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Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_content_list.json @@ -0,0 +1,1639 @@ +[ + { + "type": "text", + "text": "Q-DETR: An Efficient Low-Bit Quantized Detection Transformer", + "text_level": 1, + "bbox": [ + 153, + 130, + 816, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sheng Xu $^{1\\dagger}$ , Yanjing Li $^{1\\dagger}$ , Mingbao Lin $^{3}$ , Peng Gao $^{4}$ , Guodong Guo $^{5}$ , Jinhu Lu $^{1,2}$ , Baochang Zhang $^{1,2*}$ $^{1}$ Beihang University \n $^{2}$ Zhongguancun Laboratory \n $^{3}$ Tencent \n $^{4}$ Shanghai AI Laboratory \n $^{5}$ UNIUBI Research, Universal Ubiquitous Co.", + "bbox": [ + 86, + 178, + 895, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by $6.6\\times$ and achieve $39.4\\%$ AP, with only $2.6\\%$ performance gaps than its real-valued counterpart on the COCO dataset1.", + "bbox": [ + 76, + 300, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 707, + 209, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem.", + "bbox": [ + 75, + 732, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b47e025e70e302f5e79025c7b330255d3d8a381daa5d068aee71250b90faccb5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 270, + 629, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/58e77532541a7f2ba0fc9047e639c676fc6a1902b28eff415a9f5bd61e81e899.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 271, + 756, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/18b15d8ecd08b2a6746d8a20492c258c57b9109c76d5d9a7c04afb4562f715f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 271, + 885, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8156cf2f15f19b131f79b7183987c36c7b62f255802f7021454e16e457f5de81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 349, + 627, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3adddb20ddfb6562d837c9002e09030289bca8f8a4171abca63cc56fc35c6e37.jpg", + "image_caption": [ + "(b) 4-bit DETR-R50" + ], + "image_footnote": [], + "bbox": [ + 635, + 349, + 754, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/43ddb4a0e46f89a0a644c9d7bacbd5db54540eea7587e8f33923960758423819.jpg", + "image_caption": [ + "Figure 1. The histogram of query values $\\mathbf{q}$ (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9]." + ], + "image_footnote": [], + "bbox": [ + 763, + 359, + 885, + 428 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources.", + "bbox": [ + 496, + 598, + 890, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal contribution.", + "bbox": [ + 99, + 862, + 215, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author: bczhang@buaa.edu.cn", + "bbox": [ + 102, + 876, + 354, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code: https://github.com/SteveTsui/Q-DETR", + "bbox": [ + 102, + 888, + 424, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3842", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/212d2dd96265f5ff199cdad769f4646e2b479ae54c58646fc765cdb77f0c6adb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 88, + 462, + 143 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7ea89e0832bcf3d9a3ff705e69ca60c51428f4d85b5ada2bcfce4e4ddef14d22.jpg", + "image_caption": [ + "(a) Real-valued DETR-R50", + "(b) 4-bit DETR-R50", + "Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly." + ], + "image_footnote": [], + "bbox": [ + 84, + 156, + 462, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched.", + "bbox": [ + 75, + 366, + 468, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves $76.9\\%$ $\\mathrm{AP}_{50}$ , leaving a $6.4\\%$ performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary.", + "bbox": [ + 75, + 444, + 468, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines.", + "bbox": [ + 496, + 378, + 890, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 497, + 640, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a $2 \\sim 4$ -bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At", + "bbox": [ + 496, + 523, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3843", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e14e6d7bf16502bdbbfef0806f218e3f421ce352046ef7f791139d22bbb35d7a.jpg", + "image_caption": [ + "Architecture of quantized decoder" + ], + "image_footnote": [], + "bbox": [ + 99, + 111, + 444, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7401aae9e52ea80a8fb67f38f65d8a5a1a3a60a044a3d502a6bba7bb018998ab.jpg", + "image_caption": [ + "Learning Q-DETR with DRD", + "Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively." + ], + "image_footnote": [], + "bbox": [ + 457, + 108, + 883, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example.", + "bbox": [ + 75, + 392, + 468, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR.", + "bbox": [ + 75, + 458, + 470, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively.", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Challenge of Quantizing DETR", + "text_level": 1, + "bbox": [ + 498, + 390, + 825, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Quantized DETR baseline", + "text_level": 1, + "bbox": [ + 500, + 417, + 736, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow $\\mathrm{LSQ + [2]}$ to introduce a general framework of asymmetric activation quantization and symmetric weight quantization:", + "bbox": [ + 498, + 443, + 892, + 521 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {x} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\left(\\boldsymbol {x} - z\\right)}{\\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \\right\\} \\right\\lceil , \\mathbf {w} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\mathbf {w}}{\\alpha_ {\\mathbf {w}}}, Q _ {n} ^ {\\mathbf {w}}, Q _ {p} ^ {\\mathbf {w}} \\right\\} \\right\\rceil , \\\\ Q _ {a} (x) = \\alpha_ {x} \\circ \\mathbf {x} _ {q} + z, \\quad Q _ {w} (x) = \\alpha_ {\\mathbf {w}} \\circ \\mathbf {w} _ {q}, \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 536, + 890, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\operatorname{clip}\\{y, r_1, r_2\\}$ clips the input $y$ with value bounds $r_1$ and $r_2$ ; the $[y]$ rounds $y$ to its nearest integer; the $\\circ$ denotes the channel-wise multiplication. And $Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1$ , $Q_n^{\\mathbf{w}} = -2^{b-1}$ , $Q_p^{\\mathbf{w}} = 2^{b-1} - 1$ are the discrete bounds for $a$ -bit activations and $b$ -bit weights. $x$ generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as:", + "bbox": [ + 498, + 594, + 890, + 733 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {Q} - \\operatorname {F C} (\\boldsymbol {x}) = Q _ {a} (\\boldsymbol {x}) \\cdot Q _ {w} (\\mathbf {w}) = \\alpha_ {x} \\alpha_ {\\mathbf {w}} \\circ \\left(\\boldsymbol {x} _ {q} \\odot \\mathbf {w} _ {q} + z / \\alpha_ {x} \\circ \\mathbf {w} _ {q}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 750, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\cdot$ denotes the matrix multiplication and $\\odot$ denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation.", + "bbox": [ + 498, + 777, + 890, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output $\\mathbf{E}$ , DETR performs co-attention between object queries $\\mathbf{O}$ and the vi", + "bbox": [ + 498, + 839, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3844", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a5c972047c20bda899b5fbf274b37c7127f9b4a5c59762ec87268a7689ec6b8c.jpg", + "image_caption": [ + "Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules." + ], + "image_footnote": [], + "bbox": [ + 99, + 133, + 450, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sual features $\\mathbf{E}$ , which are formulated as:", + "bbox": [ + 76, + 334, + 349, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {q} = \\mathrm {Q - F C} (\\mathbf {O}), \\mathbf {k}, \\mathbf {v} = \\mathrm {Q - F C} (\\mathbf {E})\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 359, + 383, + 376 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {i} = \\operatorname {s o f t m a x} \\left(Q _ {a} (\\mathbf {q}) _ {i} \\cdot Q _ {a} (\\mathbf {k}) _ {i} ^ {\\top} / \\sqrt {d}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 380, + 468, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} _ {i} = Q _ {a} (\\mathbf {A}) _ {i} \\cdot Q _ {a} (\\mathbf {v}) _ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 401, + 305, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{D}$ is the multi-head co-attention module, i.e., the coattended feature for the object query. The $d$ denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query.", + "bbox": [ + 75, + 429, + 468, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Challenge Analysis", + "text_level": 1, + "bbox": [ + 76, + 559, + 261, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation.", + "bbox": [ + 75, + 583, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e., $(1) + (2) + (3)$ , brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to $2.1\\%$ in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "graded information representation is the main obstacle to a better quantized DETR.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. The Proposed Q-DETR", + "text_level": 1, + "bbox": [ + 498, + 143, + 722, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Information Bottleneck of Q-DETR", + "text_level": 1, + "bbox": [ + 500, + 170, + 808, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts $\\mathcal{T}$ and $\\mathcal{S}$ , respectively.", + "bbox": [ + 496, + 196, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is:", + "bbox": [ + 496, + 290, + 892, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta^ {S}} I (X; \\mathbf {E} ^ {S}) - \\beta I (\\mathbf {E} ^ {S}, \\mathbf {q} ^ {S}; \\boldsymbol {y} ^ {G T}) - \\gamma I (\\mathbf {q} ^ {S}; \\mathbf {q} ^ {\\mathcal {T}}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 454, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{q}^T$ and $\\mathbf{q}^S$ represent the queries in the teacher and student DETR methods as predefined in Eq. (3); $\\beta$ and $\\gamma$ are the Lagrange multipliers [35]; $\\theta^S$ is the parameters of the student; and $I(\\cdot)$ returns the mutual information of two input variables. The first item $I(X; \\mathbf{E}^S)$ minimizes information between input and visual features $\\mathbf{E}^S$ to extract task-oriented hints [40]. The second item $I(\\mathbf{E}^S, \\mathbf{q}^S; \\boldsymbol{y}^{GT})$ maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression.", + "bbox": [ + 496, + 496, + 892, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core issue of this paper is to solve the third item $I(\\mathbf{q}^S;\\mathbf{q}^T)$ , which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as:", + "bbox": [ + 498, + 681, + 890, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI (\\mathbf {q} ^ {\\mathcal {S}}; \\mathbf {q} ^ {\\mathcal {T}}) = H (\\mathbf {q} ^ {\\mathcal {S}}) - H (\\mathbf {q} ^ {\\mathcal {S}} | \\mathbf {q} ^ {\\mathcal {T}}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 772, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H(\\mathbf{q}^S)$ returns the self information entropy expected to be maximized while $H(\\mathbf{q}^S|\\mathbf{q}^T)$ is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes", + "bbox": [ + 496, + 809, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "(1) Quantizing backbone (2) Quantizing encoder (3) Quantizing MHA of decoder (4) Quantizing MLPs", + "bbox": [ + 83, + 114, + 478, + 125 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3845", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the two items, which is explicitly defined as:", + "bbox": [ + 76, + 90, + 374, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\theta} H (\\mathbf {q} ^ {S ^ {*}} | \\mathbf {q} ^ {\\mathcal {T}}), \\\\ s. t. \\quad \\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\underset {\\mathbf {q} ^ {\\mathcal {S}}} {\\arg \\max } H (\\mathbf {q} ^ {\\mathcal {S}}). \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 114, + 467, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query $\\mathbf{q}^{S^*}$ and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's.", + "bbox": [ + 75, + 178, + 468, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Distribution Rectification Distillation", + "text_level": 1, + "bbox": [ + 76, + 277, + 397, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy, $H(\\mathbf{q}^S)$ can be implicitly expanded as:", + "bbox": [ + 75, + 301, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) = - \\int_ {\\mathbf {q} _ {i} ^ {\\mathcal {S}} \\in \\mathbf {q} ^ {\\mathcal {S}}} p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right) \\log p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 369, + 468, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, an explicit form of $H(\\mathbf{q}^S)$ can only be parameterized with a regular distribution $p(\\mathbf{q}_i^S)$ . Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean $\\mu (\\mathbf{q}^S)$ and variance $\\sigma (\\mathbf{q}^S)$ of query $\\mathbf{q}^S$ whose distribution is then modeled as $\\mathbf{q}^S\\sim \\mathcal{N}(\\mu (\\mathbf{q}^S),\\sigma (\\mathbf{q}^S))$ . Then, the self-information entropy of the student query can be proceeded as:", + "bbox": [ + 75, + 414, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} H (\\mathbf {q} ^ {\\mathcal {S}}) = - \\mathbb {E} [ \\log \\mathcal {N} (\\mu (\\mathbf {q} ^ {\\mathcal {S}}), \\sigma (\\mathbf {q} ^ {\\mathcal {S}})) ] \\\\ = - \\mathbb {E} [ \\log [ (2 \\pi \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}) ^ {\\frac {1}{2}} \\exp (- \\frac {(\\mathbf {q} _ {i} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})) ^ {2}}{2 \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}})) ] \\\\ = \\frac {1}{2} \\log 2 \\pi \\sigma \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) ^ {2}. \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 573, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above objective reaches its maximum of $H(\\mathbf{q}^{S^*}) = (1/2) \\log 2\\pi e[\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}]$ when $\\mathbf{q}^{S^*} = [\\mathbf{q}^S - \\mu(\\mathbf{q}^S)] / [\\sqrt{\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}}]$ where $\\epsilon_{\\mathbf{q}^S} = 1e^{-5}$ is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter $\\beta_{\\mathbf{q}^S}$ is added to move the mean value. A learnable scaling parameter $\\gamma_{\\mathbf{q}^S}$ is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows:", + "bbox": [ + 75, + 674, + 468, + 851 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\frac {\\mathbf {q} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})}{\\sqrt {\\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2} + \\epsilon_ {\\mathbf {q} ^ {\\mathcal {S}}}}} \\gamma_ {\\mathbf {q} ^ {\\mathcal {S}}} + \\beta_ {\\mathbf {q} ^ {\\mathcal {S}}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 859, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which case the maximum self-information entropy of student query becomes $H(\\mathbf{q}^{\\mathcal{S}^*}) = (1/2) \\log 2\\pi e[(\\sigma_{\\mathbf{q}^{\\mathcal{S}}}^2 + \\epsilon_{\\mathbf{q}^{\\mathcal{S}}}) / \\gamma_{\\mathbf{q}^{\\mathcal{S}}}^2]$ . Therefore, in the forward propagation, we can obtain the current optimal query $\\mathbf{q}^{\\mathcal{S}^*}$ via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents.", + "bbox": [ + 496, + 90, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by $\\pmb{y}^{GT} = \\{c_i^{GT}, b_i^{GT}\\}_{i=1}^{N_{gt}}$ as a set of ground-truth objects where $N_{gt}$ is the number of foregrounds, $c_i^{GT}$ and $b_i^{GT}$ respectively represent the class and coordinate (bound- ing box) for the $i$ -th object. In DETR, each query is associated with an object. Therefore, we can obtain $N$ objects for teacher and student as well, denoted as $\\pmb{y}^S = \\{c_j^S, b_j^S\\}_{j=1}^N$ and $\\pmb{y}^T = \\{c_j^T, b_j^T\\}_{j=1}^N$ .", + "bbox": [ + 496, + 186, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify \"well-matched\" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as:", + "bbox": [ + 496, + 342, + 890, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {i} = \\max _ {1 \\leq j \\leq N} \\operatorname {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {S}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 472, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{GIOU}(\\cdot)$ is the generalized intersection over union function [32]. Each $G_{i}$ reflects the \"closeness\" of student proposals to the $i$ -th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as:", + "bbox": [ + 496, + 503, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nb _ {j} ^ {\\mathcal {S}} = \\left\\{ \\begin{array}{l l} b _ {j} ^ {\\mathcal {S}}, & \\text {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {\\mathcal {S}}\\right) > \\tau G _ {i}, \\forall i \\\\ \\varnothing , & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 589, + 890, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a threshold controlling the proportion of distilled queries. After removing object-empty $(\\varnothing)$ queries in $\\tilde{\\pmb{q}}^S$ , we form a distillation-desired query set of students denoted as $\\tilde{\\pmb{q}}^S$ associated with its object set $\\tilde{\\pmb{y}}^S = \\{\\tilde{c}_j^S, \\tilde{b}_j^S\\}_{j=1}^N$ . Correspondingly, we can obtain a teacher query set $\\tilde{\\pmb{y}}^T = \\{\\tilde{c}_j^T, \\tilde{b}_j^T\\}_{j=1}^N$ . For the $j$ -th student query, its corresponding teacher query is matched as:", + "bbox": [ + 496, + 632, + 890, + 743 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {c} _ {j} ^ {\\mathcal {T}}, \\tilde {b} _ {j} ^ {\\mathcal {T}} = \\underset {\\tilde {c} _ {k} ^ {\\mathcal {T}}, \\tilde {b} _ {k} ^ {\\mathcal {T}}} {\\arg \\max } \\sum_ {k = 1} ^ {N} \\mu_ {1} \\operatorname {G I o U} \\left(\\tilde {b} _ {j} ^ {\\mathcal {S}}, b _ {k} ^ {\\mathcal {T}}\\right) - \\mu_ {2} \\| \\tilde {b} _ {j} ^ {\\mathcal {S}} - b _ {k} ^ {\\mathcal {T}} \\| _ {1}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 753, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu_{1} = 2$ and $\\mu_{2} = 5$ control the matching function, values of which is to follow [4].", + "bbox": [ + 496, + 809, + 888, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the upper-level optimization after rectification in Eq. (6) becomes:", + "bbox": [ + 496, + 839, + 888, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} H \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}} \\mid \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 878, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3846", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between $\\tilde{\\mathbf{q}}^{S^*}$ and $\\tilde{\\mathbf{q}}^T$ , optima of which, i.e., $\\tilde{\\mathbf{q}}^{S^*} = \\tilde{\\mathbf{q}}^T$ , is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes:", + "bbox": [ + 76, + 90, + 468, + 165 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D R D} \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right) = \\mathbb {E} \\left[ \\left\\| \\tilde {\\mathbf {D}} ^ {\\mathcal {S} ^ {*}} - \\tilde {\\mathbf {D}} ^ {\\mathcal {T}} \\right\\| _ {2} \\right], \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 176, + 468, + 194 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where we use the Euclidean distance of co-attented feature $\\tilde{\\mathbf{D}}$ (see Eq. 3) containing the information query $\\tilde{\\mathbf{q}}$ for optimization.", + "bbox": [ + 76, + 205, + 468, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are:", + "bbox": [ + 76, + 251, + 468, + 311 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {G T} \\left(\\boldsymbol {y} ^ {G T}, \\boldsymbol {y} ^ {\\mathcal {S}}\\right) + \\lambda \\mathcal {L} _ {D R D} \\left(\\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {T}}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 319, + 468, + 337 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L_{GT}$ is the common detection loss for missions such as proposal classification and coordinate regression [4], and $\\lambda$ is a tradeoff hyper-parameter.", + "bbox": [ + 76, + 345, + 468, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 404, + 207, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves.", + "bbox": [ + 76, + 430, + 468, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 530, + 395, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP, $\\mathrm{AP}_{50}$ (default VOC metric), and $\\mathrm{AP}_{75}$ . We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list $\\mathrm{AP}_{50}$ , $\\mathrm{AP}_{75}$ , $\\mathrm{AP}_s$ , $\\mathrm{AP}_m$ , and $\\mathrm{AP}_l$ .", + "bbox": [ + 76, + 553, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f81fb84b5bb6aab549b17b32fa5da6cc62eb498e5c10813514540515dba9c182.jpg", + "image_caption": [ + "(a) Effect of $\\tau$ and $\\lambda$ ." + ], + "image_footnote": [], + "bbox": [ + 511, + 102, + 676, + 199 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/47952eabf7f40ca87b81667b8ca2c1c9243c9c288b2ab9cb3103439d10a90646.jpg", + "image_caption": [ + "(b) Mutual information curves.", + "Figure 5. (a) We select $\\tau$ and $\\lambda$ using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of $I(X; \\mathbf{E})$ and $I(\\boldsymbol{y}^{GT}; \\mathbf{E}, \\mathbf{q})$ (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR)." + ], + "image_footnote": [], + "bbox": [ + 702, + 102, + 870, + 199 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of $1e^{-4}$ . We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP50 on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP50 on VOC and 44.4% AP on COCO) as teacher network.", + "bbox": [ + 498, + 338, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 604, + 651, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyper-parameter selection. As mentioned above, we select hyper-parameters $\\tau$ and $\\lambda$ in this part using the 4-bit Q-DETR model. We show the model performance $(\\mathrm{AP}_{50})$ with different setups of hyper-parameters $\\{\\tau ,\\lambda \\}$ in Fig.5 (a), where we conduct ablative experiments on the baseline $+\\mathrm{DA}(\\mathrm{AP}_{50} = 78.8\\%)$ . As can be seen, the performances increase first and then decrease with the increase of $\\tau$ from left to right. Since $\\tau$ controls the proportion of selected distillation-desired queries, we show that the full-imitation $(\\tau = 0)$ performs worse than the vanilla baseline with no distillation $(\\tau = 1)$ , showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of $\\tau$ from left to right. The Q-DETR obtains better performances with $\\tau$ set as 0.5 and 0.6. With the varying value of $\\lambda$ , we find $\\{\\lambda ,\\tau \\} = \\{2.5,0.6\\}$ boost the performance of Q-DETR most, achieving $82.7\\%$ AP on VOC test2007. Based on the ablative study above, we set hyper-parameters $\\tau$ and $\\lambda$ as 0.6 and 2.5", + "bbox": [ + 498, + 628, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3847", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/714db789979e193ffa0cab743198c4ee6537499428e88f61c41805171caa2c36.jpg", + "table_caption": [ + "Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching." + ], + "table_footnote": [], + "table_body": "
Method#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)
Real-valued32-32-3283.3----
Baseline4-4-878.03-3-876.82-2-869.7
+DA4-4-878.83-3-878.02-2-871.6
+FQM4-4-881.53-3-880.92-2-874.9
+DA+FQM(Q-DETR)4-4-882.73-3-882.12-2-876.4
", + "bbox": [ + 78, + 167, + 468, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for the experiments in this paper.", + "bbox": [ + 76, + 308, + 294, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on $\\mathrm{AP}_{50}$ (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%.", + "bbox": [ + 75, + 321, + 468, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test $\\mathrm{AP}_{50}$ to quantify $I(\\boldsymbol{y}^{GT};\\mathbf{E},\\mathbf{q})$ . We employ a reconstruction decoder to decode the encoded feature $\\mathbf{E}$ to reconstruct the input and quantify $I(X;\\mathbf{E})$ using the $\\ell_1$ loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods.", + "bbox": [ + 75, + 489, + 468, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Results on PASCAL VOC", + "text_level": 1, + "bbox": [ + 76, + 664, + 310, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e. $1333 \\times 800$ . We mainly discuss the $\\mathrm{AP}_{50}$ (default VOC metric) in the following.", + "bbox": [ + 75, + 688, + 468, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/82eed12095fb7a4f5a22f0bdd3105b3808bf5341e615bf02f5f30004c2ceeb53.jpg", + "table_caption": [ + "Table 2. We report AP, $\\mathrm{AP}_{50}$ , and $\\mathrm{AP}_{75}$ (\\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations." + ], + "table_footnote": [], + "table_body": "
ModelMethod#BitsAP\\( AP_{50} \\)\\( AP_{75} \\)
DETR-R50Real-valued32-32-3259.583.364.7
Percentile8-8-854.779.260.1
VT-PTQ57.682.363.1
LSQ49.776.953.0
Baseline4-4-851.378.054.1
Q-DETR57.182.761.5
LSQ47.075.349.1
Baseline3-3-849.276.851.8
Q-DETR56.882.161.2
LSQ42.668.244.8
Baseline2-2-844.069.745.8
Q-DETR50.776.454.1
SMCA-DETR -R50Real-valued32-32-3256.783.762.0
Percentile8-8-854.779.260.1
VT-PTQ55.983.061.3
LSQ49.678.653.4
Baseline4-4-850.779.555.4
Q-DETR56.283.361.6
LSQ47.776.551.7
Baseline3-3-849.977.553.6
Q-DETR54.382.659.5
LSQ42.369.744.8
Baseline2-2-843.970.446.1
Q-DETR50.276.752.6
", + "bbox": [ + 501, + 155, + 890, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and bit-width, which significantly validates the effectiveness of our method.", + "bbox": [ + 498, + 564, + 888, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by $6.3\\%$ , $5.1\\%$ and $3.8\\%$ on $\\mathrm{AP}_{50}$ , a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance.", + "bbox": [ + 498, + 595, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Results on COCO", + "text_level": 1, + "bbox": [ + 500, + 710, + 671, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3.", + "bbox": [ + 498, + 734, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3848", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/75a9dded57022f71844b11e49ff060da2adeb508c57fa60eb2467e4cd037cde3.jpg", + "table_caption": [ + "Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations." + ], + "table_footnote": [], + "table_body": "
ModelMethod#BitsSize(MB)OPs(G)APAP50AP75APsAPmAPl
DETR-R50Real-valued32-32-32159.3285.5142.062.444.220.545.861.1
Percentile8-8-839.8323.0138.6-----
VT-PTQ41.2-----
LSQ33.353.733.912.837.051.6
Baseline4-4-819.9213.0234.155.335.414.338.053.8
Q-DETR39.460.241.417.743.459.9
LSQ31.052.332.111.333.948.5
Baseline3-3-815.037.6132.352.232.912.335.450.3
Q-DETR36.155.937.514.639.455.2
LSQ24.744.626.56.325.342.7
Baseline2-2-810.035.3226.646.626.58.428.244.4
Q-DETR31.451.331.611.634.349.6
SMCA-DETR-R50Real-valued32-32-32164.7586.6541.062.243.621.944.359.1
Percentile8-8-841.1923.6637.558.540.117.639.155.9
VT-PTQ40.261.042.620.342.957.7
LSQ33.955.035.013.237.251.4
Baseline4-4-820.5913.4835.056.436.415.638.352.5
Q-DETR38.359.739.817.741.756.8
LSQ30.152.631.411.933.446.6
Baseline3-3-815.688.0531.853.732.612.635.249.8
Q-DETR35.056.336.915.039.053.1
LSQ23.942.224.29.426.237.5
Baseline2-2-810.844.5425.444.325.28.427.240.3
Q-DETR30.551.831.812.033.248.0
", + "bbox": [ + 91, + 127, + 875, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "detectors. We follow [40] to calculate memory usage, by adding $32 \\times$ the number of real-valued weights and $a \\times$ the number of quantized weights in the $a$ -bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds $\\left\\{\\frac{1}{32}, \\frac{1}{16}, \\frac{1}{8}\\right\\}$ of the number of $\\{2,3,4\\}$ -bit multiplications equals the OPs following [24].", + "bbox": [ + 75, + 535, + 468, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of $2/3/4$ -bit baseline by $4.8\\%$ , $3.8\\%$ and $5.1\\%$ AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed $2/3/4$ -bit Q-DETR achieves computation acceleration and storage savings by $16.07 \\times / 11.23 \\times / 6.57 \\times$ and $15.88 \\times / 10.60 \\times / 7.99 \\times$ . The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection.", + "bbox": [ + 75, + 657, + 468, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the SMCA-DETR-R50 model, we observe similar", + "bbox": [ + 96, + 883, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates $6.42 \\times$ with only a $2.7\\%$ performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods.", + "bbox": [ + 496, + 535, + 893, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 630, + 619, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. We effectively employ a distribution alignment module to solve inner-level and a foreground-aware query matching scheme to solve upper level. As a result, Q-DETR significantly boosts performance of low-bit DETR. Extensive experiments show that Q-DETR surpasses state-of-the-arts in DETR quantization.", + "bbox": [ + 496, + 657, + 890, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 828, + 687, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China under Grant 62141604, 62076016, Beijing Natural Science Foundation L223024.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3849", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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In Proc. of CVPR, pages 7920-7928, 2018. 2" + ], + "bbox": [ + 501, + 90, + 890, + 244 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3851", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_model.json b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8dc59a1f38ea2a171c563689dfa5ffc351bba418 --- /dev/null +++ b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.131, + 0.818, + 0.152 + ], + "angle": 0, + "content": "Q-DETR: An Efficient Low-Bit Quantized Detection Transformer" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.179, + 0.896, + 0.235 + ], + "angle": 0, + "content": "Sheng Xu\\(^{1\\dagger}\\), Yanjing Li\\(^{1\\dagger}\\), Mingbao Lin\\(^{3}\\), Peng Gao\\(^{4}\\), Guodong Guo\\(^{5}\\), Jinhu Lu\\(^{1,2}\\), Baochang Zhang\\(^{1,2*}\\) \n\\(^{1}\\) Beihang University \n\\(^{2}\\) Zhongguancun Laboratory \n\\(^{3}\\) Tencent \n\\(^{4}\\) Shanghai AI Laboratory \n\\(^{5}\\) UNIUBI Research, Universal Ubiquitous Co." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.681 + ], + "angle": 0, + "content": "The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by \\(6.6\\times\\) and achieve \\(39.4\\%\\) AP, with only \\(2.6\\%\\) performance gaps than its real-valued counterpart on the COCO dataset1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.708, + 0.21, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.271, + 0.63, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.272, + 0.758, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.272, + 0.887, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.35, + 0.629, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.35, + 0.756, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.361, + 0.886, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.429, + 0.756, + 0.44 + ], + "angle": 0, + "content": "(b) 4-bit DETR-R50" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.571 + ], + "angle": 0, + "content": "Figure 1. The histogram of query values \\(\\mathbf{q}\\) (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.863, + 0.216, + 0.876 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.877, + 0.355, + 0.888 + ], + "angle": 0, + "content": "* Corresponding author: bczhang@buaa.edu.cn" + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.889, + 0.426, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code: https://github.com/SteveTsui/Q-DETR" + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.863, + 0.426, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3842" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.464, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.146, + 0.356, + 0.157 + ], + "angle": 0, + "content": "(a) Real-valued DETR-R50" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.157, + 0.464, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.213, + 0.335, + 0.225 + ], + "angle": 0, + "content": "(b) 4-bit DETR-R50" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.237, + 0.47, + 0.334 + ], + "angle": 0, + "content": "Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.469, + 0.442 + ], + "angle": 0, + "content": "simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.822 + ], + "angle": 0, + "content": "In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves \\(76.9\\%\\) \\(\\mathrm{AP}_{50}\\), leaving a \\(6.4\\%\\) performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.379 + ], + "angle": 0, + "content": "tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.484 + ], + "angle": 0, + "content": "This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.641, + 0.513 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a \\(2 \\sim 4\\)-bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3843" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.154, + 0.095, + 0.373, + 0.109 + ], + "angle": 0, + "content": "Architecture of quantized decoder" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.112, + 0.446, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.096, + 0.756, + 0.11 + ], + "angle": 0, + "content": "Learning Q-DETR with DRD" + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.109, + 0.884, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.894, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.47, + 0.455 + ], + "angle": 0, + "content": "the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.471, + 0.789 + ], + "angle": 0, + "content": "Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.391, + 0.826, + 0.41 + ], + "angle": 0, + "content": "3. The Challenge of Quantizing DETR" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.738, + 0.435 + ], + "angle": 0, + "content": "3.1. Quantized DETR baseline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.444, + 0.893, + 0.522 + ], + "angle": 0, + "content": "We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow \\(\\mathrm{LSQ + [2]}\\) to introduce a general framework of asymmetric activation quantization and symmetric weight quantization:" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.537, + 0.891, + 0.594 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {x} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\left(\\boldsymbol {x} - z\\right)}{\\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \\right\\} \\right\\lceil , \\mathbf {w} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\mathbf {w}}{\\alpha_ {\\mathbf {w}}}, Q _ {n} ^ {\\mathbf {w}}, Q _ {p} ^ {\\mathbf {w}} \\right\\} \\right\\rceil , \\\\ Q _ {a} (x) = \\alpha_ {x} \\circ \\mathbf {x} _ {q} + z, \\quad Q _ {w} (x) = \\alpha_ {\\mathbf {w}} \\circ \\mathbf {w} _ {q}, \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.892, + 0.734 + ], + "angle": 0, + "content": "where \\(\\operatorname{clip}\\{y, r_1, r_2\\}\\) clips the input \\(y\\) with value bounds \\(r_1\\) and \\(r_2\\); the \\([y]\\) rounds \\(y\\) to its nearest integer; the \\(\\circ\\) denotes the channel-wise multiplication. And \\(Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1\\), \\(Q_n^{\\mathbf{w}} = -2^{b-1}\\), \\(Q_p^{\\mathbf{w}} = 2^{b-1} - 1\\) are the discrete bounds for \\(a\\)-bit activations and \\(b\\)-bit weights. \\(x\\) generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.75, + 0.892, + 0.778 + ], + "angle": 0, + "content": "\\[\n\\operatorname {Q} - \\operatorname {F C} (\\boldsymbol {x}) = Q _ {a} (\\boldsymbol {x}) \\cdot Q _ {w} (\\mathbf {w}) = \\alpha_ {x} \\alpha_ {\\mathbf {w}} \\circ \\left(\\boldsymbol {x} _ {q} \\odot \\mathbf {w} _ {q} + z / \\alpha_ {x} \\circ \\mathbf {w} _ {q}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.778, + 0.892, + 0.839 + ], + "angle": 0, + "content": "where \\(\\cdot\\) denotes the matrix multiplication and \\(\\odot\\) denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.893, + 0.902 + ], + "angle": 0, + "content": "In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output \\(\\mathbf{E}\\), DETR performs co-attention between object queries \\(\\mathbf{O}\\) and the vi" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3844" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.115, + 0.48, + 0.126 + ], + "angle": 0, + "content": "(1) Quantizing backbone (2) Quantizing encoder (3) Quantizing MHA of decoder (4) Quantizing MLPs" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.135, + 0.452, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.28, + 0.47, + 0.308 + ], + "angle": 0, + "content": "Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.351, + 0.35 + ], + "angle": 0, + "content": "sual features \\(\\mathbf{E}\\), which are formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.36, + 0.384, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathbf {q} = \\mathrm {Q - F C} (\\mathbf {O}), \\mathbf {k}, \\mathbf {v} = \\mathrm {Q - F C} (\\mathbf {E})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.381, + 0.469, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {i} = \\operatorname {s o f t m a x} \\left(Q _ {a} (\\mathbf {q}) _ {i} \\cdot Q _ {a} (\\mathbf {k}) _ {i} ^ {\\top} / \\sqrt {d}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.402, + 0.306, + 0.418 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} _ {i} = Q _ {a} (\\mathbf {A}) _ {i} \\cdot Q _ {a} (\\mathbf {v}) _ {i},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.551 + ], + "angle": 0, + "content": "where \\(\\mathbf{D}\\) is the multi-head co-attention module, i.e., the coattended feature for the object query. The \\(d\\) denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.262, + 0.577 + ], + "angle": 0, + "content": "3.2. Challenge Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.469, + 0.704 + ], + "angle": 0, + "content": "Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e., \\((1) + (2) + (3)\\), brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to \\(2.1\\%\\) in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "graded information representation is the main obstacle to a better quantized DETR." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.144, + 0.723, + 0.162 + ], + "angle": 0, + "content": "4. The Proposed Q-DETR" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.171, + 0.81, + 0.188 + ], + "angle": 0, + "content": "4.1. Information Bottleneck of Q-DETR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.289 + ], + "angle": 0, + "content": "To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts \\(\\mathcal{T}\\) and \\(\\mathcal{S}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.893, + 0.44 + ], + "angle": 0, + "content": "Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.455, + 0.892, + 0.48 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta^ {S}} I (X; \\mathbf {E} ^ {S}) - \\beta I (\\mathbf {E} ^ {S}, \\mathbf {q} ^ {S}; \\boldsymbol {y} ^ {G T}) - \\gamma I (\\mathbf {q} ^ {S}; \\mathbf {q} ^ {\\mathcal {T}}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.679 + ], + "angle": 0, + "content": "where \\(\\mathbf{q}^T\\) and \\(\\mathbf{q}^S\\) represent the queries in the teacher and student DETR methods as predefined in Eq. (3); \\(\\beta\\) and \\(\\gamma\\) are the Lagrange multipliers [35]; \\(\\theta^S\\) is the parameters of the student; and \\(I(\\cdot)\\) returns the mutual information of two input variables. The first item \\(I(X; \\mathbf{E}^S)\\) minimizes information between input and visual features \\(\\mathbf{E}^S\\) to extract task-oriented hints [40]. The second item \\(I(\\mathbf{E}^S, \\mathbf{q}^S; \\boldsymbol{y}^{GT})\\) maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.682, + 0.892, + 0.756 + ], + "angle": 0, + "content": "The core issue of this paper is to solve the third item \\( I(\\mathbf{q}^S;\\mathbf{q}^T) \\), which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.773, + 0.892, + 0.793 + ], + "angle": 0, + "content": "\\[\nI (\\mathbf {q} ^ {\\mathcal {S}}; \\mathbf {q} ^ {\\mathcal {T}}) = H (\\mathbf {q} ^ {\\mathcal {S}}) - H (\\mathbf {q} ^ {\\mathcal {S}} | \\mathbf {q} ^ {\\mathcal {T}}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.902 + ], + "angle": 0, + "content": "where \\( H(\\mathbf{q}^S) \\) returns the self information entropy expected to be maximized while \\( H(\\mathbf{q}^S|\\mathbf{q}^T) \\) is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3845" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.375, + 0.107 + ], + "angle": 0, + "content": "the two items, which is explicitly defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.115, + 0.468, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\theta} H (\\mathbf {q} ^ {S ^ {*}} | \\mathbf {q} ^ {\\mathcal {T}}), \\\\ s. t. \\quad \\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\underset {\\mathbf {q} ^ {\\mathcal {S}}} {\\arg \\max } H (\\mathbf {q} ^ {\\mathcal {S}}). \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.179, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query \\(\\mathbf{q}^{S^*}\\) and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.279, + 0.398, + 0.293 + ], + "angle": 0, + "content": "4.2. Distribution Rectification Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.469, + 0.362 + ], + "angle": 0, + "content": "Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy, \\( H(\\mathbf{q}^S) \\) can be implicitly expanded as:" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.371, + 0.469, + 0.406 + ], + "angle": 0, + "content": "\\[\nH \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) = - \\int_ {\\mathbf {q} _ {i} ^ {\\mathcal {S}} \\in \\mathbf {q} ^ {\\mathcal {S}}} p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right) \\log p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.469, + 0.567 + ], + "angle": 0, + "content": "However, an explicit form of \\( H(\\mathbf{q}^S) \\) can only be parameterized with a regular distribution \\( p(\\mathbf{q}_i^S) \\). Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean \\( \\mu (\\mathbf{q}^S) \\) and variance \\( \\sigma (\\mathbf{q}^S) \\) of query \\( \\mathbf{q}^S \\) whose distribution is then modeled as \\( \\mathbf{q}^S\\sim \\mathcal{N}(\\mu (\\mathbf{q}^S),\\sigma (\\mathbf{q}^S)) \\). Then, the self-information entropy of the student query can be proceeded as:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.574, + 0.469, + 0.674 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} H (\\mathbf {q} ^ {\\mathcal {S}}) = - \\mathbb {E} [ \\log \\mathcal {N} (\\mu (\\mathbf {q} ^ {\\mathcal {S}}), \\sigma (\\mathbf {q} ^ {\\mathcal {S}})) ] \\\\ = - \\mathbb {E} [ \\log [ (2 \\pi \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}) ^ {\\frac {1}{2}} \\exp (- \\frac {(\\mathbf {q} _ {i} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})) ^ {2}}{2 \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}})) ] \\\\ = \\frac {1}{2} \\log 2 \\pi \\sigma \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) ^ {2}. \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.469, + 0.852 + ], + "angle": 0, + "content": "The above objective reaches its maximum of \\( H(\\mathbf{q}^{S^*}) = (1/2) \\log 2\\pi e[\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}]\\) when \\(\\mathbf{q}^{S^*} = [\\mathbf{q}^S - \\mu(\\mathbf{q}^S)] / [\\sqrt{\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}}]\\) where \\(\\epsilon_{\\mathbf{q}^S} = 1e^{-5}\\) is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter \\(\\beta_{\\mathbf{q}^S}\\) is added to move the mean value. A learnable scaling parameter \\(\\gamma_{\\mathbf{q}^S}\\) is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.86, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\frac {\\mathbf {q} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})}{\\sqrt {\\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2} + \\epsilon_ {\\mathbf {q} ^ {\\mathcal {S}}}}} \\gamma_ {\\mathbf {q} ^ {\\mathcal {S}}} + \\beta_ {\\mathbf {q} ^ {\\mathcal {S}}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.188 + ], + "angle": 0, + "content": "in which case the maximum self-information entropy of student query becomes \\( H(\\mathbf{q}^{\\mathcal{S}^*}) = (1/2) \\log 2\\pi e[(\\sigma_{\\mathbf{q}^{\\mathcal{S}}}^2 + \\epsilon_{\\mathbf{q}^{\\mathcal{S}}}) / \\gamma_{\\mathbf{q}^{\\mathcal{S}}}^2] \\). Therefore, in the forward propagation, we can obtain the current optimal query \\( \\mathbf{q}^{\\mathcal{S}^*} \\) via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.188, + 0.892, + 0.344 + ], + "angle": 0, + "content": "Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by \\(\\pmb{y}^{GT} = \\{c_i^{GT}, b_i^{GT}\\}_{i=1}^{N_{gt}}\\) as a set of ground-truth objects where \\(N_{gt}\\) is the number of foregrounds, \\(c_i^{GT}\\) and \\(b_i^{GT}\\) respectively represent the class and coordinate (bound- ing box) for the \\(i\\)-th object. In DETR, each query is associated with an object. Therefore, we can obtain \\(N\\) objects for teacher and student as well, denoted as \\(\\pmb{y}^S = \\{c_j^S, b_j^S\\}_{j=1}^N\\) and \\(\\pmb{y}^T = \\{c_j^T, b_j^T\\}_{j=1}^N\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.476 + ], + "angle": 0, + "content": "The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify \"well-matched\" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.473, + 0.891, + 0.497 + ], + "angle": 0, + "content": "\\[\nG _ {i} = \\max _ {1 \\leq j \\leq N} \\operatorname {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {S}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.58 + ], + "angle": 0, + "content": "where \\(\\mathrm{GIOU}(\\cdot)\\) is the generalized intersection over union function [32]. Each \\(G_{i}\\) reflects the \"closeness\" of student proposals to the \\(i\\)-th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.59, + 0.891, + 0.623 + ], + "angle": 0, + "content": "\\[\nb _ {j} ^ {\\mathcal {S}} = \\left\\{ \\begin{array}{l l} b _ {j} ^ {\\mathcal {S}}, & \\text {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {\\mathcal {S}}\\right) > \\tau G _ {i}, \\forall i \\\\ \\varnothing , & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.744 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a threshold controlling the proportion of distilled queries. After removing object-empty \\((\\varnothing)\\) queries in \\(\\tilde{\\pmb{q}}^S\\), we form a distillation-desired query set of students denoted as \\(\\tilde{\\pmb{q}}^S\\) associated with its object set \\(\\tilde{\\pmb{y}}^S = \\{\\tilde{c}_j^S, \\tilde{b}_j^S\\}_{j=1}^N\\). Correspondingly, we can obtain a teacher query set \\(\\tilde{\\pmb{y}}^T = \\{\\tilde{c}_j^T, \\tilde{b}_j^T\\}_{j=1}^N\\). For the \\(j\\)-th student query, its corresponding teacher query is matched as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.755, + 0.891, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\tilde {c} _ {j} ^ {\\mathcal {T}}, \\tilde {b} _ {j} ^ {\\mathcal {T}} = \\underset {\\tilde {c} _ {k} ^ {\\mathcal {T}}, \\tilde {b} _ {k} ^ {\\mathcal {T}}} {\\arg \\max } \\sum_ {k = 1} ^ {N} \\mu_ {1} \\operatorname {G I o U} \\left(\\tilde {b} _ {j} ^ {\\mathcal {S}}, b _ {k} ^ {\\mathcal {T}}\\right) - \\mu_ {2} \\| \\tilde {b} _ {j} ^ {\\mathcal {S}} - b _ {k} ^ {\\mathcal {T}} \\| _ {1}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.89, + 0.839 + ], + "angle": 0, + "content": "where \\(\\mu_{1} = 2\\) and \\(\\mu_{2} = 5\\) control the matching function, values of which is to follow [4]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.89, + 0.87 + ], + "angle": 0, + "content": "Finally, the upper-level optimization after rectification in Eq. (6) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.88, + 0.891, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} H \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}} \\mid \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right). \\tag {13}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3846" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between \\(\\tilde{\\mathbf{q}}^{S^*}\\) and \\(\\tilde{\\mathbf{q}}^T\\), optima of which, i.e., \\(\\tilde{\\mathbf{q}}^{S^*} = \\tilde{\\mathbf{q}}^T\\), is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.177, + 0.469, + 0.195 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D R D} \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right) = \\mathbb {E} \\left[ \\left\\| \\tilde {\\mathbf {D}} ^ {\\mathcal {S} ^ {*}} - \\tilde {\\mathbf {D}} ^ {\\mathcal {T}} \\right\\| _ {2} \\right], \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.206, + 0.469, + 0.25 + ], + "angle": 0, + "content": "where we use the Euclidean distance of co-attented feature \\(\\tilde{\\mathbf{D}}\\) (see Eq. 3) containing the information query \\(\\tilde{\\mathbf{q}}\\) for optimization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.252, + 0.469, + 0.312 + ], + "angle": 0, + "content": "In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.32, + 0.469, + 0.338 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {G T} \\left(\\boldsymbol {y} ^ {G T}, \\boldsymbol {y} ^ {\\mathcal {S}}\\right) + \\lambda \\mathcal {L} _ {D R D} \\left(\\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {T}}\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.347, + 0.469, + 0.392 + ], + "angle": 0, + "content": "where \\( L_{GT} \\) is the common detection loss for missions such as proposal classification and coordinate regression [4], and \\( \\lambda \\) is a tradeoff hyper-parameter." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.405, + 0.209, + 0.423 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.469, + 0.522 + ], + "angle": 0, + "content": "In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.396, + 0.546 + ], + "angle": 0, + "content": "5.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.469, + 0.795 + ], + "angle": 0, + "content": "Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP, \\(\\mathrm{AP}_{50}\\) (default VOC metric), and \\(\\mathrm{AP}_{75}\\). We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list \\(\\mathrm{AP}_{50}\\), \\(\\mathrm{AP}_{75}\\), \\(\\mathrm{AP}_s\\), \\(\\mathrm{AP}_m\\), and \\(\\mathrm{AP}_l\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.103, + 0.677, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.204, + 0.655, + 0.215 + ], + "angle": 0, + "content": "(a) Effect of \\(\\tau\\) and \\(\\lambda\\)." + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.103, + 0.871, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.204, + 0.875, + 0.215 + ], + "angle": 0, + "content": "(b) Mutual information curves." + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.228, + 0.892, + 0.312 + ], + "angle": 0, + "content": "Figure 5. (a) We select \\(\\tau\\) and \\(\\lambda\\) using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of \\(I(X; \\mathbf{E})\\) and \\(I(\\boldsymbol{y}^{GT}; \\mathbf{E}, \\mathbf{q})\\) (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.339, + 0.892, + 0.596 + ], + "angle": 0, + "content": "the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of \\(1e^{-4}\\). We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP50 on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP50 on VOC and 44.4% AP on COCO) as teacher network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.653, + 0.621 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Hyper-parameter selection. As mentioned above, we select hyper-parameters \\(\\tau\\) and \\(\\lambda\\) in this part using the 4-bit Q-DETR model. We show the model performance \\((\\mathrm{AP}_{50})\\) with different setups of hyper-parameters \\(\\{\\tau ,\\lambda \\}\\) in Fig.5 (a), where we conduct ablative experiments on the baseline \\(+\\mathrm{DA}(\\mathrm{AP}_{50} = 78.8\\%)\\). As can be seen, the performances increase first and then decrease with the increase of \\(\\tau\\) from left to right. Since \\(\\tau\\) controls the proportion of selected distillation-desired queries, we show that the full-imitation \\((\\tau = 0)\\) performs worse than the vanilla baseline with no distillation \\((\\tau = 1)\\), showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of \\(\\tau\\) from left to right. The Q-DETR obtains better performances with \\(\\tau\\) set as 0.5 and 0.6. With the varying value of \\(\\lambda\\), we find \\(\\{\\lambda ,\\tau \\} = \\{2.5,0.6\\}\\) boost the performance of Q-DETR most, achieving \\(82.7\\%\\) AP on VOC test2007. Based on the ablative study above, we set hyper-parameters \\(\\tau\\) and \\(\\lambda\\) as 0.6 and 2.5" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3847" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.16 + ], + "angle": 0, + "content": "Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.169, + 0.47, + 0.282 + ], + "angle": 0, + "content": "
Method#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)
Real-valued32-32-3283.3----
Baseline4-4-878.03-3-876.82-2-869.7
+DA4-4-878.83-3-878.02-2-871.6
+FQM4-4-881.53-3-880.92-2-874.9
+DA+FQM(Q-DETR)4-4-882.73-3-882.12-2-876.4
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.309, + 0.295, + 0.323 + ], + "angle": 0, + "content": "for the experiments in this paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.488 + ], + "angle": 0, + "content": "Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on \\(\\mathrm{AP}_{50}\\) (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test \\(\\mathrm{AP}_{50}\\) to quantify \\(I(\\boldsymbol{y}^{GT};\\mathbf{E},\\mathbf{q})\\). We employ a reconstruction decoder to decode the encoded feature \\(\\mathbf{E}\\) to reconstruct the input and quantify \\(I(X;\\mathbf{E})\\) using the \\(\\ell_1\\) loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.312, + 0.681 + ], + "angle": 0, + "content": "5.3. Results on PASCAL VOC" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.795 + ], + "angle": 0, + "content": "We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e. \\(1333 \\times 800\\). We mainly discuss the \\(\\mathrm{AP}_{50}\\) (default VOC metric) in the following." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.145 + ], + "angle": 0, + "content": "Table 2. We report AP, \\(\\mathrm{AP}_{50}\\), and \\(\\mathrm{AP}_{75}\\) (\\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.156, + 0.892, + 0.538 + ], + "angle": 0, + "content": "
ModelMethod#BitsAP\\( AP_{50} \\)\\( AP_{75} \\)
DETR-R50Real-valued32-32-3259.583.364.7
Percentile8-8-854.779.260.1
VT-PTQ57.682.363.1
LSQ49.776.953.0
Baseline4-4-851.378.054.1
Q-DETR57.182.761.5
LSQ47.075.349.1
Baseline3-3-849.276.851.8
Q-DETR56.882.161.2
LSQ42.668.244.8
Baseline2-2-844.069.745.8
Q-DETR50.776.454.1
SMCA-DETR -R50Real-valued32-32-3256.783.762.0
Percentile8-8-854.779.260.1
VT-PTQ55.983.061.3
LSQ49.678.653.4
Baseline4-4-850.779.555.4
Q-DETR56.283.361.6
LSQ47.776.551.7
Baseline3-3-849.977.553.6
Q-DETR54.382.659.5
LSQ42.369.744.8
Baseline2-2-843.970.446.1
Q-DETR50.276.752.6
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.89, + 0.594 + ], + "angle": 0, + "content": "and bit-width, which significantly validates the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.596, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by \\(6.3\\%\\), \\(5.1\\%\\) and \\(3.8\\%\\) on \\(\\mathrm{AP}_{50}\\), a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.673, + 0.726 + ], + "angle": 0, + "content": "5.4. Results on COCO" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.735, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3848" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.128, + 0.877, + 0.511 + ], + "angle": 0, + "content": "
ModelMethod#BitsSize(MB)OPs(G)APAP50AP75APsAPmAPl
DETR-R50Real-valued32-32-32159.3285.5142.062.444.220.545.861.1
Percentile8-8-839.8323.0138.6-----
VT-PTQ41.2-----
LSQ33.353.733.912.837.051.6
Baseline4-4-819.9213.0234.155.335.414.338.053.8
Q-DETR39.460.241.417.743.459.9
LSQ31.052.332.111.333.948.5
Baseline3-3-815.037.6132.352.232.912.335.450.3
Q-DETR36.155.937.514.639.455.2
LSQ24.744.626.56.325.342.7
Baseline2-2-810.035.3226.646.626.58.428.244.4
Q-DETR31.451.331.611.634.349.6
SMCA-DETR-R50Real-valued32-32-32164.7586.6541.062.243.621.944.359.1
Percentile8-8-841.1923.6637.558.540.117.639.155.9
VT-PTQ40.261.042.620.342.957.7
LSQ33.955.035.013.237.251.4
Baseline4-4-820.5913.4835.056.436.415.638.352.5
Q-DETR38.359.739.817.741.756.8
LSQ30.152.631.411.933.446.6
Baseline3-3-815.688.0531.853.732.612.635.249.8
Q-DETR35.056.336.915.039.053.1
LSQ23.942.224.29.426.237.5
Baseline2-2-810.844.5425.444.325.28.427.240.3
Q-DETR30.551.831.812.033.248.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.657 + ], + "angle": 0, + "content": "detectors. We follow [40] to calculate memory usage, by adding \\(32 \\times\\) the number of real-valued weights and \\(a \\times\\) the number of quantized weights in the \\(a\\)-bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds \\(\\left\\{\\frac{1}{32}, \\frac{1}{16}, \\frac{1}{8}\\right\\}\\) of the number of \\(\\{2,3,4\\}\\)-bit multiplications equals the OPs following [24]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.884 + ], + "angle": 0, + "content": "We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of \\(2/3/4\\)-bit baseline by \\(4.8\\%\\), \\(3.8\\%\\) and \\(5.1\\%\\) AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed \\(2/3/4\\)-bit Q-DETR achieves computation acceleration and storage savings by \\(16.07 \\times / 11.23 \\times / 6.57 \\times\\) and \\(15.88 \\times / 10.60 \\times / 7.99 \\times\\). The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.885, + 0.47, + 0.9 + ], + "angle": 0, + "content": "For the SMCA-DETR-R50 model, we observe similar" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.895, + 0.613 + ], + "angle": 0, + "content": "performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates \\(6.42 \\times\\) with only a \\(2.7\\%\\) performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.631, + 0.62, + 0.647 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.81 + ], + "angle": 0, + "content": "This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. We effectively employ a distribution alignment module to solve inner-level and a foreground-aware query matching scheme to solve upper level. As a result, Q-DETR significantly boosts performance of low-bit DETR. Extensive experiments show that Q-DETR surpasses state-of-the-arts in DETR quantization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.829, + 0.688, + 0.846 + ], + "angle": 0, + "content": "7. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China under Grant 62141604, 62076016, Beijing Natural Science Foundation L223024." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3849" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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In Proc. of CVPR, pages 7920-7928, 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3851" + } + ] +] \ No newline at end of file diff --git a/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_origin.pdf b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7ba4dae682b1b3e9de601e7dc65a952b22f0969d --- /dev/null +++ b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cbe3e699bd106e1f172fdfec4ae00867abe303ab9f18fae13d3a396aedf62df1 +size 2500769 diff --git a/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/full.md b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2e420c18209fa480a4e7703f622fc5d518beab80 --- /dev/null +++ b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/full.md @@ -0,0 +1,337 @@ +# Q-DETR: An Efficient Low-Bit Quantized Detection Transformer + +Sheng Xu $^{1\dagger}$ , Yanjing Li $^{1\dagger}$ , Mingbao Lin $^{3}$ , Peng Gao $^{4}$ , Guodong Guo $^{5}$ , Jinhu Lu $^{1,2}$ , Baochang Zhang $^{1,2*}$ $^{1}$ Beihang University + $^{2}$ Zhongguancun Laboratory + $^{3}$ Tencent + $^{4}$ Shanghai AI Laboratory + $^{5}$ UNIUBI Research, Universal Ubiquitous Co. + +# Abstract + +The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by $6.6\times$ and achieve $39.4\%$ AP, with only $2.6\%$ performance gaps than its real-valued counterpart on the COCO dataset1. + +# 1. Introduction + +Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem. + +![](images/b47e025e70e302f5e79025c7b330255d3d8a381daa5d068aee71250b90faccb5.jpg) + +![](images/58e77532541a7f2ba0fc9047e639c676fc6a1902b28eff415a9f5bd61e81e899.jpg) + +![](images/18b15d8ecd08b2a6746d8a20492c258c57b9109c76d5d9a7c04afb4562f715f8.jpg) + +![](images/8156cf2f15f19b131f79b7183987c36c7b62f255802f7021454e16e457f5de81.jpg) + +![](images/3adddb20ddfb6562d837c9002e09030289bca8f8a4171abca63cc56fc35c6e37.jpg) +(b) 4-bit DETR-R50 + +![](images/43ddb4a0e46f89a0a644c9d7bacbd5db54540eea7587e8f33923960758423819.jpg) +Figure 1. The histogram of query values $\mathbf{q}$ (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9]. + +Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources. + +Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset + +![](images/212d2dd96265f5ff199cdad769f4646e2b479ae54c58646fc765cdb77f0c6adb.jpg) + +![](images/7ea89e0832bcf3d9a3ff705e69ca60c51428f4d85b5ada2bcfce4e4ddef14d22.jpg) +(a) Real-valued DETR-R50 +(b) 4-bit DETR-R50 +Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly. + +simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched. + +In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves $76.9\%$ $\mathrm{AP}_{50}$ , leaving a $6.4\%$ performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary. + +To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica + +tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation. + +This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines. + +# 2. Related Work + +Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a $2 \sim 4$ -bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At + +![](images/e14e6d7bf16502bdbbfef0806f218e3f421ce352046ef7f791139d22bbb35d7a.jpg) +Architecture of quantized decoder + +![](images/7401aae9e52ea80a8fb67f38f65d8a5a1a3a60a044a3d502a6bba7bb018998ab.jpg) +Learning Q-DETR with DRD +Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively. + +the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example. + +Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR. + +However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively. + +# 3. The Challenge of Quantizing DETR + +# 3.1. Quantized DETR baseline + +We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow $\mathrm{LSQ + [2]}$ to introduce a general framework of asymmetric activation quantization and symmetric weight quantization: + +$$ +\begin{array}{l} \boldsymbol {x} _ {q} = \left\lfloor \operatorname {c l i p} \left\{\frac {\left(\boldsymbol {x} - z\right)}{\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \right\} \right\lceil , \mathbf {w} _ {q} = \left\lfloor \operatorname {c l i p} \left\{\frac {\mathbf {w}}{\alpha_ {\mathbf {w}}}, Q _ {n} ^ {\mathbf {w}}, Q _ {p} ^ {\mathbf {w}} \right\} \right\rceil , \\ Q _ {a} (x) = \alpha_ {x} \circ \mathbf {x} _ {q} + z, \quad Q _ {w} (x) = \alpha_ {\mathbf {w}} \circ \mathbf {w} _ {q}, \tag {1} \\ \end{array} +$$ + +where $\operatorname{clip}\{y, r_1, r_2\}$ clips the input $y$ with value bounds $r_1$ and $r_2$ ; the $[y]$ rounds $y$ to its nearest integer; the $\circ$ denotes the channel-wise multiplication. And $Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1$ , $Q_n^{\mathbf{w}} = -2^{b-1}$ , $Q_p^{\mathbf{w}} = 2^{b-1} - 1$ are the discrete bounds for $a$ -bit activations and $b$ -bit weights. $x$ generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as: + +$$ +\operatorname {Q} - \operatorname {F C} (\boldsymbol {x}) = Q _ {a} (\boldsymbol {x}) \cdot Q _ {w} (\mathbf {w}) = \alpha_ {x} \alpha_ {\mathbf {w}} \circ \left(\boldsymbol {x} _ {q} \odot \mathbf {w} _ {q} + z / \alpha_ {x} \circ \mathbf {w} _ {q}\right), \tag {2} +$$ + +where $\cdot$ denotes the matrix multiplication and $\odot$ denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation. + +In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output $\mathbf{E}$ , DETR performs co-attention between object queries $\mathbf{O}$ and the vi + +![](images/a5c972047c20bda899b5fbf274b37c7127f9b4a5c59762ec87268a7689ec6b8c.jpg) +Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules. + +sual features $\mathbf{E}$ , which are formulated as: + +$$ +\mathbf {q} = \mathrm {Q - F C} (\mathbf {O}), \mathbf {k}, \mathbf {v} = \mathrm {Q - F C} (\mathbf {E}) +$$ + +$$ +\mathbf {A} _ {i} = \operatorname {s o f t m a x} \left(Q _ {a} (\mathbf {q}) _ {i} \cdot Q _ {a} (\mathbf {k}) _ {i} ^ {\top} / \sqrt {d}\right), \tag {3} +$$ + +$$ +\mathbf {D} _ {i} = Q _ {a} (\mathbf {A}) _ {i} \cdot Q _ {a} (\mathbf {v}) _ {i}, +$$ + +where $\mathbf{D}$ is the multi-head co-attention module, i.e., the coattended feature for the object query. The $d$ denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query. + +# 3.2. Challenge Analysis + +Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation. + +We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e., $(1) + (2) + (3)$ , brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to $2.1\%$ in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de + +graded information representation is the main obstacle to a better quantized DETR. + +# 4. The Proposed Q-DETR + +# 4.1. Information Bottleneck of Q-DETR + +To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts $\mathcal{T}$ and $\mathcal{S}$ , respectively. + +Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is: + +$$ +\min _ {\theta^ {S}} I (X; \mathbf {E} ^ {S}) - \beta I (\mathbf {E} ^ {S}, \mathbf {q} ^ {S}; \boldsymbol {y} ^ {G T}) - \gamma I (\mathbf {q} ^ {S}; \mathbf {q} ^ {\mathcal {T}}), \tag {4} +$$ + +where $\mathbf{q}^T$ and $\mathbf{q}^S$ represent the queries in the teacher and student DETR methods as predefined in Eq. (3); $\beta$ and $\gamma$ are the Lagrange multipliers [35]; $\theta^S$ is the parameters of the student; and $I(\cdot)$ returns the mutual information of two input variables. The first item $I(X; \mathbf{E}^S)$ minimizes information between input and visual features $\mathbf{E}^S$ to extract task-oriented hints [40]. The second item $I(\mathbf{E}^S, \mathbf{q}^S; \boldsymbol{y}^{GT})$ maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression. + +The core issue of this paper is to solve the third item $I(\mathbf{q}^S;\mathbf{q}^T)$ , which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as: + +$$ +I (\mathbf {q} ^ {\mathcal {S}}; \mathbf {q} ^ {\mathcal {T}}) = H (\mathbf {q} ^ {\mathcal {S}}) - H (\mathbf {q} ^ {\mathcal {S}} | \mathbf {q} ^ {\mathcal {T}}), \tag {5} +$$ + +where $H(\mathbf{q}^S)$ returns the self information entropy expected to be maximized while $H(\mathbf{q}^S|\mathbf{q}^T)$ is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes + +the two items, which is explicitly defined as: + +$$ +\begin{array}{l} \min _ {\theta} H (\mathbf {q} ^ {S ^ {*}} | \mathbf {q} ^ {\mathcal {T}}), \\ s. t. \quad \mathbf {q} ^ {\mathcal {S} ^ {*}} = \underset {\mathbf {q} ^ {\mathcal {S}}} {\arg \max } H (\mathbf {q} ^ {\mathcal {S}}). \tag {6} \\ \end{array} +$$ + +Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query $\mathbf{q}^{S^*}$ and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's. + +# 4.2. Distribution Rectification Distillation + +Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy, $H(\mathbf{q}^S)$ can be implicitly expanded as: + +$$ +H \left(\mathbf {q} ^ {\mathcal {S}}\right) = - \int_ {\mathbf {q} _ {i} ^ {\mathcal {S}} \in \mathbf {q} ^ {\mathcal {S}}} p \left(\mathbf {q} _ {i} ^ {\mathcal {S}}\right) \log p \left(\mathbf {q} _ {i} ^ {\mathcal {S}}\right). \tag {7} +$$ + +However, an explicit form of $H(\mathbf{q}^S)$ can only be parameterized with a regular distribution $p(\mathbf{q}_i^S)$ . Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean $\mu (\mathbf{q}^S)$ and variance $\sigma (\mathbf{q}^S)$ of query $\mathbf{q}^S$ whose distribution is then modeled as $\mathbf{q}^S\sim \mathcal{N}(\mu (\mathbf{q}^S),\sigma (\mathbf{q}^S))$ . Then, the self-information entropy of the student query can be proceeded as: + +$$ +\begin{array}{l} H (\mathbf {q} ^ {\mathcal {S}}) = - \mathbb {E} [ \log \mathcal {N} (\mu (\mathbf {q} ^ {\mathcal {S}}), \sigma (\mathbf {q} ^ {\mathcal {S}})) ] \\ = - \mathbb {E} [ \log [ (2 \pi \sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2}) ^ {\frac {1}{2}} \exp (- \frac {(\mathbf {q} _ {i} ^ {\mathcal {S}} - \mu (\mathbf {q} ^ {\mathcal {S}})) ^ {2}}{2 \sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2}})) ] \\ = \frac {1}{2} \log 2 \pi \sigma \left(\mathbf {q} ^ {\mathcal {S}}\right) ^ {2}. \tag {8} \\ \end{array} +$$ + +The above objective reaches its maximum of $H(\mathbf{q}^{S^*}) = (1/2) \log 2\pi e[\sigma(\mathbf{q}^S)^2 + \epsilon_{\mathbf{q}^S}]$ when $\mathbf{q}^{S^*} = [\mathbf{q}^S - \mu(\mathbf{q}^S)] / [\sqrt{\sigma(\mathbf{q}^S)^2 + \epsilon_{\mathbf{q}^S}}]$ where $\epsilon_{\mathbf{q}^S} = 1e^{-5}$ is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter $\beta_{\mathbf{q}^S}$ is added to move the mean value. A learnable scaling parameter $\gamma_{\mathbf{q}^S}$ is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows: + +$$ +\mathbf {q} ^ {\mathcal {S} ^ {*}} = \frac {\mathbf {q} ^ {\mathcal {S}} - \mu (\mathbf {q} ^ {\mathcal {S}})}{\sqrt {\sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2} + \epsilon_ {\mathbf {q} ^ {\mathcal {S}}}}} \gamma_ {\mathbf {q} ^ {\mathcal {S}}} + \beta_ {\mathbf {q} ^ {\mathcal {S}}}, \tag {9} +$$ + +in which case the maximum self-information entropy of student query becomes $H(\mathbf{q}^{\mathcal{S}^*}) = (1/2) \log 2\pi e[(\sigma_{\mathbf{q}^{\mathcal{S}}}^2 + \epsilon_{\mathbf{q}^{\mathcal{S}}}) / \gamma_{\mathbf{q}^{\mathcal{S}}}^2]$ . Therefore, in the forward propagation, we can obtain the current optimal query $\mathbf{q}^{\mathcal{S}^*}$ via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents. + +Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by $\pmb{y}^{GT} = \{c_i^{GT}, b_i^{GT}\}_{i=1}^{N_{gt}}$ as a set of ground-truth objects where $N_{gt}$ is the number of foregrounds, $c_i^{GT}$ and $b_i^{GT}$ respectively represent the class and coordinate (bound- ing box) for the $i$ -th object. In DETR, each query is associated with an object. Therefore, we can obtain $N$ objects for teacher and student as well, denoted as $\pmb{y}^S = \{c_j^S, b_j^S\}_{j=1}^N$ and $\pmb{y}^T = \{c_j^T, b_j^T\}_{j=1}^N$ . + +The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify "well-matched" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as: + +$$ +G _ {i} = \max _ {1 \leq j \leq N} \operatorname {G I o U} \left(b _ {i} ^ {G T}, b _ {j} ^ {S}\right), \tag {10} +$$ + +where $\mathrm{GIOU}(\cdot)$ is the generalized intersection over union function [32]. Each $G_{i}$ reflects the "closeness" of student proposals to the $i$ -th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as: + +$$ +b _ {j} ^ {\mathcal {S}} = \left\{ \begin{array}{l l} b _ {j} ^ {\mathcal {S}}, & \text {G I o U} \left(b _ {i} ^ {G T}, b _ {j} ^ {\mathcal {S}}\right) > \tau G _ {i}, \forall i \\ \varnothing , & \text {o t h e r w i s e}, \end{array} \right. \tag {11} +$$ + +where $\tau$ is a threshold controlling the proportion of distilled queries. After removing object-empty $(\varnothing)$ queries in $\tilde{\pmb{q}}^S$ , we form a distillation-desired query set of students denoted as $\tilde{\pmb{q}}^S$ associated with its object set $\tilde{\pmb{y}}^S = \{\tilde{c}_j^S, \tilde{b}_j^S\}_{j=1}^N$ . Correspondingly, we can obtain a teacher query set $\tilde{\pmb{y}}^T = \{\tilde{c}_j^T, \tilde{b}_j^T\}_{j=1}^N$ . For the $j$ -th student query, its corresponding teacher query is matched as: + +$$ +\tilde {c} _ {j} ^ {\mathcal {T}}, \tilde {b} _ {j} ^ {\mathcal {T}} = \underset {\tilde {c} _ {k} ^ {\mathcal {T}}, \tilde {b} _ {k} ^ {\mathcal {T}}} {\arg \max } \sum_ {k = 1} ^ {N} \mu_ {1} \operatorname {G I o U} \left(\tilde {b} _ {j} ^ {\mathcal {S}}, b _ {k} ^ {\mathcal {T}}\right) - \mu_ {2} \| \tilde {b} _ {j} ^ {\mathcal {S}} - b _ {k} ^ {\mathcal {T}} \| _ {1}, \tag {12} +$$ + +where $\mu_{1} = 2$ and $\mu_{2} = 5$ control the matching function, values of which is to follow [4]. + +Finally, the upper-level optimization after rectification in Eq. (6) becomes: + +$$ +\min _ {\theta} H \left(\tilde {\mathbf {q}} ^ {\mathcal {S} ^ {*}} \mid \tilde {\mathbf {q}} ^ {\mathcal {T}}\right). \tag {13} +$$ + +Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between $\tilde{\mathbf{q}}^{S^*}$ and $\tilde{\mathbf{q}}^T$ , optima of which, i.e., $\tilde{\mathbf{q}}^{S^*} = \tilde{\mathbf{q}}^T$ , is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes: + +$$ +\mathcal {L} _ {D R D} \left(\tilde {\mathbf {q}} ^ {\mathcal {S} ^ {*}}, \tilde {\mathbf {q}} ^ {\mathcal {T}}\right) = \mathbb {E} \left[ \left\| \tilde {\mathbf {D}} ^ {\mathcal {S} ^ {*}} - \tilde {\mathbf {D}} ^ {\mathcal {T}} \right\| _ {2} \right], \tag {14} +$$ + +where we use the Euclidean distance of co-attented feature $\tilde{\mathbf{D}}$ (see Eq. 3) containing the information query $\tilde{\mathbf{q}}$ for optimization. + +In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are: + +$$ +\mathcal {L} = \mathcal {L} _ {G T} \left(\boldsymbol {y} ^ {G T}, \boldsymbol {y} ^ {\mathcal {S}}\right) + \lambda \mathcal {L} _ {D R D} \left(\tilde {\boldsymbol {\mathbf {q}}} ^ {\mathcal {S} ^ {*}}, \tilde {\boldsymbol {\mathbf {q}}} ^ {\mathcal {T}}\right), \tag {15} +$$ + +where $L_{GT}$ is the common detection loss for missions such as proposal classification and coordinate regression [4], and $\lambda$ is a tradeoff hyper-parameter. + +# 5. Experiments + +In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves. + +# 5.1. Datasets and Implementation Details + +Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP, $\mathrm{AP}_{50}$ (default VOC metric), and $\mathrm{AP}_{75}$ . We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list $\mathrm{AP}_{50}$ , $\mathrm{AP}_{75}$ , $\mathrm{AP}_s$ , $\mathrm{AP}_m$ , and $\mathrm{AP}_l$ . + +Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train + +![](images/f81fb84b5bb6aab549b17b32fa5da6cc62eb498e5c10813514540515dba9c182.jpg) +(a) Effect of $\tau$ and $\lambda$ . + +![](images/47952eabf7f40ca87b81667b8ca2c1c9243c9c288b2ab9cb3103439d10a90646.jpg) +(b) Mutual information curves. +Figure 5. (a) We select $\tau$ and $\lambda$ using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of $I(X; \mathbf{E})$ and $I(\boldsymbol{y}^{GT}; \mathbf{E}, \mathbf{q})$ (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR). + +the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of $1e^{-4}$ . We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP50 on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP50 on VOC and 44.4% AP on COCO) as teacher network. + +# 5.2. Ablation Study + +Hyper-parameter selection. As mentioned above, we select hyper-parameters $\tau$ and $\lambda$ in this part using the 4-bit Q-DETR model. We show the model performance $(\mathrm{AP}_{50})$ with different setups of hyper-parameters $\{\tau ,\lambda \}$ in Fig.5 (a), where we conduct ablative experiments on the baseline $+\mathrm{DA}(\mathrm{AP}_{50} = 78.8\%)$ . As can be seen, the performances increase first and then decrease with the increase of $\tau$ from left to right. Since $\tau$ controls the proportion of selected distillation-desired queries, we show that the full-imitation $(\tau = 0)$ performs worse than the vanilla baseline with no distillation $(\tau = 1)$ , showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of $\tau$ from left to right. The Q-DETR obtains better performances with $\tau$ set as 0.5 and 0.6. With the varying value of $\lambda$ , we find $\{\lambda ,\tau \} = \{2.5,0.6\}$ boost the performance of Q-DETR most, achieving $82.7\%$ AP on VOC test2007. Based on the ablative study above, we set hyper-parameters $\tau$ and $\lambda$ as 0.6 and 2.5 + +Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching. + +
Method#Bits\(AP_{50}\)#Bits\(AP_{50}\)#Bits\(AP_{50}\)
Real-valued32-32-3283.3----
Baseline4-4-878.03-3-876.82-2-869.7
+DA4-4-878.83-3-878.02-2-871.6
+FQM4-4-881.53-3-880.92-2-874.9
+DA+FQM(Q-DETR)4-4-882.73-3-882.12-2-876.4
+ +for the experiments in this paper. + +Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on $\mathrm{AP}_{50}$ (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%. + +Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test $\mathrm{AP}_{50}$ to quantify $I(\boldsymbol{y}^{GT};\mathbf{E},\mathbf{q})$ . We employ a reconstruction decoder to decode the encoded feature $\mathbf{E}$ to reconstruct the input and quantify $I(X;\mathbf{E})$ using the $\ell_1$ loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods. + +# 5.3. Results on PASCAL VOC + +We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e. $1333 \times 800$ . We mainly discuss the $\mathrm{AP}_{50}$ (default VOC metric) in the following. + +We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture + +Table 2. We report AP, $\mathrm{AP}_{50}$ , and $\mathrm{AP}_{75}$ (\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. + +
ModelMethod#BitsAP\( AP_{50} \)\( AP_{75} \)
DETR-R50Real-valued32-32-3259.583.364.7
Percentile8-8-854.779.260.1
VT-PTQ57.682.363.1
LSQ49.776.953.0
Baseline4-4-851.378.054.1
Q-DETR57.182.761.5
LSQ47.075.349.1
Baseline3-3-849.276.851.8
Q-DETR56.882.161.2
LSQ42.668.244.8
Baseline2-2-844.069.745.8
Q-DETR50.776.454.1
SMCA-DETR -R50Real-valued32-32-3256.783.762.0
Percentile8-8-854.779.260.1
VT-PTQ55.983.061.3
LSQ49.678.653.4
Baseline4-4-850.779.555.4
Q-DETR56.283.361.6
LSQ47.776.551.7
Baseline3-3-849.977.553.6
Q-DETR54.382.659.5
LSQ42.369.744.8
Baseline2-2-843.970.446.1
Q-DETR50.276.752.6
+ +and bit-width, which significantly validates the effectiveness of our method. + +Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by $6.3\%$ , $5.1\%$ and $3.8\%$ on $\mathrm{AP}_{50}$ , a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance. + +# 5.4. Results on COCO + +We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3. + +Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various + +Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations. + +
ModelMethod#BitsSize(MB)OPs(G)APAP50AP75APsAPmAPl
DETR-R50Real-valued32-32-32159.3285.5142.062.444.220.545.861.1
Percentile8-8-839.8323.0138.6-----
VT-PTQ41.2-----
LSQ33.353.733.912.837.051.6
Baseline4-4-819.9213.0234.155.335.414.338.053.8
Q-DETR39.460.241.417.743.459.9
LSQ31.052.332.111.333.948.5
Baseline3-3-815.037.6132.352.232.912.335.450.3
Q-DETR36.155.937.514.639.455.2
LSQ24.744.626.56.325.342.7
Baseline2-2-810.035.3226.646.626.58.428.244.4
Q-DETR31.451.331.611.634.349.6
SMCA-DETR-R50Real-valued32-32-32164.7586.6541.062.243.621.944.359.1
Percentile8-8-841.1923.6637.558.540.117.639.155.9
VT-PTQ40.261.042.620.342.957.7
LSQ33.955.035.013.237.251.4
Baseline4-4-820.5913.4835.056.436.415.638.352.5
Q-DETR38.359.739.817.741.756.8
LSQ30.152.631.411.933.446.6
Baseline3-3-815.688.0531.853.732.612.635.249.8
Q-DETR35.056.336.915.039.053.1
LSQ23.942.224.29.426.237.5
Baseline2-2-810.844.5425.444.325.28.427.240.3
Q-DETR30.551.831.812.033.248.0
+ +detectors. We follow [40] to calculate memory usage, by adding $32 \times$ the number of real-valued weights and $a \times$ the number of quantized weights in the $a$ -bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds $\left\{\frac{1}{32}, \frac{1}{16}, \frac{1}{8}\right\}$ of the number of $\{2,3,4\}$ -bit multiplications equals the OPs following [24]. + +We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of $2/3/4$ -bit baseline by $4.8\%$ , $3.8\%$ and $5.1\%$ AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed $2/3/4$ -bit Q-DETR achieves computation acceleration and storage savings by $16.07 \times / 11.23 \times / 6.57 \times$ and $15.88 \times / 10.60 \times / 7.99 \times$ . The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection. + +For the SMCA-DETR-R50 model, we observe similar + +performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates $6.42 \times$ with only a $2.7\%$ performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods. + +# 6. Conclusion + +This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. 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In Proc. of CVPR, pages 7920-7928, 2018. 2 \ No newline at end of file diff --git a/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/images.zip b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a9c033bbe6cb510bdd3f41ff1e2facb26e43bf24 --- /dev/null +++ b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:991fa9241a32959dd39bf535169cabaa6a3c959a312e20f1faa342782d12619f +size 555590 diff --git a/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/layout.json b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..30d603cd46c04c9ea9889926b3fc06b6b9594d27 --- /dev/null +++ b/2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/layout.json @@ -0,0 +1,9926 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 94, + 103, + 500, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 103, + 500, + 120 + ], + "spans": [ + { + "bbox": [ + 94, + 103, + 500, + 120 + ], + "type": "text", + "content": "Q-DETR: An Efficient Low-Bit Quantized Detection Transformer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "spans": [ + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": "Sheng Xu" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Yanjing Li" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Mingbao Lin" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Peng Gao" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Guodong Guo" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Jinhu Lu" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": ", Baochang Zhang" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": " Beihang University \n" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": " Zhongguancun Laboratory \n" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": " Tencent \n" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": " Shanghai AI Laboratory \n" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 53, + 141, + 548, + 186 + ], + "type": "text", + "content": " UNIUBI Research, Universal Ubiquitous Co." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "text", + "content": "The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by " + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "6.6\\times" + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "text", + "content": " and achieve " + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "39.4\\%" + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "text", + "content": " AP, with only " + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 47, + 238, + 290, + 539 + ], + "type": "text", + "content": " performance gaps than its real-valued counterpart on the COCO dataset1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "text", + "content": "Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 214, + 385, + 277 + ], + "blocks": [ + { + "bbox": [ + 310, + 214, + 385, + 277 + ], + "lines": [ + { + "bbox": [ + 310, + 214, + 385, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 214, + 385, + 277 + ], + "type": "image", + "image_path": "b47e025e70e302f5e79025c7b330255d3d8a381daa5d068aee71250b90faccb5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 390, + 215, + 463, + 275 + ], + "blocks": [ + { + "bbox": [ + 390, + 215, + 463, + 275 + ], + "lines": [ + { + "bbox": [ + 390, + 215, + 463, + 275 + ], + "spans": [ + { + "bbox": [ + 390, + 215, + 463, + 275 + ], + "type": "image", + "image_path": "58e77532541a7f2ba0fc9047e639c676fc6a1902b28eff415a9f5bd61e81e899.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 468, + 215, + 542, + 277 + ], + "blocks": [ + { + "bbox": [ + 468, + 215, + 542, + 277 + ], + "lines": [ + { + "bbox": [ + 468, + 215, + 542, + 277 + ], + "spans": [ + { + "bbox": [ + 468, + 215, + 542, + 277 + ], + "type": "image", + "image_path": "18b15d8ecd08b2a6746d8a20492c258c57b9109c76d5d9a7c04afb4562f715f8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 277, + 384, + 340 + ], + "blocks": [ + { + "bbox": [ + 309, + 277, + 384, + 340 + ], + "lines": [ + { + "bbox": [ + 309, + 277, + 384, + 340 + ], + "spans": [ + { + "bbox": [ + 309, + 277, + 384, + 340 + ], + "type": "image", + "image_path": "8156cf2f15f19b131f79b7183987c36c7b62f255802f7021454e16e457f5de81.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 389, + 277, + 462, + 338 + ], + "blocks": [ + { + "bbox": [ + 389, + 277, + 462, + 338 + ], + "lines": [ + { + "bbox": [ + 389, + 277, + 462, + 338 + ], + "spans": [ + { + "bbox": [ + 389, + 277, + 462, + 338 + ], + "type": "image", + "image_path": "3adddb20ddfb6562d837c9002e09030289bca8f8a4171abca63cc56fc35c6e37.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 339, + 462, + 348 + ], + "lines": [ + { + "bbox": [ + 397, + 339, + 462, + 348 + ], + "spans": [ + { + "bbox": [ + 397, + 339, + 462, + 348 + ], + "type": "text", + "content": "(b) 4-bit DETR-R50" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 467, + 285, + 542, + 339 + ], + "blocks": [ + { + "bbox": [ + 467, + 285, + 542, + 339 + ], + "lines": [ + { + "bbox": [ + 467, + 285, + 542, + 339 + ], + "spans": [ + { + "bbox": [ + 467, + 285, + 542, + 339 + ], + "type": "image", + "image_path": "43ddb4a0e46f89a0a644c9d7bacbd5db54540eea7587e8f33923960758423819.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "type": "text", + "content": "Figure 1. The histogram of query values " + }, + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "type": "text", + "content": " (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9]." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "content": "Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 683, + 132, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 683, + 132, + 693 + ], + "spans": [ + { + "bbox": [ + 61, + 683, + 132, + 693 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 61, + 683, + 132, + 693 + ], + "type": "text", + "content": " Equal contribution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 63, + 694, + 217, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 694, + 217, + 703 + ], + "spans": [ + { + "bbox": [ + 63, + 694, + 217, + 703 + ], + "type": "text", + "content": "* Corresponding author: bczhang@buaa.edu.cn" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 63, + 704, + 260, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 704, + 260, + 712 + ], + "spans": [ + { + "bbox": [ + 63, + 704, + 260, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 63, + 704, + 260, + 712 + ], + "type": "text", + "content": "Code: https://github.com/SteveTsui/Q-DETR" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3842" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 283, + 114 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 283, + 114 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 283, + 114 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 283, + 114 + ], + "type": "image", + "image_path": "212d2dd96265f5ff199cdad769f4646e2b479ae54c58646fc765cdb77f0c6adb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 124, + 283, + 168 + ], + "blocks": [ + { + "bbox": [ + 116, + 115, + 217, + 124 + ], + "lines": [ + { + "bbox": [ + 116, + 115, + 217, + 124 + ], + "spans": [ + { + "bbox": [ + 116, + 115, + 217, + 124 + ], + "type": "text", + "content": "(a) Real-valued DETR-R50" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 52, + 124, + 283, + 168 + ], + "lines": [ + { + "bbox": [ + 52, + 124, + 283, + 168 + ], + "spans": [ + { + "bbox": [ + 52, + 124, + 283, + 168 + ], + "type": "image", + "image_path": "7ea89e0832bcf3d9a3ff705e69ca60c51428f4d85b5ada2bcfce4e4ddef14d22.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 129, + 168, + 205, + 178 + ], + "lines": [ + { + "bbox": [ + 129, + 168, + 205, + 178 + ], + "spans": [ + { + "bbox": [ + 129, + 168, + 205, + 178 + ], + "type": "text", + "content": "(b) 4-bit DETR-R50" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 187, + 287, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 287, + 264 + ], + "type": "text", + "content": "Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 290, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 350 + ], + "type": "text", + "content": "simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "text", + "content": "In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves " + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "inline_equation", + "content": "76.9\\%" + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "text", + "content": ", leaving a " + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "inline_equation", + "content": "6.4\\%" + }, + { + "bbox": [ + 46, + 352, + 287, + 651 + ], + "type": "text", + "content": " performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 300, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 383 + ], + "type": "text", + "content": "This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": "Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "2 \\sim 4" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": "-bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3843" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 88, + 272, + 243 + ], + "blocks": [ + { + "bbox": [ + 94, + 75, + 228, + 86 + ], + "lines": [ + { + "bbox": [ + 94, + 75, + 228, + 86 + ], + "spans": [ + { + "bbox": [ + 94, + 75, + 228, + 86 + ], + "type": "text", + "content": "Architecture of quantized decoder" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 88, + 272, + 243 + ], + "lines": [ + { + "bbox": [ + 61, + 88, + 272, + 243 + ], + "spans": [ + { + "bbox": [ + 61, + 88, + 272, + 243 + ], + "type": "image", + "image_path": "e14e6d7bf16502bdbbfef0806f218e3f421ce352046ef7f791139d22bbb35d7a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 280, + 86, + 541, + 243 + ], + "blocks": [ + { + "bbox": [ + 347, + 76, + 462, + 87 + ], + "lines": [ + { + "bbox": [ + 347, + 76, + 462, + 87 + ], + "spans": [ + { + "bbox": [ + 347, + 76, + 462, + 87 + ], + "type": "text", + "content": "Learning Q-DETR with DRD" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 280, + 86, + 541, + 243 + ], + "lines": [ + { + "bbox": [ + 280, + 86, + 541, + 243 + ], + "spans": [ + { + "bbox": [ + 280, + 86, + 541, + 243 + ], + "type": "image", + "image_path": "7401aae9e52ea80a8fb67f38f65d8a5a1a3a60a044a3d502a6bba7bb018998ab.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 547, + 291 + ], + "type": "text", + "content": "Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 311, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 360 + ], + "type": "text", + "content": "the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 363, + 288, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 288, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 288, + 624 + ], + "type": "text", + "content": "Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 309, + 505, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 505, + 324 + ], + "type": "text", + "content": "3. The Challenge of Quantizing DETR" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 331, + 451, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 451, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 451, + 344 + ], + "type": "text", + "content": "3.1. Quantized DETR baseline" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 351, + 546, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 546, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 546, + 413 + ], + "type": "text", + "content": "We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow " + }, + { + "bbox": [ + 305, + 351, + 546, + 413 + ], + "type": "inline_equation", + "content": "\\mathrm{LSQ + [2]}" + }, + { + "bbox": [ + 305, + 351, + 546, + 413 + ], + "type": "text", + "content": " to introduce a general framework of asymmetric activation quantization and symmetric weight quantization:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 425, + 545, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 425, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 309, + 425, + 545, + 470 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {x} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\left(\\boldsymbol {x} - z\\right)}{\\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \\right\\} \\right\\lceil , \\mathbf {w} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\mathbf {w}}{\\alpha_ {\\mathbf {w}}}, Q _ {n} ^ {\\mathbf {w}}, Q _ {p} ^ {\\mathbf {w}} \\right\\} \\right\\rceil , \\\\ Q _ {a} (x) = \\alpha_ {x} \\circ \\mathbf {x} _ {q} + z, \\quad Q _ {w} (x) = \\alpha_ {\\mathbf {w}} \\circ \\mathbf {w} _ {q}, \\tag {1} \\\\ \\end{array}", + "image_path": "235f957b7795aaa2d4dd2682e55a0a4a9de523c6587911e259ccabec8dd456b0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\operatorname{clip}\\{y, r_1, r_2\\}" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " clips the input " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " with value bounds " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "r_2" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": "; the " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "[y]" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " rounds " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " to its nearest integer; the " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " denotes the channel-wise multiplication. And " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "Q_n^{\\mathbf{w}} = -2^{b-1}" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "Q_p^{\\mathbf{w}} = 2^{b-1} - 1" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " are the discrete bounds for " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": "-bit activations and " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": "-bit weights. " + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 471, + 545, + 581 + ], + "type": "text", + "content": " generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 594, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 545, + 616 + ], + "type": "interline_equation", + "content": "\\operatorname {Q} - \\operatorname {F C} (\\boldsymbol {x}) = Q _ {a} (\\boldsymbol {x}) \\cdot Q _ {w} (\\mathbf {w}) = \\alpha_ {x} \\alpha_ {\\mathbf {w}} \\circ \\left(\\boldsymbol {x} _ {q} \\odot \\mathbf {w} _ {q} + z / \\alpha_ {x} \\circ \\mathbf {w} _ {q}\\right), \\tag {2}", + "image_path": "f2d8982a35150db20af413cba38281de662c35a1d05842b89db87bd9b2d32d19.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "text", + "content": " denotes the matrix multiplication and " + }, + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 305, + 616, + 545, + 664 + ], + "type": "text", + "content": " denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "text", + "content": "In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output " + }, + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "text", + "content": ", DETR performs co-attention between object queries " + }, + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 305, + 665, + 546, + 714 + ], + "type": "text", + "content": " and the vi" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3844" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 106, + 276, + 208 + ], + "blocks": [ + { + "bbox": [ + 61, + 106, + 276, + 208 + ], + "lines": [ + { + "bbox": [ + 61, + 106, + 276, + 208 + ], + "spans": [ + { + "bbox": [ + 61, + 106, + 276, + 208 + ], + "type": "image", + "image_path": "a5c972047c20bda899b5fbf274b37c7127f9b4a5c59762ec87268a7689ec6b8c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "type": "text", + "content": "Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 265, + 214, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 214, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 214, + 277 + ], + "type": "text", + "content": "sual features " + }, + { + "bbox": [ + 47, + 265, + 214, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 265, + 214, + 277 + ], + "type": "text", + "content": ", which are formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 285, + 235, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 285, + 235, + 298 + ], + "spans": [ + { + "bbox": [ + 91, + 285, + 235, + 298 + ], + "type": "interline_equation", + "content": "\\mathbf {q} = \\mathrm {Q - F C} (\\mathbf {O}), \\mathbf {k}, \\mathbf {v} = \\mathrm {Q - F C} (\\mathbf {E})", + "image_path": "19d60b9308198896fefbb1afc5deaef1fff2f8024ede69dcf9457cb85a5e1d2b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 301, + 287, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 301, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 86, + 301, + 287, + 316 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {i} = \\operatorname {s o f t m a x} \\left(Q _ {a} (\\mathbf {q}) _ {i} \\cdot Q _ {a} (\\mathbf {k}) _ {i} ^ {\\top} / \\sqrt {d}\\right), \\tag {3}", + "image_path": "95d13e19e36a6e1bc43db3e332443945577af69221d9b3d34496f78c9133a3f8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 86, + 318, + 187, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 318, + 187, + 331 + ], + "spans": [ + { + "bbox": [ + 86, + 318, + 187, + 331 + ], + "type": "interline_equation", + "content": "\\mathbf {D} _ {i} = Q _ {a} (\\mathbf {A}) _ {i} \\cdot Q _ {a} (\\mathbf {v}) _ {i},", + "image_path": "9172fe7ee7d33c72e45baf04a106796116103ef2f8e3905aae2d952fb9a9e432.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "text", + "content": " is the multi-head co-attention module, i.e., the coattended feature for the object query. The " + }, + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 340, + 287, + 436 + ], + "type": "text", + "content": " denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 443, + 160, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 160, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 160, + 456 + ], + "type": "text", + "content": "3.2. Challenge Analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "type": "text", + "content": "Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e., " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "(1) + (2) + (3)" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ", brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "graded information representation is the main obstacle to a better quantized DETR." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 114, + 442, + 128 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 114, + 442, + 128 + ], + "spans": [ + { + "bbox": [ + 305, + 114, + 442, + 128 + ], + "type": "text", + "content": "4. The Proposed Q-DETR" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 135, + 495, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 135, + 495, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 135, + 495, + 148 + ], + "type": "text", + "content": "4.1. Information Bottleneck of Q-DETR" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": "To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts " + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 230, + 546, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 546, + 348 + ], + "type": "text", + "content": "Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 360, + 545, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 360, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 315, + 360, + 545, + 380 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta^ {S}} I (X; \\mathbf {E} ^ {S}) - \\beta I (\\mathbf {E} ^ {S}, \\mathbf {q} ^ {S}; \\boldsymbol {y} ^ {G T}) - \\gamma I (\\mathbf {q} ^ {S}; \\mathbf {q} ^ {\\mathcal {T}}), \\tag {4}", + "image_path": "ed665607cb4335132c377a2a006491d1d57b879b52ac6e4aeca2a6a6ba81c3cf.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^T" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^S" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " represent the queries in the teacher and student DETR methods as predefined in Eq. (3); " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " are the Lagrange multipliers [35]; " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\theta^S" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " is the parameters of the student; and " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " returns the mutual information of two input variables. The first item " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "I(X; \\mathbf{E}^S)" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " minimizes information between input and visual features " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^S" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " to extract task-oriented hints [40]. The second item " + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "inline_equation", + "content": "I(\\mathbf{E}^S, \\mathbf{q}^S; \\boldsymbol{y}^{GT})" + }, + { + "bbox": [ + 304, + 393, + 546, + 537 + ], + "type": "text", + "content": " maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 540, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 540, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 540, + 545, + 598 + ], + "type": "text", + "content": "The core issue of this paper is to solve the third item " + }, + { + "bbox": [ + 305, + 540, + 545, + 598 + ], + "type": "inline_equation", + "content": "I(\\mathbf{q}^S;\\mathbf{q}^T)" + }, + { + "bbox": [ + 305, + 540, + 545, + 598 + ], + "type": "text", + "content": ", which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 352, + 612, + 545, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 612, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 352, + 612, + 545, + 628 + ], + "type": "interline_equation", + "content": "I (\\mathbf {q} ^ {\\mathcal {S}}; \\mathbf {q} ^ {\\mathcal {T}}) = H (\\mathbf {q} ^ {\\mathcal {S}}) - H (\\mathbf {q} ^ {\\mathcal {S}} | \\mathbf {q} ^ {\\mathcal {T}}), \\tag {5}", + "image_path": "7f9edace7dcd9bade7a02b53d689b41befd24c71146794f304f46b0ed97d52bc.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^S)" + }, + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "text", + "content": " returns the self information entropy expected to be maximized while " + }, + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^S|\\mathbf{q}^T)" + }, + { + "bbox": [ + 304, + 641, + 546, + 714 + ], + "type": "text", + "content": " is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 91, + 293, + 99 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 91, + 293, + 99 + ], + "spans": [ + { + "bbox": [ + 51, + 91, + 293, + 99 + ], + "type": "text", + "content": "(1) Quantizing backbone (2) Quantizing encoder (3) Quantizing MHA of decoder (4) Quantizing MLPs" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3845" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "text", + "content": "the two items, which is explicitly defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 91, + 286, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 91, + 286, + 135 + ], + "spans": [ + { + "bbox": [ + 104, + 91, + 286, + 135 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\theta} H (\\mathbf {q} ^ {S ^ {*}} | \\mathbf {q} ^ {\\mathcal {T}}), \\\\ s. t. \\quad \\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\underset {\\mathbf {q} ^ {\\mathcal {S}}} {\\arg \\max } H (\\mathbf {q} ^ {\\mathcal {S}}). \\tag {6} \\\\ \\end{array}", + "image_path": "e16d95ec0877dc3ca3b88f1d501aadee4728648499fe39f60a663b8e69c89b57.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 141, + 287, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 141, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 141, + 287, + 214 + ], + "type": "text", + "content": "Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query " + }, + { + "bbox": [ + 46, + 141, + 287, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^{S^*}" + }, + { + "bbox": [ + 46, + 141, + 287, + 214 + ], + "type": "text", + "content": " and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 220, + 243, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 220, + 243, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 220, + 243, + 232 + ], + "type": "text", + "content": "4.2. Distribution Rectification Distillation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": "Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy, " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^S)" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": " can be implicitly expanded as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 89, + 293, + 287, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 293, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 89, + 293, + 287, + 321 + ], + "type": "interline_equation", + "content": "H \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) = - \\int_ {\\mathbf {q} _ {i} ^ {\\mathcal {S}} \\in \\mathbf {q} ^ {\\mathcal {S}}} p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right) \\log p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right). \\tag {7}", + "image_path": "b1992f77cc4a826db5bc777e7f82a6c69681d37a186933eba2bbedefe62a1c5e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": "However, an explicit form of " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^S)" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": " can only be parameterized with a regular distribution " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "p(\\mathbf{q}_i^S)" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": ". Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{q}^S)" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\sigma (\\mathbf{q}^S)" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": " of query " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^S" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": " whose distribution is then modeled as " + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^S\\sim \\mathcal{N}(\\mu (\\mathbf{q}^S),\\sigma (\\mathbf{q}^S))" + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": ". Then, the self-information entropy of the student query can be proceeded as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 49, + 454, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 454, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 454, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} H (\\mathbf {q} ^ {\\mathcal {S}}) = - \\mathbb {E} [ \\log \\mathcal {N} (\\mu (\\mathbf {q} ^ {\\mathcal {S}}), \\sigma (\\mathbf {q} ^ {\\mathcal {S}})) ] \\\\ = - \\mathbb {E} [ \\log [ (2 \\pi \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}) ^ {\\frac {1}{2}} \\exp (- \\frac {(\\mathbf {q} _ {i} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})) ^ {2}}{2 \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}})) ] \\\\ = \\frac {1}{2} \\log 2 \\pi \\sigma \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) ^ {2}. \\tag {8} \\\\ \\end{array}", + "image_path": "429501c595e8c8b85a5038ccd2235fda911cc3dd27db4e999a848866366526d6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": "The above objective reaches its maximum of " + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^{S^*}) = (1/2) \\log 2\\pi e[\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}]" + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^{S^*} = [\\mathbf{q}^S - \\mu(\\mathbf{q}^S)] / [\\sqrt{\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}}]" + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathbf{q}^S} = 1e^{-5}" + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": " is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter " + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathbf{q}^S}" + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": " is added to move the mean value. A learnable scaling parameter " + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathbf{q}^S}" + }, + { + "bbox": [ + 46, + 534, + 287, + 674 + ], + "type": "text", + "content": " is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 87, + 681, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 681, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 87, + 681, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\frac {\\mathbf {q} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})}{\\sqrt {\\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2} + \\epsilon_ {\\mathbf {q} ^ {\\mathcal {S}}}}} \\gamma_ {\\mathbf {q} ^ {\\mathcal {S}}} + \\beta_ {\\mathbf {q} ^ {\\mathcal {S}}}, \\tag {9}", + "image_path": "809e58dd26faa9d3b73854fd67656d57f97dccab3b6979ff68b6597ce28d724e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "text", + "content": "in which case the maximum self-information entropy of student query becomes " + }, + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "inline_equation", + "content": "H(\\mathbf{q}^{\\mathcal{S}^*}) = (1/2) \\log 2\\pi e[(\\sigma_{\\mathbf{q}^{\\mathcal{S}}}^2 + \\epsilon_{\\mathbf{q}^{\\mathcal{S}}}) / \\gamma_{\\mathbf{q}^{\\mathcal{S}}}^2]" + }, + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "text", + "content": ". Therefore, in the forward propagation, we can obtain the current optimal query " + }, + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\mathbf{q}^{\\mathcal{S}^*}" + }, + { + "bbox": [ + 304, + 72, + 545, + 148 + ], + "type": "text", + "content": " via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": "Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "\\pmb{y}^{GT} = \\{c_i^{GT}, b_i^{GT}\\}_{i=1}^{N_{gt}}" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " as a set of ground-truth objects where " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "N_{gt}" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " is the number of foregrounds, " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "c_i^{GT}" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "b_i^{GT}" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " respectively represent the class and coordinate (bound- ing box) for the " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": "-th object. In DETR, each query is associated with an object. Therefore, we can obtain " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " objects for teacher and student as well, denoted as " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "\\pmb{y}^S = \\{c_j^S, b_j^S\\}_{j=1}^N" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "inline_equation", + "content": "\\pmb{y}^T = \\{c_j^T, b_j^T\\}_{j=1}^N" + }, + { + "bbox": [ + 304, + 148, + 545, + 272 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 271, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 376 + ], + "type": "text", + "content": "The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify \"well-matched\" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 364, + 374, + 545, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 374, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 364, + 374, + 545, + 393 + ], + "type": "interline_equation", + "content": "G _ {i} = \\max _ {1 \\leq j \\leq N} \\operatorname {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {S}\\right), \\tag {10}", + "image_path": "b5fc2601eea40d3e852c09993636ba2b71c569d1f9c547eb500d6e1c8ed9d494.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\mathrm{GIOU}(\\cdot)" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": " is the generalized intersection over union function [32]. Each " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": " reflects the \"closeness\" of student proposals to the " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": "-th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 467, + 545, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 467, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 340, + 467, + 545, + 493 + ], + "type": "interline_equation", + "content": "b _ {j} ^ {\\mathcal {S}} = \\left\\{ \\begin{array}{l l} b _ {j} ^ {\\mathcal {S}}, & \\text {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {\\mathcal {S}}\\right) > \\tau G _ {i}, \\forall i \\\\ \\varnothing , & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {11}", + "image_path": "27f626d29da25fde79924bdf59a9226613c9b53c912bd0b6e147fe267409a89d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": " is a threshold controlling the proportion of distilled queries. After removing object-empty " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "(\\varnothing)" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": " queries in " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{q}}^S" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": ", we form a distillation-desired query set of students denoted as " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{q}}^S" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": " associated with its object set " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{y}}^S = \\{\\tilde{c}_j^S, \\tilde{b}_j^S\\}_{j=1}^N" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": ". Correspondingly, we can obtain a teacher query set " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{y}}^T = \\{\\tilde{c}_j^T, \\tilde{b}_j^T\\}_{j=1}^N" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": ". For the " + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 501, + 545, + 589 + ], + "type": "text", + "content": "-th student query, its corresponding teacher query is matched as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 597, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 545, + 640 + ], + "type": "interline_equation", + "content": "\\tilde {c} _ {j} ^ {\\mathcal {T}}, \\tilde {b} _ {j} ^ {\\mathcal {T}} = \\underset {\\tilde {c} _ {k} ^ {\\mathcal {T}}, \\tilde {b} _ {k} ^ {\\mathcal {T}}} {\\arg \\max } \\sum_ {k = 1} ^ {N} \\mu_ {1} \\operatorname {G I o U} \\left(\\tilde {b} _ {j} ^ {\\mathcal {S}}, b _ {k} ^ {\\mathcal {T}}\\right) - \\mu_ {2} \\| \\tilde {b} _ {j} ^ {\\mathcal {S}} - b _ {k} ^ {\\mathcal {T}} \\| _ {1}, \\tag {12}", + "image_path": "b12101d3ec30ebb0f58168b4760a5c93bf45b7d3d6471648a27a2a0d2416f230.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "inline_equation", + "content": "\\mu_{1} = 2" + }, + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "inline_equation", + "content": "\\mu_{2} = 5" + }, + { + "bbox": [ + 304, + 641, + 544, + 664 + ], + "type": "text", + "content": " control the matching function, values of which is to follow [4]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 544, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 544, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 544, + 689 + ], + "type": "text", + "content": "Finally, the upper-level optimization after rectification in Eq. (6) becomes:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 389, + 696, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 696, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 389, + 696, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} H \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}} \\mid \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right). \\tag {13}", + "image_path": "268b44323f44df2d3266dc06c810cb2ddadbc50e3350d3192ba9c680377c3b24.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3846" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": "Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{q}}^{S^*}" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{q}}^T" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": ", optima of which, i.e., " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{q}}^{S^*} = \\tilde{\\mathbf{q}}^T" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": ", is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 140, + 287, + 154 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 140, + 287, + 154 + ], + "spans": [ + { + "bbox": [ + 86, + 140, + 287, + 154 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D R D} \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right) = \\mathbb {E} \\left[ \\left\\| \\tilde {\\mathbf {D}} ^ {\\mathcal {S} ^ {*}} - \\tilde {\\mathbf {D}} ^ {\\mathcal {T}} \\right\\| _ {2} \\right], \\tag {14}", + "image_path": "a9d034c35c66f716c94401b6ed132e5b41db19f53fbcbdbb6060511e8cf11118.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "text", + "content": "where we use the Euclidean distance of co-attented feature " + }, + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{D}}" + }, + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "text", + "content": " (see Eq. 3) containing the information query " + }, + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{q}}" + }, + { + "bbox": [ + 47, + 163, + 287, + 198 + ], + "type": "text", + "content": " for optimization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 199, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 287, + 247 + ], + "type": "text", + "content": "In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 253, + 287, + 267 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 253, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 85, + 253, + 287, + 267 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {G T} \\left(\\boldsymbol {y} ^ {G T}, \\boldsymbol {y} ^ {\\mathcal {S}}\\right) + \\lambda \\mathcal {L} _ {D R D} \\left(\\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {T}}\\right), \\tag {15}", + "image_path": "5c50b00dce018522b91b34e0751bb679e9adb26339ed177e9fceea4074820b4f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "inline_equation", + "content": "L_{GT}" + }, + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "text", + "content": " is the common detection loss for missions such as proposal classification and coordinate regression [4], and " + }, + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 274, + 287, + 310 + ], + "type": "text", + "content": " is a tradeoff hyper-parameter." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 320, + 127, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 127, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 127, + 335 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 341, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 287, + 413 + ], + "type": "text", + "content": "In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 420, + 242, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 242, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 242, + 432 + ], + "type": "text", + "content": "5.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": "Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP, " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": " (default VOC metric), and " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": ". We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_s" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_m" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_l" + }, + { + "bbox": [ + 47, + 438, + 287, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 81, + 414, + 158 + ], + "blocks": [ + { + "bbox": [ + 313, + 81, + 414, + 158 + ], + "lines": [ + { + "bbox": [ + 313, + 81, + 414, + 158 + ], + "spans": [ + { + "bbox": [ + 313, + 81, + 414, + 158 + ], + "type": "image", + "image_path": "f81fb84b5bb6aab549b17b32fa5da6cc62eb498e5c10813514540515dba9c182.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "lines": [ + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "spans": [ + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "type": "text", + "content": "(a) Effect of " + }, + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 331, + 161, + 400, + 170 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 430, + 81, + 533, + 158 + ], + "blocks": [ + { + "bbox": [ + 430, + 81, + 533, + 158 + ], + "lines": [ + { + "bbox": [ + 430, + 81, + 533, + 158 + ], + "spans": [ + { + "bbox": [ + 430, + 81, + 533, + 158 + ], + "type": "image", + "image_path": "47952eabf7f40ca87b81667b8ca2c1c9243c9c288b2ab9cb3103439d10a90646.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 161, + 535, + 170 + ], + "lines": [ + { + "bbox": [ + 435, + 161, + 535, + 170 + ], + "spans": [ + { + "bbox": [ + 435, + 161, + 535, + 170 + ], + "type": "text", + "content": "(b) Mutual information curves." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "text", + "content": "Figure 5. (a) We select " + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "text", + "content": " using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of " + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "inline_equation", + "content": "I(X; \\mathbf{E})" + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "inline_equation", + "content": "I(\\boldsymbol{y}^{GT}; \\mathbf{E}, \\mathbf{q})" + }, + { + "bbox": [ + 305, + 180, + 545, + 247 + ], + "type": "text", + "content": " (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 268, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 268, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 268, + 545, + 472 + ], + "type": "text", + "content": "the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of " + }, + { + "bbox": [ + 305, + 268, + 545, + 472 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 305, + 268, + 545, + 472 + ], + "type": "text", + "content": ". We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP50 on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP50 on VOC and 44.4% AP on COCO) as teacher network." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "type": "text", + "content": "5.2. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": "Hyper-parameter selection. As mentioned above, we select hyper-parameters " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " in this part using the 4-bit Q-DETR model. We show the model performance " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\mathrm{AP}_{50})" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " with different setups of hyper-parameters " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\tau ,\\lambda \\}" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " in Fig.5 (a), where we conduct ablative experiments on the baseline " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "+\\mathrm{DA}(\\mathrm{AP}_{50} = 78.8\\%)" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": ". As can be seen, the performances increase first and then decrease with the increase of " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " from left to right. Since " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " controls the proportion of selected distillation-desired queries, we show that the full-imitation " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\tau = 0)" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " performs worse than the vanilla baseline with no distillation " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\tau = 1)" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": ", showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " from left to right. The Q-DETR obtains better performances with " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " set as 0.5 and 0.6. With the varying value of " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": ", we find " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\lambda ,\\tau \\} = \\{2.5,0.6\\}" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " boost the performance of Q-DETR most, achieving " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "82.7\\%" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " AP on VOC test2007. Based on the ablative study above, we set hyper-parameters " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 498, + 545, + 713 + ], + "type": "text", + "content": " as 0.6 and 2.5" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3847" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 133, + 287, + 223 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 126 + ], + "type": "text", + "content": "Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 133, + 287, + 223 + ], + "lines": [ + { + "bbox": [ + 48, + 133, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 48, + 133, + 287, + 223 + ], + "type": "table", + "html": "
Method#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)#Bits\\(AP_{50}\\)
Real-valued32-32-3283.3----
Baseline4-4-878.03-3-876.82-2-869.7
+DA4-4-878.83-3-878.02-2-871.6
+FQM4-4-881.53-3-880.92-2-874.9
+DA+FQM(Q-DETR)4-4-882.73-3-882.12-2-876.4
", + "image_path": "714db789979e193ffa0cab743198c4ee6537499428e88f61c41805171caa2c36.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 244, + 180, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 244, + 180, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 180, + 255 + ], + "type": "text", + "content": "for the experiments in this paper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 255, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 386 + ], + "type": "text", + "content": "Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on " + }, + { + "bbox": [ + 46, + 255, + 287, + 386 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 255, + 287, + 386 + ], + "type": "text", + "content": " (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": "Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test " + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": " to quantify " + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "inline_equation", + "content": "I(\\boldsymbol{y}^{GT};\\mathbf{E},\\mathbf{q})" + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": ". We employ a reconstruction decoder to decode the encoded feature " + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": " to reconstruct the input and quantify " + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "inline_equation", + "content": "I(X;\\mathbf{E})" + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": " using the " + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": " loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 190, + 539 + ], + "type": "text", + "content": "5.3. Results on PASCAL VOC" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": "We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e. " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "1333 \\times 800" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": ". We mainly discuss the " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": " (default VOC metric) in the following." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 123, + 545, + 426 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "text", + "content": "Table 2. We report AP, " + }, + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "text", + "content": " (\\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 123, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 307, + 123, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 307, + 123, + 545, + 426 + ], + "type": "table", + "html": "
ModelMethod#BitsAP\\( AP_{50} \\)\\( AP_{75} \\)
DETR-R50Real-valued32-32-3259.583.364.7
Percentile8-8-854.779.260.1
VT-PTQ57.682.363.1
LSQ49.776.953.0
Baseline4-4-851.378.054.1
Q-DETR57.182.761.5
LSQ47.075.349.1
Baseline3-3-849.276.851.8
Q-DETR56.882.161.2
LSQ42.668.244.8
Baseline2-2-844.069.745.8
Q-DETR50.776.454.1
SMCA-DETR -R50Real-valued32-32-3256.783.762.0
Percentile8-8-854.779.260.1
VT-PTQ55.983.061.3
LSQ49.678.653.4
Baseline4-4-850.779.555.4
Q-DETR56.283.361.6
LSQ47.776.551.7
Baseline3-3-849.977.553.6
Q-DETR54.382.659.5
LSQ42.369.744.8
Baseline2-2-843.970.446.1
Q-DETR50.276.752.6
", + "image_path": "82eed12095fb7a4f5a22f0bdd3105b3808bf5341e615bf02f5f30004c2ceeb53.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 447, + 544, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 544, + 470 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 544, + 470 + ], + "type": "text", + "content": "and bit-width, which significantly validates the effectiveness of our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "content": "Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by " + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "6.3\\%" + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 305, + 472, + 545, + 555 + ], + "type": "text", + "content": ", a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 563, + 411, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 411, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 411, + 574 + ], + "type": "text", + "content": "5.4. Results on COCO" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 582, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 582, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 582, + 545, + 665 + ], + "type": "text", + "content": "We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3848" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 101, + 536, + 404 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 101, + 536, + 404 + ], + "lines": [ + { + "bbox": [ + 56, + 101, + 536, + 404 + ], + "spans": [ + { + "bbox": [ + 56, + 101, + 536, + 404 + ], + "type": "table", + "html": "
ModelMethod#BitsSize(MB)OPs(G)APAP50AP75APsAPmAPl
DETR-R50Real-valued32-32-32159.3285.5142.062.444.220.545.861.1
Percentile8-8-839.8323.0138.6-----
VT-PTQ41.2-----
LSQ33.353.733.912.837.051.6
Baseline4-4-819.9213.0234.155.335.414.338.053.8
Q-DETR39.460.241.417.743.459.9
LSQ31.052.332.111.333.948.5
Baseline3-3-815.037.6132.352.232.912.335.450.3
Q-DETR36.155.937.514.639.455.2
LSQ24.744.626.56.325.342.7
Baseline2-2-810.035.3226.646.626.58.428.244.4
Q-DETR31.451.331.611.634.349.6
SMCA-DETR-R50Real-valued32-32-32164.7586.6541.062.243.621.944.359.1
Percentile8-8-841.1923.6637.558.540.117.639.155.9
VT-PTQ40.261.042.620.342.957.7
LSQ33.955.035.013.237.251.4
Baseline4-4-820.5913.4835.056.436.415.638.352.5
Q-DETR38.359.739.817.741.756.8
LSQ30.152.631.411.933.446.6
Baseline3-3-815.688.0531.853.732.612.635.249.8
Q-DETR35.056.336.915.039.053.1
LSQ23.942.224.29.426.237.5
Baseline2-2-810.844.5425.444.325.28.427.240.3
Q-DETR30.551.831.812.033.248.0
", + "image_path": "75a9dded57022f71844b11e49ff060da2adeb508c57fa60eb2467e4cd037cde3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": "detectors. We follow [40] to calculate memory usage, by adding " + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "inline_equation", + "content": "32 \\times" + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": " the number of real-valued weights and " + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "inline_equation", + "content": "a \\times" + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": " the number of quantized weights in the " + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": "-bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds " + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\left\\{\\frac{1}{32}, \\frac{1}{16}, \\frac{1}{8}\\right\\}" + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": " of the number of " + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\{2,3,4\\}" + }, + { + "bbox": [ + 46, + 424, + 287, + 520 + ], + "type": "text", + "content": "-bit multiplications equals the OPs following [24]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "2/3/4" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "-bit baseline by " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": " AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "2/3/4" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "-bit Q-DETR achieves computation acceleration and storage savings by " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "16.07 \\times / 11.23 \\times / 6.57 \\times" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "inline_equation", + "content": "15.88 \\times / 10.60 \\times / 7.99 \\times" + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": ". The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 700, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 700, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 700, + 287, + 712 + ], + "type": "text", + "content": "For the SMCA-DETR-R50 model, we observe similar" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "text", + "content": "performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates " + }, + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "inline_equation", + "content": "6.42 \\times" + }, + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "text", + "content": " with only a " + }, + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 304, + 424, + 547, + 485 + ], + "type": "text", + "content": " performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 499, + 379, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 499, + 379, + 512 + ], + "spans": [ + { + "bbox": [ + 306, + 499, + 379, + 512 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "text", + "content": "This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. We effectively employ a distribution alignment module to solve inner-level and a foreground-aware query matching scheme to solve upper level. As a result, Q-DETR significantly boosts performance of low-bit DETR. Extensive experiments show that Q-DETR surpasses state-of-the-arts in DETR quantization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 656, + 421, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 656, + 421, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 656, + 421, + 670 + ], + "type": "text", + "content": "7. Acknowledgements" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China under Grant 62141604, 62076016, Beijing Natural Science Foundation L223024." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3849" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Trained ternary quantization. In Proc. of ICLR, pages 1-10, 2017. 2" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 307, + 107, + 545, + 150 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 107, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 307, + 107, + 545, + 150 + ], + "type": "text", + "content": "[47] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. In Proc. of ICLR, pages 1-16, 2020. 3" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 307, + 152, + 545, + 194 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 152, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 307, + 152, + 545, + 194 + ], + "type": "text", + "content": "[48] Bohan Zhuang, Chunhua Shen, Mingkui Tan, Lingqiao Liu, and Ian Reid. Towards effective low-bitwidth convolutional neural networks. In Proc. of CVPR, pages 7920-7928, 2018. 2" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3851" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_content_list.json b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e0ed2bc9cbbd5fe0f1dac8bd79c18caf7f8b6c5a --- /dev/null +++ b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_content_list.json @@ -0,0 +1,1527 @@ +[ + { + "type": "text", + "text": "QPGesture: Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation", + "text_level": 1, + "bbox": [ + 116, + 128, + 854, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sicheng Yang $^{1}$ Zhiyong Wu $^{2,1,4}$ Minglei Li $^{2}$ Zhensong Zhang $^{3}$", + "bbox": [ + 205, + 202, + 763, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lei Hao3 Weihong Bao1 Haolin Zhuang1", + "bbox": [ + 302, + 220, + 663, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Tsinghua University $^{2}$ Huawei Cloud Computing Technologies Co., Ltd", + "bbox": [ + 186, + 238, + 784, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 Huawei Noah's Ark Lab 4 The Chinese University of Hong Kong", + "bbox": [ + 210, + 256, + 759, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yangsc21, bwh21, zhuanghl21}@mails.tsinghua.edu.cn zywu@sz.tsinghua.edu.cn", + "bbox": [ + 145, + 276, + 821, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{liminglei29, zhangzhensong, haolei5}@huawei.com", + "bbox": [ + 271, + 295, + 694, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture.", + "bbox": [ + 75, + 376, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e35abe3c93774187015fffd290bc71c99c77f4a716874f885f457d34433d322c.jpg", + "image_caption": [ + "Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2]." + ], + "image_footnote": [], + "bbox": [ + 501, + 344, + 714, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ebbf56ed8b02233525afdee7b734883d1b9987eb94f993c2944da32b50605a90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 345, + 890, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures.", + "bbox": [ + 496, + 522, + 890, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models.", + "bbox": [ + 496, + 568, + 892, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2321", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8d6095f716cf4912c526deb9e6e83fd023966593a8d27477e9378310725d4c9.jpg", + "image_caption": [ + "Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates." + ], + "image_footnote": [], + "bbox": [ + 89, + 97, + 880, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text.", + "bbox": [ + 75, + 349, + 472, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon.", + "bbox": [ + 75, + 684, + 468, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of our work are:", + "bbox": [ + 96, + 838, + 364, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We present a novel quantization-based motion matching framework for speech-driven gesture generation.", + "bbox": [ + 94, + 869, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization.", + "- We design a phase guidance strategy to select optimal audio and text candidates for motion matching.", + "- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework." + ], + "bbox": [ + 517, + 349, + 890, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 511, + 640, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality.", + "bbox": [ + 496, + 537, + 890, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2322", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/588f51f05d2070063f33b8c5f910136474356f75b8e40df2f83722a9aea7b1da.jpg", + "image_caption": [ + "Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 467, + 231 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code.", + "bbox": [ + 75, + 332, + 468, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task.", + "bbox": [ + 75, + 487, + 470, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7].", + "bbox": [ + 75, + 686, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "based motion matching with phase guidance.", + "bbox": [ + 498, + 90, + 797, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Approach", + "text_level": 1, + "bbox": [ + 500, + 117, + 648, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step.", + "bbox": [ + 496, + 143, + 893, + 295 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Learning a discrete latent space representation", + "text_level": 1, + "bbox": [ + 500, + 301, + 890, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence $\\mathbf{G} \\in \\mathbb{R}^{T \\times D_g}$ , where $T$ denotes the number of gestures and $D_g$ pose dimension. We first adopt a 1D temporal convolution network $E_g$ to encode the joint sequence $\\mathbf{G}$ to context-aware features $\\mathbf{g} \\in \\mathbb{R}^{T' \\times C}$ , where $T' = T / d$ , $d$ is the temporal down-sampling rate, and $C$ is the channel dimension of features. This process could be written as $\\mathbf{g} = E_g(\\mathbf{G})$ . Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook $\\mathcal{Z}_g$ elements $\\mathbf{g_q} \\in \\mathbb{R}^{T' \\times C}$ , where $\\mathbf{g_q} \\in \\mathcal{Z}_g^T$ , $\\mathcal{Z}_g$ is a set of $C_b$ codes of dimension $n_z$ , we quantize $\\mathbf{g}$ by mapping each temporal feature $\\mathbf{g}_i$ to its closest codebook element $z_j$ as $\\mathbf{q}(.)$ :", + "bbox": [ + 496, + 324, + 892, + 542 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {g} _ {\\mathbf {q}, i} = \\mathbf {q} (\\mathbf {g}) = \\arg \\min _ {\\mathbf {z} _ {j} \\in \\mathcal {Z} _ {g}} \\| \\mathbf {g} _ {i} - \\mathbf {z} _ {j} \\| \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 547, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A following de-convolutional decoder $D_g$ projects $\\mathbf{g_q}$ back to the motion space as a pose sequence $\\hat{\\mathbf{G}}_1$ , which can be formulated as", + "bbox": [ + 496, + 578, + 890, + 625 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {G}} _ {1} = D _ {g} \\left(\\mathbf {g} _ {q}\\right) = D _ {g} \\left(\\mathbf {q} \\left(E _ {g} (\\mathbf {G})\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 631, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Thus the encoder, decoder and codebook can be trained by optimizing:", + "bbox": [ + 496, + 656, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {g e s t u r e} \\left(E _ {g}, D _ {g}, \\mathcal {Z} _ {g}\\right)} = \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G}\\right) + \\left\\| \\operatorname {s g} [ \\mathbf {g} ] - \\mathbf {g} _ {\\mathbf {q}} \\right\\| \\tag {3} \\\\ + \\beta \\| \\mathbf {g} - \\mathrm {s g} [ \\mathbf {g _ {q}} ] \\| \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 693, + 890, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rec}$ is the reconstruction loss that constrains the predicted joint sequence to ground truth, $\\mathrm{sg}[\\cdot ]$ denotes the stop-gradient operation, and the term $\\| \\mathbf{g} - \\mathrm{sg}\\left[\\mathbf{g_q}\\right]\\|$ is the \"commitment loss\" with weighting factor $\\beta$ [42].", + "bbox": [ + 496, + 737, + 890, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture:", + "bbox": [ + 496, + 797, + 890, + 844 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G} _ {1}\\right) = \\left\\| \\hat {\\mathbf {G}} _ {1} - \\mathbf {G} _ {1} \\right\\| _ {1} + \\alpha_ {1} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime} - \\mathbf {G} _ {1} ^ {\\prime} \\right\\| _ {1} \\tag {4} \\\\ + \\alpha_ {2} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime \\prime} - \\mathbf {G} _ {1} ^ {\\prime \\prime} \\right\\| _ {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 848, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2323", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input $\\mathbf{G}$ i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints.", + "bbox": [ + 76, + 90, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation $\\mathbf{z}$ , for each time step $i$ , the quantization module replaces the original representation $\\mathbf{z}$ by $\\hat{\\mathbf{z}} = \\mathbf{a}_{\\mathbf{q},i}$ from $\\mathcal{Z}_a$ , which contains a set of $C_b'$ codes of dimension $n_z'$ .", + "bbox": [ + 75, + 167, + 470, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Motion Matching based on Audio and Text", + "text_level": 1, + "bbox": [ + 76, + 311, + 441, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our motion matching algorithm takes a discrete text sequence $\\mathbf{t} = [\\mathbf{t}_0, \\mathbf{t}_1, \\dots, \\mathbf{t}_{T' - 1}]$ , a discrete audio sequence $\\mathbf{a_q} = [\\mathbf{a_{q,0}}, \\mathbf{a_{q,1}}, \\dots, \\mathbf{a_{q,T'}} - 1]$ , and one initial previous pose code $\\mathbf{g}_{-1}$ , and optionally a sequence of control masks $\\mathbf{M} = [\\mathbf{m}_0, \\mathbf{m}_1, \\dots, \\mathbf{m}_{T' - 1}]$ . The outputs are audio-based candidate $\\mathbf{C}_a = [\\mathbf{c}_{0,a}, \\mathbf{c}_{1,a}, \\dots, \\mathbf{c}_{T' - 1,a}]$ and text-based candidate $\\mathbf{C}_t = [\\mathbf{c}_{0,t}, \\mathbf{c}_{1,t}, \\dots, \\mathbf{c}_{T' - 1,t}]$ . $T'$ denotes the number of speech segments during inference.", + "bbox": [ + 75, + 335, + 468, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1.", + "bbox": [ + 75, + 455, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To find the appropriate output gesture sequence $\\mathbf{C}_a$ and $\\mathbf{C}_t$ from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code $\\mathbf{g}_{-1}$ for every $T$ frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code $\\mathbf{g}_{-1}$ and the joints corresponding to each code $\\mathbf{g_q}$ in the codebook to get the pose-based pre-candidate $\\hat{\\mathbf{C}}_g = \\left\\{\\hat{\\mathbf{C}}_g^0,\\hat{\\mathbf{C}}_g^1,\\dots ,\\hat{\\mathbf{C}}_g^{C_b}\\right\\}$ . In the first iteration, the previous pose code $\\mathbf{g}_{-1}$ is initialized by either randomly sampling a code from codebook $\\mathcal{Z}_g$ or set to be the code with the most frequent occurrences in the codebook (the code of mean pose).", + "bbox": [ + 75, + 561, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence $\\mathbf{F}_a = [\\mathbf{F}_{a,0},\\mathbf{F}_{a,1},\\dots ,\\mathbf{F}_{a,T^{\\prime} - 1}]$ . To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database,", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/561973762b93813c2f17ca25b1a35de12b0254e7490a0b52ef0bc487c6fce9ae.jpg", + "image_caption": [ + "Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding." + ], + "image_footnote": [], + "bbox": [ + 514, + 94, + 880, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we calculate the audio feature similarity of the corresponding code per $d$ frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate $\\hat{\\mathbf{C}}_a = \\left\\{\\hat{\\mathbf{C}}_a^0,\\hat{\\mathbf{C}}_a^1,\\dots ,\\hat{\\mathbf{C}}_a^{C_b}\\right\\}$ . Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2).", + "bbox": [ + 496, + 335, + 890, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence $\\mathbf{F}_t$ . For every clip in the database, we calculate the text features cosine similarity of the corresponding code per $d$ frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is $\\hat{\\mathbf{C}}_t = \\left\\{\\hat{\\mathbf{C}}_t^0,\\hat{\\mathbf{C}}_t^1,\\dots ,\\hat{\\mathbf{C}}_t^{C_b}\\right\\}$", + "bbox": [ + 496, + 463, + 890, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate $\\mathbf{C}_a$ based on $\\hat{\\mathbf{C}}_g$ and $\\hat{\\mathbf{C}}_a$ , and text candidate $\\mathbf{C}_t$ based on $\\hat{\\mathbf{C}}_g$ and $\\hat{\\mathbf{C}}_t$ . Then we select the final gesture from $\\mathbf{C}_a$ and $\\mathbf{C}_t$ according to the phase guide.", + "bbox": [ + 496, + 602, + 890, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Phase-Guided Gesture Generation", + "text_level": 1, + "bbox": [ + 500, + 762, + 802, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network $E_{p}$ to a latent space of the motion $\\mathbf{G}$ , which can be formulated as", + "bbox": [ + 496, + 786, + 890, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} = E _ {p} (\\mathbf {G}) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2324", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{L} \\in \\mathbb{R}^{T \\times M}$ , $M$ is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of $\\mathbf{L}$ and create the zero-indexed matrix of Fourier coefficients $\\mathbf{c} \\in \\mathbb{C}^{M \\times K + 1}$ , $K = \\left\\lfloor \\frac{T}{2} \\right\\rfloor$ , written as $\\mathbf{c} = FFT(\\mathbf{L})$ . Power spectrum $\\mathbf{p} \\in \\mathbb{R}^{M \\times K + 1}$ for each channel is $\\mathbf{p}_{i,j} = \\frac{2}{T} |\\mathbf{c}_{i,j}|^2$ , where $i$ is the channel index and $j$ is the index for the frequency bands. Assumed that there are $T$ points in a time window of $N$ seconds. The periodic parameters are computed by:", + "bbox": [ + 75, + 167, + 470, + 334 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {i} = \\sqrt {\\frac {2}{T} \\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {F} _ {i} = \\frac {\\sum_ {j = 1} ^ {K} \\left(\\mathbf {f} _ {j} \\cdot \\mathbf {p} _ {i , j}\\right)}{\\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {B} _ {i} = \\frac {\\mathbf {c} _ {i , 0}}{T}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 345, + 480, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{f} = (0,1 / N,2 / N,\\dots ,K / N)$ is frequencies vector.", + "bbox": [ + 76, + 405, + 464, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Phase shift $\\mathbf{S} \\in \\mathbb{R}^{M}$ for each latent curve $\\mathbf{S}_i$ can be predicted by a fully connected layer $FC$ , which can be formulated as:", + "bbox": [ + 76, + 420, + 468, + 464 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(s _ {x}, s _ {y}\\right) = F C \\left(\\mathbf {L} _ {i}\\right), \\quad \\mathbf {S} _ {i} = \\operatorname {a t a n 2} \\left(s _ {y}, s _ {x}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 477, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each temporal motion $\\mathbf{G}$ , within a centered time window $\\mathcal{T} = \\left[-\\frac{t_1 - t_0}{2}, -\\frac{t_1 - t_0}{2} + \\frac{t_1 - t_0}{N - 1}, \\dots, \\frac{t_1 - t_0}{2}\\right]$ , where $t_0 \\leq t \\leq t_1$ , the decoder $D_p$ takes all periodic parameters as its input, and maps back to the original motion curves:", + "bbox": [ + 76, + 503, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} = f (\\mathcal {T}; \\mathbf {A}, \\mathbf {F}, \\mathbf {B}, \\mathbf {S}) = \\mathbf {A} \\cdot \\sin (2 \\pi \\cdot (\\mathbf {F} \\cdot \\mathcal {T} - \\mathrm {S})) + \\mathbf {B} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 580, + 468, + 599 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {G}} _ {2} = h (\\hat {\\mathbf {L}}) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 622, + 468, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding $\\mathbf{L}$ .", + "bbox": [ + 76, + 647, + 468, + 693 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p h a s e}} = \\mathcal {L} _ {\\text {p h a s e - r e c o n}} (\\mathbf {G}, \\hat {\\mathbf {G}} _ {\\mathbf {2}}) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 702, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After training, phase manifold $\\mathcal{P}$ of a sample motion which captures a lot of \"information\" about the current state of the original time series data is", + "bbox": [ + 76, + 731, + 468, + 776 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {2 i - 1} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\sin \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right), \\quad \\mathcal {P} _ {2 i} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\cos \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 786, + 478, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{P}\\in \\mathbb{R}^{2M}$", + "bbox": [ + 76, + 824, + 194, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cd14b049e39e037f1f7483572bf9e42dc51f401e83431c1b48b65f82f73d9a31.jpg", + "image_caption": [ + "(a) Rotational velocity space." + ], + "image_footnote": [], + "bbox": [ + 640, + 90, + 753, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9a85253e41749a017c6eb2d233aa80676278ef9c6d5884fc5322a6b1d88fc5e6.jpg", + "image_caption": [ + "(b) Latent space learned by convolutional and fully connected." + ], + "image_footnote": [], + "bbox": [ + 601, + 166, + 792, + 251 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87d56a2a641907bb6ccf00d30892b695b58b7d39df493cc4926c5267511b14f6.jpg", + "image_caption": [ + "(c) Phase space.", + "Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding" + ], + "image_footnote": [], + "bbox": [ + 601, + 276, + 790, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements.", + "bbox": [ + 496, + 489, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames $N_{strid}$ of the manifold phase $\\mathcal{P}_{-1}$ corresponding to the frame of the initial code and the first frames of the manifold phase $\\mathcal{P}_{a/t}$ corresponding to the audio/text candidate $\\mathbf{C}_a$ and $\\mathbf{C}_t$ within $N_{phase}$ frames, which can be written as $\\text{concat}[\\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \\mathcal{P}_{a/t}^{[N_{strid}]}$ and $\\text{concat}[\\mathcal{P}_{-1}^{[-N_{strid}]}, \\mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}]$ . Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm.", + "bbox": [ + 496, + 611, + 890, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 844, + 630, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2325", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0470df749c2bb5a1b8fc216dd32923a97d3fcabb6e82c2b4178c8d4c41ca6196.jpg", + "image_caption": [ + "(a) The phase manifold of the seed code to be matched.", + "Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate $\\mathbf{C}_a$ and text candidate $\\mathbf{C}_t$ ." + ], + "image_footnote": [], + "bbox": [ + 112, + 90, + 243, + 231 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/57417fdb192726bd1146df1f316eeadc16acca6950440f41e27169beadb2f486.jpg", + "image_caption": [ + "(b) The phase manifold of the candidate to be matched." + ], + "image_footnote": [], + "bbox": [ + 307, + 90, + 441, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers \"wayne\" (male speaker) and \"kieks\" (female speaker), and constructed separate databases for our experiments.", + "bbox": [ + 75, + 364, + 467, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers. $3 \\times 3$ rotation matrix features are computed as gesture sequences, with pose dimension $D_{g}$ is 9. Down-sampling rate $d$ is 8. The size $C_b$ of codebook $\\mathcal{Z}_g$ is set to 512 with dimension $n_z$ is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of $T = 240$ (4 seconds), using the ADAM [22] optimizer (learning rate is e-4, $\\beta_{1} = 0.5$ , $\\beta_{2} = 0.98$ ) with a batch size of 128 for 200 epochs. We set $\\beta = 0.1$ for Equation (3) and $\\alpha_{1} = 1$ , $\\alpha_{2} = 1$ for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with $d = 32$ . As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of $10^{-4}$ and a batch size of 128. The number of phase channels $M$ is set to 8. To calculate the phase similarity, the number of frames is set to $N_{phase} = 8$ and $N_{stride} = 3$ . The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook $\\mathcal{Z}_q$ .", + "bbox": [ + 76, + 489, + 467, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis", + "bbox": [ + 75, + 839, + 467, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tance [25], $H\\left(\\boldsymbol{h}^{(1)}, \\boldsymbol{h}^{(2)}\\right) = \\sqrt{1 - \\sum_{i} \\sqrt{h_{i}^{(1)} \\cdot h_{i}^{(2)}}}$ between the histograms $\\boldsymbol{h}^{(1)}$ and $\\boldsymbol{h}^{(2)}$ . The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements.", + "bbox": [ + 496, + 89, + 890, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparison to Existing Methods", + "text_level": 1, + "bbox": [ + 498, + 285, + 790, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921 $(44\\%)$ and 3837.068 $(39\\%)$ than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space.", + "bbox": [ + 496, + 309, + 890, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants \"How human-like does the gesture motion appear?\" In terms of appropriateness evaluation, each evaluation page asked participants \"How appropriate are the gestures for the speech?\" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) \"Excellent\", \"Good\", \"Fair\", \"Poor\", and \"Bad\". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1.", + "bbox": [ + 496, + 551, + 890, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2326", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/757f145197ca1987b82db9a9ec0d786620bbdc560532551ea6ee9746940e829c.jpg", + "table_caption": [ + "Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with $95\\%$ confidence intervals." + ], + "table_footnote": [], + "table_body": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
Ground Truth (GT)0.00.00.03.79 ± 0.193.62 ± 0.21
End2End [47]0.14664.99016739.9783.64 ± 0.113.23 ± 0.14
Trimodal [46]0.15548.32212869.983.31 ± 0.173.20 ± 0.19
StyleGestures [5]0.13635.8429846.9273.66 ± 0.083.30 ± 0.11
KNN [17]0.36443.03012470.0612.38 ± 0.102.35 ± 0.13
CaMN [31]0.14952.49610549.4553.65 ± 0.163.29 ± 0.15
Ours0.13619.9215742.2814.00 ± 0.143.66 ± 0.23
", + "bbox": [ + 130, + 155, + 844, + 305 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6dfe09e8ede19086ddb846edce9657e08b0dd8581c359ecbbbdd3f8d7f27733a.jpg", + "table_caption": [ + "Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric." + ], + "table_footnote": [], + "table_body": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
w/o wavvq + WavLM0.15119.9436009.8593.87 ± 0.213.64 ± 0.21
w/o audio0.13420.4015871.0443.87 ± 0.213.63 ± 0.20
w/o text0.11823.9296389.8663.57 ± 0.293.41 ± 0.23
w/o phase0.13819.1955759.1673.90 ± 0.113.65 ± 0.17
w/o motion matching (GRU + codebook)0.14030.40411642.6413.78 ± 0.143.43 ± 0.16
Ours0.13619.9215742.2814.07 ± 0.153.77 ± 0.21
", + "bbox": [ + 107, + 340, + 870, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more \"related to the semantics\" with \"more natural\", while our method \"lacking power and exaggerated gestures\" compared to GT. More details regarding the user study are shown in the supplementary material.", + "bbox": [ + 75, + 513, + 470, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 632, + 241, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video.", + "bbox": [ + 75, + 656, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively.", + "bbox": [ + 75, + 733, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant.", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d19feb63e29ec809be67e210cb72e7bb433171fcebf1e2d8fedd0a4df462551a.jpg", + "image_caption": [ + "Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance." + ], + "image_footnote": [], + "bbox": [ + 501, + 512, + 890, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2327", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by $10.483(53\\%)$ and 6460.202 $(107\\%)$ , respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space.", + "bbox": [ + 75, + 90, + 472, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed.", + "bbox": [ + 75, + 349, + 472, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Controllability", + "text_level": 1, + "bbox": [ + 76, + 724, + 227, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold $\\mathbf{r}$ , the search can be restricted to consider only codes corresponding to wrists above $\\mathbf{r}$ . Here is an example. The most frequent gesture in the database of \"wayne\" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that \"wayne\" is a habitual right-handed", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/749f1ef66e344cf56d62a37d3348d75b94bad3f0d20cfb26f296570fea7e7d5d.jpg", + "image_caption": [ + "Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker." + ], + "image_footnote": [], + "bbox": [ + 583, + 90, + 803, + 308 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons.", + "bbox": [ + 496, + 401, + 893, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 505, + 750, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures.", + "bbox": [ + 496, + 530, + 893, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 784, + 660, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030).", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2328", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Blender. https://www.blender.org/. 6", + "[2] Mixamo. https://www MIXamo.com/. 1", + "[3] Chaitanya Ahuja, Dong Won Lee, Ryo Ishii, and Louis-Philippe Morency. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 3408-3418, 2022. 3" + ], + "bbox": [ + 501, + 92, + 890, + 893 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2330", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_model.json b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..84eec0bfaf4dfb0d4a5a285c40eb058c0431c69e --- /dev/null +++ b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.117, + 0.13, + 0.856, + 0.177 + ], + "angle": 0, + "content": "QPGesture: Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation" + }, + { + "type": "text", + "bbox": [ + 0.206, + 0.203, + 0.764, + 0.222 + ], + "angle": 0, + "content": "Sicheng Yang\\(^{1}\\) Zhiyong Wu\\(^{2,1,4}\\) Minglei Li\\(^{2}\\) Zhensong Zhang\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.303, + 0.222, + 0.664, + 0.239 + ], + "angle": 0, + "content": "Lei Hao3 Weihong Bao1 Haolin Zhuang1" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.239, + 0.785, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\) Tsinghua University \\(^{2}\\) Huawei Cloud Computing Technologies Co., Ltd" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.257, + 0.76, + 0.275 + ], + "angle": 0, + "content": "3 Huawei Noah's Ark Lab 4 The Chinese University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.277, + 0.823, + 0.293 + ], + "angle": 0, + "content": "{yangsc21, bwh21, zhuanghl21}@mails.tsinghua.edu.cn zywu@sz.tsinghua.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.296, + 0.695, + 0.31 + ], + "angle": 0, + "content": "{liminglei29, zhangzhensong, haolei5}@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.345, + 0.715, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.346, + 0.891, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.468, + 0.893, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.569 + ], + "angle": 0, + "content": "erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.825 + ], + "angle": 0, + "content": "Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2321" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.098, + 0.882, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.267, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.681 + ], + "angle": 0, + "content": "challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.835 + ], + "angle": 0, + "content": "The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.839, + 0.365, + 0.852 + ], + "angle": 0, + "content": "The main contributions of our work are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We present a novel quantization-based motion matching framework for speech-driven gesture generation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.35, + 0.892, + 0.396 + ], + "angle": 0, + "content": "- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.408, + 0.892, + 0.439 + ], + "angle": 0, + "content": "- We design a phase guidance strategy to select optimal audio and text candidates for motion matching." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.451, + 0.892, + 0.495 + ], + "angle": 0, + "content": "- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.35, + 0.892, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.642, + 0.528 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.854 + ], + "angle": 0, + "content": "End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.902 + ], + "angle": 0, + "content": "As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2322" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.468, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.471, + 0.302 + ], + "angle": 0, + "content": "Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.47, + 0.485 + ], + "angle": 0, + "content": "identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.471, + 0.683 + ], + "angle": 0, + "content": "Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.799, + 0.107 + ], + "angle": 0, + "content": "based motion matching with phase guidance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.118, + 0.649, + 0.136 + ], + "angle": 0, + "content": "3. Our Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.144, + 0.894, + 0.296 + ], + "angle": 0, + "content": "Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.892, + 0.319 + ], + "angle": 0, + "content": "3.1. Learning a discrete latent space representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.893, + 0.543 + ], + "angle": 0, + "content": "Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence \\(\\mathbf{G} \\in \\mathbb{R}^{T \\times D_g}\\), where \\(T\\) denotes the number of gestures and \\(D_g\\) pose dimension. We first adopt a 1D temporal convolution network \\(E_g\\) to encode the joint sequence \\(\\mathbf{G}\\) to context-aware features \\(\\mathbf{g} \\in \\mathbb{R}^{T' \\times C}\\), where \\(T' = T / d\\), \\(d\\) is the temporal down-sampling rate, and \\(C\\) is the channel dimension of features. This process could be written as \\(\\mathbf{g} = E_g(\\mathbf{G})\\). Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook \\(\\mathcal{Z}_g\\) elements \\(\\mathbf{g_q} \\in \\mathbb{R}^{T' \\times C}\\), where \\(\\mathbf{g_q} \\in \\mathcal{Z}_g^T\\), \\(\\mathcal{Z}_g\\) is a set of \\(C_b\\) codes of dimension \\(n_z\\), we quantize \\(\\mathbf{g}\\) by mapping each temporal feature \\(\\mathbf{g}_i\\) to its closest codebook element \\(z_j\\) as \\(\\mathbf{q}(.)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.549, + 0.892, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\mathbf {g} _ {\\mathbf {q}, i} = \\mathbf {q} (\\mathbf {g}) = \\arg \\min _ {\\mathbf {z} _ {j} \\in \\mathcal {Z} _ {g}} \\| \\mathbf {g} _ {i} - \\mathbf {z} _ {j} \\| \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.626 + ], + "angle": 0, + "content": "A following de-convolutional decoder \\(D_g\\) projects \\(\\mathbf{g_q}\\) back to the motion space as a pose sequence \\(\\hat{\\mathbf{G}}_1\\), which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.632, + 0.892, + 0.651 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {G}} _ {1} = D _ {g} \\left(\\mathbf {g} _ {q}\\right) = D _ {g} \\left(\\mathbf {q} \\left(E _ {g} (\\mathbf {G})\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Thus the encoder, decoder and codebook can be trained by optimizing:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.694, + 0.891, + 0.732 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {g e s t u r e} \\left(E _ {g}, D _ {g}, \\mathcal {Z} _ {g}\\right)} = \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G}\\right) + \\left\\| \\operatorname {s g} [ \\mathbf {g} ] - \\mathbf {g} _ {\\mathbf {q}} \\right\\| \\tag {3} \\\\ + \\beta \\| \\mathbf {g} - \\mathrm {s g} [ \\mathbf {g _ {q}} ] \\| \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.892, + 0.799 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rec}\\) is the reconstruction loss that constrains the predicted joint sequence to ground truth, \\(\\mathrm{sg}[\\cdot ]\\) denotes the stop-gradient operation, and the term \\(\\| \\mathbf{g} - \\mathrm{sg}\\left[\\mathbf{g_q}\\right]\\|\\) is the \"commitment loss\" with weighting factor \\(\\beta\\) [42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.799, + 0.892, + 0.845 + ], + "angle": 0, + "content": "Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.849, + 0.891, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G} _ {1}\\right) = \\left\\| \\hat {\\mathbf {G}} _ {1} - \\mathbf {G} _ {1} \\right\\| _ {1} + \\alpha_ {1} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime} - \\mathbf {G} _ {1} ^ {\\prime} \\right\\| _ {1} \\tag {4} \\\\ + \\alpha_ {2} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime \\prime} - \\mathbf {G} _ {1} ^ {\\prime \\prime} \\right\\| _ {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2323" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input \\(\\mathbf{G}\\) i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.306 + ], + "angle": 0, + "content": "Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation \\(\\mathbf{z}\\), for each time step \\(i\\), the quantization module replaces the original representation \\(\\mathbf{z}\\) by \\(\\hat{\\mathbf{z}} = \\mathbf{a}_{\\mathbf{q},i}\\) from \\(\\mathcal{Z}_a\\), which contains a set of \\(C_b'\\) codes of dimension \\(n_z'\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.312, + 0.442, + 0.328 + ], + "angle": 0, + "content": "3.2. Motion Matching based on Audio and Text" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.469, + 0.456 + ], + "angle": 0, + "content": "Our motion matching algorithm takes a discrete text sequence \\(\\mathbf{t} = [\\mathbf{t}_0, \\mathbf{t}_1, \\dots, \\mathbf{t}_{T' - 1}]\\), a discrete audio sequence \\(\\mathbf{a_q} = [\\mathbf{a_{q,0}}, \\mathbf{a_{q,1}}, \\dots, \\mathbf{a_{q,T'}} - 1]\\), and one initial previous pose code \\(\\mathbf{g}_{-1}\\), and optionally a sequence of control masks \\(\\mathbf{M} = [\\mathbf{m}_0, \\mathbf{m}_1, \\dots, \\mathbf{m}_{T' - 1}]\\). The outputs are audio-based candidate \\(\\mathbf{C}_a = [\\mathbf{c}_{0,a}, \\mathbf{c}_{1,a}, \\dots, \\mathbf{c}_{T' - 1,a}]\\) and text-based candidate \\(\\mathbf{C}_t = [\\mathbf{c}_{0,t}, \\mathbf{c}_{1,t}, \\dots, \\mathbf{c}_{T' - 1,t}]\\). \\(T'\\) denotes the number of speech segments during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.469, + 0.562 + ], + "angle": 0, + "content": "Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.765 + ], + "angle": 0, + "content": "To find the appropriate output gesture sequence \\(\\mathbf{C}_a\\) and \\(\\mathbf{C}_t\\) from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code \\(\\mathbf{g}_{-1}\\) for every \\(T\\) frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code \\(\\mathbf{g}_{-1}\\) and the joints corresponding to each code \\(\\mathbf{g_q}\\) in the codebook to get the pose-based pre-candidate \\(\\hat{\\mathbf{C}}_g = \\left\\{\\hat{\\mathbf{C}}_g^0,\\hat{\\mathbf{C}}_g^1,\\dots ,\\hat{\\mathbf{C}}_g^{C_b}\\right\\}\\). In the first iteration, the previous pose code \\(\\mathbf{g}_{-1}\\) is initialized by either randomly sampling a code from codebook \\(\\mathcal{Z}_g\\) or set to be the code with the most frequent occurrences in the codebook (the code of mean pose)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence \\(\\mathbf{F}_a = [\\mathbf{F}_{a,0},\\mathbf{F}_{a,1},\\dots ,\\mathbf{F}_{a,T^{\\prime} - 1}]\\). To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database," + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.095, + 0.882, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.463 + ], + "angle": 0, + "content": "we calculate the audio feature similarity of the corresponding code per \\(d\\) frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate \\(\\hat{\\mathbf{C}}_a = \\left\\{\\hat{\\mathbf{C}}_a^0,\\hat{\\mathbf{C}}_a^1,\\dots ,\\hat{\\mathbf{C}}_a^{C_b}\\right\\}\\). Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence \\(\\mathbf{F}_t\\). For every clip in the database, we calculate the text features cosine similarity of the corresponding code per \\(d\\) frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is \\(\\hat{\\mathbf{C}}_t = \\left\\{\\hat{\\mathbf{C}}_t^0,\\hat{\\mathbf{C}}_t^1,\\dots ,\\hat{\\mathbf{C}}_t^{C_b}\\right\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.756 + ], + "angle": 0, + "content": "Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate \\(\\mathbf{C}_a\\) based on \\(\\hat{\\mathbf{C}}_g\\) and \\(\\hat{\\mathbf{C}}_a\\), and text candidate \\(\\mathbf{C}_t\\) based on \\(\\hat{\\mathbf{C}}_g\\) and \\(\\hat{\\mathbf{C}}_t\\). Then we select the final gesture from \\(\\mathbf{C}_a\\) and \\(\\mathbf{C}_t\\) according to the phase guide." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.803, + 0.779 + ], + "angle": 0, + "content": "3.3. Phase-Guided Gesture Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.892, + 0.876 + ], + "angle": 0, + "content": "To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network \\( E_{p} \\) to a latent space of the motion \\( \\mathbf{G} \\), which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} = E _ {p} (\\mathbf {G}) \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2324" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.167 + ], + "angle": 0, + "content": "where \\(\\mathbf{L} \\in \\mathbb{R}^{T \\times M}\\), \\(M\\) is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.335 + ], + "angle": 0, + "content": "It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of \\(\\mathbf{L}\\) and create the zero-indexed matrix of Fourier coefficients \\(\\mathbf{c} \\in \\mathbb{C}^{M \\times K + 1}\\), \\(K = \\left\\lfloor \\frac{T}{2} \\right\\rfloor\\), written as \\(\\mathbf{c} = FFT(\\mathbf{L})\\). Power spectrum \\(\\mathbf{p} \\in \\mathbb{R}^{M \\times K + 1}\\) for each channel is \\(\\mathbf{p}_{i,j} = \\frac{2}{T} |\\mathbf{c}_{i,j}|^2\\), where \\(i\\) is the channel index and \\(j\\) is the index for the frequency bands. Assumed that there are \\(T\\) points in a time window of \\(N\\) seconds. The periodic parameters are computed by:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.346, + 0.482, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {i} = \\sqrt {\\frac {2}{T} \\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {F} _ {i} = \\frac {\\sum_ {j = 1} ^ {K} \\left(\\mathbf {f} _ {j} \\cdot \\mathbf {p} _ {i , j}\\right)}{\\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {B} _ {i} = \\frac {\\mathbf {c} _ {i , 0}}{T}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.406, + 0.465, + 0.421 + ], + "angle": 0, + "content": "where \\(\\mathbf{f} = (0,1 / N,2 / N,\\dots ,K / N)\\) is frequencies vector." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.421, + 0.469, + 0.465 + ], + "angle": 0, + "content": "Phase shift \\(\\mathbf{S} \\in \\mathbb{R}^{M}\\) for each latent curve \\(\\mathbf{S}_i\\) can be predicted by a fully connected layer \\(FC\\), which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.478, + 0.47, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\left(s _ {x}, s _ {y}\\right) = F C \\left(\\mathbf {L} _ {i}\\right), \\quad \\mathbf {S} _ {i} = \\operatorname {a t a n 2} \\left(s _ {y}, s _ {x}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.505, + 0.469, + 0.573 + ], + "angle": 0, + "content": "For each temporal motion \\(\\mathbf{G}\\), within a centered time window \\(\\mathcal{T} = \\left[-\\frac{t_1 - t_0}{2}, -\\frac{t_1 - t_0}{2} + \\frac{t_1 - t_0}{N - 1}, \\dots, \\frac{t_1 - t_0}{2}\\right]\\), where \\(t_0 \\leq t \\leq t_1\\), the decoder \\(D_p\\) takes all periodic parameters as its input, and maps back to the original motion curves:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.582, + 0.469, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} = f (\\mathcal {T}; \\mathbf {A}, \\mathbf {F}, \\mathbf {B}, \\mathbf {S}) = \\mathbf {A} \\cdot \\sin (2 \\pi \\cdot (\\mathbf {F} \\cdot \\mathcal {T} - \\mathrm {S})) + \\mathbf {B} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.623, + 0.469, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {G}} _ {2} = h (\\hat {\\mathbf {L}}) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.469, + 0.694 + ], + "angle": 0, + "content": "The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding \\(\\mathbf{L}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.703, + 0.469, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p h a s e}} = \\mathcal {L} _ {\\text {p h a s e - r e c o n}} (\\mathbf {G}, \\hat {\\mathbf {G}} _ {\\mathbf {2}}) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.732, + 0.469, + 0.777 + ], + "angle": 0, + "content": "After training, phase manifold \\(\\mathcal{P}\\) of a sample motion which captures a lot of \"information\" about the current state of the original time series data is" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.787, + 0.48, + 0.825 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {2 i - 1} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\sin \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right), \\quad \\mathcal {P} _ {2 i} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\cos \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.825, + 0.195, + 0.839 + ], + "angle": 0, + "content": "where \\(\\mathcal{P}\\in \\mathbb{R}^{2M}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.091, + 0.754, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.149, + 0.774, + 0.161 + ], + "angle": 0, + "content": "(a) Rotational velocity space." + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.167, + 0.793, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.259, + 0.86, + 0.272 + ], + "angle": 0, + "content": "(b) Latent space learned by convolutional and fully connected." + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.277, + 0.792, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.654, + 0.37, + 0.739, + 0.382 + ], + "angle": 0, + "content": "(c) Phase space." + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.464 + ], + "angle": 0, + "content": "Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.61 + ], + "angle": 0, + "content": "a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.832 + ], + "angle": 0, + "content": "The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames \\( N_{strid} \\) of the manifold phase \\( \\mathcal{P}_{-1} \\) corresponding to the frame of the initial code and the first frames of the manifold phase \\( \\mathcal{P}_{a/t} \\) corresponding to the audio/text candidate \\( \\mathbf{C}_a \\) and \\( \\mathbf{C}_t \\) within \\( N_{phase} \\) frames, which can be written as \\( \\text{concat}[\\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \\mathcal{P}_{a/t}^{[N_{strid}]} \\) and \\( \\text{concat}[\\mathcal{P}_{-1}^{[-N_{strid}]}, \\mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}] \\). Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.632, + 0.862 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "2325" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.092, + 0.245, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.239, + 0.271, + 0.264 + ], + "angle": 0, + "content": "(a) The phase manifold of the seed code to be matched." + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.092, + 0.442, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.239, + 0.468, + 0.264 + ], + "angle": 0, + "content": "(b) The phase manifold of the candidate to be matched." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.47, + 0.332 + ], + "angle": 0, + "content": "Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate \\(\\mathbf{C}_a\\) and text candidate \\(\\mathbf{C}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.468, + 0.486 + ], + "angle": 0, + "content": "edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers \"wayne\" (male speaker) and \"kieks\" (female speaker), and constructed separate databases for our experiments." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.49, + 0.468, + 0.837 + ], + "angle": 0, + "content": "Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers. \\(3 \\times 3\\) rotation matrix features are computed as gesture sequences, with pose dimension \\(D_{g}\\) is 9. Down-sampling rate \\(d\\) is 8. The size \\(C_b\\) of codebook \\(\\mathcal{Z}_g\\) is set to 512 with dimension \\(n_z\\) is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of \\(T = 240\\) (4 seconds), using the ADAM [22] optimizer (learning rate is e-4, \\(\\beta_{1} = 0.5\\), \\(\\beta_{2} = 0.98\\)) with a batch size of 128 for 200 epochs. We set \\(\\beta = 0.1\\) for Equation (3) and \\(\\alpha_{1} = 1\\), \\(\\alpha_{2} = 1\\) for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with \\(d = 32\\). As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of \\(10^{-4}\\) and a batch size of 128. The number of phase channels \\(M\\) is set to 8. To calculate the phase similarity, the number of frames is set to \\(N_{phase} = 8\\) and \\(N_{stride} = 3\\). The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook \\(\\mathcal{Z}_q\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.275 + ], + "angle": 0, + "content": "tance [25], \\( H\\left(\\boldsymbol{h}^{(1)}, \\boldsymbol{h}^{(2)}\\right) = \\sqrt{1 - \\sum_{i} \\sqrt{h_{i}^{(1)} \\cdot h_{i}^{(2)}}} \\) between the histograms \\( \\boldsymbol{h}^{(1)} \\) and \\( \\boldsymbol{h}^{(2)} \\). The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.286, + 0.791, + 0.303 + ], + "angle": 0, + "content": "4.1. Comparison to Existing Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.552 + ], + "angle": 0, + "content": "We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921 \\((44\\%)\\) and 3837.068 \\((39\\%)\\) than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.853 + ], + "angle": 0, + "content": "User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants \"How human-like does the gesture motion appear?\" In terms of appropriateness evaluation, each evaluation page asked participants \"How appropriate are the gestures for the speech?\" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) \"Excellent\", \"Good\", \"Fair\", \"Poor\", and \"Bad\". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2326" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with \\(95\\%\\) confidence intervals." + }, + { + "type": "table", + "bbox": [ + 0.132, + 0.156, + 0.846, + 0.306 + ], + "angle": 0, + "content": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
Ground Truth (GT)0.00.00.03.79 ± 0.193.62 ± 0.21
End2End [47]0.14664.99016739.9783.64 ± 0.113.23 ± 0.14
Trimodal [46]0.15548.32212869.983.31 ± 0.173.20 ± 0.19
StyleGestures [5]0.13635.8429846.9273.66 ± 0.083.30 ± 0.11
KNN [17]0.36443.03012470.0612.38 ± 0.102.35 ± 0.13
CaMN [31]0.14952.49610549.4553.65 ± 0.163.29 ± 0.15
Ours0.13619.9215742.2814.00 ± 0.143.66 ± 0.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.211, + 0.318, + 0.759, + 0.332 + ], + "angle": 0, + "content": "Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.342, + 0.871, + 0.491 + ], + "angle": 0, + "content": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
w/o wavvq + WavLM0.15119.9436009.8593.87 ± 0.213.64 ± 0.21
w/o audio0.13420.4015871.0443.87 ± 0.213.63 ± 0.20
w/o text0.11823.9296389.8663.57 ± 0.293.41 ± 0.23
w/o phase0.13819.1955759.1673.90 ± 0.113.65 ± 0.17
w/o motion matching (GRU + codebook)0.14030.40411642.6413.78 ± 0.143.43 ± 0.16
Ours0.13619.9215742.2814.07 ± 0.153.77 ± 0.21
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.471, + 0.622 + ], + "angle": 0, + "content": "likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more \"related to the semantics\" with \"more natural\", while our method \"lacking power and exaggerated gestures\" compared to GT. More details regarding the user study are shown in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.242, + 0.648 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.81 + ], + "angle": 0, + "content": "We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.513, + 0.892, + 0.575 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2327" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.349 + ], + "angle": 0, + "content": "guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by \\(10.483(53\\%)\\) and 6460.202 \\((107\\%)\\), respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.712 + ], + "angle": 0, + "content": "User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.228, + 0.74 + ], + "angle": 0, + "content": "4.3. Controllability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold \\( \\mathbf{r} \\), the search can be restricted to consider only codes corresponding to wrists above \\( \\mathbf{r} \\). Here is an example. The most frequent gesture in the database of \"wayne\" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that \"wayne\" is a habitual right-handed" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.092, + 0.805, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.321, + 0.895, + 0.378 + ], + "angle": 0, + "content": "Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.895, + 0.493 + ], + "angle": 0, + "content": "speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.75, + 0.523 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.773 + ], + "angle": 0, + "content": "In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.661, + 0.803 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2328" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.116, + 0.332, + 0.129 + ], + "angle": 0, + "content": "[1] Blender. https://www.blender.org/. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.131, + 0.345, + 0.143 + ], + "angle": 0, + "content": "[2] Mixamo. https://www MIXamo.com/. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.145, + 0.469, + 0.227 + ], + "angle": 0, + "content": "[3] Chaitanya Ahuja, Dong Won Lee, Ryo Ishii, and Louis-Philippe Morency. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 3408-3418, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2330" + } + ] +] \ No newline at end of file diff --git a/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_origin.pdf b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..906911b2f6a3645ad91ca4dfe20495f01f07737a --- /dev/null +++ b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:457e80688616409e5e6c779ae7482d5046fbb5889f1347b1076e277fb10f301d +size 3685455 diff --git a/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/full.md b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1dc3f15c4db14cb9ad450e57dddcf1bc9c0c1c2a --- /dev/null +++ b/2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/full.md @@ -0,0 +1,315 @@ +# QPGesture: Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation + +Sicheng Yang $^{1}$ Zhiyong Wu $^{2,1,4}$ Minglei Li $^{2}$ Zhensong Zhang $^{3}$ + +Lei Hao3 Weihong Bao1 Haolin Zhuang1 + +$^{1}$ Tsinghua University $^{2}$ Huawei Cloud Computing Technologies Co., Ltd + +3 Huawei Noah's Ark Lab 4 The Chinese University of Hong Kong + +{yangsc21, bwh21, zhuanghl21}@mails.tsinghua.edu.cn zywu@sz.tsinghua.edu.cn + +{liminglei29, zhangzhensong, haolei5}@huawei.com + +# Abstract + +Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture. + +# 1. Introduction + +Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen + +![](images/e35abe3c93774187015fffd290bc71c99c77f4a716874f885f457d34433d322c.jpg) +Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2]. + +![](images/ebbf56ed8b02233525afdee7b734883d1b9987eb94f993c2944da32b50605a90.jpg) + +erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures. + +Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models. + +Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering + +![](images/c8d6095f716cf4912c526deb9e6e83fd023966593a8d27477e9378310725d4c9.jpg) +Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates. + +challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text. + +The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon. + +The main contributions of our work are: + +- We present a novel quantization-based motion matching framework for speech-driven gesture generation. + +- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization. +- We design a phase guidance strategy to select optimal audio and text candidates for motion matching. +- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework. + +# 2. Related Work + +End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality. + +As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker + +![](images/588f51f05d2070063f33b8c5f910136474356f75b8e40df2f83722a9aea7b1da.jpg) +Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features. + +identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code. + +Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task. + +Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7]. + +In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech + +based motion matching with phase guidance. + +# 3. Our Approach + +Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step. + +# 3.1. Learning a discrete latent space representation + +Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence $\mathbf{G} \in \mathbb{R}^{T \times D_g}$ , where $T$ denotes the number of gestures and $D_g$ pose dimension. We first adopt a 1D temporal convolution network $E_g$ to encode the joint sequence $\mathbf{G}$ to context-aware features $\mathbf{g} \in \mathbb{R}^{T' \times C}$ , where $T' = T / d$ , $d$ is the temporal down-sampling rate, and $C$ is the channel dimension of features. This process could be written as $\mathbf{g} = E_g(\mathbf{G})$ . Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook $\mathcal{Z}_g$ elements $\mathbf{g_q} \in \mathbb{R}^{T' \times C}$ , where $\mathbf{g_q} \in \mathcal{Z}_g^T$ , $\mathcal{Z}_g$ is a set of $C_b$ codes of dimension $n_z$ , we quantize $\mathbf{g}$ by mapping each temporal feature $\mathbf{g}_i$ to its closest codebook element $z_j$ as $\mathbf{q}(.)$ : + +$$ +\mathbf {g} _ {\mathbf {q}, i} = \mathbf {q} (\mathbf {g}) = \arg \min _ {\mathbf {z} _ {j} \in \mathcal {Z} _ {g}} \| \mathbf {g} _ {i} - \mathbf {z} _ {j} \| \tag {1} +$$ + +A following de-convolutional decoder $D_g$ projects $\mathbf{g_q}$ back to the motion space as a pose sequence $\hat{\mathbf{G}}_1$ , which can be formulated as + +$$ +\hat {\mathbf {G}} _ {1} = D _ {g} \left(\mathbf {g} _ {q}\right) = D _ {g} \left(\mathbf {q} \left(E _ {g} (\mathbf {G})\right)\right) \tag {2} +$$ + +Thus the encoder, decoder and codebook can be trained by optimizing: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {g e s t u r e} \left(E _ {g}, D _ {g}, \mathcal {Z} _ {g}\right)} = \mathcal {L} _ {\text {r e c}} \left(\hat {\mathbf {G}} _ {1}, \mathbf {G}\right) + \left\| \operatorname {s g} [ \mathbf {g} ] - \mathbf {g} _ {\mathbf {q}} \right\| \tag {3} \\ + \beta \| \mathbf {g} - \mathrm {s g} [ \mathbf {g _ {q}} ] \| \\ \end{array} +$$ + +where $\mathcal{L}_{rec}$ is the reconstruction loss that constrains the predicted joint sequence to ground truth, $\mathrm{sg}[\cdot ]$ denotes the stop-gradient operation, and the term $\| \mathbf{g} - \mathrm{sg}\left[\mathbf{g_q}\right]\|$ is the "commitment loss" with weighting factor $\beta$ [42]. + +Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {r e c}} \left(\hat {\mathbf {G}} _ {1}, \mathbf {G} _ {1}\right) = \left\| \hat {\mathbf {G}} _ {1} - \mathbf {G} _ {1} \right\| _ {1} + \alpha_ {1} \left\| \hat {\mathbf {G}} _ {1} ^ {\prime} - \mathbf {G} _ {1} ^ {\prime} \right\| _ {1} \tag {4} \\ + \alpha_ {2} \left\| \hat {\mathbf {G}} _ {1} ^ {\prime \prime} - \mathbf {G} _ {1} ^ {\prime \prime} \right\| _ {1} \\ \end{array} +$$ + +And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input $\mathbf{G}$ i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints. + +Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation $\mathbf{z}$ , for each time step $i$ , the quantization module replaces the original representation $\mathbf{z}$ by $\hat{\mathbf{z}} = \mathbf{a}_{\mathbf{q},i}$ from $\mathcal{Z}_a$ , which contains a set of $C_b'$ codes of dimension $n_z'$ . + +# 3.2. Motion Matching based on Audio and Text + +Our motion matching algorithm takes a discrete text sequence $\mathbf{t} = [\mathbf{t}_0, \mathbf{t}_1, \dots, \mathbf{t}_{T' - 1}]$ , a discrete audio sequence $\mathbf{a_q} = [\mathbf{a_{q,0}}, \mathbf{a_{q,1}}, \dots, \mathbf{a_{q,T'}} - 1]$ , and one initial previous pose code $\mathbf{g}_{-1}$ , and optionally a sequence of control masks $\mathbf{M} = [\mathbf{m}_0, \mathbf{m}_1, \dots, \mathbf{m}_{T' - 1}]$ . The outputs are audio-based candidate $\mathbf{C}_a = [\mathbf{c}_{0,a}, \mathbf{c}_{1,a}, \dots, \mathbf{c}_{T' - 1,a}]$ and text-based candidate $\mathbf{C}_t = [\mathbf{c}_{0,t}, \mathbf{c}_{1,t}, \dots, \mathbf{c}_{T' - 1,t}]$ . $T'$ denotes the number of speech segments during inference. + +Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1. + +To find the appropriate output gesture sequence $\mathbf{C}_a$ and $\mathbf{C}_t$ from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code $\mathbf{g}_{-1}$ for every $T$ frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code $\mathbf{g}_{-1}$ and the joints corresponding to each code $\mathbf{g_q}$ in the codebook to get the pose-based pre-candidate $\hat{\mathbf{C}}_g = \left\{\hat{\mathbf{C}}_g^0,\hat{\mathbf{C}}_g^1,\dots ,\hat{\mathbf{C}}_g^{C_b}\right\}$ . In the first iteration, the previous pose code $\mathbf{g}_{-1}$ is initialized by either randomly sampling a code from codebook $\mathcal{Z}_g$ or set to be the code with the most frequent occurrences in the codebook (the code of mean pose). + +Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence $\mathbf{F}_a = [\mathbf{F}_{a,0},\mathbf{F}_{a,1},\dots ,\mathbf{F}_{a,T^{\prime} - 1}]$ . To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database, + +![](images/561973762b93813c2f17ca25b1a35de12b0254e7490a0b52ef0bc487c6fce9ae.jpg) +Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding. + +we calculate the audio feature similarity of the corresponding code per $d$ frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate $\hat{\mathbf{C}}_a = \left\{\hat{\mathbf{C}}_a^0,\hat{\mathbf{C}}_a^1,\dots ,\hat{\mathbf{C}}_a^{C_b}\right\}$ . Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2). + +Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence $\mathbf{F}_t$ . For every clip in the database, we calculate the text features cosine similarity of the corresponding code per $d$ frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is $\hat{\mathbf{C}}_t = \left\{\hat{\mathbf{C}}_t^0,\hat{\mathbf{C}}_t^1,\dots ,\hat{\mathbf{C}}_t^{C_b}\right\}$ + +Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate $\mathbf{C}_a$ based on $\hat{\mathbf{C}}_g$ and $\hat{\mathbf{C}}_a$ , and text candidate $\mathbf{C}_t$ based on $\hat{\mathbf{C}}_g$ and $\hat{\mathbf{C}}_t$ . Then we select the final gesture from $\mathbf{C}_a$ and $\mathbf{C}_t$ according to the phase guide. + +# 3.3. Phase-Guided Gesture Generation + +To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network $E_{p}$ to a latent space of the motion $\mathbf{G}$ , which can be formulated as + +$$ +\mathbf {L} = E _ {p} (\mathbf {G}) \tag {5} +$$ + +where $\mathbf{L} \in \mathbb{R}^{T \times M}$ , $M$ is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle. + +It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of $\mathbf{L}$ and create the zero-indexed matrix of Fourier coefficients $\mathbf{c} \in \mathbb{C}^{M \times K + 1}$ , $K = \left\lfloor \frac{T}{2} \right\rfloor$ , written as $\mathbf{c} = FFT(\mathbf{L})$ . Power spectrum $\mathbf{p} \in \mathbb{R}^{M \times K + 1}$ for each channel is $\mathbf{p}_{i,j} = \frac{2}{T} |\mathbf{c}_{i,j}|^2$ , where $i$ is the channel index and $j$ is the index for the frequency bands. Assumed that there are $T$ points in a time window of $N$ seconds. The periodic parameters are computed by: + +$$ +\mathbf {A} _ {i} = \sqrt {\frac {2}{T} \sum_ {j = 1} ^ {K} \mathbf {p} _ {i , j}}, \quad \mathbf {F} _ {i} = \frac {\sum_ {j = 1} ^ {K} \left(\mathbf {f} _ {j} \cdot \mathbf {p} _ {i , j}\right)}{\sum_ {j = 1} ^ {K} \mathbf {p} _ {i , j}}, \quad \mathbf {B} _ {i} = \frac {\mathbf {c} _ {i , 0}}{T}, \tag {6} +$$ + +where $\mathbf{f} = (0,1 / N,2 / N,\dots ,K / N)$ is frequencies vector. + +Phase shift $\mathbf{S} \in \mathbb{R}^{M}$ for each latent curve $\mathbf{S}_i$ can be predicted by a fully connected layer $FC$ , which can be formulated as: + +$$ +\left(s _ {x}, s _ {y}\right) = F C \left(\mathbf {L} _ {i}\right), \quad \mathbf {S} _ {i} = \operatorname {a t a n 2} \left(s _ {y}, s _ {x}\right) \tag {7} +$$ + +For each temporal motion $\mathbf{G}$ , within a centered time window $\mathcal{T} = \left[-\frac{t_1 - t_0}{2}, -\frac{t_1 - t_0}{2} + \frac{t_1 - t_0}{N - 1}, \dots, \frac{t_1 - t_0}{2}\right]$ , where $t_0 \leq t \leq t_1$ , the decoder $D_p$ takes all periodic parameters as its input, and maps back to the original motion curves: + +$$ +\hat {\mathbf {L}} = f (\mathcal {T}; \mathbf {A}, \mathbf {F}, \mathbf {B}, \mathbf {S}) = \mathbf {A} \cdot \sin (2 \pi \cdot (\mathbf {F} \cdot \mathcal {T} - \mathrm {S})) + \mathbf {B} \tag {8} +$$ + +$$ +\hat {\mathbf {G}} _ {2} = h (\hat {\mathbf {L}}) \tag {9} +$$ + +The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding $\mathbf{L}$ . + +$$ +\mathcal {L} _ {\text {p h a s e}} = \mathcal {L} _ {\text {p h a s e - r e c o n}} (\mathbf {G}, \hat {\mathbf {G}} _ {\mathbf {2}}) \tag {10} +$$ + +After training, phase manifold $\mathcal{P}$ of a sample motion which captures a lot of "information" about the current state of the original time series data is + +$$ +\mathcal {P} _ {2 i - 1} ^ {(t)} = \mathrm {A} _ {i} ^ {(t)} \cdot \sin \left(2 \pi \cdot \mathrm {S} _ {i} ^ {(t)}\right), \quad \mathcal {P} _ {2 i} ^ {(t)} = \mathrm {A} _ {i} ^ {(t)} \cdot \cos \left(2 \pi \cdot \mathrm {S} _ {i} ^ {(t)}\right) \tag {11} +$$ + +where $\mathcal{P}\in \mathbb{R}^{2M}$ + +We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto + +![](images/cd14b049e39e037f1f7483572bf9e42dc51f401e83431c1b48b65f82f73d9a31.jpg) +(a) Rotational velocity space. + +![](images/9a85253e41749a017c6eb2d233aa80676278ef9c6d5884fc5322a6b1d88fc5e6.jpg) +(b) Latent space learned by convolutional and fully connected. + +![](images/87d56a2a641907bb6ccf00d30892b695b58b7d39df493cc4926c5267511b14f6.jpg) +(c) Phase space. +Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding + +a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements. + +The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames $N_{strid}$ of the manifold phase $\mathcal{P}_{-1}$ corresponding to the frame of the initial code and the first frames of the manifold phase $\mathcal{P}_{a/t}$ corresponding to the audio/text candidate $\mathbf{C}_a$ and $\mathbf{C}_t$ within $N_{phase}$ frames, which can be written as $\text{concat}[\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \mathcal{P}_{a/t}^{[N_{strid}]}$ and $\text{concat}[\mathcal{P}_{-1}^{[-N_{strid}]}, \mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}]$ . Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm. + +# 4. Experiments + +Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl + +![](images/0470df749c2bb5a1b8fc216dd32923a97d3fcabb6e82c2b4178c8d4c41ca6196.jpg) +(a) The phase manifold of the seed code to be matched. +Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate $\mathbf{C}_a$ and text candidate $\mathbf{C}_t$ . + +![](images/57417fdb192726bd1146df1f316eeadc16acca6950440f41e27169beadb2f486.jpg) +(b) The phase manifold of the candidate to be matched. + +edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers "wayne" (male speaker) and "kieks" (female speaker), and constructed separate databases for our experiments. + +Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers. $3 \times 3$ rotation matrix features are computed as gesture sequences, with pose dimension $D_{g}$ is 9. Down-sampling rate $d$ is 8. The size $C_b$ of codebook $\mathcal{Z}_g$ is set to 512 with dimension $n_z$ is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of $T = 240$ (4 seconds), using the ADAM [22] optimizer (learning rate is e-4, $\beta_{1} = 0.5$ , $\beta_{2} = 0.98$ ) with a batch size of 128 for 200 epochs. We set $\beta = 0.1$ for Equation (3) and $\alpha_{1} = 1$ , $\alpha_{2} = 1$ for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with $d = 32$ . As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of $10^{-4}$ and a batch size of 128. The number of phase channels $M$ is set to 8. To calculate the phase similarity, the number of frames is set to $N_{phase} = 8$ and $N_{stride} = 3$ . The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook $\mathcal{Z}_q$ . + +Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis + +tance [25], $H\left(\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}\right) = \sqrt{1 - \sum_{i} \sqrt{h_{i}^{(1)} \cdot h_{i}^{(2)}}}$ between the histograms $\boldsymbol{h}^{(1)}$ and $\boldsymbol{h}^{(2)}$ . The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements. + +# 4.1. Comparison to Existing Methods + +We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921 $(44\%)$ and 3837.068 $(39\%)$ than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space. + +User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants "How human-like does the gesture motion appear?" In terms of appropriateness evaluation, each evaluation page asked participants "How appropriate are the gestures for the speech?" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) "Excellent", "Good", "Fair", "Poor", and "Bad". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1. + +Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human + +Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with $95\%$ confidence intervals. + +
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
Ground Truth (GT)0.00.00.03.79 ± 0.193.62 ± 0.21
End2End [47]0.14664.99016739.9783.64 ± 0.113.23 ± 0.14
Trimodal [46]0.15548.32212869.983.31 ± 0.173.20 ± 0.19
StyleGestures [5]0.13635.8429846.9273.66 ± 0.083.30 ± 0.11
KNN [17]0.36443.03012470.0612.38 ± 0.102.35 ± 0.13
CaMN [31]0.14952.49610549.4553.65 ± 0.163.29 ± 0.15
Ours0.13619.9215742.2814.00 ± 0.143.66 ± 0.23
+ +Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric. + +
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
w/o wavvq + WavLM0.15119.9436009.8593.87 ± 0.213.64 ± 0.21
w/o audio0.13420.4015871.0443.87 ± 0.213.63 ± 0.20
w/o text0.11823.9296389.8663.57 ± 0.293.41 ± 0.23
w/o phase0.13819.1955759.1673.90 ± 0.113.65 ± 0.17
w/o motion matching (GRU + codebook)0.14030.40411642.6413.78 ± 0.143.43 ± 0.16
Ours0.13619.9215742.2814.07 ± 0.153.77 ± 0.21
+ +likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more "related to the semantics" with "more natural", while our method "lacking power and exaggerated gestures" compared to GT. More details regarding the user study are shown in the supplementary material. + +# 4.2. Ablation Studies + +Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video. + +We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively. + +Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant. + +![](images/d19feb63e29ec809be67e210cb72e7bb433171fcebf1e2d8fedd0a4df462551a.jpg) +Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance. + +The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase + +guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by $10.483(53\%)$ and 6460.202 $(107\%)$ , respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space. + +User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed. + +# 4.3. Controllability + +Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold $\mathbf{r}$ , the search can be restricted to consider only codes corresponding to wrists above $\mathbf{r}$ . Here is an example. The most frequent gesture in the database of "wayne" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that "wayne" is a habitual right-handed + +![](images/749f1ef66e344cf56d62a37d3348d75b94bad3f0d20cfb26f296570fea7e7d5d.jpg) +Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker. + +speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons. + +# 5. Discussion and Conclusion + +In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures. + +# Acknowledgments + +This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030). + +# References + +[1] Blender. https://www.blender.org/. 6 +[2] Mixamo. https://www MIXamo.com/. 1 +[3] Chaitanya Ahuja, Dong Won Lee, Ryo Ishii, and Louis-Philippe Morency. No gestures left behind: Learning relationships between spoken language and freeform gestures. In Findings of the Association for Computational Linguistics: EMNLP, volume EMNLP 2020 of Findings of ACL, pages 1884–1895, 2020. 6 +[4] Chaitanya Ahuja, Dong Won Lee, Yukiko I. Nakano, and Louis-Philippe Morency. 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+ ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 290, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 290, + 574 + ], + "type": "text", + "content": "Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 273, + 437, + 361 + ], + "blocks": [ + { + "bbox": [ + 307, + 273, + 437, + 361 + ], + "lines": [ + { + "bbox": [ + 307, + 273, + 437, + 361 + ], + "spans": [ + { + "bbox": [ + 307, + 273, + 437, + 361 + ], + "type": "image", + "image_path": "e35abe3c93774187015fffd290bc71c99c77f4a716874f885f457d34433d322c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 370, + 546, + 393 + ], + "lines": [ + { + "bbox": [ + 305, + 370, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 546, + 393 + ], + "type": "text", + "content": "Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2]." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 440, + 274, + 545, + 361 + ], + "blocks": [ + { + "bbox": [ + 440, + 274, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 440, + 274, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 440, + 274, + 545, + 361 + ], + "type": "image", + "image_path": "ebbf56ed8b02233525afdee7b734883d1b9987eb94f993c2944da32b50605a90.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 414, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 450 + ], + "type": "text", + "content": "erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 450, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 653 + ], + "type": "text", + "content": "Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2321" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 77, + 539, + 198 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 539, + 198 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 539, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 539, + 198 + ], + "type": "image", + "image_path": "c8d6095f716cf4912c526deb9e6e83fd023966593a8d27477e9378310725d4c9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 211, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 211, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 547, + 257 + ], + "type": "text", + "content": "Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 539 + ], + "type": "text", + "content": "challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 542, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 661 + ], + "type": "text", + "content": "The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 664, + 223, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 664, + 223, + 674 + ], + "spans": [ + { + "bbox": [ + 59, + 664, + 223, + 674 + ], + "type": "text", + "content": "The main contributions of our work are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We present a novel quantization-based motion matching framework for speech-driven gesture generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 277, + 545, + 392 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 277, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 277, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 317, + 277, + 545, + 313 + ], + "type": "text", + "content": "- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 323, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 323, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 317, + 323, + 545, + 347 + ], + "type": "text", + "content": "- We design a phase guidance strategy to select optimal audio and text candidates for motion matching." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 357, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 357, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 317, + 357, + 545, + 392 + ], + "type": "text", + "content": "- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 405, + 392, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 392, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 392, + 418 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 676 + ], + "type": "text", + "content": "End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2322" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 286, + 183 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 286, + 183 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 286, + 183 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 286, + 183 + ], + "type": "image", + "image_path": "588f51f05d2070063f33b8c5f910136474356f75b8e40df2f83722a9aea7b1da.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 288, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 288, + 239 + ], + "type": "text", + "content": "Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 263, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 384 + ], + "type": "text", + "content": "identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 386, + 288, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 288, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 288, + 540 + ], + "type": "text", + "content": "Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "content": "Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 488, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 488, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 488, + 84 + ], + "type": "text", + "content": "based motion matching with phase guidance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 93, + 397, + 107 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 93, + 397, + 107 + ], + "spans": [ + { + "bbox": [ + 306, + 93, + 397, + 107 + ], + "type": "text", + "content": "3. Our Approach" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 114, + 547, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 114, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 114, + 547, + 234 + ], + "type": "text", + "content": "Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 239, + 545, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 545, + 252 + ], + "type": "text", + "content": "3.1. Learning a discrete latent space representation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": "Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{G} \\in \\mathbb{R}^{T \\times D_g}" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " denotes the number of gestures and " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "D_g" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " pose dimension. We first adopt a 1D temporal convolution network " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "E_g" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " to encode the joint sequence " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " to context-aware features " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g} \\in \\mathbb{R}^{T' \\times C}" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "T' = T / d" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " is the temporal down-sampling rate, and " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " is the channel dimension of features. This process could be written as " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = E_g(\\mathbf{G})" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ". Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_g" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " elements " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g_q} \\in \\mathbb{R}^{T' \\times C}" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g_q} \\in \\mathcal{Z}_g^T" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_g" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " is a set of " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "C_b" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " codes of dimension " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "n_z" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ", we quantize " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " by mapping each temporal feature " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_i" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " to its closest codebook element " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "z_j" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{q}(.)" + }, + { + "bbox": [ + 304, + 257, + 546, + 430 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 434, + 545, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 434, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 351, + 434, + 545, + 453 + ], + "type": "interline_equation", + "content": "\\mathbf {g} _ {\\mathbf {q}, i} = \\mathbf {q} (\\mathbf {g}) = \\arg \\min _ {\\mathbf {z} _ {j} \\in \\mathcal {Z} _ {g}} \\| \\mathbf {g} _ {i} - \\mathbf {z} _ {j} \\| \\tag {1}", + "image_path": "d366ca65c435b49a7e91140041888023b0a381e7eef57071427b19960f0d40e1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "text", + "content": "A following de-convolutional decoder " + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "inline_equation", + "content": "D_g" + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "text", + "content": " projects " + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{g_q}" + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "text", + "content": " back to the motion space as a pose sequence " + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_1" + }, + { + "bbox": [ + 304, + 458, + 545, + 495 + ], + "type": "text", + "content": ", which can be formulated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 356, + 500, + 545, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 500, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 356, + 500, + 545, + 515 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {G}} _ {1} = D _ {g} \\left(\\mathbf {g} _ {q}\\right) = D _ {g} \\left(\\mathbf {q} \\left(E _ {g} (\\mathbf {G})\\right)\\right) \\tag {2}", + "image_path": "1e58d0b21e2316b61b6ed9c0782d49d3da91f4e9f69101ed94a03297cd2c41eb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "content": "Thus the encoder, decoder and codebook can be trained by optimizing:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 549, + 545, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 549, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 313, + 549, + 545, + 579 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {g e s t u r e} \\left(E _ {g}, D _ {g}, \\mathcal {Z} _ {g}\\right)} = \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G}\\right) + \\left\\| \\operatorname {s g} [ \\mathbf {g} ] - \\mathbf {g} _ {\\mathbf {q}} \\right\\| \\tag {3} \\\\ + \\beta \\| \\mathbf {g} - \\mathrm {s g} [ \\mathbf {g _ {q}} ] \\| \\\\ \\end{array}", + "image_path": "525c4d9be5f5efa23119a07c992452e38d81a063397ada5399b1471dd59663c1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": " is the reconstruction loss that constrains the predicted joint sequence to ground truth, " + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}[\\cdot ]" + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": " denotes the stop-gradient operation, and the term " + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{g} - \\mathrm{sg}\\left[\\mathbf{g_q}\\right]\\|" + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": " is the \"commitment loss\" with weighting factor " + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": " [42]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 632, + 545, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 669 + ], + "type": "text", + "content": "Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 672, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 672, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 315, + 672, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G} _ {1}\\right) = \\left\\| \\hat {\\mathbf {G}} _ {1} - \\mathbf {G} _ {1} \\right\\| _ {1} + \\alpha_ {1} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime} - \\mathbf {G} _ {1} ^ {\\prime} \\right\\| _ {1} \\tag {4} \\\\ + \\alpha_ {2} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime \\prime} - \\mathbf {G} _ {1} ^ {\\prime \\prime} \\right\\| _ {1} \\\\ \\end{array}", + "image_path": "ac5190f2199894e06ae7f216612e819b8803f00a1e2faa7760dd05ee42bf512a.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "2323" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": "And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": " i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": "Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": ", for each time step " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": ", the quantization module replaces the original representation " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}} = \\mathbf{a}_{\\mathbf{q},i}" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_a" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": ", which contains a set of " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "C_b'" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": " codes of dimension " + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "inline_equation", + "content": "n_z'" + }, + { + "bbox": [ + 46, + 133, + 288, + 242 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 247, + 270, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 270, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 270, + 259 + ], + "type": "text", + "content": "3.2. Motion Matching based on Audio and Text" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": "Our motion matching algorithm takes a discrete text sequence " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{t} = [\\mathbf{t}_0, \\mathbf{t}_1, \\dots, \\mathbf{t}_{T' - 1}]" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": ", a discrete audio sequence " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{a_q} = [\\mathbf{a_{q,0}}, \\mathbf{a_{q,1}}, \\dots, \\mathbf{a_{q,T'}} - 1]" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": ", and one initial previous pose code " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{-1}" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": ", and optionally a sequence of control masks " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{M} = [\\mathbf{m}_0, \\mathbf{m}_1, \\dots, \\mathbf{m}_{T' - 1}]" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": ". The outputs are audio-based candidate " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a = [\\mathbf{c}_{0,a}, \\mathbf{c}_{1,a}, \\dots, \\mathbf{c}_{T' - 1,a}]" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": " and text-based candidate " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t = [\\mathbf{c}_{0,t}, \\mathbf{c}_{1,t}, \\dots, \\mathbf{c}_{T' - 1,t}]" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "inline_equation", + "content": "T'" + }, + { + "bbox": [ + 46, + 266, + 287, + 361 + ], + "type": "text", + "content": " denotes the number of speech segments during inference." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 445 + ], + "type": "text", + "content": "Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": "To find the appropriate output gesture sequence " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " for every " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " and the joints corresponding to each code " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{g_q}" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " in the codebook to get the pose-based pre-candidate " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_g = \\left\\{\\hat{\\mathbf{C}}_g^0,\\hat{\\mathbf{C}}_g^1,\\dots ,\\hat{\\mathbf{C}}_g^{C_b}\\right\\}" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": ". In the first iteration, the previous pose code " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " is initialized by either randomly sampling a code from codebook " + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_g" + }, + { + "bbox": [ + 46, + 445, + 287, + 605 + ], + "type": "text", + "content": " or set to be the code with the most frequent occurrences in the codebook (the code of mean pose)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a = [\\mathbf{F}_{a,0},\\mathbf{F}_{a,1},\\dots ,\\mathbf{F}_{a,T^{\\prime} - 1}]" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database," + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 315, + 75, + 539, + 148 + ], + "blocks": [ + { + "bbox": [ + 315, + 75, + 539, + 148 + ], + "lines": [ + { + "bbox": [ + 315, + 75, + 539, + 148 + ], + "spans": [ + { + "bbox": [ + 315, + 75, + 539, + 148 + ], + "type": "image", + "image_path": "561973762b93813c2f17ca25b1a35de12b0254e7490a0b52ef0bc487c6fce9ae.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 159, + 545, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 248 + ], + "type": "text", + "content": "Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "text", + "content": "we calculate the audio feature similarity of the corresponding code per " + }, + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "text", + "content": " frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate " + }, + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_a = \\left\\{\\hat{\\mathbf{C}}_a^0,\\hat{\\mathbf{C}}_a^1,\\dots ,\\hat{\\mathbf{C}}_a^{C_b}\\right\\}" + }, + { + "bbox": [ + 304, + 266, + 545, + 366 + ], + "type": "text", + "content": ". Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "text", + "content": "Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence " + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "text", + "content": ". For every clip in the database, we calculate the text features cosine similarity of the corresponding code per " + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "text", + "content": " frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is " + }, + { + "bbox": [ + 304, + 367, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_t = \\left\\{\\hat{\\mathbf{C}}_t^0,\\hat{\\mathbf{C}}_t^1,\\dots ,\\hat{\\mathbf{C}}_t^{C_b}\\right\\}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": "Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_g" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_a" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": ", and text candidate " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_g" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_t" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": ". Then we select the final gesture from " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 304, + 477, + 545, + 598 + ], + "type": "text", + "content": " according to the phase guide." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 604, + 491, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 491, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 491, + 616 + ], + "type": "text", + "content": "3.3. Phase-Guided Gesture Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "text", + "content": "To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network " + }, + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "inline_equation", + "content": "E_{p}" + }, + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "text", + "content": " to a latent space of the motion " + }, + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 623, + 545, + 693 + ], + "type": "text", + "content": ", which can be formulated as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 399, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 399, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {L} = E _ {p} (\\mathbf {G}) \\tag {5}", + "image_path": "95ffdbaa1b3b916f7090097067d62aec1f2d65773ca928840a629043662dc61d.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "2324" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{L} \\in \\mathbb{R}^{T \\times M}" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": "It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " and create the zero-indexed matrix of Fourier coefficients " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{C}^{M \\times K + 1}" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "K = \\left\\lfloor \\frac{T}{2} \\right\\rfloor" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": ", written as " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = FFT(\\mathbf{L})" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": ". Power spectrum " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^{M \\times K + 1}" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " for each channel is " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{i,j} = \\frac{2}{T} |\\mathbf{c}_{i,j}|^2" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " is the channel index and " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " is the index for the frequency bands. Assumed that there are " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " points in a time window of " + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 133, + 288, + 265 + ], + "type": "text", + "content": " seconds. The periodic parameters are computed by:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 274, + 294, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 294, + 320 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 294, + 320 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {i} = \\sqrt {\\frac {2}{T} \\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {F} _ {i} = \\frac {\\sum_ {j = 1} ^ {K} \\left(\\mathbf {f} _ {j} \\cdot \\mathbf {p} _ {i , j}\\right)}{\\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {B} _ {i} = \\frac {\\mathbf {c} _ {i , 0}}{T}, \\tag {6}", + "image_path": "9eee794f615d4aa1becd51fe24cbc5a5a2737a1a17aee4372dff692000ce37cc.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 321, + 284, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 321, + 284, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 284, + 333 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 321, + 284, + 333 + ], + "type": "inline_equation", + "content": "\\mathbf{f} = (0,1 / N,2 / N,\\dots ,K / N)" + }, + { + "bbox": [ + 47, + 321, + 284, + 333 + ], + "type": "text", + "content": " is frequencies vector." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "text", + "content": "Phase shift " + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "text", + "content": " for each latent curve " + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_i" + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "text", + "content": " can be predicted by a fully connected layer " + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "inline_equation", + "content": "FC" + }, + { + "bbox": [ + 47, + 333, + 287, + 368 + ], + "type": "text", + "content": ", which can be formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 378, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 378, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 76, + 378, + 287, + 392 + ], + "type": "interline_equation", + "content": "\\left(s _ {x}, s _ {y}\\right) = F C \\left(\\mathbf {L} _ {i}\\right), \\quad \\mathbf {S} _ {i} = \\operatorname {a t a n 2} \\left(s _ {y}, s _ {x}\\right) \\tag {7}", + "image_path": "ea774453f1e43beb438054699929e1a794f2da54f62875a23c9565bf353b853e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "content": "For each temporal motion " + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "content": ", within a centered time window " + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\left[-\\frac{t_1 - t_0}{2}, -\\frac{t_1 - t_0}{2} + \\frac{t_1 - t_0}{N - 1}, \\dots, \\frac{t_1 - t_0}{2}\\right]" + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "inline_equation", + "content": "t_0 \\leq t \\leq t_1" + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "content": ", the decoder " + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "inline_equation", + "content": "D_p" + }, + { + "bbox": [ + 47, + 399, + 287, + 453 + ], + "type": "text", + "content": " takes all periodic parameters as its input, and maps back to the original motion curves:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 460, + 287, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 460, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 52, + 460, + 287, + 475 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} = f (\\mathcal {T}; \\mathbf {A}, \\mathbf {F}, \\mathbf {B}, \\mathbf {S}) = \\mathbf {A} \\cdot \\sin (2 \\pi \\cdot (\\mathbf {F} \\cdot \\mathcal {T} - \\mathrm {S})) + \\mathbf {B} \\tag {8}", + "image_path": "13c050a45c8f035343daf5e14948bd82f9fd74107968999b9c64d2b85419843b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 493, + 287, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 493, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 141, + 493, + 287, + 507 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {G}} _ {2} = h (\\hat {\\mathbf {L}}) \\tag {9}", + "image_path": "43d8010218ebccb767a1686a426c1d4d164d26d174ed2a88e1df5137d18d0f17.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 513, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 549 + ], + "type": "text", + "content": "The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding " + }, + { + "bbox": [ + 47, + 513, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 47, + 513, + 287, + 549 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 100, + 556, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 556, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 100, + 556, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p h a s e}} = \\mathcal {L} _ {\\text {p h a s e - r e c o n}} (\\mathbf {G}, \\hat {\\mathbf {G}} _ {\\mathbf {2}}) \\tag {10}", + "image_path": "0add48818ceff1ce50f0b712e15a2cb9c39e27490007ef70231833ca77b6823d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 579, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 287, + 615 + ], + "type": "text", + "content": "After training, phase manifold " + }, + { + "bbox": [ + 47, + 579, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 47, + 579, + 287, + 615 + ], + "type": "text", + "content": " of a sample motion which captures a lot of \"information\" about the current state of the original time series data is" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 623, + 293, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 293, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 293, + 653 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {2 i - 1} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\sin \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right), \\quad \\mathcal {P} _ {2 i} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\cos \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right) \\tag {11}", + "image_path": "ef6cacdb943580146e6b3776474873858bf66738f8497f68e748f6ffaa3a901c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 653, + 119, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 119, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 119, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 653, + 119, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{P}\\in \\mathbb{R}^{2M}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 392, + 72, + 461, + 114 + ], + "blocks": [ + { + "bbox": [ + 392, + 72, + 461, + 114 + ], + "lines": [ + { + "bbox": [ + 392, + 72, + 461, + 114 + ], + "spans": [ + { + "bbox": [ + 392, + 72, + 461, + 114 + ], + "type": "image", + "image_path": "cd14b049e39e037f1f7483572bf9e42dc51f401e83431c1b48b65f82f73d9a31.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 378, + 118, + 473, + 127 + ], + "lines": [ + { + "bbox": [ + 378, + 118, + 473, + 127 + ], + "spans": [ + { + "bbox": [ + 378, + 118, + 473, + 127 + ], + "type": "text", + "content": "(a) Rotational velocity space." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 368, + 132, + 485, + 199 + ], + "blocks": [ + { + "bbox": [ + 368, + 132, + 485, + 199 + ], + "lines": [ + { + "bbox": [ + 368, + 132, + 485, + 199 + ], + "spans": [ + { + "bbox": [ + 368, + 132, + 485, + 199 + ], + "type": "image", + "image_path": "9a85253e41749a017c6eb2d233aa80676278ef9c6d5884fc5322a6b1d88fc5e6.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 205, + 526, + 215 + ], + "lines": [ + { + "bbox": [ + 325, + 205, + 526, + 215 + ], + "spans": [ + { + "bbox": [ + 325, + 205, + 526, + 215 + ], + "type": "text", + "content": "(b) Latent space learned by convolutional and fully connected." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 368, + 219, + 484, + 287 + ], + "blocks": [ + { + "bbox": [ + 368, + 219, + 484, + 287 + ], + "lines": [ + { + "bbox": [ + 368, + 219, + 484, + 287 + ], + "spans": [ + { + "bbox": [ + 368, + 219, + 484, + 287 + ], + "type": "image", + "image_path": "87d56a2a641907bb6ccf00d30892b695b58b7d39df493cc4926c5267511b14f6.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 293, + 452, + 302 + ], + "lines": [ + { + "bbox": [ + 400, + 293, + 452, + 302 + ], + "spans": [ + { + "bbox": [ + 400, + 293, + 452, + 302 + ], + "type": "text", + "content": "(c) Phase space." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 312, + 545, + 367 + ], + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 367 + ], + "type": "text", + "content": "Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": "a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": "The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "N_{strid}" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " of the manifold phase " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{-1}" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " corresponding to the frame of the initial code and the first frames of the manifold phase " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{a/t}" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " corresponding to the audio/text candidate " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "N_{phase}" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " frames, which can be written as " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\text{concat}[\\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \\mathcal{P}_{a/t}^{[N_{strid}]}" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\text{concat}[\\mathcal{P}_{-1}^{[-N_{strid}]}, \\mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}]" + }, + { + "bbox": [ + 304, + 484, + 545, + 658 + ], + "type": "text", + "content": ". Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 386, + 682 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2325" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 72, + 149, + 183 + ], + "blocks": [ + { + "bbox": [ + 69, + 72, + 149, + 183 + ], + "lines": [ + { + "bbox": [ + 69, + 72, + 149, + 183 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 149, + 183 + ], + "type": "image", + "image_path": "0470df749c2bb5a1b8fc216dd32923a97d3fcabb6e82c2b4178c8d4c41ca6196.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 189, + 165, + 209 + ], + "lines": [ + { + "bbox": [ + 47, + 189, + 165, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 165, + 209 + ], + "type": "text", + "content": "(a) The phase manifold of the seed code to be matched." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "type": "text", + "content": "Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate " + }, + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_a" + }, + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "type": "text", + "content": " and text candidate " + }, + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_t" + }, + { + "bbox": [ + 46, + 218, + 287, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 188, + 72, + 270, + 183 + ], + "blocks": [ + { + "bbox": [ + 188, + 72, + 270, + 183 + ], + "lines": [ + { + "bbox": [ + 188, + 72, + 270, + 183 + ], + "spans": [ + { + "bbox": [ + 188, + 72, + 270, + 183 + ], + "type": "image", + "image_path": "57417fdb192726bd1146df1f316eeadc16acca6950440f41e27169beadb2f486.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 168, + 189, + 286, + 209 + ], + "lines": [ + { + "bbox": [ + 168, + 189, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 168, + 189, + 286, + 209 + ], + "type": "text", + "content": "(b) The phase manifold of the candidate to be matched." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "type": "text", + "content": "edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers \"wayne\" (male speaker) and \"kieks\" (female speaker), and constructed separate databases for our experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": "Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers. " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " rotation matrix features are computed as gesture sequences, with pose dimension " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "D_{g}" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " is 9. Down-sampling rate " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " is 8. The size " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "C_b" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " of codebook " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_g" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " is set to 512 with dimension " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "n_z" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "T = 240" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " (4 seconds), using the ADAM [22] optimizer (learning rate is e-4, " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.5" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.98" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": ") with a batch size of 128 for 200 epochs. We set " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " for Equation (3) and " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\alpha_{1} = 1" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\alpha_{2} = 1" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "d = 32" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": ". As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " and a batch size of 128. The number of phase channels " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " is set to 8. To calculate the phase similarity, the number of frames is set to " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "N_{phase} = 8" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "N_{stride} = 3" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": ". The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook " + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_q" + }, + { + "bbox": [ + 47, + 388, + 286, + 662 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "type": "text", + "content": "Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "text", + "content": "tance [25], " + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "inline_equation", + "content": "H\\left(\\boldsymbol{h}^{(1)}, \\boldsymbol{h}^{(2)}\\right) = \\sqrt{1 - \\sum_{i} \\sqrt{h_{i}^{(1)} \\cdot h_{i}^{(2)}}}" + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "text", + "content": " between the histograms " + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\boldsymbol{h}^{(1)}" + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\boldsymbol{h}^{(2)}" + }, + { + "bbox": [ + 304, + 71, + 545, + 217 + ], + "type": "text", + "content": ". The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 226, + 484, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 226, + 484, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 226, + 484, + 239 + ], + "type": "text", + "content": "4.1. Comparison to Existing Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "text", + "content": "We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921 " + }, + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "inline_equation", + "content": "(44\\%)" + }, + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "text", + "content": " and 3837.068 " + }, + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "inline_equation", + "content": "(39\\%)" + }, + { + "bbox": [ + 304, + 245, + 545, + 437 + ], + "type": "text", + "content": " than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 437, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 675 + ], + "type": "text", + "content": "User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants \"How human-like does the gesture motion appear?\" In terms of appropriateness evaluation, each evaluation page asked participants \"How appropriate are the gestures for the speech?\" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) \"Excellent\", \"Good\", \"Fair\", \"Poor\", and \"Bad\". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2326" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 123, + 517, + 242 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with " + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": " confidence intervals." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 80, + 123, + 517, + 242 + ], + "lines": [ + { + "bbox": [ + 80, + 123, + 517, + 242 + ], + "spans": [ + { + "bbox": [ + 80, + 123, + 517, + 242 + ], + "type": "table", + "html": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
Ground Truth (GT)0.00.00.03.79 ± 0.193.62 ± 0.21
End2End [47]0.14664.99016739.9783.64 ± 0.113.23 ± 0.14
Trimodal [46]0.15548.32212869.983.31 ± 0.173.20 ± 0.19
StyleGestures [5]0.13635.8429846.9273.66 ± 0.083.30 ± 0.11
KNN [17]0.36443.03012470.0612.38 ± 0.102.35 ± 0.13
CaMN [31]0.14952.49610549.4553.65 ± 0.163.29 ± 0.15
Ours0.13619.9215742.2814.00 ± 0.143.66 ± 0.23
", + "image_path": "757f145197ca1987b82db9a9ec0d786620bbdc560532551ea6ee9746940e829c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 66, + 270, + 533, + 388 + ], + "blocks": [ + { + "bbox": [ + 129, + 251, + 464, + 262 + ], + "lines": [ + { + "bbox": [ + 129, + 251, + 464, + 262 + ], + "spans": [ + { + "bbox": [ + 129, + 251, + 464, + 262 + ], + "type": "text", + "content": "Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 270, + 533, + 388 + ], + "lines": [ + { + "bbox": [ + 66, + 270, + 533, + 388 + ], + "spans": [ + { + "bbox": [ + 66, + 270, + 533, + 388 + ], + "type": "table", + "html": "
NameObjective evaluationSubjective evaluation
Hellinger distance average↓FGD on feature space↓FGD on raw data space↓Human-likenessAppropriateness
w/o wavvq + WavLM0.15119.9436009.8593.87 ± 0.213.64 ± 0.21
w/o audio0.13420.4015871.0443.87 ± 0.213.63 ± 0.20
w/o text0.11823.9296389.8663.57 ± 0.293.41 ± 0.23
w/o phase0.13819.1955759.1673.90 ± 0.113.65 ± 0.17
w/o motion matching (GRU + codebook)0.14030.40411642.6413.78 ± 0.143.43 ± 0.16
Ours0.13619.9215742.2814.07 ± 0.153.77 ± 0.21
", + "image_path": "6dfe09e8ede19086ddb846edce9657e08b0dd8581c359ecbbbdd3f8d7f27733a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "text", + "content": "likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more \"related to the semantics\" with \"more natural\", while our method \"lacking power and exaggerated gestures\" compared to GT. More details regarding the user study are shown in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 501, + 148, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 148, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 148, + 513 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 520, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 581 + ], + "type": "text", + "content": "Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "content": "We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 406, + 545, + 455 + ], + "blocks": [ + { + "bbox": [ + 307, + 406, + 545, + 455 + ], + "lines": [ + { + "bbox": [ + 307, + 406, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 307, + 406, + 545, + 455 + ], + "type": "image", + "image_path": "d19feb63e29ec809be67e210cb72e7bb433171fcebf1e2d8fedd0a4df462551a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 463, + 545, + 486 + ], + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 486 + ], + "type": "text", + "content": "Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2327" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "10.483(53\\%)" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": " and 6460.202 " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "(107\\%)" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": ", respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 563 + ], + "type": "text", + "content": "User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 574, + 139, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 139, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 139, + 586 + ], + "type": "text", + "content": "4.3. Controllability" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", the search can be restricted to consider only codes corresponding to wrists above " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". Here is an example. The most frequent gesture in the database of \"wayne\" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that \"wayne\" is a habitual right-handed" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 357, + 72, + 492, + 244 + ], + "blocks": [ + { + "bbox": [ + 357, + 72, + 492, + 244 + ], + "lines": [ + { + "bbox": [ + 357, + 72, + 492, + 244 + ], + "spans": [ + { + "bbox": [ + 357, + 72, + 492, + 244 + ], + "type": "image", + "image_path": "749f1ef66e344cf56d62a37d3348d75b94bad3f0d20cfb26f296570fea7e7d5d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 254, + 547, + 299 + ], + "lines": [ + { + "bbox": [ + 304, + 254, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 547, + 299 + ], + "type": "text", + "content": "Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 318, + 547, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 547, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 547, + 390 + ], + "type": "text", + "content": "speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 400, + 459, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 459, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 459, + 414 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 420, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 612 + ], + "type": "text", + "content": "In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2328" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 203, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 203, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 203, + 102 + ], + "type": "text", + "content": "[1] Blender. https://www.blender.org/. 6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 103, + 211, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 103, + 211, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 211, + 113 + ], + "type": "text", + "content": "[2] Mixamo. https://www MIXamo.com/. 1" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 114, + 287, + 179 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 287, + 179 + ], + "type": "text", + "content": "[3] Chaitanya Ahuja, Dong Won Lee, Ryo Ishii, and Louis-Philippe Morency. 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A: Self-Train on Unlabeled Images!", + "text_level": 1, + "bbox": [ + 76, + 128, + 893, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego", + "bbox": [ + 143, + 203, + 823, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 287, + 313, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA.", + "bbox": [ + 75, + 321, + 473, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 728, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the", + "bbox": [ + 75, + 753, + 470, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/03965e14b1009cd2745e52bb2345565fe94bb6775fa4da04f0c07e16fd5652aa.jpg", + "image_caption": [ + "Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image $I$ without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers $(Q,A)$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 271, + 893, + 486 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets.", + "bbox": [ + 496, + 580, + 893, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content", + "bbox": [ + 496, + 674, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* work done while at NEC Labs America", + "bbox": [ + 99, + 886, + 320, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15005", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3e4b943819c4228181fd9f28b9570fa942cc03b174fa245b394684d05216f4f0.jpg", + "image_caption": [ + "Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning." + ], + "image_footnote": [], + "bbox": [ + 89, + 87, + 571, + 286 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1338f0d6729f7208a8733a9fd6cc12ec31588ca937e3217f748b7773fd568866.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 89, + 880, + 282 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "than a short caption can describe).", + "bbox": [ + 76, + 363, + 305, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase \"this is a\". We convert each caption into a boolean question where the correct answer is \"yes\" by inserting the caption into the template is this a ? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between \"yes\" and \"no\" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers \"no\" to at least $5\\%$ of the questions, increasing to $15\\%$ as the diversity of captions increases (adjusted by top- $p$ parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image.", + "bbox": [ + 75, + 382, + 473, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model $\\mathrm{VQG}_{IC}$ . Next, we use $\\mathrm{VQG}_{IC}$ as a teacher to", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pseudolabel unlabeled images by sampling questions and answers from $\\mathrm{VQG}_{IC}$ with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset.", + "bbox": [ + 496, + 363, + 893, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Benefits: SelTDA allows us generate synthetic training data by approximating the distribution $P(Q, A|I)$ of the target VQA task, where $Q, A, I$ represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows:", + "bbox": [ + 496, + 438, + 895, + 694 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs.", + "2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed.", + "3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets." + ], + "bbox": [ + 511, + 702, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15006", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation.", + "bbox": [ + 75, + 114, + 468, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization.", + "bbox": [ + 75, + 296, + 470, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model.", + "bbox": [ + 75, + 492, + 470, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 299, + 591, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to pseudolabel an unlabeled image $I$ with a generated question-answer pair $(Q, A)$ using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model $\\mathrm{VQG_{IC}}$ to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating $P(Q, A|I)$ that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image.", + "bbox": [ + 496, + 325, + 893, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The Teacher: Direct Image-Conditional VQG", + "text_level": 1, + "bbox": [ + 500, + 696, + 885, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image $I$ , a question $Q$ and answer $A$ , the VQA student must approximate $P(Q \\mid Q, I)$ , while the teacher model must approximate $P(Q, A \\mid I)$ . Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate $P(Q \\mid I, A)$ , that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15007", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1b844b835973f755de7d2b3a15912d25d1506e699186fd4ae59ac4648da7d292.jpg", + "image_caption": [ + "Figure 3. Overview of the proposed framework. We first create the teacher $\\mathrm{VQG}_{IC}$ (§3.1), use $\\mathrm{VQG}_{IC}$ to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 895, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/07eb44d222a5f5a01e155ae42d95abd930b5fc2bd92482ff77ed3650a8b213c0.jpg", + "image_caption": [ + "Question: what is the cat wearing? \nAnswers: necktie, tie" + ], + "image_footnote": [], + "bbox": [ + 91, + 277, + 187, + 347 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7028f5f12d0e2415bc374ecca7788f763487cfe32d46aa2b05fde2e063073630.jpg", + "image_caption": [ + "Question: how is the egg cooked? Answer: fried" + ], + "image_footnote": [], + "bbox": [ + 93, + 386, + 218, + 460 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cd87a2039c4183818b9a7151627b2c40bcf3c0a3ac083fd466f88d2721d854a1.jpg", + "image_caption": [ + "Question: how many items of food are present here? \nAnswers: 2" + ], + "image_footnote": [], + "bbox": [ + 305, + 277, + 421, + 347 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f9013b0e122b47e981b019a685a592fdfae273ed025e4b6d73924bb935ca1efe.jpg", + "image_caption": [ + "Question: what activity is the baby learning? Answer: feeding, eating, nutrition" + ], + "image_footnote": [], + "bbox": [ + 313, + 385, + 415, + 462 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5a3885a05ec6c2ed434e18984c44ea16a9b1692d2cec15620b7b0584800ea3dd.jpg", + "image_caption": [ + "Question: what color is the sky in the picture? \nAnswers: clear, blue" + ], + "image_footnote": [], + "bbox": [ + 519, + 277, + 632, + 345 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8943e59bbb0aa9f14364f1d18c10b2466ffc22b68ab75b92f522a3b67c6b3f48.jpg", + "image_caption": [ + "Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration" + ], + "image_footnote": [], + "bbox": [ + 504, + 387, + 640, + 459 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/42a7928b3661f35b2ac5d7a2a0b66f6aa08229493cfa4d92c5cce7d9373ad563.jpg", + "image_caption": [ + "Question: what city is this? \nAnswers: london, uk" + ], + "image_footnote": [], + "bbox": [ + 718, + 277, + 830, + 345 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5188f6d8d4c231fd410025f49ec9f6ebb416f7a22adce852c9cdc6f462bf5d53.jpg", + "image_caption": [ + "Question: what is the name of this party? Answer: baby shower", + "Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning)." + ], + "image_footnote": [], + "bbox": [ + 725, + 386, + 852, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "approaches, we develop an image-conditional approach $(\\mathrm{VQG}_{IC})$ that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions $P(Y|I)$ , where $Y$ is often a distribution over a (finite) label space.", + "bbox": [ + 75, + 577, + 472, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To create the $\\mathrm{VQG}_{IC}$ teacher that approximates $P(Q,A|I)$ , we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate $P(T|I)$ , where $T = (Q,A)$ . Let $\\mathcal{D}_{QA}$ be a question-answer dataset we wish to create a teacher from. For a sample $(Q,A,I)\\in \\mathcal{D}_{QA}$ , we transform it into a target sequence of tokens $y_{1:N} = (y_1,y_2,\\dots y_n)$ by entering $(Q,A)$ into a structured template of the form \"Question: ? Answer: .\" where and are replaced by the content of $Q$ and $A$ respectively. Once $y_{1:N} = (y_1,y_2,\\dots y_n)$ is", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "obtained, we train the model by optimizing", + "bbox": [ + 500, + 577, + 787, + 593 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V Q G}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 604, + 892, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "over all question-image-answer pairs in $\\mathcal{D}_{QA}$ , where $x$ is the latent encoded features in the standard encoder-decoder architecture and $\\theta$ represents the VLM parameters. The $\\mathrm{VQG_{IC}}$ thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that $\\mathrm{VQG_{IC}}$ is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of $P(T|I)$ , having been exposed to a diverse number of images and paired text. The $\\mathrm{VQG_{IC}}$ teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair $(Q', A')$ is generated jointly as a text $T'$ , allowing us to sample from $P(T|I)$ .", + "bbox": [ + 496, + 655, + 893, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Training the Student with Unlabeled Data", + "text_level": 1, + "bbox": [ + 500, + 847, + 857, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the VQGIC teacher model has been obtained, self-training with unlabeled data can proceed. To produce a", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15008", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pseudolabel $(Q', A')$ for an unlabeled image $I_u$ , we first obtain $\\mathbf{L}_{1:N} = \\mathrm{VQG_{IC}}(I_u)$ , where $\\mathbf{L}_{1:N}$ are the logits of the decoder. The logits $\\mathbf{L}_{1:N}$ define a distribution $P(L_N \\mid L_{1:N-1})$ over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text $T'$ from $P(L_N \\mid L_{1:N-1})$ . The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair $(Q', A')$ from the decoded text $T'$ . This pair $(Q', A') = T'$ is a sample from $P(T|I)$ , and reflects textual knowledge about the content of an image known to the VLM.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form $(Q', A', I_u)$ , representing self-generated training data $\\mathcal{D}_{QA}'$ in the style of a target dataset $\\mathcal{D}_{QA}$ . We then augment the real dataset $\\mathcal{D}_{QA}$ with the self-generated question-answer pairs on unlabeled images $\\mathcal{D}_{QA}'$ to create a self-augmented training dataset $\\mathcal{D}_{\\mathrm{Aug}QA} = \\mathcal{D}_{QA}' \\cup \\mathcal{D}_{QA}$ . The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss", + "bbox": [ + 75, + 272, + 473, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V Q A}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x _ {n}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 494, + 472, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_{n}$ is the $n$ -th element of the multimodal sequence embeddings $\\mathbf{X}_{1:N}$ produced by $\\mathrm{VLM}(Q, I; \\theta)$ , $Q, I$ are the question and image, $y_{1:N}$ is the sequence of answer tokens, and $\\theta$ represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels $(Q', A')$ be generated even when $\\mathcal{D}_{QA}$ is small, and few pairs are available for adapting the teacher $\\mathrm{VQG}_{IC}$ ? Knowledge about the content of the image in a textual form $P(T|I)$ is already well-learned by the VLM from which we initialize $\\mathrm{VQG}_{IC}$ . Thus, $\\mathcal{D}_{QA}$ only needs sufficient pairs to teach $\\mathrm{VQG}_{IC}$ how to construct annotations matching the style of $\\mathcal{D}_{QA}$ .", + "bbox": [ + 75, + 544, + 472, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4b2ac891bc4bcf4b33b4e44e2b6b93430ddbd5054e0149181ab6abe4221cb0af.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelA-OKVQA
ValidationTest
(a)ViLBERT [34]49.141.5
(b)LXMERT [46]51.441.6
(c)KRISP [36]51.942.2
(d)GPV-2 [18]60.353.7
(e)BLIP [26]57.1
(f)\\( BLIP_{\\text{VQAv2}} \\) [26]67.859.5
(g)BLIP + SelTDA62.154.5
% gain w.r.t baseline+5.0
% gain w.r.t best prior work+1.8+0.8
(h)\\( BLIP_{\\text{VQAv2}} + SelTDA \\)68.959.5
% gain w.r.t baseline+1.1+0.0
% gain w.r.t best prior work+8.6+5.8
", + "bbox": [ + 529, + 88, + 866, + 329 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d60f2b11b45af6a8eb85ab73e614439db12331d8b98f1de32b18fdc7e5670f73.jpg", + "table_caption": [ + "Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs." + ], + "table_footnote": [], + "table_body": "
ModelArtVQA Accuracy
OverallGrounded
(a)BAN [22]22.4-
(b)BLIP [26]21.3681.71
(c)VIKING [12]55.578.74
(d)VIKINGVLM55.981.9
(e)BLIP + SelTDA21.6883.86
% gain w.r.t baseline+0.32+2.15
(f)VIKINGVLM + SelTDA56.8683.86
% gain w.r.t baseline+0.92+1.96
", + "bbox": [ + 519, + 380, + 874, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions.", + "bbox": [ + 498, + 571, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of $480 \\times 480$ and an image size of $384 \\times 384$ for VQG. For all datasets, we use the official training, validation, and test splits.", + "bbox": [ + 496, + 625, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top- $p$ of 0.92. Additional experiments and visualizations can be found in the supplemental material.", + "bbox": [ + 496, + 700, + 893, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Self-Training: A-OKVQA & ArtVQA", + "text_level": 1, + "bbox": [ + 498, + 816, + 828, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15009", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e8cd2dcac3f0ee0c15a91b64e997d82ef1b409d9c6fa25891da37d31eee41fc4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Question TypeWell-Posed QuestionAnswers CorrectAnswerable% of Total (95% CI)
External Knowledge73%62%70%29.6% - 50.00%
Visual Identification94%88%94%11.18% - 27.65 %
Visual Reasoning83%70%80%32.54% - 53.17%
Overall (95% CI)71.16% - 87.96%59.77% - 78.98%68.83% - 86.22%
", + "bbox": [ + 125, + 88, + 843, + 186 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the $95\\%$ confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about $79.5\\%$ on the validation set.", + "bbox": [ + 75, + 196, + 892, + 226 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9b5a2ef978d058822c9a3043cdda23a29dda1114974be441603f10370c689fc7.jpg", + "image_caption": [ + "Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE." + ], + "image_footnote": [], + "bbox": [ + 112, + 244, + 375, + 366 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d2b0cf5b89d1ad3dd5343369cccf1d07ca9f3e4b27cfec84a32030d19e925ed5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 246, + 599, + 364 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4ca10f4794329ee94ff924f1bfc11d327de68edfaaa390acc945da36e4f3a8e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 640, + 246, + 864, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/983aa70c3c59d8d9f24f1fe9ed408ee2eef44725a6b8cbaf944c32bf50704548.jpg", + "image_caption": [ + "Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA." + ], + "image_footnote": [], + "bbox": [ + 78, + 453, + 468, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when $447k$ real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions.", + "bbox": [ + 496, + 455, + 893, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablations & Analysis of Pseudolabels", + "text_level": 1, + "bbox": [ + 498, + 648, + 821, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. \"what is this object?\"). Next, we show using t-SNE [47] that the teacher model learns to copy the \"style\" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse.", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15010", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3693bf927c7c923c6428dbc133ac1a877e66dd1f0cb304068b8a69c2d123068f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ImagesQuestionsMultiplierAccuracy% GainQuestions/Image
LabeledUnlabeledRealSyntheticTotal
17,000017,000017,0001x (baseline)57.11N/A
17,000017,00017,00034,0002x57.85+0.741 / 1
17,000017,00034,00051,0003x60.01+2.902 / 1
17,000017,00051,00068,0004x59.73+2.623 / 1
17,000017,000017k1x (baseline)57.11N/A
17,0008,50017,00017,00034,0002x60.69+3.572 / 1
17,00017,00017,00034,00051,0003x62.09+4.982 / 1
17,00025,50017,00051,00068,0004x61.31+4.202 / 1
", + "bbox": [ + 114, + 88, + 854, + 268 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3731eaa068471b7de94b7fc946dae82b588deb480588b73e0e64f2ea40fec558.jpg", + "table_caption": [ + "Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used." + ], + "table_footnote": [], + "table_body": "
# of Real + Synthetic QA PairsRobustness Test SetsAvg. % IncreaseRobustness Total
RealSyntheticMultiplierAdVQAVQA-CEVQA-Rephrasings
(a)17,0000×131.0651.4365.880148.37
(b)17,0002,000×1.137.0952.9667.94+3.21157.99
(c)17,0004,500×1.336.9953.1567.98+3.25158.12
(d)17,0008,000×1.537.3453.3367.57+3.29158.24
(e)17,00012,000×1.737.4352.6267.35+3.01157.4
(f)17,00017,000×236.9552.0566.95+2.53155.95
(g)17,00034,000×336.8951.0065.64+1.72153.53
(h)17,00051,000×436.0650.2564.78+0.91151.09
Max % increase on each dataset+6.03+1.9+2.1+9.87
", + "bbox": [ + 76, + 320, + 890, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA.", + "bbox": [ + 75, + 526, + 892, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4).", + "bbox": [ + 75, + 580, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is $50\\%$ the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling.", + "bbox": [ + 75, + 672, + 470, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Robustness", + "text_level": 1, + "bbox": [ + 76, + 847, + 200, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA", + "bbox": [ + 496, + 580, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15011", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a $2.1\\%$ performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Domain Generalization", + "text_level": 1, + "bbox": [ + 76, + 252, + 292, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers.", + "bbox": [ + 75, + 276, + 472, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Numerical Reasoning", + "text_level": 1, + "bbox": [ + 76, + 589, + 279, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Numerical reasoning is required to answer questions such as \"how many sheep are looking at the camera\". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of $29.81\\%$ and $24.71\\%$ on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of $3.63\\%$ and $10.57\\%$ . These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly,", + "bbox": [ + 75, + 613, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b5c17177a6ca2b91968a9b008bd5cf438fe644bb3d2a37d4f0fb3b0c598b3be4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelTarget (0-shot)
ArtVQAPathVQARSVQA
Baseline (BLIP)31.6525.0937.78
BLIP + SelTDA38.0326.7638.99
% gain w.r.t baseline+6.38+1.67+1.1
", + "bbox": [ + 500, + 88, + 893, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9feb7d8d7bd8b618442127438956b19aaa391b5e6b915ffc5c7c90f14127caa4.jpg", + "table_caption": [ + "Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA." + ], + "table_footnote": [], + "table_body": "
Initialization# Training PairsNumerical Reasoning
RealSynthVQAv2VQA-Rephrasings
BLIPVQAv217000013.4913.06
BLIPVQAv217000200038.7333.74
BLIPVQAv217000450040.435.91
BLIPVQAv217000800042.936.5
BLIPVQAv2170001200043.337.77
max % gain w.r.t baseline+29.81+24.71
BLIP1700001.421.29
BLIP17000170004.5311.44
BLIP17000340005.0511.77
BLIP17000510004.2611.86
max % gain w.r.t baseline+3.63+10.57
", + "bbox": [ + 503, + 247, + 888, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA). $\\mathrm{BLIP}_{\\mathit{VQAv2}}$ indicates transfer learning from VQAv2, and BLIP indicates direct finetuning.", + "bbox": [ + 498, + 473, + 893, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word \"how\" is a high-probability word to start a question with, and is naturally followed by \"many\" (Fig 6) resulting in numerical questions being generated.", + "bbox": [ + 498, + 547, + 893, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion & Future Work", + "text_level": 1, + "bbox": [ + 500, + 645, + 754, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. Finally, self-training is yet to be explored with recently developed billion-parameter VLMs [9, 25].", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15012", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andy Brock, Aida Nematzadeh, Sahand Sharifzadeh, Nikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. Flamingo: a visual language model for few-shot learning. 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In Hugo Larochelle, Marc'Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and HsuanTien Lin, editors, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020. 2, 3" + ], + "bbox": [ + 501, + 92, + 893, + 539 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15015", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_model.json b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d40c970944340dfddfa406737a216f1c6ca7b981 --- /dev/null +++ b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_model.json @@ -0,0 +1,2147 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.13, + 0.895, + 0.178 + ], + "angle": 0, + "content": "Q: How to Specialize Large Vision-Language Models to Data-Scarce VQA Tasks? A: Self-Train on Unlabeled Images!" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.204, + 0.825, + 0.242 + ], + "angle": 0, + "content": "Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.314, + 0.306 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.729, + 0.21, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.471, + 0.877 + ], + "angle": 0, + "content": "Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.272, + 0.895, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.496, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image \\(I\\) without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers \\((Q,A)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.674 + ], + "angle": 0, + "content": "data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.321, + 0.9 + ], + "angle": 0, + "content": "* work done while at NEC Labs America" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "15005" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.088, + 0.573, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.09, + 0.882, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.895, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.306, + 0.379 + ], + "angle": 0, + "content": "than a short caption can describe)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.474, + 0.671 + ], + "angle": 0, + "content": "Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase \"this is a\". We convert each caption into a boolean question where the correct answer is \"yes\" by inserting the caption into the template is this a ? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between \"yes\" and \"no\" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers \"no\" to at least \\(5\\%\\) of the questions, increasing to \\(15\\%\\) as the diversity of captions increases (adjusted by top-\\(p\\) parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model \\(\\mathrm{VQG}_{IC}\\). Next, we use \\(\\mathrm{VQG}_{IC}\\) as a teacher to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.895, + 0.439 + ], + "angle": 0, + "content": "pseudolabel unlabeled images by sampling questions and answers from \\(\\mathrm{VQG}_{IC}\\) with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.896, + 0.695 + ], + "angle": 0, + "content": "Benefits: SelTDA allows us generate synthetic training data by approximating the distribution \\( P(Q, A|I) \\) of the target VQA task, where \\( Q, A, I \\) represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.703, + 0.894, + 0.748 + ], + "angle": 0, + "content": "1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.756, + 0.895, + 0.832 + ], + "angle": 0, + "content": "2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.703, + 0.895, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15006" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.297 + ], + "angle": 0, + "content": "Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.493 + ], + "angle": 0, + "content": "Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.471, + 0.841 + ], + "angle": 0, + "content": "Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.593, + 0.317 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.895, + 0.689 + ], + "angle": 0, + "content": "Our goal is to pseudolabel an unlabeled image \\( I \\) with a generated question-answer pair \\( (Q, A) \\) using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model \\( \\mathrm{VQG_{IC}} \\) to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating \\( P(Q, A|I) \\) that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.887, + 0.714 + ], + "angle": 0, + "content": "3.1. The Teacher: Direct Image-Conditional VQG" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image \\( I \\), a question \\( Q \\) and answer \\( A \\), the VQA student must approximate \\( P(Q \\mid Q, I) \\), while the teacher model must approximate \\( P(Q, A \\mid I) \\). Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate \\( P(Q \\mid I, A) \\), that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15007" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.896, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.895, + 0.261 + ], + "angle": 0, + "content": "Figure 3. Overview of the proposed framework. We first create the teacher \\(\\mathrm{VQG}_{IC}\\) (§3.1), use \\(\\mathrm{VQG}_{IC}\\) to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.279, + 0.189, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.358, + 0.264, + 0.379 + ], + "angle": 0, + "content": "Question: what is the cat wearing? \nAnswers: necktie, tie" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.387, + 0.22, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.476, + 0.258, + 0.497 + ], + "angle": 0, + "content": "Question: how is the egg cooked? Answer: fried" + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.279, + 0.422, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.352, + 0.47, + 0.382 + ], + "angle": 0, + "content": "Question: how many items of food are present here? \nAnswers: 2" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.386, + 0.416, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.47, + 0.47, + 0.502 + ], + "angle": 0, + "content": "Question: what activity is the baby learning? Answer: feeding, eating, nutrition" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.279, + 0.633, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.352, + 0.671, + 0.382 + ], + "angle": 0, + "content": "Question: what color is the sky in the picture? \nAnswers: clear, blue" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.388, + 0.642, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.466, + 0.653, + 0.507 + ], + "angle": 0, + "content": "Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.279, + 0.831, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.358, + 0.848, + 0.379 + ], + "angle": 0, + "content": "Question: what city is this? \nAnswers: london, uk" + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.387, + 0.853, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.47, + 0.88, + 0.501 + ], + "angle": 0, + "content": "Question: what is the name of this party? Answer: baby shower" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.523, + 0.893, + 0.552 + ], + "angle": 0, + "content": "Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.473, + 0.684 + ], + "angle": 0, + "content": "approaches, we develop an image-conditional approach \\((\\mathrm{VQG}_{IC})\\) that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions \\(P(Y|I)\\), where \\(Y\\) is often a distribution over a (finite) label space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To create the \\(\\mathrm{VQG}_{IC}\\) teacher that approximates \\(P(Q,A|I)\\), we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate \\(P(T|I)\\), where \\(T = (Q,A)\\). Let \\(\\mathcal{D}_{QA}\\) be a question-answer dataset we wish to create a teacher from. For a sample \\((Q,A,I)\\in \\mathcal{D}_{QA}\\), we transform it into a target sequence of tokens \\(y_{1:N} = (y_1,y_2,\\dots y_n)\\) by entering \\((Q,A)\\) into a structured template of the form \"Question: ? Answer: .\" where and are replaced by the content of \\(Q\\) and \\(A\\) respectively. Once \\(y_{1:N} = (y_1,y_2,\\dots y_n)\\) is" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.578, + 0.788, + 0.594 + ], + "angle": 0, + "content": "obtained, we train the model by optimizing" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.605, + 0.893, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {V Q G}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.895, + 0.838 + ], + "angle": 0, + "content": "over all question-image-answer pairs in \\(\\mathcal{D}_{QA}\\), where \\(x\\) is the latent encoded features in the standard encoder-decoder architecture and \\(\\theta\\) represents the VLM parameters. The \\(\\mathrm{VQG_{IC}}\\) thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that \\(\\mathrm{VQG_{IC}}\\) is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of \\(P(T|I)\\), having been exposed to a diverse number of images and paired text. The \\(\\mathrm{VQG_{IC}}\\) teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair \\((Q', A')\\) is generated jointly as a text \\(T'\\), allowing us to sample from \\(P(T|I)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.859, + 0.864 + ], + "angle": 0, + "content": "3.2. Training the Student with Unlabeled Data" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Once the VQGIC teacher model has been obtained, self-training with unlabeled data can proceed. To produce a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15008" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.272 + ], + "angle": 0, + "content": "pseudolabel \\((Q', A')\\) for an unlabeled image \\(I_u\\), we first obtain \\(\\mathbf{L}_{1:N} = \\mathrm{VQG_{IC}}(I_u)\\), where \\(\\mathbf{L}_{1:N}\\) are the logits of the decoder. The logits \\(\\mathbf{L}_{1:N}\\) define a distribution \\(P(L_N \\mid L_{1:N-1})\\) over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text \\(T'\\) from \\(P(L_N \\mid L_{1:N-1})\\). The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair \\((Q', A')\\) from the decoded text \\(T'\\). This pair \\((Q', A') = T'\\) is a sample from \\(P(T|I)\\), and reflects textual knowledge about the content of an image known to the VLM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.474, + 0.486 + ], + "angle": 0, + "content": "We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form \\((Q', A', I_u)\\), representing self-generated training data \\(\\mathcal{D}_{QA}'\\) in the style of a target dataset \\(\\mathcal{D}_{QA}\\). We then augment the real dataset \\(\\mathcal{D}_{QA}\\) with the self-generated question-answer pairs on unlabeled images \\(\\mathcal{D}_{QA}'\\) to create a self-augmented training dataset \\(\\mathcal{D}_{\\mathrm{Aug}QA} = \\mathcal{D}_{QA}' \\cup \\mathcal{D}_{QA}\\). The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.495, + 0.473, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {V Q A}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x _ {n}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.473, + 0.729 + ], + "angle": 0, + "content": "where \\( x_{n} \\) is the \\( n \\)-th element of the multimodal sequence embeddings \\( \\mathbf{X}_{1:N} \\) produced by \\( \\mathrm{VLM}(Q, I; \\theta) \\), \\( Q, I \\) are the question and image, \\( y_{1:N} \\) is the sequence of answer tokens, and \\( \\theta \\) represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels \\( (Q', A') \\) be generated even when \\( \\mathcal{D}_{QA} \\) is small, and few pairs are available for adapting the teacher \\( \\mathrm{VQG}_{IC} \\)? Knowledge about the content of the image in a textual form \\( P(T|I) \\) is already well-learned by the VLM from which we initialize \\( \\mathrm{VQG}_{IC} \\). Thus, \\( \\mathcal{D}_{QA} \\) only needs sufficient pairs to teach \\( \\mathrm{VQG}_{IC} \\) how to construct annotations matching the style of \\( \\mathcal{D}_{QA} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.21, + 0.758 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch" + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.089, + 0.867, + 0.33 + ], + "angle": 0, + "content": "
ModelA-OKVQA
ValidationTest
(a)ViLBERT [34]49.141.5
(b)LXMERT [46]51.441.6
(c)KRISP [36]51.942.2
(d)GPV-2 [18]60.353.7
(e)BLIP [26]57.1
(f)\\( BLIP_{\\text{VQAv2}} \\) [26]67.859.5
(g)BLIP + SelTDA62.154.5
% gain w.r.t baseline+5.0
% gain w.r.t best prior work+1.8+0.8
(h)\\( BLIP_{\\text{VQAv2}} + SelTDA \\)68.959.5
% gain w.r.t baseline+1.1+0.0
% gain w.r.t best prior work+8.6+5.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.339, + 0.895, + 0.369 + ], + "angle": 0, + "content": "Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.381, + 0.875, + 0.564 + ], + "angle": 0, + "content": "
ModelArtVQA Accuracy
OverallGrounded
(a)BAN [22]22.4-
(b)BLIP [26]21.3681.71
(c)VIKING [12]55.578.74
(d)VIKINGVLM55.981.9
(e)BLIP + SelTDA21.6883.86
% gain w.r.t baseline+0.32+2.15
(f)VIKINGVLM + SelTDA56.8683.86
% gain w.r.t baseline+0.92+1.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.601 + ], + "angle": 0, + "content": "Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.702 + ], + "angle": 0, + "content": "size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of \\(480 \\times 480\\) and an image size of \\(384 \\times 384\\) for VQG. For all datasets, we use the official training, validation, and test splits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.809 + ], + "angle": 0, + "content": "Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top-\\(p\\) of 0.92. Additional experiments and visualizations can be found in the supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.817, + 0.829, + 0.835 + ], + "angle": 0, + "content": "4.1. Self-Training: A-OKVQA & ArtVQA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15009" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.126, + 0.089, + 0.844, + 0.187 + ], + "angle": 0, + "content": "
Question TypeWell-Posed QuestionAnswers CorrectAnswerable% of Total (95% CI)
External Knowledge73%62%70%29.6% - 50.00%
Visual Identification94%88%94%11.18% - 27.65 %
Visual Reasoning83%70%80%32.54% - 53.17%
Overall (95% CI)71.16% - 87.96%59.77% - 78.98%68.83% - 86.22%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.198, + 0.893, + 0.227 + ], + "angle": 0, + "content": "Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the \\(95\\%\\) confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about \\(79.5\\%\\) on the validation set." + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.246, + 0.376, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.247, + 0.6, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.247, + 0.865, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.388, + 0.893, + 0.43 + ], + "angle": 0, + "content": "Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.454, + 0.469, + 0.757 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.766, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.639 + ], + "angle": 0, + "content": "self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when \\(447k\\) real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.65, + 0.822, + 0.667 + ], + "angle": 0, + "content": "4.2. Ablations & Analysis of Pseudolabels" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. \"what is this object?\"). Next, we show using t-SNE [47] that the teacher model learns to copy the \"style\" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15010" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.089, + 0.855, + 0.269 + ], + "angle": 0, + "content": "
ImagesQuestionsMultiplierAccuracy% GainQuestions/Image
LabeledUnlabeledRealSyntheticTotal
17,000017,000017,0001x (baseline)57.11N/A
17,000017,00017,00034,0002x57.85+0.741 / 1
17,000017,00034,00051,0003x60.01+2.902 / 1
17,000017,00051,00068,0004x59.73+2.623 / 1
17,000017,000017k1x (baseline)57.11N/A
17,0008,50017,00017,00034,0002x60.69+3.572 / 1
17,00017,00017,00034,00051,0003x62.09+4.982 / 1
17,00025,50017,00051,00068,0004x61.31+4.202 / 1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.279, + 0.893, + 0.309 + ], + "angle": 0, + "content": "Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.321, + 0.891, + 0.518 + ], + "angle": 0, + "content": "
# of Real + Synthetic QA PairsRobustness Test SetsAvg. % IncreaseRobustness Total
RealSyntheticMultiplierAdVQAVQA-CEVQA-Rephrasings
(a)17,0000×131.0651.4365.880148.37
(b)17,0002,000×1.137.0952.9667.94+3.21157.99
(c)17,0004,500×1.336.9953.1567.98+3.25158.12
(d)17,0008,000×1.537.3453.3367.57+3.29158.24
(e)17,00012,000×1.737.4352.6267.35+3.01157.4
(f)17,00017,000×236.9552.0566.95+2.53155.95
(g)17,00034,000×336.8951.0065.64+1.72153.53
(h)17,00051,000×436.0650.2564.78+0.91151.09
Max % increase on each dataset+6.03+1.9+2.1+9.87
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.527, + 0.893, + 0.556 + ], + "angle": 0, + "content": "Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.673 + ], + "angle": 0, + "content": "We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.471, + 0.84 + ], + "angle": 0, + "content": "Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is \\(50\\%\\) the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.202, + 0.863 + ], + "angle": 0, + "content": "4.3. Robustness" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.901 + ], + "angle": 0, + "content": "known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15011" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a \\(2.1\\%\\) performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.253, + 0.293, + 0.269 + ], + "angle": 0, + "content": "4.4. Domain Generalization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.581 + ], + "angle": 0, + "content": "We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.59, + 0.28, + 0.607 + ], + "angle": 0, + "content": "4.5. Numerical Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Numerical reasoning is required to answer questions such as \"how many sheep are looking at the camera\". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of \\(29.81\\%\\) and \\(24.71\\%\\) on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of \\(3.63\\%\\) and \\(10.57\\%\\). These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly," + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.895, + 0.189 + ], + "angle": 0, + "content": "
ModelTarget (0-shot)
ArtVQAPathVQARSVQA
Baseline (BLIP)31.6525.0937.78
BLIP + SelTDA38.0326.7638.99
% gain w.r.t baseline+6.38+1.67+1.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.2, + 0.895, + 0.229 + ], + "angle": 0, + "content": "Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.248, + 0.89, + 0.464 + ], + "angle": 0, + "content": "
Initialization# Training PairsNumerical Reasoning
RealSynthVQAv2VQA-Rephrasings
BLIPVQAv217000013.4913.06
BLIPVQAv217000200038.7333.74
BLIPVQAv217000450040.435.91
BLIPVQAv217000800042.936.5
BLIPVQAv2170001200043.337.77
max % gain w.r.t baseline+29.81+24.71
BLIP1700001.421.29
BLIP17000170004.5311.44
BLIP17000340005.0511.77
BLIP17000510004.2611.86
max % gain w.r.t baseline+3.63+10.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.474, + 0.894, + 0.517 + ], + "angle": 0, + "content": "Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA). \\(\\mathrm{BLIP}_{\\mathit{VQAv2}}\\) indicates transfer learning from VQAv2, and BLIP indicates direct finetuning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.549, + 0.894, + 0.625 + ], + "angle": 0, + "content": "even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word \"how\" is a high-probability word to start a question with, and is naturally followed by \"many\" (Fig 6) resulting in numerical questions being generated." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.646, + 0.755, + 0.663 + ], + "angle": 0, + "content": "5. Conclusion & Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. Finally, self-training is yet to be explored with recently developed billion-parameter VLMs [9, 25]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15012" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.473, + 0.253 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andy Brock, Aida Nematzadeh, Sahand Sharifzadeh, Nikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. Flamingo: a visual language model for few-shot learning. 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In Hugo Larochelle, Marc'Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and HsuanTien Lin, editors, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.895, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15015" + } + ] +] \ No newline at end of file diff --git a/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_origin.pdf b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7424f805bd0628c52ea600981480e775c2417632 --- /dev/null +++ b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dd8d00e86ab67f2d528189de92527ab8a97340e22ba1c18774fd107ca36767ad +size 2959329 diff --git a/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/full.md b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/full.md new file mode 100644 index 0000000000000000000000000000000000000000..58d82716d1df567759a99ac0ef2c2005b362f8a5 --- /dev/null +++ b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/full.md @@ -0,0 +1,274 @@ +# Q: How to Specialize Large Vision-Language Models to Data-Scarce VQA Tasks? A: Self-Train on Unlabeled Images! + +Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego + +# Abstract + +Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA. + +# 1. Introduction + +Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the + +![](images/03965e14b1009cd2745e52bb2345565fe94bb6775fa4da04f0c07e16fd5652aa.jpg) +Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image $I$ without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers $(Q,A)$ . + +data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets. + +Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content + +![](images/3e4b943819c4228181fd9f28b9570fa942cc03b174fa245b394684d05216f4f0.jpg) +Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning. + +![](images/1338f0d6729f7208a8733a9fd6cc12ec31588ca937e3217f748b7773fd568866.jpg) + +than a short caption can describe). + +Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase "this is a". We convert each caption into a boolean question where the correct answer is "yes" by inserting the caption into the template is this a ? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between "yes" and "no" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers "no" to at least $5\%$ of the questions, increasing to $15\%$ as the diversity of captions increases (adjusted by top- $p$ parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image. + +Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model $\mathrm{VQG}_{IC}$ . Next, we use $\mathrm{VQG}_{IC}$ as a teacher to + +pseudolabel unlabeled images by sampling questions and answers from $\mathrm{VQG}_{IC}$ with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset. + +Benefits: SelTDA allows us generate synthetic training data by approximating the distribution $P(Q, A|I)$ of the target VQA task, where $Q, A, I$ represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows: + +1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs. +2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed. +3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets. + +# 2. Related Work + +Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation. + +Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization. + +Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model. + +Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self + +training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image. + +# 3. Method + +Our goal is to pseudolabel an unlabeled image $I$ with a generated question-answer pair $(Q, A)$ using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model $\mathrm{VQG_{IC}}$ to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating $P(Q, A|I)$ that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image. + +# 3.1. The Teacher: Direct Image-Conditional VQG + +Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image $I$ , a question $Q$ and answer $A$ , the VQA student must approximate $P(Q \mid Q, I)$ , while the teacher model must approximate $P(Q, A \mid I)$ . Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate $P(Q \mid I, A)$ , that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG + +![](images/1b844b835973f755de7d2b3a15912d25d1506e699186fd4ae59ac4648da7d292.jpg) +Figure 3. Overview of the proposed framework. We first create the teacher $\mathrm{VQG}_{IC}$ (§3.1), use $\mathrm{VQG}_{IC}$ to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language. + +![](images/07eb44d222a5f5a01e155ae42d95abd930b5fc2bd92482ff77ed3650a8b213c0.jpg) +Question: what is the cat wearing? +Answers: necktie, tie + +![](images/7028f5f12d0e2415bc374ecca7788f763487cfe32d46aa2b05fde2e063073630.jpg) +Question: how is the egg cooked? Answer: fried + +![](images/cd87a2039c4183818b9a7151627b2c40bcf3c0a3ac083fd466f88d2721d854a1.jpg) +Question: how many items of food are present here? +Answers: 2 + +![](images/f9013b0e122b47e981b019a685a592fdfae273ed025e4b6d73924bb935ca1efe.jpg) +Question: what activity is the baby learning? Answer: feeding, eating, nutrition + +![](images/5a3885a05ec6c2ed434e18984c44ea16a9b1692d2cec15620b7b0584800ea3dd.jpg) +Question: what color is the sky in the picture? +Answers: clear, blue + +![](images/8943e59bbb0aa9f14364f1d18c10b2466ffc22b68ab75b92f522a3b67c6b3f48.jpg) +Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration + +![](images/42a7928b3661f35b2ac5d7a2a0b66f6aa08229493cfa4d92c5cce7d9373ad563.jpg) +Question: what city is this? +Answers: london, uk + +![](images/5188f6d8d4c231fd410025f49ec9f6ebb416f7a22adce852c9cdc6f462bf5d53.jpg) +Question: what is the name of this party? Answer: baby shower +Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning). + +approaches, we develop an image-conditional approach $(\mathrm{VQG}_{IC})$ that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions $P(Y|I)$ , where $Y$ is often a distribution over a (finite) label space. + +To create the $\mathrm{VQG}_{IC}$ teacher that approximates $P(Q,A|I)$ , we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate $P(T|I)$ , where $T = (Q,A)$ . Let $\mathcal{D}_{QA}$ be a question-answer dataset we wish to create a teacher from. For a sample $(Q,A,I)\in \mathcal{D}_{QA}$ , we transform it into a target sequence of tokens $y_{1:N} = (y_1,y_2,\dots y_n)$ by entering $(Q,A)$ into a structured template of the form "Question: ? Answer: ." where and are replaced by the content of $Q$ and $A$ respectively. Once $y_{1:N} = (y_1,y_2,\dots y_n)$ is + +obtained, we train the model by optimizing + +$$ +\mathcal {L} _ {\mathrm {V Q G}} = - \sum_ {n = 1} ^ {N} \log P _ {\theta} \left(y _ {n} \mid y _ {< n}, x\right) \tag {1} +$$ + +over all question-image-answer pairs in $\mathcal{D}_{QA}$ , where $x$ is the latent encoded features in the standard encoder-decoder architecture and $\theta$ represents the VLM parameters. The $\mathrm{VQG_{IC}}$ thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that $\mathrm{VQG_{IC}}$ is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of $P(T|I)$ , having been exposed to a diverse number of images and paired text. The $\mathrm{VQG_{IC}}$ teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair $(Q', A')$ is generated jointly as a text $T'$ , allowing us to sample from $P(T|I)$ . + +# 3.2. Training the Student with Unlabeled Data + +Once the VQGIC teacher model has been obtained, self-training with unlabeled data can proceed. To produce a + +pseudolabel $(Q', A')$ for an unlabeled image $I_u$ , we first obtain $\mathbf{L}_{1:N} = \mathrm{VQG_{IC}}(I_u)$ , where $\mathbf{L}_{1:N}$ are the logits of the decoder. The logits $\mathbf{L}_{1:N}$ define a distribution $P(L_N \mid L_{1:N-1})$ over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text $T'$ from $P(L_N \mid L_{1:N-1})$ . The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair $(Q', A')$ from the decoded text $T'$ . This pair $(Q', A') = T'$ is a sample from $P(T|I)$ , and reflects textual knowledge about the content of an image known to the VLM. + +We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form $(Q', A', I_u)$ , representing self-generated training data $\mathcal{D}_{QA}'$ in the style of a target dataset $\mathcal{D}_{QA}$ . We then augment the real dataset $\mathcal{D}_{QA}$ with the self-generated question-answer pairs on unlabeled images $\mathcal{D}_{QA}'$ to create a self-augmented training dataset $\mathcal{D}_{\mathrm{Aug}QA} = \mathcal{D}_{QA}' \cup \mathcal{D}_{QA}$ . The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss + +$$ +\mathcal {L} _ {\mathrm {V Q A}} = - \sum_ {n = 1} ^ {N} \log P _ {\theta} \left(y _ {n} \mid y _ {< n}, x _ {n}\right) \tag {2} +$$ + +where $x_{n}$ is the $n$ -th element of the multimodal sequence embeddings $\mathbf{X}_{1:N}$ produced by $\mathrm{VLM}(Q, I; \theta)$ , $Q, I$ are the question and image, $y_{1:N}$ is the sequence of answer tokens, and $\theta$ represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels $(Q', A')$ be generated even when $\mathcal{D}_{QA}$ is small, and few pairs are available for adapting the teacher $\mathrm{VQG}_{IC}$ ? Knowledge about the content of the image in a textual form $P(T|I)$ is already well-learned by the VLM from which we initialize $\mathrm{VQG}_{IC}$ . Thus, $\mathcal{D}_{QA}$ only needs sufficient pairs to teach $\mathrm{VQG}_{IC}$ how to construct annotations matching the style of $\mathcal{D}_{QA}$ . + +# 4. Experiments + +Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch + +
ModelA-OKVQA
ValidationTest
(a)ViLBERT [34]49.141.5
(b)LXMERT [46]51.441.6
(c)KRISP [36]51.942.2
(d)GPV-2 [18]60.353.7
(e)BLIP [26]57.1
(f)\( BLIP_{\text{VQAv2}} \) [26]67.859.5
(g)BLIP + SelTDA62.154.5
% gain w.r.t baseline+5.0
% gain w.r.t best prior work+1.8+0.8
(h)\( BLIP_{\text{VQAv2}} + SelTDA \)68.959.5
% gain w.r.t baseline+1.1+0.0
% gain w.r.t best prior work+8.6+5.8
+ +Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs. + +
ModelArtVQA Accuracy
OverallGrounded
(a)BAN [22]22.4-
(b)BLIP [26]21.3681.71
(c)VIKING [12]55.578.74
(d)VIKINGVLM55.981.9
(e)BLIP + SelTDA21.6883.86
% gain w.r.t baseline+0.32+2.15
(f)VIKINGVLM + SelTDA56.8683.86
% gain w.r.t baseline+0.92+1.96
+ +Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions. + +size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of $480 \times 480$ and an image size of $384 \times 384$ for VQG. For all datasets, we use the official training, validation, and test splits. + +Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top- $p$ of 0.92. Additional experiments and visualizations can be found in the supplemental material. + +# 4.1. Self-Training: A-OKVQA & ArtVQA + +We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi + +
Question TypeWell-Posed QuestionAnswers CorrectAnswerable% of Total (95% CI)
External Knowledge73%62%70%29.6% - 50.00%
Visual Identification94%88%94%11.18% - 27.65 %
Visual Reasoning83%70%80%32.54% - 53.17%
Overall (95% CI)71.16% - 87.96%59.77% - 78.98%68.83% - 86.22%
+ +Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the $95\%$ confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about $79.5\%$ on the validation set. + +![](images/9b5a2ef978d058822c9a3043cdda23a29dda1114974be441603f10370c689fc7.jpg) +Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE. + +![](images/d2b0cf5b89d1ad3dd5343369cccf1d07ca9f3e4b27cfec84a32030d19e925ed5.jpg) + +![](images/4ca10f4794329ee94ff924f1bfc11d327de68edfaaa390acc945da36e4f3a8e8.jpg) + +![](images/983aa70c3c59d8d9f24f1fe9ed408ee2eef44725a6b8cbaf944c32bf50704548.jpg) +Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA. + +tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that + +self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when $447k$ real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions. + +# 4.2. Ablations & Analysis of Pseudolabels + +We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. "what is this object?"). Next, we show using t-SNE [47] that the teacher model learns to copy the "style" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse. + +
ImagesQuestionsMultiplierAccuracy% GainQuestions/Image
LabeledUnlabeledRealSyntheticTotal
17,000017,000017,0001x (baseline)57.11N/A
17,000017,00017,00034,0002x57.85+0.741 / 1
17,000017,00034,00051,0003x60.01+2.902 / 1
17,000017,00051,00068,0004x59.73+2.623 / 1
17,000017,000017k1x (baseline)57.11N/A
17,0008,50017,00017,00034,0002x60.69+3.572 / 1
17,00017,00017,00034,00051,0003x62.09+4.982 / 1
17,00025,50017,00051,00068,0004x61.31+4.202 / 1
+ +Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used. + +
# of Real + Synthetic QA PairsRobustness Test SetsAvg. % IncreaseRobustness Total
RealSyntheticMultiplierAdVQAVQA-CEVQA-Rephrasings
(a)17,0000×131.0651.4365.880148.37
(b)17,0002,000×1.137.0952.9667.94+3.21157.99
(c)17,0004,500×1.336.9953.1567.98+3.25158.12
(d)17,0008,000×1.537.3453.3367.57+3.29158.24
(e)17,00012,000×1.737.4352.6267.35+3.01157.4
(f)17,00017,000×236.9552.0566.95+2.53155.95
(g)17,00034,000×336.8951.0065.64+1.72153.53
(h)17,00051,000×436.0650.2564.78+0.91151.09
Max % increase on each dataset+6.03+1.9+2.1+9.87
+ +Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA. + +We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4). + +Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is $50\%$ the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling. + +# 4.3. Robustness + +We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three + +known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA + +models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a $2.1\%$ performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA. + +# 4.4. Domain Generalization + +We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers. + +# 4.5. Numerical Reasoning + +Numerical reasoning is required to answer questions such as "how many sheep are looking at the camera". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of $29.81\%$ and $24.71\%$ on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of $3.63\%$ and $10.57\%$ . These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly, + +
ModelTarget (0-shot)
ArtVQAPathVQARSVQA
Baseline (BLIP)31.6525.0937.78
BLIP + SelTDA38.0326.7638.99
% gain w.r.t baseline+6.38+1.67+1.1
+ +Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA. + +
Initialization# Training PairsNumerical Reasoning
RealSynthVQAv2VQA-Rephrasings
BLIPVQAv217000013.4913.06
BLIPVQAv217000200038.7333.74
BLIPVQAv217000450040.435.91
BLIPVQAv217000800042.936.5
BLIPVQAv2170001200043.337.77
max % gain w.r.t baseline+29.81+24.71
BLIP1700001.421.29
BLIP17000170004.5311.44
BLIP17000340005.0511.77
BLIP17000510004.2611.86
max % gain w.r.t baseline+3.63+10.57
+ +Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA). $\mathrm{BLIP}_{\mathit{VQAv2}}$ indicates transfer learning from VQAv2, and BLIP indicates direct finetuning. + +even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word "how" is a high-probability word to start a question with, and is naturally followed by "many" (Fig 6) resulting in numerical questions being generated. + +# 5. Conclusion & Future Work + +We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. 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In Hugo Larochelle, Marc'Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and HsuanTien Lin, editors, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020. 2, 3 \ No newline at end of file diff --git a/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/images.zip b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ab01a7f92858598694ff8c2ba401a54d1c80bcb6 --- /dev/null +++ b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d23fd07c291ef2fa858018ded50b414e690c744eec309693084cc81ee70f3f7c +size 701461 diff --git a/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/layout.json b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1795fdbd8054bf30be285b119acd847ae02257cc --- /dev/null +++ b/2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/layout.json @@ -0,0 +1,8488 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 547, + 140 + ], + "type": "text", + "content": "Q: How to Specialize Large Vision-Language Models to Data-Scarce VQA Tasks? A: Self-Train on Unlabeled Images!" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 161, + 504, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 161, + 504, + 191 + ], + "spans": [ + { + "bbox": [ + 88, + 161, + 504, + 191 + ], + "type": "text", + "content": "Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "spans": [ + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 255, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 290, + 542 + ], + "type": "text", + "content": "Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 597, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 288, + 694 + ], + "type": "text", + "content": "Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 215, + 547, + 385 + ], + "blocks": [ + { + "bbox": [ + 306, + 215, + 547, + 385 + ], + "lines": [ + { + "bbox": [ + 306, + 215, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 215, + 547, + 385 + ], + "type": "image", + "image_path": "03965e14b1009cd2745e52bb2345565fe94bb6775fa4da04f0c07e16fd5652aa.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "type": "text", + "content": "Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image " + }, + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "type": "text", + "content": " without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers " + }, + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "type": "inline_equation", + "content": "(Q,A)" + }, + { + "bbox": [ + 305, + 392, + 547, + 437 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 460, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 533 + ], + "type": "text", + "content": "data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "content": "Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 196, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 196, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 196, + 712 + ], + "type": "text", + "content": "* work done while at NEC Labs America" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "15005" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 69, + 350, + 227 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 350, + 227 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 350, + 227 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 350, + 227 + ], + "type": "image", + "image_path": "3e4b943819c4228181fd9f28b9570fa942cc03b174fa245b394684d05216f4f0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 547, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 547, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 547, + 268 + ], + "type": "text", + "content": "Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 360, + 71, + 539, + 224 + ], + "blocks": [ + { + "bbox": [ + 360, + 71, + 539, + 224 + ], + "lines": [ + { + "bbox": [ + 360, + 71, + 539, + 224 + ], + "spans": [ + { + "bbox": [ + 360, + 71, + 539, + 224 + ], + "type": "image", + "image_path": "1338f0d6729f7208a8733a9fd6cc12ec31588ca937e3217f748b7773fd568866.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 288, + 187, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 187, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 187, + 300 + ], + "type": "text", + "content": "than a short caption can describe)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "text", + "content": "Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase \"this is a\". We convert each caption into a boolean question where the correct answer is \"yes\" by inserting the caption into the template is this a ? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between \"yes\" and \"no\" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers \"no\" to at least " + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "text", + "content": " of the questions, increasing to " + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "text", + "content": " as the diversity of captions increases (adjusted by top-" + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 303, + 290, + 531 + ], + "type": "text", + "content": " parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model " + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": ". Next, we use " + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": " as a teacher to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 288, + 547, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 547, + 347 + ], + "type": "text", + "content": "pseudolabel unlabeled images by sampling questions and answers from " + }, + { + "bbox": [ + 304, + 288, + 547, + 347 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 304, + 288, + 547, + 347 + ], + "type": "text", + "content": " with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "text", + "content": "Benefits: SelTDA allows us generate synthetic training data by approximating the distribution " + }, + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "inline_equation", + "content": "P(Q, A|I)" + }, + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "text", + "content": " of the target VQA task, where " + }, + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "inline_equation", + "content": "Q, A, I" + }, + { + "bbox": [ + 304, + 347, + 548, + 550 + ], + "type": "text", + "content": " represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 556, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 313, + 556, + 547, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 556, + 547, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 556, + 547, + 592 + ], + "type": "text", + "content": "1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 598, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 598, + 547, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 598, + 547, + 658 + ], + "type": "text", + "content": "2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 665, + 547, + 713 + ], + "type": "text", + "content": "3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15006" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 235 + ], + "type": "text", + "content": "Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 235, + 288, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 390 + ], + "type": "text", + "content": "Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 288, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 288, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 288, + 666 + ], + "type": "text", + "content": "Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 237, + 362, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 362, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 362, + 251 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "content": "Our goal is to pseudolabel an unlabeled image " + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "content": " with a generated question-answer pair " + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "inline_equation", + "content": "(Q, A)" + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "content": " using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model " + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG_{IC}}" + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "content": " to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating " + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "inline_equation", + "content": "P(Q, A|I)" + }, + { + "bbox": [ + 304, + 258, + 547, + 545 + ], + "type": "text", + "content": " that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 552, + 542, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 542, + 565 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 542, + 565 + ], + "type": "text", + "content": "3.1. The Teacher: Direct Image-Conditional VQG" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", a question " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and answer " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", the VQA student must approximate " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "P(Q \\mid Q, I)" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", while the teacher model must approximate " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "P(Q, A \\mid I)" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ". Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "P(Q \\mid I, A)" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15007" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 548, + 175 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 548, + 175 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 548, + 175 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 548, + 175 + ], + "type": "image", + "image_path": "1b844b835973f755de7d2b3a15912d25d1506e699186fd4ae59ac4648da7d292.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "type": "text", + "content": "Figure 3. Overview of the proposed framework. We first create the teacher " + }, + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "type": "text", + "content": " (§3.1), use " + }, + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 182, + 547, + 206 + ], + "type": "text", + "content": " to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 220, + 115, + 275 + ], + "blocks": [ + { + "bbox": [ + 56, + 220, + 115, + 275 + ], + "lines": [ + { + "bbox": [ + 56, + 220, + 115, + 275 + ], + "spans": [ + { + "bbox": [ + 56, + 220, + 115, + 275 + ], + "type": "image", + "image_path": "07eb44d222a5f5a01e155ae42d95abd930b5fc2bd92482ff77ed3650a8b213c0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 57, + 283, + 161, + 300 + ], + "lines": [ + { + "bbox": [ + 57, + 283, + 161, + 300 + ], + "spans": [ + { + "bbox": [ + 57, + 283, + 161, + 300 + ], + "type": "text", + "content": "Question: what is the cat wearing? \nAnswers: necktie, tie" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 57, + 306, + 134, + 365 + ], + "blocks": [ + { + "bbox": [ + 57, + 306, + 134, + 365 + ], + "lines": [ + { + "bbox": [ + 57, + 306, + 134, + 365 + ], + "spans": [ + { + "bbox": [ + 57, + 306, + 134, + 365 + ], + "type": "image", + "image_path": "7028f5f12d0e2415bc374ecca7788f763487cfe32d46aa2b05fde2e063073630.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 57, + 376, + 157, + 393 + ], + "lines": [ + { + "bbox": [ + 57, + 376, + 157, + 393 + ], + "spans": [ + { + "bbox": [ + 57, + 376, + 157, + 393 + ], + "type": "text", + "content": "Question: how is the egg cooked? Answer: fried" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 187, + 220, + 258, + 275 + ], + "blocks": [ + { + "bbox": [ + 187, + 220, + 258, + 275 + ], + "lines": [ + { + "bbox": [ + 187, + 220, + 258, + 275 + ], + "spans": [ + { + "bbox": [ + 187, + 220, + 258, + 275 + ], + "type": "image", + "image_path": "cd87a2039c4183818b9a7151627b2c40bcf3c0a3ac083fd466f88d2721d854a1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 278, + 287, + 302 + ], + "lines": [ + { + "bbox": [ + 182, + 278, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 182, + 278, + 287, + 302 + ], + "type": "text", + "content": "Question: how many items of food are present here? \nAnswers: 2" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 192, + 305, + 254, + 366 + ], + "blocks": [ + { + "bbox": [ + 192, + 305, + 254, + 366 + ], + "lines": [ + { + "bbox": [ + 192, + 305, + 254, + 366 + ], + "spans": [ + { + "bbox": [ + 192, + 305, + 254, + 366 + ], + "type": "image", + "image_path": "f9013b0e122b47e981b019a685a592fdfae273ed025e4b6d73924bb935ca1efe.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 372, + 287, + 397 + ], + "lines": [ + { + "bbox": [ + 182, + 372, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 182, + 372, + 287, + 397 + ], + "type": "text", + "content": "Question: what activity is the baby learning? Answer: feeding, eating, nutrition" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 318, + 220, + 387, + 274 + ], + "blocks": [ + { + "bbox": [ + 318, + 220, + 387, + 274 + ], + "lines": [ + { + "bbox": [ + 318, + 220, + 387, + 274 + ], + "spans": [ + { + "bbox": [ + 318, + 220, + 387, + 274 + ], + "type": "image", + "image_path": "5a3885a05ec6c2ed434e18984c44ea16a9b1692d2cec15620b7b0584800ea3dd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 278, + 410, + 302 + ], + "lines": [ + { + "bbox": [ + 310, + 278, + 410, + 302 + ], + "spans": [ + { + "bbox": [ + 310, + 278, + 410, + 302 + ], + "type": "text", + "content": "Question: what color is the sky in the picture? \nAnswers: clear, blue" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 307, + 392, + 364 + ], + "blocks": [ + { + "bbox": [ + 309, + 307, + 392, + 364 + ], + "lines": [ + { + "bbox": [ + 309, + 307, + 392, + 364 + ], + "spans": [ + { + "bbox": [ + 309, + 307, + 392, + 364 + ], + "type": "image", + "image_path": "8943e59bbb0aa9f14364f1d18c10b2466ffc22b68ab75b92f522a3b67c6b3f48.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 369, + 399, + 401 + ], + "lines": [ + { + "bbox": [ + 309, + 369, + 399, + 401 + ], + "spans": [ + { + "bbox": [ + 309, + 369, + 399, + 401 + ], + "type": "text", + "content": "Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 440, + 220, + 508, + 274 + ], + "blocks": [ + { + "bbox": [ + 440, + 220, + 508, + 274 + ], + "lines": [ + { + "bbox": [ + 440, + 220, + 508, + 274 + ], + "spans": [ + { + "bbox": [ + 440, + 220, + 508, + 274 + ], + "type": "image", + "image_path": "42a7928b3661f35b2ac5d7a2a0b66f6aa08229493cfa4d92c5cce7d9373ad563.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 283, + 518, + 300 + ], + "lines": [ + { + "bbox": [ + 435, + 283, + 518, + 300 + ], + "spans": [ + { + "bbox": [ + 435, + 283, + 518, + 300 + ], + "type": "text", + "content": "Question: what city is this? \nAnswers: london, uk" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 444, + 306, + 522, + 365 + ], + "blocks": [ + { + "bbox": [ + 444, + 306, + 522, + 365 + ], + "lines": [ + { + "bbox": [ + 444, + 306, + 522, + 365 + ], + "spans": [ + { + "bbox": [ + 444, + 306, + 522, + 365 + ], + "type": "image", + "image_path": "5188f6d8d4c231fd410025f49ec9f6ebb416f7a22adce852c9cdc6f462bf5d53.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 372, + 538, + 396 + ], + "lines": [ + { + "bbox": [ + 435, + 372, + 538, + 396 + ], + "spans": [ + { + "bbox": [ + 435, + 372, + 538, + 396 + ], + "type": "text", + "content": "Question: what is the name of this party? Answer: baby shower" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": "Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning)." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "text", + "content": "approaches, we develop an image-conditional approach " + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "inline_equation", + "content": "(\\mathrm{VQG}_{IC})" + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "text", + "content": " that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions " + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "inline_equation", + "content": "P(Y|I)" + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 457, + 289, + 541 + ], + "type": "text", + "content": " is often a distribution over a (finite) label space." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "To create the " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " teacher that approximates " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "P(Q,A|I)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ", we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "P(T|I)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "T = (Q,A)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " be a question-answer dataset we wish to create a teacher from. For a sample " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "(Q,A,I)\\in \\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ", we transform it into a target sequence of tokens " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "y_{1:N} = (y_1,y_2,\\dots y_n)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " by entering " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "(Q,A)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " into a structured template of the form \"Question: ? Answer: .\" where and are replaced by the content of " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " respectively. Once " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "y_{1:N} = (y_1,y_2,\\dots y_n)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 457, + 482, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 482, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 482, + 470 + ], + "type": "text", + "content": "obtained, we train the model by optimizing" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 351, + 479, + 546, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 479, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 351, + 479, + 546, + 510 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {V Q G}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x\\right) \\tag {1}", + "image_path": "a443189e13c7c708c6f17d806a5139e1079f261ce99acfa510d17bbcce8b023c.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": "over all question-image-answer pairs in " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " is the latent encoded features in the standard encoder-decoder architecture and " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " represents the VLM parameters. The " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG_{IC}}" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG_{IC}}" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "P(T|I)" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": ", having been exposed to a diverse number of images and paired text. The " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG_{IC}}" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "(Q', A')" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": " is generated jointly as a text " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "T'" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": ", allowing us to sample from " + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "inline_equation", + "content": "P(T|I)" + }, + { + "bbox": [ + 304, + 519, + 547, + 663 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 671, + 525, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 525, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 525, + 684 + ], + "type": "text", + "content": "3.2. Training the Student with Unlabeled Data" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Once the VQGIC teacher model has been obtained, self-training with unlabeled data can proceed. To produce a" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15008" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "pseudolabel " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "(Q', A')" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " for an unlabeled image " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "I_u" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ", we first obtain " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{1:N} = \\mathrm{VQG_{IC}}(I_u)" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{1:N}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " are the logits of the decoder. The logits " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{1:N}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " define a distribution " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "P(L_N \\mid L_{1:N-1})" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "T'" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "P(L_N \\mid L_{1:N-1})" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ". The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "(Q', A')" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " from the decoded text " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "T'" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ". This pair " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "(Q', A') = T'" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " is a sample from " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "P(T|I)" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ", and reflects textual knowledge about the content of an image known to the VLM." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": "We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "(Q', A', I_u)" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": ", representing self-generated training data " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}'" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": " in the style of a target dataset " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": ". We then augment the real dataset " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": " with the self-generated question-answer pairs on unlabeled images " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}'" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": " to create a self-augmented training dataset " + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{Aug}QA} = \\mathcal{D}_{QA}' \\cup \\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 216, + 290, + 384 + ], + "type": "text", + "content": ". The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 90, + 392, + 289, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 392, + 289, + 425 + ], + "spans": [ + { + "bbox": [ + 90, + 392, + 289, + 425 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {V Q A}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {< n}, x _ {n}\\right) \\tag {2}", + "image_path": "371bd8170c8ca77cb20a2e8ed3157eb11224001e252f81e7108006983f73aee9.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": "-th element of the multimodal sequence embeddings " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{1:N}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " produced by " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{VLM}(Q, I; \\theta)" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "Q, I" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " are the question and image, " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "y_{1:N}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " is the sequence of answer tokens, and " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "(Q', A')" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " be generated even when " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " is small, and few pairs are available for adapting the teacher " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": "? Knowledge about the content of the image in a textual form " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "P(T|I)" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " is already well-learned by the VLM from which we initialize " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": ". Thus, " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " only needs sufficient pairs to teach " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{VQG}_{IC}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": " how to construct annotations matching the style of " + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{QA}" + }, + { + "bbox": [ + 46, + 431, + 289, + 577 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 324, + 70, + 530, + 261 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 530, + 261 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 530, + 261 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 530, + 261 + ], + "type": "table", + "html": "
ModelA-OKVQA
ValidationTest
(a)ViLBERT [34]49.141.5
(b)LXMERT [46]51.441.6
(c)KRISP [36]51.942.2
(d)GPV-2 [18]60.353.7
(e)BLIP [26]57.1
(f)\\( BLIP_{\\text{VQAv2}} \\) [26]67.859.5
(g)BLIP + SelTDA62.154.5
% gain w.r.t baseline+5.0
% gain w.r.t best prior work+1.8+0.8
(h)\\( BLIP_{\\text{VQAv2}} + SelTDA \\)68.959.5
% gain w.r.t baseline+1.1+0.0
% gain w.r.t best prior work+8.6+5.8
", + "image_path": "4b2ac891bc4bcf4b33b4e44e2b6b93430ddbd5054e0149181ab6abe4221cb0af.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 318, + 301, + 535, + 446 + ], + "blocks": [ + { + "bbox": [ + 305, + 268, + 547, + 292 + ], + "lines": [ + { + "bbox": [ + 305, + 268, + 547, + 292 + ], + "spans": [ + { + "bbox": [ + 305, + 268, + 547, + 292 + ], + "type": "text", + "content": "Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 301, + 535, + 446 + ], + "lines": [ + { + "bbox": [ + 318, + 301, + 535, + 446 + ], + "spans": [ + { + "bbox": [ + 318, + 301, + 535, + 446 + ], + "type": "table", + "html": "
ModelArtVQA Accuracy
OverallGrounded
(a)BAN [22]22.4-
(b)BLIP [26]21.3681.71
(c)VIKING [12]55.578.74
(d)VIKINGVLM55.981.9
(e)BLIP + SelTDA21.6883.86
% gain w.r.t baseline+0.32+2.15
(f)VIKINGVLM + SelTDA56.8683.86
% gain w.r.t baseline+0.92+1.96
", + "image_path": "d60f2b11b45af6a8eb85ab73e614439db12331d8b98f1de32b18fdc7e5670f73.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 453, + 545, + 475 + ], + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 475 + ], + "type": "text", + "content": "Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": "size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "480 \\times 480" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": " and an image size of " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": " for VQG. For all datasets, we use the official training, validation, and test splits." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 640 + ], + "type": "text", + "content": "Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top-" + }, + { + "bbox": [ + 304, + 555, + 547, + 640 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 555, + 547, + 640 + ], + "type": "text", + "content": " of 0.92. Additional experiments and visualizations can be found in the supplemental material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 647, + 507, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 647, + 507, + 661 + ], + "spans": [ + { + "bbox": [ + 305, + 647, + 507, + 661 + ], + "type": "text", + "content": "4.1. Self-Training: A-OKVQA & ArtVQA" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15009" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 70, + 516, + 148 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 516, + 148 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 516, + 148 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 516, + 148 + ], + "type": "table", + "html": "
Question TypeWell-Posed QuestionAnswers CorrectAnswerable% of Total (95% CI)
External Knowledge73%62%70%29.6% - 50.00%
Visual Identification94%88%94%11.18% - 27.65 %
Visual Reasoning83%70%80%32.54% - 53.17%
Overall (95% CI)71.16% - 87.96%59.77% - 78.98%68.83% - 86.22%
", + "image_path": "e8cd2dcac3f0ee0c15a91b64e997d82ef1b409d9c6fa25891da37d31eee41fc4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "type": "text", + "content": "Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the " + }, + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "type": "text", + "content": " confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about " + }, + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "type": "inline_equation", + "content": "79.5\\%" + }, + { + "bbox": [ + 46, + 156, + 546, + 179 + ], + "type": "text", + "content": " on the validation set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 69, + 194, + 230, + 290 + ], + "blocks": [ + { + "bbox": [ + 69, + 194, + 230, + 290 + ], + "lines": [ + { + "bbox": [ + 69, + 194, + 230, + 290 + ], + "spans": [ + { + "bbox": [ + 69, + 194, + 230, + 290 + ], + "type": "image", + "image_path": "9b5a2ef978d058822c9a3043cdda23a29dda1114974be441603f10370c689fc7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 307, + 546, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 307, + 546, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 546, + 340 + ], + "type": "text", + "content": "Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 231, + 195, + 367, + 289 + ], + "blocks": [ + { + "bbox": [ + 231, + 195, + 367, + 289 + ], + "lines": [ + { + "bbox": [ + 231, + 195, + 367, + 289 + ], + "spans": [ + { + "bbox": [ + 231, + 195, + 367, + 289 + ], + "type": "image", + "image_path": "d2b0cf5b89d1ad3dd5343369cccf1d07ca9f3e4b27cfec84a32030d19e925ed5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 392, + 195, + 529, + 281 + ], + "blocks": [ + { + "bbox": [ + 392, + 195, + 529, + 281 + ], + "lines": [ + { + "bbox": [ + 392, + 195, + 529, + 281 + ], + "spans": [ + { + "bbox": [ + 392, + 195, + 529, + 281 + ], + "type": "image", + "image_path": "4ca10f4794329ee94ff924f1bfc11d327de68edfaaa390acc945da36e4f3a8e8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 48, + 359, + 287, + 599 + ], + "blocks": [ + { + "bbox": [ + 48, + 359, + 287, + 599 + ], + "lines": [ + { + "bbox": [ + 48, + 359, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 48, + 359, + 287, + 599 + ], + "type": "image", + "image_path": "983aa70c3c59d8d9f24f1fe9ed408ee2eef44725a6b8cbaf944c32bf50704548.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 606, + 287, + 628 + ], + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 628 + ], + "type": "text", + "content": "Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "content": "self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when " + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "inline_equation", + "content": "447k" + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "content": " real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 514, + 503, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 503, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 503, + 528 + ], + "type": "text", + "content": "4.2. Ablations & Analysis of Pseudolabels" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. \"what is this object?\"). Next, we show using t-SNE [47] that the teacher model learns to copy the \"style\" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15010" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 523, + 213 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 523, + 213 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 523, + 213 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 523, + 213 + ], + "type": "table", + "html": "
ImagesQuestionsMultiplierAccuracy% GainQuestions/Image
LabeledUnlabeledRealSyntheticTotal
17,000017,000017,0001x (baseline)57.11N/A
17,000017,00017,00034,0002x57.85+0.741 / 1
17,000017,00034,00051,0003x60.01+2.902 / 1
17,000017,00051,00068,0004x59.73+2.623 / 1
17,000017,000017k1x (baseline)57.11N/A
17,0008,50017,00017,00034,0002x60.69+3.572 / 1
17,00017,00017,00034,00051,0003x62.09+4.982 / 1
17,00025,50017,00051,00068,0004x61.31+4.202 / 1
", + "image_path": "3693bf927c7c923c6428dbc133ac1a877e66dd1f0cb304068b8a69c2d123068f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 254, + 545, + 410 + ], + "blocks": [ + { + "bbox": [ + 46, + 220, + 546, + 244 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 546, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 546, + 244 + ], + "type": "text", + "content": "Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 254, + 545, + 410 + ], + "lines": [ + { + "bbox": [ + 47, + 254, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 545, + 410 + ], + "type": "table", + "html": "
# of Real + Synthetic QA PairsRobustness Test SetsAvg. % IncreaseRobustness Total
RealSyntheticMultiplierAdVQAVQA-CEVQA-Rephrasings
(a)17,0000×131.0651.4365.880148.37
(b)17,0002,000×1.137.0952.9667.94+3.21157.99
(c)17,0004,500×1.336.9953.1567.98+3.25158.12
(d)17,0008,000×1.537.3453.3367.57+3.29158.24
(e)17,00012,000×1.737.4352.6267.35+3.01157.4
(f)17,00017,000×236.9552.0566.95+2.53155.95
(g)17,00034,000×336.8951.0065.64+1.72153.53
(h)17,00051,000×436.0650.2564.78+0.91151.09
Max % increase on each dataset+6.03+1.9+2.1+9.87
", + "image_path": "3731eaa068471b7de94b7fc946dae82b588deb480588b73e0e64f2ea40fec558.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "text", + "content": "Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "type": "text", + "content": "We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "content": "Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is " + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "content": " the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 123, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 123, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 123, + 683 + ], + "type": "text", + "content": "4.3. Robustness" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 713 + ], + "type": "text", + "content": "known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15011" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": " performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 200, + 179, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 200, + 179, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 200, + 179, + 213 + ], + "type": "text", + "content": "4.4. Domain Generalization" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 219, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 460 + ], + "type": "text", + "content": "We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 467, + 171, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 171, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 171, + 480 + ], + "type": "text", + "content": "4.5. Numerical Reasoning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": "Numerical reasoning is required to answer questions such as \"how many sheep are looking at the camera\". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of " + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "inline_equation", + "content": "29.81\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "inline_equation", + "content": "24.71\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": " on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of " + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "inline_equation", + "content": "3.63\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "inline_equation", + "content": "10.57\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": ". These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly," + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 547, + 149 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 149 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 149 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 149 + ], + "type": "table", + "html": "
ModelTarget (0-shot)
ArtVQAPathVQARSVQA
Baseline (BLIP)31.6525.0937.78
BLIP + SelTDA38.0326.7638.99
% gain w.r.t baseline+6.38+1.67+1.1
", + "image_path": "b5c17177a6ca2b91968a9b008bd5cf438fe644bb3d2a37d4f0fb3b0c598b3be4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 196, + 544, + 367 + ], + "blocks": [ + { + "bbox": [ + 305, + 158, + 547, + 181 + ], + "lines": [ + { + "bbox": [ + 305, + 158, + 547, + 181 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 547, + 181 + ], + "type": "text", + "content": "Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 196, + 544, + 367 + ], + "lines": [ + { + "bbox": [ + 308, + 196, + 544, + 367 + ], + "spans": [ + { + "bbox": [ + 308, + 196, + 544, + 367 + ], + "type": "table", + "html": "
Initialization# Training PairsNumerical Reasoning
RealSynthVQAv2VQA-Rephrasings
BLIPVQAv217000013.4913.06
BLIPVQAv217000200038.7333.74
BLIPVQAv217000450040.435.91
BLIPVQAv217000800042.936.5
BLIPVQAv2170001200043.337.77
max % gain w.r.t baseline+29.81+24.71
BLIP1700001.421.29
BLIP17000170004.5311.44
BLIP17000340005.0511.77
BLIP17000510004.2611.86
max % gain w.r.t baseline+3.63+10.57
", + "image_path": "9feb7d8d7bd8b618442127438956b19aaa391b5e6b915ffc5c7c90f14127caa4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 375, + 547, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 375, + 547, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 547, + 409 + ], + "type": "text", + "content": "Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA). " + }, + { + "bbox": [ + 305, + 375, + 547, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{BLIP}_{\\mathit{VQAv2}}" + }, + { + "bbox": [ + 305, + 375, + 547, + 409 + ], + "type": "text", + "content": " indicates transfer learning from VQAv2, and BLIP indicates direct finetuning." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 434, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 547, + 495 + ], + "type": "text", + "content": "even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word \"how\" is a high-probability word to start a question with, and is naturally followed by \"many\" (Fig 6) resulting in numerical questions being generated." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 511, + 462, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 462, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 462, + 525 + ], + "type": "text", + "content": "5. Conclusion & Future Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. Finally, self-training is yet to be explored with recently developed billion-parameter VLMs [9, 25]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15012" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 289, + 712 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 200 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 200 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 200 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andy Brock, Aida Nematzadeh, Sahand Sharifzadeh, Nikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. Flamingo: a visual language model for few-shot learning. ArXiv, abs/2204.14198, 2022.3" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 202, + 288, + 236 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 202, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 53, + 202, + 288, + 236 + ], + "type": "text", + "content": "[2] Pratyay Banerjee, Tejas Gokhale, Yezhou Yang, and Chitta Baral. Weaqa: Weak supervision via captions for visual question answering. In FINDINGS, 2021. 1, 3" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 237, + 289, + 599 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 237, + 289, + 599 + ], + "spans": [ + { + "bbox": [ + 53, + 237, + 289, + 599 + ], + "type": "text", + "content": "[3] Rishi Bommasani, Drew A. Hudson, Ehsan Adeli, Russ Altman, Simran Arora, Sydney von Arx, Michael S. Bernstein, Jeannette Bohg, Antoine Bosselut, Emma Brunskill, Erik Brynjolfsson, S. 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However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly $2 \\times 10^{7}$ . After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets.", + "bbox": [ + 75, + 301, + 473, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 650, + 207, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33].", + "bbox": [ + 75, + 676, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db40156e128a461ecd37c539efa1d54a46b49714b55d52f4c1dafc1fd816ed7d.jpg", + "image_caption": [ + "Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged." + ], + "image_footnote": [], + "bbox": [ + 537, + 268, + 857, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively.", + "bbox": [ + 496, + 566, + 890, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal contribution.", + "bbox": [ + 94, + 886, + 205, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22302", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62].", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44].", + "bbox": [ + 75, + 242, + 472, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows:", + "bbox": [ + 75, + 424, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of $10^{7}$ , our method can generate more than $2 \\times 10^{14}$ possible pairs for contrastive learning.", + "- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images." + ], + "bbox": [ + 94, + 662, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights.", + "bbox": [ + 517, + 90, + 890, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 223, + 640, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling.", + "bbox": [ + 498, + 250, + 890, + 295 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Blind Image Quality Assessment", + "text_level": 1, + "bbox": [ + 500, + 301, + 785, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77].", + "bbox": [ + 496, + 325, + 890, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16].", + "bbox": [ + 496, + 491, + 890, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43].", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images.", + "bbox": [ + 498, + 794, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Self-supervised Learning", + "text_level": 1, + "bbox": [ + 500, + 847, + 728, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22303", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision.", + "bbox": [ + 73, + 90, + 468, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27].", + "bbox": [ + 75, + 198, + 468, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3.", + "bbox": [ + 75, + 393, + 468, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Image Degradation Modelling", + "text_level": 1, + "bbox": [ + 76, + 491, + 344, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic.", + "bbox": [ + 73, + 515, + 468, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 753, + 166, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To excavate the potential of the \"pre-training and finetuning\" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Reviewing the Framework of SSL", + "text_level": 1, + "bbox": [ + 500, + 90, + 795, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set.", + "bbox": [ + 496, + 113, + 890, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as:", + "bbox": [ + 496, + 371, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {I n f o N C E}} = - \\log \\frac {\\exp (q \\cdot k _ {+} / \\tau)}{\\sum_ {i = 0} ^ {N} \\exp (q \\cdot k _ {i} / \\tau)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 547, + 890, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $q$ is an encoded query, $k_{i}$ is the $i$ -th encoded key of a dictionary consisting of $N$ samples, and $k_{+}$ is a single key that matches $q$ . And $\\tau$ is a temperature hyper-parameter.", + "bbox": [ + 496, + 594, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Degradation Space", + "text_level": 1, + "bbox": [ + 500, + 650, + 681, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing,", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22304", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b1232fd1c076a3948f9f6d6900587cad67094a7c8f5aa47b7f22ea694026bc4b.jpg", + "image_caption": [ + "Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 869, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible.", + "bbox": [ + 75, + 349, + 468, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image $\\mathbf{y}$ , the process can be formulated as:", + "bbox": [ + 75, + 425, + 470, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\mathcal {D} (\\mathbf {y}; w, p), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 679, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}$ denotes the function of degradation. $w$ represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And $p\\in \\{0,1\\}$ indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled:", + "bbox": [ + 75, + 708, + 468, + 829 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\mathcal {D} ^ {o} (\\mathbf {y}) = \\mathcal {D} _ {o} \\left(\\dots \\mathcal {D} _ {1} (\\mathbf {y}; w _ {1}, p _ {1}) \\dots ; w _ {o}, p _ {o}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 840, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $o$ is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "degradation type, involving multiple repeated processes of $\\mathcal{D}^o (\\mathbf{x})$ , where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2.", + "bbox": [ + 496, + 349, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is $2 \\times \\sum_{i=1}^{9} \\mathbf{C}_{9}^{i} \\times \\mathbf{A}_{i}^{i} \\approx 2 \\times 10^{7}$ .", + "bbox": [ + 496, + 441, + 892, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Quality-aware Pretext Task", + "text_level": 1, + "bbox": [ + 500, + 667, + 746, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities.", + "bbox": [ + 496, + 693, + 890, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Suppose we have $N$ images $\\mathbf{y}^{(1)},\\dots ,\\mathbf{y}^{(N)}$ . As shown in Fig. 3, each image $\\mathbf{y}^{(n)}$ will be differently augmented by $K$ degradation compositions, obtaining different \"views\" $\\mathbf{x}_1^{(n)},\\dots ,\\mathbf{x}_K^{(n)}$ that own consistent content but with different perceptual qualities. Then we extract a \"query\" (or \"anchor\") and a \"key\" patch that originates from the same view $\\mathbf{x}_k^{(n)}$ but with different locations, denoted $\\mathbf{x}_{k,i}^{(n)}$ and $\\mathbf{x}_{k,j}^{(n)}$ respectively. The query and key are considered as a positive pair due to their consistent content and degrada", + "bbox": [ + 496, + 755, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22305", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/70f2387e572644c152be2fa6cbfc89b14cf7e9b18708f4e96acbd26651b06331.jpg", + "image_caption": [ + "Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss)." + ], + "image_footnote": [], + "bbox": [ + 76, + 89, + 869, + 315 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/022847d98af6aede2f8c880e0e7e2c15f7b5670f44ce8938da9dec248e8b3cf0.jpg", + "table_caption": [ + "Table 1. Comparison of two types of pretext tasks, where $\\tilde{k}$ represents a degradation/augmentation type different from $k$ , $\\tilde{n}$ is an image different from $n$ , and * denotes an arbitrary value." + ], + "table_footnote": [], + "table_body": "
Pretext taskPositive PairNegative Pair
semantic-aware(x(nk,i), x(nk,j))(x(n)*, x(n*))
quality-aware(x(nk,i), x(nk,j))(x(n)*, x(n*), x(nk,*))
", + "bbox": [ + 89, + 446, + 450, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different \"views\" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around $10\\%$ . Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1.", + "bbox": [ + 75, + 532, + 468, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $\\mathcal{F}$ denote the transformation of the encoder network. Given an input patch $\\mathbf{x}_{k,i}^{(n)}$ , the encoded feature can be noted as $\\mathbf{f}_{k,i}^{(n)} = \\mathcal{F}(\\mathbf{x}_{k,i}^{(n)}) / ||\\mathcal{F}(\\mathbf{x}_{k,i}^{(n)})||$ , after a $\\mathcal{L}_2$ normalization", + "bbox": [ + 75, + 849, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows:", + "bbox": [ + 498, + 395, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {Q C}} = - \\beta \\cdot \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau\\right)}{\\sum_ {\\tilde {k} \\neq k} ^ {K} \\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {\\tilde {k} , j} ^ {(n)} / \\tau\\right)} \\tag {4} \\\\ - \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau)}{\\sum_ {\\bar {n} \\neq n} ^ {N} \\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k ^ {\\prime} , j} ^ {(\\bar {n})} / \\tau)}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 452, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs. $\\beta$ is a coefficient for balancing.", + "bbox": [ + 496, + 546, + 890, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating $2 \\times 10^{14}$ possible pairs during the pre-training phase.", + "bbox": [ + 496, + 592, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 744, + 633, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Criteria", + "text_level": 1, + "bbox": [ + 500, + 770, + 790, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22306", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a937e77c4275ccc663ea29d1fd5de9fbe434f7824337aefd939afef9d9f8cab2.jpg", + "table_caption": [ + "Table 2. Details of selected BIQA datasets." + ], + "table_footnote": [], + "table_body": "
DatasetSizeResolutionMOS Range
BID [12]586480P~2112P0~5
CLIVE [20]1,162500P~640P0~100
KonIQ10K [29]10,073768P0~100
SPAQ [17]11,1251080P~4368P0~100
FLIVE [79]39,810160P~700P0~100
", + "bbox": [ + 99, + 114, + 442, + 204 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2.", + "bbox": [ + 75, + 217, + 468, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a $80\\%$ training set and a $20\\%$ testing set randomly.", + "bbox": [ + 75, + 373, + 468, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 520, + 294, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages:", + "bbox": [ + 75, + 542, + 468, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters, $\\beta$ and $\\tau$ in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs.", + "bbox": [ + 75, + 623, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size $320 \\times 320$ pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with SOTA BIQA Methods", + "text_level": 1, + "bbox": [ + 498, + 237, + 841, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to $0.8875(+3.0\\%)$ of SRCC and $0.9109(+4.6\\%)$ of PLCC in BID, $0.8947(+4.0\\%)$ of SRCC and $0.9141(+2.4\\%)$ of PLCC in CLIVE, $0.9271(+1.1\\%)$ of SRCC and $0.9413(+1.3\\%)$ of PLCC in KonIQ10K, $0.9250(+0.8\\%)$ of SRCC and $0.9279(+0.7\\%)$ of PLCC in SPAQ, and $0.5746(+0.9\\%)$ of SRCC and $0.6748(+1.4\\%)$ of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training).", + "bbox": [ + 496, + 260, + 890, + 472 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training.", + "bbox": [ + 496, + 473, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios.", + "bbox": [ + 496, + 667, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{\\dagger}$ Results in FLIVE follow an aligned train/test split with CONTRIQUE. When using random $80\\% / 20\\%$ splits, SRCC is 0.5746, PLCC is 0.6748.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22307", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/50abb59ae2cdd7e251c02d74b35b3038f3ea3addb7075535188941e624a490d6.jpg", + "table_caption": [ + "Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “ $\\star$ ” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods." + ], + "table_footnote": [], + "table_body": "
MethodBIDCLIVEKonIQ10KSPAQFLIVE
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE [48]0.47720.47130.45360.46760.52600.47450.69730.68500.10480.1409
ILNIQE [85]0.49460.45380.45310.51140.50290.49560.71940.6540.21880.2547
BRISQUE [47]0.57360.54010.60050.62110.71500.70160.80210.80560.32010.3561
BMPRI [46]0.51540.45830.48680.52290.65770.65460.75010.75440.27370.3146
CNNIQA [31]0.61630.61440.62690.60080.68520.68370.79590.79880.30590.2850
WaDIQAm-NR [4]0.65260.63590.69160.73040.72940.75380.83970.84490.43460.4303
SFA [38]0.82020.82530.80370.82130.88820.89660.90570.90690.54150.6260
DB-CNN [89]0.84500.85900.84430.86240.87800.88670.90990.91330.55370.6518
HyperIQA [60]0.85440.85850.85460.87090.90750.92050.91550.91880.53540.6228
PaQ-2-PiQ* [79]--0.8400.8500.8700.880--0.5710.623
CONRTIQUE* [44]--0.8540.8900.8960.901--0.5800.641
UNIQUE* [90]0.8580.8730.8540.8900.8960.901----
MUSIQ* [32]----0.9160.9280.9170.9210.5660.661
TReS* [21]--0.8460.8770.9150.928--0.5540.625
ResNet500.84230.85210.85270.88070.91210.92700.91610.92070.55140.6354
QPT-ResNet500.88750.91090.89470.91410.92710.94130.92500.92790.6104†0.6770
", + "bbox": [ + 138, + 142, + 831, + 380 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7c531eaee968ea33a79c66d01d447870069826bfd049e7e579320d495aae2bf8.jpg", + "table_caption": [ + "Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters." + ], + "table_footnote": [], + "table_body": "
MethodsPre-trained TypeBIDCLIVEKonIQ10K
SRCCPLCCSRCCPLCCSRCCPLCC
HyperIQAOriginal0.86650.88830.85530.87160.89900.9190
QPT0.8982+3.17%0.9061+1.78%0.8743+1.90%0.8732+0.16%0.9066+0.76%0.9241+0.51%
TResOriginal0.75410.79180.84360.87930.89580.9097
QPT0.7936+3.95%0.8037+1.19%0.8666+2.30%0.8882+0.89%0.9052+0.94%0.9150+0.53%
", + "bbox": [ + 96, + 434, + 867, + 527 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/42cb970374eb50b5925a166828bba9ad6874ddea271275a54f61d113d3fbe7db.jpg", + "table_caption": [ + "Table 5. Cross-dataset evaluation. Results of SRCC are reported." + ], + "table_footnote": [], + "table_body": "
TrainTestDBCNNHyperIQACONTRIQUEQPT
KIQ10kCLIVE0.7550.7850.7310.8208
KIQ10kBID0.8160.819-0.8247
CLIVEBID0.7620.756-0.8449
CLIVEKIQ10k0.7540.7720.6760.7494
", + "bbox": [ + 81, + 566, + 462, + 633 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/832513cb052b86691f2537b2679141af30e3ec6dfeb6995c7b48b17e96cf3d17.jpg", + "table_caption": [ + "Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE." + ], + "table_footnote": [], + "table_body": "
Percentage of ImageNetBIDCLIVE
SRCCPLCCSRCCPLCC
20%0.83110.83050.81150.8203
50%0.87600.89730.88680.9007
100%0.88750.91090.89470.9141
", + "bbox": [ + 84, + 689, + 455, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 784, + 240, + 799 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use $20\\%$ , $50\\%$ and $100\\%$ percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/534709f66f8a01e2fa9623b9d37218d588935827053838443732b211e0f948fa.jpg", + "table_caption": [ + "Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE." + ], + "table_footnote": [], + "table_body": "
NetworkParamsBIDCLIVE
SRCCPLCCSRCCPLCC
MBViTV2-1004.900.87460.87990.86400.8914
MBViTV2-15010.590.87820.89760.87020.8970
MBViTV2-20018.450.88210.89600.88940.9006
ResNet-1811.690.86790.88050.86100.8795
ResNet-3421.800.87420.90010.87800.8871
ResNet-5025.560.88750.91090.89470.9141
", + "bbox": [ + 501, + 579, + 885, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only $50\\%$ of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61].", + "bbox": [ + 496, + 717, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22308", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3ba41b7b697a9a2d847b95a99bfec60c99fcf52ad21271f697b95046ad0203ba.jpg", + "table_caption": [ + "Table 8. Impact on the composition of negative samples." + ], + "table_footnote": [], + "table_body": "
InterIntraBIDCLIVE
SRCCPLCCSRCCPLCC
✓✓0.88750.91090.89470.9141
✓×0.87020.90510.87210.8994
×✓0.83990.83570.80840.8142
××0.70780.77310.74950.7493
", + "bbox": [ + 125, + 107, + 415, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6202046e3b964be34837536ae12cbffbb5b7de5b85c844f1a5df9b041d499ed0.jpg", + "image_caption": [ + "(a) Results in BID" + ], + "image_footnote": [], + "bbox": [ + 91, + 200, + 272, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26cf8107b5392dfa02cb357907d1f25db978effc89a468d0ba144b42c15e1676.jpg", + "image_caption": [ + "(b) Results in CLIVE", + "Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially." + ], + "image_footnote": [], + "bbox": [ + 277, + 200, + 452, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of $\\{53\\mathrm{h}, 61\\mathrm{h}, 75\\mathrm{h}\\}$ , MBViTV2s of $\\{66\\mathrm{h}, 92\\mathrm{h}, 109\\mathrm{h}\\}$ , respectively). We did not use larger networks out of tradeoffs, which can be tried in future work.", + "bbox": [ + 75, + 398, + 468, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e., $K - 1$ ), the number of inter-sample ones (i.e., $N \\cdot K$ ), which contain both different content and degradation types, is larger.", + "bbox": [ + 75, + 474, + 468, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results.", + "bbox": [ + 75, + 611, + 470, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Comparisons with other pretext tasks", + "text_level": 1, + "bbox": [ + 76, + 801, + 401, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations.", + "bbox": [ + 75, + 824, + 468, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Linear probing evaluation. In this way, the weights of", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/404c36d40aaded9abc81940101e22f87f200ff8b93887377b94499098db25358.jpg", + "table_caption": [ + "Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID." + ], + "table_footnote": [], + "table_body": "
skipshuffletwo-orderSRCCPLCC
✓✓✓0.88750.9109
✓✓×0.88280.9075
✓××0.87450.9029
×××0.86260.8864
", + "bbox": [ + 563, + 125, + 826, + 191 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/077c848e92ec4eaf8a8d1be882a85911740269667737c004307fc0a28c061ce4.jpg", + "table_caption": [ + "Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE." + ], + "table_footnote": [], + "table_body": "
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
Supervised0.76780.78600.71280.7668
MoCo0.73670.73570.67960.7154
QPT0.82420.81750.76130.7938
", + "bbox": [ + 553, + 241, + 834, + 308 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8b42bc2b17037940568d514289e5c399665dfd3271eb641a05c8ff7514bb0bc7.jpg", + "table_caption": [ + "Table 11. Comparisons of end-to-end fine-tuning evaluation using different pretext tasks in BID and CLIVE." + ], + "table_footnote": [], + "table_body": "
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
w/o0.70780.77310.74950.7493
Supervised0.84230.85210.85270.8807
MoCo0.85310.87240.84940.8615
QPT0.88750.91090.89470.9141
", + "bbox": [ + 553, + 357, + 834, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "encoder are frozen for feature extraction directly. As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by $8.75\\%$ of SRCC in BID and $8.17\\%$ in CLIVE.", + "bbox": [ + 496, + 452, + 890, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios.", + "bbox": [ + 496, + 498, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 647, + 617, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. By introducing diverse degradation types and compositions, we construct a degradation space that contains $2 \\times 10^{7}$ possible degradations, to simulate more complicated and realistic distorted images. To constrain the learning process, we proposed the QC-Loss that treats patch pairs extracted from the same degraded images as positive ones. And other pairs are noted as negative ones, including degradation-based and content-based ones. After pre-trained on ImageNet using QPT, BIQA models obtain significant improvements on five BIQA benchmark datasets. Moreover, QPT can be easily integrated with current SOTA methods by replacing their pre-trained weights, showing good generalization ability.", + "bbox": [ + 496, + 672, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22309", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sewoong Ahn, Yeji Choi, and Kwangjin Yoon. Deep learning-based distortion sensitivity prediction for full-reference image quality assessment. In CVPR Workshops, pages 344-353. Computer Vision Foundation / IEEE, 2021.", + "[2] Saleh Albelwi. Survey on self-supervised learning: Auxiliary pretext tasks and contrastive learning methods in imaging. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.131, + 0.843, + 0.153 + ], + "angle": 0, + "content": "Quality-aware Pre-trained Models for Blind Image Quality Assessment" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.18, + 0.731, + 0.218 + ], + "angle": 0, + "content": "Kai Zhao†, Kun Yuan†, Ming Sun, Mading Li and Xing Wen Kuaishou Technology" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.22, + 0.751, + 0.234 + ], + "angle": 0, + "content": "{zhaokai05,yuankun03,sunming03,limading,wenxing}@kuaishou.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.312, + 0.284 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.621 + ], + "angle": 0, + "content": "Blind image quality assessment (BIQA) aims to automatically evaluate the perceived quality of a single image, whose performance has been improved by deep learning-based methods in recent years. However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly \\(2 \\times 10^{7}\\). After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.651, + 0.208, + 0.667 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.47, + 0.875 + ], + "angle": 0, + "content": "With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33]." + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.269, + 0.859, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.206, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22302" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.424 + ], + "angle": 0, + "content": "Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.473, + 0.651 + ], + "angle": 0, + "content": "In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.663, + 0.47, + 0.769 + ], + "angle": 0, + "content": "- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of \\(10^{7}\\), our method can generate more than \\(2 \\times 10^{14}\\) possible pairs for contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.663, + 0.471, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.224, + 0.642, + 0.24 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.296 + ], + "angle": 0, + "content": "In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.787, + 0.319 + ], + "angle": 0, + "content": "2.1. Blind Image Quality Assessment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.492 + ], + "angle": 0, + "content": "Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.658 + ], + "angle": 0, + "content": "In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.84 + ], + "angle": 0, + "content": "In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.729, + 0.864 + ], + "angle": 0, + "content": "2.2. Self-supervised Learning" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22303" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.075, + 0.092, + 0.469, + 0.198 + ], + "angle": 0, + "content": "[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.469, + 0.394 + ], + "angle": 0, + "content": "Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.469, + 0.484 + ], + "angle": 0, + "content": "Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.492, + 0.345, + 0.509 + ], + "angle": 0, + "content": "2.3. Image Degradation Modelling" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.516, + 0.469, + 0.743 + ], + "angle": 0, + "content": "Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.168, + 0.77 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To excavate the potential of the \"pre-training and finetuning\" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.796, + 0.107 + ], + "angle": 0, + "content": "3.1. Reviewing the Framework of SSL" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.372 + ], + "angle": 0, + "content": "SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.538 + ], + "angle": 0, + "content": "In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.548, + 0.891, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {I n f o N C E}} = - \\log \\frac {\\exp (q \\cdot k _ {+} / \\tau)}{\\sum_ {i = 0} ^ {N} \\exp (q \\cdot k _ {i} / \\tau)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.891, + 0.641 + ], + "angle": 0, + "content": "where \\( q \\) is an encoded query, \\( k_{i} \\) is the \\( i \\)-th encoded key of a dictionary consisting of \\( N \\) samples, and \\( k_{+} \\) is a single key that matches \\( q \\). And \\( \\tau \\) is a temperature hyper-parameter." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.682, + 0.667 + ], + "angle": 0, + "content": "3.2. Degradation Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22304" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.87, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.305, + 0.894, + 0.335 + ], + "angle": 0, + "content": "Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.426 + ], + "angle": 0, + "content": "compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.471, + 0.668 + ], + "angle": 0, + "content": "Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image \\( \\mathbf{y} \\), the process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.68, + 0.47, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\mathcal {D} (\\mathbf {y}; w, p), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.83 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}\\) denotes the function of degradation. \\(w\\) represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And \\(p\\in \\{0,1\\}\\) indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.842, + 0.47, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\mathcal {D} ^ {o} (\\mathbf {y}) = \\mathcal {D} _ {o} \\left(\\dots \\mathcal {D} _ {1} (\\mathbf {y}; w _ {1}, p _ {1}) \\dots ; w _ {o}, p _ {o}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(o\\) is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.44 + ], + "angle": 0, + "content": "degradation type, involving multiple repeated processes of \\(\\mathcal{D}^o (\\mathbf{x})\\), where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.893, + 0.656 + ], + "angle": 0, + "content": "The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is \\(2 \\times \\sum_{i=1}^{9} \\mathbf{C}_{9}^{i} \\times \\mathbf{A}_{i}^{i} \\approx 2 \\times 10^{7}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.669, + 0.747, + 0.685 + ], + "angle": 0, + "content": "3.3. Quality-aware Pretext Task" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.755 + ], + "angle": 0, + "content": "Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Suppose we have \\(N\\) images \\(\\mathbf{y}^{(1)},\\dots ,\\mathbf{y}^{(N)}\\). As shown in Fig. 3, each image \\(\\mathbf{y}^{(n)}\\) will be differently augmented by \\(K\\) degradation compositions, obtaining different \"views\" \\(\\mathbf{x}_1^{(n)},\\dots ,\\mathbf{x}_K^{(n)}\\) that own consistent content but with different perceptual qualities. Then we extract a \"query\" (or \"anchor\") and a \"key\" patch that originates from the same view \\(\\mathbf{x}_k^{(n)}\\) but with different locations, denoted \\(\\mathbf{x}_{k,i}^{(n)}\\) and \\(\\mathbf{x}_{k,j}^{(n)}\\) respectively. The query and key are considered as a positive pair due to their consistent content and degrada" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22305" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.09, + 0.87, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss)." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.395, + 0.471, + 0.438 + ], + "angle": 0, + "content": "Table 1. Comparison of two types of pretext tasks, where \\( \\tilde{k} \\) represents a degradation/augmentation type different from \\( k \\), \\( \\tilde{n} \\) is an image different from \\( n \\), and * denotes an arbitrary value." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.448, + 0.452, + 0.52 + ], + "angle": 0, + "content": "
Pretext taskPositive PairNegative Pair
semantic-aware(x(nk,i), x(nk,j))(x(n)*, x(n*))
quality-aware(x(nk,i), x(nk,j))(x(n)*, x(n*), x(nk,*))
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.849 + ], + "angle": 0, + "content": "tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different \"views\" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around \\(10\\%\\). Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.851, + 0.469, + 0.904 + ], + "angle": 0, + "content": "Let \\(\\mathcal{F}\\) denote the transformation of the encoder network. Given an input patch \\(\\mathbf{x}_{k,i}^{(n)}\\), the encoded feature can be noted as \\(\\mathbf{f}_{k,i}^{(n)} = \\mathcal{F}(\\mathbf{x}_{k,i}^{(n)}) / ||\\mathcal{F}(\\mathbf{x}_{k,i}^{(n)})||\\), after a \\(\\mathcal{L}_2\\) normalization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.396, + 0.892, + 0.443 + ], + "angle": 0, + "content": "for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.453, + 0.892, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {Q C}} = - \\beta \\cdot \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau\\right)}{\\sum_ {\\tilde {k} \\neq k} ^ {K} \\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {\\tilde {k} , j} ^ {(n)} / \\tau\\right)} \\tag {4} \\\\ - \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau)}{\\sum_ {\\bar {n} \\neq n} ^ {N} \\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k ^ {\\prime} , j} ^ {(\\bar {n})} / \\tau)}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.592 + ], + "angle": 0, + "content": "where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs. \\(\\beta\\) is a coefficient for balancing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.73 + ], + "angle": 0, + "content": "To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating \\(2 \\times 10^{14}\\) possible pairs during the pre-training phase." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.745, + 0.634, + 0.763 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.791, + 0.787 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Criteria" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22306" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.09, + 0.402, + 0.103 + ], + "angle": 0, + "content": "Table 2. Details of selected BIQA datasets." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.115, + 0.444, + 0.205 + ], + "angle": 0, + "content": "
DatasetSizeResolutionMOS Range
BID [12]586480P~2112P0~5
CLIVE [20]1,162500P~640P0~100
KonIQ10K [29]10,073768P0~100
SPAQ [17]11,1251080P~4368P0~100
FLIVE [79]39,810160P~700P0~100
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.47, + 0.355 + ], + "angle": 0, + "content": "images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a \\(80\\%\\) training set and a \\(20\\%\\) testing set randomly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.521, + 0.295, + 0.537 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.47, + 0.605 + ], + "angle": 0, + "content": "Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.777 + ], + "angle": 0, + "content": "Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters, \\(\\beta\\) and \\(\\tau\\) in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size \\(320 \\times 320\\) pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.238, + 0.843, + 0.254 + ], + "angle": 0, + "content": "4.3. Comparison with SOTA BIQA Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.473 + ], + "angle": 0, + "content": "We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to \\(0.8875(+3.0\\%)\\) of SRCC and \\(0.9109(+4.6\\%)\\) of PLCC in BID, \\(0.8947(+4.0\\%)\\) of SRCC and \\(0.9141(+2.4\\%)\\) of PLCC in CLIVE, \\(0.9271(+1.1\\%)\\) of SRCC and \\(0.9413(+1.3\\%)\\) of PLCC in KonIQ10K, \\(0.9250(+0.8\\%)\\) of SRCC and \\(0.9279(+0.7\\%)\\) of PLCC in SPAQ, and \\(0.5746(+0.9\\%)\\) of SRCC and \\(0.6748(+1.4\\%)\\) of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(^{\\dagger}\\)Results in FLIVE follow an aligned train/test split with CONTRIQUE. When using random \\(80\\% / 20\\%\\) splits, SRCC is 0.5746, PLCC is 0.6748." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22307" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “\\(\\star\\)” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.143, + 0.832, + 0.381 + ], + "angle": 0, + "content": "
MethodBIDCLIVEKonIQ10KSPAQFLIVE
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE [48]0.47720.47130.45360.46760.52600.47450.69730.68500.10480.1409
ILNIQE [85]0.49460.45380.45310.51140.50290.49560.71940.6540.21880.2547
BRISQUE [47]0.57360.54010.60050.62110.71500.70160.80210.80560.32010.3561
BMPRI [46]0.51540.45830.48680.52290.65770.65460.75010.75440.27370.3146
CNNIQA [31]0.61630.61440.62690.60080.68520.68370.79590.79880.30590.2850
WaDIQAm-NR [4]0.65260.63590.69160.73040.72940.75380.83970.84490.43460.4303
SFA [38]0.82020.82530.80370.82130.88820.89660.90570.90690.54150.6260
DB-CNN [89]0.84500.85900.84430.86240.87800.88670.90990.91330.55370.6518
HyperIQA [60]0.85440.85850.85460.87090.90750.92050.91550.91880.53540.6228
PaQ-2-PiQ* [79]--0.8400.8500.8700.880--0.5710.623
CONRTIQUE* [44]--0.8540.8900.8960.901--0.5800.641
UNIQUE* [90]0.8580.8730.8540.8900.8960.901----
MUSIQ* [32]----0.9160.9280.9170.9210.5660.661
TReS* [21]--0.8460.8770.9150.928--0.5540.625
ResNet500.84230.85210.85270.88070.91210.92700.91610.92070.55140.6354
QPT-ResNet500.88750.91090.89470.91410.92710.94130.92500.92790.6104†0.6770
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.395, + 0.893, + 0.425 + ], + "angle": 0, + "content": "Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.435, + 0.868, + 0.529 + ], + "angle": 0, + "content": "
MethodsPre-trained TypeBIDCLIVEKonIQ10K
SRCCPLCCSRCCPLCCSRCCPLCC
HyperIQAOriginal0.86650.88830.85530.87160.89900.9190
QPT0.8982+3.17%0.9061+1.78%0.8743+1.90%0.8732+0.16%0.9066+0.76%0.9241+0.51%
TResOriginal0.75410.79180.84360.87930.89580.9097
QPT0.7936+3.95%0.8037+1.19%0.8666+2.30%0.8882+0.89%0.9052+0.94%0.9150+0.53%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.541, + 0.465, + 0.556 + ], + "angle": 0, + "content": "Table 5. Cross-dataset evaluation. Results of SRCC are reported." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.567, + 0.464, + 0.634 + ], + "angle": 0, + "content": "
TrainTestDBCNNHyperIQACONTRIQUEQPT
KIQ10kCLIVE0.7550.7850.7310.8208
KIQ10kBID0.8160.819-0.8247
CLIVEBID0.7620.756-0.8449
CLIVEKIQ10k0.7540.7720.6760.7494
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.651, + 0.47, + 0.68 + ], + "angle": 0, + "content": "Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.69, + 0.457, + 0.768 + ], + "angle": 0, + "content": "
Percentage of ImageNetBIDCLIVE
SRCCPLCCSRCCPLCC
20%0.83110.83050.81150.8203
50%0.87600.89730.88680.9007
100%0.88750.91090.89470.9141
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.241, + 0.8 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use \\(20\\%\\), \\(50\\%\\) and \\(100\\%\\) percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.541, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.58, + 0.886, + 0.7 + ], + "angle": 0, + "content": "
NetworkParamsBIDCLIVE
SRCCPLCCSRCCPLCC
MBViTV2-1004.900.87460.87990.86400.8914
MBViTV2-15010.590.87820.89760.87020.8970
MBViTV2-20018.450.88210.89600.88940.9006
ResNet-1811.690.86790.88050.86100.8795
ResNet-3421.800.87420.90010.87800.8871
ResNet-5025.560.88750.91090.89470.9141
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.793 + ], + "angle": 0, + "content": "downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only \\(50\\%\\) of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22308" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.105, + 0.09, + 0.442, + 0.104 + ], + "angle": 0, + "content": "Table 8. Impact on the composition of negative samples." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.108, + 0.416, + 0.191 + ], + "angle": 0, + "content": "
InterIntraBIDCLIVE
SRCCPLCCSRCCPLCC
✓✓0.88750.91090.89470.9141
✓×0.87020.90510.87210.8994
×✓0.83990.83570.80840.8142
××0.70780.77310.74950.7493
" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.201, + 0.273, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.305, + 0.23, + 0.317 + ], + "angle": 0, + "content": "(a) Results in BID" + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.202, + 0.454, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.309, + 0.305, + 0.424, + 0.316 + ], + "angle": 0, + "content": "(b) Results in CLIVE" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.47, + 0.386 + ], + "angle": 0, + "content": "Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.476 + ], + "angle": 0, + "content": "performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of \\(\\{53\\mathrm{h}, 61\\mathrm{h}, 75\\mathrm{h}\\}\\), MBViTV2s of \\(\\{66\\mathrm{h}, 92\\mathrm{h}, 109\\mathrm{h}\\}\\), respectively). We did not use larger networks out of tradeoffs, which can be tried in future work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e., \\( K - 1 \\)), the number of inter-sample ones (i.e., \\( N \\cdot K \\)), which contain both different content and degradation types, is larger." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.793 + ], + "angle": 0, + "content": "Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.402, + 0.818 + ], + "angle": 0, + "content": "4.5. Comparisons with other pretext tasks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.885 + ], + "angle": 0, + "content": "We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Linear probing evaluation. In this way, the weights of" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID." + }, + { + "type": "table", + "bbox": [ + 0.565, + 0.125, + 0.828, + 0.193 + ], + "angle": 0, + "content": "
skipshuffletwo-orderSRCCPLCC
✓✓✓0.88750.9109
✓✓×0.88280.9075
✓××0.87450.9029
×××0.86260.8864
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.206, + 0.892, + 0.233 + ], + "angle": 0, + "content": "Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE." + }, + { + "type": "table", + "bbox": [ + 0.555, + 0.242, + 0.836, + 0.309 + ], + "angle": 0, + "content": "
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
Supervised0.76780.78600.71280.7668
MoCo0.73670.73570.67960.7154
QPT0.82420.81750.76130.7938
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.322, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Table 11. Comparisons of end-to-end fine-tuning evaluation using different pretext tasks in BID and CLIVE." + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.358, + 0.835, + 0.435 + ], + "angle": 0, + "content": "
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
w/o0.70780.77310.74950.7493
Supervised0.84230.85210.85270.8807
MoCo0.85310.87240.84940.8615
QPT0.88750.91090.89470.9141
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.498 + ], + "angle": 0, + "content": "encoder are frozen for feature extraction directly. As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by \\(8.75\\%\\) of SRCC in BID and \\(8.17\\%\\) in CLIVE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.634 + ], + "angle": 0, + "content": "End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.619, + 0.663 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. By introducing diverse degradation types and compositions, we construct a degradation space that contains \\(2 \\times 10^{7}\\) possible degradations, to simulate more complicated and realistic distorted images. To constrain the learning process, we proposed the QC-Loss that treats patch pairs extracted from the same degraded images as positive ones. And other pairs are noted as negative ones, including degradation-based and content-based ones. After pre-trained on ImageNet using QPT, BIQA models obtain significant improvements on five BIQA benchmark datasets. Moreover, QPT can be easily integrated with current SOTA methods by replacing their pre-trained weights, showing good generalization ability." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22309" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Sewoong Ahn, Yeji Choi, and Kwangjin Yoon. Deep learning-based distortion sensitivity prediction for full-reference image quality assessment. In CVPR Workshops, pages 344-353. Computer Vision Foundation / IEEE, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Saleh Albelwi. 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IEEE, 2021." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "22313" + } + ] +] \ No newline at end of file diff --git a/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/8d41dca5-5365-455a-824a-8a417d4e7839_origin.pdf b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/8d41dca5-5365-455a-824a-8a417d4e7839_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2f60a2e17f9b47a177733b48b11c733c6fa63359 --- /dev/null +++ b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/8d41dca5-5365-455a-824a-8a417d4e7839_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91ca1d87541ea0d8658992249008da7c0aa7403e705e6f38834812de2ae4b832 +size 5796394 diff --git a/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/full.md b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0d9483f415889f4c0bd661272690bcdcd0fb6625 --- /dev/null +++ b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/full.md @@ -0,0 +1,333 @@ +# Quality-aware Pre-trained Models for Blind Image Quality Assessment + +Kai Zhao†, Kun Yuan†, Ming Sun, Mading Li and Xing Wen Kuaishou Technology + +{zhaokai05,yuankun03,sunming03,limading,wenxing}@kuaishou.com + +# Abstract + +Blind image quality assessment (BIQA) aims to automatically evaluate the perceived quality of a single image, whose performance has been improved by deep learning-based methods in recent years. However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly $2 \times 10^{7}$ . After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets. + +# 1. Introduction + +With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33]. + +![](images/db40156e128a461ecd37c539efa1d54a46b49714b55d52f4c1dafc1fd816ed7d.jpg) +Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged. + +Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively. + +Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers + +propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62]. + +Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44]. + +In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows: + +- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of $10^{7}$ , our method can generate more than $2 \times 10^{14}$ possible pairs for contrastive learning. +- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images. + +- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights. + +# 2. Related Work + +In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling. + +# 2.1. Blind Image Quality Assessment + +Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77]. + +In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16]. + +Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43]. + +In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images. + +# 2.2. Self-supervised Learning + +SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose + +[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision. + +Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27]. + +Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3. + +# 2.3. Image Degradation Modelling + +Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic. + +# 3. Method + +To excavate the potential of the "pre-training and finetuning" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective. + +# 3.1. Reviewing the Framework of SSL + +SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set. + +In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as: + +$$ +\mathcal {L} _ {\text {I n f o N C E}} = - \log \frac {\exp (q \cdot k _ {+} / \tau)}{\sum_ {i = 0} ^ {N} \exp (q \cdot k _ {i} / \tau)}, \tag {1} +$$ + +where $q$ is an encoded query, $k_{i}$ is the $i$ -th encoded key of a dictionary consisting of $N$ samples, and $k_{+}$ is a single key that matches $q$ . And $\tau$ is a temperature hyper-parameter. + +# 3.2. Degradation Space + +To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing, + +![](images/b1232fd1c076a3948f9f6d6900587cad67094a7c8f5aa47b7f22ea694026bc4b.jpg) +Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions. + +compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible. + +Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image $\mathbf{y}$ , the process can be formulated as: + +$$ +\mathbf {x} = \mathcal {D} (\mathbf {y}; w, p), \tag {2} +$$ + +where $\mathcal{D}$ denotes the function of degradation. $w$ represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And $p\in \{0,1\}$ indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled: + +$$ +\mathbf {x} = \mathcal {D} ^ {o} (\mathbf {y}) = \mathcal {D} _ {o} \left(\dots \mathcal {D} _ {1} (\mathbf {y}; w _ {1}, p _ {1}) \dots ; w _ {o}, p _ {o}\right), \tag {3} +$$ + +where $o$ is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order + +degradation type, involving multiple repeated processes of $\mathcal{D}^o (\mathbf{x})$ , where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2. + +The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is $2 \times \sum_{i=1}^{9} \mathbf{C}_{9}^{i} \times \mathbf{A}_{i}^{i} \approx 2 \times 10^{7}$ . + +# 3.3. Quality-aware Pretext Task + +Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities. + +Suppose we have $N$ images $\mathbf{y}^{(1)},\dots ,\mathbf{y}^{(N)}$ . As shown in Fig. 3, each image $\mathbf{y}^{(n)}$ will be differently augmented by $K$ degradation compositions, obtaining different "views" $\mathbf{x}_1^{(n)},\dots ,\mathbf{x}_K^{(n)}$ that own consistent content but with different perceptual qualities. Then we extract a "query" (or "anchor") and a "key" patch that originates from the same view $\mathbf{x}_k^{(n)}$ but with different locations, denoted $\mathbf{x}_{k,i}^{(n)}$ and $\mathbf{x}_{k,j}^{(n)}$ respectively. The query and key are considered as a positive pair due to their consistent content and degrada + +![](images/70f2387e572644c152be2fa6cbfc89b14cf7e9b18708f4e96acbd26651b06331.jpg) +Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss). + +Table 1. Comparison of two types of pretext tasks, where $\tilde{k}$ represents a degradation/augmentation type different from $k$ , $\tilde{n}$ is an image different from $n$ , and * denotes an arbitrary value. + +
Pretext taskPositive PairNegative Pair
semantic-aware(x(nk,i), x(nk,j))(x(n)*, x(n*))
quality-aware(x(nk,i), x(nk,j))(x(n)*, x(n*), x(nk,*))
+ +tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different "views" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around $10\%$ . Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1. + +Let $\mathcal{F}$ denote the transformation of the encoder network. Given an input patch $\mathbf{x}_{k,i}^{(n)}$ , the encoded feature can be noted as $\mathbf{f}_{k,i}^{(n)} = \mathcal{F}(\mathbf{x}_{k,i}^{(n)}) / ||\mathcal{F}(\mathbf{x}_{k,i}^{(n)})||$ , after a $\mathcal{L}_2$ normalization + +for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {Q C}} = - \beta \cdot \log \sum_ {k = 1} ^ {K} \frac {\exp \left(\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k , j} ^ {(n)} / \tau\right)}{\sum_ {\tilde {k} \neq k} ^ {K} \exp \left(\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {\tilde {k} , j} ^ {(n)} / \tau\right)} \tag {4} \\ - \log \sum_ {k = 1} ^ {K} \frac {\exp (\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k , j} ^ {(n)} / \tau)}{\sum_ {\bar {n} \neq n} ^ {N} \sum_ {k ^ {\prime} = 1} ^ {K} \exp (\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k ^ {\prime} , j} ^ {(\bar {n})} / \tau)}, \\ \end{array} +$$ + +where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs. $\beta$ is a coefficient for balancing. + +To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating $2 \times 10^{14}$ possible pairs during the pre-training phase. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Criteria + +Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073 + +Table 2. Details of selected BIQA datasets. + +
DatasetSizeResolutionMOS Range
BID [12]586480P~2112P0~5
CLIVE [20]1,162500P~640P0~100
KonIQ10K [29]10,073768P0~100
SPAQ [17]11,1251080P~4368P0~100
FLIVE [79]39,810160P~700P0~100
+ +images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2. + +Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a $80\%$ training set and a $20\%$ testing set randomly. + +# 4.2. Implementation Details + +Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages: + +Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters, $\beta$ and $\tau$ in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs. + +Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size $320 \times 320$ pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments + +are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results. + +# 4.3. Comparison with SOTA BIQA Methods + +We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to $0.8875(+3.0\%)$ of SRCC and $0.9109(+4.6\%)$ of PLCC in BID, $0.8947(+4.0\%)$ of SRCC and $0.9141(+2.4\%)$ of PLCC in CLIVE, $0.9271(+1.1\%)$ of SRCC and $0.9413(+1.3\%)$ of PLCC in KonIQ10K, $0.9250(+0.8\%)$ of SRCC and $0.9279(+0.7\%)$ of PLCC in SPAQ, and $0.5746(+0.9\%)$ of SRCC and $0.6748(+1.4\%)$ of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training). + +Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training. + +Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios. + +Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “ $\star$ ” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods. + +
MethodBIDCLIVEKonIQ10KSPAQFLIVE
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE [48]0.47720.47130.45360.46760.52600.47450.69730.68500.10480.1409
ILNIQE [85]0.49460.45380.45310.51140.50290.49560.71940.6540.21880.2547
BRISQUE [47]0.57360.54010.60050.62110.71500.70160.80210.80560.32010.3561
BMPRI [46]0.51540.45830.48680.52290.65770.65460.75010.75440.27370.3146
CNNIQA [31]0.61630.61440.62690.60080.68520.68370.79590.79880.30590.2850
WaDIQAm-NR [4]0.65260.63590.69160.73040.72940.75380.83970.84490.43460.4303
SFA [38]0.82020.82530.80370.82130.88820.89660.90570.90690.54150.6260
DB-CNN [89]0.84500.85900.84430.86240.87800.88670.90990.91330.55370.6518
HyperIQA [60]0.85440.85850.85460.87090.90750.92050.91550.91880.53540.6228
PaQ-2-PiQ* [79]--0.8400.8500.8700.880--0.5710.623
CONRTIQUE* [44]--0.8540.8900.8960.901--0.5800.641
UNIQUE* [90]0.8580.8730.8540.8900.8960.901----
MUSIQ* [32]----0.9160.9280.9170.9210.5660.661
TReS* [21]--0.8460.8770.9150.928--0.5540.625
ResNet500.84230.85210.85270.88070.91210.92700.91610.92070.55140.6354
QPT-ResNet500.88750.91090.89470.91410.92710.94130.92500.92790.6104†0.6770
+ +Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters. + +
MethodsPre-trained TypeBIDCLIVEKonIQ10K
SRCCPLCCSRCCPLCCSRCCPLCC
HyperIQAOriginal0.86650.88830.85530.87160.89900.9190
QPT0.8982+3.17%0.9061+1.78%0.8743+1.90%0.8732+0.16%0.9066+0.76%0.9241+0.51%
TResOriginal0.75410.79180.84360.87930.89580.9097
QPT0.7936+3.95%0.8037+1.19%0.8666+2.30%0.8882+0.89%0.9052+0.94%0.9150+0.53%
+ +Table 5. Cross-dataset evaluation. Results of SRCC are reported. + +
TrainTestDBCNNHyperIQACONTRIQUEQPT
KIQ10kCLIVE0.7550.7850.7310.8208
KIQ10kBID0.8160.819-0.8247
CLIVEBID0.7620.756-0.8449
CLIVEKIQ10k0.7540.7720.6760.7494
+ +Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE. + +
Percentage of ImageNetBIDCLIVE
SRCCPLCCSRCCPLCC
20%0.83110.83050.81150.8203
50%0.87600.89730.88680.9007
100%0.88750.91090.89470.9141
+ +# 4.4. Ablation Studies + +Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use $20\%$ , $50\%$ and $100\%$ percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the + +Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE. + +
NetworkParamsBIDCLIVE
SRCCPLCCSRCCPLCC
MBViTV2-1004.900.87460.87990.86400.8914
MBViTV2-15010.590.87820.89760.87020.8970
MBViTV2-20018.450.88210.89600.88940.9006
ResNet-1811.690.86790.88050.86100.8795
ResNet-3421.800.87420.90010.87800.8871
ResNet-5025.560.88750.91090.89470.9141
+ +downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only $50\%$ of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61]. + +Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream + +Table 8. Impact on the composition of negative samples. + +
InterIntraBIDCLIVE
SRCCPLCCSRCCPLCC
✓✓0.88750.91090.89470.9141
✓×0.87020.90510.87210.8994
×✓0.83990.83570.80840.8142
××0.70780.77310.74950.7493
+ +![](images/6202046e3b964be34837536ae12cbffbb5b7de5b85c844f1a5df9b041d499ed0.jpg) +(a) Results in BID + +![](images/26cf8107b5392dfa02cb357907d1f25db978effc89a468d0ba144b42c15e1676.jpg) +(b) Results in CLIVE +Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially. + +performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of $\{53\mathrm{h}, 61\mathrm{h}, 75\mathrm{h}\}$ , MBViTV2s of $\{66\mathrm{h}, 92\mathrm{h}, 109\mathrm{h}\}$ , respectively). We did not use larger networks out of tradeoffs, which can be tried in future work. + +Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e., $K - 1$ ), the number of inter-sample ones (i.e., $N \cdot K$ ), which contain both different content and degradation types, is larger. + +Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results. + +# 4.5. Comparisons with other pretext tasks + +We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations. + +Linear probing evaluation. In this way, the weights of + +Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID. + +
skipshuffletwo-orderSRCCPLCC
✓✓✓0.88750.9109
✓✓×0.88280.9075
✓××0.87450.9029
×××0.86260.8864
+ +Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE. + +
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
Supervised0.76780.78600.71280.7668
MoCo0.73670.73570.67960.7154
QPT0.82420.81750.76130.7938
+ +Table 11. Comparisons of end-to-end fine-tuning evaluation using different pretext tasks in BID and CLIVE. + +
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
w/o0.70780.77310.74950.7493
Supervised0.84230.85210.85270.8807
MoCo0.85310.87240.84940.8615
QPT0.88750.91090.89470.9141
+ +encoder are frozen for feature extraction directly. As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by $8.75\%$ of SRCC in BID and $8.17\%$ in CLIVE. + +End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios. + +# 5. Conclusion + +In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. 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IEEE, 2021. \ No newline at end of file diff --git a/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/images.zip b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a13c023cb0db116f3ff67caf96854d00627e12c6 --- /dev/null +++ b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:25fa3839a0599c312ad9f50cd89e2f876e8b0b392a05b598545c2aa30d6588b5 +size 589395 diff --git a/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/layout.json b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3b4e6a4c7935d1c60a167502430d86aa4eacccf3 --- /dev/null +++ b/2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/layout.json @@ -0,0 +1,9182 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "spans": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "text", + "content": "Quality-aware Pre-trained Models for Blind Image Quality Assessment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "spans": [ + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "type": "text", + "content": "Kai Zhao†, Kun Yuan†, Ming Sun, Mading Li and Xing Wen Kuaishou Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 131, + 174, + 459, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 174, + 459, + 185 + ], + "spans": [ + { + "bbox": [ + 131, + 174, + 459, + 185 + ], + "type": "text", + "content": "{zhaokai05,yuankun03,sunming03,limading,wenxing}@kuaishou.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 190, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 190, + 224 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 190, + 224 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 491 + ], + "type": "text", + "content": "Blind image quality assessment (BIQA) aims to automatically evaluate the perceived quality of a single image, whose performance has been improved by deep learning-based methods in recent years. However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly " + }, + { + "bbox": [ + 46, + 239, + 290, + 491 + ], + "type": "inline_equation", + "content": "2 \\times 10^{7}" + }, + { + "bbox": [ + 46, + 239, + 290, + 491 + ], + "type": "text", + "content": ". After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 515, + 127, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 127, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 127, + 528 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 536, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 693 + ], + "type": "text", + "content": "With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33]." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 329, + 213, + 525, + 347 + ], + "blocks": [ + { + "bbox": [ + 329, + 213, + 525, + 347 + ], + "lines": [ + { + "bbox": [ + 329, + 213, + 525, + 347 + ], + "spans": [ + { + "bbox": [ + 329, + 213, + 525, + 347 + ], + "type": "image", + "image_path": "db40156e128a461ecd37c539efa1d54a46b49714b55d52f4c1dafc1fd816ed7d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 359, + 545, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 437 + ], + "type": "text", + "content": "Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 569 + ], + "type": "text", + "content": "Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "type": "text", + "content": " Equal contribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22302" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "type": "text", + "content": "Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 336, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 289, + 515 + ], + "type": "text", + "content": "In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 525, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "text", + "content": "- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of " + }, + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "10^{7}" + }, + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "text", + "content": ", our method can generate more than " + }, + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "2 \\times 10^{14}" + }, + { + "bbox": [ + 58, + 525, + 287, + 609 + ], + "type": "text", + "content": " possible pairs for contrastive learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 617, + 288, + 713 + ], + "type": "text", + "content": "- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 168 + ], + "type": "text", + "content": "- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 177, + 392, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 177, + 392, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 177, + 392, + 190 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "type": "text", + "content": "In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 239, + 481, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 481, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 481, + 252 + ], + "type": "text", + "content": "2.1. Blind Image Quality Assessment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "content": "Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "content": "In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 629, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 665 + ], + "type": "text", + "content": "In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 446, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 446, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 446, + 684 + ], + "type": "text", + "content": "2.2. Self-supervised Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22303" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 45, + 72, + 287, + 156 + ], + "type": "text", + "content": "[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 287, + 312 + ], + "type": "text", + "content": "Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 312, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 383 + ], + "type": "text", + "content": "Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 389, + 211, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 211, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 211, + 403 + ], + "type": "text", + "content": "2.3. Image Degradation Modelling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 408, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 408, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 45, + 408, + 287, + 588 + ], + "type": "text", + "content": "Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 102, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 102, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 102, + 609 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "To excavate the potential of the \"pre-training and finetuning\" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 487, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 487, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 487, + 84 + ], + "type": "text", + "content": "3.1. Reviewing the Framework of SSL" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "type": "text", + "content": "SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 294, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 426 + ], + "type": "text", + "content": "In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 347, + 434, + 545, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 434, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 347, + 434, + 545, + 463 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {I n f o N C E}} = - \\log \\frac {\\exp (q \\cdot k _ {+} / \\tau)}{\\sum_ {i = 0} ^ {N} \\exp (q \\cdot k _ {i} / \\tau)}, \\tag {1}", + "image_path": "bd90e6d5d029ab03dca2b5cb7c45b8d010f088a612dadcccc191d5742d78fd72.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": " is an encoded query, " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": "-th encoded key of a dictionary consisting of " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": " samples, and " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "k_{+}" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": " is a single key that matches " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": ". And " + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": " is a temperature hyper-parameter." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 515, + 417, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 417, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 417, + 528 + ], + "type": "text", + "content": "3.2. Degradation Space" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22304" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 532, + 231 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 532, + 231 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 532, + 231 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 532, + 231 + ], + "type": "image", + "image_path": "b1232fd1c076a3948f9f6d6900587cad67094a7c8f5aa47b7f22ea694026bc4b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 241, + 547, + 265 + ], + "lines": [ + { + "bbox": [ + 46, + 241, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 547, + 265 + ], + "type": "text", + "content": "Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "content": "compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 288, + 529 + ], + "type": "text", + "content": "Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image " + }, + { + "bbox": [ + 46, + 337, + 288, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 337, + 288, + 529 + ], + "type": "text", + "content": ", the process can be formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 538, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 538, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 132, + 538, + 287, + 552 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\mathcal {D} (\\mathbf {y}; w, p), \\tag {2}", + "image_path": "8c8987bddc0b7953b324ff46c138cd7df3720967c1c3d467261da27464be0fed.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " denotes the function of degradation. " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "p\\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 60, + 666, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 666, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 60, + 666, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\mathcal {D} ^ {o} (\\mathbf {y}) = \\mathcal {D} _ {o} \\left(\\dots \\mathcal {D} _ {1} (\\mathbf {y}; w _ {1}, p _ {1}) \\dots ; w _ {o}, p _ {o}\\right), \\tag {3}", + "image_path": "92c3593fdbb7744a802f31c125b22d0be3ce3833ad2144a2a3b99d07f60bba62.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "content": "degradation type, involving multiple repeated processes of " + }, + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^o (\\mathbf{x})" + }, + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "content": ", where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 350, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 546, + 519 + ], + "type": "text", + "content": "The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is " + }, + { + "bbox": [ + 304, + 350, + 546, + 519 + ], + "type": "inline_equation", + "content": "2 \\times \\sum_{i=1}^{9} \\mathbf{C}_{9}^{i} \\times \\mathbf{A}_{i}^{i} \\approx 2 \\times 10^{7}" + }, + { + "bbox": [ + 304, + 350, + 546, + 519 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 529, + 457, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 457, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 457, + 542 + ], + "type": "text", + "content": "3.3. Quality-aware Pretext Task" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 549, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 597 + ], + "type": "text", + "content": "Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": "Suppose we have " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(1)},\\dots ,\\mathbf{y}^{(N)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": ". As shown in Fig. 3, each image " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{(n)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " will be differently augmented by " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " degradation compositions, obtaining different \"views\" " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1^{(n)},\\dots ,\\mathbf{x}_K^{(n)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " that own consistent content but with different perceptual qualities. Then we extract a \"query\" (or \"anchor\") and a \"key\" patch that originates from the same view " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_k^{(n)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " but with different locations, denoted " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{k,i}^{(n)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{k,j}^{(n)}" + }, + { + "bbox": [ + 304, + 598, + 546, + 714 + ], + "type": "text", + "content": " respectively. The query and key are considered as a positive pair due to their consistent content and degrada" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22305" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 71, + 532, + 250 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 532, + 250 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 532, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 532, + 250 + ], + "type": "image", + "image_path": "70f2387e572644c152be2fa6cbfc89b14cf7e9b18708f4e96acbd26651b06331.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 547, + 304 + ], + "type": "text", + "content": "Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 354, + 276, + 411 + ], + "blocks": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": "Table 1. Comparison of two types of pretext tasks, where " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "\\tilde{k}" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": " represents a degradation/augmentation type different from " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "\\tilde{n}" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": " is an image different from " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": ", and * denotes an arbitrary value." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 354, + 276, + 411 + ], + "lines": [ + { + "bbox": [ + 55, + 354, + 276, + 411 + ], + "spans": [ + { + "bbox": [ + 55, + 354, + 276, + 411 + ], + "type": "table", + "html": "
Pretext taskPositive PairNegative Pair
semantic-aware(x(nk,i), x(nk,j))(x(n)*, x(n*))
quality-aware(x(nk,i), x(nk,j))(x(n)*, x(n*), x(nk,*))
", + "image_path": "022847d98af6aede2f8c880e0e7e2c15f7b5670f44ce8938da9dec248e8b3cf0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 422, + 287, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 672 + ], + "type": "text", + "content": "tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different \"views\" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around " + }, + { + "bbox": [ + 46, + 422, + 287, + 672 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 672 + ], + "type": "text", + "content": ". Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "content": " denote the transformation of the encoder network. Given an input patch " + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{k,i}^{(n)}" + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "content": ", the encoded feature can be noted as " + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{k,i}^{(n)} = \\mathcal{F}(\\mathbf{x}_{k,i}^{(n)}) / ||\\mathcal{F}(\\mathbf{x}_{k,i}^{(n)})||" + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "content": ", after a " + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 673, + 287, + 715 + ], + "type": "text", + "content": " normalization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 313, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 313, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 313, + 545, + 350 + ], + "type": "text", + "content": "for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 327, + 358, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 358, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 327, + 358, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {Q C}} = - \\beta \\cdot \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau\\right)}{\\sum_ {\\tilde {k} \\neq k} ^ {K} \\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {\\tilde {k} , j} ^ {(n)} / \\tau\\right)} \\tag {4} \\\\ - \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau)}{\\sum_ {\\bar {n} \\neq n} ^ {N} \\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k ^ {\\prime} , j} ^ {(\\bar {n})} / \\tau)}, \\\\ \\end{array}", + "image_path": "76aaf9b50a5f0ffbc1173d08534350887facc0928ad353b21769ab3b7480613e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "text", + "content": "where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs. " + }, + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "text", + "content": " is a coefficient for balancing." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 469, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 578 + ], + "type": "text", + "content": "To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating " + }, + { + "bbox": [ + 304, + 469, + 545, + 578 + ], + "type": "inline_equation", + "content": "2 \\times 10^{14}" + }, + { + "bbox": [ + 304, + 469, + 545, + 578 + ], + "type": "text", + "content": " possible pairs during the pre-training phase." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 590, + 388, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 590, + 388, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 590, + 388, + 604 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 610, + 484, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 484, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 484, + 623 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Criteria" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22306" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 91, + 271, + 162 + ], + "blocks": [ + { + "bbox": [ + 88, + 71, + 246, + 81 + ], + "lines": [ + { + "bbox": [ + 88, + 71, + 246, + 81 + ], + "spans": [ + { + "bbox": [ + 88, + 71, + 246, + 81 + ], + "type": "text", + "content": "Table 2. Details of selected BIQA datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 91, + 271, + 162 + ], + "lines": [ + { + "bbox": [ + 61, + 91, + 271, + 162 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 271, + 162 + ], + "type": "table", + "html": "
DatasetSizeResolutionMOS Range
BID [12]586480P~2112P0~5
CLIVE [20]1,162500P~640P0~100
KonIQ10K [29]10,073768P0~100
SPAQ [17]11,1251080P~4368P0~100
FLIVE [79]39,810160P~700P0~100
", + "image_path": "a937e77c4275ccc663ea29d1fd5de9fbe434f7824337aefd939afef9d9f8cab2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 172, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 287, + 281 + ], + "type": "text", + "content": "images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "text", + "content": "Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a " + }, + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "text", + "content": " training set and a " + }, + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 296, + 287, + 405 + ], + "type": "text", + "content": " testing set randomly." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 412, + 180, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 180, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 180, + 425 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 479 + ], + "type": "text", + "content": "Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "text", + "content": "Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters, " + }, + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 494, + 287, + 615 + ], + "type": "text", + "content": " in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "320 \\times 320" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 188, + 515, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 188, + 515, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 515, + 201 + ], + "type": "text", + "content": "4.3. Comparison with SOTA BIQA Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": "We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.8875(+3.0\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of SRCC and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9109(+4.6\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of PLCC in BID, " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.8947(+4.0\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of SRCC and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9141(+2.4\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of PLCC in CLIVE, " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9271(+1.1\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of SRCC and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9413(+1.3\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of PLCC in KonIQ10K, " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9250(+0.8\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of SRCC and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.9279(+0.7\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of PLCC in SPAQ, and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.5746(+0.9\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of SRCC and " + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "inline_equation", + "content": "0.6748(+1.4\\%)" + }, + { + "bbox": [ + 304, + 206, + 545, + 374 + ], + "type": "text", + "content": " of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 375, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 529 + ], + "type": "text", + "content": "Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 529, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 685 + ], + "type": "text", + "content": "Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "Results in FLIVE follow an aligned train/test split with CONTRIQUE. When using random " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "80\\% / 20\\%" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " splits, SRCC is 0.5746, PLCC is 0.6748." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22307" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 113, + 509, + 301 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 113, + 509, + 301 + ], + "lines": [ + { + "bbox": [ + 85, + 113, + 509, + 301 + ], + "spans": [ + { + "bbox": [ + 85, + 113, + 509, + 301 + ], + "type": "table", + "html": "
MethodBIDCLIVEKonIQ10KSPAQFLIVE
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
NIQE [48]0.47720.47130.45360.46760.52600.47450.69730.68500.10480.1409
ILNIQE [85]0.49460.45380.45310.51140.50290.49560.71940.6540.21880.2547
BRISQUE [47]0.57360.54010.60050.62110.71500.70160.80210.80560.32010.3561
BMPRI [46]0.51540.45830.48680.52290.65770.65460.75010.75440.27370.3146
CNNIQA [31]0.61630.61440.62690.60080.68520.68370.79590.79880.30590.2850
WaDIQAm-NR [4]0.65260.63590.69160.73040.72940.75380.83970.84490.43460.4303
SFA [38]0.82020.82530.80370.82130.88820.89660.90570.90690.54150.6260
DB-CNN [89]0.84500.85900.84430.86240.87800.88670.90990.91330.55370.6518
HyperIQA [60]0.85440.85850.85460.87090.90750.92050.91550.91880.53540.6228
PaQ-2-PiQ* [79]--0.8400.8500.8700.880--0.5710.623
CONRTIQUE* [44]--0.8540.8900.8960.901--0.5800.641
UNIQUE* [90]0.8580.8730.8540.8900.8960.901----
MUSIQ* [32]----0.9160.9280.9170.9210.5660.661
TReS* [21]--0.8460.8770.9150.928--0.5540.625
ResNet500.84230.85210.85270.88070.91210.92700.91610.92070.55140.6354
QPT-ResNet500.88750.91090.89470.91410.92710.94130.92500.92790.6104†0.6770
", + "image_path": "50abb59ae2cdd7e251c02d74b35b3038f3ea3addb7075535188941e624a490d6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 59, + 344, + 531, + 418 + ], + "blocks": [ + { + "bbox": [ + 46, + 312, + 546, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 546, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 546, + 336 + ], + "type": "text", + "content": "Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 344, + 531, + 418 + ], + "lines": [ + { + "bbox": [ + 59, + 344, + 531, + 418 + ], + "spans": [ + { + "bbox": [ + 59, + 344, + 531, + 418 + ], + "type": "table", + "html": "
MethodsPre-trained TypeBIDCLIVEKonIQ10K
SRCCPLCCSRCCPLCCSRCCPLCC
HyperIQAOriginal0.86650.88830.85530.87160.89900.9190
QPT0.8982+3.17%0.9061+1.78%0.8743+1.90%0.8732+0.16%0.9066+0.76%0.9241+0.51%
TResOriginal0.75410.79180.84360.87930.89580.9097
QPT0.7936+3.95%0.8037+1.19%0.8666+2.30%0.8882+0.89%0.9052+0.94%0.9150+0.53%
", + "image_path": "7c531eaee968ea33a79c66d01d447870069826bfd049e7e579320d495aae2bf8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 449, + 283, + 502 + ], + "blocks": [ + { + "bbox": [ + 49, + 428, + 284, + 440 + ], + "lines": [ + { + "bbox": [ + 49, + 428, + 284, + 440 + ], + "spans": [ + { + "bbox": [ + 49, + 428, + 284, + 440 + ], + "type": "text", + "content": "Table 5. Cross-dataset evaluation. Results of SRCC are reported." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 449, + 283, + 502 + ], + "lines": [ + { + "bbox": [ + 50, + 449, + 283, + 502 + ], + "spans": [ + { + "bbox": [ + 50, + 449, + 283, + 502 + ], + "type": "table", + "html": "
TrainTestDBCNNHyperIQACONTRIQUEQPT
KIQ10kCLIVE0.7550.7850.7310.8208
KIQ10kBID0.8160.819-0.8247
CLIVEBID0.7620.756-0.8449
CLIVEKIQ10k0.7540.7720.6760.7494
", + "image_path": "42cb970374eb50b5925a166828bba9ad6874ddea271275a54f61d113d3fbe7db.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 52, + 546, + 279, + 608 + ], + "blocks": [ + { + "bbox": [ + 47, + 515, + 287, + 538 + ], + "lines": [ + { + "bbox": [ + 47, + 515, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 287, + 538 + ], + "type": "text", + "content": "Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 546, + 279, + 608 + ], + "lines": [ + { + "bbox": [ + 52, + 546, + 279, + 608 + ], + "spans": [ + { + "bbox": [ + 52, + 546, + 279, + 608 + ], + "type": "table", + "html": "
Percentage of ImageNetBIDCLIVE
SRCCPLCCSRCCPLCC
20%0.83110.83050.81150.8203
50%0.87600.89730.88680.9007
100%0.88750.91090.89470.9141
", + "image_path": "832513cb052b86691f2537b2679141af30e3ec6dfeb6995c7b48b17e96cf3d17.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 621, + 147, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 147, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 147, + 633 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": " percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 459, + 542, + 554 + ], + "blocks": [ + { + "bbox": [ + 305, + 428, + 545, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 428, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 428, + 545, + 449 + ], + "type": "text", + "content": "Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 459, + 542, + 554 + ], + "lines": [ + { + "bbox": [ + 307, + 459, + 542, + 554 + ], + "spans": [ + { + "bbox": [ + 307, + 459, + 542, + 554 + ], + "type": "table", + "html": "
NetworkParamsBIDCLIVE
SRCCPLCCSRCCPLCC
MBViTV2-1004.900.87460.87990.86400.8914
MBViTV2-15010.590.87820.89760.87020.8970
MBViTV2-20018.450.88210.89600.88940.9006
ResNet-1811.690.86790.88050.86100.8795
ResNet-3421.800.87420.90010.87800.8871
ResNet-5025.560.88750.91090.89470.9141
", + "image_path": "534709f66f8a01e2fa9623b9d37218d588935827053838443732b211e0f948fa.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 568, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 628 + ], + "type": "text", + "content": "downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only " + }, + { + "bbox": [ + 304, + 568, + 545, + 628 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 568, + 545, + 628 + ], + "type": "text", + "content": " of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22308" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 85, + 254, + 151 + ], + "blocks": [ + { + "bbox": [ + 64, + 71, + 270, + 82 + ], + "lines": [ + { + "bbox": [ + 64, + 71, + 270, + 82 + ], + "spans": [ + { + "bbox": [ + 64, + 71, + 270, + 82 + ], + "type": "text", + "content": "Table 8. Impact on the composition of negative samples." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 85, + 254, + 151 + ], + "lines": [ + { + "bbox": [ + 77, + 85, + 254, + 151 + ], + "spans": [ + { + "bbox": [ + 77, + 85, + 254, + 151 + ], + "type": "table", + "html": "
InterIntraBIDCLIVE
SRCCPLCCSRCCPLCC
✓✓0.88750.91090.89470.9141
✓×0.87020.90510.87210.8994
×✓0.83990.83570.80840.8142
××0.70780.77310.74950.7493
", + "image_path": "3ba41b7b697a9a2d847b95a99bfec60c99fcf52ad21271f697b95046ad0203ba.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 56, + 159, + 167, + 237 + ], + "blocks": [ + { + "bbox": [ + 56, + 159, + 167, + 237 + ], + "lines": [ + { + "bbox": [ + 56, + 159, + 167, + 237 + ], + "spans": [ + { + "bbox": [ + 56, + 159, + 167, + 237 + ], + "type": "image", + "image_path": "6202046e3b964be34837536ae12cbffbb5b7de5b85c844f1a5df9b041d499ed0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 241, + 140, + 251 + ], + "lines": [ + { + "bbox": [ + 81, + 241, + 140, + 251 + ], + "spans": [ + { + "bbox": [ + 81, + 241, + 140, + 251 + ], + "type": "text", + "content": "(a) Results in BID" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 159, + 277, + 238 + ], + "blocks": [ + { + "bbox": [ + 170, + 159, + 277, + 238 + ], + "lines": [ + { + "bbox": [ + 170, + 159, + 277, + 238 + ], + "spans": [ + { + "bbox": [ + 170, + 159, + 277, + 238 + ], + "type": "image", + "image_path": "26cf8107b5392dfa02cb357907d1f25db978effc89a468d0ba144b42c15e1676.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 189, + 241, + 259, + 250 + ], + "lines": [ + { + "bbox": [ + 189, + 241, + 259, + 250 + ], + "spans": [ + { + "bbox": [ + 189, + 241, + 259, + 250 + ], + "type": "text", + "content": "(b) Results in CLIVE" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "type": "text", + "content": "Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "text", + "content": "performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of " + }, + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\{53\\mathrm{h}, 61\\mathrm{h}, 75\\mathrm{h}\\}" + }, + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "text", + "content": ", MBViTV2s of " + }, + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\{66\\mathrm{h}, 92\\mathrm{h}, 109\\mathrm{h}\\}" + }, + { + "bbox": [ + 46, + 316, + 287, + 376 + ], + "type": "text", + "content": ", respectively). We did not use larger networks out of tradeoffs, which can be tried in future work." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "text", + "content": "Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e., " + }, + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "inline_equation", + "content": "K - 1" + }, + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "text", + "content": "), the number of inter-sample ones (i.e., " + }, + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "inline_equation", + "content": "N \\cdot K" + }, + { + "bbox": [ + 46, + 376, + 287, + 484 + ], + "type": "text", + "content": "), which contain both different content and degradation types, is larger." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 484, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 628 + ], + "type": "text", + "content": "Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "type": "text", + "content": "4.5. Comparisons with other pretext tasks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 700 + ], + "type": "text", + "content": "We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Linear probing evaluation. In this way, the weights of" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 345, + 99, + 506, + 152 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 93 + ], + "type": "text", + "content": "Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 345, + 99, + 506, + 152 + ], + "lines": [ + { + "bbox": [ + 345, + 99, + 506, + 152 + ], + "spans": [ + { + "bbox": [ + 345, + 99, + 506, + 152 + ], + "type": "table", + "html": "
skipshuffletwo-orderSRCCPLCC
✓✓✓0.88750.9109
✓✓×0.88280.9075
✓××0.87450.9029
×××0.86260.8864
", + "image_path": "404c36d40aaded9abc81940101e22f87f200ff8b93887377b94499098db25358.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 339, + 191, + 511, + 244 + ], + "blocks": [ + { + "bbox": [ + 305, + 163, + 545, + 184 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 184 + ], + "type": "text", + "content": "Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 339, + 191, + 511, + 244 + ], + "lines": [ + { + "bbox": [ + 339, + 191, + 511, + 244 + ], + "spans": [ + { + "bbox": [ + 339, + 191, + 511, + 244 + ], + "type": "table", + "html": "
Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
Supervised0.76780.78600.71280.7668
MoCo0.73670.73570.67960.7154
QPT0.82420.81750.76130.7938
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Pretext taskBIDCLIVE
SRCCPLCCSRCCPLCC
w/o0.70780.77310.74950.7493
Supervised0.84230.85210.85270.8807
MoCo0.85310.87240.84940.8615
QPT0.88750.91090.89470.9141
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As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by " + }, + { + "bbox": [ + 304, + 358, + 545, + 394 + ], + "type": "inline_equation", + "content": "8.75\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 394 + ], + "type": "text", + "content": " of SRCC in BID and " + }, + { + "bbox": [ + 304, + 358, + 545, + 394 + ], + "type": "inline_equation", + "content": "8.17\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 394 + ], + "type": "text", + "content": " in CLIVE." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 395, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 502 + ], + "type": "text", + "content": "End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. By introducing diverse degradation types and compositions, we construct a degradation space that contains " + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 10^{7}" + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": " possible degradations, to simulate more complicated and realistic distorted images. To constrain the learning process, we proposed the QC-Loss that treats patch pairs extracted from the same degraded images as positive ones. And other pairs are noted as negative ones, including degradation-based and content-based ones. After pre-trained on ImageNet using QPT, BIQA models obtain significant improvements on five BIQA benchmark datasets. Moreover, QPT can be easily integrated with current SOTA methods by replacing their pre-trained weights, showing good generalization ability." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22309" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Sewoong Ahn, Yeji Choi, and Kwangjin Yoon. 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The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks." + ], + "image_footnote": [], + "bbox": [ + 81, + 239, + 893, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 532, + 313, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods.", + "bbox": [ + 75, + 566, + 473, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 828, + 209, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image style transfer aims at transferring the artistic style of a reference image to a content image, where the output image should have the style (e.g., colors, textures, strokes,", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and tones) of the reference and the content information of the content image. Great advances [4, 5, 13, 14, 39, 40, 63] have been made in the area of image style transfer, where the arbitrary style transfer (AST) has become one of the main research focuses. Given a trained model, AST algorithms [8, 26, 33] can perform style transfer on arbitrary unseen content-style pairs in a zero-shot manner, such that it enables more practical applications1.", + "bbox": [ + 496, + 534, + 892, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing AST algorithms, including the statistics-based methods [1,26,35,60] and the patch-based methods [6,47], deliver remarkable style transfer results by matching the artistic style information of the stylized image and the style reference. However, taking the high-fidelity artwork generation as the ultimate goal of image style transfer, all existing methods can still be improved since there are few mechanisms to guarantee a high artistic fidelity of the stylized image. A few existing work [3,59] accommodate the adversarial loss [15] into the style transfer framework to enhance the image quality. However, the performance improvement is hindered by the heterogeneous optimization objectives of high image quality and faithful image stylization.", + "bbox": [ + 496, + 656, + 893, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we introduce visual fidelity as a new eval", + "bbox": [ + 517, + 852, + 890, + 867 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The codes of this paper are available at https://github.com/siyuhuang/QuantArt", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5947", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows:", + "bbox": [ + 75, + 316, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization.", + "- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result.", + "- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods." + ], + "bbox": [ + 94, + 657, + 467, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 845, + 218, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55].", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures.", + "bbox": [ + 496, + 199, + 892, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space.", + "bbox": [ + 496, + 488, + 890, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation.", + "bbox": [ + 496, + 642, + 890, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5948", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Visual Fidelity for Image Style Transfer", + "text_level": 1, + "bbox": [ + 76, + 239, + 433, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image style transfer aims to transfer a content image $c$ , e.g., a photo, to a stylized image $y$ by a given style reference $s$ , e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as", + "bbox": [ + 75, + 266, + 472, + 401 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Style fidelity: The style similarity between $y$ and $s$ , which is often evaluated by the Gram matrix [13, 34].", + "- Content fidelity: The content similarity between $y$ and $c$ , which is often evaluated by the perceptual loss [28] or the LPIPS distance [62].", + "- Visual fidelity: The realness of the generated image $y$ . Since all real artwork images belong to a distribution $\\mathcal{T}$ , a generated image $y$ tends to have a higher visual fidelity if it is closer to distribution $\\mathcal{T}$ ." + ], + "bbox": [ + 94, + 412, + 468, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm $(\\alpha = 0)$ faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image.", + "bbox": [ + 75, + 568, + 468, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution $\\mathcal{T}$ in the representation space, where the centroids of all clusters form an artwork codebook $\\mathcal{Z}_{art}$ . When making inferences, we replace the feature map at each position with its nearest centroid in $\\mathcal{Z}_{art}$ . In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ea0e806e62a1fc5ccb96922919a21ca5a693d33b46dfdcc3492e9b0dcfa18a8b.jpg", + "image_caption": [ + "Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer $w / o$ and $w/$ latent feature quantizing, respectively." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation $y$ to be close to one of the centroids of the artwork distribution $\\mathcal{T}$ but far away from the reference $s$ . We introduce more details of QuantArt in the following Section 4.", + "bbox": [ + 498, + 383, + 893, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Our Approach", + "text_level": 1, + "bbox": [ + 500, + 477, + 648, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Framework Overview", + "text_level": 1, + "bbox": [ + 500, + 503, + 705, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level $\\alpha \\in [0,1]$ between the SGA outputs. In the following, we discuss more details of QuantArt.", + "bbox": [ + 496, + 527, + 890, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Learning Auto-Encoders and Codebooks", + "text_level": 1, + "bbox": [ + 500, + 815, + 849, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first extract the features of the content image $c$ and the style reference $s$ with two convolutional encoders $E_{C}$ and $E_{S}$ , then decode the features back into images $c_{rec}$ and $s_{rec}$ with two convolutional decoders $D_{C}$ and $D_{S}$ , respec", + "bbox": [ + 498, + 840, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5949", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ac25ffe5b4ab261433e08b77ad601a9d322b24f4884808a2e54416059d33fcfb.jpg", + "image_caption": [ + "(a) Training Stage-1: learning the auto-encoders" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 344, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ac2d2a1f0fbd65a1b319b91a45858f1b3a822d9d1adb4ced8ebae617da6563fd.jpg", + "image_caption": [ + "(b) Training Stage-2: learning the SGA modules" + ], + "image_footnote": [], + "bbox": [ + 83, + 214, + 339, + 319 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d1280cbf44fcdffee8a747dc2454d6a529fe42a215bd417e1ad5cf3bb1376029.jpg", + "image_caption": [ + "(c) Inference Stage" + ], + "image_footnote": [], + "bbox": [ + 359, + 87, + 893, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tively as", + "bbox": [ + 76, + 428, + 137, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {r e c} = D _ {C} \\left(E _ {C} (c)\\right), \\quad s _ {r e c} = D _ {S} \\left(E _ {S} (s)\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 450, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is distinct from the general neural style transfer methods, which use the VGG [48] or ResNet [18] network pretrained on natural image datasets (e.g., ImageNet [7]) as the image encoder to extract features of both content and style images. To optimize encoder $E_{C}$ and decoder $D_{C}$ , the reconstruction loss is", + "bbox": [ + 75, + 476, + 468, + 565 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {A E} \\left(E _ {C}, D _ {C}\\right) = \\left| \\left| c _ {r e c} - c \\right| \\right| + \\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 575, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{adv}$ is the adversarial training loss and $\\mathbb{D}_C$ is the corresponding discriminator network,", + "bbox": [ + 76, + 599, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right) = \\log \\mathbb {D} _ {C} (c) + \\log \\left(1 - \\mathbb {D} _ {C} \\left(c _ {r e c}\\right)\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 638, + 467, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$E_{S}$ and $D_{S}$ are also optimized by the reconstruction loss $\\mathcal{L}_{AE}(E_S,D_S)$ as formulated in Eq. 2.", + "bbox": [ + 76, + 670, + 468, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we build two codebooks $\\mathcal{Z}_{photo},\\mathcal{Z}_{art}\\in \\mathbb{R}^{N\\times d}$ to model the distributions of the photo dataset and artwork dataset, where $N$ is the number of entries in the codebook and $d$ is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as", + "bbox": [ + 75, + 699, + 468, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {c} = \\hat {E} _ {C} (c), \\quad z _ {s} = \\hat {E} _ {S} (s). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 797, + 468, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then apply vector quantization [52] to the latent features to get the quantized features $\\hat{z}_c$ and $\\hat{z}_s$ , where the vector quantization operator $Q_{\\mathcal{Z}}(z)$ is formulated as", + "bbox": [ + 76, + 824, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {\\mathcal {Z}} (z) := \\underset {\\mathbf {z} _ {k} \\in \\mathcal {Z}} {\\arg \\min } \\| z - \\mathbf {z} _ {k} \\|, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 878, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cb46f7ecfb30c4d4905d235429f0f9382bea836832666ccdfbecf1fcbed1de7e.jpg", + "image_caption": [ + "Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively. $\\mathbb{Q}$ denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters $\\alpha$ , $\\beta \\in [0,1]$ .", + "Figure 4. The vector quantization operator $Q_{\\mathcal{Z}}(z)$ in Eq. 5." + ], + "image_footnote": [], + "bbox": [ + 529, + 430, + 857, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_k$ is the $k$ -th entry in the codebook $\\mathcal{Z}$ . As illustrated in Fig. 4, $z$ is replaced with the nearest neighbour entry in the codebook $\\mathcal{Z}$ via $Q_{\\mathcal{Z}}(z)$ . The quantized features $\\hat{z}_c$ and $\\hat{z}_s$ are collected from codebooks $\\mathcal{Z}_{photo}$ and $\\mathcal{Z}_{art}$ as", + "bbox": [ + 498, + 563, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} _ {c} = Q _ {\\mathcal {Z} _ {\\text {p h o t o}}} \\left(z _ {c}\\right), \\quad \\hat {z} _ {s} = Q _ {\\mathcal {Z} _ {\\text {a r t}}} \\left(z _ {s}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 635, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The quantized features $\\hat{z}_c$ and $\\hat{z}_s$ are decoded into images $\\hat{c}_{rec}$ and $\\hat{s}_{rec}$ via the decoders $\\hat{D}_C$ and $\\hat{D}_S$ , as", + "bbox": [ + 498, + 662, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {c} _ {r e c} = \\hat {D} _ {C} (\\hat {z} _ {c}), \\quad \\hat {s} _ {r e c} = \\hat {D} _ {S} (\\hat {z} _ {s}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 704, + 890, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By following [52], we optimize the codebook $\\mathcal{Z}_{\\text{photo}}$ jointly with the reconstruction loss in Eq. 2. The reconstruction loss for encoder $\\hat{E}_C$ , decoder $\\hat{D}_C$ , and codebook $\\mathcal{Z}_{\\text{photo}}$ is", + "bbox": [ + 498, + 734, + 890, + 780 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\hat {A E}} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}, \\mathcal {Z} _ {\\text {p h o t o}}\\right) = \\mathcal {L} _ {A E} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}\\right) + \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 791, + 890, + 810 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\left| \\left| \\left| \\mathbf {s g} \\left[ z _ {c} \\right] - \\hat {z} _ {c} \\right| \\right| \\right| + \\left| \\left| \\mathbf {s g} \\left[ \\hat {z} _ {c} \\right] - z _ {c} \\right| \\right| \\right|,\n$$\n", + "text_format": "latex", + "bbox": [ + 660, + 811, + 880, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathfrak{sg}[\\cdot ]$ indicates the stop gradient operator. The second term in Eq. 8 optimizes the codebook $\\mathcal{Z}_{photo}$ , while, the third term in Eq. 8 forces the latent feature $z_{c}$ to be close to the nearest neighbor entry in $\\mathcal{Z}_{photo}$ . $\\hat{E}_S$ , $\\hat{D}_S$ , and $\\mathcal{Z}_{art}$ are", + "bbox": [ + 498, + 839, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5950", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/160f7f6d0f3d8ada59a5ab01001c878a8323a7adfe37719c6c6e5c63c755a993.jpg", + "image_caption": [ + "Figure 5. The SGA module proposed for feature style transfer." + ], + "image_footnote": [], + "bbox": [ + 127, + 90, + 415, + 203 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "also optimized by the loss function $\\mathcal{L}_{\\hat{A}E}(\\hat{E}_S, \\hat{D}_S, \\mathcal{Z}_{art})$ as formulated in Eq. 8.", + "bbox": [ + 76, + 241, + 468, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features.", + "bbox": [ + 76, + 272, + 468, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Style Transfer with Style Guided Attention", + "text_level": 1, + "bbox": [ + 76, + 354, + 442, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature $z_{c} \\in \\mathbb{R}^{d}$ and style reference feature $z_{s} \\in \\mathbb{R}^{d}$ as inputs, then outputs the stylized feature vector $z_{y} \\in \\mathbb{R}^{d}$ . It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query $q$ , key $k$ , and value $v$ as inputs,", + "bbox": [ + 76, + 378, + 468, + 530 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t n} (q, k, v) = \\operatorname {s o f t m a x} \\left(f _ {q} (q) f _ {k} (k)\\right) f _ {v} (v) + q, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 537, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{q}, f_{k}, f_{v}$ are the embedding layers. The first attention block is a self-attention block that all its input heads $q, k, v$ accept the transformed content feature $\\tilde{z}_{c} = \\mathrm{ResBlock}(z_{c})$ . The second attention block takes $\\tilde{z}_{c}$ as $q$ , and the style reference feature $z_{s}$ as $k$ and $v$ . The output of the SGA module is formulated as", + "bbox": [ + 76, + 563, + 468, + 652 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {y} = \\operatorname {S G A} \\left(z _ {c}, z _ {s}\\right) = \\operatorname {A t t n} \\left(\\operatorname {A t t n} \\left(\\tilde {z} _ {c}, \\tilde {z} _ {c}, \\tilde {z} _ {c}\\right), z _ {s}, z _ {s}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 661, + 468, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for $M$ times to achieve a better style transfer performance.", + "bbox": [ + 76, + 686, + 468, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The objective function for $\\mathrm{SGA}(z_c, z_s)$ includes the content loss $\\mathcal{L}_{\\text {content }}$ , style loss $\\mathcal{L}_{\\text {style }}$ , and adversarial training loss $\\mathcal{L}_{\\text {featadv }}$", + "bbox": [ + 76, + 792, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S G A} = \\mathcal {L} _ {\\text {c o n t e n t}} + \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {f e a t a d v}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 845, + 468, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 869, + 122, + 883 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n t e n t}} = \\left| \\left| z _ {y} - z _ {c} \\right| \\right|, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 883, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t y l e}} = \\left| \\left| \\mu \\left(z _ {y}\\right) - \\mu \\left(z _ {s}\\right) \\right| \\right| + \\left| \\left| \\sigma \\left(z _ {y}\\right) - \\sigma \\left(z _ {s}\\right) \\right| \\right|, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 90, + 890, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t a d v}} = \\log \\mathbb {D} _ {S G A} \\left(z _ {s}\\right) + \\log \\left(1 - \\mathbb {D} _ {S G A} \\left(z _ {y}\\right)\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 112, + 890, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mu (\\cdot)$ and $\\sigma (\\cdot)$ denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss $\\mathcal{L}_{featadv}$ is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features.", + "bbox": [ + 498, + 133, + 890, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt another SGA module to transfer the quantized features $\\hat{z}_c$ and $\\hat{z}_s$ , as", + "bbox": [ + 498, + 268, + 890, + 299 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} _ {y} = Q _ {\\mathcal {Z} _ {a r t}} \\left(\\mathrm {S} \\hat {\\mathrm {G A}} \\left(\\hat {z} _ {c}, \\hat {z} _ {s}\\right)\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 309, + 890, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\hat{\\mathrm{SGA}} (\\cdot ,\\cdot)$ and $\\mathrm{SGA}(\\cdot ,\\cdot)$ have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook $Q_{\\mathcal{Z}_{art}}$ to ensure that the output is on the latent space of the decoder $\\hat{D}_S$ . The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as", + "bbox": [ + 498, + 335, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S \\hat {G} A} = \\mathcal {L} _ {S G A} + | | \\operatorname {s g} [ \\hat {z} _ {y} ] - z _ {y} ] | | \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 438, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Inference", + "text_level": 1, + "bbox": [ + 500, + 464, + 609, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature $z_{y}$ and stylized quantized feature $\\hat{z}_{y}$ by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have", + "bbox": [ + 498, + 487, + 890, + 607 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t e s t} = \\oplus_ {\\alpha} \\left(\\oplus_ {\\beta} \\left(\\hat {z} _ {y}, \\hat {z} _ {c}\\right), \\oplus_ {\\beta} \\left(z _ {y}, z _ {c}\\right)\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 617, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{c}$ and $\\hat{z}_{c}$ are the content features, and $\\oplus$ is the weighted sum operator as $\\oplus_{p}(a,b) = pa + (1 - p)b$ . $z_{test}$ is decoded into a stylized image with a fused decoder $\\bar{D}_S = \\oplus_\\alpha (\\hat{D}_S, D_S)$ . $\\beta$ controls the style fidelity, and a larger $\\alpha$ results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt $(\\alpha, \\beta)$ provides a simple and easy-to-understand handle grip for users to adjust the style transfer results.", + "bbox": [ + 498, + 643, + 890, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2.", + "bbox": [ + 496, + 779, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5951", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 76, + 114, + 269, + 131 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the \"genre\" tag of \"landscape\" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to $256 \\times 256$ pixels.", + "bbox": [ + 75, + 138, + 468, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of $16 \\times 16$ and a feature dimension of 256. The codebook has $N = 1024$ entries and an entry dimension of $d = 256$ . The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of $4.5 \\times 10^{-6}$ , and a training epoch of 50. The loss weights of $\\mathcal{L}_{AE}$ , $\\mathcal{L}_{codebook}$ , $\\mathcal{L}_{content}$ , $\\mathcal{L}_{style}$ , and $\\mathcal{L}_{adv}$ are set to 1, 1, 1, 10, and 0.8, respectively.", + "bbox": [ + 75, + 319, + 470, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Multi-Fidelity Image Style Transfer", + "text_level": 1, + "bbox": [ + 76, + 510, + 387, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our QuantArt $(\\alpha, \\beta)$ method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations $(\\alpha, \\beta)$ . When the style fidelity $\\beta = 0$ , the model simply reconstructs the input content image. With $\\beta = 1$ and visual fidelity $\\alpha \\rightarrow 1$ , the generated images look more vivid but lose some texture details in the style reference. Note that neither $\\alpha = 0$ or $\\alpha = 1$ performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application.", + "bbox": [ + 75, + 534, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparing with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 76, + 724, + 437, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo).", + "bbox": [ + 75, + 750, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0ea38468e5bfb276d569aad85470814cc8b043d7aaccf68370804f3491193cb7.jpg", + "image_caption": [ + "Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters $\\alpha$ and $\\beta$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 890, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23].", + "bbox": [ + 496, + 369, + 890, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with $\\alpha = 0$ faithfully transfers the texture from input style images, while QuantArt with $\\alpha = 1$ paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up.", + "bbox": [ + 496, + 446, + 890, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity", + "bbox": [ + 496, + 568, + 892, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5952", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e964907757c64c85ee7a27697627f8715b94151b611710cbc5ad040647f0e637.jpg", + "image_caption": [ + "Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 498 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b8031b1d9c0d7d137e10bbc43c159f0de46daaf27a75aa6ca842e763f474e160.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively." + ], + "table_footnote": [], + "table_body": "
Metric ↓AdaINWCTLinearWCTArtFlowEFDMStyleSwapAvatarNetSANetAdaAttNStyTR2Ours (α,β)
(0,0)(0,1)(1,1)
LPIPS ↓0.6810.6950.6570.6030.6520.6070.7060.6860.6330.5140.1590.5650.581
Gram loss (×103) ↓0.1630.2820.1720.1010.4021.3570.7180.1200.2460.386-0.3950.864
FID ↓36.61865.19348.15628.89951.07074.16858.17827.08025.89430.893-25.59017.787
ArtFID ↓63.240112.22981.45247.93686.007120.803100.96447.35643.91048.284-41.62329.695
", + "bbox": [ + 80, + 551, + 890, + 623 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7a1f2709943b9df147ab823a32df2c9faa3d8daa8a328e5939b374777b5934ec.jpg", + "table_caption": [ + "Table 2. Inference time (seconds) of a ${256} \\times {256}$ image with a NVIDIA Tesla V100 GPU." + ], + "table_footnote": [], + "table_body": "
ArtFlowStyleSwapAvatarNetSANetAdaAttNStyTR2Ours
0.0680.0430.1240.0070.0500.0550.045
", + "bbox": [ + 78, + 662, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods.", + "bbox": [ + 75, + 700, + 468, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Human Evaluation", + "text_level": 1, + "bbox": [ + 76, + 786, + 261, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since image style transfer is a highly subjective task, we further examine our model with human evaluation.", + "bbox": [ + 75, + 809, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare", + "bbox": [ + 75, + 840, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of $43.5\\%$ , $51.9\\%$ , and $40.2\\%$ , respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms.", + "bbox": [ + 496, + 637, + 893, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5953", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ea829693dccf9eccfff22df3be7907edaa320f041d58d5fefd289eb61864477.jpg", + "image_caption": [ + "Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants." + ], + "image_footnote": [], + "bbox": [ + 88, + 90, + 460, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ec0c8b7c38d60a90feb3b500c505578a52640aecf1be85c0ed716e51f816b71f.jpg", + "image_caption": [ + "Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only $40.6\\%$ participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions." + ], + "image_footnote": [], + "bbox": [ + 78, + 250, + 253, + 330 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/613c40009b5f91ef1043a14331813d61d890f57bce3b95c76aa289865b6bab3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 269, + 250, + 460, + 334 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of $i$ a real artwork image $s$ and $ii$ a photo stylized according to the reference of $s$ . The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants.", + "bbox": [ + 75, + 435, + 472, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material.", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6c91ee916ea84960fa663fccc51d51c496db39f08518208c4df8ce24a2c31ef4.jpg", + "table_caption": [ + "Table 3. An ablation study of the design choices of QuantArt." + ], + "table_footnote": [], + "table_body": "
Complete model, α = 1, code size 16×16LPIPS ↓Gram ↓FID ↓
0.5810.86417.787
Remove Quantization in SGA0.5450.99318.757
Remove all Quantizations (i.e., α = 0)0.5650.39525.590
Code size 8×80.6561.07827.741
Code size 32×320.5130.79828.663
Remove self-attention in SGA0.5840.88319.025
Remove ResBlock in SGA0.6081.84127.177
Replace SGA with StyTR2 decoder layer [8]0.5390.87526.299
Shared encoders0.5880.78830.806
Shared encoders and decoders0.5930.89135.830
", + "bbox": [ + 504, + 102, + 888, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 237, + 653, + 253 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a $16 \\times 16$ patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of $16 \\times 16$ is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction.", + "bbox": [ + 496, + 260, + 893, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 619, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. The experiments on Photo-to-Artwork, Artwork-to-Artwork, and Photo-to-Photo transfer settings have shown that our method achieves higher visual fidelity along with comparable content and style fidelities compared with the state-of-the-art methods.", + "bbox": [ + 496, + 619, + 890, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by NIH grant 5U54CA225088-03. 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In CVPR, pages 3663-3672, 2019. 3" + ], + "bbox": [ + 501, + 92, + 890, + 885 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5956", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_model.json b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8a8403a4210622927505ace3e15732e0c9c588bb --- /dev/null +++ b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_model.json @@ -0,0 +1,2541 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.131, + 0.859, + 0.154 + ], + "angle": 0, + "content": "QuantArt: Quantizing Image Style Transfer Towards High Visual Fidelity" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.181, + 0.261, + 0.199 + ], + "angle": 0, + "content": "Siyu Huang\\*" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.182, + 0.362, + 0.198 + ], + "angle": 0, + "content": "Jie An\\*" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.199, + 0.381, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Harvard University" + }, + { + "type": "text", + "bbox": [ + 0.397, + 0.182, + 0.506, + 0.199 + ], + "angle": 0, + "content": "Donglai Wei3" + }, + { + "type": "text", + "bbox": [ + 0.4, + 0.199, + 0.6, + 0.217 + ], + "angle": 0, + "content": "\\(^{2}\\)University of Rochester" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.182, + 0.635, + 0.199 + ], + "angle": 0, + "content": "Jiebo Luo" + }, + { + "type": "text", + "bbox": [ + 0.648, + 0.182, + 0.82, + 0.199 + ], + "angle": 0, + "content": "Hanspeter Pfister" + }, + { + "type": "text", + "bbox": [ + 0.619, + 0.199, + 0.751, + 0.217 + ], + "angle": 0, + "content": "3Boston College" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.22, + 0.399, + 0.234 + ], + "angle": 0, + "content": "{huang, pfister}@seas.harvard.com" + }, + { + "type": "text", + "bbox": [ + 0.421, + 0.22, + 0.667, + 0.234 + ], + "angle": 0, + "content": "{jan6,jluo}@cs.ROchester.edu" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.22, + 0.849, + 0.234 + ], + "angle": 0, + "content": "donglai.wei@bc.edu" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.241, + 0.895, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.507, + 0.868, + 0.522 + ], + "angle": 0, + "content": "Figure 1. The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.534, + 0.314, + 0.55 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.474, + 0.81 + ], + "angle": 0, + "content": "The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.829, + 0.21, + 0.845 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Image style transfer aims at transferring the artistic style of a reference image to a content image, where the output image should have the style (e.g., colors, textures, strokes," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.893, + 0.656 + ], + "angle": 0, + "content": "and tones) of the reference and the content information of the content image. Great advances [4, 5, 13, 14, 39, 40, 63] have been made in the area of image style transfer, where the arbitrary style transfer (AST) has become one of the main research focuses. Given a trained model, AST algorithms [8, 26, 33] can perform style transfer on arbitrary unseen content-style pairs in a zero-shot manner, such that it enables more practical applications1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.895, + 0.852 + ], + "angle": 0, + "content": "Existing AST algorithms, including the statistics-based methods [1,26,35,60] and the patch-based methods [6,47], deliver remarkable style transfer results by matching the artistic style information of the stylized image and the style reference. However, taking the high-fidelity artwork generation as the ultimate goal of image style transfer, all existing methods can still be improved since there are few mechanisms to guarantee a high artistic fidelity of the stylized image. A few existing work [3,59] accommodate the adversarial loss [15] into the style transfer framework to enhance the image quality. However, the performance improvement is hindered by the heterogeneous optimization objectives of high image quality and faithful image stylization." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.853, + 0.892, + 0.868 + ], + "angle": 0, + "content": "In this work, we introduce visual fidelity as a new eval" + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1The codes of this paper are available at https://github.com/siyuhuang/QuantArt" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5947" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.317 + ], + "angle": 0, + "content": "uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.651 + ], + "angle": 0, + "content": "We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.658, + 0.468, + 0.703 + ], + "angle": 0, + "content": "- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.708, + 0.468, + 0.768 + ], + "angle": 0, + "content": "- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.773, + 0.468, + 0.832 + ], + "angle": 0, + "content": "- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.658, + 0.468, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.22, + 0.86 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.893, + 0.485 + ], + "angle": 0, + "content": "Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.639 + ], + "angle": 0, + "content": "In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5948" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.24, + 0.434, + 0.259 + ], + "angle": 0, + "content": "3. Visual Fidelity for Image Style Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.473, + 0.402 + ], + "angle": 0, + "content": "Image style transfer aims to transfer a content image \\( c \\), e.g., a photo, to a stylized image \\( y \\) by a given style reference \\( s \\), e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.413, + 0.468, + 0.442 + ], + "angle": 0, + "content": "- Style fidelity: The style similarity between \\( y \\) and \\( s \\), which is often evaluated by the Gram matrix [13, 34]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.448, + 0.469, + 0.492 + ], + "angle": 0, + "content": "- Content fidelity: The content similarity between \\( y \\) and \\( c \\), which is often evaluated by the perceptual loss [28] or the LPIPS distance [62]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.498, + 0.469, + 0.557 + ], + "angle": 0, + "content": "- Visual fidelity: The realness of the generated image \\( y \\). Since all real artwork images belong to a distribution \\( \\mathcal{T} \\), a generated image \\( y \\) tends to have a higher visual fidelity if it is closer to distribution \\( \\mathcal{T} \\)." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.413, + 0.469, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm \\((\\alpha = 0)\\) faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution \\(\\mathcal{T}\\) in the representation space, where the centroids of all clusters form an artwork codebook \\(\\mathcal{Z}_{art}\\). When making inferences, we replace the feature map at each position with its nearest centroid in \\(\\mathcal{Z}_{art}\\). In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.275, + 0.895, + 0.358 + ], + "angle": 0, + "content": "Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer \\( w / o \\) and \\( w/ \\) latent feature quantizing, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.894, + 0.46 + ], + "angle": 0, + "content": "illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation \\( y \\) to be close to one of the centroids of the artwork distribution \\( \\mathcal{T} \\) but far away from the reference \\( s \\). We introduce more details of QuantArt in the following Section 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.478, + 0.649, + 0.496 + ], + "angle": 0, + "content": "4. Our Approach" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.505, + 0.706, + 0.52 + ], + "angle": 0, + "content": "4.1. Framework Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.801 + ], + "angle": 0, + "content": "In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level \\(\\alpha \\in [0,1]\\) between the SGA outputs. In the following, we discuss more details of QuantArt." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.85, + 0.832 + ], + "angle": 0, + "content": "4.2. Learning Auto-Encoders and Codebooks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We first extract the features of the content image \\( c \\) and the style reference \\( s \\) with two convolutional encoders \\( E_{C} \\) and \\( E_{S} \\), then decode the features back into images \\( c_{rec} \\) and \\( s_{rec} \\) with two convolutional decoders \\( D_{C} \\) and \\( D_{S} \\), respec" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5949" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.345, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.196, + 0.34, + 0.207 + ], + "angle": 0, + "content": "(a) Training Stage-1: learning the auto-encoders" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.215, + 0.341, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.325, + 0.341, + 0.337 + ], + "angle": 0, + "content": "(b) Training Stage-2: learning the SGA modules" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.088, + 0.895, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.327, + 0.676, + 0.34 + ], + "angle": 0, + "content": "(c) Inference Stage" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.894, + 0.409 + ], + "angle": 0, + "content": "Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively. \\(\\mathbb{Q}\\) denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters \\(\\alpha\\), \\(\\beta \\in [0,1]\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.138, + 0.442 + ], + "angle": 0, + "content": "tively as" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.452, + 0.469, + 0.468 + ], + "angle": 0, + "content": "\\[\nc _ {r e c} = D _ {C} \\left(E _ {C} (c)\\right), \\quad s _ {r e c} = D _ {S} \\left(E _ {S} (s)\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.566 + ], + "angle": 0, + "content": "This is distinct from the general neural style transfer methods, which use the VGG [48] or ResNet [18] network pretrained on natural image datasets (e.g., ImageNet [7]) as the image encoder to extract features of both content and style images. To optimize encoder \\( E_{C} \\) and decoder \\( D_{C} \\), the reconstruction loss is" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.576, + 0.469, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {A E} \\left(E _ {C}, D _ {C}\\right) = \\left| \\left| c _ {r e c} - c \\right| \\right| + \\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.601, + 0.469, + 0.631 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{adv}\\) is the adversarial training loss and \\(\\mathbb{D}_C\\) is the corresponding discriminator network," + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.64, + 0.468, + 0.669 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right) = \\log \\mathbb {D} _ {C} (c) + \\log \\left(1 - \\mathbb {D} _ {C} \\left(c _ {r e c}\\right)\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.671, + 0.469, + 0.699 + ], + "angle": 0, + "content": "\\(E_{S}\\) and \\(D_{S}\\) are also optimized by the reconstruction loss \\(\\mathcal{L}_{AE}(E_S,D_S)\\) as formulated in Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.469, + 0.791 + ], + "angle": 0, + "content": "Next, we build two codebooks \\(\\mathcal{Z}_{photo},\\mathcal{Z}_{art}\\in \\mathbb{R}^{N\\times d}\\) to model the distributions of the photo dataset and artwork dataset, where \\(N\\) is the number of entries in the codebook and \\(d\\) is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.798, + 0.469, + 0.816 + ], + "angle": 0, + "content": "\\[\nz _ {c} = \\hat {E} _ {C} (c), \\quad z _ {s} = \\hat {E} _ {S} (s). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.87 + ], + "angle": 0, + "content": "We then apply vector quantization [52] to the latent features to get the quantized features \\(\\hat{z}_c\\) and \\(\\hat{z}_s\\), where the vector quantization operator \\(Q_{\\mathcal{Z}}(z)\\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.879, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\nQ _ {\\mathcal {Z}} (z) := \\underset {\\mathbf {z} _ {k} \\in \\mathcal {Z}} {\\arg \\min } \\| z - \\mathbf {z} _ {k} \\|, \\tag {5}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.431, + 0.859, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.529, + 0.871, + 0.544 + ], + "angle": 0, + "content": "Figure 4. The vector quantization operator \\( Q_{\\mathcal{Z}}(z) \\) in Eq. 5." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.564, + 0.892, + 0.625 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_k\\) is the \\(k\\)-th entry in the codebook \\(\\mathcal{Z}\\). As illustrated in Fig. 4, \\(z\\) is replaced with the nearest neighbour entry in the codebook \\(\\mathcal{Z}\\) via \\(Q_{\\mathcal{Z}}(z)\\). The quantized features \\(\\hat{z}_c\\) and \\(\\hat{z}_s\\) are collected from codebooks \\(\\mathcal{Z}_{photo}\\) and \\(\\mathcal{Z}_{art}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.636, + 0.891, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\hat {z} _ {c} = Q _ {\\mathcal {Z} _ {\\text {p h o t o}}} \\left(z _ {c}\\right), \\quad \\hat {z} _ {s} = Q _ {\\mathcal {Z} _ {\\text {a r t}}} \\left(z _ {s}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.664, + 0.891, + 0.695 + ], + "angle": 0, + "content": "The quantized features \\(\\hat{z}_c\\) and \\(\\hat{z}_s\\) are decoded into images \\(\\hat{c}_{rec}\\) and \\(\\hat{s}_{rec}\\) via the decoders \\(\\hat{D}_C\\) and \\(\\hat{D}_S\\), as" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.705, + 0.891, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\hat {c} _ {r e c} = \\hat {D} _ {C} (\\hat {z} _ {c}), \\quad \\hat {s} _ {r e c} = \\hat {D} _ {S} (\\hat {z} _ {s}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.735, + 0.891, + 0.781 + ], + "angle": 0, + "content": "By following [52], we optimize the codebook \\(\\mathcal{Z}_{\\text{photo}}\\) jointly with the reconstruction loss in Eq. 2. The reconstruction loss for encoder \\(\\hat{E}_C\\), decoder \\(\\hat{D}_C\\), and codebook \\(\\mathcal{Z}_{\\text{photo}}\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.792, + 0.891, + 0.811 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\hat {A E}} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}, \\mathcal {Z} _ {\\text {p h o t o}}\\right) = \\mathcal {L} _ {A E} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}\\right) + \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.661, + 0.813, + 0.882, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\left. \\left| \\left| \\left| \\mathbf {s g} \\left[ z _ {c} \\right] - \\hat {z} _ {c} \\right| \\right| \\right| + \\left| \\left| \\mathbf {s g} \\left[ \\hat {z} _ {c} \\right] - z _ {c} \\right| \\right| \\right|,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathfrak{sg}[\\cdot ]\\) indicates the stop gradient operator. The second term in Eq. 8 optimizes the codebook \\(\\mathcal{Z}_{photo}\\), while, the third term in Eq. 8 forces the latent feature \\(z_{c}\\) to be close to the nearest neighbor entry in \\(\\mathcal{Z}_{photo}\\). \\(\\hat{E}_S\\), \\(\\hat{D}_S\\), and \\(\\mathcal{Z}_{art}\\) are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5950" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.092, + 0.416, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.087, + 0.212, + 0.46, + 0.227 + ], + "angle": 0, + "content": "Figure 5. The SGA module proposed for feature style transfer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.242, + 0.47, + 0.272 + ], + "angle": 0, + "content": "also optimized by the loss function \\(\\mathcal{L}_{\\hat{A}E}(\\hat{E}_S, \\hat{D}_S, \\mathcal{Z}_{art})\\) as formulated in Eq. 8." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.47, + 0.348 + ], + "angle": 0, + "content": "After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.356, + 0.443, + 0.372 + ], + "angle": 0, + "content": "4.3. Style Transfer with Style Guided Attention" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.531 + ], + "angle": 0, + "content": "To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature \\( z_{c} \\in \\mathbb{R}^{d} \\) and style reference feature \\( z_{s} \\in \\mathbb{R}^{d} \\) as inputs, then outputs the stylized feature vector \\( z_{y} \\in \\mathbb{R}^{d} \\). It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query \\( q \\), key \\( k \\), and value \\( v \\) as inputs," + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.539, + 0.47, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t n} (q, k, v) = \\operatorname {s o f t m a x} \\left(f _ {q} (q) f _ {k} (k)\\right) f _ {v} (v) + q, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.564, + 0.47, + 0.654 + ], + "angle": 0, + "content": "where \\( f_{q}, f_{k}, f_{v} \\) are the embedding layers. The first attention block is a self-attention block that all its input heads \\( q, k, v \\) accept the transformed content feature \\( \\tilde{z}_{c} = \\mathrm{ResBlock}(z_{c}) \\). The second attention block takes \\( \\tilde{z}_{c} \\) as \\( q \\), and the style reference feature \\( z_{s} \\) as \\( k \\) and \\( v \\). The output of the SGA module is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.662, + 0.469, + 0.68 + ], + "angle": 0, + "content": "\\[\nz _ {y} = \\operatorname {S G A} \\left(z _ {c}, z _ {s}\\right) = \\operatorname {A t t n} \\left(\\operatorname {A t t n} \\left(\\tilde {z} _ {c}, \\tilde {z} _ {c}, \\tilde {z} _ {c}\\right), z _ {s}, z _ {s}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.687, + 0.469, + 0.792 + ], + "angle": 0, + "content": "Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for \\(M\\) times to achieve a better style transfer performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.793, + 0.469, + 0.839 + ], + "angle": 0, + "content": "The objective function for \\(\\mathrm{SGA}(z_c, z_s)\\) includes the content loss \\(\\mathcal{L}_{\\text {content }}\\), style loss \\(\\mathcal{L}_{\\text {style }}\\), and adversarial training loss \\(\\mathcal{L}_{\\text {featadv }}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.847, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S G A} = \\mathcal {L} _ {\\text {c o n t e n t}} + \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {f e a t a d v}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.124, + 0.884 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.885, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n t e n t}} = \\left| \\left| z _ {y} - z _ {c} \\right| \\right|, \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.092, + 0.892, + 0.108 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t y l e}} = \\left| \\left| \\mu \\left(z _ {y}\\right) - \\mu \\left(z _ {s}\\right) \\right| \\right| + \\left| \\left| \\sigma \\left(z _ {y}\\right) - \\sigma \\left(z _ {s}\\right) \\right| \\right|, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.113, + 0.892, + 0.129 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t a d v}} = \\log \\mathbb {D} _ {S G A} \\left(z _ {s}\\right) + \\log \\left(1 - \\mathbb {D} _ {S G A} \\left(z _ {y}\\right)\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.134, + 0.892, + 0.268 + ], + "angle": 0, + "content": "\\(\\mu (\\cdot)\\) and \\(\\sigma (\\cdot)\\) denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss \\(\\mathcal{L}_{featadv}\\) is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.27, + 0.892, + 0.3 + ], + "angle": 0, + "content": "We adopt another SGA module to transfer the quantized features \\(\\hat{z}_c\\) and \\(\\hat{z}_s\\), as" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.31, + 0.892, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\hat {z} _ {y} = Q _ {\\mathcal {Z} _ {a r t}} \\left(\\mathrm {S} \\hat {\\mathrm {G A}} \\left(\\hat {z} _ {c}, \\hat {z} _ {s}\\right)\\right). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.892, + 0.428 + ], + "angle": 0, + "content": "\\(\\hat{\\mathrm{SGA}} (\\cdot ,\\cdot)\\) and \\(\\mathrm{SGA}(\\cdot ,\\cdot)\\) have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook \\(Q_{\\mathcal{Z}_{art}}\\) to ensure that the output is on the latent space of the decoder \\(\\hat{D}_S\\). The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.439, + 0.892, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S \\hat {G} A} = \\mathcal {L} _ {S G A} + | | \\operatorname {s g} [ \\hat {z} _ {y} ] - z _ {y} ] | | \\tag {16}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.465, + 0.61, + 0.479 + ], + "angle": 0, + "content": "4.4. Inference" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.892, + 0.608 + ], + "angle": 0, + "content": "Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature \\( z_{y} \\) and stylized quantized feature \\( \\hat{z}_{y} \\) by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.618, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\nz _ {t e s t} = \\oplus_ {\\alpha} \\left(\\oplus_ {\\beta} \\left(\\hat {z} _ {y}, \\hat {z} _ {c}\\right), \\oplus_ {\\beta} \\left(z _ {y}, z _ {c}\\right)\\right), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.644, + 0.892, + 0.78 + ], + "angle": 0, + "content": "where \\( z_{c} \\) and \\( \\hat{z}_{c} \\) are the content features, and \\( \\oplus \\) is the weighted sum operator as \\( \\oplus_{p}(a,b) = pa + (1 - p)b \\). \\( z_{test} \\) is decoded into a stylized image with a fused decoder \\( \\bar{D}_S = \\oplus_\\alpha (\\hat{D}_S, D_S) \\). \\( \\beta \\) controls the style fidelity, and a larger \\( \\alpha \\) results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt \\( (\\alpha, \\beta) \\) provides a simple and easy-to-understand handle grip for users to adjust the style transfer results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5951" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.271, + 0.132 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.47, + 0.319 + ], + "angle": 0, + "content": "Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the \"genre\" tag of \"landscape\" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to \\(256 \\times 256\\) pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.502 + ], + "angle": 0, + "content": "Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of \\( 16 \\times 16 \\) and a feature dimension of 256. The codebook has \\( N = 1024 \\) entries and an entry dimension of \\( d = 256 \\). The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of \\( 4.5 \\times 10^{-6} \\), and a training epoch of 50. The loss weights of \\( \\mathcal{L}_{AE} \\), \\( \\mathcal{L}_{codebook} \\), \\( \\mathcal{L}_{content} \\), \\( \\mathcal{L}_{style} \\), and \\( \\mathcal{L}_{adv} \\) are set to 1, 1, 1, 10, and 0.8, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.388, + 0.527 + ], + "angle": 0, + "content": "5.2. Multi-Fidelity Image Style Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Our QuantArt \\((\\alpha, \\beta)\\) method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations \\((\\alpha, \\beta)\\). When the style fidelity \\(\\beta = 0\\), the model simply reconstructs the input content image. With \\(\\beta = 1\\) and visual fidelity \\(\\alpha \\rightarrow 1\\), the generated images look more vivid but lose some texture details in the style reference. Note that neither \\(\\alpha = 0\\) or \\(\\alpha = 1\\) performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.439, + 0.743 + ], + "angle": 0, + "content": "5.3. Comparing with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.825 + ], + "angle": 0, + "content": "For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.326, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters \\(\\alpha\\) and \\(\\beta\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.446 + ], + "angle": 0, + "content": "ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with \\(\\alpha = 0\\) faithfully transfers the texture from input style images, while QuantArt with \\(\\alpha = 1\\) paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5952" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.502, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details." + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.538, + 0.885, + 0.552 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.553, + 0.891, + 0.624 + ], + "angle": 0, + "content": "
Metric ↓AdaINWCTLinearWCTArtFlowEFDMStyleSwapAvatarNetSANetAdaAttNStyTR2Ours (α,β)
(0,0)(0,1)(1,1)
LPIPS ↓0.6810.6950.6570.6030.6520.6070.7060.6860.6330.5140.1590.5650.581
Gram loss (×103) ↓0.1630.2820.1720.1010.4021.3570.7180.1200.2460.386-0.3950.864
FID ↓36.61865.19348.15628.89951.07074.16858.17827.08025.89430.893-25.59017.787
ArtFID ↓63.240112.22981.45247.93686.007120.803100.96447.35643.91048.284-41.62329.695
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.636, + 0.47, + 0.661 + ], + "angle": 0, + "content": "Table 2. Inference time (seconds) of a \\( {256} \\times {256} \\) image with a NVIDIA Tesla V100 GPU." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.663, + 0.469, + 0.688 + ], + "angle": 0, + "content": "
ArtFlowStyleSwapAvatarNetSANetAdaAttNStyTR2Ours
0.0680.0430.1240.0070.0500.0550.045
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.777 + ], + "angle": 0, + "content": "of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.262, + 0.801 + ], + "angle": 0, + "content": "5.4. Human Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Since image style transfer is a highly subjective task, we further examine our model with human evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.895, + 0.865 + ], + "angle": 0, + "content": "AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of \\(43.5\\%\\), \\(51.9\\%\\), and \\(40.2\\%\\), respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5953" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.092, + 0.462, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.204, + 0.47, + 0.234 + ], + "angle": 0, + "content": "Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.25, + 0.254, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.251, + 0.462, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.412 + ], + "angle": 0, + "content": "Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only \\(40.6\\%\\) participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.473, + 0.754 + ], + "angle": 0, + "content": "test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of \\( i \\) a real artwork image \\( s \\) and \\( ii \\) a photo stylized according to the reference of \\( s \\). The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material." + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.09, + 0.879, + 0.103 + ], + "angle": 0, + "content": "Table 3. An ablation study of the design choices of QuantArt." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.103, + 0.89, + 0.226 + ], + "angle": 0, + "content": "
Complete model, α = 1, code size 16×16LPIPS ↓Gram ↓FID ↓
0.5810.86417.787
Remove Quantization in SGA0.5450.99318.757
Remove all Quantizations (i.e., α = 0)0.5650.39525.590
Code size 8×80.6561.07827.741
Code size 32×320.5130.79828.663
Remove self-attention in SGA0.5840.88319.025
Remove ResBlock in SGA0.6081.84127.177
Replace SGA with StyTR2 decoder layer [8]0.5390.87526.299
Shared encoders0.5880.78830.806
Shared encoders and decoders0.5930.89135.830
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.655, + 0.254 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.593 + ], + "angle": 0, + "content": "As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a \\(16 \\times 16\\) patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of \\(16 \\times 16\\) is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.6, + 0.62, + 0.615 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.848 + ], + "angle": 0, + "content": "In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. The experiments on Photo-to-Artwork, Artwork-to-Artwork, and Photo-to-Photo transfer settings have shown that our method achieves higher visual fidelity along with comparable content and style fidelities compared with the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by NIH grant 5U54CA225088-03. The computations in this paper were run on the FASRC Cannon cluster supported by Harvard." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5954" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Jie An, Siyu Huang, Yibing Song, Dejing Dou, Wei Liu, and Jiebo Luo. Artflow: Unbiased image style transfer via reversible neural flows. In CVPR, pages 862-871, 2021. 1, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Jie An, Haoyi Xiong, Jun Huan, and Jiebo Luo. Ultrafast photorealistic style transfer via neural architecture search. 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In CVPR, pages 3663-3672, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.886 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5956" + } + ] +] \ No newline at end of file diff --git a/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_origin.pdf b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..926eb5a93ca81fc6525d448957ebd9d1fb3ef7e6 --- /dev/null +++ b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d74cac926bdf6e7e878e5c935cf0192e964b4f03753745ea0baa3bb08e1a1ef3 +size 2614713 diff --git a/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/full.md b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3eb32668410b3cd663a0015c7bb209d5e900069d --- /dev/null +++ b/2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/full.md @@ -0,0 +1,377 @@ +# QuantArt: Quantizing Image Style Transfer Towards High Visual Fidelity + +Siyu Huang\* + +Jie An\* + +$^{1}$ Harvard University + +Donglai Wei3 + +$^{2}$ University of Rochester + +Jiebo Luo + +Hanspeter Pfister + +3Boston College + +{huang, pfister}@seas.harvard.com + +{jan6,jluo}@cs.ROchester.edu + +donglai.wei@bc.edu + +![](images/42bc59bb7f4a090c0a7d01879c5b898b0bdfe8704f57ddb9a7a2b4eeb8bf2ba8.jpg) +Figure 1. The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks. + +# Abstract + +The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods. + +# 1. Introduction + +Image style transfer aims at transferring the artistic style of a reference image to a content image, where the output image should have the style (e.g., colors, textures, strokes, + +and tones) of the reference and the content information of the content image. Great advances [4, 5, 13, 14, 39, 40, 63] have been made in the area of image style transfer, where the arbitrary style transfer (AST) has become one of the main research focuses. Given a trained model, AST algorithms [8, 26, 33] can perform style transfer on arbitrary unseen content-style pairs in a zero-shot manner, such that it enables more practical applications1. + +Existing AST algorithms, including the statistics-based methods [1,26,35,60] and the patch-based methods [6,47], deliver remarkable style transfer results by matching the artistic style information of the stylized image and the style reference. However, taking the high-fidelity artwork generation as the ultimate goal of image style transfer, all existing methods can still be improved since there are few mechanisms to guarantee a high artistic fidelity of the stylized image. A few existing work [3,59] accommodate the adversarial loss [15] into the style transfer framework to enhance the image quality. However, the performance improvement is hindered by the heterogeneous optimization objectives of high image quality and faithful image stylization. + +In this work, we introduce visual fidelity as a new eval + +uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution. + +We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows: + +- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization. +- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result. +- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods. + +# 2. Related Work + +Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55]. + +Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner. + +Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures. + +In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space. + +Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation. + +Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel + +oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization. + +# 3. Visual Fidelity for Image Style Transfer + +Image style transfer aims to transfer a content image $c$ , e.g., a photo, to a stylized image $y$ by a given style reference $s$ , e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as + +- Style fidelity: The style similarity between $y$ and $s$ , which is often evaluated by the Gram matrix [13, 34]. +- Content fidelity: The content similarity between $y$ and $c$ , which is often evaluated by the perceptual loss [28] or the LPIPS distance [62]. +- Visual fidelity: The realness of the generated image $y$ . Since all real artwork images belong to a distribution $\mathcal{T}$ , a generated image $y$ tends to have a higher visual fidelity if it is closer to distribution $\mathcal{T}$ . + +Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm $(\alpha = 0)$ faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image. + +To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution $\mathcal{T}$ in the representation space, where the centroids of all clusters form an artwork codebook $\mathcal{Z}_{art}$ . When making inferences, we replace the feature map at each position with its nearest centroid in $\mathcal{Z}_{art}$ . In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As + +![](images/ea0e806e62a1fc5ccb96922919a21ca5a693d33b46dfdcc3492e9b0dcfa18a8b.jpg) +Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer $w / o$ and $w/$ latent feature quantizing, respectively. + +illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation $y$ to be close to one of the centroids of the artwork distribution $\mathcal{T}$ but far away from the reference $s$ . We introduce more details of QuantArt in the following Section 4. + +# 4. Our Approach + +# 4.1. Framework Overview + +In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level $\alpha \in [0,1]$ between the SGA outputs. In the following, we discuss more details of QuantArt. + +# 4.2. Learning Auto-Encoders and Codebooks + +We first extract the features of the content image $c$ and the style reference $s$ with two convolutional encoders $E_{C}$ and $E_{S}$ , then decode the features back into images $c_{rec}$ and $s_{rec}$ with two convolutional decoders $D_{C}$ and $D_{S}$ , respec + +![](images/ac25ffe5b4ab261433e08b77ad601a9d322b24f4884808a2e54416059d33fcfb.jpg) +(a) Training Stage-1: learning the auto-encoders + +![](images/ac2d2a1f0fbd65a1b319b91a45858f1b3a822d9d1adb4ced8ebae617da6563fd.jpg) +(b) Training Stage-2: learning the SGA modules + +![](images/d1280cbf44fcdffee8a747dc2454d6a529fe42a215bd417e1ad5cf3bb1376029.jpg) +(c) Inference Stage + +tively as + +$$ +c _ {r e c} = D _ {C} \left(E _ {C} (c)\right), \quad s _ {r e c} = D _ {S} \left(E _ {S} (s)\right). \tag {1} +$$ + +This is distinct from the general neural style transfer methods, which use the VGG [48] or ResNet [18] network pretrained on natural image datasets (e.g., ImageNet [7]) as the image encoder to extract features of both content and style images. To optimize encoder $E_{C}$ and decoder $D_{C}$ , the reconstruction loss is + +$$ +\mathcal {L} _ {A E} \left(E _ {C}, D _ {C}\right) = \left| \left| c _ {r e c} - c \right| \right| + \mathcal {L} _ {a d v} \left(E _ {C}, D _ {C}, \mathbb {D} _ {C}\right), \tag {2} +$$ + +where $\mathcal{L}_{adv}$ is the adversarial training loss and $\mathbb{D}_C$ is the corresponding discriminator network, + +$$ +\mathcal {L} _ {a d v} \left(E _ {C}, D _ {C}, \mathbb {D} _ {C}\right) = \log \mathbb {D} _ {C} (c) + \log \left(1 - \mathbb {D} _ {C} \left(c _ {r e c}\right)\right). \tag {3} +$$ + +$E_{S}$ and $D_{S}$ are also optimized by the reconstruction loss $\mathcal{L}_{AE}(E_S,D_S)$ as formulated in Eq. 2. + +Next, we build two codebooks $\mathcal{Z}_{photo},\mathcal{Z}_{art}\in \mathbb{R}^{N\times d}$ to model the distributions of the photo dataset and artwork dataset, where $N$ is the number of entries in the codebook and $d$ is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as + +$$ +z _ {c} = \hat {E} _ {C} (c), \quad z _ {s} = \hat {E} _ {S} (s). \tag {4} +$$ + +We then apply vector quantization [52] to the latent features to get the quantized features $\hat{z}_c$ and $\hat{z}_s$ , where the vector quantization operator $Q_{\mathcal{Z}}(z)$ is formulated as + +$$ +Q _ {\mathcal {Z}} (z) := \underset {\mathbf {z} _ {k} \in \mathcal {Z}} {\arg \min } \| z - \mathbf {z} _ {k} \|, \tag {5} +$$ + +![](images/cb46f7ecfb30c4d4905d235429f0f9382bea836832666ccdfbecf1fcbed1de7e.jpg) +Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively. $\mathbb{Q}$ denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters $\alpha$ , $\beta \in [0,1]$ . +Figure 4. The vector quantization operator $Q_{\mathcal{Z}}(z)$ in Eq. 5. + +where $\mathbf{z}_k$ is the $k$ -th entry in the codebook $\mathcal{Z}$ . As illustrated in Fig. 4, $z$ is replaced with the nearest neighbour entry in the codebook $\mathcal{Z}$ via $Q_{\mathcal{Z}}(z)$ . The quantized features $\hat{z}_c$ and $\hat{z}_s$ are collected from codebooks $\mathcal{Z}_{photo}$ and $\mathcal{Z}_{art}$ as + +$$ +\hat {z} _ {c} = Q _ {\mathcal {Z} _ {\text {p h o t o}}} \left(z _ {c}\right), \quad \hat {z} _ {s} = Q _ {\mathcal {Z} _ {\text {a r t}}} \left(z _ {s}\right), \tag {6} +$$ + +The quantized features $\hat{z}_c$ and $\hat{z}_s$ are decoded into images $\hat{c}_{rec}$ and $\hat{s}_{rec}$ via the decoders $\hat{D}_C$ and $\hat{D}_S$ , as + +$$ +\hat {c} _ {r e c} = \hat {D} _ {C} (\hat {z} _ {c}), \quad \hat {s} _ {r e c} = \hat {D} _ {S} (\hat {z} _ {s}). \tag {7} +$$ + +By following [52], we optimize the codebook $\mathcal{Z}_{\text{photo}}$ jointly with the reconstruction loss in Eq. 2. The reconstruction loss for encoder $\hat{E}_C$ , decoder $\hat{D}_C$ , and codebook $\mathcal{Z}_{\text{photo}}$ is + +$$ +\mathcal {L} _ {\hat {A E}} \left(\hat {E} _ {C}, \hat {D} _ {C}, \mathcal {Z} _ {\text {p h o t o}}\right) = \mathcal {L} _ {A E} \left(\hat {E} _ {C}, \hat {D} _ {C}\right) + \tag {8} +$$ + +$$ +\left. \left| \left| \left| \mathbf {s g} \left[ z _ {c} \right] - \hat {z} _ {c} \right| \right| \right| + \left| \left| \mathbf {s g} \left[ \hat {z} _ {c} \right] - z _ {c} \right| \right| \right|, +$$ + +where $\mathfrak{sg}[\cdot ]$ indicates the stop gradient operator. The second term in Eq. 8 optimizes the codebook $\mathcal{Z}_{photo}$ , while, the third term in Eq. 8 forces the latent feature $z_{c}$ to be close to the nearest neighbor entry in $\mathcal{Z}_{photo}$ . $\hat{E}_S$ , $\hat{D}_S$ , and $\mathcal{Z}_{art}$ are + +![](images/160f7f6d0f3d8ada59a5ab01001c878a8323a7adfe37719c6c6e5c63c755a993.jpg) +Figure 5. The SGA module proposed for feature style transfer. + +also optimized by the loss function $\mathcal{L}_{\hat{A}E}(\hat{E}_S, \hat{D}_S, \mathcal{Z}_{art})$ as formulated in Eq. 8. + +After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features. + +# 4.3. Style Transfer with Style Guided Attention + +To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature $z_{c} \in \mathbb{R}^{d}$ and style reference feature $z_{s} \in \mathbb{R}^{d}$ as inputs, then outputs the stylized feature vector $z_{y} \in \mathbb{R}^{d}$ . It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query $q$ , key $k$ , and value $v$ as inputs, + +$$ +\operatorname {A t t n} (q, k, v) = \operatorname {s o f t m a x} \left(f _ {q} (q) f _ {k} (k)\right) f _ {v} (v) + q, \tag {9} +$$ + +where $f_{q}, f_{k}, f_{v}$ are the embedding layers. The first attention block is a self-attention block that all its input heads $q, k, v$ accept the transformed content feature $\tilde{z}_{c} = \mathrm{ResBlock}(z_{c})$ . The second attention block takes $\tilde{z}_{c}$ as $q$ , and the style reference feature $z_{s}$ as $k$ and $v$ . The output of the SGA module is formulated as + +$$ +z _ {y} = \operatorname {S G A} \left(z _ {c}, z _ {s}\right) = \operatorname {A t t n} \left(\operatorname {A t t n} \left(\tilde {z} _ {c}, \tilde {z} _ {c}, \tilde {z} _ {c}\right), z _ {s}, z _ {s}\right). \tag {10} +$$ + +Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for $M$ times to achieve a better style transfer performance. + +The objective function for $\mathrm{SGA}(z_c, z_s)$ includes the content loss $\mathcal{L}_{\text {content }}$ , style loss $\mathcal{L}_{\text {style }}$ , and adversarial training loss $\mathcal{L}_{\text {featadv }}$ + +$$ +\mathcal {L} _ {S G A} = \mathcal {L} _ {\text {c o n t e n t}} + \mathcal {L} _ {\text {s t y l e}} + \mathcal {L} _ {\text {f e a t a d v}} \tag {11} +$$ + +where + +$$ +\mathcal {L} _ {\text {c o n t e n t}} = \left| \left| z _ {y} - z _ {c} \right| \right|, \tag {12} +$$ + +$$ +\mathcal {L} _ {\text {s t y l e}} = \left| \left| \mu \left(z _ {y}\right) - \mu \left(z _ {s}\right) \right| \right| + \left| \left| \sigma \left(z _ {y}\right) - \sigma \left(z _ {s}\right) \right| \right|, \tag {13} +$$ + +$$ +\mathcal {L} _ {\text {f e a t a d v}} = \log \mathbb {D} _ {S G A} \left(z _ {s}\right) + \log \left(1 - \mathbb {D} _ {S G A} \left(z _ {y}\right)\right). \tag {14} +$$ + +$\mu (\cdot)$ and $\sigma (\cdot)$ denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss $\mathcal{L}_{featadv}$ is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features. + +We adopt another SGA module to transfer the quantized features $\hat{z}_c$ and $\hat{z}_s$ , as + +$$ +\hat {z} _ {y} = Q _ {\mathcal {Z} _ {a r t}} \left(\mathrm {S} \hat {\mathrm {G A}} \left(\hat {z} _ {c}, \hat {z} _ {s}\right)\right). \tag {15} +$$ + +$\hat{\mathrm{SGA}} (\cdot ,\cdot)$ and $\mathrm{SGA}(\cdot ,\cdot)$ have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook $Q_{\mathcal{Z}_{art}}$ to ensure that the output is on the latent space of the decoder $\hat{D}_S$ . The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as + +$$ +\mathcal {L} _ {S \hat {G} A} = \mathcal {L} _ {S G A} + | | \operatorname {s g} [ \hat {z} _ {y} ] - z _ {y} ] | | \tag {16} +$$ + +# 4.4. Inference + +Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature $z_{y}$ and stylized quantized feature $\hat{z}_{y}$ by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have + +$$ +z _ {t e s t} = \oplus_ {\alpha} \left(\oplus_ {\beta} \left(\hat {z} _ {y}, \hat {z} _ {c}\right), \oplus_ {\beta} \left(z _ {y}, z _ {c}\right)\right), \tag {17} +$$ + +where $z_{c}$ and $\hat{z}_{c}$ are the content features, and $\oplus$ is the weighted sum operator as $\oplus_{p}(a,b) = pa + (1 - p)b$ . $z_{test}$ is decoded into a stylized image with a fused decoder $\bar{D}_S = \oplus_\alpha (\hat{D}_S, D_S)$ . $\beta$ controls the style fidelity, and a larger $\alpha$ results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt $(\alpha, \beta)$ provides a simple and easy-to-understand handle grip for users to adjust the style transfer results. + +Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2. + +# 5. Experiments + +# 5.1. Experiment Settings + +Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the "genre" tag of "landscape" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to $256 \times 256$ pixels. + +Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of $16 \times 16$ and a feature dimension of 256. The codebook has $N = 1024$ entries and an entry dimension of $d = 256$ . The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of $4.5 \times 10^{-6}$ , and a training epoch of 50. The loss weights of $\mathcal{L}_{AE}$ , $\mathcal{L}_{codebook}$ , $\mathcal{L}_{content}$ , $\mathcal{L}_{style}$ , and $\mathcal{L}_{adv}$ are set to 1, 1, 1, 10, and 0.8, respectively. + +# 5.2. Multi-Fidelity Image Style Transfer + +Our QuantArt $(\alpha, \beta)$ method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations $(\alpha, \beta)$ . When the style fidelity $\beta = 0$ , the model simply reconstructs the input content image. With $\beta = 1$ and visual fidelity $\alpha \rightarrow 1$ , the generated images look more vivid but lose some texture details in the style reference. Note that neither $\alpha = 0$ or $\alpha = 1$ performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application. + +# 5.3. Comparing with State-of-the-Art Methods + +For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo). + +Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ + +![](images/0ea38468e5bfb276d569aad85470814cc8b043d7aaccf68370804f3491193cb7.jpg) +Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters $\alpha$ and $\beta$ . + +ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23]. + +Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with $\alpha = 0$ faithfully transfers the texture from input style images, while QuantArt with $\alpha = 1$ paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up. + +Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity + +![](images/e964907757c64c85ee7a27697627f8715b94151b611710cbc5ad040647f0e637.jpg) +Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details. + +Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively. + +
Metric ↓AdaINWCTLinearWCTArtFlowEFDMStyleSwapAvatarNetSANetAdaAttNStyTR2Ours (α,β)
(0,0)(0,1)(1,1)
LPIPS ↓0.6810.6950.6570.6030.6520.6070.7060.6860.6330.5140.1590.5650.581
Gram loss (×103) ↓0.1630.2820.1720.1010.4021.3570.7180.1200.2460.386-0.3950.864
FID ↓36.61865.19348.15628.89951.07074.16858.17827.08025.89430.893-25.59017.787
ArtFID ↓63.240112.22981.45247.93686.007120.803100.96447.35643.91048.284-41.62329.695
+ +Table 2. Inference time (seconds) of a ${256} \times {256}$ image with a NVIDIA Tesla V100 GPU. + +
ArtFlowStyleSwapAvatarNetSANetAdaAttNStyTR2Ours
0.0680.0430.1240.0070.0500.0550.045
+ +of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods. + +# 5.4. Human Evaluation + +Since image style transfer is a highly subjective task, we further examine our model with human evaluation. + +User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare + +AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of $43.5\%$ , $51.9\%$ , and $40.2\%$ , respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms. + +Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion + +![](images/5ea829693dccf9eccfff22df3be7907edaa320f041d58d5fefd289eb61864477.jpg) +Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants. + +![](images/ec0c8b7c38d60a90feb3b500c505578a52640aecf1be85c0ed716e51f816b71f.jpg) +Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only $40.6\%$ participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions. + +![](images/613c40009b5f91ef1043a14331813d61d890f57bce3b95c76aa289865b6bab3d.jpg) + +test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of $i$ a real artwork image $s$ and $ii$ a photo stylized according to the reference of $s$ . The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants. + +We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material. + +Table 3. An ablation study of the design choices of QuantArt. + +
Complete model, α = 1, code size 16×16LPIPS ↓Gram ↓FID ↓
0.5810.86417.787
Remove Quantization in SGA0.5450.99318.757
Remove all Quantizations (i.e., α = 0)0.5650.39525.590
Code size 8×80.6561.07827.741
Code size 32×320.5130.79828.663
Remove self-attention in SGA0.5840.88319.025
Remove ResBlock in SGA0.6081.84127.177
Replace SGA with StyTR2 decoder layer [8]0.5390.87526.299
Shared encoders0.5880.78830.806
Shared encoders and decoders0.5930.89135.830
+ +# 5.5. Ablation Study + +As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a $16 \times 16$ patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of $16 \times 16$ is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction. + +# 6. Conclusion + +In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. 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The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 143, + 422, + 192, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 422, + 192, + 435 + ], + "spans": [ + { + "bbox": [ + 143, + 422, + 192, + 435 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 449, + 290, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 290, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 290, + 641 + ], + "type": "text", + "content": "The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Image style transfer aims at transferring the artistic style of a reference image to a content image, where the output image should have the style (e.g., colors, textures, strokes," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 423, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 546, + 519 + ], + "type": "text", + "content": "and tones) of the reference and the content information of the content image. Great advances [4, 5, 13, 14, 39, 40, 63] have been made in the area of image style transfer, where the arbitrary style transfer (AST) has become one of the main research focuses. Given a trained model, AST algorithms [8, 26, 33] can perform style transfer on arbitrary unseen content-style pairs in a zero-shot manner, such that it enables more practical applications1." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 520, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 547, + 674 + ], + "type": "text", + "content": "Existing AST algorithms, including the statistics-based methods [1,26,35,60] and the patch-based methods [6,47], deliver remarkable style transfer results by matching the artistic style information of the stylized image and the style reference. However, taking the high-fidelity artwork generation as the ultimate goal of image style transfer, all existing methods can still be improved since there are few mechanisms to guarantee a high artistic fidelity of the stylized image. A few existing work [3,59] accommodate the adversarial loss [15] into the style transfer framework to enhance the image quality. However, the performance improvement is hindered by the heterogeneous optimization objectives of high image quality and faithful image stylization." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 675, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 675, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 317, + 675, + 545, + 687 + ], + "type": "text", + "content": "In this work, we introduce visual fidelity as a new eval" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1The codes of this paper are available at https://github.com/siyuhuang/QuantArt" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5947" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 515 + ], + "type": "text", + "content": "We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 521, + 286, + 658 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 521, + 286, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 521, + 286, + 556 + ], + "spans": [ + { + "bbox": [ + 59, + 521, + 286, + 556 + ], + "type": "text", + "content": "- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 560, + 286, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 560, + 286, + 608 + ], + "spans": [ + { + "bbox": [ + 58, + 560, + 286, + 608 + ], + "type": "text", + "content": "- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 612, + 286, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 612, + 286, + 658 + ], + "spans": [ + { + "bbox": [ + 58, + 612, + 286, + 658 + ], + "type": "text", + "content": "- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 670, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 134, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 158, + 546, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 546, + 384 + ], + "type": "text", + "content": "Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 387, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 506 + ], + "type": "text", + "content": "In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 509, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 687 + ], + "type": "text", + "content": "Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5948" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 190, + 265, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 190, + 265, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 265, + 205 + ], + "type": "text", + "content": "3. Visual Fidelity for Image Style Transfer" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "text", + "content": "Image style transfer aims to transfer a content image " + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "text", + "content": ", e.g., a photo, to a stylized image " + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "text", + "content": " by a given style reference " + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 211, + 289, + 318 + ], + "type": "text", + "content": ", e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 327, + 287, + 441 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "spans": [ + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "text", + "content": "- Style fidelity: The style similarity between " + }, + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 58, + 327, + 286, + 350 + ], + "type": "text", + "content": ", which is often evaluated by the Gram matrix [13, 34]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "text", + "content": "- Content fidelity: The content similarity between " + }, + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 58, + 354, + 287, + 389 + ], + "type": "text", + "content": ", which is often evaluated by the perceptual loss [28] or the LPIPS distance [62]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "content": "- Visual fidelity: The realness of the generated image " + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "content": ". Since all real artwork images belong to a distribution " + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "content": ", a generated image " + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "content": " tends to have a higher visual fidelity if it is closer to distribution " + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 58, + 394, + 287, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "content": "Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm " + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha = 0)" + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "content": " faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " in the representation space, where the centroids of all clusters form an artwork codebook " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{art}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": ". When making inferences, we replace the feature map at each position with its nearest centroid in " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{art}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": ". In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 210 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 210 + ], + "type": "image", + "image_path": "ea0e806e62a1fc5ccb96922919a21ca5a693d33b46dfdcc3492e9b0dcfa18a8b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "type": "text", + "content": "Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer " + }, + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 305, + 217, + 547, + 283 + ], + "type": "text", + "content": " latent feature quantizing, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "text", + "content": "illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation " + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "text", + "content": " to be close to one of the centroids of the artwork distribution " + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "text", + "content": " but far away from the reference " + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 304, + 547, + 364 + ], + "type": "text", + "content": ". We introduce more details of QuantArt in the following Section 4." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 378, + 397, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 397, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 397, + 392 + ], + "type": "text", + "content": "4. Our Approach" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 399, + 432, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 432, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 432, + 411 + ], + "type": "text", + "content": "4.1. Framework Overview" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\alpha \\in [0,1]" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": " between the SGA outputs. In the following, we discuss more details of QuantArt." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 646, + 520, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 520, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 520, + 658 + ], + "type": "text", + "content": "4.2. Learning Auto-Encoders and Codebooks" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "text", + "content": "We first extract the features of the content image " + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "text", + "content": " and the style reference " + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "text", + "content": " with two convolutional encoders " + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "inline_equation", + "content": "E_{C}" + }, + { + "bbox": [ + 305, + 666, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + 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style images. To optimize encoder " + }, + { + "bbox": [ + 46, + 377, + 287, + 448 + ], + "type": "inline_equation", + "content": "E_{C}" + }, + { + "bbox": [ + 46, + 377, + 287, + 448 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 46, + 377, + 287, + 448 + ], + "type": "inline_equation", + "content": "D_{C}" + }, + { + "bbox": [ + 46, + 377, + 287, + 448 + ], + "type": "text", + "content": ", the reconstruction loss is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 456, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 456, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 53, + 456, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {A E} \\left(E _ {C}, D _ {C}\\right) = \\left| \\left| c _ {r e c} - c \\right| \\right| + \\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right), \\tag {2}", + "image_path": "44281c347878445ea70b19bfcb35bfc2f86d5f6d1c77f7b2260b71e7ec54353f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "content": " is the adversarial training loss and " + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathbb{D}_C" + }, + { + "bbox": [ + 47, + 475, + 287, + 499 + ], + "type": "text", + "content": " is the corresponding discriminator network," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 506, + 286, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 506, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 53, + 506, + 286, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right) = \\log \\mathbb {D} _ {C} (c) + \\log \\left(1 - \\mathbb {D} _ {C} \\left(c _ {r e c}\\right)\\right). \\tag {3}", + "image_path": "48ddf26fd1909260dc2476ddee54fb4a2f45b03c3e3086fb129df11cc1a7e0b2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "inline_equation", + "content": "E_{S}" + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "inline_equation", + "content": "D_{S}" + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "text", + "content": " are also optimized by the reconstruction loss " + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{AE}(E_S,D_S)" + }, + { + "bbox": [ + 47, + 531, + 287, + 553 + ], + "type": "text", + "content": " as formulated in Eq. 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "text", + "content": "Next, we build two codebooks " + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{photo},\\mathcal{Z}_{art}\\in \\mathbb{R}^{N\\times d}" + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "text", + "content": " to model the distributions of the photo dataset and artwork dataset, where " + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "text", + "content": " is the number of entries in the codebook and " + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 554, + 287, + 626 + ], + "type": "text", + "content": " is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 632, + 287, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 632, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 287, + 646 + ], + "type": "interline_equation", + "content": "z _ {c} = \\hat {E} _ {C} (c), \\quad z _ {s} = \\hat {E} _ {S} (s). \\tag {4}", + "image_path": "438b897a8fc7008a80a6910ca4c17a0fae9d1a87a0c71190a901d72f2dabee7e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "text", + "content": "We then apply vector quantization [52] to the latent features to get the quantized features " + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\hat{z}_c" + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\hat{z}_s" + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "text", + "content": ", where the vector quantization operator " + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "Q_{\\mathcal{Z}}(z)" + }, + { + "bbox": [ + 47, + 653, + 287, + 689 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 696, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 696, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 287, + 715 + ], + "type": "interline_equation", + "content": "Q _ {\\mathcal {Z}} (z) := \\underset {\\mathbf {z} _ {k} \\in \\mathcal {Z}} {\\arg \\min } \\| z - \\mathbf {z} _ {k} \\|, \\tag {5}", + "image_path": "b36db66bbab199f58f4a96db4ae28baabdfe3a2955ef781ff06e78de33b82978.jpg" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 324, + 341, + 525, + 410 + ], + "blocks": [ + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "text", + "content": "Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively. " + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}" + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "text", + "content": " denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters " + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "inline_equation", + "content": "\\beta \\in [0,1]" + }, + { + "bbox": [ + 46, + 278, + 547, + 323 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 324, + 341, + 525, + 410 + ], + "lines": [ + { + "bbox": [ + 324, + 341, + 525, + 410 + ], + "spans": [ + { + "bbox": [ + 324, + 341, + 525, + 410 + ], + "type": "image", + "image_path": "cb46f7ecfb30c4d4905d235429f0f9382bea836832666ccdfbecf1fcbed1de7e.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 418, + 533, + 430 + ], + "lines": [ + { + "bbox": [ + 317, + 418, + 533, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 418, + 533, + 430 + ], + "type": "text", + "content": "Figure 4. The vector quantization operator " + }, + { + "bbox": [ + 317, + 418, + 533, + 430 + ], + "type": "inline_equation", + "content": "Q_{\\mathcal{Z}}(z)" + }, + { + "bbox": [ + 317, + 418, + 533, + 430 + ], + "type": "text", + "content": " in Eq. 5." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_k" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": "-th entry in the codebook " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": ". As illustrated in Fig. 4, " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": " is replaced with the nearest neighbour entry in the codebook " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "inline_equation", + "content": "Q_{\\mathcal{Z}}(z)" + }, + { + "bbox": [ + 305, + 446, + 545, + 495 + ], + "type": "text", + "content": ". 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The second term in Eq. 8 optimizes the codebook " + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{photo}" + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": ", while, the third term in Eq. 8 forces the latent feature " + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "z_{c}" + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": " to be close to the nearest neighbor entry in " + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{photo}" + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": ". 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The SGA module proposed for feature style transfer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 191, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 191, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 287, + 215 + ], + "type": "text", + "content": "also optimized by the loss function " + }, + { + "bbox": [ + 47, + 191, + 287, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\hat{A}E}(\\hat{E}_S, \\hat{D}_S, \\mathcal{Z}_{art})" + }, + { + "bbox": [ + 47, + 191, + 287, + 215 + ], + "type": "text", + "content": " as formulated in Eq. 8." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 216, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 275 + ], + "type": "text", + "content": "After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 281, + 271, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 271, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 271, + 294 + ], + "type": "text", + "content": "4.3. Style Transfer with Style Guided Attention" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": "To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "z_{c} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": " and style reference feature " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "z_{s} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": " as inputs, then outputs the stylized feature vector " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "z_{y} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": ". It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 300, + 287, + 420 + ], + "type": "text", + "content": " as inputs," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 426, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 426, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 64, + 426, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t n} (q, k, v) = \\operatorname {s o f t m a x} \\left(f _ {q} (q) f _ {k} (k)\\right) f _ {v} (v) + q, \\tag {9}", + "image_path": "6312e0ffe68111c0ff1d62b42b3741de9ecf139e76bdfa3d6fd6b9fc1df60104.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "f_{q}, f_{k}, f_{v}" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": " are the embedding layers. The first attention block is a self-attention block that all its input heads " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "q, k, v" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": " accept the transformed content feature " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\tilde{z}_{c} = \\mathrm{ResBlock}(z_{c})" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": ". The second attention block takes " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\tilde{z}_{c}" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": ", and the style reference feature " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "z_{s}" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 446, + 287, + 517 + ], + "type": "text", + "content": ". The output of the SGA module is formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 524, + 287, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 524, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 56, + 524, + 287, + 538 + ], + "type": "interline_equation", + "content": "z _ {y} = \\operatorname {S G A} \\left(z _ {c}, z _ {s}\\right) = \\operatorname {A t t n} \\left(\\operatorname {A t t n} \\left(\\tilde {z} _ {c}, \\tilde {z} _ {c}, \\tilde {z} _ {c}\\right), z _ {s}, z _ {s}\\right). \\tag {10}", + "image_path": "1e9bcfdbc5cad57787c7633f136c3051a57f1469d48ea150f4dc6ca0c3525d67.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 544, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 287, + 627 + ], + "type": "text", + "content": "Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for " + }, + { + "bbox": [ + 47, + 544, + 287, + 627 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 544, + 287, + 627 + ], + "type": "text", + "content": " times to achieve a better style transfer performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "text", + "content": "The objective function for " + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{SGA}(z_c, z_s)" + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "text", + "content": " includes the content loss " + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {content }}" + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "text", + "content": ", style loss " + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {style }}" + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "text", + "content": ", and adversarial training loss " + }, + { + "bbox": [ + 47, + 628, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {featadv }}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 670, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 670, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 86, + 670, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S G A} = \\mathcal {L} _ {\\text {c o n t e n t}} + \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {f e a t a d v}} \\tag {11}", + "image_path": "c2947643c10121e22c74382f491d3a2c04b1f50f78a55071014734ac849eacf7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 75, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 75, + 700 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 75, + 700 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 119, + 700, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 700, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 119, + 700, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n t e n t}} = \\left| \\left| z _ {y} - z _ {c} \\right| \\right|, \\tag {12}", + "image_path": "1bf5bbd15bfb7e1a0426f352e64ff03137b0413579840053c2582c31db750e3a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 72, + 545, + 85 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 72, + 545, + 85 + ], + "spans": [ + { + "bbox": [ + 320, + 72, + 545, + 85 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t y l e}} = \\left| \\left| \\mu \\left(z _ {y}\\right) - \\mu \\left(z _ {s}\\right) \\right| \\right| + \\left| \\left| \\sigma \\left(z _ {y}\\right) - \\sigma \\left(z _ {s}\\right) \\right| \\right|, \\tag {13}", + "image_path": "882b2e006964b00ddd4bef31a43e916c36368474fd0178a9bdf6d33e25d0b49c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 89, + 545, + 102 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 89, + 545, + 102 + ], + "spans": [ + { + "bbox": [ + 315, + 89, + 545, + 102 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t a d v}} = \\log \\mathbb {D} _ {S G A} \\left(z _ {s}\\right) + \\log \\left(1 - \\mathbb {D} _ {S G A} \\left(z _ {y}\\right)\\right). \\tag {14}", + "image_path": "68913fecfa17c22a1b6256fabbe94a2f9e0adc9f1e3ad4b3d9588096e81bcc47.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mu (\\cdot)" + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "text", + "content": " denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss " + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{featadv}" + }, + { + "bbox": [ + 305, + 106, + 545, + 212 + ], + "type": "text", + "content": " is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "text", + "content": "We adopt another SGA module to transfer the quantized features " + }, + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "inline_equation", + "content": "\\hat{z}_c" + }, + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "inline_equation", + "content": "\\hat{z}_s" + }, + { + "bbox": [ + 305, + 213, + 545, + 237 + ], + "type": "text", + "content": ", as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 370, + 245, + 545, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 245, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 370, + 245, + 545, + 259 + ], + "type": "interline_equation", + "content": "\\hat {z} _ {y} = Q _ {\\mathcal {Z} _ {a r t}} \\left(\\mathrm {S} \\hat {\\mathrm {G A}} \\left(\\hat {z} _ {c}, \\hat {z} _ {s}\\right)\\right). \\tag {15}", + "image_path": "5a8eb32a6652c4d0c09947f805bf5121ab781c29b21994944383154c532f3f32.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\hat{\\mathrm{SGA}} (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{SGA}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "text", + "content": " have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook " + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "inline_equation", + "content": "Q_{\\mathcal{Z}_{art}}" + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "text", + "content": " to ensure that the output is on the latent space of the decoder " + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\hat{D}_S" + }, + { + "bbox": [ + 305, + 266, + 545, + 338 + ], + "type": "text", + "content": ". The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 357, + 347, + 545, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 347, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 357, + 347, + 545, + 361 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S \\hat {G} A} = \\mathcal {L} _ {S G A} + | | \\operatorname {s g} [ \\hat {z} _ {y} ] - z _ {y} ] | | \\tag {16}", + "image_path": "73d3ee2c84489e0cd440710d2327e4ad0fa44d743952954e7a8591b7c3a14bea.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 368, + 373, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 368, + 373, + 379 + ], + "spans": [ + { + "bbox": [ + 306, + 368, + 373, + 379 + ], + "type": "text", + "content": "4.4. Inference" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "text", + "content": "Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature " + }, + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "inline_equation", + "content": "z_{y}" + }, + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "text", + "content": " and stylized quantized feature " + }, + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "inline_equation", + "content": "\\hat{z}_{y}" + }, + { + "bbox": [ + 305, + 386, + 545, + 481 + ], + "type": "text", + "content": " by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 350, + 489, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 489, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 350, + 489, + 545, + 503 + ], + "type": "interline_equation", + "content": "z _ {t e s t} = \\oplus_ {\\alpha} \\left(\\oplus_ {\\beta} \\left(\\hat {z} _ {y}, \\hat {z} _ {c}\\right), \\oplus_ {\\beta} \\left(z _ {y}, z _ {c}\\right)\\right), \\tag {17}", + "image_path": "8769c9279b99408db8faae3bc817a6a0b8f966922077736e40653104ab14d562.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "z_{c}" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\hat{z}_{c}" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " are the content features, and " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " is the weighted sum operator as " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\oplus_{p}(a,b) = pa + (1 - p)b" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "z_{test}" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " is decoded into a stylized image with a fused decoder " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\bar{D}_S = \\oplus_\\alpha (\\hat{D}_S, D_S)" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " controls the style fidelity, and a larger " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt " + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "inline_equation", + "content": "(\\alpha, \\beta)" + }, + { + "bbox": [ + 305, + 510, + 545, + 617 + ], + "type": "text", + "content": " provides a simple and easy-to-understand handle grip for users to adjust the style transfer results." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "content": "Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5951" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 165, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 165, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 165, + 104 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 252 + ], + "type": "text", + "content": "Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the \"genre\" tag of \"landscape\" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to " + }, + { + "bbox": [ + 46, + 110, + 287, + 252 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 110, + 287, + 252 + ], + "type": "text", + "content": " pixels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": "Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": " and a feature dimension of 256. The codebook has " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "N = 1024" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": " entries and an entry dimension of " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "d = 256" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ". The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "4.5 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ", and a training epoch of 50. The loss weights of " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{AE}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{codebook}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{content}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{style}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 46, + 253, + 288, + 397 + ], + "type": "text", + "content": " are set to 1, 1, 1, 10, and 0.8, respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 404, + 237, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 237, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 237, + 417 + ], + "type": "text", + "content": "5.2. Multi-Fidelity Image Style Transfer" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": "Our QuantArt " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "(\\alpha, \\beta)" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "(\\alpha, \\beta)" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ". When the style fidelity " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", the model simply reconstructs the input content image. With " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " and visual fidelity " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\alpha \\rightarrow 1" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", the generated images look more vivid but lose some texture details in the style reference. Note that neither " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 574, + 268, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 268, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 268, + 588 + ], + "type": "text", + "content": "5.3. Comparing with State-of-the-Art Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "content": "For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 255 + ], + "type": "image", + "image_path": "0ea38468e5bfb276d569aad85470814cc8b043d7aaccf68370804f3491193cb7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "type": "text", + "content": "Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters " + }, + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 258, + 545, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 293, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 353 + ], + "type": "text", + "content": "ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "text", + "content": "Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with " + }, + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "text", + "content": " faithfully transfers the texture from input style images, while QuantArt with " + }, + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 304, + 354, + 545, + 449 + ], + "type": "text", + "content": " paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 450, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 714 + ], + "type": "text", + "content": "Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5952" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 395 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 395 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 395 + ], + "type": "image", + "image_path": "e964907757c64c85ee7a27697627f8715b94151b611710cbc5ad040647f0e637.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 397, + 546, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 397, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 546, + 420 + ], + "type": "text", + "content": "Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 437, + 545, + 494 + ], + "blocks": [ + { + "bbox": [ + 51, + 426, + 541, + 437 + ], + "lines": [ + { + "bbox": [ + 51, + 426, + 541, + 437 + ], + "spans": [ + { + "bbox": [ + 51, + 426, + 541, + 437 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 437, + 545, + 494 + ], + "lines": [ + { + "bbox": [ + 49, + 437, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 49, + 437, + 545, + 494 + ], + "type": "table", + "html": "
Metric ↓AdaINWCTLinearWCTArtFlowEFDMStyleSwapAvatarNetSANetAdaAttNStyTR2Ours (α,β)
(0,0)(0,1)(1,1)
LPIPS ↓0.6810.6950.6570.6030.6520.6070.7060.6860.6330.5140.1590.5650.581
Gram loss (×103) ↓0.1630.2820.1720.1010.4021.3570.7180.1200.2460.386-0.3950.864
FID ↓36.61865.19348.15628.89951.07074.16858.17827.08025.89430.893-25.59017.787
ArtFID ↓63.240112.22981.45247.93686.007120.803100.96447.35643.91048.284-41.62329.695
", + "image_path": "b8031b1d9c0d7d137e10bbc43c159f0de46daaf27a75aa6ca842e763f474e160.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 525, + 287, + 544 + ], + "blocks": [ + { + "bbox": [ + 47, + 503, + 287, + 523 + ], + "lines": [ + { + "bbox": [ + 47, + 503, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 287, + 523 + ], + "type": "text", + "content": "Table 2. Inference time (seconds) of a " + }, + { + "bbox": [ + 47, + 503, + 287, + 523 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 47, + 503, + 287, + 523 + ], + "type": "text", + "content": " image with a NVIDIA Tesla V100 GPU." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 525, + 287, + 544 + ], + "lines": [ + { + "bbox": [ + 48, + 525, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 48, + 525, + 287, + 544 + ], + "type": "table", + "html": "
ArtFlowStyleSwapAvatarNetSANetAdaAttNStyTR2Ours
0.0680.0430.1240.0070.0500.0550.045
", + "image_path": "7a1f2709943b9df147ab823a32df2c9faa3d8daa8a328e5939b374777b5934ec.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 555, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 615 + ], + "type": "text", + "content": "of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 623, + 160, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 160, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 160, + 634 + ], + "type": "text", + "content": "5.4. Human Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 665 + ], + "type": "text", + "content": "Since image style transfer is a highly subjective task, we further examine our model with human evaluation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": "User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "text", + "content": "AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of " + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "inline_equation", + "content": "43.5\\%" + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "inline_equation", + "content": "51.9\\%" + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "inline_equation", + "content": "40.2\\%" + }, + { + "bbox": [ + 304, + 505, + 547, + 685 + ], + "type": "text", + "content": ", respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5953" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 72, + 282, + 158 + ], + "blocks": [ + { + "bbox": [ + 54, + 72, + 282, + 158 + ], + "lines": [ + { + "bbox": [ + 54, + 72, + 282, + 158 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 282, + 158 + ], + "type": "image", + "image_path": "5ea829693dccf9eccfff22df3be7907edaa320f041d58d5fefd289eb61864477.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 161, + 287, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 161, + 287, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 161, + 287, + 185 + ], + "type": "text", + "content": "Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 198, + 155, + 262 + ], + "blocks": [ + { + "bbox": [ + 48, + 198, + 155, + 262 + ], + "lines": [ + { + "bbox": [ + 48, + 198, + 155, + 262 + ], + "spans": [ + { + "bbox": [ + 48, + 198, + 155, + 262 + ], + "type": "image", + "image_path": "ec0c8b7c38d60a90feb3b500c505578a52640aecf1be85c0ed716e51f816b71f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 289, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 326 + ], + "type": "text", + "content": "Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only " + }, + { + "bbox": [ + 46, + 270, + 289, + 326 + ], + "type": "inline_equation", + "content": "40.6\\%" + }, + { + "bbox": [ + 46, + 270, + 289, + 326 + ], + "type": "text", + "content": " participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 165, + 198, + 282, + 265 + ], + "blocks": [ + { + "bbox": [ + 165, + 198, + 282, + 265 + ], + "lines": [ + { + "bbox": [ + 165, + 198, + 282, + 265 + ], + "spans": [ + { + "bbox": [ + 165, + 198, + 282, + 265 + ], + "type": "image", + "image_path": "613c40009b5f91ef1043a14331813d61d890f57bce3b95c76aa289865b6bab3d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "content": "test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of " + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "content": " a real artwork image " + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "inline_equation", + "content": "ii" + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "content": " a photo stylized according to the reference of " + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 345, + 289, + 597 + ], + "type": "text", + "content": ". The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 81, + 544, + 178 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 537, + 81 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 537, + 81 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 537, + 81 + ], + "type": "text", + "content": "Table 3. An ablation study of the design choices of QuantArt." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 81, + 544, + 178 + ], + "lines": [ + { + "bbox": [ + 309, + 81, + 544, + 178 + ], + "spans": [ + { + "bbox": [ + 309, + 81, + 544, + 178 + ], + "type": "table", + "html": "
Complete model, α = 1, code size 16×16LPIPS ↓Gram ↓FID ↓
0.5810.86417.787
Remove Quantization in SGA0.5450.99318.757
Remove all Quantizations (i.e., α = 0)0.5650.39525.590
Code size 8×80.6561.07827.741
Code size 32×320.5130.79828.663
Remove self-attention in SGA0.5840.88319.025
Remove ResBlock in SGA0.6081.84127.177
Replace SGA with StyTR2 decoder layer [8]0.5390.87526.299
Shared encoders0.5880.78830.806
Shared encoders and decoders0.5930.89135.830
", + "image_path": "6c91ee916ea84960fa663fccc51d51c496db39f08518208c4df8ce24a2c31ef4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 188, + 400, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 400, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 400, + 201 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "text", + "content": "As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a " + }, + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "text", + "content": " patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of " + }, + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 304, + 206, + 547, + 469 + ], + "type": "text", + "content": " is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 491, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 671 + ], + "type": "text", + "content": "In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. The experiments on Photo-to-Artwork, Artwork-to-Artwork, and Photo-to-Photo transfer settings have shown that our method achieves higher visual fidelity along with comparable content and style fidelities compared with the state-of-the-art methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by NIH grant 5U54CA225088-03. 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To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments.", + "bbox": [ + 75, + 344, + 473, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 603, + 209, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks.", + "bbox": [ + 75, + 628, + 468, + 796 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24,", + "bbox": [ + 75, + 797, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f1e089957a4f5afcd2ebab912a669f305db80ccb8a17b9b534093268daeac94.jpg", + "image_caption": [ + "Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes." + ], + "image_footnote": [], + "bbox": [ + 517, + 306, + 874, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention.", + "bbox": [ + 496, + 612, + 892, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Work done during at LG Electronics", + "bbox": [ + 94, + 886, + 295, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8529", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective.", + "bbox": [ + 76, + 90, + 472, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 508, + 227, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Latent Space Image Manipulation", + "text_level": 1, + "bbox": [ + 76, + 532, + 375, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data.", + "bbox": [ + 76, + 554, + 472, + 843 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. 3D Object Manipulation", + "text_level": 1, + "bbox": [ + 76, + 848, + 302, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM).", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes.", + "bbox": [ + 496, + 257, + 893, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Efficient Geometry-Aware 3D GANs (EG3D)", + "text_level": 1, + "bbox": [ + 500, + 386, + 879, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature $z$ into intermediate latent feature $w$ , then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature $w$ . Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency.", + "bbox": [ + 496, + 409, + 893, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 664, + 591, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature $w_{s}$ , which is obtained from a source image $I_{s}$ , is manipulated to target latent feature $w_{t}$ . Then, from $w_{t}$ , EG3D generates the viewpoint-wise target image $I_{t}^{n}$ whose quantity vector is estimated by $\\hat{Q}_t^n$ . For multi-view consistency, the quantifier is trained so that every $\\hat{Q}_t^n$ follows the target quantity vector $Q_{t}$ and the variance of $\\hat{Q}_t^n$ is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature $w_{s}$ to the target $w_{t}$", + "bbox": [ + 496, + 689, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8530", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b24e269e9ea4abf3566d9de1f36de188c122501d211e89cd3e9aba054a0ca214.jpg", + "image_caption": [ + "Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 890, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in the latent space, referring to $Q_{t}$ and the estimated source quantity vector $\\hat{Q}_s$ . For training the navigator, the estimated attribute quantity vector $\\hat{Q}_t$ is defined by the average of $\\hat{Q}_t^n$ over $n$ , which is used to form a loss (i.e., the squared error between $Q_{t}$ and $\\hat{Q}_t$ for accurate manipulation), while preserving the identity of $I_{s}$ .", + "bbox": [ + 75, + 373, + 468, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.Custom Attribute Quantifier", + "text_level": 1, + "bbox": [ + 76, + 474, + 333, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity $q$ of the custom attribute from the image $x$ . We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset $\\mathcal{D}_a$ , and the consistency dataset $\\mathcal{D}_c$ . The former is used to train user-defined attributes, and the latter is used to train multi-view consistency.", + "bbox": [ + 75, + 498, + 470, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Attribute Dataset Custom attributes are specified with a small amount of labeled dataset $\\mathcal{D}_a$ provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset $\\mathcal{D}_a = \\{x_a,q_a\\}$ with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in $\\mathcal{D}_a$ , we first equally divide the quantity range of [0, 1] into $M$ groups and divide the dataset $\\mathcal{D}_a$ into $M$ groups in the order of attribute change. Each group comprises $\\Omega_{a}$ images. Then, the quantity label $q_{a}$ for each image in the $m$ -th group $G_{m}$ in $\\mathcal{D}_a$ is assigned to the value of $\\frac{m - 1}{M - 1}$ . To mitigate the lack of samples in $\\mathcal{D}_a$ , synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in $G_{m}$ with that in $G_{m + 1}$ using Cutmix of the combination ratio $\\gamma$ , the quantity label $q_{a}$ is assigned to $\\frac{m - \\gamma}{M - 1}$ . Since $\\gamma$ is sampled from the uniform distribution [0, 1], the dense", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "quantity labels are sufficient to train the quantifier for regression, yielding any quantity in $[0,1]$ . Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition.", + "bbox": [ + 496, + 373, + 890, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consistency Dataset We construct the consistency dataset $\\mathcal{D}_c = \\{x_c\\}$ using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset $\\mathcal{D}_c$ is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature $w$ , we generate $V$ images $\\{x_c^1, x_c^2, \\dots, x_c^V\\}$ using different $V$ camera viewpoints. Finally, the consistency dataset $\\mathcal{D}_c$ is constructed using $\\Omega_c$ random latent features, so it consists of multi-view images of $\\Omega_c$ different objects.", + "bbox": [ + 496, + 455, + 892, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated $\\hat{q}_a$ and label $q_{a}$ for an input sample $x_{a}$ in $\\mathcal{D}_a$ . The second term is the variance for the estimated $\\hat{q}_c$ vector for $V$ multiview images for a single object in the consistency dataset, where $\\hat{q}_c^v$ is the estimated quantity of $x_c^v$ in $\\mathcal{D}_c$ . Quantifier training loss $\\mathcal{L}_q$ is given by", + "bbox": [ + 496, + 627, + 893, + 765 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {q} = \\sum_ {x _ {a} \\in \\mathcal {D} _ {a}} \\left(q _ {a} - \\hat {q} _ {a}\\right) ^ {2} + \\lambda_ {c} \\sum_ {v = 1} ^ {V} \\sum_ {x _ {c} ^ {v} \\in \\mathcal {D} _ {c}} \\left(\\hat {q} _ {c} ^ {v} - \\bar {\\hat {q}} _ {c} ^ {v}\\right) ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 772, + 890, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\bar{\\hat{q}}_c^v$ is the mean of $\\hat{q}_c^v$ over all $v$ , and $\\lambda_c$ is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of $M$ images sampled, one from each group in $\\mathcal{D}_a$ , and $M$ objects sampled from $\\mathcal{D}_c$ .", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8531", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For $K$ attributes estimation, $K$ quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar $q^{(k)}$ from the $k$ -th quantifier is concatenated to create $K$ -dimensional quantity vector $Q = [q^{(1)}, q^{(2)}, \\dots, q^{(K)}]$ . A quantity vector can be designed by a combination of various quantifiers, depending on an application.", + "bbox": [ + 76, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Multi-Attribute Navigator", + "text_level": 1, + "bbox": [ + 76, + 204, + 316, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space $\\mathcal{W}+$ , where the source feature $w_{s}$ is changed into the target feature $w_{t}$ with the guidance of $\\hat{Q}_s$ and $Q_{t}$ . We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature $f_{Q}$ . Second, layer-wise attention controller (LAC) estimates which layer among the $L$ layer-wise mappers (LWMs) to attend each attribute manipulation.", + "bbox": [ + 75, + 227, + 468, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "AFR converts $\\hat{Q}_s$ and $Q_{t}$ to a 512-dimensional attribute quantity feature $f_{Q}$ . First, $\\hat{Q}_s$ and $Q_{t}$ are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature $f_{Q}$ . The input vector with 1024 dimensions is generated by concatenating $w_{s}$ and $f_{Q}$ , and then, the input vector is fed to each LWM. From the input vector, $l$ -th LWM generates $w_{\\Delta}^{l}$ , which represents the movement on the latent space for $l$ -th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers.", + "bbox": [ + 75, + 439, + 468, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LAC outputs the layer-wise attention vector $a = [a_1, a_2, \\dots, a_L]$ from attribute quantity feature $f_{Q}$ . And the target latent feature $w_{t}$ is generated as follows:", + "bbox": [ + 76, + 619, + 468, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\\Delta} ^ {l}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 232, + 671, + 468, + 689 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} = \\left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \\dots , w _ {t} ^ {L} \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 691, + 468, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of $[0,1]$ .", + "bbox": [ + 75, + 715, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss and Training The navigator is trained such that $\\hat{Q}_t$ follows $Q_t$ , while the identity between $I_s$ and $I_t$ is preserved. To this end, we randomly generate $Q_t$ during the", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select $J$ attributes to train out of a total of $K$ attributes at every training iteration. That is, training attribute set $\\mathcal{T}$ is generated as follows:", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} = \\left\\{\\tau_ {1}, \\tau_ {2}, \\dots , \\tau_ {J} \\right\\} \\subset \\{1, 2, \\dots , K \\}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 157, + 890, + 174 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, $Q_{t}$ is generated by replacing $J$ elements of $\\hat{Q}_{s}$ with $J$ random target values $(q_{t})$ . To ensure that the navigator performs well within the entire range of [0, 1], we use $q_{t}$ randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity.", + "bbox": [ + 496, + 181, + 890, + 289 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For view consistency in manipulation, we generate multi-view target images from $w_{t}$ . Using $N$ random camera viewpoint $p_t^n$ , $N$ multi-view images $I_{t}^{n}$ are generated. And target quantity vector $\\hat{Q}_t^n$ is calculated from $I_{t}^{n}$ , then $\\hat{Q}_t$ is calculated as the average of $\\hat{Q}_t^n$ vectors.", + "bbox": [ + 496, + 290, + 890, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the random target attribute quantity $Q_{t}$ and random source latent $w_{s}$ , we train the navigator by minimizing the losses, which can be grouped into three main subsets:", + "bbox": [ + 496, + 364, + 890, + 410 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {n} = \\mathcal {L} _ {Q} \\left(Q _ {t}, \\hat {Q} _ {t}\\right) + \\mathcal {L} _ {i d} \\left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\\right) + \\mathcal {L} _ {a} (a). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 417, + 890, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The quantity loss $\\mathcal{L}_Q$ guides the navigator to manipulate the image according to the target attribute quantity. $J$ -dimensional quantity vector $Q^{\\prime}$ for training attributes set $\\mathcal{T}$ is generated as follows:", + "bbox": [ + 496, + 439, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ ^ {\\prime} = \\left[ q ^ {(\\tau_ {1})}, q ^ {(\\tau_ {2})}, \\dots , q ^ {(\\tau_ {J})} \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 505, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "And the quantity loss consists of two MSE terms between quantity vectors as", + "bbox": [ + 496, + 530, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {Q} = \\left\\| Q _ {t} ^ {\\prime} - \\hat {Q} _ {t} ^ {\\prime} \\right\\| _ {2} ^ {2} + \\lambda_ {q} \\left\\| Q _ {t} - \\hat {Q} _ {t} \\right\\| _ {2} ^ {2}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 565, + 890, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{q}$ is the hyper-parameter for balancing the loss. In quantity loss, the first term is for $J$ attributes in $\\mathcal{T}$ and the second term is for all $K$ attributes. Because random target quantities are given for $J$ attributes out of a total of $K$ attributes, $K - J$ attributes of $Q_{t}$ are from $\\hat{Q}_s$ . Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity.", + "bbox": [ + 496, + 589, + 890, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The identity loss $\\mathcal{L}_{id}$ is designed by", + "bbox": [ + 519, + 695, + 756, + 710 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i d} = \\left\\| w _ {t} - w _ {s} \\right\\| _ {2} ^ {2} + \\frac {\\lambda_ {L}}{N} \\sum_ {n = 1} ^ {N} \\operatorname {L P I P S} \\left(I _ {s}, I _ {t} ^ {n}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 715, + 890, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{L}$ is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images.", + "bbox": [ + 496, + 762, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The third term, $\\mathcal{L}_n$ , is a regularization loss for layer-wise attention as", + "bbox": [ + 496, + 823, + 890, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a} = | \\alpha - \\bar {a} |, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 849, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{a}$ denotes the average of $a_{l}$ over $l$ , and $\\alpha$ is the hyperparameter for the target average value of attention.", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8532", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1bc818af15eef30a32286bc9eb5235e9dd86ade081db26e7aad42c1f4ba9117c.jpg", + "image_caption": [ + "Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 476, + 209, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 502, + 294, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes.", + "bbox": [ + 75, + 526, + 468, + 632 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Custom Attribute Quantifier For the attribute dataset $\\mathcal{D}_a$ of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed $\\mathcal{D}_a$ for each attribute. We constructed each $\\mathcal{D}_a$ for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each $\\mathcal{D}_a$ for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed $\\mathcal{D}_a$ , each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing $\\mathcal{D}_a$ are provided in the supplement. For the consistency dataset $\\mathcal{D}_c$ , we used $V = 10$ , $\\Omega_c = 10,000$ . We trained the quantifier for 50 epochs with a batch size of $M$ . We set", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/341b0542f1919a8cdf8b1f792a347285b30d6eb91d097c1108646a4ff5de9409.jpg", + "image_caption": [ + "Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes. $(\\dagger =$ custom attributes implemented via manually constructed $D_{a}$" + ], + "image_footnote": [], + "bbox": [ + 503, + 88, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\lambda_{c}$ to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training.", + "bbox": [ + 498, + 455, + 890, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate $w_{s}$ with truncation factor $\\phi = 0.7$ during navigator training. We set hyper-parameters $\\lambda_{q} = 0.5$ , $\\lambda_{L} = 0.1$ , $\\alpha = 0.5$ , and $N = 2$ .", + "bbox": [ + 498, + 489, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.Custom Attribute Manipulation", + "text_level": 1, + "bbox": [ + 500, + 575, + 782, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity $q_{t}$ normalized in the range [0,1]. Regardless of the source attribute quantity $\\hat{q}_{s}$ of the source image $I_{s}$ , the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When $q_{t}$ approaches 0, they are both expressionless; when $q_{t}$ approaches 1, they both smile broadly.", + "bbox": [ + 496, + 598, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8533", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/50d956ab4bffc06e87b6ad9701b55a46a8981de876e054d71e9d334b0312a7d1.jpg", + "image_caption": [ + "Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 467, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique.", + "bbox": [ + 75, + 297, + 468, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement.", + "bbox": [ + 75, + 329, + 468, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 643, + 217, + 659 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement.", + "bbox": [ + 75, + 667, + 468, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The resultant image $I_{\\theta}^{\\phi}$ was manipulated from the source image $I^{\\phi}$ using the $\\theta$ -th target value $(\\phi = 1, \\dots, \\Phi, \\theta =$", + "bbox": [ + 75, + 819, + 468, + 849 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/73b423b5074fcaf092c0a66855729c51355ded3a1a2853e5539dd2c115c0dfa2.jpg", + "image_caption": [ + "Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0." + ], + "image_footnote": [], + "bbox": [ + 500, + 87, + 890, + 356 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3466cac5575d1ee5658ac4d4ed68d65c58f7d97649fba66d58cec73a3f281c35.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile." + ], + "image_footnote": [], + "bbox": [ + 503, + 445, + 890, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$1, \\dots, \\Theta)$ . In addition, we used Face++ [1] to measure $r_{\\theta}^{\\phi}$ which is the resultant attribute quantity of $I_{\\theta}^{\\phi}$ .", + "bbox": [ + 500, + 691, + 890, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "*StyleFlow originally used Microsoft Face API [22] as a quantifier, but Microsoft no longer supports it. Therefore, we used Face++ [1] as a quantifier for StyleFlow implementation on EG3D.", + "bbox": [ + 75, + 862, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8534", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4fcf46b25655e84ff5299b8070eaffcec964ddcd7d705009f376bcd6f2f43582.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAgeSmileGenderEyeglasses
σm↓Ed↓ρ↑σv↓σm↓Ed↓ρ↑σv↓Acc. ↑Ed↓Acc. ↑Ed↓
StyleFlow8.400.37321.32.30437.380.38229.94.85983%0.58696%0.510
StyleFlow+Q10.460.33122.12.30427.490.32034.42.63578%0.67079%0.486
Ours8.030.24532.62.23521.500.21051.02.25595%0.53796%0.468
", + "bbox": [ + 91, + 89, + 874, + 179 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "across multiple manipulated views.", + "bbox": [ + 75, + 252, + 312, + 267 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation $\\sigma_{m,\\theta}$ of the $\\theta$ -th resultant quantities $\\{r_\\theta^1,\\dots ,r_\\theta^\\Phi \\}$ , the evaluation metric $\\sigma_{m}$ is the mean of $\\sigma_{m,\\theta}$ . Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance $E_{d}$ between the embeddings of two manipulated images, which were generated using two adjacent target values, as", + "bbox": [ + 75, + 267, + 468, + 434 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nE _ {d} = \\frac {1}{(\\Theta - 1) \\Phi} \\sum_ {\\theta = 1} ^ {\\Theta - 1} \\sum_ {\\phi = 1} ^ {\\Phi} \\| F \\left(I _ {\\theta + 1} ^ {\\phi}\\right) - F \\left(I _ {\\theta} ^ {\\phi}\\right) \\|, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 440, + 468, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $F$ is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio $\\rho$ between attribute manipulation and identity preservation as $\\frac{(r_{\\Theta} - r_1)}{(\\Theta - 1)E_d}$ . Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images $\\{I_\\theta^{\\phi,1}, I_\\theta^{\\phi,2}, I_\\theta^{\\phi,3}\\}$ and measured the resultant attribute quantities $\\{r_\\theta^{\\phi,1}, r_\\theta^{\\phi,2}, r_\\theta^{\\phi,3}\\}$ . From the standard deviation $\\sigma_{v,\\theta}^{\\phi}$ of the resultant attribute quantities, the evaluation metric $\\sigma_v$ is the mean of $\\sigma_{v,\\theta}^{\\phi}$ .", + "bbox": [ + 75, + 489, + 468, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted experiments with $\\Phi = 100$ and $\\Theta = 8$ . As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++.", + "bbox": [ + 75, + 651, + 468, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case).", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/65bf801bd10f1647efe1966bc789a98aa6dfd3679c54cdcacb680e86329218ee.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness $(\\sigma_{m})$ , manipulation accuracy (Acc.), identity preservation $(E_{d})$ , manipulation efficiency $(\\rho)$ , and view consistency $(\\sigma_{v})$ . Our method gives the best results." + ], + "table_footnote": [], + "table_body": "
MethodAgeSmile
σm↓Ed↓ρ↑σm↓Ed↓ρ↑
Talk-to-Edit14.30.22132.922.60.21240.9
StyleFlow16.90.19528.429.10.09988.9
Ours10.90.22547.220.20.10396.6
", + "bbox": [ + 501, + 250, + 888, + 342 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness $(\\sigma_{m})$ , identity preservation $(E_{d})$ , and manipulation efficiency $(\\rho)$ .", + "bbox": [ + 498, + 348, + 893, + 419 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b24c83074bb6cf30e6be56200cd916e06c304a23144a2ed51d4a06396f8be75f.jpg", + "image_caption": [ + "Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength." + ], + "image_footnote": [], + "bbox": [ + 501, + 435, + 890, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations.", + "bbox": [ + 496, + 656, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness $\\sigma_{m}$ . In the $E_{d}$ score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score $\\rho$ . This result implies that our method better preserves identity when an attribute changes by the same quantity.", + "bbox": [ + 496, + 795, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8535", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/26ce4651b79af4022ffb8a6f8a817136cffda45cbc391f02c34bb9a421c8d573.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Modelσm↓Acc.↑Ed↓
Designw/o LAC module15.8496.0%0.415
w/o AFR module15.3789.0%0.387
Trainingw/o entireatts. in LQ14.7887.5%0.405
w/o intermediate Qt15.6597.0%0.402
Full model14.7695.5%0.365
", + "bbox": [ + 78, + 88, + 475, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness $(\\sigma_{m})$ , accuracy, and identity preservation $(E_{d})$ .", + "bbox": [ + 75, + 200, + 470, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength.", + "bbox": [ + 75, + 271, + 470, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 481, + 230, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in $\\mathcal{L}_Q$ , intermediate target quantity). In the ablation study on the LAC module, we generated $w_{t}$ by adding $w_{\\Delta}$ to $w_{s}$ . In the ablation study on the AFR module, we generated $f_{Q}$ by concatenating $\\hat{Q}_{s}$ and $Q_{t}$ , then repeating it. When entire attributes are not used in $\\mathcal{L}_Q$ , we trained the navigator with $\\lambda_q = 0$ . When an intermediate target quantity is not used, we trained the navigator by randomly sampling $q_{t}$ value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness $\\sigma_{m}$ from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from $87.5\\%$ to $95.5\\%$ . Using intermediate target quantity in navigator training improved the manipulation exactness $\\sigma_{m}$ from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended.", + "bbox": [ + 75, + 506, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcda9631a4a613ddff274b065263ff8380d2e3c2b2918692c26231ed06e72270.jpg", + "image_caption": [ + "Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation $\\sigma_v$ (a lower value is better)." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 686, + 178 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0053102007f163eb5229b4e49f7c77e4883b10d9358053ef1d7e7459895bfb0f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 98, + 887, + 157 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset $\\mathcal{D}_c$ by setting $\\lambda_c = 0$ . In the ablation study on the navigator, we trained the navigator without multi-view images by setting $N = 1$ . Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency.", + "bbox": [ + 496, + 246, + 890, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 430, + 617, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of $[0,1]$ . This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments.", + "bbox": [ + 496, + 455, + 890, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement.", + "bbox": [ + 496, + 632, + 890, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Further discussion of the potential negative social impacts is provided in the supplement.", + "bbox": [ + 498, + 768, + 890, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8536", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Face++ face detection api. https://www faceplusplus.com/. 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Mofan-erf: Morphable facial neural radiance field. arXiv preprint arXiv:2112.02308, 2021. 2" + ], + "bbox": [ + 501, + 92, + 892, + 527 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8538", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_model.json b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d9abdc15f27ea0624ac952d2529d1476dca9001b --- /dev/null +++ b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_model.json @@ -0,0 +1,2079 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.131, + 0.885, + 0.154 + ], + "angle": 0, + "content": "Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.18, + 0.221, + 0.198 + ], + "angle": 0, + "content": "Hoseok Do1,2" + }, + { + "type": "text", + "bbox": [ + 0.259, + 0.18, + 0.391, + 0.2 + ], + "angle": 0, + "content": "EunKyung Yoo" + }, + { + "type": "text", + "bbox": [ + 0.43, + 0.18, + 0.574, + 0.2 + ], + "angle": 0, + "content": "Taehyeong \\(\\mathrm{Kim}^{3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.605, + 0.181, + 0.688, + 0.198 + ], + "angle": 0, + "content": "Chul Lee" + }, + { + "type": "text", + "bbox": [ + 0.728, + 0.181, + 0.859, + 0.199 + ], + "angle": 0, + "content": "Jin young Choi" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.206, + 0.699, + 0.223 + ], + "angle": 0, + "content": "\\(^{1}\\)AI Lab, CTO Division, LG Electronics, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.224, + 0.859, + 0.242 + ], + "angle": 0, + "content": "\\(^{2}\\)ASRI, Dept. of Electrical and Computer Engineering, Seoul National University, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.242, + 0.78, + 0.26 + ], + "angle": 0, + "content": "\\(^{3}\\)Dept. of Biosystems Engineering, Seoul National University, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.262, + 0.778, + 0.277 + ], + "angle": 0, + "content": "{hoseok.do, eunkyung.ryu, clee.lee} \\(@\\) lge.com, {hoseok03, taehyeong.kim, jychoi} \\(@\\) snu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.312, + 0.314, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.474, + 0.572 + ], + "angle": 0, + "content": "While 3D-based GAN techniques have been successfully applied to render photo-realistic 3D images with a variety of attributes while preserving view consistency, there has been little research on how to fine-control 3D images without limiting to a specific category of objects of their properties. To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.604, + 0.21, + 0.62 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.797 + ], + "angle": 0, + "content": "Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.307, + 0.875, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.522, + 0.895, + 0.606 + ], + "angle": 0, + "content": "Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.893, + 0.87 + ], + "angle": 0, + "content": "26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.296, + 0.9 + ], + "angle": 0, + "content": "†Work done during at LG Electronics" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8529" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.501 + ], + "angle": 0, + "content": "tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.51, + 0.228, + 0.525 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.533, + 0.377, + 0.55 + ], + "angle": 0, + "content": "2.1. Latent Space Image Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.555, + 0.473, + 0.844 + ], + "angle": 0, + "content": "StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.849, + 0.303, + 0.866 + ], + "angle": 0, + "content": "2.2. 3D Object Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": "new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.379 + ], + "angle": 0, + "content": "There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.387, + 0.88, + 0.403 + ], + "angle": 0, + "content": "2.3. Efficient Geometry-Aware 3D GANs (EG3D)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.653 + ], + "angle": 0, + "content": "EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature \\( z \\) into intermediate latent feature \\( w \\), then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature \\( w \\). Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.593, + 0.681 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature \\( w_{s} \\), which is obtained from a source image \\( I_{s} \\), is manipulated to target latent feature \\( w_{t} \\). Then, from \\( w_{t} \\), EG3D generates the viewpoint-wise target image \\( I_{t}^{n} \\) whose quantity vector is estimated by \\( \\hat{Q}_t^n \\). For multi-view consistency, the quantifier is trained so that every \\( \\hat{Q}_t^n \\) follows the target quantity vector \\( Q_{t} \\) and the variance of \\( \\hat{Q}_t^n \\) is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature \\( w_{s} \\) to the target \\( w_{t} \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "8530" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.891, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.893, + 0.364 + ], + "angle": 0, + "content": "Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.47, + 0.466 + ], + "angle": 0, + "content": "in the latent space, referring to \\( Q_{t} \\) and the estimated source quantity vector \\( \\hat{Q}_s \\). For training the navigator, the estimated attribute quantity vector \\( \\hat{Q}_t \\) is defined by the average of \\( \\hat{Q}_t^n \\) over \\( n \\), which is used to form a loss (i.e., the squared error between \\( Q_{t} \\) and \\( \\hat{Q}_t \\) for accurate manipulation), while preserving the identity of \\( I_{s} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.334, + 0.491 + ], + "angle": 0, + "content": "3.1.Custom Attribute Quantifier" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.471, + 0.635 + ], + "angle": 0, + "content": "The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity \\( q \\) of the custom attribute from the image \\( x \\). We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset \\( \\mathcal{D}_a \\), and the consistency dataset \\( \\mathcal{D}_c \\). The former is used to train user-defined attributes, and the latter is used to train multi-view consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Attribute Dataset Custom attributes are specified with a small amount of labeled dataset \\(\\mathcal{D}_a\\) provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset \\(\\mathcal{D}_a = \\{x_a,q_a\\}\\) with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in \\(\\mathcal{D}_a\\), we first equally divide the quantity range of [0, 1] into \\(M\\) groups and divide the dataset \\(\\mathcal{D}_a\\) into \\(M\\) groups in the order of attribute change. Each group comprises \\(\\Omega_{a}\\) images. Then, the quantity label \\(q_{a}\\) for each image in the \\(m\\)-th group \\(G_{m}\\) in \\(\\mathcal{D}_a\\) is assigned to the value of \\(\\frac{m - 1}{M - 1}\\). To mitigate the lack of samples in \\(\\mathcal{D}_a\\), synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in \\(G_{m}\\) with that in \\(G_{m + 1}\\) using Cutmix of the combination ratio \\(\\gamma\\), the quantity label \\(q_{a}\\) is assigned to \\(\\frac{m - \\gamma}{M - 1}\\). Since \\(\\gamma\\) is sampled from the uniform distribution [0, 1], the dense" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.892, + 0.45 + ], + "angle": 0, + "content": "quantity labels are sufficient to train the quantifier for regression, yielding any quantity in \\([0,1]\\). Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.893, + 0.624 + ], + "angle": 0, + "content": "Consistency Dataset We construct the consistency dataset \\(\\mathcal{D}_c = \\{x_c\\}\\) using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset \\(\\mathcal{D}_c\\) is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature \\(w\\), we generate \\(V\\) images \\(\\{x_c^1, x_c^2, \\dots, x_c^V\\}\\) using different \\(V\\) camera viewpoints. Finally, the consistency dataset \\(\\mathcal{D}_c\\) is constructed using \\(\\Omega_c\\) random latent features, so it consists of multi-view images of \\(\\Omega_c\\) different objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.766 + ], + "angle": 0, + "content": "Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated \\(\\hat{q}_a\\) and label \\(q_{a}\\) for an input sample \\(x_{a}\\) in \\(\\mathcal{D}_a\\). The second term is the variance for the estimated \\(\\hat{q}_c\\) vector for \\(V\\) multiview images for a single object in the consistency dataset, where \\(\\hat{q}_c^v\\) is the estimated quantity of \\(x_c^v\\) in \\(\\mathcal{D}_c\\). Quantifier training loss \\(\\mathcal{L}_q\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.773, + 0.892, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {q} = \\sum_ {x _ {a} \\in \\mathcal {D} _ {a}} \\left(q _ {a} - \\hat {q} _ {a}\\right) ^ {2} + \\lambda_ {c} \\sum_ {v = 1} ^ {V} \\sum_ {x _ {c} ^ {v} \\in \\mathcal {D} _ {c}} \\left(\\hat {q} _ {c} ^ {v} - \\bar {\\hat {q}} _ {c} ^ {v}\\right) ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\bar{\\hat{q}}_c^v\\) is the mean of \\(\\hat{q}_c^v\\) over all \\(v\\), and \\(\\lambda_c\\) is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of \\(M\\) images sampled, one from each group in \\(\\mathcal{D}_a\\), and \\(M\\) objects sampled from \\(\\mathcal{D}_c\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8531" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "For \\(K\\) attributes estimation, \\(K\\) quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar \\(q^{(k)}\\) from the \\(k\\)-th quantifier is concatenated to create \\(K\\)-dimensional quantity vector \\(Q = [q^{(1)}, q^{(2)}, \\dots, q^{(K)}]\\). A quantity vector can be designed by a combination of various quantifiers, depending on an application." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.205, + 0.317, + 0.22 + ], + "angle": 0, + "content": "3.2. Multi-Attribute Navigator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.47, + 0.439 + ], + "angle": 0, + "content": "Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space \\(\\mathcal{W}+\\), where the source feature \\(w_{s}\\) is changed into the target feature \\(w_{t}\\) with the guidance of \\(\\hat{Q}_s\\) and \\(Q_{t}\\). We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature \\(f_{Q}\\). Second, layer-wise attention controller (LAC) estimates which layer among the \\(L\\) layer-wise mappers (LWMs) to attend each attribute manipulation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.62 + ], + "angle": 0, + "content": "AFR converts \\(\\hat{Q}_s\\) and \\(Q_{t}\\) to a 512-dimensional attribute quantity feature \\(f_{Q}\\). First, \\(\\hat{Q}_s\\) and \\(Q_{t}\\) are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature \\(f_{Q}\\). The input vector with 1024 dimensions is generated by concatenating \\(w_{s}\\) and \\(f_{Q}\\), and then, the input vector is fed to each LWM. From the input vector, \\(l\\)-th LWM generates \\(w_{\\Delta}^{l}\\), which represents the movement on the latent space for \\(l\\)-th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.621, + 0.47, + 0.667 + ], + "angle": 0, + "content": "LAC outputs the layer-wise attention vector \\( a = [a_1, a_2, \\dots, a_L] \\) from attribute quantity feature \\( f_{Q} \\). And the target latent feature \\( w_{t} \\) is generated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.233, + 0.672, + 0.469, + 0.69 + ], + "angle": 0, + "content": "\\[\nw _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\\Delta} ^ {l}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.693, + 0.469, + 0.711 + ], + "angle": 0, + "content": "\\[\nw _ {t} = \\left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \\dots , w _ {t} ^ {L} \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of \\([0,1]\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Loss and Training The navigator is trained such that \\(\\hat{Q}_t\\) follows \\(Q_t\\), while the identity between \\(I_s\\) and \\(I_t\\) is preserved. To this end, we randomly generate \\(Q_t\\) during the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select \\( J \\) attributes to train out of a total of \\( K \\) attributes at every training iteration. That is, training attribute set \\( \\mathcal{T} \\) is generated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.159, + 0.892, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} = \\left\\{\\tau_ {1}, \\tau_ {2}, \\dots , \\tau_ {J} \\right\\} \\subset \\{1, 2, \\dots , K \\}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Then, \\( Q_{t} \\) is generated by replacing \\( J \\) elements of \\( \\hat{Q}_{s} \\) with \\( J \\) random target values \\( (q_{t}) \\). To ensure that the navigator performs well within the entire range of [0, 1], we use \\( q_{t} \\) randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.366 + ], + "angle": 0, + "content": "For view consistency in manipulation, we generate multi-view target images from \\( w_{t} \\). Using \\( N \\) random camera viewpoint \\( p_t^n \\), \\( N \\) multi-view images \\( I_{t}^{n} \\) are generated. And target quantity vector \\( \\hat{Q}_t^n \\) is calculated from \\( I_{t}^{n} \\), then \\( \\hat{Q}_t \\) is calculated as the average of \\( \\hat{Q}_t^n \\) vectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.411 + ], + "angle": 0, + "content": "With the random target attribute quantity \\( Q_{t} \\) and random source latent \\( w_{s} \\), we train the navigator by minimizing the losses, which can be grouped into three main subsets:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.418, + 0.892, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {n} = \\mathcal {L} _ {Q} \\left(Q _ {t}, \\hat {Q} _ {t}\\right) + \\mathcal {L} _ {i d} \\left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\\right) + \\mathcal {L} _ {a} (a). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.5 + ], + "angle": 0, + "content": "The quantity loss \\(\\mathcal{L}_Q\\) guides the navigator to manipulate the image according to the target attribute quantity. \\(J\\)-dimensional quantity vector \\(Q^{\\prime}\\) for training attributes set \\(\\mathcal{T}\\) is generated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.506, + 0.892, + 0.525 + ], + "angle": 0, + "content": "\\[\nQ ^ {\\prime} = \\left[ q ^ {(\\tau_ {1})}, q ^ {(\\tau_ {2})}, \\dots , q ^ {(\\tau_ {J})} \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.561 + ], + "angle": 0, + "content": "And the quantity loss consists of two MSE terms between quantity vectors as" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.566, + 0.892, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {Q} = \\left\\| Q _ {t} ^ {\\prime} - \\hat {Q} _ {t} ^ {\\prime} \\right\\| _ {2} ^ {2} + \\lambda_ {q} \\left\\| Q _ {t} - \\hat {Q} _ {t} \\right\\| _ {2} ^ {2}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.892, + 0.696 + ], + "angle": 0, + "content": "where \\(\\lambda_{q}\\) is the hyper-parameter for balancing the loss. In quantity loss, the first term is for \\(J\\) attributes in \\(\\mathcal{T}\\) and the second term is for all \\(K\\) attributes. Because random target quantities are given for \\(J\\) attributes out of a total of \\(K\\) attributes, \\(K - J\\) attributes of \\(Q_{t}\\) are from \\(\\hat{Q}_s\\). Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.696, + 0.758, + 0.711 + ], + "angle": 0, + "content": "The identity loss \\(\\mathcal{L}_{id}\\) is designed by" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.717, + 0.892, + 0.758 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i d} = \\left\\| w _ {t} - w _ {s} \\right\\| _ {2} ^ {2} + \\frac {\\lambda_ {L}}{N} \\sum_ {n = 1} ^ {N} \\operatorname {L P I P S} \\left(I _ {s}, I _ {t} ^ {n}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.824 + ], + "angle": 0, + "content": "where \\(\\lambda_{L}\\) is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.892, + 0.851 + ], + "angle": 0, + "content": "The third term, \\(\\mathcal{L}_n\\), is a regularization loss for layer-wise attention as" + }, + { + "type": "equation", + "bbox": [ + 0.646, + 0.85, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a} = | \\alpha - \\bar {a} |, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( \\bar{a} \\) denotes the average of \\( a_{l} \\) over \\( l \\), and \\( \\alpha \\) is the hyperparameter for the target average value of attention." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8532" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.393, + 0.47, + 0.464 + ], + "angle": 0, + "content": "Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.477, + 0.21, + 0.494 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.503, + 0.295, + 0.519 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.633 + ], + "angle": 0, + "content": "We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Custom Attribute Quantifier For the attribute dataset \\(\\mathcal{D}_a\\) of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed \\(\\mathcal{D}_a\\) for each attribute. We constructed each \\(\\mathcal{D}_a\\) for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each \\(\\mathcal{D}_a\\) for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed \\(\\mathcal{D}_a\\), each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing \\(\\mathcal{D}_a\\) are provided in the supplement. For the consistency dataset \\(\\mathcal{D}_c\\), we used \\(V = 10\\), \\(\\Omega_c = 10,000\\). We trained the quantifier for 50 epochs with a batch size of \\(M\\). We set" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.089, + 0.892, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.369, + 0.892, + 0.443 + ], + "angle": 0, + "content": "Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes. \\((\\dagger =\\) custom attributes implemented via manually constructed \\(D_{a}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.456, + 0.892, + 0.488 + ], + "angle": 0, + "content": "\\(\\lambda_{c}\\) to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate \\( w_{s} \\) with truncation factor \\( \\phi = 0.7 \\) during navigator training. We set hyper-parameters \\( \\lambda_{q} = 0.5 \\), \\( \\lambda_{L} = 0.1 \\), \\( \\alpha = 0.5 \\), and \\( N = 2 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.783, + 0.592 + ], + "angle": 0, + "content": "4.2.Custom Attribute Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.81 + ], + "angle": 0, + "content": "As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity \\( q_{t} \\) normalized in the range [0,1]. Regardless of the source attribute quantity \\( \\hat{q}_{s} \\) of the source image \\( I_{s} \\), the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When \\( q_{t} \\) approaches 0, they are both expressionless; when \\( q_{t} \\) approaches 1, they both smile broadly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8533" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.289 + ], + "angle": 0, + "content": "Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.469, + 0.328 + ], + "angle": 0, + "content": "cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.631 + ], + "angle": 0, + "content": "To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.644, + 0.218, + 0.66 + ], + "angle": 0, + "content": "4.3. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.469, + 0.819 + ], + "angle": 0, + "content": "In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.82, + 0.469, + 0.851 + ], + "angle": 0, + "content": "The resultant image \\(I_{\\theta}^{\\phi}\\) was manipulated from the source image \\(I^{\\phi}\\) using the \\(\\theta\\)-th target value \\((\\phi = 1, \\dots, \\Phi, \\theta =\\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.9 + ], + "angle": 0, + "content": "*StyleFlow originally used Microsoft Face API [22] as a quantifier, but Microsoft no longer supports it. Therefore, we used Face++ [1] as a quantifier for StyleFlow implementation on EG3D." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.088, + 0.892, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.361, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.446, + 0.891, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.636, + 0.892, + 0.678 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.692, + 0.891, + 0.727 + ], + "angle": 0, + "content": "\\(1, \\dots, \\Theta)\\). In addition, we used Face++ [1] to measure \\(r_{\\theta}^{\\phi}\\) which is the resultant attribute quantity of \\(I_{\\theta}^{\\phi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8534" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.09, + 0.875, + 0.18 + ], + "angle": 0, + "content": "
MethodAgeSmileGenderEyeglasses
σm↓Ed↓ρ↑σv↓σm↓Ed↓ρ↑σv↓Acc. ↑Ed↓Acc. ↑Ed↓
StyleFlow8.400.37321.32.30437.380.38229.94.85983%0.58696%0.510
StyleFlow+Q10.460.33122.12.30427.490.32034.42.63578%0.67079%0.486
Ours8.030.24532.62.23521.500.21051.02.25595%0.53796%0.468
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.188, + 0.894, + 0.232 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness \\((\\sigma_{m})\\), manipulation accuracy (Acc.), identity preservation \\((E_{d})\\), manipulation efficiency \\((\\rho)\\), and view consistency \\((\\sigma_{v})\\). Our method gives the best results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.313, + 0.268 + ], + "angle": 0, + "content": "across multiple manipulated views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.435 + ], + "angle": 0, + "content": "Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation \\(\\sigma_{m,\\theta}\\) of the \\(\\theta\\)-th resultant quantities \\(\\{r_\\theta^1,\\dots ,r_\\theta^\\Phi \\}\\), the evaluation metric \\(\\sigma_{m}\\) is the mean of \\(\\sigma_{m,\\theta}\\). Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance \\(E_{d}\\) between the embeddings of two manipulated images, which were generated using two adjacent target values, as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.441, + 0.47, + 0.484 + ], + "angle": 0, + "content": "\\[\nE _ {d} = \\frac {1}{(\\Theta - 1) \\Phi} \\sum_ {\\theta = 1} ^ {\\Theta - 1} \\sum_ {\\phi = 1} ^ {\\Phi} \\| F \\left(I _ {\\theta + 1} ^ {\\phi}\\right) - F \\left(I _ {\\theta} ^ {\\phi}\\right) \\|, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.652 + ], + "angle": 0, + "content": "where \\(F\\) is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio \\(\\rho\\) between attribute manipulation and identity preservation as \\(\\frac{(r_{\\Theta} - r_1)}{(\\Theta - 1)E_d}\\). Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images \\(\\{I_\\theta^{\\phi,1}, I_\\theta^{\\phi,2}, I_\\theta^{\\phi,3}\\}\\) and measured the resultant attribute quantities \\(\\{r_\\theta^{\\phi,1}, r_\\theta^{\\phi,2}, r_\\theta^{\\phi,3}\\}\\). From the standard deviation \\(\\sigma_{v,\\theta}^{\\phi}\\) of the resultant attribute quantities, the evaluation metric \\(\\sigma_v\\) is the mean of \\(\\sigma_{v,\\theta}^{\\phi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.47, + 0.743 + ], + "angle": 0, + "content": "We conducted experiments with \\(\\Phi = 100\\) and \\(\\Theta = 8\\). As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.251, + 0.89, + 0.343 + ], + "angle": 0, + "content": "
MethodAgeSmile
σm↓Ed↓ρ↑σm↓Ed↓ρ↑
Talk-to-Edit14.30.22132.922.60.21240.9
StyleFlow16.90.19528.429.10.09988.9
Ours10.90.22547.220.20.10396.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.349, + 0.894, + 0.42 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness \\((\\sigma_{m})\\), identity preservation \\((E_{d})\\), and manipulation efficiency \\((\\rho)\\)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.436, + 0.892, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.577, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness \\(\\sigma_{m}\\). In the \\(E_{d}\\) score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score \\(\\rho\\). This result implies that our method better preserves identity when an attribute changes by the same quantity." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8535" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.477, + 0.198 + ], + "angle": 0, + "content": "
Modelσm↓Acc.↑Ed↓
Designw/o LAC module15.8496.0%0.415
w/o AFR module15.3789.0%0.387
Trainingw/o entireatts. in LQ14.7887.5%0.405
w/o intermediate Qt15.6597.0%0.402
Full model14.7695.5%0.365
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.201, + 0.471, + 0.258 + ], + "angle": 0, + "content": "Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness \\((\\sigma_{m})\\), accuracy, and identity preservation \\((E_{d})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.468 + ], + "angle": 0, + "content": "In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.231, + 0.499 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in \\(\\mathcal{L}_Q\\), intermediate target quantity). In the ablation study on the LAC module, we generated \\(w_{t}\\) by adding \\(w_{\\Delta}\\) to \\(w_{s}\\). In the ablation study on the AFR module, we generated \\(f_{Q}\\) by concatenating \\(\\hat{Q}_{s}\\) and \\(Q_{t}\\), then repeating it. When entire attributes are not used in \\(\\mathcal{L}_Q\\), we trained the navigator with \\(\\lambda_q = 0\\). When an intermediate target quantity is not used, we trained the navigator by randomly sampling \\(q_{t}\\) value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness \\(\\sigma_{m}\\) from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from \\(87.5\\%\\) to \\(95.5\\%\\). Using intermediate target quantity in navigator training improved the manipulation exactness \\(\\sigma_{m}\\) from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.092, + 0.687, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.099, + 0.888, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.227 + ], + "angle": 0, + "content": "Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation \\(\\sigma_v\\) (a lower value is better)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.414 + ], + "angle": 0, + "content": "View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset \\(\\mathcal{D}_c\\) by setting \\(\\lambda_c = 0\\). In the ablation study on the navigator, we trained the navigator without multi-view images by setting \\(N = 1\\). Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.431, + 0.619, + 0.446 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of \\([0,1]\\). This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.769 + ], + "angle": 0, + "content": "Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.77, + 0.891, + 0.8 + ], + "angle": 0, + "content": "Further discussion of the potential negative social impacts is provided in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8536" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.155 + ], + "angle": 0, + "content": "[1] Face++ face detection api. https://www faceplusplus.com/. 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Mofan-erf: Morphable facial neural radiance field. arXiv preprint arXiv:2112.02308, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8538" + } + ] +] \ No newline at end of file diff --git a/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_origin.pdf b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0362f8ced6ffd1eae8122d1458f721f6f82b606a --- /dev/null +++ b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a265eda34a3dc06d1751dd779d0ae5b5931d46655b9ab2b1ece3f40d8f5bb822 +size 6193360 diff --git a/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/full.md b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a4b695fb38bb01ac284f8e220c3faaaffa70082c --- /dev/null +++ b/2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/full.md @@ -0,0 +1,306 @@ +# Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis + +Hoseok Do1,2 + +EunKyung Yoo + +Taehyeong $\mathrm{Kim}^{3\dagger}$ + +Chul Lee + +Jin young Choi + +$^{1}$ AI Lab, CTO Division, LG Electronics, South Korea + +$^{2}$ ASRI, Dept. of Electrical and Computer Engineering, Seoul National University, South Korea + +$^{3}$ Dept. of Biosystems Engineering, Seoul National University, South Korea + +{hoseok.do, eunkyung.ryu, clee.lee} $@$ lge.com, {hoseok03, taehyeong.kim, jychoi} $@$ snu.ac.kr + +# Abstract + +While 3D-based GAN techniques have been successfully applied to render photo-realistic 3D images with a variety of attributes while preserving view consistency, there has been little research on how to fine-control 3D images without limiting to a specific category of objects of their properties. To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments. + +# 1. Introduction + +Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks. + +Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24, + +![](images/4f1e089957a4f5afcd2ebab912a669f305db80ccb8a17b9b534093268daeac94.jpg) +Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes. + +26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention. + +Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti + +tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective. + +# 2. Related Works + +# 2.1. Latent Space Image Manipulation + +StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data. + +# 2.2. 3D Object Manipulation + +There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce + +new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM). + +There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes. + +# 2.3. Efficient Geometry-Aware 3D GANs (EG3D) + +EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature $z$ into intermediate latent feature $w$ , then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature $w$ . Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency. + +# 3. Method + +We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature $w_{s}$ , which is obtained from a source image $I_{s}$ , is manipulated to target latent feature $w_{t}$ . Then, from $w_{t}$ , EG3D generates the viewpoint-wise target image $I_{t}^{n}$ whose quantity vector is estimated by $\hat{Q}_t^n$ . For multi-view consistency, the quantifier is trained so that every $\hat{Q}_t^n$ follows the target quantity vector $Q_{t}$ and the variance of $\hat{Q}_t^n$ is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature $w_{s}$ to the target $w_{t}$ + +![](images/b24e269e9ea4abf3566d9de1f36de188c122501d211e89cd3e9aba054a0ca214.jpg) +Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity. + +in the latent space, referring to $Q_{t}$ and the estimated source quantity vector $\hat{Q}_s$ . For training the navigator, the estimated attribute quantity vector $\hat{Q}_t$ is defined by the average of $\hat{Q}_t^n$ over $n$ , which is used to form a loss (i.e., the squared error between $Q_{t}$ and $\hat{Q}_t$ for accurate manipulation), while preserving the identity of $I_{s}$ . + +# 3.1.Custom Attribute Quantifier + +The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity $q$ of the custom attribute from the image $x$ . We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset $\mathcal{D}_a$ , and the consistency dataset $\mathcal{D}_c$ . The former is used to train user-defined attributes, and the latter is used to train multi-view consistency. + +Attribute Dataset Custom attributes are specified with a small amount of labeled dataset $\mathcal{D}_a$ provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset $\mathcal{D}_a = \{x_a,q_a\}$ with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in $\mathcal{D}_a$ , we first equally divide the quantity range of [0, 1] into $M$ groups and divide the dataset $\mathcal{D}_a$ into $M$ groups in the order of attribute change. Each group comprises $\Omega_{a}$ images. Then, the quantity label $q_{a}$ for each image in the $m$ -th group $G_{m}$ in $\mathcal{D}_a$ is assigned to the value of $\frac{m - 1}{M - 1}$ . To mitigate the lack of samples in $\mathcal{D}_a$ , synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in $G_{m}$ with that in $G_{m + 1}$ using Cutmix of the combination ratio $\gamma$ , the quantity label $q_{a}$ is assigned to $\frac{m - \gamma}{M - 1}$ . Since $\gamma$ is sampled from the uniform distribution [0, 1], the dense + +quantity labels are sufficient to train the quantifier for regression, yielding any quantity in $[0,1]$ . Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition. + +Consistency Dataset We construct the consistency dataset $\mathcal{D}_c = \{x_c\}$ using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset $\mathcal{D}_c$ is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature $w$ , we generate $V$ images $\{x_c^1, x_c^2, \dots, x_c^V\}$ using different $V$ camera viewpoints. Finally, the consistency dataset $\mathcal{D}_c$ is constructed using $\Omega_c$ random latent features, so it consists of multi-view images of $\Omega_c$ different objects. + +Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated $\hat{q}_a$ and label $q_{a}$ for an input sample $x_{a}$ in $\mathcal{D}_a$ . The second term is the variance for the estimated $\hat{q}_c$ vector for $V$ multiview images for a single object in the consistency dataset, where $\hat{q}_c^v$ is the estimated quantity of $x_c^v$ in $\mathcal{D}_c$ . Quantifier training loss $\mathcal{L}_q$ is given by + +$$ +\mathcal {L} _ {q} = \sum_ {x _ {a} \in \mathcal {D} _ {a}} \left(q _ {a} - \hat {q} _ {a}\right) ^ {2} + \lambda_ {c} \sum_ {v = 1} ^ {V} \sum_ {x _ {c} ^ {v} \in \mathcal {D} _ {c}} \left(\hat {q} _ {c} ^ {v} - \bar {\hat {q}} _ {c} ^ {v}\right) ^ {2}, \tag {1} +$$ + +where $\bar{\hat{q}}_c^v$ is the mean of $\hat{q}_c^v$ over all $v$ , and $\lambda_c$ is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of $M$ images sampled, one from each group in $\mathcal{D}_a$ , and $M$ objects sampled from $\mathcal{D}_c$ . + +For $K$ attributes estimation, $K$ quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar $q^{(k)}$ from the $k$ -th quantifier is concatenated to create $K$ -dimensional quantity vector $Q = [q^{(1)}, q^{(2)}, \dots, q^{(K)}]$ . A quantity vector can be designed by a combination of various quantifiers, depending on an application. + +# 3.2. Multi-Attribute Navigator + +Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space $\mathcal{W}+$ , where the source feature $w_{s}$ is changed into the target feature $w_{t}$ with the guidance of $\hat{Q}_s$ and $Q_{t}$ . We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature $f_{Q}$ . Second, layer-wise attention controller (LAC) estimates which layer among the $L$ layer-wise mappers (LWMs) to attend each attribute manipulation. + +AFR converts $\hat{Q}_s$ and $Q_{t}$ to a 512-dimensional attribute quantity feature $f_{Q}$ . First, $\hat{Q}_s$ and $Q_{t}$ are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature $f_{Q}$ . The input vector with 1024 dimensions is generated by concatenating $w_{s}$ and $f_{Q}$ , and then, the input vector is fed to each LWM. From the input vector, $l$ -th LWM generates $w_{\Delta}^{l}$ , which represents the movement on the latent space for $l$ -th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers. + +LAC outputs the layer-wise attention vector $a = [a_1, a_2, \dots, a_L]$ from attribute quantity feature $f_{Q}$ . And the target latent feature $w_{t}$ is generated as follows: + +$$ +w _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\Delta} ^ {l}, \tag {2} +$$ + +$$ +w _ {t} = \left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \dots , w _ {t} ^ {L} \right]. \tag {3} +$$ + +Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of $[0,1]$ . + +Loss and Training The navigator is trained such that $\hat{Q}_t$ follows $Q_t$ , while the identity between $I_s$ and $I_t$ is preserved. To this end, we randomly generate $Q_t$ during the + +training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select $J$ attributes to train out of a total of $K$ attributes at every training iteration. That is, training attribute set $\mathcal{T}$ is generated as follows: + +$$ +\mathcal {T} = \left\{\tau_ {1}, \tau_ {2}, \dots , \tau_ {J} \right\} \subset \{1, 2, \dots , K \}. \tag {4} +$$ + +Then, $Q_{t}$ is generated by replacing $J$ elements of $\hat{Q}_{s}$ with $J$ random target values $(q_{t})$ . To ensure that the navigator performs well within the entire range of [0, 1], we use $q_{t}$ randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity. + +For view consistency in manipulation, we generate multi-view target images from $w_{t}$ . Using $N$ random camera viewpoint $p_t^n$ , $N$ multi-view images $I_{t}^{n}$ are generated. And target quantity vector $\hat{Q}_t^n$ is calculated from $I_{t}^{n}$ , then $\hat{Q}_t$ is calculated as the average of $\hat{Q}_t^n$ vectors. + +With the random target attribute quantity $Q_{t}$ and random source latent $w_{s}$ , we train the navigator by minimizing the losses, which can be grouped into three main subsets: + +$$ +\mathcal {L} _ {n} = \mathcal {L} _ {Q} \left(Q _ {t}, \hat {Q} _ {t}\right) + \mathcal {L} _ {i d} \left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\right) + \mathcal {L} _ {a} (a). \tag {5} +$$ + +The quantity loss $\mathcal{L}_Q$ guides the navigator to manipulate the image according to the target attribute quantity. $J$ -dimensional quantity vector $Q^{\prime}$ for training attributes set $\mathcal{T}$ is generated as follows: + +$$ +Q ^ {\prime} = \left[ q ^ {(\tau_ {1})}, q ^ {(\tau_ {2})}, \dots , q ^ {(\tau_ {J})} \right]. \tag {6} +$$ + +And the quantity loss consists of two MSE terms between quantity vectors as + +$$ +\mathcal {L} _ {Q} = \left\| Q _ {t} ^ {\prime} - \hat {Q} _ {t} ^ {\prime} \right\| _ {2} ^ {2} + \lambda_ {q} \left\| Q _ {t} - \hat {Q} _ {t} \right\| _ {2} ^ {2}, \tag {7} +$$ + +where $\lambda_{q}$ is the hyper-parameter for balancing the loss. In quantity loss, the first term is for $J$ attributes in $\mathcal{T}$ and the second term is for all $K$ attributes. Because random target quantities are given for $J$ attributes out of a total of $K$ attributes, $K - J$ attributes of $Q_{t}$ are from $\hat{Q}_s$ . Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity. + +The identity loss $\mathcal{L}_{id}$ is designed by + +$$ +\mathcal {L} _ {i d} = \left\| w _ {t} - w _ {s} \right\| _ {2} ^ {2} + \frac {\lambda_ {L}}{N} \sum_ {n = 1} ^ {N} \operatorname {L P I P S} \left(I _ {s}, I _ {t} ^ {n}\right), \tag {8} +$$ + +where $\lambda_{L}$ is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images. + +The third term, $\mathcal{L}_n$ , is a regularization loss for layer-wise attention as + +$$ +\mathcal {L} _ {a} = | \alpha - \bar {a} |, \tag {9} +$$ + +where $\bar{a}$ denotes the average of $a_{l}$ over $l$ , and $\alpha$ is the hyperparameter for the target average value of attention. + +![](images/1bc818af15eef30a32286bc9eb5235e9dd86ade081db26e7aad42c1f4ba9117c.jpg) +Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0. + +# 4. Experiments + +# 4.1. Implementation Details + +We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes. + +Custom Attribute Quantifier For the attribute dataset $\mathcal{D}_a$ of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed $\mathcal{D}_a$ for each attribute. We constructed each $\mathcal{D}_a$ for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each $\mathcal{D}_a$ for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed $\mathcal{D}_a$ , each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing $\mathcal{D}_a$ are provided in the supplement. For the consistency dataset $\mathcal{D}_c$ , we used $V = 10$ , $\Omega_c = 10,000$ . We trained the quantifier for 50 epochs with a batch size of $M$ . We set + +![](images/341b0542f1919a8cdf8b1f792a347285b30d6eb91d097c1108646a4ff5de9409.jpg) +Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes. $(\dagger =$ custom attributes implemented via manually constructed $D_{a}$ + +$\lambda_{c}$ to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training. + +Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate $w_{s}$ with truncation factor $\phi = 0.7$ during navigator training. We set hyper-parameters $\lambda_{q} = 0.5$ , $\lambda_{L} = 0.1$ , $\alpha = 0.5$ , and $N = 2$ . + +# 4.2.Custom Attribute Manipulation + +As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity $q_{t}$ normalized in the range [0,1]. Regardless of the source attribute quantity $\hat{q}_{s}$ of the source image $I_{s}$ , the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When $q_{t}$ approaches 0, they are both expressionless; when $q_{t}$ approaches 1, they both smile broadly. + +Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be + +![](images/50d956ab4bffc06e87b6ad9701b55a46a8981de876e054d71e9d334b0312a7d1.jpg) +Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images. + +cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique. + +To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement. + +# 4.3. Comparisons + +In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement. + +The resultant image $I_{\theta}^{\phi}$ was manipulated from the source image $I^{\phi}$ using the $\theta$ -th target value $(\phi = 1, \dots, \Phi, \theta =$ + +![](images/73b423b5074fcaf092c0a66855729c51355ded3a1a2853e5539dd2c115c0dfa2.jpg) +Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0. + +![](images/3466cac5575d1ee5658ac4d4ed68d65c58f7d97649fba66d58cec73a3f281c35.jpg) +Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile. + +$1, \dots, \Theta)$ . In addition, we used Face++ [1] to measure $r_{\theta}^{\phi}$ which is the resultant attribute quantity of $I_{\theta}^{\phi}$ . + +Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency + +
MethodAgeSmileGenderEyeglasses
σm↓Ed↓ρ↑σv↓σm↓Ed↓ρ↑σv↓Acc. ↑Ed↓Acc. ↑Ed↓
StyleFlow8.400.37321.32.30437.380.38229.94.85983%0.58696%0.510
StyleFlow+Q10.460.33122.12.30427.490.32034.42.63578%0.67079%0.486
Ours8.030.24532.62.23521.500.21051.02.25595%0.53796%0.468
+ +across multiple manipulated views. + +Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation $\sigma_{m,\theta}$ of the $\theta$ -th resultant quantities $\{r_\theta^1,\dots ,r_\theta^\Phi \}$ , the evaluation metric $\sigma_{m}$ is the mean of $\sigma_{m,\theta}$ . Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance $E_{d}$ between the embeddings of two manipulated images, which were generated using two adjacent target values, as + +$$ +E _ {d} = \frac {1}{(\Theta - 1) \Phi} \sum_ {\theta = 1} ^ {\Theta - 1} \sum_ {\phi = 1} ^ {\Phi} \| F \left(I _ {\theta + 1} ^ {\phi}\right) - F \left(I _ {\theta} ^ {\phi}\right) \|, \tag {10} +$$ + +where $F$ is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio $\rho$ between attribute manipulation and identity preservation as $\frac{(r_{\Theta} - r_1)}{(\Theta - 1)E_d}$ . Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images $\{I_\theta^{\phi,1}, I_\theta^{\phi,2}, I_\theta^{\phi,3}\}$ and measured the resultant attribute quantities $\{r_\theta^{\phi,1}, r_\theta^{\phi,2}, r_\theta^{\phi,3}\}$ . From the standard deviation $\sigma_{v,\theta}^{\phi}$ of the resultant attribute quantities, the evaluation metric $\sigma_v$ is the mean of $\sigma_{v,\theta}^{\phi}$ . + +We conducted experiments with $\Phi = 100$ and $\Theta = 8$ . As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++. + +Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case). + +Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness $(\sigma_{m})$ , manipulation accuracy (Acc.), identity preservation $(E_{d})$ , manipulation efficiency $(\rho)$ , and view consistency $(\sigma_{v})$ . Our method gives the best results. + +
MethodAgeSmile
σm↓Ed↓ρ↑σm↓Ed↓ρ↑
Talk-to-Edit14.30.22132.922.60.21240.9
StyleFlow16.90.19528.429.10.09988.9
Ours10.90.22547.220.20.10396.6
+ +Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness $(\sigma_{m})$ , identity preservation $(E_{d})$ , and manipulation efficiency $(\rho)$ . + +![](images/b24c83074bb6cf30e6be56200cd916e06c304a23144a2ed51d4a06396f8be75f.jpg) +Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength. + +Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations. + +As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness $\sigma_{m}$ . In the $E_{d}$ score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score $\rho$ . This result implies that our method better preserves identity when an attribute changes by the same quantity. + +
Modelσm↓Acc.↑Ed↓
Designw/o LAC module15.8496.0%0.415
w/o AFR module15.3789.0%0.387
Trainingw/o entireatts. in LQ14.7887.5%0.405
w/o intermediate Qt15.6597.0%0.402
Full model14.7695.5%0.365
+ +Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness $(\sigma_{m})$ , accuracy, and identity preservation $(E_{d})$ . + +In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength. + +# 4.4. Ablation Study + +Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in $\mathcal{L}_Q$ , intermediate target quantity). In the ablation study on the LAC module, we generated $w_{t}$ by adding $w_{\Delta}$ to $w_{s}$ . In the ablation study on the AFR module, we generated $f_{Q}$ by concatenating $\hat{Q}_{s}$ and $Q_{t}$ , then repeating it. When entire attributes are not used in $\mathcal{L}_Q$ , we trained the navigator with $\lambda_q = 0$ . When an intermediate target quantity is not used, we trained the navigator by randomly sampling $q_{t}$ value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness $\sigma_{m}$ from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from $87.5\%$ to $95.5\%$ . Using intermediate target quantity in navigator training improved the manipulation exactness $\sigma_{m}$ from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended. + +![](images/bcda9631a4a613ddff274b065263ff8380d2e3c2b2918692c26231ed06e72270.jpg) +Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation $\sigma_v$ (a lower value is better). + +![](images/0053102007f163eb5229b4e49f7c77e4883b10d9358053ef1d7e7459895bfb0f.jpg) + +View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset $\mathcal{D}_c$ by setting $\lambda_c = 0$ . In the ablation study on the navigator, we trained the navigator without multi-view images by setting $N = 1$ . Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency. + +# 5. Conclusion + +Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of $[0,1]$ . This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments. + +Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement. + +Further discussion of the potential negative social impacts is provided in the supplement. + +Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)] + +# References + +[1] Face++ face detection api. https://www faceplusplus.com/. Accessed: 2023-02-23. 2, 6 +[2] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Styleflow: Attribute-conditioned exploration of stylegan-generated images using conditional continuous normalizing flows. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023-6032, 2019. 3 +[43] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 4 +[44] Xiaoming Zhao, Fangchang Ma, David Guera, Zhile Ren, Alexander G Schwing, and Alex Colburn. Generative multiplane images: Making a 2d gan 3d-aware. arXiv preprint arXiv:2207.10642, 2022. 2 +[45] Yiyu Zhuang, Hao Zhu, Xusen Sun, and Xun Cao. 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To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 498, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 631 + ], + "type": "text", + "content": "Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "content": "Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24," + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 317, + 243, + 535, + 410 + ], + "blocks": [ + { + "bbox": [ + 317, + 243, + 535, + 410 + ], + "lines": [ + { + "bbox": [ + 317, + 243, + 535, + 410 + ], + "spans": [ + { + "bbox": [ + 317, + 243, + 535, + 410 + ], + "type": "image", + "image_path": "4f1e089957a4f5afcd2ebab912a669f305db80ccb8a17b9b534093268daeac94.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 413, + 547, + 479 + ], + "lines": [ + { + "bbox": [ + 305, + 413, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 547, + 479 + ], + "type": "text", + "content": "Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 485, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 546, + 689 + ], + "type": "text", + "content": "26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 181, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 181, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 181, + 712 + ], + "type": "text", + "content": "†Work done during at LG Electronics" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8529" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 396 + ], + "type": "text", + "content": "tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 403, + 139, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 139, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 139, + 415 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 422, + 230, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 230, + 435 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 230, + 435 + ], + "type": "text", + "content": "2.1. Latent Space Image Manipulation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 439, + 289, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 289, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 289, + 668 + ], + "type": "text", + "content": "StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 672, + 185, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 185, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 185, + 685 + ], + "type": "text", + "content": "2.2. 3D Object Manipulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": "new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "type": "text", + "content": "There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 306, + 538, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 306, + 538, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 306, + 538, + 319 + ], + "type": "text", + "content": "2.3. Efficient Geometry-Aware 3D GANs (EG3D)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "text", + "content": "EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature " + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "text", + "content": " into intermediate latent feature " + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "text", + "content": ", then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature " + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 324, + 547, + 517 + ], + "type": "text", + "content": ". Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 526, + 362, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 362, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 362, + 539 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": "We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": ", which is obtained from a source image " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": ", is manipulated to target latent feature " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": ". Then, from " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": ", EG3D generates the viewpoint-wise target image " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{t}^{n}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": " whose quantity vector is estimated by " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": ". For multi-view consistency, the quantifier is trained so that every " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": " follows the target quantity vector " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": " and the variance of " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": " is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "text", + "content": " to the target " + }, + { + "bbox": [ + 304, + 546, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{t}" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "8530" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 236 + ], + "type": "image", + "image_path": "b24e269e9ea4abf3566d9de1f36de188c122501d211e89cd3e9aba054a0ca214.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 546, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 546, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 546, + 288 + ], + "type": "text", + "content": "Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": "in the latent space, referring to " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": " and the estimated source quantity vector " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\hat{Q}_s" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": ". For training the navigator, the estimated attribute quantity vector " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": " is defined by the average of " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": ", which is used to form a loss (i.e., the squared error between " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": " for accurate manipulation), while preserving the identity of " + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 46, + 296, + 287, + 369 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 376, + 204, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 204, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 204, + 388 + ], + "type": "text", + "content": "3.1.Custom Attribute Quantifier" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "content": "The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity " + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "content": " of the custom attribute from the image " + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "content": ". We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset " + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "content": ", and the consistency dataset " + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 46, + 395, + 288, + 502 + ], + "type": "text", + "content": ". The former is used to train user-defined attributes, and the latter is used to train multi-view consistency." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Attribute Dataset Custom attributes are specified with a small amount of labeled dataset " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a = \\{x_a,q_a\\}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ", we first equally divide the quantity range of [0, 1] into " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " groups and divide the dataset " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " groups in the order of attribute change. Each group comprises " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Omega_{a}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " images. Then, the quantity label " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "q_{a}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " for each image in the " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "-th group " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{m}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " is assigned to the value of " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\frac{m - 1}{M - 1}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ". To mitigate the lack of samples in " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ", synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{m}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " with that in " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{m + 1}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " using Cutmix of the combination ratio " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ", the quantity label " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "q_{a}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " is assigned to " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\frac{m - \\gamma}{M - 1}" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " is sampled from the uniform distribution [0, 1], the dense" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 296, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 545, + 356 + ], + "type": "text", + "content": "quantity labels are sufficient to train the quantifier for regression, yielding any quantity in " + }, + { + "bbox": [ + 304, + 296, + 545, + 356 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 304, + 296, + 545, + 356 + ], + "type": "text", + "content": ". Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": "Consistency Dataset We construct the consistency dataset " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c = \\{x_c\\}" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\{x_c^1, x_c^2, \\dots, x_c^V\\}" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " using different " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " camera viewpoints. Finally, the consistency dataset " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " is constructed using " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\Omega_c" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " random latent features, so it consists of multi-view images of " + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\Omega_c" + }, + { + "bbox": [ + 304, + 361, + 546, + 494 + ], + "type": "text", + "content": " different objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": "Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\hat{q}_a" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " and label " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "q_{a}" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " for an input sample " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": ". The second term is the variance for the estimated " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\hat{q}_c" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " vector for " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " multiview images for a single object in the consistency dataset, where " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\hat{q}_c^v" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " is the estimated quantity of " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "x_c^v" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": ". Quantifier training loss " + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_q" + }, + { + "bbox": [ + 304, + 497, + 547, + 606 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 612, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 612, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 314, + 612, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {q} = \\sum_ {x _ {a} \\in \\mathcal {D} _ {a}} \\left(q _ {a} - \\hat {q} _ {a}\\right) ^ {2} + \\lambda_ {c} \\sum_ {v = 1} ^ {V} \\sum_ {x _ {c} ^ {v} \\in \\mathcal {D} _ {c}} \\left(\\hat {q} _ {c} ^ {v} - \\bar {\\hat {q}} _ {c} ^ {v}\\right) ^ {2}, \\tag {1}", + "image_path": "8381fa4a8f621d959212680aa7422679c0690926a9ce477188efb3a16da5e14e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\hat{q}}_c^v" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " is the mean of " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{q}_c^v" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " over all " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_c" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " images sampled, one from each group in " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " objects sampled from " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "8531" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " attributes estimation, " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "q^{(k)}" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": "-th quantifier is concatenated to create " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": "-dimensional quantity vector " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "Q = [q^{(1)}, q^{(2)}, \\dots, q^{(K)}]" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": ". A quantity vector can be designed by a combination of various quantifiers, depending on an application." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 162, + 194, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 162, + 194, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 194, + 174 + ], + "type": "text", + "content": "3.2. Multi-Attribute Navigator" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": "Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": ", where the source feature " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": " is changed into the target feature " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": " with the guidance of " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "\\hat{Q}_s" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": ". We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": ". Second, layer-wise attention controller (LAC) estimates which layer among the " + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 180, + 287, + 347 + ], + "type": "text", + "content": " layer-wise mappers (LWMs) to attend each attribute manipulation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": "AFR converts " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\hat{Q}_s" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": " to a 512-dimensional attribute quantity feature " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": ". First, " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\hat{Q}_s" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": " are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": ". The input vector with 1024 dimensions is generated by concatenating " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": ", and then, the input vector is fed to each LWM. From the input vector, " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": "-th LWM generates " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "w_{\\Delta}^{l}" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": ", which represents the movement on the latent space for " + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 348, + 287, + 491 + ], + "type": "text", + "content": "-th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "text", + "content": "LAC outputs the layer-wise attention vector " + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "inline_equation", + "content": "a = [a_1, a_2, \\dots, a_L]" + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "text", + "content": " from attribute quantity feature " + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "text", + "content": ". And the target latent feature " + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 47, + 491, + 287, + 528 + ], + "type": "text", + "content": " is generated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 142, + 532, + 287, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 532, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 142, + 532, + 287, + 546 + ], + "type": "interline_equation", + "content": "w _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\\Delta} ^ {l}, \\tag {2}", + "image_path": "49e301fe44ae5244deebd207299050c5ceaf611ce9f37412d534534eef536531.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 548, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 548, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 117, + 548, + 287, + 563 + ], + "type": "interline_equation", + "content": "w _ {t} = \\left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \\dots , w _ {t} ^ {L} \\right]. \\tag {3}", + "image_path": "2ef69783cd2c132217c90991094a7a8141edeffd3d3d987256665fc4ee09ad74.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 567, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 665 + ], + "type": "text", + "content": "Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of " + }, + { + "bbox": [ + 46, + 567, + 287, + 665 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 46, + 567, + 287, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Loss and Training The navigator is trained such that " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " follows " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "Q_t" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": ", while the identity between " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "I_s" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " is preserved. To this end, we randomly generate " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "Q_t" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " during the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " attributes to train out of a total of " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " attributes at every training iteration. That is, training attribute set " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " is generated as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 343, + 125, + 545, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 125, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 343, + 125, + 545, + 138 + ], + "type": "interline_equation", + "content": "\\mathcal {T} = \\left\\{\\tau_ {1}, \\tau_ {2}, \\dots , \\tau_ {J} \\right\\} \\subset \\{1, 2, \\dots , K \\}. \\tag {4}", + "image_path": "089b8ae3c6274113f9e3d03f8d7fe194b647a267becc1bdd38f203e47a70bdb3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": "Then, " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": " is generated by replacing " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": " elements of " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\hat{Q}_{s}" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": " random target values " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "(q_{t})" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": ". To ensure that the navigator performs well within the entire range of [0, 1], we use " + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 304, + 144, + 545, + 229 + ], + "type": "text", + "content": " randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": "For view consistency in manipulation, we generate multi-view target images from " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": ". Using " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " random camera viewpoint " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "p_t^n" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " multi-view images " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "I_{t}^{n}" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " are generated. And target quantity vector " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " is calculated from " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "I_{t}^{n}" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " is calculated as the average of " + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\hat{Q}_t^n" + }, + { + "bbox": [ + 304, + 230, + 545, + 289 + ], + "type": "text", + "content": " vectors." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "text", + "content": "With the random target attribute quantity " + }, + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "text", + "content": " and random source latent " + }, + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 304, + 289, + 545, + 325 + ], + "type": "text", + "content": ", we train the navigator by minimizing the losses, which can be grouped into three main subsets:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 331, + 545, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 331, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 318, + 331, + 545, + 344 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {n} = \\mathcal {L} _ {Q} \\left(Q _ {t}, \\hat {Q} _ {t}\\right) + \\mathcal {L} _ {i d} \\left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\\right) + \\mathcal {L} _ {a} (a). \\tag {5}", + "image_path": "9956577356ff2ba6f21b3d64972e449e56b428384fe628c52c58a94ff9464b7c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "content": "The quantity loss " + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_Q" + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "content": " guides the navigator to manipulate the image according to the target attribute quantity. " + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "content": "-dimensional quantity vector " + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "Q^{\\prime}" + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "content": " for training attributes set " + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 348, + 545, + 396 + ], + "type": "text", + "content": " is generated as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 364, + 400, + 545, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 400, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 364, + 400, + 545, + 415 + ], + "type": "interline_equation", + "content": "Q ^ {\\prime} = \\left[ q ^ {(\\tau_ {1})}, q ^ {(\\tau_ {2})}, \\dots , q ^ {(\\tau_ {J})} \\right]. \\tag {6}", + "image_path": "efa339e4519188a247881559f8b7e3e7c4d3c523c5da7af62a1fe75c9b7e566a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 420, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 444 + ], + "type": "text", + "content": "And the quantity loss consists of two MSE terms between quantity vectors as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 348, + 448, + 545, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 448, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 348, + 448, + 545, + 463 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {Q} = \\left\\| Q _ {t} ^ {\\prime} - \\hat {Q} _ {t} ^ {\\prime} \\right\\| _ {2} ^ {2} + \\lambda_ {q} \\left\\| Q _ {t} - \\hat {Q} _ {t} \\right\\| _ {2} ^ {2}, \\tag {7}", + "image_path": "5c675a9abd6a4bed2420ea6c1c127d5bf8b5e987091977d94375722c38a7050a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\lambda_{q}" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " is the hyper-parameter for balancing the loss. In quantity loss, the first term is for " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " attributes in " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " and the second term is for all " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " attributes. Because random target quantities are given for " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " attributes out of a total of " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " attributes, " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "K - J" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " attributes of " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": " are from " + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\hat{Q}_s" + }, + { + "bbox": [ + 304, + 467, + 545, + 551 + ], + "type": "text", + "content": ". Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 551, + 463, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 551, + 463, + 563 + ], + "spans": [ + { + "bbox": [ + 318, + 551, + 463, + 563 + ], + "type": "text", + "content": "The identity loss " + }, + { + "bbox": [ + 318, + 551, + 463, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{id}" + }, + { + "bbox": [ + 318, + 551, + 463, + 563 + ], + "type": "text", + "content": " is designed by" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 333, + 567, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 567, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 333, + 567, + 545, + 600 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i d} = \\left\\| w _ {t} - w _ {s} \\right\\| _ {2} ^ {2} + \\frac {\\lambda_ {L}}{N} \\sum_ {n = 1} ^ {N} \\operatorname {L P I P S} \\left(I _ {s}, I _ {t} ^ {n}\\right), \\tag {8}", + "image_path": "c401eef7069230c19762468ce3a2c5f30fa0aece1210aa681eaee619b17fee82.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 604, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 604, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\lambda_{L}" + }, + { + "bbox": [ + 304, + 604, + 545, + 652 + ], + "type": "text", + "content": " is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 652, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 545, + 673 + ], + "type": "text", + "content": "The third term, " + }, + { + "bbox": [ + 304, + 652, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_n" + }, + { + "bbox": [ + 304, + 652, + 545, + 673 + ], + "type": "text", + "content": ", is a regularization loss for layer-wise attention as" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 395, + 673, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 673, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 395, + 673, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a} = | \\alpha - \\bar {a} |, \\tag {9}", + "image_path": "6124de08593e4073132b3cd1d24d28fa60883088c7acd83139c02c38880a6fb4.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{a}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " denotes the average of " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "a_{l}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the hyperparameter for the target average value of attention." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8532" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 308 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 308 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 308 + ], + "type": "image", + "image_path": "1bc818af15eef30a32286bc9eb5235e9dd86ade081db26e7aad42c1f4ba9117c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 311, + 287, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 367 + ], + "type": "text", + "content": "Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 377, + 128, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 377, + 128, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 377, + 128, + 391 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 398, + 180, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 398, + 180, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 398, + 180, + 411 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": "We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "Custom Attribute Quantifier For the attribute dataset " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " for each attribute. We constructed each " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ", each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_a" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " are provided in the supplement. For the consistency dataset " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ", we used " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "V = 10" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\Omega_c = 10,000" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ". We trained the quantifier for 50 epochs with a batch size of " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ". We set" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 308, + 70, + 545, + 289 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 545, + 289 + ], + "type": "image", + "image_path": "341b0542f1919a8cdf8b1f792a347285b30d6eb91d097c1108646a4ff5de9409.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "type": "text", + "content": "Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes. " + }, + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "type": "inline_equation", + "content": "(\\dagger =" + }, + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "type": "text", + "content": " custom attributes implemented via manually constructed " + }, + { + "bbox": [ + 305, + 292, + 545, + 350 + ], + "type": "inline_equation", + "content": "D_{a}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 361, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 305, + 361, + 545, + 386 + ], + "type": "text", + "content": " to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": "Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " with truncation factor " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\phi = 0.7" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " during navigator training. We set hyper-parameters " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\lambda_{q} = 0.5" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\lambda_{L} = 0.1" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "N = 2" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 456, + 479, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 479, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 479, + 468 + ], + "type": "text", + "content": "4.2.Custom Attribute Manipulation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": "As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity " + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": " normalized in the range [0,1]. Regardless of the source attribute quantity " + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\hat{q}_{s}" + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": " of the source image " + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": ", the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When " + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": " approaches 0, they are both expressionless; when " + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": " approaches 1, they both smile broadly." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8533" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 286, + 192 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 192 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 192 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 192 + ], + "type": "image", + "image_path": "50d956ab4bffc06e87b6ad9701b55a46a8981de876e054d71e9d334b0312a7d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 287, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 228 + ], + "type": "text", + "content": "Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 236, + 287, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 259 + ], + "type": "text", + "content": "cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 261, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 499 + ], + "type": "text", + "content": "To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 510, + 133, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 133, + 522 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 133, + 522 + ], + "type": "text", + "content": "4.3. Comparisons" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 529, + 287, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 648 + ], + "type": "text", + "content": "In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "text", + "content": "The resultant image " + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "inline_equation", + "content": "I_{\\theta}^{\\phi}" + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "text", + "content": " was manipulated from the source image " + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "inline_equation", + "content": "I^{\\phi}" + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "text", + "content": " using the " + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "text", + "content": "-th target value " + }, + { + "bbox": [ + 46, + 649, + 287, + 673 + ], + "type": "inline_equation", + "content": "(\\phi = 1, \\dots, \\Phi, \\theta =" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 545, + 282 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 282 + ], + "type": "image", + "image_path": "73b423b5074fcaf092c0a66855729c51355ded3a1a2853e5539dd2c115c0dfa2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 285, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 305, + 285, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 545, + 340 + ], + "type": "text", + "content": "Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 353, + 545, + 497 + ], + "blocks": [ + { + "bbox": [ + 308, + 353, + 545, + 497 + ], + "lines": [ + { + "bbox": [ + 308, + 353, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 308, + 353, + 545, + 497 + ], + "type": "image", + "image_path": "3466cac5575d1ee5658ac4d4ed68d65c58f7d97649fba66d58cec73a3f281c35.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 503, + 545, + 536 + ], + "lines": [ + { + "bbox": [ + 305, + 503, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 545, + 536 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "inline_equation", + "content": "1, \\dots, \\Theta)" + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "text", + "content": ". In addition, we used Face++ [1] to measure " + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "inline_equation", + "content": "r_{\\theta}^{\\phi}" + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "text", + "content": " which is the resultant attribute quantity of " + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "inline_equation", + "content": "I_{\\theta}^{\\phi}" + }, + { + "bbox": [ + 306, + 548, + 545, + 575 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "text", + "content": "*StyleFlow originally used Microsoft Face API [22] as a quantifier, but Microsoft no longer supports it. Therefore, we used Face++ [1] as a quantifier for StyleFlow implementation on EG3D." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8534" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 71, + 535, + 142 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 535, + 142 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 535, + 142 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 535, + 142 + ], + "type": "table", + "html": "
MethodAgeSmileGenderEyeglasses
σm↓Ed↓ρ↑σv↓σm↓Ed↓ρ↑σv↓Acc. ↑Ed↓Acc. ↑Ed↓
StyleFlow8.400.37321.32.30437.380.38229.94.85983%0.58696%0.510
StyleFlow+Q10.460.33122.12.30427.490.32034.42.63578%0.67079%0.486
Ours8.030.24532.62.23521.500.21051.02.25595%0.53796%0.468
", + "image_path": "4fcf46b25655e84ff5299b8070eaffcec964ddcd7d705009f376bcd6f2f43582.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 200, + 191, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 191, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 191, + 212 + ], + "type": "text", + "content": "across multiple manipulated views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": "Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\sigma_{m,\\theta}" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": "-th resultant quantities " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\{r_\\theta^1,\\dots ,r_\\theta^\\Phi \\}" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": ", the evaluation metric " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\sigma_{m}" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": " is the mean of " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\sigma_{m,\\theta}" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": ". Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance " + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "inline_equation", + "content": "E_{d}" + }, + { + "bbox": [ + 46, + 212, + 287, + 344 + ], + "type": "text", + "content": " between the embeddings of two manipulated images, which were generated using two adjacent target values, as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 349, + 287, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 349, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 63, + 349, + 287, + 383 + ], + "type": "interline_equation", + "content": "E _ {d} = \\frac {1}{(\\Theta - 1) \\Phi} \\sum_ {\\theta = 1} ^ {\\Theta - 1} \\sum_ {\\phi = 1} ^ {\\Phi} \\| F \\left(I _ {\\theta + 1} ^ {\\phi}\\right) - F \\left(I _ {\\theta} ^ {\\phi}\\right) \\|, \\tag {10}", + "image_path": "c6f95bc20618f74527ce9d6b74cb63a375181e1b85ac94c717b1c8c96dcfe256.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": " is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": " between attribute manipulation and identity preservation as " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\frac{(r_{\\Theta} - r_1)}{(\\Theta - 1)E_d}" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": ". Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\{I_\\theta^{\\phi,1}, I_\\theta^{\\phi,2}, I_\\theta^{\\phi,3}\\}" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": " and measured the resultant attribute quantities " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\{r_\\theta^{\\phi,1}, r_\\theta^{\\phi,2}, r_\\theta^{\\phi,3}\\}" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": ". From the standard deviation " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\sigma_{v,\\theta}^{\\phi}" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": " of the resultant attribute quantities, the evaluation metric " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\sigma_v" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": " is the mean of " + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\sigma_{v,\\theta}^{\\phi}" + }, + { + "bbox": [ + 46, + 388, + 287, + 516 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "text", + "content": "We conducted experiments with " + }, + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\Phi = 100" + }, + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\Theta = 8" + }, + { + "bbox": [ + 46, + 516, + 287, + 588 + ], + "type": "text", + "content": ". As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case)." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 198, + 544, + 271 + ], + "blocks": [ + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "lines": [ + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness " + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "inline_equation", + "content": "(\\sigma_{m})" + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "text", + "content": ", manipulation accuracy (Acc.), identity preservation " + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "inline_equation", + "content": "(E_{d})" + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "text", + "content": ", manipulation efficiency " + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "text", + "content": ", and view consistency " + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "inline_equation", + "content": "(\\sigma_{v})" + }, + { + "bbox": [ + 46, + 148, + 547, + 183 + ], + "type": "text", + "content": ". Our method gives the best results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 198, + 544, + 271 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 544, + 271 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 544, + 271 + ], + "type": "table", + "html": "
MethodAgeSmile
σm↓Ed↓ρ↑σm↓Ed↓ρ↑
Talk-to-Edit14.30.22132.922.60.21240.9
StyleFlow16.90.19528.429.10.09988.9
Ours10.90.22547.220.20.10396.6
", + "image_path": "65bf801bd10f1647efe1966bc789a98aa6dfd3679c54cdcacb680e86329218ee.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "lines": [ + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness " + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "inline_equation", + "content": "(\\sigma_{m})" + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "text", + "content": ", identity preservation " + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "inline_equation", + "content": "(E_{d})" + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "text", + "content": ", and manipulation efficiency " + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 305, + 276, + 547, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 345, + 545, + 452 + ], + "blocks": [ + { + "bbox": [ + 307, + 345, + 545, + 452 + ], + "lines": [ + { + "bbox": [ + 307, + 345, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 307, + 345, + 545, + 452 + ], + "type": "image", + "image_path": "b24c83074bb6cf30e6be56200cd916e06c304a23144a2ed51d4a06396f8be75f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 456, + 546, + 502 + ], + "lines": [ + { + "bbox": [ + 305, + 456, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 546, + 502 + ], + "type": "text", + "content": "Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 520, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 628 + ], + "type": "text", + "content": "Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": "As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness " + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{m}" + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": ". In the " + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "inline_equation", + "content": "E_{d}" + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": " score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score " + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": ". This result implies that our method better preserves identity when an attribute changes by the same quantity." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8535" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 291, + 156 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 291, + 156 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 291, + 156 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 291, + 156 + ], + "type": "table", + "html": "
Modelσm↓Acc.↑Ed↓
Designw/o LAC module15.8496.0%0.415
w/o AFR module15.3789.0%0.387
Trainingw/o entireatts. in LQ14.7887.5%0.405
w/o intermediate Qt15.6597.0%0.402
Full model14.7695.5%0.365
", + "image_path": "26ce4651b79af4022ffb8a6f8a817136cffda45cbc391f02c34bb9a421c8d573.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "type": "text", + "content": "Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness " + }, + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "type": "inline_equation", + "content": "(\\sigma_{m})" + }, + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "type": "text", + "content": ", accuracy, and identity preservation " + }, + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "type": "inline_equation", + "content": "(E_{d})" + }, + { + "bbox": [ + 46, + 159, + 288, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 215, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 370 + ], + "type": "text", + "content": "In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 141, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 141, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 141, + 395 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": "Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_Q" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ", intermediate target quantity). In the ablation study on the LAC module, we generated " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " by adding " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "w_{\\Delta}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ". In the ablation study on the AFR module, we generated " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{Q}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " by concatenating " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{Q}_{s}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ", then repeating it. When entire attributes are not used in " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_Q" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ", we trained the navigator with " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_q = 0" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ". When an intermediate target quantity is not used, we trained the navigator by randomly sampling " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{m}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "87.5\\%" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "95.5\\%" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": ". Using intermediate target quantity in navigator training improved the manipulation exactness " + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{m}" + }, + { + "bbox": [ + 46, + 401, + 288, + 714 + ], + "type": "text", + "content": " from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 420, + 141 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 420, + 141 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 420, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 420, + 141 + ], + "type": "image", + "image_path": "bcda9631a4a613ddff274b065263ff8380d2e3c2b2918692c26231ed06e72270.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 146, + 545, + 179 + ], + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 179 + ], + "type": "text", + "content": "Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation " + }, + { + "bbox": [ + 305, + 146, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\sigma_v" + }, + { + "bbox": [ + 305, + 146, + 545, + 179 + ], + "type": "text", + "content": " (a lower value is better)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 425, + 78, + 543, + 125 + ], + "blocks": [ + { + "bbox": [ + 425, + 78, + 543, + 125 + ], + "lines": [ + { + "bbox": [ + 425, + 78, + 543, + 125 + ], + "spans": [ + { + "bbox": [ + 425, + 78, + 543, + 125 + ], + "type": "image", + "image_path": "0053102007f163eb5229b4e49f7c77e4883b10d9358053ef1d7e7459895bfb0f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "text", + "content": "View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset " + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "text", + "content": " by setting " + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "inline_equation", + "content": "\\lambda_c = 0" + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "text", + "content": ". In the ablation study on the navigator, we trained the navigator without multi-view images by setting " + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 304, + 195, + 545, + 327 + ], + "type": "text", + "content": ". Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 341, + 378, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 341, + 378, + 353 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 378, + 353 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "content": "Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of " + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "content": ". This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 501, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 609 + ], + "type": "text", + "content": "Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "type": "text", + "content": "Further discussion of the potential negative social impacts is provided in the supplement." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8536" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "text", + "content": "[1] Face++ face detection api. https://www faceplusplus.com/. 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Mofan-erf: Morphable facial neural radiance field. arXiv preprint arXiv:2112.02308, 2021. 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "8538" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_content_list.json b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fcb9267c071a1103529109884e07a0ce1577c99f --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_content_list.json @@ -0,0 +1,1700 @@ +[ + { + "type": "text", + "text": "Quantum Multi-Model Fitting", + "text_level": 1, + "bbox": [ + 330, + 130, + 640, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Matteo Farina1 Luca Magri2 Willi Menapace1", + "bbox": [ + 281, + 179, + 683, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Elisa Ricci $^{1,3}$ Vladislav Golyanik $^{4}$ Federica Arrigoni $^{2}$", + "bbox": [ + 253, + 198, + 715, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Trento 2Politecnico di Milano 3Fondazione Bruno Kessler 4MPI for Informatics, SIC", + "bbox": [ + 166, + 217, + 803, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.", + "bbox": [ + 73, + 300, + 473, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 571, + 209, + 588 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them.", + "bbox": [ + 73, + 598, + 468, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fd51112c3082f1c75d16cc57985fc1ad1a29c5de439eb310cb472cbc369f7b5a.jpg", + "image_caption": [ + "Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49]." + ], + "image_footnote": [], + "bbox": [ + 504, + 267, + 691, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c73c3852b6acb3a794c6aa5a57af836b73e0ec7194e9fbdd27e1761dd9a37656.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 276, + 875, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including $\\mathcal{NP}$ -hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC?", + "bbox": [ + 496, + 506, + 893, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal", + "bbox": [ + 496, + 734, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13640", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few.", + "bbox": [ + 75, + 287, + 472, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF.", + "bbox": [ + 75, + 409, + 473, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. In summary, the primary technical contributions of this paper are the following:", + "bbox": [ + 76, + 671, + 468, + 700 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs;", + "- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models;", + "- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware." + ], + "bbox": [ + 94, + 703, + 468, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 500, + 89, + 627, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The QUBO formulation in a binary search space is an optimization problem of the following form:", + "bbox": [ + 498, + 114, + 890, + 146 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {y} \\in \\mathbb {R} ^ {d}} \\mathbf {y} ^ {\\mathsf {T}} Q \\mathbf {y} + \\mathbf {s} ^ {\\mathsf {T}} \\mathbf {y}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 155, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbb{B}^d$ denotes the set of binary vectors of length $d$ , $Q \\in \\mathbb{R}^{d \\times d}$ is a real symmetric matrix and, in a QUBO with $d$ variables, their linear coefficients are packed into $\\mathbf{s} \\in \\mathbb{R}^d$ . When the problem is subject to linear constraints of the form $A\\mathbf{y} = \\mathbf{b}$ , a common approach is to relax such constraints and reformulate the QUBO as:", + "bbox": [ + 498, + 194, + 890, + 285 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {y} \\in \\mathbb {B} ^ {d}} \\mathbf {y} ^ {\\top} Q \\mathbf {y} + \\mathbf {s} ^ {\\top} \\mathbf {y} + \\lambda | | A \\mathbf {y} - \\mathbf {b} | | _ {2} ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 295, + 890, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\lambda$ must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to:", + "bbox": [ + 498, + 333, + 890, + 363 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {y} \\in B ^ {d}} \\mathbf {y} ^ {\\top} \\tilde {Q} \\mathbf {y} + \\tilde {\\mathbf {s}} ^ {\\top} \\mathbf {y} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 373, + 890, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where the following simple substitutions are implied:", + "bbox": [ + 500, + 412, + 852, + 428 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {Q} = Q + \\lambda A ^ {\\mathsf {T}} A, \\quad \\tilde {\\mathbf {s}} = \\mathbf {s} - 2 \\lambda A ^ {\\mathsf {T}} \\mathbf {b} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 438, + 890, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the proof, the reader can refer to, e.g., Birdal et al. [6].", + "bbox": [ + 498, + 468, + 885, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector $\\mathbf{y}$ ), while each coupler models an element of $Q$ (i.e., the coupler between the physical qubits $i$ and $j$ maps to entry $Q_{ij}$ ). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s.", + "bbox": [ + 496, + 487, + 890, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having $d$ nodes (called logical qubits $^1$ ), corresponding to the $d$ entries of $\\mathbf{y}$ and edges corresponding to the non-zero entries of $Q$ .", + "bbox": [ + 496, + 669, + 890, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such", + "bbox": [ + 496, + 775, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "Hereafter we will sometimes omit the term \"logical\" or \"physical\" as it will be clear from the context which type of qubits are being involved.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13641", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling.", + "bbox": [ + 75, + 151, + 470, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures.", + "bbox": [ + 75, + 422, + 468, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 585, + 287, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems.", + "bbox": [ + 75, + 612, + 468, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem formulation", + "text_level": 1, + "bbox": [ + 76, + 696, + 274, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a set of data points $X = \\{x_{1},\\dots,x_{n}\\}$ and a set $\\Theta = \\{\\theta_1,\\ldots ,\\theta_m\\}$ of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from $\\Theta$ the \"best\" models that describe all the data $X$ . Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Choice of Optimization Objective", + "text_level": 1, + "bbox": [ + 498, + 220, + 794, + 237 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by $P$ and defined as:", + "bbox": [ + 496, + 243, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP [ i, j ] = \\left\\{ \\begin{array}{l l} 1 & \\text {i f e r r o r} \\left(x _ {i}, \\theta_ {j}\\right) < \\epsilon \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 449, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where: $x_{i}$ and $\\theta_{j}$ are the $i$ -th point in the dataset and the $j$ -th sampled model respectively; error expresses the residual of point $x_{i}$ w.r.t. model $\\theta_{j}$ and $\\epsilon$ is the inlier threshold to assign the point to the model. $P$ is a matrix of size is $n \\times m$ , where $n$ and $m$ are the number of points and models, respectively. Intuitively, the columns of $P$ represent the consensus sets of models, while the rows are points' preference sets.", + "bbox": [ + 496, + 497, + 890, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of $P$ that explain all the rows. More formally:", + "bbox": [ + 496, + 603, + 890, + 662 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} \\geqslant \\mathbb {1} _ {n} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 672, + 890, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbb{1}$ denotes a vector of ones (whose length is given as subscript) and $\\mathbf{z}$ is a binary vector representing which models (i.e., columns of the preference matrix $P$ ) are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy.", + "bbox": [ + 496, + 704, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13642", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by $k$ ) is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly $k$ models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work:", + "bbox": [ + 76, + 301, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} = \\mathbb {1} _ {n}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 339, + 468, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation.", + "bbox": [ + 75, + 369, + 470, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. QUBO Formulation", + "text_level": 1, + "bbox": [ + 76, + 454, + 267, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences:", + "bbox": [ + 75, + 477, + 468, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ = 0, \\quad \\mathbf {s} = \\mathbb {1} _ {m}, \\quad A = P, \\quad \\mathbf {b} = \\mathbb {1} _ {n} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 623, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where optimization is carried out over $\\mathbf{z} \\in \\mathbb{B}^m$ , that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that:", + "bbox": [ + 75, + 647, + 468, + 693 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {Q} = \\lambda P ^ {\\mathsf {T}} P, \\quad \\tilde {\\mathbf {s}} = \\mathbb {1} _ {m} - 2 \\lambda P ^ {\\mathsf {T}} \\mathbb {1} _ {n} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 699, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where no matrix of quadratic coefficients is present in $\\widetilde{Q}$ as the considered formulation only contains linear terms, i.e., $Q = 0$ . Hence, Problem (7) can be turned into a QUBO of the form (3), namely:", + "bbox": [ + 76, + 724, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\lambda \\mathbf {z} ^ {\\top} (P ^ {\\top} P) \\mathbf {z} + \\left(\\mathbb {1} _ {m} - 2 \\lambda P ^ {\\top} \\mathbb {1} _ {n}\\right) ^ {\\top} \\mathbf {z}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 792, + 468, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF.", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 DEQUMF" + ], + "code_body": "Require: $P,s$ \nwhile $|P$ .columns $\\vert >s$ do subproblems $= \\text{ColumnPartition}(P,s)$ $i\\gets 0$ \nwhile $i < |$ subproblems|do $\\mathcal{J}_i\\gets$ models in the $i$ -th subproblem $P_{\\mathcal{I}_i}\\gets P$ retaining only the $\\mathcal{J}_i$ columns $\\mathbf{z}_i = \\mathrm{QUMF}(P_{\\mathcal{I}_i})$ remove from $P$ columns $P_{\\mathcal{I}_i}[:,1 - \\mathbf{z}_i]$ $i\\gets i + 1$ \nend while \nend while \n $\\mathbf{z}\\gets \\mathrm{QUMF}(P)$ \nreturn $P[:,\\mathbf{z}]$", + "bbox": [ + 500, + 107, + 803, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Iterative Decomposed Set-Cover", + "text_level": 1, + "bbox": [ + 500, + 334, + 784, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of $m$ . In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix $P$ and reduces the dimension of the problem to fit the number of available physical qubits.", + "bbox": [ + 496, + 358, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix $P$ , at each iteration we partition the columns of $P$ into multiple submatrices $P_{\\mathcal{J}_i}$ , where $\\mathcal{J}_i$ indicates the set of selected column indices and $|\\mathcal{J}_i| = s$ . We choose the subproblem size $s$ so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by $P_{\\mathcal{J}_i}$ is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector $\\mathbf{z}_i$ that represents the subset of selected models for the current subproblem. Note that models not selected in $\\mathbf{z}_i$ are unlikely to be solutions to the original problem since, by construction, $\\mathbf{z}_i$ maximizes the coverage on all points with only the restricted subset of models $\\mathcal{J}_i$ . Then, after all subproblems have been solved, we prune $P$ by retaining only the columns that are selected in the corresponding optimal $\\mathbf{z}_i$ . This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2).", + "bbox": [ + 496, + 479, + 892, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We iteratively apply the above procedure until the number of remaining columns in $P$ falls below $s$ , at which point the problem is directly and reliably solved using QUMF.", + "bbox": [ + 496, + 752, + 893, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Related Work", + "text_level": 1, + "bbox": [ + 500, + 814, + 640, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13643", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7974b62aff55b9686262afa416fda5adb67ad6385a2a793ec744d99befaf0f52.jpg", + "image_caption": [ + "Figure 2. Illustration of the iterative pruning technique applied to $P$ in DEQUMF over consecutive iterations. At time $t$ , $P$ is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time $t + 1$ , models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 433, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Multi-Model Fitting", + "text_level": 1, + "bbox": [ + 76, + 398, + 269, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods.", + "bbox": [ + 75, + 422, + 468, + 482 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50].", + "bbox": [ + 75, + 483, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5].", + "bbox": [ + 75, + 604, + 468, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective2. However, there are sub", + "bbox": [ + 75, + 785, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals.", + "bbox": [ + 500, + 90, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantum Computer Vision", + "text_level": 1, + "bbox": [ + 500, + 239, + 746, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series.", + "bbox": [ + 498, + 263, + 890, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence.", + "bbox": [ + 498, + 491, + 892, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All available approaches can be classified into single QUBO (\"one sweep\") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on", + "bbox": [ + 498, + 674, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2The same objective is considered but constraints are different: RANSACOV [29] allows for overlapping models, resulting in an inequality constraint, see Problem (6); instead, we consider disjoint models, using an equality constraint, see Problem (7). For a fair comparison, we slightly modify RANSACOV, replacing the inequality with an equality constraint.", + "bbox": [ + 75, + 838, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13644", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4).", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach.", + "bbox": [ + 75, + 212, + 470, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs.", + "bbox": [ + 75, + 545, + 468, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fcc2996690464e415e76d60e81fea03f4dd8a3a6afc5952afa587cac738f4d6a.jpg", + "image_caption": [ + "Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points $n$ is fixed to $n = 30$ , the number of ground-truth structures is fixed to $k = 5$ , and the number of sampled models $m$ is arranged on the x-axis." + ], + "image_footnote": [], + "bbox": [ + 506, + 93, + 883, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/619b7500bcc91c415825961aeb7cebdf7c7724f9f8b038a27fdef64f56e84587.jpg", + "image_caption": [ + "Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44]." + ], + "image_footnote": [], + "bbox": [ + 542, + 291, + 846, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of $20\\mu s$", + "bbox": [ + 496, + 474, + 890, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Selection of $\\lambda$ . In every experiment, we set $\\lambda = 1.1$ . This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for $\\lambda$ by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for $\\lambda$ generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error.", + "bbox": [ + 496, + 510, + 892, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Synthetic Data", + "text_level": 1, + "bbox": [ + 500, + 686, + 650, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions.", + "bbox": [ + 496, + 709, + 890, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Small-scale Data. In this experiment, we select a subset of $n = 30$ points. The number of ground-truth models is fixed to $k = 5$ , and additional $m - k$ excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma", + "bbox": [ + 496, + 758, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3We refer to optimal solution probability as the ratio between the anneals ended in a globally optimal state and the total number of anneals.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13645", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b1d0c7c65a8de500bfb6816dcef9456944eab3bf387f56d4b33115b8f8ef4fa4.jpg", + "image_caption": [ + "Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points $n$ is fixed to $n = 250$ , the number of ground-truth structures is fixed to $k = 5$ , and the number of sampled models $m$ (corresponding to the dimension of the search space) is arranged on the x-axis." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 464, + 224 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online $^4$ , that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1.", + "bbox": [ + 75, + 305, + 468, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware.", + "bbox": [ + 75, + 426, + 470, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph.", + "bbox": [ + 75, + 613, + 468, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the $k = 5$ ground-truth models) as well as all of the $n = 250$", + "bbox": [ + 76, + 830, + 470, + 875 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29].", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range $[0,10]\\%$ for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed.", + "bbox": [ + 496, + 198, + 892, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Real Data", + "text_level": 1, + "bbox": [ + 500, + 340, + 612, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA).", + "bbox": [ + 496, + 363, + 890, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments.", + "bbox": [ + 496, + 426, + 892, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach5 perform reasonably well, with DEQUMF (SA) being on par with the state of the art.", + "bbox": [ + 496, + 580, + 890, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art.", + "bbox": [ + 496, + 750, + 890, + 854 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "5We are not able to run QUMF on Traffic2 due to the limited amount of GPU time available in our monthly subscription combined with the large dimension of the dataset, hence results are not reported.", + "bbox": [ + 500, + 862, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "4https://fusiello.github.io/demo/cov/index.html", + "bbox": [ + 93, + 886, + 465, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13646", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ffa7645a9363dc96703d2bf7013f6576a9a7ca69ab66a5ad671ff1497a898627.jpg", + "table_caption": [ + "Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15]." + ], + "table_footnote": [], + "table_body": "
Multi-X [4]J-Linkage [44]T-Linkage [28]RPA [30]RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
Traffic3 [45]mean0.321.580.480.190.355.148.740.55
median00.340.1900.192.857.500.28
Traffic2 [45]mean0.091.751.310.140.546.04-0.10
median000003.17-0
York [15]mean-2.851.441.080.1912.29-0.74
median-1.800003.78-0
", + "bbox": [ + 81, + 103, + 883, + 220 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6abed28e600689162ff25dafc369b56d246880e045c7ba4bdb9e0f953fba51bf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
mean9.793.8516.220.77
median7.973.5411.00.18
", + "bbox": [ + 81, + 234, + 467, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Comparison with Quantum State-of-the-art", + "text_level": 1, + "bbox": [ + 76, + 332, + 447, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online6, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers.", + "bbox": [ + 75, + 354, + 468, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider $10\\%$ and $20\\%$ of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3.", + "bbox": [ + 75, + 595, + 468, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios.", + "bbox": [ + 75, + 732, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 76, + 821, + 199, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate", + "bbox": [ + 76, + 847, + 468, + 877 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/899d8c2d8f1036da7ad55186c19fe50bccebfb4b55f052aa7a4c129939cb5159.jpg", + "table_caption": [ + "Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49]." + ], + "table_footnote": [], + "table_body": "
AlgorithmOutlier ratio
10%20%Full sequences
QUMF (SA)7.2211.3413.23
DEQUMF2.4110.5316.17
DEQUMF (SA)6.268.2810.83
HQC-RF [17]3.7137.045.84
", + "bbox": [ + 549, + 234, + 841, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49].", + "bbox": [ + 498, + 339, + 890, + 367 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cca06efa4822d1a5eeafcc75d43abbb4354bc89338573e739da3c9a71476f8fa.jpg", + "image_caption": [ + "DEQUMF (SA)" + ], + "image_footnote": [], + "bbox": [ + 506, + 375, + 696, + 430 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2718e7988b4c7a55ad82a54a0355278d565bf2da9c76213bd044f29b0d0c68e6.jpg", + "image_caption": [ + "HQC-RF [17]", + "Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with $20\\%$ outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves $8.49\\%$ error." + ], + "image_footnote": [], + "bbox": [ + 696, + 375, + 885, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work.", + "bbox": [ + 496, + 536, + 890, + 627 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 646, + 617, + 661 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research.", + "bbox": [ + 496, + 672, + 890, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN.", + "bbox": [ + 496, + 787, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "$^{6}$ https://github.com/dadung/HQC-robust-fitting", + "bbox": [ + 93, + 886, + 450, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13647", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sameer Agarwal, Jongwoo Lim, Lihi Zelnik-manor, Pietro Perona, David Kriegman, and Serge Belongie. Beyond pairwise clustering. 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IEEE, 2005. 5" + ], + "bbox": [ + 501, + 92, + 890, + 893 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13649", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_model.json b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_model.json new file mode 100644 index 0000000000000000000000000000000000000000..69d1dfc3a2509f8000a562b3d11dff2dd2832292 --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_model.json @@ -0,0 +1,2354 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.331, + 0.131, + 0.642, + 0.154 + ], + "angle": 0, + "content": "Quantum Multi-Model Fitting" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.18, + 0.684, + 0.199 + ], + "angle": 0, + "content": "Matteo Farina1 Luca Magri2 Willi Menapace1" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.199, + 0.717, + 0.218 + ], + "angle": 0, + "content": "Elisa Ricci\\(^{1,3}\\) Vladislav Golyanik\\(^{4}\\) Federica Arrigoni\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.218, + 0.804, + 0.234 + ], + "angle": 0, + "content": "1University of Trento 2Politecnico di Milano 3Fondazione Bruno Kessler 4MPI for Informatics, SIC" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.301, + 0.474, + 0.529 + ], + "angle": 0, + "content": "Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.573, + 0.21, + 0.589 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.599, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.268, + 0.692, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.277, + 0.876, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.403, + 0.895, + 0.501 + ], + "angle": 0, + "content": "Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.895, + 0.735 + ], + "angle": 0, + "content": "vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including \\(\\mathcal{NP}\\)-hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13640" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.41 + ], + "angle": 0, + "content": "Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.474, + 0.668 + ], + "angle": 0, + "content": "This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.672, + 0.47, + 0.702 + ], + "angle": 0, + "content": "Contributions. In summary, the primary technical contributions of this paper are the following:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.704, + 0.469, + 0.735 + ], + "angle": 0, + "content": "- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.741, + 0.469, + 0.772 + ], + "angle": 0, + "content": "- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.778, + 0.469, + 0.824 + ], + "angle": 0, + "content": "- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.704, + 0.469, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.628, + 0.108 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.116, + 0.892, + 0.147 + ], + "angle": 0, + "content": "The QUBO formulation in a binary search space is an optimization problem of the following form:" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.156, + 0.892, + 0.183 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {y} \\in \\mathbb {R} ^ {d}} \\mathbf {y} ^ {\\mathsf {T}} Q \\mathbf {y} + \\mathbf {s} ^ {\\mathsf {T}} \\mathbf {y}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.195, + 0.892, + 0.286 + ], + "angle": 0, + "content": "where \\(\\mathbb{B}^d\\) denotes the set of binary vectors of length \\(d\\), \\(Q \\in \\mathbb{R}^{d \\times d}\\) is a real symmetric matrix and, in a QUBO with \\(d\\) variables, their linear coefficients are packed into \\(\\mathbf{s} \\in \\mathbb{R}^d\\). When the problem is subject to linear constraints of the form \\(A\\mathbf{y} = \\mathbf{b}\\), a common approach is to relax such constraints and reformulate the QUBO as:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.296, + 0.892, + 0.323 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {y} \\in \\mathbb {B} ^ {d}} \\mathbf {y} ^ {\\top} Q \\mathbf {y} + \\mathbf {s} ^ {\\top} \\mathbf {y} + \\lambda | | A \\mathbf {y} - \\mathbf {b} | | _ {2} ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.334, + 0.892, + 0.364 + ], + "angle": 0, + "content": "where \\(\\lambda\\) must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to:" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.374, + 0.892, + 0.403 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {y} \\in B ^ {d}} \\mathbf {y} ^ {\\top} \\tilde {Q} \\mathbf {y} + \\tilde {\\mathbf {s}} ^ {\\top} \\mathbf {y} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.413, + 0.853, + 0.429 + ], + "angle": 0, + "content": "where the following simple substitutions are implied:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.439, + 0.892, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\tilde {Q} = Q + \\lambda A ^ {\\mathsf {T}} A, \\quad \\tilde {\\mathbf {s}} = \\mathbf {s} - 2 \\lambda A ^ {\\mathsf {T}} \\mathbf {b} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.469, + 0.886, + 0.485 + ], + "angle": 0, + "content": "For the proof, the reader can refer to, e.g., Birdal et al. [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector \\(\\mathbf{y}\\)), while each coupler models an element of \\(Q\\) (i.e., the coupler between the physical qubits \\(i\\) and \\(j\\) maps to entry \\(Q_{ij}\\)). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.892, + 0.775 + ], + "angle": 0, + "content": "Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having \\(d\\) nodes (called logical qubits\\(^1\\)), corresponding to the \\(d\\) entries of \\(\\mathbf{y}\\) and edges corresponding to the non-zero entries of \\(Q\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.892, + 0.867 + ], + "angle": 0, + "content": "The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Hereafter we will sometimes omit the term \"logical\" or \"physical\" as it will be clear from the context which type of qubits are being involved." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13641" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.424 + ], + "angle": 0, + "content": "Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.576 + ], + "angle": 0, + "content": "It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.289, + 0.604 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.689 + ], + "angle": 0, + "content": "In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.276, + 0.712 + ], + "angle": 0, + "content": "3.1. Problem formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Consider a set of data points \\( X = \\{x_{1},\\dots,x_{n}\\} \\) and a set \\( \\Theta = \\{\\theta_1,\\ldots ,\\theta_m\\} \\) of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from \\( \\Theta \\) the \"best\" models that describe all the data \\( X \\). Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.221, + 0.795, + 0.238 + ], + "angle": 0, + "content": "3.2. Choice of Optimization Objective" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.44 + ], + "angle": 0, + "content": "In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by \\( P \\) and defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.45, + 0.892, + 0.49 + ], + "angle": 0, + "content": "\\[\nP [ i, j ] = \\left\\{ \\begin{array}{l l} 1 & \\text {i f e r r o r} \\left(x _ {i}, \\theta_ {j}\\right) < \\epsilon \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.604 + ], + "angle": 0, + "content": "where: \\( x_{i} \\) and \\( \\theta_{j} \\) are the \\( i \\)-th point in the dataset and the \\( j \\)-th sampled model respectively; error expresses the residual of point \\( x_{i} \\) w.r.t. model \\( \\theta_{j} \\) and \\( \\epsilon \\) is the inlier threshold to assign the point to the model. \\( P \\) is a matrix of size is \\( n \\times m \\), where \\( n \\) and \\( m \\) are the number of points and models, respectively. Intuitively, the columns of \\( P \\) represent the consensus sets of models, while the rows are points' preference sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.664 + ], + "angle": 0, + "content": "In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of \\( P \\) that explain all the rows. More formally:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.673, + 0.891, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} \\geqslant \\mathbb {1} _ {n} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.856 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\) denotes a vector of ones (whose length is given as subscript) and \\(\\mathbf{z}\\) is a binary vector representing which models (i.e., columns of the preference matrix \\(P\\)) are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13642" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by \\( k \\)) is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly \\( k \\) models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.47, + 0.334 + ], + "angle": 0, + "content": "These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.34, + 0.47, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} = \\mathbb {1} _ {n}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.471, + 0.448 + ], + "angle": 0, + "content": "The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.269, + 0.47 + ], + "angle": 0, + "content": "3.3. QUBO Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.624, + 0.469, + 0.64 + ], + "angle": 0, + "content": "\\[\nQ = 0, \\quad \\mathbf {s} = \\mathbb {1} _ {m}, \\quad A = P, \\quad \\mathbf {b} = \\mathbb {1} _ {n} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.694 + ], + "angle": 0, + "content": "where optimization is carried out over \\(\\mathbf{z} \\in \\mathbb{B}^m\\), that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.7, + 0.469, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\tilde {Q} = \\lambda P ^ {\\mathsf {T}} P, \\quad \\tilde {\\mathbf {s}} = \\mathbb {1} _ {m} - 2 \\lambda P ^ {\\mathsf {T}} \\mathbb {1} _ {n} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.726, + 0.47, + 0.788 + ], + "angle": 0, + "content": "where no matrix of quadratic coefficients is present in \\(\\widetilde{Q}\\) as the considered formulation only contains linear terms, i.e., \\(Q = 0\\). Hence, Problem (7) can be turned into a QUBO of the form (3), namely:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.794, + 0.469, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\lambda \\mathbf {z} ^ {\\top} (P ^ {\\top} P) \\mathbf {z} + \\left(\\mathbb {1} _ {m} - 2 \\lambda P ^ {\\top} \\mathbb {1} _ {n}\\right) ^ {\\top} \\mathbf {z}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF." + }, + { + "type": "code_caption", + "bbox": [ + 0.502, + 0.091, + 0.664, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 DEQUMF" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.108, + 0.805, + 0.306 + ], + "angle": 0, + "content": "Require: \\(P,s\\) \nwhile \\(|P\\) .columns \\(\\vert >s\\) do subproblems \\(= \\text{ColumnPartition}(P,s)\\) \\(i\\gets 0\\) \nwhile \\(i < |\\) subproblems|do \\(\\mathcal{J}_i\\gets\\) models in the \\(i\\) -th subproblem \\(P_{\\mathcal{I}_i}\\gets P\\) retaining only the \\(\\mathcal{J}_i\\) columns \\(\\mathbf{z}_i = \\mathrm{QUMF}(P_{\\mathcal{I}_i})\\) remove from \\(P\\) columns \\(P_{\\mathcal{I}_i}[:,1 - \\mathbf{z}_i]\\) \\(i\\gets i + 1\\) \nend while \nend while \n\\(\\mathbf{z}\\gets \\mathrm{QUMF}(P)\\) \nreturn \\(P[:,\\mathbf{z}]\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.335, + 0.785, + 0.351 + ], + "angle": 0, + "content": "3.4. Iterative Decomposed Set-Cover" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.48 + ], + "angle": 0, + "content": "While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of \\( m \\). In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix \\( P \\) and reduces the dimension of the problem to fit the number of available physical qubits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.893, + 0.752 + ], + "angle": 0, + "content": "Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix \\(P\\), at each iteration we partition the columns of \\(P\\) into multiple submatrices \\(P_{\\mathcal{J}_i}\\), where \\(\\mathcal{J}_i\\) indicates the set of selected column indices and \\(|\\mathcal{J}_i| = s\\). We choose the subproblem size \\(s\\) so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by \\(P_{\\mathcal{J}_i}\\) is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector \\(\\mathbf{z}_i\\) that represents the subset of selected models for the current subproblem. Note that models not selected in \\(\\mathbf{z}_i\\) are unlikely to be solutions to the original problem since, by construction, \\(\\mathbf{z}_i\\) maximizes the coverage on all points with only the restricted subset of models \\(\\mathcal{J}_i\\). Then, after all subproblems have been solved, we prune \\(P\\) by retaining only the columns that are selected in the corresponding optimal \\(\\mathbf{z}_i\\). This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.894, + 0.799 + ], + "angle": 0, + "content": "We iteratively apply the above procedure until the number of remaining columns in \\( P \\) falls below \\( s \\), at which point the problem is directly and reliably solved using QUMF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.642, + 0.83 + ], + "angle": 0, + "content": "4. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.434, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.473, + 0.385 + ], + "angle": 0, + "content": "Figure 2. Illustration of the iterative pruning technique applied to \\( P \\) in DEQUMF over consecutive iterations. At time \\( t \\), \\( P \\) is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time \\( t + 1 \\), models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.4, + 0.27, + 0.417 + ], + "angle": 0, + "content": "4.1. Multi-Model Fitting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.483 + ], + "angle": 0, + "content": "Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.785 + ], + "angle": 0, + "content": "Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.47, + 0.831 + ], + "angle": 0, + "content": "Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective2. However, there are sub" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.894, + 0.228 + ], + "angle": 0, + "content": "stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.24, + 0.747, + 0.258 + ], + "angle": 0, + "content": "4.2. Quantum Computer Vision" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.265, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.492, + 0.893, + 0.674 + ], + "angle": 0, + "content": "Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.894, + 0.901 + ], + "angle": 0, + "content": "All available approaches can be classified into single QUBO (\"one sweep\") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.839, + 0.47, + 0.902 + ], + "angle": 0, + "content": "2The same objective is considered but constraints are different: RANSACOV [29] allows for overlapping models, resulting in an inequality constraint, see Problem (6); instead, we consider disjoint models, using an equality constraint, see Problem (7). For a fair comparison, we slightly modify RANSACOV, replacing the inequality with an equality constraint." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13644" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.544 + ], + "angle": 0, + "content": "Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.696 + ], + "angle": 0, + "content": "Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.21, + 0.726 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.094, + 0.885, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.229, + 0.895, + 0.286 + ], + "angle": 0, + "content": "Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points \\( n \\) is fixed to \\( n = 30 \\), the number of ground-truth structures is fixed to \\( k = 5 \\), and the number of sampled models \\( m \\) is arranged on the x-axis." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.292, + 0.847, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.425, + 0.893, + 0.466 + ], + "angle": 0, + "content": "Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.507 + ], + "angle": 0, + "content": "AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of \\(20\\mu s\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.893, + 0.678 + ], + "angle": 0, + "content": "Selection of \\(\\lambda\\). In every experiment, we set \\(\\lambda = 1.1\\). This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for \\(\\lambda\\) by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for \\(\\lambda\\) generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.687, + 0.651, + 0.703 + ], + "angle": 0, + "content": "5.1. Synthetic Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.892, + 0.756 + ], + "angle": 0, + "content": "We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.866 + ], + "angle": 0, + "content": "Small-scale Data. In this experiment, we select a subset of \\( n = 30 \\) points. The number of ground-truth models is fixed to \\( k = 5 \\), and additional \\( m - k \\) excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3We refer to optimal solution probability as the ratio between the anneals ended in a globally optimal state and the total number of anneals." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13645" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.465, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.472, + 0.302 + ], + "angle": 0, + "content": "Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points \\( n \\) is fixed to \\( n = 250 \\), the number of ground-truth structures is fixed to \\( k = 5 \\), and the number of sampled models \\( m \\) (corresponding to the dimension of the search space) is arranged on the x-axis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.427 + ], + "angle": 0, + "content": "trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online\\(^4\\), that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.471, + 0.609 + ], + "angle": 0, + "content": "Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.827 + ], + "angle": 0, + "content": "Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.831, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the \\( k = 5 \\) ground-truth models) as well as all of the \\( n = 250 \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.893, + 0.334 + ], + "angle": 0, + "content": "Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range \\([0,10]\\%\\) for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.341, + 0.613, + 0.355 + ], + "angle": 0, + "content": "5.2. Real Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.424 + ], + "angle": 0, + "content": "In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.893, + 0.579 + ], + "angle": 0, + "content": "AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.747 + ], + "angle": 0, + "content": "Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach5 perform reasonably well, with DEQUMF (SA) being on par with the state of the art." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.856 + ], + "angle": 0, + "content": "York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.893, + 0.901 + ], + "angle": 0, + "content": "5We are not able to run QUMF on Traffic2 due to the limited amount of GPU time available in our monthly subscription combined with the large dimension of the dataset, hence results are not reported." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.466, + 0.901 + ], + "angle": 0, + "content": "4https://fusiello.github.io/demo/cov/index.html" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13646" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.089, + 0.866, + 0.103 + ], + "angle": 0, + "content": "Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.104, + 0.885, + 0.222 + ], + "angle": 0, + "content": "
Multi-X [4]J-Linkage [44]T-Linkage [28]RPA [30]RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
Traffic3 [45]mean0.321.580.480.190.355.148.740.55
median00.340.1900.192.857.500.28
Traffic2 [45]mean0.091.751.310.140.546.04-0.10
median000003.17-0
York [15]mean-2.851.441.080.1912.29-0.74
median-1.800003.78-0
" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.235, + 0.468, + 0.289 + ], + "angle": 0, + "content": "
RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
mean9.793.8516.220.77
median7.973.5411.00.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.301, + 0.47, + 0.329 + ], + "angle": 0, + "content": "Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.333, + 0.449, + 0.349 + ], + "angle": 0, + "content": "5.3. Comparison with Quantum State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.47, + 0.596 + ], + "angle": 0, + "content": "Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online6, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.732 + ], + "angle": 0, + "content": "We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider \\(10\\%\\) and \\(20\\%\\) of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.809 + ], + "angle": 0, + "content": "HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.823, + 0.2, + 0.838 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.848, + 0.469, + 0.878 + ], + "angle": 0, + "content": "Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate" + }, + { + "type": "table", + "bbox": [ + 0.55, + 0.235, + 0.842, + 0.33 + ], + "angle": 0, + "content": "
AlgorithmOutlier ratio
10%20%Full sequences
QUMF (SA)7.2211.3413.23
DEQUMF2.4110.5316.17
DEQUMF (SA)6.268.2810.83
HQC-RF [17]3.7137.045.84
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.34, + 0.892, + 0.368 + ], + "angle": 0, + "content": "Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49]." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.375, + 0.697, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.434, + 0.672, + 0.449 + ], + "angle": 0, + "content": "DEQUMF (SA)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.375, + 0.886, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.434, + 0.833, + 0.449 + ], + "angle": 0, + "content": "HQC-RF [17]" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with \\(20\\%\\) outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves \\(8.49\\%\\) error." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.628 + ], + "angle": 0, + "content": "with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.619, + 0.662 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.763 + ], + "angle": 0, + "content": "We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.789, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.452, + 0.901 + ], + "angle": 0, + "content": "\\(^{6}\\)https://github.com/dadung/HQC-robust-fitting" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13647" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.183 + ], + "angle": 0, + "content": "[1] Sameer Agarwal, Jongwoo Lim, Lihi Zelnik-manor, Pietro Perona, David Kriegman, and Serge Belongie. Beyond pairwise clustering. 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IEEE, 2005. 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13649" + } + ] +] \ No newline at end of file diff --git a/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_origin.pdf b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ddb6c021c385fdaf22af3554f0b6ecf60ee572fc --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:efa440e9e9345381e649d0226fe7dd99e77258d67335dd17da4fd8d77553a365 +size 1107758 diff --git a/2023/Quantum Multi-Model Fitting/full.md b/2023/Quantum Multi-Model Fitting/full.md new file mode 100644 index 0000000000000000000000000000000000000000..83cd847f38c59a9069ac46537459f91a6ef49e7b --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/full.md @@ -0,0 +1,339 @@ +# Quantum Multi-Model Fitting + +Matteo Farina1 Luca Magri2 Willi Menapace1 + +Elisa Ricci $^{1,3}$ Vladislav Golyanik $^{4}$ Federica Arrigoni $^{2}$ + +1University of Trento 2Politecnico di Milano 3Fondazione Bruno Kessler 4MPI for Informatics, SIC + +# Abstract + +Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf. + +# 1. Introduction + +Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them. + +Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro + +![](images/fd51112c3082f1c75d16cc57985fc1ad1a29c5de439eb310cb472cbc369f7b5a.jpg) +Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49]. + +![](images/c73c3852b6acb3a794c6aa5a57af836b73e0ec7194e9fbdd27e1761dd9a37656.jpg) + +vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including $\mathcal{NP}$ -hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC? + +Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal + +lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data. + +Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few. + +This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF. + +Contributions. In summary, the primary technical contributions of this paper are the following: + +- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs; +- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models; +- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware. + +The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively. + +# 2. Background + +The QUBO formulation in a binary search space is an optimization problem of the following form: + +$$ +\min _ {\mathbf {y} \in \mathbb {R} ^ {d}} \mathbf {y} ^ {\mathsf {T}} Q \mathbf {y} + \mathbf {s} ^ {\mathsf {T}} \mathbf {y}, \tag {1} +$$ + +where $\mathbb{B}^d$ denotes the set of binary vectors of length $d$ , $Q \in \mathbb{R}^{d \times d}$ is a real symmetric matrix and, in a QUBO with $d$ variables, their linear coefficients are packed into $\mathbf{s} \in \mathbb{R}^d$ . When the problem is subject to linear constraints of the form $A\mathbf{y} = \mathbf{b}$ , a common approach is to relax such constraints and reformulate the QUBO as: + +$$ +\min _ {\mathbf {y} \in \mathbb {B} ^ {d}} \mathbf {y} ^ {\top} Q \mathbf {y} + \mathbf {s} ^ {\top} \mathbf {y} + \lambda | | A \mathbf {y} - \mathbf {b} | | _ {2} ^ {2}, \tag {2} +$$ + +where $\lambda$ must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to: + +$$ +\min _ {\mathbf {y} \in B ^ {d}} \mathbf {y} ^ {\top} \tilde {Q} \mathbf {y} + \tilde {\mathbf {s}} ^ {\top} \mathbf {y} \tag {3} +$$ + +where the following simple substitutions are implied: + +$$ +\tilde {Q} = Q + \lambda A ^ {\mathsf {T}} A, \quad \tilde {\mathbf {s}} = \mathbf {s} - 2 \lambda A ^ {\mathsf {T}} \mathbf {b} \tag {4} +$$ + +For the proof, the reader can refer to, e.g., Birdal et al. [6]. + +Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector $\mathbf{y}$ ), while each coupler models an element of $Q$ (i.e., the coupler between the physical qubits $i$ and $j$ maps to entry $Q_{ij}$ ). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s. + +Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having $d$ nodes (called logical qubits $^1$ ), corresponding to the $d$ entries of $\mathbf{y}$ and edges corresponding to the non-zero entries of $Q$ . + +The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such + +constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding. + +Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling. + +It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures. + +# 3. The Proposed Method + +In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems. + +# 3.1. Problem formulation + +Consider a set of data points $X = \{x_{1},\dots,x_{n}\}$ and a set $\Theta = \{\theta_1,\ldots ,\theta_m\}$ of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from $\Theta$ the "best" models that describe all the data $X$ . Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different + +interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm. + +# 3.2. Choice of Optimization Objective + +In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by $P$ and defined as: + +$$ +P [ i, j ] = \left\{ \begin{array}{l l} 1 & \text {i f e r r o r} \left(x _ {i}, \theta_ {j}\right) < \epsilon \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {5} +$$ + +where: $x_{i}$ and $\theta_{j}$ are the $i$ -th point in the dataset and the $j$ -th sampled model respectively; error expresses the residual of point $x_{i}$ w.r.t. model $\theta_{j}$ and $\epsilon$ is the inlier threshold to assign the point to the model. $P$ is a matrix of size is $n \times m$ , where $n$ and $m$ are the number of points and models, respectively. Intuitively, the columns of $P$ represent the consensus sets of models, while the rows are points' preference sets. + +In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of $P$ that explain all the rows. More formally: + +$$ +\min _ {\mathbf {z} \in \mathbb {B} ^ {m}} \mathbb {1} _ {m} ^ {\mathsf {T}} \mathbf {z} \quad \text {s . t .} P \mathbf {z} \geqslant \mathbb {1} _ {n} \tag {6} +$$ + +where $\mathbb{1}$ denotes a vector of ones (whose length is given as subscript) and $\mathbf{z}$ is a binary vector representing which models (i.e., columns of the preference matrix $P$ ) are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy. + +Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a + +computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by $k$ ) is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly $k$ models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint. + +These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work: + +$$ +\min _ {\mathbf {z} \in \mathbb {B} ^ {m}} \mathbb {1} _ {m} ^ {\mathsf {T}} \mathbf {z} \quad \text {s . t .} P \mathbf {z} = \mathbb {1} _ {n}. \tag {7} +$$ + +The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation. + +# 3.3. QUBO Formulation + +Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences: + +$$ +Q = 0, \quad \mathbf {s} = \mathbb {1} _ {m}, \quad A = P, \quad \mathbf {b} = \mathbb {1} _ {n} \tag {8} +$$ + +where optimization is carried out over $\mathbf{z} \in \mathbb{B}^m$ , that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that: + +$$ +\tilde {Q} = \lambda P ^ {\mathsf {T}} P, \quad \tilde {\mathbf {s}} = \mathbb {1} _ {m} - 2 \lambda P ^ {\mathsf {T}} \mathbb {1} _ {n} \tag {9} +$$ + +where no matrix of quadratic coefficients is present in $\widetilde{Q}$ as the considered formulation only contains linear terms, i.e., $Q = 0$ . Hence, Problem (7) can be turned into a QUBO of the form (3), namely: + +$$ +\min _ {\mathbf {z} \in \mathbb {B} ^ {m}} \lambda \mathbf {z} ^ {\top} (P ^ {\top} P) \mathbf {z} + \left(\mathbb {1} _ {m} - 2 \lambda P ^ {\top} \mathbb {1} _ {n}\right) ^ {\top} \mathbf {z}. \tag {10} +$$ + +Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF. + +Algorithm 1 DEQUMF +Require: $P,s$ +while $|P$ .columns $\vert >s$ do subproblems $= \text{ColumnPartition}(P,s)$ $i\gets 0$ +while $i < |$ subproblems|do $\mathcal{J}_i\gets$ models in the $i$ -th subproblem $P_{\mathcal{I}_i}\gets P$ retaining only the $\mathcal{J}_i$ columns $\mathbf{z}_i = \mathrm{QUMF}(P_{\mathcal{I}_i})$ remove from $P$ columns $P_{\mathcal{I}_i}[:,1 - \mathbf{z}_i]$ $i\gets i + 1$ +end while +end while + $\mathbf{z}\gets \mathrm{QUMF}(P)$ +return $P[:,\mathbf{z}]$ + +# 3.4. Iterative Decomposed Set-Cover + +While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of $m$ . In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix $P$ and reduces the dimension of the problem to fit the number of available physical qubits. + +Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix $P$ , at each iteration we partition the columns of $P$ into multiple submatrices $P_{\mathcal{J}_i}$ , where $\mathcal{J}_i$ indicates the set of selected column indices and $|\mathcal{J}_i| = s$ . We choose the subproblem size $s$ so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by $P_{\mathcal{J}_i}$ is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector $\mathbf{z}_i$ that represents the subset of selected models for the current subproblem. Note that models not selected in $\mathbf{z}_i$ are unlikely to be solutions to the original problem since, by construction, $\mathbf{z}_i$ maximizes the coverage on all points with only the restricted subset of models $\mathcal{J}_i$ . Then, after all subproblems have been solved, we prune $P$ by retaining only the columns that are selected in the corresponding optimal $\mathbf{z}_i$ . This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2). + +We iteratively apply the above procedure until the number of remaining columns in $P$ falls below $s$ , at which point the problem is directly and reliably solved using QUMF. + +# 4. Related Work + +The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting. + +![](images/7974b62aff55b9686262afa416fda5adb67ad6385a2a793ec744d99befaf0f52.jpg) +Figure 2. Illustration of the iterative pruning technique applied to $P$ in DEQUMF over consecutive iterations. At time $t$ , $P$ is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time $t + 1$ , models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded. + +# 4.1. Multi-Model Fitting + +Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods. + +Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50]. + +Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5]. + +Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective2. However, there are sub + +stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals. + +# 4.2. Quantum Computer Vision + +Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series. + +Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence. + +All available approaches can be classified into single QUBO ("one sweep") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on + +current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4). + +Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach. + +Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs. + +# 5. Experiments + +In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the + +![](images/fcc2996690464e415e76d60e81fea03f4dd8a3a6afc5952afa587cac738f4d6a.jpg) +Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points $n$ is fixed to $n = 30$ , the number of ground-truth structures is fixed to $k = 5$ , and the number of sampled models $m$ is arranged on the x-axis. + +![](images/619b7500bcc91c415825961aeb7cebdf7c7724f9f8b038a27fdef64f56e84587.jpg) +Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44]. + +AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of $20\mu s$ + +Selection of $\lambda$ . In every experiment, we set $\lambda = 1.1$ . This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for $\lambda$ by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for $\lambda$ generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error. + +# 5.1. Synthetic Data + +We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions. + +Small-scale Data. In this experiment, we select a subset of $n = 30$ points. The number of ground-truth models is fixed to $k = 5$ , and additional $m - k$ excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma + +![](images/b1d0c7c65a8de500bfb6816dcef9456944eab3bf387f56d4b33115b8f8ef4fa4.jpg) +Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points $n$ is fixed to $n = 250$ , the number of ground-truth structures is fixed to $k = 5$ , and the number of sampled models $m$ (corresponding to the dimension of the search space) is arranged on the x-axis. + +trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online $^4$ , that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1. + +Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware. + +Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph. + +Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the $k = 5$ ground-truth models) as well as all of the $n = 250$ + +points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29]. + +Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range $[0,10]\%$ for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed. + +# 5.2. Real Data + +In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA). + +AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments. + +Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach5 perform reasonably well, with DEQUMF (SA) being on par with the state of the art. + +York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art. + +Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15]. + +
Multi-X [4]J-Linkage [44]T-Linkage [28]RPA [30]RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
Traffic3 [45]mean0.321.580.480.190.355.148.740.55
median00.340.1900.192.857.500.28
Traffic2 [45]mean0.091.751.310.140.546.04-0.10
median000003.17-0
York [15]mean-2.851.441.080.1912.29-0.74
median-1.800003.78-0
+ +
RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
mean9.793.8516.220.77
median7.973.5411.00.18
+ +# 5.3. Comparison with Quantum State-of-the-art + +Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online6, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers. + +We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider $10\%$ and $20\%$ of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3. + +HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios. + +# 6. Limitations + +Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate + +Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49]. + +
AlgorithmOutlier ratio
10%20%Full sequences
QUMF (SA)7.2211.3413.23
DEQUMF2.4110.5316.17
DEQUMF (SA)6.268.2810.83
HQC-RF [17]3.7137.045.84
+ +Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49]. + +![](images/cca06efa4822d1a5eeafcc75d43abbb4354bc89338573e739da3c9a71476f8fa.jpg) +DEQUMF (SA) + +![](images/2718e7988b4c7a55ad82a54a0355278d565bf2da9c76213bd044f29b0d0c68e6.jpg) +HQC-RF [17] +Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with $20\%$ outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves $8.49\%$ error. + +with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work. + +# 7. Conclusion + +We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research. + +Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN. + +# References + +[1] Sameer Agarwal, Jongwoo Lim, Lihi Zelnik-manor, Pietro Perona, David Kriegman, and Serge Belongie. Beyond pairwise clustering. 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IEEE, 2005. 5 \ No newline at end of file diff --git a/2023/Quantum Multi-Model Fitting/images.zip b/2023/Quantum Multi-Model Fitting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8ec4c735baaf139e688a33dd12fba2b8ffbdf7e8 --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7e75c5f13c1aa62737c9362e0091d832e206a8b01a4902b52190b7e97387ab7d +size 207594 diff --git a/2023/Quantum Multi-Model Fitting/layout.json b/2023/Quantum Multi-Model Fitting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e8ea83921f8195a1ba80d4b7a869c08beec89daa --- /dev/null +++ b/2023/Quantum Multi-Model Fitting/layout.json @@ -0,0 +1,9305 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 202, + 103, + 392, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 202, + 103, + 392, + 121 + ], + "spans": [ + { + "bbox": [ + 202, + 103, + 392, + 121 + ], + "type": "text", + "content": "Quantum Multi-Model Fitting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 172, + 142, + 418, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 172, + 142, + 418, + 157 + ], + "spans": [ + { + "bbox": [ + 172, + 142, + 418, + 157 + ], + "type": "text", + "content": "Matteo Farina1 Luca Magri2 Willi Menapace1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "spans": [ + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "text", + "content": "Elisa Ricci" + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "text", + "content": " Vladislav Golyanik" + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "text", + "content": " Federica Arrigoni" + }, + { + "bbox": [ + 155, + 157, + 438, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 172, + 492, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 172, + 492, + 185 + ], + "spans": [ + { + "bbox": [ + 102, + 172, + 492, + 185 + ], + "type": "text", + "content": "1University of Trento 2Politecnico di Milano 3Fondazione Bruno Kessler 4MPI for Informatics, SIC" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 238, + 290, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 238, + 290, + 418 + ], + "spans": [ + { + "bbox": [ + 45, + 238, + 290, + 418 + ], + "type": "text", + "content": "Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 453, + 128, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 128, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 128, + 466 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 474, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 474, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 45, + 474, + 287, + 653 + ], + "type": "text", + "content": "Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 212, + 423, + 310 + ], + "blocks": [ + { + "bbox": [ + 309, + 212, + 423, + 310 + ], + "lines": [ + { + "bbox": [ + 309, + 212, + 423, + 310 + ], + "spans": [ + { + "bbox": [ + 309, + 212, + 423, + 310 + ], + "type": "image", + "image_path": "fd51112c3082f1c75d16cc57985fc1ad1a29c5de439eb310cb472cbc369f7b5a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 319, + 547, + 396 + ], + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 396 + ], + "type": "text", + "content": "Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49]." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 432, + 219, + 536, + 299 + ], + "blocks": [ + { + "bbox": [ + 432, + 219, + 536, + 299 + ], + "lines": [ + { + "bbox": [ + 432, + 219, + 536, + 299 + ], + "spans": [ + { + "bbox": [ + 432, + 219, + 536, + 299 + ], + "type": "image", + "image_path": "c73c3852b6acb3a794c6aa5a57af836b73e0ec7194e9fbdd27e1761dd9a37656.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 401, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 547, + 582 + ], + "type": "text", + "content": "vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including " + }, + { + "bbox": [ + 304, + 401, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{NP}" + }, + { + "bbox": [ + 304, + 401, + 547, + 582 + ], + "type": "text", + "content": "-hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC?" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "type": "text", + "content": "Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13640" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 324 + ], + "type": "text", + "content": "Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 324, + 290, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 290, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 290, + 529 + ], + "type": "text", + "content": "This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "type": "text", + "content": "Contributions. In summary, the primary technical contributions of this paper are the following:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 557, + 287, + 652 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 557, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 557, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 58, + 557, + 287, + 582 + ], + "type": "text", + "content": "- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 586, + 287, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 586, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 58, + 586, + 287, + 611 + ], + "type": "text", + "content": "- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "type": "text", + "content": "- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 91, + 545, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 91, + 545, + 116 + ], + "spans": [ + { + "bbox": [ + 305, + 91, + 545, + 116 + ], + "type": "text", + "content": "The QUBO formulation in a binary search space is an optimization problem of the following form:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 385, + 123, + 545, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 123, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 385, + 123, + 545, + 144 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {y} \\in \\mathbb {R} ^ {d}} \\mathbf {y} ^ {\\mathsf {T}} Q \\mathbf {y} + \\mathbf {s} ^ {\\mathsf {T}} \\mathbf {y}, \\tag {1}", + "image_path": "d8f3467251ab0ee8870f427b2bb0545b186409077967e26540937f21f39209a3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\mathbb{B}^d" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": " denotes the set of binary vectors of length " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": " is a real symmetric matrix and, in a QUBO with " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": " variables, their linear coefficients are packed into " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\mathbf{s} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": ". When the problem is subject to linear constraints of the form " + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "inline_equation", + "content": "A\\mathbf{y} = \\mathbf{b}" + }, + { + "bbox": [ + 305, + 154, + 545, + 226 + ], + "type": "text", + "content": ", a common approach is to relax such constraints and reformulate the QUBO as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 352, + 234, + 545, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 234, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 352, + 234, + 545, + 255 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {y} \\in \\mathbb {B} ^ {d}} \\mathbf {y} ^ {\\top} Q \\mathbf {y} + \\mathbf {s} ^ {\\top} \\mathbf {y} + \\lambda | | A \\mathbf {y} - \\mathbf {b} | | _ {2} ^ {2}, \\tag {2}", + "image_path": "ada31301cffaac03bc1331f08e334bd4b4271921eb7f8986f64ee5c97d257731.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 264, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 264, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 305, + 264, + 545, + 288 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 264, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 264, + 545, + 288 + ], + "type": "text", + "content": " must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 387, + 296, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 296, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 387, + 296, + 545, + 319 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {y} \\in B ^ {d}} \\mathbf {y} ^ {\\top} \\tilde {Q} \\mathbf {y} + \\tilde {\\mathbf {s}} ^ {\\top} \\mathbf {y} \\tag {3}", + "image_path": "eae64602ad496545c710c66f3710b4c708b0d7c621cb6665483337500031f55c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 327, + 522, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 522, + 339 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 522, + 339 + ], + "type": "text", + "content": "where the following simple substitutions are implied:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 349, + 347, + 545, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 347, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 349, + 347, + 545, + 361 + ], + "type": "interline_equation", + "content": "\\tilde {Q} = Q + \\lambda A ^ {\\mathsf {T}} A, \\quad \\tilde {\\mathbf {s}} = \\mathbf {s} - 2 \\lambda A ^ {\\mathsf {T}} \\mathbf {b} \\tag {4}", + "image_path": "aaba97e1e8a3035eed44a074f28c04f4646d9ae38976f78d722278de3eaeeb40.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 371, + 542, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 542, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 542, + 384 + ], + "type": "text", + "content": "For the proof, the reader can refer to, e.g., Birdal et al. [6]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": "Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector " + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": "), while each coupler models an element of " + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": " (i.e., the coupler between the physical qubits " + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": " maps to entry " + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q_{ij}" + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": "). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": "Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having " + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": " nodes (called logical qubits" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": "), corresponding to the " + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": " entries of " + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": " and edges corresponding to the non-zero entries of " + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 530, + 545, + 613 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 614, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 545, + 686 + ], + "type": "text", + "content": "The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "Hereafter we will sometimes omit the term \"logical\" or \"physical\" as it will be clear from the context which type of qubits are being involved." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13641" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 335 + ], + "type": "text", + "content": "Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": "It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 464, + 176, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 176, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 176, + 478 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 485, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 545 + ], + "type": "text", + "content": "In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 168, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 168, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 168, + 563 + ], + "type": "text", + "content": "3.1. Problem formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Consider a set of data points " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "X = \\{x_{1},\\dots,x_{n}\\}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and a set " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Theta = \\{\\theta_1,\\ldots ,\\theta_m\\}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " the \"best\" models that describe all the data " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ". Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 175, + 486, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 175, + 486, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 486, + 188 + ], + "type": "text", + "content": "3.2. Choice of Optimization Objective" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 193, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 348 + ], + "type": "text", + "content": "In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by " + }, + { + "bbox": [ + 304, + 193, + 545, + 348 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 193, + 545, + 348 + ], + "type": "text", + "content": " and defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 353, + 356, + 545, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 356, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 353, + 356, + 545, + 388 + ], + "type": "interline_equation", + "content": "P [ i, j ] = \\left\\{ \\begin{array}{l l} 1 & \\text {i f e r r o r} \\left(x _ {i}, \\theta_ {j}\\right) < \\epsilon \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}", + "image_path": "cad7b4c0522a519886c33f1cb43d3f4cf587796310353fdecf94c42e133a17d8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": "where: " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": "-th point in the dataset and the " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": "-th sampled model respectively; error expresses the residual of point " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " w.r.t. model " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " is the inlier threshold to assign the point to the model. " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " is a matrix of size is " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "n \\times m" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " are the number of points and models, respectively. Intuitively, the columns of " + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 394, + 545, + 478 + ], + "type": "text", + "content": " represent the consensus sets of models, while the rows are points' preference sets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "content": "In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of " + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "content": " that explain all the rows. More formally:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 373, + 533, + 545, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 533, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 373, + 533, + 545, + 552 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} \\geqslant \\mathbb {1} _ {n} \\tag {6}", + "image_path": "8dbe2519ccc94826c219a8ea35aac1257787db1cc39a2b888683e92d99b1785e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "content": " denotes a vector of ones (whose length is given as subscript) and " + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "content": " is a binary vector representing which models (i.e., columns of the preference matrix " + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "content": ") are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13642" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by " + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": ") is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly " + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": " models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 239, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 287, + 264 + ], + "type": "text", + "content": "These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 112, + 269, + 287, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 269, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 112, + 269, + 287, + 289 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} = \\mathbb {1} _ {n}. \\tag {7}", + "image_path": "ba310b6a82c19f9607b057cd438bc69446a690c2bca0f7e57d224123ed6936b1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 288, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 354 + ], + "type": "text", + "content": "The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 164, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 164, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 164, + 372 + ], + "type": "text", + "content": "3.3. QUBO Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 378, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 485 + ], + "type": "text", + "content": "Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 494, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 494, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 82, + 494, + 287, + 506 + ], + "type": "interline_equation", + "content": "Q = 0, \\quad \\mathbf {s} = \\mathbb {1} _ {m}, \\quad A = P, \\quad \\mathbf {b} = \\mathbb {1} _ {n} \\tag {8}", + "image_path": "d511fc0b15e52703d8e6d9d28e0db36a44402b426de95c388516ba6170a6ef62.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 513, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 549 + ], + "type": "text", + "content": "where optimization is carried out over " + }, + { + "bbox": [ + 46, + 513, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in \\mathbb{B}^m" + }, + { + "bbox": [ + 46, + 513, + 287, + 549 + ], + "type": "text", + "content": ", that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 554, + 287, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 554, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 93, + 554, + 287, + 569 + ], + "type": "interline_equation", + "content": "\\tilde {Q} = \\lambda P ^ {\\mathsf {T}} P, \\quad \\tilde {\\mathbf {s}} = \\mathbb {1} _ {m} - 2 \\lambda P ^ {\\mathsf {T}} \\mathbb {1} _ {n} \\tag {9}", + "image_path": "7ab131c2e1c2c95f8793064f9db18d8d9fcc0ff02e3f5adb508045f5543bbbb2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "text", + "content": "where no matrix of quadratic coefficients is present in " + }, + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}" + }, + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "text", + "content": " as the considered formulation only contains linear terms, i.e., " + }, + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "inline_equation", + "content": "Q = 0" + }, + { + "bbox": [ + 47, + 574, + 287, + 624 + ], + "type": "text", + "content": ". Hence, Problem (7) can be turned into a QUBO of the form (3), namely:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 82, + 628, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 628, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 82, + 628, + 287, + 648 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\lambda \\mathbf {z} ^ {\\top} (P ^ {\\top} P) \\mathbf {z} + \\left(\\mathbb {1} _ {m} - 2 \\lambda P ^ {\\top} \\mathbb {1} _ {n}\\right) ^ {\\top} \\mathbf {z}. \\tag {10}", + "image_path": "14c56da334b5fdefde1a2a802d5b936ab58be12a594927f62e518594aac20ffc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF." + } + ] + } + ], + "index": 11 + }, + { + "type": "code", + "bbox": [ + 306, + 85, + 492, + 242 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 406, + 83 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 406, + 83 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 406, + 83 + ], + "type": "text", + "content": "Algorithm 1 DEQUMF" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "lines": [ + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": "Require: " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "P,s" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " \nwhile " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "|P" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " .columns " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "\\vert >s" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " do subproblems " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "= \\text{ColumnPartition}(P,s)" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "i\\gets 0" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " \nwhile " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "i < |" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " subproblems|do " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{J}_i\\gets" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " models in the " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " -th subproblem " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{I}_i}\\gets P" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " retaining only the " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{J}_i" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " columns " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i = \\mathrm{QUMF}(P_{\\mathcal{I}_i})" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " remove from " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " columns " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{I}_i}[:,1 - \\mathbf{z}_i]" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "i\\gets i + 1" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " \nend while \nend while \n" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\gets \\mathrm{QUMF}(P)" + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "text", + "content": " \nreturn " + }, + { + "bbox": [ + 306, + 85, + 492, + 242 + ], + "type": "inline_equation", + "content": "P[:,\\mathbf{z}]" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "code_body" + } + ], + "index": 13, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 265, + 480, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 265, + 480, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 265, + 480, + 277 + ], + "type": "text", + "content": "3.4. Iterative Decomposed Set-Cover" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": "While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": ". In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix " + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 284, + 545, + 380 + ], + "type": "text", + "content": " and reduces the dimension of the problem to fit the number of available physical qubits." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": "Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": ", at each iteration we partition the columns of " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " into multiple submatrices " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{J}_i}" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{J}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " indicates the set of selected column indices and " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "|\\mathcal{J}_i| = s" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": ". We choose the subproblem size " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{J}_i}" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " that represents the subset of selected models for the current subproblem. Note that models not selected in " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " are unlikely to be solutions to the original problem since, by construction, " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " maximizes the coverage on all points with only the restricted subset of models " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathcal{J}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": ". Then, after all subproblems have been solved, we prune " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": " by retaining only the columns that are selected in the corresponding optimal " + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 380, + 546, + 595 + ], + "type": "text", + "content": ". This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "text", + "content": "We iteratively apply the above procedure until the number of remaining columns in " + }, + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "text", + "content": " falls below " + }, + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 596, + 547, + 632 + ], + "type": "text", + "content": ", at which point the problem is directly and reliably solved using QUMF." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 645, + 392, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 392, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 392, + 657 + ], + "type": "text", + "content": "4. Related Work" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13643" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 265, + 219 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 265, + 219 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 265, + 219 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 265, + 219 + ], + "type": "image", + "image_path": "7974b62aff55b9686262afa416fda5adb67ad6385a2a793ec744d99befaf0f52.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "text", + "content": "Figure 2. Illustration of the iterative pruning technique applied to " + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "text", + "content": " in DEQUMF over consecutive iterations. At time " + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "text", + "content": " is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time " + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 46, + 225, + 289, + 304 + ], + "type": "text", + "content": ", models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 316, + 165, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 165, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 165, + 330 + ], + "type": "text", + "content": "4.1. Multi-Model Fitting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 382 + ], + "type": "text", + "content": "Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 383, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 287, + 477 + ], + "type": "text", + "content": "Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 479, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 621 + ], + "type": "text", + "content": "Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 622, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 658 + ], + "type": "text", + "content": "Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective2. However, there are sub" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 180 + ], + "type": "text", + "content": "stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 190, + 457, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 190, + 457, + 204 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 457, + 204 + ], + "type": "text", + "content": "4.2. Quantum Computer Vision" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 209, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 388 + ], + "type": "text", + "content": "Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 389, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 389, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 389, + 546, + 533 + ], + "type": "text", + "content": "Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 547, + 713 + ], + "type": "text", + "content": "All available approaches can be classified into single QUBO (\"one sweep\") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": "2The same objective is considered but constraints are different: RANSACOV [29] allows for overlapping models, resulting in an inequality constraint, see Problem (6); instead, we consider disjoint models, using an equality constraint, see Problem (7). For a fair comparison, we slightly modify RANSACOV, replacing the inequality with an equality constraint." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13644" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 288, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 430 + ], + "type": "text", + "content": "Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 432, + 287, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 551 + ], + "type": "text", + "content": "Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 310, + 74, + 541, + 177 + ], + "blocks": [ + { + "bbox": [ + 310, + 74, + 541, + 177 + ], + "lines": [ + { + "bbox": [ + 310, + 74, + 541, + 177 + ], + "spans": [ + { + "bbox": [ + 310, + 74, + 541, + 177 + ], + "type": "image", + "image_path": "fcc2996690464e415e76d60e81fea03f4dd8a3a6afc5952afa587cac738f4d6a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "lines": [ + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "text", + "content": "Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points " + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "text", + "content": " is fixed to " + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "inline_equation", + "content": "n = 30" + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "text", + "content": ", the number of ground-truth structures is fixed to " + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "inline_equation", + "content": "k = 5" + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "text", + "content": ", and the number of sampled models " + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 181, + 547, + 226 + ], + "type": "text", + "content": " is arranged on the x-axis." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 332, + 231, + 518, + 334 + ], + "blocks": [ + { + "bbox": [ + 332, + 231, + 518, + 334 + ], + "lines": [ + { + "bbox": [ + 332, + 231, + 518, + 334 + ], + "spans": [ + { + "bbox": [ + 332, + 231, + 518, + 334 + ], + "type": "image", + "image_path": "619b7500bcc91c415825961aeb7cebdf7c7724f9f8b038a27fdef64f56e84587.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 336, + 546, + 369 + ], + "lines": [ + { + "bbox": [ + 304, + 336, + 546, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 546, + 369 + ], + "type": "text", + "content": "Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 376, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 401 + ], + "type": "text", + "content": "AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of " + }, + { + "bbox": [ + 304, + 376, + 545, + 401 + ], + "type": "inline_equation", + "content": "20\\mu s" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "content": "Selection of " + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "content": ". In every experiment, we set " + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\lambda = 1.1" + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "content": ". This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for " + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "content": " by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for " + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 404, + 546, + 536 + ], + "type": "text", + "content": " generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 544, + 398, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 398, + 556 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 398, + 556 + ], + "type": "text", + "content": "5.1. Synthetic Data" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 562, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 598 + ], + "type": "text", + "content": "We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "text", + "content": "Small-scale Data. In this experiment, we select a subset of " + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "inline_equation", + "content": "n = 30" + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "text", + "content": " points. The number of ground-truth models is fixed to " + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "inline_equation", + "content": "k = 5" + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "text", + "content": ", and additional " + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "inline_equation", + "content": "m - k" + }, + { + "bbox": [ + 304, + 601, + 545, + 685 + ], + "type": "text", + "content": " excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "3We refer to optimal solution probability as the ratio between the anneals ended in a globally optimal state and the total number of anneals." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13645" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 284, + 178 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 284, + 178 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 284, + 178 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 284, + 178 + ], + "type": "image", + "image_path": "b1d0c7c65a8de500bfb6816dcef9456944eab3bf387f56d4b33115b8f8ef4fa4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "text", + "content": "Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points " + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "text", + "content": " is fixed to " + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "inline_equation", + "content": "n = 250" + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "text", + "content": ", the number of ground-truth structures is fixed to " + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "inline_equation", + "content": "k = 5" + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "text", + "content": ", and the number of sampled models " + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 182, + 288, + 239 + ], + "type": "text", + "content": " (corresponding to the dimension of the search space) is arranged on the x-axis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 242, + 287, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 338 + ], + "type": "text", + "content": "trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online" + }, + { + "bbox": [ + 46, + 242, + 287, + 338 + ], + "type": "inline_equation", + "content": "^4" + }, + { + "bbox": [ + 46, + 242, + 287, + 338 + ], + "type": "text", + "content": ", that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 288, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 482 + ], + "type": "text", + "content": "Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 654 + ], + "type": "text", + "content": "Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "type": "text", + "content": "Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the " + }, + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "type": "inline_equation", + "content": "k = 5" + }, + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "type": "text", + "content": " ground-truth models) as well as all of the " + }, + { + "bbox": [ + 47, + 658, + 288, + 693 + ], + "type": "inline_equation", + "content": "n = 250" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 157, + 546, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 546, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 546, + 264 + ], + "type": "text", + "content": "Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range " + }, + { + "bbox": [ + 304, + 157, + 546, + 264 + ], + "type": "inline_equation", + "content": "[0,10]\\%" + }, + { + "bbox": [ + 304, + 157, + 546, + 264 + ], + "type": "text", + "content": " for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 270, + 375, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 375, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 375, + 281 + ], + "type": "text", + "content": "5.2. Real Data" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 288, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 335 + ], + "type": "text", + "content": "In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 338, + 546, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 546, + 458 + ], + "type": "text", + "content": "AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": "Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach5 perform reasonably well, with DEQUMF (SA) being on par with the state of the art." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 677 + ], + "type": "text", + "content": "York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 546, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 546, + 713 + ], + "type": "text", + "content": "5We are not able to run QUMF on Traffic2 due to the limited amount of GPU time available in our monthly subscription combined with the large dimension of the dataset, hence results are not reported." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "type": "text", + "content": "4https://fusiello.github.io/demo/cov/index.html" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13646" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 82, + 541, + 175 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 529, + 81 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 529, + 81 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 529, + 81 + ], + "type": "text", + "content": "Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 82, + 541, + 175 + ], + "lines": [ + { + "bbox": [ + 50, + 82, + 541, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 82, + 541, + 175 + ], + "type": "table", + "html": "
Multi-X [4]J-Linkage [44]T-Linkage [28]RPA [30]RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
Traffic3 [45]mean0.321.580.480.190.355.148.740.55
median00.340.1900.192.857.500.28
Traffic2 [45]mean0.091.751.310.140.546.04-0.10
median000003.17-0
York [15]mean-2.851.441.080.1912.29-0.74
median-1.800003.78-0
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RANSACOV [29]QUMF (SA)DEQUMFDEQUMF (SA)
mean9.793.8516.220.77
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", + "image_path": "6abed28e600689162ff25dafc369b56d246880e045c7ba4bdb9e0f953fba51bf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 263, + 274, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 263, + 274, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 274, + 276 + ], + "type": "text", + "content": "5.3. Comparison with Quantum State-of-the-art" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 281, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 472 + ], + "type": "text", + "content": "Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online6, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": "We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "type": "text", + "content": "HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 651, + 122, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 122, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 122, + 663 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "content": "Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 336, + 186, + 515, + 261 + ], + "blocks": [ + { + "bbox": [ + 46, + 238, + 287, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 287, + 260 + ], + "type": "text", + "content": "Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 336, + 186, + 515, + 261 + ], + "lines": [ + { + "bbox": [ + 336, + 186, + 515, + 261 + ], + "spans": [ + { + "bbox": [ + 336, + 186, + 515, + 261 + ], + "type": "table", + "html": "
AlgorithmOutlier ratio
10%20%Full sequences
QUMF (SA)7.2211.3413.23
DEQUMF2.4110.5316.17
DEQUMF (SA)6.268.2810.83
HQC-RF [17]3.7137.045.84
", + "image_path": "899d8c2d8f1036da7ad55186c19fe50bccebfb4b55f052aa7a4c129939cb5159.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 269, + 545, + 291 + ], + "lines": [ + { + "bbox": [ + 305, + 269, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 545, + 291 + ], + "type": "text", + "content": "Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 297, + 426, + 341 + ], + "blocks": [ + { + "bbox": [ + 310, + 297, + 426, + 341 + ], + "lines": [ + { + "bbox": [ + 310, + 297, + 426, + 341 + ], + "spans": [ + { + "bbox": [ + 310, + 297, + 426, + 341 + ], + "type": "image", + "image_path": "cca06efa4822d1a5eeafcc75d43abbb4354bc89338573e739da3c9a71476f8fa.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 343, + 411, + 355 + ], + "lines": [ + { + "bbox": [ + 343, + 343, + 411, + 355 + ], + "spans": [ + { + "bbox": [ + 343, + 343, + 411, + 355 + ], + "type": "text", + "content": "DEQUMF (SA)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 426, + 297, + 542, + 341 + ], + "blocks": [ + { + "bbox": [ + 426, + 297, + 542, + 341 + ], + "lines": [ + { + "bbox": [ + 426, + 297, + 542, + 341 + ], + "spans": [ + { + "bbox": [ + 426, + 297, + 542, + 341 + ], + "type": "image", + "image_path": "2718e7988b4c7a55ad82a54a0355278d565bf2da9c76213bd044f29b0d0c68e6.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 452, + 343, + 509, + 355 + ], + "lines": [ + { + "bbox": [ + 452, + 343, + 509, + 355 + ], + "spans": [ + { + "bbox": [ + 452, + 343, + 509, + 355 + ], + "type": "text", + "content": "HQC-RF [17]" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "type": "text", + "content": "Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with " + }, + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "type": "text", + "content": " outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves " + }, + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "type": "inline_equation", + "content": "8.49\\%" + }, + { + "bbox": [ + 304, + 363, + 545, + 418 + ], + "type": "text", + "content": " error." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 425, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 497 + ], + "type": "text", + "content": "with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 512, + 378, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 378, + 524 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 378, + 524 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 604 + ], + "type": "text", + "content": "We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 624, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 276, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 276, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 276, + 713 + ], + "type": "inline_equation", + "content": "^{6}" + }, + { + "bbox": [ + 57, + 702, + 276, + 713 + ], + "type": "text", + "content": "https://github.com/dadung/HQC-robust-fitting" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13647" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Sameer Agarwal, Jongwoo Lim, Lihi Zelnik-manor, Pietro Perona, David Kriegman, and Serge Belongie. 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IEEE, 2005. 5" + } + ] + } + ], + "index": 29 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13649" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_content_list.json b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b3036c8efc02012443838b2c74bbcfabf220d286 --- /dev/null +++ b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_content_list.json @@ -0,0 +1,1631 @@ +[ + { + "type": "text", + "text": "Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification", + "text_level": 1, + "bbox": [ + 84, + 128, + 883, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jie Zhang $^{1}$ , Yongshan Zhang $^{2,1*}$ , Yicong Zhou $^{1*}$", + "bbox": [ + 295, + 202, + 676, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Computer and Information Science, University of Macau, Macau, China $^{2}$ School of Computer Science, China University of Geosciences, Wuhan, China", + "bbox": [ + 133, + 220, + 833, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jiezh1997@gmail.com, yszhang.cug@gmail.com, yicongzhou@um.edu.m", + "bbox": [ + 199, + 258, + 766, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyperspectral image (HSI) classification aims at assigning a unique label for every pixel to identify categories of different land covers. Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. In this pyramid framework, QSSPN progressively learns feature representations by cascading QSSN blocks and performs classification with a softmax classifier. It is the first attempt to introduce quantum theory in HSI processing model design. Substantial experiments are conducted on three HSI datasets to verify the superiority of the proposed QSSPN framework over the state-of-the-art methods.", + "bbox": [ + 73, + 340, + 472, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 792, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. Each HSI contains two spatial dimensions and one spectral di", + "bbox": [ + 75, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f8e92293ecb73eba639865db402b61a405202b3924c0e52d8206f1a103228dcd.jpg", + "image_caption": [ + "Figure 1. Performance comparison between the proposed QSSPN framework and existing methods. Average accuracies on Indian Pines dataset are presented." + ], + "image_footnote": [], + "bbox": [ + 513, + 330, + 854, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49].", + "bbox": [ + 496, + 566, + 890, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and $K$ -nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 94, + 886, + 227, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9925", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm.", + "bbox": [ + 75, + 90, + 472, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38].", + "bbox": [ + 75, + 335, + 472, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks", + "bbox": [ + 75, + 659, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this article are summarized as follows.", + "bbox": [ + 498, + 181, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising.", + "- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations.", + "- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity." + ], + "bbox": [ + 517, + 218, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion.", + "bbox": [ + 496, + 455, + 890, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 573, + 640, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45].", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9926", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f55728ced1a6ba370d2c5c93235a61a3535ba4fc48139753d716f3d45a213148.jpg", + "image_caption": [ + "Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 467, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection.", + "bbox": [ + 75, + 398, + 472, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 762, + 168, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2.", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 90, + 640, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in $N$ -dimensional Hilbert space $\\mathcal{H}^N$ . We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations $\\left|\\cdot \\right\\rangle$ and $\\langle \\cdot |$ denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors $\\{\\left|\\phi_n\\right\\rangle \\}_{n = 1}^N$ , we can represent the states of quantum system $|\\psi \\rangle$ as follows*:", + "bbox": [ + 496, + 113, + 893, + 387 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n| \\psi \\rangle = \\sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \\theta_ {n}} | \\phi_ {n} \\rangle , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 397, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $A_{n}$ is a probability amplitude satisfying $\\sum_{N}|A_{n}|^{2} = 1$ , $i$ is the imaginary unit and $\\theta_{n}$ indicates the phase. A simple example of basis state vectors for $\\mathcal{H}^N$ is standard unit basis. Detailedly, the standard basis of $\\mathcal{H}^2$ is formed by column vectors $|0\\rangle_2 = [1,0]^T$ and $|1\\rangle_2 = [0,1]^T$ . Here, we use the notation", + "bbox": [ + 498, + 448, + 893, + 541 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left| n \\right\\rangle_ {N}, n = 0, 1, \\dots , N - 1 \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 551, + 890, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to represent the standard basis of $\\mathcal{H}^N$ . Accordingly, $\\langle n|_N$ denotes the conjugate transpose of $|n\\rangle_N$ . All components of $|n\\rangle_N$ are 0 except the $n$ -th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states.", + "bbox": [ + 496, + 579, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reversible unitary operator $U$ describes the state's evolution in QC, mapping the initial states $|\\psi_{initial}\\rangle$ to final states $|\\psi_{final}\\rangle$ . These operators manipulate the phases $\\theta_{n}$ and amplitudes $A_{n}$ by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators $\\{\\Pi_m = |\\phi_m\\rangle \\langle \\phi_m|\\}_{m = 1}^M$ . According to the Born rule [28], $\\Pi_{m}$ projects the state $|\\psi_{final}\\rangle$ to the corresponding basis state $|\\phi_m\\rangle$ with a probability:", + "bbox": [ + 496, + 640, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = T r \\left(\\Pi_ {m} \\rho\\right) = \\left\\langle \\phi_ {m} \\mid \\psi_ {\\text {f i n a l}} \\right\\rangle \\left\\langle \\psi_ {\\text {f i n a l}} \\mid \\phi_ {m} \\right\\rangle , \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 818, + 890, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|$ is the density matrix representation of $|\\psi_{final}\\rangle$ and $\\sum_{M}P(|\\phi_{m}\\rangle) = 1$ . $|\\cdot \\rangle \\langle \\cdot |$ denotes the", + "bbox": [ + 496, + 845, + 890, + 878 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "*Only pure states are considered in this paper.", + "bbox": [ + 516, + 887, + 761, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9927", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e07cba4561baba1f2b8e0f9c2aea9c4e04b9ce0181a5c2168beb225e437b9a6e.jpg", + "image_caption": [ + "Figure 3. Illustration of data mapping in QSSN. The state representation $|\\psi \\rangle$ encodes data from original space to Hilbert space: $\\mathcal{R} \\to \\mathcal{H}$ . The MFM outputs a feature vector mapped from $|\\psi \\rangle$ to feature space: $\\mathcal{H} \\to \\mathcal{F}$ ." + ], + "image_footnote": [], + "bbox": [ + 80, + 98, + 467, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "outer product and $\\langle \\cdot |\\cdot \\rangle$ denotes the inner product of $\\langle \\cdot |$ and $|\\cdot \\rangle$ . Eq. (3) can be rewritten as:", + "bbox": [ + 76, + 301, + 470, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = \\left\\langle \\phi_ {m} \\right| \\rho \\left| \\phi_ {m} \\right\\rangle = \\left(\\left\\langle \\psi_ {f i n a l} \\mid \\phi_ {m} \\right\\rangle\\right) ^ {2} \\tag {4} \\\\ = \\sum_ {n _ {1}} ^ {N - 1} \\sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\\theta_ {n _ {1}} - \\theta_ {n _ {2}})} \\langle \\phi_ {m} | n _ {1} \\rangle \\langle n _ {2} | \\phi_ {m} \\rangle . \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 342, + 468, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here we neglect the subscript $N$ of $|n\\rangle_N$ for simplicity. In Eq. (4), the size of $|n\\rangle$ is $N$ . For the same measurement operator $\\Pi_m \\sim |\\phi_m\\rangle$ , the output $P(|\\phi_m\\rangle)$ depends on all pairs of $A_{n_1}$ and $A_{n_2}$ and their correlations $(\\theta_{n_1} - \\theta_{n_2})$ . PVM yields values $P_{res} = [P(|\\phi_1\\rangle), P(|\\phi_2\\rangle), \\ldots, P(|\\phi_M\\rangle)]$ corresponding to the selected projection operators $\\{\\Pi_m\\}_{m=1}^M$ , reflecting the state of quantum system.", + "bbox": [ + 76, + 414, + 468, + 535 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28].", + "bbox": [ + 75, + 536, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Quantum-Inspired Spectral-Spatial Network", + "text_level": 1, + "bbox": [ + 76, + 590, + 457, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $X \\in \\mathcal{R}^{H \\times W \\times B}$ be the HSI with $H$ pixels in height, $W$ pixels in width, and $B$ spectral bands. Taking the $(i,j)$ -th pixel as center, information in a small cuboid $x_{i,j} \\in \\mathcal{R}^{P \\times P \\times B}$ with $P \\times P$ pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad $X$ with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification.", + "bbox": [ + 75, + 611, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases $\\Theta_{i,j} \\in R^{P \\times P \\times B}$ for all elements $x_{i',j',k'}'$ in $x_{i,j}$ . Phases play an important role in encoding data $x_{i,j}$ in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase $\\theta_{i',j',k'}$ for each element $x_{i',j',k'}'$ . Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each $x_{i',j',k'}'$ , the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have $B$ channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in $3\\times 3$ pixel windows. The following asymmetric convolution layers [37] with $3\\times 1$ and $1\\times 3$ kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases $\\Theta_{i,j}$ . Before we encode each HSI cuboid into complex finite-dimensional Hilbert space $\\mathcal{H}^K$ ( $K = P\\times P\\times B$ ), we reshape the HSI cuboid $x_{i,j}$ and the corresponding phase cuboid $\\Theta_{i,j}$ as follow:", + "bbox": [ + 496, + 90, + 892, + 348 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} x ^ {v e c} = \\left[ x _ {0} ^ {\\prime}, \\dots , x _ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P} ^ {\\prime}, \\dots , x _ {K - 1} ^ {\\prime} \\right], \\tag {5} \\\\ \\Theta^ {v e c} = \\left[ \\theta_ {0}, \\dots , \\theta_ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P}, \\dots , \\theta_ {K - 1} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 356, + 892, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $i', j' \\in [0 : P - 1]$ and $k' \\in [0 : B - 1]$ . Then phase vector $x^{vec}$ and original data vector $x^{vec}$ are used in the state vector representation $|x_{i,j}\\rangle$ as follows:", + "bbox": [ + 496, + 398, + 892, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| x _ {i, j} \\right\\rangle = \\sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \\theta_ {n}} \\left| n \\right\\rangle_ {K}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 455, + 890, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (6), $A_{n}$ can be obtained as:", + "bbox": [ + 500, + 507, + 725, + 522 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {n} = \\sqrt {\\frac {x _ {n} ^ {v e c}}{\\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 532, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{n}^{vec}$ indicates the $n$ -th element in $x^{vec}$ . In Eq. (6), $x_{i,j}$ can be represented by a complex vector $|x_{i,j}\\rangle = [A_0e^{i\\theta_0}, A_1e^{i\\theta_1}, \\ldots, A_{K-1}e^{i\\theta_{K-1}}]$ in $\\mathcal{H}^K$ . As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode $x_{i,j}$ in $|x_{i,j}\\rangle$ is neglecting the imaginary parts $e^{i\\theta}$ (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations.", + "bbox": [ + 496, + 583, + 892, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation $(MO)$ to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as $PVM(\\Pi_m,\\rho)$ : using a density matrix $\\rho$ to represent the state of quantum system $\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|$ and then applying the matrix manipulation (matrix product and trace)", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9928", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with operators $\\{\\Pi_m\\}_{m=1}^M$ . For each $\\Pi_m$ , we get the probability $P(|\\phi_m\\rangle)$ . Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D _ {i, j} = \\left| x _ {i, j} \\right\\rangle \\left\\langle x _ {i, j} \\right| \\tag {8} \\\\ = \\sum_ {n = 0} ^ {K - 1} \\sum_ {n ^ {\\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\\prime}} e ^ {i \\left(\\theta_ {n} - \\theta_ {n ^ {\\prime}}\\right)} \\left| n ^ {\\prime} \\right\\rangle \\left\\langle n \\right|, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 164, + 467, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $|n^{\\prime}\\rangle \\langle n|$ represents a square matrix with $P\\times P\\times B$ rows and columns that all components are 0 except the $(n,n^{\\prime})$ -th component is 1. Each term in the density matrix $D_{i,j}$ is the multiplication of $A_{n}$ and $A_{n^{\\prime}}$ with a coefficient $e^{i(\\theta_n - \\theta_{n^{\\prime}})}$ . Empirically, this is similar to fusing information of each pair of elements $x_{n}^{vec}$ and $x_{n^{\\prime}}^{vec}$ . Phases $\\theta_{n}$ and $\\theta_{n^{\\prime}}$ are predicted by PPM. We hope the imaginary part $e^{i(\\theta_n - \\theta_{n^{\\prime}})}$ can dynamically modulate the correlations between $x_{n}^{vec}$ and $x_{n^{\\prime}}^{vec}$ . In each pair, the location and band of $x_{n}^{vec}$ and $x_{n^{\\prime}}^{vec}$ may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result $P(|\\phi_m\\rangle)$ corresponding to $\\Pi_{m}$ . Note that PVM has corresponding operations applied on physic devices. There are constraints of operations $\\Pi_{m}$ in their mathematical formulation in quantum theory. We use an abstract representation of PVM as $PVM(\\Pi_m,\\rho)\\rightarrow PVM(Operator_m,\\rho)$ . To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers $FC_{m}$ with depth 3 as $Operator_{m}$ . The MO generates a feature point as follows:", + "bbox": [ + 76, + 232, + 468, + 580 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf e a _ {m} = M O \\left(F C _ {m}, D _ {i, j}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 590, + 467, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D_{i,j}$ stores the fusion information of each element pair, $x_{n}^{vec}$ and $x_{n'}^{vec}$ . $MO$ is an operation that feeds $D_{i,j}$ into the operator $FC_{m}$ to efficiently aggregate spatial and spectral information. Given $M$ operators $\\{FC_{m}\\}_{m=1}^{M}$ , we can get an $M$ -dimensional feature vector $F^{vec} = [fea_{1},fea_{2},\\ldots,fea_{M}]$ . Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus, $M$ should be carefully designed for preserving important factors in data.", + "bbox": [ + 76, + 617, + 467, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the steps above, QSSN extracts an $M$ -dimensional feature vector from input cuboid $x_{i,j}$ with the size of $P \\times P \\times B$ . Furthermore, we introduce a new notation $N$ -QSSN to denote the learned vector representation $F^{vec}$ with the size of $(P \\times P \\times N) \\times 1$ . The output feature vector $F^{vec}$ is reshaped into a 3-D feature cuboid $F^{cub}$ with the size of $P \\times P \\times N$ . In $N$ -QSSN, the size of $M$ to denote the number of $MO$ is determined by", + "bbox": [ + 76, + 753, + 467, + 873 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM = P \\times P \\times N. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 886, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The outcome of $N$ -QSSN $F^{cub}$ has same spatial resolution as $x_{i,j}$ . The input HSI cuboid $x_{i,j}$ has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The $N$ -QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the $N$ -QSSN blocks.", + "bbox": [ + 500, + 90, + 890, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. QSSN-based Pyramid Framework", + "text_level": 1, + "bbox": [ + 500, + 285, + 799, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from $x_{i,j}$ , followed by a classifier to identify the land-cover category of the center pixel (i.e., the $(i,j)$ -th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks, $N_{1}$ -QSSN and $N_{2}$ -QSSN are stacked in a hierarchical manner. Specifically, for $N_{1}$ -QSSN, we take an original cuboid with the size of $P \\times P \\times B$ as input to learn the feature cuboid with the size of $P \\times P \\times N_{1}$ as output. Sequentially, for $N_{2}$ -QSSN, we use the feature representation with the size of $P \\times P \\times N_{1}$ learned from $N_{1}$ -QSSN as input to extract the feature cuboid with the size of $P \\times P \\times N_{2}$ as output. In our setting, $B > N_{1} > N_{2}$ , meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information.", + "bbox": [ + 498, + 325, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN- $L$ to indicate QSSPN with $L$ QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2.", + "bbox": [ + 498, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9929", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e78b27c82abcc3fc36fc035ea7499e2a5cbf7a1cce9289a4971f1aa1faeee347.jpg", + "table_caption": [ + "Table 1. Classification results and model analysis of different methods on HSI datasets." + ], + "table_footnote": [], + "table_body": "
DatasetsMetricsSSANSSRNRvTHiTSSFTTQSSPN-1QSSPN-2QSSPN-3
IPOA (%)89.4691.8583.8590.5996.3590.3692.6695.87
AA (%)85.9981.5179.6786.7189.9989.9393.3496.40
κ(%)88.0490.7381.6889.2795.8289.0591.6895.34
Params.148.83K735.88K10.78M49.60M148.50K910.50K1.13M1.17M
FLOPs7.88M212.48M17.83M345.88M3.66M34.54M52.75M55.59M
PUOA (%)99.1599.6397.3799.4399.5299.3899.4499.71
AA (%)98.7099.2995.8699.0999.2098.6198.8999.43
κ(%)98.8799.5196.5299.2499.3699.1799.2599.61
Params.94.63K396.99K9.77M42.41M148.03K609.16K666.38K700.52K
FLOPs5.57M108.04M16.83M190.85M3.66M10.25M14.89M17.66M
SAOA (%)98.9299.3198.1199.3899.5399.5499.6399.66
AA (%)99.3399.7098.8399.7099.7299.6199.6599.81
κ(%)98.8099.2397.9099.3199.4799.4999.5999.63
Params.149.71K750K10.82M50M148.50K926.90K1.16M1.20M
FLOPs7.97M216.8417.80M354.42M3.66M35.87M54.82M57.67M
", + "bbox": [ + 120, + 104, + 846, + 337 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0a3d453e62156373300ea4c7b96c04c9def9c0a7a1279cab52f65154a92bb263.jpg", + "table_caption": [ + "Table 2. Settings of channel reduction in QSSPN-L" + ], + "table_footnote": [ + "* $\\lfloor B / 2\\rfloor$ represents the greatest integer less than or equal to $B / 2$ ." + ], + "table_body": "
ModelsBandsN1N2N3
QSSPN-1B30--
QSSPN-2B[B/2]*30-
QSSPN-3B[B/2]5030
", + "bbox": [ + 135, + 377, + 411, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 498, + 209, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Details", + "text_level": 1, + "bbox": [ + 76, + 523, + 261, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with $145 \\times 145$ pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises $512 \\times 217$ pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are $610 \\times 340$ pixels with 103 bands to record nine classes of ground truths.", + "bbox": [ + 75, + 550, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36].", + "bbox": [ + 496, + 363, + 890, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. We adopt the Adam [22] optimizer with learning rate $1e^{-3}$ to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size $9 \\times 9 \\times B$ for all methods. For all datasets, we randomly select $10\\%$ , $5\\%$ and $85\\%$ labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients $(\\kappa)$ . Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM.", + "bbox": [ + 496, + 409, + 892, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Classification Results", + "text_level": 1, + "bbox": [ + 500, + 648, + 700, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 reports the results of OA, AA and $\\kappa$ on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves $96.40\\%$ AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). On the Salinas and Pavia University", + "bbox": [ + 496, + 672, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9930", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/983bc1a0572e84ade2690e37efa08117c0568becc045568807257b4c0e76910f.jpg", + "image_caption": [ + "(a) Ground truth" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 176, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6f29871000e34acad89591d7d29526e7a246475530e3c708301cb9386d72c547.jpg", + "image_caption": [ + "(b) RvT" + ], + "image_footnote": [], + "bbox": [ + 181, + 88, + 279, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f2c52b8480dd822d494923b36535d1f42ad9d9b6b49c85655268ee4ab3734253.jpg", + "image_caption": [ + "(c) HiT" + ], + "image_footnote": [], + "bbox": [ + 281, + 88, + 379, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9de2d9ef3efda918599785a4208421a40c341ad6b3a1b563898118588c577cb1.jpg", + "image_caption": [ + "(d) SSAN" + ], + "image_footnote": [], + "bbox": [ + 380, + 88, + 480, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c93307d69ee867a99c21fafa59cd12bc70d11ecad4450a07e3735bd73640c98.jpg", + "image_caption": [ + "(e)SSRN" + ], + "image_footnote": [], + "bbox": [ + 480, + 88, + 580, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d544eba9f0b0a91fbec61b481443d5befb4339f286effb910122d996478add4.jpg", + "image_caption": [ + "(f) QSSPN-1" + ], + "image_footnote": [], + "bbox": [ + 583, + 88, + 681, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e2a52ef3a4666ca26de0baeebb5c72a75ca2db8bbec4b786108474a3b157323.jpg", + "image_caption": [ + "(g) QSSPN-2" + ], + "image_footnote": [], + "bbox": [ + 684, + 88, + 782, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e99060f463733fc1faa62206fdd7332da1429200b2c8e6ce678f462fa484605.jpg", + "image_caption": [ + "(h) QSSPN-3" + ], + "image_footnote": [], + "bbox": [ + 785, + 88, + 887, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86a5ce48d8d8468be751198ee61df9747eefdc07460ef9345f9be007da4f1012.jpg", + "image_caption": [ + "(a) Ground truth" + ], + "image_footnote": [], + "bbox": [ + 80, + 215, + 176, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d06af8208275af5b014ac6cdbf7e93214b63f85a9cfbc329a211fb870ea3376.jpg", + "image_caption": [ + "(b) RvT" + ], + "image_footnote": [], + "bbox": [ + 181, + 215, + 279, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/91d6478a19804e673b3f9a8eecdfde41eeb5e4b40aa1c12ead4d9b5025296fef.jpg", + "image_caption": [ + "Figure 4. Classification maps of different methods for the Indian Pines dataset.", + "(c) HiT" + ], + "image_footnote": [], + "bbox": [ + 281, + 215, + 379, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a9f9743234b2d1f88ead07c874e3408d1b1e2e3de4b61a7a5461d2f1c18a2aaa.jpg", + "image_caption": [ + "(d) SSAN" + ], + "image_footnote": [], + "bbox": [ + 380, + 215, + 480, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/88aee164703f9470d2d6ca281a4f0b395e5a4453e170ff15a5a2af14e6267e42.jpg", + "image_caption": [ + "(e) SSRN" + ], + "image_footnote": [], + "bbox": [ + 480, + 215, + 580, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8519a95fdd0c60f122a96c1112c1a315f799db8537d2730a774c7300db4693dd.jpg", + "image_caption": [ + "(f) QSSPN-1" + ], + "image_footnote": [], + "bbox": [ + 583, + 215, + 681, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4ed2d0528c3c03bd2de342a5fe14e3a30e2722566ee0037f7a46d3e8646104dd.jpg", + "image_caption": [ + "(g) QSSPN-2" + ], + "image_footnote": [], + "bbox": [ + 684, + 215, + 782, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ad3a407872a098030c7a4351a07c5f13ed534751d1f764947aa09a930eb4487.jpg", + "image_caption": [ + "(h) QSSPN-3" + ], + "image_footnote": [], + "bbox": [ + 785, + 215, + 885, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9400aafd9a45c03ea4d8d2f156381249570fec071ea3e0ffa4a9e1d3905a0427.jpg", + "image_caption": [ + "Figure 5. Classification maps of different methods for the Pavia University dataset.", + "(a) Original data", + "Figure 6. Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 402, + 267, + 511 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/378545ef6b20edd948cdafa28996a4e55c02d40dbd5446b6e6ee805749a1d20c.jpg", + "image_caption": [ + "(b) Spectral-spatial representation" + ], + "image_footnote": [], + "bbox": [ + 281, + 402, + 465, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "datasets, our methods obtain $0.1\\%$ and $0.3\\%$ improvement with respect to $\\kappa$ , respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps.", + "bbox": [ + 75, + 582, + 468, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of $\\{15\\%, 20\\%, 25\\%, 30\\%\\}$ . Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c53b855bef662a16dbe534cdf2f7c84dc480c6e3dd7bc4bfaeeca64b1aa182cc.jpg", + "image_caption": [ + "Figure 7. OA of different models for the Indian Pines dataset with different training sizes." + ], + "image_footnote": [], + "bbox": [ + 521, + 419, + 836, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "increases. Overall, QSSPN-3 surpasses other methods, achieving $99.11\\%$ OA with a $30\\%$ training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples.", + "bbox": [ + 496, + 638, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 726, + 651, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode, $\\theta_{i',j',k'} = 0, i', j' \\in [0:P - 1], k' \\in [0:B - 1]$ ), the model has the worst performance compared with other models. The spatial phase mode (i.e., $\\theta_{i',j',0} = \\theta_{i',j',1} = \\dots = \\theta_{i',j',B - 1}$ ) considers spatial", + "bbox": [ + 496, + 750, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9931", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b749d08ad8d7fb98b5baf4cb2d2e3884782fc679732be847d555dd64a94c700.jpg", + "table_caption": [ + "Table 3. Effectiveness of phase on the Indian Pines dataset." + ], + "table_footnote": [], + "table_body": "
ModeParams.FLOPsOA (%)κ (%)
No phase717.13K18.92M86.8685.10
Spatial phase708.74K18.22M89.1887.74
Spectral phase705.68K17.97M88.6687.09
All1.13M52.75M92.6691.68
", + "bbox": [ + 91, + 114, + 455, + 195 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d54f1fc8eab06e49d4443f8e54480b5f21e595db2d3ebc634490dbe743e0116e.jpg", + "table_caption": [ + "Table 4. Effectiveness of pyramid structure on the Indian Pines dataset." + ], + "table_footnote": [ + "* $L$ indicates the QSSPN- $L$ model.", + "* Channel indicates the dimension of the learned feature cuboid for classification." + ], + "table_body": "
LChannelParams.FLOPsOA (%)κ (%)
110571.18K32.97M82.7280.45
130910.5K34.54M90.3689.05
1501.26M36.69M91.6390.49
2301.14M52.75M91.9390.84
3301.17M55.59M92.9391.96
", + "bbox": [ + 94, + 250, + 452, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e., $\\theta_{0,0,k'} = \\theta_{0,1,k'} = \\dots = \\theta_{P-1,P-1,k'}$ ) only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance.", + "bbox": [ + 75, + 407, + 468, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Parameter Sensitivity Study", + "text_level": 1, + "bbox": [ + 76, + 556, + 328, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated.", + "bbox": [ + 75, + 580, + 468, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement.", + "bbox": [ + 75, + 657, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks,", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba16aad61381aafb9d2293491a56f955d0f5e3ea607e052d7f0e34a197ea59a1.jpg", + "image_caption": [ + "(a) Indian Pines" + ], + "image_footnote": [], + "bbox": [ + 506, + 99, + 694, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c031429a9e373234cb3888ce59df701a059dc83ce88f5ebeedd4ce1c00c9815d.jpg", + "image_caption": [ + "(b) Salinas" + ], + "image_footnote": [], + "bbox": [ + 699, + 98, + 890, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22a84439773468dc4bc42d9e490ac214f42b5f9245ffc48bf91a2ff896047fee.jpg", + "image_caption": [ + "(c) Indian Pines" + ], + "image_footnote": [], + "bbox": [ + 506, + 222, + 689, + 320 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf729a5b1a18154005d0a56dd16b0f012ad4d2c98adfc7d6b326313d97faf048.jpg", + "image_caption": [ + "(d) Salinas", + "Figure 8. OA of QSSPN with different patch sizes and depths." + ], + "image_footnote": [], + "bbox": [ + 704, + 222, + 890, + 319 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g. $82.72\\%$ OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g. $91.63\\%$ OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure.", + "bbox": [ + 496, + 378, + 892, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 622, + 617, + 637 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications.", + "bbox": [ + 496, + 652, + 890, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST).", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9932", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Isabel Cecilia Contreras Acosta, Mahdi Khodadadzadeh, Laura Tusa, Pedram Ghamisi, and Richard Gloaguen. 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Rotation-invariant attention network for hyperspectral image classification. IEEE Transactions on Image Processing, 2022. 2", + "[47] Zilong Zhong, Jonathan Li, Zhiming Luo, and Michael Chapman. Spectral-spatial residual network for hyperspectral image classification: A 3-d deep learning framework. IEEE Transactions on Geoscience and Remote Sensing, 56(2):847-858, 2017. 2, 6", + "[48] Zilong Zhong, Ying Li, Lingfei Ma, Jonathan Li, and Wei-Shi Zheng. Spectral-spatial transformer network for hyperspectral image classification: A factorized architecture search framework. IEEE Transactions on Geoscience and Remote Sensing, 60:1-15, 2021. 2", + "[49] Arthur Zimek, Erich Schubert, and Hans-Peter Kriegel. A survey on unsupervised outlier detection in high-dimensional numerical data. Statistical Analysis and Data Mining: The ASA Data Science Journal, 5(5):363-387, 2012. 1, 4" + ], + "bbox": [ + 501, + 92, + 890, + 414 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9934", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_model.json b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..50b39747cafbd93bf3da6143d7dc816c8d6499b9 --- /dev/null +++ b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_model.json @@ -0,0 +1,2431 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.13, + 0.885, + 0.175 + ], + "angle": 0, + "content": "Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.203, + 0.678, + 0.222 + ], + "angle": 0, + "content": "Jie Zhang\\(^{1}\\), Yongshan Zhang\\(^{2,1*}\\), Yicong Zhou\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.222, + 0.834, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\) Department of Computer and Information Science, University of Macau, Macau, China \\(^{2}\\) School of Computer Science, China University of Geosciences, Wuhan, China" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.26, + 0.767, + 0.275 + ], + "angle": 0, + "content": "jiezh1997@gmail.com, yszhang.cug@gmail.com, yicongzhou@um.edu.m" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.342, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Hyperspectral image (HSI) classification aims at assigning a unique label for every pixel to identify categories of different land covers. Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. In this pyramid framework, QSSPN progressively learns feature representations by cascading QSSN blocks and performs classification with a softmax classifier. It is the first attempt to introduce quantum theory in HSI processing model design. Substantial experiments are conducted on three HSI datasets to verify the superiority of the proposed QSSPN framework over the state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.793, + 0.21, + 0.808 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.818, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. Each HSI contains two spatial dimensions and one spectral di" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.331, + 0.856, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.513, + 0.895, + 0.556 + ], + "angle": 0, + "content": "Figure 1. Performance comparison between the proposed QSSPN framework and existing methods. Average accuracies on Indian Pines dataset are presented." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.703 + ], + "angle": 0, + "content": "mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and \\(K\\)-nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.228, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9925" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.334 + ], + "angle": 0, + "content": "in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.655 + ], + "angle": 0, + "content": "Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.183, + 0.892, + 0.211 + ], + "angle": 0, + "content": "The contributions of this article are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.219, + 0.892, + 0.28 + ], + "angle": 0, + "content": "- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.289, + 0.892, + 0.35 + ], + "angle": 0, + "content": "- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.358, + 0.892, + 0.448 + ], + "angle": 0, + "content": "- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.219, + 0.892, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.561 + ], + "angle": 0, + "content": "The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.642, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9926" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.468, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.471, + 0.38 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.473, + 0.732 + ], + "angle": 0, + "content": "Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.763, + 0.169, + 0.779 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.642, + 0.106 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.895, + 0.388 + ], + "angle": 0, + "content": "Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in \\(N\\)-dimensional Hilbert space \\(\\mathcal{H}^N\\). We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations \\(\\left|\\cdot \\right\\rangle\\) and \\(\\langle \\cdot |\\) denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors \\(\\{\\left|\\phi_n\\right\\rangle \\}_{n = 1}^N\\), we can represent the states of quantum system \\(|\\psi \\rangle\\) as follows*:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.398, + 0.892, + 0.44 + ], + "angle": 0, + "content": "\\[\n| \\psi \\rangle = \\sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \\theta_ {n}} | \\phi_ {n} \\rangle , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.894, + 0.542 + ], + "angle": 0, + "content": "where \\(A_{n}\\) is a probability amplitude satisfying \\(\\sum_{N}|A_{n}|^{2} = 1\\), \\(i\\) is the imaginary unit and \\(\\theta_{n}\\) indicates the phase. A simple example of basis state vectors for \\(\\mathcal{H}^N\\) is standard unit basis. Detailedly, the standard basis of \\(\\mathcal{H}^2\\) is formed by column vectors \\(|0\\rangle_2 = [1,0]^T\\) and \\(|1\\rangle_2 = [0,1]^T\\). Here, we use the notation" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.552, + 0.892, + 0.57 + ], + "angle": 0, + "content": "\\[\n\\left| n \\right\\rangle_ {N}, n = 0, 1, \\dots , N - 1 \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.641 + ], + "angle": 0, + "content": "to represent the standard basis of \\(\\mathcal{H}^N\\). Accordingly, \\(\\langle n|_N\\) denotes the conjugate transpose of \\(|n\\rangle_N\\). All components of \\(|n\\rangle_N\\) are 0 except the \\(n\\)-th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.809 + ], + "angle": 0, + "content": "The reversible unitary operator \\(U\\) describes the state's evolution in QC, mapping the initial states \\(|\\psi_{initial}\\rangle\\) to final states \\(|\\psi_{final}\\rangle\\). These operators manipulate the phases \\(\\theta_{n}\\) and amplitudes \\(A_{n}\\) by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators \\(\\{\\Pi_m = |\\phi_m\\rangle \\langle \\phi_m|\\}_{m = 1}^M\\). According to the Born rule [28], \\(\\Pi_{m}\\) projects the state \\(|\\psi_{final}\\rangle\\) to the corresponding basis state \\(|\\phi_m\\rangle\\) with a probability:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.819, + 0.892, + 0.837 + ], + "angle": 0, + "content": "\\[\nP \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = T r \\left(\\Pi_ {m} \\rho\\right) = \\left\\langle \\phi_ {m} \\mid \\psi_ {\\text {f i n a l}} \\right\\rangle \\left\\langle \\psi_ {\\text {f i n a l}} \\mid \\phi_ {m} \\right\\rangle , \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.847, + 0.892, + 0.88 + ], + "angle": 0, + "content": "where \\(\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|\\) is the density matrix representation of \\(|\\psi_{final}\\rangle\\) and \\(\\sum_{M}P(|\\phi_{m}\\rangle) = 1\\). \\(|\\cdot \\rangle \\langle \\cdot |\\) denotes the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.517, + 0.888, + 0.763, + 0.901 + ], + "angle": 0, + "content": "*Only pure states are considered in this paper." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9927" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.099, + 0.468, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.228, + 0.471, + 0.286 + ], + "angle": 0, + "content": "Figure 3. Illustration of data mapping in QSSN. The state representation \\(|\\psi \\rangle\\) encodes data from original space to Hilbert space: \\(\\mathcal{R} \\to \\mathcal{H}\\). The MFM outputs a feature vector mapped from \\(|\\psi \\rangle\\) to feature space: \\(\\mathcal{H} \\to \\mathcal{F}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.471, + 0.336 + ], + "angle": 0, + "content": "outer product and \\(\\langle \\cdot |\\cdot \\rangle\\) denotes the inner product of \\(\\langle \\cdot |\\) and \\(|\\cdot \\rangle\\) . Eq. (3) can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.343, + 0.47, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = \\left\\langle \\phi_ {m} \\right| \\rho \\left| \\phi_ {m} \\right\\rangle = \\left(\\left\\langle \\psi_ {f i n a l} \\mid \\phi_ {m} \\right\\rangle\\right) ^ {2} \\tag {4} \\\\ = \\sum_ {n _ {1}} ^ {N - 1} \\sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\\theta_ {n _ {1}} - \\theta_ {n _ {2}})} \\langle \\phi_ {m} | n _ {1} \\rangle \\langle n _ {2} | \\phi_ {m} \\rangle . \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.415, + 0.469, + 0.536 + ], + "angle": 0, + "content": "Here we neglect the subscript \\(N\\) of \\(|n\\rangle_N\\) for simplicity. In Eq. (4), the size of \\(|n\\rangle\\) is \\(N\\). For the same measurement operator \\(\\Pi_m \\sim |\\phi_m\\rangle\\), the output \\(P(|\\phi_m\\rangle)\\) depends on all pairs of \\(A_{n_1}\\) and \\(A_{n_2}\\) and their correlations \\((\\theta_{n_1} - \\theta_{n_2})\\). PVM yields values \\(P_{res} = [P(|\\phi_1\\rangle), P(|\\phi_2\\rangle), \\ldots, P(|\\phi_M\\rangle)]\\) corresponding to the selected projection operators \\(\\{\\Pi_m\\}_{m=1}^M\\), reflecting the state of quantum system." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.582 + ], + "angle": 0, + "content": "We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.458, + 0.607 + ], + "angle": 0, + "content": "3.2. Quantum-Inspired Spectral-Spatial Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.469, + 0.763 + ], + "angle": 0, + "content": "Let \\( X \\in \\mathcal{R}^{H \\times W \\times B} \\) be the HSI with \\( H \\) pixels in height, \\( W \\) pixels in width, and \\( B \\) spectral bands. Taking the \\( (i,j) \\)-th pixel as center, information in a small cuboid \\( x_{i,j} \\in \\mathcal{R}^{P \\times P \\times B} \\) with \\( P \\times P \\) pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad \\( X \\) with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases \\(\\Theta_{i,j} \\in R^{P \\times P \\times B}\\) for all elements \\(x_{i',j',k'}'\\) in \\(x_{i,j}\\). Phases play an important role in encoding data \\(x_{i,j}\\) in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.893, + 0.349 + ], + "angle": 0, + "content": "distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase \\(\\theta_{i',j',k'}\\) for each element \\(x_{i',j',k'}'\\). Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each \\(x_{i',j',k'}'\\), the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have \\(B\\) channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in \\(3\\times 3\\) pixel windows. The following asymmetric convolution layers [37] with \\(3\\times 1\\) and \\(1\\times 3\\) kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases \\(\\Theta_{i,j}\\). Before we encode each HSI cuboid into complex finite-dimensional Hilbert space \\(\\mathcal{H}^K\\) (\\(K = P\\times P\\times B\\)), we reshape the HSI cuboid \\(x_{i,j}\\) and the corresponding phase cuboid \\(\\Theta_{i,j}\\) as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.357, + 0.893, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} x ^ {v e c} = \\left[ x _ {0} ^ {\\prime}, \\dots , x _ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P} ^ {\\prime}, \\dots , x _ {K - 1} ^ {\\prime} \\right], \\tag {5} \\\\ \\Theta^ {v e c} = \\left[ \\theta_ {0}, \\dots , \\theta_ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P}, \\dots , \\theta_ {K - 1} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.893, + 0.448 + ], + "angle": 0, + "content": "where \\(i', j' \\in [0 : P - 1]\\) and \\(k' \\in [0 : B - 1]\\). Then phase vector \\(x^{vec}\\) and original data vector \\(x^{vec}\\) are used in the state vector representation \\(|x_{i,j}\\rangle\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.457, + 0.892, + 0.499 + ], + "angle": 0, + "content": "\\[\n\\left| x _ {i, j} \\right\\rangle = \\sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \\theta_ {n}} \\left| n \\right\\rangle_ {K}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.508, + 0.726, + 0.523 + ], + "angle": 0, + "content": "In Eq. (6), \\(A_{n}\\) can be obtained as:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.534, + 0.892, + 0.575 + ], + "angle": 0, + "content": "\\[\nA _ {n} = \\sqrt {\\frac {x _ {n} ^ {v e c}}{\\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.78 + ], + "angle": 0, + "content": "where \\(x_{n}^{vec}\\) indicates the \\(n\\)-th element in \\(x^{vec}\\). In Eq. (6), \\(x_{i,j}\\) can be represented by a complex vector \\(|x_{i,j}\\rangle = [A_0e^{i\\theta_0}, A_1e^{i\\theta_1}, \\ldots, A_{K-1}e^{i\\theta_{K-1}}]\\) in \\(\\mathcal{H}^K\\). As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode \\(x_{i,j}\\) in \\(|x_{i,j}\\rangle\\) is neglecting the imaginary parts \\(e^{i\\theta}\\) (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation \\((MO)\\) to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as \\(PVM(\\Pi_m,\\rho)\\): using a density matrix \\(\\rho\\) to represent the state of quantum system \\(\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|\\) and then applying the matrix manipulation (matrix product and trace)" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9928" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "with operators \\(\\{\\Pi_m\\}_{m=1}^M\\). For each \\(\\Pi_m\\), we get the probability \\(P(|\\phi_m\\rangle)\\). Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.165, + 0.468, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D _ {i, j} = \\left| x _ {i, j} \\right\\rangle \\left\\langle x _ {i, j} \\right| \\tag {8} \\\\ = \\sum_ {n = 0} ^ {K - 1} \\sum_ {n ^ {\\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\\prime}} e ^ {i \\left(\\theta_ {n} - \\theta_ {n ^ {\\prime}}\\right)} \\left| n ^ {\\prime} \\right\\rangle \\left\\langle n \\right|, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.233, + 0.47, + 0.581 + ], + "angle": 0, + "content": "where \\( |n^{\\prime}\\rangle \\langle n| \\) represents a square matrix with \\( P\\times P\\times B \\) rows and columns that all components are 0 except the \\( (n,n^{\\prime}) \\)-th component is 1. Each term in the density matrix \\( D_{i,j} \\) is the multiplication of \\( A_{n} \\) and \\( A_{n^{\\prime}} \\) with a coefficient \\( e^{i(\\theta_n - \\theta_{n^{\\prime}})} \\). Empirically, this is similar to fusing information of each pair of elements \\( x_{n}^{vec} \\) and \\( x_{n^{\\prime}}^{vec} \\). Phases \\( \\theta_{n} \\) and \\( \\theta_{n^{\\prime}} \\) are predicted by PPM. We hope the imaginary part \\( e^{i(\\theta_n - \\theta_{n^{\\prime}})} \\) can dynamically modulate the correlations between \\( x_{n}^{vec} \\) and \\( x_{n^{\\prime}}^{vec} \\). In each pair, the location and band of \\( x_{n}^{vec} \\) and \\( x_{n^{\\prime}}^{vec} \\) may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result \\( P(|\\phi_m\\rangle) \\) corresponding to \\( \\Pi_{m} \\). Note that PVM has corresponding operations applied on physic devices. There are constraints of operations \\( \\Pi_{m} \\) in their mathematical formulation in quantum theory. We use an abstract representation of PVM as \\( PVM(\\Pi_m,\\rho)\\rightarrow PVM(Operator_m,\\rho) \\). To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers \\( FC_{m} \\) with depth 3 as \\( Operator_{m} \\). The MO generates a feature point as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.592, + 0.468, + 0.608 + ], + "angle": 0, + "content": "\\[\nf e a _ {m} = M O \\left(F C _ {m}, D _ {i, j}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.618, + 0.468, + 0.753 + ], + "angle": 0, + "content": "where \\(D_{i,j}\\) stores the fusion information of each element pair, \\(x_{n}^{vec}\\) and \\(x_{n'}^{vec}\\). \\(MO\\) is an operation that feeds \\(D_{i,j}\\) into the operator \\(FC_{m}\\) to efficiently aggregate spatial and spectral information. Given \\(M\\) operators \\(\\{FC_{m}\\}_{m=1}^{M}\\), we can get an \\(M\\)-dimensional feature vector \\(F^{vec} = [fea_{1},fea_{2},\\ldots,fea_{M}]\\). Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus, \\(M\\) should be carefully designed for preserving important factors in data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.754, + 0.468, + 0.874 + ], + "angle": 0, + "content": "Following the steps above, QSSN extracts an \\(M\\)-dimensional feature vector from input cuboid \\(x_{i,j}\\) with the size of \\(P \\times P \\times B\\). Furthermore, we introduce a new notation \\(N\\)-QSSN to denote the learned vector representation \\(F^{vec}\\) with the size of \\((P \\times P \\times N) \\times 1\\). The output feature vector \\(F^{vec}\\) is reshaped into a 3-D feature cuboid \\(F^{cub}\\) with the size of \\(P \\times P \\times N\\). In \\(N\\)-QSSN, the size of \\(M\\) to denote the number of \\(MO\\) is determined by" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "\\[\nM = P \\times P \\times N. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.892, + 0.227 + ], + "angle": 0, + "content": "The outcome of \\( N \\)-QSSN \\( F^{cub} \\) has same spatial resolution as \\( x_{i,j} \\). The input HSI cuboid \\( x_{i,j} \\) has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The \\( N \\)-QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the \\( N \\)-QSSN blocks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.286, + 0.8, + 0.303 + ], + "angle": 0, + "content": "3.3. QSSN-based Pyramid Framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.326, + 0.892, + 0.763 + ], + "angle": 0, + "content": "It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from \\( x_{i,j} \\), followed by a classifier to identify the land-cover category of the center pixel (i.e., the \\( (i,j) \\)-th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks, \\( N_{1} \\)-QSSN and \\( N_{2} \\)-QSSN are stacked in a hierarchical manner. Specifically, for \\( N_{1} \\)-QSSN, we take an original cuboid with the size of \\( P \\times P \\times B \\) as input to learn the feature cuboid with the size of \\( P \\times P \\times N_{1} \\) as output. Sequentially, for \\( N_{2} \\)-QSSN, we use the feature representation with the size of \\( P \\times P \\times N_{1} \\) learned from \\( N_{1} \\)-QSSN as input to extract the feature cuboid with the size of \\( P \\times P \\times N_{2} \\) as output. In our setting, \\( B > N_{1} > N_{2} \\), meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN- \\(L\\) to indicate QSSPN with \\(L\\) QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9929" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.225, + 0.09, + 0.744, + 0.103 + ], + "angle": 0, + "content": "Table 1. Classification results and model analysis of different methods on HSI datasets." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.106, + 0.847, + 0.338 + ], + "angle": 0, + "content": "
DatasetsMetricsSSANSSRNRvTHiTSSFTTQSSPN-1QSSPN-2QSSPN-3
IPOA (%)89.4691.8583.8590.5996.3590.3692.6695.87
AA (%)85.9981.5179.6786.7189.9989.9393.3496.40
κ(%)88.0490.7381.6889.2795.8289.0591.6895.34
Params.148.83K735.88K10.78M49.60M148.50K910.50K1.13M1.17M
FLOPs7.88M212.48M17.83M345.88M3.66M34.54M52.75M55.59M
PUOA (%)99.1599.6397.3799.4399.5299.3899.4499.71
AA (%)98.7099.2995.8699.0999.2098.6198.8999.43
κ(%)98.8799.5196.5299.2499.3699.1799.2599.61
Params.94.63K396.99K9.77M42.41M148.03K609.16K666.38K700.52K
FLOPs5.57M108.04M16.83M190.85M3.66M10.25M14.89M17.66M
SAOA (%)98.9299.3198.1199.3899.5399.5499.6399.66
AA (%)99.3399.7098.8399.7099.7299.6199.6599.81
κ(%)98.8099.2397.9099.3199.4799.4999.5999.63
Params.149.71K750K10.82M50M148.50K926.90K1.16M1.20M
FLOPs7.97M216.8417.80M354.42M3.66M35.87M54.82M57.67M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.362, + 0.427, + 0.376 + ], + "angle": 0, + "content": "Table 2. Settings of channel reduction in QSSPN-L" + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.378, + 0.413, + 0.444 + ], + "angle": 0, + "content": "
ModelsBandsN1N2N3
QSSPN-1B30--
QSSPN-2B[B/2]*30-
QSSPN-3B[B/2]5030
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.145, + 0.444, + 0.412, + 0.471 + ], + "angle": 0, + "content": "* \\(\\lfloor B / 2\\rfloor\\) represents the greatest integer less than or equal to \\(B / 2\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.499, + 0.21, + 0.516 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.525, + 0.263, + 0.542 + ], + "angle": 0, + "content": "4.1. Experiment Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with \\(145 \\times 145\\) pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises \\(512 \\times 217\\) pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are \\(610 \\times 340\\) pixels with 103 bands to record nine classes of ground truths." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.409 + ], + "angle": 0, + "content": "els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.637 + ], + "angle": 0, + "content": "Setup. We adopt the Adam [22] optimizer with learning rate \\(1e^{-3}\\) to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size \\(9 \\times 9 \\times B\\) for all methods. For all datasets, we randomly select \\(10\\%\\), \\(5\\%\\) and \\(85\\%\\) labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients \\((\\kappa)\\). Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.702, + 0.665 + ], + "angle": 0, + "content": "4.2. Classification Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 reports the results of OA, AA and \\(\\kappa\\) on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves \\(96.40\\%\\) AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). On the Salinas and Pavia University" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9930" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.177, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.169, + 0.173, + 0.18 + ], + "angle": 0, + "content": "(a) Ground truth" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.089, + 0.28, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.169, + 0.252, + 0.181 + ], + "angle": 0, + "content": "(b) RvT" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.089, + 0.38, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.169, + 0.351, + 0.18 + ], + "angle": 0, + "content": "(c) HiT" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.089, + 0.481, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.169, + 0.46, + 0.18 + ], + "angle": 0, + "content": "(d) SSAN" + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.089, + 0.581, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.169, + 0.56, + 0.18 + ], + "angle": 0, + "content": "(e)SSRN" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.089, + 0.683, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.169, + 0.669, + 0.18 + ], + "angle": 0, + "content": "(f) QSSPN-1" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.089, + 0.784, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.169, + 0.772, + 0.18 + ], + "angle": 0, + "content": "(g) QSSPN-2" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.089, + 0.888, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.802, + 0.169, + 0.873, + 0.18 + ], + "angle": 0, + "content": "(h) QSSPN-3" + }, + { + "type": "image_caption", + "bbox": [ + 0.25, + 0.188, + 0.718, + 0.202 + ], + "angle": 0, + "content": "Figure 4. Classification maps of different methods for the Indian Pines dataset." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.216, + 0.178, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.355, + 0.173, + 0.367 + ], + "angle": 0, + "content": "(a) Ground truth" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.216, + 0.28, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.209, + 0.355, + 0.252, + 0.367 + ], + "angle": 0, + "content": "(b) RvT" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.216, + 0.38, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.355, + 0.351, + 0.367 + ], + "angle": 0, + "content": "(c) HiT" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.216, + 0.481, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.355, + 0.46, + 0.367 + ], + "angle": 0, + "content": "(d) SSAN" + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.216, + 0.581, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.355, + 0.56, + 0.367 + ], + "angle": 0, + "content": "(e) SSRN" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.216, + 0.683, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.355, + 0.668, + 0.367 + ], + "angle": 0, + "content": "(f) QSSPN-1" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.216, + 0.784, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.7, + 0.355, + 0.772, + 0.367 + ], + "angle": 0, + "content": "(g) QSSPN-2" + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.216, + 0.887, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.355, + 0.873, + 0.367 + ], + "angle": 0, + "content": "(h) QSSPN-3" + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.375, + 0.729, + 0.388 + ], + "angle": 0, + "content": "Figure 5. Classification maps of different methods for the Pavia University dataset." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.404, + 0.268, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.515, + 0.218, + 0.527 + ], + "angle": 0, + "content": "(a) Original data" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.404, + 0.467, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.515, + 0.464, + 0.527 + ], + "angle": 0, + "content": "(b) Spectral-spatial representation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.539, + 0.469, + 0.567 + ], + "angle": 0, + "content": "Figure 6. Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.718 + ], + "angle": 0, + "content": "datasets, our methods obtain \\(0.1\\%\\) and \\(0.3\\%\\) improvement with respect to \\(\\kappa\\), respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of \\(\\{15\\%, 20\\%, 25\\%, 30\\%\\}\\). Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.42, + 0.837, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.595, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Figure 7. OA of different models for the Indian Pines dataset with different training sizes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.716 + ], + "angle": 0, + "content": "increases. Overall, QSSPN-3 surpasses other methods, achieving \\(99.11\\%\\) OA with a \\(30\\%\\) training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.653, + 0.743 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode, \\(\\theta_{i',j',k'} = 0, i', j' \\in [0:P - 1], k' \\in [0:B - 1]\\)), the model has the worst performance compared with other models. The spatial phase mode (i.e., \\(\\theta_{i',j',0} = \\theta_{i',j',1} = \\dots = \\theta_{i',j',B - 1}\\)) considers spatial" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9931" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.09, + 0.448, + 0.104 + ], + "angle": 0, + "content": "Table 3. Effectiveness of phase on the Indian Pines dataset." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.116, + 0.457, + 0.196 + ], + "angle": 0, + "content": "
ModeParams.FLOPsOA (%)κ (%)
No phase717.13K18.92M86.8685.10
Spatial phase708.74K18.22M89.1887.74
Spectral phase705.68K17.97M88.6687.09
All1.13M52.75M92.6691.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.211, + 0.454, + 0.239 + ], + "angle": 0, + "content": "Table 4. Effectiveness of pyramid structure on the Indian Pines dataset." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.251, + 0.454, + 0.345 + ], + "angle": 0, + "content": "
LChannelParams.FLOPsOA (%)κ (%)
110571.18K32.97M82.7280.45
130910.5K34.54M90.3689.05
1501.26M36.69M91.6390.49
2301.14M52.75M91.9390.84
3301.17M55.59M92.9391.96
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.108, + 0.346, + 0.295, + 0.358 + ], + "angle": 0, + "content": "* \\(L\\) indicates the QSSPN- \\(L\\) model." + }, + { + "type": "table_footnote", + "bbox": [ + 0.108, + 0.358, + 0.453, + 0.382 + ], + "angle": 0, + "content": "* Channel indicates the dimension of the learned feature cuboid for classification." + }, + { + "type": "list", + "bbox": [ + 0.108, + 0.346, + 0.453, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.47, + 0.543 + ], + "angle": 0, + "content": "information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e., \\(\\theta_{0,0,k'} = \\theta_{0,1,k'} = \\dots = \\theta_{P-1,P-1,k'}\\)) only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.33, + 0.574 + ], + "angle": 0, + "content": "4.4. Parameter Sensitivity Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.657 + ], + "angle": 0, + "content": "To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks," + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.1, + 0.695, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.201, + 0.641, + 0.213 + ], + "angle": 0, + "content": "(a) Indian Pines" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.099, + 0.891, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.201, + 0.825, + 0.213 + ], + "angle": 0, + "content": "(b) Salinas" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.223, + 0.69, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.323, + 0.64, + 0.335 + ], + "angle": 0, + "content": "(c) Indian Pines" + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.223, + 0.891, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.323, + 0.826, + 0.335 + ], + "angle": 0, + "content": "(d) Salinas" + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.347, + 0.88, + 0.362 + ], + "angle": 0, + "content": "Figure 8. OA of QSSPN with different patch sizes and depths." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.893, + 0.593 + ], + "angle": 0, + "content": "QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g. \\(82.72\\%\\) OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g. \\(91.63\\%\\) OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.623, + 0.619, + 0.638 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.836 + ], + "angle": 0, + "content": "In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9932" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[1] Isabel Cecilia Contreras Acosta, Mahdi Khodadadzadeh, Laura Tusa, Pedram Ghamisi, and Richard Gloaguen. A machine learning framework for drill-core mineral mapping using hyperspectral and high-resolution mineralogical data fusion. 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Statistical Analysis and Data Mining: The ASA Data Science Journal, 5(5):363-387, 2012. 1, 4" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9934" + } + ] +] \ No newline at end of file diff --git a/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_origin.pdf b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8a0b819da7c8595b2206249b205ffdf239e48e23 --- /dev/null +++ b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c53bc627c547fcf0b5c68e05595706200f50a3987137d05f9e46e919e0a63ab4 +size 781765 diff --git a/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/full.md b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d5113d2b8477695fa196e4f94d7301a677a93d3e --- /dev/null +++ b/2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/full.md @@ -0,0 +1,338 @@ +# Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification + +Jie Zhang $^{1}$ , Yongshan Zhang $^{2,1*}$ , Yicong Zhou $^{1*}$ + +$^{1}$ Department of Computer and Information Science, University of Macau, Macau, China $^{2}$ School of Computer Science, China University of Geosciences, Wuhan, China + +jiezh1997@gmail.com, yszhang.cug@gmail.com, yicongzhou@um.edu.m + +# Abstract + +Hyperspectral image (HSI) classification aims at assigning a unique label for every pixel to identify categories of different land covers. Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. In this pyramid framework, QSSPN progressively learns feature representations by cascading QSSN blocks and performs classification with a softmax classifier. It is the first attempt to introduce quantum theory in HSI processing model design. Substantial experiments are conducted on three HSI datasets to verify the superiority of the proposed QSSPN framework over the state-of-the-art methods. + +# 1. Introduction + +Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. Each HSI contains two spatial dimensions and one spectral di + +![](images/f8e92293ecb73eba639865db402b61a405202b3924c0e52d8206f1a103228dcd.jpg) +Figure 1. Performance comparison between the proposed QSSPN framework and existing methods. Average accuracies on Indian Pines dataset are presented. + +mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49]. + +In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and $K$ -nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification + +in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm. + +Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38]. + +Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks + +and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network. + +The contributions of this article are summarized as follows. + +- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising. +- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations. +- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity. + +The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion. + +# 2. Related Work + +Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45]. + +![](images/f55728ced1a6ba370d2c5c93235a61a3535ba4fc48139753d716f3d45a213148.jpg) +Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom. + +Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection. + +# 3. Method + +This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2. + +# 3.1. Preliminaries + +Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in $N$ -dimensional Hilbert space $\mathcal{H}^N$ . We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations $\left|\cdot \right\rangle$ and $\langle \cdot |$ denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors $\{\left|\phi_n\right\rangle \}_{n = 1}^N$ , we can represent the states of quantum system $|\psi \rangle$ as follows*: + +$$ +| \psi \rangle = \sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \theta_ {n}} | \phi_ {n} \rangle , \tag {1} +$$ + +where $A_{n}$ is a probability amplitude satisfying $\sum_{N}|A_{n}|^{2} = 1$ , $i$ is the imaginary unit and $\theta_{n}$ indicates the phase. A simple example of basis state vectors for $\mathcal{H}^N$ is standard unit basis. Detailedly, the standard basis of $\mathcal{H}^2$ is formed by column vectors $|0\rangle_2 = [1,0]^T$ and $|1\rangle_2 = [0,1]^T$ . Here, we use the notation + +$$ +\left| n \right\rangle_ {N}, n = 0, 1, \dots , N - 1 \tag {2} +$$ + +to represent the standard basis of $\mathcal{H}^N$ . Accordingly, $\langle n|_N$ denotes the conjugate transpose of $|n\rangle_N$ . All components of $|n\rangle_N$ are 0 except the $n$ -th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states. + +The reversible unitary operator $U$ describes the state's evolution in QC, mapping the initial states $|\psi_{initial}\rangle$ to final states $|\psi_{final}\rangle$ . These operators manipulate the phases $\theta_{n}$ and amplitudes $A_{n}$ by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators $\{\Pi_m = |\phi_m\rangle \langle \phi_m|\}_{m = 1}^M$ . According to the Born rule [28], $\Pi_{m}$ projects the state $|\psi_{final}\rangle$ to the corresponding basis state $|\phi_m\rangle$ with a probability: + +$$ +P \left(\left| \phi_ {m} \right\rangle\right) = T r \left(\Pi_ {m} \rho\right) = \left\langle \phi_ {m} \mid \psi_ {\text {f i n a l}} \right\rangle \left\langle \psi_ {\text {f i n a l}} \mid \phi_ {m} \right\rangle , \tag {3} +$$ + +where $\rho = |\psi_{final}\rangle \langle \psi_{final}|$ is the density matrix representation of $|\psi_{final}\rangle$ and $\sum_{M}P(|\phi_{m}\rangle) = 1$ . $|\cdot \rangle \langle \cdot |$ denotes the + +![](images/e07cba4561baba1f2b8e0f9c2aea9c4e04b9ce0181a5c2168beb225e437b9a6e.jpg) +Figure 3. Illustration of data mapping in QSSN. The state representation $|\psi \rangle$ encodes data from original space to Hilbert space: $\mathcal{R} \to \mathcal{H}$ . The MFM outputs a feature vector mapped from $|\psi \rangle$ to feature space: $\mathcal{H} \to \mathcal{F}$ . + +outer product and $\langle \cdot |\cdot \rangle$ denotes the inner product of $\langle \cdot |$ and $|\cdot \rangle$ . Eq. (3) can be rewritten as: + +$$ +\begin{array}{l} P \left(\left| \phi_ {m} \right\rangle\right) = \left\langle \phi_ {m} \right| \rho \left| \phi_ {m} \right\rangle = \left(\left\langle \psi_ {f i n a l} \mid \phi_ {m} \right\rangle\right) ^ {2} \tag {4} \\ = \sum_ {n _ {1}} ^ {N - 1} \sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\theta_ {n _ {1}} - \theta_ {n _ {2}})} \langle \phi_ {m} | n _ {1} \rangle \langle n _ {2} | \phi_ {m} \rangle . \\ \end{array} +$$ + +Here we neglect the subscript $N$ of $|n\rangle_N$ for simplicity. In Eq. (4), the size of $|n\rangle$ is $N$ . For the same measurement operator $\Pi_m \sim |\phi_m\rangle$ , the output $P(|\phi_m\rangle)$ depends on all pairs of $A_{n_1}$ and $A_{n_2}$ and their correlations $(\theta_{n_1} - \theta_{n_2})$ . PVM yields values $P_{res} = [P(|\phi_1\rangle), P(|\phi_2\rangle), \ldots, P(|\phi_M\rangle)]$ corresponding to the selected projection operators $\{\Pi_m\}_{m=1}^M$ , reflecting the state of quantum system. + +We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28]. + +# 3.2. Quantum-Inspired Spectral-Spatial Network + +Let $X \in \mathcal{R}^{H \times W \times B}$ be the HSI with $H$ pixels in height, $W$ pixels in width, and $B$ spectral bands. Taking the $(i,j)$ -th pixel as center, information in a small cuboid $x_{i,j} \in \mathcal{R}^{P \times P \times B}$ with $P \times P$ pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad $X$ with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification. + +Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases $\Theta_{i,j} \in R^{P \times P \times B}$ for all elements $x_{i',j',k'}'$ in $x_{i,j}$ . Phases play an important role in encoding data $x_{i,j}$ in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class + +distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase $\theta_{i',j',k'}$ for each element $x_{i',j',k'}'$ . Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each $x_{i',j',k'}'$ , the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have $B$ channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in $3\times 3$ pixel windows. The following asymmetric convolution layers [37] with $3\times 1$ and $1\times 3$ kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases $\Theta_{i,j}$ . Before we encode each HSI cuboid into complex finite-dimensional Hilbert space $\mathcal{H}^K$ ( $K = P\times P\times B$ ), we reshape the HSI cuboid $x_{i,j}$ and the corresponding phase cuboid $\Theta_{i,j}$ as follow: + +$$ +\begin{array}{l} x ^ {v e c} = \left[ x _ {0} ^ {\prime}, \dots , x _ {i ^ {\prime} + j ^ {\prime} \times P + k ^ {\prime} \times P \times P} ^ {\prime}, \dots , x _ {K - 1} ^ {\prime} \right], \tag {5} \\ \Theta^ {v e c} = \left[ \theta_ {0}, \dots , \theta_ {i ^ {\prime} + j ^ {\prime} \times P + k ^ {\prime} \times P \times P}, \dots , \theta_ {K - 1} \right], \\ \end{array} +$$ + +where $i', j' \in [0 : P - 1]$ and $k' \in [0 : B - 1]$ . Then phase vector $x^{vec}$ and original data vector $x^{vec}$ are used in the state vector representation $|x_{i,j}\rangle$ as follows: + +$$ +\left| x _ {i, j} \right\rangle = \sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \theta_ {n}} \left| n \right\rangle_ {K}. \tag {6} +$$ + +In Eq. (6), $A_{n}$ can be obtained as: + +$$ +A _ {n} = \sqrt {\frac {x _ {n} ^ {v e c}}{\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \tag {7} +$$ + +where $x_{n}^{vec}$ indicates the $n$ -th element in $x^{vec}$ . In Eq. (6), $x_{i,j}$ can be represented by a complex vector $|x_{i,j}\rangle = [A_0e^{i\theta_0}, A_1e^{i\theta_1}, \ldots, A_{K-1}e^{i\theta_{K-1}}]$ in $\mathcal{H}^K$ . As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode $x_{i,j}$ in $|x_{i,j}\rangle$ is neglecting the imaginary parts $e^{i\theta}$ (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations. + +Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation $(MO)$ to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as $PVM(\Pi_m,\rho)$ : using a density matrix $\rho$ to represent the state of quantum system $\rho = |\psi_{final}\rangle \langle \psi_{final}|$ and then applying the matrix manipulation (matrix product and trace) + +with operators $\{\Pi_m\}_{m=1}^M$ . For each $\Pi_m$ , we get the probability $P(|\phi_m\rangle)$ . Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by + +$$ +\begin{array}{l} D _ {i, j} = \left| x _ {i, j} \right\rangle \left\langle x _ {i, j} \right| \tag {8} \\ = \sum_ {n = 0} ^ {K - 1} \sum_ {n ^ {\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\prime}} e ^ {i \left(\theta_ {n} - \theta_ {n ^ {\prime}}\right)} \left| n ^ {\prime} \right\rangle \left\langle n \right|, \\ \end{array} +$$ + +where $|n^{\prime}\rangle \langle n|$ represents a square matrix with $P\times P\times B$ rows and columns that all components are 0 except the $(n,n^{\prime})$ -th component is 1. Each term in the density matrix $D_{i,j}$ is the multiplication of $A_{n}$ and $A_{n^{\prime}}$ with a coefficient $e^{i(\theta_n - \theta_{n^{\prime}})}$ . Empirically, this is similar to fusing information of each pair of elements $x_{n}^{vec}$ and $x_{n^{\prime}}^{vec}$ . Phases $\theta_{n}$ and $\theta_{n^{\prime}}$ are predicted by PPM. We hope the imaginary part $e^{i(\theta_n - \theta_{n^{\prime}})}$ can dynamically modulate the correlations between $x_{n}^{vec}$ and $x_{n^{\prime}}^{vec}$ . In each pair, the location and band of $x_{n}^{vec}$ and $x_{n^{\prime}}^{vec}$ may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result $P(|\phi_m\rangle)$ corresponding to $\Pi_{m}$ . Note that PVM has corresponding operations applied on physic devices. There are constraints of operations $\Pi_{m}$ in their mathematical formulation in quantum theory. We use an abstract representation of PVM as $PVM(\Pi_m,\rho)\rightarrow PVM(Operator_m,\rho)$ . To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers $FC_{m}$ with depth 3 as $Operator_{m}$ . The MO generates a feature point as follows: + +$$ +f e a _ {m} = M O \left(F C _ {m}, D _ {i, j}\right), \tag {9} +$$ + +where $D_{i,j}$ stores the fusion information of each element pair, $x_{n}^{vec}$ and $x_{n'}^{vec}$ . $MO$ is an operation that feeds $D_{i,j}$ into the operator $FC_{m}$ to efficiently aggregate spatial and spectral information. Given $M$ operators $\{FC_{m}\}_{m=1}^{M}$ , we can get an $M$ -dimensional feature vector $F^{vec} = [fea_{1},fea_{2},\ldots,fea_{M}]$ . Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus, $M$ should be carefully designed for preserving important factors in data. + +Following the steps above, QSSN extracts an $M$ -dimensional feature vector from input cuboid $x_{i,j}$ with the size of $P \times P \times B$ . Furthermore, we introduce a new notation $N$ -QSSN to denote the learned vector representation $F^{vec}$ with the size of $(P \times P \times N) \times 1$ . The output feature vector $F^{vec}$ is reshaped into a 3-D feature cuboid $F^{cub}$ with the size of $P \times P \times N$ . In $N$ -QSSN, the size of $M$ to denote the number of $MO$ is determined by + +$$ +M = P \times P \times N. \tag {10} +$$ + +The outcome of $N$ -QSSN $F^{cub}$ has same spatial resolution as $x_{i,j}$ . The input HSI cuboid $x_{i,j}$ has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The $N$ -QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the $N$ -QSSN blocks. + +# 3.3. QSSN-based Pyramid Framework + +It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from $x_{i,j}$ , followed by a classifier to identify the land-cover category of the center pixel (i.e., the $(i,j)$ -th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks, $N_{1}$ -QSSN and $N_{2}$ -QSSN are stacked in a hierarchical manner. Specifically, for $N_{1}$ -QSSN, we take an original cuboid with the size of $P \times P \times B$ as input to learn the feature cuboid with the size of $P \times P \times N_{1}$ as output. Sequentially, for $N_{2}$ -QSSN, we use the feature representation with the size of $P \times P \times N_{1}$ learned from $N_{1}$ -QSSN as input to extract the feature cuboid with the size of $P \times P \times N_{2}$ as output. In our setting, $B > N_{1} > N_{2}$ , meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information. + +The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN- $L$ to indicate QSSPN with $L$ QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2. + +Table 1. Classification results and model analysis of different methods on HSI datasets. + +
DatasetsMetricsSSANSSRNRvTHiTSSFTTQSSPN-1QSSPN-2QSSPN-3
IPOA (%)89.4691.8583.8590.5996.3590.3692.6695.87
AA (%)85.9981.5179.6786.7189.9989.9393.3496.40
κ(%)88.0490.7381.6889.2795.8289.0591.6895.34
Params.148.83K735.88K10.78M49.60M148.50K910.50K1.13M1.17M
FLOPs7.88M212.48M17.83M345.88M3.66M34.54M52.75M55.59M
PUOA (%)99.1599.6397.3799.4399.5299.3899.4499.71
AA (%)98.7099.2995.8699.0999.2098.6198.8999.43
κ(%)98.8799.5196.5299.2499.3699.1799.2599.61
Params.94.63K396.99K9.77M42.41M148.03K609.16K666.38K700.52K
FLOPs5.57M108.04M16.83M190.85M3.66M10.25M14.89M17.66M
SAOA (%)98.9299.3198.1199.3899.5399.5499.6399.66
AA (%)99.3399.7098.8399.7099.7299.6199.6599.81
κ(%)98.8099.2397.9099.3199.4799.4999.5999.63
Params.149.71K750K10.82M50M148.50K926.90K1.16M1.20M
FLOPs7.97M216.8417.80M354.42M3.66M35.87M54.82M57.67M
+ +Table 2. Settings of channel reduction in QSSPN-L + +
ModelsBandsN1N2N3
QSSPN-1B30--
QSSPN-2B[B/2]*30-
QSSPN-3B[B/2]5030
+ +* $\lfloor B / 2\rfloor$ represents the greatest integer less than or equal to $B / 2$ . + +# 4. Experiments + +# 4.1. Experiment Details + +Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with $145 \times 145$ pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises $512 \times 217$ pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are $610 \times 340$ pixels with 103 bands to record nine classes of ground truths. + +Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod + +els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36]. + +Setup. We adopt the Adam [22] optimizer with learning rate $1e^{-3}$ to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size $9 \times 9 \times B$ for all methods. For all datasets, we randomly select $10\%$ , $5\%$ and $85\%$ labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients $(\kappa)$ . Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM. + +# 4.2. Classification Results + +Tab. 1 reports the results of OA, AA and $\kappa$ on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves $96.40\%$ AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). On the Salinas and Pavia University + +![](images/983bc1a0572e84ade2690e37efa08117c0568becc045568807257b4c0e76910f.jpg) +(a) Ground truth + +![](images/6f29871000e34acad89591d7d29526e7a246475530e3c708301cb9386d72c547.jpg) +(b) RvT + +![](images/f2c52b8480dd822d494923b36535d1f42ad9d9b6b49c85655268ee4ab3734253.jpg) +(c) HiT + +![](images/9de2d9ef3efda918599785a4208421a40c341ad6b3a1b563898118588c577cb1.jpg) +(d) SSAN + +![](images/9c93307d69ee867a99c21fafa59cd12bc70d11ecad4450a07e3735bd73640c98.jpg) +(e)SSRN + +![](images/2d544eba9f0b0a91fbec61b481443d5befb4339f286effb910122d996478add4.jpg) +(f) QSSPN-1 + +![](images/0e2a52ef3a4666ca26de0baeebb5c72a75ca2db8bbec4b786108474a3b157323.jpg) +(g) QSSPN-2 + +![](images/8e99060f463733fc1faa62206fdd7332da1429200b2c8e6ce678f462fa484605.jpg) +(h) QSSPN-3 + +![](images/86a5ce48d8d8468be751198ee61df9747eefdc07460ef9345f9be007da4f1012.jpg) +(a) Ground truth + +![](images/8d06af8208275af5b014ac6cdbf7e93214b63f85a9cfbc329a211fb870ea3376.jpg) +(b) RvT + +![](images/91d6478a19804e673b3f9a8eecdfde41eeb5e4b40aa1c12ead4d9b5025296fef.jpg) +Figure 4. Classification maps of different methods for the Indian Pines dataset. +(c) HiT + +![](images/a9f9743234b2d1f88ead07c874e3408d1b1e2e3de4b61a7a5461d2f1c18a2aaa.jpg) +(d) SSAN + +![](images/88aee164703f9470d2d6ca281a4f0b395e5a4453e170ff15a5a2af14e6267e42.jpg) +(e) SSRN + +![](images/8519a95fdd0c60f122a96c1112c1a315f799db8537d2730a774c7300db4693dd.jpg) +(f) QSSPN-1 + +![](images/4ed2d0528c3c03bd2de342a5fe14e3a30e2722566ee0037f7a46d3e8646104dd.jpg) +(g) QSSPN-2 + +![](images/8ad3a407872a098030c7a4351a07c5f13ed534751d1f764947aa09a930eb4487.jpg) +(h) QSSPN-3 + +![](images/9400aafd9a45c03ea4d8d2f156381249570fec071ea3e0ffa4a9e1d3905a0427.jpg) +Figure 5. Classification maps of different methods for the Pavia University dataset. +(a) Original data +Figure 6. Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset. + +![](images/378545ef6b20edd948cdafa28996a4e55c02d40dbd5446b6e6ee805749a1d20c.jpg) +(b) Spectral-spatial representation + +datasets, our methods obtain $0.1\%$ and $0.3\%$ improvement with respect to $\kappa$ , respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps. + +To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of $\{15\%, 20\%, 25\%, 30\%\}$ . Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size + +![](images/c53b855bef662a16dbe534cdf2f7c84dc480c6e3dd7bc4bfaeeca64b1aa182cc.jpg) +Figure 7. OA of different models for the Indian Pines dataset with different training sizes. + +increases. Overall, QSSPN-3 surpasses other methods, achieving $99.11\%$ OA with a $30\%$ training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples. + +# 4.3. Ablation Study + +Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode, $\theta_{i',j',k'} = 0, i', j' \in [0:P - 1], k' \in [0:B - 1]$ ), the model has the worst performance compared with other models. The spatial phase mode (i.e., $\theta_{i',j',0} = \theta_{i',j',1} = \dots = \theta_{i',j',B - 1}$ ) considers spatial + +Table 3. Effectiveness of phase on the Indian Pines dataset. + +
ModeParams.FLOPsOA (%)κ (%)
No phase717.13K18.92M86.8685.10
Spatial phase708.74K18.22M89.1887.74
Spectral phase705.68K17.97M88.6687.09
All1.13M52.75M92.6691.68
+ +Table 4. Effectiveness of pyramid structure on the Indian Pines dataset. + +
LChannelParams.FLOPsOA (%)κ (%)
110571.18K32.97M82.7280.45
130910.5K34.54M90.3689.05
1501.26M36.69M91.6390.49
2301.14M52.75M91.9390.84
3301.17M55.59M92.9391.96
+ +* $L$ indicates the QSSPN- $L$ model. +* Channel indicates the dimension of the learned feature cuboid for classification. + +information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e., $\theta_{0,0,k'} = \theta_{0,1,k'} = \dots = \theta_{P-1,P-1,k'}$ ) only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance. + +# 4.4. Parameter Sensitivity Study + +To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated. + +Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement. + +Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks, + +![](images/ba16aad61381aafb9d2293491a56f955d0f5e3ea607e052d7f0e34a197ea59a1.jpg) +(a) Indian Pines + +![](images/c031429a9e373234cb3888ce59df701a059dc83ce88f5ebeedd4ce1c00c9815d.jpg) +(b) Salinas + +![](images/22a84439773468dc4bc42d9e490ac214f42b5f9245ffc48bf91a2ff896047fee.jpg) +(c) Indian Pines + +![](images/cf729a5b1a18154005d0a56dd16b0f012ad4d2c98adfc7d6b326313d97faf048.jpg) +(d) Salinas +Figure 8. OA of QSSPN with different patch sizes and depths. + +QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g. $82.72\%$ OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g. $91.63\%$ OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure. + +# 5. Conclusion + +In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications. + +Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST). + +# References + +[1] Isabel Cecilia Contreras Acosta, Mahdi Khodadadzadeh, Laura Tusa, Pedram Ghamisi, and Richard Gloaguen. A machine learning framework for drill-core mineral mapping using hyperspectral and high-resolution mineralogical data fusion. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 12(12):4829-4842, 2019. 1 +[2] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. 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A survey on unsupervised outlier detection in high-dimensional numerical data. 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Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. 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Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "content": "Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. 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Average accuracies on Indian Pines dataset are presented." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 556 + ], + "type": "text", + "content": "mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "-nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9925" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "content": "in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "content": "Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": "Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 144, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 144, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 305, + 144, + 545, + 167 + ], + "type": "text", + "content": "The contributions of this article are summarized as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 173, + 545, + 354 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 173, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 173, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 317, + 173, + 545, + 221 + ], + "type": "text", + "content": "- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "type": "text", + "content": "- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 283, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 283, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 317, + 283, + 545, + 354 + ], + "type": "text", + "content": "- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 361, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 444 + ], + "type": "text", + "content": "The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9926" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 286, + 235 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 286, + 235 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 286, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 286, + 235 + ], + "type": "image", + "image_path": "f55728ced1a6ba370d2c5c93235a61a3535ba4fc48139753d716f3d45a213148.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 244, + 288, + 300 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 288, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 288, + 300 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 289, + 579 + ], + "type": "text", + "content": "Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 604, + 103, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 103, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 103, + 616 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 392, + 83 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": "Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": "-dimensional Hilbert space " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^N" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": ". We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\left|\\cdot \\right\\rangle" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\langle \\cdot |" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": " denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\{\\left|\\phi_n\\right\\rangle \\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": ", we can represent the states of quantum system " + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "inline_equation", + "content": "|\\psi \\rangle" + }, + { + "bbox": [ + 304, + 90, + 547, + 307 + ], + "type": "text", + "content": " as follows*:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 374, + 315, + 545, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 315, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 374, + 315, + 545, + 348 + ], + "type": "interline_equation", + "content": "| \\psi \\rangle = \\sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \\theta_ {n}} | \\phi_ {n} \\rangle , \\tag {1}", + "image_path": "70fd66e3672e6c2ebf7815c134aebfd69218d2808ff0534b7ca84a69c25e10b0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " is a probability amplitude satisfying " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "\\sum_{N}|A_{n}|^{2} = 1" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " is the imaginary unit and " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "\\theta_{n}" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " indicates the phase. A simple example of basis state vectors for " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^N" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " is standard unit basis. Detailedly, the standard basis of " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^2" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " is formed by column vectors " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "|0\\rangle_2 = [1,0]^T" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "inline_equation", + "content": "|1\\rangle_2 = [0,1]^T" + }, + { + "bbox": [ + 305, + 355, + 547, + 429 + ], + "type": "text", + "content": ". Here, we use the notation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 369, + 437, + 545, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 437, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 369, + 437, + 545, + 451 + ], + "type": "interline_equation", + "content": "\\left| n \\right\\rangle_ {N}, n = 0, 1, \\dots , N - 1 \\tag {2}", + "image_path": "a53d0d74c15c0149674436a852ce156ce9484eb2684c3ea1720404f37afc6c82.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": "to represent the standard basis of " + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^N" + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": ". Accordingly, " + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\langle n|_N" + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": " denotes the conjugate transpose of " + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "inline_equation", + "content": "|n\\rangle_N" + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": ". All components of " + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "inline_equation", + "content": "|n\\rangle_N" + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": " are 0 except the " + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 459, + 545, + 507 + ], + "type": "text", + "content": "-th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": "The reversible unitary operator " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " describes the state's evolution in QC, mapping the initial states " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "|\\psi_{initial}\\rangle" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " to final states " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "|\\psi_{final}\\rangle" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": ". These operators manipulate the phases " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "\\theta_{n}" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " and amplitudes " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "\\{\\Pi_m = |\\phi_m\\rangle \\langle \\phi_m|\\}_{m = 1}^M" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": ". According to the Born rule [28], " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "\\Pi_{m}" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " projects the state " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "|\\psi_{final}\\rangle" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " to the corresponding basis state " + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "inline_equation", + "content": "|\\phi_m\\rangle" + }, + { + "bbox": [ + 304, + 507, + 547, + 640 + ], + "type": "text", + "content": " with a probability:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 648, + 545, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 648, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 313, + 648, + 545, + 662 + ], + "type": "interline_equation", + "content": "P \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = T r \\left(\\Pi_ {m} \\rho\\right) = \\left\\langle \\phi_ {m} \\mid \\psi_ {\\text {f i n a l}} \\right\\rangle \\left\\langle \\psi_ {\\text {f i n a l}} \\mid \\phi_ {m} \\right\\rangle , \\tag {3}", + "image_path": "e3ac3f448985d503870d825f9fd16fe8de301be6f0a79fa810d8792ea46dd101.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|" + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "content": " is the density matrix representation of " + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "inline_equation", + "content": "|\\psi_{final}\\rangle" + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\sum_{M}P(|\\phi_{m}\\rangle) = 1" + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "inline_equation", + "content": "|\\cdot \\rangle \\langle \\cdot |" + }, + { + "bbox": [ + 304, + 670, + 545, + 696 + ], + "type": "text", + "content": " denotes the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 316, + 703, + 466, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 703, + 466, + 713 + ], + "spans": [ + { + "bbox": [ + 316, + 703, + 466, + 713 + ], + "type": "text", + "content": "*Only pure states are considered in this paper." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9927" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 78, + 286, + 170 + ], + "blocks": [ + { + "bbox": [ + 49, + 78, + 286, + 170 + ], + "lines": [ + { + "bbox": [ + 49, + 78, + 286, + 170 + ], + "spans": [ + { + "bbox": [ + 49, + 78, + 286, + 170 + ], + "type": "image", + "image_path": "e07cba4561baba1f2b8e0f9c2aea9c4e04b9ce0181a5c2168beb225e437b9a6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "lines": [ + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "text", + "content": "Figure 3. Illustration of data mapping in QSSN. The state representation " + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "inline_equation", + "content": "|\\psi \\rangle" + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "text", + "content": " encodes data from original space to Hilbert space: " + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{R} \\to \\mathcal{H}" + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "text", + "content": ". The MFM outputs a feature vector mapped from " + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "inline_equation", + "content": "|\\psi \\rangle" + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "text", + "content": " to feature space: " + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{H} \\to \\mathcal{F}" + }, + { + "bbox": [ + 47, + 180, + 288, + 226 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "text", + "content": "outer product and " + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\langle \\cdot |\\cdot \\rangle" + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "text", + "content": " denotes the inner product of " + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\langle \\cdot |" + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "inline_equation", + "content": "|\\cdot \\rangle" + }, + { + "bbox": [ + 47, + 239, + 288, + 266 + ], + "type": "text", + "content": " . Eq. (3) can be rewritten as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 271, + 287, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 271, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 64, + 271, + 287, + 322 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = \\left\\langle \\phi_ {m} \\right| \\rho \\left| \\phi_ {m} \\right\\rangle = \\left(\\left\\langle \\psi_ {f i n a l} \\mid \\phi_ {m} \\right\\rangle\\right) ^ {2} \\tag {4} \\\\ = \\sum_ {n _ {1}} ^ {N - 1} \\sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\\theta_ {n _ {1}} - \\theta_ {n _ {2}})} \\langle \\phi_ {m} | n _ {1} \\rangle \\langle n _ {2} | \\phi_ {m} \\rangle . \\\\ \\end{array}", + "image_path": "d98e9deb8012729f1faa263518d92a103702ff529c1b2a67587624d79e9bca54.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": "Here we neglect the subscript " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "|n\\rangle_N" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " for simplicity. In Eq. (4), the size of " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "|n\\rangle" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": ". For the same measurement operator " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "\\Pi_m \\sim |\\phi_m\\rangle" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": ", the output " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "P(|\\phi_m\\rangle)" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " depends on all pairs of " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "A_{n_1}" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "A_{n_2}" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " and their correlations " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "(\\theta_{n_1} - \\theta_{n_2})" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": ". PVM yields values " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "P_{res} = [P(|\\phi_1\\rangle), P(|\\phi_2\\rangle), \\ldots, P(|\\phi_M\\rangle)]" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": " corresponding to the selected projection operators " + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "inline_equation", + "content": "\\{\\Pi_m\\}_{m=1}^M" + }, + { + "bbox": [ + 47, + 328, + 287, + 424 + ], + "type": "text", + "content": ", reflecting the state of quantum system." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "content": "We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 468, + 280, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 280, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 280, + 480 + ], + "type": "text", + "content": "3.2. Quantum-Inspired Spectral-Spatial Network" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "X \\in \\mathcal{R}^{H \\times W \\times B}" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " be the HSI with " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " pixels in height, " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " pixels in width, and " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " spectral bands. Taking the " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": "-th pixel as center, information in a small cuboid " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "x_{i,j} \\in \\mathcal{R}^{P \\times P \\times B}" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "P \\times P" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad " + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": " with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Theta_{i,j} \\in R^{P \\times P \\times B}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " for all elements " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "x_{i',j',k'}'" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". Phases play an important role in encoding data " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": "distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "\\theta_{i',j',k'}" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " for each element " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "x_{i',j',k'}'" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": ". Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "x_{i',j',k'}'" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": ", the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " pixel windows. The following asymmetric convolution layers [37] with " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "3\\times 1" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "1\\times 3" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "\\Theta_{i,j}" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": ". Before we encode each HSI cuboid into complex finite-dimensional Hilbert space " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^K" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "K = P\\times P\\times B" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": "), we reshape the HSI cuboid " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " and the corresponding phase cuboid " + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "inline_equation", + "content": "\\Theta_{i,j}" + }, + { + "bbox": [ + 304, + 72, + 546, + 276 + ], + "type": "text", + "content": " as follow:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 334, + 282, + 546, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 282, + 546, + 310 + ], + "spans": [ + { + "bbox": [ + 334, + 282, + 546, + 310 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} x ^ {v e c} = \\left[ x _ {0} ^ {\\prime}, \\dots , x _ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P} ^ {\\prime}, \\dots , x _ {K - 1} ^ {\\prime} \\right], \\tag {5} \\\\ \\Theta^ {v e c} = \\left[ \\theta_ {0}, \\dots , \\theta_ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P}, \\dots , \\theta_ {K - 1} \\right], \\\\ \\end{array}", + "image_path": "971f1ebeab89ce80be77c8d26d84753f148f694c5af2adc477e9112db688fe6d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "inline_equation", + "content": "i', j' \\in [0 : P - 1]" + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "inline_equation", + "content": "k' \\in [0 : B - 1]" + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": ". Then phase vector " + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "inline_equation", + "content": "x^{vec}" + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": " and original data vector " + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "inline_equation", + "content": "x^{vec}" + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": " are used in the state vector representation " + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "inline_equation", + "content": "|x_{i,j}\\rangle" + }, + { + "bbox": [ + 304, + 316, + 546, + 354 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 369, + 361, + 545, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 361, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 369, + 361, + 545, + 395 + ], + "type": "interline_equation", + "content": "\\left| x _ {i, j} \\right\\rangle = \\sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \\theta_ {n}} \\left| n \\right\\rangle_ {K}. \\tag {6}", + "image_path": "f44704747879e8e5f3f5afc8f35eebed9cabe887f913725c54d131da78f08648.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 402, + 444, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 444, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 444, + 414 + ], + "type": "text", + "content": "In Eq. (6), " + }, + { + "bbox": [ + 306, + 402, + 444, + 414 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 306, + 402, + 444, + 414 + ], + "type": "text", + "content": " can be obtained as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 378, + 422, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 422, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 378, + 422, + 545, + 455 + ], + "type": "interline_equation", + "content": "A _ {n} = \\sqrt {\\frac {x _ {n} ^ {v e c}}{\\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \\tag {7}", + "image_path": "6f2faf658575e8186c7cedde9af3f0ad405832c4bb098c16fa747fec93bb81e4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "x_{n}^{vec}" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": "-th element in " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "x^{vec}" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": ". In Eq. (6), " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " can be represented by a complex vector " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "|x_{i,j}\\rangle = [A_0e^{i\\theta_0}, A_1e^{i\\theta_1}, \\ldots, A_{K-1}e^{i\\theta_{K-1}}]" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^K" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": ". As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "|x_{i,j}\\rangle" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " is neglecting the imaginary parts " + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "inline_equation", + "content": "e^{i\\theta}" + }, + { + "bbox": [ + 304, + 462, + 546, + 617 + ], + "type": "text", + "content": " (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "(MO)" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "PVM(\\Pi_m,\\rho)" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ": using a density matrix " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " to represent the state of quantum system " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " and then applying the matrix manipulation (matrix product and trace)" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9928" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "with operators " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\{\\Pi_m\\}_{m=1}^M" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". For each " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\Pi_m" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ", we get the probability " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "P(|\\phi_m\\rangle)" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 89, + 130, + 286, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 130, + 286, + 177 + ], + "spans": [ + { + "bbox": [ + 89, + 130, + 286, + 177 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D _ {i, j} = \\left| x _ {i, j} \\right\\rangle \\left\\langle x _ {i, j} \\right| \\tag {8} \\\\ = \\sum_ {n = 0} ^ {K - 1} \\sum_ {n ^ {\\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\\prime}} e ^ {i \\left(\\theta_ {n} - \\theta_ {n ^ {\\prime}}\\right)} \\left| n ^ {\\prime} \\right\\rangle \\left\\langle n \\right|, \\\\ \\end{array}", + "image_path": "538301c67c87ff56e20b58093d56306ac160adf88c57b0fc9e5d9203de434cea.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "|n^{\\prime}\\rangle \\langle n|" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " represents a square matrix with " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "P\\times P\\times B" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " rows and columns that all components are 0 except the " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "(n,n^{\\prime})" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": "-th component is 1. Each term in the density matrix " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "D_{i,j}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " is the multiplication of " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "A_{n^{\\prime}}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " with a coefficient " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "e^{i(\\theta_n - \\theta_{n^{\\prime}})}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". Empirically, this is similar to fusing information of each pair of elements " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n^{\\prime}}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". Phases " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\theta_{n}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\theta_{n^{\\prime}}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " are predicted by PPM. We hope the imaginary part " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "e^{i(\\theta_n - \\theta_{n^{\\prime}})}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " can dynamically modulate the correlations between " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n^{\\prime}}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". In each pair, the location and band of " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "x_{n^{\\prime}}^{vec}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "P(|\\phi_m\\rangle)" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\Pi_{m}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". Note that PVM has corresponding operations applied on physic devices. There are constraints of operations " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\Pi_{m}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " in their mathematical formulation in quantum theory. We use an abstract representation of PVM as " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "PVM(\\Pi_m,\\rho)\\rightarrow PVM(Operator_m,\\rho)" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "FC_{m}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": " with depth 3 as " + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "inline_equation", + "content": "Operator_{m}" + }, + { + "bbox": [ + 47, + 184, + 287, + 460 + ], + "type": "text", + "content": ". The MO generates a feature point as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 109, + 468, + 286, + 481 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 468, + 286, + 481 + ], + "spans": [ + { + "bbox": [ + 109, + 468, + 286, + 481 + ], + "type": "interline_equation", + "content": "f e a _ {m} = M O \\left(F C _ {m}, D _ {i, j}\\right), \\tag {9}", + "image_path": "66ac801f027c3f01acb8fda29c71cd84ebdc2973b62c5f7f122b54369a1bd42e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "D_{i,j}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " stores the fusion information of each element pair, " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "x_{n}^{vec}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "x_{n'}^{vec}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "MO" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " is an operation that feeds " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "D_{i,j}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " into the operator " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "FC_{m}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " to efficiently aggregate spatial and spectral information. Given " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " operators " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "\\{FC_{m}\\}_{m=1}^{M}" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": ", we can get an " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": "-dimensional feature vector " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "F^{vec} = [fea_{1},fea_{2},\\ldots,fea_{M}]" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": ". Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus, " + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 489, + 286, + 596 + ], + "type": "text", + "content": " should be carefully designed for preserving important factors in data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": "Following the steps above, QSSN extracts an " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": "-dimensional feature vector from input cuboid " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " with the size of " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "P \\times P \\times B" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": ". Furthermore, we introduce a new notation " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": "-QSSN to denote the learned vector representation " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "F^{vec}" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " with the size of " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "(P \\times P \\times N) \\times 1" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": ". The output feature vector " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "F^{vec}" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " is reshaped into a 3-D feature cuboid " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "F^{cub}" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " with the size of " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "P \\times P \\times N" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": ". In " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": "-QSSN, the size of " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " to denote the number of " + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "inline_equation", + "content": "MO" + }, + { + "bbox": [ + 47, + 597, + 286, + 692 + ], + "type": "text", + "content": " is determined by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 129, + 702, + 286, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 129, + 702, + 286, + 712 + ], + "type": "interline_equation", + "content": "M = P \\times P \\times N. \\tag {10}", + "image_path": "5320f4260880b38eea555ef7e9d6ad7a9522b24d838b392c41e33485ce40e0b2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": "The outcome of " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": "-QSSN " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "F^{cub}" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": " has same spatial resolution as " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": ". The input HSI cuboid " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": " has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": "-QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the " + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 72, + 545, + 179 + ], + "type": "text", + "content": "-QSSN blocks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 226, + 489, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 226, + 489, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 226, + 489, + 239 + ], + "type": "text", + "content": "3.3. QSSN-based Pyramid Framework" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "x_{i,j}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": ", followed by a classifier to identify the land-cover category of the center pixel (i.e., the " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks, " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{1}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-QSSN and " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{2}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-QSSN are stacked in a hierarchical manner. Specifically, for " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{1}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-QSSN, we take an original cuboid with the size of " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "P \\times P \\times B" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": " as input to learn the feature cuboid with the size of " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "P \\times P \\times N_{1}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": " as output. Sequentially, for " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{2}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-QSSN, we use the feature representation with the size of " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "P \\times P \\times N_{1}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": " learned from " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{1}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": "-QSSN as input to extract the feature cuboid with the size of " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "P \\times P \\times N_{2}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": " as output. In our setting, " + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "inline_equation", + "content": "B > N_{1} > N_{2}" + }, + { + "bbox": [ + 305, + 258, + 545, + 604 + ], + "type": "text", + "content": ", meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": "The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN- " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " to indicate QSSPN with " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9929" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 83, + 518, + 267 + ], + "blocks": [ + { + "bbox": [ + 137, + 71, + 455, + 81 + ], + "lines": [ + { + "bbox": [ + 137, + 71, + 455, + 81 + ], + "spans": [ + { + "bbox": [ + 137, + 71, + 455, + 81 + ], + "type": "text", + "content": "Table 1. Classification results and model analysis of different methods on HSI datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 83, + 518, + 267 + ], + "lines": [ + { + "bbox": [ + 74, + 83, + 518, + 267 + ], + "spans": [ + { + "bbox": [ + 74, + 83, + 518, + 267 + ], + "type": "table", + "html": "
DatasetsMetricsSSANSSRNRvTHiTSSFTTQSSPN-1QSSPN-2QSSPN-3
IPOA (%)89.4691.8583.8590.5996.3590.3692.6695.87
AA (%)85.9981.5179.6786.7189.9989.9393.3496.40
κ(%)88.0490.7381.6889.2795.8289.0591.6895.34
Params.148.83K735.88K10.78M49.60M148.50K910.50K1.13M1.17M
FLOPs7.88M212.48M17.83M345.88M3.66M34.54M52.75M55.59M
PUOA (%)99.1599.6397.3799.4399.5299.3899.4499.71
AA (%)98.7099.2995.8699.0999.2098.6198.8999.43
κ(%)98.8799.5196.5299.2499.3699.1799.2599.61
Params.94.63K396.99K9.77M42.41M148.03K609.16K666.38K700.52K
FLOPs5.57M108.04M16.83M190.85M3.66M10.25M14.89M17.66M
SAOA (%)98.9299.3198.1199.3899.5399.5499.6399.66
AA (%)99.3399.7098.8399.7099.7299.6199.6599.81
κ(%)98.8099.2397.9099.3199.4799.4999.5999.63
Params.149.71K750K10.82M50M148.50K926.90K1.16M1.20M
FLOPs7.97M216.8417.80M354.42M3.66M35.87M54.82M57.67M
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ModelsBandsN1N2N3
QSSPN-1B30--
QSSPN-2B[B/2]*30-
QSSPN-3B[B/2]5030
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Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 415, + 160, + 429 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 160, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 160, + 429 + ], + "type": "text", + "content": "4.1. Experiment Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "text", + "content": "Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with " + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "inline_equation", + "content": "145 \\times 145" + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "text", + "content": " pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises " + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "inline_equation", + "content": "512 \\times 217" + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "text", + "content": " pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are " + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "inline_equation", + "content": "610 \\times 340" + }, + { + "bbox": [ + 46, + 436, + 287, + 628 + ], + "type": "text", + "content": " pixels with 103 bands to record nine classes of ground truths." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 288, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 323 + ], + "type": "text", + "content": "els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": "Setup. We adopt the Adam [22] optimizer with learning rate " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "1e^{-3}" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": " to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "9 \\times 9 \\times B" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": " for all methods. For all datasets, we randomly select " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "85\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": " labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients " + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "inline_equation", + "content": "(\\kappa)" + }, + { + "bbox": [ + 304, + 324, + 546, + 504 + ], + "type": "text", + "content": ". Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 514, + 429, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 429, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 429, + 526 + ], + "type": "text", + "content": "4.2. Classification Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": "Tab. 1 reports the results of OA, AA and " + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": " on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves " + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "inline_equation", + "content": "96.40\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": " AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). 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Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 172, + 319, + 285, + 405 + ], + "blocks": [ + { + "bbox": [ + 172, + 319, + 285, + 405 + ], + "lines": [ + { + "bbox": [ + 172, + 319, + 285, + 405 + ], + "spans": [ + { + "bbox": [ + 172, + 319, + 285, + 405 + ], + "type": "image", + "image_path": "378545ef6b20edd948cdafa28996a4e55c02d40dbd5446b6e6ee805749a1d20c.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 174, + 407, + 283, + 417 + ], + "lines": [ + { + "bbox": [ + 174, + 407, + 283, + 417 + ], + "spans": [ + { + "bbox": [ + 174, + 407, + 283, + 417 + ], + "type": "text", + "content": "(b) Spectral-spatial representation" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": "datasets, our methods obtain " + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": " improvement with respect to " + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": ", respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\{15\\%, 20\\%, 25\\%, 30\\%\\}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ". Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size" + } + ] + } + ], + "index": 40 + }, + { + "type": "image", + "bbox": [ + 319, + 332, + 512, + 460 + ], + "blocks": [ + { + "bbox": [ + 319, + 332, + 512, + 460 + ], + "lines": [ + { + "bbox": [ + 319, + 332, + 512, + 460 + ], + "spans": [ + { + "bbox": [ + 319, + 332, + 512, + 460 + ], + "type": "image", + "image_path": "c53b855bef662a16dbe534cdf2f7c84dc480c6e3dd7bc4bfaeeca64b1aa182cc.jpg" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 471, + 545, + 493 + ], + "lines": [ + { + "bbox": [ + 306, + 471, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 545, + 493 + ], + "type": "text", + "content": "Figure 7. OA of different models for the Indian Pines dataset with different training sizes." + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "image_caption" + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "content": "increases. Overall, QSSPN-3 surpasses other methods, achieving " + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "inline_equation", + "content": "99.11\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "content": " OA with a " + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "content": " training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 306, + 575, + 399, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 399, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 399, + 588 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode, " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i',j',k'} = 0, i', j' \\in [0:P - 1], k' \\in [0:B - 1]" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "), the model has the worst performance compared with other models. The spatial phase mode (i.e., " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i',j',0} = \\theta_{i',j',1} = \\dots = \\theta_{i',j',B - 1}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ") considers spatial" + } + ] + } + ], + "index": 45 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "9931" + } + ] + } + ], + "index": 46 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 91, + 279, + 155 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 274, + 82 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 274, + 82 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 274, + 82 + ], + "type": "text", + "content": "Table 3. Effectiveness of phase on the Indian Pines dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 91, + 279, + 155 + ], + "lines": [ + { + "bbox": [ + 56, + 91, + 279, + 155 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 279, + 155 + ], + "type": "table", + "html": "
ModeParams.FLOPsOA (%)κ (%)
No phase717.13K18.92M86.8685.10
Spatial phase708.74K18.22M89.1887.74
Spectral phase705.68K17.97M88.6687.09
All1.13M52.75M92.6691.68
", + "image_path": "8b749d08ad8d7fb98b5baf4cb2d2e3884782fc679732be847d555dd64a94c700.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 58, + 198, + 277, + 273 + ], + "blocks": [ + { + "bbox": [ + 56, + 167, + 277, + 189 + ], + "lines": [ + { + "bbox": [ + 56, + 167, + 277, + 189 + ], + "spans": [ + { + "bbox": [ + 56, + 167, + 277, + 189 + ], + "type": "text", + "content": "Table 4. Effectiveness of pyramid structure on the Indian Pines dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 198, + 277, + 273 + ], + "lines": [ + { + "bbox": [ + 58, + 198, + 277, + 273 + ], + "spans": [ + { + "bbox": [ + 58, + 198, + 277, + 273 + ], + "type": "table", + "html": "
LChannelParams.FLOPsOA (%)κ (%)
110571.18K32.97M82.7280.45
130910.5K34.54M90.3689.05
1501.26M36.69M91.6390.49
2301.14M52.75M91.9390.84
3301.17M55.59M92.9391.96
", + "image_path": "d54f1fc8eab06e49d4443f8e54480b5f21e595db2d3ebc634490dbe743e0116e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "lines": [ + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "spans": [ + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "type": "text", + "content": "* " + }, + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "type": "text", + "content": " indicates the QSSPN- " + }, + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 66, + 274, + 180, + 283 + ], + "type": "text", + "content": " model." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 66, + 283, + 277, + 302 + ], + "lines": [ + { + "bbox": [ + 66, + 283, + 277, + 302 + ], + "spans": [ + { + "bbox": [ + 66, + 283, + 277, + 302 + ], + "type": "text", + "content": "* Channel indicates the dimension of the learned feature cuboid for classification." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": "information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e., " + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "inline_equation", + "content": "\\theta_{0,0,k'} = \\theta_{0,1,k'} = \\dots = \\theta_{P-1,P-1,k'}" + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": ") only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "type": "text", + "content": "4.4. Parameter Sensitivity Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 460, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 520 + ], + "type": "text", + "content": "To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "content": "Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks," + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 79, + 425, + 157 + ], + "blocks": [ + { + "bbox": [ + 310, + 79, + 425, + 157 + ], + "lines": [ + { + "bbox": [ + 310, + 79, + 425, + 157 + ], + "spans": [ + { + "bbox": [ + 310, + 79, + 425, + 157 + ], + "type": "image", + "image_path": "ba16aad61381aafb9d2293491a56f955d0f5e3ea607e052d7f0e34a197ea59a1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 159, + 392, + 168 + ], + "lines": [ + { + "bbox": [ + 340, + 159, + 392, + 168 + ], + "spans": [ + { + "bbox": [ + 340, + 159, + 392, + 168 + ], + "type": "text", + "content": "(a) Indian Pines" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 428, + 78, + 545, + 157 + ], + "blocks": [ + { + "bbox": [ + 428, + 78, + 545, + 157 + ], + "lines": [ + { + "bbox": [ + 428, + 78, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 428, + 78, + 545, + 157 + ], + "type": "image", + "image_path": "c031429a9e373234cb3888ce59df701a059dc83ce88f5ebeedd4ce1c00c9815d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 159, + 504, + 168 + ], + "lines": [ + { + "bbox": [ + 468, + 159, + 504, + 168 + ], + "spans": [ + { + "bbox": [ + 468, + 159, + 504, + 168 + ], + "type": "text", + "content": "(b) Salinas" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 176, + 422, + 254 + ], + "blocks": [ + { + "bbox": [ + 310, + 176, + 422, + 254 + ], + "lines": [ + { + "bbox": [ + 310, + 176, + 422, + 254 + ], + "spans": [ + { + "bbox": [ + 310, + 176, + 422, + 254 + ], + "type": "image", + "image_path": "22a84439773468dc4bc42d9e490ac214f42b5f9245ffc48bf91a2ff896047fee.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 255, + 391, + 265 + ], + "lines": [ + { + "bbox": [ + 339, + 255, + 391, + 265 + ], + "spans": [ + { + "bbox": [ + 339, + 255, + 391, + 265 + ], + "type": "text", + "content": "(c) Indian Pines" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 431, + 176, + 545, + 253 + ], + "blocks": [ + { + "bbox": [ + 431, + 176, + 545, + 253 + ], + "lines": [ + { + "bbox": [ + 431, + 176, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 431, + 176, + 545, + 253 + ], + "type": "image", + "image_path": "cf729a5b1a18154005d0a56dd16b0f012ad4d2c98adfc7d6b326313d97faf048.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 255, + 505, + 265 + ], + "lines": [ + { + "bbox": [ + 470, + 255, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 470, + 255, + 505, + 265 + ], + "type": "text", + "content": "(d) Salinas" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 274, + 538, + 286 + ], + "lines": [ + { + "bbox": [ + 312, + 274, + 538, + 286 + ], + "spans": [ + { + "bbox": [ + 312, + 274, + 538, + 286 + ], + "type": "text", + "content": "Figure 8. OA of QSSPN with different patch sizes and depths." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "content": "QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g. " + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "inline_equation", + "content": "82.72\\%" + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "content": " OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g. " + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "inline_equation", + "content": "91.63\\%" + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "content": " OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 493, + 378, + 505 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 493, + 378, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 493, + 378, + 505 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "type": "text", + "content": "In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST)." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9932" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 158 + ], + "type": "text", + "content": "[1] Isabel Cecilia Contreras Acosta, Mahdi Khodadadzadeh, Laura Tusa, Pedram Ghamisi, and Richard Gloaguen. 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Statistical Analysis and Data Mining: The ASA Data Science Journal, 5(5):363-387, 2012. 1, 4" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9934" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_content_list.json b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..976fac5d8c2b638c3adc14a69dca7bbb0600729c --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_content_list.json @@ -0,0 +1,1263 @@ +[ + { + "type": "text", + "text": "Query-Centric Trajectory Prediction", + "text_level": 1, + "bbox": [ + 297, + 130, + 671, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zikang Zhou $^{1,2}$ Jianping Wang $^{1,2}$ Yung-Hui Li $^{3}$ Yu-Kai Huang $^{4}$ $^{1}$ City University of Hong Kong $^{2}$ City University of Hong Kong Shenzhen Research Institute \n $^{3}$ Hon Hai Research Institute $^{4}$ Carnegie Mellon University", + "bbox": [ + 109, + 178, + 851, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zikanzhou2-c@my.cityu.edu.hk", + "bbox": [ + 359, + 237, + 609, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 285, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the future trajectories of surrounding agents is essential for autonomous vehicles to operate safely. This paper presents QCNet, a modeling framework toward pushing the boundaries of trajectory prediction. First, we identify that the agent-centric modeling scheme used by existing approaches requires re-normalizing and re-encoding the input whenever the observation window slides forward, leading to redundant computations during online prediction. To overcome this limitation and achieve faster inference, we introduce a query-centric paradigm for scene encoding, which enables the reuse of past computations by learning representations independent of the global spacetime coordinate system. Sharing the invariant scene features among all target agents further allows the parallelism of multi-agent trajectory decoding. Second, even given rich encodings of the scene, existing decoding strategies struggle to capture the multimodality inherent in agents' future behavior, especially when the prediction horizon is long. To tackle this challenge, we first employ anchor-free queries to generate trajectory proposals in a recurrent fashion, which allows the model to utilize different scene contexts when decoding waypoints at different horizons. A refinement module then takes the trajectory proposals as anchors and leverages anchor-based queries to refine the trajectories further. By supplying adaptive and high-quality anchors to the refinement module, our query-based decoder can better deal with the multimodality in the output of trajectory prediction. Our approach ranks $1^{st}$ on Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming all methods on all main metrics by a large margin. Meanwhile, our model can achieve streaming scene encoding and parallel multi-agent decoding thanks to the query-centric design ethos.", + "bbox": [ + 75, + 316, + 473, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 829, + 209, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Making safe decisions for autonomous vehicles requires accurate predictions of surrounding agents' future trajectories. In recent years, learning-based methods have been", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/49918b1b7df75fa3d356a17c43f25747238f528ddca67d6ad8e2f7e0c6ca5ef5.jpg", + "image_caption": [ + "agent history", + "Figure 1. Illustration of our query-centric reference frame, where we build a local coordinate system for each spatial-temporal element, including map polygons and agent states at all time steps. In the attention-based encoder, all scene elements' queries are derived and updated in their local reference frames." + ], + "image_footnote": [], + "bbox": [ + 503, + 285, + 697, + 430 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48b83e0e98bd6607728ccfee4ed95cf6072e635517f50389aea718dd7e6e509d.jpg", + "image_caption": [ + "reference frame of agent state", + "$\\rightarrow$ reference frame of map polygon" + ], + "image_footnote": [], + "bbox": [ + 697, + 286, + 890, + 430 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "widely used for trajectory prediction [14, 31, 37, 38, 46, 56]. Despite the considerable efforts made to enhance models' forecasting ability, there is still a long way to go before fully addressing the problem of trajectory prediction. Why is this task so challenging, and what inability lies in existing approaches? We attempt to answer these questions from the following two perspectives:", + "bbox": [ + 496, + 532, + 890, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(i) While the flourishing forecasting models have achieved impressive performance on trajectory prediction benchmarks [7, 13, 49], today's most advanced architectures specialized for this task [37, 38, 46, 56] fail to process the heterogeneous traffic scenes efficiently. In an autonomous driving system, data frames arrive at the prediction module sequentially as a stream of sparse scene context, including the high-definition vector map and the surrounding agents' kinematic states. A model must learn expressive representations of these scene elements to achieve accurate forecasts. With the continuing development of modeling techniques for sparse context encoding [14, 31, 50], the research community has witnessed rapid progress toward more powerful trajectory predictors. Notably, factorized attention-based Transformers [37, 38, 56] have recently raised prediction accuracy to an unprecedented level. However, they require learning attention-based representations for each spatial-", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17863", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "temporal scene element and suffer from prohibitively high costs when processing dense traffic scenes. As every minimal delay may lead to catastrophic accidents in autonomous driving, the unmet need for real-time predictions has limited the applicability of state-of-the-art approaches.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(ii) The immense uncertainty in the output of trajectory prediction, which grows explosively as the prediction horizon lengthens, has troubled the research community constantly. For example, a vehicle at an intersection may turn or go straight depending on the driver's long-term goal. To avoid missing any potential behavior, a model must learn to capture the underlying multimodal distribution rather than simply predicting the most frequent mode. This learning task is challenging since only one possibility is logged in each training sample. To ease the learning difficulty, a body of works utilizes handcrafted anchors as guidance for multimodal prediction [6, 12, 39, 53, 55]. Their effectiveness, however, is subject to the quality of the anchors. Typically, these methods fail to work well when few anchors can precisely cover the ground truth. This problem is exacerbated in long-term prediction, where the search space for anchors is much larger. Some other works [10, 31, 38, 46, 56] circumvent this issue by directly predicting multiple trajectories, albeit at the risk of mode collapse and training instability [33, 41]. Due to the lack of spatial priors, these methods also fail to produce accurate long-term forecasts.", + "bbox": [ + 75, + 170, + 470, + 488 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The analysis above drives us to propose a trajectory prediction framework, termed as QCNet, to overcome the limitations of previous solutions. First, we note that it is possible to achieve faster online inference while also benefiting from the power of factorized attention, but the agent-centric encoding scheme [25, 27, 46, 56] used by existing methods serves as an impediment. Each time a new data frame arrives, the observation window slides one step forward and overlaps with its predecessor substantially, which provides opportunities for models to reuse the previously computed encodings. However, agent-centric approaches require normalizing the input based on the latest agent states' positions, necessitating the re-encoding of scene elements whenever the observation window slides forward. To address this issue, we introduce a query-centric paradigm for scene encoding (see Fig. 1). The crux of our design ethos lies in processing all scene elements in their local spacetime reference frames and learning representations independent of the global coordinates. This strategy enables us to cache and reuse the previously computed encodings, spreading the computation across all observation windows and thereby reducing inference latency. The invariant scene features can also be shared among all target agents in the scene to enable the parallelism of multi-agent decoding. Second, to better utilize the scene encodings for multimodal and long-term prediction, we use anchor-free queries to retrieve the scene context recurrently and let them decode a short seg", + "bbox": [ + 75, + 493, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ment of future waypoints at each recurrence. This recurrent mechanism eases the modeling burden on the queries by allowing them to focus on different scene contexts when predicting waypoints at different horizons. The high-quality trajectories predicted by the recurrent decoder serve as dynamic anchors in the subsequent refinement module, where we use anchor-based queries to refine the trajectory proposals based on the scene context. As a result, our query-based decoding pipeline incorporates the flexibility of anchor-free methods into anchor-based solutions, taking the best of both worlds to facilitate multimodal and long-term prediction.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our proposed query-centric encoding paradigm is the first that can exploit the sequential nature of trajectory prediction to achieve fast online inference. Besides, our query-based decoder exhibits superior performance for multimodal and long-term prediction. Experiments show that our approach achieves state-of-the-art results, ranking $1^{\\text{st}}$ on two large-scale motion forecasting benchmarks [7, 49].", + "bbox": [ + 496, + 257, + 890, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 377, + 640, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene context fusion encodes rich information for trajectory prediction. Early work rasterizes world states as multichannel images and employs classic convolutional neural networks for learning [5,6,10,21]. Due to the lossy rendering, limited receptive field, and prohibitively high cost of raster-based methods, the research community has turned to a vector-based encoding scheme [14, 31, 50]. With the use of permutation-invariant set operators such as pooling [3, 12, 14, 20, 46], graph convolution [11, 31, 36, 53], and attention mechanism [24, 26, 30, 32, 34, 52], vector-based methods can efficiently aggregate sparse information in traffic scenes. Several powerful trajectory prediction models have recently adopted Transformers [47] with factorized attention as their encoders [18, 37, 38, 56]. Although these models improve efficiency by learning agent-centric representations hierarchically [56] or encoding the whole scene in a shared coordinate system [38], their scalability is still limited by the computational complexity of factorized attention. In comparison, our encoder inherits the representational power of factorized attention while achieving more efficient scene context fusion by using a query-centric encoding paradigm, which goes beyond agent-centric modeling and enables streaming trajectory prediction.", + "bbox": [ + 496, + 402, + 890, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multimodal future distribution is a widely adopted output form of trajectory prediction, given that world states are partially observable and agents' intentions are highly uncertain. While generative models naturally fit multimodal prediction [20, 28, 40, 45], sampling from latent variables introduces test-time stochasticity, which is undesirable for safety-critical applications such as autonomous driving. Another line of research tackles multimodality by decoding a discrete set of trajectories from the encoded scene context [6, 10, 31, 55]. Since only one mode is ob-", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17864", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "served in training data, predicting multiple diverse futures is challenging. Anchor-based methods achieve this with the guidance of anchors, which facilitate multimodal prediction by leveraging predefined maneuvers [12], candidate trajectories [6, 39], or map-adaptive goals [53, 55]. However, the quality of these anchors significantly impacts prediction performance. By contrast, anchor-free methods output multiple hypotheses freely at the risk of mode collapse and training instability [10, 31, 38, 46]. Our decoding pipeline takes advantage of both anchor-based and anchor-free solutions, with an anchor-free module generating adaptive anchors in a data-driven manner and an anchor-based module refining these anchors based on the scene context.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 301, + 184, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Input and Output Formulation", + "text_level": 1, + "bbox": [ + 76, + 327, + 349, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a scenario with $A$ agents surrounding the autonomous vehicle. During online running, the perception module supplies a stream of agent states to the prediction module at a fixed interval, where each agent state is associated with its spatial-temporal position and geometric attributes. For example, the $i$ -th agent's state at time step $t$ comprises the spatial position $\\mathbf{p}_i^t = (\\mathbf{p}_{i,x}^t,\\mathbf{p}_{i,y}^t)$ , the angular position $\\theta_{i}^{t}$ (i.e., the yaw angle), the temporal position $t$ (i.e., the time step), and the velocity $\\mathbf{v}_i^t$ . We also add the motion vector $\\mathbf{p}_i^t -\\mathbf{p}_i^{t - 1}$ to the geometric attributes similar to some baselines [31, 56]. Besides, the prediction module has access to $M$ polygons on the high-definition map (e.g., lanes and crosswalks), where each map polygon is annotated with sampled points and semantic attributes (e.g., the user type of a lane). Given the map information and the agent states within an observation window of $T$ time steps, the prediction module is tasked with forecasting $K$ future trajectories for each target agent over a horizon of $T^{\\prime}$ time steps and assigning a probability score for each forecast.", + "bbox": [ + 75, + 349, + 472, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Query-Centric Scene Context Encoding", + "text_level": 1, + "bbox": [ + 76, + 650, + 416, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first step of trajectory prediction is to encode the scene input. Recent research has found factorized attention incredibly effective for scene encoding [37, 38, 56]. These approaches let a query element attend to key/value elements along one axis at a time, which results in temporal attention, agent-map attention, and social attention (i.e., agent-agent attention) with the complexity of $\\mathcal{O}(AT^2)$ , $\\mathcal{O}(ATM)$ , and $\\mathcal{O}(A^2T)$ , respectively. Unlike typical encoding strategies that first apply a temporal network to squeeze the time dimension and then perform agent-map and agent-agent fusions at the current time step only, factorized attention conducts fusions at every past time step within the observation window. As a result, factorized attention can capture more information, such as how the relations between agents and map elements evolve over the observation horizon. How", + "bbox": [ + 75, + 674, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ever, its scalability is limited by the cubic complexity of each fusion operation. In extreme circumstances involving hundreds of agents and map elements, such models may fail to emit predictions promptly. We ask: is it possible to reduce the inference latency during online prediction while enjoying the representational power of factorized attention?", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before diving into our solution, recall that trajectory prediction is a streaming processing task: when a new data frame arrives, we put it in the queue and drop the oldest one. Thus, the latest observation window has $T - 1$ time steps overlapping with its predecessor. This fact motivates us to raise another question: can we reuse the overlapped time steps' encodings computed previously after the observation window slides forward? Unfortunately, this idea is infeasible owing to the normalization requirement for trajectory prediction: existing methods employ an agent-centric encoding paradigm for spatially roto-translation invariance [25, 27, 46, 56], where each agent is encoded in the local coordinate frame determined by its current time step's position and yaw angle. Each time the observation window slides forward, the \"current time step\" also shifts accordingly, and the geometric attributes of all scene elements need to be re-normalized based on the positions of the latest agent states. Due to the variation in input, we are forced to re-encode all time steps' elements even though the observation windows largely overlap.", + "bbox": [ + 496, + 184, + 893, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the analysis above, we identify that the evolving spacetime coordinate systems hinder the reuse of previously computed encodings. To address this issue, we introduce a query-centric encoding paradigm for learning representations independent of scene elements' global coordinates. Specifically, we establish a local spacetime coordinate system for each scene element that a query vector derives from, processing query elements' features in their local reference frames. Then, we inject the relative spatial-temporal positions into the key and value elements when performing attention-based scene context fusion. We elaborate on the encoding process in the following paragraphs.", + "bbox": [ + 496, + 488, + 893, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Spacetime Coordinate System. Figure 1 shows an example of scene elements' local coordinate systems. For the $i$ -th agent's state at time step $t$ , the local coordinate frame is determined by the reference spatial-temporal position $(\\mathbf{p}_i^t, t)$ and the reference direction $\\theta_i^t$ , where $\\mathbf{p}_i^t$ and $\\theta_i^t$ are the agent state's spatial and angular positions, respectively. For lanes and crosswalks, we choose the position and orientation at the entry point of the centerline as the reference. In this way, we build local coordinate systems canonically for all the scene elements considered, resulting in one dedicated local frame per map polygon and $T$ reference frames per agent within any observation window.", + "bbox": [ + 496, + 671, + 893, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene Element Embedding. For each spatial-temporal scene element, such as an agent state or a lane, we compute the polar coordinates of all geometric attributes (e.g.,", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17865", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the velocity and motion vector of an agent state, the positions of all sampled points on a lane) relative to the spatial point and direction referenced by the element's local frame. Then, we transform each polar coordinate into Fourier features [22, 35, 44] to facilitate learning high-frequency signals. For each agent state and each sampled point on the map, the Fourier features are concatenated with the semantic attributes (e.g., an agent's category) and passed through a multi-layer perceptron (MLP) to obtain an embedding. To further produce polygon-level representations for lanes and crosswalks, we apply attention-based pooling on the embeddings of sampled points within each map polygon. These operations result in agent embeddings of shape $[A, T, D]$ and map embeddings of shape $[M, D]$ , where $D$ denotes the hidden feature dimension. Benefiting from modeling in local reference frames, the embedding of each agent state/map polygon has only one instance and can be reused in the subsequent observation windows. In contrast, agent-centric approaches have to copy all inputs multiple times, encode each copy relative to one of the $A$ agents' current position and heading, and re-encode all inputs whenever the observation window slides forward, leading to much more overhead during online inference.", + "bbox": [ + 75, + 90, + 472, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relative Spatial-Temporal Positional Embedding. We prepare the relative positional embeddings for scene element pairs, which will be incorporated into the attention-based operators to help the model be aware of the difference between two elements' local coordinate frames. For an element with absolute spatial-temporal position $(\\mathbf{p}_i^t,\\boldsymbol {\\theta}_i^t,t)$ and another with $(\\mathbf{p}_j^s,\\boldsymbol {\\theta}_j^s,s)$ , we use a 4D descriptor to summarize their relative position, whose components are the relative distance $\\left\\| \\mathbf{p}_j^s -\\mathbf{p}_i^t\\right\\| _2$ , the relative direction $\\mathrm{atan2}(\\mathbf{p}_{j,y}^{s} - \\mathbf{p}_{i,y}^{t},\\mathbf{p}_{j,x}^{s} - \\mathbf{p}_{i,x}^{t}) - \\boldsymbol{\\theta}_{i}^{t}$ , the relative orientation $\\boldsymbol{\\theta}_j^s -\\boldsymbol{\\theta}_i^t$ and the time gap $s - t$ . Since we can easily reconstruct one element's absolute position from another with the help of the descriptor, we have preserved all spatial-temporal position information of the scene element pair. Then, we transform the 4D descriptor into Fourier features and pass them through an MLP to produce the relative positional embedding $\\mathbf{r}_{j\\rightarrow i}^{s\\rightarrow t}$ . If any of the two scene elements are static (e.g., static map polygons), we can omit the superscript and denote the embedding as $\\mathbf{r}_{j\\rightarrow i}$ .", + "bbox": [ + 75, + 439, + 472, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Self-Attention for Map Encoding. We employ self-attention to model the relationships among map elements, after which the updated map encodings will enrich the agent features and assist trajectory decoding. For the $i$ -th map polygon, we derive a query vector from its embedding $\\mathbf{m}_i$ and let it attend to the neighboring lanes and crosswalks $\\{\\mathbf{m}_j\\}_{j\\in \\mathcal{N}_i}$ , where $\\mathcal{N}_i$ denotes the neighbor set of the polygon. To incorporate spatial awareness for map encoding, we generate the $j$ -th key/value vector from the concatenation of $\\mathbf{m}_j$ and the relative positional embedding, i.e., $[\\mathbf{m}_j;\\mathbf{r}_{j\\rightarrow i}]$ . Since each triple of $(\\mathbf{m}_i,\\mathbf{m}_j,\\mathbf{r}_{j\\rightarrow i})$ input to the attention", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4139b4329f7a463095a56cfdeca10d0337167b4ce19f34f758e29438f01a482b.jpg", + "image_caption": [ + "Figure 2. Overview of the encoder in an online mode. After reusing the encodings computed in previous observation windows (blue), the complexity of factorized attention goes from $\\mathcal{O}(AT^2) + \\mathcal{O}(ATM) + \\mathcal{O}(A^2T)$ to $\\mathcal{O}(AT) + \\mathcal{O}(AM) + \\mathcal{O}(A^2)$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 893, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "layer is independent of the global spacetime coordinate system, the output map encodings $\\{\\mathbf{m}_i^{\\prime}\\}_{i = 1}^{M}$ are also invariant under transformations of the global reference frame. Thus, they can be shared across all agents and all time steps and can even be pre-computed offline, thereby avoiding redundant computation suffered by agent-centric modeling.", + "bbox": [ + 496, + 286, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Factorized Attention for Agent Encoding. To help the agent embeddings capture more information, we also consider factorized attention across agent time steps, among agents, and between agents and maps. Take the $i$ -th agent at time step $t$ as an example. Given the query vector derived from the agent state's embedding $\\mathbf{a}_i^t$ , we employ temporal attention by computing the key and value vectors based on $\\{[\\mathbf{a}_i^s;\\mathbf{r}_{i\\rightarrow i}^{s\\rightarrow t}]\\}_{s = t - \\tau}^{t - 1}$ , which are the $i$ -th agent's embeddings from time step $t - \\tau$ ( $0 < \\tau < T$ ) to time step $t - 1$ and the corresponding relative positional embeddings. Likewise, the key and value vectors for agent-map and social attention are derived from $\\{[\\mathbf{m}_j';\\mathbf{r}_{j\\rightarrow i}]\\}_{j\\in \\mathcal{N}_i}$ and $\\{[\\mathbf{a}_j^t;\\mathbf{r}_{j\\rightarrow i}^{t\\rightarrow t}]\\}_{j\\in \\mathcal{N}_i}$ , respectively, where the neighbor set $\\mathcal{N}_i$ is determined by a distance threshold of 50 meters. As a result of updating the initially invariant queries with invariant keys and values, the outputs of these layers are also invariant. We stack the temporal, the agent-map, and the social attention sequentially as one fusion block and repeat such blocks $L_{\\mathrm{enc}}$ times.", + "bbox": [ + 496, + 380, + 892, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thanks to the query-centric modeling, all the agent and map encodings are unique and fixed no matter from which spacetime coordinate system we view them (i.e., roto-translation invariance for the space dimension and translation invariance for the time dimension), enabling the model to reuse past computations and operate streamingly. During online prediction, we can cache the encodings computed in previous observation windows and incrementally update the scene representation. As shown in Fig. 2, our model only performs factorized attention for the $A$ incoming agent states when a new data frame arrives, resulting in temporal attention with $\\mathcal{O}(AT)$ complexity, agent-map attention with $\\mathcal{O}(AM)$ complexity, and social attention with $\\mathcal{O}(A^2)$ complexity. All of these operations are an order less expensive than their non-streaming counterpart. Finally, we update the cached tensors using the newly computed encodings.", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17866", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/55bc5cc5fc0a1dce8112241111669c479a13735df6797f1d2d1e5711525d06fd.jpg", + "image_caption": [ + "Figure 3. Overview of the decoding pipeline. An anchor-free module generates trajectory proposals recurrently based on the encoded scene context. These proposals act as the anchors in the refinement module, where an anchor-based decoder refines the anchor trajectories and assigns a probability score for each hypothesis." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 883, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Query-Based Trajectory Decoding", + "text_level": 1, + "bbox": [ + 76, + 318, + 377, + 334 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The second step of trajectory prediction is to utilize the scene encodings output by the encoder to decode $K$ future trajectories for each target agent, which is non-trivial since the encoder returns only one set of feature embeddings. Inspired by the progress in object detection, some recent works [18, 32, 37, 46] employ DETR-like decoders [4] to deal with such a one-to-many problem, where multiple learnable queries cross-attend the scene encodings and decode trajectories. However, these models suffer from training instability and mode collapse like other anchor-free approaches. Moreover, they do not perform well in long-term prediction, where the forecasting task is much more challenging due to the explosive uncertainty in the distant future. Our query-based decoder overcomes these limitations by utilizing a recurrent, anchor-free proposal module to generate adaptive trajectory anchors, followed by an anchor-based module that further refines the initial proposals. An overview of our decoding pipeline is shown in Fig. 3. In the following, we will illustrate the components of the decoder in detail.", + "bbox": [ + 75, + 340, + 472, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Mode2Scene and Mode2Mode Attention. Both the proposal and refinement modules use a DETR-like architecture. Similar to the concept of object queries in DETR [4], each query takes charge of decoding one of the $K$ trajectory modes. In the Mode2Scene attention, we use cross-attention layers to update the mode queries with multiple contexts, including the history encodings of the target agent, the map encodings, and the neighboring agents' encodings. Following the Mode2Scene attention, the $K$ mode queries \"talk\" to each other via the Mode2Mode self-attention to improve the diversity of multiple modes.", + "bbox": [ + 75, + 643, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reference Frames of Mode Queries. To predict the trajectories of multiple agents in parallel, we share the same set of scene encodings among all target agents in the scene. As these encodings are derived from their local spacetime coordinate systems, we need to project them into each target agent's current viewpoint to achieve the same effect as", + "bbox": [ + 75, + 810, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "agent-centric modeling. To this end, we hallucinate a coordinate frame for each mode query based on the corresponding target agent's current position and yaw angle. When updating the query embeddings via Mode2Scene attention, the scene elements' positions relative to the queries are incorporated into the keys and values, which is similar to what we have done for the encoder.", + "bbox": [ + 496, + 319, + 890, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Anchor-Free Trajectory Proposal. We use learnable, anchor-free queries to propose initial trajectories. These proposals will later act as anchors in the refinement module. Compared with anchor-based methods that attempt to cover the ground truth with densely sampled handcrafted anchors [6, 19], our proposal module generates $K$ adaptive anchors in a data-driven manner. Thanks to the cross-attention layers, the mode queries can retrieve the scene context and quickly narrow the search space for anchors. The self-attention layer further allows the queries to collaborate with each other when generating trajectory proposals.", + "bbox": [ + 496, + 426, + 892, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Over an extended prediction horizon, an agent can travel a long distance, and its surrounding environment may vary quickly. As a result, it is hard to summarize all information required for decoding a long sequence into a single query embedding. To ease the queries' burden of context extraction and improve the anchors' quality, we generalize the DETR-like decoder to a recurrent fashion. Using $T_{\\mathrm{rec}}$ recurrent steps, the context-aware mode queries only decode $T^{\\prime} / T_{\\mathrm{rec}}$ future waypoints via an MLP at the end of each recurrent step. At the subsequent recurrence, these queries become the input again and extract the scene context relevant to the next few waypoints' prediction. For efficiency, $T_{\\mathrm{rec}}$ is far smaller than the prediction horizon $T^{\\prime}$ . We also find that using much more recurrent steps is unnecessary.", + "bbox": [ + 496, + 595, + 892, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Anchor-Based Trajectory Refinement. Anchor-free decoding can be a two-edged sword: despite its flexibility, the unstable training process may lead to mode collapse occasionally. On the other hand, the randomly initialized mode queries must adapt to all target agents in all scenes and lack the scenario-specific bias, which may result in non-", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17867", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "compliant predictions, such as trajectories that violate the laws of motion or break the traffic rules conveyed by the high-definition map. We are thus motivated to employ an anchor-based module to refine the proposals further. Taking the output of the proposal module as anchors, we let the refinement module predict the offset to the proposed trajectories and estimate the likelihood of each hypothesis. This module also adopts a DETR-like architecture, but its mode queries are derived from the proposed trajectory anchors instead of randomly initialized. Specifically, a small GRU [8] is used to embed each trajectory anchor, and we take its final hidden state as the mode query. These anchor-based queries provide explicit spatial prior for the model, enabling the attention layers to localize the context of interest more easily.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Training Objectives", + "text_level": 1, + "bbox": [ + 76, + 311, + 264, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following HiVT [56], we parameterize the $i$ -th agent's future trajectory as a mixture of Laplace distributions:", + "bbox": [ + 76, + 334, + 468, + 364 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(\\left\\{\\mathbf {p} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T ^ {\\prime}}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {i, k} \\prod_ {t = 1} ^ {T ^ {\\prime}} \\text {L a p l a c e} \\left(\\mathbf {p} _ {i} ^ {t} \\mid \\boldsymbol {\\mu} _ {i, k} ^ {t}, \\mathbf {b} _ {i, k} ^ {t}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 375, + 468, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\{\\pi_{i,k}\\}_{k=1}^{K}$ are the mixing coefficients, and the $k$ -th mixture component's Laplace density at time step $t$ is parameterized by the location $\\pmb{\\mu}_{i,k}^t$ and the scale $\\mathbf{b}_{i,k}^t$ . We then use a classification loss $\\mathcal{L}_{\\mathrm{cls}}$ to optimize the mixing coefficients predicted by the refinement module. This loss minimizes the negative log-likelihood of Eq. (1), and we stop the gradients of the locations and scales to optimize the mixing coefficients only. On the other hand, we adopt the winner-take-all strategy [29] to optimize the locations and scales output by the proposal and refinement modules, which conducts backpropagation on the best-predicted proposal and its refinement only. For stabilization, the refinement module stops the gradients of the proposed trajectory anchors. The final loss function combines the trajectory proposal loss $\\mathcal{L}_{\\mathrm{propose}}$ , the trajectory refinement loss $\\mathcal{L}_{\\mathrm{refine}}$ , and the classification loss $\\mathcal{L}_{\\mathrm{cls}}$ for end-to-end training:", + "bbox": [ + 75, + 426, + 472, + 667 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {p r o p o s e}} + \\mathcal {L} _ {\\text {r e f i n e}} + \\lambda \\mathcal {L} _ {\\text {c l s}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 678, + 468, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where we use $\\lambda$ to balance regression and classification.", + "bbox": [ + 76, + 704, + 446, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 731, + 209, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 756, + 284, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We use Argoverse 1 [7] and Argoverse 2 [49], two large-scale motion forecasting datasets, to test the efficacy of our approach. The Argoverse 1 dataset collects 323,557 sequences of data from Miami and Pittsburgh, while the Argoverse 2 dataset contains 250,000 scenarios spanning six cities. Both datasets have a sampled rate of $10\\mathrm{Hz}$ . For the Argoverse 1 dataset, models need to predict agents' 3-second future trajectories given the 2-second", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "observations of history. The Argoverse 2 dataset, in comparison, is featured by improved data diversity, higher data quality, a larger observation window of 5 seconds, and a longer prediction horizon of 6 seconds. Using these two datasets, we intend to examine models' forecasting capability on various data distributions and prediction horizons.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Following the standard evaluation protocol, we adopt metrics including minimum Average Displacement Error $(\\min\\mathrm{ADE}_K)$ , minimum Final Displacement Error $(\\min\\mathrm{FDE}_K)$ , Brier-minimum Final Displacement Error (b-minFDE $K$ ), and Miss Rate $(\\mathrm{MR}_K)$ for evaluation. The metric $\\min\\mathrm{ADE}_K$ calculates the $\\ell_2$ distance in meters between the ground-truth trajectory and the best of $K$ predicted trajectories as an average of all future time steps. On the other hand, the metric $\\min\\mathrm{FDE}_K$ only concerns the prediction error at the final time step to emphasize long-term performance. To further measure the performance of uncertainty estimation, the metric b-minFDE $K$ adds $(1 - \\hat{\\pi})^2$ to the final-step error, where $\\hat{\\pi}$ denotes the best-predicted trajectory's probability score that the model assigns. Moreover, the metric $\\mathrm{MR}_K$ is used for counting the ratio of cases where $\\min\\mathrm{FDE}_K$ exceeds 2 meters. As a common practice, $K$ is selected as 1 and 6. If a model outputs more than $K$ trajectories, only the predictions with the top- $K$ probability scores are considered during evaluation.", + "bbox": [ + 496, + 181, + 892, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State of the Art", + "text_level": 1, + "bbox": [ + 500, + 479, + 792, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with the strongest baselines on the Argoverse 1 and the Argoverse 2 motion forecasting benchmarks [7, 49]. We first conduct experiments on the Argoverse 2 dataset [49], which favors solutions that work well on long-term prediction, given that its prediction horizon is as long as 6 seconds. The results are shown in Tab. 1. Even without ensembling, QCNet has already outperformed all previous approaches on the Argoverse 2 test set in terms of $\\min\\mathrm{ADE}_6$ , $\\min\\mathrm{FDE}_6$ , $\\min\\mathrm{ADE}_1$ , and $\\min\\mathrm{FDE}_1$ . After using ensembling techniques similar to other entries, QCNet surpasses all methods on all metrics by a large margin. We also evaluate our model on the Argoverse 1 dataset [7] to better understand the generalizability of our approach. Although the performance on the Argoverse 1 benchmark has saturated for years [49], Tab. 2 shows that QCNet significantly advances state-of-the-art on most metrics. As of the time we submitted the paper, QCNet ranks $1^{st}$ on the leaderboards of Argoverse 1 and Argoverse 2, outperforming all published and unpublished works on the two benchmarks. Please refer to the supplementary material for more results on Argoverse 2 [49] and Waymo Open Motion Dataset [13].", + "bbox": [ + 496, + 503, + 890, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 830, + 653, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Scene Context Fusion. We study the effects of scene context fusion in Tab. 3. The first question we answer is whether factorized attention is worth it. If no fac", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17868", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/501c3b5e59995674cb29ff64a9368d75b1dee593a121c6933d6f59ab185677c3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓minADE1↓minFDE1↓MR1↓
THOMAS [17]2.160.881.510.201.954.710.64
GoRela [9]2.010.761.480.221.824.620.66
MTR [42]1.980.731.440.151.744.390.58
GANet [48]1.960.721.340.171.774.480.59
QML* [43]1.950.691.390.191.844.980.62
BANet* [54]1.920.711.360.191.794.610.60
QCNet (w/o ensemble)1.910.651.290.161.694.300.59
QCNet (w/ ensemble)1.780.621.190.141.563.960.55
", + "bbox": [ + 112, + 88, + 854, + 212 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a0d7cc45388c8146e08d96b9707384cd1c7e6af53343ef1b17382c30f6d10c5b.jpg", + "table_caption": [ + "Table 1. Quantitative results on the Argoverse 2 motion forecasting leaderboard [1] ranked by b-minFDE6. Baselines that are known to have used ensembling are marked with symbol “*”. For each metric, the best result is in bold and the second best result is underlined." + ], + "table_footnote": [], + "table_body": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓
LaneGCN [31]2.060.871.360.16
mmTransformer [32]2.030.841.340.15
DenseTNT [19]1.980.881.280.13
TPCN [50]1.930.821.240.13
SceneTransformer [38]1.890.801.230.13
HOME+GOHOME [15, 16]1.860.891.290.08
HiVT [56]1.840.771.170.13
MultiPath++ [46]1.790.791.210.13
GANet [48]1.790.811.160.12
PAGA [11]1.760.801.210.11
DCMS [51]1.760.771.140.11
Wayformer [37]1.740.771.160.12
Ours1.690.731.070.11
", + "bbox": [ + 78, + 253, + 468, + 436 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7113f9d51eec42e5179cb017446b62e5134cb6b11a6de4b276de47a76832ddff.jpg", + "table_caption": [ + "Table 2. Quantitative results on the Argoverse 1 motion forecasting leaderboard [2]. The leaderboard is sorted by b-minFDE6." + ], + "table_footnote": [], + "table_body": "
ModelOnline Inference (ms)minADE6↓minFDE6↓MR6↓
w/o reusew/ reuse
QCNet (Lenc = 0)8±11±00.761.330.18
QCNet (Lenc = 1)64±110±10.741.300.17
QCNet (Lenc = 2)82±113±10.731.270.16
", + "bbox": [ + 76, + 479, + 468, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Models' performance and inference latency evaluated on the Argoverse 2 validation set. We use an A40 GPU to measure encoders' online inference latency in the densest traffic scene involving 190 agents and 169 map polygons.", + "bbox": [ + 75, + 561, + 468, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "torized attention-based fusion blocks are employed, the encoder does not involve information interactions along different axes of the scene. Even so, the decoder has access to all information required for predictions thanks to the Mode2Scene layers. As shown in the first row of Tab. 3, our model can offer solid prediction performance without fusing the scene context. But after feeding our decoder with the fused encodings, the model gains considerable improvement over its non-fusion variant. Moreover, increasing the number of fusion blocks yields better results on all metrics, demonstrating the effectiveness of factorized attention. However, the resulting inference latency is not amenable to real-time applications such as autonomous driving, making this modeling choice less appealing for widespread adoption. Fortunately, our query-centric paradigm allows the reuse of computations from previous observation windows during online prediction, which goes beyond agent-centric approaches such as HiVT [56]. As shown in Tab. 3, caching", + "bbox": [ + 75, + 628, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and reusing the previously computed encodings drastically lowers the online inference latency in the densest traffic scene. Such a \"free lunch\" also provides headroom to design a more advanced decoder for stronger performance.", + "bbox": [ + 496, + 256, + 890, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Component Study of the Decoder. As demonstrated in Tab. 4, all layers in the decoder contribute to the performance to a certain degree. First, although the factorized attention in the encoder has already brought context awareness to the agent features, we find that using the target agent's history encodings alone is insufficient for accurate trajectory proposals. We hypothesize that injecting the map and social information into the anchor-free decoder can explicitly provide the queries with the future context, enabling them to narrow the search space for initial trajectories. On the other hand, the map and social information can also help the anchor-based queries identify those unrealistic predictions, such as trajectories that break the traffic rules or collide with static objects on the road. As a result, the role of our refinement module is more than simply trajectory smoothing [23, 51]. Table 4 also shows that removing the Mode2Mode self-attention in either the proposal or the refinement module will harm the long-term accuracy and the diversity of multiple hypotheses.", + "bbox": [ + 496, + 316, + 892, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 demonstrates the effects of the recurrent mechanism and the refinement module on different datasets. On Argoverse 1, most agents merely exhibit trivial behavior, and the scene context usually does not have significant variation within the 3-second prediction horizon. For this reason, our design choices only bring marginal improvement when evaluated on this dataset. However, on the more challenging Argoverse 2 dataset where the prediction horizon is 6 seconds, increasing the number of recurrent steps from 1 (i.e., no recurrence) to 3 leads to much better long-term performance, and the refinement module offers a dramatic improvement in terms of both accuracy and multimodality. We also notice that using much more recurrent steps is redundant: when increasing the number from 3 to 6, the model performance on Argoverse 2 cannot be further improved.", + "bbox": [ + 496, + 606, + 890, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 845, + 681, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present some qualitative results on the Argoverse 2 validation set. Comparing Fig. 4a and Fig. 4b, we can see", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17869", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/05175261e24baff49392bd0eac04fb4187299b89903ddcee6b3f1557216a04d8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TimeProposal ModuleRefinement Moduleb-minFDE6↓minADE6↓minFDE6↓MR6↓
MapSocialModeTimeMapSocialMode
✓✓2.220.821.580.22
✓✓✓2.040.781.430.19
✓✓✓2.180.811.550.22
✓✓✓2.060.791.480.21
✓✓✓✓2.020.771.400.19
✓✓✓✓✓✓1.990.741.330.17
✓✓✓✓✓✓✓1.940.741.300.17
✓✓✓✓✓✓✓1.970.741.310.17
✓✓✓✓✓✓✓1.910.731.290.17
✓✓✓✓✓✓✓✓1.900.731.270.16
", + "bbox": [ + 109, + 88, + 857, + 255 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a164a7e5428f72ae5854a3bc49af38dbb05211ec118078dacf423d0b73467b9.jpg", + "image_caption": [ + "(a) w/o recurrence & w/o refinement" + ], + "image_footnote": [], + "bbox": [ + 112, + 275, + 357, + 575 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c7c3957988cf9490b84c30f88d4fd7e4c85c85dfa2ec8140f1142881d53f7040.jpg", + "image_caption": [ + "(b) w/ recurrence & w/o refinement" + ], + "image_footnote": [], + "bbox": [ + 359, + 275, + 604, + 575 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0fe86ebba88ed038a8dbf7039b61872c2642ca8ed5c0064ab1eafb7b6270fa66.jpg", + "image_caption": [ + "(c) w/ recurrence & w/ refinement", + "Figure 4. Qualitative results on the Argoverse 2 validation set. The target agents' bounding boxes and ground-truth trajectories are shown in purple, and models' predictions are shown in pink." + ], + "image_footnote": [], + "bbox": [ + 607, + 275, + 852, + 575 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c8a86ef58e5e8bd591f6970774c5bc23bb0b2fd4da7b678e2011e80456d893ed.jpg", + "table_caption": [ + "Table 4. Ablation study on the components of the decoder. Experimental results are based on the Argoverse 2 validation set." + ], + "table_footnote": [], + "table_body": "
Dataset#Recurrent StepRefinementb-minFDE6↓minFDE6↓MR6↓
Argoverse 1 (3-sec pred.)1 (3 sec/step)×1.580.920.09
2 (1.5 sec/step)×1.570.900.08
3 (1 sec/step)×1.560.900.08
3 (1 sec/step)✓1.550.890.08
Argoverse 2 (6-sec pred.)1 (6 sec/step)×2.101.470.20
2 (3 sec/step)×2.041.420.19
3 (2 sec/step)×2.021.400.19
3 (2 sec/step)✓1.901.270.16
6 (1 sec/step)✓1.901.270.16
", + "bbox": [ + 78, + 626, + 468, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Effects of the trajectory proposal and refinement modules on datasets with varying difficulty levels and prediction horizons.", + "bbox": [ + 75, + 772, + 468, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that the recurrent mechanism of the proposal module can reduce the prediction error in the long term. Figure 4c further demonstrates the effectiveness of the refinement module, which improves the diversity of multiple hypotheses and the smoothness of the predicted trajectories.", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 627, + 619, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces QCNet, a neural architecture that overcomes some important challenges in trajectory prediction. Powered by the design ethos of query-centric modeling, QCNet maintains the representational capability of factorized attention while enjoying much faster inference. It achieves multimodal and long-term prediction by employing a recurrent, anchor-free trajectory proposal module and an anchor-based refinement module. QCNet exhibits unprecedented performance on large-scale trajectory prediction datasets, demonstrating the effectiveness of its designs.", + "bbox": [ + 496, + 652, + 890, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 815, + 660, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by Hong Kong Research Grant Council under GRF 11200220, Science and Technology Innovation Committee Foundation of Shenzhen under Grant No. JCYJ20200109143223052.", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17870", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Argoverse 2: Motion forecasting competition. https://eval.ai/web/challenges/challenge-page/1719/overview. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 1, 2, 3, 6, 7" + ], + "bbox": [ + 78, + 90, + 470, + 626 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17873", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_model.json b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8edeebc73dc7c4a5963cfcd6382a6669a9947753 --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_model.json @@ -0,0 +1,1927 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.298, + 0.131, + 0.673, + 0.154 + ], + "angle": 0, + "content": "Query-Centric Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.179, + 0.852, + 0.234 + ], + "angle": 0, + "content": "Zikang Zhou\\(^{1,2}\\) Jianping Wang\\(^{1,2}\\) Yung-Hui Li\\(^{3}\\) Yu-Kai Huang\\(^{4}\\) \n\\(^{1}\\)City University of Hong Kong \\(^{2}\\)City University of Hong Kong Shenzhen Research Institute \n\\(^{3}\\)Hon Hai Research Institute \\(^{4}\\)Carnegie Mellon University" + }, + { + "type": "text", + "bbox": [ + 0.36, + 0.238, + 0.611, + 0.251 + ], + "angle": 0, + "content": "zikanzhou2-c@my.cityu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.804 + ], + "angle": 0, + "content": "Predicting the future trajectories of surrounding agents is essential for autonomous vehicles to operate safely. This paper presents QCNet, a modeling framework toward pushing the boundaries of trajectory prediction. First, we identify that the agent-centric modeling scheme used by existing approaches requires re-normalizing and re-encoding the input whenever the observation window slides forward, leading to redundant computations during online prediction. To overcome this limitation and achieve faster inference, we introduce a query-centric paradigm for scene encoding, which enables the reuse of past computations by learning representations independent of the global spacetime coordinate system. Sharing the invariant scene features among all target agents further allows the parallelism of multi-agent trajectory decoding. Second, even given rich encodings of the scene, existing decoding strategies struggle to capture the multimodality inherent in agents' future behavior, especially when the prediction horizon is long. To tackle this challenge, we first employ anchor-free queries to generate trajectory proposals in a recurrent fashion, which allows the model to utilize different scene contexts when decoding waypoints at different horizons. A refinement module then takes the trajectory proposals as anchors and leverages anchor-based queries to refine the trajectories further. By supplying adaptive and high-quality anchors to the refinement module, our query-based decoder can better deal with the multimodality in the output of trajectory prediction. Our approach ranks \\(1^{st}\\) on Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming all methods on all main metrics by a large margin. Meanwhile, our model can achieve streaming scene encoding and parallel multi-agent decoding thanks to the query-centric design ethos." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.21, + 0.847 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Making safe decisions for autonomous vehicles requires accurate predictions of surrounding agents' future trajectories. In recent years, learning-based methods have been" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.286, + 0.698, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.437, + 0.665, + 0.452 + ], + "angle": 0, + "content": "agent history" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.287, + 0.892, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.431, + 0.871, + 0.441 + ], + "angle": 0, + "content": "reference frame of agent state" + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.445, + 0.88, + 0.455 + ], + "angle": 0, + "content": "\\(\\rightarrow\\) reference frame of map polygon" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.526 + ], + "angle": 0, + "content": "Figure 1. Illustration of our query-centric reference frame, where we build a local coordinate system for each spatial-temporal element, including map polygons and agent states at all time steps. In the attention-based encoder, all scene elements' queries are derived and updated in their local reference frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.64 + ], + "angle": 0, + "content": "widely used for trajectory prediction [14, 31, 37, 38, 46, 56]. Despite the considerable efforts made to enhance models' forecasting ability, there is still a long way to go before fully addressing the problem of trajectory prediction. Why is this task so challenging, and what inability lies in existing approaches? We attempt to answer these questions from the following two perspectives:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.901 + ], + "angle": 0, + "content": "(i) While the flourishing forecasting models have achieved impressive performance on trajectory prediction benchmarks [7, 13, 49], today's most advanced architectures specialized for this task [37, 38, 46, 56] fail to process the heterogeneous traffic scenes efficiently. In an autonomous driving system, data frames arrive at the prediction module sequentially as a stream of sparse scene context, including the high-definition vector map and the surrounding agents' kinematic states. A model must learn expressive representations of these scene elements to achieve accurate forecasts. With the continuing development of modeling techniques for sparse context encoding [14, 31, 50], the research community has witnessed rapid progress toward more powerful trajectory predictors. Notably, factorized attention-based Transformers [37, 38, 56] have recently raised prediction accuracy to an unprecedented level. However, they require learning attention-based representations for each spatial-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17863" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "temporal scene element and suffer from prohibitively high costs when processing dense traffic scenes. As every minimal delay may lead to catastrophic accidents in autonomous driving, the unmet need for real-time predictions has limited the applicability of state-of-the-art approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.171, + 0.472, + 0.489 + ], + "angle": 0, + "content": "(ii) The immense uncertainty in the output of trajectory prediction, which grows explosively as the prediction horizon lengthens, has troubled the research community constantly. For example, a vehicle at an intersection may turn or go straight depending on the driver's long-term goal. To avoid missing any potential behavior, a model must learn to capture the underlying multimodal distribution rather than simply predicting the most frequent mode. This learning task is challenging since only one possibility is logged in each training sample. To ease the learning difficulty, a body of works utilizes handcrafted anchors as guidance for multimodal prediction [6, 12, 39, 53, 55]. Their effectiveness, however, is subject to the quality of the anchors. Typically, these methods fail to work well when few anchors can precisely cover the ground truth. This problem is exacerbated in long-term prediction, where the search space for anchors is much larger. Some other works [10, 31, 38, 46, 56] circumvent this issue by directly predicting multiple trajectories, albeit at the risk of mode collapse and training instability [33, 41]. Due to the lack of spatial priors, these methods also fail to produce accurate long-term forecasts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.472, + 0.902 + ], + "angle": 0, + "content": "The analysis above drives us to propose a trajectory prediction framework, termed as QCNet, to overcome the limitations of previous solutions. First, we note that it is possible to achieve faster online inference while also benefiting from the power of factorized attention, but the agent-centric encoding scheme [25, 27, 46, 56] used by existing methods serves as an impediment. Each time a new data frame arrives, the observation window slides one step forward and overlaps with its predecessor substantially, which provides opportunities for models to reuse the previously computed encodings. However, agent-centric approaches require normalizing the input based on the latest agent states' positions, necessitating the re-encoding of scene elements whenever the observation window slides forward. To address this issue, we introduce a query-centric paradigm for scene encoding (see Fig. 1). The crux of our design ethos lies in processing all scene elements in their local spacetime reference frames and learning representations independent of the global coordinates. This strategy enables us to cache and reuse the previously computed encodings, spreading the computation across all observation windows and thereby reducing inference latency. The invariant scene features can also be shared among all target agents in the scene to enable the parallelism of multi-agent decoding. Second, to better utilize the scene encodings for multimodal and long-term prediction, we use anchor-free queries to retrieve the scene context recurrently and let them decode a short seg" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "ment of future waypoints at each recurrence. This recurrent mechanism eases the modeling burden on the queries by allowing them to focus on different scene contexts when predicting waypoints at different horizons. The high-quality trajectories predicted by the recurrent decoder serve as dynamic anchors in the subsequent refinement module, where we use anchor-based queries to refine the trajectory proposals based on the scene context. As a result, our query-based decoding pipeline incorporates the flexibility of anchor-free methods into anchor-based solutions, taking the best of both worlds to facilitate multimodal and long-term prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Our proposed query-centric encoding paradigm is the first that can exploit the sequential nature of trajectory prediction to achieve fast online inference. Besides, our query-based decoder exhibits superior performance for multimodal and long-term prediction. Experiments show that our approach achieves state-of-the-art results, ranking \\(1^{\\text{st}}\\) on two large-scale motion forecasting benchmarks [7, 49]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.378, + 0.642, + 0.394 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Scene context fusion encodes rich information for trajectory prediction. Early work rasterizes world states as multichannel images and employs classic convolutional neural networks for learning [5,6,10,21]. Due to the lossy rendering, limited receptive field, and prohibitively high cost of raster-based methods, the research community has turned to a vector-based encoding scheme [14, 31, 50]. With the use of permutation-invariant set operators such as pooling [3, 12, 14, 20, 46], graph convolution [11, 31, 36, 53], and attention mechanism [24, 26, 30, 32, 34, 52], vector-based methods can efficiently aggregate sparse information in traffic scenes. Several powerful trajectory prediction models have recently adopted Transformers [47] with factorized attention as their encoders [18, 37, 38, 56]. Although these models improve efficiency by learning agent-centric representations hierarchically [56] or encoding the whole scene in a shared coordinate system [38], their scalability is still limited by the computational complexity of factorized attention. In comparison, our encoder inherits the representational power of factorized attention while achieving more efficient scene context fusion by using a query-centric encoding paradigm, which goes beyond agent-centric modeling and enables streaming trajectory prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Multimodal future distribution is a widely adopted output form of trajectory prediction, given that world states are partially observable and agents' intentions are highly uncertain. While generative models naturally fit multimodal prediction [20, 28, 40, 45], sampling from latent variables introduces test-time stochasticity, which is undesirable for safety-critical applications such as autonomous driving. Another line of research tackles multimodality by decoding a discrete set of trajectories from the encoded scene context [6, 10, 31, 55]. Since only one mode is ob-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17864" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "served in training data, predicting multiple diverse futures is challenging. Anchor-based methods achieve this with the guidance of anchors, which facilitate multimodal prediction by leveraging predefined maneuvers [12], candidate trajectories [6, 39], or map-adaptive goals [53, 55]. However, the quality of these anchors significantly impacts prediction performance. By contrast, anchor-free methods output multiple hypotheses freely at the risk of mode collapse and training instability [10, 31, 38, 46]. Our decoding pipeline takes advantage of both anchor-based and anchor-free solutions, with an anchor-free module generating adaptive anchors in a data-driven manner and an anchor-based module refining these anchors based on the scene context." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.303, + 0.186, + 0.32 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.328, + 0.351, + 0.344 + ], + "angle": 0, + "content": "3.1. Input and Output Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.473, + 0.642 + ], + "angle": 0, + "content": "Consider a scenario with \\(A\\) agents surrounding the autonomous vehicle. During online running, the perception module supplies a stream of agent states to the prediction module at a fixed interval, where each agent state is associated with its spatial-temporal position and geometric attributes. For example, the \\(i\\)-th agent's state at time step \\(t\\) comprises the spatial position \\(\\mathbf{p}_i^t = (\\mathbf{p}_{i,x}^t,\\mathbf{p}_{i,y}^t)\\), the angular position \\(\\theta_{i}^{t}\\) (i.e., the yaw angle), the temporal position \\(t\\) (i.e., the time step), and the velocity \\(\\mathbf{v}_i^t\\). We also add the motion vector \\(\\mathbf{p}_i^t -\\mathbf{p}_i^{t - 1}\\) to the geometric attributes similar to some baselines [31, 56]. Besides, the prediction module has access to \\(M\\) polygons on the high-definition map (e.g., lanes and crosswalks), where each map polygon is annotated with sampled points and semantic attributes (e.g., the user type of a lane). Given the map information and the agent states within an observation window of \\(T\\) time steps, the prediction module is tasked with forecasting \\(K\\) future trajectories for each target agent over a horizon of \\(T^{\\prime}\\) time steps and assigning a probability score for each forecast." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.418, + 0.667 + ], + "angle": 0, + "content": "3.2. Query-Centric Scene Context Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.901 + ], + "angle": 0, + "content": "The first step of trajectory prediction is to encode the scene input. Recent research has found factorized attention incredibly effective for scene encoding [37, 38, 56]. These approaches let a query element attend to key/value elements along one axis at a time, which results in temporal attention, agent-map attention, and social attention (i.e., agent-agent attention) with the complexity of \\(\\mathcal{O}(AT^2)\\), \\(\\mathcal{O}(ATM)\\), and \\(\\mathcal{O}(A^2T)\\), respectively. Unlike typical encoding strategies that first apply a temporal network to squeeze the time dimension and then perform agent-map and agent-agent fusions at the current time step only, factorized attention conducts fusions at every past time step within the observation window. As a result, factorized attention can capture more information, such as how the relations between agents and map elements evolve over the observation horizon. How" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.183 + ], + "angle": 0, + "content": "ever, its scalability is limited by the cubic complexity of each fusion operation. In extreme circumstances involving hundreds of agents and map elements, such models may fail to emit predictions promptly. We ask: is it possible to reduce the inference latency during online prediction while enjoying the representational power of factorized attention?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.487 + ], + "angle": 0, + "content": "Before diving into our solution, recall that trajectory prediction is a streaming processing task: when a new data frame arrives, we put it in the queue and drop the oldest one. Thus, the latest observation window has \\( T - 1 \\) time steps overlapping with its predecessor. This fact motivates us to raise another question: can we reuse the overlapped time steps' encodings computed previously after the observation window slides forward? Unfortunately, this idea is infeasible owing to the normalization requirement for trajectory prediction: existing methods employ an agent-centric encoding paradigm for spatially roto-translation invariance [25, 27, 46, 56], where each agent is encoded in the local coordinate frame determined by its current time step's position and yaw angle. Each time the observation window slides forward, the \"current time step\" also shifts accordingly, and the geometric attributes of all scene elements need to be re-normalized based on the positions of the latest agent states. Due to the variation in input, we are forced to re-encode all time steps' elements even though the observation windows largely overlap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.672 + ], + "angle": 0, + "content": "Based on the analysis above, we identify that the evolving spacetime coordinate systems hinder the reuse of previously computed encodings. To address this issue, we introduce a query-centric encoding paradigm for learning representations independent of scene elements' global coordinates. Specifically, we establish a local spacetime coordinate system for each scene element that a query vector derives from, processing query elements' features in their local reference frames. Then, we inject the relative spatial-temporal positions into the key and value elements when performing attention-based scene context fusion. We elaborate on the encoding process in the following paragraphs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.853 + ], + "angle": 0, + "content": "Local Spacetime Coordinate System. Figure 1 shows an example of scene elements' local coordinate systems. For the \\(i\\)-th agent's state at time step \\(t\\), the local coordinate frame is determined by the reference spatial-temporal position \\((\\mathbf{p}_i^t, t)\\) and the reference direction \\(\\theta_i^t\\), where \\(\\mathbf{p}_i^t\\) and \\(\\theta_i^t\\) are the agent state's spatial and angular positions, respectively. For lanes and crosswalks, we choose the position and orientation at the entry point of the centerline as the reference. In this way, we build local coordinate systems canonically for all the scene elements considered, resulting in one dedicated local frame per map polygon and \\(T\\) reference frames per agent within any observation window." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Scene Element Embedding. For each spatial-temporal scene element, such as an agent state or a lane, we compute the polar coordinates of all geometric attributes (e.g.," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17865" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.439 + ], + "angle": 0, + "content": "the velocity and motion vector of an agent state, the positions of all sampled points on a lane) relative to the spatial point and direction referenced by the element's local frame. Then, we transform each polar coordinate into Fourier features [22, 35, 44] to facilitate learning high-frequency signals. For each agent state and each sampled point on the map, the Fourier features are concatenated with the semantic attributes (e.g., an agent's category) and passed through a multi-layer perceptron (MLP) to obtain an embedding. To further produce polygon-level representations for lanes and crosswalks, we apply attention-based pooling on the embeddings of sampled points within each map polygon. These operations result in agent embeddings of shape \\([A, T, D]\\) and map embeddings of shape \\([M, D]\\), where \\(D\\) denotes the hidden feature dimension. Benefiting from modeling in local reference frames, the embedding of each agent state/map polygon has only one instance and can be reused in the subsequent observation windows. In contrast, agent-centric approaches have to copy all inputs multiple times, encode each copy relative to one of the \\(A\\) agents' current position and heading, and re-encode all inputs whenever the observation window slides forward, leading to much more overhead during online inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.473, + 0.734 + ], + "angle": 0, + "content": "Relative Spatial-Temporal Positional Embedding. We prepare the relative positional embeddings for scene element pairs, which will be incorporated into the attention-based operators to help the model be aware of the difference between two elements' local coordinate frames. For an element with absolute spatial-temporal position \\((\\mathbf{p}_i^t,\\boldsymbol {\\theta}_i^t,t)\\) and another with \\((\\mathbf{p}_j^s,\\boldsymbol {\\theta}_j^s,s)\\), we use a 4D descriptor to summarize their relative position, whose components are the relative distance \\(\\left\\| \\mathbf{p}_j^s -\\mathbf{p}_i^t\\right\\| _2\\), the relative direction \\(\\mathrm{atan2}(\\mathbf{p}_{j,y}^{s} - \\mathbf{p}_{i,y}^{t},\\mathbf{p}_{j,x}^{s} - \\mathbf{p}_{i,x}^{t}) - \\boldsymbol{\\theta}_{i}^{t}\\), the relative orientation \\(\\boldsymbol{\\theta}_j^s -\\boldsymbol{\\theta}_i^t\\) and the time gap \\(s - t\\). Since we can easily reconstruct one element's absolute position from another with the help of the descriptor, we have preserved all spatial-temporal position information of the scene element pair. Then, we transform the 4D descriptor into Fourier features and pass them through an MLP to produce the relative positional embedding \\(\\mathbf{r}_{j\\rightarrow i}^{s\\rightarrow t}\\). If any of the two scene elements are static (e.g., static map polygons), we can omit the superscript and denote the embedding as \\(\\mathbf{r}_{j\\rightarrow i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Self-Attention for Map Encoding. We employ self-attention to model the relationships among map elements, after which the updated map encodings will enrich the agent features and assist trajectory decoding. For the \\(i\\)-th map polygon, we derive a query vector from its embedding \\(\\mathbf{m}_i\\) and let it attend to the neighboring lanes and crosswalks \\(\\{\\mathbf{m}_j\\}_{j\\in \\mathcal{N}_i}\\), where \\(\\mathcal{N}_i\\) denotes the neighbor set of the polygon. To incorporate spatial awareness for map encoding, we generate the \\(j\\)-th key/value vector from the concatenation of \\(\\mathbf{m}_j\\) and the relative positional embedding, i.e., \\([\\mathbf{m}_j;\\mathbf{r}_{j\\rightarrow i}]\\). Since each triple of \\((\\mathbf{m}_i,\\mathbf{m}_j,\\mathbf{r}_{j\\rightarrow i})\\) input to the attention" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.895, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 2. Overview of the encoder in an online mode. After reusing the encodings computed in previous observation windows (blue), the complexity of factorized attention goes from \\(\\mathcal{O}(AT^2) + \\mathcal{O}(ATM) + \\mathcal{O}(A^2T)\\) to \\(\\mathcal{O}(AT) + \\mathcal{O}(AM) + \\mathcal{O}(A^2)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.379 + ], + "angle": 0, + "content": "layer is independent of the global spacetime coordinate system, the output map encodings \\(\\{\\mathbf{m}_i^{\\prime}\\}_{i = 1}^{M}\\) are also invariant under transformations of the global reference frame. Thus, they can be shared across all agents and all time steps and can even be pre-computed offline, thereby avoiding redundant computation suffered by agent-centric modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.656 + ], + "angle": 0, + "content": "Factorized Attention for Agent Encoding. To help the agent embeddings capture more information, we also consider factorized attention across agent time steps, among agents, and between agents and maps. Take the \\(i\\)-th agent at time step \\(t\\) as an example. Given the query vector derived from the agent state's embedding \\(\\mathbf{a}_i^t\\), we employ temporal attention by computing the key and value vectors based on \\(\\{[\\mathbf{a}_i^s;\\mathbf{r}_{i\\rightarrow i}^{s\\rightarrow t}]\\}_{s = t - \\tau}^{t - 1}\\), which are the \\(i\\)-th agent's embeddings from time step \\(t - \\tau\\) (\\(0 < \\tau < T\\)) to time step \\(t - 1\\) and the corresponding relative positional embeddings. Likewise, the key and value vectors for agent-map and social attention are derived from \\(\\{[\\mathbf{m}_j';\\mathbf{r}_{j\\rightarrow i}]\\}_{j\\in \\mathcal{N}_i}\\) and \\(\\{[\\mathbf{a}_j^t;\\mathbf{r}_{j\\rightarrow i}^{t\\rightarrow t}]\\}_{j\\in \\mathcal{N}_i}\\), respectively, where the neighbor set \\(\\mathcal{N}_i\\) is determined by a distance threshold of 50 meters. As a result of updating the initially invariant queries with invariant keys and values, the outputs of these layers are also invariant. We stack the temporal, the agent-map, and the social attention sequentially as one fusion block and repeat such blocks \\(L_{\\mathrm{enc}}\\) times." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Thanks to the query-centric modeling, all the agent and map encodings are unique and fixed no matter from which spacetime coordinate system we view them (i.e., roto-translation invariance for the space dimension and translation invariance for the time dimension), enabling the model to reuse past computations and operate streamingly. During online prediction, we can cache the encodings computed in previous observation windows and incrementally update the scene representation. As shown in Fig. 2, our model only performs factorized attention for the \\(A\\) incoming agent states when a new data frame arrives, resulting in temporal attention with \\(\\mathcal{O}(AT)\\) complexity, agent-map attention with \\(\\mathcal{O}(AM)\\) complexity, and social attention with \\(\\mathcal{O}(A^2)\\) complexity. All of these operations are an order less expensive than their non-streaming counterpart. Finally, we update the cached tensors using the newly computed encodings." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17866" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.092, + 0.885, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.895, + 0.316 + ], + "angle": 0, + "content": "Figure 3. Overview of the decoding pipeline. An anchor-free module generates trajectory proposals recurrently based on the encoded scene context. These proposals act as the anchors in the refinement module, where an anchor-based decoder refines the anchor trajectories and assigns a probability score for each hypothesis." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.319, + 0.379, + 0.335 + ], + "angle": 0, + "content": "3.3. Query-Based Trajectory Decoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.643 + ], + "angle": 0, + "content": "The second step of trajectory prediction is to utilize the scene encodings output by the encoder to decode \\( K \\) future trajectories for each target agent, which is non-trivial since the encoder returns only one set of feature embeddings. Inspired by the progress in object detection, some recent works [18, 32, 37, 46] employ DETR-like decoders [4] to deal with such a one-to-many problem, where multiple learnable queries cross-attend the scene encodings and decode trajectories. However, these models suffer from training instability and mode collapse like other anchor-free approaches. Moreover, they do not perform well in long-term prediction, where the forecasting task is much more challenging due to the explosive uncertainty in the distant future. Our query-based decoder overcomes these limitations by utilizing a recurrent, anchor-free proposal module to generate adaptive trajectory anchors, followed by an anchor-based module that further refines the initial proposals. An overview of our decoding pipeline is shown in Fig. 3. In the following, we will illustrate the components of the decoder in detail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Mode2Scene and Mode2Mode Attention. Both the proposal and refinement modules use a DETR-like architecture. Similar to the concept of object queries in DETR [4], each query takes charge of decoding one of the \\(K\\) trajectory modes. In the Mode2Scene attention, we use cross-attention layers to update the mode queries with multiple contexts, including the history encodings of the target agent, the map encodings, and the neighboring agents' encodings. Following the Mode2Scene attention, the \\(K\\) mode queries \"talk\" to each other via the Mode2Mode self-attention to improve the diversity of multiple modes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Reference Frames of Mode Queries. To predict the trajectories of multiple agents in parallel, we share the same set of scene encodings among all target agents in the scene. As these encodings are derived from their local spacetime coordinate systems, we need to project them into each target agent's current viewpoint to achieve the same effect as" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.424 + ], + "angle": 0, + "content": "agent-centric modeling. To this end, we hallucinate a coordinate frame for each mode query based on the corresponding target agent's current position and yaw angle. When updating the query embeddings via Mode2Scene attention, the scene elements' positions relative to the queries are incorporated into the keys and values, which is similar to what we have done for the encoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.893, + 0.594 + ], + "angle": 0, + "content": "Anchor-Free Trajectory Proposal. We use learnable, anchor-free queries to propose initial trajectories. These proposals will later act as anchors in the refinement module. Compared with anchor-based methods that attempt to cover the ground truth with densely sampled handcrafted anchors [6, 19], our proposal module generates \\( K \\) adaptive anchors in a data-driven manner. Thanks to the cross-attention layers, the mode queries can retrieve the scene context and quickly narrow the search space for anchors. The self-attention layer further allows the queries to collaborate with each other when generating trajectory proposals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.893, + 0.808 + ], + "angle": 0, + "content": "Over an extended prediction horizon, an agent can travel a long distance, and its surrounding environment may vary quickly. As a result, it is hard to summarize all information required for decoding a long sequence into a single query embedding. To ease the queries' burden of context extraction and improve the anchors' quality, we generalize the DETR-like decoder to a recurrent fashion. Using \\( T_{\\mathrm{rec}} \\) recurrent steps, the context-aware mode queries only decode \\( T^{\\prime} / T_{\\mathrm{rec}} \\) future waypoints via an MLP at the end of each recurrent step. At the subsequent recurrence, these queries become the input again and extract the scene context relevant to the next few waypoints' prediction. For efficiency, \\( T_{\\mathrm{rec}} \\) is far smaller than the prediction horizon \\( T^{\\prime} \\). We also find that using much more recurrent steps is unnecessary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Anchor-Based Trajectory Refinement. Anchor-free decoding can be a two-edged sword: despite its flexibility, the unstable training process may lead to mode collapse occasionally. On the other hand, the randomly initialized mode queries must adapt to all target agents in all scenes and lack the scenario-specific bias, which may result in non-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17867" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "compliant predictions, such as trajectories that violate the laws of motion or break the traffic rules conveyed by the high-definition map. We are thus motivated to employ an anchor-based module to refine the proposals further. Taking the output of the proposal module as anchors, we let the refinement module predict the offset to the proposed trajectories and estimate the likelihood of each hypothesis. This module also adopts a DETR-like architecture, but its mode queries are derived from the proposed trajectory anchors instead of randomly initialized. Specifically, a small GRU [8] is used to embed each trajectory anchor, and we take its final hidden state as the mode query. These anchor-based queries provide explicit spatial prior for the model, enabling the attention layers to localize the context of interest more easily." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.312, + 0.266, + 0.328 + ], + "angle": 0, + "content": "3.4. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.47, + 0.366 + ], + "angle": 0, + "content": "Following HiVT [56], we parameterize the \\(i\\)-th agent's future trajectory as a mixture of Laplace distributions:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.375, + 0.47, + 0.417 + ], + "angle": 0, + "content": "\\[\nf \\left(\\left\\{\\mathbf {p} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T ^ {\\prime}}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {i, k} \\prod_ {t = 1} ^ {T ^ {\\prime}} \\text {L a p l a c e} \\left(\\mathbf {p} _ {i} ^ {t} \\mid \\boldsymbol {\\mu} _ {i, k} ^ {t}, \\mathbf {b} _ {i, k} ^ {t}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.473, + 0.669 + ], + "angle": 0, + "content": "where \\(\\{\\pi_{i,k}\\}_{k=1}^{K}\\) are the mixing coefficients, and the \\(k\\)-th mixture component's Laplace density at time step \\(t\\) is parameterized by the location \\(\\pmb{\\mu}_{i,k}^t\\) and the scale \\(\\mathbf{b}_{i,k}^t\\). We then use a classification loss \\(\\mathcal{L}_{\\mathrm{cls}}\\) to optimize the mixing coefficients predicted by the refinement module. This loss minimizes the negative log-likelihood of Eq. (1), and we stop the gradients of the locations and scales to optimize the mixing coefficients only. On the other hand, we adopt the winner-take-all strategy [29] to optimize the locations and scales output by the proposal and refinement modules, which conducts backpropagation on the best-predicted proposal and its refinement only. For stabilization, the refinement module stops the gradients of the proposed trajectory anchors. The final loss function combines the trajectory proposal loss \\(\\mathcal{L}_{\\mathrm{propose}}\\), the trajectory refinement loss \\(\\mathcal{L}_{\\mathrm{refine}}\\), and the classification loss \\(\\mathcal{L}_{\\mathrm{cls}}\\) for end-to-end training:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.679, + 0.469, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {p r o p o s e}} + \\mathcal {L} _ {\\text {r e f i n e}} + \\lambda \\mathcal {L} _ {\\text {c l s}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.447, + 0.72 + ], + "angle": 0, + "content": "where we use \\(\\lambda\\) to balance regression and classification." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.21, + 0.749 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.285, + 0.773 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Datasets. We use Argoverse 1 [7] and Argoverse 2 [49], two large-scale motion forecasting datasets, to test the efficacy of our approach. The Argoverse 1 dataset collects 323,557 sequences of data from Miami and Pittsburgh, while the Argoverse 2 dataset contains 250,000 scenarios spanning six cities. Both datasets have a sampled rate of \\(10\\mathrm{Hz}\\). For the Argoverse 1 dataset, models need to predict agents' 3-second future trajectories given the 2-second" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "observations of history. The Argoverse 2 dataset, in comparison, is featured by improved data diversity, higher data quality, a larger observation window of 5 seconds, and a longer prediction horizon of 6 seconds. Using these two datasets, we intend to examine models' forecasting capability on various data distributions and prediction horizons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Metrics. Following the standard evaluation protocol, we adopt metrics including minimum Average Displacement Error \\((\\min\\mathrm{ADE}_K)\\), minimum Final Displacement Error \\((\\min\\mathrm{FDE}_K)\\), Brier-minimum Final Displacement Error (b-minFDE \\(K\\)), and Miss Rate \\((\\mathrm{MR}_K)\\) for evaluation. The metric \\(\\min\\mathrm{ADE}_K\\) calculates the \\(\\ell_2\\) distance in meters between the ground-truth trajectory and the best of \\(K\\) predicted trajectories as an average of all future time steps. On the other hand, the metric \\(\\min\\mathrm{FDE}_K\\) only concerns the prediction error at the final time step to emphasize long-term performance. To further measure the performance of uncertainty estimation, the metric b-minFDE \\(K\\) adds \\((1 - \\hat{\\pi})^2\\) to the final-step error, where \\(\\hat{\\pi}\\) denotes the best-predicted trajectory's probability score that the model assigns. Moreover, the metric \\(\\mathrm{MR}_K\\) is used for counting the ratio of cases where \\(\\min\\mathrm{FDE}_K\\) exceeds 2 meters. As a common practice, \\(K\\) is selected as 1 and 6. If a model outputs more than \\(K\\) trajectories, only the predictions with the top-\\(K\\) probability scores are considered during evaluation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.481, + 0.794, + 0.496 + ], + "angle": 0, + "content": "4.2. Comparison with State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.822 + ], + "angle": 0, + "content": "We compare our method with the strongest baselines on the Argoverse 1 and the Argoverse 2 motion forecasting benchmarks [7, 49]. We first conduct experiments on the Argoverse 2 dataset [49], which favors solutions that work well on long-term prediction, given that its prediction horizon is as long as 6 seconds. The results are shown in Tab. 1. Even without ensembling, QCNet has already outperformed all previous approaches on the Argoverse 2 test set in terms of \\(\\min\\mathrm{ADE}_6\\), \\(\\min\\mathrm{FDE}_6\\), \\(\\min\\mathrm{ADE}_1\\), and \\(\\min\\mathrm{FDE}_1\\). After using ensembling techniques similar to other entries, QCNet surpasses all methods on all metrics by a large margin. We also evaluate our model on the Argoverse 1 dataset [7] to better understand the generalizability of our approach. Although the performance on the Argoverse 1 benchmark has saturated for years [49], Tab. 2 shows that QCNet significantly advances state-of-the-art on most metrics. As of the time we submitted the paper, QCNet ranks \\(1^{st}\\) on the leaderboards of Argoverse 1 and Argoverse 2, outperforming all published and unpublished works on the two benchmarks. Please refer to the supplementary material for more results on Argoverse 2 [49] and Waymo Open Motion Dataset [13]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.654, + 0.848 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Effects of Scene Context Fusion. We study the effects of scene context fusion in Tab. 3. The first question we answer is whether factorized attention is worth it. If no fac" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17868" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.113, + 0.089, + 0.855, + 0.213 + ], + "angle": 0, + "content": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓minADE1↓minFDE1↓MR1↓
THOMAS [17]2.160.881.510.201.954.710.64
GoRela [9]2.010.761.480.221.824.620.66
MTR [42]1.980.731.440.151.744.390.58
GANet [48]1.960.721.340.171.774.480.59
QML* [43]1.950.691.390.191.844.980.62
BANet* [54]1.920.711.360.191.794.610.60
QCNet (w/o ensemble)1.910.651.290.161.694.300.59
QCNet (w/ ensemble)1.780.621.190.141.563.960.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.217, + 0.892, + 0.245 + ], + "angle": 0, + "content": "Table 1. Quantitative results on the Argoverse 2 motion forecasting leaderboard [1] ranked by b-minFDE6. Baselines that are known to have used ensembling are marked with symbol “*”. For each metric, the best result is in bold and the second best result is underlined." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.255, + 0.47, + 0.438 + ], + "angle": 0, + "content": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓
LaneGCN [31]2.060.871.360.16
mmTransformer [32]2.030.841.340.15
DenseTNT [19]1.980.881.280.13
TPCN [50]1.930.821.240.13
SceneTransformer [38]1.890.801.230.13
HOME+GOHOME [15, 16]1.860.891.290.08
HiVT [56]1.840.771.170.13
MultiPath++ [46]1.790.791.210.13
GANet [48]1.790.811.160.12
PAGA [11]1.760.801.210.11
DCMS [51]1.760.771.140.11
Wayformer [37]1.740.771.160.12
Ours1.690.731.070.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.443, + 0.469, + 0.471 + ], + "angle": 0, + "content": "Table 2. Quantitative results on the Argoverse 1 motion forecasting leaderboard [2]. The leaderboard is sorted by b-minFDE6." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.481, + 0.47, + 0.557 + ], + "angle": 0, + "content": "
ModelOnline Inference (ms)minADE6↓minFDE6↓MR6↓
w/o reusew/ reuse
QCNet (Lenc = 0)8±11±00.761.330.18
QCNet (Lenc = 1)64±110±10.741.300.17
QCNet (Lenc = 2)82±113±10.731.270.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.618 + ], + "angle": 0, + "content": "Table 3. Models' performance and inference latency evaluated on the Argoverse 2 validation set. We use an A40 GPU to measure encoders' online inference latency in the densest traffic scene involving 190 agents and 169 map polygons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.902 + ], + "angle": 0, + "content": "torized attention-based fusion blocks are employed, the encoder does not involve information interactions along different axes of the scene. Even so, the decoder has access to all information required for predictions thanks to the Mode2Scene layers. As shown in the first row of Tab. 3, our model can offer solid prediction performance without fusing the scene context. But after feeding our decoder with the fused encodings, the model gains considerable improvement over its non-fusion variant. Moreover, increasing the number of fusion blocks yields better results on all metrics, demonstrating the effectiveness of factorized attention. However, the resulting inference latency is not amenable to real-time applications such as autonomous driving, making this modeling choice less appealing for widespread adoption. Fortunately, our query-centric paradigm allows the reuse of computations from previous observation windows during online prediction, which goes beyond agent-centric approaches such as HiVT [56]. As shown in Tab. 3, caching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.317 + ], + "angle": 0, + "content": "and reusing the previously computed encodings drastically lowers the online inference latency in the densest traffic scene. Such a \"free lunch\" also provides headroom to design a more advanced decoder for stronger performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.893, + 0.605 + ], + "angle": 0, + "content": "Component Study of the Decoder. As demonstrated in Tab. 4, all layers in the decoder contribute to the performance to a certain degree. First, although the factorized attention in the encoder has already brought context awareness to the agent features, we find that using the target agent's history encodings alone is insufficient for accurate trajectory proposals. We hypothesize that injecting the map and social information into the anchor-free decoder can explicitly provide the queries with the future context, enabling them to narrow the search space for initial trajectories. On the other hand, the map and social information can also help the anchor-based queries identify those unrealistic predictions, such as trajectories that break the traffic rules or collide with static objects on the road. As a result, the role of our refinement module is more than simply trajectory smoothing [23, 51]. Table 4 also shows that removing the Mode2Mode self-attention in either the proposal or the refinement module will harm the long-term accuracy and the diversity of multiple hypotheses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.834 + ], + "angle": 0, + "content": "Table 5 demonstrates the effects of the recurrent mechanism and the refinement module on different datasets. On Argoverse 1, most agents merely exhibit trivial behavior, and the scene context usually does not have significant variation within the 3-second prediction horizon. For this reason, our design choices only bring marginal improvement when evaluated on this dataset. However, on the more challenging Argoverse 2 dataset where the prediction horizon is 6 seconds, increasing the number of recurrent steps from 1 (i.e., no recurrence) to 3 leads to much better long-term performance, and the refinement module offers a dramatic improvement in terms of both accuracy and multimodality. We also notice that using much more recurrent steps is redundant: when increasing the number from 3 to 6, the model performance on Argoverse 2 cannot be further improved." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.682, + 0.862 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We present some qualitative results on the Argoverse 2 validation set. Comparing Fig. 4a and Fig. 4b, we can see" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17869" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.111, + 0.089, + 0.858, + 0.256 + ], + "angle": 0, + "content": "
TimeProposal ModuleRefinement Moduleb-minFDE6↓minADE6↓minFDE6↓MR6↓
MapSocialModeTimeMapSocialMode
✓✓2.220.821.580.22
✓✓✓2.040.781.430.19
✓✓✓2.180.811.550.22
✓✓✓2.060.791.480.21
✓✓✓✓2.020.771.400.19
✓✓✓✓✓✓1.990.741.330.17
✓✓✓✓✓✓✓1.940.741.300.17
✓✓✓✓✓✓✓1.970.741.310.17
✓✓✓✓✓✓✓1.910.731.290.17
✓✓✓✓✓✓✓✓1.900.731.270.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.118, + 0.259, + 0.851, + 0.273 + ], + "angle": 0, + "content": "Table 4. Ablation study on the components of the decoder. Experimental results are based on the Argoverse 2 validation set." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.276, + 0.359, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.139, + 0.579, + 0.334, + 0.589 + ], + "angle": 0, + "content": "(a) w/o recurrence & w/o refinement" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.276, + 0.605, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.579, + 0.577, + 0.589 + ], + "angle": 0, + "content": "(b) w/ recurrence & w/o refinement" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.276, + 0.853, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.579, + 0.821, + 0.589 + ], + "angle": 0, + "content": "(c) w/ recurrence & w/ refinement" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.593, + 0.891, + 0.621 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on the Argoverse 2 validation set. The target agents' bounding boxes and ground-truth trajectories are shown in purple, and models' predictions are shown in pink." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.627, + 0.469, + 0.769 + ], + "angle": 0, + "content": "
Dataset#Recurrent StepRefinementb-minFDE6↓minFDE6↓MR6↓
Argoverse 1 (3-sec pred.)1 (3 sec/step)×1.580.920.09
2 (1.5 sec/step)×1.570.900.08
3 (1 sec/step)×1.560.900.08
3 (1 sec/step)✓1.550.890.08
Argoverse 2 (6-sec pred.)1 (6 sec/step)×2.101.470.20
2 (3 sec/step)×2.041.420.19
3 (2 sec/step)×2.021.400.19
3 (2 sec/step)✓1.901.270.16
6 (1 sec/step)✓1.901.270.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.773, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Table 5. Effects of the trajectory proposal and refinement modules on datasets with varying difficulty levels and prediction horizons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "that the recurrent mechanism of the proposal module can reduce the prediction error in the long term. Figure 4c further demonstrates the effectiveness of the refinement module, which improves the diversity of multiple hypotheses and the smoothness of the predicted trajectories." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.628, + 0.62, + 0.643 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.804 + ], + "angle": 0, + "content": "This paper introduces QCNet, a neural architecture that overcomes some important challenges in trajectory prediction. Powered by the design ethos of query-centric modeling, QCNet maintains the representational capability of factorized attention while enjoying much faster inference. It achieves multimodal and long-term prediction by employing a recurrent, anchor-free trajectory proposal module and an anchor-based refinement module. QCNet exhibits unprecedented performance on large-scale trajectory prediction datasets, demonstrating the effectiveness of its designs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.661, + 0.833 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.9 + ], + "angle": 0, + "content": "This work was partially supported by Hong Kong Research Grant Council under GRF 11200220, Science and Technology Innovation Committee Foundation of Shenzhen under Grant No. JCYJ20200109143223052." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17870" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Argoverse 2: Motion forecasting competition. https://eval.ai/web/challenges/challenge-page/1719/overview. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 1, 2, 3, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.627 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17873" + } + ] +] \ No newline at end of file diff --git a/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_origin.pdf b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c8a2cec6b1178a0eae2bb41fdc9100e30dc42b50 --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/c4e71a3e-e61f-4cf4-92ef-2463bb7fd739_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d6e217869afb59f2f3b980034c51e0294691b409e226ca207f3c37518b1c747 +size 1109771 diff --git a/2023/Query-Centric Trajectory Prediction/full.md b/2023/Query-Centric Trajectory Prediction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0cd1c889950c9be2784414583fa2074e34c9f0f6 --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/full.md @@ -0,0 +1,251 @@ +# Query-Centric Trajectory Prediction + +Zikang Zhou $^{1,2}$ Jianping Wang $^{1,2}$ Yung-Hui Li $^{3}$ Yu-Kai Huang $^{4}$ $^{1}$ City University of Hong Kong $^{2}$ City University of Hong Kong Shenzhen Research Institute + $^{3}$ Hon Hai Research Institute $^{4}$ Carnegie Mellon University + +zikanzhou2-c@my.cityu.edu.hk + +# Abstract + +Predicting the future trajectories of surrounding agents is essential for autonomous vehicles to operate safely. This paper presents QCNet, a modeling framework toward pushing the boundaries of trajectory prediction. First, we identify that the agent-centric modeling scheme used by existing approaches requires re-normalizing and re-encoding the input whenever the observation window slides forward, leading to redundant computations during online prediction. To overcome this limitation and achieve faster inference, we introduce a query-centric paradigm for scene encoding, which enables the reuse of past computations by learning representations independent of the global spacetime coordinate system. Sharing the invariant scene features among all target agents further allows the parallelism of multi-agent trajectory decoding. Second, even given rich encodings of the scene, existing decoding strategies struggle to capture the multimodality inherent in agents' future behavior, especially when the prediction horizon is long. To tackle this challenge, we first employ anchor-free queries to generate trajectory proposals in a recurrent fashion, which allows the model to utilize different scene contexts when decoding waypoints at different horizons. A refinement module then takes the trajectory proposals as anchors and leverages anchor-based queries to refine the trajectories further. By supplying adaptive and high-quality anchors to the refinement module, our query-based decoder can better deal with the multimodality in the output of trajectory prediction. Our approach ranks $1^{st}$ on Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming all methods on all main metrics by a large margin. Meanwhile, our model can achieve streaming scene encoding and parallel multi-agent decoding thanks to the query-centric design ethos. + +# 1. Introduction + +Making safe decisions for autonomous vehicles requires accurate predictions of surrounding agents' future trajectories. In recent years, learning-based methods have been + +![](images/49918b1b7df75fa3d356a17c43f25747238f528ddca67d6ad8e2f7e0c6ca5ef5.jpg) +agent history +Figure 1. Illustration of our query-centric reference frame, where we build a local coordinate system for each spatial-temporal element, including map polygons and agent states at all time steps. In the attention-based encoder, all scene elements' queries are derived and updated in their local reference frames. + +![](images/48b83e0e98bd6607728ccfee4ed95cf6072e635517f50389aea718dd7e6e509d.jpg) +reference frame of agent state +$\rightarrow$ reference frame of map polygon + +widely used for trajectory prediction [14, 31, 37, 38, 46, 56]. Despite the considerable efforts made to enhance models' forecasting ability, there is still a long way to go before fully addressing the problem of trajectory prediction. Why is this task so challenging, and what inability lies in existing approaches? We attempt to answer these questions from the following two perspectives: + +(i) While the flourishing forecasting models have achieved impressive performance on trajectory prediction benchmarks [7, 13, 49], today's most advanced architectures specialized for this task [37, 38, 46, 56] fail to process the heterogeneous traffic scenes efficiently. In an autonomous driving system, data frames arrive at the prediction module sequentially as a stream of sparse scene context, including the high-definition vector map and the surrounding agents' kinematic states. A model must learn expressive representations of these scene elements to achieve accurate forecasts. With the continuing development of modeling techniques for sparse context encoding [14, 31, 50], the research community has witnessed rapid progress toward more powerful trajectory predictors. Notably, factorized attention-based Transformers [37, 38, 56] have recently raised prediction accuracy to an unprecedented level. However, they require learning attention-based representations for each spatial- + +temporal scene element and suffer from prohibitively high costs when processing dense traffic scenes. As every minimal delay may lead to catastrophic accidents in autonomous driving, the unmet need for real-time predictions has limited the applicability of state-of-the-art approaches. + +(ii) The immense uncertainty in the output of trajectory prediction, which grows explosively as the prediction horizon lengthens, has troubled the research community constantly. For example, a vehicle at an intersection may turn or go straight depending on the driver's long-term goal. To avoid missing any potential behavior, a model must learn to capture the underlying multimodal distribution rather than simply predicting the most frequent mode. This learning task is challenging since only one possibility is logged in each training sample. To ease the learning difficulty, a body of works utilizes handcrafted anchors as guidance for multimodal prediction [6, 12, 39, 53, 55]. Their effectiveness, however, is subject to the quality of the anchors. Typically, these methods fail to work well when few anchors can precisely cover the ground truth. This problem is exacerbated in long-term prediction, where the search space for anchors is much larger. Some other works [10, 31, 38, 46, 56] circumvent this issue by directly predicting multiple trajectories, albeit at the risk of mode collapse and training instability [33, 41]. Due to the lack of spatial priors, these methods also fail to produce accurate long-term forecasts. + +The analysis above drives us to propose a trajectory prediction framework, termed as QCNet, to overcome the limitations of previous solutions. First, we note that it is possible to achieve faster online inference while also benefiting from the power of factorized attention, but the agent-centric encoding scheme [25, 27, 46, 56] used by existing methods serves as an impediment. Each time a new data frame arrives, the observation window slides one step forward and overlaps with its predecessor substantially, which provides opportunities for models to reuse the previously computed encodings. However, agent-centric approaches require normalizing the input based on the latest agent states' positions, necessitating the re-encoding of scene elements whenever the observation window slides forward. To address this issue, we introduce a query-centric paradigm for scene encoding (see Fig. 1). The crux of our design ethos lies in processing all scene elements in their local spacetime reference frames and learning representations independent of the global coordinates. This strategy enables us to cache and reuse the previously computed encodings, spreading the computation across all observation windows and thereby reducing inference latency. The invariant scene features can also be shared among all target agents in the scene to enable the parallelism of multi-agent decoding. Second, to better utilize the scene encodings for multimodal and long-term prediction, we use anchor-free queries to retrieve the scene context recurrently and let them decode a short seg + +ment of future waypoints at each recurrence. This recurrent mechanism eases the modeling burden on the queries by allowing them to focus on different scene contexts when predicting waypoints at different horizons. The high-quality trajectories predicted by the recurrent decoder serve as dynamic anchors in the subsequent refinement module, where we use anchor-based queries to refine the trajectory proposals based on the scene context. As a result, our query-based decoding pipeline incorporates the flexibility of anchor-free methods into anchor-based solutions, taking the best of both worlds to facilitate multimodal and long-term prediction. + +Our proposed query-centric encoding paradigm is the first that can exploit the sequential nature of trajectory prediction to achieve fast online inference. Besides, our query-based decoder exhibits superior performance for multimodal and long-term prediction. Experiments show that our approach achieves state-of-the-art results, ranking $1^{\text{st}}$ on two large-scale motion forecasting benchmarks [7, 49]. + +# 2. Related Work + +Scene context fusion encodes rich information for trajectory prediction. Early work rasterizes world states as multichannel images and employs classic convolutional neural networks for learning [5,6,10,21]. Due to the lossy rendering, limited receptive field, and prohibitively high cost of raster-based methods, the research community has turned to a vector-based encoding scheme [14, 31, 50]. With the use of permutation-invariant set operators such as pooling [3, 12, 14, 20, 46], graph convolution [11, 31, 36, 53], and attention mechanism [24, 26, 30, 32, 34, 52], vector-based methods can efficiently aggregate sparse information in traffic scenes. Several powerful trajectory prediction models have recently adopted Transformers [47] with factorized attention as their encoders [18, 37, 38, 56]. Although these models improve efficiency by learning agent-centric representations hierarchically [56] or encoding the whole scene in a shared coordinate system [38], their scalability is still limited by the computational complexity of factorized attention. In comparison, our encoder inherits the representational power of factorized attention while achieving more efficient scene context fusion by using a query-centric encoding paradigm, which goes beyond agent-centric modeling and enables streaming trajectory prediction. + +Multimodal future distribution is a widely adopted output form of trajectory prediction, given that world states are partially observable and agents' intentions are highly uncertain. While generative models naturally fit multimodal prediction [20, 28, 40, 45], sampling from latent variables introduces test-time stochasticity, which is undesirable for safety-critical applications such as autonomous driving. Another line of research tackles multimodality by decoding a discrete set of trajectories from the encoded scene context [6, 10, 31, 55]. Since only one mode is ob- + +served in training data, predicting multiple diverse futures is challenging. Anchor-based methods achieve this with the guidance of anchors, which facilitate multimodal prediction by leveraging predefined maneuvers [12], candidate trajectories [6, 39], or map-adaptive goals [53, 55]. However, the quality of these anchors significantly impacts prediction performance. By contrast, anchor-free methods output multiple hypotheses freely at the risk of mode collapse and training instability [10, 31, 38, 46]. Our decoding pipeline takes advantage of both anchor-based and anchor-free solutions, with an anchor-free module generating adaptive anchors in a data-driven manner and an anchor-based module refining these anchors based on the scene context. + +# 3. Approach + +# 3.1. Input and Output Formulation + +Consider a scenario with $A$ agents surrounding the autonomous vehicle. During online running, the perception module supplies a stream of agent states to the prediction module at a fixed interval, where each agent state is associated with its spatial-temporal position and geometric attributes. For example, the $i$ -th agent's state at time step $t$ comprises the spatial position $\mathbf{p}_i^t = (\mathbf{p}_{i,x}^t,\mathbf{p}_{i,y}^t)$ , the angular position $\theta_{i}^{t}$ (i.e., the yaw angle), the temporal position $t$ (i.e., the time step), and the velocity $\mathbf{v}_i^t$ . We also add the motion vector $\mathbf{p}_i^t -\mathbf{p}_i^{t - 1}$ to the geometric attributes similar to some baselines [31, 56]. Besides, the prediction module has access to $M$ polygons on the high-definition map (e.g., lanes and crosswalks), where each map polygon is annotated with sampled points and semantic attributes (e.g., the user type of a lane). Given the map information and the agent states within an observation window of $T$ time steps, the prediction module is tasked with forecasting $K$ future trajectories for each target agent over a horizon of $T^{\prime}$ time steps and assigning a probability score for each forecast. + +# 3.2. Query-Centric Scene Context Encoding + +The first step of trajectory prediction is to encode the scene input. Recent research has found factorized attention incredibly effective for scene encoding [37, 38, 56]. These approaches let a query element attend to key/value elements along one axis at a time, which results in temporal attention, agent-map attention, and social attention (i.e., agent-agent attention) with the complexity of $\mathcal{O}(AT^2)$ , $\mathcal{O}(ATM)$ , and $\mathcal{O}(A^2T)$ , respectively. Unlike typical encoding strategies that first apply a temporal network to squeeze the time dimension and then perform agent-map and agent-agent fusions at the current time step only, factorized attention conducts fusions at every past time step within the observation window. As a result, factorized attention can capture more information, such as how the relations between agents and map elements evolve over the observation horizon. How + +ever, its scalability is limited by the cubic complexity of each fusion operation. In extreme circumstances involving hundreds of agents and map elements, such models may fail to emit predictions promptly. We ask: is it possible to reduce the inference latency during online prediction while enjoying the representational power of factorized attention? + +Before diving into our solution, recall that trajectory prediction is a streaming processing task: when a new data frame arrives, we put it in the queue and drop the oldest one. Thus, the latest observation window has $T - 1$ time steps overlapping with its predecessor. This fact motivates us to raise another question: can we reuse the overlapped time steps' encodings computed previously after the observation window slides forward? Unfortunately, this idea is infeasible owing to the normalization requirement for trajectory prediction: existing methods employ an agent-centric encoding paradigm for spatially roto-translation invariance [25, 27, 46, 56], where each agent is encoded in the local coordinate frame determined by its current time step's position and yaw angle. Each time the observation window slides forward, the "current time step" also shifts accordingly, and the geometric attributes of all scene elements need to be re-normalized based on the positions of the latest agent states. Due to the variation in input, we are forced to re-encode all time steps' elements even though the observation windows largely overlap. + +Based on the analysis above, we identify that the evolving spacetime coordinate systems hinder the reuse of previously computed encodings. To address this issue, we introduce a query-centric encoding paradigm for learning representations independent of scene elements' global coordinates. Specifically, we establish a local spacetime coordinate system for each scene element that a query vector derives from, processing query elements' features in their local reference frames. Then, we inject the relative spatial-temporal positions into the key and value elements when performing attention-based scene context fusion. We elaborate on the encoding process in the following paragraphs. + +Local Spacetime Coordinate System. Figure 1 shows an example of scene elements' local coordinate systems. For the $i$ -th agent's state at time step $t$ , the local coordinate frame is determined by the reference spatial-temporal position $(\mathbf{p}_i^t, t)$ and the reference direction $\theta_i^t$ , where $\mathbf{p}_i^t$ and $\theta_i^t$ are the agent state's spatial and angular positions, respectively. For lanes and crosswalks, we choose the position and orientation at the entry point of the centerline as the reference. In this way, we build local coordinate systems canonically for all the scene elements considered, resulting in one dedicated local frame per map polygon and $T$ reference frames per agent within any observation window. + +Scene Element Embedding. For each spatial-temporal scene element, such as an agent state or a lane, we compute the polar coordinates of all geometric attributes (e.g., + +the velocity and motion vector of an agent state, the positions of all sampled points on a lane) relative to the spatial point and direction referenced by the element's local frame. Then, we transform each polar coordinate into Fourier features [22, 35, 44] to facilitate learning high-frequency signals. For each agent state and each sampled point on the map, the Fourier features are concatenated with the semantic attributes (e.g., an agent's category) and passed through a multi-layer perceptron (MLP) to obtain an embedding. To further produce polygon-level representations for lanes and crosswalks, we apply attention-based pooling on the embeddings of sampled points within each map polygon. These operations result in agent embeddings of shape $[A, T, D]$ and map embeddings of shape $[M, D]$ , where $D$ denotes the hidden feature dimension. Benefiting from modeling in local reference frames, the embedding of each agent state/map polygon has only one instance and can be reused in the subsequent observation windows. In contrast, agent-centric approaches have to copy all inputs multiple times, encode each copy relative to one of the $A$ agents' current position and heading, and re-encode all inputs whenever the observation window slides forward, leading to much more overhead during online inference. + +Relative Spatial-Temporal Positional Embedding. We prepare the relative positional embeddings for scene element pairs, which will be incorporated into the attention-based operators to help the model be aware of the difference between two elements' local coordinate frames. For an element with absolute spatial-temporal position $(\mathbf{p}_i^t,\boldsymbol {\theta}_i^t,t)$ and another with $(\mathbf{p}_j^s,\boldsymbol {\theta}_j^s,s)$ , we use a 4D descriptor to summarize their relative position, whose components are the relative distance $\left\| \mathbf{p}_j^s -\mathbf{p}_i^t\right\| _2$ , the relative direction $\mathrm{atan2}(\mathbf{p}_{j,y}^{s} - \mathbf{p}_{i,y}^{t},\mathbf{p}_{j,x}^{s} - \mathbf{p}_{i,x}^{t}) - \boldsymbol{\theta}_{i}^{t}$ , the relative orientation $\boldsymbol{\theta}_j^s -\boldsymbol{\theta}_i^t$ and the time gap $s - t$ . Since we can easily reconstruct one element's absolute position from another with the help of the descriptor, we have preserved all spatial-temporal position information of the scene element pair. Then, we transform the 4D descriptor into Fourier features and pass them through an MLP to produce the relative positional embedding $\mathbf{r}_{j\rightarrow i}^{s\rightarrow t}$ . If any of the two scene elements are static (e.g., static map polygons), we can omit the superscript and denote the embedding as $\mathbf{r}_{j\rightarrow i}$ . + +Self-Attention for Map Encoding. We employ self-attention to model the relationships among map elements, after which the updated map encodings will enrich the agent features and assist trajectory decoding. For the $i$ -th map polygon, we derive a query vector from its embedding $\mathbf{m}_i$ and let it attend to the neighboring lanes and crosswalks $\{\mathbf{m}_j\}_{j\in \mathcal{N}_i}$ , where $\mathcal{N}_i$ denotes the neighbor set of the polygon. To incorporate spatial awareness for map encoding, we generate the $j$ -th key/value vector from the concatenation of $\mathbf{m}_j$ and the relative positional embedding, i.e., $[\mathbf{m}_j;\mathbf{r}_{j\rightarrow i}]$ . Since each triple of $(\mathbf{m}_i,\mathbf{m}_j,\mathbf{r}_{j\rightarrow i})$ input to the attention + +![](images/4139b4329f7a463095a56cfdeca10d0337167b4ce19f34f758e29438f01a482b.jpg) +Figure 2. Overview of the encoder in an online mode. After reusing the encodings computed in previous observation windows (blue), the complexity of factorized attention goes from $\mathcal{O}(AT^2) + \mathcal{O}(ATM) + \mathcal{O}(A^2T)$ to $\mathcal{O}(AT) + \mathcal{O}(AM) + \mathcal{O}(A^2)$ . + +layer is independent of the global spacetime coordinate system, the output map encodings $\{\mathbf{m}_i^{\prime}\}_{i = 1}^{M}$ are also invariant under transformations of the global reference frame. Thus, they can be shared across all agents and all time steps and can even be pre-computed offline, thereby avoiding redundant computation suffered by agent-centric modeling. + +Factorized Attention for Agent Encoding. To help the agent embeddings capture more information, we also consider factorized attention across agent time steps, among agents, and between agents and maps. Take the $i$ -th agent at time step $t$ as an example. Given the query vector derived from the agent state's embedding $\mathbf{a}_i^t$ , we employ temporal attention by computing the key and value vectors based on $\{[\mathbf{a}_i^s;\mathbf{r}_{i\rightarrow i}^{s\rightarrow t}]\}_{s = t - \tau}^{t - 1}$ , which are the $i$ -th agent's embeddings from time step $t - \tau$ ( $0 < \tau < T$ ) to time step $t - 1$ and the corresponding relative positional embeddings. Likewise, the key and value vectors for agent-map and social attention are derived from $\{[\mathbf{m}_j';\mathbf{r}_{j\rightarrow i}]\}_{j\in \mathcal{N}_i}$ and $\{[\mathbf{a}_j^t;\mathbf{r}_{j\rightarrow i}^{t\rightarrow t}]\}_{j\in \mathcal{N}_i}$ , respectively, where the neighbor set $\mathcal{N}_i$ is determined by a distance threshold of 50 meters. As a result of updating the initially invariant queries with invariant keys and values, the outputs of these layers are also invariant. We stack the temporal, the agent-map, and the social attention sequentially as one fusion block and repeat such blocks $L_{\mathrm{enc}}$ times. + +Thanks to the query-centric modeling, all the agent and map encodings are unique and fixed no matter from which spacetime coordinate system we view them (i.e., roto-translation invariance for the space dimension and translation invariance for the time dimension), enabling the model to reuse past computations and operate streamingly. During online prediction, we can cache the encodings computed in previous observation windows and incrementally update the scene representation. As shown in Fig. 2, our model only performs factorized attention for the $A$ incoming agent states when a new data frame arrives, resulting in temporal attention with $\mathcal{O}(AT)$ complexity, agent-map attention with $\mathcal{O}(AM)$ complexity, and social attention with $\mathcal{O}(A^2)$ complexity. All of these operations are an order less expensive than their non-streaming counterpart. Finally, we update the cached tensors using the newly computed encodings. + +![](images/55bc5cc5fc0a1dce8112241111669c479a13735df6797f1d2d1e5711525d06fd.jpg) +Figure 3. Overview of the decoding pipeline. An anchor-free module generates trajectory proposals recurrently based on the encoded scene context. These proposals act as the anchors in the refinement module, where an anchor-based decoder refines the anchor trajectories and assigns a probability score for each hypothesis. + +# 3.3. Query-Based Trajectory Decoding + +The second step of trajectory prediction is to utilize the scene encodings output by the encoder to decode $K$ future trajectories for each target agent, which is non-trivial since the encoder returns only one set of feature embeddings. Inspired by the progress in object detection, some recent works [18, 32, 37, 46] employ DETR-like decoders [4] to deal with such a one-to-many problem, where multiple learnable queries cross-attend the scene encodings and decode trajectories. However, these models suffer from training instability and mode collapse like other anchor-free approaches. Moreover, they do not perform well in long-term prediction, where the forecasting task is much more challenging due to the explosive uncertainty in the distant future. Our query-based decoder overcomes these limitations by utilizing a recurrent, anchor-free proposal module to generate adaptive trajectory anchors, followed by an anchor-based module that further refines the initial proposals. An overview of our decoding pipeline is shown in Fig. 3. In the following, we will illustrate the components of the decoder in detail. + +Mode2Scene and Mode2Mode Attention. Both the proposal and refinement modules use a DETR-like architecture. Similar to the concept of object queries in DETR [4], each query takes charge of decoding one of the $K$ trajectory modes. In the Mode2Scene attention, we use cross-attention layers to update the mode queries with multiple contexts, including the history encodings of the target agent, the map encodings, and the neighboring agents' encodings. Following the Mode2Scene attention, the $K$ mode queries "talk" to each other via the Mode2Mode self-attention to improve the diversity of multiple modes. + +Reference Frames of Mode Queries. To predict the trajectories of multiple agents in parallel, we share the same set of scene encodings among all target agents in the scene. As these encodings are derived from their local spacetime coordinate systems, we need to project them into each target agent's current viewpoint to achieve the same effect as + +agent-centric modeling. To this end, we hallucinate a coordinate frame for each mode query based on the corresponding target agent's current position and yaw angle. When updating the query embeddings via Mode2Scene attention, the scene elements' positions relative to the queries are incorporated into the keys and values, which is similar to what we have done for the encoder. + +Anchor-Free Trajectory Proposal. We use learnable, anchor-free queries to propose initial trajectories. These proposals will later act as anchors in the refinement module. Compared with anchor-based methods that attempt to cover the ground truth with densely sampled handcrafted anchors [6, 19], our proposal module generates $K$ adaptive anchors in a data-driven manner. Thanks to the cross-attention layers, the mode queries can retrieve the scene context and quickly narrow the search space for anchors. The self-attention layer further allows the queries to collaborate with each other when generating trajectory proposals. + +Over an extended prediction horizon, an agent can travel a long distance, and its surrounding environment may vary quickly. As a result, it is hard to summarize all information required for decoding a long sequence into a single query embedding. To ease the queries' burden of context extraction and improve the anchors' quality, we generalize the DETR-like decoder to a recurrent fashion. Using $T_{\mathrm{rec}}$ recurrent steps, the context-aware mode queries only decode $T^{\prime} / T_{\mathrm{rec}}$ future waypoints via an MLP at the end of each recurrent step. At the subsequent recurrence, these queries become the input again and extract the scene context relevant to the next few waypoints' prediction. For efficiency, $T_{\mathrm{rec}}$ is far smaller than the prediction horizon $T^{\prime}$ . We also find that using much more recurrent steps is unnecessary. + +Anchor-Based Trajectory Refinement. Anchor-free decoding can be a two-edged sword: despite its flexibility, the unstable training process may lead to mode collapse occasionally. On the other hand, the randomly initialized mode queries must adapt to all target agents in all scenes and lack the scenario-specific bias, which may result in non- + +compliant predictions, such as trajectories that violate the laws of motion or break the traffic rules conveyed by the high-definition map. We are thus motivated to employ an anchor-based module to refine the proposals further. Taking the output of the proposal module as anchors, we let the refinement module predict the offset to the proposed trajectories and estimate the likelihood of each hypothesis. This module also adopts a DETR-like architecture, but its mode queries are derived from the proposed trajectory anchors instead of randomly initialized. Specifically, a small GRU [8] is used to embed each trajectory anchor, and we take its final hidden state as the mode query. These anchor-based queries provide explicit spatial prior for the model, enabling the attention layers to localize the context of interest more easily. + +# 3.4. Training Objectives + +Following HiVT [56], we parameterize the $i$ -th agent's future trajectory as a mixture of Laplace distributions: + +$$ +f \left(\left\{\mathbf {p} _ {i} ^ {t} \right\} _ {t = 1} ^ {T ^ {\prime}}\right) = \sum_ {k = 1} ^ {K} \pi_ {i, k} \prod_ {t = 1} ^ {T ^ {\prime}} \text {L a p l a c e} \left(\mathbf {p} _ {i} ^ {t} \mid \boldsymbol {\mu} _ {i, k} ^ {t}, \mathbf {b} _ {i, k} ^ {t}\right), \tag {1} +$$ + +where $\{\pi_{i,k}\}_{k=1}^{K}$ are the mixing coefficients, and the $k$ -th mixture component's Laplace density at time step $t$ is parameterized by the location $\pmb{\mu}_{i,k}^t$ and the scale $\mathbf{b}_{i,k}^t$ . We then use a classification loss $\mathcal{L}_{\mathrm{cls}}$ to optimize the mixing coefficients predicted by the refinement module. This loss minimizes the negative log-likelihood of Eq. (1), and we stop the gradients of the locations and scales to optimize the mixing coefficients only. On the other hand, we adopt the winner-take-all strategy [29] to optimize the locations and scales output by the proposal and refinement modules, which conducts backpropagation on the best-predicted proposal and its refinement only. For stabilization, the refinement module stops the gradients of the proposed trajectory anchors. The final loss function combines the trajectory proposal loss $\mathcal{L}_{\mathrm{propose}}$ , the trajectory refinement loss $\mathcal{L}_{\mathrm{refine}}$ , and the classification loss $\mathcal{L}_{\mathrm{cls}}$ for end-to-end training: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p r o p o s e}} + \mathcal {L} _ {\text {r e f i n e}} + \lambda \mathcal {L} _ {\text {c l s}}, \tag {2} +$$ + +where we use $\lambda$ to balance regression and classification. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. We use Argoverse 1 [7] and Argoverse 2 [49], two large-scale motion forecasting datasets, to test the efficacy of our approach. The Argoverse 1 dataset collects 323,557 sequences of data from Miami and Pittsburgh, while the Argoverse 2 dataset contains 250,000 scenarios spanning six cities. Both datasets have a sampled rate of $10\mathrm{Hz}$ . For the Argoverse 1 dataset, models need to predict agents' 3-second future trajectories given the 2-second + +observations of history. The Argoverse 2 dataset, in comparison, is featured by improved data diversity, higher data quality, a larger observation window of 5 seconds, and a longer prediction horizon of 6 seconds. Using these two datasets, we intend to examine models' forecasting capability on various data distributions and prediction horizons. + +Metrics. Following the standard evaluation protocol, we adopt metrics including minimum Average Displacement Error $(\min\mathrm{ADE}_K)$ , minimum Final Displacement Error $(\min\mathrm{FDE}_K)$ , Brier-minimum Final Displacement Error (b-minFDE $K$ ), and Miss Rate $(\mathrm{MR}_K)$ for evaluation. The metric $\min\mathrm{ADE}_K$ calculates the $\ell_2$ distance in meters between the ground-truth trajectory and the best of $K$ predicted trajectories as an average of all future time steps. On the other hand, the metric $\min\mathrm{FDE}_K$ only concerns the prediction error at the final time step to emphasize long-term performance. To further measure the performance of uncertainty estimation, the metric b-minFDE $K$ adds $(1 - \hat{\pi})^2$ to the final-step error, where $\hat{\pi}$ denotes the best-predicted trajectory's probability score that the model assigns. Moreover, the metric $\mathrm{MR}_K$ is used for counting the ratio of cases where $\min\mathrm{FDE}_K$ exceeds 2 meters. As a common practice, $K$ is selected as 1 and 6. If a model outputs more than $K$ trajectories, only the predictions with the top- $K$ probability scores are considered during evaluation. + +# 4.2. Comparison with State of the Art + +We compare our method with the strongest baselines on the Argoverse 1 and the Argoverse 2 motion forecasting benchmarks [7, 49]. We first conduct experiments on the Argoverse 2 dataset [49], which favors solutions that work well on long-term prediction, given that its prediction horizon is as long as 6 seconds. The results are shown in Tab. 1. Even without ensembling, QCNet has already outperformed all previous approaches on the Argoverse 2 test set in terms of $\min\mathrm{ADE}_6$ , $\min\mathrm{FDE}_6$ , $\min\mathrm{ADE}_1$ , and $\min\mathrm{FDE}_1$ . After using ensembling techniques similar to other entries, QCNet surpasses all methods on all metrics by a large margin. We also evaluate our model on the Argoverse 1 dataset [7] to better understand the generalizability of our approach. Although the performance on the Argoverse 1 benchmark has saturated for years [49], Tab. 2 shows that QCNet significantly advances state-of-the-art on most metrics. As of the time we submitted the paper, QCNet ranks $1^{st}$ on the leaderboards of Argoverse 1 and Argoverse 2, outperforming all published and unpublished works on the two benchmarks. Please refer to the supplementary material for more results on Argoverse 2 [49] and Waymo Open Motion Dataset [13]. + +# 4.3. Ablation Study + +Effects of Scene Context Fusion. We study the effects of scene context fusion in Tab. 3. The first question we answer is whether factorized attention is worth it. If no fac + +
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓minADE1↓minFDE1↓MR1↓
THOMAS [17]2.160.881.510.201.954.710.64
GoRela [9]2.010.761.480.221.824.620.66
MTR [42]1.980.731.440.151.744.390.58
GANet [48]1.960.721.340.171.774.480.59
QML* [43]1.950.691.390.191.844.980.62
BANet* [54]1.920.711.360.191.794.610.60
QCNet (w/o ensemble)1.910.651.290.161.694.300.59
QCNet (w/ ensemble)1.780.621.190.141.563.960.55
+ +Table 1. Quantitative results on the Argoverse 2 motion forecasting leaderboard [1] ranked by b-minFDE6. Baselines that are known to have used ensembling are marked with symbol “*”. For each metric, the best result is in bold and the second best result is underlined. + +
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓
LaneGCN [31]2.060.871.360.16
mmTransformer [32]2.030.841.340.15
DenseTNT [19]1.980.881.280.13
TPCN [50]1.930.821.240.13
SceneTransformer [38]1.890.801.230.13
HOME+GOHOME [15, 16]1.860.891.290.08
HiVT [56]1.840.771.170.13
MultiPath++ [46]1.790.791.210.13
GANet [48]1.790.811.160.12
PAGA [11]1.760.801.210.11
DCMS [51]1.760.771.140.11
Wayformer [37]1.740.771.160.12
Ours1.690.731.070.11
+ +Table 2. Quantitative results on the Argoverse 1 motion forecasting leaderboard [2]. The leaderboard is sorted by b-minFDE6. + +
ModelOnline Inference (ms)minADE6↓minFDE6↓MR6↓
w/o reusew/ reuse
QCNet (Lenc = 0)8±11±00.761.330.18
QCNet (Lenc = 1)64±110±10.741.300.17
QCNet (Lenc = 2)82±113±10.731.270.16
+ +Table 3. Models' performance and inference latency evaluated on the Argoverse 2 validation set. We use an A40 GPU to measure encoders' online inference latency in the densest traffic scene involving 190 agents and 169 map polygons. + +torized attention-based fusion blocks are employed, the encoder does not involve information interactions along different axes of the scene. Even so, the decoder has access to all information required for predictions thanks to the Mode2Scene layers. As shown in the first row of Tab. 3, our model can offer solid prediction performance without fusing the scene context. But after feeding our decoder with the fused encodings, the model gains considerable improvement over its non-fusion variant. Moreover, increasing the number of fusion blocks yields better results on all metrics, demonstrating the effectiveness of factorized attention. However, the resulting inference latency is not amenable to real-time applications such as autonomous driving, making this modeling choice less appealing for widespread adoption. Fortunately, our query-centric paradigm allows the reuse of computations from previous observation windows during online prediction, which goes beyond agent-centric approaches such as HiVT [56]. As shown in Tab. 3, caching + +and reusing the previously computed encodings drastically lowers the online inference latency in the densest traffic scene. Such a "free lunch" also provides headroom to design a more advanced decoder for stronger performance. + +Component Study of the Decoder. As demonstrated in Tab. 4, all layers in the decoder contribute to the performance to a certain degree. First, although the factorized attention in the encoder has already brought context awareness to the agent features, we find that using the target agent's history encodings alone is insufficient for accurate trajectory proposals. We hypothesize that injecting the map and social information into the anchor-free decoder can explicitly provide the queries with the future context, enabling them to narrow the search space for initial trajectories. On the other hand, the map and social information can also help the anchor-based queries identify those unrealistic predictions, such as trajectories that break the traffic rules or collide with static objects on the road. As a result, the role of our refinement module is more than simply trajectory smoothing [23, 51]. Table 4 also shows that removing the Mode2Mode self-attention in either the proposal or the refinement module will harm the long-term accuracy and the diversity of multiple hypotheses. + +Table 5 demonstrates the effects of the recurrent mechanism and the refinement module on different datasets. On Argoverse 1, most agents merely exhibit trivial behavior, and the scene context usually does not have significant variation within the 3-second prediction horizon. For this reason, our design choices only bring marginal improvement when evaluated on this dataset. However, on the more challenging Argoverse 2 dataset where the prediction horizon is 6 seconds, increasing the number of recurrent steps from 1 (i.e., no recurrence) to 3 leads to much better long-term performance, and the refinement module offers a dramatic improvement in terms of both accuracy and multimodality. We also notice that using much more recurrent steps is redundant: when increasing the number from 3 to 6, the model performance on Argoverse 2 cannot be further improved. + +# 4.4. Qualitative Results + +We present some qualitative results on the Argoverse 2 validation set. Comparing Fig. 4a and Fig. 4b, we can see + +
TimeProposal ModuleRefinement Moduleb-minFDE6↓minADE6↓minFDE6↓MR6↓
MapSocialModeTimeMapSocialMode
✓✓2.220.821.580.22
✓✓✓2.040.781.430.19
✓✓✓2.180.811.550.22
✓✓✓2.060.791.480.21
✓✓✓✓2.020.771.400.19
✓✓✓✓✓✓1.990.741.330.17
✓✓✓✓✓✓✓1.940.741.300.17
✓✓✓✓✓✓✓1.970.741.310.17
✓✓✓✓✓✓✓1.910.731.290.17
✓✓✓✓✓✓✓✓1.900.731.270.16
+ +![](images/5a164a7e5428f72ae5854a3bc49af38dbb05211ec118078dacf423d0b73467b9.jpg) +(a) w/o recurrence & w/o refinement + +![](images/c7c3957988cf9490b84c30f88d4fd7e4c85c85dfa2ec8140f1142881d53f7040.jpg) +(b) w/ recurrence & w/o refinement + +![](images/0fe86ebba88ed038a8dbf7039b61872c2642ca8ed5c0064ab1eafb7b6270fa66.jpg) +(c) w/ recurrence & w/ refinement +Figure 4. Qualitative results on the Argoverse 2 validation set. The target agents' bounding boxes and ground-truth trajectories are shown in purple, and models' predictions are shown in pink. + +Table 4. Ablation study on the components of the decoder. Experimental results are based on the Argoverse 2 validation set. + +
Dataset#Recurrent StepRefinementb-minFDE6↓minFDE6↓MR6↓
Argoverse 1 (3-sec pred.)1 (3 sec/step)×1.580.920.09
2 (1.5 sec/step)×1.570.900.08
3 (1 sec/step)×1.560.900.08
3 (1 sec/step)✓1.550.890.08
Argoverse 2 (6-sec pred.)1 (6 sec/step)×2.101.470.20
2 (3 sec/step)×2.041.420.19
3 (2 sec/step)×2.021.400.19
3 (2 sec/step)✓1.901.270.16
6 (1 sec/step)✓1.901.270.16
+ +Table 5. Effects of the trajectory proposal and refinement modules on datasets with varying difficulty levels and prediction horizons. + +that the recurrent mechanism of the proposal module can reduce the prediction error in the long term. Figure 4c further demonstrates the effectiveness of the refinement module, which improves the diversity of multiple hypotheses and the smoothness of the predicted trajectories. + +# 5. Conclusion + +This paper introduces QCNet, a neural architecture that overcomes some important challenges in trajectory prediction. Powered by the design ethos of query-centric modeling, QCNet maintains the representational capability of factorized attention while enjoying much faster inference. It achieves multimodal and long-term prediction by employing a recurrent, anchor-free trajectory proposal module and an anchor-based refinement module. QCNet exhibits unprecedented performance on large-scale trajectory prediction datasets, demonstrating the effectiveness of its designs. + +# Acknowledgement + +This work was partially supported by Hong Kong Research Grant Council under GRF 11200220, Science and Technology Innovation Committee Foundation of Shenzhen under Grant No. JCYJ20200109143223052. + +# References + +[1] Argoverse 2: Motion forecasting competition. https://eval.ai/web/challenges/challenge-page/1719/overview. Accessed: 2022-11-11. 7 +[2] Argoverse motion forecasting competition. https://eval.ai/web/challenges/challenge-page/454/overview. Accessed: 2022-11-11. 7 +[3] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 1, 2, 3, 6, 7 \ No newline at end of file diff --git a/2023/Query-Centric Trajectory Prediction/images.zip b/2023/Query-Centric Trajectory Prediction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..9b5e1fd34d21044aa9aa32c6d0af112e688b7e73 --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fdfaa8169ca7f0ba5c07238d1bdac077d51cb6cbb35a1d06dd0de96ffbdc92a6 +size 423322 diff --git a/2023/Query-Centric Trajectory Prediction/layout.json b/2023/Query-Centric Trajectory Prediction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bb06d7d4c7e9ce075b809ed5d5c5a879fd63bca6 --- /dev/null +++ b/2023/Query-Centric Trajectory Prediction/layout.json @@ -0,0 +1,8152 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 182, + 103, + 411, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 103, + 411, + 121 + ], + "spans": [ + { + "bbox": [ + 182, + 103, + 411, + 121 + ], + "type": "text", + "content": "Query-Centric Trajectory Prediction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "spans": [ + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": "Zikang Zhou" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": " Jianping Wang" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": " Yung-Hui Li" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": " Yu-Kai Huang" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": "City University of Hong Kong " + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": "City University of Hong Kong Shenzhen Research Institute \n" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": "Hon Hai Research Institute " + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 67, + 141, + 521, + 185 + ], + "type": "text", + "content": "Carnegie Mellon University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 220, + 188, + 373, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 188, + 373, + 198 + ], + "spans": [ + { + "bbox": [ + 220, + 188, + 373, + 198 + ], + "type": "text", + "content": "zikanzhou2-c@my.cityu.edu.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 251, + 290, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 636 + ], + "type": "text", + "content": "Predicting the future trajectories of surrounding agents is essential for autonomous vehicles to operate safely. This paper presents QCNet, a modeling framework toward pushing the boundaries of trajectory prediction. First, we identify that the agent-centric modeling scheme used by existing approaches requires re-normalizing and re-encoding the input whenever the observation window slides forward, leading to redundant computations during online prediction. To overcome this limitation and achieve faster inference, we introduce a query-centric paradigm for scene encoding, which enables the reuse of past computations by learning representations independent of the global spacetime coordinate system. Sharing the invariant scene features among all target agents further allows the parallelism of multi-agent trajectory decoding. Second, even given rich encodings of the scene, existing decoding strategies struggle to capture the multimodality inherent in agents' future behavior, especially when the prediction horizon is long. To tackle this challenge, we first employ anchor-free queries to generate trajectory proposals in a recurrent fashion, which allows the model to utilize different scene contexts when decoding waypoints at different horizons. A refinement module then takes the trajectory proposals as anchors and leverages anchor-based queries to refine the trajectories further. By supplying adaptive and high-quality anchors to the refinement module, our query-based decoder can better deal with the multimodality in the output of trajectory prediction. Our approach ranks " + }, + { + "bbox": [ + 46, + 251, + 290, + 636 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 46, + 251, + 290, + 636 + ], + "type": "text", + "content": " on Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming all methods on all main metrics by a large margin. Meanwhile, our model can achieve streaming scene encoding and parallel multi-agent decoding thanks to the query-centric design ethos." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Making safe decisions for autonomous vehicles requires accurate predictions of surrounding agents' future trajectories. 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Illustration of our query-centric reference frame, where we build a local coordinate system for each spatial-temporal element, including map polygons and agent states at all time steps. In the attention-based encoder, all scene elements' queries are derived and updated in their local reference frames." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 227, + 545, + 341 + ], + "blocks": [ + { + "bbox": [ + 427, + 227, + 545, + 341 + ], + "lines": [ + { + "bbox": [ + 427, + 227, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 427, + 227, + 545, + 341 + ], + "type": "image", + "image_path": "48b83e0e98bd6607728ccfee4ed95cf6072e635517f50389aea718dd7e6e509d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 433, + 341, + 533, + 349 + ], + "lines": [ + { + "bbox": [ + 433, + 341, + 533, + 349 + ], + "spans": [ + { + "bbox": [ + 433, + 341, + 533, + 349 + ], + "type": "text", + "content": "reference frame of agent state" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 433, + 352, + 538, + 360 + ], + "lines": [ + { + "bbox": [ + 433, + 352, + 538, + 360 + ], + "spans": [ + { + "bbox": [ + 433, + 352, + 538, + 360 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 433, + 352, + 538, + 360 + ], + "type": "text", + "content": " reference frame of map polygon" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 422, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 506 + ], + "type": "text", + "content": "widely used for trajectory prediction [14, 31, 37, 38, 46, 56]. Despite the considerable efforts made to enhance models' forecasting ability, there is still a long way to go before fully addressing the problem of trajectory prediction. Why is this task so challenging, and what inability lies in existing approaches? We attempt to answer these questions from the following two perspectives:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "(i) While the flourishing forecasting models have achieved impressive performance on trajectory prediction benchmarks [7, 13, 49], today's most advanced architectures specialized for this task [37, 38, 46, 56] fail to process the heterogeneous traffic scenes efficiently. In an autonomous driving system, data frames arrive at the prediction module sequentially as a stream of sparse scene context, including the high-definition vector map and the surrounding agents' kinematic states. A model must learn expressive representations of these scene elements to achieve accurate forecasts. With the continuing development of modeling techniques for sparse context encoding [14, 31, 50], the research community has witnessed rapid progress toward more powerful trajectory predictors. Notably, factorized attention-based Transformers [37, 38, 56] have recently raised prediction accuracy to an unprecedented level. However, they require learning attention-based representations for each spatial-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17863" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "temporal scene element and suffer from prohibitively high costs when processing dense traffic scenes. As every minimal delay may lead to catastrophic accidents in autonomous driving, the unmet need for real-time predictions has limited the applicability of state-of-the-art approaches." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 135, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 135, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 135, + 288, + 387 + ], + "type": "text", + "content": "(ii) The immense uncertainty in the output of trajectory prediction, which grows explosively as the prediction horizon lengthens, has troubled the research community constantly. For example, a vehicle at an intersection may turn or go straight depending on the driver's long-term goal. To avoid missing any potential behavior, a model must learn to capture the underlying multimodal distribution rather than simply predicting the most frequent mode. This learning task is challenging since only one possibility is logged in each training sample. To ease the learning difficulty, a body of works utilizes handcrafted anchors as guidance for multimodal prediction [6, 12, 39, 53, 55]. Their effectiveness, however, is subject to the quality of the anchors. Typically, these methods fail to work well when few anchors can precisely cover the ground truth. This problem is exacerbated in long-term prediction, where the search space for anchors is much larger. Some other works [10, 31, 38, 46, 56] circumvent this issue by directly predicting multiple trajectories, albeit at the risk of mode collapse and training instability [33, 41]. Due to the lack of spatial priors, these methods also fail to produce accurate long-term forecasts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "type": "text", + "content": "The analysis above drives us to propose a trajectory prediction framework, termed as QCNet, to overcome the limitations of previous solutions. First, we note that it is possible to achieve faster online inference while also benefiting from the power of factorized attention, but the agent-centric encoding scheme [25, 27, 46, 56] used by existing methods serves as an impediment. Each time a new data frame arrives, the observation window slides one step forward and overlaps with its predecessor substantially, which provides opportunities for models to reuse the previously computed encodings. However, agent-centric approaches require normalizing the input based on the latest agent states' positions, necessitating the re-encoding of scene elements whenever the observation window slides forward. To address this issue, we introduce a query-centric paradigm for scene encoding (see Fig. 1). The crux of our design ethos lies in processing all scene elements in their local spacetime reference frames and learning representations independent of the global coordinates. This strategy enables us to cache and reuse the previously computed encodings, spreading the computation across all observation windows and thereby reducing inference latency. The invariant scene features can also be shared among all target agents in the scene to enable the parallelism of multi-agent decoding. Second, to better utilize the scene encodings for multimodal and long-term prediction, we use anchor-free queries to retrieve the scene context recurrently and let them decode a short seg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "ment of future waypoints at each recurrence. This recurrent mechanism eases the modeling burden on the queries by allowing them to focus on different scene contexts when predicting waypoints at different horizons. The high-quality trajectories predicted by the recurrent decoder serve as dynamic anchors in the subsequent refinement module, where we use anchor-based queries to refine the trajectory proposals based on the scene context. As a result, our query-based decoding pipeline incorporates the flexibility of anchor-free methods into anchor-based solutions, taking the best of both worlds to facilitate multimodal and long-term prediction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 204, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 288 + ], + "type": "text", + "content": "Our proposed query-centric encoding paradigm is the first that can exploit the sequential nature of trajectory prediction to achieve fast online inference. Besides, our query-based decoder exhibits superior performance for multimodal and long-term prediction. Experiments show that our approach achieves state-of-the-art results, ranking " + }, + { + "bbox": [ + 304, + 204, + 545, + 288 + ], + "type": "inline_equation", + "content": "1^{\\text{st}}" + }, + { + "bbox": [ + 304, + 204, + 545, + 288 + ], + "type": "text", + "content": " on two large-scale motion forecasting benchmarks [7, 49]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 319, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 594 + ], + "type": "text", + "content": "Scene context fusion encodes rich information for trajectory prediction. Early work rasterizes world states as multichannel images and employs classic convolutional neural networks for learning [5,6,10,21]. Due to the lossy rendering, limited receptive field, and prohibitively high cost of raster-based methods, the research community has turned to a vector-based encoding scheme [14, 31, 50]. With the use of permutation-invariant set operators such as pooling [3, 12, 14, 20, 46], graph convolution [11, 31, 36, 53], and attention mechanism [24, 26, 30, 32, 34, 52], vector-based methods can efficiently aggregate sparse information in traffic scenes. Several powerful trajectory prediction models have recently adopted Transformers [47] with factorized attention as their encoders [18, 37, 38, 56]. Although these models improve efficiency by learning agent-centric representations hierarchically [56] or encoding the whole scene in a shared coordinate system [38], their scalability is still limited by the computational complexity of factorized attention. In comparison, our encoder inherits the representational power of factorized attention while achieving more efficient scene context fusion by using a query-centric encoding paradigm, which goes beyond agent-centric modeling and enables streaming trajectory prediction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Multimodal future distribution is a widely adopted output form of trajectory prediction, given that world states are partially observable and agents' intentions are highly uncertain. While generative models naturally fit multimodal prediction [20, 28, 40, 45], sampling from latent variables introduces test-time stochasticity, which is undesirable for safety-critical applications such as autonomous driving. Another line of research tackles multimodality by decoding a discrete set of trajectories from the encoded scene context [6, 10, 31, 55]. Since only one mode is ob-" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17864" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "served in training data, predicting multiple diverse futures is challenging. Anchor-based methods achieve this with the guidance of anchors, which facilitate multimodal prediction by leveraging predefined maneuvers [12], candidate trajectories [6, 39], or map-adaptive goals [53, 55]. However, the quality of these anchors significantly impacts prediction performance. By contrast, anchor-free methods output multiple hypotheses freely at the risk of mode collapse and training instability [10, 31, 38, 46]. Our decoding pipeline takes advantage of both anchor-based and anchor-free solutions, with an anchor-free module generating adaptive anchors in a data-driven manner and an anchor-based module refining these anchors based on the scene context." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 239, + 113, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 113, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 113, + 253 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 259, + 214, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 214, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 214, + 272 + ], + "type": "text", + "content": "3.1. Input and Output Formulation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": "Consider a scenario with " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " agents surrounding the autonomous vehicle. During online running, the perception module supplies a stream of agent states to the prediction module at a fixed interval, where each agent state is associated with its spatial-temporal position and geometric attributes. For example, the " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": "-th agent's state at time step " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " comprises the spatial position " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^t = (\\mathbf{p}_{i,x}^t,\\mathbf{p}_{i,y}^t)" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": ", the angular position " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\theta_{i}^{t}" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " (i.e., the yaw angle), the temporal position " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " (i.e., the time step), and the velocity " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^t" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": ". We also add the motion vector " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^t -\\mathbf{p}_i^{t - 1}" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " to the geometric attributes similar to some baselines [31, 56]. Besides, the prediction module has access to " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " polygons on the high-definition map (e.g., lanes and crosswalks), where each map polygon is annotated with sampled points and semantic attributes (e.g., the user type of a lane). Given the map information and the agent states within an observation window of " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " time steps, the prediction module is tasked with forecasting " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " future trajectories for each target agent over a horizon of " + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "inline_equation", + "content": "T^{\\prime}" + }, + { + "bbox": [ + 46, + 277, + 289, + 508 + ], + "type": "text", + "content": " time steps and assigning a probability score for each forecast." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 515, + 255, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 255, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 255, + 528 + ], + "type": "text", + "content": "3.2. Query-Centric Scene Context Encoding" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "text", + "content": "The first step of trajectory prediction is to encode the scene input. Recent research has found factorized attention incredibly effective for scene encoding [37, 38, 56]. These approaches let a query element attend to key/value elements along one axis at a time, which results in temporal attention, agent-map attention, and social attention (i.e., agent-agent attention) with the complexity of " + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(AT^2)" + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(ATM)" + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(A^2T)" + }, + { + "bbox": [ + 46, + 534, + 289, + 713 + ], + "type": "text", + "content": ", respectively. Unlike typical encoding strategies that first apply a temporal network to squeeze the time dimension and then perform agent-map and agent-agent fusions at the current time step only, factorized attention conducts fusions at every past time step within the observation window. As a result, factorized attention can capture more information, such as how the relations between agents and map elements evolve over the observation horizon. How" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "ever, its scalability is limited by the cubic complexity of each fusion operation. In extreme circumstances involving hundreds of agents and map elements, such models may fail to emit predictions promptly. We ask: is it possible to reduce the inference latency during online prediction while enjoying the representational power of factorized attention?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 146, + 547, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 547, + 385 + ], + "type": "text", + "content": "Before diving into our solution, recall that trajectory prediction is a streaming processing task: when a new data frame arrives, we put it in the queue and drop the oldest one. Thus, the latest observation window has " + }, + { + "bbox": [ + 304, + 146, + 547, + 385 + ], + "type": "inline_equation", + "content": "T - 1" + }, + { + "bbox": [ + 304, + 146, + 547, + 385 + ], + "type": "text", + "content": " time steps overlapping with its predecessor. This fact motivates us to raise another question: can we reuse the overlapped time steps' encodings computed previously after the observation window slides forward? Unfortunately, this idea is infeasible owing to the normalization requirement for trajectory prediction: existing methods employ an agent-centric encoding paradigm for spatially roto-translation invariance [25, 27, 46, 56], where each agent is encoded in the local coordinate frame determined by its current time step's position and yaw angle. Each time the observation window slides forward, the \"current time step\" also shifts accordingly, and the geometric attributes of all scene elements need to be re-normalized based on the positions of the latest agent states. Due to the variation in input, we are forced to re-encode all time steps' elements even though the observation windows largely overlap." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 387, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 532 + ], + "type": "text", + "content": "Based on the analysis above, we identify that the evolving spacetime coordinate systems hinder the reuse of previously computed encodings. To address this issue, we introduce a query-centric encoding paradigm for learning representations independent of scene elements' global coordinates. Specifically, we establish a local spacetime coordinate system for each scene element that a query vector derives from, processing query elements' features in their local reference frames. Then, we inject the relative spatial-temporal positions into the key and value elements when performing attention-based scene context fusion. We elaborate on the encoding process in the following paragraphs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": "Local Spacetime Coordinate System. Figure 1 shows an example of scene elements' local coordinate systems. For the " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": "-th agent's state at time step " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": ", the local coordinate frame is determined by the reference spatial-temporal position " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}_i^t, t)" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": " and the reference direction " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\theta_i^t" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^t" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\theta_i^t" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": " are the agent state's spatial and angular positions, respectively. For lanes and crosswalks, we choose the position and orientation at the entry point of the centerline as the reference. In this way, we build local coordinate systems canonically for all the scene elements considered, resulting in one dedicated local frame per map polygon and " + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 532, + 547, + 675 + ], + "type": "text", + "content": " reference frames per agent within any observation window." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Scene Element Embedding. For each spatial-temporal scene element, such as an agent state or a lane, we compute the polar coordinates of all geometric attributes (e.g.," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17865" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "content": "the velocity and motion vector of an agent state, the positions of all sampled points on a lane) relative to the spatial point and direction referenced by the element's local frame. Then, we transform each polar coordinate into Fourier features [22, 35, 44] to facilitate learning high-frequency signals. For each agent state and each sampled point on the map, the Fourier features are concatenated with the semantic attributes (e.g., an agent's category) and passed through a multi-layer perceptron (MLP) to obtain an embedding. To further produce polygon-level representations for lanes and crosswalks, we apply attention-based pooling on the embeddings of sampled points within each map polygon. These operations result in agent embeddings of shape " + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "[A, T, D]" + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "content": " and map embeddings of shape " + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "[M, D]" + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "content": " denotes the hidden feature dimension. Benefiting from modeling in local reference frames, the embedding of each agent state/map polygon has only one instance and can be reused in the subsequent observation windows. In contrast, agent-centric approaches have to copy all inputs multiple times, encode each copy relative to one of the " + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 72, + 289, + 347 + ], + "type": "text", + "content": " agents' current position and heading, and re-encode all inputs whenever the observation window slides forward, leading to much more overhead during online inference." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": "Relative Spatial-Temporal Positional Embedding. We prepare the relative positional embeddings for scene element pairs, which will be incorporated into the attention-based operators to help the model be aware of the difference between two elements' local coordinate frames. For an element with absolute spatial-temporal position " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}_i^t,\\boldsymbol {\\theta}_i^t,t)" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": " and another with " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}_j^s,\\boldsymbol {\\theta}_j^s,s)" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": ", we use a 4D descriptor to summarize their relative position, whose components are the relative distance " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\left\\| \\mathbf{p}_j^s -\\mathbf{p}_i^t\\right\\| _2" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": ", the relative direction " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mathrm{atan2}(\\mathbf{p}_{j,y}^{s} - \\mathbf{p}_{i,y}^{t},\\mathbf{p}_{j,x}^{s} - \\mathbf{p}_{i,x}^{t}) - \\boldsymbol{\\theta}_{i}^{t}" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": ", the relative orientation " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\theta}_j^s -\\boldsymbol{\\theta}_i^t" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": " and the time gap " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "s - t" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": ". Since we can easily reconstruct one element's absolute position from another with the help of the descriptor, we have preserved all spatial-temporal position information of the scene element pair. Then, we transform the 4D descriptor into Fourier features and pass them through an MLP to produce the relative positional embedding " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{j\\rightarrow i}^{s\\rightarrow t}" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": ". If any of the two scene elements are static (e.g., static map polygons), we can omit the superscript and denote the embedding as " + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{j\\rightarrow i}" + }, + { + "bbox": [ + 46, + 348, + 289, + 581 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Self-Attention for Map Encoding. We employ self-attention to model the relationships among map elements, after which the updated map encodings will enrich the agent features and assist trajectory decoding. For the " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "-th map polygon, we derive a query vector from its embedding " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_i" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and let it attend to the neighboring lanes and crosswalks " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{m}_j\\}_{j\\in \\mathcal{N}_i}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " denotes the neighbor set of the polygon. To incorporate spatial awareness for map encoding, we generate the " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "-th key/value vector from the concatenation of " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_j" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and the relative positional embedding, i.e., " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "[\\mathbf{m}_j;\\mathbf{r}_{j\\rightarrow i}]" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": ". Since each triple of " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{m}_i,\\mathbf{m}_j,\\mathbf{r}_{j\\rightarrow i})" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " input to the attention" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 547, + 176 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 547, + 176 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 547, + 176 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 547, + 176 + ], + "type": "image", + "image_path": "4139b4329f7a463095a56cfdeca10d0337167b4ce19f34f758e29438f01a482b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "type": "text", + "content": "Figure 2. Overview of the encoder in an online mode. After reusing the encodings computed in previous observation windows (blue), the complexity of factorized attention goes from " + }, + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(AT^2) + \\mathcal{O}(ATM) + \\mathcal{O}(A^2T)" + }, + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(AT) + \\mathcal{O}(AM) + \\mathcal{O}(A^2)" + }, + { + "bbox": [ + 304, + 177, + 547, + 222 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 227, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 545, + 300 + ], + "type": "text", + "content": "layer is independent of the global spacetime coordinate system, the output map encodings " + }, + { + "bbox": [ + 304, + 227, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{m}_i^{\\prime}\\}_{i = 1}^{M}" + }, + { + "bbox": [ + 304, + 227, + 545, + 300 + ], + "type": "text", + "content": " are also invariant under transformations of the global reference frame. Thus, they can be shared across all agents and all time steps and can even be pre-computed offline, thereby avoiding redundant computation suffered by agent-centric modeling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": "Factorized Attention for Agent Encoding. To help the agent embeddings capture more information, we also consider factorized attention across agent time steps, among agents, and between agents and maps. Take the " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": "-th agent at time step " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " as an example. Given the query vector derived from the agent state's embedding " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^t" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": ", we employ temporal attention by computing the key and value vectors based on " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\{[\\mathbf{a}_i^s;\\mathbf{r}_{i\\rightarrow i}^{s\\rightarrow t}]\\}_{s = t - \\tau}^{t - 1}" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": ", which are the " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": "-th agent's embeddings from time step " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "t - \\tau" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "0 < \\tau < T" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": ") to time step " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " and the corresponding relative positional embeddings. Likewise, the key and value vectors for agent-map and social attention are derived from " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\{[\\mathbf{m}_j';\\mathbf{r}_{j\\rightarrow i}]\\}_{j\\in \\mathcal{N}_i}" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\{[\\mathbf{a}_j^t;\\mathbf{r}_{j\\rightarrow i}^{t\\rightarrow t}]\\}_{j\\in \\mathcal{N}_i}" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": ", respectively, where the neighbor set " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " is determined by a distance threshold of 50 meters. As a result of updating the initially invariant queries with invariant keys and values, the outputs of these layers are also invariant. We stack the temporal, the agent-map, and the social attention sequentially as one fusion block and repeat such blocks " + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{enc}}" + }, + { + "bbox": [ + 304, + 301, + 546, + 519 + ], + "type": "text", + "content": " times." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "Thanks to the query-centric modeling, all the agent and map encodings are unique and fixed no matter from which spacetime coordinate system we view them (i.e., roto-translation invariance for the space dimension and translation invariance for the time dimension), enabling the model to reuse past computations and operate streamingly. During online prediction, we can cache the encodings computed in previous observation windows and incrementally update the scene representation. As shown in Fig. 2, our model only performs factorized attention for the " + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": " incoming agent states when a new data frame arrives, resulting in temporal attention with " + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(AT)" + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": " complexity, agent-map attention with " + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(AM)" + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": " complexity, and social attention with " + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(A^2)" + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": " complexity. All of these operations are an order less expensive than their non-streaming counterpart. Finally, we update the cached tensors using the newly computed encodings." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17866" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 541, + 212 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 541, + 212 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 541, + 212 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 541, + 212 + ], + "type": "image", + "image_path": "55bc5cc5fc0a1dce8112241111669c479a13735df6797f1d2d1e5711525d06fd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 547, + 250 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 547, + 250 + ], + "type": "text", + "content": "Figure 3. Overview of the decoding pipeline. An anchor-free module generates trajectory proposals recurrently based on the encoded scene context. These proposals act as the anchors in the refinement module, where an anchor-based decoder refines the anchor trajectories and assigns a probability score for each hypothesis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 252, + 231, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 231, + 265 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 231, + 265 + ], + "type": "text", + "content": "3.3. Query-Based Trajectory Decoding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 289, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 509 + ], + "type": "text", + "content": "The second step of trajectory prediction is to utilize the scene encodings output by the encoder to decode " + }, + { + "bbox": [ + 46, + 270, + 289, + 509 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 270, + 289, + 509 + ], + "type": "text", + "content": " future trajectories for each target agent, which is non-trivial since the encoder returns only one set of feature embeddings. Inspired by the progress in object detection, some recent works [18, 32, 37, 46] employ DETR-like decoders [4] to deal with such a one-to-many problem, where multiple learnable queries cross-attend the scene encodings and decode trajectories. However, these models suffer from training instability and mode collapse like other anchor-free approaches. Moreover, they do not perform well in long-term prediction, where the forecasting task is much more challenging due to the explosive uncertainty in the distant future. Our query-based decoder overcomes these limitations by utilizing a recurrent, anchor-free proposal module to generate adaptive trajectory anchors, followed by an anchor-based module that further refines the initial proposals. An overview of our decoding pipeline is shown in Fig. 3. In the following, we will illustrate the components of the decoder in detail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "text", + "content": "Mode2Scene and Mode2Mode Attention. Both the proposal and refinement modules use a DETR-like architecture. Similar to the concept of object queries in DETR [4], each query takes charge of decoding one of the " + }, + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "text", + "content": " trajectory modes. In the Mode2Scene attention, we use cross-attention layers to update the mode queries with multiple contexts, including the history encodings of the target agent, the map encodings, and the neighboring agents' encodings. Following the Mode2Scene attention, the " + }, + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 510, + 287, + 641 + ], + "type": "text", + "content": " mode queries \"talk\" to each other via the Mode2Mode self-attention to improve the diversity of multiple modes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "content": "Reference Frames of Mode Queries. To predict the trajectories of multiple agents in parallel, we share the same set of scene encodings among all target agents in the scene. As these encodings are derived from their local spacetime coordinate systems, we need to project them into each target agent's current viewpoint to achieve the same effect as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 253, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 335 + ], + "type": "text", + "content": "agent-centric modeling. To this end, we hallucinate a coordinate frame for each mode query based on the corresponding target agent's current position and yaw angle. When updating the query embeddings via Mode2Scene attention, the scene elements' positions relative to the queries are incorporated into the keys and values, which is similar to what we have done for the encoder." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 338, + 546, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 546, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 546, + 470 + ], + "type": "text", + "content": "Anchor-Free Trajectory Proposal. We use learnable, anchor-free queries to propose initial trajectories. These proposals will later act as anchors in the refinement module. Compared with anchor-based methods that attempt to cover the ground truth with densely sampled handcrafted anchors [6, 19], our proposal module generates " + }, + { + "bbox": [ + 304, + 338, + 546, + 470 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 338, + 546, + 470 + ], + "type": "text", + "content": " adaptive anchors in a data-driven manner. Thanks to the cross-attention layers, the mode queries can retrieve the scene context and quickly narrow the search space for anchors. The self-attention layer further allows the queries to collaborate with each other when generating trajectory proposals." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "content": "Over an extended prediction horizon, an agent can travel a long distance, and its surrounding environment may vary quickly. As a result, it is hard to summarize all information required for decoding a long sequence into a single query embedding. To ease the queries' burden of context extraction and improve the anchors' quality, we generalize the DETR-like decoder to a recurrent fashion. Using " + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "content": " recurrent steps, the context-aware mode queries only decode " + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "inline_equation", + "content": "T^{\\prime} / T_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "content": " future waypoints via an MLP at the end of each recurrent step. At the subsequent recurrence, these queries become the input again and extract the scene context relevant to the next few waypoints' prediction. For efficiency, " + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "content": " is far smaller than the prediction horizon " + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "inline_equation", + "content": "T^{\\prime}" + }, + { + "bbox": [ + 304, + 472, + 546, + 639 + ], + "type": "text", + "content": ". We also find that using much more recurrent steps is unnecessary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Anchor-Based Trajectory Refinement. Anchor-free decoding can be a two-edged sword: despite its flexibility, the unstable training process may lead to mode collapse occasionally. On the other hand, the randomly initialized mode queries must adapt to all target agents in all scenes and lack the scenario-specific bias, which may result in non-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17867" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "compliant predictions, such as trajectories that violate the laws of motion or break the traffic rules conveyed by the high-definition map. We are thus motivated to employ an anchor-based module to refine the proposals further. Taking the output of the proposal module as anchors, we let the refinement module predict the offset to the proposed trajectories and estimate the likelihood of each hypothesis. This module also adopts a DETR-like architecture, but its mode queries are derived from the proposed trajectory anchors instead of randomly initialized. Specifically, a small GRU [8] is used to embed each trajectory anchor, and we take its final hidden state as the mode query. These anchor-based queries provide explicit spatial prior for the model, enabling the attention layers to localize the context of interest more easily." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 247, + 162, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 162, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 162, + 259 + ], + "type": "text", + "content": "3.4. Training Objectives" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 265, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 287, + 289 + ], + "type": "text", + "content": "Following HiVT [56], we parameterize the " + }, + { + "bbox": [ + 47, + 265, + 287, + 289 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 265, + 287, + 289 + ], + "type": "text", + "content": "-th agent's future trajectory as a mixture of Laplace distributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 297, + 287, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 297, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 52, + 297, + 287, + 330 + ], + "type": "interline_equation", + "content": "f \\left(\\left\\{\\mathbf {p} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T ^ {\\prime}}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {i, k} \\prod_ {t = 1} ^ {T ^ {\\prime}} \\text {L a p l a c e} \\left(\\mathbf {p} _ {i} ^ {t} \\mid \\boldsymbol {\\mu} _ {i, k} ^ {t}, \\mathbf {b} _ {i, k} ^ {t}\\right), \\tag {1}", + "image_path": "6342383cf39cd93bb4ef6bcc1ea135fd5c8dfb33ff1ba5b71dadd2afc3ce303d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\{\\pi_{i,k}\\}_{k=1}^{K}" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": " are the mixing coefficients, and the " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": "-th mixture component's Laplace density at time step " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": " is parameterized by the location " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{i,k}^t" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": " and the scale " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{i,k}^t" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": ". We then use a classification loss " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": " to optimize the mixing coefficients predicted by the refinement module. This loss minimizes the negative log-likelihood of Eq. (1), and we stop the gradients of the locations and scales to optimize the mixing coefficients only. On the other hand, we adopt the winner-take-all strategy [29] to optimize the locations and scales output by the proposal and refinement modules, which conducts backpropagation on the best-predicted proposal and its refinement only. For stabilization, the refinement module stops the gradients of the proposed trajectory anchors. The final loss function combines the trajectory proposal loss " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{propose}}" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": ", the trajectory refinement loss " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{refine}}" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": ", and the classification loss " + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 338, + 289, + 529 + ], + "type": "text", + "content": " for end-to-end training:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 537, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 537, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 104, + 537, + 287, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {p r o p o s e}} + \\mathcal {L} _ {\\text {r e f i n e}} + \\lambda \\mathcal {L} _ {\\text {c l s}}, \\tag {2}", + "image_path": "0f2e381dbbc1f98aefc48d7a9ac4208918192db6f58792f1969916578841f3e7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "text", + "content": "where we use " + }, + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 558, + 273, + 570 + ], + "type": "text", + "content": " to balance regression and classification." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 599, + 174, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 174, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 174, + 612 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "Datasets. We use Argoverse 1 [7] and Argoverse 2 [49], two large-scale motion forecasting datasets, to test the efficacy of our approach. The Argoverse 1 dataset collects 323,557 sequences of data from Miami and Pittsburgh, while the Argoverse 2 dataset contains 250,000 scenarios spanning six cities. Both datasets have a sampled rate of " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ". For the Argoverse 1 dataset, models need to predict agents' 3-second future trajectories given the 2-second" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "observations of history. The Argoverse 2 dataset, in comparison, is featured by improved data diversity, higher data quality, a larger observation window of 5 seconds, and a longer prediction horizon of 6 seconds. Using these two datasets, we intend to examine models' forecasting capability on various data distributions and prediction horizons." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": "Metrics. Following the standard evaluation protocol, we adopt metrics including minimum Average Displacement Error " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "(\\min\\mathrm{ADE}_K)" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": ", minimum Final Displacement Error " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "(\\min\\mathrm{FDE}_K)" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": ", Brier-minimum Final Displacement Error (b-minFDE " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": "), and Miss Rate " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "(\\mathrm{MR}_K)" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " for evaluation. The metric " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " calculates the " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " distance in meters between the ground-truth trajectory and the best of " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " predicted trajectories as an average of all future time steps. On the other hand, the metric " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " only concerns the prediction error at the final time step to emphasize long-term performance. To further measure the performance of uncertainty estimation, the metric b-minFDE " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " adds " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "(1 - \\hat{\\pi})^2" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " to the final-step error, where " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " denotes the best-predicted trajectory's probability score that the model assigns. Moreover, the metric " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\mathrm{MR}_K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " is used for counting the ratio of cases where " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " exceeds 2 meters. As a common practice, " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " is selected as 1 and 6. If a model outputs more than " + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " trajectories, only the predictions with the top-" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 144, + 546, + 372 + ], + "type": "text", + "content": " probability scores are considered during evaluation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 380, + 485, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 485, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 485, + 392 + ], + "type": "text", + "content": "4.2. Comparison with State of the Art" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": "We compare our method with the strongest baselines on the Argoverse 1 and the Argoverse 2 motion forecasting benchmarks [7, 49]. We first conduct experiments on the Argoverse 2 dataset [49], which favors solutions that work well on long-term prediction, given that its prediction horizon is as long as 6 seconds. The results are shown in Tab. 1. Even without ensembling, QCNet has already outperformed all previous approaches on the Argoverse 2 test set in terms of " + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_6" + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_6" + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_1" + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_1" + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": ". After using ensembling techniques similar to other entries, QCNet surpasses all methods on all metrics by a large margin. We also evaluate our model on the Argoverse 1 dataset [7] to better understand the generalizability of our approach. Although the performance on the Argoverse 1 benchmark has saturated for years [49], Tab. 2 shows that QCNet significantly advances state-of-the-art on most metrics. As of the time we submitted the paper, QCNet ranks " + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 399, + 545, + 651 + ], + "type": "text", + "content": " on the leaderboards of Argoverse 1 and Argoverse 2, outperforming all published and unpublished works on the two benchmarks. Please refer to the supplementary material for more results on Argoverse 2 [49] and Waymo Open Motion Dataset [13]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Effects of Scene Context Fusion. We study the effects of scene context fusion in Tab. 3. The first question we answer is whether factorized attention is worth it. If no fac" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17868" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 523, + 168 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 523, + 168 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 523, + 168 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 523, + 168 + ], + "type": "table", + "html": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓minADE1↓minFDE1↓MR1↓
THOMAS [17]2.160.881.510.201.954.710.64
GoRela [9]2.010.761.480.221.824.620.66
MTR [42]1.980.731.440.151.744.390.58
GANet [48]1.960.721.340.171.774.480.59
QML* [43]1.950.691.390.191.844.980.62
BANet* [54]1.920.711.360.191.794.610.60
QCNet (w/o ensemble)1.910.651.290.161.694.300.59
QCNet (w/ ensemble)1.780.621.190.141.563.960.55
", + "image_path": "501c3b5e59995674cb29ff64a9368d75b1dee593a121c6933d6f59ab185677c3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 201, + 287, + 346 + ], + "blocks": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "type": "text", + "content": "Table 1. Quantitative results on the Argoverse 2 motion forecasting leaderboard [1] ranked by b-minFDE6. Baselines that are known to have used ensembling are marked with symbol “*”. For each metric, the best result is in bold and the second best result is underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 201, + 287, + 346 + ], + "lines": [ + { + "bbox": [ + 48, + 201, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 48, + 201, + 287, + 346 + ], + "type": "table", + "html": "
Methodb-minFDE6↓minADE6↓minFDE6↓MR6↓
LaneGCN [31]2.060.871.360.16
mmTransformer [32]2.030.841.340.15
DenseTNT [19]1.980.881.280.13
TPCN [50]1.930.821.240.13
SceneTransformer [38]1.890.801.230.13
HOME+GOHOME [15, 16]1.860.891.290.08
HiVT [56]1.840.771.170.13
MultiPath++ [46]1.790.791.210.13
GANet [48]1.790.811.160.12
PAGA [11]1.760.801.210.11
DCMS [51]1.760.771.140.11
Wayformer [37]1.740.771.160.12
Ours1.690.731.070.11
", + "image_path": "a0d7cc45388c8146e08d96b9707384cd1c7e6af53343ef1b17382c30f6d10c5b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 47, + 380, + 287, + 441 + ], + "blocks": [ + { + "bbox": [ + 47, + 350, + 287, + 373 + ], + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 373 + ], + "type": "text", + "content": "Table 2. Quantitative results on the Argoverse 1 motion forecasting leaderboard [2]. The leaderboard is sorted by b-minFDE6." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 380, + 287, + 441 + ], + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 441 + ], + "type": "table", + "html": "
ModelOnline Inference (ms)minADE6↓minFDE6↓MR6↓
w/o reusew/ reuse
QCNet (Lenc = 0)8±11±00.761.330.18
QCNet (Lenc = 1)64±110±10.741.300.17
QCNet (Lenc = 2)82±113±10.731.270.16
", + "image_path": "7113f9d51eec42e5179cb017446b62e5134cb6b11a6de4b276de47a76832ddff.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "type": "text", + "content": "Table 3. Models' performance and inference latency evaluated on the Argoverse 2 validation set. We use an A40 GPU to measure encoders' online inference latency in the densest traffic scene involving 190 agents and 169 map polygons." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "content": "torized attention-based fusion blocks are employed, the encoder does not involve information interactions along different axes of the scene. Even so, the decoder has access to all information required for predictions thanks to the Mode2Scene layers. As shown in the first row of Tab. 3, our model can offer solid prediction performance without fusing the scene context. But after feeding our decoder with the fused encodings, the model gains considerable improvement over its non-fusion variant. Moreover, increasing the number of fusion blocks yields better results on all metrics, demonstrating the effectiveness of factorized attention. However, the resulting inference latency is not amenable to real-time applications such as autonomous driving, making this modeling choice less appealing for widespread adoption. Fortunately, our query-centric paradigm allows the reuse of computations from previous observation windows during online prediction, which goes beyond agent-centric approaches such as HiVT [56]. As shown in Tab. 3, caching" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 203, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 251 + ], + "type": "text", + "content": "and reusing the previously computed encodings drastically lowers the online inference latency in the densest traffic scene. Such a \"free lunch\" also provides headroom to design a more advanced decoder for stronger performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 251, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 479 + ], + "type": "text", + "content": "Component Study of the Decoder. As demonstrated in Tab. 4, all layers in the decoder contribute to the performance to a certain degree. First, although the factorized attention in the encoder has already brought context awareness to the agent features, we find that using the target agent's history encodings alone is insufficient for accurate trajectory proposals. We hypothesize that injecting the map and social information into the anchor-free decoder can explicitly provide the queries with the future context, enabling them to narrow the search space for initial trajectories. On the other hand, the map and social information can also help the anchor-based queries identify those unrealistic predictions, such as trajectories that break the traffic rules or collide with static objects on the road. As a result, the role of our refinement module is more than simply trajectory smoothing [23, 51]. Table 4 also shows that removing the Mode2Mode self-attention in either the proposal or the refinement module will harm the long-term accuracy and the diversity of multiple hypotheses." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 480, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 660 + ], + "type": "text", + "content": "Table 5 demonstrates the effects of the recurrent mechanism and the refinement module on different datasets. On Argoverse 1, most agents merely exhibit trivial behavior, and the scene context usually does not have significant variation within the 3-second prediction horizon. For this reason, our design choices only bring marginal improvement when evaluated on this dataset. However, on the more challenging Argoverse 2 dataset where the prediction horizon is 6 seconds, increasing the number of recurrent steps from 1 (i.e., no recurrence) to 3 leads to much better long-term performance, and the refinement module offers a dramatic improvement in terms of both accuracy and multimodality. We also notice that using much more recurrent steps is redundant: when increasing the number from 3 to 6, the model performance on Argoverse 2 cannot be further improved." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We present some qualitative results on the Argoverse 2 validation set. Comparing Fig. 4a and Fig. 4b, we can see" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17869" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 525, + 202 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 525, + 202 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 525, + 202 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 525, + 202 + ], + "type": "table", + "html": "
TimeProposal ModuleRefinement Moduleb-minFDE6↓minADE6↓minFDE6↓MR6↓
MapSocialModeTimeMapSocialMode
✓✓2.220.821.580.22
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✓✓✓✓✓✓✓1.970.741.310.17
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✓✓✓✓✓✓✓✓1.900.731.270.16
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Dataset#Recurrent StepRefinementb-minFDE6↓minFDE6↓MR6↓
Argoverse 1 (3-sec pred.)1 (3 sec/step)×1.580.920.09
2 (1.5 sec/step)×1.570.900.08
3 (1 sec/step)×1.560.900.08
3 (1 sec/step)✓1.550.890.08
Argoverse 2 (6-sec pred.)1 (6 sec/step)×2.101.470.20
2 (3 sec/step)×2.041.420.19
3 (2 sec/step)×2.021.400.19
3 (2 sec/step)✓1.901.270.16
6 (1 sec/step)✓1.901.270.16
", + "image_path": "c8a86ef58e5e8bd591f6970774c5bc23bb0b2fd4da7b678e2011e80456d893ed.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 612, + 287, + 635 + ], + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 635 + ], + "type": "text", + "content": "Table 5. Effects of the trajectory proposal and refinement modules on datasets with varying difficulty levels and prediction horizons." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "that the recurrent mechanism of the proposal module can reduce the prediction error in the long term. Figure 4c further demonstrates the effectiveness of the refinement module, which improves the diversity of multiple hypotheses and the smoothness of the predicted trajectories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 517, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 636 + ], + "type": "text", + "content": "This paper introduces QCNet, a neural architecture that overcomes some important challenges in trajectory prediction. Powered by the design ethos of query-centric modeling, QCNet maintains the representational capability of factorized attention while enjoying much faster inference. It achieves multimodal and long-term prediction by employing a recurrent, anchor-free trajectory proposal module and an anchor-based refinement module. QCNet exhibits unprecedented performance on large-scale trajectory prediction datasets, demonstrating the effectiveness of its designs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "This work was partially supported by Hong Kong Research Grant Council under GRF 11200220, Science and Technology Innovation Committee Foundation of Shenzhen under Grant No. JCYJ20200109143223052." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17870" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Argoverse 2: Motion forecasting competition. https://eval.ai/web/challenges/challenge-page/1719/overview. 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Hivt: Hierarchical vector transformer for multi-agent motion prediction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 1, 2, 3, 6, 7" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17873" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_content_list.json b/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b1fcb3d8a1e148e9bc0653ad7f1c2a960c400b6e --- /dev/null +++ b/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_content_list.json @@ -0,0 +1,1382 @@ +[ + { + "type": "text", + "text": "Query-Dependent Video Representation for Moment Retrieval and Highlight Detection", + "text_level": 1, + "bbox": [ + 250, + 162, + 719, + 201 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "WonJun Moon $^{1,\\ast}$ , Sangeek Hyun $^{1,\\ast}$ , SangUk Park $^{2}$ , Dongchan Park $^{2}$ , Jae-Pil Heo $^{1,\\star}$ , Sungkyunkwan University, Pyler", + "bbox": [ + 154, + 226, + 815, + 261 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wjun0830, hsi1032, jaepilheo}@g.skku.edu, {psycoder, cto}@pyler.tech", + "bbox": [ + 179, + 263, + 784, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 312, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, video moment retrieval and highlight detection (MR/HD) are being spotlighted as the demand for video understanding is drastically increased. The key objective of MR/HD is to localize the moment and estimate clip-wise accordance level, i.e., saliency score, to the given text query. Although the recent transformer-based models brought some advances, we found that these methods do not fully exploit the information of a given query. For example, the relevance between text query and video contents is sometimes neglected when predicting the moment and its saliency. To tackle this issue, we introduce Query-Dependent DETR (QD-DETR), a detection transformer tailored for MR/HD. As we observe the insignificant role of a given query in transformer architectures, our encoding module starts with cross-attention layers to explicitly inject the context of text query into video representation. Then, to enhance the model's capability of exploiting the query information, we manipulate the video-query pairs to produce irrelevant pairs. Such negative (irrelevant) video-query pairs are trained to yield low saliency scores, which in turn, encourages the model to estimate precise accordance between query-video pairs. Lastly, we present an input-adaptive saliency predictor which adaptively defines the criterion of saliency scores for the given video-query pairs. Our extensive studies verify the importance of building the query-dependent representation for MR/HD. Specifically, QD-DETR outperforms state-of-the-art methods on QVHighlights, TVSum, and Charades-STA datasets. Codes are available at github.com/wjun0830/QD-DETR.", + "bbox": [ + 75, + 338, + 473, + 725 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 752, + 208, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Along with the advance of digital devices and platforms, video is now one of the most desired data types for consumers [2, 48]. Although the large information capacity of videos might be beneficial in many aspects, e.g., informative", + "bbox": [ + 75, + 776, + 470, + 834 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$\\checkmark$ Positive Query: Man with curly hair speaks directly to camera", + "$\\times$ Negative Query: Kids exercise in front of parked cars." + ], + "bbox": [ + 552, + 312, + 857, + 333 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a86f160e33c2691cedb409bae525d3850524cf1f8249fd972f6a8404e08f1c0e.jpg", + "image_caption": [ + "Figure 1. Comparison of highlight-ness (saliency score) when relevant and non-relevant queries are given. We found that the existing work only uses queries to play an insignificant role, thereby may not be capable of detecting negative queries and video-query relevance; saliency scores for clips in ground-truth (GT) moments are low and equivalent for positive and negative queries. On the other hand, query-dependent representations of QD-DETR result in corresponding saliency scores to the video-query relevance and precisely localized moments." + ], + "image_footnote": [], + "bbox": [ + 502, + 336, + 890, + 476 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and entertaining, inspecting the videos is time-consuming, so that it is hard to capture the desired moments [1,2].", + "bbox": [ + 497, + 625, + 892, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Indeed, the need to retrieve user-requested or highlight moments within videos is greatly raised. Numerous research efforts were put into the search for the requested moments in the video [1, 12, 13, 30] and summarizing the video highlights [4, 33, 47, 57]. Recently, Moment-DETR [23] further spotlighted the topic by proposing a QVHighlights dataset that enables the model to perform both tasks, retrieving the moments with their highlight-ness, simultaneously.", + "bbox": [ + 497, + 656, + 894, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When describing the moment, one of the most favored types of query is the natural language sentence (text) [1]. While early methods utilized convolution networks [14, 44, 59], recent approaches have shown that deploying the attention mechanism of transformer architecture is more effective to fuse the text query into the video representation. For example, Moment-DETR [23] introduced the transformer", + "bbox": [ + 497, + 769, + 895, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution", + "bbox": [ + 100, + 843, + 213, + 853 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author", + "bbox": [ + 102, + 855, + 230, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23023", + "bbox": [ + 463, + 887, + 504, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "architecture which processes both text and video tokens as input by modifying the detection transformer (DETR), and UMT [31] proposed transformer architectures to take multimodal sources, e.g., video and audio. Also, they utilized the text queries in the transformer decoder. Although they brought breakthroughs in the field of MR/HD with seminal architectures, they overlooked the role of the text query. To validate our claim, we investigate the Moment-DETR [23] in terms of the impact of text query in MR/HD (Fig.1). Given the video clips with a relevant positive query and an irrelevant negative query, we observe that the baseline often neglects the given text query when estimating the query-relevance scores, i.e., saliency scores, for each video clip.", + "bbox": [ + 75, + 125, + 472, + 305 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose Query-Dependent DETR (QD-DETR) that produces query-dependent video representation. Our key focus is to ensure that the model's prediction for each clip is highly dependent on the query. First, to fully utilize the contextual information in the query, we revise the transformer encoder to be equipped with cross-attention layers at the very first layers. By inserting a video as the query and a text as the key and value of the cross-attention layers, our encoder enforces the engagement of the text query in extracting video representation. Then, in order to not only inject a lot of textual information into the video feature but also make it fully exploited, we leverage the negative video-query pairs generated by mixing the original pairs. Specifically, the model is learned to suppress the saliency scores of such negative (irrelevant) pairs. Our expectation is the increased contribution of the text query in prediction since the videos will be sometimes required to yield high saliency scores and sometimes low ones depending on whether the text query is relevant or not. Lastly, to apply the dynamic criterion to mark highlights for each instance, we deploy a saliency token to represent the entire video and utilize it as an input-adaptive saliency criterion. With all components combined, our QD-DETR produces query-dependent video representation by integrating source and query modalities. This further allows the use of positional queries [29] in the transformer decoder. Overall, our superior performances over the existing approaches validate the significance of the role of text query for MR/HD.", + "bbox": [ + 75, + 305, + 472, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 77, + 709, + 218, + 723 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Moment Retrieval and Highlight Detection", + "text_level": 1, + "bbox": [ + 77, + 733, + 440, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "MR is the task of localizing the moment relevant to the given text description. Popular approaches are modeling the cross-modal interaction between text query-video pair [32, 54, 56] or understanding the context of the temporal relation among video clips [1, 59]. On the other hand, TVT [24] exploited the additional data, i.e., subtitle, to capture the moment, and FVMR [14] enhanced the model in terms of inference speed for efficient MR.", + "bbox": [ + 75, + 755, + 472, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from the MR, HD aims to measure the clipwise importance level of the given video [41, 52]. Due to its popularity and applicability, HD can be divided into several branches. From the perspective of annotation, we can categorize HD into supervised, weakly supervised, and unsupervised HD. Supervised HD [15, 41, 50] utilizes fine-grained highlight scores, which are very expensive to collect and annotate [49]. On the other hand, weakly supervised HD [5, 36, 49] learns to detect segments as highlights with video event labels, and finally, unsupervised HD [4, 22, 33, 38] does not require any annotations. Also, while the task is often implemented only with the video, there are works to employ the extra data modalities. Generally, multi-modality was taken into account by using the natural language query to find the desired thumbnail [30] and using additional sources, i.e., audio, to predict highlights [3, 53].", + "bbox": [ + 497, + 125, + 894, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the MR/HD share a common objective to localize or discover the desired part of the given video, they have been studied separately. To handle these tasks at once, Moment-DETR [23] proposed the QVHighlights dataset, which contains a human-written text query and its corresponding moment with clip-level saliency labels. They also introduced the modified version of detection transformer (DETR [6]) to localize the query-relevant moments and their saliency scores. Following them, UMT [31] focused on processing multi-modal data by utilizing both video and audio features. Different from recent works deploying transformer architectures, here we concentrate on producing a query-dependent representation with the transformer.", + "bbox": [ + 497, + 347, + 895, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Detection Transformers", + "text_level": 1, + "bbox": [ + 499, + 540, + 719, + 554 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DETR [6], an end-to-end object detector based on vision transformers, is one of the very recent works that utilize the transformer architectures for computer vision [11,42]. Although DETR suffered from slow convergence, it simplifies the prediction process by eliminating the need for anchor generation and non-maximum suppression. Since then, along with the advance in DETR [10, 25, 60], DETR-like architectures have been popular in downstream tasks in both the image [8, 9, 20, 58] and video domains [23, 51]. Some of these works focused on analyzing the role of the decoder query and discovered that using the positional information speeds up the training and also enhances the detection performance [29, 34]. On the other hand, there are trials to extend the application of DETR on multi-modal data [21, 23], especially dealing with the query from different modalities, i.e., text, for detection (or retrieval). They generally handle the multi-modal data by simply forwarding them together to the transformer. In this paper, we also focus on handling the multi-modal data based on DETR-like architecture. However, different from the aforementioned techniques, we concentrate on the query-dependency of the prediction results.", + "bbox": [ + 497, + 562, + 895, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23024", + "bbox": [ + 463, + 887, + 505, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d660976ee35c69d277aaa39e3c913b05f31a8a86da29fa087230ae61ca5af7a8.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed QD-DETR architecture. Given a video and text query, we first extract video and text features from the frozen backbones. These video and text features are forwarded into the cross-attention transformer (Sec. 3.1). This process ensures the consistent contribution of text queries to the video tokens and together with negative pair learning (Sec. 3.2), builds query-dependent video representation. Then, accompanied by the saliency token (Sec. 3.3), video tokens are given to the transformer encoder. In this procedure, the saliency token is transformed into the adaptive saliency prediction criteria. The outputs of the encoder are then, processed to compute losses for both HD and MR. Specifically, the encoder's output tokens are directly projected to saliency scores and optimized for HD, and also provided to the transformer decoder with the learnable moment queries to estimate the query-described moments. Finally, losses for MR are computed by the discrepancy between predicted and their corresponding GT moments." + ], + "image_footnote": [], + "bbox": [ + 77, + 123, + 890, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Query-Dependent DETR", + "text_level": 1, + "bbox": [ + 75, + 458, + 314, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moment retrieval and highlight detection have the common objective to find preferred moments with the text query. Given a video of $L$ clips and a text query with $N$ words, we denote their representations as $\\{v_{1}, v_{2}, \\dots, v_{L}\\}$ and $\\{t_{1}, t_{2}, \\dots, t_{N}\\}$ extracted by frozen video and text encoders, respectively. With these representations, the main objective is to localize the center coordinate $m_{c}$ and width $m_{\\sigma}$ within the video and rank the highlight score (saliency score) $\\{s_{1}, s_{2}, \\dots, s_{L}\\}$ for each clip. A straightforward approach to utilize transformer [11, 43] for the MR is to make a moment-wise prediction as a set of clips [23], or generating the moment according to the clip-wise predictions [31]. To exploit the multi-modal information, e.g., video and text query, they either simply concatenated the features across the modalities or inserted the texts to form the moment query to the transformer decoder. However, we claim that the relationship between the video and text query should be carefully considered rather than a simple concatenation since MR/HD requires every video clip to be conditionally assessed with the text queries.", + "bbox": [ + 75, + 486, + 472, + 764 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our overall architecture is described in Fig. 2, following the design of concrete baseline, Moment-DETR [23]. Given a video and query representation extracted from fixed backbones, QD-DETR first transforms the video representation to be query-dependent using cross-attention layers. To further enhance the query-awareness of video representations, we incorporate irrelevant video-query pairs with a low saliency", + "bbox": [ + 75, + 769, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for the learning objective. Then, along with the transformer encoder-decoder architectures, the saliency token is defined that turns into an adaptive saliency predictor when attended by the specific video instance.", + "bbox": [ + 497, + 459, + 894, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Cross-Attentive Transformer Encoder", + "text_level": 1, + "bbox": [ + 497, + 524, + 828, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this subsection, we use italic letters to represent query, key, and value of the cross-attention layers. The key objective of the encoder for MR/HD is to produce clip-wise representations equipped with information regarding the degree of query-relevance since these features are directly used for retrieving the query-matched moments and predicting clip-wise saliency scores. However, the encoding process of existing works may not ensure the query conditioning on every clip. For example, Moment-DETR [23] naively concatenated the video with the query for input to the self-attention layers, which may result in an insignificant role of the query if the high similarities among the video clips overwhelm the contribution of the text query. On the other hand, UMT [31] utilizes the text query only for the synthesis of a moment query in the transformer decoder so thus resulting video representations are not associated with the text query.", + "bbox": [ + 497, + 547, + 894, + 769 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To take the textual contexts into every video clip representation, we deploy cross-attention layers between the source and the query modalities at the very first layers of the encoder. This ensures the consistent contribution of the query, thereby extracting query-dependent video representation. In detail, whereas the query for cross-attention layers is prepared by projecting the video clips as $Q_{v} = [p_{q}(v_{1}),\\dots,p_{q}(v_{L})]$ , the", + "bbox": [ + 497, + 769, + 895, + 868 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23025", + "bbox": [ + 463, + 887, + 505, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4ea1714826ce73f8a10547dcddf1e9ec9efc479d268679d8e40f2e80a6126076.jpg", + "image_caption": [ + "Figure 3. Illustration of negative pair learning. Typical HL loss is defined only with a positive video-query pair, which is insufficient to learn various degrees of query-relevance. On the other hand, our negative pair learning enforces the model to yield different scores for a video depending on the query and to be learned to suppress saliency scores for the negative query." + ], + "image_footnote": [], + "bbox": [ + 87, + 138, + 468, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "key and value are computed with the query text features as $K_{t} = [p_{k}(t_{1}),\\dots,p_{k}(t_{N})]$ and $V_{t} = [p_{v}(t_{1}),\\dots,p_{v}(t_{N})]$ . $p_q(\\cdot), p_k(\\cdot)$ , and $p_v(\\cdot)$ are projection layers for query, key, and value. Then, the cross-attention layer operates as follows:", + "bbox": [ + 75, + 370, + 472, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(Q _ {v}, K _ {t}, V _ {t}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {v} K _ {t} ^ {T}}{\\sqrt {d}}\\right) V _ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 447, + 468, + 480 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d$ is the dimension of the projected key, value, and query. Since the softmax scores are distributed only over the query elements, video clips are expressed with the weighted sum of the text queries in proportion to the similarity to texts. Attention scores are then projected through MLP and integrated into the original video representations as the typical transformer layers. For the rest of the paper, we define the query-dependent video tokens, i.e., the output of cross-attention layers, as $X = \\{x_{v}^{1}, x_{v}^{2}, \\ldots, x_{v}^{L}\\}$ .", + "bbox": [ + 75, + 488, + 468, + 615 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning from Negative Relationship", + "text_level": 1, + "bbox": [ + 75, + 622, + 400, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the cross-attention layers explicitly fuse the video and query features for intermediate video clip representations to engage the query information in an architectural way, we argue that given video-text pairs lack diversity to learn the general relationship. For instance, many consecutive clips in a single video often share similar appearances, and the similarity to a specific query will not be highly distinguishable, thereby, the text query may not much affect the prediction.", + "bbox": [ + 75, + 644, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we consider the relationships between irrelevant pairs of videos inspired by many recognition practices [17, 26, 27, 35] that learn discriminative features across different categories. To implement such relationships, we define given training video-query pairs as positive pairs and mix the video and query from different pairs to construct negative pairs. Fig. 3 illustrates the ways to augment such negative pairs", + "bbox": [ + 75, + 769, + 470, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and utilize them with positive pairs in training. While the video clips in positive pairs are trained to yield segmented saliency scores according to the query-relevance, irrelevant negative video-query pairs are enforced to have the lowest saliency scores. Formally, the loss function for suppressing the saliency of negative pairs $x_{v}^{\\mathrm{neg}}$ are expressed as follows:", + "bbox": [ + 497, + 125, + 892, + 209 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {n e g}} = - \\log \\left(1 - S \\left(x _ {v} ^ {\\text {n e g}}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 216, + 892, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S(\\cdot)$ is the saliency score predictor. This training scheme can also prevent the model from predicting the moments and highlights solely based on the inter-relationship among video clips without consideration of the query-relevance since the same video instance should be predicted differently depending on whether the positive or negative query is given.", + "bbox": [ + 497, + 239, + 894, + 336 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Input-Adaptive Saliency Predictor", + "text_level": 1, + "bbox": [ + 497, + 343, + 800, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Naive implementation for saliency predictor $S(\\cdot)$ would be stacking one or more fully-connected layers. However, such a general head provides identical criteria for the saliency prediction of every video-query pair, neglecting the diverse nature of video and natural language query pairs. This violates our key idea to extract query-dependent video representation.", + "bbox": [ + 497, + 364, + 892, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we define the saliency token $x_{s}$ to be utilized as an input-adaptive saliency predictor. Briefly, the saliency token is a randomly initialized learnable vector that becomes an input-adaptive predictor when added to the sequence of encoded video tokens and projected through the transformer encoder. To illustrate, as shown in Fig. 2, we first concatenate the saliency token with the query-dependent video tokens $X$ . We process these tokens to the transformer encoder which makes the saliency token to be re-organized with the input-dependent contexts. Consequently, saliency and video tokens are projected by a corresponding single fully-connected layer with weights, $w_{s}$ and $w_{v}$ , respectively, where their scaled-dot product becomes the saliency scores. Formally, saliency score $S(x_{v}^{i})$ is computed as follows:", + "bbox": [ + 497, + 461, + 894, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS \\left(x _ {v} ^ {i}\\right) = \\frac {\\boldsymbol {w} _ {s} ^ {T} \\boldsymbol {x} _ {s} \\cdot \\boldsymbol {w} _ {v} ^ {T} x _ {v} ^ {i}}{\\sqrt {d}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 661, + 892, + 693 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d$ is the channel dimension of projected tokens.", + "bbox": [ + 497, + 699, + 853, + 713 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Decoder and Objectives", + "text_level": 1, + "bbox": [ + 497, + 720, + 719, + 735 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transformer Decoder. Recently, understanding the role of the query in the detection transformer is being spotlighted [29, 34]. It is verified that designing the query with the positional information helps not only for acceleration of training but also for enhancing accuracy. Yet, it is hard to directly employ these studies in tasks handling multi-modal data, e.g., MR/HD, since multi-modal data often have different definitions of position; the position can be understood as time in the video and word order in the text.", + "bbox": [ + 497, + 741, + 892, + 865 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Highlight detection loss", + "bbox": [ + 368, + 127, + 482, + 137 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23026", + "bbox": [ + 463, + 887, + 505, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "On the contrary, our architectural design eliminates the need to feed the text query to the decoder since the query information is already taken into the video representations. To this end, we modify the 2D dynamic anchor boxes [29] to represent 1D moments in the video. Specifically, we utilize the center coordinate $m_{c}$ and the duration $m_{\\sigma}$ of the moments to design the queries. Similarly to the previous way in the image domain, we pool the features around the center coordinate and modulate the cross-attention map with the moment duration. Then, the coordinates and durations are layer-wisely revised.", + "bbox": [ + 75, + 125, + 472, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Functions. Training objectives for QD-DETR include loss functions for MR/HD, respectively. First, objective functions for MR, in which the key focus is to locate the desired moments, are adopted from the baseline [23]. Moment retrieval loss $L_{\\mathrm{mr}}$ measures the discrepancy between the GT moment and the predicted counterpart. It consists of a $L1$ loss and a generalized IoU loss $L_{\\mathrm{gIoU}}(\\cdot)$ from previous work [37] with minor modification to localize temporal moments. Additionally, the cross-entropy loss is used to classify the predicted moments as $\\hat{y}$ either to foreground and background by $L_{\\mathrm{CE}} = -\\sum_{y \\in Y} y \\log(\\hat{y})$ where $\\{\\mathrm{fg}, \\mathrm{bg}\\} \\subset Y$ . Thus, $L_{\\mathrm{mr}}$ is defined as follows:", + "bbox": [ + 75, + 300, + 473, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {m r}} = \\lambda_ {L 1} | | m - \\hat {m} | | + \\lambda_ {\\mathrm {g I o U}} L _ {\\mathrm {g I o U}} (m, \\hat {m}) + \\lambda_ {\\mathrm {C E}} L _ {\\mathrm {C E}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 479, + 470, + 495 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $m$ and $\\hat{m}$ are ground-truth moment and its correspond prediction containing center coordinate $m_{c}$ and duration $m_{\\sigma}$ . Also, $\\lambda_{*}$ are hyperparameters for balancing the losses.", + "bbox": [ + 75, + 505, + 470, + 548 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss functions for HD are to estimate the saliency score. It comprises two components; margin ranking loss $L_{\\mathrm{margin}}$ and rank-aware contrastive loss $L_{\\mathrm{cont}}$ . Following [23], the margin rank loss operates with two pairs of high-rank and low-rank clips. To be specific, the high-rank clips are ensured to retain higher saliency scores than both the low-rank clips within the GT moment and the negative clips outside the GT moment. In short, $L_{\\mathrm{margin}}$ is defined as:", + "bbox": [ + 75, + 549, + 470, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {m a r g i n}} = \\max (0, \\Delta + S \\left(x ^ {\\text {l o w}}\\right) - S \\left(x ^ {\\text {h i g h}}\\right)) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 671, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta$ is the margin, $S(\\cdot)$ is the saliency score estimator, and $x^{\\mathrm{high}}$ and $x^{\\mathrm{low}}$ are video tokens from two pairs of high and low-rank clips, respectively. In addition to margin loss which only indirectly guides the saliency predictor, we employ rank-aware contrastive loss [18] to learn the precisely segmented saliency levels with the contrastive loss. Given the maximum rank value $R$ , each clip in the mini-batch has a saliency score lower than $R$ . Then, we iterate the batch for $R$ times, each time utilizing the samples with higher saliency scores than the iteration index ( $r \\in \\{0, 1, \\dots, R - 1\\}$ ) to build the positive set $X_r^{\\mathrm{pos}}$ . Samples with a lower rank than the iteration index are included in the negative set $X_r^{\\mathrm{neg}}$ . Then,", + "bbox": [ + 75, + 700, + 472, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the rank-aware contrastive loss $L_{\\mathrm{cont}}$ is defined as:", + "bbox": [ + 499, + 125, + 830, + 138 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c o n t}} = - \\sum_ {r = 1} ^ {R} \\log \\frac {\\sum_ {x \\in X _ {r} ^ {\\text {p o s}}} \\exp (S (x) / \\tau)}{\\sum_ {x \\in \\left(X _ {r} ^ {\\text {p o s}} \\cup X _ {r} ^ {\\text {n e g}}\\right)} \\exp (S (x) / \\tau)} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 148, + 892, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature scaling parameter. Note that, $X_{\\tau}^{\\mathrm{neg}}$ also include all clips in negative pairs $x_{v}^{\\mathrm{neg}}$ defined in Sec. 3.2. Finally with margin loss and rank-aware contrastive loss, $L_{\\mathrm{hl}}$ and total loss function $L_{\\mathrm{total}}$ are defined as follows:", + "bbox": [ + 497, + 194, + 892, + 251 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {h l}} = \\lambda_ {\\text {m a r g i n}} L _ {\\text {m a r g i n}} + \\lambda_ {\\text {c o n t}} L _ {\\text {c o n t}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 260, + 892, + 276 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {t o t a l}} = L _ {\\mathrm {h l}} + L _ {\\mathrm {m r}} + \\lambda_ {\\mathrm {n e g}} L _ {\\mathrm {n e g}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 277, + 892, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 499, + 302, + 616, + 317 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 499, + 325, + 705, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and Evaluation Metrics. For the evaluation, we validate the effectiveness of query-dependent source representation on QVHighlights [23], TVSum [40], Charades-STA [13]. QVHighlights is the most recently publicized dataset for both moment retrieval and highlight detection. It is also the only dataset that has annotations for both tasks. In detail, QVHighlights consists of over 10,000 videos annotated with human-written text queries. It provides a fair benchmark as the evaluation for the test split can only be measured through submitting the prediction to the QVHighlights server1. Charades-STA and TVSum are the dataset for moment retrieval and video summarization, respectively. Each of them contains 9,848 videos regarding indoor activities and 50 videos of various genres, e.g., news, documentary, and vlog. For all datasets, we follow the data splits from the existing works [23, 31].", + "bbox": [ + 497, + 346, + 894, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To measure the performances, we use the same evaluation metrics used in the baselines. Specifically, recall@1 with IoU thresholds 0.5 and 0.7, and mean average precision (mAP) at different thresholds. Similarly, we use mAP and HIT@1 for evaluating the highlight detection. HIT@1 is computed through the hit ratio of the highest-scored clip.", + "bbox": [ + 497, + 568, + 892, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 499, + 657, + 700, + 673 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare QD-DETR against baselines in MR and HD throughout Tab. 1, Tab. 3, and Tab. 2. Our experiments with multi-modal sources, i.e., video with audio, are implemented by simply concatenating the video and audio along the channel axis. Throughout the tables, we use bolds to denote the best scores.", + "bbox": [ + 497, + 679, + 892, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Tab. 1, the task is to jointly learn and predict MR/HD. As observed, our QD-DETR outperforms state-of-the-art (SOTA) approaches with all evaluation metrics. Among methods utilizing the video source, QD-DETR shows a dramatic increase with stricter metrics with high IOU; it outperforms previous SOTA by large margins up", + "bbox": [ + 497, + 762, + 892, + 847 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1 https://codalab.lisn.upsaclay.fr/competitions/6937", + "bbox": [ + 517, + 853, + 786, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23027", + "bbox": [ + 463, + 887, + 504, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/17ba11897741b48417c63a267da5fe53c3f0729a51b4e360bb5398a2ae9b38d5.jpg", + "table_caption": [ + "Table 1. Performance comparison on QVHighlights test split. V and A in the Src column denote video and audio, respectively, representing the modalities of the source data. Our experiments are averaged over five runs and $\\pm$ denotes the standard deviation." + ], + "table_footnote": [], + "table_body": "
MethodSrcMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
BeautyThumb [39]V-----14.3620.88
DVSE [30]V-----18.7521.79
MCN [1]V11.412.7224.948.2210.67--
CAL [12]V25.4911.5423.407.659.89--
XML [24]V41.8330.3544.6331.7332.1434.4955.25
XML+ [24]V46.6933.4647.8934.6734.9035.3855.06
Moment-DETR [23]V52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
QD-DETR (Ours)V62.40±1.144.98±0.862.52±0.639.88±0.739.86±0.638.94±0.462.40±1.4
UMT [31]V+A56.2341.1853.3837.0136.1238.1859.99
QD-DETR (Ours)V+A63.06±1.045.10±0.763.04±0.940.10±1.040.19±0.639.04±0.362.87±0.6
", + "bbox": [ + 95, + 157, + 870, + 328 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e172e88f6e9dd6c454767b837a18e2bcd35308c865965894e13f0f7782a9a2a2.jpg", + "table_caption": [ + "Table 2. Highlight detection performance comparison on TVsum dataset." + ], + "table_footnote": [], + "table_body": "
MethodSrcVTVUGAMSPKPRFMBKBTDSAvg.
sLSTM [57]V41.146.246.347.744.846.145.240.647.145.545.1
SG [33]V42.347.247.548.945.647.346.441.748.346.646.2
LIM-S [49]V55.942.961.254.060.347.543.266.369.162.656.3
Trailer [45]V61.354.665.760.859.170.158.264.765.668.162.8
SL-Module [50]V86.568.774.986.279.063.258.972.678.964.073.3
QD-DETR (Ours)V88.287.485.685.085.886.976.491.389.273.785.0
MINI-Net [19]V+A80.668.378.281.878.165.857.875.080.265.573.2
TCG [53]V+A85.071.481.978.680.275.571.677.378.668.176.8
Joint-VA [3]V+A83.757.378.586.180.169.270.073.097.467.576.3
UMT [31]V+A87.581.588.278.881.487.076.086.984.479.683.1
QD-DETR (Ours)V+A87.691.790.288.384.188.378.791.287.877.786.6
", + "bbox": [ + 139, + 363, + 823, + 522 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c4e935c3e40d098a0612fd450190056a8e3a34740198990b99712b91a7ef7d73.jpg", + "table_caption": [ + "Table 3. Charades dataset. $\\dagger$ denotes the method using the video and audio as the source. $\\mathrm{SF + C}$ stands for Slowfast and CLIP features." + ], + "table_footnote": [], + "table_body": "
MethodfeatR1@0.5R1@0.7MethodfeatR1@0.5R1@0.7
SAPVGG27.4213.36CTRLC3D23.638.89
TripNetVGG36.6114.50ACLC3D30.4812.20
SM-RLVGG24.3611.17RWM-RLC3D36.70-
MANVGG41.2420.54MANC3D46.5322.72
2D-TANVGG40.9422.85DEBUGC3D37.3917.69
FVMRVGG42.3624.14VSLNetC3D47.3130.19
UMT†VGG48.3129.25OursC3D50.6731.02
OursVGG52.7731.13M-DETRSF+C53.6331.37
Ours†VGG55.5134.17OursSF+C57.3132.55
", + "bbox": [ + 78, + 576, + 468, + 692 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to $36\\%$ in R1@0.7 and mAP@0.75. On the other hand, QD-DETR with video and audio sources boosts $11.84\\%$ on average of the metrics for MR compared to the SOTA method employing the multi-modal source data. These results verify the importance of emphasizing the source (video-only or video+audio) descriptive contexts in the text queries.", + "bbox": [ + 75, + 723, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results in Tab. 3 also compare MR performances against the models using VGG [7,14,31,46,55,59], C3D [13,16,28,32,55,56], and Slowfast (SF) and CLIP features [23] on Charades dataset. For a fair comparison, we enumerate", + "bbox": [ + 75, + 809, + 470, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "each method with its backbone and compare within it. For each feature from VGG, C3D, and $\\mathrm{SF + C}$ , we follow the data preparation settings from UMT [31], VSLNet [56], and Moment-DETR [23]. As reported, we validate that our model surpasses the existing SOTA methods in every type of feature.", + "bbox": [ + 497, + 542, + 892, + 624 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For video highlight detection in Tab. 2, we follow the protocols from the previous work [31]. Specifically, we train the model for each category and average the mAP scores. Out of 10 categories, QD-DETR outperforms baselines on 9 categories when the only video source is available, and 8 categories when both video and audio are available. Overall, compared to methods with video-only and multi-modal sources, QD-DETR establishes new SOTA performances by improving by $4.2\\%$ in average compared to the previous SOTA model.", + "bbox": [ + 497, + 625, + 894, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 499, + 774, + 650, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To investigate the effectiveness of each component in our work, we conduct an extensive ablation study in Tab. 4. Note that, CATE and DAM denote cross-attentive transformer encoder and dynamic anchor moments, respectively. Rows (b) to (e) show the effectiveness of each component compared to", + "bbox": [ + 497, + 796, + 894, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23028", + "bbox": [ + 463, + 887, + 505, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7e1e9dbab5c615803e366858508c8fb2758d1e4b4dc8a447fc04721197e1b462.jpg", + "table_caption": [ + "Table 4. Ablation study on QVHighlights val split. CATE and DAM stands for cross-attentive transformer encoder and using dynamic anchor moments as the decoder query, respectively. All the quantities are averaged over 5 runs." + ], + "table_footnote": [], + "table_body": "
CATENeg. PairSaliency TokenDAMMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
(a)52.8933.0254.8229.4030.7335.6955.60
(b)✓56.1638.7156.4833.4234.0737.1458.34
(c)✓58.6939.8358.3934.8435.4039.0262.81
(d)✓55.4837.0055.8126.7532.8437.4858.59
(e)✓53.1935.9155.5832.5533.3335.6855.56
(f)✓✓57.7242.3559.1038.1638.0336.5657.44
(g)✓✓59.5742.1259.1936.6336.7638.6461.62
(h)✓✓60.0040.9759.2135.4135.8939.0662.88
(i)✓✓✓60.3242.3959.4736.7936.9339.2162.76
(j)✓✓✓✓62.6846.6662.2341.8241.2239.1363.03
", + "bbox": [ + 119, + 163, + 845, + 334 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a62571bd5984ace8068cc9c920e7bfaf1c6c2436a545f5f68a6307dcf2784306.jpg", + "table_caption": [ + "Table 5. Ablation study on cross-attention transformer encoder. We compare ours against the deepened transformer encoder with self-attention layers to validate that the performance gain does not come from additional parameters. SATE and CATE each indicate the transformer encoder only with self-attention layers and our transformer encoder. The numbers in the parenthesis denote the number of layers. For the experiment with $\\dagger$ , we only use the query features as the condition in the encoder and only the video representations are processed by the decoder." + ], + "table_footnote": [], + "table_body": "
T2VMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
Moment-DETR (SATE 2)52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
Moment-DETR (SATE 4)53.60±1.235.81±0.954.55±0.830.64±0.731.74±0.435.96±0.256.56±0.9
Moment-DETR (CATE 4)55.10±0.737.02±0.956.21±0.332.00±0.933.19±0.636.43±0.356.98±0.6
Moment-DETR (CATE 4)†56.16±1.238.71±1.156.48±0.833.42±0.734.07±0.637.14±0.458.34±0.4
QD-DETR (SATE 4)†60.48±0.745.21±1.060.84±0.540.45±0.740.12±0.638.66±0.261.29±1.0
QD-DETR (CATE 4)†62.68±1.146.66±0.662.23±1.041.82±0.941.22±0.439.13±0.363.03±0.5
", + "bbox": [ + 115, + 423, + 850, + 543 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f9f83d68d6afd571326eef548b593903c4eee81bbb86a5b269cb84fa69eed0ac.jpg", + "image_caption": [ + "Figure 4. Ablation study in terms of saliency scores. We plot the histograms of the average value of saliency scores in each video when the positive and negative text queries are given. For positive scores, we only account the scores within GT moments. The average value of each histogram are visualized by the dotted line. The decrease in the overlap between histograms and the increase in the gap between average values confirms the gradual improvements of significance of the query in extracting video representation." + ], + "image_footnote": [], + "bbox": [ + 90, + 568, + 460, + 769 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the baseline (a). To explain, whereas (e) only boosts the MR performances since it only affects the transformer decoder, (b), (c), and (d) are especially beneficial for both MR/HD tasks since they are focused on query-dependent video representations; (b) ensures the contributions of text query in the video representation, (c) fully exploits the contexts of the text query, and (d) provides input-adaptive saliency predictor instead of MLP. Moreover, while our components are verified that they are all complementary to others, DAM's effectiveness is especially dependent on the usage of CATE (compare between $\\{(a,e)\\}$ and $\\{(b,f),(i,j)\\}$ ). We claim that this is because DAM exploits the position information of the input tokens to capture the corresponding moments. However, without CATE, input tokens are a mixture of multi-modal tokens, thereby providing confusing position information.", + "bbox": [ + 497, + 566, + 894, + 774 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To provide in-depth examinations of each component, we inspect the difference between the positive and the negative saliency scores in Fig. 4. Since the role of text query is trivial in our baseline, each distribution significantly overlies on top of the other. Then, as we add CATE and negative pair learning, we observe a consistent decrease in overlapped", + "bbox": [ + 497, + 783, + 894, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23029", + "bbox": [ + 463, + 887, + 504, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67d07897ce050568b87a5b1df74a5ace352ca8594eba538c76ceb53b5889315b.jpg", + "image_caption": [ + "Figure 5. Visualization of results predicted by QD-DETR. Predicted and ground-truth moments are bounded by the lines. Blue, green, and red lines indicate the saliency scores for positive, semi-positive, and negative queries. The positive saliency scores are consistently higher than the others, while the scores for semi-positive are higher than the ones for the negative." + ], + "image_footnote": [], + "bbox": [ + 82, + 123, + 890, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "areas and a larger gap between the average saliency scores of positive and negative histograms. Also, we believe that the widely-distributed histogram of saliency scores for the 'CATE+Neg_pair' is due to using an identical criterion for saliency prediction for diverse video-query representations. By employing an input-adaptive saliency predictor, we notice that scores for positive queries are in almost optimal shape.", + "bbox": [ + 75, + 394, + 468, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, some might ask whether CATE benefits the training because of additional encoder layers. To answer this, we conduct another ablation study in Tab. 5. Briefly, since our transformer encoder utilizes 2 cross-attention layers and 2 self-attention layers, we conduct comparisons against the transformer encoder composed of 4 self-attention layers (SATE). First, we compare CATE and SATE on MomentDETR; by comparing the results in $2^{\\mathrm{nd}}$ and $3^{\\mathrm{rd}}$ rows, we find that CATE is much more beneficial than SATE even with the same number of layers. Furthermore, the last two rows show comparisons within QD-DETR architecture that has the same tendency. These results clearly demonstrate that the improvements from CATE are mainly from emphasizing the role of the text query rather than additional layers.", + "bbox": [ + 75, + 491, + 470, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 75, + 692, + 258, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we study how the query-dependent video representation sensitively reacts to the change in the contexts of the text query. In Fig. 5, the measured saliency scores according to the video-query relevance are visualized. We found that the more the query is relevant to the video clips, the higher the saliency scores retained for the query. For instance, whereas the negative query that is totally irrelevant to the video instance has the lowest scores, the scores for semi-positive reside between the positive and the negative ones. Also, we find that QD-DETR sometimes provides a more precise moment prediction than a given ground-truth", + "bbox": [ + 75, + 714, + 470, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "moment, as can be seen with the temporal box bounded by the dotted lines. We believe that the tendency of a bit higher saliency scores at non-relevant clips for a positive query is due to the information mixing in the self-attention layers.", + "bbox": [ + 497, + 394, + 892, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation and Conclusion", + "text_level": 1, + "bbox": [ + 497, + 459, + 749, + 473 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation As elaborated in the paper, we aim to highlight the role of the text query in retrieving the relevant moments and estimating their accordance level with the given text query. Likewise, the proposed components expect a given query to maintain a meaningful context. If not, and noisy text queries are provided, i.e., mismatched or irrelevant ground truth texts, the training may not be effective as reported.", + "bbox": [ + 497, + 482, + 892, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion Although the advent of transformer architecture has been powerful for MR/HD, investigation of the role of text query has been lacking in such architectures. Therefore, we focused on studying the role of the text query. As we found that the textual information is not fully exploited in expressing the video representations, we designed the cross-attentive transformer encoder and proposed a negative-pair training scheme. Cross-attentive encoder assures the query's contributions while extracting video representation, and negative-pair training enforces the model to learn the relationship between query and video by preventing solving the problems without consideration of the query. Finally, to preserve the diversity of query-dependent video representation, we defined the saliency token to be an input-adaptive saliency predictor. Extensive experiments validated the strength of QD-DETR with superior performances.", + "bbox": [ + 497, + 584, + 894, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported in part by MSIT/IITP (No. 2022-0-00680, 2019-0-00421, 2020-0-01821, 2021-0-02068), and MSIT&KNPA/KIPoT (Police Lab 2.0, No. 210121M06).", + "bbox": [ + 497, + 809, + 894, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23030", + "bbox": [ + 463, + 887, + 505, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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International Conference on Learning Representations, ICLR 2021, 2021. 2" + ], + "bbox": [ + 78, + 125, + 470, + 706 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23033", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_model.json b/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0dafaa7c293094ec64e18d1c4acb674186222995 --- /dev/null +++ b/2023/Query-Dependent Video Representation for Moment Retrieval and Highlight Detection/244f80b9-7720-4627-a98e-406a817fbf7d_model.json @@ -0,0 +1,2092 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.251, + 0.163, + 0.72, + 0.203 + ], + "angle": 0, + "content": "Query-Dependent Video Representation for Moment Retrieval and Highlight Detection" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.228, + 0.816, + 0.262 + ], + "angle": 0, + "content": "WonJun Moon\\(^{1,\\ast}\\), Sangeek Hyun\\(^{1,\\ast}\\), SangUk Park\\(^{2}\\), Dongchan Park\\(^{2}\\), Jae-Pil Heo\\(^{1,\\star}\\), Sungkyunkwan University, Pyler" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.264, + 0.785, + 0.278 + ], + "angle": 0, + "content": "{wjun0830, hsi1032, jaepilheo}@g.skku.edu, {psycoder, cto}@pyler.tech" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.339, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Recently, video moment retrieval and highlight detection (MR/HD) are being spotlighted as the demand for video understanding is drastically increased. The key objective of MR/HD is to localize the moment and estimate clip-wise accordance level, i.e., saliency score, to the given text query. Although the recent transformer-based models brought some advances, we found that these methods do not fully exploit the information of a given query. For example, the relevance between text query and video contents is sometimes neglected when predicting the moment and its saliency. To tackle this issue, we introduce Query-Dependent DETR (QD-DETR), a detection transformer tailored for MR/HD. As we observe the insignificant role of a given query in transformer architectures, our encoding module starts with cross-attention layers to explicitly inject the context of text query into video representation. Then, to enhance the model's capability of exploiting the query information, we manipulate the video-query pairs to produce irrelevant pairs. Such negative (irrelevant) video-query pairs are trained to yield low saliency scores, which in turn, encourages the model to estimate precise accordance between query-video pairs. Lastly, we present an input-adaptive saliency predictor which adaptively defines the criterion of saliency scores for the given video-query pairs. Our extensive studies verify the importance of building the query-dependent representation for MR/HD. Specifically, QD-DETR outperforms state-of-the-art methods on QVHighlights, TVSum, and Charades-STA datasets. Codes are available at github.com/wjun0830/QD-DETR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.753, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.777, + 0.471, + 0.835 + ], + "angle": 0, + "content": "Along with the advance of digital devices and platforms, video is now one of the most desired data types for consumers [2, 48]. Although the large information capacity of videos might be beneficial in many aspects, e.g., informative" + }, + { + "type": "text", + "bbox": [ + 0.554, + 0.313, + 0.858, + 0.325 + ], + "angle": 0, + "content": "\\(\\checkmark\\) Positive Query: Man with curly hair speaks directly to camera" + }, + { + "type": "text", + "bbox": [ + 0.554, + 0.325, + 0.82, + 0.334 + ], + "angle": 0, + "content": "\\(\\times\\) Negative Query: Kids exercise in front of parked cars." + }, + { + "type": "list", + "bbox": [ + 0.554, + 0.313, + 0.858, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.337, + 0.892, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.598 + ], + "angle": 0, + "content": "Figure 1. Comparison of highlight-ness (saliency score) when relevant and non-relevant queries are given. We found that the existing work only uses queries to play an insignificant role, thereby may not be capable of detecting negative queries and video-query relevance; saliency scores for clips in ground-truth (GT) moments are low and equivalent for positive and negative queries. On the other hand, query-dependent representations of QD-DETR result in corresponding saliency scores to the video-query relevance and precisely localized moments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.894, + 0.655 + ], + "angle": 0, + "content": "and entertaining, inspecting the videos is time-consuming, so that it is hard to capture the desired moments [1,2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.895, + 0.768 + ], + "angle": 0, + "content": "Indeed, the need to retrieve user-requested or highlight moments within videos is greatly raised. Numerous research efforts were put into the search for the requested moments in the video [1, 12, 13, 30] and summarizing the video highlights [4, 33, 47, 57]. Recently, Moment-DETR [23] further spotlighted the topic by proposing a QVHighlights dataset that enables the model to perform both tasks, retrieving the moments with their highlight-ness, simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.896, + 0.868 + ], + "angle": 0, + "content": "When describing the moment, one of the most favored types of query is the natural language sentence (text) [1]. While early methods utilized convolution networks [14, 44, 59], recent approaches have shown that deploying the attention mechanism of transformer architecture is more effective to fuse the text query into the video representation. For example, Moment-DETR [23] introduced the transformer" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.844, + 0.214, + 0.855 + ], + "angle": 0, + "content": "* Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.856, + 0.231, + 0.867 + ], + "angle": 0, + "content": "* Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.102, + 0.844, + 0.231, + 0.867 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "23023" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.306 + ], + "angle": 0, + "content": "architecture which processes both text and video tokens as input by modifying the detection transformer (DETR), and UMT [31] proposed transformer architectures to take multimodal sources, e.g., video and audio. Also, they utilized the text queries in the transformer decoder. Although they brought breakthroughs in the field of MR/HD with seminal architectures, they overlooked the role of the text query. To validate our claim, we investigate the Moment-DETR [23] in terms of the impact of text query in MR/HD (Fig.1). Given the video clips with a relevant positive query and an irrelevant negative query, we observe that the baseline often neglects the given text query when estimating the query-relevance scores, i.e., saliency scores, for each video clip." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.473, + 0.695 + ], + "angle": 0, + "content": "To this end, we propose Query-Dependent DETR (QD-DETR) that produces query-dependent video representation. Our key focus is to ensure that the model's prediction for each clip is highly dependent on the query. First, to fully utilize the contextual information in the query, we revise the transformer encoder to be equipped with cross-attention layers at the very first layers. By inserting a video as the query and a text as the key and value of the cross-attention layers, our encoder enforces the engagement of the text query in extracting video representation. Then, in order to not only inject a lot of textual information into the video feature but also make it fully exploited, we leverage the negative video-query pairs generated by mixing the original pairs. Specifically, the model is learned to suppress the saliency scores of such negative (irrelevant) pairs. Our expectation is the increased contribution of the text query in prediction since the videos will be sometimes required to yield high saliency scores and sometimes low ones depending on whether the text query is relevant or not. Lastly, to apply the dynamic criterion to mark highlights for each instance, we deploy a saliency token to represent the entire video and utilize it as an input-adaptive saliency criterion. With all components combined, our QD-DETR produces query-dependent video representation by integrating source and query modalities. This further allows the use of positional queries [29] in the transformer decoder. Overall, our superior performances over the existing approaches validate the significance of the role of text query for MR/HD." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.22, + 0.724 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.734, + 0.442, + 0.749 + ], + "angle": 0, + "content": "2.1. Moment Retrieval and Highlight Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.473, + 0.868 + ], + "angle": 0, + "content": "MR is the task of localizing the moment relevant to the given text description. Popular approaches are modeling the cross-modal interaction between text query-video pair [32, 54, 56] or understanding the context of the temporal relation among video clips [1, 59]. On the other hand, TVT [24] exploited the additional data, i.e., subtitle, to capture the moment, and FVMR [14] enhanced the model in terms of inference speed for efficient MR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Different from the MR, HD aims to measure the clipwise importance level of the given video [41, 52]. Due to its popularity and applicability, HD can be divided into several branches. From the perspective of annotation, we can categorize HD into supervised, weakly supervised, and unsupervised HD. Supervised HD [15, 41, 50] utilizes fine-grained highlight scores, which are very expensive to collect and annotate [49]. On the other hand, weakly supervised HD [5, 36, 49] learns to detect segments as highlights with video event labels, and finally, unsupervised HD [4, 22, 33, 38] does not require any annotations. Also, while the task is often implemented only with the video, there are works to employ the extra data modalities. Generally, multi-modality was taken into account by using the natural language query to find the desired thumbnail [30] and using additional sources, i.e., audio, to predict highlights [3, 53]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.897, + 0.528 + ], + "angle": 0, + "content": "Although the MR/HD share a common objective to localize or discover the desired part of the given video, they have been studied separately. To handle these tasks at once, Moment-DETR [23] proposed the QVHighlights dataset, which contains a human-written text query and its corresponding moment with clip-level saliency labels. They also introduced the modified version of detection transformer (DETR [6]) to localize the query-relevant moments and their saliency scores. Following them, UMT [31] focused on processing multi-modal data by utilizing both video and audio features. Different from recent works deploying transformer architectures, here we concentrate on producing a query-dependent representation with the transformer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.72, + 0.555 + ], + "angle": 0, + "content": "2.2. Detection Transformers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.897, + 0.868 + ], + "angle": 0, + "content": "DETR [6], an end-to-end object detector based on vision transformers, is one of the very recent works that utilize the transformer architectures for computer vision [11,42]. Although DETR suffered from slow convergence, it simplifies the prediction process by eliminating the need for anchor generation and non-maximum suppression. Since then, along with the advance in DETR [10, 25, 60], DETR-like architectures have been popular in downstream tasks in both the image [8, 9, 20, 58] and video domains [23, 51]. Some of these works focused on analyzing the role of the decoder query and discovered that using the positional information speeds up the training and also enhances the detection performance [29, 34]. On the other hand, there are trials to extend the application of DETR on multi-modal data [21, 23], especially dealing with the query from different modalities, i.e., text, for detection (or retrieval). They generally handle the multi-modal data by simply forwarding them together to the transformer. In this paper, we also focus on handling the multi-modal data based on DETR-like architecture. However, different from the aforementioned techniques, we concentrate on the query-dependency of the prediction results." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "23024" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.124, + 0.891, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.334, + 0.896, + 0.438 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed QD-DETR architecture. Given a video and text query, we first extract video and text features from the frozen backbones. These video and text features are forwarded into the cross-attention transformer (Sec. 3.1). This process ensures the consistent contribution of text queries to the video tokens and together with negative pair learning (Sec. 3.2), builds query-dependent video representation. Then, accompanied by the saliency token (Sec. 3.3), video tokens are given to the transformer encoder. In this procedure, the saliency token is transformed into the adaptive saliency prediction criteria. The outputs of the encoder are then, processed to compute losses for both HD and MR. Specifically, the encoder's output tokens are directly projected to saliency scores and optimized for HD, and also provided to the transformer decoder with the learnable moment queries to estimate the query-described moments. Finally, losses for MR are computed by the discrepancy between predicted and their corresponding GT moments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.459, + 0.315, + 0.475 + ], + "angle": 0, + "content": "3. Query-Dependent DETR" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Moment retrieval and highlight detection have the common objective to find preferred moments with the text query. Given a video of \\( L \\) clips and a text query with \\( N \\) words, we denote their representations as \\( \\{v_{1}, v_{2}, \\dots, v_{L}\\} \\) and \\( \\{t_{1}, t_{2}, \\dots, t_{N}\\} \\) extracted by frozen video and text encoders, respectively. With these representations, the main objective is to localize the center coordinate \\( m_{c} \\) and width \\( m_{\\sigma} \\) within the video and rank the highlight score (saliency score) \\( \\{s_{1}, s_{2}, \\dots, s_{L}\\} \\) for each clip. A straightforward approach to utilize transformer [11, 43] for the MR is to make a moment-wise prediction as a set of clips [23], or generating the moment according to the clip-wise predictions [31]. To exploit the multi-modal information, e.g., video and text query, they either simply concatenated the features across the modalities or inserted the texts to form the moment query to the transformer decoder. However, we claim that the relationship between the video and text query should be carefully considered rather than a simple concatenation since MR/HD requires every video clip to be conditionally assessed with the text queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Our overall architecture is described in Fig. 2, following the design of concrete baseline, Moment-DETR [23]. Given a video and query representation extracted from fixed backbones, QD-DETR first transforms the video representation to be query-dependent using cross-attention layers. To further enhance the query-awareness of video representations, we incorporate irrelevant video-query pairs with a low saliency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.518 + ], + "angle": 0, + "content": "for the learning objective. Then, along with the transformer encoder-decoder architectures, the saliency token is defined that turns into an adaptive saliency predictor when attended by the specific video instance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.526, + 0.83, + 0.54 + ], + "angle": 0, + "content": "3.1. Cross-Attentive Transformer Encoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.895, + 0.77 + ], + "angle": 0, + "content": "In this subsection, we use italic letters to represent query, key, and value of the cross-attention layers. The key objective of the encoder for MR/HD is to produce clip-wise representations equipped with information regarding the degree of query-relevance since these features are directly used for retrieving the query-matched moments and predicting clip-wise saliency scores. However, the encoding process of existing works may not ensure the query conditioning on every clip. For example, Moment-DETR [23] naively concatenated the video with the query for input to the self-attention layers, which may result in an insignificant role of the query if the high similarities among the video clips overwhelm the contribution of the text query. On the other hand, UMT [31] utilizes the text query only for the synthesis of a moment query in the transformer decoder so thus resulting video representations are not associated with the text query." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.896, + 0.869 + ], + "angle": 0, + "content": "To take the textual contexts into every video clip representation, we deploy cross-attention layers between the source and the query modalities at the very first layers of the encoder. This ensures the consistent contribution of the query, thereby extracting query-dependent video representation. In detail, whereas the query for cross-attention layers is prepared by projecting the video clips as \\( Q_{v} = [p_{q}(v_{1}),\\dots,p_{q}(v_{L})] \\), the" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "23025" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.369, + 0.128, + 0.484, + 0.138 + ], + "angle": 0, + "content": "Highlight detection loss" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.139, + 0.47, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.471, + 0.348 + ], + "angle": 0, + "content": "Figure 3. Illustration of negative pair learning. Typical HL loss is defined only with a positive video-query pair, which is insufficient to learn various degrees of query-relevance. On the other hand, our negative pair learning enforces the model to yield different scores for a video depending on the query and to be learned to suppress saliency scores for the negative query." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.371, + 0.473, + 0.44 + ], + "angle": 0, + "content": "key and value are computed with the query text features as \\( K_{t} = [p_{k}(t_{1}),\\dots,p_{k}(t_{N})] \\) and \\( V_{t} = [p_{v}(t_{1}),\\dots,p_{v}(t_{N})] \\). \\( p_q(\\cdot), p_k(\\cdot) \\), and \\( p_v(\\cdot) \\) are projection layers for query, key, and value. Then, the cross-attention layer operates as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.448, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(Q _ {v}, K _ {t}, V _ {t}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {v} K _ {t} ^ {T}}{\\sqrt {d}}\\right) V _ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.47, + 0.616 + ], + "angle": 0, + "content": "where \\(d\\) is the dimension of the projected key, value, and query. Since the softmax scores are distributed only over the query elements, video clips are expressed with the weighted sum of the text queries in proportion to the similarity to texts. Attention scores are then projected through MLP and integrated into the original video representations as the typical transformer layers. For the rest of the paper, we define the query-dependent video tokens, i.e., the output of cross-attention layers, as \\(X = \\{x_{v}^{1}, x_{v}^{2}, \\ldots, x_{v}^{L}\\}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.623, + 0.4, + 0.639 + ], + "angle": 0, + "content": "3.2. Learning from Negative Relationship" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.769 + ], + "angle": 0, + "content": "While the cross-attention layers explicitly fuse the video and query features for intermediate video clip representations to engage the query information in an architectural way, we argue that given video-text pairs lack diversity to learn the general relationship. For instance, many consecutive clips in a single video often share similar appearances, and the similarity to a specific query will not be highly distinguishable, thereby, the text query may not much affect the prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Thus, we consider the relationships between irrelevant pairs of videos inspired by many recognition practices [17, 26, 27, 35] that learn discriminative features across different categories. To implement such relationships, we define given training video-query pairs as positive pairs and mix the video and query from different pairs to construct negative pairs. Fig. 3 illustrates the ways to augment such negative pairs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.894, + 0.21 + ], + "angle": 0, + "content": "and utilize them with positive pairs in training. While the video clips in positive pairs are trained to yield segmented saliency scores according to the query-relevance, irrelevant negative video-query pairs are enforced to have the lowest saliency scores. Formally, the loss function for suppressing the saliency of negative pairs \\( x_{v}^{\\mathrm{neg}} \\) are expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.217, + 0.893, + 0.234 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {n e g}} = - \\log \\left(1 - S \\left(x _ {v} ^ {\\text {n e g}}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.24, + 0.895, + 0.337 + ], + "angle": 0, + "content": "where \\( S(\\cdot) \\) is the saliency score predictor. This training scheme can also prevent the model from predicting the moments and highlights solely based on the inter-relationship among video clips without consideration of the query-relevance since the same video instance should be predicted differently depending on whether the positive or negative query is given." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.344, + 0.8, + 0.36 + ], + "angle": 0, + "content": "3.3. Input-Adaptive Saliency Predictor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.894, + 0.461 + ], + "angle": 0, + "content": "Naive implementation for saliency predictor \\( S(\\cdot) \\) would be stacking one or more fully-connected layers. However, such a general head provides identical criteria for the saliency prediction of every video-query pair, neglecting the diverse nature of video and natural language query pairs. This violates our key idea to extract query-dependent video representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.895, + 0.656 + ], + "angle": 0, + "content": "Thus, we define the saliency token \\( x_{s} \\) to be utilized as an input-adaptive saliency predictor. Briefly, the saliency token is a randomly initialized learnable vector that becomes an input-adaptive predictor when added to the sequence of encoded video tokens and projected through the transformer encoder. To illustrate, as shown in Fig. 2, we first concatenate the saliency token with the query-dependent video tokens \\( X \\). We process these tokens to the transformer encoder which makes the saliency token to be re-organized with the input-dependent contexts. Consequently, saliency and video tokens are projected by a corresponding single fully-connected layer with weights, \\( w_{s} \\) and \\( w_{v} \\), respectively, where their scaled-dot product becomes the saliency scores. Formally, saliency score \\( S(x_{v}^{i}) \\) is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.662, + 0.893, + 0.694 + ], + "angle": 0, + "content": "\\[\nS \\left(x _ {v} ^ {i}\\right) = \\frac {\\boldsymbol {w} _ {s} ^ {T} \\boldsymbol {x} _ {s} \\cdot \\boldsymbol {w} _ {v} ^ {T} x _ {v} ^ {i}}{\\sqrt {d}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.7, + 0.855, + 0.714 + ], + "angle": 0, + "content": "where \\(d\\) is the channel dimension of projected tokens." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.721, + 0.72, + 0.736 + ], + "angle": 0, + "content": "3.4. Decoder and Objectives" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.894, + 0.866 + ], + "angle": 0, + "content": "Transformer Decoder. Recently, understanding the role of the query in the detection transformer is being spotlighted [29, 34]. It is verified that designing the query with the positional information helps not only for acceleration of training but also for enhancing accuracy. Yet, it is hard to directly employ these studies in tasks handling multi-modal data, e.g., MR/HD, since multi-modal data often have different definitions of position; the position can be understood as time in the video and word order in the text." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "23026" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.473, + 0.279 + ], + "angle": 0, + "content": "On the contrary, our architectural design eliminates the need to feed the text query to the decoder since the query information is already taken into the video representations. To this end, we modify the 2D dynamic anchor boxes [29] to represent 1D moments in the video. Specifically, we utilize the center coordinate \\( m_{c} \\) and the duration \\( m_{\\sigma} \\) of the moments to design the queries. Similarly to the previous way in the image domain, we pool the features around the center coordinate and modulate the cross-attention map with the moment duration. Then, the coordinates and durations are layer-wisely revised." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.466 + ], + "angle": 0, + "content": "Loss Functions. Training objectives for QD-DETR include loss functions for MR/HD, respectively. First, objective functions for MR, in which the key focus is to locate the desired moments, are adopted from the baseline [23]. Moment retrieval loss \\( L_{\\mathrm{mr}} \\) measures the discrepancy between the GT moment and the predicted counterpart. It consists of a \\( L1 \\) loss and a generalized IoU loss \\( L_{\\mathrm{gIoU}}(\\cdot) \\) from previous work [37] with minor modification to localize temporal moments. Additionally, the cross-entropy loss is used to classify the predicted moments as \\( \\hat{y} \\) either to foreground and background by \\( L_{\\mathrm{CE}} = -\\sum_{y \\in Y} y \\log(\\hat{y}) \\) where \\( \\{\\mathrm{fg}, \\mathrm{bg}\\} \\subset Y \\). Thus, \\( L_{\\mathrm{mr}} \\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.48, + 0.471, + 0.496 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {m r}} = \\lambda_ {L 1} | | m - \\hat {m} | | + \\lambda_ {\\mathrm {g I o U}} L _ {\\mathrm {g I o U}} (m, \\hat {m}) + \\lambda_ {\\mathrm {C E}} L _ {\\mathrm {C E}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.549 + ], + "angle": 0, + "content": "where \\(m\\) and \\(\\hat{m}\\) are ground-truth moment and its correspond prediction containing center coordinate \\(m_{c}\\) and duration \\(m_{\\sigma}\\). Also, \\(\\lambda_{*}\\) are hyperparameters for balancing the losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.472, + 0.661 + ], + "angle": 0, + "content": "Loss functions for HD are to estimate the saliency score. It comprises two components; margin ranking loss \\( L_{\\mathrm{margin}} \\) and rank-aware contrastive loss \\( L_{\\mathrm{cont}} \\). Following [23], the margin rank loss operates with two pairs of high-rank and low-rank clips. To be specific, the high-rank clips are ensured to retain higher saliency scores than both the low-rank clips within the GT moment and the negative clips outside the GT moment. In short, \\( L_{\\mathrm{margin}} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.672, + 0.47, + 0.689 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {m a r g i n}} = \\max (0, \\Delta + S \\left(x ^ {\\text {l o w}}\\right) - S \\left(x ^ {\\text {h i g h}}\\right)) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.473, + 0.867 + ], + "angle": 0, + "content": "where \\(\\Delta\\) is the margin, \\(S(\\cdot)\\) is the saliency score estimator, and \\(x^{\\mathrm{high}}\\) and \\(x^{\\mathrm{low}}\\) are video tokens from two pairs of high and low-rank clips, respectively. In addition to margin loss which only indirectly guides the saliency predictor, we employ rank-aware contrastive loss [18] to learn the precisely segmented saliency levels with the contrastive loss. Given the maximum rank value \\(R\\), each clip in the mini-batch has a saliency score lower than \\(R\\). Then, we iterate the batch for \\(R\\) times, each time utilizing the samples with higher saliency scores than the iteration index (\\(r \\in \\{0, 1, \\dots, R - 1\\}\\)) to build the positive set \\(X_r^{\\mathrm{pos}}\\). Samples with a lower rank than the iteration index are included in the negative set \\(X_r^{\\mathrm{neg}}\\). Then," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.831, + 0.14 + ], + "angle": 0, + "content": "the rank-aware contrastive loss \\( L_{\\mathrm{cont}} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.149, + 0.894, + 0.186 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c o n t}} = - \\sum_ {r = 1} ^ {R} \\log \\frac {\\sum_ {x \\in X _ {r} ^ {\\text {p o s}}} \\exp (S (x) / \\tau)}{\\sum_ {x \\in \\left(X _ {r} ^ {\\text {p o s}} \\cup X _ {r} ^ {\\text {n e g}}\\right)} \\exp (S (x) / \\tau)} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.195, + 0.894, + 0.252 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature scaling parameter. Note that, \\(X_{\\tau}^{\\mathrm{neg}}\\) also include all clips in negative pairs \\(x_{v}^{\\mathrm{neg}}\\) defined in Sec. 3.2. Finally with margin loss and rank-aware contrastive loss, \\(L_{\\mathrm{hl}}\\) and total loss function \\(L_{\\mathrm{total}}\\) are defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.261, + 0.893, + 0.277 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {h l}} = \\lambda_ {\\text {m a r g i n}} L _ {\\text {m a r g i n}} + \\lambda_ {\\text {c o n t}} L _ {\\text {c o n t}}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.278, + 0.893, + 0.295 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {t o t a l}} = L _ {\\mathrm {h l}} + L _ {\\mathrm {m r}} + \\lambda_ {\\mathrm {n e g}} L _ {\\mathrm {n e g}}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.304, + 0.617, + 0.318 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.326, + 0.707, + 0.341 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.895, + 0.569 + ], + "angle": 0, + "content": "Dataset and Evaluation Metrics. For the evaluation, we validate the effectiveness of query-dependent source representation on QVHighlights [23], TVSum [40], Charades-STA [13]. QVHighlights is the most recently publicized dataset for both moment retrieval and highlight detection. It is also the only dataset that has annotations for both tasks. In detail, QVHighlights consists of over 10,000 videos annotated with human-written text queries. It provides a fair benchmark as the evaluation for the test split can only be measured through submitting the prediction to the QVHighlights server1. Charades-STA and TVSum are the dataset for moment retrieval and video summarization, respectively. Each of them contains 9,848 videos regarding indoor activities and 50 videos of various genres, e.g., news, documentary, and vlog. For all datasets, we follow the data splits from the existing works [23, 31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.894, + 0.652 + ], + "angle": 0, + "content": "To measure the performances, we use the same evaluation metrics used in the baselines. Specifically, recall@1 with IoU thresholds 0.5 and 0.7, and mean average precision (mAP) at different thresholds. Similarly, we use mAP and HIT@1 for evaluating the highlight detection. HIT@1 is computed through the hit ratio of the highest-scored clip." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.702, + 0.674 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.894, + 0.763 + ], + "angle": 0, + "content": "We compare QD-DETR against baselines in MR and HD throughout Tab. 1, Tab. 3, and Tab. 2. Our experiments with multi-modal sources, i.e., video with audio, are implemented by simply concatenating the video and audio along the channel axis. Throughout the tables, we use bolds to denote the best scores." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.894, + 0.848 + ], + "angle": 0, + "content": "In Tab. 1, the task is to jointly learn and predict MR/HD. As observed, our QD-DETR outperforms state-of-the-art (SOTA) approaches with all evaluation metrics. Among methods utilizing the video source, QD-DETR shows a dramatic increase with stricter metrics with high IOU; it outperforms previous SOTA by large margins up" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.854, + 0.788, + 0.867 + ], + "angle": 0, + "content": "1 https://codalab.lisn.upsaclay.fr/competitions/6937" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "23027" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.121, + 0.894, + 0.147 + ], + "angle": 0, + "content": "Table 1. Performance comparison on QVHighlights test split. V and A in the Src column denote video and audio, respectively, representing the modalities of the source data. Our experiments are averaged over five runs and \\(\\pm\\) denotes the standard deviation." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.158, + 0.872, + 0.33 + ], + "angle": 0, + "content": "
MethodSrcMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
BeautyThumb [39]V-----14.3620.88
DVSE [30]V-----18.7521.79
MCN [1]V11.412.7224.948.2210.67--
CAL [12]V25.4911.5423.407.659.89--
XML [24]V41.8330.3544.6331.7332.1434.4955.25
XML+ [24]V46.6933.4647.8934.6734.9035.3855.06
Moment-DETR [23]V52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
QD-DETR (Ours)V62.40±1.144.98±0.862.52±0.639.88±0.739.86±0.638.94±0.462.40±1.4
UMT [31]V+A56.2341.1853.3837.0136.1238.1859.99
QD-DETR (Ours)V+A63.06±1.045.10±0.763.04±0.940.10±1.040.19±0.639.04±0.362.87±0.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.267, + 0.341, + 0.7, + 0.354 + ], + "angle": 0, + "content": "Table 2. Highlight detection performance comparison on TVsum dataset." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.364, + 0.825, + 0.523 + ], + "angle": 0, + "content": "
MethodSrcVTVUGAMSPKPRFMBKBTDSAvg.
sLSTM [57]V41.146.246.347.744.846.145.240.647.145.545.1
SG [33]V42.347.247.548.945.647.346.441.748.346.646.2
LIM-S [49]V55.942.961.254.060.347.543.266.369.162.656.3
Trailer [45]V61.354.665.760.859.170.158.264.765.668.162.8
SL-Module [50]V86.568.774.986.279.063.258.972.678.964.073.3
QD-DETR (Ours)V88.287.485.685.085.886.976.491.389.273.785.0
MINI-Net [19]V+A80.668.378.281.878.165.857.875.080.265.573.2
TCG [53]V+A85.071.481.978.680.275.571.677.378.668.176.8
Joint-VA [3]V+A83.757.378.586.180.169.270.073.097.467.576.3
UMT [31]V+A87.581.588.278.881.487.076.086.984.479.683.1
QD-DETR (Ours)V+A87.691.790.288.384.188.378.791.287.877.786.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.541, + 0.47, + 0.566 + ], + "angle": 0, + "content": "Table 3. Charades dataset. \\(\\dagger\\) denotes the method using the video and audio as the source. \\(\\mathrm{SF + C}\\) stands for Slowfast and CLIP features." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.577, + 0.47, + 0.693 + ], + "angle": 0, + "content": "
MethodfeatR1@0.5R1@0.7MethodfeatR1@0.5R1@0.7
SAPVGG27.4213.36CTRLC3D23.638.89
TripNetVGG36.6114.50ACLC3D30.4812.20
SM-RLVGG24.3611.17RWM-RLC3D36.70-
MANVGG41.2420.54MANC3D46.5322.72
2D-TANVGG40.9422.85DEBUGC3D37.3917.69
FVMRVGG42.3624.14VSLNetC3D47.3130.19
UMT†VGG48.3129.25OursC3D50.6731.02
OursVGG52.7731.13M-DETRSF+C53.6331.37
Ours†VGG55.5134.17OursSF+C57.3132.55
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.47, + 0.809 + ], + "angle": 0, + "content": "to \\(36\\%\\) in R1@0.7 and mAP@0.75. On the other hand, QD-DETR with video and audio sources boosts \\(11.84\\%\\) on average of the metrics for MR compared to the SOTA method employing the multi-modal source data. These results verify the importance of emphasizing the source (video-only or video+audio) descriptive contexts in the text queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.867 + ], + "angle": 0, + "content": "Results in Tab. 3 also compare MR performances against the models using VGG [7,14,31,46,55,59], C3D [13,16,28,32,55,56], and Slowfast (SF) and CLIP features [23] on Charades dataset. For a fair comparison, we enumerate" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.894, + 0.625 + ], + "angle": 0, + "content": "each method with its backbone and compare within it. For each feature from VGG, C3D, and \\(\\mathrm{SF + C}\\), we follow the data preparation settings from UMT [31], VSLNet [56], and Moment-DETR [23]. As reported, we validate that our model surpasses the existing SOTA methods in every type of feature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.895, + 0.764 + ], + "angle": 0, + "content": "For video highlight detection in Tab. 2, we follow the protocols from the previous work [31]. Specifically, we train the model for each category and average the mAP scores. Out of 10 categories, QD-DETR outperforms baselines on 9 categories when the only video source is available, and 8 categories when both video and audio are available. Overall, compared to methods with video-only and multi-modal sources, QD-DETR establishes new SOTA performances by improving by \\(4.2\\%\\) in average compared to the previous SOTA model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.775, + 0.651, + 0.79 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.895, + 0.868 + ], + "angle": 0, + "content": "To investigate the effectiveness of each component in our work, we conduct an extensive ablation study in Tab. 4. Note that, CATE and DAM denote cross-attentive transformer encoder and dynamic anchor moments, respectively. Rows (b) to (e) show the effectiveness of each component compared to" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "23028" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.128, + 0.892, + 0.154 + ], + "angle": 0, + "content": "Table 4. Ablation study on QVHighlights val split. CATE and DAM stands for cross-attentive transformer encoder and using dynamic anchor moments as the decoder query, respectively. All the quantities are averaged over 5 runs." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.164, + 0.847, + 0.336 + ], + "angle": 0, + "content": "
CATENeg. PairSaliency TokenDAMMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
(a)52.8933.0254.8229.4030.7335.6955.60
(b)✓56.1638.7156.4833.4234.0737.1458.34
(c)✓58.6939.8358.3934.8435.4039.0262.81
(d)✓55.4837.0055.8126.7532.8437.4858.59
(e)✓53.1935.9155.5832.5533.3335.6855.56
(f)✓✓57.7242.3559.1038.1638.0336.5657.44
(g)✓✓59.5742.1259.1936.6336.7638.6461.62
(h)✓✓60.0040.9759.2135.4135.8939.0662.88
(i)✓✓✓60.3242.3959.4736.7936.9339.2162.76
(j)✓✓✓✓62.6846.6662.2341.8241.2239.1363.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.35, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Table 5. Ablation study on cross-attention transformer encoder. We compare ours against the deepened transformer encoder with self-attention layers to validate that the performance gain does not come from additional parameters. SATE and CATE each indicate the transformer encoder only with self-attention layers and our transformer encoder. The numbers in the parenthesis denote the number of layers. For the experiment with \\(\\dagger\\), we only use the query features as the condition in the encoder and only the video representations are processed by the decoder." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.424, + 0.851, + 0.545 + ], + "angle": 0, + "content": "
T2VMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
Moment-DETR (SATE 2)52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
Moment-DETR (SATE 4)53.60±1.235.81±0.954.55±0.830.64±0.731.74±0.435.96±0.256.56±0.9
Moment-DETR (CATE 4)55.10±0.737.02±0.956.21±0.332.00±0.933.19±0.636.43±0.356.98±0.6
Moment-DETR (CATE 4)†56.16±1.238.71±1.156.48±0.833.42±0.734.07±0.637.14±0.458.34±0.4
QD-DETR (SATE 4)†60.48±0.745.21±1.060.84±0.540.45±0.740.12±0.638.66±0.261.29±1.0
QD-DETR (CATE 4)†62.68±1.146.66±0.662.23±1.041.82±0.941.22±0.439.13±0.363.03±0.5
" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.569, + 0.462, + 0.77 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.882 + ], + "angle": 0, + "content": "Figure 4. Ablation study in terms of saliency scores. We plot the histograms of the average value of saliency scores in each video when the positive and negative text queries are given. For positive scores, we only account the scores within GT moments. The average value of each histogram are visualized by the dotted line. The decrease in the overlap between histograms and the increase in the gap between average values confirms the gradual improvements of significance of the query in extracting video representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.895, + 0.775 + ], + "angle": 0, + "content": "the baseline (a). To explain, whereas (e) only boosts the MR performances since it only affects the transformer decoder, (b), (c), and (d) are especially beneficial for both MR/HD tasks since they are focused on query-dependent video representations; (b) ensures the contributions of text query in the video representation, (c) fully exploits the contexts of the text query, and (d) provides input-adaptive saliency predictor instead of MLP. Moreover, while our components are verified that they are all complementary to others, DAM's effectiveness is especially dependent on the usage of CATE (compare between \\(\\{(a,e)\\}\\) and \\(\\{(b,f),(i,j)\\}\\)). We claim that this is because DAM exploits the position information of the input tokens to capture the corresponding moments. However, without CATE, input tokens are a mixture of multi-modal tokens, thereby providing confusing position information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.895, + 0.868 + ], + "angle": 0, + "content": "To provide in-depth examinations of each component, we inspect the difference between the positive and the negative saliency scores in Fig. 4. Since the role of text query is trivial in our baseline, each distribution significantly overlies on top of the other. Then, as we add CATE and negative pair learning, we observe a consistent decrease in overlapped" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "23029" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.124, + 0.891, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.893, + 0.381 + ], + "angle": 0, + "content": "Figure 5. Visualization of results predicted by QD-DETR. Predicted and ground-truth moments are bounded by the lines. Blue, green, and red lines indicate the saliency scores for positive, semi-positive, and negative queries. The positive saliency scores are consistently higher than the others, while the scores for semi-positive are higher than the ones for the negative." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.47, + 0.492 + ], + "angle": 0, + "content": "areas and a larger gap between the average saliency scores of positive and negative histograms. Also, we believe that the widely-distributed histogram of saliency scores for the 'CATE+Neg_pair' is due to using an identical criterion for saliency prediction for diverse video-query representations. By employing an input-adaptive saliency predictor, we notice that scores for positive queries are in almost optimal shape." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.685 + ], + "angle": 0, + "content": "In addition, some might ask whether CATE benefits the training because of additional encoder layers. To answer this, we conduct another ablation study in Tab. 5. Briefly, since our transformer encoder utilizes 2 cross-attention layers and 2 self-attention layers, we conduct comparisons against the transformer encoder composed of 4 self-attention layers (SATE). First, we compare CATE and SATE on MomentDETR; by comparing the results in \\(2^{\\mathrm{nd}}\\) and \\(3^{\\mathrm{rd}}\\) rows, we find that CATE is much more beneficial than SATE even with the same number of layers. Furthermore, the last two rows show comparisons within QD-DETR architecture that has the same tendency. These results clearly demonstrate that the improvements from CATE are mainly from emphasizing the role of the text query rather than additional layers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.693, + 0.26, + 0.708 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.471, + 0.867 + ], + "angle": 0, + "content": "In this subsection, we study how the query-dependent video representation sensitively reacts to the change in the contexts of the text query. In Fig. 5, the measured saliency scores according to the video-query relevance are visualized. We found that the more the query is relevant to the video clips, the higher the saliency scores retained for the query. For instance, whereas the negative query that is totally irrelevant to the video instance has the lowest scores, the scores for semi-positive reside between the positive and the negative ones. Also, we find that QD-DETR sometimes provides a more precise moment prediction than a given ground-truth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.893, + 0.451 + ], + "angle": 0, + "content": "moment, as can be seen with the temporal box bounded by the dotted lines. We believe that the tendency of a bit higher saliency scores at non-relevant clips for a positive query is due to the information mixing in the self-attention layers." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.46, + 0.75, + 0.475 + ], + "angle": 0, + "content": "5. Limitation and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Limitation As elaborated in the paper, we aim to highlight the role of the text query in retrieving the relevant moments and estimating their accordance level with the given text query. Likewise, the proposed components expect a given query to maintain a meaningful context. If not, and noisy text queries are provided, i.e., mismatched or irrelevant ground truth texts, the training may not be effective as reported." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.806 + ], + "angle": 0, + "content": "Conclusion Although the advent of transformer architecture has been powerful for MR/HD, investigation of the role of text query has been lacking in such architectures. Therefore, we focused on studying the role of the text query. As we found that the textual information is not fully exploited in expressing the video representations, we designed the cross-attentive transformer encoder and proposed a negative-pair training scheme. Cross-attentive encoder assures the query's contributions while extracting video representation, and negative-pair training enforces the model to learn the relationship between query and video by preventing solving the problems without consideration of the query. Finally, to preserve the diversity of query-dependent video representation, we defined the saliency token to be an input-adaptive saliency predictor. Extensive experiments validated the strength of QD-DETR with superior performances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.867 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported in part by MSIT/IITP (No. 2022-0-00680, 2019-0-00421, 2020-0-01821, 2021-0-02068), and MSIT&KNPA/KIPoT (Police Lab 2.0, No. 210121M06)." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.506, + 0.898 + ], + "angle": 0, + "content": "23030" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.473, + 0.212 + ], + "angle": 0, + "content": "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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The key objective of MR/HD is to localize the moment and estimate clip-wise accordance level, i.e., saliency score, to the given text query. Although the recent transformer-based models brought some advances, we found that these methods do not fully exploit the information of a given query. For example, the relevance between text query and video contents is sometimes neglected when predicting the moment and its saliency. To tackle this issue, we introduce Query-Dependent DETR (QD-DETR), a detection transformer tailored for MR/HD. As we observe the insignificant role of a given query in transformer architectures, our encoding module starts with cross-attention layers to explicitly inject the context of text query into video representation. Then, to enhance the model's capability of exploiting the query information, we manipulate the video-query pairs to produce irrelevant pairs. Such negative (irrelevant) video-query pairs are trained to yield low saliency scores, which in turn, encourages the model to estimate precise accordance between query-video pairs. Lastly, we present an input-adaptive saliency predictor which adaptively defines the criterion of saliency scores for the given video-query pairs. Our extensive studies verify the importance of building the query-dependent representation for MR/HD. Specifically, QD-DETR outperforms state-of-the-art methods on QVHighlights, TVSum, and Charades-STA datasets. Codes are available at github.com/wjun0830/QD-DETR. + +# 1. Introduction + +Along with the advance of digital devices and platforms, video is now one of the most desired data types for consumers [2, 48]. Although the large information capacity of videos might be beneficial in many aspects, e.g., informative + +$\checkmark$ Positive Query: Man with curly hair speaks directly to camera +$\times$ Negative Query: Kids exercise in front of parked cars. + +![](images/a86f160e33c2691cedb409bae525d3850524cf1f8249fd972f6a8404e08f1c0e.jpg) +Figure 1. Comparison of highlight-ness (saliency score) when relevant and non-relevant queries are given. We found that the existing work only uses queries to play an insignificant role, thereby may not be capable of detecting negative queries and video-query relevance; saliency scores for clips in ground-truth (GT) moments are low and equivalent for positive and negative queries. On the other hand, query-dependent representations of QD-DETR result in corresponding saliency scores to the video-query relevance and precisely localized moments. + +and entertaining, inspecting the videos is time-consuming, so that it is hard to capture the desired moments [1,2]. + +Indeed, the need to retrieve user-requested or highlight moments within videos is greatly raised. Numerous research efforts were put into the search for the requested moments in the video [1, 12, 13, 30] and summarizing the video highlights [4, 33, 47, 57]. Recently, Moment-DETR [23] further spotlighted the topic by proposing a QVHighlights dataset that enables the model to perform both tasks, retrieving the moments with their highlight-ness, simultaneously. + +When describing the moment, one of the most favored types of query is the natural language sentence (text) [1]. While early methods utilized convolution networks [14, 44, 59], recent approaches have shown that deploying the attention mechanism of transformer architecture is more effective to fuse the text query into the video representation. For example, Moment-DETR [23] introduced the transformer + +architecture which processes both text and video tokens as input by modifying the detection transformer (DETR), and UMT [31] proposed transformer architectures to take multimodal sources, e.g., video and audio. Also, they utilized the text queries in the transformer decoder. Although they brought breakthroughs in the field of MR/HD with seminal architectures, they overlooked the role of the text query. To validate our claim, we investigate the Moment-DETR [23] in terms of the impact of text query in MR/HD (Fig.1). Given the video clips with a relevant positive query and an irrelevant negative query, we observe that the baseline often neglects the given text query when estimating the query-relevance scores, i.e., saliency scores, for each video clip. + +To this end, we propose Query-Dependent DETR (QD-DETR) that produces query-dependent video representation. Our key focus is to ensure that the model's prediction for each clip is highly dependent on the query. First, to fully utilize the contextual information in the query, we revise the transformer encoder to be equipped with cross-attention layers at the very first layers. By inserting a video as the query and a text as the key and value of the cross-attention layers, our encoder enforces the engagement of the text query in extracting video representation. Then, in order to not only inject a lot of textual information into the video feature but also make it fully exploited, we leverage the negative video-query pairs generated by mixing the original pairs. Specifically, the model is learned to suppress the saliency scores of such negative (irrelevant) pairs. Our expectation is the increased contribution of the text query in prediction since the videos will be sometimes required to yield high saliency scores and sometimes low ones depending on whether the text query is relevant or not. Lastly, to apply the dynamic criterion to mark highlights for each instance, we deploy a saliency token to represent the entire video and utilize it as an input-adaptive saliency criterion. With all components combined, our QD-DETR produces query-dependent video representation by integrating source and query modalities. This further allows the use of positional queries [29] in the transformer decoder. Overall, our superior performances over the existing approaches validate the significance of the role of text query for MR/HD. + +# 2. Related Work + +# 2.1. Moment Retrieval and Highlight Detection + +MR is the task of localizing the moment relevant to the given text description. Popular approaches are modeling the cross-modal interaction between text query-video pair [32, 54, 56] or understanding the context of the temporal relation among video clips [1, 59]. On the other hand, TVT [24] exploited the additional data, i.e., subtitle, to capture the moment, and FVMR [14] enhanced the model in terms of inference speed for efficient MR. + +Different from the MR, HD aims to measure the clipwise importance level of the given video [41, 52]. Due to its popularity and applicability, HD can be divided into several branches. From the perspective of annotation, we can categorize HD into supervised, weakly supervised, and unsupervised HD. Supervised HD [15, 41, 50] utilizes fine-grained highlight scores, which are very expensive to collect and annotate [49]. On the other hand, weakly supervised HD [5, 36, 49] learns to detect segments as highlights with video event labels, and finally, unsupervised HD [4, 22, 33, 38] does not require any annotations. Also, while the task is often implemented only with the video, there are works to employ the extra data modalities. Generally, multi-modality was taken into account by using the natural language query to find the desired thumbnail [30] and using additional sources, i.e., audio, to predict highlights [3, 53]. + +Although the MR/HD share a common objective to localize or discover the desired part of the given video, they have been studied separately. To handle these tasks at once, Moment-DETR [23] proposed the QVHighlights dataset, which contains a human-written text query and its corresponding moment with clip-level saliency labels. They also introduced the modified version of detection transformer (DETR [6]) to localize the query-relevant moments and their saliency scores. Following them, UMT [31] focused on processing multi-modal data by utilizing both video and audio features. Different from recent works deploying transformer architectures, here we concentrate on producing a query-dependent representation with the transformer. + +# 2.2. Detection Transformers + +DETR [6], an end-to-end object detector based on vision transformers, is one of the very recent works that utilize the transformer architectures for computer vision [11,42]. Although DETR suffered from slow convergence, it simplifies the prediction process by eliminating the need for anchor generation and non-maximum suppression. Since then, along with the advance in DETR [10, 25, 60], DETR-like architectures have been popular in downstream tasks in both the image [8, 9, 20, 58] and video domains [23, 51]. Some of these works focused on analyzing the role of the decoder query and discovered that using the positional information speeds up the training and also enhances the detection performance [29, 34]. On the other hand, there are trials to extend the application of DETR on multi-modal data [21, 23], especially dealing with the query from different modalities, i.e., text, for detection (or retrieval). They generally handle the multi-modal data by simply forwarding them together to the transformer. In this paper, we also focus on handling the multi-modal data based on DETR-like architecture. However, different from the aforementioned techniques, we concentrate on the query-dependency of the prediction results. + +![](images/d660976ee35c69d277aaa39e3c913b05f31a8a86da29fa087230ae61ca5af7a8.jpg) +Figure 2. Overview of the proposed QD-DETR architecture. Given a video and text query, we first extract video and text features from the frozen backbones. These video and text features are forwarded into the cross-attention transformer (Sec. 3.1). This process ensures the consistent contribution of text queries to the video tokens and together with negative pair learning (Sec. 3.2), builds query-dependent video representation. Then, accompanied by the saliency token (Sec. 3.3), video tokens are given to the transformer encoder. In this procedure, the saliency token is transformed into the adaptive saliency prediction criteria. The outputs of the encoder are then, processed to compute losses for both HD and MR. Specifically, the encoder's output tokens are directly projected to saliency scores and optimized for HD, and also provided to the transformer decoder with the learnable moment queries to estimate the query-described moments. Finally, losses for MR are computed by the discrepancy between predicted and their corresponding GT moments. + +# 3. Query-Dependent DETR + +Moment retrieval and highlight detection have the common objective to find preferred moments with the text query. Given a video of $L$ clips and a text query with $N$ words, we denote their representations as $\{v_{1}, v_{2}, \dots, v_{L}\}$ and $\{t_{1}, t_{2}, \dots, t_{N}\}$ extracted by frozen video and text encoders, respectively. With these representations, the main objective is to localize the center coordinate $m_{c}$ and width $m_{\sigma}$ within the video and rank the highlight score (saliency score) $\{s_{1}, s_{2}, \dots, s_{L}\}$ for each clip. A straightforward approach to utilize transformer [11, 43] for the MR is to make a moment-wise prediction as a set of clips [23], or generating the moment according to the clip-wise predictions [31]. To exploit the multi-modal information, e.g., video and text query, they either simply concatenated the features across the modalities or inserted the texts to form the moment query to the transformer decoder. However, we claim that the relationship between the video and text query should be carefully considered rather than a simple concatenation since MR/HD requires every video clip to be conditionally assessed with the text queries. + +Our overall architecture is described in Fig. 2, following the design of concrete baseline, Moment-DETR [23]. Given a video and query representation extracted from fixed backbones, QD-DETR first transforms the video representation to be query-dependent using cross-attention layers. To further enhance the query-awareness of video representations, we incorporate irrelevant video-query pairs with a low saliency + +for the learning objective. Then, along with the transformer encoder-decoder architectures, the saliency token is defined that turns into an adaptive saliency predictor when attended by the specific video instance. + +# 3.1. Cross-Attentive Transformer Encoder + +In this subsection, we use italic letters to represent query, key, and value of the cross-attention layers. The key objective of the encoder for MR/HD is to produce clip-wise representations equipped with information regarding the degree of query-relevance since these features are directly used for retrieving the query-matched moments and predicting clip-wise saliency scores. However, the encoding process of existing works may not ensure the query conditioning on every clip. For example, Moment-DETR [23] naively concatenated the video with the query for input to the self-attention layers, which may result in an insignificant role of the query if the high similarities among the video clips overwhelm the contribution of the text query. On the other hand, UMT [31] utilizes the text query only for the synthesis of a moment query in the transformer decoder so thus resulting video representations are not associated with the text query. + +To take the textual contexts into every video clip representation, we deploy cross-attention layers between the source and the query modalities at the very first layers of the encoder. This ensures the consistent contribution of the query, thereby extracting query-dependent video representation. In detail, whereas the query for cross-attention layers is prepared by projecting the video clips as $Q_{v} = [p_{q}(v_{1}),\dots,p_{q}(v_{L})]$ , the + +![](images/4ea1714826ce73f8a10547dcddf1e9ec9efc479d268679d8e40f2e80a6126076.jpg) +Figure 3. Illustration of negative pair learning. Typical HL loss is defined only with a positive video-query pair, which is insufficient to learn various degrees of query-relevance. On the other hand, our negative pair learning enforces the model to yield different scores for a video depending on the query and to be learned to suppress saliency scores for the negative query. + +key and value are computed with the query text features as $K_{t} = [p_{k}(t_{1}),\dots,p_{k}(t_{N})]$ and $V_{t} = [p_{v}(t_{1}),\dots,p_{v}(t_{N})]$ . $p_q(\cdot), p_k(\cdot)$ , and $p_v(\cdot)$ are projection layers for query, key, and value. Then, the cross-attention layer operates as follows: + +$$ +\operatorname {A t t e n t i o n} \left(Q _ {v}, K _ {t}, V _ {t}\right) = \operatorname {s o f t m a x} \left(\frac {Q _ {v} K _ {t} ^ {T}}{\sqrt {d}}\right) V _ {t}, \tag {1} +$$ + +where $d$ is the dimension of the projected key, value, and query. Since the softmax scores are distributed only over the query elements, video clips are expressed with the weighted sum of the text queries in proportion to the similarity to texts. Attention scores are then projected through MLP and integrated into the original video representations as the typical transformer layers. For the rest of the paper, we define the query-dependent video tokens, i.e., the output of cross-attention layers, as $X = \{x_{v}^{1}, x_{v}^{2}, \ldots, x_{v}^{L}\}$ . + +# 3.2. Learning from Negative Relationship + +While the cross-attention layers explicitly fuse the video and query features for intermediate video clip representations to engage the query information in an architectural way, we argue that given video-text pairs lack diversity to learn the general relationship. For instance, many consecutive clips in a single video often share similar appearances, and the similarity to a specific query will not be highly distinguishable, thereby, the text query may not much affect the prediction. + +Thus, we consider the relationships between irrelevant pairs of videos inspired by many recognition practices [17, 26, 27, 35] that learn discriminative features across different categories. To implement such relationships, we define given training video-query pairs as positive pairs and mix the video and query from different pairs to construct negative pairs. Fig. 3 illustrates the ways to augment such negative pairs + +and utilize them with positive pairs in training. While the video clips in positive pairs are trained to yield segmented saliency scores according to the query-relevance, irrelevant negative video-query pairs are enforced to have the lowest saliency scores. Formally, the loss function for suppressing the saliency of negative pairs $x_{v}^{\mathrm{neg}}$ are expressed as follows: + +$$ +L _ {\text {n e g}} = - \log \left(1 - S \left(x _ {v} ^ {\text {n e g}}\right)\right), \tag {2} +$$ + +where $S(\cdot)$ is the saliency score predictor. This training scheme can also prevent the model from predicting the moments and highlights solely based on the inter-relationship among video clips without consideration of the query-relevance since the same video instance should be predicted differently depending on whether the positive or negative query is given. + +# 3.3. Input-Adaptive Saliency Predictor + +Naive implementation for saliency predictor $S(\cdot)$ would be stacking one or more fully-connected layers. However, such a general head provides identical criteria for the saliency prediction of every video-query pair, neglecting the diverse nature of video and natural language query pairs. This violates our key idea to extract query-dependent video representation. + +Thus, we define the saliency token $x_{s}$ to be utilized as an input-adaptive saliency predictor. Briefly, the saliency token is a randomly initialized learnable vector that becomes an input-adaptive predictor when added to the sequence of encoded video tokens and projected through the transformer encoder. To illustrate, as shown in Fig. 2, we first concatenate the saliency token with the query-dependent video tokens $X$ . We process these tokens to the transformer encoder which makes the saliency token to be re-organized with the input-dependent contexts. Consequently, saliency and video tokens are projected by a corresponding single fully-connected layer with weights, $w_{s}$ and $w_{v}$ , respectively, where their scaled-dot product becomes the saliency scores. Formally, saliency score $S(x_{v}^{i})$ is computed as follows: + +$$ +S \left(x _ {v} ^ {i}\right) = \frac {\boldsymbol {w} _ {s} ^ {T} \boldsymbol {x} _ {s} \cdot \boldsymbol {w} _ {v} ^ {T} x _ {v} ^ {i}}{\sqrt {d}}, \tag {3} +$$ + +where $d$ is the channel dimension of projected tokens. + +# 3.4. Decoder and Objectives + +Transformer Decoder. Recently, understanding the role of the query in the detection transformer is being spotlighted [29, 34]. It is verified that designing the query with the positional information helps not only for acceleration of training but also for enhancing accuracy. Yet, it is hard to directly employ these studies in tasks handling multi-modal data, e.g., MR/HD, since multi-modal data often have different definitions of position; the position can be understood as time in the video and word order in the text. + +On the contrary, our architectural design eliminates the need to feed the text query to the decoder since the query information is already taken into the video representations. To this end, we modify the 2D dynamic anchor boxes [29] to represent 1D moments in the video. Specifically, we utilize the center coordinate $m_{c}$ and the duration $m_{\sigma}$ of the moments to design the queries. Similarly to the previous way in the image domain, we pool the features around the center coordinate and modulate the cross-attention map with the moment duration. Then, the coordinates and durations are layer-wisely revised. + +Loss Functions. Training objectives for QD-DETR include loss functions for MR/HD, respectively. First, objective functions for MR, in which the key focus is to locate the desired moments, are adopted from the baseline [23]. Moment retrieval loss $L_{\mathrm{mr}}$ measures the discrepancy between the GT moment and the predicted counterpart. It consists of a $L1$ loss and a generalized IoU loss $L_{\mathrm{gIoU}}(\cdot)$ from previous work [37] with minor modification to localize temporal moments. Additionally, the cross-entropy loss is used to classify the predicted moments as $\hat{y}$ either to foreground and background by $L_{\mathrm{CE}} = -\sum_{y \in Y} y \log(\hat{y})$ where $\{\mathrm{fg}, \mathrm{bg}\} \subset Y$ . Thus, $L_{\mathrm{mr}}$ is defined as follows: + +$$ +L _ {\mathrm {m r}} = \lambda_ {L 1} | | m - \hat {m} | | + \lambda_ {\mathrm {g I o U}} L _ {\mathrm {g I o U}} (m, \hat {m}) + \lambda_ {\mathrm {C E}} L _ {\mathrm {C E}}, \tag {4} +$$ + +where $m$ and $\hat{m}$ are ground-truth moment and its correspond prediction containing center coordinate $m_{c}$ and duration $m_{\sigma}$ . Also, $\lambda_{*}$ are hyperparameters for balancing the losses. + +Loss functions for HD are to estimate the saliency score. It comprises two components; margin ranking loss $L_{\mathrm{margin}}$ and rank-aware contrastive loss $L_{\mathrm{cont}}$ . Following [23], the margin rank loss operates with two pairs of high-rank and low-rank clips. To be specific, the high-rank clips are ensured to retain higher saliency scores than both the low-rank clips within the GT moment and the negative clips outside the GT moment. In short, $L_{\mathrm{margin}}$ is defined as: + +$$ +L _ {\text {m a r g i n}} = \max (0, \Delta + S \left(x ^ {\text {l o w}}\right) - S \left(x ^ {\text {h i g h}}\right)) \tag {5} +$$ + +where $\Delta$ is the margin, $S(\cdot)$ is the saliency score estimator, and $x^{\mathrm{high}}$ and $x^{\mathrm{low}}$ are video tokens from two pairs of high and low-rank clips, respectively. In addition to margin loss which only indirectly guides the saliency predictor, we employ rank-aware contrastive loss [18] to learn the precisely segmented saliency levels with the contrastive loss. Given the maximum rank value $R$ , each clip in the mini-batch has a saliency score lower than $R$ . Then, we iterate the batch for $R$ times, each time utilizing the samples with higher saliency scores than the iteration index ( $r \in \{0, 1, \dots, R - 1\}$ ) to build the positive set $X_r^{\mathrm{pos}}$ . Samples with a lower rank than the iteration index are included in the negative set $X_r^{\mathrm{neg}}$ . Then, + +the rank-aware contrastive loss $L_{\mathrm{cont}}$ is defined as: + +$$ +L _ {\text {c o n t}} = - \sum_ {r = 1} ^ {R} \log \frac {\sum_ {x \in X _ {r} ^ {\text {p o s}}} \exp (S (x) / \tau)}{\sum_ {x \in \left(X _ {r} ^ {\text {p o s}} \cup X _ {r} ^ {\text {n e g}}\right)} \exp (S (x) / \tau)} \tag {6} +$$ + +where $\tau$ is a temperature scaling parameter. Note that, $X_{\tau}^{\mathrm{neg}}$ also include all clips in negative pairs $x_{v}^{\mathrm{neg}}$ defined in Sec. 3.2. Finally with margin loss and rank-aware contrastive loss, $L_{\mathrm{hl}}$ and total loss function $L_{\mathrm{total}}$ are defined as follows: + +$$ +L _ {\mathrm {h l}} = \lambda_ {\text {m a r g i n}} L _ {\text {m a r g i n}} + \lambda_ {\text {c o n t}} L _ {\text {c o n t}}, \tag {7} +$$ + +$$ +L _ {\text {t o t a l}} = L _ {\mathrm {h l}} + L _ {\mathrm {m r}} + \lambda_ {\mathrm {n e g}} L _ {\mathrm {n e g}}. \tag {8} +$$ + +# 4. Evaluation + +# 4.1. Experimental Settings + +Dataset and Evaluation Metrics. For the evaluation, we validate the effectiveness of query-dependent source representation on QVHighlights [23], TVSum [40], Charades-STA [13]. QVHighlights is the most recently publicized dataset for both moment retrieval and highlight detection. It is also the only dataset that has annotations for both tasks. In detail, QVHighlights consists of over 10,000 videos annotated with human-written text queries. It provides a fair benchmark as the evaluation for the test split can only be measured through submitting the prediction to the QVHighlights server1. Charades-STA and TVSum are the dataset for moment retrieval and video summarization, respectively. Each of them contains 9,848 videos regarding indoor activities and 50 videos of various genres, e.g., news, documentary, and vlog. For all datasets, we follow the data splits from the existing works [23, 31]. + +To measure the performances, we use the same evaluation metrics used in the baselines. Specifically, recall@1 with IoU thresholds 0.5 and 0.7, and mean average precision (mAP) at different thresholds. Similarly, we use mAP and HIT@1 for evaluating the highlight detection. HIT@1 is computed through the hit ratio of the highest-scored clip. + +# 4.2. Experimental Results + +We compare QD-DETR against baselines in MR and HD throughout Tab. 1, Tab. 3, and Tab. 2. Our experiments with multi-modal sources, i.e., video with audio, are implemented by simply concatenating the video and audio along the channel axis. Throughout the tables, we use bolds to denote the best scores. + +In Tab. 1, the task is to jointly learn and predict MR/HD. As observed, our QD-DETR outperforms state-of-the-art (SOTA) approaches with all evaluation metrics. Among methods utilizing the video source, QD-DETR shows a dramatic increase with stricter metrics with high IOU; it outperforms previous SOTA by large margins up + +Table 1. Performance comparison on QVHighlights test split. V and A in the Src column denote video and audio, respectively, representing the modalities of the source data. Our experiments are averaged over five runs and $\pm$ denotes the standard deviation. + +
MethodSrcMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
BeautyThumb [39]V-----14.3620.88
DVSE [30]V-----18.7521.79
MCN [1]V11.412.7224.948.2210.67--
CAL [12]V25.4911.5423.407.659.89--
XML [24]V41.8330.3544.6331.7332.1434.4955.25
XML+ [24]V46.6933.4647.8934.6734.9035.3855.06
Moment-DETR [23]V52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
QD-DETR (Ours)V62.40±1.144.98±0.862.52±0.639.88±0.739.86±0.638.94±0.462.40±1.4
UMT [31]V+A56.2341.1853.3837.0136.1238.1859.99
QD-DETR (Ours)V+A63.06±1.045.10±0.763.04±0.940.10±1.040.19±0.639.04±0.362.87±0.6
+ +Table 2. Highlight detection performance comparison on TVsum dataset. + +
MethodSrcVTVUGAMSPKPRFMBKBTDSAvg.
sLSTM [57]V41.146.246.347.744.846.145.240.647.145.545.1
SG [33]V42.347.247.548.945.647.346.441.748.346.646.2
LIM-S [49]V55.942.961.254.060.347.543.266.369.162.656.3
Trailer [45]V61.354.665.760.859.170.158.264.765.668.162.8
SL-Module [50]V86.568.774.986.279.063.258.972.678.964.073.3
QD-DETR (Ours)V88.287.485.685.085.886.976.491.389.273.785.0
MINI-Net [19]V+A80.668.378.281.878.165.857.875.080.265.573.2
TCG [53]V+A85.071.481.978.680.275.571.677.378.668.176.8
Joint-VA [3]V+A83.757.378.586.180.169.270.073.097.467.576.3
UMT [31]V+A87.581.588.278.881.487.076.086.984.479.683.1
QD-DETR (Ours)V+A87.691.790.288.384.188.378.791.287.877.786.6
+ +Table 3. Charades dataset. $\dagger$ denotes the method using the video and audio as the source. $\mathrm{SF + C}$ stands for Slowfast and CLIP features. + +
MethodfeatR1@0.5R1@0.7MethodfeatR1@0.5R1@0.7
SAPVGG27.4213.36CTRLC3D23.638.89
TripNetVGG36.6114.50ACLC3D30.4812.20
SM-RLVGG24.3611.17RWM-RLC3D36.70-
MANVGG41.2420.54MANC3D46.5322.72
2D-TANVGG40.9422.85DEBUGC3D37.3917.69
FVMRVGG42.3624.14VSLNetC3D47.3130.19
UMT†VGG48.3129.25OursC3D50.6731.02
OursVGG52.7731.13M-DETRSF+C53.6331.37
Ours†VGG55.5134.17OursSF+C57.3132.55
+ +to $36\%$ in R1@0.7 and mAP@0.75. On the other hand, QD-DETR with video and audio sources boosts $11.84\%$ on average of the metrics for MR compared to the SOTA method employing the multi-modal source data. These results verify the importance of emphasizing the source (video-only or video+audio) descriptive contexts in the text queries. + +Results in Tab. 3 also compare MR performances against the models using VGG [7,14,31,46,55,59], C3D [13,16,28,32,55,56], and Slowfast (SF) and CLIP features [23] on Charades dataset. For a fair comparison, we enumerate + +each method with its backbone and compare within it. For each feature from VGG, C3D, and $\mathrm{SF + C}$ , we follow the data preparation settings from UMT [31], VSLNet [56], and Moment-DETR [23]. As reported, we validate that our model surpasses the existing SOTA methods in every type of feature. + +For video highlight detection in Tab. 2, we follow the protocols from the previous work [31]. Specifically, we train the model for each category and average the mAP scores. Out of 10 categories, QD-DETR outperforms baselines on 9 categories when the only video source is available, and 8 categories when both video and audio are available. Overall, compared to methods with video-only and multi-modal sources, QD-DETR establishes new SOTA performances by improving by $4.2\%$ in average compared to the previous SOTA model. + +# 4.3. Ablation study + +To investigate the effectiveness of each component in our work, we conduct an extensive ablation study in Tab. 4. Note that, CATE and DAM denote cross-attentive transformer encoder and dynamic anchor moments, respectively. Rows (b) to (e) show the effectiveness of each component compared to + +Table 4. Ablation study on QVHighlights val split. CATE and DAM stands for cross-attentive transformer encoder and using dynamic anchor moments as the decoder query, respectively. All the quantities are averaged over 5 runs. + +
CATENeg. PairSaliency TokenDAMMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
(a)52.8933.0254.8229.4030.7335.6955.60
(b)✓56.1638.7156.4833.4234.0737.1458.34
(c)✓58.6939.8358.3934.8435.4039.0262.81
(d)✓55.4837.0055.8126.7532.8437.4858.59
(e)✓53.1935.9155.5832.5533.3335.6855.56
(f)✓✓57.7242.3559.1038.1638.0336.5657.44
(g)✓✓59.5742.1259.1936.6336.7638.6461.62
(h)✓✓60.0040.9759.2135.4135.8939.0662.88
(i)✓✓✓60.3242.3959.4736.7936.9339.2162.76
(j)✓✓✓✓62.6846.6662.2341.8241.2239.1363.03
+ +Table 5. Ablation study on cross-attention transformer encoder. We compare ours against the deepened transformer encoder with self-attention layers to validate that the performance gain does not come from additional parameters. SATE and CATE each indicate the transformer encoder only with self-attention layers and our transformer encoder. The numbers in the parenthesis denote the number of layers. For the experiment with $\dagger$ , we only use the query features as the condition in the encoder and only the video representations are processed by the decoder. + +
T2VMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
Moment-DETR (SATE 2)52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
Moment-DETR (SATE 4)53.60±1.235.81±0.954.55±0.830.64±0.731.74±0.435.96±0.256.56±0.9
Moment-DETR (CATE 4)55.10±0.737.02±0.956.21±0.332.00±0.933.19±0.636.43±0.356.98±0.6
Moment-DETR (CATE 4)†56.16±1.238.71±1.156.48±0.833.42±0.734.07±0.637.14±0.458.34±0.4
QD-DETR (SATE 4)†60.48±0.745.21±1.060.84±0.540.45±0.740.12±0.638.66±0.261.29±1.0
QD-DETR (CATE 4)†62.68±1.146.66±0.662.23±1.041.82±0.941.22±0.439.13±0.363.03±0.5
+ +![](images/f9f83d68d6afd571326eef548b593903c4eee81bbb86a5b269cb84fa69eed0ac.jpg) +Figure 4. Ablation study in terms of saliency scores. We plot the histograms of the average value of saliency scores in each video when the positive and negative text queries are given. For positive scores, we only account the scores within GT moments. The average value of each histogram are visualized by the dotted line. The decrease in the overlap between histograms and the increase in the gap between average values confirms the gradual improvements of significance of the query in extracting video representation. + +the baseline (a). To explain, whereas (e) only boosts the MR performances since it only affects the transformer decoder, (b), (c), and (d) are especially beneficial for both MR/HD tasks since they are focused on query-dependent video representations; (b) ensures the contributions of text query in the video representation, (c) fully exploits the contexts of the text query, and (d) provides input-adaptive saliency predictor instead of MLP. Moreover, while our components are verified that they are all complementary to others, DAM's effectiveness is especially dependent on the usage of CATE (compare between $\{(a,e)\}$ and $\{(b,f),(i,j)\}$ ). We claim that this is because DAM exploits the position information of the input tokens to capture the corresponding moments. However, without CATE, input tokens are a mixture of multi-modal tokens, thereby providing confusing position information. + +To provide in-depth examinations of each component, we inspect the difference between the positive and the negative saliency scores in Fig. 4. Since the role of text query is trivial in our baseline, each distribution significantly overlies on top of the other. Then, as we add CATE and negative pair learning, we observe a consistent decrease in overlapped + +![](images/67d07897ce050568b87a5b1df74a5ace352ca8594eba538c76ceb53b5889315b.jpg) +Figure 5. Visualization of results predicted by QD-DETR. Predicted and ground-truth moments are bounded by the lines. Blue, green, and red lines indicate the saliency scores for positive, semi-positive, and negative queries. The positive saliency scores are consistently higher than the others, while the scores for semi-positive are higher than the ones for the negative. + +areas and a larger gap between the average saliency scores of positive and negative histograms. Also, we believe that the widely-distributed histogram of saliency scores for the 'CATE+Neg_pair' is due to using an identical criterion for saliency prediction for diverse video-query representations. By employing an input-adaptive saliency predictor, we notice that scores for positive queries are in almost optimal shape. + +In addition, some might ask whether CATE benefits the training because of additional encoder layers. To answer this, we conduct another ablation study in Tab. 5. Briefly, since our transformer encoder utilizes 2 cross-attention layers and 2 self-attention layers, we conduct comparisons against the transformer encoder composed of 4 self-attention layers (SATE). First, we compare CATE and SATE on MomentDETR; by comparing the results in $2^{\mathrm{nd}}$ and $3^{\mathrm{rd}}$ rows, we find that CATE is much more beneficial than SATE even with the same number of layers. Furthermore, the last two rows show comparisons within QD-DETR architecture that has the same tendency. These results clearly demonstrate that the improvements from CATE are mainly from emphasizing the role of the text query rather than additional layers. + +# 4.4. Qualitative Results + +In this subsection, we study how the query-dependent video representation sensitively reacts to the change in the contexts of the text query. In Fig. 5, the measured saliency scores according to the video-query relevance are visualized. We found that the more the query is relevant to the video clips, the higher the saliency scores retained for the query. For instance, whereas the negative query that is totally irrelevant to the video instance has the lowest scores, the scores for semi-positive reside between the positive and the negative ones. Also, we find that QD-DETR sometimes provides a more precise moment prediction than a given ground-truth + +moment, as can be seen with the temporal box bounded by the dotted lines. We believe that the tendency of a bit higher saliency scores at non-relevant clips for a positive query is due to the information mixing in the self-attention layers. + +# 5. Limitation and Conclusion + +Limitation As elaborated in the paper, we aim to highlight the role of the text query in retrieving the relevant moments and estimating their accordance level with the given text query. Likewise, the proposed components expect a given query to maintain a meaningful context. If not, and noisy text queries are provided, i.e., mismatched or irrelevant ground truth texts, the training may not be effective as reported. + +Conclusion Although the advent of transformer architecture has been powerful for MR/HD, investigation of the role of text query has been lacking in such architectures. Therefore, we focused on studying the role of the text query. As we found that the textual information is not fully exploited in expressing the video representations, we designed the cross-attentive transformer encoder and proposed a negative-pair training scheme. Cross-attentive encoder assures the query's contributions while extracting video representation, and negative-pair training enforces the model to learn the relationship between query and video by preventing solving the problems without consideration of the query. Finally, to preserve the diversity of query-dependent video representation, we defined the saliency token to be an input-adaptive saliency predictor. Extensive experiments validated the strength of QD-DETR with superior performances. + +Acknowledgements. This work was supported in part by MSIT/IITP (No. 2022-0-00680, 2019-0-00421, 2020-0-01821, 2021-0-02068), and MSIT&KNPA/KIPoT (Police Lab 2.0, No. 210121M06). + +# References + +[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the IEEE international conference on computer vision, pages 5803-5812, 2017. 1, 2, 6 +[2] Evlampios Apostolidis, Eleni Adamantidou, Alexandros I Metsai, Vasileios Mezaris, and Ioannis Patras. Video summarization using deep neural networks: A survey. Proceedings of the IEEE, 109(11):1838-1863, 2021. 1 +[3] Taivanbat Badamdorj, Mrigank Rochan, Yang Wang, and Li Cheng. Joint visual and audio learning for video highlight detection. 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The key objective of MR/HD is to localize the moment and estimate clip-wise accordance level, i.e., saliency score, to the given text query. Although the recent transformer-based models brought some advances, we found that these methods do not fully exploit the information of a given query. For example, the relevance between text query and video contents is sometimes neglected when predicting the moment and its saliency. To tackle this issue, we introduce Query-Dependent DETR (QD-DETR), a detection transformer tailored for MR/HD. As we observe the insignificant role of a given query in transformer architectures, our encoding module starts with cross-attention layers to explicitly inject the context of text query into video representation. Then, to enhance the model's capability of exploiting the query information, we manipulate the video-query pairs to produce irrelevant pairs. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 654, + 280, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 654, + 280, + 703 + ], + "spans": [ + { + "bbox": [ + 45, + 654, + 280, + 703 + ], + "type": "text", + "content": "Along with the advance of digital devices and platforms, video is now one of the most desired data types for consumers [2, 48]. Although the large information capacity of videos might be beneficial in many aspects, e.g., informative" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 329, + 263, + 510, + 281 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 329, + 263, + 510, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 263, + 510, + 273 + ], + "spans": [ + { + "bbox": [ + 329, + 263, + 510, + 273 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 329, + 263, + 510, + 273 + ], + "type": "text", + "content": " Positive Query: Man with curly hair speaks directly to camera" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 329, + 273, + 487, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 273, + 487, + 281 + ], + "spans": [ + { + "bbox": [ + 329, + 273, + 487, + 281 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 329, + 273, + 487, + 281 + ], + "type": "text", + "content": " Negative Query: Kids exercise in front of parked cars." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 299, + 283, + 530, + 401 + ], + "blocks": [ + { + "bbox": [ + 299, + 283, + 530, + 401 + ], + "lines": [ + { + "bbox": [ + 299, + 283, + 530, + 401 + ], + "spans": [ + { + "bbox": [ + 299, + 283, + 530, + 401 + ], + "type": "image", + "image_path": "a86f160e33c2691cedb409bae525d3850524cf1f8249fd972f6a8404e08f1c0e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 406, + 531, + 503 + ], + "lines": [ + { + "bbox": [ + 296, + 406, + 531, + 503 + ], + "spans": [ + { + "bbox": [ + 296, + 406, + 531, + 503 + ], + "type": "text", + "content": "Figure 1. Comparison of highlight-ness (saliency score) when relevant and non-relevant queries are given. We found that the existing work only uses queries to play an insignificant role, thereby may not be capable of detecting negative queries and video-query relevance; saliency scores for clips in ground-truth (GT) moments are low and equivalent for positive and negative queries. On the other hand, query-dependent representations of QD-DETR result in corresponding saliency scores to the video-query relevance and precisely localized moments." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 527, + 531, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 527, + 531, + 551 + ], + "spans": [ + { + "bbox": [ + 296, + 527, + 531, + 551 + ], + "type": "text", + "content": "and entertaining, inspecting the videos is time-consuming, so that it is hard to capture the desired moments [1,2]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 553, + 532, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 553, + 532, + 646 + ], + "spans": [ + { + "bbox": [ + 296, + 553, + 532, + 646 + ], + "type": "text", + "content": "Indeed, the need to retrieve user-requested or highlight moments within videos is greatly raised. Numerous research efforts were put into the search for the requested moments in the video [1, 12, 13, 30] and summarizing the video highlights [4, 33, 47, 57]. Recently, Moment-DETR [23] further spotlighted the topic by proposing a QVHighlights dataset that enables the model to perform both tasks, retrieving the moments with their highlight-ness, simultaneously." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 648, + 533, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 533, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 533, + 730 + ], + "type": "text", + "content": "When describing the moment, one of the most favored types of query is the natural language sentence (text) [1]. While early methods utilized convolution networks [14, 44, 59], recent approaches have shown that deploying the attention mechanism of transformer architecture is more effective to fuse the text query into the video representation. For example, Moment-DETR [23] introduced the transformer" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 710, + 127, + 719 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 710, + 127, + 719 + ], + "spans": [ + { + "bbox": [ + 60, + 710, + 127, + 719 + ], + "type": "text", + "content": "* Equal contribution" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 61, + 720, + 137, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 720, + 137, + 730 + ], + "spans": [ + { + "bbox": [ + 61, + 720, + 137, + 730 + ], + "type": "text", + "content": "* Corresponding author" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "text", + "content": "23023" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 257 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 257 + ], + "type": "text", + "content": "architecture which processes both text and video tokens as input by modifying the detection transformer (DETR), and UMT [31] proposed transformer architectures to take multimodal sources, e.g., video and audio. Also, they utilized the text queries in the transformer decoder. Although they brought breakthroughs in the field of MR/HD with seminal architectures, they overlooked the role of the text query. To validate our claim, we investigate the Moment-DETR [23] in terms of the impact of text query in MR/HD (Fig.1). Given the video clips with a relevant positive query and an irrelevant negative query, we observe that the baseline often neglects the given text query when estimating the query-relevance scores, i.e., saliency scores, for each video clip." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 257, + 281, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 257, + 281, + 585 + ], + "spans": [ + { + "bbox": [ + 45, + 257, + 281, + 585 + ], + "type": "text", + "content": "To this end, we propose Query-Dependent DETR (QD-DETR) that produces query-dependent video representation. Our key focus is to ensure that the model's prediction for each clip is highly dependent on the query. First, to fully utilize the contextual information in the query, we revise the transformer encoder to be equipped with cross-attention layers at the very first layers. By inserting a video as the query and a text as the key and value of the cross-attention layers, our encoder enforces the engagement of the text query in extracting video representation. Then, in order to not only inject a lot of textual information into the video feature but also make it fully exploited, we leverage the negative video-query pairs generated by mixing the original pairs. Specifically, the model is learned to suppress the saliency scores of such negative (irrelevant) pairs. Our expectation is the increased contribution of the text query in prediction since the videos will be sometimes required to yield high saliency scores and sometimes low ones depending on whether the text query is relevant or not. Lastly, to apply the dynamic criterion to mark highlights for each instance, we deploy a saliency token to represent the entire video and utilize it as an input-adaptive saliency criterion. With all components combined, our QD-DETR produces query-dependent video representation by integrating source and query modalities. This further allows the use of positional queries [29] in the transformer decoder. Overall, our superior performances over the existing approaches validate the significance of the role of text query for MR/HD." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 597, + 130, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 130, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 130, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 618, + 262, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 262, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 262, + 630 + ], + "type": "text", + "content": "2.1. Moment Retrieval and Highlight Detection" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 636, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 281, + 730 + ], + "type": "text", + "content": "MR is the task of localizing the moment relevant to the given text description. Popular approaches are modeling the cross-modal interaction between text query-video pair [32, 54, 56] or understanding the context of the temporal relation among video clips [1, 59]. On the other hand, TVT [24] exploited the additional data, i.e., subtitle, to capture the moment, and FVMR [14] enhanced the model in terms of inference speed for efficient MR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 106, + 532, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 532, + 293 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 532, + 293 + ], + "type": "text", + "content": "Different from the MR, HD aims to measure the clipwise importance level of the given video [41, 52]. Due to its popularity and applicability, HD can be divided into several branches. From the perspective of annotation, we can categorize HD into supervised, weakly supervised, and unsupervised HD. Supervised HD [15, 41, 50] utilizes fine-grained highlight scores, which are very expensive to collect and annotate [49]. On the other hand, weakly supervised HD [5, 36, 49] learns to detect segments as highlights with video event labels, and finally, unsupervised HD [4, 22, 33, 38] does not require any annotations. Also, while the task is often implemented only with the video, there are works to employ the extra data modalities. Generally, multi-modality was taken into account by using the natural language query to find the desired thumbnail [30] and using additional sources, i.e., audio, to predict highlights [3, 53]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 293, + 533, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 293, + 533, + 444 + ], + "spans": [ + { + "bbox": [ + 296, + 293, + 533, + 444 + ], + "type": "text", + "content": "Although the MR/HD share a common objective to localize or discover the desired part of the given video, they have been studied separately. To handle these tasks at once, Moment-DETR [23] proposed the QVHighlights dataset, which contains a human-written text query and its corresponding moment with clip-level saliency labels. They also introduced the modified version of detection transformer (DETR [6]) to localize the query-relevant moments and their saliency scores. Following them, UMT [31] focused on processing multi-modal data by utilizing both video and audio features. Different from recent works deploying transformer architectures, here we concentrate on producing a query-dependent representation with the transformer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 297, + 455, + 428, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 455, + 428, + 467 + ], + "spans": [ + { + "bbox": [ + 297, + 455, + 428, + 467 + ], + "type": "text", + "content": "2.2. Detection Transformers" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 474, + 533, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 474, + 533, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 474, + 533, + 730 + ], + "type": "text", + "content": "DETR [6], an end-to-end object detector based on vision transformers, is one of the very recent works that utilize the transformer architectures for computer vision [11,42]. Although DETR suffered from slow convergence, it simplifies the prediction process by eliminating the need for anchor generation and non-maximum suppression. Since then, along with the advance in DETR [10, 25, 60], DETR-like architectures have been popular in downstream tasks in both the image [8, 9, 20, 58] and video domains [23, 51]. Some of these works focused on analyzing the role of the decoder query and discovered that using the positional information speeds up the training and also enhances the detection performance [29, 34]. On the other hand, there are trials to extend the application of DETR on multi-modal data [21, 23], especially dealing with the query from different modalities, i.e., text, for detection (or retrieval). They generally handle the multi-modal data by simply forwarding them together to the transformer. In this paper, we also focus on handling the multi-modal data based on DETR-like architecture. However, different from the aforementioned techniques, we concentrate on the query-dependency of the prediction results." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "text", + "content": "23024" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 46, + 104, + 530, + 274 + ], + "blocks": [ + { + "bbox": [ + 46, + 104, + 530, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 104, + 530, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 104, + 530, + 274 + ], + "type": "image", + "image_path": "d660976ee35c69d277aaa39e3c913b05f31a8a86da29fa087230ae61ca5af7a8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 281, + 533, + 368 + ], + "lines": [ + { + "bbox": [ + 45, + 281, + 533, + 368 + ], + "spans": [ + { + "bbox": [ + 45, + 281, + 533, + 368 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed QD-DETR architecture. Given a video and text query, we first extract video and text features from the frozen backbones. These video and text features are forwarded into the cross-attention transformer (Sec. 3.1). This process ensures the consistent contribution of text queries to the video tokens and together with negative pair learning (Sec. 3.2), builds query-dependent video representation. Then, accompanied by the saliency token (Sec. 3.3), video tokens are given to the transformer encoder. In this procedure, the saliency token is transformed into the adaptive saliency prediction criteria. The outputs of the encoder are then, processed to compute losses for both HD and MR. Specifically, the encoder's output tokens are directly projected to saliency scores and optimized for HD, and also provided to the transformer decoder with the learnable moment queries to estimate the query-described moments. Finally, losses for MR are computed by the discrepancy between predicted and their corresponding GT moments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 386, + 187, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 386, + 187, + 399 + ], + "spans": [ + { + "bbox": [ + 45, + 386, + 187, + 399 + ], + "type": "text", + "content": "3. Query-Dependent DETR" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "spans": [ + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": "Moment retrieval and highlight detection have the common objective to find preferred moments with the text query. Given a video of " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " clips and a text query with " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " words, we denote their representations as " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "\\{v_{1}, v_{2}, \\dots, v_{L}\\}" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "\\{t_{1}, t_{2}, \\dots, t_{N}\\}" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " extracted by frozen video and text encoders, respectively. With these representations, the main objective is to localize the center coordinate " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " and width " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "m_{\\sigma}" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " within the video and rank the highlight score (saliency score) " + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "inline_equation", + "content": "\\{s_{1}, s_{2}, \\dots, s_{L}\\}" + }, + { + "bbox": [ + 45, + 410, + 281, + 644 + ], + "type": "text", + "content": " for each clip. A straightforward approach to utilize transformer [11, 43] for the MR is to make a moment-wise prediction as a set of clips [23], or generating the moment according to the clip-wise predictions [31]. To exploit the multi-modal information, e.g., video and text query, they either simply concatenated the features across the modalities or inserted the texts to form the moment query to the transformer decoder. However, we claim that the relationship between the video and text query should be carefully considered rather than a simple concatenation since MR/HD requires every video clip to be conditionally assessed with the text queries." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "content": "Our overall architecture is described in Fig. 2, following the design of concrete baseline, Moment-DETR [23]. Given a video and query representation extracted from fixed backbones, QD-DETR first transforms the video representation to be query-dependent using cross-attention layers. To further enhance the query-awareness of video representations, we incorporate irrelevant video-query pairs with a low saliency" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 387, + 532, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 387, + 532, + 436 + ], + "spans": [ + { + "bbox": [ + 296, + 387, + 532, + 436 + ], + "type": "text", + "content": "for the learning objective. Then, along with the transformer encoder-decoder architectures, the saliency token is defined that turns into an adaptive saliency predictor when attended by the specific video instance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 442, + 493, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 442, + 493, + 454 + ], + "spans": [ + { + "bbox": [ + 296, + 442, + 493, + 454 + ], + "type": "text", + "content": "3.1. Cross-Attentive Transformer Encoder" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 461, + 532, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 461, + 532, + 648 + ], + "spans": [ + { + "bbox": [ + 296, + 461, + 532, + 648 + ], + "type": "text", + "content": "In this subsection, we use italic letters to represent query, key, and value of the cross-attention layers. The key objective of the encoder for MR/HD is to produce clip-wise representations equipped with information regarding the degree of query-relevance since these features are directly used for retrieving the query-matched moments and predicting clip-wise saliency scores. However, the encoding process of existing works may not ensure the query conditioning on every clip. For example, Moment-DETR [23] naively concatenated the video with the query for input to the self-attention layers, which may result in an insignificant role of the query if the high similarities among the video clips overwhelm the contribution of the text query. On the other hand, UMT [31] utilizes the text query only for the synthesis of a moment query in the transformer decoder so thus resulting video representations are not associated with the text query." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 648, + 533, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 533, + 731 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 533, + 731 + ], + "type": "text", + "content": "To take the textual contexts into every video clip representation, we deploy cross-attention layers between the source and the query modalities at the very first layers of the encoder. This ensures the consistent contribution of the query, thereby extracting query-dependent video representation. In detail, whereas the query for cross-attention layers is prepared by projecting the video clips as " + }, + { + "bbox": [ + 296, + 648, + 533, + 731 + ], + "type": "inline_equation", + "content": "Q_{v} = [p_{q}(v_{1}),\\dots,p_{q}(v_{L})]" + }, + { + "bbox": [ + 296, + 648, + 533, + 731 + ], + "type": "text", + "content": ", the" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "text", + "content": "23025" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 117, + 279, + 226 + ], + "blocks": [ + { + "bbox": [ + 52, + 117, + 279, + 226 + ], + "lines": [ + { + "bbox": [ + 52, + 117, + 279, + 226 + ], + "spans": [ + { + "bbox": [ + 52, + 117, + 279, + 226 + ], + "type": "image", + "image_path": "4ea1714826ce73f8a10547dcddf1e9ec9efc479d268679d8e40f2e80a6126076.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 227, + 280, + 293 + ], + "lines": [ + { + "bbox": [ + 45, + 227, + 280, + 293 + ], + "spans": [ + { + "bbox": [ + 45, + 227, + 280, + 293 + ], + "type": "text", + "content": "Figure 3. Illustration of negative pair learning. Typical HL loss is defined only with a positive video-query pair, which is insufficient to learn various degrees of query-relevance. On the other hand, our negative pair learning enforces the model to yield different scores for a video depending on the query and to be learned to suppress saliency scores for the negative query." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "spans": [ + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "content": "key and value are computed with the query text features as " + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "inline_equation", + "content": "K_{t} = [p_{k}(t_{1}),\\dots,p_{k}(t_{N})]" + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "inline_equation", + "content": "V_{t} = [p_{v}(t_{1}),\\dots,p_{v}(t_{N})]" + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "inline_equation", + "content": "p_q(\\cdot), p_k(\\cdot)" + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "inline_equation", + "content": "p_v(\\cdot)" + }, + { + "bbox": [ + 45, + 312, + 281, + 370 + ], + "type": "text", + "content": " are projection layers for query, key, and value. Then, the cross-attention layer operates as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 377, + 279, + 405 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 377, + 279, + 405 + ], + "spans": [ + { + "bbox": [ + 61, + 377, + 279, + 405 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} \\left(Q _ {v}, K _ {t}, V _ {t}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {v} K _ {t} ^ {T}}{\\sqrt {d}}\\right) V _ {t}, \\tag {1}", + "image_path": "b1200843a650e9d1a03e94dd035278ab9094a4fa173a352f240e71214fd72cf3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "spans": [ + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "text", + "content": " is the dimension of the projected key, value, and query. Since the softmax scores are distributed only over the query elements, video clips are expressed with the weighted sum of the text queries in proportion to the similarity to texts. Attention scores are then projected through MLP and integrated into the original video representations as the typical transformer layers. For the rest of the paper, we define the query-dependent video tokens, i.e., the output of cross-attention layers, as " + }, + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "inline_equation", + "content": "X = \\{x_{v}^{1}, x_{v}^{2}, \\ldots, x_{v}^{L}\\}" + }, + { + "bbox": [ + 45, + 411, + 279, + 518 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 524, + 238, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 524, + 238, + 538 + ], + "spans": [ + { + "bbox": [ + 45, + 524, + 238, + 538 + ], + "type": "text", + "content": "3.2. Learning from Negative Relationship" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 543, + 279, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 543, + 279, + 647 + ], + "spans": [ + { + "bbox": [ + 45, + 543, + 279, + 647 + ], + "type": "text", + "content": "While the cross-attention layers explicitly fuse the video and query features for intermediate video clip representations to engage the query information in an architectural way, we argue that given video-text pairs lack diversity to learn the general relationship. For instance, many consecutive clips in a single video often share similar appearances, and the similarity to a specific query will not be highly distinguishable, thereby, the text query may not much affect the prediction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "content": "Thus, we consider the relationships between irrelevant pairs of videos inspired by many recognition practices [17, 26, 27, 35] that learn discriminative features across different categories. To implement such relationships, we define given training video-query pairs as positive pairs and mix the video and query from different pairs to construct negative pairs. Fig. 3 illustrates the ways to augment such negative pairs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 106, + 531, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 531, + 176 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 531, + 176 + ], + "type": "text", + "content": "and utilize them with positive pairs in training. While the video clips in positive pairs are trained to yield segmented saliency scores according to the query-relevance, irrelevant negative video-query pairs are enforced to have the lowest saliency scores. Formally, the loss function for suppressing the saliency of negative pairs " + }, + { + "bbox": [ + 296, + 106, + 531, + 176 + ], + "type": "inline_equation", + "content": "x_{v}^{\\mathrm{neg}}" + }, + { + "bbox": [ + 296, + 106, + 531, + 176 + ], + "type": "text", + "content": " are expressed as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 348, + 182, + 531, + 197 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 182, + 531, + 197 + ], + "spans": [ + { + "bbox": [ + 348, + 182, + 531, + 197 + ], + "type": "interline_equation", + "content": "L _ {\\text {n e g}} = - \\log \\left(1 - S \\left(x _ {v} ^ {\\text {n e g}}\\right)\\right), \\tag {2}", + "image_path": "68b261359a1cf848cf24a7cba5a8ac84a92f553149fa27989a31d67620727ac9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 202, + 532, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 202, + 532, + 283 + ], + "spans": [ + { + "bbox": [ + 296, + 202, + 532, + 283 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 202, + 532, + 283 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 296, + 202, + 532, + 283 + ], + "type": "text", + "content": " is the saliency score predictor. This training scheme can also prevent the model from predicting the moments and highlights solely based on the inter-relationship among video clips without consideration of the query-relevance since the same video instance should be predicted differently depending on whether the positive or negative query is given." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 289, + 476, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 289, + 476, + 303 + ], + "spans": [ + { + "bbox": [ + 296, + 289, + 476, + 303 + ], + "type": "text", + "content": "3.3. Input-Adaptive Saliency Predictor" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 307, + 531, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 307, + 531, + 388 + ], + "spans": [ + { + "bbox": [ + 296, + 307, + 531, + 388 + ], + "type": "text", + "content": "Naive implementation for saliency predictor " + }, + { + "bbox": [ + 296, + 307, + 531, + 388 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 296, + 307, + 531, + 388 + ], + "type": "text", + "content": " would be stacking one or more fully-connected layers. However, such a general head provides identical criteria for the saliency prediction of every video-query pair, neglecting the diverse nature of video and natural language query pairs. This violates our key idea to extract query-dependent video representation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "spans": [ + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": "Thus, we define the saliency token " + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": " to be utilized as an input-adaptive saliency predictor. Briefly, the saliency token is a randomly initialized learnable vector that becomes an input-adaptive predictor when added to the sequence of encoded video tokens and projected through the transformer encoder. To illustrate, as shown in Fig. 2, we first concatenate the saliency token with the query-dependent video tokens " + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": ". We process these tokens to the transformer encoder which makes the saliency token to be re-organized with the input-dependent contexts. Consequently, saliency and video tokens are projected by a corresponding single fully-connected layer with weights, " + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "inline_equation", + "content": "w_{v}" + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": ", respectively, where their scaled-dot product becomes the saliency scores. Formally, saliency score " + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "inline_equation", + "content": "S(x_{v}^{i})" + }, + { + "bbox": [ + 296, + 389, + 532, + 552 + ], + "type": "text", + "content": " is computed as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 354, + 557, + 531, + 584 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 557, + 531, + 584 + ], + "spans": [ + { + "bbox": [ + 354, + 557, + 531, + 584 + ], + "type": "interline_equation", + "content": "S \\left(x _ {v} ^ {i}\\right) = \\frac {\\boldsymbol {w} _ {s} ^ {T} \\boldsymbol {x} _ {s} \\cdot \\boldsymbol {w} _ {v} ^ {T} x _ {v} ^ {i}}{\\sqrt {d}}, \\tag {3}", + "image_path": "731a1ccf79d5dcf7335c28472385f316bc93cebfe0bd7213761a90bc5a93a83c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 589, + 508, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 589, + 508, + 601 + ], + "spans": [ + { + "bbox": [ + 296, + 589, + 508, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 589, + 508, + 601 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 296, + 589, + 508, + 601 + ], + "type": "text", + "content": " is the channel dimension of projected tokens." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 607, + 428, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 607, + 428, + 619 + ], + "spans": [ + { + "bbox": [ + 296, + 607, + 428, + 619 + ], + "type": "text", + "content": "3.4. Decoder and Objectives" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": "Transformer Decoder. Recently, understanding the role of the query in the detection transformer is being spotlighted [29, 34]. It is verified that designing the query with the positional information helps not only for acceleration of training but also for enhancing accuracy. Yet, it is hard to directly employ these studies in tasks handling multi-modal data, e.g., MR/HD, since multi-modal data often have different definitions of position; the position can be understood as time in the video and word order in the text." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 219, + 107, + 287, + 116 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 219, + 107, + 287, + 116 + ], + "spans": [ + { + "bbox": [ + 219, + 107, + 287, + 116 + ], + "type": "text", + "content": "Highlight detection loss" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "text", + "content": "23026" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": "On the contrary, our architectural design eliminates the need to feed the text query to the decoder since the query information is already taken into the video representations. To this end, we modify the 2D dynamic anchor boxes [29] to represent 1D moments in the video. Specifically, we utilize the center coordinate " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " and the duration " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "m_{\\sigma}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " of the moments to design the queries. Similarly to the previous way in the image domain, we pool the features around the center coordinate and modulate the cross-attention map with the moment duration. Then, the coordinates and durations are layer-wisely revised." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "spans": [ + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": "Loss Functions. Training objectives for QD-DETR include loss functions for MR/HD, respectively. First, objective functions for MR, in which the key focus is to locate the desired moments, are adopted from the baseline [23]. Moment retrieval loss " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mr}}" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " measures the discrepancy between the GT moment and the predicted counterpart. It consists of a " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " loss and a generalized IoU loss " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{gIoU}}(\\cdot)" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " from previous work [37] with minor modification to localize temporal moments. Additionally, the cross-entropy loss is used to classify the predicted moments as " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " either to foreground and background by " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CE}} = -\\sum_{y \\in Y} y \\log(\\hat{y})" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{fg}, \\mathrm{bg}\\} \\subset Y" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": ". Thus, " + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mr}}" + }, + { + "bbox": [ + 45, + 253, + 282, + 392 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 404, + 280, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 404, + 280, + 417 + ], + "spans": [ + { + "bbox": [ + 56, + 404, + 280, + 417 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {m r}} = \\lambda_ {L 1} | | m - \\hat {m} | | + \\lambda_ {\\mathrm {g I o U}} L _ {\\mathrm {g I o U}} (m, \\hat {m}) + \\lambda_ {\\mathrm {C E}} L _ {\\mathrm {C E}}, \\tag {4}", + "image_path": "b21475f5e417a2ed6aeeafb261ac82fa0d4760b45e54e1e466aec7b5aabbf5f9.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "spans": [ + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "inline_equation", + "content": "\\hat{m}" + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": " are ground-truth moment and its correspond prediction containing center coordinate " + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": " and duration " + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "inline_equation", + "content": "m_{\\sigma}" + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": ". Also, " + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "inline_equation", + "content": "\\lambda_{*}" + }, + { + "bbox": [ + 45, + 426, + 280, + 462 + ], + "type": "text", + "content": " are hyperparameters for balancing the losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "spans": [ + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "text", + "content": "Loss functions for HD are to estimate the saliency score. It comprises two components; margin ranking loss " + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{margin}}" + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "text", + "content": " and rank-aware contrastive loss " + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{cont}}" + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "text", + "content": ". Following [23], the margin rank loss operates with two pairs of high-rank and low-rank clips. To be specific, the high-rank clips are ensured to retain higher saliency scores than both the low-rank clips within the GT moment and the negative clips outside the GT moment. In short, " + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{margin}}" + }, + { + "bbox": [ + 45, + 463, + 280, + 556 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 565, + 279, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 565, + 279, + 580 + ], + "spans": [ + { + "bbox": [ + 68, + 565, + 279, + 580 + ], + "type": "interline_equation", + "content": "L _ {\\text {m a r g i n}} = \\max (0, \\Delta + S \\left(x ^ {\\text {l o w}}\\right) - S \\left(x ^ {\\text {h i g h}}\\right)) \\tag {5}", + "image_path": "3b8323e7b4af541840ba4f739de032a44e9400841b05cb0a97124829970a5381.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": " is the margin, " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": " is the saliency score estimator, and " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{high}}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{low}}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": " are video tokens from two pairs of high and low-rank clips, respectively. In addition to margin loss which only indirectly guides the saliency predictor, we employ rank-aware contrastive loss [18] to learn the precisely segmented saliency levels with the contrastive loss. Given the maximum rank value " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ", each clip in the mini-batch has a saliency score lower than " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ". Then, we iterate the batch for " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": " times, each time utilizing the samples with higher saliency scores than the iteration index (" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "r \\in \\{0, 1, \\dots, R - 1\\}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ") to build the positive set " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "X_r^{\\mathrm{pos}}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ". Samples with a lower rank than the iteration index are included in the negative set " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "X_r^{\\mathrm{neg}}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ". Then," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 297, + 106, + 494, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 494, + 117 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 494, + 117 + ], + "type": "text", + "content": "the rank-aware contrastive loss " + }, + { + "bbox": [ + 297, + 106, + 494, + 117 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{cont}}" + }, + { + "bbox": [ + 297, + 106, + 494, + 117 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 310, + 125, + 531, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 125, + 531, + 156 + ], + "spans": [ + { + "bbox": [ + 310, + 125, + 531, + 156 + ], + "type": "interline_equation", + "content": "L _ {\\text {c o n t}} = - \\sum_ {r = 1} ^ {R} \\log \\frac {\\sum_ {x \\in X _ {r} ^ {\\text {p o s}}} \\exp (S (x) / \\tau)}{\\sum_ {x \\in \\left(X _ {r} ^ {\\text {p o s}} \\cup X _ {r} ^ {\\text {n e g}}\\right)} \\exp (S (x) / \\tau)} \\tag {6}", + "image_path": "04c803cae242c49bc9a52f7186ecd4c0b4f883f0b487c7c3771fa95f62624147.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "spans": [ + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": " is a temperature scaling parameter. Note that, " + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "inline_equation", + "content": "X_{\\tau}^{\\mathrm{neg}}" + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": " also include all clips in negative pairs " + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "inline_equation", + "content": "x_{v}^{\\mathrm{neg}}" + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": " defined in Sec. 3.2. Finally with margin loss and rank-aware contrastive loss, " + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{hl}}" + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": " and total loss function " + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{total}}" + }, + { + "bbox": [ + 296, + 164, + 531, + 212 + ], + "type": "text", + "content": " are defined as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 348, + 219, + 531, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 219, + 531, + 233 + ], + "spans": [ + { + "bbox": [ + 348, + 219, + 531, + 233 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {h l}} = \\lambda_ {\\text {m a r g i n}} L _ {\\text {m a r g i n}} + \\lambda_ {\\text {c o n t}} L _ {\\text {c o n t}}, \\tag {7}", + "image_path": "64a4c31e090e3ff09e131c8bb625a41e95c476412b9f33d86fc055e0b14fe06f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 354, + 234, + 531, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 234, + 531, + 248 + ], + "spans": [ + { + "bbox": [ + 354, + 234, + 531, + 248 + ], + "type": "interline_equation", + "content": "L _ {\\text {t o t a l}} = L _ {\\mathrm {h l}} + L _ {\\mathrm {m r}} + \\lambda_ {\\mathrm {n e g}} L _ {\\mathrm {n e g}}. \\tag {8}", + "image_path": "f760cea7c78a07e546129314077546e78ecb8f9dc7a8a33af6c3dfcbaa11dd9b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 255, + 367, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 255, + 367, + 267 + ], + "spans": [ + { + "bbox": [ + 297, + 255, + 367, + 267 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 274, + 420, + 287 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 274, + 420, + 287 + ], + "spans": [ + { + "bbox": [ + 297, + 274, + 420, + 287 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 292, + 532, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 292, + 532, + 479 + ], + "spans": [ + { + "bbox": [ + 296, + 292, + 532, + 479 + ], + "type": "text", + "content": "Dataset and Evaluation Metrics. For the evaluation, we validate the effectiveness of query-dependent source representation on QVHighlights [23], TVSum [40], Charades-STA [13]. QVHighlights is the most recently publicized dataset for both moment retrieval and highlight detection. It is also the only dataset that has annotations for both tasks. In detail, QVHighlights consists of over 10,000 videos annotated with human-written text queries. It provides a fair benchmark as the evaluation for the test split can only be measured through submitting the prediction to the QVHighlights server1. Charades-STA and TVSum are the dataset for moment retrieval and video summarization, respectively. Each of them contains 9,848 videos regarding indoor activities and 50 videos of various genres, e.g., news, documentary, and vlog. For all datasets, we follow the data splits from the existing works [23, 31]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 479, + 531, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 479, + 531, + 548 + ], + "spans": [ + { + "bbox": [ + 296, + 479, + 531, + 548 + ], + "type": "text", + "content": "To measure the performances, we use the same evaluation metrics used in the baselines. Specifically, recall@1 with IoU thresholds 0.5 and 0.7, and mean average precision (mAP) at different thresholds. Similarly, we use mAP and HIT@1 for evaluating the highlight detection. HIT@1 is computed through the hit ratio of the highest-scored clip." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 554, + 417, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 554, + 417, + 567 + ], + "spans": [ + { + "bbox": [ + 297, + 554, + 417, + 567 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 572, + 531, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 572, + 531, + 642 + ], + "spans": [ + { + "bbox": [ + 296, + 572, + 531, + 642 + ], + "type": "text", + "content": "We compare QD-DETR against baselines in MR and HD throughout Tab. 1, Tab. 3, and Tab. 2. Our experiments with multi-modal sources, i.e., video with audio, are implemented by simply concatenating the video and audio along the channel axis. Throughout the tables, we use bolds to denote the best scores." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 642, + 531, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 642, + 531, + 714 + ], + "spans": [ + { + "bbox": [ + 296, + 642, + 531, + 714 + ], + "type": "text", + "content": "In Tab. 1, the task is to jointly learn and predict MR/HD. As observed, our QD-DETR outperforms state-of-the-art (SOTA) approaches with all evaluation metrics. Among methods utilizing the video source, QD-DETR shows a dramatic increase with stricter metrics with high IOU; it outperforms previous SOTA by large margins up" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 308, + 719, + 468, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 719, + 468, + 730 + ], + "spans": [ + { + "bbox": [ + 308, + 719, + 468, + 730 + ], + "type": "text", + "content": "1 https://codalab.lisn.upsaclay.fr/competitions/6937" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "text", + "content": "23027" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 133, + 518, + 277 + ], + "blocks": [ + { + "bbox": [ + 45, + 101, + 531, + 123 + ], + "lines": [ + { + "bbox": [ + 45, + 101, + 531, + 123 + ], + "spans": [ + { + "bbox": [ + 45, + 101, + 531, + 123 + ], + "type": "text", + "content": "Table 1. Performance comparison on QVHighlights test split. V and A in the Src column denote video and audio, respectively, representing the modalities of the source data. Our experiments are averaged over five runs and " + }, + { + "bbox": [ + 45, + 101, + 531, + 123 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 45, + 101, + 531, + 123 + ], + "type": "text", + "content": " denotes the standard deviation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 133, + 518, + 277 + ], + "lines": [ + { + "bbox": [ + 57, + 133, + 518, + 277 + ], + "spans": [ + { + "bbox": [ + 57, + 133, + 518, + 277 + ], + "type": "table", + "html": "
MethodSrcMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
BeautyThumb [39]V-----14.3620.88
DVSE [30]V-----18.7521.79
MCN [1]V11.412.7224.948.2210.67--
CAL [12]V25.4911.5423.407.659.89--
XML [24]V41.8330.3544.6331.7332.1434.4955.25
XML+ [24]V46.6933.4647.8934.6734.9035.3855.06
Moment-DETR [23]V52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
QD-DETR (Ours)V62.40±1.144.98±0.862.52±0.639.88±0.739.86±0.638.94±0.462.40±1.4
UMT [31]V+A56.2341.1853.3837.0136.1238.1859.99
QD-DETR (Ours)V+A63.06±1.045.10±0.763.04±0.940.10±1.040.19±0.639.04±0.362.87±0.6
", + "image_path": "17ba11897741b48417c63a267da5fe53c3f0729a51b4e360bb5398a2ae9b38d5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 83, + 306, + 490, + 440 + ], + "blocks": [ + { + "bbox": [ + 158, + 287, + 416, + 298 + ], + "lines": [ + { + "bbox": [ + 158, + 287, + 416, + 298 + ], + "spans": [ + { + "bbox": [ + 158, + 287, + 416, + 298 + ], + "type": "text", + "content": "Table 2. Highlight detection performance comparison on TVsum dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 306, + 490, + 440 + ], + "lines": [ + { + "bbox": [ + 83, + 306, + 490, + 440 + ], + "spans": [ + { + "bbox": [ + 83, + 306, + 490, + 440 + ], + "type": "table", + "html": "
MethodSrcVTVUGAMSPKPRFMBKBTDSAvg.
sLSTM [57]V41.146.246.347.744.846.145.240.647.145.545.1
SG [33]V42.347.247.548.945.647.346.441.748.346.646.2
LIM-S [49]V55.942.961.254.060.347.543.266.369.162.656.3
Trailer [45]V61.354.665.760.859.170.158.264.765.668.162.8
SL-Module [50]V86.568.774.986.279.063.258.972.678.964.073.3
QD-DETR (Ours)V88.287.485.685.085.886.976.491.389.273.785.0
MINI-Net [19]V+A80.668.378.281.878.165.857.875.080.265.573.2
TCG [53]V+A85.071.481.978.680.275.571.677.378.668.176.8
Joint-VA [3]V+A83.757.378.586.180.169.270.073.097.467.576.3
UMT [31]V+A87.581.588.278.881.487.076.086.984.479.683.1
QD-DETR (Ours)V+A87.691.790.288.384.188.378.791.287.877.786.6
", + "image_path": "e172e88f6e9dd6c454767b837a18e2bcd35308c865965894e13f0f7782a9a2a2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 47, + 485, + 279, + 583 + ], + "blocks": [ + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "lines": [ + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "spans": [ + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "type": "text", + "content": "Table 3. Charades dataset. " + }, + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "type": "text", + "content": " denotes the method using the video and audio as the source. " + }, + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\mathrm{SF + C}" + }, + { + "bbox": [ + 45, + 455, + 279, + 476 + ], + "type": "text", + "content": " stands for Slowfast and CLIP features." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 485, + 279, + 583 + ], + "lines": [ + { + "bbox": [ + 47, + 485, + 279, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 279, + 583 + ], + "type": "table", + "html": "
MethodfeatR1@0.5R1@0.7MethodfeatR1@0.5R1@0.7
SAPVGG27.4213.36CTRLC3D23.638.89
TripNetVGG36.6114.50ACLC3D30.4812.20
SM-RLVGG24.3611.17RWM-RLC3D36.70-
MANVGG41.2420.54MANC3D46.5322.72
2D-TANVGG40.9422.85DEBUGC3D37.3917.69
FVMRVGG42.3624.14VSLNetC3D47.3130.19
UMT†VGG48.3129.25OursC3D50.6731.02
OursVGG52.7731.13M-DETRSF+C53.6331.37
Ours†VGG55.5134.17OursSF+C57.3132.55
", + "image_path": "c4e935c3e40d098a0612fd450190056a8e3a34740198990b99712b91a7ef7d73.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "spans": [ + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "text", + "content": "to " + }, + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "inline_equation", + "content": "36\\%" + }, + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "text", + "content": " in R1@0.7 and mAP@0.75. On the other hand, QD-DETR with video and audio sources boosts " + }, + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "inline_equation", + "content": "11.84\\%" + }, + { + "bbox": [ + 45, + 609, + 279, + 681 + ], + "type": "text", + "content": " on average of the metrics for MR compared to the SOTA method employing the multi-modal source data. These results verify the importance of emphasizing the source (video-only or video+audio) descriptive contexts in the text queries." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": "Results in Tab. 3 also compare MR performances against the models using VGG [7,14,31,46,55,59], C3D [13,16,28,32,55,56], and Slowfast (SF) and CLIP features [23] on Charades dataset. For a fair comparison, we enumerate" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 457, + 531, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 457, + 531, + 526 + ], + "spans": [ + { + "bbox": [ + 296, + 457, + 531, + 526 + ], + "type": "text", + "content": "each method with its backbone and compare within it. For each feature from VGG, C3D, and " + }, + { + "bbox": [ + 296, + 457, + 531, + 526 + ], + "type": "inline_equation", + "content": "\\mathrm{SF + C}" + }, + { + "bbox": [ + 296, + 457, + 531, + 526 + ], + "type": "text", + "content": ", we follow the data preparation settings from UMT [31], VSLNet [56], and Moment-DETR [23]. As reported, we validate that our model surpasses the existing SOTA methods in every type of feature." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 527, + 532, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 527, + 532, + 643 + ], + "spans": [ + { + "bbox": [ + 296, + 527, + 532, + 643 + ], + "type": "text", + "content": "For video highlight detection in Tab. 2, we follow the protocols from the previous work [31]. Specifically, we train the model for each category and average the mAP scores. Out of 10 categories, QD-DETR outperforms baselines on 9 categories when the only video source is available, and 8 categories when both video and audio are available. Overall, compared to methods with video-only and multi-modal sources, QD-DETR establishes new SOTA performances by improving by " + }, + { + "bbox": [ + 296, + 527, + 532, + 643 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 296, + 527, + 532, + 643 + ], + "type": "text", + "content": " in average compared to the previous SOTA model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 652, + 387, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 652, + 387, + 665 + ], + "spans": [ + { + "bbox": [ + 297, + 652, + 387, + 665 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 671, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 532, + 730 + ], + "type": "text", + "content": "To investigate the effectiveness of each component in our work, we conduct an extensive ablation study in Tab. 4. Note that, CATE and DAM denote cross-attentive transformer encoder and dynamic anchor moments, respectively. Rows (b) to (e) show the effectiveness of each component compared to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "text", + "content": "23028" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 138, + 503, + 282 + ], + "blocks": [ + { + "bbox": [ + 45, + 107, + 530, + 129 + ], + "lines": [ + { + "bbox": [ + 45, + 107, + 530, + 129 + ], + "spans": [ + { + "bbox": [ + 45, + 107, + 530, + 129 + ], + "type": "text", + "content": "Table 4. Ablation study on QVHighlights val split. CATE and DAM stands for cross-attentive transformer encoder and using dynamic anchor moments as the decoder query, respectively. All the quantities are averaged over 5 runs." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 138, + 503, + 282 + ], + "lines": [ + { + "bbox": [ + 71, + 138, + 503, + 282 + ], + "spans": [ + { + "bbox": [ + 71, + 138, + 503, + 282 + ], + "type": "table", + "html": "
CATENeg. PairSaliency TokenDAMMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
(a)52.8933.0254.8229.4030.7335.6955.60
(b)✓56.1638.7156.4833.4234.0737.1458.34
(c)✓58.6939.8358.3934.8435.4039.0262.81
(d)✓55.4837.0055.8126.7532.8437.4858.59
(e)✓53.1935.9155.5832.5533.3335.6855.56
(f)✓✓57.7242.3559.1038.1638.0336.5657.44
(g)✓✓59.5742.1259.1936.6336.7638.6461.62
(h)✓✓60.0040.9759.2135.4135.8939.0662.88
(i)✓✓✓60.3242.3959.4736.7936.9339.2162.76
(j)✓✓✓✓62.6846.6662.2341.8241.2239.1363.03
", + "image_path": "7e1e9dbab5c615803e366858508c8fb2758d1e4b4dc8a447fc04721197e1b462.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 69, + 357, + 506, + 458 + ], + "blocks": [ + { + "bbox": [ + 45, + 294, + 532, + 348 + ], + "lines": [ + { + "bbox": [ + 45, + 294, + 532, + 348 + ], + "spans": [ + { + "bbox": [ + 45, + 294, + 532, + 348 + ], + "type": "text", + "content": "Table 5. Ablation study on cross-attention transformer encoder. We compare ours against the deepened transformer encoder with self-attention layers to validate that the performance gain does not come from additional parameters. SATE and CATE each indicate the transformer encoder only with self-attention layers and our transformer encoder. The numbers in the parenthesis denote the number of layers. For the experiment with " + }, + { + "bbox": [ + 45, + 294, + 532, + 348 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 45, + 294, + 532, + 348 + ], + "type": "text", + "content": ", we only use the query features as the condition in the encoder and only the video representations are processed by the decoder." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 357, + 506, + 458 + ], + "lines": [ + { + "bbox": [ + 69, + 357, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 69, + 357, + 506, + 458 + ], + "type": "table", + "html": "
T2VMRHD
R1mAP>= Very Good
@0.5@0.7@0.5@0.75Avg.mAPHIT@1
Moment-DETR (SATE 2)52.89±2.333.02±1.754.82±1.729.40±1.730.73±1.435.69±0.555.60±1.6
Moment-DETR (SATE 4)53.60±1.235.81±0.954.55±0.830.64±0.731.74±0.435.96±0.256.56±0.9
Moment-DETR (CATE 4)55.10±0.737.02±0.956.21±0.332.00±0.933.19±0.636.43±0.356.98±0.6
Moment-DETR (CATE 4)†56.16±1.238.71±1.156.48±0.833.42±0.734.07±0.637.14±0.458.34±0.4
QD-DETR (SATE 4)†60.48±0.745.21±1.060.84±0.540.45±0.740.12±0.638.66±0.261.29±1.0
QD-DETR (CATE 4)†62.68±1.146.66±0.662.23±1.041.82±0.941.22±0.439.13±0.363.03±0.5
", + "image_path": "a62571bd5984ace8068cc9c920e7bfaf1c6c2436a545f5f68a6307dcf2784306.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 54, + 479, + 274, + 648 + ], + "blocks": [ + { + "bbox": [ + 54, + 479, + 274, + 648 + ], + "lines": [ + { + "bbox": [ + 54, + 479, + 274, + 648 + ], + "spans": [ + { + "bbox": [ + 54, + 479, + 274, + 648 + ], + "type": "image", + "image_path": "f9f83d68d6afd571326eef548b593903c4eee81bbb86a5b269cb84fa69eed0ac.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 656, + 281, + 742 + ], + "lines": [ + { + "bbox": [ + 45, + 656, + 281, + 742 + ], + "spans": [ + { + "bbox": [ + 45, + 656, + 281, + 742 + ], + "type": "text", + "content": "Figure 4. Ablation study in terms of saliency scores. We plot the histograms of the average value of saliency scores in each video when the positive and negative text queries are given. For positive scores, we only account the scores within GT moments. The average value of each histogram are visualized by the dotted line. The decrease in the overlap between histograms and the increase in the gap between average values confirms the gradual improvements of significance of the query in extracting video representation." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "spans": [ + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "text", + "content": "the baseline (a). To explain, whereas (e) only boosts the MR performances since it only affects the transformer decoder, (b), (c), and (d) are especially beneficial for both MR/HD tasks since they are focused on query-dependent video representations; (b) ensures the contributions of text query in the video representation, (c) fully exploits the contexts of the text query, and (d) provides input-adaptive saliency predictor instead of MLP. Moreover, while our components are verified that they are all complementary to others, DAM's effectiveness is especially dependent on the usage of CATE (compare between " + }, + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "inline_equation", + "content": "\\{(a,e)\\}" + }, + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "inline_equation", + "content": "\\{(b,f),(i,j)\\}" + }, + { + "bbox": [ + 296, + 477, + 532, + 652 + ], + "type": "text", + "content": "). We claim that this is because DAM exploits the position information of the input tokens to capture the corresponding moments. However, without CATE, input tokens are a mixture of multi-modal tokens, thereby providing confusing position information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 660, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 532, + 730 + ], + "type": "text", + "content": "To provide in-depth examinations of each component, we inspect the difference between the positive and the negative saliency scores in Fig. 4. Since the role of text query is trivial in our baseline, each distribution significantly overlies on top of the other. Then, as we add CATE and negative pair learning, we observe a consistent decrease in overlapped" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 300, + 756 + ], + "type": "text", + "content": "23029" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 104, + 530, + 281 + ], + "blocks": [ + { + "bbox": [ + 49, + 104, + 530, + 281 + ], + "lines": [ + { + "bbox": [ + 49, + 104, + 530, + 281 + ], + "spans": [ + { + "bbox": [ + 49, + 104, + 530, + 281 + ], + "type": "image", + "image_path": "67d07897ce050568b87a5b1df74a5ace352ca8594eba538c76ceb53b5889315b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 287, + 531, + 320 + ], + "lines": [ + { + "bbox": [ + 45, + 287, + 531, + 320 + ], + "spans": [ + { + "bbox": [ + 45, + 287, + 531, + 320 + ], + "type": "text", + "content": "Figure 5. Visualization of results predicted by QD-DETR. Predicted and ground-truth moments are bounded by the lines. Blue, green, and red lines indicate the saliency scores for positive, semi-positive, and negative queries. The positive saliency scores are consistently higher than the others, while the scores for semi-positive are higher than the ones for the negative." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 332, + 279, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 332, + 279, + 414 + ], + "spans": [ + { + "bbox": [ + 45, + 332, + 279, + 414 + ], + "type": "text", + "content": "areas and a larger gap between the average saliency scores of positive and negative histograms. Also, we believe that the widely-distributed histogram of saliency scores for the 'CATE+Neg_pair' is due to using an identical criterion for saliency prediction for diverse video-query representations. By employing an input-adaptive saliency predictor, we notice that scores for positive queries are in almost optimal shape." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "spans": [ + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "text", + "content": "In addition, some might ask whether CATE benefits the training because of additional encoder layers. To answer this, we conduct another ablation study in Tab. 5. Briefly, since our transformer encoder utilizes 2 cross-attention layers and 2 self-attention layers, we conduct comparisons against the transformer encoder composed of 4 self-attention layers (SATE). First, we compare CATE and SATE on MomentDETR; by comparing the results in " + }, + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "inline_equation", + "content": "2^{\\mathrm{nd}}" + }, + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "inline_equation", + "content": "3^{\\mathrm{rd}}" + }, + { + "bbox": [ + 45, + 414, + 280, + 576 + ], + "type": "text", + "content": " rows, we find that CATE is much more beneficial than SATE even with the same number of layers. Furthermore, the last two rows show comparisons within QD-DETR architecture that has the same tendency. These results clearly demonstrate that the improvements from CATE are mainly from emphasizing the role of the text query rather than additional layers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 583, + 154, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 583, + 154, + 596 + ], + "spans": [ + { + "bbox": [ + 45, + 583, + 154, + 596 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 602, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 602, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 602, + 280, + 730 + ], + "type": "text", + "content": "In this subsection, we study how the query-dependent video representation sensitively reacts to the change in the contexts of the text query. In Fig. 5, the measured saliency scores according to the video-query relevance are visualized. We found that the more the query is relevant to the video clips, the higher the saliency scores retained for the query. For instance, whereas the negative query that is totally irrelevant to the video instance has the lowest scores, the scores for semi-positive reside between the positive and the negative ones. Also, we find that QD-DETR sometimes provides a more precise moment prediction than a given ground-truth" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 332, + 531, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 332, + 531, + 379 + ], + "spans": [ + { + "bbox": [ + 296, + 332, + 531, + 379 + ], + "type": "text", + "content": "moment, as can be seen with the temporal box bounded by the dotted lines. We believe that the tendency of a bit higher saliency scores at non-relevant clips for a positive query is due to the information mixing in the self-attention layers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 387, + 446, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 387, + 446, + 399 + ], + "spans": [ + { + "bbox": [ + 296, + 387, + 446, + 399 + ], + "type": "text", + "content": "5. Limitation and Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 406, + 531, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 406, + 531, + 489 + ], + "spans": [ + { + "bbox": [ + 296, + 406, + 531, + 489 + ], + "type": "text", + "content": "Limitation As elaborated in the paper, we aim to highlight the role of the text query in retrieving the relevant moments and estimating their accordance level with the given text query. Likewise, the proposed components expect a given query to maintain a meaningful context. If not, and noisy text queries are provided, i.e., mismatched or irrelevant ground truth texts, the training may not be effective as reported." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 492, + 532, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 492, + 532, + 678 + ], + "spans": [ + { + "bbox": [ + 296, + 492, + 532, + 678 + ], + "type": "text", + "content": "Conclusion Although the advent of transformer architecture has been powerful for MR/HD, investigation of the role of text query has been lacking in such architectures. Therefore, we focused on studying the role of the text query. As we found that the textual information is not fully exploited in expressing the video representations, we designed the cross-attentive transformer encoder and proposed a negative-pair training scheme. Cross-attentive encoder assures the query's contributions while extracting video representation, and negative-pair training enforces the model to learn the relationship between query and video by preventing solving the problems without consideration of the query. Finally, to preserve the diversity of query-dependent video representation, we defined the saliency token to be an input-adaptive saliency predictor. Extensive experiments validated the strength of QD-DETR with superior performances." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 682, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 532, + 730 + ], + "type": "text", + "content": "Acknowledgements. This work was supported in part by MSIT/IITP (No. 2022-0-00680, 2019-0-00421, 2020-0-01821, 2021-0-02068), and MSIT&KNPA/KIPoT (Police Lab 2.0, No. 210121M06)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 301, + 756 + ], + "type": "text", + "content": "23030" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 281, + 730 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 51, + 124, + 281, + 178 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 281, + 178 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 281, + 178 + ], + "type": "text", + "content": "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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International Conference on Learning Representations, ICLR 2021, 2021. 2" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "23033" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_content_list.json b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e99dd10eaf965e32599417cbc5dd5da003ba21 --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_content_list.json @@ -0,0 +1,1245 @@ +[ + { + "type": "text", + "text": "$R^2$ Former: Unified Retrieval and Reranking Transformer for Place Recognition", + "text_level": 1, + "bbox": [ + 83, + 128, + 887, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sijie Zhu $^{1,2,\\dagger}$ , Linjie Yang $^{1}$ , Chen Chen $^{2}$ , Mubarak Shah $^{2}$ , Xiaohui Shen $^{1}$ , Heng Wang $^{1}$ , ByteDance $^{2}$ Center for Research in Computer Vision, University of Central Florida", + "bbox": [ + 158, + 179, + 846, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sijiezhu,linjie.yang,heng.wang,shenxiaohui.kevin}@bytedance.com,{chen.chen,shah}@crcv.ucf.edu", + "bbox": [ + 86, + 218, + 921, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Place Recognition (VPR) estimates the location of query images by matching them with images in a reference database. Conventional methods generally adopt aggregated CNN features for global retrieval and RANSAC-based geometric verification for reranking. However, RANSAC only employs geometric information but ignores other possible information that could be useful for reranking, e.g. local feature correlations, and attention values. In this paper, we propose a unified place recognition framework that handles both retrieval and reranking with a novel transformer model, named $R^2$ Former. The proposed reranking module takes feature correlation, attention value, and xy coordinates into account, and learns to determine whether the image pair is from the same location. The whole pipeline is end-to-end trainable and the reranking module alone can also be adopted on other CNN or transformer backbones as a generic component. Remarkably, $R^2$ Former significantly outperforms state-of-the-art methods on major VPR datasets with much less inference time and memory consumption. It also achieves the state-of-the-art on the hold-out MSLS challenge set and could serve as a simple yet strong solution for real-world large-scale applications. Experiments also show vision transformer tokens are comparable and sometimes better than CNN local features on local matching. The code is released at https://github.com/Jeff-Zilence/R2Former.", + "bbox": [ + 75, + 301, + 473, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 726, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Place Recognition (VPR) aims to localize query images from unknown locations by matching them with a set of reference images from known locations. It has great potential for robotics [47], navigation [41], autonomous driving [9], augmented reality (AR) applications. Previous works [26, 53] generally formulate VPR as a retrieval problem with two stages, i.e. global retrieval, and reranking. The global retrieval stage usually applies aggregation", + "bbox": [ + 75, + 752, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/75aaabf6c94297b6f622e9a3e58b255ed60584a8ffcf5b56414ae4bd42781ee0.jpg", + "image_caption": [ + "Figure 1. An overview of conventional pipeline and our unified framework. Both our global retrieval and reranking modules are end-to-end trainable transformer layers, which achieve state-of-the-art performance with much less computational cost." + ], + "image_footnote": [], + "bbox": [ + 501, + 266, + 890, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "methods (e.g. NetVLAD [3] and GeM [43]) on top of CNN (Convolutional Neural Network) to retrieve top candidates from a large reference database. While some works [3, 6] only adopt global retrieval, current state-of-the-art methods [26, 53] conduct reranking (i.e. geometric verification with RANSAC [19]) on the top-k (e.g. $k = 100$ ) candidates to further confirm the matches, typically leading to a significant performance boost. However, geometric information is not the only information that could be useful for reranking, and task-relevant information could be learned with a data-driven module to further boost performance. Besides, the current reranking process requires a relatively large inference time and memory footprint (typically over 1s and 1MB per image), which cannot scale to real-world applications with large QPS (Queries Per Second) and reference database ( $>1\\mathrm{M}$ images).", + "bbox": [ + 496, + 612, + 892, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently vision transformer [17] has achieved significant performance on a wide range of vision tasks, and has been shown to have a high potential for VPR [53] (Sec. 2).", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† This work was done during the first author's internship at ByteDance", + "bbox": [ + 99, + 886, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19370", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the predominant local features [26, 53] are still based on CNN backbones, due to the built-in feature locality with limited receptive fields. Although vision transformer [17] considers each patch as an input token and naturally encodes local information, the local information might be overwritten with global information by the strong global correlation between all tokens in every layer. Therefore, it is still unclear how vision transformer tokens perform in local matching as compared to CNN local features in this field.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we integrate the global retrieval and reranking into one unified framework employing only transformers (Fig. 1), abbreviated as $R^2$ Former, which is simple, efficient, and effective. The global retrieval is tackled based on the class token without additional aggregation modules [3,43] and the other image tokens are adopted as local features. Different from geometric verification which focuses on geometric information between local feature pairs, we feed the correlation between the tokens (local features) of a pair of images, xy coordinates of tokens, and their attention information to transformer modules, so that the module can learn task-relevant information that could be useful for reranking. The global retrieval and reranking parts can be either trained in an end-to-end manner or tuned alternatively with a more stable convergence. The proposed reranking module can also be adopted on other CNN or transformer backbones, and our comparison shows that vision transformer tokens are comparable to CNN local features in terms of reranking performance (Table 6).", + "bbox": [ + 75, + 229, + 472, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Without bells and whistles, the proposed method outperforms both retrieval-only and retrieval+reranking state-of-the-art methods on a wide range of VPR datasets. The proposed method follows a very efficient design and applies linear layers for dimension reduction: i.e. only 256 and $500 \\times 131$ for global and local feature dimensions and only 32 for transformer dimension of reranking module, thus is significantly faster ( $>4.7 \\times \\mathrm{QPS}$ ) with much less ( $< 22\\%$ ) memory consumption than previous methods [26, 53]. Both the global and local features are extracted from the same backbone model only once, and the reranking of top-k candidates is finished with only one forward pass by computing the reranking scores of all candidate pairs in parallel within one batch. The reranking speed can be further boosted by parallel computing on multiple GPUs with $>20 \\times$ speedup over previous methods [26, 53]. We demonstrate that the proposed reranking module also learns to focus on good local matches like RANSAC [19]. We summarize our contributions as follows:", + "bbox": [ + 75, + 518, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A unified retrieval and reranking framework for place recognition employing pure transformers, which demonstrates that vision transformer tokens are comparable and sometimes better than CNN local features in terms of reranking or local matching.", + "- A novel transformer-based reranking module that learns" + ], + "bbox": [ + 76, + 810, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to attend to the correlation of informative local feature pairs. It can be combined with either CNN or transformer backbones with better performance and efficiency than other reranking methods, e.g. RANSAC.", + "bbox": [ + 509, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments showing state-of-the-art performance on a wide range of place recognition datasets with significantly less ( $< 22\\%$ ) inference latency and memory consumption than previous reranking-based methods.", + "bbox": [ + 500, + 152, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 224, + 640, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Place Recognition. Visual place recognition (VPR) [2, 21, 38, 39, 47, 58, 60] is traditionally addressed with nearest neighbor search on aggregated [28] hand-crafted features [12, 37]. The current predominant methods [3-6, 26, 53] are based on CNN [27, 46] feature extractors with trainable aggregation layer, e.g. NetVLAD [3], CRN [30], or light-weighted pooling layer, e.g. GeM [43], R-MAC [24]. Numerous works [7, 20, 22, 23, 34, 54, 55] follow NetVLAD [3] to further improve the global representation for retrieval. Recently, Berton [6] et al. introduce a benchmark for VPR and implement a wide range of global-retrieval-based methods in the same framework. CosPlace [4] et al. propose an extremely large dataset and formulate the problem differently as classification using orientation information.", + "bbox": [ + 496, + 250, + 893, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to global retrieval, recent state-of-the-art VPR methods [26, 53] apply reranking on the top retrieved candidates. Patch-NetVLAD [26] adopts NetVLAD [3] model as their backbone for global retrieval and applies RANSAC [19] based geometric verification on multi-scale patch descriptors. TransVPR [53] adds multiple transformer layers on the top of CNN backbones to extract both global and local features. An additional attention module is then deployed to select important local features as the input of RANSAC [19]. Other local matching methods from related tasks, e.g. SuperGlue [15,44] and DELG [10], are also evaluated for VPR. However, they both have a lower accuracy with a much slower inference speed [53]. Recently, there are several recent learning-based reranking methods from related tasks, e.g. landmark matching [31,48] and local matching [29]. While they either fail to generalize [31,48] on VPR (Table 4) or have a very different problem setting [29], i.e. computing point-to-point correspondence between two given images without global retrieval. To summarize, current state-of-the-art VPR methods rely on RANSAC, and methods from related tasks do not generalize well when directly applied to VPR. Our method takes one step forward to integrate retrieval and reranking into one unified VPR framework with pure transformers.", + "bbox": [ + 496, + 463, + 893, + 825 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision Transformer. Transformer [52] is first proposed for NLP (Natural Language Processing) tasks as a generic architecture without inductive bias. It is recently introduced to vision tasks as vision transformer [17] (ViT) by simply considering each image patch as a token. The vanilla ViT", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19371", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dcd0ac18f460a95c5412df5ba73d86faa745bb96c5a79be92754b610504d48c8.jpg", + "image_caption": [ + "Figure 2. An overview of the proposed framework. Both the global and local features are extracted as the class token and patch tokens, followed by dimension reduction using linear layers. The important local features are then selected based on the attention map (Fig. 3) and fed into the reranking module. Both the global retrieval and reranking modules consist of only transformer and linear layers." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 843, + 366 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[17] requires large-scale training datasets (e.g. ImageNet-21k [14]) to achieve comparable results as CNN [27], and Deit [51] proposes a data-efficient training strategy for ViT which outperforms CNN on standard ImageNet-1k. The recent VG benchmark [6] adopts vanilla ViT without modifying the input resolution which could be suboptimal, while it already shows competitive performance on global retrieval. TransVPR [53] adopts multiple transformer layers, while the backbone feature extractor is still based on CNN. We hypothesize the power of vision transformer is not fully exploited for VPR and it is interesting to know how vision transformer tokens perform on reranking/local matching as compared with the predominant CNN local feature.", + "bbox": [ + 75, + 425, + 472, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. $R^2$ Former", + "text_level": 1, + "bbox": [ + 76, + 632, + 191, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first formulate the problem and training objective of the proposed method in Sec. 3.1. Then we describe global retrieval and reranking stages in Sec. 3.2 and Sec. 3.3 respectively. Fig. 2 shows an overview of $R^2$ Former.", + "bbox": [ + 75, + 657, + 468, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation and Training Objective", + "text_level": 1, + "bbox": [ + 76, + 726, + 465, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed framework consists of two stages, i.e. global retrieval, and reranking. Given a set of query images $\\{I_q\\}$ and reference images $\\{I_r\\}$ , the objective of global retrieval is to learn an embedding space in which each query $I_{q}$ is close to its corresponding positive reference image $I_{r}$ . During training, reference images from the same location as the query image are defined as positive samples, and the typical threshold is set as 10 meters. We follow the common practice of previous works [3,6] to find the nearest reference image for each query in the embedding space as the", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "final positive sample. Other reference images with distances greater than 25 meters are considered as negative samples. Partial negative mining [6] is conducted to select the hardest negative samples from a random subset. We denote the global embedding features of query, positive samples, and negative samples as $E_{q}, E_{p}, E_{n}$ and the global retrieval loss is trained with margin triplet loss:", + "bbox": [ + 496, + 425, + 893, + 532 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e t r i e v a l}} = \\max \\left(\\left| \\left| E _ {q} - E _ {p} \\right| \\right| ^ {2} - \\left| \\left| E _ {q} - E _ {n} \\right| \\right| ^ {2} + m, 0\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 539, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here $||.||^2$ denotes squared L2 norm and $m$ is the margin.", + "bbox": [ + 498, + 564, + 879, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reranking module takes the local features of two images as input and generates two-logit scores $\\mathbb{L}$ as the output of a binary classification, representing the likelihoods for True or False matches. We feed both positive and negative query-reference pairs to the reranking module during training and the cross entropy $(CE)$ loss is formulated as:", + "bbox": [ + 496, + 580, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e r a n k i n g}} = C E \\left(\\operatorname {S o f t m a x} \\left(\\mathbb {L} _ {q r}\\right), \\mathbb {I} _ {q r}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 679, + 890, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{L}$ and $\\mathbb{I}$ denote the logits scores and ground-truth labels for the query-reference pairs. Although the partial negative mining [6] is shown to perform better than full negative mining for global retrieval in [6], the objective of the reranking module is to distinguish top-k retrieved candidates which are harder than partial negative samples [6]. To make sure the reranking module sees top-k hardest samples during training, we first freeze the global retrieval module and train the reranking module with randomly selected negative samples from the top-k hardest samples of the full database. The retrieval and reranking modules are then finetuned together with partial negative mining for better performance. Details are provided in Sec. 4.2.", + "bbox": [ + 496, + 703, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19372", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Global Retrieval Module", + "text_level": 1, + "bbox": [ + 76, + 90, + 305, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe the components of our vision transformer backbone for VPR and how the final global/local features are generated. As shown in Fig. 2, the query and reference images share the same backbone transformer encoder and there is no additional aggregation [3, 43] or key-point [15] extraction module for global and local feature generation. In other words, all the features and intermediate data are directly generated using only transformers.", + "bbox": [ + 75, + 114, + 470, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ViT for Place Recognition. An input image $I \\in \\mathbb{R}^{h \\times w \\times c}$ is first divided into small $p \\times p$ patches ( $p = 16$ by default) and converted into a number of tokens $T \\in \\mathbb{R}^{n \\times d}$ by linear projection as the input of transformer encoders. Here $n, d$ denote the number and dimension of tokens, and $h, w, c$ denote the height, width, and number of channels in input images. In addition to the $n$ patch tokens, ViT [17] adds an additional learnable class token to aggregate classification information from each layer, which serves as a simple alternative for feature aggregation. Then we adopt the learnable position embedding $PE \\in \\mathbb{R}^{(n + 1) \\times d}$ from ViT [17] and add it to each token to provide positional information. Different from previous work [6] using the fixed training resolution of ViT [17], we conduct 2D interpolation on the positional embedding so that the input resolution can be arbitrary and we use the most widely used resolution ( $640 \\times 480$ ) for our method.", + "bbox": [ + 75, + 234, + 473, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Global Attention. On the bottom right of Fig. 2, we provide the detailed inner architecture of the transformer encoder, which has $L$ cascaded basic transformer [52] layers. The key component is the multi-head attention module, which adopts three linear projections to convert the input token into query, key and value, denoted as $Q, K, V$ with dimension $d$ . The basic attention is computed as $\\text{softmax}(QK^{\\top} / d)V$ (T means transpose), and a multi-head attention module performs this attention procedure in parallel for multiple heads with their final outputs concatenated. The multi-head attention module can model stronger global correlation than CNN with a limited receptive field, which helps information aggregation for global representation. However, it might reduce the locality of each token which could be harmful to local matching, we demonstrate that transformer tokens perform well as local features compared to CNN as shown in Table 6.", + "bbox": [ + 75, + 492, + 470, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dimension Reduction. We feed the output class token from the last transformer layer into a linear layer to generate the global feature with only 256 dimensions. The local features are generated by applying a linear head on the output patch tokens of the penultimate transformer layer and the dimension is reduced to 128 to achieve a small memory consumption. Both global and local features are L2 normalized after reduction. The dimension reduction ensures a much smaller (Table 3) total feature dimensions than previous reranking-based methods.", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/68bad915b4afab613365c64f0742d4718b52b37d059b3345752f683856302b5d.jpg", + "image_caption": [ + "Figure 3. Illustration of attention generation and token selection." + ], + "image_footnote": [], + "bbox": [ + 522, + 87, + 867, + 352 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Reranking Transformer Module", + "text_level": 1, + "bbox": [ + 500, + 393, + 785, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe the attention-based local feature selection and the workflow inside our reranking transformer module.", + "bbox": [ + 496, + 417, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attention-based Selection. For large-scale scenarios, local features occupy the majority of memory, thus reducing the number of local features is important for real-world deployment. Previous works [3,26,53] usually use $640 \\times 480$ as image resolution, resulting in 1200 patch tokens. However, only a small portion of them are informative to determine the location of the image, e.g. buildings, trees, roads, etc. Previous works either leverage all the local features from multiple scales [26] or adopt additional modules [53] to generate attention maps, which filter local features with a certain threshold during local matching. On the contrary, we leverage the natural attention map within our transformer module and only save a fixed number of local features (e.g. 500) with top attention values, resulting in a much lower memory cost and simpler extraction pipeline.", + "bbox": [ + 496, + 448, + 892, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $(n + 1) \\times (n + 1)$ attention matrix of the last transformer layer in Fig. 3 is formulated as $\\text{softmax}(QK^{\\top} / d)$ in Sec. 3.2. It represents the contribution from each input token to each output token. Since the output class (CLS) token is the only one that connects to the global embedding feature, the CLS token output channel of the matrix $((n + 1)$ -dimensional vector for $n$ patches and CLS token) represents the contribution from input tokens to the global feature, which corresponds to the importance of each patch. We reshape the $n$ -dimensional vector corresponding to $n$ patches as $h / p \\times w / p$ attention map to sort all the tokens and we select the top-500 tokens that are likely to cover the informative regions (bottom right of Fig. 3). The attention value and x,y coordinates are saved along with each local feature, resulting in $128 + 3 = 131$ dimensions.", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19373", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Correlation-based Reranking. RANSAC-based [19] geometric verification only leverages the top-1 matched pairs for all local features, but ignores other important information that could be useful for reranking, i.e. the correlation, and attention value. Local feature pairs with higher correlation/similarity have higher probabilities to be correct local matches, and an image pair with more correct local matches is more likely to represent the same place. Also, high attention values of the local patches could indicate the importance of the local feature pairs. Therefore, our reranking module is designed to maintain the correlation, attention, and positional information for all the local feature pairs in a correlation matrix, resulting in 7 dimensions (Fig. 2) denoted as $(x,y,A,x',y',A',S)$ . $x,y,x',y'$ denote the coordinates of the two patches in the query and reference images. $A,A'$ denotes the attention values of the two patches. $S$ is the cosine similarity between the 128-dimensional local features. Since each image has 500 selected features/tokens, there are $500\\times 500$ pairs, resulting in a $500\\times 500\\times 7$ correlation matrix. The correlation matrix contains the major information for all the feature pairs and allows the model to learn whatever is useful to determine whether the two images are from the same location.", + "bbox": [ + 76, + 90, + 472, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To reduce the computation, we select the 5 nearest neighbors of each token in the feature space to produce two $500 \\times 5 \\times 7$ matrices, as the other feature pairs with large distances are likely to be wrong matches. They are concatenated together and fed to a linear layer, resulting in a $1000 \\times 5 \\times 32$ matrix. We then leverage the strong global correlation modeling of transformer [52] to aggregate the large matrix as a reranking score to determine whether the input pair is a correct match. First, we adopt \"Transformer Block-1\" to extract important information from the top-5 pairs as one output class token. Then \"Transformer Block-2\" extracts aggregates the information from the 1000 tokens as a single 32-dimension vector (the class token). The two transformer blocks are multiple transformer layers with linear projection and standard Sinusoidal positional embedding [52]. Finally, the vector is converted into 2 channels by a linear head as a binary classification (i.e. True vs False).", + "bbox": [ + 76, + 439, + 472, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 714, + 202, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 739, + 364, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our model on MSLS (Mapillary Street-Level Sequences) [55] dataset, which covers a wide range of real-world scenarios for VPR, e.g. different cities, viewpoint variation, day/night, and season changes. The performance in urban scenarios (e.g. Pitts30k [50], Tokyo24/7 [49]) can be further improved by finetuning on Pitts30k. For evaluation, we use standard train/val/test split [6, 26, 53, 55] on major datasets, including MSLS Val [55], MSLS Challenge [55], Pitts30k [50], Tokyo 24/7 [49], R-SF (Revisited San", + "bbox": [ + 76, + 763, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Francisco) [6, 11, 33, 45], St Lucia [40]. The MSLS Challenge [55] is a hold-out set whose labels are not released, but researchers can submit the predictions on their challenge server to get the performance. For the other datasets with location labels, we follow previous works [6, 26, 53] to use 25 meters as the threshold for correct localization and report recall@k (k=1,5,10) as evaluation metrics. We also report detailed computational costs, including inference time for extraction/retrieval/matching, feature dimensions, GFLOPs, and memory footprint (Table 3).", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 253, + 718, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method is implemented using PyTorch [42]. The models are trained on 8 Tesla-V100 GPUs. All images are resized to $640 \\times 480$ for training and evaluation. The reranking is conducted on top-100 candidates and we set margin $m = 0.1$ . We use ViT-S [17] (12 layers with 384 dimensions) architecture as our default backbone and the module is initialized with off-the-shelf pre-trained weights [51] on ImageNet-1k [14]. The transformers in the reranking module use a small dimension of 32 with only 2 and 6 layers for Transformer Block-1 and Block-2 respectively, thus resulting in a very small computational cost.", + "bbox": [ + 496, + 276, + 893, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The global retrieval and the reranking module can be trained jointly in an end-to-end manner, but we train them separately (Sec. 3.1) by default to achieve a stable convergence and better accuracy. The global retrieval module is trained following common practice [6]. The reranking module is trained from scratch following the standard pipeline of training transformers, i.e. AdamW [36] optimizer with cosine learning rate schedule [35]. The initial learning rate is 0.0005 with 64 triplets per batch. Each triplet only samples one hard negative reference image which is randomly selected from the top-100 hardest samples from the MSLS training set of the corresponding query. Given that the global embedding features do not change during this stage, the global hard negative mining only needs to be conducted once and can be efficiently computed on GPU in 3 hours. We precompute the hard negative list of all queries for the training of the reranking module, which is more efficient than the full mining implementation of the VG benchmark [6]. The reranking module is trained for 50 epochs and we select the model with the highest recall@5 on the validation set. The global retrieval and reranking module are then finetuned together with partial negative mining [6]. More details are included in supplementary material.", + "bbox": [ + 496, + 443, + 893, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-art", + "text_level": 1, + "bbox": [ + 500, + 801, + 794, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we compare the proposed method with previous state-of-the-art methods, including NetVLAD [3], SFRS [23], SP-SuperGlue [15, 44], Patch-NetVLAD [26], and TransVPR [53]. We further compare our method with the best configurations in the recent VG benchmark [6].", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19374", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5ba1a5ed6841f6ed0da36930543ce40bf1c6b96eda1f4c795bfcbf55410cf42d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MSLS Val [55]MSLS Challenge [55]Pitts30k [50]Tokyo 24/7 [49]
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
NetVLAD [3]60.874.379.535.147.451.781.991.293.764.878.481.6
SFRS [23]69.280.383.141.552.056.389.494.795.985.491.193.3
SP-SuperGlue [15,44]78.181.984.350.656.958.387.294.896.488.290.290.2
Patch-NetVLAD [26]79.586.287.748.157.660.588.794.595.986.088.690.5
TransVPR [53]86.891.292.463.974.077.589.094.996.279.082.285.1
Ours89.795.096.273.085.988.891.195.296.388.691.491.7
", + "bbox": [ + 81, + 87, + 893, + 202 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b4e5b083469c36213e5f77ce9256e71fddaf6aa13485a3c00757f7f73871b602.jpg", + "table_caption": [ + "Table 1. Comparison of our method with previous state-of-the-art results on major VPR datasets. Our model is trained on MSLS and tested on MSLS Val and Challenge set. Our model is further finetuned on Pitts30k for urban scenarios, i.e. Pitts30k, Tokyo 24/7." + ], + "table_footnote": [], + "table_body": "
Features Dim ↓GFLOPs ↓Trained on MSLS - R@1
Pitts30kMSLS ValMSLS Chall.Tok. 24/7R-SFSt Lucia
ResNet101 + GeM [6,43]102486.2977.277.0*55.551.046.991.6
ResNet101 + NetVLAD [3,6]6553686.0680.881.1*61.559.056.195.1
CCT384 + NetVLAD [6,25]2457618.5385.183.8*61.470.365.998.4
Ours w/o Reranking25625.9076.379.356.245.747.594.3
Ours65500†48.50†88.489.773.072.772.199.7
", + "bbox": [ + 81, + 241, + 883, + 345 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4b3a28f30c5e15d54219b2b675bb8a1824a26f12ea5beb152620af2a3ee49595.jpg", + "table_caption": [ + "Table 2. Comparison following the protocol of the recent VG benchmark [6] on major datasets in terms of R@1. The models are trained on MSLS and directly tested on all datasets w/o finetuning. † The dimensions and GFLOPs are computed by adding the numbers of global retrieval and reranking together, i.e. $Dim = 256 + 500 \\times (128 + 3)$ and $GFLOPs = 25.90 + 100 \\times 0.226$ ." + ], + "table_footnote": [], + "table_body": "
Feature Dim ↓Latency per Query (ms) ↓Memory Footprint (GB) ↓
GlobalLocalExtractionRetrievalRerankingMSLS Val1M Images
ResNet101 + NetVLAD [3,6]65536N/A9.602.33N/A4.79244.14
Patch-NetVLAD-s [26]512936 × 5129.290.08952.8537.601917.29
Patch-NetVLAD-p [26]40962826 × 40969.360.198377.17908.3046315.85
TransVPR [53]2561200 × 2566.200.071757.7022.721158.53
Ours256500 × (128+3)8.810.07202.374.79244.01
", + "bbox": [ + 76, + 396, + 890, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison of computational cost in terms of feature dimension, latency, and memory footprint. All the methods are measured on MSLS Val (18,871 database images) using the same CPU and GPU (RTX A5000). Reranking is conducted on top-100 candidates. \"Patch-NetVLAD-p\" and \"Patch-NetVLAD-s\" denote the performance and speed-oriented versions.", + "bbox": [ + 75, + 503, + 892, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also provide a detailed comparison with state-of-the-art methods [6,26,53] on computational cost. Other works [1, 16, 18, 57, 59, 62] on related tasks with different settings are not included.", + "bbox": [ + 75, + 565, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 1, the proposed method significantly outperforms state-of-the-art methods on MSLS Val and Challenge set with absolute R@1 improvement of $2.9\\%$ and $9.1\\%$ respectively. Benefiting from large-scale training, our method also achieves state-of-the-art R@1 on Pitts30k and Tokyo24/7. Small-scale dataset [50] with weak supervision is not enough to train a data-driven reranking module, and training on one large-scale dataset with good generalization on all datasets is more desirable for real-world deployment. (Details in supp. material.)", + "bbox": [ + 75, + 626, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 2, we select the best-performing models in the VG benchmark [6] and compare them with our method on major datasets. Eynsham [13] dataset is not included because it has a different camera type (gray-scale) and resolution. * denotes reproduced results using the official MSLS [55] validation code and pre-trained models [6]. Table 2 shows that our model trained on MSLS generalizes well on all the other datasets and significantly outperforms the best", + "bbox": [ + 75, + 777, + 470, + 897 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "models in the VG benchmark [6] with comparable computational cost.", + "bbox": [ + 496, + 565, + 890, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 3, we compare the computational cost of our method with previous global retrieval methods and retrieval+reranking methods. Apparently, the inference latency of extraction and retrieval is negligible as compared to the reranking latency of previous works. Our method is significantly faster than all the other reranking-based methods because our reranking process is only one network forward pass on GPU and can be easily accelerated by parallel computing, e.g. reranking on 4 GPUs takes only $47.17\\mathrm{ms}$ per query $(20.2\\times$ speedup over previous reranking-based methods [26, 53]). However, it is not straightforward to accelerate RANSAC-based geometric verification with multiprocessing. Previous works [26, 53] generally follow the standard implementation of OpenCV [8]. In addition, the local feature dimension of our method is the smallest among all the reranking-based methods, specifically, we only save 500 important local features with very small dimensions $(128 + 3)$ for each image. In total, it only needs $4.79\\mathrm{GB}$ of memory for the MSLS validation set which is much smaller $(189\\times$ reduction) than $908.3\\mathrm{GB}$ of Patch-NetVLAD-p.", + "bbox": [ + 496, + 595, + 892, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19375", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5e7fc2a9215e758d72be0236c9422d12f91653766579de4b47052799f4c69a15.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
R@1R@5R@10
No Reranking79.390.892.6
RANSAC [19]84.993.094.5
RRT [48]81.291.993.1
CVNet [32]73.486.891.4
Ours89.795.096.2
", + "bbox": [ + 112, + 88, + 401, + 184 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0d60b4df628cc3502e3f1202bfa81a0ee1a26357066f3a6741f525a45ede398d.jpg", + "table_caption": [ + "Table 4. Comparison with different reranking methods (top-100 candidates reranked) using our backbone on MSLS Val." + ], + "table_footnote": [], + "table_body": "
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking + Mining88.493.494.9
Reranking + Mining + Finetune89.795.096.2
End-to-end Training87.393.595.4
", + "bbox": [ + 455, + 88, + 877, + 184 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/758d3e963f4deab84d7c697e2d47145c3eb3898acce327f2afeea2c78761bdbb.jpg", + "table_caption": [ + "Table 5. Ablation study on training strategy. We freeze the global retrieval module by default when training the reranking module." + ], + "table_footnote": [], + "table_body": "
ArchitectureR@1R@5R@10
Ours w/o \nRerankingViT-Small79.390.892.6
ResNet50 + GeM79.690.992.6
ViT-Base84.992.794.5
Ours w/ \nRANSACViT-Small84.993.094.5
ResNet50 + GeM84.391.493.0
ViT-Base87.093.094.6
OursViT-Small89.795.096.2
ResNet50 + GeM88.493.695.3
ViT-Base90.095.196.9
", + "bbox": [ + 84, + 229, + 457, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Even for datasets with over 1M reference images (e.g. R-SF dataset), the memory footprint is only 244.01 GB which can fit in a typical server or high-end desktop. It can be further reduced to 122 GB by using float16 instead of float32, with which we observe no performance drop on R-SF. However, other reranking-based methods typically require much larger ( $>4\\times$ ) memory, which cannot scale to large-scale real-world scenarios with 1M reference images. Given the unified design, outstanding performance, strong efficiency, and scalability of our method, it could serve as a well-balanced solution for real-world large-scale applications.", + "bbox": [ + 75, + 455, + 467, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 633, + 228, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Reranking Methods. In Table 4, we adopt the same global and local features from our default backbone and compare different reranking methods. “No Reranking” denotes our model with only global retrieval. “RANSAC” [19] follows the pipeline of state-of-the-art methods [26, 53] using $1.5 \\times$ of the patch size. “RRT” [48] is not proposed for VPR, nevertheless, we train it on the top of our backbone for comparison. “CVNet” [31] does not provide the training code, we thus adopt their pre-trained model trained on Google Landmark [56]. Remarkably, our reranking module significantly outperforms RANSAC [19] based geometric verification using much less ( $< 22\\%$ ) inference time (Table 3). It also outperforms two recent state-of-the-art reranking methods on landmark retrieval, indicating the superiority of our reranking module.", + "bbox": [ + 75, + 657, + 467, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Strategies. In Table 5, we compare our method", + "bbox": [ + 83, + 885, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d651fe9edbd8dd65d590606374a6359b2951ae308c09864ce5ef2bbbc86fc95d.jpg", + "table_caption": [ + "Table 6. Ablation study on MSLS Val with different backbone architectures, including ResNet50+GeM [27,43], ViT Small [17], ViT Base [17]. Transformer tokens perform on par with CNN local features in terms of reranking/local matching." + ], + "table_footnote": [], + "table_body": "
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking Module
Remove Positional Embedding86.493.294.7
Remove Transformer Block-185.593.895.0
Remove Transformer Block-281.992.894.6
Replace Top-5 w/ Top-186.693.894.7
Reranking Input
Remove Attention Selection83.692.894.1
Remove xy Coordinates Value85.093.594.7
Remove Attention Value86.193.594.3
Remove Correlation Value31.859.272.8
", + "bbox": [ + 511, + 229, + 875, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Ablation study on model components. We freeze the global retrieval module so that the global and local features are the same for different ablations. All ablations are trained with partial negative mining [6]. The components are defined in Sec. 3.", + "bbox": [ + 498, + 419, + 890, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "based on different training strategies. “No Reranking” uses only global retrieval, and “Reranking” denotes training reranking module with partial negative mining on a fixed global retrieval module. “Reranking+Mining” means training the reranking module with our global negative mining by randomly selecting one negative sample from the 100 global hardest samples. “Reranking+Mining+Finetune” further finetunes retrieval and reranking module together. “End-to-end Training” directly trains global retrieval and reranking module from the beginning in an end-to-end manner with partial negative mining. All the strategies with reranking outperform previous state-of-the-art methods on $\\mathbb{R}@\\mathbb{5}$ , and training the global retrieval and reranking module separately with a carefully designed strategy achieves the best performance. The results indicate that global hard negative mining is helpful for training the reranking module. End-to-end training is also a good trade-off between simplicity and performance.", + "bbox": [ + 496, + 492, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different Backbones. In Table 6, we combine our reranking module with different backbone retrieval modules, including ViT-Small (default), ResNet50+GeM [27, 43] and ViT-Base. We follow [6] to add L2 normalization before the pooling layer but do not freeze or remove any convolutional layer. The attention map of ResNet50+GeM is generated following CAM [61]. The ResNet50+GeM model achieves competitive results for both global retrieval and reranking. It also significantly outperforms previous", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19376", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc49f31c6d459fcf2f21b329e6076f3add35a360cb153f5178dc12fda3ebce61.jpg", + "image_caption": [ + "Figure 4. Visualization of attention map and matched pairs. Green and red boxes in (f) indicate correct and wrong predictions." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 890, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "works [26, 53], indicating that our reranking module is a generic component for both CNN and transformer backbone architectures. With similar global retrieval performance and the same reranking method (RANSAC or Ours), the ViT-Small model achieves slightly better performance than ResNet50+GeM, which means the transformer token is a good alternative for local matching as compared with CNN local feature. Furthermore, we adopt a larger backbone ViT-Base, which achieves significant performance improvement on global retrieval and RANSAC-based reranking over ViT-Small. However, the overall performance of our ViT-Base model has very small performance improvement (mainly on $\\mathbb{R}@\\mathbb{10}$ ), which indicates a possible bottleneck of the proposed framework. Components Ablation. In Table 7, we use the \"Reranking\" configuration in Table 5 as a baseline and ablate different components to check the importance of each component of our method. For simplicity, we freeze the global retrieval module and all the models are trained with partial negative mining. We have the following observations. (1) The most important components are the Transformer Block-2 and Correlation Value, and removing them causes a significant performance drop. This indicates that the feature correlation contributes most to the final decision. (2) When we replace the attention-based feature selection with random selection, the model becomes unstable and the performance drops moderately. (3) Removing other components, i.e. Transformer Block-1, xy Coordinates Value, Attention Value (defined in Sec. 3.2), causes a slight performance drop, indicating the effectiveness of these blocks for performance purposes. (4) We observe negligible performance drop when removing positional embedding or replacing top-5 pairs selection with top-1, which means the Sinusoidal positional embedding does not help much and the top-1 pair contains most of the", + "bbox": [ + 76, + 369, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "information that is needed for reranking.", + "bbox": [ + 500, + 369, + 767, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 500, + 411, + 635, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 4, we show a detailed case where the global retrieval fails on the top-3 results. Fig. 4 (b) and (c) show the attention map and the selected patches, which cover most of the informative regions for reranking. Both RANSAC and our method work well on reranking the top-100 candidates and our method finds more correct reference images in the top-3 results (Fig. 4 (f)). Although our reranking module is not as explainable as RANSAC, the transformer still focuses on specific patch pairs and we plot the top-20 pairs with the highest attention in the reranking module. As shown in Fig. 4 (d) and (e), our reranking also focuses on meaningful pairs and most of them are correct matches. As compared with RANSAC, our matched pairs may not have tight geometric consistency, but they may provide different information for the reranking as adjusted according to the task-relevant training data.", + "bbox": [ + 496, + 435, + 890, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 693, + 617, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a unified retrieval and reranking framework for place recognition with only transformers. We for the first time show that vision transformer tokens are comparable to or even better than CNN local feature in terms of reranking. Our reranking module is generic and can be adopted on other CNN or transformer backbones. Remarkably, it significantly outperforms previous methods on major datasets with much less inference time and memory consumption. Our method can also provide possible matched local pairs like RANSAC and could be improved with geometric modeling in the future. We discuss the limitations and societal impact in the supplementary material.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19377", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Amar Ali-bey, Brahim Chaib-draa, and Philippe Giguere. Mixvpr: Feature mixing for visual place recognition. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1162-1171, 2022. 6" + ], + "bbox": [ + 78, + 90, + 468, + 767 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19380", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_model.json b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0d66408286462126e497b8fbd2ff1356c641e618 --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_model.json @@ -0,0 +1,1949 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.13, + 0.888, + 0.153 + ], + "angle": 0, + "content": "\\(R^2\\)Former: Unified Retrieval and Reranking Transformer for Place Recognition" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.18, + 0.847, + 0.217 + ], + "angle": 0, + "content": "Sijie Zhu\\(^{1,2,\\dagger}\\), Linjie Yang\\(^{1}\\), Chen Chen\\(^{2}\\), Mubarak Shah\\(^{2}\\), Xiaohui Shen\\(^{1}\\), Heng Wang\\(^{1}\\), ByteDance\\(^{2}\\) Center for Research in Computer Vision, University of Central Florida" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.219, + 0.922, + 0.234 + ], + "angle": 0, + "content": "{sijiezhu,linjie.yang,heng.wang,shenxiaohui.kevin}@bytedance.com,{chen.chen,shah}@crcv.ucf.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.695 + ], + "angle": 0, + "content": "Visual Place Recognition (VPR) estimates the location of query images by matching them with images in a reference database. Conventional methods generally adopt aggregated CNN features for global retrieval and RANSAC-based geometric verification for reranking. However, RANSAC only employs geometric information but ignores other possible information that could be useful for reranking, e.g. local feature correlations, and attention values. In this paper, we propose a unified place recognition framework that handles both retrieval and reranking with a novel transformer model, named \\(R^2\\)Former. The proposed reranking module takes feature correlation, attention value, and xy coordinates into account, and learns to determine whether the image pair is from the same location. The whole pipeline is end-to-end trainable and the reranking module alone can also be adopted on other CNN or transformer backbones as a generic component. Remarkably, \\(R^2\\)Former significantly outperforms state-of-the-art methods on major VPR datasets with much less inference time and memory consumption. It also achieves the state-of-the-art on the hold-out MSLS challenge set and could serve as a simple yet strong solution for real-world large-scale applications. Experiments also show vision transformer tokens are comparable and sometimes better than CNN local features on local matching. The code is released at https://github.com/Jeff-Zilence/R2Former." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.727, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Visual Place Recognition (VPR) aims to localize query images from unknown locations by matching them with a set of reference images from known locations. It has great potential for robotics [47], navigation [41], autonomous driving [9], augmented reality (AR) applications. Previous works [26, 53] generally formulate VPR as a retrieval problem with two stages, i.e. global retrieval, and reranking. The global retrieval stage usually applies aggregation" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.267, + 0.891, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.54, + 0.894, + 0.596 + ], + "angle": 0, + "content": "Figure 1. An overview of conventional pipeline and our unified framework. Both our global retrieval and reranking modules are end-to-end trainable transformer layers, which achieve state-of-the-art performance with much less computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.893, + 0.854 + ], + "angle": 0, + "content": "methods (e.g. NetVLAD [3] and GeM [43]) on top of CNN (Convolutional Neural Network) to retrieve top candidates from a large reference database. While some works [3, 6] only adopt global retrieval, current state-of-the-art methods [26, 53] conduct reranking (i.e. geometric verification with RANSAC [19]) on the top-k (e.g. \\( k = 100 \\)) candidates to further confirm the matches, typically leading to a significant performance boost. However, geometric information is not the only information that could be useful for reranking, and task-relevant information could be learned with a data-driven module to further boost performance. Besides, the current reranking process requires a relatively large inference time and memory footprint (typically over 1s and 1MB per image), which cannot scale to real-world applications with large QPS (Queries Per Second) and reference database (\\( >1\\mathrm{M} \\) images)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recently vision transformer [17] has achieved significant performance on a wide range of vision tasks, and has been shown to have a high potential for VPR [53] (Sec. 2)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.47, + 0.9 + ], + "angle": 0, + "content": "† This work was done during the first author's internship at ByteDance" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19370" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "However, the predominant local features [26, 53] are still based on CNN backbones, due to the built-in feature locality with limited receptive fields. Although vision transformer [17] considers each patch as an input token and naturally encodes local information, the local information might be overwritten with global information by the strong global correlation between all tokens in every layer. Therefore, it is still unclear how vision transformer tokens perform in local matching as compared to CNN local features in this field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.518 + ], + "angle": 0, + "content": "In this paper, we integrate the global retrieval and reranking into one unified framework employing only transformers (Fig. 1), abbreviated as \\( R^2 \\)Former, which is simple, efficient, and effective. The global retrieval is tackled based on the class token without additional aggregation modules [3,43] and the other image tokens are adopted as local features. Different from geometric verification which focuses on geometric information between local feature pairs, we feed the correlation between the tokens (local features) of a pair of images, xy coordinates of tokens, and their attention information to transformer modules, so that the module can learn task-relevant information that could be useful for reranking. The global retrieval and reranking parts can be either trained in an end-to-end manner or tuned alternatively with a more stable convergence. The proposed reranking module can also be adopted on other CNN or transformer backbones, and our comparison shows that vision transformer tokens are comparable to CNN local features in terms of reranking performance (Table 6)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Without bells and whistles, the proposed method outperforms both retrieval-only and retrieval+reranking state-of-the-art methods on a wide range of VPR datasets. The proposed method follows a very efficient design and applies linear layers for dimension reduction: i.e. only 256 and \\(500 \\times 131\\) for global and local feature dimensions and only 32 for transformer dimension of reranking module, thus is significantly faster (\\(>4.7 \\times \\mathrm{QPS}\\)) with much less (\\(< 22\\%\\)) memory consumption than previous methods [26, 53]. Both the global and local features are extracted from the same backbone model only once, and the reranking of top-k candidates is finished with only one forward pass by computing the reranking scores of all candidate pairs in parallel within one batch. The reranking speed can be further boosted by parallel computing on multiple GPUs with \\(>20 \\times\\) speedup over previous methods [26, 53]. We demonstrate that the proposed reranking module also learns to focus on good local matches like RANSAC [19]. We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.47, + 0.886 + ], + "angle": 0, + "content": "- A unified retrieval and reranking framework for place recognition employing pure transformers, which demonstrates that vision transformer tokens are comparable and sometimes better than CNN local features in terms of reranking or local matching." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- A novel transformer-based reranking module that learns" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "to attend to the correlation of informative local feature pairs. It can be combined with either CNN or transformer backbones with better performance and efficiency than other reranking methods, e.g. RANSAC." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.153, + 0.894, + 0.213 + ], + "angle": 0, + "content": "- Extensive experiments showing state-of-the-art performance on a wide range of place recognition datasets with significantly less (\\(< 22\\%\\)) inference latency and memory consumption than previous reranking-based methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.226, + 0.642, + 0.242 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.463 + ], + "angle": 0, + "content": "Visual Place Recognition. Visual place recognition (VPR) [2, 21, 38, 39, 47, 58, 60] is traditionally addressed with nearest neighbor search on aggregated [28] hand-crafted features [12, 37]. The current predominant methods [3-6, 26, 53] are based on CNN [27, 46] feature extractors with trainable aggregation layer, e.g. NetVLAD [3], CRN [30], or light-weighted pooling layer, e.g. GeM [43], R-MAC [24]. Numerous works [7, 20, 22, 23, 34, 54, 55] follow NetVLAD [3] to further improve the global representation for retrieval. Recently, Berton [6] et al. introduce a benchmark for VPR and implement a wide range of global-retrieval-based methods in the same framework. CosPlace [4] et al. propose an extremely large dataset and formulate the problem differently as classification using orientation information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.895, + 0.827 + ], + "angle": 0, + "content": "In addition to global retrieval, recent state-of-the-art VPR methods [26, 53] apply reranking on the top retrieved candidates. Patch-NetVLAD [26] adopts NetVLAD [3] model as their backbone for global retrieval and applies RANSAC [19] based geometric verification on multi-scale patch descriptors. TransVPR [53] adds multiple transformer layers on the top of CNN backbones to extract both global and local features. An additional attention module is then deployed to select important local features as the input of RANSAC [19]. Other local matching methods from related tasks, e.g. SuperGlue [15,44] and DELG [10], are also evaluated for VPR. However, they both have a lower accuracy with a much slower inference speed [53]. Recently, there are several recent learning-based reranking methods from related tasks, e.g. landmark matching [31,48] and local matching [29]. While they either fail to generalize [31,48] on VPR (Table 4) or have a very different problem setting [29], i.e. computing point-to-point correspondence between two given images without global retrieval. To summarize, current state-of-the-art VPR methods rely on RANSAC, and methods from related tasks do not generalize well when directly applied to VPR. Our method takes one step forward to integrate retrieval and reranking into one unified VPR framework with pure transformers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Vision Transformer. Transformer [52] is first proposed for NLP (Natural Language Processing) tasks as a generic architecture without inductive bias. It is recently introduced to vision tasks as vision transformer [17] (ViT) by simply considering each image patch as a token. The vanilla ViT" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19371" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.844, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.895, + 0.412 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed framework. Both the global and local features are extracted as the class token and patch tokens, followed by dimension reduction using linear layers. The important local features are then selected based on the attention map (Fig. 3) and fed into the reranking module. Both the global retrieval and reranking modules consist of only transformer and linear layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.473, + 0.624 + ], + "angle": 0, + "content": "[17] requires large-scale training datasets (e.g. ImageNet-21k [14]) to achieve comparable results as CNN [27], and Deit [51] proposes a data-efficient training strategy for ViT which outperforms CNN on standard ImageNet-1k. The recent VG benchmark [6] adopts vanilla ViT without modifying the input resolution which could be suboptimal, while it already shows competitive performance on global retrieval. TransVPR [53] adopts multiple transformer layers, while the backbone feature extractor is still based on CNN. We hypothesize the power of vision transformer is not fully exploited for VPR and it is interesting to know how vision transformer tokens perform on reranking/local matching as compared with the predominant CNN local feature." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.192, + 0.65 + ], + "angle": 0, + "content": "3. \\(R^2\\) Former" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.721 + ], + "angle": 0, + "content": "We first formulate the problem and training objective of the proposed method in Sec. 3.1. Then we describe global retrieval and reranking stages in Sec. 3.2 and Sec. 3.3 respectively. Fig. 2 shows an overview of \\( R^2 \\)Former." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.466, + 0.743 + ], + "angle": 0, + "content": "3.1. Problem Formulation and Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The proposed framework consists of two stages, i.e. global retrieval, and reranking. Given a set of query images \\(\\{I_q\\}\\) and reference images \\(\\{I_r\\}\\), the objective of global retrieval is to learn an embedding space in which each query \\(I_{q}\\) is close to its corresponding positive reference image \\(I_{r}\\). During training, reference images from the same location as the query image are defined as positive samples, and the typical threshold is set as 10 meters. We follow the common practice of previous works [3,6] to find the nearest reference image for each query in the embedding space as the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.895, + 0.533 + ], + "angle": 0, + "content": "final positive sample. Other reference images with distances greater than 25 meters are considered as negative samples. Partial negative mining [6] is conducted to select the hardest negative samples from a random subset. We denote the global embedding features of query, positive samples, and negative samples as \\( E_{q}, E_{p}, E_{n} \\) and the global retrieval loss is trained with margin triplet loss:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.54, + 0.892, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e t r i e v a l}} = \\max \\left(\\left| \\left| E _ {q} - E _ {p} \\right| \\right| ^ {2} - \\left| \\left| E _ {q} - E _ {n} \\right| \\right| ^ {2} + m, 0\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.88, + 0.581 + ], + "angle": 0, + "content": "Here \\(||.||^2\\) denotes squared L2 norm and \\(m\\) is the margin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.672 + ], + "angle": 0, + "content": "The reranking module takes the local features of two images as input and generates two-logit scores \\(\\mathbb{L}\\) as the output of a binary classification, representing the likelihoods for True or False matches. We feed both positive and negative query-reference pairs to the reranking module during training and the cross entropy \\((CE)\\) loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.68, + 0.891, + 0.696 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e r a n k i n g}} = C E \\left(\\operatorname {S o f t m a x} \\left(\\mathbb {L} _ {q r}\\right), \\mathbb {I} _ {q r}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.902 + ], + "angle": 0, + "content": "\\(\\mathbb{L}\\) and \\(\\mathbb{I}\\) denote the logits scores and ground-truth labels for the query-reference pairs. Although the partial negative mining [6] is shown to perform better than full negative mining for global retrieval in [6], the objective of the reranking module is to distinguish top-k retrieved candidates which are harder than partial negative samples [6]. To make sure the reranking module sees top-k hardest samples during training, we first freeze the global retrieval module and train the reranking module with randomly selected negative samples from the top-k hardest samples of the full database. The retrieval and reranking modules are then finetuned together with partial negative mining for better performance. Details are provided in Sec. 4.2." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19372" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.307, + 0.106 + ], + "angle": 0, + "content": "3.2. Global Retrieval Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.471, + 0.236 + ], + "angle": 0, + "content": "We describe the components of our vision transformer backbone for VPR and how the final global/local features are generated. As shown in Fig. 2, the query and reference images share the same backbone transformer encoder and there is no additional aggregation [3, 43] or key-point [15] extraction module for global and local feature generation. In other words, all the features and intermediate data are directly generated using only transformers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.236, + 0.474, + 0.493 + ], + "angle": 0, + "content": "ViT for Place Recognition. An input image \\( I \\in \\mathbb{R}^{h \\times w \\times c} \\) is first divided into small \\( p \\times p \\) patches (\\( p = 16 \\) by default) and converted into a number of tokens \\( T \\in \\mathbb{R}^{n \\times d} \\) by linear projection as the input of transformer encoders. Here \\( n, d \\) denote the number and dimension of tokens, and \\( h, w, c \\) denote the height, width, and number of channels in input images. In addition to the \\( n \\) patch tokens, ViT [17] adds an additional learnable class token to aggregate classification information from each layer, which serves as a simple alternative for feature aggregation. Then we adopt the learnable position embedding \\( PE \\in \\mathbb{R}^{(n + 1) \\times d} \\) from ViT [17] and add it to each token to provide positional information. Different from previous work [6] using the fixed training resolution of ViT [17], we conduct 2D interpolation on the positional embedding so that the input resolution can be arbitrary and we use the most widely used resolution (\\( 640 \\times 480 \\)) for our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.471, + 0.75 + ], + "angle": 0, + "content": "Global Attention. On the bottom right of Fig. 2, we provide the detailed inner architecture of the transformer encoder, which has \\( L \\) cascaded basic transformer [52] layers. The key component is the multi-head attention module, which adopts three linear projections to convert the input token into query, key and value, denoted as \\( Q, K, V \\) with dimension \\( d \\). The basic attention is computed as \\( \\text{softmax}(QK^{\\top} / d)V \\) (T means transpose), and a multi-head attention module performs this attention procedure in parallel for multiple heads with their final outputs concatenated. The multi-head attention module can model stronger global correlation than CNN with a limited receptive field, which helps information aggregation for global representation. However, it might reduce the locality of each token which could be harmful to local matching, we demonstrate that transformer tokens perform well as local features compared to CNN as shown in Table 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Dimension Reduction. We feed the output class token from the last transformer layer into a linear layer to generate the global feature with only 256 dimensions. The local features are generated by applying a linear head on the output patch tokens of the penultimate transformer layer and the dimension is reduced to 128 to achieve a small memory consumption. Both global and local features are L2 normalized after reduction. The dimension reduction ensures a much smaller (Table 3) total feature dimensions than previous reranking-based methods." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.088, + 0.868, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.36, + 0.888, + 0.374 + ], + "angle": 0, + "content": "Figure 3. Illustration of attention generation and token selection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.394, + 0.787, + 0.41 + ], + "angle": 0, + "content": "3.3. Reranking Transformer Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.448 + ], + "angle": 0, + "content": "We describe the attention-based local feature selection and the workflow inside our reranking transformer module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.893, + 0.675 + ], + "angle": 0, + "content": "Attention-based Selection. For large-scale scenarios, local features occupy the majority of memory, thus reducing the number of local features is important for real-world deployment. Previous works [3,26,53] usually use \\(640 \\times 480\\) as image resolution, resulting in 1200 patch tokens. However, only a small portion of them are informative to determine the location of the image, e.g. buildings, trees, roads, etc. Previous works either leverage all the local features from multiple scales [26] or adopt additional modules [53] to generate attention maps, which filter local features with a certain threshold during local matching. On the contrary, we leverage the natural attention map within our transformer module and only save a fixed number of local features (e.g. 500) with top attention values, resulting in a much lower memory cost and simpler extraction pipeline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "The \\((n + 1) \\times (n + 1)\\) attention matrix of the last transformer layer in Fig. 3 is formulated as \\(\\text{softmax}(QK^{\\top} / d)\\) in Sec. 3.2. It represents the contribution from each input token to each output token. Since the output class (CLS) token is the only one that connects to the global embedding feature, the CLS token output channel of the matrix \\(((n + 1)\\)-dimensional vector for \\(n\\) patches and CLS token) represents the contribution from input tokens to the global feature, which corresponds to the importance of each patch. We reshape the \\(n\\)-dimensional vector corresponding to \\(n\\) patches as \\(h / p \\times w / p\\) attention map to sort all the tokens and we select the top-500 tokens that are likely to cover the informative regions (bottom right of Fig. 3). The attention value and x,y coordinates are saved along with each local feature, resulting in \\(128 + 3 = 131\\) dimensions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19373" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.438 + ], + "angle": 0, + "content": "Correlation-based Reranking. RANSAC-based [19] geometric verification only leverages the top-1 matched pairs for all local features, but ignores other important information that could be useful for reranking, i.e. the correlation, and attention value. Local feature pairs with higher correlation/similarity have higher probabilities to be correct local matches, and an image pair with more correct local matches is more likely to represent the same place. Also, high attention values of the local patches could indicate the importance of the local feature pairs. Therefore, our reranking module is designed to maintain the correlation, attention, and positional information for all the local feature pairs in a correlation matrix, resulting in 7 dimensions (Fig. 2) denoted as \\((x,y,A,x',y',A',S)\\). \\(x,y,x',y'\\) denote the coordinates of the two patches in the query and reference images. \\(A,A'\\) denotes the attention values of the two patches. \\(S\\) is the cosine similarity between the 128-dimensional local features. Since each image has 500 selected features/tokens, there are \\(500\\times 500\\) pairs, resulting in a \\(500\\times 500\\times 7\\) correlation matrix. The correlation matrix contains the major information for all the feature pairs and allows the model to learn whatever is useful to determine whether the two images are from the same location." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.473, + 0.698 + ], + "angle": 0, + "content": "To reduce the computation, we select the 5 nearest neighbors of each token in the feature space to produce two \\(500 \\times 5 \\times 7\\) matrices, as the other feature pairs with large distances are likely to be wrong matches. They are concatenated together and fed to a linear layer, resulting in a \\(1000 \\times 5 \\times 32\\) matrix. We then leverage the strong global correlation modeling of transformer [52] to aggregate the large matrix as a reranking score to determine whether the input pair is a correct match. First, we adopt \"Transformer Block-1\" to extract important information from the top-5 pairs as one output class token. Then \"Transformer Block-2\" extracts aggregates the information from the 1000 tokens as a single 32-dimension vector (the class token). The two transformer blocks are multiple transformer layers with linear projection and standard Sinusoidal positional embedding [52]. Finally, the vector is converted into 2 channels by a linear head as a binary classification (i.e. True vs False)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.715, + 0.203, + 0.731 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.365, + 0.756 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We train our model on MSLS (Mapillary Street-Level Sequences) [55] dataset, which covers a wide range of real-world scenarios for VPR, e.g. different cities, viewpoint variation, day/night, and season changes. The performance in urban scenarios (e.g. Pitts30k [50], Tokyo24/7 [49]) can be further improved by finetuning on Pitts30k. For evaluation, we use standard train/val/test split [6, 26, 53, 55] on major datasets, including MSLS Val [55], MSLS Challenge [55], Pitts30k [50], Tokyo 24/7 [49], R-SF (Revisited San" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "Francisco) [6, 11, 33, 45], St Lucia [40]. The MSLS Challenge [55] is a hold-out set whose labels are not released, but researchers can submit the predictions on their challenge server to get the performance. For the other datasets with location labels, we follow previous works [6, 26, 53] to use 25 meters as the threshold for correct localization and report recall@k (k=1,5,10) as evaluation metrics. We also report detailed computational costs, including inference time for extraction/retrieval/matching, feature dimensions, GFLOPs, and memory footprint (Table 3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.254, + 0.719, + 0.27 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.895, + 0.444 + ], + "angle": 0, + "content": "The proposed method is implemented using PyTorch [42]. The models are trained on 8 Tesla-V100 GPUs. All images are resized to \\(640 \\times 480\\) for training and evaluation. The reranking is conducted on top-100 candidates and we set margin \\(m = 0.1\\). We use ViT-S [17] (12 layers with 384 dimensions) architecture as our default backbone and the module is initialized with off-the-shelf pre-trained weights [51] on ImageNet-1k [14]. The transformers in the reranking module use a small dimension of 32 with only 2 and 6 layers for Transformer Block-1 and Block-2 respectively, thus resulting in a very small computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.895, + 0.793 + ], + "angle": 0, + "content": "The global retrieval and the reranking module can be trained jointly in an end-to-end manner, but we train them separately (Sec. 3.1) by default to achieve a stable convergence and better accuracy. The global retrieval module is trained following common practice [6]. The reranking module is trained from scratch following the standard pipeline of training transformers, i.e. AdamW [36] optimizer with cosine learning rate schedule [35]. The initial learning rate is 0.0005 with 64 triplets per batch. Each triplet only samples one hard negative reference image which is randomly selected from the top-100 hardest samples from the MSLS training set of the corresponding query. Given that the global embedding features do not change during this stage, the global hard negative mining only needs to be conducted once and can be efficiently computed on GPU in 3 hours. We precompute the hard negative list of all queries for the training of the reranking module, which is more efficient than the full mining implementation of the VG benchmark [6]. The reranking module is trained for 50 epochs and we select the model with the highest recall@5 on the validation set. The global retrieval and reranking module are then finetuned together with partial negative mining [6]. More details are included in supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.795, + 0.818 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this section, we compare the proposed method with previous state-of-the-art methods, including NetVLAD [3], SFRS [23], SP-SuperGlue [15, 44], Patch-NetVLAD [26], and TransVPR [53]. We further compare our method with the best configurations in the recent VG benchmark [6]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "19374" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.088, + 0.894, + 0.203 + ], + "angle": 0, + "content": "
MSLS Val [55]MSLS Challenge [55]Pitts30k [50]Tokyo 24/7 [49]
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
NetVLAD [3]60.874.379.535.147.451.781.991.293.764.878.481.6
SFRS [23]69.280.383.141.552.056.389.494.795.985.491.193.3
SP-SuperGlue [15,44]78.181.984.350.656.958.387.294.896.488.290.290.2
Patch-NetVLAD [26]79.586.287.748.157.660.588.794.595.986.088.690.5
TransVPR [53]86.891.292.463.974.077.589.094.996.279.082.285.1
Ours89.795.096.273.085.988.891.195.296.388.691.491.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.207, + 0.893, + 0.234 + ], + "angle": 0, + "content": "Table 1. Comparison of our method with previous state-of-the-art results on major VPR datasets. Our model is trained on MSLS and tested on MSLS Val and Challenge set. Our model is further finetuned on Pitts30k for urban scenarios, i.e. Pitts30k, Tokyo 24/7." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.242, + 0.885, + 0.346 + ], + "angle": 0, + "content": "
Features Dim ↓GFLOPs ↓Trained on MSLS - R@1
Pitts30kMSLS ValMSLS Chall.Tok. 24/7R-SFSt Lucia
ResNet101 + GeM [6,43]102486.2977.277.0*55.551.046.991.6
ResNet101 + NetVLAD [3,6]6553686.0680.881.1*61.559.056.195.1
CCT384 + NetVLAD [6,25]2457618.5385.183.8*61.470.365.998.4
Ours w/o Reranking25625.9076.379.356.245.747.594.3
Ours65500†48.50†88.489.773.072.772.199.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.348, + 0.893, + 0.391 + ], + "angle": 0, + "content": "Table 2. Comparison following the protocol of the recent VG benchmark [6] on major datasets in terms of R@1. The models are trained on MSLS and directly tested on all datasets w/o finetuning. † The dimensions and GFLOPs are computed by adding the numbers of global retrieval and reranking together, i.e. \\( Dim = 256 + 500 \\times (128 + 3) \\) and \\( GFLOPs = 25.90 + 100 \\times 0.226 \\)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.397, + 0.892, + 0.501 + ], + "angle": 0, + "content": "
Feature Dim ↓Latency per Query (ms) ↓Memory Footprint (GB) ↓
GlobalLocalExtractionRetrievalRerankingMSLS Val1M Images
ResNet101 + NetVLAD [3,6]65536N/A9.602.33N/A4.79244.14
Patch-NetVLAD-s [26]512936 × 5129.290.08952.8537.601917.29
Patch-NetVLAD-p [26]40962826 × 40969.360.198377.17908.3046315.85
TransVPR [53]2561200 × 2566.200.071757.7022.721158.53
Ours256500 × (128+3)8.810.07202.374.79244.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.504, + 0.893, + 0.547 + ], + "angle": 0, + "content": "Table 3. Comparison of computational cost in terms of feature dimension, latency, and memory footprint. All the methods are measured on MSLS Val (18,871 database images) using the same CPU and GPU (RTX A5000). Reranking is conducted on top-100 candidates. \"Patch-NetVLAD-p\" and \"Patch-NetVLAD-s\" denote the performance and speed-oriented versions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.469, + 0.626 + ], + "angle": 0, + "content": "We also provide a detailed comparison with state-of-the-art methods [6,26,53] on computational cost. Other works [1, 16, 18, 57, 59, 62] on related tasks with different settings are not included." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.777 + ], + "angle": 0, + "content": "As shown in Table 1, the proposed method significantly outperforms state-of-the-art methods on MSLS Val and Challenge set with absolute R@1 improvement of \\(2.9\\%\\) and \\(9.1\\%\\) respectively. Benefiting from large-scale training, our method also achieves state-of-the-art R@1 on Pitts30k and Tokyo24/7. Small-scale dataset [50] with weak supervision is not enough to train a data-driven reranking module, and training on one large-scale dataset with good generalization on all datasets is more desirable for real-world deployment. (Details in supp. material.)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.471, + 0.898 + ], + "angle": 0, + "content": "In Table 2, we select the best-performing models in the VG benchmark [6] and compare them with our method on major datasets. Eynsham [13] dataset is not included because it has a different camera type (gray-scale) and resolution. * denotes reproduced results using the official MSLS [55] validation code and pre-trained models [6]. Table 2 shows that our model trained on MSLS generalizes well on all the other datasets and significantly outperforms the best" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.595 + ], + "angle": 0, + "content": "models in the VG benchmark [6] with comparable computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.898 + ], + "angle": 0, + "content": "In Table 3, we compare the computational cost of our method with previous global retrieval methods and retrieval+reranking methods. Apparently, the inference latency of extraction and retrieval is negligible as compared to the reranking latency of previous works. Our method is significantly faster than all the other reranking-based methods because our reranking process is only one network forward pass on GPU and can be easily accelerated by parallel computing, e.g. reranking on 4 GPUs takes only \\(47.17\\mathrm{ms}\\) per query \\((20.2\\times\\) speedup over previous reranking-based methods [26, 53]). However, it is not straightforward to accelerate RANSAC-based geometric verification with multiprocessing. Previous works [26, 53] generally follow the standard implementation of OpenCV [8]. In addition, the local feature dimension of our method is the smallest among all the reranking-based methods, specifically, we only save 500 important local features with very small dimensions \\((128 + 3)\\) for each image. In total, it only needs \\(4.79\\mathrm{GB}\\) of memory for the MSLS validation set which is much smaller \\((189\\times\\) reduction) than \\(908.3\\mathrm{GB}\\) of Patch-NetVLAD-p." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19375" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.113, + 0.089, + 0.402, + 0.185 + ], + "angle": 0, + "content": "
R@1R@5R@10
No Reranking79.390.892.6
RANSAC [19]84.993.094.5
RRT [48]81.291.993.1
CVNet [32]73.486.891.4
Ours89.795.096.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.189, + 0.438, + 0.217 + ], + "angle": 0, + "content": "Table 4. Comparison with different reranking methods (top-100 candidates reranked) using our backbone on MSLS Val." + }, + { + "type": "table", + "bbox": [ + 0.457, + 0.089, + 0.878, + 0.185 + ], + "angle": 0, + "content": "
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking + Mining88.493.494.9
Reranking + Mining + Finetune89.795.096.2
End-to-end Training87.393.595.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.452, + 0.188, + 0.885, + 0.217 + ], + "angle": 0, + "content": "Table 5. Ablation study on training strategy. We freeze the global retrieval module by default when training the reranking module." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.23, + 0.459, + 0.375 + ], + "angle": 0, + "content": "
ArchitectureR@1R@5R@10
Ours w/o \nRerankingViT-Small79.390.892.6
ResNet50 + GeM79.690.992.6
ViT-Base84.992.794.5
Ours w/ \nRANSACViT-Small84.993.094.5
ResNet50 + GeM84.391.493.0
ViT-Base87.093.094.6
OursViT-Small89.795.096.2
ResNet50 + GeM88.493.695.3
ViT-Base90.095.196.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.378, + 0.468, + 0.434 + ], + "angle": 0, + "content": "Table 6. Ablation study on MSLS Val with different backbone architectures, including ResNet50+GeM [27,43], ViT Small [17], ViT Base [17]. Transformer tokens perform on par with CNN local features in terms of reranking/local matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.468, + 0.622 + ], + "angle": 0, + "content": "Even for datasets with over 1M reference images (e.g. R-SF dataset), the memory footprint is only 244.01 GB which can fit in a typical server or high-end desktop. It can be further reduced to 122 GB by using float16 instead of float32, with which we observe no performance drop on R-SF. However, other reranking-based methods typically require much larger (\\(>4\\times\\)) memory, which cannot scale to large-scale real-world scenarios with 1M reference images. Given the unified design, outstanding performance, strong efficiency, and scalability of our method, it could serve as a well-balanced solution for real-world large-scale applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.229, + 0.65 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.885 + ], + "angle": 0, + "content": "Reranking Methods. In Table 4, we adopt the same global and local features from our default backbone and compare different reranking methods. “No Reranking” denotes our model with only global retrieval. “RANSAC” [19] follows the pipeline of state-of-the-art methods [26, 53] using \\(1.5 \\times\\) of the patch size. “RRT” [48] is not proposed for VPR, nevertheless, we train it on the top of our backbone for comparison. “CVNet” [31] does not provide the training code, we thus adopt their pre-trained model trained on Google Landmark [56]. Remarkably, our reranking module significantly outperforms RANSAC [19] based geometric verification using much less (\\(< 22\\%\\)) inference time (Table 3). It also outperforms two recent state-of-the-art reranking methods on landmark retrieval, indicating the superiority of our reranking module." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Training Strategies. In Table 5, we compare our method" + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.23, + 0.876, + 0.417 + ], + "angle": 0, + "content": "
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking Module
Remove Positional Embedding86.493.294.7
Remove Transformer Block-185.593.895.0
Remove Transformer Block-281.992.894.6
Replace Top-5 w/ Top-186.693.894.7
Reranking Input
Remove Attention Selection83.692.894.1
Remove xy Coordinates Value85.093.594.7
Remove Attention Value86.193.594.3
Remove Correlation Value31.859.272.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.42, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Table 7. Ablation study on model components. We freeze the global retrieval module so that the global and local features are the same for different ablations. All ablations are trained with partial negative mining [6]. The components are defined in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.765 + ], + "angle": 0, + "content": "based on different training strategies. “No Reranking” uses only global retrieval, and “Reranking” denotes training reranking module with partial negative mining on a fixed global retrieval module. “Reranking+Mining” means training the reranking module with our global negative mining by randomly selecting one negative sample from the 100 global hardest samples. “Reranking+Mining+Finetune” further finetunes retrieval and reranking module together. “End-to-end Training” directly trains global retrieval and reranking module from the beginning in an end-to-end manner with partial negative mining. All the strategies with reranking outperform previous state-of-the-art methods on \\(\\mathbb{R}@\\mathbb{5}\\), and training the global retrieval and reranking module separately with a carefully designed strategy achieves the best performance. The results indicate that global hard negative mining is helpful for training the reranking module. End-to-end training is also a good trade-off between simplicity and performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different Backbones. In Table 6, we combine our reranking module with different backbone retrieval modules, including ViT-Small (default), ResNet50+GeM [27, 43] and ViT-Base. We follow [6] to add L2 normalization before the pooling layer but do not freeze or remove any convolutional layer. The attention map of ResNet50+GeM is generated following CAM [61]. The ResNet50+GeM model achieves competitive results for both global retrieval and reranking. It also significantly outperforms previous" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19376" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.092, + 0.892, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.337, + 0.856, + 0.351 + ], + "angle": 0, + "content": "Figure 4. Visualization of attention map and matched pairs. Green and red boxes in (f) indicate correct and wrong predictions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.371, + 0.473, + 0.901 + ], + "angle": 0, + "content": "works [26, 53], indicating that our reranking module is a generic component for both CNN and transformer backbone architectures. With similar global retrieval performance and the same reranking method (RANSAC or Ours), the ViT-Small model achieves slightly better performance than ResNet50+GeM, which means the transformer token is a good alternative for local matching as compared with CNN local feature. Furthermore, we adopt a larger backbone ViT-Base, which achieves significant performance improvement on global retrieval and RANSAC-based reranking over ViT-Small. However, the overall performance of our ViT-Base model has very small performance improvement (mainly on \\(\\mathbb{R}@\\mathbb{10}\\)), which indicates a possible bottleneck of the proposed framework. Components Ablation. In Table 7, we use the \"Reranking\" configuration in Table 5 as a baseline and ablate different components to check the importance of each component of our method. For simplicity, we freeze the global retrieval module and all the models are trained with partial negative mining. We have the following observations. (1) The most important components are the Transformer Block-2 and Correlation Value, and removing them causes a significant performance drop. This indicates that the feature correlation contributes most to the final decision. (2) When we replace the attention-based feature selection with random selection, the model becomes unstable and the performance drops moderately. (3) Removing other components, i.e. Transformer Block-1, xy Coordinates Value, Attention Value (defined in Sec. 3.2), causes a slight performance drop, indicating the effectiveness of these blocks for performance purposes. (4) We observe negligible performance drop when removing positional embedding or replacing top-5 pairs selection with top-1, which means the Sinusoidal positional embedding does not help much and the top-1 pair contains most of the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.371, + 0.768, + 0.385 + ], + "angle": 0, + "content": "information that is needed for reranking." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.412, + 0.637, + 0.427 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.678 + ], + "angle": 0, + "content": "In Fig. 4, we show a detailed case where the global retrieval fails on the top-3 results. Fig. 4 (b) and (c) show the attention map and the selected patches, which cover most of the informative regions for reranking. Both RANSAC and our method work well on reranking the top-100 candidates and our method finds more correct reference images in the top-3 results (Fig. 4 (f)). Although our reranking module is not as explainable as RANSAC, the transformer still focuses on specific patch pairs and we plot the top-20 pairs with the highest attention in the reranking module. As shown in Fig. 4 (d) and (e), our reranking also focuses on meaningful pairs and most of them are correct matches. As compared with RANSAC, our matched pairs may not have tight geometric consistency, but they may provide different information for the reranking as adjusted according to the task-relevant training data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.618, + 0.709 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose a unified retrieval and reranking framework for place recognition with only transformers. We for the first time show that vision transformer tokens are comparable to or even better than CNN local feature in terms of reranking. Our reranking module is generic and can be adopted on other CNN or transformer backbones. Remarkably, it significantly outperforms previous methods on major datasets with much less inference time and memory consumption. Our method can also provide possible matched local pairs like RANSAC and could be improved with geometric modeling in the future. We discuss the limitations and societal impact in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19377" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Amar Ali-bey, Brahim Chaib-draa, and Philippe Giguere. Mixvpr: Feature mixing for visual place recognition. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1162-1171, 2022. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.768 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "19380" + } + ] +] \ No newline at end of file diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_origin.pdf b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..81e2a126beec0284ae0bf534d901857a6f74b306 --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/2ca4068a-0a96-471c-b512-c2d7b65af9b6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c0ef72df334c74bc3709e1aea5e1d978cfb703cc85419b810b643f883d674d5 +size 2137183 diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/full.md b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ba3c92ec9babee6fb4ef1bd75f7dfde288ef744e --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/full.md @@ -0,0 +1,251 @@ +# $R^2$ Former: Unified Retrieval and Reranking Transformer for Place Recognition + +Sijie Zhu $^{1,2,\dagger}$ , Linjie Yang $^{1}$ , Chen Chen $^{2}$ , Mubarak Shah $^{2}$ , Xiaohui Shen $^{1}$ , Heng Wang $^{1}$ , ByteDance $^{2}$ Center for Research in Computer Vision, University of Central Florida + +{sijiezhu,linjie.yang,heng.wang,shenxiaohui.kevin}@bytedance.com,{chen.chen,shah}@crcv.ucf.edu + +# Abstract + +Visual Place Recognition (VPR) estimates the location of query images by matching them with images in a reference database. Conventional methods generally adopt aggregated CNN features for global retrieval and RANSAC-based geometric verification for reranking. However, RANSAC only employs geometric information but ignores other possible information that could be useful for reranking, e.g. local feature correlations, and attention values. In this paper, we propose a unified place recognition framework that handles both retrieval and reranking with a novel transformer model, named $R^2$ Former. The proposed reranking module takes feature correlation, attention value, and xy coordinates into account, and learns to determine whether the image pair is from the same location. The whole pipeline is end-to-end trainable and the reranking module alone can also be adopted on other CNN or transformer backbones as a generic component. Remarkably, $R^2$ Former significantly outperforms state-of-the-art methods on major VPR datasets with much less inference time and memory consumption. It also achieves the state-of-the-art on the hold-out MSLS challenge set and could serve as a simple yet strong solution for real-world large-scale applications. Experiments also show vision transformer tokens are comparable and sometimes better than CNN local features on local matching. The code is released at https://github.com/Jeff-Zilence/R2Former. + +# 1. Introduction + +Visual Place Recognition (VPR) aims to localize query images from unknown locations by matching them with a set of reference images from known locations. It has great potential for robotics [47], navigation [41], autonomous driving [9], augmented reality (AR) applications. Previous works [26, 53] generally formulate VPR as a retrieval problem with two stages, i.e. global retrieval, and reranking. The global retrieval stage usually applies aggregation + +![](images/75aaabf6c94297b6f622e9a3e58b255ed60584a8ffcf5b56414ae4bd42781ee0.jpg) +Figure 1. An overview of conventional pipeline and our unified framework. Both our global retrieval and reranking modules are end-to-end trainable transformer layers, which achieve state-of-the-art performance with much less computational cost. + +methods (e.g. NetVLAD [3] and GeM [43]) on top of CNN (Convolutional Neural Network) to retrieve top candidates from a large reference database. While some works [3, 6] only adopt global retrieval, current state-of-the-art methods [26, 53] conduct reranking (i.e. geometric verification with RANSAC [19]) on the top-k (e.g. $k = 100$ ) candidates to further confirm the matches, typically leading to a significant performance boost. However, geometric information is not the only information that could be useful for reranking, and task-relevant information could be learned with a data-driven module to further boost performance. Besides, the current reranking process requires a relatively large inference time and memory footprint (typically over 1s and 1MB per image), which cannot scale to real-world applications with large QPS (Queries Per Second) and reference database ( $>1\mathrm{M}$ images). + +Recently vision transformer [17] has achieved significant performance on a wide range of vision tasks, and has been shown to have a high potential for VPR [53] (Sec. 2). + +However, the predominant local features [26, 53] are still based on CNN backbones, due to the built-in feature locality with limited receptive fields. Although vision transformer [17] considers each patch as an input token and naturally encodes local information, the local information might be overwritten with global information by the strong global correlation between all tokens in every layer. Therefore, it is still unclear how vision transformer tokens perform in local matching as compared to CNN local features in this field. + +In this paper, we integrate the global retrieval and reranking into one unified framework employing only transformers (Fig. 1), abbreviated as $R^2$ Former, which is simple, efficient, and effective. The global retrieval is tackled based on the class token without additional aggregation modules [3,43] and the other image tokens are adopted as local features. Different from geometric verification which focuses on geometric information between local feature pairs, we feed the correlation between the tokens (local features) of a pair of images, xy coordinates of tokens, and their attention information to transformer modules, so that the module can learn task-relevant information that could be useful for reranking. The global retrieval and reranking parts can be either trained in an end-to-end manner or tuned alternatively with a more stable convergence. The proposed reranking module can also be adopted on other CNN or transformer backbones, and our comparison shows that vision transformer tokens are comparable to CNN local features in terms of reranking performance (Table 6). + +Without bells and whistles, the proposed method outperforms both retrieval-only and retrieval+reranking state-of-the-art methods on a wide range of VPR datasets. The proposed method follows a very efficient design and applies linear layers for dimension reduction: i.e. only 256 and $500 \times 131$ for global and local feature dimensions and only 32 for transformer dimension of reranking module, thus is significantly faster ( $>4.7 \times \mathrm{QPS}$ ) with much less ( $< 22\%$ ) memory consumption than previous methods [26, 53]. Both the global and local features are extracted from the same backbone model only once, and the reranking of top-k candidates is finished with only one forward pass by computing the reranking scores of all candidate pairs in parallel within one batch. The reranking speed can be further boosted by parallel computing on multiple GPUs with $>20 \times$ speedup over previous methods [26, 53]. We demonstrate that the proposed reranking module also learns to focus on good local matches like RANSAC [19]. We summarize our contributions as follows: + +- A unified retrieval and reranking framework for place recognition employing pure transformers, which demonstrates that vision transformer tokens are comparable and sometimes better than CNN local features in terms of reranking or local matching. +- A novel transformer-based reranking module that learns + +to attend to the correlation of informative local feature pairs. It can be combined with either CNN or transformer backbones with better performance and efficiency than other reranking methods, e.g. RANSAC. + +- Extensive experiments showing state-of-the-art performance on a wide range of place recognition datasets with significantly less ( $< 22\%$ ) inference latency and memory consumption than previous reranking-based methods. + +# 2. Related Work + +Visual Place Recognition. Visual place recognition (VPR) [2, 21, 38, 39, 47, 58, 60] is traditionally addressed with nearest neighbor search on aggregated [28] hand-crafted features [12, 37]. The current predominant methods [3-6, 26, 53] are based on CNN [27, 46] feature extractors with trainable aggregation layer, e.g. NetVLAD [3], CRN [30], or light-weighted pooling layer, e.g. GeM [43], R-MAC [24]. Numerous works [7, 20, 22, 23, 34, 54, 55] follow NetVLAD [3] to further improve the global representation for retrieval. Recently, Berton [6] et al. introduce a benchmark for VPR and implement a wide range of global-retrieval-based methods in the same framework. CosPlace [4] et al. propose an extremely large dataset and formulate the problem differently as classification using orientation information. + +In addition to global retrieval, recent state-of-the-art VPR methods [26, 53] apply reranking on the top retrieved candidates. Patch-NetVLAD [26] adopts NetVLAD [3] model as their backbone for global retrieval and applies RANSAC [19] based geometric verification on multi-scale patch descriptors. TransVPR [53] adds multiple transformer layers on the top of CNN backbones to extract both global and local features. An additional attention module is then deployed to select important local features as the input of RANSAC [19]. Other local matching methods from related tasks, e.g. SuperGlue [15,44] and DELG [10], are also evaluated for VPR. However, they both have a lower accuracy with a much slower inference speed [53]. Recently, there are several recent learning-based reranking methods from related tasks, e.g. landmark matching [31,48] and local matching [29]. While they either fail to generalize [31,48] on VPR (Table 4) or have a very different problem setting [29], i.e. computing point-to-point correspondence between two given images without global retrieval. To summarize, current state-of-the-art VPR methods rely on RANSAC, and methods from related tasks do not generalize well when directly applied to VPR. Our method takes one step forward to integrate retrieval and reranking into one unified VPR framework with pure transformers. + +Vision Transformer. Transformer [52] is first proposed for NLP (Natural Language Processing) tasks as a generic architecture without inductive bias. It is recently introduced to vision tasks as vision transformer [17] (ViT) by simply considering each image patch as a token. The vanilla ViT + +![](images/dcd0ac18f460a95c5412df5ba73d86faa745bb96c5a79be92754b610504d48c8.jpg) +Figure 2. An overview of the proposed framework. Both the global and local features are extracted as the class token and patch tokens, followed by dimension reduction using linear layers. The important local features are then selected based on the attention map (Fig. 3) and fed into the reranking module. Both the global retrieval and reranking modules consist of only transformer and linear layers. + +[17] requires large-scale training datasets (e.g. ImageNet-21k [14]) to achieve comparable results as CNN [27], and Deit [51] proposes a data-efficient training strategy for ViT which outperforms CNN on standard ImageNet-1k. The recent VG benchmark [6] adopts vanilla ViT without modifying the input resolution which could be suboptimal, while it already shows competitive performance on global retrieval. TransVPR [53] adopts multiple transformer layers, while the backbone feature extractor is still based on CNN. We hypothesize the power of vision transformer is not fully exploited for VPR and it is interesting to know how vision transformer tokens perform on reranking/local matching as compared with the predominant CNN local feature. + +# 3. $R^2$ Former + +We first formulate the problem and training objective of the proposed method in Sec. 3.1. Then we describe global retrieval and reranking stages in Sec. 3.2 and Sec. 3.3 respectively. Fig. 2 shows an overview of $R^2$ Former. + +# 3.1. Problem Formulation and Training Objective + +The proposed framework consists of two stages, i.e. global retrieval, and reranking. Given a set of query images $\{I_q\}$ and reference images $\{I_r\}$ , the objective of global retrieval is to learn an embedding space in which each query $I_{q}$ is close to its corresponding positive reference image $I_{r}$ . During training, reference images from the same location as the query image are defined as positive samples, and the typical threshold is set as 10 meters. We follow the common practice of previous works [3,6] to find the nearest reference image for each query in the embedding space as the + +final positive sample. Other reference images with distances greater than 25 meters are considered as negative samples. Partial negative mining [6] is conducted to select the hardest negative samples from a random subset. We denote the global embedding features of query, positive samples, and negative samples as $E_{q}, E_{p}, E_{n}$ and the global retrieval loss is trained with margin triplet loss: + +$$ +\mathcal {L} _ {\text {r e t r i e v a l}} = \max \left(\left| \left| E _ {q} - E _ {p} \right| \right| ^ {2} - \left| \left| E _ {q} - E _ {n} \right| \right| ^ {2} + m, 0\right). \tag {1} +$$ + +Here $||.||^2$ denotes squared L2 norm and $m$ is the margin. + +The reranking module takes the local features of two images as input and generates two-logit scores $\mathbb{L}$ as the output of a binary classification, representing the likelihoods for True or False matches. We feed both positive and negative query-reference pairs to the reranking module during training and the cross entropy $(CE)$ loss is formulated as: + +$$ +\mathcal {L} _ {\text {r e r a n k i n g}} = C E \left(\operatorname {S o f t m a x} \left(\mathbb {L} _ {q r}\right), \mathbb {I} _ {q r}\right). \tag {2} +$$ + +$\mathbb{L}$ and $\mathbb{I}$ denote the logits scores and ground-truth labels for the query-reference pairs. Although the partial negative mining [6] is shown to perform better than full negative mining for global retrieval in [6], the objective of the reranking module is to distinguish top-k retrieved candidates which are harder than partial negative samples [6]. To make sure the reranking module sees top-k hardest samples during training, we first freeze the global retrieval module and train the reranking module with randomly selected negative samples from the top-k hardest samples of the full database. The retrieval and reranking modules are then finetuned together with partial negative mining for better performance. Details are provided in Sec. 4.2. + +# 3.2. Global Retrieval Module + +We describe the components of our vision transformer backbone for VPR and how the final global/local features are generated. As shown in Fig. 2, the query and reference images share the same backbone transformer encoder and there is no additional aggregation [3, 43] or key-point [15] extraction module for global and local feature generation. In other words, all the features and intermediate data are directly generated using only transformers. + +ViT for Place Recognition. An input image $I \in \mathbb{R}^{h \times w \times c}$ is first divided into small $p \times p$ patches ( $p = 16$ by default) and converted into a number of tokens $T \in \mathbb{R}^{n \times d}$ by linear projection as the input of transformer encoders. Here $n, d$ denote the number and dimension of tokens, and $h, w, c$ denote the height, width, and number of channels in input images. In addition to the $n$ patch tokens, ViT [17] adds an additional learnable class token to aggregate classification information from each layer, which serves as a simple alternative for feature aggregation. Then we adopt the learnable position embedding $PE \in \mathbb{R}^{(n + 1) \times d}$ from ViT [17] and add it to each token to provide positional information. Different from previous work [6] using the fixed training resolution of ViT [17], we conduct 2D interpolation on the positional embedding so that the input resolution can be arbitrary and we use the most widely used resolution ( $640 \times 480$ ) for our method. + +Global Attention. On the bottom right of Fig. 2, we provide the detailed inner architecture of the transformer encoder, which has $L$ cascaded basic transformer [52] layers. The key component is the multi-head attention module, which adopts three linear projections to convert the input token into query, key and value, denoted as $Q, K, V$ with dimension $d$ . The basic attention is computed as $\text{softmax}(QK^{\top} / d)V$ (T means transpose), and a multi-head attention module performs this attention procedure in parallel for multiple heads with their final outputs concatenated. The multi-head attention module can model stronger global correlation than CNN with a limited receptive field, which helps information aggregation for global representation. However, it might reduce the locality of each token which could be harmful to local matching, we demonstrate that transformer tokens perform well as local features compared to CNN as shown in Table 6. + +Dimension Reduction. We feed the output class token from the last transformer layer into a linear layer to generate the global feature with only 256 dimensions. The local features are generated by applying a linear head on the output patch tokens of the penultimate transformer layer and the dimension is reduced to 128 to achieve a small memory consumption. Both global and local features are L2 normalized after reduction. The dimension reduction ensures a much smaller (Table 3) total feature dimensions than previous reranking-based methods. + +![](images/68bad915b4afab613365c64f0742d4718b52b37d059b3345752f683856302b5d.jpg) +Figure 3. Illustration of attention generation and token selection. + +# 3.3. Reranking Transformer Module + +We describe the attention-based local feature selection and the workflow inside our reranking transformer module. + +Attention-based Selection. For large-scale scenarios, local features occupy the majority of memory, thus reducing the number of local features is important for real-world deployment. Previous works [3,26,53] usually use $640 \times 480$ as image resolution, resulting in 1200 patch tokens. However, only a small portion of them are informative to determine the location of the image, e.g. buildings, trees, roads, etc. Previous works either leverage all the local features from multiple scales [26] or adopt additional modules [53] to generate attention maps, which filter local features with a certain threshold during local matching. On the contrary, we leverage the natural attention map within our transformer module and only save a fixed number of local features (e.g. 500) with top attention values, resulting in a much lower memory cost and simpler extraction pipeline. + +The $(n + 1) \times (n + 1)$ attention matrix of the last transformer layer in Fig. 3 is formulated as $\text{softmax}(QK^{\top} / d)$ in Sec. 3.2. It represents the contribution from each input token to each output token. Since the output class (CLS) token is the only one that connects to the global embedding feature, the CLS token output channel of the matrix $((n + 1)$ -dimensional vector for $n$ patches and CLS token) represents the contribution from input tokens to the global feature, which corresponds to the importance of each patch. We reshape the $n$ -dimensional vector corresponding to $n$ patches as $h / p \times w / p$ attention map to sort all the tokens and we select the top-500 tokens that are likely to cover the informative regions (bottom right of Fig. 3). The attention value and x,y coordinates are saved along with each local feature, resulting in $128 + 3 = 131$ dimensions. + +Correlation-based Reranking. RANSAC-based [19] geometric verification only leverages the top-1 matched pairs for all local features, but ignores other important information that could be useful for reranking, i.e. the correlation, and attention value. Local feature pairs with higher correlation/similarity have higher probabilities to be correct local matches, and an image pair with more correct local matches is more likely to represent the same place. Also, high attention values of the local patches could indicate the importance of the local feature pairs. Therefore, our reranking module is designed to maintain the correlation, attention, and positional information for all the local feature pairs in a correlation matrix, resulting in 7 dimensions (Fig. 2) denoted as $(x,y,A,x',y',A',S)$ . $x,y,x',y'$ denote the coordinates of the two patches in the query and reference images. $A,A'$ denotes the attention values of the two patches. $S$ is the cosine similarity between the 128-dimensional local features. Since each image has 500 selected features/tokens, there are $500\times 500$ pairs, resulting in a $500\times 500\times 7$ correlation matrix. The correlation matrix contains the major information for all the feature pairs and allows the model to learn whatever is useful to determine whether the two images are from the same location. + +To reduce the computation, we select the 5 nearest neighbors of each token in the feature space to produce two $500 \times 5 \times 7$ matrices, as the other feature pairs with large distances are likely to be wrong matches. They are concatenated together and fed to a linear layer, resulting in a $1000 \times 5 \times 32$ matrix. We then leverage the strong global correlation modeling of transformer [52] to aggregate the large matrix as a reranking score to determine whether the input pair is a correct match. First, we adopt "Transformer Block-1" to extract important information from the top-5 pairs as one output class token. Then "Transformer Block-2" extracts aggregates the information from the 1000 tokens as a single 32-dimension vector (the class token). The two transformer blocks are multiple transformer layers with linear projection and standard Sinusoidal positional embedding [52]. Finally, the vector is converted into 2 channels by a linear head as a binary classification (i.e. True vs False). + +# 4. Experiment + +# 4.1. Datasets and Evaluation Metrics + +We train our model on MSLS (Mapillary Street-Level Sequences) [55] dataset, which covers a wide range of real-world scenarios for VPR, e.g. different cities, viewpoint variation, day/night, and season changes. The performance in urban scenarios (e.g. Pitts30k [50], Tokyo24/7 [49]) can be further improved by finetuning on Pitts30k. For evaluation, we use standard train/val/test split [6, 26, 53, 55] on major datasets, including MSLS Val [55], MSLS Challenge [55], Pitts30k [50], Tokyo 24/7 [49], R-SF (Revisited San + +Francisco) [6, 11, 33, 45], St Lucia [40]. The MSLS Challenge [55] is a hold-out set whose labels are not released, but researchers can submit the predictions on their challenge server to get the performance. For the other datasets with location labels, we follow previous works [6, 26, 53] to use 25 meters as the threshold for correct localization and report recall@k (k=1,5,10) as evaluation metrics. We also report detailed computational costs, including inference time for extraction/retrieval/matching, feature dimensions, GFLOPs, and memory footprint (Table 3). + +# 4.2. Implementation Details + +The proposed method is implemented using PyTorch [42]. The models are trained on 8 Tesla-V100 GPUs. All images are resized to $640 \times 480$ for training and evaluation. The reranking is conducted on top-100 candidates and we set margin $m = 0.1$ . We use ViT-S [17] (12 layers with 384 dimensions) architecture as our default backbone and the module is initialized with off-the-shelf pre-trained weights [51] on ImageNet-1k [14]. The transformers in the reranking module use a small dimension of 32 with only 2 and 6 layers for Transformer Block-1 and Block-2 respectively, thus resulting in a very small computational cost. + +The global retrieval and the reranking module can be trained jointly in an end-to-end manner, but we train them separately (Sec. 3.1) by default to achieve a stable convergence and better accuracy. The global retrieval module is trained following common practice [6]. The reranking module is trained from scratch following the standard pipeline of training transformers, i.e. AdamW [36] optimizer with cosine learning rate schedule [35]. The initial learning rate is 0.0005 with 64 triplets per batch. Each triplet only samples one hard negative reference image which is randomly selected from the top-100 hardest samples from the MSLS training set of the corresponding query. Given that the global embedding features do not change during this stage, the global hard negative mining only needs to be conducted once and can be efficiently computed on GPU in 3 hours. We precompute the hard negative list of all queries for the training of the reranking module, which is more efficient than the full mining implementation of the VG benchmark [6]. The reranking module is trained for 50 epochs and we select the model with the highest recall@5 on the validation set. The global retrieval and reranking module are then finetuned together with partial negative mining [6]. More details are included in supplementary material. + +# 4.3. Comparison with State-of-the-art + +In this section, we compare the proposed method with previous state-of-the-art methods, including NetVLAD [3], SFRS [23], SP-SuperGlue [15, 44], Patch-NetVLAD [26], and TransVPR [53]. We further compare our method with the best configurations in the recent VG benchmark [6]. + +
MSLS Val [55]MSLS Challenge [55]Pitts30k [50]Tokyo 24/7 [49]
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
NetVLAD [3]60.874.379.535.147.451.781.991.293.764.878.481.6
SFRS [23]69.280.383.141.552.056.389.494.795.985.491.193.3
SP-SuperGlue [15,44]78.181.984.350.656.958.387.294.896.488.290.290.2
Patch-NetVLAD [26]79.586.287.748.157.660.588.794.595.986.088.690.5
TransVPR [53]86.891.292.463.974.077.589.094.996.279.082.285.1
Ours89.795.096.273.085.988.891.195.296.388.691.491.7
+ +Table 1. Comparison of our method with previous state-of-the-art results on major VPR datasets. Our model is trained on MSLS and tested on MSLS Val and Challenge set. Our model is further finetuned on Pitts30k for urban scenarios, i.e. Pitts30k, Tokyo 24/7. + +
Features Dim ↓GFLOPs ↓Trained on MSLS - R@1
Pitts30kMSLS ValMSLS Chall.Tok. 24/7R-SFSt Lucia
ResNet101 + GeM [6,43]102486.2977.277.0*55.551.046.991.6
ResNet101 + NetVLAD [3,6]6553686.0680.881.1*61.559.056.195.1
CCT384 + NetVLAD [6,25]2457618.5385.183.8*61.470.365.998.4
Ours w/o Reranking25625.9076.379.356.245.747.594.3
Ours65500†48.50†88.489.773.072.772.199.7
+ +Table 2. Comparison following the protocol of the recent VG benchmark [6] on major datasets in terms of R@1. The models are trained on MSLS and directly tested on all datasets w/o finetuning. † The dimensions and GFLOPs are computed by adding the numbers of global retrieval and reranking together, i.e. $Dim = 256 + 500 \times (128 + 3)$ and $GFLOPs = 25.90 + 100 \times 0.226$ . + +
Feature Dim ↓Latency per Query (ms) ↓Memory Footprint (GB) ↓
GlobalLocalExtractionRetrievalRerankingMSLS Val1M Images
ResNet101 + NetVLAD [3,6]65536N/A9.602.33N/A4.79244.14
Patch-NetVLAD-s [26]512936 × 5129.290.08952.8537.601917.29
Patch-NetVLAD-p [26]40962826 × 40969.360.198377.17908.3046315.85
TransVPR [53]2561200 × 2566.200.071757.7022.721158.53
Ours256500 × (128+3)8.810.07202.374.79244.01
+ +Table 3. Comparison of computational cost in terms of feature dimension, latency, and memory footprint. All the methods are measured on MSLS Val (18,871 database images) using the same CPU and GPU (RTX A5000). Reranking is conducted on top-100 candidates. "Patch-NetVLAD-p" and "Patch-NetVLAD-s" denote the performance and speed-oriented versions. + +We also provide a detailed comparison with state-of-the-art methods [6,26,53] on computational cost. Other works [1, 16, 18, 57, 59, 62] on related tasks with different settings are not included. + +As shown in Table 1, the proposed method significantly outperforms state-of-the-art methods on MSLS Val and Challenge set with absolute R@1 improvement of $2.9\%$ and $9.1\%$ respectively. Benefiting from large-scale training, our method also achieves state-of-the-art R@1 on Pitts30k and Tokyo24/7. Small-scale dataset [50] with weak supervision is not enough to train a data-driven reranking module, and training on one large-scale dataset with good generalization on all datasets is more desirable for real-world deployment. (Details in supp. material.) + +In Table 2, we select the best-performing models in the VG benchmark [6] and compare them with our method on major datasets. Eynsham [13] dataset is not included because it has a different camera type (gray-scale) and resolution. * denotes reproduced results using the official MSLS [55] validation code and pre-trained models [6]. Table 2 shows that our model trained on MSLS generalizes well on all the other datasets and significantly outperforms the best + +models in the VG benchmark [6] with comparable computational cost. + +In Table 3, we compare the computational cost of our method with previous global retrieval methods and retrieval+reranking methods. Apparently, the inference latency of extraction and retrieval is negligible as compared to the reranking latency of previous works. Our method is significantly faster than all the other reranking-based methods because our reranking process is only one network forward pass on GPU and can be easily accelerated by parallel computing, e.g. reranking on 4 GPUs takes only $47.17\mathrm{ms}$ per query $(20.2\times$ speedup over previous reranking-based methods [26, 53]). However, it is not straightforward to accelerate RANSAC-based geometric verification with multiprocessing. Previous works [26, 53] generally follow the standard implementation of OpenCV [8]. In addition, the local feature dimension of our method is the smallest among all the reranking-based methods, specifically, we only save 500 important local features with very small dimensions $(128 + 3)$ for each image. In total, it only needs $4.79\mathrm{GB}$ of memory for the MSLS validation set which is much smaller $(189\times$ reduction) than $908.3\mathrm{GB}$ of Patch-NetVLAD-p. + +
R@1R@5R@10
No Reranking79.390.892.6
RANSAC [19]84.993.094.5
RRT [48]81.291.993.1
CVNet [32]73.486.891.4
Ours89.795.096.2
+ +Table 4. Comparison with different reranking methods (top-100 candidates reranked) using our backbone on MSLS Val. + +
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking + Mining88.493.494.9
Reranking + Mining + Finetune89.795.096.2
End-to-end Training87.393.595.4
+ +Table 5. Ablation study on training strategy. We freeze the global retrieval module by default when training the reranking module. + +
ArchitectureR@1R@5R@10
Ours w/o +RerankingViT-Small79.390.892.6
ResNet50 + GeM79.690.992.6
ViT-Base84.992.794.5
Ours w/ +RANSACViT-Small84.993.094.5
ResNet50 + GeM84.391.493.0
ViT-Base87.093.094.6
OursViT-Small89.795.096.2
ResNet50 + GeM88.493.695.3
ViT-Base90.095.196.9
+ +Even for datasets with over 1M reference images (e.g. R-SF dataset), the memory footprint is only 244.01 GB which can fit in a typical server or high-end desktop. It can be further reduced to 122 GB by using float16 instead of float32, with which we observe no performance drop on R-SF. However, other reranking-based methods typically require much larger ( $>4\times$ ) memory, which cannot scale to large-scale real-world scenarios with 1M reference images. Given the unified design, outstanding performance, strong efficiency, and scalability of our method, it could serve as a well-balanced solution for real-world large-scale applications. + +# 4.4. Ablation Study + +Reranking Methods. In Table 4, we adopt the same global and local features from our default backbone and compare different reranking methods. “No Reranking” denotes our model with only global retrieval. “RANSAC” [19] follows the pipeline of state-of-the-art methods [26, 53] using $1.5 \times$ of the patch size. “RRT” [48] is not proposed for VPR, nevertheless, we train it on the top of our backbone for comparison. “CVNet” [31] does not provide the training code, we thus adopt their pre-trained model trained on Google Landmark [56]. Remarkably, our reranking module significantly outperforms RANSAC [19] based geometric verification using much less ( $< 22\%$ ) inference time (Table 3). It also outperforms two recent state-of-the-art reranking methods on landmark retrieval, indicating the superiority of our reranking module. + +Training Strategies. In Table 5, we compare our method + +Table 6. Ablation study on MSLS Val with different backbone architectures, including ResNet50+GeM [27,43], ViT Small [17], ViT Base [17]. Transformer tokens perform on par with CNN local features in terms of reranking/local matching. + +
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking Module
Remove Positional Embedding86.493.294.7
Remove Transformer Block-185.593.895.0
Remove Transformer Block-281.992.894.6
Replace Top-5 w/ Top-186.693.894.7
Reranking Input
Remove Attention Selection83.692.894.1
Remove xy Coordinates Value85.093.594.7
Remove Attention Value86.193.594.3
Remove Correlation Value31.859.272.8
+ +Table 7. Ablation study on model components. We freeze the global retrieval module so that the global and local features are the same for different ablations. All ablations are trained with partial negative mining [6]. The components are defined in Sec. 3. + +based on different training strategies. “No Reranking” uses only global retrieval, and “Reranking” denotes training reranking module with partial negative mining on a fixed global retrieval module. “Reranking+Mining” means training the reranking module with our global negative mining by randomly selecting one negative sample from the 100 global hardest samples. “Reranking+Mining+Finetune” further finetunes retrieval and reranking module together. “End-to-end Training” directly trains global retrieval and reranking module from the beginning in an end-to-end manner with partial negative mining. All the strategies with reranking outperform previous state-of-the-art methods on $\mathbb{R}@\mathbb{5}$ , and training the global retrieval and reranking module separately with a carefully designed strategy achieves the best performance. The results indicate that global hard negative mining is helpful for training the reranking module. End-to-end training is also a good trade-off between simplicity and performance. + +Different Backbones. In Table 6, we combine our reranking module with different backbone retrieval modules, including ViT-Small (default), ResNet50+GeM [27, 43] and ViT-Base. We follow [6] to add L2 normalization before the pooling layer but do not freeze or remove any convolutional layer. The attention map of ResNet50+GeM is generated following CAM [61]. The ResNet50+GeM model achieves competitive results for both global retrieval and reranking. It also significantly outperforms previous + +![](images/bc49f31c6d459fcf2f21b329e6076f3add35a360cb153f5178dc12fda3ebce61.jpg) +Figure 4. Visualization of attention map and matched pairs. Green and red boxes in (f) indicate correct and wrong predictions. + +works [26, 53], indicating that our reranking module is a generic component for both CNN and transformer backbone architectures. With similar global retrieval performance and the same reranking method (RANSAC or Ours), the ViT-Small model achieves slightly better performance than ResNet50+GeM, which means the transformer token is a good alternative for local matching as compared with CNN local feature. Furthermore, we adopt a larger backbone ViT-Base, which achieves significant performance improvement on global retrieval and RANSAC-based reranking over ViT-Small. However, the overall performance of our ViT-Base model has very small performance improvement (mainly on $\mathbb{R}@\mathbb{10}$ ), which indicates a possible bottleneck of the proposed framework. Components Ablation. In Table 7, we use the "Reranking" configuration in Table 5 as a baseline and ablate different components to check the importance of each component of our method. For simplicity, we freeze the global retrieval module and all the models are trained with partial negative mining. We have the following observations. (1) The most important components are the Transformer Block-2 and Correlation Value, and removing them causes a significant performance drop. This indicates that the feature correlation contributes most to the final decision. (2) When we replace the attention-based feature selection with random selection, the model becomes unstable and the performance drops moderately. (3) Removing other components, i.e. Transformer Block-1, xy Coordinates Value, Attention Value (defined in Sec. 3.2), causes a slight performance drop, indicating the effectiveness of these blocks for performance purposes. (4) We observe negligible performance drop when removing positional embedding or replacing top-5 pairs selection with top-1, which means the Sinusoidal positional embedding does not help much and the top-1 pair contains most of the + +information that is needed for reranking. + +# 4.5. Visualization + +In Fig. 4, we show a detailed case where the global retrieval fails on the top-3 results. Fig. 4 (b) and (c) show the attention map and the selected patches, which cover most of the informative regions for reranking. Both RANSAC and our method work well on reranking the top-100 candidates and our method finds more correct reference images in the top-3 results (Fig. 4 (f)). Although our reranking module is not as explainable as RANSAC, the transformer still focuses on specific patch pairs and we plot the top-20 pairs with the highest attention in the reranking module. As shown in Fig. 4 (d) and (e), our reranking also focuses on meaningful pairs and most of them are correct matches. As compared with RANSAC, our matched pairs may not have tight geometric consistency, but they may provide different information for the reranking as adjusted according to the task-relevant training data. + +# 5. Conclusion + +We propose a unified retrieval and reranking framework for place recognition with only transformers. We for the first time show that vision transformer tokens are comparable to or even better than CNN local feature in terms of reranking. Our reranking module is generic and can be adopted on other CNN or transformer backbones. Remarkably, it significantly outperforms previous methods on major datasets with much less inference time and memory consumption. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1162-1171, 2022. 6 \ No newline at end of file diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/images.zip b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7ac71d0071fa09822b5c38124b77134302f96f7c --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d42a36217f6dc84edf9528cfab41d64bd579faace1c034aa7388b8721e75e8e4 +size 677726 diff --git a/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/layout.json b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..95fa17205be94e683c63e51c180c5575b0138094 --- /dev/null +++ b/2023/R2Former_ Unified Retrieval and Reranking Transformer for Place Recognition/layout.json @@ -0,0 +1,7469 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 51, + 102, + 543, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 102, + 543, + 121 + ], + "spans": [ + { + "bbox": [ + 51, + 102, + 543, + 121 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 51, + 102, + 543, + 121 + ], + "type": "text", + "content": "Former: Unified Retrieval and Reranking Transformer for Place Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "spans": [ + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": "Sijie Zhu" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{1,2,\\dagger}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", Linjie Yang" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", Chen Chen" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", Mubarak Shah" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", Xiaohui Shen" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", Heng Wang" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": ", ByteDance" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 142, + 518, + 171 + ], + "type": "text", + "content": " Center for Research in Computer Vision, University of Central Florida" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 173, + 564, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 173, + 564, + 185 + ], + "spans": [ + { + "bbox": [ + 53, + 173, + 564, + 185 + ], + "type": "text", + "content": "{sijiezhu,linjie.yang,heng.wang,shenxiaohui.kevin}@bytedance.com,{chen.chen,shah}@crcv.ucf.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "content": "Visual Place Recognition (VPR) estimates the location of query images by matching them with images in a reference database. Conventional methods generally adopt aggregated CNN features for global retrieval and RANSAC-based geometric verification for reranking. However, RANSAC only employs geometric information but ignores other possible information that could be useful for reranking, e.g. local feature correlations, and attention values. In this paper, we propose a unified place recognition framework that handles both retrieval and reranking with a novel transformer model, named " + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "content": "Former. The proposed reranking module takes feature correlation, attention value, and xy coordinates into account, and learns to determine whether the image pair is from the same location. The whole pipeline is end-to-end trainable and the reranking module alone can also be adopted on other CNN or transformer backbones as a generic component. Remarkably, " + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 239, + 290, + 550 + ], + "type": "text", + "content": "Former significantly outperforms state-of-the-art methods on major VPR datasets with much less inference time and memory consumption. It also achieves the state-of-the-art on the hold-out MSLS challenge set and could serve as a simple yet strong solution for real-world large-scale applications. Experiments also show vision transformer tokens are comparable and sometimes better than CNN local features on local matching. The code is released at https://github.com/Jeff-Zilence/R2Former." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 575, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "type": "text", + "content": "Visual Place Recognition (VPR) aims to localize query images from unknown locations by matching them with a set of reference images from known locations. It has great potential for robotics [47], navigation [41], autonomous driving [9], augmented reality (AR) applications. Previous works [26, 53] generally formulate VPR as a retrieval problem with two stages, i.e. global retrieval, and reranking. The global retrieval stage usually applies aggregation" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 211, + 545, + 425 + ], + "blocks": [ + { + "bbox": [ + 307, + 211, + 545, + 425 + ], + "lines": [ + { + "bbox": [ + 307, + 211, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 307, + 211, + 545, + 425 + ], + "type": "image", + "image_path": "75aaabf6c94297b6f622e9a3e58b255ed60584a8ffcf5b56414ae4bd42781ee0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "lines": [ + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "type": "text", + "content": "Figure 1. An overview of conventional pipeline and our unified framework. Both our global retrieval and reranking modules are end-to-end trainable transformer layers, which achieve state-of-the-art performance with much less computational cost." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "text", + "content": "methods (e.g. NetVLAD [3] and GeM [43]) on top of CNN (Convolutional Neural Network) to retrieve top candidates from a large reference database. While some works [3, 6] only adopt global retrieval, current state-of-the-art methods [26, 53] conduct reranking (i.e. geometric verification with RANSAC [19]) on the top-k (e.g. " + }, + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "inline_equation", + "content": "k = 100" + }, + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "text", + "content": ") candidates to further confirm the matches, typically leading to a significant performance boost. However, geometric information is not the only information that could be useful for reranking, and task-relevant information could be learned with a data-driven module to further boost performance. Besides, the current reranking process requires a relatively large inference time and memory footprint (typically over 1s and 1MB per image), which cannot scale to real-world applications with large QPS (Queries Per Second) and reference database (" + }, + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "inline_equation", + "content": ">1\\mathrm{M}" + }, + { + "bbox": [ + 304, + 485, + 546, + 676 + ], + "type": "text", + "content": " images)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Recently vision transformer [17] has achieved significant performance on a wide range of vision tasks, and has been shown to have a high potential for VPR [53] (Sec. 2)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 287, + 712 + ], + "type": "text", + "content": "† This work was done during the first author's internship at ByteDance" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19370" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "However, the predominant local features [26, 53] are still based on CNN backbones, due to the built-in feature locality with limited receptive fields. Although vision transformer [17] considers each patch as an input token and naturally encodes local information, the local information might be overwritten with global information by the strong global correlation between all tokens in every layer. Therefore, it is still unclear how vision transformer tokens perform in local matching as compared to CNN local features in this field." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 410 + ], + "type": "text", + "content": "In this paper, we integrate the global retrieval and reranking into one unified framework employing only transformers (Fig. 1), abbreviated as " + }, + { + "bbox": [ + 46, + 182, + 289, + 410 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 182, + 289, + 410 + ], + "type": "text", + "content": "Former, which is simple, efficient, and effective. The global retrieval is tackled based on the class token without additional aggregation modules [3,43] and the other image tokens are adopted as local features. Different from geometric verification which focuses on geometric information between local feature pairs, we feed the correlation between the tokens (local features) of a pair of images, xy coordinates of tokens, and their attention information to transformer modules, so that the module can learn task-relevant information that could be useful for reranking. The global retrieval and reranking parts can be either trained in an end-to-end manner or tuned alternatively with a more stable convergence. The proposed reranking module can also be adopted on other CNN or transformer backbones, and our comparison shows that vision transformer tokens are comparable to CNN local features in terms of reranking performance (Table 6)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "content": "Without bells and whistles, the proposed method outperforms both retrieval-only and retrieval+reranking state-of-the-art methods on a wide range of VPR datasets. The proposed method follows a very efficient design and applies linear layers for dimension reduction: i.e. only 256 and " + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "inline_equation", + "content": "500 \\times 131" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "content": " for global and local feature dimensions and only 32 for transformer dimension of reranking module, thus is significantly faster (" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "inline_equation", + "content": ">4.7 \\times \\mathrm{QPS}" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "content": ") with much less (" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "inline_equation", + "content": "< 22\\%" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "content": ") memory consumption than previous methods [26, 53]. Both the global and local features are extracted from the same backbone model only once, and the reranking of top-k candidates is finished with only one forward pass by computing the reranking scores of all candidate pairs in parallel within one batch. The reranking speed can be further boosted by parallel computing on multiple GPUs with " + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "inline_equation", + "content": ">20 \\times" + }, + { + "bbox": [ + 46, + 411, + 289, + 639 + ], + "type": "text", + "content": " speedup over previous methods [26, 53]. We demonstrate that the proposed reranking module also learns to focus on good local matches like RANSAC [19]. We summarize our contributions as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 642, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 701 + ], + "type": "text", + "content": "- A unified retrieval and reranking framework for place recognition employing pure transformers, which demonstrates that vision transformer tokens are comparable and sometimes better than CNN local features in terms of reranking or local matching." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "- A novel transformer-based reranking module that learns" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 312, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 545, + 120 + ], + "type": "text", + "content": "to attend to the correlation of informative local feature pairs. It can be combined with either CNN or transformer backbones with better performance and efficiency than other reranking methods, e.g. RANSAC." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 121, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 547, + 168 + ], + "type": "text", + "content": "- Extensive experiments showing state-of-the-art performance on a wide range of place recognition datasets with significantly less (" + }, + { + "bbox": [ + 306, + 121, + 547, + 168 + ], + "type": "inline_equation", + "content": "< 22\\%" + }, + { + "bbox": [ + 306, + 121, + 547, + 168 + ], + "type": "text", + "content": ") inference latency and memory consumption than previous reranking-based methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 178, + 392, + 191 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 392, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 392, + 191 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "content": "Visual Place Recognition. Visual place recognition (VPR) [2, 21, 38, 39, 47, 58, 60] is traditionally addressed with nearest neighbor search on aggregated [28] hand-crafted features [12, 37]. The current predominant methods [3-6, 26, 53] are based on CNN [27, 46] feature extractors with trainable aggregation layer, e.g. NetVLAD [3], CRN [30], or light-weighted pooling layer, e.g. GeM [43], R-MAC [24]. Numerous works [7, 20, 22, 23, 34, 54, 55] follow NetVLAD [3] to further improve the global representation for retrieval. Recently, Berton [6] et al. introduce a benchmark for VPR and implement a wide range of global-retrieval-based methods in the same framework. CosPlace [4] et al. propose an extremely large dataset and formulate the problem differently as classification using orientation information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 367, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 547, + 654 + ], + "type": "text", + "content": "In addition to global retrieval, recent state-of-the-art VPR methods [26, 53] apply reranking on the top retrieved candidates. Patch-NetVLAD [26] adopts NetVLAD [3] model as their backbone for global retrieval and applies RANSAC [19] based geometric verification on multi-scale patch descriptors. TransVPR [53] adds multiple transformer layers on the top of CNN backbones to extract both global and local features. An additional attention module is then deployed to select important local features as the input of RANSAC [19]. Other local matching methods from related tasks, e.g. SuperGlue [15,44] and DELG [10], are also evaluated for VPR. However, they both have a lower accuracy with a much slower inference speed [53]. Recently, there are several recent learning-based reranking methods from related tasks, e.g. landmark matching [31,48] and local matching [29]. While they either fail to generalize [31,48] on VPR (Table 4) or have a very different problem setting [29], i.e. computing point-to-point correspondence between two given images without global retrieval. To summarize, current state-of-the-art VPR methods rely on RANSAC, and methods from related tasks do not generalize well when directly applied to VPR. Our method takes one step forward to integrate retrieval and reranking into one unified VPR framework with pure transformers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Vision Transformer. Transformer [52] is first proposed for NLP (Natural Language Processing) tasks as a generic architecture without inductive bias. It is recently introduced to vision tasks as vision transformer [17] (ViT) by simply considering each image patch as a token. The vanilla ViT" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19371" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 516, + 290 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 516, + 290 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 516, + 290 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 516, + 290 + ], + "type": "image", + "image_path": "dcd0ac18f460a95c5412df5ba73d86faa745bb96c5a79be92754b610504d48c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 547, + 326 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed framework. Both the global and local features are extracted as the class token and patch tokens, followed by dimension reduction using linear layers. The important local features are then selected based on the attention map (Fig. 3) and fed into the reranking module. Both the global retrieval and reranking modules consist of only transformer and linear layers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 337, + 289, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 289, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 289, + 494 + ], + "type": "text", + "content": "[17] requires large-scale training datasets (e.g. ImageNet-21k [14]) to achieve comparable results as CNN [27], and Deit [51] proposes a data-efficient training strategy for ViT which outperforms CNN on standard ImageNet-1k. The recent VG benchmark [6] adopts vanilla ViT without modifying the input resolution which could be suboptimal, while it already shows competitive performance on global retrieval. TransVPR [53] adopts multiple transformer layers, while the backbone feature extractor is still based on CNN. We hypothesize the power of vision transformer is not fully exploited for VPR and it is interesting to know how vision transformer tokens perform on reranking/local matching as compared with the predominant CNN local feature." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 501, + 117, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 117, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 117, + 514 + ], + "type": "text", + "content": "3. " + }, + { + "bbox": [ + 47, + 501, + 117, + 514 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 47, + 501, + 117, + 514 + ], + "type": "text", + "content": " Former" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 571 + ], + "type": "text", + "content": "We first formulate the problem and training objective of the proposed method in Sec. 3.1. Then we describe global retrieval and reranking stages in Sec. 3.2 and Sec. 3.3 respectively. Fig. 2 shows an overview of " + }, + { + "bbox": [ + 46, + 521, + 287, + 571 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 521, + 287, + 571 + ], + "type": "text", + "content": "Former." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 575, + 285, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 285, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 285, + 588 + ], + "type": "text", + "content": "3.1. Problem Formulation and Training Objective" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "The proposed framework consists of two stages, i.e. global retrieval, and reranking. Given a set of query images " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{I_q\\}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and reference images " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{I_r\\}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", the objective of global retrieval is to learn an embedding space in which each query " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_{q}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is close to its corresponding positive reference image " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_{r}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". During training, reference images from the same location as the query image are defined as positive samples, and the typical threshold is set as 10 meters. We follow the common practice of previous works [3,6] to find the nearest reference image for each query in the embedding space as the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 337, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 547, + 422 + ], + "type": "text", + "content": "final positive sample. Other reference images with distances greater than 25 meters are considered as negative samples. Partial negative mining [6] is conducted to select the hardest negative samples from a random subset. We denote the global embedding features of query, positive samples, and negative samples as " + }, + { + "bbox": [ + 304, + 337, + 547, + 422 + ], + "type": "inline_equation", + "content": "E_{q}, E_{p}, E_{n}" + }, + { + "bbox": [ + 304, + 337, + 547, + 422 + ], + "type": "text", + "content": " and the global retrieval loss is trained with margin triplet loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 427, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 427, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 312, + 427, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e t r i e v a l}} = \\max \\left(\\left| \\left| E _ {q} - E _ {p} \\right| \\right| ^ {2} - \\left| \\left| E _ {q} - E _ {n} \\right| \\right| ^ {2} + m, 0\\right). \\tag {1}", + "image_path": "77e131046876f9e23c1bf30c2e1d303b6a2619e90e11450364f6a3025ff2c4bf.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "inline_equation", + "content": "||.||^2" + }, + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "text", + "content": " denotes squared L2 norm and " + }, + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 447, + 538, + 460 + ], + "type": "text", + "content": " is the margin." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": "The reranking module takes the local features of two images as input and generates two-logit scores " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " as the output of a binary classification, representing the likelihoods for True or False matches. We feed both positive and negative query-reference pairs to the reranking module during training and the cross entropy " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "(CE)" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " loss is formulated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 348, + 538, + 545, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 538, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 348, + 538, + 545, + 551 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e r a n k i n g}} = C E \\left(\\operatorname {S o f t m a x} \\left(\\mathbb {L} _ {q r}\\right), \\mathbb {I} _ {q r}\\right). \\tag {2}", + "image_path": "2f9f191b521e12c5137f79262427e9d81748a8c0eafa7c04cc86afacdfd25112.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " denote the logits scores and ground-truth labels for the query-reference pairs. Although the partial negative mining [6] is shown to perform better than full negative mining for global retrieval in [6], the objective of the reranking module is to distinguish top-k retrieved candidates which are harder than partial negative samples [6]. To make sure the reranking module sees top-k hardest samples during training, we first freeze the global retrieval module and train the reranking module with randomly selected negative samples from the top-k hardest samples of the full database. The retrieval and reranking modules are then finetuned together with partial negative mining for better performance. Details are provided in Sec. 4.2." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19372" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 187, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 187, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 187, + 83 + ], + "type": "text", + "content": "3.2. Global Retrieval Module" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 288, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 288, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 288, + 186 + ], + "type": "text", + "content": "We describe the components of our vision transformer backbone for VPR and how the final global/local features are generated. As shown in Fig. 2, the query and reference images share the same backbone transformer encoder and there is no additional aggregation [3, 43] or key-point [15] extraction module for global and local feature generation. In other words, all the features and intermediate data are directly generated using only transformers." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": "ViT for Place Recognition. An input image " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " is first divided into small " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "p \\times p" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " patches (" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "p = 16" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " by default) and converted into a number of tokens " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{n \\times d}" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " by linear projection as the input of transformer encoders. Here " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "n, d" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " denote the number and dimension of tokens, and " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "h, w, c" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " denote the height, width, and number of channels in input images. In addition to the " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " patch tokens, ViT [17] adds an additional learnable class token to aggregate classification information from each layer, which serves as a simple alternative for feature aggregation. Then we adopt the learnable position embedding " + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "PE \\in \\mathbb{R}^{(n + 1) \\times d}" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": " from ViT [17] and add it to each token to provide positional information. Different from previous work [6] using the fixed training resolution of ViT [17], we conduct 2D interpolation on the positional embedding so that the input resolution can be arbitrary and we use the most widely used resolution (" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 46, + 186, + 290, + 390 + ], + "type": "text", + "content": ") for our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "content": "Global Attention. On the bottom right of Fig. 2, we provide the detailed inner architecture of the transformer encoder, which has " + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "content": " cascaded basic transformer [52] layers. The key component is the multi-head attention module, which adopts three linear projections to convert the input token into query, key and value, denoted as " + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "inline_equation", + "content": "Q, K, V" + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "content": " with dimension " + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "content": ". The basic attention is computed as " + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "inline_equation", + "content": "\\text{softmax}(QK^{\\top} / d)V" + }, + { + "bbox": [ + 46, + 390, + 288, + 594 + ], + "type": "text", + "content": " (T means transpose), and a multi-head attention module performs this attention procedure in parallel for multiple heads with their final outputs concatenated. The multi-head attention module can model stronger global correlation than CNN with a limited receptive field, which helps information aggregation for global representation. However, it might reduce the locality of each token which could be harmful to local matching, we demonstrate that transformer tokens perform well as local features compared to CNN as shown in Table 6." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Dimension Reduction. We feed the output class token from the last transformer layer into a linear layer to generate the global feature with only 256 dimensions. The local features are generated by applying a linear head on the output patch tokens of the penultimate transformer layer and the dimension is reduced to 128 to achieve a small memory consumption. Both global and local features are L2 normalized after reduction. The dimension reduction ensures a much smaller (Table 3) total feature dimensions than previous reranking-based methods." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 320, + 69, + 531, + 279 + ], + "blocks": [ + { + "bbox": [ + 320, + 69, + 531, + 279 + ], + "lines": [ + { + "bbox": [ + 320, + 69, + 531, + 279 + ], + "spans": [ + { + "bbox": [ + 320, + 69, + 531, + 279 + ], + "type": "image", + "image_path": "68bad915b4afab613365c64f0742d4718b52b37d059b3345752f683856302b5d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 285, + 543, + 296 + ], + "lines": [ + { + "bbox": [ + 307, + 285, + 543, + 296 + ], + "spans": [ + { + "bbox": [ + 307, + 285, + 543, + 296 + ], + "type": "text", + "content": "Figure 3. Illustration of attention generation and token selection." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 312, + 481, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 481, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 481, + 324 + ], + "type": "text", + "content": "3.3. Reranking Transformer Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 331, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 354 + ], + "type": "text", + "content": "We describe the attention-based local feature selection and the workflow inside our reranking transformer module." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 355, + 546, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 546, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 546, + 534 + ], + "type": "text", + "content": "Attention-based Selection. For large-scale scenarios, local features occupy the majority of memory, thus reducing the number of local features is important for real-world deployment. Previous works [3,26,53] usually use " + }, + { + "bbox": [ + 304, + 355, + 546, + 534 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 304, + 355, + 546, + 534 + ], + "type": "text", + "content": " as image resolution, resulting in 1200 patch tokens. However, only a small portion of them are informative to determine the location of the image, e.g. buildings, trees, roads, etc. Previous works either leverage all the local features from multiple scales [26] or adopt additional modules [53] to generate attention maps, which filter local features with a certain threshold during local matching. On the contrary, we leverage the natural attention map within our transformer module and only save a fixed number of local features (e.g. 500) with top attention values, resulting in a much lower memory cost and simpler extraction pipeline." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "(n + 1) \\times (n + 1)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " attention matrix of the last transformer layer in Fig. 3 is formulated as " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\text{softmax}(QK^{\\top} / d)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " in Sec. 3.2. It represents the contribution from each input token to each output token. Since the output class (CLS) token is the only one that connects to the global embedding feature, the CLS token output channel of the matrix " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "((n + 1)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "-dimensional vector for " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " patches and CLS token) represents the contribution from input tokens to the global feature, which corresponds to the importance of each patch. We reshape the " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "-dimensional vector corresponding to " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " patches as " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "h / p \\times w / p" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " attention map to sort all the tokens and we select the top-500 tokens that are likely to cover the informative regions (bottom right of Fig. 3). The attention value and x,y coordinates are saved along with each local feature, resulting in " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "128 + 3 = 131" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " dimensions." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19373" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": "Correlation-based Reranking. RANSAC-based [19] geometric verification only leverages the top-1 matched pairs for all local features, but ignores other important information that could be useful for reranking, i.e. the correlation, and attention value. Local feature pairs with higher correlation/similarity have higher probabilities to be correct local matches, and an image pair with more correct local matches is more likely to represent the same place. Also, high attention values of the local patches could indicate the importance of the local feature pairs. Therefore, our reranking module is designed to maintain the correlation, attention, and positional information for all the local feature pairs in a correlation matrix, resulting in 7 dimensions (Fig. 2) denoted as " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "(x,y,A,x',y',A',S)" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "x,y,x',y'" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " denote the coordinates of the two patches in the query and reference images. " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "A,A'" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " denotes the attention values of the two patches. " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " is the cosine similarity between the 128-dimensional local features. Since each image has 500 selected features/tokens, there are " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "500\\times 500" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " pairs, resulting in a " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "500\\times 500\\times 7" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " correlation matrix. The correlation matrix contains the major information for all the feature pairs and allows the model to learn whatever is useful to determine whether the two images are from the same location." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "text", + "content": "To reduce the computation, we select the 5 nearest neighbors of each token in the feature space to produce two " + }, + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "inline_equation", + "content": "500 \\times 5 \\times 7" + }, + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "text", + "content": " matrices, as the other feature pairs with large distances are likely to be wrong matches. They are concatenated together and fed to a linear layer, resulting in a " + }, + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "inline_equation", + "content": "1000 \\times 5 \\times 32" + }, + { + "bbox": [ + 47, + 348, + 289, + 552 + ], + "type": "text", + "content": " matrix. We then leverage the strong global correlation modeling of transformer [52] to aggregate the large matrix as a reranking score to determine whether the input pair is a correct match. First, we adopt \"Transformer Block-1\" to extract important information from the top-5 pairs as one output class token. Then \"Transformer Block-2\" extracts aggregates the information from the 1000 tokens as a single 32-dimension vector (the class token). The two transformer blocks are multiple transformer layers with linear projection and standard Sinusoidal positional embedding [52]. Finally, the vector is converted into 2 channels by a linear head as a binary classification (i.e. True vs False)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 566, + 124, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 124, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 124, + 578 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 586, + 223, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 223, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 223, + 598 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 288, + 715 + ], + "type": "text", + "content": "We train our model on MSLS (Mapillary Street-Level Sequences) [55] dataset, which covers a wide range of real-world scenarios for VPR, e.g. different cities, viewpoint variation, day/night, and season changes. The performance in urban scenarios (e.g. Pitts30k [50], Tokyo24/7 [49]) can be further improved by finetuning on Pitts30k. For evaluation, we use standard train/val/test split [6, 26, 53, 55] on major datasets, including MSLS Val [55], MSLS Challenge [55], Pitts30k [50], Tokyo 24/7 [49], R-SF (Revisited San" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "Francisco) [6, 11, 33, 45], St Lucia [40]. The MSLS Challenge [55] is a hold-out set whose labels are not released, but researchers can submit the predictions on their challenge server to get the performance. For the other datasets with location labels, we follow previous works [6, 26, 53] to use 25 meters as the threshold for correct localization and report recall@k (k=1,5,10) as evaluation metrics. We also report detailed computational costs, including inference time for extraction/retrieval/matching, feature dimensions, GFLOPs, and memory footprint (Table 3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 201, + 440, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 201, + 440, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 201, + 440, + 213 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "text", + "content": "The proposed method is implemented using PyTorch [42]. The models are trained on 8 Tesla-V100 GPUs. All images are resized to " + }, + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "text", + "content": " for training and evaluation. The reranking is conducted on top-100 candidates and we set margin " + }, + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "inline_equation", + "content": "m = 0.1" + }, + { + "bbox": [ + 304, + 219, + 547, + 351 + ], + "type": "text", + "content": ". We use ViT-S [17] (12 layers with 384 dimensions) architecture as our default backbone and the module is initialized with off-the-shelf pre-trained weights [51] on ImageNet-1k [14]. The transformers in the reranking module use a small dimension of 32 with only 2 and 6 layers for Transformer Block-1 and Block-2 respectively, thus resulting in a very small computational cost." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 351, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 547, + 628 + ], + "type": "text", + "content": "The global retrieval and the reranking module can be trained jointly in an end-to-end manner, but we train them separately (Sec. 3.1) by default to achieve a stable convergence and better accuracy. The global retrieval module is trained following common practice [6]. The reranking module is trained from scratch following the standard pipeline of training transformers, i.e. AdamW [36] optimizer with cosine learning rate schedule [35]. The initial learning rate is 0.0005 with 64 triplets per batch. Each triplet only samples one hard negative reference image which is randomly selected from the top-100 hardest samples from the MSLS training set of the corresponding query. Given that the global embedding features do not change during this stage, the global hard negative mining only needs to be conducted once and can be efficiently computed on GPU in 3 hours. We precompute the hard negative list of all queries for the training of the reranking module, which is more efficient than the full mining implementation of the VG benchmark [6]. The reranking module is trained for 50 epochs and we select the model with the highest recall@5 on the validation set. The global retrieval and reranking module are then finetuned together with partial negative mining [6]. More details are included in supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 635, + 486, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 486, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 486, + 647 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-art" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "In this section, we compare the proposed method with previous state-of-the-art methods, including NetVLAD [3], SFRS [23], SP-SuperGlue [15, 44], Patch-NetVLAD [26], and TransVPR [53]. We further compare our method with the best configurations in the recent VG benchmark [6]." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19374" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 69, + 547, + 160 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 547, + 160 + ], + "type": "table", + "html": "
MSLS Val [55]MSLS Challenge [55]Pitts30k [50]Tokyo 24/7 [49]
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
NetVLAD [3]60.874.379.535.147.451.781.991.293.764.878.481.6
SFRS [23]69.280.383.141.552.056.389.494.795.985.491.193.3
SP-SuperGlue [15,44]78.181.984.350.656.958.387.294.896.488.290.290.2
Patch-NetVLAD [26]79.586.287.748.157.660.588.794.595.986.088.690.5
TransVPR [53]86.891.292.463.974.077.589.094.996.279.082.285.1
Ours89.795.096.273.085.988.891.195.296.388.691.491.7
", + "image_path": "5ba1a5ed6841f6ed0da36930543ce40bf1c6b96eda1f4c795bfcbf55410cf42d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 191, + 541, + 274 + ], + "blocks": [ + { + "bbox": [ + 47, + 163, + 546, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 163, + 546, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 546, + 185 + ], + "type": "text", + "content": "Table 1. Comparison of our method with previous state-of-the-art results on major VPR datasets. Our model is trained on MSLS and tested on MSLS Val and Challenge set. Our model is further finetuned on Pitts30k for urban scenarios, i.e. Pitts30k, Tokyo 24/7." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 191, + 541, + 274 + ], + "lines": [ + { + "bbox": [ + 50, + 191, + 541, + 274 + ], + "spans": [ + { + "bbox": [ + 50, + 191, + 541, + 274 + ], + "type": "table", + "html": "
Features Dim ↓GFLOPs ↓Trained on MSLS - R@1
Pitts30kMSLS ValMSLS Chall.Tok. 24/7R-SFSt Lucia
ResNet101 + GeM [6,43]102486.2977.277.0*55.551.046.991.6
ResNet101 + NetVLAD [3,6]6553686.0680.881.1*61.559.056.195.1
CCT384 + NetVLAD [6,25]2457618.5385.183.8*61.470.365.998.4
Ours w/o Reranking25625.9076.379.356.245.747.594.3
Ours65500†48.50†88.489.773.072.772.199.7
", + "image_path": "b4e5b083469c36213e5f77ce9256e71fddaf6aa13485a3c00757f7f73871b602.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 47, + 314, + 545, + 396 + ], + "blocks": [ + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "type": "text", + "content": "Table 2. Comparison following the protocol of the recent VG benchmark [6] on major datasets in terms of R@1. The models are trained on MSLS and directly tested on all datasets w/o finetuning. † The dimensions and GFLOPs are computed by adding the numbers of global retrieval and reranking together, i.e. " + }, + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "type": "inline_equation", + "content": "Dim = 256 + 500 \\times (128 + 3)" + }, + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "type": "inline_equation", + "content": "GFLOPs = 25.90 + 100 \\times 0.226" + }, + { + "bbox": [ + 46, + 275, + 546, + 309 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 314, + 545, + 396 + ], + "lines": [ + { + "bbox": [ + 47, + 314, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 545, + 396 + ], + "type": "table", + "html": "
Feature Dim ↓Latency per Query (ms) ↓Memory Footprint (GB) ↓
GlobalLocalExtractionRetrievalRerankingMSLS Val1M Images
ResNet101 + NetVLAD [3,6]65536N/A9.602.33N/A4.79244.14
Patch-NetVLAD-s [26]512936 × 5129.290.08952.8537.601917.29
Patch-NetVLAD-p [26]40962826 × 40969.360.198377.17908.3046315.85
TransVPR [53]2561200 × 2566.200.071757.7022.721158.53
Ours256500 × (128+3)8.810.07202.374.79244.01
", + "image_path": "4b3a28f30c5e15d54219b2b675bb8a1824a26f12ea5beb152620af2a3ee49595.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 546, + 433 + ], + "lines": [ + { + "bbox": [ + 46, + 399, + 546, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 546, + 433 + ], + "type": "text", + "content": "Table 3. Comparison of computational cost in terms of feature dimension, latency, and memory footprint. All the methods are measured on MSLS Val (18,871 database images) using the same CPU and GPU (RTX A5000). Reranking is conducted on top-100 candidates. \"Patch-NetVLAD-p\" and \"Patch-NetVLAD-s\" denote the performance and speed-oriented versions." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 448, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 495 + ], + "type": "text", + "content": "We also provide a detailed comparison with state-of-the-art methods [6,26,53] on computational cost. Other works [1, 16, 18, 57, 59, 62] on related tasks with different settings are not included." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": "As shown in Table 1, the proposed method significantly outperforms state-of-the-art methods on MSLS Val and Challenge set with absolute R@1 improvement of " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "9.1\\%" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": " respectively. Benefiting from large-scale training, our method also achieves state-of-the-art R@1 on Pitts30k and Tokyo24/7. Small-scale dataset [50] with weak supervision is not enough to train a data-driven reranking module, and training on one large-scale dataset with good generalization on all datasets is more desirable for real-world deployment. (Details in supp. material.)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 288, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 288, + 711 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 288, + 711 + ], + "type": "text", + "content": "In Table 2, we select the best-performing models in the VG benchmark [6] and compare them with our method on major datasets. Eynsham [13] dataset is not included because it has a different camera type (gray-scale) and resolution. * denotes reproduced results using the official MSLS [55] validation code and pre-trained models [6]. Table 2 shows that our model trained on MSLS generalizes well on all the other datasets and significantly outperforms the best" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 471 + ], + "type": "text", + "content": "models in the VG benchmark [6] with comparable computational cost." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": "In Table 3, we compare the computational cost of our method with previous global retrieval methods and retrieval+reranking methods. Apparently, the inference latency of extraction and retrieval is negligible as compared to the reranking latency of previous works. Our method is significantly faster than all the other reranking-based methods because our reranking process is only one network forward pass on GPU and can be easily accelerated by parallel computing, e.g. reranking on 4 GPUs takes only " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "47.17\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " per query " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "(20.2\\times" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " speedup over previous reranking-based methods [26, 53]). However, it is not straightforward to accelerate RANSAC-based geometric verification with multiprocessing. Previous works [26, 53] generally follow the standard implementation of OpenCV [8]. In addition, the local feature dimension of our method is the smallest among all the reranking-based methods, specifically, we only save 500 important local features with very small dimensions " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "(128 + 3)" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " for each image. In total, it only needs " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "4.79\\mathrm{GB}" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " of memory for the MSLS validation set which is much smaller " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "(189\\times" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " reduction) than " + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "inline_equation", + "content": "908.3\\mathrm{GB}" + }, + { + "bbox": [ + 304, + 472, + 546, + 711 + ], + "type": "text", + "content": " of Patch-NetVLAD-p." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19375" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 246, + 146 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 246, + 146 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 246, + 146 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 246, + 146 + ], + "type": "table", + "html": "
R@1R@5R@10
No Reranking79.390.892.6
RANSAC [19]84.993.094.5
RRT [48]81.291.993.1
CVNet [32]73.486.891.4
Ours89.795.096.2
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R@1R@5R@10
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Reranking86.694.195.0
Reranking + Mining88.493.494.9
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ArchitectureR@1R@5R@10
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ResNet50 + GeM79.690.992.6
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Ours w/ \nRANSACViT-Small84.993.094.5
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", + "image_path": "758d3e963f4deab84d7c697e2d47145c3eb3898acce327f2afeea2c78761bdbb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 361, + 286, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 286, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 286, + 492 + ], + "type": "text", + "content": "Even for datasets with over 1M reference images (e.g. R-SF dataset), the memory footprint is only 244.01 GB which can fit in a typical server or high-end desktop. It can be further reduced to 122 GB by using float16 instead of float32, with which we observe no performance drop on R-SF. However, other reranking-based methods typically require much larger (" + }, + { + "bbox": [ + 46, + 361, + 286, + 492 + ], + "type": "inline_equation", + "content": ">4\\times" + }, + { + "bbox": [ + 46, + 361, + 286, + 492 + ], + "type": "text", + "content": ") memory, which cannot scale to large-scale real-world scenarios with 1M reference images. Given the unified design, outstanding performance, strong efficiency, and scalability of our method, it could serve as a well-balanced solution for real-world large-scale applications." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 502, + 140, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 140, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 140, + 514 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "text", + "content": "Reranking Methods. In Table 4, we adopt the same global and local features from our default backbone and compare different reranking methods. “No Reranking” denotes our model with only global retrieval. “RANSAC” [19] follows the pipeline of state-of-the-art methods [26, 53] using " + }, + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "inline_equation", + "content": "1.5 \\times" + }, + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "text", + "content": " of the patch size. “RRT” [48] is not proposed for VPR, nevertheless, we train it on the top of our backbone for comparison. “CVNet” [31] does not provide the training code, we thus adopt their pre-trained model trained on Google Landmark [56]. Remarkably, our reranking module significantly outperforms RANSAC [19] based geometric verification using much less (" + }, + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "inline_equation", + "content": "< 22\\%" + }, + { + "bbox": [ + 46, + 521, + 286, + 700 + ], + "type": "text", + "content": ") inference time (Table 3). It also outperforms two recent state-of-the-art reranking methods on landmark retrieval, indicating the superiority of our reranking module." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 51, + 701, + 286, + 713 + ], + "type": "text", + "content": "Training Strategies. In Table 5, we compare our method" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 313, + 182, + 536, + 330 + ], + "blocks": [ + { + "bbox": [ + 46, + 299, + 286, + 343 + ], + "lines": [ + { + "bbox": [ + 46, + 299, + 286, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 286, + 343 + ], + "type": "text", + "content": "Table 6. Ablation study on MSLS Val with different backbone architectures, including ResNet50+GeM [27,43], ViT Small [17], ViT Base [17]. Transformer tokens perform on par with CNN local features in terms of reranking/local matching." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 182, + 536, + 330 + ], + "lines": [ + { + "bbox": [ + 313, + 182, + 536, + 330 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 536, + 330 + ], + "type": "table", + "html": "
R@1R@5R@10
No Reranking79.390.892.6
Reranking86.694.195.0
Reranking Module
Remove Positional Embedding86.493.294.7
Remove Transformer Block-185.593.895.0
Remove Transformer Block-281.992.894.6
Replace Top-5 w/ Top-186.693.894.7
Reranking Input
Remove Attention Selection83.692.894.1
Remove xy Coordinates Value85.093.594.7
Remove Attention Value86.193.594.3
Remove Correlation Value31.859.272.8
", + "image_path": "d651fe9edbd8dd65d590606374a6359b2951ae308c09864ce5ef2bbbc86fc95d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "lines": [ + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "type": "text", + "content": "Table 7. Ablation study on model components. We freeze the global retrieval module so that the global and local features are the same for different ablations. All ablations are trained with partial negative mining [6]. The components are defined in Sec. 3." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "text", + "content": "based on different training strategies. “No Reranking” uses only global retrieval, and “Reranking” denotes training reranking module with partial negative mining on a fixed global retrieval module. “Reranking+Mining” means training the reranking module with our global negative mining by randomly selecting one negative sample from the 100 global hardest samples. “Reranking+Mining+Finetune” further finetunes retrieval and reranking module together. “End-to-end Training” directly trains global retrieval and reranking module from the beginning in an end-to-end manner with partial negative mining. All the strategies with reranking outperform previous state-of-the-art methods on " + }, + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{5}" + }, + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "text", + "content": ", and training the global retrieval and reranking module separately with a carefully designed strategy achieves the best performance. The results indicate that global hard negative mining is helpful for training the reranking module. End-to-end training is also a good trade-off between simplicity and performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Different Backbones. In Table 6, we combine our reranking module with different backbone retrieval modules, including ViT-Small (default), ResNet50+GeM [27, 43] and ViT-Base. We follow [6] to add L2 normalization before the pooling layer but do not freeze or remove any convolutional layer. The attention map of ResNet50+GeM is generated following CAM [61]. The ResNet50+GeM model achieves competitive results for both global retrieval and reranking. It also significantly outperforms previous" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19376" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 545, + 261 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 545, + 261 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 545, + 261 + ], + "type": "image", + "image_path": "bc49f31c6d459fcf2f21b329e6076f3add35a360cb153f5178dc12fda3ebce61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 266, + 523, + 277 + ], + "lines": [ + { + "bbox": [ + 67, + 266, + 523, + 277 + ], + "spans": [ + { + "bbox": [ + 67, + 266, + 523, + 277 + ], + "type": "text", + "content": "Figure 4. Visualization of attention map and matched pairs. Green and red boxes in (f) indicate correct and wrong predictions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 293, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 289, + 713 + ], + "type": "text", + "content": "works [26, 53], indicating that our reranking module is a generic component for both CNN and transformer backbone architectures. With similar global retrieval performance and the same reranking method (RANSAC or Ours), the ViT-Small model achieves slightly better performance than ResNet50+GeM, which means the transformer token is a good alternative for local matching as compared with CNN local feature. Furthermore, we adopt a larger backbone ViT-Base, which achieves significant performance improvement on global retrieval and RANSAC-based reranking over ViT-Small. However, the overall performance of our ViT-Base model has very small performance improvement (mainly on " + }, + { + "bbox": [ + 47, + 293, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{10}" + }, + { + "bbox": [ + 47, + 293, + 289, + 713 + ], + "type": "text", + "content": "), which indicates a possible bottleneck of the proposed framework. Components Ablation. In Table 7, we use the \"Reranking\" configuration in Table 5 as a baseline and ablate different components to check the importance of each component of our method. For simplicity, we freeze the global retrieval module and all the models are trained with partial negative mining. We have the following observations. (1) The most important components are the Transformer Block-2 and Correlation Value, and removing them causes a significant performance drop. This indicates that the feature correlation contributes most to the final decision. (2) When we replace the attention-based feature selection with random selection, the model becomes unstable and the performance drops moderately. (3) Removing other components, i.e. Transformer Block-1, xy Coordinates Value, Attention Value (defined in Sec. 3.2), causes a slight performance drop, indicating the effectiveness of these blocks for performance purposes. (4) We observe negligible performance drop when removing positional embedding or replacing top-5 pairs selection with top-1, which means the Sinusoidal positional embedding does not help much and the top-1 pair contains most of the" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 293, + 470, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 470, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 470, + 304 + ], + "type": "text", + "content": "information that is needed for reranking." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 326, + 389, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 326, + 389, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 326, + 389, + 338 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 345, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 536 + ], + "type": "text", + "content": "In Fig. 4, we show a detailed case where the global retrieval fails on the top-3 results. Fig. 4 (b) and (c) show the attention map and the selected patches, which cover most of the informative regions for reranking. Both RANSAC and our method work well on reranking the top-100 candidates and our method finds more correct reference images in the top-3 results (Fig. 4 (f)). Although our reranking module is not as explainable as RANSAC, the transformer still focuses on specific patch pairs and we plot the top-20 pairs with the highest attention in the reranking module. As shown in Fig. 4 (d) and (e), our reranking also focuses on meaningful pairs and most of them are correct matches. As compared with RANSAC, our matched pairs may not have tight geometric consistency, but they may provide different information for the reranking as adjusted according to the task-relevant training data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 549, + 378, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 378, + 561 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 378, + 561 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We propose a unified retrieval and reranking framework for place recognition with only transformers. We for the first time show that vision transformer tokens are comparable to or even better than CNN local feature in terms of reranking. Our reranking module is generic and can be adopted on other CNN or transformer backbones. Remarkably, it significantly outperforms previous methods on major datasets with much less inference time and memory consumption. Our method can also provide possible matched local pairs like RANSAC and could be improved with geometric modeling in the future. We discuss the limitations and societal impact in the supplementary material." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19377" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Amar Ali-bey, Brahim Chaib-draa, and Philippe Giguere. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1162-1171, 2022. 6" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19380" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_content_list.json b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bc58ab1a28fe8c201b65e00d063b6da302c6367e --- /dev/null +++ b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_content_list.json @@ -0,0 +1,1603 @@ +[ + { + "type": "text", + "text": "RA-CLIP: Retrieval Augmented Contrastive Language-Image Pre-training", + "text_level": 1, + "bbox": [ + 107, + 128, + 864, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chen-Wei Xie*, Siyang Sun*, Xiong Xiong*, Yun Zheng, Deli Zhao, Jingren Zhou \nAlibaba Group", + "bbox": [ + 158, + 180, + 810, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{eniac.xcw,siyang.ssy,moxiong.xx,zhengyun.zy}@alibaba-inc.com zhaodeli@gmail.com,jingren.zhou@alibaba-inc.com", + "bbox": [ + 215, + 218, + 754, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contrastive Language-Image Pre-training (CLIP) is attracting increasing attention for its impressive zero-shot recognition performance on different down-stream tasks. However, training CLIP is data-hungry and requires lots of image-text pairs to memorize various semantic concepts. In this paper, we propose a novel and efficient framework: Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to augment embeddings by online retrieval. Specifically, we sample part of image-text data as a hold-out reference set. Given an input image, relevant image-text pairs are retrieved from the reference set to enrich the representation of input image. This process can be considered as an open-book exam: with the reference set as a cheat sheet, the proposed method doesn't need to memorize all visual concepts in the training data. It explores how to recognize visual concepts by exploiting correspondence between images and texts in the cheat sheet. The proposed RA-CLIP implements this idea and comprehensive experiments are conducted to show how RA-CLIP works. Performances on 10 image classification datasets and 2 object detection datasets show that RA-CLIP outperforms vanilla CLIP baseline by a large margin on zero-shot image classification task $(+12.7\\%)$ , linear probe image classification task $(+6.9\\%)$ and zero-shot ROI classification task $(+2.8\\%)$ .", + "bbox": [ + 76, + 318, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional visual representation learning systems are trained to predict a fixed set of predetermined image categories [12, 16, 22, 34]. This limits their transferability since additional labeled training data are required to recognize new visual concepts. Recently, vision-language pre-training approaches such as CLIP [29] emerge as a promising alternative which introduces text description as supervision. CLIP aligns image modality and text modality by learning a", + "bbox": [ + 75, + 753, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/794085a01f645c9bd211db4fdcb0ac0ef577894884364619a51c8dc2e35a5c57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 285, + 596, + 362 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d6b7f809887ee3e14f5438f6c21f42fa94ef31c028a57ccdf8a1eb0d489289f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 286, + 694, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/27e9145605541a005cc7f848eb4fd2a607ec8fe6c4d5d956eb193640f91eba0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 286, + 794, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0a251a4cd8a93706f45a9c3ce8cd1080a4e663a7b28aeb841fb3d9c9fb60a56e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 286, + 893, + 361 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/704356f9a3d08e3fb73d4724c75cc9fd0c803aadd1adfe380a6c5367d4abfe2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 372, + 594, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/422ea2ffee9fe4aac571c5735c9ed39e5295f942acdf7fea1007140e3ae6bbf2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 372, + 694, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/14c8e2616dad18db9c6694ce955783cf0f16d95eb1f94df7c9d560099d5b4094.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 372, + 792, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0069551945500f7602cfe09c692432ec0c4ac8148bec772dfac637a6b4f74eda.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 372, + 893, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/991e2695e32b35a29a9127e35f95fa2946b01a61e910c0e5e85f4e521c9e4658.jpg", + "image_caption": [ + "Figure 1. Transferring the CLIP and RA-CLIP to 12 down-stream visual recognition datasets for zero-shot evaluation. Our RA-CLIP achieves better results in 10 out of 12 datasets, and brings $+12.7\\%$ averaged improvements on the 10 image classification datasets and $2.8\\%$ averaged improvements on the 2 object detection datasets.." + ], + "image_footnote": [], + "bbox": [ + 503, + 455, + 594, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dd2aaf194e46d0cf15338ceea44d77de7add6c962c0a4388d175b478ce1cf18c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 455, + 694, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81c4d1c8708780021404caf655148ead60a53729cc01a6676d0f26563b7ec316.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 455, + 792, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5ecdd1dbe143b2419a11587a9d43c97adc6deacf6be2393379474b9efb8d77da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 455, + 893, + 530 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "modality-shared representation. During pre-training, CLIP learns to pull matched image-text pairs together and push non-matched pairs apart. After pre-training, CLIP can be transferred to zero-shot image classification task: categories can be referred by textual descriptions, and the image classification task can be converted to image-to-text retrieval task. Experimental results show that CLIP performs well on zero-shot image classification task, e.g., for ImageNet zero-shot classification task, CLIP can match the accuracy of ImageNet pre-trained ResNet50, even that CLIP doesn't use any of the 1.28 million training examples of ImageNet for training.", + "bbox": [ + 496, + 628, + 893, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the impressive zero-shot performance, CLIP requires lots of image-text pairs to train encoders and memorize various semantic concepts, which limits its applications since it is not affordable for most laboratories and companies. Recent works [24, 25] try to alleviate this limitation by taking full advantage of existing data and", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*indicates equal contribution.", + "bbox": [ + 94, + 886, + 253, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19265", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "train encoders to memorize concepts as many as possible, e.g., DeCLIP [24] explores widespread supervision from given image-text pairs, and SLIP [25] introduces self-supervised learning which helps encoders learn better visual representation.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel and efficient way to make use of image-text pairs. We sample part of image-text data as a hold-out reference set. Given an input image, our model first retrieves similar images from the reference set with an unsupervised pre-trained image retrieval model, then we use the relationship between retrieved images and texts to augment the representation of input image. A heuristic explanation of the idea is that, it can be considered as an open-book exam: our model doesn't have to memorize all visual concepts in the training data, but learns to recognize visual concepts with the help of a cheat sheet (i.e., the reference set). We propose a framework called Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to implement this idea. Although using the same amount of image-text data with the vanilla CLIP, RA-CLIP achieves better zero-shot classification performance and linear probe classification performance.", + "bbox": [ + 75, + 167, + 470, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are three-fold:", + "bbox": [ + 96, + 424, + 313, + 436 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- For contrastive language-image pre-training (CLIP), we present a novel and efficient utilization of image-text pairs. Concretely, we construct a hold-out reference set composed by image-text pairs. Given an input image, we find relevant image-text pairs and use them to help us build better representation for the input image.", + "- We propose Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP), a framework to implement the idea described above. We conduct comprehensive experiments to validate the effectiveness of each block. Visualization results are also provided to explain how RA-CLIP works.", + "- We compare the proposed RA-CLIP with previous methods on a dozen of commonly used visual recognition benchmarks. Experimental results show that our proposed method significantly outperforms vanilla CLIP baseline and other recently proposed methods." + ], + "bbox": [ + 93, + 450, + 468, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 761, + 217, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Contrastive Language Image Pre-training", + "text_level": 1, + "bbox": [ + 76, + 786, + 433, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CLIP [29] introduces a new paradigm for visual representation learning. Given image-text pairs as training data, CLIP learns a visual encoder and a textual encoder to align images and text sentences. Different from previous visual recognition system which can only recognize categories specified by the training set, CLIP can be flexibly", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "transferred to new categories. Given new categories, CLIP extends them into text sentences and feed them into the text encoder to obtain categories embeddings. Experimental results show that CLIP can match the accuracy of ImageNet trained ResNet50, even that CLIP didn't use any of the 1.28 million training examples of ImageNet during pre-training. Despite the impressive transfer performance, CLIP is quite data-hungry, it needs tens of millions or more image-text pairs for pre-training [1, 18, 29, 41, 42]. To decrease the amount of training data, recent works [24, 25] try to introduce as much as supervision from existing datasets to help CLIP train better encoders.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel and efficient methods to make better use of image-text pairs. Different from previous methods that only use image-text pairs to train encoders, we also use them to construct a reference set which can provide supplementary information for the encoder. Given an input image, we find relevant images along with their text descriptions from the reference set, these image-text pairs contain information that can help us describe the input image, thus we use them to augment original CLIP's image representation.", + "bbox": [ + 496, + 277, + 890, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Knowledge-Enhanced Models", + "text_level": 1, + "bbox": [ + 500, + 454, + 764, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Structured external knowledge has also been included to improve the zero-shot performance, K-Lite [33] enriches entities in natural language with WordNet and Wiktionary, the motivation is straightforward, some concepts like \"zebra\" may have less training example in the training set, by introducing a knowledge base, \"zebra\" can be extended to a more general description: \"Zebras are African equines with distinctive black-and-white striped coats\". CLIP-event [23] also introduces structured external knowledge to construct hard negative text descriptions for images during training. ASIF [26] builds a relative representation for image and text respectively and aligns image modality and text modality with image-text pairs.", + "bbox": [ + 496, + 482, + 890, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently large language models have shown impressive zero-shot and few-shot performance on various downstream NLP tasks, massive parameters have to be introduced to encode the knowledge that will be used. Previous works Atlas [17] and RETRO [2] introduce an external non-parametric knowledge base to store the information, which significantly reduces the parameters of their model, e.g., Atlas outperforms a 540B model with $50 \\times$ fewer parameters.", + "bbox": [ + 496, + 684, + 890, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The methods mentioned above mainly focus on providing more information for individual modalities. Different from them, we utilize the correspondence between imagetext pairs in the reference set, which helps us align visual concepts and textual concepts.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19266", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/df2450e9ef9d0c9f22dab9e15eeab6f0588f0df001a99ebf27f77fa6ac3a429c.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed RA-CLIP. Given an input image, RA-CLIP retrieves K most similar image-text pairs from the reference set, which provide informative descriptions for the input image, thus we feed them into the Retrieval Augmented Module (RAM) to enrich the representation of input image." + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 867, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Zero-shot Visual Recognition", + "text_level": 1, + "bbox": [ + 76, + 388, + 338, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero-shot visual recognition can be categorized into two generations: the traditional class-level zero-shot setting and recently popular task-level zero-shot setting [33]. The traditional class-level zero-shot aims at recognizing objects that belong to categories that are not included in the training set. The task-level zero-shot like CLIP [29] is more practical in real-world applications, the model is trained by hundreds of millions of image-text pairs and is directly evaluated on image classification task, by prompting category names into sentence descriptions [1, 18, 29, 41, 42].", + "bbox": [ + 75, + 415, + 470, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Memorizing visual and textual concepts for down-stream zero-shot tasks usually requires lots of image-text pairs. In this paper, we propose that, besides using image-text pairs to train image encoder and text encoder, we can also introduce a reference set to help the model align visual concepts and textual concepts.", + "bbox": [ + 75, + 568, + 468, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 676, + 168, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present the details of our proposed Retrieval Augmented Language Image Pre-training (RA-CLIP). An overview of RA-CLIP is summarized in Figure 2. Given $N$ image-text pairs $\\{I_i,T_i\\}_{i = 1}^N$ as training data, where $I_{i}$ is the $i$ -th image in the dataset and $T_{i}$ is its corresponding text description. Different from previous Contrastive Language Image Pre-training (CLIP) method that only uses $\\{I_i,T_i\\}_{i = 1}^N$ to train encoders, we propose a novel utilization of the image-text pairs. Specifically, we split $\\{I_i,T_i\\}_{i = 1}^N$ into two disjoint sets: training set $\\mathcal{T}$ and reference set $\\mathcal{R}$ . Given $I_{i}$ as input image, we first feed it into the image encoder to obtain the initial image embedding $\\mathbf{v}_i$ , following previous method CLIP. After that,", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "we retrieve $K$ most similar images $\\{\\mathbf{r}_k^I\\}_{k = 1}^K$ from $\\mathcal{R}$ as well as their corresponding text sentences $\\{\\mathbf{r}_k^T\\}_{k = 1}^K$ . $\\{\\mathbf{r}_k^I\\}_{k = 1}^K$ and $\\{\\mathbf{r}_k^T\\}_{k = 1}^K$ provide informative description for $I_{i}$ , so we use them to augment $\\mathbf{v}_i$ by a proposed Retrieval Augmented Module (RAM). The augmented image embedding is output as $\\mathbf{v}_i'$ . The text branch of RA-CLIP is like the one of CLIP.", + "bbox": [ + 498, + 388, + 893, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dual-Encoder Architecture", + "text_level": 1, + "bbox": [ + 500, + 511, + 746, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The dual-encoder architecture consists of an image encoder and a text encoder. The image encoder used in our experiments is a Vision Transformer [12]. Given an image $I_{i}$ , we take the embedding of the [CLS] token and normalize it by its L2-norm to obtain the representation of $I_{i}$ , which is a $d$ -dimension feature vector $\\mathbf{v}_i$ . The text encoder is also a Transformer. Given a sequence of input text $T_{i}$ , the text encoder transforms and normalizes $T_{i}$ into another $d$ -dimension feature vector $\\mathbf{t}_i$ .", + "bbox": [ + 498, + 537, + 890, + 675 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview of RA-CLIP", + "text_level": 1, + "bbox": [ + 500, + 691, + 709, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reference Set Construction. Multi-modal image-text pairs naturally establish the connection between images and texts. Different images and text descriptions of the same concept can provide informative description of this concept. Inspired by this observation, we construct the reference set $\\mathcal{R}$ by random sampling 1.6M (about 1/10 amount of our total training data) image-text pairs from original train set. Ablation experiments will show that commonly used image-text datasets such as YFCC [35], CC12M [5] and LAION [32] can be used as reference data. We also exploit how the amount of image-text pairs effect the final performance. Please refer to Section 4.2.2 for more details.", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19267", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reference Image-Text Retrieval. Given an input image $I_{i}$ , RA-CLIP retrieves $K$ most similar images $\\{\\mathbf{r}_k^I\\}_{k=1}^K$ from the reference set as well as their corresponding text descriptions $\\{\\mathbf{r}_k^T\\}_{k=1}^K$ . Concretely, we first extract the embeddings of the images in reference set, with an unsupervised pre-trained image encoder (e.g., DINO) for a fairer comparison. This process can be pre-computed offline. Given an input image $I_{i}$ as query, we also extract the embedding of $I_{i}$ with the same model, then use the embedding to retrieve $K$ most similar images from the reference set. The retrieval process can be conducted efficiently by existing libraries like Faiss [19]. Finally, we get $K$ images $\\{\\mathbf{r}_k^I\\}_{k=1}^K$ and their corresponding text sentences $\\{\\mathbf{r}_k^T\\}_{k=1}^K$ , which are sent to the Retrieval Augmented Module (RAM) to obtain augmented image representation.", + "bbox": [ + 76, + 90, + 472, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Retrieval Augmented Module (RAM). We propose a novel Retrieval Augmented Module (RAM), which first extracts the embeddings of each retrieved $\\mathbf{r}_k^I$ and $\\mathbf{r}_k^T$ :", + "bbox": [ + 76, + 325, + 470, + 371 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {k} ^ {I} = \\phi (\\mathbf {r} _ {k} ^ {I}),\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 380, + 313, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {k} ^ {T} = \\psi \\left(\\mathbf {r} _ {k} ^ {T}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 397, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that $\\phi$ and $\\psi$ are pre-trained uni-modal encoders for image and text respectively. They are frozen during the training stage, so Equation 1 can be pre-computed before training.", + "bbox": [ + 76, + 429, + 468, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After that, RAM uses $\\{\\mathbf{e}_k^I\\}_{k=1}^K$ and $\\{\\mathbf{e}_k^T\\}_{k=1}^K$ to augment $\\mathbf{v}_i$ . RAM first introduces a Multi-head Attention [37] block which takes $\\mathbf{v}_i$ as query, $\\{\\mathbf{e}_k^I\\}_{k=1}^K$ as key and $\\{\\mathbf{e}_k^T\\}_{k=1}^K$ as value to obtain text-augmented embedding $\\mathbf{a}_i^T$ :", + "bbox": [ + 76, + 489, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {i} ^ {T} = \\text {M u l t i h e a d A t t n} (\\mathbf {v} _ {i}, \\left\\{\\mathbf {e} _ {k} ^ {I} \\right\\} _ {k = 1} ^ {K}, \\left\\{\\mathbf {e} _ {k} ^ {T} \\right\\} _ {k = 1} ^ {K}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 571, + 468, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Equation 2, $\\mathbf{v}_i$ learns to weight and aggregate $\\{\\mathbf{e}_k^T\\}_{k=1}^K$ according to the relationship between $\\mathbf{v}_i$ and $\\{\\mathbf{e}_k^I\\}_{k=1}^K$ . The aggregated text embedding $\\mathbf{a}_i^T$ will be used to augment $\\mathbf{v}_i$ .", + "bbox": [ + 76, + 604, + 468, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Likewise, RAM also computes image-augmented embedding $\\mathbf{a}_i^I$ by aggregating $\\{\\mathbf{e}_k^I\\}_{k=1}^K$ in a similar way:", + "bbox": [ + 76, + 660, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {i} ^ {I} = M u l t i h e a d A t t n (\\mathbf {v} _ {i}, \\left\\{\\mathbf {e} _ {k} ^ {T} \\right\\} _ {k = 1} ^ {K}, \\left\\{\\mathbf {e} _ {k} ^ {I} \\right\\} _ {k = 1} ^ {K}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 703, + 468, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, RAM outputs the augmented image embedding $\\mathbf{v}_i'$ :", + "bbox": [ + 76, + 734, + 468, + 751 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {i} ^ {\\prime} = \\mathbf {v} _ {i} + \\mathbf {a} _ {i} ^ {T} + \\mathbf {a} _ {i} ^ {I}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 762, + 468, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "as illustrated in Figure 3.", + "bbox": [ + 76, + 792, + 243, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Loss Function.", + "text_level": 1, + "bbox": [ + 76, + 816, + 225, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the training stage, we follow previous contrastive learning methods [29] and use InfoNCE loss [36] to train our framework. Concretely, given a batch of $N$ image-text pairs $\\{I_i, T_i\\}_{i=1}^N$ as training data, RA-CLIP produces", + "bbox": [ + 76, + 840, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/754ebaea9800a5bab4401e3a1f3e4c0da82fa00ef38838d3bab1fd2440b97b3c.jpg", + "image_caption": [ + "Figure 3. The proposed Retrieval Augmented Module (RAM)." + ], + "image_footnote": [], + "bbox": [ + 513, + 90, + 880, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the augmented image embeddings and the text embeddings: $\\{\\mathbf{v}_i',\\mathbf{t}_i\\}_{i = 1}^N$ , then we compute text-to-image contrastive loss $\\mathcal{L}_{t2v}$ and image-to-text contrastive loss $\\mathcal{L}_{v2t}$ ..", + "bbox": [ + 500, + 348, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v 2 t} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {i} ^ {\\prime}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {j} ^ {\\prime}\\right) / \\tau\\right)}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 405, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t 2 v} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {i}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {j}\\right) / \\tau\\right)}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 454, + 890, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ is the batch size, and $\\tau$ is a temperature factor, which is initialized as 0.07 and trained end-to-end. $\\sigma$ computes the cosine similarity between two vectors. The total loss of our framework is:", + "bbox": [ + 496, + 498, + 890, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {t 2 v} + \\mathcal {L} _ {v 2 t}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 573, + 890, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 632, + 624, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous works [24, 25, 39], we pre-train our framework on YFCC dataset [35], then evaluate the performance of zero-shot classification and linear probe classification on commonly used visual recognition benchmarks. Besides that, we also follow RegionCLIP [43] and evaluate the zero-shot ROI classification performance on two widely used object detection datasets, i.e., MS COCO [7] and LVIS [15].", + "bbox": [ + 496, + 657, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first describe the implementation details in Section 4.1, including datasets, evaluation metrics, model architecture and optimization details. Then we conduct ablation experiments in Section 4.2 to validate the effectiveness of our proposed method and analyse the effectiveness of each component. Finally, we compare our proposed method with recently proposed CLIP variants like MS-CLIP [39], DeCLIP [24] and SLIP [25] in Section 4.3.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19268", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/613bcbf5148904dde7b1bf82886a6258a41a5766d54b2a431a42e55da2614918.jpg", + "table_caption": [ + "Table 1. Ablation experiments on zero-shot ImageNet classification." + ], + "table_footnote": [], + "table_body": "
IDMethodInit. of Image Enc.Init. of Text Enc.Pretrain DatasetReference DatasetφψImageNet Top-1
1CLIPViT rand.BERTYFCC×××37.7
2CLIPDINO-SSentenceTYFCC×××21.0
3CLIPViT IN1KBERTYFCC×××46.1
4CLIPViT rand.BERTYFCC+CC×××42.1
5RA-CLIPViT rand.BERTYFCCYFCCSentenceTDINO-S53.5
6RA-CLIPViT rand.BERTYFCCCCSentenceTDINO-S54.5
7RA-CLIPViT rand.BERTYFCCLAIONSentenceTDINO-S54.2
8RA-CLIPViT rand.BERTYFCCCCText EncoderDINO-S54.4
", + "bbox": [ + 99, + 114, + 867, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 287, + 294, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset All the experiments are conducted on public available datasets. For a fair comparison, we follow previous works [24, 25, 39] and use YFCC [35] for pretraining. We follow CLIP [29] and use the 15 million English subset of YFCC for pre-training. For the reference set used in our framework, we test three different image-text datasets, including the YFCC15M described above, CC12M [5] and LAION [32]. By default, we random sample 1,600,000 image-text pairs (about 1/10 amount of our pre-train dataset) from corresponding dataset to construct the reference set. 10 widely used visual recognition datasets are used to evaluate the zero-shot classification performance and linear probe classification performance, including ImageNet [10], ImageNet V2 [30], CIFAR 10 [21], CIFAR 100 [21], Caltech 101 [13], Oxford Pets [27], SUN397 [38], Food 101 [3], DTD [8] and Stanford Dogs [20]. Following RegionCLIP [43], two object detection datasets are used to evaluate the zero-shot ROI classification performance, i.e., COCO [7] and LVIS [15]. More details about the datasets can be found in our supplement.", + "bbox": [ + 75, + 316, + 470, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics The metrics used to evaluate image classification on all datasets are top-1 accuracy except for Oxford Pets, and Caltech101, which are measured by mean accuracy over classes as in CLIP [29]. The evaluation metric for COCO and LVIS is box Average Precision (AP) as used in RegionCLIP [43].", + "bbox": [ + 76, + 623, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architecture By default, the image encoder is a random initialized ViT-B/32 [12], which has 12 layers of Transformer blocks. Each Transformer block has 12 attention heads and the hidden size is set to 768. The text encoder is BERT-base [11], which shares similar scale with the image encoder, i.e., 12 layers of Transformer blocks, 12 attention heads in each Transformer block and 768 hidden size. We also try smaller text encoder from scratch while comparing with previous state-of-the-arts in Section 4.3. The output of the text encoder and image encoder are projected to 384-dim by linear projection. We adopt DINO-S/8 [4] as the image retriever and the uni-modal image encoder $\\phi$", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "described in Section 3.2, which is pre-trained on ImageNet 1K [10] with self-supervised method. Meanwhile, we adopt Sentence Transformer (SentenceT) [31] as the uni-modal text encoder $\\psi$ , which is a 6-layer Transformer. For our proposed Retrieval Augmented Module (RAM), we use 6 layers of cross-attention blocks. We truncate the input text tokens so that they have a maximum length of 77. The input image is resized to $224 \\times 224$ .", + "bbox": [ + 496, + 289, + 893, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization We implement our framework with PyTorch [28]. All pre-training experiments are conducted on 8 NVIDIA Tesla A100 GPUs. Batch size is set to 4096. The framework is trained for 32 epochs with LAMB optimizer [40] and an initial learning rate of $2.5\\mathrm{e - }3$ . The learning rate follows a cosine decay schedule with 5 epochs of linear warm-up. Weight decay is set to 0.2. For data augmentation, we random crop a $224\\times 224$ patch from the input image, then conduct random horizontal flip, random color distortions, random gaussian blur and RandAugment [9], following previous works [6, 24, 25]. Training details of down-stream tasks (e.g., linear probe classification) can be found in our supplement.", + "bbox": [ + 496, + 411, + 893, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 619, + 653, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first validate the effectiveness of our proposed method by comparing RA-CLIP and CLIP trained on the same dataset. After that, we build reference sets by sampling image-text pairs from different datasets (YFCC, CC or LAION) and sampling different amounts of image-text pairs from the same dataset to see if the reference set is sensitive to these two factors. Since we introduce pre-trained DINO-S/8 ( $\\phi$ in Section 3.2) and SentenceT ( $\\psi$ in Section 3.2) to extract reference embeddings, we also discuss how these models effect the final performance. At last, ablation experiments with different K-value and different design choices of RAM are provided.", + "bbox": [ + 496, + 642, + 893, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Effectiveness of the Retrieval Augmented CLIP", + "text_level": 1, + "bbox": [ + 500, + 845, + 883, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To validate the effectiveness of our proposed method, we train and test CLIP and RA-CLIP with the same dataset.", + "bbox": [ + 500, + 869, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19269", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/151efcc3388e6f6cb4c1db8dc93634b9d759e47a7e125f015daeca8f3bf2ce69.jpg", + "image_caption": [ + "Figure 4. Zero-shot classification performance of RA-CLIP with different amounts of reference data. Five different scales of reference sets are used, i.e., 1K, 10K, 100K, 1.6M, and 10M." + ], + "image_footnote": [], + "bbox": [ + 122, + 95, + 421, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For CLIP, we use YFCC15M for pre-training, and evaluate the zero-shot performance on ImageNet. For RA-CLIP, we random sample 1.6 million image-text pairs (about 1/10 amount of entire dataset) from YFCC15M to construct the reference set, and use the other 13 million image-text pairs for training. Experimental results can be found in Table 1, RA-CLIP (experiment ID 5) outperforms CLIP (experiment ID 1) by a large margin (53.5% vs 37.7%), which validates the effectiveness of RA-CLIP.", + "bbox": [ + 75, + 325, + 468, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide a heuristic explanation for this comparison. The pipeline of training and testing CLIP may be considered as a closed-book exam. In the training stage, CLIP trains encoders to learn visual and textual concepts in the training data. In the testing stage, given a test query image, CLIP may return a false prediction if it didn't memorize related concepts of the test image. Different from CLIP, the training and testing of RA-CLIP can be considered as an open-book exam. In the training stage, RA-CLIP doesn't have to memorize all concepts in the training data, but learns how to recognize an image with a help of a cheat-sheet (i.e., the reference set). In the testing stage, given a test query image, RA-CLIP can look up the cheat-sheet (i.e., the reference set) and finds related knowledge about the query image, then uses the knowledge to enrich the representation of input image.", + "bbox": [ + 75, + 462, + 470, + 704 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Different image-text data as reference set", + "text_level": 1, + "bbox": [ + 76, + 724, + 416, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since the reference set is the core component of RA-CLIP, we then analyse if RA-CLIP provides significant improvements while using different datasets or different amounts of image-text pairs as reference sets.", + "bbox": [ + 75, + 750, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Different dataset as reference set. We adopt another two widely used datasets to construct the reference set, i.e., CC12M and LAION. We sample 1.6 million image-text pairs from CC12M to construct the reference set, and use YFCC15M for RA-CLIP pre-training. We also train CLIP on the combination of the reference set and YFCC15M.", + "bbox": [ + 75, + 810, + 470, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/46c29975b2eaed116e95511a45dfea0937e800ea582b194988eb6fe47d808600.jpg", + "table_caption": [ + "Table 2. Different design choices of Retrieval Augmented Module (RAM). All models are trained on YFCC15M with CC1.6M as reference set and evaluated on zero-shot ImageNet classification." + ], + "table_footnote": [], + "table_body": "
MethodAugment ImageAugment TextFusion TypeKImageNet Top-1
RAM✓XaiT6452.1
RAM✓XaiT + aiI6451.8
RAM✓XaiT + aiI + vi6454.5
RAM✓XaiT + aiI + vi1654.3
RAM✓XaiT + aiI + vi12853.9
RAM✓✓aiT + aiI + vi6453.1
", + "bbox": [ + 506, + 142, + 883, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By comparing experiment 6 and experiment 4 in Table 1, we can see that RA-CLIP still outperforms CLIP with significant improvement(54.5% v.s. 42.1%). We then conduct similar experiments with 1.6 million image-text pairs from LAION as reference set, which achieves 54.2% top-1 accuracy on ImageNet. Experiments above show that the commonly used datasets like YFCC15M, CC12M, LAION can be used as reference set and provide similar performance.", + "bbox": [ + 496, + 297, + 890, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Different amounts of reference data. We then test the performance of reference sets with different amounts of image-text pairs. 5 reference sets are constructed by sample 1K, 10K, 100K, 1.6M, 10M image-text pairs from CC12M. YFCC15M is used as training data. The performance of RA-CLIP with these 5 different reference sets is illustrated in Figure 4. We can see that introducing more image-text pairs as reference set usually brings better performance. Since the horizontal axis of Figure 4 is plotted in log-space, we can conclude that performance is getting saturated while introducing more image-text pairs as reference set.", + "bbox": [ + 496, + 435, + 892, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.3 Ablation of pre-trained SentenceT and DINO", + "text_level": 1, + "bbox": [ + 498, + 619, + 870, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Two frozen pre-trained uni-modal encoders are introduced in RA-CLIP to process image-text data of the reference set: SentenceT and DINO-S/8. It is necessary for us to show if the improvement described above is brought by these two encoders. We re-implement CLIP with frozen SentenceT as text encoder and frozen DINO-S/8 as image encoder, linear projection layer is appended after each encoder to obtain final embeddings. We train the CLIP model on YFCC15M, the zero-shot classification performance on ImageNet is $21.0\\%$ , referred as experiment 2 in Table 1, which is significantly lower than CLIP baseline (experiment 1). Experimental results show that although the pre-trained SentenceT and DINO-S provide promising results on uni-modal tasks, they provide poor performance on multi-modal alignment task.", + "bbox": [ + 496, + 643, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also prove that, SentenceT is not necessary for our final performance. We re-implemented RA-CLIP by", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19270", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ae07675e5d9cb8f2f0fa3edae297a2c1c8b8f6d44920438c8db3c2804bcb5a13.jpg", + "table_caption": [ + "Table 3. Zero-shot image classification performance and linear probe classification performance on 10 downstream datasets (\\%). RA-CLIP* denotes the model that trains a text encoder with width = 512 and head = 8 from scratch." + ], + "table_footnote": [], + "table_body": "
Evaluation TypeMethodImageNetImageNetV2PetsCIFAR10CIFAR100SUN397Food101Caltech101DTDDogsAvg.
Zero-shotK-Lite [33]45.3----------
CLIP [29]37.732.816.176.048.650.821.869.828.311.139.3
MS-CLIP [39]36.730.2-------5.6-
SLIP [25]38.333.328.372.245.345.144.765.921.811.840.7
DeCLIP [24]43.236.130.272.139.751.646.970.124.211.742.6
RA-CLIP*51.245.450.589.461.845.743.976.124.622.051.1
RA-CLIP53.547.249.089.462.346.543.876.925.626.152.0
Linear probeCLIP [29]63.551.369.891.774.164.769.184.966.550.568.6
MS-CLIP [39]68.149.862.187.266.771.776.081.669.446.167.9
SLIP [25]68.152.175.490.575.373.577.187.271.152.672.3
DeCLIP [24]69.253.176.588.671.675.979.388.069.149.972.1
RA-CLIP*73.362.388.294.978.460.765.586.865.575.575.1
RA-CLIP72.961.988.295.278.961.166.587.266.676.075.5
", + "bbox": [ + 80, + 128, + 888, + 337 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "replacing SentenceT with the text encoder of RA-CLIP, the zero-shot performance on ImageNet is $54.4\\%$ (experiment 8), which is comparable with the one used SentenceT (experiment 6). We also note that, although replacing SentenceT with the text encoder of RA-CLIP can provide similar performance, the text encoder of RA-CLIP is trained end-to-end, thus the embeddings of the reference text cannot be pre-computed off-line before training, which introduces more computation cost. So we use SentenceT by default.", + "bbox": [ + 75, + 359, + 468, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DINO-S/8 in Section 3.2 uses ImageNet 1K for self-supervised learning, extracting reference images on-the-fly during training with the image encoder is much more time-consuming due to the time of reading, pre-processing and extracting images. So we test if CLIP can achieve comparable or better performance than RA-CLIP if it uses ImageNet data for pre-training. Concretely, we use the ViT-B/32 pre-trained on ImageNet 21K and fine-tuned on ImageNet-1K to initialize the image encoder of CLIP. Then train the CLIP on YFCC15M, the classification performance is referred as experiment 3 in Table 1. Initializing the image encoder by ImageNet pre-trained model brings significant improvements (46.1% v.s. 37.7%). However, it is not zero-shot evaluation anymore. We can see that RA-CLIP (53.5%) still outperforms this strong CLIP baseline.", + "bbox": [ + 75, + 511, + 470, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.4 Different hyper-parameters and design choices", + "text_level": 1, + "bbox": [ + 76, + 756, + 457, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different K-value in retrieval process. We train RA-CLIP by retrieving different amounts $(K = 16, 64, 128)$ of image-text pairs from the reference set for each query image. Experimental results are shown in row 3, 4 and 5 of Table 2. RA-CLIP provides stable performance with different $K$ values, and the model with $K = 64$ performs slightly better than the others.", + "bbox": [ + 75, + 779, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different design choices of RAM architecture. We", + "bbox": [ + 96, + 885, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "further test different design choices of RAM architecture in Table 2. Firstly, we take $\\mathbf{a}_i^T$ as the final augmented representation. In this case, RAM gathers related information from the reference texts and produces final embedding, the result is $52.1\\%$ . After that, we fuse $\\mathbf{a}_i^T$ and $\\mathbf{a}_i^I$ , which provides similar performance $(51.8\\%)$ . Finally, we take $\\mathbf{a}_i^T + \\mathbf{a}_i^I + \\mathbf{v}_i$ as the final image embedding to fuse information from original image encoder and the reference data, which performs best $(54.5\\%)$ among the three different variants as expected.", + "bbox": [ + 496, + 359, + 890, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Augment both image and text representation. Since experiments above have validated the effectiveness of RA-CLIP, a straightforward question is: will this idea improve CLIP's text representation? To validate that, we use SentenceT to retrieve relevant image-text pairs for input text sentence, then apply similar augmentation to the text embedding. However, it leads to a slightly worse performance $53.1\\%$ as shown in Table 2. We conjecture that text sentence is less informative and the retrieved image-text pairs are more diverse and may not bring correct information.", + "bbox": [ + 496, + 512, + 892, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 676, + 638, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we compare RA-CLIP with CLIP and recently proposed CLIP-variant on two down-stream visual recognition tasks: zero-shot image classification and linear probe image classification. Evaluations are conducted on 10 widely used visual recognition benchmarks. Note that some previous works (e.g., DeCLIP [24]) train a text encoder with width $= 512$ and head $= 8$ from scratch, thus we follow them and re-implemented the RA-CLIP for a fair comparison, the results are denoted as RA-CLIP*. Besides that, we also follow RegionCLIP to evaluate the zero-shot ROI classification performance on MS COCO and LVIS.", + "bbox": [ + 496, + 702, + 890, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zero-shot image classification Previous methods usually take YFCC15M or its augmented version as train set.", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19271", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d056aa6013eb86d398328169bdb8176ff6c2f42886549f7ae5cc3fefe832809.jpg", + "image_caption": [ + "Figure 5. Case study for RA-CLIP in image classification. The retrieved images and texts enrich the representation of input image." + ], + "image_footnote": [], + "bbox": [ + 125, + 94, + 848, + 368 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7950bb3e1af5af99c2ffd8ddfa095e66105fedbb3b35f63352667e68d5a1c832.jpg", + "table_caption": [ + "Table 4. Zero-shot ROI classification on COCO and LVIS (%)" + ], + "table_footnote": [], + "table_body": "
MethodLVISCOCO
APAPsAPmAPIAPAPsAPmAPI
Regin CLIP21.68.731.045.744.421.951.061.8
Region RA-CLIP23.210.934.244.948.429.357.961.9
", + "bbox": [ + 78, + 446, + 468, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thus random sample 1.6M image-text from YFCC15M as reference set, and use the other 13M image-text pairs as train set. We report the performance of RA-CLIP on all 10 datasets as well as the results of previous methods CLIP [29], K-lite [33], SLIP [25], DeCLIP [24] and MS-CLIP [39] shown in Table 3. RA-CLIP shows superior performance than previous state-of-the-art methods.", + "bbox": [ + 75, + 545, + 468, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also compare with OpenAI's CLIP model trained on 400 million image-text pairs. To reduce the training cost, we use OpenAI's CLIP-B/32 to initialize the image encoder, text encoders, $\\phi$ and $\\psi$ of RA-CLIP, then freeze them and train the other modules on YFCC15M. The model achieves $68.2\\%$ top-1 accuracy on ImageNet, significantly better than OpenAI's CLIP-B/32 (63.3%).", + "bbox": [ + 75, + 654, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 5, we also provide some visualization to help us understand how RA-CLIP works. The image-text pairs retrieved from the reference set can introduce additional important information that can help RA-CLIP make correct predictions.", + "bbox": [ + 75, + 762, + 468, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Linear probe image classification Following previous methods, we also conduct linear probe image classification experiments to test the transferability of the learned image representation. We fix the pre-trained image encoder of our", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "trained CLIP and RA-CLIP, then train a linear classifier to conduct image classification on down-stream datasets. Experimental results are shown in Table 3. RA-CLIP achieves better performance than previous methods CLIP, MS-CLIP, SLIP and DeCLIP, bringing $2.8\\%$ (75.1% v.s. $72.3\\%$ ) averaged improvements.", + "bbox": [ + 496, + 422, + 890, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Zero-shot ROI classification Following previous work RegionCLIP [43], we transfer the proposed RA-CLIP to object detection task on COCO [7] and LVIS [15] datasets to test the performance of ROI classification. Following RegionCLIP [43], we use ground-truth bounding boxes as region proposals, then apply RA-CLIP and CLIP to classify the proposals, following a RCNN [14] pipeline.", + "bbox": [ + 496, + 515, + 890, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We report results on the validation set of LVIS and COCO in Table 4. We can see that RA-CLIP still outperforms CLIP on these two benchmarks, bringing $1.6\\%$ improvement on LVIS and $4.0\\%$ improvement on COCO. Note that the proposed RA-CLIP performs much better on small objects and medium objects.", + "bbox": [ + 496, + 623, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 734, + 619, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel and efficient utilization of image-text pairs. Different from previous Contrastive Language Image Pre-training methods that only use imagetext pairs to train encoders, we also use image-text pairs to construct a reference set. Given an input image, we find relevant images as well as corresponding texts in the reference set and use them to enrich the representation of the input image. Experiments on zero-shot classification and linear probe classification validate the effectiveness of our methods.", + "bbox": [ + 496, + 760, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19272", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. Flamingo: a visual language model for few-shot learning. 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Pattern Recog., pages 16793-16803, 2022. 4, 5, 8" + ], + "bbox": [ + 503, + 92, + 890, + 542 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19274", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_model.json b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cbbf9432495d6ebbb188574fd71502f7250075bd --- /dev/null +++ b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.13, + 0.865, + 0.155 + ], + "angle": 0, + "content": "RA-CLIP: Retrieval Augmented Contrastive Language-Image Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.159, + 0.181, + 0.812, + 0.217 + ], + "angle": 0, + "content": "Chen-Wei Xie*, Siyang Sun*, Xiong Xiong*, Yun Zheng, Deli Zhao, Jingren Zhou \nAlibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.219, + 0.756, + 0.252 + ], + "angle": 0, + "content": "{eniac.xcw,siyang.ssy,moxiong.xx,zhengyun.zy}@alibaba-inc.com zhaodeli@gmail.com,jingren.zhou@alibaba-inc.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.697 + ], + "angle": 0, + "content": "Contrastive Language-Image Pre-training (CLIP) is attracting increasing attention for its impressive zero-shot recognition performance on different down-stream tasks. However, training CLIP is data-hungry and requires lots of image-text pairs to memorize various semantic concepts. In this paper, we propose a novel and efficient framework: Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to augment embeddings by online retrieval. Specifically, we sample part of image-text data as a hold-out reference set. Given an input image, relevant image-text pairs are retrieved from the reference set to enrich the representation of input image. This process can be considered as an open-book exam: with the reference set as a cheat sheet, the proposed method doesn't need to memorize all visual concepts in the training data. It explores how to recognize visual concepts by exploiting correspondence between images and texts in the cheat sheet. The proposed RA-CLIP implements this idea and comprehensive experiments are conducted to show how RA-CLIP works. Performances on 10 image classification datasets and 2 object detection datasets show that RA-CLIP outperforms vanilla CLIP baseline by a large margin on zero-shot image classification task \\((+12.7\\%)\\), linear probe image classification task \\((+6.9\\%)\\) and zero-shot ROI classification task \\((+2.8\\%)\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Traditional visual representation learning systems are trained to predict a fixed set of predetermined image categories [12, 16, 22, 34]. This limits their transferability since additional labeled training data are required to recognize new visual concepts. Recently, vision-language pre-training approaches such as CLIP [29] emerge as a promising alternative which introduces text description as supervision. CLIP aligns image modality and text modality by learning a" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.286, + 0.597, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.287, + 0.696, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.287, + 0.795, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.804, + 0.287, + 0.895, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.373, + 0.596, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.373, + 0.695, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.373, + 0.794, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.373, + 0.895, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.457, + 0.596, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.457, + 0.695, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.457, + 0.794, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.457, + 0.895, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.545, + 0.895, + 0.616 + ], + "angle": 0, + "content": "Figure 1. Transferring the CLIP and RA-CLIP to 12 down-stream visual recognition datasets for zero-shot evaluation. Our RA-CLIP achieves better results in 10 out of 12 datasets, and brings \\(+12.7\\%\\) averaged improvements on the 10 image classification datasets and \\(2.8\\%\\) averaged improvements on the 2 object detection datasets.." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.81 + ], + "angle": 0, + "content": "modality-shared representation. During pre-training, CLIP learns to pull matched image-text pairs together and push non-matched pairs apart. After pre-training, CLIP can be transferred to zero-shot image classification task: categories can be referred by textual descriptions, and the image classification task can be converted to image-to-text retrieval task. Experimental results show that CLIP performs well on zero-shot image classification task, e.g., for ImageNet zero-shot classification task, CLIP can match the accuracy of ImageNet pre-trained ResNet50, even that CLIP doesn't use any of the 1.28 million training examples of ImageNet for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Despite the impressive zero-shot performance, CLIP requires lots of image-text pairs to train encoders and memorize various semantic concepts, which limits its applications since it is not affordable for most laboratories and companies. Recent works [24, 25] try to alleviate this limitation by taking full advantage of existing data and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.254, + 0.901 + ], + "angle": 0, + "content": "*indicates equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19265" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "train encoders to memorize concepts as many as possible, e.g., DeCLIP [24] explores widespread supervision from given image-text pairs, and SLIP [25] introduces self-supervised learning which helps encoders learn better visual representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.424 + ], + "angle": 0, + "content": "In this paper, we propose a novel and efficient way to make use of image-text pairs. We sample part of image-text data as a hold-out reference set. Given an input image, our model first retrieves similar images from the reference set with an unsupervised pre-trained image retrieval model, then we use the relationship between retrieved images and texts to augment the representation of input image. A heuristic explanation of the idea is that, it can be considered as an open-book exam: our model doesn't have to memorize all visual concepts in the training data, but learns to recognize visual concepts with the help of a cheat sheet (i.e., the reference set). We propose a framework called Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to implement this idea. Although using the same amount of image-text data with the vanilla CLIP, RA-CLIP achieves better zero-shot classification performance and linear probe classification performance." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.425, + 0.314, + 0.438 + ], + "angle": 0, + "content": "Our contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.452, + 0.469, + 0.556 + ], + "angle": 0, + "content": "- For contrastive language-image pre-training (CLIP), we present a novel and efficient utilization of image-text pairs. Concretely, we construct a hold-out reference set composed by image-text pairs. Given an input image, we find relevant image-text pairs and use them to help us build better representation for the input image." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.569, + 0.469, + 0.658 + ], + "angle": 0, + "content": "- We propose Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP), a framework to implement the idea described above. We conduct comprehensive experiments to validate the effectiveness of each block. Visualization results are also provided to explain how RA-CLIP works." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.671, + 0.468, + 0.745 + ], + "angle": 0, + "content": "- We compare the proposed RA-CLIP with previous methods on a dozen of commonly used visual recognition benchmarks. Experimental results show that our proposed method significantly outperforms vanilla CLIP baseline and other recently proposed methods." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.452, + 0.469, + 0.745 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.762, + 0.218, + 0.777 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.434, + 0.803 + ], + "angle": 0, + "content": "2.1. Contrastive Language Image Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "CLIP [29] introduces a new paradigm for visual representation learning. Given image-text pairs as training data, CLIP learns a visual encoder and a textual encoder to align images and text sentences. Different from previous visual recognition system which can only recognize categories specified by the training set, CLIP can be flexibly" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "transferred to new categories. Given new categories, CLIP extends them into text sentences and feed them into the text encoder to obtain categories embeddings. Experimental results show that CLIP can match the accuracy of ImageNet trained ResNet50, even that CLIP didn't use any of the 1.28 million training examples of ImageNet during pre-training. Despite the impressive transfer performance, CLIP is quite data-hungry, it needs tens of millions or more image-text pairs for pre-training [1, 18, 29, 41, 42]. To decrease the amount of training data, recent works [24, 25] try to introduce as much as supervision from existing datasets to help CLIP train better encoders." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.43 + ], + "angle": 0, + "content": "In this paper, we propose a novel and efficient methods to make better use of image-text pairs. Different from previous methods that only use image-text pairs to train encoders, we also use them to construct a reference set which can provide supplementary information for the encoder. Given an input image, we find relevant images along with their text descriptions from the reference set, these image-text pairs contain information that can help us describe the input image, thus we use them to augment original CLIP's image representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.766, + 0.47 + ], + "angle": 0, + "content": "2.2. Knowledge-Enhanced Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.679 + ], + "angle": 0, + "content": "Structured external knowledge has also been included to improve the zero-shot performance, K-Lite [33] enriches entities in natural language with WordNet and Wiktionary, the motivation is straightforward, some concepts like \"zebra\" may have less training example in the training set, by introducing a knowledge base, \"zebra\" can be extended to a more general description: \"Zebras are African equines with distinctive black-and-white striped coats\". CLIP-event [23] also introduces structured external knowledge to construct hard negative text descriptions for images during training. ASIF [26] builds a relative representation for image and text respectively and aligns image modality and text modality with image-text pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.82 + ], + "angle": 0, + "content": "Recently large language models have shown impressive zero-shot and few-shot performance on various downstream NLP tasks, massive parameters have to be introduced to encode the knowledge that will be used. Previous works Atlas [17] and RETRO [2] introduce an external non-parametric knowledge base to store the information, which significantly reduces the parameters of their model, e.g., Atlas outperforms a 540B model with \\(50 \\times\\) fewer parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The methods mentioned above mainly focus on providing more information for individual modalities. Different from them, we utilize the correspondence between imagetext pairs in the reference set, which helps us align visual concepts and textual concepts." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19266" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.091, + 0.868, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.335, + 0.895, + 0.38 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed RA-CLIP. Given an input image, RA-CLIP retrieves K most similar image-text pairs from the reference set, which provide informative descriptions for the input image, thus we feed them into the Retrieval Augmented Module (RAM) to enrich the representation of input image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.39, + 0.339, + 0.407 + ], + "angle": 0, + "content": "2.3. Zero-shot Visual Recognition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.567 + ], + "angle": 0, + "content": "Zero-shot visual recognition can be categorized into two generations: the traditional class-level zero-shot setting and recently popular task-level zero-shot setting [33]. The traditional class-level zero-shot aims at recognizing objects that belong to categories that are not included in the training set. The task-level zero-shot like CLIP [29] is more practical in real-world applications, the model is trained by hundreds of millions of image-text pairs and is directly evaluated on image classification task, by prompting category names into sentence descriptions [1, 18, 29, 41, 42]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.66 + ], + "angle": 0, + "content": "Memorizing visual and textual concepts for down-stream zero-shot tasks usually requires lots of image-text pairs. In this paper, we propose that, besides using image-text pairs to train image encoder and text encoder, we can also introduce a reference set to help the model align visual concepts and textual concepts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.169, + 0.693 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this section, we present the details of our proposed Retrieval Augmented Language Image Pre-training (RA-CLIP). An overview of RA-CLIP is summarized in Figure 2. Given \\(N\\) image-text pairs \\(\\{I_i,T_i\\}_{i = 1}^N\\) as training data, where \\(I_{i}\\) is the \\(i\\)-th image in the dataset and \\(T_{i}\\) is its corresponding text description. Different from previous Contrastive Language Image Pre-training (CLIP) method that only uses \\(\\{I_i,T_i\\}_{i = 1}^N\\) to train encoders, we propose a novel utilization of the image-text pairs. Specifically, we split \\(\\{I_i,T_i\\}_{i = 1}^N\\) into two disjoint sets: training set \\(\\mathcal{T}\\) and reference set \\(\\mathcal{R}\\). Given \\(I_{i}\\) as input image, we first feed it into the image encoder to obtain the initial image embedding \\(\\mathbf{v}_i\\), following previous method CLIP. After that," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.39, + 0.895, + 0.496 + ], + "angle": 0, + "content": "we retrieve \\(K\\) most similar images \\(\\{\\mathbf{r}_k^I\\}_{k = 1}^K\\) from \\(\\mathcal{R}\\) as well as their corresponding text sentences \\(\\{\\mathbf{r}_k^T\\}_{k = 1}^K\\). \\(\\{\\mathbf{r}_k^I\\}_{k = 1}^K\\) and \\(\\{\\mathbf{r}_k^T\\}_{k = 1}^K\\) provide informative description for \\(I_{i}\\), so we use them to augment \\(\\mathbf{v}_i\\) by a proposed Retrieval Augmented Module (RAM). The augmented image embedding is output as \\(\\mathbf{v}_i'\\). The text branch of RA-CLIP is like the one of CLIP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.747, + 0.527 + ], + "angle": 0, + "content": "3.1. Dual-Encoder Architecture" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.539, + 0.892, + 0.676 + ], + "angle": 0, + "content": "The dual-encoder architecture consists of an image encoder and a text encoder. The image encoder used in our experiments is a Vision Transformer [12]. Given an image \\( I_{i} \\), we take the embedding of the [CLS] token and normalize it by its L2-norm to obtain the representation of \\( I_{i} \\), which is a \\( d \\)-dimension feature vector \\( \\mathbf{v}_i \\). The text encoder is also a Transformer. Given a sequence of input text \\( T_{i} \\), the text encoder transforms and normalizes \\( T_{i} \\) into another \\( d \\)-dimension feature vector \\( \\mathbf{t}_i \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.71, + 0.708 + ], + "angle": 0, + "content": "3.2. Overview of RA-CLIP" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Reference Set Construction. Multi-modal image-text pairs naturally establish the connection between images and texts. Different images and text descriptions of the same concept can provide informative description of this concept. Inspired by this observation, we construct the reference set \\(\\mathcal{R}\\) by random sampling 1.6M (about 1/10 amount of our total training data) image-text pairs from original train set. Ablation experiments will show that commonly used image-text datasets such as YFCC [35], CC12M [5] and LAION [32] can be used as reference data. We also exploit how the amount of image-text pairs effect the final performance. Please refer to Section 4.2.2 for more details." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19267" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.325 + ], + "angle": 0, + "content": "Reference Image-Text Retrieval. Given an input image \\(I_{i}\\), RA-CLIP retrieves \\(K\\) most similar images \\(\\{\\mathbf{r}_k^I\\}_{k=1}^K\\) from the reference set as well as their corresponding text descriptions \\(\\{\\mathbf{r}_k^T\\}_{k=1}^K\\). Concretely, we first extract the embeddings of the images in reference set, with an unsupervised pre-trained image encoder (e.g., DINO) for a fairer comparison. This process can be pre-computed offline. Given an input image \\(I_{i}\\) as query, we also extract the embedding of \\(I_{i}\\) with the same model, then use the embedding to retrieve \\(K\\) most similar images from the reference set. The retrieval process can be conducted efficiently by existing libraries like Faiss [19]. Finally, we get \\(K\\) images \\(\\{\\mathbf{r}_k^I\\}_{k=1}^K\\) and their corresponding text sentences \\(\\{\\mathbf{r}_k^T\\}_{k=1}^K\\), which are sent to the Retrieval Augmented Module (RAM) to obtain augmented image representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.326, + 0.472, + 0.372 + ], + "angle": 0, + "content": "Retrieval Augmented Module (RAM). We propose a novel Retrieval Augmented Module (RAM), which first extracts the embeddings of each retrieved \\(\\mathbf{r}_k^I\\) and \\(\\mathbf{r}_k^T\\):" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.381, + 0.314, + 0.399 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {k} ^ {I} = \\phi (\\mathbf {r} _ {k} ^ {I}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.398, + 0.469, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {k} ^ {T} = \\psi \\left(\\mathbf {r} _ {k} ^ {T}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.47, + 0.49 + ], + "angle": 0, + "content": "Note that \\(\\phi\\) and \\(\\psi\\) are pre-trained uni-modal encoders for image and text respectively. They are frozen during the training stage, so Equation 1 can be pre-computed before training." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.49, + 0.47, + 0.563 + ], + "angle": 0, + "content": "After that, RAM uses \\(\\{\\mathbf{e}_k^I\\}_{k=1}^K\\) and \\(\\{\\mathbf{e}_k^T\\}_{k=1}^K\\) to augment \\(\\mathbf{v}_i\\). RAM first introduces a Multi-head Attention [37] block which takes \\(\\mathbf{v}_i\\) as query, \\(\\{\\mathbf{e}_k^I\\}_{k=1}^K\\) as key and \\(\\{\\mathbf{e}_k^T\\}_{k=1}^K\\) as value to obtain text-augmented embedding \\(\\mathbf{a}_i^T\\):" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.572, + 0.47, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {i} ^ {T} = \\text {M u l t i h e a d A t t n} (\\mathbf {v} _ {i}, \\left\\{\\mathbf {e} _ {k} ^ {I} \\right\\} _ {k = 1} ^ {K}, \\left\\{\\mathbf {e} _ {k} ^ {T} \\right\\} _ {k = 1} ^ {K}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.605, + 0.469, + 0.66 + ], + "angle": 0, + "content": "In Equation 2, \\(\\mathbf{v}_i\\) learns to weight and aggregate \\(\\{\\mathbf{e}_k^T\\}_{k=1}^K\\) according to the relationship between \\(\\mathbf{v}_i\\) and \\(\\{\\mathbf{e}_k^I\\}_{k=1}^K\\). The aggregated text embedding \\(\\mathbf{a}_i^T\\) will be used to augment \\(\\mathbf{v}_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.661, + 0.469, + 0.695 + ], + "angle": 0, + "content": "Likewise, RAM also computes image-augmented embedding \\(\\mathbf{a}_i^I\\) by aggregating \\(\\{\\mathbf{e}_k^I\\}_{k=1}^K\\) in a similar way:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.704, + 0.47, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {i} ^ {I} = M u l t i h e a d A t t n (\\mathbf {v} _ {i}, \\left\\{\\mathbf {e} _ {k} ^ {T} \\right\\} _ {k = 1} ^ {K}, \\left\\{\\mathbf {e} _ {k} ^ {I} \\right\\} _ {k = 1} ^ {K}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.736, + 0.469, + 0.752 + ], + "angle": 0, + "content": "Finally, RAM outputs the augmented image embedding \\(\\mathbf{v}_i'\\):" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.763, + 0.469, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {i} ^ {\\prime} = \\mathbf {v} _ {i} + \\mathbf {a} _ {i} ^ {T} + \\mathbf {a} _ {i} ^ {I}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.793, + 0.245, + 0.808 + ], + "angle": 0, + "content": "as illustrated in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.227, + 0.832 + ], + "angle": 0, + "content": "3.3. Loss Function." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "At the training stage, we follow previous contrastive learning methods [29] and use InfoNCE loss [36] to train our framework. Concretely, given a batch of \\( N \\) image-text pairs \\( \\{I_i, T_i\\}_{i=1}^N \\) as training data, RA-CLIP produces" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.092, + 0.882, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.318, + 0.882, + 0.334 + ], + "angle": 0, + "content": "Figure 3. The proposed Retrieval Augmented Module (RAM)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.349, + 0.892, + 0.394 + ], + "angle": 0, + "content": "the augmented image embeddings and the text embeddings: \\(\\{\\mathbf{v}_i',\\mathbf{t}_i\\}_{i = 1}^N\\) , then we compute text-to-image contrastive loss \\(\\mathcal{L}_{t2v}\\) and image-to-text contrastive loss \\(\\mathcal{L}_{v2t}\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.406, + 0.891, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v 2 t} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {i} ^ {\\prime}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {j} ^ {\\prime}\\right) / \\tau\\right)}\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.455, + 0.891, + 0.493 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t 2 v} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {i}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {j}\\right) / \\tau\\right)}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.56 + ], + "angle": 0, + "content": "where \\(N\\) is the batch size, and \\(\\tau\\) is a temperature factor, which is initialized as 0.07 and trained end-to-end. \\(\\sigma\\) computes the cosine similarity between two vectors. The total loss of our framework is:" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.574, + 0.891, + 0.589 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {t 2 v} + \\mathcal {L} _ {v 2 t}. \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.625, + 0.65 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Following previous works [24, 25, 39], we pre-train our framework on YFCC dataset [35], then evaluate the performance of zero-shot classification and linear probe classification on commonly used visual recognition benchmarks. Besides that, we also follow RegionCLIP [43] and evaluate the zero-shot ROI classification performance on two widely used object detection datasets, i.e., MS COCO [7] and LVIS [15]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We first describe the implementation details in Section 4.1, including datasets, evaluation metrics, model architecture and optimization details. Then we conduct ablation experiments in Section 4.2 to validate the effectiveness of our proposed method and analyse the effectiveness of each component. Finally, we compare our proposed method with recently proposed CLIP variants like MS-CLIP [39], DeCLIP [24] and SLIP [25] in Section 4.3." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19268" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.283, + 0.09, + 0.687, + 0.104 + ], + "angle": 0, + "content": "Table 1. Ablation experiments on zero-shot ImageNet classification." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.115, + 0.868, + 0.265 + ], + "angle": 0, + "content": "
IDMethodInit. of Image Enc.Init. of Text Enc.Pretrain DatasetReference DatasetφψImageNet Top-1
1CLIPViT rand.BERTYFCC×××37.7
2CLIPDINO-SSentenceTYFCC×××21.0
3CLIPViT IN1KBERTYFCC×××46.1
4CLIPViT rand.BERTYFCC+CC×××42.1
5RA-CLIPViT rand.BERTYFCCYFCCSentenceTDINO-S53.5
6RA-CLIPViT rand.BERTYFCCCCSentenceTDINO-S54.5
7RA-CLIPViT rand.BERTYFCCLAIONSentenceTDINO-S54.2
8RA-CLIPViT rand.BERTYFCCCCText EncoderDINO-S54.4
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.289, + 0.295, + 0.306 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.471, + 0.62 + ], + "angle": 0, + "content": "Dataset All the experiments are conducted on public available datasets. For a fair comparison, we follow previous works [24, 25, 39] and use YFCC [35] for pretraining. We follow CLIP [29] and use the 15 million English subset of YFCC for pre-training. For the reference set used in our framework, we test three different image-text datasets, including the YFCC15M described above, CC12M [5] and LAION [32]. By default, we random sample 1,600,000 image-text pairs (about 1/10 amount of our pre-train dataset) from corresponding dataset to construct the reference set. 10 widely used visual recognition datasets are used to evaluate the zero-shot classification performance and linear probe classification performance, including ImageNet [10], ImageNet V2 [30], CIFAR 10 [21], CIFAR 100 [21], Caltech 101 [13], Oxford Pets [27], SUN397 [38], Food 101 [3], DTD [8] and Stanford Dogs [20]. Following RegionCLIP [43], two object detection datasets are used to evaluate the zero-shot ROI classification performance, i.e., COCO [7] and LVIS [15]. More details about the datasets can be found in our supplement." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.624, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Metrics The metrics used to evaluate image classification on all datasets are top-1 accuracy except for Oxford Pets, and Caltech101, which are measured by mean accuracy over classes as in CLIP [29]. The evaluation metric for COCO and LVIS is box Average Precision (AP) as used in RegionCLIP [43]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Architecture By default, the image encoder is a random initialized ViT-B/32 [12], which has 12 layers of Transformer blocks. Each Transformer block has 12 attention heads and the hidden size is set to 768. The text encoder is BERT-base [11], which shares similar scale with the image encoder, i.e., 12 layers of Transformer blocks, 12 attention heads in each Transformer block and 768 hidden size. We also try smaller text encoder from scratch while comparing with previous state-of-the-arts in Section 4.3. The output of the text encoder and image encoder are projected to 384-dim by linear projection. We adopt DINO-S/8 [4] as the image retriever and the uni-modal image encoder \\(\\phi\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.895, + 0.41 + ], + "angle": 0, + "content": "described in Section 3.2, which is pre-trained on ImageNet 1K [10] with self-supervised method. Meanwhile, we adopt Sentence Transformer (SentenceT) [31] as the uni-modal text encoder \\(\\psi\\), which is a 6-layer Transformer. For our proposed Retrieval Augmented Module (RAM), we use 6 layers of cross-attention blocks. We truncate the input text tokens so that they have a maximum length of 77. The input image is resized to \\(224 \\times 224\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.895, + 0.609 + ], + "angle": 0, + "content": "Optimization We implement our framework with PyTorch [28]. All pre-training experiments are conducted on 8 NVIDIA Tesla A100 GPUs. Batch size is set to 4096. The framework is trained for 32 epochs with LAMB optimizer [40] and an initial learning rate of \\(2.5\\mathrm{e - }3\\). The learning rate follows a cosine decay schedule with 5 epochs of linear warm-up. Weight decay is set to 0.2. For data augmentation, we random crop a \\(224\\times 224\\) patch from the input image, then conduct random horizontal flip, random color distortions, random gaussian blur and RandAugment [9], following previous works [6, 24, 25]. Training details of down-stream tasks (e.g., linear probe classification) can be found in our supplement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.655, + 0.636 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.894, + 0.825 + ], + "angle": 0, + "content": "In this section, we first validate the effectiveness of our proposed method by comparing RA-CLIP and CLIP trained on the same dataset. After that, we build reference sets by sampling image-text pairs from different datasets (YFCC, CC or LAION) and sampling different amounts of image-text pairs from the same dataset to see if the reference set is sensitive to these two factors. Since we introduce pre-trained DINO-S/8 (\\(\\phi\\) in Section 3.2) and SentenceT (\\(\\psi\\) in Section 3.2) to extract reference embeddings, we also discuss how these models effect the final performance. At last, ablation experiments with different K-value and different design choices of RAM are provided." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.885, + 0.862 + ], + "angle": 0, + "content": "4.2.1 Effectiveness of the Retrieval Augmented CLIP" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of our proposed method, we train and test CLIP and RA-CLIP with the same dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19269" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.096, + 0.422, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.256, + 0.472, + 0.298 + ], + "angle": 0, + "content": "Figure 4. Zero-shot classification performance of RA-CLIP with different amounts of reference data. Five different scales of reference sets are used, i.e., 1K, 10K, 100K, 1.6M, and 10M." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.461 + ], + "angle": 0, + "content": "For CLIP, we use YFCC15M for pre-training, and evaluate the zero-shot performance on ImageNet. For RA-CLIP, we random sample 1.6 million image-text pairs (about 1/10 amount of entire dataset) from YFCC15M to construct the reference set, and use the other 13 million image-text pairs for training. Experimental results can be found in Table 1, RA-CLIP (experiment ID 5) outperforms CLIP (experiment ID 1) by a large margin (53.5% vs 37.7%), which validates the effectiveness of RA-CLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.471, + 0.705 + ], + "angle": 0, + "content": "We provide a heuristic explanation for this comparison. The pipeline of training and testing CLIP may be considered as a closed-book exam. In the training stage, CLIP trains encoders to learn visual and textual concepts in the training data. In the testing stage, given a test query image, CLIP may return a false prediction if it didn't memorize related concepts of the test image. Different from CLIP, the training and testing of RA-CLIP can be considered as an open-book exam. In the training stage, RA-CLIP doesn't have to memorize all concepts in the training data, but learns how to recognize an image with a help of a cheat-sheet (i.e., the reference set). In the testing stage, given a test query image, RA-CLIP can look up the cheat-sheet (i.e., the reference set) and finds related knowledge about the query image, then uses the knowledge to enrich the representation of input image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.418, + 0.74 + ], + "angle": 0, + "content": "4.2.2 Different image-text data as reference set" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Since the reference set is the core component of RA-CLIP, we then analyse if RA-CLIP provides significant improvements while using different datasets or different amounts of image-text pairs as reference sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Different dataset as reference set. We adopt another two widely used datasets to construct the reference set, i.e., CC12M and LAION. We sample 1.6 million image-text pairs from CC12M to construct the reference set, and use YFCC15M for RA-CLIP pre-training. We also train CLIP on the combination of the reference set and YFCC15M." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 2. Different design choices of Retrieval Augmented Module (RAM). All models are trained on YFCC15M with CC1.6M as reference set and evaluated on zero-shot ImageNet classification." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.143, + 0.885, + 0.273 + ], + "angle": 0, + "content": "
MethodAugment ImageAugment TextFusion TypeKImageNet Top-1
RAM✓XaiT6452.1
RAM✓XaiT + aiI6451.8
RAM✓XaiT + aiI + vi6454.5
RAM✓XaiT + aiI + vi1654.3
RAM✓XaiT + aiI + vi12853.9
RAM✓✓aiT + aiI + vi6453.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.435 + ], + "angle": 0, + "content": "By comparing experiment 6 and experiment 4 in Table 1, we can see that RA-CLIP still outperforms CLIP with significant improvement(54.5% v.s. 42.1%). We then conduct similar experiments with 1.6 million image-text pairs from LAION as reference set, which achieves 54.2% top-1 accuracy on ImageNet. Experiments above show that the commonly used datasets like YFCC15M, CC12M, LAION can be used as reference set and provide similar performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.893, + 0.602 + ], + "angle": 0, + "content": "Different amounts of reference data. We then test the performance of reference sets with different amounts of image-text pairs. 5 reference sets are constructed by sample 1K, 10K, 100K, 1.6M, 10M image-text pairs from CC12M. YFCC15M is used as training data. The performance of RA-CLIP with these 5 different reference sets is illustrated in Figure 4. We can see that introducing more image-text pairs as reference set usually brings better performance. Since the horizontal axis of Figure 4 is plotted in log-space, we can conclude that performance is getting saturated while introducing more image-text pairs as reference set." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.62, + 0.871, + 0.636 + ], + "angle": 0, + "content": "4.2.3 Ablation of pre-trained SentenceT and DINO" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Two frozen pre-trained uni-modal encoders are introduced in RA-CLIP to process image-text data of the reference set: SentenceT and DINO-S/8. It is necessary for us to show if the improvement described above is brought by these two encoders. We re-implement CLIP with frozen SentenceT as text encoder and frozen DINO-S/8 as image encoder, linear projection layer is appended after each encoder to obtain final embeddings. We train the CLIP model on YFCC15M, the zero-shot classification performance on ImageNet is \\(21.0\\%\\), referred as experiment 2 in Table 1, which is significantly lower than CLIP baseline (experiment 1). Experimental results show that although the pre-trained SentenceT and DINO-S provide promising results on uni-modal tasks, they provide poor performance on multi-modal alignment task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also prove that, SentenceT is not necessary for our final performance. We re-implemented RA-CLIP by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19270" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 3. Zero-shot image classification performance and linear probe classification performance on 10 downstream datasets (\\%). RA-CLIP* denotes the model that trains a text encoder with width = 512 and head = 8 from scratch." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.13, + 0.89, + 0.338 + ], + "angle": 0, + "content": "
Evaluation TypeMethodImageNetImageNetV2PetsCIFAR10CIFAR100SUN397Food101Caltech101DTDDogsAvg.
Zero-shotK-Lite [33]45.3----------
CLIP [29]37.732.816.176.048.650.821.869.828.311.139.3
MS-CLIP [39]36.730.2-------5.6-
SLIP [25]38.333.328.372.245.345.144.765.921.811.840.7
DeCLIP [24]43.236.130.272.139.751.646.970.124.211.742.6
RA-CLIP*51.245.450.589.461.845.743.976.124.622.051.1
RA-CLIP53.547.249.089.462.346.543.876.925.626.152.0
Linear probeCLIP [29]63.551.369.891.774.164.769.184.966.550.568.6
MS-CLIP [39]68.149.862.187.266.771.776.081.669.446.167.9
SLIP [25]68.152.175.490.575.373.577.187.271.152.672.3
DeCLIP [24]69.253.176.588.671.675.979.388.069.149.972.1
RA-CLIP*73.362.388.294.978.460.765.586.865.575.575.1
RA-CLIP72.961.988.295.278.961.166.587.266.676.075.5
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.512 + ], + "angle": 0, + "content": "replacing SentenceT with the text encoder of RA-CLIP, the zero-shot performance on ImageNet is \\(54.4\\%\\) (experiment 8), which is comparable with the one used SentenceT (experiment 6). We also note that, although replacing SentenceT with the text encoder of RA-CLIP can provide similar performance, the text encoder of RA-CLIP is trained end-to-end, thus the embeddings of the reference text cannot be pre-computed off-line before training, which introduces more computation cost. So we use SentenceT by default." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.471, + 0.74 + ], + "angle": 0, + "content": "DINO-S/8 in Section 3.2 uses ImageNet 1K for self-supervised learning, extracting reference images on-the-fly during training with the image encoder is much more time-consuming due to the time of reading, pre-processing and extracting images. So we test if CLIP can achieve comparable or better performance than RA-CLIP if it uses ImageNet data for pre-training. Concretely, we use the ViT-B/32 pre-trained on ImageNet 21K and fine-tuned on ImageNet-1K to initialize the image encoder of CLIP. Then train the CLIP on YFCC15M, the classification performance is referred as experiment 3 in Table 1. Initializing the image encoder by ImageNet pre-trained model brings significant improvements (46.1% v.s. 37.7%). However, it is not zero-shot evaluation anymore. We can see that RA-CLIP (53.5%) still outperforms this strong CLIP baseline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.458, + 0.773 + ], + "angle": 0, + "content": "4.2.4 Different hyper-parameters and design choices" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Different K-value in retrieval process. We train RA-CLIP by retrieving different amounts \\((K = 16, 64, 128)\\) of image-text pairs from the reference set for each query image. Experimental results are shown in row 3, 4 and 5 of Table 2. RA-CLIP provides stable performance with different \\(K\\) values, and the model with \\(K = 64\\) performs slightly better than the others." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Different design choices of RAM architecture. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.512 + ], + "angle": 0, + "content": "further test different design choices of RAM architecture in Table 2. Firstly, we take \\(\\mathbf{a}_i^T\\) as the final augmented representation. In this case, RAM gathers related information from the reference texts and produces final embedding, the result is \\(52.1\\%\\). After that, we fuse \\(\\mathbf{a}_i^T\\) and \\(\\mathbf{a}_i^I\\), which provides similar performance \\((51.8\\%)\\). Finally, we take \\(\\mathbf{a}_i^T + \\mathbf{a}_i^I + \\mathbf{v}_i\\) as the final image embedding to fuse information from original image encoder and the reference data, which performs best \\((54.5\\%)\\) among the three different variants as expected." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.893, + 0.665 + ], + "angle": 0, + "content": "Augment both image and text representation. Since experiments above have validated the effectiveness of RA-CLIP, a straightforward question is: will this idea improve CLIP's text representation? To validate that, we use SentenceT to retrieve relevant image-text pairs for input text sentence, then apply similar augmentation to the text embedding. However, it leads to a slightly worse performance \\(53.1\\%\\) as shown in Table 2. We conjecture that text sentence is less informative and the retrieved image-text pairs are more diverse and may not bring correct information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.64, + 0.694 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.869 + ], + "angle": 0, + "content": "In this section, we compare RA-CLIP with CLIP and recently proposed CLIP-variant on two down-stream visual recognition tasks: zero-shot image classification and linear probe image classification. Evaluations are conducted on 10 widely used visual recognition benchmarks. Note that some previous works (e.g., DeCLIP [24]) train a text encoder with width \\(= 512\\) and head \\(= 8\\) from scratch, thus we follow them and re-implemented the RA-CLIP for a fair comparison, the results are denoted as RA-CLIP*. Besides that, we also follow RegionCLIP to evaluate the zero-shot ROI classification performance on MS COCO and LVIS." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Zero-shot image classification Previous methods usually take YFCC15M or its augmented version as train set." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19271" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.095, + 0.849, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.383, + 0.87, + 0.399 + ], + "angle": 0, + "content": "Figure 5. Case study for RA-CLIP in image classification. The retrieved images and texts enrich the representation of input image." + }, + { + "type": "table_caption", + "bbox": [ + 0.086, + 0.422, + 0.46, + 0.436 + ], + "angle": 0, + "content": "Table 4. Zero-shot ROI classification on COCO and LVIS (%)" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.447, + 0.47, + 0.515 + ], + "angle": 0, + "content": "
MethodLVISCOCO
APAPsAPmAPIAPAPsAPmAPI
Regin CLIP21.68.731.045.744.421.951.061.8
Region RA-CLIP23.210.934.244.948.429.357.961.9
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.652 + ], + "angle": 0, + "content": "We thus random sample 1.6M image-text from YFCC15M as reference set, and use the other 13M image-text pairs as train set. We report the performance of RA-CLIP on all 10 datasets as well as the results of previous methods CLIP [29], K-lite [33], SLIP [25], DeCLIP [24] and MS-CLIP [39] shown in Table 3. RA-CLIP shows superior performance than previous state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.76 + ], + "angle": 0, + "content": "We also compare with OpenAI's CLIP model trained on 400 million image-text pairs. To reduce the training cost, we use OpenAI's CLIP-B/32 to initialize the image encoder, text encoders, \\(\\phi\\) and \\(\\psi\\) of RA-CLIP, then freeze them and train the other modules on YFCC15M. The model achieves \\(68.2\\%\\) top-1 accuracy on ImageNet, significantly better than OpenAI's CLIP-B/32 (63.3%)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.838 + ], + "angle": 0, + "content": "In Figure 5, we also provide some visualization to help us understand how RA-CLIP works. The image-text pairs retrieved from the reference set can introduce additional important information that can help RA-CLIP make correct predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Linear probe image classification Following previous methods, we also conduct linear probe image classification experiments to test the transferability of the learned image representation. We fix the pre-trained image encoder of our" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.514 + ], + "angle": 0, + "content": "trained CLIP and RA-CLIP, then train a linear classifier to conduct image classification on down-stream datasets. Experimental results are shown in Table 3. RA-CLIP achieves better performance than previous methods CLIP, MS-CLIP, SLIP and DeCLIP, bringing \\(2.8\\%\\) (75.1% v.s. \\(72.3\\%\\)) averaged improvements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Zero-shot ROI classification Following previous work RegionCLIP [43], we transfer the proposed RA-CLIP to object detection task on COCO [7] and LVIS [15] datasets to test the performance of ROI classification. Following RegionCLIP [43], we use ground-truth bounding boxes as region proposals, then apply RA-CLIP and CLIP to classify the proposals, following a RCNN [14] pipeline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.716 + ], + "angle": 0, + "content": "We report results on the validation set of LVIS and COCO in Table 4. We can see that RA-CLIP still outperforms CLIP on these two benchmarks, bringing \\(1.6\\%\\) improvement on LVIS and \\(4.0\\%\\) improvement on COCO. Note that the proposed RA-CLIP performs much better on small objects and medium objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.62, + 0.751 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this paper, we propose a novel and efficient utilization of image-text pairs. Different from previous Contrastive Language Image Pre-training methods that only use imagetext pairs to train encoders, we also use image-text pairs to construct a reference set. Given an input image, we find relevant images as well as corresponding texts in the reference set and use them to enrich the representation of the input image. Experiments on zero-shot classification and linear probe classification validate the effectiveness of our methods." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19272" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.255 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. Flamingo: a visual language model for few-shot learning. 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Pattern Recog., pages 16793-16803, 2022. 4, 5, 8" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19274" + } + ] +] \ No newline at end of file diff --git a/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_origin.pdf b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..482154c9630091001c91d542aaec650418974ee2 --- /dev/null +++ b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/459b769d-d1fe-4e25-9ca1-08382651f316_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91a99e68753b29a872a71c1b52c849bd94fde6ea6dd15dd31f47db9fd82f7c30 +size 1416777 diff --git a/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/full.md b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bc480f9a33fb993e38ae08bfa3e77c32e848ab15 --- /dev/null +++ b/2023/RA-CLIP_ Retrieval Augmented Contrastive Language-Image Pre-Training/full.md @@ -0,0 +1,310 @@ +# RA-CLIP: Retrieval Augmented Contrastive Language-Image Pre-training + +Chen-Wei Xie*, Siyang Sun*, Xiong Xiong*, Yun Zheng, Deli Zhao, Jingren Zhou +Alibaba Group + +{eniac.xcw,siyang.ssy,moxiong.xx,zhengyun.zy}@alibaba-inc.com zhaodeli@gmail.com,jingren.zhou@alibaba-inc.com + +# Abstract + +Contrastive Language-Image Pre-training (CLIP) is attracting increasing attention for its impressive zero-shot recognition performance on different down-stream tasks. However, training CLIP is data-hungry and requires lots of image-text pairs to memorize various semantic concepts. In this paper, we propose a novel and efficient framework: Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to augment embeddings by online retrieval. Specifically, we sample part of image-text data as a hold-out reference set. Given an input image, relevant image-text pairs are retrieved from the reference set to enrich the representation of input image. This process can be considered as an open-book exam: with the reference set as a cheat sheet, the proposed method doesn't need to memorize all visual concepts in the training data. It explores how to recognize visual concepts by exploiting correspondence between images and texts in the cheat sheet. The proposed RA-CLIP implements this idea and comprehensive experiments are conducted to show how RA-CLIP works. Performances on 10 image classification datasets and 2 object detection datasets show that RA-CLIP outperforms vanilla CLIP baseline by a large margin on zero-shot image classification task $(+12.7\%)$ , linear probe image classification task $(+6.9\%)$ and zero-shot ROI classification task $(+2.8\%)$ . + +# 1. Introduction + +Traditional visual representation learning systems are trained to predict a fixed set of predetermined image categories [12, 16, 22, 34]. This limits their transferability since additional labeled training data are required to recognize new visual concepts. Recently, vision-language pre-training approaches such as CLIP [29] emerge as a promising alternative which introduces text description as supervision. CLIP aligns image modality and text modality by learning a + +![](images/794085a01f645c9bd211db4fdcb0ac0ef577894884364619a51c8dc2e35a5c57.jpg) + +![](images/d6b7f809887ee3e14f5438f6c21f42fa94ef31c028a57ccdf8a1eb0d489289f4.jpg) + +![](images/27e9145605541a005cc7f848eb4fd2a607ec8fe6c4d5d956eb193640f91eba0a.jpg) + +![](images/0a251a4cd8a93706f45a9c3ce8cd1080a4e663a7b28aeb841fb3d9c9fb60a56e.jpg) + +![](images/704356f9a3d08e3fb73d4724c75cc9fd0c803aadd1adfe380a6c5367d4abfe2f.jpg) + +![](images/422ea2ffee9fe4aac571c5735c9ed39e5295f942acdf7fea1007140e3ae6bbf2.jpg) + +![](images/14c8e2616dad18db9c6694ce955783cf0f16d95eb1f94df7c9d560099d5b4094.jpg) + +![](images/0069551945500f7602cfe09c692432ec0c4ac8148bec772dfac637a6b4f74eda.jpg) + +![](images/991e2695e32b35a29a9127e35f95fa2946b01a61e910c0e5e85f4e521c9e4658.jpg) +Figure 1. Transferring the CLIP and RA-CLIP to 12 down-stream visual recognition datasets for zero-shot evaluation. Our RA-CLIP achieves better results in 10 out of 12 datasets, and brings $+12.7\%$ averaged improvements on the 10 image classification datasets and $2.8\%$ averaged improvements on the 2 object detection datasets.. + +![](images/dd2aaf194e46d0cf15338ceea44d77de7add6c962c0a4388d175b478ce1cf18c.jpg) + +![](images/81c4d1c8708780021404caf655148ead60a53729cc01a6676d0f26563b7ec316.jpg) + +![](images/5ecdd1dbe143b2419a11587a9d43c97adc6deacf6be2393379474b9efb8d77da.jpg) + +modality-shared representation. During pre-training, CLIP learns to pull matched image-text pairs together and push non-matched pairs apart. After pre-training, CLIP can be transferred to zero-shot image classification task: categories can be referred by textual descriptions, and the image classification task can be converted to image-to-text retrieval task. Experimental results show that CLIP performs well on zero-shot image classification task, e.g., for ImageNet zero-shot classification task, CLIP can match the accuracy of ImageNet pre-trained ResNet50, even that CLIP doesn't use any of the 1.28 million training examples of ImageNet for training. + +Despite the impressive zero-shot performance, CLIP requires lots of image-text pairs to train encoders and memorize various semantic concepts, which limits its applications since it is not affordable for most laboratories and companies. Recent works [24, 25] try to alleviate this limitation by taking full advantage of existing data and + +train encoders to memorize concepts as many as possible, e.g., DeCLIP [24] explores widespread supervision from given image-text pairs, and SLIP [25] introduces self-supervised learning which helps encoders learn better visual representation. + +In this paper, we propose a novel and efficient way to make use of image-text pairs. We sample part of image-text data as a hold-out reference set. Given an input image, our model first retrieves similar images from the reference set with an unsupervised pre-trained image retrieval model, then we use the relationship between retrieved images and texts to augment the representation of input image. A heuristic explanation of the idea is that, it can be considered as an open-book exam: our model doesn't have to memorize all visual concepts in the training data, but learns to recognize visual concepts with the help of a cheat sheet (i.e., the reference set). We propose a framework called Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to implement this idea. Although using the same amount of image-text data with the vanilla CLIP, RA-CLIP achieves better zero-shot classification performance and linear probe classification performance. + +Our contributions are three-fold: + +- For contrastive language-image pre-training (CLIP), we present a novel and efficient utilization of image-text pairs. Concretely, we construct a hold-out reference set composed by image-text pairs. Given an input image, we find relevant image-text pairs and use them to help us build better representation for the input image. +- We propose Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP), a framework to implement the idea described above. We conduct comprehensive experiments to validate the effectiveness of each block. Visualization results are also provided to explain how RA-CLIP works. +- We compare the proposed RA-CLIP with previous methods on a dozen of commonly used visual recognition benchmarks. Experimental results show that our proposed method significantly outperforms vanilla CLIP baseline and other recently proposed methods. + +# 2. Related Work + +# 2.1. Contrastive Language Image Pre-training + +CLIP [29] introduces a new paradigm for visual representation learning. Given image-text pairs as training data, CLIP learns a visual encoder and a textual encoder to align images and text sentences. Different from previous visual recognition system which can only recognize categories specified by the training set, CLIP can be flexibly + +transferred to new categories. Given new categories, CLIP extends them into text sentences and feed them into the text encoder to obtain categories embeddings. Experimental results show that CLIP can match the accuracy of ImageNet trained ResNet50, even that CLIP didn't use any of the 1.28 million training examples of ImageNet during pre-training. Despite the impressive transfer performance, CLIP is quite data-hungry, it needs tens of millions or more image-text pairs for pre-training [1, 18, 29, 41, 42]. To decrease the amount of training data, recent works [24, 25] try to introduce as much as supervision from existing datasets to help CLIP train better encoders. + +In this paper, we propose a novel and efficient methods to make better use of image-text pairs. Different from previous methods that only use image-text pairs to train encoders, we also use them to construct a reference set which can provide supplementary information for the encoder. Given an input image, we find relevant images along with their text descriptions from the reference set, these image-text pairs contain information that can help us describe the input image, thus we use them to augment original CLIP's image representation. + +# 2.2. Knowledge-Enhanced Models + +Structured external knowledge has also been included to improve the zero-shot performance, K-Lite [33] enriches entities in natural language with WordNet and Wiktionary, the motivation is straightforward, some concepts like "zebra" may have less training example in the training set, by introducing a knowledge base, "zebra" can be extended to a more general description: "Zebras are African equines with distinctive black-and-white striped coats". CLIP-event [23] also introduces structured external knowledge to construct hard negative text descriptions for images during training. ASIF [26] builds a relative representation for image and text respectively and aligns image modality and text modality with image-text pairs. + +Recently large language models have shown impressive zero-shot and few-shot performance on various downstream NLP tasks, massive parameters have to be introduced to encode the knowledge that will be used. Previous works Atlas [17] and RETRO [2] introduce an external non-parametric knowledge base to store the information, which significantly reduces the parameters of their model, e.g., Atlas outperforms a 540B model with $50 \times$ fewer parameters. + +The methods mentioned above mainly focus on providing more information for individual modalities. Different from them, we utilize the correspondence between imagetext pairs in the reference set, which helps us align visual concepts and textual concepts. + +![](images/df2450e9ef9d0c9f22dab9e15eeab6f0588f0df001a99ebf27f77fa6ac3a429c.jpg) +Figure 2. Overview of the proposed RA-CLIP. Given an input image, RA-CLIP retrieves K most similar image-text pairs from the reference set, which provide informative descriptions for the input image, thus we feed them into the Retrieval Augmented Module (RAM) to enrich the representation of input image. + +# 2.3. Zero-shot Visual Recognition + +Zero-shot visual recognition can be categorized into two generations: the traditional class-level zero-shot setting and recently popular task-level zero-shot setting [33]. The traditional class-level zero-shot aims at recognizing objects that belong to categories that are not included in the training set. The task-level zero-shot like CLIP [29] is more practical in real-world applications, the model is trained by hundreds of millions of image-text pairs and is directly evaluated on image classification task, by prompting category names into sentence descriptions [1, 18, 29, 41, 42]. + +Memorizing visual and textual concepts for down-stream zero-shot tasks usually requires lots of image-text pairs. In this paper, we propose that, besides using image-text pairs to train image encoder and text encoder, we can also introduce a reference set to help the model align visual concepts and textual concepts. + +# 3. Method + +In this section, we present the details of our proposed Retrieval Augmented Language Image Pre-training (RA-CLIP). An overview of RA-CLIP is summarized in Figure 2. Given $N$ image-text pairs $\{I_i,T_i\}_{i = 1}^N$ as training data, where $I_{i}$ is the $i$ -th image in the dataset and $T_{i}$ is its corresponding text description. Different from previous Contrastive Language Image Pre-training (CLIP) method that only uses $\{I_i,T_i\}_{i = 1}^N$ to train encoders, we propose a novel utilization of the image-text pairs. Specifically, we split $\{I_i,T_i\}_{i = 1}^N$ into two disjoint sets: training set $\mathcal{T}$ and reference set $\mathcal{R}$ . Given $I_{i}$ as input image, we first feed it into the image encoder to obtain the initial image embedding $\mathbf{v}_i$ , following previous method CLIP. After that, + +we retrieve $K$ most similar images $\{\mathbf{r}_k^I\}_{k = 1}^K$ from $\mathcal{R}$ as well as their corresponding text sentences $\{\mathbf{r}_k^T\}_{k = 1}^K$ . $\{\mathbf{r}_k^I\}_{k = 1}^K$ and $\{\mathbf{r}_k^T\}_{k = 1}^K$ provide informative description for $I_{i}$ , so we use them to augment $\mathbf{v}_i$ by a proposed Retrieval Augmented Module (RAM). The augmented image embedding is output as $\mathbf{v}_i'$ . The text branch of RA-CLIP is like the one of CLIP. + +# 3.1. Dual-Encoder Architecture + +The dual-encoder architecture consists of an image encoder and a text encoder. The image encoder used in our experiments is a Vision Transformer [12]. Given an image $I_{i}$ , we take the embedding of the [CLS] token and normalize it by its L2-norm to obtain the representation of $I_{i}$ , which is a $d$ -dimension feature vector $\mathbf{v}_i$ . The text encoder is also a Transformer. Given a sequence of input text $T_{i}$ , the text encoder transforms and normalizes $T_{i}$ into another $d$ -dimension feature vector $\mathbf{t}_i$ . + +# 3.2. Overview of RA-CLIP + +Reference Set Construction. Multi-modal image-text pairs naturally establish the connection between images and texts. Different images and text descriptions of the same concept can provide informative description of this concept. Inspired by this observation, we construct the reference set $\mathcal{R}$ by random sampling 1.6M (about 1/10 amount of our total training data) image-text pairs from original train set. Ablation experiments will show that commonly used image-text datasets such as YFCC [35], CC12M [5] and LAION [32] can be used as reference data. We also exploit how the amount of image-text pairs effect the final performance. Please refer to Section 4.2.2 for more details. + +Reference Image-Text Retrieval. Given an input image $I_{i}$ , RA-CLIP retrieves $K$ most similar images $\{\mathbf{r}_k^I\}_{k=1}^K$ from the reference set as well as their corresponding text descriptions $\{\mathbf{r}_k^T\}_{k=1}^K$ . Concretely, we first extract the embeddings of the images in reference set, with an unsupervised pre-trained image encoder (e.g., DINO) for a fairer comparison. This process can be pre-computed offline. Given an input image $I_{i}$ as query, we also extract the embedding of $I_{i}$ with the same model, then use the embedding to retrieve $K$ most similar images from the reference set. The retrieval process can be conducted efficiently by existing libraries like Faiss [19]. Finally, we get $K$ images $\{\mathbf{r}_k^I\}_{k=1}^K$ and their corresponding text sentences $\{\mathbf{r}_k^T\}_{k=1}^K$ , which are sent to the Retrieval Augmented Module (RAM) to obtain augmented image representation. + +Retrieval Augmented Module (RAM). We propose a novel Retrieval Augmented Module (RAM), which first extracts the embeddings of each retrieved $\mathbf{r}_k^I$ and $\mathbf{r}_k^T$ : + +$$ +\mathbf {e} _ {k} ^ {I} = \phi (\mathbf {r} _ {k} ^ {I}), +$$ + +$$ +\mathbf {e} _ {k} ^ {T} = \psi \left(\mathbf {r} _ {k} ^ {T}\right). \tag {1} +$$ + +Note that $\phi$ and $\psi$ are pre-trained uni-modal encoders for image and text respectively. They are frozen during the training stage, so Equation 1 can be pre-computed before training. + +After that, RAM uses $\{\mathbf{e}_k^I\}_{k=1}^K$ and $\{\mathbf{e}_k^T\}_{k=1}^K$ to augment $\mathbf{v}_i$ . RAM first introduces a Multi-head Attention [37] block which takes $\mathbf{v}_i$ as query, $\{\mathbf{e}_k^I\}_{k=1}^K$ as key and $\{\mathbf{e}_k^T\}_{k=1}^K$ as value to obtain text-augmented embedding $\mathbf{a}_i^T$ : + +$$ +\mathbf {a} _ {i} ^ {T} = \text {M u l t i h e a d A t t n} (\mathbf {v} _ {i}, \left\{\mathbf {e} _ {k} ^ {I} \right\} _ {k = 1} ^ {K}, \left\{\mathbf {e} _ {k} ^ {T} \right\} _ {k = 1} ^ {K}). \tag {2} +$$ + +In Equation 2, $\mathbf{v}_i$ learns to weight and aggregate $\{\mathbf{e}_k^T\}_{k=1}^K$ according to the relationship between $\mathbf{v}_i$ and $\{\mathbf{e}_k^I\}_{k=1}^K$ . The aggregated text embedding $\mathbf{a}_i^T$ will be used to augment $\mathbf{v}_i$ . + +Likewise, RAM also computes image-augmented embedding $\mathbf{a}_i^I$ by aggregating $\{\mathbf{e}_k^I\}_{k=1}^K$ in a similar way: + +$$ +\mathbf {a} _ {i} ^ {I} = M u l t i h e a d A t t n (\mathbf {v} _ {i}, \left\{\mathbf {e} _ {k} ^ {T} \right\} _ {k = 1} ^ {K}, \left\{\mathbf {e} _ {k} ^ {I} \right\} _ {k = 1} ^ {K}). \tag {3} +$$ + +Finally, RAM outputs the augmented image embedding $\mathbf{v}_i'$ : + +$$ +\mathbf {v} _ {i} ^ {\prime} = \mathbf {v} _ {i} + \mathbf {a} _ {i} ^ {T} + \mathbf {a} _ {i} ^ {I}, \tag {4} +$$ + +as illustrated in Figure 3. + +# 3.3. Loss Function. + +At the training stage, we follow previous contrastive learning methods [29] and use InfoNCE loss [36] to train our framework. Concretely, given a batch of $N$ image-text pairs $\{I_i, T_i\}_{i=1}^N$ as training data, RA-CLIP produces + +![](images/754ebaea9800a5bab4401e3a1f3e4c0da82fa00ef38838d3bab1fd2440b97b3c.jpg) +Figure 3. The proposed Retrieval Augmented Module (RAM). + +the augmented image embeddings and the text embeddings: $\{\mathbf{v}_i',\mathbf{t}_i\}_{i = 1}^N$ , then we compute text-to-image contrastive loss $\mathcal{L}_{t2v}$ and image-to-text contrastive loss $\mathcal{L}_{v2t}$ .. + +$$ +\mathcal {L} _ {v 2 t} = - \log \left(\frac {\exp \left(\sigma \left(\mathbf {t} _ {i} , \mathbf {v} _ {i} ^ {\prime}\right) / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\sigma \left(\mathbf {t} _ {i} , \mathbf {v} _ {j} ^ {\prime}\right) / \tau\right)}\right), \tag {5} +$$ + +$$ +\mathcal {L} _ {t 2 v} = - \log \left(\frac {\exp \left(\sigma \left(\mathbf {v} _ {i} ^ {\prime} , \mathbf {t} _ {i}\right) / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\sigma \left(\mathbf {v} _ {i} ^ {\prime} , \mathbf {t} _ {j}\right) / \tau\right)}\right), \tag {6} +$$ + +where $N$ is the batch size, and $\tau$ is a temperature factor, which is initialized as 0.07 and trained end-to-end. $\sigma$ computes the cosine similarity between two vectors. The total loss of our framework is: + +$$ +\mathcal {L} = \mathcal {L} _ {t 2 v} + \mathcal {L} _ {v 2 t}. \tag {7} +$$ + +# 4. Experiment + +Following previous works [24, 25, 39], we pre-train our framework on YFCC dataset [35], then evaluate the performance of zero-shot classification and linear probe classification on commonly used visual recognition benchmarks. Besides that, we also follow RegionCLIP [43] and evaluate the zero-shot ROI classification performance on two widely used object detection datasets, i.e., MS COCO [7] and LVIS [15]. + +We first describe the implementation details in Section 4.1, including datasets, evaluation metrics, model architecture and optimization details. Then we conduct ablation experiments in Section 4.2 to validate the effectiveness of our proposed method and analyse the effectiveness of each component. Finally, we compare our proposed method with recently proposed CLIP variants like MS-CLIP [39], DeCLIP [24] and SLIP [25] in Section 4.3. + +Table 1. Ablation experiments on zero-shot ImageNet classification. + +
IDMethodInit. of Image Enc.Init. of Text Enc.Pretrain DatasetReference DatasetφψImageNet Top-1
1CLIPViT rand.BERTYFCC×××37.7
2CLIPDINO-SSentenceTYFCC×××21.0
3CLIPViT IN1KBERTYFCC×××46.1
4CLIPViT rand.BERTYFCC+CC×××42.1
5RA-CLIPViT rand.BERTYFCCYFCCSentenceTDINO-S53.5
6RA-CLIPViT rand.BERTYFCCCCSentenceTDINO-S54.5
7RA-CLIPViT rand.BERTYFCCLAIONSentenceTDINO-S54.2
8RA-CLIPViT rand.BERTYFCCCCText EncoderDINO-S54.4
+ +# 4.1. Implementation Details + +Dataset All the experiments are conducted on public available datasets. For a fair comparison, we follow previous works [24, 25, 39] and use YFCC [35] for pretraining. We follow CLIP [29] and use the 15 million English subset of YFCC for pre-training. For the reference set used in our framework, we test three different image-text datasets, including the YFCC15M described above, CC12M [5] and LAION [32]. By default, we random sample 1,600,000 image-text pairs (about 1/10 amount of our pre-train dataset) from corresponding dataset to construct the reference set. 10 widely used visual recognition datasets are used to evaluate the zero-shot classification performance and linear probe classification performance, including ImageNet [10], ImageNet V2 [30], CIFAR 10 [21], CIFAR 100 [21], Caltech 101 [13], Oxford Pets [27], SUN397 [38], Food 101 [3], DTD [8] and Stanford Dogs [20]. Following RegionCLIP [43], two object detection datasets are used to evaluate the zero-shot ROI classification performance, i.e., COCO [7] and LVIS [15]. More details about the datasets can be found in our supplement. + +Metrics The metrics used to evaluate image classification on all datasets are top-1 accuracy except for Oxford Pets, and Caltech101, which are measured by mean accuracy over classes as in CLIP [29]. The evaluation metric for COCO and LVIS is box Average Precision (AP) as used in RegionCLIP [43]. + +Architecture By default, the image encoder is a random initialized ViT-B/32 [12], which has 12 layers of Transformer blocks. Each Transformer block has 12 attention heads and the hidden size is set to 768. The text encoder is BERT-base [11], which shares similar scale with the image encoder, i.e., 12 layers of Transformer blocks, 12 attention heads in each Transformer block and 768 hidden size. We also try smaller text encoder from scratch while comparing with previous state-of-the-arts in Section 4.3. The output of the text encoder and image encoder are projected to 384-dim by linear projection. We adopt DINO-S/8 [4] as the image retriever and the uni-modal image encoder $\phi$ + +described in Section 3.2, which is pre-trained on ImageNet 1K [10] with self-supervised method. Meanwhile, we adopt Sentence Transformer (SentenceT) [31] as the uni-modal text encoder $\psi$ , which is a 6-layer Transformer. For our proposed Retrieval Augmented Module (RAM), we use 6 layers of cross-attention blocks. We truncate the input text tokens so that they have a maximum length of 77. The input image is resized to $224 \times 224$ . + +Optimization We implement our framework with PyTorch [28]. All pre-training experiments are conducted on 8 NVIDIA Tesla A100 GPUs. Batch size is set to 4096. The framework is trained for 32 epochs with LAMB optimizer [40] and an initial learning rate of $2.5\mathrm{e - }3$ . The learning rate follows a cosine decay schedule with 5 epochs of linear warm-up. Weight decay is set to 0.2. For data augmentation, we random crop a $224\times 224$ patch from the input image, then conduct random horizontal flip, random color distortions, random gaussian blur and RandAugment [9], following previous works [6, 24, 25]. Training details of down-stream tasks (e.g., linear probe classification) can be found in our supplement. + +# 4.2. Ablation Study + +In this section, we first validate the effectiveness of our proposed method by comparing RA-CLIP and CLIP trained on the same dataset. After that, we build reference sets by sampling image-text pairs from different datasets (YFCC, CC or LAION) and sampling different amounts of image-text pairs from the same dataset to see if the reference set is sensitive to these two factors. Since we introduce pre-trained DINO-S/8 ( $\phi$ in Section 3.2) and SentenceT ( $\psi$ in Section 3.2) to extract reference embeddings, we also discuss how these models effect the final performance. At last, ablation experiments with different K-value and different design choices of RAM are provided. + +# 4.2.1 Effectiveness of the Retrieval Augmented CLIP + +To validate the effectiveness of our proposed method, we train and test CLIP and RA-CLIP with the same dataset. + +![](images/151efcc3388e6f6cb4c1db8dc93634b9d759e47a7e125f015daeca8f3bf2ce69.jpg) +Figure 4. Zero-shot classification performance of RA-CLIP with different amounts of reference data. Five different scales of reference sets are used, i.e., 1K, 10K, 100K, 1.6M, and 10M. + +For CLIP, we use YFCC15M for pre-training, and evaluate the zero-shot performance on ImageNet. For RA-CLIP, we random sample 1.6 million image-text pairs (about 1/10 amount of entire dataset) from YFCC15M to construct the reference set, and use the other 13 million image-text pairs for training. Experimental results can be found in Table 1, RA-CLIP (experiment ID 5) outperforms CLIP (experiment ID 1) by a large margin (53.5% vs 37.7%), which validates the effectiveness of RA-CLIP. + +We provide a heuristic explanation for this comparison. The pipeline of training and testing CLIP may be considered as a closed-book exam. In the training stage, CLIP trains encoders to learn visual and textual concepts in the training data. In the testing stage, given a test query image, CLIP may return a false prediction if it didn't memorize related concepts of the test image. Different from CLIP, the training and testing of RA-CLIP can be considered as an open-book exam. In the training stage, RA-CLIP doesn't have to memorize all concepts in the training data, but learns how to recognize an image with a help of a cheat-sheet (i.e., the reference set). In the testing stage, given a test query image, RA-CLIP can look up the cheat-sheet (i.e., the reference set) and finds related knowledge about the query image, then uses the knowledge to enrich the representation of input image. + +# 4.2.2 Different image-text data as reference set + +Since the reference set is the core component of RA-CLIP, we then analyse if RA-CLIP provides significant improvements while using different datasets or different amounts of image-text pairs as reference sets. + +Different dataset as reference set. We adopt another two widely used datasets to construct the reference set, i.e., CC12M and LAION. We sample 1.6 million image-text pairs from CC12M to construct the reference set, and use YFCC15M for RA-CLIP pre-training. We also train CLIP on the combination of the reference set and YFCC15M. + +Table 2. Different design choices of Retrieval Augmented Module (RAM). All models are trained on YFCC15M with CC1.6M as reference set and evaluated on zero-shot ImageNet classification. + +
MethodAugment ImageAugment TextFusion TypeKImageNet Top-1
RAM✓XaiT6452.1
RAM✓XaiT + aiI6451.8
RAM✓XaiT + aiI + vi6454.5
RAM✓XaiT + aiI + vi1654.3
RAM✓XaiT + aiI + vi12853.9
RAM✓✓aiT + aiI + vi6453.1
+ +By comparing experiment 6 and experiment 4 in Table 1, we can see that RA-CLIP still outperforms CLIP with significant improvement(54.5% v.s. 42.1%). We then conduct similar experiments with 1.6 million image-text pairs from LAION as reference set, which achieves 54.2% top-1 accuracy on ImageNet. Experiments above show that the commonly used datasets like YFCC15M, CC12M, LAION can be used as reference set and provide similar performance. + +Different amounts of reference data. We then test the performance of reference sets with different amounts of image-text pairs. 5 reference sets are constructed by sample 1K, 10K, 100K, 1.6M, 10M image-text pairs from CC12M. YFCC15M is used as training data. The performance of RA-CLIP with these 5 different reference sets is illustrated in Figure 4. We can see that introducing more image-text pairs as reference set usually brings better performance. Since the horizontal axis of Figure 4 is plotted in log-space, we can conclude that performance is getting saturated while introducing more image-text pairs as reference set. + +# 4.2.3 Ablation of pre-trained SentenceT and DINO + +Two frozen pre-trained uni-modal encoders are introduced in RA-CLIP to process image-text data of the reference set: SentenceT and DINO-S/8. It is necessary for us to show if the improvement described above is brought by these two encoders. We re-implement CLIP with frozen SentenceT as text encoder and frozen DINO-S/8 as image encoder, linear projection layer is appended after each encoder to obtain final embeddings. We train the CLIP model on YFCC15M, the zero-shot classification performance on ImageNet is $21.0\%$ , referred as experiment 2 in Table 1, which is significantly lower than CLIP baseline (experiment 1). Experimental results show that although the pre-trained SentenceT and DINO-S provide promising results on uni-modal tasks, they provide poor performance on multi-modal alignment task. + +We also prove that, SentenceT is not necessary for our final performance. We re-implemented RA-CLIP by + +Table 3. Zero-shot image classification performance and linear probe classification performance on 10 downstream datasets (\%). RA-CLIP* denotes the model that trains a text encoder with width = 512 and head = 8 from scratch. + +
Evaluation TypeMethodImageNetImageNetV2PetsCIFAR10CIFAR100SUN397Food101Caltech101DTDDogsAvg.
Zero-shotK-Lite [33]45.3----------
CLIP [29]37.732.816.176.048.650.821.869.828.311.139.3
MS-CLIP [39]36.730.2-------5.6-
SLIP [25]38.333.328.372.245.345.144.765.921.811.840.7
DeCLIP [24]43.236.130.272.139.751.646.970.124.211.742.6
RA-CLIP*51.245.450.589.461.845.743.976.124.622.051.1
RA-CLIP53.547.249.089.462.346.543.876.925.626.152.0
Linear probeCLIP [29]63.551.369.891.774.164.769.184.966.550.568.6
MS-CLIP [39]68.149.862.187.266.771.776.081.669.446.167.9
SLIP [25]68.152.175.490.575.373.577.187.271.152.672.3
DeCLIP [24]69.253.176.588.671.675.979.388.069.149.972.1
RA-CLIP*73.362.388.294.978.460.765.586.865.575.575.1
RA-CLIP72.961.988.295.278.961.166.587.266.676.075.5
+ +replacing SentenceT with the text encoder of RA-CLIP, the zero-shot performance on ImageNet is $54.4\%$ (experiment 8), which is comparable with the one used SentenceT (experiment 6). We also note that, although replacing SentenceT with the text encoder of RA-CLIP can provide similar performance, the text encoder of RA-CLIP is trained end-to-end, thus the embeddings of the reference text cannot be pre-computed off-line before training, which introduces more computation cost. So we use SentenceT by default. + +DINO-S/8 in Section 3.2 uses ImageNet 1K for self-supervised learning, extracting reference images on-the-fly during training with the image encoder is much more time-consuming due to the time of reading, pre-processing and extracting images. So we test if CLIP can achieve comparable or better performance than RA-CLIP if it uses ImageNet data for pre-training. Concretely, we use the ViT-B/32 pre-trained on ImageNet 21K and fine-tuned on ImageNet-1K to initialize the image encoder of CLIP. Then train the CLIP on YFCC15M, the classification performance is referred as experiment 3 in Table 1. Initializing the image encoder by ImageNet pre-trained model brings significant improvements (46.1% v.s. 37.7%). However, it is not zero-shot evaluation anymore. We can see that RA-CLIP (53.5%) still outperforms this strong CLIP baseline. + +# 4.2.4 Different hyper-parameters and design choices + +Different K-value in retrieval process. We train RA-CLIP by retrieving different amounts $(K = 16, 64, 128)$ of image-text pairs from the reference set for each query image. Experimental results are shown in row 3, 4 and 5 of Table 2. RA-CLIP provides stable performance with different $K$ values, and the model with $K = 64$ performs slightly better than the others. + +Different design choices of RAM architecture. We + +further test different design choices of RAM architecture in Table 2. Firstly, we take $\mathbf{a}_i^T$ as the final augmented representation. In this case, RAM gathers related information from the reference texts and produces final embedding, the result is $52.1\%$ . After that, we fuse $\mathbf{a}_i^T$ and $\mathbf{a}_i^I$ , which provides similar performance $(51.8\%)$ . Finally, we take $\mathbf{a}_i^T + \mathbf{a}_i^I + \mathbf{v}_i$ as the final image embedding to fuse information from original image encoder and the reference data, which performs best $(54.5\%)$ among the three different variants as expected. + +Augment both image and text representation. Since experiments above have validated the effectiveness of RA-CLIP, a straightforward question is: will this idea improve CLIP's text representation? To validate that, we use SentenceT to retrieve relevant image-text pairs for input text sentence, then apply similar augmentation to the text embedding. However, it leads to a slightly worse performance $53.1\%$ as shown in Table 2. We conjecture that text sentence is less informative and the retrieved image-text pairs are more diverse and may not bring correct information. + +# 4.3. Main Results + +In this section, we compare RA-CLIP with CLIP and recently proposed CLIP-variant on two down-stream visual recognition tasks: zero-shot image classification and linear probe image classification. Evaluations are conducted on 10 widely used visual recognition benchmarks. Note that some previous works (e.g., DeCLIP [24]) train a text encoder with width $= 512$ and head $= 8$ from scratch, thus we follow them and re-implemented the RA-CLIP for a fair comparison, the results are denoted as RA-CLIP*. Besides that, we also follow RegionCLIP to evaluate the zero-shot ROI classification performance on MS COCO and LVIS. + +Zero-shot image classification Previous methods usually take YFCC15M or its augmented version as train set. + +![](images/9d056aa6013eb86d398328169bdb8176ff6c2f42886549f7ae5cc3fefe832809.jpg) +Figure 5. Case study for RA-CLIP in image classification. The retrieved images and texts enrich the representation of input image. + +Table 4. Zero-shot ROI classification on COCO and LVIS (%) + +
MethodLVISCOCO
APAPsAPmAPIAPAPsAPmAPI
Regin CLIP21.68.731.045.744.421.951.061.8
Region RA-CLIP23.210.934.244.948.429.357.961.9
+ +We thus random sample 1.6M image-text from YFCC15M as reference set, and use the other 13M image-text pairs as train set. We report the performance of RA-CLIP on all 10 datasets as well as the results of previous methods CLIP [29], K-lite [33], SLIP [25], DeCLIP [24] and MS-CLIP [39] shown in Table 3. RA-CLIP shows superior performance than previous state-of-the-art methods. + +We also compare with OpenAI's CLIP model trained on 400 million image-text pairs. To reduce the training cost, we use OpenAI's CLIP-B/32 to initialize the image encoder, text encoders, $\phi$ and $\psi$ of RA-CLIP, then freeze them and train the other modules on YFCC15M. The model achieves $68.2\%$ top-1 accuracy on ImageNet, significantly better than OpenAI's CLIP-B/32 (63.3%). + +In Figure 5, we also provide some visualization to help us understand how RA-CLIP works. The image-text pairs retrieved from the reference set can introduce additional important information that can help RA-CLIP make correct predictions. + +Linear probe image classification Following previous methods, we also conduct linear probe image classification experiments to test the transferability of the learned image representation. We fix the pre-trained image encoder of our + +trained CLIP and RA-CLIP, then train a linear classifier to conduct image classification on down-stream datasets. Experimental results are shown in Table 3. RA-CLIP achieves better performance than previous methods CLIP, MS-CLIP, SLIP and DeCLIP, bringing $2.8\%$ (75.1% v.s. $72.3\%$ ) averaged improvements. + +Zero-shot ROI classification Following previous work RegionCLIP [43], we transfer the proposed RA-CLIP to object detection task on COCO [7] and LVIS [15] datasets to test the performance of ROI classification. Following RegionCLIP [43], we use ground-truth bounding boxes as region proposals, then apply RA-CLIP and CLIP to classify the proposals, following a RCNN [14] pipeline. + +We report results on the validation set of LVIS and COCO in Table 4. We can see that RA-CLIP still outperforms CLIP on these two benchmarks, bringing $1.6\%$ improvement on LVIS and $4.0\%$ improvement on COCO. Note that the proposed RA-CLIP performs much better on small objects and medium objects. + +# 5. Conclusion + +In this paper, we propose a novel and efficient utilization of image-text pairs. Different from previous Contrastive Language Image Pre-training methods that only use imagetext pairs to train encoders, we also use image-text pairs to construct a reference set. Given an input image, we find relevant images as well as corresponding texts in the reference set and use them to enrich the representation of the input image. 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However, training CLIP is data-hungry and requires lots of image-text pairs to memorize various semantic concepts. In this paper, we propose a novel and efficient framework: Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to augment embeddings by online retrieval. Specifically, we sample part of image-text data as a hold-out reference set. Given an input image, relevant image-text pairs are retrieved from the reference set to enrich the representation of input image. This process can be considered as an open-book exam: with the reference set as a cheat sheet, the proposed method doesn't need to memorize all visual concepts in the training data. It explores how to recognize visual concepts by exploiting correspondence between images and texts in the cheat sheet. The proposed RA-CLIP implements this idea and comprehensive experiments are conducted to show how RA-CLIP works. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "content": "Traditional visual representation learning systems are trained to predict a fixed set of predetermined image categories [12, 16, 22, 34]. This limits their transferability since additional labeled training data are required to recognize new visual concepts. Recently, vision-language pre-training approaches such as CLIP [29] emerge as a promising alternative which introduces text description as supervision. 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Transferring the CLIP and RA-CLIP to 12 down-stream visual recognition datasets for zero-shot evaluation. 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During pre-training, CLIP learns to pull matched image-text pairs together and push non-matched pairs apart. After pre-training, CLIP can be transferred to zero-shot image classification task: categories can be referred by textual descriptions, and the image classification task can be converted to image-to-text retrieval task. Experimental results show that CLIP performs well on zero-shot image classification task, e.g., for ImageNet zero-shot classification task, CLIP can match the accuracy of ImageNet pre-trained ResNet50, even that CLIP doesn't use any of the 1.28 million training examples of ImageNet for training." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Despite the impressive zero-shot performance, CLIP requires lots of image-text pairs to train encoders and memorize various semantic concepts, which limits its applications since it is not affordable for most laboratories and companies. Recent works [24, 25] try to alleviate this limitation by taking full advantage of existing data and" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 155, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 155, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 155, + 713 + ], + "type": "text", + "content": "*indicates equal contribution." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19265" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "train encoders to memorize concepts as many as possible, e.g., DeCLIP [24] explores widespread supervision from given image-text pairs, and SLIP [25] introduces self-supervised learning which helps encoders learn better visual representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 335 + ], + "type": "text", + "content": "In this paper, we propose a novel and efficient way to make use of image-text pairs. We sample part of image-text data as a hold-out reference set. Given an input image, our model first retrieves similar images from the reference set with an unsupervised pre-trained image retrieval model, then we use the relationship between retrieved images and texts to augment the representation of input image. A heuristic explanation of the idea is that, it can be considered as an open-book exam: our model doesn't have to memorize all visual concepts in the training data, but learns to recognize visual concepts with the help of a cheat sheet (i.e., the reference set). We propose a framework called Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP) to implement this idea. Although using the same amount of image-text data with the vanilla CLIP, RA-CLIP achieves better zero-shot classification performance and linear probe classification performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 336, + 192, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 336, + 192, + 346 + ], + "spans": [ + { + "bbox": [ + 59, + 336, + 192, + 346 + ], + "type": "text", + "content": "Our contributions are three-fold:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 357, + 287, + 590 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 57, + 357, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 357, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 57, + 357, + 287, + 440 + ], + "type": "text", + "content": "- For contrastive language-image pre-training (CLIP), we present a novel and efficient utilization of image-text pairs. Concretely, we construct a hold-out reference set composed by image-text pairs. Given an input image, we find relevant image-text pairs and use them to help us build better representation for the input image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 450, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 450, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 57, + 450, + 287, + 521 + ], + "type": "text", + "content": "- We propose Retrieval Augmented Contrastive Language-Image Pre-training (RA-CLIP), a framework to implement the idea described above. We conduct comprehensive experiments to validate the effectiveness of each block. Visualization results are also provided to explain how RA-CLIP works." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 531, + 286, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 531, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 57, + 531, + 286, + 590 + ], + "type": "text", + "content": "- We compare the proposed RA-CLIP with previous methods on a dozen of commonly used visual recognition benchmarks. Experimental results show that our proposed method significantly outperforms vanilla CLIP baseline and other recently proposed methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 603, + 133, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 133, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 133, + 615 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 623, + 265, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 265, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 265, + 635 + ], + "type": "text", + "content": "2.1. Contrastive Language Image Pre-training" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "CLIP [29] introduces a new paradigm for visual representation learning. Given image-text pairs as training data, CLIP learns a visual encoder and a textual encoder to align images and text sentences. Different from previous visual recognition system which can only recognize categories specified by the training set, CLIP can be flexibly" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "transferred to new categories. Given new categories, CLIP extends them into text sentences and feed them into the text encoder to obtain categories embeddings. Experimental results show that CLIP can match the accuracy of ImageNet trained ResNet50, even that CLIP didn't use any of the 1.28 million training examples of ImageNet during pre-training. Despite the impressive transfer performance, CLIP is quite data-hungry, it needs tens of millions or more image-text pairs for pre-training [1, 18, 29, 41, 42]. To decrease the amount of training data, recent works [24, 25] try to introduce as much as supervision from existing datasets to help CLIP train better encoders." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 220, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 340 + ], + "type": "text", + "content": "In this paper, we propose a novel and efficient methods to make better use of image-text pairs. Different from previous methods that only use image-text pairs to train encoders, we also use them to construct a reference set which can provide supplementary information for the encoder. Given an input image, we find relevant images along with their text descriptions from the reference set, these image-text pairs contain information that can help us describe the input image, thus we use them to augment original CLIP's image representation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "type": "text", + "content": "2.2. Knowledge-Enhanced Models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 382, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 537 + ], + "type": "text", + "content": "Structured external knowledge has also been included to improve the zero-shot performance, K-Lite [33] enriches entities in natural language with WordNet and Wiktionary, the motivation is straightforward, some concepts like \"zebra\" may have less training example in the training set, by introducing a knowledge base, \"zebra\" can be extended to a more general description: \"Zebras are African equines with distinctive black-and-white striped coats\". CLIP-event [23] also introduces structured external knowledge to construct hard negative text descriptions for images during training. ASIF [26] builds a relative representation for image and text respectively and aligns image modality and text modality with image-text pairs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 542, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 649 + ], + "type": "text", + "content": "Recently large language models have shown impressive zero-shot and few-shot performance on various downstream NLP tasks, massive parameters have to be introduced to encode the knowledge that will be used. Previous works Atlas [17] and RETRO [2] introduce an external non-parametric knowledge base to store the information, which significantly reduces the parameters of their model, e.g., Atlas outperforms a 540B model with " + }, + { + "bbox": [ + 304, + 542, + 545, + 649 + ], + "type": "inline_equation", + "content": "50 \\times" + }, + { + "bbox": [ + 304, + 542, + 545, + 649 + ], + "type": "text", + "content": " fewer parameters." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "The methods mentioned above mainly focus on providing more information for individual modalities. Different from them, we utilize the correspondence between imagetext pairs in the reference set, which helps us align visual concepts and textual concepts." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19266" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 531, + 255 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 531, + 255 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 531, + 255 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 531, + 255 + ], + "type": "image", + "image_path": "df2450e9ef9d0c9f22dab9e15eeab6f0588f0df001a99ebf27f77fa6ac3a429c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 265, + 547, + 300 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 547, + 300 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed RA-CLIP. Given an input image, RA-CLIP retrieves K most similar image-text pairs from the reference set, which provide informative descriptions for the input image, thus we feed them into the Retrieval Augmented Module (RAM) to enrich the representation of input image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 308, + 207, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 207, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 207, + 322 + ], + "type": "text", + "content": "2.3. Zero-shot Visual Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "type": "text", + "content": "Zero-shot visual recognition can be categorized into two generations: the traditional class-level zero-shot setting and recently popular task-level zero-shot setting [33]. The traditional class-level zero-shot aims at recognizing objects that belong to categories that are not included in the training set. The task-level zero-shot like CLIP [29] is more practical in real-world applications, the model is trained by hundreds of millions of image-text pairs and is directly evaluated on image classification task, by prompting category names into sentence descriptions [1, 18, 29, 41, 42]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 522 + ], + "type": "text", + "content": "Memorizing visual and textual concepts for down-stream zero-shot tasks usually requires lots of image-text pairs. In this paper, we propose that, besides using image-text pairs to train image encoder and text encoder, we can also introduce a reference set to help the model align visual concepts and textual concepts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 536, + 103, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 103, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 103, + 548 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "In this section, we present the details of our proposed Retrieval Augmented Language Image Pre-training (RA-CLIP). An overview of RA-CLIP is summarized in Figure 2. Given " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " image-text pairs " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i,T_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " as training data, where " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "-th image in the dataset and " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " is its corresponding text description. Different from previous Contrastive Language Image Pre-training (CLIP) method that only uses " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i,T_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " to train encoders, we propose a novel utilization of the image-text pairs. Specifically, we split " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i,T_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " into two disjoint sets: training set " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " and reference set " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " as input image, we first feed it into the image encoder to obtain the initial image embedding " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", following previous method CLIP. After that," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": "we retrieve " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " most similar images " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^I\\}_{k = 1}^K" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " as well as their corresponding text sentences " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^T\\}_{k = 1}^K" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^I\\}_{k = 1}^K" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^T\\}_{k = 1}^K" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " provide informative description for " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": ", so we use them to augment " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": " by a proposed Retrieval Augmented Module (RAM). The augmented image embedding is output as " + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i'" + }, + { + "bbox": [ + 305, + 308, + 547, + 392 + ], + "type": "text", + "content": ". The text branch of RA-CLIP is like the one of CLIP." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 405, + 457, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 457, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 457, + 417 + ], + "type": "text", + "content": "3.1. Dual-Encoder Architecture" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": "The dual-encoder architecture consists of an image encoder and a text encoder. The image encoder used in our experiments is a Vision Transformer [12]. Given an image " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": ", we take the embedding of the [CLS] token and normalize it by its L2-norm to obtain the representation of " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": ", which is a " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": "-dimension feature vector " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": ". The text encoder is also a Transformer. Given a sequence of input text " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": ", the text encoder transforms and normalizes " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": " into another " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": "-dimension feature vector " + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_i" + }, + { + "bbox": [ + 305, + 426, + 545, + 535 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 548, + 434, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 434, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 434, + 560 + ], + "type": "text", + "content": "3.2. Overview of RA-CLIP" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Reference Set Construction. Multi-modal image-text pairs naturally establish the connection between images and texts. Different images and text descriptions of the same concept can provide informative description of this concept. Inspired by this observation, we construct the reference set " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " by random sampling 1.6M (about 1/10 amount of our total training data) image-text pairs from original train set. Ablation experiments will show that commonly used image-text datasets such as YFCC [35], CC12M [5] and LAION [32] can be used as reference data. We also exploit how the amount of image-text pairs effect the final performance. Please refer to Section 4.2.2 for more details." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19267" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": "Reference Image-Text Retrieval. Given an input image " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": ", RA-CLIP retrieves " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " most similar images " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^I\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " from the reference set as well as their corresponding text descriptions " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^T\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": ". Concretely, we first extract the embeddings of the images in reference set, with an unsupervised pre-trained image encoder (e.g., DINO) for a fairer comparison. This process can be pre-computed offline. Given an input image " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " as query, we also extract the embedding of " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " with the same model, then use the embedding to retrieve " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " most similar images from the reference set. The retrieval process can be conducted efficiently by existing libraries like Faiss [19]. Finally, we get " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^I\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": " and their corresponding text sentences " + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{r}_k^T\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 72, + 289, + 257 + ], + "type": "text", + "content": ", which are sent to the Retrieval Augmented Module (RAM) to obtain augmented image representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "text", + "content": "Retrieval Augmented Module (RAM). We propose a novel Retrieval Augmented Module (RAM), which first extracts the embeddings of each retrieved " + }, + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_k^I" + }, + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_k^T" + }, + { + "bbox": [ + 47, + 258, + 288, + 294 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 138, + 301, + 192, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 301, + 192, + 316 + ], + "spans": [ + { + "bbox": [ + 138, + 301, + 192, + 316 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {k} ^ {I} = \\phi (\\mathbf {r} _ {k} ^ {I}),", + "image_path": "7a45066c231b47a156edb1b5bfa120ebbbe1e896f4a77e019f751dc180637761.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 140, + 315, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 315, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 140, + 315, + 287, + 332 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {k} ^ {T} = \\psi \\left(\\mathbf {r} _ {k} ^ {T}\\right). \\tag {1}", + "image_path": "abd2a980b00f5679ae408504d842c2bb1c42efbd29e073716dacb370652252ac.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 47, + 340, + 287, + 388 + ], + "type": "text", + "content": " are pre-trained uni-modal encoders for image and text respectively. They are frozen during the training stage, so Equation 1 can be pre-computed before training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "text", + "content": "After that, RAM uses " + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{e}_k^I\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{e}_k^T\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "text", + "content": " to augment " + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 47, + 388, + 287, + 445 + ], + "type": "text", + "content": ". 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The aggregated text embedding " + }, + { + "bbox": [ + 47, + 479, + 287, + 522 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^T" + }, + { + "bbox": [ + 47, + 479, + 287, + 522 + ], + "type": "text", + "content": " will be used to augment " + }, + { + "bbox": [ + 47, + 479, + 287, + 522 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 47, + 479, + 287, + 522 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "text", + "content": "Likewise, RAM also computes image-augmented embedding " + }, + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^I" + }, + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "text", + "content": " by aggregating " + }, + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{e}_k^I\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 523, + 287, + 550 + ], + "type": "text", + "content": " in a similar way:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 60, + 557, + 287, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 557, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 60, + 557, + 287, + 576 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {i} ^ {I} = M u l t i h e a d A t t n (\\mathbf {v} _ {i}, \\left\\{\\mathbf {e} _ {k} ^ {T} \\right\\} _ {k = 1} ^ {K}, \\left\\{\\mathbf {e} _ {k} ^ {I} \\right\\} _ {k = 1} ^ {K}). \\tag {3}", + "image_path": "16ff30665a030b0d90c6f3909f5069fc8174c19520ab00bf955cd2be454fab45.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 582, + 287, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 595 + ], + "type": "text", + "content": "Finally, RAM outputs the augmented image embedding " + }, + { + "bbox": [ + 47, + 582, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i'" + }, + { + "bbox": [ + 47, + 582, + 287, + 595 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 124, + 604, + 287, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 604, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 124, + 604, + 287, + 619 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {i} ^ {\\prime} = \\mathbf {v} _ {i} + \\mathbf {a} _ {i} ^ {T} + \\mathbf {a} _ {i} ^ {I}, \\tag {4}", + "image_path": "fb63d27e185a918430a0e92f1a8e5c9bda81e969263edbe93af39aa79696384f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 628, + 149, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 149, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 149, + 639 + ], + "type": "text", + "content": "as illustrated in Figure 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 647, + 138, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 138, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 138, + 658 + ], + "type": "text", + "content": "3.3. Loss Function." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "content": "At the training stage, we follow previous contrastive learning methods [29] and use InfoNCE loss [36] to train our framework. Concretely, given a batch of " + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "content": " image-text pairs " + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i, T_i\\}_{i=1}^N" + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "content": " as training data, RA-CLIP produces" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 314, + 72, + 539, + 241 + ], + "blocks": [ + { + "bbox": [ + 314, + 72, + 539, + 241 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 539, + 241 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 539, + 241 + ], + "type": "image", + "image_path": "754ebaea9800a5bab4401e3a1f3e4c0da82fa00ef38838d3bab1fd2440b97b3c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 311, + 251, + 539, + 264 + ], + "lines": [ + { + "bbox": [ + 311, + 251, + 539, + 264 + ], + "spans": [ + { + "bbox": [ + 311, + 251, + 539, + 264 + ], + "type": "text", + "content": "Figure 3. The proposed Retrieval Augmented Module (RAM)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "text", + "content": "the augmented image embeddings and the text embeddings: " + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{v}_i',\\mathbf{t}_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "text", + "content": " , then we compute text-to-image contrastive loss " + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{t2v}" + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "text", + "content": " and image-to-text contrastive loss " + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{v2t}" + }, + { + "bbox": [ + 306, + 276, + 545, + 312 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 343, + 321, + 545, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 321, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 343, + 321, + 545, + 352 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v 2 t} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {i} ^ {\\prime}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {t} _ {i} , \\mathbf {v} _ {j} ^ {\\prime}\\right) / \\tau\\right)}\\right), \\tag {5}", + "image_path": "0b2c31356e371b20fc65f7992ed2f7d7dbfbaf1663d53dffe6598c986ae08bb8.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 343, + 360, + 545, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 360, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 343, + 360, + 545, + 390 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t 2 v} = - \\log \\left(\\frac {\\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {i}\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\sigma \\left(\\mathbf {v} _ {i} ^ {\\prime} , \\mathbf {t} _ {j}\\right) / \\tau\\right)}\\right), \\tag {6}", + "image_path": "20339d60687c8b698c6ca2095dd0c87fb689dd157400ead19184e20cbb3a0026.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " is the batch size, and " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " is a temperature factor, which is initialized as 0.07 and trained end-to-end. " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " computes the cosine similarity between two vectors. The total loss of our framework is:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 388, + 454, + 545, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 454, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 388, + 454, + 545, + 466 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {t 2 v} + \\mathcal {L} _ {v 2 t}. \\tag {7}", + "image_path": "76c1b94ded36d9433002f0669503a6eed56577754c4e734d9add07ffcafcfb4c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 501, + 382, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 382, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 382, + 514 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "content": "Following previous works [24, 25, 39], we pre-train our framework on YFCC dataset [35], then evaluate the performance of zero-shot classification and linear probe classification on commonly used visual recognition benchmarks. Besides that, we also follow RegionCLIP [43] and evaluate the zero-shot ROI classification performance on two widely used object detection datasets, i.e., MS COCO [7] and LVIS [15]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We first describe the implementation details in Section 4.1, including datasets, evaluation metrics, model architecture and optimization details. Then we conduct ablation experiments in Section 4.2 to validate the effectiveness of our proposed method and analyse the effectiveness of each component. Finally, we compare our proposed method with recently proposed CLIP variants like MS-CLIP [39], DeCLIP [24] and SLIP [25] in Section 4.3." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19268" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 91, + 531, + 209 + ], + "blocks": [ + { + "bbox": [ + 173, + 71, + 420, + 82 + ], + "lines": [ + { + "bbox": [ + 173, + 71, + 420, + 82 + ], + "spans": [ + { + "bbox": [ + 173, + 71, + 420, + 82 + ], + "type": "text", + "content": "Table 1. Ablation experiments on zero-shot ImageNet classification." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 91, + 531, + 209 + ], + "lines": [ + { + "bbox": [ + 61, + 91, + 531, + 209 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 531, + 209 + ], + "type": "table", + "html": "
IDMethodInit. of Image Enc.Init. of Text Enc.Pretrain DatasetReference DatasetφψImageNet Top-1
1CLIPViT rand.BERTYFCC×××37.7
2CLIPDINO-SSentenceTYFCC×××21.0
3CLIPViT IN1KBERTYFCC×××46.1
4CLIPViT rand.BERTYFCC+CC×××42.1
5RA-CLIPViT rand.BERTYFCCYFCCSentenceTDINO-S53.5
6RA-CLIPViT rand.BERTYFCCCCSentenceTDINO-S54.5
7RA-CLIPViT rand.BERTYFCCLAIONSentenceTDINO-S54.2
8RA-CLIPViT rand.BERTYFCCCCText EncoderDINO-S54.4
", + "image_path": "613bcbf5148904dde7b1bf82886a6258a41a5766d54b2a431a42e55da2614918.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 228, + 180, + 242 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 180, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 180, + 242 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 288, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 288, + 491 + ], + "type": "text", + "content": "Dataset All the experiments are conducted on public available datasets. For a fair comparison, we follow previous works [24, 25, 39] and use YFCC [35] for pretraining. We follow CLIP [29] and use the 15 million English subset of YFCC for pre-training. For the reference set used in our framework, we test three different image-text datasets, including the YFCC15M described above, CC12M [5] and LAION [32]. By default, we random sample 1,600,000 image-text pairs (about 1/10 amount of our pre-train dataset) from corresponding dataset to construct the reference set. 10 widely used visual recognition datasets are used to evaluate the zero-shot classification performance and linear probe classification performance, including ImageNet [10], ImageNet V2 [30], CIFAR 10 [21], CIFAR 100 [21], Caltech 101 [13], Oxford Pets [27], SUN397 [38], Food 101 [3], DTD [8] and Stanford Dogs [20]. Following RegionCLIP [43], two object detection datasets are used to evaluate the zero-shot ROI classification performance, i.e., COCO [7] and LVIS [15]. More details about the datasets can be found in our supplement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 494, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 287, + 567 + ], + "type": "text", + "content": "Metrics The metrics used to evaluate image classification on all datasets are top-1 accuracy except for Oxford Pets, and Caltech101, which are measured by mean accuracy over classes as in CLIP [29]. The evaluation metric for COCO and LVIS is box Average Precision (AP) as used in RegionCLIP [43]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Architecture By default, the image encoder is a random initialized ViT-B/32 [12], which has 12 layers of Transformer blocks. Each Transformer block has 12 attention heads and the hidden size is set to 768. The text encoder is BERT-base [11], which shares similar scale with the image encoder, i.e., 12 layers of Transformer blocks, 12 attention heads in each Transformer block and 768 hidden size. We also try smaller text encoder from scratch while comparing with previous state-of-the-arts in Section 4.3. The output of the text encoder and image encoder are projected to 384-dim by linear projection. We adopt DINO-S/8 [4] as the image retriever and the uni-modal image encoder " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "text", + "content": "described in Section 3.2, which is pre-trained on ImageNet 1K [10] with self-supervised method. Meanwhile, we adopt Sentence Transformer (SentenceT) [31] as the uni-modal text encoder " + }, + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "text", + "content": ", which is a 6-layer Transformer. For our proposed Retrieval Augmented Module (RAM), we use 6 layers of cross-attention blocks. We truncate the input text tokens so that they have a maximum length of 77. The input image is resized to " + }, + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 229, + 547, + 324 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "text", + "content": "Optimization We implement our framework with PyTorch [28]. All pre-training experiments are conducted on 8 NVIDIA Tesla A100 GPUs. Batch size is set to 4096. The framework is trained for 32 epochs with LAMB optimizer [40] and an initial learning rate of " + }, + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "inline_equation", + "content": "2.5\\mathrm{e - }3" + }, + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "text", + "content": ". The learning rate follows a cosine decay schedule with 5 epochs of linear warm-up. Weight decay is set to 0.2. For data augmentation, we random crop a " + }, + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "inline_equation", + "content": "224\\times 224" + }, + { + "bbox": [ + 304, + 326, + 547, + 482 + ], + "type": "text", + "content": " patch from the input image, then conduct random horizontal flip, random color distortions, random gaussian blur and RandAugment [9], following previous works [6, 24, 25]. Training details of down-stream tasks (e.g., linear probe classification) can be found in our supplement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 491, + 400, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 400, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 400, + 503 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "text", + "content": "In this section, we first validate the effectiveness of our proposed method by comparing RA-CLIP and CLIP trained on the same dataset. After that, we build reference sets by sampling image-text pairs from different datasets (YFCC, CC or LAION) and sampling different amounts of image-text pairs from the same dataset to see if the reference set is sensitive to these two factors. Since we introduce pre-trained DINO-S/8 (" + }, + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "text", + "content": " in Section 3.2) and SentenceT (" + }, + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 509, + 547, + 653 + ], + "type": "text", + "content": " in Section 3.2) to extract reference embeddings, we also discuss how these models effect the final performance. At last, ablation experiments with different K-value and different design choices of RAM are provided." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 670, + 541, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 541, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 541, + 682 + ], + "type": "text", + "content": "4.2.1 Effectiveness of the Retrieval Augmented CLIP" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of our proposed method, we train and test CLIP and RA-CLIP with the same dataset." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19269" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 76, + 258, + 190 + ], + "blocks": [ + { + "bbox": [ + 75, + 76, + 258, + 190 + ], + "lines": [ + { + "bbox": [ + 75, + 76, + 258, + 190 + ], + "spans": [ + { + "bbox": [ + 75, + 76, + 258, + 190 + ], + "type": "image", + "image_path": "151efcc3388e6f6cb4c1db8dc93634b9d759e47a7e125f015daeca8f3bf2ce69.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 202, + 288, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 288, + 236 + ], + "type": "text", + "content": "Figure 4. Zero-shot classification performance of RA-CLIP with different amounts of reference data. Five different scales of reference sets are used, i.e., 1K, 10K, 100K, 1.6M, and 10M." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 365 + ], + "type": "text", + "content": "For CLIP, we use YFCC15M for pre-training, and evaluate the zero-shot performance on ImageNet. For RA-CLIP, we random sample 1.6 million image-text pairs (about 1/10 amount of entire dataset) from YFCC15M to construct the reference set, and use the other 13 million image-text pairs for training. Experimental results can be found in Table 1, RA-CLIP (experiment ID 5) outperforms CLIP (experiment ID 1) by a large margin (53.5% vs 37.7%), which validates the effectiveness of RA-CLIP." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 366, + 288, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 288, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 288, + 558 + ], + "type": "text", + "content": "We provide a heuristic explanation for this comparison. The pipeline of training and testing CLIP may be considered as a closed-book exam. In the training stage, CLIP trains encoders to learn visual and textual concepts in the training data. In the testing stage, given a test query image, CLIP may return a false prediction if it didn't memorize related concepts of the test image. Different from CLIP, the training and testing of RA-CLIP can be considered as an open-book exam. In the training stage, RA-CLIP doesn't have to memorize all concepts in the training data, but learns how to recognize an image with a help of a cheat-sheet (i.e., the reference set). In the testing stage, given a test query image, RA-CLIP can look up the cheat-sheet (i.e., the reference set) and finds related knowledge about the query image, then uses the knowledge to enrich the representation of input image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 255, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 255, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 255, + 586 + ], + "type": "text", + "content": "4.2.2 Different image-text data as reference set" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 641 + ], + "type": "text", + "content": "Since the reference set is the core component of RA-CLIP, we then analyse if RA-CLIP provides significant improvements while using different datasets or different amounts of image-text pairs as reference sets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 712 + ], + "type": "text", + "content": "Different dataset as reference set. We adopt another two widely used datasets to construct the reference set, i.e., CC12M and LAION. We sample 1.6 million image-text pairs from CC12M to construct the reference set, and use YFCC15M for RA-CLIP pre-training. We also train CLIP on the combination of the reference set and YFCC15M." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 310, + 113, + 541, + 216 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 104 + ], + "type": "text", + "content": "Table 2. Different design choices of Retrieval Augmented Module (RAM). All models are trained on YFCC15M with CC1.6M as reference set and evaluated on zero-shot ImageNet classification." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 113, + 541, + 216 + ], + "lines": [ + { + "bbox": [ + 310, + 113, + 541, + 216 + ], + "spans": [ + { + "bbox": [ + 310, + 113, + 541, + 216 + ], + "type": "table", + "html": "
MethodAugment ImageAugment TextFusion TypeKImageNet Top-1
RAM✓XaiT6452.1
RAM✓XaiT + aiI6451.8
RAM✓XaiT + aiI + vi6454.5
RAM✓XaiT + aiI + vi1654.3
RAM✓XaiT + aiI + vi12853.9
RAM✓✓aiT + aiI + vi6453.1
", + "image_path": "46c29975b2eaed116e95511a45dfea0937e800ea582b194988eb6fe47d808600.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 236, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 344 + ], + "type": "text", + "content": "By comparing experiment 6 and experiment 4 in Table 1, we can see that RA-CLIP still outperforms CLIP with significant improvement(54.5% v.s. 42.1%). We then conduct similar experiments with 1.6 million image-text pairs from LAION as reference set, which achieves 54.2% top-1 accuracy on ImageNet. Experiments above show that the commonly used datasets like YFCC15M, CC12M, LAION can be used as reference set and provide similar performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 345, + 546, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 546, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 546, + 476 + ], + "type": "text", + "content": "Different amounts of reference data. We then test the performance of reference sets with different amounts of image-text pairs. 5 reference sets are constructed by sample 1K, 10K, 100K, 1.6M, 10M image-text pairs from CC12M. YFCC15M is used as training data. The performance of RA-CLIP with these 5 different reference sets is illustrated in Figure 4. We can see that introducing more image-text pairs as reference set usually brings better performance. Since the horizontal axis of Figure 4 is plotted in log-space, we can conclude that performance is getting saturated while introducing more image-text pairs as reference set." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 491, + 533, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 533, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 533, + 503 + ], + "type": "text", + "content": "4.2.3 Ablation of pre-trained SentenceT and DINO" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "content": "Two frozen pre-trained uni-modal encoders are introduced in RA-CLIP to process image-text data of the reference set: SentenceT and DINO-S/8. It is necessary for us to show if the improvement described above is brought by these two encoders. We re-implement CLIP with frozen SentenceT as text encoder and frozen DINO-S/8 as image encoder, linear projection layer is appended after each encoder to obtain final embeddings. We train the CLIP model on YFCC15M, the zero-shot classification performance on ImageNet is " + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "inline_equation", + "content": "21.0\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "content": ", referred as experiment 2 in Table 1, which is significantly lower than CLIP baseline (experiment 1). Experimental results show that although the pre-trained SentenceT and DINO-S provide promising results on uni-modal tasks, they provide poor performance on multi-modal alignment task." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We also prove that, SentenceT is not necessary for our final performance. We re-implemented RA-CLIP by" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19270" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 102, + 544, + 267 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 3. Zero-shot image classification performance and linear probe classification performance on 10 downstream datasets (\\%). RA-CLIP* denotes the model that trains a text encoder with width = 512 and head = 8 from scratch." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 102, + 544, + 267 + ], + "lines": [ + { + "bbox": [ + 49, + 102, + 544, + 267 + ], + "spans": [ + { + "bbox": [ + 49, + 102, + 544, + 267 + ], + "type": "table", + "html": "
Evaluation TypeMethodImageNetImageNetV2PetsCIFAR10CIFAR100SUN397Food101Caltech101DTDDogsAvg.
Zero-shotK-Lite [33]45.3----------
CLIP [29]37.732.816.176.048.650.821.869.828.311.139.3
MS-CLIP [39]36.730.2-------5.6-
SLIP [25]38.333.328.372.245.345.144.765.921.811.840.7
DeCLIP [24]43.236.130.272.139.751.646.970.124.211.742.6
RA-CLIP*51.245.450.589.461.845.743.976.124.622.051.1
RA-CLIP53.547.249.089.462.346.543.876.925.626.152.0
Linear probeCLIP [29]63.551.369.891.774.164.769.184.966.550.568.6
MS-CLIP [39]68.149.862.187.266.771.776.081.669.446.167.9
SLIP [25]68.152.175.490.575.373.577.187.271.152.672.3
DeCLIP [24]69.253.176.588.671.675.979.388.069.149.972.1
RA-CLIP*73.362.388.294.978.460.765.586.865.575.575.1
RA-CLIP72.961.988.295.278.961.166.587.266.676.075.5
", + "image_path": "ae07675e5d9cb8f2f0fa3edae297a2c1c8b8f6d44920438c8db3c2804bcb5a13.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 285, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 405 + ], + "type": "text", + "content": "replacing SentenceT with the text encoder of RA-CLIP, the zero-shot performance on ImageNet is " + }, + { + "bbox": [ + 46, + 285, + 287, + 405 + ], + "type": "inline_equation", + "content": "54.4\\%" + }, + { + "bbox": [ + 46, + 285, + 287, + 405 + ], + "type": "text", + "content": " (experiment 8), which is comparable with the one used SentenceT (experiment 6). We also note that, although replacing SentenceT with the text encoder of RA-CLIP can provide similar performance, the text encoder of RA-CLIP is trained end-to-end, thus the embeddings of the reference text cannot be pre-computed off-line before training, which introduces more computation cost. So we use SentenceT by default." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 405, + 288, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 288, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 288, + 586 + ], + "type": "text", + "content": "DINO-S/8 in Section 3.2 uses ImageNet 1K for self-supervised learning, extracting reference images on-the-fly during training with the image encoder is much more time-consuming due to the time of reading, pre-processing and extracting images. So we test if CLIP can achieve comparable or better performance than RA-CLIP if it uses ImageNet data for pre-training. Concretely, we use the ViT-B/32 pre-trained on ImageNet 21K and fine-tuned on ImageNet-1K to initialize the image encoder of CLIP. Then train the CLIP on YFCC15M, the classification performance is referred as experiment 3 in Table 1. Initializing the image encoder by ImageNet pre-trained model brings significant improvements (46.1% v.s. 37.7%). However, it is not zero-shot evaluation anymore. We can see that RA-CLIP (53.5%) still outperforms this strong CLIP baseline." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 599, + 280, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 280, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 280, + 612 + ], + "type": "text", + "content": "4.2.4 Different hyper-parameters and design choices" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "content": "Different K-value in retrieval process. We train RA-CLIP by retrieving different amounts " + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "inline_equation", + "content": "(K = 16, 64, 128)" + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "content": " of image-text pairs from the reference set for each query image. Experimental results are shown in row 3, 4 and 5 of Table 2. RA-CLIP provides stable performance with different " + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "content": " values, and the model with " + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "inline_equation", + "content": "K = 64" + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "content": " performs slightly better than the others." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "content": "Different design choices of RAM architecture. We" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": "further test different design choices of RAM architecture in Table 2. Firstly, we take " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^T" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " as the final augmented representation. In this case, RAM gathers related information from the reference texts and produces final embedding, the result is " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "52.1\\%" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": ". After that, we fuse " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^T" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^I" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": ", which provides similar performance " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "(51.8\\%)" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": ". Finally, we take " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i^T + \\mathbf{a}_i^I + \\mathbf{v}_i" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " as the final image embedding to fuse information from original image encoder and the reference data, which performs best " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "(54.5\\%)" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " among the three different variants as expected." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 406, + 546, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 546, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 546, + 526 + ], + "type": "text", + "content": "Augment both image and text representation. Since experiments above have validated the effectiveness of RA-CLIP, a straightforward question is: will this idea improve CLIP's text representation? To validate that, we use SentenceT to retrieve relevant image-text pairs for input text sentence, then apply similar augmentation to the text embedding. However, it leads to a slightly worse performance " + }, + { + "bbox": [ + 304, + 406, + 546, + 526 + ], + "type": "inline_equation", + "content": "53.1\\%" + }, + { + "bbox": [ + 304, + 406, + 546, + 526 + ], + "type": "text", + "content": " as shown in Table 2. We conjecture that text sentence is less informative and the retrieved image-text pairs are more diverse and may not bring correct information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 536, + 391, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 391, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 391, + 549 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "text", + "content": "In this section, we compare RA-CLIP with CLIP and recently proposed CLIP-variant on two down-stream visual recognition tasks: zero-shot image classification and linear probe image classification. Evaluations are conducted on 10 widely used visual recognition benchmarks. Note that some previous works (e.g., DeCLIP [24]) train a text encoder with width " + }, + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "inline_equation", + "content": "= 512" + }, + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "text", + "content": " and head " + }, + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "inline_equation", + "content": "= 8" + }, + { + "bbox": [ + 304, + 556, + 545, + 688 + ], + "type": "text", + "content": " from scratch, thus we follow them and re-implemented the RA-CLIP for a fair comparison, the results are denoted as RA-CLIP*. Besides that, we also follow RegionCLIP to evaluate the zero-shot ROI classification performance on MS COCO and LVIS." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Zero-shot image classification Previous methods usually take YFCC15M or its augmented version as train set." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19271" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 75, + 519, + 292 + ], + "blocks": [ + { + "bbox": [ + 77, + 75, + 519, + 292 + ], + "lines": [ + { + "bbox": [ + 77, + 75, + 519, + 292 + ], + "spans": [ + { + "bbox": [ + 77, + 75, + 519, + 292 + ], + "type": "image", + "image_path": "9d056aa6013eb86d398328169bdb8176ff6c2f42886549f7ae5cc3fefe832809.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 303, + 532, + 316 + ], + "lines": [ + { + "bbox": [ + 59, + 303, + 532, + 316 + ], + "spans": [ + { + "bbox": [ + 59, + 303, + 532, + 316 + ], + "type": "text", + "content": "Figure 5. Case study for RA-CLIP in image classification. The retrieved images and texts enrich the representation of input image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 354, + 287, + 407 + ], + "blocks": [ + { + "bbox": [ + 52, + 334, + 281, + 345 + ], + "lines": [ + { + "bbox": [ + 52, + 334, + 281, + 345 + ], + "spans": [ + { + "bbox": [ + 52, + 334, + 281, + 345 + ], + "type": "text", + "content": "Table 4. Zero-shot ROI classification on COCO and LVIS (%)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 354, + 287, + 407 + ], + "lines": [ + { + "bbox": [ + 48, + 354, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 48, + 354, + 287, + 407 + ], + "type": "table", + "html": "
MethodLVISCOCO
APAPsAPmAPIAPAPsAPmAPI
Regin CLIP21.68.731.045.744.421.951.061.8
Region RA-CLIP23.210.934.244.948.429.357.961.9
", + "image_path": "7950bb3e1af5af99c2ffd8ddfa095e66105fedbb3b35f63352667e68d5a1c832.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 432, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 516 + ], + "type": "text", + "content": "We thus random sample 1.6M image-text from YFCC15M as reference set, and use the other 13M image-text pairs as train set. We report the performance of RA-CLIP on all 10 datasets as well as the results of previous methods CLIP [29], K-lite [33], SLIP [25], DeCLIP [24] and MS-CLIP [39] shown in Table 3. RA-CLIP shows superior performance than previous state-of-the-art methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "content": "We also compare with OpenAI's CLIP model trained on 400 million image-text pairs. To reduce the training cost, we use OpenAI's CLIP-B/32 to initialize the image encoder, text encoders, " + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "content": " of RA-CLIP, then freeze them and train the other modules on YFCC15M. The model achieves " + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "inline_equation", + "content": "68.2\\%" + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "content": " top-1 accuracy on ImageNet, significantly better than OpenAI's CLIP-B/32 (63.3%)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 604, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 663 + ], + "type": "text", + "content": "In Figure 5, we also provide some visualization to help us understand how RA-CLIP works. The image-text pairs retrieved from the reference set can introduce additional important information that can help RA-CLIP make correct predictions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Linear probe image classification Following previous methods, we also conduct linear probe image classification experiments to test the transferability of the learned image representation. We fix the pre-trained image encoder of our" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "content": "trained CLIP and RA-CLIP, then train a linear classifier to conduct image classification on down-stream datasets. Experimental results are shown in Table 3. RA-CLIP achieves better performance than previous methods CLIP, MS-CLIP, SLIP and DeCLIP, bringing " + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "content": " (75.1% v.s. " + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "inline_equation", + "content": "72.3\\%" + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "content": ") averaged improvements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 408, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 545, + 493 + ], + "type": "text", + "content": "Zero-shot ROI classification Following previous work RegionCLIP [43], we transfer the proposed RA-CLIP to object detection task on COCO [7] and LVIS [15] datasets to test the performance of ROI classification. Following RegionCLIP [43], we use ground-truth bounding boxes as region proposals, then apply RA-CLIP and CLIP to classify the proposals, following a RCNN [14] pipeline." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "text", + "content": "We report results on the validation set of LVIS and COCO in Table 4. We can see that RA-CLIP still outperforms CLIP on these two benchmarks, bringing " + }, + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "text", + "content": " improvement on LVIS and " + }, + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "inline_equation", + "content": "4.0\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 567 + ], + "type": "text", + "content": " improvement on COCO. Note that the proposed RA-CLIP performs much better on small objects and medium objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 582, + 379, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 379, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 379, + 594 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "type": "text", + "content": "In this paper, we propose a novel and efficient utilization of image-text pairs. Different from previous Contrastive Language Image Pre-training methods that only use imagetext pairs to train encoders, we also use image-text pairs to construct a reference set. Given an input image, we find relevant images as well as corresponding texts in the reference set and use them to enrich the representation of the input image. Experiments on zero-shot classification and linear probe classification validate the effectiveness of our methods." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19272" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 201 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 201 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Pattern Recog., pages 16793-16803, 2022. 4, 5, 8" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19274" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_content_list.json b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1e8108ba16e156330080425f0e5ed2d0f2bee66e --- /dev/null +++ b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_content_list.json @@ -0,0 +1,2120 @@ +[ + { + "type": "text", + "text": "REC-MV: REconstructing 3D Dynamic Cloth from Monocular Videos", + "text_level": 1, + "bbox": [ + 130, + 130, + 836, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lingteng Qiu $^{1*}$ Guanying Chen $^{1,2*}$ Jiapeng Zhou $^{1}$ Mutian Xu $^{1}$ Junle Wang $^{3}$ Xiaoguang Han $^{1,2\\dagger}$ $^{1}$ SSE, CUHKSZ $^{2}$ FNii, CUHKSZ $^{3}$ Tencent", + "bbox": [ + 214, + 179, + 753, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstructing dynamic 3D garment surfaces with open boundaries from monocular videos is an important problem as it provides a practical and low-cost solution for clothes digitization. Recent neural rendering methods achieve high-quality dynamic clothed human reconstruction results from monocular video, but these methods cannot separate the garment surface from the body. Moreover, despite existing garment reconstruction methods based on feature curve representation demonstrating impressive results for garment reconstruction from a single image, they struggle to generate temporally consistent surfaces for the video input. To address the above limitations, in this paper, we formulate this task as an optimization problem of 3D garment feature curves and surface reconstruction from monocular video. We introduce a novel approach, called REC-MV, to jointly optimize the explicit feature curves and the implicit signed distance field (SDF) of the garments. Then the open garment meshes can be extracted via garment template registration in the canonical space. Experiments on multiple casually captured datasets show that our approach outperforms existing methods and can produce high-quality dynamic garment surfaces. The source code is available at https://github.com/GAP-LAB-CUHK-SZ/REC-MV.", + "bbox": [ + 73, + 306, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 684, + 207, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "High-fidelity clothes digitization plays an essential role in various human-related vision applications such as virtual shopping, film, and gaming. In our daily life, humans are always in a moving status, driving their clothes to move together. To realize this very common scenario, it is indispensable to gain dynamic garments in real applications. Thanks to the rapid development of mobile devices in terms of digital cameras, processors, and storage, shooting a monocular video in the wild becomes highly convenient and accessible for general customers. In this paper,", + "bbox": [ + 75, + 710, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3b12c49523ed62d8478876006ca4ca2a4bb06d23131e2b5ecaf8d7b907fb2d80.jpg", + "image_caption": [ + "Figure 1. Can we extract dynamic 3D garments from monocular videos? The answer is Yes! By jointly optimizing the dynamic feature curves and garment surface followed by non-rigid template registration, our method can reconstruct high-fidelity and temporally consistent garment meshes with open boundaries." + ], + "image_footnote": [], + "bbox": [ + 504, + 273, + 893, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "our goal is definite – extracting dynamic 3D garments from monocular videos, which is significantly meaningful and valuable for practical applications, but is yet an uncultivated land with many challenges.", + "bbox": [ + 496, + 574, + 892, + 635 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We attempt to seek a new solution to this open problem and start by revisiting existing works from two main-streams. i) Leveraging the success of neural rendering methods [35, 37, 57], several works are able to reconstruct dynamic clothed humans from monocular videos [8, 19, 29, 47, 49], by representing the body surface with an implicit function in the canonical space and apply skinning based deformation for motion modeling. One naive way to achieve our goal is: first to get the clothed human through these methods and separate the garments from human bodies. However, such a separation job requires laborious and non-trivial processing by professional artists, which is neither straightforward nor feasible for general application scenarios. ii) As for garment reconstruction, many methods [5, 10, 20, 61, 62] make it possible to reconstruct high-quality garment meshes from single-view images in the wild. Specifically, ReEF [62] estimates 3D fea", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution.", + "bbox": [ + 63, + 875, + 181, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author: hanxiaoguang@cuhk.edu.cn.", + "bbox": [ + 63, + 887, + 354, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4637", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ture curves* and an implicit surface field [34] for non-rigid garment template registration. Nonetheless, these methods struggle to produce temporally consistent surfaces when taking videos as inputs.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above discussion motivates us to combine the merits of both the dynamic surface modeling in recent neural rendering methods and the explicit curve representation for garment modeling. To this end, we try to delineate a new path towards our goal: optimizing dynamic explicit feature curves and implicit garment surface from monocular videos, to extract temporally consistent garment meshes with open boundaries. We represent the explicit curves and implicit surface in the canonical space with skinning-based motion modeling, and optimize them by 2D supervision automatically extracted from the video (e.g., image intensities, garment masks, and visible feature curves). After that, the open garment meshes can be extracted by a garment template registration in the canonical space (see Fig. 1).", + "bbox": [ + 73, + 155, + 468, + 367 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We strive to probe this path as follows: (1) As a feature curve is a point set whose deformation has a high degree of freedom, directly optimizing the per-point offsets often leads to undesired self-intersection and spike artifacts. To better regularize the deformation of curves, we introduce an intersection-free curve deformation method to maintain the order of feature curves. (2) We optimize the 3D feature curves using 2D projection loss measured by the estimated 2D visible curves, where the key challenge is to accurately compute the visibility of curves. To address this problem, we propose a surface-aware curve visibility estimation method based on the implicit garment surface and z-buffer. (3) To ensure the accuracy of curve visibility estimation during the optimization process, the curves should always be right on the garment surface. We therefore introduce a progressive curve and surface evolution strategy to jointly update the curves and surface while imposing the on-surface regularization for curves.", + "bbox": [ + 73, + 371, + 470, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, the main contributions of this work are:", + "bbox": [ + 96, + 647, + 459, + 662 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce REC-MV, to our best knowledge, the first method to reconstruct dynamic and open loose garments from the monocular video.", + "- We propose a new approach for joint optimization of explicit feature curves and implicit garment surface from monocular video, based on carefully designed intersection-free curve deformation, surface-aware curve visibility estimation, and progressive curve and surface evolution methods.", + "- Extensive evaluations on casually captured monocular videos demonstrate that our method outperforms existing methods." + ], + "bbox": [ + 94, + 669, + 468, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human Reconstruction from Single-view Image. Traditional methods for human reconstruction often adopt a parametric human model (e.g., SMPL [32] or SCAPE [4]) and can only recover a naked 3D body [23, 24]. To increase the surface details, free-form deformations can be applied to the mesh vertices to model small geometry variations caused by the clothing [2, 3, 26, 43, 52].", + "bbox": [ + 496, + 118, + 890, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent methods propose to utilize implicit surface representations [34, 38] to reconstruct 3D clothed human with an arbitrary topology. Specifically, PIFu and PIFuhd [44, 45] extract pixel-aligned spatial features from images as the input for implicit surface function for occupancy prediction. Follow-up methods then integrates 3D-aligned features to improve the results [6, 15-18, 56, 58]. As these methods only consider single-image reconstruction, they cannot produce temporally consistent results for video input.", + "bbox": [ + 496, + 226, + 890, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human Reconstruction from Monocular Video. Inspired by the success of neural rendering methods [35, 37, 57] in scene reconstruction, many methods have been proposed to reconstruct 3D human from sparse-view [31, 41, 53, 55, 60] or monocular [19, 47, 49] videos.", + "bbox": [ + 496, + 366, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Anim-NeRF [8], Neuman [21] and HumanNeRF [49] introduce methods based on neural radiance field (NeRF) [35] to reconstruct an animatable avatar from monocular video. These methods transform a 3D point in the observation space to the canonical space by inverse-skinning, and then perform volume rendering in the canonical space. A-NeRF [47] additionally adopt a skeleton-relative encoding strategy. AvATAR [29] proposes a monocular human volumetric capture method, but requires reconstructing an avatar from multiple 3D scans in advance.", + "bbox": [ + 496, + 443, + 890, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Garment Reconstruction from Images. Reconstructing garment mesh from images enables many applications like virtual try-on and content creation. Existing methods reconstruct the clothing as a separate layer on top of the body [7, 22, 25, 42, 48, 51]. Among them, several methods address the challenging problem of garment reconstruction from single-view image [5, 10, 20, 36, 61, 62]. MGN [5] learns a per-category parametric model from a large-scale clothing dataset. BCNet [20] first reconstructs a coarse template and then refines the surface details with a displacement network. AnchorUDF [59] adopts the unsigned distance field (UDF) [9] to represent the open surface mesh. SMPlicit [10] proposes a generative model to reconstruct layered garments from a single image. DeepFasion3D [61] reconstructs the surface with occupancy network [34] and applies non-rigid ICP to register the clothing template. ReEF [62] registers explicit clothing template to the implicit field learned from pixel-aligned implicit function. However, as these single-image methods do not consider clothing motion, they are not suitable for dynamic gar", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "* feature curves of the garment (e.g., necklines, hemlines) can provide critical cues for determining the shape contours of the garment.", + "bbox": [ + 65, + 875, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4638", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c05b4122433502f378ddbb7982115a06b03ef498cd88d2bd49969a9a1e79e035.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 94, + 264, + 203 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7d369701113cb4dd33ffa847cf85a04375cb6ea4d19f755d9b57901d6f3c36b7.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed REC-MV. (a) Starting from a surface template, we initialize the canonical curves by solving Eq. (3), and apply a handle-based deformation to initialize the canonical implicit surface. (b) Given an $i$ -th frame, canonical curves are deformed to the camera view space to compute the projection loss based on the surface-aware visibility estimation. (c) Similarly, the canonical surface is deform to the camera view to compute the photometric loss by differentiable rendering. The curves and surface are jointly optimized to enable a progressive co-evolution. (d) Last, the open garment meshes can be extracted by template registration in the canonical space." + ], + "image_footnote": [], + "bbox": [ + 267, + 94, + 785, + 316 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/63b369c6a7e6a6a3b610fa82900be97be17607bc792b51bcd366a26ff12d05f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 95, + 888, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ment reconstruction.", + "bbox": [ + 76, + 422, + 215, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Among methods related to garment reconstruction from videos, Li et al. [28] introduce a method to learn physics-aware clothing deformation from monocular videos, but assumes the template scans for the body and clothing are provided [13]. Garment Avatar [14] proposes a multi-view patterned cloth tracking algorithm, requiring the subject to wear clothing with specific patterns. SCARF represents the layered clothing using radiance field [11] on top of the SMPL-X model [40] from monocular video. In contrast, our method first reconstructs the explicit 3D garment curves and surfaces, and then extracts the garment mesh via template registration.", + "bbox": [ + 75, + 438, + 468, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 631, + 168, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a monocular video with $N_{i}$ frames depicting a moving person $\\{I_t|t = 1,\\dots ,N_i\\}$ , REC-MV aims to reconstruct high-fidelity and space-time coherent open garment meshes. This is a challenging problem as it requires a method to simultaneously capture the shape contours, local surface details, and the motion of the garment.", + "bbox": [ + 75, + 656, + 468, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Observing that feature curves (e.g., necklines, hemlines) provide critical cues for determining the shape contours of garment [61] and implicit signed distance function (SDF) can well represent a detailed closed surface [19], we propose to first optimize the explicit 3D feature curves and implicit garment surfaces from the video, and then apply non-rigid clothing template registration to extract the open garment meshes (see Fig. 2).", + "bbox": [ + 75, + 747, + 470, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preprocessing. We generate the initial shape parameter $\\beta$ , camera intrinsic $\\pi$ , and per-frame SMPL [32] pose param", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "eters $\\{\\pmb {\\theta}_t|t = 1,\\dots ,N_i\\}$ using Videoavatar [3]. To identify the garment regions in 2D images, we apply the existing garment parsing method [27] to estimate the garment masks. Our method also requires 2D visible curves $\\zeta =$ $\\{\\zeta_{l,t}|l = 1,\\ldots N_l,t = 1,\\ldots ,N_i\\}$ for 3D curve recovery, where $N_{l}$ denotes the number of curves. Note that the 2D visible curves can be automatically produced by parsing boundaries of the garment mask (more details in the supplementary material).", + "bbox": [ + 496, + 422, + 893, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. To utilize the information that exists in the entire video for dynamic garment reconstruction, we represent the explicit feature curve and implicit garment surface in the canonical space (Sec. 3.1). For a specific time step, we adopt the skeleton-based skinning and non-rigid deformation modeling to map the canonical curves and surfaces to the camera view space (Sec. 3.2). As the given 2D curves only contain visible points, to optimize the 3D feature curves from 2D projection error, we propose a surface-aware approach to compute the visibility of the 3D feature curve based on z-buffer (Sec. 3.3). In terms of implicit surface optimization, we minimize the photometric loss between the rendered and input image based on the differentiable surface rendering technique (Sec. 3.4). Then the adopted loss functions for joint optimization of curves and surfaces are described (Sec. 3.5). Last, the open garment meshes can be extracted by registering an explicit garment template to the recovered curves and implicit surfaces in the canonical space (more details in the supplementary material). Then the garment meshes can be deformed based on the SMPL poses.", + "bbox": [ + 496, + 583, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4639", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Feature Curve and Surface Representation", + "text_level": 1, + "bbox": [ + 76, + 90, + 442, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explicit Surface Template. Following DeepFashion3D [61], we employ several surface templates, each contains a pre-defined set of 3D feature curves $\\mathbf{L} = \\{\\mathbf{L}_i | i = 1, \\dots, N_l\\}$ extracted from the garment boundaries, where $N_l$ is the number of feature curves (see our supplementary materials for more details). The surface templates will be used for garment surface initialization and the pre-defined feature curves will be used for curve initialization†.", + "bbox": [ + 76, + 116, + 468, + 238 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intersection-free Curve Deformation. A straightforward idea is to represent a feature curve as a discrete point set, and directly estimate the 3D deformation offset for each point during optimization. However, this unstructured curve representation struggles to maintain the order of the points and often generate spike artifacts due to the high degree of freedom of the deformation.", + "bbox": [ + 75, + 241, + 470, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address this issue, we introduce a novel intersection-free curve deformation method, in which the point's deformation at each step is controlled by the curve center and two orthogonal directions (see Fig. 3 for illustration). Formally, given a curve $\\mathcal{C}$ of $N_{p}$ points with center $\\mathbf{p_c}$ , the updated position of $i$ -th point $\\mathcal{C}(i)$ is defined as", + "bbox": [ + 75, + 348, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} ^ {\\prime} (i) = \\mathbf {p} _ {\\mathbf {c}} + S _ {i} ^ {d} \\mathbf {n} _ {\\mathbf {i}} ^ {\\mathbf {d}} + S _ {i} ^ {c} \\mathbf {n} ^ {\\mathbf {c}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 452, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{n_i^d}$ is the direction from the curve center to the current point $\\mathcal{C}(i)$ , and $\\mathbf{n}^{\\mathbf{c}} = \\frac{1}{N_p - 1}\\sum_{i = 1}^{N_p}(\\mathbf{n_i^d}\\times \\mathbf{n_{i - 1}^d})$ is the direction perpendicular to the current feature curve plane. $S_{i}^{d}\\in \\mathbb{R}$ and $S_{i}^{c}\\in \\mathbb{R}$ are learnable parameters specifying the step size of the deformation.", + "bbox": [ + 76, + 484, + 468, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed intersection-free curve deformation can well preserve the order of points in the curve, which largely reduced the difficulty of optimization compared to the direct offset estimation approach.", + "bbox": [ + 76, + 566, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implicit SDF in Canonical Space. Unsigned distance field (UDF) [9] is an implicit function that can represent an open surface. However, as UDF is not differentiable at points close to the surface, it is non-trivial to integrate UDF with differentiable surface rendering to take advantage of supervision from 2D photometric loss. We therefore adopt the SDF to represent a closed garment surface for surface geometry recovery, followed by garment template registration to extract the open surface.", + "bbox": [ + 75, + 630, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is common to represent the whole surface with a single SDF for human reconstruction [19]. However, as our goal is to reconstruct separate clothes, using a single SDF to represent both the upper clothes and bottom clothes (e.g., skirt) increases the difficulty of template registration (i.e., splitting the upper and bottom clothes requires highly accurate waist curves).", + "bbox": [ + 75, + 768, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/97f26a46e27995ce8e675fd909c2af1e80eb7cc434878d75ae472ee90cb5b51d.jpg", + "image_caption": [ + "Figure 3. Illustration of the intersection-free curve deformation." + ], + "image_footnote": [], + "bbox": [ + 555, + 97, + 846, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enable better template registration, we consider three different surface types (i.e., upper-clothing, bottom-clothing, and upper-bottom) according to the garment types, and represent each surface type as the zero-isosurface of an independent SDF in the canonical space. The SDF is expressed by an MLP $f$ with learnable weights $\\eta$ :", + "bbox": [ + 496, + 258, + 890, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS (\\eta) = \\{\\mathbf {p} \\in \\mathbb {R} ^ {3} | f (\\mathbf {p}; \\eta) = 0 \\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 357, + 800, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the sake of simplicity and without loss of generality, we illustrate our method in reconstructing a single surface type later in this section.", + "bbox": [ + 496, + 380, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Skinning Based Motion Modeling", + "text_level": 1, + "bbox": [ + 500, + 433, + 795, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We model large body motions by linear blend skinning (LBS) transformation based on the SMPL [32] model, and utilize a non-rigid deformation field to account for fine-grained deformations.", + "bbox": [ + 496, + 455, + 890, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Skinning Transformation. Given a SMPL body with shape parameter $\\beta$ and a pose parameter $\\theta_{i}$ in $i$ -th frame, a point $\\mathbf{p}$ on the body surface in canonical space with skinning weights $w(\\mathbf{p})$ can be warped to camera view space via skinning transformation $\\mathcal{W}$ .", + "bbox": [ + 496, + 518, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notably, the skinning weights $w(\\mathbf{p})$ are only defined for points on the SMPL surface. To warp arbitrary points in the canonical space to camera view, we use the diffused skinning strategy [30] to propagate the skinning weights of SMPL body vertices to the entire canonical space, and store the weights in a voxel grid of size $256 \\times 256 \\times 256$ . Then we can obtain the skinning weights by trilinear interpolation.", + "bbox": [ + 496, + 595, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Non-rigid Deformation. Skinning deformation enables the garment surface to deform in a way consistent with the body's large-scale motion [16]. However, the motion of details and garment parts that are far away from body cannot be fully represented by skinning transformation [19]. Hence, a non-rigid deformation MLP is used to model these fine-grained changes. Specifically, we design an MLP $\\mathcal{D}$ with learnable parameters $\\phi$ to model garment surface's non-rigid deformation:", + "bbox": [ + 496, + 703, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} ^ {\\prime} = \\mathcal {D} (\\mathbf {p}, \\mathbf {h}, E (\\mathbf {p}); \\phi), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 845, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{p}'$ is the deformed point of the input point $\\mathbf{p}$ in the canonical space, $\\mathbf{h}$ is the latent code of the current frame,", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "† including templates for uppers, dresses, coats, pants, and skirts.", + "bbox": [ + 65, + 886, + 411, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4640", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and $E(\\mathbf{p})$ of $\\mathbf{p}$ is the position encoding [35] to represent the high-frequency information of spatial points.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, combining $\\mathcal{D}$ with skinning transformation field $\\mathcal{W}$ , we could define a deformation field $\\Phi(\\cdot) = \\mathcal{W}(\\mathcal{D}(\\cdot))$ to warp any points in the canonical space to the camera view.", + "bbox": [ + 76, + 121, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. 3D Feature Curves from 2D Projections", + "text_level": 1, + "bbox": [ + 76, + 175, + 416, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 3D feature curve will be optimized by minimizing the distance between its 2D projection on the image plane and the provided 2D visible curves. The key challenge here is how to compute the visibility of the 3D curves in the camera view. We first introduce a curve initialization strategy based on rigid transformation, and then propose a surface-aware curve visibility estimation method to support accurate non-rigid curves optimization.", + "bbox": [ + 75, + 198, + 468, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature Curve Initialization. We start from the predefined feature curve sets $\\mathbf{L} = \\{\\mathbf{L}_i|i = 1,\\dots ,N_l\\}$ provided in the garment template. To reduce the difficulty of curve optimization, we perform a rigid curve initialization by directly minimizing the Chamfer Distance (CD) between the projected curves on the camera view space and the corresponding visible 2D curves $\\zeta$ as", + "bbox": [ + 75, + 321, + 468, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns, \\mathbf {t}, \\mathbf {R} = \\underset {s, \\mathbf {t}, \\mathbf {R}} {\\arg \\min } \\operatorname {C D} \\left(\\Pi (\\mathcal {W} (\\bar {\\mathbf {L}} _ {i})) , \\zeta_ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 436, + 468, + 463 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {L}} _ {i} = s \\mathbf {R} \\left(\\mathbf {L} _ {i}\\right) + \\mathbf {t}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 465, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Pi$ is the projection matrix, $\\bar{\\mathbf{L}}_i$ is the transformed feature curve. $\\mathbf{t} \\in \\mathbb{R}^3$ , $\\mathbf{R} \\in SO(3)$ , and $s \\in \\mathbb{R}$ are the optimized translation, rotation, and scaling parameters, respectively.", + "bbox": [ + 75, + 494, + 468, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our implementation, we execute 150 gradient descent iterations to solve the rigid transformation parameters. After rigid optimization, we set $\\widetilde{\\mathbf{L}}$ as the initial position for the feature curve sets $\\{\\mathcal{C}_i|i = 1,\\dots ,N_l\\}$ for later non-rigid optimization.", + "bbox": [ + 75, + 555, + 468, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Surface-aware Curve Visibility Estimation. As the 2D feature curve $\\zeta$ only contains visible points, it is essential to identify the visible points of the 3D curve $\\mathcal{C}$ in camera space. A naive solution is to consider a point $\\mathcal{C}(i)$ as visible if the cosine similarity between the view direction $\\mathbf{v}$ and $\\mathbf{n_i^d}$ (i.e., the direction from curve center to the $i$ -th point) in view-pose is less than 0. However, this approach will produce wrong judgments when a curve is occluded by other body parts.", + "bbox": [ + 75, + 632, + 468, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To tackle this problem, a surface-aware curve visibility estimation method is proposed. Specifically, we generate an explicit mesh $\\mathbf{T}_{\\mathbf{s}}$ from implicit surface $S(\\eta)$ in canonical space via marching cube [33]. Next, we deform $\\mathbf{T}_{\\mathbf{s}}$ to camera view space via the deformation field $\\Phi (\\mathbf{T}_{\\mathbf{s}})$ . Then, we can check if a feature curve point $\\Phi (\\mathcal{C}(i))$ is occluded by the explicit mesh in view space based on z-buffer:", + "bbox": [ + 75, + 768, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV _ {\\mathcal {C} (i)} = \\operatorname {z b u f f e r} _ {-} \\operatorname {t e s t} \\left(\\Phi (\\mathcal {C} (i)), \\Phi (\\mathbf {T} _ {\\mathbf {s}})\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 883, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, we find that the 3D curve $\\mathcal{C}$ might sometimes move outside or have a scale larger than the explicit mesh $\\mathbf{T_s}$ , there will be some errors if only depending on the z-buffer testing between $\\mathcal{C}(i)$ and $\\mathbf{T_s}$ . We therefore make use of the SMPL surface to improve the visibility estimation, by checking if the nearest point of $\\mathcal{C}(i)$ on the SMPL body is occluded in the camera view space in a similar way. Note that this is feasible as in our intersection-free curve deformation, the correspondences between $\\mathcal{C}(i)$ and its nearest vertex in the SMPL body are almost unchanged during optimization. Then a curve point is considered as visible if it passes both visibility checks.", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Progressive Curve and Surface Co-evolution.", + "text_level": 1, + "bbox": [ + 498, + 285, + 879, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The surface of the garment is represented by the implicit SDF. As the feature curve visibility estimation depends on the garment surface, the curves and surface have to evolve consistently. To ensure the accuracy of curve visibility during the optimization process, we jointly optimize the curves and surface while imposing a regularization that the curves lie on the zero-isosurface of the SDF. The implicit surface is minimized by the photometric loss based on differentiable surface rendering.", + "bbox": [ + 496, + 309, + 890, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Curve-aware Surface Initialization. A good initialization for the implicit SDF $S(\\eta)$ can reduce the optimization difficulty and improve the performance, especially for the long skirt and dress. Thanks to our curve-aware garment representation, we can utilize the initialized feature curve $\\bar{\\mathbf{L}}$ computed in Eq. (4) to enable a better shape initialization. Specifically, we apply a handle-based deformation [46] to deform a surface template such that its feature curves are aligned with $\\bar{\\mathbf{L}}$ . Then, we apply IGR [12] to initialize the implicit surface $S(\\eta)$ by fitting the deformed template.", + "bbox": [ + 496, + 449, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Differentiable Surface Rendering. To reconstruct high-fidelity geometry, following the SelfRecon [19], we find the intersection points $\\mathbf{p}$ on the surface and make them differentiable (more details can be found in supplementary).", + "bbox": [ + 496, + 603, + 890, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the intersection points $\\mathbf{p}$ , we compute its gradient $\\mathbf{n_p} = \\nabla f(\\mathbf{p};\\eta)$ and transform the camera view to canonical space as $\\mathbf{v_p}$ by the Jacobian matrix of the deformed point $\\Phi (\\mathbf{p})$ (more details can be found in supplementary). To better account for the changes in the illumination, we also take a per-frame latent code $\\mathbf{z}$ as input to the color rendering network $f_{c}$ . Then, the surface color $C_{\\mathbf{p}}$ of point $\\mathbf{p}$ can be computed as", + "bbox": [ + 496, + 665, + 890, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC _ {\\mathbf {p}} = f _ {c} \\left(\\mathbf {p}, \\mathbf {n} _ {\\mathbf {p}}, \\mathbf {v} _ {\\mathbf {p}}, \\mathbf {z}, E (\\mathbf {p}); \\psi\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 800, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 830, + 643, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function consists of two parts, one part is for the feature curves optimization and the other is for garment surfaces optimization.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4641", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.1 Explicit Feature Curve Loss", + "text_level": 1, + "bbox": [ + 76, + 90, + 326, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The optimization of feature curves relies on the 2D projection loss, a curve slope regularization loss, and an on-surface regularization loss that ensures the feature curves are on the garment surface.", + "bbox": [ + 75, + 114, + 468, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Curve Projection Loss. Given SMPL pose parameter $\\theta_{i}$ and the camera projection matrix $\\Pi$ , we warp predicted feature curve $\\mathcal{C}$ to camera view space via deformation field $\\Phi$ , and compute project loss $\\mathcal{L}_{proj}$ measured by 2D visible curves $\\zeta$ using Chamfer Distance (CD):", + "bbox": [ + 75, + 178, + 468, + 253 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p r o j} = \\mathrm {C D} \\left(V _ {\\mathcal {C}} \\otimes \\Pi (\\Phi (\\mathcal {C})), \\zeta\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 266, + 468, + 284 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $V_{\\mathcal{C}}$ is the visibility mask of curves, and symbol $\\otimes$ indicates the mask selection operator.", + "bbox": [ + 75, + 295, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Curve Slope Regularization. To maintain the curvature of 3D curve $\\mathcal{C}$ , we design a slope loss $\\mathcal{L}_{slop}$ to regularize that the slope is consistent between adjacent points", + "bbox": [ + 76, + 328, + 468, + 375 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s l o p} = \\sum_ {i = 1} ^ {N _ {p}} (1 - \\cos < \\mathbf {s} _ {i + 1}, \\mathbf {s} _ {i} >) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 386, + 468, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{s}_i = \\mathcal{C}(i + 1) - \\mathcal{C}(i)$ , $N_{p}$ is the point number in the curve, and $\\cos < \\infty$ is the cosine similarity function.", + "bbox": [ + 75, + 440, + 468, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On-surface Regularization. In addition, the feature curves are required to be on the corresponding garment surface. Hence, we introduce an as near as possible loss $\\mathcal{L}_{anap}$ as:", + "bbox": [ + 75, + 473, + 468, + 520 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a n a p} = \\sum_ {i = 1} ^ {N _ {p}} | f (\\mathcal {C} (i); \\eta) | \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 531, + 468, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall explicit feature curve loss can be written as:", + "bbox": [ + 76, + 585, + 446, + 599 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c u r v e}} = \\lambda_ {\\text {p r o j}} \\mathcal {L} _ {\\text {p r o j}} + \\lambda_ {\\text {s l o p}} \\mathcal {L} _ {\\text {s l o p}} + \\lambda_ {\\text {a n a p}} \\mathcal {L} _ {\\text {a n a p}} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 614, + 468, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{proj},\\lambda_{slop}$ and $\\lambda_{anap}$ are loss weights.", + "bbox": [ + 76, + 645, + 383, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5.2 Garment Surface Loss", + "text_level": 1, + "bbox": [ + 76, + 680, + 287, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a monocular video with $N_{i}$ frames, the learnable parameter in implicit surface reconstruction is denoted as $\\Theta$ :", + "bbox": [ + 75, + 704, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Theta} = \\left\\{\\eta , \\phi , \\psi \\right\\} \\cup \\left\\{\\mathbf {h} _ {i}, \\mathbf {z} _ {i} \\mid i = 1, \\dots , N _ {i} \\right\\} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 747, + 468, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Surface Rendering Loss. For a pixel within the garment mask, we compute the ray's intersection point $\\mathbf{p}$ on the canonical surface $S(\\eta)$ and apply surface rendering network to predict the color $C_{\\mathbf{p}}$ (see Eq. (6)). Then the photometric loss can be computed as", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R G B} = \\frac {1}{| \\mathcal {R} |} \\sum_ {\\mathbf {p} \\in \\mathcal {R}} \\left| C _ {\\mathbf {p}} (\\boldsymbol {\\Theta}) - I _ {\\mathbf {p}} \\right|, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 866, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ is the sample point set, $I_{\\mathbf{p}}$ is the corresponding ground-truth pixel color from the input images.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mask-guided Implicit Consistency Loss. To better optimize implicit surface, following SelfRecon [19], we periodically extract explicit surface meshes $\\mathbf{T}_{\\mathbf{s}}$ in canonical space from SDF $f$ and use a differentiable renderer [50] to iteratively optimize $\\mathbf{T}_{\\mathbf{s}}$ by a mask loss using the surface mask. Then the updated explicit surface $\\hat{\\mathbf{T}}_{\\mathbf{s}}$ will be used to supervise the implicit SDF $f$ as", + "bbox": [ + 498, + 123, + 890, + 229 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m c o n s} = \\frac {1}{| \\hat {\\mathbf {T}} _ {\\mathbf {s}} |} \\sum_ {\\mathbf {p} \\in \\hat {\\mathbf {T}} _ {\\mathbf {s}}} | f (\\mathbf {p}; \\eta) |. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 234, + 890, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Curve-guided Implicit Consistency Loss. We find that the explicit mesh $\\hat{\\mathbf{T}}_{\\mathrm{s}}$ updated by the mask loss might contain holes or even collapse in some surface areas, which will harm the learning of implicit surface (see in Fig. 9). To address this issue, we design an explicit curve and surface consistency loss. Specifically, for a specific feature curve $\\mathcal{C}$ that belongs to two implicit surfaces (e.g., waist curve belongs to both the upper-clothing and bottom-clothing), we generate its closed surface $\\mathbf{T}_{\\mathcal{C}}$ and then sample $N_{a}$ points from $\\mathbf{T}_{\\mathcal{C}}$ to constrain the implicit SDF $f$ as", + "bbox": [ + 498, + 281, + 890, + 434 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c c o n s} = \\frac {1}{| \\mathbf {T} _ {\\mathcal {C}} |} \\sum_ {\\mathbf {p} \\in \\mathbf {T} _ {\\mathcal {C}}} | f (\\mathbf {p}; \\eta) |. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 439, + 890, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Common Implicit Loss. Eikonal loss $\\mathcal{L}_{eik}$ [12] is included to make the implicit function the signed distance function. To avoid distortion of non-rigid transformation, a rigid loss [39] $\\mathcal{L}_{arap}$ is computed to constrain the non-rigid deformation. We also compute normal loss $\\mathcal{L}_{norm}$ in canonical space to further refine the surface [19]. Moreover, we compute the skeleton smoothness loss [54] to reduce the high-frequency jitter of SMPL poses among frames (more details can be found in supplementary).", + "bbox": [ + 498, + 483, + 890, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall implicit surface loss can be written as:", + "bbox": [ + 517, + 619, + 851, + 633 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i m s} = \\mathcal {L} _ {R G B} + \\lambda_ {m c o n s} \\mathcal {L} _ {m c o n s} + \\lambda_ {c c o n s} \\mathcal {L} _ {c c o n s} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 641, + 890, + 665 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {a r a p} \\mathcal {L} _ {a r a p} + \\lambda_ {e i k} \\mathcal {L} _ {e i k} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}},\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 661, + 844, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{\\text{arap}}, \\lambda_{\\text{mcons}}, \\lambda_{\\text{ccons}}, \\lambda_{\\text{eik}},$ and $\\lambda_{\\text{norm}}$ are the loss weights.", + "bbox": [ + 500, + 681, + 888, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 724, + 630, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since there is no existing method for open garment meshes reconstruction from monocular videos, we compare with three state-of-the-art single-image methods, namely BCNet [20], ClothWild [36], and ReEF [62].", + "bbox": [ + 498, + 750, + 890, + 810 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation on Synthetic Dataset", + "text_level": 1, + "bbox": [ + 500, + 816, + 782, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since there is no public real dataset for evaluating dynamic garment reconstruction, we adopt four video sequences from the synthetic data generated by SelfRecon [19] for quantitative evaluation.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4642", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c4226bba4b85f08e9a8fef0eb1a81718ecedd0118073ed39e53a650db57d4ad1.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison on the synthetic dataset. From left to right in each example: the ground-truth mesh, results of BCNet [20], ClothedWild [36], ReEF [62], and Ours." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 883, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2cc13f2f8e26bc47649966972e3f153f54c731da6aea0291a2af6a051f6312f9.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on real datasets between BCNet [20], ClothWild [36], ReEF [62], and our method. Upper clothes are visualized in red color, while bottom clothes and dresses are visualized in blue color. Note that BCNet and ClothWild cannot model dresses." + ], + "image_footnote": [], + "bbox": [ + 76, + 257, + 890, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first employ Blender [1] to extract the ground-truth garment mesh from the provided clothed human mesh of the first frame. To measure the accuracy of the reconstructed meshes, we compute the Chamfer distance (CD) between the ground-truth and estimated meshes. To evaluate the temporal consistency of the reconstructed meshes for the video sequence, we measure the consistency of corresponding vertices (CCV), which is the root mean square error of the corresponding vertices distances in adjacent frames.", + "bbox": [ + 75, + 496, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We test our method and the baseline methods on these four video sequences. Table 1 shows that our method achieves the best results in the metrics of CD and CCV on all four videos, demonstrating the effectiveness of our method in reconstructing accurate and temporally consistent dynamic garment meshes. From the results of high errors in the CCV, we can clearly see that single-image methods fail to maintain the consistency of the reconstruction for the video input. Figure 4 compares the visual results, in which our method produces detailed and accurate garments that are mostly close to the ground-truth surfaces.", + "bbox": [ + 75, + 633, + 470, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation on Real-world Videos", + "text_level": 1, + "bbox": [ + 76, + 815, + 366, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We then qualitatively evaluate our method on the PeopleSnapshot [3] and a dataset captured by ourselves. These testing videos include a diverse variety of garments categories, including upper-cloth, dress, coats, pants, and skirts.", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e95dc6e07356b1aa5c198791e4b0cb900719e252941bf3d87b151bb4288e5ccf.jpg", + "table_caption": [ + "Table 1. Quantitative results on four synthetic sequences. We compare the Chamfer distance (CD) between the ground-truth and reconstructed surfaces (in $cm$ ), as well as the consistency of corresponding vertices (CCV) between adjacent frames." + ], + "table_footnote": [], + "table_body": "
MethodFemale1Female3Male1Male2
CDCCVCDCCVCDCCVCDCCV
BCNet [20]3.1847.2013.4476.1862.9298.6045.2347.128
ClothedWild [36]2.424-2.075-2.782-3.980-
ReEF [62]1.8103.7821.9244.3222.0056.7942.8653.579
Ours1.8040.5971.6411.0641.7360.4841.8120.433
", + "bbox": [ + 503, + 555, + 890, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 shows the visual comparisons. The results of the baseline methods are predicted using a single image as input. Our method can faithfully reconstruct the layouts and surface details of the garments. In contrast, BCNet [20] and ClothWild [36] cannot accurately predict the garment layouts and produce over-smooth surfaces.", + "bbox": [ + 496, + 652, + 893, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also demonstrate our dynamic reconstruction results in Fig. 6. We can see that our method can produce spacetime coherent results for different garment types (including the challenging dresses) from monocular videos, which is difficult to achieve with single-image methods.", + "bbox": [ + 496, + 744, + 893, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 829, + 653, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We next conduct ablation study for different components of our method (more results in our supplementary material). Curve Visibility Estimation. As shown in Fig. 7, sim", + "bbox": [ + 496, + 852, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4643", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/23aa9d3ee69e4cf78ac6cb3b01642407c57cc80d727f7882b8004aeda967af2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 87, + 166, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9eab54e38b3ddc914547eb333c3b01fcfc2847aa11f486bc28c20c0bc62e497e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 174, + 89, + 281, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d9538ab2313c16a7445715009a771f4072a53ae0b96a7e9affaf7d5a9912fe2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 88, + 377, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/286bd9cfdf8e94fb8066e1b6e80869ab5b26613f20a74a5f36bab47ee4677359.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 88, + 473, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4de8f3507800811a84cc184341e55680bd1140fb984cf1fe35fa3120d5edc348.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 183, + 166, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/44ee80d6c057bd5aba6a5a31fb1f018f8325a4b73e0bb9fc428f3f58bde9b9a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 176, + 184, + 276, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/85de9297105ef055a5830a3f78a4799651f79f17d0dd9397f65296f7a8b9bf6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 184, + 377, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4315e4b211cec1282a51163e58e117ba10e6cecfcfa4f729910bc374dbaca7b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 184, + 472, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dcecc9c16201e9992afba4ca814712339560872a8428918bb3eed02049a6611b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 88, + 584, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e3be3dcdc1d4c92c9c6cae7a41c66e692d8971ba472e4ce5ebf9a887164bc7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 586, + 88, + 691, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/590e11158fa22e1a8022f72898c369f375be00c695961ec94b4d691539d709a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 183, + 583, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83ec3b394a906d75f57f39638459aa65b7b5cf4964d1d348d3b99b89641813ce.jpg", + "image_caption": [ + "ur frames in a monocular video." + ], + "image_footnote": [], + "bbox": [ + 586, + 184, + 691, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/102cb020732abde71912e74c1ddaff384c54ff987a3f531f8d72a0a3541e312b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 88, + 790, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b97b082c6ee865c5e32cfeeba0cd3b5642f5e122182f599cb0977287c1e4ad26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 183, + 790, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/836b40200a58c8b4db25efef8f95a96b2e80dd1d258ac5dd6d49d6312585f443.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 799, + 89, + 883, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a57e8de2e7cccb1ae132592a4eae536063f3b0ca1ada7816a0e1b1bd4cb0537f.jpg", + "image_caption": [ + "(a) Curve Normal" + ], + "image_footnote": [], + "bbox": [ + 84, + 328, + 181, + 376 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd64f50717aa150c1251f86115084fbbaf39ac9c059a75de7143fdcf909aeaa4.jpg", + "image_caption": [ + "(b) w/o Implicit Surface" + ], + "image_footnote": [], + "bbox": [ + 183, + 330, + 276, + 376 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/223fbe665da5003bcb187a1c3abb32695a98b05a5206749ed89e814a4dfe1667.jpg", + "image_caption": [ + "(c) w/o SMPL" + ], + "image_footnote": [], + "bbox": [ + 277, + 330, + 370, + 376 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f186949018f3d561bca6be1a79bd593ff861ae5ffcb7feda27163aa6a9d38694.jpg", + "image_caption": [ + "(d) Surface-aware", + "Figure 7. Ablation study of curve visibility estimation method." + ], + "image_footnote": [], + "bbox": [ + 372, + 329, + 468, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ply using normal direction for visibility estimation leads to worse results, while using both the implicit SDF and SMPL surfaces for z-buffer testing produces the best result.", + "bbox": [ + 76, + 438, + 468, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Explicit Curve Losses. Figure 8 (a) shows that without the curve slop loss $\\mathcal{L}_{slop}$ , the optimized curves will contain noise and artifacts. As shown in Fig. 8 (b), the proposed on-surface regularization (i.e., $\\mathcal{L}_{anap}$ ) can well constrain the curves to be on the surface and produce much more accurate fitting results, demonstrating the implicit surface helps the optimization of curves.", + "bbox": [ + 76, + 487, + 468, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Curve-guided Consistency Loss. To improve the optimization of the implicit surface, we use curves to regularize the surface. Figure 9 shows that this regularization effectively improves the surface geometry, verifying that curves benefit the optimization of surfaces.", + "bbox": [ + 76, + 595, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 689, + 194, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a new framework for dynamic garment reconstruction from monocular videos, by formulating this task as an optimization problem of dynamic 3D curves and surface recovery, followed by garment template registration. To solve this problem, we introduce a novel approach, called REC-MV, to jointly optimize the curves and surface from 2D supervision in a progressive co-evolution manner. Experimental results show that our method can reconstruct high-fidelity dynamic garments meshes with open boundaries, significantly outperforming existing methods.", + "bbox": [ + 75, + 715, + 468, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our method can only reconstruct common garment categories whose contours can be represented by", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc08e93cf39adc4f040bef778a40ee7a4bc9266b57b334a32ae147927c097c14.jpg", + "image_caption": [ + "(a) $\\mathrm{w / o}\\mathcal{L}_{slop}$" + ], + "image_footnote": [], + "bbox": [ + 519, + 313, + 645, + 425 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d86ed5350ff42348e6e4baeb431cce0b943d65549fb31658bca2d84a37d12e80.jpg", + "image_caption": [ + "(b) $\\mathrm{w / o}$ $\\mathcal{L}_{anap}$" + ], + "image_footnote": [], + "bbox": [ + 645, + 313, + 756, + 424 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7ef37cd970c33cdb32741fe7c71a1575178ae08aba787897d680a6253293e14e.jpg", + "image_caption": [ + "(c) Both" + ], + "image_footnote": [], + "bbox": [ + 756, + 314, + 880, + 425 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/39d3e506edb20c3648f7f138bcb9ca20304409a9c75c5056dda4307ab09eebde.jpg", + "image_caption": [ + "Figure 8. Ablation study of the explicit curve losses." + ], + "image_footnote": [], + "bbox": [ + 532, + 462, + 689, + 574 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94f0581cc88290b029f33065aece1f7bd024fbb102573391496f4af9078ec2b3.jpg", + "image_caption": [ + "Figure 9. Results of w/o and w/ the curve-guided consistency loss." + ], + "image_footnote": [], + "bbox": [ + 694, + 470, + 779, + 575 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/49b733f4355c3972236b81d198959e8c3e8a662b3155f8a448f947f2fb4303f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 782, + 472, + 867, + 575 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {w / o} \\mathcal {L} _ {c c o n s}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 584, + 599, + 595 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {w} / \\mathcal {L} _ {c c o n s}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 584, + 679, + 595 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {w / o} \\mathcal {L} _ {c c o n s}\n$$\n", + "text_format": "latex", + "bbox": [ + 702, + 584, + 769, + 595 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {w /} \\mathcal {L} _ {c c o n s}\n$$\n", + "text_format": "latex", + "bbox": [ + 792, + 584, + 851, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "feature curves. Additionally, our method requires the moving person to be observed from different angles.", + "bbox": [ + 498, + 641, + 890, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No.JCYJ20220530143604010, the National Key R&D Program of China with grant No.2018YFB1800800, by NSFC No. 62202409, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No.2017ZT07X152 and No.2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No.2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No.ZDSYS201707251409055). It was also sponsored by CCF-Tencent Open Research Fund.", + "bbox": [ + 496, + 672, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4644", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Blender. https://www.blender.org/. 2021.7", + "[2] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single RGB camera. In CVPR, 2019. 2", + "[3] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. Video based reconstruction of 3d people models. In CVPR, 2018. 2, 3, 7", + "[4] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. SCAPE: shape completion and animation of people. 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Learning anchored unsigned distance functions with gradient direction alignment for single-view garment reconstruction. In ICCV, 2021. 2", + "[60] Fuqiang Zhao, Wei Yang, Jiakai Zhang, Pei Lin, Yingliang Zhang, Jingyi Yu, and Lan Xu. Humanerf: Efficiently generated human radiance field from sparse inputs. In CVPR, 2021. 2", + "[61] Heming Zhu, Yu Cao, Hang Jin, Weikai Chen, Dong Du, Zhangye Wang, Shuguang Cui, and Xiaoguang Han. Deep fashion3d: A dataset and benchmark for 3d garment reconstruction from single images. In ECCV, 2020. 1, 2, 3, 4", + "[62] Heming Zhu, Lingteng Qiu, Yuda Qiu, and Xiaoguang Han. Registering explicit to implicit: Towards high-fidelity garment mesh reconstruction from single images. In CVPR, 2022. 1, 2, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 868 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4646", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_model.json b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8270ea4c4a0966cbf82392f4256cfd248bec5e4d --- /dev/null +++ b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_model.json @@ -0,0 +1,2849 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.131, + 0.838, + 0.152 + ], + "angle": 0, + "content": "REC-MV: REconstructing 3D Dynamic Cloth from Monocular Videos" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.18, + 0.754, + 0.24 + ], + "angle": 0, + "content": "Lingteng Qiu\\(^{1*}\\) Guanying Chen\\(^{1,2*}\\) Jiapeng Zhou\\(^{1}\\) Mutian Xu\\(^{1}\\) Junle Wang\\(^{3}\\) Xiaoguang Han\\(^{1,2\\dagger}\\) \n\\(^{1}\\)SSE, CUHKSZ \\(^{2}\\)FNii, CUHKSZ \\(^{3}\\)Tencent" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.307, + 0.474, + 0.655 + ], + "angle": 0, + "content": "Reconstructing dynamic 3D garment surfaces with open boundaries from monocular videos is an important problem as it provides a practical and low-cost solution for clothes digitization. Recent neural rendering methods achieve high-quality dynamic clothed human reconstruction results from monocular video, but these methods cannot separate the garment surface from the body. Moreover, despite existing garment reconstruction methods based on feature curve representation demonstrating impressive results for garment reconstruction from a single image, they struggle to generate temporally consistent surfaces for the video input. To address the above limitations, in this paper, we formulate this task as an optimization problem of 3D garment feature curves and surface reconstruction from monocular video. We introduce a novel approach, called REC-MV, to jointly optimize the explicit feature curves and the implicit signed distance field (SDF) of the garments. Then the open garment meshes can be extracted via garment template registration in the canonical space. Experiments on multiple casually captured datasets show that our approach outperforms existing methods and can produce high-quality dynamic garment surfaces. The source code is available at https://github.com/GAP-LAB-CUHK-SZ/REC-MV." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.685, + 0.208, + 0.7 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.47, + 0.864 + ], + "angle": 0, + "content": "High-fidelity clothes digitization plays an essential role in various human-related vision applications such as virtual shopping, film, and gaming. In our daily life, humans are always in a moving status, driving their clothes to move together. To realize this very common scenario, it is indispensable to gain dynamic garments in real applications. Thanks to the rapid development of mobile devices in terms of digital cameras, processors, and storage, shooting a monocular video in the wild becomes highly convenient and accessible for general customers. In this paper," + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.275, + 0.895, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.461, + 0.894, + 0.531 + ], + "angle": 0, + "content": "Figure 1. Can we extract dynamic 3D garments from monocular videos? The answer is Yes! By jointly optimizing the dynamic feature curves and garment surface followed by non-rigid template registration, our method can reconstruct high-fidelity and temporally consistent garment meshes with open boundaries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.893, + 0.636 + ], + "angle": 0, + "content": "our goal is definite – extracting dynamic 3D garments from monocular videos, which is significantly meaningful and valuable for practical applications, but is yet an uncultivated land with many challenges." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We attempt to seek a new solution to this open problem and start by revisiting existing works from two main-streams. i) Leveraging the success of neural rendering methods [35, 37, 57], several works are able to reconstruct dynamic clothed humans from monocular videos [8, 19, 29, 47, 49], by representing the body surface with an implicit function in the canonical space and apply skinning based deformation for motion modeling. One naive way to achieve our goal is: first to get the clothed human through these methods and separate the garments from human bodies. However, such a separation job requires laborious and non-trivial processing by professional artists, which is neither straightforward nor feasible for general application scenarios. ii) As for garment reconstruction, many methods [5, 10, 20, 61, 62] make it possible to reconstruct high-quality garment meshes from single-view images in the wild. Specifically, ReEF [62] estimates 3D fea" + }, + { + "type": "page_footnote", + "bbox": [ + 0.065, + 0.875, + 0.183, + 0.888 + ], + "angle": 0, + "content": "* Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.065, + 0.888, + 0.355, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author: hanxiaoguang@cuhk.edu.cn." + }, + { + "type": "list", + "bbox": [ + 0.065, + 0.875, + 0.355, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4637" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "ture curves* and an implicit surface field [34] for non-rigid garment template registration. Nonetheless, these methods struggle to produce temporally consistent surfaces when taking videos as inputs." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.156, + 0.47, + 0.368 + ], + "angle": 0, + "content": "The above discussion motivates us to combine the merits of both the dynamic surface modeling in recent neural rendering methods and the explicit curve representation for garment modeling. To this end, we try to delineate a new path towards our goal: optimizing dynamic explicit feature curves and implicit garment surface from monocular videos, to extract temporally consistent garment meshes with open boundaries. We represent the explicit curves and implicit surface in the canonical space with skinning-based motion modeling, and optimize them by 2D supervision automatically extracted from the video (e.g., image intensities, garment masks, and visible feature curves). After that, the open garment meshes can be extracted by a garment template registration in the canonical space (see Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.372, + 0.471, + 0.644 + ], + "angle": 0, + "content": "We strive to probe this path as follows: (1) As a feature curve is a point set whose deformation has a high degree of freedom, directly optimizing the per-point offsets often leads to undesired self-intersection and spike artifacts. To better regularize the deformation of curves, we introduce an intersection-free curve deformation method to maintain the order of feature curves. (2) We optimize the 3D feature curves using 2D projection loss measured by the estimated 2D visible curves, where the key challenge is to accurately compute the visibility of curves. To address this problem, we propose a surface-aware curve visibility estimation method based on the implicit garment surface and z-buffer. (3) To ensure the accuracy of curve visibility estimation during the optimization process, the curves should always be right on the garment surface. We therefore introduce a progressive curve and surface evolution strategy to jointly update the curves and surface while imposing the on-surface regularization for curves." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.648, + 0.46, + 0.663 + ], + "angle": 0, + "content": "To summarize, the main contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.67, + 0.469, + 0.715 + ], + "angle": 0, + "content": "- We introduce REC-MV, to our best knowledge, the first method to reconstruct dynamic and open loose garments from the monocular video." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.716, + 0.469, + 0.806 + ], + "angle": 0, + "content": "- We propose a new approach for joint optimization of explicit feature curves and implicit garment surface from monocular video, based on carefully designed intersection-free curve deformation, surface-aware curve visibility estimation, and progressive curve and surface evolution methods." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.807, + 0.469, + 0.852 + ], + "angle": 0, + "content": "- Extensive evaluations on casually captured monocular videos demonstrate that our method outperforms existing methods." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.67, + 0.469, + 0.852 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.066, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "* feature curves of the garment (e.g., necklines, hemlines) can provide critical cues for determining the shape contours of the garment." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.119, + 0.892, + 0.225 + ], + "angle": 0, + "content": "Human Reconstruction from Single-view Image. Traditional methods for human reconstruction often adopt a parametric human model (e.g., SMPL [32] or SCAPE [4]) and can only recover a naked 3D body [23, 24]. To increase the surface details, free-form deformations can be applied to the mesh vertices to model small geometry variations caused by the clothing [2, 3, 26, 43, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.227, + 0.892, + 0.363 + ], + "angle": 0, + "content": "Recent methods propose to utilize implicit surface representations [34, 38] to reconstruct 3D clothed human with an arbitrary topology. Specifically, PIFu and PIFuhd [44, 45] extract pixel-aligned spatial features from images as the input for implicit surface function for occupancy prediction. Follow-up methods then integrates 3D-aligned features to improve the results [6, 15-18, 56, 58]. As these methods only consider single-image reconstruction, they cannot produce temporally consistent results for video input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Human Reconstruction from Monocular Video. Inspired by the success of neural rendering methods [35, 37, 57] in scene reconstruction, many methods have been proposed to reconstruct 3D human from sparse-view [31, 41, 53, 55, 60] or monocular [19, 47, 49] videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Anim-NeRF [8], Neuman [21] and HumanNeRF [49] introduce methods based on neural radiance field (NeRF) [35] to reconstruct an animatable avatar from monocular video. These methods transform a 3D point in the observation space to the canonical space by inverse-skinning, and then perform volume rendering in the canonical space. A-NeRF [47] additionally adopt a skeleton-relative encoding strategy. AvATAR [29] proposes a monocular human volumetric capture method, but requires reconstructing an avatar from multiple 3D scans in advance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Garment Reconstruction from Images. Reconstructing garment mesh from images enables many applications like virtual try-on and content creation. Existing methods reconstruct the clothing as a separate layer on top of the body [7, 22, 25, 42, 48, 51]. Among them, several methods address the challenging problem of garment reconstruction from single-view image [5, 10, 20, 36, 61, 62]. MGN [5] learns a per-category parametric model from a large-scale clothing dataset. BCNet [20] first reconstructs a coarse template and then refines the surface details with a displacement network. AnchorUDF [59] adopts the unsigned distance field (UDF) [9] to represent the open surface mesh. SMPlicit [10] proposes a generative model to reconstruct layered garments from a single image. DeepFasion3D [61] reconstructs the surface with occupancy network [34] and applies non-rigid ICP to register the clothing template. ReEF [62] registers explicit clothing template to the implicit field learned from pixel-aligned implicit function. However, as these single-image methods do not consider clothing motion, they are not suitable for dynamic gar" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4638" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.095, + 0.266, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.095, + 0.787, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.097, + 0.89, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.894, + 0.397 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed REC-MV. (a) Starting from a surface template, we initialize the canonical curves by solving Eq. (3), and apply a handle-based deformation to initialize the canonical implicit surface. (b) Given an \\(i\\)-th frame, canonical curves are deformed to the camera view space to compute the projection loss based on the surface-aware visibility estimation. (c) Similarly, the canonical surface is deform to the camera view to compute the photometric loss by differentiable rendering. The curves and surface are jointly optimized to enable a progressive co-evolution. (d) Last, the open garment meshes can be extracted by template registration in the canonical space." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.217, + 0.437 + ], + "angle": 0, + "content": "ment reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.62 + ], + "angle": 0, + "content": "Among methods related to garment reconstruction from videos, Li et al. [28] introduce a method to learn physics-aware clothing deformation from monocular videos, but assumes the template scans for the body and clothing are provided [13]. Garment Avatar [14] proposes a multi-view patterned cloth tracking algorithm, requiring the subject to wear clothing with specific patterns. SCARF represents the layered clothing using radiance field [11] on top of the SMPL-X model [40] from monocular video. In contrast, our method first reconstructs the explicit 3D garment curves and surfaces, and then extracts the garment mesh via template registration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.632, + 0.169, + 0.646 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.747 + ], + "angle": 0, + "content": "Given a monocular video with \\( N_{i} \\) frames depicting a moving person \\( \\{I_t|t = 1,\\dots ,N_i\\} \\), REC-MV aims to reconstruct high-fidelity and space-time coherent open garment meshes. This is a challenging problem as it requires a method to simultaneously capture the shape contours, local surface details, and the motion of the garment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.471, + 0.869 + ], + "angle": 0, + "content": "Observing that feature curves (e.g., necklines, hemlines) provide critical cues for determining the shape contours of garment [61] and implicit signed distance function (SDF) can well represent a detailed closed surface [19], we propose to first optimize the explicit 3D feature curves and implicit garment surfaces from the video, and then apply non-rigid clothing template registration to extract the open garment meshes (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Preprocessing. We generate the initial shape parameter \\(\\beta\\), camera intrinsic \\(\\pi\\), and per-frame SMPL [32] pose param" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.56 + ], + "angle": 0, + "content": "eters \\(\\{\\pmb {\\theta}_t|t = 1,\\dots ,N_i\\}\\) using Videoavatar [3]. To identify the garment regions in 2D images, we apply the existing garment parsing method [27] to estimate the garment masks. Our method also requires 2D visible curves \\(\\zeta =\\) \\(\\{\\zeta_{l,t}|l = 1,\\ldots N_l,t = 1,\\ldots ,N_i\\}\\) for 3D curve recovery, where \\(N_{l}\\) denotes the number of curves. Note that the 2D visible curves can be automatically produced by parsing boundaries of the garment mask (more details in the supplementary material)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Overview. To utilize the information that exists in the entire video for dynamic garment reconstruction, we represent the explicit feature curve and implicit garment surface in the canonical space (Sec. 3.1). For a specific time step, we adopt the skeleton-based skinning and non-rigid deformation modeling to map the canonical curves and surfaces to the camera view space (Sec. 3.2). As the given 2D curves only contain visible points, to optimize the 3D feature curves from 2D projection error, we propose a surface-aware approach to compute the visibility of the 3D feature curve based on z-buffer (Sec. 3.3). In terms of implicit surface optimization, we minimize the photometric loss between the rendered and input image based on the differentiable surface rendering technique (Sec. 3.4). Then the adopted loss functions for joint optimization of curves and surfaces are described (Sec. 3.5). Last, the open garment meshes can be extracted by registering an explicit garment template to the recovered curves and implicit surfaces in the canonical space (more details in the supplementary material). Then the garment meshes can be deformed based on the SMPL poses." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4639" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.443, + 0.108 + ], + "angle": 0, + "content": "3.1. Feature Curve and Surface Representation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.117, + 0.47, + 0.239 + ], + "angle": 0, + "content": "Explicit Surface Template. Following DeepFashion3D [61], we employ several surface templates, each contains a pre-defined set of 3D feature curves \\(\\mathbf{L} = \\{\\mathbf{L}_i | i = 1, \\dots, N_l\\}\\) extracted from the garment boundaries, where \\(N_l\\) is the number of feature curves (see our supplementary materials for more details). The surface templates will be used for garment surface initialization and the pre-defined feature curves will be used for curve initialization†." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.471, + 0.348 + ], + "angle": 0, + "content": "Intersection-free Curve Deformation. A straightforward idea is to represent a feature curve as a discrete point set, and directly estimate the 3D deformation offset for each point during optimization. However, this unstructured curve representation struggles to maintain the order of the points and often generate spike artifacts due to the high degree of freedom of the deformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.442 + ], + "angle": 0, + "content": "To address this issue, we introduce a novel intersection-free curve deformation method, in which the point's deformation at each step is controlled by the curve center and two orthogonal directions (see Fig. 3 for illustration). Formally, given a curve \\(\\mathcal{C}\\) of \\(N_{p}\\) points with center \\(\\mathbf{p_c}\\), the updated position of \\(i\\)-th point \\(\\mathcal{C}(i)\\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.453, + 0.47, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} ^ {\\prime} (i) = \\mathbf {p} _ {\\mathbf {c}} + S _ {i} ^ {d} \\mathbf {n} _ {\\mathbf {i}} ^ {\\mathbf {d}} + S _ {i} ^ {c} \\mathbf {n} ^ {\\mathbf {c}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.47, + 0.566 + ], + "angle": 0, + "content": "where \\(\\mathbf{n_i^d}\\) is the direction from the curve center to the current point \\(\\mathcal{C}(i)\\), and \\(\\mathbf{n}^{\\mathbf{c}} = \\frac{1}{N_p - 1}\\sum_{i = 1}^{N_p}(\\mathbf{n_i^d}\\times \\mathbf{n_{i - 1}^d})\\) is the direction perpendicular to the current feature curve plane. \\(S_{i}^{d}\\in \\mathbb{R}\\) and \\(S_{i}^{c}\\in \\mathbb{R}\\) are learnable parameters specifying the step size of the deformation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.567, + 0.47, + 0.629 + ], + "angle": 0, + "content": "The proposed intersection-free curve deformation can well preserve the order of points in the curve, which largely reduced the difficulty of optimization compared to the direct offset estimation approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Implicit SDF in Canonical Space. Unsigned distance field (UDF) [9] is an implicit function that can represent an open surface. However, as UDF is not differentiable at points close to the surface, it is non-trivial to integrate UDF with differentiable surface rendering to take advantage of supervision from 2D photometric loss. We therefore adopt the SDF to represent a closed garment surface for surface geometry recovery, followed by garment template registration to extract the open surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.769, + 0.47, + 0.875 + ], + "angle": 0, + "content": "It is common to represent the whole surface with a single SDF for human reconstruction [19]. However, as our goal is to reconstruct separate clothes, using a single SDF to represent both the upper clothes and bottom clothes (e.g., skirt) increases the difficulty of template registration (i.e., splitting the upper and bottom clothes requires highly accurate waist curves)." + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.098, + 0.848, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.223, + 0.885, + 0.238 + ], + "angle": 0, + "content": "Figure 3. Illustration of the intersection-free curve deformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.26, + 0.892, + 0.352 + ], + "angle": 0, + "content": "To enable better template registration, we consider three different surface types (i.e., upper-clothing, bottom-clothing, and upper-bottom) according to the garment types, and represent each surface type as the zero-isosurface of an independent SDF in the canonical space. The SDF is expressed by an MLP \\( f \\) with learnable weights \\( \\eta \\):" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.358, + 0.802, + 0.377 + ], + "angle": 0, + "content": "\\[\nS (\\eta) = \\{\\mathbf {p} \\in \\mathbb {R} ^ {3} | f (\\mathbf {p}; \\eta) = 0 \\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.427 + ], + "angle": 0, + "content": "For the sake of simplicity and without loss of generality, we illustrate our method in reconstructing a single surface type later in this section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.434, + 0.796, + 0.451 + ], + "angle": 0, + "content": "3.2. Skinning Based Motion Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.518 + ], + "angle": 0, + "content": "We model large body motions by linear blend skinning (LBS) transformation based on the SMPL [32] model, and utilize a non-rigid deformation field to account for fine-grained deformations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Skinning Transformation. Given a SMPL body with shape parameter \\(\\beta\\) and a pose parameter \\(\\theta_{i}\\) in \\(i\\)-th frame, a point \\(\\mathbf{p}\\) on the body surface in canonical space with skinning weights \\(w(\\mathbf{p})\\) can be warped to camera view space via skinning transformation \\(\\mathcal{W}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Notably, the skinning weights \\( w(\\mathbf{p}) \\) are only defined for points on the SMPL surface. To warp arbitrary points in the canonical space to camera view, we use the diffused skinning strategy [30] to propagate the skinning weights of SMPL body vertices to the entire canonical space, and store the weights in a voxel grid of size \\( 256 \\times 256 \\times 256 \\). Then we can obtain the skinning weights by trilinear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Non-rigid Deformation. Skinning deformation enables the garment surface to deform in a way consistent with the body's large-scale motion [16]. However, the motion of details and garment parts that are far away from body cannot be fully represented by skinning transformation [19]. Hence, a non-rigid deformation MLP is used to model these fine-grained changes. Specifically, we design an MLP \\(\\mathcal{D}\\) with learnable parameters \\(\\phi\\) to model garment surface's non-rigid deformation:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.847, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} ^ {\\prime} = \\mathcal {D} (\\mathbf {p}, \\mathbf {h}, E (\\mathbf {p}); \\phi), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}'\\) is the deformed point of the input point \\(\\mathbf{p}\\) in the canonical space, \\(\\mathbf{h}\\) is the latent code of the current frame," + }, + { + "type": "page_footnote", + "bbox": [ + 0.066, + 0.887, + 0.412, + 0.901 + ], + "angle": 0, + "content": "† including templates for uppers, dresses, coats, pants, and skirts." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4640" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "and \\( E(\\mathbf{p}) \\) of \\( \\mathbf{p} \\) is the position encoding [35] to represent the high-frequency information of spatial points." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.122, + 0.469, + 0.168 + ], + "angle": 0, + "content": "Finally, combining \\(\\mathcal{D}\\) with skinning transformation field \\(\\mathcal{W}\\), we could define a deformation field \\(\\Phi(\\cdot) = \\mathcal{W}(\\mathcal{D}(\\cdot))\\) to warp any points in the canonical space to the camera view." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.176, + 0.418, + 0.192 + ], + "angle": 0, + "content": "3.3. 3D Feature Curves from 2D Projections" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.469, + 0.319 + ], + "angle": 0, + "content": "The 3D feature curve will be optimized by minimizing the distance between its 2D projection on the image plane and the provided 2D visible curves. The key challenge here is how to compute the visibility of the 3D curves in the camera view. We first introduce a curve initialization strategy based on rigid transformation, and then propose a surface-aware curve visibility estimation method to support accurate non-rigid curves optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.469, + 0.428 + ], + "angle": 0, + "content": "Feature Curve Initialization. We start from the predefined feature curve sets \\(\\mathbf{L} = \\{\\mathbf{L}_i|i = 1,\\dots ,N_l\\}\\) provided in the garment template. To reduce the difficulty of curve optimization, we perform a rigid curve initialization by directly minimizing the Chamfer Distance (CD) between the projected curves on the camera view space and the corresponding visible 2D curves \\(\\zeta\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.438, + 0.469, + 0.464 + ], + "angle": 0, + "content": "\\[\ns, \\mathbf {t}, \\mathbf {R} = \\underset {s, \\mathbf {t}, \\mathbf {R}} {\\arg \\min } \\operatorname {C D} \\left(\\Pi (\\mathcal {W} (\\bar {\\mathbf {L}} _ {i})) , \\zeta_ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.467, + 0.469, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {L}} _ {i} = s \\mathbf {R} \\left(\\mathbf {L} _ {i}\\right) + \\mathbf {t}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.469, + 0.555 + ], + "angle": 0, + "content": "where \\(\\Pi\\) is the projection matrix, \\(\\bar{\\mathbf{L}}_i\\) is the transformed feature curve. \\(\\mathbf{t} \\in \\mathbb{R}^3\\), \\(\\mathbf{R} \\in SO(3)\\), and \\(s \\in \\mathbb{R}\\) are the optimized translation, rotation, and scaling parameters, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.469, + 0.631 + ], + "angle": 0, + "content": "In our implementation, we execute 150 gradient descent iterations to solve the rigid transformation parameters. After rigid optimization, we set \\(\\widetilde{\\mathbf{L}}\\) as the initial position for the feature curve sets \\(\\{\\mathcal{C}_i|i = 1,\\dots ,N_l\\}\\) for later non-rigid optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.469, + 0.769 + ], + "angle": 0, + "content": "Surface-aware Curve Visibility Estimation. As the 2D feature curve \\(\\zeta\\) only contains visible points, it is essential to identify the visible points of the 3D curve \\(\\mathcal{C}\\) in camera space. A naive solution is to consider a point \\(\\mathcal{C}(i)\\) as visible if the cosine similarity between the view direction \\(\\mathbf{v}\\) and \\(\\mathbf{n_i^d}\\) (i.e., the direction from curve center to the \\(i\\)-th point) in view-pose is less than 0. However, this approach will produce wrong judgments when a curve is occluded by other body parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.469, + 0.875 + ], + "angle": 0, + "content": "To tackle this problem, a surface-aware curve visibility estimation method is proposed. Specifically, we generate an explicit mesh \\(\\mathbf{T}_{\\mathbf{s}}\\) from implicit surface \\(S(\\eta)\\) in canonical space via marching cube [33]. Next, we deform \\(\\mathbf{T}_{\\mathbf{s}}\\) to camera view space via the deformation field \\(\\Phi (\\mathbf{T}_{\\mathbf{s}})\\). Then, we can check if a feature curve point \\(\\Phi (\\mathcal{C}(i))\\) is occluded by the explicit mesh in view space based on z-buffer:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.885, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\nV _ {\\mathcal {C} (i)} = \\operatorname {z b u f f e r} _ {-} \\operatorname {t e s t} \\left(\\Phi (\\mathcal {C} (i)), \\Phi (\\mathbf {T} _ {\\mathbf {s}})\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "However, we find that the 3D curve \\(\\mathcal{C}\\) might sometimes move outside or have a scale larger than the explicit mesh \\(\\mathbf{T_s}\\), there will be some errors if only depending on the z-buffer testing between \\(\\mathcal{C}(i)\\) and \\(\\mathbf{T_s}\\). We therefore make use of the SMPL surface to improve the visibility estimation, by checking if the nearest point of \\(\\mathcal{C}(i)\\) on the SMPL body is occluded in the camera view space in a similar way. Note that this is feasible as in our intersection-free curve deformation, the correspondences between \\(\\mathcal{C}(i)\\) and its nearest vertex in the SMPL body are almost unchanged during optimization. Then a curve point is considered as visible if it passes both visibility checks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.286, + 0.88, + 0.302 + ], + "angle": 0, + "content": "3.4. Progressive Curve and Surface Co-evolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.446 + ], + "angle": 0, + "content": "The surface of the garment is represented by the implicit SDF. As the feature curve visibility estimation depends on the garment surface, the curves and surface have to evolve consistently. To ensure the accuracy of curve visibility during the optimization process, we jointly optimize the curves and surface while imposing a regularization that the curves lie on the zero-isosurface of the SDF. The implicit surface is minimized by the photometric loss based on differentiable surface rendering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.601 + ], + "angle": 0, + "content": "Curve-aware Surface Initialization. A good initialization for the implicit SDF \\(S(\\eta)\\) can reduce the optimization difficulty and improve the performance, especially for the long skirt and dress. Thanks to our curve-aware garment representation, we can utilize the initialized feature curve \\(\\bar{\\mathbf{L}}\\) computed in Eq. (4) to enable a better shape initialization. Specifically, we apply a handle-based deformation [46] to deform a surface template such that its feature curves are aligned with \\(\\bar{\\mathbf{L}}\\). Then, we apply IGR [12] to initialize the implicit surface \\(S(\\eta)\\) by fitting the deformed template." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.891, + 0.664 + ], + "angle": 0, + "content": "Differentiable Surface Rendering. To reconstruct high-fidelity geometry, following the SelfRecon [19], we find the intersection points \\(\\mathbf{p}\\) on the surface and make them differentiable (more details can be found in supplementary)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.786 + ], + "angle": 0, + "content": "After obtaining the intersection points \\(\\mathbf{p}\\), we compute its gradient \\(\\mathbf{n_p} = \\nabla f(\\mathbf{p};\\eta)\\) and transform the camera view to canonical space as \\(\\mathbf{v_p}\\) by the Jacobian matrix of the deformed point \\(\\Phi (\\mathbf{p})\\) (more details can be found in supplementary). To better account for the changes in the illumination, we also take a per-frame latent code \\(\\mathbf{z}\\) as input to the color rendering network \\(f_{c}\\). Then, the surface color \\(C_{\\mathbf{p}}\\) of point \\(\\mathbf{p}\\) can be computed as" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.801, + 0.891, + 0.818 + ], + "angle": 0, + "content": "\\[\nC _ {\\mathbf {p}} = f _ {c} \\left(\\mathbf {p}, \\mathbf {n} _ {\\mathbf {p}}, \\mathbf {v} _ {\\mathbf {p}}, \\mathbf {z}, E (\\mathbf {p}); \\psi\\right). \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.645, + 0.845 + ], + "angle": 0, + "content": "3.5. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The overall loss function consists of two parts, one part is for the feature curves optimization and the other is for garment surfaces optimization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4641" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.327, + 0.106 + ], + "angle": 0, + "content": "3.5.1 Explicit Feature Curve Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.469, + 0.176 + ], + "angle": 0, + "content": "The optimization of feature curves relies on the 2D projection loss, a curve slope regularization loss, and an on-surface regularization loss that ensures the feature curves are on the garment surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.179, + 0.469, + 0.255 + ], + "angle": 0, + "content": "Feature Curve Projection Loss. Given SMPL pose parameter \\(\\theta_{i}\\) and the camera projection matrix \\(\\Pi\\), we warp predicted feature curve \\(\\mathcal{C}\\) to camera view space via deformation field \\(\\Phi\\), and compute project loss \\(\\mathcal{L}_{proj}\\) measured by 2D visible curves \\(\\zeta\\) using Chamfer Distance (CD):" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.267, + 0.469, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p r o j} = \\mathrm {C D} \\left(V _ {\\mathcal {C}} \\otimes \\Pi (\\Phi (\\mathcal {C})), \\zeta\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.469, + 0.327 + ], + "angle": 0, + "content": "where \\(V_{\\mathcal{C}}\\) is the visibility mask of curves, and symbol \\(\\otimes\\) indicates the mask selection operator." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.329, + 0.469, + 0.375 + ], + "angle": 0, + "content": "Feature Curve Slope Regularization. To maintain the curvature of 3D curve \\(\\mathcal{C}\\), we design a slope loss \\(\\mathcal{L}_{slop}\\) to regularize that the slope is consistent between adjacent points" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.387, + 0.469, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s l o p} = \\sum_ {i = 1} ^ {N _ {p}} (1 - \\cos < \\mathbf {s} _ {i + 1}, \\mathbf {s} _ {i} >) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.469, + 0.471 + ], + "angle": 0, + "content": "where \\(\\mathbf{s}_i = \\mathcal{C}(i + 1) - \\mathcal{C}(i)\\), \\(N_{p}\\) is the point number in the curve, and \\(\\cos < \\infty\\) is the cosine similarity function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.469, + 0.521 + ], + "angle": 0, + "content": "On-surface Regularization. In addition, the feature curves are required to be on the corresponding garment surface. Hence, we introduce an as near as possible loss \\(\\mathcal{L}_{anap}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.532, + 0.469, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a n a p} = \\sum_ {i = 1} ^ {N _ {p}} | f (\\mathcal {C} (i); \\eta) | \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.586, + 0.447, + 0.6 + ], + "angle": 0, + "content": "The overall explicit feature curve loss can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.615, + 0.469, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c u r v e}} = \\lambda_ {\\text {p r o j}} \\mathcal {L} _ {\\text {p r o j}} + \\lambda_ {\\text {s l o p}} \\mathcal {L} _ {\\text {s l o p}} + \\lambda_ {\\text {a n a p}} \\mathcal {L} _ {\\text {a n a p}} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.646, + 0.385, + 0.663 + ], + "angle": 0, + "content": "where \\(\\lambda_{proj},\\lambda_{slop}\\) and \\(\\lambda_{anap}\\) are loss weights." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.289, + 0.696 + ], + "angle": 0, + "content": "3.5.2 Garment Surface Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.736 + ], + "angle": 0, + "content": "For a monocular video with \\(N_{i}\\) frames, the learnable parameter in implicit surface reconstruction is denoted as \\(\\Theta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.748, + 0.469, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Theta} = \\left\\{\\eta , \\phi , \\psi \\right\\} \\cup \\left\\{\\mathbf {h} _ {i}, \\mathbf {z} _ {i} \\mid i = 1, \\dots , N _ {i} \\right\\} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.855 + ], + "angle": 0, + "content": "Surface Rendering Loss. For a pixel within the garment mask, we compute the ray's intersection point \\(\\mathbf{p}\\) on the canonical surface \\(S(\\eta)\\) and apply surface rendering network to predict the color \\(C_{\\mathbf{p}}\\) (see Eq. (6)). Then the photometric loss can be computed as" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.867, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R G B} = \\frac {1}{| \\mathcal {R} |} \\sum_ {\\mathbf {p} \\in \\mathcal {R}} \\left| C _ {\\mathbf {p}} (\\boldsymbol {\\Theta}) - I _ {\\mathbf {p}} \\right|, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) is the sample point set, \\(I_{\\mathbf{p}}\\) is the corresponding ground-truth pixel color from the input images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.124, + 0.892, + 0.23 + ], + "angle": 0, + "content": "Mask-guided Implicit Consistency Loss. To better optimize implicit surface, following SelfRecon [19], we periodically extract explicit surface meshes \\(\\mathbf{T}_{\\mathbf{s}}\\) in canonical space from SDF \\(f\\) and use a differentiable renderer [50] to iteratively optimize \\(\\mathbf{T}_{\\mathbf{s}}\\) by a mask loss using the surface mask. Then the updated explicit surface \\(\\hat{\\mathbf{T}}_{\\mathbf{s}}\\) will be used to supervise the implicit SDF \\(f\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.235, + 0.892, + 0.275 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m c o n s} = \\frac {1}{| \\hat {\\mathbf {T}} _ {\\mathbf {s}} |} \\sum_ {\\mathbf {p} \\in \\hat {\\mathbf {T}} _ {\\mathbf {s}}} | f (\\mathbf {p}; \\eta) |. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.282, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Curve-guided Implicit Consistency Loss. We find that the explicit mesh \\(\\hat{\\mathbf{T}}_{\\mathrm{s}}\\) updated by the mask loss might contain holes or even collapse in some surface areas, which will harm the learning of implicit surface (see in Fig. 9). To address this issue, we design an explicit curve and surface consistency loss. Specifically, for a specific feature curve \\(\\mathcal{C}\\) that belongs to two implicit surfaces (e.g., waist curve belongs to both the upper-clothing and bottom-clothing), we generate its closed surface \\(\\mathbf{T}_{\\mathcal{C}}\\) and then sample \\(N_{a}\\) points from \\(\\mathbf{T}_{\\mathcal{C}}\\) to constrain the implicit SDF \\(f\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.44, + 0.892, + 0.476 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c c o n s} = \\frac {1}{| \\mathbf {T} _ {\\mathcal {C}} |} \\sum_ {\\mathbf {p} \\in \\mathbf {T} _ {\\mathcal {C}}} | f (\\mathbf {p}; \\eta) |. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.484, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Common Implicit Loss. Eikonal loss \\(\\mathcal{L}_{eik}\\) [12] is included to make the implicit function the signed distance function. To avoid distortion of non-rigid transformation, a rigid loss [39] \\(\\mathcal{L}_{arap}\\) is computed to constrain the non-rigid deformation. We also compute normal loss \\(\\mathcal{L}_{norm}\\) in canonical space to further refine the surface [19]. Moreover, we compute the skeleton smoothness loss [54] to reduce the high-frequency jitter of SMPL poses among frames (more details can be found in supplementary)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.62, + 0.852, + 0.635 + ], + "angle": 0, + "content": "The overall implicit surface loss can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.642, + 0.892, + 0.666 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i m s} = \\mathcal {L} _ {R G B} + \\lambda_ {m c o n s} \\mathcal {L} _ {m c o n s} + \\lambda_ {c c o n s} \\mathcal {L} _ {c c o n s} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.662, + 0.846, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {a r a p} \\mathcal {L} _ {a r a p} + \\lambda_ {e i k} \\mathcal {L} _ {e i k} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.683, + 0.89, + 0.713 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\text{arap}}, \\lambda_{\\text{mcons}}, \\lambda_{\\text{ccons}}, \\lambda_{\\text{eik}},\\) and \\(\\lambda_{\\text{norm}}\\) are the loss weights." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.632, + 0.741 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.811 + ], + "angle": 0, + "content": "Since there is no existing method for open garment meshes reconstruction from monocular videos, we compare with three state-of-the-art single-image methods, namely BCNet [20], ClothWild [36], and ReEF [62]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.783, + 0.833 + ], + "angle": 0, + "content": "4.1. Evaluation on Synthetic Dataset" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since there is no public real dataset for evaluating dynamic garment reconstruction, we adopt four video sequences from the synthetic data generated by SelfRecon [19] for quantitative evaluation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4642" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.885, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.895, + 0.245 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison on the synthetic dataset. From left to right in each example: the ground-truth mesh, results of BCNet [20], ClothedWild [36], ReEF [62], and Ours." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.258, + 0.892, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.442, + 0.895, + 0.473 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on real datasets between BCNet [20], ClothWild [36], ReEF [62], and our method. Upper clothes are visualized in red color, while bottom clothes and dresses are visualized in blue color. Note that BCNet and ClothWild cannot model dresses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.47, + 0.633 + ], + "angle": 0, + "content": "We first employ Blender [1] to extract the ground-truth garment mesh from the provided clothed human mesh of the first frame. To measure the accuracy of the reconstructed meshes, we compute the Chamfer distance (CD) between the ground-truth and estimated meshes. To evaluate the temporal consistency of the reconstructed meshes for the video sequence, we measure the consistency of corresponding vertices (CCV), which is the root mean square error of the corresponding vertices distances in adjacent frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.471, + 0.803 + ], + "angle": 0, + "content": "We test our method and the baseline methods on these four video sequences. Table 1 shows that our method achieves the best results in the metrics of CD and CCV on all four videos, demonstrating the effectiveness of our method in reconstructing accurate and temporally consistent dynamic garment meshes. From the results of high errors in the CCV, we can clearly see that single-image methods fail to maintain the consistency of the reconstruction for the video input. Figure 4 compares the visual results, in which our method produces detailed and accurate garments that are mostly close to the ground-truth surfaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.367, + 0.831 + ], + "angle": 0, + "content": "4.2. Evaluation on Real-world Videos" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We then qualitatively evaluate our method on the PeopleSnapshot [3] and a dataset captured by ourselves. These testing videos include a diverse variety of garments categories, including upper-cloth, dress, coats, pants, and skirts." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.497, + 0.893, + 0.554 + ], + "angle": 0, + "content": "Table 1. Quantitative results on four synthetic sequences. We compare the Chamfer distance (CD) between the ground-truth and reconstructed surfaces (in \\( cm \\)), as well as the consistency of corresponding vertices (CCV) between adjacent frames." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.556, + 0.892, + 0.628 + ], + "angle": 0, + "content": "
MethodFemale1Female3Male1Male2
CDCCVCDCCVCDCCVCDCCV
BCNet [20]3.1847.2013.4476.1862.9298.6045.2347.128
ClothedWild [36]2.424-2.075-2.782-3.980-
ReEF [62]1.8103.7821.9244.3222.0056.7942.8653.579
Ours1.8040.5971.6411.0641.7360.4841.8120.433
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.894, + 0.744 + ], + "angle": 0, + "content": "Figure 5 shows the visual comparisons. The results of the baseline methods are predicted using a single image as input. Our method can faithfully reconstruct the layouts and surface details of the garments. In contrast, BCNet [20] and ClothWild [36] cannot accurately predict the garment layouts and produce over-smooth surfaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.894, + 0.821 + ], + "angle": 0, + "content": "We also demonstrate our dynamic reconstruction results in Fig. 6. We can see that our method can produce spacetime coherent results for different garment types (including the challenging dresses) from monocular videos, which is difficult to achieve with single-image methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.655, + 0.846 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.853, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We next conduct ablation study for different components of our method (more results in our supplementary material). Curve Visibility Estimation. As shown in Fig. 7, sim" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.088, + 0.168, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.09, + 0.282, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.089, + 0.378, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.089, + 0.474, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.184, + 0.168, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.177, + 0.185, + 0.277, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.185, + 0.378, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.185, + 0.473, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.089, + 0.585, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.089, + 0.692, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.184, + 0.584, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.185, + 0.692, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.792, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.184, + 0.792, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.09, + 0.885, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.285, + 0.891, + 0.3 + ], + "angle": 0, + "content": "ur frames in a monocular video." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.329, + 0.182, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.38, + 0.172, + 0.391 + ], + "angle": 0, + "content": "(a) Curve Normal" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.331, + 0.277, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.38, + 0.288, + 0.391 + ], + "angle": 0, + "content": "(b) w/o Implicit Surface" + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.331, + 0.371, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.295, + 0.38, + 0.363, + 0.391 + ], + "angle": 0, + "content": "(c) w/o SMPL" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.33, + 0.47, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.38, + 0.464, + 0.391 + ], + "angle": 0, + "content": "(d) Surface-aware" + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.396, + 0.46, + 0.41 + ], + "angle": 0, + "content": "Figure 7. Ablation study of curve visibility estimation method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.439, + 0.47, + 0.485 + ], + "angle": 0, + "content": "ply using normal direction for visibility estimation leads to worse results, while using both the implicit SDF and SMPL surfaces for z-buffer testing produces the best result." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.488, + 0.47, + 0.594 + ], + "angle": 0, + "content": "Explicit Curve Losses. Figure 8 (a) shows that without the curve slop loss \\(\\mathcal{L}_{slop}\\), the optimized curves will contain noise and artifacts. As shown in Fig. 8 (b), the proposed on-surface regularization (i.e., \\(\\mathcal{L}_{anap}\\)) can well constrain the curves to be on the surface and produce much more accurate fitting results, demonstrating the implicit surface helps the optimization of curves." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.597, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Curve-guided Consistency Loss. To improve the optimization of the implicit surface, we use curves to regularize the surface. Figure 9 shows that this regularization effectively improves the surface geometry, verifying that curves benefit the optimization of surfaces." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.69, + 0.196, + 0.705 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.868 + ], + "angle": 0, + "content": "We have presented a new framework for dynamic garment reconstruction from monocular videos, by formulating this task as an optimization problem of dynamic 3D curves and surface recovery, followed by garment template registration. To solve this problem, we introduce a novel approach, called REC-MV, to jointly optimize the curves and surface from 2D supervision in a progressive co-evolution manner. Experimental results show that our method can reconstruct high-fidelity dynamic garments meshes with open boundaries, significantly outperforming existing methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Limitations. Our method can only reconstruct common garment categories whose contours can be represented by" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.314, + 0.646, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.427, + 0.608, + 0.44 + ], + "angle": 0, + "content": "(a) \\(\\mathrm{w / o}\\mathcal{L}_{slop}\\)" + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.314, + 0.757, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.427, + 0.735, + 0.44 + ], + "angle": 0, + "content": "(b) \\(\\mathrm{w / o}\\) \\(\\mathcal{L}_{anap}\\)" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.315, + 0.882, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.427, + 0.846, + 0.438 + ], + "angle": 0, + "content": "(c) Both" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.444, + 0.852, + 0.458 + ], + "angle": 0, + "content": "Figure 8. Ablation study of the explicit curve losses." + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.463, + 0.691, + 0.575 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.472, + 0.781, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.473, + 0.868, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.585, + 0.6, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathrm {w / o} \\mathcal {L} _ {c c o n s}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.585, + 0.681, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathrm {w} / \\mathcal {L} _ {c c o n s}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.704, + 0.585, + 0.77, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathrm {w / o} \\mathcal {L} _ {c c o n s}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.793, + 0.585, + 0.852, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathrm {w /} \\mathcal {L} _ {c c o n s}\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.601, + 0.891, + 0.615 + ], + "angle": 0, + "content": "Figure 9. Results of w/o and w/ the curve-guided consistency loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.642, + 0.892, + 0.672 + ], + "angle": 0, + "content": "feature curves. Additionally, our method requires the moving person to be observed from different angles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No.JCYJ20220530143604010, the National Key R&D Program of China with grant No.2018YFB1800800, by NSFC No. 62202409, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No.2017ZT07X152 and No.2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No.2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No.ZDSYS201707251409055). It was also sponsored by CCF-Tencent Open Research Fund." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4644" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.442, + 0.131 + ], + "angle": 0, + "content": "[1] Blender. https://www.blender.org/. 2021.7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.133, + 0.47, + 0.187 + ], + "angle": 0, + "content": "[2] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single RGB camera. In CVPR, 2019. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.19, + 0.469, + 0.233 + ], + "angle": 0, + "content": "[3] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. 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In CVPR, 2022. 1, 2, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.869 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4646" + } + ] +] \ No newline at end of file diff --git a/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_origin.pdf b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6e53a5a2aae31e9fd31edd67a6dcfb08bd65ad88 --- /dev/null +++ b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/dc096b27-b9fa-424b-94dc-3477e0e0fc0c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:445f48beaea3c1f58037b693717001b186ac549bf2c73cb4c8389b873d329e96 +size 3258291 diff --git a/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/full.md b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4dafd90618218b8044097cdd676192be99ca998c --- /dev/null +++ b/2023/REC-MV_ REconstructing 3D Dynamic Cloth From Monocular Videos/full.md @@ -0,0 +1,434 @@ +# REC-MV: REconstructing 3D Dynamic Cloth from Monocular Videos + +Lingteng Qiu $^{1*}$ Guanying Chen $^{1,2*}$ Jiapeng Zhou $^{1}$ Mutian Xu $^{1}$ Junle Wang $^{3}$ Xiaoguang Han $^{1,2\dagger}$ $^{1}$ SSE, CUHKSZ $^{2}$ FNii, CUHKSZ $^{3}$ Tencent + +# Abstract + +Reconstructing dynamic 3D garment surfaces with open boundaries from monocular videos is an important problem as it provides a practical and low-cost solution for clothes digitization. Recent neural rendering methods achieve high-quality dynamic clothed human reconstruction results from monocular video, but these methods cannot separate the garment surface from the body. Moreover, despite existing garment reconstruction methods based on feature curve representation demonstrating impressive results for garment reconstruction from a single image, they struggle to generate temporally consistent surfaces for the video input. To address the above limitations, in this paper, we formulate this task as an optimization problem of 3D garment feature curves and surface reconstruction from monocular video. We introduce a novel approach, called REC-MV, to jointly optimize the explicit feature curves and the implicit signed distance field (SDF) of the garments. Then the open garment meshes can be extracted via garment template registration in the canonical space. Experiments on multiple casually captured datasets show that our approach outperforms existing methods and can produce high-quality dynamic garment surfaces. The source code is available at https://github.com/GAP-LAB-CUHK-SZ/REC-MV. + +# 1. Introduction + +High-fidelity clothes digitization plays an essential role in various human-related vision applications such as virtual shopping, film, and gaming. In our daily life, humans are always in a moving status, driving their clothes to move together. To realize this very common scenario, it is indispensable to gain dynamic garments in real applications. Thanks to the rapid development of mobile devices in terms of digital cameras, processors, and storage, shooting a monocular video in the wild becomes highly convenient and accessible for general customers. In this paper, + +![](images/3b12c49523ed62d8478876006ca4ca2a4bb06d23131e2b5ecaf8d7b907fb2d80.jpg) +Figure 1. Can we extract dynamic 3D garments from monocular videos? The answer is Yes! By jointly optimizing the dynamic feature curves and garment surface followed by non-rigid template registration, our method can reconstruct high-fidelity and temporally consistent garment meshes with open boundaries. + +our goal is definite – extracting dynamic 3D garments from monocular videos, which is significantly meaningful and valuable for practical applications, but is yet an uncultivated land with many challenges. + +We attempt to seek a new solution to this open problem and start by revisiting existing works from two main-streams. i) Leveraging the success of neural rendering methods [35, 37, 57], several works are able to reconstruct dynamic clothed humans from monocular videos [8, 19, 29, 47, 49], by representing the body surface with an implicit function in the canonical space and apply skinning based deformation for motion modeling. One naive way to achieve our goal is: first to get the clothed human through these methods and separate the garments from human bodies. However, such a separation job requires laborious and non-trivial processing by professional artists, which is neither straightforward nor feasible for general application scenarios. ii) As for garment reconstruction, many methods [5, 10, 20, 61, 62] make it possible to reconstruct high-quality garment meshes from single-view images in the wild. Specifically, ReEF [62] estimates 3D fea + +ture curves* and an implicit surface field [34] for non-rigid garment template registration. Nonetheless, these methods struggle to produce temporally consistent surfaces when taking videos as inputs. + +The above discussion motivates us to combine the merits of both the dynamic surface modeling in recent neural rendering methods and the explicit curve representation for garment modeling. To this end, we try to delineate a new path towards our goal: optimizing dynamic explicit feature curves and implicit garment surface from monocular videos, to extract temporally consistent garment meshes with open boundaries. We represent the explicit curves and implicit surface in the canonical space with skinning-based motion modeling, and optimize them by 2D supervision automatically extracted from the video (e.g., image intensities, garment masks, and visible feature curves). After that, the open garment meshes can be extracted by a garment template registration in the canonical space (see Fig. 1). + +We strive to probe this path as follows: (1) As a feature curve is a point set whose deformation has a high degree of freedom, directly optimizing the per-point offsets often leads to undesired self-intersection and spike artifacts. To better regularize the deformation of curves, we introduce an intersection-free curve deformation method to maintain the order of feature curves. (2) We optimize the 3D feature curves using 2D projection loss measured by the estimated 2D visible curves, where the key challenge is to accurately compute the visibility of curves. To address this problem, we propose a surface-aware curve visibility estimation method based on the implicit garment surface and z-buffer. (3) To ensure the accuracy of curve visibility estimation during the optimization process, the curves should always be right on the garment surface. We therefore introduce a progressive curve and surface evolution strategy to jointly update the curves and surface while imposing the on-surface regularization for curves. + +To summarize, the main contributions of this work are: + +- We introduce REC-MV, to our best knowledge, the first method to reconstruct dynamic and open loose garments from the monocular video. +- We propose a new approach for joint optimization of explicit feature curves and implicit garment surface from monocular video, based on carefully designed intersection-free curve deformation, surface-aware curve visibility estimation, and progressive curve and surface evolution methods. +- Extensive evaluations on casually captured monocular videos demonstrate that our method outperforms existing methods. + +# 2. Related Work + +Human Reconstruction from Single-view Image. Traditional methods for human reconstruction often adopt a parametric human model (e.g., SMPL [32] or SCAPE [4]) and can only recover a naked 3D body [23, 24]. To increase the surface details, free-form deformations can be applied to the mesh vertices to model small geometry variations caused by the clothing [2, 3, 26, 43, 52]. + +Recent methods propose to utilize implicit surface representations [34, 38] to reconstruct 3D clothed human with an arbitrary topology. Specifically, PIFu and PIFuhd [44, 45] extract pixel-aligned spatial features from images as the input for implicit surface function for occupancy prediction. Follow-up methods then integrates 3D-aligned features to improve the results [6, 15-18, 56, 58]. As these methods only consider single-image reconstruction, they cannot produce temporally consistent results for video input. + +Human Reconstruction from Monocular Video. Inspired by the success of neural rendering methods [35, 37, 57] in scene reconstruction, many methods have been proposed to reconstruct 3D human from sparse-view [31, 41, 53, 55, 60] or monocular [19, 47, 49] videos. + +Anim-NeRF [8], Neuman [21] and HumanNeRF [49] introduce methods based on neural radiance field (NeRF) [35] to reconstruct an animatable avatar from monocular video. These methods transform a 3D point in the observation space to the canonical space by inverse-skinning, and then perform volume rendering in the canonical space. A-NeRF [47] additionally adopt a skeleton-relative encoding strategy. AvATAR [29] proposes a monocular human volumetric capture method, but requires reconstructing an avatar from multiple 3D scans in advance. + +Garment Reconstruction from Images. Reconstructing garment mesh from images enables many applications like virtual try-on and content creation. Existing methods reconstruct the clothing as a separate layer on top of the body [7, 22, 25, 42, 48, 51]. Among them, several methods address the challenging problem of garment reconstruction from single-view image [5, 10, 20, 36, 61, 62]. MGN [5] learns a per-category parametric model from a large-scale clothing dataset. BCNet [20] first reconstructs a coarse template and then refines the surface details with a displacement network. AnchorUDF [59] adopts the unsigned distance field (UDF) [9] to represent the open surface mesh. SMPlicit [10] proposes a generative model to reconstruct layered garments from a single image. DeepFasion3D [61] reconstructs the surface with occupancy network [34] and applies non-rigid ICP to register the clothing template. ReEF [62] registers explicit clothing template to the implicit field learned from pixel-aligned implicit function. However, as these single-image methods do not consider clothing motion, they are not suitable for dynamic gar + +![](images/c05b4122433502f378ddbb7982115a06b03ef498cd88d2bd49969a9a1e79e035.jpg) + +![](images/7d369701113cb4dd33ffa847cf85a04375cb6ea4d19f755d9b57901d6f3c36b7.jpg) +Figure 2. Overview of the proposed REC-MV. (a) Starting from a surface template, we initialize the canonical curves by solving Eq. (3), and apply a handle-based deformation to initialize the canonical implicit surface. (b) Given an $i$ -th frame, canonical curves are deformed to the camera view space to compute the projection loss based on the surface-aware visibility estimation. (c) Similarly, the canonical surface is deform to the camera view to compute the photometric loss by differentiable rendering. The curves and surface are jointly optimized to enable a progressive co-evolution. (d) Last, the open garment meshes can be extracted by template registration in the canonical space. + +![](images/63b369c6a7e6a6a3b610fa82900be97be17607bc792b51bcd366a26ff12d05f8.jpg) + +ment reconstruction. + +Among methods related to garment reconstruction from videos, Li et al. [28] introduce a method to learn physics-aware clothing deformation from monocular videos, but assumes the template scans for the body and clothing are provided [13]. Garment Avatar [14] proposes a multi-view patterned cloth tracking algorithm, requiring the subject to wear clothing with specific patterns. SCARF represents the layered clothing using radiance field [11] on top of the SMPL-X model [40] from monocular video. In contrast, our method first reconstructs the explicit 3D garment curves and surfaces, and then extracts the garment mesh via template registration. + +# 3. Method + +Given a monocular video with $N_{i}$ frames depicting a moving person $\{I_t|t = 1,\dots ,N_i\}$ , REC-MV aims to reconstruct high-fidelity and space-time coherent open garment meshes. This is a challenging problem as it requires a method to simultaneously capture the shape contours, local surface details, and the motion of the garment. + +Observing that feature curves (e.g., necklines, hemlines) provide critical cues for determining the shape contours of garment [61] and implicit signed distance function (SDF) can well represent a detailed closed surface [19], we propose to first optimize the explicit 3D feature curves and implicit garment surfaces from the video, and then apply non-rigid clothing template registration to extract the open garment meshes (see Fig. 2). + +Preprocessing. We generate the initial shape parameter $\beta$ , camera intrinsic $\pi$ , and per-frame SMPL [32] pose param + +eters $\{\pmb {\theta}_t|t = 1,\dots ,N_i\}$ using Videoavatar [3]. To identify the garment regions in 2D images, we apply the existing garment parsing method [27] to estimate the garment masks. Our method also requires 2D visible curves $\zeta =$ $\{\zeta_{l,t}|l = 1,\ldots N_l,t = 1,\ldots ,N_i\}$ for 3D curve recovery, where $N_{l}$ denotes the number of curves. Note that the 2D visible curves can be automatically produced by parsing boundaries of the garment mask (more details in the supplementary material). + +Overview. To utilize the information that exists in the entire video for dynamic garment reconstruction, we represent the explicit feature curve and implicit garment surface in the canonical space (Sec. 3.1). For a specific time step, we adopt the skeleton-based skinning and non-rigid deformation modeling to map the canonical curves and surfaces to the camera view space (Sec. 3.2). As the given 2D curves only contain visible points, to optimize the 3D feature curves from 2D projection error, we propose a surface-aware approach to compute the visibility of the 3D feature curve based on z-buffer (Sec. 3.3). In terms of implicit surface optimization, we minimize the photometric loss between the rendered and input image based on the differentiable surface rendering technique (Sec. 3.4). Then the adopted loss functions for joint optimization of curves and surfaces are described (Sec. 3.5). Last, the open garment meshes can be extracted by registering an explicit garment template to the recovered curves and implicit surfaces in the canonical space (more details in the supplementary material). Then the garment meshes can be deformed based on the SMPL poses. + +# 3.1. Feature Curve and Surface Representation + +Explicit Surface Template. Following DeepFashion3D [61], we employ several surface templates, each contains a pre-defined set of 3D feature curves $\mathbf{L} = \{\mathbf{L}_i | i = 1, \dots, N_l\}$ extracted from the garment boundaries, where $N_l$ is the number of feature curves (see our supplementary materials for more details). The surface templates will be used for garment surface initialization and the pre-defined feature curves will be used for curve initialization†. + +Intersection-free Curve Deformation. A straightforward idea is to represent a feature curve as a discrete point set, and directly estimate the 3D deformation offset for each point during optimization. However, this unstructured curve representation struggles to maintain the order of the points and often generate spike artifacts due to the high degree of freedom of the deformation. + +To address this issue, we introduce a novel intersection-free curve deformation method, in which the point's deformation at each step is controlled by the curve center and two orthogonal directions (see Fig. 3 for illustration). Formally, given a curve $\mathcal{C}$ of $N_{p}$ points with center $\mathbf{p_c}$ , the updated position of $i$ -th point $\mathcal{C}(i)$ is defined as + +$$ +\mathcal {C} ^ {\prime} (i) = \mathbf {p} _ {\mathbf {c}} + S _ {i} ^ {d} \mathbf {n} _ {\mathbf {i}} ^ {\mathbf {d}} + S _ {i} ^ {c} \mathbf {n} ^ {\mathbf {c}}, \tag {1} +$$ + +where $\mathbf{n_i^d}$ is the direction from the curve center to the current point $\mathcal{C}(i)$ , and $\mathbf{n}^{\mathbf{c}} = \frac{1}{N_p - 1}\sum_{i = 1}^{N_p}(\mathbf{n_i^d}\times \mathbf{n_{i - 1}^d})$ is the direction perpendicular to the current feature curve plane. $S_{i}^{d}\in \mathbb{R}$ and $S_{i}^{c}\in \mathbb{R}$ are learnable parameters specifying the step size of the deformation. + +The proposed intersection-free curve deformation can well preserve the order of points in the curve, which largely reduced the difficulty of optimization compared to the direct offset estimation approach. + +Implicit SDF in Canonical Space. Unsigned distance field (UDF) [9] is an implicit function that can represent an open surface. However, as UDF is not differentiable at points close to the surface, it is non-trivial to integrate UDF with differentiable surface rendering to take advantage of supervision from 2D photometric loss. We therefore adopt the SDF to represent a closed garment surface for surface geometry recovery, followed by garment template registration to extract the open surface. + +It is common to represent the whole surface with a single SDF for human reconstruction [19]. However, as our goal is to reconstruct separate clothes, using a single SDF to represent both the upper clothes and bottom clothes (e.g., skirt) increases the difficulty of template registration (i.e., splitting the upper and bottom clothes requires highly accurate waist curves). + +![](images/97f26a46e27995ce8e675fd909c2af1e80eb7cc434878d75ae472ee90cb5b51d.jpg) +Figure 3. Illustration of the intersection-free curve deformation. + +To enable better template registration, we consider three different surface types (i.e., upper-clothing, bottom-clothing, and upper-bottom) according to the garment types, and represent each surface type as the zero-isosurface of an independent SDF in the canonical space. The SDF is expressed by an MLP $f$ with learnable weights $\eta$ : + +$$ +S (\eta) = \{\mathbf {p} \in \mathbb {R} ^ {3} | f (\mathbf {p}; \eta) = 0 \}. +$$ + +For the sake of simplicity and without loss of generality, we illustrate our method in reconstructing a single surface type later in this section. + +# 3.2. Skinning Based Motion Modeling + +We model large body motions by linear blend skinning (LBS) transformation based on the SMPL [32] model, and utilize a non-rigid deformation field to account for fine-grained deformations. + +Skinning Transformation. Given a SMPL body with shape parameter $\beta$ and a pose parameter $\theta_{i}$ in $i$ -th frame, a point $\mathbf{p}$ on the body surface in canonical space with skinning weights $w(\mathbf{p})$ can be warped to camera view space via skinning transformation $\mathcal{W}$ . + +Notably, the skinning weights $w(\mathbf{p})$ are only defined for points on the SMPL surface. To warp arbitrary points in the canonical space to camera view, we use the diffused skinning strategy [30] to propagate the skinning weights of SMPL body vertices to the entire canonical space, and store the weights in a voxel grid of size $256 \times 256 \times 256$ . Then we can obtain the skinning weights by trilinear interpolation. + +Non-rigid Deformation. Skinning deformation enables the garment surface to deform in a way consistent with the body's large-scale motion [16]. However, the motion of details and garment parts that are far away from body cannot be fully represented by skinning transformation [19]. Hence, a non-rigid deformation MLP is used to model these fine-grained changes. Specifically, we design an MLP $\mathcal{D}$ with learnable parameters $\phi$ to model garment surface's non-rigid deformation: + +$$ +\mathbf {p} ^ {\prime} = \mathcal {D} (\mathbf {p}, \mathbf {h}, E (\mathbf {p}); \phi), \tag {2} +$$ + +where $\mathbf{p}'$ is the deformed point of the input point $\mathbf{p}$ in the canonical space, $\mathbf{h}$ is the latent code of the current frame, + +and $E(\mathbf{p})$ of $\mathbf{p}$ is the position encoding [35] to represent the high-frequency information of spatial points. + +Finally, combining $\mathcal{D}$ with skinning transformation field $\mathcal{W}$ , we could define a deformation field $\Phi(\cdot) = \mathcal{W}(\mathcal{D}(\cdot))$ to warp any points in the canonical space to the camera view. + +# 3.3. 3D Feature Curves from 2D Projections + +The 3D feature curve will be optimized by minimizing the distance between its 2D projection on the image plane and the provided 2D visible curves. The key challenge here is how to compute the visibility of the 3D curves in the camera view. We first introduce a curve initialization strategy based on rigid transformation, and then propose a surface-aware curve visibility estimation method to support accurate non-rigid curves optimization. + +Feature Curve Initialization. We start from the predefined feature curve sets $\mathbf{L} = \{\mathbf{L}_i|i = 1,\dots ,N_l\}$ provided in the garment template. To reduce the difficulty of curve optimization, we perform a rigid curve initialization by directly minimizing the Chamfer Distance (CD) between the projected curves on the camera view space and the corresponding visible 2D curves $\zeta$ as + +$$ +s, \mathbf {t}, \mathbf {R} = \underset {s, \mathbf {t}, \mathbf {R}} {\arg \min } \operatorname {C D} \left(\Pi (\mathcal {W} (\bar {\mathbf {L}} _ {i})) , \zeta_ {i}\right), \tag {3} +$$ + +$$ +\bar {\mathbf {L}} _ {i} = s \mathbf {R} \left(\mathbf {L} _ {i}\right) + \mathbf {t}, \tag {4} +$$ + +where $\Pi$ is the projection matrix, $\bar{\mathbf{L}}_i$ is the transformed feature curve. $\mathbf{t} \in \mathbb{R}^3$ , $\mathbf{R} \in SO(3)$ , and $s \in \mathbb{R}$ are the optimized translation, rotation, and scaling parameters, respectively. + +In our implementation, we execute 150 gradient descent iterations to solve the rigid transformation parameters. After rigid optimization, we set $\widetilde{\mathbf{L}}$ as the initial position for the feature curve sets $\{\mathcal{C}_i|i = 1,\dots ,N_l\}$ for later non-rigid optimization. + +Surface-aware Curve Visibility Estimation. As the 2D feature curve $\zeta$ only contains visible points, it is essential to identify the visible points of the 3D curve $\mathcal{C}$ in camera space. A naive solution is to consider a point $\mathcal{C}(i)$ as visible if the cosine similarity between the view direction $\mathbf{v}$ and $\mathbf{n_i^d}$ (i.e., the direction from curve center to the $i$ -th point) in view-pose is less than 0. However, this approach will produce wrong judgments when a curve is occluded by other body parts. + +To tackle this problem, a surface-aware curve visibility estimation method is proposed. Specifically, we generate an explicit mesh $\mathbf{T}_{\mathbf{s}}$ from implicit surface $S(\eta)$ in canonical space via marching cube [33]. Next, we deform $\mathbf{T}_{\mathbf{s}}$ to camera view space via the deformation field $\Phi (\mathbf{T}_{\mathbf{s}})$ . Then, we can check if a feature curve point $\Phi (\mathcal{C}(i))$ is occluded by the explicit mesh in view space based on z-buffer: + +$$ +V _ {\mathcal {C} (i)} = \operatorname {z b u f f e r} _ {-} \operatorname {t e s t} \left(\Phi (\mathcal {C} (i)), \Phi (\mathbf {T} _ {\mathbf {s}})\right). \tag {5} +$$ + +However, we find that the 3D curve $\mathcal{C}$ might sometimes move outside or have a scale larger than the explicit mesh $\mathbf{T_s}$ , there will be some errors if only depending on the z-buffer testing between $\mathcal{C}(i)$ and $\mathbf{T_s}$ . We therefore make use of the SMPL surface to improve the visibility estimation, by checking if the nearest point of $\mathcal{C}(i)$ on the SMPL body is occluded in the camera view space in a similar way. Note that this is feasible as in our intersection-free curve deformation, the correspondences between $\mathcal{C}(i)$ and its nearest vertex in the SMPL body are almost unchanged during optimization. Then a curve point is considered as visible if it passes both visibility checks. + +# 3.4. Progressive Curve and Surface Co-evolution. + +The surface of the garment is represented by the implicit SDF. As the feature curve visibility estimation depends on the garment surface, the curves and surface have to evolve consistently. To ensure the accuracy of curve visibility during the optimization process, we jointly optimize the curves and surface while imposing a regularization that the curves lie on the zero-isosurface of the SDF. The implicit surface is minimized by the photometric loss based on differentiable surface rendering. + +Curve-aware Surface Initialization. A good initialization for the implicit SDF $S(\eta)$ can reduce the optimization difficulty and improve the performance, especially for the long skirt and dress. Thanks to our curve-aware garment representation, we can utilize the initialized feature curve $\bar{\mathbf{L}}$ computed in Eq. (4) to enable a better shape initialization. Specifically, we apply a handle-based deformation [46] to deform a surface template such that its feature curves are aligned with $\bar{\mathbf{L}}$ . Then, we apply IGR [12] to initialize the implicit surface $S(\eta)$ by fitting the deformed template. + +Differentiable Surface Rendering. To reconstruct high-fidelity geometry, following the SelfRecon [19], we find the intersection points $\mathbf{p}$ on the surface and make them differentiable (more details can be found in supplementary). + +After obtaining the intersection points $\mathbf{p}$ , we compute its gradient $\mathbf{n_p} = \nabla f(\mathbf{p};\eta)$ and transform the camera view to canonical space as $\mathbf{v_p}$ by the Jacobian matrix of the deformed point $\Phi (\mathbf{p})$ (more details can be found in supplementary). To better account for the changes in the illumination, we also take a per-frame latent code $\mathbf{z}$ as input to the color rendering network $f_{c}$ . Then, the surface color $C_{\mathbf{p}}$ of point $\mathbf{p}$ can be computed as + +$$ +C _ {\mathbf {p}} = f _ {c} \left(\mathbf {p}, \mathbf {n} _ {\mathbf {p}}, \mathbf {v} _ {\mathbf {p}}, \mathbf {z}, E (\mathbf {p}); \psi\right). \tag {6} +$$ + +# 3.5. Loss Function + +The overall loss function consists of two parts, one part is for the feature curves optimization and the other is for garment surfaces optimization. + +# 3.5.1 Explicit Feature Curve Loss + +The optimization of feature curves relies on the 2D projection loss, a curve slope regularization loss, and an on-surface regularization loss that ensures the feature curves are on the garment surface. + +Feature Curve Projection Loss. Given SMPL pose parameter $\theta_{i}$ and the camera projection matrix $\Pi$ , we warp predicted feature curve $\mathcal{C}$ to camera view space via deformation field $\Phi$ , and compute project loss $\mathcal{L}_{proj}$ measured by 2D visible curves $\zeta$ using Chamfer Distance (CD): + +$$ +\mathcal {L} _ {p r o j} = \mathrm {C D} \left(V _ {\mathcal {C}} \otimes \Pi (\Phi (\mathcal {C})), \zeta\right) \tag {7} +$$ + +where $V_{\mathcal{C}}$ is the visibility mask of curves, and symbol $\otimes$ indicates the mask selection operator. + +Feature Curve Slope Regularization. To maintain the curvature of 3D curve $\mathcal{C}$ , we design a slope loss $\mathcal{L}_{slop}$ to regularize that the slope is consistent between adjacent points + +$$ +\mathcal {L} _ {s l o p} = \sum_ {i = 1} ^ {N _ {p}} (1 - \cos < \mathbf {s} _ {i + 1}, \mathbf {s} _ {i} >) \tag {8} +$$ + +where $\mathbf{s}_i = \mathcal{C}(i + 1) - \mathcal{C}(i)$ , $N_{p}$ is the point number in the curve, and $\cos < \infty$ is the cosine similarity function. + +On-surface Regularization. In addition, the feature curves are required to be on the corresponding garment surface. Hence, we introduce an as near as possible loss $\mathcal{L}_{anap}$ as: + +$$ +\mathcal {L} _ {a n a p} = \sum_ {i = 1} ^ {N _ {p}} | f (\mathcal {C} (i); \eta) | \tag {9} +$$ + +The overall explicit feature curve loss can be written as: + +$$ +\mathcal {L} _ {\text {c u r v e}} = \lambda_ {\text {p r o j}} \mathcal {L} _ {\text {p r o j}} + \lambda_ {\text {s l o p}} \mathcal {L} _ {\text {s l o p}} + \lambda_ {\text {a n a p}} \mathcal {L} _ {\text {a n a p}} \tag {10} +$$ + +where $\lambda_{proj},\lambda_{slop}$ and $\lambda_{anap}$ are loss weights. + +# 3.5.2 Garment Surface Loss + +For a monocular video with $N_{i}$ frames, the learnable parameter in implicit surface reconstruction is denoted as $\Theta$ : + +$$ +\boldsymbol {\Theta} = \left\{\eta , \phi , \psi \right\} \cup \left\{\mathbf {h} _ {i}, \mathbf {z} _ {i} \mid i = 1, \dots , N _ {i} \right\} \tag {11} +$$ + +Surface Rendering Loss. For a pixel within the garment mask, we compute the ray's intersection point $\mathbf{p}$ on the canonical surface $S(\eta)$ and apply surface rendering network to predict the color $C_{\mathbf{p}}$ (see Eq. (6)). Then the photometric loss can be computed as + +$$ +\mathcal {L} _ {R G B} = \frac {1}{| \mathcal {R} |} \sum_ {\mathbf {p} \in \mathcal {R}} \left| C _ {\mathbf {p}} (\boldsymbol {\Theta}) - I _ {\mathbf {p}} \right|, \tag {12} +$$ + +where $\mathcal{R}$ is the sample point set, $I_{\mathbf{p}}$ is the corresponding ground-truth pixel color from the input images. + +Mask-guided Implicit Consistency Loss. To better optimize implicit surface, following SelfRecon [19], we periodically extract explicit surface meshes $\mathbf{T}_{\mathbf{s}}$ in canonical space from SDF $f$ and use a differentiable renderer [50] to iteratively optimize $\mathbf{T}_{\mathbf{s}}$ by a mask loss using the surface mask. Then the updated explicit surface $\hat{\mathbf{T}}_{\mathbf{s}}$ will be used to supervise the implicit SDF $f$ as + +$$ +\mathcal {L} _ {m c o n s} = \frac {1}{| \hat {\mathbf {T}} _ {\mathbf {s}} |} \sum_ {\mathbf {p} \in \hat {\mathbf {T}} _ {\mathbf {s}}} | f (\mathbf {p}; \eta) |. \tag {13} +$$ + +Curve-guided Implicit Consistency Loss. We find that the explicit mesh $\hat{\mathbf{T}}_{\mathrm{s}}$ updated by the mask loss might contain holes or even collapse in some surface areas, which will harm the learning of implicit surface (see in Fig. 9). To address this issue, we design an explicit curve and surface consistency loss. Specifically, for a specific feature curve $\mathcal{C}$ that belongs to two implicit surfaces (e.g., waist curve belongs to both the upper-clothing and bottom-clothing), we generate its closed surface $\mathbf{T}_{\mathcal{C}}$ and then sample $N_{a}$ points from $\mathbf{T}_{\mathcal{C}}$ to constrain the implicit SDF $f$ as + +$$ +\mathcal {L} _ {c c o n s} = \frac {1}{| \mathbf {T} _ {\mathcal {C}} |} \sum_ {\mathbf {p} \in \mathbf {T} _ {\mathcal {C}}} | f (\mathbf {p}; \eta) |. \tag {14} +$$ + +Common Implicit Loss. Eikonal loss $\mathcal{L}_{eik}$ [12] is included to make the implicit function the signed distance function. To avoid distortion of non-rigid transformation, a rigid loss [39] $\mathcal{L}_{arap}$ is computed to constrain the non-rigid deformation. We also compute normal loss $\mathcal{L}_{norm}$ in canonical space to further refine the surface [19]. Moreover, we compute the skeleton smoothness loss [54] to reduce the high-frequency jitter of SMPL poses among frames (more details can be found in supplementary). + +The overall implicit surface loss can be written as: + +$$ +\mathcal {L} _ {i m s} = \mathcal {L} _ {R G B} + \lambda_ {m c o n s} \mathcal {L} _ {m c o n s} + \lambda_ {c c o n s} \mathcal {L} _ {c c o n s} \tag {15} +$$ + +$$ +\lambda_ {a r a p} \mathcal {L} _ {a r a p} + \lambda_ {e i k} \mathcal {L} _ {e i k} + \lambda_ {\text {n o r m}} \mathcal {L} _ {\text {n o r m}}, +$$ + +where $\lambda_{\text{arap}}, \lambda_{\text{mcons}}, \lambda_{\text{ccons}}, \lambda_{\text{eik}},$ and $\lambda_{\text{norm}}$ are the loss weights. + +# 4. Experiments + +Since there is no existing method for open garment meshes reconstruction from monocular videos, we compare with three state-of-the-art single-image methods, namely BCNet [20], ClothWild [36], and ReEF [62]. + +# 4.1. Evaluation on Synthetic Dataset + +Since there is no public real dataset for evaluating dynamic garment reconstruction, we adopt four video sequences from the synthetic data generated by SelfRecon [19] for quantitative evaluation. + +![](images/c4226bba4b85f08e9a8fef0eb1a81718ecedd0118073ed39e53a650db57d4ad1.jpg) +Figure 4. Qualitative comparison on the synthetic dataset. From left to right in each example: the ground-truth mesh, results of BCNet [20], ClothedWild [36], ReEF [62], and Ours. + +![](images/2cc13f2f8e26bc47649966972e3f153f54c731da6aea0291a2af6a051f6312f9.jpg) +Figure 5. Qualitative comparison on real datasets between BCNet [20], ClothWild [36], ReEF [62], and our method. Upper clothes are visualized in red color, while bottom clothes and dresses are visualized in blue color. Note that BCNet and ClothWild cannot model dresses. + +We first employ Blender [1] to extract the ground-truth garment mesh from the provided clothed human mesh of the first frame. To measure the accuracy of the reconstructed meshes, we compute the Chamfer distance (CD) between the ground-truth and estimated meshes. To evaluate the temporal consistency of the reconstructed meshes for the video sequence, we measure the consistency of corresponding vertices (CCV), which is the root mean square error of the corresponding vertices distances in adjacent frames. + +We test our method and the baseline methods on these four video sequences. Table 1 shows that our method achieves the best results in the metrics of CD and CCV on all four videos, demonstrating the effectiveness of our method in reconstructing accurate and temporally consistent dynamic garment meshes. From the results of high errors in the CCV, we can clearly see that single-image methods fail to maintain the consistency of the reconstruction for the video input. Figure 4 compares the visual results, in which our method produces detailed and accurate garments that are mostly close to the ground-truth surfaces. + +# 4.2. Evaluation on Real-world Videos + +We then qualitatively evaluate our method on the PeopleSnapshot [3] and a dataset captured by ourselves. These testing videos include a diverse variety of garments categories, including upper-cloth, dress, coats, pants, and skirts. + +Table 1. Quantitative results on four synthetic sequences. We compare the Chamfer distance (CD) between the ground-truth and reconstructed surfaces (in $cm$ ), as well as the consistency of corresponding vertices (CCV) between adjacent frames. + +
MethodFemale1Female3Male1Male2
CDCCVCDCCVCDCCVCDCCV
BCNet [20]3.1847.2013.4476.1862.9298.6045.2347.128
ClothedWild [36]2.424-2.075-2.782-3.980-
ReEF [62]1.8103.7821.9244.3222.0056.7942.8653.579
Ours1.8040.5971.6411.0641.7360.4841.8120.433
+ +Figure 5 shows the visual comparisons. The results of the baseline methods are predicted using a single image as input. Our method can faithfully reconstruct the layouts and surface details of the garments. In contrast, BCNet [20] and ClothWild [36] cannot accurately predict the garment layouts and produce over-smooth surfaces. + +We also demonstrate our dynamic reconstruction results in Fig. 6. We can see that our method can produce spacetime coherent results for different garment types (including the challenging dresses) from monocular videos, which is difficult to achieve with single-image methods. + +# 4.3. Ablation Study + +We next conduct ablation study for different components of our method (more results in our supplementary material). Curve Visibility Estimation. As shown in Fig. 7, sim + +![](images/23aa9d3ee69e4cf78ac6cb3b01642407c57cc80d727f7882b8004aeda967af2f.jpg) + +![](images/9eab54e38b3ddc914547eb333c3b01fcfc2847aa11f486bc28c20c0bc62e497e.jpg) + +![](images/4d9538ab2313c16a7445715009a771f4072a53ae0b96a7e9affaf7d5a9912fe2.jpg) + +![](images/286bd9cfdf8e94fb8066e1b6e80869ab5b26613f20a74a5f36bab47ee4677359.jpg) + +![](images/4de8f3507800811a84cc184341e55680bd1140fb984cf1fe35fa3120d5edc348.jpg) + +![](images/44ee80d6c057bd5aba6a5a31fb1f018f8325a4b73e0bb9fc428f3f58bde9b9a1.jpg) + +![](images/85de9297105ef055a5830a3f78a4799651f79f17d0dd9397f65296f7a8b9bf6b.jpg) + +![](images/4315e4b211cec1282a51163e58e117ba10e6cecfcfa4f729910bc374dbaca7b4.jpg) + +![](images/dcecc9c16201e9992afba4ca814712339560872a8428918bb3eed02049a6611b.jpg) + +![](images/8e3be3dcdc1d4c92c9c6cae7a41c66e692d8971ba472e4ce5ebf9a887164bc7d.jpg) + +![](images/590e11158fa22e1a8022f72898c369f375be00c695961ec94b4d691539d709a3.jpg) + +![](images/83ec3b394a906d75f57f39638459aa65b7b5cf4964d1d348d3b99b89641813ce.jpg) +ur frames in a monocular video. + +![](images/102cb020732abde71912e74c1ddaff384c54ff987a3f531f8d72a0a3541e312b.jpg) + +![](images/b97b082c6ee865c5e32cfeeba0cd3b5642f5e122182f599cb0977287c1e4ad26.jpg) + +![](images/836b40200a58c8b4db25efef8f95a96b2e80dd1d258ac5dd6d49d6312585f443.jpg) + +![](images/a57e8de2e7cccb1ae132592a4eae536063f3b0ca1ada7816a0e1b1bd4cb0537f.jpg) +(a) Curve Normal + +![](images/cd64f50717aa150c1251f86115084fbbaf39ac9c059a75de7143fdcf909aeaa4.jpg) +(b) w/o Implicit Surface + +![](images/223fbe665da5003bcb187a1c3abb32695a98b05a5206749ed89e814a4dfe1667.jpg) +(c) w/o SMPL + +![](images/f186949018f3d561bca6be1a79bd593ff861ae5ffcb7feda27163aa6a9d38694.jpg) +(d) Surface-aware +Figure 7. Ablation study of curve visibility estimation method. + +ply using normal direction for visibility estimation leads to worse results, while using both the implicit SDF and SMPL surfaces for z-buffer testing produces the best result. + +Explicit Curve Losses. Figure 8 (a) shows that without the curve slop loss $\mathcal{L}_{slop}$ , the optimized curves will contain noise and artifacts. As shown in Fig. 8 (b), the proposed on-surface regularization (i.e., $\mathcal{L}_{anap}$ ) can well constrain the curves to be on the surface and produce much more accurate fitting results, demonstrating the implicit surface helps the optimization of curves. + +Curve-guided Consistency Loss. To improve the optimization of the implicit surface, we use curves to regularize the surface. Figure 9 shows that this regularization effectively improves the surface geometry, verifying that curves benefit the optimization of surfaces. + +# 5. Conclusion + +We have presented a new framework for dynamic garment reconstruction from monocular videos, by formulating this task as an optimization problem of dynamic 3D curves and surface recovery, followed by garment template registration. To solve this problem, we introduce a novel approach, called REC-MV, to jointly optimize the curves and surface from 2D supervision in a progressive co-evolution manner. Experimental results show that our method can reconstruct high-fidelity dynamic garments meshes with open boundaries, significantly outperforming existing methods. + +Limitations. Our method can only reconstruct common garment categories whose contours can be represented by + +![](images/cc08e93cf39adc4f040bef778a40ee7a4bc9266b57b334a32ae147927c097c14.jpg) +(a) $\mathrm{w / o}\mathcal{L}_{slop}$ + +![](images/d86ed5350ff42348e6e4baeb431cce0b943d65549fb31658bca2d84a37d12e80.jpg) +(b) $\mathrm{w / o}$ $\mathcal{L}_{anap}$ + +![](images/7ef37cd970c33cdb32741fe7c71a1575178ae08aba787897d680a6253293e14e.jpg) +(c) Both + +![](images/39d3e506edb20c3648f7f138bcb9ca20304409a9c75c5056dda4307ab09eebde.jpg) +Figure 8. Ablation study of the explicit curve losses. + +![](images/94f0581cc88290b029f33065aece1f7bd024fbb102573391496f4af9078ec2b3.jpg) +Figure 9. Results of w/o and w/ the curve-guided consistency loss. + +![](images/49b733f4355c3972236b81d198959e8c3e8a662b3155f8a448f947f2fb4303f7.jpg) + +$$ +\mathrm {w / o} \mathcal {L} _ {c c o n s} +$$ + +$$ +\mathrm {w} / \mathcal {L} _ {c c o n s} +$$ + +$$ +\mathrm {w / o} \mathcal {L} _ {c c o n s} +$$ + +$$ +\mathrm {w /} \mathcal {L} _ {c c o n s} +$$ + +feature curves. Additionally, our method requires the moving person to be observed from different angles. + +Acknowledgement. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No.JCYJ20220530143604010, the National Key R&D Program of China with grant No.2018YFB1800800, by NSFC No. 62202409, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No.2017ZT07X152 and No.2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No.2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No.ZDSYS201707251409055). It was also sponsored by CCF-Tencent Open Research Fund. + +# References + +[1] Blender. https://www.blender.org/. 2021.7 +[2] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single RGB camera. In CVPR, 2019. 2 +[3] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. Video based reconstruction of 3d people models. 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Registering explicit to implicit: Towards high-fidelity garment mesh reconstruction from single images. 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Recent neural rendering methods achieve high-quality dynamic clothed human reconstruction results from monocular video, but these methods cannot separate the garment surface from the body. Moreover, despite existing garment reconstruction methods based on feature curve representation demonstrating impressive results for garment reconstruction from a single image, they struggle to generate temporally consistent surfaces for the video input. To address the above limitations, in this paper, we formulate this task as an optimization problem of 3D garment feature curves and surface reconstruction from monocular video. We introduce a novel approach, called REC-MV, to jointly optimize the explicit feature curves and the implicit signed distance field (SDF) of the garments. Then the open garment meshes can be extracted via garment template registration in the canonical space. Experiments on multiple casually captured datasets show that our approach outperforms existing methods and can produce high-quality dynamic garment surfaces. The source code is available at https://github.com/GAP-LAB-CUHK-SZ/REC-MV." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 542, + 127, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 542, + 127, + 554 + ], + "spans": [ + { + "bbox": [ + 47, + 542, + 127, + 554 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 684 + ], + "type": "text", + "content": "High-fidelity clothes digitization plays an essential role in various human-related vision applications such as virtual shopping, film, and gaming. In our daily life, humans are always in a moving status, driving their clothes to move together. To realize this very common scenario, it is indispensable to gain dynamic garments in real applications. Thanks to the rapid development of mobile devices in terms of digital cameras, processors, and storage, shooting a monocular video in the wild becomes highly convenient and accessible for general customers. In this paper," + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 217, + 547, + 363 + ], + "blocks": [ + { + "bbox": [ + 309, + 217, + 547, + 363 + ], + "lines": [ + { + "bbox": [ + 309, + 217, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 309, + 217, + 547, + 363 + ], + "type": "image", + "image_path": "3b12c49523ed62d8478876006ca4ca2a4bb06d23131e2b5ecaf8d7b907fb2d80.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 365, + 547, + 420 + ], + "lines": [ + { + "bbox": [ + 305, + 365, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 547, + 420 + ], + "type": "text", + "content": "Figure 1. Can we extract dynamic 3D garments from monocular videos? The answer is Yes! By jointly optimizing the dynamic feature curves and garment surface followed by non-rigid template registration, our method can reconstruct high-fidelity and temporally consistent garment meshes with open boundaries." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 455, + 546, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 546, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 546, + 503 + ], + "type": "text", + "content": "our goal is definite – extracting dynamic 3D garments from monocular videos, which is significantly meaningful and valuable for practical applications, but is yet an uncultivated land with many challenges." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "We attempt to seek a new solution to this open problem and start by revisiting existing works from two main-streams. i) Leveraging the success of neural rendering methods [35, 37, 57], several works are able to reconstruct dynamic clothed humans from monocular videos [8, 19, 29, 47, 49], by representing the body surface with an implicit function in the canonical space and apply skinning based deformation for motion modeling. One naive way to achieve our goal is: first to get the clothed human through these methods and separate the garments from human bodies. However, such a separation job requires laborious and non-trivial processing by professional artists, which is neither straightforward nor feasible for general application scenarios. ii) As for garment reconstruction, many methods [5, 10, 20, 61, 62] make it possible to reconstruct high-quality garment meshes from single-view images in the wild. Specifically, ReEF [62] estimates 3D fea" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 39, + 693, + 111, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 39, + 693, + 111, + 703 + ], + "spans": [ + { + "bbox": [ + 39, + 693, + 111, + 703 + ], + "type": "text", + "content": "* Equal contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 39, + 703, + 217, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 39, + 703, + 217, + 712 + ], + "spans": [ + { + "bbox": [ + 39, + 703, + 217, + 712 + ], + "type": "text", + "content": "† Corresponding author: hanxiaoguang@cuhk.edu.cn." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4637" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "ture curves* and an implicit surface field [34] for non-rigid garment template registration. Nonetheless, these methods struggle to produce temporally consistent surfaces when taking videos as inputs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 123, + 287, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 123, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 45, + 123, + 287, + 291 + ], + "type": "text", + "content": "The above discussion motivates us to combine the merits of both the dynamic surface modeling in recent neural rendering methods and the explicit curve representation for garment modeling. To this end, we try to delineate a new path towards our goal: optimizing dynamic explicit feature curves and implicit garment surface from monocular videos, to extract temporally consistent garment meshes with open boundaries. We represent the explicit curves and implicit surface in the canonical space with skinning-based motion modeling, and optimize them by 2D supervision automatically extracted from the video (e.g., image intensities, garment masks, and visible feature curves). After that, the open garment meshes can be extracted by a garment template registration in the canonical space (see Fig. 1)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 294, + 288, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 294, + 288, + 510 + ], + "spans": [ + { + "bbox": [ + 45, + 294, + 288, + 510 + ], + "type": "text", + "content": "We strive to probe this path as follows: (1) As a feature curve is a point set whose deformation has a high degree of freedom, directly optimizing the per-point offsets often leads to undesired self-intersection and spike artifacts. To better regularize the deformation of curves, we introduce an intersection-free curve deformation method to maintain the order of feature curves. (2) We optimize the 3D feature curves using 2D projection loss measured by the estimated 2D visible curves, where the key challenge is to accurately compute the visibility of curves. To address this problem, we propose a surface-aware curve visibility estimation method based on the implicit garment surface and z-buffer. (3) To ensure the accuracy of curve visibility estimation during the optimization process, the curves should always be right on the garment surface. We therefore introduce a progressive curve and surface evolution strategy to jointly update the curves and surface while imposing the on-surface regularization for curves." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 513, + 281, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 513, + 281, + 525 + ], + "spans": [ + { + "bbox": [ + 59, + 513, + 281, + 525 + ], + "type": "text", + "content": "To summarize, the main contributions of this work are:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 530, + 287, + 674 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 530, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 530, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 58, + 530, + 287, + 566 + ], + "type": "text", + "content": "- We introduce REC-MV, to our best knowledge, the first method to reconstruct dynamic and open loose garments from the monocular video." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 567, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 567, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 58, + 567, + 287, + 638 + ], + "type": "text", + "content": "- We propose a new approach for joint optimization of explicit feature curves and implicit garment surface from monocular video, based on carefully designed intersection-free curve deformation, surface-aware curve visibility estimation, and progressive curve and surface evolution methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 639, + 287, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 639, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 58, + 639, + 287, + 674 + ], + "type": "text", + "content": "- Extensive evaluations on casually captured monocular videos demonstrate that our method outperforms existing methods." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 94, + 545, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 94, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 94, + 545, + 178 + ], + "type": "text", + "content": "Human Reconstruction from Single-view Image. Traditional methods for human reconstruction often adopt a parametric human model (e.g., SMPL [32] or SCAPE [4]) and can only recover a naked 3D body [23, 24]. To increase the surface details, free-form deformations can be applied to the mesh vertices to model small geometry variations caused by the clothing [2, 3, 26, 43, 52]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 179, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 179, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 545, + 287 + ], + "type": "text", + "content": "Recent methods propose to utilize implicit surface representations [34, 38] to reconstruct 3D clothed human with an arbitrary topology. Specifically, PIFu and PIFuhd [44, 45] extract pixel-aligned spatial features from images as the input for implicit surface function for occupancy prediction. Follow-up methods then integrates 3D-aligned features to improve the results [6, 15-18, 56, 58]. As these methods only consider single-image reconstruction, they cannot produce temporally consistent results for video input." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 290, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 350 + ], + "type": "text", + "content": "Human Reconstruction from Monocular Video. Inspired by the success of neural rendering methods [35, 37, 57] in scene reconstruction, many methods have been proposed to reconstruct 3D human from sparse-view [31, 41, 53, 55, 60] or monocular [19, 47, 49] videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": "Anim-NeRF [8], Neuman [21] and HumanNeRF [49] introduce methods based on neural radiance field (NeRF) [35] to reconstruct an animatable avatar from monocular video. These methods transform a 3D point in the observation space to the canonical space by inverse-skinning, and then perform volume rendering in the canonical space. A-NeRF [47] additionally adopt a skeleton-relative encoding strategy. AvATAR [29] proposes a monocular human volumetric capture method, but requires reconstructing an avatar from multiple 3D scans in advance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Garment Reconstruction from Images. Reconstructing garment mesh from images enables many applications like virtual try-on and content creation. Existing methods reconstruct the clothing as a separate layer on top of the body [7, 22, 25, 42, 48, 51]. Among them, several methods address the challenging problem of garment reconstruction from single-view image [5, 10, 20, 36, 61, 62]. MGN [5] learns a per-category parametric model from a large-scale clothing dataset. BCNet [20] first reconstructs a coarse template and then refines the surface details with a displacement network. AnchorUDF [59] adopts the unsigned distance field (UDF) [9] to represent the open surface mesh. SMPlicit [10] proposes a generative model to reconstruct layered garments from a single image. DeepFasion3D [61] reconstructs the surface with occupancy network [34] and applies non-rigid ICP to register the clothing template. ReEF [62] registers explicit clothing template to the implicit field learned from pixel-aligned implicit function. However, as these single-image methods do not consider clothing motion, they are not suitable for dynamic gar" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 40, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 40, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 40, + 693, + 287, + 713 + ], + "type": "text", + "content": "* feature curves of the garment (e.g., necklines, hemlines) can provide critical cues for determining the shape contours of the garment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4638" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 75, + 162, + 161 + ], + "blocks": [ + { + "bbox": [ + 49, + 75, + 162, + 161 + ], + "lines": [ + { + "bbox": [ + 49, + 75, + 162, + 161 + ], + "spans": [ + { + "bbox": [ + 49, + 75, + 162, + 161 + ], + "type": "image", + "image_path": "c05b4122433502f378ddbb7982115a06b03ef498cd88d2bd49969a9a1e79e035.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 75, + 481, + 251 + ], + "blocks": [ + { + "bbox": [ + 164, + 75, + 481, + 251 + ], + "lines": [ + { + "bbox": [ + 164, + 75, + 481, + 251 + ], + "spans": [ + { + "bbox": [ + 164, + 75, + 481, + 251 + ], + "type": "image", + "image_path": "7d369701113cb4dd33ffa847cf85a04375cb6ea4d19f755d9b57901d6f3c36b7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 547, + 314 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed REC-MV. (a) Starting from a surface template, we initialize the canonical curves by solving Eq. (3), and apply a handle-based deformation to initialize the canonical implicit surface. (b) Given an " + }, + { + "bbox": [ + 46, + 258, + 547, + 314 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 258, + 547, + 314 + ], + "type": "text", + "content": "-th frame, canonical curves are deformed to the camera view space to compute the projection loss based on the surface-aware visibility estimation. (c) Similarly, the canonical surface is deform to the camera view to compute the photometric loss by differentiable rendering. The curves and surface are jointly optimized to enable a progressive co-evolution. (d) Last, the open garment meshes can be extracted by template registration in the canonical space." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 483, + 76, + 544, + 250 + ], + "blocks": [ + { + "bbox": [ + 483, + 76, + 544, + 250 + ], + "lines": [ + { + "bbox": [ + 483, + 76, + 544, + 250 + ], + "spans": [ + { + "bbox": [ + 483, + 76, + 544, + 250 + ], + "type": "image", + "image_path": "63b369c6a7e6a6a3b610fa82900be97be17607bc792b51bcd366a26ff12d05f8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 335, + 132, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 132, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 132, + 346 + ], + "type": "text", + "content": "ment reconstruction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 347, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 491 + ], + "type": "text", + "content": "Among methods related to garment reconstruction from videos, Li et al. [28] introduce a method to learn physics-aware clothing deformation from monocular videos, but assumes the template scans for the body and clothing are provided [13]. Garment Avatar [14] proposes a multi-view patterned cloth tracking algorithm, requiring the subject to wear clothing with specific patterns. SCARF represents the layered clothing using radiance field [11] on top of the SMPL-X model [40] from monocular video. In contrast, our method first reconstructs the explicit 3D garment curves and surfaces, and then extracts the garment mesh via template registration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 500, + 103, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 103, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 103, + 511 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": "Given a monocular video with " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "N_{i}" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": " frames depicting a moving person " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\{I_t|t = 1,\\dots ,N_i\\}" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": ", REC-MV aims to reconstruct high-fidelity and space-time coherent open garment meshes. This is a challenging problem as it requires a method to simultaneously capture the shape contours, local surface details, and the motion of the garment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": "Observing that feature curves (e.g., necklines, hemlines) provide critical cues for determining the shape contours of garment [61] and implicit signed distance function (SDF) can well represent a detailed closed surface [19], we propose to first optimize the explicit 3D feature curves and implicit garment surfaces from the video, and then apply non-rigid clothing template registration to extract the open garment meshes (see Fig. 2)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Preprocessing. We generate the initial shape parameter " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", camera intrinsic " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", and per-frame SMPL [32] pose param" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "content": "eters " + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\{\\pmb {\\theta}_t|t = 1,\\dots ,N_i\\}" + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "content": " using Videoavatar [3]. To identify the garment regions in 2D images, we apply the existing garment parsing method [27] to estimate the garment masks. Our method also requires 2D visible curves " + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\zeta =" + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\{\\zeta_{l,t}|l = 1,\\ldots N_l,t = 1,\\ldots ,N_i\\}" + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "content": " for 3D curve recovery, where " + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "content": " denotes the number of curves. Note that the 2D visible curves can be automatically produced by parsing boundaries of the garment mask (more details in the supplementary material)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": "Overview. To utilize the information that exists in the entire video for dynamic garment reconstruction, we represent the explicit feature curve and implicit garment surface in the canonical space (Sec. 3.1). For a specific time step, we adopt the skeleton-based skinning and non-rigid deformation modeling to map the canonical curves and surfaces to the camera view space (Sec. 3.2). As the given 2D curves only contain visible points, to optimize the 3D feature curves from 2D projection error, we propose a surface-aware approach to compute the visibility of the 3D feature curve based on z-buffer (Sec. 3.3). In terms of implicit surface optimization, we minimize the photometric loss between the rendered and input image based on the differentiable surface rendering technique (Sec. 3.4). Then the adopted loss functions for joint optimization of curves and surfaces are described (Sec. 3.5). Last, the open garment meshes can be extracted by registering an explicit garment template to the recovered curves and implicit surfaces in the canonical space (more details in the supplementary material). Then the garment meshes can be deformed based on the SMPL poses." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4639" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "type": "text", + "content": "3.1. Feature Curve and Surface Representation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "text", + "content": "Explicit Surface Template. Following DeepFashion3D [61], we employ several surface templates, each contains a pre-defined set of 3D feature curves " + }, + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = \\{\\mathbf{L}_i | i = 1, \\dots, N_l\\}" + }, + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "text", + "content": " extracted from the garment boundaries, where " + }, + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "inline_equation", + "content": "N_l" + }, + { + "bbox": [ + 47, + 92, + 287, + 189 + ], + "type": "text", + "content": " is the number of feature curves (see our supplementary materials for more details). The surface templates will be used for garment surface initialization and the pre-defined feature curves will be used for curve initialization†." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 191, + 288, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 288, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 288, + 275 + ], + "type": "text", + "content": "Intersection-free Curve Deformation. A straightforward idea is to represent a feature curve as a discrete point set, and directly estimate the 3D deformation offset for each point during optimization. However, this unstructured curve representation struggles to maintain the order of the points and often generate spike artifacts due to the high degree of freedom of the deformation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": "To address this issue, we introduce a novel intersection-free curve deformation method, in which the point's deformation at each step is controlled by the curve center and two orthogonal directions (see Fig. 3 for illustration). Formally, given a curve " + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": " points with center " + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{p_c}" + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": ", the updated position of " + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": "-th point " + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 46, + 276, + 287, + 350 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 358, + 287, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 358, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 102, + 358, + 287, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {C} ^ {\\prime} (i) = \\mathbf {p} _ {\\mathbf {c}} + S _ {i} ^ {d} \\mathbf {n} _ {\\mathbf {i}} ^ {\\mathbf {d}} + S _ {i} ^ {c} \\mathbf {n} ^ {\\mathbf {c}}, \\tag {1}", + "image_path": "4a3040f97d688e6ed59bd4210da18fe0586528ad4edb46e86ea678320fd9388c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathbf{n_i^d}" + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": " is the direction from the curve center to the current point " + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathbf{n}^{\\mathbf{c}} = \\frac{1}{N_p - 1}\\sum_{i = 1}^{N_p}(\\mathbf{n_i^d}\\times \\mathbf{n_{i - 1}^d})" + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": " is the direction perpendicular to the current feature curve plane. " + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "inline_equation", + "content": "S_{i}^{d}\\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "inline_equation", + "content": "S_{i}^{c}\\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 384, + 287, + 448 + ], + "type": "text", + "content": " are learnable parameters specifying the step size of the deformation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "type": "text", + "content": "The proposed intersection-free curve deformation can well preserve the order of points in the curve, which largely reduced the difficulty of optimization compared to the direct offset estimation approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": "Implicit SDF in Canonical Space. Unsigned distance field (UDF) [9] is an implicit function that can represent an open surface. However, as UDF is not differentiable at points close to the surface, it is non-trivial to integrate UDF with differentiable surface rendering to take advantage of supervision from 2D photometric loss. We therefore adopt the SDF to represent a closed garment surface for surface geometry recovery, followed by garment template registration to extract the open surface." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": "It is common to represent the whole surface with a single SDF for human reconstruction [19]. However, as our goal is to reconstruct separate clothes, using a single SDF to represent both the upper clothes and bottom clothes (e.g., skirt) increases the difficulty of template registration (i.e., splitting the upper and bottom clothes requires highly accurate waist curves)." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 340, + 77, + 518, + 168 + ], + "blocks": [ + { + "bbox": [ + 340, + 77, + 518, + 168 + ], + "lines": [ + { + "bbox": [ + 340, + 77, + 518, + 168 + ], + "spans": [ + { + "bbox": [ + 340, + 77, + 518, + 168 + ], + "type": "image", + "image_path": "97f26a46e27995ce8e675fd909c2af1e80eb7cc434878d75ae472ee90cb5b51d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 176, + 541, + 188 + ], + "lines": [ + { + "bbox": [ + 309, + 176, + 541, + 188 + ], + "spans": [ + { + "bbox": [ + 309, + 176, + 541, + 188 + ], + "type": "text", + "content": "Figure 3. Illustration of the intersection-free curve deformation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "text", + "content": "To enable better template registration, we consider three different surface types (i.e., upper-clothing, bottom-clothing, and upper-bottom) according to the garment types, and represent each surface type as the zero-isosurface of an independent SDF in the canonical space. The SDF is expressed by an MLP " + }, + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "text", + "content": " with learnable weights " + }, + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 205, + 545, + 278 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 360, + 283, + 490, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 283, + 490, + 298 + ], + "spans": [ + { + "bbox": [ + 360, + 283, + 490, + 298 + ], + "type": "interline_equation", + "content": "S (\\eta) = \\{\\mathbf {p} \\in \\mathbb {R} ^ {3} | f (\\mathbf {p}; \\eta) = 0 \\}.", + "image_path": "a0b2d58c14106c4e9c33a3bd3d001413a71f20e61020b93d59c1a42eadc4570f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 301, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 338 + ], + "type": "text", + "content": "For the sake of simplicity and without loss of generality, we illustrate our method in reconstructing a single surface type later in this section." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 343, + 487, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 343, + 487, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 343, + 487, + 357 + ], + "type": "text", + "content": "3.2. Skinning Based Motion Modeling" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 361, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 410 + ], + "type": "text", + "content": "We model large body motions by linear blend skinning (LBS) transformation based on the SMPL [32] model, and utilize a non-rigid deformation field to account for fine-grained deformations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": "Skinning Transformation. Given a SMPL body with shape parameter " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": " and a pose parameter " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": "-th frame, a point " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": " on the body surface in canonical space with skinning weights " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "w(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": " can be warped to camera view space via skinning transformation " + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 411, + 545, + 471 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "text", + "content": "Notably, the skinning weights " + }, + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "w(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "text", + "content": " are only defined for points on the SMPL surface. To warp arbitrary points in the canonical space to camera view, we use the diffused skinning strategy [30] to propagate the skinning weights of SMPL body vertices to the entire canonical space, and store the weights in a voxel grid of size " + }, + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 256" + }, + { + "bbox": [ + 304, + 472, + 545, + 555 + ], + "type": "text", + "content": ". Then we can obtain the skinning weights by trilinear interpolation." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": "Non-rigid Deformation. Skinning deformation enables the garment surface to deform in a way consistent with the body's large-scale motion [16]. However, the motion of details and garment parts that are far away from body cannot be fully represented by skinning transformation [19]. Hence, a non-rigid deformation MLP is used to model these fine-grained changes. Specifically, we design an MLP " + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": " with learnable parameters " + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": " to model garment surface's non-rigid deformation:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 371, + 670, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 670, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 371, + 670, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathbf {p} ^ {\\prime} = \\mathcal {D} (\\mathbf {p}, \\mathbf {h}, E (\\mathbf {p}); \\phi), \\tag {2}", + "image_path": "364f121883e9c5b0b785e5a927c0cd080e2fd997d3622c69651eb76bedee64d6.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}'" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " is the deformed point of the input point " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " in the canonical space, " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " is the latent code of the current frame," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 40, + 702, + 252, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 40, + 702, + 252, + 713 + ], + "spans": [ + { + "bbox": [ + 40, + 702, + 252, + 713 + ], + "type": "text", + "content": "† including templates for uppers, dresses, coats, pants, and skirts." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4640" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "E(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is the position encoding [35] to represent the high-frequency information of spatial points." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "text", + "content": "Finally, combining " + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "text", + "content": " with skinning transformation field " + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "text", + "content": ", we could define a deformation field " + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot) = \\mathcal{W}(\\mathcal{D}(\\cdot))" + }, + { + "bbox": [ + 47, + 96, + 287, + 133 + ], + "type": "text", + "content": " to warp any points in the canonical space to the camera view." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 139, + 255, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 139, + 255, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 255, + 152 + ], + "type": "text", + "content": "3.3. 3D Feature Curves from 2D Projections" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "text", + "content": "The 3D feature curve will be optimized by minimizing the distance between its 2D projection on the image plane and the provided 2D visible curves. The key challenge here is how to compute the visibility of the 3D curves in the camera view. We first introduce a curve initialization strategy based on rigid transformation, and then propose a surface-aware curve visibility estimation method to support accurate non-rigid curves optimization." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "text", + "content": "Feature Curve Initialization. We start from the predefined feature curve sets " + }, + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = \\{\\mathbf{L}_i|i = 1,\\dots ,N_l\\}" + }, + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "text", + "content": " provided in the garment template. To reduce the difficulty of curve optimization, we perform a rigid curve initialization by directly minimizing the Chamfer Distance (CD) between the projected curves on the camera view space and the corresponding visible 2D curves " + }, + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 255, + 287, + 338 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 346, + 287, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 346, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 83, + 346, + 287, + 367 + ], + "type": "interline_equation", + "content": "s, \\mathbf {t}, \\mathbf {R} = \\underset {s, \\mathbf {t}, \\mathbf {R}} {\\arg \\min } \\operatorname {C D} \\left(\\Pi (\\mathcal {W} (\\bar {\\mathbf {L}} _ {i})) , \\zeta_ {i}\\right), \\tag {3}", + "image_path": "7dff9977413bb969bb59e5303ca64fad2365b4833f738851dfdb001aa285d610.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 100, + 369, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 369, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 100, + 369, + 287, + 384 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {L}} _ {i} = s \\mathbf {R} \\left(\\mathbf {L} _ {i}\\right) + \\mathbf {t}, \\tag {4}", + "image_path": "6c1c810ca7be6f449db73fdc45cd42139fb6b64c7090f74931a3530fe3ef2118.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": " is the projection matrix, " + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": " is the transformed feature curve. " + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in SO(3)" + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 392, + 287, + 439 + ], + "type": "text", + "content": " are the optimized translation, rotation, and scaling parameters, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "text", + "content": "In our implementation, we execute 150 gradient descent iterations to solve the rigid transformation parameters. After rigid optimization, we set " + }, + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{L}}" + }, + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "text", + "content": " as the initial position for the feature curve sets " + }, + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{C}_i|i = 1,\\dots ,N_l\\}" + }, + { + "bbox": [ + 46, + 440, + 287, + 499 + ], + "type": "text", + "content": " for later non-rigid optimization." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": "Surface-aware Curve Visibility Estimation. As the 2D feature curve " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " only contains visible points, it is essential to identify the visible points of the 3D curve " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " in camera space. A naive solution is to consider a point " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " as visible if the cosine similarity between the view direction " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{n_i^d}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " (i.e., the direction from curve center to the " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": "-th point) in view-pose is less than 0. However, this approach will produce wrong judgments when a curve is occluded by other body parts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": "To tackle this problem, a surface-aware curve visibility estimation method is proposed. Specifically, we generate an explicit mesh " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbf{s}}" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": " from implicit surface " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "S(\\eta)" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": " in canonical space via marching cube [33]. Next, we deform " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbf{s}}" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": " to camera view space via the deformation field " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\Phi (\\mathbf{T}_{\\mathbf{s}})" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": ". Then, we can check if a feature curve point " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\Phi (\\mathcal{C}(i))" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": " is occluded by the explicit mesh in view space based on z-buffer:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 86, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "V _ {\\mathcal {C} (i)} = \\operatorname {z b u f f e r} _ {-} \\operatorname {t e s t} \\left(\\Phi (\\mathcal {C} (i)), \\Phi (\\mathbf {T} _ {\\mathbf {s}})\\right). \\tag {5}", + "image_path": "c370acfd6fbdbc5ee21ea6da39b690559738977ce07563047951d456253b07d9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "However, we find that the 3D curve " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " might sometimes move outside or have a scale larger than the explicit mesh " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{T_s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": ", there will be some errors if only depending on the z-buffer testing between " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{T_s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": ". We therefore make use of the SMPL surface to improve the visibility estimation, by checking if the nearest point of " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " on the SMPL body is occluded in the camera view space in a similar way. Note that this is feasible as in our intersection-free curve deformation, the correspondences between " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " and its nearest vertex in the SMPL body are almost unchanged during optimization. Then a curve point is considered as visible if it passes both visibility checks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 226, + 538, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 226, + 538, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 226, + 538, + 239 + ], + "type": "text", + "content": "3.4. Progressive Curve and Surface Co-evolution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 245, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 353 + ], + "type": "text", + "content": "The surface of the garment is represented by the implicit SDF. As the feature curve visibility estimation depends on the garment surface, the curves and surface have to evolve consistently. To ensure the accuracy of curve visibility during the optimization process, we jointly optimize the curves and surface while imposing a regularization that the curves lie on the zero-isosurface of the SDF. The implicit surface is minimized by the photometric loss based on differentiable surface rendering." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "content": "Curve-aware Surface Initialization. A good initialization for the implicit SDF " + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "inline_equation", + "content": "S(\\eta)" + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "content": " can reduce the optimization difficulty and improve the performance, especially for the long skirt and dress. Thanks to our curve-aware garment representation, we can utilize the initialized feature curve " + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{L}}" + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "content": " computed in Eq. (4) to enable a better shape initialization. Specifically, we apply a handle-based deformation [46] to deform a surface template such that its feature curves are aligned with " + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{L}}" + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "content": ". Then, we apply IGR [12] to initialize the implicit surface " + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "inline_equation", + "content": "S(\\eta)" + }, + { + "bbox": [ + 304, + 356, + 545, + 475 + ], + "type": "text", + "content": " by fitting the deformed template." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "content": "Differentiable Surface Rendering. To reconstruct high-fidelity geometry, following the SelfRecon [19], we find the intersection points " + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 478, + 545, + 525 + ], + "type": "text", + "content": " on the surface and make them differentiable (more details can be found in supplementary)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": "After obtaining the intersection points " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": ", we compute its gradient " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{n_p} = \\nabla f(\\mathbf{p};\\eta)" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " and transform the camera view to canonical space as " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{v_p}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " by the Jacobian matrix of the deformed point " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\Phi (\\mathbf{p})" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " (more details can be found in supplementary). To better account for the changes in the illumination, we also take a per-frame latent code " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " as input to the color rendering network " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": ". Then, the surface color " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "C_{\\mathbf{p}}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " of point " + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 527, + 545, + 622 + ], + "type": "text", + "content": " can be computed as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 353, + 634, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 634, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 353, + 634, + 545, + 647 + ], + "type": "interline_equation", + "content": "C _ {\\mathbf {p}} = f _ {c} \\left(\\mathbf {p}, \\mathbf {n} _ {\\mathbf {p}}, \\mathbf {v} _ {\\mathbf {p}}, \\mathbf {z}, E (\\mathbf {p}); \\psi\\right). \\tag {6}", + "image_path": "39044420c9e35d367446c8a6c8c98333ad57cbba3a9a2e4e44e7b2a14d671a4f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 658, + 394, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 394, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 394, + 669 + ], + "type": "text", + "content": "3.5. Loss Function" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "The overall loss function consists of two parts, one part is for the feature curves optimization and the other is for garment surfaces optimization." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4641" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "text", + "content": "3.5.1 Explicit Feature Curve Loss" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "type": "text", + "content": "The optimization of feature curves relies on the 2D projection loss, a curve slope regularization loss, and an on-surface regularization loss that ensures the feature curves are on the garment surface." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": "Feature Curve Projection Loss. Given SMPL pose parameter " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": " and the camera projection matrix " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": ", we warp predicted feature curve " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": " to camera view space via deformation field " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": ", and compute project loss " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{proj}" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": " measured by 2D visible curves " + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 141, + 287, + 201 + ], + "type": "text", + "content": " using Chamfer Distance (CD):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 211, + 287, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 211, + 287, + 225 + ], + "spans": [ + { + "bbox": [ + 101, + 211, + 287, + 225 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p r o j} = \\mathrm {C D} \\left(V _ {\\mathcal {C}} \\otimes \\Pi (\\Phi (\\mathcal {C})), \\zeta\\right) \\tag {7}", + "image_path": "344ac041cc67b79d2b73e232eaf35fe150d28795095178ece6d71d5ca203c8ff.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "inline_equation", + "content": "V_{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "content": " is the visibility mask of curves, and symbol " + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 234, + 287, + 258 + ], + "type": "text", + "content": " indicates the mask selection operator." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "text", + "content": "Feature Curve Slope Regularization. To maintain the curvature of 3D curve " + }, + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "text", + "content": ", we design a slope loss " + }, + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{slop}" + }, + { + "bbox": [ + 47, + 260, + 287, + 297 + ], + "type": "text", + "content": " to regularize that the slope is consistent between adjacent points" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 306, + 287, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 306, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 94, + 306, + 287, + 339 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s l o p} = \\sum_ {i = 1} ^ {N _ {p}} (1 - \\cos < \\mathbf {s} _ {i + 1}, \\mathbf {s} _ {i} >) \\tag {8}", + "image_path": "d267437fa110a4835d14c51d5ce42baa803c05f3e3964b76d4462092d0734e5c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i = \\mathcal{C}(i + 1) - \\mathcal{C}(i)" + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": " is the point number in the curve, and " + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\cos < \\infty" + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": " is the cosine similarity function." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 375, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 412 + ], + "type": "text", + "content": "On-surface Regularization. In addition, the feature curves are required to be on the corresponding garment surface. Hence, we introduce an as near as possible loss " + }, + { + "bbox": [ + 46, + 375, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anap}" + }, + { + "bbox": [ + 46, + 375, + 287, + 412 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 115, + 421, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 421, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 115, + 421, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a n a p} = \\sum_ {i = 1} ^ {N _ {p}} | f (\\mathcal {C} (i); \\eta) | \\tag {9}", + "image_path": "ec28824b2ffc21d32b15035abc899192f585e829f6c0abec4dc8185bee0dc3bf.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 464, + 273, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 273, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 273, + 475 + ], + "type": "text", + "content": "The overall explicit feature curve loss can be written as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 487, + 287, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 487, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 56, + 487, + 287, + 501 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c u r v e}} = \\lambda_ {\\text {p r o j}} \\mathcal {L} _ {\\text {p r o j}} + \\lambda_ {\\text {s l o p}} \\mathcal {L} _ {\\text {s l o p}} + \\lambda_ {\\text {a n a p}} \\mathcal {L} _ {\\text {a n a p}} \\tag {10}", + "image_path": "65afa0ba3091bbedab13b8d0fd2b122c74940ac565059972c95e5e4d050f4509.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "inline_equation", + "content": "\\lambda_{proj},\\lambda_{slop}" + }, + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "inline_equation", + "content": "\\lambda_{anap}" + }, + { + "bbox": [ + 47, + 511, + 235, + 525 + ], + "type": "text", + "content": " are loss weights." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 539, + 176, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 176, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 176, + 551 + ], + "type": "text", + "content": "3.5.2 Garment Surface Loss" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "text", + "content": "For a monocular video with " + }, + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "inline_equation", + "content": "N_{i}" + }, + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "text", + "content": " frames, the learnable parameter in implicit surface reconstruction is denoted as " + }, + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 558, + 287, + 582 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 85, + 592, + 287, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 592, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 85, + 592, + 287, + 605 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Theta} = \\left\\{\\eta , \\phi , \\psi \\right\\} \\cup \\left\\{\\mathbf {h} _ {i}, \\mathbf {z} _ {i} \\mid i = 1, \\dots , N _ {i} \\right\\} \\tag {11}", + "image_path": "9b0e3e1cb2b294f65629d987eb8ccce5c3bea0391d08fe9c8b7c807de01fe39e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "Surface Rendering Loss. For a pixel within the garment mask, we compute the ray's intersection point " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " on the canonical surface " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "S(\\eta)" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " and apply surface rendering network to predict the color " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "C_{\\mathbf{p}}" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " (see Eq. (6)). Then the photometric loss can be computed as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 97, + 686, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 686, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 97, + 686, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R G B} = \\frac {1}{| \\mathcal {R} |} \\sum_ {\\mathbf {p} \\in \\mathcal {R}} \\left| C _ {\\mathbf {p}} (\\boldsymbol {\\Theta}) - I _ {\\mathbf {p}} \\right|, \\tag {12}", + "image_path": "84226296661f35a57afd932609772634f8516185b78e5e4ccb0cc26929974be7.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " is the sample point set, " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "I_{\\mathbf{p}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " is the corresponding ground-truth pixel color from the input images." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": "Mask-guided Implicit Consistency Loss. To better optimize implicit surface, following SelfRecon [19], we periodically extract explicit surface meshes " + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": " in canonical space from SDF " + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": " and use a differentiable renderer [50] to iteratively optimize " + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": " by a mask loss using the surface mask. Then the updated explicit surface " + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}_{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": " will be used to supervise the implicit SDF " + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 98, + 545, + 182 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 361, + 186, + 545, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 186, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 361, + 186, + 545, + 217 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m c o n s} = \\frac {1}{| \\hat {\\mathbf {T}} _ {\\mathbf {s}} |} \\sum_ {\\mathbf {p} \\in \\hat {\\mathbf {T}} _ {\\mathbf {s}}} | f (\\mathbf {p}; \\eta) |. \\tag {13}", + "image_path": "272f71fa842dcc0a63e9e71b9b7c92d817f0e0176aa092cadc4c3147eaa41b8d.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": "Curve-guided Implicit Consistency Loss. We find that the explicit mesh " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}_{\\mathrm{s}}" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " updated by the mask loss might contain holes or even collapse in some surface areas, which will harm the learning of implicit surface (see in Fig. 9). To address this issue, we design an explicit curve and surface consistency loss. Specifically, for a specific feature curve " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " that belongs to two implicit surfaces (e.g., waist curve belongs to both the upper-clothing and bottom-clothing), we generate its closed surface " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathcal{C}}" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " and then sample " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "N_{a}" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " points from " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathcal{C}}" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " to constrain the implicit SDF " + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 223, + 545, + 344 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 361, + 348, + 545, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 348, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 361, + 348, + 545, + 376 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c c o n s} = \\frac {1}{| \\mathbf {T} _ {\\mathcal {C}} |} \\sum_ {\\mathbf {p} \\in \\mathbf {T} _ {\\mathcal {C}}} | f (\\mathbf {p}; \\eta) |. \\tag {14}", + "image_path": "708143297caae6981ef54e18af10b32b5796c46fe0d4e0c2de66e75c8afdfae2.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "text", + "content": "Common Implicit Loss. Eikonal loss " + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{eik}" + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "text", + "content": " [12] is included to make the implicit function the signed distance function. To avoid distortion of non-rigid transformation, a rigid loss [39] " + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{arap}" + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "text", + "content": " is computed to constrain the non-rigid deformation. We also compute normal loss " + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{norm}" + }, + { + "bbox": [ + 305, + 383, + 545, + 491 + ], + "type": "text", + "content": " in canonical space to further refine the surface [19]. Moreover, we compute the skeleton smoothness loss [54] to reduce the high-frequency jitter of SMPL poses among frames (more details can be found in supplementary)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 317, + 491, + 521, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 491, + 521, + 502 + ], + "spans": [ + { + "bbox": [ + 317, + 491, + 521, + 502 + ], + "type": "text", + "content": "The overall implicit surface loss can be written as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 317, + 508, + 545, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 508, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 317, + 508, + 545, + 527 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i m s} = \\mathcal {L} _ {R G B} + \\lambda_ {m c o n s} \\mathcal {L} _ {m c o n s} + \\lambda_ {c c o n s} \\mathcal {L} _ {c c o n s} \\tag {15}", + "image_path": "3d877099a3ffac42017c744b61f9f471db6493df6cfdb8b94ee591c5f3730b5e.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 353, + 524, + 517, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 524, + 517, + 536 + ], + "spans": [ + { + "bbox": [ + 353, + 524, + 517, + 536 + ], + "type": "interline_equation", + "content": "\\lambda_ {a r a p} \\mathcal {L} _ {a r a p} + \\lambda_ {e i k} \\mathcal {L} _ {e i k} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}},", + "image_path": "efae26cf7840c6b2939f41435723b8e6de3b259328ae1003a954e4727656da67.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_{\\text{arap}}, \\lambda_{\\text{mcons}}, \\lambda_{\\text{ccons}}, \\lambda_{\\text{eik}}," + }, + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_{\\text{norm}}" + }, + { + "bbox": [ + 306, + 540, + 544, + 564 + ], + "type": "text", + "content": " are the loss weights." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 574, + 386, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 386, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 386, + 586 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 594, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 642 + ], + "type": "text", + "content": "Since there is no existing method for open garment meshes reconstruction from monocular videos, we compare with three state-of-the-art single-image methods, namely BCNet [20], ClothWild [36], and ReEF [62]." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 647, + 479, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 479, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 479, + 659 + ], + "type": "text", + "content": "4.1. Evaluation on Synthetic Dataset" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Since there is no public real dataset for evaluating dynamic garment reconstruction, we adopt four video sequences from the synthetic data generated by SelfRecon [19] for quantitative evaluation." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4642" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 541, + 167 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 541, + 167 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 541, + 167 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 541, + 167 + ], + "type": "image", + "image_path": "c4226bba4b85f08e9a8fef0eb1a81718ecedd0118073ed39e53a650db57d4ad1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 194 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison on the synthetic dataset. From left to right in each example: the ground-truth mesh, results of BCNet [20], ClothedWild [36], ReEF [62], and Ours." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 204, + 545, + 350 + ], + "blocks": [ + { + "bbox": [ + 47, + 204, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 47, + 204, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 545, + 350 + ], + "type": "image", + "image_path": "2cc13f2f8e26bc47649966972e3f153f54c731da6aea0291a2af6a051f6312f9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 350, + 547, + 374 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 547, + 374 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on real datasets between BCNet [20], ClothWild [36], ReEF [62], and our method. Upper clothes are visualized in red color, while bottom clothes and dresses are visualized in blue color. Note that BCNet and ClothWild cannot model dresses." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 393, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 287, + 501 + ], + "type": "text", + "content": "We first employ Blender [1] to extract the ground-truth garment mesh from the provided clothed human mesh of the first frame. To measure the accuracy of the reconstructed meshes, we compute the Chamfer distance (CD) between the ground-truth and estimated meshes. To evaluate the temporal consistency of the reconstructed meshes for the video sequence, we measure the consistency of corresponding vertices (CCV), which is the root mean square error of the corresponding vertices distances in adjacent frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 502, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 635 + ], + "type": "text", + "content": "We test our method and the baseline methods on these four video sequences. Table 1 shows that our method achieves the best results in the metrics of CD and CCV on all four videos, demonstrating the effectiveness of our method in reconstructing accurate and temporally consistent dynamic garment meshes. From the results of high errors in the CCV, we can clearly see that single-image methods fail to maintain the consistency of the reconstruction for the video input. Figure 4 compares the visual results, in which our method produces detailed and accurate garments that are mostly close to the ground-truth surfaces." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 646, + 224, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 224, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 224, + 658 + ], + "type": "text", + "content": "4.2. Evaluation on Real-world Videos" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We then qualitatively evaluate our method on the PeopleSnapshot [3] and a dataset captured by ourselves. These testing videos include a diverse variety of garments categories, including upper-cloth, dress, coats, pants, and skirts." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 440, + 545, + 497 + ], + "blocks": [ + { + "bbox": [ + 305, + 393, + 546, + 438 + ], + "lines": [ + { + "bbox": [ + 305, + 393, + 546, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 546, + 438 + ], + "type": "text", + "content": "Table 1. Quantitative results on four synthetic sequences. We compare the Chamfer distance (CD) between the ground-truth and reconstructed surfaces (in " + }, + { + "bbox": [ + 305, + 393, + 546, + 438 + ], + "type": "inline_equation", + "content": "cm" + }, + { + "bbox": [ + 305, + 393, + 546, + 438 + ], + "type": "text", + "content": "), as well as the consistency of corresponding vertices (CCV) between adjacent frames." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 440, + 545, + 497 + ], + "lines": [ + { + "bbox": [ + 308, + 440, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 308, + 440, + 545, + 497 + ], + "type": "table", + "html": "
MethodFemale1Female3Male1Male2
CDCCVCDCCVCDCCVCDCCV
BCNet [20]3.1847.2013.4476.1862.9298.6045.2347.128
ClothedWild [36]2.424-2.075-2.782-3.980-
ReEF [62]1.8103.7821.9244.3222.0056.7942.8653.579
Ours1.8040.5971.6411.0641.7360.4841.8120.433
", + "image_path": "e95dc6e07356b1aa5c198791e4b0cb900719e252941bf3d87b151bb4288e5ccf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "type": "text", + "content": "Figure 5 shows the visual comparisons. The results of the baseline methods are predicted using a single image as input. Our method can faithfully reconstruct the layouts and surface details of the garments. In contrast, BCNet [20] and ClothWild [36] cannot accurately predict the garment layouts and produce over-smooth surfaces." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 590, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 547, + 650 + ], + "type": "text", + "content": "We also demonstrate our dynamic reconstruction results in Fig. 6. We can see that our method can produce spacetime coherent results for different garment types (including the challenging dresses) from monocular videos, which is difficult to achieve with single-image methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 657, + 400, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 400, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 400, + 670 + ], + "type": "text", + "content": "4.3. 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Ablation study of curve visibility estimation method." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 347, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 287, + 384 + ], + "type": "text", + "content": "ply using normal direction for visibility estimation leads to worse results, while using both the implicit SDF and SMPL surfaces for z-buffer testing produces the best result." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "text", + "content": "Explicit Curve Losses. Figure 8 (a) shows that without the curve slop loss " + }, + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{slop}" + }, + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "text", + "content": ", the optimized curves will contain noise and artifacts. As shown in Fig. 8 (b), the proposed on-surface regularization (i.e., " + }, + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anap}" + }, + { + "bbox": [ + 47, + 386, + 287, + 470 + ], + "type": "text", + "content": ") can well constrain the curves to be on the surface and produce much more accurate fitting results, demonstrating the implicit surface helps the optimization of curves." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 472, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 287, + 533 + ], + "type": "text", + "content": "Curve-guided Consistency Loss. To improve the optimization of the implicit surface, we use curves to regularize the surface. Figure 9 shows that this regularization effectively improves the surface geometry, verifying that curves benefit the optimization of surfaces." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 546, + 119, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 119, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 119, + 558 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": "We have presented a new framework for dynamic garment reconstruction from monocular videos, by formulating this task as an optimization problem of dynamic 3D curves and surface recovery, followed by garment template registration. To solve this problem, we introduce a novel approach, called REC-MV, to jointly optimize the curves and surface from 2D supervision in a progressive co-evolution manner. Experimental results show that our method can reconstruct high-fidelity dynamic garments meshes with open boundaries, significantly outperforming existing methods." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Limitations. Our method can only reconstruct common garment categories whose contours can be represented by" + } + ] + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 318, + 248, + 395, + 337 + ], + "blocks": [ + { + "bbox": [ + 318, + 248, + 395, + 337 + ], + "lines": [ + { + "bbox": [ + 318, + 248, + 395, + 337 + ], + "spans": [ + { + "bbox": [ + 318, + 248, + 395, + 337 + ], + "type": "image", + "image_path": "cc08e93cf39adc4f040bef778a40ee7a4bc9266b57b334a32ae147927c097c14.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 338, + 372, + 348 + ], + "lines": [ + { + "bbox": [ + 326, + 338, + 372, + 348 + ], + "spans": [ + { + "bbox": [ + 326, + 338, + 372, + 348 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 326, + 338, + 372, + 348 + ], + "type": "inline_equation", + "content": "\\mathrm{w / o}\\mathcal{L}_{slop}" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 395, + 248, + 463, + 336 + ], + "blocks": [ + { + "bbox": [ + 395, + 248, + 463, + 336 + ], + "lines": [ + { + "bbox": [ + 395, + 248, + 463, + 336 + ], + "spans": [ + { + "bbox": [ + 395, + 248, + 463, + 336 + ], + "type": "image", + "image_path": "d86ed5350ff42348e6e4baeb431cce0b943d65549fb31658bca2d84a37d12e80.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 338, + 449, + 348 + ], + "lines": [ + { + "bbox": [ + 400, + 338, + 449, + 348 + ], + "spans": [ + { + "bbox": [ + 400, + 338, + 449, + 348 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 400, + 338, + 449, + 348 + ], + "type": "inline_equation", + "content": "\\mathrm{w / o}" + }, + { + "bbox": [ + 400, + 338, + 449, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anap}" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 463, + 249, + 539, + 337 + ], + "blocks": [ + { + "bbox": [ + 463, + 249, + 539, + 337 + ], + "lines": [ + { + "bbox": [ + 463, + 249, + 539, + 337 + ], + "spans": [ + { + "bbox": [ + 463, + 249, + 539, + 337 + ], + "type": "image", + "image_path": "7ef37cd970c33cdb32741fe7c71a1575178ae08aba787897d680a6253293e14e.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 488, + 338, + 517, + 346 + ], + "lines": [ + { + "bbox": [ + 488, + 338, + 517, + 346 + ], + "spans": [ + { + "bbox": [ + 488, + 338, + 517, + 346 + ], + "type": "text", + "content": "(c) Both" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 326, + 366, + 422, + 455 + ], + "blocks": [ + { + "bbox": [ + 329, + 351, + 521, + 362 + ], + "lines": [ + { + "bbox": [ + 329, + 351, + 521, + 362 + ], + "spans": [ + { + "bbox": [ + 329, + 351, + 521, + 362 + ], + "type": "text", + "content": "Figure 8. 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Additionally, our method requires the moving person to be observed from different angles." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgement. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No.JCYJ20220530143604010, the National Key R&D Program of China with grant No.2018YFB1800800, by NSFC No. 62202409, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No.2017ZT07X152 and No.2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No.2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No.ZDSYS201707251409055). 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Ross $^{2}$ , Alireza Fathi $^{2}$ , $^{1}$ University of California, Los Angeles, $^{2}$ Google Research", + "bbox": [ + 143, + 202, + 823, + 257 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2885fe2a4a23575f25aa37fbb74917d7593077933c05623b714035fd7d1bcebc.jpg", + "image_caption": [ + "Figure 1. We augment a visual-language model with the ability to retrieve multiple knowledge entries from a diverse set of knowledge sources, which helps generation. Both retriever and generator are trained jointly, end-to-end, by optimizing a language modeling objective." + ], + "image_footnote": [], + "bbox": [ + 132, + 282, + 820, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 472, + 313, + 488 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose an end-to-end Retrieval-Augmented Visual Language Model (REVEAL) that learns to encode world knowledge into a large-scale memory, and to retrieve from it to answer knowledge-intensive queries. REVEAL consists of four key components: the memory, the encoder, the retriever and the generator. The large-scale memory encodes various sources of multimodal world knowledge (e.g. image-text pairs, question answering pairs, knowledge graph triplets, etc.) via a unified encoder. The retriever finds the most relevant knowledge entries in the memory, and the generator fuses the retrieved knowledge with the input query to produce the output. A key novelty in our approach is that the memory, encoder, retriever and generator are all pre-trained end-to-end on a massive amount of data. Furthermore, our approach can use a diverse set of multimodal knowledge sources, which is shown to result in significant gains. We show that REVEAL achieves state-of-the-art results on visual question answering and image captioning. The project page of this work is reveal.github.io.", + "bbox": [ + 73, + 505, + 473, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 821, + 209, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent large-scale models such as T5 [33], GPT-3 [4], PaLM [9], CoCa [49], Flamingo [2], BEIT-3 [43] and", + "bbox": [ + 76, + 847, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "PaLI [7] have demonstrated the ability to store substantial amounts of world knowledge, when scaled to tens of billions of parameters and trained on vast text and image corpora. These models achieve state-of-the-art results in downstream tasks such as image captioning, visual question answering and open vocabulary recognition. Yet, these models have a number of drawbacks: (i) they require massive scale, of parameters, data and computation, and (ii) they need to be re-trained every time the world knowledge is updated.", + "bbox": [ + 500, + 473, + 893, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address these issues, we adopt a different approach. Instead of statically compiling world knowledge into model weights, we transform the knowledge into a key-value memory through neural representation learning. Our model learns to utilize the memory for answering knowledge-intensive queries. By decoupling the knowledge memorization from reasoning, we enable our model to leverage various external sources of knowledge (e.g., Wikipedia passages and images [37], the WikiData knowledge graph [40], Web imagetext pairs [5] and visual question answering data [12]). This enables the model parameters to focus on understanding the query and conducting reasoning, rather than being dedicated to memorization.", + "bbox": [ + 496, + 612, + 895, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Retrieval-augmented models have attracted a fair amount of attention in the fields of NLP [14, 18] and computer vision [13,25]. Typically, these models often use a pre-existing single-modality backbone to encode and retrieve information from the knowledge corpus. Such approaches do not leverage all available modalities in the query and knowl", + "bbox": [ + 496, + 811, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done when Ziniu was an intern at Google.", + "bbox": [ + 94, + 888, + 403, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23369", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "edge corpora, and hence they might not find the information that is most helpful for generating the model output. A key novelty in our approach is that we encode and store various sources of multimodal world knowledge into a unified memory, which the retriever can access via multimodal query encodings, to find the most relevant information from across complementary sources. Our multimodal memory and retriever are pre-trained end-to-end together together with the rest of the model, on a massive amount of data and using diverse knowledge sources.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key challenge of pre-training the multimodal retriever end-to-end is the lack of direct supervision. There is no ground-truth indicating which knowledge entries are most helpful for answering knowledge-intensive queries. Some of the existing works in NLP [14, 23, 34] propose to acquire training signal by assessing the usefulness of each retrieved knowledge entry independently for helping language modelling. This approach is inefficient, as it involves estimating hundreds of retrieved knowledge entries independently, and also inaccurate as it discards the dependency between different knowledge entries in the retrieval set. In contrast, we propose to get this training signal while simultaneously considering multiple retrieved knowledge entries, by introducing an attentive fusion layer that injects retrieval score into the attention calculation procedure. This enables the retrieval module to be differentiable and jointly pre-trained with the rest of the model.", + "bbox": [ + 75, + 242, + 472, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our key contributions are as follows:", + "bbox": [ + 96, + 500, + 423, + 513 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We are the first to propose an end-to-end pre-training paradigm that learns to index into a large-scale memory to solve knowledge-intensive visual-language tasks.", + "- Our method can construct a large-scale memory by encoding various sources of multimodal world knowledge, including Wikipedia passage, web images with alt-text captions, and knowledge graph triplets.", + "- REVEAL achieves state-of-the-art performance on several knowledge-intensive visual question answering and image captioning datasets. Notably on the OKVQA benchmark, REVEAL achieves a new state-of-the-art, $59.1\\%$ accuracy, while using order of magnitude fewer parameters than previous works." + ], + "bbox": [ + 94, + 513, + 468, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work and Background", + "text_level": 1, + "bbox": [ + 76, + 724, + 362, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge-based Visual Question Answering. To evaluate a model's ability to comprehend multimodal world knowledge not easily inferred from input data, several knowledge-based Visual Question Answering (VQA) datasets have been introduced. KB-VQA [41] and FVQA [42] design questions that can be answered by retrieving relevant triplets from domain-specific structured knowledge graphs. OK-VQA [29] improves these datasets by necessitating the use of external knowledge, which goes beyond what can be directly observed in the input images. More recently, A-", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "OKVQA [35] offers further improvements to OK-VQA by exclusively selecting questions that demand both external knowledge and commonsense reasoning about the image scenes. To tackle knowledge-based VQA tasks, many approaches have been proposed to incorporate external knowledge into visual-language models. One line of research uses explicit knowledge from structured knowledge graphs [11, 15, 31, 44] or unstructured text corpora [27, 28, 46]. The key component for these works is the knowledge retriever. Some works [11, 28, 31, 46] utilize off-the-shelf vision detection models to generate image tags for knowledge retrieval, while others train the retrieval model via distant supervision [27] or auxiliary tasks (e.g. entity linking) [13]. Another research direction aims to incorporate implicit knowledge from pre-trained Large Language Models, such as GPT-3 [4] or PaLM [9]. These approaches utilize off-the-shelf image caption models to convert images into text, feed them into a language model, and use the generated text output as augmented knowledge [13, 24, 48]. Our work follows the first direction, augmenting a vision-language model with an explicit knowledge retriever. The main distinction is that we propose an end-to-end training framework to jointly learn the answer generator and retriever, rather than using a fixed or predefined knowledge retrieval.", + "bbox": [ + 496, + 90, + 895, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-End Training of Retrieval-Augmented Models. Given the advantage of knowledge retrieval, a key question is how to get learning signal to train the retrieval model. For tasks with annotated retrieval ground-truth, retrieval training can be conducted via standard contrastive learning [22]. However, most tasks do not provide clear indications of which knowledge entries are relevant for generating answers. To this end, a series of studies have investigated retrieval training using supervision derived from downstream tasks. REALM [14] trains a single-document retriever by concatenating each retrieved result with the query, to calculate the final loss independently. A similar approach has been used by EMDR² [34] for multi-document retrieval training. FIDKD [17] proposes to use the aggregated attention score calculated by the generator as a distillation signal to train the retriever. Atlas [18] further introduces a perplexity distillation loss and a leave-one-out variant. Our REVEAL proposes to inject the retrieval scores directly into an attentive fusion module, enabling to train the retriever to directly optimize downstream tasks as well as pre-training objectives.", + "bbox": [ + 496, + 470, + 893, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 784, + 591, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose a Retrieval-Augmented Visual Language Model (REVEAL), which learns to use knowledge from different sources for solving knowledge-intensive tasks. For both pre-training and fine-tuning, our goal is to learn the distribution $P(y \\mid x)$ to generate a textual output $y$ conditioned on a multimodal input query $x$ . REVEAL contains", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23370", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6be7ed32586e08a00590f51f7e7587a4d834835f6f8483ba6fa0b9047484a740.jpg", + "image_caption": [ + "Figure 2. The overall workflow of REVEAL consists of four main steps: (a) encode a multimodal input into a sequence of token embeddings and a summarized query embedding; (b) encode each knowledge entry from different corpus into unified key and value embedding pairs, where key is used to index the memory and value contains full information of the knowledge; (c) retrieve top-K most similar knowledge items from different knowledge sources, and return the pre-computed in-memory value embeddings and re-encoded value; and (d) fuse the top-K knowledge items via attentive knowledge fusion layer by injecting the retrieval score as a prior during attention calculation. This facilitates REVEAL's key novelty: the memory, encoder, retriever and the generator can be jointly trained in an end-to-end manner." + ], + "image_footnote": [], + "bbox": [ + 76, + 61, + 883, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "four components: knowledge encoding, memory, retrieval and generation. Given an input query $x$ , we first retrieve $K$ possibly helpful entries $M = \\{m_1, \\dots, m_K\\}$ from the memory corpora $\\mathcal{M}$ . Each $m$ is a memory entry containing the encoded single key embedding and a sequence of value embeddings (we will describe how to encode knowledge items into memory entries in Sec. 3.2). With it, the retriever can use embedding similarity to find relevant memory entries. We model this retrieval process as sampling from distribution $p(M \\mid x)$ . Then, we condition on both the retrieved set $M$ and the original input query $x$ to generate the output $y$ , modeled as $p(y \\mid x, M)$ . To obtain the overall likelihood of generating $y$ , we treat $M$ as a latent variable from the entire memory $\\mathcal{M}$ and marginalize over it yielding:", + "bbox": [ + 75, + 364, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (y \\mid x) = \\sum_ {M \\subset \\tilde {\\mathcal {M}}} \\underbrace {p (M \\mid x)} _ {\\text {r e t r i e v a l}} \\cdot \\underbrace {p (y \\mid x , M)} _ {\\text {g e n e r a t i o n}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 590, + 470, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, this marginal probability involves an intractable summation over all size- $K$ subsets of the memory corpora $\\tilde{\\mathcal{M}}$ . We approximate this instead by using the top- $K$ entries in memory with the highest probability under $p(M \\mid x)$ . This is reasonable if most of the unrelated memory entries do not contribute to the generation. Note that we use an online memory that is updated as the knowledge encoder is trained end-to-end with the rest of the model.", + "bbox": [ + 75, + 641, + 468, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 illustrates the overall workflow of REVEAL, and we describe each component in this section. In particular, in Sec. 3.1 we describe how the query is encoded. In Sec. 3.2 we go over how the multimodal knowledge memory is constructed and updated during pre-training. Next, we describe how we retrieve the memory entries that are most relevant to the input query in Sec. 3.3. Finally, in Sec. 3.4 we describe the generator that fuses the query and retrieved knowledge and decodes them into the generated text.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Query Encoding", + "text_level": 1, + "bbox": [ + 498, + 363, + 663, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 (a) depicts how the input image-text query is encoded. We use a base visual-language encoder $b(\\cdot)$ to turn the query input and each knowledge item (with potentially different modalities e.g. text-only, image-only or image-text pairs) into a sequence of embeddings (tokens). We adopt a Vision Transformer (ViT) [10] to encode the images and we use a lower-layer $^{1}$ T5 encoder [33] to encode the texts. We add a projection layer on top of the ViT model to map the image tokens into the same space as the text tokens. We then concatenate the two modalities together. We use an upper-layer T5 module as both the query Head $\\phi_{Query}(\\cdot)$ and the key Head $\\phi_{Key}(\\cdot)$ to compute the query embedding and memory keys. We take the output of the first [CLS] tokens followed by a linear projection and L2-normalization to summarize the input into a $d$ -dimensional embedding.", + "bbox": [ + 496, + 387, + 893, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Memory", + "text_level": 1, + "bbox": [ + 500, + 625, + 602, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 (b) shows how memory is constructed and updated by encoding knowledge items. Our approach differs from previous works primarily by leveraging a diverse set of multimodal knowledge corpora (WikiData knowledge graph,Wikimedia passages and images, Web image-text pairs). Throughout the paper, we denote each corpus as $\\mathcal{C}^j = \\{z_1^j,\\dots ,z_N^j\\}$ , in which each $z_{i}^{j}\\in \\mathcal{C}^{j}$ is a knowledge item that could be an image-text pair, text only, image only, or a knowledge graph triplet. We denote the unified knowledge corpus as $\\tilde{\\mathcal{C}} = \\mathcal{C}^1\\cup \\mathcal{C}^2\\dots \\cup \\mathcal{C}^S$ that combines $|\\tilde{\\mathcal{C}} | = S$ different knowledge corpora. We encode the external knowledge corpora into a unified memory $\\tilde{\\mathcal{M}} = [\\mathcal{M}^1,\\ldots ,\\mathcal{M}^{|\\tilde{\\mathcal{C}} |}]$ Each knowledge item $z_{i}$ is encoded into a key/value pair $m_{i} = (\\mathrm{Emb}_{\\mathrm{Key}}(z_{i}),\\mathrm{Emb}_{\\mathrm{Value}}(z_{i}))$ in memory. Each key", + "bbox": [ + 496, + 648, + 893, + 864 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1We denote the last $l$ layers of a T5 encoder as 'upper-layer', and the remaining ones including the token embedding layer as 'lower-layer'.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23371", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathsf{Emb}_{\\mathsf{Key}}(z) = \\phi_{\\mathsf{Key}}(b(z)) \\in \\mathbb{R}^d$ is a $d$ -dimensional embedding vector encoded via Key Head. Each value is a sequence of token embeddings representing the full information of knowledge item $z$ . We follow a similar procedure as in [14] to precompute key/value embeddings of knowledge items from different sources and index them in a unified knowledge memory. We continuously re-compute the memory key/value embeddings as the model parameters get updated during the pre-training phase. We update the memory $\\tilde{\\mathcal{M}}$ asynchronously at every 1000 training steps.", + "bbox": [ + 75, + 89, + 472, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Scaling Memory by Compression A naive solution for encoding the memory value is to keep the whole sequence of tokens for each knowledge item. Then, the generator could fuse the input query and the top-K retrieved memory values by concatenating all their tokens together and feeding them into a Transformer Encoder-Decoder pipeline [23]. This approach has two issues: (1) storing hundreds of millions of knowledge items in memory is impractical given that each memory value would consist of hundreds of tokens; (2) transformer encoder has quadratic complexity with respect to the total number of tokens times $K$ for self-attention.", + "bbox": [ + 75, + 246, + 472, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we propose to use the Perceiver architecture [19] as the Value Head to encode and compress knowledge items. The Perceiver model uses a transformer decoder $\\psi(\\cdot)$ with learnable $c$ -length latent embeddings to compress the full token sequence into an arbitrary length $c$ , such that $\\mathrm{Emb}_{\\mathrm{Value}}(z) = \\psi(b(z)) \\in \\mathbb{R}^{c \\times d}$ (In our experiments we use $c = 32$ ). This lets us retrieve top-K memory entries for K as large as a hundred. To make the compressed embeddings generated by Perceiver more expressive, we add two additional regularizations. The first one is a disentangled regularization [16] that forces every two output tokens to be linearly de-correlated $\\mathcal{L}_{\\mathrm{decor}} = \\sum_{i,j=1}^{K} \\left\\| \\mathrm{Covariance}(\\psi(b(z_i)), \\psi(b(z_j))) \\right\\|_F^2$ , and the second one is an alignment regularization that minimizes the distance of L2-Norm between the query and compressed knowledge embedding: $\\mathcal{L}_{\\mathrm{align}} = \\left| 1 - \\frac{\\sum_z \\| \\psi(b(z)) \\|_2}{\\sum_x \\| b(x) \\|_2} \\right|$ .", + "bbox": [ + 75, + 415, + 473, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Retriever", + "text_level": 1, + "bbox": [ + 76, + 704, + 187, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 2 (c) shows REVEAL's retrieval procedure. Given the input query $x$ , the retriever's task is to find top-K memory entries $M$ with the highest probability $p(M \\mid x)$ which we approximate as $p(M \\mid x) = \\prod_{m \\in M} p(m \\mid x)$ by retrieving each entry independently. Note that we retrieve from a large-scale unified memory $\\tilde{\\mathcal{M}} = [\\mathcal{M}^1, \\dots, \\mathcal{M}^{|\\tilde{\\mathcal{C}}|}]$ that is constructed from a diverse set of knowledge sources. To help the query to better choose the most appropriate knowledge sources, we learn a gating function that models the probability of retrieving from each memory corpus. With the corpus gating, for $m_i^j \\in \\mathcal{M}^j$ we re-weight $p(m^j \\mid x)$ by", + "bbox": [ + 75, + 731, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/41f024044c16f67d827a4b96e98813bfb4011d91f5feb41460ed45e6757a150d.jpg", + "image_caption": [ + "Figure 3. Detailed procedure of attentive knowledge fusion module. We inject retrieval probability as a prior to knowledge token embeddings, so the retriever can receive gradients via back-propagating over {self/cross} -attention part." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 883, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the computed corpus gating score:", + "bbox": [ + 498, + 305, + 730, + 320 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p \\left(m _ {i} ^ {j} \\mid x\\right) = p \\left(\\mathcal {M} ^ {j} \\mid x\\right) \\cdot p \\left(m _ {i} ^ {j} \\mid x; \\mathcal {M} ^ {j}\\right) (2) \\\\ = G a t e _ {\\mathcal {M} ^ {j}} (x) \\cdot \\frac {\\exp \\left(R e l \\left(x , m _ {i} ^ {j}\\right) / \\tau\\right)}{\\sum_ {m _ {k} ^ {j} \\in \\mathcal {M} ^ {j}} \\exp \\left(R e l \\left(x , m _ {k} ^ {j}\\right) / \\tau\\right)} (3) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 328, + 892, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Gate_{\\mathcal{M}^j}(x) = \\mathrm{Softmax}(W \\cdot \\mathrm{Emb}_{\\mathrm{Query}}(x) + b)[j]$ is a softmax gating that assigns a score to each memory corpus $M^j$ , with $W$ and $b$ as function parameters. $Rel(x, m_i^j)$ models relevance score between query $x$ and each memory entry via embedding dot product, such that $Rel(x, m_i^j) = \\mathrm{Emb}_{\\mathrm{Query}}(x)^T \\cdot \\mathrm{Emb}_{\\mathrm{Key}}(z_i^j)$ . where $z_i$ is the knowledge item corresponding to the memory entry $m_i$ and $\\tau$ is the temperature parameter.", + "bbox": [ + 496, + 398, + 893, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After identifying the top-K memory entries, the retriever passes the pre-computed in-memory key and value embeddings to the generator. In the meantime, to support end-to-end training of the encoders, we also re-encode a small portion (i.e., $10\\%$ ) of the retrieved knowledge items $z_{i}$ from scratch. In this way, the memory encoders could be updated with moderate computational cost. We concatenate the re-encoded knowledge with in-memory ones to construct the final top-K retrieved key/value embeddings.", + "bbox": [ + 496, + 521, + 893, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Generator", + "text_level": 1, + "bbox": [ + 500, + 666, + 617, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 2 (d) shows how the query and the retrieved knowledge items are fused to generate the output answer. All $K$ retrieved memory values are concatenated with the query embedding, which is feasible due to the Perceiver module utilized as the value head $\\psi(\\cdot)$ , compressing each knowledge item into a short sequence. We denote the concatenated query embedding and memory values as $X = [b(x), \\psi(b(z_1)), \\dots, \\psi(b(z_K))] \\in \\mathbb{R}^{(I + c \\cdot K) \\times d}$ , where $I$ is the number of tokens of the input query $x$ and $c$ is the number of compressed tokens. To guide the generator towards attending to the most important items in $X$ and facilitate backpropagation of gradients to the retriever, we propose an attentive fusion module $f(\\cdot)$ capable of incorporating the retriever score as a prior for calculating", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23372", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/2628aa98b7ca5471a025707d5201821ffe490cf010eda4b20a31c2adf169ccc3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Knowledge SourceCorpus SizeType of TextAvg. Text Length
WIT [37]5,233,186Wikipedia Passage258
CC12M [5]10,009,901Alt-Text Caption37
VQA-V2 [12]123,287Question Answer111
WikiData [40]4,947,397Linearized Triplets326
", + "bbox": [ + 81, + 89, + 467, + 164 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2e8027d65284762575dde37f82b044aef6ca2eae7fd26c1c334422eddd403e15.jpg", + "table_caption": [ + "Table 1. Statistics of the knowledge sources used." + ], + "table_footnote": [], + "table_body": "
Model NameT5 VariantImage Encoder# params.GFLOPs
REVEAL-BaseT5-BaseViT-B/160.4B120
REVEAL-LargeT5-LargeViT-L/161.4B528
REVEALT5-LargeViT-g/142.1B795
", + "bbox": [ + 94, + 204, + 447, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Model configuration of different REVEAL variants.", + "bbox": [ + 93, + 270, + 450, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cross-knowledge attention. The detailed procedure is illustrated in Figure 3. We firstly compute a latent soft attention mask over $X$ as $\\text{Mask}_{\\text{att}} = [1, p(z_1|x), \\ldots, p(z_K|x)]$ . Finally, we pass the fused representation $f(X, \\text{Mask}_{\\text{att}})$ into a T5 decoder module $g(\\cdot)$ to generate the textual output.", + "bbox": [ + 75, + 311, + 470, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Generative Pre-Training", + "text_level": 1, + "bbox": [ + 76, + 401, + 307, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The existing VQA datasets are not large enough for training a complex multi-component model like ours from scratch. Therefore, we pre-train our model on a massive image-text corpus. In Sec. 4.1 we go over the details of our pre-training data and objective. Then in Sec. 4.2 we introduce the various sources of knowledge used in our experiments. Finally, in Sec. 4.3 we describe the pre-training implementation details.", + "bbox": [ + 75, + 426, + 470, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Pre-Training Objective", + "text_level": 1, + "bbox": [ + 76, + 542, + 290, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We pre-train our model on the Web-Image-Text dataset [51], a large-scale corpus containing 3 billion image alt-text caption pairs collected from the public Web. Since the dataset is noisy, we add a filter to remove data points whose captions are shorter than 50 characters. This yields roughly 1.3 billion image caption pairs for pre-training.", + "bbox": [ + 75, + 566, + 468, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We denote the pre-training Web-Image-Text dataset [51] as $\\mathcal{D}$ . We use the text generation objective used in Wang et al. [45]) to pre-train our model on $\\mathcal{D}$ . Given an image-text example $x = (\\mathrm{img},\\mathrm{txt})$ from $\\mathcal{D}$ , we randomly sample a prefix length $T_{p}$ . We feed $x_{< T_p}$ that contains the text prefix and image to the model as input and our objective is to generate $x_{\\geq T_p}$ containing the rest of the text as output. The training goal is to condition on $x_{< T_p}$ and autoregressively generate the remaining text sequence $x_{\\geq T_p}$ :", + "bbox": [ + 75, + 657, + 468, + 784 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {P r e f i x L M}} = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\log p \\left(x _ {\\geq T _ {p}} \\mid x < T _ {p}\\right) \\right] \\tag {4} \\\\ = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\sum_ {i \\geq T _ {p}} \\log p \\left(x _ {i} \\mid x _ {< i}\\right) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 794, + 468, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Warm Starting the Model In order to pre-train all components of our model end-to-end, we need to warm start the retriever at a good state. Otherwise, if starting with random", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "weights, the retriever would often return irrelevant memory items that would never generate useful training signals.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To avoid this cold-start problem, we propose to construct an initial retrieval dataset with pseudo ground-truth knowledge to give the pre-training a reasonable head start. We create a modified version of the Wikipedia-Image-Text (WIT) [37] dataset for this purpose. Each image-caption pair in WIT also comes with a corresponding Wikipedia passage (words surrounding the text). We put together the surrounding passage with the query image and use it as the pseudo ground-truth knowledge that corresponds to the input query. As the passage provides rich information about the image and caption, it definitely is useful for initializing the model. To avoid the model from relying on low-level image features for retrieval, we apply random data augmentation to the input query image. Given this modified dataset that contains pseudo retrieval ground-truth, we train the query and memory key embeddings by optimizing the following contrastive loss:", + "bbox": [ + 496, + 122, + 892, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n t r a}} = - \\log \\operatorname {S o f t m a x} \\left(\\operatorname {E m b} _ {\\text {Q u e r y}} (x) ^ {T} \\operatorname {E m b} _ {\\text {K e y}} (\\hat {z})\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 391, + 867, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{z}$ represents the pseudo ground-truth knowledge entry corresponding to the input query $x$ .", + "bbox": [ + 498, + 421, + 890, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Knowledge Sources", + "text_level": 1, + "bbox": [ + 500, + 463, + 686, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the following four sources of knowledge in our experiments: Wikipedia-Image-Text (WIT) [37] consists of the images in Wikipedia, as well as their alt-text captions and contextualized text passages. Conceptual (CC12M) [5] contains web images paired with alt-text captions. It includes many long-tail entities. VQA-v2 [12] is a visual question answering dataset. We merge all question-answer pairs per image into a single passage. WikiData [40] is a structural knowledge graph encoding relations between Wikipedia entities. We linearize all relational triplets per entity into a textual passage following the procedure of [32]. We have listed the statistical details of these knowledge sources in Table 1.", + "bbox": [ + 496, + 487, + 892, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 695, + 715, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Incorporating all the components introduced above, REVEAL can be directly pre-trained over large-scale image caption datasets after proper initialization. As our model architecture is based on T5 and ViT, we use pre-trained ViT checkpoints from [50] and pre-trained T5 checkpoints from [33] to initialize the encoder parameters. The query head, key head and attentive fusion layers are initialized from upper T5, while the base text encoder is initialized from lower T5. The combination of these modules can be found in Table 2 for three three model variants, REVEAL-Base, REVEAL-Large and REVEAL, of which the largest REVEAL model has around 2 billion parameters.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23373", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2ab41171529bcfd777b1bb4e2209d2eb92e617c116aad485ae3d818c48fedbe2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VQA Model NameKnowledge SourcesAccuracy (%)Memory (GB)
MUTAN+AN [29]Wikipedia + ConceptNet27.8-
ConceptBERT [11]Wikipedia33.7-
KRISP [28]Wikipedia + ConceptNet38.4-
Visual Retriever-Reader [27]Google Search39.2-
MAVEx [46]Wikipedia+ConceptNet+Google Images39.4-
KAT-Explicit [13]Wikidata44.31.5
PICa-Base [48]Frozen GPT-343.3350
PICa-Full [48]Frozen GPT-348.0350
KAT [13] (Single)Wikidata + Frozen GPT-353.11.5 + 352+ 500
KAT [13] (Ensemble)Wikidata + Frozen GPT-354.44.6 + 352 + 500
ReVIVE [24] (Single)Wikidata + Frozen GPT-356.61.5 + 354 + 500
ReVIVE [24] (Ensemble)Wikidata+Frozen GPT-358.04.6 + 354 + 500
REVEAL-BaseWIT + CC12M + Wikidata + VQA-255.20.8 + 7.5 + 744
REVEAL-LargeWIT + CC12M + Wikidata + VQA-258.02.8 + 10 + 993
REVEALWIT + CC12M + Wikidata + VQA-259.14.2 + 10 + 993
", + "bbox": [ + 148, + 51, + 820, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Distributed Online Retrieval. Finding the top-k most-relevant knowledge entries is a standard Maximum Inner Product Search (MIPS) problem. There are approximate search algorithms [8, 36] that scale sub-linearly with the size of the knowledge corpus $|C|$ . We use TPU-KNN [8] to conduct distributed MIPS search, by splitting and storing the memory embeddings across all training devices. The query is synced to each device, which retrieves approximate top-K results from its own memory. Then these results are combined to compute the global top-K retrieved items.", + "bbox": [ + 75, + 372, + 472, + 525 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-Training Pipeline. We first train the multimodal retriever on our modified version of the Wikipedia Image Text (WIT) dataset via $\\mathcal{L}_{\\text{contra}}$ . We use the Adafactor optimizer without momentum ( $\\beta_{1} = 0$ , $\\beta_{2} = 0.999$ ), with weight decay of $0.001^{2}$ , and with a peak learning rate of 6e4, to train for 10 epochs. We use this checkpoint to warm-start our generative pre-training. We set the number of retrieved knowledge entries as $K = 10$ during pre-training, and use adafactor with a peak learning rate of 1e-3 and inverse squared root learning rate scheduler with 10,000 linear warm-up steps. We use $\\mathcal{L}_{\\text{PrefixLM}}$ as the main objective, adding $\\mathcal{L}_{\\text{contra}}$ , $\\mathcal{L}_{\\text{decor}}$ and $\\mathcal{L}_{\\text{align}}$ weighted by 0.01. We use a batch size of 4096 across 256 CloudTPUv4 chips and train for about 5 days.", + "bbox": [ + 75, + 527, + 473, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 767, + 282, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our proposed method on knowledge-based VQA in Sec. 5.1 and image captioning in Sec. 5.2. We then conduct ablation studies in Sec. 5.3 to analyze the impact of each model component on overall performance.", + "bbox": [ + 75, + 797, + 470, + 859 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/08bac58654cb3b7276b5a492f354ba6fab65eeb974f82a2bea755f0bee017927.jpg", + "table_caption": [ + "Table 3. Visual Question Answering results on OK-VQA, compared with existing methods that use different knowledge sources. For the memory cost, we assume all models use bfloat16. Green means on-device model parameters that are learnable, Blue means on-device memory of frozen model parameters, and Red means CPU/disk storage cost that are not involved in computation." + ], + "table_footnote": [], + "table_body": "
VQA Model NameAccuracy (%)
ViLBERT [26]30.6
LXMERT [38]30.7
ClipCap [30]30.9
KRISP [28]33.7
GPV-2 [21]48.6
REVEAL-Base50.4
REVEAL-Large51.5
REVEAL52.2
", + "bbox": [ + 571, + 369, + 820, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Visual Question Answering results on A-OKVQA.", + "bbox": [ + 513, + 518, + 875, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Evaluating on Knowledge-Based VQA", + "text_level": 1, + "bbox": [ + 500, + 559, + 828, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "One of the most knowledge intensive visual-language tasks is knowledge-based visual question answering (VQA), exemplified by the OK-VQA [29] and A-OKVQA [35] benchmarks. To finetune our pre-trained model on these VQA tasks, we use the same generative objective where the model takes in an image question pair as input and generates the text answer as output. There are a few differences between the fine-tuning and the pre-training stages: 1) we set the number of retrieved knowledge entries to $K = 50$ , so the model is able to retrieve sufficient supporting evidence; 2) we freeze the whole base V-L encoder to stabilize training; and 3) we use a batch size of 128, with the Adafactor optimizer, a peak learning rate of 1e-4. We use the soft VQA accuracy metric [3] to evaluate the model's generated answer.", + "bbox": [ + 496, + 583, + 893, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our results on OKVQA and A-OKVQA datasets are shown in Table 3 and Table 4 respectively. For OKVQA, earlier attempts that incorporate a fixed knowledge retriever report results that are below $45\\%$ . Recently a series of works utilize large language models (e.g. GPT-3) as implicit knowledge sources, which achieve much better performance", + "bbox": [ + 496, + 810, + 895, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2The remaining experiments use the same optimizer configuration.", + "bbox": [ + 94, + 886, + 447, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23374", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8ac53a0bb6b3fc4a4978a0202b0abf33fa2fad7c4fcd72d63e9502b9fa129dc4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model NameMSCOCONoCaps# params.
Flamingo [2]138.1-80B
VinVL [52]140.9105.10.4B
SimVLM [45]143.3112.21.5B
CoCa [49]143.6122.42.1B
REVEAL-Base141.1115.80.4B
REVEAL-Large144.5121.31.4B
REVEAL145.4123.02.1B
", + "bbox": [ + 109, + 79, + 434, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Image Captioning results on MSCOCO (Karpathy-test split) and NoCaps (val set). Evaluated using the CIDEr metric.", + "bbox": [ + 76, + 199, + 468, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with the trade-off of a huge computational cost. REVEAL achieves higher performance than those methods without relying on such large language models3. Compared with the previous state-of-the-art, KAT and ReVIVE, which also utilizes T5-Large as a generator, REVEAL achieves accuracy of $59.1\\%$ , which is $+6.0\\%$ higher than the single KAT [13] model and $+2.5\\%$ higher than ReVIVE [24].", + "bbox": [ + 75, + 256, + 468, + 361 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On A-OKVQA, REVEAL achieves $52.2\\%$ accuracy, which is $+3.6\\%$ higher than the previous best, GPV-2 [21]. We also show two examples of these datasets in Figure 4. All these results show that, with proper end-to-end retrieval training and a diverse set of knowledge sources, REVEAL can learn to retrieve meaningful knowledge entries, and achieve promising results without relying on a large language model.", + "bbox": [ + 75, + 363, + 472, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Evaluating on Image Captioning", + "text_level": 1, + "bbox": [ + 76, + 481, + 364, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also evaluate REVEAL on image captioning benchmarks: MSCOCO Captions [6] and NoCaps [1]. We follow the evaluation protocol used in [49]. We directly fine-tune our generator model on the MSCOCO training split via cross-entropy generative objective. We measure our performance on the MSCOCO test split and NoCaps val set with the CIDEr metric [39]. The results of these two datasets are shown in Table 5. Note that REVEAL achieves better results than strong recent baselines such as SimVLM [45] and CoCa [49] on both benchmarks. Notably, REVEAL -Large with 1.4B parameters outperforms the 2.1B-parameter CoCa model and is significantly better than 80B-parameter Flamingo model [2].", + "bbox": [ + 75, + 505, + 472, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Analyzing Effects of Key Model Components", + "text_level": 1, + "bbox": [ + 76, + 714, + 457, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the following we study which design choices contribute most to the model's performance. We focus on three research questions: (1) Does utilizing multiple knowledge sources enhance performance? (2) Does the proposed attentive fusion surpass existing end-to-end retrieval training methods?", + "bbox": [ + 75, + 738, + 468, + 814 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38c375cf6c0f9d40307f96db9860a09ef28f6c1badeaff0776ac64795f16702a.jpg", + "image_caption": [ + "Figure 4. VQA Examples. REVEAL is able to use knowledge from different sources to correctly answer the question. We show more examples in Figure 1-3 of Supplementary Material, indicating that our model can retrieve and use items from diverse knowledge sources to correctly solve different input query." + ], + "image_footnote": [], + "bbox": [ + 504, + 79, + 874, + 232 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(3) Can we add knowledge by only updating the memory without modifying model parameters?", + "bbox": [ + 496, + 340, + 890, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analyzing multiple knowledge sources. A major distinction of REVEAL compared to previous retrieval-augmented approaches is its capacity to utilize a diverse set of knowledge sources during inference. To assess the relative importance of each data source and the efficacy of retrieving from various corpora, we conduct two ablation studies: 1) Only-One-Left: employing a single knowledge source to evaluate the outcomes; and 2) Leave-One-Out: excluding one knowledge source from the complete set $\\mathcal{C}$ . These ablation studies are executed using the REVEAL Base, evaluated on the OKVQA validation set under the aforementioned conditions. As shown in Figure 5, among the four knowledge sources utilized in this paper, WIT is the most informative, with the highest accuracy when used in isolation (53.1The remaining three corpora, CC12M, VQA-v2, and WikiData, do not offer the same level of informativeness as WIT when utilized independently. However, excluding any of these corpora from the complete dataset results in performance decreases of $1.3\\%$ , $0.6\\%$ , and $1.1\\%$ , respectively. This observation implies that these knowledge sources effectively complement one another, contributing valuable information to enhance performance. To further substantiate this hypothesis, we perform an additional experiment involving pairs of knowledge sources, as illustrated in Figure 6. Notably, even when paired with an informative knowledge source such as WIT, incorporating an extra corpus consistently leads to performance improvements.", + "bbox": [ + 496, + 372, + 893, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analyzing different retrieval training methods. Another core component of REVEAL is the attentive fusion layer, which supports efficient joint training of the retriever and generator. We investigate its performance compared to two existing retrieval training method categories: 1) a frozen retriever based on ALIGN [20] representations; 2) end-to-end retrieval training methods including Attention Distill [17], EMDR² [47], and Perplexity Distill [18].", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3As shown in the last column of Table 3, REVEAL stores external knowledge as value embeddings on disk, occupying 993GB of space. The key embeddings consume 10GB space and are kept in TPU memory for fast lookup. On the other hand, KAT and REVIVE need to load the entire 350GB GPT-3 model in the GPU/TPU memory. Furthermore, storing WikiData on disk consumes 500GB of disk memory.", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23375", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d0df5c0d0bbdcc4cf7dc27b908727660bd9cdf2c54e1a6f54318a6d4946f9cb9.jpg", + "image_caption": [ + "Figure 5. OKVQA Accuracy of REVEAL using 1) Only-One-Left: only use a single knowledge source; 2) Leave-One-Out: use all without this knowledge source." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 267, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e02aaf069bc4d099fbdfb1bbec61edc8a51e1a6402b1e34cf4edc4c27e49551.jpg", + "image_caption": [ + "Figure 6. OKVQA Accuracy of REVEAL using all Pair of Knowledge Sources. Results show that combining multiple sources could consistently improve performance." + ], + "image_footnote": [], + "bbox": [ + 281, + 88, + 480, + 199 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4c3678263a9a9c77b8043c3ff219d7a844a49293a81f433b57e2fe4f61084074.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Retrieval MethodAcc@10Acc@100OKVQA Acc.GFLOPs
ALIGN [20] (fixed)0.6380.79344.7-
Attention Distill [17]0.6740.83545.9119
EMDR2 [47]0.6910.86946.5561
Perplexity Distill [18]0.7040.88646.7561
Ours (Attentive Fusion)0.7260.89447.3120
", + "bbox": [ + 78, + 303, + 468, + 404 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Analysis of Retrieval Training Method: We train REVEAL-Base (frozen generator, only train randomly initialized retriever) to retrieve from the WIT dataset (only text passage without image), and show the retrieval accuracy at the first 10 or 100 results, as well as fine-tuned OKVQA accuracy.", + "bbox": [ + 75, + 406, + 470, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We use the pre-trained REVEAL-Base model, fix the generator and randomly initialize the retriever (query head and key head). We utilize our modified version of WIT dataset with pseudo ground-truth retrieved labels as the evaluation corpus. We evaluate retrieval performance by checking whether the correct passage appears in top-10/100 results. For the ALIGNN model, we directly evaluate the retrieval results from the pre-trained checkpoint, while for other models, we perform retrieval-augmented training on the WIT dataset. To prevent the model from relying on image similarity for accurate results, we only use text passages as knowledge entries and discard images. Subsequently, we finetune the model on OKVQA and report its accuracy. The results are presented in Table 6. We observe that directly using pretrained encoder does not perform well, even with a strong model like ALIGNN. Moreover, among the various end-to-end retrieval training approaches, our attentive fusion method attains better accuracy in both retrieval and OKVQA tasks. Importantly, our technique exhibits a computational cost (quantified by GFLOPs) comparable to that of attention distillation, yet significantly lower than $\\mathrm{EMDR}^2$ and Perplexity distillation. This indicates that our proposed method is more efficient and effective for pre-training retrieval-augmented visual-language models.", + "bbox": [ + 75, + 506, + 470, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analyzing Knowledge Modification. One advantage of utilizing knowledge memory is that we could easily add or", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/09aaa27b58b8df4167608888e1f3ac520c8361912c7af0fea3e7b09fb79ffe1c.jpg", + "image_caption": [ + "Figure 7. Study of Knowledge Update. The blue curve shows result by removing certain percentage of knowledge during both fine-tuning and inference stage. The orange curve shows results by still first removing the knowledge, and then adding the knowledge back during inference, which simulates the knowledge update." + ], + "image_footnote": [], + "bbox": [ + 526, + 87, + 864, + 223 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "update knowledge entries without re-training model's parameters. To validate this, we conducted ablation studies in which we removed a specific percentage of knowledge entries from the corpora and assessed the performance of the REVEAL-Base model on the OKVQA dataset. Subsequently, we add the removed knowledge back into the corpora, allowing the trained model to make predictions using the complete set of corpora. This approach ensured that the removed knowledge was not seen by the model during fine-tuning, enabling us to test its ability to accurately retrieve and utilize that knowledge for problem-solving.", + "bbox": [ + 496, + 324, + 893, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results are illustrated in Figure 7, with the blue curves representing the inference outcomes without the removed knowledge and the orange curve depicting the results after adding the removed knowledge back. A notable performance improvement was observed upon reintroducing the knowledge (orange curve) compared to the outcomes with the removed knowledge (blue curve). Specifically, for the model fine-tuned with only $10\\%$ of the knowledge, the reintroduction of the removed knowledge resulted in an accuracy of 51.8 (+6.7 higher than when removed). This finding demonstrates that the REVEAL model can swiftly adapt to new knowledge by merely updating the memory, obviating the need for re-training model parameters.", + "bbox": [ + 496, + 492, + 895, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 707, + 619, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents an end-to-end Retrieval-augmented Visual Language model (REVEAL), which contains a knowledge retriever that learns to utilize a diverse set of knowledge sources with different modality. The retriever is trained jointly with the generator to return multiple knowledge entries. We pre-train REVEAL on a massive image-text corpus with four diverse knowledge corpora, and achieves state-of-the-art results on knowledge-intensive visual question answering and image caption tasks. In the future we'd explore the ability of this model to be used for attribution, and applying it to broader class of multimodal tasks.", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23376", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Harsh Agrawal, Peter Anderson, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, and Stefan Lee. nocaps: novel object captioning at scale. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 8947-8956. 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Computer Vision Foundation / IEEE, 2021. 7" + ], + "bbox": [ + 501, + 92, + 893, + 652 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23379", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/REVEAL_ Retrieval-Augmented Visual-Language Pre-Training With Multi-Source Multimodal Knowledge Memory/ec28663c-769a-4a6f-bc32-f0643a00e7d2_model.json b/2023/REVEAL_ Retrieval-Augmented Visual-Language Pre-Training With Multi-Source Multimodal Knowledge Memory/ec28663c-769a-4a6f-bc32-f0643a00e7d2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7a0aa8235c7a3b0b249241c9a1c81aabbbd4b0d7 --- /dev/null +++ b/2023/REVEAL_ Retrieval-Augmented Visual-Language Pre-Training With Multi-Source Multimodal Knowledge Memory/ec28663c-769a-4a6f-bc32-f0643a00e7d2_model.json @@ -0,0 +1,2037 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "REVEAL: Retrieval-Augmented Visual-Language Pre-Training with Multi-Source Multimodal Knowledge Memory" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.203, + 0.825, + 0.258 + ], + "angle": 0, + "content": "Ziniu Hu\\(^{1*}\\), Ahmet Iscen\\(^{2}\\), Chen Sun\\(^{2}\\), Zirui Wang\\(^{2}\\), Kai-Wei Chang\\(^{1}\\), Yizhou Sun\\(^{1}\\), Cordelia Schmid\\(^{2}\\), David A. Ross\\(^{2}\\), Alireza Fathi\\(^{2}\\), \\(^{1}\\)University of California, Los Angeles, \\(^{2}\\)Google Research" + }, + { + "type": "image", + "bbox": [ + 0.133, + 0.284, + 0.821, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.425, + 0.895, + 0.454 + ], + "angle": 0, + "content": "Figure 1. We augment a visual-language model with the ability to retrieve multiple knowledge entries from a diverse set of knowledge sources, which helps generation. Both retriever and generator are trained jointly, end-to-end, by optimizing a language modeling objective." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.473, + 0.314, + 0.489 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.506, + 0.474, + 0.793 + ], + "angle": 0, + "content": "In this paper, we propose an end-to-end Retrieval-Augmented Visual Language Model (REVEAL) that learns to encode world knowledge into a large-scale memory, and to retrieve from it to answer knowledge-intensive queries. REVEAL consists of four key components: the memory, the encoder, the retriever and the generator. The large-scale memory encodes various sources of multimodal world knowledge (e.g. image-text pairs, question answering pairs, knowledge graph triplets, etc.) via a unified encoder. The retriever finds the most relevant knowledge entries in the memory, and the generator fuses the retrieved knowledge with the input query to produce the output. A key novelty in our approach is that the memory, encoder, retriever and generator are all pre-trained end-to-end on a massive amount of data. Furthermore, our approach can use a diverse set of multimodal knowledge sources, which is shown to result in significant gains. We show that REVEAL achieves state-of-the-art results on visual question answering and image captioning. The project page of this work is reveal.github.io." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.21, + 0.837 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.848, + 0.471, + 0.879 + ], + "angle": 0, + "content": "Recent large-scale models such as T5 [33], GPT-3 [4], PaLM [9], CoCa [49], Flamingo [2], BEIT-3 [43] and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.474, + 0.895, + 0.611 + ], + "angle": 0, + "content": "PaLI [7] have demonstrated the ability to store substantial amounts of world knowledge, when scaled to tens of billions of parameters and trained on vast text and image corpora. These models achieve state-of-the-art results in downstream tasks such as image captioning, visual question answering and open vocabulary recognition. Yet, these models have a number of drawbacks: (i) they require massive scale, of parameters, data and computation, and (ii) they need to be re-trained every time the world knowledge is updated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.896, + 0.809 + ], + "angle": 0, + "content": "To address these issues, we adopt a different approach. Instead of statically compiling world knowledge into model weights, we transform the knowledge into a key-value memory through neural representation learning. Our model learns to utilize the memory for answering knowledge-intensive queries. By decoupling the knowledge memorization from reasoning, we enable our model to leverage various external sources of knowledge (e.g., Wikipedia passages and images [37], the WikiData knowledge graph [40], Web imagetext pairs [5] and visual question answering data [12]). This enables the model parameters to focus on understanding the query and conducting reasoning, rather than being dedicated to memorization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Retrieval-augmented models have attracted a fair amount of attention in the fields of NLP [14, 18] and computer vision [13,25]. Typically, these models often use a pre-existing single-modality backbone to encode and retrieve information from the knowledge corpus. Such approaches do not leverage all available modalities in the query and knowl" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.889, + 0.405, + 0.902 + ], + "angle": 0, + "content": "*This work was done when Ziniu was an intern at Google." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23369" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "edge corpora, and hence they might not find the information that is most helpful for generating the model output. A key novelty in our approach is that we encode and store various sources of multimodal world knowledge into a unified memory, which the retriever can access via multimodal query encodings, to find the most relevant information from across complementary sources. Our multimodal memory and retriever are pre-trained end-to-end together together with the rest of the model, on a massive amount of data and using diverse knowledge sources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.497 + ], + "angle": 0, + "content": "A key challenge of pre-training the multimodal retriever end-to-end is the lack of direct supervision. There is no ground-truth indicating which knowledge entries are most helpful for answering knowledge-intensive queries. Some of the existing works in NLP [14, 23, 34] propose to acquire training signal by assessing the usefulness of each retrieved knowledge entry independently for helping language modelling. This approach is inefficient, as it involves estimating hundreds of retrieved knowledge entries independently, and also inaccurate as it discards the dependency between different knowledge entries in the retrieval set. In contrast, we propose to get this training signal while simultaneously considering multiple retrieved knowledge entries, by introducing an attentive fusion layer that injects retrieval score into the attention calculation procedure. This enables the retrieval module to be differentiable and jointly pre-trained with the rest of the model." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.5, + 0.424, + 0.514 + ], + "angle": 0, + "content": "In summary, our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.515, + 0.468, + 0.559 + ], + "angle": 0, + "content": "- We are the first to propose an end-to-end pre-training paradigm that learns to index into a large-scale memory to solve knowledge-intensive visual-language tasks." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.561, + 0.47, + 0.62 + ], + "angle": 0, + "content": "- Our method can construct a large-scale memory by encoding various sources of multimodal world knowledge, including Wikipedia passage, web images with alt-text captions, and knowledge graph triplets." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.62, + 0.47, + 0.711 + ], + "angle": 0, + "content": "- REVEAL achieves state-of-the-art performance on several knowledge-intensive visual question answering and image captioning datasets. Notably on the OKVQA benchmark, REVEAL achieves a new state-of-the-art, \\(59.1\\%\\) accuracy, while using order of magnitude fewer parameters than previous works." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.515, + 0.47, + 0.711 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.364, + 0.742 + ], + "angle": 0, + "content": "2. Related Work and Background" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Knowledge-based Visual Question Answering. To evaluate a model's ability to comprehend multimodal world knowledge not easily inferred from input data, several knowledge-based Visual Question Answering (VQA) datasets have been introduced. KB-VQA [41] and FVQA [42] design questions that can be answered by retrieving relevant triplets from domain-specific structured knowledge graphs. OK-VQA [29] improves these datasets by necessitating the use of external knowledge, which goes beyond what can be directly observed in the input images. More recently, A-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.896, + 0.455 + ], + "angle": 0, + "content": "OKVQA [35] offers further improvements to OK-VQA by exclusively selecting questions that demand both external knowledge and commonsense reasoning about the image scenes. To tackle knowledge-based VQA tasks, many approaches have been proposed to incorporate external knowledge into visual-language models. One line of research uses explicit knowledge from structured knowledge graphs [11, 15, 31, 44] or unstructured text corpora [27, 28, 46]. The key component for these works is the knowledge retriever. Some works [11, 28, 31, 46] utilize off-the-shelf vision detection models to generate image tags for knowledge retrieval, while others train the retrieval model via distant supervision [27] or auxiliary tasks (e.g. entity linking) [13]. Another research direction aims to incorporate implicit knowledge from pre-trained Large Language Models, such as GPT-3 [4] or PaLM [9]. These approaches utilize off-the-shelf image caption models to convert images into text, feed them into a language model, and use the generated text output as augmented knowledge [13, 24, 48]. Our work follows the first direction, augmenting a vision-language model with an explicit knowledge retriever. The main distinction is that we propose an end-to-end training framework to jointly learn the answer generator and retriever, rather than using a fixed or predefined knowledge retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.895, + 0.775 + ], + "angle": 0, + "content": "End-to-End Training of Retrieval-Augmented Models. Given the advantage of knowledge retrieval, a key question is how to get learning signal to train the retrieval model. For tasks with annotated retrieval ground-truth, retrieval training can be conducted via standard contrastive learning [22]. However, most tasks do not provide clear indications of which knowledge entries are relevant for generating answers. To this end, a series of studies have investigated retrieval training using supervision derived from downstream tasks. REALM [14] trains a single-document retriever by concatenating each retrieved result with the query, to calculate the final loss independently. A similar approach has been used by EMDR² [34] for multi-document retrieval training. FIDKD [17] proposes to use the aggregated attention score calculated by the generator as a distillation signal to train the retriever. Atlas [18] further introduces a perplexity distillation loss and a leave-one-out variant. Our REVEAL proposes to inject the retrieval scores directly into an attentive fusion module, enabling to train the retriever to directly optimize downstream tasks as well as pre-training objectives." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.593, + 0.801 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We propose a Retrieval-Augmented Visual Language Model (REVEAL), which learns to use knowledge from different sources for solving knowledge-intensive tasks. For both pre-training and fine-tuning, our goal is to learn the distribution \\( P(y \\mid x) \\) to generate a textual output \\( y \\) conditioned on a multimodal input query \\( x \\). REVEAL contains" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.063, + 0.885, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.895, + 0.34 + ], + "angle": 0, + "content": "Figure 2. The overall workflow of REVEAL consists of four main steps: (a) encode a multimodal input into a sequence of token embeddings and a summarized query embedding; (b) encode each knowledge entry from different corpus into unified key and value embedding pairs, where key is used to index the memory and value contains full information of the knowledge; (c) retrieve top-K most similar knowledge items from different knowledge sources, and return the pre-computed in-memory value embeddings and re-encoded value; and (d) fuse the top-K knowledge items via attentive knowledge fusion layer by injecting the retrieval score as a prior during attention calculation. This facilitates REVEAL's key novelty: the memory, encoder, retriever and the generator can be jointly trained in an end-to-end manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.577 + ], + "angle": 0, + "content": "four components: knowledge encoding, memory, retrieval and generation. Given an input query \\( x \\), we first retrieve \\( K \\) possibly helpful entries \\( M = \\{m_1, \\dots, m_K\\} \\) from the memory corpora \\( \\mathcal{M} \\). Each \\( m \\) is a memory entry containing the encoded single key embedding and a sequence of value embeddings (we will describe how to encode knowledge items into memory entries in Sec. 3.2). With it, the retriever can use embedding similarity to find relevant memory entries. We model this retrieval process as sampling from distribution \\( p(M \\mid x) \\). Then, we condition on both the retrieved set \\( M \\) and the original input query \\( x \\) to generate the output \\( y \\), modeled as \\( p(y \\mid x, M) \\). To obtain the overall likelihood of generating \\( y \\), we treat \\( M \\) as a latent variable from the entire memory \\( \\mathcal{M} \\) and marginalize over it yielding:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.591, + 0.472, + 0.63 + ], + "angle": 0, + "content": "\\[\np (y \\mid x) = \\sum_ {M \\subset \\tilde {\\mathcal {M}}} \\underbrace {p (M \\mid x)} _ {\\text {r e t r i e v a l}} \\cdot \\underbrace {p (y \\mid x , M)} _ {\\text {g e n e r a t i o n}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.763 + ], + "angle": 0, + "content": "However, this marginal probability involves an intractable summation over all size-\\(K\\) subsets of the memory corpora \\(\\tilde{\\mathcal{M}}\\). We approximate this instead by using the top-\\(K\\) entries in memory with the highest probability under \\(p(M \\mid x)\\). This is reasonable if most of the unrelated memory entries do not contribute to the generation. Note that we use an online memory that is updated as the knowledge encoder is trained end-to-end with the rest of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 2 illustrates the overall workflow of REVEAL, and we describe each component in this section. In particular, in Sec. 3.1 we describe how the query is encoded. In Sec. 3.2 we go over how the multimodal knowledge memory is constructed and updated during pre-training. Next, we describe how we retrieve the memory entries that are most relevant to the input query in Sec. 3.3. Finally, in Sec. 3.4 we describe the generator that fuses the query and retrieved knowledge and decodes them into the generated text." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.364, + 0.665, + 0.381 + ], + "angle": 0, + "content": "3.1. Query Encoding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.895, + 0.616 + ], + "angle": 0, + "content": "Figure 2 (a) depicts how the input image-text query is encoded. We use a base visual-language encoder \\( b(\\cdot) \\) to turn the query input and each knowledge item (with potentially different modalities e.g. text-only, image-only or image-text pairs) into a sequence of embeddings (tokens). We adopt a Vision Transformer (ViT) [10] to encode the images and we use a lower-layer\\(^{1}\\) T5 encoder [33] to encode the texts. We add a projection layer on top of the ViT model to map the image tokens into the same space as the text tokens. We then concatenate the two modalities together. We use an upper-layer T5 module as both the query Head \\( \\phi_{Query}(\\cdot) \\) and the key Head \\( \\phi_{Key}(\\cdot) \\) to compute the query embedding and memory keys. We take the output of the first [CLS] tokens followed by a linear projection and L2-normalization to summarize the input into a \\( d \\)-dimensional embedding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.626, + 0.604, + 0.643 + ], + "angle": 0, + "content": "3.2. Memory" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.895, + 0.865 + ], + "angle": 0, + "content": "Figure 2 (b) shows how memory is constructed and updated by encoding knowledge items. Our approach differs from previous works primarily by leveraging a diverse set of multimodal knowledge corpora (WikiData knowledge graph,Wikimedia passages and images, Web image-text pairs). Throughout the paper, we denote each corpus as \\(\\mathcal{C}^j = \\{z_1^j,\\dots ,z_N^j\\}\\) , in which each \\(z_{i}^{j}\\in \\mathcal{C}^{j}\\) is a knowledge item that could be an image-text pair, text only, image only, or a knowledge graph triplet. We denote the unified knowledge corpus as \\(\\tilde{\\mathcal{C}} = \\mathcal{C}^1\\cup \\mathcal{C}^2\\dots \\cup \\mathcal{C}^S\\) that combines \\(|\\tilde{\\mathcal{C}} | = S\\) different knowledge corpora. We encode the external knowledge corpora into a unified memory \\(\\tilde{\\mathcal{M}} = [\\mathcal{M}^1,\\ldots ,\\mathcal{M}^{|\\tilde{\\mathcal{C}} |}]\\) Each knowledge item \\(z_{i}\\) is encoded into a key/value pair \\(m_{i} = (\\mathrm{Emb}_{\\mathrm{Key}}(z_{i}),\\mathrm{Emb}_{\\mathrm{Value}}(z_{i}))\\) in memory. Each key" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1We denote the last \\(l\\) layers of a T5 encoder as 'upper-layer', and the remaining ones including the token embedding layer as 'lower-layer'." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23371" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.473, + 0.244 + ], + "angle": 0, + "content": "\\(\\mathsf{Emb}_{\\mathsf{Key}}(z) = \\phi_{\\mathsf{Key}}(b(z)) \\in \\mathbb{R}^d\\) is a \\(d\\)-dimensional embedding vector encoded via Key Head. Each value is a sequence of token embeddings representing the full information of knowledge item \\(z\\). We follow a similar procedure as in [14] to precompute key/value embeddings of knowledge items from different sources and index them in a unified knowledge memory. We continuously re-compute the memory key/value embeddings as the model parameters get updated during the pre-training phase. We update the memory \\(\\tilde{\\mathcal{M}}\\) asynchronously at every 1000 training steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.473, + 0.414 + ], + "angle": 0, + "content": "Scaling Memory by Compression A naive solution for encoding the memory value is to keep the whole sequence of tokens for each knowledge item. Then, the generator could fuse the input query and the top-K retrieved memory values by concatenating all their tokens together and feeding them into a Transformer Encoder-Decoder pipeline [23]. This approach has two issues: (1) storing hundreds of millions of knowledge items in memory is impractical given that each memory value would consist of hundreds of tokens; (2) transformer encoder has quadratic complexity with respect to the total number of tokens times \\( K \\) for self-attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Therefore, we propose to use the Perceiver architecture [19] as the Value Head to encode and compress knowledge items. The Perceiver model uses a transformer decoder \\(\\psi(\\cdot)\\) with learnable \\(c\\)-length latent embeddings to compress the full token sequence into an arbitrary length \\(c\\), such that \\(\\mathrm{Emb}_{\\mathrm{Value}}(z) = \\psi(b(z)) \\in \\mathbb{R}^{c \\times d}\\) (In our experiments we use \\(c = 32\\)). This lets us retrieve top-K memory entries for K as large as a hundred. To make the compressed embeddings generated by Perceiver more expressive, we add two additional regularizations. The first one is a disentangled regularization [16] that forces every two output tokens to be linearly de-correlated \\(\\mathcal{L}_{\\mathrm{decor}} = \\sum_{i,j=1}^{K} \\left\\| \\mathrm{Covariance}(\\psi(b(z_i)), \\psi(b(z_j))) \\right\\|_F^2\\), and the second one is an alignment regularization that minimizes the distance of L2-Norm between the query and compressed knowledge embedding: \\(\\mathcal{L}_{\\mathrm{align}} = \\left| 1 - \\frac{\\sum_z \\| \\psi(b(z)) \\|_2}{\\sum_x \\| b(x) \\|_2} \\right|\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.705, + 0.188, + 0.721 + ], + "angle": 0, + "content": "3.3. Retriever" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Figure 2 (c) shows REVEAL's retrieval procedure. Given the input query \\( x \\), the retriever's task is to find top-K memory entries \\( M \\) with the highest probability \\( p(M \\mid x) \\) which we approximate as \\( p(M \\mid x) = \\prod_{m \\in M} p(m \\mid x) \\) by retrieving each entry independently. Note that we retrieve from a large-scale unified memory \\( \\tilde{\\mathcal{M}} = [\\mathcal{M}^1, \\dots, \\mathcal{M}^{|\\tilde{\\mathcal{C}}|}] \\) that is constructed from a diverse set of knowledge sources. To help the query to better choose the most appropriate knowledge sources, we learn a gating function that models the probability of retrieving from each memory corpus. With the corpus gating, for \\( m_i^j \\in \\mathcal{M}^j \\) we re-weight \\( p(m^j \\mid x) \\) by" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.885, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.224, + 0.896, + 0.281 + ], + "angle": 0, + "content": "Figure 3. Detailed procedure of attentive knowledge fusion module. We inject retrieval probability as a prior to knowledge token embeddings, so the retriever can receive gradients via back-propagating over {self/cross} -attention part." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.306, + 0.731, + 0.321 + ], + "angle": 0, + "content": "the computed corpus gating score:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.329, + 0.893, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p \\left(m _ {i} ^ {j} \\mid x\\right) = p \\left(\\mathcal {M} ^ {j} \\mid x\\right) \\cdot p \\left(m _ {i} ^ {j} \\mid x; \\mathcal {M} ^ {j}\\right) (2) \\\\ = G a t e _ {\\mathcal {M} ^ {j}} (x) \\cdot \\frac {\\exp \\left(R e l \\left(x , m _ {i} ^ {j}\\right) / \\tau\\right)}{\\sum_ {m _ {k} ^ {j} \\in \\mathcal {M} ^ {j}} \\exp \\left(R e l \\left(x , m _ {k} ^ {j}\\right) / \\tau\\right)} (3) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.895, + 0.522 + ], + "angle": 0, + "content": "where \\(Gate_{\\mathcal{M}^j}(x) = \\mathrm{Softmax}(W \\cdot \\mathrm{Emb}_{\\mathrm{Query}}(x) + b)[j]\\) is a softmax gating that assigns a score to each memory corpus \\(M^j\\), with \\(W\\) and \\(b\\) as function parameters. \\(Rel(x, m_i^j)\\) models relevance score between query \\(x\\) and each memory entry via embedding dot product, such that \\(Rel(x, m_i^j) = \\mathrm{Emb}_{\\mathrm{Query}}(x)^T \\cdot \\mathrm{Emb}_{\\mathrm{Key}}(z_i^j)\\). where \\(z_i\\) is the knowledge item corresponding to the memory entry \\(m_i\\) and \\(\\tau\\) is the temperature parameter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.895, + 0.658 + ], + "angle": 0, + "content": "After identifying the top-K memory entries, the retriever passes the pre-computed in-memory key and value embeddings to the generator. In the meantime, to support end-to-end training of the encoders, we also re-encode a small portion (i.e., \\(10\\%\\) ) of the retrieved knowledge items \\(z_{i}\\) from scratch. In this way, the memory encoders could be updated with moderate computational cost. We concatenate the re-encoded knowledge with in-memory ones to construct the final top-K retrieved key/value embeddings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.618, + 0.681 + ], + "angle": 0, + "content": "3.4. Generator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Figure 2 (d) shows how the query and the retrieved knowledge items are fused to generate the output answer. All \\(K\\) retrieved memory values are concatenated with the query embedding, which is feasible due to the Perceiver module utilized as the value head \\(\\psi(\\cdot)\\), compressing each knowledge item into a short sequence. We denote the concatenated query embedding and memory values as \\(X = [b(x), \\psi(b(z_1)), \\dots, \\psi(b(z_K))] \\in \\mathbb{R}^{(I + c \\cdot K) \\times d}\\), where \\(I\\) is the number of tokens of the input query \\(x\\) and \\(c\\) is the number of compressed tokens. To guide the generator towards attending to the most important items in \\(X\\) and facilitate backpropagation of gradients to the retriever, we propose an attentive fusion module \\(f(\\cdot)\\) capable of incorporating the retriever score as a prior for calculating" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23372" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.165 + ], + "angle": 0, + "content": "
Knowledge SourceCorpus SizeType of TextAvg. Text Length
WIT [37]5,233,186Wikipedia Passage258
CC12M [5]10,009,901Alt-Text Caption37
VQA-V2 [12]123,287Question Answer111
WikiData [40]4,947,397Linearized Triplets326
" + }, + { + "type": "table_caption", + "bbox": [ + 0.125, + 0.176, + 0.42, + 0.19 + ], + "angle": 0, + "content": "Table 1. Statistics of the knowledge sources used." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.205, + 0.449, + 0.269 + ], + "angle": 0, + "content": "
Model NameT5 VariantImage Encoder# params.GFLOPs
REVEAL-BaseT5-BaseViT-B/160.4B120
REVEAL-LargeT5-LargeViT-L/161.4B528
REVEALT5-LargeViT-g/142.1B795
" + }, + { + "type": "table_caption", + "bbox": [ + 0.094, + 0.271, + 0.451, + 0.285 + ], + "angle": 0, + "content": "Table 2. Model configuration of different REVEAL variants." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.471, + 0.388 + ], + "angle": 0, + "content": "cross-knowledge attention. The detailed procedure is illustrated in Figure 3. We firstly compute a latent soft attention mask over \\( X \\) as \\( \\text{Mask}_{\\text{att}} = [1, p(z_1|x), \\ldots, p(z_K|x)] \\). Finally, we pass the fused representation \\( f(X, \\text{Mask}_{\\text{att}}) \\) into a T5 decoder module \\( g(\\cdot) \\) to generate the textual output." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.402, + 0.308, + 0.42 + ], + "angle": 0, + "content": "4. Generative Pre-Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.471, + 0.534 + ], + "angle": 0, + "content": "The existing VQA datasets are not large enough for training a complex multi-component model like ours from scratch. Therefore, we pre-train our model on a massive image-text corpus. In Sec. 4.1 we go over the details of our pre-training data and objective. Then in Sec. 4.2 we introduce the various sources of knowledge used in our experiments. Finally, in Sec. 4.3 we describe the pre-training implementation details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.292, + 0.56 + ], + "angle": 0, + "content": "4.1. Pre-Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.469, + 0.657 + ], + "angle": 0, + "content": "We pre-train our model on the Web-Image-Text dataset [51], a large-scale corpus containing 3 billion image alt-text caption pairs collected from the public Web. Since the dataset is noisy, we add a filter to remove data points whose captions are shorter than 50 characters. This yields roughly 1.3 billion image caption pairs for pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.785 + ], + "angle": 0, + "content": "We denote the pre-training Web-Image-Text dataset [51] as \\(\\mathcal{D}\\). We use the text generation objective used in Wang et al. [45]) to pre-train our model on \\(\\mathcal{D}\\). Given an image-text example \\(x = (\\mathrm{img},\\mathrm{txt})\\) from \\(\\mathcal{D}\\), we randomly sample a prefix length \\(T_{p}\\). We feed \\(x_{< T_p}\\) that contains the text prefix and image to the model as input and our objective is to generate \\(x_{\\geq T_p}\\) containing the rest of the text as output. The training goal is to condition on \\(x_{< T_p}\\) and autoregressively generate the remaining text sequence \\(x_{\\geq T_p}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.795, + 0.47, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {P r e f i x L M}} = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\log p \\left(x _ {\\geq T _ {p}} \\mid x < T _ {p}\\right) \\right] \\tag {4} \\\\ = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\sum_ {i \\geq T _ {p}} \\log p \\left(x _ {i} \\mid x _ {< i}\\right) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Warm Starting the Model In order to pre-train all components of our model end-to-end, we need to warm start the retriever at a good state. Otherwise, if starting with random" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.891, + 0.122 + ], + "angle": 0, + "content": "weights, the retriever would often return irrelevant memory items that would never generate useful training signals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.893, + 0.379 + ], + "angle": 0, + "content": "To avoid this cold-start problem, we propose to construct an initial retrieval dataset with pseudo ground-truth knowledge to give the pre-training a reasonable head start. We create a modified version of the Wikipedia-Image-Text (WIT) [37] dataset for this purpose. Each image-caption pair in WIT also comes with a corresponding Wikipedia passage (words surrounding the text). We put together the surrounding passage with the query image and use it as the pseudo ground-truth knowledge that corresponds to the input query. As the passage provides rich information about the image and caption, it definitely is useful for initializing the model. To avoid the model from relying on low-level image features for retrieval, we apply random data augmentation to the input query image. Given this modified dataset that contains pseudo retrieval ground-truth, we train the query and memory key embeddings by optimizing the following contrastive loss:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.392, + 0.868, + 0.41 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n t r a}} = - \\log \\operatorname {S o f t m a x} \\left(\\operatorname {E m b} _ {\\text {Q u e r y}} (x) ^ {T} \\operatorname {E m b} _ {\\text {K e y}} (\\hat {z})\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.891, + 0.453 + ], + "angle": 0, + "content": "where \\(\\hat{z}\\) represents the pseudo ground-truth knowledge entry corresponding to the input query \\(x\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.464, + 0.687, + 0.48 + ], + "angle": 0, + "content": "4.2. Knowledge Sources" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.893, + 0.683 + ], + "angle": 0, + "content": "We use the following four sources of knowledge in our experiments: Wikipedia-Image-Text (WIT) [37] consists of the images in Wikipedia, as well as their alt-text captions and contextualized text passages. Conceptual (CC12M) [5] contains web images paired with alt-text captions. It includes many long-tail entities. VQA-v2 [12] is a visual question answering dataset. We merge all question-answer pairs per image into a single passage. WikiData [40] is a structural knowledge graph encoding relations between Wikipedia entities. We linearize all relational triplets per entity into a textual passage following the procedure of [32]. We have listed the statistical details of these knowledge sources in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.716, + 0.712 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Incorporating all the components introduced above, REVEAL can be directly pre-trained over large-scale image caption datasets after proper initialization. As our model architecture is based on T5 and ViT, we use pre-trained ViT checkpoints from [50] and pre-trained T5 checkpoints from [33] to initialize the encoder parameters. The query head, key head and attentive fusion layers are initialized from upper T5, while the base text encoder is initialized from lower T5. The combination of these modules can be found in Table 2 for three three model variants, REVEAL-Base, REVEAL-Large and REVEAL, of which the largest REVEAL model has around 2 billion parameters." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23373" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.149, + 0.053, + 0.821, + 0.302 + ], + "angle": 0, + "content": "
VQA Model NameKnowledge SourcesAccuracy (%)Memory (GB)
MUTAN+AN [29]Wikipedia + ConceptNet27.8-
ConceptBERT [11]Wikipedia33.7-
KRISP [28]Wikipedia + ConceptNet38.4-
Visual Retriever-Reader [27]Google Search39.2-
MAVEx [46]Wikipedia+ConceptNet+Google Images39.4-
KAT-Explicit [13]Wikidata44.31.5
PICa-Base [48]Frozen GPT-343.3350
PICa-Full [48]Frozen GPT-348.0350
KAT [13] (Single)Wikidata + Frozen GPT-353.11.5 + 352+ 500
KAT [13] (Ensemble)Wikidata + Frozen GPT-354.44.6 + 352 + 500
ReVIVE [24] (Single)Wikidata + Frozen GPT-356.61.5 + 354 + 500
ReVIVE [24] (Ensemble)Wikidata+Frozen GPT-358.04.6 + 354 + 500
REVEAL-BaseWIT + CC12M + Wikidata + VQA-255.20.8 + 7.5 + 744
REVEAL-LargeWIT + CC12M + Wikidata + VQA-258.02.8 + 10 + 993
REVEALWIT + CC12M + Wikidata + VQA-259.14.2 + 10 + 993
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.305, + 0.895, + 0.349 + ], + "angle": 0, + "content": "Table 3. Visual Question Answering results on OK-VQA, compared with existing methods that use different knowledge sources. For the memory cost, we assume all models use bfloat16. Green means on-device model parameters that are learnable, Blue means on-device memory of frozen model parameters, and Red means CPU/disk storage cost that are not involved in computation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.473, + 0.526 + ], + "angle": 0, + "content": "Distributed Online Retrieval. Finding the top-k most-relevant knowledge entries is a standard Maximum Inner Product Search (MIPS) problem. There are approximate search algorithms [8, 36] that scale sub-linearly with the size of the knowledge corpus \\( |C| \\). We use TPU-KNN [8] to conduct distributed MIPS search, by splitting and storing the memory embeddings across all training devices. The query is synced to each device, which retrieves approximate top-K results from its own memory. Then these results are combined to compute the global top-K retrieved items." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.474, + 0.742 + ], + "angle": 0, + "content": "Pre-Training Pipeline. We first train the multimodal retriever on our modified version of the Wikipedia Image Text (WIT) dataset via \\(\\mathcal{L}_{\\text{contra}}\\). We use the Adafactor optimizer without momentum (\\(\\beta_{1} = 0\\), \\(\\beta_{2} = 0.999\\)), with weight decay of \\(0.001^{2}\\), and with a peak learning rate of 6e4, to train for 10 epochs. We use this checkpoint to warm-start our generative pre-training. We set the number of retrieved knowledge entries as \\(K = 10\\) during pre-training, and use adafactor with a peak learning rate of 1e-3 and inverse squared root learning rate scheduler with 10,000 linear warm-up steps. We use \\(\\mathcal{L}_{\\text{PrefixLM}}\\) as the main objective, adding \\(\\mathcal{L}_{\\text{contra}}\\), \\(\\mathcal{L}_{\\text{decor}}\\) and \\(\\mathcal{L}_{\\text{align}}\\) weighted by 0.01. We use a batch size of 4096 across 256 CloudTPUv4 chips and train for about 5 days." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.768, + 0.283, + 0.786 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.471, + 0.86 + ], + "angle": 0, + "content": "We evaluate our proposed method on knowledge-based VQA in Sec. 5.1 and image captioning in Sec. 5.2. We then conduct ablation studies in Sec. 5.3 to analyze the impact of each model component on overall performance." + }, + { + "type": "table", + "bbox": [ + 0.572, + 0.371, + 0.821, + 0.517 + ], + "angle": 0, + "content": "
VQA Model NameAccuracy (%)
ViLBERT [26]30.6
LXMERT [38]30.7
ClipCap [30]30.9
KRISP [28]33.7
GPV-2 [21]48.6
REVEAL-Base50.4
REVEAL-Large51.5
REVEAL52.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.52, + 0.877, + 0.535 + ], + "angle": 0, + "content": "Table 4. Visual Question Answering results on A-OKVQA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.83, + 0.577 + ], + "angle": 0, + "content": "5.1. Evaluating on Knowledge-Based VQA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.809 + ], + "angle": 0, + "content": "One of the most knowledge intensive visual-language tasks is knowledge-based visual question answering (VQA), exemplified by the OK-VQA [29] and A-OKVQA [35] benchmarks. To finetune our pre-trained model on these VQA tasks, we use the same generative objective where the model takes in an image question pair as input and generates the text answer as output. There are a few differences between the fine-tuning and the pre-training stages: 1) we set the number of retrieved knowledge entries to \\( K = 50 \\), so the model is able to retrieve sufficient supporting evidence; 2) we freeze the whole base V-L encoder to stabilize training; and 3) we use a batch size of 128, with the Adafactor optimizer, a peak learning rate of 1e-4. We use the soft VQA accuracy metric [3] to evaluate the model's generated answer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Our results on OKVQA and A-OKVQA datasets are shown in Table 3 and Table 4 respectively. For OKVQA, earlier attempts that incorporate a fixed knowledge retriever report results that are below \\(45\\%\\). Recently a series of works utilize large language models (e.g. GPT-3) as implicit knowledge sources, which achieve much better performance" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.448, + 0.902 + ], + "angle": 0, + "content": "2The remaining experiments use the same optimizer configuration." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23374" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.08, + 0.435, + 0.198 + ], + "angle": 0, + "content": "
Model NameMSCOCONoCaps# params.
Flamingo [2]138.1-80B
VinVL [52]140.9105.10.4B
SimVLM [45]143.3112.21.5B
CoCa [49]143.6122.42.1B
REVEAL-Base141.1115.80.4B
REVEAL-Large144.5121.31.4B
REVEAL145.4123.02.1B
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.2, + 0.47, + 0.228 + ], + "angle": 0, + "content": "Table 5. Image Captioning results on MSCOCO (Karpathy-test split) and NoCaps (val set). Evaluated using the CIDEr metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.47, + 0.362 + ], + "angle": 0, + "content": "with the trade-off of a huge computational cost. REVEAL achieves higher performance than those methods without relying on such large language models3. Compared with the previous state-of-the-art, KAT and ReVIVE, which also utilizes T5-Large as a generator, REVEAL achieves accuracy of \\(59.1\\%\\), which is \\(+6.0\\%\\) higher than the single KAT [13] model and \\(+2.5\\%\\) higher than ReVIVE [24]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.471 + ], + "angle": 0, + "content": "On A-OKVQA, REVEAL achieves \\(52.2\\%\\) accuracy, which is \\(+3.6\\%\\) higher than the previous best, GPV-2 [21]. We also show two examples of these datasets in Figure 4. All these results show that, with proper end-to-end retrieval training and a diverse set of knowledge sources, REVEAL can learn to retrieve meaningful knowledge entries, and achieve promising results without relying on a large language model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.365, + 0.499 + ], + "angle": 0, + "content": "5.2. Evaluating on Image Captioning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.704 + ], + "angle": 0, + "content": "We also evaluate REVEAL on image captioning benchmarks: MSCOCO Captions [6] and NoCaps [1]. We follow the evaluation protocol used in [49]. We directly fine-tune our generator model on the MSCOCO training split via cross-entropy generative objective. We measure our performance on the MSCOCO test split and NoCaps val set with the CIDEr metric [39]. The results of these two datasets are shown in Table 5. Note that REVEAL achieves better results than strong recent baselines such as SimVLM [45] and CoCa [49] on both benchmarks. Notably, REVEAL -Large with 1.4B parameters outperforms the 2.1B-parameter CoCa model and is significantly better than 80B-parameter Flamingo model [2]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.715, + 0.458, + 0.733 + ], + "angle": 0, + "content": "5.3. Analyzing Effects of Key Model Components" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.739, + 0.47, + 0.815 + ], + "angle": 0, + "content": "In the following we study which design choices contribute most to the model's performance. We focus on three research questions: (1) Does utilizing multiple knowledge sources enhance performance? (2) Does the proposed attentive fusion surpass existing end-to-end retrieval training methods?" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.08, + 0.875, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Figure 4. VQA Examples. REVEAL is able to use knowledge from different sources to correctly answer the question. We show more examples in Figure 1-3 of Supplementary Material, indicating that our model can retrieve and use items from diverse knowledge sources to correctly solve different input query." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.372 + ], + "angle": 0, + "content": "(3) Can we add knowledge by only updating the memory without modifying model parameters?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Analyzing multiple knowledge sources. A major distinction of REVEAL compared to previous retrieval-augmented approaches is its capacity to utilize a diverse set of knowledge sources during inference. To assess the relative importance of each data source and the efficacy of retrieving from various corpora, we conduct two ablation studies: 1) Only-One-Left: employing a single knowledge source to evaluate the outcomes; and 2) Leave-One-Out: excluding one knowledge source from the complete set \\(\\mathcal{C}\\). These ablation studies are executed using the REVEAL Base, evaluated on the OKVQA validation set under the aforementioned conditions. As shown in Figure 5, among the four knowledge sources utilized in this paper, WIT is the most informative, with the highest accuracy when used in isolation (53.1The remaining three corpora, CC12M, VQA-v2, and WikiData, do not offer the same level of informativeness as WIT when utilized independently. However, excluding any of these corpora from the complete dataset results in performance decreases of \\(1.3\\%\\), \\(0.6\\%\\), and \\(1.1\\%\\), respectively. This observation implies that these knowledge sources effectively complement one another, contributing valuable information to enhance performance. To further substantiate this hypothesis, we perform an additional experiment involving pairs of knowledge sources, as illustrated in Figure 6. Notably, even when paired with an informative knowledge source such as WIT, incorporating an extra corpus consistently leads to performance improvements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Analyzing different retrieval training methods. Another core component of REVEAL is the attentive fusion layer, which supports efficient joint training of the retriever and generator. We investigate its performance compared to two existing retrieval training method categories: 1) a frozen retriever based on ALIGN [20] representations; 2) end-to-end retrieval training methods including Attention Distill [17], EMDR² [47], and Perplexity Distill [18]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.827, + 0.47, + 0.901 + ], + "angle": 0, + "content": "3As shown in the last column of Table 3, REVEAL stores external knowledge as value embeddings on disk, occupying 993GB of space. The key embeddings consume 10GB space and are kept in TPU memory for fast lookup. On the other hand, KAT and REVIVE need to load the entire 350GB GPT-3 model in the GPU/TPU memory. Furthermore, storing WikiData on disk consumes 500GB of disk memory." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23375" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.085, + 0.089, + 0.268, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.203, + 0.268, + 0.287 + ], + "angle": 0, + "content": "Figure 5. OKVQA Accuracy of REVEAL using 1) Only-One-Left: only use a single knowledge source; 2) Leave-One-Out: use all without this knowledge source." + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.089, + 0.481, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.281, + 0.203, + 0.466, + 0.287 + ], + "angle": 0, + "content": "Figure 6. OKVQA Accuracy of REVEAL using all Pair of Knowledge Sources. Results show that combining multiple sources could consistently improve performance." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.304, + 0.47, + 0.405 + ], + "angle": 0, + "content": "
Retrieval MethodAcc@10Acc@100OKVQA Acc.GFLOPs
ALIGN [20] (fixed)0.6380.79344.7-
Attention Distill [17]0.6740.83545.9119
EMDR2 [47]0.6910.86946.5561
Perplexity Distill [18]0.7040.88646.7561
Ours (Attentive Fusion)0.7260.89447.3120
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.407, + 0.472, + 0.478 + ], + "angle": 0, + "content": "Table 6. Analysis of Retrieval Training Method: We train REVEAL-Base (frozen generator, only train randomly initialized retriever) to retrieve from the WIT dataset (only text passage without image), and show the retrieval accuracy at the first 10 or 100 results, as well as fine-tuned OKVQA accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.472, + 0.869 + ], + "angle": 0, + "content": "We use the pre-trained REVEAL-Base model, fix the generator and randomly initialize the retriever (query head and key head). We utilize our modified version of WIT dataset with pseudo ground-truth retrieved labels as the evaluation corpus. We evaluate retrieval performance by checking whether the correct passage appears in top-10/100 results. For the ALIGNN model, we directly evaluate the retrieval results from the pre-trained checkpoint, while for other models, we perform retrieval-augmented training on the WIT dataset. To prevent the model from relying on image similarity for accurate results, we only use text passages as knowledge entries and discard images. Subsequently, we finetune the model on OKVQA and report its accuracy. The results are presented in Table 6. We observe that directly using pretrained encoder does not perform well, even with a strong model like ALIGNN. Moreover, among the various end-to-end retrieval training approaches, our attentive fusion method attains better accuracy in both retrieval and OKVQA tasks. Importantly, our technique exhibits a computational cost (quantified by GFLOPs) comparable to that of attention distillation, yet significantly lower than \\(\\mathrm{EMDR}^2\\) and Perplexity distillation. This indicates that our proposed method is more efficient and effective for pre-training retrieval-augmented visual-language models." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Analyzing Knowledge Modification. One advantage of utilizing knowledge memory is that we could easily add or" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.088, + 0.865, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.225, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Figure 7. Study of Knowledge Update. The blue curve shows result by removing certain percentage of knowledge during both fine-tuning and inference stage. The orange curve shows results by still first removing the knowledge, and then adding the knowledge back during inference, which simulates the knowledge update." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.491 + ], + "angle": 0, + "content": "update knowledge entries without re-training model's parameters. To validate this, we conducted ablation studies in which we removed a specific percentage of knowledge entries from the corpora and assessed the performance of the REVEAL-Base model on the OKVQA dataset. Subsequently, we add the removed knowledge back into the corpora, allowing the trained model to make predictions using the complete set of corpora. This approach ensured that the removed knowledge was not seen by the model during fine-tuning, enabling us to test its ability to accurately retrieve and utilize that knowledge for problem-solving." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.897, + 0.69 + ], + "angle": 0, + "content": "The results are illustrated in Figure 7, with the blue curves representing the inference outcomes without the removed knowledge and the orange curve depicting the results after adding the removed knowledge back. A notable performance improvement was observed upon reintroducing the knowledge (orange curve) compared to the outcomes with the removed knowledge (blue curve). Specifically, for the model fine-tuned with only \\(10\\%\\) of the knowledge, the reintroduction of the removed knowledge resulted in an accuracy of 51.8 (+6.7 higher than when removed). This finding demonstrates that the REVEAL model can swiftly adapt to new knowledge by merely updating the memory, obviating the need for re-training model parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.62, + 0.723 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.903 + ], + "angle": 0, + "content": "This paper presents an end-to-end Retrieval-augmented Visual Language model (REVEAL), which contains a knowledge retriever that learns to utilize a diverse set of knowledge sources with different modality. The retriever is trained jointly with the generator to return multiple knowledge entries. We pre-train REVEAL on a massive image-text corpus with four diverse knowledge corpora, and achieves state-of-the-art results on knowledge-intensive visual question answering and image caption tasks. In the future we'd explore the ability of this model to be used for attribution, and applying it to broader class of multimodal tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23376" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Harsh Agrawal, Peter Anderson, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, and Stefan Lee. nocaps: novel object captioning at scale. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 8947-8956. 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Ross $^{2}$ , Alireza Fathi $^{2}$ , $^{1}$ University of California, Los Angeles, $^{2}$ Google Research + +![](images/2885fe2a4a23575f25aa37fbb74917d7593077933c05623b714035fd7d1bcebc.jpg) +Figure 1. We augment a visual-language model with the ability to retrieve multiple knowledge entries from a diverse set of knowledge sources, which helps generation. Both retriever and generator are trained jointly, end-to-end, by optimizing a language modeling objective. + +# Abstract + +In this paper, we propose an end-to-end Retrieval-Augmented Visual Language Model (REVEAL) that learns to encode world knowledge into a large-scale memory, and to retrieve from it to answer knowledge-intensive queries. REVEAL consists of four key components: the memory, the encoder, the retriever and the generator. The large-scale memory encodes various sources of multimodal world knowledge (e.g. image-text pairs, question answering pairs, knowledge graph triplets, etc.) via a unified encoder. The retriever finds the most relevant knowledge entries in the memory, and the generator fuses the retrieved knowledge with the input query to produce the output. A key novelty in our approach is that the memory, encoder, retriever and generator are all pre-trained end-to-end on a massive amount of data. Furthermore, our approach can use a diverse set of multimodal knowledge sources, which is shown to result in significant gains. We show that REVEAL achieves state-of-the-art results on visual question answering and image captioning. The project page of this work is reveal.github.io. + +# 1. Introduction + +Recent large-scale models such as T5 [33], GPT-3 [4], PaLM [9], CoCa [49], Flamingo [2], BEIT-3 [43] and + +PaLI [7] have demonstrated the ability to store substantial amounts of world knowledge, when scaled to tens of billions of parameters and trained on vast text and image corpora. These models achieve state-of-the-art results in downstream tasks such as image captioning, visual question answering and open vocabulary recognition. Yet, these models have a number of drawbacks: (i) they require massive scale, of parameters, data and computation, and (ii) they need to be re-trained every time the world knowledge is updated. + +To address these issues, we adopt a different approach. Instead of statically compiling world knowledge into model weights, we transform the knowledge into a key-value memory through neural representation learning. Our model learns to utilize the memory for answering knowledge-intensive queries. By decoupling the knowledge memorization from reasoning, we enable our model to leverage various external sources of knowledge (e.g., Wikipedia passages and images [37], the WikiData knowledge graph [40], Web imagetext pairs [5] and visual question answering data [12]). This enables the model parameters to focus on understanding the query and conducting reasoning, rather than being dedicated to memorization. + +Retrieval-augmented models have attracted a fair amount of attention in the fields of NLP [14, 18] and computer vision [13,25]. Typically, these models often use a pre-existing single-modality backbone to encode and retrieve information from the knowledge corpus. Such approaches do not leverage all available modalities in the query and knowl + +edge corpora, and hence they might not find the information that is most helpful for generating the model output. A key novelty in our approach is that we encode and store various sources of multimodal world knowledge into a unified memory, which the retriever can access via multimodal query encodings, to find the most relevant information from across complementary sources. Our multimodal memory and retriever are pre-trained end-to-end together together with the rest of the model, on a massive amount of data and using diverse knowledge sources. + +A key challenge of pre-training the multimodal retriever end-to-end is the lack of direct supervision. There is no ground-truth indicating which knowledge entries are most helpful for answering knowledge-intensive queries. Some of the existing works in NLP [14, 23, 34] propose to acquire training signal by assessing the usefulness of each retrieved knowledge entry independently for helping language modelling. This approach is inefficient, as it involves estimating hundreds of retrieved knowledge entries independently, and also inaccurate as it discards the dependency between different knowledge entries in the retrieval set. In contrast, we propose to get this training signal while simultaneously considering multiple retrieved knowledge entries, by introducing an attentive fusion layer that injects retrieval score into the attention calculation procedure. This enables the retrieval module to be differentiable and jointly pre-trained with the rest of the model. + +In summary, our key contributions are as follows: + +- We are the first to propose an end-to-end pre-training paradigm that learns to index into a large-scale memory to solve knowledge-intensive visual-language tasks. +- Our method can construct a large-scale memory by encoding various sources of multimodal world knowledge, including Wikipedia passage, web images with alt-text captions, and knowledge graph triplets. +- REVEAL achieves state-of-the-art performance on several knowledge-intensive visual question answering and image captioning datasets. Notably on the OKVQA benchmark, REVEAL achieves a new state-of-the-art, $59.1\%$ accuracy, while using order of magnitude fewer parameters than previous works. + +# 2. Related Work and Background + +Knowledge-based Visual Question Answering. To evaluate a model's ability to comprehend multimodal world knowledge not easily inferred from input data, several knowledge-based Visual Question Answering (VQA) datasets have been introduced. KB-VQA [41] and FVQA [42] design questions that can be answered by retrieving relevant triplets from domain-specific structured knowledge graphs. OK-VQA [29] improves these datasets by necessitating the use of external knowledge, which goes beyond what can be directly observed in the input images. More recently, A- + +OKVQA [35] offers further improvements to OK-VQA by exclusively selecting questions that demand both external knowledge and commonsense reasoning about the image scenes. To tackle knowledge-based VQA tasks, many approaches have been proposed to incorporate external knowledge into visual-language models. One line of research uses explicit knowledge from structured knowledge graphs [11, 15, 31, 44] or unstructured text corpora [27, 28, 46]. The key component for these works is the knowledge retriever. Some works [11, 28, 31, 46] utilize off-the-shelf vision detection models to generate image tags for knowledge retrieval, while others train the retrieval model via distant supervision [27] or auxiliary tasks (e.g. entity linking) [13]. Another research direction aims to incorporate implicit knowledge from pre-trained Large Language Models, such as GPT-3 [4] or PaLM [9]. These approaches utilize off-the-shelf image caption models to convert images into text, feed them into a language model, and use the generated text output as augmented knowledge [13, 24, 48]. Our work follows the first direction, augmenting a vision-language model with an explicit knowledge retriever. The main distinction is that we propose an end-to-end training framework to jointly learn the answer generator and retriever, rather than using a fixed or predefined knowledge retrieval. + +End-to-End Training of Retrieval-Augmented Models. Given the advantage of knowledge retrieval, a key question is how to get learning signal to train the retrieval model. For tasks with annotated retrieval ground-truth, retrieval training can be conducted via standard contrastive learning [22]. However, most tasks do not provide clear indications of which knowledge entries are relevant for generating answers. To this end, a series of studies have investigated retrieval training using supervision derived from downstream tasks. REALM [14] trains a single-document retriever by concatenating each retrieved result with the query, to calculate the final loss independently. A similar approach has been used by EMDR² [34] for multi-document retrieval training. FIDKD [17] proposes to use the aggregated attention score calculated by the generator as a distillation signal to train the retriever. Atlas [18] further introduces a perplexity distillation loss and a leave-one-out variant. Our REVEAL proposes to inject the retrieval scores directly into an attentive fusion module, enabling to train the retriever to directly optimize downstream tasks as well as pre-training objectives. + +# 3. Method + +We propose a Retrieval-Augmented Visual Language Model (REVEAL), which learns to use knowledge from different sources for solving knowledge-intensive tasks. For both pre-training and fine-tuning, our goal is to learn the distribution $P(y \mid x)$ to generate a textual output $y$ conditioned on a multimodal input query $x$ . REVEAL contains + +![](images/6be7ed32586e08a00590f51f7e7587a4d834835f6f8483ba6fa0b9047484a740.jpg) +Figure 2. The overall workflow of REVEAL consists of four main steps: (a) encode a multimodal input into a sequence of token embeddings and a summarized query embedding; (b) encode each knowledge entry from different corpus into unified key and value embedding pairs, where key is used to index the memory and value contains full information of the knowledge; (c) retrieve top-K most similar knowledge items from different knowledge sources, and return the pre-computed in-memory value embeddings and re-encoded value; and (d) fuse the top-K knowledge items via attentive knowledge fusion layer by injecting the retrieval score as a prior during attention calculation. This facilitates REVEAL's key novelty: the memory, encoder, retriever and the generator can be jointly trained in an end-to-end manner. + +four components: knowledge encoding, memory, retrieval and generation. Given an input query $x$ , we first retrieve $K$ possibly helpful entries $M = \{m_1, \dots, m_K\}$ from the memory corpora $\mathcal{M}$ . Each $m$ is a memory entry containing the encoded single key embedding and a sequence of value embeddings (we will describe how to encode knowledge items into memory entries in Sec. 3.2). With it, the retriever can use embedding similarity to find relevant memory entries. We model this retrieval process as sampling from distribution $p(M \mid x)$ . Then, we condition on both the retrieved set $M$ and the original input query $x$ to generate the output $y$ , modeled as $p(y \mid x, M)$ . To obtain the overall likelihood of generating $y$ , we treat $M$ as a latent variable from the entire memory $\mathcal{M}$ and marginalize over it yielding: + +$$ +p (y \mid x) = \sum_ {M \subset \tilde {\mathcal {M}}} \underbrace {p (M \mid x)} _ {\text {r e t r i e v a l}} \cdot \underbrace {p (y \mid x , M)} _ {\text {g e n e r a t i o n}}. \tag {1} +$$ + +However, this marginal probability involves an intractable summation over all size- $K$ subsets of the memory corpora $\tilde{\mathcal{M}}$ . We approximate this instead by using the top- $K$ entries in memory with the highest probability under $p(M \mid x)$ . This is reasonable if most of the unrelated memory entries do not contribute to the generation. Note that we use an online memory that is updated as the knowledge encoder is trained end-to-end with the rest of the model. + +Figure 2 illustrates the overall workflow of REVEAL, and we describe each component in this section. In particular, in Sec. 3.1 we describe how the query is encoded. In Sec. 3.2 we go over how the multimodal knowledge memory is constructed and updated during pre-training. Next, we describe how we retrieve the memory entries that are most relevant to the input query in Sec. 3.3. Finally, in Sec. 3.4 we describe the generator that fuses the query and retrieved knowledge and decodes them into the generated text. + +# 3.1. Query Encoding + +Figure 2 (a) depicts how the input image-text query is encoded. We use a base visual-language encoder $b(\cdot)$ to turn the query input and each knowledge item (with potentially different modalities e.g. text-only, image-only or image-text pairs) into a sequence of embeddings (tokens). We adopt a Vision Transformer (ViT) [10] to encode the images and we use a lower-layer $^{1}$ T5 encoder [33] to encode the texts. We add a projection layer on top of the ViT model to map the image tokens into the same space as the text tokens. We then concatenate the two modalities together. We use an upper-layer T5 module as both the query Head $\phi_{Query}(\cdot)$ and the key Head $\phi_{Key}(\cdot)$ to compute the query embedding and memory keys. We take the output of the first [CLS] tokens followed by a linear projection and L2-normalization to summarize the input into a $d$ -dimensional embedding. + +# 3.2. Memory + +Figure 2 (b) shows how memory is constructed and updated by encoding knowledge items. Our approach differs from previous works primarily by leveraging a diverse set of multimodal knowledge corpora (WikiData knowledge graph,Wikimedia passages and images, Web image-text pairs). Throughout the paper, we denote each corpus as $\mathcal{C}^j = \{z_1^j,\dots ,z_N^j\}$ , in which each $z_{i}^{j}\in \mathcal{C}^{j}$ is a knowledge item that could be an image-text pair, text only, image only, or a knowledge graph triplet. We denote the unified knowledge corpus as $\tilde{\mathcal{C}} = \mathcal{C}^1\cup \mathcal{C}^2\dots \cup \mathcal{C}^S$ that combines $|\tilde{\mathcal{C}} | = S$ different knowledge corpora. We encode the external knowledge corpora into a unified memory $\tilde{\mathcal{M}} = [\mathcal{M}^1,\ldots ,\mathcal{M}^{|\tilde{\mathcal{C}} |}]$ Each knowledge item $z_{i}$ is encoded into a key/value pair $m_{i} = (\mathrm{Emb}_{\mathrm{Key}}(z_{i}),\mathrm{Emb}_{\mathrm{Value}}(z_{i}))$ in memory. Each key + +$\mathsf{Emb}_{\mathsf{Key}}(z) = \phi_{\mathsf{Key}}(b(z)) \in \mathbb{R}^d$ is a $d$ -dimensional embedding vector encoded via Key Head. Each value is a sequence of token embeddings representing the full information of knowledge item $z$ . We follow a similar procedure as in [14] to precompute key/value embeddings of knowledge items from different sources and index them in a unified knowledge memory. We continuously re-compute the memory key/value embeddings as the model parameters get updated during the pre-training phase. We update the memory $\tilde{\mathcal{M}}$ asynchronously at every 1000 training steps. + +Scaling Memory by Compression A naive solution for encoding the memory value is to keep the whole sequence of tokens for each knowledge item. Then, the generator could fuse the input query and the top-K retrieved memory values by concatenating all their tokens together and feeding them into a Transformer Encoder-Decoder pipeline [23]. This approach has two issues: (1) storing hundreds of millions of knowledge items in memory is impractical given that each memory value would consist of hundreds of tokens; (2) transformer encoder has quadratic complexity with respect to the total number of tokens times $K$ for self-attention. + +Therefore, we propose to use the Perceiver architecture [19] as the Value Head to encode and compress knowledge items. The Perceiver model uses a transformer decoder $\psi(\cdot)$ with learnable $c$ -length latent embeddings to compress the full token sequence into an arbitrary length $c$ , such that $\mathrm{Emb}_{\mathrm{Value}}(z) = \psi(b(z)) \in \mathbb{R}^{c \times d}$ (In our experiments we use $c = 32$ ). This lets us retrieve top-K memory entries for K as large as a hundred. To make the compressed embeddings generated by Perceiver more expressive, we add two additional regularizations. The first one is a disentangled regularization [16] that forces every two output tokens to be linearly de-correlated $\mathcal{L}_{\mathrm{decor}} = \sum_{i,j=1}^{K} \left\| \mathrm{Covariance}(\psi(b(z_i)), \psi(b(z_j))) \right\|_F^2$ , and the second one is an alignment regularization that minimizes the distance of L2-Norm between the query and compressed knowledge embedding: $\mathcal{L}_{\mathrm{align}} = \left| 1 - \frac{\sum_z \| \psi(b(z)) \|_2}{\sum_x \| b(x) \|_2} \right|$ . + +# 3.3. Retriever + +Figure 2 (c) shows REVEAL's retrieval procedure. Given the input query $x$ , the retriever's task is to find top-K memory entries $M$ with the highest probability $p(M \mid x)$ which we approximate as $p(M \mid x) = \prod_{m \in M} p(m \mid x)$ by retrieving each entry independently. Note that we retrieve from a large-scale unified memory $\tilde{\mathcal{M}} = [\mathcal{M}^1, \dots, \mathcal{M}^{|\tilde{\mathcal{C}}|}]$ that is constructed from a diverse set of knowledge sources. To help the query to better choose the most appropriate knowledge sources, we learn a gating function that models the probability of retrieving from each memory corpus. With the corpus gating, for $m_i^j \in \mathcal{M}^j$ we re-weight $p(m^j \mid x)$ by + +![](images/41f024044c16f67d827a4b96e98813bfb4011d91f5feb41460ed45e6757a150d.jpg) +Figure 3. Detailed procedure of attentive knowledge fusion module. We inject retrieval probability as a prior to knowledge token embeddings, so the retriever can receive gradients via back-propagating over {self/cross} -attention part. + +the computed corpus gating score: + +$$ +\begin{array}{l} p \left(m _ {i} ^ {j} \mid x\right) = p \left(\mathcal {M} ^ {j} \mid x\right) \cdot p \left(m _ {i} ^ {j} \mid x; \mathcal {M} ^ {j}\right) (2) \\ = G a t e _ {\mathcal {M} ^ {j}} (x) \cdot \frac {\exp \left(R e l \left(x , m _ {i} ^ {j}\right) / \tau\right)}{\sum_ {m _ {k} ^ {j} \in \mathcal {M} ^ {j}} \exp \left(R e l \left(x , m _ {k} ^ {j}\right) / \tau\right)} (3) \\ \end{array} +$$ + +where $Gate_{\mathcal{M}^j}(x) = \mathrm{Softmax}(W \cdot \mathrm{Emb}_{\mathrm{Query}}(x) + b)[j]$ is a softmax gating that assigns a score to each memory corpus $M^j$ , with $W$ and $b$ as function parameters. $Rel(x, m_i^j)$ models relevance score between query $x$ and each memory entry via embedding dot product, such that $Rel(x, m_i^j) = \mathrm{Emb}_{\mathrm{Query}}(x)^T \cdot \mathrm{Emb}_{\mathrm{Key}}(z_i^j)$ . where $z_i$ is the knowledge item corresponding to the memory entry $m_i$ and $\tau$ is the temperature parameter. + +After identifying the top-K memory entries, the retriever passes the pre-computed in-memory key and value embeddings to the generator. In the meantime, to support end-to-end training of the encoders, we also re-encode a small portion (i.e., $10\%$ ) of the retrieved knowledge items $z_{i}$ from scratch. In this way, the memory encoders could be updated with moderate computational cost. We concatenate the re-encoded knowledge with in-memory ones to construct the final top-K retrieved key/value embeddings. + +# 3.4. Generator + +Figure 2 (d) shows how the query and the retrieved knowledge items are fused to generate the output answer. All $K$ retrieved memory values are concatenated with the query embedding, which is feasible due to the Perceiver module utilized as the value head $\psi(\cdot)$ , compressing each knowledge item into a short sequence. We denote the concatenated query embedding and memory values as $X = [b(x), \psi(b(z_1)), \dots, \psi(b(z_K))] \in \mathbb{R}^{(I + c \cdot K) \times d}$ , where $I$ is the number of tokens of the input query $x$ and $c$ is the number of compressed tokens. To guide the generator towards attending to the most important items in $X$ and facilitate backpropagation of gradients to the retriever, we propose an attentive fusion module $f(\cdot)$ capable of incorporating the retriever score as a prior for calculating + +
Knowledge SourceCorpus SizeType of TextAvg. Text Length
WIT [37]5,233,186Wikipedia Passage258
CC12M [5]10,009,901Alt-Text Caption37
VQA-V2 [12]123,287Question Answer111
WikiData [40]4,947,397Linearized Triplets326
+ +Table 1. Statistics of the knowledge sources used. + +
Model NameT5 VariantImage Encoder# params.GFLOPs
REVEAL-BaseT5-BaseViT-B/160.4B120
REVEAL-LargeT5-LargeViT-L/161.4B528
REVEALT5-LargeViT-g/142.1B795
+ +Table 2. Model configuration of different REVEAL variants. + +cross-knowledge attention. The detailed procedure is illustrated in Figure 3. We firstly compute a latent soft attention mask over $X$ as $\text{Mask}_{\text{att}} = [1, p(z_1|x), \ldots, p(z_K|x)]$ . Finally, we pass the fused representation $f(X, \text{Mask}_{\text{att}})$ into a T5 decoder module $g(\cdot)$ to generate the textual output. + +# 4. Generative Pre-Training + +The existing VQA datasets are not large enough for training a complex multi-component model like ours from scratch. Therefore, we pre-train our model on a massive image-text corpus. In Sec. 4.1 we go over the details of our pre-training data and objective. Then in Sec. 4.2 we introduce the various sources of knowledge used in our experiments. Finally, in Sec. 4.3 we describe the pre-training implementation details. + +# 4.1. Pre-Training Objective + +We pre-train our model on the Web-Image-Text dataset [51], a large-scale corpus containing 3 billion image alt-text caption pairs collected from the public Web. Since the dataset is noisy, we add a filter to remove data points whose captions are shorter than 50 characters. This yields roughly 1.3 billion image caption pairs for pre-training. + +We denote the pre-training Web-Image-Text dataset [51] as $\mathcal{D}$ . We use the text generation objective used in Wang et al. [45]) to pre-train our model on $\mathcal{D}$ . Given an image-text example $x = (\mathrm{img},\mathrm{txt})$ from $\mathcal{D}$ , we randomly sample a prefix length $T_{p}$ . We feed $x_{< T_p}$ that contains the text prefix and image to the model as input and our objective is to generate $x_{\geq T_p}$ containing the rest of the text as output. The training goal is to condition on $x_{< T_p}$ and autoregressively generate the remaining text sequence $x_{\geq T_p}$ : + +$$ +\begin{array}{l} \mathcal {L} _ {\text {P r e f i x L M}} = - \mathbb {E} _ {x \sim \mathcal {D}} \left[ \log p \left(x _ {\geq T _ {p}} \mid x < T _ {p}\right) \right] \tag {4} \\ = - \mathbb {E} _ {x \sim \mathcal {D}} \left[ \sum_ {i \geq T _ {p}} \log p \left(x _ {i} \mid x _ {< i}\right) \right]. \\ \end{array} +$$ + +Warm Starting the Model In order to pre-train all components of our model end-to-end, we need to warm start the retriever at a good state. Otherwise, if starting with random + +weights, the retriever would often return irrelevant memory items that would never generate useful training signals. + +To avoid this cold-start problem, we propose to construct an initial retrieval dataset with pseudo ground-truth knowledge to give the pre-training a reasonable head start. We create a modified version of the Wikipedia-Image-Text (WIT) [37] dataset for this purpose. Each image-caption pair in WIT also comes with a corresponding Wikipedia passage (words surrounding the text). We put together the surrounding passage with the query image and use it as the pseudo ground-truth knowledge that corresponds to the input query. As the passage provides rich information about the image and caption, it definitely is useful for initializing the model. To avoid the model from relying on low-level image features for retrieval, we apply random data augmentation to the input query image. Given this modified dataset that contains pseudo retrieval ground-truth, we train the query and memory key embeddings by optimizing the following contrastive loss: + +$$ +\mathcal {L} _ {\text {c o n t r a}} = - \log \operatorname {S o f t m a x} \left(\operatorname {E m b} _ {\text {Q u e r y}} (x) ^ {T} \operatorname {E m b} _ {\text {K e y}} (\hat {z})\right) +$$ + +where $\hat{z}$ represents the pseudo ground-truth knowledge entry corresponding to the input query $x$ . + +# 4.2. Knowledge Sources + +We use the following four sources of knowledge in our experiments: Wikipedia-Image-Text (WIT) [37] consists of the images in Wikipedia, as well as their alt-text captions and contextualized text passages. Conceptual (CC12M) [5] contains web images paired with alt-text captions. It includes many long-tail entities. VQA-v2 [12] is a visual question answering dataset. We merge all question-answer pairs per image into a single passage. WikiData [40] is a structural knowledge graph encoding relations between Wikipedia entities. We linearize all relational triplets per entity into a textual passage following the procedure of [32]. We have listed the statistical details of these knowledge sources in Table 1. + +# 4.3. Implementation Details + +Incorporating all the components introduced above, REVEAL can be directly pre-trained over large-scale image caption datasets after proper initialization. As our model architecture is based on T5 and ViT, we use pre-trained ViT checkpoints from [50] and pre-trained T5 checkpoints from [33] to initialize the encoder parameters. The query head, key head and attentive fusion layers are initialized from upper T5, while the base text encoder is initialized from lower T5. The combination of these modules can be found in Table 2 for three three model variants, REVEAL-Base, REVEAL-Large and REVEAL, of which the largest REVEAL model has around 2 billion parameters. + +
VQA Model NameKnowledge SourcesAccuracy (%)Memory (GB)
MUTAN+AN [29]Wikipedia + ConceptNet27.8-
ConceptBERT [11]Wikipedia33.7-
KRISP [28]Wikipedia + ConceptNet38.4-
Visual Retriever-Reader [27]Google Search39.2-
MAVEx [46]Wikipedia+ConceptNet+Google Images39.4-
KAT-Explicit [13]Wikidata44.31.5
PICa-Base [48]Frozen GPT-343.3350
PICa-Full [48]Frozen GPT-348.0350
KAT [13] (Single)Wikidata + Frozen GPT-353.11.5 + 352+ 500
KAT [13] (Ensemble)Wikidata + Frozen GPT-354.44.6 + 352 + 500
ReVIVE [24] (Single)Wikidata + Frozen GPT-356.61.5 + 354 + 500
ReVIVE [24] (Ensemble)Wikidata+Frozen GPT-358.04.6 + 354 + 500
REVEAL-BaseWIT + CC12M + Wikidata + VQA-255.20.8 + 7.5 + 744
REVEAL-LargeWIT + CC12M + Wikidata + VQA-258.02.8 + 10 + 993
REVEALWIT + CC12M + Wikidata + VQA-259.14.2 + 10 + 993
+ +Distributed Online Retrieval. Finding the top-k most-relevant knowledge entries is a standard Maximum Inner Product Search (MIPS) problem. There are approximate search algorithms [8, 36] that scale sub-linearly with the size of the knowledge corpus $|C|$ . We use TPU-KNN [8] to conduct distributed MIPS search, by splitting and storing the memory embeddings across all training devices. The query is synced to each device, which retrieves approximate top-K results from its own memory. Then these results are combined to compute the global top-K retrieved items. + +Pre-Training Pipeline. We first train the multimodal retriever on our modified version of the Wikipedia Image Text (WIT) dataset via $\mathcal{L}_{\text{contra}}$ . We use the Adafactor optimizer without momentum ( $\beta_{1} = 0$ , $\beta_{2} = 0.999$ ), with weight decay of $0.001^{2}$ , and with a peak learning rate of 6e4, to train for 10 epochs. We use this checkpoint to warm-start our generative pre-training. We set the number of retrieved knowledge entries as $K = 10$ during pre-training, and use adafactor with a peak learning rate of 1e-3 and inverse squared root learning rate scheduler with 10,000 linear warm-up steps. We use $\mathcal{L}_{\text{PrefixLM}}$ as the main objective, adding $\mathcal{L}_{\text{contra}}$ , $\mathcal{L}_{\text{decor}}$ and $\mathcal{L}_{\text{align}}$ weighted by 0.01. We use a batch size of 4096 across 256 CloudTPUv4 chips and train for about 5 days. + +# 5. Experimental Results + +We evaluate our proposed method on knowledge-based VQA in Sec. 5.1 and image captioning in Sec. 5.2. We then conduct ablation studies in Sec. 5.3 to analyze the impact of each model component on overall performance. + +Table 3. Visual Question Answering results on OK-VQA, compared with existing methods that use different knowledge sources. For the memory cost, we assume all models use bfloat16. Green means on-device model parameters that are learnable, Blue means on-device memory of frozen model parameters, and Red means CPU/disk storage cost that are not involved in computation. + +
VQA Model NameAccuracy (%)
ViLBERT [26]30.6
LXMERT [38]30.7
ClipCap [30]30.9
KRISP [28]33.7
GPV-2 [21]48.6
REVEAL-Base50.4
REVEAL-Large51.5
REVEAL52.2
+ +Table 4. Visual Question Answering results on A-OKVQA. + +# 5.1. Evaluating on Knowledge-Based VQA + +One of the most knowledge intensive visual-language tasks is knowledge-based visual question answering (VQA), exemplified by the OK-VQA [29] and A-OKVQA [35] benchmarks. To finetune our pre-trained model on these VQA tasks, we use the same generative objective where the model takes in an image question pair as input and generates the text answer as output. There are a few differences between the fine-tuning and the pre-training stages: 1) we set the number of retrieved knowledge entries to $K = 50$ , so the model is able to retrieve sufficient supporting evidence; 2) we freeze the whole base V-L encoder to stabilize training; and 3) we use a batch size of 128, with the Adafactor optimizer, a peak learning rate of 1e-4. We use the soft VQA accuracy metric [3] to evaluate the model's generated answer. + +Our results on OKVQA and A-OKVQA datasets are shown in Table 3 and Table 4 respectively. For OKVQA, earlier attempts that incorporate a fixed knowledge retriever report results that are below $45\%$ . Recently a series of works utilize large language models (e.g. GPT-3) as implicit knowledge sources, which achieve much better performance + +
Model NameMSCOCONoCaps# params.
Flamingo [2]138.1-80B
VinVL [52]140.9105.10.4B
SimVLM [45]143.3112.21.5B
CoCa [49]143.6122.42.1B
REVEAL-Base141.1115.80.4B
REVEAL-Large144.5121.31.4B
REVEAL145.4123.02.1B
+ +Table 5. Image Captioning results on MSCOCO (Karpathy-test split) and NoCaps (val set). Evaluated using the CIDEr metric. + +with the trade-off of a huge computational cost. REVEAL achieves higher performance than those methods without relying on such large language models3. Compared with the previous state-of-the-art, KAT and ReVIVE, which also utilizes T5-Large as a generator, REVEAL achieves accuracy of $59.1\%$ , which is $+6.0\%$ higher than the single KAT [13] model and $+2.5\%$ higher than ReVIVE [24]. + +On A-OKVQA, REVEAL achieves $52.2\%$ accuracy, which is $+3.6\%$ higher than the previous best, GPV-2 [21]. We also show two examples of these datasets in Figure 4. All these results show that, with proper end-to-end retrieval training and a diverse set of knowledge sources, REVEAL can learn to retrieve meaningful knowledge entries, and achieve promising results without relying on a large language model. + +# 5.2. Evaluating on Image Captioning + +We also evaluate REVEAL on image captioning benchmarks: MSCOCO Captions [6] and NoCaps [1]. We follow the evaluation protocol used in [49]. We directly fine-tune our generator model on the MSCOCO training split via cross-entropy generative objective. We measure our performance on the MSCOCO test split and NoCaps val set with the CIDEr metric [39]. The results of these two datasets are shown in Table 5. Note that REVEAL achieves better results than strong recent baselines such as SimVLM [45] and CoCa [49] on both benchmarks. Notably, REVEAL -Large with 1.4B parameters outperforms the 2.1B-parameter CoCa model and is significantly better than 80B-parameter Flamingo model [2]. + +# 5.3. Analyzing Effects of Key Model Components + +In the following we study which design choices contribute most to the model's performance. We focus on three research questions: (1) Does utilizing multiple knowledge sources enhance performance? (2) Does the proposed attentive fusion surpass existing end-to-end retrieval training methods? + +![](images/38c375cf6c0f9d40307f96db9860a09ef28f6c1badeaff0776ac64795f16702a.jpg) +Figure 4. VQA Examples. REVEAL is able to use knowledge from different sources to correctly answer the question. We show more examples in Figure 1-3 of Supplementary Material, indicating that our model can retrieve and use items from diverse knowledge sources to correctly solve different input query. + +(3) Can we add knowledge by only updating the memory without modifying model parameters? + +Analyzing multiple knowledge sources. A major distinction of REVEAL compared to previous retrieval-augmented approaches is its capacity to utilize a diverse set of knowledge sources during inference. To assess the relative importance of each data source and the efficacy of retrieving from various corpora, we conduct two ablation studies: 1) Only-One-Left: employing a single knowledge source to evaluate the outcomes; and 2) Leave-One-Out: excluding one knowledge source from the complete set $\mathcal{C}$ . These ablation studies are executed using the REVEAL Base, evaluated on the OKVQA validation set under the aforementioned conditions. As shown in Figure 5, among the four knowledge sources utilized in this paper, WIT is the most informative, with the highest accuracy when used in isolation (53.1The remaining three corpora, CC12M, VQA-v2, and WikiData, do not offer the same level of informativeness as WIT when utilized independently. However, excluding any of these corpora from the complete dataset results in performance decreases of $1.3\%$ , $0.6\%$ , and $1.1\%$ , respectively. This observation implies that these knowledge sources effectively complement one another, contributing valuable information to enhance performance. To further substantiate this hypothesis, we perform an additional experiment involving pairs of knowledge sources, as illustrated in Figure 6. Notably, even when paired with an informative knowledge source such as WIT, incorporating an extra corpus consistently leads to performance improvements. + +Analyzing different retrieval training methods. Another core component of REVEAL is the attentive fusion layer, which supports efficient joint training of the retriever and generator. We investigate its performance compared to two existing retrieval training method categories: 1) a frozen retriever based on ALIGN [20] representations; 2) end-to-end retrieval training methods including Attention Distill [17], EMDR² [47], and Perplexity Distill [18]. + +![](images/d0df5c0d0bbdcc4cf7dc27b908727660bd9cdf2c54e1a6f54318a6d4946f9cb9.jpg) +Figure 5. OKVQA Accuracy of REVEAL using 1) Only-One-Left: only use a single knowledge source; 2) Leave-One-Out: use all without this knowledge source. + +![](images/4e02aaf069bc4d099fbdfb1bbec61edc8a51e1a6402b1e34cf4edc4c27e49551.jpg) +Figure 6. OKVQA Accuracy of REVEAL using all Pair of Knowledge Sources. Results show that combining multiple sources could consistently improve performance. + +
Retrieval MethodAcc@10Acc@100OKVQA Acc.GFLOPs
ALIGN [20] (fixed)0.6380.79344.7-
Attention Distill [17]0.6740.83545.9119
EMDR2 [47]0.6910.86946.5561
Perplexity Distill [18]0.7040.88646.7561
Ours (Attentive Fusion)0.7260.89447.3120
+ +Table 6. Analysis of Retrieval Training Method: We train REVEAL-Base (frozen generator, only train randomly initialized retriever) to retrieve from the WIT dataset (only text passage without image), and show the retrieval accuracy at the first 10 or 100 results, as well as fine-tuned OKVQA accuracy. + +We use the pre-trained REVEAL-Base model, fix the generator and randomly initialize the retriever (query head and key head). We utilize our modified version of WIT dataset with pseudo ground-truth retrieved labels as the evaluation corpus. We evaluate retrieval performance by checking whether the correct passage appears in top-10/100 results. For the ALIGNN model, we directly evaluate the retrieval results from the pre-trained checkpoint, while for other models, we perform retrieval-augmented training on the WIT dataset. To prevent the model from relying on image similarity for accurate results, we only use text passages as knowledge entries and discard images. Subsequently, we finetune the model on OKVQA and report its accuracy. The results are presented in Table 6. We observe that directly using pretrained encoder does not perform well, even with a strong model like ALIGNN. Moreover, among the various end-to-end retrieval training approaches, our attentive fusion method attains better accuracy in both retrieval and OKVQA tasks. Importantly, our technique exhibits a computational cost (quantified by GFLOPs) comparable to that of attention distillation, yet significantly lower than $\mathrm{EMDR}^2$ and Perplexity distillation. This indicates that our proposed method is more efficient and effective for pre-training retrieval-augmented visual-language models. + +Analyzing Knowledge Modification. One advantage of utilizing knowledge memory is that we could easily add or + +![](images/09aaa27b58b8df4167608888e1f3ac520c8361912c7af0fea3e7b09fb79ffe1c.jpg) +Figure 7. Study of Knowledge Update. The blue curve shows result by removing certain percentage of knowledge during both fine-tuning and inference stage. The orange curve shows results by still first removing the knowledge, and then adding the knowledge back during inference, which simulates the knowledge update. + +update knowledge entries without re-training model's parameters. To validate this, we conducted ablation studies in which we removed a specific percentage of knowledge entries from the corpora and assessed the performance of the REVEAL-Base model on the OKVQA dataset. Subsequently, we add the removed knowledge back into the corpora, allowing the trained model to make predictions using the complete set of corpora. This approach ensured that the removed knowledge was not seen by the model during fine-tuning, enabling us to test its ability to accurately retrieve and utilize that knowledge for problem-solving. + +The results are illustrated in Figure 7, with the blue curves representing the inference outcomes without the removed knowledge and the orange curve depicting the results after adding the removed knowledge back. A notable performance improvement was observed upon reintroducing the knowledge (orange curve) compared to the outcomes with the removed knowledge (blue curve). Specifically, for the model fine-tuned with only $10\%$ of the knowledge, the reintroduction of the removed knowledge resulted in an accuracy of 51.8 (+6.7 higher than when removed). This finding demonstrates that the REVEAL model can swiftly adapt to new knowledge by merely updating the memory, obviating the need for re-training model parameters. + +# 6. Conclusion + +This paper presents an end-to-end Retrieval-augmented Visual Language model (REVEAL), which contains a knowledge retriever that learns to utilize a diverse set of knowledge sources with different modality. The retriever is trained jointly with the generator to return multiple knowledge entries. We pre-train REVEAL on a massive image-text corpus with four diverse knowledge corpora, and achieves state-of-the-art results on knowledge-intensive visual question answering and image caption tasks. In the future we'd explore the ability of this model to be used for attribution, and applying it to broader class of multimodal tasks. + +# References + +[1] Harsh Agrawal, Peter Anderson, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, and Stefan Lee. nocaps: novel object captioning at scale. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 8947-8956. 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We augment a visual-language model with the ability to retrieve multiple knowledge entries from a diverse set of knowledge sources, which helps generation. Both retriever and generator are trained jointly, end-to-end, by optimizing a language modeling objective." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 374, + 192, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 374, + 192, + 387 + ], + "spans": [ + { + "bbox": [ + 143, + 374, + 192, + 387 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 400, + 290, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 400, + 290, + 628 + ], + "spans": [ + { + "bbox": [ + 45, + 400, + 290, + 628 + ], + "type": "text", + "content": "In this paper, we propose an end-to-end Retrieval-Augmented Visual Language Model (REVEAL) that learns to encode world knowledge into a large-scale memory, and to retrieve from it to answer knowledge-intensive queries. REVEAL consists of four key components: the memory, the encoder, the retriever and the generator. The large-scale memory encodes various sources of multimodal world knowledge (e.g. image-text pairs, question answering pairs, knowledge graph triplets, etc.) via a unified encoder. The retriever finds the most relevant knowledge entries in the memory, and the generator fuses the retrieved knowledge with the input query to produce the output. A key novelty in our approach is that the memory, encoder, retriever and generator are all pre-trained end-to-end on a massive amount of data. Furthermore, our approach can use a diverse set of multimodal knowledge sources, which is shown to result in significant gains. We show that REVEAL achieves state-of-the-art results on visual question answering and image captioning. The project page of this work is reveal.github.io." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 288, + 696 + ], + "type": "text", + "content": "Recent large-scale models such as T5 [33], GPT-3 [4], PaLM [9], CoCa [49], Flamingo [2], BEIT-3 [43] and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 375, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 375, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 375, + 547, + 483 + ], + "type": "text", + "content": "PaLI [7] have demonstrated the ability to store substantial amounts of world knowledge, when scaled to tens of billions of parameters and trained on vast text and image corpora. These models achieve state-of-the-art results in downstream tasks such as image captioning, visual question answering and open vocabulary recognition. Yet, these models have a number of drawbacks: (i) they require massive scale, of parameters, data and computation, and (ii) they need to be re-trained every time the world knowledge is updated." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 485, + 548, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 548, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 548, + 640 + ], + "type": "text", + "content": "To address these issues, we adopt a different approach. Instead of statically compiling world knowledge into model weights, we transform the knowledge into a key-value memory through neural representation learning. Our model learns to utilize the memory for answering knowledge-intensive queries. By decoupling the knowledge memorization from reasoning, we enable our model to leverage various external sources of knowledge (e.g., Wikipedia passages and images [37], the WikiData knowledge graph [40], Web imagetext pairs [5] and visual question answering data [12]). This enables the model parameters to focus on understanding the query and conducting reasoning, rather than being dedicated to memorization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 643, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 548, + 715 + ], + "type": "text", + "content": "Retrieval-augmented models have attracted a fair amount of attention in the fields of NLP [14, 18] and computer vision [13,25]. Typically, these models often use a pre-existing single-modality backbone to encode and retrieve information from the knowledge corpus. Such approaches do not leverage all available modalities in the query and knowl" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 704, + 247, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 704, + 247, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 704, + 247, + 714 + ], + "type": "text", + "content": "*This work was done when Ziniu was an intern at Google." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23369" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "edge corpora, and hence they might not find the information that is most helpful for generating the model output. A key novelty in our approach is that we encode and store various sources of multimodal world knowledge into a unified memory, which the retriever can access via multimodal query encodings, to find the most relevant information from across complementary sources. Our multimodal memory and retriever are pre-trained end-to-end together together with the rest of the model, on a massive amount of data and using diverse knowledge sources." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 393 + ], + "type": "text", + "content": "A key challenge of pre-training the multimodal retriever end-to-end is the lack of direct supervision. There is no ground-truth indicating which knowledge entries are most helpful for answering knowledge-intensive queries. Some of the existing works in NLP [14, 23, 34] propose to acquire training signal by assessing the usefulness of each retrieved knowledge entry independently for helping language modelling. This approach is inefficient, as it involves estimating hundreds of retrieved knowledge entries independently, and also inaccurate as it discards the dependency between different knowledge entries in the retrieval set. In contrast, we propose to get this training signal while simultaneously considering multiple retrieved knowledge entries, by introducing an attentive fusion layer that injects retrieval score into the attention calculation procedure. This enables the retrieval module to be differentiable and jointly pre-trained with the rest of the model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 396, + 259, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 396, + 259, + 407 + ], + "spans": [ + { + "bbox": [ + 59, + 396, + 259, + 407 + ], + "type": "text", + "content": "In summary, our key contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 407, + 287, + 563 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 407, + 286, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 407, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 58, + 407, + 286, + 442 + ], + "type": "text", + "content": "- We are the first to propose an end-to-end pre-training paradigm that learns to index into a large-scale memory to solve knowledge-intensive visual-language tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 444, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 444, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 58, + 444, + 287, + 491 + ], + "type": "text", + "content": "- Our method can construct a large-scale memory by encoding various sources of multimodal world knowledge, including Wikipedia passage, web images with alt-text captions, and knowledge graph triplets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 491, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 491, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 58, + 491, + 287, + 563 + ], + "type": "text", + "content": "- REVEAL achieves state-of-the-art performance on several knowledge-intensive visual question answering and image captioning datasets. Notably on the OKVQA benchmark, REVEAL achieves a new state-of-the-art, " + }, + { + "bbox": [ + 58, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "59.1\\%" + }, + { + "bbox": [ + 58, + 491, + 287, + 563 + ], + "type": "text", + "content": " accuracy, while using order of magnitude fewer parameters than previous works." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 574, + 222, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 222, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 222, + 587 + ], + "type": "text", + "content": "2. Related Work and Background" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Knowledge-based Visual Question Answering. To evaluate a model's ability to comprehend multimodal world knowledge not easily inferred from input data, several knowledge-based Visual Question Answering (VQA) datasets have been introduced. KB-VQA [41] and FVQA [42] design questions that can be answered by retrieving relevant triplets from domain-specific structured knowledge graphs. OK-VQA [29] improves these datasets by necessitating the use of external knowledge, which goes beyond what can be directly observed in the input images. More recently, A-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 548, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 548, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 548, + 360 + ], + "type": "text", + "content": "OKVQA [35] offers further improvements to OK-VQA by exclusively selecting questions that demand both external knowledge and commonsense reasoning about the image scenes. To tackle knowledge-based VQA tasks, many approaches have been proposed to incorporate external knowledge into visual-language models. One line of research uses explicit knowledge from structured knowledge graphs [11, 15, 31, 44] or unstructured text corpora [27, 28, 46]. The key component for these works is the knowledge retriever. Some works [11, 28, 31, 46] utilize off-the-shelf vision detection models to generate image tags for knowledge retrieval, while others train the retrieval model via distant supervision [27] or auxiliary tasks (e.g. entity linking) [13]. Another research direction aims to incorporate implicit knowledge from pre-trained Large Language Models, such as GPT-3 [4] or PaLM [9]. These approaches utilize off-the-shelf image caption models to convert images into text, feed them into a language model, and use the generated text output as augmented knowledge [13, 24, 48]. Our work follows the first direction, augmenting a vision-language model with an explicit knowledge retriever. The main distinction is that we propose an end-to-end training framework to jointly learn the answer generator and retriever, rather than using a fixed or predefined knowledge retrieval." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 373, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 613 + ], + "type": "text", + "content": "End-to-End Training of Retrieval-Augmented Models. Given the advantage of knowledge retrieval, a key question is how to get learning signal to train the retrieval model. For tasks with annotated retrieval ground-truth, retrieval training can be conducted via standard contrastive learning [22]. However, most tasks do not provide clear indications of which knowledge entries are relevant for generating answers. To this end, a series of studies have investigated retrieval training using supervision derived from downstream tasks. REALM [14] trains a single-document retriever by concatenating each retrieved result with the query, to calculate the final loss independently. A similar approach has been used by EMDR² [34] for multi-document retrieval training. FIDKD [17] proposes to use the aggregated attention score calculated by the generator as a distillation signal to train the retriever. Atlas [18] further introduces a perplexity distillation loss and a leave-one-out variant. Our REVEAL proposes to inject the retrieval scores directly into an attentive fusion module, enabling to train the retriever to directly optimize downstream tasks as well as pre-training objectives." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 621, + 362, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 362, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 362, + 634 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "We propose a Retrieval-Augmented Visual Language Model (REVEAL), which learns to use knowledge from different sources for solving knowledge-intensive tasks. For both pre-training and fine-tuning, our goal is to learn the distribution " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "P(y \\mid x)" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " to generate a textual output " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " conditioned on a multimodal input query " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ". REVEAL contains" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23370" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 49, + 541, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 49, + 541, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 49, + 541, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 49, + 541, + 198 + ], + "type": "image", + "image_path": "6be7ed32586e08a00590f51f7e7587a4d834835f6f8483ba6fa0b9047484a740.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 269 + ], + "type": "text", + "content": "Figure 2. The overall workflow of REVEAL consists of four main steps: (a) encode a multimodal input into a sequence of token embeddings and a summarized query embedding; (b) encode each knowledge entry from different corpus into unified key and value embedding pairs, where key is used to index the memory and value contains full information of the knowledge; (c) retrieve top-K most similar knowledge items from different knowledge sources, and return the pre-computed in-memory value embeddings and re-encoded value; and (d) fuse the top-K knowledge items via attentive knowledge fusion layer by injecting the retrieval score as a prior during attention calculation. This facilitates REVEAL's key novelty: the memory, encoder, retriever and the generator can be jointly trained in an end-to-end manner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": "four components: knowledge encoding, memory, retrieval and generation. Given an input query " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ", we first retrieve " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " possibly helpful entries " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "M = \\{m_1, \\dots, m_K\\}" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " from the memory corpora " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ". Each " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " is a memory entry containing the encoded single key embedding and a sequence of value embeddings (we will describe how to encode knowledge items into memory entries in Sec. 3.2). With it, the retriever can use embedding similarity to find relevant memory entries. We model this retrieval process as sampling from distribution " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "p(M \\mid x)" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ". Then, we condition on both the retrieved set " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " and the original input query " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " to generate the output " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ", modeled as " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "p(y \\mid x, M)" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ". To obtain the overall likelihood of generating " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": ", we treat " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " as a latent variable from the entire memory " + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": " and marginalize over it yielding:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 81, + 468, + 288, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 468, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 81, + 468, + 288, + 498 + ], + "type": "interline_equation", + "content": "p (y \\mid x) = \\sum_ {M \\subset \\tilde {\\mathcal {M}}} \\underbrace {p (M \\mid x)} _ {\\text {r e t r i e v a l}} \\cdot \\underbrace {p (y \\mid x , M)} _ {\\text {g e n e r a t i o n}}. \\tag {1}", + "image_path": "8da01e7f864d1fea692bdf3e787ae8a5fc6dff4394a3c3c7e8c359cc2af31276.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "content": "However, this marginal probability involves an intractable summation over all size-" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "content": " subsets of the memory corpora " + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{M}}" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "content": ". We approximate this instead by using the top-" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "content": " entries in memory with the highest probability under " + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "inline_equation", + "content": "p(M \\mid x)" + }, + { + "bbox": [ + 46, + 508, + 287, + 604 + ], + "type": "text", + "content": ". This is reasonable if most of the unrelated memory entries do not contribute to the generation. Note that we use an online memory that is updated as the knowledge encoder is trained end-to-end with the rest of the model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Figure 2 illustrates the overall workflow of REVEAL, and we describe each component in this section. In particular, in Sec. 3.1 we describe how the query is encoded. In Sec. 3.2 we go over how the multimodal knowledge memory is constructed and updated during pre-training. Next, we describe how we retrieve the memory entries that are most relevant to the input query in Sec. 3.3. Finally, in Sec. 3.4 we describe the generator that fuses the query and retrieved knowledge and decodes them into the generated text." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 288, + 406, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 406, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 406, + 301 + ], + "type": "text", + "content": "3.1. Query Encoding" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": "Figure 2 (a) depicts how the input image-text query is encoded. We use a base visual-language encoder " + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "inline_equation", + "content": "b(\\cdot)" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": " to turn the query input and each knowledge item (with potentially different modalities e.g. text-only, image-only or image-text pairs) into a sequence of embeddings (tokens). We adopt a Vision Transformer (ViT) [10] to encode the images and we use a lower-layer" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": " T5 encoder [33] to encode the texts. We add a projection layer on top of the ViT model to map the image tokens into the same space as the text tokens. We then concatenate the two modalities together. We use an upper-layer T5 module as both the query Head " + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "inline_equation", + "content": "\\phi_{Query}(\\cdot)" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": " and the key Head " + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "inline_equation", + "content": "\\phi_{Key}(\\cdot)" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": " to compute the query embedding and memory keys. We take the output of the first [CLS] tokens followed by a linear projection and L2-normalization to summarize the input into a " + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 307, + 547, + 487 + ], + "type": "text", + "content": "-dimensional embedding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 495, + 369, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 369, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 369, + 509 + ], + "type": "text", + "content": "3.2. Memory" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": "Figure 2 (b) shows how memory is constructed and updated by encoding knowledge items. Our approach differs from previous works primarily by leveraging a diverse set of multimodal knowledge corpora (WikiData knowledge graph,Wikimedia passages and images, Web image-text pairs). Throughout the paper, we denote each corpus as " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^j = \\{z_1^j,\\dots ,z_N^j\\}" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " , in which each " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "z_{i}^{j}\\in \\mathcal{C}^{j}" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " is a knowledge item that could be an image-text pair, text only, image only, or a knowledge graph triplet. We denote the unified knowledge corpus as " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{C}} = \\mathcal{C}^1\\cup \\mathcal{C}^2\\dots \\cup \\mathcal{C}^S" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " that combines " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "|\\tilde{\\mathcal{C}} | = S" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " different knowledge corpora. We encode the external knowledge corpora into a unified memory " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{M}} = [\\mathcal{M}^1,\\ldots ,\\mathcal{M}^{|\\tilde{\\mathcal{C}} |}]" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " Each knowledge item " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " is encoded into a key/value pair " + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "inline_equation", + "content": "m_{i} = (\\mathrm{Emb}_{\\mathrm{Key}}(z_{i}),\\mathrm{Emb}_{\\mathrm{Value}}(z_{i}))" + }, + { + "bbox": [ + 304, + 514, + 547, + 685 + ], + "type": "text", + "content": " in memory. Each key" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1We denote the last " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " layers of a T5 encoder as 'upper-layer', and the remaining ones including the token embedding layer as 'lower-layer'." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23371" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathsf{Emb}_{\\mathsf{Key}}(z) = \\phi_{\\mathsf{Key}}(b(z)) \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "text", + "content": "-dimensional embedding vector encoded via Key Head. Each value is a sequence of token embeddings representing the full information of knowledge item " + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "text", + "content": ". We follow a similar procedure as in [14] to precompute key/value embeddings of knowledge items from different sources and index them in a unified knowledge memory. We continuously re-compute the memory key/value embeddings as the model parameters get updated during the pre-training phase. We update the memory " + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{M}}" + }, + { + "bbox": [ + 46, + 71, + 289, + 193 + ], + "type": "text", + "content": " asynchronously at every 1000 training steps." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 289, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 289, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 289, + 327 + ], + "type": "text", + "content": "Scaling Memory by Compression A naive solution for encoding the memory value is to keep the whole sequence of tokens for each knowledge item. Then, the generator could fuse the input query and the top-K retrieved memory values by concatenating all their tokens together and feeding them into a Transformer Encoder-Decoder pipeline [23]. This approach has two issues: (1) storing hundreds of millions of knowledge items in memory is impractical given that each memory value would consist of hundreds of tokens; (2) transformer encoder has quadratic complexity with respect to the total number of tokens times " + }, + { + "bbox": [ + 46, + 195, + 289, + 327 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 195, + 289, + 327 + ], + "type": "text", + "content": " for self-attention." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": "Therefore, we propose to use the Perceiver architecture [19] as the Value Head to encode and compress knowledge items. The Perceiver model uses a transformer decoder " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": " with learnable " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": "-length latent embeddings to compress the full token sequence into an arbitrary length " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "\\mathrm{Emb}_{\\mathrm{Value}}(z) = \\psi(b(z)) \\in \\mathbb{R}^{c \\times d}" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": " (In our experiments we use " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "c = 32" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": "). This lets us retrieve top-K memory entries for K as large as a hundred. To make the compressed embeddings generated by Perceiver more expressive, we add two additional regularizations. The first one is a disentangled regularization [16] that forces every two output tokens to be linearly de-correlated " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{decor}} = \\sum_{i,j=1}^{K} \\left\\| \\mathrm{Covariance}(\\psi(b(z_i)), \\psi(b(z_j))) \\right\\|_F^2" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": ", and the second one is an alignment regularization that minimizes the distance of L2-Norm between the query and compressed knowledge embedding: " + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{align}} = \\left| 1 - \\frac{\\sum_z \\| \\psi(b(z)) \\|_2}{\\sum_x \\| b(x) \\|_2} \\right|" + }, + { + "bbox": [ + 46, + 329, + 290, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 558, + 115, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 115, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 115, + 571 + ], + "type": "text", + "content": "3.3. Retriever" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": "Figure 2 (c) shows REVEAL's retrieval procedure. Given the input query " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": ", the retriever's task is to find top-K memory entries " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " with the highest probability " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(M \\mid x)" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " which we approximate as " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(M \\mid x) = \\prod_{m \\in M} p(m \\mid x)" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " by retrieving each entry independently. Note that we retrieve from a large-scale unified memory " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{M}} = [\\mathcal{M}^1, \\dots, \\mathcal{M}^{|\\tilde{\\mathcal{C}}|}]" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " that is constructed from a diverse set of knowledge sources. To help the query to better choose the most appropriate knowledge sources, we learn a gating function that models the probability of retrieving from each memory corpus. With the corpus gating, for " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "m_i^j \\in \\mathcal{M}^j" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " we re-weight " + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(m^j \\mid x)" + }, + { + "bbox": [ + 46, + 579, + 289, + 715 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 541, + 170 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 541, + 170 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 541, + 170 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 541, + 170 + ], + "type": "image", + "image_path": "41f024044c16f67d827a4b96e98813bfb4011d91f5feb41460ed45e6757a150d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 177, + 548, + 222 + ], + "lines": [ + { + "bbox": [ + 304, + 177, + 548, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 548, + 222 + ], + "type": "text", + "content": "Figure 3. Detailed procedure of attentive knowledge fusion module. We inject retrieval probability as a prior to knowledge token embeddings, so the retriever can receive gradients via back-propagating over {self/cross} -attention part." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 242, + 447, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 242, + 447, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 447, + 254 + ], + "type": "text", + "content": "the computed corpus gating score:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 319, + 260, + 546, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 260, + 546, + 310 + ], + "spans": [ + { + "bbox": [ + 319, + 260, + 546, + 310 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p \\left(m _ {i} ^ {j} \\mid x\\right) = p \\left(\\mathcal {M} ^ {j} \\mid x\\right) \\cdot p \\left(m _ {i} ^ {j} \\mid x; \\mathcal {M} ^ {j}\\right) (2) \\\\ = G a t e _ {\\mathcal {M} ^ {j}} (x) \\cdot \\frac {\\exp \\left(R e l \\left(x , m _ {i} ^ {j}\\right) / \\tau\\right)}{\\sum_ {m _ {k} ^ {j} \\in \\mathcal {M} ^ {j}} \\exp \\left(R e l \\left(x , m _ {k} ^ {j}\\right) / \\tau\\right)} (3) \\\\ \\end{array}", + "image_path": "aed59fcc4232b98489db6ee60f1a0fb1d99f96a8aeb6cac6fdd1062a0ad709b6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "Gate_{\\mathcal{M}^j}(x) = \\mathrm{Softmax}(W \\cdot \\mathrm{Emb}_{\\mathrm{Query}}(x) + b)[j]" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " is a softmax gating that assigns a score to each memory corpus " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "M^j" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " as function parameters. " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "Rel(x, m_i^j)" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " models relevance score between query " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " and each memory entry via embedding dot product, such that " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "Rel(x, m_i^j) = \\mathrm{Emb}_{\\mathrm{Query}}(x)^T \\cdot \\mathrm{Emb}_{\\mathrm{Key}}(z_i^j)" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": ". where " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "z_i" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " is the knowledge item corresponding to the memory entry " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "m_i" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 316, + 547, + 413 + ], + "type": "text", + "content": " is the temperature parameter." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "text", + "content": "After identifying the top-K memory entries, the retriever passes the pre-computed in-memory key and value embeddings to the generator. In the meantime, to support end-to-end training of the encoders, we also re-encode a small portion (i.e., " + }, + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "text", + "content": " ) of the retrieved knowledge items " + }, + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 304, + 413, + 547, + 521 + ], + "type": "text", + "content": " from scratch. In this way, the memory encoders could be updated with moderate computational cost. We concatenate the re-encoded knowledge with in-memory ones to construct the final top-K retrieved key/value embeddings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 378, + 539 + ], + "type": "text", + "content": "3.4. Generator" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "Figure 2 (d) shows how the query and the retrieved knowledge items are fused to generate the output answer. All " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " retrieved memory values are concatenated with the query embedding, which is feasible due to the Perceiver module utilized as the value head " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": ", compressing each knowledge item into a short sequence. We denote the concatenated query embedding and memory values as " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "X = [b(x), \\psi(b(z_1)), \\dots, \\psi(b(z_K))] \\in \\mathbb{R}^{(I + c \\cdot K) \\times d}" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " is the number of tokens of the input query " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " is the number of compressed tokens. To guide the generator towards attending to the most important items in " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " and facilitate backpropagation of gradients to the retriever, we propose an attentive fusion module " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " capable of incorporating the retriever score as a prior for calculating" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23372" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 286, + 130 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 130 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 130 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 130 + ], + "type": "table", + "html": "
Knowledge SourceCorpus SizeType of TextAvg. Text Length
WIT [37]5,233,186Wikipedia Passage258
CC12M [5]10,009,901Alt-Text Caption37
VQA-V2 [12]123,287Question Answer111
WikiData [40]4,947,397Linearized Triplets326
", + "image_path": "2628aa98b7ca5471a025707d5201821ffe490cf010eda4b20a31c2adf169ccc3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 162, + 274, + 213 + ], + "blocks": [ + { + "bbox": [ + 76, + 139, + 257, + 150 + ], + "lines": [ + { + "bbox": [ + 76, + 139, + 257, + 150 + ], + "spans": [ + { + "bbox": [ + 76, + 139, + 257, + 150 + ], + "type": "text", + "content": "Table 1. Statistics of the knowledge sources used." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 162, + 274, + 213 + ], + "lines": [ + { + "bbox": [ + 58, + 162, + 274, + 213 + ], + "spans": [ + { + "bbox": [ + 58, + 162, + 274, + 213 + ], + "type": "table", + "html": "
Model NameT5 VariantImage Encoder# params.GFLOPs
REVEAL-BaseT5-BaseViT-B/160.4B120
REVEAL-LargeT5-LargeViT-L/161.4B528
REVEALT5-LargeViT-g/142.1B795
", + "image_path": "2e8027d65284762575dde37f82b044aef6ca2eae7fd26c1c334422eddd403e15.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 214, + 276, + 225 + ], + "lines": [ + { + "bbox": [ + 57, + 214, + 276, + 225 + ], + "spans": [ + { + "bbox": [ + 57, + 214, + 276, + 225 + ], + "type": "text", + "content": "Table 2. Model configuration of different REVEAL variants." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "content": "cross-knowledge attention. The detailed procedure is illustrated in Figure 3. We firstly compute a latent soft attention mask over " + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\text{Mask}_{\\text{att}} = [1, p(z_1|x), \\ldots, p(z_K|x)]" + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "content": ". Finally, we pass the fused representation " + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "inline_equation", + "content": "f(X, \\text{Mask}_{\\text{att}})" + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "content": " into a T5 decoder module " + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 247, + 288, + 307 + ], + "type": "text", + "content": " to generate the textual output." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 318, + 188, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 188, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 188, + 332 + ], + "type": "text", + "content": "4. Generative Pre-Training" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 338, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 422 + ], + "type": "text", + "content": "The existing VQA datasets are not large enough for training a complex multi-component model like ours from scratch. Therefore, we pre-train our model on a massive image-text corpus. In Sec. 4.1 we go over the details of our pre-training data and objective. Then in Sec. 4.2 we introduce the various sources of knowledge used in our experiments. Finally, in Sec. 4.3 we describe the pre-training implementation details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 430, + 178, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 178, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 178, + 443 + ], + "type": "text", + "content": "4.1. Pre-Training Objective" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 520 + ], + "type": "text", + "content": "We pre-train our model on the Web-Image-Text dataset [51], a large-scale corpus containing 3 billion image alt-text caption pairs collected from the public Web. Since the dataset is noisy, we add a filter to remove data points whose captions are shorter than 50 characters. This yields roughly 1.3 billion image caption pairs for pre-training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": "We denote the pre-training Web-Image-Text dataset [51] as " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": ". We use the text generation objective used in Wang et al. [45]) to pre-train our model on " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": ". Given an image-text example " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "x = (\\mathrm{img},\\mathrm{txt})" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": ", we randomly sample a prefix length " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "T_{p}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": ". We feed " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "x_{< T_p}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": " that contains the text prefix and image to the model as input and our objective is to generate " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "x_{\\geq T_p}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": " containing the rest of the text as output. The training goal is to condition on " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "x_{< T_p}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": " and autoregressively generate the remaining text sequence " + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "inline_equation", + "content": "x_{\\geq T_p}" + }, + { + "bbox": [ + 46, + 521, + 287, + 621 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 629, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 629, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 87, + 629, + 287, + 669 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {P r e f i x L M}} = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\log p \\left(x _ {\\geq T _ {p}} \\mid x < T _ {p}\\right) \\right] \\tag {4} \\\\ = - \\mathbb {E} _ {x \\sim \\mathcal {D}} \\left[ \\sum_ {i \\geq T _ {p}} \\log p \\left(x _ {i} \\mid x _ {< i}\\right) \\right]. \\\\ \\end{array}", + "image_path": "2ba062847a748126ac2678ae9f44f7d86c9184c048fd13bab3ea484d7451cd56.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "Warm Starting the Model In order to pre-train all components of our model end-to-end, we need to warm start the retriever at a good state. Otherwise, if starting with random" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "weights, the retriever would often return irrelevant memory items that would never generate useful training signals." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 97, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 546, + 300 + ], + "type": "text", + "content": "To avoid this cold-start problem, we propose to construct an initial retrieval dataset with pseudo ground-truth knowledge to give the pre-training a reasonable head start. We create a modified version of the Wikipedia-Image-Text (WIT) [37] dataset for this purpose. Each image-caption pair in WIT also comes with a corresponding Wikipedia passage (words surrounding the text). We put together the surrounding passage with the query image and use it as the pseudo ground-truth knowledge that corresponds to the input query. As the passage provides rich information about the image and caption, it definitely is useful for initializing the model. To avoid the model from relying on low-level image features for retrieval, we apply random data augmentation to the input query image. Given this modified dataset that contains pseudo retrieval ground-truth, we train the query and memory key embeddings by optimizing the following contrastive loss:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 319, + 310, + 531, + 324 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 310, + 531, + 324 + ], + "spans": [ + { + "bbox": [ + 319, + 310, + 531, + 324 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n t r a}} = - \\log \\operatorname {S o f t m a x} \\left(\\operatorname {E m b} _ {\\text {Q u e r y}} (x) ^ {T} \\operatorname {E m b} _ {\\text {K e y}} (\\hat {z})\\right)", + "image_path": "ef8913ef4e2ff62e6eaf2e0061d1d7d7c222d2d5583e248fc06156ec09793fbe.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "text", + "content": " represents the pseudo ground-truth knowledge entry corresponding to the input query " + }, + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 334, + 545, + 358 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 367, + 420, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 367, + 420, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 367, + 420, + 380 + ], + "type": "text", + "content": "4.2. Knowledge Sources" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": "We use the following four sources of knowledge in our experiments: Wikipedia-Image-Text (WIT) [37] consists of the images in Wikipedia, as well as their alt-text captions and contextualized text passages. Conceptual (CC12M) [5] contains web images paired with alt-text captions. It includes many long-tail entities. VQA-v2 [12] is a visual question answering dataset. We merge all question-answer pairs per image into a single passage. WikiData [40] is a structural knowledge graph encoding relations between Wikipedia entities. We linearize all relational triplets per entity into a textual passage following the procedure of [32]. We have listed the statistical details of these knowledge sources in Table 1." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 551, + 438, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 438, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 438, + 563 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Incorporating all the components introduced above, REVEAL can be directly pre-trained over large-scale image caption datasets after proper initialization. As our model architecture is based on T5 and ViT, we use pre-trained ViT checkpoints from [50] and pre-trained T5 checkpoints from [33] to initialize the encoder parameters. The query head, key head and attentive fusion layers are initialized from upper T5, while the base text encoder is initialized from lower T5. The combination of these modules can be found in Table 2 for three three model variants, REVEAL-Base, REVEAL-Large and REVEAL, of which the largest REVEAL model has around 2 billion parameters." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23373" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 91, + 41, + 502, + 239 + ], + "blocks": [ + { + "bbox": [ + 91, + 41, + 502, + 239 + ], + "lines": [ + { + "bbox": [ + 91, + 41, + 502, + 239 + ], + "spans": [ + { + "bbox": [ + 91, + 41, + 502, + 239 + ], + "type": "table", + "html": "
VQA Model NameKnowledge SourcesAccuracy (%)Memory (GB)
MUTAN+AN [29]Wikipedia + ConceptNet27.8-
ConceptBERT [11]Wikipedia33.7-
KRISP [28]Wikipedia + ConceptNet38.4-
Visual Retriever-Reader [27]Google Search39.2-
MAVEx [46]Wikipedia+ConceptNet+Google Images39.4-
KAT-Explicit [13]Wikidata44.31.5
PICa-Base [48]Frozen GPT-343.3350
PICa-Full [48]Frozen GPT-348.0350
KAT [13] (Single)Wikidata + Frozen GPT-353.11.5 + 352+ 500
KAT [13] (Ensemble)Wikidata + Frozen GPT-354.44.6 + 352 + 500
ReVIVE [24] (Single)Wikidata + Frozen GPT-356.61.5 + 354 + 500
ReVIVE [24] (Ensemble)Wikidata+Frozen GPT-358.04.6 + 354 + 500
REVEAL-BaseWIT + CC12M + Wikidata + VQA-255.20.8 + 7.5 + 744
REVEAL-LargeWIT + CC12M + Wikidata + VQA-258.02.8 + 10 + 993
REVEALWIT + CC12M + Wikidata + VQA-259.14.2 + 10 + 993
", + "image_path": "2ab41171529bcfd777b1bb4e2209d2eb92e617c116aad485ae3d818c48fedbe2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 295, + 289, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 289, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 289, + 416 + ], + "type": "text", + "content": "Distributed Online Retrieval. Finding the top-k most-relevant knowledge entries is a standard Maximum Inner Product Search (MIPS) problem. There are approximate search algorithms [8, 36] that scale sub-linearly with the size of the knowledge corpus " + }, + { + "bbox": [ + 46, + 295, + 289, + 416 + ], + "type": "inline_equation", + "content": "|C|" + }, + { + "bbox": [ + 46, + 295, + 289, + 416 + ], + "type": "text", + "content": ". We use TPU-KNN [8] to conduct distributed MIPS search, by splitting and storing the memory embeddings across all training devices. The query is synced to each device, which retrieves approximate top-K results from its own memory. Then these results are combined to compute the global top-K retrieved items." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": "Pre-Training Pipeline. We first train the multimodal retriever on our modified version of the Wikipedia Image Text (WIT) dataset via " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{contra}}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": ". We use the Adafactor optimizer without momentum (" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": "), with weight decay of " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "0.001^{2}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": ", and with a peak learning rate of 6e4, to train for 10 epochs. We use this checkpoint to warm-start our generative pre-training. We set the number of retrieved knowledge entries as " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "K = 10" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": " during pre-training, and use adafactor with a peak learning rate of 1e-3 and inverse squared root learning rate scheduler with 10,000 linear warm-up steps. We use " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{PrefixLM}}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": " as the main objective, adding " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{contra}}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{decor}}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{align}}" + }, + { + "bbox": [ + 46, + 418, + 290, + 587 + ], + "type": "text", + "content": " weighted by 0.01. We use a batch size of 4096 across 256 CloudTPUv4 chips and train for about 5 days." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 608, + 173, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 608, + 173, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 608, + 173, + 622 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 632, + 288, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 288, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 288, + 681 + ], + "type": "text", + "content": "We evaluate our proposed method on knowledge-based VQA in Sec. 5.1 and image captioning in Sec. 5.2. We then conduct ablation studies in Sec. 5.3 to analyze the impact of each model component on overall performance." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 350, + 293, + 502, + 409 + ], + "blocks": [ + { + "bbox": [ + 46, + 241, + 547, + 276 + ], + "lines": [ + { + "bbox": [ + 46, + 241, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 547, + 276 + ], + "type": "text", + "content": "Table 3. Visual Question Answering results on OK-VQA, compared with existing methods that use different knowledge sources. For the memory cost, we assume all models use bfloat16. Green means on-device model parameters that are learnable, Blue means on-device memory of frozen model parameters, and Red means CPU/disk storage cost that are not involved in computation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 350, + 293, + 502, + 409 + ], + "lines": [ + { + "bbox": [ + 350, + 293, + 502, + 409 + ], + "spans": [ + { + "bbox": [ + 350, + 293, + 502, + 409 + ], + "type": "table", + "html": "
VQA Model NameAccuracy (%)
ViLBERT [26]30.6
LXMERT [38]30.7
ClipCap [30]30.9
KRISP [28]33.7
GPV-2 [21]48.6
REVEAL-Base50.4
REVEAL-Large51.5
REVEAL52.2
", + "image_path": "08bac58654cb3b7276b5a492f354ba6fab65eeb974f82a2bea755f0bee017927.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 314, + 411, + 536, + 423 + ], + "lines": [ + { + "bbox": [ + 314, + 411, + 536, + 423 + ], + "spans": [ + { + "bbox": [ + 314, + 411, + 536, + 423 + ], + "type": "text", + "content": "Table 4. Visual Question Answering results on A-OKVQA." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 443, + 507, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 507, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 507, + 456 + ], + "type": "text", + "content": "5.1. Evaluating on Knowledge-Based VQA" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 462, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 640 + ], + "type": "text", + "content": "One of the most knowledge intensive visual-language tasks is knowledge-based visual question answering (VQA), exemplified by the OK-VQA [29] and A-OKVQA [35] benchmarks. To finetune our pre-trained model on these VQA tasks, we use the same generative objective where the model takes in an image question pair as input and generates the text answer as output. There are a few differences between the fine-tuning and the pre-training stages: 1) we set the number of retrieved knowledge entries to " + }, + { + "bbox": [ + 304, + 462, + 547, + 640 + ], + "type": "inline_equation", + "content": "K = 50" + }, + { + "bbox": [ + 304, + 462, + 547, + 640 + ], + "type": "text", + "content": ", so the model is able to retrieve sufficient supporting evidence; 2) we freeze the whole base V-L encoder to stabilize training; and 3) we use a batch size of 128, with the Adafactor optimizer, a peak learning rate of 1e-4. We use the soft VQA accuracy metric [3] to evaluate the model's generated answer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "text", + "content": "Our results on OKVQA and A-OKVQA datasets are shown in Table 3 and Table 4 respectively. For OKVQA, earlier attempts that incorporate a fixed knowledge retriever report results that are below " + }, + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "text", + "content": ". Recently a series of works utilize large language models (e.g. GPT-3) as implicit knowledge sources, which achieve much better performance" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 274, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 274, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 274, + 714 + ], + "type": "text", + "content": "2The remaining experiments use the same optimizer configuration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23374" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 63, + 266, + 156 + ], + "blocks": [ + { + "bbox": [ + 67, + 63, + 266, + 156 + ], + "lines": [ + { + "bbox": [ + 67, + 63, + 266, + 156 + ], + "spans": [ + { + "bbox": [ + 67, + 63, + 266, + 156 + ], + "type": "table", + "html": "
Model NameMSCOCONoCaps# params.
Flamingo [2]138.1-80B
VinVL [52]140.9105.10.4B
SimVLM [45]143.3112.21.5B
CoCa [49]143.6122.42.1B
REVEAL-Base141.1115.80.4B
REVEAL-Large144.5121.31.4B
REVEAL145.4123.02.1B
", + "image_path": "8ac53a0bb6b3fc4a4978a0202b0abf33fa2fad7c4fcd72d63e9502b9fa129dc4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 158, + 287, + 180 + ], + "lines": [ + { + "bbox": [ + 47, + 158, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 287, + 180 + ], + "type": "text", + "content": "Table 5. Image Captioning results on MSCOCO (Karpathy-test split) and NoCaps (val set). Evaluated using the CIDEr metric." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "text", + "content": "with the trade-off of a huge computational cost. REVEAL achieves higher performance than those methods without relying on such large language models3. Compared with the previous state-of-the-art, KAT and ReVIVE, which also utilizes T5-Large as a generator, REVEAL achieves accuracy of " + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "inline_equation", + "content": "59.1\\%" + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "text", + "content": ", which is " + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "inline_equation", + "content": "+6.0\\%" + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "text", + "content": " higher than the single KAT [13] model and " + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "inline_equation", + "content": "+2.5\\%" + }, + { + "bbox": [ + 46, + 203, + 287, + 286 + ], + "type": "text", + "content": " higher than ReVIVE [24]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "text", + "content": "On A-OKVQA, REVEAL achieves " + }, + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "inline_equation", + "content": "52.2\\%" + }, + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "text", + "content": " accuracy, which is " + }, + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "inline_equation", + "content": "+3.6\\%" + }, + { + "bbox": [ + 46, + 288, + 289, + 373 + ], + "type": "text", + "content": " higher than the previous best, GPV-2 [21]. We also show two examples of these datasets in Figure 4. All these results show that, with proper end-to-end retrieval training and a diverse set of knowledge sources, REVEAL can learn to retrieve meaningful knowledge entries, and achieve promising results without relying on a large language model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 381, + 223, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 223, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 223, + 395 + ], + "type": "text", + "content": "5.2. Evaluating on Image Captioning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 289, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 557 + ], + "type": "text", + "content": "We also evaluate REVEAL on image captioning benchmarks: MSCOCO Captions [6] and NoCaps [1]. We follow the evaluation protocol used in [49]. We directly fine-tune our generator model on the MSCOCO training split via cross-entropy generative objective. We measure our performance on the MSCOCO test split and NoCaps val set with the CIDEr metric [39]. The results of these two datasets are shown in Table 5. Note that REVEAL achieves better results than strong recent baselines such as SimVLM [45] and CoCa [49] on both benchmarks. Notably, REVEAL -Large with 1.4B parameters outperforms the 2.1B-parameter CoCa model and is significantly better than 80B-parameter Flamingo model [2]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 566, + 280, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 280, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 280, + 580 + ], + "type": "text", + "content": "5.3. Analyzing Effects of Key Model Components" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 585, + 287, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 585, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 46, + 585, + 287, + 645 + ], + "type": "text", + "content": "In the following we study which design choices contribute most to the model's performance. We focus on three research questions: (1) Does utilizing multiple knowledge sources enhance performance? (2) Does the proposed attentive fusion surpass existing end-to-end retrieval training methods?" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 63, + 535, + 184 + ], + "blocks": [ + { + "bbox": [ + 309, + 63, + 535, + 184 + ], + "lines": [ + { + "bbox": [ + 309, + 63, + 535, + 184 + ], + "spans": [ + { + "bbox": [ + 309, + 63, + 535, + 184 + ], + "type": "image", + "image_path": "38c375cf6c0f9d40307f96db9860a09ef28f6c1badeaff0776ac64795f16702a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "type": "text", + "content": "Figure 4. VQA Examples. REVEAL is able to use knowledge from different sources to correctly answer the question. We show more examples in Figure 1-3 of Supplementary Material, indicating that our model can retrieve and use items from diverse knowledge sources to correctly solve different input query." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 270, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 294 + ], + "type": "text", + "content": "(3) Can we add knowledge by only updating the memory without modifying model parameters?" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "content": "Analyzing multiple knowledge sources. A major distinction of REVEAL compared to previous retrieval-augmented approaches is its capacity to utilize a diverse set of knowledge sources during inference. To assess the relative importance of each data source and the efficacy of retrieving from various corpora, we conduct two ablation studies: 1) Only-One-Left: employing a single knowledge source to evaluate the outcomes; and 2) Leave-One-Out: excluding one knowledge source from the complete set " + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "content": ". These ablation studies are executed using the REVEAL Base, evaluated on the OKVQA validation set under the aforementioned conditions. As shown in Figure 5, among the four knowledge sources utilized in this paper, WIT is the most informative, with the highest accuracy when used in isolation (53.1The remaining three corpora, CC12M, VQA-v2, and WikiData, do not offer the same level of informativeness as WIT when utilized independently. However, excluding any of these corpora from the complete dataset results in performance decreases of " + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 295, + 547, + 617 + ], + "type": "text", + "content": ", respectively. This observation implies that these knowledge sources effectively complement one another, contributing valuable information to enhance performance. To further substantiate this hypothesis, we perform an additional experiment involving pairs of knowledge sources, as illustrated in Figure 6. Notably, even when paired with an informative knowledge source such as WIT, incorporating an extra corpus consistently leads to performance improvements." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Analyzing different retrieval training methods. Another core component of REVEAL is the attentive fusion layer, which supports efficient joint training of the retriever and generator. We investigate its performance compared to two existing retrieval training method categories: 1) a frozen retriever based on ALIGN [20] representations; 2) end-to-end retrieval training methods including Attention Distill [17], EMDR² [47], and Perplexity Distill [18]." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "3As shown in the last column of Table 3, REVEAL stores external knowledge as value embeddings on disk, occupying 993GB of space. The key embeddings consume 10GB space and are kept in TPU memory for fast lookup. On the other hand, KAT and REVIVE need to load the entire 350GB GPT-3 model in the GPU/TPU memory. Furthermore, storing WikiData on disk consumes 500GB of disk memory." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23375" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 164, + 158 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 164, + 158 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 164, + 158 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 164, + 158 + ], + "type": "image", + "image_path": "d0df5c0d0bbdcc4cf7dc27b908727660bd9cdf2c54e1a6f54318a6d4946f9cb9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 160, + 164, + 227 + ], + "lines": [ + { + "bbox": [ + 50, + 160, + 164, + 227 + ], + "spans": [ + { + "bbox": [ + 50, + 160, + 164, + 227 + ], + "type": "text", + "content": "Figure 5. OKVQA Accuracy of REVEAL using 1) Only-One-Left: only use a single knowledge source; 2) Leave-One-Out: use all without this knowledge source." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 172, + 70, + 294, + 158 + ], + "blocks": [ + { + "bbox": [ + 172, + 70, + 294, + 158 + ], + "lines": [ + { + "bbox": [ + 172, + 70, + 294, + 158 + ], + "spans": [ + { + "bbox": [ + 172, + 70, + 294, + 158 + ], + "type": "image", + "image_path": "4e02aaf069bc4d099fbdfb1bbec61edc8a51e1a6402b1e34cf4edc4c27e49551.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 171, + 160, + 285, + 227 + ], + "lines": [ + { + "bbox": [ + 171, + 160, + 285, + 227 + ], + "spans": [ + { + "bbox": [ + 171, + 160, + 285, + 227 + ], + "type": "text", + "content": "Figure 6. OKVQA Accuracy of REVEAL using all Pair of Knowledge Sources. Results show that combining multiple sources could consistently improve performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 240, + 287, + 320 + ], + "blocks": [ + { + "bbox": [ + 48, + 240, + 287, + 320 + ], + "lines": [ + { + "bbox": [ + 48, + 240, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 48, + 240, + 287, + 320 + ], + "type": "table", + "html": "
Retrieval MethodAcc@10Acc@100OKVQA Acc.GFLOPs
ALIGN [20] (fixed)0.6380.79344.7-
Attention Distill [17]0.6740.83545.9119
EMDR2 [47]0.6910.86946.5561
Perplexity Distill [18]0.7040.88646.7561
Ours (Attentive Fusion)0.7260.89447.3120
", + "image_path": "4c3678263a9a9c77b8043c3ff219d7a844a49293a81f433b57e2fe4f61084074.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 322, + 288, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 322, + 288, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 288, + 378 + ], + "type": "text", + "content": "Table 6. Analysis of Retrieval Training Method: We train REVEAL-Base (frozen generator, only train randomly initialized retriever) to retrieve from the WIT dataset (only text passage without image), and show the retrieval accuracy at the first 10 or 100 results, as well as fine-tuned OKVQA accuracy." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 401, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 688 + ], + "type": "text", + "content": "We use the pre-trained REVEAL-Base model, fix the generator and randomly initialize the retriever (query head and key head). We utilize our modified version of WIT dataset with pseudo ground-truth retrieved labels as the evaluation corpus. We evaluate retrieval performance by checking whether the correct passage appears in top-10/100 results. For the ALIGNN model, we directly evaluate the retrieval results from the pre-trained checkpoint, while for other models, we perform retrieval-augmented training on the WIT dataset. To prevent the model from relying on image similarity for accurate results, we only use text passages as knowledge entries and discard images. Subsequently, we finetune the model on OKVQA and report its accuracy. The results are presented in Table 6. We observe that directly using pretrained encoder does not perform well, even with a strong model like ALIGNN. Moreover, among the various end-to-end retrieval training approaches, our attentive fusion method attains better accuracy in both retrieval and OKVQA tasks. Importantly, our technique exhibits a computational cost (quantified by GFLOPs) comparable to that of attention distillation, yet significantly lower than " + }, + { + "bbox": [ + 46, + 401, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{EMDR}^2" + }, + { + "bbox": [ + 46, + 401, + 288, + 688 + ], + "type": "text", + "content": " and Perplexity distillation. This indicates that our proposed method is more efficient and effective for pre-training retrieval-augmented visual-language models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Analyzing Knowledge Modification. One advantage of utilizing knowledge memory is that we could easily add or" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 322, + 69, + 529, + 177 + ], + "blocks": [ + { + "bbox": [ + 322, + 69, + 529, + 177 + ], + "lines": [ + { + "bbox": [ + 322, + 69, + 529, + 177 + ], + "spans": [ + { + "bbox": [ + 322, + 69, + 529, + 177 + ], + "type": "image", + "image_path": "09aaa27b58b8df4167608888e1f3ac520c8361912c7af0fea3e7b09fb79ffe1c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 178, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 304, + 178, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 547, + 234 + ], + "type": "text", + "content": "Figure 7. Study of Knowledge Update. The blue curve shows result by removing certain percentage of knowledge during both fine-tuning and inference stage. The orange curve shows results by still first removing the knowledge, and then adding the knowledge back during inference, which simulates the knowledge update." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 257, + 547, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 388 + ], + "type": "text", + "content": "update knowledge entries without re-training model's parameters. To validate this, we conducted ablation studies in which we removed a specific percentage of knowledge entries from the corpora and assessed the performance of the REVEAL-Base model on the OKVQA dataset. Subsequently, we add the removed knowledge back into the corpora, allowing the trained model to make predictions using the complete set of corpora. This approach ensured that the removed knowledge was not seen by the model during fine-tuning, enabling us to test its ability to accurately retrieve and utilize that knowledge for problem-solving." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 390, + 548, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 548, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 548, + 546 + ], + "type": "text", + "content": "The results are illustrated in Figure 7, with the blue curves representing the inference outcomes without the removed knowledge and the orange curve depicting the results after adding the removed knowledge back. A notable performance improvement was observed upon reintroducing the knowledge (orange curve) compared to the outcomes with the removed knowledge (blue curve). Specifically, for the model fine-tuned with only " + }, + { + "bbox": [ + 304, + 390, + 548, + 546 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 390, + 548, + 546 + ], + "type": "text", + "content": " of the knowledge, the reintroduction of the removed knowledge resulted in an accuracy of 51.8 (+6.7 higher than when removed). This finding demonstrates that the REVEAL model can swiftly adapt to new knowledge by merely updating the memory, obviating the need for re-training model parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 560, + 379, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 379, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 379, + 572 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "This paper presents an end-to-end Retrieval-augmented Visual Language model (REVEAL), which contains a knowledge retriever that learns to utilize a diverse set of knowledge sources with different modality. The retriever is trained jointly with the generator to return multiple knowledge entries. We pre-train REVEAL on a massive image-text corpus with four diverse knowledge corpora, and achieves state-of-the-art results on knowledge-intensive visual question answering and image caption tasks. In the future we'd explore the ability of this model to be used for attribution, and applying it to broader class of multimodal tasks." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23376" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Harsh Agrawal, Peter Anderson, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, and Stefan Lee. nocaps: novel object captioning at scale. 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Computer Vision Foundation / IEEE, 2021. 7" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23379" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_content_list.json b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ef739cdf283280faf6a2c29437053cd3e208ffbb --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_content_list.json @@ -0,0 +1,1746 @@ +[ + { + "type": "text", + "text": "RGB no more: Minimally-decoded JPEG Vision Transformers", + "text_level": 1, + "bbox": [ + 169, + 130, + 800, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jeongsoo Park Justin Johnson University of Michigan {jespark, justincj}@umich.edu", + "bbox": [ + 326, + 181, + 643, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 255, + 313, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most neural networks for computer vision are designed to infer using RGB images. However, these RGB images are commonly encoded in JPEG before saving to disk; decoding them imposes an unavoidable overhead for RGB networks. Instead, our work focuses on training Vision Transformers (ViT) directly from the encoded features of JPEG. This way, we can avoid most of the decoding overhead, accelerating data load. Existing works have studied this aspect but they focus on CNNs. Due to how these encoded features are structured, CNNs require heavy modification to their architecture to accept such data. Here, we show that this is not the case for ViTs. In addition, we tackle data augmentation directly on these encoded features, which to our knowledge, has not been explored in-depth for training in this setting. With these two improvements – ViT and data augmentation – we show that our ViT-Ti model achieves up to $39.2\\%$ faster training and $17.9\\%$ faster inference with no accuracy loss compared to the RGB counterpart.", + "bbox": [ + 75, + 287, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 568, + 209, + 584 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural networks that process images typically receive their inputs as regular grids of RGB pixel values. This spatial-domain representation is intuitive, and matches the way that images are displayed on digital devices (e.g. LCD panels with RGB sub-pixels). However, images are often stored on disk as compressed JPEG files that instead use frequency-domain representations for images. In this paper we design neural networks that can directly process images encoded in the frequency domain.", + "bbox": [ + 73, + 594, + 468, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Networks that process frequency-domain images have the potential for much faster data loading. JPEG files store image data using Huffman codes; these are decoded to (frequency-domain) discrete cosine transform (DCT) coefficients then converted to (spatial-domain) RGB pixels before being fed to the neural network (Fig. 1). Networks that process DCT coefficients can avoid the expensive DCT to RGB conversion; we show in Sec. 3 that this can reduce the theoretical cost of data loading by up to $85\\%$ . Data is typi", + "bbox": [ + 75, + 729, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e392f363c8dd64c7baa17f7b9354a8c90944fb50cc480f5f9701b26a5f6b981f.jpg", + "image_caption": [ + "Figure 1. Our proposed training process. The typical process requires full decoding as well as patch extraction to train. In contrast, our process does not since the DCT coefficients are already saved in block-wise fashion. As ViTs work on image patches, we can directly feed these coefficients to the network." + ], + "image_footnote": [], + "bbox": [ + 503, + 255, + 893, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cally loaded by the CPU while the network runs on a GPU or other accelerator; more efficient data loading can thus reduce CPU bottlenecks and accelerate the entire pipeline.", + "bbox": [ + 496, + 554, + 893, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We are not the first to design networks that process frequency-domain images. The work of Gueguen et al. [1] and Xu et al. [2] are most similar to ours: they show how standard CNN architectures such as ResNet [3] and MobileNetV2 [4] can be modified to input DCT rather than RGB and trained to accuracies comparable to their standard formulations. We improve upon these pioneering efforts in two key ways: architecture and data augmentation.", + "bbox": [ + 496, + 604, + 893, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adapting a CNN architecture designed for RGB inputs to instead receive DCT is nontrivial. The DCT representation of an $H \\times W \\times 3$ RGB image consists of a $\\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8$ tensor of luma data and two $\\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8$ tensors of chroma data. The CNN architecture must be modified both to accept lower-resolution inputs (e.g. by skipping the first few stages of a ResNet50 and adding capacity to later stages) and to accept heterogeneously-sized luma and chroma data (e.g. by encoding them with separate pathways).", + "bbox": [ + 496, + 729, + 893, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We overcome these challenges by using Vision Trans", + "bbox": [ + 519, + 872, + 890, + 888 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code available at https://github.com/JeongsooP/RGB-no-more", + "bbox": [ + 94, + 873, + 433, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22334", + "bbox": [ + 478, + 938, + 519, + 950 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formers (ViTs) [5] rather than CNNs. ViTs use a patch embedding layer to encode non-overlapping image patches into vectors, which are processed using a Transformer [6]. This is a perfect match to DCT representations, which also represent non-overlapping RGB image patches as vectors. We show that ViTs can be easily adapted to DCT inputs by modifying only the initial patch embedding layer and leaving the rest of the architecture unchanged.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data augmentation is critical for training accurate networks; this is especially true for ViTs [7-9]. However, standard image augmentations such as resizing, cropping, flipping, color jittering, etc. are expressed as transformations on RGB images; prior work [1,2] on neural networks with DCT inputs thus implement data augmentation by converting DCT to RGB, augmenting in RGB, then converting back to DCT before passing the image to the network. This negates all of the potential training-time efficiency gains of using DCT representations; improvements can only be realized during inference when augmentations are not used.", + "bbox": [ + 75, + 212, + 468, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We overcome this limitation by augmenting DCT image representations directly, avoiding any DCT to RGB conversions during training. We show how all image augmentations used by RandAugment [10] can be implemented on DCT representations. Some standard augmentations such as image rotation and shearing are costly to implement in DCT, so we also introduce several new augmentations which are natural for DCT.", + "bbox": [ + 75, + 378, + 468, + 497 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using these insights, we train ViT-S and ViT-Ti models on ImageNet [11, 12] which match the accuracy of their RGB counterparts. Compared to an RGB equivalent, our ViT-Ti model is up to $39.2\\%$ faster per training iteration and $17.9\\%$ faster during inference. We believe that these results demonstrate the benefits of neural networks that ingest frequency-domain image representations.", + "bbox": [ + 75, + 498, + 468, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 616, + 218, + 632 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training in the frequency domain is extensively explored in the recent studies. They consider JPEG [1, 2, 13-21], DCT [22-29] or video CODECs [30-33] with a primary focus on increasing the throughput of the model by skipping most of the decoding steps. Many of these works base their model architecture on CNNs. However, adapting CNNs to accept frequency input requires nontrivial modification to the architecture [1,2,17,18,30]. More recent studies [34,35] explore training from a neural compressor [36-45] instead of an existing compression algorithms [46-49]. This approach, however, requires transcoding the existing data to their neural compressed format, increasing overhead. We instead use Vision Transformers [5, 7, 8, 50] on the JPEG-encoded data. Our approach has two advantages: (1) patchwise architecture of ViTs is better suited for existing compression algorithms, (2) does not require any transcoding; it can work on any JPEG images.", + "bbox": [ + 75, + 643, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1787745d3c6fd5d58f8411f401c0bcd11ddd1c874b2532e1f0463f8f87c4526f.jpg", + "image_caption": [ + "Figure 2. Process of applying $8 \\times 8$ DCT to the input image. The input image is sliced into $8 \\times 8$ patches and the DCT is applied to each patch. The DCT bases are shown on the right." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 893, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data augmentation directly on the frequency domain has been studied in several works. Gueguen et al. [1] suggested augmenting on RGB and converting back to DCT. Wiles et al. [34] used an augmentation network that is tailored towards their neural compressor. Others focus on a more classical approach such as sharpening [51-57], resizing [58-65], watermarking [66-72], segmentation [73-77], flip and 90-degree rotation [21, 78], scalar operations [79], and forgery detection [80-82] via analyzing the properties of JPEG and DCT. However, to our knowledge, no other works have thoroughly studied the effect of DCT augmentation during frequency-domain training.", + "bbox": [ + 496, + 277, + 890, + 459 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Speeding up ViTs has been rigorously studied. These either utilize CNN-hybrid architectures to reduce computation [83-89], speed up attention by sparsifying [90-93], linearizing [94, 95], or through other techniques such as pruning [96-99], bottlenecking [100], or approximation [101]. While we only consider the plain ViT architecture in this paper, we want to emphasize that faster data loading is imperative to fully take advantage of these speed-ups as models can only infer as fast as the data loading speed.", + "bbox": [ + 496, + 460, + 890, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 500, + 609, + 629, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Here, we discuss Discrete Cosine Transform (DCT) and JPEG compression process. They are crucial to designing a model and DCT data augmentations in the later sections.", + "bbox": [ + 496, + 635, + 890, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Discrete cosine transform decomposes a finite data sequence into a sum of discrete-frequency cosine functions. It is a transformation from the spatial domain to the frequency domain. We will focus on $8 \\times 8$ DCT since it is a transform used in JPEG. Let $x \\in \\mathbb{R}^{8 \\times 8}$ be a $8 \\times 8$ image patch. Then its DCT transform $X \\in \\mathbb{R}^{8 \\times 8}$ is given by:", + "bbox": [ + 496, + 683, + 890, + 773 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nX _ {u, v} = \\frac {\\alpha_ {u} \\alpha_ {v}}{4} \\sum_ {m, n} x _ {m, n} \\cos \\left[ \\frac {\\pi (2 m + 1) u}{1 6} \\right] \\cos \\left[ \\frac {\\pi (2 n + 1) v}{1 6} \\right] \\tag {3.1}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 776, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Where $\\alpha_{i} = 1 / \\sqrt{2}$ if $i = 0$ , else 1, $u,v,m,n\\in [0..7]$ . Figure 2 shows how the DCT is applied to an image in JPEG. The original image patch can be reconstructed by a weighted sum of the DCT bases (Fig. 2) and their corresponding coefficients $X_{u,v}$ . For the standard JPEG setting,", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22335", + "bbox": [ + 478, + 938, + 519, + 950 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/db5c0a0489b16cdb18183e6456fbc4c136dd95f2d344b9e0a1d449cbd872faf7.jpg", + "image_caption": [ + "Figure 3. A simplified JPEG compression process. An RGB image is first converted to YCbCr, then transformed to DCT space. They are then encoded into binary codes and written to disk. Decoding follows the inverse of this process." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 472, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the pixel-space min/max value of $[-128, 127]$ , is scaled up by $8 \\times$ to $[-1024, 1016]$ . The proof of this property is shown in the supplementary material. This property is necessary to implement several DCT augmentations in Sec. 5.", + "bbox": [ + 75, + 327, + 467, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "JPEG [46, 47, 102] is a widely used compression algorithm that is designed to encode images generated by digital photography. The encoding process is as follows:", + "bbox": [ + 75, + 390, + 467, + 435 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) $H\\times W\\times 3$ RGB image is given as input", + "(b) RGB is converted to YCbCr color space", + "(c) $\\mathrm{CbCr}$ channels are downsampled to $\\frac{H}{2} \\times \\frac{W}{2}$", + "(d) Values are shifted from [0,255] to [-128,127]", + "(e) DCT is applied to non-overlapping $8\\times 8$ pixel patches", + "(f) DCT coefficients are quantized", + "(g) Run-length encoding(RLE) compresses the coefficients", + "(h) RLE symbols are encoded using Huffman coding" + ], + "bbox": [ + 83, + 443, + 468, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A simplified illustration of this process is shown in Figure 3. YCbCr is a color space where $\\mathbf{Y}$ represents luma (i.e. brightness) and $\\mathrm{Cb}$ , $\\mathrm{Cr}$ signifies chroma (i.e. color) of the image. Step (e) produces a data of size $\\mathbf{Y} \\in \\mathbb{R}^{1 \\times \\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8}$ , $\\mathbf{U} \\in \\mathbb{R}^{2 \\times \\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8}$ for $\\mathbf{Y}$ and $\\mathrm{CbCr}$ channel respectively. These $8 \\times 8$ DCT coefficients are referred to as DCT Blocks in the later sections.", + "bbox": [ + 75, + 573, + 468, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compute cost to decode JPEG can be analyzed by counting the number of operations (OPs) for the inverse of the above process. Consider decoding a single $8 \\times 8$ patch. Our proposed scheme decodes step (h) - (f) with a computation cost of $3N_{s} + 128$ OPs where $N_{s} \\in [1..64]$ : number of RLE symbols. Full JPEG decoding, on the other hand, requires $3N_{s} + 1717$ OPs. If we suppose $N_{s} = 32$ , then the compute cost is 224 and 1813 OPs respectively, where our scheme theoretically saves computation by $87.6\\%$ . The details of these values are shown in the supplementary material.", + "bbox": [ + 75, + 681, + 468, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Model Architecture", + "text_level": 1, + "bbox": [ + 76, + 844, + 264, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Designing a neural network that works on JPEG-encoded DCT coefficients can be challenging. In Sec. 3, we", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "showed that JPEG downsamples $\\mathrm{CbCr}$ channels to $\\frac{H}{2} \\times \\frac{W}{2}$ . This spatial disparity must be addressed before training in DCT. An existing work by Gueguen et al. [1] suggested several new CNN architectures which include (1) upsampling, (2) downsampling, and (3) late-concatenation. The first two architectures either upsample $\\mathrm{CbCr}$ to match the dimension of Y or downsample Y to match $\\mathrm{CbCr}$ . However, doing so results in (1) redundant computation or (2) loss of information due to resizing. The third approach, late-concatenation, computes them separately and concatenates them further down the network. However, this requires substantial modification of the CNN architecture, making adaptation to existing models difficult.", + "bbox": [ + 496, + 89, + 890, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We believe that ViTs are better suited to deal with this unique characteristic of JPEG. Vision transformers work on patches of an image [5, 7-9]. Considering that JPEG DCT already extracts $8 \\times 8$ patches from an image (Sec. 3 (e)), we can employ them by modifying only the initial embedding layer. This allows easier integration into other ViTs as the rest of the architecture can remain untouched.", + "bbox": [ + 496, + 287, + 890, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, in this section, we propose several patch-embedding strategies that are plausible solutions to this problem. These modified patch embedding layers are illustrated in Fig. 4. The architecture that follows is identical to the plain ViT defined in [5,7,50].", + "bbox": [ + 496, + 393, + 890, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Grouped embedding generates embeddings by grouping the $8 \\times 8$ DCT blocks together from the corresponding patch position. Consider a DCT input $\\mathbf{Y}$ , $\\mathbf{U}$ defined in Sec. 3. Grouped embedding collects DCT blocks such that for patch size $p^2$ , $\\mathbf{Y} \\to \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}$ and $\\mathbf{U} \\to \\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{2p^2}{4}}$ where the channel and block size are flattened to the last dimension. Then, this is concatenated along the last axis as $(\\mathbf{Y}_r, \\mathbf{U}_r) \\to \\mathbf{Y}\\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{3p^2}{2}}$ which will then be embedded as $\\mathbf{z}: \\mathbf{Y}\\mathbf{U}_r \\to \\mathbf{z} \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times E}$ where $\\mathbf{z}$ is the generated embedding and $E$ is the embedding size.", + "bbox": [ + 496, + 470, + 890, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Separate embedding generates separate embeddings for each DCT block in a patch. A DCT input $\\mathbf{Y},\\mathbf{U}$ is reshaped as $\\mathbf{Y}\\rightarrow \\mathbf{Y}_r\\in \\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{p^2}{64}\\times 64},\\mathbf{U}\\rightarrow \\mathbf{U}_r\\in$ $\\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{2p^2}{4\\cdot 64}\\times 64}$ which is embedded separately for each block: $(\\mathbf{Y}_r,\\mathbf{U}_r)\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times \\frac{3p^2}{2\\cdot 64}\\times \\frac{E}{NB}}$ where $N_{B} =$ number of blocks $= \\frac{3p^2}{2\\cdot 64}$ . This is then mixed using a linear layer to generate a final embedding $\\mathbf{z}\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times E}$ . Our intuition behind this strategy is that the information each block holds might be critical, thus training a specialized linear layer for each block could yield better results.", + "bbox": [ + 496, + 640, + 890, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concatenated embedding embeds and concatenates the DCT blocks from $\\mathbf{Y}$ , $\\mathbf{U}$ separately. Our intuition is that since $\\mathbf{Y}$ and $\\mathbf{U}$ represent different information (luma and chroma), designing specialized layers that handle each in-", + "bbox": [ + 496, + 816, + 890, + 876 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2Assume $p = 16n,n\\in \\mathbb{N}$ .For $p < 16$ , check the supplementary.", + "bbox": [ + 514, + 886, + 867, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22336", + "bbox": [ + 478, + 938, + 517, + 949 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/583b009aaa27acf885dcb25951d56cde4730e1d8abda2bc2308d68ebce239aa3.jpg", + "image_caption": [ + "Figure 4. Proposed embedding strategies. We first collect $8 \\times 8$ DCT blocks until it matches the patch size. Then, these blocks can be embedded using one of the strategies. Grouped embedding groups all of the collected blocks and embeds them together. Separate embedding embeds each block separately and mixes it. Concatenated embedding embeds $\\mathbf{Y}$ and $\\mathbf{U}$ separately and concatenates them." + ], + "image_footnote": [], + "bbox": [ + 122, + 90, + 851, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "formation separately may be necessary. However, this generates more embeddings per image patch than the plain model. To keep the overall size even, we reduce the size of each embedding to 2/3. An embedding formula is $\\mathbf{Y} \\rightarrow \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}$ , $\\mathbf{U} \\rightarrow \\mathbf{U}_r \\in \\mathbb{R}^{2 \\times \\frac{H}{2p} \\times \\frac{W}{2p} \\times p^2}$ , which is then embedded separately per channel type: $\\mathbf{Y}_r \\rightarrow \\mathbf{z}_Y \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times \\frac{2E}{3}}$ , $\\mathbf{U}_r \\rightarrow \\mathbf{z}_U \\in \\mathbb{R}^{\\frac{2HW}{4p \\cdot p} \\times \\frac{2E}{3}}$ then concatenated $(\\mathbf{z}_Y, \\mathbf{z}_U) \\rightarrow \\mathbf{z} \\in \\mathbb{R}^{\\frac{3HW}{2p \\cdot p} \\times \\frac{2E}{3}}$ to generate an embedding $\\mathbf{z}$ .", + "bbox": [ + 76, + 367, + 472, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sub-block conversion [64] can be applied as an alternate way to embed a patch. Consider ViT architecture of patch size 16. For simplicity, assume only the Y channel is present. To form a patch size of $16 \\times 16$ , four $8 \\times 8$ DCT blocks have to be grouped together. One strategy is to embed these directly through the linear layer. Another approach is to convert them into a single $16 \\times 16$ block and embed them. In other words, we embed the DCT patches from a $16 \\times 16$ DCT. There exists a way to efficiently extract these $16 \\times 16$ DCT from the smaller $8 \\times 8$ DCT blocks and vice versa known as sub-block conversion [64]. This technique can allow us to extract a native DCT patch of different sizes, potentially yielding better results. We also use this technique to implement several augmentations in Sec. 5.", + "bbox": [ + 75, + 497, + 472, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. DCT Augmentation", + "text_level": 1, + "bbox": [ + 76, + 723, + 266, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data augmentation has been a vital component in training robust networks [10, 103-108]. However, augmenting the DCT, as well as training with it, has not been studied in depth. There exist several prior works for some augmentations such as sharpening or resizing as discussed in Sec. 2, but most other RGB augments lack their DCT counterparts.", + "bbox": [ + 75, + 750, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing work by Gueguen et al. [1] proposed converting DCT to RGB, augmenting in RGB, and converting it back to DCT. However, this incurs expensive RGB/DCT conversion as shown in Sec. 3. More recent work by Wiles et", + "bbox": [ + 75, + 840, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "al. [34] used a specialized augmentation network that augments their neural-compressed format. Doing so, however, sacrifices versatility as it requires training and can't be reliably generalized to other resolutions or data.", + "bbox": [ + 496, + 367, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our approach is different. We instead implement augmentations directly on DCT by analyzing its properties. That way, we can avoid converting to RGB or relying on a trained augmentation network. In other words, our method is fast, flexible, and works on virtually any data, so long as it is represented in DCT. Thus, in this section, we implement all augmentations used in RandAugment [10] as well as suggest new augmentations that are meaningful for DCT. We mark the ones we suggest using an asterisk(*)", + "bbox": [ + 496, + 428, + 892, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are largely two different types of DCT augmentation: photometric and geometric. Each of which uses different key properties of the DCT. While these augmentations are not meant to precisely reproduce RGB augmentations, most of our implementations approximate the RGB counterparts reasonably well. The overview of the augmentations and their similarity metrics are shown in Fig. 6.", + "bbox": [ + 496, + 564, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Photometric augmentation", + "text_level": 1, + "bbox": [ + 500, + 678, + 741, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Photometric augmentation alters a metric of an image, which includes brightness or sharpness. Our implementation of this can be roughly categorized into two: DC component-based and frequency component-based augmentation. Both use the attributes of a DCT coefficient.", + "bbox": [ + 496, + 702, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DC Component-based augmentation only alters the DCT coefficient without frequency $(X_{0,0})$ , which is simply a scaled sum of all pixel values in the block (Eq. (3.1)). Altering this value will affect all pixels in the block evenly. This property can be used in two ways – either when we have to modify a value uniformly across all pixels, or when we have to approximate a value of the pixels in a block.", + "bbox": [ + 496, + 779, + 890, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Brightness augmentation alters the brightness of the im", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22337", + "bbox": [ + 478, + 938, + 517, + 950 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1697da140a2cb1d0c061efb38c8b8b4f8c4998ee81e94546aff0f82ffc2fde87.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 109, + 88, + 439, + 212 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4c56f1ff74fd2a7e203d16864861bed72aa302c9dc32328b3bcda2fc0affc003.jpg", + "image_caption": [ + "Figure 5. A visualization of different DCT augmentation types. Orange-colored coefficients are augmented and saved as blue. The bottom two examples illustrate Translate and Resize." + ], + "image_footnote": [], + "bbox": [ + 109, + 212, + 437, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "age. Considering that the image is represented in YCbCr color space, we can implement this augmentation by simply modifying the DC component of the Y channel. Let $Y_{u,v}^{h,w}$ denote a $u$ , $v$ -th DCT coefficient of Y at block position $h$ , $w$ . Then our implementation $f$ is the following where $t \\in \\mathbb{R}$ .", + "bbox": [ + 75, + 402, + 468, + 477 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {u, v}: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}Y _ {0, 0} ^ {h, w} + t \\cdot \\text {m e a n} (\\operatorname {a b s} \\left(Y _ {0, 0}\\right))&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.1}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 479, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrast modifies the distance between the bright and dark values in the image. Since DCT coefficients are zero-centered by design (Sec. 3 (d)) and the brightness of a block can be approximated using the DC component $Y_{0,0}$ , we can categorize the non-negative component as 'bright' and the negative component as 'dark'. Therefore, multiplying $Y_{0,0}$ with $t \\in [0,\\infty)$ can adjust the contrast of the image. The implementation is $f:Y_{0,0}^{h,w} \\to tY_{0,0}^{h,w}$ . Similarly, Equalize applies histogram equalization to $Y_{0,0}$ .", + "bbox": [ + 75, + 511, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Color (Saturation) augmentation apply the same equation of Contrast to $U$ (DCT coefficient of $\\mathrm{CbCr}$ ), instead of $Y$ . This augments the saturation as illustrated in Fig. 6.", + "bbox": [ + 76, + 648, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "AutoContrast scales the values so that the brightest and darkest value in an image becomes the brightest and darkest possible value. These values are approximated using $X_{0,0}$ in the same way as Contrast. In Sec. 3, we showed that the min/max value of the DCT in JPEG is $[-1024, 1016]$ . Thus, our implementation $f$ is as follows.", + "bbox": [ + 75, + 694, + 468, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}\\frac {Y _ {0 , 0} ^ {h , w} - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)}{\\operatorname* {m a x} \\left(Y _ {0 , 0}\\right) - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)} \\cdot 2 0 4 0 - 1 0 2 4&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.2}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 787, + 467, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "AutoSaturation* applies the formula in AutoContrast to $U$ . This allows the DCT to utilize the full range of the color.", + "bbox": [ + 76, + 837, + 468, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frequency component-based augmentation uses non-DC components $(X_{u,v}, u, v \\neq 0)$ . Altering the amplitude of", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "these changes the intensity of the corresponding cosine signal in the pixel space. Here, we designed three augmentations each affecting frequency differently.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sharpness augmentation adjusts a sharpness of an image. Typically in RGB, this utilizes a convolution kernel to achieve such an effect. However, in DCT, several studies show that this can be implemented by adjusting the frequency components of the DCT [51-57]. They show that sharper images will generally have a higher frequency as there are more sudden changes around the sharp edges. Using this property, we implement Sharpness by linearly altering the frequency components. If $t > 0$ , the following equation sharpens the image. Otherwise, it blurs it.", + "bbox": [ + 496, + 138, + 890, + 289 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf: Y _ {u, v} ^ {h, w} \\rightarrow Y _ {u, v} ^ {h, w} \\cdot \\max \\left(1 + \\frac {t u}{7}, 0\\right) \\max \\left(1 + \\frac {t v}{7}, 0\\right) \\tag {5.3}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 291, + 890, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MidfreqAug* augmentation is similar to sharpness but instead of peaking the augmentation strength at the highest frequency $(u, v = 7)$ , we peaked it at the middle frequency $(u, v \\in \\{3, 4\\})$ . We expect the results to be similar to Sharpness, but possibly with less noise.", + "bbox": [ + 496, + 315, + 890, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FreqEnhance* multiplies all frequency components uniformly with a positive factor $t \\in [0, \\infty)$ . The augmentation is simply $f: Y_{u,v}^{h,w} \\to tY_{u,v}^{h,w}$ , $u, v \\neq 0$ . We believe that this allows us to see the impact of a frequency component with respect to the model performance.", + "bbox": [ + 496, + 392, + 890, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Photometric - special case. There are some augmentations that do not categorize into either of the above augmentations. Invert simply flips the sign of all DCT coefficients. This is because the coefficients are virtually zero-centered. Posterize quantizes $X_{0,0}$ to lower bits. Solarize uses $X_{0,0}$ to determine whether or not the DCT block should be inverted. SolarizeAdd adds a preset value to $X_{0,0}$ if it is below threshold. Grayscale replaces $U$ with zeros, removing color information. ChromaDrop* instead drops the Cb or Cr channel randomly, removing only half of the color information.", + "bbox": [ + 496, + 473, + 890, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Geometric augmentation", + "text_level": 1, + "bbox": [ + 500, + 641, + 725, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometric augmentation modifies the image plane geometrically. An example of this augmentation includes translation, rotation, or shearing. There are two main subcategories of geometric augmentation – block-wise and subblock conversion-based augmentation.", + "bbox": [ + 496, + 666, + 890, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Block-wise augmentation treats the DCT block positions similarly to pixel positions. Translate can be implemented by moving the positions $h, w$ of each $X^{h,w}$ and filling the blank with zeros. Cutout follows a similar process where we crop blocks out and fill them with zeros.", + "bbox": [ + 496, + 747, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Flipping the DCT coefficients utilize the fact that odd-column or odd-row DCT bases are odd-symmetric [78]. Flip is performed by flipping the position of the blocks and then flipping the individual DCT blocks. Define $R = \\mathrm{diag}(1, -1, 1, -1, \\ldots, -1)$ of matching size. Then, the per", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22338", + "bbox": [ + 478, + 938, + 517, + 950 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8529e97412e4550bfff2b91d206b5746eb1f29afc3980c67446d94ba6de142ac.jpg", + "image_caption": [ + "Figure 6. A visualization of RGB augmentations and their DCT counterparts. $/S$ or $/B$ indicates 'sharpen' or 'blur' on sharpness-related augmentations. Resize has been compared where they scale the image up by 2. PSNR and SSIM are calculated for each DCT augmentation. We observe that most DCT augmentations resemble RGB augmentations. Augmentations such as grayscale, cutout, and flip are identical to RGB. However, other augmentations including equalize and contrast are not exactly equal to RGB." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 890, + 300 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "block flipping operation is as follows.", + "bbox": [ + 76, + 382, + 328, + 398 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}X ^ {h, w} R&\\text {i f h o r i z o n t a l f l i p}\\\\R X ^ {h, w}&\\text {i f v e r t i c a l f l i p}\\end{array}\\right\\} \\tag {5.4}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 400, + 468, + 433 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rotate90 is implemented using a transpose with flipping [78]. We first rotate the block position $h, w$ and rotate each $X^{h,w}$ by 90 degrees. The per-block rotation is defined as:", + "bbox": [ + 76, + 435, + 468, + 479 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}(X ^ {h, w}) ^ {T} R&\\text {c l o c k w i s e}\\\\R (X ^ {h, w}) ^ {T}&\\text {c o u n t e r - c l o c k w i s e}\\end{array}\\right\\} \\tag {5.5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 481, + 468, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sub-block conversion-based augmentation uses the relationship between the DCT block and its smaller sub-blocks. This allows us to efficiently calculate the DCT of different DCT bases without the need to do inverse transform (e.g. $8 \\times 8$ DCT $\\leftrightarrow$ $32 \\times 32$ DCT). The relationship studied by Jiang and Feng [64] is as follows. Let $X_{N \\times M}^{h,w}$ be the DCT coefficient block of $N \\times M$ DCT at block position $h, w$ . Then, there exists a conversion matrix $A$ such that:", + "bbox": [ + 75, + 518, + 468, + 637 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX _ {L N \\times M N} = A _ {L, N} \\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] A _ {M, N} ^ {T} \\tag {5.6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 638, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Where $A_{L,N}$ is a $LN \\times LN$ matrix that converts the $L$ number of $N$ 1-D DCT blocks into a single $LN$ DCT block. The decomposition of $X_{LN \\times MN}$ DCT blocks into $L \\times M$ DCT blocks of $X_{N \\times N}$ follows a similar process:", + "bbox": [ + 75, + 691, + 468, + 753 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] = A _ {L, N} ^ {- 1} X _ {L N \\times M N} A _ {M, N} ^ {- 1 ^ {T}} \\tag {5.7}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 753, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Derivation of $A$ is given in the supplementary material.", + "bbox": [ + 76, + 810, + 441, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Resize can be implemented if we can understand how to resize individual DCT blocks. Suppose that there exists a way to resize $X_{4 \\times 4}$ to $X_{8 \\times 8}$ by padding. Then, to up-sample $X_{8 \\times 8}$ while keeping the $8 \\times 8$ sliced structure of JPEG DCT, we can first decompose $X_{8 \\times 8}$ into four $X_{4 \\times 4}$", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "using sub-block conversion. Then, we can individually resize each $X_{4 \\times 4}$ to $X_{8 \\times 8}$ . This gives us four $X_{8 \\times 8}$ blocks upsampled from one $X_{8 \\times 8}$ . Downsampling can follow a similar process. We first combine four adjacent $X_{8 \\times 8}$ into a single $X_{16 \\times 16}$ using sub-block conversion. Then, we resize $X_{16 \\times 16}$ down to $X_{8 \\times 8}$ . This process is shown in Fig. 5.", + "bbox": [ + 498, + 382, + 890, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This technique to resize each individual DCT block is known as sub-band approximation and has been studied by Mukherjee and Mitra [65]. Their work shows that if $X_{N\\times N}(k,l)$ is a $(k,l)$ -th coefficient of a $X_{N\\times N}$ block, then, the approximate relationship is:", + "bbox": [ + 498, + 474, + 890, + 550 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX _ {L N \\times M N} (k, l) \\approx \\left\\{ \\begin{array}{l l} \\sqrt {L M} X _ {N \\times N} (k, l) & 0 \\leq k, l \\leq N - 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5.8}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 551, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Using this, we can upsample $L \\times M$ times by resizing each $X_{N \\times N}$ to $X_{LN \\times MN}$ and decomposing them to $L \\times M$ $X_{N \\times N}$ . $L \\times M$ downsampling combines $L \\times M$ adjacent $X_{N \\times N}$ to form $X_{LN \\times MN}$ and resize it to $X_{N \\times N}$ . An arbitrary resizing of $\\frac{P}{Q} \\times \\frac{R}{S}$ can be done by first upsampling $P \\times R$ times and downsampling the result by $Q \\times S$ .", + "bbox": [ + 498, + 597, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rotate is implemented using the rotational property of the Fourier transform [112-114]. This property denotes that the Fourier transform of a rotated function is equal to rotating the Fourier transform of a function. To use this property, we slightly alter the Eq. (5.6). Instead of combining the blocks to $X_{LN\\times MN}$ DCT, we combine them to the discrete Fourier transform (DFT) coefficients. Define $D_{N\\times N}$ as the DFT coefficient block of size $N\\times N$ . Then, the rotation is done by combining $L\\times M X_{N\\times N}$ to $D_{LN\\times MN}$ , rotating it, and decomposing it back to $L\\times M X_{N\\times N}$ using the modified Eq. (5.7). This can be further improved using the lossless 90-degree rotation to minimize the lossy arbitrary-degree rotation. The details of this DFT conversion are shown in the supplementary material.", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22339", + "bbox": [ + 478, + 938, + 517, + 950 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ecd4e1fc4fa181d41aef6b4871b724d04256a0a1ba33e5705d79a6a41b04b647.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ArchitectureColor SpaceAug. SpaceEmbed. FLOPsDecodeAugmentTrain Data LoadModel Fwd/BwdTrain PipelineEval Data LoadModel FwdEval PipelineVal Acc (%)
(↓ Performance)Latency per img (ms)Throughput per GPU (FPS)
ViT-Ti [50]RGBRGB28.9M3.683.08571.5832.8493.8641.42898.7638.074.1
ViT-S [50]RGBRGB57.8M3.623.01558.0355.7352.1660.21174.5610.576.5
ViT-S* [50]RGBRGB57.8M3.692.63574.7716.8489.0680.32335.1644.275.6
SwinV2-T* [109]RGBRGB20.8M3.612.98489.8231.5231.6614.8809.5516.279.0*
ResNet50 [110]RGBRGB------688.21226.8639.176.1
JPEG-TiDCTDCT16.1M1.422.62816.2857.2687.6775.32847.5752.375.1
JPEG-SDCTDCT30.5M1.492.40824.8364.3360.5782.91139.7711.176.5
JPEG-S*DCTDCT30.5M1.422.37821.7764.0665.8793.12384.1711.875.8
JPEG-S*◇DCTRGB to DCT30.5M3.625.98425.3751.9372.3748.72382.4721.076.3
SwinV2-T*DCTDCT13.0M1.402.47752.0241.9235.9664.2824.9578.079.4
ResNet50◇ [1] [2]DCTRGB to DCT------785.75969.8753.576.1
(↓ Improvements)(Reduction▼)(Speed-ups▲)
JPEG-Ti vs ViT-Ti-44.4 %-61.4 %-14.9 %+42.8 %+2.9 %+39.2 %+20.9 %-1.8 %+17.9 %+1.0
JPEG-S vs ViT-S-47.2 %-58.8 %-20.3 %+47.8 %+2.4 %+2.4 %+18.6 %-3.0 %+16.5 %+0.0
JPEG-S* ViT-S*-47.2 %-61.5 %-9.9 %+43.0 %+6.6 %+36.2 %+16.6 %+2.1 %+10.5 %+0.2
JPEG-S* vs JPEG-S*◇+0.0 %-60.8 %-60.4 %+93.2 %+1.6 %+78.8 %+5.9 %+0.1 %-1.3 %-0.5
SwinV2-T* (DCT vs RGB)-37.7 %-61.2 %-17.1 %+53.5 %+4.5 %+1.9 %+8.0 %+1.9 %+12.0 %+0.4
", + "bbox": [ + 101, + 85, + 870, + 325 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Model throughput per GPU for each pipeline element and accuracy. Embed. FLOPs shows the FLOPs needed to generate patch embeddings. Decode and Augment indicates the per-image processing latency during training. Val Acc shows the accuracy on the ImageNet validation set. 'JPEG-' prefix indicates that it is a ViT trained using JPEG DCT coefficients. Model with \\* symbol is trained using mixed precision [111]. $\\diamondsuit$ models are trained using the pipeline suggested by Gueguen et al. [1]. \\*SwinV2 models are trained using the same recipe as in [50] for a fair comparison. The details of these measurements are shown in the supplementary material.", + "bbox": [ + 75, + 334, + 893, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shear is identically implemented as Rotate where instead of rotating $D_{LN \\times MN}$ , we shear it. This is because we can apply the same property [112] for each axis.", + "bbox": [ + 76, + 417, + 470, + 465 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 76, + 479, + 209, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we compare our models trained in DCT space with the RGB models. We show that the DCT models achieve similar accuracy but perform notably faster than the RGB models. First, we compare the throughput and accuracy of the RGB and DCT models. Then, we compare the DCT embedding strategies covered in Sec. 4. Lastly, we conduct an ablation study on the DCT data augmentation.", + "bbox": [ + 75, + 505, + 468, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details. All experiments are conducted with PyTorch [115]. We extract DCT coefficients using a modified version of libjpeg [116] and TorchJPEG [117]. All timing measurements are performed using $2 \\times$ A40 GPUs and 8 cores from an Intel Xeon 6226R CPU, and all throughputs are reported per GPU. We used fvcore [118] to obtain the FLOPs. All models are trained on ImageNet [11, 12], which we resize on-disk to $512 \\times 512$ prior to training. We re-implement a ViT training pipeline in PyTorch, carefully following the recipe suggested by Beyer et al. [50] which uses random resized crop, random flip, RandAugment [10] and Mixup [119] with a global batch size of 1024. All plain ViT models are trained with a patch size of 16. SwinV2 model [109] uses a patch size of 4, a window size of 8, and a global batch size of 512. '-S' models are trained for 90 epochs. '-Ti' and SwinV2 models are instead trained for 300 epochs using the same recipe in [50]. Following [50], we randomly sample $1\\%$ of the train set to use for validation. Our RGB ResNet-50 baseline uses the V1", + "bbox": [ + 75, + 613, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "weights from Torchvision [110]. There exist recent works with improved training recipes for ResNets [120, 121], but this is orthogonal to our work. The DCT ResNet-50 uses the model proposed by Gueguen et al. [1] and Xu et al. [2].", + "bbox": [ + 498, + 417, + 893, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Main results", + "text_level": 1, + "bbox": [ + 500, + 494, + 633, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The hyperparameter settings for the models are given in the supplementary material. Tab. 1 shows the comprehensive result from our experiment. Both the ViT and CNN models show equivalent accuracy to their RGB counterparts. However, loading directly from JPEG DCT reduces decoding latency by up to $61.5\\%$ . We see a similar effect on the augmentation latency to a lesser extent. Additionally, as the input size has been halved by JPEG (Sec. 3), we observe that the FLOPs needed to generate embeddings are reduced by up to $47.2\\%$ . These speed-ups boost throughput for DCT models. Most notably, our JPEG-Ti model showed $39.2\\%$ and $17.9\\%$ faster training and evaluation. Our augmentation scheme improves train data loading throughput by $93.2\\%$ versus the one by Gueguen et al. [1], which must convert DCT to RGB, augment, and convert it back to DCT.", + "bbox": [ + 496, + 521, + 890, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "While training as-is still reaps the benefits of faster data loading, we can observe that the JPEG-S model is bottlenecked by model forward and backward passes. One option is to employ mixed precision training [111]. This allows us to fully realize the data loading speed-ups by accelerating the model with minor accuracy loss. We observe that our JPEG-S model trained using mixed precision is $36.2\\%$ faster during training time compared to the RGB counterpart. We believe most other faster models discussed in Sec. 2 will also benefit from this speed-up.", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22340", + "bbox": [ + 478, + 938, + 519, + 950 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3ae9513160d224f3a9b6386392f42602d93046633e1f4d5d3586e0927cdc2a45.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PhotometricGeometricAccuracy
SubsetResizeDC basedFreq. basedSpecial caseBlock-wiseSub-block basedRGBDCT
(Avg. latency (ms) ↓)
RGB2.170.611.340.671.231.28--
DCT2.790.370.540.340.429.31--
(Ablation ↓)
All✓✓✓✓✓✓76.574.6
No sub-block✓✓✓✓✓✗76.275.1
No block-wise✓✓✓✓✗✗76.072.6
No Special-case✓✓✓✗✗✗76.373.3
No Freq. based✓✓✗✗✗✗75.974.2
No DC based✓✗✗✗✗✗74.475.5
Best Subset✓Brightness, Contrast, Color, AutoContrast, AutoSaturation, Sharpness, MidfreqAug, Posterize, Grayscale, ChromaDrop, Translate, Cutout, Rotate90✗76.5*76.5
", + "bbox": [ + 101, + 88, + 870, + 281 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e792387cfea2390901cf2bd206d6fc93e26e611f2abb3f6588dd5f2c5b6f2f40.jpg", + "table_caption": [ + "Table 2. Data augmentation ablation study on ViT-S. At the bottom row, we report the best subset we found and train both the RGB and DCT models from it. *RGB accuracy is obtained with MidfreqAug removed, since it is analogous to Sharpness in RGB as shown in Fig. 6." + ], + "table_footnote": [], + "table_body": "
GroupedSeparateConcat.Sub-blockAcc
✓--✓76.5
-✓-✓74.7
--✓✓71.3
✓---74.6
-✓--73.8
--✓-71.3
", + "bbox": [ + 120, + 330, + 428, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Embedding strategy ablation study on ViT-S. We see that grouped embedding with sub-block outperforms other strategies.", + "bbox": [ + 75, + 433, + 470, + 464 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2. Embedding strategies", + "text_level": 1, + "bbox": [ + 76, + 474, + 279, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To see which patch embedding scheme is most suitable for DCT, we performed an ablation study in Tab. 3. We ablate on the embedding strategies and the sub-block conversion technique discussed in Sec. 4 on ViT-S. The results show two things. One is that the simplest strategy-grouped embedding-is best, and that sub-block conversion is important to achieve high accuracy. We believe this indicates that (1) all blocks in an image patch relay information of that patch as a whole; they should not be separately inferred, and (2) it is more natural for the model to deduce the information in a patch if the sub-blocks are fused together. The best strategy is used throughout the DCT models in Tab. 1.", + "bbox": [ + 75, + 500, + 470, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Augmentation", + "text_level": 1, + "bbox": [ + 76, + 695, + 222, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As discussed in Sec. 5, data augmentation is crucial to train a well-performing model. However, many existing studies [9, 10, 103-108] are tuned toward RGB augmentations; we cannot assume that the existing work's result would be consistent on DCT. In other words, some DCT augmentations could have a different impact on both the accuracy and throughput of the model compared to RGB. Therefore, we perform an ablation study on data augmentations discussed in Sec. 5 and report the result in Tab. 2. We perform ablation by varying the subset of augmentations used in RandAugment [10] on ViT-S. The experiment is performed separately for RGB and DCT with their re", + "bbox": [ + 75, + 719, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "spective augmentation sets. The results show that while sub-block-based augmentations (e.g. rotate, shear) are prohibitively expensive to do directly on DCT, it is not as important to train a model. We report the best augmentation subset we found without sub-block-based augmentations at the bottom row. In addition, we train an RGB model using this subset and compare the accuracy. We can see that the RGB model performs identically to the DCT model, and the subset does not unfairly favor DCT over RGB models.", + "bbox": [ + 496, + 334, + 893, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 497, + 619, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we demonstrated that vision transformers can be accelerated significantly by directly training from the DCT coefficients of JPEG. We proposed several DCT embedding strategies for ViT, as well as reasonable augmentations that can be directly carried out on the DCT coefficients. The throughput of our model is considerably faster with virtually no accuracy loss compared to RGB.", + "bbox": [ + 496, + 527, + 893, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RGB has been widely used for as long as computer vision existed. Many computer vision schemes regard retrieving RGB as a necessary cost; they have not considered the potential of direct encoded-space training in-depth. We wanted to show the capability of this approach, as well as demonstrate that recovering RGB is not always necessary.", + "bbox": [ + 496, + 638, + 893, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Encoded-space training can be adapted to nearly all scenarios that require loading some compressed data from storage. From mobile devices to powerful data centers, there are no situations where they wouldn't benefit from faster loading speed. As we only considered the plain ViT architecture, there is still more to be gained by adapting our findings to the existing efficient architectures. Future studies may also consider a better augmentation strategy to improve the performance further. We hope that the techniques shown in this paper prove to be an adequate foundation for future encoded-space research.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22341", + "bbox": [ + 478, + 938, + 517, + 950 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lionel Gueguen, Alex Sergeev, Ben Kadlec, Rosanne Liu, and Jason Yosinski. Faster Neural Networks Straight from JPEG. Advances in Neural Information Processing Systems, 31, 2018. 1, 2, 3, 4, 7", + "[2] Kai Xu, Minghai Qin, Fei Sun, Yuhao Wang, Yen-Kuang Chen, and Fengbo Ren. Learning in the frequency domain. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 1, 2, 7", + "[3] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 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NeurIPS, 2021. 7" + ], + "bbox": [ + 501, + 90, + 890, + 607 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "22346", + "bbox": [ + 478, + 938, + 519, + 950 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_model.json b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d3ee9d416e15143917ce977e2e65dce6c6e53755 --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_model.json @@ -0,0 +1,3086 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.17, + 0.131, + 0.802, + 0.152 + ], + "angle": 0, + "content": "RGB no more: Minimally-decoded JPEG Vision Transformers" + }, + { + "type": "text", + "bbox": [ + 0.327, + 0.182, + 0.644, + 0.234 + ], + "angle": 0, + "content": "Jeongsoo Park Justin Johnson University of Michigan {jespark, justincj}@umich.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.256, + 0.314, + 0.273 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.474, + 0.562 + ], + "angle": 0, + "content": "Most neural networks for computer vision are designed to infer using RGB images. However, these RGB images are commonly encoded in JPEG before saving to disk; decoding them imposes an unavoidable overhead for RGB networks. Instead, our work focuses on training Vision Transformers (ViT) directly from the encoded features of JPEG. This way, we can avoid most of the decoding overhead, accelerating data load. Existing works have studied this aspect but they focus on CNNs. Due to how these encoded features are structured, CNNs require heavy modification to their architecture to accept such data. Here, we show that this is not the case for ViTs. In addition, we tackle data augmentation directly on these encoded features, which to our knowledge, has not been explored in-depth for training in this setting. With these two improvements – ViT and data augmentation – we show that our ViT-Ti model achieves up to \\(39.2\\%\\) faster training and \\(17.9\\%\\) faster inference with no accuracy loss compared to the RGB counterpart." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.569, + 0.21, + 0.585 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.595, + 0.47, + 0.731 + ], + "angle": 0, + "content": "Neural networks that process images typically receive their inputs as regular grids of RGB pixel values. This spatial-domain representation is intuitive, and matches the way that images are displayed on digital devices (e.g. LCD panels with RGB sub-pixels). However, images are often stored on disk as compressed JPEG files that instead use frequency-domain representations for images. In this paper we design neural networks that can directly process images encoded in the frequency domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Networks that process frequency-domain images have the potential for much faster data loading. JPEG files store image data using Huffman codes; these are decoded to (frequency-domain) discrete cosine transform (DCT) coefficients then converted to (spatial-domain) RGB pixels before being fed to the neural network (Fig. 1). Networks that process DCT coefficients can avoid the expensive DCT to RGB conversion; we show in Sec. 3 that this can reduce the theoretical cost of data loading by up to \\(85\\%\\). Data is typi" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.256, + 0.895, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.472, + 0.895, + 0.542 + ], + "angle": 0, + "content": "Figure 1. Our proposed training process. The typical process requires full decoding as well as patch extraction to train. In contrast, our process does not since the DCT coefficients are already saved in block-wise fashion. As ViTs work on image patches, we can directly feed these coefficients to the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.555, + 0.895, + 0.601 + ], + "angle": 0, + "content": "cally loaded by the CPU while the network runs on a GPU or other accelerator; more efficient data loading can thus reduce CPU bottlenecks and accelerate the entire pipeline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.894, + 0.728 + ], + "angle": 0, + "content": "We are not the first to design networks that process frequency-domain images. The work of Gueguen et al. [1] and Xu et al. [2] are most similar to ours: they show how standard CNN architectures such as ResNet [3] and MobileNetV2 [4] can be modified to input DCT rather than RGB and trained to accuracies comparable to their standard formulations. We improve upon these pioneering efforts in two key ways: architecture and data augmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.894, + 0.869 + ], + "angle": 0, + "content": "Adapting a CNN architecture designed for RGB inputs to instead receive DCT is nontrivial. The DCT representation of an \\( H \\times W \\times 3 \\) RGB image consists of a \\( \\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8 \\) tensor of luma data and two \\( \\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8 \\) tensors of chroma data. The CNN architecture must be modified both to accept lower-resolution inputs (e.g. by skipping the first few stages of a ResNet50 and adding capacity to later stages) and to accept heterogeneously-sized luma and chroma data (e.g. by encoding them with separate pathways)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.873, + 0.892, + 0.889 + ], + "angle": 0, + "content": "We overcome these challenges by using Vision Trans" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.874, + 0.434, + 0.888 + ], + "angle": 0, + "content": "\\(^{1}\\)Code available at https://github.com/JeongsooP/RGB-no-more" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.521, + 0.951 + ], + "angle": 0, + "content": "22334" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "formers (ViTs) [5] rather than CNNs. ViTs use a patch embedding layer to encode non-overlapping image patches into vectors, which are processed using a Transformer [6]. This is a perfect match to DCT representations, which also represent non-overlapping RGB image patches as vectors. We show that ViTs can be easily adapted to DCT inputs by modifying only the initial patch embedding layer and leaving the rest of the architecture unchanged." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.378 + ], + "angle": 0, + "content": "Data augmentation is critical for training accurate networks; this is especially true for ViTs [7-9]. However, standard image augmentations such as resizing, cropping, flipping, color jittering, etc. are expressed as transformations on RGB images; prior work [1,2] on neural networks with DCT inputs thus implement data augmentation by converting DCT to RGB, augmenting in RGB, then converting back to DCT before passing the image to the network. This negates all of the potential training-time efficiency gains of using DCT representations; improvements can only be realized during inference when augmentations are not used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.498 + ], + "angle": 0, + "content": "We overcome this limitation by augmenting DCT image representations directly, avoiding any DCT to RGB conversions during training. We show how all image augmentations used by RandAugment [10] can be implemented on DCT representations. Some standard augmentations such as image rotation and shearing are costly to implement in DCT, so we also introduce several new augmentations which are natural for DCT." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Using these insights, we train ViT-S and ViT-Ti models on ImageNet [11, 12] which match the accuracy of their RGB counterparts. Compared to an RGB equivalent, our ViT-Ti model is up to \\(39.2\\%\\) faster per training iteration and \\(17.9\\%\\) faster during inference. We believe that these results demonstrate the benefits of neural networks that ingest frequency-domain image representations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.617, + 0.22, + 0.633 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Training in the frequency domain is extensively explored in the recent studies. They consider JPEG [1, 2, 13-21], DCT [22-29] or video CODECs [30-33] with a primary focus on increasing the throughput of the model by skipping most of the decoding steps. Many of these works base their model architecture on CNNs. However, adapting CNNs to accept frequency input requires nontrivial modification to the architecture [1,2,17,18,30]. More recent studies [34,35] explore training from a neural compressor [36-45] instead of an existing compression algorithms [46-49]. This approach, however, requires transcoding the existing data to their neural compressed format, increasing overhead. We instead use Vision Transformers [5, 7, 8, 50] on the JPEG-encoded data. Our approach has two advantages: (1) patchwise architecture of ViTs is better suited for existing compression algorithms, (2) does not require any transcoding; it can work on any JPEG images." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.895, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.222, + 0.894, + 0.265 + ], + "angle": 0, + "content": "Figure 2. Process of applying \\(8 \\times 8\\) DCT to the input image. The input image is sliced into \\(8 \\times 8\\) patches and the DCT is applied to each patch. The DCT bases are shown on the right." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Data augmentation directly on the frequency domain has been studied in several works. Gueguen et al. [1] suggested augmenting on RGB and converting back to DCT. Wiles et al. [34] used an augmentation network that is tailored towards their neural compressor. Others focus on a more classical approach such as sharpening [51-57], resizing [58-65], watermarking [66-72], segmentation [73-77], flip and 90-degree rotation [21, 78], scalar operations [79], and forgery detection [80-82] via analyzing the properties of JPEG and DCT. However, to our knowledge, no other works have thoroughly studied the effect of DCT augmentation during frequency-domain training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Speeding up ViTs has been rigorously studied. These either utilize CNN-hybrid architectures to reduce computation [83-89], speed up attention by sparsifying [90-93], linearizing [94, 95], or through other techniques such as pruning [96-99], bottlenecking [100], or approximation [101]. While we only consider the plain ViT architecture in this paper, we want to emphasize that faster data loading is imperative to fully take advantage of these speed-ups as models can only infer as fast as the data loading speed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.63, + 0.629 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Here, we discuss Discrete Cosine Transform (DCT) and JPEG compression process. They are crucial to designing a model and DCT data augmentations in the later sections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.892, + 0.774 + ], + "angle": 0, + "content": "Discrete cosine transform decomposes a finite data sequence into a sum of discrete-frequency cosine functions. It is a transformation from the spatial domain to the frequency domain. We will focus on \\(8 \\times 8\\) DCT since it is a transform used in JPEG. Let \\(x \\in \\mathbb{R}^{8 \\times 8}\\) be a \\(8 \\times 8\\) image patch. Then its DCT transform \\(X \\in \\mathbb{R}^{8 \\times 8}\\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.777, + 0.892, + 0.825 + ], + "angle": 0, + "content": "\\[\nX _ {u, v} = \\frac {\\alpha_ {u} \\alpha_ {v}}{4} \\sum_ {m, n} x _ {m, n} \\cos \\left[ \\frac {\\pi (2 m + 1) u}{1 6} \\right] \\cos \\left[ \\frac {\\pi (2 n + 1) v}{1 6} \\right] \\tag {3.1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Where \\(\\alpha_{i} = 1 / \\sqrt{2}\\) if \\(i = 0\\), else 1, \\(u,v,m,n\\in [0..7]\\). Figure 2 shows how the DCT is applied to an image in JPEG. The original image patch can be reconstructed by a weighted sum of the DCT bases (Fig. 2) and their corresponding coefficients \\(X_{u,v}\\). For the standard JPEG setting," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.521, + 0.951 + ], + "angle": 0, + "content": "22335" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.47, + 0.315 + ], + "angle": 0, + "content": "Figure 3. A simplified JPEG compression process. An RGB image is first converted to YCbCr, then transformed to DCT space. They are then encoded into binary codes and written to disk. Decoding follows the inverse of this process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.468, + 0.388 + ], + "angle": 0, + "content": "the pixel-space min/max value of \\([-128, 127]\\), is scaled up by \\(8 \\times\\) to \\([-1024, 1016]\\). The proof of this property is shown in the supplementary material. This property is necessary to implement several DCT augmentations in Sec. 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.468, + 0.436 + ], + "angle": 0, + "content": "JPEG [46, 47, 102] is a widely used compression algorithm that is designed to encode images generated by digital photography. The encoding process is as follows:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.444, + 0.381, + 0.458 + ], + "angle": 0, + "content": "(a) \\(H\\times W\\times 3\\) RGB image is given as input" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.459, + 0.377, + 0.473 + ], + "angle": 0, + "content": "(b) RGB is converted to YCbCr color space" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.473, + 0.403, + 0.49 + ], + "angle": 0, + "content": "(c) \\(\\mathrm{CbCr}\\) channels are downsampled to \\(\\frac{H}{2} \\times \\frac{W}{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.49, + 0.408, + 0.505 + ], + "angle": 0, + "content": "(d) Values are shifted from [0,255] to [-128,127]" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.506, + 0.469, + 0.521 + ], + "angle": 0, + "content": "(e) DCT is applied to non-overlapping \\(8\\times 8\\) pixel patches" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.522, + 0.319, + 0.536 + ], + "angle": 0, + "content": "(f) DCT coefficients are quantized" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.537, + 0.469, + 0.552 + ], + "angle": 0, + "content": "(g) Run-length encoding(RLE) compresses the coefficients" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.553, + 0.437, + 0.568 + ], + "angle": 0, + "content": "(h) RLE symbols are encoded using Huffman coding" + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.444, + 0.469, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.469, + 0.679 + ], + "angle": 0, + "content": "A simplified illustration of this process is shown in Figure 3. YCbCr is a color space where \\(\\mathbf{Y}\\) represents luma (i.e. brightness) and \\(\\mathrm{Cb}\\), \\(\\mathrm{Cr}\\) signifies chroma (i.e. color) of the image. Step (e) produces a data of size \\(\\mathbf{Y} \\in \\mathbb{R}^{1 \\times \\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8}\\), \\(\\mathbf{U} \\in \\mathbb{R}^{2 \\times \\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8}\\) for \\(\\mathbf{Y}\\) and \\(\\mathrm{CbCr}\\) channel respectively. These \\(8 \\times 8\\) DCT coefficients are referred to as DCT Blocks in the later sections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Compute cost to decode JPEG can be analyzed by counting the number of operations (OPs) for the inverse of the above process. Consider decoding a single \\(8 \\times 8\\) patch. Our proposed scheme decodes step (h) - (f) with a computation cost of \\(3N_{s} + 128\\) OPs where \\(N_{s} \\in [1..64]\\): number of RLE symbols. Full JPEG decoding, on the other hand, requires \\(3N_{s} + 1717\\) OPs. If we suppose \\(N_{s} = 32\\), then the compute cost is 224 and 1813 OPs respectively, where our scheme theoretically saves computation by \\(87.6\\%\\). The details of these values are shown in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.266, + 0.86 + ], + "angle": 0, + "content": "4. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Designing a neural network that works on JPEG-encoded DCT coefficients can be challenging. In Sec. 3, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.287 + ], + "angle": 0, + "content": "showed that JPEG downsamples \\(\\mathrm{CbCr}\\) channels to \\(\\frac{H}{2} \\times \\frac{W}{2}\\). This spatial disparity must be addressed before training in DCT. An existing work by Gueguen et al. [1] suggested several new CNN architectures which include (1) upsampling, (2) downsampling, and (3) late-concatenation. The first two architectures either upsample \\(\\mathrm{CbCr}\\) to match the dimension of Y or downsample Y to match \\(\\mathrm{CbCr}\\). However, doing so results in (1) redundant computation or (2) loss of information due to resizing. The third approach, late-concatenation, computes them separately and concatenates them further down the network. However, this requires substantial modification of the CNN architecture, making adaptation to existing models difficult." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.392 + ], + "angle": 0, + "content": "We believe that ViTs are better suited to deal with this unique characteristic of JPEG. Vision transformers work on patches of an image [5, 7-9]. Considering that JPEG DCT already extracts \\(8 \\times 8\\) patches from an image (Sec. 3 (e)), we can employ them by modifying only the initial embedding layer. This allows easier integration into other ViTs as the rest of the architecture can remain untouched." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.469 + ], + "angle": 0, + "content": "Therefore, in this section, we propose several patch-embedding strategies that are plausible solutions to this problem. These modified patch embedding layers are illustrated in Fig. 4. The architecture that follows is identical to the plain ViT defined in [5,7,50]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.892, + 0.638 + ], + "angle": 0, + "content": "Grouped embedding generates embeddings by grouping the \\(8 \\times 8\\) DCT blocks together from the corresponding patch position. Consider a DCT input \\(\\mathbf{Y}\\), \\(\\mathbf{U}\\) defined in Sec. 3. Grouped embedding collects DCT blocks such that for patch size \\(p^2\\), \\(\\mathbf{Y} \\to \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}\\) and \\(\\mathbf{U} \\to \\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{2p^2}{4}}\\) where the channel and block size are flattened to the last dimension. Then, this is concatenated along the last axis as \\((\\mathbf{Y}_r, \\mathbf{U}_r) \\to \\mathbf{Y}\\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{3p^2}{2}}\\) which will then be embedded as \\(\\mathbf{z}: \\mathbf{Y}\\mathbf{U}_r \\to \\mathbf{z} \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times E}\\) where \\(\\mathbf{z}\\) is the generated embedding and \\(E\\) is the embedding size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.814 + ], + "angle": 0, + "content": "Separate embedding generates separate embeddings for each DCT block in a patch. A DCT input \\(\\mathbf{Y},\\mathbf{U}\\) is reshaped as \\(\\mathbf{Y}\\rightarrow \\mathbf{Y}_r\\in \\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{p^2}{64}\\times 64},\\mathbf{U}\\rightarrow \\mathbf{U}_r\\in\\) \\(\\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{2p^2}{4\\cdot 64}\\times 64}\\) which is embedded separately for each block: \\((\\mathbf{Y}_r,\\mathbf{U}_r)\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times \\frac{3p^2}{2\\cdot 64}\\times \\frac{E}{NB}}\\) where \\(N_{B} =\\) number of blocks \\(= \\frac{3p^2}{2\\cdot 64}\\). This is then mixed using a linear layer to generate a final embedding \\(\\mathbf{z}\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times E}\\). Our intuition behind this strategy is that the information each block holds might be critical, thus training a specialized linear layer for each block could yield better results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.877 + ], + "angle": 0, + "content": "Concatenated embedding embeds and concatenates the DCT blocks from \\(\\mathbf{Y}\\), \\(\\mathbf{U}\\) separately. Our intuition is that since \\(\\mathbf{Y}\\) and \\(\\mathbf{U}\\) represent different information (luma and chroma), designing specialized layers that handle each in-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.868, + 0.901 + ], + "angle": 0, + "content": "2Assume \\(p = 16n,n\\in \\mathbb{N}\\) .For \\(p < 16\\) , check the supplementary." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.519, + 0.95 + ], + "angle": 0, + "content": "22336" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.092, + 0.852, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Figure 4. Proposed embedding strategies. We first collect \\(8 \\times 8\\) DCT blocks until it matches the patch size. Then, these blocks can be embedded using one of the strategies. Grouped embedding groups all of the collected blocks and embeds them together. Separate embedding embeds each block separately and mixes it. Concatenated embedding embeds \\(\\mathbf{Y}\\) and \\(\\mathbf{U}\\) separately and concatenates them." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.368, + 0.473, + 0.496 + ], + "angle": 0, + "content": "formation separately may be necessary. However, this generates more embeddings per image patch than the plain model. To keep the overall size even, we reduce the size of each embedding to 2/3. An embedding formula is \\(\\mathbf{Y} \\rightarrow \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}\\), \\(\\mathbf{U} \\rightarrow \\mathbf{U}_r \\in \\mathbb{R}^{2 \\times \\frac{H}{2p} \\times \\frac{W}{2p} \\times p^2}\\), which is then embedded separately per channel type: \\(\\mathbf{Y}_r \\rightarrow \\mathbf{z}_Y \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times \\frac{2E}{3}}\\), \\(\\mathbf{U}_r \\rightarrow \\mathbf{z}_U \\in \\mathbb{R}^{\\frac{2HW}{4p \\cdot p} \\times \\frac{2E}{3}}\\) then concatenated \\((\\mathbf{z}_Y, \\mathbf{z}_U) \\rightarrow \\mathbf{z} \\in \\mathbb{R}^{\\frac{3HW}{2p \\cdot p} \\times \\frac{2E}{3}}\\) to generate an embedding \\(\\mathbf{z}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.473, + 0.71 + ], + "angle": 0, + "content": "Sub-block conversion [64] can be applied as an alternate way to embed a patch. Consider ViT architecture of patch size 16. For simplicity, assume only the Y channel is present. To form a patch size of \\(16 \\times 16\\), four \\(8 \\times 8\\) DCT blocks have to be grouped together. One strategy is to embed these directly through the linear layer. Another approach is to convert them into a single \\(16 \\times 16\\) block and embed them. In other words, we embed the DCT patches from a \\(16 \\times 16\\) DCT. There exists a way to efficiently extract these \\(16 \\times 16\\) DCT from the smaller \\(8 \\times 8\\) DCT blocks and vice versa known as sub-block conversion [64]. This technique can allow us to extract a native DCT patch of different sizes, potentially yielding better results. We also use this technique to implement several augmentations in Sec. 5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.267, + 0.74 + ], + "angle": 0, + "content": "5. DCT Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.841 + ], + "angle": 0, + "content": "Data augmentation has been a vital component in training robust networks [10, 103-108]. However, augmenting the DCT, as well as training with it, has not been studied in depth. There exist several prior works for some augmentations such as sharpening or resizing as discussed in Sec. 2, but most other RGB augments lack their DCT counterparts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Existing work by Gueguen et al. [1] proposed converting DCT to RGB, augmenting in RGB, and converting it back to DCT. However, this incurs expensive RGB/DCT conversion as shown in Sec. 3. More recent work by Wiles et" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.428 + ], + "angle": 0, + "content": "al. [34] used a specialized augmentation network that augments their neural-compressed format. Doing so, however, sacrifices versatility as it requires training and can't be reliably generalized to other resolutions or data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.565 + ], + "angle": 0, + "content": "Our approach is different. We instead implement augmentations directly on DCT by analyzing its properties. That way, we can avoid converting to RGB or relying on a trained augmentation network. In other words, our method is fast, flexible, and works on virtually any data, so long as it is represented in DCT. Thus, in this section, we implement all augmentations used in RandAugment [10] as well as suggest new augmentations that are meaningful for DCT. We mark the ones we suggest using an asterisk(*)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.671 + ], + "angle": 0, + "content": "There are largely two different types of DCT augmentation: photometric and geometric. Each of which uses different key properties of the DCT. While these augmentations are not meant to precisely reproduce RGB augmentations, most of our implementations approximate the RGB counterparts reasonably well. The overview of the augmentations and their similarity metrics are shown in Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.742, + 0.695 + ], + "angle": 0, + "content": "5.1. Photometric augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.778 + ], + "angle": 0, + "content": "Photometric augmentation alters a metric of an image, which includes brightness or sharpness. Our implementation of this can be roughly categorized into two: DC component-based and frequency component-based augmentation. Both use the attributes of a DCT coefficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.885 + ], + "angle": 0, + "content": "DC Component-based augmentation only alters the DCT coefficient without frequency \\((X_{0,0})\\), which is simply a scaled sum of all pixel values in the block (Eq. (3.1)). Altering this value will affect all pixels in the block evenly. This property can be used in two ways – either when we have to modify a value uniformly across all pixels, or when we have to approximate a value of the pixels in a block." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Brightness augmentation alters the brightness of the im" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.519, + 0.951 + ], + "angle": 0, + "content": "22337" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.089, + 0.44, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.213, + 0.438, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.47, + 0.389 + ], + "angle": 0, + "content": "Figure 5. A visualization of different DCT augmentation types. Orange-colored coefficients are augmented and saved as blue. The bottom two examples illustrate Translate and Resize." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.469, + 0.478 + ], + "angle": 0, + "content": "age. Considering that the image is represented in YCbCr color space, we can implement this augmentation by simply modifying the DC component of the Y channel. Let \\(Y_{u,v}^{h,w}\\) denote a \\(u\\), \\(v\\)-th DCT coefficient of Y at block position \\(h\\), \\(w\\). Then our implementation \\(f\\) is the following where \\(t \\in \\mathbb{R}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.481, + 0.469, + 0.51 + ], + "angle": 0, + "content": "\\[\nf _ {u, v}: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}Y _ {0, 0} ^ {h, w} + t \\cdot \\text {m e a n} (\\operatorname {a b s} \\left(Y _ {0, 0}\\right))&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.469, + 0.649 + ], + "angle": 0, + "content": "Contrast modifies the distance between the bright and dark values in the image. Since DCT coefficients are zero-centered by design (Sec. 3 (d)) and the brightness of a block can be approximated using the DC component \\( Y_{0,0} \\), we can categorize the non-negative component as 'bright' and the negative component as 'dark'. Therefore, multiplying \\( Y_{0,0} \\) with \\( t \\in [0,\\infty) \\) can adjust the contrast of the image. The implementation is \\( f:Y_{0,0}^{h,w} \\to tY_{0,0}^{h,w} \\). Similarly, Equalize applies histogram equalization to \\( Y_{0,0} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.65, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Color (Saturation) augmentation apply the same equation of Contrast to \\( U \\) (DCT coefficient of \\( \\mathrm{CbCr} \\)), instead of \\( Y \\). This augments the saturation as illustrated in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.469, + 0.786 + ], + "angle": 0, + "content": "AutoContrast scales the values so that the brightest and darkest value in an image becomes the brightest and darkest possible value. These values are approximated using \\( X_{0,0} \\) in the same way as Contrast. In Sec. 3, we showed that the min/max value of the DCT in JPEG is \\([-1024, 1016]\\). Thus, our implementation \\( f \\) is as follows." + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.788, + 0.468, + 0.837 + ], + "angle": 0, + "content": "\\[\nf: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}\\frac {Y _ {0 , 0} ^ {h , w} - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)}{\\operatorname* {m a x} \\left(Y _ {0 , 0}\\right) - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)} \\cdot 2 0 4 0 - 1 0 2 4&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.838, + 0.469, + 0.868 + ], + "angle": 0, + "content": "AutoSaturation* applies the formula in AutoContrast to \\( U \\). This allows the DCT to utilize the full range of the color." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Frequency component-based augmentation uses non-DC components \\((X_{u,v}, u, v \\neq 0)\\). Altering the amplitude of" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "these changes the intensity of the corresponding cosine signal in the pixel space. Here, we designed three augmentations each affecting frequency differently." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Sharpness augmentation adjusts a sharpness of an image. Typically in RGB, this utilizes a convolution kernel to achieve such an effect. However, in DCT, several studies show that this can be implemented by adjusting the frequency components of the DCT [51-57]. They show that sharper images will generally have a higher frequency as there are more sudden changes around the sharp edges. Using this property, we implement Sharpness by linearly altering the frequency components. If \\( t > 0 \\), the following equation sharpens the image. Otherwise, it blurs it." + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.292, + 0.892, + 0.312 + ], + "angle": 0, + "content": "\\[\nf: Y _ {u, v} ^ {h, w} \\rightarrow Y _ {u, v} ^ {h, w} \\cdot \\max \\left(1 + \\frac {t u}{7}, 0\\right) \\max \\left(1 + \\frac {t v}{7}, 0\\right) \\tag {5.3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.391 + ], + "angle": 0, + "content": "MidfreqAug* augmentation is similar to sharpness but instead of peaking the augmentation strength at the highest frequency \\((u, v = 7)\\), we peaked it at the middle frequency \\((u, v \\in \\{3, 4\\})\\). We expect the results to be similar to Sharpness, but possibly with less noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.469 + ], + "angle": 0, + "content": "FreqEnhance* multiplies all frequency components uniformly with a positive factor \\( t \\in [0, \\infty) \\). The augmentation is simply \\( f: Y_{u,v}^{h,w} \\to tY_{u,v}^{h,w} \\), \\( u, v \\neq 0 \\). We believe that this allows us to see the impact of a frequency component with respect to the model performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Photometric - special case. There are some augmentations that do not categorize into either of the above augmentations. Invert simply flips the sign of all DCT coefficients. This is because the coefficients are virtually zero-centered. Posterize quantizes \\( X_{0,0} \\) to lower bits. Solarize uses \\( X_{0,0} \\) to determine whether or not the DCT block should be inverted. SolarizeAdd adds a preset value to \\( X_{0,0} \\) if it is below threshold. Grayscale replaces \\( U \\) with zeros, removing color information. ChromaDrop* instead drops the Cb or Cr channel randomly, removing only half of the color information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.727, + 0.658 + ], + "angle": 0, + "content": "5.2. Geometric augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Geometric augmentation modifies the image plane geometrically. An example of this augmentation includes translation, rotation, or shearing. There are two main subcategories of geometric augmentation – block-wise and subblock conversion-based augmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.892, + 0.823 + ], + "angle": 0, + "content": "Block-wise augmentation treats the DCT block positions similarly to pixel positions. Translate can be implemented by moving the positions \\( h, w \\) of each \\( X^{h,w} \\) and filling the blank with zeros. Cutout follows a similar process where we crop blocks out and fill them with zeros." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Flipping the DCT coefficients utilize the fact that odd-column or odd-row DCT bases are odd-symmetric [78]. Flip is performed by flipping the position of the blocks and then flipping the individual DCT blocks. Define \\( R = \\mathrm{diag}(1, -1, 1, -1, \\ldots, -1) \\) of matching size. Then, the per" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.519, + 0.951 + ], + "angle": 0, + "content": "22338" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.891, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.313, + 0.893, + 0.37 + ], + "angle": 0, + "content": "Figure 6. A visualization of RGB augmentations and their DCT counterparts. \\(/S\\) or \\(/B\\) indicates 'sharpen' or 'blur' on sharpness-related augmentations. Resize has been compared where they scale the image up by 2. PSNR and SSIM are calculated for each DCT augmentation. We observe that most DCT augmentations resemble RGB augmentations. Augmentations such as grayscale, cutout, and flip are identical to RGB. However, other augmentations including equalize and contrast are not exactly equal to RGB." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.383, + 0.329, + 0.399 + ], + "angle": 0, + "content": "block flipping operation is as follows." + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.401, + 0.469, + 0.434 + ], + "angle": 0, + "content": "\\[\nf ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}X ^ {h, w} R&\\text {i f h o r i z o n t a l f l i p}\\\\R X ^ {h, w}&\\text {i f v e r t i c a l f l i p}\\end{array}\\right\\} \\tag {5.4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.436, + 0.469, + 0.48 + ], + "angle": 0, + "content": "Rotate90 is implemented using a transpose with flipping [78]. We first rotate the block position \\( h, w \\) and rotate each \\( X^{h,w} \\) by 90 degrees. The per-block rotation is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.482, + 0.469, + 0.517 + ], + "angle": 0, + "content": "\\[\nf ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}(X ^ {h, w}) ^ {T} R&\\text {c l o c k w i s e}\\\\R (X ^ {h, w}) ^ {T}&\\text {c o u n t e r - c l o c k w i s e}\\end{array}\\right\\} \\tag {5.5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.469, + 0.638 + ], + "angle": 0, + "content": "Sub-block conversion-based augmentation uses the relationship between the DCT block and its smaller sub-blocks. This allows us to efficiently calculate the DCT of different DCT bases without the need to do inverse transform (e.g. \\(8 \\times 8\\) DCT \\(\\leftrightarrow\\) \\(32 \\times 32\\) DCT). The relationship studied by Jiang and Feng [64] is as follows. Let \\(X_{N \\times M}^{h,w}\\) be the DCT coefficient block of \\(N \\times M\\) DCT at block position \\(h, w\\). Then, there exists a conversion matrix \\(A\\) such that:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.64, + 0.469, + 0.692 + ], + "angle": 0, + "content": "\\[\nX _ {L N \\times M N} = A _ {L, N} \\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] A _ {M, N} ^ {T} \\tag {5.6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.469, + 0.754 + ], + "angle": 0, + "content": "Where \\( A_{L,N} \\) is a \\( LN \\times LN \\) matrix that converts the \\( L \\) number of \\( N \\) 1-D DCT blocks into a single \\( LN \\) DCT block. The decomposition of \\( X_{LN \\times MN} \\) DCT blocks into \\( L \\times M \\) DCT blocks of \\( X_{N \\times N} \\) follows a similar process:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.755, + 0.469, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] = A _ {L, N} ^ {- 1} X _ {L N \\times M N} A _ {M, N} ^ {- 1 ^ {T}} \\tag {5.7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.442, + 0.825 + ], + "angle": 0, + "content": "Derivation of \\(A\\) is given in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Resize can be implemented if we can understand how to resize individual DCT blocks. Suppose that there exists a way to resize \\( X_{4 \\times 4} \\) to \\( X_{8 \\times 8} \\) by padding. Then, to up-sample \\( X_{8 \\times 8} \\) while keeping the \\( 8 \\times 8 \\) sliced structure of JPEG DCT, we can first decompose \\( X_{8 \\times 8} \\) into four \\( X_{4 \\times 4} \\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.383, + 0.892, + 0.474 + ], + "angle": 0, + "content": "using sub-block conversion. Then, we can individually resize each \\( X_{4 \\times 4} \\) to \\( X_{8 \\times 8} \\). This gives us four \\( X_{8 \\times 8} \\) blocks upsampled from one \\( X_{8 \\times 8} \\). Downsampling can follow a similar process. We first combine four adjacent \\( X_{8 \\times 8} \\) into a single \\( X_{16 \\times 16} \\) using sub-block conversion. Then, we resize \\( X_{16 \\times 16} \\) down to \\( X_{8 \\times 8} \\). This process is shown in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.476, + 0.892, + 0.551 + ], + "angle": 0, + "content": "This technique to resize each individual DCT block is known as sub-band approximation and has been studied by Mukherjee and Mitra [65]. Their work shows that if \\( X_{N\\times N}(k,l) \\) is a \\( (k,l) \\)-th coefficient of a \\( X_{N\\times N} \\) block, then, the approximate relationship is:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.553, + 0.891, + 0.597 + ], + "angle": 0, + "content": "\\[\nX _ {L N \\times M N} (k, l) \\approx \\left\\{ \\begin{array}{l l} \\sqrt {L M} X _ {N \\times N} (k, l) & 0 \\leq k, l \\leq N - 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5.8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Using this, we can upsample \\( L \\times M \\) times by resizing each \\( X_{N \\times N} \\) to \\( X_{LN \\times MN} \\) and decomposing them to \\( L \\times M \\) \\( X_{N \\times N} \\). \\( L \\times M \\) downsampling combines \\( L \\times M \\) adjacent \\( X_{N \\times N} \\) to form \\( X_{LN \\times MN} \\) and resize it to \\( X_{N \\times N} \\). An arbitrary resizing of \\( \\frac{P}{Q} \\times \\frac{R}{S} \\) can be done by first upsampling \\( P \\times R \\) times and downsampling the result by \\( Q \\times S \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Rotate is implemented using the rotational property of the Fourier transform [112-114]. This property denotes that the Fourier transform of a rotated function is equal to rotating the Fourier transform of a function. To use this property, we slightly alter the Eq. (5.6). Instead of combining the blocks to \\(X_{LN\\times MN}\\) DCT, we combine them to the discrete Fourier transform (DFT) coefficients. Define \\(D_{N\\times N}\\) as the DFT coefficient block of size \\(N\\times N\\). Then, the rotation is done by combining \\(L\\times M X_{N\\times N}\\) to \\(D_{LN\\times MN}\\), rotating it, and decomposing it back to \\(L\\times M X_{N\\times N}\\) using the modified Eq. (5.7). This can be further improved using the lossless 90-degree rotation to minimize the lossy arbitrary-degree rotation. The details of this DFT conversion are shown in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.519, + 0.951 + ], + "angle": 0, + "content": "22339" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.086, + 0.872, + 0.326 + ], + "angle": 0, + "content": "
ArchitectureColor SpaceAug. SpaceEmbed. FLOPsDecodeAugmentTrain Data LoadModel Fwd/BwdTrain PipelineEval Data LoadModel FwdEval PipelineVal Acc (%)
(↓ Performance)Latency per img (ms)Throughput per GPU (FPS)
ViT-Ti [50]RGBRGB28.9M3.683.08571.5832.8493.8641.42898.7638.074.1
ViT-S [50]RGBRGB57.8M3.623.01558.0355.7352.1660.21174.5610.576.5
ViT-S* [50]RGBRGB57.8M3.692.63574.7716.8489.0680.32335.1644.275.6
SwinV2-T* [109]RGBRGB20.8M3.612.98489.8231.5231.6614.8809.5516.279.0*
ResNet50 [110]RGBRGB------688.21226.8639.176.1
JPEG-TiDCTDCT16.1M1.422.62816.2857.2687.6775.32847.5752.375.1
JPEG-SDCTDCT30.5M1.492.40824.8364.3360.5782.91139.7711.176.5
JPEG-S*DCTDCT30.5M1.422.37821.7764.0665.8793.12384.1711.875.8
JPEG-S*◇DCTRGB to DCT30.5M3.625.98425.3751.9372.3748.72382.4721.076.3
SwinV2-T*DCTDCT13.0M1.402.47752.0241.9235.9664.2824.9578.079.4
ResNet50◇ [1] [2]DCTRGB to DCT------785.75969.8753.576.1
(↓ Improvements)(Reduction▼)(Speed-ups▲)
JPEG-Ti vs ViT-Ti-44.4 %-61.4 %-14.9 %+42.8 %+2.9 %+39.2 %+20.9 %-1.8 %+17.9 %+1.0
JPEG-S vs ViT-S-47.2 %-58.8 %-20.3 %+47.8 %+2.4 %+2.4 %+18.6 %-3.0 %+16.5 %+0.0
JPEG-S* ViT-S*-47.2 %-61.5 %-9.9 %+43.0 %+6.6 %+36.2 %+16.6 %+2.1 %+10.5 %+0.2
JPEG-S* vs JPEG-S*◇+0.0 %-60.8 %-60.4 %+93.2 %+1.6 %+78.8 %+5.9 %+0.1 %-1.3 %-0.5
SwinV2-T* (DCT vs RGB)-37.7 %-61.2 %-17.1 %+53.5 %+4.5 %+1.9 %+8.0 %+1.9 %+12.0 %+0.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.335, + 0.895, + 0.406 + ], + "angle": 0, + "content": "Table 1. Model throughput per GPU for each pipeline element and accuracy. Embed. FLOPs shows the FLOPs needed to generate patch embeddings. Decode and Augment indicates the per-image processing latency during training. Val Acc shows the accuracy on the ImageNet validation set. 'JPEG-' prefix indicates that it is a ViT trained using JPEG DCT coefficients. Model with \\* symbol is trained using mixed precision [111]. \\(\\diamondsuit\\) models are trained using the pipeline suggested by Gueguen et al. [1]. \\*SwinV2 models are trained using the same recipe as in [50] for a fair comparison. The details of these measurements are shown in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.419, + 0.471, + 0.466 + ], + "angle": 0, + "content": "Shear is identically implemented as Rotate where instead of rotating \\( D_{LN \\times MN} \\), we shear it. This is because we can apply the same property [112] for each axis." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.21, + 0.496 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.612 + ], + "angle": 0, + "content": "In this section, we compare our models trained in DCT space with the RGB models. We show that the DCT models achieve similar accuracy but perform notably faster than the RGB models. First, we compare the throughput and accuracy of the RGB and DCT models. Then, we compare the DCT embedding strategies covered in Sec. 4. Lastly, we conduct an ablation study on the DCT data augmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. All experiments are conducted with PyTorch [115]. We extract DCT coefficients using a modified version of libjpeg [116] and TorchJPEG [117]. All timing measurements are performed using \\(2 \\times\\) A40 GPUs and 8 cores from an Intel Xeon 6226R CPU, and all throughputs are reported per GPU. We used fvcore [118] to obtain the FLOPs. All models are trained on ImageNet [11, 12], which we resize on-disk to \\(512 \\times 512\\) prior to training. We re-implement a ViT training pipeline in PyTorch, carefully following the recipe suggested by Beyer et al. [50] which uses random resized crop, random flip, RandAugment [10] and Mixup [119] with a global batch size of 1024. All plain ViT models are trained with a patch size of 16. SwinV2 model [109] uses a patch size of 4, a window size of 8, and a global batch size of 512. '-S' models are trained for 90 epochs. '-Ti' and SwinV2 models are instead trained for 300 epochs using the same recipe in [50]. Following [50], we randomly sample \\(1\\%\\) of the train set to use for validation. Our RGB ResNet-50 baseline uses the V1" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.419, + 0.895, + 0.481 + ], + "angle": 0, + "content": "weights from Torchvision [110]. There exist recent works with improved training recipes for ResNets [120, 121], but this is orthogonal to our work. The DCT ResNet-50 uses the model proposed by Gueguen et al. [1] and Xu et al. [2]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.634, + 0.51 + ], + "angle": 0, + "content": "6.1. Main results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.748 + ], + "angle": 0, + "content": "The hyperparameter settings for the models are given in the supplementary material. Tab. 1 shows the comprehensive result from our experiment. Both the ViT and CNN models show equivalent accuracy to their RGB counterparts. However, loading directly from JPEG DCT reduces decoding latency by up to \\(61.5\\%\\). We see a similar effect on the augmentation latency to a lesser extent. Additionally, as the input size has been halved by JPEG (Sec. 3), we observe that the FLOPs needed to generate embeddings are reduced by up to \\(47.2\\%\\). These speed-ups boost throughput for DCT models. Most notably, our JPEG-Ti model showed \\(39.2\\%\\) and \\(17.9\\%\\) faster training and evaluation. Our augmentation scheme improves train data loading throughput by \\(93.2\\%\\) versus the one by Gueguen et al. [1], which must convert DCT to RGB, augment, and convert it back to DCT." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "While training as-is still reaps the benefits of faster data loading, we can observe that the JPEG-S model is bottlenecked by model forward and backward passes. One option is to employ mixed precision training [111]. This allows us to fully realize the data loading speed-ups by accelerating the model with minor accuracy loss. We observe that our JPEG-S model trained using mixed precision is \\(36.2\\%\\) faster during training time compared to the RGB counterpart. We believe most other faster models discussed in Sec. 2 will also benefit from this speed-up." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.939, + 0.52, + 0.951 + ], + "angle": 0, + "content": "22340" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.872, + 0.282 + ], + "angle": 0, + "content": "
PhotometricGeometricAccuracy
SubsetResizeDC basedFreq. basedSpecial caseBlock-wiseSub-block basedRGBDCT
(Avg. latency (ms) ↓)
RGB2.170.611.340.671.231.28--
DCT2.790.370.540.340.429.31--
(Ablation ↓)
All✓✓✓✓✓✓76.574.6
No sub-block✓✓✓✓✓✗76.275.1
No block-wise✓✓✓✓✗✗76.072.6
No Special-case✓✓✓✗✗✗76.373.3
No Freq. based✓✓✗✗✗✗75.974.2
No DC based✓✗✗✗✗✗74.475.5
Best Subset✓Brightness, Contrast, Color, AutoContrast, AutoSaturation, Sharpness, MidfreqAug, Posterize, Grayscale, ChromaDrop, Translate, Cutout, Rotate90✗76.5*76.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.292, + 0.895, + 0.322 + ], + "angle": 0, + "content": "Table 2. Data augmentation ablation study on ViT-S. At the bottom row, we report the best subset we found and train both the RGB and DCT models from it. *RGB accuracy is obtained with MidfreqAug removed, since it is analogous to Sharpness in RGB as shown in Fig. 6." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.331, + 0.429, + 0.426 + ], + "angle": 0, + "content": "
GroupedSeparateConcat.Sub-blockAcc
✓--✓76.5
-✓-✓74.7
--✓✓71.3
✓---74.6
-✓--73.8
--✓-71.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.434, + 0.471, + 0.465 + ], + "angle": 0, + "content": "Table 3. Embedding strategy ablation study on ViT-S. We see that grouped embedding with sub-block outperforms other strategies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.476, + 0.281, + 0.493 + ], + "angle": 0, + "content": "6.2. Embedding strategies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.683 + ], + "angle": 0, + "content": "To see which patch embedding scheme is most suitable for DCT, we performed an ablation study in Tab. 3. We ablate on the embedding strategies and the sub-block conversion technique discussed in Sec. 4 on ViT-S. The results show two things. One is that the simplest strategy-grouped embedding-is best, and that sub-block conversion is important to achieve high accuracy. We believe this indicates that (1) all blocks in an image patch relay information of that patch as a whole; they should not be separately inferred, and (2) it is more natural for the model to deduce the information in a patch if the sub-blocks are fused together. The best strategy is used throughout the DCT models in Tab. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.223, + 0.712 + ], + "angle": 0, + "content": "6.3. Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As discussed in Sec. 5, data augmentation is crucial to train a well-performing model. However, many existing studies [9, 10, 103-108] are tuned toward RGB augmentations; we cannot assume that the existing work's result would be consistent on DCT. In other words, some DCT augmentations could have a different impact on both the accuracy and throughput of the model compared to RGB. Therefore, we perform an ablation study on data augmentations discussed in Sec. 5 and report the result in Tab. 2. We perform ablation by varying the subset of augmentations used in RandAugment [10] on ViT-S. The experiment is performed separately for RGB and DCT with their re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.895, + 0.471 + ], + "angle": 0, + "content": "spective augmentation sets. The results show that while sub-block-based augmentations (e.g. rotate, shear) are prohibitively expensive to do directly on DCT, it is not as important to train a model. We report the best augmentation subset we found without sub-block-based augmentations at the bottom row. In addition, we train an RGB model using this subset and compare the accuracy. We can see that the RGB model performs identically to the DCT model, and the subset does not unfairly favor DCT over RGB models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.62, + 0.515 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.894, + 0.636 + ], + "angle": 0, + "content": "In this paper, we demonstrated that vision transformers can be accelerated significantly by directly training from the DCT coefficients of JPEG. We proposed several DCT embedding strategies for ViT, as well as reasonable augmentations that can be directly carried out on the DCT coefficients. The throughput of our model is considerably faster with virtually no accuracy loss compared to RGB." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.894, + 0.732 + ], + "angle": 0, + "content": "RGB has been widely used for as long as computer vision existed. Many computer vision schemes regard retrieving RGB as a necessary cost; they have not considered the potential of direct encoded-space training in-depth. We wanted to show the capability of this approach, as well as demonstrate that recovering RGB is not always necessary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Encoded-space training can be adapted to nearly all scenarios that require loading some compressed data from storage. From mobile devices to powerful data centers, there are no situations where they wouldn't benefit from faster loading speed. As we only considered the plain ViT architecture, there is still more to be gained by adapting our findings to the existing efficient architectures. Future studies may also consider a better augmentation strategy to improve the performance further. We hope that the techniques shown in this paper prove to be an adequate foundation for future encoded-space research." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.939, + 0.518, + 0.951 + ], + "angle": 0, + "content": "22341" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.469, + 0.17 + ], + "angle": 0, + "content": "[1] Lionel Gueguen, Alex Sergeev, Ben Kadlec, Rosanne Liu, and Jason Yosinski. Faster Neural Networks Straight from JPEG. Advances in Neural Information Processing Systems, 31, 2018. 1, 2, 3, 4, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.095, + 0.176, + 0.469, + 0.232 + ], + "angle": 0, + "content": "[2] Kai Xu, Minghai Qin, Fei Sun, Yuhao Wang, Yen-Kuang Chen, and Fengbo Ren. Learning in the frequency domain. 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NeurIPS, 2021. 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.939, + 0.52, + 0.951 + ], + "angle": 0, + "content": "22346" + } + ] +] \ No newline at end of file diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_origin.pdf b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..738cf71be4d3f8ad17f4491b50b56771199c8dd4 --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/2da81411-0f32-4a64-8564-8877ef6902a3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7013e7cc5ab5fc5281ef9c9dbcb021a76ada2f9054f1ce85aa0563e2d75d5994 +size 2925509 diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/full.md b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d24176d6f1e5b4ee3dfde2d7b902fc1e56bc0b1c --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/full.md @@ -0,0 +1,390 @@ +# RGB no more: Minimally-decoded JPEG Vision Transformers + +Jeongsoo Park Justin Johnson University of Michigan {jespark, justincj}@umich.edu + +# Abstract + +Most neural networks for computer vision are designed to infer using RGB images. However, these RGB images are commonly encoded in JPEG before saving to disk; decoding them imposes an unavoidable overhead for RGB networks. Instead, our work focuses on training Vision Transformers (ViT) directly from the encoded features of JPEG. This way, we can avoid most of the decoding overhead, accelerating data load. Existing works have studied this aspect but they focus on CNNs. Due to how these encoded features are structured, CNNs require heavy modification to their architecture to accept such data. Here, we show that this is not the case for ViTs. In addition, we tackle data augmentation directly on these encoded features, which to our knowledge, has not been explored in-depth for training in this setting. With these two improvements – ViT and data augmentation – we show that our ViT-Ti model achieves up to $39.2\%$ faster training and $17.9\%$ faster inference with no accuracy loss compared to the RGB counterpart. + +# 1. Introduction + +Neural networks that process images typically receive their inputs as regular grids of RGB pixel values. This spatial-domain representation is intuitive, and matches the way that images are displayed on digital devices (e.g. LCD panels with RGB sub-pixels). However, images are often stored on disk as compressed JPEG files that instead use frequency-domain representations for images. In this paper we design neural networks that can directly process images encoded in the frequency domain. + +Networks that process frequency-domain images have the potential for much faster data loading. JPEG files store image data using Huffman codes; these are decoded to (frequency-domain) discrete cosine transform (DCT) coefficients then converted to (spatial-domain) RGB pixels before being fed to the neural network (Fig. 1). Networks that process DCT coefficients can avoid the expensive DCT to RGB conversion; we show in Sec. 3 that this can reduce the theoretical cost of data loading by up to $85\%$ . Data is typi + +![](images/e392f363c8dd64c7baa17f7b9354a8c90944fb50cc480f5f9701b26a5f6b981f.jpg) +Figure 1. Our proposed training process. The typical process requires full decoding as well as patch extraction to train. In contrast, our process does not since the DCT coefficients are already saved in block-wise fashion. As ViTs work on image patches, we can directly feed these coefficients to the network. + +cally loaded by the CPU while the network runs on a GPU or other accelerator; more efficient data loading can thus reduce CPU bottlenecks and accelerate the entire pipeline. + +We are not the first to design networks that process frequency-domain images. The work of Gueguen et al. [1] and Xu et al. [2] are most similar to ours: they show how standard CNN architectures such as ResNet [3] and MobileNetV2 [4] can be modified to input DCT rather than RGB and trained to accuracies comparable to their standard formulations. We improve upon these pioneering efforts in two key ways: architecture and data augmentation. + +Adapting a CNN architecture designed for RGB inputs to instead receive DCT is nontrivial. The DCT representation of an $H \times W \times 3$ RGB image consists of a $\frac{H}{8} \times \frac{W}{8} \times 8 \times 8$ tensor of luma data and two $\frac{H}{16} \times \frac{W}{16} \times 8 \times 8$ tensors of chroma data. The CNN architecture must be modified both to accept lower-resolution inputs (e.g. by skipping the first few stages of a ResNet50 and adding capacity to later stages) and to accept heterogeneously-sized luma and chroma data (e.g. by encoding them with separate pathways). + +We overcome these challenges by using Vision Trans + +formers (ViTs) [5] rather than CNNs. ViTs use a patch embedding layer to encode non-overlapping image patches into vectors, which are processed using a Transformer [6]. This is a perfect match to DCT representations, which also represent non-overlapping RGB image patches as vectors. We show that ViTs can be easily adapted to DCT inputs by modifying only the initial patch embedding layer and leaving the rest of the architecture unchanged. + +Data augmentation is critical for training accurate networks; this is especially true for ViTs [7-9]. However, standard image augmentations such as resizing, cropping, flipping, color jittering, etc. are expressed as transformations on RGB images; prior work [1,2] on neural networks with DCT inputs thus implement data augmentation by converting DCT to RGB, augmenting in RGB, then converting back to DCT before passing the image to the network. This negates all of the potential training-time efficiency gains of using DCT representations; improvements can only be realized during inference when augmentations are not used. + +We overcome this limitation by augmenting DCT image representations directly, avoiding any DCT to RGB conversions during training. We show how all image augmentations used by RandAugment [10] can be implemented on DCT representations. Some standard augmentations such as image rotation and shearing are costly to implement in DCT, so we also introduce several new augmentations which are natural for DCT. + +Using these insights, we train ViT-S and ViT-Ti models on ImageNet [11, 12] which match the accuracy of their RGB counterparts. Compared to an RGB equivalent, our ViT-Ti model is up to $39.2\%$ faster per training iteration and $17.9\%$ faster during inference. We believe that these results demonstrate the benefits of neural networks that ingest frequency-domain image representations. + +# 2. Related Work + +Training in the frequency domain is extensively explored in the recent studies. They consider JPEG [1, 2, 13-21], DCT [22-29] or video CODECs [30-33] with a primary focus on increasing the throughput of the model by skipping most of the decoding steps. Many of these works base their model architecture on CNNs. However, adapting CNNs to accept frequency input requires nontrivial modification to the architecture [1,2,17,18,30]. More recent studies [34,35] explore training from a neural compressor [36-45] instead of an existing compression algorithms [46-49]. This approach, however, requires transcoding the existing data to their neural compressed format, increasing overhead. We instead use Vision Transformers [5, 7, 8, 50] on the JPEG-encoded data. Our approach has two advantages: (1) patchwise architecture of ViTs is better suited for existing compression algorithms, (2) does not require any transcoding; it can work on any JPEG images. + +![](images/1787745d3c6fd5d58f8411f401c0bcd11ddd1c874b2532e1f0463f8f87c4526f.jpg) +Figure 2. Process of applying $8 \times 8$ DCT to the input image. The input image is sliced into $8 \times 8$ patches and the DCT is applied to each patch. The DCT bases are shown on the right. + +Data augmentation directly on the frequency domain has been studied in several works. Gueguen et al. [1] suggested augmenting on RGB and converting back to DCT. Wiles et al. [34] used an augmentation network that is tailored towards their neural compressor. Others focus on a more classical approach such as sharpening [51-57], resizing [58-65], watermarking [66-72], segmentation [73-77], flip and 90-degree rotation [21, 78], scalar operations [79], and forgery detection [80-82] via analyzing the properties of JPEG and DCT. However, to our knowledge, no other works have thoroughly studied the effect of DCT augmentation during frequency-domain training. + +Speeding up ViTs has been rigorously studied. These either utilize CNN-hybrid architectures to reduce computation [83-89], speed up attention by sparsifying [90-93], linearizing [94, 95], or through other techniques such as pruning [96-99], bottlenecking [100], or approximation [101]. While we only consider the plain ViT architecture in this paper, we want to emphasize that faster data loading is imperative to fully take advantage of these speed-ups as models can only infer as fast as the data loading speed. + +# 3. Background + +Here, we discuss Discrete Cosine Transform (DCT) and JPEG compression process. They are crucial to designing a model and DCT data augmentations in the later sections. + +Discrete cosine transform decomposes a finite data sequence into a sum of discrete-frequency cosine functions. It is a transformation from the spatial domain to the frequency domain. We will focus on $8 \times 8$ DCT since it is a transform used in JPEG. Let $x \in \mathbb{R}^{8 \times 8}$ be a $8 \times 8$ image patch. Then its DCT transform $X \in \mathbb{R}^{8 \times 8}$ is given by: + +$$ +X _ {u, v} = \frac {\alpha_ {u} \alpha_ {v}}{4} \sum_ {m, n} x _ {m, n} \cos \left[ \frac {\pi (2 m + 1) u}{1 6} \right] \cos \left[ \frac {\pi (2 n + 1) v}{1 6} \right] \tag {3.1} +$$ + +Where $\alpha_{i} = 1 / \sqrt{2}$ if $i = 0$ , else 1, $u,v,m,n\in [0..7]$ . Figure 2 shows how the DCT is applied to an image in JPEG. The original image patch can be reconstructed by a weighted sum of the DCT bases (Fig. 2) and their corresponding coefficients $X_{u,v}$ . For the standard JPEG setting, + +![](images/db5c0a0489b16cdb18183e6456fbc4c136dd95f2d344b9e0a1d449cbd872faf7.jpg) +Figure 3. A simplified JPEG compression process. An RGB image is first converted to YCbCr, then transformed to DCT space. They are then encoded into binary codes and written to disk. Decoding follows the inverse of this process. + +the pixel-space min/max value of $[-128, 127]$ , is scaled up by $8 \times$ to $[-1024, 1016]$ . The proof of this property is shown in the supplementary material. This property is necessary to implement several DCT augmentations in Sec. 5. + +JPEG [46, 47, 102] is a widely used compression algorithm that is designed to encode images generated by digital photography. The encoding process is as follows: + +(a) $H\times W\times 3$ RGB image is given as input +(b) RGB is converted to YCbCr color space +(c) $\mathrm{CbCr}$ channels are downsampled to $\frac{H}{2} \times \frac{W}{2}$ +(d) Values are shifted from [0,255] to [-128,127] +(e) DCT is applied to non-overlapping $8\times 8$ pixel patches +(f) DCT coefficients are quantized +(g) Run-length encoding(RLE) compresses the coefficients +(h) RLE symbols are encoded using Huffman coding + +A simplified illustration of this process is shown in Figure 3. YCbCr is a color space where $\mathbf{Y}$ represents luma (i.e. brightness) and $\mathrm{Cb}$ , $\mathrm{Cr}$ signifies chroma (i.e. color) of the image. Step (e) produces a data of size $\mathbf{Y} \in \mathbb{R}^{1 \times \frac{H}{8} \times \frac{W}{8} \times 8 \times 8}$ , $\mathbf{U} \in \mathbb{R}^{2 \times \frac{H}{16} \times \frac{W}{16} \times 8 \times 8}$ for $\mathbf{Y}$ and $\mathrm{CbCr}$ channel respectively. These $8 \times 8$ DCT coefficients are referred to as DCT Blocks in the later sections. + +Compute cost to decode JPEG can be analyzed by counting the number of operations (OPs) for the inverse of the above process. Consider decoding a single $8 \times 8$ patch. Our proposed scheme decodes step (h) - (f) with a computation cost of $3N_{s} + 128$ OPs where $N_{s} \in [1..64]$ : number of RLE symbols. Full JPEG decoding, on the other hand, requires $3N_{s} + 1717$ OPs. If we suppose $N_{s} = 32$ , then the compute cost is 224 and 1813 OPs respectively, where our scheme theoretically saves computation by $87.6\%$ . The details of these values are shown in the supplementary material. + +# 4. Model Architecture + +Designing a neural network that works on JPEG-encoded DCT coefficients can be challenging. In Sec. 3, we + +showed that JPEG downsamples $\mathrm{CbCr}$ channels to $\frac{H}{2} \times \frac{W}{2}$ . This spatial disparity must be addressed before training in DCT. An existing work by Gueguen et al. [1] suggested several new CNN architectures which include (1) upsampling, (2) downsampling, and (3) late-concatenation. The first two architectures either upsample $\mathrm{CbCr}$ to match the dimension of Y or downsample Y to match $\mathrm{CbCr}$ . However, doing so results in (1) redundant computation or (2) loss of information due to resizing. The third approach, late-concatenation, computes them separately and concatenates them further down the network. However, this requires substantial modification of the CNN architecture, making adaptation to existing models difficult. + +We believe that ViTs are better suited to deal with this unique characteristic of JPEG. Vision transformers work on patches of an image [5, 7-9]. Considering that JPEG DCT already extracts $8 \times 8$ patches from an image (Sec. 3 (e)), we can employ them by modifying only the initial embedding layer. This allows easier integration into other ViTs as the rest of the architecture can remain untouched. + +Therefore, in this section, we propose several patch-embedding strategies that are plausible solutions to this problem. These modified patch embedding layers are illustrated in Fig. 4. The architecture that follows is identical to the plain ViT defined in [5,7,50]. + +Grouped embedding generates embeddings by grouping the $8 \times 8$ DCT blocks together from the corresponding patch position. Consider a DCT input $\mathbf{Y}$ , $\mathbf{U}$ defined in Sec. 3. Grouped embedding collects DCT blocks such that for patch size $p^2$ , $\mathbf{Y} \to \mathbf{Y}_r \in \mathbb{R}^{\frac{H}{p} \times \frac{W}{p} \times p^2}$ and $\mathbf{U} \to \mathbf{U}_r \in \mathbb{R}^{\frac{H}{p} \times \frac{W}{p} \times \frac{2p^2}{4}}$ where the channel and block size are flattened to the last dimension. Then, this is concatenated along the last axis as $(\mathbf{Y}_r, \mathbf{U}_r) \to \mathbf{Y}\mathbf{U}_r \in \mathbb{R}^{\frac{H}{p} \times \frac{W}{p} \times \frac{3p^2}{2}}$ which will then be embedded as $\mathbf{z}: \mathbf{Y}\mathbf{U}_r \to \mathbf{z} \in \mathbb{R}^{\frac{HW}{p \cdot p} \times E}$ where $\mathbf{z}$ is the generated embedding and $E$ is the embedding size. + +Separate embedding generates separate embeddings for each DCT block in a patch. A DCT input $\mathbf{Y},\mathbf{U}$ is reshaped as $\mathbf{Y}\rightarrow \mathbf{Y}_r\in \mathbb{R}^{\frac{H}{p}\times \frac{W}{p}\times \frac{p^2}{64}\times 64},\mathbf{U}\rightarrow \mathbf{U}_r\in$ $\mathbb{R}^{\frac{H}{p}\times \frac{W}{p}\times \frac{2p^2}{4\cdot 64}\times 64}$ which is embedded separately for each block: $(\mathbf{Y}_r,\mathbf{U}_r)\to \mathbf{z}\in \mathbb{R}^{\frac{HW}{p\cdot p}\times \frac{3p^2}{2\cdot 64}\times \frac{E}{NB}}$ where $N_{B} =$ number of blocks $= \frac{3p^2}{2\cdot 64}$ . This is then mixed using a linear layer to generate a final embedding $\mathbf{z}\to \mathbf{z}\in \mathbb{R}^{\frac{HW}{p\cdot p}\times E}$ . Our intuition behind this strategy is that the information each block holds might be critical, thus training a specialized linear layer for each block could yield better results. + +Concatenated embedding embeds and concatenates the DCT blocks from $\mathbf{Y}$ , $\mathbf{U}$ separately. Our intuition is that since $\mathbf{Y}$ and $\mathbf{U}$ represent different information (luma and chroma), designing specialized layers that handle each in- + +![](images/583b009aaa27acf885dcb25951d56cde4730e1d8abda2bc2308d68ebce239aa3.jpg) +Figure 4. Proposed embedding strategies. We first collect $8 \times 8$ DCT blocks until it matches the patch size. Then, these blocks can be embedded using one of the strategies. Grouped embedding groups all of the collected blocks and embeds them together. Separate embedding embeds each block separately and mixes it. Concatenated embedding embeds $\mathbf{Y}$ and $\mathbf{U}$ separately and concatenates them. + +formation separately may be necessary. However, this generates more embeddings per image patch than the plain model. To keep the overall size even, we reduce the size of each embedding to 2/3. An embedding formula is $\mathbf{Y} \rightarrow \mathbf{Y}_r \in \mathbb{R}^{\frac{H}{p} \times \frac{W}{p} \times p^2}$ , $\mathbf{U} \rightarrow \mathbf{U}_r \in \mathbb{R}^{2 \times \frac{H}{2p} \times \frac{W}{2p} \times p^2}$ , which is then embedded separately per channel type: $\mathbf{Y}_r \rightarrow \mathbf{z}_Y \in \mathbb{R}^{\frac{HW}{p \cdot p} \times \frac{2E}{3}}$ , $\mathbf{U}_r \rightarrow \mathbf{z}_U \in \mathbb{R}^{\frac{2HW}{4p \cdot p} \times \frac{2E}{3}}$ then concatenated $(\mathbf{z}_Y, \mathbf{z}_U) \rightarrow \mathbf{z} \in \mathbb{R}^{\frac{3HW}{2p \cdot p} \times \frac{2E}{3}}$ to generate an embedding $\mathbf{z}$ . + +Sub-block conversion [64] can be applied as an alternate way to embed a patch. Consider ViT architecture of patch size 16. For simplicity, assume only the Y channel is present. To form a patch size of $16 \times 16$ , four $8 \times 8$ DCT blocks have to be grouped together. One strategy is to embed these directly through the linear layer. Another approach is to convert them into a single $16 \times 16$ block and embed them. In other words, we embed the DCT patches from a $16 \times 16$ DCT. There exists a way to efficiently extract these $16 \times 16$ DCT from the smaller $8 \times 8$ DCT blocks and vice versa known as sub-block conversion [64]. This technique can allow us to extract a native DCT patch of different sizes, potentially yielding better results. We also use this technique to implement several augmentations in Sec. 5. + +# 5. DCT Augmentation + +Data augmentation has been a vital component in training robust networks [10, 103-108]. However, augmenting the DCT, as well as training with it, has not been studied in depth. There exist several prior works for some augmentations such as sharpening or resizing as discussed in Sec. 2, but most other RGB augments lack their DCT counterparts. + +Existing work by Gueguen et al. [1] proposed converting DCT to RGB, augmenting in RGB, and converting it back to DCT. However, this incurs expensive RGB/DCT conversion as shown in Sec. 3. More recent work by Wiles et + +al. [34] used a specialized augmentation network that augments their neural-compressed format. Doing so, however, sacrifices versatility as it requires training and can't be reliably generalized to other resolutions or data. + +Our approach is different. We instead implement augmentations directly on DCT by analyzing its properties. That way, we can avoid converting to RGB or relying on a trained augmentation network. In other words, our method is fast, flexible, and works on virtually any data, so long as it is represented in DCT. Thus, in this section, we implement all augmentations used in RandAugment [10] as well as suggest new augmentations that are meaningful for DCT. We mark the ones we suggest using an asterisk(*) + +There are largely two different types of DCT augmentation: photometric and geometric. Each of which uses different key properties of the DCT. While these augmentations are not meant to precisely reproduce RGB augmentations, most of our implementations approximate the RGB counterparts reasonably well. The overview of the augmentations and their similarity metrics are shown in Fig. 6. + +# 5.1. Photometric augmentation + +Photometric augmentation alters a metric of an image, which includes brightness or sharpness. Our implementation of this can be roughly categorized into two: DC component-based and frequency component-based augmentation. Both use the attributes of a DCT coefficient. + +DC Component-based augmentation only alters the DCT coefficient without frequency $(X_{0,0})$ , which is simply a scaled sum of all pixel values in the block (Eq. (3.1)). Altering this value will affect all pixels in the block evenly. This property can be used in two ways – either when we have to modify a value uniformly across all pixels, or when we have to approximate a value of the pixels in a block. + +Brightness augmentation alters the brightness of the im + +![](images/1697da140a2cb1d0c061efb38c8b8b4f8c4998ee81e94546aff0f82ffc2fde87.jpg) + +![](images/4c56f1ff74fd2a7e203d16864861bed72aa302c9dc32328b3bcda2fc0affc003.jpg) +Figure 5. A visualization of different DCT augmentation types. Orange-colored coefficients are augmented and saved as blue. The bottom two examples illustrate Translate and Resize. + +age. Considering that the image is represented in YCbCr color space, we can implement this augmentation by simply modifying the DC component of the Y channel. Let $Y_{u,v}^{h,w}$ denote a $u$ , $v$ -th DCT coefficient of Y at block position $h$ , $w$ . Then our implementation $f$ is the following where $t \in \mathbb{R}$ . + +$$ +f _ {u, v}: Y _ {u, v} ^ {h, w} \rightarrow \left\{\begin{array}{l l}Y _ {0, 0} ^ {h, w} + t \cdot \text {m e a n} (\operatorname {a b s} \left(Y _ {0, 0}\right))&\text {i f} u, v = 0\\Y _ {u, v} ^ {h, w}&\text {o t h e r w i s e}\end{array}\right\} \tag {5.1} +$$ + +Contrast modifies the distance between the bright and dark values in the image. Since DCT coefficients are zero-centered by design (Sec. 3 (d)) and the brightness of a block can be approximated using the DC component $Y_{0,0}$ , we can categorize the non-negative component as 'bright' and the negative component as 'dark'. Therefore, multiplying $Y_{0,0}$ with $t \in [0,\infty)$ can adjust the contrast of the image. The implementation is $f:Y_{0,0}^{h,w} \to tY_{0,0}^{h,w}$ . Similarly, Equalize applies histogram equalization to $Y_{0,0}$ . + +Color (Saturation) augmentation apply the same equation of Contrast to $U$ (DCT coefficient of $\mathrm{CbCr}$ ), instead of $Y$ . This augments the saturation as illustrated in Fig. 6. + +AutoContrast scales the values so that the brightest and darkest value in an image becomes the brightest and darkest possible value. These values are approximated using $X_{0,0}$ in the same way as Contrast. In Sec. 3, we showed that the min/max value of the DCT in JPEG is $[-1024, 1016]$ . Thus, our implementation $f$ is as follows. + +$$ +f: Y _ {u, v} ^ {h, w} \rightarrow \left\{\begin{array}{l l}\frac {Y _ {0 , 0} ^ {h , w} - \operatorname* {m i n} \left(Y _ {0 , 0}\right)}{\operatorname* {m a x} \left(Y _ {0 , 0}\right) - \operatorname* {m i n} \left(Y _ {0 , 0}\right)} \cdot 2 0 4 0 - 1 0 2 4&\text {i f} u, v = 0\\Y _ {u, v} ^ {h, w}&\text {o t h e r w i s e}\end{array}\right\} \tag {5.2} +$$ + +AutoSaturation* applies the formula in AutoContrast to $U$ . This allows the DCT to utilize the full range of the color. + +Frequency component-based augmentation uses non-DC components $(X_{u,v}, u, v \neq 0)$ . Altering the amplitude of + +these changes the intensity of the corresponding cosine signal in the pixel space. Here, we designed three augmentations each affecting frequency differently. + +Sharpness augmentation adjusts a sharpness of an image. Typically in RGB, this utilizes a convolution kernel to achieve such an effect. However, in DCT, several studies show that this can be implemented by adjusting the frequency components of the DCT [51-57]. They show that sharper images will generally have a higher frequency as there are more sudden changes around the sharp edges. Using this property, we implement Sharpness by linearly altering the frequency components. If $t > 0$ , the following equation sharpens the image. Otherwise, it blurs it. + +$$ +f: Y _ {u, v} ^ {h, w} \rightarrow Y _ {u, v} ^ {h, w} \cdot \max \left(1 + \frac {t u}{7}, 0\right) \max \left(1 + \frac {t v}{7}, 0\right) \tag {5.3} +$$ + +MidfreqAug* augmentation is similar to sharpness but instead of peaking the augmentation strength at the highest frequency $(u, v = 7)$ , we peaked it at the middle frequency $(u, v \in \{3, 4\})$ . We expect the results to be similar to Sharpness, but possibly with less noise. + +FreqEnhance* multiplies all frequency components uniformly with a positive factor $t \in [0, \infty)$ . The augmentation is simply $f: Y_{u,v}^{h,w} \to tY_{u,v}^{h,w}$ , $u, v \neq 0$ . We believe that this allows us to see the impact of a frequency component with respect to the model performance. + +Photometric - special case. There are some augmentations that do not categorize into either of the above augmentations. Invert simply flips the sign of all DCT coefficients. This is because the coefficients are virtually zero-centered. Posterize quantizes $X_{0,0}$ to lower bits. Solarize uses $X_{0,0}$ to determine whether or not the DCT block should be inverted. SolarizeAdd adds a preset value to $X_{0,0}$ if it is below threshold. Grayscale replaces $U$ with zeros, removing color information. ChromaDrop* instead drops the Cb or Cr channel randomly, removing only half of the color information. + +# 5.2. Geometric augmentation + +Geometric augmentation modifies the image plane geometrically. An example of this augmentation includes translation, rotation, or shearing. There are two main subcategories of geometric augmentation – block-wise and subblock conversion-based augmentation. + +Block-wise augmentation treats the DCT block positions similarly to pixel positions. Translate can be implemented by moving the positions $h, w$ of each $X^{h,w}$ and filling the blank with zeros. Cutout follows a similar process where we crop blocks out and fill them with zeros. + +Flipping the DCT coefficients utilize the fact that odd-column or odd-row DCT bases are odd-symmetric [78]. Flip is performed by flipping the position of the blocks and then flipping the individual DCT blocks. Define $R = \mathrm{diag}(1, -1, 1, -1, \ldots, -1)$ of matching size. Then, the per + +![](images/8529e97412e4550bfff2b91d206b5746eb1f29afc3980c67446d94ba6de142ac.jpg) +Figure 6. A visualization of RGB augmentations and their DCT counterparts. $/S$ or $/B$ indicates 'sharpen' or 'blur' on sharpness-related augmentations. Resize has been compared where they scale the image up by 2. PSNR and SSIM are calculated for each DCT augmentation. We observe that most DCT augmentations resemble RGB augmentations. Augmentations such as grayscale, cutout, and flip are identical to RGB. However, other augmentations including equalize and contrast are not exactly equal to RGB. + +block flipping operation is as follows. + +$$ +f ^ {X}: X ^ {h, w} \rightarrow \left\{\begin{array}{l l}X ^ {h, w} R&\text {i f h o r i z o n t a l f l i p}\\R X ^ {h, w}&\text {i f v e r t i c a l f l i p}\end{array}\right\} \tag {5.4} +$$ + +Rotate90 is implemented using a transpose with flipping [78]. We first rotate the block position $h, w$ and rotate each $X^{h,w}$ by 90 degrees. The per-block rotation is defined as: + +$$ +f ^ {X}: X ^ {h, w} \rightarrow \left\{\begin{array}{l l}(X ^ {h, w}) ^ {T} R&\text {c l o c k w i s e}\\R (X ^ {h, w}) ^ {T}&\text {c o u n t e r - c l o c k w i s e}\end{array}\right\} \tag {5.5} +$$ + +Sub-block conversion-based augmentation uses the relationship between the DCT block and its smaller sub-blocks. This allows us to efficiently calculate the DCT of different DCT bases without the need to do inverse transform (e.g. $8 \times 8$ DCT $\leftrightarrow$ $32 \times 32$ DCT). The relationship studied by Jiang and Feng [64] is as follows. Let $X_{N \times M}^{h,w}$ be the DCT coefficient block of $N \times M$ DCT at block position $h, w$ . Then, there exists a conversion matrix $A$ such that: + +$$ +X _ {L N \times M N} = A _ {L, N} \left[ \begin{array}{c c c} X _ {N \times N} ^ {0, 0} & \dots & X _ {N \times N} ^ {0, M - 1} \\ \vdots & \ddots & \vdots \\ X _ {N \times N} ^ {L - 1, 0} & \dots & X _ {N \times N} ^ {L - 1, M - 1} \end{array} \right] A _ {M, N} ^ {T} \tag {5.6} +$$ + +Where $A_{L,N}$ is a $LN \times LN$ matrix that converts the $L$ number of $N$ 1-D DCT blocks into a single $LN$ DCT block. The decomposition of $X_{LN \times MN}$ DCT blocks into $L \times M$ DCT blocks of $X_{N \times N}$ follows a similar process: + +$$ +\left[ \begin{array}{c c c} X _ {N \times N} ^ {0, 0} & \dots & X _ {N \times N} ^ {0, M - 1} \\ \vdots & \ddots & \vdots \\ X _ {N \times N} ^ {L - 1, 0} & \dots & X _ {N \times N} ^ {L - 1, M - 1} \end{array} \right] = A _ {L, N} ^ {- 1} X _ {L N \times M N} A _ {M, N} ^ {- 1 ^ {T}} \tag {5.7} +$$ + +Derivation of $A$ is given in the supplementary material. + +Resize can be implemented if we can understand how to resize individual DCT blocks. Suppose that there exists a way to resize $X_{4 \times 4}$ to $X_{8 \times 8}$ by padding. Then, to up-sample $X_{8 \times 8}$ while keeping the $8 \times 8$ sliced structure of JPEG DCT, we can first decompose $X_{8 \times 8}$ into four $X_{4 \times 4}$ + +using sub-block conversion. Then, we can individually resize each $X_{4 \times 4}$ to $X_{8 \times 8}$ . This gives us four $X_{8 \times 8}$ blocks upsampled from one $X_{8 \times 8}$ . Downsampling can follow a similar process. We first combine four adjacent $X_{8 \times 8}$ into a single $X_{16 \times 16}$ using sub-block conversion. Then, we resize $X_{16 \times 16}$ down to $X_{8 \times 8}$ . This process is shown in Fig. 5. + +This technique to resize each individual DCT block is known as sub-band approximation and has been studied by Mukherjee and Mitra [65]. Their work shows that if $X_{N\times N}(k,l)$ is a $(k,l)$ -th coefficient of a $X_{N\times N}$ block, then, the approximate relationship is: + +$$ +X _ {L N \times M N} (k, l) \approx \left\{ \begin{array}{l l} \sqrt {L M} X _ {N \times N} (k, l) & 0 \leq k, l \leq N - 1 \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {5.8} +$$ + +Using this, we can upsample $L \times M$ times by resizing each $X_{N \times N}$ to $X_{LN \times MN}$ and decomposing them to $L \times M$ $X_{N \times N}$ . $L \times M$ downsampling combines $L \times M$ adjacent $X_{N \times N}$ to form $X_{LN \times MN}$ and resize it to $X_{N \times N}$ . An arbitrary resizing of $\frac{P}{Q} \times \frac{R}{S}$ can be done by first upsampling $P \times R$ times and downsampling the result by $Q \times S$ . + +Rotate is implemented using the rotational property of the Fourier transform [112-114]. This property denotes that the Fourier transform of a rotated function is equal to rotating the Fourier transform of a function. To use this property, we slightly alter the Eq. (5.6). Instead of combining the blocks to $X_{LN\times MN}$ DCT, we combine them to the discrete Fourier transform (DFT) coefficients. Define $D_{N\times N}$ as the DFT coefficient block of size $N\times N$ . Then, the rotation is done by combining $L\times M X_{N\times N}$ to $D_{LN\times MN}$ , rotating it, and decomposing it back to $L\times M X_{N\times N}$ using the modified Eq. (5.7). This can be further improved using the lossless 90-degree rotation to minimize the lossy arbitrary-degree rotation. The details of this DFT conversion are shown in the supplementary material. + +
ArchitectureColor SpaceAug. SpaceEmbed. FLOPsDecodeAugmentTrain Data LoadModel Fwd/BwdTrain PipelineEval Data LoadModel FwdEval PipelineVal Acc (%)
(↓ Performance)Latency per img (ms)Throughput per GPU (FPS)
ViT-Ti [50]RGBRGB28.9M3.683.08571.5832.8493.8641.42898.7638.074.1
ViT-S [50]RGBRGB57.8M3.623.01558.0355.7352.1660.21174.5610.576.5
ViT-S* [50]RGBRGB57.8M3.692.63574.7716.8489.0680.32335.1644.275.6
SwinV2-T* [109]RGBRGB20.8M3.612.98489.8231.5231.6614.8809.5516.279.0*
ResNet50 [110]RGBRGB------688.21226.8639.176.1
JPEG-TiDCTDCT16.1M1.422.62816.2857.2687.6775.32847.5752.375.1
JPEG-SDCTDCT30.5M1.492.40824.8364.3360.5782.91139.7711.176.5
JPEG-S*DCTDCT30.5M1.422.37821.7764.0665.8793.12384.1711.875.8
JPEG-S*◇DCTRGB to DCT30.5M3.625.98425.3751.9372.3748.72382.4721.076.3
SwinV2-T*DCTDCT13.0M1.402.47752.0241.9235.9664.2824.9578.079.4
ResNet50◇ [1] [2]DCTRGB to DCT------785.75969.8753.576.1
(↓ Improvements)(Reduction▼)(Speed-ups▲)
JPEG-Ti vs ViT-Ti-44.4 %-61.4 %-14.9 %+42.8 %+2.9 %+39.2 %+20.9 %-1.8 %+17.9 %+1.0
JPEG-S vs ViT-S-47.2 %-58.8 %-20.3 %+47.8 %+2.4 %+2.4 %+18.6 %-3.0 %+16.5 %+0.0
JPEG-S* ViT-S*-47.2 %-61.5 %-9.9 %+43.0 %+6.6 %+36.2 %+16.6 %+2.1 %+10.5 %+0.2
JPEG-S* vs JPEG-S*◇+0.0 %-60.8 %-60.4 %+93.2 %+1.6 %+78.8 %+5.9 %+0.1 %-1.3 %-0.5
SwinV2-T* (DCT vs RGB)-37.7 %-61.2 %-17.1 %+53.5 %+4.5 %+1.9 %+8.0 %+1.9 %+12.0 %+0.4
+ +Table 1. Model throughput per GPU for each pipeline element and accuracy. Embed. FLOPs shows the FLOPs needed to generate patch embeddings. Decode and Augment indicates the per-image processing latency during training. Val Acc shows the accuracy on the ImageNet validation set. 'JPEG-' prefix indicates that it is a ViT trained using JPEG DCT coefficients. Model with \* symbol is trained using mixed precision [111]. $\diamondsuit$ models are trained using the pipeline suggested by Gueguen et al. [1]. \*SwinV2 models are trained using the same recipe as in [50] for a fair comparison. The details of these measurements are shown in the supplementary material. + +Shear is identically implemented as Rotate where instead of rotating $D_{LN \times MN}$ , we shear it. This is because we can apply the same property [112] for each axis. + +# 6. Experiments + +In this section, we compare our models trained in DCT space with the RGB models. We show that the DCT models achieve similar accuracy but perform notably faster than the RGB models. First, we compare the throughput and accuracy of the RGB and DCT models. Then, we compare the DCT embedding strategies covered in Sec. 4. Lastly, we conduct an ablation study on the DCT data augmentation. + +Implementation Details. All experiments are conducted with PyTorch [115]. We extract DCT coefficients using a modified version of libjpeg [116] and TorchJPEG [117]. All timing measurements are performed using $2 \times$ A40 GPUs and 8 cores from an Intel Xeon 6226R CPU, and all throughputs are reported per GPU. We used fvcore [118] to obtain the FLOPs. All models are trained on ImageNet [11, 12], which we resize on-disk to $512 \times 512$ prior to training. We re-implement a ViT training pipeline in PyTorch, carefully following the recipe suggested by Beyer et al. [50] which uses random resized crop, random flip, RandAugment [10] and Mixup [119] with a global batch size of 1024. All plain ViT models are trained with a patch size of 16. SwinV2 model [109] uses a patch size of 4, a window size of 8, and a global batch size of 512. '-S' models are trained for 90 epochs. '-Ti' and SwinV2 models are instead trained for 300 epochs using the same recipe in [50]. Following [50], we randomly sample $1\%$ of the train set to use for validation. Our RGB ResNet-50 baseline uses the V1 + +weights from Torchvision [110]. There exist recent works with improved training recipes for ResNets [120, 121], but this is orthogonal to our work. The DCT ResNet-50 uses the model proposed by Gueguen et al. [1] and Xu et al. [2]. + +# 6.1. Main results + +The hyperparameter settings for the models are given in the supplementary material. Tab. 1 shows the comprehensive result from our experiment. Both the ViT and CNN models show equivalent accuracy to their RGB counterparts. However, loading directly from JPEG DCT reduces decoding latency by up to $61.5\%$ . We see a similar effect on the augmentation latency to a lesser extent. Additionally, as the input size has been halved by JPEG (Sec. 3), we observe that the FLOPs needed to generate embeddings are reduced by up to $47.2\%$ . These speed-ups boost throughput for DCT models. Most notably, our JPEG-Ti model showed $39.2\%$ and $17.9\%$ faster training and evaluation. Our augmentation scheme improves train data loading throughput by $93.2\%$ versus the one by Gueguen et al. [1], which must convert DCT to RGB, augment, and convert it back to DCT. + +While training as-is still reaps the benefits of faster data loading, we can observe that the JPEG-S model is bottlenecked by model forward and backward passes. One option is to employ mixed precision training [111]. This allows us to fully realize the data loading speed-ups by accelerating the model with minor accuracy loss. We observe that our JPEG-S model trained using mixed precision is $36.2\%$ faster during training time compared to the RGB counterpart. We believe most other faster models discussed in Sec. 2 will also benefit from this speed-up. + +
PhotometricGeometricAccuracy
SubsetResizeDC basedFreq. basedSpecial caseBlock-wiseSub-block basedRGBDCT
(Avg. latency (ms) ↓)
RGB2.170.611.340.671.231.28--
DCT2.790.370.540.340.429.31--
(Ablation ↓)
All✓✓✓✓✓✓76.574.6
No sub-block✓✓✓✓✓✗76.275.1
No block-wise✓✓✓✓✗✗76.072.6
No Special-case✓✓✓✗✗✗76.373.3
No Freq. based✓✓✗✗✗✗75.974.2
No DC based✓✗✗✗✗✗74.475.5
Best Subset✓Brightness, Contrast, Color, AutoContrast, AutoSaturation, Sharpness, MidfreqAug, Posterize, Grayscale, ChromaDrop, Translate, Cutout, Rotate90✗76.5*76.5
+ +Table 2. Data augmentation ablation study on ViT-S. At the bottom row, we report the best subset we found and train both the RGB and DCT models from it. *RGB accuracy is obtained with MidfreqAug removed, since it is analogous to Sharpness in RGB as shown in Fig. 6. + +
GroupedSeparateConcat.Sub-blockAcc
✓--✓76.5
-✓-✓74.7
--✓✓71.3
✓---74.6
-✓--73.8
--✓-71.3
+ +Table 3. Embedding strategy ablation study on ViT-S. We see that grouped embedding with sub-block outperforms other strategies. + +# 6.2. Embedding strategies + +To see which patch embedding scheme is most suitable for DCT, we performed an ablation study in Tab. 3. We ablate on the embedding strategies and the sub-block conversion technique discussed in Sec. 4 on ViT-S. The results show two things. One is that the simplest strategy-grouped embedding-is best, and that sub-block conversion is important to achieve high accuracy. We believe this indicates that (1) all blocks in an image patch relay information of that patch as a whole; they should not be separately inferred, and (2) it is more natural for the model to deduce the information in a patch if the sub-blocks are fused together. The best strategy is used throughout the DCT models in Tab. 1. + +# 6.3. Augmentation + +As discussed in Sec. 5, data augmentation is crucial to train a well-performing model. However, many existing studies [9, 10, 103-108] are tuned toward RGB augmentations; we cannot assume that the existing work's result would be consistent on DCT. In other words, some DCT augmentations could have a different impact on both the accuracy and throughput of the model compared to RGB. Therefore, we perform an ablation study on data augmentations discussed in Sec. 5 and report the result in Tab. 2. We perform ablation by varying the subset of augmentations used in RandAugment [10] on ViT-S. The experiment is performed separately for RGB and DCT with their re + +spective augmentation sets. The results show that while sub-block-based augmentations (e.g. rotate, shear) are prohibitively expensive to do directly on DCT, it is not as important to train a model. We report the best augmentation subset we found without sub-block-based augmentations at the bottom row. In addition, we train an RGB model using this subset and compare the accuracy. We can see that the RGB model performs identically to the DCT model, and the subset does not unfairly favor DCT over RGB models. + +# 7. Conclusion + +In this paper, we demonstrated that vision transformers can be accelerated significantly by directly training from the DCT coefficients of JPEG. We proposed several DCT embedding strategies for ViT, as well as reasonable augmentations that can be directly carried out on the DCT coefficients. The throughput of our model is considerably faster with virtually no accuracy loss compared to RGB. + +RGB has been widely used for as long as computer vision existed. Many computer vision schemes regard retrieving RGB as a necessary cost; they have not considered the potential of direct encoded-space training in-depth. We wanted to show the capability of this approach, as well as demonstrate that recovering RGB is not always necessary. + +Encoded-space training can be adapted to nearly all scenarios that require loading some compressed data from storage. From mobile devices to powerful data centers, there are no situations where they wouldn't benefit from faster loading speed. As we only considered the plain ViT architecture, there is still more to be gained by adapting our findings to the existing efficient architectures. Future studies may also consider a better augmentation strategy to improve the performance further. We hope that the techniques shown in this paper prove to be an adequate foundation for future encoded-space research. + +# References + +[1] Lionel Gueguen, Alex Sergeev, Ben Kadlec, Rosanne Liu, and Jason Yosinski. Faster Neural Networks Straight from JPEG. 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NeurIPS, 2021. 7 \ No newline at end of file diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/images.zip b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..89b4c172e3bb8920f9cf0fa0127eb3c4abd9083f --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:efb456d2d2e766c1eeebe8a5b60577249294509f458f34a5770606807ea8f9f3 +size 712590 diff --git a/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/layout.json b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e607655067c88290c61caa2d6aadf2f7ee630b12 --- /dev/null +++ b/2023/RGB No More_ Minimally-Decoded JPEG Vision Transformers/layout.json @@ -0,0 +1,12866 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 104, + 103, + 490, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 103, + 490, + 120 + ], + "spans": [ + { + "bbox": [ + 104, + 103, + 490, + 120 + ], + "type": "text", + "content": "RGB no more: Minimally-decoded JPEG Vision Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 200, + 144, + 394, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 200, + 144, + 394, + 185 + ], + "spans": [ + { + "bbox": [ + 200, + 144, + 394, + 185 + ], + "type": "text", + "content": "Jeongsoo Park Justin Johnson University of Michigan {jespark, justincj}@umich.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "spans": [ + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": "Most neural networks for computer vision are designed to infer using RGB images. However, these RGB images are commonly encoded in JPEG before saving to disk; decoding them imposes an unavoidable overhead for RGB networks. Instead, our work focuses on training Vision Transformers (ViT) directly from the encoded features of JPEG. This way, we can avoid most of the decoding overhead, accelerating data load. Existing works have studied this aspect but they focus on CNNs. Due to how these encoded features are structured, CNNs require heavy modification to their architecture to accept such data. Here, we show that this is not the case for ViTs. In addition, we tackle data augmentation directly on these encoded features, which to our knowledge, has not been explored in-depth for training in this setting. With these two improvements – ViT and data augmentation – we show that our ViT-Ti model achieves up to " + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "inline_equation", + "content": "39.2\\%" + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": " faster training and " + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "inline_equation", + "content": "17.9\\%" + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": " faster inference with no accuracy loss compared to the RGB counterpart." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 450, + 128, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 450, + 128, + 463 + ], + "spans": [ + { + "bbox": [ + 47, + 450, + 128, + 463 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 471, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 471, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 45, + 471, + 287, + 578 + ], + "type": "text", + "content": "Neural networks that process images typically receive their inputs as regular grids of RGB pixel values. This spatial-domain representation is intuitive, and matches the way that images are displayed on digital devices (e.g. LCD panels with RGB sub-pixels). However, images are often stored on disk as compressed JPEG files that instead use frequency-domain representations for images. In this paper we design neural networks that can directly process images encoded in the frequency domain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "content": "Networks that process frequency-domain images have the potential for much faster data loading. JPEG files store image data using Huffman codes; these are decoded to (frequency-domain) discrete cosine transform (DCT) coefficients then converted to (spatial-domain) RGB pixels before being fed to the neural network (Fig. 1). Networks that process DCT coefficients can avoid the expensive DCT to RGB conversion; we show in Sec. 3 that this can reduce the theoretical cost of data loading by up to " + }, + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "inline_equation", + "content": "85\\%" + }, + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "content": ". Data is typi" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 202, + 547, + 365 + ], + "blocks": [ + { + "bbox": [ + 308, + 202, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 308, + 202, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 308, + 202, + 547, + 365 + ], + "type": "image", + "image_path": "e392f363c8dd64c7baa17f7b9354a8c90944fb50cc480f5f9701b26a5f6b981f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 373, + 547, + 429 + ], + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 429 + ], + "type": "text", + "content": "Figure 1. Our proposed training process. The typical process requires full decoding as well as patch extraction to train. In contrast, our process does not since the DCT coefficients are already saved in block-wise fashion. As ViTs work on image patches, we can directly feed these coefficients to the network." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 439, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 439, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 439, + 547, + 475 + ], + "type": "text", + "content": "cally loaded by the CPU while the network runs on a GPU or other accelerator; more efficient data loading can thus reduce CPU bottlenecks and accelerate the entire pipeline." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 479, + 547, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 576 + ], + "type": "text", + "content": "We are not the first to design networks that process frequency-domain images. The work of Gueguen et al. [1] and Xu et al. [2] are most similar to ours: they show how standard CNN architectures such as ResNet [3] and MobileNetV2 [4] can be modified to input DCT rather than RGB and trained to accuracies comparable to their standard formulations. We improve upon these pioneering efforts in two key ways: architecture and data augmentation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "text", + "content": "Adapting a CNN architecture designed for RGB inputs to instead receive DCT is nontrivial. The DCT representation of an " + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "inline_equation", + "content": "H \\times W \\times 3" + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "text", + "content": " RGB image consists of a " + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "inline_equation", + "content": "\\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8" + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "text", + "content": " tensor of luma data and two " + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "inline_equation", + "content": "\\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8" + }, + { + "bbox": [ + 304, + 578, + 547, + 688 + ], + "type": "text", + "content": " tensors of chroma data. The CNN architecture must be modified both to accept lower-resolution inputs (e.g. by skipping the first few stages of a ResNet50 and adding capacity to later stages) and to accept heterogeneously-sized luma and chroma data (e.g. by encoding them with separate pathways)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 691, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 691, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 318, + 691, + 545, + 704 + ], + "type": "text", + "content": "We overcome these challenges by using Vision Trans" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 692, + 265, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 692, + 265, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 692, + 265, + 703 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 692, + 265, + 703 + ], + "type": "text", + "content": "Code available at https://github.com/JeongsooP/RGB-no-more" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "text", + "content": "22334" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "formers (ViTs) [5] rather than CNNs. ViTs use a patch embedding layer to encode non-overlapping image patches into vectors, which are processed using a Transformer [6]. This is a perfect match to DCT representations, which also represent non-overlapping RGB image patches as vectors. We show that ViTs can be easily adapted to DCT inputs by modifying only the initial patch embedding layer and leaving the rest of the architecture unchanged." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 299 + ], + "type": "text", + "content": "Data augmentation is critical for training accurate networks; this is especially true for ViTs [7-9]. However, standard image augmentations such as resizing, cropping, flipping, color jittering, etc. are expressed as transformations on RGB images; prior work [1,2] on neural networks with DCT inputs thus implement data augmentation by converting DCT to RGB, augmenting in RGB, then converting back to DCT before passing the image to the network. This negates all of the potential training-time efficiency gains of using DCT representations; improvements can only be realized during inference when augmentations are not used." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 394 + ], + "type": "text", + "content": "We overcome this limitation by augmenting DCT image representations directly, avoiding any DCT to RGB conversions during training. We show how all image augmentations used by RandAugment [10] can be implemented on DCT representations. Some standard augmentations such as image rotation and shearing are costly to implement in DCT, so we also introduce several new augmentations which are natural for DCT." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "text", + "content": "Using these insights, we train ViT-S and ViT-Ti models on ImageNet [11, 12] which match the accuracy of their RGB counterparts. Compared to an RGB equivalent, our ViT-Ti model is up to " + }, + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "inline_equation", + "content": "39.2\\%" + }, + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "text", + "content": " faster per training iteration and " + }, + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "inline_equation", + "content": "17.9\\%" + }, + { + "bbox": [ + 46, + 395, + 287, + 479 + ], + "type": "text", + "content": " faster during inference. We believe that these results demonstrate the benefits of neural networks that ingest frequency-domain image representations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 488, + 134, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 134, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 134, + 501 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": "Training in the frequency domain is extensively explored in the recent studies. They consider JPEG [1, 2, 13-21], DCT [22-29] or video CODECs [30-33] with a primary focus on increasing the throughput of the model by skipping most of the decoding steps. Many of these works base their model architecture on CNNs. However, adapting CNNs to accept frequency input requires nontrivial modification to the architecture [1,2,17,18,30]. More recent studies [34,35] explore training from a neural compressor [36-45] instead of an existing compression algorithms [46-49]. This approach, however, requires transcoding the existing data to their neural compressed format, increasing overhead. We instead use Vision Transformers [5, 7, 8, 50] on the JPEG-encoded data. Our approach has two advantages: (1) patchwise architecture of ViTs is better suited for existing compression algorithms, (2) does not require any transcoding; it can work on any JPEG images." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 547, + 167 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 547, + 167 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 547, + 167 + ], + "type": "image", + "image_path": "1787745d3c6fd5d58f8411f401c0bcd11ddd1c874b2532e1f0463f8f87c4526f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "type": "text", + "content": "Figure 2. Process of applying " + }, + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "type": "text", + "content": " DCT to the input image. The input image is sliced into " + }, + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 305, + 175, + 547, + 209 + ], + "type": "text", + "content": " patches and the DCT is applied to each patch. The DCT bases are shown on the right." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 220, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 364 + ], + "type": "text", + "content": "Data augmentation directly on the frequency domain has been studied in several works. Gueguen et al. [1] suggested augmenting on RGB and converting back to DCT. Wiles et al. [34] used an augmentation network that is tailored towards their neural compressor. Others focus on a more classical approach such as sharpening [51-57], resizing [58-65], watermarking [66-72], segmentation [73-77], flip and 90-degree rotation [21, 78], scalar operations [79], and forgery detection [80-82] via analyzing the properties of JPEG and DCT. However, to our knowledge, no other works have thoroughly studied the effect of DCT augmentation during frequency-domain training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 474 + ], + "type": "text", + "content": "Speeding up ViTs has been rigorously studied. These either utilize CNN-hybrid architectures to reduce computation [83-89], speed up attention by sparsifying [90-93], linearizing [94, 95], or through other techniques such as pruning [96-99], bottlenecking [100], or approximation [101]. While we only consider the plain ViT architecture in this paper, we want to emphasize that faster data loading is imperative to fully take advantage of these speed-ups as models can only infer as fast as the data loading speed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 483, + 385, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 385, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 385, + 498 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 503, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 539 + ], + "type": "text", + "content": "Here, we discuss Discrete Cosine Transform (DCT) and JPEG compression process. They are crucial to designing a model and DCT data augmentations in the later sections." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "content": "Discrete cosine transform decomposes a finite data sequence into a sum of discrete-frequency cosine functions. It is a transformation from the spatial domain to the frequency domain. We will focus on " + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "content": " DCT since it is a transform used in JPEG. Let " + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{8 \\times 8}" + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "content": " be a " + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "content": " image patch. Then its DCT transform " + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{8 \\times 8}" + }, + { + "bbox": [ + 304, + 541, + 545, + 613 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 615, + 545, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 615, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 615, + 545, + 653 + ], + "type": "interline_equation", + "content": "X _ {u, v} = \\frac {\\alpha_ {u} \\alpha_ {v}}{4} \\sum_ {m, n} x _ {m, n} \\cos \\left[ \\frac {\\pi (2 m + 1) u}{1 6} \\right] \\cos \\left[ \\frac {\\pi (2 n + 1) v}{1 6} \\right] \\tag {3.1}", + "image_path": "e557e5d0d1d31097b531642416c984adad830395f248b95ec35071de7238bada.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_{i} = 1 / \\sqrt{2}" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "i = 0" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ", else 1, " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "u,v,m,n\\in [0..7]" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ". Figure 2 shows how the DCT is applied to an image in JPEG. The original image patch can be reconstructed by a weighted sum of the DCT bases (Fig. 2) and their corresponding coefficients " + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "X_{u,v}" + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": ". For the standard JPEG setting," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "text", + "content": "22335" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 289, + 196 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 196 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 196 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 196 + ], + "type": "image", + "image_path": "db5c0a0489b16cdb18183e6456fbc4c136dd95f2d344b9e0a1d449cbd872faf7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 287, + 249 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 287, + 249 + ], + "type": "text", + "content": "Figure 3. A simplified JPEG compression process. An RGB image is first converted to YCbCr, then transformed to DCT space. They are then encoded into binary codes and written to disk. Decoding follows the inverse of this process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "text", + "content": "the pixel-space min/max value of " + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "inline_equation", + "content": "[-128, 127]" + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "text", + "content": ", is scaled up by " + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "inline_equation", + "content": "[-1024, 1016]" + }, + { + "bbox": [ + 46, + 259, + 286, + 307 + ], + "type": "text", + "content": ". The proof of this property is shown in the supplementary material. This property is necessary to implement several DCT augmentations in Sec. 5." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 309, + 286, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 286, + 345 + ], + "type": "text", + "content": "JPEG [46, 47, 102] is a widely used compression algorithm that is designed to encode images generated by digital photography. The encoding process is as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 351, + 287, + 449 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 51, + 351, + 233, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 351, + 233, + 362 + ], + "spans": [ + { + "bbox": [ + 51, + 351, + 233, + 362 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 51, + 351, + 233, + 362 + ], + "type": "inline_equation", + "content": "H\\times W\\times 3" + }, + { + "bbox": [ + 51, + 351, + 233, + 362 + ], + "type": "text", + "content": " RGB image is given as input" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 363, + 230, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 363, + 230, + 374 + ], + "spans": [ + { + "bbox": [ + 51, + 363, + 230, + 374 + ], + "type": "text", + "content": "(b) RGB is converted to YCbCr color space" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "spans": [ + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "type": "text", + "content": " channels are downsampled to " + }, + { + "bbox": [ + 51, + 374, + 246, + 388 + ], + "type": "inline_equation", + "content": "\\frac{H}{2} \\times \\frac{W}{2}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 388, + 249, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 388, + 249, + 399 + ], + "spans": [ + { + "bbox": [ + 51, + 388, + 249, + 399 + ], + "type": "text", + "content": "(d) Values are shifted from [0,255] to [-128,127]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 400, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 400, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 51, + 400, + 287, + 412 + ], + "type": "text", + "content": "(e) DCT is applied to non-overlapping " + }, + { + "bbox": [ + 51, + 400, + 287, + 412 + ], + "type": "inline_equation", + "content": "8\\times 8" + }, + { + "bbox": [ + 51, + 400, + 287, + 412 + ], + "type": "text", + "content": " pixel patches" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 413, + 195, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 413, + 195, + 424 + ], + "spans": [ + { + "bbox": [ + 52, + 413, + 195, + 424 + ], + "type": "text", + "content": "(f) DCT coefficients are quantized" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 425, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 425, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 51, + 425, + 287, + 437 + ], + "type": "text", + "content": "(g) Run-length encoding(RLE) compresses the coefficients" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 437, + 267, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 437, + 267, + 449 + ], + "spans": [ + { + "bbox": [ + 51, + 437, + 267, + 449 + ], + "type": "text", + "content": "(h) RLE symbols are encoded using Huffman coding" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": "A simplified illustration of this process is shown in Figure 3. YCbCr is a color space where " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " represents luma (i.e. brightness) and " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathrm{Cb}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathrm{Cr}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " signifies chroma (i.e. color) of the image. Step (e) produces a data of size " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\mathbb{R}^{1 \\times \\frac{H}{8} \\times \\frac{W}{8} \\times 8 \\times 8}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{U} \\in \\mathbb{R}^{2 \\times \\frac{H}{16} \\times \\frac{W}{16} \\times 8 \\times 8}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " channel respectively. These " + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": " DCT coefficients are referred to as DCT Blocks in the later sections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": "Compute cost to decode JPEG can be analyzed by counting the number of operations (OPs) for the inverse of the above process. Consider decoding a single " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": " patch. Our proposed scheme decodes step (h) - (f) with a computation cost of " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "3N_{s} + 128" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": " OPs where " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "N_{s} \\in [1..64]" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": ": number of RLE symbols. Full JPEG decoding, on the other hand, requires " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "3N_{s} + 1717" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": " OPs. If we suppose " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "N_{s} = 32" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": ", then the compute cost is 224 and 1813 OPs respectively, where our scheme theoretically saves computation by " + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "inline_equation", + "content": "87.6\\%" + }, + { + "bbox": [ + 46, + 540, + 287, + 659 + ], + "type": "text", + "content": ". The details of these values are shown in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 669, + 162, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 162, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 162, + 681 + ], + "type": "text", + "content": "4. Model Architecture" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Designing a neural network that works on JPEG-encoded DCT coefficients can be challenging. In Sec. 3, we" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "content": "showed that JPEG downsamples " + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "content": " channels to " + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\frac{H}{2} \\times \\frac{W}{2}" + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "content": ". This spatial disparity must be addressed before training in DCT. An existing work by Gueguen et al. [1] suggested several new CNN architectures which include (1) upsampling, (2) downsampling, and (3) late-concatenation. The first two architectures either upsample " + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "content": " to match the dimension of Y or downsample Y to match " + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 304, + 71, + 545, + 227 + ], + "type": "text", + "content": ". However, doing so results in (1) redundant computation or (2) loss of information due to resizing. The third approach, late-concatenation, computes them separately and concatenates them further down the network. However, this requires substantial modification of the CNN architecture, making adaptation to existing models difficult." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 228, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 310 + ], + "type": "text", + "content": "We believe that ViTs are better suited to deal with this unique characteristic of JPEG. Vision transformers work on patches of an image [5, 7-9]. Considering that JPEG DCT already extracts " + }, + { + "bbox": [ + 304, + 228, + 545, + 310 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 228, + 545, + 310 + ], + "type": "text", + "content": " patches from an image (Sec. 3 (e)), we can employ them by modifying only the initial embedding layer. This allows easier integration into other ViTs as the rest of the architecture can remain untouched." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 312, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 371 + ], + "type": "text", + "content": "Therefore, in this section, we propose several patch-embedding strategies that are plausible solutions to this problem. These modified patch embedding layers are illustrated in Fig. 4. The architecture that follows is identical to the plain ViT defined in [5,7,50]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": "Grouped embedding generates embeddings by grouping the " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " DCT blocks together from the corresponding patch position. Consider a DCT input " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " defined in Sec. 3. Grouped embedding collects DCT blocks such that for patch size " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "p^2" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\to \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{U} \\to \\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{2p^2}{4}}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " where the channel and block size are flattened to the last dimension. Then, this is concatenated along the last axis as " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "(\\mathbf{Y}_r, \\mathbf{U}_r) \\to \\mathbf{Y}\\mathbf{U}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times \\frac{3p^2}{2}}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " which will then be embedded as " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{z}: \\mathbf{Y}\\mathbf{U}_r \\to \\mathbf{z} \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times E}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " is the generated embedding and " + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 373, + 545, + 505 + ], + "type": "text", + "content": " is the embedding size." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": "Separate embedding generates separate embeddings for each DCT block in a patch. A DCT input " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{Y},\\mathbf{U}" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": " is reshaped as " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}\\rightarrow \\mathbf{Y}_r\\in \\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{p^2}{64}\\times 64},\\mathbf{U}\\rightarrow \\mathbf{U}_r\\in" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\frac{H}{p}\\times \\frac{W}{p}\\times \\frac{2p^2}{4\\cdot 64}\\times 64}" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": " which is embedded separately for each block: " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "(\\mathbf{Y}_r,\\mathbf{U}_r)\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times \\frac{3p^2}{2\\cdot 64}\\times \\frac{E}{NB}}" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "N_{B} =" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": " number of blocks " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "= \\frac{3p^2}{2\\cdot 64}" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": ". This is then mixed using a linear layer to generate a final embedding " + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\to \\mathbf{z}\\in \\mathbb{R}^{\\frac{HW}{p\\cdot p}\\times E}" + }, + { + "bbox": [ + 304, + 507, + 545, + 644 + ], + "type": "text", + "content": ". Our intuition behind this strategy is that the information each block holds might be critical, thus training a specialized linear layer for each block could yield better results." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "content": "Concatenated embedding embeds and concatenates the DCT blocks from " + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "content": " separately. Our intuition is that since " + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 647, + 545, + 694 + ], + "type": "text", + "content": " represent different information (luma and chroma), designing specialized layers that handle each in-" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "text", + "content": "2Assume " + }, + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "inline_equation", + "content": "p = 16n,n\\in \\mathbb{N}" + }, + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "text", + "content": " .For " + }, + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "inline_equation", + "content": "p < 16" + }, + { + "bbox": [ + 315, + 702, + 531, + 713 + ], + "type": "text", + "content": " , check the supplementary." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 743, + 317, + 752 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 317, + 752 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 317, + 752 + ], + "type": "text", + "content": "22336" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 72, + 521, + 238 + ], + "blocks": [ + { + "bbox": [ + 75, + 72, + 521, + 238 + ], + "lines": [ + { + "bbox": [ + 75, + 72, + 521, + 238 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 521, + 238 + ], + "type": "image", + "image_path": "583b009aaa27acf885dcb25951d56cde4730e1d8abda2bc2308d68ebce239aa3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "text", + "content": "Figure 4. Proposed embedding strategies. We first collect " + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "text", + "content": " DCT blocks until it matches the patch size. Then, these blocks can be embedded using one of the strategies. Grouped embedding groups all of the collected blocks and embeds them together. Separate embedding embeds each block separately and mixes it. Concatenated embedding embeds " + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 247, + 547, + 282 + ], + "type": "text", + "content": " separately and concatenates them." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": "formation separately may be necessary. However, this generates more embeddings per image patch than the plain model. To keep the overall size even, we reduce the size of each embedding to 2/3. An embedding formula is " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\rightarrow \\mathbf{Y}_r \\in \\mathbb{R}^{\\frac{H}{p} \\times \\frac{W}{p} \\times p^2}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{U} \\rightarrow \\mathbf{U}_r \\in \\mathbb{R}^{2 \\times \\frac{H}{2p} \\times \\frac{W}{2p} \\times p^2}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": ", which is then embedded separately per channel type: " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_r \\rightarrow \\mathbf{z}_Y \\in \\mathbb{R}^{\\frac{HW}{p \\cdot p} \\times \\frac{2E}{3}}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_r \\rightarrow \\mathbf{z}_U \\in \\mathbb{R}^{\\frac{2HW}{4p \\cdot p} \\times \\frac{2E}{3}}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": " then concatenated " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_Y, \\mathbf{z}_U) \\rightarrow \\mathbf{z} \\in \\mathbb{R}^{\\frac{3HW}{2p \\cdot p} \\times \\frac{2E}{3}}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": " to generate an embedding " + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 291, + 289, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": "Sub-block conversion [64] can be applied as an alternate way to embed a patch. Consider ViT architecture of patch size 16. For simplicity, assume only the Y channel is present. To form a patch size of " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": ", four " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": " DCT blocks have to be grouped together. One strategy is to embed these directly through the linear layer. Another approach is to convert them into a single " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": " block and embed them. In other words, we embed the DCT patches from a " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": " DCT. There exists a way to efficiently extract these " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": " DCT from the smaller " + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 394, + 289, + 562 + ], + "type": "text", + "content": " DCT blocks and vice versa known as sub-block conversion [64]. This technique can allow us to extract a native DCT patch of different sizes, potentially yielding better results. We also use this technique to implement several augmentations in Sec. 5." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 573, + 163, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 163, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 163, + 586 + ], + "type": "text", + "content": "5. DCT Augmentation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": "Data augmentation has been a vital component in training robust networks [10, 103-108]. However, augmenting the DCT, as well as training with it, has not been studied in depth. There exist several prior works for some augmentations such as sharpening or resizing as discussed in Sec. 2, but most other RGB augments lack their DCT counterparts." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "text", + "content": "Existing work by Gueguen et al. [1] proposed converting DCT to RGB, augmenting in RGB, and converting it back to DCT. However, this incurs expensive RGB/DCT conversion as shown in Sec. 3. More recent work by Wiles et" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 291, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 338 + ], + "type": "text", + "content": "al. [34] used a specialized augmentation network that augments their neural-compressed format. Doing so, however, sacrifices versatility as it requires training and can't be reliably generalized to other resolutions or data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 339, + 546, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 546, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 546, + 447 + ], + "type": "text", + "content": "Our approach is different. We instead implement augmentations directly on DCT by analyzing its properties. That way, we can avoid converting to RGB or relying on a trained augmentation network. In other words, our method is fast, flexible, and works on virtually any data, so long as it is represented in DCT. Thus, in this section, we implement all augmentations used in RandAugment [10] as well as suggest new augmentations that are meaningful for DCT. We mark the ones we suggest using an asterisk(*)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 447, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 531 + ], + "type": "text", + "content": "There are largely two different types of DCT augmentation: photometric and geometric. Each of which uses different key properties of the DCT. While these augmentations are not meant to precisely reproduce RGB augmentations, most of our implementations approximate the RGB counterparts reasonably well. The overview of the augmentations and their similarity metrics are shown in Fig. 6." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 537, + 454, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 454, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 454, + 550 + ], + "type": "text", + "content": "5.1. Photometric augmentation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "type": "text", + "content": "Photometric augmentation alters a metric of an image, which includes brightness or sharpness. Our implementation of this can be roughly categorized into two: DC component-based and frequency component-based augmentation. Both use the attributes of a DCT coefficient." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 700 + ], + "type": "text", + "content": "DC Component-based augmentation only alters the DCT coefficient without frequency " + }, + { + "bbox": [ + 304, + 617, + 545, + 700 + ], + "type": "inline_equation", + "content": "(X_{0,0})" + }, + { + "bbox": [ + 304, + 617, + 545, + 700 + ], + "type": "text", + "content": ", which is simply a scaled sum of all pixel values in the block (Eq. (3.1)). Altering this value will affect all pixels in the block evenly. This property can be used in two ways – either when we have to modify a value uniformly across all pixels, or when we have to approximate a value of the pixels in a block." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Brightness augmentation alters the brightness of the im" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "text", + "content": "22337" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 70, + 269, + 168 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 269, + 168 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 269, + 168 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 269, + 168 + ], + "type": "image", + "image_path": "1697da140a2cb1d0c061efb38c8b8b4f8c4998ee81e94546aff0f82ffc2fde87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 67, + 168, + 268, + 266 + ], + "blocks": [ + { + "bbox": [ + 67, + 168, + 268, + 266 + ], + "lines": [ + { + "bbox": [ + 67, + 168, + 268, + 266 + ], + "spans": [ + { + "bbox": [ + 67, + 168, + 268, + 266 + ], + "type": "image", + "image_path": "4c56f1ff74fd2a7e203d16864861bed72aa302c9dc32328b3bcda2fc0affc003.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 287, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 308 + ], + "type": "text", + "content": "Figure 5. A visualization of different DCT augmentation types. Orange-colored coefficients are augmented and saved as blue. The bottom two examples illustrate Translate and Resize." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": "age. Considering that the image is represented in YCbCr color space, we can implement this augmentation by simply modifying the DC component of the Y channel. Let " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "Y_{u,v}^{h,w}" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": " denote a " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": "-th DCT coefficient of Y at block position " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": ". Then our implementation " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": " is the following where " + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 380, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 380, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 53, + 380, + 287, + 403 + ], + "type": "interline_equation", + "content": "f _ {u, v}: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}Y _ {0, 0} ^ {h, w} + t \\cdot \\text {m e a n} (\\operatorname {a b s} \\left(Y _ {0, 0}\\right))&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.1}", + "image_path": "eda8683c59afc3e2a6cc95071ee65807454bc717b12f62bfd38435e82adc029b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": "Contrast modifies the distance between the bright and dark values in the image. Since DCT coefficients are zero-centered by design (Sec. 3 (d)) and the brightness of a block can be approximated using the DC component " + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "inline_equation", + "content": "Y_{0,0}" + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": ", we can categorize the non-negative component as 'bright' and the negative component as 'dark'. Therefore, multiplying " + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "inline_equation", + "content": "Y_{0,0}" + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "inline_equation", + "content": "t \\in [0,\\infty)" + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": " can adjust the contrast of the image. The implementation is " + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "inline_equation", + "content": "f:Y_{0,0}^{h,w} \\to tY_{0,0}^{h,w}" + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": ". Similarly, Equalize applies histogram equalization to " + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "inline_equation", + "content": "Y_{0,0}" + }, + { + "bbox": [ + 46, + 405, + 287, + 514 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "text", + "content": "Color (Saturation) augmentation apply the same equation of Contrast to " + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "text", + "content": " (DCT coefficient of " + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathrm{CbCr}" + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "text", + "content": "), instead of " + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 47, + 514, + 287, + 550 + ], + "type": "text", + "content": ". This augments the saturation as illustrated in Fig. 6." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "text", + "content": "AutoContrast scales the values so that the brightest and darkest value in an image becomes the brightest and darkest possible value. These values are approximated using " + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "inline_equation", + "content": "X_{0,0}" + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "text", + "content": " in the same way as Contrast. In Sec. 3, we showed that the min/max value of the DCT in JPEG is " + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "inline_equation", + "content": "[-1024, 1016]" + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "text", + "content": ". Thus, our implementation " + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 550, + 287, + 622 + ], + "type": "text", + "content": " is as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 624, + 286, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 286, + 662 + ], + "type": "interline_equation", + "content": "f: Y _ {u, v} ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}\\frac {Y _ {0 , 0} ^ {h , w} - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)}{\\operatorname* {m a x} \\left(Y _ {0 , 0}\\right) - \\operatorname* {m i n} \\left(Y _ {0 , 0}\\right)} \\cdot 2 0 4 0 - 1 0 2 4&\\text {i f} u, v = 0\\\\Y _ {u, v} ^ {h, w}&\\text {o t h e r w i s e}\\end{array}\\right\\} \\tag {5.2}", + "image_path": "7f6793a960650e4d90bd4f148fa917bd3f551ff5656a869f8f7809e240cac41f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 663, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 287, + 687 + ], + "type": "text", + "content": "AutoSaturation* applies the formula in AutoContrast to " + }, + { + "bbox": [ + 47, + 663, + 287, + 687 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 47, + 663, + 287, + 687 + ], + "type": "text", + "content": ". This allows the DCT to utilize the full range of the color." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Frequency component-based augmentation uses non-DC components " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "(X_{u,v}, u, v \\neq 0)" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": ". Altering the amplitude of" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "these changes the intensity of the corresponding cosine signal in the pixel space. Here, we designed three augmentations each affecting frequency differently." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 110, + 545, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 229 + ], + "type": "text", + "content": "Sharpness augmentation adjusts a sharpness of an image. Typically in RGB, this utilizes a convolution kernel to achieve such an effect. However, in DCT, several studies show that this can be implemented by adjusting the frequency components of the DCT [51-57]. They show that sharper images will generally have a higher frequency as there are more sudden changes around the sharp edges. Using this property, we implement Sharpness by linearly altering the frequency components. If " + }, + { + "bbox": [ + 304, + 110, + 545, + 229 + ], + "type": "inline_equation", + "content": "t > 0" + }, + { + "bbox": [ + 304, + 110, + 545, + 229 + ], + "type": "text", + "content": ", the following equation sharpens the image. Otherwise, it blurs it." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 231, + 545, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 231, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 311, + 231, + 545, + 247 + ], + "type": "interline_equation", + "content": "f: Y _ {u, v} ^ {h, w} \\rightarrow Y _ {u, v} ^ {h, w} \\cdot \\max \\left(1 + \\frac {t u}{7}, 0\\right) \\max \\left(1 + \\frac {t v}{7}, 0\\right) \\tag {5.3}", + "image_path": "1f040df17b53e8fcccce68e06c6de6d7bd563f84bcc07e41e36b5f0af546f0fc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "text", + "content": "MidfreqAug* augmentation is similar to sharpness but instead of peaking the augmentation strength at the highest frequency " + }, + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "inline_equation", + "content": "(u, v = 7)" + }, + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "text", + "content": ", we peaked it at the middle frequency " + }, + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "inline_equation", + "content": "(u, v \\in \\{3, 4\\})" + }, + { + "bbox": [ + 304, + 250, + 545, + 309 + ], + "type": "text", + "content": ". We expect the results to be similar to Sharpness, but possibly with less noise." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "text", + "content": "FreqEnhance* multiplies all frequency components uniformly with a positive factor " + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "inline_equation", + "content": "t \\in [0, \\infty)" + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "text", + "content": ". The augmentation is simply " + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "inline_equation", + "content": "f: Y_{u,v}^{h,w} \\to tY_{u,v}^{h,w}" + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "inline_equation", + "content": "u, v \\neq 0" + }, + { + "bbox": [ + 304, + 311, + 545, + 371 + ], + "type": "text", + "content": ". We believe that this allows us to see the impact of a frequency component with respect to the model performance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": "Photometric - special case. There are some augmentations that do not categorize into either of the above augmentations. Invert simply flips the sign of all DCT coefficients. This is because the coefficients are virtually zero-centered. Posterize quantizes " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "X_{0,0}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": " to lower bits. Solarize uses " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "X_{0,0}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": " to determine whether or not the DCT block should be inverted. SolarizeAdd adds a preset value to " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "X_{0,0}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": " if it is below threshold. Grayscale replaces " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": " with zeros, removing color information. ChromaDrop* instead drops the Cb or Cr channel randomly, removing only half of the color information." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 508, + 444, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 444, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 444, + 521 + ], + "type": "text", + "content": "5.2. Geometric augmentation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "content": "Geometric augmentation modifies the image plane geometrically. An example of this augmentation includes translation, rotation, or shearing. There are two main subcategories of geometric augmentation – block-wise and subblock conversion-based augmentation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "text", + "content": "Block-wise augmentation treats the DCT block positions similarly to pixel positions. Translate can be implemented by moving the positions " + }, + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "text", + "content": " of each " + }, + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "inline_equation", + "content": "X^{h,w}" + }, + { + "bbox": [ + 304, + 592, + 545, + 651 + ], + "type": "text", + "content": " and filling the blank with zeros. Cutout follows a similar process where we crop blocks out and fill them with zeros." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Flipping the DCT coefficients utilize the fact that odd-column or odd-row DCT bases are odd-symmetric [78]. Flip is performed by flipping the position of the blocks and then flipping the individual DCT blocks. Define " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "R = \\mathrm{diag}(1, -1, 1, -1, \\ldots, -1)" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " of matching size. Then, the per" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "text", + "content": "22338" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 545, + 238 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 545, + 238 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 545, + 238 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 545, + 238 + ], + "type": "image", + "image_path": "8529e97412e4550bfff2b91d206b5746eb1f29afc3980c67446d94ba6de142ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "type": "text", + "content": "Figure 6. A visualization of RGB augmentations and their DCT counterparts. " + }, + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "type": "inline_equation", + "content": "/S" + }, + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "type": "inline_equation", + "content": "/B" + }, + { + "bbox": [ + 46, + 247, + 546, + 293 + ], + "type": "text", + "content": " indicates 'sharpen' or 'blur' on sharpness-related augmentations. Resize has been compared where they scale the image up by 2. PSNR and SSIM are calculated for each DCT augmentation. We observe that most DCT augmentations resemble RGB augmentations. Augmentations such as grayscale, cutout, and flip are identical to RGB. However, other augmentations including equalize and contrast are not exactly equal to RGB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 303, + 201, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 303, + 201, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 201, + 316 + ], + "type": "text", + "content": "block flipping operation is as follows." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 317, + 287, + 343 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 317, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 61, + 317, + 287, + 343 + ], + "type": "interline_equation", + "content": "f ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}X ^ {h, w} R&\\text {i f h o r i z o n t a l f l i p}\\\\R X ^ {h, w}&\\text {i f v e r t i c a l f l i p}\\end{array}\\right\\} \\tag {5.4}", + "image_path": "2f0ec504c3c0d60d60650761c943469676aa0f835cb54e1ddfbdc605004f4ba9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "text", + "content": "Rotate90 is implemented using a transpose with flipping [78]. We first rotate the block position " + }, + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "text", + "content": " and rotate each " + }, + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "inline_equation", + "content": "X^{h,w}" + }, + { + "bbox": [ + 47, + 345, + 287, + 380 + ], + "type": "text", + "content": " by 90 degrees. The per-block rotation is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 381, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 381, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 53, + 381, + 287, + 409 + ], + "type": "interline_equation", + "content": "f ^ {X}: X ^ {h, w} \\rightarrow \\left\\{\\begin{array}{l l}(X ^ {h, w}) ^ {T} R&\\text {c l o c k w i s e}\\\\R (X ^ {h, w}) ^ {T}&\\text {c o u n t e r - c l o c k w i s e}\\end{array}\\right\\} \\tag {5.5}", + "image_path": "7f4f99e8d603935503b62e09bc12b29889b54eea7a1b52600b0fb42c5a0c2694.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": "Sub-block conversion-based augmentation uses the relationship between the DCT block and its smaller sub-blocks. This allows us to efficiently calculate the DCT of different DCT bases without the need to do inverse transform (e.g. " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": " DCT " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": " DCT). The relationship studied by Jiang and Feng [64] is as follows. Let " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "X_{N \\times M}^{h,w}" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": " be the DCT coefficient block of " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "N \\times M" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": " DCT at block position " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": ". Then, there exists a conversion matrix " + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 411, + 287, + 505 + ], + "type": "text", + "content": " such that:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 506, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 506, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 287, + 548 + ], + "type": "interline_equation", + "content": "X _ {L N \\times M N} = A _ {L, N} \\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] A _ {M, N} ^ {T} \\tag {5.6}", + "image_path": "8e09a0ecea1ddc6224110a0c97969118caf6b3f1f79ed93b250ec7352f75468c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "A_{L,N}" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "LN \\times LN" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " matrix that converts the " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " number of " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " 1-D DCT blocks into a single " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "LN" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " DCT block. The decomposition of " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "X_{LN \\times MN}" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " DCT blocks into " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "L \\times M" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " DCT blocks of " + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "inline_equation", + "content": "X_{N \\times N}" + }, + { + "bbox": [ + 46, + 548, + 287, + 597 + ], + "type": "text", + "content": " follows a similar process:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 597, + 287, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 597, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 58, + 597, + 287, + 640 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{c c c} X _ {N \\times N} ^ {0, 0} & \\dots & X _ {N \\times N} ^ {0, M - 1} \\\\ \\vdots & \\ddots & \\vdots \\\\ X _ {N \\times N} ^ {L - 1, 0} & \\dots & X _ {N \\times N} ^ {L - 1, M - 1} \\end{array} \\right] = A _ {L, N} ^ {- 1} X _ {L N \\times M N} A _ {M, N} ^ {- 1 ^ {T}} \\tag {5.7}", + "image_path": "a0a8bfeaf7a3d0d62c566b9dfe5e4f5d95f171e020534e91085b696c9031d036.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 642, + 270, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 270, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 270, + 653 + ], + "type": "text", + "content": "Derivation of " + }, + { + "bbox": [ + 47, + 642, + 270, + 653 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 642, + 270, + 653 + ], + "type": "text", + "content": " is given in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Resize can be implemented if we can understand how to resize individual DCT blocks. Suppose that there exists a way to resize " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{4 \\times 4}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " by padding. Then, to up-sample " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " while keeping the " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " sliced structure of JPEG DCT, we can first decompose " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " into four " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{4 \\times 4}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": "using sub-block conversion. Then, we can individually resize each " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{4 \\times 4}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": ". This gives us four " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": " blocks upsampled from one " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": ". Downsampling can follow a similar process. We first combine four adjacent " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": " into a single " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{16 \\times 16}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": " using sub-block conversion. Then, we resize " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{16 \\times 16}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": " down to " + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "inline_equation", + "content": "X_{8 \\times 8}" + }, + { + "bbox": [ + 305, + 303, + 545, + 375 + ], + "type": "text", + "content": ". This process is shown in Fig. 5." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "text", + "content": "This technique to resize each individual DCT block is known as sub-band approximation and has been studied by Mukherjee and Mitra [65]. Their work shows that if " + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "inline_equation", + "content": "X_{N\\times N}(k,l)" + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "inline_equation", + "content": "(k,l)" + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "text", + "content": "-th coefficient of a " + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "inline_equation", + "content": "X_{N\\times N}" + }, + { + "bbox": [ + 305, + 376, + 545, + 436 + ], + "type": "text", + "content": " block, then, the approximate relationship is:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 437, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 545, + 472 + ], + "type": "interline_equation", + "content": "X _ {L N \\times M N} (k, l) \\approx \\left\\{ \\begin{array}{l l} \\sqrt {L M} X _ {N \\times N} (k, l) & 0 \\leq k, l \\leq N - 1 \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5.8}", + "image_path": "d0f963233a011aad8dacc200fb6868e04ca4f1934696ab3f56fd1f76072cc169.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": "Using this, we can upsample " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "L \\times M" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " times by resizing each " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{N \\times N}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{LN \\times MN}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " and decomposing them to " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "L \\times M" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{N \\times N}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "L \\times M" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " downsampling combines " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "L \\times M" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " adjacent " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{N \\times N}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " to form " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{LN \\times MN}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " and resize it to " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "X_{N \\times N}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": ". An arbitrary resizing of " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\frac{P}{Q} \\times \\frac{R}{S}" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " can be done by first upsampling " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "P \\times R" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": " times and downsampling the result by " + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "inline_equation", + "content": "Q \\times S" + }, + { + "bbox": [ + 305, + 473, + 545, + 544 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Rotate is implemented using the rotational property of the Fourier transform [112-114]. This property denotes that the Fourier transform of a rotated function is equal to rotating the Fourier transform of a function. To use this property, we slightly alter the Eq. (5.6). Instead of combining the blocks to " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "X_{LN\\times MN}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " DCT, we combine them to the discrete Fourier transform (DFT) coefficients. Define " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{N\\times N}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " as the DFT coefficient block of size " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": ". Then, the rotation is done by combining " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "L\\times M X_{N\\times N}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{LN\\times MN}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": ", rotating it, and decomposing it back to " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "L\\times M X_{N\\times N}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " using the modified Eq. (5.7). This can be further improved using the lossless 90-degree rotation to minimize the lossy arbitrary-degree rotation. The details of this DFT conversion are shown in the supplementary material." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "text", + "content": "22339" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 68, + 533, + 258 + ], + "blocks": [ + { + "bbox": [ + 62, + 68, + 533, + 258 + ], + "lines": [ + { + "bbox": [ + 62, + 68, + 533, + 258 + ], + "spans": [ + { + "bbox": [ + 62, + 68, + 533, + 258 + ], + "type": "table", + "html": "
ArchitectureColor SpaceAug. SpaceEmbed. FLOPsDecodeAugmentTrain Data LoadModel Fwd/BwdTrain PipelineEval Data LoadModel FwdEval PipelineVal Acc (%)
(↓ Performance)Latency per img (ms)Throughput per GPU (FPS)
ViT-Ti [50]RGBRGB28.9M3.683.08571.5832.8493.8641.42898.7638.074.1
ViT-S [50]RGBRGB57.8M3.623.01558.0355.7352.1660.21174.5610.576.5
ViT-S* [50]RGBRGB57.8M3.692.63574.7716.8489.0680.32335.1644.275.6
SwinV2-T* [109]RGBRGB20.8M3.612.98489.8231.5231.6614.8809.5516.279.0*
ResNet50 [110]RGBRGB------688.21226.8639.176.1
JPEG-TiDCTDCT16.1M1.422.62816.2857.2687.6775.32847.5752.375.1
JPEG-SDCTDCT30.5M1.492.40824.8364.3360.5782.91139.7711.176.5
JPEG-S*DCTDCT30.5M1.422.37821.7764.0665.8793.12384.1711.875.8
JPEG-S*◇DCTRGB to DCT30.5M3.625.98425.3751.9372.3748.72382.4721.076.3
SwinV2-T*DCTDCT13.0M1.402.47752.0241.9235.9664.2824.9578.079.4
ResNet50◇ [1] [2]DCTRGB to DCT------785.75969.8753.576.1
(↓ Improvements)(Reduction▼)(Speed-ups▲)
JPEG-Ti vs ViT-Ti-44.4 %-61.4 %-14.9 %+42.8 %+2.9 %+39.2 %+20.9 %-1.8 %+17.9 %+1.0
JPEG-S vs ViT-S-47.2 %-58.8 %-20.3 %+47.8 %+2.4 %+2.4 %+18.6 %-3.0 %+16.5 %+0.0
JPEG-S* ViT-S*-47.2 %-61.5 %-9.9 %+43.0 %+6.6 %+36.2 %+16.6 %+2.1 %+10.5 %+0.2
JPEG-S* vs JPEG-S*◇+0.0 %-60.8 %-60.4 %+93.2 %+1.6 %+78.8 %+5.9 %+0.1 %-1.3 %-0.5
SwinV2-T* (DCT vs RGB)-37.7 %-61.2 %-17.1 %+53.5 %+4.5 %+1.9 %+8.0 %+1.9 %+12.0 %+0.4
", + "image_path": "ecd4e1fc4fa181d41aef6b4871b724d04256a0a1ba33e5705d79a6a41b04b647.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 265, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 547, + 321 + ], + "type": "text", + "content": "Table 1. Model throughput per GPU for each pipeline element and accuracy. Embed. FLOPs shows the FLOPs needed to generate patch embeddings. Decode and Augment indicates the per-image processing latency during training. Val Acc shows the accuracy on the ImageNet validation set. 'JPEG-' prefix indicates that it is a ViT trained using JPEG DCT coefficients. Model with \\* symbol is trained using mixed precision [111]. " + }, + { + "bbox": [ + 46, + 265, + 547, + 321 + ], + "type": "inline_equation", + "content": "\\diamondsuit" + }, + { + "bbox": [ + 46, + 265, + 547, + 321 + ], + "type": "text", + "content": " models are trained using the pipeline suggested by Gueguen et al. [1]. \\*SwinV2 models are trained using the same recipe as in [50] for a fair comparison. The details of these measurements are shown in the supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 331, + 288, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 288, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 288, + 369 + ], + "type": "text", + "content": "Shear is identically implemented as Rotate where instead of rotating " + }, + { + "bbox": [ + 47, + 331, + 288, + 369 + ], + "type": "inline_equation", + "content": "D_{LN \\times MN}" + }, + { + "bbox": [ + 47, + 331, + 288, + 369 + ], + "type": "text", + "content": ", we shear it. This is because we can apply the same property [112] for each axis." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 380, + 128, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 128, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 128, + 392 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 400, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 484 + ], + "type": "text", + "content": "In this section, we compare our models trained in DCT space with the RGB models. We show that the DCT models achieve similar accuracy but perform notably faster than the RGB models. First, we compare the throughput and accuracy of the RGB and DCT models. Then, we compare the DCT embedding strategies covered in Sec. 4. Lastly, we conduct an ablation study on the DCT data augmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": "Implementation Details. All experiments are conducted with PyTorch [115]. We extract DCT coefficients using a modified version of libjpeg [116] and TorchJPEG [117]. All timing measurements are performed using " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": " A40 GPUs and 8 cores from an Intel Xeon 6226R CPU, and all throughputs are reported per GPU. We used fvcore [118] to obtain the FLOPs. All models are trained on ImageNet [11, 12], which we resize on-disk to " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": " prior to training. We re-implement a ViT training pipeline in PyTorch, carefully following the recipe suggested by Beyer et al. [50] which uses random resized crop, random flip, RandAugment [10] and Mixup [119] with a global batch size of 1024. All plain ViT models are trained with a patch size of 16. SwinV2 model [109] uses a patch size of 4, a window size of 8, and a global batch size of 512. '-S' models are trained for 90 epochs. '-Ti' and SwinV2 models are instead trained for 300 epochs using the same recipe in [50]. Following [50], we randomly sample " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": " of the train set to use for validation. Our RGB ResNet-50 baseline uses the V1" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 331, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 547, + 380 + ], + "type": "text", + "content": "weights from Torchvision [110]. There exist recent works with improved training recipes for ResNets [120, 121], but this is orthogonal to our work. The DCT ResNet-50 uses the model proposed by Gueguen et al. [1] and Xu et al. [2]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 392, + 388, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 388, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 388, + 403 + ], + "type": "text", + "content": "6.1. Main results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": "The hyperparameter settings for the models are given in the supplementary material. Tab. 1 shows the comprehensive result from our experiment. Both the ViT and CNN models show equivalent accuracy to their RGB counterparts. However, loading directly from JPEG DCT reduces decoding latency by up to " + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "inline_equation", + "content": "61.5\\%" + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": ". We see a similar effect on the augmentation latency to a lesser extent. Additionally, as the input size has been halved by JPEG (Sec. 3), we observe that the FLOPs needed to generate embeddings are reduced by up to " + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "inline_equation", + "content": "47.2\\%" + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": ". These speed-ups boost throughput for DCT models. Most notably, our JPEG-Ti model showed " + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "inline_equation", + "content": "39.2\\%" + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "inline_equation", + "content": "17.9\\%" + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": " faster training and evaluation. Our augmentation scheme improves train data loading throughput by " + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "inline_equation", + "content": "93.2\\%" + }, + { + "bbox": [ + 304, + 413, + 545, + 592 + ], + "type": "text", + "content": " versus the one by Gueguen et al. [1], which must convert DCT to RGB, augment, and convert it back to DCT." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "While training as-is still reaps the benefits of faster data loading, we can observe that the JPEG-S model is bottlenecked by model forward and backward passes. One option is to employ mixed precision training [111]. This allows us to fully realize the data loading speed-ups by accelerating the model with minor accuracy loss. We observe that our JPEG-S model trained using mixed precision is " + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "inline_equation", + "content": "36.2\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": " faster during training time compared to the RGB counterpart. We believe most other faster models discussed in Sec. 2 will also benefit from this speed-up." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 318, + 753 + ], + "type": "text", + "content": "22340" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 533, + 223 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 533, + 223 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 533, + 223 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 533, + 223 + ], + "type": "table", + "html": "
PhotometricGeometricAccuracy
SubsetResizeDC basedFreq. basedSpecial caseBlock-wiseSub-block basedRGBDCT
(Avg. latency (ms) ↓)
RGB2.170.611.340.671.231.28--
DCT2.790.370.540.340.429.31--
(Ablation ↓)
All✓✓✓✓✓✓76.574.6
No sub-block✓✓✓✓✓✗76.275.1
No block-wise✓✓✓✓✗✗76.072.6
No Special-case✓✓✓✗✗✗76.373.3
No Freq. based✓✓✗✗✗✗75.974.2
No DC based✓✗✗✗✗✗74.475.5
Best Subset✓Brightness, Contrast, Color, AutoContrast, AutoSaturation, Sharpness, MidfreqAug, Posterize, Grayscale, ChromaDrop, Translate, Cutout, Rotate90✗76.5*76.5
", + "image_path": "3ae9513160d224f3a9b6386392f42602d93046633e1f4d5d3586e0927cdc2a45.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 74, + 262, + 262, + 337 + ], + "blocks": [ + { + "bbox": [ + 46, + 231, + 547, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 231, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 547, + 255 + ], + "type": "text", + "content": "Table 2. Data augmentation ablation study on ViT-S. At the bottom row, we report the best subset we found and train both the RGB and DCT models from it. *RGB accuracy is obtained with MidfreqAug removed, since it is analogous to Sharpness in RGB as shown in Fig. 6." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 262, + 262, + 337 + ], + "lines": [ + { + "bbox": [ + 74, + 262, + 262, + 337 + ], + "spans": [ + { + "bbox": [ + 74, + 262, + 262, + 337 + ], + "type": "table", + "html": "
GroupedSeparateConcat.Sub-blockAcc
✓--✓76.5
-✓-✓74.7
--✓✓71.3
✓---74.6
-✓--73.8
--✓-71.3
", + "image_path": "e792387cfea2390901cf2bd206d6fc93e26e611f2abb3f6588dd5f2c5b6f2f40.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 343, + 288, + 368 + ], + "lines": [ + { + "bbox": [ + 46, + 343, + 288, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 288, + 368 + ], + "type": "text", + "content": "Table 3. Embedding strategy ablation study on ViT-S. We see that grouped embedding with sub-block outperforms other strategies." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 376, + 171, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 171, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 171, + 390 + ], + "type": "text", + "content": "6.2. Embedding strategies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 288, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 540 + ], + "type": "text", + "content": "To see which patch embedding scheme is most suitable for DCT, we performed an ablation study in Tab. 3. We ablate on the embedding strategies and the sub-block conversion technique discussed in Sec. 4 on ViT-S. The results show two things. One is that the simplest strategy-grouped embedding-is best, and that sub-block conversion is important to achieve high accuracy. We believe this indicates that (1) all blocks in an image patch relay information of that patch as a whole; they should not be separately inferred, and (2) it is more natural for the model to deduce the information in a patch if the sub-blocks are fused together. The best strategy is used throughout the DCT models in Tab. 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 551, + 136, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 136, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 136, + 563 + ], + "type": "text", + "content": "6.3. Augmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": "As discussed in Sec. 5, data augmentation is crucial to train a well-performing model. However, many existing studies [9, 10, 103-108] are tuned toward RGB augmentations; we cannot assume that the existing work's result would be consistent on DCT. In other words, some DCT augmentations could have a different impact on both the accuracy and throughput of the model compared to RGB. Therefore, we perform an ablation study on data augmentations discussed in Sec. 5 and report the result in Tab. 2. We perform ablation by varying the subset of augmentations used in RandAugment [10] on ViT-S. The experiment is performed separately for RGB and DCT with their re" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 265, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 547, + 373 + ], + "type": "text", + "content": "spective augmentation sets. The results show that while sub-block-based augmentations (e.g. rotate, shear) are prohibitively expensive to do directly on DCT, it is not as important to train a model. We report the best augmentation subset we found without sub-block-based augmentations at the bottom row. In addition, we train an RGB model using this subset and compare the accuracy. We can see that the RGB model performs identically to the DCT model, and the subset does not unfairly favor DCT over RGB models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 394, + 379, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 379, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 379, + 407 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 418, + 547, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 503 + ], + "type": "text", + "content": "In this paper, we demonstrated that vision transformers can be accelerated significantly by directly training from the DCT coefficients of JPEG. We proposed several DCT embedding strategies for ViT, as well as reasonable augmentations that can be directly carried out on the DCT coefficients. The throughput of our model is considerably faster with virtually no accuracy loss compared to RGB." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "content": "RGB has been widely used for as long as computer vision existed. Many computer vision schemes regard retrieving RGB as a necessary cost; they have not considered the potential of direct encoded-space training in-depth. We wanted to show the capability of this approach, as well as demonstrate that recovering RGB is not always necessary." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Encoded-space training can be adapted to nearly all scenarios that require loading some compressed data from storage. From mobile devices to powerful data centers, there are no situations where they wouldn't benefit from faster loading speed. As we only considered the plain ViT architecture, there is still more to be gained by adapting our findings to the existing efficient architectures. Future studies may also consider a better augmentation strategy to improve the performance further. We hope that the techniques shown in this paper prove to be an adequate foundation for future encoded-space research." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "spans": [ + { + "bbox": [ + 293, + 743, + 317, + 753 + ], + "type": "text", + "content": "22341" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 58, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Lionel Gueguen, Alex Sergeev, Ben Kadlec, Rosanne Liu, and Jason Yosinski. 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In this work, we present a new solution termed $\\text{RGBD}^2$ that sequentially generates novel RGBD views along a camera trajectory, and the scene geometry is simply the fusion result of these views. More specifically, we maintain an intermediate surface mesh used for rendering new RGBD views, which subsequently becomes complete by an inpainting network; each rendered RGBD view is later back-projected as a partial surface and is supplemented into the intermediate mesh. The use of intermediate mesh and camera projection helps solve the tough problem of multi-view inconsistency. We practically implement the RGBD inpainting network as a versatile RGBD diffusion model, which is previously used for 2D generative modeling; we make a modification to its reverse diffusion process to enable our use. We evaluate our approach on the task of 3D scene synthesis from sparse RGBD inputs; extensive experiments on the ScanNet dataset demonstrate the superiority of our approach over existing ones. Project page: https://jblei.site/proj/rgbd-diffusion.", + "bbox": [ + 75, + 338, + 473, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 641, + 208, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scene synthesis is an essential requirement for many practical applications. The resulting scene representation can be readily utilized in diverse fields, such as virtual reality, augmented reality, computer graphics, and game development. Nevertheless, conventional approaches to scene synthesis usually involve reconstructing scenes (e.g., indoor scenes with varying sizes) by fitting given observations, such as multi-view images or point clouds. The increasing prevalence of RGB/RGBD scanning devices has established multi-view data as a favored input modality, driving and promoting technical advancements in the realm of scene reconstruction from multi-view images.", + "bbox": [ + 75, + 661, + 468, + 827 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural Radiance Fields (NeRFs) [42] have demonstrated", + "bbox": [ + 95, + 828, + 468, + 842 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e6ecad3a716aaec0762ce18756dbc183a05ef24ace83a615449604ad12029d9b.jpg", + "image_caption": [ + "$t = 0$" + ], + "image_footnote": [], + "bbox": [ + 539, + 333, + 616, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/53b0650c244c28dfec3bb61f36829b0d0b05ae02b12665db35da6d88bf4373fe.jpg", + "image_caption": [ + "$t = 1$" + ], + "image_footnote": [], + "bbox": [ + 640, + 313, + 719, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2243ea2d0b580b4866865ad361f81750e3dc49c46829e9367f2702740c808cc6.jpg", + "image_caption": [ + "$t = 2$" + ], + "image_footnote": [], + "bbox": [ + 734, + 311, + 848, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/af5a9859a8d6bfe2519f5304edb9d69ce0dede25a2ccee65dff034ec4fd8bc9d.jpg", + "image_caption": [ + "$t = 3$" + ], + "image_footnote": [], + "bbox": [ + 544, + 404, + 660, + 476 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0db275be78bb69072dbb509103945ff4f2626fa62702882a75254c49bec4dece.jpg", + "image_caption": [ + "Final Result", + "Figure 1. Illustration of Our Generative Scene Synthesis. We incrementally reconstruct the scene geometry by inpainting RGBD views as the camera moves in the scene." + ], + "image_footnote": [], + "bbox": [ + 705, + 404, + 843, + 480 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "potential in this regard, yet they are not exempt from limitations. NeRFs are designed to reconstruct complete scenes by fitting multi-view images, and they cannot generate or infer missing parts when the input is inevitably incomplete or missing. While recently some studies [3,5,8,56,63] have attempted to equip NeRFs with generative and extrapolation capabilities, this functionality relies on a comparatively short representation with limited elements (e.g. typically, the length of a global latent code is much shorter than that of an image: $(F = 512) \\ll (H \\times W = 128 \\times 128 = 16,384)$ ) that significantly constrains their capacity to accurately capture fine-grained details in the observed data. Consequently, the effectiveness of these methods has only been established for certain categories of canonical objects, such as faces or cars [8, 63], or relatively small toy scenes [5].", + "bbox": [ + 497, + 546, + 892, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce a novel task of generative scene synthesis from sparse RGBD views, which involves learning across multiple scenes to later enable scene synthesis from a sparse set of multi-view RGBD images. This task presents a challenging setting wherein a desired solution should simultaneously (1) preserve observed regions, hallucinate missing parts of the scene, (2) eliminate additional computational costs during inference for each individual test scene, (3) en", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 86 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Correspondence to Kui Jia: .", + "bbox": [ + 99, + 853, + 381, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8422", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sure exact 3D consistency, and (4) maintain scalability to scenes with unfixed scales.", + "bbox": [ + 75, + 125, + 468, + 153 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We will elaborate on them in detail as follows. Firstly, to maximize the preservation of intricate details while simultaneously hallucinating potentially absent parts that may become more pronounced when views are exceedingly sparse, we perform straightforward reconstruction whose details come from images that can describe fine structures using a maximum of $H \\times W$ elements (i.e. an image size) in a view completion manner. This is particularly compatible with diffusion models that operate at full image resolution with an inpainting mechanism. We also found that RGBD diffusion models greatly simplify the training complexity of a completion model, thanks to their versatile generative ability to inpaint missing RGBD pixels while preserving the integrity of known regions through a convenient training process solely operated on complete RGBD data. Secondly, our method employs back-projection that requires no optimization, thus eliminating the necessity for test-time training for each individual scene, ultimately leading to a significant enhancement in test-time efficiency. Thirdly, to ensure consistency among multi-view images, an intermediate mesh representation is utilized as a means of bridging the 2D domain (i.e. multi-view RGBD images) with the 3D domain (i.e. the 3D intermediate mesh) through the aid of camera projection. Fourthly, to enable our method to handle scenes of indeterminate sizes, we utilize images with freely designated poses as the input representation. Such manner naturally ensures SE(3) equivariance, and thus offers scalability due to the ease with which the range of the generated content can be controlled by simply specifying their camera extrinsic matrices.", + "bbox": [ + 75, + 157, + 472, + 570 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our proposal involves generating multi-view consistent RGBD views along a predetermined camera trajectory, using an intermediate mesh to render novel RGBD images that are subsequently inpainted using a diffusion model, and transforming each RGBD view into a 3D partial mesh via back-projection, and finally merging it with the intermediate scene mesh to produce the final output. Specifically, our proposed approach initiates by ingesting multiple posed RGBD images as input and utilizing back-projection to construct an intermediate scene mesh. This mesh encompasses color attributes that facilitate the rendering of RGBD images from the representation under arbitrarily specified camera viewpoints. Once a camera pose is selected from the test-time rendering trajectory, the intermediate mesh is rendered to generate a new RGBD image for this pose. Notably, the test-time view typically exhibits only slight overlap with the known cameras, leading to naturally partially rendered RGBD images. To fill the gaps in the incomplete view, we employ an inpainting network implemented as an RGBD diffusion model with minor modifications to its reverse sampling process. The resulting inpainted out", + "bbox": [ + 75, + 576, + 472, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "put is then back-projected into 3D space, forming a partial mesh that complements the entire intermediate scene mesh. We iterate these steps until all test-time camera viewpoints are covered, and the intermediate scene mesh gradually becomes complete during this process. The final output of our pipeline is the mesh outcome acquired from the last step.", + "bbox": [ + 497, + 125, + 890, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments on ScanNet [12] dataset demonstrate the superiority of our approach over existing solutions on the task of scene synthesis from sparse RGBD inputs.", + "bbox": [ + 497, + 209, + 890, + 251 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 497, + 254, + 650, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we provide a brief review of the literature related to diffusion models, 3D representations and generative manners, scene synthesis, and view synthesis.", + "bbox": [ + 497, + 271, + 890, + 313 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Models. In recent years, the field of 2D computer vision has experienced a surge of interest in diffusion-based generative models [20,65,67]. These models have prompted the development of image generative modeling approaches, such as GLIDE [45], unCLIP [53], Imagen [61], and Latent Diffusion Models [57], as well as the invention of sampling schedulers [20, 26, 36, 66] and guiding methods [15, 22]. Furthermore, these models have been applied to a broad range of image processing tasks, including image inpainting [37], image translation [4, 57, 60, 82], video generation [23, 25, 76], super-resolution [21, 32, 62], and image editing [2, 27, 40]. More recently, some researchers have adapted these techniques from 2D to the 3D domain, as demonstrated by methods such as [39, 51, 88, 92]. Our approach harnesses such versatility by adopting an iterative denoising strategy like [37], and utilizing a masked inpainting technique that operates on the projected RGBD views to synthesize image content.", + "bbox": [ + 497, + 314, + 892, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Representations and Generative Manners. A variety of representations, including voxels [81, 85], point clouds [1, 39, 68, 87, 92], meshes [17, 44, 70, 71, 79], implicit surfaces [10, 30, 31, 41, 48, 72-74, 88, 91], multi-view images [11, 19, 34, 35, 86], and neural radiance fields [3, 8, 9, 13, 42, 43, 49, 56, 63, 80], have been proposed, each with its own unique advantages over the others. This has also motivated researchers to combine them with distinct generative approaches, such as VAEs [28], GANs [16], normalizing flows [54], auto-regressive models [24, 75], and the latest diffusion models [20], resulting in an extensive range of applications [1, 8, 39, 41, 44, 48, 63, 85, 87, 92]. However, most existing methods have limitations in their representation capability, such as cubically scaled-up memory consumption, or a fixed number of points, which makes them difficult to apply to scenes of uncertain scales, and poor equivariance, which only allows them to handle canonically-posed objects. In this paper, we address these issues by focusing on the generation of multi-view RGBD images that can capture intricate structures using $H \\times W$ pixels created by a diffusion model. This approach reduces memory complexity from $\\mathcal{O}(HWD)$ to $\\mathcal{O}(HW)$ and increases expressive", + "bbox": [ + 497, + 562, + 892, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8423", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ability from $\\mathcal{O}(F)$ to $\\mathcal{O}(HW)$ .", + "bbox": [ + 75, + 125, + 285, + 138 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene Synthesis. In this area, there are two primary research directions. The first pertains to learning configurations, including graphs [33, 38, 77, 90], top-down views [55, 78], and scene composition [50, 83]. The second line of research involves direct learning from the appearance of a scene [13, 42, 43, 49, 80], thereby obviating the necessity for specialized synthesized datasets required by the aforementioned methods. Our approach relies solely on RGBD scans, which are readily available from scanning devices, reducing the need for manual annotation. It accurately reconstructs a clean geometry based on the sparse-view input and can effectively hallucinate missing parts, especially when the input views are highly sparse.", + "bbox": [ + 75, + 138, + 468, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "View Synthesis. The arrival of NeRF [42] has significantly advanced the field of view synthesis. While a considerable amount of research has been dedicated to the view synthesis of object-level instances [7, 18, 47, 64], only a few studies have focused on simple scenes [5, 14, 58]. Additionally, some studies have explored techniques for improving performance using sparse inputs [46, 56]. In this paper, we aim to recover scene-level geometry from sparse RGBD images without relying on NeRFs.", + "bbox": [ + 75, + 319, + 468, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 75, + 448, + 201, + 463 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make our paper self-contained, we provide some preliminary knowledge about DDPM [20] and DDIM [66].", + "bbox": [ + 75, + 467, + 468, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition. Given an image $\\mathbf{x}_0\\sim q(\\mathbf{x}_0)$ , the forward diffusion process is a Markov chain that sequentially produces noisy images $\\mathbf{x}_1,\\dots ,\\mathbf{x}_T$ scheduled by a set of constants $\\{\\beta_t\\in (0,1)\\}_{t = 1}^T$ where $T$ is the total number of iterations and $\\beta_{1} < \\beta_{2} < \\ldots < \\beta_{T}$ :", + "bbox": [ + 75, + 496, + 468, + 565 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 131, + 566, + 411, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A nice property of using i.i.d. Gaussian distribution is that we can sample the noisy image $\\mathbf{x}_t$ easily based on $\\mathbf{x}_0$ in a closed form without computing all the intermediates:", + "bbox": [ + 75, + 591, + 468, + 633 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha}} _ {t} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 139, + 640, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} = \\prod_{s = 1}^{t}\\alpha_{s}$ . The reverse diffusion process is another Markov chain starting from $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})$ parameterized by a trainable $\\theta$ :", + "bbox": [ + 75, + 663, + 468, + 707 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 714, + 468, + 730 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{\\Sigma}_{\\theta}(\\mathbf{x}_t,t) = \\sigma_t^2\\mathbf{I} = \\eta \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t\\mathbf{I}$ [66] is independent of $\\theta$ and $\\mathbf{x}_t$ , and $\\mu_{\\theta}(\\mathbf{x}_t,t)$ can be derived from a noise estimator $\\epsilon_{\\theta}(\\mathbf{x}_t,t)$ via:", + "bbox": [ + 75, + 737, + 468, + 780 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {o}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 115, + 788, + 425, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We practically implement the noise estimator $\\epsilon_{\\theta}(\\mathbf{x}_t,t)$ as a UNet [57, 59] parameterized by $\\theta$ . However, in our case, it is also conditioned on $\\hat{\\mathbf{x}}_0$ which will be detailed in Sec. 4.2.", + "bbox": [ + 75, + 826, + 468, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training. To train the noise estimator $\\epsilon_{\\theta}(\\mathbf{x}_t,t)$ , we adopt the simplified training objective [20]:", + "bbox": [ + 497, + 125, + 890, + 153 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {t, \\epsilon_ {t}, \\mathbf {x} _ {0}} \\left[ \\| \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {t}, t) - \\epsilon_ {t} \\| ^ {2} \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 163, + 860, + 185 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the time step $t\\sim \\mathcal{U}\\{1,T\\}$ is uniformly sampled, $\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ is a standard Gaussian noise, and the image $\\mathbf{x}_0\\sim q(\\mathbf{x}_0)$ is randomly drawn from the data distribution.", + "bbox": [ + 497, + 195, + 890, + 238 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inference. We employ a strided DDIM [66] scheduler to progressively recover the clean image from $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ to $\\mathbf{x}_0$ with a subset of $S$ (usually $S\\ll T$ ) steps $\\{\\tau_i\\}_{i = 1}^S$", + "bbox": [ + 497, + 248, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {\\tau_ {i - 1}} \\leftarrow \\sqrt {\\bar {\\alpha} _ {\\tau_ {i - 1}}} \\left(\\frac {\\mathbf {x} _ {\\tau_ {i}} - \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}} , \\tau_ {i})}{\\sqrt {\\bar {\\alpha} _ {\\tau_ {i}}}}\\right) + \\\\ \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i - 1}} - \\sigma_ {\\tau_ {i}} ^ {2}} \\cdot \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}}, \\tau_ {i}) + \\sigma_ {\\tau_ {i}} ^ {2} \\epsilon_ {\\tau_ {i}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 311, + 865, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\tau_i} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ is a standard Gaussian noise. It is interesting that setting $\\eta = 0$ implies $\\forall i$ , $\\sigma_{\\tau_i} \\equiv 0$ , making the inference process deterministic. Nevertheless, diversity can still be achieved by choosing a different $\\mathbf{x}_T$ from $\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ .", + "bbox": [ + 497, + 378, + 890, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Approach", + "text_level": 1, + "bbox": [ + 499, + 437, + 606, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we introduce a new scene synthesis approach that relies on the sequential generation of RGBD frames using a trained RGBD diffusion model conditioned on views rendered under a test-time camera trajectory from a sparse set of input RGBD images. Our approach leverages the generative ability of diffusion models to synthesize missing visual appearance (color) and geometry details (depth) while rigorously preserving visible regions by image inpainting. Such an incremental view inpainting process is interleaved with the back-projection, mesh fusion, and mesh rendering procedures to achieve global 3D consistency among distinct temporal frames.", + "bbox": [ + 497, + 458, + 890, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section is organized as follow. In Sec. 4.1, we will start by introducing the overall framework of repeatedly converting the RGBD image into a partial 3D mesh and performing RGBD inpainting for rendered views in a progressive manner. Later in Sec. 4.2, we will elaborate more on the details of the conditional RGBD diffusion model for rendered view inpainting based on a trained DDPM [20].", + "bbox": [ + 497, + 623, + 890, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Incremental View Inpainting Fashion", + "text_level": 1, + "bbox": [ + 497, + 723, + 821, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, given a sparse set of $N$ RGBD views $\\{\\mathbf{I}_i\\}_{i=1}^N$ with their associated camera intrinsic $\\mathbf{K}$ and extrinsic $\\{\\mathbf{R}_i\\}_{i=1}^N$ matrices, and additionally a camera trajectory composed of $M$ viewpoints $\\{\\mathbf{T}_j\\}_{j=1}^M$ with the same intrinsic matrix, the essence of our method is to progressively synthesize RGBD images $\\mathbf{O}_j$ at each specified novel view $\\mathbf{T}_j$ . The generated novel-view frames should be consistent with $\\{\\mathbf{I}_i\\}_{i=1}^N$ in both geometry and appearance. The final output should be a consistent 3D", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8424", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/af0fdedf317ec3fac38e7e2af6ab146b2bfc5c1b75537a7c20b1b1a72e6886e8.jpg", + "image_caption": [ + "Figure 2. 3D Scene Synthesis via Incremental View Inpainting. Given a sparse set of RGBD images $\\{\\mathbf{I}_i\\}_{i=1}^N$ with camera intrinsic $\\mathbf{K}$ and extrinsic $\\{\\mathbf{R}_i\\}_{i=1}^N$ matrices, our goal is to generate a coherent 3D scene mesh $\\mathcal{S}$ via predicting RGBD frames $\\{\\mathbf{O}_j\\}_{j=1}^M$ along a novel-view trajectory $\\{\\mathbf{T}_j\\}_{j=1}^M$ . To achieve this goal, we firstly fuse the inputs of $\\{\\mathbf{I}_i\\}_{i=1}^N$ into an initial mesh $\\mathcal{S}_1$ , and then render it to obtain an incomplete image $\\hat{\\mathbf{O}}_1$ that is later inpainted to obtain $\\mathbf{O}_1$ using a RGBD diffusion model. After that, $\\mathbf{O}_1$ is back-projected and integrated with $\\mathcal{S}_1$ to produce a more complete scene, $\\mathcal{S}_2$ . By iteratively repeating this process, we can progressively obtain $\\mathcal{S}_2, \\dots, \\mathcal{S}_M$ . Finally, the fused result $\\mathcal{S}_{M+1}$ is the eventual desired output $\\mathcal{S}$ . Gray dashed lines “- - ” denote omitted and unvisualized steps." + ], + "image_footnote": [], + "bbox": [ + 85, + 125, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "colored mesh $S$ converted from the back-projection result $\\left( \\cup_{j=1}^{M} \\phi_{2 \\to 3}(\\mathbf{O}_j) \\right) \\cup \\left( \\cup_{i=1}^{N} \\phi_{2 \\to 3}(\\mathbf{I}_i) \\right)$ . Please also refer to Algorithm 1 for a detailed description of the procedure.", + "bbox": [ + 75, + 456, + 470, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Incremental RGBD View Inpainting", + "text_level": 1, + "bbox": [ + 80, + 505, + 406, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: RGBD images $\\{\\mathbf{I}_i\\}_{i=1}^N$ with camera extrinsics $\\{\\mathbf{R}_i\\}_{i=1}^N$ , a novel trajectory of M extrinsics $\\{\\mathbf{T}_j\\}_{j=1}^M$ .", + "bbox": [ + 80, + 524, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {1} \\leftarrow \\cup_ {i = 1} ^ {N} \\phi_ {2 \\rightarrow 3} (\\mathbf {I} _ {i})\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 554, + 233, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for $j = 1$ to $M$ do", + "bbox": [ + 95, + 568, + 220, + 581 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {\\hat {O}} _ {j} \\leftarrow \\phi_ {3 \\rightarrow 2} (\\mathbf {T} _ {j})\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 581, + 236, + 596 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\triangleright$ novel-view rendering", + "bbox": [ + 312, + 583, + 468, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {O} _ {j} \\leftarrow f (\\hat {\\mathbf {O}} _ {j})\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 597, + 210, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "RGBD inpainting", + "bbox": [ + 337, + 598, + 468, + 610 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {j + 1} \\leftarrow \\mathcal {S} _ {j} \\cup \\phi_ {2 \\rightarrow 3} (\\mathbf {O} _ {j})\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 612, + 284, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\triangleright$ mesh fusion", + "bbox": [ + 373, + 612, + 467, + 624 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 95, + 627, + 147, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "return $\\mathcal{S}_{M + 1}$", + "bbox": [ + 95, + 640, + 186, + 653 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rendering and Back-projection. The operator $\\phi_{3\\rightarrow 2}$ is implemented as mesh rasterization, which allows for the rendering of a partial RGBD image $\\hat{\\mathbf{O}}_j$ from a mesh $S_{j}$ . This approach offers the advantage of producing a clean visibility mask $\\mathbf{m}_j$ , which is not possible with NeRFs [42]. The back-projection operator $\\phi_{2\\rightarrow 3}$ is responsible for the conversion from a depth map into a point cloud, where the connectivity between points is inherited from the connectivity of the 2D pixel grid. Furthermore, mesh faces that are either in close proximity to the viewpoint or exhibit slender characteristics are filtered out to ensure accuracy.", + "bbox": [ + 75, + 666, + 468, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Challenges and Solutions. To circumvent the limitations", + "bbox": [ + 75, + 819, + 468, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "posed by potential 3D inconsistency in both geometry and appearance, as well as the challenge of solely handling specific canonically-posed scenes, we propose several strategies to address these issues. Firstly, our method for synthesizing novel views combines rendering (mesh rasterization) and inpainting techniques, and interleaves the view synthesis process with online RGBD fusion via back-projection and mesh combination. The use of perspective camera projection ensures strict adherence to 3D constraints, resulting in visually consistent and accurate synthesized views. In concrete terms, we begin by rendering the mesh $S_{j}$ under view $\\mathbf{T}_{j}$ using a rendering operation $\\phi_{3\\rightarrow 2}(\\mathbf{T}_{j})$ . This process yields an incomplete RGBD image $\\hat{\\mathbf{O}}_j$ with missing regions, which is subsequently inpainted using a diffusion model described in detail in Sec. 4.2, resulting in a complete image $\\mathbf{O}_j$ . Once image $\\mathbf{O}_j$ has been generated for view $\\mathbf{T}_j$ , it can be fused into a 3D mesh via $S_{j + 1} = \\phi_{2\\rightarrow 3}(\\mathbf{O}_j)\\cup S_j$ using a back-projection operator $\\phi_{2\\rightarrow 3}$ . Secondly, our solution reduces the learning difficulty and can handle noncanonical scenes by decomposing the 3D scene as a Markov chain of temporal RGBD images rendered from arbitrarily specified novel viewpoints. The applicability of handling scenes with arbitrary scaling, movement, and posing is attributed to the utilization of two SE(3) equivariant operators, namely $\\phi_{3\\rightarrow 2}$ and $\\phi_{2\\rightarrow 3}$ , as well as the independence of absolute coordinates. Moreover, the presence of redundant information in adjacent frames, combined with our suggested decomposition rule, facilitates the minimization of learning complexity in an auto-regressive manner.", + "bbox": [ + 499, + 456, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1 To simplify notations, we disregard certain arguments in operators $\\phi_{3\\to 2}$ and $\\phi_{2\\to 3}$ , such as the camera intrinsic matrix $\\mathbf{K}$ .", + "bbox": [ + 75, + 842, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8425", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In accordance with the Markov chain decomposition principle, the distribution of the scene can be expressed as the joint distribution of view frames:", + "bbox": [ + 75, + 125, + 470, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathcal {S}) = \\prod_ {j} p (\\mathbf {O} _ {j} \\mid \\{\\mathbf {O} _ {s} \\} _ {s = 1} ^ {j - 1}, \\{\\mathbf {I} _ {s} \\} _ {s = 1} ^ {N})\n$$\n", + "text_format": "latex", + "bbox": [ + 139, + 174, + 406, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the prediction of $\\mathbf{O}_j$ is based on the fusion result of all the previously known frames $\\{\\mathbf{O}_s\\}_{s=1}^{j-1} \\cup \\{\\mathbf{I}_s\\}_{s=1}^N$ .", + "bbox": [ + 75, + 205, + 470, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. RGBD Diffusion for Rendered View Inpainting", + "text_level": 1, + "bbox": [ + 75, + 241, + 468, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we describe the implementation details of the way to employ diffusion models to inpaint the missing regions of the RGBD image $\\hat{\\mathbf{O}}_j$ with a binary mask $\\mathbf{m}_j$ obtained by rendering visibility, where the value of 1 is assigned to the corresponding ray that intersects with the geometry surface, while 0 is assigned to all other cases, both of which are rendered by projecting $S_{j}$ under a novel viewpoint $\\mathbf{T}_j$ . It is noteworthy that only those pixels located where $\\mathbf{m}_j = 0$ in $\\hat{\\mathbf{O}}_j$ are considered invalid, and therefore, are entirely filled with zeros (i.e., $\\hat{\\mathbf{O}}_j\\odot \\mathbf{m}_j\\equiv \\hat{\\mathbf{O}}_j$ ).", + "bbox": [ + 75, + 262, + 468, + 404 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6906c4f13e23c97d09c549e269e678c9755500f0cd73c536b2bbdb1580ea17f9.jpg", + "image_caption": [ + "Figure 3. RGBD Diffusion for Rendered View Inpainting. In each iteration, we utilize a forward diffusion step to sample the visible region $\\mathbf{x}_t^{\\mathrm{vis}}$ (top) from the incomplete input $\\hat{\\mathbf{x}}_0$ , while employing a denoising diffusion step to obtain the complementary content $\\mathbf{x}_t^{\\mathrm{invis}}$ (bottom) from the output $\\mathbf{x}_{t + 1}$ generated in the previous iteration $t + 1$ ." + ], + "image_footnote": [], + "bbox": [ + 80, + 412, + 467, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A Single Reverse Diffusion Step for $\\mathbf{T}_j$ at Time $t$ .2 We initialize the clean diffusion sample $\\hat{\\mathbf{x}}_0$ at time $t = 0$ as $\\hat{\\mathbf{O}}_j$ , and those noisy samples at time $0 < t \\leq T$ are denoted as $\\mathbf{x}_t$ . To ensure 3D consistency, we seek to predict the invisible region $\\mathbf{x}_0^{\\mathrm{vis}}$ while preserving the visible portion $\\mathbf{x}_0^{\\mathrm{vis}}$ unaltered. We follow [37] and modify the standard denoising process to meet our needs. At each reverse diffusion step $t$ , we use the forward diffusion process defined by the Eqn. (1) to sample a visible region $\\mathbf{x}_t^{\\mathrm{vis}}$ masked by $\\mathbf{m}$ , and the reverse diffusion step defined by Eqn. (2) to sample a full part from $\\mathbf{x}_{t+1}$ which is later masked by $1 - \\mathbf{m}$ to form an invisible region $\\mathbf{x}_t^{\\mathrm{vis}}$ .", + "bbox": [ + 75, + 634, + 468, + 802 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {\\text {v i s}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} + (1 - \\bar {\\alpha} _ {t}) \\epsilon_ {t} ^ {\\text {v i s}} \\odot \\mathbf {m}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 809, + 389, + 826 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {\\text {i n v i s}} = \\left(\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {t}, t\\right) + \\sigma_ {t} \\epsilon_ {t} ^ {\\text {i n v i s}}\\right) \\odot (1 - \\mathbf {m})\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 122, + 843, + 140 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon_t^{\\mathrm{vis}},\\epsilon_t^{\\mathrm{invis}}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ . The noisy image $\\mathbf{x}_t$ can be simply calculated as the sum of $\\mathbf{x}_t^{\\mathrm{vis}}$ and $\\mathbf{x}_t^{\\mathrm{invis}}$ , as expressed by $\\mathbf{x}_t = \\mathbf{x}_t^{\\mathrm{vis}} + \\mathbf{x}_t^{\\mathrm{invis}}$", + "bbox": [ + 497, + 144, + 890, + 188 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diffusion Network. We implement the diffusion model as a UNet [57, 59] conditioned on the observed region $\\mathbf{x}_0$ . We input the concatenation of $\\mathbf{x}_t$ and $\\hat{\\mathbf{x}}_0$ into the network.", + "bbox": [ + 497, + 193, + 890, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Classifier-free Guidance. To further enhance the controllability of the generation process, we introduce a classifier-free guidance [22] mechanism. Specifically, we train a unified network $\\epsilon_{\\theta}$ comprising of an unconditional model $\\epsilon_{\\theta}(\\mathbf{x}_t,\\mathbf{c},t)$ , where the shared variable $\\mathbf{c}$ is incorporated, and a conditional model $\\epsilon_{\\theta}(\\mathbf{x}_t,\\hat{\\mathbf{x}}_0,t)$ . In this way, the predicted noise $\\tilde{\\epsilon}_{\\theta}$ can be recomputed as follows:", + "bbox": [ + 497, + 237, + 892, + 334 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\epsilon} _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) = \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) + \\beta \\times [ \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) ]\n$$\n", + "text_format": "latex", + "bbox": [ + 497, + 345, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta \\geq 0$ is the guidance factor, being responsible for the trade-off between sampling quality and diversity [22].", + "bbox": [ + 497, + 371, + 890, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 499, + 406, + 631, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We conducted experiments on the ScanNetV2 [12] dataset, which was pre-processed by removing redundant frames [69]. For training, we used the first 1,293 scenes, while for metric evaluation, we randomly selected 18 scenes with over 50 views each from the remaining as our test set. We also evaluated under various sparsity settings (5%, 10%, 20%, and 50%) by uniformly down-sampling views.", + "bbox": [ + 497, + 423, + 890, + 533 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison. We compared against the neural graphics primitive (NGP) [43], which has demonstrated impressive performance in scene modeling with high efficiency. To enhance its geometric quality, we incorporated a depth supervision (DS) loss [13] to build an improved variant called DS-NGP [13, 43]. We also compare against Neural RGBD (N-RGBD) [3], which recovers implicit surfaces from RGBD scans, and Dense Depth Prior (DDP) [56], which learns a NeRF utilizing view completion from sparse RGBD views.", + "bbox": [ + 497, + 534, + 890, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. For assessing the visual quality of RGB images, we adopted the peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [89] that is based on the AlexNet [29] backbone. To evaluate the geometry quality, we computed the mean squared error (MSE) on depth maps, and sample 10,000 points uniformly on meshes constructed via back-projection to evaluate the chamfer distance (CD) and completeness (Comp.) with a threshold of $0.1\\mathrm{m}$ . We also measured the computational time required to execute different stages of the method. For LPIPS, MSE, and CD, the lower the better; for PSNR, SSIM, and Comp., the higher the better. All reported metrics are averaged across the test scenes.", + "bbox": [ + 497, + 672, + 892, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2 For notational simplicity, we ignore the novel camera subscript $j$ in the following part of this Sec. 4.2 since all notations we consider here are derived from the same camera $\\mathbf{T}_j$ .", + "bbox": [ + 75, + 831, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8426", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our model has 157M parameters and was trained for three days on 7 NVIDIA 3090-Ti GPUs, using a batch size of 280. The learning rate was initialized at $1 \\times 10^{-4}$ and reduced to $1 \\times 10^{-6}$ over a period of 300 epochs, utilizing a cosine annealing strategy. The image resolution is $128 \\times 128$ with a rendering chunk size of 7.", + "bbox": [ + 75, + 125, + 468, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Ablation Studies", + "text_level": 1, + "bbox": [ + 75, + 216, + 240, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conducted ablation studies to validate the effectiveness of each component in our proposal. Results concluded here are nontrivial and a bit nuanced.", + "bbox": [ + 75, + 235, + 468, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Different Ingredients. We examined the anticipated efficacy of the proposed conditioning and inpainting components in our approach. Table 2 displays the numerical results, and Figure 5-(a-c) presents the visualizations. The combined use of conditioning and inpainting yields superior visual performance compared to the ground truth. Nevertheless, when the model is conditioned, the impact of inpainting on geometric quality becomes less crucial. Moreover, as more views are provided, the stochastic generation process becomes increasingly deterministic, resulting in structures that more closely resemble the ground truth.", + "bbox": [ + 75, + 277, + 468, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Guidance Scale. The guidance factor $\\beta$ significantly affects the conditioning effect on the results. To investigate the optimal $\\beta$ under various settings, we conducted experiments with $\\beta$ chosen from 0.0, 0.5, 1.0, 2.0, and 5.0, respectively, and evaluated their performance. Quantitative results are presented in Table 3. It is interesting that only a suitable value of $\\beta$ (1.0 or 2.0) yields optimal performance, while smaller or larger values of $\\beta$ result in underperformance. Surprisingly, for geometric recovery (MSE and CD), the optimal value of $\\beta$ appears to increase as the percentage gets larger. For a scene with a percentage $\\geq 50\\%$ , the best value of $\\beta$ is amazingly greater than 5.0. However, such a large percentage is not optimal for visual appearance. This is because using a larger value of $\\beta$ at a low percentage can cause the generated results to deviate unexpectedly from the ground truth. Our visualization, presented in Figure 5-(a, c, d), indicates that using an unconditional model ( $\\beta = 0$ ) leads to undesired and bizarre geometric structures since the network fails to understand the context provided by known views. However, excessively large values of $\\beta$ also oversaturate the color (e.g. row “(d)” at $5\\%$ ), making the visual appearance unrealistic.", + "bbox": [ + 75, + 429, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Randomness and Trajectories. We investigated", + "bbox": [ + 75, + 733, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/667411f8f3865b6c8e79adda100c3b6508f4409591d5fa6d5e6d301c7079e91f.jpg", + "image_caption": [ + "(a) original" + ], + "image_footnote": [], + "bbox": [ + 78, + 761, + 181, + 825 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7702e27e95d9ba0b58d343044003fd82de25acb8fad3a9d4964eacad22452589.jpg", + "image_caption": [ + "(b) seed" + ], + "image_footnote": [], + "bbox": [ + 181, + 761, + 290, + 825 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2154a1da3631d63db816ecaeaf07bf4f163bbe22e7be25dca39303cfdc022432.jpg", + "image_caption": [ + "(c) trajectory", + "Figure 4. Diverse results obtained by changing the (b) random seed and (c) camera trajectory based on (a) the original scene." + ], + "image_footnote": [], + "bbox": [ + 292, + 761, + 468, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the impact of employing different random seeds and camera trajectories on the results. Such obtained meshes are visualized in Figure 4. As diffusion models inherently include randomness in their reverse sampling process, by switching to a different random seed, we can obtain another outcome. Moreover, the camera trajectory can affect the rough shape of the scene. It is promising that our approach can yield controllable and editable results, as it is capable of generating various and appealing outcomes by simply altering these two factors.", + "bbox": [ + 497, + 125, + 890, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Generative Scene Synthesis", + "text_level": 1, + "bbox": [ + 499, + 268, + 744, + 283 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated the performance of our method against other similar approaches on this task through extensive experiments under various sparsity settings. Table 1 presents the time required by different methods across various stages. Our approach stands out for its efficiency, as it eliminates the need for additional optimization on individual test scenes during inference. Quantitative results are shown in", + "bbox": [ + 497, + 286, + 890, + 383 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9de6690d162a6143c813316609d1cf96aa26da7b018ffc99b9c212b8e1f58d3e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TimeBackendRepre.TrainingOptimizationRendering
(DS-)NGP [13,43]CUDA C++NeRF—~ 3 min.~ 0.05 sec.
N-RGBD [3]PyTorchNeRF—~ 2 hours~ 2 sec.
DDP [56]PyTorchNeRF~ 1 day~ 1 hour~ 1 sec.
OursPyTorchMesh~ 3 days—~ 3 sec.
", + "bbox": [ + 502, + 387, + 889, + 442 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Efficiency Comparison of Different Methods. It details their distinct implementation backends, the underlying representation (Repre.) methods, and the time required for training on multiple training scenes, optimization on a single test scene, and rendering a single view after per-scene optimization.", + "bbox": [ + 497, + 444, + 890, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. We observe that our approach exhibits a clear advantage in visual metrics over the others when the provided views are extremely sparse (5%). Interestingly, our method consistently achieves the best performance in all the geometry-related metrics. Qualitative results are presented in Figure 6. DS-NGP [13, 43] and DDP [56] struggle to accurately recover geometry due to their inability to hallucinate and extrapolate missing regions. In comparison, N-RGBD [3] can achieve better surface completion results by learning and extrapolating neural implicit surfaces. However, their performance significantly degrades when input views are extraordinarily sparse (5%). In contrast, our method consistently exhibits plausible appearance that closely resembles the ground truth, particularly in scenarios with sparse-view inputs.", + "bbox": [ + 497, + 511, + 890, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Discussions", + "text_level": 1, + "bbox": [ + 499, + 725, + 620, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Limitations. Our current implementation has several limitations that may impact its usefulness in some scenarios. Firstly, it is incapable of handling color discrepancies caused by lighting variations. Secondly, it lacks surface extrapolation capabilities that can be provided through implicit field representation. Lastly, the limited receptive field of our design is confined to the observable volume of the current camera view and may result in inconsistent and discontinuous predictions, particularly in the case of a large", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8427", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/46f79f39df215acde508ada52afddb44f33a572f7c9961c4f8181f543552cea9.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Ablation studies of the effects of conditioning (Cond., $\\beta = 1$ ) and inpainting (Inpa.) on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. The combined use of conditioning and inpainting leads to superior performance in visual metrics, and inpainting plays a less significant role in terms of geometric results when the model is conditioned." + ], + "table_body": "
FactorsVisual
PSNRcolorSSIMcolorLPIPScolor
Cond.Inpa.5%10%20%50%5%10%20%50%5%10%20%
9.339.309.279.450.3310.3300.3300.3330.6370.6360.637
✓12.414.716.517.90.4110.4960.5570.5830.5200.4460.393
✓12.513.614.716.10.4440.4730.5130.5560.4490.4090.362
✓✓14.616.017.418.40.5220.5550.5930.6030.4480.3990.359
", + "bbox": [ + 80, + 123, + 510, + 193 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/173abf0b0692c917257c43a90b3f997c1ef5f5315e03d56bec5d516b852b3789.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.3091.3041.3101.29330612777246317580.5130.5980.7110.862
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.8970.8080.6620.595116369917699.00.7510.8170.8870.928
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
", + "bbox": [ + 515, + 124, + 887, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16a16ca21b2bbf6f0ae8f5b6ffd337d3337f94e06fc9d7abff4b1fca291bee98.jpg", + "image_caption": [ + "Figure 5. Qualitative results of ablation studies on the task of scene synthesis from sparse RGBD inputs. \"(a)\", \"(b)\" and \"(c)\" correspond to the second (w/o conditioning, $\\beta = 0$ ), third (w/o inpainting, $\\beta = 1$ ) and fourth (w/ all, $\\beta = 1$ ) rows of Table 2, and \"(d)\" corresponds to the last (w/ all, $\\beta = 5$ ) row of Table 3. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. It is clear that the third row basically shows the most favorable appearance." + ], + "image_footnote": [], + "bbox": [ + 112, + 247, + 850, + 521 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c8ac30557c05f2c600d45e4088fc8d9bc9f7d153df912f90b827475979ceb93c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Ablation studies of the effects of guidance factor $\\beta$ on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. A larger $\\beta$ ideally strengthens the conditioning effect. The visual metrics are found to be the best when $\\beta$ is set to 1 or 2. Interestingly, the optimal value of $\\beta$ for the best geometry appears to increase as views become denser. However, setting such a large value of $\\beta$ (e.g. $\\beta = 5$ ) leads to sub-optimal visual results." + ], + "table_body": "
Guidance Factor βVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
0.012.414.716.517.90.4110.4960.5570.5830.5200.4460.3930.359
0.513.215.517.118.20.4520.5300.5780.5960.4960.4180.3740.347
1.014.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
2.014.515.817.518.40.5320.5610.5980.6060.4390.3930.3520.334
5.013.314.917.118.20.4880.5310.5790.5980.4750.4180.3670.342
", + "bbox": [ + 84, + 604, + 504, + 684 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ebe76dcff26da2bfcff157665d2b2d79d9e7e0cc3999122f9aa009aeb48a9edf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Geometric
MSEdepthCDmeshComp meshes@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.9990.8450.7720.71919806062231110.6530.8180.8940.933
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
0.8940.8000.6540.593156251514487.20.7530.8460.9100.936
0.9920.8560.6630.5822551167617587.20.7470.8420.9080.934
", + "bbox": [ + 509, + 604, + 887, + 682 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "circular camera trajectory.", + "bbox": [ + 75, + 750, + 252, + 764 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Future Works. To improve our design, potential areas of investigation include: (1) Modeling color smoothness and variation, as demonstrated by NeRF [42]. (2) Supporting advanced physical lighting effects, such as SVBRDF, as implemented in TANGO [9]. (3) Incorporating appearance/surface extrapolation by learning an implicit field, such as NeRF [42, 43] or SDF [3, 80]. (4) Exploring gener", + "bbox": [ + 75, + 769, + 470, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ative [5] or estimable [6, 84] camera trajectories for scene synthesis. (5) Investigating reconstruction from sparse-view RGB inputs only, using depth inpainting/estimation following the reverse sampling technique proposed in [37] by utilizing a versatile RGBD diffusion model. (6) Leveraging the multi-modal [52] or generative [57] power of large-scale pre-trained models, such as the recently widespread Stable Diffusion [57].", + "bbox": [ + 497, + 750, + 890, + 861 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8428", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/032b1f18eb7aa9a8ebc0c1f758cbfbdb79d8edaaaf1b76722737fe3fe9acdf14.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
NGP10.412.414.417.40.2930.3770.4370.4980.5820.4760.4150.376
DS-NGP10.111.913.515.30.2050.2810.3210.3610.6050.5330.5030.476
N-RGBD14.116.518.420.00.4010.5130.5950.6520.4900.3840.3200.287
DDP14.116.118.320.90.4180.5040.5990.7020.5170.4100.3290.259
Ours14.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
", + "bbox": [ + 80, + 117, + 504, + 197 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c36dd93338924116b9ce9f8f642442f7260ec1efbe2b1d57c92ad25fe2dc5b45.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
7.017.397.376.5229994229731667680660.2890.4460.6460.850
2.301.691.441.17536217017682300.5290.7220.8450.918
1.511.231.211.133503134512106430.7050.8190.8570.872
1.441.050.940.88236310136374510.5070.6240.7190.812
0.820.800.680.6210589021561000.7470.8390.9090.936
", + "bbox": [ + 509, + 119, + 887, + 195 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Quantitative comparison with other approaches on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. Our approach outperforms other methods consistently in terms of geometric metrics as the sparsity varies. However, our method only show a definitive visual advantage across various visual metrics when the input views are highly sparse (5%).", + "bbox": [ + 75, + 199, + 892, + 249 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c97d438b48dfd90f6ad29adce2d16f48e00053657fc853040f8b4d1d097eb941.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison results with DS-NGP [13,43], DDP [56], N-RGBD [3] on the task of scene synthesis from sparse RGBD inputs. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. Our approach produces images that exhibit a close resemblance to the ground truth (GT), while comparative methods may result in inferior outcomes, especially when dealing with excessively sparse input views and outward-looking cameras." + ], + "image_footnote": [], + "bbox": [ + 112, + 252, + 855, + 790 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8429", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3D point clouds. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 40-49. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826–5835, October 2021. 2" + ], + "bbox": [ + 78, + 125, + 468, + 526 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "8434", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/a2d21046-a37a-4e32-b58b-aa13bd3ca238_model.json b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/a2d21046-a37a-4e32-b58b-aa13bd3ca238_model.json new file mode 100644 index 0000000000000000000000000000000000000000..27361205cc43a9007487d1f3c5efa99eecc0ce87 --- /dev/null +++ b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/a2d21046-a37a-4e32-b58b-aa13bd3ca238_model.json @@ -0,0 +1,2822 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.087 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.162, + 0.755, + 0.205 + ], + "angle": 0, + "content": "RGBD2: Generative Scene Synthesis via Incremental View Inpainting using RGBD Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.32, + 0.228, + 0.649, + 0.246 + ], + "angle": 0, + "content": "Jiabao Lei\\(^{1}\\), Jiapeng Tang\\(^{2}\\), Kui Jia\\(^{1,3,\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.246, + 0.642, + 0.262 + ], + "angle": 0, + "content": "\\(^{1}\\)South China University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.262, + 0.72, + 0.278 + ], + "angle": 0, + "content": "\\(^{2}\\)Technical University of Munich, \\(^{3}\\)Peng Cheng Laboratory" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.339, + 0.474, + 0.631 + ], + "angle": 0, + "content": "We address the challenge of recovering an underlying scene geometry and colors from a sparse set of RGBD view observations. In this work, we present a new solution termed \\( \\text{RGBD}^2 \\) that sequentially generates novel RGBD views along a camera trajectory, and the scene geometry is simply the fusion result of these views. More specifically, we maintain an intermediate surface mesh used for rendering new RGBD views, which subsequently becomes complete by an inpainting network; each rendered RGBD view is later back-projected as a partial surface and is supplemented into the intermediate mesh. The use of intermediate mesh and camera projection helps solve the tough problem of multi-view inconsistency. We practically implement the RGBD inpainting network as a versatile RGBD diffusion model, which is previously used for 2D generative modeling; we make a modification to its reverse diffusion process to enable our use. We evaluate our approach on the task of 3D scene synthesis from sparse RGBD inputs; extensive experiments on the ScanNet dataset demonstrate the superiority of our approach over existing ones. Project page: https://jblei.site/proj/rgbd-diffusion." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.642, + 0.21, + 0.656 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.662, + 0.47, + 0.828 + ], + "angle": 0, + "content": "Scene synthesis is an essential requirement for many practical applications. The resulting scene representation can be readily utilized in diverse fields, such as virtual reality, augmented reality, computer graphics, and game development. Nevertheless, conventional approaches to scene synthesis usually involve reconstructing scenes (e.g., indoor scenes with varying sizes) by fitting given observations, such as multi-view images or point clouds. The increasing prevalence of RGB/RGBD scanning devices has established multi-view data as a favored input modality, driving and promoting technical advancements in the realm of scene reconstruction from multi-view images." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.829, + 0.47, + 0.843 + ], + "angle": 0, + "content": "Neural Radiance Fields (NeRFs) [42] have demonstrated" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.334, + 0.617, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.385, + 0.596, + 0.395 + ], + "angle": 0, + "content": "\\(t = 0\\)" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.314, + 0.721, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.661, + 0.385, + 0.697, + 0.395 + ], + "angle": 0, + "content": "\\(t = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.312, + 0.85, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.385, + 0.812, + 0.395 + ], + "angle": 0, + "content": "\\(t = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.406, + 0.661, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.483, + 0.621, + 0.494 + ], + "angle": 0, + "content": "\\(t = 3\\)" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.406, + 0.844, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.483, + 0.82, + 0.494 + ], + "angle": 0, + "content": "Final Result" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.498, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Illustration of Our Generative Scene Synthesis. We incrementally reconstruct the scene geometry by inpainting RGBD views as the camera moves in the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.893, + 0.756 + ], + "angle": 0, + "content": "potential in this regard, yet they are not exempt from limitations. NeRFs are designed to reconstruct complete scenes by fitting multi-view images, and they cannot generate or infer missing parts when the input is inevitably incomplete or missing. While recently some studies [3,5,8,56,63] have attempted to equip NeRFs with generative and extrapolation capabilities, this functionality relies on a comparatively short representation with limited elements (e.g. typically, the length of a global latent code is much shorter than that of an image: \\((F = 512) \\ll (H \\times W = 128 \\times 128 = 16,384)\\)) that significantly constrains their capacity to accurately capture fine-grained details in the observed data. Consequently, the effectiveness of these methods has only been established for certain categories of canonical objects, such as faces or cars [8, 63], or relatively small toy scenes [5]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We introduce a novel task of generative scene synthesis from sparse RGBD views, which involves learning across multiple scenes to later enable scene synthesis from a sparse set of multi-view RGBD images. This task presents a challenging setting wherein a desired solution should simultaneously (1) preserve observed regions, hallucinate missing parts of the scene, (2) eliminate additional computational costs during inference for each individual test scene, (3) en" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.854, + 0.383, + 0.867 + ], + "angle": 0, + "content": "\\(\\dagger\\) Correspondence to Kui Jia: ." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8422" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.47, + 0.154 + ], + "angle": 0, + "content": "sure exact 3D consistency, and (4) maintain scalability to scenes with unfixed scales." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.158, + 0.473, + 0.571 + ], + "angle": 0, + "content": "We will elaborate on them in detail as follows. Firstly, to maximize the preservation of intricate details while simultaneously hallucinating potentially absent parts that may become more pronounced when views are exceedingly sparse, we perform straightforward reconstruction whose details come from images that can describe fine structures using a maximum of \\( H \\times W \\) elements (i.e. an image size) in a view completion manner. This is particularly compatible with diffusion models that operate at full image resolution with an inpainting mechanism. We also found that RGBD diffusion models greatly simplify the training complexity of a completion model, thanks to their versatile generative ability to inpaint missing RGBD pixels while preserving the integrity of known regions through a convenient training process solely operated on complete RGBD data. Secondly, our method employs back-projection that requires no optimization, thus eliminating the necessity for test-time training for each individual scene, ultimately leading to a significant enhancement in test-time efficiency. Thirdly, to ensure consistency among multi-view images, an intermediate mesh representation is utilized as a means of bridging the 2D domain (i.e. multi-view RGBD images) with the 3D domain (i.e. the 3D intermediate mesh) through the aid of camera projection. Fourthly, to enable our method to handle scenes of indeterminate sizes, we utilize images with freely designated poses as the input representation. Such manner naturally ensures SE(3) equivariance, and thus offers scalability due to the ease with which the range of the generated content can be controlled by simply specifying their camera extrinsic matrices." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.577, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Our proposal involves generating multi-view consistent RGBD views along a predetermined camera trajectory, using an intermediate mesh to render novel RGBD images that are subsequently inpainted using a diffusion model, and transforming each RGBD view into a 3D partial mesh via back-projection, and finally merging it with the intermediate scene mesh to produce the final output. Specifically, our proposed approach initiates by ingesting multiple posed RGBD images as input and utilizing back-projection to construct an intermediate scene mesh. This mesh encompasses color attributes that facilitate the rendering of RGBD images from the representation under arbitrarily specified camera viewpoints. Once a camera pose is selected from the test-time rendering trajectory, the intermediate mesh is rendered to generate a new RGBD image for this pose. Notably, the test-time view typically exhibits only slight overlap with the known cameras, leading to naturally partially rendered RGBD images. To fill the gaps in the incomplete view, we employ an inpainting network implemented as an RGBD diffusion model with minor modifications to its reverse sampling process. The resulting inpainted out" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.21 + ], + "angle": 0, + "content": "put is then back-projected into 3D space, forming a partial mesh that complements the entire intermediate scene mesh. We iterate these steps until all test-time camera viewpoints are covered, and the intermediate scene mesh gradually becomes complete during this process. The final output of our pipeline is the mesh outcome acquired from the last step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.21, + 0.892, + 0.252 + ], + "angle": 0, + "content": "Extensive experiments on ScanNet [12] dataset demonstrate the superiority of our approach over existing solutions on the task of scene synthesis from sparse RGBD inputs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.255, + 0.651, + 0.269 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.892, + 0.314 + ], + "angle": 0, + "content": "In this section, we provide a brief review of the literature related to diffusion models, 3D representations and generative manners, scene synthesis, and view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.315, + 0.893, + 0.562 + ], + "angle": 0, + "content": "Diffusion Models. In recent years, the field of 2D computer vision has experienced a surge of interest in diffusion-based generative models [20,65,67]. These models have prompted the development of image generative modeling approaches, such as GLIDE [45], unCLIP [53], Imagen [61], and Latent Diffusion Models [57], as well as the invention of sampling schedulers [20, 26, 36, 66] and guiding methods [15, 22]. Furthermore, these models have been applied to a broad range of image processing tasks, including image inpainting [37], image translation [4, 57, 60, 82], video generation [23, 25, 76], super-resolution [21, 32, 62], and image editing [2, 27, 40]. More recently, some researchers have adapted these techniques from 2D to the 3D domain, as demonstrated by methods such as [39, 51, 88, 92]. Our approach harnesses such versatility by adopting an iterative denoising strategy like [37], and utilizing a masked inpainting technique that operates on the projected RGBD views to synthesize image content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.894, + 0.868 + ], + "angle": 0, + "content": "3D Representations and Generative Manners. A variety of representations, including voxels [81, 85], point clouds [1, 39, 68, 87, 92], meshes [17, 44, 70, 71, 79], implicit surfaces [10, 30, 31, 41, 48, 72-74, 88, 91], multi-view images [11, 19, 34, 35, 86], and neural radiance fields [3, 8, 9, 13, 42, 43, 49, 56, 63, 80], have been proposed, each with its own unique advantages over the others. This has also motivated researchers to combine them with distinct generative approaches, such as VAEs [28], GANs [16], normalizing flows [54], auto-regressive models [24, 75], and the latest diffusion models [20], resulting in an extensive range of applications [1, 8, 39, 41, 44, 48, 63, 85, 87, 92]. However, most existing methods have limitations in their representation capability, such as cubically scaled-up memory consumption, or a fixed number of points, which makes them difficult to apply to scenes of uncertain scales, and poor equivariance, which only allows them to handle canonically-posed objects. In this paper, we address these issues by focusing on the generation of multi-view RGBD images that can capture intricate structures using \\( H \\times W \\) pixels created by a diffusion model. This approach reduces memory complexity from \\( \\mathcal{O}(HWD) \\) to \\( \\mathcal{O}(HW) \\) and increases expressive" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8423" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.126, + 0.286, + 0.14 + ], + "angle": 0, + "content": "ability from \\(\\mathcal{O}(F)\\) to \\(\\mathcal{O}(HW)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.469, + 0.319 + ], + "angle": 0, + "content": "Scene Synthesis. In this area, there are two primary research directions. The first pertains to learning configurations, including graphs [33, 38, 77, 90], top-down views [55, 78], and scene composition [50, 83]. The second line of research involves direct learning from the appearance of a scene [13, 42, 43, 49, 80], thereby obviating the necessity for specialized synthesized datasets required by the aforementioned methods. Our approach relies solely on RGBD scans, which are readily available from scanning devices, reducing the need for manual annotation. It accurately reconstructs a clean geometry based on the sparse-view input and can effectively hallucinate missing parts, especially when the input views are highly sparse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.469, + 0.445 + ], + "angle": 0, + "content": "View Synthesis. The arrival of NeRF [42] has significantly advanced the field of view synthesis. While a considerable amount of research has been dedicated to the view synthesis of object-level instances [7, 18, 47, 64], only a few studies have focused on simple scenes [5, 14, 58]. Additionally, some studies have explored techniques for improving performance using sparse inputs [46, 56]. In this paper, we aim to recover scene-level geometry from sparse RGBD images without relying on NeRFs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.449, + 0.203, + 0.464 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.469, + 0.497 + ], + "angle": 0, + "content": "To make our paper self-contained, we provide some preliminary knowledge about DDPM [20] and DDIM [66]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.497, + 0.469, + 0.566 + ], + "angle": 0, + "content": "Definition. Given an image \\(\\mathbf{x}_0\\sim q(\\mathbf{x}_0)\\), the forward diffusion process is a Markov chain that sequentially produces noisy images \\(\\mathbf{x}_1,\\dots ,\\mathbf{x}_T\\) scheduled by a set of constants \\(\\{\\beta_t\\in (0,1)\\}_{t = 1}^T\\) where \\(T\\) is the total number of iterations and \\(\\beta_{1} < \\beta_{2} < \\ldots < \\beta_{T}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.567, + 0.413, + 0.584 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.469, + 0.634 + ], + "angle": 0, + "content": "A nice property of using i.i.d. Gaussian distribution is that we can sample the noisy image \\(\\mathbf{x}_t\\) easily based on \\(\\mathbf{x}_0\\) in a closed form without computing all the intermediates:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.641, + 0.469, + 0.658 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha}} _ {t} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.469, + 0.708 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} = \\prod_{s = 1}^{t}\\alpha_{s}\\). The reverse diffusion process is another Markov chain starting from \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})\\) parameterized by a trainable \\(\\theta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.716, + 0.469, + 0.731 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.469, + 0.781 + ], + "angle": 0, + "content": "where \\(\\pmb{\\Sigma}_{\\theta}(\\mathbf{x}_t,t) = \\sigma_t^2\\mathbf{I} = \\eta \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t\\mathbf{I}\\) [66] is independent of \\(\\theta\\) and \\(\\mathbf{x}_t\\), and \\(\\mu_{\\theta}(\\mathbf{x}_t,t)\\) can be derived from a noise estimator \\(\\epsilon_{\\theta}(\\mathbf{x}_t,t)\\) via:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.789, + 0.426, + 0.821 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {o}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.827, + 0.469, + 0.869 + ], + "angle": 0, + "content": "We practically implement the noise estimator \\(\\epsilon_{\\theta}(\\mathbf{x}_t,t)\\) as a UNet [57, 59] parameterized by \\(\\theta\\). However, in our case, it is also conditioned on \\(\\hat{\\mathbf{x}}_0\\) which will be detailed in Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.154 + ], + "angle": 0, + "content": "Training. To train the noise estimator \\(\\epsilon_{\\theta}(\\mathbf{x}_t,t)\\) , we adopt the simplified training objective [20]:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.164, + 0.862, + 0.186 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {t, \\epsilon_ {t}, \\mathbf {x} _ {0}} \\left[ \\| \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {t}, t) - \\epsilon_ {t} \\| ^ {2} \\right]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.196, + 0.892, + 0.239 + ], + "angle": 0, + "content": "where the time step \\(t\\sim \\mathcal{U}\\{1,T\\}\\) is uniformly sampled, \\(\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) is a standard Gaussian noise, and the image \\(\\mathbf{x}_0\\sim q(\\mathbf{x}_0)\\) is randomly drawn from the data distribution." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.249, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Inference. We employ a strided DDIM [66] scheduler to progressively recover the clean image from \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) to \\(\\mathbf{x}_0\\) with a subset of \\(S\\) (usually \\(S\\ll T\\)) steps \\(\\{\\tau_i\\}_{i = 1}^S\\)" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.312, + 0.866, + 0.37 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {\\tau_ {i - 1}} \\leftarrow \\sqrt {\\bar {\\alpha} _ {\\tau_ {i - 1}}} \\left(\\frac {\\mathbf {x} _ {\\tau_ {i}} - \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}} , \\tau_ {i})}{\\sqrt {\\bar {\\alpha} _ {\\tau_ {i}}}}\\right) + \\\\ \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i - 1}} - \\sigma_ {\\tau_ {i}} ^ {2}} \\cdot \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}}, \\tau_ {i}) + \\sigma_ {\\tau_ {i}} ^ {2} \\epsilon_ {\\tau_ {i}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.436 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\tau_i} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\) is a standard Gaussian noise. It is interesting that setting \\(\\eta = 0\\) implies \\(\\forall i\\), \\(\\sigma_{\\tau_i} \\equiv 0\\), making the inference process deterministic. Nevertheless, diversity can still be achieved by choosing a different \\(\\mathbf{x}_T\\) from \\(\\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.608, + 0.455 + ], + "angle": 0, + "content": "4. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.624 + ], + "angle": 0, + "content": "In this work, we introduce a new scene synthesis approach that relies on the sequential generation of RGBD frames using a trained RGBD diffusion model conditioned on views rendered under a test-time camera trajectory from a sparse set of input RGBD images. Our approach leverages the generative ability of diffusion models to synthesize missing visual appearance (color) and geometry details (depth) while rigorously preserving visible regions by image inpainting. Such an incremental view inpainting process is interleaved with the back-projection, mesh fusion, and mesh rendering procedures to achieve global 3D consistency among distinct temporal frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.721 + ], + "angle": 0, + "content": "This section is organized as follow. In Sec. 4.1, we will start by introducing the overall framework of repeatedly converting the RGBD image into a partial 3D mesh and performing RGBD inpainting for rendered views in a progressive manner. Later in Sec. 4.2, we will elaborate more on the details of the conditional RGBD diffusion model for rendered view inpainting based on a trained DDPM [20]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.724, + 0.822, + 0.739 + ], + "angle": 0, + "content": "4.1. Incremental View Inpainting Fashion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.867 + ], + "angle": 0, + "content": "As shown in Figure 2, given a sparse set of \\(N\\) RGBD views \\(\\{\\mathbf{I}_i\\}_{i=1}^N\\) with their associated camera intrinsic \\(\\mathbf{K}\\) and extrinsic \\(\\{\\mathbf{R}_i\\}_{i=1}^N\\) matrices, and additionally a camera trajectory composed of \\(M\\) viewpoints \\(\\{\\mathbf{T}_j\\}_{j=1}^M\\) with the same intrinsic matrix, the essence of our method is to progressively synthesize RGBD images \\(\\mathbf{O}_j\\) at each specified novel view \\(\\mathbf{T}_j\\). The generated novel-view frames should be consistent with \\(\\{\\mathbf{I}_i\\}_{i=1}^N\\) in both geometry and appearance. The final output should be a consistent 3D" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8424" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.127, + 0.891, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.37, + 0.893, + 0.45 + ], + "angle": 0, + "content": "Figure 2. 3D Scene Synthesis via Incremental View Inpainting. Given a sparse set of RGBD images \\(\\{\\mathbf{I}_i\\}_{i=1}^N\\) with camera intrinsic \\(\\mathbf{K}\\) and extrinsic \\(\\{\\mathbf{R}_i\\}_{i=1}^N\\) matrices, our goal is to generate a coherent 3D scene mesh \\(\\mathcal{S}\\) via predicting RGBD frames \\(\\{\\mathbf{O}_j\\}_{j=1}^M\\) along a novel-view trajectory \\(\\{\\mathbf{T}_j\\}_{j=1}^M\\). To achieve this goal, we firstly fuse the inputs of \\(\\{\\mathbf{I}_i\\}_{i=1}^N\\) into an initial mesh \\(\\mathcal{S}_1\\), and then render it to obtain an incomplete image \\(\\hat{\\mathbf{O}}_1\\) that is later inpainted to obtain \\(\\mathbf{O}_1\\) using a RGBD diffusion model. After that, \\(\\mathbf{O}_1\\) is back-projected and integrated with \\(\\mathcal{S}_1\\) to produce a more complete scene, \\(\\mathcal{S}_2\\). By iteratively repeating this process, we can progressively obtain \\(\\mathcal{S}_2, \\dots, \\mathcal{S}_M\\). Finally, the fused result \\(\\mathcal{S}_{M+1}\\) is the eventual desired output \\(\\mathcal{S}\\). Gray dashed lines “- - ” denote omitted and unvisualized steps." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.457, + 0.471, + 0.499 + ], + "angle": 0, + "content": "colored mesh \\( S \\) converted from the back-projection result \\( \\left( \\cup_{j=1}^{M} \\phi_{2 \\to 3}(\\mathbf{O}_j) \\right) \\cup \\left( \\cup_{i=1}^{N} \\phi_{2 \\to 3}(\\mathbf{I}_i) \\right) \\). Please also refer to Algorithm 1 for a detailed description of the procedure." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.507, + 0.407, + 0.521 + ], + "angle": 0, + "content": "Algorithm 1 Incremental RGBD View Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.525, + 0.469, + 0.555 + ], + "angle": 0, + "content": "Require: RGBD images \\(\\{\\mathbf{I}_i\\}_{i=1}^N\\) with camera extrinsics \\(\\{\\mathbf{R}_i\\}_{i=1}^N\\), a novel trajectory of M extrinsics \\(\\{\\mathbf{T}_j\\}_{j=1}^M\\)." + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.555, + 0.235, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {1} \\leftarrow \\cup_ {i = 1} ^ {N} \\phi_ {2 \\rightarrow 3} (\\mathbf {I} _ {i})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.57, + 0.221, + 0.582 + ], + "angle": 0, + "content": "for \\( j = 1 \\) to \\( M \\) do" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.583, + 0.237, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathbf {\\hat {O}} _ {j} \\leftarrow \\phi_ {3 \\rightarrow 2} (\\mathbf {T} _ {j})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.314, + 0.584, + 0.469, + 0.596 + ], + "angle": 0, + "content": "\\(\\triangleright\\) novel-view rendering" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.598, + 0.211, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\mathbf {O} _ {j} \\leftarrow f (\\hat {\\mathbf {O}} _ {j})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.338, + 0.599, + 0.469, + 0.611 + ], + "angle": 0, + "content": "RGBD inpainting" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.613, + 0.285, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {j + 1} \\leftarrow \\mathcal {S} _ {j} \\cup \\phi_ {2 \\rightarrow 3} (\\mathbf {O} _ {j})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.374, + 0.613, + 0.468, + 0.625 + ], + "angle": 0, + "content": "\\(\\triangleright\\) mesh fusion" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.628, + 0.149, + 0.638 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.641, + 0.187, + 0.654 + ], + "angle": 0, + "content": "return \\(\\mathcal{S}_{M + 1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.47, + 0.819 + ], + "angle": 0, + "content": "Rendering and Back-projection. The operator \\(\\phi_{3\\rightarrow 2}\\) is implemented as mesh rasterization, which allows for the rendering of a partial RGBD image \\(\\hat{\\mathbf{O}}_j\\) from a mesh \\(S_{j}\\). This approach offers the advantage of producing a clean visibility mask \\(\\mathbf{m}_j\\), which is not possible with NeRFs [42]. The back-projection operator \\(\\phi_{2\\rightarrow 3}\\) is responsible for the conversion from a depth map into a point cloud, where the connectivity between points is inherited from the connectivity of the 2D pixel grid. Furthermore, mesh faces that are either in close proximity to the viewpoint or exhibit slender characteristics are filtered out to ensure accuracy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.82, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Challenges and Solutions. To circumvent the limitations" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.457, + 0.892, + 0.86 + ], + "angle": 0, + "content": "posed by potential 3D inconsistency in both geometry and appearance, as well as the challenge of solely handling specific canonically-posed scenes, we propose several strategies to address these issues. Firstly, our method for synthesizing novel views combines rendering (mesh rasterization) and inpainting techniques, and interleaves the view synthesis process with online RGBD fusion via back-projection and mesh combination. The use of perspective camera projection ensures strict adherence to 3D constraints, resulting in visually consistent and accurate synthesized views. In concrete terms, we begin by rendering the mesh \\( S_{j} \\) under view \\( \\mathbf{T}_{j} \\) using a rendering operation \\( \\phi_{3\\rightarrow 2}(\\mathbf{T}_{j}) \\). This process yields an incomplete RGBD image \\( \\hat{\\mathbf{O}}_j \\) with missing regions, which is subsequently inpainted using a diffusion model described in detail in Sec. 4.2, resulting in a complete image \\( \\mathbf{O}_j \\). Once image \\( \\mathbf{O}_j \\) has been generated for view \\( \\mathbf{T}_j \\), it can be fused into a 3D mesh via \\( S_{j + 1} = \\phi_{2\\rightarrow 3}(\\mathbf{O}_j)\\cup S_j \\) using a back-projection operator \\( \\phi_{2\\rightarrow 3} \\). Secondly, our solution reduces the learning difficulty and can handle noncanonical scenes by decomposing the 3D scene as a Markov chain of temporal RGBD images rendered from arbitrarily specified novel viewpoints. The applicability of handling scenes with arbitrary scaling, movement, and posing is attributed to the utilization of two SE(3) equivariant operators, namely \\( \\phi_{3\\rightarrow 2} \\) and \\( \\phi_{2\\rightarrow 3} \\), as well as the independence of absolute coordinates. Moreover, the presence of redundant information in adjacent frames, combined with our suggested decomposition rule, facilitates the minimization of learning complexity in an auto-regressive manner." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.843, + 0.469, + 0.867 + ], + "angle": 0, + "content": "1 To simplify notations, we disregard certain arguments in operators \\( \\phi_{3\\to 2} \\) and \\( \\phi_{2\\to 3} \\), such as the camera intrinsic matrix \\( \\mathbf{K} \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8425" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.471, + 0.168 + ], + "angle": 0, + "content": "In accordance with the Markov chain decomposition principle, the distribution of the scene can be expressed as the joint distribution of view frames:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.175, + 0.407, + 0.205 + ], + "angle": 0, + "content": "\\[\np (\\mathcal {S}) = \\prod_ {j} p (\\mathbf {O} _ {j} \\mid \\{\\mathbf {O} _ {s} \\} _ {s = 1} ^ {j - 1}, \\{\\mathbf {I} _ {s} \\} _ {s = 1} ^ {N})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.206, + 0.471, + 0.237 + ], + "angle": 0, + "content": "where the prediction of \\(\\mathbf{O}_j\\) is based on the fusion result of all the previously known frames \\(\\{\\mathbf{O}_s\\}_{s=1}^{j-1} \\cup \\{\\mathbf{I}_s\\}_{s=1}^N\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.242, + 0.47, + 0.258 + ], + "angle": 0, + "content": "4.2. RGBD Diffusion for Rendered View Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.263, + 0.47, + 0.406 + ], + "angle": 0, + "content": "In this section, we describe the implementation details of the way to employ diffusion models to inpaint the missing regions of the RGBD image \\(\\hat{\\mathbf{O}}_j\\) with a binary mask \\(\\mathbf{m}_j\\) obtained by rendering visibility, where the value of 1 is assigned to the corresponding ray that intersects with the geometry surface, while 0 is assigned to all other cases, both of which are rendered by projecting \\(S_{j}\\) under a novel viewpoint \\(\\mathbf{T}_j\\). It is noteworthy that only those pixels located where \\(\\mathbf{m}_j = 0\\) in \\(\\hat{\\mathbf{O}}_j\\) are considered invalid, and therefore, are entirely filled with zeros (i.e., \\(\\hat{\\mathbf{O}}_j\\odot \\mathbf{m}_j\\equiv \\hat{\\mathbf{O}}_j\\))." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.413, + 0.468, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.63 + ], + "angle": 0, + "content": "Figure 3. RGBD Diffusion for Rendered View Inpainting. In each iteration, we utilize a forward diffusion step to sample the visible region \\(\\mathbf{x}_t^{\\mathrm{vis}}\\) (top) from the incomplete input \\(\\hat{\\mathbf{x}}_0\\), while employing a denoising diffusion step to obtain the complementary content \\(\\mathbf{x}_t^{\\mathrm{invis}}\\) (bottom) from the output \\(\\mathbf{x}_{t + 1}\\) generated in the previous iteration \\(t + 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.804 + ], + "angle": 0, + "content": "A Single Reverse Diffusion Step for \\(\\mathbf{T}_j\\) at Time \\(t\\).2 We initialize the clean diffusion sample \\(\\hat{\\mathbf{x}}_0\\) at time \\(t = 0\\) as \\(\\hat{\\mathbf{O}}_j\\), and those noisy samples at time \\(0 < t \\leq T\\) are denoted as \\(\\mathbf{x}_t\\). To ensure 3D consistency, we seek to predict the invisible region \\(\\mathbf{x}_0^{\\mathrm{vis}}\\) while preserving the visible portion \\(\\mathbf{x}_0^{\\mathrm{vis}}\\) unaltered. We follow [37] and modify the standard denoising process to meet our needs. At each reverse diffusion step \\(t\\), we use the forward diffusion process defined by the Eqn. (1) to sample a visible region \\(\\mathbf{x}_t^{\\mathrm{vis}}\\) masked by \\(\\mathbf{m}\\), and the reverse diffusion step defined by Eqn. (2) to sample a full part from \\(\\mathbf{x}_{t+1}\\) which is later masked by \\(1 - \\mathbf{m}\\) to form an invisible region \\(\\mathbf{x}_t^{\\mathrm{vis}}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.81, + 0.39, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {\\text {v i s}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} + (1 - \\bar {\\alpha} _ {t}) \\epsilon_ {t} ^ {\\text {v i s}} \\odot \\mathbf {m}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.832, + 0.47, + 0.867 + ], + "angle": 0, + "content": "2 For notational simplicity, we ignore the novel camera subscript \\( j \\) in the following part of this Sec. 4.2 since all notations we consider here are derived from the same camera \\( \\mathbf{T}_j \\)." + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.123, + 0.845, + 0.141 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {\\text {i n v i s}} = \\left(\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {t}, t\\right) + \\sigma_ {t} \\epsilon_ {t} ^ {\\text {i n v i s}}\\right) \\odot (1 - \\mathbf {m})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.145, + 0.892, + 0.189 + ], + "angle": 0, + "content": "where \\(\\epsilon_t^{\\mathrm{vis}},\\epsilon_t^{\\mathrm{invis}}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) . The noisy image \\(\\mathbf{x}_t\\) can be simply calculated as the sum of \\(\\mathbf{x}_t^{\\mathrm{vis}}\\) and \\(\\mathbf{x}_t^{\\mathrm{invis}}\\) , as expressed by \\(\\mathbf{x}_t = \\mathbf{x}_t^{\\mathrm{vis}} + \\mathbf{x}_t^{\\mathrm{invis}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.194, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Diffusion Network. We implement the diffusion model as a UNet [57, 59] conditioned on the observed region \\(\\mathbf{x}_0\\). We input the concatenation of \\(\\mathbf{x}_t\\) and \\(\\hat{\\mathbf{x}}_0\\) into the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.893, + 0.335 + ], + "angle": 0, + "content": "Classifier-free Guidance. To further enhance the controllability of the generation process, we introduce a classifier-free guidance [22] mechanism. Specifically, we train a unified network \\(\\epsilon_{\\theta}\\) comprising of an unconditional model \\(\\epsilon_{\\theta}(\\mathbf{x}_t,\\mathbf{c},t)\\), where the shared variable \\(\\mathbf{c}\\) is incorporated, and a conditional model \\(\\epsilon_{\\theta}(\\mathbf{x}_t,\\hat{\\mathbf{x}}_0,t)\\). In this way, the predicted noise \\(\\tilde{\\epsilon}_{\\theta}\\) can be recomputed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.346, + 0.892, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\epsilon} _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) = \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) + \\beta \\times [ \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.402 + ], + "angle": 0, + "content": "where \\(\\beta \\geq 0\\) is the guidance factor, being responsible for the trade-off between sampling quality and diversity [22]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.407, + 0.633, + 0.423 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Dataset. We conducted experiments on the ScanNetV2 [12] dataset, which was pre-processed by removing redundant frames [69]. For training, we used the first 1,293 scenes, while for metric evaluation, we randomly selected 18 scenes with over 50 views each from the remaining as our test set. We also evaluated under various sparsity settings (5%, 10%, 20%, and 50%) by uniformly down-sampling views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Comparison. We compared against the neural graphics primitive (NGP) [43], which has demonstrated impressive performance in scene modeling with high efficiency. To enhance its geometric quality, we incorporated a depth supervision (DS) loss [13] to build an improved variant called DS-NGP [13, 43]. We also compare against Neural RGBD (N-RGBD) [3], which recovers implicit surfaces from RGBD scans, and Dense Depth Prior (DDP) [56], which learns a NeRF utilizing view completion from sparse RGBD views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Evaluation Metrics. For assessing the visual quality of RGB images, we adopted the peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [89] that is based on the AlexNet [29] backbone. To evaluate the geometry quality, we computed the mean squared error (MSE) on depth maps, and sample 10,000 points uniformly on meshes constructed via back-projection to evaluate the chamfer distance (CD) and completeness (Comp.) with a threshold of \\(0.1\\mathrm{m}\\). We also measured the computational time required to execute different stages of the method. For LPIPS, MSE, and CD, the lower the better; for PSNR, SSIM, and Comp., the higher the better. All reported metrics are averaged across the test scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8426" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.47, + 0.21 + ], + "angle": 0, + "content": "Implementation Details. Our model has 157M parameters and was trained for three days on 7 NVIDIA 3090-Ti GPUs, using a batch size of 280. The learning rate was initialized at \\(1 \\times 10^{-4}\\) and reduced to \\(1 \\times 10^{-6}\\) over a period of 300 epochs, utilizing a cosine annealing strategy. The image resolution is \\(128 \\times 128\\) with a rendering chunk size of 7." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.217, + 0.242, + 0.23 + ], + "angle": 0, + "content": "5.1. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.236, + 0.469, + 0.277 + ], + "angle": 0, + "content": "We conducted ablation studies to validate the effectiveness of each component in our proposal. Results concluded here are nontrivial and a bit nuanced." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.469, + 0.43 + ], + "angle": 0, + "content": "Effects of Different Ingredients. We examined the anticipated efficacy of the proposed conditioning and inpainting components in our approach. Table 2 displays the numerical results, and Figure 5-(a-c) presents the visualizations. The combined use of conditioning and inpainting yields superior visual performance compared to the ground truth. Nevertheless, when the model is conditioned, the impact of inpainting on geometric quality becomes less crucial. Moreover, as more views are provided, the stochastic generation process becomes increasingly deterministic, resulting in structures that more closely resemble the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Effects of Guidance Scale. The guidance factor \\(\\beta\\) significantly affects the conditioning effect on the results. To investigate the optimal \\(\\beta\\) under various settings, we conducted experiments with \\(\\beta\\) chosen from 0.0, 0.5, 1.0, 2.0, and 5.0, respectively, and evaluated their performance. Quantitative results are presented in Table 3. It is interesting that only a suitable value of \\(\\beta\\) (1.0 or 2.0) yields optimal performance, while smaller or larger values of \\(\\beta\\) result in underperformance. Surprisingly, for geometric recovery (MSE and CD), the optimal value of \\(\\beta\\) appears to increase as the percentage gets larger. For a scene with a percentage \\(\\geq 50\\%\\), the best value of \\(\\beta\\) is amazingly greater than 5.0. However, such a large percentage is not optimal for visual appearance. This is because using a larger value of \\(\\beta\\) at a low percentage can cause the generated results to deviate unexpectedly from the ground truth. Our visualization, presented in Figure 5-(a, c, d), indicates that using an unconditional model (\\(\\beta = 0\\)) leads to undesired and bizarre geometric structures since the network fails to understand the context provided by known views. However, excessively large values of \\(\\beta\\) also oversaturate the color (e.g. row “(d)” at \\(5\\%\\)), making the visual appearance unrealistic." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Effects of Randomness and Trajectories. We investigated" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.762, + 0.182, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.836, + 0.167, + 0.849 + ], + "angle": 0, + "content": "(a) original" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.762, + 0.291, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.207, + 0.836, + 0.26, + 0.848 + ], + "angle": 0, + "content": "(b) seed" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.762, + 0.469, + 0.836 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.837, + 0.421, + 0.849 + ], + "angle": 0, + "content": "(c) trajectory" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.854, + 0.469, + 0.879 + ], + "angle": 0, + "content": "Figure 4. Diverse results obtained by changing the (b) random seed and (c) camera trajectory based on (a) the original scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.264 + ], + "angle": 0, + "content": "the impact of employing different random seeds and camera trajectories on the results. Such obtained meshes are visualized in Figure 4. As diffusion models inherently include randomness in their reverse sampling process, by switching to a different random seed, we can obtain another outcome. Moreover, the camera trajectory can affect the rough shape of the scene. It is promising that our approach can yield controllable and editable results, as it is capable of generating various and appealing outcomes by simply altering these two factors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.269, + 0.746, + 0.284 + ], + "angle": 0, + "content": "5.2. Generative Scene Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.384 + ], + "angle": 0, + "content": "We evaluated the performance of our method against other similar approaches on this task through extensive experiments under various sparsity settings. Table 1 presents the time required by different methods across various stages. Our approach stands out for its efficiency, as it eliminates the need for additional optimization on individual test scenes during inference. Quantitative results are shown in" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.388, + 0.89, + 0.444 + ], + "angle": 0, + "content": "
TimeBackendRepre.TrainingOptimizationRendering
(DS-)NGP [13,43]CUDA C++NeRF—~ 3 min.~ 0.05 sec.
N-RGBD [3]PyTorchNeRF—~ 2 hours~ 2 sec.
DDP [56]PyTorchNeRF~ 1 day~ 1 hour~ 1 sec.
OursPyTorchMesh~ 3 days—~ 3 sec.
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Table 1. Efficiency Comparison of Different Methods. It details their distinct implementation backends, the underlying representation (Repre.) methods, and the time required for training on multiple training scenes, optimization on a single test scene, and rendering a single view after per-scene optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Table 4. We observe that our approach exhibits a clear advantage in visual metrics over the others when the provided views are extremely sparse (5%). Interestingly, our method consistently achieves the best performance in all the geometry-related metrics. Qualitative results are presented in Figure 6. DS-NGP [13, 43] and DDP [56] struggle to accurately recover geometry due to their inability to hallucinate and extrapolate missing regions. In comparison, N-RGBD [3] can achieve better surface completion results by learning and extrapolating neural implicit surfaces. However, their performance significantly degrades when input views are extraordinarily sparse (5%). In contrast, our method consistently exhibits plausible appearance that closely resembles the ground truth, particularly in scenarios with sparse-view inputs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.621, + 0.739 + ], + "angle": 0, + "content": "6. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Limitations. Our current implementation has several limitations that may impact its usefulness in some scenarios. Firstly, it is incapable of handling color discrepancies caused by lighting variations. Secondly, it lacks surface extrapolation capabilities that can be provided through implicit field representation. Lastly, the limited receptive field of our design is confined to the observable volume of the current camera view and may result in inconsistent and discontinuous predictions, particularly in the case of a large" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8427" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.124, + 0.511, + 0.194 + ], + "angle": 0, + "content": "
FactorsVisual
PSNRcolorSSIMcolorLPIPScolor
Cond.Inpa.5%10%20%50%5%10%20%50%5%10%20%
9.339.309.279.450.3310.3300.3300.3330.6370.6360.637
✓12.414.716.517.90.4110.4960.5570.5830.5200.4460.393
✓12.513.614.716.10.4440.4730.5130.5560.4490.4090.362
✓✓14.616.017.418.40.5220.5550.5930.6030.4480.3990.359
" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.125, + 0.888, + 0.194 + ], + "angle": 0, + "content": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.3091.3041.3101.29330612777246317580.5130.5980.7110.862
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.8970.8080.6620.595116369917699.00.7510.8170.8870.928
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.196, + 0.893, + 0.246 + ], + "angle": 0, + "content": "Table 2. Ablation studies of the effects of conditioning (Cond., \\(\\beta = 1\\)) and inpainting (Inpa.) on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. The combined use of conditioning and inpainting leads to superior performance in visual metrics, and inpainting plays a less significant role in terms of geometric results when the model is conditioned." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.248, + 0.852, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.525, + 0.893, + 0.601 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of ablation studies on the task of scene synthesis from sparse RGBD inputs. \"(a)\", \"(b)\" and \"(c)\" correspond to the second (w/o conditioning, \\(\\beta = 0\\)), third (w/o inpainting, \\(\\beta = 1\\)) and fourth (w/ all, \\(\\beta = 1\\)) rows of Table 2, and \"(d)\" corresponds to the last (w/ all, \\(\\beta = 5\\)) row of Table 3. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. It is clear that the third row basically shows the most favorable appearance." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.605, + 0.505, + 0.685 + ], + "angle": 0, + "content": "
Guidance Factor βVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
0.012.414.716.517.90.4110.4960.5570.5830.5200.4460.3930.359
0.513.215.517.118.20.4520.5300.5780.5960.4960.4180.3740.347
1.014.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
2.014.515.817.518.40.5320.5610.5980.6060.4390.3930.3520.334
5.013.314.917.118.20.4880.5310.5790.5980.4750.4180.3670.342
" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.605, + 0.888, + 0.684 + ], + "angle": 0, + "content": "
Geometric
MSEdepthCDmeshComp meshes@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.9990.8450.7720.71919806062231110.6530.8180.8940.933
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
0.8940.8000.6540.593156251514487.20.7530.8460.9100.936
0.9920.8560.6630.5822551167617587.20.7470.8420.9080.934
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.686, + 0.893, + 0.737 + ], + "angle": 0, + "content": "Table 3. Ablation studies of the effects of guidance factor \\(\\beta\\) on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. A larger \\(\\beta\\) ideally strengthens the conditioning effect. The visual metrics are found to be the best when \\(\\beta\\) is set to 1 or 2. Interestingly, the optimal value of \\(\\beta\\) for the best geometry appears to increase as views become denser. However, setting such a large value of \\(\\beta\\) (e.g. \\(\\beta = 5\\)) leads to sub-optimal visual results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.751, + 0.253, + 0.765 + ], + "angle": 0, + "content": "circular camera trajectory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.471, + 0.867 + ], + "angle": 0, + "content": "Future Works. To improve our design, potential areas of investigation include: (1) Modeling color smoothness and variation, as demonstrated by NeRF [42]. (2) Supporting advanced physical lighting effects, such as SVBRDF, as implemented in TANGO [9]. (3) Incorporating appearance/surface extrapolation by learning an implicit field, such as NeRF [42, 43] or SDF [3, 80]. (4) Exploring gener" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.862 + ], + "angle": 0, + "content": "ative [5] or estimable [6, 84] camera trajectories for scene synthesis. (5) Investigating reconstruction from sparse-view RGB inputs only, using depth inpainting/estimation following the reverse sampling technique proposed in [37] by utilizing a versatile RGBD diffusion model. (6) Leveraging the multi-modal [52] or generative [57] power of large-scale pre-trained models, such as the recently widespread Stable Diffusion [57]." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8428" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.118, + 0.505, + 0.198 + ], + "angle": 0, + "content": "
MethodsVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
NGP10.412.414.417.40.2930.3770.4370.4980.5820.4760.4150.376
DS-NGP10.111.913.515.30.2050.2810.3210.3610.6050.5330.5030.476
N-RGBD14.116.518.420.00.4010.5130.5950.6520.4900.3840.3200.287
DDP14.116.118.320.90.4180.5040.5990.7020.5170.4100.3290.259
Ours14.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.12, + 0.889, + 0.197 + ], + "angle": 0, + "content": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
7.017.397.376.5229994229731667680660.2890.4460.6460.850
2.301.691.441.17536217017682300.5290.7220.8450.918
1.511.231.211.133503134512106430.7050.8190.8570.872
1.441.050.940.88236310136374510.5070.6240.7190.812
0.820.800.680.6210589021561000.7470.8390.9090.936
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.2, + 0.893, + 0.25 + ], + "angle": 0, + "content": "Table 4. Quantitative comparison with other approaches on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. Our approach outperforms other methods consistently in terms of geometric metrics as the sparsity varies. However, our method only show a definitive visual advantage across various visual metrics when the input views are highly sparse (5%)." + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.253, + 0.856, + 0.791 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.793, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison results with DS-NGP [13,43], DDP [56], N-RGBD [3] on the task of scene synthesis from sparse RGBD inputs. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. Our approach produces images that exhibit a close resemblance to the ground truth (GT), while comparative methods may result in inferior outcomes, especially when dealing with excessively sparse input views and outward-looking cameras." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8429" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.163, + 0.47, + 0.252 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3D point clouds. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 40-49. 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In this work, we present a new solution termed $\text{RGBD}^2$ that sequentially generates novel RGBD views along a camera trajectory, and the scene geometry is simply the fusion result of these views. More specifically, we maintain an intermediate surface mesh used for rendering new RGBD views, which subsequently becomes complete by an inpainting network; each rendered RGBD view is later back-projected as a partial surface and is supplemented into the intermediate mesh. The use of intermediate mesh and camera projection helps solve the tough problem of multi-view inconsistency. We practically implement the RGBD inpainting network as a versatile RGBD diffusion model, which is previously used for 2D generative modeling; we make a modification to its reverse diffusion process to enable our use. We evaluate our approach on the task of 3D scene synthesis from sparse RGBD inputs; extensive experiments on the ScanNet dataset demonstrate the superiority of our approach over existing ones. Project page: https://jblei.site/proj/rgbd-diffusion. + +# 1. Introduction + +Scene synthesis is an essential requirement for many practical applications. The resulting scene representation can be readily utilized in diverse fields, such as virtual reality, augmented reality, computer graphics, and game development. Nevertheless, conventional approaches to scene synthesis usually involve reconstructing scenes (e.g., indoor scenes with varying sizes) by fitting given observations, such as multi-view images or point clouds. The increasing prevalence of RGB/RGBD scanning devices has established multi-view data as a favored input modality, driving and promoting technical advancements in the realm of scene reconstruction from multi-view images. + +Neural Radiance Fields (NeRFs) [42] have demonstrated + +![](images/e6ecad3a716aaec0762ce18756dbc183a05ef24ace83a615449604ad12029d9b.jpg) +$t = 0$ + +![](images/53b0650c244c28dfec3bb61f36829b0d0b05ae02b12665db35da6d88bf4373fe.jpg) +$t = 1$ + +![](images/2243ea2d0b580b4866865ad361f81750e3dc49c46829e9367f2702740c808cc6.jpg) +$t = 2$ + +![](images/af5a9859a8d6bfe2519f5304edb9d69ce0dede25a2ccee65dff034ec4fd8bc9d.jpg) +$t = 3$ + +![](images/0db275be78bb69072dbb509103945ff4f2626fa62702882a75254c49bec4dece.jpg) +Final Result +Figure 1. Illustration of Our Generative Scene Synthesis. We incrementally reconstruct the scene geometry by inpainting RGBD views as the camera moves in the scene. + +potential in this regard, yet they are not exempt from limitations. NeRFs are designed to reconstruct complete scenes by fitting multi-view images, and they cannot generate or infer missing parts when the input is inevitably incomplete or missing. While recently some studies [3,5,8,56,63] have attempted to equip NeRFs with generative and extrapolation capabilities, this functionality relies on a comparatively short representation with limited elements (e.g. typically, the length of a global latent code is much shorter than that of an image: $(F = 512) \ll (H \times W = 128 \times 128 = 16,384)$ ) that significantly constrains their capacity to accurately capture fine-grained details in the observed data. Consequently, the effectiveness of these methods has only been established for certain categories of canonical objects, such as faces or cars [8, 63], or relatively small toy scenes [5]. + +We introduce a novel task of generative scene synthesis from sparse RGBD views, which involves learning across multiple scenes to later enable scene synthesis from a sparse set of multi-view RGBD images. This task presents a challenging setting wherein a desired solution should simultaneously (1) preserve observed regions, hallucinate missing parts of the scene, (2) eliminate additional computational costs during inference for each individual test scene, (3) en + +sure exact 3D consistency, and (4) maintain scalability to scenes with unfixed scales. + +We will elaborate on them in detail as follows. Firstly, to maximize the preservation of intricate details while simultaneously hallucinating potentially absent parts that may become more pronounced when views are exceedingly sparse, we perform straightforward reconstruction whose details come from images that can describe fine structures using a maximum of $H \times W$ elements (i.e. an image size) in a view completion manner. This is particularly compatible with diffusion models that operate at full image resolution with an inpainting mechanism. We also found that RGBD diffusion models greatly simplify the training complexity of a completion model, thanks to their versatile generative ability to inpaint missing RGBD pixels while preserving the integrity of known regions through a convenient training process solely operated on complete RGBD data. Secondly, our method employs back-projection that requires no optimization, thus eliminating the necessity for test-time training for each individual scene, ultimately leading to a significant enhancement in test-time efficiency. Thirdly, to ensure consistency among multi-view images, an intermediate mesh representation is utilized as a means of bridging the 2D domain (i.e. multi-view RGBD images) with the 3D domain (i.e. the 3D intermediate mesh) through the aid of camera projection. Fourthly, to enable our method to handle scenes of indeterminate sizes, we utilize images with freely designated poses as the input representation. Such manner naturally ensures SE(3) equivariance, and thus offers scalability due to the ease with which the range of the generated content can be controlled by simply specifying their camera extrinsic matrices. + +Our proposal involves generating multi-view consistent RGBD views along a predetermined camera trajectory, using an intermediate mesh to render novel RGBD images that are subsequently inpainted using a diffusion model, and transforming each RGBD view into a 3D partial mesh via back-projection, and finally merging it with the intermediate scene mesh to produce the final output. Specifically, our proposed approach initiates by ingesting multiple posed RGBD images as input and utilizing back-projection to construct an intermediate scene mesh. This mesh encompasses color attributes that facilitate the rendering of RGBD images from the representation under arbitrarily specified camera viewpoints. Once a camera pose is selected from the test-time rendering trajectory, the intermediate mesh is rendered to generate a new RGBD image for this pose. Notably, the test-time view typically exhibits only slight overlap with the known cameras, leading to naturally partially rendered RGBD images. To fill the gaps in the incomplete view, we employ an inpainting network implemented as an RGBD diffusion model with minor modifications to its reverse sampling process. The resulting inpainted out + +put is then back-projected into 3D space, forming a partial mesh that complements the entire intermediate scene mesh. We iterate these steps until all test-time camera viewpoints are covered, and the intermediate scene mesh gradually becomes complete during this process. The final output of our pipeline is the mesh outcome acquired from the last step. + +Extensive experiments on ScanNet [12] dataset demonstrate the superiority of our approach over existing solutions on the task of scene synthesis from sparse RGBD inputs. + +# 2. Related Works + +In this section, we provide a brief review of the literature related to diffusion models, 3D representations and generative manners, scene synthesis, and view synthesis. + +Diffusion Models. In recent years, the field of 2D computer vision has experienced a surge of interest in diffusion-based generative models [20,65,67]. These models have prompted the development of image generative modeling approaches, such as GLIDE [45], unCLIP [53], Imagen [61], and Latent Diffusion Models [57], as well as the invention of sampling schedulers [20, 26, 36, 66] and guiding methods [15, 22]. Furthermore, these models have been applied to a broad range of image processing tasks, including image inpainting [37], image translation [4, 57, 60, 82], video generation [23, 25, 76], super-resolution [21, 32, 62], and image editing [2, 27, 40]. More recently, some researchers have adapted these techniques from 2D to the 3D domain, as demonstrated by methods such as [39, 51, 88, 92]. Our approach harnesses such versatility by adopting an iterative denoising strategy like [37], and utilizing a masked inpainting technique that operates on the projected RGBD views to synthesize image content. + +3D Representations and Generative Manners. A variety of representations, including voxels [81, 85], point clouds [1, 39, 68, 87, 92], meshes [17, 44, 70, 71, 79], implicit surfaces [10, 30, 31, 41, 48, 72-74, 88, 91], multi-view images [11, 19, 34, 35, 86], and neural radiance fields [3, 8, 9, 13, 42, 43, 49, 56, 63, 80], have been proposed, each with its own unique advantages over the others. This has also motivated researchers to combine them with distinct generative approaches, such as VAEs [28], GANs [16], normalizing flows [54], auto-regressive models [24, 75], and the latest diffusion models [20], resulting in an extensive range of applications [1, 8, 39, 41, 44, 48, 63, 85, 87, 92]. However, most existing methods have limitations in their representation capability, such as cubically scaled-up memory consumption, or a fixed number of points, which makes them difficult to apply to scenes of uncertain scales, and poor equivariance, which only allows them to handle canonically-posed objects. In this paper, we address these issues by focusing on the generation of multi-view RGBD images that can capture intricate structures using $H \times W$ pixels created by a diffusion model. This approach reduces memory complexity from $\mathcal{O}(HWD)$ to $\mathcal{O}(HW)$ and increases expressive + +ability from $\mathcal{O}(F)$ to $\mathcal{O}(HW)$ . + +Scene Synthesis. In this area, there are two primary research directions. The first pertains to learning configurations, including graphs [33, 38, 77, 90], top-down views [55, 78], and scene composition [50, 83]. The second line of research involves direct learning from the appearance of a scene [13, 42, 43, 49, 80], thereby obviating the necessity for specialized synthesized datasets required by the aforementioned methods. Our approach relies solely on RGBD scans, which are readily available from scanning devices, reducing the need for manual annotation. It accurately reconstructs a clean geometry based on the sparse-view input and can effectively hallucinate missing parts, especially when the input views are highly sparse. + +View Synthesis. The arrival of NeRF [42] has significantly advanced the field of view synthesis. While a considerable amount of research has been dedicated to the view synthesis of object-level instances [7, 18, 47, 64], only a few studies have focused on simple scenes [5, 14, 58]. Additionally, some studies have explored techniques for improving performance using sparse inputs [46, 56]. In this paper, we aim to recover scene-level geometry from sparse RGBD images without relying on NeRFs. + +# 3. Preliminary + +To make our paper self-contained, we provide some preliminary knowledge about DDPM [20] and DDIM [66]. + +Definition. Given an image $\mathbf{x}_0\sim q(\mathbf{x}_0)$ , the forward diffusion process is a Markov chain that sequentially produces noisy images $\mathbf{x}_1,\dots ,\mathbf{x}_T$ scheduled by a set of constants $\{\beta_t\in (0,1)\}_{t = 1}^T$ where $T$ is the total number of iterations and $\beta_{1} < \beta_{2} < \ldots < \beta_{T}$ : + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1}, \beta_ {t} \mathbf {I}\right) +$$ + +A nice property of using i.i.d. Gaussian distribution is that we can sample the noisy image $\mathbf{x}_t$ easily based on $\mathbf{x}_0$ in a closed form without computing all the intermediates: + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {0}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {\bar {\alpha}} _ {t} \mathbf {x} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right) \tag {1} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \prod_{s = 1}^{t}\alpha_{s}$ . The reverse diffusion process is another Markov chain starting from $\mathbf{x}_T\sim \mathcal{N}(\mathbf{x}_T;\mathbf{0},\mathbf{I})$ parameterized by a trainable $\theta$ : + +$$ +p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \mu_ {\theta} \left(\mathbf {x} _ {t}, t\right), \boldsymbol {\Sigma} _ {\theta} \left(\mathbf {x} _ {t}, t\right)\right) \tag {2} +$$ + +where $\pmb{\Sigma}_{\theta}(\mathbf{x}_t,t) = \sigma_t^2\mathbf{I} = \eta \frac{1 - \bar{\alpha}_{t - 1}}{1 - \bar{\alpha}_t}\beta_t\mathbf{I}$ [66] is independent of $\theta$ and $\mathbf{x}_t$ , and $\mu_{\theta}(\mathbf{x}_t,t)$ can be derived from a noise estimator $\epsilon_{\theta}(\mathbf{x}_t,t)$ via: + +$$ +\mu_ {\theta} (\mathbf {x} _ {t}, \mathbf {x} _ {o}) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} (\mathbf {x} _ {t}, t)\right) +$$ + +We practically implement the noise estimator $\epsilon_{\theta}(\mathbf{x}_t,t)$ as a UNet [57, 59] parameterized by $\theta$ . However, in our case, it is also conditioned on $\hat{\mathbf{x}}_0$ which will be detailed in Sec. 4.2. + +Training. To train the noise estimator $\epsilon_{\theta}(\mathbf{x}_t,t)$ , we adopt the simplified training objective [20]: + +$$ +\min _ {\theta} \mathbb {E} _ {t, \epsilon_ {t}, \mathbf {x} _ {0}} \left[ \| \epsilon_ {\theta} (\sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {t}, t) - \epsilon_ {t} \| ^ {2} \right] +$$ + +where the time step $t\sim \mathcal{U}\{1,T\}$ is uniformly sampled, $\epsilon_t\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ is a standard Gaussian noise, and the image $\mathbf{x}_0\sim q(\mathbf{x}_0)$ is randomly drawn from the data distribution. + +Inference. We employ a strided DDIM [66] scheduler to progressively recover the clean image from $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ to $\mathbf{x}_0$ with a subset of $S$ (usually $S\ll T$ ) steps $\{\tau_i\}_{i = 1}^S$ + +$$ +\begin{array}{l} \mathbf {x} _ {\tau_ {i - 1}} \leftarrow \sqrt {\bar {\alpha} _ {\tau_ {i - 1}}} \left(\frac {\mathbf {x} _ {\tau_ {i}} - \sqrt {1 - \bar {\alpha} _ {\tau_ {i}}} \epsilon_ {\theta} (\mathbf {x} _ {\tau_ {i}} , \tau_ {i})}{\sqrt {\bar {\alpha} _ {\tau_ {i}}}}\right) + \\ \sqrt {1 - \bar {\alpha} _ {\tau_ {i - 1}} - \sigma_ {\tau_ {i}} ^ {2}} \cdot \epsilon_ {\theta} (\mathbf {x} _ {\tau_ {i}}, \tau_ {i}) + \sigma_ {\tau_ {i}} ^ {2} \epsilon_ {\tau_ {i}} \\ \end{array} +$$ + +where $\epsilon_{\tau_i} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ is a standard Gaussian noise. It is interesting that setting $\eta = 0$ implies $\forall i$ , $\sigma_{\tau_i} \equiv 0$ , making the inference process deterministic. Nevertheless, diversity can still be achieved by choosing a different $\mathbf{x}_T$ from $\mathcal{N}(\mathbf{0}, \mathbf{I})$ . + +# 4. Approach + +In this work, we introduce a new scene synthesis approach that relies on the sequential generation of RGBD frames using a trained RGBD diffusion model conditioned on views rendered under a test-time camera trajectory from a sparse set of input RGBD images. Our approach leverages the generative ability of diffusion models to synthesize missing visual appearance (color) and geometry details (depth) while rigorously preserving visible regions by image inpainting. Such an incremental view inpainting process is interleaved with the back-projection, mesh fusion, and mesh rendering procedures to achieve global 3D consistency among distinct temporal frames. + +This section is organized as follow. In Sec. 4.1, we will start by introducing the overall framework of repeatedly converting the RGBD image into a partial 3D mesh and performing RGBD inpainting for rendered views in a progressive manner. Later in Sec. 4.2, we will elaborate more on the details of the conditional RGBD diffusion model for rendered view inpainting based on a trained DDPM [20]. + +# 4.1. Incremental View Inpainting Fashion + +As shown in Figure 2, given a sparse set of $N$ RGBD views $\{\mathbf{I}_i\}_{i=1}^N$ with their associated camera intrinsic $\mathbf{K}$ and extrinsic $\{\mathbf{R}_i\}_{i=1}^N$ matrices, and additionally a camera trajectory composed of $M$ viewpoints $\{\mathbf{T}_j\}_{j=1}^M$ with the same intrinsic matrix, the essence of our method is to progressively synthesize RGBD images $\mathbf{O}_j$ at each specified novel view $\mathbf{T}_j$ . The generated novel-view frames should be consistent with $\{\mathbf{I}_i\}_{i=1}^N$ in both geometry and appearance. The final output should be a consistent 3D + +![](images/af0fdedf317ec3fac38e7e2af6ab146b2bfc5c1b75537a7c20b1b1a72e6886e8.jpg) +Figure 2. 3D Scene Synthesis via Incremental View Inpainting. Given a sparse set of RGBD images $\{\mathbf{I}_i\}_{i=1}^N$ with camera intrinsic $\mathbf{K}$ and extrinsic $\{\mathbf{R}_i\}_{i=1}^N$ matrices, our goal is to generate a coherent 3D scene mesh $\mathcal{S}$ via predicting RGBD frames $\{\mathbf{O}_j\}_{j=1}^M$ along a novel-view trajectory $\{\mathbf{T}_j\}_{j=1}^M$ . To achieve this goal, we firstly fuse the inputs of $\{\mathbf{I}_i\}_{i=1}^N$ into an initial mesh $\mathcal{S}_1$ , and then render it to obtain an incomplete image $\hat{\mathbf{O}}_1$ that is later inpainted to obtain $\mathbf{O}_1$ using a RGBD diffusion model. After that, $\mathbf{O}_1$ is back-projected and integrated with $\mathcal{S}_1$ to produce a more complete scene, $\mathcal{S}_2$ . By iteratively repeating this process, we can progressively obtain $\mathcal{S}_2, \dots, \mathcal{S}_M$ . Finally, the fused result $\mathcal{S}_{M+1}$ is the eventual desired output $\mathcal{S}$ . Gray dashed lines “- - ” denote omitted and unvisualized steps. + +colored mesh $S$ converted from the back-projection result $\left( \cup_{j=1}^{M} \phi_{2 \to 3}(\mathbf{O}_j) \right) \cup \left( \cup_{i=1}^{N} \phi_{2 \to 3}(\mathbf{I}_i) \right)$ . Please also refer to Algorithm 1 for a detailed description of the procedure. + +# Algorithm 1 Incremental RGBD View Inpainting + +Require: RGBD images $\{\mathbf{I}_i\}_{i=1}^N$ with camera extrinsics $\{\mathbf{R}_i\}_{i=1}^N$ , a novel trajectory of M extrinsics $\{\mathbf{T}_j\}_{j=1}^M$ . + +$$ +\mathcal {S} _ {1} \leftarrow \cup_ {i = 1} ^ {N} \phi_ {2 \rightarrow 3} (\mathbf {I} _ {i}) +$$ + +for $j = 1$ to $M$ do + +$$ +\mathbf {\hat {O}} _ {j} \leftarrow \phi_ {3 \rightarrow 2} (\mathbf {T} _ {j}) +$$ + +$\triangleright$ novel-view rendering + +$$ +\mathbf {O} _ {j} \leftarrow f (\hat {\mathbf {O}} _ {j}) +$$ + +RGBD inpainting + +$$ +\mathcal {S} _ {j + 1} \leftarrow \mathcal {S} _ {j} \cup \phi_ {2 \rightarrow 3} (\mathbf {O} _ {j}) +$$ + +$\triangleright$ mesh fusion + +end for + +return $\mathcal{S}_{M + 1}$ + +Rendering and Back-projection. The operator $\phi_{3\rightarrow 2}$ is implemented as mesh rasterization, which allows for the rendering of a partial RGBD image $\hat{\mathbf{O}}_j$ from a mesh $S_{j}$ . This approach offers the advantage of producing a clean visibility mask $\mathbf{m}_j$ , which is not possible with NeRFs [42]. The back-projection operator $\phi_{2\rightarrow 3}$ is responsible for the conversion from a depth map into a point cloud, where the connectivity between points is inherited from the connectivity of the 2D pixel grid. Furthermore, mesh faces that are either in close proximity to the viewpoint or exhibit slender characteristics are filtered out to ensure accuracy. + +Challenges and Solutions. To circumvent the limitations + +posed by potential 3D inconsistency in both geometry and appearance, as well as the challenge of solely handling specific canonically-posed scenes, we propose several strategies to address these issues. Firstly, our method for synthesizing novel views combines rendering (mesh rasterization) and inpainting techniques, and interleaves the view synthesis process with online RGBD fusion via back-projection and mesh combination. The use of perspective camera projection ensures strict adherence to 3D constraints, resulting in visually consistent and accurate synthesized views. In concrete terms, we begin by rendering the mesh $S_{j}$ under view $\mathbf{T}_{j}$ using a rendering operation $\phi_{3\rightarrow 2}(\mathbf{T}_{j})$ . This process yields an incomplete RGBD image $\hat{\mathbf{O}}_j$ with missing regions, which is subsequently inpainted using a diffusion model described in detail in Sec. 4.2, resulting in a complete image $\mathbf{O}_j$ . Once image $\mathbf{O}_j$ has been generated for view $\mathbf{T}_j$ , it can be fused into a 3D mesh via $S_{j + 1} = \phi_{2\rightarrow 3}(\mathbf{O}_j)\cup S_j$ using a back-projection operator $\phi_{2\rightarrow 3}$ . Secondly, our solution reduces the learning difficulty and can handle noncanonical scenes by decomposing the 3D scene as a Markov chain of temporal RGBD images rendered from arbitrarily specified novel viewpoints. The applicability of handling scenes with arbitrary scaling, movement, and posing is attributed to the utilization of two SE(3) equivariant operators, namely $\phi_{3\rightarrow 2}$ and $\phi_{2\rightarrow 3}$ , as well as the independence of absolute coordinates. Moreover, the presence of redundant information in adjacent frames, combined with our suggested decomposition rule, facilitates the minimization of learning complexity in an auto-regressive manner. + +In accordance with the Markov chain decomposition principle, the distribution of the scene can be expressed as the joint distribution of view frames: + +$$ +p (\mathcal {S}) = \prod_ {j} p (\mathbf {O} _ {j} \mid \{\mathbf {O} _ {s} \} _ {s = 1} ^ {j - 1}, \{\mathbf {I} _ {s} \} _ {s = 1} ^ {N}) +$$ + +where the prediction of $\mathbf{O}_j$ is based on the fusion result of all the previously known frames $\{\mathbf{O}_s\}_{s=1}^{j-1} \cup \{\mathbf{I}_s\}_{s=1}^N$ . + +# 4.2. RGBD Diffusion for Rendered View Inpainting + +In this section, we describe the implementation details of the way to employ diffusion models to inpaint the missing regions of the RGBD image $\hat{\mathbf{O}}_j$ with a binary mask $\mathbf{m}_j$ obtained by rendering visibility, where the value of 1 is assigned to the corresponding ray that intersects with the geometry surface, while 0 is assigned to all other cases, both of which are rendered by projecting $S_{j}$ under a novel viewpoint $\mathbf{T}_j$ . It is noteworthy that only those pixels located where $\mathbf{m}_j = 0$ in $\hat{\mathbf{O}}_j$ are considered invalid, and therefore, are entirely filled with zeros (i.e., $\hat{\mathbf{O}}_j\odot \mathbf{m}_j\equiv \hat{\mathbf{O}}_j$ ). + +![](images/6906c4f13e23c97d09c549e269e678c9755500f0cd73c536b2bbdb1580ea17f9.jpg) +Figure 3. RGBD Diffusion for Rendered View Inpainting. In each iteration, we utilize a forward diffusion step to sample the visible region $\mathbf{x}_t^{\mathrm{vis}}$ (top) from the incomplete input $\hat{\mathbf{x}}_0$ , while employing a denoising diffusion step to obtain the complementary content $\mathbf{x}_t^{\mathrm{invis}}$ (bottom) from the output $\mathbf{x}_{t + 1}$ generated in the previous iteration $t + 1$ . + +A Single Reverse Diffusion Step for $\mathbf{T}_j$ at Time $t$ .2 We initialize the clean diffusion sample $\hat{\mathbf{x}}_0$ at time $t = 0$ as $\hat{\mathbf{O}}_j$ , and those noisy samples at time $0 < t \leq T$ are denoted as $\mathbf{x}_t$ . To ensure 3D consistency, we seek to predict the invisible region $\mathbf{x}_0^{\mathrm{vis}}$ while preserving the visible portion $\mathbf{x}_0^{\mathrm{vis}}$ unaltered. We follow [37] and modify the standard denoising process to meet our needs. At each reverse diffusion step $t$ , we use the forward diffusion process defined by the Eqn. (1) to sample a visible region $\mathbf{x}_t^{\mathrm{vis}}$ masked by $\mathbf{m}$ , and the reverse diffusion step defined by Eqn. (2) to sample a full part from $\mathbf{x}_{t+1}$ which is later masked by $1 - \mathbf{m}$ to form an invisible region $\mathbf{x}_t^{\mathrm{vis}}$ . + +$$ +\mathbf {x} _ {t} ^ {\text {v i s}} = \sqrt {\bar {\alpha} _ {t}} \hat {\mathbf {x}} _ {0} + (1 - \bar {\alpha} _ {t}) \epsilon_ {t} ^ {\text {v i s}} \odot \mathbf {m} +$$ + +$$ +\mathbf {x} _ {t} ^ {\text {i n v i s}} = \left(\mu_ {\theta} \left(\mathbf {x} _ {t}, \hat {\mathbf {x}} _ {t}, t\right) + \sigma_ {t} \epsilon_ {t} ^ {\text {i n v i s}}\right) \odot (1 - \mathbf {m}) +$$ + +where $\epsilon_t^{\mathrm{vis}},\epsilon_t^{\mathrm{invis}}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ . The noisy image $\mathbf{x}_t$ can be simply calculated as the sum of $\mathbf{x}_t^{\mathrm{vis}}$ and $\mathbf{x}_t^{\mathrm{invis}}$ , as expressed by $\mathbf{x}_t = \mathbf{x}_t^{\mathrm{vis}} + \mathbf{x}_t^{\mathrm{invis}}$ + +Diffusion Network. We implement the diffusion model as a UNet [57, 59] conditioned on the observed region $\mathbf{x}_0$ . We input the concatenation of $\mathbf{x}_t$ and $\hat{\mathbf{x}}_0$ into the network. + +Classifier-free Guidance. To further enhance the controllability of the generation process, we introduce a classifier-free guidance [22] mechanism. Specifically, we train a unified network $\epsilon_{\theta}$ comprising of an unconditional model $\epsilon_{\theta}(\mathbf{x}_t,\mathbf{c},t)$ , where the shared variable $\mathbf{c}$ is incorporated, and a conditional model $\epsilon_{\theta}(\mathbf{x}_t,\hat{\mathbf{x}}_0,t)$ . In this way, the predicted noise $\tilde{\epsilon}_{\theta}$ can be recomputed as follows: + +$$ +\tilde {\epsilon} _ {\boldsymbol {\theta}} (\mathbf {x} _ {t}, \hat {\mathbf {x}} _ {0}, t) = \epsilon_ {\boldsymbol {\theta}} (\mathbf {x} _ {t}, \mathbf {c}, t) + \beta \times [ \epsilon_ {\boldsymbol {\theta}} (\mathbf {x} _ {t}, \hat {\mathbf {x}} _ {0}, t) - \epsilon_ {\boldsymbol {\theta}} (\mathbf {x} _ {t}, \mathbf {c}, t) ] +$$ + +where $\beta \geq 0$ is the guidance factor, being responsible for the trade-off between sampling quality and diversity [22]. + +# 5. Experiments + +Dataset. We conducted experiments on the ScanNetV2 [12] dataset, which was pre-processed by removing redundant frames [69]. For training, we used the first 1,293 scenes, while for metric evaluation, we randomly selected 18 scenes with over 50 views each from the remaining as our test set. We also evaluated under various sparsity settings (5%, 10%, 20%, and 50%) by uniformly down-sampling views. + +Comparison. We compared against the neural graphics primitive (NGP) [43], which has demonstrated impressive performance in scene modeling with high efficiency. To enhance its geometric quality, we incorporated a depth supervision (DS) loss [13] to build an improved variant called DS-NGP [13, 43]. We also compare against Neural RGBD (N-RGBD) [3], which recovers implicit surfaces from RGBD scans, and Dense Depth Prior (DDP) [56], which learns a NeRF utilizing view completion from sparse RGBD views. + +Evaluation Metrics. For assessing the visual quality of RGB images, we adopted the peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [89] that is based on the AlexNet [29] backbone. To evaluate the geometry quality, we computed the mean squared error (MSE) on depth maps, and sample 10,000 points uniformly on meshes constructed via back-projection to evaluate the chamfer distance (CD) and completeness (Comp.) with a threshold of $0.1\mathrm{m}$ . We also measured the computational time required to execute different stages of the method. For LPIPS, MSE, and CD, the lower the better; for PSNR, SSIM, and Comp., the higher the better. All reported metrics are averaged across the test scenes. + +Implementation Details. Our model has 157M parameters and was trained for three days on 7 NVIDIA 3090-Ti GPUs, using a batch size of 280. The learning rate was initialized at $1 \times 10^{-4}$ and reduced to $1 \times 10^{-6}$ over a period of 300 epochs, utilizing a cosine annealing strategy. The image resolution is $128 \times 128$ with a rendering chunk size of 7. + +# 5.1. Ablation Studies + +We conducted ablation studies to validate the effectiveness of each component in our proposal. Results concluded here are nontrivial and a bit nuanced. + +Effects of Different Ingredients. We examined the anticipated efficacy of the proposed conditioning and inpainting components in our approach. Table 2 displays the numerical results, and Figure 5-(a-c) presents the visualizations. The combined use of conditioning and inpainting yields superior visual performance compared to the ground truth. Nevertheless, when the model is conditioned, the impact of inpainting on geometric quality becomes less crucial. Moreover, as more views are provided, the stochastic generation process becomes increasingly deterministic, resulting in structures that more closely resemble the ground truth. + +Effects of Guidance Scale. The guidance factor $\beta$ significantly affects the conditioning effect on the results. To investigate the optimal $\beta$ under various settings, we conducted experiments with $\beta$ chosen from 0.0, 0.5, 1.0, 2.0, and 5.0, respectively, and evaluated their performance. Quantitative results are presented in Table 3. It is interesting that only a suitable value of $\beta$ (1.0 or 2.0) yields optimal performance, while smaller or larger values of $\beta$ result in underperformance. Surprisingly, for geometric recovery (MSE and CD), the optimal value of $\beta$ appears to increase as the percentage gets larger. For a scene with a percentage $\geq 50\%$ , the best value of $\beta$ is amazingly greater than 5.0. However, such a large percentage is not optimal for visual appearance. This is because using a larger value of $\beta$ at a low percentage can cause the generated results to deviate unexpectedly from the ground truth. Our visualization, presented in Figure 5-(a, c, d), indicates that using an unconditional model ( $\beta = 0$ ) leads to undesired and bizarre geometric structures since the network fails to understand the context provided by known views. However, excessively large values of $\beta$ also oversaturate the color (e.g. row “(d)” at $5\%$ ), making the visual appearance unrealistic. + +Effects of Randomness and Trajectories. We investigated + +![](images/667411f8f3865b6c8e79adda100c3b6508f4409591d5fa6d5e6d301c7079e91f.jpg) +(a) original + +![](images/7702e27e95d9ba0b58d343044003fd82de25acb8fad3a9d4964eacad22452589.jpg) +(b) seed + +![](images/2154a1da3631d63db816ecaeaf07bf4f163bbe22e7be25dca39303cfdc022432.jpg) +(c) trajectory +Figure 4. Diverse results obtained by changing the (b) random seed and (c) camera trajectory based on (a) the original scene. + +the impact of employing different random seeds and camera trajectories on the results. Such obtained meshes are visualized in Figure 4. As diffusion models inherently include randomness in their reverse sampling process, by switching to a different random seed, we can obtain another outcome. Moreover, the camera trajectory can affect the rough shape of the scene. It is promising that our approach can yield controllable and editable results, as it is capable of generating various and appealing outcomes by simply altering these two factors. + +# 5.2. Generative Scene Synthesis + +We evaluated the performance of our method against other similar approaches on this task through extensive experiments under various sparsity settings. Table 1 presents the time required by different methods across various stages. Our approach stands out for its efficiency, as it eliminates the need for additional optimization on individual test scenes during inference. Quantitative results are shown in + +
TimeBackendRepre.TrainingOptimizationRendering
(DS-)NGP [13,43]CUDA C++NeRF—~ 3 min.~ 0.05 sec.
N-RGBD [3]PyTorchNeRF—~ 2 hours~ 2 sec.
DDP [56]PyTorchNeRF~ 1 day~ 1 hour~ 1 sec.
OursPyTorchMesh~ 3 days—~ 3 sec.
+ +Table 1. Efficiency Comparison of Different Methods. It details their distinct implementation backends, the underlying representation (Repre.) methods, and the time required for training on multiple training scenes, optimization on a single test scene, and rendering a single view after per-scene optimization. + +Table 4. We observe that our approach exhibits a clear advantage in visual metrics over the others when the provided views are extremely sparse (5%). Interestingly, our method consistently achieves the best performance in all the geometry-related metrics. Qualitative results are presented in Figure 6. DS-NGP [13, 43] and DDP [56] struggle to accurately recover geometry due to their inability to hallucinate and extrapolate missing regions. In comparison, N-RGBD [3] can achieve better surface completion results by learning and extrapolating neural implicit surfaces. However, their performance significantly degrades when input views are extraordinarily sparse (5%). In contrast, our method consistently exhibits plausible appearance that closely resembles the ground truth, particularly in scenarios with sparse-view inputs. + +# 6. Discussions + +Limitations. Our current implementation has several limitations that may impact its usefulness in some scenarios. Firstly, it is incapable of handling color discrepancies caused by lighting variations. Secondly, it lacks surface extrapolation capabilities that can be provided through implicit field representation. Lastly, the limited receptive field of our design is confined to the observable volume of the current camera view and may result in inconsistent and discontinuous predictions, particularly in the case of a large + +
FactorsVisual
PSNRcolorSSIMcolorLPIPScolor
Cond.Inpa.5%10%20%50%5%10%20%50%5%10%20%
9.339.309.279.450.3310.3300.3300.3330.6370.6360.637
✓12.414.716.517.90.4110.4960.5570.5830.5200.4460.393
✓12.513.614.716.10.4440.4730.5130.5560.4490.4090.362
✓✓14.616.017.418.40.5220.5550.5930.6030.4480.3990.359
+ +Table 2. Ablation studies of the effects of conditioning (Cond., $\beta = 1$ ) and inpainting (Inpa.) on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. The combined use of conditioning and inpainting leads to superior performance in visual metrics, and inpainting plays a less significant role in terms of geometric results when the model is conditioned. + +
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.3091.3041.3101.29330612777246317580.5130.5980.7110.862
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.8970.8080.6620.595116369917699.00.7510.8170.8870.928
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
+ +![](images/16a16ca21b2bbf6f0ae8f5b6ffd337d3337f94e06fc9d7abff4b1fca291bee98.jpg) +Figure 5. Qualitative results of ablation studies on the task of scene synthesis from sparse RGBD inputs. "(a)", "(b)" and "(c)" correspond to the second (w/o conditioning, $\beta = 0$ ), third (w/o inpainting, $\beta = 1$ ) and fourth (w/ all, $\beta = 1$ ) rows of Table 2, and "(d)" corresponds to the last (w/ all, $\beta = 5$ ) row of Table 3. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. It is clear that the third row basically shows the most favorable appearance. + +
Guidance Factor βVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
0.012.414.716.517.90.4110.4960.5570.5830.5200.4460.3930.359
0.513.215.517.118.20.4520.5300.5780.5960.4960.4180.3740.347
1.014.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
2.014.515.817.518.40.5320.5610.5980.6060.4390.3930.3520.334
5.013.314.917.118.20.4880.5310.5790.5980.4750.4180.3670.342
+ +Table 3. Ablation studies of the effects of guidance factor $\beta$ on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. A larger $\beta$ ideally strengthens the conditioning effect. The visual metrics are found to be the best when $\beta$ is set to 1 or 2. Interestingly, the optimal value of $\beta$ for the best geometry appears to increase as views become denser. However, setting such a large value of $\beta$ (e.g. $\beta = 5$ ) leads to sub-optimal visual results. + +
Geometric
MSEdepthCDmeshComp meshes@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.9990.8450.7720.71919806062231110.6530.8180.8940.933
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
0.8940.8000.6540.593156251514487.20.7530.8460.9100.936
0.9920.8560.6630.5822551167617587.20.7470.8420.9080.934
+ +circular camera trajectory. + +Future Works. To improve our design, potential areas of investigation include: (1) Modeling color smoothness and variation, as demonstrated by NeRF [42]. (2) Supporting advanced physical lighting effects, such as SVBRDF, as implemented in TANGO [9]. (3) Incorporating appearance/surface extrapolation by learning an implicit field, such as NeRF [42, 43] or SDF [3, 80]. (4) Exploring gener + +ative [5] or estimable [6, 84] camera trajectories for scene synthesis. (5) Investigating reconstruction from sparse-view RGB inputs only, using depth inpainting/estimation following the reverse sampling technique proposed in [37] by utilizing a versatile RGBD diffusion model. (6) Leveraging the multi-modal [52] or generative [57] power of large-scale pre-trained models, such as the recently widespread Stable Diffusion [57]. + +
MethodsVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
NGP10.412.414.417.40.2930.3770.4370.4980.5820.4760.4150.376
DS-NGP10.111.913.515.30.2050.2810.3210.3610.6050.5330.5030.476
N-RGBD14.116.518.420.00.4010.5130.5950.6520.4900.3840.3200.287
DDP14.116.118.320.90.4180.5040.5990.7020.5170.4100.3290.259
Ours14.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
+ +
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
7.017.397.376.5229994229731667680660.2890.4460.6460.850
2.301.691.441.17536217017682300.5290.7220.8450.918
1.511.231.211.133503134512106430.7050.8190.8570.872
1.441.050.940.88236310136374510.5070.6240.7190.812
0.820.800.680.6210589021561000.7470.8390.9090.936
+ +Table 4. Quantitative comparison with other approaches on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. Our approach outperforms other methods consistently in terms of geometric metrics as the sparsity varies. However, our method only show a definitive visual advantage across various visual metrics when the input views are highly sparse (5%). + +![](images/c97d438b48dfd90f6ad29adce2d16f48e00053657fc853040f8b4d1d097eb941.jpg) +Figure 6. Qualitative comparison results with DS-NGP [13,43], DDP [56], N-RGBD [3] on the task of scene synthesis from sparse RGBD inputs. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826–5835, October 2021. 2 \ No newline at end of file diff --git a/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/images.zip b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..39f732c8318b6fe8414b74cf75434b4910ae3188 --- /dev/null +++ b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ba3b62daf586204db72751f35373cacc459bba516d22b5640ef545a43f836e96 +size 780968 diff --git a/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/layout.json b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d36ced849e6441927e6c76373e0b7fa53cc52c20 --- /dev/null +++ b/2023/RGBD2_ Generative Scene Synthesis via Incremental View Inpainting Using RGBD Diffusion Models/layout.json @@ -0,0 +1,12019 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 129, + 136, + 449, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 136, + 449, + 172 + ], + "spans": [ + { + "bbox": [ + 129, + 136, + 449, + 172 + ], + "type": "text", + "content": "RGBD2: Generative Scene Synthesis via Incremental View Inpainting using RGBD Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "spans": [ + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "text", + "content": "Jiabao Lei" + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "text", + "content": ", Jiapeng Tang" + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "text", + "content": ", Kui Jia" + }, + { + "bbox": [ + 190, + 191, + 386, + 207 + ], + "type": "inline_equation", + "content": "^{1,3,\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 195, + 207, + 381, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 195, + 207, + 381, + 220 + ], + "spans": [ + { + "bbox": [ + 195, + 207, + 381, + 220 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 195, + 207, + 381, + 220 + ], + "type": "text", + "content": "South China University of Technology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "spans": [ + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "type": "text", + "content": "Technical University of Munich, " + }, + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 145, + 220, + 428, + 234 + ], + "type": "text", + "content": "Peng Cheng Laboratory" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "spans": [ + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 285, + 282, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 282, + 531 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 282, + 531 + ], + "type": "text", + "content": "We address the challenge of recovering an underlying scene geometry and colors from a sparse set of RGBD view observations. In this work, we present a new solution termed " + }, + { + "bbox": [ + 45, + 285, + 282, + 531 + ], + "type": "inline_equation", + "content": "\\text{RGBD}^2" + }, + { + "bbox": [ + 45, + 285, + 282, + 531 + ], + "type": "text", + "content": " that sequentially generates novel RGBD views along a camera trajectory, and the scene geometry is simply the fusion result of these views. More specifically, we maintain an intermediate surface mesh used for rendering new RGBD views, which subsequently becomes complete by an inpainting network; each rendered RGBD view is later back-projected as a partial surface and is supplemented into the intermediate mesh. The use of intermediate mesh and camera projection helps solve the tough problem of multi-view inconsistency. We practically implement the RGBD inpainting network as a versatile RGBD diffusion model, which is previously used for 2D generative modeling; we make a modification to its reverse diffusion process to enable our use. 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The resulting scene representation can be readily utilized in diverse fields, such as virtual reality, augmented reality, computer graphics, and game development. Nevertheless, conventional approaches to scene synthesis usually involve reconstructing scenes (e.g., indoor scenes with varying sizes) by fitting given observations, such as multi-view images or point clouds. The increasing prevalence of RGB/RGBD scanning devices has established multi-view data as a favored input modality, driving and promoting technical advancements in the realm of scene reconstruction from multi-view images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 57, + 698, + 279, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 698, + 279, + 709 + ], + "spans": [ + { + "bbox": [ + 57, + 698, + 279, + 709 + ], + "type": "text", + "content": "Neural Radiance Fields (NeRFs) [42] have demonstrated" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 321, + 281, + 367, + 321 + ], + "blocks": [ + { + "bbox": [ + 321, + 281, + 367, + 321 + ], + "lines": [ + { + "bbox": [ + 321, + 281, + 367, + 321 + ], + "spans": [ + { + "bbox": [ + 321, + 281, + 367, + 321 + ], + "type": "image", + "image_path": "e6ecad3a716aaec0762ce18756dbc183a05ef24ace83a615449604ad12029d9b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 324, + 354, + 332 + ], + "lines": [ + { + "bbox": [ + 333, + 324, + 354, + 332 + ], + "spans": [ + { + "bbox": [ + 333, + 324, + 354, + 332 + ], + "type": "inline_equation", + "content": "t = 0" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 381, + 264, + 428, + 321 + ], + "blocks": [ + { + "bbox": [ + 381, + 264, + 428, + 321 + ], + "lines": [ + { + "bbox": [ + 381, + 264, + 428, + 321 + ], + "spans": [ + { + "bbox": [ + 381, + 264, + 428, + 321 + ], + "type": "image", + "image_path": "53b0650c244c28dfec3bb61f36829b0d0b05ae02b12665db35da6d88bf4373fe.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 393, + 324, + 414, + 332 + ], + "lines": [ + { + "bbox": [ + 393, + 324, + 414, + 332 + ], + "spans": [ + { + "bbox": [ + 393, + 324, + 414, + 332 + ], + "type": "inline_equation", + "content": "t = 1" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 437, + 262, + 505, + 321 + ], + "blocks": [ + { + "bbox": [ + 437, + 262, + 505, + 321 + ], + "lines": [ + { + "bbox": [ + 437, + 262, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 437, + 262, + 505, + 321 + ], + "type": "image", + "image_path": "2243ea2d0b580b4866865ad361f81750e3dc49c46829e9367f2702740c808cc6.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 324, + 483, + 332 + ], + "lines": [ + { + "bbox": [ + 460, + 324, + 483, + 332 + ], + "spans": [ + { + "bbox": [ + 460, + 324, + 483, + 332 + ], + "type": "inline_equation", + "content": "t = 2" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 324, + 341, + 393, + 401 + ], + "blocks": [ + { + "bbox": [ + 324, + 341, + 393, + 401 + ], + "lines": [ + { + "bbox": [ + 324, + 341, + 393, + 401 + ], + "spans": [ + { + "bbox": [ + 324, + 341, + 393, + 401 + ], + "type": "image", + "image_path": "af5a9859a8d6bfe2519f5304edb9d69ce0dede25a2ccee65dff034ec4fd8bc9d.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 348, + 406, + 369, + 415 + ], + "lines": [ + { + "bbox": [ + 348, + 406, + 369, + 415 + ], + "spans": [ + { + "bbox": [ + 348, + 406, + 369, + 415 + ], + "type": "inline_equation", + "content": "t = 3" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 420, + 341, + 502, + 405 + ], + "blocks": [ + { + "bbox": [ + 420, + 341, + 502, + 405 + ], + "lines": [ + { + "bbox": [ + 420, + 341, + 502, + 405 + ], + "spans": [ + { + "bbox": [ + 420, + 341, + 502, + 405 + ], + "type": "image", + "image_path": "0db275be78bb69072dbb509103945ff4f2626fa62702882a75254c49bec4dece.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 442, + 406, + 487, + 415 + ], + "lines": [ + { + "bbox": [ + 442, + 406, + 487, + 415 + ], + "spans": [ + { + "bbox": [ + 442, + 406, + 487, + 415 + ], + "type": "text", + "content": "Final Result" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 419, + 530, + 452 + ], + "lines": [ + { + "bbox": [ + 296, + 419, + 530, + 452 + ], + "spans": [ + { + "bbox": [ + 296, + 419, + 530, + 452 + ], + "type": "text", + "content": "Figure 1. Illustration of Our Generative Scene Synthesis. We incrementally reconstruct the scene geometry by inpainting RGBD views as the camera moves in the scene." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 460, + 531, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 460, + 531, + 636 + ], + "spans": [ + { + "bbox": [ + 296, + 460, + 531, + 636 + ], + "type": "text", + "content": "potential in this regard, yet they are not exempt from limitations. NeRFs are designed to reconstruct complete scenes by fitting multi-view images, and they cannot generate or infer missing parts when the input is inevitably incomplete or missing. While recently some studies [3,5,8,56,63] have attempted to equip NeRFs with generative and extrapolation capabilities, this functionality relies on a comparatively short representation with limited elements (e.g. typically, the length of a global latent code is much shorter than that of an image: " + }, + { + "bbox": [ + 296, + 460, + 531, + 636 + ], + "type": "inline_equation", + "content": "(F = 512) \\ll (H \\times W = 128 \\times 128 = 16,384)" + }, + { + "bbox": [ + 296, + 460, + 531, + 636 + ], + "type": "text", + "content": ") that significantly constrains their capacity to accurately capture fine-grained details in the observed data. Consequently, the effectiveness of these methods has only been established for certain categories of canonical objects, such as faces or cars [8, 63], or relatively small toy scenes [5]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "We introduce a novel task of generative scene synthesis from sparse RGBD views, which involves learning across multiple scenes to later enable scene synthesis from a sparse set of multi-view RGBD images. This task presents a challenging setting wherein a desired solution should simultaneously (1) preserve observed regions, hallucinate missing parts of the scene, (2) eliminate additional computational costs during inference for each individual test scene, (3) en" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 73 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 73 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 73 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 719, + 227, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 719, + 227, + 730 + ], + "spans": [ + { + "bbox": [ + 59, + 719, + 227, + 730 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 59, + 719, + 227, + 730 + ], + "type": "text", + "content": " Correspondence to Kui Jia: ." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8422" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "type": "text", + "content": "sure exact 3D consistency, and (4) maintain scalability to scenes with unfixed scales." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 133, + 281, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 133, + 281, + 480 + ], + "spans": [ + { + "bbox": [ + 45, + 133, + 281, + 480 + ], + "type": "text", + "content": "We will elaborate on them in detail as follows. Firstly, to maximize the preservation of intricate details while simultaneously hallucinating potentially absent parts that may become more pronounced when views are exceedingly sparse, we perform straightforward reconstruction whose details come from images that can describe fine structures using a maximum of " + }, + { + "bbox": [ + 45, + 133, + 281, + 480 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 45, + 133, + 281, + 480 + ], + "type": "text", + "content": " elements (i.e. an image size) in a view completion manner. This is particularly compatible with diffusion models that operate at full image resolution with an inpainting mechanism. We also found that RGBD diffusion models greatly simplify the training complexity of a completion model, thanks to their versatile generative ability to inpaint missing RGBD pixels while preserving the integrity of known regions through a convenient training process solely operated on complete RGBD data. Secondly, our method employs back-projection that requires no optimization, thus eliminating the necessity for test-time training for each individual scene, ultimately leading to a significant enhancement in test-time efficiency. Thirdly, to ensure consistency among multi-view images, an intermediate mesh representation is utilized as a means of bridging the 2D domain (i.e. multi-view RGBD images) with the 3D domain (i.e. the 3D intermediate mesh) through the aid of camera projection. Fourthly, to enable our method to handle scenes of indeterminate sizes, we utilize images with freely designated poses as the input representation. Such manner naturally ensures SE(3) equivariance, and thus offers scalability due to the ease with which the range of the generated content can be controlled by simply specifying their camera extrinsic matrices." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 485, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 485, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 485, + 281, + 730 + ], + "type": "text", + "content": "Our proposal involves generating multi-view consistent RGBD views along a predetermined camera trajectory, using an intermediate mesh to render novel RGBD images that are subsequently inpainted using a diffusion model, and transforming each RGBD view into a 3D partial mesh via back-projection, and finally merging it with the intermediate scene mesh to produce the final output. Specifically, our proposed approach initiates by ingesting multiple posed RGBD images as input and utilizing back-projection to construct an intermediate scene mesh. This mesh encompasses color attributes that facilitate the rendering of RGBD images from the representation under arbitrarily specified camera viewpoints. Once a camera pose is selected from the test-time rendering trajectory, the intermediate mesh is rendered to generate a new RGBD image for this pose. Notably, the test-time view typically exhibits only slight overlap with the known cameras, leading to naturally partially rendered RGBD images. To fill the gaps in the incomplete view, we employ an inpainting network implemented as an RGBD diffusion model with minor modifications to its reverse sampling process. The resulting inpainted out" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": "put is then back-projected into 3D space, forming a partial mesh that complements the entire intermediate scene mesh. We iterate these steps until all test-time camera viewpoints are covered, and the intermediate scene mesh gradually becomes complete during this process. The final output of our pipeline is the mesh outcome acquired from the last step." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 176, + 530, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 176, + 530, + 212 + ], + "spans": [ + { + "bbox": [ + 296, + 176, + 530, + 212 + ], + "type": "text", + "content": "Extensive experiments on ScanNet [12] dataset demonstrate the superiority of our approach over existing solutions on the task of scene synthesis from sparse RGBD inputs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 214, + 387, + 226 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 214, + 387, + 226 + ], + "spans": [ + { + "bbox": [ + 296, + 214, + 387, + 226 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 229, + 530, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 229, + 530, + 264 + ], + "spans": [ + { + "bbox": [ + 296, + 229, + 530, + 264 + ], + "type": "text", + "content": "In this section, we provide a brief review of the literature related to diffusion models, 3D representations and generative manners, scene synthesis, and view synthesis." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 265, + 531, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 265, + 531, + 473 + ], + "spans": [ + { + "bbox": [ + 296, + 265, + 531, + 473 + ], + "type": "text", + "content": "Diffusion Models. In recent years, the field of 2D computer vision has experienced a surge of interest in diffusion-based generative models [20,65,67]. These models have prompted the development of image generative modeling approaches, such as GLIDE [45], unCLIP [53], Imagen [61], and Latent Diffusion Models [57], as well as the invention of sampling schedulers [20, 26, 36, 66] and guiding methods [15, 22]. Furthermore, these models have been applied to a broad range of image processing tasks, including image inpainting [37], image translation [4, 57, 60, 82], video generation [23, 25, 76], super-resolution [21, 32, 62], and image editing [2, 27, 40]. More recently, some researchers have adapted these techniques from 2D to the 3D domain, as demonstrated by methods such as [39, 51, 88, 92]. Our approach harnesses such versatility by adopting an iterative denoising strategy like [37], and utilizing a masked inpainting technique that operates on the projected RGBD views to synthesize image content." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "text", + "content": "3D Representations and Generative Manners. A variety of representations, including voxels [81, 85], point clouds [1, 39, 68, 87, 92], meshes [17, 44, 70, 71, 79], implicit surfaces [10, 30, 31, 41, 48, 72-74, 88, 91], multi-view images [11, 19, 34, 35, 86], and neural radiance fields [3, 8, 9, 13, 42, 43, 49, 56, 63, 80], have been proposed, each with its own unique advantages over the others. This has also motivated researchers to combine them with distinct generative approaches, such as VAEs [28], GANs [16], normalizing flows [54], auto-regressive models [24, 75], and the latest diffusion models [20], resulting in an extensive range of applications [1, 8, 39, 41, 44, 48, 63, 85, 87, 92]. However, most existing methods have limitations in their representation capability, such as cubically scaled-up memory consumption, or a fixed number of points, which makes them difficult to apply to scenes of uncertain scales, and poor equivariance, which only allows them to handle canonically-posed objects. In this paper, we address these issues by focusing on the generation of multi-view RGBD images that can capture intricate structures using " + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "text", + "content": " pixels created by a diffusion model. This approach reduces memory complexity from " + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(HWD)" + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(HW)" + }, + { + "bbox": [ + 296, + 474, + 531, + 730 + ], + "type": "text", + "content": " and increases expressive" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8423" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "text", + "content": "ability from " + }, + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(F)" + }, + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(HW)" + }, + { + "bbox": [ + 45, + 106, + 170, + 117 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 117, + 279, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 117, + 279, + 268 + ], + "spans": [ + { + "bbox": [ + 45, + 117, + 279, + 268 + ], + "type": "text", + "content": "Scene Synthesis. In this area, there are two primary research directions. The first pertains to learning configurations, including graphs [33, 38, 77, 90], top-down views [55, 78], and scene composition [50, 83]. The second line of research involves direct learning from the appearance of a scene [13, 42, 43, 49, 80], thereby obviating the necessity for specialized synthesized datasets required by the aforementioned methods. Our approach relies solely on RGBD scans, which are readily available from scanning devices, reducing the need for manual annotation. It accurately reconstructs a clean geometry based on the sparse-view input and can effectively hallucinate missing parts, especially when the input views are highly sparse." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 269, + 279, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 269, + 279, + 374 + ], + "spans": [ + { + "bbox": [ + 45, + 269, + 279, + 374 + ], + "type": "text", + "content": "View Synthesis. The arrival of NeRF [42] has significantly advanced the field of view synthesis. While a considerable amount of research has been dedicated to the view synthesis of object-level instances [7, 18, 47, 64], only a few studies have focused on simple scenes [5, 14, 58]. Additionally, some studies have explored techniques for improving performance using sparse inputs [46, 56]. In this paper, we aim to recover scene-level geometry from sparse RGBD images without relying on NeRFs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 378, + 120, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 120, + 390 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 120, + 390 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 394, + 279, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 394, + 279, + 418 + ], + "spans": [ + { + "bbox": [ + 45, + 394, + 279, + 418 + ], + "type": "text", + "content": "To make our paper self-contained, we provide some preliminary knowledge about DDPM [20] and DDIM [66]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "spans": [ + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": "Definition. Given an image " + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0\\sim q(\\mathbf{x}_0)" + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": ", the forward diffusion process is a Markov chain that sequentially produces noisy images " + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1,\\dots ,\\mathbf{x}_T" + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": " scheduled by a set of constants " + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\in (0,1)\\}_{t = 1}^T" + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": " is the total number of iterations and " + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "inline_equation", + "content": "\\beta_{1} < \\beta_{2} < \\ldots < \\beta_{T}" + }, + { + "bbox": [ + 45, + 418, + 279, + 476 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 78, + 477, + 245, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 477, + 245, + 491 + ], + "spans": [ + { + "bbox": [ + 78, + 477, + 245, + 491 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right)", + "image_path": "523ab63c0532f1466abd81b5dd5d495ecc4acf3461e7e296a81727c7f3136151.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "text", + "content": "A nice property of using i.i.d. Gaussian distribution is that we can sample the noisy image " + }, + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "text", + "content": " easily based on " + }, + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 45, + 498, + 279, + 533 + ], + "type": "text", + "content": " in a closed form without computing all the intermediates:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 539, + 279, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 539, + 279, + 554 + ], + "spans": [ + { + "bbox": [ + 83, + 539, + 279, + 554 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha}} _ {t} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right) \\tag {1}", + "image_path": "f20500b796f3aae50d7bee9f441d064a9a982237ccaeb14a37cd156668920822.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "spans": [ + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{s = 1}^{t}\\alpha_{s}" + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "content": ". The reverse diffusion process is another Markov chain starting from " + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "content": " parameterized by a trainable " + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 559, + 279, + 596 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 602, + 279, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 602, + 279, + 615 + ], + "spans": [ + { + "bbox": [ + 68, + 602, + 279, + 615 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right) \\tag {2}", + "image_path": "1c1d95805026c09007ae9c4024361abc612bfcef5c6293405042dc7aaef927f3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "spans": [ + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_{\\theta}(\\mathbf{x}_t,t) = \\sigma_t^2\\mathbf{I} = \\eta \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t\\mathbf{I}" + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": " [66] is independent of " + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": " can be derived from a noise estimator " + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 45, + 621, + 279, + 657 + ], + "type": "text", + "content": " via:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 664, + 253, + 691 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 664, + 253, + 691 + ], + "spans": [ + { + "bbox": [ + 69, + 664, + 253, + 691 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} (\\mathbf {x} _ {t}, \\mathbf {x} _ {o}) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right)", + "image_path": "715de9dda9c9e4b37738eccef9ed900786a25c86a8e18b0ca124b52c7cf43a32.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "spans": [ + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "text", + "content": "We practically implement the noise estimator " + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "text", + "content": " as a UNet [57, 59] parameterized by " + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "text", + "content": ". However, in our case, it is also conditioned on " + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_0" + }, + { + "bbox": [ + 45, + 696, + 279, + 731 + ], + "type": "text", + "content": " which will be detailed in Sec. 4.2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": "Training. To train the noise estimator " + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": " , we adopt the simplified training objective [20]:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 138, + 512, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 138, + 512, + 156 + ], + "spans": [ + { + "bbox": [ + 314, + 138, + 512, + 156 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {t, \\epsilon_ {t}, \\mathbf {x} _ {0}} \\left[ \\| \\epsilon_ {\\theta} (\\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {t}, t) - \\epsilon_ {t} \\| ^ {2} \\right]", + "image_path": "520aff74e1228740b0e3fe489041d11bfb23194ba6f7cd402d456bce09e180b0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "spans": [ + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "text", + "content": "where the time step " + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "inline_equation", + "content": "t\\sim \\mathcal{U}\\{1,T\\}" + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "text", + "content": " is uniformly sampled, " + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "text", + "content": " is a standard Gaussian noise, and the image " + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0\\sim q(\\mathbf{x}_0)" + }, + { + "bbox": [ + 296, + 165, + 530, + 201 + ], + "type": "text", + "content": " is randomly drawn from the data distribution." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "spans": [ + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "content": "Inference. We employ a strided DDIM [66] scheduler to progressively recover the clean image from " + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "content": " with a subset of " + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "content": " (usually " + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "inline_equation", + "content": "S\\ll T" + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "text", + "content": ") steps " + }, + { + "bbox": [ + 296, + 209, + 530, + 246 + ], + "type": "inline_equation", + "content": "\\{\\tau_i\\}_{i = 1}^S" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 311, + 262, + 515, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 262, + 515, + 311 + ], + "spans": [ + { + "bbox": [ + 311, + 262, + 515, + 311 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {\\tau_ {i - 1}} \\leftarrow \\sqrt {\\bar {\\alpha} _ {\\tau_ {i - 1}}} \\left(\\frac {\\mathbf {x} _ {\\tau_ {i}} - \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}} , \\tau_ {i})}{\\sqrt {\\bar {\\alpha} _ {\\tau_ {i}}}}\\right) + \\\\ \\sqrt {1 - \\bar {\\alpha} _ {\\tau_ {i - 1}} - \\sigma_ {\\tau_ {i}} ^ {2}} \\cdot \\epsilon_ {\\theta} (\\mathbf {x} _ {\\tau_ {i}}, \\tau_ {i}) + \\sigma_ {\\tau_ {i}} ^ {2} \\epsilon_ {\\tau_ {i}} \\\\ \\end{array}", + "image_path": "05808e57f77b684f662edbff7f38541378010ec74a48f68ebd998b75271305f6.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "spans": [ + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\tau_i} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": " is a standard Gaussian noise. It is interesting that setting " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\eta = 0" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": " implies " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\forall i" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\sigma_{\\tau_i} \\equiv 0" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": ", making the inference process deterministic. Nevertheless, diversity can still be achieved by choosing a different " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 296, + 319, + 530, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 297, + 368, + 361, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 368, + 361, + 383 + ], + "spans": [ + { + "bbox": [ + 297, + 368, + 361, + 383 + ], + "type": "text", + "content": "4. Approach" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 386, + 530, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 386, + 530, + 525 + ], + "spans": [ + { + "bbox": [ + 296, + 386, + 530, + 525 + ], + "type": "text", + "content": "In this work, we introduce a new scene synthesis approach that relies on the sequential generation of RGBD frames using a trained RGBD diffusion model conditioned on views rendered under a test-time camera trajectory from a sparse set of input RGBD images. Our approach leverages the generative ability of diffusion models to synthesize missing visual appearance (color) and geometry details (depth) while rigorously preserving visible regions by image inpainting. Such an incremental view inpainting process is interleaved with the back-projection, mesh fusion, and mesh rendering procedures to achieve global 3D consistency among distinct temporal frames." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 525, + 530, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 525, + 530, + 607 + ], + "spans": [ + { + "bbox": [ + 296, + 525, + 530, + 607 + ], + "type": "text", + "content": "This section is organized as follow. In Sec. 4.1, we will start by introducing the overall framework of repeatedly converting the RGBD image into a partial 3D mesh and performing RGBD inpainting for rendered views in a progressive manner. Later in Sec. 4.2, we will elaborate more on the details of the conditional RGBD diffusion model for rendered view inpainting based on a trained DDPM [20]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 609, + 489, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 609, + 489, + 622 + ], + "spans": [ + { + "bbox": [ + 296, + 609, + 489, + 622 + ], + "type": "text", + "content": "4.1. Incremental View Inpainting Fashion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "As shown in Figure 2, given a sparse set of " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " RGBD views " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " with their associated camera intrinsic " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " and extrinsic " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " matrices, and additionally a camera trajectory composed of " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " viewpoints " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{T}_j\\}_{j=1}^M" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " with the same intrinsic matrix, the essence of our method is to progressively synthesize RGBD images " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_j" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " at each specified novel view " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": ". The generated novel-view frames should be consistent with " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " in both geometry and appearance. The final output should be a consistent 3D" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8424" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 106, + 530, + 301 + ], + "blocks": [ + { + "bbox": [ + 51, + 106, + 530, + 301 + ], + "lines": [ + { + "bbox": [ + 51, + 106, + 530, + 301 + ], + "spans": [ + { + "bbox": [ + 51, + 106, + 530, + 301 + ], + "type": "image", + "image_path": "af0fdedf317ec3fac38e7e2af6ab146b2bfc5c1b75537a7c20b1b1a72e6886e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "lines": [ + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "spans": [ + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": "Figure 2. 3D Scene Synthesis via Incremental View Inpainting. Given a sparse set of RGBD images " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " with camera intrinsic " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " and extrinsic " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " matrices, our goal is to generate a coherent 3D scene mesh " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " via predicting RGBD frames " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{O}_j\\}_{j=1}^M" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " along a novel-view trajectory " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{T}_j\\}_{j=1}^M" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": ". To achieve this goal, we firstly fuse the inputs of " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " into an initial mesh " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_1" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": ", and then render it to obtain an incomplete image " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_1" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " that is later inpainted to obtain " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_1" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " using a RGBD diffusion model. After that, " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_1" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " is back-projected and integrated with " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_1" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " to produce a more complete scene, " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_2" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": ". By iteratively repeating this process, we can progressively obtain " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_2, \\dots, \\mathcal{S}_M" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": ". Finally, the fused result " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{M+1}" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": " is the eventual desired output " + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 45, + 311, + 531, + 378 + ], + "type": "text", + "content": ". Gray dashed lines “- - ” denote omitted and unvisualized steps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "spans": [ + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "text", + "content": "colored mesh " + }, + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "text", + "content": " converted from the back-projection result " + }, + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "inline_equation", + "content": "\\left( \\cup_{j=1}^{M} \\phi_{2 \\to 3}(\\mathbf{O}_j) \\right) \\cup \\left( \\cup_{i=1}^{N} \\phi_{2 \\to 3}(\\mathbf{I}_i) \\right)" + }, + { + "bbox": [ + 45, + 384, + 280, + 420 + ], + "type": "text", + "content": ". Please also refer to Algorithm 1 for a detailed description of the procedure." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 426, + 242, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 426, + 242, + 438 + ], + "spans": [ + { + "bbox": [ + 48, + 426, + 242, + 438 + ], + "type": "text", + "content": "Algorithm 1 Incremental RGBD View Inpainting" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "spans": [ + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "text", + "content": "Require: RGBD images " + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "text", + "content": " with camera extrinsics " + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "text", + "content": ", a novel trajectory of M extrinsics " + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{T}_j\\}_{j=1}^M" + }, + { + "bbox": [ + 48, + 442, + 279, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 467, + 139, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 467, + 139, + 479 + ], + "spans": [ + { + "bbox": [ + 57, + 467, + 139, + 479 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {1} \\leftarrow \\cup_ {i = 1} ^ {N} \\phi_ {2 \\rightarrow 3} (\\mathbf {I} _ {i})", + "image_path": "7a1eb7c1ebf3e88882331d54b3bb7f961220a8dd8a21ddf82960a2e191bd0aa6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 479, + 131, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ 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"index": 7 + }, + { + "bbox": [ + 186, + 491, + 279, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 491, + 279, + 501 + ], + "spans": [ + { + "bbox": [ + 186, + 491, + 279, + 501 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 186, + 491, + 279, + 501 + ], + "type": "text", + "content": " novel-view rendering" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 71, + 503, + 125, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 503, + 125, + 515 + ], + "spans": [ + { + "bbox": [ + 71, + 503, + 125, + 515 + ], + "type": "interline_equation", + "content": "\\mathbf {O} _ {j} \\leftarrow f (\\hat {\\mathbf {O}} _ {j})", + "image_path": "86439a89201d4631cfde99f6d7422a42080a8c24a6117f0e207c55ac65a823b5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 201, + 504, + 279, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 201, + 504, + 279, + 514 + ], + "spans": [ + { + "bbox": [ + 201, + 504, + 279, + 514 + ], + "type": "text", + "content": "RGBD inpainting" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 71, + 516, + 169, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 516, + 169, + 527 + ], + "spans": [ + { + "bbox": [ + 71, + 516, + 169, + 527 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {j + 1} \\leftarrow \\mathcal {S} _ {j} \\cup \\phi_ {2 \\rightarrow 3} (\\mathbf {O} _ {j})", + "image_path": "0b410640af9836f8f947c25f198ba22f8d53b7fed6fb29017025035ff33e1fb9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 222, + 516, + 278, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 222, + 516, + 278, + 526 + ], + "spans": [ + { + "bbox": [ + 222, + 516, + 278, + 526 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 222, + 516, + 278, + 526 + ], + "type": "text", + "content": " mesh fusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 57, + 528, + 88, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 528, + 88, + 537 + ], + "spans": [ + { + "bbox": [ + 57, + 528, + 88, + 537 + ], + "type": "text", + "content": "end for" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 57, + 539, + 111, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 539, + 111, + 550 + ], + "spans": [ + { + "bbox": [ + 57, + 539, + 111, + 550 + ], + "type": "text", + "content": "return " + }, + { + "bbox": [ + 57, + 539, + 111, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{M + 1}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "spans": [ + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": "Rendering and Back-projection. The operator " + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "inline_equation", + "content": "\\phi_{3\\rightarrow 2}" + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": " is implemented as mesh rasterization, which allows for the rendering of a partial RGBD image " + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": " from a mesh " + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": ". This approach offers the advantage of producing a clean visibility mask " + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_j" + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": ", which is not possible with NeRFs [42]. The back-projection operator " + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "inline_equation", + "content": "\\phi_{2\\rightarrow 3}" + }, + { + "bbox": [ + 45, + 561, + 279, + 689 + ], + "type": "text", + "content": " is responsible for the conversion from a depth map into a point cloud, where the connectivity between points is inherited from the connectivity of the 2D pixel grid. Furthermore, mesh faces that are either in close proximity to the viewpoint or exhibit slender characteristics are filtered out to ensure accuracy." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 45, + 690, + 279, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 690, + 279, + 701 + ], + "spans": [ + { + "bbox": [ + 45, + 690, + 279, + 701 + ], + "type": "text", + "content": "Challenges and Solutions. To circumvent the limitations" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "spans": [ + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": "posed by potential 3D inconsistency in both geometry and appearance, as well as the challenge of solely handling specific canonically-posed scenes, we propose several strategies to address these issues. Firstly, our method for synthesizing novel views combines rendering (mesh rasterization) and inpainting techniques, and interleaves the view synthesis process with online RGBD fusion via back-projection and mesh combination. The use of perspective camera projection ensures strict adherence to 3D constraints, resulting in visually consistent and accurate synthesized views. In concrete terms, we begin by rendering the mesh " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " under view " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{j}" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " using a rendering operation " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\phi_{3\\rightarrow 2}(\\mathbf{T}_{j})" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": ". This process yields an incomplete RGBD image " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " with missing regions, which is subsequently inpainted using a diffusion model described in detail in Sec. 4.2, resulting in a complete image " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_j" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": ". Once image " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_j" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " has been generated for view " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": ", it can be fused into a 3D mesh via " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "S_{j + 1} = \\phi_{2\\rightarrow 3}(\\mathbf{O}_j)\\cup S_j" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " using a back-projection operator " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\phi_{2\\rightarrow 3}" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": ". Secondly, our solution reduces the learning difficulty and can handle noncanonical scenes by decomposing the 3D scene as a Markov chain of temporal RGBD images rendered from arbitrarily specified novel viewpoints. The applicability of handling scenes with arbitrary scaling, movement, and posing is attributed to the utilization of two SE(3) equivariant operators, namely " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\phi_{3\\rightarrow 2}" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "inline_equation", + "content": "\\phi_{2\\rightarrow 3}" + }, + { + "bbox": [ + 297, + 384, + 530, + 724 + ], + "type": "text", + "content": ", as well as the independence of absolute coordinates. Moreover, the presence of redundant information in adjacent frames, combined with our suggested decomposition rule, facilitates the minimization of learning complexity in an auto-regressive manner." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "text", + "content": "1 To simplify notations, we disregard certain arguments in operators " + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\phi_{3\\to 2}" + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\phi_{2\\to 3}" + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "text", + "content": ", such as the camera intrinsic matrix " + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8425" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 280, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 280, + 141 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 280, + 141 + ], + "type": "text", + "content": "In accordance with the Markov chain decomposition principle, the distribution of the scene can be expressed as the joint distribution of view frames:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 147, + 242, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 147, + 242, + 172 + ], + "spans": [ + { + "bbox": [ + 83, + 147, + 242, + 172 + ], + "type": "interline_equation", + "content": "p (\\mathcal {S}) = \\prod_ {j} p (\\mathbf {O} _ {j} \\mid \\{\\mathbf {O} _ {s} \\} _ {s = 1} ^ {j - 1}, \\{\\mathbf {I} _ {s} \\} _ {s = 1} ^ {N})", + "image_path": "26683a6128c29e9f4e594ab3ccf9615484cdd57c1182423557e1d947b9dea414.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "spans": [ + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "text", + "content": "where the prediction of " + }, + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_j" + }, + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "text", + "content": " is based on the fusion result of all the previously known frames " + }, + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{O}_s\\}_{s=1}^{j-1} \\cup \\{\\mathbf{I}_s\\}_{s=1}^N" + }, + { + "bbox": [ + 45, + 173, + 280, + 199 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 203, + 279, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 203, + 279, + 217 + ], + "spans": [ + { + "bbox": [ + 45, + 203, + 279, + 217 + ], + "type": "text", + "content": "4.2. RGBD Diffusion for Rendered View Inpainting" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "spans": [ + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": "In this section, we describe the implementation details of the way to employ diffusion models to inpaint the missing regions of the RGBD image " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": " with a binary mask " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_j" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": " obtained by rendering visibility, where the value of 1 is assigned to the corresponding ray that intersects with the geometry surface, while 0 is assigned to all other cases, both of which are rendered by projecting " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": " under a novel viewpoint " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": ". It is noteworthy that only those pixels located where " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_j = 0" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": " are considered invalid, and therefore, are entirely filled with zeros (i.e., " + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j\\odot \\mathbf{m}_j\\equiv \\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 45, + 221, + 279, + 341 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 48, + 347, + 278, + 457 + ], + "blocks": [ + { + "bbox": [ + 48, + 347, + 278, + 457 + ], + "lines": [ + { + "bbox": [ + 48, + 347, + 278, + 457 + ], + "spans": [ + { + "bbox": [ + 48, + 347, + 278, + 457 + ], + "type": "image", + "image_path": "6906c4f13e23c97d09c549e269e678c9755500f0cd73c536b2bbdb1580ea17f9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "lines": [ + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "spans": [ + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": "Figure 3. RGBD Diffusion for Rendered View Inpainting. In each iteration, we utilize a forward diffusion step to sample the visible region " + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{vis}}" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": " (top) from the incomplete input " + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_0" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": ", while employing a denoising diffusion step to obtain the complementary content " + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{invis}}" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": " (bottom) from the output " + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t + 1}" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": " generated in the previous iteration " + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 45, + 465, + 279, + 530 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "spans": [ + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": "A Single Reverse Diffusion Step for " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " at Time " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": ".2 We initialize the clean diffusion sample " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_0" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{O}}_j" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": ", and those noisy samples at time " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "0 < t \\leq T" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " are denoted as " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": ". To ensure 3D consistency, we seek to predict the invisible region " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{vis}}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " while preserving the visible portion " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{vis}}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " unaltered. We follow [37] and modify the standard denoising process to meet our needs. At each reverse diffusion step " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": ", we use the forward diffusion process defined by the Eqn. (1) to sample a visible region " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{vis}}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " masked by " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": ", and the reverse diffusion step defined by Eqn. (2) to sample a full part from " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t+1}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " which is later masked by " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "1 - \\mathbf{m}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": " to form an invisible region " + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{vis}}" + }, + { + "bbox": [ + 45, + 534, + 279, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 682, + 232, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 682, + 232, + 696 + ], + "spans": [ + { + "bbox": [ + 93, + 682, + 232, + 696 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} ^ {\\text {v i s}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} + (1 - \\bar {\\alpha} _ {t}) \\epsilon_ {t} ^ {\\text {v i s}} \\odot \\mathbf {m}", + "image_path": "29d8ecc65595c8f8353b65231f10e48a7482751b0aa65f9765e083d1b6fce8ed.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 324, + 103, + 502, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 103, + 502, + 118 + ], + "spans": [ + { + "bbox": [ + 324, + 103, + 502, + 118 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} ^ {\\text {i n v i s}} = \\left(\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {t}, t\\right) + \\sigma_ {t} \\epsilon_ {t} ^ {\\text {i n v i s}}\\right) \\odot (1 - \\mathbf {m})", + "image_path": "ba46c768b72d1cbe9aed3ba44e83e4e1a16ffe611677a56d922271a2082f78c7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "spans": [ + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "inline_equation", + "content": "\\epsilon_t^{\\mathrm{vis}},\\epsilon_t^{\\mathrm{invis}}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "content": " . The noisy image " + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "content": " can be simply calculated as the sum of " + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{vis}}" + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{invis}}" + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "text", + "content": " , as expressed by " + }, + { + "bbox": [ + 296, + 122, + 530, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t = \\mathbf{x}_t^{\\mathrm{vis}} + \\mathbf{x}_t^{\\mathrm{invis}}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "spans": [ + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "text", + "content": "Diffusion Network. We implement the diffusion model as a UNet [57, 59] conditioned on the observed region " + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "text", + "content": ". We input the concatenation of " + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_0" + }, + { + "bbox": [ + 296, + 163, + 530, + 197 + ], + "type": "text", + "content": " into the network." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "spans": [ + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": "Classifier-free Guidance. To further enhance the controllability of the generation process, we introduce a classifier-free guidance [22] mechanism. Specifically, we train a unified network " + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": " comprising of an unconditional model " + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,\\mathbf{c},t)" + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": ", where the shared variable " + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": " is incorporated, and a conditional model " + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,\\hat{\\mathbf{x}}_0,t)" + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": ". In this way, the predicted noise " + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\theta}" + }, + { + "bbox": [ + 296, + 200, + 531, + 282 + ], + "type": "text", + "content": " can be recomputed as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 291, + 530, + 305 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 291, + 530, + 305 + ], + "spans": [ + { + "bbox": [ + 296, + 291, + 530, + 305 + ], + "type": "interline_equation", + "content": "\\tilde {\\epsilon} _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) = \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) + \\beta \\times [ \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\hat {\\mathbf {x}} _ {0}, t) - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {t}, \\mathbf {c}, t) ]", + "image_path": "c7dc537cdcc061f59afd74d4d28c4b2121d2f3d23f9dbff1c8d15c844a65fef5.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 313, + 530, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 313, + 530, + 338 + ], + "spans": [ + { + "bbox": [ + 296, + 313, + 530, + 338 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 313, + 530, + 338 + ], + "type": "inline_equation", + "content": "\\beta \\geq 0" + }, + { + "bbox": [ + 296, + 313, + 530, + 338 + ], + "type": "text", + "content": " is the guidance factor, being responsible for the trade-off between sampling quality and diversity [22]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 342, + 376, + 356 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 342, + 376, + 356 + ], + "spans": [ + { + "bbox": [ + 297, + 342, + 376, + 356 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 357, + 530, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 357, + 530, + 449 + ], + "spans": [ + { + "bbox": [ + 296, + 357, + 530, + 449 + ], + "type": "text", + "content": "Dataset. We conducted experiments on the ScanNetV2 [12] dataset, which was pre-processed by removing redundant frames [69]. For training, we used the first 1,293 scenes, while for metric evaluation, we randomly selected 18 scenes with over 50 views each from the remaining as our test set. We also evaluated under various sparsity settings (5%, 10%, 20%, and 50%) by uniformly down-sampling views." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 450, + 530, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 450, + 530, + 565 + ], + "spans": [ + { + "bbox": [ + 296, + 450, + 530, + 565 + ], + "type": "text", + "content": "Comparison. We compared against the neural graphics primitive (NGP) [43], which has demonstrated impressive performance in scene modeling with high efficiency. To enhance its geometric quality, we incorporated a depth supervision (DS) loss [13] to build an improved variant called DS-NGP [13, 43]. We also compare against Neural RGBD (N-RGBD) [3], which recovers implicit surfaces from RGBD scans, and Dense Depth Prior (DDP) [56], which learns a NeRF utilizing view completion from sparse RGBD views." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "text", + "content": "Evaluation Metrics. For assessing the visual quality of RGB images, we adopted the peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [89] that is based on the AlexNet [29] backbone. To evaluate the geometry quality, we computed the mean squared error (MSE) on depth maps, and sample 10,000 points uniformly on meshes constructed via back-projection to evaluate the chamfer distance (CD) and completeness (Comp.) with a threshold of " + }, + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{m}" + }, + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "text", + "content": ". We also measured the computational time required to execute different stages of the method. For LPIPS, MSE, and CD, the lower the better; for PSNR, SSIM, and Comp., the higher the better. All reported metrics are averaged across the test scenes." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "text", + "content": "2 For notational simplicity, we ignore the novel camera subscript " + }, + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "text", + "content": " in the following part of this Sec. 4.2 since all notations we consider here are derived from the same camera " + }, + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j" + }, + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8426" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "text", + "content": "Implementation Details. Our model has 157M parameters and was trained for three days on 7 NVIDIA 3090-Ti GPUs, using a batch size of 280. The learning rate was initialized at " + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "text", + "content": " and reduced to " + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "text", + "content": " over a period of 300 epochs, utilizing a cosine annealing strategy. The image resolution is " + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 45, + 106, + 279, + 176 + ], + "type": "text", + "content": " with a rendering chunk size of 7." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 182, + 143, + 193 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 182, + 143, + 193 + ], + "spans": [ + { + "bbox": [ + 45, + 182, + 143, + 193 + ], + "type": "text", + "content": "5.1. Ablation Studies" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 198, + 279, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 198, + 279, + 233 + ], + "spans": [ + { + "bbox": [ + 45, + 198, + 279, + 233 + ], + "type": "text", + "content": "We conducted ablation studies to validate the effectiveness of each component in our proposal. Results concluded here are nontrivial and a bit nuanced." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 234, + 279, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 234, + 279, + 362 + ], + "spans": [ + { + "bbox": [ + 45, + 234, + 279, + 362 + ], + "type": "text", + "content": "Effects of Different Ingredients. We examined the anticipated efficacy of the proposed conditioning and inpainting components in our approach. Table 2 displays the numerical results, and Figure 5-(a-c) presents the visualizations. The combined use of conditioning and inpainting yields superior visual performance compared to the ground truth. Nevertheless, when the model is conditioned, the impact of inpainting on geometric quality becomes less crucial. Moreover, as more views are provided, the stochastic generation process becomes increasingly deterministic, resulting in structures that more closely resemble the ground truth." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "spans": [ + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": "Effects of Guidance Scale. The guidance factor " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " significantly affects the conditioning effect on the results. To investigate the optimal " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " under various settings, we conducted experiments with " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " chosen from 0.0, 0.5, 1.0, 2.0, and 5.0, respectively, and evaluated their performance. Quantitative results are presented in Table 3. It is interesting that only a suitable value of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " (1.0 or 2.0) yields optimal performance, while smaller or larger values of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " result in underperformance. Surprisingly, for geometric recovery (MSE and CD), the optimal value of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " appears to increase as the percentage gets larger. For a scene with a percentage " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\geq 50\\%" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": ", the best value of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " is amazingly greater than 5.0. However, such a large percentage is not optimal for visual appearance. This is because using a larger value of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " at a low percentage can cause the generated results to deviate unexpectedly from the ground truth. Our visualization, presented in Figure 5-(a, c, d), indicates that using an unconditional model (" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": ") leads to undesired and bizarre geometric structures since the network fails to understand the context provided by known views. However, excessively large values of " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": " also oversaturate the color (e.g. row “(d)” at " + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 45, + 362, + 279, + 618 + ], + "type": "text", + "content": "), making the visual appearance unrealistic." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 618, + 279, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 618, + 279, + 630 + ], + "spans": [ + { + "bbox": [ + 45, + 618, + 279, + 630 + ], + "type": "text", + "content": "Effects of Randomness and Trajectories. We investigated" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 47, + 641, + 108, + 695 + ], + "blocks": [ + { + "bbox": [ + 47, + 641, + 108, + 695 + ], + "lines": [ + { + "bbox": [ + 47, + 641, + 108, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 108, + 695 + ], + "type": "image", + "image_path": "667411f8f3865b6c8e79adda100c3b6508f4409591d5fa6d5e6d301c7079e91f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 703, + 99, + 714 + ], + "lines": [ + { + "bbox": [ + 55, + 703, + 99, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 703, + 99, + 714 + ], + "type": "text", + "content": "(a) original" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 108, + 641, + 173, + 695 + ], + "blocks": [ + { + "bbox": [ + 108, + 641, + 173, + 695 + ], + "lines": [ + { + "bbox": [ + 108, + 641, + 173, + 695 + ], + "spans": [ + { + "bbox": [ + 108, + 641, + 173, + 695 + ], + "type": "image", + "image_path": "7702e27e95d9ba0b58d343044003fd82de25acb8fad3a9d4964eacad22452589.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 123, + 703, + 154, + 714 + ], + "lines": [ + { + "bbox": [ + 123, + 703, + 154, + 714 + ], + "spans": [ + { + "bbox": [ + 123, + 703, + 154, + 714 + ], + "type": "text", + "content": "(b) seed" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 174, + 641, + 279, + 703 + ], + "blocks": [ + { + "bbox": [ + 174, + 641, + 279, + 703 + ], + "lines": [ + { + "bbox": [ + 174, + 641, + 279, + 703 + ], + "spans": [ + { + "bbox": [ + 174, + 641, + 279, + 703 + ], + "type": "image", + "image_path": "2154a1da3631d63db816ecaeaf07bf4f163bbe22e7be25dca39303cfdc022432.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 199, + 704, + 250, + 714 + ], + "lines": [ + { + "bbox": [ + 199, + 704, + 250, + 714 + ], + "spans": [ + { + "bbox": [ + 199, + 704, + 250, + 714 + ], + "type": "text", + "content": "(c) trajectory" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 719, + 279, + 740 + ], + "lines": [ + { + "bbox": [ + 45, + 719, + 279, + 740 + ], + "spans": [ + { + "bbox": [ + 45, + 719, + 279, + 740 + ], + "type": "text", + "content": "Figure 4. Diverse results obtained by changing the (b) random seed and (c) camera trajectory based on (a) the original scene." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 106, + 530, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 222 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 222 + ], + "type": "text", + "content": "the impact of employing different random seeds and camera trajectories on the results. Such obtained meshes are visualized in Figure 4. As diffusion models inherently include randomness in their reverse sampling process, by switching to a different random seed, we can obtain another outcome. Moreover, the camera trajectory can affect the rough shape of the scene. It is promising that our approach can yield controllable and editable results, as it is capable of generating various and appealing outcomes by simply altering these two factors." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 226, + 443, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 226, + 443, + 239 + ], + "spans": [ + { + "bbox": [ + 297, + 226, + 443, + 239 + ], + "type": "text", + "content": "5.2. Generative Scene Synthesis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 241, + 530, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 241, + 530, + 323 + ], + "spans": [ + { + "bbox": [ + 296, + 241, + 530, + 323 + ], + "type": "text", + "content": "We evaluated the performance of our method against other similar approaches on this task through extensive experiments under various sparsity settings. Table 1 presents the time required by different methods across various stages. Our approach stands out for its efficiency, as it eliminates the need for additional optimization on individual test scenes during inference. Quantitative results are shown in" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 299, + 326, + 529, + 373 + ], + "blocks": [ + { + "bbox": [ + 299, + 326, + 529, + 373 + ], + "lines": [ + { + "bbox": [ + 299, + 326, + 529, + 373 + ], + "spans": [ + { + "bbox": [ + 299, + 326, + 529, + 373 + ], + "type": "table", + "html": "
TimeBackendRepre.TrainingOptimizationRendering
(DS-)NGP [13,43]CUDA C++NeRF—~ 3 min.~ 0.05 sec.
N-RGBD [3]PyTorchNeRF—~ 2 hours~ 2 sec.
DDP [56]PyTorchNeRF~ 1 day~ 1 hour~ 1 sec.
OursPyTorchMesh~ 3 days—~ 3 sec.
", + "image_path": "9de6690d162a6143c813316609d1cf96aa26da7b018ffc99b9c212b8e1f58d3e.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 374, + 530, + 428 + ], + "lines": [ + { + "bbox": [ + 296, + 374, + 530, + 428 + ], + "spans": [ + { + "bbox": [ + 296, + 374, + 530, + 428 + ], + "type": "text", + "content": "Table 1. Efficiency Comparison of Different Methods. It details their distinct implementation backends, the underlying representation (Repre.) methods, and the time required for training on multiple training scenes, optimization on a single test scene, and rendering a single view after per-scene optimization." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 431, + 530, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 431, + 530, + 606 + ], + "spans": [ + { + "bbox": [ + 296, + 431, + 530, + 606 + ], + "type": "text", + "content": "Table 4. We observe that our approach exhibits a clear advantage in visual metrics over the others when the provided views are extremely sparse (5%). Interestingly, our method consistently achieves the best performance in all the geometry-related metrics. Qualitative results are presented in Figure 6. DS-NGP [13, 43] and DDP [56] struggle to accurately recover geometry due to their inability to hallucinate and extrapolate missing regions. In comparison, N-RGBD [3] can achieve better surface completion results by learning and extrapolating neural implicit surfaces. However, their performance significantly degrades when input views are extraordinarily sparse (5%). In contrast, our method consistently exhibits plausible appearance that closely resembles the ground truth, particularly in scenarios with sparse-view inputs." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 297, + 611, + 369, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 611, + 369, + 622 + ], + "spans": [ + { + "bbox": [ + 297, + 611, + 369, + 622 + ], + "type": "text", + "content": "6. Discussions" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "Limitations. Our current implementation has several limitations that may impact its usefulness in some scenarios. Firstly, it is incapable of handling color discrepancies caused by lighting variations. Secondly, it lacks surface extrapolation capabilities that can be provided through implicit field representation. Lastly, the limited receptive field of our design is confined to the observable volume of the current camera view and may result in inconsistent and discontinuous predictions, particularly in the case of a large" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8427" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 104, + 304, + 163 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 304, + 163 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 304, + 163 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 304, + 163 + ], + "type": "table", + "html": "
FactorsVisual
PSNRcolorSSIMcolorLPIPScolor
Cond.Inpa.5%10%20%50%5%10%20%50%5%10%20%
9.339.309.279.450.3310.3300.3300.3330.6370.6360.637
✓12.414.716.517.90.4110.4960.5570.5830.5200.4460.393
✓12.513.614.716.10.4440.4730.5130.5560.4490.4090.362
✓✓14.616.017.418.40.5220.5550.5930.6030.4480.3990.359
", + "image_path": "46f79f39df215acde508ada52afddb44f33a572f7c9961c4f8181f543552cea9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 45, + 165, + 531, + 207 + ], + "lines": [ + { + "bbox": [ + 45, + 165, + 531, + 207 + ], + "spans": [ + { + "bbox": [ + 45, + 165, + 531, + 207 + ], + "type": "text", + "content": "Table 2. Ablation studies of the effects of conditioning (Cond., " + }, + { + "bbox": [ + 45, + 165, + 531, + 207 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 45, + 165, + 531, + 207 + ], + "type": "text", + "content": ") and inpainting (Inpa.) on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. The combined use of conditioning and inpainting leads to superior performance in visual metrics, and inpainting plays a less significant role in terms of geometric results when the model is conditioned." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 307, + 105, + 528, + 163 + ], + "blocks": [ + { + "bbox": [ + 307, + 105, + 528, + 163 + ], + "lines": [ + { + "bbox": [ + 307, + 105, + 528, + 163 + ], + "spans": [ + { + "bbox": [ + 307, + 105, + 528, + 163 + ], + "type": "table", + "html": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.3091.3041.3101.29330612777246317580.5130.5980.7110.862
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.8970.8080.6620.595116369917699.00.7510.8170.8870.928
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
", + "image_path": "173abf0b0692c917257c43a90b3f997c1ef5f5315e03d56bec5d516b852b3789.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 67, + 208, + 506, + 439 + ], + "blocks": [ + { + "bbox": [ + 67, + 208, + 506, + 439 + ], + "lines": [ + { + "bbox": [ + 67, + 208, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 67, + 208, + 506, + 439 + ], + "type": "image", + "image_path": "16a16ca21b2bbf6f0ae8f5b6ffd337d3337f94e06fc9d7abff4b1fca291bee98.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "lines": [ + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "spans": [ + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "text", + "content": "Figure 5. Qualitative results of ablation studies on the task of scene synthesis from sparse RGBD inputs. \"(a)\", \"(b)\" and \"(c)\" correspond to the second (w/o conditioning, " + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "text", + "content": "), third (w/o inpainting, " + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "text", + "content": ") and fourth (w/ all, " + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "text", + "content": ") rows of Table 2, and \"(d)\" corresponds to the last (w/ all, " + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "inline_equation", + "content": "\\beta = 5" + }, + { + "bbox": [ + 45, + 442, + 531, + 506 + ], + "type": "text", + "content": ") row of Table 3. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. It is clear that the third row basically shows the most favorable appearance." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 509, + 300, + 576 + ], + "blocks": [ + { + "bbox": [ + 50, + 509, + 300, + 576 + ], + "lines": [ + { + "bbox": [ + 50, + 509, + 300, + 576 + ], + "spans": [ + { + "bbox": [ + 50, + 509, + 300, + 576 + ], + "type": "table", + "html": "
Guidance Factor βVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
0.012.414.716.517.90.4110.4960.5570.5830.5200.4460.3930.359
0.513.215.517.118.20.4520.5300.5780.5960.4960.4180.3740.347
1.014.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
2.014.515.817.518.40.5320.5610.5980.6060.4390.3930.3520.334
5.013.314.917.118.20.4880.5310.5790.5980.4750.4180.3670.342
", + "image_path": "c8ac30557c05f2c600d45e4088fc8d9bc9f7d153df912f90b827475979ceb93c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "lines": [ + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "spans": [ + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": "Table 3. Ablation studies of the effects of guidance factor " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": " on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. A larger " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": " ideally strengthens the conditioning effect. The visual metrics are found to be the best when " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": " is set to 1 or 2. Interestingly, the optimal value of " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": " for the best geometry appears to increase as views become denser. However, setting such a large value of " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": " (e.g. " + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "inline_equation", + "content": "\\beta = 5" + }, + { + "bbox": [ + 45, + 577, + 531, + 620 + ], + "type": "text", + "content": ") leads to sub-optimal visual results." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 303, + 509, + 528, + 575 + ], + "blocks": [ + { + "bbox": [ + 303, + 509, + 528, + 575 + ], + "lines": [ + { + "bbox": [ + 303, + 509, + 528, + 575 + ], + "spans": [ + { + "bbox": [ + 303, + 509, + 528, + 575 + ], + "type": "table", + "html": "
Geometric
MSEdepthCDmeshComp meshes@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
1.0010.8370.7610.73019348504431490.6000.7810.8810.931
0.9990.8450.7720.71919806062231110.6530.8180.8940.933
0.8250.8050.6880.62810589021561000.7470.8390.9090.936
0.8940.8000.6540.593156251514487.20.7530.8460.9100.936
0.9920.8560.6630.5822551167617587.20.7470.8420.9080.934
", + "image_path": "ebe76dcff26da2bfcff157665d2b2d79d9e7e0cc3999122f9aa009aeb48a9edf.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 632, + 150, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 632, + 150, + 644 + ], + "spans": [ + { + "bbox": [ + 45, + 632, + 150, + 644 + ], + "type": "text", + "content": "circular camera trajectory." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "content": "Future Works. To improve our design, potential areas of investigation include: (1) Modeling color smoothness and variation, as demonstrated by NeRF [42]. (2) Supporting advanced physical lighting effects, such as SVBRDF, as implemented in TANGO [9]. (3) Incorporating appearance/surface extrapolation by learning an implicit field, such as NeRF [42, 43] or SDF [3, 80]. (4) Exploring gener" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 632, + 530, + 725 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 632, + 530, + 725 + ], + "spans": [ + { + "bbox": [ + 296, + 632, + 530, + 725 + ], + "type": "text", + "content": "ative [5] or estimable [6, 84] camera trajectories for scene synthesis. (5) Investigating reconstruction from sparse-view RGB inputs only, using depth inpainting/estimation following the reverse sampling technique proposed in [37] by utilizing a versatile RGBD diffusion model. (6) Leveraging the multi-modal [52] or generative [57] power of large-scale pre-trained models, such as the recently widespread Stable Diffusion [57]." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8428" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 99, + 300, + 166 + ], + "blocks": [ + { + "bbox": [ + 48, + 99, + 300, + 166 + ], + "lines": [ + { + "bbox": [ + 48, + 99, + 300, + 166 + ], + "spans": [ + { + "bbox": [ + 48, + 99, + 300, + 166 + ], + "type": "table", + "html": "
MethodsVisual
PSNRcolorSSIMcolorLPIPScolor
5%10%20%50%5%10%20%50%5%10%20%50%
NGP10.412.414.417.40.2930.3770.4370.4980.5820.4760.4150.376
DS-NGP10.111.913.515.30.2050.2810.3210.3610.6050.5330.5030.476
N-RGBD14.116.518.420.00.4010.5130.5950.6520.4900.3840.3200.287
DDP14.116.118.320.90.4180.5040.5990.7020.5170.4100.3290.259
Ours14.616.017.418.40.5220.5550.5930.6030.4480.3990.3590.338
", + "image_path": "032b1f18eb7aa9a8ebc0c1f758cbfbdb79d8edaaaf1b76722737fe3fe9acdf14.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 303, + 101, + 528, + 165 + ], + "blocks": [ + { + "bbox": [ + 303, + 101, + 528, + 165 + ], + "lines": [ + { + "bbox": [ + 303, + 101, + 528, + 165 + ], + "spans": [ + { + "bbox": [ + 303, + 101, + 528, + 165 + ], + "type": "table", + "html": "
Geometric
MSEdepthCDmeshComp_mesh@0.1m
5%10%20%50%5%10%20%50%5%10%20%50%
7.017.397.376.5229994229731667680660.2890.4460.6460.850
2.301.691.441.17536217017682300.5290.7220.8450.918
1.511.231.211.133503134512106430.7050.8190.8570.872
1.441.050.940.88236310136374510.5070.6240.7190.812
0.820.800.680.6210589021561000.7470.8390.9090.936
", + "image_path": "c36dd93338924116b9ce9f8f642442f7260ec1efbe2b1d57c92ad25fe2dc5b45.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 168, + 531, + 210 + ], + "lines": [ + { + "bbox": [ + 45, + 168, + 531, + 210 + ], + "spans": [ + { + "bbox": [ + 45, + 168, + 531, + 210 + ], + "type": "text", + "content": "Table 4. Quantitative comparison with other approaches on visual (color images) and geometric (depth maps and meshes) results on the task of scene synthesis from sparse RGBD inputs. Our approach outperforms other methods consistently in terms of geometric metrics as the sparsity varies. However, our method only show a definitive visual advantage across various visual metrics when the input views are highly sparse (5%)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 67, + 213, + 509, + 666 + ], + "blocks": [ + { + "bbox": [ + 67, + 213, + 509, + 666 + ], + "lines": [ + { + "bbox": [ + 67, + 213, + 509, + 666 + ], + "spans": [ + { + "bbox": [ + 67, + 213, + 509, + 666 + ], + "type": "image", + "image_path": "c97d438b48dfd90f6ad29adce2d16f48e00053657fc853040f8b4d1d097eb941.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 667, + 531, + 732 + ], + "lines": [ + { + "bbox": [ + 45, + 667, + 531, + 732 + ], + "spans": [ + { + "bbox": [ + 45, + 667, + 531, + 732 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison results with DS-NGP [13,43], DDP [56], N-RGBD [3] on the task of scene synthesis from sparse RGBD inputs. Each image in the grid consists of four sub-images, with two located at the lower-right corner displaying rendered RGBD images generated from either NeRFs (others) or meshes (ours), and the other two positioned at the top-left corner and underneath, respectively, showcasing the back-projected triangular meshes captured from a close-up perspective. Our approach produces images that exhibit a close resemblance to the ground truth (GT), while comparative methods may result in inferior outcomes, especially when dealing with excessively sparse input views and outward-looking cameras." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8429" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 51, + 137, + 279, + 728 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 51, + 137, + 279, + 212 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 137, + 279, + 212 + ], + "spans": [ + { + "bbox": [ + 51, + 137, + 279, + 212 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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As this technology gains popularity, there is a growing concern about its potential security risks. However, there has been limited exploration into the robustness of these models from an adversarial perspective. Existing research has primarily focused on untargeted settings, and lacks holistic consideration for reliability (attack success rate) and stealthiness (imperceptibility).", + "bbox": [ + 75, + 323, + 472, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models via inconspicuous examples. By formulating the example crafting as an optimization process and solving it using a genetic-based method, our proposed attack can generate imperceptible prompts for text-to-image generation models in a reliable way. Evaluation of six popular text-to-image generation models demonstrates the efficiency and stealthiness of our attack in both white-box and black-box settings. To allow the community to build on top of our findings, we've made the artifacts available1.", + "bbox": [ + 75, + 460, + 472, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 654, + 209, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The text-to-image generation has captured widespread attention from the research community with its creative and realistic image generation capability [52, 55, 56]. The ability to generate text-consistent images from natural language descriptions could potentially bring tremendous benefits to many areas of life, such as multimedia editing, computer-aided design, and art creation [23, 27, 37, 43].", + "bbox": [ + 75, + 680, + 468, + 785 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Driven by recent advances in models trained with large datasets [42, 57] and multimodal learning [45] (e.g., diffusion models [17]), text-to-image generation has made significant progress in synthesizing high-fidelity and photorealistic images, such as DALL-E [43], DALL-E 2 [42] and Imagen [45]. At the same time, there are a growing num", + "bbox": [ + 75, + 786, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b94be0ae3da8f7e0d45a3b0f124aa802285a028829448d335a900d217bd75352.jpg", + "image_caption": [ + "Figure 1. Examples of RIATIG attacks. The top texts are the adversarial prompts, and the bottom texts are the target models. The first row represents the target images, while the second row represents the adversarial image generated by the prompt." + ], + "image_footnote": [], + "bbox": [ + 511, + 292, + 888, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ber of ethical concerns about the potential misuse of this technology [36,45,53]. Generative models could be used to generate synthetic video/audio/images of individuals (e.g., Deepfakes [14]), or synthetic contents with harmful stereotypes, violence, or obscenities [10, 45, 53]. To prevent the generation of such harmful content, content moderation filters are deployed in public APIs (e.g., DALL·E 2) to filter unsafe text prompts that may lead to harmful content. However, despite their best intentions, existing model-based text filters remain susceptible to adaptive adversarial attacks.", + "bbox": [ + 496, + 609, + 893, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) have been shown to be vulnerable to adversarial examples [9, 31, 32]. By applying these techniques, it is possible to craft an adversarial text that looks natural to bypass the content filters, yet generates a completely different category of potentially malicious images. However, the adversarial attacks on text-to-image generators are less explored. To the best of our knowledge, there are two closely related studies [15, 36]. Nevertheless, two challenges remain:", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code is available at: https://github.com/WUSTL-CSPL/RIATIG", + "bbox": [ + 94, + 886, + 441, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20585", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1) Reliability. One significant limitation is that the existing works [15, 36] do not offer a reliable method to find adversarial examples. [15] discovers that DALL-E 2 has certain hidden vocabularies that can be used to generate images with some absurd (non-natural) prompts; however, this vocabulary is often limited and not stealthy (natural). Built on evocative prompting, [36] crafts adversarial examples via the morphological similarity between existing words. However, it is very difficult to find texts with such linguistic similarity, and as a result, it can be challenging for this method to be adopted and generalized in different scenarios.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2) Stealthiness. The existing approaches can only craft adversarial examples that appear to be non-natural compared to normal texts or retain similar meanings, making them easily filtered and recognized by human examiners. For example, [15] crafts Apoploe vesrreaaitais to represent bugs, and [36] crafts falaiscoglieklippantilado to represent cliff. Also, [36] combines creepy and spooky into creepokey to generate an image that looks creepy and scary, yet the inferred meaning of this new word is highly related to the generated image, limiting its stealthiness.", + "bbox": [ + 75, + 262, + 472, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models using natural examples. To achieve this, we first formulate the generation of the adversarial examples as an optimization problem and apply genetic-based optimization methods to solve it, thus making our methods much more reliable in finding working adversarial examples. Furthermore, in order to improve the stealthiness, we propose a new text mutation technique to generate adversarial text that is visually and semantically similar to its normal version (some example results are shown in Figure 1).", + "bbox": [ + 75, + 414, + 472, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "RIATIG is evaluated on six popular text-to-image models with both white-box and black-box attack settings. Experimental results show that compared with the state-of-the-art text-to-image-oriented adversarial attacks, RIATIG demonstrates significantly better performance in terms of attack effectiveness and sample quality. Overall, the contributions of this work are summarized as follows:", + "bbox": [ + 75, + 582, + 472, + 688 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We are the first to systematically analyze the adversarial robustness of text-to-image generation models in both the white-box and black-box settings.", + "- We propose genetic-based optimization methods to find natural adversarial examples reliably.", + "- We evaluate our attacks on six popular text-to-image generation models and compare our attacks with five baselines. The evaluation results show that our methods achieve a much higher success rate and sample quality, raising awareness of improving and securing the robustness of text-to-image models." + ], + "bbox": [ + 96, + 702, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-Image Generation. The research towards text-to-image generation starts with the work proposed by Mansimov et al. [33], which extends the Deep Recurrent Attention Writer (DRAW) [20] model to condition on image captions using a soft attention mechanism. Xu et al. [52] further propose a multi-stage attentional GAN (AttnGAN) to force the model to focus on the fine-grained information at the word level, leading to the generation of more semantically matched images. To address the limitations of the multi-stage methods, e.g., low-quality initial images and repeated use of the same word representations, Zhu et al. [58] propose a dynamic memory GAN (DM-GAN), which uses a memory network to write and read encoded prior dynamically in each image-refined process. To further improve the quality of the generator, Tao et al. [49] propose a deep Fusion Generative Adversarial Network (DF-GAN) that performs deep fusion between text and visual features. Recently, a set of large-scale text-to-image generation models are proposed and released, demonstrating promising performance. DALL-E, an autoregressive transformer model trained on 250 million web-crawled image-text pairs [43], achieves zero-shot high-quality image generation on the MS-COCO dataset. Its updated version, DALL-E 2, adopts contrastive model CLIP [42]. By feeding a text caption and using a diffusion model to generate an image conditioned on the image embedding, DALL-E 2 can synthesize amazingly photorealistic images. Imagen is another state-of-the-art text-to-image generator built on the combination of a transformer trained on text data and a high-fidelity diffusion model, achieving a very high generation performance.", + "bbox": [ + 496, + 122, + 893, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial Attacks on Text-to-Image Generators. The adversarial robustness of text-to-image generation is a relatively less studied topic. [15] is the pioneering work that studies the vulnerability of text-to-image generators, such as DALL-E 2. They found it is possible to leverage gibberish text in the target image to evade content filters by using such gibberish texts as prompts rather than semantically equivalent text. However, most of the gibberish text does not reliably produce a specific category of images. Later, Millière proposes two methods of crafting adversarial text to generate specific pictures [36]. The first solution is macaronic prompting, which composes multilingual subword segments to generate specific types of images. The second approach is evocative prompting, a strategy that uses prompts possessing similarity of broad morphological features to generate semantic-consistent images with real concepts. In addition, Struppek shows that replacing a single character in the text with visually similar non-Latin characters can induce cultural biases into the generated images or even hide complete objects in the generated images. However, their method is untargeted, i.e., they cannot generate", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20586", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/49f154a6fe6f50e7f75320193b801e4ae422265724547fc6fa6fe846e1d4379d.jpg", + "image_caption": [ + "Figure 2. Working mechanism of a text-to-image generator." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 460, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "specific attacker selected images.", + "bbox": [ + 76, + 223, + 297, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. System and Threat Model", + "text_level": 1, + "bbox": [ + 76, + 250, + 318, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-Image Generation Model. Figure 2 represents the working mechanism of text-to-image generation models considered in this work, consisting of three parts: a text encoder, a transformation network, and a decoder. In the text encoder, the text prompt is first converted to tokens by a tokenizer. Each token is mapped to a text encoding by looking up the mapping dictionary of the embedding models. The transformation model maps the text encoding to a corresponding image encoding that captures the semantic information contained in the text encoding. Finally, the decoder generates an image based on image encoding that is a visual representation of the text prompt. As shown in Figure 2, the image generated by DALL-E 2 with prompt A bowl of soup that is also a portal to another dimension is photorealistic and has aligned semantic meaning.", + "bbox": [ + 75, + 279, + 468, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Threat Model. We consider both white-box and black-box settings to evaluate the different capabilities of the adversary. In the white-box setting, the adversary has full knowledge of the target model such as model architecture as well as its parameters. In the black-box setting, the adversary does not know the internal information of the model or training data. It is only capable of querying the model with supplied input and obtaining the output. Different from classification models [8, 21, 24, 28], the generation models cannot return confidence scores to the adversary.", + "bbox": [ + 75, + 508, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 76, + 672, + 210, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 696, + 279, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A text-to-image generation model $\\mathcal{G}:\\mathcal{X}\\to \\mathcal{Y}$ maps text space $\\mathcal{X}$ to image space $\\mathcal{V}$ . Since $\\mathcal{G}$ is trained on semantically-aligned text-image pairs, a well-trained model should generate images that are semantically identical to the input text. Given an arbitrary target image $y_{t}$ , which corresponds to its naive text prompt $x_{t}$ , the adversary aims to craft an adversarial example $x^{*}$ that generates a semantically similar image to $y_{t}$ , with the premise that $x^{*}$ is semantically dissimilar from $x_{t}$ enough to evade detection. This is an optimization program that can be formulated as", + "bbox": [ + 75, + 720, + 468, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {x ^ {*}} {\\operatorname {a r g m a x}} S _ {i} \\left(\\mathcal {G} \\left(x ^ {*}\\right), y _ {t}\\right) \\text {s . t .} D _ {t} \\left(x ^ {*}, x _ {t}\\right) > \\eta , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 878, + 468, + 904 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S_{i}$ is a semantic similarity function of images, $D_{t}$ is a function measuring the semantic distance of texts, and $\\eta$ is the threshold of the semantic dissimilarity of $x_{t}$ and $x^{*}$ .", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Challenges and Overview", + "text_level": 1, + "bbox": [ + 500, + 143, + 732, + 160 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Challenges. Designing a reliable and imperceptible adversarial attack against text-to-image models can face several challenges. Firstly, unlike existing work on textual adversarial attacks [8,24,28], where the output of the model is a finite number of classes (e.g., positive and negative in sentiment analysis), the output of a text-to-image model is a high-dimensional continuous class with nearly infinite combinations. This characteristic makes it difficult to measure the effectiveness of the attacks. One possible solution is to measure the semantic distance of images, however, existing approaches only focus on category-level semantic distance [11, 16], which cannot handle the complex sentence context similarity. For example, simply representing a blue double decker school bus parking in let by school bus will lose important context information such as the color, size of the bus, and its surrounding environment. Second, since words can serve as discrete tokens in a sentence, it is impossible to optimize the input words directly by computing the gradient of the loss function with respect to the input word even assuming white-box knowledge in the adversary [8]. Third, unlike image domains where small perturbations can go unnoticed, any changes in the text domain are perceptible [8,28,29] and easily detectable by human examiners.", + "bbox": [ + 496, + 170, + 890, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Attack Overview. We adopt a genetic-based approach to iteratively optimize the input samples towards the target samples, followed by a quality fine-tuning stage to further improve the imperceptibility. First, the mutation stage generates a large number of variants that are semantically and visually similar to the input text, then the text-to-image generation model outputs images accordingly. A similarity measurement is implemented to compute the quality of mutated examples, allowing us to select the best offspring, which will enter a crossover stage to exchange the desirable traits to obtain a better population for the next-round iteration. The loop ends when the generated images are highly similar to the target images yet the adversarial text is distinct from the target text. Then the result samples go through the quality fine-tuning stage where we propose two techniques to further improve the imperceptibility of adversarial examples. In the following section, we will first introduce the similarity measurement for the offspring selection (§4.3), then elaborate on the genetic-based optimization with mutation and crossover scheme (§4.4), before finally describing the sample quality improvement procedure (§4.5).", + "bbox": [ + 496, + 522, + 890, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.3. Similarity Measurement", + "text_level": 1, + "bbox": [ + 500, + 847, + 723, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To find a suitable measurement metric, we need to consider the natural continuity of visual space and find a proper", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20587", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f302ac0845059f8a31c02ec81b319ecdc1ecb0a119ba15d6feced44393b7e3b.jpg", + "image_caption": [ + "Figure 3. Overview of the RIATIG attack." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 467, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "representation of image semantic information. Recently, there is a growing research interest in learning image representation from text [40, 46, 57], which maps images into a semantic-rich embedding space by jointly learning with textual data. Among these efforts, the CLIP proposed by OpenAI has been trained on large-scale (i.e., 400 million) web-crawled image-text pairs [40], which can efficiently represent visual concepts aligned with the corresponding textual information. Motivated by its powerful capability, we adopt the pre-trained image encoder of CLIP to encode two images and then calculate the cosine distance between the encoded vectors measuring the similarity as", + "bbox": [ + 75, + 253, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} (\\mathcal {G} (x), y) = \\frac {E _ {i} (\\mathcal {G} (x)) \\cdot E _ {i} (y)}{\\| E _ {i} (\\mathcal {G} (x)) \\| \\| E _ {i} (y) \\|.} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 446, + 468, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarly, we utilize the text encoder to encode the text and calculate the cosine distance as their semantic distance,", + "bbox": [ + 76, + 491, + 468, + 521 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {t} (x, x ^ {*}) = 1 - \\frac {E _ {t} (x) \\cdot E _ {t} \\left(x ^ {*}\\right)}{\\| E _ {t} (x) \\| \\| E _ {t} \\left(x ^ {*}\\right) \\|.} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 532, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When the semantic distance is above a certain threshold, the two texts are considered not semantically similar.", + "bbox": [ + 76, + 578, + 468, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Genetic-based Optimization", + "text_level": 1, + "bbox": [ + 76, + 619, + 328, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Genetic algorithms are heuristic optimization methods that are inspired by nature selection. By evolving a population of candidates towards better solutions with performing mutation and crossover [22], the genetic algorithms can search a large solution space effectively [25], making them well suited in the optimization over the multi-dimensional input space. Therefore, in this work, we adopt a genetic-based algorithm to solve the target optimization problem. To be specific, the optimization process starts with an input text that is semantically dissimilar from the target images. The mutation is used to generate different variants to explore the search space and increase the diversity of the population. To generate initial high-quality variants, RIATIG first generates a large pool of mutated candidates, rendering the execution of crossover and mutation more effective. In each generation, we select the samples with the highest fitness score for crossover and mutation to generate the next", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Adversarial Example Generation" + ], + "code_body": "1 Input: Original text $x$ target text $x_{t}$ with associated target image $y_{t}$ mutation probability $p_m$ population size $M,N,K$ maximum iterations $c_{max}$ ,control parameter $\\alpha ,\\beta$ \n2 Output: Adversarial examples sets $T^{*}$ \n3 $G_0\\gets \\text{Mutate}(x,p_m,M)\\triangleright$ initialize population \n4 for $c = 0$ to $c_{max}$ do \n5 $Z_{c}\\gets S_{i}(\\mathcal{G}(G_{c}),yt)\\triangleright$ update score by Eq.2 \n6 $I_{c}\\gets \\text{argsort}(Z_{c})[: - 1]$ \n7 $E_{c}\\gets G_{c}[I_{c}][:K];F_{c}\\gets Z_{c}[I_{c}][:K]$ \n8 $s_c\\gets F_c[0]^\\triangleright$ For mutation prob update \n9 $p_m\\gets \\alpha \\cdot p_{m - 1} + \\frac{\\beta}{|s_c - s_{c - 1}|}$ \n10 $P_{c}\\gets \\text{Softmax}(F_{c})\\triangleright$ normalize to prob \n11 for $i = 1$ to $N$ do \n12 parent1,parent2 $\\leftarrow$ Sample $(E_c,P_c)\\triangleright$ sample two parents from $E_{c}$ with prob $P_{c}$ \n13 childi $\\leftarrow$ Crossover(parent1, parent2) \n14 gi $\\leftarrow$ Mutate(childi,pm,1) \n15 $G_{c + 1}\\gets G_{c + 1}\\cup \\{g_i\\} \\triangleright$ append to new generation \n16 if $S_{i}(\\mathcal{G}(g_{i}),y_{t}) > \\epsilon$ and $D_t(g_i,x_t) > \\eta$ then \n17 | $T\\gets T\\cup \\{g_i\\} \\triangleright$ append to sample sets \n18 end \n19 end \n20 end \n21 $T^{*}\\gets \\text{FineTune}(T)\\triangleright$ Fine tune samples by strategy in Section 4.5 \n22 return $T^{*}$", + "bbox": [ + 503, + 112, + 866, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "generation of text samples. Cosine similarity scores calculated by Eq. 2 between the two images are the fitness score of the genetic algorithm.", + "bbox": [ + 496, + 479, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Crossover Scheme. Crossover is used to exchange the desirable traits between the chosen populations, thereby possibly generating an even better population. For the crossover scheme used in RIATIG, a new sentence is synthesized by a pair of parent sentences. The probability of each population being selected as a parent is proportional to their fitness score, giving the beneficial traits a higher probability to stay.", + "bbox": [ + 496, + 530, + 892, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mutation Scheme. RIATIG performs sentence-level mutation. Each sentence has a mutation probability of $p_m$ to be selected. The proper selection of $p_m$ is very critical. When it is too high, the beneficial traits may be mutated without crossover to generate better offsprings. On the other hand, very small $p_m$ will make most of the populations unchanged, causing insufficient mutations to escape the local maximum. To address the challenge, $p_m$ can be adaptively updated using a momentum mutation-based method [50] by", + "bbox": [ + 496, + 638, + 890, + 776 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {m} = \\alpha \\cdot p _ {m - 1} + \\frac {\\beta}{\\left| S _ {i} - S _ {i - 1} \\right|}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 786, + 890, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are scaling factors, and $S_{i}$ denotes the maximum fitness score across the populations in $i$ -th generation.", + "bbox": [ + 496, + 824, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mutation process occurs for each selected sentence, which is divided into two stages. In the first stage, we identify the important words in the original sentence that need to", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20588", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be mutated. In the second stage, we propose two strategies to slightly modify a word while preserving its semantics.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage-1: Selection of Important Word. Because 1) the search space for mutation is very huge; and 2) most of the mutation variants do not play significant roles to improve the fitness score, identifying the most important words that contribute to fitness scores is crucial to improve the effectiveness of mutation. When we assume white-box knowledge, gradient information can be used to measure the importance, calculating the gradient of the fitness score with respect to the embedding of each word by", + "bbox": [ + 75, + 125, + 472, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng _ {x _ {n}} = \\frac {\\partial S _ {i} \\left(\\mathcal {G} \\left(e _ {n}\\right) , y _ {t}\\right)}{\\partial e _ {n}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 268, + 468, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $e_n$ is the embedding of word $x_n$ , $y_t$ is the target image, $\\mathcal{G}$ is the generation model, and $S_i$ is the semantic similarity function defined in Eq. 2. When we assume black-box knowledge, the importance of a word is estimated by calculating the change in fitness scores before and after deleting the word, such a calculation process is defined as", + "bbox": [ + 75, + 306, + 468, + 398 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng _ {x _ {n}} = S _ {i} (\\mathcal {G} (e), y _ {t}) - S _ {i} (\\mathcal {G} \\left(e _ {\\backslash e _ {n}}\\right), y _ {t}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 407, + 468, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $e$ is the embedding vectors of sentence $x$ , $e \\backslash e_n$ is the embedding vectors after deleting the word $x_n$ from $x$ . After that, we normalize the important scores as", + "bbox": [ + 75, + 434, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {x _ {n}} = \\frac {e ^ {\\| g _ {x _ {n}} \\|}}{\\sum_ {i = 1} ^ {N} e ^ {\\| g _ {x _ {i}} \\Vert}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 488, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then each word $x_{n}$ has a probability of $I_{x_n}$ to be selected.", + "bbox": [ + 75, + 534, + 464, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage-2: Word Mutation. Since our goal is to generate adversarial text to be visually and semantically similar to normal text for human understanding, we consider two types of mutation strategies that are used in natural language processing fields [28,29,51]. The first one is to inject character-level typos that mimic the grammar mistakes people may make. The rationale is that the semantic meaning of the text is very likely to be preserved after a few character changes [44]. More specifically, we adopt three types of text manipulations: (1) Insert extra spaces into words; (2) Swap the position of two characters randomly except for the first and last characters; (3) Delete one random character except for the first and last characters. The second type of text manipulation is to replace characters/words with visually or semantically similar counterparts. As for visually similar substitution, we utilize the LEET Speak Alphabet [7], which replaces characters in ways that play on the similarity of glyphs. For example, we may replace the letter $l$ with the number $l$ , the letter $o$ with the number $o$ , etc.", + "bbox": [ + 75, + 551, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the semantically similar substitution, we adopt the Word2vec model [34] to transform the words into embedding vectors, and then compute the cosine distance as the similarity measurement to select the nearest neighbors. A", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "threshold is used to filter out candidates with large distances. Due to the large search space of optimization, only replacing it with target-irrelevant sentences will weaken the mutation, making it hard to find variants that generate images closer to the target. To solve this problem, we use the target sentences to perform semantic substitution, and the words with a close distance are filtered out. In addition, we adopt the WordNet [35] to decide the part-of-speech (POS) tag of the word, filtering out the candidates with different POS to maintain grammatical fluency. After filtering, we select the top-M nearest neighbors into the candidate pool. Next, Google's one billion-word language model [13] is used to filter out words that do not fit within the context surroundings. To that end, we first fit words in the candidate pools with the surrounding context, then calculate their language scores that measure the fluency of the sentences, keeping the top-N word with the highest scores.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Sample Quality Improvement", + "text_level": 1, + "bbox": [ + 498, + 357, + 764, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the adversarial examples, we further improve the quality of adversarial text based on two key observations. First, the presuppositions (e.g., on, in, etc.) in the sentences have little impact on the semantic meanings of generated images compared to the nouns and verbs. Second, the text embedding in the text-to-image generation model usually uses a dictionary to represent a finite set of possible words [52, 58], meaning that the deliberately misspell out-of-vocabulary will be mapped to unknown. With the first observation, we iteratively replace or add all predefined presuppositions in different positions of sentences and test their naturality. The presuppositions with the highest naturality are chosen to improve the samples. We then further fine-tune the quality of samples based on the second observation. For example, both paking and parnikg are out-of-vocabulary words that are mapped to the unknown, and they are regarded as the same words by the text-to-image generation models. However, since the first word has fewer modifications, it is closer to an ordinary text and is preferred. Therefore, with white-box knowledge, we can test whether the adversarial text is the out-of-vocabulary words by feeding it to the embedding models. In the black-box attack setting, we adopt the GloVe embedding models [38] pre-trained on the Common Crawl dataset containing 2.2 million vocabularies as a surrogate embedding model.", + "bbox": [ + 496, + 381, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 498, + 773, + 633, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 500, + 797, + 692, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We choose the initial texts, target texts, and target images from the Microsoft COCO [30] dataset, a popular benchmark for training and evaluating text-to-image generation models. The dataset includes 82,783 training images and 40,504 testing images, each with 5 text descriptions.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20589", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Target Models. To evaluate the performance of our proposed attack, we choose three representative public text-to-image generation models: AttnGAN [52], DM-GAN [58], and DF-GAN [49]. We use the pre-trained models on the COCO dataset released in their official GitHub repository [1, 4, 5] as the target models. We also choose three large-scale proprietary models: DALL-E [43], DALL-E 2 [42], and Imagen [45]. None of the above have officially released their pre-trained models, nor public APIs except DALL-E 2. Therefore, for DALL-E, we adopt the released pre-trained models of DALL-E mini [3], which achieves comparable performance to that of DALL-E. Similarly, for Imagen, we adopt the pre-trained models released by Hugging Face [6]. For DALL-E 2, though a public API exists2, only 15 free credits are granted to each account, so we first train adversarial examples on LAION's pre-trained model [2], then access the APIs to check if it was transferred successfully.", + "bbox": [ + 76, + 90, + 472, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Setup. In our experiment, we attacked the AttnGAN, DM-GAN, and DF-GAN in white-box settings, and we attacked DALL-E, DALL-E 2,Imagen in black-box settings, which means we can only query the model and get the generated images. We set the initial population size $M$ , the total population size $N$ , and the selected population size $K$ to 300, 50, and 25, respectively. The initial mutation probability $p_m$ is set to 0.8. Ten adversarial examples are generated for each model. For each generation, we randomly select a target image and a semantic unrelated text from the COCO dataset. For example, we select the target images with the meaning a clock is flying in the blue sky and the original text a red double decker bus parking in let.", + "bbox": [ + 76, + 351, + 472, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with Baselines. To the best of our knowledge, there are only two related studies [15, 36] for a targeted adversarial attack against text-to-image generation models. [15] proposes a hidden vocabulary attack (HiddVocab) on DALL-E 2 and [36] implements macaronic prompting (MacPrompt) and evocative prompting (EvoPrompt) attacks against DALL-E mini and DALL-E 2. For a comprehensive comparison, we also include [48], which is a homolytic substitution-based attack (HomoSubs) to cause image content obfuscation. We also include one state-of-the-art textual adversarial attack, TextFooler [24]. Since their attack does not involve image generation, we change the posterior tasks to match our settings and apply our proposed similarity metric to guide the optimization.", + "bbox": [ + 76, + 551, + 472, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 773, + 261, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of our attack, we evaluate both attack effectiveness and adversarial sample imperceptibility. The imperceptibility measure consists of two parts: semantic meaning similarity and sentence naturality.", + "bbox": [ + 76, + 797, + 468, + 858 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of Generated Images. We adopt the method", + "bbox": [ + 76, + 861, + 468, + 877 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of R-precision, a widely-used metric in text-to-image generation models [27, 39, 52, 54, 58] to measure whether the generated image is semantically aligned with the given text description. Specifically, we use the generated images to perform a retrieval experiment by querying a candidate set of text descriptions that consist of one ground truth and 99 randomly selected mismatched descriptions. The ViLT model [26], which achieves state-of-the-art performance on image-text retrieval tasks, is used here. We examine the top $R$ ranked retrieval results and consider our attacks successful when the ground truth appears in the retrieval. We evaluate the effectiveness when R is 1 (R-1) and R is 3 (R-3).", + "bbox": [ + 500, + 90, + 890, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sentence Semantic Meaning. Following [24, 28], we first adopt the Universal Sentence Encoder [12] to encode the adversarial sentence and target sentence into high dimensional vectors, and then their cosine similarity score are calculated to measure the semantic similarity.", + "bbox": [ + 500, + 277, + 890, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sentence Naturality. The adversarial examples should look natural, similar to normal sentences in the real world. In our experiment, we calculate the perplexity (PPL) of the adversarial examples with GPT-2 [41], which is trained on a large corpus of real-world sentences. PPL measures how likely the model is to generate the input text sequence, representing the fluency of the adversarial examples. Generally, the sample with lower PPL is more natural.", + "bbox": [ + 500, + 357, + 890, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Evaluation Results", + "text_level": 1, + "bbox": [ + 500, + 489, + 679, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "White-box Attacks. The results for white-box attacks are shown in Table 1. It is seen that RIATIG succeeds in generating all adversarial examples in DM-GAN and DF-GAN, and can succeed in generating 9 out of 10 samples in AttnGAN when we examine top-3 recall results. The recall precision drops when we only examine top-1 recall results. This phenomenon might be caused by the image generation quality of the target model, since the DM-GAN and AttnGAN achieve an average R-precision of $85.47\\%$ [52] and $88.56\\%$ [58] on COCO datasets. Furthermore, a low semantic distance means there is a low semantic relevance between the adversarial text and the text used to generate the target images. The low PPL means our adversarial text is fluent and natural as compared to the normal text. On the other hand, due to the limited-size and monolingual datasets that these three models are trained on, the baselines can not succeed in generating adversarial examples.", + "bbox": [ + 500, + 518, + 890, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Black-box Attacks. The results for black-box attacks are shown in Table 2. RIATIG achieves a high R-precision as compared to the baseline methods. HomoSubs and TextFooler are designed for untargeted attacks, and cannot be easily adapted for targeted attacks. HiddVocab does not provide a reliable method for finding adversarial examples and can achieve only a $40\\%$ success rate against DALL-E 2. Though MacPrompt and EvoPrompt can achieve a higher", + "bbox": [ + 500, + 780, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ DALL·E 2 API: https://openai.com/dall-e-2/", + "bbox": [ + 94, + 886, + 336, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20590", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d1e9f183385f1f07534a2438542c43d3f87208d82ae891d37084f5768f761d5.jpg", + "image_caption": [ + "Figure 4. Examples of our adversarial attack results against DALL-E mini, DALL-E 2, and Imagen." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 883, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dbc8bdb423b7e8139f16eb0f698c3e0fb80b0030d3fc70d39383281a26df06f6.jpg", + "table_caption": [ + "Table 1. The results of the white-box attacks against AttnGAN, DM-GAN, and DF-GAN." + ], + "table_footnote": [ + "Note: R-1 and R-3 represent the R-precision when $\\mathrm{R} = 1$ and $\\mathrm{R} = 3$ , respectively. PPL represents the perplexity of sentences." + ], + "table_body": "
ModelR-1 ↑R-3 ↑Semantic Distance ↓PPL ↓
AttnGAN [52]8/109/100.24522.63
DM-GAN [58]8/1010/100.27420.16
DF-GAN [49]9/1010/100.34558.81
", + "bbox": [ + 83, + 366, + 464, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "precision rate, due to their loosely formulated linguistic methods, MacPrompt and EvoPrompt do not always guarantee to find an adversarial example. In addition, MacPrompt adopts the compositional prompts by combining two semantically similar words resulting in a higher semantic distance. For example, it combines creepy and spooky into creepepy and uses the sentence A very creepepy person to generate a person that looks creepy and spooky. As a result, the semantic meaning between the adversarial examples and the target is still very close, making them highly perceptible. Also, these generated words can break the fluency and naturalness of the sentences, resulting in a high PPL. For EvoPrompt, since it relies on broad morphological similarity, the semantic difference is quite low. However, the crafted sentences can seem meaningless, again breaking the naturality of the sentences, e.g., using prompt rygamera pultris to generate the images of fishes.", + "bbox": [ + 75, + 474, + 468, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 744, + 230, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Mutation Strategy. To evaluate the effectiveness of our proposed mutation strategy, we conducted a comparative analysis with a random mutation approach, which employed insert, swap, and delete operations. Table 3 presents the results of our experiments, indicating that our mutations significantly outperformed random mutations, particularly in black-box settings.", + "bbox": [ + 75, + 773, + 467, + 881 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Influence of Target Images. To further analyze the im", + "bbox": [ + 76, + 885, + 467, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c92f269e4f280b8d87f501dd9fd2dbcc0e75897682df51744159a8d9724997e8.jpg", + "table_caption": [ + "Table 2. The results of the black-box attacks against DALL-E mini, DALL-E 2, and Imagen." + ], + "table_footnote": [ + "Note: Sem. Dist. represents semantic distance." + ], + "table_body": "
ModelMethodsR-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DALL-E mini [43]HiddVocab [15]3/103/100.175284.78
MacPrompt [36]8/108/100.466814.61
EvoPrompt [36]6/106/100.145662.97
HomoSubs [48]0/100/100.091115.84
TextFooer [24]0/100/100.181848.41
RIATIG9/1010/100.27420.16
DALL-E 2 [42]HiddVocab [15]4/104/100.165162.71
MacPrompt [36]9/109/100.394931.31
EvoPrompt [36]7/107/100.176139.39
HomoSubs [48]0/100/100.06981.69
TextFooer [24]0/100/100.182624.88
RIATIG10/1010/100.27872.03
Imagen [45]HiddVocab [15]2/102/100.185073.74
MacPrompt [36]6/106/100.425694.73
EvoPrompt [36]4/104/100.165607.66
HomoSubs [48]0/100/100.081103.53
TextFooer [24]0/100/100.162231.10
RIATIG10/1010/100.23704.09
", + "bbox": [ + 501, + 366, + 893, + 612 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f411338327ca8bb5c9e9aa593806173c1282f88a0131f693bbc71e1a2d61f288.jpg", + "table_caption": [ + "Table 3. Attack performance using random mutation strategy." + ], + "table_footnote": [], + "table_body": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DM-GAN7/108/100.14867.93
DF-GAN1/102/100.12882.80
DALL·E mini0/100/100.172111.82
", + "bbox": [ + 511, + 667, + 879, + 724 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/49cb1b4891980834e9e6e6a902b6ba8be8b436661a9189f92636ff597d307521.jpg", + "table_caption": [ + "Table 4. The mean and variance of evaluation metrics under different selections of target images." + ], + "table_footnote": [], + "table_body": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN9.2(±0.42)/109.8(±0.42)/100.31±0.04596.33±297.02
DALL-E mini9.7(±0.48)/109.9(±0.32)/100.28±0.03475.83±180.53
", + "bbox": [ + 501, + 781, + 890, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pact of target image selection on attack performance, we conducted ten experiments of the sample training process, with each experiment utilizing a different target image that", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20591", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0b4fee9d0cb83d6f52cad8e22d2e086eead7334234528e0f3c2acb00e55c2bb5.jpg", + "table_caption": [ + "Table 5. The attack performance by using different substitution methods against DF-GAN and DALL-E mini." + ], + "table_footnote": [ + "Note: Sub. Meth. represents substitution method." + ], + "table_body": "
ModelSub. Meth.R-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DF-GAN [49]Word2vec [34]9/1010/100.336558.81
Glove [34]8/109/100.331836.96
WordNet [35]5/107/100.358580.49
DALLE mini [43]Word2vec [34]9/1010/100.268420.16
Glove [34]7/109/100.311797.63
WordNet [35]4/106/100.368522.34
", + "bbox": [ + 78, + 128, + 473, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1a1927022d7e63a75e521b8618bbfaa463324f181d8ddbe71a35926341b3985d.jpg", + "table_caption": [ + "Table 6. The attack performance of 50 additional experiments." + ], + "table_footnote": [], + "table_body": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN42/5046/500.22838.28
DALL·E mini45/5047/500.34640.78
", + "bbox": [ + 89, + 273, + 457, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shared the same semantic meaning. The results, as presented in Table 4, indicate that our attacks demonstrated high robustness across varying target images.", + "bbox": [ + 76, + 345, + 467, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness of Example Generation. One important property of RIATIG is that the adversarial text can be reliably associated with specific visual concepts when used as a prompt. We evaluated the sample robustness of DALL-E mini, DALL-E 2, andImagen. Specifically, we feed the same adversarial text to the target model ten times and calculated the average R-precision. The results show that RIATIG can achieve a $100\\%$ R-3.", + "bbox": [ + 76, + 393, + 467, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Substitution Methods. In our mutation strategy, one of the most important parts is the semantic word substitution, which is essential for optimizing the fitness scores and improving the sample quality. To identify a suitable approach for substitution, we evaluate three different approaches, namely Glove models [38], WordNet models [35] and Word2vec models [34]. We evaluate two target generation models (DF-GAN [49] and DALL-E mini [43]) in both white-box and black-box settings. For all three approaches, we select the substitute word from the top 30 results. For each target model and substitution approach, we start with ten identical benign text and target images and generate ten adversarial samples accordingly to evaluate the performance. The results are shown in Table 5. It is seen that Word2vec performs better than Glove and WordNet with respect to R-precision and PPL for the attack against DF-GAN, and Word2vec performs better than the others with respect to all three performance metrics when attacking DALL-E mini. We hypothesize that it is probably caused by the larger semantic vocabulary of Word2vec.", + "bbox": [ + 76, + 518, + 467, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attack Performance with More Evaluations. To comprehensively evaluate the scalability of our attack, we trained 50 additional samples, each with distinct sources and targets. The results of this larger-scale evaluation are in Table 6, showing consistent performance of our attack strategy.", + "bbox": [ + 76, + 824, + 467, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 500, + 90, + 612, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Security Impacts. To prevent the malicious use of text-to-image generation models such as spreading misinformation (e.g., deepfake) [18], generating biased and inappropriate contents (e.g., stereotyping, pornography, violence) [10, 47], content moderation filters are deployed to filter harmful inputs. However, as we demonstrated, it is possible to craft a completely unrelated sentence to generate target images with black-box knowledge. Thus, it is important to consider the security risks of latest AI models.", + "bbox": [ + 496, + 118, + 890, + 255 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Possible Defense. There are several possible defenses. First, a rule-based text filter could be deployed to remove redundant spaces and wrong words before generating images. To evaluate this defense, we tested the adversarial text using Grammarly and found that $20\\%$ of the samples could bypass the text filtering. For example, the sentence \"a fruit stand display with bananas and starlit skies\" was able to evade detection because this rule-based tool does not inspect the semantic meaning of the sentence. Second, one may consider using an image filter to prevent harmful images from being displayed to users. However, training such an image filter may require non-trivial efforts in collecting a large number of datasets. Moreover, the scope of harmful images can sometimes be difficult to define, such as with deep fake images. Another possible defense mechanism lies in the enhancement of the text-to-image generation models by adversarial training, which is one of the most effective defensive approaches against adversarial examples in the image and text domains [19, 24]. The model can be trained using both the original and adversarial text sharing the same associated images as the original text. However, it requires non-trivial efforts when facing a huge volume of adversarial examples as the modern text-to-image generation models are based on large-scale training datasets (e.g., Imagen [45] trains on about 460M image-text pairs).", + "bbox": [ + 496, + 258, + 890, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose an adversarial attack against the text-to-image generation models. We propose a two-stage attack framework to craft an effective adversarial example, where we find a workable adversarial example in the first stage, followed by a sample quality fine-tuning in the second stage. Through extensive evaluation, we can generate highly natural and semantically unrelated examples, allowing for successful attacks. We hope this work will raise awareness of potential security risks and aid the development of more effective defenses.", + "bbox": [ + 496, + 675, + 890, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was partially supported by the NSF ( CNS-1916926, CNS-2038995, CNS-2154930, CNS-2229427, CNS-2238635), ARO (W911NF2010141).", + "bbox": [ + 496, + 844, + 890, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20592", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Attngan implementation. https://github.com/taoxugit/AttnGAN. Accessed: 2022-10-01.", + "[2] Dall-e 2 laion implementation. https://github.com/LAION-AI/dalle2-laion. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019." + ], + "bbox": [ + 501, + 92, + 893, + 849 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20594", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_model.json b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..15c177cabe11620e9032e4522b6c280810140245 --- /dev/null +++ b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.809, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.13, + 0.895, + 0.178 + ], + "angle": 0, + "content": "RIATIG: Reliable and Imperceptible Adversarial Text-to-Image Generation with Natural Prompts" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.203, + 0.732, + 0.222 + ], + "angle": 0, + "content": "Han Liu\\(^{1}\\), Yuhao Wu\\(^{1}\\), Shixuan Zhai\\(^{1}\\), Bo Yuan\\(^{2}\\), Ning Zhang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.222, + 0.714, + 0.241 + ], + "angle": 0, + "content": "\\(^{1}\\)Washington University in St. Louis, \\(^{2}\\)Rutgers University" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.242, + 0.782, + 0.258 + ], + "angle": 0, + "content": "{h.liul,yuhao.wu,zhais,zhang.ning}@wustl.edu,bo.yuan@soe.rutgers.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.46 + ], + "angle": 0, + "content": "The field of text-to-image generation has made remarkable strides in creating high-fidelity and photorealistic images. As this technology gains popularity, there is a growing concern about its potential security risks. However, there has been limited exploration into the robustness of these models from an adversarial perspective. Existing research has primarily focused on untargeted settings, and lacks holistic consideration for reliability (attack success rate) and stealthiness (imperceptibility)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.473, + 0.627 + ], + "angle": 0, + "content": "In this paper, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models via inconspicuous examples. By formulating the example crafting as an optimization process and solving it using a genetic-based method, our proposed attack can generate imperceptible prompts for text-to-image generation models in a reliable way. Evaluation of six popular text-to-image generation models demonstrates the efficiency and stealthiness of our attack in both white-box and black-box settings. To allow the community to build on top of our findings, we've made the artifacts available1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.655, + 0.21, + 0.672 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.47, + 0.786 + ], + "angle": 0, + "content": "The text-to-image generation has captured widespread attention from the research community with its creative and realistic image generation capability [52, 55, 56]. The ability to generate text-consistent images from natural language descriptions could potentially bring tremendous benefits to many areas of life, such as multimedia editing, computer-aided design, and art creation [23, 27, 37, 43]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.471, + 0.879 + ], + "angle": 0, + "content": "Driven by recent advances in models trained with large datasets [42, 57] and multimodal learning [45] (e.g., diffusion models [17]), text-to-image generation has made significant progress in synthesizing high-fidelity and photorealistic images, such as DALL-E [43], DALL-E 2 [42] and Imagen [45]. At the same time, there are a growing num" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.293, + 0.889, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.521, + 0.895, + 0.579 + ], + "angle": 0, + "content": "Figure 1. Examples of RIATIG attacks. The top texts are the adversarial prompts, and the bottom texts are the target models. The first row represents the target images, while the second row represents the adversarial image generated by the prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.895, + 0.763 + ], + "angle": 0, + "content": "ber of ethical concerns about the potential misuse of this technology [36,45,53]. Generative models could be used to generate synthetic video/audio/images of individuals (e.g., Deepfakes [14]), or synthetic contents with harmful stereotypes, violence, or obscenities [10, 45, 53]. To prevent the generation of such harmful content, content moderation filters are deployed in public APIs (e.g., DALL·E 2) to filter unsafe text prompts that may lead to harmful content. However, despite their best intentions, existing model-based text filters remain susceptible to adaptive adversarial attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) have been shown to be vulnerable to adversarial examples [9, 31, 32]. By applying these techniques, it is possible to craft an adversarial text that looks natural to bypass the content filters, yet generates a completely different category of potentially malicious images. However, the adversarial attacks on text-to-image generators are less explored. To the best of our knowledge, there are two closely related studies [15, 36]. Nevertheless, two challenges remain:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.442, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Code is available at: https://github.com/WUSTL-CSPL/RIATIG" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20585" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "1) Reliability. One significant limitation is that the existing works [15, 36] do not offer a reliable method to find adversarial examples. [15] discovers that DALL-E 2 has certain hidden vocabularies that can be used to generate images with some absurd (non-natural) prompts; however, this vocabulary is often limited and not stealthy (natural). Built on evocative prompting, [36] crafts adversarial examples via the morphological similarity between existing words. However, it is very difficult to find texts with such linguistic similarity, and as a result, it can be challenging for this method to be adopted and generalized in different scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.263, + 0.473, + 0.414 + ], + "angle": 0, + "content": "2) Stealthiness. The existing approaches can only craft adversarial examples that appear to be non-natural compared to normal texts or retain similar meanings, making them easily filtered and recognized by human examiners. For example, [15] crafts Apoploe vesrreaaitais to represent bugs, and [36] crafts falaiscoglieklippantilado to represent cliff. Also, [36] combines creepy and spooky into creepokey to generate an image that looks creepy and scary, yet the inferred meaning of this new word is highly related to the generated image, limiting its stealthiness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.473, + 0.583 + ], + "angle": 0, + "content": "To address these challenges, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models using natural examples. To achieve this, we first formulate the generation of the adversarial examples as an optimization problem and apply genetic-based optimization methods to solve it, thus making our methods much more reliable in finding working adversarial examples. Furthermore, in order to improve the stealthiness, we propose a new text mutation technique to generate adversarial text that is visually and semantically similar to its normal version (some example results are shown in Figure 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.473, + 0.689 + ], + "angle": 0, + "content": "RIATIG is evaluated on six popular text-to-image models with both white-box and black-box attack settings. Experimental results show that compared with the state-of-the-art text-to-image-oriented adversarial attacks, RIATIG demonstrates significantly better performance in terms of attack effectiveness and sample quality. Overall, the contributions of this work are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.703, + 0.47, + 0.748 + ], + "angle": 0, + "content": "- We are the first to systematically analyze the adversarial robustness of text-to-image generation models in both the white-box and black-box settings." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.764, + 0.47, + 0.794 + ], + "angle": 0, + "content": "- We propose genetic-based optimization methods to find natural adversarial examples reliably." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.81, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We evaluate our attacks on six popular text-to-image generation models and compare our attacks with five baselines. The evaluation results show that our methods achieve a much higher success rate and sample quality, raising awareness of improving and securing the robustness of text-to-image models." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.703, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Text-to-Image Generation. The research towards text-to-image generation starts with the work proposed by Mansimov et al. [33], which extends the Deep Recurrent Attention Writer (DRAW) [20] model to condition on image captions using a soft attention mechanism. Xu et al. [52] further propose a multi-stage attentional GAN (AttnGAN) to force the model to focus on the fine-grained information at the word level, leading to the generation of more semantically matched images. To address the limitations of the multi-stage methods, e.g., low-quality initial images and repeated use of the same word representations, Zhu et al. [58] propose a dynamic memory GAN (DM-GAN), which uses a memory network to write and read encoded prior dynamically in each image-refined process. To further improve the quality of the generator, Tao et al. [49] propose a deep Fusion Generative Adversarial Network (DF-GAN) that performs deep fusion between text and visual features. Recently, a set of large-scale text-to-image generation models are proposed and released, demonstrating promising performance. DALL-E, an autoregressive transformer model trained on 250 million web-crawled image-text pairs [43], achieves zero-shot high-quality image generation on the MS-COCO dataset. Its updated version, DALL-E 2, adopts contrastive model CLIP [42]. By feeding a text caption and using a diffusion model to generate an image conditioned on the image embedding, DALL-E 2 can synthesize amazingly photorealistic images. Imagen is another state-of-the-art text-to-image generator built on the combination of a transformer trained on text data and a high-fidelity diffusion model, achieving a very high generation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Adversarial Attacks on Text-to-Image Generators. The adversarial robustness of text-to-image generation is a relatively less studied topic. [15] is the pioneering work that studies the vulnerability of text-to-image generators, such as DALL-E 2. They found it is possible to leverage gibberish text in the target image to evade content filters by using such gibberish texts as prompts rather than semantically equivalent text. However, most of the gibberish text does not reliably produce a specific category of images. Later, Millière proposes two methods of crafting adversarial text to generate specific pictures [36]. The first solution is macaronic prompting, which composes multilingual subword segments to generate specific types of images. The second approach is evocative prompting, a strategy that uses prompts possessing similarity of broad morphological features to generate semantic-consistent images with real concepts. In addition, Struppek shows that replacing a single character in the text with visually similar non-Latin characters can induce cultural biases into the generated images or even hide complete objects in the generated images. However, their method is untargeted, i.e., they cannot generate" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20586" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.089, + 0.462, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.186, + 0.451, + 0.201 + ], + "angle": 0, + "content": "Figure 2. Working mechanism of a text-to-image generator." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.224, + 0.299, + 0.24 + ], + "angle": 0, + "content": "specific attacker selected images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.251, + 0.32, + 0.269 + ], + "angle": 0, + "content": "3. System and Threat Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.47, + 0.508 + ], + "angle": 0, + "content": "Text-to-Image Generation Model. Figure 2 represents the working mechanism of text-to-image generation models considered in this work, consisting of three parts: a text encoder, a transformation network, and a decoder. In the text encoder, the text prompt is first converted to tokens by a tokenizer. Each token is mapped to a text encoding by looking up the mapping dictionary of the embedding models. The transformation model maps the text encoding to a corresponding image encoding that captures the semantic information contained in the text encoding. Finally, the decoder generates an image based on image encoding that is a visual representation of the text prompt. As shown in Figure 2, the image generated by DALL-E 2 with prompt A bowl of soup that is also a portal to another dimension is photorealistic and has aligned semantic meaning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.47, + 0.664 + ], + "angle": 0, + "content": "Threat Model. We consider both white-box and black-box settings to evaluate the different capabilities of the adversary. In the white-box setting, the adversary has full knowledge of the target model such as model architecture as well as its parameters. In the black-box setting, the adversary does not know the internal information of the model or training data. It is only capable of querying the model with supplied input and obtaining the output. Different from classification models [8, 21, 24, 28], the generation models cannot return confidence scores to the adversary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.673, + 0.212, + 0.691 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.698, + 0.28, + 0.714 + ], + "angle": 0, + "content": "4.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.721, + 0.47, + 0.873 + ], + "angle": 0, + "content": "A text-to-image generation model \\(\\mathcal{G}:\\mathcal{X}\\to \\mathcal{Y}\\) maps text space \\(\\mathcal{X}\\) to image space \\(\\mathcal{V}\\). Since \\(\\mathcal{G}\\) is trained on semantically-aligned text-image pairs, a well-trained model should generate images that are semantically identical to the input text. Given an arbitrary target image \\(y_{t}\\), which corresponds to its naive text prompt \\(x_{t}\\), the adversary aims to craft an adversarial example \\(x^{*}\\) that generates a semantically similar image to \\(y_{t}\\), with the premise that \\(x^{*}\\) is semantically dissimilar from \\(x_{t}\\) enough to evade detection. This is an optimization program that can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.88, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\underset {x ^ {*}} {\\operatorname {a r g m a x}} S _ {i} \\left(\\mathcal {G} \\left(x ^ {*}\\right), y _ {t}\\right) \\text {s . t .} D _ {t} \\left(x ^ {*}, x _ {t}\\right) > \\eta , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "where \\( S_{i} \\) is a semantic similarity function of images, \\( D_{t} \\) is a function measuring the semantic distance of texts, and \\( \\eta \\) is the threshold of the semantic dissimilarity of \\( x_{t} \\) and \\( x^{*} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.145, + 0.733, + 0.161 + ], + "angle": 0, + "content": "4.2. Challenges and Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Challenges. Designing a reliable and imperceptible adversarial attack against text-to-image models can face several challenges. Firstly, unlike existing work on textual adversarial attacks [8,24,28], where the output of the model is a finite number of classes (e.g., positive and negative in sentiment analysis), the output of a text-to-image model is a high-dimensional continuous class with nearly infinite combinations. This characteristic makes it difficult to measure the effectiveness of the attacks. One possible solution is to measure the semantic distance of images, however, existing approaches only focus on category-level semantic distance [11, 16], which cannot handle the complex sentence context similarity. For example, simply representing a blue double decker school bus parking in let by school bus will lose important context information such as the color, size of the bus, and its surrounding environment. Second, since words can serve as discrete tokens in a sentence, it is impossible to optimize the input words directly by computing the gradient of the loss function with respect to the input word even assuming white-box knowledge in the adversary [8]. Third, unlike image domains where small perturbations can go unnoticed, any changes in the text domain are perceptible [8,28,29] and easily detectable by human examiners." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.841 + ], + "angle": 0, + "content": "Attack Overview. We adopt a genetic-based approach to iteratively optimize the input samples towards the target samples, followed by a quality fine-tuning stage to further improve the imperceptibility. First, the mutation stage generates a large number of variants that are semantically and visually similar to the input text, then the text-to-image generation model outputs images accordingly. A similarity measurement is implemented to compute the quality of mutated examples, allowing us to select the best offspring, which will enter a crossover stage to exchange the desirable traits to obtain a better population for the next-round iteration. The loop ends when the generated images are highly similar to the target images yet the adversarial text is distinct from the target text. Then the result samples go through the quality fine-tuning stage where we propose two techniques to further improve the imperceptibility of adversarial examples. In the following section, we will first introduce the similarity measurement for the offspring selection (§4.3), then elaborate on the genetic-based optimization with mutation and crossover scheme (§4.4), before finally describing the sample quality improvement procedure (§4.5)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.724, + 0.864 + ], + "angle": 0, + "content": "4.3. Similarity Measurement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To find a suitable measurement metric, we need to consider the natural continuity of visual space and find a proper" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20587" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.211, + 0.398, + 0.225 + ], + "angle": 0, + "content": "Figure 3. Overview of the RIATIG attack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.435 + ], + "angle": 0, + "content": "representation of image semantic information. Recently, there is a growing research interest in learning image representation from text [40, 46, 57], which maps images into a semantic-rich embedding space by jointly learning with textual data. Among these efforts, the CLIP proposed by OpenAI has been trained on large-scale (i.e., 400 million) web-crawled image-text pairs [40], which can efficiently represent visual concepts aligned with the corresponding textual information. Motivated by its powerful capability, we adopt the pre-trained image encoder of CLIP to encode two images and then calculate the cosine distance between the encoded vectors measuring the similarity as" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.447, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\nS _ {i} (\\mathcal {G} (x), y) = \\frac {E _ {i} (\\mathcal {G} (x)) \\cdot E _ {i} (y)}{\\| E _ {i} (\\mathcal {G} (x)) \\| \\| E _ {i} (y) \\|.} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.492, + 0.47, + 0.522 + ], + "angle": 0, + "content": "Similarly, we utilize the text encoder to encode the text and calculate the cosine distance as their semantic distance," + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.533, + 0.47, + 0.567 + ], + "angle": 0, + "content": "\\[\nD _ {t} (x, x ^ {*}) = 1 - \\frac {E _ {t} (x) \\cdot E _ {t} \\left(x ^ {*}\\right)}{\\| E _ {t} (x) \\| \\| E _ {t} \\left(x ^ {*}\\right) \\|.} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.579, + 0.469, + 0.609 + ], + "angle": 0, + "content": "When the semantic distance is above a certain threshold, the two texts are considered not semantically similar." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.62, + 0.329, + 0.636 + ], + "angle": 0, + "content": "4.4. Genetic-based Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Genetic algorithms are heuristic optimization methods that are inspired by nature selection. By evolving a population of candidates towards better solutions with performing mutation and crossover [22], the genetic algorithms can search a large solution space effectively [25], making them well suited in the optimization over the multi-dimensional input space. Therefore, in this work, we adopt a genetic-based algorithm to solve the target optimization problem. To be specific, the optimization process starts with an input text that is semantically dissimilar from the target images. The mutation is used to generate different variants to explore the search space and increase the diversity of the population. To generate initial high-quality variants, RIATIG first generates a large pool of mutated candidates, rendering the execution of crossover and mutation more effective. In each generation, we select the samples with the highest fitness score for crossover and mutation to generate the next" + }, + { + "type": "code_caption", + "bbox": [ + 0.511, + 0.096, + 0.824, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Adversarial Example Generation" + }, + { + "type": "algorithm", + "bbox": [ + 0.504, + 0.113, + 0.867, + 0.447 + ], + "angle": 0, + "content": "1 Input: Original text \\(x\\) target text \\(x_{t}\\) with associated target image \\(y_{t}\\) mutation probability \\(p_m\\) population size \\(M,N,K\\) maximum iterations \\(c_{max}\\) ,control parameter \\(\\alpha ,\\beta\\) \n2 Output: Adversarial examples sets \\(T^{*}\\) \n3 \\(G_0\\gets \\text{Mutate}(x,p_m,M)\\triangleright\\) initialize population \n4 for \\(c = 0\\) to \\(c_{max}\\) do \n5 \\(Z_{c}\\gets S_{i}(\\mathcal{G}(G_{c}),yt)\\triangleright\\) update score by Eq.2 \n6 \\(I_{c}\\gets \\text{argsort}(Z_{c})[: - 1]\\) \n7 \\(E_{c}\\gets G_{c}[I_{c}][:K];F_{c}\\gets Z_{c}[I_{c}][:K]\\) \n8 \\(s_c\\gets F_c[0]^\\triangleright\\) For mutation prob update \n9 \\(p_m\\gets \\alpha \\cdot p_{m - 1} + \\frac{\\beta}{|s_c - s_{c - 1}|}\\) \n10 \\(P_{c}\\gets \\text{Softmax}(F_{c})\\triangleright\\) normalize to prob \n11 for \\(i = 1\\) to \\(N\\) do \n12 parent1,parent2 \\(\\leftarrow\\) Sample \\((E_c,P_c)\\triangleright\\) sample two parents from \\(E_{c}\\) with prob \\(P_{c}\\) \n13 childi \\(\\leftarrow\\) Crossover(parent1, parent2) \n14 gi \\(\\leftarrow\\) Mutate(childi,pm,1) \n15 \\(G_{c + 1}\\gets G_{c + 1}\\cup \\{g_i\\} \\triangleright\\) append to new generation \n16 if \\(S_{i}(\\mathcal{G}(g_{i}),y_{t}) > \\epsilon\\) and \\(D_t(g_i,x_t) > \\eta\\) then \n17 | \\(T\\gets T\\cup \\{g_i\\} \\triangleright\\) append to sample sets \n18 end \n19 end \n20 end \n21 \\(T^{*}\\gets \\text{FineTune}(T)\\triangleright\\) Fine tune samples by strategy in Section 4.5 \n22 return \\(T^{*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.527 + ], + "angle": 0, + "content": "generation of text samples. Cosine similarity scores calculated by Eq. 2 between the two images are the fitness score of the genetic algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.893, + 0.637 + ], + "angle": 0, + "content": "Crossover Scheme. Crossover is used to exchange the desirable traits between the chosen populations, thereby possibly generating an even better population. For the crossover scheme used in RIATIG, a new sentence is synthesized by a pair of parent sentences. The probability of each population being selected as a parent is proportional to their fitness score, giving the beneficial traits a higher probability to stay." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.777 + ], + "angle": 0, + "content": "Mutation Scheme. RIATIG performs sentence-level mutation. Each sentence has a mutation probability of \\( p_m \\) to be selected. The proper selection of \\( p_m \\) is very critical. When it is too high, the beneficial traits may be mutated without crossover to generate better offsprings. On the other hand, very small \\( p_m \\) will make most of the populations unchanged, causing insufficient mutations to escape the local maximum. To address the challenge, \\( p_m \\) can be adaptively updated using a momentum mutation-based method [50] by" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.787, + 0.891, + 0.82 + ], + "angle": 0, + "content": "\\[\np _ {m} = \\alpha \\cdot p _ {m - 1} + \\frac {\\beta}{\\left| S _ {i} - S _ {i - 1} \\right|}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.891, + 0.855 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are scaling factors, and \\(S_{i}\\) denotes the maximum fitness score across the populations in \\(i\\)-th generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The mutation process occurs for each selected sentence, which is divided into two stages. In the first stage, we identify the important words in the original sentence that need to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20588" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "be mutated. In the second stage, we propose two strategies to slightly modify a word while preserving its semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.473, + 0.262 + ], + "angle": 0, + "content": "Stage-1: Selection of Important Word. Because 1) the search space for mutation is very huge; and 2) most of the mutation variants do not play significant roles to improve the fitness score, identifying the most important words that contribute to fitness scores is crucial to improve the effectiveness of mutation. When we assume white-box knowledge, gradient information can be used to measure the importance, calculating the gradient of the fitness score with respect to the embedding of each word by" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.27, + 0.47, + 0.304 + ], + "angle": 0, + "content": "\\[\ng _ {x _ {n}} = \\frac {\\partial S _ {i} \\left(\\mathcal {G} \\left(e _ {n}\\right) , y _ {t}\\right)}{\\partial e _ {n}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.47, + 0.399 + ], + "angle": 0, + "content": "where \\( e_n \\) is the embedding of word \\( x_n \\), \\( y_t \\) is the target image, \\( \\mathcal{G} \\) is the generation model, and \\( S_i \\) is the semantic similarity function defined in Eq. 2. When we assume black-box knowledge, the importance of a word is estimated by calculating the change in fitness scores before and after deleting the word, such a calculation process is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.408, + 0.47, + 0.427 + ], + "angle": 0, + "content": "\\[\ng _ {x _ {n}} = S _ {i} (\\mathcal {G} (e), y _ {t}) - S _ {i} (\\mathcal {G} \\left(e _ {\\backslash e _ {n}}\\right), y _ {t}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.47, + 0.48 + ], + "angle": 0, + "content": "where \\( e \\) is the embedding vectors of sentence \\( x \\), \\( e \\backslash e_n \\) is the embedding vectors after deleting the word \\( x_n \\) from \\( x \\). After that, we normalize the important scores as" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.489, + 0.47, + 0.529 + ], + "angle": 0, + "content": "\\[\nI _ {x _ {n}} = \\frac {e ^ {\\| g _ {x _ {n}} \\|}}{\\sum_ {i = 1} ^ {N} e ^ {\\| g _ {x _ {i}} \\Vert}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.465, + 0.551 + ], + "angle": 0, + "content": "Then each word \\( x_{n} \\) has a probability of \\( I_{x_n} \\) to be selected." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Stage-2: Word Mutation. Since our goal is to generate adversarial text to be visually and semantically similar to normal text for human understanding, we consider two types of mutation strategies that are used in natural language processing fields [28,29,51]. The first one is to inject character-level typos that mimic the grammar mistakes people may make. The rationale is that the semantic meaning of the text is very likely to be preserved after a few character changes [44]. More specifically, we adopt three types of text manipulations: (1) Insert extra spaces into words; (2) Swap the position of two characters randomly except for the first and last characters; (3) Delete one random character except for the first and last characters. The second type of text manipulation is to replace characters/words with visually or semantically similar counterparts. As for visually similar substitution, we utilize the LEET Speak Alphabet [7], which replaces characters in ways that play on the similarity of glyphs. For example, we may replace the letter \\(l\\) with the number \\(l\\), the letter \\(o\\) with the number \\(o\\), etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "For the semantically similar substitution, we adopt the Word2vec model [34] to transform the words into embedding vectors, and then compute the cosine distance as the similarity measurement to select the nearest neighbors. A" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "threshold is used to filter out candidates with large distances. Due to the large search space of optimization, only replacing it with target-irrelevant sentences will weaken the mutation, making it hard to find variants that generate images closer to the target. To solve this problem, we use the target sentences to perform semantic substitution, and the words with a close distance are filtered out. In addition, we adopt the WordNet [35] to decide the part-of-speech (POS) tag of the word, filtering out the candidates with different POS to maintain grammatical fluency. After filtering, we select the top-M nearest neighbors into the candidate pool. Next, Google's one billion-word language model [13] is used to filter out words that do not fit within the context surroundings. To that end, we first fit words in the candidate pools with the surrounding context, then calculate their language scores that measure the fluency of the sentences, keeping the top-N word with the highest scores." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.358, + 0.766, + 0.375 + ], + "angle": 0, + "content": "4.5. Sample Quality Improvement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.76 + ], + "angle": 0, + "content": "After obtaining the adversarial examples, we further improve the quality of adversarial text based on two key observations. First, the presuppositions (e.g., on, in, etc.) in the sentences have little impact on the semantic meanings of generated images compared to the nouns and verbs. Second, the text embedding in the text-to-image generation model usually uses a dictionary to represent a finite set of possible words [52, 58], meaning that the deliberately misspell out-of-vocabulary will be mapped to unknown. With the first observation, we iteratively replace or add all predefined presuppositions in different positions of sentences and test their naturality. The presuppositions with the highest naturality are chosen to improve the samples. We then further fine-tune the quality of samples based on the second observation. For example, both paking and parnikg are out-of-vocabulary words that are mapped to the unknown, and they are regarded as the same words by the text-to-image generation models. However, since the first word has fewer modifications, it is closer to an ordinary text and is preferred. Therefore, with white-box knowledge, we can test whether the adversarial text is the out-of-vocabulary words by feeding it to the embedding models. In the black-box attack setting, we adopt the GloVe embedding models [38] pre-trained on the Common Crawl dataset containing 2.2 million vocabularies as a surrogate embedding model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.774, + 0.634, + 0.79 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.798, + 0.694, + 0.815 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset. We choose the initial texts, target texts, and target images from the Microsoft COCO [30] dataset, a popular benchmark for training and evaluating text-to-image generation models. The dataset includes 82,783 training images and 40,504 testing images, each with 5 text descriptions." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20589" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "Target Models. To evaluate the performance of our proposed attack, we choose three representative public text-to-image generation models: AttnGAN [52], DM-GAN [58], and DF-GAN [49]. We use the pre-trained models on the COCO dataset released in their official GitHub repository [1, 4, 5] as the target models. We also choose three large-scale proprietary models: DALL-E [43], DALL-E 2 [42], and Imagen [45]. None of the above have officially released their pre-trained models, nor public APIs except DALL-E 2. Therefore, for DALL-E, we adopt the released pre-trained models of DALL-E mini [3], which achieves comparable performance to that of DALL-E. Similarly, for Imagen, we adopt the pre-trained models released by Hugging Face [6]. For DALL-E 2, though a public API exists2, only 15 free credits are granted to each account, so we first train adversarial examples on LAION's pre-trained model [2], then access the APIs to check if it was transferred successfully." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.352, + 0.473, + 0.549 + ], + "angle": 0, + "content": "Evaluation Setup. In our experiment, we attacked the AttnGAN, DM-GAN, and DF-GAN in white-box settings, and we attacked DALL-E, DALL-E 2,Imagen in black-box settings, which means we can only query the model and get the generated images. We set the initial population size \\(M\\), the total population size \\(N\\), and the selected population size \\(K\\) to 300, 50, and 25, respectively. The initial mutation probability \\(p_m\\) is set to 0.8. Ten adversarial examples are generated for each model. For each generation, we randomly select a target image and a semantic unrelated text from the COCO dataset. For example, we select the target images with the meaning a clock is flying in the blue sky and the original text a red double decker bus parking in let." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.553, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Comparison with Baselines. To the best of our knowledge, there are only two related studies [15, 36] for a targeted adversarial attack against text-to-image generation models. [15] proposes a hidden vocabulary attack (HiddVocab) on DALL-E 2 and [36] implements macaronic prompting (MacPrompt) and evocative prompting (EvoPrompt) attacks against DALL-E mini and DALL-E 2. For a comprehensive comparison, we also include [48], which is a homolytic substitution-based attack (HomoSubs) to cause image content obfuscation. We also include one state-of-the-art textual adversarial attack, TextFooler [24]. Since their attack does not involve image generation, we change the posterior tasks to match our settings and apply our proposed similarity metric to guide the optimization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.775, + 0.262, + 0.79 + ], + "angle": 0, + "content": "5.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.798, + 0.47, + 0.859 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of our attack, we evaluate both attack effectiveness and adversarial sample imperceptibility. The imperceptibility measure consists of two parts: semantic meaning similarity and sentence naturality." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.862, + 0.47, + 0.878 + ], + "angle": 0, + "content": "Effectiveness of Generated Images. We adopt the method" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "of R-precision, a widely-used metric in text-to-image generation models [27, 39, 52, 54, 58] to measure whether the generated image is semantically aligned with the given text description. Specifically, we use the generated images to perform a retrieval experiment by querying a candidate set of text descriptions that consist of one ground truth and 99 randomly selected mismatched descriptions. The ViLT model [26], which achieves state-of-the-art performance on image-text retrieval tasks, is used here. We examine the top \\(R\\) ranked retrieval results and consider our attacks successful when the ground truth appears in the retrieval. We evaluate the effectiveness when R is 1 (R-1) and R is 3 (R-3)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.278, + 0.892, + 0.354 + ], + "angle": 0, + "content": "Sentence Semantic Meaning. Following [24, 28], we first adopt the Universal Sentence Encoder [12] to encode the adversarial sentence and target sentence into high dimensional vectors, and then their cosine similarity score are calculated to measure the semantic similarity." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.358, + 0.892, + 0.48 + ], + "angle": 0, + "content": "Sentence Naturality. The adversarial examples should look natural, similar to normal sentences in the real world. In our experiment, we calculate the perplexity (PPL) of the adversarial examples with GPT-2 [41], which is trained on a large corpus of real-world sentences. PPL measures how likely the model is to generate the input text sequence, representing the fluency of the adversarial examples. Generally, the sample with lower PPL is more natural." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.491, + 0.681, + 0.505 + ], + "angle": 0, + "content": "5.3. Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.519, + 0.892, + 0.777 + ], + "angle": 0, + "content": "White-box Attacks. The results for white-box attacks are shown in Table 1. It is seen that RIATIG succeeds in generating all adversarial examples in DM-GAN and DF-GAN, and can succeed in generating 9 out of 10 samples in AttnGAN when we examine top-3 recall results. The recall precision drops when we only examine top-1 recall results. This phenomenon might be caused by the image generation quality of the target model, since the DM-GAN and AttnGAN achieve an average R-precision of \\(85.47\\%\\) [52] and \\(88.56\\%\\) [58] on COCO datasets. Furthermore, a low semantic distance means there is a low semantic relevance between the adversarial text and the text used to generate the target images. The low PPL means our adversarial text is fluent and natural as compared to the normal text. On the other hand, due to the limited-size and monolingual datasets that these three models are trained on, the baselines can not succeed in generating adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.781, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Black-box Attacks. The results for black-box attacks are shown in Table 2. RIATIG achieves a high R-precision as compared to the baseline methods. HomoSubs and TextFooler are designed for untargeted attacks, and cannot be easily adapted for targeted attacks. HiddVocab does not provide a reliable method for finding adversarial examples and can achieve only a \\(40\\%\\) success rate against DALL-E 2. Though MacPrompt and EvoPrompt can achieve a higher" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.338, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)DALL·E 2 API: https://openai.com/dall-e-2/" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20590" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.885, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.189, + 0.289, + 0.778, + 0.304 + ], + "angle": 0, + "content": "Figure 4. Examples of our adversarial attack results against DALL-E mini, DALL-E 2, and Imagen." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.328, + 0.47, + 0.355 + ], + "angle": 0, + "content": "Table 1. The results of the white-box attacks against AttnGAN, DM-GAN, and DF-GAN." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.367, + 0.465, + 0.424 + ], + "angle": 0, + "content": "
ModelR-1 ↑R-3 ↑Semantic Distance ↓PPL ↓
AttnGAN [52]8/109/100.24522.63
DM-GAN [58]8/1010/100.27420.16
DF-GAN [49]9/1010/100.34558.81
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.097, + 0.425, + 0.468, + 0.446 + ], + "angle": 0, + "content": "Note: R-1 and R-3 represent the R-precision when \\( \\mathrm{R} = 1 \\) and \\( \\mathrm{R} = 3 \\), respectively. PPL represents the perplexity of sentences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.47, + 0.732 + ], + "angle": 0, + "content": "precision rate, due to their loosely formulated linguistic methods, MacPrompt and EvoPrompt do not always guarantee to find an adversarial example. In addition, MacPrompt adopts the compositional prompts by combining two semantically similar words resulting in a higher semantic distance. For example, it combines creepy and spooky into creepepy and uses the sentence A very creepepy person to generate a person that looks creepy and spooky. As a result, the semantic meaning between the adversarial examples and the target is still very close, making them highly perceptible. Also, these generated words can break the fluency and naturalness of the sentences, resulting in a high PPL. For EvoPrompt, since it relies on broad morphological similarity, the semantic difference is quite low. However, the crafted sentences can seem meaningless, again breaking the naturality of the sentences, e.g., using prompt rygamera pultris to generate the images of fishes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.746, + 0.231, + 0.763 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.775, + 0.468, + 0.882 + ], + "angle": 0, + "content": "Effectiveness of Mutation Strategy. To evaluate the effectiveness of our proposed mutation strategy, we conducted a comparative analysis with a random mutation approach, which employed insert, swap, and delete operations. Table 3 presents the results of our experiments, indicating that our mutations significantly outperformed random mutations, particularly in black-box settings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Influence of Target Images. To further analyze the im" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.328, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Table 2. The results of the black-box attacks against DALL-E mini, DALL-E 2, and Imagen." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.367, + 0.894, + 0.613 + ], + "angle": 0, + "content": "
ModelMethodsR-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DALL-E mini [43]HiddVocab [15]3/103/100.175284.78
MacPrompt [36]8/108/100.466814.61
EvoPrompt [36]6/106/100.145662.97
HomoSubs [48]0/100/100.091115.84
TextFooer [24]0/100/100.181848.41
RIATIG9/1010/100.27420.16
DALL-E 2 [42]HiddVocab [15]4/104/100.165162.71
MacPrompt [36]9/109/100.394931.31
EvoPrompt [36]7/107/100.176139.39
HomoSubs [48]0/100/100.06981.69
TextFooer [24]0/100/100.182624.88
RIATIG10/1010/100.27872.03
Imagen [45]HiddVocab [15]2/102/100.185073.74
MacPrompt [36]6/106/100.425694.73
EvoPrompt [36]4/104/100.165607.66
HomoSubs [48]0/100/100.081103.53
TextFooer [24]0/100/100.162231.10
RIATIG10/1010/100.23704.09
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.597, + 0.614, + 0.815, + 0.625 + ], + "angle": 0, + "content": "Note: Sem. Dist. represents semantic distance." + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.643, + 0.878, + 0.658 + ], + "angle": 0, + "content": "Table 3. Attack performance using random mutation strategy." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.668, + 0.88, + 0.726 + ], + "angle": 0, + "content": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DM-GAN7/108/100.14867.93
DF-GAN1/102/100.12882.80
DALL·E mini0/100/100.172111.82
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.742, + 0.892, + 0.771 + ], + "angle": 0, + "content": "Table 4. The mean and variance of evaluation metrics under different selections of target images." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.782, + 0.892, + 0.827 + ], + "angle": 0, + "content": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN9.2(±0.42)/109.8(±0.42)/100.31±0.04596.33±297.02
DALL-E mini9.7(±0.48)/109.9(±0.32)/100.28±0.03475.83±180.53
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "pact of target image selection on attack performance, we conducted ten experiments of the sample training process, with each experiment utilizing a different target image that" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20591" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.47, + 0.119 + ], + "angle": 0, + "content": "Table 5. The attack performance by using different substitution methods against DF-GAN and DALL-E mini." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.13, + 0.474, + 0.225 + ], + "angle": 0, + "content": "
ModelSub. Meth.R-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DF-GAN [49]Word2vec [34]9/1010/100.336558.81
Glove [34]8/109/100.331836.96
WordNet [35]5/107/100.358580.49
DALLE mini [43]Word2vec [34]9/1010/100.268420.16
Glove [34]7/109/100.311797.63
WordNet [35]4/106/100.368522.34
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.168, + 0.226, + 0.398, + 0.236 + ], + "angle": 0, + "content": "Note: Sub. Meth. represents substitution method." + }, + { + "type": "table_caption", + "bbox": [ + 0.088, + 0.25, + 0.458, + 0.265 + ], + "angle": 0, + "content": "Table 6. The attack performance of 50 additional experiments." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.275, + 0.458, + 0.322 + ], + "angle": 0, + "content": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN42/5046/500.22838.28
DALL·E mini45/5047/500.34640.78
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.468, + 0.392 + ], + "angle": 0, + "content": "shared the same semantic meaning. The results, as presented in Table 4, indicate that our attacks demonstrated high robustness across varying target images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.468, + 0.516 + ], + "angle": 0, + "content": "Robustness of Example Generation. One important property of RIATIG is that the adversarial text can be reliably associated with specific visual concepts when used as a prompt. We evaluated the sample robustness of DALL-E mini, DALL-E 2, andImagen. Specifically, we feed the same adversarial text to the target model ten times and calculated the average R-precision. The results show that RIATIG can achieve a \\(100\\%\\) R-3." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.519, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Different Substitution Methods. In our mutation strategy, one of the most important parts is the semantic word substitution, which is essential for optimizing the fitness scores and improving the sample quality. To identify a suitable approach for substitution, we evaluate three different approaches, namely Glove models [38], WordNet models [35] and Word2vec models [34]. We evaluate two target generation models (DF-GAN [49] and DALL-E mini [43]) in both white-box and black-box settings. For all three approaches, we select the substitute word from the top 30 results. For each target model and substitution approach, we start with ten identical benign text and target images and generate ten adversarial samples accordingly to evaluate the performance. The results are shown in Table 5. It is seen that Word2vec performs better than Glove and WordNet with respect to R-precision and PPL for the attack against DF-GAN, and Word2vec performs better than the others with respect to all three performance metrics when attacking DALL-E mini. We hypothesize that it is probably caused by the larger semantic vocabulary of Word2vec." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.468, + 0.903 + ], + "angle": 0, + "content": "Attack Performance with More Evaluations. To comprehensively evaluate the scalability of our attack, we trained 50 additional samples, each with distinct sources and targets. The results of this larger-scale evaluation are in Table 6, showing consistent performance of our attack strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.613, + 0.107 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.119, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Security Impacts. To prevent the malicious use of text-to-image generation models such as spreading misinformation (e.g., deepfake) [18], generating biased and inappropriate contents (e.g., stereotyping, pornography, violence) [10, 47], content moderation filters are deployed to filter harmful inputs. However, as we demonstrated, it is possible to craft a completely unrelated sentence to generate target images with black-box knowledge. Thus, it is important to consider the security risks of latest AI models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Possible Defense. There are several possible defenses. First, a rule-based text filter could be deployed to remove redundant spaces and wrong words before generating images. To evaluate this defense, we tested the adversarial text using Grammarly and found that \\(20\\%\\) of the samples could bypass the text filtering. For example, the sentence \"a fruit stand display with bananas and starlit skies\" was able to evade detection because this rule-based tool does not inspect the semantic meaning of the sentence. Second, one may consider using an image filter to prevent harmful images from being displayed to users. However, training such an image filter may require non-trivial efforts in collecting a large number of datasets. Moreover, the scope of harmful images can sometimes be difficult to define, such as with deep fake images. Another possible defense mechanism lies in the enhancement of the text-to-image generation models by adversarial training, which is one of the most effective defensive approaches against adversarial examples in the image and text domains [19, 24]. The model can be trained using both the original and adversarial text sharing the same associated images as the original text. However, it requires non-trivial efforts when facing a huge volume of adversarial examples as the modern text-to-image generation models are based on large-scale training datasets (e.g., Imagen [45] trains on about 460M image-text pairs)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.618, + 0.665 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.892, + 0.826 + ], + "angle": 0, + "content": "In this paper, we propose an adversarial attack against the text-to-image generation models. We propose a two-stage attack framework to craft an effective adversarial example, where we find a workable adversarial example in the first stage, followed by a sample quality fine-tuning in the second stage. Through extensive evaluation, we can generate highly natural and semantically unrelated examples, allowing for successful attacks. We hope this work will raise awareness of potential security risks and aid the development of more effective defenses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.845, + 0.892, + 0.89 + ], + "angle": 0, + "content": "Acknowledgments This work was partially supported by the NSF ( CNS-1916926, CNS-2038995, CNS-2154930, CNS-2229427, CNS-2238635), ARO (W911NF2010141)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20592" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Attngan implementation. https://github.com/taoxugit/AttnGAN. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.851 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20594" + } + ] +] \ No newline at end of file diff --git a/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_origin.pdf b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d4e4e19b9f19f672acecf9a729be73365f606002 --- /dev/null +++ b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/caa635c4-0250-4102-a574-c4d125a4109d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:070bdc56ed574d07a44ff078816eb94cecefa2f9ecd7609979a01e2ce29a74f5 +size 2712351 diff --git a/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/full.md b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1cde7cf9b709f0651979fb727e635e061f2732f0 --- /dev/null +++ b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/full.md @@ -0,0 +1,325 @@ +# RIATIG: Reliable and Imperceptible Adversarial Text-to-Image Generation with Natural Prompts + +Han Liu $^{1}$ , Yuhao Wu $^{1}$ , Shixuan Zhai $^{1}$ , Bo Yuan $^{2}$ , Ning Zhang $^{1}$ + +$^{1}$ Washington University in St. Louis, $^{2}$ Rutgers University + +{h.liul,yuhao.wu,zhais,zhang.ning}@wustl.edu,bo.yuan@soe.rutgers.edu + +# Abstract + +The field of text-to-image generation has made remarkable strides in creating high-fidelity and photorealistic images. As this technology gains popularity, there is a growing concern about its potential security risks. However, there has been limited exploration into the robustness of these models from an adversarial perspective. Existing research has primarily focused on untargeted settings, and lacks holistic consideration for reliability (attack success rate) and stealthiness (imperceptibility). + +In this paper, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models via inconspicuous examples. By formulating the example crafting as an optimization process and solving it using a genetic-based method, our proposed attack can generate imperceptible prompts for text-to-image generation models in a reliable way. Evaluation of six popular text-to-image generation models demonstrates the efficiency and stealthiness of our attack in both white-box and black-box settings. To allow the community to build on top of our findings, we've made the artifacts available1. + +# 1. Introduction + +The text-to-image generation has captured widespread attention from the research community with its creative and realistic image generation capability [52, 55, 56]. The ability to generate text-consistent images from natural language descriptions could potentially bring tremendous benefits to many areas of life, such as multimedia editing, computer-aided design, and art creation [23, 27, 37, 43]. + +Driven by recent advances in models trained with large datasets [42, 57] and multimodal learning [45] (e.g., diffusion models [17]), text-to-image generation has made significant progress in synthesizing high-fidelity and photorealistic images, such as DALL-E [43], DALL-E 2 [42] and Imagen [45]. At the same time, there are a growing num + +![](images/b94be0ae3da8f7e0d45a3b0f124aa802285a028829448d335a900d217bd75352.jpg) +Figure 1. Examples of RIATIG attacks. The top texts are the adversarial prompts, and the bottom texts are the target models. The first row represents the target images, while the second row represents the adversarial image generated by the prompt. + +ber of ethical concerns about the potential misuse of this technology [36,45,53]. Generative models could be used to generate synthetic video/audio/images of individuals (e.g., Deepfakes [14]), or synthetic contents with harmful stereotypes, violence, or obscenities [10, 45, 53]. To prevent the generation of such harmful content, content moderation filters are deployed in public APIs (e.g., DALL·E 2) to filter unsafe text prompts that may lead to harmful content. However, despite their best intentions, existing model-based text filters remain susceptible to adaptive adversarial attacks. + +Deep neural networks (DNNs) have been shown to be vulnerable to adversarial examples [9, 31, 32]. By applying these techniques, it is possible to craft an adversarial text that looks natural to bypass the content filters, yet generates a completely different category of potentially malicious images. However, the adversarial attacks on text-to-image generators are less explored. To the best of our knowledge, there are two closely related studies [15, 36]. Nevertheless, two challenges remain: + +1) Reliability. One significant limitation is that the existing works [15, 36] do not offer a reliable method to find adversarial examples. [15] discovers that DALL-E 2 has certain hidden vocabularies that can be used to generate images with some absurd (non-natural) prompts; however, this vocabulary is often limited and not stealthy (natural). Built on evocative prompting, [36] crafts adversarial examples via the morphological similarity between existing words. However, it is very difficult to find texts with such linguistic similarity, and as a result, it can be challenging for this method to be adopted and generalized in different scenarios. + +2) Stealthiness. The existing approaches can only craft adversarial examples that appear to be non-natural compared to normal texts or retain similar meanings, making them easily filtered and recognized by human examiners. For example, [15] crafts Apoploe vesrreaaitais to represent bugs, and [36] crafts falaiscoglieklippantilado to represent cliff. Also, [36] combines creepy and spooky into creepokey to generate an image that looks creepy and scary, yet the inferred meaning of this new word is highly related to the generated image, limiting its stealthiness. + +To address these challenges, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models using natural examples. To achieve this, we first formulate the generation of the adversarial examples as an optimization problem and apply genetic-based optimization methods to solve it, thus making our methods much more reliable in finding working adversarial examples. Furthermore, in order to improve the stealthiness, we propose a new text mutation technique to generate adversarial text that is visually and semantically similar to its normal version (some example results are shown in Figure 1). + +RIATIG is evaluated on six popular text-to-image models with both white-box and black-box attack settings. Experimental results show that compared with the state-of-the-art text-to-image-oriented adversarial attacks, RIATIG demonstrates significantly better performance in terms of attack effectiveness and sample quality. Overall, the contributions of this work are summarized as follows: + +- We are the first to systematically analyze the adversarial robustness of text-to-image generation models in both the white-box and black-box settings. +- We propose genetic-based optimization methods to find natural adversarial examples reliably. +- We evaluate our attacks on six popular text-to-image generation models and compare our attacks with five baselines. The evaluation results show that our methods achieve a much higher success rate and sample quality, raising awareness of improving and securing the robustness of text-to-image models. + +# 2. Related Work + +Text-to-Image Generation. The research towards text-to-image generation starts with the work proposed by Mansimov et al. [33], which extends the Deep Recurrent Attention Writer (DRAW) [20] model to condition on image captions using a soft attention mechanism. Xu et al. [52] further propose a multi-stage attentional GAN (AttnGAN) to force the model to focus on the fine-grained information at the word level, leading to the generation of more semantically matched images. To address the limitations of the multi-stage methods, e.g., low-quality initial images and repeated use of the same word representations, Zhu et al. [58] propose a dynamic memory GAN (DM-GAN), which uses a memory network to write and read encoded prior dynamically in each image-refined process. To further improve the quality of the generator, Tao et al. [49] propose a deep Fusion Generative Adversarial Network (DF-GAN) that performs deep fusion between text and visual features. Recently, a set of large-scale text-to-image generation models are proposed and released, demonstrating promising performance. DALL-E, an autoregressive transformer model trained on 250 million web-crawled image-text pairs [43], achieves zero-shot high-quality image generation on the MS-COCO dataset. Its updated version, DALL-E 2, adopts contrastive model CLIP [42]. By feeding a text caption and using a diffusion model to generate an image conditioned on the image embedding, DALL-E 2 can synthesize amazingly photorealistic images. Imagen is another state-of-the-art text-to-image generator built on the combination of a transformer trained on text data and a high-fidelity diffusion model, achieving a very high generation performance. + +Adversarial Attacks on Text-to-Image Generators. The adversarial robustness of text-to-image generation is a relatively less studied topic. [15] is the pioneering work that studies the vulnerability of text-to-image generators, such as DALL-E 2. They found it is possible to leverage gibberish text in the target image to evade content filters by using such gibberish texts as prompts rather than semantically equivalent text. However, most of the gibberish text does not reliably produce a specific category of images. Later, Millière proposes two methods of crafting adversarial text to generate specific pictures [36]. The first solution is macaronic prompting, which composes multilingual subword segments to generate specific types of images. The second approach is evocative prompting, a strategy that uses prompts possessing similarity of broad morphological features to generate semantic-consistent images with real concepts. In addition, Struppek shows that replacing a single character in the text with visually similar non-Latin characters can induce cultural biases into the generated images or even hide complete objects in the generated images. However, their method is untargeted, i.e., they cannot generate + +![](images/49f154a6fe6f50e7f75320193b801e4ae422265724547fc6fa6fe846e1d4379d.jpg) +Figure 2. Working mechanism of a text-to-image generator. + +specific attacker selected images. + +# 3. System and Threat Model + +Text-to-Image Generation Model. Figure 2 represents the working mechanism of text-to-image generation models considered in this work, consisting of three parts: a text encoder, a transformation network, and a decoder. In the text encoder, the text prompt is first converted to tokens by a tokenizer. Each token is mapped to a text encoding by looking up the mapping dictionary of the embedding models. The transformation model maps the text encoding to a corresponding image encoding that captures the semantic information contained in the text encoding. Finally, the decoder generates an image based on image encoding that is a visual representation of the text prompt. As shown in Figure 2, the image generated by DALL-E 2 with prompt A bowl of soup that is also a portal to another dimension is photorealistic and has aligned semantic meaning. + +Threat Model. We consider both white-box and black-box settings to evaluate the different capabilities of the adversary. In the white-box setting, the adversary has full knowledge of the target model such as model architecture as well as its parameters. In the black-box setting, the adversary does not know the internal information of the model or training data. It is only capable of querying the model with supplied input and obtaining the output. Different from classification models [8, 21, 24, 28], the generation models cannot return confidence scores to the adversary. + +# 4. Methodology + +# 4.1. Problem Formulation + +A text-to-image generation model $\mathcal{G}:\mathcal{X}\to \mathcal{Y}$ maps text space $\mathcal{X}$ to image space $\mathcal{V}$ . Since $\mathcal{G}$ is trained on semantically-aligned text-image pairs, a well-trained model should generate images that are semantically identical to the input text. Given an arbitrary target image $y_{t}$ , which corresponds to its naive text prompt $x_{t}$ , the adversary aims to craft an adversarial example $x^{*}$ that generates a semantically similar image to $y_{t}$ , with the premise that $x^{*}$ is semantically dissimilar from $x_{t}$ enough to evade detection. This is an optimization program that can be formulated as + +$$ +\underset {x ^ {*}} {\operatorname {a r g m a x}} S _ {i} \left(\mathcal {G} \left(x ^ {*}\right), y _ {t}\right) \text {s . t .} D _ {t} \left(x ^ {*}, x _ {t}\right) > \eta , \tag {1} +$$ + +where $S_{i}$ is a semantic similarity function of images, $D_{t}$ is a function measuring the semantic distance of texts, and $\eta$ is the threshold of the semantic dissimilarity of $x_{t}$ and $x^{*}$ . + +# 4.2. Challenges and Overview + +Challenges. Designing a reliable and imperceptible adversarial attack against text-to-image models can face several challenges. Firstly, unlike existing work on textual adversarial attacks [8,24,28], where the output of the model is a finite number of classes (e.g., positive and negative in sentiment analysis), the output of a text-to-image model is a high-dimensional continuous class with nearly infinite combinations. This characteristic makes it difficult to measure the effectiveness of the attacks. One possible solution is to measure the semantic distance of images, however, existing approaches only focus on category-level semantic distance [11, 16], which cannot handle the complex sentence context similarity. For example, simply representing a blue double decker school bus parking in let by school bus will lose important context information such as the color, size of the bus, and its surrounding environment. Second, since words can serve as discrete tokens in a sentence, it is impossible to optimize the input words directly by computing the gradient of the loss function with respect to the input word even assuming white-box knowledge in the adversary [8]. Third, unlike image domains where small perturbations can go unnoticed, any changes in the text domain are perceptible [8,28,29] and easily detectable by human examiners. + +Attack Overview. We adopt a genetic-based approach to iteratively optimize the input samples towards the target samples, followed by a quality fine-tuning stage to further improve the imperceptibility. First, the mutation stage generates a large number of variants that are semantically and visually similar to the input text, then the text-to-image generation model outputs images accordingly. A similarity measurement is implemented to compute the quality of mutated examples, allowing us to select the best offspring, which will enter a crossover stage to exchange the desirable traits to obtain a better population for the next-round iteration. The loop ends when the generated images are highly similar to the target images yet the adversarial text is distinct from the target text. Then the result samples go through the quality fine-tuning stage where we propose two techniques to further improve the imperceptibility of adversarial examples. In the following section, we will first introduce the similarity measurement for the offspring selection (§4.3), then elaborate on the genetic-based optimization with mutation and crossover scheme (§4.4), before finally describing the sample quality improvement procedure (§4.5). + +# 4.3. Similarity Measurement + +To find a suitable measurement metric, we need to consider the natural continuity of visual space and find a proper + +![](images/0f302ac0845059f8a31c02ec81b319ecdc1ecb0a119ba15d6feced44393b7e3b.jpg) +Figure 3. Overview of the RIATIG attack. + +representation of image semantic information. Recently, there is a growing research interest in learning image representation from text [40, 46, 57], which maps images into a semantic-rich embedding space by jointly learning with textual data. Among these efforts, the CLIP proposed by OpenAI has been trained on large-scale (i.e., 400 million) web-crawled image-text pairs [40], which can efficiently represent visual concepts aligned with the corresponding textual information. Motivated by its powerful capability, we adopt the pre-trained image encoder of CLIP to encode two images and then calculate the cosine distance between the encoded vectors measuring the similarity as + +$$ +S _ {i} (\mathcal {G} (x), y) = \frac {E _ {i} (\mathcal {G} (x)) \cdot E _ {i} (y)}{\| E _ {i} (\mathcal {G} (x)) \| \| E _ {i} (y) \|.} \tag {2} +$$ + +Similarly, we utilize the text encoder to encode the text and calculate the cosine distance as their semantic distance, + +$$ +D _ {t} (x, x ^ {*}) = 1 - \frac {E _ {t} (x) \cdot E _ {t} \left(x ^ {*}\right)}{\| E _ {t} (x) \| \| E _ {t} \left(x ^ {*}\right) \|.} \tag {3} +$$ + +When the semantic distance is above a certain threshold, the two texts are considered not semantically similar. + +# 4.4. Genetic-based Optimization + +Genetic algorithms are heuristic optimization methods that are inspired by nature selection. By evolving a population of candidates towards better solutions with performing mutation and crossover [22], the genetic algorithms can search a large solution space effectively [25], making them well suited in the optimization over the multi-dimensional input space. Therefore, in this work, we adopt a genetic-based algorithm to solve the target optimization problem. To be specific, the optimization process starts with an input text that is semantically dissimilar from the target images. The mutation is used to generate different variants to explore the search space and increase the diversity of the population. To generate initial high-quality variants, RIATIG first generates a large pool of mutated candidates, rendering the execution of crossover and mutation more effective. In each generation, we select the samples with the highest fitness score for crossover and mutation to generate the next + +Algorithm 1: Adversarial Example Generation +1 Input: Original text $x$ target text $x_{t}$ with associated target image $y_{t}$ mutation probability $p_m$ population size $M,N,K$ maximum iterations $c_{max}$ ,control parameter $\alpha ,\beta$ +2 Output: Adversarial examples sets $T^{*}$ +3 $G_0\gets \text{Mutate}(x,p_m,M)\triangleright$ initialize population +4 for $c = 0$ to $c_{max}$ do +5 $Z_{c}\gets S_{i}(\mathcal{G}(G_{c}),yt)\triangleright$ update score by Eq.2 +6 $I_{c}\gets \text{argsort}(Z_{c})[: - 1]$ +7 $E_{c}\gets G_{c}[I_{c}][:K];F_{c}\gets Z_{c}[I_{c}][:K]$ +8 $s_c\gets F_c[0]^\triangleright$ For mutation prob update +9 $p_m\gets \alpha \cdot p_{m - 1} + \frac{\beta}{|s_c - s_{c - 1}|}$ +10 $P_{c}\gets \text{Softmax}(F_{c})\triangleright$ normalize to prob +11 for $i = 1$ to $N$ do +12 parent1,parent2 $\leftarrow$ Sample $(E_c,P_c)\triangleright$ sample two parents from $E_{c}$ with prob $P_{c}$ +13 childi $\leftarrow$ Crossover(parent1, parent2) +14 gi $\leftarrow$ Mutate(childi,pm,1) +15 $G_{c + 1}\gets G_{c + 1}\cup \{g_i\} \triangleright$ append to new generation +16 if $S_{i}(\mathcal{G}(g_{i}),y_{t}) > \epsilon$ and $D_t(g_i,x_t) > \eta$ then +17 | $T\gets T\cup \{g_i\} \triangleright$ append to sample sets +18 end +19 end +20 end +21 $T^{*}\gets \text{FineTune}(T)\triangleright$ Fine tune samples by strategy in Section 4.5 +22 return $T^{*}$ + +generation of text samples. Cosine similarity scores calculated by Eq. 2 between the two images are the fitness score of the genetic algorithm. + +Crossover Scheme. Crossover is used to exchange the desirable traits between the chosen populations, thereby possibly generating an even better population. For the crossover scheme used in RIATIG, a new sentence is synthesized by a pair of parent sentences. The probability of each population being selected as a parent is proportional to their fitness score, giving the beneficial traits a higher probability to stay. + +Mutation Scheme. RIATIG performs sentence-level mutation. Each sentence has a mutation probability of $p_m$ to be selected. The proper selection of $p_m$ is very critical. When it is too high, the beneficial traits may be mutated without crossover to generate better offsprings. On the other hand, very small $p_m$ will make most of the populations unchanged, causing insufficient mutations to escape the local maximum. To address the challenge, $p_m$ can be adaptively updated using a momentum mutation-based method [50] by + +$$ +p _ {m} = \alpha \cdot p _ {m - 1} + \frac {\beta}{\left| S _ {i} - S _ {i - 1} \right|}, \tag {4} +$$ + +where $\alpha$ and $\beta$ are scaling factors, and $S_{i}$ denotes the maximum fitness score across the populations in $i$ -th generation. + +The mutation process occurs for each selected sentence, which is divided into two stages. In the first stage, we identify the important words in the original sentence that need to + +be mutated. In the second stage, we propose two strategies to slightly modify a word while preserving its semantics. + +Stage-1: Selection of Important Word. Because 1) the search space for mutation is very huge; and 2) most of the mutation variants do not play significant roles to improve the fitness score, identifying the most important words that contribute to fitness scores is crucial to improve the effectiveness of mutation. When we assume white-box knowledge, gradient information can be used to measure the importance, calculating the gradient of the fitness score with respect to the embedding of each word by + +$$ +g _ {x _ {n}} = \frac {\partial S _ {i} \left(\mathcal {G} \left(e _ {n}\right) , y _ {t}\right)}{\partial e _ {n}}, \tag {5} +$$ + +where $e_n$ is the embedding of word $x_n$ , $y_t$ is the target image, $\mathcal{G}$ is the generation model, and $S_i$ is the semantic similarity function defined in Eq. 2. When we assume black-box knowledge, the importance of a word is estimated by calculating the change in fitness scores before and after deleting the word, such a calculation process is defined as + +$$ +g _ {x _ {n}} = S _ {i} (\mathcal {G} (e), y _ {t}) - S _ {i} (\mathcal {G} \left(e _ {\backslash e _ {n}}\right), y _ {t}), \tag {6} +$$ + +where $e$ is the embedding vectors of sentence $x$ , $e \backslash e_n$ is the embedding vectors after deleting the word $x_n$ from $x$ . After that, we normalize the important scores as + +$$ +I _ {x _ {n}} = \frac {e ^ {\| g _ {x _ {n}} \|}}{\sum_ {i = 1} ^ {N} e ^ {\| g _ {x _ {i}} \Vert}}. \tag {7} +$$ + +Then each word $x_{n}$ has a probability of $I_{x_n}$ to be selected. + +Stage-2: Word Mutation. Since our goal is to generate adversarial text to be visually and semantically similar to normal text for human understanding, we consider two types of mutation strategies that are used in natural language processing fields [28,29,51]. The first one is to inject character-level typos that mimic the grammar mistakes people may make. The rationale is that the semantic meaning of the text is very likely to be preserved after a few character changes [44]. More specifically, we adopt three types of text manipulations: (1) Insert extra spaces into words; (2) Swap the position of two characters randomly except for the first and last characters; (3) Delete one random character except for the first and last characters. The second type of text manipulation is to replace characters/words with visually or semantically similar counterparts. As for visually similar substitution, we utilize the LEET Speak Alphabet [7], which replaces characters in ways that play on the similarity of glyphs. For example, we may replace the letter $l$ with the number $l$ , the letter $o$ with the number $o$ , etc. + +For the semantically similar substitution, we adopt the Word2vec model [34] to transform the words into embedding vectors, and then compute the cosine distance as the similarity measurement to select the nearest neighbors. A + +threshold is used to filter out candidates with large distances. Due to the large search space of optimization, only replacing it with target-irrelevant sentences will weaken the mutation, making it hard to find variants that generate images closer to the target. To solve this problem, we use the target sentences to perform semantic substitution, and the words with a close distance are filtered out. In addition, we adopt the WordNet [35] to decide the part-of-speech (POS) tag of the word, filtering out the candidates with different POS to maintain grammatical fluency. After filtering, we select the top-M nearest neighbors into the candidate pool. Next, Google's one billion-word language model [13] is used to filter out words that do not fit within the context surroundings. To that end, we first fit words in the candidate pools with the surrounding context, then calculate their language scores that measure the fluency of the sentences, keeping the top-N word with the highest scores. + +# 4.5. Sample Quality Improvement + +After obtaining the adversarial examples, we further improve the quality of adversarial text based on two key observations. First, the presuppositions (e.g., on, in, etc.) in the sentences have little impact on the semantic meanings of generated images compared to the nouns and verbs. Second, the text embedding in the text-to-image generation model usually uses a dictionary to represent a finite set of possible words [52, 58], meaning that the deliberately misspell out-of-vocabulary will be mapped to unknown. With the first observation, we iteratively replace or add all predefined presuppositions in different positions of sentences and test their naturality. The presuppositions with the highest naturality are chosen to improve the samples. We then further fine-tune the quality of samples based on the second observation. For example, both paking and parnikg are out-of-vocabulary words that are mapped to the unknown, and they are regarded as the same words by the text-to-image generation models. However, since the first word has fewer modifications, it is closer to an ordinary text and is preferred. Therefore, with white-box knowledge, we can test whether the adversarial text is the out-of-vocabulary words by feeding it to the embedding models. In the black-box attack setting, we adopt the GloVe embedding models [38] pre-trained on the Common Crawl dataset containing 2.2 million vocabularies as a surrogate embedding model. + +# 5. Experiments + +# 5.1. Experiment Settings + +Dataset. We choose the initial texts, target texts, and target images from the Microsoft COCO [30] dataset, a popular benchmark for training and evaluating text-to-image generation models. The dataset includes 82,783 training images and 40,504 testing images, each with 5 text descriptions. + +Target Models. To evaluate the performance of our proposed attack, we choose three representative public text-to-image generation models: AttnGAN [52], DM-GAN [58], and DF-GAN [49]. We use the pre-trained models on the COCO dataset released in their official GitHub repository [1, 4, 5] as the target models. We also choose three large-scale proprietary models: DALL-E [43], DALL-E 2 [42], and Imagen [45]. None of the above have officially released their pre-trained models, nor public APIs except DALL-E 2. Therefore, for DALL-E, we adopt the released pre-trained models of DALL-E mini [3], which achieves comparable performance to that of DALL-E. Similarly, for Imagen, we adopt the pre-trained models released by Hugging Face [6]. For DALL-E 2, though a public API exists2, only 15 free credits are granted to each account, so we first train adversarial examples on LAION's pre-trained model [2], then access the APIs to check if it was transferred successfully. + +Evaluation Setup. In our experiment, we attacked the AttnGAN, DM-GAN, and DF-GAN in white-box settings, and we attacked DALL-E, DALL-E 2,Imagen in black-box settings, which means we can only query the model and get the generated images. We set the initial population size $M$ , the total population size $N$ , and the selected population size $K$ to 300, 50, and 25, respectively. The initial mutation probability $p_m$ is set to 0.8. Ten adversarial examples are generated for each model. For each generation, we randomly select a target image and a semantic unrelated text from the COCO dataset. For example, we select the target images with the meaning a clock is flying in the blue sky and the original text a red double decker bus parking in let. + +Comparison with Baselines. To the best of our knowledge, there are only two related studies [15, 36] for a targeted adversarial attack against text-to-image generation models. [15] proposes a hidden vocabulary attack (HiddVocab) on DALL-E 2 and [36] implements macaronic prompting (MacPrompt) and evocative prompting (EvoPrompt) attacks against DALL-E mini and DALL-E 2. For a comprehensive comparison, we also include [48], which is a homolytic substitution-based attack (HomoSubs) to cause image content obfuscation. We also include one state-of-the-art textual adversarial attack, TextFooler [24]. Since their attack does not involve image generation, we change the posterior tasks to match our settings and apply our proposed similarity metric to guide the optimization. + +# 5.2. Evaluation Metrics + +To demonstrate the effectiveness of our attack, we evaluate both attack effectiveness and adversarial sample imperceptibility. The imperceptibility measure consists of two parts: semantic meaning similarity and sentence naturality. + +Effectiveness of Generated Images. We adopt the method + +of R-precision, a widely-used metric in text-to-image generation models [27, 39, 52, 54, 58] to measure whether the generated image is semantically aligned with the given text description. Specifically, we use the generated images to perform a retrieval experiment by querying a candidate set of text descriptions that consist of one ground truth and 99 randomly selected mismatched descriptions. The ViLT model [26], which achieves state-of-the-art performance on image-text retrieval tasks, is used here. We examine the top $R$ ranked retrieval results and consider our attacks successful when the ground truth appears in the retrieval. We evaluate the effectiveness when R is 1 (R-1) and R is 3 (R-3). + +Sentence Semantic Meaning. Following [24, 28], we first adopt the Universal Sentence Encoder [12] to encode the adversarial sentence and target sentence into high dimensional vectors, and then their cosine similarity score are calculated to measure the semantic similarity. + +Sentence Naturality. The adversarial examples should look natural, similar to normal sentences in the real world. In our experiment, we calculate the perplexity (PPL) of the adversarial examples with GPT-2 [41], which is trained on a large corpus of real-world sentences. PPL measures how likely the model is to generate the input text sequence, representing the fluency of the adversarial examples. Generally, the sample with lower PPL is more natural. + +# 5.3. Evaluation Results + +White-box Attacks. The results for white-box attacks are shown in Table 1. It is seen that RIATIG succeeds in generating all adversarial examples in DM-GAN and DF-GAN, and can succeed in generating 9 out of 10 samples in AttnGAN when we examine top-3 recall results. The recall precision drops when we only examine top-1 recall results. This phenomenon might be caused by the image generation quality of the target model, since the DM-GAN and AttnGAN achieve an average R-precision of $85.47\%$ [52] and $88.56\%$ [58] on COCO datasets. Furthermore, a low semantic distance means there is a low semantic relevance between the adversarial text and the text used to generate the target images. The low PPL means our adversarial text is fluent and natural as compared to the normal text. On the other hand, due to the limited-size and monolingual datasets that these three models are trained on, the baselines can not succeed in generating adversarial examples. + +Black-box Attacks. The results for black-box attacks are shown in Table 2. RIATIG achieves a high R-precision as compared to the baseline methods. HomoSubs and TextFooler are designed for untargeted attacks, and cannot be easily adapted for targeted attacks. HiddVocab does not provide a reliable method for finding adversarial examples and can achieve only a $40\%$ success rate against DALL-E 2. Though MacPrompt and EvoPrompt can achieve a higher + +![](images/9d1e9f183385f1f07534a2438542c43d3f87208d82ae891d37084f5768f761d5.jpg) +Figure 4. Examples of our adversarial attack results against DALL-E mini, DALL-E 2, and Imagen. + +Table 1. The results of the white-box attacks against AttnGAN, DM-GAN, and DF-GAN. + +
ModelR-1 ↑R-3 ↑Semantic Distance ↓PPL ↓
AttnGAN [52]8/109/100.24522.63
DM-GAN [58]8/1010/100.27420.16
DF-GAN [49]9/1010/100.34558.81
+ +Note: R-1 and R-3 represent the R-precision when $\mathrm{R} = 1$ and $\mathrm{R} = 3$ , respectively. PPL represents the perplexity of sentences. + +precision rate, due to their loosely formulated linguistic methods, MacPrompt and EvoPrompt do not always guarantee to find an adversarial example. In addition, MacPrompt adopts the compositional prompts by combining two semantically similar words resulting in a higher semantic distance. For example, it combines creepy and spooky into creepepy and uses the sentence A very creepepy person to generate a person that looks creepy and spooky. As a result, the semantic meaning between the adversarial examples and the target is still very close, making them highly perceptible. Also, these generated words can break the fluency and naturalness of the sentences, resulting in a high PPL. For EvoPrompt, since it relies on broad morphological similarity, the semantic difference is quite low. However, the crafted sentences can seem meaningless, again breaking the naturality of the sentences, e.g., using prompt rygamera pultris to generate the images of fishes. + +# 5.4. Ablation Study + +Effectiveness of Mutation Strategy. To evaluate the effectiveness of our proposed mutation strategy, we conducted a comparative analysis with a random mutation approach, which employed insert, swap, and delete operations. Table 3 presents the results of our experiments, indicating that our mutations significantly outperformed random mutations, particularly in black-box settings. + +Influence of Target Images. To further analyze the im + +Table 2. The results of the black-box attacks against DALL-E mini, DALL-E 2, and Imagen. + +
ModelMethodsR-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DALL-E mini [43]HiddVocab [15]3/103/100.175284.78
MacPrompt [36]8/108/100.466814.61
EvoPrompt [36]6/106/100.145662.97
HomoSubs [48]0/100/100.091115.84
TextFooer [24]0/100/100.181848.41
RIATIG9/1010/100.27420.16
DALL-E 2 [42]HiddVocab [15]4/104/100.165162.71
MacPrompt [36]9/109/100.394931.31
EvoPrompt [36]7/107/100.176139.39
HomoSubs [48]0/100/100.06981.69
TextFooer [24]0/100/100.182624.88
RIATIG10/1010/100.27872.03
Imagen [45]HiddVocab [15]2/102/100.185073.74
MacPrompt [36]6/106/100.425694.73
EvoPrompt [36]4/104/100.165607.66
HomoSubs [48]0/100/100.081103.53
TextFooer [24]0/100/100.162231.10
RIATIG10/1010/100.23704.09
+ +Note: Sem. Dist. represents semantic distance. + +Table 3. Attack performance using random mutation strategy. + +
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DM-GAN7/108/100.14867.93
DF-GAN1/102/100.12882.80
DALL·E mini0/100/100.172111.82
+ +Table 4. The mean and variance of evaluation metrics under different selections of target images. + +
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN9.2(±0.42)/109.8(±0.42)/100.31±0.04596.33±297.02
DALL-E mini9.7(±0.48)/109.9(±0.32)/100.28±0.03475.83±180.53
+ +pact of target image selection on attack performance, we conducted ten experiments of the sample training process, with each experiment utilizing a different target image that + +Table 5. The attack performance by using different substitution methods against DF-GAN and DALL-E mini. + +
ModelSub. Meth.R-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DF-GAN [49]Word2vec [34]9/1010/100.336558.81
Glove [34]8/109/100.331836.96
WordNet [35]5/107/100.358580.49
DALLE mini [43]Word2vec [34]9/1010/100.268420.16
Glove [34]7/109/100.311797.63
WordNet [35]4/106/100.368522.34
+ +Note: Sub. Meth. represents substitution method. + +Table 6. The attack performance of 50 additional experiments. + +
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN42/5046/500.22838.28
DALL·E mini45/5047/500.34640.78
+ +shared the same semantic meaning. The results, as presented in Table 4, indicate that our attacks demonstrated high robustness across varying target images. + +Robustness of Example Generation. One important property of RIATIG is that the adversarial text can be reliably associated with specific visual concepts when used as a prompt. We evaluated the sample robustness of DALL-E mini, DALL-E 2, andImagen. Specifically, we feed the same adversarial text to the target model ten times and calculated the average R-precision. The results show that RIATIG can achieve a $100\%$ R-3. + +Different Substitution Methods. In our mutation strategy, one of the most important parts is the semantic word substitution, which is essential for optimizing the fitness scores and improving the sample quality. To identify a suitable approach for substitution, we evaluate three different approaches, namely Glove models [38], WordNet models [35] and Word2vec models [34]. We evaluate two target generation models (DF-GAN [49] and DALL-E mini [43]) in both white-box and black-box settings. For all three approaches, we select the substitute word from the top 30 results. For each target model and substitution approach, we start with ten identical benign text and target images and generate ten adversarial samples accordingly to evaluate the performance. The results are shown in Table 5. It is seen that Word2vec performs better than Glove and WordNet with respect to R-precision and PPL for the attack against DF-GAN, and Word2vec performs better than the others with respect to all three performance metrics when attacking DALL-E mini. We hypothesize that it is probably caused by the larger semantic vocabulary of Word2vec. + +Attack Performance with More Evaluations. To comprehensively evaluate the scalability of our attack, we trained 50 additional samples, each with distinct sources and targets. The results of this larger-scale evaluation are in Table 6, showing consistent performance of our attack strategy. + +# 6. Discussion + +Security Impacts. To prevent the malicious use of text-to-image generation models such as spreading misinformation (e.g., deepfake) [18], generating biased and inappropriate contents (e.g., stereotyping, pornography, violence) [10, 47], content moderation filters are deployed to filter harmful inputs. However, as we demonstrated, it is possible to craft a completely unrelated sentence to generate target images with black-box knowledge. Thus, it is important to consider the security risks of latest AI models. + +Possible Defense. There are several possible defenses. First, a rule-based text filter could be deployed to remove redundant spaces and wrong words before generating images. To evaluate this defense, we tested the adversarial text using Grammarly and found that $20\%$ of the samples could bypass the text filtering. For example, the sentence "a fruit stand display with bananas and starlit skies" was able to evade detection because this rule-based tool does not inspect the semantic meaning of the sentence. Second, one may consider using an image filter to prevent harmful images from being displayed to users. However, training such an image filter may require non-trivial efforts in collecting a large number of datasets. Moreover, the scope of harmful images can sometimes be difficult to define, such as with deep fake images. Another possible defense mechanism lies in the enhancement of the text-to-image generation models by adversarial training, which is one of the most effective defensive approaches against adversarial examples in the image and text domains [19, 24]. The model can be trained using both the original and adversarial text sharing the same associated images as the original text. However, it requires non-trivial efforts when facing a huge volume of adversarial examples as the modern text-to-image generation models are based on large-scale training datasets (e.g., Imagen [45] trains on about 460M image-text pairs). + +# 7. Conclusion + +In this paper, we propose an adversarial attack against the text-to-image generation models. We propose a two-stage attack framework to craft an effective adversarial example, where we find a workable adversarial example in the first stage, followed by a sample quality fine-tuning in the second stage. Through extensive evaluation, we can generate highly natural and semantically unrelated examples, allowing for successful attacks. We hope this work will raise awareness of potential security risks and aid the development of more effective defenses. + +Acknowledgments This work was partially supported by the NSF ( CNS-1916926, CNS-2038995, CNS-2154930, CNS-2229427, CNS-2238635), ARO (W911NF2010141). + +# References + +[1] Attngan implementation. https://github.com/taoxugit/AttnGAN. Accessed: 2022-10-01. +[2] Dall-e 2 laion implementation. https://github.com/LAION-AI/dalle2-laion. Accessed: 2022-10-01. +[3] Dall-e mini implementation. https://github.com/borisdayma/dalle-mini. Accessed: 2022-10-01. +[4] Df-gan implementation. https://github.com/tobran/DF-GAN. Accessed: 2022-10-01. +[5] Dm-gan implementation. https://github.com/MinfengZhu/DM-GAN. Accessed: 2022-10-01. +[6]Imagen implementation. https://github.com/cene555/Imagen-pytorch. Accessed: 2022-10-01. +[7] Leet speak cheat sheet. https://www.gamehouse.com/blog/leet-speak-cheat-sheet/. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019. \ No newline at end of file diff --git a/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/images.zip b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ba1e784ba9167948e7eb41f129c17de01fa2df12 --- /dev/null +++ b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:56ef14da51a263cc7e64bf5f53fa530dd7f576e33200b6c309b6524ac84bf9e2 +size 401722 diff --git a/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/layout.json b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2993411d6b2eed35d880bece1d06e365cc36b756 --- /dev/null +++ b/2023/RIATIG_ Reliable and Imperceptible Adversarial Text-to-Image Generation With Natural Prompts/layout.json @@ -0,0 +1,8372 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 102, + 547, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 102, + 547, + 140 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 547, + 140 + ], + "type": "text", + "content": "RIATIG: Reliable and Imperceptible Adversarial Text-to-Image Generation with Natural Prompts" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "spans": [ + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "content": "Han Liu" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "content": ", Yuhao Wu" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "content": ", Shixuan Zhai" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "content": ", Bo Yuan" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "text", + "content": ", Ning Zhang" + }, + { + "bbox": [ + 144, + 160, + 447, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "spans": [ + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "type": "text", + "content": "Washington University in St. Louis, " + }, + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 157, + 175, + 436, + 190 + ], + "type": "text", + "content": "Rutgers University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 191, + 478, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 191, + 478, + 204 + ], + "spans": [ + { + "bbox": [ + 111, + 191, + 478, + 204 + ], + "type": "text", + "content": "{h.liul,yuhao.wu,zhais,zhang.ning}@wustl.edu,bo.yuan@soe.rutgers.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 256, + 289, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 364 + ], + "type": "text", + "content": "The field of text-to-image generation has made remarkable strides in creating high-fidelity and photorealistic images. As this technology gains popularity, there is a growing concern about its potential security risks. However, there has been limited exploration into the robustness of these models from an adversarial perspective. Existing research has primarily focused on untargeted settings, and lacks holistic consideration for reliability (attack success rate) and stealthiness (imperceptibility)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 365, + 289, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 496 + ], + "type": "text", + "content": "In this paper, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models via inconspicuous examples. By formulating the example crafting as an optimization process and solving it using a genetic-based method, our proposed attack can generate imperceptible prompts for text-to-image generation models in a reliable way. Evaluation of six popular text-to-image generation models demonstrates the efficiency and stealthiness of our attack in both white-box and black-box settings. To allow the community to build on top of our findings, we've made the artifacts available1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "type": "text", + "content": "The text-to-image generation has captured widespread attention from the research community with its creative and realistic image generation capability [52, 55, 56]. The ability to generate text-consistent images from natural language descriptions could potentially bring tremendous benefits to many areas of life, such as multimedia editing, computer-aided design, and art creation [23, 27, 37, 43]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 623, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 288, + 696 + ], + "type": "text", + "content": "Driven by recent advances in models trained with large datasets [42, 57] and multimodal learning [45] (e.g., diffusion models [17]), text-to-image generation has made significant progress in synthesizing high-fidelity and photorealistic images, such as DALL-E [43], DALL-E 2 [42] and Imagen [45]. At the same time, there are a growing num" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 232, + 544, + 403 + ], + "blocks": [ + { + "bbox": [ + 313, + 232, + 544, + 403 + ], + "lines": [ + { + "bbox": [ + 313, + 232, + 544, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 232, + 544, + 403 + ], + "type": "image", + "image_path": "b94be0ae3da8f7e0d45a3b0f124aa802285a028829448d335a900d217bd75352.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 412, + 547, + 458 + ], + "lines": [ + { + "bbox": [ + 305, + 412, + 547, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 547, + 458 + ], + "type": "text", + "content": "Figure 1. Examples of RIATIG attacks. The top texts are the adversarial prompts, and the bottom texts are the target models. The first row represents the target images, while the second row represents the adversarial image generated by the prompt." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 604 + ], + "type": "text", + "content": "ber of ethical concerns about the potential misuse of this technology [36,45,53]. Generative models could be used to generate synthetic video/audio/images of individuals (e.g., Deepfakes [14]), or synthetic contents with harmful stereotypes, violence, or obscenities [10, 45, 53]. To prevent the generation of such harmful content, content moderation filters are deployed in public APIs (e.g., DALL·E 2) to filter unsafe text prompts that may lead to harmful content. However, despite their best intentions, existing model-based text filters remain susceptible to adaptive adversarial attacks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "Deep neural networks (DNNs) have been shown to be vulnerable to adversarial examples [9, 31, 32]. By applying these techniques, it is possible to craft an adversarial text that looks natural to bypass the content filters, yet generates a completely different category of potentially malicious images. However, the adversarial attacks on text-to-image generators are less explored. To the best of our knowledge, there are two closely related studies [15, 36]. Nevertheless, two challenges remain:" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 270, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 270, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 270, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 702, + 270, + 713 + ], + "type": "text", + "content": "Code is available at: https://github.com/WUSTL-CSPL/RIATIG" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20585" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "1) Reliability. One significant limitation is that the existing works [15, 36] do not offer a reliable method to find adversarial examples. [15] discovers that DALL-E 2 has certain hidden vocabularies that can be used to generate images with some absurd (non-natural) prompts; however, this vocabulary is often limited and not stealthy (natural). Built on evocative prompting, [36] crafts adversarial examples via the morphological similarity between existing words. However, it is very difficult to find texts with such linguistic similarity, and as a result, it can be challenging for this method to be adopted and generalized in different scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 208, + 289, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 208, + 289, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 289, + 327 + ], + "type": "text", + "content": "2) Stealthiness. The existing approaches can only craft adversarial examples that appear to be non-natural compared to normal texts or retain similar meanings, making them easily filtered and recognized by human examiners. For example, [15] crafts Apoploe vesrreaaitais to represent bugs, and [36] crafts falaiscoglieklippantilado to represent cliff. Also, [36] combines creepy and spooky into creepokey to generate an image that looks creepy and scary, yet the inferred meaning of this new word is highly related to the generated image, limiting its stealthiness." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "text", + "content": "To address these challenges, we propose RIATIG, a reliable and imperceptible adversarial attack against text-to-image models using natural examples. To achieve this, we first formulate the generation of the adversarial examples as an optimization problem and apply genetic-based optimization methods to solve it, thus making our methods much more reliable in finding working adversarial examples. Furthermore, in order to improve the stealthiness, we propose a new text mutation technique to generate adversarial text that is visually and semantically similar to its normal version (some example results are shown in Figure 1)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 461, + 289, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 289, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 289, + 545 + ], + "type": "text", + "content": "RIATIG is evaluated on six popular text-to-image models with both white-box and black-box attack settings. Experimental results show that compared with the state-of-the-art text-to-image-oriented adversarial attacks, RIATIG demonstrates significantly better performance in terms of attack effectiveness and sample quality. Overall, the contributions of this work are summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 556, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 59, + 556, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 556, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 59, + 556, + 287, + 592 + ], + "type": "text", + "content": "- We are the first to systematically analyze the adversarial robustness of text-to-image generation models in both the white-box and black-box settings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 605, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 605, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 59, + 605, + 287, + 628 + ], + "type": "text", + "content": "- We propose genetic-based optimization methods to find natural adversarial examples reliably." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 641, + 287, + 713 + ], + "type": "text", + "content": "- We evaluate our attacks on six popular text-to-image generation models and compare our attacks with five baselines. The evaluation results show that our methods achieve a much higher success rate and sample quality, raising awareness of improving and securing the robustness of text-to-image models." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 97, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 547, + 456 + ], + "type": "text", + "content": "Text-to-Image Generation. The research towards text-to-image generation starts with the work proposed by Mansimov et al. [33], which extends the Deep Recurrent Attention Writer (DRAW) [20] model to condition on image captions using a soft attention mechanism. Xu et al. [52] further propose a multi-stage attentional GAN (AttnGAN) to force the model to focus on the fine-grained information at the word level, leading to the generation of more semantically matched images. To address the limitations of the multi-stage methods, e.g., low-quality initial images and repeated use of the same word representations, Zhu et al. [58] propose a dynamic memory GAN (DM-GAN), which uses a memory network to write and read encoded prior dynamically in each image-refined process. To further improve the quality of the generator, Tao et al. [49] propose a deep Fusion Generative Adversarial Network (DF-GAN) that performs deep fusion between text and visual features. Recently, a set of large-scale text-to-image generation models are proposed and released, demonstrating promising performance. DALL-E, an autoregressive transformer model trained on 250 million web-crawled image-text pairs [43], achieves zero-shot high-quality image generation on the MS-COCO dataset. Its updated version, DALL-E 2, adopts contrastive model CLIP [42]. By feeding a text caption and using a diffusion model to generate an image conditioned on the image embedding, DALL-E 2 can synthesize amazingly photorealistic images. Imagen is another state-of-the-art text-to-image generator built on the combination of a transformer trained on text data and a high-fidelity diffusion model, achieving a very high generation performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "Adversarial Attacks on Text-to-Image Generators. The adversarial robustness of text-to-image generation is a relatively less studied topic. [15] is the pioneering work that studies the vulnerability of text-to-image generators, such as DALL-E 2. They found it is possible to leverage gibberish text in the target image to evade content filters by using such gibberish texts as prompts rather than semantically equivalent text. However, most of the gibberish text does not reliably produce a specific category of images. Later, Millière proposes two methods of crafting adversarial text to generate specific pictures [36]. The first solution is macaronic prompting, which composes multilingual subword segments to generate specific types of images. The second approach is evocative prompting, a strategy that uses prompts possessing similarity of broad morphological features to generate semantic-consistent images with real concepts. In addition, Struppek shows that replacing a single character in the text with visually similar non-Latin characters can induce cultural biases into the generated images or even hide complete objects in the generated images. However, their method is untargeted, i.e., they cannot generate" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20586" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 282, + 139 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 282, + 139 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 282, + 139 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 282, + 139 + ], + "type": "image", + "image_path": "49f154a6fe6f50e7f75320193b801e4ae422265724547fc6fa6fe846e1d4379d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 147, + 276, + 159 + ], + "lines": [ + { + "bbox": [ + 58, + 147, + 276, + 159 + ], + "spans": [ + { + "bbox": [ + 58, + 147, + 276, + 159 + ], + "type": "text", + "content": "Figure 2. Working mechanism of a text-to-image generator." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 177, + 182, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 177, + 182, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 182, + 190 + ], + "type": "text", + "content": "specific attacker selected images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 198, + 195, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 195, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 195, + 213 + ], + "type": "text", + "content": "3. System and Threat Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 221, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 402 + ], + "type": "text", + "content": "Text-to-Image Generation Model. Figure 2 represents the working mechanism of text-to-image generation models considered in this work, consisting of three parts: a text encoder, a transformation network, and a decoder. In the text encoder, the text prompt is first converted to tokens by a tokenizer. Each token is mapped to a text encoding by looking up the mapping dictionary of the embedding models. The transformation model maps the text encoding to a corresponding image encoding that captures the semantic information contained in the text encoding. Finally, the decoder generates an image based on image encoding that is a visual representation of the text prompt. As shown in Figure 2, the image generated by DALL-E 2 with prompt A bowl of soup that is also a portal to another dimension is photorealistic and has aligned semantic meaning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 525 + ], + "type": "text", + "content": "Threat Model. We consider both white-box and black-box settings to evaluate the different capabilities of the adversary. In the white-box setting, the adversary has full knowledge of the target model such as model architecture as well as its parameters. In the black-box setting, the adversary does not know the internal information of the model or training data. It is only capable of querying the model with supplied input and obtaining the output. Different from classification models [8, 21, 24, 28], the generation models cannot return confidence scores to the adversary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 129, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 129, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 129, + 547 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 552, + 171, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 171, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 171, + 565 + ], + "type": "text", + "content": "4.1. Problem Formulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": "A text-to-image generation model " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{G}:\\mathcal{X}\\to \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " maps text space " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " to image space " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " is trained on semantically-aligned text-image pairs, a well-trained model should generate images that are semantically identical to the input text. Given an arbitrary target image " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": ", which corresponds to its naive text prompt " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": ", the adversary aims to craft an adversarial example " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "x^{*}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " that generates a semantically similar image to " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": ", with the premise that " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "x^{*}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " is semantically dissimilar from " + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 46, + 571, + 287, + 691 + ], + "type": "text", + "content": " enough to evade detection. This is an optimization program that can be formulated as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 79, + 696, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 696, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 79, + 696, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\underset {x ^ {*}} {\\operatorname {a r g m a x}} S _ {i} \\left(\\mathcal {G} \\left(x ^ {*}\\right), y _ {t}\\right) \\text {s . t .} D _ {t} \\left(x ^ {*}, x _ {t}\\right) > \\eta , \\tag {1}", + "image_path": "3865df9fe7484d3fb36c05fabfc8997e506231a035c3c7b03a88927ee1258ba6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " is a semantic similarity function of images, " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " is a function measuring the semantic distance of texts, and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " is the threshold of the semantic dissimilarity of " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "x^{*}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 114, + 448, + 127 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 114, + 448, + 127 + ], + "spans": [ + { + "bbox": [ + 306, + 114, + 448, + 127 + ], + "type": "text", + "content": "4.2. Challenges and Overview" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 135, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 545, + 411 + ], + "type": "text", + "content": "Challenges. Designing a reliable and imperceptible adversarial attack against text-to-image models can face several challenges. Firstly, unlike existing work on textual adversarial attacks [8,24,28], where the output of the model is a finite number of classes (e.g., positive and negative in sentiment analysis), the output of a text-to-image model is a high-dimensional continuous class with nearly infinite combinations. This characteristic makes it difficult to measure the effectiveness of the attacks. One possible solution is to measure the semantic distance of images, however, existing approaches only focus on category-level semantic distance [11, 16], which cannot handle the complex sentence context similarity. For example, simply representing a blue double decker school bus parking in let by school bus will lose important context information such as the color, size of the bus, and its surrounding environment. Second, since words can serve as discrete tokens in a sentence, it is impossible to optimize the input words directly by computing the gradient of the loss function with respect to the input word even assuming white-box knowledge in the adversary [8]. Third, unlike image domains where small perturbations can go unnoticed, any changes in the text domain are perceptible [8,28,29] and easily detectable by human examiners." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 414, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 666 + ], + "type": "text", + "content": "Attack Overview. We adopt a genetic-based approach to iteratively optimize the input samples towards the target samples, followed by a quality fine-tuning stage to further improve the imperceptibility. First, the mutation stage generates a large number of variants that are semantically and visually similar to the input text, then the text-to-image generation model outputs images accordingly. A similarity measurement is implemented to compute the quality of mutated examples, allowing us to select the best offspring, which will enter a crossover stage to exchange the desirable traits to obtain a better population for the next-round iteration. The loop ends when the generated images are highly similar to the target images yet the adversarial text is distinct from the target text. Then the result samples go through the quality fine-tuning stage where we propose two techniques to further improve the imperceptibility of adversarial examples. In the following section, we will first introduce the similarity measurement for the offspring selection (§4.3), then elaborate on the genetic-based optimization with mutation and crossover scheme (§4.4), before finally describing the sample quality improvement procedure (§4.5)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 443, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 443, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 443, + 684 + ], + "type": "text", + "content": "4.3. Similarity Measurement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "To find a suitable measurement metric, we need to consider the natural continuity of visual space and find a proper" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20587" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 286, + 158 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 158 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 158 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 158 + ], + "type": "image", + "image_path": "0f302ac0845059f8a31c02ec81b319ecdc1ecb0a119ba15d6feced44393b7e3b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 167, + 243, + 178 + ], + "lines": [ + { + "bbox": [ + 89, + 167, + 243, + 178 + ], + "spans": [ + { + "bbox": [ + 89, + 167, + 243, + 178 + ], + "type": "text", + "content": "Figure 3. Overview of the RIATIG attack." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 201, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 344 + ], + "type": "text", + "content": "representation of image semantic information. Recently, there is a growing research interest in learning image representation from text [40, 46, 57], which maps images into a semantic-rich embedding space by jointly learning with textual data. Among these efforts, the CLIP proposed by OpenAI has been trained on large-scale (i.e., 400 million) web-crawled image-text pairs [40], which can efficiently represent visual concepts aligned with the corresponding textual information. Motivated by its powerful capability, we adopt the pre-trained image encoder of CLIP to encode two images and then calculate the cosine distance between the encoded vectors measuring the similarity as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 354, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 354, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 91, + 354, + 287, + 380 + ], + "type": "interline_equation", + "content": "S _ {i} (\\mathcal {G} (x), y) = \\frac {E _ {i} (\\mathcal {G} (x)) \\cdot E _ {i} (y)}{\\| E _ {i} (\\mathcal {G} (x)) \\| \\| E _ {i} (y) \\|.} \\tag {2}", + "image_path": "dcbffb1a7edb8b1ce6c028e47de5a99656cb8debdd036f1e5ef856b15aab993d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 389, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 287, + 413 + ], + "type": "text", + "content": "Similarly, we utilize the text encoder to encode the text and calculate the cosine distance as their semantic distance," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 91, + 422, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 422, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 91, + 422, + 287, + 449 + ], + "type": "interline_equation", + "content": "D _ {t} (x, x ^ {*}) = 1 - \\frac {E _ {t} (x) \\cdot E _ {t} \\left(x ^ {*}\\right)}{\\| E _ {t} (x) \\| \\| E _ {t} \\left(x ^ {*}\\right) \\|.} \\tag {3}", + "image_path": "fda53ef323750c4bb98c6308954c8a8508fc1aab08e04fe6390de85668649385.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 458, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 287, + 482 + ], + "type": "text", + "content": "When the semantic distance is above a certain threshold, the two texts are considered not semantically similar." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 491, + 201, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 201, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 201, + 503 + ], + "type": "text", + "content": "4.4. Genetic-based Optimization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "Genetic algorithms are heuristic optimization methods that are inspired by nature selection. By evolving a population of candidates towards better solutions with performing mutation and crossover [22], the genetic algorithms can search a large solution space effectively [25], making them well suited in the optimization over the multi-dimensional input space. Therefore, in this work, we adopt a genetic-based algorithm to solve the target optimization problem. To be specific, the optimization process starts with an input text that is semantically dissimilar from the target images. The mutation is used to generate different variants to explore the search space and increase the diversity of the population. To generate initial high-quality variants, RIATIG first generates a large pool of mutated candidates, rendering the execution of crossover and mutation more effective. In each generation, we select the samples with the highest fitness score for crossover and mutation to generate the next" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 308, + 89, + 530, + 354 + ], + "blocks": [ + { + "bbox": [ + 312, + 76, + 504, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 76, + 504, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 76, + 504, + 87 + ], + "type": "text", + "content": "Algorithm 1: Adversarial Example Generation" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "lines": [ + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "spans": [ + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": "1 Input: Original text " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " target text " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " with associated target image " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " mutation probability " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " population size " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "M,N,K" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " maximum iterations " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "c_{max}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " ,control parameter " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "\\alpha ,\\beta" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n2 Output: Adversarial examples sets " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "T^{*}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n3 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "G_0\\gets \\text{Mutate}(x,p_m,M)\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " initialize population \n4 for " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "c = 0" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "c_{max}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " do \n5 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "Z_{c}\\gets S_{i}(\\mathcal{G}(G_{c}),yt)\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " update score by Eq.2 \n6 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "I_{c}\\gets \\text{argsort}(Z_{c})[: - 1]" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n7 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "E_{c}\\gets G_{c}[I_{c}][:K];F_{c}\\gets Z_{c}[I_{c}][:K]" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n8 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "s_c\\gets F_c[0]^\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " For mutation prob update \n9 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "p_m\\gets \\alpha \\cdot p_{m - 1} + \\frac{\\beta}{|s_c - s_{c - 1}|}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n10 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "P_{c}\\gets \\text{Softmax}(F_{c})\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " normalize to prob \n11 for " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " do \n12 parent1,parent2 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " Sample " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "(E_c,P_c)\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " sample two parents from " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "E_{c}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " with prob " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "P_{c}" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " \n13 childi " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " Crossover(parent1, parent2) \n14 gi " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " Mutate(childi,pm,1) \n15 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "G_{c + 1}\\gets G_{c + 1}\\cup \\{g_i\\} \\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " append to new generation \n16 if " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "S_{i}(\\mathcal{G}(g_{i}),y_{t}) > \\epsilon" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "D_t(g_i,x_t) > \\eta" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " then \n17 | " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "T\\gets T\\cup \\{g_i\\} \\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " append to sample sets \n18 end \n19 end \n20 end \n21 " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "T^{*}\\gets \\text{FineTune}(T)\\triangleright" + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "text", + "content": " Fine tune samples by strategy in Section 4.5 \n22 return " + }, + { + "bbox": [ + 308, + 89, + 530, + 354 + ], + "type": "inline_equation", + "content": "T^{*}" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 380, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 417 + ], + "type": "text", + "content": "generation of text samples. Cosine similarity scores calculated by Eq. 2 between the two images are the fitness score of the genetic algorithm." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 420, + 546, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 546, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 546, + 504 + ], + "type": "text", + "content": "Crossover Scheme. Crossover is used to exchange the desirable traits between the chosen populations, thereby possibly generating an even better population. For the crossover scheme used in RIATIG, a new sentence is synthesized by a pair of parent sentences. The probability of each population being selected as a parent is proportional to their fitness score, giving the beneficial traits a higher probability to stay." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "content": "Mutation Scheme. RIATIG performs sentence-level mutation. Each sentence has a mutation probability of " + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "content": " to be selected. The proper selection of " + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "content": " is very critical. When it is too high, the beneficial traits may be mutated without crossover to generate better offsprings. On the other hand, very small " + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "content": " will make most of the populations unchanged, causing insufficient mutations to escape the local maximum. To address the challenge, " + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 304, + 506, + 545, + 615 + ], + "type": "text", + "content": " can be adaptively updated using a momentum mutation-based method [50] by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 623, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 623, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 359, + 623, + 545, + 649 + ], + "type": "interline_equation", + "content": "p _ {m} = \\alpha \\cdot p _ {m - 1} + \\frac {\\beta}{\\left| S _ {i} - S _ {i - 1} \\right|}, \\tag {4}", + "image_path": "4605f9641bc1eb0655a94e8c3c9c5c0bb8000506af717f472981f06d534c6a08.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": " are scaling factors, and " + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": " denotes the maximum fitness score across the populations in " + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": "-th generation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "The mutation process occurs for each selected sentence, which is divided into two stages. In the first stage, we identify the important words in the original sentence that need to" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20588" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "be mutated. In the second stage, we propose two strategies to slightly modify a word while preserving its semantics." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 289, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 289, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 289, + 207 + ], + "type": "text", + "content": "Stage-1: Selection of Important Word. Because 1) the search space for mutation is very huge; and 2) most of the mutation variants do not play significant roles to improve the fitness score, identifying the most important words that contribute to fitness scores is crucial to improve the effectiveness of mutation. When we assume white-box knowledge, gradient information can be used to measure the importance, calculating the gradient of the fitness score with respect to the embedding of each word by" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 118, + 213, + 287, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 213, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 118, + 213, + 287, + 240 + ], + "type": "interline_equation", + "content": "g _ {x _ {n}} = \\frac {\\partial S _ {i} \\left(\\mathcal {G} \\left(e _ {n}\\right) , y _ {t}\\right)}{\\partial e _ {n}}, \\tag {5}", + "image_path": "2c0e122082e276ac4bc14de7e423b4e7e24baec903be018518e08e68fcbc3cf0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "e_n" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " is the embedding of word " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "x_n" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "y_t" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " is the target image, " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " is the generation model, and " + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 46, + 243, + 287, + 316 + ], + "type": "text", + "content": " is the semantic similarity function defined in Eq. 2. When we assume black-box knowledge, the importance of a word is estimated by calculating the change in fitness scores before and after deleting the word, such a calculation process is defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 323, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 323, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 88, + 323, + 287, + 338 + ], + "type": "interline_equation", + "content": "g _ {x _ {n}} = S _ {i} (\\mathcal {G} (e), y _ {t}) - S _ {i} (\\mathcal {G} \\left(e _ {\\backslash e _ {n}}\\right), y _ {t}), \\tag {6}", + "image_path": "33d08511b289f6b5a685e174bc783b7614f3b66463f96455ac068497483435f0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": " is the embedding vectors of sentence " + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "inline_equation", + "content": "e \\backslash e_n" + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": " is the embedding vectors after deleting the word " + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "inline_equation", + "content": "x_n" + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 344, + 287, + 380 + ], + "type": "text", + "content": ". After that, we normalize the important scores as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 387, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 387, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 123, + 387, + 287, + 418 + ], + "type": "interline_equation", + "content": "I _ {x _ {n}} = \\frac {e ^ {\\| g _ {x _ {n}} \\|}}{\\sum_ {i = 1} ^ {N} e ^ {\\| g _ {x _ {i}} \\Vert}}. \\tag {7}", + "image_path": "9e9701a6ea82841887d1e932f1d4583c8ac3403fac9395e9519690b302baabc3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "text", + "content": "Then each word " + }, + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "text", + "content": " has a probability of " + }, + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "inline_equation", + "content": "I_{x_n}" + }, + { + "bbox": [ + 46, + 423, + 284, + 436 + ], + "type": "text", + "content": " to be selected." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "content": "Stage-2: Word Mutation. Since our goal is to generate adversarial text to be visually and semantically similar to normal text for human understanding, we consider two types of mutation strategies that are used in natural language processing fields [28,29,51]. The first one is to inject character-level typos that mimic the grammar mistakes people may make. The rationale is that the semantic meaning of the text is very likely to be preserved after a few character changes [44]. More specifically, we adopt three types of text manipulations: (1) Insert extra spaces into words; (2) Swap the position of two characters randomly except for the first and last characters; (3) Delete one random character except for the first and last characters. The second type of text manipulation is to replace characters/words with visually or semantically similar counterparts. As for visually similar substitution, we utilize the LEET Speak Alphabet [7], which replaces characters in ways that play on the similarity of glyphs. For example, we may replace the letter " + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "content": " with the number " + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "content": ", the letter " + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "content": " with the number " + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 437, + 287, + 664 + ], + "type": "text", + "content": ", etc." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "For the semantically similar substitution, we adopt the Word2vec model [34] to transform the words into embedding vectors, and then compute the cosine distance as the similarity measurement to select the nearest neighbors. A" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "threshold is used to filter out candidates with large distances. Due to the large search space of optimization, only replacing it with target-irrelevant sentences will weaken the mutation, making it hard to find variants that generate images closer to the target. To solve this problem, we use the target sentences to perform semantic substitution, and the words with a close distance are filtered out. In addition, we adopt the WordNet [35] to decide the part-of-speech (POS) tag of the word, filtering out the candidates with different POS to maintain grammatical fluency. After filtering, we select the top-M nearest neighbors into the candidate pool. Next, Google's one billion-word language model [13] is used to filter out words that do not fit within the context surroundings. To that end, we first fit words in the candidate pools with the surrounding context, then calculate their language scores that measure the fluency of the sentences, keeping the top-N word with the highest scores." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 283, + 468, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 283, + 468, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 468, + 297 + ], + "type": "text", + "content": "4.5. Sample Quality Improvement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 302, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 601 + ], + "type": "text", + "content": "After obtaining the adversarial examples, we further improve the quality of adversarial text based on two key observations. First, the presuppositions (e.g., on, in, etc.) in the sentences have little impact on the semantic meanings of generated images compared to the nouns and verbs. Second, the text embedding in the text-to-image generation model usually uses a dictionary to represent a finite set of possible words [52, 58], meaning that the deliberately misspell out-of-vocabulary will be mapped to unknown. With the first observation, we iteratively replace or add all predefined presuppositions in different positions of sentences and test their naturality. The presuppositions with the highest naturality are chosen to improve the samples. We then further fine-tune the quality of samples based on the second observation. For example, both paking and parnikg are out-of-vocabulary words that are mapped to the unknown, and they are regarded as the same words by the text-to-image generation models. However, since the first word has fewer modifications, it is closer to an ordinary text and is preferred. Therefore, with white-box knowledge, we can test whether the adversarial text is the out-of-vocabulary words by feeding it to the embedding models. In the black-box attack setting, we adopt the GloVe embedding models [38] pre-trained on the Common Crawl dataset containing 2.2 million vocabularies as a surrogate embedding model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 613, + 388, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 613, + 388, + 625 + ], + "spans": [ + { + "bbox": [ + 305, + 613, + 388, + 625 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 632, + 424, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 424, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 424, + 645 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Dataset. We choose the initial texts, target texts, and target images from the Microsoft COCO [30] dataset, a popular benchmark for training and evaluating text-to-image generation models. The dataset includes 82,783 training images and 40,504 testing images, each with 5 text descriptions." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20589" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": "Target Models. To evaluate the performance of our proposed attack, we choose three representative public text-to-image generation models: AttnGAN [52], DM-GAN [58], and DF-GAN [49]. We use the pre-trained models on the COCO dataset released in their official GitHub repository [1, 4, 5] as the target models. We also choose three large-scale proprietary models: DALL-E [43], DALL-E 2 [42], and Imagen [45]. None of the above have officially released their pre-trained models, nor public APIs except DALL-E 2. Therefore, for DALL-E, we adopt the released pre-trained models of DALL-E mini [3], which achieves comparable performance to that of DALL-E. Similarly, for Imagen, we adopt the pre-trained models released by Hugging Face [6]. For DALL-E 2, though a public API exists2, only 15 free credits are granted to each account, so we first train adversarial examples on LAION's pre-trained model [2], then access the APIs to check if it was transferred successfully." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "content": "Evaluation Setup. In our experiment, we attacked the AttnGAN, DM-GAN, and DF-GAN in white-box settings, and we attacked DALL-E, DALL-E 2,Imagen in black-box settings, which means we can only query the model and get the generated images. We set the initial population size " + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "content": ", the total population size " + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "content": ", and the selected population size " + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "content": " to 300, 50, and 25, respectively. The initial mutation probability " + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 47, + 278, + 289, + 434 + ], + "type": "text", + "content": " is set to 0.8. Ten adversarial examples are generated for each model. For each generation, we randomly select a target image and a semantic unrelated text from the COCO dataset. For example, we select the target images with the meaning a clock is flying in the blue sky and the original text a red double decker bus parking in let." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 437, + 289, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 289, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 289, + 605 + ], + "type": "text", + "content": "Comparison with Baselines. To the best of our knowledge, there are only two related studies [15, 36] for a targeted adversarial attack against text-to-image generation models. [15] proposes a hidden vocabulary attack (HiddVocab) on DALL-E 2 and [36] implements macaronic prompting (MacPrompt) and evocative prompting (EvoPrompt) attacks against DALL-E mini and DALL-E 2. For a comprehensive comparison, we also include [48], which is a homolytic substitution-based attack (HomoSubs) to cause image content obfuscation. We also include one state-of-the-art textual adversarial attack, TextFooler [24]. Since their attack does not involve image generation, we change the posterior tasks to match our settings and apply our proposed similarity metric to guide the optimization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "type": "text", + "content": "5.2. Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 632, + 287, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 287, + 680 + ], + "type": "text", + "content": "To demonstrate the effectiveness of our attack, we evaluate both attack effectiveness and adversarial sample imperceptibility. The imperceptibility measure consists of two parts: semantic meaning similarity and sentence naturality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 682, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 682, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 682, + 287, + 695 + ], + "type": "text", + "content": "Effectiveness of Generated Images. We adopt the method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 216 + ], + "type": "text", + "content": "of R-precision, a widely-used metric in text-to-image generation models [27, 39, 52, 54, 58] to measure whether the generated image is semantically aligned with the given text description. Specifically, we use the generated images to perform a retrieval experiment by querying a candidate set of text descriptions that consist of one ground truth and 99 randomly selected mismatched descriptions. The ViLT model [26], which achieves state-of-the-art performance on image-text retrieval tasks, is used here. We examine the top " + }, + { + "bbox": [ + 306, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 306, + 72, + 545, + 216 + ], + "type": "text", + "content": " ranked retrieval results and consider our attacks successful when the ground truth appears in the retrieval. We evaluate the effectiveness when R is 1 (R-1) and R is 3 (R-3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 220, + 545, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 220, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 545, + 280 + ], + "type": "text", + "content": "Sentence Semantic Meaning. Following [24, 28], we first adopt the Universal Sentence Encoder [12] to encode the adversarial sentence and target sentence into high dimensional vectors, and then their cosine similarity score are calculated to measure the semantic similarity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 283, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 283, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 283, + 545, + 380 + ], + "type": "text", + "content": "Sentence Naturality. The adversarial examples should look natural, similar to normal sentences in the real world. In our experiment, we calculate the perplexity (PPL) of the adversarial examples with GPT-2 [41], which is trained on a large corpus of real-world sentences. PPL measures how likely the model is to generate the input text sequence, representing the fluency of the adversarial examples. Generally, the sample with lower PPL is more natural." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 388, + 416, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 416, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 416, + 399 + ], + "type": "text", + "content": "5.3. Evaluation Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "text", + "content": "White-box Attacks. The results for white-box attacks are shown in Table 1. It is seen that RIATIG succeeds in generating all adversarial examples in DM-GAN and DF-GAN, and can succeed in generating 9 out of 10 samples in AttnGAN when we examine top-3 recall results. The recall precision drops when we only examine top-1 recall results. This phenomenon might be caused by the image generation quality of the target model, since the DM-GAN and AttnGAN achieve an average R-precision of " + }, + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "inline_equation", + "content": "85.47\\%" + }, + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "text", + "content": " [52] and " + }, + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "inline_equation", + "content": "88.56\\%" + }, + { + "bbox": [ + 306, + 411, + 545, + 615 + ], + "type": "text", + "content": " [58] on COCO datasets. Furthermore, a low semantic distance means there is a low semantic relevance between the adversarial text and the text used to generate the target images. The low PPL means our adversarial text is fluent and natural as compared to the normal text. On the other hand, due to the limited-size and monolingual datasets that these three models are trained on, the baselines can not succeed in generating adversarial examples." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 618, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 618, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 618, + 545, + 715 + ], + "type": "text", + "content": "Black-box Attacks. The results for black-box attacks are shown in Table 2. RIATIG achieves a high R-precision as compared to the baseline methods. HomoSubs and TextFooler are designed for untargeted attacks, and cannot be easily adapted for targeted attacks. HiddVocab does not provide a reliable method for finding adversarial examples and can achieve only a " + }, + { + "bbox": [ + 306, + 618, + 545, + 715 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 306, + 618, + 545, + 715 + ], + "type": "text", + "content": " success rate against DALL-E 2. Though MacPrompt and EvoPrompt can achieve a higher" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "type": "text", + "content": "DALL·E 2 API: https://openai.com/dall-e-2/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20590" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 541, + 220 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 541, + 220 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 541, + 220 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 541, + 220 + ], + "type": "image", + "image_path": "9d1e9f183385f1f07534a2438542c43d3f87208d82ae891d37084f5768f761d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 115, + 228, + 476, + 240 + ], + "lines": [ + { + "bbox": [ + 115, + 228, + 476, + 240 + ], + "spans": [ + { + "bbox": [ + 115, + 228, + 476, + 240 + ], + "type": "text", + "content": "Figure 4. Examples of our adversarial attack results against DALL-E mini, DALL-E 2, and Imagen." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 290, + 284, + 335 + ], + "blocks": [ + { + "bbox": [ + 47, + 259, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 259, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 287, + 281 + ], + "type": "text", + "content": "Table 1. The results of the white-box attacks against AttnGAN, DM-GAN, and DF-GAN." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 290, + 284, + 335 + ], + "lines": [ + { + "bbox": [ + 51, + 290, + 284, + 335 + ], + "spans": [ + { + "bbox": [ + 51, + 290, + 284, + 335 + ], + "type": "table", + "html": "
ModelR-1 ↑R-3 ↑Semantic Distance ↓PPL ↓
AttnGAN [52]8/109/100.24522.63
DM-GAN [58]8/1010/100.27420.16
DF-GAN [49]9/1010/100.34558.81
", + "image_path": "dbc8bdb423b7e8139f16eb0f698c3e0fb80b0030d3fc70d39383281a26df06f6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "lines": [ + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "spans": [ + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "type": "text", + "content": "Note: R-1 and R-3 represent the R-precision when " + }, + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "type": "inline_equation", + "content": "\\mathrm{R} = 1" + }, + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "type": "inline_equation", + "content": "\\mathrm{R} = 3" + }, + { + "bbox": [ + 59, + 336, + 286, + 353 + ], + "type": "text", + "content": ", respectively. PPL represents the perplexity of sentences." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "content": "precision rate, due to their loosely formulated linguistic methods, MacPrompt and EvoPrompt do not always guarantee to find an adversarial example. In addition, MacPrompt adopts the compositional prompts by combining two semantically similar words resulting in a higher semantic distance. For example, it combines creepy and spooky into creepepy and uses the sentence A very creepepy person to generate a person that looks creepy and spooky. As a result, the semantic meaning between the adversarial examples and the target is still very close, making them highly perceptible. Also, these generated words can break the fluency and naturalness of the sentences, resulting in a high PPL. For EvoPrompt, since it relies on broad morphological similarity, the semantic difference is quite low. However, the crafted sentences can seem meaningless, again breaking the naturality of the sentences, e.g., using prompt rygamera pultris to generate the images of fishes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 590, + 141, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 141, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 141, + 604 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 613, + 286, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 286, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 286, + 698 + ], + "type": "text", + "content": "Effectiveness of Mutation Strategy. To evaluate the effectiveness of our proposed mutation strategy, we conducted a comparative analysis with a random mutation approach, which employed insert, swap, and delete operations. Table 3 presents the results of our experiments, indicating that our mutations significantly outperformed random mutations, particularly in black-box settings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": "Influence of Target Images. To further analyze the im" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 290, + 547, + 485 + ], + "blocks": [ + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "type": "text", + "content": "Table 2. The results of the black-box attacks against DALL-E mini, DALL-E 2, and Imagen." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 290, + 547, + 485 + ], + "lines": [ + { + "bbox": [ + 307, + 290, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 307, + 290, + 547, + 485 + ], + "type": "table", + "html": "
ModelMethodsR-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DALL-E mini [43]HiddVocab [15]3/103/100.175284.78
MacPrompt [36]8/108/100.466814.61
EvoPrompt [36]6/106/100.145662.97
HomoSubs [48]0/100/100.091115.84
TextFooer [24]0/100/100.181848.41
RIATIG9/1010/100.27420.16
DALL-E 2 [42]HiddVocab [15]4/104/100.165162.71
MacPrompt [36]9/109/100.394931.31
EvoPrompt [36]7/107/100.176139.39
HomoSubs [48]0/100/100.06981.69
TextFooer [24]0/100/100.182624.88
RIATIG10/1010/100.27872.03
Imagen [45]HiddVocab [15]2/102/100.185073.74
MacPrompt [36]6/106/100.425694.73
EvoPrompt [36]4/104/100.165607.66
HomoSubs [48]0/100/100.081103.53
TextFooer [24]0/100/100.162231.10
RIATIG10/1010/100.23704.09
", + "image_path": "c92f269e4f280b8d87f501dd9fd2dbcc0e75897682df51744159a8d9724997e8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 365, + 486, + 498, + 495 + ], + "lines": [ + { + "bbox": [ + 365, + 486, + 498, + 495 + ], + "spans": [ + { + "bbox": [ + 365, + 486, + 498, + 495 + ], + "type": "text", + "content": "Note: Sem. Dist. represents semantic distance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 313, + 529, + 538, + 574 + ], + "blocks": [ + { + "bbox": [ + 313, + 509, + 537, + 521 + ], + "lines": [ + { + "bbox": [ + 313, + 509, + 537, + 521 + ], + "spans": [ + { + "bbox": [ + 313, + 509, + 537, + 521 + ], + "type": "text", + "content": "Table 3. Attack performance using random mutation strategy." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 529, + 538, + 574 + ], + "lines": [ + { + "bbox": [ + 313, + 529, + 538, + 574 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 538, + 574 + ], + "type": "table", + "html": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DM-GAN7/108/100.14867.93
DF-GAN1/102/100.12882.80
DALL·E mini0/100/100.172111.82
", + "image_path": "f411338327ca8bb5c9e9aa593806173c1282f88a0131f693bbc71e1a2d61f288.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 307, + 619, + 545, + 654 + ], + "blocks": [ + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "lines": [ + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "type": "text", + "content": "Table 4. The mean and variance of evaluation metrics under different selections of target images." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 619, + 545, + 654 + ], + "lines": [ + { + "bbox": [ + 307, + 619, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 307, + 619, + 545, + 654 + ], + "type": "table", + "html": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN9.2(±0.42)/109.8(±0.42)/100.31±0.04596.33±297.02
DALL-E mini9.7(±0.48)/109.9(±0.32)/100.28±0.03475.83±180.53
", + "image_path": "49cb1b4891980834e9e6e6a902b6ba8be8b436661a9189f92636ff597d307521.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "pact of target image selection on attack performance, we conducted ten experiments of the sample training process, with each experiment utilizing a different target image that" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20591" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 102, + 290, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "type": "text", + "content": "Table 5. The attack performance by using different substitution methods against DF-GAN and DALL-E mini." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 102, + 290, + 178 + ], + "lines": [ + { + "bbox": [ + 48, + 102, + 290, + 178 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 290, + 178 + ], + "type": "table", + "html": "
ModelSub. Meth.R-1 ↑R-3 ↑Sem. Dist. ↓PPL ↓
DF-GAN [49]Word2vec [34]9/1010/100.336558.81
Glove [34]8/109/100.331836.96
WordNet [35]5/107/100.358580.49
DALLE mini [43]Word2vec [34]9/1010/100.268420.16
Glove [34]7/109/100.311797.63
WordNet [35]4/106/100.368522.34
", + "image_path": "0b4fee9d0cb83d6f52cad8e22d2e086eead7334234528e0f3c2acb00e55c2bb5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 102, + 178, + 243, + 186 + ], + "lines": [ + { + "bbox": [ + 102, + 178, + 243, + 186 + ], + "spans": [ + { + "bbox": [ + 102, + 178, + 243, + 186 + ], + "type": "text", + "content": "Note: Sub. Meth. represents substitution method." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 55, + 217, + 280, + 255 + ], + "blocks": [ + { + "bbox": [ + 53, + 198, + 280, + 209 + ], + "lines": [ + { + "bbox": [ + 53, + 198, + 280, + 209 + ], + "spans": [ + { + "bbox": [ + 53, + 198, + 280, + 209 + ], + "type": "text", + "content": "Table 6. The attack performance of 50 additional experiments." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 217, + 280, + 255 + ], + "lines": [ + { + "bbox": [ + 55, + 217, + 280, + 255 + ], + "spans": [ + { + "bbox": [ + 55, + 217, + 280, + 255 + ], + "type": "table", + "html": "
ModelR-1↑R-3↑Sem. Dist.↓PPL↓
DF-GAN42/5046/500.22838.28
DALL·E mini45/5047/500.34640.78
", + "image_path": "1a1927022d7e63a75e521b8618bbfaa463324f181d8ddbe71a35926341b3985d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 274, + 286, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 286, + 310 + ], + "type": "text", + "content": "shared the same semantic meaning. The results, as presented in Table 4, indicate that our attacks demonstrated high robustness across varying target images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 312, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 286, + 408 + ], + "type": "text", + "content": "Robustness of Example Generation. One important property of RIATIG is that the adversarial text can be reliably associated with specific visual concepts when used as a prompt. We evaluated the sample robustness of DALL-E mini, DALL-E 2, andImagen. Specifically, we feed the same adversarial text to the target model ten times and calculated the average R-precision. The results show that RIATIG can achieve a " + }, + { + "bbox": [ + 47, + 312, + 286, + 408 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 312, + 286, + 408 + ], + "type": "text", + "content": " R-3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 411, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 286, + 651 + ], + "type": "text", + "content": "Different Substitution Methods. In our mutation strategy, one of the most important parts is the semantic word substitution, which is essential for optimizing the fitness scores and improving the sample quality. To identify a suitable approach for substitution, we evaluate three different approaches, namely Glove models [38], WordNet models [35] and Word2vec models [34]. We evaluate two target generation models (DF-GAN [49] and DALL-E mini [43]) in both white-box and black-box settings. For all three approaches, we select the substitute word from the top 30 results. For each target model and substitution approach, we start with ten identical benign text and target images and generate ten adversarial samples accordingly to evaluate the performance. The results are shown in Table 5. It is seen that Word2vec performs better than Glove and WordNet with respect to R-precision and PPL for the attack against DF-GAN, and Word2vec performs better than the others with respect to all three performance metrics when attacking DALL-E mini. We hypothesize that it is probably caused by the larger semantic vocabulary of Word2vec." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 653, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 286, + 715 + ], + "type": "text", + "content": "Attack Performance with More Evaluations. To comprehensively evaluate the scalability of our attack, we trained 50 additional samples, each with distinct sources and targets. The results of this larger-scale evaluation are in Table 6, showing consistent performance of our attack strategy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 375, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 375, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 375, + 84 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 94, + 545, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 94, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 94, + 545, + 202 + ], + "type": "text", + "content": "Security Impacts. To prevent the malicious use of text-to-image generation models such as spreading misinformation (e.g., deepfake) [18], generating biased and inappropriate contents (e.g., stereotyping, pornography, violence) [10, 47], content moderation filters are deployed to filter harmful inputs. However, as we demonstrated, it is possible to craft a completely unrelated sentence to generate target images with black-box knowledge. Thus, it is important to consider the security risks of latest AI models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 205, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 504 + ], + "type": "text", + "content": "Possible Defense. There are several possible defenses. First, a rule-based text filter could be deployed to remove redundant spaces and wrong words before generating images. To evaluate this defense, we tested the adversarial text using Grammarly and found that " + }, + { + "bbox": [ + 304, + 205, + 545, + 504 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 205, + 545, + 504 + ], + "type": "text", + "content": " of the samples could bypass the text filtering. For example, the sentence \"a fruit stand display with bananas and starlit skies\" was able to evade detection because this rule-based tool does not inspect the semantic meaning of the sentence. Second, one may consider using an image filter to prevent harmful images from being displayed to users. However, training such an image filter may require non-trivial efforts in collecting a large number of datasets. Moreover, the scope of harmful images can sometimes be difficult to define, such as with deep fake images. Another possible defense mechanism lies in the enhancement of the text-to-image generation models by adversarial training, which is one of the most effective defensive approaches against adversarial examples in the image and text domains [19, 24]. The model can be trained using both the original and adversarial text sharing the same associated images as the original text. However, it requires non-trivial efforts when facing a huge volume of adversarial examples as the modern text-to-image generation models are based on large-scale training datasets (e.g., Imagen [45] trains on about 460M image-text pairs)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 535, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 535, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 535, + 545, + 654 + ], + "type": "text", + "content": "In this paper, we propose an adversarial attack against the text-to-image generation models. We propose a two-stage attack framework to craft an effective adversarial example, where we find a workable adversarial example in the first stage, followed by a sample quality fine-tuning in the second stage. Through extensive evaluation, we can generate highly natural and semantically unrelated examples, allowing for successful attacks. We hope this work will raise awareness of potential security risks and aid the development of more effective defenses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 669, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 669, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 545, + 704 + ], + "type": "text", + "content": "Acknowledgments This work was partially supported by the NSF ( CNS-1916926, CNS-2038995, CNS-2154930, CNS-2229427, CNS-2238635), ARO (W911NF2010141)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20592" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Attngan implementation. https://github.com/taoxugit/AttnGAN. Accessed: 2022-10-01." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "type": "text", + "content": "[2] Dall-e 2 laion implementation. https://github.com/LAION-AI/dalle2-laion. Accessed: 2022-10-01." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 137, + 286, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 137, + 286, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 137, + 286, + 158 + ], + "type": "text", + "content": "[3] Dall-e mini implementation. https://github.com/borisdayma/dalle-mini. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019." + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20594" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_content_list.json b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ccae4f6aaf5d5dc8b3423334dc2370be82db0d78 --- /dev/null +++ b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_content_list.json @@ -0,0 +1,1518 @@ +[ + { + "type": "text", + "text": "RIAV-MVS: Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo", + "text_level": 1, + "bbox": [ + 86, + 130, + 880, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Changjiang Cai, Pan Ji, Qingan Yan, Yi Xu \nOPPO US Research Center, InnoPeak Technology, Inc.", + "bbox": [ + 264, + 181, + 700, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 267 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper presents a learning-based method for multiview depth estimation from posed images. Our core idea is a \"learning-to-optimize\" paradigm that iteratively indexes a plane-sweeping cost volume and regresses the depth map via a convolutional Gated Recurrent Unit (GRU). Since the cost volume plays a paramount role in encoding the multiview geometry, we aim to improve its construction both at pixel- and frame- levels. At the pixel level, we propose to break the symmetry of the Siamese network (which is typically used in MVS to extract image features) by introducing a transformer block to the reference image (but not to the source images). Such an asymmetric volume allows the network to extract global features from the reference image to predict its depth map. Given potential inaccuracies in the poses between reference and source images, we propose to incorporate a residual pose network to correct the relative poses. This essentially rectifies the cost volume at the frame level. We conduct extensive experiments on real-world MVS datasets and show that our method achieves state-of-the-art performance in terms of both within-dataset evaluation and cross-dataset generalization.", + "bbox": [ + 76, + 282, + 472, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 632, + 209, + 647 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multi-view stereo (MVS) aims to recover dense 3D geometry from multiple images captured from different viewpoints with calibrated cameras [28]. It is a fundamental problem in computer vision and has wide applications ranging from autonomous driving [12, 55], remote sensing [3], augmented reality [50], to robotics [22]. Following the seminal MVSNet [59], many learning-based methods [17, 39, 40, 52, 53, 58, 60] have been proposed, achieving great improvements against their traditional counterparts [5, 14, 19, 44], in terms of accuracy or efficiency.", + "bbox": [ + 76, + 657, + 468, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most of the learning-based MVS methods [17,39,40,52, 58,60] rely on traditional plane-sweeping [14,19] approach to generate a cost volume by comparing the CNN features of reference image and source images at several depth hypotheses, and then apply 2D or 3D convolutional encoder-decoders to aggregate and regularize the cost volume. The", + "bbox": [ + 76, + 810, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2D CNN methods [17] use multi-level features as skip connections to help decode the cost volume for depth regression. Even though the skip connections improve the depth maps, they weaken the role of cost volume and the geometry knowledge embedded therein to some extent. Hence, 2D CNN methods suffer from degraded generalization when testing on unseen domains. The 3D CNN methods [31] use soft-argmin to regress the depth map as the expectation from the cost volume distribution, and hence cannot predict the best candidate but instead an averaged one when dealing with a flat or multi-modal distribution caused by textureless, repeated, or occluded regions, etc. To mitigate these problems, we propose RIAV-MVS, a new paradigm to predict the depth via learning to recurrently index an asymmetric cost volume, obtaining improved accuracy and generalization. As depicted in Fig. 1, our RIAV-MVS features several nontrivial novel designs.", + "bbox": [ + 496, + 252, + 893, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "First, we learn to index the cost volume by approaching the correct depth planes per pixel via an index field (a grid of indices to identify the depth hypotheses), as shown in Fig. 1-(e). The proposed recurrent estimate of the index field enables the learning to be anchored at the cost volume domain. Specifically, it recurrently predicts the residual index field in a descent direction of matching cost to retrieve cost values for the next iteration. The newly updated index field is used to directly index (i.e., sampling via linear interpolation) depth hypotheses to render a depth map, which is iteratively optimized to approach the ground truth depth, making the system end-to-end trainable.", + "bbox": [ + 496, + 516, + 893, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Second, to facilitate the optimization, we propose to improve the cost volume at pixel- and frame- levels, respectively. At the pixel level, a transformer block is asymmetrically applied to the reference view (but not to the source views). By capturing long-range global context via a transformer and pixel-wise local features via CNNs, we build an asymmetric cost volume to store more accurate matching similarity cues. At the frame level, we propose a residual pose net to rectify the camera poses that are usually obtained via Visual SLAM [9, 16, 30] and inevitably contain noise. The rectified poses are used to more accurately backward warp the reference features to match the counterparts in source views.", + "bbox": [ + 496, + 704, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "919", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0dea1038c6576faf439cb8d7185940f04379a223dd76c1fdd4bd1726e5dc21d6.jpg", + "image_caption": [ + "Figure 1. Our pipeline versus RAFT [49] and IterMVS [52]. Our recurrent processing of a plane-sweep cost volume by the iteratively refined index field serves as a new design for multi-view depth estimation." + ], + "image_footnote": [], + "bbox": [ + 127, + 89, + 844, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our RIAV-MVS is depicted versus two related works RAFT [49] and IterMVS [52] as in Fig. 1. First, our method is developed using RAFT's GRU-based iterative optimization. However, RAFT operates an all-pair correlation volume (no multi-view geometry constraints) for optical flow (Fig. 1-(a) and (c)), our method is proposed for multi-view depth estimation by constructing a plane-sweep cost volume (Fig. 1-(b)). Second, IterMVS [52] iteratively predicts the depth and reconstructs a new plane-sweep cost volume using updated depth planes centered at the predicted depth (Fig. 1-(d)). Instead, as shown in Fig. 1-(e), our proposed index field serves as a new design that bridges the cost volume optimization (i.e., by learning better image features via back-propagation) and the depth map estimation (i.e., by sampling sweeping planes). It makes forward and backward learning differentiable. We conduct extensive experiments on indoor-scene datasets, including ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32]. We also performed well-designed ablation studies to verify the effectiveness and the generalization of our approach.", + "bbox": [ + 75, + 295, + 472, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 614, + 218, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth can be accurately predicted from stereo matching, which can be broadly divided into binocular stereo and multi-view stereo (MVS). The former requires calibrated setups of rectified stereo pairs, and many traditional [4, 24, 25, 43] and deep learning-based methods [7, 8, 10, 31, 33, 34, 41, 61, 62] have been proposed. Compared with binocular stereo, MVS methods estimate depth from a set of images or a video, where the camera moves and the scene is assumed static. In this section, we briefly review deep learning-based MVS methods.", + "bbox": [ + 75, + 641, + 468, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D-CNN MVS Depth Estimation: Learning-based MVS methods [17, 39, 40, 52, 53, 58-60] rely on traditional plane-sweeping [14, 19] to generate a cost volume by associating reference frame and source frames for similarity matching, followed by encoder-decoder architectures for cost volume aggregation and depth map prediction. Among them, MVSNet [59], R-MVSNet [60], and DPSNet [26] leverage", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D convolutions to regularize 4D cost volumes and regress depth maps via soft-argmin [31]. Different strategies have been introduced for cost volume construction. MVSNet [59] proposes a variance-based cost volume for multi-view similarity measurement. Cas-MVSNet [21] builds cascade cost volumes based on multi-scale feature pyramid and regresses the depth map in a multi-stage coarse-to-fine manner. Similarly, Cheng et al. propose UCS-Net [13] to build cascade adaptive thin volumes by leveraging variance-based uncertainty. CVP-MVSNet [58] builds a cost volume pyramid via multi-scale images to reduce to memory footprint. This cost volume mechanism is also adopted to other related tasks, e.g., 3D plane reconstruction in PlaneMVS [38], which leverages slanted plane sweeping to help plane reconstruction and accurate depth predictions.", + "bbox": [ + 496, + 295, + 893, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2D-CNN MVS Depth Estimation: Even though 3D convolutional methods usually deliver high accuracy, they demand a large memory footprint and computational cost. Instead, some methods, e.g., MVDepthNet [54] and DeepVideoMVS [17], generate 3D volumes by computing correlation or dot production between the extracted features of multi-view input images. The 3D cost volumes are further regularized by 2D convolutions. DeepVideoMVS [17] extracts multi-scale features. It uses the feature at half scale to construct the cost volume, and other features as the skip connections to a series of decoders for depth regression. PatchmatchNet [53] proposes an adaptive procedure mimicking PatchMatch [5] to achieve superior efficiency. 2D convolutions are much faster and more memory efficient than the 3D counterparts, making them better suitable for lightweight networks in real-time applications.", + "bbox": [ + 496, + 530, + 895, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Iterative Depth Estimation: Several methods adopt an iterative depth estimation paradigm. R-MVSNet [60] iteratively regularizes each slice of the cost volume with GRU along the depth dimension. Unlike the above mentioned cost volume-based approaches, Point-MVSNet [11] directly processes the target scene as point clouds. It first generates a coarse depth map, converts it into a point cloud and refines the point cloud iteratively to reduce the residual between the", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "920", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "estimated depth and the ground truth depth. IterMVS [52] encodes a pixel-wise probability distribution of depth in the hidden state of a GRU-based estimator. During each iteration, the multi-scale matching information is injected into the GRU to predict the depth and confidence maps to facilitate the following 3D reconstruction. The depth maps are predicted via a combined classification and regression through the probability distribution. It uses arg-min to finish \"classification\", which is not differentiable and must be detached first before the following regression operation. Unlike IterMVS, our method learns to recurrently index the cost volume to directly find the best depth candidates in an end-to-end differentiable fashion.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 300, + 168, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our learning-based end-to-end multi-view stereo system, RIAV-MVS, aims to predict depth maps from a set of images, which are different views of the same scene with known camera poses, denoted by $\\mathcal{I} = \\{I_i\\}_{i=0}^{N-1}$ . More specifically, RIAV-MVS uses one as the reference image and others as source images to infer the depth map of the reference image. Without loss of generality, we refer to the first image $I_0$ as the reference image and others as source views $\\mathcal{I}^S$ , where $S = 1,2,\\dots,N-1$ . An overview of our approach is illustrated in Fig. 2. It consists of feature extraction (Sec. 3.1), cost volume construction via plane-sweeping stereo [14, 19] (Sec. 3.2), and cost volume optimization and depth prediction (Sec. 3.3). Details will be discussed below.", + "bbox": [ + 75, + 325, + 473, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Feature Extraction", + "text_level": 1, + "bbox": [ + 76, + 545, + 261, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a reference image $I_0$ and source images $\\mathcal{I}^S$ , we extract matching features of $I_0$ and each of the $\\mathcal{I}^S$ by F-Net (see below), and a context feature for $I_0$ by C-Net (see the supplementary material for C-Net), as shown in Fig. 2.", + "bbox": [ + 75, + 568, + 470, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Matching Feature Extraction: Our feature extractor F-Net is based on PairNet [17]. It is a lightweight Feature Pyramid Network (FPN) [35] on top of the first fourteen layers of MnasNet [47]. Specifically, the reference input image $I_0 \\in \\mathbb{R}^{H \\times W}$ is spatially scaled down until 1/32 scale, and recovered up to 1/2 scale, resulting in multi-scale features $\\{f_{0,s} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times F_0}\\}$ ( $s = 2,4,8,16$ and $F_0 = 32$ for feature channels). In PairNet, $f_{0,2}$ is used to construct the cost volume, and other features are used in the skip connections to a series of decoders for depth regression. Unlike this, we add an extra fusion layer $\\mathcal{G}$ to aggregate them into a matching feature $f_0$ at 1/4 scale, as", + "bbox": [ + 75, + 628, + 468, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {0} = \\mathcal {G} \\left(\\left\\langle f _ {0, 2} \\downarrow_ {2}, f _ {0, 4}, f _ {0, 8} \\uparrow_ {2}, f _ {0, 1 6} \\uparrow_ {4} \\right\\rangle\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 813, + 468, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the fusion layer $\\mathcal{G}$ is a sequence of operations of $\\mathrm{Conv}_{3\\times 3}$ , batch normalization, ReLU, and $\\mathrm{Conv}_{1\\times 1}$ , $\\downarrow x$ and $\\uparrow x$ are downsampling and upsampling by scale $x$ , $\\langle \\cdot \\rangle$ is concatenation along channel dimension, and $f_0\\in$", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{H / 4\\times W / 4\\times F_1}$ with $F_{1} = 128$ . Similarly, F-Net (with shared weights as that for $I_0$ ) is also applied to source images $\\mathcal{L}^S$ to extract a set of matching features $f^{\\mathcal{S}} = \\{f_i\\mid i\\in \\mathcal{S}\\}$", + "bbox": [ + 496, + 89, + 890, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Global Matching Feature of Reference View: Besides the local pixel-wise features extracted from CNNs, we also leverage global long-range information to better guide the feature matching. Towards that, a transformer layer (fourhead self-attention with positional encoding) [51] is applied to the local feature $f_{0}$ of the reference image, to construct an aggregated feature $f_{0}^{a} \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times F_{1}}$ as", + "bbox": [ + 496, + 136, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {0} ^ {a} = f _ {0} + \\omega_ {\\alpha} \\sigma \\left(\\frac {\\left(f _ {0} W ^ {Q}\\right) \\left(f _ {0} W ^ {K}\\right) ^ {T}}{\\sqrt {F _ {1}}} \\left(f _ {0} W ^ {V}\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 253, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma (\\cdot)$ is the softmax operator, $\\omega_{\\alpha}$ is a learned scalar weight that is initialized to zero, and $W^{Q}, W^{K} \\in \\mathbb{R}^{F_{1} \\times hF_{1}}$ and $W^{V} \\in \\mathbb{R}^{F_{1} \\times F_{1}}$ are the projections matrices for query, key and value features, with $h = 4$ for multi-head attention. The final output $f_{0}^{a}$ contains both local and global information, which are balanced by the parameter $\\omega_{\\alpha}$ , to enhance the following cost volume construction.", + "bbox": [ + 496, + 294, + 890, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is worth noting that this transformer self-attention is only applied to the reference image, while the source features still possess the local representations from CNNs. Our asymmetric employment of this transformer layer provides the capability to better balance the high-frequency features (by high-pass CNNs) and the low-frequency features by self-attention [42, 46]. The high-frequency features are beneficial to image matching at local and structural regions, while the low-frequency ones, with noisy information suppressed by the transformer's spatial smoothing (serving as a low-pass filter), provide more global context cues for robust matching, especially for the areas full of low-texture, repeated patterns, and occlusion, etc. This way, our network can learn where to rely on global features over local features, and vice versa.", + "bbox": [ + 496, + 400, + 892, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Cost Volume Construction", + "text_level": 1, + "bbox": [ + 500, + 635, + 740, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use the global matching feature map $f_0^a$ of $I_0$ and local matching features $f^S$ of $\\mathcal{I}^S$ to build a cost volume. The cost (or matching) volume is defined on a 3D view frustum attached to the camera in perspective projection. It is generated by running the traditional plane-sweep stereo [14, 19] which uniformly samples $M_0 = 64$ plane hypotheses in the inverse depth space, s.t. $1 / d \\sim U(d_{\\min}, d_{\\max})$ . Here $d_{\\min}$ and $d_{\\max}$ are the near and far planes of the 3D frustum, respectively. Following [17], we set $d_{\\min} = 0.25$ and $d_{\\max} = 20$ meters for indoor scenes (e.g., ScanNet [15]).", + "bbox": [ + 496, + 657, + 890, + 810 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a given depth hypothesis $d$ and known camera intrinsic matrices $\\mathcal{K} = \\{K_i\\}_{i=0}^N$ and relative transformations $\\Theta = \\{R_{0,i} \\mid t_{0,i}\\}_{i=1}^N$ from reference image $I_0$ , to source image $I_i$ , a cost map is computed by i) warping source image feature $f_i$ into the reference image and ii) calculating the similarity between the reference global feature $f_0^a$ and", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "921", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ec69df47d9b7e1e15ed55ce6fd6f6bfa78e701f92dc4a1f5a8322152170163a4.jpg", + "image_caption": [ + "Figure 2. Architecture of our proposed network. It consists of a feature extraction (i.e., F-Net, a Transformer, and C-Net) block, a cost volume construction and index field GRU-based optimization block, and a residual pose block." + ], + "image_footnote": [], + "bbox": [ + 122, + 90, + 851, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the warped feature $\\tilde{f}_i$ . To generate $\\tilde{f}_i$ , we implement the homography $H$ as a backward 2D grid sampling. Specifically, a pixel $\\mathbf{p} = (u,v,1)^T$ in the reference image will be warped to its counterpart $\\tilde{\\mathbf{p}}_i$ in source image $i$ as follows:", + "bbox": [ + 75, + 359, + 470, + 422 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {p}} _ {i} = H (\\mathbf {p} \\mid d, \\mathcal {K}, \\Theta) = K _ {i} \\left(R _ {0, i} \\left(K _ {0} ^ {- 1} \\mathbf {p} d\\right) + t _ {0, i}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 444, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then $\\tilde{f}_i$ is bilinearly sampled from $f_{i}$ as $\\tilde{f}_i(\\mathbf{p}) = f_i(\\tilde{\\mathbf{p}}_i)$ . Given the warped source feature $\\tilde{f}_i$ and the reference feature $f_0^a$ , the cost volume is formulated as $C_0(d) = \\frac{1}{N - 1}\\sum_{i\\in S}\\frac{f_0^a\\cdot\\tilde{f}_i^T}{\\sqrt{F_1}}$ . This way, we can construct a cost volume for all depth candidates $\\mathcal{B}_0 = \\{d_i\\}_{i = 0}^{M_0 - 1}$ , resulting in a 3D tensor, denoted as $C_0\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0}$ .", + "bbox": [ + 76, + 483, + 470, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. GRU-based Iterative Optimization", + "text_level": 1, + "bbox": [ + 76, + 594, + 380, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We solve the depth prediction as learning to optimize the dense stereo matching problem [5, 24, 48, 57]. Given the generated cost volume $C_0$ as in Sec. 3.2, the depth estimation of the reference image is formulated as finding the best solution $D^{*} = \\mathrm{argmin}_{D}E(D,C_{0})$ , which minimizes an energy function $E(D,C_0)$ (including a data term and a smoothness term). Unfortunately, such a global minimization is NP-complete due to many discontinuity preserving energies [6]. Approximate solutions are proposed by loosening the energy function, e.g., the binocular stereo matching solved by Semi-Global Matching (SGM) [24]. In SGM, the matching cost $C_0$ is iteratively aggregated by summing the costs (of all 1D minimum cost paths that end in pixel $\\mathbf{p}$ at disparity $d^1$ ) when traversing from pixel $\\mathbf{p} - \\mathbf{r}$ to pixel $\\mathbf{p}$ in a direction $\\mathbf{r}$ (out of sixteen directions) and the best disparity at each pixel $\\mathbf{p}$ is given by $d^{*}(\\mathbf{p}) = \\mathrm{argmin}_{d}(C^{\\prime}(\\mathbf{p},d))$ with $C^\\prime$ being the aggregated cost volume. Similar to SGM,", + "bbox": [ + 75, + 618, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we do not directly optimize the energy function $E$ , but learn to process the cost volume $C_0$ .", + "bbox": [ + 500, + 362, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, several major problems still need to be solved. SGM is not differentiable due to its winner-take-all (WTA) by argmin, making it unable to train the system in an end-to-end manner. Its differentiable counterpart, SGA [62], was proposed by changing the min to sum when aggregating the cost volume, and replacing the argmin with softargmin when predicting the disparity from the optimized cost volume, but still i) the update direction $\\mathbf{r}$ when traversing from pixel $\\mathbf{p} - \\mathbf{r}$ to $\\mathbf{p}$ needs to be predefined, and ii) the softargmin focuses on measuring the distance of the expectation of disparity map to the ground truth disparity, and hence cannot handle multi-modal distributions in $C_0$ well [52].", + "bbox": [ + 496, + 397, + 892, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, towards an end-to-end, differentiable solution, we propose to use a GRU-based module to implicitly optimize the matching volume. It estimates a sequence of index fields $\\{\\phi_t\\}_{t=1}^T$ by unrolling the optimization problem to $T$ iterative updates (in a descent direction), mimicking the updates of a first-order optimizer according to [1,2,36,49]. At each iteration $t$ , the index field $\\phi_t \\in \\mathbb{R}^{H \\times W}$ is estimated as a grid of indices to iteratively better approach (i.e., closer to the ground truth) depth hypotheses having a lower matching cost. Specifically, a residual index field $\\delta \\phi_t$ is predicted as an update direction for next iteration, i.e., $\\phi_{t+1} = \\phi_t + \\delta \\phi_t$ , (analogous to the direction $\\mathbf{r}$ in SGM), which is explicitly driven by training the system (e.g., feature encoders, the transformer layer, and the residual pose net, etc.) to minimize the loss between the predicted depth maps and the ground truth. The recurrent estimate of the index field enables the learning to be directly anchored at the cost volume domain. This indexing paradigm differentiates our approach from other depth estimation methods, such as the depth regression which fuses cost volume and", + "bbox": [ + 496, + 598, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1 Abuse of notation $d$ for depth in MVS or disparity in binocular stereo", + "bbox": [ + 94, + 886, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "922", + "bbox": [ + 485, + 944, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the skipped multi-level features by 2D CNNs [17, 52, 53], and soft-argmin [31] after cost volume aggregation and regularization by 3D CNNs [21, 39, 59, 60].", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Index Field Iterative Updates: We use a 3 chained GRUs [36] to estimate a sequence of index fields, $\\{\\phi_t\\in$ $\\mathbb{R}^{H / 4\\times W / 4}\\}_{t = 1}^T$ from an initial starting point $\\phi_0$ . We use a softargmin-start from the cost volume $C_0$ , i.e., $\\phi_0 =$ $\\sum_{i = 0}^{M_1 - 1}i\\sigma (C_0)$ where $\\sigma (\\cdot)$ is the softmax operator along the last dimension of cost volume $C_0$ , to convert it to a probability of each index $i$ . This setup facilitates the convergence of our predictions. A four-layer matching pyramid $\\{C_0^i\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0 / 2^i}\\}_{i = 1}^4$ is built by repeated pooling the cost volume $C_0$ along the depth dimension with kernel size 2 as in [49]. To index the matching pyramid, we define a lookup operator analogous to the one in [36]. Given a current estimate of index field $\\phi_t$ , a 1D grid is constructed with integer offsets up to $r = \\pm 4$ around the $\\phi_t$ . The grid is used to index from each level of the matching pyramid via linear interpolation due to $\\phi_t$ being real numbers. The retrieved cost values are then concatenated into a single feature map $C_0^{\\phi_t}\\in \\mathbb{R}^{H / 4\\times W / 4\\times F_2}$ . Then the index field $\\phi_t$ , the retrieved cost features $C_0^{\\phi_t}$ , and context features $f_0^c$ are concatenated, and fed into the GRU layer, together with a latent hidden state $h_t$ . The GRU outputs a residual index field $\\delta \\phi_t$ , and a new hidden state $h_{t + 1}$ :", + "bbox": [ + 75, + 136, + 472, + 473 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta \\phi_ {t}, h _ {t + 1} \\Leftarrow \\operatorname {G R U} \\left(\\left\\langle \\phi_ {t}, C _ {0} ^ {\\phi_ {t}}, f _ {0} ^ {c} \\right\\rangle , h _ {t}\\right); \\phi_ {t + 1} \\Leftarrow \\phi_ {t} + \\delta \\phi_ {t}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 483, + 460, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upsampling and Depth Estimation: The depth map at iteration $t$ is estimated by sampling the depth hypotheses via linear interpolation given the index field $\\phi_t$ . Since $\\phi_t$ is at 1/4 resolution, we upsample it to full resolution using a convex combination of a $3 \\times 3$ neighbors as in [49]. Specifically, a weight mask $W_0 \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times (4 \\times 4 \\times 9)}$ is predicted from the hidden state $h_t$ using two convolutional layers and softmax is performed over the weights of those 9 neighbors. The final high resolution index field $\\phi_t^u$ is obtained by taking a weighted combination over the 9 neighbors, and reshaping to the resolution $\\mathrm{H} \\times \\mathrm{W}$ . Convex combination can be implemented using the einsum function in PyTorch.", + "bbox": [ + 75, + 507, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When constructing the cost volume, we use $M_0 = 64$ depth hypotheses, $\\mathcal{B}_0 = \\{d_i\\}_{i=0}^{M_0 - 1}$ . A small $M_0$ helps reduce the computation and space. If we use the upsampled index field $\\phi_t^u$ to directly sample the planes $\\mathcal{B}_0$ , we see discontinuities in the inferred depth map, even though the quantitative evaluation is not hindered. To mitigate this, we propose a coarse-to-fine pattern, and to use $M_1 = 256$ depth hypotheses $\\mathcal{B}_1 = \\{d_i\\}_{i=0}^{M_1 - 1}$ . Analogous to upsampling in optical flow or disparity in binocular stereo, the flow or disparity values themselves have to be scaled when implementing the spatial upsampling. Our depth index fields are adjusted by a scale $s_D = \\frac{M_1}{M_0} = 4$ . To mimic the convex combination before mentioned, we apply a similar weighted summation along the depth dimension when sampling depth from", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{B}_1$ . Specifically, another mask $W_{1} \\in \\mathbb{R}^{H \\times W \\times s_{D} \\times M_{0}}$ is predicted from the hidden state using three convolutional layers, and further reshaped to $H \\times W \\times M_{1}$ . Given a pixel $\\mathbf{p}$ , and the upsampled index field $\\phi_t^u$ , the final depth $D_{t}$ is estimated as", + "bbox": [ + 496, + 89, + 890, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {t} (p) = \\frac {\\sum_ {i \\in \\Omega (\\mathbf {p})} \\mathcal {B} _ {1} [ i ] W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)}{\\sum_ {i \\in \\Omega (\\mathbf {p})} W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 172, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where, we aggregate the neighbors within a radius $r = 4$ centered at the index $\\phi_t^u (\\mathbf{p})$ for a given pixel $\\mathbf{p}$ , and $\\lfloor i \\rfloor$ gives a greatest integer less than or equal to $i$ , and $[i]$ means to index the depth planes $\\mathcal{B}_1$ via linear interpolation, due to index $i$ being a real number.", + "bbox": [ + 496, + 217, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is worth mentioning that our method embeds both regression (similar to softmax in existing methods [39, 59, 60]) and classification (similar to argmin), which make it robust to multi-modal distributions, and achieving sub-pixel precision thanks to linear interpolation. Combining both classification and regression has been seen in [52], but ours does not use the argmax operator when achieving the \"classification\" purpose, thanks to our proposal of index fields estimation, which differentiably bridges the cost volume indexing and depth hypotheses sampling directly in a sub-pixel precision.", + "bbox": [ + 496, + 294, + 892, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Residual Pose Net: An accurate cost volume benefits the GRU-based iterative optimization. The quality of the generated cost volume $C_0$ is not only determined by the matching features $(f_0^a$ and $f^S$ ) (for which we have proposed asymmetric employment of the transformer layer), but also by the homography warping as in Eq. 3. However, the camera poses are, in practice, usually obtained by Visual SLAM algorithms [9, 16, 30], and inevitably contain noise. Therefore, we propose a residual pose net to rectify the camera poses for accurately backward warping the reference features to match the corresponding features in source images. We use an image-net pretrained ResNet18 [23] backbone as in [29, 56] to encode the reference image and the warped source images. Specifically, given the current estimated depth map $D_t$ at iteration $t$ , and the ground truth depth $D_{gt}$ , we warp a source image $I_i$ into the reference image through the homography defined in Eq. 3 with (noisy) ground truth camera poses $\\Theta$ and the $D_t$ or $D_{gt}$ . We randomly select $D_t$ or $D_{gt}$ with a probability $\\mathrm{prob}(D_t) = 0.6$ during network training, but always use the predicted depth $D_t$ during network inference. The input to the pose net is the concatenated $I_0$ and the warped $\\tilde{I}_i$ , and the output is an axis-angle representation, which is further converted to a residual rotation matrix $\\Delta \\theta_i$ , for an updated one $\\theta_i' = \\Delta \\theta_i \\cdot \\theta_i$ . This way, we predict the residual poses $\\Delta \\Theta = \\{\\Delta \\theta_i\\}_{i=1}^{N-1}$ for each of the source and reference pair, and perform the rectification as $\\Theta' = \\Delta \\Theta \\cdot \\Theta$ . We leverage the updated poses $\\Theta'$ to calculate a more accurate cost volume $C_1$ using Eq. 3, followed by the remaining iterations of GRU.", + "bbox": [ + 496, + 462, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "923", + "bbox": [ + 485, + 944, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss Function", + "text_level": 1, + "bbox": [ + 76, + 90, + 222, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our network is supervised on the inverse $L_{1}$ loss between the predicted depths $\\{D_t\\}_{i=1}^T$ and the ground truth $D_{gt}$ . It is evaluated over valid pixels (i.e., with non-zero ground truth depths). Following the exponentially increasing weights as in [36, 49], this depth loss is defined as", + "bbox": [ + 76, + 113, + 468, + 191 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D} = \\sum_ {t = 1} ^ {T} \\gamma^ {T - t} \\frac {1}{N _ {v}} \\sum_ {i = 0} ^ {N _ {v} - 1} \\| \\frac {1}{D _ {t} (i)} - \\frac {1}{D _ {g t} (i)} \\| _ {1} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 200, + 468, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where, $\\| \\cdot \\|_1$ measures the $l_1$ distance, $N_v$ is the number of valid pixels, and $\\gamma = 0.9$ . We also apply the photometric loss $\\mathcal{L}_P$ (as defined in [56]) to supervise the residual pose network. The total loss is then defined as $\\mathcal{L} = \\mathcal{L}_D + \\mathcal{L}_P$ .", + "bbox": [ + 76, + 258, + 470, + 319 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 333, + 209, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 359, + 179, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our experiments use four indoor-scene datasets, which have RGB-D video frames with ground truth depths and known camera poses. ScanNet [15] and DTU [27] are used in training and testing, and 7scenes [20] and RGB-D Scenes V2 [32] are evaluated for zero-shot generalization. (1) ScanNet. Our network is trained from scratch on ScanNet [15] using the official training split. We use 279k training samples and 20k validation ones. (2) DTU. Following [53,59,60], the depth range for sampling depth hypotheses is set to $d_{min} = 0.425$ and $d_{max} = 0.935$ meters. We use 27k training samples, 6k validation ones, and 1k ones for evaluation. Each sample has 5 frames. (3) 7-Scenes. We select 13 sequences from 7-Scenes for zero-shot generalization. (4) RGB-D Scenes V2. We select 8 sequences for testing. Details about train/val/test splits, training, and implementation are shown in the supplementary material.", + "bbox": [ + 75, + 382, + 470, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with Existing Methods", + "text_level": 1, + "bbox": [ + 76, + 633, + 385, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, our method is evaluated and compared with several state-of-the-art MVS methods. Our network is strictly compared with two baselines PairNet [17] and IterMVS [52], following the same training schedule and training set. We also compare ours with other MVS methods either by running the provided models or referring to the available evaluation metrics when testing on the same datasets, including ESTDepth [39], Neural RGBD [37], MVDepthNet [54], DPSNet [26], and DELTAS [45].", + "bbox": [ + 75, + 657, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Evaluation. We evaluate the depth maps using the standard metrics in [18], including mean absolute relative error (abs-rel), mean absolute error (abs), squared relative error (sq-rel), root mean square error in linear scale (rmse) and log scale (rmse-log), and inlier ratios under thresholds of $\\sigma < 1.25 / 1.25^2 / 1.25^3$ . Tab. 1 shows the results on the ScanNet benchmark of our methods and sev-", + "bbox": [ + 75, + 795, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "eral state-of-the-art MVS methods. We compare two variants of our models: i) base: a base version with our recurrent indexing cost volume, and ii) +pose,atten: a full version with residual pose and the asymmetric employment of transformer self-attention. Our full model achieves the best performance in most metrics except the inlier ratio under $\\sigma < 1.25^2$ , outperformed by DELTAS [45] and ESTD [39]. But the inlier ratio is not as essential as abs-rel and abs. Zero-shot Generalization. We evaluate the generalization performance of our method RIAV-MVS from ScanNet to other indoor datasets without any fine-tuning. Tab. 2 shows the results of the methods trained on ScanNet [15] and directly tested on 7-scenes [20] and RGB-D Scenes V2 [32]. Our models outperform the baselines, and our two variants all have strong generalization performance. Qualitative Results. Fig. 3 demonstrates the qualitative results of our method vs. baselines IterMVS [52] and PairNet [17] on the test set of ScanNet [15] and DTU [27]. Our method can make more accurate and sharp depth predictions, especially for regions near boundaries and edges. For both near and far objects, our method outperforms the baselines.", + "bbox": [ + 496, + 90, + 893, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 420, + 653, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Efficacy of Proposed Modules: Our design is verified by ablating the modules to three variants, as shown in Tab. 3-(a). The base version itself can achieve competitive performance on ScanNet and better generalization, verifying the efficacy of our novel design - cost volume recurrent indexing via index field. Further, the performance can be consistently boosted when the residual pose net (i.e., variant +pose) and transformer self-attention are added (i.e., variant +pose,atten). Therefore, each of the proposed modules can consistently help with accurate depth estimation. Tab. 3-(b) shows the benefit of using asymmetric attention over symmetric attention. We also see improvements when applying our asymmetric attention to the MVSNet [59] backbone on ScanNet and DTU test sets (see the results in parentheses). Number of GRU Iterations and Convergence: Tab. 4-(a) shows the ablation study on different number of GRU iterations $T$ . The results are obtained by running our model (the full version) on the ScanNet test set, with $T = 16, 24, 48, 64, 96$ , and 128. Running more iterations boosts our depth prediction, but after $T \\geq 96$ , the gain is marginal. View Number: We compare 3-view (i.e., 1 reference + 2 source images) and 5-view (i.e., 1 reference + 4 source images). Tab. 4-(b) shows that the more frames are used for matching, the better the depth will be. The results are obtained for the zero-shot generalization from ScanNet to 7-Scenes. Note that our full model (+pose,atten) with 3-view input outperforms the other two variants with 5-view input, showing the asymmetrical employment of the transformer self-attention can boost the prediction due to the mining of more global information. 3-view vs 5-view on", + "bbox": [ + 496, + 446, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "924", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8d758ac223a99a0a56b1c2d148f3cec30f47d5c9e1e38098be866d1f9c573a28.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodScanNet Test-Set (m)DTU Test-Set (mm)
abs-relabssq-relrmsermse-logδ < 1.25δ < 1.252abs-relabsrmse
MVDepth [54]0.11670.23010.05960.32360.16100.84530.9639---
MVDepth-FT0.11160.20870.07630.31430.15000.88040.9734---
DPSNet [26]0.12000.21040.06880.31390.16040.86400.9612---
DPSNet-FT0.09860.19980.04590.28400.13480.88800.9785---
DELTAS [45]0.09150.17100.03270.23900.12260.91470.9872---
NRGBD [37]0.10130.16570.05020.25000.13150.91600.9790---
ESTD [39]0.08120.15050.02980.21990.11040.93130.9871---
MVSNet [59]0.10320.186450.04650.27430.13850.89350.97750.014310.723525.3989
PairNet [17]0.08950.17090.06150.27340.12080.91720.98040.01299.442821.4650
IterMVS [52]0.09910.18180.05180.27330.13680.89950.97410.014610.622528.7009
Ours(base)0.08850.16050.03800.23470.11830.92110.98100.01168.288721.5806
Ours(+pose,atten)0.07340.13810.02810.20800.10300.93950.98620.00926.777118.5953
", + "bbox": [ + 119, + 89, + 856, + 275 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ca88c997d8f87e1404fd3012594369ace5f8291ccd8f3946efe42d0b3dc6a05.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation results on the test set of ScanNet [15] and the test set of DTU [27]. Error metrics (lower is better) are abs-rel, abs, sq-rel, rmse, rmse-log, while accuracy (higher is better) metrics are $\\delta < 1.25 / 1.25^2 / 1.25^3$ . Here -FT denotes finetuned on ScanNet. Bold is the best score, and underline indicates the second best one." + ], + "table_footnote": [], + "table_body": "
ScanNet ⇒ Others7-ScenesRGB-D Scenes V2
abs-relabssq-relrmseδ < 1.25abs-relabssq-relrmseδ < 1.25
NRGBD [37]0.23340.40600.21630.53580.6803-----
ESTD [39]0.14650.25280.07290.33820.8036-----
PairNet [17]0.11570.20860.06770.29260.87680.09950.13820.02790.19710.9393
IterMVS [52]0.13360.23630.10330.34250.85180.08110.12450.03400.21330.9496
Ours(base)0.11480.19990.05520.28570.87260.09670.13360.02460.18360.9427
Ours(+pose,atten)0.10000.17810.04730.26640.89670.08030.11680.02000.17030.9632
", + "bbox": [ + 120, + 340, + 849, + 452 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc85f3a3ad64ea0518e889d93c68cb6259047d8bac3a69487b9e2c41c7d023c5.jpg", + "table_caption": [ + "Table 2. Zero-shot generalization from ScanNet [15] to 7-scenes [20] and RGB-D Scenes V2 [32]. Our methods achieve better generalization. We sample the sequences every 10 frames, and each sample has 5 frames for multi-view stereo depth prediction." + ], + "table_footnote": [ + "(a) We compare three variants of our models." + ], + "table_body": "
VariantsScanNet Test-Set (m)
abs-relabsrmseδ < 1.25
Ours(base)0.08850.16050.23470.9211
Ours(+pose)0.08270.15230.22530.9277
Ours(+pose,atten)0.07340.13810.20800.9395
", + "bbox": [ + 91, + 527, + 423, + 594 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/154ac6016b4159ee677e099614f52ebad265ce8aaeb32737de38878261a6d04e.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Asymmetric attention and MVsNet backbone. DTU results are in parentheses." + ], + "table_body": "
AttentionScanNet/DTU Test-Set (m)
abs-relabsrmseδ < 1.25
Asym attenu (ours)0.07340.13810.20800.9395
Sym. attenu0.07610.14960.22530.9333
MVSNet [59]0.10320.18650.27430.8935
(0.0143)(10.7235)(25.3989)(0.8936)
MVSNet(+atten)0.10180.18530.27340.8957
(0.0123)(9.1150)(22.3525)(0.9909)
", + "bbox": [ + 452, + 505, + 805, + 603 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d07749ba2e2dcffe74c299e09814eca34091fa8cb09e821dfad7b9232fa03d09.jpg", + "table_caption": [], + "table_footnote": [ + "(a) GRU iterations" + ], + "table_body": "
Itr. Tabs-relabsδ < 1.25
160.14130.07600.9364
240.14000.07520.9375
480.13920.07470.9382
640.13920.07460.9384
960.13920.07450.9385
1280.13940.07450.9385
", + "bbox": [ + 91, + 674, + 303, + 765 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a7fe5406acd3803a9e376761a3f0dd5fbaa9dfc853b8cacda5dbcb49be4c5762.jpg", + "table_caption": [ + "Table 3. Ablation study for our proposed modules and a different backbone architecture MVSNet [59]." + ], + "table_footnote": [ + "(b) View numbers" + ], + "table_body": "
View No.abs-relabsδ < 1.25
3 (base)0.12040.21210.8603
5 (base)0.11480.19990.8726
3 (+pose)0.11620.20610.8711
5 (+pose)0.10960.19300.8840
3 (+pose,atten)0.10840.19230.8833
5 (+pose,atten)0.10000.17810.8967
", + "bbox": [ + 339, + 672, + 604, + 765 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0947001a03d2f3488f0d0aaeacbab9bc72eb1a3e0d5737b21c5d4c07657cb1ef.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Frame sampling" + ], + "table_body": "
Samplingabs-relabsδ < 1.25
s10 (base)0.08850.16050.9211
key (base)0.08380.15980.9277
s10 (+pose)0.08270.15230.9277
key (+pose)0.07890.15310.9339
s10 (+pose,atten)0.07470.13920.9382
key (+pose,atten)0.06970.13480.9472
", + "bbox": [ + 620, + 672, + 898, + 765 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study of design choices. Bold is the best, and underline indicates the second best.", + "bbox": [ + 189, + 794, + 777, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DTU: Tab. 5 shows that our model, i.e., Ours(+pose,atten) is trained/tested on DTU dataset with 3-view and 5-view input collections, respectively. We use the same training scheduling for a fair comparison. The 5-view result is worse", + "bbox": [ + 75, + 835, + 470, + 896 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "than the last row in Tab. 1 due to the lack of pretraining on ScanNet. Frame Sampling: We compare the simple view selection strategy (i.e., sampling by every 10 frames) with the heuristics [17]. Tab. 4-(c) shows that ours can be im", + "bbox": [ + 498, + 835, + 890, + 897 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "925", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c47c7743b436770eed809c68eb97122c0153d2992d349b04804a7f31d4db532.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 243, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f8ec11b074ab58990aab59a4f8706b619aaba5a71649e6241a988f033443a37a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 246, + 90, + 403, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0cbbc0b8829043b875f56ce7c5e30211631fe2dedc61fcc7ecc5a580d3f6adc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 90, + 568, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be164c96a78c32b619e206bf71cce111b184bd6065060d0d36020631554f0a47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 90, + 728, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d2accc473bb7806d6fe2a55b33be5bee30b1e894c5f2c171f932051b2233252.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 90, + 893, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22b4b953a1d3bfe2d76f0a49712c0ab98542d654cc47c90e78593d6dc3843a2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 191, + 243, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/55492bc24df457847bc73813e32e4398f7ad2fd3e9062b605147ed545e7d8145.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 245, + 191, + 403, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/111ce22ff0c78cad3ab1bd674d2b5869bad780adb157ffe098075ef161dfe4c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 191, + 566, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cbbba39d91c21b3fcefcfa61736b0ce7e0abc5cb6baa5e37f1e996894c58f4de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 191, + 730, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/379d9db278f90a491608b876a3653cc417b40db06885b77d7fe3dab8579f4ce5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 191, + 893, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/27b84bccf639331a898739c8cb7f0dbbd639495b21a3f69abbcf65e09ead5797.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 294, + 243, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f786e9b092f94cd29513f2e4a724753e83926f9e7f14bd59819d71eece491dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 294, + 403, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/78271702adc0f237f407bc1acea6d388636c61498bcb7b223e47f21be7654e72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 294, + 566, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/da6b0c05f9a4687948a8405a9c3ff781da38f74622addc9af25fda459ca1ea03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 294, + 730, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/46d7abc7927e4689cf58da9d9e4752468b1c6d8a9957f05df00a022913ad91f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 294, + 893, + 396 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4a2b0d058b3440f8a7be6e45860f57704e91ff49c9e4fee5477568e6a19935a1.jpg", + "image_caption": [ + "Ref. image" + ], + "image_footnote": [], + "bbox": [ + 80, + 397, + 243, + 496 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a511150d73d1d67648dd74537f8006aa9092fbba0a576a833850dc7070652270.jpg", + "image_caption": [ + "GT depth" + ], + "image_footnote": [], + "bbox": [ + 243, + 397, + 403, + 500 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/659a52eae79c656ce97ac87ae9513470e028a602019b5a6e811e33db1d382b37.jpg", + "image_caption": [ + "IterMVS" + ], + "image_footnote": [], + "bbox": [ + 403, + 397, + 566, + 500 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11798852638036f2a3277a6afcb29db1ebc8748f53355e9e14821dac9c9ca86e.jpg", + "image_caption": [ + "PairNet", + "Figure 3. Qualitative results on ScanNet [15] (top two rows) and DTU [27] test set. Left two columns show reference image and ground truth depth, and other columns are the estimated depth by baseline IterMVS [52], PairNet [17] and ours (the full version), respectively. Our method outperforms the baselines on thin structures, small objects and boundaries, as highlighted in green for ours and in red for the baselines. The abs-err errors (in meters) are imposed on the depth maps for comparison." + ], + "image_footnote": [], + "bbox": [ + 568, + 397, + 730, + 500 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e03640d26f9a0665e829ae3b5ef57a2d350322bc2a5daa5687abb593305ca490.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 730, + 397, + 893, + 500 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5e4bf6eb3f61a1512b0741d004e48d2d3e66c97b629b04d427d0a7a4252fe2c7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
View No. on DTUabs-rel (↓)abs (mm) (↓)rmse (↓)
3 (1 ref + 2 source)0.014911.068924.8831
5 (1 ref + 4 source)0.01198.841921.4327
", + "bbox": [ + 122, + 597, + 419, + 633 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a963a570b8306a809f37e23817acc9dcf3ebfb2943ad0f6b0cc24cb0c78aad9c.jpg", + "table_caption": [ + "Table 5. 3-view vs. 5-view training and testing on DTU [27]." + ], + "table_footnote": [], + "table_body": "
MethodsTime(fps)Mem.(MB)Param.(M)abs-rel (↓)
Ours(T=8)6.98429727.60.0760
Ours(T=12)5.91429727.60.0752
Ours(T=24)3.77429727.60.0734
IterMVS [52]22.6121710.340.0991
ESTD [39]14.08179936.20.0812
", + "bbox": [ + 109, + 664, + 434, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Comparison of run time, memory consumption, and accuracy on ScanNet [15] test set with frame dimension $320 \\times 256$ .", + "bbox": [ + 75, + 733, + 468, + 761 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "proved when the selected views have more overlapping and the baselines are suitable. Our(+pose,atten) even with simple strategy outperforms other variants with heuristic sampling, and so are our(+pose) vs our(base). Runtime Overhead: Tab. 6 shows the run-time and memory consumption when processing $320 \\times 256$ frames from the ScanNet test set. Ours (T=8/12/24) means 8, 12, and 24 GRU iterations.", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 604, + 627, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed RIAV-MVS, a novel learning-based MVS method. Our approach utilizes a convolutional GRU to iteratively optimize the index fields, which are used to access the cost volume and regress the depth. The cost volume is further improved through the application of a transformer block to the reference image and a residual pose network to correct the relative poses. Extensive experiments on ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32] have demonstrated the superior accuracy and cross-dataset generalizability of our method. Due to the plane-sweeping 3D cost volume and transformer selfattention, our method requires large memory consumption for high-resolution images. Moreover, the inference time is not as fast as other lightweight convolutional counterparts, due to the iterative update paradigm in our approach. In future work, we plan to leverage temporal information to further enhance depth estimation from posed-video streams.", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "926", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonas Adler and Ozan Öktem. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12):124007, 2017. 4", + "[2] Jonas Adler and Ozan Oktem. Learned primal-dual reconstruction. IEEE transactions on medical imaging, 37(6):1322-1332, 2018. 4", + "[3] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M Seitz, and Richard Szeliski. Building rome in a day. 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In CVPR, 2019. 2, 4" + ], + "bbox": [ + 503, + 92, + 890, + 811 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "928", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_model.json b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e7d0b45058cfcc17836c79578a7769971bb76990 --- /dev/null +++ b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/04aab7d4-b43b-496c-94a4-596185183726_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.131, + 0.882, + 0.152 + ], + "angle": 0, + "content": "RIAV-MVS: Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.182, + 0.702, + 0.217 + ], + "angle": 0, + "content": "Changjiang Cai, Pan Ji, Qingan Yan, Yi Xu \nOPPO US Research Center, InnoPeak Technology, Inc." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.268 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.284, + 0.473, + 0.603 + ], + "angle": 0, + "content": "This paper presents a learning-based method for multiview depth estimation from posed images. Our core idea is a \"learning-to-optimize\" paradigm that iteratively indexes a plane-sweeping cost volume and regresses the depth map via a convolutional Gated Recurrent Unit (GRU). Since the cost volume plays a paramount role in encoding the multiview geometry, we aim to improve its construction both at pixel- and frame- levels. At the pixel level, we propose to break the symmetry of the Siamese network (which is typically used in MVS to extract image features) by introducing a transformer block to the reference image (but not to the source images). Such an asymmetric volume allows the network to extract global features from the reference image to predict its depth map. Given potential inaccuracies in the poses between reference and source images, we propose to incorporate a residual pose network to correct the relative poses. This essentially rectifies the cost volume at the frame level. We conduct extensive experiments on real-world MVS datasets and show that our method achieves state-of-the-art performance in terms of both within-dataset evaluation and cross-dataset generalization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.633, + 0.21, + 0.648 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.659, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Multi-view stereo (MVS) aims to recover dense 3D geometry from multiple images captured from different viewpoints with calibrated cameras [28]. It is a fundamental problem in computer vision and has wide applications ranging from autonomous driving [12, 55], remote sensing [3], augmented reality [50], to robotics [22]. Following the seminal MVSNet [59], many learning-based methods [17, 39, 40, 52, 53, 58, 60] have been proposed, achieving great improvements against their traditional counterparts [5, 14, 19, 44], in terms of accuracy or efficiency." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Most of the learning-based MVS methods [17,39,40,52, 58,60] rely on traditional plane-sweeping [14,19] approach to generate a cost volume by comparing the CNN features of reference image and source images at several depth hypotheses, and then apply 2D or 3D convolutional encoder-decoders to aggregate and regularize the cost volume. The" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.51 + ], + "angle": 0, + "content": "2D CNN methods [17] use multi-level features as skip connections to help decode the cost volume for depth regression. Even though the skip connections improve the depth maps, they weaken the role of cost volume and the geometry knowledge embedded therein to some extent. Hence, 2D CNN methods suffer from degraded generalization when testing on unseen domains. The 3D CNN methods [31] use soft-argmin to regress the depth map as the expectation from the cost volume distribution, and hence cannot predict the best candidate but instead an averaged one when dealing with a flat or multi-modal distribution caused by textureless, repeated, or occluded regions, etc. To mitigate these problems, we propose RIAV-MVS, a new paradigm to predict the depth via learning to recurrently index an asymmetric cost volume, obtaining improved accuracy and generalization. As depicted in Fig. 1, our RIAV-MVS features several nontrivial novel designs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.895, + 0.699 + ], + "angle": 0, + "content": "First, we learn to index the cost volume by approaching the correct depth planes per pixel via an index field (a grid of indices to identify the depth hypotheses), as shown in Fig. 1-(e). The proposed recurrent estimate of the index field enables the learning to be anchored at the cost volume domain. Specifically, it recurrently predicts the residual index field in a descent direction of matching cost to retrieve cost values for the next iteration. The newly updated index field is used to directly index (i.e., sampling via linear interpolation) depth hypotheses to render a depth map, which is iteratively optimized to approach the ground truth depth, making the system end-to-end trainable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Second, to facilitate the optimization, we propose to improve the cost volume at pixel- and frame- levels, respectively. At the pixel level, a transformer block is asymmetrically applied to the reference view (but not to the source views). By capturing long-range global context via a transformer and pixel-wise local features via CNNs, we build an asymmetric cost volume to store more accurate matching similarity cues. At the frame level, we propose a residual pose net to rectify the camera poses that are usually obtained via Visual SLAM [9, 16, 30] and inevitably contain noise. The rectified poses are used to more accurately backward warp the reference features to match the counterparts in source views." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "919" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.09, + 0.845, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 1. Our pipeline versus RAFT [49] and IterMVS [52]. Our recurrent processing of a plane-sweep cost volume by the iteratively refined index field serves as a new design for multi-view depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.473, + 0.6 + ], + "angle": 0, + "content": "Our RIAV-MVS is depicted versus two related works RAFT [49] and IterMVS [52] as in Fig. 1. First, our method is developed using RAFT's GRU-based iterative optimization. However, RAFT operates an all-pair correlation volume (no multi-view geometry constraints) for optical flow (Fig. 1-(a) and (c)), our method is proposed for multi-view depth estimation by constructing a plane-sweep cost volume (Fig. 1-(b)). Second, IterMVS [52] iteratively predicts the depth and reconstructs a new plane-sweep cost volume using updated depth planes centered at the predicted depth (Fig. 1-(d)). Instead, as shown in Fig. 1-(e), our proposed index field serves as a new design that bridges the cost volume optimization (i.e., by learning better image features via back-propagation) and the depth map estimation (i.e., by sampling sweeping planes). It makes forward and backward learning differentiable. We conduct extensive experiments on indoor-scene datasets, including ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32]. We also performed well-designed ablation studies to verify the effectiveness and the generalization of our approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.615, + 0.22, + 0.631 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Depth can be accurately predicted from stereo matching, which can be broadly divided into binocular stereo and multi-view stereo (MVS). The former requires calibrated setups of rectified stereo pairs, and many traditional [4, 24, 25, 43] and deep learning-based methods [7, 8, 10, 31, 33, 34, 41, 61, 62] have been proposed. Compared with binocular stereo, MVS methods estimate depth from a set of images or a video, where the camera moves and the scene is assumed static. In this section, we briefly review deep learning-based MVS methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.904 + ], + "angle": 0, + "content": "3D-CNN MVS Depth Estimation: Learning-based MVS methods [17, 39, 40, 52, 53, 58-60] rely on traditional plane-sweeping [14, 19] to generate a cost volume by associating reference frame and source frames for similarity matching, followed by encoder-decoder architectures for cost volume aggregation and depth map prediction. Among them, MVSNet [59], R-MVSNet [60], and DPSNet [26] leverage" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.895, + 0.525 + ], + "angle": 0, + "content": "3D convolutions to regularize 4D cost volumes and regress depth maps via soft-argmin [31]. Different strategies have been introduced for cost volume construction. MVSNet [59] proposes a variance-based cost volume for multi-view similarity measurement. Cas-MVSNet [21] builds cascade cost volumes based on multi-scale feature pyramid and regresses the depth map in a multi-stage coarse-to-fine manner. Similarly, Cheng et al. propose UCS-Net [13] to build cascade adaptive thin volumes by leveraging variance-based uncertainty. CVP-MVSNet [58] builds a cost volume pyramid via multi-scale images to reduce to memory footprint. This cost volume mechanism is also adopted to other related tasks, e.g., 3D plane reconstruction in PlaneMVS [38], which leverages slanted plane sweeping to help plane reconstruction and accurate depth predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.896, + 0.773 + ], + "angle": 0, + "content": "2D-CNN MVS Depth Estimation: Even though 3D convolutional methods usually deliver high accuracy, they demand a large memory footprint and computational cost. Instead, some methods, e.g., MVDepthNet [54] and DeepVideoMVS [17], generate 3D volumes by computing correlation or dot production between the extracted features of multi-view input images. The 3D cost volumes are further regularized by 2D convolutions. DeepVideoMVS [17] extracts multi-scale features. It uses the feature at half scale to construct the cost volume, and other features as the skip connections to a series of decoders for depth regression. PatchmatchNet [53] proposes an adaptive procedure mimicking PatchMatch [5] to achieve superior efficiency. 2D convolutions are much faster and more memory efficient than the 3D counterparts, making them better suitable for lightweight networks in real-time applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Iterative Depth Estimation: Several methods adopt an iterative depth estimation paradigm. R-MVSNet [60] iteratively regularizes each slice of the cost volume with GRU along the depth dimension. Unlike the above mentioned cost volume-based approaches, Point-MVSNet [11] directly processes the target scene as point clouds. It first generates a coarse depth map, converts it into a point cloud and refines the point cloud iteratively to reduce the residual between the" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "920" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.288 + ], + "angle": 0, + "content": "estimated depth and the ground truth depth. IterMVS [52] encodes a pixel-wise probability distribution of depth in the hidden state of a GRU-based estimator. During each iteration, the multi-scale matching information is injected into the GRU to predict the depth and confidence maps to facilitate the following 3D reconstruction. The depth maps are predicted via a combined classification and regression through the probability distribution. It uses arg-min to finish \"classification\", which is not differentiable and must be detached first before the following regression operation. Unlike IterMVS, our method learns to recurrently index the cost volume to directly find the best depth candidates in an end-to-end differentiable fashion." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.301, + 0.169, + 0.317 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.538 + ], + "angle": 0, + "content": "Our learning-based end-to-end multi-view stereo system, RIAV-MVS, aims to predict depth maps from a set of images, which are different views of the same scene with known camera poses, denoted by \\(\\mathcal{I} = \\{I_i\\}_{i=0}^{N-1}\\). More specifically, RIAV-MVS uses one as the reference image and others as source images to infer the depth map of the reference image. Without loss of generality, we refer to the first image \\(I_0\\) as the reference image and others as source views \\(\\mathcal{I}^S\\), where \\(S = 1,2,\\dots,N-1\\). An overview of our approach is illustrated in Fig. 2. It consists of feature extraction (Sec. 3.1), cost volume construction via plane-sweeping stereo [14, 19] (Sec. 3.2), and cost volume optimization and depth prediction (Sec. 3.3). Details will be discussed below." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.546, + 0.262, + 0.561 + ], + "angle": 0, + "content": "3.1. Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.471, + 0.63 + ], + "angle": 0, + "content": "Given a reference image \\( I_0 \\) and source images \\( \\mathcal{I}^S \\), we extract matching features of \\( I_0 \\) and each of the \\( \\mathcal{I}^S \\) by F-Net (see below), and a context feature for \\( I_0 \\) by C-Net (see the supplementary material for C-Net), as shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.812 + ], + "angle": 0, + "content": "Local Matching Feature Extraction: Our feature extractor F-Net is based on PairNet [17]. It is a lightweight Feature Pyramid Network (FPN) [35] on top of the first fourteen layers of MnasNet [47]. Specifically, the reference input image \\( I_0 \\in \\mathbb{R}^{H \\times W} \\) is spatially scaled down until 1/32 scale, and recovered up to 1/2 scale, resulting in multi-scale features \\( \\{f_{0,s} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times F_0}\\} \\) (\\( s = 2,4,8,16 \\) and \\( F_0 = 32 \\) for feature channels). In PairNet, \\( f_{0,2} \\) is used to construct the cost volume, and other features are used in the skip connections to a series of decoders for depth regression. Unlike this, we add an extra fusion layer \\( \\mathcal{G} \\) to aggregate them into a matching feature \\( f_0 \\) at 1/4 scale, as" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.814, + 0.47, + 0.832 + ], + "angle": 0, + "content": "\\[\nf _ {0} = \\mathcal {G} \\left(\\left\\langle f _ {0, 2} \\downarrow_ {2}, f _ {0, 4}, f _ {0, 8} \\uparrow_ {2}, f _ {0, 1 6} \\uparrow_ {4} \\right\\rangle\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where the fusion layer \\(\\mathcal{G}\\) is a sequence of operations of \\(\\mathrm{Conv}_{3\\times 3}\\), batch normalization, ReLU, and \\(\\mathrm{Conv}_{1\\times 1}\\), \\(\\downarrow x\\) and \\(\\uparrow x\\) are downsampling and upsampling by scale \\(x\\), \\(\\langle \\cdot \\rangle\\) is concatenation along channel dimension, and \\(f_0\\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.137 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{H / 4\\times W / 4\\times F_1}\\) with \\(F_{1} = 128\\) . Similarly, F-Net (with shared weights as that for \\(I_0\\) ) is also applied to source images \\(\\mathcal{L}^S\\) to extract a set of matching features \\(f^{\\mathcal{S}} = \\{f_i\\mid i\\in \\mathcal{S}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.894, + 0.244 + ], + "angle": 0, + "content": "Global Matching Feature of Reference View: Besides the local pixel-wise features extracted from CNNs, we also leverage global long-range information to better guide the feature matching. Towards that, a transformer layer (fourhead self-attention with positional encoding) [51] is applied to the local feature \\( f_{0} \\) of the reference image, to construct an aggregated feature \\( f_{0}^{a} \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times F_{1}} \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.254, + 0.892, + 0.289 + ], + "angle": 0, + "content": "\\[\nf _ {0} ^ {a} = f _ {0} + \\omega_ {\\alpha} \\sigma \\left(\\frac {\\left(f _ {0} W ^ {Q}\\right) \\left(f _ {0} W ^ {K}\\right) ^ {T}}{\\sqrt {F _ {1}}} \\left(f _ {0} W ^ {V}\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.401 + ], + "angle": 0, + "content": "where \\(\\sigma (\\cdot)\\) is the softmax operator, \\(\\omega_{\\alpha}\\) is a learned scalar weight that is initialized to zero, and \\(W^{Q}, W^{K} \\in \\mathbb{R}^{F_{1} \\times hF_{1}}\\) and \\(W^{V} \\in \\mathbb{R}^{F_{1} \\times F_{1}}\\) are the projections matrices for query, key and value features, with \\(h = 4\\) for multi-head attention. The final output \\(f_{0}^{a}\\) contains both local and global information, which are balanced by the parameter \\(\\omega_{\\alpha}\\), to enhance the following cost volume construction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.893, + 0.627 + ], + "angle": 0, + "content": "It is worth noting that this transformer self-attention is only applied to the reference image, while the source features still possess the local representations from CNNs. Our asymmetric employment of this transformer layer provides the capability to better balance the high-frequency features (by high-pass CNNs) and the low-frequency features by self-attention [42, 46]. The high-frequency features are beneficial to image matching at local and structural regions, while the low-frequency ones, with noisy information suppressed by the transformer's spatial smoothing (serving as a low-pass filter), provide more global context cues for robust matching, especially for the areas full of low-texture, repeated patterns, and occlusion, etc. This way, our network can learn where to rely on global features over local features, and vice versa." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.741, + 0.652 + ], + "angle": 0, + "content": "3.2. Cost Volume Construction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.811 + ], + "angle": 0, + "content": "We use the global matching feature map \\( f_0^a \\) of \\( I_0 \\) and local matching features \\( f^S \\) of \\( \\mathcal{I}^S \\) to build a cost volume. The cost (or matching) volume is defined on a 3D view frustum attached to the camera in perspective projection. It is generated by running the traditional plane-sweep stereo [14, 19] which uniformly samples \\( M_0 = 64 \\) plane hypotheses in the inverse depth space, s.t. \\( 1 / d \\sim U(d_{\\min}, d_{\\max}) \\). Here \\( d_{\\min} \\) and \\( d_{\\max} \\) are the near and far planes of the 3D frustum, respectively. Following [17], we set \\( d_{\\min} = 0.25 \\) and \\( d_{\\max} = 20 \\) meters for indoor scenes (e.g., ScanNet [15])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For a given depth hypothesis \\(d\\) and known camera intrinsic matrices \\(\\mathcal{K} = \\{K_i\\}_{i=0}^N\\) and relative transformations \\(\\Theta = \\{R_{0,i} \\mid t_{0,i}\\}_{i=1}^N\\) from reference image \\(I_0\\), to source image \\(I_i\\), a cost map is computed by i) warping source image feature \\(f_i\\) into the reference image and ii) calculating the similarity between the reference global feature \\(f_0^a\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "921" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.091, + 0.852, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.895, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Architecture of our proposed network. It consists of a feature extraction (i.e., F-Net, a Transformer, and C-Net) block, a cost volume construction and index field GRU-based optimization block, and a residual pose block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.471, + 0.424 + ], + "angle": 0, + "content": "the warped feature \\(\\tilde{f}_i\\). To generate \\(\\tilde{f}_i\\), we implement the homography \\(H\\) as a backward 2D grid sampling. Specifically, a pixel \\(\\mathbf{p} = (u,v,1)^T\\) in the reference image will be warped to its counterpart \\(\\tilde{\\mathbf{p}}_i\\) in source image \\(i\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.445, + 0.47, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {p}} _ {i} = H (\\mathbf {p} \\mid d, \\mathcal {K}, \\Theta) = K _ {i} \\left(R _ {0, i} \\left(K _ {0} ^ {- 1} \\mathbf {p} d\\right) + t _ {0, i}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.484, + 0.471, + 0.586 + ], + "angle": 0, + "content": "Then \\(\\tilde{f}_i\\) is bilinearly sampled from \\(f_{i}\\) as \\(\\tilde{f}_i(\\mathbf{p}) = f_i(\\tilde{\\mathbf{p}}_i)\\). Given the warped source feature \\(\\tilde{f}_i\\) and the reference feature \\(f_0^a\\), the cost volume is formulated as \\(C_0(d) = \\frac{1}{N - 1}\\sum_{i\\in S}\\frac{f_0^a\\cdot\\tilde{f}_i^T}{\\sqrt{F_1}}\\). This way, we can construct a cost volume for all depth candidates \\(\\mathcal{B}_0 = \\{d_i\\}_{i = 0}^{M_0 - 1}\\), resulting in a 3D tensor, denoted as \\(C_0\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.595, + 0.381, + 0.612 + ], + "angle": 0, + "content": "3.3. GRU-based Iterative Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.877 + ], + "angle": 0, + "content": "We solve the depth prediction as learning to optimize the dense stereo matching problem [5, 24, 48, 57]. Given the generated cost volume \\( C_0 \\) as in Sec. 3.2, the depth estimation of the reference image is formulated as finding the best solution \\( D^{*} = \\mathrm{argmin}_{D}E(D,C_{0}) \\), which minimizes an energy function \\( E(D,C_0) \\) (including a data term and a smoothness term). Unfortunately, such a global minimization is NP-complete due to many discontinuity preserving energies [6]. Approximate solutions are proposed by loosening the energy function, e.g., the binocular stereo matching solved by Semi-Global Matching (SGM) [24]. In SGM, the matching cost \\( C_0 \\) is iteratively aggregated by summing the costs (of all 1D minimum cost paths that end in pixel \\( \\mathbf{p} \\) at disparity \\( d^1 \\)) when traversing from pixel \\( \\mathbf{p} - \\mathbf{r} \\) to pixel \\( \\mathbf{p} \\) in a direction \\( \\mathbf{r} \\) (out of sixteen directions) and the best disparity at each pixel \\( \\mathbf{p} \\) is given by \\( d^{*}(\\mathbf{p}) = \\mathrm{argmin}_{d}(C^{\\prime}(\\mathbf{p},d)) \\) with \\( C^\\prime \\) being the aggregated cost volume. Similar to SGM," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.363, + 0.892, + 0.394 + ], + "angle": 0, + "content": "we do not directly optimize the energy function \\( E \\), but learn to process the cost volume \\( C_0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.893, + 0.595 + ], + "angle": 0, + "content": "However, several major problems still need to be solved. SGM is not differentiable due to its winner-take-all (WTA) by argmin, making it unable to train the system in an end-to-end manner. Its differentiable counterpart, SGA [62], was proposed by changing the min to sum when aggregating the cost volume, and replacing the argmin with softargmin when predicting the disparity from the optimized cost volume, but still i) the update direction \\(\\mathbf{r}\\) when traversing from pixel \\(\\mathbf{p} - \\mathbf{r}\\) to \\(\\mathbf{p}\\) needs to be predefined, and ii) the softargmin focuses on measuring the distance of the expectation of disparity map to the ground truth disparity, and hence cannot handle multi-modal distributions in \\(C_0\\) well [52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Therefore, towards an end-to-end, differentiable solution, we propose to use a GRU-based module to implicitly optimize the matching volume. It estimates a sequence of index fields \\(\\{\\phi_t\\}_{t=1}^T\\) by unrolling the optimization problem to \\(T\\) iterative updates (in a descent direction), mimicking the updates of a first-order optimizer according to [1,2,36,49]. At each iteration \\(t\\), the index field \\(\\phi_t \\in \\mathbb{R}^{H \\times W}\\) is estimated as a grid of indices to iteratively better approach (i.e., closer to the ground truth) depth hypotheses having a lower matching cost. Specifically, a residual index field \\(\\delta \\phi_t\\) is predicted as an update direction for next iteration, i.e., \\(\\phi_{t+1} = \\phi_t + \\delta \\phi_t\\), (analogous to the direction \\(\\mathbf{r}\\) in SGM), which is explicitly driven by training the system (e.g., feature encoders, the transformer layer, and the residual pose net, etc.) to minimize the loss between the predicted depth maps and the ground truth. The recurrent estimate of the index field enables the learning to be directly anchored at the cost volume domain. This indexing paradigm differentiates our approach from other depth estimation methods, such as the depth regression which fuses cost volume and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.902 + ], + "angle": 0, + "content": "1 Abuse of notation \\(d\\) for depth in MVS or disparity in binocular stereo" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.511, + 0.957 + ], + "angle": 0, + "content": "922" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "the skipped multi-level features by 2D CNNs [17, 52, 53], and soft-argmin [31] after cost volume aggregation and regularization by 3D CNNs [21, 39, 59, 60]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.473, + 0.474 + ], + "angle": 0, + "content": "Index Field Iterative Updates: We use a 3 chained GRUs [36] to estimate a sequence of index fields, \\(\\{\\phi_t\\in\\) \\(\\mathbb{R}^{H / 4\\times W / 4}\\}_{t = 1}^T\\) from an initial starting point \\(\\phi_0\\). We use a softargmin-start from the cost volume \\(C_0\\), i.e., \\(\\phi_0 =\\) \\(\\sum_{i = 0}^{M_1 - 1}i\\sigma (C_0)\\) where \\(\\sigma (\\cdot)\\) is the softmax operator along the last dimension of cost volume \\(C_0\\), to convert it to a probability of each index \\(i\\). This setup facilitates the convergence of our predictions. A four-layer matching pyramid \\(\\{C_0^i\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0 / 2^i}\\}_{i = 1}^4\\) is built by repeated pooling the cost volume \\(C_0\\) along the depth dimension with kernel size 2 as in [49]. To index the matching pyramid, we define a lookup operator analogous to the one in [36]. Given a current estimate of index field \\(\\phi_t\\), a 1D grid is constructed with integer offsets up to \\(r = \\pm 4\\) around the \\(\\phi_t\\). The grid is used to index from each level of the matching pyramid via linear interpolation due to \\(\\phi_t\\) being real numbers. The retrieved cost values are then concatenated into a single feature map \\(C_0^{\\phi_t}\\in \\mathbb{R}^{H / 4\\times W / 4\\times F_2}\\). Then the index field \\(\\phi_t\\), the retrieved cost features \\(C_0^{\\phi_t}\\), and context features \\(f_0^c\\) are concatenated, and fed into the GRU layer, together with a latent hidden state \\(h_t\\). The GRU outputs a residual index field \\(\\delta \\phi_t\\), and a new hidden state \\(h_{t + 1}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.484, + 0.462, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\delta \\phi_ {t}, h _ {t + 1} \\Leftarrow \\operatorname {G R U} \\left(\\left\\langle \\phi_ {t}, C _ {0} ^ {\\phi_ {t}}, f _ {0} ^ {c} \\right\\rangle , h _ {t}\\right); \\phi_ {t + 1} \\Leftarrow \\phi_ {t} + \\delta \\phi_ {t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Upsampling and Depth Estimation: The depth map at iteration \\( t \\) is estimated by sampling the depth hypotheses via linear interpolation given the index field \\( \\phi_t \\). Since \\( \\phi_t \\) is at 1/4 resolution, we upsample it to full resolution using a convex combination of a \\( 3 \\times 3 \\) neighbors as in [49]. Specifically, a weight mask \\( W_0 \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times (4 \\times 4 \\times 9)} \\) is predicted from the hidden state \\( h_t \\) using two convolutional layers and softmax is performed over the weights of those 9 neighbors. The final high resolution index field \\( \\phi_t^u \\) is obtained by taking a weighted combination over the 9 neighbors, and reshaping to the resolution \\( \\mathrm{H} \\times \\mathrm{W} \\). Convex combination can be implemented using the einsum function in PyTorch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "When constructing the cost volume, we use \\( M_0 = 64 \\) depth hypotheses, \\( \\mathcal{B}_0 = \\{d_i\\}_{i=0}^{M_0 - 1} \\). A small \\( M_0 \\) helps reduce the computation and space. If we use the upsampled index field \\( \\phi_t^u \\) to directly sample the planes \\( \\mathcal{B}_0 \\), we see discontinuities in the inferred depth map, even though the quantitative evaluation is not hindered. To mitigate this, we propose a coarse-to-fine pattern, and to use \\( M_1 = 256 \\) depth hypotheses \\( \\mathcal{B}_1 = \\{d_i\\}_{i=0}^{M_1 - 1} \\). Analogous to upsampling in optical flow or disparity in binocular stereo, the flow or disparity values themselves have to be scaled when implementing the spatial upsampling. Our depth index fields are adjusted by a scale \\( s_D = \\frac{M_1}{M_0} = 4 \\). To mimic the convex combination before mentioned, we apply a similar weighted summation along the depth dimension when sampling depth from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\(\\mathcal{B}_1\\). Specifically, another mask \\(W_{1} \\in \\mathbb{R}^{H \\times W \\times s_{D} \\times M_{0}}\\) is predicted from the hidden state using three convolutional layers, and further reshaped to \\(H \\times W \\times M_{1}\\). Given a pixel \\(\\mathbf{p}\\), and the upsampled index field \\(\\phi_t^u\\), the final depth \\(D_{t}\\) is estimated as" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.173, + 0.892, + 0.212 + ], + "angle": 0, + "content": "\\[\nD _ {t} (p) = \\frac {\\sum_ {i \\in \\Omega (\\mathbf {p})} \\mathcal {B} _ {1} [ i ] W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)}{\\sum_ {i \\in \\Omega (\\mathbf {p})} W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.293 + ], + "angle": 0, + "content": "where, we aggregate the neighbors within a radius \\( r = 4 \\) centered at the index \\( \\phi_t^u (\\mathbf{p}) \\) for a given pixel \\( \\mathbf{p} \\), and \\( \\lfloor i \\rfloor \\) gives a greatest integer less than or equal to \\( i \\), and \\( [i] \\) means to index the depth planes \\( \\mathcal{B}_1 \\) via linear interpolation, due to index \\( i \\) being a real number." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.893, + 0.461 + ], + "angle": 0, + "content": "It is worth mentioning that our method embeds both regression (similar to softmax in existing methods [39, 59, 60]) and classification (similar to argmin), which make it robust to multi-modal distributions, and achieving sub-pixel precision thanks to linear interpolation. Combining both classification and regression has been seen in [52], but ours does not use the argmax operator when achieving the \"classification\" purpose, thanks to our proposal of index fields estimation, which differentiably bridges the cost volume indexing and depth hypotheses sampling directly in a sub-pixel precision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Residual Pose Net: An accurate cost volume benefits the GRU-based iterative optimization. The quality of the generated cost volume \\( C_0 \\) is not only determined by the matching features \\( (f_0^a \\) and \\( f^S \\)) (for which we have proposed asymmetric employment of the transformer layer), but also by the homography warping as in Eq. 3. However, the camera poses are, in practice, usually obtained by Visual SLAM algorithms [9, 16, 30], and inevitably contain noise. Therefore, we propose a residual pose net to rectify the camera poses for accurately backward warping the reference features to match the corresponding features in source images. We use an image-net pretrained ResNet18 [23] backbone as in [29, 56] to encode the reference image and the warped source images. Specifically, given the current estimated depth map \\( D_t \\) at iteration \\( t \\), and the ground truth depth \\( D_{gt} \\), we warp a source image \\( I_i \\) into the reference image through the homography defined in Eq. 3 with (noisy) ground truth camera poses \\( \\Theta \\) and the \\( D_t \\) or \\( D_{gt} \\). We randomly select \\( D_t \\) or \\( D_{gt} \\) with a probability \\( \\mathrm{prob}(D_t) = 0.6 \\) during network training, but always use the predicted depth \\( D_t \\) during network inference. The input to the pose net is the concatenated \\( I_0 \\) and the warped \\( \\tilde{I}_i \\), and the output is an axis-angle representation, which is further converted to a residual rotation matrix \\( \\Delta \\theta_i \\), for an updated one \\( \\theta_i' = \\Delta \\theta_i \\cdot \\theta_i \\). This way, we predict the residual poses \\( \\Delta \\Theta = \\{\\Delta \\theta_i\\}_{i=1}^{N-1} \\) for each of the source and reference pair, and perform the rectification as \\( \\Theta' = \\Delta \\Theta \\cdot \\Theta \\). We leverage the updated poses \\( \\Theta' \\) to calculate a more accurate cost volume \\( C_1 \\) using Eq. 3, followed by the remaining iterations of GRU." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.511, + 0.957 + ], + "angle": 0, + "content": "923" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.223, + 0.106 + ], + "angle": 0, + "content": "3.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.47, + 0.192 + ], + "angle": 0, + "content": "Our network is supervised on the inverse \\(L_{1}\\) loss between the predicted depths \\(\\{D_t\\}_{i=1}^T\\) and the ground truth \\(D_{gt}\\). It is evaluated over valid pixels (i.e., with non-zero ground truth depths). Following the exponentially increasing weights as in [36, 49], this depth loss is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.202, + 0.47, + 0.245 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D} = \\sum_ {t = 1} ^ {T} \\gamma^ {T - t} \\frac {1}{N _ {v}} \\sum_ {i = 0} ^ {N _ {v} - 1} \\| \\frac {1}{D _ {t} (i)} - \\frac {1}{D _ {g t} (i)} \\| _ {1} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.259, + 0.471, + 0.32 + ], + "angle": 0, + "content": "where, \\( \\| \\cdot \\|_1 \\) measures the \\( l_1 \\) distance, \\( N_v \\) is the number of valid pixels, and \\( \\gamma = 0.9 \\). We also apply the photometric loss \\( \\mathcal{L}_P \\) (as defined in [56]) to supervise the residual pose network. The total loss is then defined as \\( \\mathcal{L} = \\mathcal{L}_D + \\mathcal{L}_P \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.334, + 0.21, + 0.351 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.36, + 0.18, + 0.374 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.471, + 0.626 + ], + "angle": 0, + "content": "Our experiments use four indoor-scene datasets, which have RGB-D video frames with ground truth depths and known camera poses. ScanNet [15] and DTU [27] are used in training and testing, and 7scenes [20] and RGB-D Scenes V2 [32] are evaluated for zero-shot generalization. (1) ScanNet. Our network is trained from scratch on ScanNet [15] using the official training split. We use 279k training samples and 20k validation ones. (2) DTU. Following [53,59,60], the depth range for sampling depth hypotheses is set to \\( d_{min} = 0.425 \\) and \\( d_{max} = 0.935 \\) meters. We use 27k training samples, 6k validation ones, and 1k ones for evaluation. Each sample has 5 frames. (3) 7-Scenes. We select 13 sequences from 7-Scenes for zero-shot generalization. (4) RGB-D Scenes V2. We select 8 sequences for testing. Details about train/val/test splits, training, and implementation are shown in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.387, + 0.652 + ], + "angle": 0, + "content": "4.2. Comparison with Existing Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.795 + ], + "angle": 0, + "content": "In this section, our method is evaluated and compared with several state-of-the-art MVS methods. Our network is strictly compared with two baselines PairNet [17] and IterMVS [52], following the same training schedule and training set. We also compare ours with other MVS methods either by running the provided models or referring to the available evaluation metrics when testing on the same datasets, including ESTDepth [39], Neural RGBD [37], MVDepthNet [54], DPSNet [26], and DELTAS [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Quantitative Evaluation. We evaluate the depth maps using the standard metrics in [18], including mean absolute relative error (abs-rel), mean absolute error (abs), squared relative error (sq-rel), root mean square error in linear scale (rmse) and log scale (rmse-log), and inlier ratios under thresholds of \\(\\sigma < 1.25 / 1.25^2 / 1.25^3\\). Tab. 1 shows the results on the ScanNet benchmark of our methods and sev-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.41 + ], + "angle": 0, + "content": "eral state-of-the-art MVS methods. We compare two variants of our models: i) base: a base version with our recurrent indexing cost volume, and ii) +pose,atten: a full version with residual pose and the asymmetric employment of transformer self-attention. Our full model achieves the best performance in most metrics except the inlier ratio under \\(\\sigma < 1.25^2\\), outperformed by DELTAS [45] and ESTD [39]. But the inlier ratio is not as essential as abs-rel and abs. Zero-shot Generalization. We evaluate the generalization performance of our method RIAV-MVS from ScanNet to other indoor datasets without any fine-tuning. Tab. 2 shows the results of the methods trained on ScanNet [15] and directly tested on 7-scenes [20] and RGB-D Scenes V2 [32]. Our models outperform the baselines, and our two variants all have strong generalization performance. Qualitative Results. Fig. 3 demonstrates the qualitative results of our method vs. baselines IterMVS [52] and PairNet [17] on the test set of ScanNet [15] and DTU [27]. Our method can make more accurate and sharp depth predictions, especially for regions near boundaries and edges. For both near and far objects, our method outperforms the baselines." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.421, + 0.655, + 0.437 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Efficacy of Proposed Modules: Our design is verified by ablating the modules to three variants, as shown in Tab. 3-(a). The base version itself can achieve competitive performance on ScanNet and better generalization, verifying the efficacy of our novel design - cost volume recurrent indexing via index field. Further, the performance can be consistently boosted when the residual pose net (i.e., variant +pose) and transformer self-attention are added (i.e., variant +pose,atten). Therefore, each of the proposed modules can consistently help with accurate depth estimation. Tab. 3-(b) shows the benefit of using asymmetric attention over symmetric attention. We also see improvements when applying our asymmetric attention to the MVSNet [59] backbone on ScanNet and DTU test sets (see the results in parentheses). Number of GRU Iterations and Convergence: Tab. 4-(a) shows the ablation study on different number of GRU iterations \\( T \\). The results are obtained by running our model (the full version) on the ScanNet test set, with \\( T = 16, 24, 48, 64, 96 \\), and 128. Running more iterations boosts our depth prediction, but after \\( T \\geq 96 \\), the gain is marginal. View Number: We compare 3-view (i.e., 1 reference + 2 source images) and 5-view (i.e., 1 reference + 4 source images). Tab. 4-(b) shows that the more frames are used for matching, the better the depth will be. The results are obtained for the zero-shot generalization from ScanNet to 7-Scenes. Note that our full model (+pose,atten) with 3-view input outperforms the other two variants with 5-view input, showing the asymmetrical employment of the transformer self-attention can boost the prediction due to the mining of more global information. 3-view vs 5-view on" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "924" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.09, + 0.857, + 0.276 + ], + "angle": 0, + "content": "
MethodScanNet Test-Set (m)DTU Test-Set (mm)
abs-relabssq-relrmsermse-logδ < 1.25δ < 1.252abs-relabsrmse
MVDepth [54]0.11670.23010.05960.32360.16100.84530.9639---
MVDepth-FT0.11160.20870.07630.31430.15000.88040.9734---
DPSNet [26]0.12000.21040.06880.31390.16040.86400.9612---
DPSNet-FT0.09860.19980.04590.28400.13480.88800.9785---
DELTAS [45]0.09150.17100.03270.23900.12260.91470.9872---
NRGBD [37]0.10130.16570.05020.25000.13150.91600.9790---
ESTD [39]0.08120.15050.02980.21990.11040.93130.9871---
MVSNet [59]0.10320.186450.04650.27430.13850.89350.97750.014310.723525.3989
PairNet [17]0.08950.17090.06150.27340.12080.91720.98040.01299.442821.4650
IterMVS [52]0.09910.18180.05180.27330.13680.89950.97410.014610.622528.7009
Ours(base)0.08850.16050.03800.23470.11830.92110.98100.01168.288721.5806
Ours(+pose,atten)0.07340.13810.02810.20800.10300.93950.98620.00926.777118.5953
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.285, + 0.895, + 0.327 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation results on the test set of ScanNet [15] and the test set of DTU [27]. Error metrics (lower is better) are abs-rel, abs, sq-rel, rmse, rmse-log, while accuracy (higher is better) metrics are \\(\\delta < 1.25 / 1.25^2 / 1.25^3\\). Here -FT denotes finetuned on ScanNet. Bold is the best score, and underline indicates the second best one." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.342, + 0.851, + 0.453 + ], + "angle": 0, + "content": "
ScanNet ⇒ Others7-ScenesRGB-D Scenes V2
abs-relabssq-relrmseδ < 1.25abs-relabssq-relrmseδ < 1.25
NRGBD [37]0.23340.40600.21630.53580.6803-----
ESTD [39]0.14650.25280.07290.33820.8036-----
PairNet [17]0.11570.20860.06770.29260.87680.09950.13820.02790.19710.9393
IterMVS [52]0.13360.23630.10330.34250.85180.08110.12450.03400.21330.9496
Ours(base)0.11480.19990.05520.28570.87260.09670.13360.02460.18360.9427
Ours(+pose,atten)0.10000.17810.04730.26640.89670.08030.11680.02000.17030.9632
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.464, + 0.893, + 0.494 + ], + "angle": 0, + "content": "Table 2. Zero-shot generalization from ScanNet [15] to 7-scenes [20] and RGB-D Scenes V2 [32]. Our methods achieve better generalization. We sample the sequences every 10 frames, and each sample has 5 frames for multi-view stereo depth prediction." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.528, + 0.424, + 0.595 + ], + "angle": 0, + "content": "
VariantsScanNet Test-Set (m)
abs-relabsrmseδ < 1.25
Ours(base)0.08850.16050.23470.9211
Ours(+pose)0.08270.15230.22530.9277
Ours(+pose,atten)0.07340.13810.20800.9395
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.116, + 0.605, + 0.386, + 0.619 + ], + "angle": 0, + "content": "(a) We compare three variants of our models." + }, + { + "type": "table", + "bbox": [ + 0.454, + 0.506, + 0.807, + 0.604 + ], + "angle": 0, + "content": "
AttentionScanNet/DTU Test-Set (m)
abs-relabsrmseδ < 1.25
Asym attenu (ours)0.07340.13810.20800.9395
Sym. attenu0.07610.14960.22530.9333
MVSNet [59]0.10320.18650.27430.8935
(0.0143)(10.7235)(25.3989)(0.8936)
MVSNet(+atten)0.10180.18530.27340.8957
(0.0123)(9.1150)(22.3525)(0.9909)
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.449, + 0.614, + 0.86, + 0.641 + ], + "angle": 0, + "content": "(b) Asymmetric attention and MVsNet backbone. DTU results are in parentheses." + }, + { + "type": "table_caption", + "bbox": [ + 0.18, + 0.646, + 0.789, + 0.661 + ], + "angle": 0, + "content": "Table 3. Ablation study for our proposed modules and a different backbone architecture MVSNet [59]." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.675, + 0.305, + 0.766 + ], + "angle": 0, + "content": "
Itr. Tabs-relabsδ < 1.25
160.14130.07600.9364
240.14000.07520.9375
480.13920.07470.9382
640.13920.07460.9384
960.13920.07450.9385
1280.13940.07450.9385
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.14, + 0.775, + 0.253, + 0.789 + ], + "angle": 0, + "content": "(a) GRU iterations" + }, + { + "type": "table", + "bbox": [ + 0.341, + 0.674, + 0.606, + 0.766 + ], + "angle": 0, + "content": "
View No.abs-relabsδ < 1.25
3 (base)0.12040.21210.8603
5 (base)0.11480.19990.8726
3 (+pose)0.11620.20610.8711
5 (+pose)0.10960.19300.8840
3 (+pose,atten)0.10840.19230.8833
5 (+pose,atten)0.10000.17810.8967
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.407, + 0.776, + 0.516, + 0.789 + ], + "angle": 0, + "content": "(b) View numbers" + }, + { + "type": "table", + "bbox": [ + 0.622, + 0.674, + 0.9, + 0.766 + ], + "angle": 0, + "content": "
Samplingabs-relabsδ < 1.25
s10 (base)0.08850.16050.9211
key (base)0.08380.15980.9277
s10 (+pose)0.08270.15230.9277
key (+pose)0.07890.15310.9339
s10 (+pose,atten)0.07470.13920.9382
key (+pose,atten)0.06970.13480.9472
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.692, + 0.776, + 0.81, + 0.79 + ], + "angle": 0, + "content": "(c) Frame sampling" + }, + { + "type": "table_caption", + "bbox": [ + 0.19, + 0.795, + 0.779, + 0.81 + ], + "angle": 0, + "content": "Table 4. Ablation study of design choices. Bold is the best, and underline indicates the second best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.836, + 0.471, + 0.897 + ], + "angle": 0, + "content": "DTU: Tab. 5 shows that our model, i.e., Ours(+pose,atten) is trained/tested on DTU dataset with 3-view and 5-view input collections, respectively. We use the same training scheduling for a fair comparison. The 5-view result is worse" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.836, + 0.892, + 0.898 + ], + "angle": 0, + "content": "than the last row in Tab. 1 due to the lack of pretraining on ScanNet. Frame Sampling: We compare the simple view selection strategy (i.e., sampling by every 10 frames) with the heuristics [17]. Tab. 4-(c) shows that ours can be im" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "925" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.245, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.091, + 0.404, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.091, + 0.569, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.091, + 0.73, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.091, + 0.895, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.192, + 0.244, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.192, + 0.405, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.192, + 0.568, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.192, + 0.731, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.192, + 0.895, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.295, + 0.244, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.295, + 0.405, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.295, + 0.568, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.295, + 0.731, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.295, + 0.895, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.398, + 0.244, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.5, + 0.201, + 0.515 + ], + "angle": 0, + "content": "Ref. image" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.398, + 0.404, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.501, + 0.358, + 0.515 + ], + "angle": 0, + "content": "GT depth" + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.398, + 0.568, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.457, + 0.501, + 0.517, + 0.513 + ], + "angle": 0, + "content": "IterMVS" + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.398, + 0.731, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.501, + 0.676, + 0.513 + ], + "angle": 0, + "content": "PairNet" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.398, + 0.895, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.501, + 0.829, + 0.513 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.524, + 0.895, + 0.582 + ], + "angle": 0, + "content": "Figure 3. Qualitative results on ScanNet [15] (top two rows) and DTU [27] test set. Left two columns show reference image and ground truth depth, and other columns are the estimated depth by baseline IterMVS [52], PairNet [17] and ours (the full version), respectively. Our method outperforms the baselines on thin structures, small objects and boundaries, as highlighted in green for ours and in red for the baselines. The abs-err errors (in meters) are imposed on the depth maps for comparison." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.598, + 0.421, + 0.634 + ], + "angle": 0, + "content": "
View No. on DTUabs-rel (↓)abs (mm) (↓)rmse (↓)
3 (1 ref + 2 source)0.014911.068924.8831
5 (1 ref + 4 source)0.01198.841921.4327
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.635, + 0.454, + 0.649 + ], + "angle": 0, + "content": "Table 5. 3-view vs. 5-view training and testing on DTU [27]." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.665, + 0.435, + 0.732 + ], + "angle": 0, + "content": "
MethodsTime(fps)Mem.(MB)Param.(M)abs-rel (↓)
Ours(T=8)6.98429727.60.0760
Ours(T=12)5.91429727.60.0752
Ours(T=24)3.77429727.60.0734
IterMVS [52]22.6121710.340.0991
ESTD [39]14.08179936.20.0812
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Table 6. Comparison of run time, memory consumption, and accuracy on ScanNet [15] test set with frame dimension \\(320 \\times 256\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "proved when the selected views have more overlapping and the baselines are suitable. Our(+pose,atten) even with simple strategy outperforms other variants with heuristic sampling, and so are our(+pose) vs our(base). Runtime Overhead: Tab. 6 shows the run-time and memory consumption when processing \\(320 \\times 256\\) frames from the ScanNet test set. Ours (T=8/12/24) means 8, 12, and 24 GRU iterations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.628, + 0.621 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We have proposed RIAV-MVS, a novel learning-based MVS method. Our approach utilizes a convolutional GRU to iteratively optimize the index fields, which are used to access the cost volume and regress the depth. The cost volume is further improved through the application of a transformer block to the reference image and a residual pose network to correct the relative poses. Extensive experiments on ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32] have demonstrated the superior accuracy and cross-dataset generalizability of our method. Due to the plane-sweeping 3D cost volume and transformer selfattention, our method requires large memory consumption for high-resolution images. Moreover, the inference time is not as fast as other lightweight convolutional counterparts, due to the iterative update paradigm in our approach. 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Our core idea is a "learning-to-optimize" paradigm that iteratively indexes a plane-sweeping cost volume and regresses the depth map via a convolutional Gated Recurrent Unit (GRU). Since the cost volume plays a paramount role in encoding the multiview geometry, we aim to improve its construction both at pixel- and frame- levels. At the pixel level, we propose to break the symmetry of the Siamese network (which is typically used in MVS to extract image features) by introducing a transformer block to the reference image (but not to the source images). Such an asymmetric volume allows the network to extract global features from the reference image to predict its depth map. Given potential inaccuracies in the poses between reference and source images, we propose to incorporate a residual pose network to correct the relative poses. This essentially rectifies the cost volume at the frame level. We conduct extensive experiments on real-world MVS datasets and show that our method achieves state-of-the-art performance in terms of both within-dataset evaluation and cross-dataset generalization. + +# 1. Introduction + +Multi-view stereo (MVS) aims to recover dense 3D geometry from multiple images captured from different viewpoints with calibrated cameras [28]. It is a fundamental problem in computer vision and has wide applications ranging from autonomous driving [12, 55], remote sensing [3], augmented reality [50], to robotics [22]. Following the seminal MVSNet [59], many learning-based methods [17, 39, 40, 52, 53, 58, 60] have been proposed, achieving great improvements against their traditional counterparts [5, 14, 19, 44], in terms of accuracy or efficiency. + +Most of the learning-based MVS methods [17,39,40,52, 58,60] rely on traditional plane-sweeping [14,19] approach to generate a cost volume by comparing the CNN features of reference image and source images at several depth hypotheses, and then apply 2D or 3D convolutional encoder-decoders to aggregate and regularize the cost volume. The + +2D CNN methods [17] use multi-level features as skip connections to help decode the cost volume for depth regression. Even though the skip connections improve the depth maps, they weaken the role of cost volume and the geometry knowledge embedded therein to some extent. Hence, 2D CNN methods suffer from degraded generalization when testing on unseen domains. The 3D CNN methods [31] use soft-argmin to regress the depth map as the expectation from the cost volume distribution, and hence cannot predict the best candidate but instead an averaged one when dealing with a flat or multi-modal distribution caused by textureless, repeated, or occluded regions, etc. To mitigate these problems, we propose RIAV-MVS, a new paradigm to predict the depth via learning to recurrently index an asymmetric cost volume, obtaining improved accuracy and generalization. As depicted in Fig. 1, our RIAV-MVS features several nontrivial novel designs. + +First, we learn to index the cost volume by approaching the correct depth planes per pixel via an index field (a grid of indices to identify the depth hypotheses), as shown in Fig. 1-(e). The proposed recurrent estimate of the index field enables the learning to be anchored at the cost volume domain. Specifically, it recurrently predicts the residual index field in a descent direction of matching cost to retrieve cost values for the next iteration. The newly updated index field is used to directly index (i.e., sampling via linear interpolation) depth hypotheses to render a depth map, which is iteratively optimized to approach the ground truth depth, making the system end-to-end trainable. + +Second, to facilitate the optimization, we propose to improve the cost volume at pixel- and frame- levels, respectively. At the pixel level, a transformer block is asymmetrically applied to the reference view (but not to the source views). By capturing long-range global context via a transformer and pixel-wise local features via CNNs, we build an asymmetric cost volume to store more accurate matching similarity cues. At the frame level, we propose a residual pose net to rectify the camera poses that are usually obtained via Visual SLAM [9, 16, 30] and inevitably contain noise. The rectified poses are used to more accurately backward warp the reference features to match the counterparts in source views. + +![](images/0dea1038c6576faf439cb8d7185940f04379a223dd76c1fdd4bd1726e5dc21d6.jpg) +Figure 1. Our pipeline versus RAFT [49] and IterMVS [52]. Our recurrent processing of a plane-sweep cost volume by the iteratively refined index field serves as a new design for multi-view depth estimation. + +Our RIAV-MVS is depicted versus two related works RAFT [49] and IterMVS [52] as in Fig. 1. First, our method is developed using RAFT's GRU-based iterative optimization. However, RAFT operates an all-pair correlation volume (no multi-view geometry constraints) for optical flow (Fig. 1-(a) and (c)), our method is proposed for multi-view depth estimation by constructing a plane-sweep cost volume (Fig. 1-(b)). Second, IterMVS [52] iteratively predicts the depth and reconstructs a new plane-sweep cost volume using updated depth planes centered at the predicted depth (Fig. 1-(d)). Instead, as shown in Fig. 1-(e), our proposed index field serves as a new design that bridges the cost volume optimization (i.e., by learning better image features via back-propagation) and the depth map estimation (i.e., by sampling sweeping planes). It makes forward and backward learning differentiable. We conduct extensive experiments on indoor-scene datasets, including ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32]. We also performed well-designed ablation studies to verify the effectiveness and the generalization of our approach. + +# 2. Related Work + +Depth can be accurately predicted from stereo matching, which can be broadly divided into binocular stereo and multi-view stereo (MVS). The former requires calibrated setups of rectified stereo pairs, and many traditional [4, 24, 25, 43] and deep learning-based methods [7, 8, 10, 31, 33, 34, 41, 61, 62] have been proposed. Compared with binocular stereo, MVS methods estimate depth from a set of images or a video, where the camera moves and the scene is assumed static. In this section, we briefly review deep learning-based MVS methods. + +3D-CNN MVS Depth Estimation: Learning-based MVS methods [17, 39, 40, 52, 53, 58-60] rely on traditional plane-sweeping [14, 19] to generate a cost volume by associating reference frame and source frames for similarity matching, followed by encoder-decoder architectures for cost volume aggregation and depth map prediction. Among them, MVSNet [59], R-MVSNet [60], and DPSNet [26] leverage + +3D convolutions to regularize 4D cost volumes and regress depth maps via soft-argmin [31]. Different strategies have been introduced for cost volume construction. MVSNet [59] proposes a variance-based cost volume for multi-view similarity measurement. Cas-MVSNet [21] builds cascade cost volumes based on multi-scale feature pyramid and regresses the depth map in a multi-stage coarse-to-fine manner. Similarly, Cheng et al. propose UCS-Net [13] to build cascade adaptive thin volumes by leveraging variance-based uncertainty. CVP-MVSNet [58] builds a cost volume pyramid via multi-scale images to reduce to memory footprint. This cost volume mechanism is also adopted to other related tasks, e.g., 3D plane reconstruction in PlaneMVS [38], which leverages slanted plane sweeping to help plane reconstruction and accurate depth predictions. + +2D-CNN MVS Depth Estimation: Even though 3D convolutional methods usually deliver high accuracy, they demand a large memory footprint and computational cost. Instead, some methods, e.g., MVDepthNet [54] and DeepVideoMVS [17], generate 3D volumes by computing correlation or dot production between the extracted features of multi-view input images. The 3D cost volumes are further regularized by 2D convolutions. DeepVideoMVS [17] extracts multi-scale features. It uses the feature at half scale to construct the cost volume, and other features as the skip connections to a series of decoders for depth regression. PatchmatchNet [53] proposes an adaptive procedure mimicking PatchMatch [5] to achieve superior efficiency. 2D convolutions are much faster and more memory efficient than the 3D counterparts, making them better suitable for lightweight networks in real-time applications. + +Iterative Depth Estimation: Several methods adopt an iterative depth estimation paradigm. R-MVSNet [60] iteratively regularizes each slice of the cost volume with GRU along the depth dimension. Unlike the above mentioned cost volume-based approaches, Point-MVSNet [11] directly processes the target scene as point clouds. It first generates a coarse depth map, converts it into a point cloud and refines the point cloud iteratively to reduce the residual between the + +estimated depth and the ground truth depth. IterMVS [52] encodes a pixel-wise probability distribution of depth in the hidden state of a GRU-based estimator. During each iteration, the multi-scale matching information is injected into the GRU to predict the depth and confidence maps to facilitate the following 3D reconstruction. The depth maps are predicted via a combined classification and regression through the probability distribution. It uses arg-min to finish "classification", which is not differentiable and must be detached first before the following regression operation. Unlike IterMVS, our method learns to recurrently index the cost volume to directly find the best depth candidates in an end-to-end differentiable fashion. + +# 3. Method + +Our learning-based end-to-end multi-view stereo system, RIAV-MVS, aims to predict depth maps from a set of images, which are different views of the same scene with known camera poses, denoted by $\mathcal{I} = \{I_i\}_{i=0}^{N-1}$ . More specifically, RIAV-MVS uses one as the reference image and others as source images to infer the depth map of the reference image. Without loss of generality, we refer to the first image $I_0$ as the reference image and others as source views $\mathcal{I}^S$ , where $S = 1,2,\dots,N-1$ . An overview of our approach is illustrated in Fig. 2. It consists of feature extraction (Sec. 3.1), cost volume construction via plane-sweeping stereo [14, 19] (Sec. 3.2), and cost volume optimization and depth prediction (Sec. 3.3). Details will be discussed below. + +# 3.1. Feature Extraction + +Given a reference image $I_0$ and source images $\mathcal{I}^S$ , we extract matching features of $I_0$ and each of the $\mathcal{I}^S$ by F-Net (see below), and a context feature for $I_0$ by C-Net (see the supplementary material for C-Net), as shown in Fig. 2. + +Local Matching Feature Extraction: Our feature extractor F-Net is based on PairNet [17]. It is a lightweight Feature Pyramid Network (FPN) [35] on top of the first fourteen layers of MnasNet [47]. Specifically, the reference input image $I_0 \in \mathbb{R}^{H \times W}$ is spatially scaled down until 1/32 scale, and recovered up to 1/2 scale, resulting in multi-scale features $\{f_{0,s} \in \mathbb{R}^{\frac{H}{s} \times \frac{W}{s} \times F_0}\}$ ( $s = 2,4,8,16$ and $F_0 = 32$ for feature channels). In PairNet, $f_{0,2}$ is used to construct the cost volume, and other features are used in the skip connections to a series of decoders for depth regression. Unlike this, we add an extra fusion layer $\mathcal{G}$ to aggregate them into a matching feature $f_0$ at 1/4 scale, as + +$$ +f _ {0} = \mathcal {G} \left(\left\langle f _ {0, 2} \downarrow_ {2}, f _ {0, 4}, f _ {0, 8} \uparrow_ {2}, f _ {0, 1 6} \uparrow_ {4} \right\rangle\right) \tag {1} +$$ + +where the fusion layer $\mathcal{G}$ is a sequence of operations of $\mathrm{Conv}_{3\times 3}$ , batch normalization, ReLU, and $\mathrm{Conv}_{1\times 1}$ , $\downarrow x$ and $\uparrow x$ are downsampling and upsampling by scale $x$ , $\langle \cdot \rangle$ is concatenation along channel dimension, and $f_0\in$ + +$\mathbb{R}^{H / 4\times W / 4\times F_1}$ with $F_{1} = 128$ . Similarly, F-Net (with shared weights as that for $I_0$ ) is also applied to source images $\mathcal{L}^S$ to extract a set of matching features $f^{\mathcal{S}} = \{f_i\mid i\in \mathcal{S}\}$ + +Global Matching Feature of Reference View: Besides the local pixel-wise features extracted from CNNs, we also leverage global long-range information to better guide the feature matching. Towards that, a transformer layer (fourhead self-attention with positional encoding) [51] is applied to the local feature $f_{0}$ of the reference image, to construct an aggregated feature $f_{0}^{a} \in \mathbb{R}^{H / 4 \times W / 4 \times F_{1}}$ as + +$$ +f _ {0} ^ {a} = f _ {0} + \omega_ {\alpha} \sigma \left(\frac {\left(f _ {0} W ^ {Q}\right) \left(f _ {0} W ^ {K}\right) ^ {T}}{\sqrt {F _ {1}}} \left(f _ {0} W ^ {V}\right)\right) \tag {2} +$$ + +where $\sigma (\cdot)$ is the softmax operator, $\omega_{\alpha}$ is a learned scalar weight that is initialized to zero, and $W^{Q}, W^{K} \in \mathbb{R}^{F_{1} \times hF_{1}}$ and $W^{V} \in \mathbb{R}^{F_{1} \times F_{1}}$ are the projections matrices for query, key and value features, with $h = 4$ for multi-head attention. The final output $f_{0}^{a}$ contains both local and global information, which are balanced by the parameter $\omega_{\alpha}$ , to enhance the following cost volume construction. + +It is worth noting that this transformer self-attention is only applied to the reference image, while the source features still possess the local representations from CNNs. Our asymmetric employment of this transformer layer provides the capability to better balance the high-frequency features (by high-pass CNNs) and the low-frequency features by self-attention [42, 46]. The high-frequency features are beneficial to image matching at local and structural regions, while the low-frequency ones, with noisy information suppressed by the transformer's spatial smoothing (serving as a low-pass filter), provide more global context cues for robust matching, especially for the areas full of low-texture, repeated patterns, and occlusion, etc. This way, our network can learn where to rely on global features over local features, and vice versa. + +# 3.2. Cost Volume Construction + +We use the global matching feature map $f_0^a$ of $I_0$ and local matching features $f^S$ of $\mathcal{I}^S$ to build a cost volume. The cost (or matching) volume is defined on a 3D view frustum attached to the camera in perspective projection. It is generated by running the traditional plane-sweep stereo [14, 19] which uniformly samples $M_0 = 64$ plane hypotheses in the inverse depth space, s.t. $1 / d \sim U(d_{\min}, d_{\max})$ . Here $d_{\min}$ and $d_{\max}$ are the near and far planes of the 3D frustum, respectively. Following [17], we set $d_{\min} = 0.25$ and $d_{\max} = 20$ meters for indoor scenes (e.g., ScanNet [15]). + +For a given depth hypothesis $d$ and known camera intrinsic matrices $\mathcal{K} = \{K_i\}_{i=0}^N$ and relative transformations $\Theta = \{R_{0,i} \mid t_{0,i}\}_{i=1}^N$ from reference image $I_0$ , to source image $I_i$ , a cost map is computed by i) warping source image feature $f_i$ into the reference image and ii) calculating the similarity between the reference global feature $f_0^a$ and + +![](images/ec69df47d9b7e1e15ed55ce6fd6f6bfa78e701f92dc4a1f5a8322152170163a4.jpg) +Figure 2. Architecture of our proposed network. It consists of a feature extraction (i.e., F-Net, a Transformer, and C-Net) block, a cost volume construction and index field GRU-based optimization block, and a residual pose block. + +the warped feature $\tilde{f}_i$ . To generate $\tilde{f}_i$ , we implement the homography $H$ as a backward 2D grid sampling. Specifically, a pixel $\mathbf{p} = (u,v,1)^T$ in the reference image will be warped to its counterpart $\tilde{\mathbf{p}}_i$ in source image $i$ as follows: + +$$ +\tilde {\mathbf {p}} _ {i} = H (\mathbf {p} \mid d, \mathcal {K}, \Theta) = K _ {i} \left(R _ {0, i} \left(K _ {0} ^ {- 1} \mathbf {p} d\right) + t _ {0, i}\right) \tag {3} +$$ + +Then $\tilde{f}_i$ is bilinearly sampled from $f_{i}$ as $\tilde{f}_i(\mathbf{p}) = f_i(\tilde{\mathbf{p}}_i)$ . Given the warped source feature $\tilde{f}_i$ and the reference feature $f_0^a$ , the cost volume is formulated as $C_0(d) = \frac{1}{N - 1}\sum_{i\in S}\frac{f_0^a\cdot\tilde{f}_i^T}{\sqrt{F_1}}$ . This way, we can construct a cost volume for all depth candidates $\mathcal{B}_0 = \{d_i\}_{i = 0}^{M_0 - 1}$ , resulting in a 3D tensor, denoted as $C_0\in \mathbb{R}^{H / 4\times W / 4\times M_0}$ . + +# 3.3. GRU-based Iterative Optimization + +We solve the depth prediction as learning to optimize the dense stereo matching problem [5, 24, 48, 57]. Given the generated cost volume $C_0$ as in Sec. 3.2, the depth estimation of the reference image is formulated as finding the best solution $D^{*} = \mathrm{argmin}_{D}E(D,C_{0})$ , which minimizes an energy function $E(D,C_0)$ (including a data term and a smoothness term). Unfortunately, such a global minimization is NP-complete due to many discontinuity preserving energies [6]. Approximate solutions are proposed by loosening the energy function, e.g., the binocular stereo matching solved by Semi-Global Matching (SGM) [24]. In SGM, the matching cost $C_0$ is iteratively aggregated by summing the costs (of all 1D minimum cost paths that end in pixel $\mathbf{p}$ at disparity $d^1$ ) when traversing from pixel $\mathbf{p} - \mathbf{r}$ to pixel $\mathbf{p}$ in a direction $\mathbf{r}$ (out of sixteen directions) and the best disparity at each pixel $\mathbf{p}$ is given by $d^{*}(\mathbf{p}) = \mathrm{argmin}_{d}(C^{\prime}(\mathbf{p},d))$ with $C^\prime$ being the aggregated cost volume. Similar to SGM, + +we do not directly optimize the energy function $E$ , but learn to process the cost volume $C_0$ . + +However, several major problems still need to be solved. SGM is not differentiable due to its winner-take-all (WTA) by argmin, making it unable to train the system in an end-to-end manner. Its differentiable counterpart, SGA [62], was proposed by changing the min to sum when aggregating the cost volume, and replacing the argmin with softargmin when predicting the disparity from the optimized cost volume, but still i) the update direction $\mathbf{r}$ when traversing from pixel $\mathbf{p} - \mathbf{r}$ to $\mathbf{p}$ needs to be predefined, and ii) the softargmin focuses on measuring the distance of the expectation of disparity map to the ground truth disparity, and hence cannot handle multi-modal distributions in $C_0$ well [52]. + +Therefore, towards an end-to-end, differentiable solution, we propose to use a GRU-based module to implicitly optimize the matching volume. It estimates a sequence of index fields $\{\phi_t\}_{t=1}^T$ by unrolling the optimization problem to $T$ iterative updates (in a descent direction), mimicking the updates of a first-order optimizer according to [1,2,36,49]. At each iteration $t$ , the index field $\phi_t \in \mathbb{R}^{H \times W}$ is estimated as a grid of indices to iteratively better approach (i.e., closer to the ground truth) depth hypotheses having a lower matching cost. Specifically, a residual index field $\delta \phi_t$ is predicted as an update direction for next iteration, i.e., $\phi_{t+1} = \phi_t + \delta \phi_t$ , (analogous to the direction $\mathbf{r}$ in SGM), which is explicitly driven by training the system (e.g., feature encoders, the transformer layer, and the residual pose net, etc.) to minimize the loss between the predicted depth maps and the ground truth. The recurrent estimate of the index field enables the learning to be directly anchored at the cost volume domain. This indexing paradigm differentiates our approach from other depth estimation methods, such as the depth regression which fuses cost volume and + +the skipped multi-level features by 2D CNNs [17, 52, 53], and soft-argmin [31] after cost volume aggregation and regularization by 3D CNNs [21, 39, 59, 60]. + +Index Field Iterative Updates: We use a 3 chained GRUs [36] to estimate a sequence of index fields, $\{\phi_t\in$ $\mathbb{R}^{H / 4\times W / 4}\}_{t = 1}^T$ from an initial starting point $\phi_0$ . We use a softargmin-start from the cost volume $C_0$ , i.e., $\phi_0 =$ $\sum_{i = 0}^{M_1 - 1}i\sigma (C_0)$ where $\sigma (\cdot)$ is the softmax operator along the last dimension of cost volume $C_0$ , to convert it to a probability of each index $i$ . This setup facilitates the convergence of our predictions. A four-layer matching pyramid $\{C_0^i\in \mathbb{R}^{H / 4\times W / 4\times M_0 / 2^i}\}_{i = 1}^4$ is built by repeated pooling the cost volume $C_0$ along the depth dimension with kernel size 2 as in [49]. To index the matching pyramid, we define a lookup operator analogous to the one in [36]. Given a current estimate of index field $\phi_t$ , a 1D grid is constructed with integer offsets up to $r = \pm 4$ around the $\phi_t$ . The grid is used to index from each level of the matching pyramid via linear interpolation due to $\phi_t$ being real numbers. The retrieved cost values are then concatenated into a single feature map $C_0^{\phi_t}\in \mathbb{R}^{H / 4\times W / 4\times F_2}$ . Then the index field $\phi_t$ , the retrieved cost features $C_0^{\phi_t}$ , and context features $f_0^c$ are concatenated, and fed into the GRU layer, together with a latent hidden state $h_t$ . The GRU outputs a residual index field $\delta \phi_t$ , and a new hidden state $h_{t + 1}$ : + +$$ +\delta \phi_ {t}, h _ {t + 1} \Leftarrow \operatorname {G R U} \left(\left\langle \phi_ {t}, C _ {0} ^ {\phi_ {t}}, f _ {0} ^ {c} \right\rangle , h _ {t}\right); \phi_ {t + 1} \Leftarrow \phi_ {t} + \delta \phi_ {t} +$$ + +Upsampling and Depth Estimation: The depth map at iteration $t$ is estimated by sampling the depth hypotheses via linear interpolation given the index field $\phi_t$ . Since $\phi_t$ is at 1/4 resolution, we upsample it to full resolution using a convex combination of a $3 \times 3$ neighbors as in [49]. Specifically, a weight mask $W_0 \in \mathbb{R}^{H / 4 \times W / 4 \times (4 \times 4 \times 9)}$ is predicted from the hidden state $h_t$ using two convolutional layers and softmax is performed over the weights of those 9 neighbors. The final high resolution index field $\phi_t^u$ is obtained by taking a weighted combination over the 9 neighbors, and reshaping to the resolution $\mathrm{H} \times \mathrm{W}$ . Convex combination can be implemented using the einsum function in PyTorch. + +When constructing the cost volume, we use $M_0 = 64$ depth hypotheses, $\mathcal{B}_0 = \{d_i\}_{i=0}^{M_0 - 1}$ . A small $M_0$ helps reduce the computation and space. If we use the upsampled index field $\phi_t^u$ to directly sample the planes $\mathcal{B}_0$ , we see discontinuities in the inferred depth map, even though the quantitative evaluation is not hindered. To mitigate this, we propose a coarse-to-fine pattern, and to use $M_1 = 256$ depth hypotheses $\mathcal{B}_1 = \{d_i\}_{i=0}^{M_1 - 1}$ . Analogous to upsampling in optical flow or disparity in binocular stereo, the flow or disparity values themselves have to be scaled when implementing the spatial upsampling. Our depth index fields are adjusted by a scale $s_D = \frac{M_1}{M_0} = 4$ . To mimic the convex combination before mentioned, we apply a similar weighted summation along the depth dimension when sampling depth from + +$\mathcal{B}_1$ . Specifically, another mask $W_{1} \in \mathbb{R}^{H \times W \times s_{D} \times M_{0}}$ is predicted from the hidden state using three convolutional layers, and further reshaped to $H \times W \times M_{1}$ . Given a pixel $\mathbf{p}$ , and the upsampled index field $\phi_t^u$ , the final depth $D_{t}$ is estimated as + +$$ +D _ {t} (p) = \frac {\sum_ {i \in \Omega (\mathbf {p})} \mathcal {B} _ {1} [ i ] W _ {1} (\mathbf {p} , \lfloor i \rfloor)}{\sum_ {i \in \Omega (\mathbf {p})} W _ {1} (\mathbf {p} , \lfloor i \rfloor)} \tag {4} +$$ + +where, we aggregate the neighbors within a radius $r = 4$ centered at the index $\phi_t^u (\mathbf{p})$ for a given pixel $\mathbf{p}$ , and $\lfloor i \rfloor$ gives a greatest integer less than or equal to $i$ , and $[i]$ means to index the depth planes $\mathcal{B}_1$ via linear interpolation, due to index $i$ being a real number. + +It is worth mentioning that our method embeds both regression (similar to softmax in existing methods [39, 59, 60]) and classification (similar to argmin), which make it robust to multi-modal distributions, and achieving sub-pixel precision thanks to linear interpolation. Combining both classification and regression has been seen in [52], but ours does not use the argmax operator when achieving the "classification" purpose, thanks to our proposal of index fields estimation, which differentiably bridges the cost volume indexing and depth hypotheses sampling directly in a sub-pixel precision. + +Residual Pose Net: An accurate cost volume benefits the GRU-based iterative optimization. The quality of the generated cost volume $C_0$ is not only determined by the matching features $(f_0^a$ and $f^S$ ) (for which we have proposed asymmetric employment of the transformer layer), but also by the homography warping as in Eq. 3. However, the camera poses are, in practice, usually obtained by Visual SLAM algorithms [9, 16, 30], and inevitably contain noise. Therefore, we propose a residual pose net to rectify the camera poses for accurately backward warping the reference features to match the corresponding features in source images. We use an image-net pretrained ResNet18 [23] backbone as in [29, 56] to encode the reference image and the warped source images. Specifically, given the current estimated depth map $D_t$ at iteration $t$ , and the ground truth depth $D_{gt}$ , we warp a source image $I_i$ into the reference image through the homography defined in Eq. 3 with (noisy) ground truth camera poses $\Theta$ and the $D_t$ or $D_{gt}$ . We randomly select $D_t$ or $D_{gt}$ with a probability $\mathrm{prob}(D_t) = 0.6$ during network training, but always use the predicted depth $D_t$ during network inference. The input to the pose net is the concatenated $I_0$ and the warped $\tilde{I}_i$ , and the output is an axis-angle representation, which is further converted to a residual rotation matrix $\Delta \theta_i$ , for an updated one $\theta_i' = \Delta \theta_i \cdot \theta_i$ . This way, we predict the residual poses $\Delta \Theta = \{\Delta \theta_i\}_{i=1}^{N-1}$ for each of the source and reference pair, and perform the rectification as $\Theta' = \Delta \Theta \cdot \Theta$ . We leverage the updated poses $\Theta'$ to calculate a more accurate cost volume $C_1$ using Eq. 3, followed by the remaining iterations of GRU. + +# 3.4. Loss Function + +Our network is supervised on the inverse $L_{1}$ loss between the predicted depths $\{D_t\}_{i=1}^T$ and the ground truth $D_{gt}$ . It is evaluated over valid pixels (i.e., with non-zero ground truth depths). Following the exponentially increasing weights as in [36, 49], this depth loss is defined as + +$$ +\mathcal {L} _ {D} = \sum_ {t = 1} ^ {T} \gamma^ {T - t} \frac {1}{N _ {v}} \sum_ {i = 0} ^ {N _ {v} - 1} \| \frac {1}{D _ {t} (i)} - \frac {1}{D _ {g t} (i)} \| _ {1} \tag {5} +$$ + +where, $\| \cdot \|_1$ measures the $l_1$ distance, $N_v$ is the number of valid pixels, and $\gamma = 0.9$ . We also apply the photometric loss $\mathcal{L}_P$ (as defined in [56]) to supervise the residual pose network. The total loss is then defined as $\mathcal{L} = \mathcal{L}_D + \mathcal{L}_P$ . + +# 4. Experiments + +# 4.1. Datasets + +Our experiments use four indoor-scene datasets, which have RGB-D video frames with ground truth depths and known camera poses. ScanNet [15] and DTU [27] are used in training and testing, and 7scenes [20] and RGB-D Scenes V2 [32] are evaluated for zero-shot generalization. (1) ScanNet. Our network is trained from scratch on ScanNet [15] using the official training split. We use 279k training samples and 20k validation ones. (2) DTU. Following [53,59,60], the depth range for sampling depth hypotheses is set to $d_{min} = 0.425$ and $d_{max} = 0.935$ meters. We use 27k training samples, 6k validation ones, and 1k ones for evaluation. Each sample has 5 frames. (3) 7-Scenes. We select 13 sequences from 7-Scenes for zero-shot generalization. (4) RGB-D Scenes V2. We select 8 sequences for testing. Details about train/val/test splits, training, and implementation are shown in the supplementary material. + +# 4.2. Comparison with Existing Methods + +In this section, our method is evaluated and compared with several state-of-the-art MVS methods. Our network is strictly compared with two baselines PairNet [17] and IterMVS [52], following the same training schedule and training set. We also compare ours with other MVS methods either by running the provided models or referring to the available evaluation metrics when testing on the same datasets, including ESTDepth [39], Neural RGBD [37], MVDepthNet [54], DPSNet [26], and DELTAS [45]. + +Quantitative Evaluation. We evaluate the depth maps using the standard metrics in [18], including mean absolute relative error (abs-rel), mean absolute error (abs), squared relative error (sq-rel), root mean square error in linear scale (rmse) and log scale (rmse-log), and inlier ratios under thresholds of $\sigma < 1.25 / 1.25^2 / 1.25^3$ . Tab. 1 shows the results on the ScanNet benchmark of our methods and sev- + +eral state-of-the-art MVS methods. We compare two variants of our models: i) base: a base version with our recurrent indexing cost volume, and ii) +pose,atten: a full version with residual pose and the asymmetric employment of transformer self-attention. Our full model achieves the best performance in most metrics except the inlier ratio under $\sigma < 1.25^2$ , outperformed by DELTAS [45] and ESTD [39]. But the inlier ratio is not as essential as abs-rel and abs. Zero-shot Generalization. We evaluate the generalization performance of our method RIAV-MVS from ScanNet to other indoor datasets without any fine-tuning. Tab. 2 shows the results of the methods trained on ScanNet [15] and directly tested on 7-scenes [20] and RGB-D Scenes V2 [32]. Our models outperform the baselines, and our two variants all have strong generalization performance. Qualitative Results. Fig. 3 demonstrates the qualitative results of our method vs. baselines IterMVS [52] and PairNet [17] on the test set of ScanNet [15] and DTU [27]. Our method can make more accurate and sharp depth predictions, especially for regions near boundaries and edges. For both near and far objects, our method outperforms the baselines. + +# 4.3. Ablation Study + +Efficacy of Proposed Modules: Our design is verified by ablating the modules to three variants, as shown in Tab. 3-(a). The base version itself can achieve competitive performance on ScanNet and better generalization, verifying the efficacy of our novel design - cost volume recurrent indexing via index field. Further, the performance can be consistently boosted when the residual pose net (i.e., variant +pose) and transformer self-attention are added (i.e., variant +pose,atten). Therefore, each of the proposed modules can consistently help with accurate depth estimation. Tab. 3-(b) shows the benefit of using asymmetric attention over symmetric attention. We also see improvements when applying our asymmetric attention to the MVSNet [59] backbone on ScanNet and DTU test sets (see the results in parentheses). Number of GRU Iterations and Convergence: Tab. 4-(a) shows the ablation study on different number of GRU iterations $T$ . The results are obtained by running our model (the full version) on the ScanNet test set, with $T = 16, 24, 48, 64, 96$ , and 128. Running more iterations boosts our depth prediction, but after $T \geq 96$ , the gain is marginal. View Number: We compare 3-view (i.e., 1 reference + 2 source images) and 5-view (i.e., 1 reference + 4 source images). Tab. 4-(b) shows that the more frames are used for matching, the better the depth will be. The results are obtained for the zero-shot generalization from ScanNet to 7-Scenes. Note that our full model (+pose,atten) with 3-view input outperforms the other two variants with 5-view input, showing the asymmetrical employment of the transformer self-attention can boost the prediction due to the mining of more global information. 3-view vs 5-view on + +
MethodScanNet Test-Set (m)DTU Test-Set (mm)
abs-relabssq-relrmsermse-logδ < 1.25δ < 1.252abs-relabsrmse
MVDepth [54]0.11670.23010.05960.32360.16100.84530.9639---
MVDepth-FT0.11160.20870.07630.31430.15000.88040.9734---
DPSNet [26]0.12000.21040.06880.31390.16040.86400.9612---
DPSNet-FT0.09860.19980.04590.28400.13480.88800.9785---
DELTAS [45]0.09150.17100.03270.23900.12260.91470.9872---
NRGBD [37]0.10130.16570.05020.25000.13150.91600.9790---
ESTD [39]0.08120.15050.02980.21990.11040.93130.9871---
MVSNet [59]0.10320.186450.04650.27430.13850.89350.97750.014310.723525.3989
PairNet [17]0.08950.17090.06150.27340.12080.91720.98040.01299.442821.4650
IterMVS [52]0.09910.18180.05180.27330.13680.89950.97410.014610.622528.7009
Ours(base)0.08850.16050.03800.23470.11830.92110.98100.01168.288721.5806
Ours(+pose,atten)0.07340.13810.02810.20800.10300.93950.98620.00926.777118.5953
+ +Table 1. Quantitative evaluation results on the test set of ScanNet [15] and the test set of DTU [27]. Error metrics (lower is better) are abs-rel, abs, sq-rel, rmse, rmse-log, while accuracy (higher is better) metrics are $\delta < 1.25 / 1.25^2 / 1.25^3$ . Here -FT denotes finetuned on ScanNet. Bold is the best score, and underline indicates the second best one. + +
ScanNet ⇒ Others7-ScenesRGB-D Scenes V2
abs-relabssq-relrmseδ < 1.25abs-relabssq-relrmseδ < 1.25
NRGBD [37]0.23340.40600.21630.53580.6803-----
ESTD [39]0.14650.25280.07290.33820.8036-----
PairNet [17]0.11570.20860.06770.29260.87680.09950.13820.02790.19710.9393
IterMVS [52]0.13360.23630.10330.34250.85180.08110.12450.03400.21330.9496
Ours(base)0.11480.19990.05520.28570.87260.09670.13360.02460.18360.9427
Ours(+pose,atten)0.10000.17810.04730.26640.89670.08030.11680.02000.17030.9632
+ +Table 2. Zero-shot generalization from ScanNet [15] to 7-scenes [20] and RGB-D Scenes V2 [32]. Our methods achieve better generalization. We sample the sequences every 10 frames, and each sample has 5 frames for multi-view stereo depth prediction. + +
VariantsScanNet Test-Set (m)
abs-relabsrmseδ < 1.25
Ours(base)0.08850.16050.23470.9211
Ours(+pose)0.08270.15230.22530.9277
Ours(+pose,atten)0.07340.13810.20800.9395
+ +(a) We compare three variants of our models. + +
AttentionScanNet/DTU Test-Set (m)
abs-relabsrmseδ < 1.25
Asym attenu (ours)0.07340.13810.20800.9395
Sym. attenu0.07610.14960.22530.9333
MVSNet [59]0.10320.18650.27430.8935
(0.0143)(10.7235)(25.3989)(0.8936)
MVSNet(+atten)0.10180.18530.27340.8957
(0.0123)(9.1150)(22.3525)(0.9909)
+ +(b) Asymmetric attention and MVsNet backbone. DTU results are in parentheses. + +
Itr. Tabs-relabsδ < 1.25
160.14130.07600.9364
240.14000.07520.9375
480.13920.07470.9382
640.13920.07460.9384
960.13920.07450.9385
1280.13940.07450.9385
+ +(a) GRU iterations + +Table 3. Ablation study for our proposed modules and a different backbone architecture MVSNet [59]. + +
View No.abs-relabsδ < 1.25
3 (base)0.12040.21210.8603
5 (base)0.11480.19990.8726
3 (+pose)0.11620.20610.8711
5 (+pose)0.10960.19300.8840
3 (+pose,atten)0.10840.19230.8833
5 (+pose,atten)0.10000.17810.8967
+ +(b) View numbers + +
Samplingabs-relabsδ < 1.25
s10 (base)0.08850.16050.9211
key (base)0.08380.15980.9277
s10 (+pose)0.08270.15230.9277
key (+pose)0.07890.15310.9339
s10 (+pose,atten)0.07470.13920.9382
key (+pose,atten)0.06970.13480.9472
+ +(c) Frame sampling + +Table 4. Ablation study of design choices. Bold is the best, and underline indicates the second best. + +DTU: Tab. 5 shows that our model, i.e., Ours(+pose,atten) is trained/tested on DTU dataset with 3-view and 5-view input collections, respectively. We use the same training scheduling for a fair comparison. The 5-view result is worse + +than the last row in Tab. 1 due to the lack of pretraining on ScanNet. Frame Sampling: We compare the simple view selection strategy (i.e., sampling by every 10 frames) with the heuristics [17]. Tab. 4-(c) shows that ours can be im + +![](images/2c47c7743b436770eed809c68eb97122c0153d2992d349b04804a7f31d4db532.jpg) + +![](images/f8ec11b074ab58990aab59a4f8706b619aaba5a71649e6241a988f033443a37a.jpg) + +![](images/0cbbc0b8829043b875f56ce7c5e30211631fe2dedc61fcc7ecc5a580d3f6adc0.jpg) + +![](images/be164c96a78c32b619e206bf71cce111b184bd6065060d0d36020631554f0a47.jpg) + +![](images/3d2accc473bb7806d6fe2a55b33be5bee30b1e894c5f2c171f932051b2233252.jpg) + +![](images/22b4b953a1d3bfe2d76f0a49712c0ab98542d654cc47c90e78593d6dc3843a2f.jpg) + +![](images/55492bc24df457847bc73813e32e4398f7ad2fd3e9062b605147ed545e7d8145.jpg) + +![](images/111ce22ff0c78cad3ab1bd674d2b5869bad780adb157ffe098075ef161dfe4c3.jpg) + +![](images/cbbba39d91c21b3fcefcfa61736b0ce7e0abc5cb6baa5e37f1e996894c58f4de.jpg) + +![](images/379d9db278f90a491608b876a3653cc417b40db06885b77d7fe3dab8579f4ce5.jpg) + +![](images/27b84bccf639331a898739c8cb7f0dbbd639495b21a3f69abbcf65e09ead5797.jpg) + +![](images/5f786e9b092f94cd29513f2e4a724753e83926f9e7f14bd59819d71eece491dd.jpg) + +![](images/78271702adc0f237f407bc1acea6d388636c61498bcb7b223e47f21be7654e72.jpg) + +![](images/da6b0c05f9a4687948a8405a9c3ff781da38f74622addc9af25fda459ca1ea03.jpg) + +![](images/46d7abc7927e4689cf58da9d9e4752468b1c6d8a9957f05df00a022913ad91f2.jpg) + +![](images/4a2b0d058b3440f8a7be6e45860f57704e91ff49c9e4fee5477568e6a19935a1.jpg) +Ref. image + +![](images/a511150d73d1d67648dd74537f8006aa9092fbba0a576a833850dc7070652270.jpg) +GT depth + +![](images/659a52eae79c656ce97ac87ae9513470e028a602019b5a6e811e33db1d382b37.jpg) +IterMVS + +![](images/11798852638036f2a3277a6afcb29db1ebc8748f53355e9e14821dac9c9ca86e.jpg) +PairNet +Figure 3. Qualitative results on ScanNet [15] (top two rows) and DTU [27] test set. Left two columns show reference image and ground truth depth, and other columns are the estimated depth by baseline IterMVS [52], PairNet [17] and ours (the full version), respectively. Our method outperforms the baselines on thin structures, small objects and boundaries, as highlighted in green for ours and in red for the baselines. The abs-err errors (in meters) are imposed on the depth maps for comparison. + +![](images/e03640d26f9a0665e829ae3b5ef57a2d350322bc2a5daa5687abb593305ca490.jpg) +Ours + +
View No. on DTUabs-rel (↓)abs (mm) (↓)rmse (↓)
3 (1 ref + 2 source)0.014911.068924.8831
5 (1 ref + 4 source)0.01198.841921.4327
+ +Table 5. 3-view vs. 5-view training and testing on DTU [27]. + +
MethodsTime(fps)Mem.(MB)Param.(M)abs-rel (↓)
Ours(T=8)6.98429727.60.0760
Ours(T=12)5.91429727.60.0752
Ours(T=24)3.77429727.60.0734
IterMVS [52]22.6121710.340.0991
ESTD [39]14.08179936.20.0812
+ +Table 6. Comparison of run time, memory consumption, and accuracy on ScanNet [15] test set with frame dimension $320 \times 256$ . + +proved when the selected views have more overlapping and the baselines are suitable. Our(+pose,atten) even with simple strategy outperforms other variants with heuristic sampling, and so are our(+pose) vs our(base). Runtime Overhead: Tab. 6 shows the run-time and memory consumption when processing $320 \times 256$ frames from the ScanNet test set. Ours (T=8/12/24) means 8, 12, and 24 GRU iterations. + +# 5. Conclusions + +We have proposed RIAV-MVS, a novel learning-based MVS method. Our approach utilizes a convolutional GRU to iteratively optimize the index fields, which are used to access the cost volume and regress the depth. The cost volume is further improved through the application of a transformer block to the reference image and a residual pose network to correct the relative poses. Extensive experiments on ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32] have demonstrated the superior accuracy and cross-dataset generalizability of our method. Due to the plane-sweeping 3D cost volume and transformer selfattention, our method requires large memory consumption for high-resolution images. Moreover, the inference time is not as fast as other lightweight convolutional counterparts, due to the iterative update paradigm in our approach. In future work, we plan to leverage temporal information to further enhance depth estimation from posed-video streams. + +# References + +[1] Jonas Adler and Ozan Öktem. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12):124007, 2017. 4 +[2] Jonas Adler and Ozan Oktem. Learned primal-dual reconstruction. 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GA-Net: Guided aggregation net for end-to-end stereo matching. In CVPR, 2019. 2, 4 \ No newline at end of file diff --git a/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/images.zip b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a95f25c092c46c812d23b918f2bc99eef6fbf46b --- /dev/null +++ b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91bb5f428ed15d25552cb5093aae713368723985f071c81676fe38a142f11cce +size 660439 diff --git a/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/layout.json b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e10f479fba9d9cd0c633468cee0c2c0799810a35 --- /dev/null +++ b/2023/RIAV-MVS_ Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo/layout.json @@ -0,0 +1,10727 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 53, + 103, + 539, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 103, + 539, + 120 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 539, + 120 + ], + "type": "text", + "content": "RIAV-MVS: Recurrent-Indexing an Asymmetric Volume for Multi-View Stereo" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 162, + 144, + 429, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 144, + 429, + 171 + ], + "spans": [ + { + "bbox": [ + 162, + 144, + 429, + 171 + ], + "type": "text", + "content": "Changjiang Cai, Pan Ji, Qingan Yan, Yi Xu \nOPPO US Research Center, InnoPeak Technology, Inc." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 224, + 289, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 289, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 289, + 477 + ], + "type": "text", + "content": "This paper presents a learning-based method for multiview depth estimation from posed images. Our core idea is a \"learning-to-optimize\" paradigm that iteratively indexes a plane-sweeping cost volume and regresses the depth map via a convolutional Gated Recurrent Unit (GRU). Since the cost volume plays a paramount role in encoding the multiview geometry, we aim to improve its construction both at pixel- and frame- levels. At the pixel level, we propose to break the symmetry of the Siamese network (which is typically used in MVS to extract image features) by introducing a transformer block to the reference image (but not to the source images). Such an asymmetric volume allows the network to extract global features from the reference image to predict its depth map. Given potential inaccuracies in the poses between reference and source images, we propose to incorporate a residual pose network to correct the relative poses. This essentially rectifies the cost volume at the frame level. We conduct extensive experiments on real-world MVS datasets and show that our method achieves state-of-the-art performance in terms of both within-dataset evaluation and cross-dataset generalization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 501, + 128, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 128, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 128, + 513 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 521, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 641 + ], + "type": "text", + "content": "Multi-view stereo (MVS) aims to recover dense 3D geometry from multiple images captured from different viewpoints with calibrated cameras [28]. It is a fundamental problem in computer vision and has wide applications ranging from autonomous driving [12, 55], remote sensing [3], augmented reality [50], to robotics [22]. Following the seminal MVSNet [59], many learning-based methods [17, 39, 40, 52, 53, 58, 60] have been proposed, achieving great improvements against their traditional counterparts [5, 14, 19, 44], in terms of accuracy or efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "content": "Most of the learning-based MVS methods [17,39,40,52, 58,60] rely on traditional plane-sweeping [14,19] approach to generate a cost volume by comparing the CNN features of reference image and source images at several depth hypotheses, and then apply 2D or 3D convolutional encoder-decoders to aggregate and regularize the cost volume. The" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "text", + "content": "2D CNN methods [17] use multi-level features as skip connections to help decode the cost volume for depth regression. Even though the skip connections improve the depth maps, they weaken the role of cost volume and the geometry knowledge embedded therein to some extent. Hence, 2D CNN methods suffer from degraded generalization when testing on unseen domains. The 3D CNN methods [31] use soft-argmin to regress the depth map as the expectation from the cost volume distribution, and hence cannot predict the best candidate but instead an averaged one when dealing with a flat or multi-modal distribution caused by textureless, repeated, or occluded regions, etc. To mitigate these problems, we propose RIAV-MVS, a new paradigm to predict the depth via learning to recurrently index an asymmetric cost volume, obtaining improved accuracy and generalization. As depicted in Fig. 1, our RIAV-MVS features several nontrivial novel designs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 409, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 547, + 553 + ], + "type": "text", + "content": "First, we learn to index the cost volume by approaching the correct depth planes per pixel via an index field (a grid of indices to identify the depth hypotheses), as shown in Fig. 1-(e). The proposed recurrent estimate of the index field enables the learning to be anchored at the cost volume domain. Specifically, it recurrently predicts the residual index field in a descent direction of matching cost to retrieve cost values for the next iteration. The newly updated index field is used to directly index (i.e., sampling via linear interpolation) depth hypotheses to render a depth map, which is iteratively optimized to approach the ground truth depth, making the system end-to-end trainable." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "Second, to facilitate the optimization, we propose to improve the cost volume at pixel- and frame- levels, respectively. At the pixel level, a transformer block is asymmetrically applied to the reference view (but not to the source views). By capturing long-range global context via a transformer and pixel-wise local features via CNNs, we build an asymmetric cost volume to store more accurate matching similarity cues. At the frame level, we propose a residual pose net to rectify the camera poses that are usually obtained via Visual SLAM [9, 16, 30] and inevitably contain noise. The rectified poses are used to more accurately backward warp the reference features to match the counterparts in source views." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "919" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 71, + 517, + 190 + ], + "blocks": [ + { + "bbox": [ + 78, + 71, + 517, + 190 + ], + "lines": [ + { + "bbox": [ + 78, + 71, + 517, + 190 + ], + "spans": [ + { + "bbox": [ + 78, + 71, + 517, + 190 + ], + "type": "image", + "image_path": "0dea1038c6576faf439cb8d7185940f04379a223dd76c1fdd4bd1726e5dc21d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "type": "text", + "content": "Figure 1. Our pipeline versus RAFT [49] and IterMVS [52]. Our recurrent processing of a plane-sweep cost volume by the iteratively refined index field serves as a new design for multi-view depth estimation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 234, + 289, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 289, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 289, + 475 + ], + "type": "text", + "content": "Our RIAV-MVS is depicted versus two related works RAFT [49] and IterMVS [52] as in Fig. 1. First, our method is developed using RAFT's GRU-based iterative optimization. However, RAFT operates an all-pair correlation volume (no multi-view geometry constraints) for optical flow (Fig. 1-(a) and (c)), our method is proposed for multi-view depth estimation by constructing a plane-sweep cost volume (Fig. 1-(b)). Second, IterMVS [52] iteratively predicts the depth and reconstructs a new plane-sweep cost volume using updated depth planes centered at the predicted depth (Fig. 1-(d)). Instead, as shown in Fig. 1-(e), our proposed index field serves as a new design that bridges the cost volume optimization (i.e., by learning better image features via back-propagation) and the depth map estimation (i.e., by sampling sweeping planes). It makes forward and backward learning differentiable. We conduct extensive experiments on indoor-scene datasets, including ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32]. We also performed well-designed ablation studies to verify the effectiveness and the generalization of our approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 487, + 134, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 134, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 134, + 499 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 508, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 628 + ], + "type": "text", + "content": "Depth can be accurately predicted from stereo matching, which can be broadly divided into binocular stereo and multi-view stereo (MVS). The former requires calibrated setups of rectified stereo pairs, and many traditional [4, 24, 25, 43] and deep learning-based methods [7, 8, 10, 31, 33, 34, 41, 61, 62] have been proposed. Compared with binocular stereo, MVS methods estimate depth from a set of images or a video, where the camera moves and the scene is assumed static. In this section, we briefly review deep learning-based MVS methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "3D-CNN MVS Depth Estimation: Learning-based MVS methods [17, 39, 40, 52, 53, 58-60] rely on traditional plane-sweeping [14, 19] to generate a cost volume by associating reference frame and source frames for similarity matching, followed by encoder-decoder architectures for cost volume aggregation and depth map prediction. Among them, MVSNet [59], R-MVSNet [60], and DPSNet [26] leverage" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 234, + 547, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 547, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 547, + 415 + ], + "type": "text", + "content": "3D convolutions to regularize 4D cost volumes and regress depth maps via soft-argmin [31]. Different strategies have been introduced for cost volume construction. MVSNet [59] proposes a variance-based cost volume for multi-view similarity measurement. Cas-MVSNet [21] builds cascade cost volumes based on multi-scale feature pyramid and regresses the depth map in a multi-stage coarse-to-fine manner. Similarly, Cheng et al. propose UCS-Net [13] to build cascade adaptive thin volumes by leveraging variance-based uncertainty. CVP-MVSNet [58] builds a cost volume pyramid via multi-scale images to reduce to memory footprint. This cost volume mechanism is also adopted to other related tasks, e.g., 3D plane reconstruction in PlaneMVS [38], which leverages slanted plane sweeping to help plane reconstruction and accurate depth predictions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 420, + 548, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 548, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 548, + 612 + ], + "type": "text", + "content": "2D-CNN MVS Depth Estimation: Even though 3D convolutional methods usually deliver high accuracy, they demand a large memory footprint and computational cost. Instead, some methods, e.g., MVDepthNet [54] and DeepVideoMVS [17], generate 3D volumes by computing correlation or dot production between the extracted features of multi-view input images. The 3D cost volumes are further regularized by 2D convolutions. DeepVideoMVS [17] extracts multi-scale features. It uses the feature at half scale to construct the cost volume, and other features as the skip connections to a series of decoders for depth regression. PatchmatchNet [53] proposes an adaptive procedure mimicking PatchMatch [5] to achieve superior efficiency. 2D convolutions are much faster and more memory efficient than the 3D counterparts, making them better suitable for lightweight networks in real-time applications." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Iterative Depth Estimation: Several methods adopt an iterative depth estimation paradigm. R-MVSNet [60] iteratively regularizes each slice of the cost volume with GRU along the depth dimension. Unlike the above mentioned cost volume-based approaches, Point-MVSNet [11] directly processes the target scene as point clouds. It first generates a coarse depth map, converts it into a point cloud and refines the point cloud iteratively to reduce the residual between the" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "920" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "estimated depth and the ground truth depth. IterMVS [52] encodes a pixel-wise probability distribution of depth in the hidden state of a GRU-based estimator. During each iteration, the multi-scale matching information is injected into the GRU to predict the depth and confidence maps to facilitate the following 3D reconstruction. The depth maps are predicted via a combined classification and regression through the probability distribution. It uses arg-min to finish \"classification\", which is not differentiable and must be detached first before the following regression operation. Unlike IterMVS, our method learns to recurrently index the cost volume to directly find the best depth candidates in an end-to-end differentiable fashion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 238, + 103, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 103, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 103, + 251 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "content": "Our learning-based end-to-end multi-view stereo system, RIAV-MVS, aims to predict depth maps from a set of images, which are different views of the same scene with known camera poses, denoted by " + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I_i\\}_{i=0}^{N-1}" + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "content": ". More specifically, RIAV-MVS uses one as the reference image and others as source images to infer the depth map of the reference image. Without loss of generality, we refer to the first image " + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "content": " as the reference image and others as source views " + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^S" + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "inline_equation", + "content": "S = 1,2,\\dots,N-1" + }, + { + "bbox": [ + 46, + 258, + 290, + 426 + ], + "type": "text", + "content": ". An overview of our approach is illustrated in Fig. 2. It consists of feature extraction (Sec. 3.1), cost volume construction via plane-sweeping stereo [14, 19] (Sec. 3.2), and cost volume optimization and depth prediction (Sec. 3.3). Details will be discussed below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 432, + 160, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 160, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 160, + 444 + ], + "type": "text", + "content": "3.1. Feature Extraction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": "Given a reference image " + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": " and source images " + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^S" + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": ", we extract matching features of " + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": " and each of the " + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^S" + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": " by F-Net (see below), and a context feature for " + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 450, + 288, + 498 + ], + "type": "text", + "content": " by C-Net (see the supplementary material for C-Net), as shown in Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": "Local Matching Feature Extraction: Our feature extractor F-Net is based on PairNet [17]. It is a lightweight Feature Pyramid Network (FPN) [35] on top of the first fourteen layers of MnasNet [47]. Specifically, the reference input image " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "I_0 \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " is spatially scaled down until 1/32 scale, and recovered up to 1/2 scale, resulting in multi-scale features " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\{f_{0,s} \\in \\mathbb{R}^{\\frac{H}{s} \\times \\frac{W}{s} \\times F_0}\\}" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "s = 2,4,8,16" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "F_0 = 32" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " for feature channels). In PairNet, " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "f_{0,2}" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " is used to construct the cost volume, and other features are used in the skip connections to a series of decoders for depth regression. Unlike this, we add an extra fusion layer " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " to aggregate them into a matching feature " + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "inline_equation", + "content": "f_0" + }, + { + "bbox": [ + 46, + 498, + 287, + 643 + ], + "type": "text", + "content": " at 1/4 scale, as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 644, + 287, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 644, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 84, + 644, + 287, + 658 + ], + "type": "interline_equation", + "content": "f _ {0} = \\mathcal {G} \\left(\\left\\langle f _ {0, 2} \\downarrow_ {2}, f _ {0, 4}, f _ {0, 8} \\uparrow_ {2}, f _ {0, 1 6} \\uparrow_ {4} \\right\\rangle\\right) \\tag {1}", + "image_path": "153c1b2175941df4c4257511bf4e823775f947fa2f165d0f011b510cd5024028.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "where the fusion layer " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " is a sequence of operations of " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{3\\times 3}" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": ", batch normalization, ReLU, and " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{1\\times 1}" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\downarrow x" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\uparrow x" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " are downsampling and upsampling by scale " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\cdot \\rangle" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " is concatenation along channel dimension, and " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_0\\in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H / 4\\times W / 4\\times F_1}" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "F_{1} = 128" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": " . Similarly, F-Net (with shared weights as that for " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": " ) is also applied to source images " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^S" + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "text", + "content": " to extract a set of matching features " + }, + { + "bbox": [ + 304, + 71, + 545, + 108 + ], + "type": "inline_equation", + "content": "f^{\\mathcal{S}} = \\{f_i\\mid i\\in \\mathcal{S}\\}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "text", + "content": "Global Matching Feature of Reference View: Besides the local pixel-wise features extracted from CNNs, we also leverage global long-range information to better guide the feature matching. Towards that, a transformer layer (fourhead self-attention with positional encoding) [51] is applied to the local feature " + }, + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "inline_equation", + "content": "f_{0}" + }, + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "text", + "content": " of the reference image, to construct an aggregated feature " + }, + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "inline_equation", + "content": "f_{0}^{a} \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times F_{1}}" + }, + { + "bbox": [ + 304, + 108, + 547, + 193 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 321, + 201, + 545, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 201, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 321, + 201, + 545, + 228 + ], + "type": "interline_equation", + "content": "f _ {0} ^ {a} = f _ {0} + \\omega_ {\\alpha} \\sigma \\left(\\frac {\\left(f _ {0} W ^ {Q}\\right) \\left(f _ {0} W ^ {K}\\right) ^ {T}}{\\sqrt {F _ {1}}} \\left(f _ {0} W ^ {V}\\right)\\right) \\tag {2}", + "image_path": "c7fb27e9768b38bde11669cad8d92a1f2851ca0903f308bd3fe0b613c56cd4ce.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " is the softmax operator, " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\omega_{\\alpha}" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " is a learned scalar weight that is initialized to zero, and " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "W^{Q}, W^{K} \\in \\mathbb{R}^{F_{1} \\times hF_{1}}" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "W^{V} \\in \\mathbb{R}^{F_{1} \\times F_{1}}" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " are the projections matrices for query, key and value features, with " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "h = 4" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " for multi-head attention. The final output " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "f_{0}^{a}" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": " contains both local and global information, which are balanced by the parameter " + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\omega_{\\alpha}" + }, + { + "bbox": [ + 304, + 233, + 545, + 317 + ], + "type": "text", + "content": ", to enhance the following cost volume construction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 317, + 546, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 546, + 496 + ], + "type": "text", + "content": "It is worth noting that this transformer self-attention is only applied to the reference image, while the source features still possess the local representations from CNNs. Our asymmetric employment of this transformer layer provides the capability to better balance the high-frequency features (by high-pass CNNs) and the low-frequency features by self-attention [42, 46]. The high-frequency features are beneficial to image matching at local and structural regions, while the low-frequency ones, with noisy information suppressed by the transformer's spatial smoothing (serving as a low-pass filter), provide more global context cues for robust matching, especially for the areas full of low-texture, repeated patterns, and occlusion, etc. This way, our network can learn where to rely on global features over local features, and vice versa." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 503, + 453, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 453, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 453, + 516 + ], + "type": "text", + "content": "3.2. Cost Volume Construction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": "We use the global matching feature map " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "f_0^a" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " and local matching features " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "f^S" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^S" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " to build a cost volume. The cost (or matching) volume is defined on a 3D view frustum attached to the camera in perspective projection. It is generated by running the traditional plane-sweep stereo [14, 19] which uniformly samples " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "M_0 = 64" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " plane hypotheses in the inverse depth space, s.t. " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "1 / d \\sim U(d_{\\min}, d_{\\max})" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "d_{\\min}" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "d_{\\max}" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " are the near and far planes of the 3D frustum, respectively. Following [17], we set " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "d_{\\min} = 0.25" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "inline_equation", + "content": "d_{\\max} = 20" + }, + { + "bbox": [ + 304, + 521, + 545, + 642 + ], + "type": "text", + "content": " meters for indoor scenes (e.g., ScanNet [15])." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "For a given depth hypothesis " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " and known camera intrinsic matrices " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{K} = \\{K_i\\}_{i=0}^N" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " and relative transformations " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Theta = \\{R_{0,i} \\mid t_{0,i}\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " from reference image " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": ", to source image " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": ", a cost map is computed by i) warping source image feature " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_i" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " into the reference image and ii) calculating the similarity between the reference global feature " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_0^a" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "921" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 72, + 521, + 235 + ], + "blocks": [ + { + "bbox": [ + 75, + 72, + 521, + 235 + ], + "lines": [ + { + "bbox": [ + 75, + 72, + 521, + 235 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 521, + 235 + ], + "type": "image", + "image_path": "ec69df47d9b7e1e15ed55ce6fd6f6bfa78e701f92dc4a1f5a8322152170163a4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 547, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 268 + ], + "type": "text", + "content": "Figure 2. Architecture of our proposed network. It consists of a feature extraction (i.e., F-Net, a Transformer, and C-Net) block, a cost volume construction and index field GRU-based optimization block, and a residual pose block." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": "the warped feature " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": ". To generate " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": ", we implement the homography " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": " as a backward 2D grid sampling. Specifically, a pixel " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (u,v,1)^T" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": " in the reference image will be warped to its counterpart " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{p}}_i" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": " in source image " + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 285, + 288, + 335 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 352, + 287, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 352, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 56, + 352, + 287, + 369 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {p}} _ {i} = H (\\mathbf {p} \\mid d, \\mathcal {K}, \\Theta) = K _ {i} \\left(R _ {0, i} \\left(K _ {0} ^ {- 1} \\mathbf {p} d\\right) + t _ {0, i}\\right) \\tag {3}", + "image_path": "b46f55cc5dfc660d65c3c9f7e237c68ff1ce9700cd26a62f238d7911b83966a6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": "Then " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": " is bilinearly sampled from " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i(\\mathbf{p}) = f_i(\\tilde{\\mathbf{p}}_i)" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": ". Given the warped source feature " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": " and the reference feature " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "f_0^a" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": ", the cost volume is formulated as " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "C_0(d) = \\frac{1}{N - 1}\\sum_{i\\in S}\\frac{f_0^a\\cdot\\tilde{f}_i^T}{\\sqrt{F_1}}" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": ". This way, we can construct a cost volume for all depth candidates " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_0 = \\{d_i\\}_{i = 0}^{M_0 - 1}" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": ", resulting in a 3D tensor, denoted as " + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "inline_equation", + "content": "C_0\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0}" + }, + { + "bbox": [ + 47, + 383, + 288, + 464 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 471, + 233, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 233, + 484 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 233, + 484 + ], + "type": "text", + "content": "3.3. GRU-based Iterative Optimization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": "We solve the depth prediction as learning to optimize the dense stereo matching problem [5, 24, 48, 57]. Given the generated cost volume " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " as in Sec. 3.2, the depth estimation of the reference image is formulated as finding the best solution " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "D^{*} = \\mathrm{argmin}_{D}E(D,C_{0})" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": ", which minimizes an energy function " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "E(D,C_0)" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " (including a data term and a smoothness term). Unfortunately, such a global minimization is NP-complete due to many discontinuity preserving energies [6]. Approximate solutions are proposed by loosening the energy function, e.g., the binocular stereo matching solved by Semi-Global Matching (SGM) [24]. In SGM, the matching cost " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " is iteratively aggregated by summing the costs (of all 1D minimum cost paths that end in pixel " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " at disparity " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "d^1" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": ") when traversing from pixel " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{p} - \\mathbf{r}" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " to pixel " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " in a direction " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " (out of sixteen directions) and the best disparity at each pixel " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " is given by " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "d^{*}(\\mathbf{p}) = \\mathrm{argmin}_{d}(C^{\\prime}(\\mathbf{p},d))" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "inline_equation", + "content": "C^\\prime" + }, + { + "bbox": [ + 46, + 490, + 287, + 694 + ], + "type": "text", + "content": " being the aggregated cost volume. Similar to SGM," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "content": "we do not directly optimize the energy function " + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "content": ", but learn to process the cost volume " + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "content": "However, several major problems still need to be solved. SGM is not differentiable due to its winner-take-all (WTA) by argmin, making it unable to train the system in an end-to-end manner. Its differentiable counterpart, SGA [62], was proposed by changing the min to sum when aggregating the cost volume, and replacing the argmin with softargmin when predicting the disparity from the optimized cost volume, but still i) the update direction " + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "content": " when traversing from pixel " + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{p} - \\mathbf{r}" + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "content": " needs to be predefined, and ii) the softargmin focuses on measuring the distance of the expectation of disparity map to the ground truth disparity, and hence cannot handle multi-modal distributions in " + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 304, + 315, + 546, + 471 + ], + "type": "text", + "content": " well [52]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": "Therefore, towards an end-to-end, differentiable solution, we propose to use a GRU-based module to implicitly optimize the matching volume. It estimates a sequence of index fields " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{\\phi_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": " by unrolling the optimization problem to " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": " iterative updates (in a descent direction), mimicking the updates of a first-order optimizer according to [1,2,36,49]. At each iteration " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": ", the index field " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\phi_t \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": " is estimated as a grid of indices to iteratively better approach (i.e., closer to the ground truth) depth hypotheses having a lower matching cost. Specifically, a residual index field " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\delta \\phi_t" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": " is predicted as an update direction for next iteration, i.e., " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\phi_{t+1} = \\phi_t + \\delta \\phi_t" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": ", (analogous to the direction " + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": " in SGM), which is explicitly driven by training the system (e.g., feature encoders, the transformer layer, and the residual pose net, etc.) to minimize the loss between the predicted depth maps and the ground truth. The recurrent estimate of the index field enables the learning to be directly anchored at the cost volume domain. This indexing paradigm differentiates our approach from other depth estimation methods, such as the depth regression which fuses cost volume and" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "text", + "content": "1 Abuse of notation " + }, + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "text", + "content": " for depth in MVS or disparity in binocular stereo" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "text", + "content": "922" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "the skipped multi-level features by 2D CNNs [17, 52, 53], and soft-argmin [31] after cost volume aggregation and regularization by 3D CNNs [21, 39, 59, 60]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": "Index Field Iterative Updates: We use a 3 chained GRUs [36] to estimate a sequence of index fields, " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\{\\phi_t\\in" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H / 4\\times W / 4}\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " from an initial starting point " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_0" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ". We use a softargmin-start from the cost volume " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_0 =" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\sum_{i = 0}^{M_1 - 1}i\\sigma (C_0)" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " is the softmax operator along the last dimension of cost volume " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", to convert it to a probability of each index " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ". This setup facilitates the convergence of our predictions. A four-layer matching pyramid " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\{C_0^i\\in \\mathbb{R}^{H / 4\\times W / 4\\times M_0 / 2^i}\\}_{i = 1}^4" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " is built by repeated pooling the cost volume " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " along the depth dimension with kernel size 2 as in [49]. To index the matching pyramid, we define a lookup operator analogous to the one in [36]. Given a current estimate of index field " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", a 1D grid is constructed with integer offsets up to " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "r = \\pm 4" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " around the " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ". The grid is used to index from each level of the matching pyramid via linear interpolation due to " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " being real numbers. The retrieved cost values are then concatenated into a single feature map " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "C_0^{\\phi_t}\\in \\mathbb{R}^{H / 4\\times W / 4\\times F_2}" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ". Then the index field " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", the retrieved cost features " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "C_0^{\\phi_t}" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", and context features " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "f_0^c" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": " are concatenated, and fed into the GRU layer, together with a latent hidden state " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ". The GRU outputs a residual index field " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "\\delta \\phi_t" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ", and a new hidden state " + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "inline_equation", + "content": "h_{t + 1}" + }, + { + "bbox": [ + 46, + 108, + 289, + 375 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 383, + 282, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 383, + 282, + 397 + ], + "spans": [ + { + "bbox": [ + 52, + 383, + 282, + 397 + ], + "type": "interline_equation", + "content": "\\delta \\phi_ {t}, h _ {t + 1} \\Leftarrow \\operatorname {G R U} \\left(\\left\\langle \\phi_ {t}, C _ {0} ^ {\\phi_ {t}}, f _ {0} ^ {c} \\right\\rangle , h _ {t}\\right); \\phi_ {t + 1} \\Leftarrow \\phi_ {t} + \\delta \\phi_ {t}", + "image_path": "606feae712a29cac83d661c8041c72c6f66c06bd12c012bc52753146b0e4b1f5.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": "Upsampling and Depth Estimation: The depth map at iteration " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " is estimated by sampling the depth hypotheses via linear interpolation given the index field " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " is at 1/4 resolution, we upsample it to full resolution using a convex combination of a " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " neighbors as in [49]. Specifically, a weight mask " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "W_0 \\in \\mathbb{R}^{H / 4 \\times W / 4 \\times (4 \\times 4 \\times 9)}" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " is predicted from the hidden state " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " using two convolutional layers and softmax is performed over the weights of those 9 neighbors. The final high resolution index field " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi_t^u" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": " is obtained by taking a weighted combination over the 9 neighbors, and reshaping to the resolution " + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathrm{H} \\times \\mathrm{W}" + }, + { + "bbox": [ + 46, + 402, + 287, + 545 + ], + "type": "text", + "content": ". Convex combination can be implemented using the einsum function in PyTorch." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "When constructing the cost volume, we use " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "M_0 = 64" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " depth hypotheses, " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_0 = \\{d_i\\}_{i=0}^{M_0 - 1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". A small " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "M_0" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " helps reduce the computation and space. If we use the upsampled index field " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi_t^u" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " to directly sample the planes " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_0" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ", we see discontinuities in the inferred depth map, even though the quantitative evaluation is not hindered. To mitigate this, we propose a coarse-to-fine pattern, and to use " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "M_1 = 256" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " depth hypotheses " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_1 = \\{d_i\\}_{i=0}^{M_1 - 1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". Analogous to upsampling in optical flow or disparity in binocular stereo, the flow or disparity values themselves have to be scaled when implementing the spatial upsampling. Our depth index fields are adjusted by a scale " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "s_D = \\frac{M_1}{M_0} = 4" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". To mimic the convex combination before mentioned, we apply a similar weighted summation along the depth dimension when sampling depth from" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_1" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": ". Specifically, another mask " + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "W_{1} \\in \\mathbb{R}^{H \\times W \\times s_{D} \\times M_{0}}" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": " is predicted from the hidden state using three convolutional layers, and further reshaped to " + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "H \\times W \\times M_{1}" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": ". Given a pixel " + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": ", and the upsampled index field " + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\phi_t^u" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": ", the final depth " + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 71, + 545, + 131 + ], + "type": "text", + "content": " is estimated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 351, + 137, + 545, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 137, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 351, + 137, + 545, + 167 + ], + "type": "interline_equation", + "content": "D _ {t} (p) = \\frac {\\sum_ {i \\in \\Omega (\\mathbf {p})} \\mathcal {B} _ {1} [ i ] W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)}{\\sum_ {i \\in \\Omega (\\mathbf {p})} W _ {1} (\\mathbf {p} , \\lfloor i \\rfloor)} \\tag {4}", + "image_path": "a8430c35767e24367c9bf5be4a7168c7edd35f321415036c0723b336e42a9902.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": "where, we aggregate the neighbors within a radius " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "r = 4" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " centered at the index " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\phi_t^u (\\mathbf{p})" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " for a given pixel " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\lfloor i \\rfloor" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " gives a greatest integer less than or equal to " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "[i]" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " means to index the depth planes " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_1" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " via linear interpolation, due to index " + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 172, + 545, + 232 + ], + "type": "text", + "content": " being a real number." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 233, + 546, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 546, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 546, + 365 + ], + "type": "text", + "content": "It is worth mentioning that our method embeds both regression (similar to softmax in existing methods [39, 59, 60]) and classification (similar to argmin), which make it robust to multi-modal distributions, and achieving sub-pixel precision thanks to linear interpolation. Combining both classification and regression has been seen in [52], but ours does not use the argmax operator when achieving the \"classification\" purpose, thanks to our proposal of index fields estimation, which differentiably bridges the cost volume indexing and depth hypotheses sampling directly in a sub-pixel precision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": "Residual Pose Net: An accurate cost volume benefits the GRU-based iterative optimization. The quality of the generated cost volume " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "C_0" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " is not only determined by the matching features " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "(f_0^a" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "f^S" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ") (for which we have proposed asymmetric employment of the transformer layer), but also by the homography warping as in Eq. 3. However, the camera poses are, in practice, usually obtained by Visual SLAM algorithms [9, 16, 30], and inevitably contain noise. Therefore, we propose a residual pose net to rectify the camera poses for accurately backward warping the reference features to match the corresponding features in source images. We use an image-net pretrained ResNet18 [23] backbone as in [29, 56] to encode the reference image and the warped source images. Specifically, given the current estimated depth map " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_t" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " at iteration " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ", and the ground truth depth " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{gt}" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ", we warp a source image " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " into the reference image through the homography defined in Eq. 3 with (noisy) ground truth camera poses " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_t" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{gt}" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ". We randomly select " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_t" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{gt}" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " with a probability " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{prob}(D_t) = 0.6" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " during network training, but always use the predicted depth " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_t" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " during network inference. The input to the pose net is the concatenated " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " and the warped " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{I}_i" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ", and the output is an axis-angle representation, which is further converted to a residual rotation matrix " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\theta_i" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ", for an updated one " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\theta_i' = \\Delta \\theta_i \\cdot \\theta_i" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ". This way, we predict the residual poses " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\Theta = \\{\\Delta \\theta_i\\}_{i=1}^{N-1}" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " for each of the source and reference pair, and perform the rectification as " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Theta' = \\Delta \\Theta \\cdot \\Theta" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": ". We leverage the updated poses " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Theta'" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " to calculate a more accurate cost volume " + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "inline_equation", + "content": "C_1" + }, + { + "bbox": [ + 304, + 366, + 546, + 713 + ], + "type": "text", + "content": " using Eq. 3, followed by the remaining iterations of GRU." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "text", + "content": "923" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 136, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 136, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 136, + 83 + ], + "type": "text", + "content": "3.4. Loss Function" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "text", + "content": "Our network is supervised on the inverse " + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "text", + "content": " loss between the predicted depths " + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "inline_equation", + "content": "\\{D_t\\}_{i=1}^T" + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "text", + "content": " and the ground truth " + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "inline_equation", + "content": "D_{gt}" + }, + { + "bbox": [ + 47, + 90, + 287, + 152 + ], + "type": "text", + "content": ". It is evaluated over valid pixels (i.e., with non-zero ground truth depths). Following the exponentially increasing weights as in [36, 49], this depth loss is defined as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 72, + 159, + 287, + 194 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 159, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 72, + 159, + 287, + 194 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D} = \\sum_ {t = 1} ^ {T} \\gamma^ {T - t} \\frac {1}{N _ {v}} \\sum_ {i = 0} ^ {N _ {v} - 1} \\| \\frac {1}{D _ {t} (i)} - \\frac {1}{D _ {g t} (i)} \\| _ {1} \\tag {5}", + "image_path": "fca811cd11ceb599b875379ac8bbdc55ac048e3fb8772ae8c5bedccecc2d2a18.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_1" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": " measures the " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "l_1" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": " distance, " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "N_v" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": " is the number of valid pixels, and " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "\\gamma = 0.9" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": ". We also apply the photometric loss " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_P" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": " (as defined in [56]) to supervise the residual pose network. The total loss is then defined as " + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_D + \\mathcal{L}_P" + }, + { + "bbox": [ + 47, + 205, + 288, + 253 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 264, + 128, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 128, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 128, + 277 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 285, + 110, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 110, + 296 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 110, + 296 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "text", + "content": "Our experiments use four indoor-scene datasets, which have RGB-D video frames with ground truth depths and known camera poses. ScanNet [15] and DTU [27] are used in training and testing, and 7scenes [20] and RGB-D Scenes V2 [32] are evaluated for zero-shot generalization. (1) ScanNet. Our network is trained from scratch on ScanNet [15] using the official training split. We use 279k training samples and 20k validation ones. (2) DTU. Following [53,59,60], the depth range for sampling depth hypotheses is set to " + }, + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "inline_equation", + "content": "d_{min} = 0.425" + }, + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "inline_equation", + "content": "d_{max} = 0.935" + }, + { + "bbox": [ + 46, + 303, + 288, + 495 + ], + "type": "text", + "content": " meters. We use 27k training samples, 6k validation ones, and 1k ones for evaluation. Each sample has 5 frames. (3) 7-Scenes. We select 13 sequences from 7-Scenes for zero-shot generalization. (4) RGB-D Scenes V2. We select 8 sequences for testing. Details about train/val/test splits, training, and implementation are shown in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 502, + 236, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 236, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 236, + 516 + ], + "type": "text", + "content": "4.2. Comparison with Existing Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 629 + ], + "type": "text", + "content": "In this section, our method is evaluated and compared with several state-of-the-art MVS methods. Our network is strictly compared with two baselines PairNet [17] and IterMVS [52], following the same training schedule and training set. We also compare ours with other MVS methods either by running the provided models or referring to the available evaluation metrics when testing on the same datasets, including ESTDepth [39], Neural RGBD [37], MVDepthNet [54], DPSNet [26], and DELTAS [45]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": "Quantitative Evaluation. We evaluate the depth maps using the standard metrics in [18], including mean absolute relative error (abs-rel), mean absolute error (abs), squared relative error (sq-rel), root mean square error in linear scale (rmse) and log scale (rmse-log), and inlier ratios under thresholds of " + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\sigma < 1.25 / 1.25^2 / 1.25^3" + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": ". Tab. 1 shows the results on the ScanNet benchmark of our methods and sev-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "eral state-of-the-art MVS methods. We compare two variants of our models: i) base: a base version with our recurrent indexing cost volume, and ii) +pose,atten: a full version with residual pose and the asymmetric employment of transformer self-attention. Our full model achieves the best performance in most metrics except the inlier ratio under " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\sigma < 1.25^2" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", outperformed by DELTAS [45] and ESTD [39]. But the inlier ratio is not as essential as abs-rel and abs. Zero-shot Generalization. We evaluate the generalization performance of our method RIAV-MVS from ScanNet to other indoor datasets without any fine-tuning. Tab. 2 shows the results of the methods trained on ScanNet [15] and directly tested on 7-scenes [20] and RGB-D Scenes V2 [32]. Our models outperform the baselines, and our two variants all have strong generalization performance. Qualitative Results. Fig. 3 demonstrates the qualitative results of our method vs. baselines IterMVS [52] and PairNet [17] on the test set of ScanNet [15] and DTU [27]. Our method can make more accurate and sharp depth predictions, especially for regions near boundaries and edges. For both near and far objects, our method outperforms the baselines." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 333, + 400, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 333, + 400, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 333, + 400, + 346 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "content": "Efficacy of Proposed Modules: Our design is verified by ablating the modules to three variants, as shown in Tab. 3-(a). The base version itself can achieve competitive performance on ScanNet and better generalization, verifying the efficacy of our novel design - cost volume recurrent indexing via index field. Further, the performance can be consistently boosted when the residual pose net (i.e., variant +pose) and transformer self-attention are added (i.e., variant +pose,atten). Therefore, each of the proposed modules can consistently help with accurate depth estimation. Tab. 3-(b) shows the benefit of using asymmetric attention over symmetric attention. We also see improvements when applying our asymmetric attention to the MVSNet [59] backbone on ScanNet and DTU test sets (see the results in parentheses). Number of GRU Iterations and Convergence: Tab. 4-(a) shows the ablation study on different number of GRU iterations " + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "content": ". The results are obtained by running our model (the full version) on the ScanNet test set, with " + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "inline_equation", + "content": "T = 16, 24, 48, 64, 96" + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "content": ", and 128. Running more iterations boosts our depth prediction, but after " + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "inline_equation", + "content": "T \\geq 96" + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "content": ", the gain is marginal. View Number: We compare 3-view (i.e., 1 reference + 2 source images) and 5-view (i.e., 1 reference + 4 source images). Tab. 4-(b) shows that the more frames are used for matching, the better the depth will be. The results are obtained for the zero-shot generalization from ScanNet to 7-Scenes. Note that our full model (+pose,atten) with 3-view input outperforms the other two variants with 5-view input, showing the asymmetrical employment of the transformer self-attention can boost the prediction due to the mining of more global information. 3-view vs 5-view on" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "924" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 71, + 524, + 218 + ], + "blocks": [ + { + "bbox": [ + 73, + 71, + 524, + 218 + ], + "lines": [ + { + "bbox": [ + 73, + 71, + 524, + 218 + ], + "spans": [ + { + "bbox": [ + 73, + 71, + 524, + 218 + ], + "type": "table", + "html": "
MethodScanNet Test-Set (m)DTU Test-Set (mm)
abs-relabssq-relrmsermse-logδ < 1.25δ < 1.252abs-relabsrmse
MVDepth [54]0.11670.23010.05960.32360.16100.84530.9639---
MVDepth-FT0.11160.20870.07630.31430.15000.88040.9734---
DPSNet [26]0.12000.21040.06880.31390.16040.86400.9612---
DPSNet-FT0.09860.19980.04590.28400.13480.88800.9785---
DELTAS [45]0.09150.17100.03270.23900.12260.91470.9872---
NRGBD [37]0.10130.16570.05020.25000.13150.91600.9790---
ESTD [39]0.08120.15050.02980.21990.11040.93130.9871---
MVSNet [59]0.10320.186450.04650.27430.13850.89350.97750.014310.723525.3989
PairNet [17]0.08950.17090.06150.27340.12080.91720.98040.01299.442821.4650
IterMVS [52]0.09910.18180.05180.27330.13680.89950.97410.014610.622528.7009
Ours(base)0.08850.16050.03800.23470.11830.92110.98100.01168.288721.5806
Ours(+pose,atten)0.07340.13810.02810.20800.10300.93950.98620.00926.777118.5953
", + "image_path": "8d758ac223a99a0a56b1c2d148f3cec30f47d5c9e1e38098be866d1f9c573a28.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 74, + 270, + 520, + 358 + ], + "blocks": [ + { + "bbox": [ + 46, + 225, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 547, + 258 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation results on the test set of ScanNet [15] and the test set of DTU [27]. Error metrics (lower is better) are abs-rel, abs, sq-rel, rmse, rmse-log, while accuracy (higher is better) metrics are " + }, + { + "bbox": [ + 46, + 225, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\delta < 1.25 / 1.25^2 / 1.25^3" + }, + { + "bbox": [ + 46, + 225, + 547, + 258 + ], + "type": "text", + "content": ". Here -FT denotes finetuned on ScanNet. Bold is the best score, and underline indicates the second best one." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 270, + 520, + 358 + ], + "lines": [ + { + "bbox": [ + 74, + 270, + 520, + 358 + ], + "spans": [ + { + "bbox": [ + 74, + 270, + 520, + 358 + ], + "type": "table", + "html": "
ScanNet ⇒ Others7-ScenesRGB-D Scenes V2
abs-relabssq-relrmseδ < 1.25abs-relabssq-relrmseδ < 1.25
NRGBD [37]0.23340.40600.21630.53580.6803-----
ESTD [39]0.14650.25280.07290.33820.8036-----
PairNet [17]0.11570.20860.06770.29260.87680.09950.13820.02790.19710.9393
IterMVS [52]0.13360.23630.10330.34250.85180.08110.12450.03400.21330.9496
Ours(base)0.11480.19990.05520.28570.87260.09670.13360.02460.18360.9427
Ours(+pose,atten)0.10000.17810.04730.26640.89670.08030.11680.02000.17030.9632
", + "image_path": "9ca88c997d8f87e1404fd3012594369ace5f8291ccd8f3946efe42d0b3dc6a05.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 56, + 418, + 259, + 471 + ], + "blocks": [ + { + "bbox": [ + 46, + 367, + 546, + 391 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 546, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 546, + 391 + ], + "type": "text", + "content": "Table 2. Zero-shot generalization from ScanNet [15] to 7-scenes [20] and RGB-D Scenes V2 [32]. Our methods achieve better generalization. We sample the sequences every 10 frames, and each sample has 5 frames for multi-view stereo depth prediction." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 418, + 259, + 471 + ], + "lines": [ + { + "bbox": [ + 56, + 418, + 259, + 471 + ], + "spans": [ + { + "bbox": [ + 56, + 418, + 259, + 471 + ], + "type": "table", + "html": "
VariantsScanNet Test-Set (m)
abs-relabsrmseδ < 1.25
Ours(base)0.08850.16050.23470.9211
Ours(+pose)0.08270.15230.22530.9277
Ours(+pose,atten)0.07340.13810.20800.9395
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AttentionScanNet/DTU Test-Set (m)
abs-relabsrmseδ < 1.25
Asym attenu (ours)0.07340.13810.20800.9395
Sym. attenu0.07610.14960.22530.9333
MVSNet [59]0.10320.18650.27430.8935
(0.0143)(10.7235)(25.3989)(0.8936)
MVSNet(+atten)0.10180.18530.27340.8957
(0.0123)(9.1150)(22.3525)(0.9909)
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Itr. Tabs-relabsδ < 1.25
160.14130.07600.9364
240.14000.07520.9375
480.13920.07470.9382
640.13920.07460.9384
960.13920.07450.9385
1280.13940.07450.9385
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View No.abs-relabsδ < 1.25
3 (base)0.12040.21210.8603
5 (base)0.11480.19990.8726
3 (+pose)0.11620.20610.8711
5 (+pose)0.10960.19300.8840
3 (+pose,atten)0.10840.19230.8833
5 (+pose,atten)0.10000.17810.8967
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Samplingabs-relabsδ < 1.25
s10 (base)0.08850.16050.9211
key (base)0.08380.15980.9277
s10 (+pose)0.08270.15230.9277
key (+pose)0.07890.15310.9339
s10 (+pose,atten)0.07470.13920.9382
key (+pose,atten)0.06970.13480.9472
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Bold is the best, and underline indicates the second best." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 662, + 288, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 662, + 288, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 662, + 288, + 710 + ], + "type": "text", + "content": "DTU: Tab. 5 shows that our model, i.e., Ours(+pose,atten) is trained/tested on DTU dataset with 3-view and 5-view input collections, respectively. We use the same training scheduling for a fair comparison. The 5-view result is worse" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 662, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 662, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 305, + 662, + 545, + 711 + ], + "type": "text", + "content": "than the last row in Tab. 1 due to the lack of pretraining on ScanNet. Frame Sampling: We compare the simple view selection strategy (i.e., sampling by every 10 frames) with the heuristics [17]. 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Qualitative results on ScanNet [15] (top two rows) and DTU [27] test set. Left two columns show reference image and ground truth depth, and other columns are the estimated depth by baseline IterMVS [52], PairNet [17] and ours (the full version), respectively. Our method outperforms the baselines on thin structures, small objects and boundaries, as highlighted in green for ours and in red for the baselines. 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View No. on DTUabs-rel (↓)abs (mm) (↓)rmse (↓)
3 (1 ref + 2 source)0.014911.068924.8831
5 (1 ref + 4 source)0.01198.841921.4327
", + "image_path": "5e4bf6eb3f61a1512b0741d004e48d2d3e66c97b629b04d427d0a7a4252fe2c7.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_body" + } + ], + "index": 26 + }, + { + "type": "table", + "bbox": [ + 67, + 526, + 266, + 579 + ], + "blocks": [ + { + "bbox": [ + 56, + 502, + 277, + 514 + ], + "lines": [ + { + "bbox": [ + 56, + 502, + 277, + 514 + ], + "spans": [ + { + "bbox": [ + 56, + 502, + 277, + 514 + ], + "type": "text", + "content": "Table 5. 3-view vs. 5-view training and testing on DTU [27]." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 526, + 266, + 579 + ], + "lines": [ + { + "bbox": [ + 67, + 526, + 266, + 579 + ], + "spans": [ + { + "bbox": [ + 67, + 526, + 266, + 579 + ], + "type": "table", + "html": "
MethodsTime(fps)Mem.(MB)Param.(M)abs-rel (↓)
Ours(T=8)6.98429727.60.0760
Ours(T=12)5.91429727.60.0752
Ours(T=24)3.77429727.60.0734
IterMVS [52]22.6121710.340.0991
ESTD [39]14.08179936.20.0812
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Comparison of run time, memory consumption, and accuracy on ScanNet [15] test set with frame dimension " + }, + { + "bbox": [ + 46, + 581, + 287, + 603 + ], + "type": "inline_equation", + "content": "320 \\times 256" + }, + { + "bbox": [ + 46, + 581, + 287, + 603 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "proved when the selected views have more overlapping and the baselines are suitable. Our(+pose,atten) even with simple strategy outperforms other variants with heuristic sampling, and so are our(+pose) vs our(base). Runtime Overhead: Tab. 6 shows the run-time and memory consumption when processing " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "320 \\times 256" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " frames from the ScanNet test set. Ours (T=8/12/24) means 8, 12, and 24 GRU iterations." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 479, + 384, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 384, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 384, + 491 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "We have proposed RIAV-MVS, a novel learning-based MVS method. Our approach utilizes a convolutional GRU to iteratively optimize the index fields, which are used to access the cost volume and regress the depth. The cost volume is further improved through the application of a transformer block to the reference image and a residual pose network to correct the relative poses. Extensive experiments on ScanNet [15], DTU [27], 7-Scenes [20], and RGB-D Scenes V2 [32] have demonstrated the superior accuracy and cross-dataset generalizability of our method. Due to the plane-sweeping 3D cost volume and transformer selfattention, our method requires large memory consumption for high-resolution images. Moreover, the inference time is not as fast as other lightweight convolutional counterparts, due to the iterative update paradigm in our approach. 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Ltd. \n3S-Lab, Nanyang Technological University", + "bbox": [ + 176, + 179, + 790, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wuruiqi,adamduan0211}@mail.nankai.edu.cn,guochunle=nankai.edu.cn, chaizhi2@huawei.com, chongyi.li@ntu.edu.sg", + "bbox": [ + 184, + 236, + 781, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing dehazing approaches struggle to process real-world hazy images owing to the lack of paired real data and robust priors. In this work, we present a new paradigm for real image dehazing from the perspectives of synthesizing more realistic hazy data and introducing more robust priors into the network. Specifically, (1) instead of adopting the de facto physical scattering model, we rethink the degradation of real hazy images and propose a phenomenological pipeline considering diverse degradation types. (2) We propose a Real Image Dehazing network via high-quality Codebook Priors (RIDCP). Firstly, a VQGAN is pre-trained on a large-scale high-quality dataset to obtain the discrete codebook, encapsulating high-quality priors (HQPs). After replacing the negative effects brought by haze with HQPs, the decoder equipped with a novel normalized feature alignment module can effectively utilize high-quality features and produce clean results. However, although our degradation pipeline drastically mitigates the domain gap between synthetic and real data, it is still intractable to avoid it, which challenges HQPs matching in the wild. Thus, we re-calculate the distance when matching the features to the HQPs by a controllable matching operation, which facilitates finding better counterparts. We provide a recommendation to control the matching based on an explainable solution. Users can also flexibly adjust the enhancement degree as per their preference. Extensive experiments verify the effectiveness of our data synthesis pipeline and the superior performance of RIDCP in real image dehazing. Code and data are released at https://rqw.github.io/projects/RIDCP.", + "bbox": [ + 75, + 335, + 473, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 794, + 209, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image dehazing aims to recover clean images from their hazy counterparts, which is essential for computational photography and high-level tasks [20, 32]. The hazy image formulation is commonly described by a physical scattering", + "bbox": [ + 75, + 819, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d48fe80a2323503fa210d6fc19f6595a21d7a30eea755f5c8453a27c19b1ffdf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 304, + 632, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a7d108bfeb09e69b8f620cdfe849f6b61806885049bd157860521074c3da22c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 303, + 756, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/260698b543f5e33c2926f0a81cb3150dc07a1b081737e742b353bd064f5e5e3c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 303, + 883, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/092b1e12a80bb07ba35210296317fd793bb2001d33a76f0056b78c05219ce02b.jpg", + "image_caption": [ + "(a) Hazy input", + "Figure 1. Visual comparisons on a typical hazy image. The proposed method generates cleaner results than other two state-of-the-art real image dehazing approaches. The enhancement degree of our result can be flexibly adjusted by adopting different parameters in the real-domain adaptation phase. The image with a golden border is the result obtained under our recommended parameter." + ], + "image_footnote": [], + "bbox": [ + 506, + 383, + 633, + 476 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f035fd25c9d118eacb6cdad3f2d1db6388dcd5981ddb55f29dc14fa57bcd2168.jpg", + "image_caption": [ + "(b) DAD [33]", + "(d) Ours" + ], + "image_footnote": [], + "bbox": [ + 635, + 383, + 756, + 476 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/403431cbbef964eb0f038a7a8bc6035076594e6d87bb4b5e20fed3483cfe07df.jpg", + "image_caption": [ + "(c) PSD [7]" + ], + "image_footnote": [], + "bbox": [ + 759, + 383, + 885, + 476 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "model:", + "bbox": [ + 500, + 589, + 549, + 602 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\nI (x) = J (x) t (x) + A (1 - t (x)), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 604, + 890, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where $I(x)$ denotes the hazy image and $J(x)$ is its corresponding clean image. The variables $A$ and $t(x)$ are the global atmosphere light and transmission map, respectively. The transmission map $t(x) = e^{\\beta d(x)}$ depends on scene depth $d(x)$ and haze density coefficient $\\beta$ .", + "bbox": [ + 496, + 627, + 892, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given a hazy image, restoring its clean version is highly ill-posed. To mitigate the ill-posedness of this problem, various priors, e.g., dark channel prior [16], color attenuation prior [44], and color lines [12] have been proposed in existing traditional methods. Nevertheless, the statistical priors cannot cover diverse cases in real-world scenes, leading to suboptimal dehazing performance.", + "bbox": [ + 496, + 704, + 893, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the advent of deep learning, image dehazing has achieved remarkable progress. Existing methods either adopt deep networks to estimate physical parameters [5,21, 31] or directly restore haze-free images [10, 15, 27, 30, 40]. However, image dehazing neural networks perform limited generalization to real scenes, owing to the difficulty in", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "footer", + "text": "22282", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "collecting large-scale yet perfectly aligned paired training data and solving the uncertainty of the ill-posed problem without robust priors. Concretely, 1) collecting large-scale and perfectly aligned hazy images with the clean counterpart is incredibly difficult, if not impossible. Thus, most of the existing deep models use synthetic data for training, in which the hazy images are generated using Eq. (1), leading to the neglect of multiple degradation factors. There are some real hazy image datasets [2,3] with paired data, but the size and diversity are insufficient. Moreover, these datasets deviate from the hazy images captured in the wild. These shortcomings inevitably decrease the capability of deep models in real scenes. 2) Real image dehazing is a highly ill-posed issue. Generally, addressing an uncertain mapping problem often needs the support of priors. However, it is difficult to obtain robust priors that can cover the diverse scenes of real hazy images, which also limits the performance of dehazing algorithms. Recently, many studies for real image dehazing try to solve these two issues by domain adaptation from the perspective of data generation [33,39] or priors guidance [7,23], but still cannot obtain desirable results.", + "bbox": [ + 76, + 90, + 472, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a new paradigm for real image dehazing motivated by addressing the above two problems. To obtain large-scale and perfectly aligned paired training data, we rethink the degradation of hazy images by observing amounts of real hazy images and propose a novel data generation pipeline considering multiple degradation factors. In order to solve the uncertainty of the ill-posed issue, we attempt to train a VQGAN [11] on high-quality images to extract more robust high-quality priors (HQPs). The VQGAN only learns high-quality image reconstruction, so it naturally contains the robust HQPs that can help hazy features jump to the clean domain. The observation in Sec. 4.1 further verifies our motivation. Thus, we propose the Real Image Dehazing network via high-quality Codebook Priors (RIDCP). The codebook and decoder of VQGAN are fixed to provide HQPs. Then, RIDCP is equipped with an encoder that helps find the correct HQPs, and a new decoder that utilizes the features from the fixed decoder and produces the final result. Moreover, we propose a novel Normalized Feature Alignment (NFA) that can mitigate the distortion and balance the features for better fusion.", + "bbox": [ + 76, + 428, + 472, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In comparison to previous methods [6, 14, 43] that introduce codebook for image restoration, we further design a unique real domain adaptation strategy based on the characteristics of VQGAN and the statistical results. Intuitively, we propose Controllable HQPs Matching (CHM) operation that replaces the nearest-neighbour matching by imposing elaborate-designed weights on the distances between features and HQPs during the inference phase. The weights are determined by a controllable parameter $\\alpha$ and the statistical distribution gap of HQPs activation in Sec. 4.3. By adjust-", + "bbox": [ + 76, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing $\\alpha$ , the distribution of HQPs activation can be shifted. Moreover, we present a theoretically feasible solution to obtain the optimal $\\alpha$ by minimizing the Kullback-Leibler Divergence of two probability distributions. More significantly, the value of $\\alpha$ can be visually reflected as the enhancement degree as shown in Figure 1(d), and users are allowed to adjust the dehazing results as per their preference. Our CHM is effective, flexible, and explainable.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared with the state-of-the-art real image dehazing methods, e.g., DAD [33] and PSD [7], only the proposed RIDCP can effectively process the hazy images captured in the wild while generating adjustable results, which are shown in Figure 1. The contributions of our work can be summarized as follows.", + "bbox": [ + 496, + 212, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a new paradigm to push the frontier of deep learning-based image dehazing towards real scenes.", + "- We are the first to leverage the high-quality codebook prior in the real image dehazing task. The controllable HQPs matching operation is proposed to overcome the gap between synthetic and real domains and produce adjustable results.", + "- We re-formulate the degradation model of real hazy images and propose a phenomenological degradation pipeline to simulate the hazy images captured in the wild." + ], + "bbox": [ + 517, + 309, + 890, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 505, + 640, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Single Image Dehazing", + "text_level": 1, + "bbox": [ + 500, + 530, + 712, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Dehazing. The early attempts at single image dehazing consider estimating the parameters of the atmosphere scattering model presented in Eq. (1) by priors on haze-free images [4, 12, 16, 35, 44]. These methods have achieved impressive results. However, the handcrafted priors based on empirical observations are hard to perform well in diverse scenarios. For example, the assumption of DCP [16] is not available in the sky region. The proposed method obtains the priors of high-quality images by pre-training a discrete codebook on large-scale datasets, which is more reliable and comprehensive.", + "bbox": [ + 496, + 553, + 890, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the development of deep learning techniques, how to use data-driven ideology to remove haze gains a lot of attention. At the early stage, many studies [5, 21, 31] try to adopt convolutional neural networks (CNNs) to estimate the parameters of the degradation model in Eq. (1). In addition, in order to avoid accumulated errors in parameters estimation, some end-to-end networks [10, 15, 27, 30, 40] are proposed to directly estimate the haze-free image. The above learning-based methods have achieved excellent performance on synthetic datasets. However, their significant performance drop on real-world data urgently needs to be solved.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22283", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/345c0ee4dcbccd5db9e91406f932a99ad092da4ee667cff10864c4068af28e45.jpg", + "image_caption": [ + "Figure 2. Overview of our RIDCP. During the training phase, we train the dehazing network on the data synthesized by our data generation pipeline, as illustrated in (a). The network is based on the pre-trained HQPs codebook and the corresponding decoder $\\mathbf{G}_{vq}$ of VQGAN. We also design the Controllable HQPs Matching (CHM) operation for real domain adaptation by re-calculating the distance $d_{k}^{\\hat{z}} = ||\\hat{z} - z_{k}||$ between features and HQPs. (b) represents the distance re-calculation with two Voronoi diagrams, where the colored cells indicate belonging to better HQPs and the gray cells vice versa. Triangles represent features and star points represent HQPs. It can be seen that after the distance recalibration points that originally belonged to the gray cells are forced to be assigned to the colored cells by our CHM." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 576, + 369 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0364824034e4602662ec86e7e7ab940d6afcaac5d95f68710605f6f0529cd22b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 586, + 88, + 883, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Real Image Dehazing. Recently, some works pay attention to real image dehazing. One research line is to utilize GANs [13] for generating hazy data that fits the real haze domain. Shao et al. [33] design a domain adaptation strategy based on the framework of CycleGAN [?]. Yang et al. [39] propose an unpaired dehazing framework named D4. It can estimate the scene depth of hazy images and generate hazy data with different thicknesses to benefit dehazing model training. However, GANs are easy to produce artifacts in the generated results, which is harmful to training models. Another research line aims to introduce prior knowledge by loss functions or network architectures. Li et al. [23] propose a semi-supervised pipeline that adopts prior-based loss functions to train networks on the real dataset. PSD [7] adds a physical-based sub-network on the pre-trained dehazing model and further proposes a prior loss committee to fine-tune the network on real-world data in an unsupervised manner. Nevertheless, directly using handcrafted priors cannot avoid the inherent flaws of prior-based methods. In our study, we investigate overcoming the weaknesses of both types of real image dehazing methods by proposing a novel data generation pipeline and exploiting the latent high-quality priors.", + "bbox": [ + 75, + 470, + 472, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Discrete Codebook Learning", + "text_level": 1, + "bbox": [ + 76, + 830, + 334, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, a vector-quantized auto-encoder framework was proposed in VQ-VAE [36], which learns a discrete codebook in latent space. The discrete representation ef", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fectively addresses the \"posterior collapse\" issue in autoencoder [19] architecture. VQGAN [11] further improves the perceptual quality of reconstructed results by introducing adversarial supervision for codebook learning. The learned discrete codebook helps boost the performance in many low-level vision tasks including face restoration [14, 43] and image super-resolution [6]. Gu et al. [14] introduce the vector quantization technique to face restoration and design a parallel decoder to achieve a balance between visual quality and fidelity. Zhou et al. [14] cast blind face restoration as a code prediction task, and propose a Transformer-based prediction network to replace the nearest-neighbor matching operation for better matching the corresponding code. FeMaSR [6] extends the discrete codebook learning to blind super-resolution. Motivated by the exciting performance of these approaches, we are the first to leverage the high-quality codebook prior for real image dehazing. A novel and controllable HQPs matching operation is proposed to further bridge the gap between our synthetic data and real data, which is inevitable for real scenes.", + "bbox": [ + 496, + 470, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Data Preparation for Real Image Dehazing", + "text_level": 1, + "bbox": [ + 498, + 784, + 883, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Redesigning the pipeline of data generation has been demonstrated as an effective way for solving real-world low-level vision tasks [37, 38, 41]. Based on these works, we consider various degradation factors when synthesizing paired data for training the dehazing network, which can mitigate the domain gap with the real data. For concise-", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22284", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ness, we represent Eq. (1) as $I(x) = \\mathcal{P}(J(x),t(x),A)$ . The formation of the hazy image can be written as:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI (x) = J P E G \\left(\\mathcal {P} \\left(J (x) ^ {\\gamma} + \\mathcal {N}, e ^ {\\beta \\hat {d} (x)}, A + \\Delta A\\right)\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 133, + 468, + 152 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The details of Eq. (2) are introduced as follows:", + "bbox": [ + 76, + 161, + 393, + 175 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Poor light condition. $\\gamma \\in [1.5,3.0]$ is a brightness adjustment factor and $\\mathcal{N}$ is the Gaussian noise distribution. These two components can simulate poor light conditions that frequently occur in hazy weather.", + "bbox": [ + 75, + 176, + 468, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transmission map. As a key parameter in the degradation model, we adopt the depth estimation algorithm [18] to estimate depth map $d(x)$ and use $\\beta \\in [0.3, 1.5]$ to control the haze density.", + "bbox": [ + 76, + 236, + 468, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Colorful haze. To obtain diverse hazy images, the color bias of atmosphere light is considered, which is implemented by a three-channel vector $\\Delta A \\in [-0.025, 0.025]$ . The range of $A$ is in the range of [0.25, 1.0].", + "bbox": [ + 76, + 296, + 468, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "JPEG compression. We observe that dehazing algorithms amplify the JPEG artifacts. It is desirable to remove such artifacts while dehazing. $JPEG(\\cdot)$ denotes JPEG compression in the final results.", + "bbox": [ + 76, + 357, + 468, + 416 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We select 500 clean images to build the paired data, and the hazy data is generated on-the-fly during the training phase. Additionally, low light and JPEG compression appear with $50\\%$ probability in the proposed pipeline.", + "bbox": [ + 75, + 417, + 468, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 76, + 491, + 210, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key idea of our work is to adopt a discrete codebook that introduces high-quality priors (HQPs) into the dehazing network. The overall framework of the proposed method is illustrated in Figure 2. The training phase can be divided into two stages. In the first training stage, we pre-train a VQGAN [11] on high-quality data, obtaining a latent discrete codebook $\\mathcal{Z}$ with HQPs and the correspondence decoder $\\mathbf{G}_{vq}$ (Sec. 4.1). In the second stage, our RIDCP based on the pre-trained VQGAN is trained on hazy images generated by the proposed synthesis pipeline (Sec. 4.2). Moreover, in order to help the network find more accurate code, we propose a controllable adjustment feature matching strategy based on code activation distribution on high-quality images (Sec. 4.3). Besides, the details of training objectives can be found in supplementary materials.", + "bbox": [ + 75, + 516, + 468, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Latent Codebook for High-quality Priors", + "text_level": 1, + "bbox": [ + 76, + 753, + 428, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first introduce how VQGAN works briefly. Given a high-quality image patch $x$ , which is the input of the VQGAN encoder $\\mathbf{E}_{vq}$ and the corresponding outputs are the latent features $\\hat{z}$ . Then each \"pixel\" $\\hat{z}_{ij}$ of $\\hat{z}$ will be matched to the nearest HQPs in codebook $\\mathcal{Z} \\in \\mathbb{R}^{K \\times n}$ and then obtain the discrete representation $z_{ij}^q$ , which can be written as:", + "bbox": [ + 75, + 776, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i j} ^ {q} = \\mathcal {M} (\\hat {z} _ {i j}) = \\arg \\min _ {z _ {k} \\in \\mathcal {Z}} \\left(\\left\\| \\hat {z} _ {i j} - z _ {k} \\right\\| _ {2}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 880, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e74194e9ff30ee6f3f4901a26b045f4a4c698d4a94b99e0bb4671ecdfc56d97b.jpg", + "image_caption": [ + "(a) Hazy input" + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 694, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/087c517098971667c648427ec54dc762e6ebc905bf20e4c437cef73c0da42e3c.jpg", + "image_caption": [ + "(b) Reconstruction", + "Figure 3. Result reconstructed by the pre-trained VQGAN. The haze is removed but distorted textures are introduced." + ], + "image_footnote": [], + "bbox": [ + 696, + 88, + 885, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $K$ denotes the codebook size, $n$ is the channel number of $\\hat{z}$ , and $\\mathcal{M}(\\cdot)$ represents the matching operation. Finally, the input $x$ is reconstructed by $\\mathbf{G}_{vq}$ :", + "bbox": [ + 498, + 224, + 890, + 270 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {\\prime} = \\mathbf {G} _ {v q} \\left(z ^ {q}\\right) = \\mathbf {G} _ {v q} \\left(\\mathcal {M} \\left(\\mathbf {E} _ {v q} (x)\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 279, + 890, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x^{\\prime}$ is the reconstructed result.", + "bbox": [ + 498, + 299, + 736, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation 1. To understand the potential of the HQPs in the codebook and better utilize it, we made some observations on the results reconstructed by the pre-trained VQGAN. As illustrated in Figure 3, our VQGAN can remove the thin haze and recover vivid color for the hazy input without fine-tuning. We analyze that using HQPs in a matching manner can replace the degraded feature so help it jump to the high-quality domain. However, the dehazing ability of VQGAN is limited due to the difficulty in matching the correct code. Moreover, some distorted textures are produced because of the information loss during the vector-quantized phase. Thus, directly adopting the features from $\\mathbf{G}_{vq}$ is suboptimal. It is intuitive that our next step is to train an encoder $\\mathbf{E}$ that can help priors matching, and a decoder $\\mathbf{G}$ that can utilize the features reconstructed from HQPs.", + "bbox": [ + 496, + 314, + 890, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Image Dehazing via Feature Matching", + "text_level": 1, + "bbox": [ + 500, + 549, + 828, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the observation in Sec. 4.1, image dehazing is decoupled into two sub-tasks: matching correct code and removing texture distortion.", + "bbox": [ + 498, + 571, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Encoder for HQPs Matching. We follow SwinIR [25] which shows its powerful feature extraction ability for image restoration to design our encoder $\\mathbf{E}$ . Specifically, the shallow feature extraction head consists of a stack of residual layers [17] and $4\\times$ downsamples the features. Then 4 residual swim transformer blocks [28] are followed, which serve as the deep feature extraction module.", + "bbox": [ + 496, + 617, + 890, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder with Normalized Feature Alignment. We propose the Normalized Feature Alignment (NFA) to help the decoder utilize the features reconstructed from HQPs. Firstly, VQGAN tends to decrease results' fidelity due to the information loss brought by vector-quantized operation [14, 43]. Our solution is to eliminate the distortion by the guidance of features before HQPs matching. Specifically, in $i$ th layer, we adopt the deformable convolution [9] to align the features $F_{vq}^{i}$ from $\\mathbf{G}_{vq}$ with the features $F^{i}$ from $\\mathbf{G}$ , which can be written as:", + "bbox": [ + 496, + 723, + 890, + 873 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {w} ^ {i} = D C O N V \\left(F _ {v q} ^ {i}, C O N V \\left(C o n c a t \\left(F _ {v q} ^ {i}, F ^ {i}\\right)\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22285", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/abc330b88e9afa9fd791abd855ea013e30a29c22257b58665c664a2d9c5564b9.jpg", + "image_caption": [ + "Figure 4. Code activation frequencies under different situations. 'dehaze' denotes inputting real hazy images to dehazing network and 'clean' denotes feeding clean images into the pre-trained VQGAN network. 'adjusted' denotes our RIDCP equipped with the CHM under the recommended parameter with real hazy inputs." + ], + "image_footnote": [], + "bbox": [ + 73, + 88, + 472, + 193 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{w}^{i}$ denotes the features after warping and $DCONV$ is the deformable convolutional layer. $CONV$ is the convolutional layer for offset generation. In addition, we notice that the ratio of the values of $F_{w}^{i}$ and $F^{i}$ is not stable, resulting in an inadequate combination. Thus, we balance the contributions of each by forcing them to be in the same order of magnitude, which can be written as:", + "bbox": [ + 75, + 271, + 470, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {i} = F ^ {i} + \\frac {\\sum F ^ {i}}{\\sum F _ {w} ^ {i}} F _ {w} ^ {i}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 387, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Controllable HQPs Matching Operation", + "text_level": 1, + "bbox": [ + 76, + 438, + 421, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Observation 2. Our RIDCP achieves relatively satisfactory results with the help of $\\mathbf{E}$ and $\\mathbf{G}$ . However, there are still limitations, e.g., low color saturation in some challenging real data. Rather than the HQPs that already show a strong capability in reconstructing vivid results (see Observation 1), the main reason is the difficulty in finding correct HQPs, which is caused by the domain gap between synthetic data and real data. Although the domain gap is drastically reduced by our synthesis pipeline than previous works [22, 42], it is still impossible to cover all real-world hazy conditions by our pipeline.", + "bbox": [ + 75, + 462, + 468, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To verify our claim, we made an observation as follows. We randomly collect 200 high-quality clean images as input of the pre-trained VQGAN and compute the activation frequency $f_{c} \\in \\mathbb{R}^{K}$ of each code. Similarly, 200 real hazy images are fed to the dehazing network to compute the frequency $f_{h} \\in \\mathbb{R}^{K}$ . Figure 4 illustrates the activation frequencies of the codes with the top ten largest differences between $f_{h}$ and $f_{c}$ . We can see a significant distribution shift. The observation proves that the unavoidable domain gap results in a divergent matching for HQPs. Thus, HQPs still have unexplored potential.", + "bbox": [ + 75, + 628, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Controllable Matching via Distance Re-calculation. Based on the above observation, it is indispensable to match better HQPs when encountering real hazy images, i.e., priors with high frequency on clear images. Two components can affect the HQPs matching, which are the encoder $\\mathbf{E}$ and the matching operation $\\mathcal{M}(\\cdot)$ . Since it is difficult to retrain $\\mathbf{E}$ on real hazy images without reference images, defining", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a new matching operation $\\mathcal{M}'(\\cdot)$ sounds like a reasonable solution. We propose Controllable HQPs Matching (CHM) that re-calculates distances by assigning different weights during matching phase. The CHM can be written as:", + "bbox": [ + 496, + 90, + 893, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} ^ {\\prime} (\\hat {z}) = \\arg \\min _ {z _ {k} \\in Z} \\left(\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) \\times | | \\hat {z} - z _ {k} |\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 161, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{F}(\\tilde{f}_k,\\alpha)$ is the function to generate weights based on the frequency difference $\\tilde{f}_k = f_h^k -f_c^k$ and adjusted by a parameter $\\alpha$ . There are three objectives in the design of F: 1) Since higher $\\tilde{f}_k$ means less activation is needed, $\\mathbf{F}$ should be monotonic with $\\tilde{f}_k$ thus ensuring consistent trend adjustment. 2) $\\mathbf{F}(0,\\alpha)\\equiv 1$ so that HQPs with the same frequencies on clear and hazy data are not adjusted. 3) The degree of adjustment can be controlled monotonically by $\\alpha$ , e.g., $\\forall \\tilde{f}_1 > \\tilde{f}_2,\\forall \\alpha_1 > \\alpha_2\\rightarrow \\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_1)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_1)} >\\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_2)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_2)}$ . Coincidentally, the exponential function has these properties, thus $\\mathbf{F}$ can be formulated as;", + "bbox": [ + 496, + 198, + 893, + 371 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) = e ^ {a \\times \\tilde {f} _ {k}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 380, + 890, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 2(b) adopts two Voronoi diagrams to simulate the changes occurring in the high-dimensional space during feature matching. As we can see, the points originally belonging to gray cells are matched to the colored cells after distance re-calculation, i.e., finding better HQPs.", + "bbox": [ + 496, + 411, + 890, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Possible Solution of the Recommended $\\alpha$ . Our method is able to control the HQPs matching based on the above strategy. The final goal is to find a suitable $\\alpha$ to adapt the network to real domain. According to the law of large numbers, the frequencies $f_{c}^{k}, f_{h}^{k}$ can be substituted for the corresponding probabilities $P_{c}(x = z_{k}), P_{h}(x = z_{k}|\\alpha)$ . The gap between the dehazing results and the clean domain can be represented by the difference between the two probability distributions. Thus, the real domain adaptation problem is transferred into calculating an optimal parameter $\\hat{\\alpha}$ that can minimize the forward Kullback-Leibler Divergence of $P_{c}(x = z_{k})$ and $P_{h}(x = z_{k}|\\alpha)$ , which is also the maximum likelihood estimation of $\\alpha$ :", + "bbox": [ + 496, + 487, + 892, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\alpha} = \\arg \\min _ {\\alpha} K L (P _ {c} | | P _ {h}) \\\\ = a r g \\min _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) \\log \\frac {P _ {c} (x = z _ {i})}{P _ {h} (x = z _ {i} | \\alpha)} \\\\ = \\arg \\max _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} \\left(x = z _ {i}\\right) \\log P _ {h} \\left(x = z _ {i} \\mid \\alpha\\right) \\tag {9} \\\\ = a r g \\max _ {\\alpha} \\prod_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) P _ {h} (x = z _ {i} | \\alpha). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 691, + 890, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a binary search algorithm to iteratively find the approximate optimal solution for $\\hat{\\alpha}$ . The final determination is $\\hat{\\alpha} = 21.25$ and higher precision calculations have little", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22286", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/88d26bdb4ff88b2b14423ce838b3ae9f2970d3c02e7063bf83041ab2d686730e.jpg", + "image_caption": [ + "(a) Hazy image" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 197, + 462 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/87dcc4072a0e3ae6effb445ec3ceb9486e43796c339e1b7f3b0659444c896a10.jpg", + "image_caption": [ + "(b) MSBDN [10]" + ], + "image_footnote": [], + "bbox": [ + 197, + 90, + 312, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9438fbefd3a6a922574032c830484d01bf5199a7091078b293f3f5c80645bc8c.jpg", + "image_caption": [ + "(c) Dehamer [15]", + "Figure 5. Visual comparison on RTTS dataset [22]." + ], + "image_footnote": [], + "bbox": [ + 313, + 90, + 424, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c8d08b7bdbbd9c08f508c78df573cec1dcc78a113c7e3cd619ce828ef979e962.jpg", + "image_caption": [ + "(d) PSD [7]" + ], + "image_footnote": [], + "bbox": [ + 426, + 90, + 540, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f6416b3ac5c05777e4cbff4694b0c12b95df9627dbc080e3526bf75b94a8b463.jpg", + "image_caption": [ + "(e) D4 [39]" + ], + "image_footnote": [], + "bbox": [ + 540, + 90, + 653, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/91c5ca337af56e1d0656160d53aea6960f2294bc459026ac9f1023231b065bda.jpg", + "image_caption": [ + "(f) DAD [33]" + ], + "image_footnote": [], + "bbox": [ + 655, + 90, + 769, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6c20893a27786eb940f8fc0e76c4cfb737d6020eff761ec4bd3c47267f94f125.jpg", + "image_caption": [ + "(g) RIDCP" + ], + "image_footnote": [], + "bbox": [ + 769, + 90, + 883, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "effect on the results. Note that, $\\hat{\\alpha}$ may not be the determined choice for all cases. One can flexibly adjust $\\alpha$ according to their preference.", + "bbox": [ + 75, + 508, + 468, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 563, + 209, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 588, + 179, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "High-quality Datasets. In order to obtain high-quality results from the pre-trained HQPs, the VQGAN needs to be trained on large-scale datasets containing high-resolution and texture-sharp images. In our work, we use DIV2K [1] and Flickr2K [26] (containing 4,250 images) to train the first stage. Both datasets are widely used in high-quality reconstruction tasks [6,24,25].", + "bbox": [ + 75, + 612, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real Haze Datasets. We qualitatively and quantitatively evaluate our dehazing network on the RTTS dataset [22], which contains over 4,000 real hazy images with diverse scenes, resolutions, and degradation issues. Besides, we use Fattal's dataset [12] that includes 31 classic real hazy cases for further visual comparison.", + "bbox": [ + 75, + 719, + 468, + 810 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 815, + 294, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For both VQGAN and RIDCP training, we use Adam optimizer with default parameters $(\\beta_{1} = 0.9, \\beta_{2} = 0.99)$ . The learning rate is fixed to 0.0001 during the training phase and the batch size is set to 16. For data augmentation, we", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "randomly resize and crop the input into a size of $256 \\times 256$ , and flip it with a half probability. During the first training stage, our VQGAN is pre-trained on DIV2K and Flickr2K for 350K iterations. Then, the proposed RIDCP is trained on the data generated by the proposed synthesis pipeline for 10K iterations. All experiments are implemented with PyTorch framework on 4 NVIDIA V100 GPUs. The code implemented by MindSpore framework is also provided.", + "bbox": [ + 496, + 508, + 890, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 645, + 867, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the performance of the proposed method with several state-of-the-art dehazing approaches. The experiments are designed from both quantitative and qualitative perspectives. Moreover, we also conduct a user study to verify the subjective performance of our method.", + "bbox": [ + 496, + 672, + 890, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparison. Since there is no ground-truth image in real hazy datasets, we use some non-reference metrics for quantitative comparison. We first adopt the Fog Aware Density Evaluator (FADE) [8] for haze density estimation. In addition, two widely-used image quality assessment metrics, BRISQUE [29] and NIMA [34] are also included. The quantitative comparison is conducted on RTTS dataset with two dehazing methods (MSBDN [10] and Dehamer [15]) that achieve outstanding performance on synthetic hazy image datasets [22], and three real dehazing ap", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22287", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/448787017f808eda32ecab974c85693115b85210870768b5b2ac36f71b790442.jpg", + "image_caption": [ + "(a) Hazy image" + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 197, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7617defef89f897f0333934e12112046646996efba30c7f6e17a7932910e0f96.jpg", + "image_caption": [ + "(b) MSBDN [10]" + ], + "image_footnote": [], + "bbox": [ + 197, + 90, + 312, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6ece84cdb50d9eb7d477b8512b7e6ef547ca6ec6736a04f31fe6c4a1c79e9061.jpg", + "image_caption": [ + "(c) Dehamer [15]" + ], + "image_footnote": [], + "bbox": [ + 313, + 90, + 424, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ef46d2a22e4022aae4cbe9bef3328b8180774b32f18d47a88934e4823dcda7d.jpg", + "image_caption": [ + "(d) PSD [7]" + ], + "image_footnote": [], + "bbox": [ + 426, + 90, + 540, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be0ed0d7e688291c9877c4266bf5d107b0ba3beb482ba25352eb8c9bd67e00a8.jpg", + "image_caption": [ + "(e) D4 [39]", + "Figure 6. Visual comparison on Fattal's data [12]." + ], + "image_footnote": [], + "bbox": [ + 540, + 90, + 653, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/edb7893c212c44023cad1c4b1180d258d3065a34d3e87fae5d354104bc1d400f.jpg", + "image_caption": [ + "(f) DAD [33]" + ], + "image_footnote": [], + "bbox": [ + 655, + 90, + 769, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a0a7fbdc1fda89868ec1ea53f21d0c3d5a809db0a5ca9b70294ef51c2f588452.jpg", + "image_caption": [ + "(g) RIDCP" + ], + "image_footnote": [], + "bbox": [ + 769, + 90, + 883, + 227 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/329f6207be297ae7f5e8a3b0538ec4e2140fdbf73ad84cb8199155e1c3ccbee9.jpg", + "table_caption": [ + "Table 1. Quantitative comparison and user study on RTTS dataset. Red indicates the best and blue indicates the second best. 'US' shows the percentage of votes in the user study." + ], + "table_footnote": [], + "table_body": "
MethodFADE↓BRISQUE↓NIMA↑US↑
Hazy image2.48437.0114.32500.030
MSBDN [10]1.36328.7434.14010.046
Dehamer [15]1.89533.8663.86630.041
DAD [33]1.13032.7274.00550.143
PSD [7]0.92025.2394.34590.105
D4 [39]1.35833.2063.72390.079
RIDCP0.94418.7824.42670.556
", + "bbox": [ + 78, + 319, + 486, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "proaches (DAD [33], PSD [7], D4 [39]). The results are illustrated in Table 1. The proposed RIDCP achieves the best in terms of BRISQUE and NIMA, which gains $25.57\\%$ and $1.86\\%$ improvements, respectively. For FADE, our method is ranked second slightly below the PSD. However, as shown in Figure 5, PSD tends to produce over-enhanced results, which leads to an inaccurate evaluation. Overall, RIDCP achieves the best results on quantitative metrics, and subsequent experiments will further prove our superiority.", + "bbox": [ + 75, + 446, + 468, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Comparison. We perform the qualitative comparison on RTTS and Fattal's datasets, which is shown in Figure 5 and Figure 6. We can observe that Dehamer, MSBDN, and D4 cannot process the real hazy images well. PSD can produce bright results but the dehazing ability is limited. DAD is effective in haze removal, while its results suffer from color bias and dark tone. Our method generates the best perceptual results in terms of brightness, colorfulness, and haze residue compared to other methods. More results can be found in supplementary materials.", + "bbox": [ + 75, + 583, + 468, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study. We conduct a user study to evaluate the proposed method subjectively against other methods. We randomly select 100 images from RTTS dataset for comparison and invite 5 experts with image processing background and 5 naive observers as volunteers. Before the user study, we give the observer three tips: 1) The primary concern is whether the haze is removed, especially the dense haze in the distance. 2) Pay attention to whether the natural color is recovered. 3) A good method should generate artifact-free results. Afterward, the images are displayed to the observer group by group. Each group contains the input image and", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the results generated by different methods. The observer is required to choose the best one after at least 10 seconds of observation. We statistic the percentage of each method selected as the best and the final scores are listed in Table 1. The proposed RIDCP achieves the highest score and is well ahead of the second place, further demonstrating our method's superior dehazing ability.", + "bbox": [ + 496, + 273, + 893, + 380 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 390, + 653, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to verify the effectiveness of each key component, we conduct a series of ablation experiments. Generally, we discuss the effectiveness of CHM, NFA, and the phenomenological degradation pipeline in this section.", + "bbox": [ + 496, + 415, + 890, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Influence of Adjustment Parameter. The degree of real domain adaptation is controlled by parameter $\\alpha$ in Eq. (8) and one can adjust the final result flexibly by adjusting $\\alpha$ . Thus, we are curious about what influence the different $\\alpha$ will have. As Figure 7 shows, the value of $\\alpha$ and the image enhancement effect belong to a linear relationship. More visual-pleasing even over-enhanced results can be produced when $\\alpha > 0$ . Interestingly, we can obtain under-enhanced results if $\\alpha$ is adjusted in the opposite direction.", + "bbox": [ + 496, + 476, + 892, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of NFA. Our NFA can help remove the distorted textures caused by feature matching while preserving the useful information reconstructed from HQPs. The NFA can be divided into two key parts: warping operation based on deformable convolution and normalize-based addition. To analyze the role of each part, we propose 4 variants to replace NFA, which are: 1) Without any fusion operation. 2) Adding directly. 3) Normalized addition without warping. 4) Warping and direct addition. Figure 8 shows a set of comparisons. Observing the grass area in red boxes, the result of variant 1 is dark and remaining thin haze. Variants 2 and 4 also have non-homogeneous fog residues in some areas. Variant 3 generates obvious artifacts because forcing normalizing unaligned features to the same order of magnitude and adding them together makes the network difficult to train. Only the full NFA achieves the best in brightness and haze removal.", + "bbox": [ + 496, + 613, + 893, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the Phenomenological Degradation Pipeline. To prove that our proposed degradation pipeline", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22288", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a32e9c34fc6ca629646f4a427e19bb1ca3a8d73f6efdf686828d226b26704a06.jpg", + "image_caption": [ + "(a) Hazy image" + ], + "image_footnote": [], + "bbox": [ + 81, + 94, + 238, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cabbf7fcdc0a7df3f03e76880e1745dcc0b8a94a5870ad82f8656c5c39f9c8ef.jpg", + "image_caption": [ + "(b) $\\alpha = -60.0$" + ], + "image_footnote": [], + "bbox": [ + 243, + 94, + 401, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af9c13fbba79d66c21ff463c5ec2acb9c35e3249196b0d84d3fae85f7277196e.jpg", + "image_caption": [ + "(c) $\\alpha = 0.0$" + ], + "image_footnote": [], + "bbox": [ + 406, + 94, + 563, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c99718997fe2bd1adebce608e85292f0dd49bdf1285acb887d793a3880cde573.jpg", + "image_caption": [ + "(d) $\\alpha = 21.25$" + ], + "image_footnote": [], + "bbox": [ + 566, + 90, + 727, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae656ee6f9f9b5f45a9307eee306ec8857b4752025bf2624758c55f5af85eb91.jpg", + "image_caption": [ + "(e) $\\alpha = 60.0$" + ], + "image_footnote": [], + "bbox": [ + 730, + 94, + 887, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/de2120cb38c999e10baad1b4d212dc06c57bac8a0d402f87747bd7fe2f8c388f.jpg", + "image_caption": [ + "Figure 7. Results under different adjustment degrees. The proposed CHM allows users to adjust the degree of enhancement from low $(\\alpha = -60.0)$ to high $(\\alpha = 60.0)$ . The recommended value $(\\alpha = 21.25)$ facilitates the network to generate the most natural results (surrounded by the blue box). Zoom in for the best view." + ], + "image_footnote": [], + "bbox": [ + 81, + 321, + 207, + 387 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b4c188d0fcc1fa9ffad827c70879bff2479e50a5a12246a45776b675c374fbd.jpg", + "image_caption": [ + "(b) w/o fusion" + ], + "image_footnote": [], + "bbox": [ + 210, + 321, + 336, + 387 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47c84a952e95854934a27d40f549b3473a628164043ae2d61f4444260ef69b62.jpg", + "image_caption": [ + "(c) Addition" + ], + "image_footnote": [], + "bbox": [ + 336, + 321, + 465, + 387 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/abbf0e115ed88337506525a8b8c08313dc4606671afcacdf6b60dac9ede8b7fc.jpg", + "image_caption": [ + "(a) Haze", + "(d) w/o warping", + "Figure 8. Ablation results of the proposed NFA." + ], + "image_footnote": [], + "bbox": [ + 81, + 400, + 207, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f308c916a62328b65faab3685e395d76fec97f959fe3ae82727d9018261ae8c.jpg", + "image_caption": [ + "(e) w/o normalizing" + ], + "image_footnote": [], + "bbox": [ + 210, + 401, + 336, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f069f2c400a234d12b64f1ee0b53ea30f65b2df9f327582895e47bb94b303ac.jpg", + "image_caption": [ + "(f) Full NFA" + ], + "image_footnote": [], + "bbox": [ + 336, + 401, + 465, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for paired data generation can boost the capabilities of haze removal, we retrain our RIDCP on two widely-used synthetic datasets, which are OTS [22] and Haze4K [42]. Notably, Haze4K is post-processed by DAD [33]. Moreover, we replace the training set from OTS with our synthetic data for transformer-based Dehamer and CNN-based MSBDN, thus demonstrating that it can generally bring gains. The comparison results are illustrated in Figure 9. We can observe that our dehazing network cannot remove the haze under the training of OTS and Haze4K. Besides, Dehamer and MSBDN can generate results with less haze and higher brightness with the help of our training data. However, they still struggle in color recovery compared to our method, which also demonstrates the effectiveness of HQPs and our adaptation strategy.", + "bbox": [ + 75, + 505, + 472, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 738, + 191, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In this paper, we present a novel paradigm to revitalize deep dehazing networks towards the real world. Our proposed phenomenological degradation pipeline synthesizes more realistic hazy data, which achieves significant gains in haze removal. Based on our observations and analysis, we introduce the high-quality priors in VQGAN to the dehazing network and progressively leverage their power, which finally builds our real image dehazing network via high-quality codebook priors (RIDCP). Extensive experi", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8cfaa0a9a442267102e407c2992930a54792ca571acd331a18c2ccfb0ca8a80e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 321, + 601, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c2ca58416296d1c1e69a8b7fc8d2b686e1c922a71784b1f8a6619f91800ca8ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 321, + 696, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ceb76382657d338e7b3c18cf53dc16df40bb5cc77a8c72f6c78a76dc15160c87.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 321, + 792, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2b3203c74dd099c221ff29b232dd7eee20289add603b7aa44c278778b7892d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 321, + 887, + 381 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/472f7979c9af532d47e0c2f468bc14ebc4ac5242d8ce36f02036c66359a70e9d.jpg", + "image_caption": [ + "(a) Haze", + "(e) Dehamer†", + "Figure 9. Ablation results of the proposed data generation pipeline. We retrain our dehazing network on OTS (b) and Haze4K (c) to verify the effectiveness of our generation pipeline. Dehamer and MSBDN are also retrained on our synthetic data, which are marked by $\\dagger$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 395, + 601, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b70d214e4f980e9550604abb21f90e7a5c8eb341e0deba6b0be127572befd4e6.jpg", + "image_caption": [ + "(b) OTS", + "(f) MSBDN" + ], + "image_footnote": [], + "bbox": [ + 602, + 395, + 696, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/409bba2378222b66280eeddfbd3ea2da53653ad0dcb3ff0f1099787f8a1f60bb.jpg", + "image_caption": [ + "(c) Haze4K", + "(g) $\\mathbf{MSBDN}^{\\dagger}$" + ], + "image_footnote": [], + "bbox": [ + 697, + 395, + 792, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/060c05511a6c1091fdd4c4e4666c0a6bd40d2260c19c22c61fdd1771c6441f22.jpg", + "image_caption": [ + "(d) Dehamer", + "(h) Ours" + ], + "image_footnote": [], + "bbox": [ + 792, + 395, + 887, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ments show the superiority of the proposed paradigm.", + "bbox": [ + 500, + 556, + 854, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Future Work. In the process of doing our work on RIDCP, we observed that there are still some difficulties that are urgent to be addressed. We leave the challenges here and hope that future work can address them", + "bbox": [ + 498, + 571, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Existing dehazing methods including RIDCP can not process non-homogeneous haze well.", + "- Dehazing based on enhancement fashion is limited. Generative ability should be introduced for recovering extremely dense haze.", + "- We found that difficult to benchmark dehazing methods in quantitative fairly. Robust metrics for evaluating the quality of dehazing results are also needed." + ], + "bbox": [ + 517, + 640, + 890, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is funded by the National Key Research and Development Program of China (NO.2018AAA0100400), Fundamental Research Funds for the Central Universities (Nankai University, NO.63223050), China Postdoctoral Science Foundation (NO.2021M701780). We are also sponsored by CAAI-Huawei MindSpore Open Fund.", + "bbox": [ + 496, + 794, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22289", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 126-135, 2017. 6", + "[2] Codruta O Ancuti, Cosmin Ancuti, Mateu Sbert, and Radu Timofte. 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CiteSeer, 2014. 1, 2" + ], + "bbox": [ + 501, + 92, + 892, + 486 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22291", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_model.json b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e9ccddbc13441e7d70fd9c06153dd7336bb11f03 --- /dev/null +++ b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_model.json @@ -0,0 +1,2827 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.131, + 0.877, + 0.153 + ], + "angle": 0, + "content": "RIDCP: Revitalizing Real Image Dehazing via High-Quality Codebook Priors" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.18, + 0.792, + 0.235 + ], + "angle": 0, + "content": "Rui-Qi Wu1 Zheng-Peng Duan1 Chun-Le Guo1* Zhi Chai2 Chongyi Li3 \n1VCIP, CS, Nankai University \n2Hisilicon Technologies Co. Ltd. \n3S-Lab, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.185, + 0.237, + 0.782, + 0.27 + ], + "angle": 0, + "content": "{wuruiqi,adamduan0211}@mail.nankai.edu.cn,guochunle=nankai.edu.cn, chaizhi2@huawei.com, chongyi.li@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.474, + 0.789 + ], + "angle": 0, + "content": "Existing dehazing approaches struggle to process real-world hazy images owing to the lack of paired real data and robust priors. In this work, we present a new paradigm for real image dehazing from the perspectives of synthesizing more realistic hazy data and introducing more robust priors into the network. Specifically, (1) instead of adopting the de facto physical scattering model, we rethink the degradation of real hazy images and propose a phenomenological pipeline considering diverse degradation types. (2) We propose a Real Image Dehazing network via high-quality Codebook Priors (RIDCP). Firstly, a VQGAN is pre-trained on a large-scale high-quality dataset to obtain the discrete codebook, encapsulating high-quality priors (HQPs). After replacing the negative effects brought by haze with HQPs, the decoder equipped with a novel normalized feature alignment module can effectively utilize high-quality features and produce clean results. However, although our degradation pipeline drastically mitigates the domain gap between synthetic and real data, it is still intractable to avoid it, which challenges HQPs matching in the wild. Thus, we re-calculate the distance when matching the features to the HQPs by a controllable matching operation, which facilitates finding better counterparts. We provide a recommendation to control the matching based on an explainable solution. Users can also flexibly adjust the enhancement degree as per their preference. Extensive experiments verify the effectiveness of our data synthesis pipeline and the superior performance of RIDCP in real image dehazing. Code and data are released at https://rqw.github.io/projects/RIDCP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.795, + 0.21, + 0.81 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.82, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Image dehazing aims to recover clean images from their hazy counterparts, which is essential for computational photography and high-level tasks [20, 32]. The hazy image formulation is commonly described by a physical scattering" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.305, + 0.633, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.372, + 0.616, + 0.385 + ], + "angle": 0, + "content": "(a) Hazy input" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.304, + 0.758, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.371, + 0.738, + 0.384 + ], + "angle": 0, + "content": "(b) DAD [33]" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.304, + 0.885, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.371, + 0.858, + 0.385 + ], + "angle": 0, + "content": "(c) PSD [7]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.385, + 0.635, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.385, + 0.758, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.385, + 0.887, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.482, + 0.72, + 0.495 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Figure 1. Visual comparisons on a typical hazy image. The proposed method generates cleaner results than other two state-of-the-art real image dehazing approaches. The enhancement degree of our result can be flexibly adjusted by adopting different parameters in the real-domain adaptation phase. The image with a golden border is the result obtained under our recommended parameter." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.59, + 0.55, + 0.603 + ], + "angle": 0, + "content": "model:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.605, + 0.892, + 0.621 + ], + "angle": 0, + "content": "\\[\nI (x) = J (x) t (x) + A (1 - t (x)), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.704 + ], + "angle": 0, + "content": "where \\( I(x) \\) denotes the hazy image and \\( J(x) \\) is its corresponding clean image. The variables \\( A \\) and \\( t(x) \\) are the global atmosphere light and transmission map, respectively. The transmission map \\( t(x) = e^{\\beta d(x)} \\) depends on scene depth \\( d(x) \\) and haze density coefficient \\( \\beta \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.81 + ], + "angle": 0, + "content": "Given a hazy image, restoring its clean version is highly ill-posed. To mitigate the ill-posedness of this problem, various priors, e.g., dark channel prior [16], color attenuation prior [44], and color lines [12] have been proposed in existing traditional methods. Nevertheless, the statistical priors cannot cover diverse cases in real-world scenes, leading to suboptimal dehazing performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "With the advent of deep learning, image dehazing has achieved remarkable progress. Existing methods either adopt deep networks to estimate physical parameters [5,21, 31] or directly restore haze-free images [10, 15, 27, 30, 40]. However, image dehazing neural networks perform limited generalization to real scenes, owing to the difficulty in" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "22282" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.424 + ], + "angle": 0, + "content": "collecting large-scale yet perfectly aligned paired training data and solving the uncertainty of the ill-posed problem without robust priors. Concretely, 1) collecting large-scale and perfectly aligned hazy images with the clean counterpart is incredibly difficult, if not impossible. Thus, most of the existing deep models use synthetic data for training, in which the hazy images are generated using Eq. (1), leading to the neglect of multiple degradation factors. There are some real hazy image datasets [2,3] with paired data, but the size and diversity are insufficient. Moreover, these datasets deviate from the hazy images captured in the wild. These shortcomings inevitably decrease the capability of deep models in real scenes. 2) Real image dehazing is a highly ill-posed issue. Generally, addressing an uncertain mapping problem often needs the support of priors. However, it is difficult to obtain robust priors that can cover the diverse scenes of real hazy images, which also limits the performance of dehazing algorithms. Recently, many studies for real image dehazing try to solve these two issues by domain adaptation from the perspective of data generation [33,39] or priors guidance [7,23], but still cannot obtain desirable results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.473, + 0.746 + ], + "angle": 0, + "content": "In this work, we present a new paradigm for real image dehazing motivated by addressing the above two problems. To obtain large-scale and perfectly aligned paired training data, we rethink the degradation of hazy images by observing amounts of real hazy images and propose a novel data generation pipeline considering multiple degradation factors. In order to solve the uncertainty of the ill-posed issue, we attempt to train a VQGAN [11] on high-quality images to extract more robust high-quality priors (HQPs). The VQGAN only learns high-quality image reconstruction, so it naturally contains the robust HQPs that can help hazy features jump to the clean domain. The observation in Sec. 4.1 further verifies our motivation. Thus, we propose the Real Image Dehazing network via high-quality Codebook Priors (RIDCP). The codebook and decoder of VQGAN are fixed to provide HQPs. Then, RIDCP is equipped with an encoder that helps find the correct HQPs, and a new decoder that utilizes the features from the fixed decoder and produces the final result. Moreover, we propose a novel Normalized Feature Alignment (NFA) that can mitigate the distortion and balance the features for better fusion." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In comparison to previous methods [6, 14, 43] that introduce codebook for image restoration, we further design a unique real domain adaptation strategy based on the characteristics of VQGAN and the statistical results. Intuitively, we propose Controllable HQPs Matching (CHM) operation that replaces the nearest-neighbour matching by imposing elaborate-designed weights on the distances between features and HQPs during the inference phase. The weights are determined by a controllable parameter \\(\\alpha\\) and the statistical distribution gap of HQPs activation in Sec. 4.3. By adjust-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "ing \\(\\alpha\\), the distribution of HQPs activation can be shifted. Moreover, we present a theoretically feasible solution to obtain the optimal \\(\\alpha\\) by minimizing the Kullback-Leibler Divergence of two probability distributions. More significantly, the value of \\(\\alpha\\) can be visually reflected as the enhancement degree as shown in Figure 1(d), and users are allowed to adjust the dehazing results as per their preference. Our CHM is effective, flexible, and explainable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Compared with the state-of-the-art real image dehazing methods, e.g., DAD [33] and PSD [7], only the proposed RIDCP can effectively process the hazy images captured in the wild while generating adjustable results, which are shown in Figure 1. The contributions of our work can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.31, + 0.891, + 0.342 + ], + "angle": 0, + "content": "- We present a new paradigm to push the frontier of deep learning-based image dehazing towards real scenes." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.349, + 0.892, + 0.425 + ], + "angle": 0, + "content": "- We are the first to leverage the high-quality codebook prior in the real image dehazing task. The controllable HQPs matching operation is proposed to overcome the gap between synthetic and real domains and produce adjustable results." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.433, + 0.892, + 0.493 + ], + "angle": 0, + "content": "- We re-formulate the degradation model of real hazy images and propose a phenomenological degradation pipeline to simulate the hazy images captured in the wild." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.31, + 0.892, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.642, + 0.521 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.714, + 0.547 + ], + "angle": 0, + "content": "2.1. Single Image Dehazing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Image Dehazing. The early attempts at single image dehazing consider estimating the parameters of the atmosphere scattering model presented in Eq. (1) by priors on haze-free images [4, 12, 16, 35, 44]. These methods have achieved impressive results. However, the handcrafted priors based on empirical observations are hard to perform well in diverse scenarios. For example, the assumption of DCP [16] is not available in the sky region. The proposed method obtains the priors of high-quality images by pre-training a discrete codebook on large-scale datasets, which is more reliable and comprehensive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "With the development of deep learning techniques, how to use data-driven ideology to remove haze gains a lot of attention. At the early stage, many studies [5, 21, 31] try to adopt convolutional neural networks (CNNs) to estimate the parameters of the degradation model in Eq. (1). In addition, in order to avoid accumulated errors in parameters estimation, some end-to-end networks [10, 15, 27, 30, 40] are proposed to directly estimate the haze-free image. The above learning-based methods have achieved excellent performance on synthetic datasets. However, their significant performance drop on real-world data urgently needs to be solved." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "22283" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.578, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.089, + 0.885, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.379, + 0.892, + 0.464 + ], + "angle": 0, + "content": "Figure 2. Overview of our RIDCP. During the training phase, we train the dehazing network on the data synthesized by our data generation pipeline, as illustrated in (a). The network is based on the pre-trained HQPs codebook and the corresponding decoder \\(\\mathbf{G}_{vq}\\) of VQGAN. We also design the Controllable HQPs Matching (CHM) operation for real domain adaptation by re-calculating the distance \\(d_{k}^{\\hat{z}} = ||\\hat{z} - z_{k}||\\) between features and HQPs. (b) represents the distance re-calculation with two Voronoi diagrams, where the colored cells indicate belonging to better HQPs and the gray cells vice versa. Triangles represent features and star points represent HQPs. It can be seen that after the distance recalibration points that originally belonged to the gray cells are forced to be assigned to the colored cells by our CHM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.473, + 0.82 + ], + "angle": 0, + "content": "Real Image Dehazing. Recently, some works pay attention to real image dehazing. One research line is to utilize GANs [13] for generating hazy data that fits the real haze domain. Shao et al. [33] design a domain adaptation strategy based on the framework of CycleGAN [?]. Yang et al. [39] propose an unpaired dehazing framework named D4. It can estimate the scene depth of hazy images and generate hazy data with different thicknesses to benefit dehazing model training. However, GANs are easy to produce artifacts in the generated results, which is harmful to training models. Another research line aims to introduce prior knowledge by loss functions or network architectures. Li et al. [23] propose a semi-supervised pipeline that adopts prior-based loss functions to train networks on the real dataset. PSD [7] adds a physical-based sub-network on the pre-trained dehazing model and further proposes a prior loss committee to fine-tune the network on real-world data in an unsupervised manner. Nevertheless, directly using handcrafted priors cannot avoid the inherent flaws of prior-based methods. In our study, we investigate overcoming the weaknesses of both types of real image dehazing methods by proposing a novel data generation pipeline and exploiting the latent high-quality priors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.336, + 0.849 + ], + "angle": 0, + "content": "2.2. Discrete Codebook Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Recently, a vector-quantized auto-encoder framework was proposed in VQ-VAE [36], which learns a discrete codebook in latent space. The discrete representation ef" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.892, + 0.773 + ], + "angle": 0, + "content": "fectively addresses the \"posterior collapse\" issue in autoencoder [19] architecture. VQGAN [11] further improves the perceptual quality of reconstructed results by introducing adversarial supervision for codebook learning. The learned discrete codebook helps boost the performance in many low-level vision tasks including face restoration [14, 43] and image super-resolution [6]. Gu et al. [14] introduce the vector quantization technique to face restoration and design a parallel decoder to achieve a balance between visual quality and fidelity. Zhou et al. [14] cast blind face restoration as a code prediction task, and propose a Transformer-based prediction network to replace the nearest-neighbor matching operation for better matching the corresponding code. FeMaSR [6] extends the discrete codebook learning to blind super-resolution. Motivated by the exciting performance of these approaches, we are the first to leverage the high-quality codebook prior for real image dehazing. A novel and controllable HQPs matching operation is proposed to further bridge the gap between our synthetic data and real data, which is inevitable for real scenes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.785, + 0.885, + 0.803 + ], + "angle": 0, + "content": "3. Data Preparation for Real Image Dehazing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Redesigning the pipeline of data generation has been demonstrated as an effective way for solving real-world low-level vision tasks [37, 38, 41]. Based on these works, we consider various degradation factors when synthesizing paired data for training the dehazing network, which can mitigate the domain gap with the real data. For concise-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "22284" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.122 + ], + "angle": 0, + "content": "ness, we represent Eq. (1) as \\(I(x) = \\mathcal{P}(J(x),t(x),A)\\). The formation of the hazy image can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.134, + 0.469, + 0.153 + ], + "angle": 0, + "content": "\\[\nI (x) = J P E G \\left(\\mathcal {P} \\left(J (x) ^ {\\gamma} + \\mathcal {N}, e ^ {\\beta \\hat {d} (x)}, A + \\Delta A\\right)\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.162, + 0.395, + 0.176 + ], + "angle": 0, + "content": "The details of Eq. (2) are introduced as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.177, + 0.469, + 0.236 + ], + "angle": 0, + "content": "Poor light condition. \\(\\gamma \\in [1.5,3.0]\\) is a brightness adjustment factor and \\(\\mathcal{N}\\) is the Gaussian noise distribution. These two components can simulate poor light conditions that frequently occur in hazy weather." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.237, + 0.469, + 0.297 + ], + "angle": 0, + "content": "Transmission map. As a key parameter in the degradation model, we adopt the depth estimation algorithm [18] to estimate depth map \\( d(x) \\) and use \\( \\beta \\in [0.3, 1.5] \\) to control the haze density." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.297, + 0.469, + 0.357 + ], + "angle": 0, + "content": "Colorful haze. To obtain diverse hazy images, the color bias of atmosphere light is considered, which is implemented by a three-channel vector \\(\\Delta A \\in [-0.025, 0.025]\\). The range of \\(A\\) is in the range of [0.25, 1.0]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.358, + 0.469, + 0.417 + ], + "angle": 0, + "content": "JPEG compression. We observe that dehazing algorithms amplify the JPEG artifacts. It is desirable to remove such artifacts while dehazing. \\(JPEG(\\cdot)\\) denotes JPEG compression in the final results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.479 + ], + "angle": 0, + "content": "We select 500 clean images to build the paired data, and the hazy data is generated on-the-fly during the training phase. Additionally, low light and JPEG compression appear with \\(50\\%\\) probability in the proposed pipeline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.492, + 0.212, + 0.51 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.745 + ], + "angle": 0, + "content": "The key idea of our work is to adopt a discrete codebook that introduces high-quality priors (HQPs) into the dehazing network. The overall framework of the proposed method is illustrated in Figure 2. The training phase can be divided into two stages. In the first training stage, we pre-train a VQGAN [11] on high-quality data, obtaining a latent discrete codebook \\(\\mathcal{Z}\\) with HQPs and the correspondence decoder \\(\\mathbf{G}_{vq}\\) (Sec. 4.1). In the second stage, our RIDCP based on the pre-trained VQGAN is trained on hazy images generated by the proposed synthesis pipeline (Sec. 4.2). Moreover, in order to help the network find more accurate code, we propose a controllable adjustment feature matching strategy based on code activation distribution on high-quality images (Sec. 4.3). Besides, the details of training objectives can be found in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.429, + 0.77 + ], + "angle": 0, + "content": "4.1. Latent Codebook for High-quality Priors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.777, + 0.469, + 0.869 + ], + "angle": 0, + "content": "We first introduce how VQGAN works briefly. Given a high-quality image patch \\( x \\), which is the input of the VQGAN encoder \\( \\mathbf{E}_{vq} \\) and the corresponding outputs are the latent features \\( \\hat{z} \\). Then each \"pixel\" \\( \\hat{z}_{ij} \\) of \\( \\hat{z} \\) will be matched to the nearest HQPs in codebook \\( \\mathcal{Z} \\in \\mathbb{R}^{K \\times n} \\) and then obtain the discrete representation \\( z_{ij}^q \\), which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.881, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\nz _ {i j} ^ {q} = \\mathcal {M} (\\hat {z} _ {i j}) = \\arg \\min _ {z _ {k} \\in \\mathcal {Z}} \\left(\\left\\| \\hat {z} _ {i j} - z _ {k} \\right\\| _ {2}\\right), \\tag {3}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.696, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.176, + 0.643, + 0.189 + ], + "angle": 0, + "content": "(a) Hazy input" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.887, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.737, + 0.176, + 0.848, + 0.188 + ], + "angle": 0, + "content": "(b) Reconstruction" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.19, + 0.892, + 0.218 + ], + "angle": 0, + "content": "Figure 3. Result reconstructed by the pre-trained VQGAN. The haze is removed but distorted textures are introduced." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.225, + 0.892, + 0.271 + ], + "angle": 0, + "content": "where \\(K\\) denotes the codebook size, \\(n\\) is the channel number of \\(\\hat{z}\\), and \\(\\mathcal{M}(\\cdot)\\) represents the matching operation. Finally, the input \\(x\\) is reconstructed by \\(\\mathbf{G}_{vq}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.28, + 0.892, + 0.297 + ], + "angle": 0, + "content": "\\[\nx ^ {\\prime} = \\mathbf {G} _ {v q} \\left(z ^ {q}\\right) = \\mathbf {G} _ {v q} \\left(\\mathcal {M} \\left(\\mathbf {E} _ {v q} (x)\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.3, + 0.738, + 0.314 + ], + "angle": 0, + "content": "where \\(x^{\\prime}\\) is the reconstructed result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Observation 1. To understand the potential of the HQPs in the codebook and better utilize it, we made some observations on the results reconstructed by the pre-trained VQGAN. As illustrated in Figure 3, our VQGAN can remove the thin haze and recover vivid color for the hazy input without fine-tuning. We analyze that using HQPs in a matching manner can replace the degraded feature so help it jump to the high-quality domain. However, the dehazing ability of VQGAN is limited due to the difficulty in matching the correct code. Moreover, some distorted textures are produced because of the information loss during the vector-quantized phase. Thus, directly adopting the features from \\(\\mathbf{G}_{vq}\\) is suboptimal. It is intuitive that our next step is to train an encoder \\(\\mathbf{E}\\) that can help priors matching, and a decoder \\(\\mathbf{G}\\) that can utilize the features reconstructed from HQPs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.83, + 0.567 + ], + "angle": 0, + "content": "4.2. Image Dehazing via Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.617 + ], + "angle": 0, + "content": "Based on the observation in Sec. 4.1, image dehazing is decoupled into two sub-tasks: matching correct code and removing texture distortion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.723 + ], + "angle": 0, + "content": "Encoder for HQPs Matching. We follow SwinIR [25] which shows its powerful feature extraction ability for image restoration to design our encoder \\(\\mathbf{E}\\). Specifically, the shallow feature extraction head consists of a stack of residual layers [17] and \\(4\\times\\) downsamples the features. Then 4 residual swim transformer blocks [28] are followed, which serve as the deep feature extraction module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Decoder with Normalized Feature Alignment. We propose the Normalized Feature Alignment (NFA) to help the decoder utilize the features reconstructed from HQPs. Firstly, VQGAN tends to decrease results' fidelity due to the information loss brought by vector-quantized operation [14, 43]. Our solution is to eliminate the distortion by the guidance of features before HQPs matching. Specifically, in \\(i\\)th layer, we adopt the deformable convolution [9] to align the features \\(F_{vq}^{i}\\) from \\(\\mathbf{G}_{vq}\\) with the features \\(F^{i}\\) from \\(\\mathbf{G}\\), which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.884, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nF _ {w} ^ {i} = D C O N V \\left(F _ {v q} ^ {i}, C O N V \\left(C o n c a t \\left(F _ {v q} ^ {i}, F ^ {i}\\right)\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "22285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.074, + 0.089, + 0.473, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.197, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Code activation frequencies under different situations. 'dehaze' denotes inputting real hazy images to dehazing network and 'clean' denotes feeding clean images into the pre-trained VQGAN network. 'adjusted' denotes our RIDCP equipped with the CHM under the recommended parameter with real hazy inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.379 + ], + "angle": 0, + "content": "where \\( F_{w}^{i} \\) denotes the features after warping and \\( DCONV \\) is the deformable convolutional layer. \\( CONV \\) is the convolutional layer for offset generation. In addition, we notice that the ratio of the values of \\( F_{w}^{i} \\) and \\( F^{i} \\) is not stable, resulting in an inadequate combination. Thus, we balance the contributions of each by forcing them to be in the same order of magnitude, which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.388, + 0.47, + 0.423 + ], + "angle": 0, + "content": "\\[\nF ^ {i} = F ^ {i} + \\frac {\\sum F ^ {i}}{\\sum F _ {w} ^ {i}} F _ {w} ^ {i}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.439, + 0.423, + 0.457 + ], + "angle": 0, + "content": "4.3. Controllable HQPs Matching Operation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Observation 2. Our RIDCP achieves relatively satisfactory results with the help of \\(\\mathbf{E}\\) and \\(\\mathbf{G}\\). However, there are still limitations, e.g., low color saturation in some challenging real data. Rather than the HQPs that already show a strong capability in reconstructing vivid results (see Observation 1), the main reason is the difficulty in finding correct HQPs, which is caused by the domain gap between synthetic data and real data. Although the domain gap is drastically reduced by our synthesis pipeline than previous works [22, 42], it is still impossible to cover all real-world hazy conditions by our pipeline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.795 + ], + "angle": 0, + "content": "To verify our claim, we made an observation as follows. We randomly collect 200 high-quality clean images as input of the pre-trained VQGAN and compute the activation frequency \\( f_{c} \\in \\mathbb{R}^{K} \\) of each code. Similarly, 200 real hazy images are fed to the dehazing network to compute the frequency \\( f_{h} \\in \\mathbb{R}^{K} \\). Figure 4 illustrates the activation frequencies of the codes with the top ten largest differences between \\( f_{h} \\) and \\( f_{c} \\). We can see a significant distribution shift. The observation proves that the unavoidable domain gap results in a divergent matching for HQPs. Thus, HQPs still have unexplored potential." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Controllable Matching via Distance Re-calculation. Based on the above observation, it is indispensable to match better HQPs when encountering real hazy images, i.e., priors with high frequency on clear images. Two components can affect the HQPs matching, which are the encoder \\(\\mathbf{E}\\) and the matching operation \\(\\mathcal{M}(\\cdot)\\). Since it is difficult to retrain \\(\\mathbf{E}\\) on real hazy images without reference images, defining" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.152 + ], + "angle": 0, + "content": "a new matching operation \\(\\mathcal{M}'(\\cdot)\\) sounds like a reasonable solution. We propose Controllable HQPs Matching (CHM) that re-calculates distances by assigning different weights during matching phase. The CHM can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.162, + 0.892, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} ^ {\\prime} (\\hat {z}) = \\arg \\min _ {z _ {k} \\in Z} \\left(\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) \\times | | \\hat {z} - z _ {k} |\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.895, + 0.372 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}(\\tilde{f}_k,\\alpha)\\) is the function to generate weights based on the frequency difference \\(\\tilde{f}_k = f_h^k -f_c^k\\) and adjusted by a parameter \\(\\alpha\\). There are three objectives in the design of F: 1) Since higher \\(\\tilde{f}_k\\) means less activation is needed, \\(\\mathbf{F}\\) should be monotonic with \\(\\tilde{f}_k\\) thus ensuring consistent trend adjustment. 2) \\(\\mathbf{F}(0,\\alpha)\\equiv 1\\) so that HQPs with the same frequencies on clear and hazy data are not adjusted. 3) The degree of adjustment can be controlled monotonically by \\(\\alpha\\), e.g., \\(\\forall \\tilde{f}_1 > \\tilde{f}_2,\\forall \\alpha_1 > \\alpha_2\\rightarrow \\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_1)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_1)} >\\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_2)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_2)}\\). Coincidentally, the exponential function has these properties, thus \\(\\mathbf{F}\\) can be formulated as;" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.381, + 0.892, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) = e ^ {a \\times \\tilde {f} _ {k}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.488 + ], + "angle": 0, + "content": "Figure 2(b) adopts two Voronoi diagrams to simulate the changes occurring in the high-dimensional space during feature matching. As we can see, the points originally belonging to gray cells are matched to the colored cells after distance re-calculation, i.e., finding better HQPs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.893, + 0.683 + ], + "angle": 0, + "content": "Possible Solution of the Recommended \\(\\alpha\\). Our method is able to control the HQPs matching based on the above strategy. The final goal is to find a suitable \\(\\alpha\\) to adapt the network to real domain. According to the law of large numbers, the frequencies \\(f_{c}^{k}, f_{h}^{k}\\) can be substituted for the corresponding probabilities \\(P_{c}(x = z_{k}), P_{h}(x = z_{k}|\\alpha)\\). The gap between the dehazing results and the clean domain can be represented by the difference between the two probability distributions. Thus, the real domain adaptation problem is transferred into calculating an optimal parameter \\(\\hat{\\alpha}\\) that can minimize the forward Kullback-Leibler Divergence of \\(P_{c}(x = z_{k})\\) and \\(P_{h}(x = z_{k}|\\alpha)\\), which is also the maximum likelihood estimation of \\(\\alpha\\):" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.692, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\alpha} = \\arg \\min _ {\\alpha} K L (P _ {c} | | P _ {h}) \\\\ = a r g \\min _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) \\log \\frac {P _ {c} (x = z _ {i})}{P _ {h} (x = z _ {i} | \\alpha)} \\\\ = \\arg \\max _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} \\left(x = z _ {i}\\right) \\log P _ {h} \\left(x = z _ {i} \\mid \\alpha\\right) \\tag {9} \\\\ = a r g \\max _ {\\alpha} \\prod_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) P _ {h} (x = z _ {i} | \\alpha). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We use a binary search algorithm to iteratively find the approximate optimal solution for \\(\\hat{\\alpha}\\). The final determination is \\(\\hat{\\alpha} = 21.25\\) and higher precision calculations have little" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "22286" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.091, + 0.198, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.465, + 0.188, + 0.478 + ], + "angle": 0, + "content": "(a) Hazy image" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.091, + 0.313, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.465, + 0.305, + 0.478 + ], + "angle": 0, + "content": "(b) MSBDN [10]" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.091, + 0.426, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.319, + 0.465, + 0.421, + 0.478 + ], + "angle": 0, + "content": "(c) Dehamer [15]" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.091, + 0.541, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.465, + 0.519, + 0.478 + ], + "angle": 0, + "content": "(d) PSD [7]" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.091, + 0.655, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.465, + 0.633, + 0.478 + ], + "angle": 0, + "content": "(e) D4 [39]" + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.091, + 0.77, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.465, + 0.751, + 0.478 + ], + "angle": 0, + "content": "(f) DAD [33]" + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.091, + 0.885, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.465, + 0.859, + 0.478 + ], + "angle": 0, + "content": "(g) RIDCP" + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.482, + 0.637, + 0.497 + ], + "angle": 0, + "content": "Figure 5. Visual comparison on RTTS dataset [22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.556 + ], + "angle": 0, + "content": "effect on the results. Note that, \\(\\hat{\\alpha}\\) may not be the determined choice for all cases. One can flexibly adjust \\(\\alpha\\) according to their preference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.564, + 0.21, + 0.58 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.181, + 0.604 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.719 + ], + "angle": 0, + "content": "High-quality Datasets. In order to obtain high-quality results from the pre-trained HQPs, the VQGAN needs to be trained on large-scale datasets containing high-resolution and texture-sharp images. In our work, we use DIV2K [1] and Flickr2K [26] (containing 4,250 images) to train the first stage. Both datasets are widely used in high-quality reconstruction tasks [6,24,25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.811 + ], + "angle": 0, + "content": "Real Haze Datasets. We qualitatively and quantitatively evaluate our dehazing network on the RTTS dataset [22], which contains over 4,000 real hazy images with diverse scenes, resolutions, and degradation issues. Besides, we use Fattal's dataset [12] that includes 31 classic real hazy cases for further visual comparison." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.295, + 0.832 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "For both VQGAN and RIDCP training, we use Adam optimizer with default parameters \\((\\beta_{1} = 0.9, \\beta_{2} = 0.99)\\). The learning rate is fixed to 0.0001 during the training phase and the batch size is set to 16. For data augmentation, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.631 + ], + "angle": 0, + "content": "randomly resize and crop the input into a size of \\(256 \\times 256\\), and flip it with a half probability. During the first training stage, our VQGAN is pre-trained on DIV2K and Flickr2K for 350K iterations. Then, the proposed RIDCP is trained on the data generated by the proposed synthesis pipeline for 10K iterations. All experiments are implemented with PyTorch framework on 4 NVIDIA V100 GPUs. The code implemented by MindSpore framework is also provided." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.646, + 0.869, + 0.663 + ], + "angle": 0, + "content": "5.3. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.748 + ], + "angle": 0, + "content": "We compare the performance of the proposed method with several state-of-the-art dehazing approaches. The experiments are designed from both quantitative and qualitative perspectives. Moreover, we also conduct a user study to verify the subjective performance of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Quantitative Comparison. Since there is no ground-truth image in real hazy datasets, we use some non-reference metrics for quantitative comparison. We first adopt the Fog Aware Density Evaluator (FADE) [8] for haze density estimation. In addition, two widely-used image quality assessment metrics, BRISQUE [29] and NIMA [34] are also included. The quantitative comparison is conducted on RTTS dataset with two dehazing methods (MSBDN [10] and Dehamer [15]) that achieve outstanding performance on synthetic hazy image datasets [22], and three real dehazing ap" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "22287" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.198, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.229, + 0.189, + 0.243 + ], + "angle": 0, + "content": "(a) Hazy image" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.091, + 0.313, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.229, + 0.306, + 0.242 + ], + "angle": 0, + "content": "(b) MSBDN [10]" + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.091, + 0.426, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.318, + 0.229, + 0.421, + 0.242 + ], + "angle": 0, + "content": "(c) Dehamer [15]" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.091, + 0.541, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.229, + 0.52, + 0.242 + ], + "angle": 0, + "content": "(d) PSD [7]" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.091, + 0.655, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.229, + 0.633, + 0.242 + ], + "angle": 0, + "content": "(e) D4 [39]" + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.091, + 0.77, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.229, + 0.752, + 0.242 + ], + "angle": 0, + "content": "(f) DAD [33]" + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.091, + 0.885, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.229, + 0.859, + 0.242 + ], + "angle": 0, + "content": "(g) RIDCP" + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.248, + 0.632, + 0.262 + ], + "angle": 0, + "content": "Figure 6. Visual comparison on Fattal's data [12]." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.273, + 0.468, + 0.315 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison and user study on RTTS dataset. Red indicates the best and blue indicates the second best. 'US' shows the percentage of votes in the user study." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.32, + 0.487, + 0.44 + ], + "angle": 0, + "content": "
MethodFADE↓BRISQUE↓NIMA↑US↑
Hazy image2.48437.0114.32500.030
MSBDN [10]1.36328.7434.14010.046
Dehamer [15]1.89533.8663.86630.041
DAD [33]1.13032.7274.00550.143
PSD [7]0.92025.2394.34590.105
D4 [39]1.35833.2063.72390.079
RIDCP0.94418.7824.42670.556
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.584 + ], + "angle": 0, + "content": "proaches (DAD [33], PSD [7], D4 [39]). The results are illustrated in Table 1. The proposed RIDCP achieves the best in terms of BRISQUE and NIMA, which gains \\(25.57\\%\\) and \\(1.86\\%\\) improvements, respectively. For FADE, our method is ranked second slightly below the PSD. However, as shown in Figure 5, PSD tends to produce over-enhanced results, which leads to an inaccurate evaluation. Overall, RIDCP achieves the best results on quantitative metrics, and subsequent experiments will further prove our superiority." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Qualitative Comparison. We perform the qualitative comparison on RTTS and Fattal's datasets, which is shown in Figure 5 and Figure 6. We can observe that Dehamer, MSBDN, and D4 cannot process the real hazy images well. PSD can produce bright results but the dehazing ability is limited. DAD is effective in haze removal, while its results suffer from color bias and dark tone. Our method generates the best perceptual results in terms of brightness, colorfulness, and haze residue compared to other methods. More results can be found in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "User Study. We conduct a user study to evaluate the proposed method subjectively against other methods. We randomly select 100 images from RTTS dataset for comparison and invite 5 experts with image processing background and 5 naive observers as volunteers. Before the user study, we give the observer three tips: 1) The primary concern is whether the haze is removed, especially the dense haze in the distance. 2) Pay attention to whether the natural color is recovered. 3) A good method should generate artifact-free results. Afterward, the images are displayed to the observer group by group. Each group contains the input image and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.895, + 0.381 + ], + "angle": 0, + "content": "the results generated by different methods. The observer is required to choose the best one after at least 10 seconds of observation. We statistic the percentage of each method selected as the best and the final scores are listed in Table 1. The proposed RIDCP achieves the highest score and is well ahead of the second place, further demonstrating our method's superior dehazing ability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.391, + 0.654, + 0.408 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.476 + ], + "angle": 0, + "content": "In order to verify the effectiveness of each key component, we conduct a series of ablation experiments. Generally, we discuss the effectiveness of CHM, NFA, and the phenomenological degradation pipeline in this section." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.893, + 0.613 + ], + "angle": 0, + "content": "Influence of Adjustment Parameter. The degree of real domain adaptation is controlled by parameter \\(\\alpha\\) in Eq. (8) and one can adjust the final result flexibly by adjusting \\(\\alpha\\). Thus, we are curious about what influence the different \\(\\alpha\\) will have. As Figure 7 shows, the value of \\(\\alpha\\) and the image enhancement effect belong to a linear relationship. More visual-pleasing even over-enhanced results can be produced when \\(\\alpha > 0\\). Interestingly, we can obtain under-enhanced results if \\(\\alpha\\) is adjusted in the opposite direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.869 + ], + "angle": 0, + "content": "Effectiveness of NFA. Our NFA can help remove the distorted textures caused by feature matching while preserving the useful information reconstructed from HQPs. The NFA can be divided into two key parts: warping operation based on deformable convolution and normalize-based addition. To analyze the role of each part, we propose 4 variants to replace NFA, which are: 1) Without any fusion operation. 2) Adding directly. 3) Normalized addition without warping. 4) Warping and direct addition. Figure 8 shows a set of comparisons. Observing the grass area in red boxes, the result of variant 1 is dark and remaining thin haze. Variants 2 and 4 also have non-homogeneous fog residues in some areas. Variant 3 generates obvious artifacts because forcing normalizing unaligned features to the same order of magnitude and adding them together makes the network difficult to train. Only the full NFA achieves the best in brightness and haze removal." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of the Phenomenological Degradation Pipeline. To prove that our proposed degradation pipeline" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "22288" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.095, + 0.239, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.256, + 0.204, + 0.269 + ], + "angle": 0, + "content": "(a) Hazy image" + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.095, + 0.402, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.256, + 0.369, + 0.269 + ], + "angle": 0, + "content": "(b) \\(\\alpha = -60.0\\)" + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.095, + 0.564, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.256, + 0.518, + 0.269 + ], + "angle": 0, + "content": "(c) \\(\\alpha = 0.0\\)" + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.092, + 0.728, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.256, + 0.686, + 0.268 + ], + "angle": 0, + "content": "(d) \\(\\alpha = 21.25\\)" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.095, + 0.888, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.256, + 0.844, + 0.268 + ], + "angle": 0, + "content": "(e) \\(\\alpha = 60.0\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.894, + 0.313 + ], + "angle": 0, + "content": "Figure 7. Results under different adjustment degrees. The proposed CHM allows users to adjust the degree of enhancement from low \\((\\alpha = -60.0)\\) to high \\((\\alpha = 60.0)\\). The recommended value \\((\\alpha = 21.25)\\) facilitates the network to generate the most natural results (surrounded by the blue box). Zoom in for the best view." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.322, + 0.209, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.389, + 0.169, + 0.4 + ], + "angle": 0, + "content": "(a) Haze" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.323, + 0.338, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.389, + 0.311, + 0.4 + ], + "angle": 0, + "content": "(b) w/o fusion" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.323, + 0.466, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.389, + 0.439, + 0.4 + ], + "angle": 0, + "content": "(c) Addition" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.401, + 0.209, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.468, + 0.188, + 0.48 + ], + "angle": 0, + "content": "(d) w/o warping" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.402, + 0.338, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.468, + 0.332, + 0.48 + ], + "angle": 0, + "content": "(e) w/o normalizing" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.402, + 0.466, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.468, + 0.436, + 0.479 + ], + "angle": 0, + "content": "(f) Full NFA" + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.485, + 0.416, + 0.5 + ], + "angle": 0, + "content": "Figure 8. Ablation results of the proposed NFA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.734 + ], + "angle": 0, + "content": "for paired data generation can boost the capabilities of haze removal, we retrain our RIDCP on two widely-used synthetic datasets, which are OTS [22] and Haze4K [42]. Notably, Haze4K is post-processed by DAD [33]. Moreover, we replace the training set from OTS with our synthetic data for transformer-based Dehamer and CNN-based MSBDN, thus demonstrating that it can generally bring gains. The comparison results are illustrated in Figure 9. We can observe that our dehazing network cannot remove the haze under the training of OTS and Haze4K. Besides, Dehamer and MSBDN can generate results with less haze and higher brightness with the help of our training data. However, they still struggle in color recovery compared to our method, which also demonstrates the effectiveness of HQPs and our adaptation strategy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.192, + 0.754 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Conclusion. In this paper, we present a novel paradigm to revitalize deep dehazing networks towards the real world. Our proposed phenomenological degradation pipeline synthesizes more realistic hazy data, which achieves significant gains in haze removal. Based on our observations and analysis, we introduce the high-quality priors in VQGAN to the dehazing network and progressively leverage their power, which finally builds our real image dehazing network via high-quality codebook priors (RIDCP). Extensive experi" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.323, + 0.602, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.384, + 0.574, + 0.395 + ], + "angle": 0, + "content": "(a) Haze" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.323, + 0.697, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.384, + 0.67, + 0.395 + ], + "angle": 0, + "content": "(b) OTS" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.323, + 0.793, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.384, + 0.779, + 0.395 + ], + "angle": 0, + "content": "(c) Haze4K" + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.323, + 0.888, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.803, + 0.384, + 0.881, + 0.395 + ], + "angle": 0, + "content": "(d) Dehamer" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.396, + 0.602, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.457, + 0.591, + 0.471 + ], + "angle": 0, + "content": "(e) Dehamer†" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.396, + 0.697, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.613, + 0.457, + 0.685, + 0.47 + ], + "angle": 0, + "content": "(f) MSBDN" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.396, + 0.793, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.457, + 0.786, + 0.471 + ], + "angle": 0, + "content": "(g) \\(\\mathbf{MSBDN}^{\\dagger}\\)" + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.396, + 0.888, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.812, + 0.457, + 0.864, + 0.47 + ], + "angle": 0, + "content": "(h) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.476, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Figure 9. Ablation results of the proposed data generation pipeline. We retrain our dehazing network on OTS (b) and Haze4K (c) to verify the effectiveness of our generation pipeline. Dehamer and MSBDN are also retrained on our synthetic data, which are marked by \\(\\dagger\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.557, + 0.855, + 0.572 + ], + "angle": 0, + "content": "ments show the superiority of the proposed paradigm." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Limitations and Future Work. In the process of doing our work on RIDCP, we observed that there are still some difficulties that are urgent to be addressed. We leave the challenges here and hope that future work can address them" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.641, + 0.892, + 0.672 + ], + "angle": 0, + "content": "- Existing dehazing methods including RIDCP can not process non-homogeneous haze well." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.681, + 0.892, + 0.726 + ], + "angle": 0, + "content": "- Dehazing based on enhancement fashion is limited. Generative ability should be introduced for recovering extremely dense haze." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.735, + 0.892, + 0.781 + ], + "angle": 0, + "content": "- We found that difficult to benchmark dehazing methods in quantitative fairly. Robust metrics for evaluating the quality of dehazing results are also needed." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.641, + 0.892, + 0.781 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgements. This work is funded by the National Key Research and Development Program of China (NO.2018AAA0100400), Fundamental Research Funds for the Central Universities (Nankai University, NO.63223050), China Postdoctoral Science Foundation (NO.2021M701780). 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CiteSeer, 2014. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "22291" + } + ] +] \ No newline at end of file diff --git a/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_origin.pdf b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..29f68e66590f368c69cd4b6f2b5639d56b284389 --- /dev/null +++ b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/05659269-f519-4ff3-9c15-95d37cd713bf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:72e0b135acef46d8385f0fca1e936e6c6dddfe079420fb1c2411f1ff8015f61b +size 5824427 diff --git a/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/full.md b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a43cdc500bd563051a7f0335cc1069c86bd66323 --- /dev/null +++ b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/full.md @@ -0,0 +1,398 @@ +# RIDCP: Revitalizing Real Image Dehazing via High-Quality Codebook Priors + +Rui-Qi Wu1 Zheng-Peng Duan1 Chun-Le Guo1* Zhi Chai2 Chongyi Li3 +1VCIP, CS, Nankai University +2Hisilicon Technologies Co. Ltd. +3S-Lab, Nanyang Technological University + +{wuruiqi,adamduan0211}@mail.nankai.edu.cn,guochunle=nankai.edu.cn, chaizhi2@huawei.com, chongyi.li@ntu.edu.sg + +# Abstract + +Existing dehazing approaches struggle to process real-world hazy images owing to the lack of paired real data and robust priors. In this work, we present a new paradigm for real image dehazing from the perspectives of synthesizing more realistic hazy data and introducing more robust priors into the network. Specifically, (1) instead of adopting the de facto physical scattering model, we rethink the degradation of real hazy images and propose a phenomenological pipeline considering diverse degradation types. (2) We propose a Real Image Dehazing network via high-quality Codebook Priors (RIDCP). Firstly, a VQGAN is pre-trained on a large-scale high-quality dataset to obtain the discrete codebook, encapsulating high-quality priors (HQPs). After replacing the negative effects brought by haze with HQPs, the decoder equipped with a novel normalized feature alignment module can effectively utilize high-quality features and produce clean results. However, although our degradation pipeline drastically mitigates the domain gap between synthetic and real data, it is still intractable to avoid it, which challenges HQPs matching in the wild. Thus, we re-calculate the distance when matching the features to the HQPs by a controllable matching operation, which facilitates finding better counterparts. We provide a recommendation to control the matching based on an explainable solution. Users can also flexibly adjust the enhancement degree as per their preference. Extensive experiments verify the effectiveness of our data synthesis pipeline and the superior performance of RIDCP in real image dehazing. Code and data are released at https://rqw.github.io/projects/RIDCP. + +# 1. Introduction + +Image dehazing aims to recover clean images from their hazy counterparts, which is essential for computational photography and high-level tasks [20, 32]. The hazy image formulation is commonly described by a physical scattering + +![](images/d48fe80a2323503fa210d6fc19f6595a21d7a30eea755f5c8453a27c19b1ffdf.jpg) + +![](images/a7d108bfeb09e69b8f620cdfe849f6b61806885049bd157860521074c3da22c6.jpg) + +![](images/260698b543f5e33c2926f0a81cb3150dc07a1b081737e742b353bd064f5e5e3c.jpg) + +![](images/092b1e12a80bb07ba35210296317fd793bb2001d33a76f0056b78c05219ce02b.jpg) +(a) Hazy input +Figure 1. Visual comparisons on a typical hazy image. The proposed method generates cleaner results than other two state-of-the-art real image dehazing approaches. The enhancement degree of our result can be flexibly adjusted by adopting different parameters in the real-domain adaptation phase. The image with a golden border is the result obtained under our recommended parameter. + +![](images/f035fd25c9d118eacb6cdad3f2d1db6388dcd5981ddb55f29dc14fa57bcd2168.jpg) +(b) DAD [33] +(d) Ours + +![](images/403431cbbef964eb0f038a7a8bc6035076594e6d87bb4b5e20fed3483cfe07df.jpg) +(c) PSD [7] + +model: + +$$ +I (x) = J (x) t (x) + A (1 - t (x)), \tag {1} +$$ + +where $I(x)$ denotes the hazy image and $J(x)$ is its corresponding clean image. The variables $A$ and $t(x)$ are the global atmosphere light and transmission map, respectively. The transmission map $t(x) = e^{\beta d(x)}$ depends on scene depth $d(x)$ and haze density coefficient $\beta$ . + +Given a hazy image, restoring its clean version is highly ill-posed. To mitigate the ill-posedness of this problem, various priors, e.g., dark channel prior [16], color attenuation prior [44], and color lines [12] have been proposed in existing traditional methods. Nevertheless, the statistical priors cannot cover diverse cases in real-world scenes, leading to suboptimal dehazing performance. + +With the advent of deep learning, image dehazing has achieved remarkable progress. Existing methods either adopt deep networks to estimate physical parameters [5,21, 31] or directly restore haze-free images [10, 15, 27, 30, 40]. However, image dehazing neural networks perform limited generalization to real scenes, owing to the difficulty in + +collecting large-scale yet perfectly aligned paired training data and solving the uncertainty of the ill-posed problem without robust priors. Concretely, 1) collecting large-scale and perfectly aligned hazy images with the clean counterpart is incredibly difficult, if not impossible. Thus, most of the existing deep models use synthetic data for training, in which the hazy images are generated using Eq. (1), leading to the neglect of multiple degradation factors. There are some real hazy image datasets [2,3] with paired data, but the size and diversity are insufficient. Moreover, these datasets deviate from the hazy images captured in the wild. These shortcomings inevitably decrease the capability of deep models in real scenes. 2) Real image dehazing is a highly ill-posed issue. Generally, addressing an uncertain mapping problem often needs the support of priors. However, it is difficult to obtain robust priors that can cover the diverse scenes of real hazy images, which also limits the performance of dehazing algorithms. Recently, many studies for real image dehazing try to solve these two issues by domain adaptation from the perspective of data generation [33,39] or priors guidance [7,23], but still cannot obtain desirable results. + +In this work, we present a new paradigm for real image dehazing motivated by addressing the above two problems. To obtain large-scale and perfectly aligned paired training data, we rethink the degradation of hazy images by observing amounts of real hazy images and propose a novel data generation pipeline considering multiple degradation factors. In order to solve the uncertainty of the ill-posed issue, we attempt to train a VQGAN [11] on high-quality images to extract more robust high-quality priors (HQPs). The VQGAN only learns high-quality image reconstruction, so it naturally contains the robust HQPs that can help hazy features jump to the clean domain. The observation in Sec. 4.1 further verifies our motivation. Thus, we propose the Real Image Dehazing network via high-quality Codebook Priors (RIDCP). The codebook and decoder of VQGAN are fixed to provide HQPs. Then, RIDCP is equipped with an encoder that helps find the correct HQPs, and a new decoder that utilizes the features from the fixed decoder and produces the final result. Moreover, we propose a novel Normalized Feature Alignment (NFA) that can mitigate the distortion and balance the features for better fusion. + +In comparison to previous methods [6, 14, 43] that introduce codebook for image restoration, we further design a unique real domain adaptation strategy based on the characteristics of VQGAN and the statistical results. Intuitively, we propose Controllable HQPs Matching (CHM) operation that replaces the nearest-neighbour matching by imposing elaborate-designed weights on the distances between features and HQPs during the inference phase. The weights are determined by a controllable parameter $\alpha$ and the statistical distribution gap of HQPs activation in Sec. 4.3. By adjust- + +ing $\alpha$ , the distribution of HQPs activation can be shifted. Moreover, we present a theoretically feasible solution to obtain the optimal $\alpha$ by minimizing the Kullback-Leibler Divergence of two probability distributions. More significantly, the value of $\alpha$ can be visually reflected as the enhancement degree as shown in Figure 1(d), and users are allowed to adjust the dehazing results as per their preference. Our CHM is effective, flexible, and explainable. + +Compared with the state-of-the-art real image dehazing methods, e.g., DAD [33] and PSD [7], only the proposed RIDCP can effectively process the hazy images captured in the wild while generating adjustable results, which are shown in Figure 1. The contributions of our work can be summarized as follows. + +- We present a new paradigm to push the frontier of deep learning-based image dehazing towards real scenes. +- We are the first to leverage the high-quality codebook prior in the real image dehazing task. The controllable HQPs matching operation is proposed to overcome the gap between synthetic and real domains and produce adjustable results. +- We re-formulate the degradation model of real hazy images and propose a phenomenological degradation pipeline to simulate the hazy images captured in the wild. + +# 2. Related Work + +# 2.1. Single Image Dehazing + +Image Dehazing. The early attempts at single image dehazing consider estimating the parameters of the atmosphere scattering model presented in Eq. (1) by priors on haze-free images [4, 12, 16, 35, 44]. These methods have achieved impressive results. However, the handcrafted priors based on empirical observations are hard to perform well in diverse scenarios. For example, the assumption of DCP [16] is not available in the sky region. The proposed method obtains the priors of high-quality images by pre-training a discrete codebook on large-scale datasets, which is more reliable and comprehensive. + +With the development of deep learning techniques, how to use data-driven ideology to remove haze gains a lot of attention. At the early stage, many studies [5, 21, 31] try to adopt convolutional neural networks (CNNs) to estimate the parameters of the degradation model in Eq. (1). In addition, in order to avoid accumulated errors in parameters estimation, some end-to-end networks [10, 15, 27, 30, 40] are proposed to directly estimate the haze-free image. The above learning-based methods have achieved excellent performance on synthetic datasets. However, their significant performance drop on real-world data urgently needs to be solved. + +![](images/345c0ee4dcbccd5db9e91406f932a99ad092da4ee667cff10864c4068af28e45.jpg) +Figure 2. Overview of our RIDCP. During the training phase, we train the dehazing network on the data synthesized by our data generation pipeline, as illustrated in (a). The network is based on the pre-trained HQPs codebook and the corresponding decoder $\mathbf{G}_{vq}$ of VQGAN. We also design the Controllable HQPs Matching (CHM) operation for real domain adaptation by re-calculating the distance $d_{k}^{\hat{z}} = ||\hat{z} - z_{k}||$ between features and HQPs. (b) represents the distance re-calculation with two Voronoi diagrams, where the colored cells indicate belonging to better HQPs and the gray cells vice versa. Triangles represent features and star points represent HQPs. It can be seen that after the distance recalibration points that originally belonged to the gray cells are forced to be assigned to the colored cells by our CHM. + +![](images/0364824034e4602662ec86e7e7ab940d6afcaac5d95f68710605f6f0529cd22b.jpg) + +Real Image Dehazing. Recently, some works pay attention to real image dehazing. One research line is to utilize GANs [13] for generating hazy data that fits the real haze domain. Shao et al. [33] design a domain adaptation strategy based on the framework of CycleGAN [?]. Yang et al. [39] propose an unpaired dehazing framework named D4. It can estimate the scene depth of hazy images and generate hazy data with different thicknesses to benefit dehazing model training. However, GANs are easy to produce artifacts in the generated results, which is harmful to training models. Another research line aims to introduce prior knowledge by loss functions or network architectures. Li et al. [23] propose a semi-supervised pipeline that adopts prior-based loss functions to train networks on the real dataset. PSD [7] adds a physical-based sub-network on the pre-trained dehazing model and further proposes a prior loss committee to fine-tune the network on real-world data in an unsupervised manner. Nevertheless, directly using handcrafted priors cannot avoid the inherent flaws of prior-based methods. In our study, we investigate overcoming the weaknesses of both types of real image dehazing methods by proposing a novel data generation pipeline and exploiting the latent high-quality priors. + +# 2.2. Discrete Codebook Learning + +Recently, a vector-quantized auto-encoder framework was proposed in VQ-VAE [36], which learns a discrete codebook in latent space. The discrete representation ef + +fectively addresses the "posterior collapse" issue in autoencoder [19] architecture. VQGAN [11] further improves the perceptual quality of reconstructed results by introducing adversarial supervision for codebook learning. The learned discrete codebook helps boost the performance in many low-level vision tasks including face restoration [14, 43] and image super-resolution [6]. Gu et al. [14] introduce the vector quantization technique to face restoration and design a parallel decoder to achieve a balance between visual quality and fidelity. Zhou et al. [14] cast blind face restoration as a code prediction task, and propose a Transformer-based prediction network to replace the nearest-neighbor matching operation for better matching the corresponding code. FeMaSR [6] extends the discrete codebook learning to blind super-resolution. Motivated by the exciting performance of these approaches, we are the first to leverage the high-quality codebook prior for real image dehazing. A novel and controllable HQPs matching operation is proposed to further bridge the gap between our synthetic data and real data, which is inevitable for real scenes. + +# 3. Data Preparation for Real Image Dehazing + +Redesigning the pipeline of data generation has been demonstrated as an effective way for solving real-world low-level vision tasks [37, 38, 41]. Based on these works, we consider various degradation factors when synthesizing paired data for training the dehazing network, which can mitigate the domain gap with the real data. For concise- + +ness, we represent Eq. (1) as $I(x) = \mathcal{P}(J(x),t(x),A)$ . The formation of the hazy image can be written as: + +$$ +I (x) = J P E G \left(\mathcal {P} \left(J (x) ^ {\gamma} + \mathcal {N}, e ^ {\beta \hat {d} (x)}, A + \Delta A\right)\right). \tag {2} +$$ + +The details of Eq. (2) are introduced as follows: + +Poor light condition. $\gamma \in [1.5,3.0]$ is a brightness adjustment factor and $\mathcal{N}$ is the Gaussian noise distribution. These two components can simulate poor light conditions that frequently occur in hazy weather. + +Transmission map. As a key parameter in the degradation model, we adopt the depth estimation algorithm [18] to estimate depth map $d(x)$ and use $\beta \in [0.3, 1.5]$ to control the haze density. + +Colorful haze. To obtain diverse hazy images, the color bias of atmosphere light is considered, which is implemented by a three-channel vector $\Delta A \in [-0.025, 0.025]$ . The range of $A$ is in the range of [0.25, 1.0]. + +JPEG compression. We observe that dehazing algorithms amplify the JPEG artifacts. It is desirable to remove such artifacts while dehazing. $JPEG(\cdot)$ denotes JPEG compression in the final results. + +We select 500 clean images to build the paired data, and the hazy data is generated on-the-fly during the training phase. Additionally, low light and JPEG compression appear with $50\%$ probability in the proposed pipeline. + +# 4. Methodology + +The key idea of our work is to adopt a discrete codebook that introduces high-quality priors (HQPs) into the dehazing network. The overall framework of the proposed method is illustrated in Figure 2. The training phase can be divided into two stages. In the first training stage, we pre-train a VQGAN [11] on high-quality data, obtaining a latent discrete codebook $\mathcal{Z}$ with HQPs and the correspondence decoder $\mathbf{G}_{vq}$ (Sec. 4.1). In the second stage, our RIDCP based on the pre-trained VQGAN is trained on hazy images generated by the proposed synthesis pipeline (Sec. 4.2). Moreover, in order to help the network find more accurate code, we propose a controllable adjustment feature matching strategy based on code activation distribution on high-quality images (Sec. 4.3). Besides, the details of training objectives can be found in supplementary materials. + +# 4.1. Latent Codebook for High-quality Priors + +We first introduce how VQGAN works briefly. Given a high-quality image patch $x$ , which is the input of the VQGAN encoder $\mathbf{E}_{vq}$ and the corresponding outputs are the latent features $\hat{z}$ . Then each "pixel" $\hat{z}_{ij}$ of $\hat{z}$ will be matched to the nearest HQPs in codebook $\mathcal{Z} \in \mathbb{R}^{K \times n}$ and then obtain the discrete representation $z_{ij}^q$ , which can be written as: + +$$ +z _ {i j} ^ {q} = \mathcal {M} (\hat {z} _ {i j}) = \arg \min _ {z _ {k} \in \mathcal {Z}} \left(\left\| \hat {z} _ {i j} - z _ {k} \right\| _ {2}\right), \tag {3} +$$ + +![](images/e74194e9ff30ee6f3f4901a26b045f4a4c698d4a94b99e0bb4671ecdfc56d97b.jpg) +(a) Hazy input + +![](images/087c517098971667c648427ec54dc762e6ebc905bf20e4c437cef73c0da42e3c.jpg) +(b) Reconstruction +Figure 3. Result reconstructed by the pre-trained VQGAN. The haze is removed but distorted textures are introduced. + +where $K$ denotes the codebook size, $n$ is the channel number of $\hat{z}$ , and $\mathcal{M}(\cdot)$ represents the matching operation. Finally, the input $x$ is reconstructed by $\mathbf{G}_{vq}$ : + +$$ +x ^ {\prime} = \mathbf {G} _ {v q} \left(z ^ {q}\right) = \mathbf {G} _ {v q} \left(\mathcal {M} \left(\mathbf {E} _ {v q} (x)\right)\right), \tag {4} +$$ + +where $x^{\prime}$ is the reconstructed result. + +Observation 1. To understand the potential of the HQPs in the codebook and better utilize it, we made some observations on the results reconstructed by the pre-trained VQGAN. As illustrated in Figure 3, our VQGAN can remove the thin haze and recover vivid color for the hazy input without fine-tuning. We analyze that using HQPs in a matching manner can replace the degraded feature so help it jump to the high-quality domain. However, the dehazing ability of VQGAN is limited due to the difficulty in matching the correct code. Moreover, some distorted textures are produced because of the information loss during the vector-quantized phase. Thus, directly adopting the features from $\mathbf{G}_{vq}$ is suboptimal. It is intuitive that our next step is to train an encoder $\mathbf{E}$ that can help priors matching, and a decoder $\mathbf{G}$ that can utilize the features reconstructed from HQPs. + +# 4.2. Image Dehazing via Feature Matching + +Based on the observation in Sec. 4.1, image dehazing is decoupled into two sub-tasks: matching correct code and removing texture distortion. + +Encoder for HQPs Matching. We follow SwinIR [25] which shows its powerful feature extraction ability for image restoration to design our encoder $\mathbf{E}$ . Specifically, the shallow feature extraction head consists of a stack of residual layers [17] and $4\times$ downsamples the features. Then 4 residual swim transformer blocks [28] are followed, which serve as the deep feature extraction module. + +Decoder with Normalized Feature Alignment. We propose the Normalized Feature Alignment (NFA) to help the decoder utilize the features reconstructed from HQPs. Firstly, VQGAN tends to decrease results' fidelity due to the information loss brought by vector-quantized operation [14, 43]. Our solution is to eliminate the distortion by the guidance of features before HQPs matching. Specifically, in $i$ th layer, we adopt the deformable convolution [9] to align the features $F_{vq}^{i}$ from $\mathbf{G}_{vq}$ with the features $F^{i}$ from $\mathbf{G}$ , which can be written as: + +$$ +F _ {w} ^ {i} = D C O N V \left(F _ {v q} ^ {i}, C O N V \left(C o n c a t \left(F _ {v q} ^ {i}, F ^ {i}\right)\right)\right), \tag {5} +$$ + +![](images/abc330b88e9afa9fd791abd855ea013e30a29c22257b58665c664a2d9c5564b9.jpg) +Figure 4. Code activation frequencies under different situations. 'dehaze' denotes inputting real hazy images to dehazing network and 'clean' denotes feeding clean images into the pre-trained VQGAN network. 'adjusted' denotes our RIDCP equipped with the CHM under the recommended parameter with real hazy inputs. + +where $F_{w}^{i}$ denotes the features after warping and $DCONV$ is the deformable convolutional layer. $CONV$ is the convolutional layer for offset generation. In addition, we notice that the ratio of the values of $F_{w}^{i}$ and $F^{i}$ is not stable, resulting in an inadequate combination. Thus, we balance the contributions of each by forcing them to be in the same order of magnitude, which can be written as: + +$$ +F ^ {i} = F ^ {i} + \frac {\sum F ^ {i}}{\sum F _ {w} ^ {i}} F _ {w} ^ {i}. \tag {6} +$$ + +# 4.3. Controllable HQPs Matching Operation + +Observation 2. Our RIDCP achieves relatively satisfactory results with the help of $\mathbf{E}$ and $\mathbf{G}$ . However, there are still limitations, e.g., low color saturation in some challenging real data. Rather than the HQPs that already show a strong capability in reconstructing vivid results (see Observation 1), the main reason is the difficulty in finding correct HQPs, which is caused by the domain gap between synthetic data and real data. Although the domain gap is drastically reduced by our synthesis pipeline than previous works [22, 42], it is still impossible to cover all real-world hazy conditions by our pipeline. + +To verify our claim, we made an observation as follows. We randomly collect 200 high-quality clean images as input of the pre-trained VQGAN and compute the activation frequency $f_{c} \in \mathbb{R}^{K}$ of each code. Similarly, 200 real hazy images are fed to the dehazing network to compute the frequency $f_{h} \in \mathbb{R}^{K}$ . Figure 4 illustrates the activation frequencies of the codes with the top ten largest differences between $f_{h}$ and $f_{c}$ . We can see a significant distribution shift. The observation proves that the unavoidable domain gap results in a divergent matching for HQPs. Thus, HQPs still have unexplored potential. + +Controllable Matching via Distance Re-calculation. Based on the above observation, it is indispensable to match better HQPs when encountering real hazy images, i.e., priors with high frequency on clear images. Two components can affect the HQPs matching, which are the encoder $\mathbf{E}$ and the matching operation $\mathcal{M}(\cdot)$ . Since it is difficult to retrain $\mathbf{E}$ on real hazy images without reference images, defining + +a new matching operation $\mathcal{M}'(\cdot)$ sounds like a reasonable solution. We propose Controllable HQPs Matching (CHM) that re-calculates distances by assigning different weights during matching phase. The CHM can be written as: + +$$ +\mathcal {M} ^ {\prime} (\hat {z}) = \arg \min _ {z _ {k} \in Z} \left(\mathbf {F} \left(\tilde {f} _ {k}, \alpha\right) \times | | \hat {z} - z _ {k} |\right), \tag {7} +$$ + +where $\mathbf{F}(\tilde{f}_k,\alpha)$ is the function to generate weights based on the frequency difference $\tilde{f}_k = f_h^k -f_c^k$ and adjusted by a parameter $\alpha$ . There are three objectives in the design of F: 1) Since higher $\tilde{f}_k$ means less activation is needed, $\mathbf{F}$ should be monotonic with $\tilde{f}_k$ thus ensuring consistent trend adjustment. 2) $\mathbf{F}(0,\alpha)\equiv 1$ so that HQPs with the same frequencies on clear and hazy data are not adjusted. 3) The degree of adjustment can be controlled monotonically by $\alpha$ , e.g., $\forall \tilde{f}_1 > \tilde{f}_2,\forall \alpha_1 > \alpha_2\rightarrow \frac{\mathbf{F}(\tilde{f}_1,\alpha_1)}{\mathbf{F}(\tilde{f}_2,\alpha_1)} >\frac{\mathbf{F}(\tilde{f}_1,\alpha_2)}{\mathbf{F}(\tilde{f}_2,\alpha_2)}$ . Coincidentally, the exponential function has these properties, thus $\mathbf{F}$ can be formulated as; + +$$ +\mathbf {F} \left(\tilde {f} _ {k}, \alpha\right) = e ^ {a \times \tilde {f} _ {k}}. \tag {8} +$$ + +Figure 2(b) adopts two Voronoi diagrams to simulate the changes occurring in the high-dimensional space during feature matching. As we can see, the points originally belonging to gray cells are matched to the colored cells after distance re-calculation, i.e., finding better HQPs. + +Possible Solution of the Recommended $\alpha$ . Our method is able to control the HQPs matching based on the above strategy. The final goal is to find a suitable $\alpha$ to adapt the network to real domain. According to the law of large numbers, the frequencies $f_{c}^{k}, f_{h}^{k}$ can be substituted for the corresponding probabilities $P_{c}(x = z_{k}), P_{h}(x = z_{k}|\alpha)$ . The gap between the dehazing results and the clean domain can be represented by the difference between the two probability distributions. Thus, the real domain adaptation problem is transferred into calculating an optimal parameter $\hat{\alpha}$ that can minimize the forward Kullback-Leibler Divergence of $P_{c}(x = z_{k})$ and $P_{h}(x = z_{k}|\alpha)$ , which is also the maximum likelihood estimation of $\alpha$ : + +$$ +\begin{array}{l} \hat {\alpha} = \arg \min _ {\alpha} K L (P _ {c} | | P _ {h}) \\ = a r g \min _ {\alpha} \sum_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) \log \frac {P _ {c} (x = z _ {i})}{P _ {h} (x = z _ {i} | \alpha)} \\ = \arg \max _ {\alpha} \sum_ {i = 1} ^ {K} P _ {c} \left(x = z _ {i}\right) \log P _ {h} \left(x = z _ {i} \mid \alpha\right) \tag {9} \\ = a r g \max _ {\alpha} \prod_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) P _ {h} (x = z _ {i} | \alpha). \\ \end{array} +$$ + +We use a binary search algorithm to iteratively find the approximate optimal solution for $\hat{\alpha}$ . The final determination is $\hat{\alpha} = 21.25$ and higher precision calculations have little + +![](images/88d26bdb4ff88b2b14423ce838b3ae9f2970d3c02e7063bf83041ab2d686730e.jpg) +(a) Hazy image + +![](images/87dcc4072a0e3ae6effb445ec3ceb9486e43796c339e1b7f3b0659444c896a10.jpg) +(b) MSBDN [10] + +![](images/9438fbefd3a6a922574032c830484d01bf5199a7091078b293f3f5c80645bc8c.jpg) +(c) Dehamer [15] +Figure 5. Visual comparison on RTTS dataset [22]. + +![](images/c8d08b7bdbbd9c08f508c78df573cec1dcc78a113c7e3cd619ce828ef979e962.jpg) +(d) PSD [7] + +![](images/f6416b3ac5c05777e4cbff4694b0c12b95df9627dbc080e3526bf75b94a8b463.jpg) +(e) D4 [39] + +![](images/91c5ca337af56e1d0656160d53aea6960f2294bc459026ac9f1023231b065bda.jpg) +(f) DAD [33] + +![](images/6c20893a27786eb940f8fc0e76c4cfb737d6020eff761ec4bd3c47267f94f125.jpg) +(g) RIDCP + +effect on the results. Note that, $\hat{\alpha}$ may not be the determined choice for all cases. One can flexibly adjust $\alpha$ according to their preference. + +# 5. Experiments + +# 5.1. Datasets + +High-quality Datasets. In order to obtain high-quality results from the pre-trained HQPs, the VQGAN needs to be trained on large-scale datasets containing high-resolution and texture-sharp images. In our work, we use DIV2K [1] and Flickr2K [26] (containing 4,250 images) to train the first stage. Both datasets are widely used in high-quality reconstruction tasks [6,24,25]. + +Real Haze Datasets. We qualitatively and quantitatively evaluate our dehazing network on the RTTS dataset [22], which contains over 4,000 real hazy images with diverse scenes, resolutions, and degradation issues. Besides, we use Fattal's dataset [12] that includes 31 classic real hazy cases for further visual comparison. + +# 5.2. Implementation Details + +For both VQGAN and RIDCP training, we use Adam optimizer with default parameters $(\beta_{1} = 0.9, \beta_{2} = 0.99)$ . The learning rate is fixed to 0.0001 during the training phase and the batch size is set to 16. For data augmentation, we + +randomly resize and crop the input into a size of $256 \times 256$ , and flip it with a half probability. During the first training stage, our VQGAN is pre-trained on DIV2K and Flickr2K for 350K iterations. Then, the proposed RIDCP is trained on the data generated by the proposed synthesis pipeline for 10K iterations. All experiments are implemented with PyTorch framework on 4 NVIDIA V100 GPUs. The code implemented by MindSpore framework is also provided. + +# 5.3. Comparison with State-of-the-Art Methods + +We compare the performance of the proposed method with several state-of-the-art dehazing approaches. The experiments are designed from both quantitative and qualitative perspectives. Moreover, we also conduct a user study to verify the subjective performance of our method. + +Quantitative Comparison. Since there is no ground-truth image in real hazy datasets, we use some non-reference metrics for quantitative comparison. We first adopt the Fog Aware Density Evaluator (FADE) [8] for haze density estimation. In addition, two widely-used image quality assessment metrics, BRISQUE [29] and NIMA [34] are also included. The quantitative comparison is conducted on RTTS dataset with two dehazing methods (MSBDN [10] and Dehamer [15]) that achieve outstanding performance on synthetic hazy image datasets [22], and three real dehazing ap + +![](images/448787017f808eda32ecab974c85693115b85210870768b5b2ac36f71b790442.jpg) +(a) Hazy image + +![](images/7617defef89f897f0333934e12112046646996efba30c7f6e17a7932910e0f96.jpg) +(b) MSBDN [10] + +![](images/6ece84cdb50d9eb7d477b8512b7e6ef547ca6ec6736a04f31fe6c4a1c79e9061.jpg) +(c) Dehamer [15] + +![](images/8ef46d2a22e4022aae4cbe9bef3328b8180774b32f18d47a88934e4823dcda7d.jpg) +(d) PSD [7] + +![](images/be0ed0d7e688291c9877c4266bf5d107b0ba3beb482ba25352eb8c9bd67e00a8.jpg) +(e) D4 [39] +Figure 6. Visual comparison on Fattal's data [12]. + +![](images/edb7893c212c44023cad1c4b1180d258d3065a34d3e87fae5d354104bc1d400f.jpg) +(f) DAD [33] + +![](images/a0a7fbdc1fda89868ec1ea53f21d0c3d5a809db0a5ca9b70294ef51c2f588452.jpg) +(g) RIDCP + +Table 1. Quantitative comparison and user study on RTTS dataset. Red indicates the best and blue indicates the second best. 'US' shows the percentage of votes in the user study. + +
MethodFADE↓BRISQUE↓NIMA↑US↑
Hazy image2.48437.0114.32500.030
MSBDN [10]1.36328.7434.14010.046
Dehamer [15]1.89533.8663.86630.041
DAD [33]1.13032.7274.00550.143
PSD [7]0.92025.2394.34590.105
D4 [39]1.35833.2063.72390.079
RIDCP0.94418.7824.42670.556
+ +proaches (DAD [33], PSD [7], D4 [39]). The results are illustrated in Table 1. The proposed RIDCP achieves the best in terms of BRISQUE and NIMA, which gains $25.57\%$ and $1.86\%$ improvements, respectively. For FADE, our method is ranked second slightly below the PSD. However, as shown in Figure 5, PSD tends to produce over-enhanced results, which leads to an inaccurate evaluation. Overall, RIDCP achieves the best results on quantitative metrics, and subsequent experiments will further prove our superiority. + +Qualitative Comparison. We perform the qualitative comparison on RTTS and Fattal's datasets, which is shown in Figure 5 and Figure 6. We can observe that Dehamer, MSBDN, and D4 cannot process the real hazy images well. PSD can produce bright results but the dehazing ability is limited. DAD is effective in haze removal, while its results suffer from color bias and dark tone. Our method generates the best perceptual results in terms of brightness, colorfulness, and haze residue compared to other methods. More results can be found in supplementary materials. + +User Study. We conduct a user study to evaluate the proposed method subjectively against other methods. We randomly select 100 images from RTTS dataset for comparison and invite 5 experts with image processing background and 5 naive observers as volunteers. Before the user study, we give the observer three tips: 1) The primary concern is whether the haze is removed, especially the dense haze in the distance. 2) Pay attention to whether the natural color is recovered. 3) A good method should generate artifact-free results. Afterward, the images are displayed to the observer group by group. Each group contains the input image and + +the results generated by different methods. The observer is required to choose the best one after at least 10 seconds of observation. We statistic the percentage of each method selected as the best and the final scores are listed in Table 1. The proposed RIDCP achieves the highest score and is well ahead of the second place, further demonstrating our method's superior dehazing ability. + +# 5.4. Ablation Study + +In order to verify the effectiveness of each key component, we conduct a series of ablation experiments. Generally, we discuss the effectiveness of CHM, NFA, and the phenomenological degradation pipeline in this section. + +Influence of Adjustment Parameter. The degree of real domain adaptation is controlled by parameter $\alpha$ in Eq. (8) and one can adjust the final result flexibly by adjusting $\alpha$ . Thus, we are curious about what influence the different $\alpha$ will have. As Figure 7 shows, the value of $\alpha$ and the image enhancement effect belong to a linear relationship. More visual-pleasing even over-enhanced results can be produced when $\alpha > 0$ . Interestingly, we can obtain under-enhanced results if $\alpha$ is adjusted in the opposite direction. + +Effectiveness of NFA. Our NFA can help remove the distorted textures caused by feature matching while preserving the useful information reconstructed from HQPs. The NFA can be divided into two key parts: warping operation based on deformable convolution and normalize-based addition. To analyze the role of each part, we propose 4 variants to replace NFA, which are: 1) Without any fusion operation. 2) Adding directly. 3) Normalized addition without warping. 4) Warping and direct addition. Figure 8 shows a set of comparisons. Observing the grass area in red boxes, the result of variant 1 is dark and remaining thin haze. Variants 2 and 4 also have non-homogeneous fog residues in some areas. Variant 3 generates obvious artifacts because forcing normalizing unaligned features to the same order of magnitude and adding them together makes the network difficult to train. Only the full NFA achieves the best in brightness and haze removal. + +Effectiveness of the Phenomenological Degradation Pipeline. To prove that our proposed degradation pipeline + +![](images/a32e9c34fc6ca629646f4a427e19bb1ca3a8d73f6efdf686828d226b26704a06.jpg) +(a) Hazy image + +![](images/cabbf7fcdc0a7df3f03e76880e1745dcc0b8a94a5870ad82f8656c5c39f9c8ef.jpg) +(b) $\alpha = -60.0$ + +![](images/af9c13fbba79d66c21ff463c5ec2acb9c35e3249196b0d84d3fae85f7277196e.jpg) +(c) $\alpha = 0.0$ + +![](images/c99718997fe2bd1adebce608e85292f0dd49bdf1285acb887d793a3880cde573.jpg) +(d) $\alpha = 21.25$ + +![](images/ae656ee6f9f9b5f45a9307eee306ec8857b4752025bf2624758c55f5af85eb91.jpg) +(e) $\alpha = 60.0$ + +![](images/de2120cb38c999e10baad1b4d212dc06c57bac8a0d402f87747bd7fe2f8c388f.jpg) +Figure 7. Results under different adjustment degrees. The proposed CHM allows users to adjust the degree of enhancement from low $(\alpha = -60.0)$ to high $(\alpha = 60.0)$ . The recommended value $(\alpha = 21.25)$ facilitates the network to generate the most natural results (surrounded by the blue box). Zoom in for the best view. + +![](images/5b4c188d0fcc1fa9ffad827c70879bff2479e50a5a12246a45776b675c374fbd.jpg) +(b) w/o fusion + +![](images/47c84a952e95854934a27d40f549b3473a628164043ae2d61f4444260ef69b62.jpg) +(c) Addition + +![](images/abbf0e115ed88337506525a8b8c08313dc4606671afcacdf6b60dac9ede8b7fc.jpg) +(a) Haze +(d) w/o warping +Figure 8. Ablation results of the proposed NFA. + +![](images/2f308c916a62328b65faab3685e395d76fec97f959fe3ae82727d9018261ae8c.jpg) +(e) w/o normalizing + +![](images/9f069f2c400a234d12b64f1ee0b53ea30f65b2df9f327582895e47bb94b303ac.jpg) +(f) Full NFA + +for paired data generation can boost the capabilities of haze removal, we retrain our RIDCP on two widely-used synthetic datasets, which are OTS [22] and Haze4K [42]. Notably, Haze4K is post-processed by DAD [33]. Moreover, we replace the training set from OTS with our synthetic data for transformer-based Dehamer and CNN-based MSBDN, thus demonstrating that it can generally bring gains. The comparison results are illustrated in Figure 9. We can observe that our dehazing network cannot remove the haze under the training of OTS and Haze4K. Besides, Dehamer and MSBDN can generate results with less haze and higher brightness with the help of our training data. However, they still struggle in color recovery compared to our method, which also demonstrates the effectiveness of HQPs and our adaptation strategy. + +# 6. Discussion + +Conclusion. In this paper, we present a novel paradigm to revitalize deep dehazing networks towards the real world. Our proposed phenomenological degradation pipeline synthesizes more realistic hazy data, which achieves significant gains in haze removal. Based on our observations and analysis, we introduce the high-quality priors in VQGAN to the dehazing network and progressively leverage their power, which finally builds our real image dehazing network via high-quality codebook priors (RIDCP). Extensive experi + +![](images/8cfaa0a9a442267102e407c2992930a54792ca571acd331a18c2ccfb0ca8a80e.jpg) + +![](images/c2ca58416296d1c1e69a8b7fc8d2b686e1c922a71784b1f8a6619f91800ca8ef.jpg) + +![](images/ceb76382657d338e7b3c18cf53dc16df40bb5cc77a8c72f6c78a76dc15160c87.jpg) + +![](images/a2b3203c74dd099c221ff29b232dd7eee20289add603b7aa44c278778b7892d3.jpg) + +![](images/472f7979c9af532d47e0c2f468bc14ebc4ac5242d8ce36f02036c66359a70e9d.jpg) +(a) Haze +(e) Dehamer† +Figure 9. Ablation results of the proposed data generation pipeline. We retrain our dehazing network on OTS (b) and Haze4K (c) to verify the effectiveness of our generation pipeline. Dehamer and MSBDN are also retrained on our synthetic data, which are marked by $\dagger$ . + +![](images/b70d214e4f980e9550604abb21f90e7a5c8eb341e0deba6b0be127572befd4e6.jpg) +(b) OTS +(f) MSBDN + +![](images/409bba2378222b66280eeddfbd3ea2da53653ad0dcb3ff0f1099787f8a1f60bb.jpg) +(c) Haze4K +(g) $\mathbf{MSBDN}^{\dagger}$ + +![](images/060c05511a6c1091fdd4c4e4666c0a6bd40d2260c19c22c61fdd1771c6441f22.jpg) +(d) Dehamer +(h) Ours + +ments show the superiority of the proposed paradigm. + +Limitations and Future Work. In the process of doing our work on RIDCP, we observed that there are still some difficulties that are urgent to be addressed. We leave the challenges here and hope that future work can address them + +- Existing dehazing methods including RIDCP can not process non-homogeneous haze well. +- Dehazing based on enhancement fashion is limited. Generative ability should be introduced for recovering extremely dense haze. +- We found that difficult to benchmark dehazing methods in quantitative fairly. Robust metrics for evaluating the quality of dehazing results are also needed. + +Acknowledgements. This work is funded by the National Key Research and Development Program of China (NO.2018AAA0100400), Fundamental Research Funds for the Central Universities (Nankai University, NO.63223050), China Postdoctoral Science Foundation (NO.2021M701780). We are also sponsored by CAAI-Huawei MindSpore Open Fund. + +# References + +[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 126-135, 2017. 6 +[2] Codruta O Ancuti, Cosmin Ancuti, Mateu Sbert, and Radu Timofte. Dense-haze: A benchmark for image dehazing with dense-haze and haze-free images. 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CiteSeer, 2014. 1, 2 \ No newline at end of file diff --git a/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/images.zip b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c4a225162a6bb22f126a2dc9b2156c872e523a24 --- /dev/null +++ b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f06cac472a984426d22300eaec4c622b2f65a34f51e8d0cc4016508d5b22352d +size 782902 diff --git a/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/layout.json b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4ab336f7920ebb533cce2c22c7ad74614aee25ff --- /dev/null +++ b/2023/RIDCP_ Revitalizing Real Image Dehazing via High-Quality Codebook Priors/layout.json @@ -0,0 +1,10997 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "type": "text", + "content": "RIDCP: Revitalizing Real Image Dehazing via High-Quality Codebook Priors" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 142, + 484, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 142, + 484, + 186 + ], + "spans": [ + { + "bbox": [ + 108, + 142, + 484, + 186 + ], + "type": "text", + "content": "Rui-Qi Wu1 Zheng-Peng Duan1 Chun-Le Guo1* Zhi Chai2 Chongyi Li3 \n1VCIP, CS, Nankai University \n2Hisilicon Technologies Co. Ltd. \n3S-Lab, Nanyang Technological University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 187, + 478, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 187, + 478, + 213 + ], + "spans": [ + { + "bbox": [ + 113, + 187, + 478, + 213 + ], + "type": "text", + "content": "{wuruiqi,adamduan0211}@mail.nankai.edu.cn,guochunle=nankai.edu.cn, chaizhi2@huawei.com, chongyi.li@ntu.edu.sg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 241, + 191, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 191, + 253 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 191, + 253 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 266, + 290, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 290, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 290, + 624 + ], + "type": "text", + "content": "Existing dehazing approaches struggle to process real-world hazy images owing to the lack of paired real data and robust priors. In this work, we present a new paradigm for real image dehazing from the perspectives of synthesizing more realistic hazy data and introducing more robust priors into the network. Specifically, (1) instead of adopting the de facto physical scattering model, we rethink the degradation of real hazy images and propose a phenomenological pipeline considering diverse degradation types. (2) We propose a Real Image Dehazing network via high-quality Codebook Priors (RIDCP). Firstly, a VQGAN is pre-trained on a large-scale high-quality dataset to obtain the discrete codebook, encapsulating high-quality priors (HQPs). After replacing the negative effects brought by haze with HQPs, the decoder equipped with a novel normalized feature alignment module can effectively utilize high-quality features and produce clean results. However, although our degradation pipeline drastically mitigates the domain gap between synthetic and real data, it is still intractable to avoid it, which challenges HQPs matching in the wild. Thus, we re-calculate the distance when matching the features to the HQPs by a controllable matching operation, which facilitates finding better counterparts. We provide a recommendation to control the matching based on an explainable solution. Users can also flexibly adjust the enhancement degree as per their preference. Extensive experiments verify the effectiveness of our data synthesis pipeline and the superior performance of RIDCP in real image dehazing. Code and data are released at https://rqw.github.io/projects/RIDCP." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 629, + 128, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 128, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 128, + 641 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 649, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 649, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 649, + 287, + 696 + ], + "type": "text", + "content": "Image dehazing aims to recover clean images from their hazy counterparts, which is essential for computational photography and high-level tasks [20, 32]. 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Visual comparisons on a typical hazy image. The proposed method generates cleaner results than other two state-of-the-art real image dehazing approaches. The enhancement degree of our result can be flexibly adjusted by adopting different parameters in the real-domain adaptation phase. The image with a golden border is the result obtained under our recommended parameter." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 389, + 304, + 463, + 377 + ], + "blocks": [ + { + "bbox": [ + 401, + 293, + 451, + 304 + ], + "lines": [ + { + "bbox": [ + 401, + 293, + 451, + 304 + ], + "spans": [ + { + "bbox": [ + 401, + 293, + 451, + 304 + ], + "type": "text", + "content": "(b) DAD [33]" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 389, + 304, + 463, + 377 + ], + "lines": [ + { + "bbox": [ + 389, + 304, + 463, + 377 + ], + "spans": [ + { + "bbox": [ + 389, + 304, + 463, + 377 + ], + "type": "image", + "image_path": "f035fd25c9d118eacb6cdad3f2d1db6388dcd5981ddb55f29dc14fa57bcd2168.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 381, + 440, + 392 + ], + "lines": [ + { + "bbox": [ + 408, + 381, + 440, + 392 + ], + "spans": [ + { + "bbox": [ + 408, + 381, + 440, + 392 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 465, + 304, + 542, + 377 + ], + "blocks": [ + { + "bbox": [ + 482, + 293, + 525, + 304 + ], + "lines": [ + { + "bbox": [ + 482, + 293, + 525, + 304 + ], + "spans": [ + { + "bbox": [ + 482, + 293, + 525, + 304 + ], + "type": "text", + "content": "(c) PSD [7]" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 465, + 304, + 542, + 377 + ], + "lines": [ + { + "bbox": [ + 465, + 304, + 542, + 377 + ], + "spans": [ + { + "bbox": [ + 465, + 304, + 542, + 377 + ], + "type": "image", + "image_path": "403431cbbef964eb0f038a7a8bc6035076594e6d87bb4b5e20fed3483cfe07df.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 467, + 336, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 336, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 336, + 477 + ], + "type": "text", + "content": "model:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 358, + 479, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 479, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 358, + 479, + 545, + 491 + ], + "type": "interline_equation", + "content": "I (x) = J (x) t (x) + A (1 - t (x)), \\tag {1}", + "image_path": "765858cdceec1b6314e4bf2416dae9ea70330db3f21ded5ba093bccb2c3a4427.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "I(x)" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " denotes the hazy image and " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "J(x)" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " is its corresponding clean image. The variables " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "t(x)" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " are the global atmosphere light and transmission map, respectively. The transmission map " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "t(x) = e^{\\beta d(x)}" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " depends on scene depth " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "d(x)" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": " and haze density coefficient " + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 497, + 546, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "type": "text", + "content": "Given a hazy image, restoring its clean version is highly ill-posed. To mitigate the ill-posedness of this problem, various priors, e.g., dark channel prior [16], color attenuation prior [44], and color lines [12] have been proposed in existing traditional methods. Nevertheless, the statistical priors cannot cover diverse cases in real-world scenes, leading to suboptimal dehazing performance." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "With the advent of deep learning, image dehazing has achieved remarkable progress. Existing methods either adopt deep networks to estimate physical parameters [5,21, 31] or directly restore haze-free images [10, 15, 27, 30, 40]. However, image dehazing neural networks perform limited generalization to real scenes, owing to the difficulty in" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22282" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 335 + ], + "type": "text", + "content": "collecting large-scale yet perfectly aligned paired training data and solving the uncertainty of the ill-posed problem without robust priors. Concretely, 1) collecting large-scale and perfectly aligned hazy images with the clean counterpart is incredibly difficult, if not impossible. Thus, most of the existing deep models use synthetic data for training, in which the hazy images are generated using Eq. (1), leading to the neglect of multiple degradation factors. There are some real hazy image datasets [2,3] with paired data, but the size and diversity are insufficient. Moreover, these datasets deviate from the hazy images captured in the wild. These shortcomings inevitably decrease the capability of deep models in real scenes. 2) Real image dehazing is a highly ill-posed issue. Generally, addressing an uncertain mapping problem often needs the support of priors. However, it is difficult to obtain robust priors that can cover the diverse scenes of real hazy images, which also limits the performance of dehazing algorithms. Recently, many studies for real image dehazing try to solve these two issues by domain adaptation from the perspective of data generation [33,39] or priors guidance [7,23], but still cannot obtain desirable results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 339, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 289, + 590 + ], + "type": "text", + "content": "In this work, we present a new paradigm for real image dehazing motivated by addressing the above two problems. To obtain large-scale and perfectly aligned paired training data, we rethink the degradation of hazy images by observing amounts of real hazy images and propose a novel data generation pipeline considering multiple degradation factors. In order to solve the uncertainty of the ill-posed issue, we attempt to train a VQGAN [11] on high-quality images to extract more robust high-quality priors (HQPs). The VQGAN only learns high-quality image reconstruction, so it naturally contains the robust HQPs that can help hazy features jump to the clean domain. The observation in Sec. 4.1 further verifies our motivation. Thus, we propose the Real Image Dehazing network via high-quality Codebook Priors (RIDCP). The codebook and decoder of VQGAN are fixed to provide HQPs. Then, RIDCP is equipped with an encoder that helps find the correct HQPs, and a new decoder that utilizes the features from the fixed decoder and produces the final result. Moreover, we propose a novel Normalized Feature Alignment (NFA) that can mitigate the distortion and balance the features for better fusion." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "text", + "content": "In comparison to previous methods [6, 14, 43] that introduce codebook for image restoration, we further design a unique real domain adaptation strategy based on the characteristics of VQGAN and the statistical results. Intuitively, we propose Controllable HQPs Matching (CHM) operation that replaces the nearest-neighbour matching by imposing elaborate-designed weights on the distances between features and HQPs during the inference phase. The weights are determined by a controllable parameter " + }, + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "text", + "content": " and the statistical distribution gap of HQPs activation in Sec. 4.3. By adjust-" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "ing " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": ", the distribution of HQPs activation can be shifted. Moreover, we present a theoretically feasible solution to obtain the optimal " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " by minimizing the Kullback-Leibler Divergence of two probability distributions. More significantly, the value of " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " can be visually reflected as the enhancement degree as shown in Figure 1(d), and users are allowed to adjust the dehazing results as per their preference. Our CHM is effective, flexible, and explainable." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 168, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 547, + 240 + ], + "type": "text", + "content": "Compared with the state-of-the-art real image dehazing methods, e.g., DAD [33] and PSD [7], only the proposed RIDCP can effectively process the hazy images captured in the wild while generating adjustable results, which are shown in Figure 1. The contributions of our work can be summarized as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 245, + 545, + 390 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 245, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 245, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 317, + 245, + 545, + 270 + ], + "type": "text", + "content": "- We present a new paradigm to push the frontier of deep learning-based image dehazing towards real scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 276, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 276, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 317, + 276, + 545, + 336 + ], + "type": "text", + "content": "- We are the first to leverage the high-quality codebook prior in the real image dehazing task. The controllable HQPs matching operation is proposed to overcome the gap between synthetic and real domains and produce adjustable results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 342, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 342, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 317, + 342, + 545, + 390 + ], + "type": "text", + "content": "- We re-formulate the degradation model of real hazy images and propose a phenomenological degradation pipeline to simulate the hazy images captured in the wild." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 400, + 392, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 392, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 392, + 412 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 420, + 436, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 436, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 436, + 433 + ], + "type": "text", + "content": "2.1. Single Image Dehazing" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "type": "text", + "content": "Image Dehazing. The early attempts at single image dehazing consider estimating the parameters of the atmosphere scattering model presented in Eq. (1) by priors on haze-free images [4, 12, 16, 35, 44]. These methods have achieved impressive results. However, the handcrafted priors based on empirical observations are hard to perform well in diverse scenarios. For example, the assumption of DCP [16] is not available in the sky region. The proposed method obtains the priors of high-quality images by pre-training a discrete codebook on large-scale datasets, which is more reliable and comprehensive." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "With the development of deep learning techniques, how to use data-driven ideology to remove haze gains a lot of attention. At the early stage, many studies [5, 21, 31] try to adopt convolutional neural networks (CNNs) to estimate the parameters of the degradation model in Eq. (1). In addition, in order to avoid accumulated errors in parameters estimation, some end-to-end networks [10, 15, 27, 30, 40] are proposed to directly estimate the haze-free image. The above learning-based methods have achieved excellent performance on synthetic datasets. However, their significant performance drop on real-world data urgently needs to be solved." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22283" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 353, + 293 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 353, + 293 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 353, + 293 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 353, + 293 + ], + "type": "image", + "image_path": "345c0ee4dcbccd5db9e91406f932a99ad092da4ee667cff10864c4068af28e45.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "text", + "content": "Figure 2. Overview of our RIDCP. During the training phase, we train the dehazing network on the data synthesized by our data generation pipeline, as illustrated in (a). The network is based on the pre-trained HQPs codebook and the corresponding decoder " + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{vq}" + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "text", + "content": " of VQGAN. We also design the Controllable HQPs Matching (CHM) operation for real domain adaptation by re-calculating the distance " + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "inline_equation", + "content": "d_{k}^{\\hat{z}} = ||\\hat{z} - z_{k}||" + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "text", + "content": " between features and HQPs. (b) represents the distance re-calculation with two Voronoi diagrams, where the colored cells indicate belonging to better HQPs and the gray cells vice versa. Triangles represent features and star points represent HQPs. It can be seen that after the distance recalibration points that originally belonged to the gray cells are forced to be assigned to the colored cells by our CHM." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 359, + 70, + 541, + 294 + ], + "blocks": [ + { + "bbox": [ + 359, + 70, + 541, + 294 + ], + "lines": [ + { + "bbox": [ + 359, + 70, + 541, + 294 + ], + "spans": [ + { + "bbox": [ + 359, + 70, + 541, + 294 + ], + "type": "image", + "image_path": "0364824034e4602662ec86e7e7ab940d6afcaac5d95f68710605f6f0529cd22b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 373, + 289, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 649 + ], + "type": "text", + "content": "Real Image Dehazing. Recently, some works pay attention to real image dehazing. One research line is to utilize GANs [13] for generating hazy data that fits the real haze domain. Shao et al. [33] design a domain adaptation strategy based on the framework of CycleGAN [?]. Yang et al. [39] propose an unpaired dehazing framework named D4. It can estimate the scene depth of hazy images and generate hazy data with different thicknesses to benefit dehazing model training. However, GANs are easy to produce artifacts in the generated results, which is harmful to training models. Another research line aims to introduce prior knowledge by loss functions or network architectures. Li et al. [23] propose a semi-supervised pipeline that adopts prior-based loss functions to train networks on the real dataset. PSD [7] adds a physical-based sub-network on the pre-trained dehazing model and further proposes a prior loss committee to fine-tune the network on real-world data in an unsupervised manner. Nevertheless, directly using handcrafted priors cannot avoid the inherent flaws of prior-based methods. In our study, we investigate overcoming the weaknesses of both types of real image dehazing methods by proposing a novel data generation pipeline and exploiting the latent high-quality priors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 658, + 205, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 205, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 205, + 672 + ], + "type": "text", + "content": "2.2. Discrete Codebook Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Recently, a vector-quantized auto-encoder framework was proposed in VQ-VAE [36], which learns a discrete codebook in latent space. The discrete representation ef" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 373, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 612 + ], + "type": "text", + "content": "fectively addresses the \"posterior collapse\" issue in autoencoder [19] architecture. VQGAN [11] further improves the perceptual quality of reconstructed results by introducing adversarial supervision for codebook learning. The learned discrete codebook helps boost the performance in many low-level vision tasks including face restoration [14, 43] and image super-resolution [6]. Gu et al. [14] introduce the vector quantization technique to face restoration and design a parallel decoder to achieve a balance between visual quality and fidelity. Zhou et al. [14] cast blind face restoration as a code prediction task, and propose a Transformer-based prediction network to replace the nearest-neighbor matching operation for better matching the corresponding code. FeMaSR [6] extends the discrete codebook learning to blind super-resolution. Motivated by the exciting performance of these approaches, we are the first to leverage the high-quality codebook prior for real image dehazing. A novel and controllable HQPs matching operation is proposed to further bridge the gap between our synthetic data and real data, which is inevitable for real scenes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 621, + 541, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 621, + 541, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 621, + 541, + 635 + ], + "type": "text", + "content": "3. Data Preparation for Real Image Dehazing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Redesigning the pipeline of data generation has been demonstrated as an effective way for solving real-world low-level vision tasks [37, 38, 41]. Based on these works, we consider various degradation factors when synthesizing paired data for training the dehazing network, which can mitigate the domain gap with the real data. For concise-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "22284" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "ness, we represent Eq. (1) as " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "I(x) = \\mathcal{P}(J(x),t(x),A)" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ". The formation of the hazy image can be written as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 106, + 287, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 106, + 287, + 121 + ], + "spans": [ + { + "bbox": [ + 58, + 106, + 287, + 121 + ], + "type": "interline_equation", + "content": "I (x) = J P E G \\left(\\mathcal {P} \\left(J (x) ^ {\\gamma} + \\mathcal {N}, e ^ {\\beta \\hat {d} (x)}, A + \\Delta A\\right)\\right). \\tag {2}", + "image_path": "80fd98cd5dfa58e3c81cbbc9491a689331d1a83f6c2b10402b56745fcaef2062.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 128, + 241, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 128, + 241, + 139 + ], + "spans": [ + { + "bbox": [ + 47, + 128, + 241, + 139 + ], + "type": "text", + "content": "The details of Eq. (2) are introduced as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "text", + "content": "Poor light condition. " + }, + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "inline_equation", + "content": "\\gamma \\in [1.5,3.0]" + }, + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "text", + "content": " is a brightness adjustment factor and " + }, + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 140, + 287, + 186 + ], + "type": "text", + "content": " is the Gaussian noise distribution. These two components can simulate poor light conditions that frequently occur in hazy weather." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "text", + "content": "Transmission map. As a key parameter in the degradation model, we adopt the depth estimation algorithm [18] to estimate depth map " + }, + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "inline_equation", + "content": "d(x)" + }, + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\beta \\in [0.3, 1.5]" + }, + { + "bbox": [ + 47, + 187, + 287, + 235 + ], + "type": "text", + "content": " to control the haze density." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "content": "Colorful haze. To obtain diverse hazy images, the color bias of atmosphere light is considered, which is implemented by a three-channel vector " + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "inline_equation", + "content": "\\Delta A \\in [-0.025, 0.025]" + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "content": ". The range of " + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "content": " is in the range of [0.25, 1.0]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 283, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 287, + 330 + ], + "type": "text", + "content": "JPEG compression. We observe that dehazing algorithms amplify the JPEG artifacts. It is desirable to remove such artifacts while dehazing. " + }, + { + "bbox": [ + 47, + 283, + 287, + 330 + ], + "type": "inline_equation", + "content": "JPEG(\\cdot)" + }, + { + "bbox": [ + 47, + 283, + 287, + 330 + ], + "type": "text", + "content": " denotes JPEG compression in the final results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 331, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 379 + ], + "type": "text", + "content": "We select 500 clean images to build the paired data, and the hazy data is generated on-the-fly during the training phase. Additionally, low light and JPEG compression appear with " + }, + { + "bbox": [ + 46, + 331, + 287, + 379 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 331, + 287, + 379 + ], + "type": "text", + "content": " probability in the proposed pipeline." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 389, + 129, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 129, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 129, + 403 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "text", + "content": "The key idea of our work is to adopt a discrete codebook that introduces high-quality priors (HQPs) into the dehazing network. The overall framework of the proposed method is illustrated in Figure 2. The training phase can be divided into two stages. In the first training stage, we pre-train a VQGAN [11] on high-quality data, obtaining a latent discrete codebook " + }, + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "text", + "content": " with HQPs and the correspondence decoder " + }, + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{vq}" + }, + { + "bbox": [ + 46, + 409, + 287, + 590 + ], + "type": "text", + "content": " (Sec. 4.1). In the second stage, our RIDCP based on the pre-trained VQGAN is trained on hazy images generated by the proposed synthesis pipeline (Sec. 4.2). Moreover, in order to help the network find more accurate code, we propose a controllable adjustment feature matching strategy based on code activation distribution on high-quality images (Sec. 4.3). Besides, the details of training objectives can be found in supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 597, + 262, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 262, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 262, + 609 + ], + "type": "text", + "content": "4.1. Latent Codebook for High-quality Priors" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": "We first introduce how VQGAN works briefly. Given a high-quality image patch " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": ", which is the input of the VQGAN encoder " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{vq}" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": " and the corresponding outputs are the latent features " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": ". Then each \"pixel\" " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\hat{z}_{ij}" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": " will be matched to the nearest HQPs in codebook " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{Z} \\in \\mathbb{R}^{K \\times n}" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": " and then obtain the discrete representation " + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "inline_equation", + "content": "z_{ij}^q" + }, + { + "bbox": [ + 46, + 615, + 287, + 688 + ], + "type": "text", + "content": ", which can be written as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 82, + 697, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 697, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 82, + 697, + 287, + 716 + ], + "type": "interline_equation", + "content": "z _ {i j} ^ {q} = \\mathcal {M} (\\hat {z} _ {i j}) = \\arg \\min _ {z _ {k} \\in \\mathcal {Z}} \\left(\\left\\| \\hat {z} _ {i j} - z _ {k} \\right\\| _ {2}\\right), \\tag {3}", + "image_path": "3a46a9d7a68e1323681a19c92a6b3ac32f94f2229e8b2cb259d688351672beec.jpg" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 425, + 137 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 425, + 137 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 425, + 137 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 425, + 137 + ], + "type": "image", + "image_path": "e74194e9ff30ee6f3f4901a26b045f4a4c698d4a94b99e0bb4671ecdfc56d97b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 139, + 393, + 149 + ], + "lines": [ + { + "bbox": [ + 339, + 139, + 393, + 149 + ], + "spans": [ + { + "bbox": [ + 339, + 139, + 393, + 149 + ], + "type": "text", + "content": "(a) Hazy input" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 542, + 137 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 542, + 137 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 542, + 137 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 542, + 137 + ], + "type": "image", + "image_path": "087c517098971667c648427ec54dc762e6ebc905bf20e4c437cef73c0da42e3c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 451, + 139, + 518, + 148 + ], + "lines": [ + { + "bbox": [ + 451, + 139, + 518, + 148 + ], + "spans": [ + { + "bbox": [ + 451, + 139, + 518, + 148 + ], + "type": "text", + "content": "(b) Reconstruction" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 150, + 545, + 172 + ], + "lines": [ + { + "bbox": [ + 305, + 150, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 305, + 150, + 545, + 172 + ], + "type": "text", + "content": "Figure 3. Result reconstructed by the pre-trained VQGAN. The haze is removed but distorted textures are introduced." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": " denotes the codebook size, " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": " is the channel number of " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\cdot)" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": " represents the matching operation. Finally, the input " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": " is reconstructed by " + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{vq}" + }, + { + "bbox": [ + 305, + 178, + 545, + 214 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 350, + 221, + 545, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 221, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 350, + 221, + 545, + 235 + ], + "type": "interline_equation", + "content": "x ^ {\\prime} = \\mathbf {G} _ {v q} \\left(z ^ {q}\\right) = \\mathbf {G} _ {v q} \\left(\\mathcal {M} \\left(\\mathbf {E} _ {v q} (x)\\right)\\right), \\tag {4}", + "image_path": "9ff60cbf3046985f9fd012892577cdf57c734674ded9e36359e05bcdf8600c47.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 237, + 451, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 451, + 248 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 451, + 248 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 237, + 451, + 248 + ], + "type": "inline_equation", + "content": "x^{\\prime}" + }, + { + "bbox": [ + 305, + 237, + 451, + 248 + ], + "type": "text", + "content": " is the reconstructed result." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "text", + "content": "Observation 1. To understand the potential of the HQPs in the codebook and better utilize it, we made some observations on the results reconstructed by the pre-trained VQGAN. As illustrated in Figure 3, our VQGAN can remove the thin haze and recover vivid color for the hazy input without fine-tuning. We analyze that using HQPs in a matching manner can replace the degraded feature so help it jump to the high-quality domain. However, the dehazing ability of VQGAN is limited due to the difficulty in matching the correct code. Moreover, some distorted textures are produced because of the information loss during the vector-quantized phase. Thus, directly adopting the features from " + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{vq}" + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "text", + "content": " is suboptimal. It is intuitive that our next step is to train an encoder " + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "text", + "content": " that can help priors matching, and a decoder " + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 249, + 545, + 428 + ], + "type": "text", + "content": " that can utilize the features reconstructed from HQPs." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 435, + 507, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 507, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 507, + 449 + ], + "type": "text", + "content": "4.2. Image Dehazing via Feature Matching" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 453, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 488 + ], + "type": "text", + "content": "Based on the observation in Sec. 4.1, image dehazing is decoupled into two sub-tasks: matching correct code and removing texture distortion." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "text", + "content": "Encoder for HQPs Matching. We follow SwinIR [25] which shows its powerful feature extraction ability for image restoration to design our encoder " + }, + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "text", + "content": ". Specifically, the shallow feature extraction head consists of a stack of residual layers [17] and " + }, + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 304, + 489, + 545, + 572 + ], + "type": "text", + "content": " downsamples the features. Then 4 residual swim transformer blocks [28] are followed, which serve as the deep feature extraction module." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": "Decoder with Normalized Feature Alignment. We propose the Normalized Feature Alignment (NFA) to help the decoder utilize the features reconstructed from HQPs. Firstly, VQGAN tends to decrease results' fidelity due to the information loss brought by vector-quantized operation [14, 43]. Our solution is to eliminate the distortion by the guidance of features before HQPs matching. Specifically, in " + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": "th layer, we adopt the deformable convolution [9] to align the features " + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "inline_equation", + "content": "F_{vq}^{i}" + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{vq}" + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": " with the features " + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "inline_equation", + "content": "F^{i}" + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 304, + 573, + 545, + 692 + ], + "type": "text", + "content": ", which can be written as:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 314, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "F _ {w} ^ {i} = D C O N V \\left(F _ {v q} ^ {i}, C O N V \\left(C o n c a t \\left(F _ {v q} ^ {i}, F ^ {i}\\right)\\right)\\right), \\tag {5}", + "image_path": "d30396c280d3b019a0d4ba47dc56cfea43678d30d4c4682553ab80b7e55dae89.jpg" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22285" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 45, + 70, + 289, + 153 + ], + "blocks": [ + { + "bbox": [ + 45, + 70, + 289, + 153 + ], + "lines": [ + { + "bbox": [ + 45, + 70, + 289, + 153 + ], + "spans": [ + { + "bbox": [ + 45, + 70, + 289, + 153 + ], + "type": "image", + "image_path": "abc330b88e9afa9fd791abd855ea013e30a29c22257b58665c664a2d9c5564b9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": "Figure 4. Code activation frequencies under different situations. 'dehaze' denotes inputting real hazy images to dehazing network and 'clean' denotes feeding clean images into the pre-trained VQGAN network. 'adjusted' denotes our RIDCP equipped with the CHM under the recommended parameter with real hazy inputs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "inline_equation", + "content": "F_{w}^{i}" + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": " denotes the features after warping and " + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "inline_equation", + "content": "DCONV" + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": " is the deformable convolutional layer. " + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "inline_equation", + "content": "CONV" + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": " is the convolutional layer for offset generation. In addition, we notice that the ratio of the values of " + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "inline_equation", + "content": "F_{w}^{i}" + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "inline_equation", + "content": "F^{i}" + }, + { + "bbox": [ + 46, + 215, + 288, + 300 + ], + "type": "text", + "content": " is not stable, resulting in an inadequate combination. Thus, we balance the contributions of each by forcing them to be in the same order of magnitude, which can be written as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 119, + 307, + 287, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 307, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 119, + 307, + 287, + 335 + ], + "type": "interline_equation", + "content": "F ^ {i} = F ^ {i} + \\frac {\\sum F ^ {i}}{\\sum F _ {w} ^ {i}} F _ {w} ^ {i}. \\tag {6}", + "image_path": "70465eabf636c2e381ad409754af952a5bc20fa1c3951d5aee9d30db3b5d729d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 347, + 258, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 258, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 258, + 361 + ], + "type": "text", + "content": "4.3. Controllable HQPs Matching Operation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "text", + "content": "Observation 2. Our RIDCP achieves relatively satisfactory results with the help of " + }, + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 366, + 287, + 498 + ], + "type": "text", + "content": ". However, there are still limitations, e.g., low color saturation in some challenging real data. Rather than the HQPs that already show a strong capability in reconstructing vivid results (see Observation 1), the main reason is the difficulty in finding correct HQPs, which is caused by the domain gap between synthetic data and real data. Although the domain gap is drastically reduced by our synthesis pipeline than previous works [22, 42], it is still impossible to cover all real-world hazy conditions by our pipeline." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": "To verify our claim, we made an observation as follows. We randomly collect 200 high-quality clean images as input of the pre-trained VQGAN and compute the activation frequency " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "f_{c} \\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": " of each code. Similarly, 200 real hazy images are fed to the dehazing network to compute the frequency " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "f_{h} \\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": ". Figure 4 illustrates the activation frequencies of the codes with the top ten largest differences between " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "f_{h}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 46, + 498, + 287, + 629 + ], + "type": "text", + "content": ". We can see a significant distribution shift. The observation proves that the unavoidable domain gap results in a divergent matching for HQPs. Thus, HQPs still have unexplored potential." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Controllable Matching via Distance Re-calculation. Based on the above observation, it is indispensable to match better HQPs when encountering real hazy images, i.e., priors with high frequency on clear images. Two components can affect the HQPs matching, which are the encoder " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " and the matching operation " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\cdot)" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": ". Since it is difficult to retrain " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " on real hazy images without reference images, defining" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": "a new matching operation " + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{M}'(\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": " sounds like a reasonable solution. We propose Controllable HQPs Matching (CHM) that re-calculates distances by assigning different weights during matching phase. The CHM can be written as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 337, + 128, + 545, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 128, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 337, + 128, + 545, + 148 + ], + "type": "interline_equation", + "content": "\\mathcal {M} ^ {\\prime} (\\hat {z}) = \\arg \\min _ {z _ {k} \\in Z} \\left(\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) \\times | | \\hat {z} - z _ {k} |\\right), \\tag {7}", + "image_path": "8fe1289496046f8df9a27ed80bcaf100cbf6b5499cf0c5696d890d1245f5bc73.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{F}(\\tilde{f}_k,\\alpha)" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " is the function to generate weights based on the frequency difference " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\tilde{f}_k = f_h^k -f_c^k" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " and adjusted by a parameter " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": ". There are three objectives in the design of F: 1) Since higher " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\tilde{f}_k" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " means less activation is needed, " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " should be monotonic with " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\tilde{f}_k" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " thus ensuring consistent trend adjustment. 2) " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{F}(0,\\alpha)\\equiv 1" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " so that HQPs with the same frequencies on clear and hazy data are not adjusted. 3) The degree of adjustment can be controlled monotonically by " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": ", e.g., " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\forall \\tilde{f}_1 > \\tilde{f}_2,\\forall \\alpha_1 > \\alpha_2\\rightarrow \\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_1)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_1)} >\\frac{\\mathbf{F}(\\tilde{f}_1,\\alpha_2)}{\\mathbf{F}(\\tilde{f}_2,\\alpha_2)}" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": ". Coincidentally, the exponential function has these properties, thus " + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 157, + 547, + 294 + ], + "type": "text", + "content": " can be formulated as;" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 386, + 301, + 545, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 301, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 386, + 301, + 545, + 318 + ], + "type": "interline_equation", + "content": "\\mathbf {F} \\left(\\tilde {f} _ {k}, \\alpha\\right) = e ^ {a \\times \\tilde {f} _ {k}}. \\tag {8}", + "image_path": "8bd1aacb66fe6c60d961378d7dace45a651f9f7f9984b895971bd29b9102f8b5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 326, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 386 + ], + "type": "text", + "content": "Figure 2(b) adopts two Voronoi diagrams to simulate the changes occurring in the high-dimensional space during feature matching. As we can see, the points originally belonging to gray cells are matched to the colored cells after distance re-calculation, i.e., finding better HQPs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": "Possible Solution of the Recommended " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": ". Our method is able to control the HQPs matching based on the above strategy. The final goal is to find a suitable " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": " to adapt the network to real domain. According to the law of large numbers, the frequencies " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "f_{c}^{k}, f_{h}^{k}" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": " can be substituted for the corresponding probabilities " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "P_{c}(x = z_{k}), P_{h}(x = z_{k}|\\alpha)" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": ". The gap between the dehazing results and the clean domain can be represented by the difference between the two probability distributions. Thus, the real domain adaptation problem is transferred into calculating an optimal parameter " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha}" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": " that can minimize the forward Kullback-Leibler Divergence of " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "P_{c}(x = z_{k})" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "P_{h}(x = z_{k}|\\alpha)" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": ", which is also the maximum likelihood estimation of " + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 386, + 546, + 540 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 323, + 548, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 548, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 323, + 548, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\alpha} = \\arg \\min _ {\\alpha} K L (P _ {c} | | P _ {h}) \\\\ = a r g \\min _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) \\log \\frac {P _ {c} (x = z _ {i})}{P _ {h} (x = z _ {i} | \\alpha)} \\\\ = \\arg \\max _ {\\alpha} \\sum_ {i = 1} ^ {K} P _ {c} \\left(x = z _ {i}\\right) \\log P _ {h} \\left(x = z _ {i} \\mid \\alpha\\right) \\tag {9} \\\\ = a r g \\max _ {\\alpha} \\prod_ {i = 1} ^ {K} P _ {c} (x = z _ {i}) P _ {h} (x = z _ {i} | \\alpha). \\\\ \\end{array}", + "image_path": "0ae76d563f30dde11923b09495ab786ed88d6f795c655f390aeee464fa3ef140.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "We use a binary search algorithm to iteratively find the approximate optimal solution for " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha}" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": ". The final determination is " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha} = 21.25" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": " and higher precision calculations have little" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "22286" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 121, + 366 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 121, + 366 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 121, + 366 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 121, + 366 + ], + "type": "image", + "image_path": "88d26bdb4ff88b2b14423ce838b3ae9f2970d3c02e7063bf83041ab2d686730e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 368, + 115, + 378 + ], + "lines": [ + { + "bbox": [ + 58, + 368, + 115, + 378 + ], + "spans": [ + { + "bbox": [ + 58, + 368, + 115, + 378 + ], + "type": "text", + "content": "(a) Hazy image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 121, + 72, + 191, + 365 + ], + "blocks": [ + { + "bbox": [ + 121, + 72, + 191, + 365 + ], + "lines": [ + { + "bbox": [ + 121, + 72, + 191, + 365 + ], + "spans": [ + { + "bbox": [ + 121, + 72, + 191, + 365 + ], + "type": "image", + "image_path": "87dcc4072a0e3ae6effb445ec3ceb9486e43796c339e1b7f3b0659444c896a10.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 368, + 186, + 378 + ], + "lines": [ + { + "bbox": [ + 124, + 368, + 186, + 378 + ], + "spans": [ + { + "bbox": [ + 124, + 368, + 186, + 378 + ], + "type": "text", + "content": "(b) MSBDN [10]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 192, + 72, + 260, + 365 + ], + "blocks": [ + { + "bbox": [ + 192, + 72, + 260, + 365 + ], + "lines": [ + { + "bbox": [ + 192, + 72, + 260, + 365 + ], + "spans": [ + { + "bbox": [ + 192, + 72, + 260, + 365 + ], + "type": "image", + "image_path": "9438fbefd3a6a922574032c830484d01bf5199a7091078b293f3f5c80645bc8c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 368, + 257, + 378 + ], + "lines": [ + { + "bbox": [ + 195, + 368, + 257, + 378 + ], + "spans": [ + { + "bbox": [ + 195, + 368, + 257, + 378 + ], + "type": "text", + "content": "(c) Dehamer [15]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 203, + 381, + 389, + 393 + ], + "lines": [ + { + "bbox": [ + 203, + 381, + 389, + 393 + ], + "spans": [ + { + "bbox": [ + 203, + 381, + 389, + 393 + ], + "type": "text", + "content": "Figure 5. 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Note that, " + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha}" + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "content": " may not be the determined choice for all cases. One can flexibly adjust " + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "content": " according to their preference." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 446, + 128, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 128, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 128, + 459 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 466, + 110, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 110, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 110, + 478 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 485, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 569 + ], + "type": "text", + "content": "High-quality Datasets. In order to obtain high-quality results from the pre-trained HQPs, the VQGAN needs to be trained on large-scale datasets containing high-resolution and texture-sharp images. In our work, we use DIV2K [1] and Flickr2K [26] (containing 4,250 images) to train the first stage. Both datasets are widely used in high-quality reconstruction tasks [6,24,25]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 570, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 642 + ], + "type": "text", + "content": "Real Haze Datasets. We qualitatively and quantitatively evaluate our dehazing network on the RTTS dataset [22], which contains over 4,000 real hazy images with diverse scenes, resolutions, and degradation issues. Besides, we use Fattal's dataset [12] that includes 31 classic real hazy cases for further visual comparison." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 646, + 180, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 180, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 180, + 658 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "For both VQGAN and RIDCP training, we use Adam optimizer with default parameters " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9, \\beta_{2} = 0.99)" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": ". The learning rate is fixed to 0.0001 during the training phase and the batch size is set to 16. For data augmentation, we" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": "randomly resize and crop the input into a size of " + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 403, + 545, + 499 + ], + "type": "text", + "content": ", and flip it with a half probability. During the first training stage, our VQGAN is pre-trained on DIV2K and Flickr2K for 350K iterations. Then, the proposed RIDCP is trained on the data generated by the proposed synthesis pipeline for 10K iterations. All experiments are implemented with PyTorch framework on 4 NVIDIA V100 GPUs. The code implemented by MindSpore framework is also provided." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 511, + 531, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 511, + 531, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 511, + 531, + 525 + ], + "type": "text", + "content": "5.3. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 533, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 592 + ], + "type": "text", + "content": "We compare the performance of the proposed method with several state-of-the-art dehazing approaches. The experiments are designed from both quantitative and qualitative perspectives. Moreover, we also conduct a user study to verify the subjective performance of our method." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Quantitative Comparison. Since there is no ground-truth image in real hazy datasets, we use some non-reference metrics for quantitative comparison. We first adopt the Fog Aware Density Evaluator (FADE) [8] for haze density estimation. In addition, two widely-used image quality assessment metrics, BRISQUE [29] and NIMA [34] are also included. The quantitative comparison is conducted on RTTS dataset with two dehazing methods (MSBDN [10] and Dehamer [15]) that achieve outstanding performance on synthetic hazy image datasets [22], and three real dehazing ap" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "22287" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 121, + 179 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 121, + 179 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 121, + 179 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 121, + 179 + ], + "type": "image", + "image_path": "448787017f808eda32ecab974c85693115b85210870768b5b2ac36f71b790442.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 181, + 115, + 192 + ], + "lines": [ + { + "bbox": [ + 58, + 181, + 115, + 192 + ], + "spans": [ + { + "bbox": [ + 58, + 181, + 115, + 192 + ], + "type": "text", + "content": "(a) Hazy image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 121, + 72, + 191, + 180 + ], + "blocks": [ + { + "bbox": [ + 121, + 72, + 191, + 180 + ], + "lines": [ + { + "bbox": [ + 121, + 72, + 191, + 180 + ], + "spans": [ + { + "bbox": [ + 121, + 72, + 191, + 180 + ], + "type": "image", + "image_path": "7617defef89f897f0333934e12112046646996efba30c7f6e17a7932910e0f96.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 181, + 187, + 191 + ], + "lines": [ + { + "bbox": [ + 124, + 181, + 187, + 191 + ], + "spans": [ + { + "bbox": [ + 124, + 181, + 187, + 191 + ], + "type": "text", + "content": "(b) MSBDN [10]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 192, + 72, + 260, + 180 + ], + "blocks": [ + { + "bbox": [ + 192, + 72, + 260, + 180 + ], + "lines": [ + { + "bbox": [ + 192, + 72, + 260, + 180 + ], + "spans": [ + { + "bbox": [ + 192, + 72, + 260, + 180 + ], + "type": "image", + "image_path": "6ece84cdb50d9eb7d477b8512b7e6ef547ca6ec6736a04f31fe6c4a1c79e9061.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 194, + 181, + 257, + 191 + ], + "lines": [ + { + "bbox": [ + 194, + 181, + 257, + 191 + ], + "spans": [ + { + "bbox": [ + 194, + 181, + 257, + 191 + ], + "type": "text", + "content": "(c) Dehamer [15]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 261, + 72, + 331, + 180 + ], + "blocks": [ + { + "bbox": [ + 261, + 72, + 331, + 180 + ], + "lines": [ + { + "bbox": [ + 261, + 72, + 331, + 180 + ], + "spans": [ + { + "bbox": [ + 261, + 72, + 331, + 180 + ], + "type": "image", + "image_path": "8ef46d2a22e4022aae4cbe9bef3328b8180774b32f18d47a88934e4823dcda7d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 275, + 181, + 318, + 191 + ], + "lines": [ + { + "bbox": [ + 275, + 181, + 318, + 191 + ], + "spans": [ + { + "bbox": [ + 275, + 181, + 318, + 191 + ], + "type": "text", + "content": "(d) PSD [7]" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 72, + 400, + 180 + ], + "blocks": [ + { + "bbox": [ + 331, + 72, + 400, + 180 + ], + "lines": [ + { + "bbox": [ + 331, + 72, + 400, + 180 + ], + "spans": [ + { + "bbox": [ + 331, + 72, + 400, + 180 + ], + "type": "image", + "image_path": "be0ed0d7e688291c9877c4266bf5d107b0ba3beb482ba25352eb8c9bd67e00a8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 181, + 387, + 191 + ], + "lines": [ + { + "bbox": [ + 345, + 181, + 387, + 191 + ], + "spans": [ + { + "bbox": [ + 345, + 181, + 387, + 191 + ], + "type": "text", + "content": "(e) D4 [39]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 205, + 196, + 386, + 207 + ], + "lines": [ + { + "bbox": [ + 205, + 196, + 386, + 207 + ], + "spans": [ + { + "bbox": [ + 205, + 196, + 386, + 207 + ], + "type": "text", + "content": "Figure 6. Visual comparison on Fattal's data [12]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 401, + 72, + 471, + 180 + ], + "blocks": [ + { + "bbox": [ + 401, + 72, + 471, + 180 + ], + "lines": [ + { + "bbox": [ + 401, + 72, + 471, + 180 + ], + "spans": [ + { + "bbox": [ + 401, + 72, + 471, + 180 + ], + "type": "image", + "image_path": "edb7893c212c44023cad1c4b1180d258d3065a34d3e87fae5d354104bc1d400f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 181, + 460, + 191 + ], + "lines": [ + { + "bbox": [ + 411, + 181, + 460, + 191 + ], + "spans": [ + { + "bbox": [ + 411, + 181, + 460, + 191 + ], + "type": "text", + "content": "(f) DAD [33]" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 471, + 72, + 541, + 180 + ], + "blocks": [ + { + "bbox": [ + 471, + 72, + 541, + 180 + ], + "lines": [ + { + "bbox": [ + 471, + 72, + 541, + 180 + ], + "spans": [ + { + "bbox": [ + 471, + 72, + 541, + 180 + ], + "type": "image", + "image_path": "a0a7fbdc1fda89868ec1ea53f21d0c3d5a809db0a5ca9b70294ef51c2f588452.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 181, + 525, + 191 + ], + "lines": [ + { + "bbox": [ + 485, + 181, + 525, + 191 + ], + "spans": [ + { + "bbox": [ + 485, + 181, + 525, + 191 + ], + "type": "text", + "content": "(g) RIDCP" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 48, + 253, + 298, + 348 + ], + "blocks": [ + { + "bbox": [ + 47, + 216, + 286, + 249 + ], + "lines": [ + { + "bbox": [ + 47, + 216, + 286, + 249 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 286, + 249 + ], + "type": "text", + "content": "Table 1. Quantitative comparison and user study on RTTS dataset. Red indicates the best and blue indicates the second best. 'US' shows the percentage of votes in the user study." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 253, + 298, + 348 + ], + "lines": [ + { + "bbox": [ + 48, + 253, + 298, + 348 + ], + "spans": [ + { + "bbox": [ + 48, + 253, + 298, + 348 + ], + "type": "table", + "html": "
MethodFADE↓BRISQUE↓NIMA↑US↑
Hazy image2.48437.0114.32500.030
MSBDN [10]1.36328.7434.14010.046
Dehamer [15]1.89533.8663.86630.041
DAD [33]1.13032.7274.00550.143
PSD [7]0.92025.2394.34590.105
D4 [39]1.35833.2063.72390.079
RIDCP0.94418.7824.42670.556
", + "image_path": "329f6207be297ae7f5e8a3b0538ec4e2140fdbf73ad84cb8199155e1c3ccbee9.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "text", + "content": "proaches (DAD [33], PSD [7], D4 [39]). The results are illustrated in Table 1. The proposed RIDCP achieves the best in terms of BRISQUE and NIMA, which gains " + }, + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "inline_equation", + "content": "25.57\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "inline_equation", + "content": "1.86\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 462 + ], + "type": "text", + "content": " improvements, respectively. For FADE, our method is ranked second slightly below the PSD. However, as shown in Figure 5, PSD tends to produce over-enhanced results, which leads to an inaccurate evaluation. Overall, RIDCP achieves the best results on quantitative metrics, and subsequent experiments will further prove our superiority." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 462, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 582 + ], + "type": "text", + "content": "Qualitative Comparison. We perform the qualitative comparison on RTTS and Fattal's datasets, which is shown in Figure 5 and Figure 6. We can observe that Dehamer, MSBDN, and D4 cannot process the real hazy images well. PSD can produce bright results but the dehazing ability is limited. DAD is effective in haze removal, while its results suffer from color bias and dark tone. Our method generates the best perceptual results in terms of brightness, colorfulness, and haze residue compared to other methods. More results can be found in supplementary materials." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "User Study. We conduct a user study to evaluate the proposed method subjectively against other methods. We randomly select 100 images from RTTS dataset for comparison and invite 5 experts with image processing background and 5 naive observers as volunteers. Before the user study, we give the observer three tips: 1) The primary concern is whether the haze is removed, especially the dense haze in the distance. 2) Pay attention to whether the natural color is recovered. 3) A good method should generate artifact-free results. Afterward, the images are displayed to the observer group by group. Each group contains the input image and" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 217, + 547, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 547, + 301 + ], + "type": "text", + "content": "the results generated by different methods. The observer is required to choose the best one after at least 10 seconds of observation. We statistic the percentage of each method selected as the best and the final scores are listed in Table 1. The proposed RIDCP achieves the highest score and is well ahead of the second place, further demonstrating our method's superior dehazing ability." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 309, + 400, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 309, + 400, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 309, + 400, + 323 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "content": "In order to verify the effectiveness of each key component, we conduct a series of ablation experiments. Generally, we discuss the effectiveness of CHM, NFA, and the phenomenological degradation pipeline in this section." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": "Influence of Adjustment Parameter. The degree of real domain adaptation is controlled by parameter " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": " in Eq. (8) and one can adjust the final result flexibly by adjusting " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": ". Thus, we are curious about what influence the different " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": " will have. As Figure 7 shows, the value of " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": " and the image enhancement effect belong to a linear relationship. More visual-pleasing even over-enhanced results can be produced when " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha > 0" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": ". Interestingly, we can obtain under-enhanced results if " + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 377, + 546, + 485 + ], + "type": "text", + "content": " is adjusted in the opposite direction." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 486, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 688 + ], + "type": "text", + "content": "Effectiveness of NFA. Our NFA can help remove the distorted textures caused by feature matching while preserving the useful information reconstructed from HQPs. The NFA can be divided into two key parts: warping operation based on deformable convolution and normalize-based addition. To analyze the role of each part, we propose 4 variants to replace NFA, which are: 1) Without any fusion operation. 2) Adding directly. 3) Normalized addition without warping. 4) Warping and direct addition. Figure 8 shows a set of comparisons. Observing the grass area in red boxes, the result of variant 1 is dark and remaining thin haze. Variants 2 and 4 also have non-homogeneous fog residues in some areas. Variant 3 generates obvious artifacts because forcing normalizing unaligned features to the same order of magnitude and adding them together makes the network difficult to train. Only the full NFA achieves the best in brightness and haze removal." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Effectiveness of the Phenomenological Degradation Pipeline. 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Results under different adjustment degrees. The proposed CHM allows users to adjust the degree of enhancement from low " + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "inline_equation", + "content": "(\\alpha = -60.0)" + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "text", + "content": " to high " + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "inline_equation", + "content": "(\\alpha = 60.0)" + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "text", + "content": ". The recommended value " + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "inline_equation", + "content": "(\\alpha = 21.25)" + }, + { + "bbox": [ + 46, + 215, + 547, + 247 + ], + "type": "text", + "content": " facilitates the network to generate the most natural results (surrounded by the blue box). 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Ablation results of the proposed NFA." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 129, + 318, + 206, + 369 + ], + "blocks": [ + { + "bbox": [ + 129, + 318, + 206, + 369 + ], + "lines": [ + { + "bbox": [ + 129, + 318, + 206, + 369 + ], + "spans": [ + { + "bbox": [ + 129, + 318, + 206, + 369 + ], + "type": "image", + "image_path": "2f308c916a62328b65faab3685e395d76fec97f959fe3ae82727d9018261ae8c.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 130, + 370, + 203, + 380 + ], + "lines": [ + { + "bbox": [ + 130, + 370, + 203, + 380 + ], + "spans": [ + { + "bbox": [ + 130, + 370, + 203, + 380 + ], + "type": "text", + "content": "(e) w/o normalizing" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 206, + 318, + 285, + 369 + ], + "blocks": [ + { + "bbox": [ + 206, + 318, + 285, + 369 + ], + "lines": [ + { + "bbox": [ + 206, + 318, + 285, + 369 + ], + "spans": [ + { + "bbox": [ + 206, + 318, + 285, + 369 + ], + "type": "image", + "image_path": "9f069f2c400a234d12b64f1ee0b53ea30f65b2df9f327582895e47bb94b303ac.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 370, + 266, + 379 + ], + "lines": [ + { + "bbox": [ + 220, + 370, + 266, + 379 + ], + "spans": [ + { + "bbox": [ + 220, + 370, + 266, + 379 + ], + "type": "text", + "content": "(f) Full NFA" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 400, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 581 + ], + "type": "text", + "content": "for paired data generation can boost the capabilities of haze removal, we retrain our RIDCP on two widely-used synthetic datasets, which are OTS [22] and Haze4K [42]. Notably, Haze4K is post-processed by DAD [33]. Moreover, we replace the training set from OTS with our synthetic data for transformer-based Dehamer and CNN-based MSBDN, thus demonstrating that it can generally bring gains. The comparison results are illustrated in Figure 9. We can observe that our dehazing network cannot remove the haze under the training of OTS and Haze4K. Besides, Dehamer and MSBDN can generate results with less haze and higher brightness with the help of our training data. However, they still struggle in color recovery compared to our method, which also demonstrates the effectiveness of HQPs and our adaptation strategy." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 585, + 117, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 117, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 117, + 597 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Conclusion. In this paper, we present a novel paradigm to revitalize deep dehazing networks towards the real world. Our proposed phenomenological degradation pipeline synthesizes more realistic hazy data, which achieves significant gains in haze removal. Based on our observations and analysis, we introduce the high-quality priors in VQGAN to the dehazing network and progressively leverage their power, which finally builds our real image dehazing network via high-quality codebook priors (RIDCP). 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Ablation results of the proposed data generation pipeline. We retrain our dehazing network on OTS (b) and Haze4K (c) to verify the effectiveness of our generation pipeline. Dehamer and MSBDN are also retrained on our synthetic data, which are marked by " + }, + { + "bbox": [ + 306, + 376, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 306, + 376, + 545, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 369, + 313, + 426, + 360 + ], + "blocks": [ + { + "bbox": [ + 379, + 304, + 410, + 312 + ], + "lines": [ + { + "bbox": [ + 379, + 304, + 410, + 312 + ], + "spans": [ + { + "bbox": [ + 379, + 304, + 410, + 312 + ], + "type": "text", + "content": "(b) OTS" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 313, + 426, + 360 + ], + "lines": [ + { + "bbox": [ + 369, + 313, + 426, + 360 + ], + "spans": [ + { + "bbox": [ + 369, + 313, + 426, + 360 + ], + "type": "image", + "image_path": "b70d214e4f980e9550604abb21f90e7a5c8eb341e0deba6b0be127572befd4e6.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 361, + 419, + 372 + ], + "lines": [ + { + "bbox": [ + 375, + 361, + 419, + 372 + ], + "spans": [ + { + "bbox": [ + 375, + 361, + 419, + 372 + ], + "type": "text", + "content": "(f) MSBDN" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 37 + }, + { + "type": "image", + "bbox": [ + 427, + 313, + 485, + 360 + ], + "blocks": [ + { + "bbox": [ + 433, + 304, + 476, + 312 + ], + "lines": [ + { + "bbox": [ + 433, + 304, + 476, + 312 + ], + "spans": [ + { + "bbox": [ + 433, + 304, + 476, + 312 + ], + "type": "text", + "content": "(c) Haze4K" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 313, + 485, + 360 + ], + "lines": [ + { + "bbox": [ + 427, + 313, + 485, + 360 + ], + "spans": [ + { + "bbox": [ + 427, + 313, + 485, + 360 + ], + "type": "image", + "image_path": "409bba2378222b66280eeddfbd3ea2da53653ad0dcb3ff0f1099787f8a1f60bb.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 361, + 481, + 373 + ], + "lines": [ + { + "bbox": [ + 432, + 361, + 481, + 373 + ], + "spans": [ + { + "bbox": [ + 432, + 361, + 481, + 373 + ], + "type": "text", + "content": "(g) " + }, + { + "bbox": [ + 432, + 361, + 481, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{MSBDN}^{\\dagger}" + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_caption" + } + ], + "index": 39 + }, + { + "type": "image", + "bbox": [ + 485, + 313, + 543, + 360 + ], + "blocks": [ + { + "bbox": [ + 491, + 304, + 539, + 312 + ], + "lines": [ + { + "bbox": [ + 491, + 304, + 539, + 312 + ], + "spans": [ + { + "bbox": [ + 491, + 304, + 539, + 312 + ], + "type": "text", + "content": "(d) Dehamer" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 485, + 313, + 543, + 360 + ], + "lines": [ + { + "bbox": [ + 485, + 313, + 543, + 360 + ], + "spans": [ + { + "bbox": [ + 485, + 313, + 543, + 360 + ], + "type": "image", + "image_path": "060c05511a6c1091fdd4c4e4666c0a6bd40d2260c19c22c61fdd1771c6441f22.jpg" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 361, + 528, + 372 + ], + "lines": [ + { + "bbox": [ + 496, + 361, + 528, + 372 + ], + "spans": [ + { + "bbox": [ + 496, + 361, + 528, + 372 + ], + "type": "text", + "content": "(h) Ours" + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "image_caption" + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 441, + 523, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 523, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 523, + 453 + ], + "type": "text", + "content": "ments show the superiority of the proposed paradigm." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 305, + 453, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 502 + ], + "type": "text", + "content": "Limitations and Future Work. In the process of doing our work on RIDCP, we observed that there are still some difficulties that are urgent to be addressed. We leave the challenges here and hope that future work can address them" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 317, + 507, + 545, + 618 + ], + "type": "list", + "angle": 0, + "index": 49, + "blocks": [ + { + "bbox": [ + 317, + 507, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 507, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 317, + 507, + 545, + 532 + ], + "type": "text", + "content": "- Existing dehazing methods including RIDCP can not process non-homogeneous haze well." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 317, + 539, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 539, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 317, + 539, + 545, + 574 + ], + "type": "text", + "content": "- Dehazing based on enhancement fashion is limited. Generative ability should be introduced for recovering extremely dense haze." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 317, + 582, + 545, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 582, + 545, + 618 + ], + "spans": [ + { + "bbox": [ + 317, + 582, + 545, + 618 + ], + "type": "text", + "content": "- We found that difficult to benchmark dehazing methods in quantitative fairly. Robust metrics for evaluating the quality of dehazing results are also needed." + } + ] + } + ], + "index": 48 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgements. This work is funded by the National Key Research and Development Program of China (NO.2018AAA0100400), Fundamental Research Funds for the Central Universities (Nankai University, NO.63223050), China Postdoctoral Science Foundation (NO.2021M701780). 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Token mixers, as self-attention for vision transformers (ViTs), are intended to perform information communication between different spatial tokens but suffer from considerable computational cost and latency. However, directly removing them will lead to an incomplete model structure prior, and thus brings a significant accuracy drop. To this end, we first develop an RepIdentityFormer base on the reparameterizing idea, to study the token mixer free model architecture. And we then explore the improved learning paradigm to break the limitation of simple token mixer free backbone, and summarize the empirical practice into 5 guidelines. Equipped with the proposed optimization strategy, we are able to build an extremely simple vision backbone with encouraging performance, while enjoying the high efficiency during inference. Extensive experiments and ablative analysis also demonstrate that the inductive bias of network architecture, can be incorporated into simple network structure with appropriate optimization strategy. We hope this work can serve as a starting point for the exploration of optimization-driven efficient network design.", + "bbox": [ + 73, + 353, + 473, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 729, + 209, + 746 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The monumental advance in computer vision in the past few years was partly brought by the revolution of vision backbones, including convolutional neural networks (ConvNets) [13, 17, 25, 30] and vision transformers (ViTs) [14, 38]. Both of them have particular modules in their basic building blocks that aggregate information between different spatial locations, which are called token mixer [46], such as self-attention for ViTs. Although the effective", + "bbox": [ + 75, + 756, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/52123fafbd222c9d4003807e33cb96ab5dbe4aab859c22f83db9bf7326e8e7d9.jpg", + "image_caption": [ + "Figure 1. Latency analysis of different components in ViT-Base [14]. (a) For token mixer (self-attention), the latency occupies about $46.3\\%$ of the backbone. (b) Our motivation was to remove the token mixer while striving to keep the performance." + ], + "image_footnote": [], + "bbox": [ + 506, + 320, + 883, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ness of token mixer has been demonstrated on many vision tasks [5, 6, 24, 45], its computational complexity typically takes up a significant portion of the network. In practice, heavy token mixers make the vision backbone limited especially on the edge-side devices due to the issue of speed and computation cost.", + "bbox": [ + 496, + 625, + 893, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There have been several attempts in the literature to investigate efficient token mixers for slimming vision backbones [29, 31, 46]. Although those works have already achieve competitive performance with light-weight design, they do retain the token mixers, which brings non-negligible increase in latency, as illustrated in Fig. 1. The recent work [47] finds that removing the token mixer is possible but leads to performance degeneration. Those explorations in efficient token mixers inspire us to think that can we keep the vision backbone effective but removing the token mixer? The resulting token mixer free vision backbone is expected to be efficient and effective for the realistic application.", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author.", + "bbox": [ + 101, + 887, + 233, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14443", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we first review the current model architectures and learning paradigms. Most of the previous works concentrate on the improvement of the architecture while adopting the conventional supervised learning to optimize the model from scratch. Differently, we propose to adopt the simplified model architecture, and explore the learning paradigm design to fully exploit the potential of the simple model. We aim to simultaneously maintain the efficiency and efficacy of token mixer free vision backbone (namely IdentityFormer, in Fig. 1-(b)). To this end, we investigate the simple and yet effective learning strategy, knowledge distillation (KD) [18] thoroughly in the following sections.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main idea is distilling the knowledge from powerful teacher model (with token mixer) to the student model (token mixer free). We instantiate the re-parameterizing idea to enlarge the modeling capacity of student network but retain its efficiency, as shown in Fig. 2. Specifically, the simple affine transformation is introduced into student model, to replace the token mixer for training. The parameters of affine transformation can be merged into LayerNorm [2] during inference, which makes the student token mixer free finally.", + "bbox": [ + 75, + 273, + 472, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We empirically summarize the our learning strategy as the following guidelines, hope to shed light on how to learn the extremely simple model. Concretely, 1) soft distillation without using ground-truth labels is more effective; 2) using affine transformation without distillation is difficult to tailor the performance degeneration; 3) the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator; 4) teacher with large receptive field is beneficial to improve receptive field limited student; 5) loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance.", + "bbox": [ + 75, + 411, + 472, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the above guidelines, we finally obtain a token mixer free vision model with competitive performance enjoying the high efficiency, dubbed as $\\underline{\\text{RepIdentityFormer}}$ (RIFormer). RIFormer shares nearly the same macro and micro design as MetaFormer [46], but safely removing all token mixers. The quantitative results show that our networks outperform many prevailing backbones with faster inference speed on ImageNet-1K [8]. And the ablative analyses on the feature distribution and Effective Receptive Fields (ERFs) also demonstrate that the inductive bias brought by an explicit token mixer, can be implicitly incorporated into the simple network structure with appropriate optimization strategies. In summary, the main contributions of our work are as the following:", + "bbox": [ + 75, + 593, + 472, + 805 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to explore the vision backbone by developing advanced learning paradigm for simple model architecture, to satisfy the demand of realistic application.", + "- We instantiate the re-parameterizing idea to build a token mixer free vision model, RIFormer, which owns the improved modeling capacity for the inductive bias while" + ], + "bbox": [ + 76, + 810, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "enjoying the efficiency during inference.", + "bbox": [ + 511, + 90, + 782, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our proposed practical guidelines of distillation strategy has been demonstrated effective in keeping the vision backbone competitive but removing the token mixer.", + "bbox": [ + 500, + 106, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 164, + 640, + 179 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Vision Transformer Acceleration", + "text_level": 1, + "bbox": [ + 500, + 188, + 785, + 203 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision transformer is a inference slow, energy intensive backbone due to its quadratic computational cost of the self-attention, and therefore unfriendly to deploy on resource-limited edge devices, calling for compression techniques. Various technology route are designed for vision transformer slimming, such as distilling an efficient transformer with fewer depths and embedding dimensions [16,38,39,44, 51], pruning or merging unimportant tokens [3,21,28,29], applying energy efficient operations [23, 33], or designing efficient attention alternatives [4,24,31], etc. Different from these lines, our work proposes a novel angle of totally removing the complicated token mixer in a backbone while keep satisfactory performance.", + "bbox": [ + 496, + 210, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Structural Re-parameterization", + "text_level": 1, + "bbox": [ + 500, + 416, + 772, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Structural re-parameterization [12, 13, 49] is a training technique which decouples the training-time and inference-time architectures. For example, RepVGG [13] is a plain VGG-style architecture with attractive performance and speed during inference, and a powerful architecture with manually added $1 \\times 1$ branch and identity mapping branch during training. Similarly, such technique can be further extended to super large kernel ConvNets [12], MLP-like models [9], network pruning [11] and special optimizer design [10]. In this paper, we follow the technique to introduce parameters and equivalently absorb them into LN layer after training. The extra weights after proper optimization can help the model learn useful representations.", + "bbox": [ + 496, + 439, + 890, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminary and Motivation", + "text_level": 1, + "bbox": [ + 500, + 647, + 756, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we first briefly recap the concept of token mixer. Then, we revisit their inevitable side effects on inference speed through an empirical latency analysis, and thus introduce the motivation of our paper.", + "bbox": [ + 496, + 672, + 890, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Preliminary: The Concept of Token Mixer", + "text_level": 1, + "bbox": [ + 500, + 741, + 861, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The concept token mixer is a structure that performs token mixing functions in a given vision backbone. It allows information aggregation from different spatial positions [46]. For instance, self-attention module serves as the token mixer in ViT [14] by performing the attention function in parallel between components in queries, keys and values matrices, which are linearly projected from the input feature. Moreover, ResMLP [37] applies a cross-patch linear sublayer by treating Spatial MLP as token mixer. The", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14444", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e5ec6657e66492546a60c6e227dbb55d01babf3622c9b5ff50d344e01c5881f7.jpg", + "image_caption": [ + "Figure 2. Structural re-parameterization of a RIFormer block." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 447, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "computational and memory costs of the aforementioned token mixers are quadratic to the image scale.", + "bbox": [ + 75, + 270, + 468, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Motivation", + "text_level": 1, + "bbox": [ + 76, + 310, + 197, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we take our eyes on the side effects of token mixers through a quantitative latency analysis on the ViT [14] model. We start with a modified 12-layer ViT-Base model containing only input embedding, without any operation in each of its basic building blocks. Then we gradually add the operation component (e.g., LN, Attention, Channel MLP, etc.) to each basic block, and the model finally comes to ViT-Base without the global average pooling layer and the classifier head. For each model, we take a batch size of 2048 at $224^2$ resolution with one A100 GPU and calculate the average time over 30 runs to inference that batch. The whole process is repeated for three times and we take the medium number as the statistical latency. As shown in Fig. 1, after stacking the regular number of 12 layers, token mixer can bring an additional latency of 1433.6ms, occupying about $46.3\\%$ of the backbone.", + "bbox": [ + 75, + 333, + 468, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "According to the above analysis, token mixer brings significant side effects on the latency to the model, which makes it limited for realistic application. The observation naturally raises a question: can we keep the backbone effective but removing token mixer? Specifically, a recent work [47] introduces the MetaFormer model without any token mixer in its basic building block and finds that it raises a non-negligible performance degeneration. Based on those findings, we propose to exploit the full potential of the extremely simple model by incorporating the inductive bias with the advanced optimization strategies, such as knowledge distillation [18, 38, 51], structural reparameterization [12, 13], etc. And we present all the exploration details in the remaining of this work.", + "bbox": [ + 73, + 575, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Exploring RIFormer: A Roadmap", + "text_level": 1, + "bbox": [ + 76, + 800, + 388, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present a trajectory going from a fully supervised approaches for RIFormer to more advanced training paradigms. During the journey we investigate and develop different optimization schemes for transformer-like models, while maintaining the inference-time model as the", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/9cbeb8db91b898ecaa4b86ed739ae5d530c2fb8d43ca0248c47a5e3cac0f62ef.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Token MixerTraining recipeImageNet top-1 acc (%)
PoolingCE Loss75.01
IdentityCE Loss72.31
", + "bbox": [ + 511, + 92, + 880, + 138 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/e84de8f08d83ebbe1717a7449cf06d64cf841e5acec8696ffd5723ef30026b37.jpg", + "table_caption": [ + "Table 1. Results of different token mixers on MetaFormer using cross-entropy loss." + ], + "table_footnote": [], + "table_body": "
TMLabelTeacherImageNet top-1 acc (%)
Identity✓✗72.31
Identity✓hard73.51
Identity✗hard72.86
Identity✓soft73.64
Identity✗soft74.05
", + "bbox": [ + 521, + 175, + 870, + 265 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/c09368186a13384cb0cdf6ad69bc4a8ef8ff6112d5aa05a3a940f44d2df97ed3.jpg", + "table_caption": [ + "Table 2. Results of different teacher type in normal/label-free RIFformer-S12 with identity mapping as token mixer." + ], + "table_footnote": [], + "table_body": "
TMLabelKD typeImageNet top-1 acc (%)
Affine✓×72.25
Affine✓hard73.44
Affine×hard72.77
Affine✓soft72.10
Affine×soft74.07
", + "bbox": [ + 522, + 300, + 867, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 3. Results of different distillation type in normal/label-free RIFormer-S12 with affine transformation as token mixer.", + "bbox": [ + 498, + 393, + 890, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "same. The baseline RIFormer we use has exactly the same macro architecture and model size as recently-developed MetaFormer [46], the difference only lies in the fact that no token mixer is used in its basic building blocks during inference. We control the computational complexity of RIFormer-S12 models comparable to PoolFormer-S12 [46], with about 12M parameters and 1.8G MAC. All RIFormer-S12 models in this section are trained and evaluated on ImageNet-1K for 120 epochs. The details of hyper-parameters are shown in Sec.1 of the appendix. The roadmap of our exploration is as follows.", + "bbox": [ + 496, + 430, + 890, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Vision Backbone Without Token Mixer", + "text_level": 1, + "bbox": [ + 500, + 604, + 834, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our exploration is directed to remove token mixer in each basic block of a inference-time model vision backbone to obtain a higher inference speed while striving to keep the performance. Thus, we start with a RIFormer-S12 model with a fully supervised training scheme using CE loss, mainly follows [46]. As a performance reference, we compare the results with PoolFormer-S12, since it use only basic pooling operation as token mixer and the performance gap can thus, be attributed to the absence of basic token mixing function. As shown in Tab. 1, RIFormer-S12 with a trivial supervised training can lead to an unacceptable performance drop (2.7% top-1 accuracy) compared to PoolFormer-S12. The results show that without token mixer in each building block, it is limited for regular supervised learning in helping the model learn useful information from images, calling for advanced training procedure.", + "bbox": [ + 496, + 628, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We then investigate and modify a series of training paradigms to improve the inferior baseline performance,", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14445", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d67209d4231f432636aecf7fa1f27df03169140dc897229a5002d02a699c18f9.jpg", + "image_caption": [ + "(a) Overall training procedure with $L$ RIFormer blocks", + "(b) Module imitation", + "Figure 3. (a) Overall training procedure of RIFormer. Following the macro and micro design of [46], RIFormer removes token mixer in each block. (b) Module imitation technique aims to mimic the behavior of token mixer via a simple affine transformation." + ], + "image_footnote": [], + "bbox": [ + 76, + 84, + 893, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which can be summarized as 1) knowledge distillation, 2) teacher type influence, 3) structural re-parameterization, 4) the proposed module imitation technique, 5) load partial parameters from teacher. Since we aim at exploring the influence of different advanced training recipes instead of network architecture, inference-time model architecture is always kept the same at intermediate steps. Next, we share 5 useful guidelines for training RIFformer.", + "bbox": [ + 75, + 364, + 472, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Distillation Paradigm Design", + "text_level": 1, + "bbox": [ + 76, + 496, + 334, + 512 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now study the knowledge distillation [18, 38] of a RIFormaler student by a general vision backbone teacher with token mixer, and summarize how to effectively utilize the \"soft\" labels coming from the strong teacher network.", + "bbox": [ + 75, + 520, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Guideline 1: soft distillation without using ground-truth labels can be effective for student without token mixer. Basically, most of the existing KD methods are designed for models with token mixer. For example, it is common practice to help a student convnet by learning from both ground-truth labels and the soft labels predicted by a teacher convnet. Moreover, some observations from DeiT [38] show that using the hard labels instead of soft labels as a supervised target, can improves transformer significantly. In contrast, the token mixer free backbone do not have explicit patch aggregating modules in its basic block. The distillation of it is should be thus, different from that of conventional backbones. Specifically, although RIFormer shares the same macro structure as transformer, it still cannot be treated as a student transformer because we have deliberately removed the token mixer from each building block. However, we also do not prefer viewing it as a pure convnet since RIFormer bears a resemblance to transformer in terms of macro/micro-level architecture design. Therefore, we are motivated to explore a suitable KD method for RIFormer with promising performance.", + "bbox": [ + 75, + 583, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Typically, the cross-entropy objective is to assist a student network reproduce the hard accurate label, and we argue that the process may be unsuitable for RIFormer. First, the ground-truth hard label can be transformed to a soft distribution by label-smoothing regularization [35], with weights $1 - \\varepsilon$ for the true label and $\\varepsilon$ shared each classes. The unlearned uniform distribution across the negative classes is less informative, and may interfere with the learned soft distribution given by teacher. Second, $1 \\times 1$ convolutions actually dominate basic building block in RIFormer, \"mixing\" only the per-location features but not spatial information. Such a simplified design may require richer information in the supervised labels. To demonstrate this, Tab. 2 compare the performance of four different settings. The default teacher is a GFNet-H-B [31] (54M parameters). Hard distillation with true labels improves the accuracy from $72.31\\%$ to $73.51\\%$ . It shows that a teacher with token mixer has a positive effect on a student without token mixer. In fact, the combination of using a soft distillation without true labels performs the best, improving the network performance to $74.05\\%$ .", + "bbox": [ + 496, + 364, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 1. Supervised learning with true label does not seem to be the most suitable way for a crude model without token mixer. A teacher with token mixer can help to guide the training, but still fails to fully recover the performance gap from removing token mixer, calling for other strategies.", + "bbox": [ + 496, + 681, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Re-parameterization for Identity Mapping", + "text_level": 1, + "bbox": [ + 498, + 770, + 864, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Guideline 2: using affine transformation without tailored distillation, is hard to recover the performance degradation. In this part, we adopt the idea of Structural Reparameterization [9, 12, 13] methodology, which usually takes a powerful model for training and equivalently converts to a simple model during inference. Specifically, the inference-time token mixer module in RIFormer can be", + "bbox": [ + 496, + 794, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14446", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/e13896a95de0a271fe135ea670b399f082029b548bda8e3ddd272cc18b2ba2b7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TMFeatRelLayerImageNet top-1 acc (%)
Affine00-74.07
Affine400674.49
Affine600674.77
Affine800674.81
Affine8010675.08
Affine8020674.82
Affine8040675.00
Affine8020475.13
", + "bbox": [ + 93, + 88, + 454, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "viewed as an identity mapping following a LN layer. Thus, the training-time module should satisfy at least two basic requirements: 1) per-location operator for allowing equivalent transformation; 2) parametric operator for allowing extra representation ability. Accordingly, we apply an affine transformation operator to replace the identity mapping during training, which only performs channel-wise scaling and shifts, as shown in Fig. 2. The affine operator and its preceding LN layer can be converted into a LN with modified weights, thus it can be equivalently converted into an identity mapping during inference. Denote the input feature as $\\mathbf{M} \\in \\mathbb{R}^{N \\times C \\times H \\times W}$ , the affine operator can be expressed as:", + "bbox": [ + 75, + 244, + 472, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A f f i n e} (\\mathrm {M}, \\mathbf {s}, \\mathbf {t}) _ {:, i,:,:} = \\mathbf {s} _ {i} \\mathrm {M} _ {:, i,:,:} + \\mathbf {t} _ {i} - \\mathrm {M} _ {:, i,:,:}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 431, + 468, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{s} \\in \\mathbb{R}^C$ and $\\mathbf{t} \\in \\mathbb{R}^C$ are learnable weight vectors. We follow [46] to add a subtraction of the input during implementation due to the residual connection, and thus does not merge the first and third terms in Eq. 1. Then, we describe how to merge the affine transformation into its preceding LN layer, so the training-time model can be equivalently converted to model for deploy but no longer has token mixer in its blocks. We use $\\mu, \\sigma, \\gamma, \\beta$ as the mean, standard deviation and learned scaling factor and bias of the preceding LN layer. Denote $\\mathrm{T}^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}$ , $\\mathrm{T}'^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}$ respectively as the input and output of an affine residual sub-block in Fig. 2-(a). During the training time, we have:", + "bbox": [ + 75, + 457, + 472, + 641 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {T} ^ {\\prime (a)} = \\operatorname {A f f i n e} (\\mathrm {L N} (\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma , \\beta), \\mathbf {s}, \\mathbf {t}) - \\mathrm {T} ^ {(a)} \\qquad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 648, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where LN is the LN function, which is implemented by GroupNorm API in PyTorch (setting the group number as 1) following [46]. During inference time, there only exists an identity mapping followed by a LN layer in the residual sub-block. Thus, we have:", + "bbox": [ + 75, + 675, + 468, + 751 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {T} ^ {\\prime (a)} = \\operatorname {L N} \\left(\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma^ {\\prime}, \\beta^ {\\prime}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 758, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma^\\prime$ and $\\beta^\\prime$ are the weight and bias parameters of the merged LN layer. Based on the equivalence of Eq. 2 and Eq. 3, for $\\forall 1\\leq i\\leq C$ , we have:", + "bbox": [ + 75, + 787, + 470, + 835 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\pmb {\\gamma} _ {i} ^ {\\prime} = \\pmb {\\gamma} _ {i} (\\mathbf {s} _ {i} - 1), \\quad \\pmb {\\beta} _ {i} ^ {\\prime} = \\pmb {\\beta} _ {i} (\\mathbf {s} _ {i} - 1) + \\mathbf {t} _ {i}, \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 843, + 468, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proof and PyTorch-like code of the affine transformation and re-parameterization process is shown in Sec.2 and", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3d660f1a073a7b05a7d2a1cc828903c15cadd6522660ca57c949217c47043ede.jpg", + "table_caption": [ + "Table 4. Results of different module imitation setting." + ], + "table_footnote": [], + "table_body": "
Teacher (T)T.acc (%)MIImageNet top-1 acc (%)
PoolFormer-M48 [46]82.5✗73.63
Swin-B* [24]85.2✗73.12
Pyramid ViG-B [15]83.7✗73.25
GFNet-H-B [31]82.9✗74.07
PoolFormer-M48 [46]82.5✓74.83
Swin-B* [24]85.2✓74.52
Pyramid ViG-B [15]83.7✓74.25
GFNet-H-B [31]82.9✓75.13
", + "bbox": [ + 513, + 88, + 880, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 5. Results of different teachers on RIFormer-S12 w/ or w/o module imitation (MI). * indicates ImageNet-22K pre-training.", + "bbox": [ + 498, + 236, + 890, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sec.3 of the appendix, respectively. Since the LN layer does not have a pre-computed mean and standard deviation during inference time, their specific values are input adaptive, which do not affect the equivalence of transform.", + "bbox": [ + 496, + 271, + 890, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 2. Compare Tab. 3 with Tab. 2, directly applying structural re-parameterization method shows no advantages. We attribute this phenomenon to the fact that the affine transformation in the LN layer is a linear transformation that can be directly merged with the extra affine operator we introduced (if do not add any nonlinear function in between). Therefore, if both are supervised only by the output of the model, the potential of the additional parameters may not be fully exploited. Meanwhile, the isomorphic design of teacher and student inspires us to explore suitable methods for knowledge transfer of modules at each layer.", + "bbox": [ + 496, + 332, + 892, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Module Imitation", + "text_level": 1, + "bbox": [ + 500, + 507, + 671, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Guideline 3: the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator. The previous KD methods we tried only focus on the output of between teacher and student networks. We propose module imitation (MI) method, which present to utilize the useful information in the teacher's token mixer. Specifically, a pretrained PoolFormer-S12 [46] is utilized as a teacher network. As shown in Fig. 3, we expect the simple affine operator (with its preceding LN layer) to approximate the behavior of that of a basic token mixer during training. Denote $f(\\cdot), \\mathrm{T}^{(a),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M}$ as the affine operator and the input of the $m$ -th layer of RIFormal in which $\\mathcal{M}$ is the intermediate layers set we used, and $g(\\cdot), \\mathrm{T}^{(t),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M}$ are that of the teacher network, respectively. We abbreviate $\\mathrm{LN}(\\cdot, \\mu, \\sigma, \\gamma, \\beta)$ as $\\mathrm{LN}(\\cdot)$ for simplicity. The mean squared error (MSE) of the inputs between the LN layer of affine operator and token mixer can be calculated as:", + "bbox": [ + 496, + 530, + 893, + 818 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i n} = \\alpha_ {1} \\| \\mathrm {L N} (\\mathrm {T} ^ {(a), m}) - \\mathrm {L N} (\\mathrm {T} ^ {(t), m}) \\| _ {F} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 827, + 890, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{1} = 1 / NCHW$ . Note that the input feature of the current layer is the output feature of the previous one. Therefore, we propose to match the output features of this", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14447", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "block (i.e., the input features of the next subsequent block) in practice, which can be seen as a hidden state distillation in transformers [16, 19, 40, 41, 51].", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i n} ^ {\\prime} = \\alpha_ {1} \\| T ^ {(a), m + 1} - T ^ {(t), m + 1} \\| _ {F} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 147, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The hidden-state distillation based on relation matrices [16, 51] is then applied on the output feature:", + "bbox": [ + 76, + 176, + 468, + 208 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e l} = \\alpha_ {2} \\| \\mathcal {R} (\\mathrm {T} ^ {(a), m + 1}) - \\mathcal {R} (\\mathrm {T} ^ {(t), m + 1}) \\| _ {F} ^ {2}, \\qquad (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 218, + 468, + 238 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha_{2} = 1 / NH^{2}W^{2}$ , $\\mathcal{R}(T) = \\tilde{T}\\tilde{T}^{\\top}$ , $\\tilde{T}$ denotes normalize $T$ at the last dimension. Considering the MSE of the outputs between affine operator and token mixer:", + "bbox": [ + 76, + 250, + 468, + 296 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o u t} = \\alpha_ {1} \\| f (\\mathrm {L N} (\\mathrm {T} ^ {(a), m})) - g (\\mathrm {L N} (\\mathrm {T} ^ {(t), m})) \\| _ {F} ^ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 306, + 468, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Combining Eq. 6, Eq. 7 and Eq. 8, the final loss function with module imitation is defined as:", + "bbox": [ + 76, + 335, + 468, + 366 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {s o f t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {i n}} ^ {\\prime} + \\lambda_ {2} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {3} \\mathcal {L} _ {\\text {r e l}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 378, + 468, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{soft}$ is the soft logit distillation target in Sec. 4.2, $\\lambda_{1},\\lambda_{2},\\lambda_{3}$ is the hyper-parameter for seeking the balance between loss functions. In Tab. 4, Feat and Rel are number of epochs of using $(\\mathcal{L}_{in}^{\\prime},\\mathcal{L}_{out})$ and $\\mathcal{L}_{rel}$ , Layer represents the number of intermediate layers we used. The results show positive effect of module imitation on the student RIFformer in different circumstances. With a 4 layer setting and the usage of affine operator, we get the best result of $75.13\\%$ , already surpassing the PoolFormer-S12's result of $75.01\\%$ in Tab. 1. From now on, we will use this setting.", + "bbox": [ + 75, + 407, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 3. We deem a reason for that phenomenon might be that module imitation helps the affine operator implicitly benefit from the supervision of the teacher's token mixer, while not losing the convenience of explicitly merging the preceding LN layer. Besides, we find module imitation can effectively shift the feature distribution closer to the teacher network and show larger Effective Receptive Fields (ERFs). Please refer to Sec. 5.3 for details.", + "bbox": [ + 75, + 559, + 468, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Guideline 4: teacher with large receptive field is beneficial to improve student with limited receptive field. Tab. 5 compares student performance with different teacher architectures. Although GFNet-H-B [31] does not show the highest ImageNet top-1 performance among teachers, it can still serves as a better choice, no matter whether module imitation is used or not.", + "bbox": [ + 75, + 688, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 4. The fact is probably attributed to the receptive field gap between teacher and student. As explained by [1], inductive bias can be transferred from one model to another through distillation. According to this study, model with large receptive field (e.g., GFNet with learnable global filters in the frequency domain) can be better teacher for student RIFormer with limited receptive field.", + "bbox": [ + 73, + 795, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Guideline 5: loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance. Our method can be categorized as a model compression technique that aims at removing the token mixer in basic blocks for acceleration. Inspired by previous methods, including knowledge distillation [32, 34], quantization [22, 26], and model acceleration [29] that initialize the weights of the light-weight network using (or partly using) the corresponding weights of the pre-trained heavy network, we explore a suitable initialization method. Since our goal is to remove only the token mixer, the weights of the remaining part still remain and are not paid enough attention in the previous journey. We observe that initializing the weights of RIFformer (except the affine operator) with the corresponding teacher network further boosts the performance from $75.13\\%$ to $75.36\\%$ . This brings us to the final paradigm for training RIFformer.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Closing remarks. So far, we have finished our exploration and discovered a suitable paradigm for training the RIFformer. It has the approximately the same macro design with MetaFormer [46], but does not require any token mixer. Equipped with the propsoed optimization methods, RIFformer can outperform complicated models with token mixers for ImageNet-1K classification. These encouraging findings inspire us to answer the following questions in the next section. 1) The scaling behavior of such extremely simple architecture with our training paradigm. 2) The generalizability of the paradigm on different teachers.", + "bbox": [ + 496, + 349, + 890, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 532, + 633, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Image classification", + "text_level": 1, + "bbox": [ + 500, + 556, + 686, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. For ImageNet-1K [8] with 1.2M training images and 50000 validation images, we generally apply the training scheme in [46] while following the guidelines in Sec. 4. The data augmentation contains MixUp [50], CutMix [48], CutOut [52] and RandAugment [7]. As a model compression work on removing token mixer, bridging the performance gap caused by removing the token mixer is definitely our first priority, instead of proposing a strong baseline. Therefore, we use a prolonged the training epochs of 600. We also finetune the pre-trained models for 30 epochs with input resolution of $384^2$ . More details are in the appendix.", + "bbox": [ + 496, + 580, + 890, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main results. Tab. 6 shows the results of RIFormer on ImageNet classification. We pay main attention to the throughput metrics since our primary consideration is to satisfy latency requirements for edge devices. As expected, favorable speed advantage is achieved since RIFormer does not contain any token mixer in its building block, compared with other type of backbones. Surprisingly, with such fast inference, RIFormers successfully remove all token mixers using our training approach without affecting the performance. For example, RIFormer-M36 can pro", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14448", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ca39dc2a3579bf7543593f0c871b45494ceb8d404cc2f96398ffb5d4547a8d7c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Token MixerOutcome ModelImage SizeParams (M)MACs (G)Throughput (images/s)Top-1 (%)
ConvolutionRSB-ResNet-34 [17,43]224223.76653.7575.5
RSB-ResNet-50 [17,43]224264.12732.8579.8
RSB-ResNet-101 [17,43]224457.91856.4881.3
RSB-ResNet-152 [17,43]2246011.61308.2681.8
Attention▲ DeiT-S [38]224224.63092.0279.8
▲ DeiT-B [38]2248617.51348.7681.8
▲ PVT-Small [42]224253.81622.5379.8
▲ PVT-Medium [42]224446.71190.4881.2
▲ PVT-Large [42]224619.8865.3381.7
Spatial MLPMLP-Mixer-B/16 [36]2245912.71855.4576.4
ResMLP-S24 [37]224306.03228.7579.4
ResMLP-B24 [37]22411623.0298.9481.0
Swin-Mixer-T/D6 [24]256234.01625.5979.7
Swin-Mixer-B/D24 [24]2246110.41131.6081.3
2D FFTGFNet-H-Ti [31]224152.11979.5680.1
GFNet-H-S [31]224324.61434.1981.5
GFNet-B [31]224437.91771.0780.7
GFNet-H-B [31]224548.6939.2082.9
Pooling○ PoolFormer-S12 [46]224121.84160.1877.2
○ PoolFormer-S24 [46]224213.42140.2080.3
○ PoolFormer-S36 [46]224315.01440.3781.4
○ PoolFormer-M36 [46]224568.81009.4582.1
○ PoolFormer-M48 [46]2247311.6761.9382.5
None★ RIFounder-S12°224121.84899.80 (↑17.8%)76.9
★ RIFounder-S24°224213.42530.48 (↑18.2%)80.3
★ RIFounder-S36°224315.01699.94 (↑18.0%)81.3
★ RIFounder-M36°224568.81185.33 (↑17.4%)82.6
★ RIFounder-M48°2247311.6897.05 (↑17.7%)82.8
★ RIFounder-S12‡384125.41586.5178.3
★ RIFounder-S24‡3842110.0819.4081.4
★ RIFounder-S36‡3843114.7552.0782.2
★ RIFounder-M36‡3845625.9403.1583.4
★ RIFounder-M48‡3847334.1304.4383.7
", + "bbox": [ + 91, + 88, + 872, + 573 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Results of models with different types of token mixers on ImageNet-1K. denotes training with prolonged 600 epochs. denotes fine-tuning from the ImageNet pre-trained model for 30 epochs.", + "bbox": [ + 75, + 574, + 890, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cess more than 1185 images at $224^2$ resolution per second, with the top-1 accuracy of $82.6\\%$ . In comparison, the recent baseline PoolFormer-M36 [46] with a Pooling token mixer, can process 1009 images of the same size with a worse $82.1\\%$ accuracy. We also compare with an efficient backbone, GFNet [31]. It conducts token mixing via a global filter, which consists an FFT, an element-wise multiplication, and an IFFT, with a total computational complexity $\\mathcal{O}(N\\log N)$ . With a 939 throughput, GFNet-H-B gets $82.9\\%$ accuracy while our RIFformer-M48 can still reaches a comparable $82.8\\%$ accuracy with on par throughput of 897. Meanwhile, the body of inference-time RIFformer is dominated by only $1\\times 1$ conv following LN, without complex 2D FFT or attention, friendly for hardware specialization.", + "bbox": [ + 75, + 607, + 468, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, without token mixer, RIFormer cannot even perform basic token mixing operation in its building blocks. However, the ImageNet experiments demonstrate that with the proposed training paradigm, RIFormer still shows promising results. We can only deem the reason behind the", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fact might be that optimization strategy plays a key role. RIFormer is readily a starting recipe for the exploration of optimization-driven efficient network design, and rest assured of the performance with advanced training schemes.", + "bbox": [ + 496, + 608, + 890, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation studies", + "text_level": 1, + "bbox": [ + 498, + 676, + 661, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of module imitation. As an important way for the extra affine operator to learn suitable weights, module imitation is based on distillation. Therefore, we compare it with the hidden state feature distillation approach (with relations). Taking the paradigm in Sec. 4.2 by soft distillation without CE loss, we get the results in Tab. 7. More details for Sec. 5.2 can be found in Sec.4 of the appendix. With feature distillation, the accuracy is $0.46\\%$ lower than that of module imitation, showing module imitation's positive effect on the optimization of the extra weights.", + "bbox": [ + 496, + 699, + 890, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons of different acceleration strategy. Next, we discuss whether the token removing is better than other sparsification strategies. Based on the PoolFormer [46]", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14449", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08242cdedb5dd833cae1948cc2e0b7ab7786b2cd89aded2ef7b3573fb696fa8d.jpg", + "image_caption": [ + "(a) PoolFormer-S12" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 207, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7107825627d6ffe2a074d214865460790fabc41e1e0e42d48cc7ba3a3f6250d0.jpg", + "image_caption": [ + "(b) RIFormer-S12" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 336, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5795a116e98fcd19eb43041343044f4e6becfe84d4744b3e624f5c932e5ac1a0.jpg", + "image_caption": [ + "(c) RIFormer-S12 (MI)", + "Figure 4. The Effective Receptive Field (ERF) of PoolFormer-S12 and RIFlower-S12 with/without using module imitation." + ], + "image_footnote": [], + "bbox": [ + 338, + 88, + 468, + 196 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b150f51d6b8504e6af6bee99252c6cf5ffbd46e3d8f7ee5be8387fe96cb51987.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Token MixerFeature distillation schemeTop-1 (%)
IdentityNone74.05
IdentityFeature distill74.90
AffineModule imitation75.36
", + "bbox": [ + 94, + 250, + 452, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "baseline, we first construct a slim PoolFormer-S9 and PoolFormer-XS12 by reducing the depth to 9 and by maintaining about $\\frac{5}{6}$ of its width, i.e., embedding dimension, to obtain comparable inference speed with our RIFormer-S12. We also follow the soft distillation paradigm in Sec. 4.2. Tab. 8 shows the results. Directly pruning depths or width cannot render a better performance than ours without latency-hungry token mixer.", + "bbox": [ + 75, + 337, + 467, + 459 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Generalization to different teachers. In order to verify the proposed training paradigm a general compression technique, we adopt the architecture modifications in [47] for student and change teacher to the other 4 MetaFormer baselines [47], with teacher token mixer as rand matrices, pooling, separable depthwise convolutions, and attention, respectively. Tab. 9 shows that our method has a positive effect in different depth settings and teacher circumstances.", + "bbox": [ + 75, + 465, + 467, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Analysis of Module Imitation.", + "text_level": 1, + "bbox": [ + 76, + 597, + 339, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Module imitation (MI) shifts the feature distribution of the RIFformer model to be closer to the teacher. The effect of the module imitation is explicitly shown in Fig. 5. It can be observed that PoolFomer-S12 and RIFformer-S12 show a clear difference in feature distribution of Stage 1 and Stage 4. After applying the proposed module imitation, the distribution of RIFformer-S12 are basically shifted toward that of the PoolFomer-S12, demonstrating its effect on helping student learn useful knowledge from the teacher.", + "bbox": [ + 75, + 619, + 467, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Module imitation helps showing larger Effective Receptive Field (ERF). ERF [27] reflects how large an area of the image the trained model can respond to or capture information about how large an object. We follow [12, 20] to visualize the ERF via measuring the aggregated contributions of each pixel of the input to the central points of the output feature. Since RIFormer removes all token mixers, it exhibits an expectedly much smaller ERF than PoolFormer, as shown in Fig. 4. There is only a square of pixels emerg-", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/69900e83ad5c01544ec37fb1a70b40c678ee4c3e7a55a6f8e3831c497a28e158.jpg", + "image_caption": [ + "Figure 5. Visualization of the feature distribution of the first and last stage of PoolFormer-S12 and RIFormal-S12." + ], + "image_footnote": [], + "bbox": [ + 500, + 87, + 694, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c212c97c5154694105f56209d5ee329629347c4d5df8061d756c553a365eba8d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 88, + 890, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/31b57126921b2b230afbf38022084a3ad4cdaa3d017a223f3593bdc98589ae0c.jpg", + "table_caption": [ + "Table 7. Ablation study of the effectiveness of module imitation." + ], + "table_footnote": [], + "table_body": "
ModelTypeThroughputTop-1 (%)
PoolFormer-S12None4160.1875.01
PoolFormer-S9Depth5025.7174.78
PoolFormer-XS12Width4780.2875.11
RIFounder-S12TM4899.8075.36
", + "bbox": [ + 516, + 247, + 874, + 321 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b5b54cf32ec25c77801f79a4f5054a36bc85ba96232aa29a1f98425a79b032f2.jpg", + "table_caption": [ + "Table 8. Results of comparison with depth or width slimming." + ], + "table_footnote": [], + "table_body": "
Token MixerTeacherTop-1 (%)
Affine (12 layers)None72.75
Affine (12 layers)RandFormer-S12 [47]75.62
Affine (12 layers)PoolFormer V2-S12 [47]75.87
Affine (18 layers)None75.01
Affine (18 layers)ConvFormer-S18 [47]77.53
Affine (18 layers)CAFormer-S18 [47]77.26
", + "bbox": [ + 508, + 349, + 883, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. Results of generalization to other teachers.", + "bbox": [ + 540, + 457, + 846, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing with red color in the whole region, much smaller than PoolFormer. However, surprisingly, we can observe that red color widely distributed in all locations after training with module imitation. It seems that although there's no explicit structural change, module imitation still help change the learned weights and show larger ERF.", + "bbox": [ + 496, + 474, + 890, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 579, + 754, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper investigates removing token mixer of the basic building block in a vision backbone, motivated by their considerable latency cost. To keep the remaining structure still effective, we thoroughly revisits the training paradigm. We observe that appropriate optimization strategy can effectively help a token mixer-free model learn useful knowledge from another model, boosting its performance and bridge the gap caused by incomplete structure. Limitations are that more vision tasks, including detection, deblurring, etc. are not discussed, and we will work on them in the future.", + "bbox": [ + 496, + 604, + 890, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 768, + 660, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper is partly supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, Shanghai Postdoctoral Excellence Program (No.2022235), the National Natural Science Foundation of China (Grant No.61991450) and the Shenzhen Science and Technology Program (JCYJ20220818101001004).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14450", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samira Abnar, Mostafa Dehghani, and Willem Zuidema. 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In AAAI, 2020. 6" + ], + "bbox": [ + 501, + 92, + 890, + 329 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14452", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/5e2f8802-cd09-4641-a7fa-0692dcfb5f55_model.json b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/5e2f8802-cd09-4641-a7fa-0692dcfb5f55_model.json new file mode 100644 index 0000000000000000000000000000000000000000..dab74e29f512724881a9afd459e7543e29293fee --- /dev/null +++ b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/5e2f8802-cd09-4641-a7fa-0692dcfb5f55_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.131, + 0.877, + 0.153 + ], + "angle": 0, + "content": "RIFormer: Keep Your Vision Backbone Effective But Removing Token Mixer" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.179, + 0.81, + 0.288 + ], + "angle": 0, + "content": "Jiahao Wang\\(^{1,2}\\) Songyang Zhang\\(^{1*}\\) Yong Liu\\(^{3}\\) Taiqiang Wu\\(^{3}\\) Yujiu Yang\\(^{3}\\) Xihui Liu\\(^{2}\\) Kai Chen\\(^{1*}\\) Ping Luo\\(^{2}\\) Dahua Lin\\(^{1}\\) \n\\(^{1}\\)Shanghai AI Laboratory \\(^{2}\\)The University of HongKong \n\\(^{3}\\)Tsinghua Shenzhen International Graduate School \nwang-jh19@tsinghua.org.cn {zhangsongyang, chenkai, lindahua}@pjlab.org.cn \nyang.yujiu@sz.tsinghua.edu.cn xihuiliu@eee.hku.hk pluo@cs.hku.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.354, + 0.474, + 0.687 + ], + "angle": 0, + "content": "This paper studies how to keep a vision backbone effective while removing token mixers in its basic building blocks. Token mixers, as self-attention for vision transformers (ViTs), are intended to perform information communication between different spatial tokens but suffer from considerable computational cost and latency. However, directly removing them will lead to an incomplete model structure prior, and thus brings a significant accuracy drop. To this end, we first develop an RepIdentityFormer base on the reparameterizing idea, to study the token mixer free model architecture. And we then explore the improved learning paradigm to break the limitation of simple token mixer free backbone, and summarize the empirical practice into 5 guidelines. Equipped with the proposed optimization strategy, we are able to build an extremely simple vision backbone with encouraging performance, while enjoying the high efficiency during inference. Extensive experiments and ablative analysis also demonstrate that the inductive bias of network architecture, can be incorporated into simple network structure with appropriate optimization strategy. We hope this work can serve as a starting point for the exploration of optimization-driven efficient network design." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.731, + 0.21, + 0.747 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.47, + 0.879 + ], + "angle": 0, + "content": "The monumental advance in computer vision in the past few years was partly brought by the revolution of vision backbones, including convolutional neural networks (ConvNets) [13, 17, 25, 30] and vision transformers (ViTs) [14, 38]. Both of them have particular modules in their basic building blocks that aggregate information between different spatial locations, which are called token mixer [46], such as self-attention for ViTs. Although the effective" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.321, + 0.885, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.553, + 0.893, + 0.61 + ], + "angle": 0, + "content": "Figure 1. Latency analysis of different components in ViT-Base [14]. (a) For token mixer (self-attention), the latency occupies about \\(46.3\\%\\) of the backbone. (b) Our motivation was to remove the token mixer while striving to keep the performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.894, + 0.716 + ], + "angle": 0, + "content": "ness of token mixer has been demonstrated on many vision tasks [5, 6, 24, 45], its computational complexity typically takes up a significant portion of the network. In practice, heavy token mixers make the vision backbone limited especially on the edge-side devices due to the issue of speed and computation cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "There have been several attempts in the literature to investigate efficient token mixers for slimming vision backbones [29, 31, 46]. Although those works have already achieve competitive performance with light-weight design, they do retain the token mixers, which brings non-negligible increase in latency, as illustrated in Fig. 1. The recent work [47] finds that removing the token mixer is possible but leads to performance degeneration. Those explorations in efficient token mixers inspire us to think that can we keep the vision backbone effective but removing the token mixer? The resulting token mixer free vision backbone is expected to be efficient and effective for the realistic application." + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.234, + 0.901 + ], + "angle": 0, + "content": "* Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14443" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "In this work, we first review the current model architectures and learning paradigms. Most of the previous works concentrate on the improvement of the architecture while adopting the conventional supervised learning to optimize the model from scratch. Differently, we propose to adopt the simplified model architecture, and explore the learning paradigm design to fully exploit the potential of the simple model. We aim to simultaneously maintain the efficiency and efficacy of token mixer free vision backbone (namely IdentityFormer, in Fig. 1-(b)). To this end, we investigate the simple and yet effective learning strategy, knowledge distillation (KD) [18] thoroughly in the following sections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.41 + ], + "angle": 0, + "content": "Our main idea is distilling the knowledge from powerful teacher model (with token mixer) to the student model (token mixer free). We instantiate the re-parameterizing idea to enlarge the modeling capacity of student network but retain its efficiency, as shown in Fig. 2. Specifically, the simple affine transformation is introduced into student model, to replace the token mixer for training. The parameters of affine transformation can be merged into LayerNorm [2] during inference, which makes the student token mixer free finally." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.473, + 0.593 + ], + "angle": 0, + "content": "We empirically summarize the our learning strategy as the following guidelines, hope to shed light on how to learn the extremely simple model. Concretely, 1) soft distillation without using ground-truth labels is more effective; 2) using affine transformation without distillation is difficult to tailor the performance degeneration; 3) the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator; 4) teacher with large receptive field is beneficial to improve receptive field limited student; 5) loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.473, + 0.806 + ], + "angle": 0, + "content": "Based on the above guidelines, we finally obtain a token mixer free vision model with competitive performance enjoying the high efficiency, dubbed as \\( \\underline{\\text{RepIdentityFormer}} \\) (RIFormer). RIFormer shares nearly the same macro and micro design as MetaFormer [46], but safely removing all token mixers. The quantitative results show that our networks outperform many prevailing backbones with faster inference speed on ImageNet-1K [8]. And the ablative analyses on the feature distribution and Effective Receptive Fields (ERFs) also demonstrate that the inductive bias brought by an explicit token mixer, can be implicitly incorporated into the simple network structure with appropriate optimization strategies. In summary, the main contributions of our work are as the following:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.468, + 0.856 + ], + "angle": 0, + "content": "- We propose to explore the vision backbone by developing advanced learning paradigm for simple model architecture, to satisfy the demand of realistic application." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We instantiate the re-parameterizing idea to build a token mixer free vision model, RIFormer, which owns the improved modeling capacity for the inductive bias while" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.783, + 0.107 + ], + "angle": 0, + "content": "enjoying the efficiency during inference." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.107, + 0.892, + 0.151 + ], + "angle": 0, + "content": "- Our proposed practical guidelines of distillation strategy has been demonstrated effective in keeping the vision backbone competitive but removing the token mixer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.165, + 0.642, + 0.18 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.189, + 0.787, + 0.204 + ], + "angle": 0, + "content": "2.1. Vision Transformer Acceleration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Vision transformer is a inference slow, energy intensive backbone due to its quadratic computational cost of the self-attention, and therefore unfriendly to deploy on resource-limited edge devices, calling for compression techniques. Various technology route are designed for vision transformer slimming, such as distilling an efficient transformer with fewer depths and embedding dimensions [16,38,39,44, 51], pruning or merging unimportant tokens [3,21,28,29], applying energy efficient operations [23, 33], or designing efficient attention alternatives [4,24,31], etc. Different from these lines, our work proposes a novel angle of totally removing the complicated token mixer in a backbone while keep satisfactory performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.417, + 0.773, + 0.433 + ], + "angle": 0, + "content": "2.2. Structural Re-parameterization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Structural re-parameterization [12, 13, 49] is a training technique which decouples the training-time and inference-time architectures. For example, RepVGG [13] is a plain VGG-style architecture with attractive performance and speed during inference, and a powerful architecture with manually added \\(1 \\times 1\\) branch and identity mapping branch during training. Similarly, such technique can be further extended to super large kernel ConvNets [12], MLP-like models [9], network pruning [11] and special optimizer design [10]. In this paper, we follow the technique to introduce parameters and equivalently absorb them into LN layer after training. The extra weights after proper optimization can help the model learn useful representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.758, + 0.665 + ], + "angle": 0, + "content": "3. Preliminary and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.735 + ], + "angle": 0, + "content": "In this section, we first briefly recap the concept of token mixer. Then, we revisit their inevitable side effects on inference speed through an empirical latency analysis, and thus introduce the motivation of our paper." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.862, + 0.758 + ], + "angle": 0, + "content": "3.1. Preliminary: The Concept of Token Mixer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The concept token mixer is a structure that performs token mixing functions in a given vision backbone. It allows information aggregation from different spatial positions [46]. For instance, self-attention module serves as the token mixer in ViT [14] by performing the attention function in parallel between components in queries, keys and values matrices, which are linearly projected from the input feature. Moreover, ResMLP [37] applies a cross-patch linear sublayer by treating Spatial MLP as token mixer. The" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14444" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.449, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.254, + 0.456, + 0.267 + ], + "angle": 0, + "content": "Figure 2. Structural re-parameterization of a RIFormer block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.271, + 0.47, + 0.302 + ], + "angle": 0, + "content": "computational and memory costs of the aforementioned token mixers are quadratic to the image scale." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.311, + 0.199, + 0.325 + ], + "angle": 0, + "content": "3.2. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.575 + ], + "angle": 0, + "content": "In this section, we take our eyes on the side effects of token mixers through a quantitative latency analysis on the ViT [14] model. We start with a modified 12-layer ViT-Base model containing only input embedding, without any operation in each of its basic building blocks. Then we gradually add the operation component (e.g., LN, Attention, Channel MLP, etc.) to each basic block, and the model finally comes to ViT-Base without the global average pooling layer and the classifier head. For each model, we take a batch size of 2048 at \\(224^2\\) resolution with one A100 GPU and calculate the average time over 30 runs to inference that batch. The whole process is repeated for three times and we take the medium number as the statistical latency. As shown in Fig. 1, after stacking the regular number of 12 layers, token mixer can bring an additional latency of 1433.6ms, occupying about \\(46.3\\%\\) of the backbone." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.576, + 0.469, + 0.788 + ], + "angle": 0, + "content": "According to the above analysis, token mixer brings significant side effects on the latency to the model, which makes it limited for realistic application. The observation naturally raises a question: can we keep the backbone effective but removing token mixer? Specifically, a recent work [47] introduces the MetaFormer model without any token mixer in its basic building block and finds that it raises a non-negligible performance degeneration. Based on those findings, we propose to exploit the full potential of the extremely simple model by incorporating the inductive bias with the advanced optimization strategies, such as knowledge distillation [18, 38, 51], structural reparameterization [12, 13], etc. And we present all the exploration details in the remaining of this work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.389, + 0.818 + ], + "angle": 0, + "content": "4. Exploring RIFormer: A Roadmap" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we present a trajectory going from a fully supervised approaches for RIFormer to more advanced training paradigms. During the journey we investigate and develop different optimization schemes for transformer-like models, while maintaining the inference-time model as the" + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.093, + 0.882, + 0.139 + ], + "angle": 0, + "content": "
Token MixerTraining recipeImageNet top-1 acc (%)
PoolingCE Loss75.01
IdentityCE Loss72.31
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.144, + 0.892, + 0.172 + ], + "angle": 0, + "content": "Table 1. Results of different token mixers on MetaFormer using cross-entropy loss." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.176, + 0.871, + 0.266 + ], + "angle": 0, + "content": "
TMLabelTeacherImageNet top-1 acc (%)
Identity✓✗72.31
Identity✓hard73.51
Identity✗hard72.86
Identity✓soft73.64
Identity✗soft74.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.269, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Table 2. Results of different teacher type in normal/label-free RIFformer-S12 with identity mapping as token mixer." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.301, + 0.869, + 0.391 + ], + "angle": 0, + "content": "
TMLabelKD typeImageNet top-1 acc (%)
Affine✓×72.25
Affine✓hard73.44
Affine×hard72.77
Affine✓soft72.10
Affine×soft74.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.423 + ], + "angle": 0, + "content": "Table 3. Results of different distillation type in normal/label-free RIFormer-S12 with affine transformation as token mixer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.597 + ], + "angle": 0, + "content": "same. The baseline RIFormer we use has exactly the same macro architecture and model size as recently-developed MetaFormer [46], the difference only lies in the fact that no token mixer is used in its basic building blocks during inference. We control the computational complexity of RIFormer-S12 models comparable to PoolFormer-S12 [46], with about 12M parameters and 1.8G MAC. All RIFormer-S12 models in this section are trained and evaluated on ImageNet-1K for 120 epochs. The details of hyper-parameters are shown in Sec.1 of the appendix. The roadmap of our exploration is as follows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.836, + 0.621 + ], + "angle": 0, + "content": "4.1. Vision Backbone Without Token Mixer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Our exploration is directed to remove token mixer in each basic block of a inference-time model vision backbone to obtain a higher inference speed while striving to keep the performance. Thus, we start with a RIFormer-S12 model with a fully supervised training scheme using CE loss, mainly follows [46]. As a performance reference, we compare the results with PoolFormer-S12, since it use only basic pooling operation as token mixer and the performance gap can thus, be attributed to the absence of basic token mixing function. As shown in Tab. 1, RIFormer-S12 with a trivial supervised training can lead to an unacceptable performance drop (2.7% top-1 accuracy) compared to PoolFormer-S12. The results show that without token mixer in each building block, it is limited for regular supervised learning in helping the model learn useful information from images, calling for advanced training procedure." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We then investigate and modify a series of training paradigms to improve the inferior baseline performance," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14445" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.085, + 0.895, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.307, + 0.515, + 0.321 + ], + "angle": 0, + "content": "(a) Overall training procedure with \\(L\\) RIFormer blocks" + }, + { + "type": "image_caption", + "bbox": [ + 0.731, + 0.307, + 0.848, + 0.32 + ], + "angle": 0, + "content": "(b) Module imitation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Figure 3. (a) Overall training procedure of RIFormer. Following the macro and micro design of [46], RIFormer removes token mixer in each block. (b) Module imitation technique aims to mimic the behavior of token mixer via a simple affine transformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.487 + ], + "angle": 0, + "content": "which can be summarized as 1) knowledge distillation, 2) teacher type influence, 3) structural re-parameterization, 4) the proposed module imitation technique, 5) load partial parameters from teacher. Since we aim at exploring the influence of different advanced training recipes instead of network architecture, inference-time model architecture is always kept the same at intermediate steps. Next, we share 5 useful guidelines for training RIFformer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.497, + 0.336, + 0.513 + ], + "angle": 0, + "content": "4.2. Distillation Paradigm Design" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.581 + ], + "angle": 0, + "content": "We now study the knowledge distillation [18, 38] of a RIFormaler student by a general vision backbone teacher with token mixer, and summarize how to effectively utilize the \"soft\" labels coming from the strong teacher network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Guideline 1: soft distillation without using ground-truth labels can be effective for student without token mixer. Basically, most of the existing KD methods are designed for models with token mixer. For example, it is common practice to help a student convnet by learning from both ground-truth labels and the soft labels predicted by a teacher convnet. Moreover, some observations from DeiT [38] show that using the hard labels instead of soft labels as a supervised target, can improves transformer significantly. In contrast, the token mixer free backbone do not have explicit patch aggregating modules in its basic block. The distillation of it is should be thus, different from that of conventional backbones. Specifically, although RIFormer shares the same macro structure as transformer, it still cannot be treated as a student transformer because we have deliberately removed the token mixer from each building block. However, we also do not prefer viewing it as a pure convnet since RIFormer bears a resemblance to transformer in terms of macro/micro-level architecture design. Therefore, we are motivated to explore a suitable KD method for RIFormer with promising performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.682 + ], + "angle": 0, + "content": "Typically, the cross-entropy objective is to assist a student network reproduce the hard accurate label, and we argue that the process may be unsuitable for RIFormer. First, the ground-truth hard label can be transformed to a soft distribution by label-smoothing regularization [35], with weights \\(1 - \\varepsilon\\) for the true label and \\(\\varepsilon\\) shared each classes. The unlearned uniform distribution across the negative classes is less informative, and may interfere with the learned soft distribution given by teacher. Second, \\(1 \\times 1\\) convolutions actually dominate basic building block in RIFormer, \"mixing\" only the per-location features but not spatial information. Such a simplified design may require richer information in the supervised labels. To demonstrate this, Tab. 2 compare the performance of four different settings. The default teacher is a GFNet-H-B [31] (54M parameters). Hard distillation with true labels improves the accuracy from \\(72.31\\%\\) to \\(73.51\\%\\). It shows that a teacher with token mixer has a positive effect on a student without token mixer. In fact, the combination of using a soft distillation without true labels performs the best, improving the network performance to \\(74.05\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.759 + ], + "angle": 0, + "content": "Remark 1. Supervised learning with true label does not seem to be the most suitable way for a crude model without token mixer. A teacher with token mixer can help to guide the training, but still fails to fully recover the performance gap from removing token mixer, calling for other strategies." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.771, + 0.866, + 0.789 + ], + "angle": 0, + "content": "4.3. Re-parameterization for Identity Mapping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Guideline 2: using affine transformation without tailored distillation, is hard to recover the performance degradation. In this part, we adopt the idea of Structural Reparameterization [9, 12, 13] methodology, which usually takes a powerful model for training and equivalently converts to a simple model during inference. Specifically, the inference-time token mixer module in RIFormer can be" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14446" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.455, + 0.219 + ], + "angle": 0, + "content": "
TMFeatRelLayerImageNet top-1 acc (%)
Affine00-74.07
Affine400674.49
Affine600674.77
Affine800674.81
Affine8010675.08
Affine8020674.82
Affine8040675.00
Affine8020475.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.224, + 0.434, + 0.238 + ], + "angle": 0, + "content": "Table 4. Results of different module imitation setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.473, + 0.427 + ], + "angle": 0, + "content": "viewed as an identity mapping following a LN layer. Thus, the training-time module should satisfy at least two basic requirements: 1) per-location operator for allowing equivalent transformation; 2) parametric operator for allowing extra representation ability. Accordingly, we apply an affine transformation operator to replace the identity mapping during training, which only performs channel-wise scaling and shifts, as shown in Fig. 2. The affine operator and its preceding LN layer can be converted into a LN with modified weights, thus it can be equivalently converted into an identity mapping during inference. Denote the input feature as \\(\\mathbf{M} \\in \\mathbb{R}^{N \\times C \\times H \\times W}\\), the affine operator can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.433, + 0.47, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A f f i n e} (\\mathrm {M}, \\mathbf {s}, \\mathbf {t}) _ {:, i,:,:} = \\mathbf {s} _ {i} \\mathrm {M} _ {:, i,:,:} + \\mathbf {t} _ {i} - \\mathrm {M} _ {:, i,:,:}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.473, + 0.642 + ], + "angle": 0, + "content": "where \\(\\mathbf{s} \\in \\mathbb{R}^C\\) and \\(\\mathbf{t} \\in \\mathbb{R}^C\\) are learnable weight vectors. We follow [46] to add a subtraction of the input during implementation due to the residual connection, and thus does not merge the first and third terms in Eq. 1. Then, we describe how to merge the affine transformation into its preceding LN layer, so the training-time model can be equivalently converted to model for deploy but no longer has token mixer in its blocks. We use \\(\\mu, \\sigma, \\gamma, \\beta\\) as the mean, standard deviation and learned scaling factor and bias of the preceding LN layer. Denote \\(\\mathrm{T}^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}\\), \\(\\mathrm{T}'^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}\\) respectively as the input and output of an affine residual sub-block in Fig. 2-(a). During the training time, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.649, + 0.47, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathrm {T} ^ {\\prime (a)} = \\operatorname {A f f i n e} (\\mathrm {L N} (\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma , \\beta), \\mathbf {s}, \\mathbf {t}) - \\mathrm {T} ^ {(a)} \\qquad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.47, + 0.752 + ], + "angle": 0, + "content": "where LN is the LN function, which is implemented by GroupNorm API in PyTorch (setting the group number as 1) following [46]. During inference time, there only exists an identity mapping followed by a LN layer in the residual sub-block. Thus, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.76, + 0.47, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\mathrm {T} ^ {\\prime (a)} = \\operatorname {L N} \\left(\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma^ {\\prime}, \\beta^ {\\prime}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.471, + 0.836 + ], + "angle": 0, + "content": "where \\(\\gamma^\\prime\\) and \\(\\beta^\\prime\\) are the weight and bias parameters of the merged LN layer. Based on the equivalence of Eq. 2 and Eq. 3, for \\(\\forall 1\\leq i\\leq C\\), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.844, + 0.47, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\pmb {\\gamma} _ {i} ^ {\\prime} = \\pmb {\\gamma} _ {i} (\\mathbf {s} _ {i} - 1), \\quad \\pmb {\\beta} _ {i} ^ {\\prime} = \\pmb {\\beta} _ {i} (\\mathbf {s} _ {i} - 1) + \\mathbf {t} _ {i}, \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The proof and PyTorch-like code of the affine transformation and re-parameterization process is shown in Sec.2 and" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.089, + 0.882, + 0.233 + ], + "angle": 0, + "content": "
Teacher (T)T.acc (%)MIImageNet top-1 acc (%)
PoolFormer-M48 [46]82.5✗73.63
Swin-B* [24]85.2✗73.12
Pyramid ViG-B [15]83.7✗73.25
GFNet-H-B [31]82.9✗74.07
PoolFormer-M48 [46]82.5✓74.83
Swin-B* [24]85.2✓74.52
Pyramid ViG-B [15]83.7✓74.25
GFNet-H-B [31]82.9✓75.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.237, + 0.892, + 0.266 + ], + "angle": 0, + "content": "Table 5. Results of different teachers on RIFormer-S12 w/ or w/o module imitation (MI). * indicates ImageNet-22K pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Sec.3 of the appendix, respectively. Since the LN layer does not have a pre-computed mean and standard deviation during inference time, their specific values are input adaptive, which do not affect the equivalence of transform." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.893, + 0.501 + ], + "angle": 0, + "content": "Remark 2. Compare Tab. 3 with Tab. 2, directly applying structural re-parameterization method shows no advantages. We attribute this phenomenon to the fact that the affine transformation in the LN layer is a linear transformation that can be directly merged with the extra affine operator we introduced (if do not add any nonlinear function in between). Therefore, if both are supervised only by the output of the model, the potential of the additional parameters may not be fully exploited. Meanwhile, the isomorphic design of teacher and student inspires us to explore suitable methods for knowledge transfer of modules at each layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.508, + 0.673, + 0.523 + ], + "angle": 0, + "content": "4.4. Module Imitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.819 + ], + "angle": 0, + "content": "Guideline 3: the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator. The previous KD methods we tried only focus on the output of between teacher and student networks. We propose module imitation (MI) method, which present to utilize the useful information in the teacher's token mixer. Specifically, a pretrained PoolFormer-S12 [46] is utilized as a teacher network. As shown in Fig. 3, we expect the simple affine operator (with its preceding LN layer) to approximate the behavior of that of a basic token mixer during training. Denote \\( f(\\cdot), \\mathrm{T}^{(a),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M} \\) as the affine operator and the input of the \\( m \\)-th layer of RIFormal in which \\( \\mathcal{M} \\) is the intermediate layers set we used, and \\( g(\\cdot), \\mathrm{T}^{(t),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M} \\) are that of the teacher network, respectively. We abbreviate \\( \\mathrm{LN}(\\cdot, \\mu, \\sigma, \\gamma, \\beta) \\) as \\( \\mathrm{LN}(\\cdot) \\) for simplicity. The mean squared error (MSE) of the inputs between the LN layer of affine operator and token mixer can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.828, + 0.892, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i n} = \\alpha_ {1} \\| \\mathrm {L N} (\\mathrm {T} ^ {(a), m}) - \\mathrm {L N} (\\mathrm {T} ^ {(t), m}) \\| _ {F} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\alpha_{1} = 1 / NCHW\\). Note that the input feature of the current layer is the output feature of the previous one. Therefore, we propose to match the output features of this" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14447" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "block (i.e., the input features of the next subsequent block) in practice, which can be seen as a hidden state distillation in transformers [16, 19, 40, 41, 51]." + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.148, + 0.469, + 0.169 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i n} ^ {\\prime} = \\alpha_ {1} \\| T ^ {(a), m + 1} - T ^ {(t), m + 1} \\| _ {F} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.178, + 0.469, + 0.209 + ], + "angle": 0, + "content": "The hidden-state distillation based on relation matrices [16, 51] is then applied on the output feature:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.219, + 0.47, + 0.239 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e l} = \\alpha_ {2} \\| \\mathcal {R} (\\mathrm {T} ^ {(a), m + 1}) - \\mathcal {R} (\\mathrm {T} ^ {(t), m + 1}) \\| _ {F} ^ {2}, \\qquad (7)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.25, + 0.469, + 0.297 + ], + "angle": 0, + "content": "where \\(\\alpha_{2} = 1 / NH^{2}W^{2}\\), \\(\\mathcal{R}(T) = \\tilde{T}\\tilde{T}^{\\top}\\), \\(\\tilde{T}\\) denotes normalize \\(T\\) at the last dimension. Considering the MSE of the outputs between affine operator and token mixer:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.308, + 0.469, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o u t} = \\alpha_ {1} \\| f (\\mathrm {L N} (\\mathrm {T} ^ {(a), m})) - g (\\mathrm {L N} (\\mathrm {T} ^ {(t), m})) \\| _ {F} ^ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.469, + 0.367 + ], + "angle": 0, + "content": "Combining Eq. 6, Eq. 7 and Eq. 8, the final loss function with module imitation is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.38, + 0.469, + 0.398 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {s o f t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {i n}} ^ {\\prime} + \\lambda_ {2} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {3} \\mathcal {L} _ {\\text {r e l}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.469, + 0.558 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{soft}\\) is the soft logit distillation target in Sec. 4.2, \\(\\lambda_{1},\\lambda_{2},\\lambda_{3}\\) is the hyper-parameter for seeking the balance between loss functions. In Tab. 4, Feat and Rel are number of epochs of using \\((\\mathcal{L}_{in}^{\\prime},\\mathcal{L}_{out})\\) and \\(\\mathcal{L}_{rel}\\), Layer represents the number of intermediate layers we used. The results show positive effect of module imitation on the student RIFformer in different circumstances. With a 4 layer setting and the usage of affine operator, we get the best result of \\(75.13\\%\\), already surpassing the PoolFormer-S12's result of \\(75.01\\%\\) in Tab. 1. From now on, we will use this setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.469, + 0.679 + ], + "angle": 0, + "content": "Remark 3. We deem a reason for that phenomenon might be that module imitation helps the affine operator implicitly benefit from the supervision of the teacher's token mixer, while not losing the convenience of explicitly merging the preceding LN layer. Besides, we find module imitation can effectively shift the feature distribution closer to the teacher network and show larger Effective Receptive Fields (ERFs). Please refer to Sec. 5.3 for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Guideline 4: teacher with large receptive field is beneficial to improve student with limited receptive field. Tab. 5 compares student performance with different teacher architectures. Although GFNet-H-B [31] does not show the highest ImageNet top-1 performance among teachers, it can still serves as a better choice, no matter whether module imitation is used or not." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Remark 4. The fact is probably attributed to the receptive field gap between teacher and student. As explained by [1], inductive bias can be transferred from one model to another through distillation. According to this study, model with large receptive field (e.g., GFNet with learnable global filters in the frequency domain) can be better teacher for student RIFormer with limited receptive field." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "Guideline 5: loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance. Our method can be categorized as a model compression technique that aims at removing the token mixer in basic blocks for acceleration. Inspired by previous methods, including knowledge distillation [32, 34], quantization [22, 26], and model acceleration [29] that initialize the weights of the light-weight network using (or partly using) the corresponding weights of the pre-trained heavy network, we explore a suitable initialization method. Since our goal is to remove only the token mixer, the weights of the remaining part still remain and are not paid enough attention in the previous journey. We observe that initializing the weights of RIFformer (except the affine operator) with the corresponding teacher network further boosts the performance from \\(75.13\\%\\) to \\(75.36\\%\\). This brings us to the final paradigm for training RIFformer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Closing remarks. So far, we have finished our exploration and discovered a suitable paradigm for training the RIFformer. It has the approximately the same macro design with MetaFormer [46], but does not require any token mixer. Equipped with the propsoed optimization methods, RIFformer can outperform complicated models with token mixers for ImageNet-1K classification. These encouraging findings inspire us to answer the following questions in the next section. 1) The scaling behavior of such extremely simple architecture with our training paradigm. 2) The generalizability of the paradigm on different teachers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.634, + 0.55 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.687, + 0.573 + ], + "angle": 0, + "content": "5.1. Image classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Setup. For ImageNet-1K [8] with 1.2M training images and 50000 validation images, we generally apply the training scheme in [46] while following the guidelines in Sec. 4. The data augmentation contains MixUp [50], CutMix [48], CutOut [52] and RandAugment [7]. As a model compression work on removing token mixer, bridging the performance gap caused by removing the token mixer is definitely our first priority, instead of proposing a strong baseline. Therefore, we use a prolonged the training epochs of 600. We also finetune the pre-trained models for 30 epochs with input resolution of \\(384^2\\). More details are in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Main results. Tab. 6 shows the results of RIFormer on ImageNet classification. We pay main attention to the throughput metrics since our primary consideration is to satisfy latency requirements for edge devices. As expected, favorable speed advantage is achieved since RIFormer does not contain any token mixer in its building block, compared with other type of backbones. Surprisingly, with such fast inference, RIFormers successfully remove all token mixers using our training approach without affecting the performance. For example, RIFormer-M36 can pro" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14448" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.873, + 0.574 + ], + "angle": 0, + "content": "
Token MixerOutcome ModelImage SizeParams (M)MACs (G)Throughput (images/s)Top-1 (%)
ConvolutionRSB-ResNet-34 [17,43]224223.76653.7575.5
RSB-ResNet-50 [17,43]224264.12732.8579.8
RSB-ResNet-101 [17,43]224457.91856.4881.3
RSB-ResNet-152 [17,43]2246011.61308.2681.8
Attention▲ DeiT-S [38]224224.63092.0279.8
▲ DeiT-B [38]2248617.51348.7681.8
▲ PVT-Small [42]224253.81622.5379.8
▲ PVT-Medium [42]224446.71190.4881.2
▲ PVT-Large [42]224619.8865.3381.7
Spatial MLPMLP-Mixer-B/16 [36]2245912.71855.4576.4
ResMLP-S24 [37]224306.03228.7579.4
ResMLP-B24 [37]22411623.0298.9481.0
Swin-Mixer-T/D6 [24]256234.01625.5979.7
Swin-Mixer-B/D24 [24]2246110.41131.6081.3
2D FFTGFNet-H-Ti [31]224152.11979.5680.1
GFNet-H-S [31]224324.61434.1981.5
GFNet-B [31]224437.91771.0780.7
GFNet-H-B [31]224548.6939.2082.9
Pooling○ PoolFormer-S12 [46]224121.84160.1877.2
○ PoolFormer-S24 [46]224213.42140.2080.3
○ PoolFormer-S36 [46]224315.01440.3781.4
○ PoolFormer-M36 [46]224568.81009.4582.1
○ PoolFormer-M48 [46]2247311.6761.9382.5
None★ RIFounder-S12°224121.84899.80 (↑17.8%)76.9
★ RIFounder-S24°224213.42530.48 (↑18.2%)80.3
★ RIFounder-S36°224315.01699.94 (↑18.0%)81.3
★ RIFounder-M36°224568.81185.33 (↑17.4%)82.6
★ RIFounder-M48°2247311.6897.05 (↑17.7%)82.8
★ RIFounder-S12‡384125.41586.5178.3
★ RIFounder-S24‡3842110.0819.4081.4
★ RIFounder-S36‡3843114.7552.0782.2
★ RIFounder-M36‡3845625.9403.1583.4
★ RIFounder-M48‡3847334.1304.4383.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.575, + 0.891, + 0.604 + ], + "angle": 0, + "content": "Table 6. Results of models with different types of token mixers on ImageNet-1K. denotes training with prolonged 600 epochs. denotes fine-tuning from the ImageNet pre-trained model for 30 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.82 + ], + "angle": 0, + "content": "cess more than 1185 images at \\(224^2\\) resolution per second, with the top-1 accuracy of \\(82.6\\%\\). In comparison, the recent baseline PoolFormer-M36 [46] with a Pooling token mixer, can process 1009 images of the same size with a worse \\(82.1\\%\\) accuracy. We also compare with an efficient backbone, GFNet [31]. It conducts token mixing via a global filter, which consists an FFT, an element-wise multiplication, and an IFFT, with a total computational complexity \\(\\mathcal{O}(N\\log N)\\). With a 939 throughput, GFNet-H-B gets \\(82.9\\%\\) accuracy while our RIFformer-M48 can still reaches a comparable \\(82.8\\%\\) accuracy with on par throughput of 897. Meanwhile, the body of inference-time RIFformer is dominated by only \\(1\\times 1\\) conv following LN, without complex 2D FFT or attention, friendly for hardware specialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Notably, without token mixer, RIFormer cannot even perform basic token mixing operation in its building blocks. However, the ImageNet experiments demonstrate that with the proposed training paradigm, RIFormer still shows promising results. We can only deem the reason behind the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.671 + ], + "angle": 0, + "content": "fact might be that optimization strategy plays a key role. RIFormer is readily a starting recipe for the exploration of optimization-driven efficient network design, and rest assured of the performance with advanced training schemes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.677, + 0.663, + 0.692 + ], + "angle": 0, + "content": "5.2. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Effectiveness of module imitation. As an important way for the extra affine operator to learn suitable weights, module imitation is based on distillation. Therefore, we compare it with the hidden state feature distillation approach (with relations). Taking the paradigm in Sec. 4.2 by soft distillation without CE loss, we get the results in Tab. 7. More details for Sec. 5.2 can be found in Sec.4 of the appendix. With feature distillation, the accuracy is \\(0.46\\%\\) lower than that of module imitation, showing module imitation's positive effect on the optimization of the extra weights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Comparisons of different acceleration strategy. Next, we discuss whether the token removing is better than other sparsification strategies. Based on the PoolFormer [46]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14449" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.209, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.199, + 0.187, + 0.209 + ], + "angle": 0, + "content": "(a) PoolFormer-S12" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.338, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.199, + 0.311, + 0.209 + ], + "angle": 0, + "content": "(b) RIFormer-S12" + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.089, + 0.47, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.199, + 0.451, + 0.21 + ], + "angle": 0, + "content": "(c) RIFormer-S12 (MI)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.217, + 0.468, + 0.245 + ], + "angle": 0, + "content": "Figure 4. The Effective Receptive Field (ERF) of PoolFormer-S12 and RIFlower-S12 with/without using module imitation." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.25, + 0.453, + 0.312 + ], + "angle": 0, + "content": "
Token MixerFeature distillation schemeTop-1 (%)
IdentityNone74.05
IdentityFeature distill74.90
AffineModule imitation75.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.317, + 0.465, + 0.331 + ], + "angle": 0, + "content": "Table 7. Ablation study of the effectiveness of module imitation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.468, + 0.46 + ], + "angle": 0, + "content": "baseline, we first construct a slim PoolFormer-S9 and PoolFormer-XS12 by reducing the depth to 9 and by maintaining about \\(\\frac{5}{6}\\) of its width, i.e., embedding dimension, to obtain comparable inference speed with our RIFormer-S12. We also follow the soft distillation paradigm in Sec. 4.2. Tab. 8 shows the results. Directly pruning depths or width cannot render a better performance than ours without latency-hungry token mixer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.468, + 0.587 + ], + "angle": 0, + "content": "Generalization to different teachers. In order to verify the proposed training paradigm a general compression technique, we adopt the architecture modifications in [47] for student and change teacher to the other 4 MetaFormer baselines [47], with teacher token mixer as rand matrices, pooling, separable depthwise convolutions, and attention, respectively. Tab. 9 shows that our method has a positive effect in different depth settings and teacher circumstances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.598, + 0.341, + 0.614 + ], + "angle": 0, + "content": "5.3. Analysis of Module Imitation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.468, + 0.758 + ], + "angle": 0, + "content": "Module imitation (MI) shifts the feature distribution of the RIFformer model to be closer to the teacher. The effect of the module imitation is explicitly shown in Fig. 5. It can be observed that PoolFomer-S12 and RIFformer-S12 show a clear difference in feature distribution of Stage 1 and Stage 4. After applying the proposed module imitation, the distribution of RIFformer-S12 are basically shifted toward that of the PoolFomer-S12, demonstrating its effect on helping student learn useful knowledge from the teacher." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Module imitation helps showing larger Effective Receptive Field (ERF). ERF [27] reflects how large an area of the image the trained model can respond to or capture information about how large an object. We follow [12, 20] to visualize the ERF via measuring the aggregated contributions of each pixel of the input to the central points of the output feature. Since RIFormer removes all token mixers, it exhibits an expectedly much smaller ERF than PoolFormer, as shown in Fig. 4. There is only a square of pixels emerg-" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.088, + 0.696, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.891, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.217, + 0.892, + 0.244 + ], + "angle": 0, + "content": "Figure 5. Visualization of the feature distribution of the first and last stage of PoolFormer-S12 and RIFormal-S12." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.248, + 0.875, + 0.323 + ], + "angle": 0, + "content": "
ModelTypeThroughputTop-1 (%)
PoolFormer-S12None4160.1875.01
PoolFormer-S9Depth5025.7174.78
PoolFormer-XS12Width4780.2875.11
RIFounder-S12TM4899.8075.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.511, + 0.333, + 0.88, + 0.347 + ], + "angle": 0, + "content": "Table 8. Results of comparison with depth or width slimming." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.351, + 0.884, + 0.455 + ], + "angle": 0, + "content": "
Token MixerTeacherTop-1 (%)
Affine (12 layers)None72.75
Affine (12 layers)RandFormer-S12 [47]75.62
Affine (12 layers)PoolFormer V2-S12 [47]75.87
Affine (18 layers)None75.01
Affine (18 layers)ConvFormer-S18 [47]77.53
Affine (18 layers)CAFormer-S18 [47]77.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.542, + 0.458, + 0.848, + 0.471 + ], + "angle": 0, + "content": "Table 9. Results of generalization to other teachers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.567 + ], + "angle": 0, + "content": "ing with red color in the whole region, much smaller than PoolFormer. However, surprisingly, we can observe that red color widely distributed in all locations after training with module imitation. It seems that although there's no explicit structural change, module imitation still help change the learned weights and show larger ERF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.756, + 0.596 + ], + "angle": 0, + "content": "6. Limitations and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.756 + ], + "angle": 0, + "content": "This paper investigates removing token mixer of the basic building block in a vision backbone, motivated by their considerable latency cost. To keep the remaining structure still effective, we thoroughly revisits the training paradigm. We observe that appropriate optimization strategy can effectively help a token mixer-free model learn useful knowledge from another model, boosting its performance and bridge the gap caused by incomplete structure. Limitations are that more vision tasks, including detection, deblurring, etc. are not discussed, and we will work on them in the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.661, + 0.787 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This paper is partly supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, Shanghai Postdoctoral Excellence Program (No.2022235), the National Natural Science Foundation of China (Grant No.61991450) and the Shenzhen Science and Technology Program (JCYJ20220818101001004)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14450" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Samira Abnar, Mostafa Dehghani, and Willem Zuidema. 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Token mixers, as self-attention for vision transformers (ViTs), are intended to perform information communication between different spatial tokens but suffer from considerable computational cost and latency. However, directly removing them will lead to an incomplete model structure prior, and thus brings a significant accuracy drop. To this end, we first develop an RepIdentityFormer base on the reparameterizing idea, to study the token mixer free model architecture. And we then explore the improved learning paradigm to break the limitation of simple token mixer free backbone, and summarize the empirical practice into 5 guidelines. Equipped with the proposed optimization strategy, we are able to build an extremely simple vision backbone with encouraging performance, while enjoying the high efficiency during inference. Extensive experiments and ablative analysis also demonstrate that the inductive bias of network architecture, can be incorporated into simple network structure with appropriate optimization strategy. We hope this work can serve as a starting point for the exploration of optimization-driven efficient network design. + +# 1. Introduction + +The monumental advance in computer vision in the past few years was partly brought by the revolution of vision backbones, including convolutional neural networks (ConvNets) [13, 17, 25, 30] and vision transformers (ViTs) [14, 38]. Both of them have particular modules in their basic building blocks that aggregate information between different spatial locations, which are called token mixer [46], such as self-attention for ViTs. Although the effective + +![](images/52123fafbd222c9d4003807e33cb96ab5dbe4aab859c22f83db9bf7326e8e7d9.jpg) +Figure 1. Latency analysis of different components in ViT-Base [14]. (a) For token mixer (self-attention), the latency occupies about $46.3\%$ of the backbone. (b) Our motivation was to remove the token mixer while striving to keep the performance. + +ness of token mixer has been demonstrated on many vision tasks [5, 6, 24, 45], its computational complexity typically takes up a significant portion of the network. In practice, heavy token mixers make the vision backbone limited especially on the edge-side devices due to the issue of speed and computation cost. + +There have been several attempts in the literature to investigate efficient token mixers for slimming vision backbones [29, 31, 46]. Although those works have already achieve competitive performance with light-weight design, they do retain the token mixers, which brings non-negligible increase in latency, as illustrated in Fig. 1. The recent work [47] finds that removing the token mixer is possible but leads to performance degeneration. Those explorations in efficient token mixers inspire us to think that can we keep the vision backbone effective but removing the token mixer? The resulting token mixer free vision backbone is expected to be efficient and effective for the realistic application. + +In this work, we first review the current model architectures and learning paradigms. Most of the previous works concentrate on the improvement of the architecture while adopting the conventional supervised learning to optimize the model from scratch. Differently, we propose to adopt the simplified model architecture, and explore the learning paradigm design to fully exploit the potential of the simple model. We aim to simultaneously maintain the efficiency and efficacy of token mixer free vision backbone (namely IdentityFormer, in Fig. 1-(b)). To this end, we investigate the simple and yet effective learning strategy, knowledge distillation (KD) [18] thoroughly in the following sections. + +Our main idea is distilling the knowledge from powerful teacher model (with token mixer) to the student model (token mixer free). We instantiate the re-parameterizing idea to enlarge the modeling capacity of student network but retain its efficiency, as shown in Fig. 2. Specifically, the simple affine transformation is introduced into student model, to replace the token mixer for training. The parameters of affine transformation can be merged into LayerNorm [2] during inference, which makes the student token mixer free finally. + +We empirically summarize the our learning strategy as the following guidelines, hope to shed light on how to learn the extremely simple model. Concretely, 1) soft distillation without using ground-truth labels is more effective; 2) using affine transformation without distillation is difficult to tailor the performance degeneration; 3) the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator; 4) teacher with large receptive field is beneficial to improve receptive field limited student; 5) loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance. + +Based on the above guidelines, we finally obtain a token mixer free vision model with competitive performance enjoying the high efficiency, dubbed as $\underline{\text{RepIdentityFormer}}$ (RIFormer). RIFormer shares nearly the same macro and micro design as MetaFormer [46], but safely removing all token mixers. The quantitative results show that our networks outperform many prevailing backbones with faster inference speed on ImageNet-1K [8]. And the ablative analyses on the feature distribution and Effective Receptive Fields (ERFs) also demonstrate that the inductive bias brought by an explicit token mixer, can be implicitly incorporated into the simple network structure with appropriate optimization strategies. In summary, the main contributions of our work are as the following: + +- We propose to explore the vision backbone by developing advanced learning paradigm for simple model architecture, to satisfy the demand of realistic application. +- We instantiate the re-parameterizing idea to build a token mixer free vision model, RIFormer, which owns the improved modeling capacity for the inductive bias while + +enjoying the efficiency during inference. + +- Our proposed practical guidelines of distillation strategy has been demonstrated effective in keeping the vision backbone competitive but removing the token mixer. + +# 2. Related Work + +# 2.1. Vision Transformer Acceleration + +Vision transformer is a inference slow, energy intensive backbone due to its quadratic computational cost of the self-attention, and therefore unfriendly to deploy on resource-limited edge devices, calling for compression techniques. Various technology route are designed for vision transformer slimming, such as distilling an efficient transformer with fewer depths and embedding dimensions [16,38,39,44, 51], pruning or merging unimportant tokens [3,21,28,29], applying energy efficient operations [23, 33], or designing efficient attention alternatives [4,24,31], etc. Different from these lines, our work proposes a novel angle of totally removing the complicated token mixer in a backbone while keep satisfactory performance. + +# 2.2. Structural Re-parameterization + +Structural re-parameterization [12, 13, 49] is a training technique which decouples the training-time and inference-time architectures. For example, RepVGG [13] is a plain VGG-style architecture with attractive performance and speed during inference, and a powerful architecture with manually added $1 \times 1$ branch and identity mapping branch during training. Similarly, such technique can be further extended to super large kernel ConvNets [12], MLP-like models [9], network pruning [11] and special optimizer design [10]. In this paper, we follow the technique to introduce parameters and equivalently absorb them into LN layer after training. The extra weights after proper optimization can help the model learn useful representations. + +# 3. Preliminary and Motivation + +In this section, we first briefly recap the concept of token mixer. Then, we revisit their inevitable side effects on inference speed through an empirical latency analysis, and thus introduce the motivation of our paper. + +# 3.1. Preliminary: The Concept of Token Mixer + +The concept token mixer is a structure that performs token mixing functions in a given vision backbone. It allows information aggregation from different spatial positions [46]. For instance, self-attention module serves as the token mixer in ViT [14] by performing the attention function in parallel between components in queries, keys and values matrices, which are linearly projected from the input feature. Moreover, ResMLP [37] applies a cross-patch linear sublayer by treating Spatial MLP as token mixer. The + +![](images/e5ec6657e66492546a60c6e227dbb55d01babf3622c9b5ff50d344e01c5881f7.jpg) +Figure 2. Structural re-parameterization of a RIFormer block. + +computational and memory costs of the aforementioned token mixers are quadratic to the image scale. + +# 3.2. Motivation + +In this section, we take our eyes on the side effects of token mixers through a quantitative latency analysis on the ViT [14] model. We start with a modified 12-layer ViT-Base model containing only input embedding, without any operation in each of its basic building blocks. Then we gradually add the operation component (e.g., LN, Attention, Channel MLP, etc.) to each basic block, and the model finally comes to ViT-Base without the global average pooling layer and the classifier head. For each model, we take a batch size of 2048 at $224^2$ resolution with one A100 GPU and calculate the average time over 30 runs to inference that batch. The whole process is repeated for three times and we take the medium number as the statistical latency. As shown in Fig. 1, after stacking the regular number of 12 layers, token mixer can bring an additional latency of 1433.6ms, occupying about $46.3\%$ of the backbone. + +According to the above analysis, token mixer brings significant side effects on the latency to the model, which makes it limited for realistic application. The observation naturally raises a question: can we keep the backbone effective but removing token mixer? Specifically, a recent work [47] introduces the MetaFormer model without any token mixer in its basic building block and finds that it raises a non-negligible performance degeneration. Based on those findings, we propose to exploit the full potential of the extremely simple model by incorporating the inductive bias with the advanced optimization strategies, such as knowledge distillation [18, 38, 51], structural reparameterization [12, 13], etc. And we present all the exploration details in the remaining of this work. + +# 4. Exploring RIFormer: A Roadmap + +In this section, we present a trajectory going from a fully supervised approaches for RIFormer to more advanced training paradigms. During the journey we investigate and develop different optimization schemes for transformer-like models, while maintaining the inference-time model as the + +
Token MixerTraining recipeImageNet top-1 acc (%)
PoolingCE Loss75.01
IdentityCE Loss72.31
+ +Table 1. Results of different token mixers on MetaFormer using cross-entropy loss. + +
TMLabelTeacherImageNet top-1 acc (%)
Identity✓✗72.31
Identity✓hard73.51
Identity✗hard72.86
Identity✓soft73.64
Identity✗soft74.05
+ +Table 2. Results of different teacher type in normal/label-free RIFformer-S12 with identity mapping as token mixer. + +
TMLabelKD typeImageNet top-1 acc (%)
Affine✓×72.25
Affine✓hard73.44
Affine×hard72.77
Affine✓soft72.10
Affine×soft74.07
+ +Table 3. Results of different distillation type in normal/label-free RIFormer-S12 with affine transformation as token mixer. + +same. The baseline RIFormer we use has exactly the same macro architecture and model size as recently-developed MetaFormer [46], the difference only lies in the fact that no token mixer is used in its basic building blocks during inference. We control the computational complexity of RIFormer-S12 models comparable to PoolFormer-S12 [46], with about 12M parameters and 1.8G MAC. All RIFormer-S12 models in this section are trained and evaluated on ImageNet-1K for 120 epochs. The details of hyper-parameters are shown in Sec.1 of the appendix. The roadmap of our exploration is as follows. + +# 4.1. Vision Backbone Without Token Mixer + +Our exploration is directed to remove token mixer in each basic block of a inference-time model vision backbone to obtain a higher inference speed while striving to keep the performance. Thus, we start with a RIFormer-S12 model with a fully supervised training scheme using CE loss, mainly follows [46]. As a performance reference, we compare the results with PoolFormer-S12, since it use only basic pooling operation as token mixer and the performance gap can thus, be attributed to the absence of basic token mixing function. As shown in Tab. 1, RIFormer-S12 with a trivial supervised training can lead to an unacceptable performance drop (2.7% top-1 accuracy) compared to PoolFormer-S12. The results show that without token mixer in each building block, it is limited for regular supervised learning in helping the model learn useful information from images, calling for advanced training procedure. + +We then investigate and modify a series of training paradigms to improve the inferior baseline performance, + +![](images/d67209d4231f432636aecf7fa1f27df03169140dc897229a5002d02a699c18f9.jpg) +(a) Overall training procedure with $L$ RIFormer blocks +(b) Module imitation +Figure 3. (a) Overall training procedure of RIFormer. Following the macro and micro design of [46], RIFormer removes token mixer in each block. (b) Module imitation technique aims to mimic the behavior of token mixer via a simple affine transformation. + +which can be summarized as 1) knowledge distillation, 2) teacher type influence, 3) structural re-parameterization, 4) the proposed module imitation technique, 5) load partial parameters from teacher. Since we aim at exploring the influence of different advanced training recipes instead of network architecture, inference-time model architecture is always kept the same at intermediate steps. Next, we share 5 useful guidelines for training RIFformer. + +# 4.2. Distillation Paradigm Design + +We now study the knowledge distillation [18, 38] of a RIFormaler student by a general vision backbone teacher with token mixer, and summarize how to effectively utilize the "soft" labels coming from the strong teacher network. + +Guideline 1: soft distillation without using ground-truth labels can be effective for student without token mixer. Basically, most of the existing KD methods are designed for models with token mixer. For example, it is common practice to help a student convnet by learning from both ground-truth labels and the soft labels predicted by a teacher convnet. Moreover, some observations from DeiT [38] show that using the hard labels instead of soft labels as a supervised target, can improves transformer significantly. In contrast, the token mixer free backbone do not have explicit patch aggregating modules in its basic block. The distillation of it is should be thus, different from that of conventional backbones. Specifically, although RIFormer shares the same macro structure as transformer, it still cannot be treated as a student transformer because we have deliberately removed the token mixer from each building block. However, we also do not prefer viewing it as a pure convnet since RIFormer bears a resemblance to transformer in terms of macro/micro-level architecture design. Therefore, we are motivated to explore a suitable KD method for RIFormer with promising performance. + +Typically, the cross-entropy objective is to assist a student network reproduce the hard accurate label, and we argue that the process may be unsuitable for RIFormer. First, the ground-truth hard label can be transformed to a soft distribution by label-smoothing regularization [35], with weights $1 - \varepsilon$ for the true label and $\varepsilon$ shared each classes. The unlearned uniform distribution across the negative classes is less informative, and may interfere with the learned soft distribution given by teacher. Second, $1 \times 1$ convolutions actually dominate basic building block in RIFormer, "mixing" only the per-location features but not spatial information. Such a simplified design may require richer information in the supervised labels. To demonstrate this, Tab. 2 compare the performance of four different settings. The default teacher is a GFNet-H-B [31] (54M parameters). Hard distillation with true labels improves the accuracy from $72.31\%$ to $73.51\%$ . It shows that a teacher with token mixer has a positive effect on a student without token mixer. In fact, the combination of using a soft distillation without true labels performs the best, improving the network performance to $74.05\%$ . + +Remark 1. Supervised learning with true label does not seem to be the most suitable way for a crude model without token mixer. A teacher with token mixer can help to guide the training, but still fails to fully recover the performance gap from removing token mixer, calling for other strategies. + +# 4.3. Re-parameterization for Identity Mapping + +Guideline 2: using affine transformation without tailored distillation, is hard to recover the performance degradation. In this part, we adopt the idea of Structural Reparameterization [9, 12, 13] methodology, which usually takes a powerful model for training and equivalently converts to a simple model during inference. Specifically, the inference-time token mixer module in RIFormer can be + +
TMFeatRelLayerImageNet top-1 acc (%)
Affine00-74.07
Affine400674.49
Affine600674.77
Affine800674.81
Affine8010675.08
Affine8020674.82
Affine8040675.00
Affine8020475.13
+ +viewed as an identity mapping following a LN layer. Thus, the training-time module should satisfy at least two basic requirements: 1) per-location operator for allowing equivalent transformation; 2) parametric operator for allowing extra representation ability. Accordingly, we apply an affine transformation operator to replace the identity mapping during training, which only performs channel-wise scaling and shifts, as shown in Fig. 2. The affine operator and its preceding LN layer can be converted into a LN with modified weights, thus it can be equivalently converted into an identity mapping during inference. Denote the input feature as $\mathbf{M} \in \mathbb{R}^{N \times C \times H \times W}$ , the affine operator can be expressed as: + +$$ +\operatorname {A f f i n e} (\mathrm {M}, \mathbf {s}, \mathbf {t}) _ {:, i,:,:} = \mathbf {s} _ {i} \mathrm {M} _ {:, i,:,:} + \mathbf {t} _ {i} - \mathrm {M} _ {:, i,:,:}, \tag {1} +$$ + +where $\mathbf{s} \in \mathbb{R}^C$ and $\mathbf{t} \in \mathbb{R}^C$ are learnable weight vectors. We follow [46] to add a subtraction of the input during implementation due to the residual connection, and thus does not merge the first and third terms in Eq. 1. Then, we describe how to merge the affine transformation into its preceding LN layer, so the training-time model can be equivalently converted to model for deploy but no longer has token mixer in its blocks. We use $\mu, \sigma, \gamma, \beta$ as the mean, standard deviation and learned scaling factor and bias of the preceding LN layer. Denote $\mathrm{T}^{(a)} \in \mathbb{R}^{N \times C \times H \times W}$ , $\mathrm{T}'^{(a)} \in \mathbb{R}^{N \times C \times H \times W}$ respectively as the input and output of an affine residual sub-block in Fig. 2-(a). During the training time, we have: + +$$ +\mathrm {T} ^ {\prime (a)} = \operatorname {A f f i n e} (\mathrm {L N} (\mathrm {T} ^ {(a)}, \boldsymbol {\mu}, \boldsymbol {\sigma}, \gamma , \beta), \mathbf {s}, \mathbf {t}) - \mathrm {T} ^ {(a)} \qquad (2) +$$ + +where LN is the LN function, which is implemented by GroupNorm API in PyTorch (setting the group number as 1) following [46]. During inference time, there only exists an identity mapping followed by a LN layer in the residual sub-block. Thus, we have: + +$$ +\mathrm {T} ^ {\prime (a)} = \operatorname {L N} \left(\mathrm {T} ^ {(a)}, \boldsymbol {\mu}, \boldsymbol {\sigma}, \gamma^ {\prime}, \beta^ {\prime}\right), \tag {3} +$$ + +where $\gamma^\prime$ and $\beta^\prime$ are the weight and bias parameters of the merged LN layer. Based on the equivalence of Eq. 2 and Eq. 3, for $\forall 1\leq i\leq C$ , we have: + +$$ +\pmb {\gamma} _ {i} ^ {\prime} = \pmb {\gamma} _ {i} (\mathbf {s} _ {i} - 1), \quad \pmb {\beta} _ {i} ^ {\prime} = \pmb {\beta} _ {i} (\mathbf {s} _ {i} - 1) + \mathbf {t} _ {i}, \qquad (4) +$$ + +The proof and PyTorch-like code of the affine transformation and re-parameterization process is shown in Sec.2 and + +Table 4. Results of different module imitation setting. + +
Teacher (T)T.acc (%)MIImageNet top-1 acc (%)
PoolFormer-M48 [46]82.5✗73.63
Swin-B* [24]85.2✗73.12
Pyramid ViG-B [15]83.7✗73.25
GFNet-H-B [31]82.9✗74.07
PoolFormer-M48 [46]82.5✓74.83
Swin-B* [24]85.2✓74.52
Pyramid ViG-B [15]83.7✓74.25
GFNet-H-B [31]82.9✓75.13
+ +Table 5. Results of different teachers on RIFormer-S12 w/ or w/o module imitation (MI). * indicates ImageNet-22K pre-training. + +Sec.3 of the appendix, respectively. Since the LN layer does not have a pre-computed mean and standard deviation during inference time, their specific values are input adaptive, which do not affect the equivalence of transform. + +Remark 2. Compare Tab. 3 with Tab. 2, directly applying structural re-parameterization method shows no advantages. We attribute this phenomenon to the fact that the affine transformation in the LN layer is a linear transformation that can be directly merged with the extra affine operator we introduced (if do not add any nonlinear function in between). Therefore, if both are supervised only by the output of the model, the potential of the additional parameters may not be fully exploited. Meanwhile, the isomorphic design of teacher and student inspires us to explore suitable methods for knowledge transfer of modules at each layer. + +# 4.4. Module Imitation + +Guideline 3: the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator. The previous KD methods we tried only focus on the output of between teacher and student networks. We propose module imitation (MI) method, which present to utilize the useful information in the teacher's token mixer. Specifically, a pretrained PoolFormer-S12 [46] is utilized as a teacher network. As shown in Fig. 3, we expect the simple affine operator (with its preceding LN layer) to approximate the behavior of that of a basic token mixer during training. Denote $f(\cdot), \mathrm{T}^{(a),m} \in \mathbb{R}^{N \times C \times H \times W}, m \in \mathcal{M}$ as the affine operator and the input of the $m$ -th layer of RIFormal in which $\mathcal{M}$ is the intermediate layers set we used, and $g(\cdot), \mathrm{T}^{(t),m} \in \mathbb{R}^{N \times C \times H \times W}, m \in \mathcal{M}$ are that of the teacher network, respectively. We abbreviate $\mathrm{LN}(\cdot, \mu, \sigma, \gamma, \beta)$ as $\mathrm{LN}(\cdot)$ for simplicity. The mean squared error (MSE) of the inputs between the LN layer of affine operator and token mixer can be calculated as: + +$$ +\mathcal {L} _ {i n} = \alpha_ {1} \| \mathrm {L N} (\mathrm {T} ^ {(a), m}) - \mathrm {L N} (\mathrm {T} ^ {(t), m}) \| _ {F} ^ {2}, \tag {5} +$$ + +where $\alpha_{1} = 1 / NCHW$ . Note that the input feature of the current layer is the output feature of the previous one. Therefore, we propose to match the output features of this + +block (i.e., the input features of the next subsequent block) in practice, which can be seen as a hidden state distillation in transformers [16, 19, 40, 41, 51]. + +$$ +\mathcal {L} _ {i n} ^ {\prime} = \alpha_ {1} \| T ^ {(a), m + 1} - T ^ {(t), m + 1} \| _ {F} ^ {2}, \tag {6} +$$ + +The hidden-state distillation based on relation matrices [16, 51] is then applied on the output feature: + +$$ +\mathcal {L} _ {r e l} = \alpha_ {2} \| \mathcal {R} (\mathrm {T} ^ {(a), m + 1}) - \mathcal {R} (\mathrm {T} ^ {(t), m + 1}) \| _ {F} ^ {2}, \qquad (7) +$$ + +where $\alpha_{2} = 1 / NH^{2}W^{2}$ , $\mathcal{R}(T) = \tilde{T}\tilde{T}^{\top}$ , $\tilde{T}$ denotes normalize $T$ at the last dimension. Considering the MSE of the outputs between affine operator and token mixer: + +$$ +\mathcal {L} _ {o u t} = \alpha_ {1} \| f (\mathrm {L N} (\mathrm {T} ^ {(a), m})) - g (\mathrm {L N} (\mathrm {T} ^ {(t), m})) \| _ {F} ^ {2}, \tag {8} +$$ + +Combining Eq. 6, Eq. 7 and Eq. 8, the final loss function with module imitation is defined as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s o f t}} + \lambda_ {1} \mathcal {L} _ {\text {i n}} ^ {\prime} + \lambda_ {2} \mathcal {L} _ {\text {o u t}} + \lambda_ {3} \mathcal {L} _ {\text {r e l}}, \tag {9} +$$ + +where $\mathcal{L}_{soft}$ is the soft logit distillation target in Sec. 4.2, $\lambda_{1},\lambda_{2},\lambda_{3}$ is the hyper-parameter for seeking the balance between loss functions. In Tab. 4, Feat and Rel are number of epochs of using $(\mathcal{L}_{in}^{\prime},\mathcal{L}_{out})$ and $\mathcal{L}_{rel}$ , Layer represents the number of intermediate layers we used. The results show positive effect of module imitation on the student RIFformer in different circumstances. With a 4 layer setting and the usage of affine operator, we get the best result of $75.13\%$ , already surpassing the PoolFormer-S12's result of $75.01\%$ in Tab. 1. From now on, we will use this setting. + +Remark 3. We deem a reason for that phenomenon might be that module imitation helps the affine operator implicitly benefit from the supervision of the teacher's token mixer, while not losing the convenience of explicitly merging the preceding LN layer. Besides, we find module imitation can effectively shift the feature distribution closer to the teacher network and show larger Effective Receptive Fields (ERFs). Please refer to Sec. 5.3 for details. + +Guideline 4: teacher with large receptive field is beneficial to improve student with limited receptive field. Tab. 5 compares student performance with different teacher architectures. Although GFNet-H-B [31] does not show the highest ImageNet top-1 performance among teachers, it can still serves as a better choice, no matter whether module imitation is used or not. + +Remark 4. The fact is probably attributed to the receptive field gap between teacher and student. As explained by [1], inductive bias can be transferred from one model to another through distillation. According to this study, model with large receptive field (e.g., GFNet with learnable global filters in the frequency domain) can be better teacher for student RIFormer with limited receptive field. + +Guideline 5: loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance. Our method can be categorized as a model compression technique that aims at removing the token mixer in basic blocks for acceleration. Inspired by previous methods, including knowledge distillation [32, 34], quantization [22, 26], and model acceleration [29] that initialize the weights of the light-weight network using (or partly using) the corresponding weights of the pre-trained heavy network, we explore a suitable initialization method. Since our goal is to remove only the token mixer, the weights of the remaining part still remain and are not paid enough attention in the previous journey. We observe that initializing the weights of RIFformer (except the affine operator) with the corresponding teacher network further boosts the performance from $75.13\%$ to $75.36\%$ . This brings us to the final paradigm for training RIFformer. + +Closing remarks. So far, we have finished our exploration and discovered a suitable paradigm for training the RIFformer. It has the approximately the same macro design with MetaFormer [46], but does not require any token mixer. Equipped with the propsoed optimization methods, RIFformer can outperform complicated models with token mixers for ImageNet-1K classification. These encouraging findings inspire us to answer the following questions in the next section. 1) The scaling behavior of such extremely simple architecture with our training paradigm. 2) The generalizability of the paradigm on different teachers. + +# 5. Experiments + +# 5.1. Image classification + +Setup. For ImageNet-1K [8] with 1.2M training images and 50000 validation images, we generally apply the training scheme in [46] while following the guidelines in Sec. 4. The data augmentation contains MixUp [50], CutMix [48], CutOut [52] and RandAugment [7]. As a model compression work on removing token mixer, bridging the performance gap caused by removing the token mixer is definitely our first priority, instead of proposing a strong baseline. Therefore, we use a prolonged the training epochs of 600. We also finetune the pre-trained models for 30 epochs with input resolution of $384^2$ . More details are in the appendix. + +Main results. Tab. 6 shows the results of RIFormer on ImageNet classification. We pay main attention to the throughput metrics since our primary consideration is to satisfy latency requirements for edge devices. As expected, favorable speed advantage is achieved since RIFormer does not contain any token mixer in its building block, compared with other type of backbones. Surprisingly, with such fast inference, RIFormers successfully remove all token mixers using our training approach without affecting the performance. For example, RIFormer-M36 can pro + +
Token MixerOutcome ModelImage SizeParams (M)MACs (G)Throughput (images/s)Top-1 (%)
ConvolutionRSB-ResNet-34 [17,43]224223.76653.7575.5
RSB-ResNet-50 [17,43]224264.12732.8579.8
RSB-ResNet-101 [17,43]224457.91856.4881.3
RSB-ResNet-152 [17,43]2246011.61308.2681.8
Attention▲ DeiT-S [38]224224.63092.0279.8
▲ DeiT-B [38]2248617.51348.7681.8
▲ PVT-Small [42]224253.81622.5379.8
▲ PVT-Medium [42]224446.71190.4881.2
▲ PVT-Large [42]224619.8865.3381.7
Spatial MLPMLP-Mixer-B/16 [36]2245912.71855.4576.4
ResMLP-S24 [37]224306.03228.7579.4
ResMLP-B24 [37]22411623.0298.9481.0
Swin-Mixer-T/D6 [24]256234.01625.5979.7
Swin-Mixer-B/D24 [24]2246110.41131.6081.3
2D FFTGFNet-H-Ti [31]224152.11979.5680.1
GFNet-H-S [31]224324.61434.1981.5
GFNet-B [31]224437.91771.0780.7
GFNet-H-B [31]224548.6939.2082.9
Pooling○ PoolFormer-S12 [46]224121.84160.1877.2
○ PoolFormer-S24 [46]224213.42140.2080.3
○ PoolFormer-S36 [46]224315.01440.3781.4
○ PoolFormer-M36 [46]224568.81009.4582.1
○ PoolFormer-M48 [46]2247311.6761.9382.5
None★ RIFounder-S12°224121.84899.80 (↑17.8%)76.9
★ RIFounder-S24°224213.42530.48 (↑18.2%)80.3
★ RIFounder-S36°224315.01699.94 (↑18.0%)81.3
★ RIFounder-M36°224568.81185.33 (↑17.4%)82.6
★ RIFounder-M48°2247311.6897.05 (↑17.7%)82.8
★ RIFounder-S12‡384125.41586.5178.3
★ RIFounder-S24‡3842110.0819.4081.4
★ RIFounder-S36‡3843114.7552.0782.2
★ RIFounder-M36‡3845625.9403.1583.4
★ RIFounder-M48‡3847334.1304.4383.7
+ +Table 6. Results of models with different types of token mixers on ImageNet-1K. denotes training with prolonged 600 epochs. denotes fine-tuning from the ImageNet pre-trained model for 30 epochs. + +cess more than 1185 images at $224^2$ resolution per second, with the top-1 accuracy of $82.6\%$ . In comparison, the recent baseline PoolFormer-M36 [46] with a Pooling token mixer, can process 1009 images of the same size with a worse $82.1\%$ accuracy. We also compare with an efficient backbone, GFNet [31]. It conducts token mixing via a global filter, which consists an FFT, an element-wise multiplication, and an IFFT, with a total computational complexity $\mathcal{O}(N\log N)$ . With a 939 throughput, GFNet-H-B gets $82.9\%$ accuracy while our RIFformer-M48 can still reaches a comparable $82.8\%$ accuracy with on par throughput of 897. Meanwhile, the body of inference-time RIFformer is dominated by only $1\times 1$ conv following LN, without complex 2D FFT or attention, friendly for hardware specialization. + +Notably, without token mixer, RIFormer cannot even perform basic token mixing operation in its building blocks. However, the ImageNet experiments demonstrate that with the proposed training paradigm, RIFormer still shows promising results. We can only deem the reason behind the + +fact might be that optimization strategy plays a key role. RIFormer is readily a starting recipe for the exploration of optimization-driven efficient network design, and rest assured of the performance with advanced training schemes. + +# 5.2. Ablation studies + +Effectiveness of module imitation. As an important way for the extra affine operator to learn suitable weights, module imitation is based on distillation. Therefore, we compare it with the hidden state feature distillation approach (with relations). Taking the paradigm in Sec. 4.2 by soft distillation without CE loss, we get the results in Tab. 7. More details for Sec. 5.2 can be found in Sec.4 of the appendix. With feature distillation, the accuracy is $0.46\%$ lower than that of module imitation, showing module imitation's positive effect on the optimization of the extra weights. + +Comparisons of different acceleration strategy. Next, we discuss whether the token removing is better than other sparsification strategies. Based on the PoolFormer [46] + +![](images/08242cdedb5dd833cae1948cc2e0b7ab7786b2cd89aded2ef7b3573fb696fa8d.jpg) +(a) PoolFormer-S12 + +![](images/7107825627d6ffe2a074d214865460790fabc41e1e0e42d48cc7ba3a3f6250d0.jpg) +(b) RIFormer-S12 + +![](images/5795a116e98fcd19eb43041343044f4e6becfe84d4744b3e624f5c932e5ac1a0.jpg) +(c) RIFormer-S12 (MI) +Figure 4. The Effective Receptive Field (ERF) of PoolFormer-S12 and RIFlower-S12 with/without using module imitation. + +
Token MixerFeature distillation schemeTop-1 (%)
IdentityNone74.05
IdentityFeature distill74.90
AffineModule imitation75.36
+ +baseline, we first construct a slim PoolFormer-S9 and PoolFormer-XS12 by reducing the depth to 9 and by maintaining about $\frac{5}{6}$ of its width, i.e., embedding dimension, to obtain comparable inference speed with our RIFormer-S12. We also follow the soft distillation paradigm in Sec. 4.2. Tab. 8 shows the results. Directly pruning depths or width cannot render a better performance than ours without latency-hungry token mixer. + +Generalization to different teachers. In order to verify the proposed training paradigm a general compression technique, we adopt the architecture modifications in [47] for student and change teacher to the other 4 MetaFormer baselines [47], with teacher token mixer as rand matrices, pooling, separable depthwise convolutions, and attention, respectively. Tab. 9 shows that our method has a positive effect in different depth settings and teacher circumstances. + +# 5.3. Analysis of Module Imitation. + +Module imitation (MI) shifts the feature distribution of the RIFformer model to be closer to the teacher. The effect of the module imitation is explicitly shown in Fig. 5. It can be observed that PoolFomer-S12 and RIFformer-S12 show a clear difference in feature distribution of Stage 1 and Stage 4. After applying the proposed module imitation, the distribution of RIFformer-S12 are basically shifted toward that of the PoolFomer-S12, demonstrating its effect on helping student learn useful knowledge from the teacher. + +Module imitation helps showing larger Effective Receptive Field (ERF). ERF [27] reflects how large an area of the image the trained model can respond to or capture information about how large an object. We follow [12, 20] to visualize the ERF via measuring the aggregated contributions of each pixel of the input to the central points of the output feature. Since RIFormer removes all token mixers, it exhibits an expectedly much smaller ERF than PoolFormer, as shown in Fig. 4. There is only a square of pixels emerg- + +![](images/69900e83ad5c01544ec37fb1a70b40c678ee4c3e7a55a6f8e3831c497a28e158.jpg) +Figure 5. Visualization of the feature distribution of the first and last stage of PoolFormer-S12 and RIFormal-S12. + +![](images/c212c97c5154694105f56209d5ee329629347c4d5df8061d756c553a365eba8d.jpg) + +Table 7. Ablation study of the effectiveness of module imitation. + +
ModelTypeThroughputTop-1 (%)
PoolFormer-S12None4160.1875.01
PoolFormer-S9Depth5025.7174.78
PoolFormer-XS12Width4780.2875.11
RIFounder-S12TM4899.8075.36
+ +Table 8. Results of comparison with depth or width slimming. + +
Token MixerTeacherTop-1 (%)
Affine (12 layers)None72.75
Affine (12 layers)RandFormer-S12 [47]75.62
Affine (12 layers)PoolFormer V2-S12 [47]75.87
Affine (18 layers)None75.01
Affine (18 layers)ConvFormer-S18 [47]77.53
Affine (18 layers)CAFormer-S18 [47]77.26
+ +Table 9. Results of generalization to other teachers. + +ing with red color in the whole region, much smaller than PoolFormer. However, surprisingly, we can observe that red color widely distributed in all locations after training with module imitation. It seems that although there's no explicit structural change, module imitation still help change the learned weights and show larger ERF. + +# 6. Limitations and Conclusion + +This paper investigates removing token mixer of the basic building block in a vision backbone, motivated by their considerable latency cost. To keep the remaining structure still effective, we thoroughly revisits the training paradigm. We observe that appropriate optimization strategy can effectively help a token mixer-free model learn useful knowledge from another model, boosting its performance and bridge the gap caused by incomplete structure. Limitations are that more vision tasks, including detection, deblurring, etc. are not discussed, and we will work on them in the future. + +# Acknowledgement + +This paper is partly supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, Shanghai Postdoctoral Excellence Program (No.2022235), the National Natural Science Foundation of China (Grant No.61991450) and the Shenzhen Science and Technology Program (JCYJ20220818101001004). + +# References + +[1] Samira Abnar, Mostafa Dehghani, and Willem Zuidema. Transferring inductive biases through knowledge distillation. arXiv preprint arXiv:2006.00555, 2020. 6 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 2 +[3] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. 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Attention probe: Vision transformer distillation in the wild. In ICASSP, 2022. 2 +[40] Wenhui Wang, Hangbo Bao, Shaohan Huang, Li Dong, and Furu Wei. Minilmv2: Multi-head self-attention relation distillation for compressing pretrained transformers. In ACL, 2021. 6 +[41] Wenhui Wang, Furu Wei, Li Dong, Hangbo Bao, Nan Yang, and Ming Zhou. Minilm: Deep self-attention distillation for task-agnostic compression of pre-trained transformers. In NeurIPS, 2020. 6 +[42] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. In ICCV, 2021. 7 +[43] Ross Wightman, Hugo Touvron, and Hervé Jégou. Resnet strikes back: An improved training procedure in timm. arXiv preprint arXiv:2110.00476, 2021. 7 +[44] Kan Wu, Jinnian Zhang, Houwen Peng, Mengchen Liu, Bin Xiao, Jianlong Fu, and Lu Yuan. Tinyvit: Fast pretraining distillation for small vision transformers. In ECCV, 2022. 2 +[45] Enze Xie, Wenhai Wang, Zhiding Yu, Anima Anandkumar, Jose M Alvarez, and Ping Luo. Segformer: Simple and efficient design for semantic segmentation with transformers. In NeurIPS, 2021. 1 +[46] Weihao Yu, Mi Luo, Pan Zhou, Chenyang Si, Yichen Zhou, Xinchao Wang, Jiashi Feng, and Shuicheng Yan. Metaformer is actually what you need for vision. In CVPR, 2022. 1, 2, 3, 4, 5, 6, 7 +[47] Weihao Yu, Chenyang Si, Pan Zhou, Mi Luo, Yichen Zhou, Jiashi Feng, Shuicheng Yan, and Xinchao Wang. Metaformer baselines for vision. arXiv preprint arXiv:2210.13452, 2022. 1, 3, 8 + +[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In ICCV, 2019. 6 +[49] Sergey Zagoruyko and Nikos Komodakis. Diracnets: Training very deep neural networks without skip-connections. arXiv preprint arXiv:1706.00388, 2017. 2 +[50] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 6 +[51] Jinnian Zhang, Houwen Peng, Kan Wu, Mengchen Liu, Bin Xiao, Jianlong Fu, and Lu Yuan. Minivit: Compressing vision transformers with weight multiplexing. In CVPR, 2022, 2, 3, 6 +[52] Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. In AAAI, 2020. 6 \ No newline at end of file diff --git a/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/images.zip b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..cf4b86d9ae22b5891022983e9a16851da53848c4 --- /dev/null +++ b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:48b301e5eec6ce032f9c23168e9bce2d674c3ea2661d91b8f0a8563b146e1328 +size 573493 diff --git a/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/layout.json b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6dc8727f1dbf62d84dd000a6b9359b4e2989619f --- /dev/null +++ b/2023/RIFormer_ Keep Your Vision Backbone Effective but Removing Token Mixer/layout.json @@ -0,0 +1,8040 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 536, + 121 + ], + "type": "text", + "content": "RIFormer: Keep Your Vision Backbone Effective But Removing Token Mixer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "spans": [ + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": "Jiahao Wang" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Songyang Zhang" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Yong Liu" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Taiqiang Wu" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Yujiu Yang" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Xihui Liu" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Kai Chen" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Ping Luo" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": " Dahua Lin" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": "Shanghai AI Laboratory " + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": "The University of HongKong \n" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 97, + 141, + 495, + 228 + ], + "type": "text", + "content": "Tsinghua Shenzhen International Graduate School \nwang-jh19@tsinghua.org.cn {zhangsongyang, chenkai, lindahua}@pjlab.org.cn \nyang.yujiu@sz.tsinghua.edu.cn xihuiliu@eee.hku.hk pluo@cs.hku.hk" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "spans": [ + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 280, + 290, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 280, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 45, + 280, + 290, + 544 + ], + "type": "text", + "content": "This paper studies how to keep a vision backbone effective while removing token mixers in its basic building blocks. Token mixers, as self-attention for vision transformers (ViTs), are intended to perform information communication between different spatial tokens but suffer from considerable computational cost and latency. However, directly removing them will lead to an incomplete model structure prior, and thus brings a significant accuracy drop. To this end, we first develop an RepIdentityFormer base on the reparameterizing idea, to study the token mixer free model architecture. And we then explore the improved learning paradigm to break the limitation of simple token mixer free backbone, and summarize the empirical practice into 5 guidelines. Equipped with the proposed optimization strategy, we are able to build an extremely simple vision backbone with encouraging performance, while enjoying the high efficiency during inference. Extensive experiments and ablative analysis also demonstrate that the inductive bias of network architecture, can be incorporated into simple network structure with appropriate optimization strategy. We hope this work can serve as a starting point for the exploration of optimization-driven efficient network design." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 578, + 128, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 578, + 128, + 591 + ], + "spans": [ + { + "bbox": [ + 48, + 578, + 128, + 591 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": "The monumental advance in computer vision in the past few years was partly brought by the revolution of vision backbones, including convolutional neural networks (ConvNets) [13, 17, 25, 30] and vision transformers (ViTs) [14, 38]. Both of them have particular modules in their basic building blocks that aggregate information between different spatial locations, which are called token mixer [46], such as self-attention for ViTs. Although the effective" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 254, + 541, + 434 + ], + "blocks": [ + { + "bbox": [ + 310, + 254, + 541, + 434 + ], + "lines": [ + { + "bbox": [ + 310, + 254, + 541, + 434 + ], + "spans": [ + { + "bbox": [ + 310, + 254, + 541, + 434 + ], + "type": "image", + "image_path": "52123fafbd222c9d4003807e33cb96ab5dbe4aab859c22f83db9bf7326e8e7d9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 437, + 546, + 483 + ], + "lines": [ + { + "bbox": [ + 305, + 437, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 546, + 483 + ], + "type": "text", + "content": "Figure 1. Latency analysis of different components in ViT-Base [14]. (a) For token mixer (self-attention), the latency occupies about " + }, + { + "bbox": [ + 305, + 437, + 546, + 483 + ], + "type": "inline_equation", + "content": "46.3\\%" + }, + { + "bbox": [ + 305, + 437, + 546, + 483 + ], + "type": "text", + "content": " of the backbone. (b) Our motivation was to remove the token mixer while striving to keep the performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": "ness of token mixer has been demonstrated on many vision tasks [5, 6, 24, 45], its computational complexity typically takes up a significant portion of the network. In practice, heavy token mixers make the vision backbone limited especially on the edge-side devices due to the issue of speed and computation cost." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "There have been several attempts in the literature to investigate efficient token mixers for slimming vision backbones [29, 31, 46]. Although those works have already achieve competitive performance with light-weight design, they do retain the token mixers, which brings non-negligible increase in latency, as illustrated in Fig. 1. The recent work [47] finds that removing the token mixer is possible but leads to performance degeneration. Those explorations in efficient token mixers inspire us to think that can we keep the vision backbone effective but removing the token mixer? The resulting token mixer free vision backbone is expected to be efficient and effective for the realistic application." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 143, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 143, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 143, + 713 + ], + "type": "text", + "content": "* Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14443" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "In this work, we first review the current model architectures and learning paradigms. Most of the previous works concentrate on the improvement of the architecture while adopting the conventional supervised learning to optimize the model from scratch. Differently, we propose to adopt the simplified model architecture, and explore the learning paradigm design to fully exploit the potential of the simple model. We aim to simultaneously maintain the efficiency and efficacy of token mixer free vision backbone (namely IdentityFormer, in Fig. 1-(b)). To this end, we investigate the simple and yet effective learning strategy, knowledge distillation (KD) [18] thoroughly in the following sections." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 324 + ], + "type": "text", + "content": "Our main idea is distilling the knowledge from powerful teacher model (with token mixer) to the student model (token mixer free). We instantiate the re-parameterizing idea to enlarge the modeling capacity of student network but retain its efficiency, as shown in Fig. 2. Specifically, the simple affine transformation is introduced into student model, to replace the token mixer for training. The parameters of affine transformation can be merged into LayerNorm [2] during inference, which makes the student token mixer free finally." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 326, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 289, + 469 + ], + "type": "text", + "content": "We empirically summarize the our learning strategy as the following guidelines, hope to shed light on how to learn the extremely simple model. Concretely, 1) soft distillation without using ground-truth labels is more effective; 2) using affine transformation without distillation is difficult to tailor the performance degeneration; 3) the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator; 4) teacher with large receptive field is beneficial to improve receptive field limited student; 5) loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 470, + 289, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 289, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 289, + 638 + ], + "type": "text", + "content": "Based on the above guidelines, we finally obtain a token mixer free vision model with competitive performance enjoying the high efficiency, dubbed as " + }, + { + "bbox": [ + 46, + 470, + 289, + 638 + ], + "type": "inline_equation", + "content": "\\underline{\\text{RepIdentityFormer}}" + }, + { + "bbox": [ + 46, + 470, + 289, + 638 + ], + "type": "text", + "content": " (RIFormer). RIFormer shares nearly the same macro and micro design as MetaFormer [46], but safely removing all token mixers. The quantitative results show that our networks outperform many prevailing backbones with faster inference speed on ImageNet-1K [8]. And the ablative analyses on the feature distribution and Effective Receptive Fields (ERFs) also demonstrate that the inductive bias brought by an explicit token mixer, can be implicitly incorporated into the simple network structure with appropriate optimization strategies. In summary, the main contributions of our work are as the following:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 642, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 677 + ], + "type": "text", + "content": "- We propose to explore the vision backbone by developing advanced learning paradigm for simple model architecture, to satisfy the demand of realistic application." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "- We instantiate the re-parameterizing idea to build a token mixer free vision model, RIFormer, which owns the improved modeling capacity for the inductive bias while" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 479, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 479, + 84 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 479, + 84 + ], + "type": "text", + "content": "enjoying the efficiency during inference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 84, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 84, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 84, + 545, + 119 + ], + "type": "text", + "content": "- Our proposed practical guidelines of distillation strategy has been demonstrated effective in keeping the vision backbone competitive but removing the token mixer." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 130, + 392, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 130, + 392, + 142 + ], + "spans": [ + { + "bbox": [ + 306, + 130, + 392, + 142 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 149, + 481, + 161 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 149, + 481, + 161 + ], + "spans": [ + { + "bbox": [ + 306, + 149, + 481, + 161 + ], + "type": "text", + "content": "2.1. Vision Transformer Acceleration" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 167, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 545, + 323 + ], + "type": "text", + "content": "Vision transformer is a inference slow, energy intensive backbone due to its quadratic computational cost of the self-attention, and therefore unfriendly to deploy on resource-limited edge devices, calling for compression techniques. Various technology route are designed for vision transformer slimming, such as distilling an efficient transformer with fewer depths and embedding dimensions [16,38,39,44, 51], pruning or merging unimportant tokens [3,21,28,29], applying energy efficient operations [23, 33], or designing efficient attention alternatives [4,24,31], etc. Different from these lines, our work proposes a novel angle of totally removing the complicated token mixer in a backbone while keep satisfactory performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 330, + 473, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 473, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 473, + 342 + ], + "type": "text", + "content": "2.2. Structural Re-parameterization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 348, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 503 + ], + "type": "text", + "content": "Structural re-parameterization [12, 13, 49] is a training technique which decouples the training-time and inference-time architectures. For example, RepVGG [13] is a plain VGG-style architecture with attractive performance and speed during inference, and a powerful architecture with manually added " + }, + { + "bbox": [ + 304, + 348, + 545, + 503 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 348, + 545, + 503 + ], + "type": "text", + "content": " branch and identity mapping branch during training. Similarly, such technique can be further extended to super large kernel ConvNets [12], MLP-like models [9], network pruning [11] and special optimizer design [10]. In this paper, we follow the technique to introduce parameters and equivalently absorb them into LN layer after training. The extra weights after proper optimization can help the model learn useful representations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 513, + 463, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 463, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 463, + 526 + ], + "type": "text", + "content": "3. Preliminary and Motivation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 582 + ], + "type": "text", + "content": "In this section, we first briefly recap the concept of token mixer. Then, we revisit their inevitable side effects on inference speed through an empirical latency analysis, and thus introduce the motivation of our paper." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 587, + 527, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 527, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 527, + 600 + ], + "type": "text", + "content": "3.1. Preliminary: The Concept of Token Mixer" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The concept token mixer is a structure that performs token mixing functions in a given vision backbone. It allows information aggregation from different spatial positions [46]. For instance, self-attention module serves as the token mixer in ViT [14] by performing the attention function in parallel between components in queries, keys and values matrices, which are linearly projected from the input feature. Moreover, ResMLP [37] applies a cross-patch linear sublayer by treating Spatial MLP as token mixer. The" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14444" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 274, + 199 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 274, + 199 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 274, + 199 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 274, + 199 + ], + "type": "image", + "image_path": "e5ec6657e66492546a60c6e227dbb55d01babf3622c9b5ff50d344e01c5881f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 201, + 279, + 211 + ], + "lines": [ + { + "bbox": [ + 55, + 201, + 279, + 211 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 279, + 211 + ], + "type": "text", + "content": "Figure 2. Structural re-parameterization of a RIFormer block." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 214, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 214, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 287, + 239 + ], + "type": "text", + "content": "computational and memory costs of the aforementioned token mixers are quadratic to the image scale." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 246, + 121, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 246, + 121, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 121, + 257 + ], + "type": "text", + "content": "3.2. Motivation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "text", + "content": "In this section, we take our eyes on the side effects of token mixers through a quantitative latency analysis on the ViT [14] model. We start with a modified 12-layer ViT-Base model containing only input embedding, without any operation in each of its basic building blocks. Then we gradually add the operation component (e.g., LN, Attention, Channel MLP, etc.) to each basic block, and the model finally comes to ViT-Base without the global average pooling layer and the classifier head. For each model, we take a batch size of 2048 at " + }, + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "text", + "content": " resolution with one A100 GPU and calculate the average time over 30 runs to inference that batch. The whole process is repeated for three times and we take the medium number as the statistical latency. As shown in Fig. 1, after stacking the regular number of 12 layers, token mixer can bring an additional latency of 1433.6ms, occupying about " + }, + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "inline_equation", + "content": "46.3\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 455 + ], + "type": "text", + "content": " of the backbone." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 456, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 456, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 45, + 456, + 287, + 624 + ], + "type": "text", + "content": "According to the above analysis, token mixer brings significant side effects on the latency to the model, which makes it limited for realistic application. The observation naturally raises a question: can we keep the backbone effective but removing token mixer? Specifically, a recent work [47] introduces the MetaFormer model without any token mixer in its basic building block and finds that it raises a non-negligible performance degeneration. Based on those findings, we propose to exploit the full potential of the extremely simple model by incorporating the inductive bias with the advanced optimization strategies, such as knowledge distillation [18, 38, 51], structural reparameterization [12, 13], etc. And we present all the exploration details in the remaining of this work." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 634, + 238, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 238, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 238, + 647 + ], + "type": "text", + "content": "4. Exploring RIFormer: A Roadmap" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "In this section, we present a trajectory going from a fully supervised approaches for RIFormer to more advanced training paradigms. During the journey we investigate and develop different optimization schemes for transformer-like models, while maintaining the inference-time model as the" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 73, + 539, + 110 + ], + "blocks": [ + { + "bbox": [ + 313, + 73, + 539, + 110 + ], + "lines": [ + { + "bbox": [ + 313, + 73, + 539, + 110 + ], + "spans": [ + { + "bbox": [ + 313, + 73, + 539, + 110 + ], + "type": "table", + "html": "
Token MixerTraining recipeImageNet top-1 acc (%)
PoolingCE Loss75.01
IdentityCE Loss72.31
", + "image_path": "9cbeb8db91b898ecaa4b86ed739ae5d530c2fb8d43ca0248c47a5e3cac0f62ef.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 319, + 139, + 533, + 210 + ], + "blocks": [ + { + "bbox": [ + 305, + 114, + 545, + 136 + ], + "lines": [ + { + "bbox": [ + 305, + 114, + 545, + 136 + ], + "spans": [ + { + "bbox": [ + 305, + 114, + 545, + 136 + ], + "type": "text", + "content": "Table 1. Results of different token mixers on MetaFormer using cross-entropy loss." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 139, + 533, + 210 + ], + "lines": [ + { + "bbox": [ + 319, + 139, + 533, + 210 + ], + "spans": [ + { + "bbox": [ + 319, + 139, + 533, + 210 + ], + "type": "table", + "html": "
TMLabelTeacherImageNet top-1 acc (%)
Identity✓✗72.31
Identity✓hard73.51
Identity✗hard72.86
Identity✓soft73.64
Identity✗soft74.05
", + "image_path": "e84de8f08d83ebbe1717a7449cf06d64cf841e5acec8696ffd5723ef30026b37.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 320, + 238, + 531, + 309 + ], + "blocks": [ + { + "bbox": [ + 306, + 213, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 236 + ], + "type": "text", + "content": "Table 2. Results of different teacher type in normal/label-free RIFformer-S12 with identity mapping as token mixer." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 238, + 531, + 309 + ], + "lines": [ + { + "bbox": [ + 320, + 238, + 531, + 309 + ], + "spans": [ + { + "bbox": [ + 320, + 238, + 531, + 309 + ], + "type": "table", + "html": "
TMLabelKD typeImageNet top-1 acc (%)
Affine✓×72.25
Affine✓hard73.44
Affine×hard72.77
Affine✓soft72.10
Affine×soft74.07
", + "image_path": "c09368186a13384cb0cdf6ad69bc4a8ef8ff6112d5aa05a3a940f44d2df97ed3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": "Table 3. Results of different distillation type in normal/label-free RIFormer-S12 with affine transformation as token mixer." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 341, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 472 + ], + "type": "text", + "content": "same. The baseline RIFormer we use has exactly the same macro architecture and model size as recently-developed MetaFormer [46], the difference only lies in the fact that no token mixer is used in its basic building blocks during inference. We control the computational complexity of RIFormer-S12 models comparable to PoolFormer-S12 [46], with about 12M parameters and 1.8G MAC. All RIFormer-S12 models in this section are trained and evaluated on ImageNet-1K for 120 epochs. The details of hyper-parameters are shown in Sec.1 of the appendix. The roadmap of our exploration is as follows." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 479, + 511, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 511, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 511, + 491 + ], + "type": "text", + "content": "4.1. Vision Backbone Without Token Mixer" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "type": "text", + "content": "Our exploration is directed to remove token mixer in each basic block of a inference-time model vision backbone to obtain a higher inference speed while striving to keep the performance. Thus, we start with a RIFormer-S12 model with a fully supervised training scheme using CE loss, mainly follows [46]. As a performance reference, we compare the results with PoolFormer-S12, since it use only basic pooling operation as token mixer and the performance gap can thus, be attributed to the absence of basic token mixing function. As shown in Tab. 1, RIFormer-S12 with a trivial supervised training can lead to an unacceptable performance drop (2.7% top-1 accuracy) compared to PoolFormer-S12. The results show that without token mixer in each building block, it is limited for regular supervised learning in helping the model learn useful information from images, calling for advanced training procedure." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We then investigate and modify a series of training paradigms to improve the inferior baseline performance," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14445" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 67, + 547, + 240 + ], + "blocks": [ + { + "bbox": [ + 47, + 67, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 47, + 67, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 67, + 547, + 240 + ], + "type": "image", + "image_path": "d67209d4231f432636aecf7fa1f27df03169140dc897229a5002d02a699c18f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 129, + 243, + 315, + 254 + ], + "lines": [ + { + "bbox": [ + 129, + 243, + 315, + 254 + ], + "spans": [ + { + "bbox": [ + 129, + 243, + 315, + 254 + ], + "type": "text", + "content": "(a) Overall training procedure with " + }, + { + "bbox": [ + 129, + 243, + 315, + 254 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 129, + 243, + 315, + 254 + ], + "type": "text", + "content": " RIFormer blocks" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 447, + 243, + 518, + 253 + ], + "lines": [ + { + "bbox": [ + 447, + 243, + 518, + 253 + ], + "spans": [ + { + "bbox": [ + 447, + 243, + 518, + 253 + ], + "type": "text", + "content": "(b) Module imitation" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 260, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 546, + 282 + ], + "type": "text", + "content": "Figure 3. (a) Overall training procedure of RIFormer. Following the macro and micro design of [46], RIFormer removes token mixer in each block. (b) Module imitation technique aims to mimic the behavior of token mixer via a simple affine transformation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 289, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 385 + ], + "type": "text", + "content": "which can be summarized as 1) knowledge distillation, 2) teacher type influence, 3) structural re-parameterization, 4) the proposed module imitation technique, 5) load partial parameters from teacher. Since we aim at exploring the influence of different advanced training recipes instead of network architecture, inference-time model architecture is always kept the same at intermediate steps. Next, we share 5 useful guidelines for training RIFformer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 393, + 205, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 205, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 205, + 406 + ], + "type": "text", + "content": "4.2. Distillation Paradigm Design" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 412, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 460 + ], + "type": "text", + "content": "We now study the knowledge distillation [18, 38] of a RIFormaler student by a general vision backbone teacher with token mixer, and summarize how to effectively utilize the \"soft\" labels coming from the strong teacher network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": "Guideline 1: soft distillation without using ground-truth labels can be effective for student without token mixer. Basically, most of the existing KD methods are designed for models with token mixer. For example, it is common practice to help a student convnet by learning from both ground-truth labels and the soft labels predicted by a teacher convnet. Moreover, some observations from DeiT [38] show that using the hard labels instead of soft labels as a supervised target, can improves transformer significantly. In contrast, the token mixer free backbone do not have explicit patch aggregating modules in its basic block. The distillation of it is should be thus, different from that of conventional backbones. Specifically, although RIFormer shares the same macro structure as transformer, it still cannot be treated as a student transformer because we have deliberately removed the token mixer from each building block. However, we also do not prefer viewing it as a pure convnet since RIFormer bears a resemblance to transformer in terms of macro/micro-level architecture design. Therefore, we are motivated to explore a suitable KD method for RIFormer with promising performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": "Typically, the cross-entropy objective is to assist a student network reproduce the hard accurate label, and we argue that the process may be unsuitable for RIFormer. First, the ground-truth hard label can be transformed to a soft distribution by label-smoothing regularization [35], with weights " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "1 - \\varepsilon" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": " for the true label and " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": " shared each classes. The unlearned uniform distribution across the negative classes is less informative, and may interfere with the learned soft distribution given by teacher. Second, " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": " convolutions actually dominate basic building block in RIFormer, \"mixing\" only the per-location features but not spatial information. Such a simplified design may require richer information in the supervised labels. To demonstrate this, Tab. 2 compare the performance of four different settings. The default teacher is a GFNet-H-B [31] (54M parameters). Hard distillation with true labels improves the accuracy from " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "72.31\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "73.51\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": ". It shows that a teacher with token mixer has a positive effect on a student without token mixer. In fact, the combination of using a soft distillation without true labels performs the best, improving the network performance to " + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "inline_equation", + "content": "74.05\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 540 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 540, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 601 + ], + "type": "text", + "content": "Remark 1. Supervised learning with true label does not seem to be the most suitable way for a crude model without token mixer. A teacher with token mixer can help to guide the training, but still fails to fully recover the performance gap from removing token mixer, calling for other strategies." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 610, + 529, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 610, + 529, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 610, + 529, + 624 + ], + "type": "text", + "content": "4.3. Re-parameterization for Identity Mapping" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": "Guideline 2: using affine transformation without tailored distillation, is hard to recover the performance degradation. In this part, we adopt the idea of Structural Reparameterization [9, 12, 13] methodology, which usually takes a powerful model for training and equivalently converts to a simple model during inference. Specifically, the inference-time token mixer module in RIFormer can be" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14446" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 278, + 173 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 278, + 173 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 278, + 173 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 278, + 173 + ], + "type": "table", + "html": "
TMFeatRelLayerImageNet top-1 acc (%)
Affine00-74.07
Affine400674.49
Affine600674.77
Affine800674.81
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", + "image_path": "e13896a95de0a271fe135ea670b399f082029b548bda8e3ddd272cc18b2ba2b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 338 + ], + "type": "text", + "content": "viewed as an identity mapping following a LN layer. Thus, the training-time module should satisfy at least two basic requirements: 1) per-location operator for allowing equivalent transformation; 2) parametric operator for allowing extra representation ability. Accordingly, we apply an affine transformation operator to replace the identity mapping during training, which only performs channel-wise scaling and shifts, as shown in Fig. 2. The affine operator and its preceding LN layer can be converted into a LN with modified weights, thus it can be equivalently converted into an identity mapping during inference. Denote the input feature as " + }, + { + "bbox": [ + 46, + 194, + 289, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 194, + 289, + 338 + ], + "type": "text", + "content": ", the affine operator can be expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 342, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 342, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 61, + 342, + 287, + 357 + ], + "type": "interline_equation", + "content": "\\operatorname {A f f i n e} (\\mathrm {M}, \\mathbf {s}, \\mathbf {t}) _ {:, i,:,:} = \\mathbf {s} _ {i} \\mathrm {M} _ {:, i,:,:} + \\mathbf {t} _ {i} - \\mathrm {M} _ {:, i,:,:}, \\tag {1}", + "image_path": "f01ab2e8f20d082de04325382a3ed061e2b039e2551e85f17d9e4b828795973c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{s} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": " are learnable weight vectors. We follow [46] to add a subtraction of the input during implementation due to the residual connection, and thus does not merge the first and third terms in Eq. 1. Then, we describe how to merge the affine transformation into its preceding LN layer, so the training-time model can be equivalently converted to model for deploy but no longer has token mixer in its blocks. We use " + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mu, \\sigma, \\gamma, \\beta" + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": " as the mean, standard deviation and learned scaling factor and bias of the preceding LN layer. Denote " + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathrm{T}^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "inline_equation", + "content": "\\mathrm{T}'^{(a)} \\in \\mathbb{R}^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 362, + 289, + 508 + ], + "type": "text", + "content": " respectively as the input and output of an affine residual sub-block in Fig. 2-(a). During the training time, we have:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 514, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 514, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 53, + 514, + 287, + 529 + ], + "type": "interline_equation", + "content": "\\mathrm {T} ^ {\\prime (a)} = \\operatorname {A f f i n e} (\\mathrm {L N} (\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma , \\beta), \\mathbf {s}, \\mathbf {t}) - \\mathrm {T} ^ {(a)} \\qquad (2)", + "image_path": "c8cf656db0ceebf3cb41f00e536023a2494937835b519a12205c13e4390b3ad0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 535, + 287, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 287, + 595 + ], + "type": "text", + "content": "where LN is the LN function, which is implemented by GroupNorm API in PyTorch (setting the group number as 1) following [46]. During inference time, there only exists an identity mapping followed by a LN layer in the residual sub-block. Thus, we have:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 601, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 601, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 96, + 601, + 287, + 617 + ], + "type": "interline_equation", + "content": "\\mathrm {T} ^ {\\prime (a)} = \\operatorname {L N} \\left(\\mathrm {T} ^ {(a)}, \\boldsymbol {\\mu}, \\boldsymbol {\\sigma}, \\gamma^ {\\prime}, \\beta^ {\\prime}\\right), \\tag {3}", + "image_path": "cd901a616e82e76fcc2df0a911b8e012e1b51e7f1748552673b343d35f3df30a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "inline_equation", + "content": "\\gamma^\\prime" + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "inline_equation", + "content": "\\beta^\\prime" + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "text", + "content": " are the weight and bias parameters of the merged LN layer. Based on the equivalence of Eq. 2 and Eq. 3, for " + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "inline_equation", + "content": "\\forall 1\\leq i\\leq C" + }, + { + "bbox": [ + 46, + 624, + 288, + 662 + ], + "type": "text", + "content": ", we have:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 668, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 668, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 82, + 668, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\pmb {\\gamma} _ {i} ^ {\\prime} = \\pmb {\\gamma} _ {i} (\\mathbf {s} _ {i} - 1), \\quad \\pmb {\\beta} _ {i} ^ {\\prime} = \\pmb {\\beta} _ {i} (\\mathbf {s} _ {i} - 1) + \\mathbf {t} _ {i}, \\qquad (4)", + "image_path": "f8577ee809d27da1cc23fcf253d948a2bd5e6aab014fcf1a9a8ac8bc1d122059.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "The proof and PyTorch-like code of the affine transformation and re-parameterization process is shown in Sec.2 and" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 314, + 70, + 539, + 184 + ], + "blocks": [ + { + "bbox": [ + 69, + 177, + 265, + 188 + ], + "lines": [ + { + "bbox": [ + 69, + 177, + 265, + 188 + ], + "spans": [ + { + "bbox": [ + 69, + 177, + 265, + 188 + ], + "type": "text", + "content": "Table 4. Results of different module imitation setting." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 70, + 539, + 184 + ], + "lines": [ + { + "bbox": [ + 314, + 70, + 539, + 184 + ], + "spans": [ + { + "bbox": [ + 314, + 70, + 539, + 184 + ], + "type": "table", + "html": "
Teacher (T)T.acc (%)MIImageNet top-1 acc (%)
PoolFormer-M48 [46]82.5✗73.63
Swin-B* [24]85.2✗73.12
Pyramid ViG-B [15]83.7✗73.25
GFNet-H-B [31]82.9✗74.07
PoolFormer-M48 [46]82.5✓74.83
Swin-B* [24]85.2✓74.52
Pyramid ViG-B [15]83.7✓74.25
GFNet-H-B [31]82.9✓75.13
", + "image_path": "3d660f1a073a7b05a7d2a1cc828903c15cadd6522660ca57c949217c47043ede.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 187, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 305, + 187, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 187, + 545, + 210 + ], + "type": "text", + "content": "Table 5. Results of different teachers on RIFormer-S12 w/ or w/o module imitation (MI). * indicates ImageNet-22K pre-training." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 215, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 545, + 262 + ], + "type": "text", + "content": "Sec.3 of the appendix, respectively. Since the LN layer does not have a pre-computed mean and standard deviation during inference time, their specific values are input adaptive, which do not affect the equivalence of transform." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 263, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 546, + 396 + ], + "type": "text", + "content": "Remark 2. Compare Tab. 3 with Tab. 2, directly applying structural re-parameterization method shows no advantages. We attribute this phenomenon to the fact that the affine transformation in the LN layer is a linear transformation that can be directly merged with the extra affine operator we introduced (if do not add any nonlinear function in between). Therefore, if both are supervised only by the output of the model, the potential of the additional parameters may not be fully exploited. Meanwhile, the isomorphic design of teacher and student inspires us to explore suitable methods for knowledge transfer of modules at each layer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 402, + 411, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 411, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 411, + 414 + ], + "type": "text", + "content": "4.4. Module Imitation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": "Guideline 3: the proposed block-wise knowledge distillation, called module imitation, helps leveraging the modeling capacity of affine operator. The previous KD methods we tried only focus on the output of between teacher and student networks. We propose module imitation (MI) method, which present to utilize the useful information in the teacher's token mixer. Specifically, a pretrained PoolFormer-S12 [46] is utilized as a teacher network. As shown in Fig. 3, we expect the simple affine operator (with its preceding LN layer) to approximate the behavior of that of a basic token mixer during training. Denote " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "f(\\cdot), \\mathrm{T}^{(a),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M}" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": " as the affine operator and the input of the " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": "-th layer of RIFormal in which " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": " is the intermediate layers set we used, and " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "g(\\cdot), \\mathrm{T}^{(t),m} \\in \\mathbb{R}^{N \\times C \\times H \\times W}, m \\in \\mathcal{M}" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": " are that of the teacher network, respectively. We abbreviate " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\mathrm{LN}(\\cdot, \\mu, \\sigma, \\gamma, \\beta)" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\mathrm{LN}(\\cdot)" + }, + { + "bbox": [ + 304, + 420, + 547, + 648 + ], + "type": "text", + "content": " for simplicity. The mean squared error (MSE) of the inputs between the LN layer of affine operator and token mixer can be calculated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 340, + 655, + 545, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 655, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 340, + 655, + 545, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i n} = \\alpha_ {1} \\| \\mathrm {L N} (\\mathrm {T} ^ {(a), m}) - \\mathrm {L N} (\\mathrm {T} ^ {(t), m}) \\| _ {F} ^ {2}, \\tag {5}", + "image_path": "bcf4fbf3fb797dd7e203af75a398cb742712a2bcb25cfed26bff84dcbc0d0ab7.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{1} = 1 / NCHW" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": ". Note that the input feature of the current layer is the output feature of the previous one. Therefore, we propose to match the output features of this" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14447" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "block (i.e., the input features of the next subsequent block) in practice, which can be seen as a hidden state distillation in transformers [16, 19, 40, 41, 51]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 93, + 117, + 287, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 117, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 93, + 117, + 287, + 133 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i n} ^ {\\prime} = \\alpha_ {1} \\| T ^ {(a), m + 1} - T ^ {(t), m + 1} \\| _ {F} ^ {2}, \\tag {6}", + "image_path": "a95fda466fafdb1bb11f5a41a51963387f5bc6adb594c3c8754381648d6579de.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 287, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 165 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 165 + ], + "type": "text", + "content": "The hidden-state distillation based on relation matrices [16, 51] is then applied on the output feature:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 173, + 287, + 189 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 173, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 75, + 173, + 287, + 189 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e l} = \\alpha_ {2} \\| \\mathcal {R} (\\mathrm {T} ^ {(a), m + 1}) - \\mathcal {R} (\\mathrm {T} ^ {(t), m + 1}) \\| _ {F} ^ {2}, \\qquad (7)", + "image_path": "cb8b722232499071b95f1414d7ec33fd63bee8a6f67fd8c3411e5d0166ea8d10.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\alpha_{2} = 1 / NH^{2}W^{2}" + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(T) = \\tilde{T}\\tilde{T}^{\\top}" + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\tilde{T}" + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "content": " denotes normalize " + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 198, + 287, + 235 + ], + "type": "text", + "content": " at the last dimension. Considering the MSE of the outputs between affine operator and token mixer:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 60, + 243, + 287, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 243, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 60, + 243, + 287, + 259 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o u t} = \\alpha_ {1} \\| f (\\mathrm {L N} (\\mathrm {T} ^ {(a), m})) - g (\\mathrm {L N} (\\mathrm {T} ^ {(t), m})) \\| _ {F} ^ {2}, \\tag {8}", + "image_path": "48b69aa619b9e61473df136b394e4cc9f3289dc1648f0192b8893afdd1ae4208.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 266, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 287, + 290 + ], + "type": "text", + "content": "Combining Eq. 6, Eq. 7 and Eq. 8, the final loss function with module imitation is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 83, + 300, + 287, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 300, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 83, + 300, + 287, + 315 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {s o f t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {i n}} ^ {\\prime} + \\lambda_ {2} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {3} \\mathcal {L} _ {\\text {r e l}}, \\tag {9}", + "image_path": "374bdc97e808a132da597d13ebd2a531562e14442c22b73e93330149de55fdc9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{soft}" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": " is the soft logit distillation target in Sec. 4.2, " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2},\\lambda_{3}" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": " is the hyper-parameter for seeking the balance between loss functions. In Tab. 4, Feat and Rel are number of epochs of using " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{in}^{\\prime},\\mathcal{L}_{out})" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rel}" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": ", Layer represents the number of intermediate layers we used. The results show positive effect of module imitation on the student RIFformer in different circumstances. With a 4 layer setting and the usage of affine operator, we get the best result of " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "75.13\\%" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": ", already surpassing the PoolFormer-S12's result of " + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "inline_equation", + "content": "75.01\\%" + }, + { + "bbox": [ + 46, + 323, + 287, + 441 + ], + "type": "text", + "content": " in Tab. 1. From now on, we will use this setting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 443, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 537 + ], + "type": "text", + "content": "Remark 3. We deem a reason for that phenomenon might be that module imitation helps the affine operator implicitly benefit from the supervision of the teacher's token mixer, while not losing the convenience of explicitly merging the preceding LN layer. Besides, we find module imitation can effectively shift the feature distribution closer to the teacher network and show larger Effective Receptive Fields (ERFs). Please refer to Sec. 5.3 for details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 545, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 628 + ], + "type": "text", + "content": "Guideline 4: teacher with large receptive field is beneficial to improve student with limited receptive field. Tab. 5 compares student performance with different teacher architectures. Although GFNet-H-B [31] does not show the highest ImageNet top-1 performance among teachers, it can still serves as a better choice, no matter whether module imitation is used or not." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 45, + 630, + 287, + 713 + ], + "type": "text", + "content": "Remark 4. The fact is probably attributed to the receptive field gap between teacher and student. As explained by [1], inductive bias can be transferred from one model to another through distillation. According to this study, model with large receptive field (e.g., GFNet with learnable global filters in the frequency domain) can be better teacher for student RIFormer with limited receptive field." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "Guideline 5: loading the pre-trained weight of teacher model (except the token mixer) into student improves the convergence and performance. Our method can be categorized as a model compression technique that aims at removing the token mixer in basic blocks for acceleration. Inspired by previous methods, including knowledge distillation [32, 34], quantization [22, 26], and model acceleration [29] that initialize the weights of the light-weight network using (or partly using) the corresponding weights of the pre-trained heavy network, we explore a suitable initialization method. Since our goal is to remove only the token mixer, the weights of the remaining part still remain and are not paid enough attention in the previous journey. We observe that initializing the weights of RIFformer (except the affine operator) with the corresponding teacher network further boosts the performance from " + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "inline_equation", + "content": "75.13\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "inline_equation", + "content": "75.36\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": ". This brings us to the final paradigm for training RIFformer." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 277, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 410 + ], + "type": "text", + "content": "Closing remarks. So far, we have finished our exploration and discovered a suitable paradigm for training the RIFformer. It has the approximately the same macro design with MetaFormer [46], but does not require any token mixer. Equipped with the propsoed optimization methods, RIFformer can outperform complicated models with token mixers for ImageNet-1K classification. These encouraging findings inspire us to answer the following questions in the next section. 1) The scaling behavior of such extremely simple architecture with our training paradigm. 2) The generalizability of the paradigm on different teachers." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 441, + 420, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 420, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 420, + 453 + ], + "type": "text", + "content": "5.1. Image classification" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 460, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 592 + ], + "type": "text", + "content": "Setup. For ImageNet-1K [8] with 1.2M training images and 50000 validation images, we generally apply the training scheme in [46] while following the guidelines in Sec. 4. The data augmentation contains MixUp [50], CutMix [48], CutOut [52] and RandAugment [7]. As a model compression work on removing token mixer, bridging the performance gap caused by removing the token mixer is definitely our first priority, instead of proposing a strong baseline. Therefore, we use a prolonged the training epochs of 600. We also finetune the pre-trained models for 30 epochs with input resolution of " + }, + { + "bbox": [ + 304, + 460, + 545, + 592 + ], + "type": "inline_equation", + "content": "384^2" + }, + { + "bbox": [ + 304, + 460, + 545, + 592 + ], + "type": "text", + "content": ". More details are in the appendix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Main results. Tab. 6 shows the results of RIFormer on ImageNet classification. We pay main attention to the throughput metrics since our primary consideration is to satisfy latency requirements for edge devices. As expected, favorable speed advantage is achieved since RIFormer does not contain any token mixer in its building block, compared with other type of backbones. Surprisingly, with such fast inference, RIFormers successfully remove all token mixers using our training approach without affecting the performance. For example, RIFormer-M36 can pro" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14448" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 534, + 454 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 534, + 454 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 534, + 454 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 534, + 454 + ], + "type": "table", + "html": "
Token MixerOutcome ModelImage SizeParams (M)MACs (G)Throughput (images/s)Top-1 (%)
ConvolutionRSB-ResNet-34 [17,43]224223.76653.7575.5
RSB-ResNet-50 [17,43]224264.12732.8579.8
RSB-ResNet-101 [17,43]224457.91856.4881.3
RSB-ResNet-152 [17,43]2246011.61308.2681.8
Attention▲ DeiT-S [38]224224.63092.0279.8
▲ DeiT-B [38]2248617.51348.7681.8
▲ PVT-Small [42]224253.81622.5379.8
▲ PVT-Medium [42]224446.71190.4881.2
▲ PVT-Large [42]224619.8865.3381.7
Spatial MLPMLP-Mixer-B/16 [36]2245912.71855.4576.4
ResMLP-S24 [37]224306.03228.7579.4
ResMLP-B24 [37]22411623.0298.9481.0
Swin-Mixer-T/D6 [24]256234.01625.5979.7
Swin-Mixer-B/D24 [24]2246110.41131.6081.3
2D FFTGFNet-H-Ti [31]224152.11979.5680.1
GFNet-H-S [31]224324.61434.1981.5
GFNet-B [31]224437.91771.0780.7
GFNet-H-B [31]224548.6939.2082.9
Pooling○ PoolFormer-S12 [46]224121.84160.1877.2
○ PoolFormer-S24 [46]224213.42140.2080.3
○ PoolFormer-S36 [46]224315.01440.3781.4
○ PoolFormer-M36 [46]224568.81009.4582.1
○ PoolFormer-M48 [46]2247311.6761.9382.5
None★ RIFounder-S12°224121.84899.80 (↑17.8%)76.9
★ RIFounder-S24°224213.42530.48 (↑18.2%)80.3
★ RIFounder-S36°224315.01699.94 (↑18.0%)81.3
★ RIFounder-M36°224568.81185.33 (↑17.4%)82.6
★ RIFounder-M48°2247311.6897.05 (↑17.7%)82.8
★ RIFounder-S12‡384125.41586.5178.3
★ RIFounder-S24‡3842110.0819.4081.4
★ RIFounder-S36‡3843114.7552.0782.2
★ RIFounder-M36‡3845625.9403.1583.4
★ RIFounder-M48‡3847334.1304.4383.7
", + "image_path": "ca39dc2a3579bf7543593f0c871b45494ceb8d404cc2f96398ffb5d4547a8d7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 455, + 545, + 478 + ], + "lines": [ + { + "bbox": [ + 46, + 455, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 545, + 478 + ], + "type": "text", + "content": "Table 6. Results of models with different types of token mixers on ImageNet-1K. denotes training with prolonged 600 epochs. denotes fine-tuning from the ImageNet pre-trained model for 30 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": "cess more than 1185 images at " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " resolution per second, with the top-1 accuracy of " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "82.6\\%" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": ". In comparison, the recent baseline PoolFormer-M36 [46] with a Pooling token mixer, can process 1009 images of the same size with a worse " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "82.1\\%" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " accuracy. We also compare with an efficient backbone, GFNet [31]. It conducts token mixing via a global filter, which consists an FFT, an element-wise multiplication, and an IFFT, with a total computational complexity " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N\\log N)" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": ". With a 939 throughput, GFNet-H-B gets " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "82.9\\%" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " accuracy while our RIFformer-M48 can still reaches a comparable " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "82.8\\%" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " accuracy with on par throughput of 897. Meanwhile, the body of inference-time RIFformer is dominated by only " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " conv following LN, without complex 2D FFT or attention, friendly for hardware specialization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Notably, without token mixer, RIFormer cannot even perform basic token mixing operation in its building blocks. However, the ImageNet experiments demonstrate that with the proposed training paradigm, RIFormer still shows promising results. We can only deem the reason behind the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 482, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 531 + ], + "type": "text", + "content": "fact might be that optimization strategy plays a key role. RIFormer is readily a starting recipe for the exploration of optimization-driven efficient network design, and rest assured of the performance with advanced training schemes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 536, + 405, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 536, + 405, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 536, + 405, + 548 + ], + "type": "text", + "content": "5.2. Ablation studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 554, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 674 + ], + "type": "text", + "content": "Effectiveness of module imitation. As an important way for the extra affine operator to learn suitable weights, module imitation is based on distillation. Therefore, we compare it with the hidden state feature distillation approach (with relations). Taking the paradigm in Sec. 4.2 by soft distillation without CE loss, we get the results in Tab. 7. More details for Sec. 5.2 can be found in Sec.4 of the appendix. With feature distillation, the accuracy is " + }, + { + "bbox": [ + 304, + 554, + 545, + 674 + ], + "type": "inline_equation", + "content": "0.46\\%" + }, + { + "bbox": [ + 304, + 554, + 545, + 674 + ], + "type": "text", + "content": " lower than that of module imitation, showing module imitation's positive effect on the optimization of the extra weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "Comparisons of different acceleration strategy. Next, we discuss whether the token removing is better than other sparsification strategies. Based on the PoolFormer [46]" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14449" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 127, + 156 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 127, + 156 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 127, + 156 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 127, + 156 + ], + "type": "image", + "image_path": "08242cdedb5dd833cae1948cc2e0b7ab7786b2cd89aded2ef7b3573fb696fa8d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 157, + 114, + 165 + ], + "lines": [ + { + "bbox": [ + 61, + 157, + 114, + 165 + ], + "spans": [ + { + "bbox": [ + 61, + 157, + 114, + 165 + ], + "type": "text", + "content": "(a) PoolFormer-S12" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 206, + 156 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 206, + 156 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 206, + 156 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 206, + 156 + ], + "type": "image", + "image_path": "7107825627d6ffe2a074d214865460790fabc41e1e0e42d48cc7ba3a3f6250d0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 157, + 190, + 165 + ], + "lines": [ + { + "bbox": [ + 141, + 157, + 190, + 165 + ], + "spans": [ + { + "bbox": [ + 141, + 157, + 190, + 165 + ], + "type": "text", + "content": "(b) RIFormer-S12" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 207, + 70, + 287, + 156 + ], + "blocks": [ + { + "bbox": [ + 207, + 70, + 287, + 156 + ], + "lines": [ + { + "bbox": [ + 207, + 70, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 207, + 70, + 287, + 156 + ], + "type": "image", + "image_path": "5795a116e98fcd19eb43041343044f4e6becfe84d4744b3e624f5c932e5ac1a0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 157, + 276, + 166 + ], + "lines": [ + { + "bbox": [ + 214, + 157, + 276, + 166 + ], + "spans": [ + { + "bbox": [ + 214, + 157, + 276, + 166 + ], + "type": "text", + "content": "(c) RIFormer-S12 (MI)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 171, + 286, + 194 + ], + "lines": [ + { + "bbox": [ + 47, + 171, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 286, + 194 + ], + "type": "text", + "content": "Figure 4. The Effective Receptive Field (ERF) of PoolFormer-S12 and RIFlower-S12 with/without using module imitation." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 58, + 198, + 277, + 247 + ], + "blocks": [ + { + "bbox": [ + 58, + 198, + 277, + 247 + ], + "lines": [ + { + "bbox": [ + 58, + 198, + 277, + 247 + ], + "spans": [ + { + "bbox": [ + 58, + 198, + 277, + 247 + ], + "type": "table", + "html": "
Token MixerFeature distillation schemeTop-1 (%)
IdentityNone74.05
IdentityFeature distill74.90
AffineModule imitation75.36
", + "image_path": "b150f51d6b8504e6af6bee99252c6cf5ffbd46e3d8f7ee5be8387fe96cb51987.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 267, + 286, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 286, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 286, + 364 + ], + "type": "text", + "content": "baseline, we first construct a slim PoolFormer-S9 and PoolFormer-XS12 by reducing the depth to 9 and by maintaining about " + }, + { + "bbox": [ + 46, + 267, + 286, + 364 + ], + "type": "inline_equation", + "content": "\\frac{5}{6}" + }, + { + "bbox": [ + 46, + 267, + 286, + 364 + ], + "type": "text", + "content": " of its width, i.e., embedding dimension, to obtain comparable inference speed with our RIFormer-S12. We also follow the soft distillation paradigm in Sec. 4.2. Tab. 8 shows the results. Directly pruning depths or width cannot render a better performance than ours without latency-hungry token mixer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "content": "Generalization to different teachers. In order to verify the proposed training paradigm a general compression technique, we adopt the architecture modifications in [47] for student and change teacher to the other 4 MetaFormer baselines [47], with teacher token mixer as rand matrices, pooling, separable depthwise convolutions, and attention, respectively. Tab. 9 shows that our method has a positive effect in different depth settings and teacher circumstances." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 473, + 208, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 208, + 486 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 208, + 486 + ], + "type": "text", + "content": "5.3. Analysis of Module Imitation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 491, + 286, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 286, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 286, + 600 + ], + "type": "text", + "content": "Module imitation (MI) shifts the feature distribution of the RIFformer model to be closer to the teacher. The effect of the module imitation is explicitly shown in Fig. 5. It can be observed that PoolFomer-S12 and RIFformer-S12 show a clear difference in feature distribution of Stage 1 and Stage 4. After applying the proposed module imitation, the distribution of RIFformer-S12 are basically shifted toward that of the PoolFomer-S12, demonstrating its effect on helping student learn useful knowledge from the teacher." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Module imitation helps showing larger Effective Receptive Field (ERF). ERF [27] reflects how large an area of the image the trained model can respond to or capture information about how large an object. We follow [12, 20] to visualize the ERF via measuring the aggregated contributions of each pixel of the input to the central points of the output feature. Since RIFormer removes all token mixers, it exhibits an expectedly much smaller ERF than PoolFormer, as shown in Fig. 4. There is only a square of pixels emerg-" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 425, + 166 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 425, + 166 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 425, + 166 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 425, + 166 + ], + "type": "image", + "image_path": "69900e83ad5c01544ec37fb1a70b40c678ee4c3e7a55a6f8e3831c497a28e158.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 171, + 545, + 193 + ], + "lines": [ + { + "bbox": [ + 305, + 171, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 305, + 171, + 545, + 193 + ], + "type": "text", + "content": "Figure 5. Visualization of the feature distribution of the first and last stage of PoolFormer-S12 and RIFormal-S12." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 545, + 166 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 545, + 166 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 545, + 166 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 545, + 166 + ], + "type": "image", + "image_path": "c212c97c5154694105f56209d5ee329629347c4d5df8061d756c553a365eba8d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 316, + 196, + 535, + 255 + ], + "blocks": [ + { + "bbox": [ + 49, + 251, + 284, + 262 + ], + "lines": [ + { + "bbox": [ + 49, + 251, + 284, + 262 + ], + "spans": [ + { + "bbox": [ + 49, + 251, + 284, + 262 + ], + "type": "text", + "content": "Table 7. Ablation study of the effectiveness of module imitation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 196, + 535, + 255 + ], + "lines": [ + { + "bbox": [ + 316, + 196, + 535, + 255 + ], + "spans": [ + { + "bbox": [ + 316, + 196, + 535, + 255 + ], + "type": "table", + "html": "
ModelTypeThroughputTop-1 (%)
PoolFormer-S12None4160.1875.01
PoolFormer-S9Depth5025.7174.78
PoolFormer-XS12Width4780.2875.11
RIFounder-S12TM4899.8075.36
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Token MixerTeacherTop-1 (%)
Affine (12 layers)None72.75
Affine (12 layers)RandFormer-S12 [47]75.62
Affine (12 layers)PoolFormer V2-S12 [47]75.87
Affine (18 layers)None75.01
Affine (18 layers)ConvFormer-S18 [47]77.53
Affine (18 layers)CAFormer-S18 [47]77.26
", + "image_path": "b5b54cf32ec25c77801f79a4f5054a36bc85ba96232aa29a1f98425a79b032f2.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 362, + 518, + 373 + ], + "lines": [ + { + "bbox": [ + 331, + 362, + 518, + 373 + ], + "spans": [ + { + "bbox": [ + 331, + 362, + 518, + 373 + ], + "type": "text", + "content": "Table 9. Results of generalization to other teachers." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 376, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 449 + ], + "type": "text", + "content": "ing with red color in the whole region, much smaller than PoolFormer. However, surprisingly, we can observe that red color widely distributed in all locations after training with module imitation. It seems that although there's no explicit structural change, module imitation still help change the learned weights and show larger ERF." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 459, + 462, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 462, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 462, + 472 + ], + "type": "text", + "content": "6. Limitations and Conclusion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 598 + ], + "type": "text", + "content": "This paper investigates removing token mixer of the basic building block in a vision backbone, motivated by their considerable latency cost. To keep the remaining structure still effective, we thoroughly revisits the training paradigm. We observe that appropriate optimization strategy can effectively help a token mixer-free model learn useful knowledge from another model, boosting its performance and bridge the gap caused by incomplete structure. Limitations are that more vision tasks, including detection, deblurring, etc. are not discussed, and we will work on them in the future." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 609, + 404, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 404, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 404, + 623 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This paper is partly supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, Shanghai Postdoctoral Excellence Program (No.2022235), the National Natural Science Foundation of China (Grant No.61991450) and the Shenzhen Science and Technology Program (JCYJ20220818101001004)." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14450" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Samira Abnar, Mostafa Dehghani, and Willem Zuidema. 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In this work, we seek the synergy between two paradigms and study the emerging properties when MIM meets natural language supervision. To this end, we present a novel masked visual Reconstruction In Language semantic Space (RILS) pre-training framework, in which sentence representations, encoded by the text encoder, serve as prototypes to transform the vision-only signals into patch-sentence probabilities as semantically meaningful MIM reconstruction targets. The vision models can therefore capture useful components with structured information by predicting proper semantic of masked tokens. Better visual representations could, in turn, improve the text encoder via the image-text alignment objective, which is essential for the effective MIM target transformation. Extensive experimental results demonstrate that our method not only enjoys the best of previous MIM and CLIP but also achieves further improvements on various tasks due to their mutual benefits. RILS exhibits advanced transferability on downstream classification, detection, and segmentation, especially for low-shot regimes. Code is available at https://github.com/hustvl/RILS.", + "bbox": [ + 75, + 318, + 473, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 698, + 209, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning transferable representation lies a crucial task in deep learning. Over the past few years, natural language processing (NLP) has achieved great success in this line of research [18, 45, 60]. To explore similar trajectories in the vision domain, researchers tend to draw upon the successes of NLP and have made tremendous progress: (i) Inspired by the advanced model architecture [60] as well as self-supervised learning paradigm [18] in NLP, vision Transformers (ViT) [21, 42] and masked image modeling", + "bbox": [ + 75, + 724, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/286393bcdae264a5673a8b31c0ec496e5b2e016853b473b1d29545879f01c785.jpg", + "image_caption": [ + "Figure 1. Overview of our RILS. Recon and Contra represent masked reconstruction loss and image-text contrastive loss. During pre-training, RILS learns to perform masked image modeling and image-text contrastive simultaneously. Masked predictions and corresponding targets are transformed to probabilistic distributions in language space by leveraging text features as semantic-rich prototypes. Under such a scheme, both objective and unified and achieve mutual benefits from each other. Vision encoder obtains the ability to capture meaningful and fine-grained context information, sparking decent transfer capacity." + ], + "image_footnote": [], + "bbox": [ + 503, + 286, + 893, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(MIM) [3, 28] open a new era of self-supervised visual representation learning, and show unprecedented transferability on various tasks, especially on fine-grained tasks such as object detection [22, 39]. (ii) Inspired by the great scalability brought by leveraging web-scale collections of texts as training data in NLP [5, 48, 49, 72], CLIP [47] and ALIGN [35] bring such a principle to vision and manifest the immense potential of leveraging natural language supervision for scalable visual pre-training. Strong transferability of pre-trained visual models on low-shot regimes ensues. It also facilitates diverse applications by extracting contextualized image or text features [26, 50, 52].", + "bbox": [ + 496, + 597, + 893, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The remarkable attainment achieved by these two research lines pushes us to ponder: Is it possible to unify both masked image modeling and natural language supervision to pursuit better visual pre-training? A straightforward way towards this goal is to simply combine masked image modeling (MIM) with image-text contrastive learning (ITC) for multi-task learning. Although the naive combination is feasible to inherit the above advantages, we find it remains un-", + "bbox": [ + 496, + 780, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done while S. Yang was an intern at ARC Lab, Tencent PCG. † X. Wang and Y. Ge are the corresponding authors.", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23304", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "satisfactory due to the mutual benefits between MIM and ITC have not yet been fully explored. Motivated by this, we develop RILS, a tailored framework to seek the synergy of masked image modeling and language supervision.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The core insight of RILS is to perform masked visual reconstruction in language semantic space. Specifically, instead of reconstructing masked patches in the standalone vision space (e.g., raw pixel [28,66], low-level features [3,62] or high-level perceptions [12, 34, 63, 75]), we map patch features to a probabilistic distribution over a batch of text features as the reconstruction target, which is enabled by ITC that progressively aligns the image and text spaces. The text features serve as semantically rich prototypes and probabilistic distributions explicitly inject the semantic information onto each image patch. The MIM objective is formulated as a soft cross-entropy loss to minimize the KL divergence between text-injected probabilistic distributions of masked vision tokens and their corresponding targets. The visual model optimized by our language-assisted reconstruction objective, in turn, improves ITC with better visual representations that capture fine-grained local contexts.", + "bbox": [ + 75, + 152, + 470, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Under such a working mechanism, the two objectives (i.e., MIM and ITC) complement each other and form a unified solution for transferable and scalable visual pretraining. Note that a lot of works [34, 63, 75] have manifested the importance of semantic information in the reconstruction target of MIM objectives. However, it is abstract to pursue such a semantically rich space with visual-only signals due to its unstructured characteristics [29]. Thanks to natural language supervision, this issue is alleviated by performing masked reconstruction in language space.", + "bbox": [ + 75, + 407, + 468, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments on various downstream tasks demonstrate that our design enjoys the best of both worlds. With a vanilla ViT-B/16 as the vision model and 25-epoch pre-training on 20 million image-text pairs, RILS achieves $83.3\\%$ top-1 accuracy when fine-tune on ImageNet-1K [15], $+1.2\\%$ and $+0.6\\%$ better than the MAE [28] and CLIP [47] counterparts. Advanced performance can be consistently acquired when transfer to fine-grained tasks such as detection and segmentation. Moreover, our approach exhibits promising out-of-the-box capability under an extremely low-shot regime. RILS also demonstrates superior performance on zero-shot image classification and image-text retrieval. On ImageNet-1K benchmark, RILS obtains $45.0\\%$ zero-shot classification accuracy, $+4.7\\% / + 3.4\\%$ higher than CLIP [47]/SLIP [43] under the same training recipe. Compelling results of RILS imply the promising capacity in the unification of MIM and language supervision.", + "bbox": [ + 75, + 560, + 470, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 844, + 225, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Masked Image Modeling translates masked language modeling [18] to vision domain and learns transferable", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "visual representation by reconstructing masked signals from partial observation [3, 9, 21]. Despite following the same mask-then-reconstruction principle, MIM differs from MLM a lot in the design of reconstruction target. BEiT [3] utilizes a pre-trained d-VAE [51, 55] and reconstructs masked image patches in the offline token space. Subsequent works improve it by employing better pretrained tokenizer [19, 34, 44, 63], eased and refined multichoice tokens [37] or contextual aligner [11]. MAE [28] and SimMIM [66] demonstrate directly reconstruct masked patches in raw pixel space can also lead to favorable transferability as well as scalability. MaskFeat [62] takes handcrafted low-level HOG feature [14] as target. Other works like iBOT [75], data2vec [2] and SdAE [12] perform reconstruction in a high-level vision feature space. Different from these methods, in this work, we tap the potential when masked image modeling meets natural language supervision and propose performing masked visual reconstruction in the language semantic space.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Language Supervised Visual Pre-training learns visual representation from image-text pairs by solving generative [16, 56] or discriminative [73] pretext tasks. Recently, benefit from modern network architectures [21,41,42] and publicly available image-text datasets [8,17,57-59], CLIP [47] and ALIGN [35] unveil the tremendous transferability and scalability of this paradigm. The core technique of CLIP is aligning both vision and language modalities in a joint embedding space by global representation contrastive. Follow-up works further improve CLIP on the vision-only [43, 67] or vision-language [38, 64, 68-70] side. In this paper, we bring natural language supervision together with masked image modeling for better visual pre-training on these two paradigms.", + "bbox": [ + 496, + 378, + 892, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Our Approach", + "text_level": 1, + "bbox": [ + 500, + 607, + 648, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Architecture", + "text_level": 1, + "bbox": [ + 500, + 633, + 633, + 647 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among numerous architecture designing spaces, without loss of generalization, we adopt an asymmetric encoder-decoder architecture following MAE [28] and a dual-encoder architecture following CLIP [47] for their flexibility. As illustrated in Figure 1, RILS comprises the following three major components:", + "bbox": [ + 496, + 657, + 890, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision Encoder plays the key role in RILS and all our efforts aim to strengthen its capacity on downstream transfer. Following the trend in recent visual pre-training, we implement this encoder by a vanilla vision Transformer (ViT) [21]. It takes both intact (unmasked) image and corrupted (masked) image as inputs. Formally, input image $I$ is first divided into regular non-overlapping image patches and then encoded by a stack of Transformer blocks [60]. Meanwhile, following MAE [28], we randomly mask a large portion of image patches and leave the remaining patches to be", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23305", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "visible. This corrupted image $\\hat{I}$ is also encoded by vision encoder. We formulate the process of vision encoder as:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {V} - \\operatorname {E n c} (I) = \\{f ^ {k} | k \\in [ 1, N ] \\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 128, + 468, + 154 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {V - E n c} (\\hat {I}) = \\{\\hat {f} ^ {k} | k \\in [ 1, N ] \\backslash \\mathcal {M} \\},\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 150, + 388, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $k$ denotes the patch index and $N$ denotes image patch numbers. $f$ and $\\hat{f}$ betoken encoded patch features of intact image $I$ and corrupted image $\\hat{I}$ . $\\mathcal{M}$ indicates the index set of random masked patches.", + "bbox": [ + 76, + 175, + 468, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Language Encoder encodes input text $T$ by a stack of Transformer layers with causal masked attention [60]. This process can be simply represented by:", + "bbox": [ + 76, + 236, + 468, + 281 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L} - \\operatorname {E n c} (T) = h. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 289, + 468, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We take the output $h$ as global representation of input text. Vision Decoder consists of another series of Transformer blocks. Particularly, in our design, decoder blocks have the same dimension as encoder blocks. It takes the encoded feature $\\hat{f}$ of masked image $\\hat{I}$ along with a learnable [MASK] token as inputs, and tries to predict masked signals from corrupted view:", + "bbox": [ + 76, + 313, + 467, + 419 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {V} - \\operatorname {D e c} \\left(\\left\\{\\hat {f} ^ {k} \\mid k \\in [ 1, N ] \\backslash \\mathcal {M} \\right\\}, [ \\text {M A S K} ]\\right) = \\left\\{g ^ {k} \\mid k \\in [ 1, N ] \\right\\}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 425, + 468, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 465, + 256, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image-Text Contrastive. We leverage image-text contrastive loss to align two modalities into a joint embedding space. Specifically, given image-text pair $\\{(I,T)\\}$ , we take the mean-pooled image feature $\\bar{f} = \\frac{1}{N}\\sum_{k=1}^{N}f^k$ and $h$ in Eq. (2) as global representations for image and text. The image and text features are further projected by two projection heads and followed by a normalization:", + "bbox": [ + 76, + 489, + 468, + 595 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz ^ {I} = \\left\\| \\theta (\\bar {f}) \\right\\|, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 603, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz ^ {T} = | | \\phi (h) | |,\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 625, + 321, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\theta (\\cdot)$ and $\\phi (\\cdot)$ denotes the projection head for image and text respectively. The image-to-text contrastive loss and text-to-image contrastive loss can be represented as:", + "bbox": [ + 76, + 650, + 468, + 695 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {I 2 T}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {i} ^ {T} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {j} ^ {T} \\right\\rangle / \\sigma\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 703, + 468, + 752 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T 2 I}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {i} ^ {I} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {j} ^ {I} \\right\\rangle / \\sigma\\right)},\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 750, + 423, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $i$ and $j$ stands for the index within a mini-batch and $B$ indicates the batch size respectively. $\\sigma$ performs a learnable temperature and is jointly trained during the pretraining. The total loss of image-text contrastive learning can be formulated as:", + "bbox": [ + 76, + 795, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {C o n t r a}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {I 2 T}} + \\mathcal {L} _ {\\mathrm {T 2 I}}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 876, + 468, + 905 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Masked Visual Reconstruction in Language Semantic Space. As aforementioned, despite the mask-then-reconstruct principle of MIM is concise enough, the contiguous and unstructured characteristics in visual signal make the choice of reconstruction space non-trivial. Lots of works have manifested the great importance of performing masked reconstruction in a semantic-rich space [12, 34, 63, 75]. In this work, we build our reconstruction space from a vision-language perspective. We regard the text features as natural semantic descriptors for image patches and try to perform masked visual reconstruction in this language space. Specifically, given the encoded patch feature $f^{k}$ in Eq. (1) with $k$ being the index of patch and decoded patch feature $g^{k}$ in Eq. (3), we firstly project and normalize both features to the vision-language aligned space:", + "bbox": [ + 498, + 90, + 890, + 318 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {f} _ {i} ^ {k} = \\left| \\left| \\theta \\left(f _ {i} ^ {k}\\right) \\right| \\right|, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 642, + 328, + 890, + 354 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {g} _ {i} ^ {k} = | \\left| \\theta \\left(g _ {i} ^ {k}\\right) \\right| |,\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 349, + 745, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $i$ being the index within mini-batch. $\\theta (\\cdot)$ represents the same vision projection head in Eq. (4). The key step of our design is to map patch features to a probabilistic distributions over a bunch of text features:", + "bbox": [ + 498, + 378, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {1}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {1}\\right)} \\mid l \\in [ 1, B ] \\right\\}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 448, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {q} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {2}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {2}\\right)} \\mid l \\in [ 1, B ] \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 489, + 844, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\tau_{1}$ and $\\tau_{2}$ serve as temperatures. In this way, with the text features serve as semantic-rich prototypes, both masked prediction and corresponding target are mapped into this language semantic space. The probabilistic distributions explicitly express the context information within each patch. The reconstruction objective is to shrinking the differences between text-injected distributions of target and masked prediction by minimize the KL divergence of $p_i^k$ w.r.t. $q_i^k$ , which can be represented by:", + "bbox": [ + 498, + 539, + 890, + 675 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {R e c o n}} = \\frac {1}{| | \\mathcal {C} | | \\cdot | | \\mathcal {M} | |} \\sum_ {i \\in \\mathcal {C}} \\sum_ {k \\in \\mathcal {M}} - \\operatorname {s g} \\left[ \\boldsymbol {p} _ {i} ^ {k} \\right] \\log \\boldsymbol {q} _ {i} ^ {k}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 686, + 890, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\mathrm{sg}[\\cdot ]$ indicates stop gradient. $\\mathcal{M}$ denotes the index set of masked patches. $\\mathcal{C}$ signifies the indexes of images which are correctly aligned to corresponding text features. In other words, we only calculate reconstruction loss on images which are correctly matched with target texts in imaged-to-text matching.", + "bbox": [ + 498, + 734, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By transferring reconstruction space from standalone vision space to language space, our approach takes both MIM and ITC into a unifying landscape and achieves mutual benefits from each other. MIM always suffers from overly paying attention on low-level details which consume lots of", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23306", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e298da8b7cc482b2ce558532c05ceafd955b308998304a0e85d52226917a432b.jpg", + "image_caption": [ + "Figure 2. Architecture comparisons between MAE [28], CLIP [47], MAE+CLIP and RILS. Recon and Contra indicate masked reconstruction loss and image-text contrastive loss." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 468, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "model's capacity but of less helpful for understanding visual concepts. By leveraging text features as prototypes and transfer patch features to probabilistic distribution on language space, the low-level information inside visual signals are abandoned by the contextualized language prototypes. Better contextualized image features in turn assist vision-language alignment, leading to transferable and scalable visual pre-training.", + "bbox": [ + 75, + 435, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall Objective Function. The final objective of RILS is a weighted-sum of both image-text contrastive loss and masked reconstruction loss:", + "bbox": [ + 75, + 556, + 468, + 602 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {R I L S}} = \\lambda_ {1} \\cdot \\mathcal {L} _ {\\text {C o n t r a}} + \\lambda_ {2} \\cdot \\mathcal {L} _ {\\text {R e c o n}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 614, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\lambda_{1}$ and $\\lambda_{2}$ indicate coefficients to balance two losses.", + "bbox": [ + 76, + 641, + 426, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pre-training Setup", + "text_level": 1, + "bbox": [ + 76, + 665, + 256, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to [69], we sequentially sample image-text pairs according to filenames from recent released LAION-400M [58] dataset as our training sets. We term them as L-10M/L-20M/L-50M according to the amount of sampled unique image-text pairs (e.g., L-10M stands for the first 10 million subset of LAION-400M). Unless specified, our method is trained on L-20M for 25 epochs. We take AdamW [36] as optimizer with learning rate set to 5e-4 and a weight decay of 0.5. Learning rate linearly increases in the first epoch as warmup and decreases in the rest following the cosine learning rate decay strategy. We train our method on 32 NVIDIA V100 with a total batch size of 4096 (i.e., batch size per GPU is 128). For model architecture, we take the widely-adopted ViT-B/16 as vision encoder, 1-", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/c3b37ee9095a3b7213c75a81bea58cb5c0db4f64e356909eca679afcd9386225.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDatasetPT Epo.Lin.FT.
SimCLR [10]51.781.3
MAE [28]44.382.1
CLIP [47]L-20M25(∼ 400)67.882.7
SLIP [43]70.182.6
MAE+CLIP64.582.9
RILS71.583.3
BEiT [3]IN-1K(∼ 1.3M)800-83.2
MAE [28]160067.883.6
RILSL-50M25(∼ 1000)71.983.6
", + "bbox": [ + 532, + 87, + 859, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Image classification results on ImageNet-1K (IN-1K). PT Epo. indicates per-training epochs. Lin. and FT. is short for linear probing and end-to-end fine-tuning respectively.", + "bbox": [ + 498, + 247, + 893, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "layer Transformer block with 768-dim and 12 heads as vision decoder, and a text Transformer with 12 blocks and 512-dim as language encoder. To tokenize text inputs, following [47], we use byte-pair encoding (BPE [23]) with $49\\mathrm{K}$ vocabulary size and set the max length of each sentence to 77. During pre-training, input images are resized to $224 \\times 224$ and we set random mask ratio to $75\\%$ following [28]. Temperatures $\\tau_{1}$ and $\\tau_{2}$ in Eq. (8) are set to 0.04 and 0.1. Loss coefficients $\\lambda_{1}$ and $\\lambda_{2}$ are set to 1.0 and 0.5 by default. More pre-training setups are listed in the appendix.", + "bbox": [ + 498, + 304, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Discussion", + "text_level": 1, + "bbox": [ + 500, + 474, + 617, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are also meaningful attempts [20,34,44,63] on utilizing natural language supervision together with MIM and seem alike to ours. However, there still have some distinctions existing in the motivation and method between ours and theirs. MVP [63], MILAN [34] and BEiTv2 [44] leverage natural language supervision by a two-stage framework, while ours is fully end-to-end. We will take further discussion about two-stage methods and ours in later experiments. A related and concurrent work [20] shows some similar designs but significantly differs from our idea of reconstruction in language space. As it does not have a reproducible implementation, we do not take it into consideration for comparison.", + "bbox": [ + 498, + 501, + 890, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Main Results", + "text_level": 1, + "bbox": [ + 500, + 720, + 635, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we evaluate the representation quality of pre-training by transferring pre-trained models to various downstream tasks. We choose MAE [28] and CLIP [47] as representative methods of masked image modeling and vision-language contrastive learning. We also conduct a naive baseline (termed as MAE+CLIP) which simply combine MAE and CLIP together to perform MIM and ITC simultaneously, as a counterpart for our approach. Semantically comparisons between MAE, CLIP, MAE+CLIP and our RILS are illustrated in Figure 2.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23307", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/609a6813748562c0f1b92b20b88fc7130a152250854835af3939d1d71ad21701.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCOCOLVIS
APBAPB50APB75APMAPM50APM75APBAPB50APB75APMAPM50APM75
MAE [28]48.168.652.942.465.846.431.046.233.729.644.031.7
CLIP [47]47.769.152.342.065.945.132.348.135.130.545.932.5
SLIP [43]46.568.551.041.565.144.132.448.935.130.846.532.6
MAE+CLIP48.169.652.542.466.245.732.648.835.230.746.432.6
RILS48.570.553.242.666.845.833.850.236.531.647.833.7
", + "bbox": [ + 114, + 88, + 851, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Classification Transfer", + "text_level": 1, + "bbox": [ + 76, + 242, + 287, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Linear Probing evaluates the quality of pre-trained feature by training a linear classifier on the frozen feature. We following the the recipe in [7] and sweep over different learning rate. Results are shown in Table 1. We notice that, with 25-epochs pre-training on L-20M, MAE+CLIP only achieves $64.5\\%$ accuracy which is better than MAE but worse than CLIP. This implies the contradiction between MIM and ITC exists in such a naive combination. RILS alleviates this contradiction by elaborated design and outperforms other methods by a large margin.", + "bbox": [ + 75, + 266, + 468, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "End-to-End Fine-tuning. We follow most of setups in [28] for fine-tuning. Concretely, we fine-tune pre-trained models for 100 epochs with a warm-up of 5 epochs. Hyperparameters are all the same for all experiments except the learning rate. Results are shown in Table 1. When training with 25 epochs on L-20M, our method shows distinct advantages. Compared to MAE, CLIP and MAE+CLIP, our method exhibits $+1.2\\%$ , $+0.6\\%$ and $+0.4\\%$ gains respectively. Moreover, when we scale-up the dataset capacity from L-20M to L-50M, with 25 epochs pre-training (around 1000 equivalent epochs in the ImageNet-1K regime), our method achieves $83.6\\%$ top-1 accuracy which is on par with prior art (MAE trained on ImageNet-1K with 1600 epochs) with only $62.5\\%$ training length.", + "bbox": [ + 75, + 417, + 470, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Downstream Transfer", + "text_level": 1, + "bbox": [ + 76, + 635, + 282, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Object Detection and Segmentation. For object detection and instance segmentation, we choose COCO [40] and LVIS [27] as benchmarks. We follow the design in [39] to transfer pre-trained ViT to detection. To tame quadratic complexity within self-attention, most attention blocks in the ViT are replaced with window attention except for four global blocks to perform cross-window interaction. SimpleFPN [39] is attached to the last transform block to generate pyramid features. Modernized RPN [54] and Mask R-CNN [31] head are deployed for detecting and segmenting visual instances. All pre-trained models are fine-tuned on two benchmarks for 25 epochs with same hyper-parameters. The results are shown in Table 2. Among all methods, our RILS achieves the best results in terms of $\\mathrm{AP}^{\\mathcal{B}}$ and $\\mathrm{AP}^{\\mathcal{M}}$ on both COCO and LVIS. It's noteworthy that two benchmarks show different properties: COCO benchmark shows", + "bbox": [ + 75, + 657, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/53b8197dca98be686f9168c730ff80f6548cc9811632262ee146e8448abbaa2c.jpg", + "table_caption": [ + "Table 2. Object detection and instance segmentation results on COCO and LVIS. All models are pre-trained with ViT-B/16 for 25 epochs on L-20M. Fine-tuning recipes for different pre-trained models are the same." + ], + "table_footnote": [], + "table_body": "
MethodDatasetPT Epo.mIoU
BEiT [3]IN-1K(~ 1.3M)30045.5
80046.5
MAE [28]30045.8
160048.1
MAE [28]L-20M25(~ 400)44.2
CLIP [47]45.2
SLIP [43]45.7
MAE+CLIP45.3
RILSL-20M25(~ 400)48.1
", + "bbox": [ + 526, + 241, + 864, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3. Semantic segmentation results on ADE20K.", + "bbox": [ + 529, + 398, + 861, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "less benefits from language supervision while LVIS converses. Specifically, MAE shows leading performance on COCO but inferior performance on LVIS. We suspect this is due to the inherent distinctions in COCO and LVIS: LVIS contains 1203 visual categories which is about $15 \\times$ more than COCO, and it always suffers from the long-tail distribution. Under such circumstances, COCO requires more localization ability which MAE excel at while LVIS prefers better classification ability which natural language supervision can bring. From this perspective, when compare our RILS with the MAE+CLIP, we find our design benefits more from both MIM and ITC objectives. On both COCO and LVIS, MAE+CLIP only shows competitive performance to the winner of MAE and CLIP, but our RILS exhibits apparent improvements especially on LVIS. This indicates our design leverage masked image modeling and language supervision in a more synergistic way. We believe this kind of synergy is of great exploration value for better visual pre-training.", + "bbox": [ + 496, + 428, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic Segmentation. Experiments on semantic segmentation are conducted on the well-known ADE20K [74] dataset. We build the segmentation framework upon UperNet [65] and use the pre-trained models as encoders. Input images are resized to $512 \\times 512$ and all models are finetuned for 160K iterations. All hyper-parameters strictly follow MAE [28] and not tuned. We report the mean intersection-over-union (mIoU) in Table 3. As the results shown, our method overwhelmingly surpasses others. Specifically, with 25 epoch pre-training on L-20M, our method achieves $48.1\\mathrm{mIoU}$ , $+3.9$ and $+2.9$ higher than MAE and CLIP. Similar to the trends on LVIS, MAE+CLIP", + "bbox": [ + 496, + 719, + 892, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23308", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9b1a62bea2c1f7e5f052a138b6be8d323d6b0552185f0f59d4241c31f1904220.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPT DatasetPT Epo.Images per Class
12510
MAE [28]IN-1K(~ 1.3M)16004.3 ± (0.28)10.6 ± (0.21)22.4 ± (0.28)31.6 ± (0.02)
BEiT [3]IN-1K(~ 1.3M)8001.3 ± (0.03)2.2 ± (0.13)4.4 ± (0.21)7.4 ± (0.05)
MAE [28]L-20M25(~ 400)3.4 ± (0.12)5.2 ± (0.21)10.1 ± (0.10)14.8 ± (0.20)
CLIP [47]19.4 ± (0.18)29.2 ± (0.61)39.8 ± (0.39)46.3 ± (0.15)
SLIP [43]17.7 ± (0.33)27.2 ± (0.56)38.6 ± (0.55)46.4 ± (0.06)
MAE+CLIP21.1 ± (0.12)31.1 ± (0.94)41.6 ± (0.43)47.5 ± (0.15)
RILSL-20M25(~ 400)24.0 ± (0.27)34.6 ± (0.88)45.7 ± (0.46)51.8 ± (0.18)
", + "bbox": [ + 116, + 88, + 851, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "only gets $0.1\\mathrm{mIoU}$ gains by simply combining MIM with ITC together, far less than our approach. Furthermore, our method shows competitive or better performance when compared to prior art. Compared to MAE pre-trained on ImageNet-1K with 300 epochs, our method achieves 2.3 higher performance (48.1 vs. 45.8). When MAE is pretrained with 1600 epochs, our method achieves the same mIoU (48.1) while only requires $25\\%$ training length.", + "bbox": [ + 75, + 282, + 468, + 404 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments above demonstrate the excellent transfer capacity of our approach on fine-grained visual understanding tasks. Our design unleashes the ability to capture local details and global contexts by performing masked visual reconstruction in language semantic space.", + "bbox": [ + 75, + 405, + 470, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Label-Efficient Transfer", + "text_level": 1, + "bbox": [ + 76, + 494, + 302, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Low-shot Regime Classification. We investigate the classification performance when only very few labeled images are available. Specifically, following [1,6], we random sample 1, 2, 5, and 10 labeled images per class from ImageNet-1K training split as our training sets. Instead of end-to-end fine-tuning, we train a linear classifier on frozen features to avoid overfitting. The complete validation split of ImageNet-1K which contains $50\\mathrm{K}$ images are used to evaluate the accuracy. Table 4 shows the results.", + "bbox": [ + 75, + 518, + 468, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Specifically, compared to MAE+CLIP which only obtain slightly improvements over CLIP, our RILS outperforms both of them by a large margin. Notably, with only 10 images per class (i.e., 10K images for 1K classes), our method can achieve $51.8\\%$ top-1 accuracy.", + "bbox": [ + 75, + 657, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Low-shot Regime Detection. We further transfer the low-shot experiment to object detection on COCO [40], which requires model to localize and classify visual objects simultaneously. We randomly sample annotated images from COCO training split with different sampling ratio (range from $1\\%$ to $50\\%$ ) as our training sets. All models are end-to-end fine-tuned for 12 epochs instead of 25 to prevent overfitting. We report the average precision of detection $\\mathbf{AP}^{\\mathcal{B}}$ for comparison in Table 5. As the results shown, our method shows the best performance under a wide range of sampling ratio (from $2\\%$ to $50\\%$ ).", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c641712f1b6e254fc5c5aeec5dd860f95a47638ecf02103b32dec62adb33b79f.jpg", + "table_caption": [ + "Table 4. Extreme low-shot classification on ImageNet-1K. We random sample 1, 2, 5, 10 images per class from training split, and report logistic regression accuracy (%) on ImageNet-1K validation split. All methods use ViT-B/16 as vision encoder." + ], + "table_footnote": [], + "table_body": "
MethodCOCO Sampling Ratio
1%2%5%10%20%50%
MAE [28]0.946.1015.7623.1629.7838.10
CLIP [47]0.815.0514.9822.4929.8838.50
SLIP [43]1.114.5413.8421.9129.5337.73
MAE+CLIP0.685.2814.3323.7229.9939.24
RILS0.866.4616.9424.6931.9740.41
", + "bbox": [ + 509, + 280, + 880, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Low-shot regime object detection on COCO. We report detection performance $\\mathrm{AP}^{\\mathcal{B}}$ with 12 epochs fine-tuning. All models are pre-trained with ViT-B/16 and 25 epochs on L-20M.", + "bbox": [ + 498, + 397, + 892, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Conceptually, one of the aspirations of pre-training is to pursue efficient transfer (e.g., less trainable data, shorter training length) on downstream tasks [1, 25, 30]. Experiments in the low-shot regime show the strong out-of-the-box capacity of our RILS by performing MIM in language semantic space. The non-trivial results indicate our pretraining approach brings out label-efficient learner, showing great application value to real-world scenarios, especially when annotated data is insufficient.", + "bbox": [ + 496, + 445, + 893, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Zero-Shot Transfer", + "text_level": 1, + "bbox": [ + 500, + 590, + 686, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classification. We evaluate the zero-shot classification over 21 benchmarks including ImageNet-1K [15]. Detail of each datasets are listed in the appendix and the evaluate recipes (e.g., prompt engineering) strictly follow [43]. Results are shown in Table 6. Specifically, compared to CLIP, MAE+CLIP only achieves $+0.6\\%$ average improvements, while our RILS shows $+2.0\\%$ gains. This hints the masked image modeling objective in the naive combination has little help to image-text alignment, while ours alleviate this issue by bind two objectives in a unified landscape. On ImageNet-1K, our method achieves $45.0\\%$ accuracy, $+4.7\\% / + 3.4\\% / + 2.7\\%$ higher than CLIP, SLIP and MAE+CLIP, respectively. Among 21 benchmarks, our method outperforms others over 17 datasets, frequently with a significant margin.", + "bbox": [ + 496, + 613, + 892, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image-Text Retrieval. We study image-text retrieval on 2 benchmarks: COCO [40] and Flickr30K [46]. For both benchmarks, we use the original captions (w/o prompt) and $224 \\times 224$ resized images for retrieval. Different from zero", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23309", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e547cb9fc54193346c08f59eddc5aa1015deeb175473e9336dc2844499065fe8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFood101CIFAR10CIFAR100CUB200SUN397CarsAircraftDTDPetsCaltech101FlowersMNISTFER2013STL10EuroSATRESISC45GTSRBCountry211CLEVRSST2ImageNetAverage# Wins.
CLIP [47]55.776.046.924.450.717.84.831.553.778.431.826.837.689.022.736.924.16.820.049.140.339.32
SLIP [43]56.773.443.222.651.617.74.932.452.579.133.329.433.589.517.836.217.86.823.449.741.638.72
MAE+CLIP57.878.252.423.951.618.14.631.555.878.432.027.632.789.827.039.422.97.214.749.342.339.90
RILS58.986.255.123.451.819.55.932.859.280.733.522.640.193.228.840.219.17.816.850.045.042.317
", + "bbox": [ + 86, + 88, + 880, + 199 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9a966cbd537614a2a6934ca03096ac2c5d06d0bc4539db7cd0a77f2c923461e8.jpg", + "table_caption": [ + "Table 6. Zero-shot classification on 21 datasets. All models are trained with ViT-B/16 encoder for 25 epochs on L-20M." + ], + "table_footnote": [], + "table_body": "
MethodCOCOFlickr30K
I→TT→II→TT→I
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [47]41.8269.5079.3430.5457.1069.3028.1350.7761.1220.6140.7750.49
SLIP [43]44.5472.2082.1033.2659.6671.1431.2055.8166.0224.0545.5855.90
MAE+CLIP42.7270.6680.3631.4057.5069.6828.6252.2562.6422.6443.6753.97
RILS45.0673.3883.3634.8661.3672.7832.2156.3966.6725.4847.5557.94
", + "bbox": [ + 96, + 215, + 870, + 339 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/34bea2d9826a29fa627b43f35a0bd24a30075b327fcbe080915615797671f9d3.jpg", + "table_caption": [ + "Table 7. Zero-shot image-text retrieval. $\\mathrm{I} \\rightarrow \\mathrm{T}$ and $\\mathrm{T} \\rightarrow \\mathrm{I}$ indicate image-to-text retrieval and text-to-image retrieval." + ], + "table_footnote": [], + "table_body": "
MethodIN-AIN-RIN-SkeIN-V2ObjNetAverage
CLIP [47]9.351.228.139.817.732.3
SLIP [43]10.549.826.741.320.433.1↑0.8
MAE+CLIP11.653.931.141.619.434.4↑2.1
RILS12.155.731.443.321.035.7↑3.4
", + "bbox": [ + 96, + 362, + 447, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 8. Zero-shot out-of-distribution classification. We report the Top-1 classification accuracy (\\%) for reference.", + "bbox": [ + 75, + 474, + 468, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shot classification, retrieval requires the models to have the ability to capture fine-grained contextualized information in both images and texts. As the results in Table 7 shown, our model achieves the best among all counterparts. In particular, when compared to CLIP, our RILS shows more significant improvements than MAE+CLIP.", + "bbox": [ + 75, + 512, + 468, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness to Distribution Shift. Following CLIP [47], we also conduct zero-shot experiments on 5 out-of-distribution datasets: ImageNet Adversarial [33], ImageNet Rendition [32], ImageNetV2 [53], ImageNet Sketch [61], and ObjectNet [4]. As shown in Table 8, our method outperforms others on all five benchmarks. Specifically, RILS obtains significant improvements, $+3.4\\%$ , $+2.6\\%$ , $+1.3\\%$ better than CLIP, SLIP, and MAE+CLIP respectively.", + "bbox": [ + 75, + 602, + 468, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 736, + 228, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we ablate the designs of RILS. All experiments are conducted with ViT/B-16 vision encoder and trained on L-10M for 25 epochs. We report the classification accuracy $(\\%)$ under zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.) on ImageNet-1K.", + "bbox": [ + 75, + 762, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Comparisons with Two-stage Methods", + "text_level": 1, + "bbox": [ + 76, + 847, + 406, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As discussed above, another way to leverage both masked image modeling with image-text contrastive learn-", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing is to build a two-stage framework and learn two objectives step by step. In this section, we compare our RILS with several two-stage methods:", + "bbox": [ + 496, + 364, + 890, + 411 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathbf{MIM} \\rightarrow \\mathbf{LiT}$ indicates firstly pre-train with masked image modeling only, then follow [71] to perform locked-image text tuning on image-text pairs. Specifically, we start the second stage by fine-tuning pre-trained MAE [28].", + "bbox": [ + 496, + 410, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathbf{MIM} \\rightarrow \\mathbf{CLIP}$ denotes fully fine-tune pre-trained MAE on image-text pairs in the second stage. In this way, pre-trained model also inherit properties from both objectives.", + "bbox": [ + 496, + 470, + 890, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathbf{CLIP} \\rightarrow \\mathbf{MIM}$ stands for using pre-trained CLIP as a guidance for masked image modeling in the second stage. This paradigm has been studied in recent research such as [34, 44, 63].", + "bbox": [ + 496, + 517, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The comparison results are shown in Table 9. As the vision encoder is fully frozen during the second stage in MIM $\\rightarrow$ LiT, its performance on downstream tasks remains unchanged except for zero-shot. MIM $\\rightarrow$ CLIP slightly outperforms MAE and CLIP. CLIP $\\rightarrow$ MIM exhibits more improvements upon two base methods, but lose the ability on zero-shot classification. Our method rivals all counterparts with a more concise training pipeline.", + "bbox": [ + 496, + 579, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Comparisons on Reconstruction Space", + "text_level": 1, + "bbox": [ + 498, + 710, + 831, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The core philosophy of our design is to perform masked reconstruction in language semantic space. We ablate the effectiveness of our design by comparing to two other alternatives: raw pixel space and high-level vision space. Reconstruction in raw pixel space denotes the aforementioned MAE+CLIP which tries to reconstruct raw pixels directly. For high-level vision space, we replace the language feature $z^T$ in Eq. (8) to learnable weights with other components unchanged. In other words, similar to design in [1,7,75], we map patch features to a probabilistic distribution on a group of learnable weights. As results in Table 10 shown, our", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23310", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a6371ed24ed7179f6f307528b36b333e2ad224ddbb76531ad79b4f6dcb21e990.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodZS.Lin.FT.
MAE [28]-43.481.5
CLIP [47]32.164.182.0
MIM→LiT [71]13.243.481.5
MIM→CLIP34.464.882.2
CLIP→MIM [34,44,63]-66.282.4
RILS (E2E)37.568.582.7
", + "bbox": [ + 125, + 88, + 419, + 203 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e7634cf1fe1f609a42960f416024ea217f509941f4e45ecc6a4b9ba1a73f32cf.jpg", + "table_caption": [ + "Table 9. Comparisons with two-stage methods. All methods are trained with ViT-B/16 on L-10M for 25 epochs. Our approach rivals all two-stage methods in terms of zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.)" + ], + "table_footnote": [], + "table_body": "
Reconstruction SpaceZS.Lin.FT.
Raw Pixel Space (MAE+CLIP)34.261.982.2
High-level Vision Space [12,75]34.867.782.4
Language Semantic Space (RILS)37.568.582.7
", + "bbox": [ + 102, + 267, + 444, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Comparisons on reconstruction space. Raw pixel space denotes aforementioned MAE+CLIP which directly reconstruct RGB values. High-level vision space indicates to replace the language feature $z^T$ in Eq. (8) to a group of learnable embeddings similar to [1,7,75]. Language semantic space stands for ours. All methods are trained with ViT-B/16 for 25 epochs on L-10M.", + "bbox": [ + 75, + 347, + 467, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RILS shows better performance on all three metrics. We notice that compared to reconstruct raw pixels, the high-level space reconstruction does not show prominent advantages as in [1,7,75]. We guess this is due to the absence of multicrop augmentation and exponential moving average (EMA) strategy which play important roles inside these methods but bring significant adverse impact on training efficiency.", + "bbox": [ + 75, + 441, + 467, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Hyper-parameters Analysis", + "text_level": 1, + "bbox": [ + 76, + 559, + 323, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mask Ratio. We compare three different mask ratios in Table 11a. As results shown, randomly masking at a ratio of $75\\%$ leads to generally decent performance. Lower mask ratio $(60\\%)$ leads to $+0.8\\%$ better linear probing accuracy but impairs zero-shot performance $(-1.6\\%)$ . Higher mask ratio $(90\\%)$ acquires similar zero-shot accuracy but results in apparent decrease of $-0.9\\%$ and $-0.4\\%$ in terms of linear probing and fine-tuning. We guess this is due to lower mask ratio brings more prior information but less supervision in reconstruction, while the higher one exact converses.", + "bbox": [ + 75, + 582, + 467, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of vision decoder blocks. Performance w.r.t. number of decoder blocks are shown in Table 11b. Different decoder blocks numbers exhibit less to none differences in terms of zero-shot. As to linear probing, we detect the same trend as [28]: More vision decoder blocks leads to better linear probing accuracy. For fine-tuning, we observe almost the same accuracy but more decoder blocks seems to be slightly worse. Besides the numerical differences, when take the extra costs bring by more decoder blocks into consideration, we choose to build our RILS with one vision decoder blocks only, due to more decoder blocks introduces", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/79185acb47816215a244b17eb2400101935db6852b86915645b8463b3b8bd041.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Mask RatioZS.Lin.FT.
60%35.969.382.7
75%37.568.582.7
90%37.467.682.3
", + "bbox": [ + 552, + 88, + 839, + 151 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/743f76e8574ff8ec94b5c62302e73f53683224f03869fdcd32ed1455866d6900.jpg", + "table_caption": [ + "(a) Ablations on mask ratio. $75\\%$ generally leads to a good result except for linear probing." + ], + "table_footnote": [], + "table_body": "
Nums.ZS.Lin.FT.Rel.GHs.
137.568.582.71.0×
237.868.982.61.3×
437.369.682.51.5×
", + "bbox": [ + 545, + 179, + 844, + 239 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f1d7396a113aacd7ba49f35016871b09fa3f6946ece864e6c4ed32f123afddb7.jpg", + "table_caption": [ + "(b) Numbers of vision decoder blocks. Rel.GHs. is short for relative GPU hours." + ], + "table_footnote": [], + "table_body": "
λ1:λ2ZS.Lin.FT.
2:137.568.582.7
1:136.468.182.3
1:235.968.282.2
", + "bbox": [ + 557, + 267, + 834, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(c) Loss coefficients of $\\mathcal{L}_{\\mathrm{Contra}}$ and $\\mathcal{L}_{\\mathrm{Recon}}$ .", + "bbox": [ + 571, + 330, + 818, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 11. Ablations on the hyper-parameters of our approach. We report zero-shot (ZS.), linear probing(Lin.) and end-to-end finetuning (FT.) accuracy $(\\%)$ on ImageNet-1K. Our default setups are high-lighted in gray.", + "bbox": [ + 498, + 345, + 890, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "un-negligible training overheads. For instance, increasing the number of decoder blocks from 1 to 4 brings $0.5 \\times$ more training costs.", + "bbox": [ + 498, + 421, + 890, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Loss coefficients. The results under different loss coefficients in Eq. (6) are shown in Table 11c. We empirically observe better performance with $\\lambda_1:\\lambda_2$ setting to 2:1.", + "bbox": [ + 498, + 470, + 890, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 542, + 617, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present a unified vision representation learner RILS that subsumes masked image modeling with natural language supervision. Instead of simply combining both paradigms with limited connection, we present a novel design to perform MIM in the language semantic space. Text features from language encoder serves as basic prototypes and probabilistic distribution of masked patches explicitly. Both objectives complement each other, leading to high synergy and mutual benefits. Extensive experimental results on downstream tasks showcase our method's advanced transferability and out-of-the-box capacity. We also observe excellent properties emerge from our design, especially in the low-shot regime. We hope our work can provide a new perspective on how to utilize language supervision with masked image modeling. In the future, we will explore further scale-up of our approach in terms of both model size and data size.", + "bbox": [ + 496, + 571, + 890, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 856, + 658, + 872 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by NSFC (No. 62276108).", + "bbox": [ + 519, + 885, + 864, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23311", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. Masked siamese networks for label-efficient learning. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.131, + 0.823, + 0.154 + ], + "angle": 0, + "content": "RILS: Masked Visual Reconstruction in Language Semantic Space" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.179, + 0.905, + 0.201 + ], + "angle": 0, + "content": "Shusheng Yang\\(^{1,\\ast}\\), Yixiao Ge\\(^{2,\\dagger}\\), Kun Yi\\(^{2}\\), Dian Li\\(^{3}\\), Ying Shan\\(^{2}\\), Xiaohu Qie\\(^{4}\\), Xinggang Wang\\(^{1,\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.2, + 0.709, + 0.217 + ], + "angle": 0, + "content": "1School of EIC, Huazhong University of Science & Technology" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.217, + 0.76, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)ARC Lab, \\(^{4}\\)Tencent PCG Foundation Technology Center, \\(^{4}\\)Tencent PCG" + }, + { + "type": "text", + "bbox": [ + 0.132, + 0.238, + 0.861, + 0.251 + ], + "angle": 0, + "content": "{shushengyang, xgwang}@hust.edu.cn {yixiaoge, kunyi, goodli, yingsshan, tigerqie}@tencent.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.668 + ], + "angle": 0, + "content": "Both masked image modeling (MIM) and natural language supervision have facilitated the progress of transferable visual pre-training. In this work, we seek the synergy between two paradigms and study the emerging properties when MIM meets natural language supervision. To this end, we present a novel masked visual Reconstruction In Language semantic Space (RILS) pre-training framework, in which sentence representations, encoded by the text encoder, serve as prototypes to transform the vision-only signals into patch-sentence probabilities as semantically meaningful MIM reconstruction targets. The vision models can therefore capture useful components with structured information by predicting proper semantic of masked tokens. Better visual representations could, in turn, improve the text encoder via the image-text alignment objective, which is essential for the effective MIM target transformation. Extensive experimental results demonstrate that our method not only enjoys the best of previous MIM and CLIP but also achieves further improvements on various tasks due to their mutual benefits. RILS exhibits advanced transferability on downstream classification, detection, and segmentation, especially for low-shot regimes. Code is available at https://github.com/hustvl/RILS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.699, + 0.21, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Learning transferable representation lies a crucial task in deep learning. Over the past few years, natural language processing (NLP) has achieved great success in this line of research [18, 45, 60]. To explore similar trajectories in the vision domain, researchers tend to draw upon the successes of NLP and have made tremendous progress: (i) Inspired by the advanced model architecture [60] as well as self-supervised learning paradigm [18] in NLP, vision Transformers (ViT) [21, 42] and masked image modeling" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.287, + 0.895, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.588 + ], + "angle": 0, + "content": "Figure 1. Overview of our RILS. Recon and Contra represent masked reconstruction loss and image-text contrastive loss. During pre-training, RILS learns to perform masked image modeling and image-text contrastive simultaneously. Masked predictions and corresponding targets are transformed to probabilistic distributions in language space by leveraging text features as semantic-rich prototypes. Under such a scheme, both objective and unified and achieve mutual benefits from each other. Vision encoder obtains the ability to capture meaningful and fine-grained context information, sparking decent transfer capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.779 + ], + "angle": 0, + "content": "(MIM) [3, 28] open a new era of self-supervised visual representation learning, and show unprecedented transferability on various tasks, especially on fine-grained tasks such as object detection [22, 39]. (ii) Inspired by the great scalability brought by leveraging web-scale collections of texts as training data in NLP [5, 48, 49, 72], CLIP [47] and ALIGN [35] bring such a principle to vision and manifest the immense potential of leveraging natural language supervision for scalable visual pre-training. Strong transferability of pre-trained visual models on low-shot regimes ensues. It also facilitates diverse applications by extracting contextualized image or text features [26, 50, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.896, + 0.902 + ], + "angle": 0, + "content": "The remarkable attainment achieved by these two research lines pushes us to ponder: Is it possible to unify both masked image modeling and natural language supervision to pursuit better visual pre-training? A straightforward way towards this goal is to simply combine masked image modeling (MIM) with image-text contrastive learning (ITC) for multi-task learning. Although the naive combination is feasible to inherit the above advantages, we find it remains un-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*This work was done while S. Yang was an intern at ARC Lab, Tencent PCG. † X. Wang and Y. Ge are the corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23304" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "satisfactory due to the mutual benefits between MIM and ITC have not yet been fully explored. Motivated by this, we develop RILS, a tailored framework to seek the synergy of masked image modeling and language supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.408 + ], + "angle": 0, + "content": "The core insight of RILS is to perform masked visual reconstruction in language semantic space. Specifically, instead of reconstructing masked patches in the standalone vision space (e.g., raw pixel [28,66], low-level features [3,62] or high-level perceptions [12, 34, 63, 75]), we map patch features to a probabilistic distribution over a batch of text features as the reconstruction target, which is enabled by ITC that progressively aligns the image and text spaces. The text features serve as semantically rich prototypes and probabilistic distributions explicitly inject the semantic information onto each image patch. The MIM objective is formulated as a soft cross-entropy loss to minimize the KL divergence between text-injected probabilistic distributions of masked vision tokens and their corresponding targets. The visual model optimized by our language-assisted reconstruction objective, in turn, improves ITC with better visual representations that capture fine-grained local contexts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Under such a working mechanism, the two objectives (i.e., MIM and ITC) complement each other and form a unified solution for transferable and scalable visual pretraining. Note that a lot of works [34, 63, 75] have manifested the importance of semantic information in the reconstruction target of MIM objectives. However, it is abstract to pursue such a semantically rich space with visual-only signals due to its unstructured characteristics [29]. Thanks to natural language supervision, this issue is alleviated by performing masked reconstruction in language space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.471, + 0.833 + ], + "angle": 0, + "content": "Extensive experiments on various downstream tasks demonstrate that our design enjoys the best of both worlds. With a vanilla ViT-B/16 as the vision model and 25-epoch pre-training on 20 million image-text pairs, RILS achieves \\(83.3\\%\\) top-1 accuracy when fine-tune on ImageNet-1K [15], \\(+1.2\\%\\) and \\(+0.6\\%\\) better than the MAE [28] and CLIP [47] counterparts. Advanced performance can be consistently acquired when transfer to fine-grained tasks such as detection and segmentation. Moreover, our approach exhibits promising out-of-the-box capability under an extremely low-shot regime. RILS also demonstrates superior performance on zero-shot image classification and image-text retrieval. On ImageNet-1K benchmark, RILS obtains \\(45.0\\%\\) zero-shot classification accuracy, \\(+4.7\\% / + 3.4\\%\\) higher than CLIP [47]/SLIP [43] under the same training recipe. Compelling results of RILS imply the promising capacity in the unification of MIM and language supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.227, + 0.86 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Masked Image Modeling translates masked language modeling [18] to vision domain and learns transferable" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "visual representation by reconstructing masked signals from partial observation [3, 9, 21]. Despite following the same mask-then-reconstruction principle, MIM differs from MLM a lot in the design of reconstruction target. BEiT [3] utilizes a pre-trained d-VAE [51, 55] and reconstructs masked image patches in the offline token space. Subsequent works improve it by employing better pretrained tokenizer [19, 34, 44, 63], eased and refined multichoice tokens [37] or contextual aligner [11]. MAE [28] and SimMIM [66] demonstrate directly reconstruct masked patches in raw pixel space can also lead to favorable transferability as well as scalability. MaskFeat [62] takes handcrafted low-level HOG feature [14] as target. Other works like iBOT [75], data2vec [2] and SdAE [12] perform reconstruction in a high-level vision feature space. Different from these methods, in this work, we tap the potential when masked image modeling meets natural language supervision and propose performing masked visual reconstruction in the language semantic space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.893, + 0.593 + ], + "angle": 0, + "content": "Language Supervised Visual Pre-training learns visual representation from image-text pairs by solving generative [16, 56] or discriminative [73] pretext tasks. Recently, benefit from modern network architectures [21,41,42] and publicly available image-text datasets [8,17,57-59], CLIP [47] and ALIGN [35] unveil the tremendous transferability and scalability of this paradigm. The core technique of CLIP is aligning both vision and language modalities in a joint embedding space by global representation contrastive. Follow-up works further improve CLIP on the vision-only [43, 67] or vision-language [38, 64, 68-70] side. In this paper, we bring natural language supervision together with masked image modeling for better visual pre-training on these two paradigms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.608, + 0.649, + 0.626 + ], + "angle": 0, + "content": "3. Our Approach" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.634, + 0.648 + ], + "angle": 0, + "content": "3.1. Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Among numerous architecture designing spaces, without loss of generalization, we adopt an asymmetric encoder-decoder architecture following MAE [28] and a dual-encoder architecture following CLIP [47] for their flexibility. As illustrated in Figure 1, RILS comprises the following three major components:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Vision Encoder plays the key role in RILS and all our efforts aim to strengthen its capacity on downstream transfer. Following the trend in recent visual pre-training, we implement this encoder by a vanilla vision Transformer (ViT) [21]. It takes both intact (unmasked) image and corrupted (masked) image as inputs. Formally, input image \\(I\\) is first divided into regular non-overlapping image patches and then encoded by a stack of Transformer blocks [60]. Meanwhile, following MAE [28], we randomly mask a large portion of image patches and leave the remaining patches to be" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23305" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.122 + ], + "angle": 0, + "content": "visible. This corrupted image \\(\\hat{I}\\) is also encoded by vision encoder. We formulate the process of vision encoder as:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.129, + 0.47, + 0.155 + ], + "angle": 0, + "content": "\\[\n\\operatorname {V} - \\operatorname {E n c} (I) = \\{f ^ {k} | k \\in [ 1, N ] \\}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.151, + 0.39, + 0.169 + ], + "angle": 0, + "content": "\\[\n\\mathrm {V - E n c} (\\hat {I}) = \\{\\hat {f} ^ {k} | k \\in [ 1, N ] \\backslash \\mathcal {M} \\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.176, + 0.469, + 0.235 + ], + "angle": 0, + "content": "in which \\( k \\) denotes the patch index and \\( N \\) denotes image patch numbers. \\( f \\) and \\( \\hat{f} \\) betoken encoded patch features of intact image \\( I \\) and corrupted image \\( \\hat{I} \\). \\( \\mathcal{M} \\) indicates the index set of random masked patches." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.237, + 0.47, + 0.282 + ], + "angle": 0, + "content": "Language Encoder encodes input text \\( T \\) by a stack of Transformer layers with causal masked attention [60]. This process can be simply represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.219, + 0.29, + 0.469, + 0.306 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L} - \\operatorname {E n c} (T) = h. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.314, + 0.468, + 0.42 + ], + "angle": 0, + "content": "We take the output \\( h \\) as global representation of input text. Vision Decoder consists of another series of Transformer blocks. Particularly, in our design, decoder blocks have the same dimension as encoder blocks. It takes the encoded feature \\( \\hat{f} \\) of masked image \\( \\hat{I} \\) along with a learnable [MASK] token as inputs, and tries to predict masked signals from corrupted view:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.426, + 0.47, + 0.459 + ], + "angle": 0, + "content": "\\[\n\\operatorname {V} - \\operatorname {D e c} \\left(\\left\\{\\hat {f} ^ {k} \\mid k \\in [ 1, N ] \\backslash \\mathcal {M} \\right\\}, [ \\text {M A S K} ]\\right) = \\left\\{g ^ {k} \\mid k \\in [ 1, N ] \\right\\}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.467, + 0.258, + 0.483 + ], + "angle": 0, + "content": "3.2. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.49, + 0.469, + 0.597 + ], + "angle": 0, + "content": "Image-Text Contrastive. We leverage image-text contrastive loss to align two modalities into a joint embedding space. Specifically, given image-text pair \\(\\{(I,T)\\}\\), we take the mean-pooled image feature \\(\\bar{f} = \\frac{1}{N}\\sum_{k=1}^{N}f^k\\) and \\(h\\) in Eq. (2) as global representations for image and text. The image and text features are further projected by two projection heads and followed by a normalization:" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.604, + 0.469, + 0.63 + ], + "angle": 0, + "content": "\\[\nz ^ {I} = \\left\\| \\theta (\\bar {f}) \\right\\|, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.626, + 0.323, + 0.643 + ], + "angle": 0, + "content": "\\[\nz ^ {T} = | | \\phi (h) | |,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.651, + 0.469, + 0.696 + ], + "angle": 0, + "content": "\\(\\theta (\\cdot)\\) and \\(\\phi (\\cdot)\\) denotes the projection head for image and text respectively. The image-to-text contrastive loss and text-to-image contrastive loss can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.704, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {I 2 T}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {i} ^ {T} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {j} ^ {T} \\right\\rangle / \\sigma\\right)}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.75, + 0.424, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {T 2 I}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {i} ^ {I} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {j} ^ {I} \\right\\rangle / \\sigma\\right)},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.469, + 0.871 + ], + "angle": 0, + "content": "in which \\(i\\) and \\(j\\) stands for the index within a mini-batch and \\(B\\) indicates the batch size respectively. \\(\\sigma\\) performs a learnable temperature and is jointly trained during the pretraining. The total loss of image-text contrastive learning can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.877, + 0.469, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {C o n t r a}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {I 2 T}} + \\mathcal {L} _ {\\mathrm {T 2 I}}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Masked Visual Reconstruction in Language Semantic Space. As aforementioned, despite the mask-then-reconstruct principle of MIM is concise enough, the contiguous and unstructured characteristics in visual signal make the choice of reconstruction space non-trivial. Lots of works have manifested the great importance of performing masked reconstruction in a semantic-rich space [12, 34, 63, 75]. In this work, we build our reconstruction space from a vision-language perspective. We regard the text features as natural semantic descriptors for image patches and try to perform masked visual reconstruction in this language space. Specifically, given the encoded patch feature \\( f^{k} \\) in Eq. (1) with \\( k \\) being the index of patch and decoded patch feature \\( g^{k} \\) in Eq. (3), we firstly project and normalize both features to the vision-language aligned space:" + }, + { + "type": "equation", + "bbox": [ + 0.643, + 0.329, + 0.891, + 0.355 + ], + "angle": 0, + "content": "\\[\n\\tilde {f} _ {i} ^ {k} = \\left| \\left| \\theta \\left(f _ {i} ^ {k}\\right) \\right| \\right|, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.646, + 0.351, + 0.746, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\tilde {g} _ {i} ^ {k} = | \\left| \\theta \\left(g _ {i} ^ {k}\\right) \\right| |,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.44 + ], + "angle": 0, + "content": "with \\(i\\) being the index within mini-batch. \\(\\theta (\\cdot)\\) represents the same vision projection head in Eq. (4). The key step of our design is to map patch features to a probabilistic distributions over a bunch of text features:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.449, + 0.891, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {1}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {1}\\right)} \\mid l \\in [ 1, B ] \\right\\}, \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.491, + 0.846, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {q} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {2}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {2}\\right)} \\mid l \\in [ 1, B ] \\right\\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.54, + 0.892, + 0.676 + ], + "angle": 0, + "content": "in which \\(\\tau_{1}\\) and \\(\\tau_{2}\\) serve as temperatures. In this way, with the text features serve as semantic-rich prototypes, both masked prediction and corresponding target are mapped into this language semantic space. The probabilistic distributions explicitly express the context information within each patch. The reconstruction objective is to shrinking the differences between text-injected distributions of target and masked prediction by minimize the KL divergence of \\(p_i^k\\) w.r.t. \\(q_i^k\\), which can be represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.687, + 0.891, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {R e c o n}} = \\frac {1}{| | \\mathcal {C} | | \\cdot | | \\mathcal {M} | |} \\sum_ {i \\in \\mathcal {C}} \\sum_ {k \\in \\mathcal {M}} - \\operatorname {s g} \\left[ \\boldsymbol {p} _ {i} ^ {k} \\right] \\log \\boldsymbol {q} _ {i} ^ {k}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.735, + 0.891, + 0.825 + ], + "angle": 0, + "content": "in which \\(\\mathrm{sg}[\\cdot ]\\) indicates stop gradient. \\(\\mathcal{M}\\) denotes the index set of masked patches. \\(\\mathcal{C}\\) signifies the indexes of images which are correctly aligned to corresponding text features. In other words, we only calculate reconstruction loss on images which are correctly matched with target texts in imaged-to-text matching." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "By transferring reconstruction space from standalone vision space to language space, our approach takes both MIM and ITC into a unifying landscape and achieves mutual benefits from each other. MIM always suffers from overly paying attention on low-level details which consume lots of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.47, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.429 + ], + "angle": 0, + "content": "Figure 2. Architecture comparisons between MAE [28], CLIP [47], MAE+CLIP and RILS. Recon and Contra indicate masked reconstruction loss and image-text contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.557 + ], + "angle": 0, + "content": "model's capacity but of less helpful for understanding visual concepts. By leveraging text features as prototypes and transfer patch features to probabilistic distribution on language space, the low-level information inside visual signals are abandoned by the contextualized language prototypes. Better contextualized image features in turn assist vision-language alignment, leading to transferable and scalable visual pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Overall Objective Function. The final objective of RILS is a weighted-sum of both image-text contrastive loss and masked reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.615, + 0.47, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {R I L S}} = \\lambda_ {1} \\cdot \\mathcal {L} _ {\\text {C o n t r a}} + \\lambda_ {2} \\cdot \\mathcal {L} _ {\\text {R e c o n}}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.642, + 0.428, + 0.657 + ], + "angle": 0, + "content": "\\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) indicate coefficients to balance two losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.258, + 0.683 + ], + "angle": 0, + "content": "3.3. Pre-training Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Similar to [69], we sequentially sample image-text pairs according to filenames from recent released LAION-400M [58] dataset as our training sets. We term them as L-10M/L-20M/L-50M according to the amount of sampled unique image-text pairs (e.g., L-10M stands for the first 10 million subset of LAION-400M). Unless specified, our method is trained on L-20M for 25 epochs. We take AdamW [36] as optimizer with learning rate set to 5e-4 and a weight decay of 0.5. Learning rate linearly increases in the first epoch as warmup and decreases in the rest following the cosine learning rate decay strategy. We train our method on 32 NVIDIA V100 with a total batch size of 4096 (i.e., batch size per GPU is 128). For model architecture, we take the widely-adopted ViT-B/16 as vision encoder, 1-" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.088, + 0.86, + 0.238 + ], + "angle": 0, + "content": "
MethodDatasetPT Epo.Lin.FT.
SimCLR [10]51.781.3
MAE [28]44.382.1
CLIP [47]L-20M25(∼ 400)67.882.7
SLIP [43]70.182.6
MAE+CLIP64.582.9
RILS71.583.3
BEiT [3]IN-1K(∼ 1.3M)800-83.2
MAE [28]160067.883.6
RILSL-50M25(∼ 1000)71.983.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.248, + 0.894, + 0.291 + ], + "angle": 0, + "content": "Table 1. Image classification results on ImageNet-1K (IN-1K). PT Epo. indicates per-training epochs. Lin. and FT. is short for linear probing and end-to-end fine-tuning respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.305, + 0.892, + 0.457 + ], + "angle": 0, + "content": "layer Transformer block with 768-dim and 12 heads as vision decoder, and a text Transformer with 12 blocks and 512-dim as language encoder. To tokenize text inputs, following [47], we use byte-pair encoding (BPE [23]) with \\(49\\mathrm{K}\\) vocabulary size and set the max length of each sentence to 77. During pre-training, input images are resized to \\(224 \\times 224\\) and we set random mask ratio to \\(75\\%\\) following [28]. Temperatures \\(\\tau_{1}\\) and \\(\\tau_{2}\\) in Eq. (8) are set to 0.04 and 0.1. Loss coefficients \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are set to 1.0 and 0.5 by default. More pre-training setups are listed in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.475, + 0.618, + 0.49 + ], + "angle": 0, + "content": "3.4. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.699 + ], + "angle": 0, + "content": "There are also meaningful attempts [20,34,44,63] on utilizing natural language supervision together with MIM and seem alike to ours. However, there still have some distinctions existing in the motivation and method between ours and theirs. MVP [63], MILAN [34] and BEiTv2 [44] leverage natural language supervision by a two-stage framework, while ours is fully end-to-end. We will take further discussion about two-stage methods and ours in later experiments. A related and concurrent work [20] shows some similar designs but significantly differs from our idea of reconstruction in language space. As it does not have a reproducible implementation, we do not take it into consideration for comparison." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.721, + 0.636, + 0.737 + ], + "angle": 0, + "content": "4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In this section, we evaluate the representation quality of pre-training by transferring pre-trained models to various downstream tasks. We choose MAE [28] and CLIP [47] as representative methods of masked image modeling and vision-language contrastive learning. We also conduct a naive baseline (termed as MAE+CLIP) which simply combine MAE and CLIP together to perform MIM and ITC simultaneously, as a counterpart for our approach. Semantically comparisons between MAE, CLIP, MAE+CLIP and our RILS are illustrated in Figure 2." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23307" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.116, + 0.089, + 0.852, + 0.203 + ], + "angle": 0, + "content": "
MethodCOCOLVIS
APBAPB50APB75APMAPM50APM75APBAPB50APB75APMAPM50APM75
MAE [28]48.168.652.942.465.846.431.046.233.729.644.031.7
CLIP [47]47.769.152.342.065.945.132.348.135.130.545.932.5
SLIP [43]46.568.551.041.565.144.132.448.935.130.846.532.6
MAE+CLIP48.169.652.542.466.245.732.648.835.230.746.432.6
RILS48.570.553.242.666.845.833.850.236.531.647.833.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.207, + 0.894, + 0.237 + ], + "angle": 0, + "content": "Table 2. Object detection and instance segmentation results on COCO and LVIS. All models are pre-trained with ViT-B/16 for 25 epochs on L-20M. Fine-tuning recipes for different pre-trained models are the same." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.243, + 0.288, + 0.259 + ], + "angle": 0, + "content": "4.1. Classification Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.417 + ], + "angle": 0, + "content": "Linear Probing evaluates the quality of pre-trained feature by training a linear classifier on the frozen feature. We following the the recipe in [7] and sweep over different learning rate. Results are shown in Table 1. We notice that, with 25-epochs pre-training on L-20M, MAE+CLIP only achieves \\(64.5\\%\\) accuracy which is better than MAE but worse than CLIP. This implies the contradiction between MIM and ITC exists in such a naive combination. RILS alleviates this contradiction by elaborated design and outperforms other methods by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.471, + 0.63 + ], + "angle": 0, + "content": "End-to-End Fine-tuning. We follow most of setups in [28] for fine-tuning. Concretely, we fine-tune pre-trained models for 100 epochs with a warm-up of 5 epochs. Hyperparameters are all the same for all experiments except the learning rate. Results are shown in Table 1. When training with 25 epochs on L-20M, our method shows distinct advantages. Compared to MAE, CLIP and MAE+CLIP, our method exhibits \\(+1.2\\%\\), \\(+0.6\\%\\) and \\(+0.4\\%\\) gains respectively. Moreover, when we scale-up the dataset capacity from L-20M to L-50M, with 25 epochs pre-training (around 1000 equivalent epochs in the ImageNet-1K regime), our method achieves \\(83.6\\%\\) top-1 accuracy which is on par with prior art (MAE trained on ImageNet-1K with 1600 epochs) with only \\(62.5\\%\\) training length." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.283, + 0.65 + ], + "angle": 0, + "content": "4.2. Downstream Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Object Detection and Segmentation. For object detection and instance segmentation, we choose COCO [40] and LVIS [27] as benchmarks. We follow the design in [39] to transfer pre-trained ViT to detection. To tame quadratic complexity within self-attention, most attention blocks in the ViT are replaced with window attention except for four global blocks to perform cross-window interaction. SimpleFPN [39] is attached to the last transform block to generate pyramid features. Modernized RPN [54] and Mask R-CNN [31] head are deployed for detecting and segmenting visual instances. All pre-trained models are fine-tuned on two benchmarks for 25 epochs with same hyper-parameters. The results are shown in Table 2. Among all methods, our RILS achieves the best results in terms of \\(\\mathrm{AP}^{\\mathcal{B}}\\) and \\(\\mathrm{AP}^{\\mathcal{M}}\\) on both COCO and LVIS. It's noteworthy that two benchmarks show different properties: COCO benchmark shows" + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.242, + 0.865, + 0.396 + ], + "angle": 0, + "content": "
MethodDatasetPT Epo.mIoU
BEiT [3]IN-1K(~ 1.3M)30045.5
80046.5
MAE [28]30045.8
160048.1
MAE [28]L-20M25(~ 400)44.2
CLIP [47]45.2
SLIP [43]45.7
MAE+CLIP45.3
RILSL-20M25(~ 400)48.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.53, + 0.399, + 0.862, + 0.414 + ], + "angle": 0, + "content": "Table 3. Semantic segmentation results on ADE20K." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.717 + ], + "angle": 0, + "content": "less benefits from language supervision while LVIS converses. Specifically, MAE shows leading performance on COCO but inferior performance on LVIS. We suspect this is due to the inherent distinctions in COCO and LVIS: LVIS contains 1203 visual categories which is about \\(15 \\times\\) more than COCO, and it always suffers from the long-tail distribution. Under such circumstances, COCO requires more localization ability which MAE excel at while LVIS prefers better classification ability which natural language supervision can bring. From this perspective, when compare our RILS with the MAE+CLIP, we find our design benefits more from both MIM and ITC objectives. On both COCO and LVIS, MAE+CLIP only shows competitive performance to the winner of MAE and CLIP, but our RILS exhibits apparent improvements especially on LVIS. This indicates our design leverage masked image modeling and language supervision in a more synergistic way. We believe this kind of synergy is of great exploration value for better visual pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Semantic Segmentation. Experiments on semantic segmentation are conducted on the well-known ADE20K [74] dataset. We build the segmentation framework upon UperNet [65] and use the pre-trained models as encoders. Input images are resized to \\(512 \\times 512\\) and all models are finetuned for 160K iterations. All hyper-parameters strictly follow MAE [28] and not tuned. We report the mean intersection-over-union (mIoU) in Table 3. As the results shown, our method overwhelmingly surpasses others. Specifically, with 25 epoch pre-training on L-20M, our method achieves \\(48.1\\mathrm{mIoU}\\), \\(+3.9\\) and \\(+2.9\\) higher than MAE and CLIP. Similar to the trends on LVIS, MAE+CLIP" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23308" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.117, + 0.089, + 0.852, + 0.242 + ], + "angle": 0, + "content": "
MethodPT DatasetPT Epo.Images per Class
12510
MAE [28]IN-1K(~ 1.3M)16004.3 ± (0.28)10.6 ± (0.21)22.4 ± (0.28)31.6 ± (0.02)
BEiT [3]IN-1K(~ 1.3M)8001.3 ± (0.03)2.2 ± (0.13)4.4 ± (0.21)7.4 ± (0.05)
MAE [28]L-20M25(~ 400)3.4 ± (0.12)5.2 ± (0.21)10.1 ± (0.10)14.8 ± (0.20)
CLIP [47]19.4 ± (0.18)29.2 ± (0.61)39.8 ± (0.39)46.3 ± (0.15)
SLIP [43]17.7 ± (0.33)27.2 ± (0.56)38.6 ± (0.55)46.4 ± (0.06)
MAE+CLIP21.1 ± (0.12)31.1 ± (0.94)41.6 ± (0.43)47.5 ± (0.15)
RILSL-20M25(~ 400)24.0 ± (0.27)34.6 ± (0.88)45.7 ± (0.46)51.8 ± (0.18)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.246, + 0.894, + 0.276 + ], + "angle": 0, + "content": "Table 4. Extreme low-shot classification on ImageNet-1K. We random sample 1, 2, 5, 10 images per class from training split, and report logistic regression accuracy (%) on ImageNet-1K validation split. All methods use ViT-B/16 as vision encoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.47, + 0.405 + ], + "angle": 0, + "content": "only gets \\(0.1\\mathrm{mIoU}\\) gains by simply combining MIM with ITC together, far less than our approach. Furthermore, our method shows competitive or better performance when compared to prior art. Compared to MAE pre-trained on ImageNet-1K with 300 epochs, our method achieves 2.3 higher performance (48.1 vs. 45.8). When MAE is pretrained with 1600 epochs, our method achieves the same mIoU (48.1) while only requires \\(25\\%\\) training length." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.471, + 0.482 + ], + "angle": 0, + "content": "Experiments above demonstrate the excellent transfer capacity of our approach on fine-grained visual understanding tasks. Our design unleashes the ability to capture local details and global contexts by performing masked visual reconstruction in language semantic space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.303, + 0.51 + ], + "angle": 0, + "content": "4.3. Label-Efficient Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Low-shot Regime Classification. We investigate the classification performance when only very few labeled images are available. Specifically, following [1,6], we random sample 1, 2, 5, and 10 labeled images per class from ImageNet-1K training split as our training sets. Instead of end-to-end fine-tuning, we train a linear classifier on frozen features to avoid overfitting. The complete validation split of ImageNet-1K which contains \\(50\\mathrm{K}\\) images are used to evaluate the accuracy. Table 4 shows the results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Specifically, compared to MAE+CLIP which only obtain slightly improvements over CLIP, our RILS outperforms both of them by a large margin. Notably, with only 10 images per class (i.e., 10K images for 1K classes), our method can achieve \\(51.8\\%\\) top-1 accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Low-shot Regime Detection. We further transfer the low-shot experiment to object detection on COCO [40], which requires model to localize and classify visual objects simultaneously. We randomly sample annotated images from COCO training split with different sampling ratio (range from \\(1\\%\\) to \\(50\\%\\)) as our training sets. All models are end-to-end fine-tuned for 12 epochs instead of 25 to prevent overfitting. We report the average precision of detection \\(\\mathbf{AP}^{\\mathcal{B}}\\) for comparison in Table 5. As the results shown, our method shows the best performance under a wide range of sampling ratio (from \\(2\\%\\) to \\(50\\%\\))." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.281, + 0.882, + 0.395 + ], + "angle": 0, + "content": "
MethodCOCO Sampling Ratio
1%2%5%10%20%50%
MAE [28]0.946.1015.7623.1629.7838.10
CLIP [47]0.815.0514.9822.4929.8838.50
SLIP [43]1.114.5413.8421.9129.5337.73
MAE+CLIP0.685.2814.3323.7229.9939.24
RILS0.866.4616.9424.6931.9740.41
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.398, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Table 5. Low-shot regime object detection on COCO. We report detection performance \\(\\mathrm{AP}^{\\mathcal{B}}\\) with 12 epochs fine-tuning. All models are pre-trained with ViT-B/16 and 25 epochs on L-20M." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.894, + 0.583 + ], + "angle": 0, + "content": "Conceptually, one of the aspirations of pre-training is to pursue efficient transfer (e.g., less trainable data, shorter training length) on downstream tasks [1, 25, 30]. Experiments in the low-shot regime show the strong out-of-the-box capacity of our RILS by performing MIM in language semantic space. The non-trivial results indicate our pretraining approach brings out label-efficient learner, showing great application value to real-world scenarios, especially when annotated data is insufficient." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.687, + 0.606 + ], + "angle": 0, + "content": "4.4. Zero-Shot Transfer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.841 + ], + "angle": 0, + "content": "Classification. We evaluate the zero-shot classification over 21 benchmarks including ImageNet-1K [15]. Detail of each datasets are listed in the appendix and the evaluate recipes (e.g., prompt engineering) strictly follow [43]. Results are shown in Table 6. Specifically, compared to CLIP, MAE+CLIP only achieves \\(+0.6\\%\\) average improvements, while our RILS shows \\(+2.0\\%\\) gains. This hints the masked image modeling objective in the naive combination has little help to image-text alignment, while ours alleviate this issue by bind two objectives in a unified landscape. On ImageNet-1K, our method achieves \\(45.0\\%\\) accuracy, \\(+4.7\\% / + 3.4\\% / + 2.7\\%\\) higher than CLIP, SLIP and MAE+CLIP, respectively. Among 21 benchmarks, our method outperforms others over 17 datasets, frequently with a significant margin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Image-Text Retrieval. We study image-text retrieval on 2 benchmarks: COCO [40] and Flickr30K [46]. For both benchmarks, we use the original captions (w/o prompt) and \\(224 \\times 224\\) resized images for retrieval. Different from zero" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23309" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.089, + 0.881, + 0.2 + ], + "angle": 0, + "content": "
MethodFood101CIFAR10CIFAR100CUB200SUN397CarsAircraftDTDPetsCaltech101FlowersMNISTFER2013STL10EuroSATRESISC45GTSRBCountry211CLEVRSST2ImageNetAverage# Wins.
CLIP [47]55.776.046.924.450.717.84.831.553.778.431.826.837.689.022.736.924.16.820.049.140.339.32
SLIP [43]56.773.443.222.651.617.74.932.452.579.133.329.433.589.517.836.217.86.823.449.741.638.72
MAE+CLIP57.878.252.423.951.618.14.631.555.878.432.027.632.789.827.039.422.97.214.749.342.339.90
RILS58.986.255.123.451.819.55.932.859.280.733.522.640.193.228.840.219.17.816.850.045.042.317
" + }, + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.201, + 0.847, + 0.215 + ], + "angle": 0, + "content": "Table 6. Zero-shot classification on 21 datasets. All models are trained with ViT-B/16 encoder for 25 epochs on L-20M." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.217, + 0.872, + 0.34 + ], + "angle": 0, + "content": "
MethodCOCOFlickr30K
I→TT→II→TT→I
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [47]41.8269.5079.3430.5457.1069.3028.1350.7761.1220.6140.7750.49
SLIP [43]44.5472.2082.1033.2659.6671.1431.2055.8166.0224.0545.5855.90
MAE+CLIP42.7270.6680.3631.4057.5069.6828.6252.2562.6422.6443.6753.97
RILS45.0673.3883.3634.8661.3672.7832.2156.3966.6725.4847.5557.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.141, + 0.343, + 0.825, + 0.357 + ], + "angle": 0, + "content": "Table 7. Zero-shot image-text retrieval. \\( \\mathrm{I} \\rightarrow \\mathrm{T} \\) and \\( \\mathrm{T} \\rightarrow \\mathrm{I} \\) indicate image-to-text retrieval and text-to-image retrieval." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.363, + 0.449, + 0.472 + ], + "angle": 0, + "content": "
MethodIN-AIN-RIN-SkeIN-V2ObjNetAverage
CLIP [47]9.351.228.139.817.732.3
SLIP [43]10.549.826.741.320.433.1↑0.8
MAE+CLIP11.653.931.141.619.434.4↑2.1
RILS12.155.731.443.321.035.7↑3.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.504 + ], + "angle": 0, + "content": "Table 8. Zero-shot out-of-distribution classification. We report the Top-1 classification accuracy (\\%) for reference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.603 + ], + "angle": 0, + "content": "shot classification, retrieval requires the models to have the ability to capture fine-grained contextualized information in both images and texts. As the results in Table 7 shown, our model achieves the best among all counterparts. In particular, when compared to CLIP, our RILS shows more significant improvements than MAE+CLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.725 + ], + "angle": 0, + "content": "Robustness to Distribution Shift. Following CLIP [47], we also conduct zero-shot experiments on 5 out-of-distribution datasets: ImageNet Adversarial [33], ImageNet Rendition [32], ImageNetV2 [53], ImageNet Sketch [61], and ObjectNet [4]. As shown in Table 8, our method outperforms others on all five benchmarks. Specifically, RILS obtains significant improvements, \\(+3.4\\%\\), \\(+2.6\\%\\), \\(+1.3\\%\\) better than CLIP, SLIP, and MAE+CLIP respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.737, + 0.229, + 0.755 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.469, + 0.839 + ], + "angle": 0, + "content": "In this section, we ablate the designs of RILS. All experiments are conducted with ViT/B-16 vision encoder and trained on L-10M for 25 epochs. We report the classification accuracy \\((\\%)\\) under zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.) on ImageNet-1K." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.407, + 0.865 + ], + "angle": 0, + "content": "5.1. Comparisons with Two-stage Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As discussed above, another way to leverage both masked image modeling with image-text contrastive learn-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.412 + ], + "angle": 0, + "content": "ing is to build a two-stage framework and learn two objectives step by step. In this section, we compare our RILS with several two-stage methods:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.472 + ], + "angle": 0, + "content": "\\(\\mathbf{MIM} \\rightarrow \\mathbf{LiT}\\) indicates firstly pre-train with masked image modeling only, then follow [71] to perform locked-image text tuning on image-text pairs. Specifically, we start the second stage by fine-tuning pre-trained MAE [28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.892, + 0.518 + ], + "angle": 0, + "content": "\\(\\mathbf{MIM} \\rightarrow \\mathbf{CLIP}\\) denotes fully fine-tune pre-trained MAE on image-text pairs in the second stage. In this way, pre-trained model also inherit properties from both objectives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.579 + ], + "angle": 0, + "content": "\\(\\mathbf{CLIP} \\rightarrow \\mathbf{MIM}\\) stands for using pre-trained CLIP as a guidance for masked image modeling in the second stage. This paradigm has been studied in recent research such as [34, 44, 63]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.701 + ], + "angle": 0, + "content": "The comparison results are shown in Table 9. As the vision encoder is fully frozen during the second stage in MIM \\(\\rightarrow\\) LiT, its performance on downstream tasks remains unchanged except for zero-shot. MIM \\(\\rightarrow\\) CLIP slightly outperforms MAE and CLIP. CLIP \\(\\rightarrow\\) MIM exhibits more improvements upon two base methods, but lose the ability on zero-shot classification. Our method rivals all counterparts with a more concise training pipeline." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.711, + 0.833, + 0.728 + ], + "angle": 0, + "content": "5.2. Comparisons on Reconstruction Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The core philosophy of our design is to perform masked reconstruction in language semantic space. We ablate the effectiveness of our design by comparing to two other alternatives: raw pixel space and high-level vision space. Reconstruction in raw pixel space denotes the aforementioned MAE+CLIP which tries to reconstruct raw pixels directly. For high-level vision space, we replace the language feature \\( z^T \\) in Eq. (8) to learnable weights with other components unchanged. In other words, similar to design in [1,7,75], we map patch features to a probabilistic distribution on a group of learnable weights. As results in Table 10 shown, our" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23310" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.126, + 0.089, + 0.42, + 0.204 + ], + "angle": 0, + "content": "
MethodZS.Lin.FT.
MAE [28]-43.481.5
CLIP [47]32.164.182.0
MIM→LiT [71]13.243.481.5
MIM→CLIP34.464.882.2
CLIP→MIM [34,44,63]-66.282.4
RILS (E2E)37.568.582.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.207, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 9. Comparisons with two-stage methods. All methods are trained with ViT-B/16 on L-10M for 25 epochs. Our approach rivals all two-stage methods in terms of zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.)" + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.268, + 0.445, + 0.337 + ], + "angle": 0, + "content": "
Reconstruction SpaceZS.Lin.FT.
Raw Pixel Space (MAE+CLIP)34.261.982.2
High-level Vision Space [12,75]34.867.782.4
Language Semantic Space (RILS)37.568.582.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.468, + 0.432 + ], + "angle": 0, + "content": "Table 10. Comparisons on reconstruction space. Raw pixel space denotes aforementioned MAE+CLIP which directly reconstruct RGB values. High-level vision space indicates to replace the language feature \\( z^T \\) in Eq. (8) to a group of learnable embeddings similar to [1,7,75]. Language semantic space stands for ours. All methods are trained with ViT-B/16 for 25 epochs on L-10M." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.468, + 0.548 + ], + "angle": 0, + "content": "RILS shows better performance on all three metrics. We notice that compared to reconstruct raw pixels, the high-level space reconstruction does not show prominent advantages as in [1,7,75]. We guess this is due to the absence of multicrop augmentation and exponential moving average (EMA) strategy which play important roles inside these methods but bring significant adverse impact on training efficiency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.325, + 0.575 + ], + "angle": 0, + "content": "5.3. Hyper-parameters Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Mask Ratio. We compare three different mask ratios in Table 11a. As results shown, randomly masking at a ratio of \\(75\\%\\) leads to generally decent performance. Lower mask ratio \\((60\\%)\\) leads to \\(+0.8\\%\\) better linear probing accuracy but impairs zero-shot performance \\((-1.6\\%)\\). Higher mask ratio \\((90\\%)\\) acquires similar zero-shot accuracy but results in apparent decrease of \\(-0.9\\%\\) and \\(-0.4\\%\\) in terms of linear probing and fine-tuning. We guess this is due to lower mask ratio brings more prior information but less supervision in reconstruction, while the higher one exact converses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Number of vision decoder blocks. Performance w.r.t. number of decoder blocks are shown in Table 11b. Different decoder blocks numbers exhibit less to none differences in terms of zero-shot. As to linear probing, we detect the same trend as [28]: More vision decoder blocks leads to better linear probing accuracy. For fine-tuning, we observe almost the same accuracy but more decoder blocks seems to be slightly worse. Besides the numerical differences, when take the extra costs bring by more decoder blocks into consideration, we choose to build our RILS with one vision decoder blocks only, due to more decoder blocks introduces" + }, + { + "type": "table", + "bbox": [ + 0.553, + 0.089, + 0.841, + 0.152 + ], + "angle": 0, + "content": "
Mask RatioZS.Lin.FT.
60%35.969.382.7
75%37.568.582.7
90%37.467.682.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.154, + 0.871, + 0.178 + ], + "angle": 0, + "content": "(a) Ablations on mask ratio. \\(75\\%\\) generally leads to a good result except for linear probing." + }, + { + "type": "table", + "bbox": [ + 0.547, + 0.18, + 0.846, + 0.24 + ], + "angle": 0, + "content": "
Nums.ZS.Lin.FT.Rel.GHs.
137.568.582.71.0×
237.868.982.61.3×
437.369.682.51.5×
" + }, + { + "type": "table_caption", + "bbox": [ + 0.519, + 0.242, + 0.872, + 0.266 + ], + "angle": 0, + "content": "(b) Numbers of vision decoder blocks. Rel.GHs. is short for relative GPU hours." + }, + { + "type": "table", + "bbox": [ + 0.558, + 0.268, + 0.836, + 0.33 + ], + "angle": 0, + "content": "
λ1:λ2ZS.Lin.FT.
2:137.568.582.7
1:136.468.182.3
1:235.968.282.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.573, + 0.332, + 0.819, + 0.345 + ], + "angle": 0, + "content": "(c) Loss coefficients of \\(\\mathcal{L}_{\\mathrm{Contra}}\\) and \\(\\mathcal{L}_{\\mathrm{Recon}}\\)." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.347, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Table 11. Ablations on the hyper-parameters of our approach. We report zero-shot (ZS.), linear probing(Lin.) and end-to-end finetuning (FT.) accuracy \\((\\%)\\) on ImageNet-1K. Our default setups are high-lighted in gray." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.891, + 0.468 + ], + "angle": 0, + "content": "un-negligible training overheads. For instance, increasing the number of decoder blocks from 1 to 4 brings \\(0.5 \\times\\) more training costs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.472, + 0.891, + 0.517 + ], + "angle": 0, + "content": "Loss coefficients. The results under different loss coefficients in Eq. (6) are shown in Table 11c. We empirically observe better performance with \\(\\lambda_1:\\lambda_2\\) setting to 2:1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.544, + 0.618, + 0.558 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.83 + ], + "angle": 0, + "content": "In this work, we present a unified vision representation learner RILS that subsumes masked image modeling with natural language supervision. Instead of simply combining both paradigms with limited connection, we present a novel design to perform MIM in the language semantic space. Text features from language encoder serves as basic prototypes and probabilistic distribution of masked patches explicitly. Both objectives complement each other, leading to high synergy and mutual benefits. Extensive experimental results on downstream tasks showcase our method's advanced transferability and out-of-the-box capacity. We also observe excellent properties emerge from our design, especially in the low-shot regime. We hope our work can provide a new perspective on how to utilize language supervision with masked image modeling. In the future, we will explore further scale-up of our approach in terms of both model size and data size." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.857, + 0.66, + 0.873 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.866, + 0.901 + ], + "angle": 0, + "content": "This work was supported by NSFC (No. 62276108)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23311" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. Masked siamese networks for label-efficient learning. 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In this work, we seek the synergy between two paradigms and study the emerging properties when MIM meets natural language supervision. To this end, we present a novel masked visual Reconstruction In Language semantic Space (RILS) pre-training framework, in which sentence representations, encoded by the text encoder, serve as prototypes to transform the vision-only signals into patch-sentence probabilities as semantically meaningful MIM reconstruction targets. The vision models can therefore capture useful components with structured information by predicting proper semantic of masked tokens. Better visual representations could, in turn, improve the text encoder via the image-text alignment objective, which is essential for the effective MIM target transformation. Extensive experimental results demonstrate that our method not only enjoys the best of previous MIM and CLIP but also achieves further improvements on various tasks due to their mutual benefits. RILS exhibits advanced transferability on downstream classification, detection, and segmentation, especially for low-shot regimes. Code is available at https://github.com/hustvl/RILS. + +# 1. Introduction + +Learning transferable representation lies a crucial task in deep learning. Over the past few years, natural language processing (NLP) has achieved great success in this line of research [18, 45, 60]. To explore similar trajectories in the vision domain, researchers tend to draw upon the successes of NLP and have made tremendous progress: (i) Inspired by the advanced model architecture [60] as well as self-supervised learning paradigm [18] in NLP, vision Transformers (ViT) [21, 42] and masked image modeling + +![](images/286393bcdae264a5673a8b31c0ec496e5b2e016853b473b1d29545879f01c785.jpg) +Figure 1. Overview of our RILS. Recon and Contra represent masked reconstruction loss and image-text contrastive loss. During pre-training, RILS learns to perform masked image modeling and image-text contrastive simultaneously. Masked predictions and corresponding targets are transformed to probabilistic distributions in language space by leveraging text features as semantic-rich prototypes. Under such a scheme, both objective and unified and achieve mutual benefits from each other. Vision encoder obtains the ability to capture meaningful and fine-grained context information, sparking decent transfer capacity. + +(MIM) [3, 28] open a new era of self-supervised visual representation learning, and show unprecedented transferability on various tasks, especially on fine-grained tasks such as object detection [22, 39]. (ii) Inspired by the great scalability brought by leveraging web-scale collections of texts as training data in NLP [5, 48, 49, 72], CLIP [47] and ALIGN [35] bring such a principle to vision and manifest the immense potential of leveraging natural language supervision for scalable visual pre-training. Strong transferability of pre-trained visual models on low-shot regimes ensues. It also facilitates diverse applications by extracting contextualized image or text features [26, 50, 52]. + +The remarkable attainment achieved by these two research lines pushes us to ponder: Is it possible to unify both masked image modeling and natural language supervision to pursuit better visual pre-training? A straightforward way towards this goal is to simply combine masked image modeling (MIM) with image-text contrastive learning (ITC) for multi-task learning. Although the naive combination is feasible to inherit the above advantages, we find it remains un- + +satisfactory due to the mutual benefits between MIM and ITC have not yet been fully explored. Motivated by this, we develop RILS, a tailored framework to seek the synergy of masked image modeling and language supervision. + +The core insight of RILS is to perform masked visual reconstruction in language semantic space. Specifically, instead of reconstructing masked patches in the standalone vision space (e.g., raw pixel [28,66], low-level features [3,62] or high-level perceptions [12, 34, 63, 75]), we map patch features to a probabilistic distribution over a batch of text features as the reconstruction target, which is enabled by ITC that progressively aligns the image and text spaces. The text features serve as semantically rich prototypes and probabilistic distributions explicitly inject the semantic information onto each image patch. The MIM objective is formulated as a soft cross-entropy loss to minimize the KL divergence between text-injected probabilistic distributions of masked vision tokens and their corresponding targets. The visual model optimized by our language-assisted reconstruction objective, in turn, improves ITC with better visual representations that capture fine-grained local contexts. + +Under such a working mechanism, the two objectives (i.e., MIM and ITC) complement each other and form a unified solution for transferable and scalable visual pretraining. Note that a lot of works [34, 63, 75] have manifested the importance of semantic information in the reconstruction target of MIM objectives. However, it is abstract to pursue such a semantically rich space with visual-only signals due to its unstructured characteristics [29]. Thanks to natural language supervision, this issue is alleviated by performing masked reconstruction in language space. + +Extensive experiments on various downstream tasks demonstrate that our design enjoys the best of both worlds. With a vanilla ViT-B/16 as the vision model and 25-epoch pre-training on 20 million image-text pairs, RILS achieves $83.3\%$ top-1 accuracy when fine-tune on ImageNet-1K [15], $+1.2\%$ and $+0.6\%$ better than the MAE [28] and CLIP [47] counterparts. Advanced performance can be consistently acquired when transfer to fine-grained tasks such as detection and segmentation. Moreover, our approach exhibits promising out-of-the-box capability under an extremely low-shot regime. RILS also demonstrates superior performance on zero-shot image classification and image-text retrieval. On ImageNet-1K benchmark, RILS obtains $45.0\%$ zero-shot classification accuracy, $+4.7\% / + 3.4\%$ higher than CLIP [47]/SLIP [43] under the same training recipe. Compelling results of RILS imply the promising capacity in the unification of MIM and language supervision. + +# 2. Related Works + +Masked Image Modeling translates masked language modeling [18] to vision domain and learns transferable + +visual representation by reconstructing masked signals from partial observation [3, 9, 21]. Despite following the same mask-then-reconstruction principle, MIM differs from MLM a lot in the design of reconstruction target. BEiT [3] utilizes a pre-trained d-VAE [51, 55] and reconstructs masked image patches in the offline token space. Subsequent works improve it by employing better pretrained tokenizer [19, 34, 44, 63], eased and refined multichoice tokens [37] or contextual aligner [11]. MAE [28] and SimMIM [66] demonstrate directly reconstruct masked patches in raw pixel space can also lead to favorable transferability as well as scalability. MaskFeat [62] takes handcrafted low-level HOG feature [14] as target. Other works like iBOT [75], data2vec [2] and SdAE [12] perform reconstruction in a high-level vision feature space. Different from these methods, in this work, we tap the potential when masked image modeling meets natural language supervision and propose performing masked visual reconstruction in the language semantic space. + +Language Supervised Visual Pre-training learns visual representation from image-text pairs by solving generative [16, 56] or discriminative [73] pretext tasks. Recently, benefit from modern network architectures [21,41,42] and publicly available image-text datasets [8,17,57-59], CLIP [47] and ALIGN [35] unveil the tremendous transferability and scalability of this paradigm. The core technique of CLIP is aligning both vision and language modalities in a joint embedding space by global representation contrastive. Follow-up works further improve CLIP on the vision-only [43, 67] or vision-language [38, 64, 68-70] side. In this paper, we bring natural language supervision together with masked image modeling for better visual pre-training on these two paradigms. + +# 3. Our Approach + +# 3.1. Architecture + +Among numerous architecture designing spaces, without loss of generalization, we adopt an asymmetric encoder-decoder architecture following MAE [28] and a dual-encoder architecture following CLIP [47] for their flexibility. As illustrated in Figure 1, RILS comprises the following three major components: + +Vision Encoder plays the key role in RILS and all our efforts aim to strengthen its capacity on downstream transfer. Following the trend in recent visual pre-training, we implement this encoder by a vanilla vision Transformer (ViT) [21]. It takes both intact (unmasked) image and corrupted (masked) image as inputs. Formally, input image $I$ is first divided into regular non-overlapping image patches and then encoded by a stack of Transformer blocks [60]. Meanwhile, following MAE [28], we randomly mask a large portion of image patches and leave the remaining patches to be + +visible. This corrupted image $\hat{I}$ is also encoded by vision encoder. We formulate the process of vision encoder as: + +$$ +\operatorname {V} - \operatorname {E n c} (I) = \{f ^ {k} | k \in [ 1, N ] \}, \tag {1} +$$ + +$$ +\mathrm {V - E n c} (\hat {I}) = \{\hat {f} ^ {k} | k \in [ 1, N ] \backslash \mathcal {M} \}, +$$ + +in which $k$ denotes the patch index and $N$ denotes image patch numbers. $f$ and $\hat{f}$ betoken encoded patch features of intact image $I$ and corrupted image $\hat{I}$ . $\mathcal{M}$ indicates the index set of random masked patches. + +Language Encoder encodes input text $T$ by a stack of Transformer layers with causal masked attention [60]. This process can be simply represented by: + +$$ +\mathrm {L} - \operatorname {E n c} (T) = h. \tag {2} +$$ + +We take the output $h$ as global representation of input text. Vision Decoder consists of another series of Transformer blocks. Particularly, in our design, decoder blocks have the same dimension as encoder blocks. It takes the encoded feature $\hat{f}$ of masked image $\hat{I}$ along with a learnable [MASK] token as inputs, and tries to predict masked signals from corrupted view: + +$$ +\operatorname {V} - \operatorname {D e c} \left(\left\{\hat {f} ^ {k} \mid k \in [ 1, N ] \backslash \mathcal {M} \right\}, [ \text {M A S K} ]\right) = \left\{g ^ {k} \mid k \in [ 1, N ] \right\}. \tag {3} +$$ + +# 3.2. Training Objective + +Image-Text Contrastive. We leverage image-text contrastive loss to align two modalities into a joint embedding space. Specifically, given image-text pair $\{(I,T)\}$ , we take the mean-pooled image feature $\bar{f} = \frac{1}{N}\sum_{k=1}^{N}f^k$ and $h$ in Eq. (2) as global representations for image and text. The image and text features are further projected by two projection heads and followed by a normalization: + +$$ +z ^ {I} = \left\| \theta (\bar {f}) \right\|, \tag {4} +$$ + +$$ +z ^ {T} = | | \phi (h) | |, +$$ + +$\theta (\cdot)$ and $\phi (\cdot)$ denotes the projection head for image and text respectively. The image-to-text contrastive loss and text-to-image contrastive loss can be represented as: + +$$ +\mathcal {L} _ {\mathrm {I 2 T}} = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\left\langle z _ {i} ^ {I} , z _ {i} ^ {T} \right\rangle / \sigma\right)}{\sum_ {j = 1} ^ {B} \exp \left(\left\langle z _ {i} ^ {I} , z _ {j} ^ {T} \right\rangle / \sigma\right)}, \tag {5} +$$ + +$$ +\mathcal {L} _ {\mathrm {T 2 I}} = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\left\langle z _ {i} ^ {T} , z _ {i} ^ {I} \right\rangle / \sigma\right)}{\sum_ {j = 1} ^ {B} \exp \left(\left\langle z _ {i} ^ {T} , z _ {j} ^ {I} \right\rangle / \sigma\right)}, +$$ + +in which $i$ and $j$ stands for the index within a mini-batch and $B$ indicates the batch size respectively. $\sigma$ performs a learnable temperature and is jointly trained during the pretraining. The total loss of image-text contrastive learning can be formulated as: + +$$ +\mathcal {L} _ {\text {C o n t r a}} = \frac {1}{2} \left(\mathcal {L} _ {\mathrm {I 2 T}} + \mathcal {L} _ {\mathrm {T 2 I}}\right). \tag {6} +$$ + +Masked Visual Reconstruction in Language Semantic Space. As aforementioned, despite the mask-then-reconstruct principle of MIM is concise enough, the contiguous and unstructured characteristics in visual signal make the choice of reconstruction space non-trivial. Lots of works have manifested the great importance of performing masked reconstruction in a semantic-rich space [12, 34, 63, 75]. In this work, we build our reconstruction space from a vision-language perspective. We regard the text features as natural semantic descriptors for image patches and try to perform masked visual reconstruction in this language space. Specifically, given the encoded patch feature $f^{k}$ in Eq. (1) with $k$ being the index of patch and decoded patch feature $g^{k}$ in Eq. (3), we firstly project and normalize both features to the vision-language aligned space: + +$$ +\tilde {f} _ {i} ^ {k} = \left| \left| \theta \left(f _ {i} ^ {k}\right) \right| \right|, \tag {7} +$$ + +$$ +\tilde {g} _ {i} ^ {k} = | \left| \theta \left(g _ {i} ^ {k}\right) \right| |, +$$ + +with $i$ being the index within mini-batch. $\theta (\cdot)$ represents the same vision projection head in Eq. (4). The key step of our design is to map patch features to a probabilistic distributions over a bunch of text features: + +$$ +\boldsymbol {p} _ {i} ^ {k} = \left\{\frac {\exp \left(\left\langle \tilde {f} _ {i} ^ {k} , z _ {l} ^ {T} \right\rangle / \tau_ {1}\right)}{\sum_ {j = 1} ^ {B} \exp \left(\left\langle \tilde {f} _ {i} ^ {k} , z _ {j} ^ {T} \right\rangle / \tau_ {1}\right)} \mid l \in [ 1, B ] \right\}, \tag {8} +$$ + +$$ +\boldsymbol {q} _ {i} ^ {k} = \left\{\frac {\exp \left(\left\langle \tilde {g} _ {i} ^ {k} , z _ {l} ^ {T} \right\rangle / \tau_ {2}\right)}{\sum_ {j = 1} ^ {B} \exp \left(\left\langle \tilde {g} _ {i} ^ {k} , z _ {j} ^ {T} \right\rangle / \tau_ {2}\right)} \mid l \in [ 1, B ] \right\}, +$$ + +in which $\tau_{1}$ and $\tau_{2}$ serve as temperatures. In this way, with the text features serve as semantic-rich prototypes, both masked prediction and corresponding target are mapped into this language semantic space. The probabilistic distributions explicitly express the context information within each patch. The reconstruction objective is to shrinking the differences between text-injected distributions of target and masked prediction by minimize the KL divergence of $p_i^k$ w.r.t. $q_i^k$ , which can be represented by: + +$$ +\mathcal {L} _ {\text {R e c o n}} = \frac {1}{| | \mathcal {C} | | \cdot | | \mathcal {M} | |} \sum_ {i \in \mathcal {C}} \sum_ {k \in \mathcal {M}} - \operatorname {s g} \left[ \boldsymbol {p} _ {i} ^ {k} \right] \log \boldsymbol {q} _ {i} ^ {k}, \tag {9} +$$ + +in which $\mathrm{sg}[\cdot ]$ indicates stop gradient. $\mathcal{M}$ denotes the index set of masked patches. $\mathcal{C}$ signifies the indexes of images which are correctly aligned to corresponding text features. In other words, we only calculate reconstruction loss on images which are correctly matched with target texts in imaged-to-text matching. + +By transferring reconstruction space from standalone vision space to language space, our approach takes both MIM and ITC into a unifying landscape and achieves mutual benefits from each other. MIM always suffers from overly paying attention on low-level details which consume lots of + +![](images/e298da8b7cc482b2ce558532c05ceafd955b308998304a0e85d52226917a432b.jpg) +Figure 2. Architecture comparisons between MAE [28], CLIP [47], MAE+CLIP and RILS. Recon and Contra indicate masked reconstruction loss and image-text contrastive loss. + +model's capacity but of less helpful for understanding visual concepts. By leveraging text features as prototypes and transfer patch features to probabilistic distribution on language space, the low-level information inside visual signals are abandoned by the contextualized language prototypes. Better contextualized image features in turn assist vision-language alignment, leading to transferable and scalable visual pre-training. + +Overall Objective Function. The final objective of RILS is a weighted-sum of both image-text contrastive loss and masked reconstruction loss: + +$$ +\mathcal {L} _ {\text {R I L S}} = \lambda_ {1} \cdot \mathcal {L} _ {\text {C o n t r a}} + \lambda_ {2} \cdot \mathcal {L} _ {\text {R e c o n}}. \tag {10} +$$ + +$\lambda_{1}$ and $\lambda_{2}$ indicate coefficients to balance two losses. + +# 3.3. Pre-training Setup + +Similar to [69], we sequentially sample image-text pairs according to filenames from recent released LAION-400M [58] dataset as our training sets. We term them as L-10M/L-20M/L-50M according to the amount of sampled unique image-text pairs (e.g., L-10M stands for the first 10 million subset of LAION-400M). Unless specified, our method is trained on L-20M for 25 epochs. We take AdamW [36] as optimizer with learning rate set to 5e-4 and a weight decay of 0.5. Learning rate linearly increases in the first epoch as warmup and decreases in the rest following the cosine learning rate decay strategy. We train our method on 32 NVIDIA V100 with a total batch size of 4096 (i.e., batch size per GPU is 128). For model architecture, we take the widely-adopted ViT-B/16 as vision encoder, 1- + +
MethodDatasetPT Epo.Lin.FT.
SimCLR [10]51.781.3
MAE [28]44.382.1
CLIP [47]L-20M25(∼ 400)67.882.7
SLIP [43]70.182.6
MAE+CLIP64.582.9
RILS71.583.3
BEiT [3]IN-1K(∼ 1.3M)800-83.2
MAE [28]160067.883.6
RILSL-50M25(∼ 1000)71.983.6
+ +Table 1. Image classification results on ImageNet-1K (IN-1K). PT Epo. indicates per-training epochs. Lin. and FT. is short for linear probing and end-to-end fine-tuning respectively. + +layer Transformer block with 768-dim and 12 heads as vision decoder, and a text Transformer with 12 blocks and 512-dim as language encoder. To tokenize text inputs, following [47], we use byte-pair encoding (BPE [23]) with $49\mathrm{K}$ vocabulary size and set the max length of each sentence to 77. During pre-training, input images are resized to $224 \times 224$ and we set random mask ratio to $75\%$ following [28]. Temperatures $\tau_{1}$ and $\tau_{2}$ in Eq. (8) are set to 0.04 and 0.1. Loss coefficients $\lambda_{1}$ and $\lambda_{2}$ are set to 1.0 and 0.5 by default. More pre-training setups are listed in the appendix. + +# 3.4. Discussion + +There are also meaningful attempts [20,34,44,63] on utilizing natural language supervision together with MIM and seem alike to ours. However, there still have some distinctions existing in the motivation and method between ours and theirs. MVP [63], MILAN [34] and BEiTv2 [44] leverage natural language supervision by a two-stage framework, while ours is fully end-to-end. We will take further discussion about two-stage methods and ours in later experiments. A related and concurrent work [20] shows some similar designs but significantly differs from our idea of reconstruction in language space. As it does not have a reproducible implementation, we do not take it into consideration for comparison. + +# 4. Main Results + +In this section, we evaluate the representation quality of pre-training by transferring pre-trained models to various downstream tasks. We choose MAE [28] and CLIP [47] as representative methods of masked image modeling and vision-language contrastive learning. We also conduct a naive baseline (termed as MAE+CLIP) which simply combine MAE and CLIP together to perform MIM and ITC simultaneously, as a counterpart for our approach. Semantically comparisons between MAE, CLIP, MAE+CLIP and our RILS are illustrated in Figure 2. + +
MethodCOCOLVIS
APBAPB50APB75APMAPM50APM75APBAPB50APB75APMAPM50APM75
MAE [28]48.168.652.942.465.846.431.046.233.729.644.031.7
CLIP [47]47.769.152.342.065.945.132.348.135.130.545.932.5
SLIP [43]46.568.551.041.565.144.132.448.935.130.846.532.6
MAE+CLIP48.169.652.542.466.245.732.648.835.230.746.432.6
RILS48.570.553.242.666.845.833.850.236.531.647.833.7
+ +# 4.1. Classification Transfer + +Linear Probing evaluates the quality of pre-trained feature by training a linear classifier on the frozen feature. We following the the recipe in [7] and sweep over different learning rate. Results are shown in Table 1. We notice that, with 25-epochs pre-training on L-20M, MAE+CLIP only achieves $64.5\%$ accuracy which is better than MAE but worse than CLIP. This implies the contradiction between MIM and ITC exists in such a naive combination. RILS alleviates this contradiction by elaborated design and outperforms other methods by a large margin. + +End-to-End Fine-tuning. We follow most of setups in [28] for fine-tuning. Concretely, we fine-tune pre-trained models for 100 epochs with a warm-up of 5 epochs. Hyperparameters are all the same for all experiments except the learning rate. Results are shown in Table 1. When training with 25 epochs on L-20M, our method shows distinct advantages. Compared to MAE, CLIP and MAE+CLIP, our method exhibits $+1.2\%$ , $+0.6\%$ and $+0.4\%$ gains respectively. Moreover, when we scale-up the dataset capacity from L-20M to L-50M, with 25 epochs pre-training (around 1000 equivalent epochs in the ImageNet-1K regime), our method achieves $83.6\%$ top-1 accuracy which is on par with prior art (MAE trained on ImageNet-1K with 1600 epochs) with only $62.5\%$ training length. + +# 4.2. Downstream Transfer + +Object Detection and Segmentation. For object detection and instance segmentation, we choose COCO [40] and LVIS [27] as benchmarks. We follow the design in [39] to transfer pre-trained ViT to detection. To tame quadratic complexity within self-attention, most attention blocks in the ViT are replaced with window attention except for four global blocks to perform cross-window interaction. SimpleFPN [39] is attached to the last transform block to generate pyramid features. Modernized RPN [54] and Mask R-CNN [31] head are deployed for detecting and segmenting visual instances. All pre-trained models are fine-tuned on two benchmarks for 25 epochs with same hyper-parameters. The results are shown in Table 2. Among all methods, our RILS achieves the best results in terms of $\mathrm{AP}^{\mathcal{B}}$ and $\mathrm{AP}^{\mathcal{M}}$ on both COCO and LVIS. It's noteworthy that two benchmarks show different properties: COCO benchmark shows + +Table 2. Object detection and instance segmentation results on COCO and LVIS. All models are pre-trained with ViT-B/16 for 25 epochs on L-20M. Fine-tuning recipes for different pre-trained models are the same. + +
MethodDatasetPT Epo.mIoU
BEiT [3]IN-1K(~ 1.3M)30045.5
80046.5
MAE [28]30045.8
160048.1
MAE [28]L-20M25(~ 400)44.2
CLIP [47]45.2
SLIP [43]45.7
MAE+CLIP45.3
RILSL-20M25(~ 400)48.1
+ +Table 3. Semantic segmentation results on ADE20K. + +less benefits from language supervision while LVIS converses. Specifically, MAE shows leading performance on COCO but inferior performance on LVIS. We suspect this is due to the inherent distinctions in COCO and LVIS: LVIS contains 1203 visual categories which is about $15 \times$ more than COCO, and it always suffers from the long-tail distribution. Under such circumstances, COCO requires more localization ability which MAE excel at while LVIS prefers better classification ability which natural language supervision can bring. From this perspective, when compare our RILS with the MAE+CLIP, we find our design benefits more from both MIM and ITC objectives. On both COCO and LVIS, MAE+CLIP only shows competitive performance to the winner of MAE and CLIP, but our RILS exhibits apparent improvements especially on LVIS. This indicates our design leverage masked image modeling and language supervision in a more synergistic way. We believe this kind of synergy is of great exploration value for better visual pre-training. + +Semantic Segmentation. Experiments on semantic segmentation are conducted on the well-known ADE20K [74] dataset. We build the segmentation framework upon UperNet [65] and use the pre-trained models as encoders. Input images are resized to $512 \times 512$ and all models are finetuned for 160K iterations. All hyper-parameters strictly follow MAE [28] and not tuned. We report the mean intersection-over-union (mIoU) in Table 3. As the results shown, our method overwhelmingly surpasses others. Specifically, with 25 epoch pre-training on L-20M, our method achieves $48.1\mathrm{mIoU}$ , $+3.9$ and $+2.9$ higher than MAE and CLIP. Similar to the trends on LVIS, MAE+CLIP + +
MethodPT DatasetPT Epo.Images per Class
12510
MAE [28]IN-1K(~ 1.3M)16004.3 ± (0.28)10.6 ± (0.21)22.4 ± (0.28)31.6 ± (0.02)
BEiT [3]IN-1K(~ 1.3M)8001.3 ± (0.03)2.2 ± (0.13)4.4 ± (0.21)7.4 ± (0.05)
MAE [28]L-20M25(~ 400)3.4 ± (0.12)5.2 ± (0.21)10.1 ± (0.10)14.8 ± (0.20)
CLIP [47]19.4 ± (0.18)29.2 ± (0.61)39.8 ± (0.39)46.3 ± (0.15)
SLIP [43]17.7 ± (0.33)27.2 ± (0.56)38.6 ± (0.55)46.4 ± (0.06)
MAE+CLIP21.1 ± (0.12)31.1 ± (0.94)41.6 ± (0.43)47.5 ± (0.15)
RILSL-20M25(~ 400)24.0 ± (0.27)34.6 ± (0.88)45.7 ± (0.46)51.8 ± (0.18)
+ +only gets $0.1\mathrm{mIoU}$ gains by simply combining MIM with ITC together, far less than our approach. Furthermore, our method shows competitive or better performance when compared to prior art. Compared to MAE pre-trained on ImageNet-1K with 300 epochs, our method achieves 2.3 higher performance (48.1 vs. 45.8). When MAE is pretrained with 1600 epochs, our method achieves the same mIoU (48.1) while only requires $25\%$ training length. + +Experiments above demonstrate the excellent transfer capacity of our approach on fine-grained visual understanding tasks. Our design unleashes the ability to capture local details and global contexts by performing masked visual reconstruction in language semantic space. + +# 4.3. Label-Efficient Transfer + +Low-shot Regime Classification. We investigate the classification performance when only very few labeled images are available. Specifically, following [1,6], we random sample 1, 2, 5, and 10 labeled images per class from ImageNet-1K training split as our training sets. Instead of end-to-end fine-tuning, we train a linear classifier on frozen features to avoid overfitting. The complete validation split of ImageNet-1K which contains $50\mathrm{K}$ images are used to evaluate the accuracy. Table 4 shows the results. + +Specifically, compared to MAE+CLIP which only obtain slightly improvements over CLIP, our RILS outperforms both of them by a large margin. Notably, with only 10 images per class (i.e., 10K images for 1K classes), our method can achieve $51.8\%$ top-1 accuracy. + +Low-shot Regime Detection. We further transfer the low-shot experiment to object detection on COCO [40], which requires model to localize and classify visual objects simultaneously. We randomly sample annotated images from COCO training split with different sampling ratio (range from $1\%$ to $50\%$ ) as our training sets. All models are end-to-end fine-tuned for 12 epochs instead of 25 to prevent overfitting. We report the average precision of detection $\mathbf{AP}^{\mathcal{B}}$ for comparison in Table 5. As the results shown, our method shows the best performance under a wide range of sampling ratio (from $2\%$ to $50\%$ ). + +Table 4. Extreme low-shot classification on ImageNet-1K. We random sample 1, 2, 5, 10 images per class from training split, and report logistic regression accuracy (%) on ImageNet-1K validation split. All methods use ViT-B/16 as vision encoder. + +
MethodCOCO Sampling Ratio
1%2%5%10%20%50%
MAE [28]0.946.1015.7623.1629.7838.10
CLIP [47]0.815.0514.9822.4929.8838.50
SLIP [43]1.114.5413.8421.9129.5337.73
MAE+CLIP0.685.2814.3323.7229.9939.24
RILS0.866.4616.9424.6931.9740.41
+ +Table 5. Low-shot regime object detection on COCO. We report detection performance $\mathrm{AP}^{\mathcal{B}}$ with 12 epochs fine-tuning. All models are pre-trained with ViT-B/16 and 25 epochs on L-20M. + +Conceptually, one of the aspirations of pre-training is to pursue efficient transfer (e.g., less trainable data, shorter training length) on downstream tasks [1, 25, 30]. Experiments in the low-shot regime show the strong out-of-the-box capacity of our RILS by performing MIM in language semantic space. The non-trivial results indicate our pretraining approach brings out label-efficient learner, showing great application value to real-world scenarios, especially when annotated data is insufficient. + +# 4.4. Zero-Shot Transfer + +Classification. We evaluate the zero-shot classification over 21 benchmarks including ImageNet-1K [15]. Detail of each datasets are listed in the appendix and the evaluate recipes (e.g., prompt engineering) strictly follow [43]. Results are shown in Table 6. Specifically, compared to CLIP, MAE+CLIP only achieves $+0.6\%$ average improvements, while our RILS shows $+2.0\%$ gains. This hints the masked image modeling objective in the naive combination has little help to image-text alignment, while ours alleviate this issue by bind two objectives in a unified landscape. On ImageNet-1K, our method achieves $45.0\%$ accuracy, $+4.7\% / + 3.4\% / + 2.7\%$ higher than CLIP, SLIP and MAE+CLIP, respectively. Among 21 benchmarks, our method outperforms others over 17 datasets, frequently with a significant margin. + +Image-Text Retrieval. We study image-text retrieval on 2 benchmarks: COCO [40] and Flickr30K [46]. For both benchmarks, we use the original captions (w/o prompt) and $224 \times 224$ resized images for retrieval. Different from zero + +
MethodFood101CIFAR10CIFAR100CUB200SUN397CarsAircraftDTDPetsCaltech101FlowersMNISTFER2013STL10EuroSATRESISC45GTSRBCountry211CLEVRSST2ImageNetAverage# Wins.
CLIP [47]55.776.046.924.450.717.84.831.553.778.431.826.837.689.022.736.924.16.820.049.140.339.32
SLIP [43]56.773.443.222.651.617.74.932.452.579.133.329.433.589.517.836.217.86.823.449.741.638.72
MAE+CLIP57.878.252.423.951.618.14.631.555.878.432.027.632.789.827.039.422.97.214.749.342.339.90
RILS58.986.255.123.451.819.55.932.859.280.733.522.640.193.228.840.219.17.816.850.045.042.317
+ +Table 6. Zero-shot classification on 21 datasets. All models are trained with ViT-B/16 encoder for 25 epochs on L-20M. + +
MethodCOCOFlickr30K
I→TT→II→TT→I
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [47]41.8269.5079.3430.5457.1069.3028.1350.7761.1220.6140.7750.49
SLIP [43]44.5472.2082.1033.2659.6671.1431.2055.8166.0224.0545.5855.90
MAE+CLIP42.7270.6680.3631.4057.5069.6828.6252.2562.6422.6443.6753.97
RILS45.0673.3883.3634.8661.3672.7832.2156.3966.6725.4847.5557.94
+ +Table 7. Zero-shot image-text retrieval. $\mathrm{I} \rightarrow \mathrm{T}$ and $\mathrm{T} \rightarrow \mathrm{I}$ indicate image-to-text retrieval and text-to-image retrieval. + +
MethodIN-AIN-RIN-SkeIN-V2ObjNetAverage
CLIP [47]9.351.228.139.817.732.3
SLIP [43]10.549.826.741.320.433.1↑0.8
MAE+CLIP11.653.931.141.619.434.4↑2.1
RILS12.155.731.443.321.035.7↑3.4
+ +Table 8. Zero-shot out-of-distribution classification. We report the Top-1 classification accuracy (\%) for reference. + +shot classification, retrieval requires the models to have the ability to capture fine-grained contextualized information in both images and texts. As the results in Table 7 shown, our model achieves the best among all counterparts. In particular, when compared to CLIP, our RILS shows more significant improvements than MAE+CLIP. + +Robustness to Distribution Shift. Following CLIP [47], we also conduct zero-shot experiments on 5 out-of-distribution datasets: ImageNet Adversarial [33], ImageNet Rendition [32], ImageNetV2 [53], ImageNet Sketch [61], and ObjectNet [4]. As shown in Table 8, our method outperforms others on all five benchmarks. Specifically, RILS obtains significant improvements, $+3.4\%$ , $+2.6\%$ , $+1.3\%$ better than CLIP, SLIP, and MAE+CLIP respectively. + +# 5. Ablation Study + +In this section, we ablate the designs of RILS. All experiments are conducted with ViT/B-16 vision encoder and trained on L-10M for 25 epochs. We report the classification accuracy $(\%)$ under zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.) on ImageNet-1K. + +# 5.1. Comparisons with Two-stage Methods + +As discussed above, another way to leverage both masked image modeling with image-text contrastive learn- + +ing is to build a two-stage framework and learn two objectives step by step. In this section, we compare our RILS with several two-stage methods: + +$\mathbf{MIM} \rightarrow \mathbf{LiT}$ indicates firstly pre-train with masked image modeling only, then follow [71] to perform locked-image text tuning on image-text pairs. Specifically, we start the second stage by fine-tuning pre-trained MAE [28]. + +$\mathbf{MIM} \rightarrow \mathbf{CLIP}$ denotes fully fine-tune pre-trained MAE on image-text pairs in the second stage. In this way, pre-trained model also inherit properties from both objectives. + +$\mathbf{CLIP} \rightarrow \mathbf{MIM}$ stands for using pre-trained CLIP as a guidance for masked image modeling in the second stage. This paradigm has been studied in recent research such as [34, 44, 63]. + +The comparison results are shown in Table 9. As the vision encoder is fully frozen during the second stage in MIM $\rightarrow$ LiT, its performance on downstream tasks remains unchanged except for zero-shot. MIM $\rightarrow$ CLIP slightly outperforms MAE and CLIP. CLIP $\rightarrow$ MIM exhibits more improvements upon two base methods, but lose the ability on zero-shot classification. Our method rivals all counterparts with a more concise training pipeline. + +# 5.2. Comparisons on Reconstruction Space + +The core philosophy of our design is to perform masked reconstruction in language semantic space. We ablate the effectiveness of our design by comparing to two other alternatives: raw pixel space and high-level vision space. Reconstruction in raw pixel space denotes the aforementioned MAE+CLIP which tries to reconstruct raw pixels directly. For high-level vision space, we replace the language feature $z^T$ in Eq. (8) to learnable weights with other components unchanged. In other words, similar to design in [1,7,75], we map patch features to a probabilistic distribution on a group of learnable weights. As results in Table 10 shown, our + +
MethodZS.Lin.FT.
MAE [28]-43.481.5
CLIP [47]32.164.182.0
MIM→LiT [71]13.243.481.5
MIM→CLIP34.464.882.2
CLIP→MIM [34,44,63]-66.282.4
RILS (E2E)37.568.582.7
+ +Table 9. Comparisons with two-stage methods. All methods are trained with ViT-B/16 on L-10M for 25 epochs. Our approach rivals all two-stage methods in terms of zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.) + +
Reconstruction SpaceZS.Lin.FT.
Raw Pixel Space (MAE+CLIP)34.261.982.2
High-level Vision Space [12,75]34.867.782.4
Language Semantic Space (RILS)37.568.582.7
+ +Table 10. Comparisons on reconstruction space. Raw pixel space denotes aforementioned MAE+CLIP which directly reconstruct RGB values. High-level vision space indicates to replace the language feature $z^T$ in Eq. (8) to a group of learnable embeddings similar to [1,7,75]. Language semantic space stands for ours. All methods are trained with ViT-B/16 for 25 epochs on L-10M. + +RILS shows better performance on all three metrics. We notice that compared to reconstruct raw pixels, the high-level space reconstruction does not show prominent advantages as in [1,7,75]. We guess this is due to the absence of multicrop augmentation and exponential moving average (EMA) strategy which play important roles inside these methods but bring significant adverse impact on training efficiency. + +# 5.3. Hyper-parameters Analysis + +Mask Ratio. We compare three different mask ratios in Table 11a. As results shown, randomly masking at a ratio of $75\%$ leads to generally decent performance. Lower mask ratio $(60\%)$ leads to $+0.8\%$ better linear probing accuracy but impairs zero-shot performance $(-1.6\%)$ . Higher mask ratio $(90\%)$ acquires similar zero-shot accuracy but results in apparent decrease of $-0.9\%$ and $-0.4\%$ in terms of linear probing and fine-tuning. We guess this is due to lower mask ratio brings more prior information but less supervision in reconstruction, while the higher one exact converses. + +Number of vision decoder blocks. Performance w.r.t. number of decoder blocks are shown in Table 11b. Different decoder blocks numbers exhibit less to none differences in terms of zero-shot. As to linear probing, we detect the same trend as [28]: More vision decoder blocks leads to better linear probing accuracy. For fine-tuning, we observe almost the same accuracy but more decoder blocks seems to be slightly worse. Besides the numerical differences, when take the extra costs bring by more decoder blocks into consideration, we choose to build our RILS with one vision decoder blocks only, due to more decoder blocks introduces + +
Mask RatioZS.Lin.FT.
60%35.969.382.7
75%37.568.582.7
90%37.467.682.3
+ +(a) Ablations on mask ratio. $75\%$ generally leads to a good result except for linear probing. + +
Nums.ZS.Lin.FT.Rel.GHs.
137.568.582.71.0×
237.868.982.61.3×
437.369.682.51.5×
+ +(b) Numbers of vision decoder blocks. Rel.GHs. is short for relative GPU hours. + +
λ1:λ2ZS.Lin.FT.
2:137.568.582.7
1:136.468.182.3
1:235.968.282.2
+ +(c) Loss coefficients of $\mathcal{L}_{\mathrm{Contra}}$ and $\mathcal{L}_{\mathrm{Recon}}$ . + +Table 11. Ablations on the hyper-parameters of our approach. We report zero-shot (ZS.), linear probing(Lin.) and end-to-end finetuning (FT.) accuracy $(\%)$ on ImageNet-1K. Our default setups are high-lighted in gray. + +un-negligible training overheads. For instance, increasing the number of decoder blocks from 1 to 4 brings $0.5 \times$ more training costs. + +Loss coefficients. The results under different loss coefficients in Eq. (6) are shown in Table 11c. We empirically observe better performance with $\lambda_1:\lambda_2$ setting to 2:1. + +# 6. Conclusion + +In this work, we present a unified vision representation learner RILS that subsumes masked image modeling with natural language supervision. Instead of simply combining both paradigms with limited connection, we present a novel design to perform MIM in the language semantic space. Text features from language encoder serves as basic prototypes and probabilistic distribution of masked patches explicitly. Both objectives complement each other, leading to high synergy and mutual benefits. Extensive experimental results on downstream tasks showcase our method's advanced transferability and out-of-the-box capacity. We also observe excellent properties emerge from our design, especially in the low-shot regime. We hope our work can provide a new perspective on how to utilize language supervision with masked image modeling. In the future, we will explore further scale-up of our approach in terms of both model size and data size. + +# Acknowledgement + +This work was supported by NSFC (No. 62276108). + +# References + +[1] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. Masked siamese networks for label-efficient learning. 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International Journal of Computer Vision, 2019. 5 +[75] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. ibot: Image bert pre-training with online tokenizer. arXiv preprint arXiv:2111.07832, 2021. 2, 3, 7, 8 \ No newline at end of file diff --git a/2023/RILS_ Masked Visual Reconstruction in Language Semantic Space/images.zip b/2023/RILS_ Masked Visual Reconstruction in Language Semantic Space/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8cc5b9b198c2756c0f380e97cc4becaa7b6fbb9c --- /dev/null +++ b/2023/RILS_ Masked Visual Reconstruction in Language Semantic Space/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6582c42cb22c95d096aaf9d749fb6b68c7c3c429954cfd01508b78c28ff5cb65 +size 524650 diff --git a/2023/RILS_ Masked Visual Reconstruction in Language Semantic Space/layout.json b/2023/RILS_ Masked Visual Reconstruction in Language Semantic Space/layout.json new file mode 100644 index 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], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 529 + ], + "type": "text", + "content": "Both masked image modeling (MIM) and natural language supervision have facilitated the progress of transferable visual pre-training. In this work, we seek the synergy between two paradigms and study the emerging properties when MIM meets natural language supervision. To this end, we present a novel masked visual Reconstruction In Language semantic Space (RILS) pre-training framework, in which sentence representations, encoded by the text encoder, serve as prototypes to transform the vision-only signals into patch-sentence probabilities as semantically meaningful MIM reconstruction targets. The vision models can therefore capture useful components with structured information by predicting proper semantic of masked tokens. Better visual representations could, in turn, improve the text encoder via the image-text alignment objective, which is essential for the effective MIM target transformation. Extensive experimental results demonstrate that our method not only enjoys the best of previous MIM and CLIP but also achieves further improvements on various tasks due to their mutual benefits. RILS exhibits advanced transferability on downstream classification, detection, and segmentation, especially for low-shot regimes. Code is available at https://github.com/hustvl/RILS." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 574, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 684 + ], + "type": "text", + "content": "Learning transferable representation lies a crucial task in deep learning. Over the past few years, natural language processing (NLP) has achieved great success in this line of research [18, 45, 60]. To explore similar trajectories in the vision domain, researchers tend to draw upon the successes of NLP and have made tremendous progress: (i) Inspired by the advanced model architecture [60] as well as self-supervised learning paradigm [18] in NLP, vision Transformers (ViT) [21, 42] and masked image modeling" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 227, + 547, + 346 + ], + "blocks": [ + { + "bbox": [ + 308, + 227, + 547, + 346 + ], + "lines": [ + { + "bbox": [ + 308, + 227, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 308, + 227, + 547, + 346 + ], + "type": "image", + "image_path": "286393bcdae264a5673a8b31c0ec496e5b2e016853b473b1d29545879f01c785.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 354, + 547, + 465 + ], + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 465 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 465 + ], + "type": "text", + "content": "Figure 1. Overview of our RILS. Recon and Contra represent masked reconstruction loss and image-text contrastive loss. During pre-training, RILS learns to perform masked image modeling and image-text contrastive simultaneously. Masked predictions and corresponding targets are transformed to probabilistic distributions in language space by leveraging text features as semantic-rich prototypes. Under such a scheme, both objective and unified and achieve mutual benefits from each other. Vision encoder obtains the ability to capture meaningful and fine-grained context information, sparking decent transfer capacity." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "type": "text", + "content": "(MIM) [3, 28] open a new era of self-supervised visual representation learning, and show unprecedented transferability on various tasks, especially on fine-grained tasks such as object detection [22, 39]. (ii) Inspired by the great scalability brought by leveraging web-scale collections of texts as training data in NLP [5, 48, 49, 72], CLIP [47] and ALIGN [35] bring such a principle to vision and manifest the immense potential of leveraging natural language supervision for scalable visual pre-training. Strong transferability of pre-trained visual models on low-shot regimes ensues. It also facilitates diverse applications by extracting contextualized image or text features [26, 50, 52]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 548, + 714 + ], + "type": "text", + "content": "The remarkable attainment achieved by these two research lines pushes us to ponder: Is it possible to unify both masked image modeling and natural language supervision to pursuit better visual pre-training? A straightforward way towards this goal is to simply combine masked image modeling (MIM) with image-text contrastive learning (ITC) for multi-task learning. Although the naive combination is feasible to inherit the above advantages, we find it remains un-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": "*This work was done while S. Yang was an intern at ARC Lab, Tencent PCG. † X. Wang and Y. Ge are the corresponding authors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23304" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "satisfactory due to the mutual benefits between MIM and ITC have not yet been fully explored. Motivated by this, we develop RILS, a tailored framework to seek the synergy of masked image modeling and language supervision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "type": "text", + "content": "The core insight of RILS is to perform masked visual reconstruction in language semantic space. Specifically, instead of reconstructing masked patches in the standalone vision space (e.g., raw pixel [28,66], low-level features [3,62] or high-level perceptions [12, 34, 63, 75]), we map patch features to a probabilistic distribution over a batch of text features as the reconstruction target, which is enabled by ITC that progressively aligns the image and text spaces. The text features serve as semantically rich prototypes and probabilistic distributions explicitly inject the semantic information onto each image patch. The MIM objective is formulated as a soft cross-entropy loss to minimize the KL divergence between text-injected probabilistic distributions of masked vision tokens and their corresponding targets. The visual model optimized by our language-assisted reconstruction objective, in turn, improves ITC with better visual representations that capture fine-grained local contexts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 443 + ], + "type": "text", + "content": "Under such a working mechanism, the two objectives (i.e., MIM and ITC) complement each other and form a unified solution for transferable and scalable visual pretraining. Note that a lot of works [34, 63, 75] have manifested the importance of semantic information in the reconstruction target of MIM objectives. However, it is abstract to pursue such a semantically rich space with visual-only signals due to its unstructured characteristics [29]. Thanks to natural language supervision, this issue is alleviated by performing masked reconstruction in language space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": "Extensive experiments on various downstream tasks demonstrate that our design enjoys the best of both worlds. With a vanilla ViT-B/16 as the vision model and 25-epoch pre-training on 20 million image-text pairs, RILS achieves " + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "inline_equation", + "content": "83.3\\%" + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": " top-1 accuracy when fine-tune on ImageNet-1K [15], " + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "inline_equation", + "content": "+1.2\\%" + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "inline_equation", + "content": "+0.6\\%" + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": " better than the MAE [28] and CLIP [47] counterparts. Advanced performance can be consistently acquired when transfer to fine-grained tasks such as detection and segmentation. Moreover, our approach exhibits promising out-of-the-box capability under an extremely low-shot regime. RILS also demonstrates superior performance on zero-shot image classification and image-text retrieval. On ImageNet-1K benchmark, RILS obtains " + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "inline_equation", + "content": "45.0\\%" + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": " zero-shot classification accuracy, " + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "inline_equation", + "content": "+4.7\\% / + 3.4\\%" + }, + { + "bbox": [ + 46, + 444, + 288, + 659 + ], + "type": "text", + "content": " higher than CLIP [47]/SLIP [43] under the same training recipe. Compelling results of RILS imply the promising capacity in the unification of MIM and language supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 669, + 138, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 138, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 138, + 681 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "Masked Image Modeling translates masked language modeling [18] to vision domain and learns transferable" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "visual representation by reconstructing masked signals from partial observation [3, 9, 21]. Despite following the same mask-then-reconstruction principle, MIM differs from MLM a lot in the design of reconstruction target. BEiT [3] utilizes a pre-trained d-VAE [51, 55] and reconstructs masked image patches in the offline token space. Subsequent works improve it by employing better pretrained tokenizer [19, 34, 44, 63], eased and refined multichoice tokens [37] or contextual aligner [11]. MAE [28] and SimMIM [66] demonstrate directly reconstruct masked patches in raw pixel space can also lead to favorable transferability as well as scalability. MaskFeat [62] takes handcrafted low-level HOG feature [14] as target. Other works like iBOT [75], data2vec [2] and SdAE [12] perform reconstruction in a high-level vision feature space. Different from these methods, in this work, we tap the potential when masked image modeling meets natural language supervision and propose performing masked visual reconstruction in the language semantic space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 469 + ], + "type": "text", + "content": "Language Supervised Visual Pre-training learns visual representation from image-text pairs by solving generative [16, 56] or discriminative [73] pretext tasks. Recently, benefit from modern network architectures [21,41,42] and publicly available image-text datasets [8,17,57-59], CLIP [47] and ALIGN [35] unveil the tremendous transferability and scalability of this paradigm. The core technique of CLIP is aligning both vision and language modalities in a joint embedding space by global representation contrastive. Follow-up works further improve CLIP on the vision-only [43, 67] or vision-language [38, 64, 68-70] side. In this paper, we bring natural language supervision together with masked image modeling for better visual pre-training on these two paradigms." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 481, + 397, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 481, + 397, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 397, + 495 + ], + "type": "text", + "content": "3. Our Approach" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 502, + 388, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 388, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 388, + 513 + ], + "type": "text", + "content": "3.1. Architecture" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": "Among numerous architecture designing spaces, without loss of generalization, we adopt an asymmetric encoder-decoder architecture following MAE [28] and a dual-encoder architecture following CLIP [47] for their flexibility. As illustrated in Figure 1, RILS comprises the following three major components:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "Vision Encoder plays the key role in RILS and all our efforts aim to strengthen its capacity on downstream transfer. Following the trend in recent visual pre-training, we implement this encoder by a vanilla vision Transformer (ViT) [21]. It takes both intact (unmasked) image and corrupted (masked) image as inputs. Formally, input image " + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": " is first divided into regular non-overlapping image patches and then encoded by a stack of Transformer blocks [60]. Meanwhile, following MAE [28], we randomly mask a large portion of image patches and leave the remaining patches to be" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23305" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "visible. This corrupted image " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " is also encoded by vision encoder. We formulate the process of vision encoder as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 102, + 287, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 102, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 95, + 102, + 287, + 122 + ], + "type": "interline_equation", + "content": "\\operatorname {V} - \\operatorname {E n c} (I) = \\{f ^ {k} | k \\in [ 1, N ] \\}, \\tag {1}", + "image_path": "4fd5c16294bb6445ce37afe4cf9df62150fc4842e67937ea76c3654c988f2cde.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 96, + 119, + 238, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 119, + 238, + 133 + ], + "spans": [ + { + "bbox": [ + 96, + 119, + 238, + 133 + ], + "type": "interline_equation", + "content": "\\mathrm {V - E n c} (\\hat {I}) = \\{\\hat {f} ^ {k} | k \\in [ 1, N ] \\backslash \\mathcal {M} \\},", + "image_path": "95743f1f84e7f0237b9982dee654018c9ca3a8ad09d254e49686fb12f1ee8874.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " denotes the patch index and " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " denotes image patch numbers. " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " betoken encoded patch features of intact image " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " and corrupted image " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 139, + 287, + 186 + ], + "type": "text", + "content": " indicates the index set of random masked patches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 187, + 287, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 187, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 287, + 223 + ], + "type": "text", + "content": "Language Encoder encodes input text " + }, + { + "bbox": [ + 47, + 187, + 287, + 223 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 187, + 287, + 223 + ], + "type": "text", + "content": " by a stack of Transformer layers with causal masked attention [60]. This process can be simply represented by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 229, + 287, + 242 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 229, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 134, + 229, + 287, + 242 + ], + "type": "interline_equation", + "content": "\\mathrm {L} - \\operatorname {E n c} (T) = h. \\tag {2}", + "image_path": "cb580e46c5e8bbe7d54ade85e87b2b27d940c636e0474d00bf277f82e6418490.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "text", + "content": "We take the output " + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "text", + "content": " as global representation of input text. Vision Decoder consists of another series of Transformer blocks. Particularly, in our design, decoder blocks have the same dimension as encoder blocks. It takes the encoded feature " + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "text", + "content": " of masked image " + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 47, + 248, + 286, + 332 + ], + "type": "text", + "content": " along with a learnable [MASK] token as inputs, and tries to predict masked signals from corrupted view:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 337, + 287, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 287, + 363 + ], + "type": "interline_equation", + "content": "\\operatorname {V} - \\operatorname {D e c} \\left(\\left\\{\\hat {f} ^ {k} \\mid k \\in [ 1, N ] \\backslash \\mathcal {M} \\right\\}, [ \\text {M A S K} ]\\right) = \\left\\{g ^ {k} \\mid k \\in [ 1, N ] \\right\\}. \\tag {3}", + "image_path": "1f2e8e1401c1066d748aa897280e4bf2be75cf32e3860853840b3850e417fb4f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 369, + 157, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 157, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 157, + 382 + ], + "type": "text", + "content": "3.2. Training Objective" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "text", + "content": "Image-Text Contrastive. We leverage image-text contrastive loss to align two modalities into a joint embedding space. Specifically, given image-text pair " + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\{(I,T)\\}" + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "text", + "content": ", we take the mean-pooled image feature " + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\bar{f} = \\frac{1}{N}\\sum_{k=1}^{N}f^k" + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 388, + 287, + 472 + ], + "type": "text", + "content": " in Eq. (2) as global representations for image and text. The image and text features are further projected by two projection heads and followed by a normalization:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 138, + 478, + 287, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 478, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 138, + 478, + 287, + 498 + ], + "type": "interline_equation", + "content": "z ^ {I} = \\left\\| \\theta (\\bar {f}) \\right\\|, \\tag {4}", + "image_path": "5424020922202c0715c194e4c008376ede57142bcb5a64a828e8ab2a633c79c2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 138, + 495, + 197, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 495, + 197, + 509 + ], + "spans": [ + { + "bbox": [ + 138, + 495, + 197, + 509 + ], + "type": "interline_equation", + "content": "z ^ {T} = | | \\phi (h) | |,", + "image_path": "9485a42bb7aad5384200e773925e7faed87a7436c9eb188ad73b493919f9e096.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "type": "inline_equation", + "content": "\\theta (\\cdot)" + }, + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 47, + 515, + 287, + 551 + ], + "type": "text", + "content": " denotes the projection head for image and text respectively. The image-to-text contrastive loss and text-to-image contrastive loss can be represented as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 73, + 557, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 557, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 73, + 557, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {I 2 T}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {i} ^ {T} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {I} , z _ {j} ^ {T} \\right\\rangle / \\sigma\\right)}, \\tag {5}", + "image_path": "3409af7390a4da986b44a86ce971050e17f4fe30c96ad85e71ae6c2c0a90a5a8.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 74, + 594, + 259, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 594, + 259, + 625 + ], + "spans": [ + { + "bbox": [ + 74, + 594, + 259, + 625 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {T 2 I}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {i} ^ {I} \\right\\rangle / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle z _ {i} ^ {T} , z _ {j} ^ {I} \\right\\rangle / \\sigma\\right)},", + "image_path": "73e478388fba785fc20292b197a4c44c65064a6d9228c871f30c16c463f3f136.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "content": " stands for the index within a mini-batch and " + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "content": " indicates the batch size respectively. " + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 630, + 287, + 689 + ], + "type": "text", + "content": " performs a learnable temperature and is jointly trained during the pretraining. The total loss of image-text contrastive learning can be formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 108, + 694, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 694, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 108, + 694, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {C o n t r a}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {I 2 T}} + \\mathcal {L} _ {\\mathrm {T 2 I}}\\right). \\tag {6}", + "image_path": "06e5239d8eddf433195b83019d360db156099a0fab1ea30dae6133db75e1d19b.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "text", + "content": "Masked Visual Reconstruction in Language Semantic Space. As aforementioned, despite the mask-then-reconstruct principle of MIM is concise enough, the contiguous and unstructured characteristics in visual signal make the choice of reconstruction space non-trivial. Lots of works have manifested the great importance of performing masked reconstruction in a semantic-rich space [12, 34, 63, 75]. In this work, we build our reconstruction space from a vision-language perspective. We regard the text features as natural semantic descriptors for image patches and try to perform masked visual reconstruction in this language space. Specifically, given the encoded patch feature " + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "f^{k}" + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "text", + "content": " in Eq. (1) with " + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "text", + "content": " being the index of patch and decoded patch feature " + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "g^{k}" + }, + { + "bbox": [ + 305, + 72, + 545, + 252 + ], + "type": "text", + "content": " in Eq. (3), we firstly project and normalize both features to the vision-language aligned space:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 393, + 260, + 545, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 260, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 393, + 260, + 545, + 281 + ], + "type": "interline_equation", + "content": "\\tilde {f} _ {i} ^ {k} = \\left| \\left| \\theta \\left(f _ {i} ^ {k}\\right) \\right| \\right|, \\tag {7}", + "image_path": "3774aa372291c7df6c5aa11cfa7d12375ab7d94d260f6fad4d5b11e3fcebc16b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 395, + 277, + 456, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 277, + 456, + 291 + ], + "spans": [ + { + "bbox": [ + 395, + 277, + 456, + 291 + ], + "type": "interline_equation", + "content": "\\tilde {g} _ {i} ^ {k} = | \\left| \\theta \\left(g _ {i} ^ {k}\\right) \\right| |,", + "image_path": "55512c0cb13355848e91d15d1b2172859f4cece74dcd624cdcc927f8ab586e34.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": " being the index within mini-batch. " + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\theta (\\cdot)" + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": " represents the same vision projection head in Eq. (4). The key step of our design is to map patch features to a probabilistic distributions over a bunch of text features:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 331, + 355, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 355, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 331, + 355, + 545, + 392 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {1}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {f} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {1}\\right)} \\mid l \\in [ 1, B ] \\right\\}, \\tag {8}", + "image_path": "a68987e508bb6b4b4d704141222a829bb3a3112ddef3e850cbd7255cbec84410.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 333, + 388, + 517, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 388, + 517, + 418 + ], + "spans": [ + { + "bbox": [ + 333, + 388, + 517, + 418 + ], + "type": "interline_equation", + "content": "\\boldsymbol {q} _ {i} ^ {k} = \\left\\{\\frac {\\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {l} ^ {T} \\right\\rangle / \\tau_ {2}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\left\\langle \\tilde {g} _ {i} ^ {k} , z _ {j} ^ {T} \\right\\rangle / \\tau_ {2}\\right)} \\mid l \\in [ 1, B ] \\right\\},", + "image_path": "300785efe8acae2834cbfbcefad7c12ca4bc64592c4bf416989234de6d5b25d3.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\tau_{1}" + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\tau_{2}" + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "content": " serve as temperatures. In this way, with the text features serve as semantic-rich prototypes, both masked prediction and corresponding target are mapped into this language semantic space. The probabilistic distributions explicitly express the context information within each patch. The reconstruction objective is to shrinking the differences between text-injected distributions of target and masked prediction by minimize the KL divergence of " + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "inline_equation", + "content": "p_i^k" + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "content": " w.r.t. " + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "inline_equation", + "content": "q_i^k" + }, + { + "bbox": [ + 305, + 427, + 545, + 535 + ], + "type": "text", + "content": ", which can be represented by:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 321, + 544, + 545, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 544, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 321, + 544, + 545, + 572 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {R e c o n}} = \\frac {1}{| | \\mathcal {C} | | \\cdot | | \\mathcal {M} | |} \\sum_ {i \\in \\mathcal {C}} \\sum_ {k \\in \\mathcal {M}} - \\operatorname {s g} \\left[ \\boldsymbol {p} _ {i} ^ {k} \\right] \\log \\boldsymbol {q} _ {i} ^ {k}, \\tag {9}", + "image_path": "21a97f73275c7a360f6fa1381dcc06aa452c9b7ed85bc980211c0e2a5cc5172e.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}[\\cdot ]" + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "text", + "content": " indicates stop gradient. " + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "text", + "content": " denotes the index set of masked patches. " + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 305, + 582, + 545, + 653 + ], + "type": "text", + "content": " signifies the indexes of images which are correctly aligned to corresponding text features. In other words, we only calculate reconstruction loss on images which are correctly matched with target texts in imaged-to-text matching." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "By transferring reconstruction space from standalone vision space to language space, our approach takes both MIM and ITC into a unifying landscape and achieves mutual benefits from each other. MIM always suffers from overly paying attention on low-level details which consume lots of" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23306" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 287, + 295 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 295 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 295 + ], + "type": "image", + "image_path": "e298da8b7cc482b2ce558532c05ceafd955b308998304a0e85d52226917a432b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 288, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 339 + ], + "type": "text", + "content": "Figure 2. Architecture comparisons between MAE [28], CLIP [47], MAE+CLIP and RILS. Recon and Contra indicate masked reconstruction loss and image-text contrastive loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 345, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 441 + ], + "type": "text", + "content": "model's capacity but of less helpful for understanding visual concepts. By leveraging text features as prototypes and transfer patch features to probabilistic distribution on language space, the low-level information inside visual signals are abandoned by the contextualized language prototypes. Better contextualized image features in turn assist vision-language alignment, leading to transferable and scalable visual pre-training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "type": "text", + "content": "Overall Objective Function. The final objective of RILS is a weighted-sum of both image-text contrastive loss and masked reconstruction loss:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 487, + 287, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 487, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 91, + 487, + 287, + 499 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {R I L S}} = \\lambda_ {1} \\cdot \\mathcal {L} _ {\\text {C o n t r a}} + \\lambda_ {2} \\cdot \\mathcal {L} _ {\\text {R e c o n}}. \\tag {10}", + "image_path": "49c706ecec68e61fa7039d55f7bb5a092d8d34b4af358657323effa347aeeb0e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 47, + 508, + 261, + 520 + ], + "type": "text", + "content": " indicate coefficients to balance two losses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 527, + 157, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 157, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 157, + 540 + ], + "type": "text", + "content": "3.3. Pre-training Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Similar to [69], we sequentially sample image-text pairs according to filenames from recent released LAION-400M [58] dataset as our training sets. We term them as L-10M/L-20M/L-50M according to the amount of sampled unique image-text pairs (e.g., L-10M stands for the first 10 million subset of LAION-400M). Unless specified, our method is trained on L-20M for 25 epochs. We take AdamW [36] as optimizer with learning rate set to 5e-4 and a weight decay of 0.5. Learning rate linearly increases in the first epoch as warmup and decreases in the rest following the cosine learning rate decay strategy. We train our method on 32 NVIDIA V100 with a total batch size of 4096 (i.e., batch size per GPU is 128). For model architecture, we take the widely-adopted ViT-B/16 as vision encoder, 1-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 326, + 69, + 526, + 188 + ], + "blocks": [ + { + "bbox": [ + 326, + 69, + 526, + 188 + ], + "lines": [ + { + "bbox": [ + 326, + 69, + 526, + 188 + ], + "spans": [ + { + "bbox": [ + 326, + 69, + 526, + 188 + ], + "type": "table", + "html": "
MethodDatasetPT Epo.Lin.FT.
SimCLR [10]51.781.3
MAE [28]44.382.1
CLIP [47]L-20M25(∼ 400)67.882.7
SLIP [43]70.182.6
MAE+CLIP64.582.9
RILS71.583.3
BEiT [3]IN-1K(∼ 1.3M)800-83.2
MAE [28]160067.883.6
RILSL-50M25(∼ 1000)71.983.6
", + "image_path": "c3b37ee9095a3b7213c75a81bea58cb5c0db4f64e356909eca679afcd9386225.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 196, + 547, + 230 + ], + "lines": [ + { + "bbox": [ + 305, + 196, + 547, + 230 + ], + "spans": [ + { + "bbox": [ + 305, + 196, + 547, + 230 + ], + "type": "text", + "content": "Table 1. Image classification results on ImageNet-1K (IN-1K). PT Epo. indicates per-training epochs. Lin. and FT. is short for linear probing and end-to-end fine-tuning respectively." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": "layer Transformer block with 768-dim and 12 heads as vision decoder, and a text Transformer with 12 blocks and 512-dim as language encoder. To tokenize text inputs, following [47], we use byte-pair encoding (BPE [23]) with " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "49\\mathrm{K}" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " vocabulary size and set the max length of each sentence to 77. During pre-training, input images are resized to " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " and we set random mask ratio to " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " following [28]. Temperatures " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\tau_{1}" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\tau_{2}" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " in Eq. (8) are set to 0.04 and 0.1. Loss coefficients " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 305, + 241, + 545, + 361 + ], + "type": "text", + "content": " are set to 1.0 and 0.5 by default. More pre-training setups are listed in the appendix." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 376, + 378, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 378, + 388 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 378, + 388 + ], + "type": "text", + "content": "3.4. Discussion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 397, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 553 + ], + "type": "text", + "content": "There are also meaningful attempts [20,34,44,63] on utilizing natural language supervision together with MIM and seem alike to ours. However, there still have some distinctions existing in the motivation and method between ours and theirs. MVP [63], MILAN [34] and BEiTv2 [44] leverage natural language supervision by a two-stage framework, while ours is fully end-to-end. We will take further discussion about two-stage methods and ours in later experiments. A related and concurrent work [20] shows some similar designs but significantly differs from our idea of reconstruction in language space. As it does not have a reproducible implementation, we do not take it into consideration for comparison." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 571, + 389, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 389, + 583 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 389, + 583 + ], + "type": "text", + "content": "4. Main Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "In this section, we evaluate the representation quality of pre-training by transferring pre-trained models to various downstream tasks. We choose MAE [28] and CLIP [47] as representative methods of masked image modeling and vision-language contrastive learning. We also conduct a naive baseline (termed as MAE+CLIP) which simply combine MAE and CLIP together to perform MIM and ITC simultaneously, as a counterpart for our approach. Semantically comparisons between MAE, CLIP, MAE+CLIP and our RILS are illustrated in Figure 2." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23307" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 521, + 160 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 521, + 160 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 521, + 160 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 521, + 160 + ], + "type": "table", + "html": "
MethodCOCOLVIS
APBAPB50APB75APMAPM50APM75APBAPB50APB75APMAPM50APM75
MAE [28]48.168.652.942.465.846.431.046.233.729.644.031.7
CLIP [47]47.769.152.342.065.945.132.348.135.130.545.932.5
SLIP [43]46.568.551.041.565.144.132.448.935.130.846.532.6
MAE+CLIP48.169.652.542.466.245.732.648.835.230.746.432.6
RILS48.570.553.242.666.845.833.850.236.531.647.833.7
", + "image_path": "609a6813748562c0f1b92b20b88fc7130a152250854835af3939d1d71ad21701.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 192, + 176, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 176, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 176, + 205 + ], + "type": "text", + "content": "4.1. Classification Transfer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 211, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 330 + ], + "type": "text", + "content": "Linear Probing evaluates the quality of pre-trained feature by training a linear classifier on the frozen feature. We following the the recipe in [7] and sweep over different learning rate. Results are shown in Table 1. We notice that, with 25-epochs pre-training on L-20M, MAE+CLIP only achieves " + }, + { + "bbox": [ + 46, + 211, + 287, + 330 + ], + "type": "inline_equation", + "content": "64.5\\%" + }, + { + "bbox": [ + 46, + 211, + 287, + 330 + ], + "type": "text", + "content": " accuracy which is better than MAE but worse than CLIP. This implies the contradiction between MIM and ITC exists in such a naive combination. RILS alleviates this contradiction by elaborated design and outperforms other methods by a large margin." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": "End-to-End Fine-tuning. We follow most of setups in [28] for fine-tuning. Concretely, we fine-tune pre-trained models for 100 epochs with a warm-up of 5 epochs. Hyperparameters are all the same for all experiments except the learning rate. Results are shown in Table 1. When training with 25 epochs on L-20M, our method shows distinct advantages. Compared to MAE, CLIP and MAE+CLIP, our method exhibits " + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "inline_equation", + "content": "+1.2\\%" + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "inline_equation", + "content": "+0.6\\%" + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "inline_equation", + "content": "+0.4\\%" + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": " gains respectively. Moreover, when we scale-up the dataset capacity from L-20M to L-50M, with 25 epochs pre-training (around 1000 equivalent epochs in the ImageNet-1K regime), our method achieves " + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "inline_equation", + "content": "83.6\\%" + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": " top-1 accuracy which is on par with prior art (MAE trained on ImageNet-1K with 1600 epochs) with only " + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "inline_equation", + "content": "62.5\\%" + }, + { + "bbox": [ + 46, + 331, + 288, + 498 + ], + "type": "text", + "content": " training length." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 503, + 173, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 173, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 173, + 514 + ], + "type": "text", + "content": "4.2. Downstream Transfer" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "content": "Object Detection and Segmentation. For object detection and instance segmentation, we choose COCO [40] and LVIS [27] as benchmarks. We follow the design in [39] to transfer pre-trained ViT to detection. To tame quadratic complexity within self-attention, most attention blocks in the ViT are replaced with window attention except for four global blocks to perform cross-window interaction. SimpleFPN [39] is attached to the last transform block to generate pyramid features. Modernized RPN [54] and Mask R-CNN [31] head are deployed for detecting and segmenting visual instances. All pre-trained models are fine-tuned on two benchmarks for 25 epochs with same hyper-parameters. The results are shown in Table 2. Among all methods, our RILS achieves the best results in terms of " + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{\\mathcal{B}}" + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{\\mathcal{M}}" + }, + { + "bbox": [ + 46, + 521, + 288, + 713 + ], + "type": "text", + "content": " on both COCO and LVIS. It's noteworthy that two benchmarks show different properties: COCO benchmark shows" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 322, + 191, + 529, + 313 + ], + "blocks": [ + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "type": "text", + "content": "Table 2. Object detection and instance segmentation results on COCO and LVIS. All models are pre-trained with ViT-B/16 for 25 epochs on L-20M. Fine-tuning recipes for different pre-trained models are the same." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 191, + 529, + 313 + ], + "lines": [ + { + "bbox": [ + 322, + 191, + 529, + 313 + ], + "spans": [ + { + "bbox": [ + 322, + 191, + 529, + 313 + ], + "type": "table", + "html": "
MethodDatasetPT Epo.mIoU
BEiT [3]IN-1K(~ 1.3M)30045.5
80046.5
MAE [28]30045.8
160048.1
MAE [28]L-20M25(~ 400)44.2
CLIP [47]45.2
SLIP [43]45.7
MAE+CLIP45.3
RILSL-20M25(~ 400)48.1
", + "image_path": "53b8197dca98be686f9168c730ff80f6548cc9811632262ee146e8448abbaa2c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 324, + 316, + 527, + 327 + ], + "lines": [ + { + "bbox": [ + 324, + 316, + 527, + 327 + ], + "spans": [ + { + "bbox": [ + 324, + 316, + 527, + 327 + ], + "type": "text", + "content": "Table 3. Semantic segmentation results on ADE20K." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 339, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 567 + ], + "type": "text", + "content": "less benefits from language supervision while LVIS converses. Specifically, MAE shows leading performance on COCO but inferior performance on LVIS. We suspect this is due to the inherent distinctions in COCO and LVIS: LVIS contains 1203 visual categories which is about " + }, + { + "bbox": [ + 304, + 339, + 545, + 567 + ], + "type": "inline_equation", + "content": "15 \\times" + }, + { + "bbox": [ + 304, + 339, + 545, + 567 + ], + "type": "text", + "content": " more than COCO, and it always suffers from the long-tail distribution. Under such circumstances, COCO requires more localization ability which MAE excel at while LVIS prefers better classification ability which natural language supervision can bring. From this perspective, when compare our RILS with the MAE+CLIP, we find our design benefits more from both MIM and ITC objectives. On both COCO and LVIS, MAE+CLIP only shows competitive performance to the winner of MAE and CLIP, but our RILS exhibits apparent improvements especially on LVIS. This indicates our design leverage masked image modeling and language supervision in a more synergistic way. We believe this kind of synergy is of great exploration value for better visual pre-training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": "Semantic Segmentation. Experiments on semantic segmentation are conducted on the well-known ADE20K [74] dataset. We build the segmentation framework upon UperNet [65] and use the pre-trained models as encoders. Input images are resized to " + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": " and all models are finetuned for 160K iterations. All hyper-parameters strictly follow MAE [28] and not tuned. We report the mean intersection-over-union (mIoU) in Table 3. As the results shown, our method overwhelmingly surpasses others. Specifically, with 25 epoch pre-training on L-20M, our method achieves " + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "inline_equation", + "content": "48.1\\mathrm{mIoU}" + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "inline_equation", + "content": "+3.9" + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "inline_equation", + "content": "+2.9" + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": " higher than MAE and CLIP. Similar to the trends on LVIS, MAE+CLIP" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23308" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 70, + 521, + 191 + ], + "blocks": [ + { + "bbox": [ + 71, + 70, + 521, + 191 + ], + "lines": [ + { + "bbox": [ + 71, + 70, + 521, + 191 + ], + "spans": [ + { + "bbox": [ + 71, + 70, + 521, + 191 + ], + "type": "table", + "html": "
MethodPT DatasetPT Epo.Images per Class
12510
MAE [28]IN-1K(~ 1.3M)16004.3 ± (0.28)10.6 ± (0.21)22.4 ± (0.28)31.6 ± (0.02)
BEiT [3]IN-1K(~ 1.3M)8001.3 ± (0.03)2.2 ± (0.13)4.4 ± (0.21)7.4 ± (0.05)
MAE [28]L-20M25(~ 400)3.4 ± (0.12)5.2 ± (0.21)10.1 ± (0.10)14.8 ± (0.20)
CLIP [47]19.4 ± (0.18)29.2 ± (0.61)39.8 ± (0.39)46.3 ± (0.15)
SLIP [43]17.7 ± (0.33)27.2 ± (0.56)38.6 ± (0.55)46.4 ± (0.06)
MAE+CLIP21.1 ± (0.12)31.1 ± (0.94)41.6 ± (0.43)47.5 ± (0.15)
RILSL-20M25(~ 400)24.0 ± (0.27)34.6 ± (0.88)45.7 ± (0.46)51.8 ± (0.18)
", + "image_path": "9b1a62bea2c1f7e5f052a138b6be8d323d6b0552185f0f59d4241c31f1904220.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "text", + "content": "only gets " + }, + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{mIoU}" + }, + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "text", + "content": " gains by simply combining MIM with ITC together, far less than our approach. Furthermore, our method shows competitive or better performance when compared to prior art. Compared to MAE pre-trained on ImageNet-1K with 300 epochs, our method achieves 2.3 higher performance (48.1 vs. 45.8). When MAE is pretrained with 1600 epochs, our method achieves the same mIoU (48.1) while only requires " + }, + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 224, + 287, + 320 + ], + "type": "text", + "content": " training length." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 321, + 288, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 288, + 381 + ], + "type": "text", + "content": "Experiments above demonstrate the excellent transfer capacity of our approach on fine-grained visual understanding tasks. Our design unleashes the ability to capture local details and global contexts by performing masked visual reconstruction in language semantic space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 392, + 185, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 185, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 185, + 403 + ], + "type": "text", + "content": "4.3. Label-Efficient Transfer" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 519 + ], + "type": "text", + "content": "Low-shot Regime Classification. We investigate the classification performance when only very few labeled images are available. Specifically, following [1,6], we random sample 1, 2, 5, and 10 labeled images per class from ImageNet-1K training split as our training sets. Instead of end-to-end fine-tuning, we train a linear classifier on frozen features to avoid overfitting. The complete validation split of ImageNet-1K which contains " + }, + { + "bbox": [ + 46, + 411, + 287, + 519 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 411, + 287, + 519 + ], + "type": "text", + "content": " images are used to evaluate the accuracy. Table 4 shows the results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "text", + "content": "Specifically, compared to MAE+CLIP which only obtain slightly improvements over CLIP, our RILS outperforms both of them by a large margin. Notably, with only 10 images per class (i.e., 10K images for 1K classes), our method can achieve " + }, + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "inline_equation", + "content": "51.8\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "text", + "content": " top-1 accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Low-shot Regime Detection. We further transfer the low-shot experiment to object detection on COCO [40], which requires model to localize and classify visual objects simultaneously. We randomly sample annotated images from COCO training split with different sampling ratio (range from " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": ") as our training sets. All models are end-to-end fine-tuned for 12 epochs instead of 25 to prevent overfitting. We report the average precision of detection " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{AP}^{\\mathcal{B}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " for comparison in Table 5. As the results shown, our method shows the best performance under a wide range of sampling ratio (from " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 312, + 222, + 539, + 312 + ], + "blocks": [ + { + "bbox": [ + 46, + 194, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 547, + 218 + ], + "type": "text", + "content": "Table 4. Extreme low-shot classification on ImageNet-1K. We random sample 1, 2, 5, 10 images per class from training split, and report logistic regression accuracy (%) on ImageNet-1K validation split. All methods use ViT-B/16 as vision encoder." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 222, + 539, + 312 + ], + "lines": [ + { + "bbox": [ + 312, + 222, + 539, + 312 + ], + "spans": [ + { + "bbox": [ + 312, + 222, + 539, + 312 + ], + "type": "table", + "html": "
MethodCOCO Sampling Ratio
1%2%5%10%20%50%
MAE [28]0.946.1015.7623.1629.7838.10
CLIP [47]0.815.0514.9822.4929.8838.50
SLIP [43]1.114.5413.8421.9129.5337.73
MAE+CLIP0.685.2814.3323.7229.9939.24
RILS0.866.4616.9424.6931.9740.41
", + "image_path": "c641712f1b6e254fc5c5aeec5dd860f95a47638ecf02103b32dec62adb33b79f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 315, + 546, + 350 + ], + "lines": [ + { + "bbox": [ + 305, + 315, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 546, + 350 + ], + "type": "text", + "content": "Table 5. Low-shot regime object detection on COCO. We report detection performance " + }, + { + "bbox": [ + 305, + 315, + 546, + 350 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}^{\\mathcal{B}}" + }, + { + "bbox": [ + 305, + 315, + 546, + 350 + ], + "type": "text", + "content": " with 12 epochs fine-tuning. All models are pre-trained with ViT-B/16 and 25 epochs on L-20M." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 353, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 461 + ], + "type": "text", + "content": "Conceptually, one of the aspirations of pre-training is to pursue efficient transfer (e.g., less trainable data, shorter training length) on downstream tasks [1, 25, 30]. Experiments in the low-shot regime show the strong out-of-the-box capacity of our RILS by performing MIM in language semantic space. The non-trivial results indicate our pretraining approach brings out label-efficient learner, showing great application value to real-world scenarios, especially when annotated data is insufficient." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 468, + 420, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 420, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 420, + 479 + ], + "type": "text", + "content": "4.4. Zero-Shot Transfer" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "content": "Classification. We evaluate the zero-shot classification over 21 benchmarks including ImageNet-1K [15]. Detail of each datasets are listed in the appendix and the evaluate recipes (e.g., prompt engineering) strictly follow [43]. Results are shown in Table 6. Specifically, compared to CLIP, MAE+CLIP only achieves " + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "inline_equation", + "content": "+0.6\\%" + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "content": " average improvements, while our RILS shows " + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "inline_equation", + "content": "+2.0\\%" + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "content": " gains. This hints the masked image modeling objective in the naive combination has little help to image-text alignment, while ours alleviate this issue by bind two objectives in a unified landscape. On ImageNet-1K, our method achieves " + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "inline_equation", + "content": "45.0\\%" + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "content": " accuracy, " + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "inline_equation", + "content": "+4.7\\% / + 3.4\\% / + 2.7\\%" + }, + { + "bbox": [ + 304, + 486, + 546, + 666 + ], + "type": "text", + "content": " higher than CLIP, SLIP and MAE+CLIP, respectively. Among 21 benchmarks, our method outperforms others over 17 datasets, frequently with a significant margin." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "Image-Text Retrieval. We study image-text retrieval on 2 benchmarks: COCO [40] and Flickr30K [46]. For both benchmarks, we use the original captions (w/o prompt) and " + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": " resized images for retrieval. Different from zero" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23309" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 539, + 158 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 539, + 158 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 539, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 539, + 158 + ], + "type": "table", + "html": "
MethodFood101CIFAR10CIFAR100CUB200SUN397CarsAircraftDTDPetsCaltech101FlowersMNISTFER2013STL10EuroSATRESISC45GTSRBCountry211CLEVRSST2ImageNetAverage# Wins.
CLIP [47]55.776.046.924.450.717.84.831.553.778.431.826.837.689.022.736.924.16.820.049.140.339.32
SLIP [43]56.773.443.222.651.617.74.932.452.579.133.329.433.589.517.836.217.86.823.449.741.638.72
MAE+CLIP57.878.252.423.951.618.14.631.555.878.432.027.632.789.827.039.422.97.214.749.342.339.90
RILS58.986.255.123.451.819.55.932.859.280.733.522.640.193.228.840.219.17.816.850.045.042.317
", + "image_path": "e547cb9fc54193346c08f59eddc5aa1015deeb175473e9336dc2844499065fe8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 171, + 533, + 269 + ], + "blocks": [ + { + "bbox": [ + 75, + 159, + 518, + 170 + ], + "lines": [ + { + "bbox": [ + 75, + 159, + 518, + 170 + ], + "spans": [ + { + "bbox": [ + 75, + 159, + 518, + 170 + ], + "type": "text", + "content": "Table 6. Zero-shot classification on 21 datasets. All models are trained with ViT-B/16 encoder for 25 epochs on L-20M." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 171, + 533, + 269 + ], + "lines": [ + { + "bbox": [ + 59, + 171, + 533, + 269 + ], + "spans": [ + { + "bbox": [ + 59, + 171, + 533, + 269 + ], + "type": "table", + "html": "
MethodCOCOFlickr30K
I→TT→II→TT→I
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [47]41.8269.5079.3430.5457.1069.3028.1350.7761.1220.6140.7750.49
SLIP [43]44.5472.2082.1033.2659.6671.1431.2055.8166.0224.0545.5855.90
MAE+CLIP42.7270.6680.3631.4057.5069.6828.6252.2562.6422.6443.6753.97
RILS45.0673.3883.3634.8661.3672.7832.2156.3966.6725.4847.5557.94
", + "image_path": "9a966cbd537614a2a6934ca03096ac2c5d06d0bc4539db7cd0a77f2c923461e8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 59, + 287, + 274, + 373 + ], + "blocks": [ + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "lines": [ + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "spans": [ + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "type": "text", + "content": "Table 7. Zero-shot image-text retrieval. " + }, + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "type": "inline_equation", + "content": "\\mathrm{I} \\rightarrow \\mathrm{T}" + }, + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "type": "inline_equation", + "content": "\\mathrm{T} \\rightarrow \\mathrm{I}" + }, + { + "bbox": [ + 86, + 271, + 504, + 282 + ], + "type": "text", + "content": " indicate image-to-text retrieval and text-to-image retrieval." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 287, + 274, + 373 + ], + "lines": [ + { + "bbox": [ + 59, + 287, + 274, + 373 + ], + "spans": [ + { + "bbox": [ + 59, + 287, + 274, + 373 + ], + "type": "table", + "html": "
MethodIN-AIN-RIN-SkeIN-V2ObjNetAverage
CLIP [47]9.351.228.139.817.732.3
SLIP [43]10.549.826.741.320.433.1↑0.8
MAE+CLIP11.653.931.141.619.434.4↑2.1
RILS12.155.731.443.321.035.7↑3.4
", + "image_path": "34bea2d9826a29fa627b43f35a0bd24a30075b327fcbe080915615797671f9d3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 376, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 399 + ], + "type": "text", + "content": "Table 8. Zero-shot out-of-distribution classification. We report the Top-1 classification accuracy (\\%) for reference." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 406, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 477 + ], + "type": "text", + "content": "shot classification, retrieval requires the models to have the ability to capture fine-grained contextualized information in both images and texts. As the results in Table 7 shown, our model achieves the best among all counterparts. In particular, when compared to CLIP, our RILS shows more significant improvements than MAE+CLIP." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "text", + "content": "Robustness to Distribution Shift. Following CLIP [47], we also conduct zero-shot experiments on 5 out-of-distribution datasets: ImageNet Adversarial [33], ImageNet Rendition [32], ImageNetV2 [53], ImageNet Sketch [61], and ObjectNet [4]. As shown in Table 8, our method outperforms others on all five benchmarks. Specifically, RILS obtains significant improvements, " + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "inline_equation", + "content": "+3.4\\%" + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "inline_equation", + "content": "+2.6\\%" + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "inline_equation", + "content": "+1.3\\%" + }, + { + "bbox": [ + 46, + 477, + 287, + 574 + ], + "type": "text", + "content": " better than CLIP, SLIP, and MAE+CLIP respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 583, + 140, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 140, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 140, + 597 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": "In this section, we ablate the designs of RILS. All experiments are conducted with ViT/B-16 vision encoder and trained on L-10M for 25 epochs. We report the classification accuracy " + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": " under zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.) on ImageNet-1K." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 249, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 249, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 249, + 685 + ], + "type": "text", + "content": "5.1. Comparisons with Two-stage Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "As discussed above, another way to leverage both masked image modeling with image-text contrastive learn-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 289, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 326 + ], + "type": "text", + "content": "ing is to build a two-stage framework and learn two objectives step by step. In this section, we compare our RILS with several two-stage methods:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{MIM} \\rightarrow \\mathbf{LiT}" + }, + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "type": "text", + "content": " indicates firstly pre-train with masked image modeling only, then follow [71] to perform locked-image text tuning on image-text pairs. Specifically, we start the second stage by fine-tuning pre-trained MAE [28]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 373, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{MIM} \\rightarrow \\mathbf{CLIP}" + }, + { + "bbox": [ + 304, + 373, + 545, + 410 + ], + "type": "text", + "content": " denotes fully fine-tune pre-trained MAE on image-text pairs in the second stage. In this way, pre-trained model also inherit properties from both objectives." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 410, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{CLIP} \\rightarrow \\mathbf{MIM}" + }, + { + "bbox": [ + 304, + 410, + 545, + 458 + ], + "type": "text", + "content": " stands for using pre-trained CLIP as a guidance for masked image modeling in the second stage. This paradigm has been studied in recent research such as [34, 44, 63]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": "The comparison results are shown in Table 9. As the vision encoder is fully frozen during the second stage in MIM " + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": " LiT, its performance on downstream tasks remains unchanged except for zero-shot. MIM " + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": " CLIP slightly outperforms MAE and CLIP. CLIP " + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": " MIM exhibits more improvements upon two base methods, but lose the ability on zero-shot classification. Our method rivals all counterparts with a more concise training pipeline." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 563, + 509, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 509, + 576 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 509, + 576 + ], + "type": "text", + "content": "5.2. Comparisons on Reconstruction Space" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "The core philosophy of our design is to perform masked reconstruction in language semantic space. We ablate the effectiveness of our design by comparing to two other alternatives: raw pixel space and high-level vision space. Reconstruction in raw pixel space denotes the aforementioned MAE+CLIP which tries to reconstruct raw pixels directly. For high-level vision space, we replace the language feature " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "z^T" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " in Eq. (8) to learnable weights with other components unchanged. In other words, similar to design in [1,7,75], we map patch features to a probabilistic distribution on a group of learnable weights. As results in Table 10 shown, our" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23310" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 70, + 257, + 161 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 257, + 161 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 257, + 161 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 257, + 161 + ], + "type": "table", + "html": "
MethodZS.Lin.FT.
MAE [28]-43.481.5
CLIP [47]32.164.182.0
MIM→LiT [71]13.243.481.5
MIM→CLIP34.464.882.2
CLIP→MIM [34,44,63]-66.282.4
RILS (E2E)37.568.582.7
", + "image_path": "a6371ed24ed7179f6f307528b36b333e2ad224ddbb76531ad79b4f6dcb21e990.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 63, + 212, + 272, + 266 + ], + "blocks": [ + { + "bbox": [ + 47, + 163, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 208 + ], + "type": "text", + "content": "Table 9. Comparisons with two-stage methods. All methods are trained with ViT-B/16 on L-10M for 25 epochs. Our approach rivals all two-stage methods in terms of zero-shot (ZS.), linear probing (Lin.) and end-to-end fine-tuning (FT.)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 212, + 272, + 266 + ], + "lines": [ + { + "bbox": [ + 63, + 212, + 272, + 266 + ], + "spans": [ + { + "bbox": [ + 63, + 212, + 272, + 266 + ], + "type": "table", + "html": "
Reconstruction SpaceZS.Lin.FT.
Raw Pixel Space (MAE+CLIP)34.261.982.2
High-level Vision Space [12,75]34.867.782.4
Language Semantic Space (RILS)37.568.582.7
", + "image_path": "e7634cf1fe1f609a42960f416024ea217f509941f4e45ecc6a4b9ba1a73f32cf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 275, + 286, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 286, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 286, + 342 + ], + "type": "text", + "content": "Table 10. Comparisons on reconstruction space. Raw pixel space denotes aforementioned MAE+CLIP which directly reconstruct RGB values. High-level vision space indicates to replace the language feature " + }, + { + "bbox": [ + 46, + 275, + 286, + 342 + ], + "type": "inline_equation", + "content": "z^T" + }, + { + "bbox": [ + 46, + 275, + 286, + 342 + ], + "type": "text", + "content": " in Eq. (8) to a group of learnable embeddings similar to [1,7,75]. Language semantic space stands for ours. All methods are trained with ViT-B/16 for 25 epochs on L-10M." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 286, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 286, + 434 + ], + "type": "text", + "content": "RILS shows better performance on all three metrics. We notice that compared to reconstruct raw pixels, the high-level space reconstruction does not show prominent advantages as in [1,7,75]. We guess this is due to the absence of multicrop augmentation and exponential moving average (EMA) strategy which play important roles inside these methods but bring significant adverse impact on training efficiency." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 443, + 198, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 198, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 198, + 455 + ], + "type": "text", + "content": "5.3. Hyper-parameters Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": "Mask Ratio. We compare three different mask ratios in Table 11a. As results shown, randomly masking at a ratio of " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " leads to generally decent performance. Lower mask ratio " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "(60\\%)" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " leads to " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "+0.8\\%" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " better linear probing accuracy but impairs zero-shot performance " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "(-1.6\\%)" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": ". Higher mask ratio " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "(90\\%)" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " acquires similar zero-shot accuracy but results in apparent decrease of " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "-0.9\\%" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "inline_equation", + "content": "-0.4\\%" + }, + { + "bbox": [ + 46, + 461, + 286, + 581 + ], + "type": "text", + "content": " in terms of linear probing and fine-tuning. We guess this is due to lower mask ratio brings more prior information but less supervision in reconstruction, while the higher one exact converses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Number of vision decoder blocks. Performance w.r.t. number of decoder blocks are shown in Table 11b. Different decoder blocks numbers exhibit less to none differences in terms of zero-shot. As to linear probing, we detect the same trend as [28]: More vision decoder blocks leads to better linear probing accuracy. For fine-tuning, we observe almost the same accuracy but more decoder blocks seems to be slightly worse. Besides the numerical differences, when take the extra costs bring by more decoder blocks into consideration, we choose to build our RILS with one vision decoder blocks only, due to more decoder blocks introduces" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 338, + 70, + 514, + 120 + ], + "blocks": [ + { + "bbox": [ + 338, + 70, + 514, + 120 + ], + "lines": [ + { + "bbox": [ + 338, + 70, + 514, + 120 + ], + "spans": [ + { + "bbox": [ + 338, + 70, + 514, + 120 + ], + "type": "table", + "html": "
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Nums.ZS.Lin.FT.Rel.GHs.
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λ1:λ2ZS.Lin.FT.
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", + "image_path": "f1d7396a113aacd7ba49f35016871b09fa3f6946ece864e6c4ed32f123afddb7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "lines": [ + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "spans": [ + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "type": "text", + "content": "(c) Loss coefficients of " + }, + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Contra}}" + }, + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Recon}}" + }, + { + "bbox": [ + 350, + 262, + 501, + 273 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 274, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 274, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 545, + 319 + ], + "type": "text", + "content": "Table 11. Ablations on the hyper-parameters of our approach. We report zero-shot (ZS.), linear probing(Lin.) and end-to-end finetuning (FT.) accuracy " + }, + { + "bbox": [ + 305, + 274, + 545, + 319 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 274, + 545, + 319 + ], + "type": "text", + "content": " on ImageNet-1K. Our default setups are high-lighted in gray." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 334, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 370 + ], + "type": "text", + "content": "un-negligible training overheads. For instance, increasing the number of decoder blocks from 1 to 4 brings " + }, + { + "bbox": [ + 305, + 334, + 545, + 370 + ], + "type": "inline_equation", + "content": "0.5 \\times" + }, + { + "bbox": [ + 305, + 334, + 545, + 370 + ], + "type": "text", + "content": " more training costs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "content": "Loss coefficients. The results under different loss coefficients in Eq. (6) are shown in Table 11c. We empirically observe better performance with " + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\lambda_1:\\lambda_2" + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "content": " setting to 2:1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 430, + 378, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 378, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 378, + 441 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 453, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 657 + ], + "type": "text", + "content": "In this work, we present a unified vision representation learner RILS that subsumes masked image modeling with natural language supervision. Instead of simply combining both paradigms with limited connection, we present a novel design to perform MIM in the language semantic space. Text features from language encoder serves as basic prototypes and probabilistic distribution of masked patches explicitly. Both objectives complement each other, leading to high synergy and mutual benefits. Extensive experimental results on downstream tasks showcase our method's advanced transferability and out-of-the-box capacity. We also observe excellent properties emerge from our design, especially in the low-shot regime. We hope our work can provide a new perspective on how to utilize language supervision with masked image modeling. In the future, we will explore further scale-up of our approach in terms of both model size and data size." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 678, + 403, + 691 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 678, + 403, + 691 + ], + "spans": [ + { + "bbox": [ + 306, + 678, + 403, + 691 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 701, + 529, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 529, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 529, + 713 + ], + "type": "text", + "content": "This work was supported by NSFC (No. 62276108)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23311" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. 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Venkatesh Babu", + "bbox": [ + 406, + 247, + 560, + 262 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "venky@iisc.ac.in", + "bbox": [ + 411, + 267, + 557, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision and AI Lab, Indian Institute of Science, Bangalore", + "bbox": [ + 254, + 282, + 709, + 299 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 334, + 313, + 349 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Question Answering models have been shown to suffer from language biases, where the model learns a correlation between the question and the answer, ignoring the image. While early works attempted to use question-only models or data augmentations to reduce this bias, we propose an adaptive margin loss approach having two components. The first component considers the frequency of answers within a question type in the training data, which addresses the concern of the class-imbalance causing the language biases. However, it does not take into account the answering difficulty of the samples, which impacts their learning. We address this through the second component, where instance-specific margins are learnt, allowing the model to distinguish between samples of varying complexity. We introduce a bias-injecting component to our model, and compute the instance-specific margins from the confidence of this component. We combine these with the estimated margins to consider both answer-frequency and task-complexity in the training loss. We show that, while the margin loss is effective for out-of-distribution (ood) data, the bias-injecting component is essential for generalising to indistribution (id) data. Our proposed approach, Robust Margin Loss for Visual Question Answering (RMLVQA) improves upon the existing state-of-the-art results when compared to augmentation-free methods on benchmark VQA datasets suffering from language biases, while maintaining competitive performance on id data, making our method the most robust one among all comparable methods.", + "bbox": [ + 76, + 366, + 472, + 789 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 819, + 209, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual question answering (VQA) lies at the intersection of computer vision and natural language processing. It is", + "bbox": [ + 76, + 844, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the task of answering a question based on a given image. VQA networks need to combine knowledge from both visual scene and the question to predict the answer. These systems have numerous applications such as aiding the visually impaired in understanding their surroundings, image retrieval systems in e-commerce, and robotics.", + "bbox": [ + 500, + 335, + 890, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the success of deep learning, research in VQA has made great strides in recent years [3,5,16]. However, studies have shown that deep networks may learn correlations between the question and answer alone, ignoring the image modality [3,21,36]. They fail to do multimodal reasoning, specifically, if there is a class imbalance in the answer distributions of the training and test sets. For example, if most of the questions starting with \"What color..?\" are paired with the answer \"red\" in the training data, the model memorizes this trend to answer \"red\" for all color based questions in the test set, irrespective of the image.", + "bbox": [ + 496, + 428, + 892, + 594 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One solution to this problem is to perform data augmentations in various ways [1,4,11,15,27,36,42,43,46]. These methods outperform most other debiasing techniques in the literature. However, augmentation strategies are dependent on the dataset in question and the type of biases observed, which makes the process manual and tedious. Another extensively explored solution is to learn the bias in the dataset separately using a question-only branch [9, 12, 18] and explicitly removing the learnt bias from the base model.", + "bbox": [ + 496, + 595, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Margin losses have been widely used for a number of tasks. Cao et al. [10] address the problem of long tailed recognition through an adaptive margin loss, ensuring higher cosine margin penalty for the tail classes and lower penalty for other classes. A similar adaptive cosine margin penalty has been applied to mitigate the language bias problem in VQA by a previous work [17]. Margin losses have been widely used in deep face recognition as well, where it is desired that the features of two images of the same person should be as similar as possible, whereas those of two different people should be far apart. Margin losses", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code available at https://github.com/val-iisc/RMLVQA", + "bbox": [ + 94, + 886, + 467, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11671", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "are used in this regard for facial feature discrimination to maximize the decision margin. Rather than the Euclidean space, both these margin losses project their feature spaces onto a fixed radius hypersphere. While the well known CosFace loss [41] uses cosine margin penalties like Cao et al. [10], ArcFace [14], uses angular margins to maximize the decision margins among different classes in this feature space. Angles correspond to geodesic distance on the projected hypersphere which stabilizes the training process and is shown to improve the discriminative power of face recognition models as compared to cosine margin based methods.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We believe that the language bias problem of VQA can be addressed by learning discriminative features for the biased and unbiased samples in the dataset. To this end, we implement an adaptive angular margin loss, inspired by ArcFace, as margins allow models to distinguish between different kinds of samples. However, the key question here would be how to set the adaptive margins to cater to the specific problem of language biases. Traditional models over-trust the questions over the images due to a class imbalance in the training and test set answer distributions. Hence, one way to set the margins would be to ensure that the training samples with frequent answers are given a smaller penalty due to the abundance of those answers in the dataset, whereas those with rare answers are given a higher margin value. We refer to the resultant margin values as the frequency-based margins. However, one factor that is ignored in this aspect is the answering difficulty of each sample. We argue that more margin should be given to hard samples compared to the easier ones even if the corresponding answers are frequent. In this regard, we propose the learning of instance-specific margins during training, so as to allow the model to distinguish between hard and easy samples alongside frequent and rare samples. To the best of our knowledge, this is one of the first attempts in learning margins automatically and parallelly during training. We combine these learnable margins with the frequency based margins used in prior works [17], so as to allow both frequency and complexity of data samples to control the training dynamics. To compute these learnable margins, we introduce a bias injecting module to our model that is trained using Cross-Entropy $(CE)$ loss. We show that the $CE$ loss additionally clusters the training samples based on the dataset bias itself, thereby aiding the margin loss further. We further introduce a supervised contrastive loss [23] to pull the features of samples having the same answer together, while pushing others apart.", + "bbox": [ + 75, + 261, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adaptive margin losses, with margins calculated by using frequency of answers in the dataset, perform well in the ood setting. However, we show that they cause a drop in the in-domain performance, which raises questions on their robustness. As pointed by [40], it is crucial for VQA models to perform well on both in-domain and ood data since", + "bbox": [ + 75, + 810, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the test set distribution is unknown apriori. We mitigate this issue by ensembling the outputs of the bias injecting component and the proposed learnable margin-loss trained classification head during inference. This makes the model robust to the difference in answer distributions of the training and test sets. Our overall method is called RMLVQA - Robust Margin Loss for Visual Question Answering with language biases. The key contributions of this work can be summarized as follows:", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to mitigate the well known problem of language bias in VQA models by introducing an instance-specific adaptive margin loss, to allow the use of different margins for the learning of samples with varying complexities, in addition to the use of frequency-based margins. To achieve this, we introduce a bias-injecting component and allow the margins to be computed based on prediction probabilities of this branch. We show that this clusters samples in the feature space based on the bias present in the dataset.", + "- We propose to overcome the id-ood trade-off in margin-based losses, by ensembling the outputs of the bias-injecting component and the main model.", + "- We further introduce a supervised contrastive loss that pulls features of training samples having the same ground truth answers together, while pushing apart others. This aids the margin loss further.", + "- Through extensive experiments and ablations, we show how the proposed approach achieves state-of-the-art results when compared to augmentation-free methods on the ood VQA-CP v2 dataset, while maintaining competitive performance on the id VQA v2 dataset. This makes our model the most robust one among all non-augmentation based methods." + ], + "bbox": [ + 517, + 234, + 890, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The code, hyperparameter analyses, and results on multiple datasets are shared as supplementary material.", + "bbox": [ + 498, + 619, + 890, + 651 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 662, + 640, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "VQA and the language bias problem. VQA [5, 16] is the task of answering natural language questions given an image. VQA v1 & v2 [5, 16] are widely used datasets that are used to benchmark different algorithms. However, prior works have shown that these datasets have biases which can be amplified in the trained models [2, 3, 19, 36, 37]. Specifically, in case of language bias, the model learns a correlation between the question and the answer directly. For example, if the model always predicts \"tennis\" for the sport-related questions, it can achieve around $40\\%$ accuracy on the VQA v1 dataset, as the images of the VQA datasets are from MS-COCO [28], which has many \"tennis\" related images. To effectively quantify the extent of bias in the trained models, a new dataset VQA-CP v2 [3] was created from the", + "bbox": [ + 496, + 688, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11672", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "VQA v2 dataset. In this work, we aim to solve the language bias problem of VQA, where we evaluate our models on the ood benchmark dataset VQA-CP v2 and the id VQA v2.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bias mitigation techniques. The language bias problem reduces the generalizability of the VQA models, resulting in a drop in performance when the training set answer distribution is different from that of the test set. There are three popular categories of solutions in the literature tackling this problem, which we discuss below.", + "bbox": [ + 75, + 137, + 467, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual Grounding based methods [34, 45] used human annotations as supervision to attention maps [13, 33], whereas more recent works use Grad-CAM for the same [36, 43].", + "bbox": [ + 75, + 228, + 467, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ensemble based methods use a separate question-only model to capture the bias, and further remove the bias explicitly from the base VQA model [9, 12, 35]. Apart from these techniques, Niu et al. [31] introduce a counterfactual inference framework to mitigate the biases. KV and Mittal [25] use a visually grounded question encoder such that the visual information is embedded in the question representation itself. Niu et al. [32] improve both ood generalizability and id performance through introspective knowledge distillation.", + "bbox": [ + 75, + 290, + 467, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Augmentation based methods remove bias by augmenting the dataset to make it more balanced. Some works generate counterfactual data by masking or transforming the critical objects and words, and further generating appropriate ground truth answers [11, 15, 27]. Other works introduce negative samples by shuffling the inputs (images and questions) in the minibatch to reduce bias without requiring any annotation [40, 42, 46]. Wen et al. [42] use two kinds of negative samples for balancing the dataset, and construct both question-only and vision-only models to remove the biases.", + "bbox": [ + 75, + 441, + 467, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Margin-based methods. Max-margin classifiers are used in popular machine learning algorithms like SVMs [38]. Margin losses are commonly used in many problems such as deep face recognition [7, 14, 29, 41], long tailed or class imbalanced learning [10, 22, 30] and few-shot learning [26]. Guo et al. [17] apply an adaptive cosine margin loss to discriminate the frequent and rare answers for a given question type and implement this by transforming the multimodal feature space to a fixed radius hypersphere. The adaptive margins are estimated from the training data based on the frequency of occurrence of an answer in questions of a given type, ensuring that rare answers are given more margin penalty, whereas frequent classes are given less penalty.", + "bbox": [ + 75, + 593, + 467, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed approach", + "text_level": 1, + "bbox": [ + 76, + 805, + 263, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 830, + 217, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider the problem of classification based Visual Question Answering (VQA). It is the task of answering questions based on an image. Given a dataset $\\mathcal{D}$ having", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$n$ samples, with image $v \\in \\mathcal{V}$ , question $q \\in \\mathcal{Q}$ and answer (class label) $a \\in \\mathcal{A}$ , the goal is to train a model to optimize a mapping function $f: \\mathcal{V} \\times \\mathcal{Q} \\to \\mathbb{R}^{|\\mathcal{A}|}$ to generate predictions for the given question and image. The VQA model consists of four parts: (1) image feature extractor $e_v$ , (2) question feature extractor $e_q$ , (3) the VQA model $m_f$ which fuses the image and question features to generate the joint multimodal features $\\mathbf{x}$ , (4) classifier $c$ having weights $\\mathbf{W}$ , that generates the logits $f$ . Most of the classical VQA models [4, 6, 8, 24, 44] follow this paradigm and formulate the problem as follows:", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (v, q) = c \\left(m _ {f} \\left(e _ {v} (v), e _ {q} (q)\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 268, + 890, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Standard Cross-Entropy loss. VQA models can be trained by optimizing the Cross-Entropy $(CE)$ loss $^2$ shown below:", + "bbox": [ + 496, + 295, + 890, + 338 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp \\left(f _ {i}\\right)}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp \\left(f _ {j}\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 338, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To solve the problem of language bias in VQA, the model should learn discriminative features for different answers for a given question type so that it can distinguish frequently occurring answers from rarely occurring answers, as well as those with varying complexity. However, standard $CE$ loss only favours the samples with frequently occurring answers. Normalized $CE$ loss. Before defining the margin loss, we define a reformulation of the $CE$ loss as a cosine loss [14, 41], by L2-normalizing the classifier weight vectors $\\mathbf{W_i} \\in c$ for each $a_i \\in \\mathcal{A}$ , and feature $\\mathbf{x} = m_f(e_v(v_i), e_q(q_i))$ . Therefore, we define $\\hat{\\mathbf{W}}_{\\mathrm{i}} = \\frac{\\mathbf{W}_{\\mathrm{i}}}{\\|\\mathbf{W}_{\\mathrm{i}}\\|}$ and $\\hat{\\mathbf{x}} = s\\frac{\\mathbf{x}}{\\|\\mathbf{x}\\|}$ , where $s$ is a scaling parameter. Let $\\theta_{i}$ be the angle between $\\mathbf{x}$ and $\\mathbf{W}_{\\mathrm{i}}$ . Therefore the logit for each $a_i$ is transformed as (keeping the bias term as 0 for simplicity):", + "bbox": [ + 496, + 385, + 890, + 599 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} = \\hat {\\mathbf {W}} _ {\\mathbf {i}} ^ {\\top} \\hat {\\mathbf {x}} = \\| \\hat {\\mathbf {W}} _ {\\mathbf {i}} \\| \\| \\hat {\\mathbf {x}} \\| \\cos \\theta_ {i} = s \\cos \\theta_ {i} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 609, + 890, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The joint features $\\hat{\\mathbf{x}}$ are thus distributed on a hypersphere with a radius $s$ . This makes the normalized $CE$ loss as:", + "bbox": [ + 496, + 642, + 888, + 671 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {n s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos \\theta_ {i})}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos \\theta_ {j})} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 681, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. RMLVQA", + "text_level": 1, + "bbox": [ + 500, + 733, + 614, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this subsection, we define our method, which is a Robust Margin Loss based approach for solving the problem of language biases in VQA.", + "bbox": [ + 496, + 757, + 888, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adaptive Angular Margin Loss. We introduce an adaptive angular margin loss that ensures decision margin maximization through angular margins in an adaptive way. The normalized $CE$ loss transforms the feature space to an angular space of radius $s$ . The motivation behind an adaptive", + "bbox": [ + 496, + 801, + 890, + 878 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2In this paper, all losses will be expressed as individual sample losses", + "bbox": [ + 514, + 886, + 883, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11673", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1eec2d02ecfe881596ea47683b90aed0eb4aaf89021eecd2f63cf952a8b5c45d.jpg", + "image_caption": [ + "Figure 1. Overview of our model. The orange dashed region shows the proposed bias-injecting module, trained using the $CE$ loss. The blue dashed region shows how the instance-based margins are generated and then combined with the randomized frequency-based margins to compute the final margins. The final prediction is obtained by combining the two logit heads." + ], + "image_footnote": [], + "bbox": [ + 178, + 89, + 794, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "margin instead of a constant margin is based on the root of the language bias problem in VQA. These biases occur when similar questions in the dataset are paired with the same answers most of the time, fooling the model to memorize these questions and the answers by ignoring the image completely. Thus, while some samples are overlooked because of the rarity of their corresponding answers, others are overly paid attention to. Adaptive margins allow the model to set different penalties for the varying samples, thus leading to highly discriminative features for the different training instances.", + "bbox": [ + 75, + 344, + 472, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One aspect of the adaptive margins is to ensure that the instances with frequent answers are allowed a smaller margin than those with the rare ones. We call these margins $m_{freq}$ . Similar to [17], these margins are calculated based on the question type as shown below:", + "bbox": [ + 75, + 511, + 470, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {m} _ {f r e q} ^ {k} [ i ] = \\frac {n _ {i} ^ {k} + \\epsilon}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} n _ {j} ^ {k} + \\epsilon} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 592, + 468, + 631 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nm _ {f r e q} ^ {k} [ i ] = 1 - \\bar {m} _ {f r e q} ^ {k} [ i ] \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 632, + 468, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{m}_{freq}^{k}[i]$ measures the probability of occurrence of answer $a_{i}$ in the training data for a given question type $qt_{k}$ . $n_{i}^{k}$ is the frequency of answer $a_{i}$ in the training set calculated for the given $qt_{k}$ , and $\\epsilon$ is a hyperparameter for avoiding computational overflow. $m_{freq}^{k}[i]$ is the adaptive margin for answer $a_{i} \\in \\mathcal{A}$ corresponding to $qt_{k}$ .", + "bbox": [ + 76, + 657, + 468, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The adaptive angular margin loss adds a margin penalty to the angle between the features $\\mathbf{x}$ and the classifier weights $\\mathbf{W_i}$ for the $i^{th}$ class as shown below. Since the margin is placed on the angle, it maps exactly to the \"geodesic\" distance on the hypersphere [14]. While Deng et al. [14] set a constant value for the margin, i.e. 0.5, our margins are adaptive in nature.", + "bbox": [ + 75, + 750, + 470, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {A n g u l a r} ^ {k} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos (\\theta_ {i} + m _ {f r e q} ^ {k} [ i ]))}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos (\\theta_ {j} + m _ {f r e q} ^ {k} [ j ]))}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 859, + 472, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For notational simplicity, in the coming sections, we omit $k$ from the margin and loss computations.", + "bbox": [ + 496, + 344, + 890, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Randomization of the estimated margins. Boutros et al. [7] suggest that in typical margin losses, setting constant margins can limit the generalizability and discriminative power of a model. We note that $m_{freq}[i]$ is constant for each $a_i \\in \\mathcal{A}$ for a given question type $qt_k$ over all samples in the training set. When $qt_k$ is \"how many\", the margin for the answer \"2\" is same for all the training instances belonging to this question type. We believe that setting the same high margin value for a specific rare answer in a given question type and similarly lower value for a frequently appearing answer can lead to overcorrection of the language bias, by forcing the model to focus on the rare answers more than the frequent ones. Therefore, under a given question type $qt_k$ , for every answer $a_i$ , we use a randomized version of $\\bar{m}_{freq}[i]$ , called $\\bar{m}_{ran}[i]$ in the following manner:", + "bbox": [ + 496, + 375, + 892, + 603 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {m} _ {r a n} [ i ] = \\mathcal {N} (\\bar {m} _ {f r e q} [ i ], \\sigma) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 614, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}$ is the Gaussian distribution, and $\\sigma$ is the standard deviation, which is a hyperparameter. This impedes the model from overcorrecting with respect to the rare answers, thus increasing its generalizability. Finally, we obtain the randomized margin $m_{ran}[i] = 1 - \\bar{m}_{ran}[i]$ for each $a_i\\in \\mathcal{A}$ in each $qt_{k}$ .", + "bbox": [ + 496, + 643, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instance-based margins. The frequency-based margins estimated from the training data are constant for a given question type. So, for two different questions starting with \"how many\", the margins are same for each answer, irrespective of the model's difficulty in answering these instances. Ideally if one of the samples is hard to answer, more margin should be given to its ground truth class compared to the easier one. Randomizing $m_{\\text{freq}}$ as described above does not take the complexity of each sample into account. To this end, our model learns instance-level margins during training. We augment an auxiliary classifica", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11674", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion head to the feature $\\mathbf{x}$ (the orange dashed box in Fig. 1) which is architecturally same as the original model classifier $c$ . We call this the bias-injecting component. Following Eq. 1, the formulation of this component becomes:", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {b} (v, q) = c _ {b} (\\mathbf {x}) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 161, + 468, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where, $f_{b}$ refers to the logits generated by this component and $c_{b}$ refers to the classification head. It is to be noted that while $c_{b} \\neq c$ , both are trained to predict the answers given the questions and the images. Finally, we denote $\\bar{m}_{ins} = \\text{softmax}(f_{b} / \\tau)$ as the confidence, (i.e. prediction probability) of the bias-injecting component in answering a question. Here $\\tau$ stands for temperature which is a hyperparameter to the network. We define $m_{ins} = 1 - \\bar{m}_{ins}$ as the instance-level learnable margin, obtained from the model during training. These learned margins are similar with the frequency-based margins when samples are far away from the decision boundary. However, for training instances that are close, $m_{ins}$ increases the margins if the model confidence is low for the ground truth class, and decreases the same in case the model has high confidence in predicting the ground truth answer. We combine this instance-level confidence for the ground truth class with the previously calculated $m_{ran}$ for each sample $(v, q)$ to obtain the final margins $m_{comb}$ , as shown in the blue dashed box in Fig. 1.", + "bbox": [ + 75, + 186, + 472, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nm _ {\\text {c o m b}} [ g t ] = \\beta m _ {\\text {r a n}} [ g t ] + (1 - \\beta) m _ {\\text {i n s}} [ g t ] \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 482, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$gt$ refers to the index of the ground truth class of the sample, and $\\beta$ is a hyperparameter used for combining the two margins. For all indices $l \\neq gt$ , $m_{comb}[l] = m_{ran}[l]$ . In the first few training epochs, we do not compute $m_{ins}$ as the model is in the initial stage of its learning, i.e. we set $\\beta = 1$ . As training progresses, $\\beta$ is decreased in a step-wise manner to increase the contributions from the learnt margins.", + "bbox": [ + 75, + 508, + 468, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The bias-injecting component. The bias-injecting component is a classifier appended to the features $\\mathbf{x}$ trained using the standard $CE$ loss. As the $CE$ loss is known to favour the frequently appearing answers in the training data, it automatically learns the bias in the dataset, and by backpropagating this bias into the network, it clusters samples in the feature space based on the source of the bias. This aids the margin loss as it can now separate the (frequent, rare), and the (easy, difficult) samples inside the individual clusters. Moreover, the advantage of using it to generate the learnable margins is that the bias captured is now reflected directly in $\\bar{m}_{ins}$ , which ensures that it is close to $\\bar{m}_{freq}$ , but still provides information on the answering difficulty of a samples lying close to the decision boundary. Another advantage of this component is that by learning the data bias, this module is capable of generalizing to any in-distribution data, whereas the predictions from the primary classifier $c$ favour the ood data.", + "bbox": [ + 75, + 614, + 472, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. While margin losses are effective on an ood test", + "bbox": [ + 76, + 885, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "data, they result in degraded performance on $id$ test set. To mitigate this problem, during inference time, we take advantage of both the bias-injecting component $f_{b}$ and the primary logit head $f$ , as the former is useful in making predictions for an $id$ test data, while the latter is useful in an ood setting. This makes our model robust to different data distributions. We denote by $p_{comb}$ the combined predicted answer probabilities. This is obtained by combining the predictions from $c$ and $c_{b}$ as defined below:", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\text {c o m b}} = \\alpha . \\hat {p} + (1 - \\alpha). \\hat {p} _ {b} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 238, + 890, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyperparameter controlling the weight of each logit head during inference, $\\hat{p} = \\mathrm{softmax}(f)$ are the predictions from classifier $c$ , $\\hat{p_b} = \\mathrm{softmax}(f_b / \\tau)$ are the predictions from the bias-injecting component $c_b$ . The answer predicted is therefore $\\hat{a} = \\arg\\max(p_{comb})$ . The temperature $\\tau$ is same as that defined previously for the instance-based margins.", + "bbox": [ + 496, + 265, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Supervised Contrastive (SupCon) Loss. We further separate samples in the feature space based on the SupCon loss. In addition to creating discriminative features for (frequent, rare) and (easy, difficult) samples, the SupCon loss leads to a degree of discrimination among samples with different ground truth answers in the feature space. We consider a mini-batch of size $\\mathcal{B}$ of multimodal features denoted as $\\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_{\\mathcal{B}}\\}$ and corresponding answers as $\\{a_1,a_2,\\ldots ,a_{\\mathcal{B}}\\}$ . If we consider the current sample with index $j$ , the set of positive examples from the mini-batch is denoted by $P_{j}:\\{i\\in \\mathcal{B}\\text{s.t.} a_{i} = a_{j}\\}$ . Similarly, the set of negative examples is denoted by $N_{j}:\\{i\\in$ $\\mathcal{B}\\text{s.t.} a_i\\neq a_j\\}$ . The SupCon loss [23] is defined as,", + "bbox": [ + 496, + 369, + 892, + 568 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s u p - c o n}} = \\sum_ {j \\in \\mathcal {B}} \\frac {- 1}{| P _ {j} |} \\sum_ {p \\in P _ {j}} \\log \\frac {\\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {p}} / \\tau\\right)}{\\sum_ {n \\in N _ {j}} \\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {n}} / \\tau\\right)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 577, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We set the temperature $\\tau = 1$ for all experiments as we do not find any significant improvements by changing its value.", + "bbox": [ + 496, + 636, + 890, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Total Loss: The final loss function for each sample is:", + "bbox": [ + 500, + 667, + 859, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = L _ {\\text {A n g u l a r}} \\left(m _ {\\text {c o m b}}\\right) + L _ {s} + L _ {\\sup - c o n} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 693, + 890, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{Angular}$ is the angular margin loss, $L_{s}$ is the CE loss training the bias injecting component, $L_{sup-con}$ is the SupCon loss. Our final model can be seen in Fig. 1. We name our overall method RMLVQA.", + "bbox": [ + 496, + 719, + 890, + 780 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 792, + 632, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset details. We evaluate our model on the VQACP v2 dataset (Visual Question Answering Under Changing Priors) [3], which is an ood benchmark, based on the standard evaluation metric shown by Antol et al. [5]. It was created by reorganizing the training and validation sets of the VQA v2 [16] dataset, ensuring that the distribution", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11675", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of answers for each question type in the training set and the test set are different. The training set of VQA-CP v2 contains approximately 121k images and 438k questions, the test set contains approximately 98k images and 220k questions. Following previous works, we also evaluate our model on the VQA v2 validation set.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results", + "text_level": 1, + "bbox": [ + 76, + 190, + 171, + 204 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative analysis. In Table 1, we show a comparative analysis of the performance of RMLVQA on both VQACP v2 test and VQA v2 validation sets. We report the overall accuracies along with those on \"yes/no\", \"number\" and \"other\" type questions. We observe that our method gains around $6.39\\%$ in the overall accuracy for VQA-CP in comparison with AdaVQA [17], which is the cosine margin loss trained model. We observe that AdaVQA, while performing well on VQA-CP v2, has considerably low scores for the in-domain VQA v2. With RMLVQA, the validation accuracy of VQA v2 is $59.99\\%$ , which is $13.01\\%$ higher than AdaVQA. This shows that our method is the first one trained by adaptive margins that is robust to both id and ood data. With a score of $60.41\\%$ for VQA-CP v2, the model improves upon the current state-of-the-art augmentation-free models. In addition to reporting the performance of the various models in literature on the two datasets, we show the relative difference in accuracies between VQA-CP v2 test data and VQA v2 validation data. RMLVQA outperforms all other non-augmentation based models in terms of robustness, with the lowest difference in the two accuracies (see Table 1), indicating that our method is the most robust compared to all other methods that do not use any augmentation, and perform equally well on both VQA-CP v2 and VQA v2. For all experiments, Updn [4] is our base network.", + "bbox": [ + 75, + 205, + 472, + 584 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative analysis. We further demonstrate the effectiveness of our method in Fig. 2 which provides qualitative results on the VQA-CP v2 test set for RMLVQA and the base network UpDn. In the first row, we show examples for question type \"what color\". The base network UpDn [4] focuses on the incorrect region in the image, given by attention map scores, and outputs \"blue\", the most frequent answer in the training set for the given question type. The best scoring region from the attention maps of our model is localized at the correct region in the image, and it correctly outputs \"red\", which is not a frequent answer in \"what color\". In the second example, belonging to question type \"what is the person\", we see that while the baseline outputs \"phone\", which is a frequent class under that question type, RMLVQA predicts the correct answer \"hat\", which is a rare class, thus showing the effectiveness of our method. While the baseline outputs incorrect answers, it still focuses on the correct region in the image. This crucial observation indicates that the bias in the model weights do not allow this visual information to propagate forward. Thus it still picks from the frequent answers for the given question type.", + "bbox": [ + 75, + 584, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Choice of hyperparameter $\\alpha$ for inference time combination of prediction probabilities. Choice of $\\alpha$ is crucial as it decides how much weight to put on the prediction probabilities of the bias-injecting component $c_{b}$ and the primary classifier $c$ . As VQA-CP v2 does not have a validation set, we choose $\\alpha = 0.5$ for fair evaluation. However, we report the accuracies of VQA-CP v2 test and VQA v2 validation sets for different values of $\\alpha$ in Table 2. We observe that $\\alpha = 0.5$ leads to the most robust performance of our method on both id and ood data, where the relative gap of accuracies is just $0.42\\%$ . While we already choose the optimal value of $\\alpha$ for reporting model performance, our experiments demonstrate that one can choose an appropriate value to control the tradeoff between id and ood performances.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation studies", + "text_level": 1, + "bbox": [ + 498, + 310, + 661, + 324 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this subsection, we discuss the role of each component of RMLVQA. We evaluate them on the VQA-CP v2 test and VQA v2 validation data and show the results in Table 3.", + "bbox": [ + 496, + 325, + 890, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of angular margins. We call the base adaptive angular margin loss trained model RMLVQA-Base, which only considers the frequency based margins. Compared to AdaVQA, it leads to a rise of $3.22\\%$ in the VQACP test accuracy and an increase of $2.74\\%$ in the accuracy of the VQA-v2 validation set. This shows the effectiveness of the angular margin loss over the cosine margins both in id and ood data, validating the choice of the angular margin loss for addressing the language bias problem of VQA.", + "bbox": [ + 496, + 372, + 890, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of randomization of the margins. Randomizing the margins of each answer leads to an improvement in the accuracy values of VQA-CP v2 test, as shown in Table 3. Further, we also notice that it improves the in-domain accuracy of VQA v2 by a large margin (7.12%), thus showing its effectiveness in generalizability.", + "bbox": [ + 496, + 508, + 890, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Role of the learnable margins. As explained earlier, $m_{ins}$ represents the confidence of the bias-injecting component in answering a question. We show the positive effect of adding these margins to $m_{ran}$ in Table 3 for VQA-CP v2, with a slight loss in VQA v2. In Fig. 4 we show the Spearman's rank correlation coefficient $\\rho$ between $m_{freq}$ and $m_{ins}$ for the question type 'how many' for our method (for the angular and cosine margin losses defined in Sec 3 and AdaVQA [17] respectively), averaged over the relevant samples in each training epoch. We note the following: a) $\\rho$ is high throughout, indicating that the order of margin values in $m_{ins}$ for a certain sample remains similar to that of the margin values in $m_{freq}$ for the question type to which the sample belongs. b) $\\rho$ decreases over epochs, indicating the excess information being carried by $m_{ins}$ , aiding in the discrimination of samples whose answer frequencies are similar, but have different complexities.", + "bbox": [ + 496, + 599, + 893, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Role of the bias-injecting component. In Table 3, we show that the bias-injecting component increases the model's overall accuracy by $1.47\\%$ for VQA-CP v2 $(3.65\\%)$", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11676", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Accuracy comparisons with other methods on the VQA-CP v2 and VQA v2 datasets. The methods have been grouped into different categories (separated by lines in the table): base approaches, methods using human annotations, those that modify the language encoder, models weakening the language bias in different ways, our approach RMLVQA trained with UpDn as backbone, and finally the augmentation based methods. The best performance in each column is highlighted in bold. We highlight the overall accuracy of RMLVQA on VQA-CP with an underline as it achieves state-of-the-art on augmentation-free methods. * denotes numbers shown in [17]. We report the average accuracy of our model over 5 random seeds (along the with standard deviations in the superscript). Columns ending with “-CP” denote accuracies for VQA-CP v2, others denote accuracies for VQA v2. † indicates our implementation.", + "bbox": [ + 75, + 88, + 890, + 186 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c9a157ecd17abf27d199e2724819bca53340e7bc1d5106ce9feddbbcfb4b4413.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelY/N-CPNum-CPOthers-CPOverall-CPY/NNumOthersOverallDiff
SAN [44]38.3511.1421.7424.9670.0639.2847.8452.4127.45
GVQA [3]57.9913.6822.1431.3072.0331.1734.6548.2416.94
UpDn [4]42.2711.9346.0539.7481.1842.1455.6663.4823.74
S-MRL [9]42.8512.8143.238.4641.9612.5441.3537.131.33
AttAlign [36]43.0211.8945.0039.3780.9942.5555.2263.2423.87
HINT [36]67.2710.6145.8846.7381.1842.9955.5663.3816.65
SCR [43]70.4110.4247.2948.4778.841.654.562.213.73
VGQE [25]66.3527.0846.7750.11---64.0413.93
DLR [20]70.9918.7245.5748.8776.8239.3348.5457.969.09
AdvReg [35]65.4915.4835.4841.1779.8442.3555.1662.7521.58
RUBi [9]68.6520.2843.1847.11-----
LMH* [12]70.2944.1044.8652.1565.0637.6354.6956.354.2
CF-VQA [31]90.6121.5045.6155.0581.1343.8650.1160.945.89
IntroD [32]90.7917.9246.7355.1782.4846.6054.0563.408.23
GGE-DQ [18]87.0427.7549.5957.3273.2739.9954.3959.111.79
AdaVQA † [17]70.8349.0046.2954.0247.7834.1351.1446.987.04
RMLVQA89.98±0.4645.96±0.5748.74±0.1360.41±0.3276.68±0.3737.54±0.4953.26±0.1259.990.060.42
CVL [1]45.7212.4548.3442.12-----
Unshuffling [39]47.7214.4347.2442.3978.3242.1652.8161.0818.69
RandImg [40]83.8941.6044.2055.3776.5333.8748.5757.241.87
SSL [46]86.5329.8750.0357.59---63.736.14
CSS [11]84.3749.4248.2158.9573.2539.7755.1159.910.96
CSS + CL [27]86.9949.8947.1659.1867.2738.4054.7157.291.89
Mutant [15]88.9049.6850.7861.7282.0742.5253.2862.560.84
D-VQA [42]88.9352.3250.3961.9182.1844.0157.5464.963.05
", + "bbox": [ + 130, + 196, + 841, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "What color shirt is the man with the ball wearing?", + "text_level": 1, + "bbox": [ + 326, + 556, + 647, + 568 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f65ccc7f4056b44e1d7c536091f583d44fff5e1f41a71054740023159e03061.jpg", + "image_caption": [ + "GT: Red" + ], + "image_footnote": [], + "bbox": [ + 169, + 569, + 366, + 671 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c880fba39a812860704805c8336e16025634a0d4796987c49f3c1bcf4f966bb9.jpg", + "image_caption": [ + "Baseline: Blue" + ], + "image_footnote": [], + "bbox": [ + 380, + 569, + 576, + 670 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5bf7b283eff56dab88831df9c314d610ccbf247efb41f1d3f15417d2382579c6.jpg", + "image_caption": [ + "RMLVQA: Red" + ], + "image_footnote": [], + "bbox": [ + 591, + 569, + 787, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "What is the person holding?", + "text_level": 1, + "bbox": [ + 395, + 683, + 578, + 696 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fbe26fb4a497fc0248111b8329c47a48176c9ebea328d73d2ef6c3c30549608c.jpg", + "image_caption": [ + "GT: Hat", + "(a)", + "Figure 2. Qualitative analysis of RMLVQA. We show two images from two question types in the rows. Column (a) represents the ground truth answers, column (b) represents the answers predicted by the baseline UpDn model. Column (c) represents the answer predicted by our method. The bounding boxes show the highest scored region in the attention map of the individual models." + ], + "image_footnote": [], + "bbox": [ + 166, + 699, + 367, + 803 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/032b55525c8b9d4e55224ab045fad06844e478776a7ea6868c62f23365b3d075.jpg", + "image_caption": [ + "Baseline: Phone", + "(b)" + ], + "image_footnote": [], + "bbox": [ + 380, + 699, + 578, + 801 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b69a4157255a206863ec38b14eb84286f8af9150d5325d8dace729062f9e611a.jpg", + "image_caption": [ + "RMLVQA: Hat", + "(c)" + ], + "image_footnote": [], + "bbox": [ + 593, + 699, + 792, + 801 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11677", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2cabd8991afa8a8e691998dc092974f001334a5a46c1c11c5fee794a9a04acae.jpg", + "image_caption": [ + "Figure 3. TSNE visualization of the feature space with respect to different question types for the model components, evaluated incrementally: a) RMLVQA-Base, b) Gaussian randomization, c) Bias injection" + ], + "image_footnote": [], + "bbox": [ + 86, + 104, + 519, + 236 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8c950b91dac6ac8d0421b14018cd380f8ef036bdfbeeedef944d4e38b4f405b8.jpg", + "table_caption": [ + "Table 2. Role of $\\alpha$ in the inference stage of RMLVQA." + ], + "table_footnote": [], + "table_body": "
αVQA-CP v2 TestVQA-v2 ValGap
1.060.5458.162.38
0.860.5058.831.67
0.660.3359.570.76
0.560.4159.990.42
0.459.8760.460.59
0.257.4661.263.8
0.039.4861.5422.06
", + "bbox": [ + 117, + 349, + 428, + 477 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/136b7b08fa856e504691de1fa6dfa5e3ce86f39f1538d2cf44c619573e13ae5f.jpg", + "table_caption": [ + "Table 3. Ablations. In this table we show the ablations of $RM$ -LVQA, evaluated on VQA-CP v2 test & VQA v2 val." + ], + "table_footnote": [], + "table_body": "
ModelY/NNumOthersOverallVQA v2 Val
RMLVQA-Base79.7849.6248.4957.2449.72
+Randomization83.7249.4748.3157.9756.84
+Bias Injection88.2744.1348.5559.4460.49
+Learnable Margin88.0646.6348.7459.8759.60
+SupCon Loss89.9845.9648.7460.4159.99
-Backprop89.3640.5647.8058.8059.67
", + "bbox": [ + 81, + 532, + 465, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for VQA v2). The effectiveness of this component can be understood from Fig. 3, where we show the TSNE visualizations of how answers from different question types are placed in the feature space for the components of RMLVQA. Fig. 3(a) shows that while for some question types like 'how many', 'are', answers are well separated, some others like 'do', 'are they', 'is there' are close, out of which some are entangled. Although the randomization increases flexibility of the adaptive margins, it does not disentangle these question types, as seen in Fig. 3b. Finally, in Fig. 3(c), we see that the bias-injecting component aids in separating the answers according to their question types. This is because the bias sources of VQA-CP is its question types, and hence this component clusters samples in the training set based on the same. This is crucial, as with more entanglement, the model tends to answer questions of one question type with", + "bbox": [ + 75, + 657, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/707495bf036325e7cf448736f4d3a435eb967624af6a809a28c7eadeaad65635.jpg", + "image_caption": [ + "Figure 4. Spearman's rank correlation coefficient between $\\mathbf{m}_{\\mathrm{freq}}$ and $\\mathbf{m}_{\\mathrm{ins}}$ over epochs for question type \"how many\" on VQA-CP v2 test set" + ], + "image_footnote": [], + "bbox": [ + 591, + 95, + 851, + 252 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the answers of another type. In the last row of Table 3, we also observe the effect of removing the backpropagation of the $CE$ loss (used to train the bias-injecting component) into the main network for VQA-CP v2. The classifier weights in the bias-injecting component learn the language bias in the dataset and backpropagate the same into the network, thus helping the model separate the answers across different question types in the feature space. We utilize this knowledge in the inference stage, where we combine the two logit heads, thus helping the model to generalize to both $id$ and $ood$ test data, as is evident from Tables 1 and 2.", + "bbox": [ + 496, + 325, + 890, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Role of the SupCon Loss. The addition of the SupCon loss is shown to improve the performance of our model empirically for both VQA-CP and VQA v2 as shown in Table 3.", + "bbox": [ + 496, + 491, + 890, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 542, + 617, + 558 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although margin-based losses are useful in mitigating language biases in VQA, they may not distinguish between answers of different task-complexity levels in the feature space. To distinguish between samples having similar answer frequency, but different complexity, we learn instance-based margins for each sample from the model during training. We introduce a bias-injecting component in our model and utilize its confidence in answer prediction as the instance-level margins. Being trained by the $CE$ loss, this component further clusters the training samples based on the source of the data bias, guiding the margin loss to distinguish frequent and rare answers inside each cluster. We ensemble the outputs of the bias-injecting component with those of the main model during inference to achieve state-of-the-art results among existing augmentation-free methods on the ood VQA-CP v2 dataset, while being the most robust with respect to both id and ood test sets.", + "bbox": [ + 496, + 561, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 835, + 678, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by a research grant (CRG/2021/005925) from SERB, DST, Govt. of India. Abhipsa Basu is supported by the PMRF fellowship.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11678", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10044-10054, 2020. 1, 7", + "[2] Aishwarya Agrawal, Dhruv Batra, and Devi Parikh. Analyzing the behavior of visual question answering models. arXiv preprint arXiv:1606.07356, 2016. 2", + "[3] Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. Don't just assume; look and answer: Overcoming priors for visual question answering. 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Overcoming language priors with self-supervised learning for visual question answering. arXiv preprint arXiv:2012.11528, 2020. 1, 3, 7" + ], + "bbox": [ + 501, + 92, + 890, + 614 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11680", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_model.json b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b655f62cda272b940c8935595b7d9ad4389bb793 --- /dev/null +++ b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.13, + 0.861, + 0.177 + ], + "angle": 0, + "content": "RMLVQA: A Margin Loss Approach For Visual Question Answering with Language Biases" + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.205, + 0.42, + 0.222 + ], + "angle": 0, + "content": "Abhipsa Basu" + }, + { + "type": "text", + "bbox": [ + 0.265, + 0.226, + 0.461, + 0.239 + ], + "angle": 0, + "content": "abhipsabasu@iisc.ac.in" + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.205, + 0.692, + 0.222 + ], + "angle": 0, + "content": "Sravanti Addepalli" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.226, + 0.706, + 0.238 + ], + "angle": 0, + "content": "sravantia@iisc.ac.in" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.248, + 0.562, + 0.263 + ], + "angle": 0, + "content": "R. Venkatesh Babu" + }, + { + "type": "text", + "bbox": [ + 0.413, + 0.268, + 0.558, + 0.282 + ], + "angle": 0, + "content": "venky@iisc.ac.in" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.283, + 0.71, + 0.3 + ], + "angle": 0, + "content": "Vision and AI Lab, Indian Institute of Science, Bangalore" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.335, + 0.314, + 0.351 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.367, + 0.473, + 0.79 + ], + "angle": 0, + "content": "Visual Question Answering models have been shown to suffer from language biases, where the model learns a correlation between the question and the answer, ignoring the image. While early works attempted to use question-only models or data augmentations to reduce this bias, we propose an adaptive margin loss approach having two components. The first component considers the frequency of answers within a question type in the training data, which addresses the concern of the class-imbalance causing the language biases. However, it does not take into account the answering difficulty of the samples, which impacts their learning. We address this through the second component, where instance-specific margins are learnt, allowing the model to distinguish between samples of varying complexity. We introduce a bias-injecting component to our model, and compute the instance-specific margins from the confidence of this component. We combine these with the estimated margins to consider both answer-frequency and task-complexity in the training loss. We show that, while the margin loss is effective for out-of-distribution (ood) data, the bias-injecting component is essential for generalising to indistribution (id) data. Our proposed approach, Robust Margin Loss for Visual Question Answering (RMLVQA) improves upon the existing state-of-the-art results when compared to augmentation-free methods on benchmark VQA datasets suffering from language biases, while maintaining competitive performance on id data, making our method the most robust one among all comparable methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.82, + 0.21, + 0.835 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.845, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Visual question answering (VQA) lies at the intersection of computer vision and natural language processing. It is" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.336, + 0.892, + 0.427 + ], + "angle": 0, + "content": "the task of answering a question based on a given image. VQA networks need to combine knowledge from both visual scene and the question to predict the answer. These systems have numerous applications such as aiding the visually impaired in understanding their surroundings, image retrieval systems in e-commerce, and robotics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.595 + ], + "angle": 0, + "content": "With the success of deep learning, research in VQA has made great strides in recent years [3,5,16]. However, studies have shown that deep networks may learn correlations between the question and answer alone, ignoring the image modality [3,21,36]. They fail to do multimodal reasoning, specifically, if there is a class imbalance in the answer distributions of the training and test sets. For example, if most of the questions starting with \"What color..?\" are paired with the answer \"red\" in the training data, the model memorizes this trend to answer \"red\" for all color based questions in the test set, irrespective of the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.734 + ], + "angle": 0, + "content": "One solution to this problem is to perform data augmentations in various ways [1,4,11,15,27,36,42,43,46]. These methods outperform most other debiasing techniques in the literature. However, augmentation strategies are dependent on the dataset in question and the type of biases observed, which makes the process manual and tedious. Another extensively explored solution is to learn the bias in the dataset separately using a question-only branch [9, 12, 18] and explicitly removing the learnt bias from the base model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Margin losses have been widely used for a number of tasks. Cao et al. [10] address the problem of long tailed recognition through an adaptive margin loss, ensuring higher cosine margin penalty for the tail classes and lower penalty for other classes. A similar adaptive cosine margin penalty has been applied to mitigate the language bias problem in VQA by a previous work [17]. Margin losses have been widely used in deep face recognition as well, where it is desired that the features of two images of the same person should be as similar as possible, whereas those of two different people should be far apart. Margin losses" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code available at https://github.com/val-iisc/RMLVQA" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11671" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "are used in this regard for facial feature discrimination to maximize the decision margin. Rather than the Euclidean space, both these margin losses project their feature spaces onto a fixed radius hypersphere. While the well known CosFace loss [41] uses cosine margin penalties like Cao et al. [10], ArcFace [14], uses angular margins to maximize the decision margins among different classes in this feature space. Angles correspond to geodesic distance on the projected hypersphere which stabilizes the training process and is shown to improve the discriminative power of face recognition models as compared to cosine margin based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.473, + 0.807 + ], + "angle": 0, + "content": "We believe that the language bias problem of VQA can be addressed by learning discriminative features for the biased and unbiased samples in the dataset. To this end, we implement an adaptive angular margin loss, inspired by ArcFace, as margins allow models to distinguish between different kinds of samples. However, the key question here would be how to set the adaptive margins to cater to the specific problem of language biases. Traditional models over-trust the questions over the images due to a class imbalance in the training and test set answer distributions. Hence, one way to set the margins would be to ensure that the training samples with frequent answers are given a smaller penalty due to the abundance of those answers in the dataset, whereas those with rare answers are given a higher margin value. We refer to the resultant margin values as the frequency-based margins. However, one factor that is ignored in this aspect is the answering difficulty of each sample. We argue that more margin should be given to hard samples compared to the easier ones even if the corresponding answers are frequent. In this regard, we propose the learning of instance-specific margins during training, so as to allow the model to distinguish between hard and easy samples alongside frequent and rare samples. To the best of our knowledge, this is one of the first attempts in learning margins automatically and parallelly during training. We combine these learnable margins with the frequency based margins used in prior works [17], so as to allow both frequency and complexity of data samples to control the training dynamics. To compute these learnable margins, we introduce a bias injecting module to our model that is trained using Cross-Entropy \\((CE)\\) loss. We show that the \\(CE\\) loss additionally clusters the training samples based on the dataset bias itself, thereby aiding the margin loss further. We further introduce a supervised contrastive loss [23] to pull the features of samples having the same answer together, while pushing others apart." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Adaptive margin losses, with margins calculated by using frequency of answers in the dataset, perform well in the ood setting. However, we show that they cause a drop in the in-domain performance, which raises questions on their robustness. As pointed by [40], it is crucial for VQA models to perform well on both in-domain and ood data since" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "the test set distribution is unknown apriori. We mitigate this issue by ensembling the outputs of the bias injecting component and the proposed learnable margin-loss trained classification head during inference. This makes the model robust to the difference in answer distributions of the training and test sets. Our overall method is called RMLVQA - Robust Margin Loss for Visual Question Answering with language biases. The key contributions of this work can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.236, + 0.892, + 0.386 + ], + "angle": 0, + "content": "- We propose to mitigate the well known problem of language bias in VQA models by introducing an instance-specific adaptive margin loss, to allow the use of different margins for the learning of samples with varying complexities, in addition to the use of frequency-based margins. To achieve this, we introduce a bias-injecting component and allow the margins to be computed based on prediction probabilities of this branch. We show that this clusters samples in the feature space based on the bias present in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.392, + 0.892, + 0.437 + ], + "angle": 0, + "content": "- We propose to overcome the id-ood trade-off in margin-based losses, by ensembling the outputs of the bias-injecting component and the main model." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.442, + 0.892, + 0.502 + ], + "angle": 0, + "content": "- We further introduce a supervised contrastive loss that pulls features of training samples having the same ground truth answers together, while pushing apart others. This aids the margin loss further." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.507, + 0.892, + 0.613 + ], + "angle": 0, + "content": "- Through extensive experiments and ablations, we show how the proposed approach achieves state-of-the-art results when compared to augmentation-free methods on the ood VQA-CP v2 dataset, while maintaining competitive performance on the id VQA v2 dataset. This makes our model the most robust one among all non-augmentation based methods." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.236, + 0.892, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.621, + 0.892, + 0.652 + ], + "angle": 0, + "content": "The code, hyperparameter analyses, and results on multiple datasets are shared as supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.642, + 0.681 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.902 + ], + "angle": 0, + "content": "VQA and the language bias problem. VQA [5, 16] is the task of answering natural language questions given an image. VQA v1 & v2 [5, 16] are widely used datasets that are used to benchmark different algorithms. However, prior works have shown that these datasets have biases which can be amplified in the trained models [2, 3, 19, 36, 37]. Specifically, in case of language bias, the model learns a correlation between the question and the answer directly. For example, if the model always predicts \"tennis\" for the sport-related questions, it can achieve around \\(40\\%\\) accuracy on the VQA v1 dataset, as the images of the VQA datasets are from MS-COCO [28], which has many \"tennis\" related images. To effectively quantify the extent of bias in the trained models, a new dataset VQA-CP v2 [3] was created from the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11672" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "VQA v2 dataset. In this work, we aim to solve the language bias problem of VQA, where we evaluate our models on the ood benchmark dataset VQA-CP v2 and the id VQA v2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.468, + 0.228 + ], + "angle": 0, + "content": "Bias mitigation techniques. The language bias problem reduces the generalizability of the VQA models, resulting in a drop in performance when the training set answer distribution is different from that of the test set. There are three popular categories of solutions in the literature tackling this problem, which we discuss below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.468, + 0.289 + ], + "angle": 0, + "content": "Visual Grounding based methods [34, 45] used human annotations as supervision to attention maps [13, 33], whereas more recent works use Grad-CAM for the same [36, 43]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.468, + 0.44 + ], + "angle": 0, + "content": "Ensemble based methods use a separate question-only model to capture the bias, and further remove the bias explicitly from the base VQA model [9, 12, 35]. Apart from these techniques, Niu et al. [31] introduce a counterfactual inference framework to mitigate the biases. KV and Mittal [25] use a visually grounded question encoder such that the visual information is embedded in the question representation itself. Niu et al. [32] improve both ood generalizability and id performance through introspective knowledge distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.468, + 0.593 + ], + "angle": 0, + "content": "Augmentation based methods remove bias by augmenting the dataset to make it more balanced. Some works generate counterfactual data by masking or transforming the critical objects and words, and further generating appropriate ground truth answers [11, 15, 27]. Other works introduce negative samples by shuffling the inputs (images and questions) in the minibatch to reduce bias without requiring any annotation [40, 42, 46]. Wen et al. [42] use two kinds of negative samples for balancing the dataset, and construct both question-only and vision-only models to remove the biases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.468, + 0.79 + ], + "angle": 0, + "content": "Margin-based methods. Max-margin classifiers are used in popular machine learning algorithms like SVMs [38]. Margin losses are commonly used in many problems such as deep face recognition [7, 14, 29, 41], long tailed or class imbalanced learning [10, 22, 30] and few-shot learning [26]. Guo et al. [17] apply an adaptive cosine margin loss to discriminate the frequent and rare answers for a given question type and implement this by transforming the multimodal feature space to a fixed radius hypersphere. The adaptive margins are estimated from the training data based on the frequency of occurrence of an answer in questions of a given type, ensuring that rare answers are given more margin penalty, whereas frequent classes are given less penalty." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.806, + 0.264, + 0.824 + ], + "angle": 0, + "content": "3. Proposed approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.831, + 0.218, + 0.846 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We consider the problem of classification based Visual Question Answering (VQA). It is the task of answering questions based on an image. Given a dataset \\(\\mathcal{D}\\) having" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "\\(n\\) samples, with image \\(v \\in \\mathcal{V}\\), question \\(q \\in \\mathcal{Q}\\) and answer (class label) \\(a \\in \\mathcal{A}\\), the goal is to train a model to optimize a mapping function \\(f: \\mathcal{V} \\times \\mathcal{Q} \\to \\mathbb{R}^{|\\mathcal{A}|}\\) to generate predictions for the given question and image. The VQA model consists of four parts: (1) image feature extractor \\(e_v\\), (2) question feature extractor \\(e_q\\), (3) the VQA model \\(m_f\\) which fuses the image and question features to generate the joint multimodal features \\(\\mathbf{x}\\), (4) classifier \\(c\\) having weights \\(\\mathbf{W}\\), that generates the logits \\(f\\). Most of the classical VQA models [4, 6, 8, 24, 44] follow this paradigm and formulate the problem as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.269, + 0.892, + 0.287 + ], + "angle": 0, + "content": "\\[\nf (v, q) = c \\left(m _ {f} \\left(e _ {v} (v), e _ {q} (q)\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.339 + ], + "angle": 0, + "content": "Standard Cross-Entropy loss. VQA models can be trained by optimizing the Cross-Entropy \\((CE)\\) loss\\(^2\\) shown below:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.339, + 0.892, + 0.381 + ], + "angle": 0, + "content": "\\[\nL _ {s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp \\left(f _ {i}\\right)}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp \\left(f _ {j}\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.601 + ], + "angle": 0, + "content": "To solve the problem of language bias in VQA, the model should learn discriminative features for different answers for a given question type so that it can distinguish frequently occurring answers from rarely occurring answers, as well as those with varying complexity. However, standard \\(CE\\) loss only favours the samples with frequently occurring answers. Normalized \\(CE\\) loss. Before defining the margin loss, we define a reformulation of the \\(CE\\) loss as a cosine loss [14, 41], by L2-normalizing the classifier weight vectors \\(\\mathbf{W_i} \\in c\\) for each \\(a_i \\in \\mathcal{A}\\), and feature \\(\\mathbf{x} = m_f(e_v(v_i), e_q(q_i))\\). Therefore, we define \\(\\hat{\\mathbf{W}}_{\\mathrm{i}} = \\frac{\\mathbf{W}_{\\mathrm{i}}}{\\|\\mathbf{W}_{\\mathrm{i}}\\|}\\) and \\(\\hat{\\mathbf{x}} = s\\frac{\\mathbf{x}}{\\|\\mathbf{x}\\|}\\), where \\(s\\) is a scaling parameter. Let \\(\\theta_{i}\\) be the angle between \\(\\mathbf{x}\\) and \\(\\mathbf{W}_{\\mathrm{i}}\\). Therefore the logit for each \\(a_i\\) is transformed as (keeping the bias term as 0 for simplicity):" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.611, + 0.892, + 0.632 + ], + "angle": 0, + "content": "\\[\nf _ {i} = \\hat {\\mathbf {W}} _ {\\mathbf {i}} ^ {\\top} \\hat {\\mathbf {x}} = \\| \\hat {\\mathbf {W}} _ {\\mathbf {i}} \\| \\| \\hat {\\mathbf {x}} \\| \\cos \\theta_ {i} = s \\cos \\theta_ {i} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.89, + 0.672 + ], + "angle": 0, + "content": "The joint features \\(\\hat{\\mathbf{x}}\\) are thus distributed on a hypersphere with a radius \\(s\\). This makes the normalized \\(CE\\) loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.682, + 0.892, + 0.725 + ], + "angle": 0, + "content": "\\[\nL _ {n s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos \\theta_ {i})}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos \\theta_ {j})} \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.734, + 0.616, + 0.751 + ], + "angle": 0, + "content": "3.2. RMLVQA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.758, + 0.89, + 0.803 + ], + "angle": 0, + "content": "In this subsection, we define our method, which is a Robust Margin Loss based approach for solving the problem of language biases in VQA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.803, + 0.892, + 0.879 + ], + "angle": 0, + "content": "Adaptive Angular Margin Loss. We introduce an adaptive angular margin loss that ensures decision margin maximization through angular margins in an adaptive way. The normalized \\(CE\\) loss transforms the feature space to an angular space of radius \\(s\\). The motivation behind an adaptive" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.885, + 0.901 + ], + "angle": 0, + "content": "2In this paper, all losses will be expressed as individual sample losses" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11673" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.179, + 0.09, + 0.795, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.277, + 0.895, + 0.32 + ], + "angle": 0, + "content": "Figure 1. Overview of our model. The orange dashed region shows the proposed bias-injecting module, trained using the \\(CE\\) loss. The blue dashed region shows how the instance-based margins are generated and then combined with the randomized frequency-based margins to compute the final margins. The final prediction is obtained by combining the two logit heads." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.473, + 0.51 + ], + "angle": 0, + "content": "margin instead of a constant margin is based on the root of the language bias problem in VQA. These biases occur when similar questions in the dataset are paired with the same answers most of the time, fooling the model to memorize these questions and the answers by ignoring the image completely. Thus, while some samples are overlooked because of the rarity of their corresponding answers, others are overly paid attention to. Adaptive margins allow the model to set different penalties for the varying samples, thus leading to highly discriminative features for the different training instances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.471, + 0.587 + ], + "angle": 0, + "content": "One aspect of the adaptive margins is to ensure that the instances with frequent answers are allowed a smaller margin than those with the rare ones. We call these margins \\( m_{freq} \\). Similar to [17], these margins are calculated based on the question type as shown below:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.593, + 0.469, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\bar {m} _ {f r e q} ^ {k} [ i ] = \\frac {n _ {i} ^ {k} + \\epsilon}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} n _ {j} ^ {k} + \\epsilon} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.633, + 0.469, + 0.654 + ], + "angle": 0, + "content": "\\[\nm _ {f r e q} ^ {k} [ i ] = 1 - \\bar {m} _ {f r e q} ^ {k} [ i ] \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.47, + 0.749 + ], + "angle": 0, + "content": "where \\(\\bar{m}_{freq}^{k}[i]\\) measures the probability of occurrence of answer \\(a_{i}\\) in the training data for a given question type \\(qt_{k}\\). \\(n_{i}^{k}\\) is the frequency of answer \\(a_{i}\\) in the training set calculated for the given \\(qt_{k}\\), and \\(\\epsilon\\) is a hyperparameter for avoiding computational overflow. \\(m_{freq}^{k}[i]\\) is the adaptive margin for answer \\(a_{i} \\in \\mathcal{A}\\) corresponding to \\(qt_{k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.856 + ], + "angle": 0, + "content": "The adaptive angular margin loss adds a margin penalty to the angle between the features \\(\\mathbf{x}\\) and the classifier weights \\(\\mathbf{W_i}\\) for the \\(i^{th}\\) class as shown below. Since the margin is placed on the angle, it maps exactly to the \"geodesic\" distance on the hypersphere [14]. While Deng et al. [14] set a constant value for the margin, i.e. 0.5, our margins are adaptive in nature." + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.861, + 0.473, + 0.906 + ], + "angle": 0, + "content": "\\[\nL _ {A n g u l a r} ^ {k} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos (\\theta_ {i} + m _ {f r e q} ^ {k} [ i ]))}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos (\\theta_ {j} + m _ {f r e q} ^ {k} [ j ]))}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.375 + ], + "angle": 0, + "content": "For notational simplicity, in the coming sections, we omit \\( k \\) from the margin and loss computations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.893, + 0.604 + ], + "angle": 0, + "content": "Randomization of the estimated margins. Boutros et al. [7] suggest that in typical margin losses, setting constant margins can limit the generalizability and discriminative power of a model. We note that \\( m_{freq}[i] \\) is constant for each \\( a_i \\in \\mathcal{A} \\) for a given question type \\( qt_k \\) over all samples in the training set. When \\( qt_k \\) is \"how many\", the margin for the answer \"2\" is same for all the training instances belonging to this question type. We believe that setting the same high margin value for a specific rare answer in a given question type and similarly lower value for a frequently appearing answer can lead to overcorrection of the language bias, by forcing the model to focus on the rare answers more than the frequent ones. Therefore, under a given question type \\( qt_k \\), for every answer \\( a_i \\), we use a randomized version of \\( \\bar{m}_{freq}[i] \\), called \\( \\bar{m}_{ran}[i] \\) in the following manner:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.615, + 0.892, + 0.634 + ], + "angle": 0, + "content": "\\[\n\\bar {m} _ {r a n} [ i ] = \\mathcal {N} (\\bar {m} _ {f r e q} [ i ], \\sigma) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.735 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}\\) is the Gaussian distribution, and \\(\\sigma\\) is the standard deviation, which is a hyperparameter. This impedes the model from overcorrecting with respect to the rare answers, thus increasing its generalizability. Finally, we obtain the randomized margin \\(m_{ran}[i] = 1 - \\bar{m}_{ran}[i]\\) for each \\(a_i\\in \\mathcal{A}\\) in each \\(qt_{k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Instance-based margins. The frequency-based margins estimated from the training data are constant for a given question type. So, for two different questions starting with \"how many\", the margins are same for each answer, irrespective of the model's difficulty in answering these instances. Ideally if one of the samples is hard to answer, more margin should be given to its ground truth class compared to the easier one. Randomizing \\( m_{\\text{freq}} \\) as described above does not take the complexity of each sample into account. To this end, our model learns instance-level margins during training. We augment an auxiliary classifica" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11674" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "tion head to the feature \\(\\mathbf{x}\\) (the orange dashed box in Fig. 1) which is architecturally same as the original model classifier \\(c\\). We call this the bias-injecting component. Following Eq. 1, the formulation of this component becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.162, + 0.469, + 0.178 + ], + "angle": 0, + "content": "\\[\nf _ {b} (v, q) = c _ {b} (\\mathbf {x}) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.187, + 0.473, + 0.475 + ], + "angle": 0, + "content": "where, \\( f_{b} \\) refers to the logits generated by this component and \\( c_{b} \\) refers to the classification head. It is to be noted that while \\( c_{b} \\neq c \\), both are trained to predict the answers given the questions and the images. Finally, we denote \\( \\bar{m}_{ins} = \\text{softmax}(f_{b} / \\tau) \\) as the confidence, (i.e. prediction probability) of the bias-injecting component in answering a question. Here \\( \\tau \\) stands for temperature which is a hyperparameter to the network. We define \\( m_{ins} = 1 - \\bar{m}_{ins} \\) as the instance-level learnable margin, obtained from the model during training. These learned margins are similar with the frequency-based margins when samples are far away from the decision boundary. However, for training instances that are close, \\( m_{ins} \\) increases the margins if the model confidence is low for the ground truth class, and decreases the same in case the model has high confidence in predicting the ground truth answer. We combine this instance-level confidence for the ground truth class with the previously calculated \\( m_{ran} \\) for each sample \\( (v, q) \\) to obtain the final margins \\( m_{comb} \\), as shown in the blue dashed box in Fig. 1." + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.483, + 0.469, + 0.5 + ], + "angle": 0, + "content": "\\[\nm _ {\\text {c o m b}} [ g t ] = \\beta m _ {\\text {r a n}} [ g t ] + (1 - \\beta) m _ {\\text {i n s}} [ g t ] \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.614 + ], + "angle": 0, + "content": "\\(gt\\) refers to the index of the ground truth class of the sample, and \\(\\beta\\) is a hyperparameter used for combining the two margins. For all indices \\(l \\neq gt\\), \\(m_{comb}[l] = m_{ran}[l]\\). In the first few training epochs, we do not compute \\(m_{ins}\\) as the model is in the initial stage of its learning, i.e. we set \\(\\beta = 1\\). As training progresses, \\(\\beta\\) is decreased in a step-wise manner to increase the contributions from the learnt margins." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.473, + 0.885 + ], + "angle": 0, + "content": "The bias-injecting component. The bias-injecting component is a classifier appended to the features \\( \\mathbf{x} \\) trained using the standard \\( CE \\) loss. As the \\( CE \\) loss is known to favour the frequently appearing answers in the training data, it automatically learns the bias in the dataset, and by backpropagating this bias into the network, it clusters samples in the feature space based on the source of the bias. This aids the margin loss as it can now separate the (frequent, rare), and the (easy, difficult) samples inside the individual clusters. Moreover, the advantage of using it to generate the learnable margins is that the bias captured is now reflected directly in \\( \\bar{m}_{ins} \\), which ensures that it is close to \\( \\bar{m}_{freq} \\), but still provides information on the answering difficulty of a samples lying close to the decision boundary. Another advantage of this component is that by learning the data bias, this module is capable of generalizing to any in-distribution data, whereas the predictions from the primary classifier \\( c \\) favour the ood data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Inference. While margin losses are effective on an ood test" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "data, they result in degraded performance on \\( id \\) test set. To mitigate this problem, during inference time, we take advantage of both the bias-injecting component \\( f_{b} \\) and the primary logit head \\( f \\), as the former is useful in making predictions for an \\( id \\) test data, while the latter is useful in an ood setting. This makes our model robust to different data distributions. We denote by \\( p_{comb} \\) the combined predicted answer probabilities. This is obtained by combining the predictions from \\( c \\) and \\( c_{b} \\) as defined below:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.239, + 0.892, + 0.256 + ], + "angle": 0, + "content": "\\[\np _ {\\text {c o m b}} = \\alpha . \\hat {p} + (1 - \\alpha). \\hat {p} _ {b} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.892, + 0.37 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyperparameter controlling the weight of each logit head during inference, \\(\\hat{p} = \\mathrm{softmax}(f)\\) are the predictions from classifier \\(c\\), \\(\\hat{p_b} = \\mathrm{softmax}(f_b / \\tau)\\) are the predictions from the bias-injecting component \\(c_b\\). The answer predicted is therefore \\(\\hat{a} = \\arg\\max(p_{comb})\\). The temperature \\(\\tau\\) is same as that defined previously for the instance-based margins." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.893, + 0.569 + ], + "angle": 0, + "content": "Supervised Contrastive (SupCon) Loss. We further separate samples in the feature space based on the SupCon loss. In addition to creating discriminative features for (frequent, rare) and (easy, difficult) samples, the SupCon loss leads to a degree of discrimination among samples with different ground truth answers in the feature space. We consider a mini-batch of size \\(\\mathcal{B}\\) of multimodal features denoted as \\(\\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_{\\mathcal{B}}\\}\\) and corresponding answers as \\(\\{a_1,a_2,\\ldots ,a_{\\mathcal{B}}\\}\\). If we consider the current sample with index \\(j\\), the set of positive examples from the mini-batch is denoted by \\(P_{j}:\\{i\\in \\mathcal{B}\\text{s.t.} a_{i} = a_{j}\\}\\). Similarly, the set of negative examples is denoted by \\(N_{j}:\\{i\\in\\) \\(\\mathcal{B}\\text{s.t.} a_i\\neq a_j\\}\\). The SupCon loss [23] is defined as," + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.578, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s u p - c o n}} = \\sum_ {j \\in \\mathcal {B}} \\frac {- 1}{| P _ {j} |} \\sum_ {p \\in P _ {j}} \\log \\frac {\\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {p}} / \\tau\\right)}{\\sum_ {n \\in N _ {j}} \\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {n}} / \\tau\\right)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.667 + ], + "angle": 0, + "content": "We set the temperature \\(\\tau = 1\\) for all experiments as we do not find any significant improvements by changing its value." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.668, + 0.86, + 0.682 + ], + "angle": 0, + "content": "Total Loss: The final loss function for each sample is:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.694, + 0.891, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = L _ {\\text {A n g u l a r}} \\left(m _ {\\text {c o m b}}\\right) + L _ {s} + L _ {\\sup - c o n} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.781 + ], + "angle": 0, + "content": "where \\(L_{Angular}\\) is the angular margin loss, \\(L_{s}\\) is the CE loss training the bias injecting component, \\(L_{sup-con}\\) is the SupCon loss. Our final model can be seen in Fig. 1. We name our overall method RMLVQA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.794, + 0.633, + 0.81 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset details. We evaluate our model on the VQACP v2 dataset (Visual Question Answering Under Changing Priors) [3], which is an ood benchmark, based on the standard evaluation metric shown by Antol et al. [5]. It was created by reorganizing the training and validation sets of the VQA v2 [16] dataset, ensuring that the distribution" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11675" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "of answers for each question type in the training set and the test set are different. The training set of VQA-CP v2 contains approximately 121k images and 438k questions, the test set contains approximately 98k images and 220k questions. Following previous works, we also evaluate our model on the VQA v2 validation set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.191, + 0.172, + 0.205 + ], + "angle": 0, + "content": "4.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.207, + 0.473, + 0.585 + ], + "angle": 0, + "content": "Quantitative analysis. In Table 1, we show a comparative analysis of the performance of RMLVQA on both VQACP v2 test and VQA v2 validation sets. We report the overall accuracies along with those on \"yes/no\", \"number\" and \"other\" type questions. We observe that our method gains around \\(6.39\\%\\) in the overall accuracy for VQA-CP in comparison with AdaVQA [17], which is the cosine margin loss trained model. We observe that AdaVQA, while performing well on VQA-CP v2, has considerably low scores for the in-domain VQA v2. With RMLVQA, the validation accuracy of VQA v2 is \\(59.99\\%\\), which is \\(13.01\\%\\) higher than AdaVQA. This shows that our method is the first one trained by adaptive margins that is robust to both id and ood data. With a score of \\(60.41\\%\\) for VQA-CP v2, the model improves upon the current state-of-the-art augmentation-free models. In addition to reporting the performance of the various models in literature on the two datasets, we show the relative difference in accuracies between VQA-CP v2 test data and VQA v2 validation data. RMLVQA outperforms all other non-augmentation based models in terms of robustness, with the lowest difference in the two accuracies (see Table 1), indicating that our method is the most robust compared to all other methods that do not use any augmentation, and perform equally well on both VQA-CP v2 and VQA v2. For all experiments, Updn [4] is our base network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Qualitative analysis. We further demonstrate the effectiveness of our method in Fig. 2 which provides qualitative results on the VQA-CP v2 test set for RMLVQA and the base network UpDn. In the first row, we show examples for question type \"what color\". The base network UpDn [4] focuses on the incorrect region in the image, given by attention map scores, and outputs \"blue\", the most frequent answer in the training set for the given question type. The best scoring region from the attention maps of our model is localized at the correct region in the image, and it correctly outputs \"red\", which is not a frequent answer in \"what color\". In the second example, belonging to question type \"what is the person\", we see that while the baseline outputs \"phone\", which is a frequent class under that question type, RMLVQA predicts the correct answer \"hat\", which is a rare class, thus showing the effectiveness of our method. While the baseline outputs incorrect answers, it still focuses on the correct region in the image. This crucial observation indicates that the bias in the model weights do not allow this visual information to propagate forward. Thus it still picks from the frequent answers for the given question type." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Choice of hyperparameter \\(\\alpha\\) for inference time combination of prediction probabilities. Choice of \\(\\alpha\\) is crucial as it decides how much weight to put on the prediction probabilities of the bias-injecting component \\(c_{b}\\) and the primary classifier \\(c\\). As VQA-CP v2 does not have a validation set, we choose \\(\\alpha = 0.5\\) for fair evaluation. However, we report the accuracies of VQA-CP v2 test and VQA v2 validation sets for different values of \\(\\alpha\\) in Table 2. We observe that \\(\\alpha = 0.5\\) leads to the most robust performance of our method on both id and ood data, where the relative gap of accuracies is just \\(0.42\\%\\). While we already choose the optimal value of \\(\\alpha\\) for reporting model performance, our experiments demonstrate that one can choose an appropriate value to control the tradeoff between id and ood performances." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.311, + 0.663, + 0.325 + ], + "angle": 0, + "content": "4.2. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.372 + ], + "angle": 0, + "content": "In this subsection, we discuss the role of each component of RMLVQA. We evaluate them on the VQA-CP v2 test and VQA v2 validation data and show the results in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Effectiveness of angular margins. We call the base adaptive angular margin loss trained model RMLVQA-Base, which only considers the frequency based margins. Compared to AdaVQA, it leads to a rise of \\(3.22\\%\\) in the VQACP test accuracy and an increase of \\(2.74\\%\\) in the accuracy of the VQA-v2 validation set. This shows the effectiveness of the angular margin loss over the cosine margins both in id and ood data, validating the choice of the angular margin loss for addressing the language bias problem of VQA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Effect of randomization of the margins. Randomizing the margins of each answer leads to an improvement in the accuracy values of VQA-CP v2 test, as shown in Table 3. Further, we also notice that it improves the in-domain accuracy of VQA v2 by a large margin (7.12%), thus showing its effectiveness in generalizability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.895, + 0.855 + ], + "angle": 0, + "content": "Role of the learnable margins. As explained earlier, \\( m_{ins} \\) represents the confidence of the bias-injecting component in answering a question. We show the positive effect of adding these margins to \\( m_{ran} \\) in Table 3 for VQA-CP v2, with a slight loss in VQA v2. In Fig. 4 we show the Spearman's rank correlation coefficient \\( \\rho \\) between \\( m_{freq} \\) and \\( m_{ins} \\) for the question type 'how many' for our method (for the angular and cosine margin losses defined in Sec 3 and AdaVQA [17] respectively), averaged over the relevant samples in each training epoch. We note the following: a) \\( \\rho \\) is high throughout, indicating that the order of margin values in \\( m_{ins} \\) for a certain sample remains similar to that of the margin values in \\( m_{freq} \\) for the question type to which the sample belongs. b) \\( \\rho \\) decreases over epochs, indicating the excess information being carried by \\( m_{ins} \\), aiding in the discrimination of samples whose answer frequencies are similar, but have different complexities." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Role of the bias-injecting component. In Table 3, we show that the bias-injecting component increases the model's overall accuracy by \\(1.47\\%\\) for VQA-CP v2 \\((3.65\\%)\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11676" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.187 + ], + "angle": 0, + "content": "Table 1. Accuracy comparisons with other methods on the VQA-CP v2 and VQA v2 datasets. The methods have been grouped into different categories (separated by lines in the table): base approaches, methods using human annotations, those that modify the language encoder, models weakening the language bias in different ways, our approach RMLVQA trained with UpDn as backbone, and finally the augmentation based methods. The best performance in each column is highlighted in bold. We highlight the overall accuracy of RMLVQA on VQA-CP with an underline as it achieves state-of-the-art on augmentation-free methods. * denotes numbers shown in [17]. We report the average accuracy of our model over 5 random seeds (along the with standard deviations in the superscript). Columns ending with “-CP” denote accuracies for VQA-CP v2, others denote accuracies for VQA v2. † indicates our implementation." + }, + { + "type": "table", + "bbox": [ + 0.131, + 0.198, + 0.842, + 0.542 + ], + "angle": 0, + "content": "
ModelY/N-CPNum-CPOthers-CPOverall-CPY/NNumOthersOverallDiff
SAN [44]38.3511.1421.7424.9670.0639.2847.8452.4127.45
GVQA [3]57.9913.6822.1431.3072.0331.1734.6548.2416.94
UpDn [4]42.2711.9346.0539.7481.1842.1455.6663.4823.74
S-MRL [9]42.8512.8143.238.4641.9612.5441.3537.131.33
AttAlign [36]43.0211.8945.0039.3780.9942.5555.2263.2423.87
HINT [36]67.2710.6145.8846.7381.1842.9955.5663.3816.65
SCR [43]70.4110.4247.2948.4778.841.654.562.213.73
VGQE [25]66.3527.0846.7750.11---64.0413.93
DLR [20]70.9918.7245.5748.8776.8239.3348.5457.969.09
AdvReg [35]65.4915.4835.4841.1779.8442.3555.1662.7521.58
RUBi [9]68.6520.2843.1847.11-----
LMH* [12]70.2944.1044.8652.1565.0637.6354.6956.354.2
CF-VQA [31]90.6121.5045.6155.0581.1343.8650.1160.945.89
IntroD [32]90.7917.9246.7355.1782.4846.6054.0563.408.23
GGE-DQ [18]87.0427.7549.5957.3273.2739.9954.3959.111.79
AdaVQA † [17]70.8349.0046.2954.0247.7834.1351.1446.987.04
RMLVQA89.98±0.4645.96±0.5748.74±0.1360.41±0.3276.68±0.3737.54±0.4953.26±0.1259.990.060.42
CVL [1]45.7212.4548.3442.12-----
Unshuffling [39]47.7214.4347.2442.3978.3242.1652.8161.0818.69
RandImg [40]83.8941.6044.2055.3776.5333.8748.5757.241.87
SSL [46]86.5329.8750.0357.59---63.736.14
CSS [11]84.3749.4248.2158.9573.2539.7755.1159.910.96
CSS + CL [27]86.9949.8947.1659.1867.2738.4054.7157.291.89
Mutant [15]88.9049.6850.7861.7282.0742.5253.2862.560.84
D-VQA [42]88.9352.3250.3961.9182.1844.0157.5464.963.05
" + }, + { + "type": "title", + "bbox": [ + 0.328, + 0.557, + 0.648, + 0.569 + ], + "angle": 0, + "content": "What color shirt is the man with the ball wearing?" + }, + { + "type": "image", + "bbox": [ + 0.171, + 0.57, + 0.367, + 0.672 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.671, + 0.29, + 0.681 + ], + "angle": 0, + "content": "GT: Red" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.57, + 0.578, + 0.671 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.428, + 0.671, + 0.522, + 0.681 + ], + "angle": 0, + "content": "Baseline: Blue" + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.57, + 0.789, + 0.671 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.646, + 0.672, + 0.74, + 0.683 + ], + "angle": 0, + "content": "RMLVQA: Red" + }, + { + "type": "title", + "bbox": [ + 0.396, + 0.684, + 0.579, + 0.697 + ], + "angle": 0, + "content": "What is the person holding?" + }, + { + "type": "image", + "bbox": [ + 0.168, + 0.7, + 0.368, + 0.804 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.244, + 0.804, + 0.294, + 0.814 + ], + "angle": 0, + "content": "GT: Hat" + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.817, + 0.277, + 0.83 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.7, + 0.58, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.435, + 0.804, + 0.542, + 0.814 + ], + "angle": 0, + "content": "Baseline: Phone" + }, + { + "type": "image_caption", + "bbox": [ + 0.474, + 0.817, + 0.493, + 0.83 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.594, + 0.7, + 0.793, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.804, + 0.739, + 0.814 + ], + "angle": 0, + "content": "RMLVQA: Hat" + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.817, + 0.697, + 0.83 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.841, + 0.892, + 0.883 + ], + "angle": 0, + "content": "Figure 2. Qualitative analysis of RMLVQA. We show two images from two question types in the rows. Column (a) represents the ground truth answers, column (b) represents the answers predicted by the baseline UpDn model. Column (c) represents the answer predicted by our method. The bounding boxes show the highest scored region in the attention map of the individual models." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11677" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.106, + 0.52, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.25, + 0.529, + 0.294 + ], + "angle": 0, + "content": "Figure 3. TSNE visualization of the feature space with respect to different question types for the model components, evaluated incrementally: a) RMLVQA-Base, b) Gaussian randomization, c) Bias injection" + }, + { + "type": "table_caption", + "bbox": [ + 0.106, + 0.324, + 0.441, + 0.339 + ], + "angle": 0, + "content": "Table 2. Role of \\( \\alpha \\) in the inference stage of RMLVQA." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.35, + 0.429, + 0.478 + ], + "angle": 0, + "content": "
αVQA-CP v2 TestVQA-v2 ValGap
1.060.5458.162.38
0.860.5058.831.67
0.660.3359.570.76
0.560.4159.990.42
0.459.8760.460.59
0.257.4661.263.8
0.039.4861.5422.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.495, + 0.47, + 0.523 + ], + "angle": 0, + "content": "Table 3. Ablations. In this table we show the ablations of \\( RM \\)-LVQA, evaluated on VQA-CP v2 test & VQA v2 val." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.534, + 0.466, + 0.63 + ], + "angle": 0, + "content": "
ModelY/NNumOthersOverallVQA v2 Val
RMLVQA-Base79.7849.6248.4957.2449.72
+Randomization83.7249.4748.3157.9756.84
+Bias Injection88.2744.1348.5559.4460.49
+Learnable Margin88.0646.6348.7459.8759.60
+SupCon Loss89.9845.9648.7460.4159.99
-Backprop89.3640.5647.8058.8059.67
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.903 + ], + "angle": 0, + "content": "for VQA v2). The effectiveness of this component can be understood from Fig. 3, where we show the TSNE visualizations of how answers from different question types are placed in the feature space for the components of RMLVQA. Fig. 3(a) shows that while for some question types like 'how many', 'are', answers are well separated, some others like 'do', 'are they', 'is there' are close, out of which some are entangled. Although the randomization increases flexibility of the adaptive margins, it does not disentangle these question types, as seen in Fig. 3b. Finally, in Fig. 3(c), we see that the bias-injecting component aids in separating the answers according to their question types. This is because the bias sources of VQA-CP is its question types, and hence this component clusters samples in the training set based on the same. This is crucial, as with more entanglement, the model tends to answer questions of one question type with" + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.097, + 0.852, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.557, + 0.265, + 0.888, + 0.307 + ], + "angle": 0, + "content": "Figure 4. Spearman's rank correlation coefficient between \\(\\mathbf{m}_{\\mathrm{freq}}\\) and \\(\\mathbf{m}_{\\mathrm{ins}}\\) over epochs for question type \"how many\" on VQA-CP v2 test set" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.492 + ], + "angle": 0, + "content": "the answers of another type. In the last row of Table 3, we also observe the effect of removing the backpropagation of the \\( CE \\) loss (used to train the bias-injecting component) into the main network for VQA-CP v2. The classifier weights in the bias-injecting component learn the language bias in the dataset and backpropagate the same into the network, thus helping the model separate the answers across different question types in the feature space. We utilize this knowledge in the inference stage, where we combine the two logit heads, thus helping the model to generalize to both \\( id \\) and \\( ood \\) test data, as is evident from Tables 1 and 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Role of the SupCon Loss. The addition of the SupCon loss is shown to improve the performance of our model empirically for both VQA-CP and VQA v2 as shown in Table 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.544, + 0.619, + 0.559 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.82 + ], + "angle": 0, + "content": "Although margin-based losses are useful in mitigating language biases in VQA, they may not distinguish between answers of different task-complexity levels in the feature space. To distinguish between samples having similar answer frequency, but different complexity, we learn instance-based margins for each sample from the model during training. We introduce a bias-injecting component in our model and utilize its confidence in answer prediction as the instance-level margins. Being trained by the \\(CE\\) loss, this component further clusters the training samples based on the source of the data bias, guiding the margin loss to distinguish frequent and rare answers inside each cluster. We ensemble the outputs of the bias-injecting component with those of the main model during inference to achieve state-of-the-art results among existing augmentation-free methods on the ood VQA-CP v2 dataset, while being the most robust with respect to both id and ood test sets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.837, + 0.679, + 0.853 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by a research grant (CRG/2021/005925) from SERB, DST, Govt. of India. Abhipsa Basu is supported by the PMRF fellowship." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11678" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10044-10054, 2020. 1, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.185, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Aishwarya Agrawal, Dhruv Batra, and Devi Parikh. 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Overcoming language priors with self-supervised learning for visual question answering. arXiv preprint arXiv:2012.11528, 2020. 1, 3, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11680" + } + ] +] \ No newline at end of file diff --git a/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_origin.pdf b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..744b8695059878e4241347bfc7afdeccd5b9d3cd --- /dev/null +++ b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/211c42c4-defc-46bd-b55e-243b99c5b0bb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:023dc87dc8ef48216653e811e4e262ba83597d8a0bcfad59a3bf632934b6adb2 +size 1862582 diff --git a/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/full.md b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0b001f3d95514d3e4e659c1363523a07786ecc0c --- /dev/null +++ b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/full.md @@ -0,0 +1,312 @@ +# RMLVQA: A Margin Loss Approach For Visual Question Answering with Language Biases + +Abhipsa Basu + +abhipsabasu@iisc.ac.in + +Sravanti Addepalli + +sravantia@iisc.ac.in + +R. Venkatesh Babu + +venky@iisc.ac.in + +Vision and AI Lab, Indian Institute of Science, Bangalore + +# Abstract + +Visual Question Answering models have been shown to suffer from language biases, where the model learns a correlation between the question and the answer, ignoring the image. While early works attempted to use question-only models or data augmentations to reduce this bias, we propose an adaptive margin loss approach having two components. The first component considers the frequency of answers within a question type in the training data, which addresses the concern of the class-imbalance causing the language biases. However, it does not take into account the answering difficulty of the samples, which impacts their learning. We address this through the second component, where instance-specific margins are learnt, allowing the model to distinguish between samples of varying complexity. We introduce a bias-injecting component to our model, and compute the instance-specific margins from the confidence of this component. We combine these with the estimated margins to consider both answer-frequency and task-complexity in the training loss. We show that, while the margin loss is effective for out-of-distribution (ood) data, the bias-injecting component is essential for generalising to indistribution (id) data. Our proposed approach, Robust Margin Loss for Visual Question Answering (RMLVQA) improves upon the existing state-of-the-art results when compared to augmentation-free methods on benchmark VQA datasets suffering from language biases, while maintaining competitive performance on id data, making our method the most robust one among all comparable methods. + +# 1. Introduction + +Visual question answering (VQA) lies at the intersection of computer vision and natural language processing. It is + +the task of answering a question based on a given image. VQA networks need to combine knowledge from both visual scene and the question to predict the answer. These systems have numerous applications such as aiding the visually impaired in understanding their surroundings, image retrieval systems in e-commerce, and robotics. + +With the success of deep learning, research in VQA has made great strides in recent years [3,5,16]. However, studies have shown that deep networks may learn correlations between the question and answer alone, ignoring the image modality [3,21,36]. They fail to do multimodal reasoning, specifically, if there is a class imbalance in the answer distributions of the training and test sets. For example, if most of the questions starting with "What color..?" are paired with the answer "red" in the training data, the model memorizes this trend to answer "red" for all color based questions in the test set, irrespective of the image. + +One solution to this problem is to perform data augmentations in various ways [1,4,11,15,27,36,42,43,46]. These methods outperform most other debiasing techniques in the literature. However, augmentation strategies are dependent on the dataset in question and the type of biases observed, which makes the process manual and tedious. Another extensively explored solution is to learn the bias in the dataset separately using a question-only branch [9, 12, 18] and explicitly removing the learnt bias from the base model. + +Margin losses have been widely used for a number of tasks. Cao et al. [10] address the problem of long tailed recognition through an adaptive margin loss, ensuring higher cosine margin penalty for the tail classes and lower penalty for other classes. A similar adaptive cosine margin penalty has been applied to mitigate the language bias problem in VQA by a previous work [17]. Margin losses have been widely used in deep face recognition as well, where it is desired that the features of two images of the same person should be as similar as possible, whereas those of two different people should be far apart. Margin losses + +are used in this regard for facial feature discrimination to maximize the decision margin. Rather than the Euclidean space, both these margin losses project their feature spaces onto a fixed radius hypersphere. While the well known CosFace loss [41] uses cosine margin penalties like Cao et al. [10], ArcFace [14], uses angular margins to maximize the decision margins among different classes in this feature space. Angles correspond to geodesic distance on the projected hypersphere which stabilizes the training process and is shown to improve the discriminative power of face recognition models as compared to cosine margin based methods. + +We believe that the language bias problem of VQA can be addressed by learning discriminative features for the biased and unbiased samples in the dataset. To this end, we implement an adaptive angular margin loss, inspired by ArcFace, as margins allow models to distinguish between different kinds of samples. However, the key question here would be how to set the adaptive margins to cater to the specific problem of language biases. Traditional models over-trust the questions over the images due to a class imbalance in the training and test set answer distributions. Hence, one way to set the margins would be to ensure that the training samples with frequent answers are given a smaller penalty due to the abundance of those answers in the dataset, whereas those with rare answers are given a higher margin value. We refer to the resultant margin values as the frequency-based margins. However, one factor that is ignored in this aspect is the answering difficulty of each sample. We argue that more margin should be given to hard samples compared to the easier ones even if the corresponding answers are frequent. In this regard, we propose the learning of instance-specific margins during training, so as to allow the model to distinguish between hard and easy samples alongside frequent and rare samples. To the best of our knowledge, this is one of the first attempts in learning margins automatically and parallelly during training. We combine these learnable margins with the frequency based margins used in prior works [17], so as to allow both frequency and complexity of data samples to control the training dynamics. To compute these learnable margins, we introduce a bias injecting module to our model that is trained using Cross-Entropy $(CE)$ loss. We show that the $CE$ loss additionally clusters the training samples based on the dataset bias itself, thereby aiding the margin loss further. We further introduce a supervised contrastive loss [23] to pull the features of samples having the same answer together, while pushing others apart. + +Adaptive margin losses, with margins calculated by using frequency of answers in the dataset, perform well in the ood setting. However, we show that they cause a drop in the in-domain performance, which raises questions on their robustness. As pointed by [40], it is crucial for VQA models to perform well on both in-domain and ood data since + +the test set distribution is unknown apriori. We mitigate this issue by ensembling the outputs of the bias injecting component and the proposed learnable margin-loss trained classification head during inference. This makes the model robust to the difference in answer distributions of the training and test sets. Our overall method is called RMLVQA - Robust Margin Loss for Visual Question Answering with language biases. The key contributions of this work can be summarized as follows: + +- We propose to mitigate the well known problem of language bias in VQA models by introducing an instance-specific adaptive margin loss, to allow the use of different margins for the learning of samples with varying complexities, in addition to the use of frequency-based margins. To achieve this, we introduce a bias-injecting component and allow the margins to be computed based on prediction probabilities of this branch. We show that this clusters samples in the feature space based on the bias present in the dataset. +- We propose to overcome the id-ood trade-off in margin-based losses, by ensembling the outputs of the bias-injecting component and the main model. +- We further introduce a supervised contrastive loss that pulls features of training samples having the same ground truth answers together, while pushing apart others. This aids the margin loss further. +- Through extensive experiments and ablations, we show how the proposed approach achieves state-of-the-art results when compared to augmentation-free methods on the ood VQA-CP v2 dataset, while maintaining competitive performance on the id VQA v2 dataset. This makes our model the most robust one among all non-augmentation based methods. + +The code, hyperparameter analyses, and results on multiple datasets are shared as supplementary material. + +# 2. Related Work + +VQA and the language bias problem. VQA [5, 16] is the task of answering natural language questions given an image. VQA v1 & v2 [5, 16] are widely used datasets that are used to benchmark different algorithms. However, prior works have shown that these datasets have biases which can be amplified in the trained models [2, 3, 19, 36, 37]. Specifically, in case of language bias, the model learns a correlation between the question and the answer directly. For example, if the model always predicts "tennis" for the sport-related questions, it can achieve around $40\%$ accuracy on the VQA v1 dataset, as the images of the VQA datasets are from MS-COCO [28], which has many "tennis" related images. To effectively quantify the extent of bias in the trained models, a new dataset VQA-CP v2 [3] was created from the + +VQA v2 dataset. In this work, we aim to solve the language bias problem of VQA, where we evaluate our models on the ood benchmark dataset VQA-CP v2 and the id VQA v2. + +Bias mitigation techniques. The language bias problem reduces the generalizability of the VQA models, resulting in a drop in performance when the training set answer distribution is different from that of the test set. There are three popular categories of solutions in the literature tackling this problem, which we discuss below. + +Visual Grounding based methods [34, 45] used human annotations as supervision to attention maps [13, 33], whereas more recent works use Grad-CAM for the same [36, 43]. + +Ensemble based methods use a separate question-only model to capture the bias, and further remove the bias explicitly from the base VQA model [9, 12, 35]. Apart from these techniques, Niu et al. [31] introduce a counterfactual inference framework to mitigate the biases. KV and Mittal [25] use a visually grounded question encoder such that the visual information is embedded in the question representation itself. Niu et al. [32] improve both ood generalizability and id performance through introspective knowledge distillation. + +Augmentation based methods remove bias by augmenting the dataset to make it more balanced. Some works generate counterfactual data by masking or transforming the critical objects and words, and further generating appropriate ground truth answers [11, 15, 27]. Other works introduce negative samples by shuffling the inputs (images and questions) in the minibatch to reduce bias without requiring any annotation [40, 42, 46]. Wen et al. [42] use two kinds of negative samples for balancing the dataset, and construct both question-only and vision-only models to remove the biases. + +Margin-based methods. Max-margin classifiers are used in popular machine learning algorithms like SVMs [38]. Margin losses are commonly used in many problems such as deep face recognition [7, 14, 29, 41], long tailed or class imbalanced learning [10, 22, 30] and few-shot learning [26]. Guo et al. [17] apply an adaptive cosine margin loss to discriminate the frequent and rare answers for a given question type and implement this by transforming the multimodal feature space to a fixed radius hypersphere. The adaptive margins are estimated from the training data based on the frequency of occurrence of an answer in questions of a given type, ensuring that rare answers are given more margin penalty, whereas frequent classes are given less penalty. + +# 3. Proposed approach + +# 3.1. Preliminaries + +We consider the problem of classification based Visual Question Answering (VQA). It is the task of answering questions based on an image. Given a dataset $\mathcal{D}$ having + +$n$ samples, with image $v \in \mathcal{V}$ , question $q \in \mathcal{Q}$ and answer (class label) $a \in \mathcal{A}$ , the goal is to train a model to optimize a mapping function $f: \mathcal{V} \times \mathcal{Q} \to \mathbb{R}^{|\mathcal{A}|}$ to generate predictions for the given question and image. The VQA model consists of four parts: (1) image feature extractor $e_v$ , (2) question feature extractor $e_q$ , (3) the VQA model $m_f$ which fuses the image and question features to generate the joint multimodal features $\mathbf{x}$ , (4) classifier $c$ having weights $\mathbf{W}$ , that generates the logits $f$ . Most of the classical VQA models [4, 6, 8, 24, 44] follow this paradigm and formulate the problem as follows: + +$$ +f (v, q) = c \left(m _ {f} \left(e _ {v} (v), e _ {q} (q)\right)\right) \tag {1} +$$ + +Standard Cross-Entropy loss. VQA models can be trained by optimizing the Cross-Entropy $(CE)$ loss $^2$ shown below: + +$$ +L _ {s} = \sum_ {i = 1} ^ {| \mathcal {A} |} - a _ {i} \log \frac {\exp \left(f _ {i}\right)}{\sum_ {j = 1} ^ {| \mathcal {A} |} \exp \left(f _ {j}\right)} \tag {2} +$$ + +To solve the problem of language bias in VQA, the model should learn discriminative features for different answers for a given question type so that it can distinguish frequently occurring answers from rarely occurring answers, as well as those with varying complexity. However, standard $CE$ loss only favours the samples with frequently occurring answers. Normalized $CE$ loss. Before defining the margin loss, we define a reformulation of the $CE$ loss as a cosine loss [14, 41], by L2-normalizing the classifier weight vectors $\mathbf{W_i} \in c$ for each $a_i \in \mathcal{A}$ , and feature $\mathbf{x} = m_f(e_v(v_i), e_q(q_i))$ . Therefore, we define $\hat{\mathbf{W}}_{\mathrm{i}} = \frac{\mathbf{W}_{\mathrm{i}}}{\|\mathbf{W}_{\mathrm{i}}\|}$ and $\hat{\mathbf{x}} = s\frac{\mathbf{x}}{\|\mathbf{x}\|}$ , where $s$ is a scaling parameter. Let $\theta_{i}$ be the angle between $\mathbf{x}$ and $\mathbf{W}_{\mathrm{i}}$ . Therefore the logit for each $a_i$ is transformed as (keeping the bias term as 0 for simplicity): + +$$ +f _ {i} = \hat {\mathbf {W}} _ {\mathbf {i}} ^ {\top} \hat {\mathbf {x}} = \| \hat {\mathbf {W}} _ {\mathbf {i}} \| \| \hat {\mathbf {x}} \| \cos \theta_ {i} = s \cos \theta_ {i} \tag {3} +$$ + +The joint features $\hat{\mathbf{x}}$ are thus distributed on a hypersphere with a radius $s$ . This makes the normalized $CE$ loss as: + +$$ +L _ {n s} = \sum_ {i = 1} ^ {| \mathcal {A} |} - a _ {i} \log \frac {\exp (s \cos \theta_ {i})}{\sum_ {j = 1} ^ {| \mathcal {A} |} \exp (s \cos \theta_ {j})} \tag {4} +$$ + +# 3.2. RMLVQA + +In this subsection, we define our method, which is a Robust Margin Loss based approach for solving the problem of language biases in VQA. + +Adaptive Angular Margin Loss. We introduce an adaptive angular margin loss that ensures decision margin maximization through angular margins in an adaptive way. The normalized $CE$ loss transforms the feature space to an angular space of radius $s$ . The motivation behind an adaptive + +![](images/1eec2d02ecfe881596ea47683b90aed0eb4aaf89021eecd2f63cf952a8b5c45d.jpg) +Figure 1. Overview of our model. The orange dashed region shows the proposed bias-injecting module, trained using the $CE$ loss. The blue dashed region shows how the instance-based margins are generated and then combined with the randomized frequency-based margins to compute the final margins. The final prediction is obtained by combining the two logit heads. + +margin instead of a constant margin is based on the root of the language bias problem in VQA. These biases occur when similar questions in the dataset are paired with the same answers most of the time, fooling the model to memorize these questions and the answers by ignoring the image completely. Thus, while some samples are overlooked because of the rarity of their corresponding answers, others are overly paid attention to. Adaptive margins allow the model to set different penalties for the varying samples, thus leading to highly discriminative features for the different training instances. + +One aspect of the adaptive margins is to ensure that the instances with frequent answers are allowed a smaller margin than those with the rare ones. We call these margins $m_{freq}$ . Similar to [17], these margins are calculated based on the question type as shown below: + +$$ +\bar {m} _ {f r e q} ^ {k} [ i ] = \frac {n _ {i} ^ {k} + \epsilon}{\sum_ {j = 1} ^ {| \mathcal {A} |} n _ {j} ^ {k} + \epsilon} \tag {5} +$$ + +$$ +m _ {f r e q} ^ {k} [ i ] = 1 - \bar {m} _ {f r e q} ^ {k} [ i ] \tag {6} +$$ + +where $\bar{m}_{freq}^{k}[i]$ measures the probability of occurrence of answer $a_{i}$ in the training data for a given question type $qt_{k}$ . $n_{i}^{k}$ is the frequency of answer $a_{i}$ in the training set calculated for the given $qt_{k}$ , and $\epsilon$ is a hyperparameter for avoiding computational overflow. $m_{freq}^{k}[i]$ is the adaptive margin for answer $a_{i} \in \mathcal{A}$ corresponding to $qt_{k}$ . + +The adaptive angular margin loss adds a margin penalty to the angle between the features $\mathbf{x}$ and the classifier weights $\mathbf{W_i}$ for the $i^{th}$ class as shown below. Since the margin is placed on the angle, it maps exactly to the "geodesic" distance on the hypersphere [14]. While Deng et al. [14] set a constant value for the margin, i.e. 0.5, our margins are adaptive in nature. + +$$ +L _ {A n g u l a r} ^ {k} = \sum_ {i = 1} ^ {| \mathcal {A} |} - a _ {i} \log \frac {\exp (s \cos (\theta_ {i} + m _ {f r e q} ^ {k} [ i ]))}{\sum_ {j = 1} ^ {| \mathcal {A} |} \exp (s \cos (\theta_ {j} + m _ {f r e q} ^ {k} [ j ]))} +$$ + +For notational simplicity, in the coming sections, we omit $k$ from the margin and loss computations. + +Randomization of the estimated margins. Boutros et al. [7] suggest that in typical margin losses, setting constant margins can limit the generalizability and discriminative power of a model. We note that $m_{freq}[i]$ is constant for each $a_i \in \mathcal{A}$ for a given question type $qt_k$ over all samples in the training set. When $qt_k$ is "how many", the margin for the answer "2" is same for all the training instances belonging to this question type. We believe that setting the same high margin value for a specific rare answer in a given question type and similarly lower value for a frequently appearing answer can lead to overcorrection of the language bias, by forcing the model to focus on the rare answers more than the frequent ones. Therefore, under a given question type $qt_k$ , for every answer $a_i$ , we use a randomized version of $\bar{m}_{freq}[i]$ , called $\bar{m}_{ran}[i]$ in the following manner: + +$$ +\bar {m} _ {r a n} [ i ] = \mathcal {N} (\bar {m} _ {f r e q} [ i ], \sigma) \tag {7} +$$ + +where $\mathcal{N}$ is the Gaussian distribution, and $\sigma$ is the standard deviation, which is a hyperparameter. This impedes the model from overcorrecting with respect to the rare answers, thus increasing its generalizability. Finally, we obtain the randomized margin $m_{ran}[i] = 1 - \bar{m}_{ran}[i]$ for each $a_i\in \mathcal{A}$ in each $qt_{k}$ . + +Instance-based margins. The frequency-based margins estimated from the training data are constant for a given question type. So, for two different questions starting with "how many", the margins are same for each answer, irrespective of the model's difficulty in answering these instances. Ideally if one of the samples is hard to answer, more margin should be given to its ground truth class compared to the easier one. Randomizing $m_{\text{freq}}$ as described above does not take the complexity of each sample into account. To this end, our model learns instance-level margins during training. We augment an auxiliary classifica + +tion head to the feature $\mathbf{x}$ (the orange dashed box in Fig. 1) which is architecturally same as the original model classifier $c$ . We call this the bias-injecting component. Following Eq. 1, the formulation of this component becomes: + +$$ +f _ {b} (v, q) = c _ {b} (\mathbf {x}) \tag {8} +$$ + +where, $f_{b}$ refers to the logits generated by this component and $c_{b}$ refers to the classification head. It is to be noted that while $c_{b} \neq c$ , both are trained to predict the answers given the questions and the images. Finally, we denote $\bar{m}_{ins} = \text{softmax}(f_{b} / \tau)$ as the confidence, (i.e. prediction probability) of the bias-injecting component in answering a question. Here $\tau$ stands for temperature which is a hyperparameter to the network. We define $m_{ins} = 1 - \bar{m}_{ins}$ as the instance-level learnable margin, obtained from the model during training. These learned margins are similar with the frequency-based margins when samples are far away from the decision boundary. However, for training instances that are close, $m_{ins}$ increases the margins if the model confidence is low for the ground truth class, and decreases the same in case the model has high confidence in predicting the ground truth answer. We combine this instance-level confidence for the ground truth class with the previously calculated $m_{ran}$ for each sample $(v, q)$ to obtain the final margins $m_{comb}$ , as shown in the blue dashed box in Fig. 1. + +$$ +m _ {\text {c o m b}} [ g t ] = \beta m _ {\text {r a n}} [ g t ] + (1 - \beta) m _ {\text {i n s}} [ g t ] \tag {9} +$$ + +$gt$ refers to the index of the ground truth class of the sample, and $\beta$ is a hyperparameter used for combining the two margins. For all indices $l \neq gt$ , $m_{comb}[l] = m_{ran}[l]$ . In the first few training epochs, we do not compute $m_{ins}$ as the model is in the initial stage of its learning, i.e. we set $\beta = 1$ . As training progresses, $\beta$ is decreased in a step-wise manner to increase the contributions from the learnt margins. + +The bias-injecting component. The bias-injecting component is a classifier appended to the features $\mathbf{x}$ trained using the standard $CE$ loss. As the $CE$ loss is known to favour the frequently appearing answers in the training data, it automatically learns the bias in the dataset, and by backpropagating this bias into the network, it clusters samples in the feature space based on the source of the bias. This aids the margin loss as it can now separate the (frequent, rare), and the (easy, difficult) samples inside the individual clusters. Moreover, the advantage of using it to generate the learnable margins is that the bias captured is now reflected directly in $\bar{m}_{ins}$ , which ensures that it is close to $\bar{m}_{freq}$ , but still provides information on the answering difficulty of a samples lying close to the decision boundary. Another advantage of this component is that by learning the data bias, this module is capable of generalizing to any in-distribution data, whereas the predictions from the primary classifier $c$ favour the ood data. + +Inference. While margin losses are effective on an ood test + +data, they result in degraded performance on $id$ test set. To mitigate this problem, during inference time, we take advantage of both the bias-injecting component $f_{b}$ and the primary logit head $f$ , as the former is useful in making predictions for an $id$ test data, while the latter is useful in an ood setting. This makes our model robust to different data distributions. We denote by $p_{comb}$ the combined predicted answer probabilities. This is obtained by combining the predictions from $c$ and $c_{b}$ as defined below: + +$$ +p _ {\text {c o m b}} = \alpha . \hat {p} + (1 - \alpha). \hat {p} _ {b} \tag {10} +$$ + +where $\alpha$ is a hyperparameter controlling the weight of each logit head during inference, $\hat{p} = \mathrm{softmax}(f)$ are the predictions from classifier $c$ , $\hat{p_b} = \mathrm{softmax}(f_b / \tau)$ are the predictions from the bias-injecting component $c_b$ . The answer predicted is therefore $\hat{a} = \arg\max(p_{comb})$ . The temperature $\tau$ is same as that defined previously for the instance-based margins. + +Supervised Contrastive (SupCon) Loss. We further separate samples in the feature space based on the SupCon loss. In addition to creating discriminative features for (frequent, rare) and (easy, difficult) samples, the SupCon loss leads to a degree of discrimination among samples with different ground truth answers in the feature space. We consider a mini-batch of size $\mathcal{B}$ of multimodal features denoted as $\{\mathbf{x}_1,\mathbf{x}_2,\dots ,\mathbf{x}_{\mathcal{B}}\}$ and corresponding answers as $\{a_1,a_2,\ldots ,a_{\mathcal{B}}\}$ . If we consider the current sample with index $j$ , the set of positive examples from the mini-batch is denoted by $P_{j}:\{i\in \mathcal{B}\text{s.t.} a_{i} = a_{j}\}$ . Similarly, the set of negative examples is denoted by $N_{j}:\{i\in$ $\mathcal{B}\text{s.t.} a_i\neq a_j\}$ . The SupCon loss [23] is defined as, + +$$ +L _ {\text {s u p - c o n}} = \sum_ {j \in \mathcal {B}} \frac {- 1}{| P _ {j} |} \sum_ {p \in P _ {j}} \log \frac {\exp \left(\mathbf {x} _ {\mathbf {j}} ^ {T} \mathbf {x} _ {\mathbf {p}} / \tau\right)}{\sum_ {n \in N _ {j}} \exp \left(\mathbf {x} _ {\mathbf {j}} ^ {T} \mathbf {x} _ {\mathbf {n}} / \tau\right)}, \tag {11} +$$ + +We set the temperature $\tau = 1$ for all experiments as we do not find any significant improvements by changing its value. + +Total Loss: The final loss function for each sample is: + +$$ +\mathcal {L} = L _ {\text {A n g u l a r}} \left(m _ {\text {c o m b}}\right) + L _ {s} + L _ {\sup - c o n} \tag {12} +$$ + +where $L_{Angular}$ is the angular margin loss, $L_{s}$ is the CE loss training the bias injecting component, $L_{sup-con}$ is the SupCon loss. Our final model can be seen in Fig. 1. We name our overall method RMLVQA. + +# 4. Experiments + +Dataset details. We evaluate our model on the VQACP v2 dataset (Visual Question Answering Under Changing Priors) [3], which is an ood benchmark, based on the standard evaluation metric shown by Antol et al. [5]. It was created by reorganizing the training and validation sets of the VQA v2 [16] dataset, ensuring that the distribution + +of answers for each question type in the training set and the test set are different. The training set of VQA-CP v2 contains approximately 121k images and 438k questions, the test set contains approximately 98k images and 220k questions. Following previous works, we also evaluate our model on the VQA v2 validation set. + +# 4.1. Results + +Quantitative analysis. In Table 1, we show a comparative analysis of the performance of RMLVQA on both VQACP v2 test and VQA v2 validation sets. We report the overall accuracies along with those on "yes/no", "number" and "other" type questions. We observe that our method gains around $6.39\%$ in the overall accuracy for VQA-CP in comparison with AdaVQA [17], which is the cosine margin loss trained model. We observe that AdaVQA, while performing well on VQA-CP v2, has considerably low scores for the in-domain VQA v2. With RMLVQA, the validation accuracy of VQA v2 is $59.99\%$ , which is $13.01\%$ higher than AdaVQA. This shows that our method is the first one trained by adaptive margins that is robust to both id and ood data. With a score of $60.41\%$ for VQA-CP v2, the model improves upon the current state-of-the-art augmentation-free models. In addition to reporting the performance of the various models in literature on the two datasets, we show the relative difference in accuracies between VQA-CP v2 test data and VQA v2 validation data. RMLVQA outperforms all other non-augmentation based models in terms of robustness, with the lowest difference in the two accuracies (see Table 1), indicating that our method is the most robust compared to all other methods that do not use any augmentation, and perform equally well on both VQA-CP v2 and VQA v2. For all experiments, Updn [4] is our base network. + +Qualitative analysis. We further demonstrate the effectiveness of our method in Fig. 2 which provides qualitative results on the VQA-CP v2 test set for RMLVQA and the base network UpDn. In the first row, we show examples for question type "what color". The base network UpDn [4] focuses on the incorrect region in the image, given by attention map scores, and outputs "blue", the most frequent answer in the training set for the given question type. The best scoring region from the attention maps of our model is localized at the correct region in the image, and it correctly outputs "red", which is not a frequent answer in "what color". In the second example, belonging to question type "what is the person", we see that while the baseline outputs "phone", which is a frequent class under that question type, RMLVQA predicts the correct answer "hat", which is a rare class, thus showing the effectiveness of our method. While the baseline outputs incorrect answers, it still focuses on the correct region in the image. This crucial observation indicates that the bias in the model weights do not allow this visual information to propagate forward. Thus it still picks from the frequent answers for the given question type. + +Choice of hyperparameter $\alpha$ for inference time combination of prediction probabilities. Choice of $\alpha$ is crucial as it decides how much weight to put on the prediction probabilities of the bias-injecting component $c_{b}$ and the primary classifier $c$ . As VQA-CP v2 does not have a validation set, we choose $\alpha = 0.5$ for fair evaluation. However, we report the accuracies of VQA-CP v2 test and VQA v2 validation sets for different values of $\alpha$ in Table 2. We observe that $\alpha = 0.5$ leads to the most robust performance of our method on both id and ood data, where the relative gap of accuracies is just $0.42\%$ . While we already choose the optimal value of $\alpha$ for reporting model performance, our experiments demonstrate that one can choose an appropriate value to control the tradeoff between id and ood performances. + +# 4.2. Ablation studies + +In this subsection, we discuss the role of each component of RMLVQA. We evaluate them on the VQA-CP v2 test and VQA v2 validation data and show the results in Table 3. + +Effectiveness of angular margins. We call the base adaptive angular margin loss trained model RMLVQA-Base, which only considers the frequency based margins. Compared to AdaVQA, it leads to a rise of $3.22\%$ in the VQACP test accuracy and an increase of $2.74\%$ in the accuracy of the VQA-v2 validation set. This shows the effectiveness of the angular margin loss over the cosine margins both in id and ood data, validating the choice of the angular margin loss for addressing the language bias problem of VQA. + +Effect of randomization of the margins. Randomizing the margins of each answer leads to an improvement in the accuracy values of VQA-CP v2 test, as shown in Table 3. Further, we also notice that it improves the in-domain accuracy of VQA v2 by a large margin (7.12%), thus showing its effectiveness in generalizability. + +Role of the learnable margins. As explained earlier, $m_{ins}$ represents the confidence of the bias-injecting component in answering a question. We show the positive effect of adding these margins to $m_{ran}$ in Table 3 for VQA-CP v2, with a slight loss in VQA v2. In Fig. 4 we show the Spearman's rank correlation coefficient $\rho$ between $m_{freq}$ and $m_{ins}$ for the question type 'how many' for our method (for the angular and cosine margin losses defined in Sec 3 and AdaVQA [17] respectively), averaged over the relevant samples in each training epoch. We note the following: a) $\rho$ is high throughout, indicating that the order of margin values in $m_{ins}$ for a certain sample remains similar to that of the margin values in $m_{freq}$ for the question type to which the sample belongs. b) $\rho$ decreases over epochs, indicating the excess information being carried by $m_{ins}$ , aiding in the discrimination of samples whose answer frequencies are similar, but have different complexities. + +Role of the bias-injecting component. In Table 3, we show that the bias-injecting component increases the model's overall accuracy by $1.47\%$ for VQA-CP v2 $(3.65\%)$ + +Table 1. Accuracy comparisons with other methods on the VQA-CP v2 and VQA v2 datasets. The methods have been grouped into different categories (separated by lines in the table): base approaches, methods using human annotations, those that modify the language encoder, models weakening the language bias in different ways, our approach RMLVQA trained with UpDn as backbone, and finally the augmentation based methods. The best performance in each column is highlighted in bold. We highlight the overall accuracy of RMLVQA on VQA-CP with an underline as it achieves state-of-the-art on augmentation-free methods. * denotes numbers shown in [17]. We report the average accuracy of our model over 5 random seeds (along the with standard deviations in the superscript). Columns ending with “-CP” denote accuracies for VQA-CP v2, others denote accuracies for VQA v2. † indicates our implementation. + +
ModelY/N-CPNum-CPOthers-CPOverall-CPY/NNumOthersOverallDiff
SAN [44]38.3511.1421.7424.9670.0639.2847.8452.4127.45
GVQA [3]57.9913.6822.1431.3072.0331.1734.6548.2416.94
UpDn [4]42.2711.9346.0539.7481.1842.1455.6663.4823.74
S-MRL [9]42.8512.8143.238.4641.9612.5441.3537.131.33
AttAlign [36]43.0211.8945.0039.3780.9942.5555.2263.2423.87
HINT [36]67.2710.6145.8846.7381.1842.9955.5663.3816.65
SCR [43]70.4110.4247.2948.4778.841.654.562.213.73
VGQE [25]66.3527.0846.7750.11---64.0413.93
DLR [20]70.9918.7245.5748.8776.8239.3348.5457.969.09
AdvReg [35]65.4915.4835.4841.1779.8442.3555.1662.7521.58
RUBi [9]68.6520.2843.1847.11-----
LMH* [12]70.2944.1044.8652.1565.0637.6354.6956.354.2
CF-VQA [31]90.6121.5045.6155.0581.1343.8650.1160.945.89
IntroD [32]90.7917.9246.7355.1782.4846.6054.0563.408.23
GGE-DQ [18]87.0427.7549.5957.3273.2739.9954.3959.111.79
AdaVQA † [17]70.8349.0046.2954.0247.7834.1351.1446.987.04
RMLVQA89.98±0.4645.96±0.5748.74±0.1360.41±0.3276.68±0.3737.54±0.4953.26±0.1259.990.060.42
CVL [1]45.7212.4548.3442.12-----
Unshuffling [39]47.7214.4347.2442.3978.3242.1652.8161.0818.69
RandImg [40]83.8941.6044.2055.3776.5333.8748.5757.241.87
SSL [46]86.5329.8750.0357.59---63.736.14
CSS [11]84.3749.4248.2158.9573.2539.7755.1159.910.96
CSS + CL [27]86.9949.8947.1659.1867.2738.4054.7157.291.89
Mutant [15]88.9049.6850.7861.7282.0742.5253.2862.560.84
D-VQA [42]88.9352.3250.3961.9182.1844.0157.5464.963.05
+ +# What color shirt is the man with the ball wearing? + +![](images/0f65ccc7f4056b44e1d7c536091f583d44fff5e1f41a71054740023159e03061.jpg) +GT: Red + +![](images/c880fba39a812860704805c8336e16025634a0d4796987c49f3c1bcf4f966bb9.jpg) +Baseline: Blue + +![](images/5bf7b283eff56dab88831df9c314d610ccbf247efb41f1d3f15417d2382579c6.jpg) +RMLVQA: Red + +# What is the person holding? + +![](images/fbe26fb4a497fc0248111b8329c47a48176c9ebea328d73d2ef6c3c30549608c.jpg) +GT: Hat +(a) +Figure 2. Qualitative analysis of RMLVQA. We show two images from two question types in the rows. Column (a) represents the ground truth answers, column (b) represents the answers predicted by the baseline UpDn model. Column (c) represents the answer predicted by our method. The bounding boxes show the highest scored region in the attention map of the individual models. + +![](images/032b55525c8b9d4e55224ab045fad06844e478776a7ea6868c62f23365b3d075.jpg) +Baseline: Phone +(b) + +![](images/b69a4157255a206863ec38b14eb84286f8af9150d5325d8dace729062f9e611a.jpg) +RMLVQA: Hat +(c) + +![](images/2cabd8991afa8a8e691998dc092974f001334a5a46c1c11c5fee794a9a04acae.jpg) +Figure 3. TSNE visualization of the feature space with respect to different question types for the model components, evaluated incrementally: a) RMLVQA-Base, b) Gaussian randomization, c) Bias injection + +Table 2. Role of $\alpha$ in the inference stage of RMLVQA. + +
αVQA-CP v2 TestVQA-v2 ValGap
1.060.5458.162.38
0.860.5058.831.67
0.660.3359.570.76
0.560.4159.990.42
0.459.8760.460.59
0.257.4661.263.8
0.039.4861.5422.06
+ +Table 3. Ablations. In this table we show the ablations of $RM$ -LVQA, evaluated on VQA-CP v2 test & VQA v2 val. + +
ModelY/NNumOthersOverallVQA v2 Val
RMLVQA-Base79.7849.6248.4957.2449.72
+Randomization83.7249.4748.3157.9756.84
+Bias Injection88.2744.1348.5559.4460.49
+Learnable Margin88.0646.6348.7459.8759.60
+SupCon Loss89.9845.9648.7460.4159.99
-Backprop89.3640.5647.8058.8059.67
+ +for VQA v2). The effectiveness of this component can be understood from Fig. 3, where we show the TSNE visualizations of how answers from different question types are placed in the feature space for the components of RMLVQA. Fig. 3(a) shows that while for some question types like 'how many', 'are', answers are well separated, some others like 'do', 'are they', 'is there' are close, out of which some are entangled. Although the randomization increases flexibility of the adaptive margins, it does not disentangle these question types, as seen in Fig. 3b. Finally, in Fig. 3(c), we see that the bias-injecting component aids in separating the answers according to their question types. This is because the bias sources of VQA-CP is its question types, and hence this component clusters samples in the training set based on the same. This is crucial, as with more entanglement, the model tends to answer questions of one question type with + +![](images/707495bf036325e7cf448736f4d3a435eb967624af6a809a28c7eadeaad65635.jpg) +Figure 4. Spearman's rank correlation coefficient between $\mathbf{m}_{\mathrm{freq}}$ and $\mathbf{m}_{\mathrm{ins}}$ over epochs for question type "how many" on VQA-CP v2 test set + +the answers of another type. In the last row of Table 3, we also observe the effect of removing the backpropagation of the $CE$ loss (used to train the bias-injecting component) into the main network for VQA-CP v2. The classifier weights in the bias-injecting component learn the language bias in the dataset and backpropagate the same into the network, thus helping the model separate the answers across different question types in the feature space. We utilize this knowledge in the inference stage, where we combine the two logit heads, thus helping the model to generalize to both $id$ and $ood$ test data, as is evident from Tables 1 and 2. + +Role of the SupCon Loss. The addition of the SupCon loss is shown to improve the performance of our model empirically for both VQA-CP and VQA v2 as shown in Table 3. + +# 5. Conclusion + +Although margin-based losses are useful in mitigating language biases in VQA, they may not distinguish between answers of different task-complexity levels in the feature space. To distinguish between samples having similar answer frequency, but different complexity, we learn instance-based margins for each sample from the model during training. We introduce a bias-injecting component in our model and utilize its confidence in answer prediction as the instance-level margins. Being trained by the $CE$ loss, this component further clusters the training samples based on the source of the data bias, guiding the margin loss to distinguish frequent and rare answers inside each cluster. We ensemble the outputs of the bias-injecting component with those of the main model during inference to achieve state-of-the-art results among existing augmentation-free methods on the ood VQA-CP v2 dataset, while being the most robust with respect to both id and ood test sets. + +# 6. Acknowledgments + +This work was supported by a research grant (CRG/2021/005925) from SERB, DST, Govt. of India. Abhipsa Basu is supported by the PMRF fellowship. + +# References + +[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10044-10054, 2020. 1, 7 +[2] Aishwarya Agrawal, Dhruv Batra, and Devi Parikh. 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Overcoming language priors with self-supervised learning for visual question answering. arXiv preprint arXiv:2012.11528, 2020. 1, 3, 7 \ No newline at end of file diff --git a/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/images.zip b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f9622926d56b490e65a507bdc91e0f474719bc25 --- /dev/null +++ b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a17bf492672c371b73b97964bae35a33aadd0c8f2ea9cb0d6964fb18f1988e63 +size 432271 diff --git a/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/layout.json b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5f8df241825e3085df8d6488183bbc62a55b3a32 --- /dev/null +++ b/2023/RMLVQA_ A Margin Loss Approach for Visual Question Answering With Language Biases/layout.json @@ -0,0 +1,9507 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 68, + 102, + 526, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 102, + 526, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 102, + 526, + 140 + ], + "type": "text", + "content": "RMLVQA: A Margin Loss Approach For Visual Question Answering with Language Biases" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 187, + 162, + 257, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 162, + 257, + 175 + ], + "spans": [ + { + "bbox": [ + 187, + 162, + 257, + 175 + ], + "type": "text", + "content": "Abhipsa Basu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 162, + 178, + 282, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 178, + 282, + 189 + ], + "spans": [ + { + "bbox": [ + 162, + 178, + 282, + 189 + ], + "type": "text", + "content": "abhipsabasu@iisc.ac.in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 331, + 162, + 423, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 162, + 423, + 175 + ], + "spans": [ + { + "bbox": [ + 331, + 162, + 423, + 175 + ], + "type": "text", + "content": "Sravanti Addepalli" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 323, + 178, + 432, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 178, + 432, + 188 + ], + "spans": [ + { + "bbox": [ + 323, + 178, + 432, + 188 + ], + "type": "text", + "content": "sravantia@iisc.ac.in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 249, + 196, + 343, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 249, + 196, + 343, + 208 + ], + "spans": [ + { + "bbox": [ + 249, + 196, + 343, + 208 + ], + "type": "text", + "content": "R. Venkatesh Babu" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 252, + 212, + 341, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 252, + 212, + 341, + 223 + ], + "spans": [ + { + "bbox": [ + 252, + 212, + 341, + 223 + ], + "type": "text", + "content": "venky@iisc.ac.in" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 156, + 224, + 434, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 224, + 434, + 237 + ], + "spans": [ + { + "bbox": [ + 156, + 224, + 434, + 237 + ], + "type": "text", + "content": "Vision and AI Lab, Indian Institute of Science, Bangalore" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 265, + 192, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 265, + 192, + 277 + ], + "spans": [ + { + "bbox": [ + 143, + 265, + 192, + 277 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 290, + 289, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 289, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 289, + 625 + ], + "type": "text", + "content": "Visual Question Answering models have been shown to suffer from language biases, where the model learns a correlation between the question and the answer, ignoring the image. While early works attempted to use question-only models or data augmentations to reduce this bias, we propose an adaptive margin loss approach having two components. The first component considers the frequency of answers within a question type in the training data, which addresses the concern of the class-imbalance causing the language biases. However, it does not take into account the answering difficulty of the samples, which impacts their learning. We address this through the second component, where instance-specific margins are learnt, allowing the model to distinguish between samples of varying complexity. We introduce a bias-injecting component to our model, and compute the instance-specific margins from the confidence of this component. We combine these with the estimated margins to consider both answer-frequency and task-complexity in the training loss. We show that, while the margin loss is effective for out-of-distribution (ood) data, the bias-injecting component is essential for generalising to indistribution (id) data. Our proposed approach, Robust Margin Loss for Visual Question Answering (RMLVQA) improves upon the existing state-of-the-art results when compared to augmentation-free methods on benchmark VQA datasets suffering from language biases, while maintaining competitive performance on id data, making our method the most robust one among all comparable methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 649, + 128, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 649, + 128, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 649, + 128, + 661 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 669, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 287, + 694 + ], + "type": "text", + "content": "Visual question answering (VQA) lies at the intersection of computer vision and natural language processing. It is" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 266, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 545, + 338 + ], + "type": "text", + "content": "the task of answering a question based on a given image. VQA networks need to combine knowledge from both visual scene and the question to predict the answer. These systems have numerous applications such as aiding the visually impaired in understanding their surroundings, image retrieval systems in e-commerce, and robotics." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 339, + 546, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 546, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 546, + 471 + ], + "type": "text", + "content": "With the success of deep learning, research in VQA has made great strides in recent years [3,5,16]. However, studies have shown that deep networks may learn correlations between the question and answer alone, ignoring the image modality [3,21,36]. They fail to do multimodal reasoning, specifically, if there is a class imbalance in the answer distributions of the training and test sets. For example, if most of the questions starting with \"What color..?\" are paired with the answer \"red\" in the training data, the model memorizes this trend to answer \"red\" for all color based questions in the test set, irrespective of the image." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 472, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 581 + ], + "type": "text", + "content": "One solution to this problem is to perform data augmentations in various ways [1,4,11,15,27,36,42,43,46]. These methods outperform most other debiasing techniques in the literature. However, augmentation strategies are dependent on the dataset in question and the type of biases observed, which makes the process manual and tedious. Another extensively explored solution is to learn the bias in the dataset separately using a question-only branch [9, 12, 18] and explicitly removing the learnt bias from the base model." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "Margin losses have been widely used for a number of tasks. Cao et al. [10] address the problem of long tailed recognition through an adaptive margin loss, ensuring higher cosine margin penalty for the tail classes and lower penalty for other classes. A similar adaptive cosine margin penalty has been applied to mitigate the language bias problem in VQA by a previous work [17]. Margin losses have been widely used in deep face recognition as well, where it is desired that the features of two images of the same person should be as similar as possible, whereas those of two different people should be far apart. Margin losses" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "content": "Code available at https://github.com/val-iisc/RMLVQA" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11671" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "are used in this regard for facial feature discrimination to maximize the decision margin. Rather than the Euclidean space, both these margin losses project their feature spaces onto a fixed radius hypersphere. While the well known CosFace loss [41] uses cosine margin penalties like Cao et al. [10], ArcFace [14], uses angular margins to maximize the decision margins among different classes in this feature space. Angles correspond to geodesic distance on the projected hypersphere which stabilizes the training process and is shown to improve the discriminative power of face recognition models as compared to cosine margin based methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "text", + "content": "We believe that the language bias problem of VQA can be addressed by learning discriminative features for the biased and unbiased samples in the dataset. To this end, we implement an adaptive angular margin loss, inspired by ArcFace, as margins allow models to distinguish between different kinds of samples. However, the key question here would be how to set the adaptive margins to cater to the specific problem of language biases. Traditional models over-trust the questions over the images due to a class imbalance in the training and test set answer distributions. Hence, one way to set the margins would be to ensure that the training samples with frequent answers are given a smaller penalty due to the abundance of those answers in the dataset, whereas those with rare answers are given a higher margin value. We refer to the resultant margin values as the frequency-based margins. However, one factor that is ignored in this aspect is the answering difficulty of each sample. We argue that more margin should be given to hard samples compared to the easier ones even if the corresponding answers are frequent. In this regard, we propose the learning of instance-specific margins during training, so as to allow the model to distinguish between hard and easy samples alongside frequent and rare samples. To the best of our knowledge, this is one of the first attempts in learning margins automatically and parallelly during training. We combine these learnable margins with the frequency based margins used in prior works [17], so as to allow both frequency and complexity of data samples to control the training dynamics. To compute these learnable margins, we introduce a bias injecting module to our model that is trained using Cross-Entropy " + }, + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "inline_equation", + "content": "(CE)" + }, + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "text", + "content": " loss. We show that the " + }, + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 46, + 207, + 289, + 639 + ], + "type": "text", + "content": " loss additionally clusters the training samples based on the dataset bias itself, thereby aiding the margin loss further. We further introduce a supervised contrastive loss [23] to pull the features of samples having the same answer together, while pushing others apart." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "content": "Adaptive margin losses, with margins calculated by using frequency of answers in the dataset, perform well in the ood setting. However, we show that they cause a drop in the in-domain performance, which raises questions on their robustness. As pointed by [40], it is crucial for VQA models to perform well on both in-domain and ood data since" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "the test set distribution is unknown apriori. We mitigate this issue by ensembling the outputs of the bias injecting component and the proposed learnable margin-loss trained classification head during inference. This makes the model robust to the difference in answer distributions of the training and test sets. Our overall method is called RMLVQA - Robust Margin Loss for Visual Question Answering with language biases. The key contributions of this work can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 186, + 545, + 485 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 186, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 186, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 317, + 186, + 545, + 305 + ], + "type": "text", + "content": "- We propose to mitigate the well known problem of language bias in VQA models by introducing an instance-specific adaptive margin loss, to allow the use of different margins for the learning of samples with varying complexities, in addition to the use of frequency-based margins. To achieve this, we introduce a bias-injecting component and allow the margins to be computed based on prediction probabilities of this branch. We show that this clusters samples in the feature space based on the bias present in the dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 310, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 310, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 317, + 310, + 545, + 346 + ], + "type": "text", + "content": "- We propose to overcome the id-ood trade-off in margin-based losses, by ensembling the outputs of the bias-injecting component and the main model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 350, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 350, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 317, + 350, + 545, + 397 + ], + "type": "text", + "content": "- We further introduce a supervised contrastive loss that pulls features of training samples having the same ground truth answers together, while pushing apart others. This aids the margin loss further." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 401, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 401, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 317, + 401, + 545, + 485 + ], + "type": "text", + "content": "- Through extensive experiments and ablations, we show how the proposed approach achieves state-of-the-art results when compared to augmentation-free methods on the ood VQA-CP v2 dataset, while maintaining competitive performance on the id VQA v2 dataset. This makes our model the most robust one among all non-augmentation based methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 491, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 516 + ], + "type": "text", + "content": "The code, hyperparameter analyses, and results on multiple datasets are shared as supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 525, + 392, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 392, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 392, + 539 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": "VQA and the language bias problem. VQA [5, 16] is the task of answering natural language questions given an image. VQA v1 & v2 [5, 16] are widely used datasets that are used to benchmark different algorithms. However, prior works have shown that these datasets have biases which can be amplified in the trained models [2, 3, 19, 36, 37]. Specifically, in case of language bias, the model learns a correlation between the question and the answer directly. For example, if the model always predicts \"tennis\" for the sport-related questions, it can achieve around " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": " accuracy on the VQA v1 dataset, as the images of the VQA datasets are from MS-COCO [28], which has many \"tennis\" related images. To effectively quantify the extent of bias in the trained models, a new dataset VQA-CP v2 [3] was created from the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11672" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "VQA v2 dataset. In this work, we aim to solve the language bias problem of VQA, where we evaluate our models on the ood benchmark dataset VQA-CP v2 and the id VQA v2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "type": "text", + "content": "Bias mitigation techniques. The language bias problem reduces the generalizability of the VQA models, resulting in a drop in performance when the training set answer distribution is different from that of the test set. There are three popular categories of solutions in the literature tackling this problem, which we discuss below." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 181, + 286, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 286, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 286, + 228 + ], + "type": "text", + "content": "Visual Grounding based methods [34, 45] used human annotations as supervision to attention maps [13, 33], whereas more recent works use Grad-CAM for the same [36, 43]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 230, + 286, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 286, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 286, + 348 + ], + "type": "text", + "content": "Ensemble based methods use a separate question-only model to capture the bias, and further remove the bias explicitly from the base VQA model [9, 12, 35]. Apart from these techniques, Niu et al. [31] introduce a counterfactual inference framework to mitigate the biases. KV and Mittal [25] use a visually grounded question encoder such that the visual information is embedded in the question representation itself. Niu et al. [32] improve both ood generalizability and id performance through introspective knowledge distillation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 286, + 469 + ], + "type": "text", + "content": "Augmentation based methods remove bias by augmenting the dataset to make it more balanced. Some works generate counterfactual data by masking or transforming the critical objects and words, and further generating appropriate ground truth answers [11, 15, 27]. Other works introduce negative samples by shuffling the inputs (images and questions) in the minibatch to reduce bias without requiring any annotation [40, 42, 46]. Wen et al. [42] use two kinds of negative samples for balancing the dataset, and construct both question-only and vision-only models to remove the biases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 470, + 286, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 286, + 625 + ], + "type": "text", + "content": "Margin-based methods. Max-margin classifiers are used in popular machine learning algorithms like SVMs [38]. Margin losses are commonly used in many problems such as deep face recognition [7, 14, 29, 41], long tailed or class imbalanced learning [10, 22, 30] and few-shot learning [26]. Guo et al. [17] apply an adaptive cosine margin loss to discriminate the frequent and rare answers for a given question type and implement this by transforming the multimodal feature space to a fixed radius hypersphere. The adaptive margins are estimated from the training data based on the frequency of occurrence of an answer in questions of a given type, ensuring that rare answers are given more margin penalty, whereas frequent classes are given less penalty." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 638, + 161, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 161, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 161, + 652 + ], + "type": "text", + "content": "3. Proposed approach" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 133, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 133, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 133, + 670 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "We consider the problem of classification based Visual Question Answering (VQA). It is the task of answering questions based on an image. Given a dataset " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": " having" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " samples, with image " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "v \\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", question " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "q \\in \\mathcal{Q}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and answer (class label) " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "a \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", the goal is to train a model to optimize a mapping function " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "f: \\mathcal{V} \\times \\mathcal{Q} \\to \\mathbb{R}^{|\\mathcal{A}|}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " to generate predictions for the given question and image. The VQA model consists of four parts: (1) image feature extractor " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "e_v" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", (2) question feature extractor " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "e_q" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", (3) the VQA model " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "m_f" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " which fuses the image and question features to generate the joint multimodal features " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", (4) classifier " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " having weights " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", that generates the logits " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ". Most of the classical VQA models [4, 6, 8, 24, 44] follow this paradigm and formulate the problem as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 361, + 213, + 545, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 213, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 361, + 213, + 545, + 227 + ], + "type": "interline_equation", + "content": "f (v, q) = c \\left(m _ {f} \\left(e _ {v} (v), e _ {q} (q)\\right)\\right) \\tag {1}", + "image_path": "b9d86a1bfcb4a29516d47575bf5a2b9f50285d68f9cdff79c0fa2a8c34b4e257.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "text", + "content": "Standard Cross-Entropy loss. VQA models can be trained by optimizing the Cross-Entropy " + }, + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "inline_equation", + "content": "(CE)" + }, + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "text", + "content": " loss" + }, + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 234, + 545, + 268 + ], + "type": "text", + "content": " shown below:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 357, + 268, + 545, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 268, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 357, + 268, + 545, + 301 + ], + "type": "interline_equation", + "content": "L _ {s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp \\left(f _ {i}\\right)}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp \\left(f _ {j}\\right)} \\tag {2}", + "image_path": "e32bc2d76e8f82263a5a12e11eacfb47ad62aced21e0400ebbc6082579431a4f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": "To solve the problem of language bias in VQA, the model should learn discriminative features for different answers for a given question type so that it can distinguish frequently occurring answers from rarely occurring answers, as well as those with varying complexity. However, standard " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " loss only favours the samples with frequently occurring answers. Normalized " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " loss. Before defining the margin loss, we define a reformulation of the " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " loss as a cosine loss [14, 41], by L2-normalizing the classifier weight vectors " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{W_i} \\in c" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "a_i \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": ", and feature " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = m_f(e_v(v_i), e_q(q_i))" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": ". Therefore, we define " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}_{\\mathrm{i}} = \\frac{\\mathbf{W}_{\\mathrm{i}}}{\\|\\mathbf{W}_{\\mathrm{i}}\\|}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} = s\\frac{\\mathbf{x}}{\\|\\mathbf{x}\\|}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " is a scaling parameter. Let " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " be the angle between " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{i}}" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": ". Therefore the logit for each " + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 305, + 545, + 475 + ], + "type": "text", + "content": " is transformed as (keeping the bias term as 0 for simplicity):" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 337, + 483, + 545, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 483, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 337, + 483, + 545, + 500 + ], + "type": "interline_equation", + "content": "f _ {i} = \\hat {\\mathbf {W}} _ {\\mathbf {i}} ^ {\\top} \\hat {\\mathbf {x}} = \\| \\hat {\\mathbf {W}} _ {\\mathbf {i}} \\| \\| \\hat {\\mathbf {x}} \\| \\cos \\theta_ {i} = s \\cos \\theta_ {i} \\tag {3}", + "image_path": "cd1a0aa191e8dfa954199a6b62fc5a42820804a21d97efde36081473b4f452e7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "text", + "content": "The joint features " + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "text", + "content": " are thus distributed on a hypersphere with a radius " + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "text", + "content": ". This makes the normalized " + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 509, + 544, + 532 + ], + "type": "text", + "content": " loss as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 342, + 540, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 540, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 342, + 540, + 545, + 574 + ], + "type": "interline_equation", + "content": "L _ {n s} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos \\theta_ {i})}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos \\theta_ {j})} \\tag {4}", + "image_path": "e36b45c2af8081a7cd1ee835a209d8d7590d727877d97365ca780f9af69901b7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 581, + 376, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 581, + 376, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 581, + 376, + 594 + ], + "type": "text", + "content": "3.2. RMLVQA" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 600, + 544, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 600, + 544, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 600, + 544, + 635 + ], + "type": "text", + "content": "In this subsection, we define our method, which is a Robust Margin Loss based approach for solving the problem of language biases in VQA." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "text", + "content": "Adaptive Angular Margin Loss. We introduce an adaptive angular margin loss that ensures decision margin maximization through angular margins in an adaptive way. The normalized " + }, + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "text", + "content": " loss transforms the feature space to an angular space of radius " + }, + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 635, + 545, + 696 + ], + "type": "text", + "content": ". The motivation behind an adaptive" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 541, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 541, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 541, + 713 + ], + "type": "text", + "content": "2In this paper, all losses will be expressed as individual sample losses" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11673" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 71, + 486, + 210 + ], + "blocks": [ + { + "bbox": [ + 109, + 71, + 486, + 210 + ], + "lines": [ + { + "bbox": [ + 109, + 71, + 486, + 210 + ], + "spans": [ + { + "bbox": [ + 109, + 71, + 486, + 210 + ], + "type": "image", + "image_path": "1eec2d02ecfe881596ea47683b90aed0eb4aaf89021eecd2f63cf952a8b5c45d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 219, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 45, + 219, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 45, + 219, + 547, + 253 + ], + "type": "text", + "content": "Figure 1. Overview of our model. The orange dashed region shows the proposed bias-injecting module, trained using the " + }, + { + "bbox": [ + 45, + 219, + 547, + 253 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 45, + 219, + 547, + 253 + ], + "type": "text", + "content": " loss. The blue dashed region shows how the instance-based margins are generated and then combined with the randomized frequency-based margins to compute the final margins. The final prediction is obtained by combining the two logit heads." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 273, + 289, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 289, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 289, + 403 + ], + "type": "text", + "content": "margin instead of a constant margin is based on the root of the language bias problem in VQA. These biases occur when similar questions in the dataset are paired with the same answers most of the time, fooling the model to memorize these questions and the answers by ignoring the image completely. Thus, while some samples are overlooked because of the rarity of their corresponding answers, others are overly paid attention to. Adaptive margins allow the model to set different penalties for the varying samples, thus leading to highly discriminative features for the different training instances." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 405, + 288, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 288, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 288, + 464 + ], + "type": "text", + "content": "One aspect of the adaptive margins is to ensure that the instances with frequent answers are allowed a smaller margin than those with the rare ones. We call these margins " + }, + { + "bbox": [ + 46, + 405, + 288, + 464 + ], + "type": "inline_equation", + "content": "m_{freq}" + }, + { + "bbox": [ + 46, + 405, + 288, + 464 + ], + "type": "text", + "content": ". Similar to [17], these margins are calculated based on the question type as shown below:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 469, + 287, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 469, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 102, + 469, + 287, + 500 + ], + "type": "interline_equation", + "content": "\\bar {m} _ {f r e q} ^ {k} [ i ] = \\frac {n _ {i} ^ {k} + \\epsilon}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} n _ {j} ^ {k} + \\epsilon} \\tag {5}", + "image_path": "bed8782481c85b0079b45b190bbc7bb4d89abca9985faec7223ddfaa795db6c9.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 501, + 287, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 501, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 108, + 501, + 287, + 517 + ], + "type": "interline_equation", + "content": "m _ {f r e q} ^ {k} [ i ] = 1 - \\bar {m} _ {f r e q} ^ {k} [ i ] \\tag {6}", + "image_path": "3a5972a61ac4b2ede353fb9157e6f8e8e7c2d8513dad94964b26bbb5a2ccbb78.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\bar{m}_{freq}^{k}[i]" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " measures the probability of occurrence of answer " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " in the training data for a given question type " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "qt_{k}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "n_{i}^{k}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " is the frequency of answer " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " in the training set calculated for the given " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "qt_{k}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " is a hyperparameter for avoiding computational overflow. " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "m_{freq}^{k}[i]" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " is the adaptive margin for answer " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "a_{i} \\in \\mathcal{A}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "qt_{k}" + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "text", + "content": "The adaptive angular margin loss adds a margin penalty to the angle between the features " + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "text", + "content": " and the classifier weights " + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{W_i}" + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 594, + 288, + 677 + ], + "type": "text", + "content": " class as shown below. Since the margin is placed on the angle, it maps exactly to the \"geodesic\" distance on the hypersphere [14]. While Deng et al. [14] set a constant value for the margin, i.e. 0.5, our margins are adaptive in nature." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 681, + 289, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 681, + 289, + 717 + ], + "spans": [ + { + "bbox": [ + 47, + 681, + 289, + 717 + ], + "type": "interline_equation", + "content": "L _ {A n g u l a r} ^ {k} = \\sum_ {i = 1} ^ {| \\mathcal {A} |} - a _ {i} \\log \\frac {\\exp (s \\cos (\\theta_ {i} + m _ {f r e q} ^ {k} [ i ]))}{\\sum_ {j = 1} ^ {| \\mathcal {A} |} \\exp (s \\cos (\\theta_ {j} + m _ {f r e q} ^ {k} [ j ]))}", + "image_path": "8cbc3347c747e519170e534e659a1043f08379f16525b724a5bf416132ba0e4c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 273, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 297 + ], + "type": "text", + "content": "For notational simplicity, in the coming sections, we omit " + }, + { + "bbox": [ + 304, + 273, + 545, + 297 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 273, + 545, + 297 + ], + "type": "text", + "content": " from the margin and loss computations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": "Randomization of the estimated margins. Boutros et al. [7] suggest that in typical margin losses, setting constant margins can limit the generalizability and discriminative power of a model. We note that " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "m_{freq}[i]" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": " is constant for each " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "a_i \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": " for a given question type " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "qt_k" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": " over all samples in the training set. When " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "qt_k" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": " is \"how many\", the margin for the answer \"2\" is same for all the training instances belonging to this question type. We believe that setting the same high margin value for a specific rare answer in a given question type and similarly lower value for a frequently appearing answer can lead to overcorrection of the language bias, by forcing the model to focus on the rare answers more than the frequent ones. Therefore, under a given question type " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "qt_k" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": ", for every answer " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": ", we use a randomized version of " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "\\bar{m}_{freq}[i]" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": ", called " + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "inline_equation", + "content": "\\bar{m}_{ran}[i]" + }, + { + "bbox": [ + 304, + 297, + 546, + 478 + ], + "type": "text", + "content": " in the following manner:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 370, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 370, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\bar {m} _ {r a n} [ i ] = \\mathcal {N} (\\bar {m} _ {f r e q} [ i ], \\sigma) \\tag {7}", + "image_path": "c7213f4d85af0f29a358cf324f37fc2d4d258331419c5f68e46b1fa4b94c9786.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " is the Gaussian distribution, and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " is the standard deviation, which is a hyperparameter. This impedes the model from overcorrecting with respect to the rare answers, thus increasing its generalizability. Finally, we obtain the randomized margin " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "m_{ran}[i] = 1 - \\bar{m}_{ran}[i]" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "a_i\\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " in each " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "qt_{k}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "Instance-based margins. The frequency-based margins estimated from the training data are constant for a given question type. So, for two different questions starting with \"how many\", the margins are same for each answer, irrespective of the model's difficulty in answering these instances. Ideally if one of the samples is hard to answer, more margin should be given to its ground truth class compared to the easier one. Randomizing " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "m_{\\text{freq}}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " as described above does not take the complexity of each sample into account. To this end, our model learns instance-level margins during training. We augment an auxiliary classifica" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11674" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "tion head to the feature " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " (the orange dashed box in Fig. 1) which is architecturally same as the original model classifier " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ". We call this the bias-injecting component. Following Eq. 1, the formulation of this component becomes:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 128, + 287, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 128, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 132, + 128, + 287, + 140 + ], + "type": "interline_equation", + "content": "f _ {b} (v, q) = c _ {b} (\\mathbf {x}) \\tag {8}", + "image_path": "b7dd3bd4267e42857b02acb9e81f1b22a04d551173743a190d2d9ba7c8298eee.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "f_{b}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " refers to the logits generated by this component and " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "c_{b}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " refers to the classification head. It is to be noted that while " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "c_{b} \\neq c" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": ", both are trained to predict the answers given the questions and the images. Finally, we denote " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\bar{m}_{ins} = \\text{softmax}(f_{b} / \\tau)" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " as the confidence, (i.e. prediction probability) of the bias-injecting component in answering a question. Here " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " stands for temperature which is a hyperparameter to the network. We define " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "m_{ins} = 1 - \\bar{m}_{ins}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " as the instance-level learnable margin, obtained from the model during training. These learned margins are similar with the frequency-based margins when samples are far away from the decision boundary. However, for training instances that are close, " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " increases the margins if the model confidence is low for the ground truth class, and decreases the same in case the model has high confidence in predicting the ground truth answer. We combine this instance-level confidence for the ground truth class with the previously calculated " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "m_{ran}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " for each sample " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "(v, q)" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": " to obtain the final margins " + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "inline_equation", + "content": "m_{comb}" + }, + { + "bbox": [ + 46, + 148, + 289, + 376 + ], + "type": "text", + "content": ", as shown in the blue dashed box in Fig. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 382, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 382, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 77, + 382, + 287, + 396 + ], + "type": "interline_equation", + "content": "m _ {\\text {c o m b}} [ g t ] = \\beta m _ {\\text {r a n}} [ g t ] + (1 - \\beta) m _ {\\text {i n s}} [ g t ] \\tag {9}", + "image_path": "d70b9690293c8c7c0430cd2259b046c42ca9c438ce19dace45c5e0b7bbdc620c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " refers to the index of the ground truth class of the sample, and " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " is a hyperparameter used for combining the two margins. For all indices " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "l \\neq gt" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "m_{comb}[l] = m_{ran}[l]" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": ". In the first few training epochs, we do not compute " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " as the model is in the initial stage of its learning, i.e. we set " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": ". As training progresses, " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " is decreased in a step-wise manner to increase the contributions from the learnt margins." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": "The bias-injecting component. The bias-injecting component is a classifier appended to the features " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": " trained using the standard " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": " loss. As the " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": " loss is known to favour the frequently appearing answers in the training data, it automatically learns the bias in the dataset, and by backpropagating this bias into the network, it clusters samples in the feature space based on the source of the bias. This aids the margin loss as it can now separate the (frequent, rare), and the (easy, difficult) samples inside the individual clusters. Moreover, the advantage of using it to generate the learnable margins is that the bias captured is now reflected directly in " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\bar{m}_{ins}" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": ", which ensures that it is close to " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\bar{m}_{freq}" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": ", but still provides information on the answering difficulty of a samples lying close to the decision boundary. Another advantage of this component is that by learning the data bias, this module is capable of generalizing to any in-distribution data, whereas the predictions from the primary classifier " + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 487, + 289, + 700 + ], + "type": "text", + "content": " favour the ood data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "content": "Inference. While margin losses are effective on an ood test" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "data, they result in degraded performance on " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "id" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " test set. To mitigate this problem, during inference time, we take advantage of both the bias-injecting component " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "f_{b}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " and the primary logit head " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": ", as the former is useful in making predictions for an " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "id" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " test data, while the latter is useful in an ood setting. This makes our model robust to different data distributions. We denote by " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "p_{comb}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " the combined predicted answer probabilities. This is obtained by combining the predictions from " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "c_{b}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " as defined below:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 370, + 189, + 545, + 202 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 189, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 370, + 189, + 545, + 202 + ], + "type": "interline_equation", + "content": "p _ {\\text {c o m b}} = \\alpha . \\hat {p} + (1 - \\alpha). \\hat {p} _ {b} \\tag {10}", + "image_path": "61cbd4f5c8246ddb42dc341e2361ac1ea9bc87f65fa4481cd22a35ac0d968175.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": " is a hyperparameter controlling the weight of each logit head during inference, " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\hat{p} = \\mathrm{softmax}(f)" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": " are the predictions from classifier " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\hat{p_b} = \\mathrm{softmax}(f_b / \\tau)" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": " are the predictions from the bias-injecting component " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "c_b" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": ". The answer predicted is therefore " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\hat{a} = \\arg\\max(p_{comb})" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": ". The temperature " + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 210, + 545, + 293 + ], + "type": "text", + "content": " is same as that defined previously for the instance-based margins." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": "Supervised Contrastive (SupCon) Loss. We further separate samples in the feature space based on the SupCon loss. In addition to creating discriminative features for (frequent, rare) and (easy, difficult) samples, the SupCon loss leads to a degree of discrimination among samples with different ground truth answers in the feature space. We consider a mini-batch of size " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": " of multimodal features denoted as " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_{\\mathcal{B}}\\}" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": " and corresponding answers as " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "\\{a_1,a_2,\\ldots ,a_{\\mathcal{B}}\\}" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": ". If we consider the current sample with index " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": ", the set of positive examples from the mini-batch is denoted by " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "P_{j}:\\{i\\in \\mathcal{B}\\text{s.t.} a_{i} = a_{j}\\}" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": ". Similarly, the set of negative examples is denoted by " + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "N_{j}:\\{i\\in" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{B}\\text{s.t.} a_i\\neq a_j\\}" + }, + { + "bbox": [ + 304, + 293, + 546, + 450 + ], + "type": "text", + "content": ". The SupCon loss [23] is defined as," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 457, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 457, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 318, + 457, + 545, + 503 + ], + "type": "interline_equation", + "content": "L _ {\\text {s u p - c o n}} = \\sum_ {j \\in \\mathcal {B}} \\frac {- 1}{| P _ {j} |} \\sum_ {p \\in P _ {j}} \\log \\frac {\\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {p}} / \\tau\\right)}{\\sum_ {n \\in N _ {j}} \\exp \\left(\\mathbf {x} _ {\\mathbf {j}} ^ {T} \\mathbf {x} _ {\\mathbf {n}} / \\tau\\right)}, \\tag {11}", + "image_path": "00ddde610d1ab48a9c12a0e0dc702af561fbbbb405828ff3d3d81b26294597db.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 504, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 528 + ], + "type": "text", + "content": "We set the temperature " + }, + { + "bbox": [ + 304, + 504, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 304, + 504, + 545, + 528 + ], + "type": "text", + "content": " for all experiments as we do not find any significant improvements by changing its value." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 529, + 526, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 526, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 526, + 540 + ], + "type": "text", + "content": "Total Loss: The final loss function for each sample is:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 340, + 549, + 545, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 549, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 340, + 549, + 545, + 562 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = L _ {\\text {A n g u l a r}} \\left(m _ {\\text {c o m b}}\\right) + L _ {s} + L _ {\\sup - c o n} \\tag {12}", + "image_path": "38f4fd7febcb995afe8dba31d5650ea75b1fedee86b3ddfd07b59cfbe5e9dd91.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "inline_equation", + "content": "L_{Angular}" + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "text", + "content": " is the angular margin loss, " + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "inline_equation", + "content": "L_{s}" + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "text", + "content": " is the CE loss training the bias injecting component, " + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "inline_equation", + "content": "L_{sup-con}" + }, + { + "bbox": [ + 304, + 570, + 545, + 618 + ], + "type": "text", + "content": " is the SupCon loss. Our final model can be seen in Fig. 1. We name our overall method RMLVQA." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 628, + 387, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 628, + 387, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 628, + 387, + 641 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Dataset details. We evaluate our model on the VQACP v2 dataset (Visual Question Answering Under Changing Priors) [3], which is an ood benchmark, based on the standard evaluation metric shown by Antol et al. [5]. It was created by reorganizing the training and validation sets of the VQA v2 [16] dataset, ensuring that the distribution" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11675" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "of answers for each question type in the training set and the test set are different. The training set of VQA-CP v2 contains approximately 121k images and 438k questions, the test set contains approximately 98k images and 220k questions. Following previous works, we also evaluate our model on the VQA v2 validation set." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 151, + 105, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 151, + 105, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 151, + 105, + 162 + ], + "type": "text", + "content": "4.1. Results" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "content": "Quantitative analysis. In Table 1, we show a comparative analysis of the performance of RMLVQA on both VQACP v2 test and VQA v2 validation sets. We report the overall accuracies along with those on \"yes/no\", \"number\" and \"other\" type questions. We observe that our method gains around " + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "inline_equation", + "content": "6.39\\%" + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "content": " in the overall accuracy for VQA-CP in comparison with AdaVQA [17], which is the cosine margin loss trained model. We observe that AdaVQA, while performing well on VQA-CP v2, has considerably low scores for the in-domain VQA v2. With RMLVQA, the validation accuracy of VQA v2 is " + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "inline_equation", + "content": "59.99\\%" + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "content": ", which is " + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "inline_equation", + "content": "13.01\\%" + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "content": " higher than AdaVQA. This shows that our method is the first one trained by adaptive margins that is robust to both id and ood data. With a score of " + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "inline_equation", + "content": "60.41\\%" + }, + { + "bbox": [ + 46, + 163, + 289, + 463 + ], + "type": "text", + "content": " for VQA-CP v2, the model improves upon the current state-of-the-art augmentation-free models. In addition to reporting the performance of the various models in literature on the two datasets, we show the relative difference in accuracies between VQA-CP v2 test data and VQA v2 validation data. RMLVQA outperforms all other non-augmentation based models in terms of robustness, with the lowest difference in the two accuracies (see Table 1), indicating that our method is the most robust compared to all other methods that do not use any augmentation, and perform equally well on both VQA-CP v2 and VQA v2. For all experiments, Updn [4] is our base network." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 463, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 289, + 715 + ], + "type": "text", + "content": "Qualitative analysis. We further demonstrate the effectiveness of our method in Fig. 2 which provides qualitative results on the VQA-CP v2 test set for RMLVQA and the base network UpDn. In the first row, we show examples for question type \"what color\". The base network UpDn [4] focuses on the incorrect region in the image, given by attention map scores, and outputs \"blue\", the most frequent answer in the training set for the given question type. The best scoring region from the attention maps of our model is localized at the correct region in the image, and it correctly outputs \"red\", which is not a frequent answer in \"what color\". In the second example, belonging to question type \"what is the person\", we see that while the baseline outputs \"phone\", which is a frequent class under that question type, RMLVQA predicts the correct answer \"hat\", which is a rare class, thus showing the effectiveness of our method. While the baseline outputs incorrect answers, it still focuses on the correct region in the image. This crucial observation indicates that the bias in the model weights do not allow this visual information to propagate forward. Thus it still picks from the frequent answers for the given question type." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "Choice of hyperparameter " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " for inference time combination of prediction probabilities. Choice of " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " is crucial as it decides how much weight to put on the prediction probabilities of the bias-injecting component " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "c_{b}" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " and the primary classifier " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": ". As VQA-CP v2 does not have a validation set, we choose " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " for fair evaluation. However, we report the accuracies of VQA-CP v2 test and VQA v2 validation sets for different values of " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " in Table 2. We observe that " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " leads to the most robust performance of our method on both id and ood data, where the relative gap of accuracies is just " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "0.42\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": ". While we already choose the optimal value of " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " for reporting model performance, our experiments demonstrate that one can choose an appropriate value to control the tradeoff between id and ood performances." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 246, + 405, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 246, + 405, + 257 + ], + "spans": [ + { + "bbox": [ + 305, + 246, + 405, + 257 + ], + "type": "text", + "content": "4.2. Ablation studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "type": "text", + "content": "In this subsection, we discuss the role of each component of RMLVQA. We evaluate them on the VQA-CP v2 test and VQA v2 validation data and show the results in Table 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "text", + "content": "Effectiveness of angular margins. We call the base adaptive angular margin loss trained model RMLVQA-Base, which only considers the frequency based margins. Compared to AdaVQA, it leads to a rise of " + }, + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "3.22\\%" + }, + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "text", + "content": " in the VQACP test accuracy and an increase of " + }, + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "2.74\\%" + }, + { + "bbox": [ + 304, + 295, + 545, + 403 + ], + "type": "text", + "content": " in the accuracy of the VQA-v2 validation set. This shows the effectiveness of the angular margin loss over the cosine margins both in id and ood data, validating the choice of the angular margin loss for addressing the language bias problem of VQA." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": "Effect of randomization of the margins. Randomizing the margins of each answer leads to an improvement in the accuracy values of VQA-CP v2 test, as shown in Table 3. Further, we also notice that it improves the in-domain accuracy of VQA v2 by a large margin (7.12%), thus showing its effectiveness in generalizability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": "Role of the learnable margins. As explained earlier, " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " represents the confidence of the bias-injecting component in answering a question. We show the positive effect of adding these margins to " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{ran}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " in Table 3 for VQA-CP v2, with a slight loss in VQA v2. In Fig. 4 we show the Spearman's rank correlation coefficient " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{freq}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " for the question type 'how many' for our method (for the angular and cosine margin losses defined in Sec 3 and AdaVQA [17] respectively), averaged over the relevant samples in each training epoch. We note the following: a) " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " is high throughout, indicating that the order of margin values in " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " for a certain sample remains similar to that of the margin values in " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{freq}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " for the question type to which the sample belongs. b) " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": " decreases over epochs, indicating the excess information being carried by " + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "inline_equation", + "content": "m_{ins}" + }, + { + "bbox": [ + 304, + 475, + 547, + 677 + ], + "type": "text", + "content": ", aiding in the discrimination of samples whose answer frequencies are similar, but have different complexities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Role of the bias-injecting component. In Table 3, we show that the bias-injecting component increases the model's overall accuracy by " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "1.47\\%" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " for VQA-CP v2 " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "(3.65\\%)" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11676" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 148 + ], + "type": "text", + "content": "Table 1. Accuracy comparisons with other methods on the VQA-CP v2 and VQA v2 datasets. The methods have been grouped into different categories (separated by lines in the table): base approaches, methods using human annotations, those that modify the language encoder, models weakening the language bias in different ways, our approach RMLVQA trained with UpDn as backbone, and finally the augmentation based methods. The best performance in each column is highlighted in bold. We highlight the overall accuracy of RMLVQA on VQA-CP with an underline as it achieves state-of-the-art on augmentation-free methods. * denotes numbers shown in [17]. We report the average accuracy of our model over 5 random seeds (along the with standard deviations in the superscript). Columns ending with “-CP” denote accuracies for VQA-CP v2, others denote accuracies for VQA v2. † indicates our implementation." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 80, + 156, + 515, + 429 + ], + "blocks": [ + { + "bbox": [ + 80, + 156, + 515, + 429 + ], + "lines": [ + { + "bbox": [ + 80, + 156, + 515, + 429 + ], + "spans": [ + { + "bbox": [ + 80, + 156, + 515, + 429 + ], + "type": "table", + "html": "
ModelY/N-CPNum-CPOthers-CPOverall-CPY/NNumOthersOverallDiff
SAN [44]38.3511.1421.7424.9670.0639.2847.8452.4127.45
GVQA [3]57.9913.6822.1431.3072.0331.1734.6548.2416.94
UpDn [4]42.2711.9346.0539.7481.1842.1455.6663.4823.74
S-MRL [9]42.8512.8143.238.4641.9612.5441.3537.131.33
AttAlign [36]43.0211.8945.0039.3780.9942.5555.2263.2423.87
HINT [36]67.2710.6145.8846.7381.1842.9955.5663.3816.65
SCR [43]70.4110.4247.2948.4778.841.654.562.213.73
VGQE [25]66.3527.0846.7750.11---64.0413.93
DLR [20]70.9918.7245.5748.8776.8239.3348.5457.969.09
AdvReg [35]65.4915.4835.4841.1779.8442.3555.1662.7521.58
RUBi [9]68.6520.2843.1847.11-----
LMH* [12]70.2944.1044.8652.1565.0637.6354.6956.354.2
CF-VQA [31]90.6121.5045.6155.0581.1343.8650.1160.945.89
IntroD [32]90.7917.9246.7355.1782.4846.6054.0563.408.23
GGE-DQ [18]87.0427.7549.5957.3273.2739.9954.3959.111.79
AdaVQA † [17]70.8349.0046.2954.0247.7834.1351.1446.987.04
RMLVQA89.98±0.4645.96±0.5748.74±0.1360.41±0.3276.68±0.3737.54±0.4953.26±0.1259.990.060.42
CVL [1]45.7212.4548.3442.12-----
Unshuffling [39]47.7214.4347.2442.3978.3242.1652.8161.0818.69
RandImg [40]83.8941.6044.2055.3776.5333.8748.5757.241.87
SSL [46]86.5329.8750.0357.59---63.736.14
CSS [11]84.3749.4248.2158.9573.2539.7755.1159.910.96
CSS + CL [27]86.9949.8947.1659.1867.2738.4054.7157.291.89
Mutant [15]88.9049.6850.7861.7282.0742.5253.2862.560.84
D-VQA [42]88.9352.3250.3961.9182.1844.0157.5464.963.05
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Qualitative analysis of RMLVQA. We show two images from two question types in the rows. Column (a) represents the ground truth answers, column (b) represents the answers predicted by the baseline UpDn model. Column (c) represents the answer predicted by our method. The bounding boxes show the highest scored region in the attention map of the individual models." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 233, + 554, + 354, + 635 + ], + "blocks": [ + { + "bbox": [ + 233, + 554, + 354, + 635 + ], + "lines": [ + { + "bbox": [ + 233, + 554, + 354, + 635 + ], + "spans": [ + { + "bbox": [ + 233, + 554, + 354, + 635 + ], + "type": "image", + "image_path": "032b55525c8b9d4e55224ab045fad06844e478776a7ea6868c62f23365b3d075.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 266, + 636, + 331, + 644 + ], + "lines": [ + { + "bbox": [ + 266, + 636, + 331, + 644 + ], + "spans": [ + { + "bbox": [ + 266, + 636, + 331, + 644 + ], + "type": "text", + "content": "Baseline: Phone" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 290, + 647, + 301, + 657 + ], + "lines": [ + { + "bbox": [ + 290, + 647, + 301, + 657 + ], + "spans": [ + { + "bbox": [ + 290, + 647, + 301, + 657 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 363, + 554, + 485, + 635 + ], + "blocks": [ + { + "bbox": [ + 363, + 554, + 485, + 635 + ], + "lines": [ + { + "bbox": [ + 363, + 554, + 485, + 635 + ], + "spans": [ + { + "bbox": [ + 363, + 554, + 485, + 635 + ], + "type": "image", + "image_path": "b69a4157255a206863ec38b14eb84286f8af9150d5325d8dace729062f9e611a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 636, + 452, + 644 + ], + "lines": [ + { + "bbox": [ + 397, + 636, + 452, + 644 + ], + "spans": [ + { + "bbox": [ + 397, + 636, + 452, + 644 + ], + "type": "text", + "content": "RMLVQA: Hat" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 415, + 647, + 426, + 657 + ], + "lines": [ + { + "bbox": [ + 415, + 647, + 426, + 657 + ], + "spans": [ + { + "bbox": [ + 415, + 647, + 426, + 657 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11677" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 83, + 318, + 187 + ], + "blocks": [ + { + "bbox": [ + 53, + 83, + 318, + 187 + ], + "lines": [ + { + "bbox": [ + 53, + 83, + 318, + 187 + ], + "spans": [ + { + "bbox": [ + 53, + 83, + 318, + 187 + ], + "type": "image", + "image_path": "2cabd8991afa8a8e691998dc092974f001334a5a46c1c11c5fee794a9a04acae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 323, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 323, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 323, + 232 + ], + "type": "text", + "content": "Figure 3. TSNE visualization of the feature space with respect to different question types for the model components, evaluated incrementally: a) RMLVQA-Base, b) Gaussian randomization, c) Bias injection" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 72, + 277, + 262, + 378 + ], + "blocks": [ + { + "bbox": [ + 64, + 256, + 269, + 268 + ], + "lines": [ + { + "bbox": [ + 64, + 256, + 269, + 268 + ], + "spans": [ + { + "bbox": [ + 64, + 256, + 269, + 268 + ], + "type": "text", + "content": "Table 2. Role of " + }, + { + "bbox": [ + 64, + 256, + 269, + 268 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 64, + 256, + 269, + 268 + ], + "type": "text", + "content": " in the inference stage of RMLVQA." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 277, + 262, + 378 + ], + "lines": [ + { + "bbox": [ + 72, + 277, + 262, + 378 + ], + "spans": [ + { + "bbox": [ + 72, + 277, + 262, + 378 + ], + "type": "table", + "html": "
αVQA-CP v2 TestVQA-v2 ValGap
1.060.5458.162.38
0.860.5058.831.67
0.660.3359.570.76
0.560.4159.990.42
0.459.8760.460.59
0.257.4661.263.8
0.039.4861.5422.06
", + "image_path": "8c950b91dac6ac8d0421b14018cd380f8ef036bdfbeeedef944d4e38b4f405b8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 422, + 285, + 498 + ], + "blocks": [ + { + "bbox": [ + 46, + 392, + 287, + 414 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 414 + ], + "type": "text", + "content": "Table 3. Ablations. In this table we show the ablations of " + }, + { + "bbox": [ + 46, + 392, + 287, + 414 + ], + "type": "inline_equation", + "content": "RM" + }, + { + "bbox": [ + 46, + 392, + 287, + 414 + ], + "type": "text", + "content": "-LVQA, evaluated on VQA-CP v2 test & VQA v2 val." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 422, + 285, + 498 + ], + "lines": [ + { + "bbox": [ + 50, + 422, + 285, + 498 + ], + "spans": [ + { + "bbox": [ + 50, + 422, + 285, + 498 + ], + "type": "table", + "html": "
ModelY/NNumOthersOverallVQA v2 Val
RMLVQA-Base79.7849.6248.4957.2449.72
+Randomization83.7249.4748.3157.9756.84
+Bias Injection88.2744.1348.5559.4460.49
+Learnable Margin88.0646.6348.7459.8759.60
+SupCon Loss89.9845.9648.7460.4159.99
-Backprop89.3640.5647.8058.8059.67
", + "image_path": "136b7b08fa856e504691de1fa6dfa5e3ce86f39f1538d2cf44c619573e13ae5f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "content": "for VQA v2). The effectiveness of this component can be understood from Fig. 3, where we show the TSNE visualizations of how answers from different question types are placed in the feature space for the components of RMLVQA. Fig. 3(a) shows that while for some question types like 'how many', 'are', answers are well separated, some others like 'do', 'are they', 'is there' are close, out of which some are entangled. Although the randomization increases flexibility of the adaptive margins, it does not disentangle these question types, as seen in Fig. 3b. Finally, in Fig. 3(c), we see that the bias-injecting component aids in separating the answers according to their question types. This is because the bias sources of VQA-CP is its question types, and hence this component clusters samples in the training set based on the same. This is crucial, as with more entanglement, the model tends to answer questions of one question type with" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 362, + 76, + 521, + 200 + ], + "blocks": [ + { + "bbox": [ + 362, + 76, + 521, + 200 + ], + "lines": [ + { + "bbox": [ + 362, + 76, + 521, + 200 + ], + "spans": [ + { + "bbox": [ + 362, + 76, + 521, + 200 + ], + "type": "image", + "image_path": "707495bf036325e7cf448736f4d3a435eb967624af6a809a28c7eadeaad65635.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "lines": [ + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "spans": [ + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "type": "text", + "content": "Figure 4. Spearman's rank correlation coefficient between " + }, + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_{\\mathrm{freq}}" + }, + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_{\\mathrm{ins}}" + }, + { + "bbox": [ + 340, + 209, + 543, + 243 + ], + "type": "text", + "content": " over epochs for question type \"how many\" on VQA-CP v2 test set" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "content": "the answers of another type. In the last row of Table 3, we also observe the effect of removing the backpropagation of the " + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "content": " loss (used to train the bias-injecting component) into the main network for VQA-CP v2. The classifier weights in the bias-injecting component learn the language bias in the dataset and backpropagate the same into the network, thus helping the model separate the answers across different question types in the feature space. We utilize this knowledge in the inference stage, where we combine the two logit heads, thus helping the model to generalize to both " + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "inline_equation", + "content": "id" + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "inline_equation", + "content": "ood" + }, + { + "bbox": [ + 304, + 258, + 545, + 389 + ], + "type": "text", + "content": " test data, as is evident from Tables 1 and 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 389, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 425 + ], + "type": "text", + "content": "Role of the SupCon Loss. The addition of the SupCon loss is shown to improve the performance of our model empirically for both VQA-CP and VQA v2 as shown in Table 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 430, + 378, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 378, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 378, + 442 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "text", + "content": "Although margin-based losses are useful in mitigating language biases in VQA, they may not distinguish between answers of different task-complexity levels in the feature space. To distinguish between samples having similar answer frequency, but different complexity, we learn instance-based margins for each sample from the model during training. We introduce a bias-injecting component in our model and utilize its confidence in answer prediction as the instance-level margins. Being trained by the " + }, + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "text", + "content": " loss, this component further clusters the training samples based on the source of the data bias, guiding the margin loss to distinguish frequent and rare answers inside each cluster. We ensemble the outputs of the bias-injecting component with those of the main model during inference to achieve state-of-the-art results among existing augmentation-free methods on the ood VQA-CP v2 dataset, while being the most robust with respect to both id and ood test sets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 662, + 415, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 662, + 415, + 675 + ], + "spans": [ + { + "bbox": [ + 306, + 662, + 415, + 675 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by a research grant (CRG/2021/005925) from SERB, DST, Govt. of India. 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Our diffusion model, RODIN, can produce high-fidelity 3D avatars (the first row). Our model also supports 3D avatar generation from a single portrait or text prompt, while permitting text-based semantic manipulation (second row). See the webpage for video demos." + ], + "image_footnote": [], + "bbox": [ + 84, + 243, + 607, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/711315261932b2e61905e94b43bc22d680005cd0dfd29f26d9f58b6a6384df24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 246, + 888, + 443 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 497, + 313, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper presents a 3D diffusion model that automatically generates 3D digital avatars represented as neural radiance fields (NeRFs). A significant challenge for 3D diffusion is that the memory and processing costs are prohibitive for producing high-quality results with rich details. To tackle this problem, we propose the roll-out diffusion network (RODIN), which takes a 3D NeRF model represented as multiple 2D feature maps and rolls out them onto a single 2D feature plane within which we perform 3D-aware diffusion. The RODIN model brings much-needed computational efficiency while preserving the integrity of 3D diffusion by using 3D-aware convolution that attends to projected features in the 2D plane according to their original relationships in 3D. We also use latent conditioning to orchestrate the feature generation with global coherence, leading to high-fidelity avatars and enabling semantic editing based on text prompts. Finally, we use hierarchical synthesis to further enhance details. The 3D avatars generated by our model compare favorably with those produced by existing techniques. We can generate highly detailed avatars with realistic hairstyles and facial hair. We also demonstrate 3D avatar generation from image or text, as well as text-guided editability.", + "bbox": [ + 73, + 518, + 473, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 497, + 632, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative models [2, 34] are one of the most promising ways to analyze and synthesize visual data including 2D images and 3D models. At the forefront of generative modeling is the diffusion model [14, 24, 61], which has shown phenomenal generative power for images [19,47,50,52] and videos [23,59]. Indeed, we are witnessing a 2D content creation revolution driven by the rapid advances of diffusion and generative modeling. In this paper, we aim to expand the applicability of diffusion to 3D digital avatars. We use \"digital avatars\" to refer to the traditional avatars manually created by 3D artists, as opposed to the recently emerging photorealistic avatars [8, 43]. The reason for focusing on digital avatars is twofold. On the one hand, digital avatars are widely used in movies, games, the metaverse, and the 3D industry in general. On the other hand, the available digital avatar data is very scarce as each avatar must be painstakingly created by a specialized 3D artist using a sophisticated creation pipeline [20, 35], especially for modeling hair and facial hair. All this leads to a compelling scenario for generative modeling.", + "bbox": [ + 496, + 530, + 893, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a diffusion model for automatically producing digital avatars represented as NeRFs [38], with each point describing its color radiance and density within the 3D volume. The core challenge in generating these avatars", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Intern at Microsoft Research. ‡Corresponding author. *Equal contribution. Project Webpage: https://3d-ayar-diffusion.microsoft.com", + "bbox": [ + 75, + 875, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4563", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "is the prohibitive memory and computational cost required by high-quality avatars with rich details. Without rich details, an avatar will always be somewhat \"toy-like\". To tackle this challenge, we develop RODIN, the roll-out diffusion network. We take a NeRF model represented as multiple 2D feature maps and roll out these maps onto a single 2D feature plane and perform 3D-aware diffusion within this plane. Specifically, we use the tri-plane representation [9], which represents a volume by three orthogonal feature planes. By simply rolling out the feature maps, RODIN can perform 3D-aware diffusion using an efficient 2D architecture and by drawing power from RODIN's three key ingredients.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first is the 3D-aware convolution. The 2D CNN processing used in conventional 2D diffusion cannot effectively handle feature maps originating from orthogonal planes. Rather than treating the features as plain 2D input, the 3D-aware convolution explicitly accounts for the fact that a 2D feature in one plane (of the tri-plane) is a projection from a piece of 3D data and is hence intrinsically associated with the same data's projected features in the other two planes. To encourage cross-plane communication, we involve all these associated features in the convolution and synchronize their detail synthesis according to their 3D relationship.", + "bbox": [ + 75, + 289, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second ingredient is latent conditioning. We use a latent vector to orchestrate the feature generation so that it is globally coherent in 3D, leading to better quality avatars and enabling semantic editing. We do this by using the avatars in the training dataset to train an additional image encoder which extracts a semantic latent vector serving as the conditional input to the diffusion model. This latent conditioning essentially acts as an autoencoder in orchestrating the feature generation. For semantic editability, we adopt a frozen CLIP image encoder [46] that shares the latent space with text prompts.", + "bbox": [ + 75, + 473, + 472, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The final ingredient is hierarchical synthesis. We start by generating at low resolution $(64 \\times 64)$ , followed by a diffusion-based upsampling that yields a higher resolution $(256 \\times 256)$ . When training the diffusion upsampler, it is instrumental to penalize the image-level loss that we compute in a patch-wise manner.", + "bbox": [ + 75, + 641, + 472, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "RODIN supports several application scenarios. We can use the model to generate an unlimited number of avatars from scratch, each different from the others as well as those in the training data. As shown in Figure 1, we can generate highly detailed avatars with realistic hairstyles and facial hair styled as beards, mustaches, goatees, and sideburns. Hairstyle and facial hair are essential parts of personal identity yet have been notoriously difficult to model well with existing approaches. The RODIN model also allows avatar customization, with the resulting avatar capturing the visual characteristics of a person portrayed in an image or a textual", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "description. Finally, our framework supports text-guided semantic editing.", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work shows that 3D diffusion holds great modeling power, and this power can be effectively unleashed by rolling out the feature maps onto a 2D plane, leading to rich details, including those highly desirable but extremely difficult to produce with existing techniques. It is worth noting that while this paper focuses on RODIN's application to avatars, the design of RODIN is not avatar specific. Indeed, we believe RODIN is applicable to general 3D scenes.", + "bbox": [ + 496, + 121, + 893, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 498, + 256, + 640, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The state of generative modeling [5, 14, 15, 28, 48, 65, 75] has seen rapid progress in past years. Diffusion models [14, 24, 61, 73] have recently shown unprecedented generative ability and compositional power. The most remarkable success happens in text-to-image synthesis [19, 39, 47, 50, 52], which serves as a foundation model and enables various appealing applications [21, 51, 66] previously unattainable. While diffusion models have been successfully applied to different modalities [11, 23, 26, 32], its generative capability is much less explored in 3D generation, with only a few attempts on modeling 3D primitives [36, 74, 76].", + "bbox": [ + 496, + 281, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early 3D generation works rely on either GAN [17] or VAE [29] to model the distribution of 3D shape representation like voxel grids [6, 70], point clouds [1, 7, 31, 72], mesh [33, 63] and implicit neural representation [42, 60]. However, existing works have not demonstrated the ability to produce complex 3D assets yet. Concurrent to this work, Bautista et al. [4] train a diffusion model to generate the latent vector that encodes the radiance field [38] of synthetic scenes, yet this work only produces coarse 3D geometry. In comparison, we propose a hierarchical 3D generation framework with effective 3D-aware operators, offering unprecedented 3D detail synthesis.", + "bbox": [ + 496, + 448, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of work learns 3D-aware generation by utilizing richly available 2D data. 3D-aware GANs [9, 10, 12, 16, 18, 41, 54-58, 62, 71, 77] recently attract significant research interest, which are trained to produce radiance fields with image level distribution matching. However, these methods suffer from instabilities and mode collapse of GAN training, and it is still challenging to attain authentic avatars that can be viewed from large angles. Concurrently, there are a few attempts to use diffusion models for the problem. Daniel et al. [68] proposes to synthesize novel views with a pose-conditioned 2D diffusion model, yet the results are not intrinsically 3D. Ben et al. [45] optimizes a radiance field using the supervision from a pretrained text-to-image diffusion model and produces impressive 3D objects of diverse genres. Nonetheless, pretrained 2D generative networks only offer limited 3D knowledge and inevitably lead to blurry 3D results. A high-quality generation framework in 3D space is still highly desired.", + "bbox": [ + 496, + 628, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4564", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c1b3b408b26aa7d301635b36701041490df3b18df8cffa93b6f5cda68ac98fce.jpg", + "image_caption": [ + "Figure 2. An overview of our RODIN model. We derive the latent $z$ via the mapping from image, text, or random noise, which is used to control the base diffusion model to generate $64 \\times 64$ tri-planes. We train another diffusion model to upsample this coarse result to $256 \\times 256$ tri-planes that are used to render final multi-view images with volumetric rendering and convolutional refinement. The operators used in diffusion models are designed to be 3D-aware." + ], + "image_footnote": [], + "bbox": [ + 84, + 82, + 883, + 233 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 318, + 184, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike prior methods that learn 3D-aware generation from a 2D image collection, we aim to learn the 3D avatar generation using the multi-view renderings from the Blender synthetic pipeline [69]. Rather than treating the multi-view images of the same subject as individual training samples, we fit the volumetric neural representation for each avatar, which is used to explain all the observations from different viewpoints. Thereafter we use diffusion models to characterize the distribution of these 3D instances. Our diffusion-based 3D generation is a hierarchical process — we first utilize a diffusion model to generate the coarse geometry, followed by a diffusion upsampler for detail synthesis. As illustrated in Figure 2, the whole 3D portrait generation comprises multiple training stages, which we detail in the following subsections.", + "bbox": [ + 75, + 345, + 473, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Robust 3D Representation Fitting", + "text_level": 1, + "bbox": [ + 76, + 587, + 372, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To train a generative network with explicit 3D supervision, we need an expressive 3D representation that accounts for multi-view images, which should meet the following requirements. First, we need an explicit representation that is amenable to generative network processing. Second, we require a compact representation that is memory efficient; otherwise, it would be too costly to store a myriad of such 3D instances for training. Furthermore, we expect fast representation fitting since hours of optimization as vanilla NeRF [38] would make it unaffordable to generate abundant 3D training data as required for generative modeling.", + "bbox": [ + 75, + 611, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Taking these into consideration, we adopt tri-plane representation proposed by [9] to model the neural radiance field of 3D avatars. Specifically, the 3D volume is factorized into three axis-aligned orthogonal feature planes, denoted by $\\mathbf{y}_{uv},\\mathbf{y}_{wu},\\mathbf{y}_{vw}\\in \\mathbb{R}^{H\\times W\\times C}$ , each of which has spatial resolution of $H\\times W$ and number of channel as $C$ . Compared to voxel grids, the tri-plane representation offers a considerably smaller memory footprint without sacrificial", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f13f6f6963b0d9ba426c2c211ddf7aada4ee2a41c5ba14ea5fcb3e95836bdcd5.jpg", + "image_caption": [ + "(a) $256\\times 256$ tri-plane" + ], + "image_footnote": [], + "bbox": [ + 506, + 324, + 625, + 416 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/66b831382cd7197327decfdcf504b84477fc57b66a5a1b9c98b0294e0f380ece.jpg", + "image_caption": [ + "(b) $64\\times 64$ tri-plane without random scaling" + ], + "image_footnote": [], + "bbox": [ + 633, + 325, + 751, + 416 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c918b7c3c68f7febfa51bb39ce833cc5a3d64df65ea5196ef42d847896736eb.jpg", + "image_caption": [ + "(c) $64\\times 64$ tri-plane with random scaling", + "Figure 3. While $256 \\times 256$ tri-planes give good renderings (a), the $64 \\times 64$ variant gives much worse result (b). Hence, we introduce random scaling during fitting so as to obtain a robust representation that can be effectively rendered in continuous scales (c)." + ], + "image_footnote": [], + "bbox": [ + 759, + 325, + 880, + 416 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing the expressivity. Hence, rich 3D information is explicitly memorized in the tri-plane features, and one can query the feature of the 3D point $\\pmb{p} \\in \\mathbb{R}^3$ by projecting it onto each plane and aggregating the retrieved features, i.e., $\\pmb{y_p} = \\pmb{y}_{uv}(\\pmb{p}_{uv}) + \\pmb{y}_{wu}(\\pmb{p}_{wu}) + \\pmb{y}_{vw}(\\pmb{p}_{vw})$ . With such positional feature, one can derive the density $\\sigma \\in \\mathbb{R}^{+}$ and view-dependent color $c \\in \\mathbb{R}^3$ of each 3D location given the viewing direction $d \\in \\mathbb{S}^2$ with a lightweight MLP decoder $\\mathcal{G}_{\\theta}^{\\mathrm{MLP}}$ , which can be formulated as", + "bbox": [ + 496, + 527, + 893, + 665 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} (\\boldsymbol {p}, \\boldsymbol {d}), \\sigma (\\boldsymbol {p}) = \\mathcal {G} _ {\\theta} ^ {\\mathrm {M L P}} \\left(\\boldsymbol {y} _ {\\boldsymbol {p}}, \\xi (\\boldsymbol {y} _ {\\boldsymbol {p}}), \\boldsymbol {d}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 674, + 890, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we apply the Fourier embedding operator $\\xi (\\cdot)$ [64] on the queried feature rather than the spatial coordinate. The tri-plane features and the MLP decoder are optimized such that the rendering of the neural radiance field matches the multi-view images $\\{\\pmb {x}\\}_{N_v}$ for the given subject, where $\\pmb {x}\\in \\mathbb{R}^{H_0\\times W_0\\times 3}$ . We enforce the rendered image given by volumetric rendering [37], i.e., $\\hat{\\pmb{x}} = \\mathcal{R}(\\pmb {c},\\sigma)$ , to match the corresponding ground truth with mean squared error loss. Besides, we introduce sparse, smooth, and compact regularizers to reduce the \"floating\" artifacts [3] in free space. For more tri-plane fitting details, please refer to the Appendix.", + "bbox": [ + 496, + 703, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While prior per-scene reconstruction mainly concerns the fitting quality, our 3D fitting procedure should also con", + "bbox": [ + 498, + 871, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4565", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sider several key aspects for generation purposes. First, the tri-plane features of different subjects should rigorously reside in the same domain. To achieve this, we adopt a shared MLP decoder when fitting distinct portraits, thus implicitly pushing the tri-plane features to the shared latent space recognizable by the decoder. Second, the MLP decoder has to possess some level of robustness. That is, the decoder should be tolerant to slight perturbation of tri-plane features, and thus one can still obtain plausible results even if the tri-plane features are imperfectly generated. More importantly, the decoder should be robust to varied tri-plane sizes because hierarchical 3D generation is trained on multi-resolution tri-plane features. As shown in Figure 3, when solely fitting $256 \\times 256$ tri-planes, its $64 \\times 64$ resolution variant cannot be effectively rendered. To address this, we randomly scale the tri-plane during fitting, which is instrumental in deriving multi-resolution tri-plane features simultaneously with a shared decoder.", + "bbox": [ + 75, + 90, + 472, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Latent Conditioned 3D Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 373, + 419, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now the 3D avatar generation is reduced to learning the distribution of tri-plane features, i.e., $p(\\pmb{y})$ , where $y = (\\pmb{y}_{uv},\\pmb{y}_{wu},\\pmb{y}_{vw})$ . Such generative modeling is non-trivial since $\\pmb{y}$ is highly dimensional. We leverage diffusion models for the task, which have shown compelling quality in complex image modeling.", + "bbox": [ + 75, + 397, + 468, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "On a high level, the diffusion model generates $\\pmb{y}$ by gradually reversing a Markov forward process. Starting from $\\pmb{y}_0\\sim p(\\pmb {y})$ , the forward process $q$ yields a sequence of increasing noisy latent codes $\\{\\pmb {y}_t\\mid t\\in [0,T]\\}$ according to $\\pmb{y}_{t}:= \\alpha_{t}\\pmb{y}_{0} + \\sigma_{t}\\pmb {\\epsilon}$ , where $\\pmb {\\epsilon}\\in \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ is the added Gaussian noise; $\\alpha_{t}$ and $\\sigma_t$ define a noise schedule whose log signalto-noise ratio $\\lambda_{t} = \\log [\\alpha_{t}^{2} / \\sigma_{t}^{2}]$ linearly decreases with the timestep $t$ . With sufficient noising steps, we reach a pure Gaussian noise, i.e., $\\pmb {y}_T\\sim \\mathcal{N}(\\pmb {0},\\pmb {I})$ . The generative process corresponds to reversing the above noising process, where the diffusion model is trained to denoise $\\pmb {y}_t$ into $\\pmb{y}_0$ for all $t$ using a mean squared error loss. Following [24], better generation quality can be achieved by parameterizing the diffusion model $\\hat{\\epsilon}_{\\theta}$ to predict the added noise:", + "bbox": [ + 75, + 489, + 470, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}} \\left[ \\left\\| \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\alpha_ {t} \\boldsymbol {y} _ {0} + \\sigma_ {t} \\boldsymbol {\\epsilon}, t\\right) - \\boldsymbol {\\epsilon} \\right\\| _ {2} ^ {2} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 710, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, our diffusion model training also jointly optimizes the variational lower bound loss $\\mathcal{L}_{\\mathrm{VLB}}$ as suggested in [40], which allows high-quality generation with fewer timesteps. During inference, stochastic ancestral sampler [24] is used to generate the final samples, which starts from the Gaussian noise $\\pmb{y}_T$ and sequentially produces less noisy samples $\\{\\pmb{y}_T,\\pmb{y}_{T - 1},\\dots \\}$ until reaching $\\pmb{y}_0$ .", + "bbox": [ + 75, + 750, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first train a base diffusion model to generate the coarse-level tri-planes, e.g., at $64 \\times 64$ resolution. A straightforward approach is to adopt the 2D network struc", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dfc1a6beeabb89111d0e4ab0ecbb2781fc285377fc860407863f21e55dcffc89.jpg", + "image_caption": [ + "(a)", + "Figure 4. We propose two mechanisms to ensure coherent tri-plane generation. Our 3D-aware convolution considers the 3D relationship in (a) and correlates the associated elements from separate feature planes as shown in (b). In (b), we also visualize the usage of a shared latent code to orchestrate the feature generation." + ], + "image_footnote": [], + "bbox": [ + 498, + 74, + 640, + 181 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bb17f3903a7470a654a358b6bebc391e6859b4d390bdd9aef6afbb4e9fead2fb.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 651, + 74, + 883, + 178 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ture used in the state-of-the-art image-based diffusion models for our tri-plane generation. Specifically, we can concatenate the tri-plane features in the channel dimension as in [9], which forms $\\pmb{y} = (\\pmb{y}_{uv}\\oplus \\pmb{y}_{wu}\\oplus \\pmb{y}_{vw})\\in \\mathbb{R}^{H\\times W\\times 3C}$ , and employ a well-designed 2D U-Net to model the data distribution through the denoising diffusion process. However, such a baseline model produces 3D avatars with severe artifacts. We conjecture the generation artifact comes from the incompatibility between the tri-plane representation and the 2D U-Net. As shown in Figure 4(a), intuitively, one can regard the tri-plane features as the projection of neural volume towards the frontal, bottom, and side views, respectively. Hence, the channel-wise concatenation of these orthogonal planes for CNN processing is problematic because these planes are not spatially aligned. To better handle the tri-plane representation, we make the following efforts.", + "bbox": [ + 496, + 295, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D-aware convolution. Using CNN to process channelwise concatenated tri-planes will cause the mixing of theoretically uncorrected features in terms of 3D. One simple yet effective way to address this is to spatially roll out the tri-plane features. As shown in Figure 4(b), we concatenate the tri-plane features horizontally, yielding $\\tilde{\\pmb{y}} =$ hstack $(\\pmb {y}_{uv},\\pmb {y}_{wu},\\pmb {y}_{vw})\\in \\mathbb{R}^{H\\times 3W\\times C}$ . Such feature rollout allows independent processing of feature planes. For simplicity, we subsequently use $\\pmb{y}$ to denote such input form by default. However, the tri-plane roll-out hampers crossplane communication, while the 3D generation requires the synergy of the tri-plane generation.", + "bbox": [ + 496, + 537, + 892, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To better process the tri-plane features, we need an efficient 3D operator that performs on the tri-plane rather than treating it as a plain 2D input. To achieve this, we propose 3D-aware convolution to effectively process the triplane features while respecting their 3D relationship. A point on a certain feature plane actually corresponds to an axis-aligned 3D line in the volume, which also has two corresponding line projections in other planes, as shown in Figure 4(a). The features of these corresponding locations essentially describe the same 3D primitive and should be learned synchronously. However, such a 3D relationship is neglected when employing plain 2D convolution to tri-", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4566", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "plane processing. As such, our 3D-aware convolution explicitly introduces such 3D inductive bias by attending the features of each plane to the corresponding row/column of the rest planes. In this way, we enable 3D processing capability with 2D CNNs. This 3D-aware convolution applied on the tri-plane representation, in fact, is a generic way to simplify 3D convolutions previously too costly to compute when modeling high-resolution 3D volumes.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 3D-aware convolution is depicted in Figure 4(b). Ideally, the compute for $\\mathbf{y}_{uv}$ would attend to full elements from the corresponding row/column, i.e., $\\mathbf{y}_{wu}$ and $\\mathbf{y}_{vw}$ , from other planes. For parallel computing, we simplify this and aggregate the row/column elements. Specifically, we apply the axis-wise pooling for $\\mathbf{y}_{wu}$ and $\\mathbf{y}_{vw}$ , yielding a row vector $\\mathbf{y}_{wu\\rightarrow u}\\in \\mathbb{R}^{1\\times W\\times C}$ and a column vector $\\mathbf{y}_{vw\\rightarrow v}\\in \\mathbb{R}^{H\\times 1\\times C}$ respectively. For each point of $\\mathbf{y}_{uv}$ , we can easily access the corresponding element in the aggregated vectors. We expand the aggregated vectors to the original 2D dimension (i.e., replicating the column vectors along row dimension, and vice versa) and thus derive $\\mathbf{y}_{(\\cdot)u},\\mathbf{y}_{v(\\cdot)}\\in \\mathbb{R}^{H\\times W\\times C}$ . By far, we can perform 2D convolution on the channel-wise concatenation of the feature maps, i.e., $\\mathrm{Conv2D}(\\mathbf{y}_{uv}\\oplus \\mathbf{y}_{(\\cdot)u}\\oplus \\mathbf{y}_{v(\\cdot)})$ . because $\\mathbf{y}_{uv}$ is now spatially aligned with the aggregation of the corresponding elements from other planes. The compute for $\\mathbf{y}_{vw}$ and $\\mathbf{y}_{wu}$ is conducted likewise. The 3D-aware convolution greatly enhances the cross-plane communication, and we empirically observe reduced artifacts and improved generation of thin structures like hair strands.", + "bbox": [ + 75, + 213, + 472, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Latent conditioning. We further propose to learn a latent vector to orchestrate the tri-plane generation. As shown in Figure 2, we additionally train an image encoder $\\mathcal{E}$ to extract a semantic latent vector serving as the conditional input of the base diffusion model, so essentially the whole framework is an autoencoder. To be specific, we extract the latent vector from the frontal view of each training subject, i.e., $z = \\mathcal{E}_{\\theta}(\\pmb{x}_{\\mathrm{front}})\\in \\mathbb{R}^{512}$ , and the diffusion model conditioned on $\\pmb{z}$ is trained to reconstruct the tri-plane of the same subject. We use adaptive group normalization (AdaGN) to modulate the activations of the diffusion model, where $\\pmb{z}$ is injected into every residual block, and in this way, the features of the orthogonal planes are synchronously generated according to a shared latent.", + "bbox": [ + 75, + 534, + 472, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The latent conditioning not only leads to higher generation quality but also permits a disentangled latent space, thus allowing semantic editing of generated results. To achieve better editability, we adopt a frozen CLIP image encoder [46] that has shared latent space with text prompts. We will show how the learned model produces controllable text-guided generation results.", + "bbox": [ + 75, + 747, + 470, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Another notable benefit of latent conditioning is that it allows classifier-free guidance [25], a technique typically used to boost the sampling quality in the conditional gener-", + "bbox": [ + 76, + 854, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ation. When training the diffusion model, we randomly zero the latent embedding with $20\\%$ probability, thus adapting the diffusion decoder to unconditional generation. During inference, we can steer the model toward better generation sampling according to", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) = \\lambda \\epsilon_ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) + (1 - \\lambda) \\epsilon_ {\\theta} (\\boldsymbol {y}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 178, + 890, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(\\pmb{y},\\pmb{z})$ and $\\epsilon_{\\theta}(\\pmb{y})$ are the conditional and unconditional $\\epsilon$ -predictions respectively, and $\\lambda > 0$ specifies the guidance strength.", + "bbox": [ + 496, + 205, + 890, + 251 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our latent conditioned base model thus supports both unconditional generation as well as the conditional generation that is used for portrait inversion. To account for full diversity during unconditional sampling, we additionally train a diffusion model to model the distribution of the latent $z$ , whereas the latent $y_{T}$ describes the residual variation. We include this latent diffusion model in Figure 2.", + "bbox": [ + 496, + 252, + 893, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Diffusion Tri-plane Upsampler", + "text_level": 1, + "bbox": [ + 498, + 367, + 774, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To generate high-fidelity 3D structures, we further train a diffusion super-resolution (SR) model to increase the triplane resolution from $64 \\times 64$ to $256 \\times 256$ . At this stage, the diffusion upsampler is conditioned on the low-resolution (LR) tri-plane $\\mathbf{y}^{\\mathrm{LR}}$ . Different from the base model training we parameterize the diffusion upsampler $\\mathbf{y}_{\\theta}^{\\mathrm{HR}}(\\mathbf{y}_{t}^{\\mathrm{HR}}, \\mathbf{y}^{\\mathrm{LR}}, t)$ to predict the high-resolution (HR) ground truth $\\mathbf{y}_0^{\\mathrm{HR}}$ instead of the added noise $\\epsilon$ . The 3D-aware convolution is utilized in each residual block to enhance detail synthesis.", + "bbox": [ + 496, + 390, + 893, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following prior cascaded image generation works, we apply condition augmentation to reduce the domain gap between the output from the base model and the LR conditional input for SR training. We conduct careful tuning for the tri-plane augmentation with a combination of random downsampling, Gaussian blurring and Gaussian noises, making the rendered augmented LR tri-plane resemble the base rendering output as much as possible.", + "bbox": [ + 496, + 527, + 893, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Nonetheless, we find that a tri-plane restoration with a lower $\\ell_2$ distance to the ground truth may not necessarily correspond to a satisfactory image rendering. Hence, we need to directly constrain the rendered image. Specifically, we obtain the rendered image $\\pmb{x}^{\\mathrm{HR}}\\in \\mathbb{R}^{256\\times 256\\times 3}$ from the predicted tri-plane $\\hat{\\pmb{y}}_0^{\\mathrm{HR}}$ with $\\hat{\\pmb{x}} = \\mathcal{R}(\\mathcal{G}_{\\theta}^{\\mathrm{MLP}}(\\hat{\\pmb{y}}_0^{\\mathrm{HR}}))$ , and we further penalize the perceptual loss [27] between this rendered result and the ground truth, according to", + "bbox": [ + 496, + 647, + 893, + 771 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p e r c}} = \\mathbb {E} _ {t, \\hat {\\boldsymbol {x}}} \\sum_ {l} \\| \\Psi^ {l} (\\hat {\\boldsymbol {x}}) - \\Psi^ {l} (\\boldsymbol {x}) \\| _ {2} ^ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 780, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Psi^l$ denotes the multi-level feature extraction using a pretrained VGG. Usually, the volume rendering requires stratified sampling along each ray, which is computationally prohibitive for high-resolution rendering. Hence, we compute $\\mathcal{L}_{\\mathrm{perc}}$ on random $112\\times 112$ image patches with high", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4567", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5f278f6af8d9e700b7aa0205fe34a8288bbee107b0f835041fbfe290c776f0c8.jpg", + "image_caption": [ + "Figure 5. Unconditional generation samples by our RODIN model. We visualize the mesh extracted from the generated density field." + ], + "image_footnote": [], + "bbox": [ + 91, + 84, + 877, + 292 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c88ef1d56c75134cf0defaed5e906a7893356d642c4077878284d22fac3ecf46.jpg", + "image_caption": [ + "Figure 6. Latent interpolation results for generated avatars." + ], + "image_footnote": [], + "bbox": [ + 83, + 327, + 460, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sampling importance on face region. Compared with prior 3D-aware GANs that require rendering full images, our 3D-aware SR can be easily scalable to high resolutions due to the permit of patchwise training with direct supervision.", + "bbox": [ + 75, + 513, + 468, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Modeling high-frequency detail and thin structures are particularly challenging in volumetric rendering. Thus, at this stage, we jointly train a convolution refiner [67] on our data which complements the missing details of the NeRF rendering, ultimately producing compelling $1024 \\times 1024$ image outputs.", + "bbox": [ + 75, + 575, + 470, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 684, + 209, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 709, + 294, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To train our 3D diffusion, we obtain 100K 3D avatars with a random combination of identities, expressions, hairstyles, and accessories using synthetic engine [69]. For each avatar, we render 300 multi-view images with known camera pose, which are sufficient for a high-quality radiance field reconstruction. The tri-planes for our generation have the dimension of $256 \\times 256 \\times 32$ in each feature plane. We optimize a shared MLP decoder when fitting the first 1,000 subjects. This decoder consists of 4 fully connected layers and is fixed when fitting the following subjects. Thus different subjects are fitted separately in distributed servers.", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/70f80982419a798c2637f07a15c0fcb0e8537138571ef9a202b77eb169c0e408.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Pi-GANGIRAFFEEG3DAutoencoderOurs
FID ↓78.364.640.567.426.1
", + "bbox": [ + 506, + 321, + 885, + 368 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0e99c194ed6e847f1c57655ef954cc93929ed7f39c9b8ca4d26b985e4a5e638f.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with baseline methods." + ], + "table_footnote": [], + "table_body": "
Model configurationFID↓
A. Baseline39.2
B. + Latent conditioning37.4
C. + Tri-plane roll-out28.4
D. + 3D-aware conv26.1
", + "bbox": [ + 562, + 407, + 831, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Ablation study of the proposed components.", + "bbox": [ + 537, + 500, + 854, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Both the base and upsampling diffusion networks adopt U-Net architecture to process the roll-out tri-plane features. We apply full-attention for $8^{2}$ , $16^{2}$ and $32^{2}$ scales within the network and adopt 3D-aware convolution at higher scales to enhance the details. While we generate $256^{2}$ tri-planes with the diffusion upsampler, we also render image and compute image loss at $512^{2}$ resolution, with a convolutional refinement further enhancing the details to $1024^{2}$ . For more details about the network architecture and training strategies, please refer to our Appendix.", + "bbox": [ + 496, + 532, + 890, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Unconditional Generation Results", + "text_level": 1, + "bbox": [ + 500, + 705, + 797, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 5 shows several samples generated by the RODIN model, showing the capability to synthesize high-quality 3D renderings with impressive details, e.g., glasses and hairstyle. To reflect the geometry, we extract the mesh from the generated density field using marching cubes, which demonstrates high-fidelity geometry. More uncurated samples are shown in the Appendix. We also explore the interpolation of the latent condition $z$ between two generated avatars, as shown in Figure 6, where we observe consistent high-quality interpolation results with smooth appearance transition.", + "bbox": [ + 496, + 734, + 893, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4568", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/faa47d56b5717d4a1faeeb4ba884f143131ebb75ec403dc575a420b7dca05155.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison with state-of-the-art approaches." + ], + "image_footnote": [], + "bbox": [ + 106, + 84, + 867, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison", + "text_level": 1, + "bbox": [ + 76, + 421, + 209, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with state-of-the-art 3D-aware GANs, e.g., Pi-GAN [10] and GIRAFFE [41] and EG3D [9], which learn to produce neural radiance field from 2D image supervision. Moreover, we implement an auto-encoder baseline, which leverages the multi-view supervision and reconstructs the radiance field from the latent. We differ in this baseline by using the power diffusion-based decoder with 3D-aware designs. We adapt the official implementation of prior works to 360-degree generation and retrain them using the same dataset.", + "bbox": [ + 75, + 444, + 468, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use FID score [22] to measure the quality of image renderings. As per [30], we use the features extracted from the CLIP model to compute FID, which we find better correlates the perceptual quality. Specifically, we compute the FID score using 5K generated samples. The quantitative comparison is shown in Table 1, where we see that the RODIN model induces significantly lower FID than others.", + "bbox": [ + 75, + 595, + 468, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The visual comparison in Figure 7 shows a clear quality superiority of our RODIN model over prior arts. Our method gives visually pleasing multi-view renderings with high-quality geometry, e.g., for glasses and hair, whereas 3D-aware GANs produce more artifacts due to the geometry ambiguity caused by the simple use of image supervision.", + "bbox": [ + 75, + 700, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Analysis of the RODIN model", + "text_level": 1, + "bbox": [ + 76, + 801, + 341, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Both 3D-aware convolution and latent conditioning are crucial for 3D synthesis. To prove this, we conduct the ablation study as shown in Table 2. We start from a baseline that uses a plain 2D CNN to process channel-wise concatenated tri-plane features following [9]. With latent con", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2d02a8c6b51d86a6040e06b9281fececa78e3ea608fd2ba0c417cc2177f9288.jpg", + "image_caption": [ + "Figure 8. Hierarchical generation progressively improves results." + ], + "image_footnote": [], + "bbox": [ + 516, + 412, + 875, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ditioning, we achieve a lower FID. Feeding the network with roll-out tri-plane features significantly reduces the FID score because tri-planes are no longer improperly mingled. The proposed 3D-aware convolution further improves the synthesis quality, especially for thin structures like hair and cloth texture. More visual results regarding these ablations can be found in the Appendix.", + "bbox": [ + 496, + 547, + 890, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hierarchical generation is critical for high-fidelity results. One significant benefit of this approach is that we can train different diffusion models dedicated to different scales in a supervised manner, as opposed to end-to-end synthesis with image loss. This also enables patch-wise training without the need to render full images. Thus hierarchical training allows high-resolution avatar generation without suffering the prohibitive memory issue. Figure 8 shows the progressive quality improvement after the base diffusion, diffusion upsampler, and convolution refinement, respectively. It can be seen that the diffusion upsampler is critical, largely enhancing the synthesis quality, while convolution refinement further adds delicate details.", + "bbox": [ + 496, + 656, + 892, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Diffusion upsampling training strategies. When training the tri-plane upsampler, we parameterize the model to predict the clean tri-plane ground truth at each diffusion re", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4569", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c57edd550fba1b4d1375dd2810ba4c0be6249f05d92dee1d2d7cff7d7d1e178.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 84, + 184, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6cc15b83433bd030f263b0869141497161b0b7612c6ccb540fb6642fe41cbe7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 95, + 277, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/692276c26fba94f707cbefa2b67f99e71bb9e00a9e5230473685a1728ac5f93e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 101, + 369, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6cbdfb1a54cec59a117f49349a6f5948704add05141689040a61d7b0f7d8d632.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 85, + 486, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a41c1e5ee158d94b05f7151ab91672ef546ca55ff79766e936157f8e4d65f32.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 589, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/140a627ac59286641c4ae7110020d7c3f41fd333b7d38230e634c6f4a1671506.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 589, + 92, + 687, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7b5d8907ddbbe8cc9595a9abf66090f837f67ee2bb7380fac440e91dc8d84511.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 90, + 797, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7ad01d61bba965df67dcfc4171bd80c167903d01dc4acb097e2aa569590211aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 90, + 895, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c60662bdfdb059181143ee47cc577e9276f02f5b2f38b034199971130724e955.jpg", + "image_caption": [ + "Figure 9. Results of (a) portrait inversion and (b) text-to-ayar generation." + ], + "image_footnote": [], + "bbox": [ + 80, + 172, + 285, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/523eb3ac45bcefaf02648589f01641ac228524b7b0b418723b0e200187275202.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 305, + 176, + 379, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/45091f4a42eefcb2c51270ec34b0a069af218666bfdcbd54d4baacbe336e73a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 174, + 486, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3b7a8cebdb78a56a75eeb2a6ee320b20d7f1c72da9dccc4e3e051a5123dc9a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 174, + 584, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc05e66fb1ddfb64b2a299e7ce46125dfbe04d920b130636b3ddc1e00eb05655.jpg", + "image_caption": [ + "\"A woman with afro hair in red wearing" + ], + "image_footnote": [], + "bbox": [ + 596, + 178, + 687, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e2c27a7e6ef49d701d30125ead58b9bf0a2b184d00f93b852bb3cc338a8bfbf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 174, + 785, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0257ec549a149d72590db861efffe3b083c165bcf85a14a8d446bafc93bcddaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 174, + 898, + 253 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a18267431b97fe1475325b575b12ac3738ed6422290569ffab3f56b7c6527b91.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Tri-plane level lossImage-level lossCond. augmentFID ↓
✓48.5
✓✓38.6
✓✓✓26.1
", + "bbox": [ + 86, + 303, + 459, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study of the tri-plane upsampling strategy.", + "bbox": [ + 91, + 380, + 450, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "version step. Meanwhile, conditioning augmentation is of great significance to let the model generalize to the coarse-level tri-plane generated from the base model. Besides, we observe enforcing image-level loss is beneficial to final perceptual quality. The effectiveness of these strategies are quantitatively justified in Table 3.", + "bbox": [ + 75, + 414, + 468, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Applications", + "text_level": 1, + "bbox": [ + 76, + 513, + 209, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3D portrait from a single image. We can hallucinate a 3D avatar from a single portrait by conditioning the base generator with the CLIP image embedding for that input image. Note that our goal is different from face/head reconstruction [13, 49], but to conveniently produce a personalized digital avatar for users. As shown in Figure 9(a), the generated avatars keep the main characteristics of the portrait, e.g., expression, hairstyle, glass wearing, etc., while being 360-degree renderable.", + "bbox": [ + 75, + 537, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Text-to-ayar generation. Another natural way to customize avatars is to use language guidance. To do this, we train a text-conditioned diffusion model to generate the CLIP image embedding used to semantically control the avatar generation. We use a subset of the LAION-400M dataset [53] containing portrait-text pairs to train this model. As shown in Figure 9(b), one can finely customize the avatars using detailed text descriptions.", + "bbox": [ + 75, + 674, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Text-based avatar customization. We can also semantically edit generated avatars using text prompts. For a generated avatar with the CLIP image embedding $z_{i}$ , we can obtain a direction $\\delta$ in the CLIP's text embedding based on prompt engineering [44]. We assume colinearity between the CLIP's image and text embedding, thus we obtain the manipulated embedding as $z_{i} + \\delta$ , which is used to con", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea871e55e466c7b8c6595de70af7790cc380db43fa935bcbe70bb99691451363.jpg", + "image_caption": [ + "Input", + "Reconstructed avatar with visualized mesh" + ], + "image_footnote": [], + "bbox": [ + 501, + 300, + 890, + 375 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1cc3004356753ac4b58d96ee8c77ba0477bb9a08c8488a5b7c5c5a5d71b44ff6.jpg", + "image_caption": [ + "\"Blond hair\"", + "\"Smiling\"", + "\"With sunglasses\"", + "\"Short hair\"", + "Figure 10. Results of text-guided avatar manipulation." + ], + "image_footnote": [], + "bbox": [ + 501, + 390, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dition the generative process. As shown in Figure 10, we can achieve a wide variety of disentangled and meaningful control faithful to the text prompt.", + "bbox": [ + 498, + 515, + 890, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 580, + 746, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented the RODIN model, a powerful generative model for 3D avatars. Like all generative models, the RODIN model can exhibit biases that are inherited from the data it has been trained on. Some of these biases will be harmful and lead to an unfair representation for the target application. We need to pay attention to the data that are fed into RODIN and gain a better understanding of the resulting biases.", + "bbox": [ + 496, + 608, + 890, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This model also allows users to customize avatars from a portrait or text, thus significantly lowering the barrier of personalized avatar creation. While this paper only focuses on avatars, the main ideas behind the RODIN model are applicable to the diffusion model for general 3D scenes. For future work, it would be fruitful to improve the sampling speed of the 3D diffusion model and study jointly leveraging the ample 2D data to mitigate the 3D data bottleneck.", + "bbox": [ + 496, + 732, + 890, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: We would like to thank Steve Lin for the paper proofreading. 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Cips-3d: A 3d-aware generator of gans based on conditionally-independent pixel synthesis. arXiv preprint arXiv:2110.09788, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 880 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4573", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RODIN_ A Generative Model for Sculpting 3D Digital Avatars Using Diffusion/39108314-e784-42b7-854a-19be46573cc4_model.json b/2023/RODIN_ A Generative Model for Sculpting 3D Digital Avatars Using Diffusion/39108314-e784-42b7-854a-19be46573cc4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9b14f27083e8ad11184252160fdf69d88fb65b37 --- /dev/null +++ b/2023/RODIN_ A Generative Model for Sculpting 3D Digital Avatars Using Diffusion/39108314-e784-42b7-854a-19be46573cc4_model.json @@ -0,0 +1,2642 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.131, + 0.88, + 0.153 + ], + "angle": 0, + "content": "RODIN: A Generative Model for Sculpting 3D Digital Avatars Using Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.18, + 0.812, + 0.199 + ], + "angle": 0, + "content": "Tengfei Wang\\(^{1*†}\\) Bo Zhang\\(^{2*‡}\\) Ting Zhang\\(^{2}\\) Shuyang Gu\\(^{2}\\) Jianmin Bao\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.201, + 0.895, + 0.237 + ], + "angle": 0, + "content": "Tadas Baltrusaitis\\(^{2}\\) Jingjing Shen\\(^{2}\\) Dong Chen\\(^{2}\\) Fang Wen\\(^{2}\\) Qifeng Chen\\(^{1}\\) Baining Guo\\(^{2}\\) \n\\(^{1}\\)HKUST \\({}^{2}\\)Microsoft Research" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.244, + 0.608, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.247, + 0.89, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.449, + 0.895, + 0.478 + ], + "angle": 0, + "content": "Figure 1. Our diffusion model, RODIN, can produce high-fidelity 3D avatars (the first row). Our model also supports 3D avatar generation from a single portrait or text prompt, while permitting text-based semantic manipulation (second row). See the webpage for video demos." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.498, + 0.314, + 0.515 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.52, + 0.474, + 0.868 + ], + "angle": 0, + "content": "This paper presents a 3D diffusion model that automatically generates 3D digital avatars represented as neural radiance fields (NeRFs). A significant challenge for 3D diffusion is that the memory and processing costs are prohibitive for producing high-quality results with rich details. To tackle this problem, we propose the roll-out diffusion network (RODIN), which takes a 3D NeRF model represented as multiple 2D feature maps and rolls out them onto a single 2D feature plane within which we perform 3D-aware diffusion. The RODIN model brings much-needed computational efficiency while preserving the integrity of 3D diffusion by using 3D-aware convolution that attends to projected features in the 2D plane according to their original relationships in 3D. We also use latent conditioning to orchestrate the feature generation with global coherence, leading to high-fidelity avatars and enabling semantic editing based on text prompts. Finally, we use hierarchical synthesis to further enhance details. The 3D avatars generated by our model compare favorably with those produced by existing techniques. We can generate highly detailed avatars with realistic hairstyles and facial hair. We also demonstrate 3D avatar generation from image or text, as well as text-guided editability." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.903 + ], + "angle": 0, + "content": "†Intern at Microsoft Research. ‡Corresponding author. *Equal contribution. Project Webpage: https://3d-ayar-diffusion.microsoft.com" + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.498, + 0.633, + 0.515 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.835 + ], + "angle": 0, + "content": "Generative models [2, 34] are one of the most promising ways to analyze and synthesize visual data including 2D images and 3D models. At the forefront of generative modeling is the diffusion model [14, 24, 61], which has shown phenomenal generative power for images [19,47,50,52] and videos [23,59]. Indeed, we are witnessing a 2D content creation revolution driven by the rapid advances of diffusion and generative modeling. In this paper, we aim to expand the applicability of diffusion to 3D digital avatars. We use \"digital avatars\" to refer to the traditional avatars manually created by 3D artists, as opposed to the recently emerging photorealistic avatars [8, 43]. The reason for focusing on digital avatars is twofold. On the one hand, digital avatars are widely used in movies, games, the metaverse, and the 3D industry in general. On the other hand, the available digital avatar data is very scarce as each avatar must be painstakingly created by a specialized 3D artist using a sophisticated creation pipeline [20, 35], especially for modeling hair and facial hair. All this leads to a compelling scenario for generative modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We present a diffusion model for automatically producing digital avatars represented as NeRFs [38], with each point describing its color radiance and density within the 3D volume. The core challenge in generating these avatars" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4563" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "is the prohibitive memory and computational cost required by high-quality avatars with rich details. Without rich details, an avatar will always be somewhat \"toy-like\". To tackle this challenge, we develop RODIN, the roll-out diffusion network. We take a NeRF model represented as multiple 2D feature maps and roll out these maps onto a single 2D feature plane and perform 3D-aware diffusion within this plane. Specifically, we use the tri-plane representation [9], which represents a volume by three orthogonal feature planes. By simply rolling out the feature maps, RODIN can perform 3D-aware diffusion using an efficient 2D architecture and by drawing power from RODIN's three key ingredients." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.473, + 0.472 + ], + "angle": 0, + "content": "The first is the 3D-aware convolution. The 2D CNN processing used in conventional 2D diffusion cannot effectively handle feature maps originating from orthogonal planes. Rather than treating the features as plain 2D input, the 3D-aware convolution explicitly accounts for the fact that a 2D feature in one plane (of the tri-plane) is a projection from a piece of 3D data and is hence intrinsically associated with the same data's projected features in the other two planes. To encourage cross-plane communication, we involve all these associated features in the convolution and synchronize their detail synthesis according to their 3D relationship." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.473, + 0.64 + ], + "angle": 0, + "content": "The second ingredient is latent conditioning. We use a latent vector to orchestrate the feature generation so that it is globally coherent in 3D, leading to better quality avatars and enabling semantic editing. We do this by using the avatars in the training dataset to train an additional image encoder which extracts a semantic latent vector serving as the conditional input to the diffusion model. This latent conditioning essentially acts as an autoencoder in orchestrating the feature generation. For semantic editability, we adopt a frozen CLIP image encoder [46] that shares the latent space with text prompts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.473, + 0.735 + ], + "angle": 0, + "content": "The final ingredient is hierarchical synthesis. We start by generating at low resolution \\((64 \\times 64)\\), followed by a diffusion-based upsampling that yields a higher resolution \\((256 \\times 256)\\). When training the diffusion upsampler, it is instrumental to penalize the image-level loss that we compute in a patch-wise manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "RODIN supports several application scenarios. We can use the model to generate an unlimited number of avatars from scratch, each different from the others as well as those in the training data. As shown in Figure 1, we can generate highly detailed avatars with realistic hairstyles and facial hair styled as beards, mustaches, goatees, and sideburns. Hairstyle and facial hair are essential parts of personal identity yet have been notoriously difficult to model well with existing approaches. The RODIN model also allows avatar customization, with the resulting avatar capturing the visual characteristics of a person portrayed in an image or a textual" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "description. Finally, our framework supports text-guided semantic editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.244 + ], + "angle": 0, + "content": "Our work shows that 3D diffusion holds great modeling power, and this power can be effectively unleashed by rolling out the feature maps onto a 2D plane, leading to rich details, including those highly desirable but extremely difficult to produce with existing techniques. It is worth noting that while this paper focuses on RODIN's application to avatars, the design of RODIN is not avatar specific. Indeed, we believe RODIN is applicable to general 3D scenes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.257, + 0.642, + 0.273 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.448 + ], + "angle": 0, + "content": "The state of generative modeling [5, 14, 15, 28, 48, 65, 75] has seen rapid progress in past years. Diffusion models [14, 24, 61, 73] have recently shown unprecedented generative ability and compositional power. The most remarkable success happens in text-to-image synthesis [19, 39, 47, 50, 52], which serves as a foundation model and enables various appealing applications [21, 51, 66] previously unattainable. While diffusion models have been successfully applied to different modalities [11, 23, 26, 32], its generative capability is much less explored in 3D generation, with only a few attempts on modeling 3D primitives [36, 74, 76]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Early 3D generation works rely on either GAN [17] or VAE [29] to model the distribution of 3D shape representation like voxel grids [6, 70], point clouds [1, 7, 31, 72], mesh [33, 63] and implicit neural representation [42, 60]. However, existing works have not demonstrated the ability to produce complex 3D assets yet. Concurrent to this work, Bautista et al. [4] train a diffusion model to generate the latent vector that encodes the radiance field [38] of synthetic scenes, yet this work only produces coarse 3D geometry. In comparison, we propose a hierarchical 3D generation framework with effective 3D-aware operators, offering unprecedented 3D detail synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Another line of work learns 3D-aware generation by utilizing richly available 2D data. 3D-aware GANs [9, 10, 12, 16, 18, 41, 54-58, 62, 71, 77] recently attract significant research interest, which are trained to produce radiance fields with image level distribution matching. However, these methods suffer from instabilities and mode collapse of GAN training, and it is still challenging to attain authentic avatars that can be viewed from large angles. Concurrently, there are a few attempts to use diffusion models for the problem. Daniel et al. [68] proposes to synthesize novel views with a pose-conditioned 2D diffusion model, yet the results are not intrinsically 3D. Ben et al. [45] optimizes a radiance field using the supervision from a pretrained text-to-image diffusion model and produces impressive 3D objects of diverse genres. Nonetheless, pretrained 2D generative networks only offer limited 3D knowledge and inevitably lead to blurry 3D results. A high-quality generation framework in 3D space is still highly desired." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4564" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.083, + 0.885, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.238, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Figure 2. An overview of our RODIN model. We derive the latent \\( z \\) via the mapping from image, text, or random noise, which is used to control the base diffusion model to generate \\( 64 \\times 64 \\) tri-planes. We train another diffusion model to upsample this coarse result to \\( 256 \\times 256 \\) tri-planes that are used to render final multi-view images with volumetric rendering and convolutional refinement. The operators used in diffusion models are designed to be 3D-aware." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.319, + 0.186, + 0.337 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.346, + 0.474, + 0.574 + ], + "angle": 0, + "content": "Unlike prior methods that learn 3D-aware generation from a 2D image collection, we aim to learn the 3D avatar generation using the multi-view renderings from the Blender synthetic pipeline [69]. Rather than treating the multi-view images of the same subject as individual training samples, we fit the volumetric neural representation for each avatar, which is used to explain all the observations from different viewpoints. Thereafter we use diffusion models to characterize the distribution of these 3D instances. Our diffusion-based 3D generation is a hierarchical process — we first utilize a diffusion model to generate the coarse geometry, followed by a diffusion upsampler for detail synthesis. As illustrated in Figure 2, the whole 3D portrait generation comprises multiple training stages, which we detail in the following subsections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.373, + 0.604 + ], + "angle": 0, + "content": "3.1. Robust 3D Representation Fitting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.779 + ], + "angle": 0, + "content": "To train a generative network with explicit 3D supervision, we need an expressive 3D representation that accounts for multi-view images, which should meet the following requirements. First, we need an explicit representation that is amenable to generative network processing. Second, we require a compact representation that is memory efficient; otherwise, it would be too costly to store a myriad of such 3D instances for training. Furthermore, we expect fast representation fitting since hours of optimization as vanilla NeRF [38] would make it unaffordable to generate abundant 3D training data as required for generative modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Taking these into consideration, we adopt tri-plane representation proposed by [9] to model the neural radiance field of 3D avatars. Specifically, the 3D volume is factorized into three axis-aligned orthogonal feature planes, denoted by \\(\\mathbf{y}_{uv},\\mathbf{y}_{wu},\\mathbf{y}_{vw}\\in \\mathbb{R}^{H\\times W\\times C}\\), each of which has spatial resolution of \\(H\\times W\\) and number of channel as \\(C\\). Compared to voxel grids, the tri-plane representation offers a considerably smaller memory footprint without sacrificial" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.325, + 0.627, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.419, + 0.627, + 0.43 + ], + "angle": 0, + "content": "(a) \\(256\\times 256\\) tri-plane" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.326, + 0.753, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.419, + 0.753, + 0.44 + ], + "angle": 0, + "content": "(b) \\(64\\times 64\\) tri-plane without random scaling" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.326, + 0.881, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.772, + 0.419, + 0.875, + 0.44 + ], + "angle": 0, + "content": "(c) \\(64\\times 64\\) tri-plane with random scaling" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.503 + ], + "angle": 0, + "content": "Figure 3. While \\(256 \\times 256\\) tri-planes give good renderings (a), the \\(64 \\times 64\\) variant gives much worse result (b). Hence, we introduce random scaling during fitting so as to obtain a robust representation that can be effectively rendered in continuous scales (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.666 + ], + "angle": 0, + "content": "ing the expressivity. Hence, rich 3D information is explicitly memorized in the tri-plane features, and one can query the feature of the 3D point \\( \\pmb{p} \\in \\mathbb{R}^3 \\) by projecting it onto each plane and aggregating the retrieved features, i.e., \\( \\pmb{y_p} = \\pmb{y}_{uv}(\\pmb{p}_{uv}) + \\pmb{y}_{wu}(\\pmb{p}_{wu}) + \\pmb{y}_{vw}(\\pmb{p}_{vw}) \\). With such positional feature, one can derive the density \\( \\sigma \\in \\mathbb{R}^{+} \\) and view-dependent color \\( c \\in \\mathbb{R}^3 \\) of each 3D location given the viewing direction \\( d \\in \\mathbb{S}^2 \\) with a lightweight MLP decoder \\( \\mathcal{G}_{\\theta}^{\\mathrm{MLP}} \\), which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.675, + 0.892, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} (\\boldsymbol {p}, \\boldsymbol {d}), \\sigma (\\boldsymbol {p}) = \\mathcal {G} _ {\\theta} ^ {\\mathrm {M L P}} \\left(\\boldsymbol {y} _ {\\boldsymbol {p}}, \\xi (\\boldsymbol {y} _ {\\boldsymbol {p}}), \\boldsymbol {d}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Here, we apply the Fourier embedding operator \\(\\xi (\\cdot)\\) [64] on the queried feature rather than the spatial coordinate. The tri-plane features and the MLP decoder are optimized such that the rendering of the neural radiance field matches the multi-view images \\(\\{\\pmb {x}\\}_{N_v}\\) for the given subject, where \\(\\pmb {x}\\in \\mathbb{R}^{H_0\\times W_0\\times 3}\\). We enforce the rendered image given by volumetric rendering [37], i.e., \\(\\hat{\\pmb{x}} = \\mathcal{R}(\\pmb {c},\\sigma)\\), to match the corresponding ground truth with mean squared error loss. Besides, we introduce sparse, smooth, and compact regularizers to reduce the \"floating\" artifacts [3] in free space. For more tri-plane fitting details, please refer to the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.872, + 0.892, + 0.902 + ], + "angle": 0, + "content": "While prior per-scene reconstruction mainly concerns the fitting quality, our 3D fitting procedure should also con" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4565" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "sider several key aspects for generation purposes. First, the tri-plane features of different subjects should rigorously reside in the same domain. To achieve this, we adopt a shared MLP decoder when fitting distinct portraits, thus implicitly pushing the tri-plane features to the shared latent space recognizable by the decoder. Second, the MLP decoder has to possess some level of robustness. That is, the decoder should be tolerant to slight perturbation of tri-plane features, and thus one can still obtain plausible results even if the tri-plane features are imperfectly generated. More importantly, the decoder should be robust to varied tri-plane sizes because hierarchical 3D generation is trained on multi-resolution tri-plane features. As shown in Figure 3, when solely fitting \\(256 \\times 256\\) tri-planes, its \\(64 \\times 64\\) resolution variant cannot be effectively rendered. To address this, we randomly scale the tri-plane during fitting, which is instrumental in deriving multi-resolution tri-plane features simultaneously with a shared decoder." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.374, + 0.42, + 0.39 + ], + "angle": 0, + "content": "3.2. Latent Conditioned 3D Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.47, + 0.489 + ], + "angle": 0, + "content": "Now the 3D avatar generation is reduced to learning the distribution of tri-plane features, i.e., \\( p(\\pmb{y}) \\), where \\( y = (\\pmb{y}_{uv},\\pmb{y}_{wu},\\pmb{y}_{vw}) \\). Such generative modeling is non-trivial since \\( \\pmb{y} \\) is highly dimensional. We leverage diffusion models for the task, which have shown compelling quality in complex image modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.471, + 0.701 + ], + "angle": 0, + "content": "On a high level, the diffusion model generates \\(\\pmb{y}\\) by gradually reversing a Markov forward process. Starting from \\(\\pmb{y}_0\\sim p(\\pmb {y})\\) , the forward process \\(q\\) yields a sequence of increasing noisy latent codes \\(\\{\\pmb {y}_t\\mid t\\in [0,T]\\}\\) according to \\(\\pmb{y}_{t}:= \\alpha_{t}\\pmb{y}_{0} + \\sigma_{t}\\pmb {\\epsilon}\\) , where \\(\\pmb {\\epsilon}\\in \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) is the added Gaussian noise; \\(\\alpha_{t}\\) and \\(\\sigma_t\\) define a noise schedule whose log signalto-noise ratio \\(\\lambda_{t} = \\log [\\alpha_{t}^{2} / \\sigma_{t}^{2}]\\) linearly decreases with the timestep \\(t\\) . With sufficient noising steps, we reach a pure Gaussian noise, i.e., \\(\\pmb {y}_T\\sim \\mathcal{N}(\\pmb {0},\\pmb {I})\\) . The generative process corresponds to reversing the above noising process, where the diffusion model is trained to denoise \\(\\pmb {y}_t\\) into \\(\\pmb{y}_0\\) for all \\(t\\) using a mean squared error loss. Following [24], better generation quality can be achieved by parameterizing the diffusion model \\(\\hat{\\epsilon}_{\\theta}\\) to predict the added noise:" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.712, + 0.47, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}} \\left[ \\left\\| \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\alpha_ {t} \\boldsymbol {y} _ {0} + \\sigma_ {t} \\boldsymbol {\\epsilon}, t\\right) - \\boldsymbol {\\epsilon} \\right\\| _ {2} ^ {2} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.856 + ], + "angle": 0, + "content": "In practice, our diffusion model training also jointly optimizes the variational lower bound loss \\(\\mathcal{L}_{\\mathrm{VLB}}\\) as suggested in [40], which allows high-quality generation with fewer timesteps. During inference, stochastic ancestral sampler [24] is used to generate the final samples, which starts from the Gaussian noise \\(\\pmb{y}_T\\) and sequentially produces less noisy samples \\(\\{\\pmb{y}_T,\\pmb{y}_{T - 1},\\dots \\}\\) until reaching \\(\\pmb{y}_0\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We first train a base diffusion model to generate the coarse-level tri-planes, e.g., at \\(64 \\times 64\\) resolution. A straightforward approach is to adopt the 2D network struc" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.075, + 0.642, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.184, + 0.582, + 0.194 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.075, + 0.885, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.183, + 0.779, + 0.194 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.199, + 0.894, + 0.269 + ], + "angle": 0, + "content": "Figure 4. We propose two mechanisms to ensure coherent tri-plane generation. Our 3D-aware convolution considers the 3D relationship in (a) and correlates the associated elements from separate feature planes as shown in (b). In (b), we also visualize the usage of a shared latent code to orchestrate the feature generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.538 + ], + "angle": 0, + "content": "ture used in the state-of-the-art image-based diffusion models for our tri-plane generation. Specifically, we can concatenate the tri-plane features in the channel dimension as in [9], which forms \\(\\pmb{y} = (\\pmb{y}_{uv}\\oplus \\pmb{y}_{wu}\\oplus \\pmb{y}_{vw})\\in \\mathbb{R}^{H\\times W\\times 3C}\\), and employ a well-designed 2D U-Net to model the data distribution through the denoising diffusion process. However, such a baseline model produces 3D avatars with severe artifacts. We conjecture the generation artifact comes from the incompatibility between the tri-plane representation and the 2D U-Net. As shown in Figure 4(a), intuitively, one can regard the tri-plane features as the projection of neural volume towards the frontal, bottom, and side views, respectively. Hence, the channel-wise concatenation of these orthogonal planes for CNN processing is problematic because these planes are not spatially aligned. To better handle the tri-plane representation, we make the following efforts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.893, + 0.719 + ], + "angle": 0, + "content": "3D-aware convolution. Using CNN to process channelwise concatenated tri-planes will cause the mixing of theoretically uncorrected features in terms of 3D. One simple yet effective way to address this is to spatially roll out the tri-plane features. As shown in Figure 4(b), we concatenate the tri-plane features horizontally, yielding \\(\\tilde{\\pmb{y}} =\\) hstack \\((\\pmb {y}_{uv},\\pmb {y}_{wu},\\pmb {y}_{vw})\\in \\mathbb{R}^{H\\times 3W\\times C}\\). Such feature rollout allows independent processing of feature planes. For simplicity, we subsequently use \\(\\pmb{y}\\) to denote such input form by default. However, the tri-plane roll-out hampers crossplane communication, while the 3D generation requires the synergy of the tri-plane generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To better process the tri-plane features, we need an efficient 3D operator that performs on the tri-plane rather than treating it as a plain 2D input. To achieve this, we propose 3D-aware convolution to effectively process the triplane features while respecting their 3D relationship. A point on a certain feature plane actually corresponds to an axis-aligned 3D line in the volume, which also has two corresponding line projections in other planes, as shown in Figure 4(a). The features of these corresponding locations essentially describe the same 3D primitive and should be learned synchronously. However, such a 3D relationship is neglected when employing plain 2D convolution to tri-" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4566" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "plane processing. As such, our 3D-aware convolution explicitly introduces such 3D inductive bias by attending the features of each plane to the corresponding row/column of the rest planes. In this way, we enable 3D processing capability with 2D CNNs. This 3D-aware convolution applied on the tri-plane representation, in fact, is a generic way to simplify 3D convolutions previously too costly to compute when modeling high-resolution 3D volumes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.473, + 0.532 + ], + "angle": 0, + "content": "The 3D-aware convolution is depicted in Figure 4(b). Ideally, the compute for \\( \\mathbf{y}_{uv} \\) would attend to full elements from the corresponding row/column, i.e., \\( \\mathbf{y}_{wu} \\) and \\( \\mathbf{y}_{vw} \\), from other planes. For parallel computing, we simplify this and aggregate the row/column elements. Specifically, we apply the axis-wise pooling for \\( \\mathbf{y}_{wu} \\) and \\( \\mathbf{y}_{vw} \\), yielding a row vector \\( \\mathbf{y}_{wu\\rightarrow u}\\in \\mathbb{R}^{1\\times W\\times C} \\) and a column vector \\( \\mathbf{y}_{vw\\rightarrow v}\\in \\mathbb{R}^{H\\times 1\\times C} \\) respectively. For each point of \\( \\mathbf{y}_{uv} \\), we can easily access the corresponding element in the aggregated vectors. We expand the aggregated vectors to the original 2D dimension (i.e., replicating the column vectors along row dimension, and vice versa) and thus derive \\( \\mathbf{y}_{(\\cdot)u},\\mathbf{y}_{v(\\cdot)}\\in \\mathbb{R}^{H\\times W\\times C} \\). By far, we can perform 2D convolution on the channel-wise concatenation of the feature maps, i.e., \\( \\mathrm{Conv2D}(\\mathbf{y}_{uv}\\oplus \\mathbf{y}_{(\\cdot)u}\\oplus \\mathbf{y}_{v(\\cdot)}) \\). because \\( \\mathbf{y}_{uv} \\) is now spatially aligned with the aggregation of the corresponding elements from other planes. The compute for \\( \\mathbf{y}_{vw} \\) and \\( \\mathbf{y}_{wu} \\) is conducted likewise. The 3D-aware convolution greatly enhances the cross-plane communication, and we empirically observe reduced artifacts and improved generation of thin structures like hair strands." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.473, + 0.746 + ], + "angle": 0, + "content": "Latent conditioning. We further propose to learn a latent vector to orchestrate the tri-plane generation. As shown in Figure 2, we additionally train an image encoder \\(\\mathcal{E}\\) to extract a semantic latent vector serving as the conditional input of the base diffusion model, so essentially the whole framework is an autoencoder. To be specific, we extract the latent vector from the frontal view of each training subject, i.e., \\(z = \\mathcal{E}_{\\theta}(\\pmb{x}_{\\mathrm{front}})\\in \\mathbb{R}^{512}\\), and the diffusion model conditioned on \\(\\pmb{z}\\) is trained to reconstruct the tri-plane of the same subject. We use adaptive group normalization (AdaGN) to modulate the activations of the diffusion model, where \\(\\pmb{z}\\) is injected into every residual block, and in this way, the features of the orthogonal planes are synchronously generated according to a shared latent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.472, + 0.854 + ], + "angle": 0, + "content": "The latent conditioning not only leads to higher generation quality but also permits a disentangled latent space, thus allowing semantic editing of generated results. To achieve better editability, we adopt a frozen CLIP image encoder [46] that has shared latent space with text prompts. We will show how the learned model produces controllable text-guided generation results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Another notable benefit of latent conditioning is that it allows classifier-free guidance [25], a technique typically used to boost the sampling quality in the conditional gener-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "ation. When training the diffusion model, we randomly zero the latent embedding with \\(20\\%\\) probability, thus adapting the diffusion decoder to unconditional generation. During inference, we can steer the model toward better generation sampling according to" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.179, + 0.892, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} _ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) = \\lambda \\epsilon_ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) + (1 - \\lambda) \\epsilon_ {\\theta} (\\boldsymbol {y}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.207, + 0.892, + 0.252 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(\\pmb{y},\\pmb{z})\\) and \\(\\epsilon_{\\theta}(\\pmb{y})\\) are the conditional and unconditional \\(\\epsilon\\)-predictions respectively, and \\(\\lambda > 0\\) specifies the guidance strength." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.359 + ], + "angle": 0, + "content": "Our latent conditioned base model thus supports both unconditional generation as well as the conditional generation that is used for portrait inversion. To account for full diversity during unconditional sampling, we additionally train a diffusion model to model the distribution of the latent \\( z \\), whereas the latent \\( y_{T} \\) describes the residual variation. We include this latent diffusion model in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.368, + 0.776, + 0.385 + ], + "angle": 0, + "content": "3.3. Diffusion Tri-plane Upsampler" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.895, + 0.527 + ], + "angle": 0, + "content": "To generate high-fidelity 3D structures, we further train a diffusion super-resolution (SR) model to increase the triplane resolution from \\(64 \\times 64\\) to \\(256 \\times 256\\). At this stage, the diffusion upsampler is conditioned on the low-resolution (LR) tri-plane \\(\\mathbf{y}^{\\mathrm{LR}}\\). Different from the base model training we parameterize the diffusion upsampler \\(\\mathbf{y}_{\\theta}^{\\mathrm{HR}}(\\mathbf{y}_{t}^{\\mathrm{HR}}, \\mathbf{y}^{\\mathrm{LR}}, t)\\) to predict the high-resolution (HR) ground truth \\(\\mathbf{y}_0^{\\mathrm{HR}}\\) instead of the added noise \\(\\epsilon\\). The 3D-aware convolution is utilized in each residual block to enhance detail synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Following prior cascaded image generation works, we apply condition augmentation to reduce the domain gap between the output from the base model and the LR conditional input for SR training. We conduct careful tuning for the tri-plane augmentation with a combination of random downsampling, Gaussian blurring and Gaussian noises, making the rendered augmented LR tri-plane resemble the base rendering output as much as possible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.895, + 0.772 + ], + "angle": 0, + "content": "Nonetheless, we find that a tri-plane restoration with a lower \\(\\ell_2\\) distance to the ground truth may not necessarily correspond to a satisfactory image rendering. Hence, we need to directly constrain the rendered image. Specifically, we obtain the rendered image \\(\\pmb{x}^{\\mathrm{HR}}\\in \\mathbb{R}^{256\\times 256\\times 3}\\) from the predicted tri-plane \\(\\hat{\\pmb{y}}_0^{\\mathrm{HR}}\\) with \\(\\hat{\\pmb{x}} = \\mathcal{R}(\\mathcal{G}_{\\theta}^{\\mathrm{MLP}}(\\hat{\\pmb{y}}_0^{\\mathrm{HR}}))\\), and we further penalize the perceptual loss [27] between this rendered result and the ground truth, according to" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.781, + 0.892, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p e r c}} = \\mathbb {E} _ {t, \\hat {\\boldsymbol {x}}} \\sum_ {l} \\| \\Psi^ {l} (\\hat {\\boldsymbol {x}}) - \\Psi^ {l} (\\boldsymbol {x}) \\| _ {2} ^ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\Psi^l\\) denotes the multi-level feature extraction using a pretrained VGG. Usually, the volume rendering requires stratified sampling along each ray, which is computationally prohibitive for high-resolution rendering. Hence, we compute \\(\\mathcal{L}_{\\mathrm{perc}}\\) on random \\(112\\times 112\\) image patches with high" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4567" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.085, + 0.878, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.295, + 0.878, + 0.311 + ], + "angle": 0, + "content": "Figure 5. Unconditional generation samples by our RODIN model. We visualize the mesh extracted from the generated density field." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.328, + 0.462, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.471, + 0.449, + 0.485 + ], + "angle": 0, + "content": "Figure 6. Latent interpolation results for generated avatars." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.576 + ], + "angle": 0, + "content": "sampling importance on face region. Compared with prior 3D-aware GANs that require rendering full images, our 3D-aware SR can be easily scalable to high resolutions due to the permit of patchwise training with direct supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.471, + 0.669 + ], + "angle": 0, + "content": "Modeling high-frequency detail and thin structures are particularly challenging in volumetric rendering. Thus, at this stage, we jointly train a convolution refiner [67] on our data which complements the missing details of the NeRF rendering, ultimately producing compelling \\(1024 \\times 1024\\) image outputs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.685, + 0.21, + 0.701 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.295, + 0.726 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To train our 3D diffusion, we obtain 100K 3D avatars with a random combination of identities, expressions, hairstyles, and accessories using synthetic engine [69]. For each avatar, we render 300 multi-view images with known camera pose, which are sufficient for a high-quality radiance field reconstruction. The tri-planes for our generation have the dimension of \\(256 \\times 256 \\times 32\\) in each feature plane. We optimize a shared MLP decoder when fitting the first 1,000 subjects. This decoder consists of 4 fully connected layers and is fixed when fitting the following subjects. Thus different subjects are fitted separately in distributed servers." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.323, + 0.887, + 0.369 + ], + "angle": 0, + "content": "
Pi-GANGIRAFFEEG3DAutoencoderOurs
FID ↓78.364.640.567.426.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.527, + 0.371, + 0.866, + 0.385 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with baseline methods." + }, + { + "type": "table", + "bbox": [ + 0.563, + 0.408, + 0.832, + 0.5 + ], + "angle": 0, + "content": "
Model configurationFID↓
A. Baseline39.2
B. + Latent conditioning37.4
C. + Tri-plane roll-out28.4
D. + 3D-aware conv26.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.501, + 0.855, + 0.516 + ], + "angle": 0, + "content": "Table 2. Ablation study of the proposed components." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.685 + ], + "angle": 0, + "content": "Both the base and upsampling diffusion networks adopt U-Net architecture to process the roll-out tri-plane features. We apply full-attention for \\(8^{2}\\), \\(16^{2}\\) and \\(32^{2}\\) scales within the network and adopt 3D-aware convolution at higher scales to enhance the details. While we generate \\(256^{2}\\) tri-planes with the diffusion upsampler, we also render image and compute image loss at \\(512^{2}\\) resolution, with a convolutional refinement further enhancing the details to \\(1024^{2}\\). For more details about the network architecture and training strategies, please refer to our Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.707, + 0.798, + 0.723 + ], + "angle": 0, + "content": "4.2. Unconditional Generation Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Figure 5 shows several samples generated by the RODIN model, showing the capability to synthesize high-quality 3D renderings with impressive details, e.g., glasses and hairstyle. To reflect the geometry, we extract the mesh from the generated density field using marching cubes, which demonstrates high-fidelity geometry. More uncurated samples are shown in the Appendix. We also explore the interpolation of the latent condition \\( z \\) between two generated avatars, as shown in Figure 6, where we observe consistent high-quality interpolation results with smooth appearance transition." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4568" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.085, + 0.868, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.382, + 0.68, + 0.397 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison with state-of-the-art approaches." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.21, + 0.438 + ], + "angle": 0, + "content": "4.3. Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.596 + ], + "angle": 0, + "content": "We compare our method with state-of-the-art 3D-aware GANs, e.g., Pi-GAN [10] and GIRAFFE [41] and EG3D [9], which learn to produce neural radiance field from 2D image supervision. Moreover, we implement an auto-encoder baseline, which leverages the multi-view supervision and reconstructs the radiance field from the latent. We differ in this baseline by using the power diffusion-based decoder with 3D-aware designs. We adapt the official implementation of prior works to 360-degree generation and retrain them using the same dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.702 + ], + "angle": 0, + "content": "We use FID score [22] to measure the quality of image renderings. As per [30], we use the features extracted from the CLIP model to compute FID, which we find better correlates the perceptual quality. Specifically, we compute the FID score using 5K generated samples. The quantitative comparison is shown in Table 1, where we see that the RODIN model induces significantly lower FID than others." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.793 + ], + "angle": 0, + "content": "The visual comparison in Figure 7 shows a clear quality superiority of our RODIN model over prior arts. Our method gives visually pleasing multi-view renderings with high-quality geometry, e.g., for glasses and hair, whereas 3D-aware GANs produce more artifacts due to the geometry ambiguity caused by the simple use of image supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.342, + 0.818 + ], + "angle": 0, + "content": "4.4. Analysis of the RODIN model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Both 3D-aware convolution and latent conditioning are crucial for 3D synthesis. To prove this, we conduct the ablation study as shown in Table 2. We start from a baseline that uses a plain 2D CNN to process channel-wise concatenated tri-plane features following [9]. With latent con" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.413, + 0.877, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.513, + 0.889, + 0.527 + ], + "angle": 0, + "content": "Figure 8. Hierarchical generation progressively improves results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.655 + ], + "angle": 0, + "content": "ditioning, we achieve a lower FID. Feeding the network with roll-out tri-plane features significantly reduces the FID score because tri-planes are no longer improperly mingled. The proposed 3D-aware convolution further improves the synthesis quality, especially for thin structures like hair and cloth texture. More visual results regarding these ablations can be found in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.893, + 0.852 + ], + "angle": 0, + "content": "Hierarchical generation is critical for high-fidelity results. One significant benefit of this approach is that we can train different diffusion models dedicated to different scales in a supervised manner, as opposed to end-to-end synthesis with image loss. This also enables patch-wise training without the need to render full images. Thus hierarchical training allows high-resolution avatar generation without suffering the prohibitive memory issue. Figure 8 shows the progressive quality improvement after the base diffusion, diffusion upsampler, and convolution refinement, respectively. It can be seen that the diffusion upsampler is critical, largely enhancing the synthesis quality, while convolution refinement further adds delicate details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Diffusion upsampling training strategies. When training the tri-plane upsampler, we parameterize the model to predict the clean tri-plane ground truth at each diffusion re" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4569" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.085, + 0.185, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.097, + 0.279, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.102, + 0.37, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.086, + 0.487, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.092, + 0.59, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.093, + 0.689, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.092, + 0.798, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.091, + 0.897, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.174, + 0.287, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.178, + 0.38, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.175, + 0.488, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.175, + 0.585, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.597, + 0.179, + 0.689, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.175, + 0.787, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.175, + 0.899, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.255, + 0.902, + 0.266 + ], + "angle": 0, + "content": "\"A woman with afro hair in red wearing" + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.266, + 0.392, + 0.276 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.277, + 0.704, + 0.29 + ], + "angle": 0, + "content": "Figure 9. Results of (a) portrait inversion and (b) text-to-ayar generation." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.304, + 0.46, + 0.379 + ], + "angle": 0, + "content": "
Tri-plane level lossImage-level lossCond. augmentFID ↓
✓48.5
✓✓38.6
✓✓✓26.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.381, + 0.452, + 0.395 + ], + "angle": 0, + "content": "Table 3. Ablation study of the tri-plane upsampling strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.47, + 0.507 + ], + "angle": 0, + "content": "version step. Meanwhile, conditioning augmentation is of great significance to let the model generalize to the coarse-level tri-plane generated from the base model. Besides, we observe enforcing image-level loss is beneficial to final perceptual quality. The effectiveness of these strategies are quantitatively justified in Table 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.21, + 0.531 + ], + "angle": 0, + "content": "4.5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.469, + 0.674 + ], + "angle": 0, + "content": "3D portrait from a single image. We can hallucinate a 3D avatar from a single portrait by conditioning the base generator with the CLIP image embedding for that input image. Note that our goal is different from face/head reconstruction [13, 49], but to conveniently produce a personalized digital avatar for users. As shown in Figure 9(a), the generated avatars keep the main characteristics of the portrait, e.g., expression, hairstyle, glass wearing, etc., while being 360-degree renderable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.469, + 0.795 + ], + "angle": 0, + "content": "Text-to-ayar generation. Another natural way to customize avatars is to use language guidance. To do this, we train a text-conditioned diffusion model to generate the CLIP image embedding used to semantically control the avatar generation. We use a subset of the LAION-400M dataset [53] containing portrait-text pairs to train this model. As shown in Figure 9(b), one can finely customize the avatars using detailed text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Text-based avatar customization. We can also semantically edit generated avatars using text prompts. For a generated avatar with the CLIP image embedding \\( z_{i} \\), we can obtain a direction \\( \\delta \\) in the CLIP's text embedding based on prompt engineering [44]. We assume colinearity between the CLIP's image and text embedding, thus we obtain the manipulated embedding as \\( z_{i} + \\delta \\), which is used to con" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.301, + 0.892, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.377, + 0.571, + 0.388 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.377, + 0.849, + 0.388 + ], + "angle": 0, + "content": "Reconstructed avatar with visualized mesh" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.391, + 0.891, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.468, + 0.587, + 0.477 + ], + "angle": 0, + "content": "\"Blond hair\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.468, + 0.665, + 0.477 + ], + "angle": 0, + "content": "\"Smiling\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.699, + 0.468, + 0.79, + 0.477 + ], + "angle": 0, + "content": "\"With sunglasses\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.814, + 0.468, + 0.876, + 0.477 + ], + "angle": 0, + "content": "\"Short hair\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.48, + 0.857, + 0.494 + ], + "angle": 0, + "content": "Figure 10. Results of text-guided avatar manipulation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.516, + 0.892, + 0.561 + ], + "angle": 0, + "content": "dition the generative process. As shown in Figure 10, we can achieve a wide variety of disentangled and meaningful control faithful to the text prompt." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.748, + 0.598 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.731 + ], + "angle": 0, + "content": "We have presented the RODIN model, a powerful generative model for 3D avatars. Like all generative models, the RODIN model can exhibit biases that are inherited from the data it has been trained on. Some of these biases will be harmful and lead to an unfair representation for the target application. We need to pay attention to the data that are fed into RODIN and gain a better understanding of the resulting biases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.853 + ], + "angle": 0, + "content": "This model also allows users to customize avatars from a portrait or text, thus significantly lowering the barrier of personalized avatar creation. While this paper only focuses on avatars, the main ideas behind the RODIN model are applicable to the diffusion model for general 3D scenes. For future work, it would be fruitful to improve the sampling speed of the 3D diffusion model and study jointly leveraging the ample 2D data to mitigate the 3D data bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements: We would like to thank Steve Lin for the paper proofreading. 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Our diffusion model, RODIN, can produce high-fidelity 3D avatars (the first row). Our model also supports 3D avatar generation from a single portrait or text prompt, while permitting text-based semantic manipulation (second row). See the webpage for video demos. + +![](images/711315261932b2e61905e94b43bc22d680005cd0dfd29f26d9f58b6a6384df24.jpg) + +# Abstract + +This paper presents a 3D diffusion model that automatically generates 3D digital avatars represented as neural radiance fields (NeRFs). A significant challenge for 3D diffusion is that the memory and processing costs are prohibitive for producing high-quality results with rich details. To tackle this problem, we propose the roll-out diffusion network (RODIN), which takes a 3D NeRF model represented as multiple 2D feature maps and rolls out them onto a single 2D feature plane within which we perform 3D-aware diffusion. The RODIN model brings much-needed computational efficiency while preserving the integrity of 3D diffusion by using 3D-aware convolution that attends to projected features in the 2D plane according to their original relationships in 3D. We also use latent conditioning to orchestrate the feature generation with global coherence, leading to high-fidelity avatars and enabling semantic editing based on text prompts. Finally, we use hierarchical synthesis to further enhance details. The 3D avatars generated by our model compare favorably with those produced by existing techniques. We can generate highly detailed avatars with realistic hairstyles and facial hair. We also demonstrate 3D avatar generation from image or text, as well as text-guided editability. + +# 1. Introduction + +Generative models [2, 34] are one of the most promising ways to analyze and synthesize visual data including 2D images and 3D models. At the forefront of generative modeling is the diffusion model [14, 24, 61], which has shown phenomenal generative power for images [19,47,50,52] and videos [23,59]. Indeed, we are witnessing a 2D content creation revolution driven by the rapid advances of diffusion and generative modeling. In this paper, we aim to expand the applicability of diffusion to 3D digital avatars. We use "digital avatars" to refer to the traditional avatars manually created by 3D artists, as opposed to the recently emerging photorealistic avatars [8, 43]. The reason for focusing on digital avatars is twofold. On the one hand, digital avatars are widely used in movies, games, the metaverse, and the 3D industry in general. On the other hand, the available digital avatar data is very scarce as each avatar must be painstakingly created by a specialized 3D artist using a sophisticated creation pipeline [20, 35], especially for modeling hair and facial hair. All this leads to a compelling scenario for generative modeling. + +We present a diffusion model for automatically producing digital avatars represented as NeRFs [38], with each point describing its color radiance and density within the 3D volume. The core challenge in generating these avatars + +is the prohibitive memory and computational cost required by high-quality avatars with rich details. Without rich details, an avatar will always be somewhat "toy-like". To tackle this challenge, we develop RODIN, the roll-out diffusion network. We take a NeRF model represented as multiple 2D feature maps and roll out these maps onto a single 2D feature plane and perform 3D-aware diffusion within this plane. Specifically, we use the tri-plane representation [9], which represents a volume by three orthogonal feature planes. By simply rolling out the feature maps, RODIN can perform 3D-aware diffusion using an efficient 2D architecture and by drawing power from RODIN's three key ingredients. + +The first is the 3D-aware convolution. The 2D CNN processing used in conventional 2D diffusion cannot effectively handle feature maps originating from orthogonal planes. Rather than treating the features as plain 2D input, the 3D-aware convolution explicitly accounts for the fact that a 2D feature in one plane (of the tri-plane) is a projection from a piece of 3D data and is hence intrinsically associated with the same data's projected features in the other two planes. To encourage cross-plane communication, we involve all these associated features in the convolution and synchronize their detail synthesis according to their 3D relationship. + +The second ingredient is latent conditioning. We use a latent vector to orchestrate the feature generation so that it is globally coherent in 3D, leading to better quality avatars and enabling semantic editing. We do this by using the avatars in the training dataset to train an additional image encoder which extracts a semantic latent vector serving as the conditional input to the diffusion model. This latent conditioning essentially acts as an autoencoder in orchestrating the feature generation. For semantic editability, we adopt a frozen CLIP image encoder [46] that shares the latent space with text prompts. + +The final ingredient is hierarchical synthesis. We start by generating at low resolution $(64 \times 64)$ , followed by a diffusion-based upsampling that yields a higher resolution $(256 \times 256)$ . When training the diffusion upsampler, it is instrumental to penalize the image-level loss that we compute in a patch-wise manner. + +RODIN supports several application scenarios. We can use the model to generate an unlimited number of avatars from scratch, each different from the others as well as those in the training data. As shown in Figure 1, we can generate highly detailed avatars with realistic hairstyles and facial hair styled as beards, mustaches, goatees, and sideburns. Hairstyle and facial hair are essential parts of personal identity yet have been notoriously difficult to model well with existing approaches. The RODIN model also allows avatar customization, with the resulting avatar capturing the visual characteristics of a person portrayed in an image or a textual + +description. Finally, our framework supports text-guided semantic editing. + +Our work shows that 3D diffusion holds great modeling power, and this power can be effectively unleashed by rolling out the feature maps onto a 2D plane, leading to rich details, including those highly desirable but extremely difficult to produce with existing techniques. It is worth noting that while this paper focuses on RODIN's application to avatars, the design of RODIN is not avatar specific. Indeed, we believe RODIN is applicable to general 3D scenes. + +# 2. Related Work + +The state of generative modeling [5, 14, 15, 28, 48, 65, 75] has seen rapid progress in past years. Diffusion models [14, 24, 61, 73] have recently shown unprecedented generative ability and compositional power. The most remarkable success happens in text-to-image synthesis [19, 39, 47, 50, 52], which serves as a foundation model and enables various appealing applications [21, 51, 66] previously unattainable. While diffusion models have been successfully applied to different modalities [11, 23, 26, 32], its generative capability is much less explored in 3D generation, with only a few attempts on modeling 3D primitives [36, 74, 76]. + +Early 3D generation works rely on either GAN [17] or VAE [29] to model the distribution of 3D shape representation like voxel grids [6, 70], point clouds [1, 7, 31, 72], mesh [33, 63] and implicit neural representation [42, 60]. However, existing works have not demonstrated the ability to produce complex 3D assets yet. Concurrent to this work, Bautista et al. [4] train a diffusion model to generate the latent vector that encodes the radiance field [38] of synthetic scenes, yet this work only produces coarse 3D geometry. In comparison, we propose a hierarchical 3D generation framework with effective 3D-aware operators, offering unprecedented 3D detail synthesis. + +Another line of work learns 3D-aware generation by utilizing richly available 2D data. 3D-aware GANs [9, 10, 12, 16, 18, 41, 54-58, 62, 71, 77] recently attract significant research interest, which are trained to produce radiance fields with image level distribution matching. However, these methods suffer from instabilities and mode collapse of GAN training, and it is still challenging to attain authentic avatars that can be viewed from large angles. Concurrently, there are a few attempts to use diffusion models for the problem. Daniel et al. [68] proposes to synthesize novel views with a pose-conditioned 2D diffusion model, yet the results are not intrinsically 3D. Ben et al. [45] optimizes a radiance field using the supervision from a pretrained text-to-image diffusion model and produces impressive 3D objects of diverse genres. Nonetheless, pretrained 2D generative networks only offer limited 3D knowledge and inevitably lead to blurry 3D results. A high-quality generation framework in 3D space is still highly desired. + +![](images/c1b3b408b26aa7d301635b36701041490df3b18df8cffa93b6f5cda68ac98fce.jpg) +Figure 2. An overview of our RODIN model. We derive the latent $z$ via the mapping from image, text, or random noise, which is used to control the base diffusion model to generate $64 \times 64$ tri-planes. We train another diffusion model to upsample this coarse result to $256 \times 256$ tri-planes that are used to render final multi-view images with volumetric rendering and convolutional refinement. The operators used in diffusion models are designed to be 3D-aware. + +# 3. Approach + +Unlike prior methods that learn 3D-aware generation from a 2D image collection, we aim to learn the 3D avatar generation using the multi-view renderings from the Blender synthetic pipeline [69]. Rather than treating the multi-view images of the same subject as individual training samples, we fit the volumetric neural representation for each avatar, which is used to explain all the observations from different viewpoints. Thereafter we use diffusion models to characterize the distribution of these 3D instances. Our diffusion-based 3D generation is a hierarchical process — we first utilize a diffusion model to generate the coarse geometry, followed by a diffusion upsampler for detail synthesis. As illustrated in Figure 2, the whole 3D portrait generation comprises multiple training stages, which we detail in the following subsections. + +# 3.1. Robust 3D Representation Fitting + +To train a generative network with explicit 3D supervision, we need an expressive 3D representation that accounts for multi-view images, which should meet the following requirements. First, we need an explicit representation that is amenable to generative network processing. Second, we require a compact representation that is memory efficient; otherwise, it would be too costly to store a myriad of such 3D instances for training. Furthermore, we expect fast representation fitting since hours of optimization as vanilla NeRF [38] would make it unaffordable to generate abundant 3D training data as required for generative modeling. + +Taking these into consideration, we adopt tri-plane representation proposed by [9] to model the neural radiance field of 3D avatars. Specifically, the 3D volume is factorized into three axis-aligned orthogonal feature planes, denoted by $\mathbf{y}_{uv},\mathbf{y}_{wu},\mathbf{y}_{vw}\in \mathbb{R}^{H\times W\times C}$ , each of which has spatial resolution of $H\times W$ and number of channel as $C$ . Compared to voxel grids, the tri-plane representation offers a considerably smaller memory footprint without sacrificial + +![](images/f13f6f6963b0d9ba426c2c211ddf7aada4ee2a41c5ba14ea5fcb3e95836bdcd5.jpg) +(a) $256\times 256$ tri-plane + +![](images/66b831382cd7197327decfdcf504b84477fc57b66a5a1b9c98b0294e0f380ece.jpg) +(b) $64\times 64$ tri-plane without random scaling + +![](images/2c918b7c3c68f7febfa51bb39ce833cc5a3d64df65ea5196ef42d847896736eb.jpg) +(c) $64\times 64$ tri-plane with random scaling +Figure 3. While $256 \times 256$ tri-planes give good renderings (a), the $64 \times 64$ variant gives much worse result (b). Hence, we introduce random scaling during fitting so as to obtain a robust representation that can be effectively rendered in continuous scales (c). + +ing the expressivity. Hence, rich 3D information is explicitly memorized in the tri-plane features, and one can query the feature of the 3D point $\pmb{p} \in \mathbb{R}^3$ by projecting it onto each plane and aggregating the retrieved features, i.e., $\pmb{y_p} = \pmb{y}_{uv}(\pmb{p}_{uv}) + \pmb{y}_{wu}(\pmb{p}_{wu}) + \pmb{y}_{vw}(\pmb{p}_{vw})$ . With such positional feature, one can derive the density $\sigma \in \mathbb{R}^{+}$ and view-dependent color $c \in \mathbb{R}^3$ of each 3D location given the viewing direction $d \in \mathbb{S}^2$ with a lightweight MLP decoder $\mathcal{G}_{\theta}^{\mathrm{MLP}}$ , which can be formulated as + +$$ +\boldsymbol {c} (\boldsymbol {p}, \boldsymbol {d}), \sigma (\boldsymbol {p}) = \mathcal {G} _ {\theta} ^ {\mathrm {M L P}} \left(\boldsymbol {y} _ {\boldsymbol {p}}, \xi (\boldsymbol {y} _ {\boldsymbol {p}}), \boldsymbol {d}\right). \tag {1} +$$ + +Here, we apply the Fourier embedding operator $\xi (\cdot)$ [64] on the queried feature rather than the spatial coordinate. The tri-plane features and the MLP decoder are optimized such that the rendering of the neural radiance field matches the multi-view images $\{\pmb {x}\}_{N_v}$ for the given subject, where $\pmb {x}\in \mathbb{R}^{H_0\times W_0\times 3}$ . We enforce the rendered image given by volumetric rendering [37], i.e., $\hat{\pmb{x}} = \mathcal{R}(\pmb {c},\sigma)$ , to match the corresponding ground truth with mean squared error loss. Besides, we introduce sparse, smooth, and compact regularizers to reduce the "floating" artifacts [3] in free space. For more tri-plane fitting details, please refer to the Appendix. + +While prior per-scene reconstruction mainly concerns the fitting quality, our 3D fitting procedure should also con + +sider several key aspects for generation purposes. First, the tri-plane features of different subjects should rigorously reside in the same domain. To achieve this, we adopt a shared MLP decoder when fitting distinct portraits, thus implicitly pushing the tri-plane features to the shared latent space recognizable by the decoder. Second, the MLP decoder has to possess some level of robustness. That is, the decoder should be tolerant to slight perturbation of tri-plane features, and thus one can still obtain plausible results even if the tri-plane features are imperfectly generated. More importantly, the decoder should be robust to varied tri-plane sizes because hierarchical 3D generation is trained on multi-resolution tri-plane features. As shown in Figure 3, when solely fitting $256 \times 256$ tri-planes, its $64 \times 64$ resolution variant cannot be effectively rendered. To address this, we randomly scale the tri-plane during fitting, which is instrumental in deriving multi-resolution tri-plane features simultaneously with a shared decoder. + +# 3.2. Latent Conditioned 3D Diffusion Model + +Now the 3D avatar generation is reduced to learning the distribution of tri-plane features, i.e., $p(\pmb{y})$ , where $y = (\pmb{y}_{uv},\pmb{y}_{wu},\pmb{y}_{vw})$ . Such generative modeling is non-trivial since $\pmb{y}$ is highly dimensional. We leverage diffusion models for the task, which have shown compelling quality in complex image modeling. + +On a high level, the diffusion model generates $\pmb{y}$ by gradually reversing a Markov forward process. Starting from $\pmb{y}_0\sim p(\pmb {y})$ , the forward process $q$ yields a sequence of increasing noisy latent codes $\{\pmb {y}_t\mid t\in [0,T]\}$ according to $\pmb{y}_{t}:= \alpha_{t}\pmb{y}_{0} + \sigma_{t}\pmb {\epsilon}$ , where $\pmb {\epsilon}\in \mathcal{N}(\mathbf{0},\mathbf{I})$ is the added Gaussian noise; $\alpha_{t}$ and $\sigma_t$ define a noise schedule whose log signalto-noise ratio $\lambda_{t} = \log [\alpha_{t}^{2} / \sigma_{t}^{2}]$ linearly decreases with the timestep $t$ . With sufficient noising steps, we reach a pure Gaussian noise, i.e., $\pmb {y}_T\sim \mathcal{N}(\pmb {0},\pmb {I})$ . The generative process corresponds to reversing the above noising process, where the diffusion model is trained to denoise $\pmb {y}_t$ into $\pmb{y}_0$ for all $t$ using a mean squared error loss. Following [24], better generation quality can be achieved by parameterizing the diffusion model $\hat{\epsilon}_{\theta}$ to predict the added noise: + +$$ +\mathcal {L} _ {\text {s i m p l e}} = \mathbb {E} _ {t, \boldsymbol {x} _ {0}, \boldsymbol {\epsilon}} \left[ \left\| \hat {\boldsymbol {\epsilon}} _ {\theta} \left(\alpha_ {t} \boldsymbol {y} _ {0} + \sigma_ {t} \boldsymbol {\epsilon}, t\right) - \boldsymbol {\epsilon} \right\| _ {2} ^ {2} \right]. \tag {2} +$$ + +In practice, our diffusion model training also jointly optimizes the variational lower bound loss $\mathcal{L}_{\mathrm{VLB}}$ as suggested in [40], which allows high-quality generation with fewer timesteps. During inference, stochastic ancestral sampler [24] is used to generate the final samples, which starts from the Gaussian noise $\pmb{y}_T$ and sequentially produces less noisy samples $\{\pmb{y}_T,\pmb{y}_{T - 1},\dots \}$ until reaching $\pmb{y}_0$ . + +We first train a base diffusion model to generate the coarse-level tri-planes, e.g., at $64 \times 64$ resolution. A straightforward approach is to adopt the 2D network struc + +![](images/dfc1a6beeabb89111d0e4ab0ecbb2781fc285377fc860407863f21e55dcffc89.jpg) +(a) +Figure 4. We propose two mechanisms to ensure coherent tri-plane generation. Our 3D-aware convolution considers the 3D relationship in (a) and correlates the associated elements from separate feature planes as shown in (b). In (b), we also visualize the usage of a shared latent code to orchestrate the feature generation. + +![](images/bb17f3903a7470a654a358b6bebc391e6859b4d390bdd9aef6afbb4e9fead2fb.jpg) +(b) + +ture used in the state-of-the-art image-based diffusion models for our tri-plane generation. Specifically, we can concatenate the tri-plane features in the channel dimension as in [9], which forms $\pmb{y} = (\pmb{y}_{uv}\oplus \pmb{y}_{wu}\oplus \pmb{y}_{vw})\in \mathbb{R}^{H\times W\times 3C}$ , and employ a well-designed 2D U-Net to model the data distribution through the denoising diffusion process. However, such a baseline model produces 3D avatars with severe artifacts. We conjecture the generation artifact comes from the incompatibility between the tri-plane representation and the 2D U-Net. As shown in Figure 4(a), intuitively, one can regard the tri-plane features as the projection of neural volume towards the frontal, bottom, and side views, respectively. Hence, the channel-wise concatenation of these orthogonal planes for CNN processing is problematic because these planes are not spatially aligned. To better handle the tri-plane representation, we make the following efforts. + +3D-aware convolution. Using CNN to process channelwise concatenated tri-planes will cause the mixing of theoretically uncorrected features in terms of 3D. One simple yet effective way to address this is to spatially roll out the tri-plane features. As shown in Figure 4(b), we concatenate the tri-plane features horizontally, yielding $\tilde{\pmb{y}} =$ hstack $(\pmb {y}_{uv},\pmb {y}_{wu},\pmb {y}_{vw})\in \mathbb{R}^{H\times 3W\times C}$ . Such feature rollout allows independent processing of feature planes. For simplicity, we subsequently use $\pmb{y}$ to denote such input form by default. However, the tri-plane roll-out hampers crossplane communication, while the 3D generation requires the synergy of the tri-plane generation. + +To better process the tri-plane features, we need an efficient 3D operator that performs on the tri-plane rather than treating it as a plain 2D input. To achieve this, we propose 3D-aware convolution to effectively process the triplane features while respecting their 3D relationship. A point on a certain feature plane actually corresponds to an axis-aligned 3D line in the volume, which also has two corresponding line projections in other planes, as shown in Figure 4(a). The features of these corresponding locations essentially describe the same 3D primitive and should be learned synchronously. However, such a 3D relationship is neglected when employing plain 2D convolution to tri- + +plane processing. As such, our 3D-aware convolution explicitly introduces such 3D inductive bias by attending the features of each plane to the corresponding row/column of the rest planes. In this way, we enable 3D processing capability with 2D CNNs. This 3D-aware convolution applied on the tri-plane representation, in fact, is a generic way to simplify 3D convolutions previously too costly to compute when modeling high-resolution 3D volumes. + +The 3D-aware convolution is depicted in Figure 4(b). Ideally, the compute for $\mathbf{y}_{uv}$ would attend to full elements from the corresponding row/column, i.e., $\mathbf{y}_{wu}$ and $\mathbf{y}_{vw}$ , from other planes. For parallel computing, we simplify this and aggregate the row/column elements. Specifically, we apply the axis-wise pooling for $\mathbf{y}_{wu}$ and $\mathbf{y}_{vw}$ , yielding a row vector $\mathbf{y}_{wu\rightarrow u}\in \mathbb{R}^{1\times W\times C}$ and a column vector $\mathbf{y}_{vw\rightarrow v}\in \mathbb{R}^{H\times 1\times C}$ respectively. For each point of $\mathbf{y}_{uv}$ , we can easily access the corresponding element in the aggregated vectors. We expand the aggregated vectors to the original 2D dimension (i.e., replicating the column vectors along row dimension, and vice versa) and thus derive $\mathbf{y}_{(\cdot)u},\mathbf{y}_{v(\cdot)}\in \mathbb{R}^{H\times W\times C}$ . By far, we can perform 2D convolution on the channel-wise concatenation of the feature maps, i.e., $\mathrm{Conv2D}(\mathbf{y}_{uv}\oplus \mathbf{y}_{(\cdot)u}\oplus \mathbf{y}_{v(\cdot)})$ . because $\mathbf{y}_{uv}$ is now spatially aligned with the aggregation of the corresponding elements from other planes. The compute for $\mathbf{y}_{vw}$ and $\mathbf{y}_{wu}$ is conducted likewise. The 3D-aware convolution greatly enhances the cross-plane communication, and we empirically observe reduced artifacts and improved generation of thin structures like hair strands. + +Latent conditioning. We further propose to learn a latent vector to orchestrate the tri-plane generation. As shown in Figure 2, we additionally train an image encoder $\mathcal{E}$ to extract a semantic latent vector serving as the conditional input of the base diffusion model, so essentially the whole framework is an autoencoder. To be specific, we extract the latent vector from the frontal view of each training subject, i.e., $z = \mathcal{E}_{\theta}(\pmb{x}_{\mathrm{front}})\in \mathbb{R}^{512}$ , and the diffusion model conditioned on $\pmb{z}$ is trained to reconstruct the tri-plane of the same subject. We use adaptive group normalization (AdaGN) to modulate the activations of the diffusion model, where $\pmb{z}$ is injected into every residual block, and in this way, the features of the orthogonal planes are synchronously generated according to a shared latent. + +The latent conditioning not only leads to higher generation quality but also permits a disentangled latent space, thus allowing semantic editing of generated results. To achieve better editability, we adopt a frozen CLIP image encoder [46] that has shared latent space with text prompts. We will show how the learned model produces controllable text-guided generation results. + +Another notable benefit of latent conditioning is that it allows classifier-free guidance [25], a technique typically used to boost the sampling quality in the conditional gener- + +ation. When training the diffusion model, we randomly zero the latent embedding with $20\%$ probability, thus adapting the diffusion decoder to unconditional generation. During inference, we can steer the model toward better generation sampling according to + +$$ +\hat {\epsilon} _ {\theta} (\boldsymbol {y}, \boldsymbol {z}) = \lambda \epsilon_ {\theta} (\boldsymbol {y}, \boldsymbol {z}) + (1 - \lambda) \epsilon_ {\theta} (\boldsymbol {y}), \tag {3} +$$ + +where $\epsilon_{\theta}(\pmb{y},\pmb{z})$ and $\epsilon_{\theta}(\pmb{y})$ are the conditional and unconditional $\epsilon$ -predictions respectively, and $\lambda > 0$ specifies the guidance strength. + +Our latent conditioned base model thus supports both unconditional generation as well as the conditional generation that is used for portrait inversion. To account for full diversity during unconditional sampling, we additionally train a diffusion model to model the distribution of the latent $z$ , whereas the latent $y_{T}$ describes the residual variation. We include this latent diffusion model in Figure 2. + +# 3.3. Diffusion Tri-plane Upsampler + +To generate high-fidelity 3D structures, we further train a diffusion super-resolution (SR) model to increase the triplane resolution from $64 \times 64$ to $256 \times 256$ . At this stage, the diffusion upsampler is conditioned on the low-resolution (LR) tri-plane $\mathbf{y}^{\mathrm{LR}}$ . Different from the base model training we parameterize the diffusion upsampler $\mathbf{y}_{\theta}^{\mathrm{HR}}(\mathbf{y}_{t}^{\mathrm{HR}}, \mathbf{y}^{\mathrm{LR}}, t)$ to predict the high-resolution (HR) ground truth $\mathbf{y}_0^{\mathrm{HR}}$ instead of the added noise $\epsilon$ . The 3D-aware convolution is utilized in each residual block to enhance detail synthesis. + +Following prior cascaded image generation works, we apply condition augmentation to reduce the domain gap between the output from the base model and the LR conditional input for SR training. We conduct careful tuning for the tri-plane augmentation with a combination of random downsampling, Gaussian blurring and Gaussian noises, making the rendered augmented LR tri-plane resemble the base rendering output as much as possible. + +Nonetheless, we find that a tri-plane restoration with a lower $\ell_2$ distance to the ground truth may not necessarily correspond to a satisfactory image rendering. Hence, we need to directly constrain the rendered image. Specifically, we obtain the rendered image $\pmb{x}^{\mathrm{HR}}\in \mathbb{R}^{256\times 256\times 3}$ from the predicted tri-plane $\hat{\pmb{y}}_0^{\mathrm{HR}}$ with $\hat{\pmb{x}} = \mathcal{R}(\mathcal{G}_{\theta}^{\mathrm{MLP}}(\hat{\pmb{y}}_0^{\mathrm{HR}}))$ , and we further penalize the perceptual loss [27] between this rendered result and the ground truth, according to + +$$ +\mathcal {L} _ {\text {p e r c}} = \mathbb {E} _ {t, \hat {\boldsymbol {x}}} \sum_ {l} \| \Psi^ {l} (\hat {\boldsymbol {x}}) - \Psi^ {l} (\boldsymbol {x}) \| _ {2} ^ {2}, \tag {4} +$$ + +where $\Psi^l$ denotes the multi-level feature extraction using a pretrained VGG. Usually, the volume rendering requires stratified sampling along each ray, which is computationally prohibitive for high-resolution rendering. Hence, we compute $\mathcal{L}_{\mathrm{perc}}$ on random $112\times 112$ image patches with high + +![](images/5f278f6af8d9e700b7aa0205fe34a8288bbee107b0f835041fbfe290c776f0c8.jpg) +Figure 5. Unconditional generation samples by our RODIN model. We visualize the mesh extracted from the generated density field. + +![](images/c88ef1d56c75134cf0defaed5e906a7893356d642c4077878284d22fac3ecf46.jpg) +Figure 6. Latent interpolation results for generated avatars. + +sampling importance on face region. Compared with prior 3D-aware GANs that require rendering full images, our 3D-aware SR can be easily scalable to high resolutions due to the permit of patchwise training with direct supervision. + +Modeling high-frequency detail and thin structures are particularly challenging in volumetric rendering. Thus, at this stage, we jointly train a convolution refiner [67] on our data which complements the missing details of the NeRF rendering, ultimately producing compelling $1024 \times 1024$ image outputs. + +# 4. Experiments + +# 4.1. Implementation Details + +To train our 3D diffusion, we obtain 100K 3D avatars with a random combination of identities, expressions, hairstyles, and accessories using synthetic engine [69]. For each avatar, we render 300 multi-view images with known camera pose, which are sufficient for a high-quality radiance field reconstruction. The tri-planes for our generation have the dimension of $256 \times 256 \times 32$ in each feature plane. We optimize a shared MLP decoder when fitting the first 1,000 subjects. This decoder consists of 4 fully connected layers and is fixed when fitting the following subjects. Thus different subjects are fitted separately in distributed servers. + +
Pi-GANGIRAFFEEG3DAutoencoderOurs
FID ↓78.364.640.567.426.1
+ +Table 1. Quantitative comparison with baseline methods. + +
Model configurationFID↓
A. Baseline39.2
B. + Latent conditioning37.4
C. + Tri-plane roll-out28.4
D. + 3D-aware conv26.1
+ +Table 2. Ablation study of the proposed components. + +Both the base and upsampling diffusion networks adopt U-Net architecture to process the roll-out tri-plane features. We apply full-attention for $8^{2}$ , $16^{2}$ and $32^{2}$ scales within the network and adopt 3D-aware convolution at higher scales to enhance the details. While we generate $256^{2}$ tri-planes with the diffusion upsampler, we also render image and compute image loss at $512^{2}$ resolution, with a convolutional refinement further enhancing the details to $1024^{2}$ . For more details about the network architecture and training strategies, please refer to our Appendix. + +# 4.2. Unconditional Generation Results + +Figure 5 shows several samples generated by the RODIN model, showing the capability to synthesize high-quality 3D renderings with impressive details, e.g., glasses and hairstyle. To reflect the geometry, we extract the mesh from the generated density field using marching cubes, which demonstrates high-fidelity geometry. More uncurated samples are shown in the Appendix. We also explore the interpolation of the latent condition $z$ between two generated avatars, as shown in Figure 6, where we observe consistent high-quality interpolation results with smooth appearance transition. + +![](images/faa47d56b5717d4a1faeeb4ba884f143131ebb75ec403dc575a420b7dca05155.jpg) +Figure 7. Qualitative comparison with state-of-the-art approaches. + +# 4.3. Comparison + +We compare our method with state-of-the-art 3D-aware GANs, e.g., Pi-GAN [10] and GIRAFFE [41] and EG3D [9], which learn to produce neural radiance field from 2D image supervision. Moreover, we implement an auto-encoder baseline, which leverages the multi-view supervision and reconstructs the radiance field from the latent. We differ in this baseline by using the power diffusion-based decoder with 3D-aware designs. We adapt the official implementation of prior works to 360-degree generation and retrain them using the same dataset. + +We use FID score [22] to measure the quality of image renderings. As per [30], we use the features extracted from the CLIP model to compute FID, which we find better correlates the perceptual quality. Specifically, we compute the FID score using 5K generated samples. The quantitative comparison is shown in Table 1, where we see that the RODIN model induces significantly lower FID than others. + +The visual comparison in Figure 7 shows a clear quality superiority of our RODIN model over prior arts. Our method gives visually pleasing multi-view renderings with high-quality geometry, e.g., for glasses and hair, whereas 3D-aware GANs produce more artifacts due to the geometry ambiguity caused by the simple use of image supervision. + +# 4.4. Analysis of the RODIN model + +Both 3D-aware convolution and latent conditioning are crucial for 3D synthesis. To prove this, we conduct the ablation study as shown in Table 2. We start from a baseline that uses a plain 2D CNN to process channel-wise concatenated tri-plane features following [9]. With latent con + +![](images/b2d02a8c6b51d86a6040e06b9281fececa78e3ea608fd2ba0c417cc2177f9288.jpg) +Figure 8. Hierarchical generation progressively improves results. + +ditioning, we achieve a lower FID. Feeding the network with roll-out tri-plane features significantly reduces the FID score because tri-planes are no longer improperly mingled. The proposed 3D-aware convolution further improves the synthesis quality, especially for thin structures like hair and cloth texture. More visual results regarding these ablations can be found in the Appendix. + +Hierarchical generation is critical for high-fidelity results. One significant benefit of this approach is that we can train different diffusion models dedicated to different scales in a supervised manner, as opposed to end-to-end synthesis with image loss. This also enables patch-wise training without the need to render full images. Thus hierarchical training allows high-resolution avatar generation without suffering the prohibitive memory issue. Figure 8 shows the progressive quality improvement after the base diffusion, diffusion upsampler, and convolution refinement, respectively. It can be seen that the diffusion upsampler is critical, largely enhancing the synthesis quality, while convolution refinement further adds delicate details. + +Diffusion upsampling training strategies. When training the tri-plane upsampler, we parameterize the model to predict the clean tri-plane ground truth at each diffusion re + +![](images/4c57edd550fba1b4d1375dd2810ba4c0be6249f05d92dee1d2d7cff7d7d1e178.jpg) + +![](images/6cc15b83433bd030f263b0869141497161b0b7612c6ccb540fb6642fe41cbe7c.jpg) + +![](images/692276c26fba94f707cbefa2b67f99e71bb9e00a9e5230473685a1728ac5f93e.jpg) + +![](images/6cbdfb1a54cec59a117f49349a6f5948704add05141689040a61d7b0f7d8d632.jpg) + +![](images/0a41c1e5ee158d94b05f7151ab91672ef546ca55ff79766e936157f8e4d65f32.jpg) + +![](images/140a627ac59286641c4ae7110020d7c3f41fd333b7d38230e634c6f4a1671506.jpg) + +![](images/7b5d8907ddbbe8cc9595a9abf66090f837f67ee2bb7380fac440e91dc8d84511.jpg) + +![](images/7ad01d61bba965df67dcfc4171bd80c167903d01dc4acb097e2aa569590211aa.jpg) + +![](images/c60662bdfdb059181143ee47cc577e9276f02f5b2f38b034199971130724e955.jpg) +Figure 9. Results of (a) portrait inversion and (b) text-to-ayar generation. + +![](images/523eb3ac45bcefaf02648589f01641ac228524b7b0b418723b0e200187275202.jpg) +(a) + +![](images/45091f4a42eefcb2c51270ec34b0a069af218666bfdcbd54d4baacbe336e73a1.jpg) + +![](images/e3b7a8cebdb78a56a75eeb2a6ee320b20d7f1c72da9dccc4e3e051a5123dc9a6.jpg) + +![](images/fc05e66fb1ddfb64b2a299e7ce46125dfbe04d920b130636b3ddc1e00eb05655.jpg) +"A woman with afro hair in red wearing + +![](images/2e2c27a7e6ef49d701d30125ead58b9bf0a2b184d00f93b852bb3cc338a8bfbf.jpg) + +![](images/0257ec549a149d72590db861efffe3b083c165bcf85a14a8d446bafc93bcddaf.jpg) + +
Tri-plane level lossImage-level lossCond. augmentFID ↓
✓48.5
✓✓38.6
✓✓✓26.1
+ +Table 3. Ablation study of the tri-plane upsampling strategy. + +version step. Meanwhile, conditioning augmentation is of great significance to let the model generalize to the coarse-level tri-plane generated from the base model. Besides, we observe enforcing image-level loss is beneficial to final perceptual quality. The effectiveness of these strategies are quantitatively justified in Table 3. + +# 4.5. Applications + +3D portrait from a single image. We can hallucinate a 3D avatar from a single portrait by conditioning the base generator with the CLIP image embedding for that input image. Note that our goal is different from face/head reconstruction [13, 49], but to conveniently produce a personalized digital avatar for users. As shown in Figure 9(a), the generated avatars keep the main characteristics of the portrait, e.g., expression, hairstyle, glass wearing, etc., while being 360-degree renderable. + +Text-to-ayar generation. Another natural way to customize avatars is to use language guidance. To do this, we train a text-conditioned diffusion model to generate the CLIP image embedding used to semantically control the avatar generation. We use a subset of the LAION-400M dataset [53] containing portrait-text pairs to train this model. As shown in Figure 9(b), one can finely customize the avatars using detailed text descriptions. + +Text-based avatar customization. We can also semantically edit generated avatars using text prompts. For a generated avatar with the CLIP image embedding $z_{i}$ , we can obtain a direction $\delta$ in the CLIP's text embedding based on prompt engineering [44]. We assume colinearity between the CLIP's image and text embedding, thus we obtain the manipulated embedding as $z_{i} + \delta$ , which is used to con + +![](images/ea871e55e466c7b8c6595de70af7790cc380db43fa935bcbe70bb99691451363.jpg) +Input +Reconstructed avatar with visualized mesh + +![](images/1cc3004356753ac4b58d96ee8c77ba0477bb9a08c8488a5b7c5c5a5d71b44ff6.jpg) +"Blond hair" +"Smiling" +"With sunglasses" +"Short hair" +Figure 10. Results of text-guided avatar manipulation. + +dition the generative process. As shown in Figure 10, we can achieve a wide variety of disentangled and meaningful control faithful to the text prompt. + +# 5. Discussion and Conclusion + +We have presented the RODIN model, a powerful generative model for 3D avatars. Like all generative models, the RODIN model can exhibit biases that are inherited from the data it has been trained on. Some of these biases will be harmful and lead to an unfair representation for the target application. We need to pay attention to the data that are fed into RODIN and gain a better understanding of the resulting biases. + +This model also allows users to customize avatars from a portrait or text, thus significantly lowering the barrier of personalized avatar creation. While this paper only focuses on avatars, the main ideas behind the RODIN model are applicable to the diffusion model for general 3D scenes. For future work, it would be fruitful to improve the sampling speed of the 3D diffusion model and study jointly leveraging the ample 2D data to mitigate the 3D data bottleneck. + +Acknowledgements: We would like to thank Steve Lin for the paper proofreading. We also thank anonymous reviewers for their constructive comments. + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. 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Our diffusion model, RODIN, can produce high-fidelity 3D avatars (the first row). Our model also supports 3D avatar generation from a single portrait or text prompt, while permitting text-based semantic manipulation (second row). See the webpage for video demos." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 381, + 195, + 544, + 351 + ], + "blocks": [ + { + "bbox": [ + 381, + 195, + 544, + 351 + ], + "lines": [ + { + "bbox": [ + 381, + 195, + 544, + 351 + ], + "spans": [ + { + "bbox": [ + 381, + 195, + 544, + 351 + ], + "type": "image", + "image_path": "711315261932b2e61905e94b43bc22d680005cd0dfd29f26d9f58b6a6384df24.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 394, + 192, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 394, + 192, + 407 + ], + "spans": [ + { + "bbox": [ + 143, + 394, + 192, + 407 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 411, + 290, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 411, + 290, + 687 + ], + "spans": [ + { + "bbox": [ + 45, + 411, + 290, + 687 + ], + "type": "text", + "content": "This paper presents a 3D diffusion model that automatically generates 3D digital avatars represented as neural radiance fields (NeRFs). A significant challenge for 3D diffusion is that the memory and processing costs are prohibitive for producing high-quality results with rich details. To tackle this problem, we propose the roll-out diffusion network (RODIN), which takes a 3D NeRF model represented as multiple 2D feature maps and rolls out them onto a single 2D feature plane within which we perform 3D-aware diffusion. The RODIN model brings much-needed computational efficiency while preserving the integrity of 3D diffusion by using 3D-aware convolution that attends to projected features in the 2D plane according to their original relationships in 3D. We also use latent conditioning to orchestrate the feature generation with global coherence, leading to high-fidelity avatars and enabling semantic editing based on text prompts. Finally, we use hierarchical synthesis to further enhance details. The 3D avatars generated by our model compare favorably with those produced by existing techniques. We can generate highly detailed avatars with realistic hairstyles and facial hair. We also demonstrate 3D avatar generation from image or text, as well as text-guided editability." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 394, + 387, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 394, + 387, + 407 + ], + "spans": [ + { + "bbox": [ + 307, + 394, + 387, + 407 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 420, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 661 + ], + "type": "text", + "content": "Generative models [2, 34] are one of the most promising ways to analyze and synthesize visual data including 2D images and 3D models. At the forefront of generative modeling is the diffusion model [14, 24, 61], which has shown phenomenal generative power for images [19,47,50,52] and videos [23,59]. Indeed, we are witnessing a 2D content creation revolution driven by the rapid advances of diffusion and generative modeling. In this paper, we aim to expand the applicability of diffusion to 3D digital avatars. We use \"digital avatars\" to refer to the traditional avatars manually created by 3D artists, as opposed to the recently emerging photorealistic avatars [8, 43]. The reason for focusing on digital avatars is twofold. On the one hand, digital avatars are widely used in movies, games, the metaverse, and the 3D industry in general. On the other hand, the available digital avatar data is very scarce as each avatar must be painstakingly created by a specialized 3D artist using a sophisticated creation pipeline [20, 35], especially for modeling hair and facial hair. All this leads to a compelling scenario for generative modeling." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "We present a diffusion model for automatically producing digital avatars represented as NeRFs [38], with each point describing its color radiance and density within the 3D volume. The core challenge in generating these avatars" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "text", + "content": "†Intern at Microsoft Research. ‡Corresponding author. *Equal contribution. Project Webpage: https://3d-ayar-diffusion.microsoft.com" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "4563" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "is the prohibitive memory and computational cost required by high-quality avatars with rich details. Without rich details, an avatar will always be somewhat \"toy-like\". To tackle this challenge, we develop RODIN, the roll-out diffusion network. We take a NeRF model represented as multiple 2D feature maps and roll out these maps onto a single 2D feature plane and perform 3D-aware diffusion within this plane. Specifically, we use the tri-plane representation [9], which represents a volume by three orthogonal feature planes. By simply rolling out the feature maps, RODIN can perform 3D-aware diffusion using an efficient 2D architecture and by drawing power from RODIN's three key ingredients." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 229, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 289, + 373 + ], + "type": "text", + "content": "The first is the 3D-aware convolution. The 2D CNN processing used in conventional 2D diffusion cannot effectively handle feature maps originating from orthogonal planes. Rather than treating the features as plain 2D input, the 3D-aware convolution explicitly accounts for the fact that a 2D feature in one plane (of the tri-plane) is a projection from a piece of 3D data and is hence intrinsically associated with the same data's projected features in the other two planes. To encourage cross-plane communication, we involve all these associated features in the convolution and synchronize their detail synthesis according to their 3D relationship." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 375, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 289, + 506 + ], + "type": "text", + "content": "The second ingredient is latent conditioning. We use a latent vector to orchestrate the feature generation so that it is globally coherent in 3D, leading to better quality avatars and enabling semantic editing. We do this by using the avatars in the training dataset to train an additional image encoder which extracts a semantic latent vector serving as the conditional input to the diffusion model. This latent conditioning essentially acts as an autoencoder in orchestrating the feature generation. For semantic editability, we adopt a frozen CLIP image encoder [46] that shares the latent space with text prompts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "text", + "content": "The final ingredient is hierarchical synthesis. We start by generating at low resolution " + }, + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "inline_equation", + "content": "(64 \\times 64)" + }, + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "text", + "content": ", followed by a diffusion-based upsampling that yields a higher resolution " + }, + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "inline_equation", + "content": "(256 \\times 256)" + }, + { + "bbox": [ + 46, + 508, + 289, + 582 + ], + "type": "text", + "content": ". When training the diffusion upsampler, it is instrumental to penalize the image-level loss that we compute in a patch-wise manner." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "RODIN supports several application scenarios. We can use the model to generate an unlimited number of avatars from scratch, each different from the others as well as those in the training data. As shown in Figure 1, we can generate highly detailed avatars with realistic hairstyles and facial hair styled as beards, mustaches, goatees, and sideburns. Hairstyle and facial hair are essential parts of personal identity yet have been notoriously difficult to model well with existing approaches. The RODIN model also allows avatar customization, with the resulting avatar capturing the visual characteristics of a person portrayed in an image or a textual" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "description. Finally, our framework supports text-guided semantic editing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 96, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 193 + ], + "type": "text", + "content": "Our work shows that 3D diffusion holds great modeling power, and this power can be effectively unleashed by rolling out the feature maps onto a 2D plane, leading to rich details, including those highly desirable but extremely difficult to produce with existing techniques. It is worth noting that while this paper focuses on RODIN's application to avatars, the design of RODIN is not avatar specific. Indeed, we believe RODIN is applicable to general 3D scenes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 203, + 392, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 203, + 392, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 203, + 392, + 216 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 223, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 354 + ], + "type": "text", + "content": "The state of generative modeling [5, 14, 15, 28, 48, 65, 75] has seen rapid progress in past years. Diffusion models [14, 24, 61, 73] have recently shown unprecedented generative ability and compositional power. The most remarkable success happens in text-to-image synthesis [19, 39, 47, 50, 52], which serves as a foundation model and enables various appealing applications [21, 51, 66] previously unattainable. While diffusion models have been successfully applied to different modalities [11, 23, 26, 32], its generative capability is much less explored in 3D generation, with only a few attempts on modeling 3D primitives [36, 74, 76]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "type": "text", + "content": "Early 3D generation works rely on either GAN [17] or VAE [29] to model the distribution of 3D shape representation like voxel grids [6, 70], point clouds [1, 7, 31, 72], mesh [33, 63] and implicit neural representation [42, 60]. However, existing works have not demonstrated the ability to produce complex 3D assets yet. Concurrent to this work, Bautista et al. [4] train a diffusion model to generate the latent vector that encodes the radiance field [38] of synthetic scenes, yet this work only produces coarse 3D geometry. In comparison, we propose a hierarchical 3D generation framework with effective 3D-aware operators, offering unprecedented 3D detail synthesis." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "type": "text", + "content": "Another line of work learns 3D-aware generation by utilizing richly available 2D data. 3D-aware GANs [9, 10, 12, 16, 18, 41, 54-58, 62, 71, 77] recently attract significant research interest, which are trained to produce radiance fields with image level distribution matching. However, these methods suffer from instabilities and mode collapse of GAN training, and it is still challenging to attain authentic avatars that can be viewed from large angles. Concurrently, there are a few attempts to use diffusion models for the problem. Daniel et al. [68] proposes to synthesize novel views with a pose-conditioned 2D diffusion model, yet the results are not intrinsically 3D. Ben et al. [45] optimizes a radiance field using the supervision from a pretrained text-to-image diffusion model and produces impressive 3D objects of diverse genres. Nonetheless, pretrained 2D generative networks only offer limited 3D knowledge and inevitably lead to blurry 3D results. A high-quality generation framework in 3D space is still highly desired." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4564" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 65, + 541, + 185 + ], + "blocks": [ + { + "bbox": [ + 52, + 65, + 541, + 185 + ], + "lines": [ + { + "bbox": [ + 52, + 65, + 541, + 185 + ], + "spans": [ + { + "bbox": [ + 52, + 65, + 541, + 185 + ], + "type": "image", + "image_path": "c1b3b408b26aa7d301635b36701041490df3b18df8cffa93b6f5cda68ac98fce.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "text", + "content": "Figure 2. An overview of our RODIN model. We derive the latent " + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "text", + "content": " via the mapping from image, text, or random noise, which is used to control the base diffusion model to generate " + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "text", + "content": " tri-planes. We train another diffusion model to upsample this coarse result to " + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 188, + 547, + 234 + ], + "type": "text", + "content": " tri-planes that are used to render final multi-view images with volumetric rendering and convolutional refinement. The operators used in diffusion models are designed to be 3D-aware." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 252, + 113, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 113, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 113, + 266 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 274, + 290, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 290, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 290, + 454 + ], + "type": "text", + "content": "Unlike prior methods that learn 3D-aware generation from a 2D image collection, we aim to learn the 3D avatar generation using the multi-view renderings from the Blender synthetic pipeline [69]. Rather than treating the multi-view images of the same subject as individual training samples, we fit the volumetric neural representation for each avatar, which is used to explain all the observations from different viewpoints. Thereafter we use diffusion models to characterize the distribution of these 3D instances. Our diffusion-based 3D generation is a hierarchical process — we first utilize a diffusion model to generate the coarse geometry, followed by a diffusion upsampler for detail synthesis. As illustrated in Figure 2, the whole 3D portrait generation comprises multiple training stages, which we detail in the following subsections." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 465, + 228, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 228, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 228, + 478 + ], + "type": "text", + "content": "3.1. Robust 3D Representation Fitting" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "text", + "content": "To train a generative network with explicit 3D supervision, we need an expressive 3D representation that accounts for multi-view images, which should meet the following requirements. First, we need an explicit representation that is amenable to generative network processing. Second, we require a compact representation that is memory efficient; otherwise, it would be too costly to store a myriad of such 3D instances for training. Furthermore, we expect fast representation fitting since hours of optimization as vanilla NeRF [38] would make it unaffordable to generate abundant 3D training data as required for generative modeling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Taking these into consideration, we adopt tri-plane representation proposed by [9] to model the neural radiance field of 3D avatars. Specifically, the 3D volume is factorized into three axis-aligned orthogonal feature planes, denoted by " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{uv},\\mathbf{y}_{wu},\\mathbf{y}_{vw}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ", each of which has spatial resolution of " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " and number of channel as " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ". Compared to voxel grids, the tri-plane representation offers a considerably smaller memory footprint without sacrificial" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 257, + 383, + 330 + ], + "blocks": [ + { + "bbox": [ + 310, + 257, + 383, + 330 + ], + "lines": [ + { + "bbox": [ + 310, + 257, + 383, + 330 + ], + "spans": [ + { + "bbox": [ + 310, + 257, + 383, + 330 + ], + "type": "image", + "image_path": "f13f6f6963b0d9ba426c2c211ddf7aada4ee2a41c5ba14ea5fcb3e95836bdcd5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 331, + 383, + 340 + ], + "lines": [ + { + "bbox": [ + 313, + 331, + 383, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 383, + 340 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 313, + 331, + 383, + 340 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 313, + 331, + 383, + 340 + ], + "type": "text", + "content": " tri-plane" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 388, + 258, + 460, + 330 + ], + "blocks": [ + { + "bbox": [ + 388, + 258, + 460, + 330 + ], + "lines": [ + { + "bbox": [ + 388, + 258, + 460, + 330 + ], + "spans": [ + { + "bbox": [ + 388, + 258, + 460, + 330 + ], + "type": "image", + "image_path": "66b831382cd7197327decfdcf504b84477fc57b66a5a1b9c98b0294e0f380ece.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 331, + 460, + 348 + ], + "lines": [ + { + "bbox": [ + 392, + 331, + 460, + 348 + ], + "spans": [ + { + "bbox": [ + 392, + 331, + 460, + 348 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 392, + 331, + 460, + 348 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 392, + 331, + 460, + 348 + ], + "type": "text", + "content": " tri-plane without random scaling" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 465, + 258, + 539, + 330 + ], + "blocks": [ + { + "bbox": [ + 465, + 258, + 539, + 330 + ], + "lines": [ + { + "bbox": [ + 465, + 258, + 539, + 330 + ], + "spans": [ + { + "bbox": [ + 465, + 258, + 539, + 330 + ], + "type": "image", + "image_path": "2c918b7c3c68f7febfa51bb39ce833cc5a3d64df65ea5196ef42d847896736eb.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 472, + 331, + 535, + 348 + ], + "lines": [ + { + "bbox": [ + 472, + 331, + 535, + 348 + ], + "spans": [ + { + "bbox": [ + 472, + 331, + 535, + 348 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 472, + 331, + 535, + 348 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 472, + 331, + 535, + 348 + ], + "type": "text", + "content": " tri-plane with random scaling" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "type": "text", + "content": "Figure 3. While " + }, + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "type": "text", + "content": " tri-planes give good renderings (a), the " + }, + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 353, + 547, + 398 + ], + "type": "text", + "content": " variant gives much worse result (b). Hence, we introduce random scaling during fitting so as to obtain a robust representation that can be effectively rendered in continuous scales (c)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": "ing the expressivity. Hence, rich 3D information is explicitly memorized in the tri-plane features, and one can query the feature of the 3D point " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "\\pmb{p} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": " by projecting it onto each plane and aggregating the retrieved features, i.e., " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "\\pmb{y_p} = \\pmb{y}_{uv}(\\pmb{p}_{uv}) + \\pmb{y}_{wu}(\\pmb{p}_{wu}) + \\pmb{y}_{vw}(\\pmb{p}_{vw})" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": ". With such positional feature, one can derive the density " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}^{+}" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": " and view-dependent color " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": " of each 3D location given the viewing direction " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "d \\in \\mathbb{S}^2" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": " with a lightweight MLP decoder " + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{\\mathrm{MLP}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 527 + ], + "type": "text", + "content": ", which can be formulated as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 534, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 534, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 348, + 534, + 545, + 550 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} (\\boldsymbol {p}, \\boldsymbol {d}), \\sigma (\\boldsymbol {p}) = \\mathcal {G} _ {\\theta} ^ {\\mathrm {M L P}} \\left(\\boldsymbol {y} _ {\\boldsymbol {p}}, \\xi (\\boldsymbol {y} _ {\\boldsymbol {p}}), \\boldsymbol {d}\\right). \\tag {1}", + "image_path": "2f495be19161fa01865e8e9ff6a5bf8830dabf2282155b911f44e37e5b943201.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": "Here, we apply the Fourier embedding operator " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\xi (\\cdot)" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": " [64] on the queried feature rather than the spatial coordinate. The tri-plane features and the MLP decoder are optimized such that the rendering of the neural radiance field matches the multi-view images " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\{\\pmb {x}\\}_{N_v}" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": " for the given subject, where " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb {x}\\in \\mathbb{R}^{H_0\\times W_0\\times 3}" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": ". We enforce the rendered image given by volumetric rendering [37], i.e., " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{x}} = \\mathcal{R}(\\pmb {c},\\sigma)" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": ", to match the corresponding ground truth with mean squared error loss. Besides, we introduce sparse, smooth, and compact regularizers to reduce the \"floating\" artifacts [3] in free space. For more tri-plane fitting details, please refer to the Appendix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 690, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 690, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 690, + 545, + 714 + ], + "type": "text", + "content": "While prior per-scene reconstruction mainly concerns the fitting quality, our 3D fitting procedure should also con" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4565" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": "sider several key aspects for generation purposes. First, the tri-plane features of different subjects should rigorously reside in the same domain. To achieve this, we adopt a shared MLP decoder when fitting distinct portraits, thus implicitly pushing the tri-plane features to the shared latent space recognizable by the decoder. Second, the MLP decoder has to possess some level of robustness. That is, the decoder should be tolerant to slight perturbation of tri-plane features, and thus one can still obtain plausible results even if the tri-plane features are imperfectly generated. More importantly, the decoder should be robust to varied tri-plane sizes because hierarchical 3D generation is trained on multi-resolution tri-plane features. As shown in Figure 3, when solely fitting " + }, + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": " tri-planes, its " + }, + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": " resolution variant cannot be effectively rendered. To address this, we randomly scale the tri-plane during fitting, which is instrumental in deriving multi-resolution tri-plane features simultaneously with a shared decoder." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 296, + 257, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 296, + 257, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 296, + 257, + 308 + ], + "type": "text", + "content": "3.2. Latent Conditioned 3D Diffusion Model" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": "Now the 3D avatar generation is reduced to learning the distribution of tri-plane features, i.e., " + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "inline_equation", + "content": "p(\\pmb{y})" + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "inline_equation", + "content": "y = (\\pmb{y}_{uv},\\pmb{y}_{wu},\\pmb{y}_{vw})" + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": ". Such generative modeling is non-trivial since " + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 315, + 287, + 387 + ], + "type": "text", + "content": " is highly dimensional. We leverage diffusion models for the task, which have shown compelling quality in complex image modeling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": "On a high level, the diffusion model generates " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " by gradually reversing a Markov forward process. Starting from " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{y}_0\\sim p(\\pmb {y})" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " , the forward process " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " yields a sequence of increasing noisy latent codes " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\{\\pmb {y}_t\\mid t\\in [0,T]\\}" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " according to " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{t}:= \\alpha_{t}\\pmb{y}_{0} + \\sigma_{t}\\pmb {\\epsilon}" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb {\\epsilon}\\in \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " is the added Gaussian noise; " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\sigma_t" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " define a noise schedule whose log signalto-noise ratio " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\lambda_{t} = \\log [\\alpha_{t}^{2} / \\sigma_{t}^{2}]" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " linearly decreases with the timestep " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " . With sufficient noising steps, we reach a pure Gaussian noise, i.e., " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb {y}_T\\sim \\mathcal{N}(\\pmb {0},\\pmb {I})" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " . The generative process corresponds to reversing the above noising process, where the diffusion model is trained to denoise " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb {y}_t" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{y}_0" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " using a mean squared error loss. Following [24], better generation quality can be achieved by parameterizing the diffusion model " + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{\\theta}" + }, + { + "bbox": [ + 46, + 388, + 288, + 555 + ], + "type": "text", + "content": " to predict the added noise:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 563, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 563, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 72, + 563, + 287, + 585 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {t, \\boldsymbol {x} _ {0}, \\boldsymbol {\\epsilon}} \\left[ \\left\\| \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\alpha_ {t} \\boldsymbol {y} _ {0} + \\sigma_ {t} \\boldsymbol {\\epsilon}, t\\right) - \\boldsymbol {\\epsilon} \\right\\| _ {2} ^ {2} \\right]. \\tag {2}", + "image_path": "d64fb92ee7129e98c9500891007375c12456e04cac9cd790e26db7071ddfdd0b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": "In practice, our diffusion model training also jointly optimizes the variational lower bound loss " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VLB}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " as suggested in [40], which allows high-quality generation with fewer timesteps. During inference, stochastic ancestral sampler [24] is used to generate the final samples, which starts from the Gaussian noise " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{y}_T" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " and sequentially produces less noisy samples " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_T,\\pmb{y}_{T - 1},\\dots \\}" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": " until reaching " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{y}_0" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "We first train a base diffusion model to generate the coarse-level tri-planes, e.g., at " + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": " resolution. A straightforward approach is to adopt the 2D network struc" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 305, + 59, + 392, + 144 + ], + "blocks": [ + { + "bbox": [ + 305, + 59, + 392, + 144 + ], + "lines": [ + { + "bbox": [ + 305, + 59, + 392, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 59, + 392, + 144 + ], + "type": "image", + "image_path": "dfc1a6beeabb89111d0e4ab0ecbb2781fc285377fc860407863f21e55dcffc89.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 145, + 356, + 153 + ], + "lines": [ + { + "bbox": [ + 345, + 145, + 356, + 153 + ], + "spans": [ + { + "bbox": [ + 345, + 145, + 356, + 153 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 157, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 304, + 157, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 547, + 213 + ], + "type": "text", + "content": "Figure 4. We propose two mechanisms to ensure coherent tri-plane generation. Our 3D-aware convolution considers the 3D relationship in (a) and correlates the associated elements from separate feature planes as shown in (b). In (b), we also visualize the usage of a shared latent code to orchestrate the feature generation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 399, + 59, + 541, + 141 + ], + "blocks": [ + { + "bbox": [ + 399, + 59, + 541, + 141 + ], + "lines": [ + { + "bbox": [ + 399, + 59, + 541, + 141 + ], + "spans": [ + { + "bbox": [ + 399, + 59, + 541, + 141 + ], + "type": "image", + "image_path": "bb17f3903a7470a654a358b6bebc391e6859b4d390bdd9aef6afbb4e9fead2fb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 465, + 144, + 476, + 153 + ], + "lines": [ + { + "bbox": [ + 465, + 144, + 476, + 153 + ], + "spans": [ + { + "bbox": [ + 465, + 144, + 476, + 153 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 234, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 426 + ], + "type": "text", + "content": "ture used in the state-of-the-art image-based diffusion models for our tri-plane generation. Specifically, we can concatenate the tri-plane features in the channel dimension as in [9], which forms " + }, + { + "bbox": [ + 304, + 234, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\pmb{y} = (\\pmb{y}_{uv}\\oplus \\pmb{y}_{wu}\\oplus \\pmb{y}_{vw})\\in \\mathbb{R}^{H\\times W\\times 3C}" + }, + { + "bbox": [ + 304, + 234, + 545, + 426 + ], + "type": "text", + "content": ", and employ a well-designed 2D U-Net to model the data distribution through the denoising diffusion process. However, such a baseline model produces 3D avatars with severe artifacts. We conjecture the generation artifact comes from the incompatibility between the tri-plane representation and the 2D U-Net. As shown in Figure 4(a), intuitively, one can regard the tri-plane features as the projection of neural volume towards the frontal, bottom, and side views, respectively. Hence, the channel-wise concatenation of these orthogonal planes for CNN processing is problematic because these planes are not spatially aligned. To better handle the tri-plane representation, we make the following efforts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "text", + "content": "3D-aware convolution. Using CNN to process channelwise concatenated tri-planes will cause the mixing of theoretically uncorrected features in terms of 3D. One simple yet effective way to address this is to spatially roll out the tri-plane features. As shown in Figure 4(b), we concatenate the tri-plane features horizontally, yielding " + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{y}} =" + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "text", + "content": " hstack " + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "inline_equation", + "content": "(\\pmb {y}_{uv},\\pmb {y}_{wu},\\pmb {y}_{vw})\\in \\mathbb{R}^{H\\times 3W\\times C}" + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "text", + "content": ". Such feature rollout allows independent processing of feature planes. For simplicity, we subsequently use " + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 304, + 426, + 546, + 569 + ], + "type": "text", + "content": " to denote such input form by default. However, the tri-plane roll-out hampers crossplane communication, while the 3D generation requires the synergy of the tri-plane generation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "To better process the tri-plane features, we need an efficient 3D operator that performs on the tri-plane rather than treating it as a plain 2D input. To achieve this, we propose 3D-aware convolution to effectively process the triplane features while respecting their 3D relationship. A point on a certain feature plane actually corresponds to an axis-aligned 3D line in the volume, which also has two corresponding line projections in other planes, as shown in Figure 4(a). The features of these corresponding locations essentially describe the same 3D primitive and should be learned synchronously. However, such a 3D relationship is neglected when employing plain 2D convolution to tri-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4566" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "plane processing. As such, our 3D-aware convolution explicitly introduces such 3D inductive bias by attending the features of each plane to the corresponding row/column of the rest planes. In this way, we enable 3D processing capability with 2D CNNs. This 3D-aware convolution applied on the tri-plane representation, in fact, is a generic way to simplify 3D convolutions previously too costly to compute when modeling high-resolution 3D volumes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": "The 3D-aware convolution is depicted in Figure 4(b). Ideally, the compute for " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{uv}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " would attend to full elements from the corresponding row/column, i.e., " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{wu}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{vw}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": ", from other planes. For parallel computing, we simplify this and aggregate the row/column elements. Specifically, we apply the axis-wise pooling for " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{wu}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{vw}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": ", yielding a row vector " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{wu\\rightarrow u}\\in \\mathbb{R}^{1\\times W\\times C}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " and a column vector " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{vw\\rightarrow v}\\in \\mathbb{R}^{H\\times 1\\times C}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " respectively. For each point of " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{uv}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": ", we can easily access the corresponding element in the aggregated vectors. We expand the aggregated vectors to the original 2D dimension (i.e., replicating the column vectors along row dimension, and vice versa) and thus derive " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{(\\cdot)u},\\mathbf{y}_{v(\\cdot)}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": ". By far, we can perform 2D convolution on the channel-wise concatenation of the feature maps, i.e., " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv2D}(\\mathbf{y}_{uv}\\oplus \\mathbf{y}_{(\\cdot)u}\\oplus \\mathbf{y}_{v(\\cdot)})" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": ". because " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{uv}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " is now spatially aligned with the aggregation of the corresponding elements from other planes. The compute for " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{vw}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{wu}" + }, + { + "bbox": [ + 46, + 169, + 289, + 421 + ], + "type": "text", + "content": " is conducted likewise. The 3D-aware convolution greatly enhances the cross-plane communication, and we empirically observe reduced artifacts and improved generation of thin structures like hair strands." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "content": "Latent conditioning. We further propose to learn a latent vector to orchestrate the tri-plane generation. As shown in Figure 2, we additionally train an image encoder " + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "content": " to extract a semantic latent vector serving as the conditional input of the base diffusion model, so essentially the whole framework is an autoencoder. To be specific, we extract the latent vector from the frontal view of each training subject, i.e., " + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "inline_equation", + "content": "z = \\mathcal{E}_{\\theta}(\\pmb{x}_{\\mathrm{front}})\\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "content": ", and the diffusion model conditioned on " + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "content": " is trained to reconstruct the tri-plane of the same subject. We use adaptive group normalization (AdaGN) to modulate the activations of the diffusion model, where " + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 46, + 423, + 289, + 590 + ], + "type": "text", + "content": " is injected into every residual block, and in this way, the features of the orthogonal planes are synchronously generated according to a shared latent." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 592, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 288, + 676 + ], + "type": "text", + "content": "The latent conditioning not only leads to higher generation quality but also permits a disentangled latent space, thus allowing semantic editing of generated results. To achieve better editability, we adopt a frozen CLIP image encoder [46] that has shared latent space with text prompts. We will show how the learned model produces controllable text-guided generation results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "type": "text", + "content": "Another notable benefit of latent conditioning is that it allows classifier-free guidance [25], a technique typically used to boost the sampling quality in the conditional gener-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "ation. When training the diffusion model, we randomly zero the latent embedding with " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " probability, thus adapting the diffusion decoder to unconditional generation. During inference, we can steer the model toward better generation sampling according to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 346, + 141, + 545, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 141, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 346, + 141, + 545, + 155 + ], + "type": "interline_equation", + "content": "\\hat {\\epsilon} _ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) = \\lambda \\epsilon_ {\\theta} (\\boldsymbol {y}, \\boldsymbol {z}) + (1 - \\lambda) \\epsilon_ {\\theta} (\\boldsymbol {y}), \\tag {3}", + "image_path": "2498d571bacc3630a035791bef3f6dec4992bf5d4d7e88da4398bb245cc5c7c8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\pmb{y},\\pmb{z})" + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\pmb{y})" + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "content": " are the conditional and unconditional " + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "content": "-predictions respectively, and " + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 304, + 163, + 545, + 199 + ], + "type": "text", + "content": " specifies the guidance strength." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "text", + "content": "Our latent conditioned base model thus supports both unconditional generation as well as the conditional generation that is used for portrait inversion. To account for full diversity during unconditional sampling, we additionally train a diffusion model to model the distribution of the latent " + }, + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "text", + "content": ", whereas the latent " + }, + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "inline_equation", + "content": "y_{T}" + }, + { + "bbox": [ + 304, + 200, + 547, + 284 + ], + "type": "text", + "content": " describes the residual variation. We include this latent diffusion model in Figure 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 291, + 474, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 291, + 474, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 291, + 474, + 304 + ], + "type": "text", + "content": "3.3. Diffusion Tri-plane Upsampler" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": "To generate high-fidelity 3D structures, we further train a diffusion super-resolution (SR) model to increase the triplane resolution from " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": ". At this stage, the diffusion upsampler is conditioned on the low-resolution (LR) tri-plane " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{LR}}" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": ". Different from the base model training we parameterize the diffusion upsampler " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\theta}^{\\mathrm{HR}}(\\mathbf{y}_{t}^{\\mathrm{HR}}, \\mathbf{y}^{\\mathrm{LR}}, t)" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": " to predict the high-resolution (HR) ground truth " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_0^{\\mathrm{HR}}" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": " instead of the added noise " + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 309, + 547, + 417 + ], + "type": "text", + "content": ". The 3D-aware convolution is utilized in each residual block to enhance detail synthesis." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 418, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 513 + ], + "type": "text", + "content": "Following prior cascaded image generation works, we apply condition augmentation to reduce the domain gap between the output from the base model and the LR conditional input for SR training. We conduct careful tuning for the tri-plane augmentation with a combination of random downsampling, Gaussian blurring and Gaussian noises, making the rendered augmented LR tri-plane resemble the base rendering output as much as possible." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "content": "Nonetheless, we find that a tri-plane restoration with a lower " + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "content": " distance to the ground truth may not necessarily correspond to a satisfactory image rendering. Hence, we need to directly constrain the rendered image. Specifically, we obtain the rendered image " + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{\\mathrm{HR}}\\in \\mathbb{R}^{256\\times 256\\times 3}" + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "content": " from the predicted tri-plane " + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{y}}_0^{\\mathrm{HR}}" + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{x}} = \\mathcal{R}(\\mathcal{G}_{\\theta}^{\\mathrm{MLP}}(\\hat{\\pmb{y}}_0^{\\mathrm{HR}}))" + }, + { + "bbox": [ + 304, + 513, + 547, + 611 + ], + "type": "text", + "content": ", and we further penalize the perceptual loss [27] between this rendered result and the ground truth, according to" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 351, + 618, + 545, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 618, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 351, + 618, + 545, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p e r c}} = \\mathbb {E} _ {t, \\hat {\\boldsymbol {x}}} \\sum_ {l} \\| \\Psi^ {l} (\\hat {\\boldsymbol {x}}) - \\Psi^ {l} (\\boldsymbol {x}) \\| _ {2} ^ {2}, \\tag {4}", + "image_path": "6369ea03fa779c24129090983d4ece685fe946d17b5dded84a697fe9f1641c9f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\Psi^l" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " denotes the multi-level feature extraction using a pretrained VGG. Usually, the volume rendering requires stratified sampling along each ray, which is computationally prohibitive for high-resolution rendering. Hence, we compute " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perc}}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " on random " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "112\\times 112" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " image patches with high" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4567" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 67, + 537, + 232 + ], + "blocks": [ + { + "bbox": [ + 56, + 67, + 537, + 232 + ], + "lines": [ + { + "bbox": [ + 56, + 67, + 537, + 232 + ], + "spans": [ + { + "bbox": [ + 56, + 67, + 537, + 232 + ], + "type": "image", + "image_path": "5f278f6af8d9e700b7aa0205fe34a8288bbee107b0f835041fbfe290c776f0c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 233, + 537, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 233, + 537, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 537, + 246 + ], + "type": "text", + "content": "Figure 5. Unconditional generation samples by our RODIN model. We visualize the mesh extracted from the generated density field." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 259, + 282, + 371 + ], + "blocks": [ + { + "bbox": [ + 51, + 259, + 282, + 371 + ], + "lines": [ + { + "bbox": [ + 51, + 259, + 282, + 371 + ], + "spans": [ + { + "bbox": [ + 51, + 259, + 282, + 371 + ], + "type": "image", + "image_path": "c88ef1d56c75134cf0defaed5e906a7893356d642c4077878284d22fac3ecf46.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 373, + 274, + 384 + ], + "lines": [ + { + "bbox": [ + 59, + 373, + 274, + 384 + ], + "spans": [ + { + "bbox": [ + 59, + 373, + 274, + 384 + ], + "type": "text", + "content": "Figure 6. Latent interpolation results for generated avatars." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 407, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 456 + ], + "type": "text", + "content": "sampling importance on face region. Compared with prior 3D-aware GANs that require rendering full images, our 3D-aware SR can be easily scalable to high resolutions due to the permit of patchwise training with direct supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 456, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 288, + 529 + ], + "type": "text", + "content": "Modeling high-frequency detail and thin structures are particularly challenging in volumetric rendering. Thus, at this stage, we jointly train a convolution refiner [67] on our data which complements the missing details of the NeRF rendering, ultimately producing compelling " + }, + { + "bbox": [ + 46, + 456, + 288, + 529 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 456, + 288, + 529 + ], + "type": "text", + "content": " image outputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 542, + 128, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 542, + 128, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 542, + 128, + 555 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 562, + 180, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 180, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 180, + 574 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "To train our 3D diffusion, we obtain 100K 3D avatars with a random combination of identities, expressions, hairstyles, and accessories using synthetic engine [69]. For each avatar, we render 300 multi-view images with known camera pose, which are sufficient for a high-quality radiance field reconstruction. The tri-planes for our generation have the dimension of " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 32" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " in each feature plane. We optimize a shared MLP decoder when fitting the first 1,000 subjects. This decoder consists of 4 fully connected layers and is fixed when fitting the following subjects. Thus different subjects are fitted separately in distributed servers." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 255, + 542, + 292 + ], + "blocks": [ + { + "bbox": [ + 310, + 255, + 542, + 292 + ], + "lines": [ + { + "bbox": [ + 310, + 255, + 542, + 292 + ], + "spans": [ + { + "bbox": [ + 310, + 255, + 542, + 292 + ], + "type": "table", + "html": "
Pi-GANGIRAFFEEG3DAutoencoderOurs
FID ↓78.364.640.567.426.1
", + "image_path": "70f80982419a798c2637f07a15c0fcb0e8537138571ef9a202b77eb169c0e408.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 344, + 323, + 509, + 396 + ], + "blocks": [ + { + "bbox": [ + 322, + 293, + 529, + 304 + ], + "lines": [ + { + "bbox": [ + 322, + 293, + 529, + 304 + ], + "spans": [ + { + "bbox": [ + 322, + 293, + 529, + 304 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with baseline methods." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 344, + 323, + 509, + 396 + ], + "lines": [ + { + "bbox": [ + 344, + 323, + 509, + 396 + ], + "spans": [ + { + "bbox": [ + 344, + 323, + 509, + 396 + ], + "type": "table", + "html": "
Model configurationFID↓
A. Baseline39.2
B. + Latent conditioning37.4
C. + Tri-plane roll-out28.4
D. + 3D-aware conv26.1
", + "image_path": "0e99c194ed6e847f1c57655ef954cc93929ed7f39c9b8ca4d26b985e4a5e638f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 396, + 523, + 408 + ], + "lines": [ + { + "bbox": [ + 329, + 396, + 523, + 408 + ], + "spans": [ + { + "bbox": [ + 329, + 396, + 523, + 408 + ], + "type": "text", + "content": "Table 2. Ablation study of the proposed components." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": "Both the base and upsampling diffusion networks adopt U-Net architecture to process the roll-out tri-plane features. We apply full-attention for " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "8^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "16^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "32^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": " scales within the network and adopt 3D-aware convolution at higher scales to enhance the details. While we generate " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": " tri-planes with the diffusion upsampler, we also render image and compute image loss at " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "512^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": " resolution, with a convolutional refinement further enhancing the details to " + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 542 + ], + "type": "text", + "content": ". For more details about the network architecture and training strategies, please refer to our Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 559, + 488, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 559, + 488, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 559, + 488, + 572 + ], + "type": "text", + "content": "4.2. Unconditional Generation Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 712 + ], + "type": "text", + "content": "Figure 5 shows several samples generated by the RODIN model, showing the capability to synthesize high-quality 3D renderings with impressive details, e.g., glasses and hairstyle. To reflect the geometry, we extract the mesh from the generated density field using marching cubes, which demonstrates high-fidelity geometry. More uncurated samples are shown in the Appendix. We also explore the interpolation of the latent condition " + }, + { + "bbox": [ + 304, + 582, + 547, + 712 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 582, + 547, + 712 + ], + "type": "text", + "content": " between two generated avatars, as shown in Figure 6, where we observe consistent high-quality interpolation results with smooth appearance transition." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4568" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 67, + 531, + 300 + ], + "blocks": [ + { + "bbox": [ + 65, + 67, + 531, + 300 + ], + "lines": [ + { + "bbox": [ + 65, + 67, + 531, + 300 + ], + "spans": [ + { + "bbox": [ + 65, + 67, + 531, + 300 + ], + "type": "image", + "image_path": "faa47d56b5717d4a1faeeb4ba884f143131ebb75ec403dc575a420b7dca05155.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 302, + 416, + 314 + ], + "lines": [ + { + "bbox": [ + 176, + 302, + 416, + 314 + ], + "spans": [ + { + "bbox": [ + 176, + 302, + 416, + 314 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison with state-of-the-art approaches." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 334, + 128, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 128, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 128, + 346 + ], + "type": "text", + "content": "4.3. Comparison" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 472 + ], + "type": "text", + "content": "We compare our method with state-of-the-art 3D-aware GANs, e.g., Pi-GAN [10] and GIRAFFE [41] and EG3D [9], which learn to produce neural radiance field from 2D image supervision. Moreover, we implement an auto-encoder baseline, which leverages the multi-view supervision and reconstructs the radiance field from the latent. We differ in this baseline by using the power diffusion-based decoder with 3D-aware designs. We adapt the official implementation of prior works to 360-degree generation and retrain them using the same dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 555 + ], + "type": "text", + "content": "We use FID score [22] to measure the quality of image renderings. As per [30], we use the features extracted from the CLIP model to compute FID, which we find better correlates the perceptual quality. Specifically, we compute the FID score using 5K generated samples. The quantitative comparison is shown in Table 1, where we see that the RODIN model induces significantly lower FID than others." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "type": "text", + "content": "The visual comparison in Figure 7 shows a clear quality superiority of our RODIN model over prior arts. Our method gives visually pleasing multi-view renderings with high-quality geometry, e.g., for glasses and hair, whereas 3D-aware GANs produce more artifacts due to the geometry ambiguity caused by the simple use of image supervision." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "text", + "content": "4.4. Analysis of the RODIN model" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Both 3D-aware convolution and latent conditioning are crucial for 3D synthesis. To prove this, we conduct the ablation study as shown in Table 2. We start from a baseline that uses a plain 2D CNN to process channel-wise concatenated tri-plane features following [9]. With latent con" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 327, + 536, + 403 + ], + "blocks": [ + { + "bbox": [ + 316, + 327, + 536, + 403 + ], + "lines": [ + { + "bbox": [ + 316, + 327, + 536, + 403 + ], + "spans": [ + { + "bbox": [ + 316, + 327, + 536, + 403 + ], + "type": "image", + "image_path": "b2d02a8c6b51d86a6040e06b9281fececa78e3ea608fd2ba0c417cc2177f9288.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 406, + 544, + 417 + ], + "lines": [ + { + "bbox": [ + 307, + 406, + 544, + 417 + ], + "spans": [ + { + "bbox": [ + 307, + 406, + 544, + 417 + ], + "type": "text", + "content": "Figure 8. Hierarchical generation progressively improves results." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 434, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 518 + ], + "type": "text", + "content": "ditioning, we achieve a lower FID. Feeding the network with roll-out tri-plane features significantly reduces the FID score because tri-planes are no longer improperly mingled. The proposed 3D-aware convolution further improves the synthesis quality, especially for thin structures like hair and cloth texture. More visual results regarding these ablations can be found in the Appendix." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 520, + 546, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 546, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 546, + 674 + ], + "type": "text", + "content": "Hierarchical generation is critical for high-fidelity results. One significant benefit of this approach is that we can train different diffusion models dedicated to different scales in a supervised manner, as opposed to end-to-end synthesis with image loss. This also enables patch-wise training without the need to render full images. Thus hierarchical training allows high-resolution avatar generation without suffering the prohibitive memory issue. Figure 8 shows the progressive quality improvement after the base diffusion, diffusion upsampler, and convolution refinement, respectively. It can be seen that the diffusion upsampler is critical, largely enhancing the synthesis quality, while convolution refinement further adds delicate details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Diffusion upsampling training strategies. 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Results of (a) portrait inversion and (b) text-to-ayar generation." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 187, + 140, + 232, + 201 + ], + "blocks": [ + { + "bbox": [ + 187, + 140, + 232, + 201 + ], + "lines": [ + { + "bbox": [ + 187, + 140, + 232, + 201 + ], + "spans": [ + { + "bbox": [ + 187, + 140, + 232, + 201 + ], + "type": "image", + "image_path": "523eb3ac45bcefaf02648589f01641ac228524b7b0b418723b0e200187275202.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 229, + 210, + 239, + 218 + ], + "lines": [ + { + "bbox": [ + 229, + 210, + 239, + 218 + ], + "spans": [ + { + "bbox": [ + 229, + 210, + 239, + 218 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 235, + 138, + 298, + 201 + ], + "blocks": [ + { + "bbox": [ + 235, + 138, + 298, + 201 + ], + "lines": [ + { + "bbox": [ + 235, + 138, + 298, + 201 + ], + "spans": [ + { + "bbox": [ + 235, + 138, + 298, + 201 + ], + "type": "image", + "image_path": "45091f4a42eefcb2c51270ec34b0a069af218666bfdcbd54d4baacbe336e73a1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 299, + 138, + 358, + 201 + ], + "blocks": [ + { + "bbox": [ + 299, + 138, + 358, + 201 + ], + "lines": [ + { + "bbox": [ + 299, + 138, + 358, + 201 + ], + "spans": [ + { + "bbox": [ + 299, + 138, + 358, + 201 + ], + "type": "image", + "image_path": "e3b7a8cebdb78a56a75eeb2a6ee320b20d7f1c72da9dccc4e3e051a5123dc9a6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 365, + 141, + 421, + 201 + ], + "blocks": [ + { + "bbox": [ + 365, + 141, + 421, + 201 + ], + "lines": [ + { + "bbox": [ + 365, + 141, + 421, + 201 + ], + "spans": [ + { + "bbox": [ + 365, + 141, + 421, + 201 + ], + "type": "image", + "image_path": "fc05e66fb1ddfb64b2a299e7ce46125dfbe04d920b130636b3ddc1e00eb05655.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 201, + 552, + 210 + ], + "lines": [ + { + "bbox": [ + 421, + 201, + 552, + 210 + ], + "spans": [ + { + "bbox": [ + 421, + 201, + 552, + 210 + ], + "type": "text", + "content": "\"A woman with afro hair in red wearing" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 425, + 138, + 481, + 201 + ], + "blocks": [ + { + "bbox": [ + 425, + 138, + 481, + 201 + ], + "lines": [ + { + "bbox": [ + 425, + 138, + 481, + 201 + ], + "spans": [ + { + "bbox": [ + 425, + 138, + 481, + 201 + ], + "type": "image", + "image_path": "2e2c27a7e6ef49d701d30125ead58b9bf0a2b184d00f93b852bb3cc338a8bfbf.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 488, + 138, + 550, + 201 + ], + "blocks": [ + { + "bbox": [ + 488, + 138, + 550, + 201 + ], + "lines": [ + { + "bbox": [ + 488, + 138, + 550, + 201 + ], + "spans": [ + { + "bbox": [ + 488, + 138, + 550, + 201 + ], + "type": "image", + "image_path": "0257ec549a149d72590db861efffe3b083c165bcf85a14a8d446bafc93bcddaf.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 53, + 240, + 281, + 300 + ], + "blocks": [ + { + "bbox": [ + 53, + 240, + 281, + 300 + ], + "lines": [ + { + "bbox": [ + 53, + 240, + 281, + 300 + ], + "spans": [ + { + "bbox": [ + 53, + 240, + 281, + 300 + ], + "type": "table", + "html": "
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", + "image_path": "a18267431b97fe1475325b575b12ac3738ed6422290569ffab3f56b7c6527b91.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 56, + 301, + 276, + 312 + ], + "lines": [ + { + "bbox": [ + 56, + 301, + 276, + 312 + ], + "spans": [ + { + "bbox": [ + 56, + 301, + 276, + 312 + ], + "type": "text", + "content": "Table 3. Ablation study of the tri-plane upsampling strategy." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 328, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 287, + 401 + ], + "type": "text", + "content": "version step. Meanwhile, conditioning augmentation is of great significance to let the model generalize to the coarse-level tri-plane generated from the base model. Besides, we observe enforcing image-level loss is beneficial to final perceptual quality. The effectiveness of these strategies are quantitatively justified in Table 3." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 47, + 407, + 128, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 128, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 128, + 420 + ], + "type": "text", + "content": "4.5. Applications" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 426, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 533 + ], + "type": "text", + "content": "3D portrait from a single image. We can hallucinate a 3D avatar from a single portrait by conditioning the base generator with the CLIP image embedding for that input image. Note that our goal is different from face/head reconstruction [13, 49], but to conveniently produce a personalized digital avatar for users. As shown in Figure 9(a), the generated avatars keep the main characteristics of the portrait, e.g., expression, hairstyle, glass wearing, etc., while being 360-degree renderable." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 534, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 629 + ], + "type": "text", + "content": "Text-to-ayar generation. Another natural way to customize avatars is to use language guidance. To do this, we train a text-conditioned diffusion model to generate the CLIP image embedding used to semantically control the avatar generation. We use a subset of the LAION-400M dataset [53] containing portrait-text pairs to train this model. As shown in Figure 9(b), one can finely customize the avatars using detailed text descriptions." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Text-based avatar customization. We can also semantically edit generated avatars using text prompts. For a generated avatar with the CLIP image embedding " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ", we can obtain a direction " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " in the CLIP's text embedding based on prompt engineering [44]. We assume colinearity between the CLIP's image and text embedding, thus we obtain the manipulated embedding as " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{i} + \\delta" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ", which is used to con" + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 307, + 238, + 545, + 297 + ], + "blocks": [ + { + "bbox": [ + 307, + 238, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 307, + 238, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 307, + 238, + 545, + 297 + ], + "type": "image", + "image_path": "ea871e55e466c7b8c6595de70af7790cc380db43fa935bcbe70bb99691451363.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 298, + 349, + 307 + ], + "lines": [ + { + "bbox": [ + 331, + 298, + 349, + 307 + ], + "spans": [ + { + "bbox": [ + 331, + 298, + 349, + 307 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 381, + 298, + 519, + 307 + ], + "lines": [ + { + "bbox": [ + 381, + 298, + 519, + 307 + ], + "spans": [ + { + "bbox": [ + 381, + 298, + 519, + 307 + ], + "type": "text", + "content": "Reconstructed avatar with visualized mesh" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 307, + 309, + 545, + 369 + ], + "blocks": [ + { + "bbox": [ + 307, + 309, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 307, + 309, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 309, + 545, + 369 + ], + "type": "image", + "image_path": "1cc3004356753ac4b58d96ee8c77ba0477bb9a08c8488a5b7c5c5a5d71b44ff6.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 370, + 359, + 377 + ], + "lines": [ + { + "bbox": [ + 317, + 370, + 359, + 377 + ], + "spans": [ + { + "bbox": [ + 317, + 370, + 359, + 377 + ], + "type": "text", + "content": "\"Blond hair\"" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 375, + 370, + 406, + 377 + ], + "lines": [ + { + "bbox": [ + 375, + 370, + 406, + 377 + ], + "spans": [ + { + "bbox": [ + 375, + 370, + 406, + 377 + ], + "type": "text", + "content": "\"Smiling\"" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 370, + 483, + 377 + ], + "lines": [ + { + "bbox": [ + 427, + 370, + 483, + 377 + ], + "spans": [ + { + "bbox": [ + 427, + 370, + 483, + 377 + ], + "type": "text", + "content": "\"With sunglasses\"" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 498, + 370, + 536, + 377 + ], + "lines": [ + { + "bbox": [ + 498, + 370, + 536, + 377 + ], + "spans": [ + { + "bbox": [ + 498, + 370, + 536, + 377 + ], + "type": "text", + "content": "\"Short hair\"" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 327, + 380, + 524, + 391 + ], + "lines": [ + { + "bbox": [ + 327, + 380, + 524, + 391 + ], + "spans": [ + { + "bbox": [ + 327, + 380, + 524, + 391 + ], + "type": "text", + "content": "Figure 10. Results of text-guided avatar manipulation." + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 408, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 408, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 408, + 545, + 444 + ], + "type": "text", + "content": "dition the generative process. As shown in Figure 10, we can achieve a wide variety of disentangled and meaningful control faithful to the text prompt." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 460, + 457, + 473 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 457, + 473 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 457, + 473 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 482, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 578 + ], + "type": "text", + "content": "We have presented the RODIN model, a powerful generative model for 3D avatars. Like all generative models, the RODIN model can exhibit biases that are inherited from the data it has been trained on. Some of these biases will be harmful and lead to an unfair representation for the target application. We need to pay attention to the data that are fed into RODIN and gain a better understanding of the resulting biases." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "content": "This model also allows users to customize avatars from a portrait or text, thus significantly lowering the barrier of personalized avatar creation. While this paper only focuses on avatars, the main ideas behind the RODIN model are applicable to the diffusion model for general 3D scenes. For future work, it would be fruitful to improve the sampling speed of the 3D diffusion model and study jointly leveraging the ample 2D data to mitigate the 3D data bottleneck." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements: We would like to thank Steve Lin for the paper proofreading. 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Cips-3d: A 3d-aware generator of gans based on conditionally-independent pixel synthesis. arXiv preprint arXiv:2110.09788, 2021. 2" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4573" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_content_list.json b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..49a9c3c3e539f824ff1fb3807f311b3488c96688 --- /dev/null +++ b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_content_list.json @@ -0,0 +1,1524 @@ +[ + { + "type": "text", + "text": "RONO: Robust Discriminative Learning with Noisy Labels for 2D-3D Cross-Modal Retrieval", + "text_level": 1, + "bbox": [ + 187, + 130, + 782, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yanglin Feng", + "bbox": [ + 132, + 203, + 246, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hongyuan Zhu", + "bbox": [ + 287, + 203, + 416, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1College of Computer Science, Sichuan University \n3Sichuan Zhiqian Technology Co., Ltd", + "bbox": [ + 96, + 220, + 429, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dezhong Peng $^{1,3,4}$", + "bbox": [ + 457, + 203, + 602, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xi Peng1", + "bbox": [ + 643, + 203, + 715, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Peng Hu1*", + "bbox": [ + 758, + 203, + 841, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Institute for Infocomm Research (I²R), A*STAR, Singapore \n $^{4}$ Chengdu Ruibei Yingle Information Technology Co., Ltd", + "bbox": [ + 457, + 220, + 874, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, with the advent of Metaverse and AI Generated Content, cross-modal retrieval becomes popular with a burst of 2D and 3D data. However, this problem is challenging given the heterogeneous structure and semantic discrepancies. Moreover, imperfect annotations are ubiquitous given the ambiguous 2D and 3D content, thus inevitably producing noisy labels to degrade the learning performance. To tackle the problem, this paper proposes a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data. Specifically, one novel Robust Discriminative Center Learning mechanism (RDCL) is proposed in RONO to adaptively distinguish clean and noisy samples for respectively providing them with positive and negative optimization directions, thus mitigating the negative impact of noisy labels. Besides, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information inside the noisy data by minimizing the cross-modal and semantic discrepancy between common space and label space simultaneously. Comprehensive mathematical analyses are given to theoretically prove the noise tolerance of the proposed method. Furthermore, we conduct extensive experiments on four 3D-model multimodal datasets to verify the effectiveness of our method by comparing it with 15 state-of-the-art methods. Code is available at https://github.com/penghu-cs/RONO.", + "bbox": [ + 75, + 323, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 729, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Point-cloud retrieval (PCR) is fundamental and crucial for processing and analyzing 3D data [14], which could provide the direct technical support of the 3D data search engine, thus embracing compelling application prospects and practical value in the fields of robotics [7, 32], autonomous driving [23, 31], virtual/augmented reality [9], and medicine [29], etc. Different from 2D images, 3D point clouds could depict the internal architecture and ex", + "bbox": [ + 75, + 755, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ternal appearance of objects from distinct views/modalities. Hence, PCR is often accompanied by retrieving across diverse modalities, termed 2D-3D cross-modal retrieval [19].", + "bbox": [ + 500, + 292, + 890, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the other hand, it is extremely expensive and labor-intensive to label such a huge amount of data points [17, 41], not to mention the additional challenges of the missing color and texture of the point clouds. In order to reduce the labeling cost, we could utilize open source or low-cost annotation tools (e.g., point-cloud-annotation-tool [18], LabelHub, etc.), hence it will inevitably introduce label noise due to the non-expert annotation. However, almost all existing works excessively rely on well-labeled data [19, 20, 44], thus making them vulnerable to noisy labels and leading to unavoidable performance degradation.", + "bbox": [ + 496, + 339, + 892, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the aforementioned issues, we propose a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data as shown in Figure 1. Our RONO framework consists of two mechanisms: 1) a novel Robust Discriminative Center Learning mechanism (RDCL) to robustly and discriminatively tackle clean and noisy samples, and 2) a Shared Space Consistency Learning mechanism (SSCL) to alleviate and even eliminate the heterogeneity and semantic gaps across different modalities.", + "bbox": [ + 496, + 507, + 893, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "More specifically, RDCL is presented to adaptively divide the noisy data into clean and noisy samples based on the memorization effect of deep neural networks (DNNs) [3], and then endowing them with positive and negative optimization directions, respectively. In brief, RDCL could compact the clean points to the corresponding category centers while scattering the noisy ones apart away from the noisy centers in the common space, thus alleviating the interference of noisy labels. In addition, our SSCL aims at mitigating the inherent gaps in the common space, i.e., the heterogeneity and semantic gaps. On the one hand, to bridge the heterogeneity gap across different modalities, our SSCL enforces modality-specific samples from the same instance collapse into a single point in the common space, thus producing modality-invariant representations. On the other hand, our SSCL narrows the gap between the representation space and shared label space to explicitly elimi", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Peng Hu (penghu.ml@gmail.com).", + "bbox": [ + 94, + 886, + 410, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11610", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5f3682d314260462355518a027708f5981e88e88bf5604391393e969f377bf84.jpg", + "image_caption": [ + "Figure 1. The pipeline of our robust 2D-3D retrieval framework (RONO). First, modality-specific extractors project different modalities $\\{\\mathcal{X}_j,\\mathcal{Y}_j\\}_{j = 1}^M$ into a common space. Second, our Robust Discriminative Center Learning mechanism (RDCL) is conducted in the common space to divide the clean and noisy data while rectifying the optimization direction of noisy ones, leading to robustness against noisy labels. Finally, RONO employs a Shared Space Consistency Learning mechanism (SSCL) to bridge the intrinsic gaps between common space and label space. To be specific, SSCL narrows the cross-modal gap by a Multimodal Gap loss (MG) while minimizing the semantic discrepancy between the common space and label space using a Common Representations Classification loss (CRC) $\\mathcal{L}_{\\mathrm{rc}}$ , thus endowing representations with modality-invariant discrimination." + ], + "image_footnote": [], + "bbox": [ + 137, + 87, + 831, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "nate the semantic discrepancy, thus encapsulating common discrimination into common representations. Our main contributions can be summarized as follows:", + "bbox": [ + 75, + 479, + 470, + 525 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a robust 2D-3D cross-modal retrieval framework (RONO) to robustly learn the common discriminative and modality-invariant representations from noisy labels. To the best of our knowledge, this work could be one of the first attempts to learn with noisy labels for 2D-3D cross-modal retrieval.", + "- To mitigate the impact of noisy labels, a novel Robust Discriminative Center Learning mechanism (RDCL) is proposed to adaptively distinguish clean and noisy samples, and then provide them with positive and negative optimization directions, respectively.", + "- To construct discriminative and modality-invariant representations, a Shared Space Consistency Learning mechanism (SSCL) is presented to alleviate the intrinsic gaps across heterogeneity, representation, and label spaces.", + "- We theoretically and experimentally demonstrate the robustness of the proposed method under both synthetic symmetric/asymmetric and real-world noisy labels. Our RONO remarkably outperforms the state-of-the-art methods on 3D object benchmarks of different scales with noisy labels without bells and whistles." + ], + "bbox": [ + 94, + 536, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 478, + 640, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Cross-modal Retrieval", + "text_level": 1, + "bbox": [ + 500, + 505, + 709, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, cross-modal retrieval has attracted more and more attention from academia and industry due to its flexible search [17, 39, 40]. The most popular solution is to project multimodal data into a common space, resulting in retrieving related content in the space across different modalities. They could be roughly classified into unsupervised and supervised methods. More specifically, 1) one typical kind of unsupervised method is Canonical Correlation Analysis (CCA) and its variants [1, 35, 45]. They aim to map multimodal inputs into a common space by maximizing the correlation across different modalities. 2) With the help of label information, supervised methods could encapsulate the discrimination into the shared space, thus suiting the downstream retrieval task better. To learn discriminative representations, some shallow methods utilize Fisher criterion [6] to project different modalities into a latent common space [20, 30]. To capture the high nonlinearity in multimodal data, Deep Neural Networks (DNNs) are introduced to learn discriminative and modality-invariant representations [28, 34, 44].", + "bbox": [ + 496, + 529, + 890, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Learning with Noisy Labels", + "text_level": 1, + "bbox": [ + 500, + 845, + 750, + 862 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the ubiquitous imperfect annotations in the training data, numerous methods have been presented to im", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11611", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prove the robustness of DNNs against noisy labels. The existing works could be grouped into three main categories: 1) Architecture-based methods focus on modifying the DNN architecture to model the noise transition matrix [5, 8, 11]. However, it is still an open issue to accurately estimate noise transition due to the unpredictable and complex noise. 2) Samples-based methods generally learn from clean samples while weakening the adverse impact of noisy ones by re-weighting samples and refurbishing the labels [2, 25]. However, they require some additional well-labeled data, which is difficult and even impossible to satisfy in real-world applications. To address the problem, some methods adaptively divide the training data into clean and noisy sets based on the memorization effect of DNNs [3] for robust DNN training [13, 24]. 3) Loss-based methods mainly focus on designing robust optimization objectives to guide DNNs learning from noisy labels [10, 16, 26, 37, 43]. Although these robust loss functions could alleviate DNNs overfitting on noisy labels, they may lead DNNs to underfit the clean and hard samples.", + "bbox": [ + 75, + 90, + 472, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 407, + 287, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 433, + 279, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, some notations are defined for a clear presentation. Boldface lowercase $\\pmb{x}$ and plain letters $M, N$ represent column vectors and scalars, respectively. Give a $K$ -category multimodal dataset $\\mathcal{D} = \\{\\mathcal{M}_j\\}_{j=1}^M = \\{\\mathcal{X}_j, \\mathcal{Y}_j\\}_{j=1}^M$ , where $M$ is the number of modalities, $N$ is the number of samples in one modality, $\\mathcal{M}_j = \\{(x_i^j, y_i^j)\\}_{i=1}^N$ is the $j$ -th modality, $x_i^j \\in \\mathbb{R}^{d_j}$ is the $i$ -th sample from the $j$ -th modality, $d_j$ is the dimension of the $j$ -th modality and $y_i^j$ is the corresponding label of $x_i^j$ that may be incorrect.", + "bbox": [ + 75, + 458, + 468, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To alleviate the influence of corrupted labels, a robust 2D-3D retrieval framework (RONO) is proposed to robustly learn discrimination from noisy labels while bridging the cross-modal gap. In the framework, we present a Robust Discriminative Center Learning mechanism (RDCL) to reduce the negative impact of unreliable labels, and a Shared Space Consistency Learning mechanism (SSCL) to simultaneously narrow the semantic and heterogeneity gaps. The overall objective function is shown as follows:", + "bbox": [ + 75, + 599, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\underbrace {\\mathcal {L} _ {r d c}} _ {R D C L} + \\underbrace {\\beta_ {m g} \\mathcal {L} _ {m g} + \\beta_ {c r c} \\mathcal {L} _ {c r c}} _ {S S C L}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 748, + 468, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rdc}$ is the loss function adopted by RDCL (see Equation (4)), $\\mathcal{L}_{mg}$ and $\\mathcal{L}_{crc}$ are the loss functions employed by SSCL (see Equations (5) and (6)), and $\\beta_{mg}$ and $\\beta_{crc}$ are the trade-off parameters. Our RONO could be optimized by descending Equation (1) with stochastic gradient descent. In the following sections, we will elaborate on each component of our RONO.", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Robust Discriminative Center Learning", + "text_level": 1, + "bbox": [ + 500, + 90, + 841, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To encapsulate the discrimination into the common space, we enforce the samples with the same category compact to the shared clustering centers, while escaping from other centering centers. First, we formulate a contrastive center error $t$ to measure the semantic difference between the estimated representations and the clustering centers as follows:", + "bbox": [ + 496, + 113, + 893, + 218 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i} ^ {j} = \\frac {\\sum_ {k} ^ {K} e ^ {\\left(\\mathbf {c} _ {k \\neq y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}}{K - 1} - e ^ {\\left(\\mathbf {c} _ {k = y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 222, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z_{i}^{j} = f_{j}(\\pmb{x}_{i}^{j})\\in \\mathbb{R}^{d_{c}}$ is the $d_{c}$ -D common representation of the $\\pmb{x}_i^j$ , $f_{j}:\\mathbb{R}^{d_{j}}\\to \\mathbb{R}^{d_{c}}$ is the input space to common space mapping function, $\\pmb {c}_i = \\frac{1}{|\\mathcal{Z}_i|}\\sum_{\\pmb {z}\\in \\mathcal{Z}_i}\\pmb {z}$ is the center of $i$ -th category, and $\\mathcal{Z}_i$ is the set of the $i$ -th category in the common space. In Equation (2), the dot product is exploited to measure the similarity between a given point and a clustering center in the common space. Obviously, minimizing Equation (2) could maximize the within-class similarities while minimizing the between-class ones, thus endowing the common representations with discrimination. Thus, we could formulate a vanilla loss of RDCL as below:", + "bbox": [ + 496, + 271, + 892, + 441 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r d c} ^ {\\prime} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} t _ {i} ^ {j}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 452, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, such a learning paradigm of Equation (3) will utilize all samples to train networks indiscriminately, thus leading to overfitting on corrupted labels like traditional supervision methods, especially under high noise rates.", + "bbox": [ + 496, + 498, + 890, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To investigate the impact of noisy labels on $\\mathcal{L}_{rdc}^{\\prime}$ , we conduct some visualized experiments on noisy labels and true labels as shown in Figure 2. From the figure, one could observe that although $\\mathcal{L}_{rdc}^{\\prime}$ makes the networks overfitting to corrupted labels (see Figures 2b and 2f), it could capture the correct discrimination to compact the samples with corrupted labels to the correct clusters in the early training stage (see Figures 2c and 2g), which is well known as the memorization effect of DNNs [3]. That is to say, the similarities between points and the assigned clusters could be markedly distinguishable after a short training period for the samples with correct and corrupt labels. Inspired by the observation, we propose a Robust Discriminative Center loss (RDC) to adaptively discriminate the clean and noisy samples according to $t$ , and then apply a bias to endow them with positive and negative optimization direction. Thus, we rewrite Equation (3) as follows:", + "bbox": [ + 496, + 559, + 892, + 815 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r d c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} \\left[ (1 - v) t _ {i} ^ {j} - v | t _ {i} ^ {j} + \\alpha | \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 820, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $v\\in [0,1]$ is a dynamically increasing balanced parameter increasing from 0 to 1 with the number of epoch lin", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11612", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5169172ff861dae6b230b3aaa4f914022b4260109cbe3d22239ac6f4b0fff69a.jpg", + "image_caption": [ + "(a) Baseline [19]" + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 277, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8df2a74aa902c3c2958ed749a29086a7c5ac8c5f597fff6b6d7eee6aa58dee9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5d94271e5e17b82514d19a4edebdf636df67ebc22bdf0e7faa71c4dc8f61a8c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 88, + 687, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bc198c729bad7e083dc3d1243b38dc5279e7f486e11d50750d5c6637d8efad4a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 89, + 890, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d60a308fbf943c58d2145e1c517d13b85c3d0edcbff469cd43d360f6f08ee595.jpg", + "image_caption": [ + "(e) Baseline [19]" + ], + "image_footnote": [], + "bbox": [ + 80, + 223, + 274, + 337 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/610d9e26c1e39d36d70969c01d504ed947b9207c80d406ca0dedd974427dd8c5.jpg", + "image_caption": [ + "(b) $\\mathcal{L}_{rdc}^{\\prime}$", + "(f) $\\mathcal{L}_{rdc}^{\\prime}$" + ], + "image_footnote": [], + "bbox": [ + 282, + 223, + 480, + 337 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f3652a3696cdbf5fc8bede1314c4b52d1e9039b3908d4f5829c7772b48daf320.jpg", + "image_caption": [ + "(c) $\\mathcal{L}_{rdc}^{\\prime}$ after 5 epochs", + "(g) $\\mathcal{L}_{rdc}^{\\prime}$ after 5 epochs", + "Figure 2. (a), (b), (c) and (d) show the density vs. the similarity between common representations and noisy centers, and (e), (f), (g) and (h) show the density vs. the similarity between common representations and clean centers for the test set after the training under 0.4 symmetric noise. Moreover, (a) and (e) are trained with the Cross-Modal Center loss (CMC) [19], (b) and (f) are trained with vanilla RDCL loss $\\mathcal{L}_{rdc}^{\\prime}$ of Equation (3), (c) and (g) are trained for only 5 epochs with $\\mathcal{L}_{rdc}^{\\prime}$ and (d) and (h) are trained with the proposed Robust Discriminative Center loss (RDC). It can be found that after short training periods with vanilla RDCL loss, both true and false labeled samples are compacted to their real category centers, and false labeled samples are not similar to their mislabeled category centers. Adopting RDC for training could maintain and reinforce the robustness of the results, which makes the samples in noisy set adaptively avoid being similar to the mislabeled category centers and maintain their similarity to the real category centers, while CMC could hardly achieve." + ], + "image_footnote": [], + "bbox": [ + 490, + 223, + 684, + 337 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5fbe530347785e29565210d77dca011f599632315ef58d628b343fcfdf231367.jpg", + "image_caption": [ + "(d) $\\mathcal{L}_{rdc}$", + "(h) $\\mathcal{L}_{rdc}$" + ], + "image_footnote": [], + "bbox": [ + 694, + 223, + 890, + 337 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "early within up to 30 epochs, and $\\alpha \\in [-e,e]$ is a threshold for clean-noise separation. In our training stage, $v$ gradually increases from 0 to 1. More specifically, our RDC will focus on learning simple patterns before fitting on the corrupted labels in the early stage. With further training, our RDC will make the second item dominant to explicitly separate samples into clean and noisy sets, and assign them with correct optimization directions. Surprisingly, our RDC could accurately cluster noisy samples into their correct centers regardless of the corrupted supervision as shown in the visualization results of Figures 2d and 2h, thus embracing robustness against noisy labels.", + "bbox": [ + 75, + 503, + 468, + 685 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Shared Space Consistency Learning", + "text_level": 1, + "bbox": [ + 76, + 695, + 388, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although our RDCL could achieve robustness against noisy labels, the cross-modal learning paradigm is frequently affected by the inherent gaps across different modalities. More specifically, due to the randomness of the category centers caused by the random initialization of DNNs, blindly increasing the discrimination between points and centers would lead to losing the intrinsic information inside the data, thus degrading the retrieval performance. To handle the problem, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information by narrowing the heterogeneity and semantic gaps simultaneously.", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, in order to further alleviate or even eliminate the inherent gap across different modalities, we adopt a Multimodal Gap loss (MG) to maximize the mutual information between different modalities from the instance-based perspective [16], which could be formulated as:", + "bbox": [ + 496, + 503, + 890, + 578 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m g} = - \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} l o g \\left(\\frac {\\sum_ {k} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {i} ^ {k}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}{\\sum_ {l} ^ {N} \\sum_ {m} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {l} ^ {m}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 584, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature parameter. By minimizing Equation (5), the discrepancy across different modalities could be reduced to project cross-modal samples into a common space, thus narrowing the heterogeneity gap.", + "bbox": [ + 496, + 631, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, in addition to the heterogeneity gap, the semantic discrepancy will also degrade the performance since distinct modalities intrinsically belong to the same label space. To eliminate the discrepancy, we propose a Common Representations Classification loss (CRC) to narrow the gap between the common space and label space. Specifically, a shared classifier is employed to bridge the common space and label space, and then minimize the difference between classification predictions and labels. To alleviate the influence of noisy labels, the robust MAE loss is utilized to minimize the difference as follows:", + "bbox": [ + 496, + 691, + 890, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c r c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} | g \\left(\\boldsymbol {z} _ {i} ^ {j}, \\Gamma\\right) - y _ {i} ^ {j} |, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 859, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11613", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g(z_i^j, \\Gamma)$ is a common classifier with parameters $\\Gamma$ shared by all modalities.", + "bbox": [ + 76, + 89, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Theoretical Justification", + "text_level": 1, + "bbox": [ + 76, + 128, + 299, + 145 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following previous works [10, 26], we could indicate that our joint loss function $\\mathcal{L}$ is robust against both symmetric and asymmetric label noise. Since DNNs are noise tolerant in the early training stage [3], we only discuss the robustness of our method during the latter training stage as $v$ has dynamically increased to 1.", + "bbox": [ + 76, + 152, + 468, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Property 1 $\\exists \\alpha \\in [-e,e],RDC$ satisfies:", + "bbox": [ + 76, + 253, + 349, + 270 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {i = 1} ^ {K} \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), i) = (K - 1) \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), y ^ {*}) + C \\quad \\boldsymbol {x} \\in \\mathcal {X}, \\forall f, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 279, + 483, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rdc}(f(\\pmb{x}), y^{*})$ is the loss function to compute $\\mathcal{L}_{rdc}$ with the common representations $f(\\pmb{x})$ and $K$ -category true label $y^{*}$ , and $C$ is a constant.", + "bbox": [ + 76, + 333, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Property 2 There exist upper and lower definite boundaries for $\\mathcal{L}_{rdc}$ .", + "bbox": [ + 76, + 388, + 468, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 1 If the above properties are satisfied, RDC with appropriate $\\alpha$ is noise tolerant against symmetric (or uniform) and asymmetric (or class conditional) noisy labels.", + "bbox": [ + 75, + 430, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 2 [10] When symmetric noise rate $\\eta < 1 - \\frac{1}{K}$ , MAE is robust against symmetric (or uniform) noisy labels. Defining the risk of the classifier is $R_{\\mathcal{L}_{mae}}(f)$ , $f^{*}$ is the global minimizers of $R_{\\mathcal{L}_{mae}}(f)$ , $\\mathcal{L}_{mae}(f(\\pmb{x}),y)$ is the calculation of MAE, when $R_{\\mathcal{L}_{mae}}(f^{*}) = 0$ , $0 \\leq \\mathcal{L}_{mae}(f(\\pmb{x}),i) \\leq \\frac{C}{K-1} = 2, \\forall i$ and any category-wide noise rate is less than the rate of being clean $\\eta_{ij} \\leq 1 - \\eta_y$ , MAE is robust against asymmetric (or class conditional) noisy labels.", + "bbox": [ + 76, + 484, + 468, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 3 [21, 26] Assuming there are $n$ noise tolerant loss functions $\\{\\mathcal{L}_i\\}_{i=1}^n$ , and $n$ trade-off hyperparameters $\\{\\gamma_i\\}_{i=1}^n$ , then $\\mathcal{L} = \\sum_{i=1}^n \\gamma_i \\mathcal{L}_i$ is noise tolerant.", + "bbox": [ + 76, + 633, + 468, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The elaborate proofs for Property 1, Property 2, and Lemma 1 can be found in our Complementary Materials. Property 1 and Property 2 can be obtained by mathematical derivation. For Lemma 1, we denote the risk of representation extractor $f$ with clean data $\\{x, y^*\\}$ on our RDC as $R(f) = \\mathbb{E}_{x, y^*} \\mathcal{L}_{rdc}$ , and the risk with noisy labels as $R^\\eta(f) = \\mathbb{E}_{x, y} \\mathcal{L}_{rdc}$ . If $f^*$ and $f_\\eta^*$ are respectively the global minimizers of $R(f)$ and $R^\\eta(f)$ , we require to prove $f^*$ is also a global minimizer of noisy risk $R^\\eta(f)$ for $\\mathcal{L}_{rdc}$ that is robust against noisy labels. For Lemma 2 and Lemma 3, the theoretical proofs are provided in [10] and [21, 26], respectively.", + "bbox": [ + 76, + 689, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to Lemma 1 and Lemma 2, our RDC and CRC are theoretically robust against both symmetric and", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "asymmetric noisy labels. Moreover, our MG is also noise tolerant with noisy labels since it is unsupervised and independent of labels. Therefore, according to Lemma 3, we could draw the conclusion that our joint loss function $\\mathcal{L}$ is noise tolerant against noisy labels.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 179, + 633, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate our RONO, we conduct extensive comparison experiments on four 3D multimodal datasets with different scales, i.e., 3D MNIST [38], RGB-D object [22], ModelNet10 [36] and ModelNet40 [36] datasets.", + "bbox": [ + 496, + 204, + 890, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 273, + 705, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, our RONO is implemented in PyTorch and its optimization process could be found in our Complementary Materials. All the experiments are carried out on GeForce RTX 1080Ti GPUs. Four widely-used 3D multimodal datasets are utilized for evaluation, which are briefly introduced below:", + "bbox": [ + 496, + 296, + 890, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3D MNIST [38]: It is a small-scale 3D model dataset collected in Kaggle which contains 6000 image-point cloud pairs. The point cloud samples are generated from the MNIST dataset. We divide the dataset into 2 subsets: 5000 and 1000 pairs for training and testing sets, respectively.", + "bbox": [ + 496, + 387, + 890, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RGB-D object [22]: It is a large-scale dataset containing 300 common family objects belonging to 51 categories. The dataset has 207,621 image-point cloud pairs, which of each has a $640 \\times 480$ image and a point-cloud object with 1000 to 5000 points. We split the dataset into 200,000 and 7,621 pairs for training and testing sets, respectively.", + "bbox": [ + 496, + 462, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ModelNet10 [36]: It is a 10-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 2,468 and 908 for training and testing sets, respectively.", + "bbox": [ + 496, + 553, + 890, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ModelNet40 [36]: It is a 40-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 9,840 and 3,991 for training and testing sets, respectively.", + "bbox": [ + 496, + 598, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our experiments, we compare our RONO with 15 state-of-the-art methods that include 5 unsupervised methods (i.e., CCA [15], DCCA [1], DCCAE [35], UCCH [17] and DGCPN [42]) and 10 supervised ones (i.e., GMA [30], MvDA [20], AGAH [12], DADH [4], DAGNN [28], ALGCN [27], DSCMR [44], MRL [16], CLF [19] and CLF [19] + MAE [10]). Note that, CLF+MAE is a variant of CLF [19] with a robust MAE [10].", + "bbox": [ + 496, + 643, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Most of the experiments are conducted on bimodal settings to evaluate two cross-modal tasks: using images as queries to retrieve the point-cloud samples (Image $\\rightarrow$ Point Cloud), using point-cloud samples as queries to retrieve the images (Point Cloud $\\rightarrow$ Image). Without loss of generality, several experiments are conducted across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40. We use the widely-used mean Average Precision (mAP) score to evaluate the retrieval performance. We", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11614", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7c571f4108fd03f2311cd98dd1df7cb960364006fb323a59a7725d9109ec719a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.4150.4150.4150.4150.4140.4140.4140.4140.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.4490.4380.4260.4150.4370.4320.4230.4140.0900.0850.0880.0890.0870.0830.0870.086
MvDA [20]0.4810.4610.4320.3280.4820.4610.4310.3230.1330.1320.1280.1120.1320.1330.1090.102
AGAH [12]0.6880.5570.1280.1080.6800.5480.1220.1160.6080.3790.1950.0900.6010.3800.1940.090
DADH [4]0.7350.6320.4030.2900.7270.6140.3820.2860.6260.3340.1360.0620.6180.3260.1350.062
DAGNN [28]0.8830.8500.7490.4450.8790.8450.7430.4350.7070.6370.5200.3150.7150.6350.5130.313
ALGCN [27]0.8740.8400.7570.4010.8680.8310.7480.3850.6730.5010.3980.2040.6700.5010.4140.200
DSCMR [44]0.9080.8120.5120.2190.8960.8110.4720.1400.7270.6710.5320.2900.7310.6730.5230.275
MRL [16]0.9550.9370.9180.7850.9440.9310.9050.7910.7110.6460.6100.4980.7090.6230.5980.487
CLF [19]0.8900.8110.4600.1240.8720.7930.4260.1200.7230.6610.3460.1110.7030.6340.3430.106
CLF [19]+MAE [10]0.8100.8120.5010.1220.8090.8110.4830.1220.7050.6260.4260.1870.7030.6240.3990.167
Ours0.9620.9520.9310.8310.9480.9340.9150.8280.7740.7370.7360.7060.7710.7300.7290.700
", + "bbox": [ + 81, + 88, + 890, + 361 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6b407398999444ad7647a2b7425621bf316b470d1cdaf511b6ee29751f59bf5c.jpg", + "table_caption": [ + "Table 1. Performance comparison in terms of mAP under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + ], + "table_footnote": [], + "table_body": "
MethodModelNet10 [36]ModelNet40 [36]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.6250.6250.6250.6250.6270.6270.6270.6270.5320.5320.5320.5320.5310.5310.5310.531
DCCA [1]0.6840.6840.6840.6840.6770.6770.6770.6770.5840.5840.5840.5840.5690.5690.5690.569
DCCAE [35]0.7030.7030.7030.7030.6930.6930.6930.6930.5930.5930.5930.5930.5720.5720.5720.572
DGCPN [42]0.7650.7650.7650.7650.7590.7590.7590.7590.7050.7050.7050.7050.6970.6970.6970.697
UCCH [17]0.7710.7710.7710.7710.7700.7700.7700.7700.7550.7550.7550.7550.7390.7390.7390.739
GMA [30]0.6500.6170.5850.5210.6460.5790.5500.4970.5250.4850.4660.4480.5150.4870.4590.437
MvDA [20]0.4940.4580.4490.3900.4640.4280.4060.3280.4200.3730.3290.3160.4120.3700.3000.271
AGAH [12]0.8530.7360.5830.4250.8370.6990.5490.4080.8090.7320.6870.5680.7830.7360.6640.554
DADH [4]0.8600.7720.6700.5540.8380.7680.6580.5530.8180.7430.6760.5810.7820.7480.6570.586
DAGNN [28]0.8440.8000.7540.4220.8360.8100.7630.4480.8020.7230.6350.4020.7980.7280.6430.412
ALGCN [27]0.7880.5970.4260.2820.7970.5890.4400.2690.7660.5380.4260.2980.7630.5370.4030.279
DSCMR [44]0.8490.7580.6660.3240.8360.7320.6370.3070.8240.7880.6870.3280.8110.7850.6940.339
MRL [16]0.8760.8700.8630.8320.8610.8570.8480.8230.8330.8290.8280.8180.8240.8260.8200.817
CLF [19]0.8490.7820.6200.3650.8380.7640.5950.3870.8220.7780.6240.3150.8150.7710.5870.295
CLF [19]+MAE[10]0.8530.7520.6790.3430.8380.7160.6590.3730.8270.7580.6510.3840.8160.7490.6400.372
Ours0.8920.8770.8700.8360.8900.8750.8610.8300.8770.8580.8380.8230.8720.8540.8380.821
", + "bbox": [ + 81, + 414, + 888, + 689 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Performance comparison under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the ModelNet10 and ModelNet40 datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined.", + "bbox": [ + 76, + 698, + 892, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "conduct the comparison experiments under both synthetic symmetric and asymmetric label noise for comprehensive evaluation. Due to the space limitation, we only evaluate the robustness against asymmetric label noise on 3D MNIST and RGB-D object datasets. More extra experimental results could be found in our Complementary Materials. For a comprehensive evaluation, the symmetric noise rates are set as 0.2, 0.4, 0.6, and 0.8, and the asymmetric ones are set as 0.1, 0.2, and 0.4.", + "bbox": [ + 75, + 739, + 470, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with the State-of-the-Arts", + "text_level": 1, + "bbox": [ + 500, + 739, + 831, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We apply 2D-3D cross-modal retrieval on four 3D model multimodal datasets to evaluate the robustness of our RONO and the baselines. The experimental results under symmetric noise are reported in Tables 1 and 2, and ones under asymmetric noise are reported in Table 3. From these experimental results, we could obtain the following observations:", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- Noisy labels could remarkably reduce the retrieval per", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11615", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e8c1e01763170a6e841bed905717321129e2924b286a5432e7752afce408d78f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
00.10.20.400.10.20.400.10.20.400.10.20.4
CCA [15]0.4150.4150.4150.4150.4150.4150.4150.4150.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.5140.4440.4360.4150.5000.4350.4170.3960.1260.0890.0850.0730.1210.0850.0810.069
MvDA [20]0.5300.4720.4070.3700.5080.4720.3970.3520.1880.1880.1590.1420.1990.1680.1390.124
AGAH [12]0.9670.7300.6110.5190.9610.7290.5890.5120.6520.6030.4440.3560.6280.5590.4360.361
DADH [4]0.9710.8480.7180.5700.9690.8250.7010.5720.7720.7230.5890.5240.7610.7030.5720.511
DAGNN [28]0.9270.8940.8710.6840.9270.8930.8640.6910.7410.7040.6460.5630.7240.6890.6310.554
ALGCN [27]0.9080.8760.8600.6350.9000.8710.8520.6410.7170.6850.6170.5260.6910.6780.5980.531
DSCMR [44]0.9630.9140.8690.7110.9450.9060.8620.7040.7740.7550.7110.6730.7680.7380.7000.659
MRL [16]0.9630.9590.9440.7920.9450.9400.9220.7620.7230.6550.6350.6020.7190.6520.6360.599
CLF [19]0.9830.9450.9240.8090.9580.9320.9200.8020.7720.7710.7340.6740.7660.7590.7210.659
CLF [19]+MAE[10]0.9710.9420.9210.7960.9510.9300.9180.7830.7520.7580.7200.6510.7410.7500.7120.637
Ours0.9830.9610.9580.9120.9680.9470.9380.8970.7790.7730.7280.6810.7710.7560.7210.669
", + "bbox": [ + 81, + 88, + 890, + 363 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formance of supervised methods. Their performance will be degraded rapidly as the noise rate increases. Especially, when the noise rate is high, supervised methods tend to perform worse than unsupervised ones, or even fail to fit the data.", + "bbox": [ + 107, + 428, + 468, + 503 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- For the symmetric noise, our RONO achieves remarkably better results than supervised (e.g., CLF, DAGNN, DSCMR, etc.), which demonstrates the robustness of our method against noisy labels. Besides, our RONO could utilize noisy labels to overcome the unsupervised methods (e.g., UCCH, DGCPN, etc.), thus indicating that additional label information could improve performance even if it contains noise.", + "- Our RONO is superior to a strong baseline (i.e., MRL) that is a noise-tolerate cross-modal method. Especially, our method could achieve 0.703 in terms of mAP under 0.8 noise on the large-scale RGB-D object dataset, which is higher than MRL (0.493) by 0.210, thus demonstrating the effectiveness of our adaptive optimization strategy for clean and noisy data.", + "- For asymmetric noise, the extremely perplexing class conditional noise will degrade the performance of the memorization effect of DNNs, however, our RONO still achieves superior robustness against noisy labels.", + "- Our RONO shows superiority even without the addition of synthetic label noise, demonstrating that well-annotated datasets also contain noise impacting the performance of each non-robust method." + ], + "bbox": [ + 94, + 512, + 468, + 888 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4495a42d427a8a810147b12b84f6c5413f903994667d2b13e7423d0c80531dba.jpg", + "table_caption": [ + "Table 3. Performance comparison under the asymmetric noise rates of 0, 0.1, 0.2, and 0.4 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + ], + "table_footnote": [], + "table_body": "
RDCLSSCL3D MNIST [38]ModelNet40 [36]
LrdcLmgLcrcImg→PntPnt→ImgImg→PntPnt→Img
0.40.80.40.80.40.8
✓✓✓0.9520.8310.9340.8280.8580.824
L′rdc✓✓0.8910.3420.8990.3140.8150.670
✓✓0.8410.6750.8320.6710.8210.777
✓✓0.9290.6150.9270.5640.7930.551
✓✓0.9300.7090.9140.7060.8040.673
✓0.6410.4230.6350.4290.7350.608
✓0.6610.6610.6600.6600.4440.444
✓0.5270.3480.5370.2750.7250.484
", + "bbox": [ + 504, + 425, + 893, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation studies for RONO on the 3D MNIST and ModelNet40 datasets with 0.4 symmetric noise. $\\checkmark$ stands for use.", + "bbox": [ + 498, + 590, + 890, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 643, + 653, + 660 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we investigate the contribution of each proposed component (i.e., loss $\\mathcal{L}_{rdc}$ , $\\mathcal{L}_{mg}$ and $\\mathcal{L}_{crc}$ ) to 2D-3D retrieval with noisy labels. For a comprehensive comparison, we ablate each component from the framework and conduct the variants with the same experimental settings on two distinct datasets (i.e., 3D MNIST and ModelNet40). The results are shown in Table 4. From the table, one could draw the following observation: 1) RONO with/without any component will improve/drop retrieval performance, which indicates that each component contributes to our framework. 2) Replacing RCD (i.e., $\\mathcal{L}_{rdc}$ ) with the vanilla loss of RDCL (i.e., $\\mathcal{L}_{rdc}^{\\prime}$ ) will result in remarkable performance degradation, thus demonstrating the effectiveness of differentiated optimization for clean and noisy data, especially for high noise rates.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11616", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6f35e736dfa907279016eacec918404f0e382b7bb53130f3111d4a68a30fe70b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ηQryImgMshPnt
RetrvImgMshPntImgMshPntImgMshPnt
0CLF0.9030.8980.8830.8910.8730.8820.8870.8830.881
Ours0.9110.9010.8910.8990.9010.8830.8910.8940.891
0.2CLF0.8250.8300.8250.8310.8500.8480.8290.8500.851
Ours0.8740.8720.8810.8830.8910.8890.8750.8840.890
0.4CLF0.6830.7490.7610.7370.8160.8290.7460.8280.848
Ours0.8580.8760.8630.8620.8810.8750.8590.8750.875
0.6CLF0.5600.5890.6270.5690.6810.7290.6040.7250.794
Ours0.8420.8530.8510.8570.8570.8620.8430.8680.872
0.8CLF0.3110.3160.3610.3230.3920.4000.3650.3850.559
Ours0.8280.8420.8420.8420.8680.8660.8410.8640.868
", + "bbox": [ + 81, + 88, + 472, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance comparison of CLF [19] and our RONO under the symmetric noise rates of 0, 0.2, 0.4, 0.6 and 0.8 on trimodal ModelNet40 dataset [36]. The highest mAPs are shown in bold. For a convenience presentation, we abbreviate Image, Mesh, Point cloud, Query, and Retrieval to Img, Msh, Pnt, Qry, and Retrv, respectively.", + "bbox": [ + 75, + 290, + 470, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Further Comparison with CLF", + "text_level": 1, + "bbox": [ + 76, + 400, + 352, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To comprehensively evaluate our RONO, we conduct various 2D-3D cross-modal retrieval and visualization experiments across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40 [36], by comparing RONO with state-of-the-art CLF [19]. The comparison results are shown in Table 5 and Figures 3 and 4. Due to space limitation, more cross-modal and in-domain comparison results could be found in our Complementary Materials.", + "bbox": [ + 75, + 422, + 468, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From the experimental results, one could observe that: 1) Regardless of noise rates, our RONO show stronger robustness against noisy labels across three modalities. 2) Our RONO could obtain more discriminative clusters compared to CLR, which demonstrates the robustness of our RONO. 3) Our RONO could achieve more correct retrieved results while CLF fails on the same queries, indicating that our method has stronger robustness and is consistent with our quantitative results.", + "bbox": [ + 75, + 560, + 470, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 709, + 194, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel 2D-3D cross-modal retrieval framework to robustly learn discriminative and modality-invariant representations with noisy labels, termed RONO. To be specific, our RONO employs a novel Robust Discriminative Center Learning mechanism (RDCL) to endow clean and noisy samples with correct optimization directions, while a Shared Space Consistency Learning mechanism (SSCL) to guarantee the cross-modal and semantic consistency across different modalities in the common space. Comprehensive mathematical analyses are provided to theoretically prove the noise tolerance of our RONO.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/21613b3f5dd1a7b6559c054f6f67ba3e5289f33f80b5f85d0295ffd0a4a40cda.jpg", + "image_caption": [ + "(a) CLF" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 692, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/665871952dda2bec5c2cbe80bb7f55401a3ac9ac0ac67b5ee99d73ed16512f08.jpg", + "image_caption": [ + "(b) Ours" + ], + "image_footnote": [], + "bbox": [ + 702, + 88, + 890, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/028306bbaa728e64ce89842ab1eb5bc118e300b2ec13f246bfe1d17cbb365687.jpg", + "image_caption": [ + "Figure 3. The representation visualization on the testing set of ModelNet40 by using t-SNE method [33]. CLF and our RONO are trained under 0.4 symmetric label noise. Samples from the same category are rendered with the same color, and ones from the same modality are rendered with the same marker.", + "Figure 4. Top-5 retrieved results of CLF and our RONO under 0.4 label noise on the tri-modal ModelNet40 dataset. Green boxes indicate correct retrieval, while red boxes indicate wrong retrieval." + ], + "image_footnote": [], + "bbox": [ + 501, + 344, + 893, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Furthermore, we conduct extensive experiments compared to 15 state-of-the-art methods on four 3D model multimodal datasets to demonstrate the robustness of the proposed method against synthetic and real label noise.", + "bbox": [ + 498, + 632, + 890, + 693 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 709, + 658, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the National Key R&D Program of China under Grant 2020YFB1406702, the National Natural Science Foundation of China (Grants No. 62102274, 62176171, and U19A2078), Sichuan Science and Technology Planning Project (Grants No. 2021YFS0389, 2021YFG0317, 2021YFG0301, 2022YFQ0014, and 2022YFH0021), Fundamental Research Funds for the Central Universities, A\\*STAR AME Programmatic Funding A18A2b0046, RobotHTPO Seed Fund under Project C211518008 and EDB Space Technology Development Grant under Project S22-19016-STDP.", + "bbox": [ + 498, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11617", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Galen Andrew, Raman Arora, Jeff Bilmes, and Karen Livescu. 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IEEE transactions on neural networks, 17(1):233-238, 2006. 2" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11619", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_model.json b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8632e40f58723179f217a843e81df1758da7a7b1 --- /dev/null +++ b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.189, + 0.131, + 0.784, + 0.175 + ], + "angle": 0, + "content": "RONO: Robust Discriminative Learning with Noisy Labels for 2D-3D Cross-Modal Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.204, + 0.248, + 0.222 + ], + "angle": 0, + "content": "Yanglin Feng" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.204, + 0.418, + 0.222 + ], + "angle": 0, + "content": "Hongyuan Zhu" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.222, + 0.43, + 0.257 + ], + "angle": 0, + "content": "1College of Computer Science, Sichuan University \n3Sichuan Zhiqian Technology Co., Ltd" + }, + { + "type": "text", + "bbox": [ + 0.458, + 0.204, + 0.603, + 0.222 + ], + "angle": 0, + "content": "Dezhong Peng\\(^{1,3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.644, + 0.204, + 0.717, + 0.222 + ], + "angle": 0, + "content": "Xi Peng1" + }, + { + "type": "text", + "bbox": [ + 0.759, + 0.204, + 0.843, + 0.222 + ], + "angle": 0, + "content": "Peng Hu1*" + }, + { + "type": "text", + "bbox": [ + 0.458, + 0.222, + 0.875, + 0.257 + ], + "angle": 0, + "content": "\\(^{2}\\)Institute for Infocomm Research (I²R), A*STAR, Singapore \n\\(^{4}\\)Chengdu Ruibei Yingle Information Technology Co., Ltd" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.702 + ], + "angle": 0, + "content": "Recently, with the advent of Metaverse and AI Generated Content, cross-modal retrieval becomes popular with a burst of 2D and 3D data. However, this problem is challenging given the heterogeneous structure and semantic discrepancies. Moreover, imperfect annotations are ubiquitous given the ambiguous 2D and 3D content, thus inevitably producing noisy labels to degrade the learning performance. To tackle the problem, this paper proposes a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data. Specifically, one novel Robust Discriminative Center Learning mechanism (RDCL) is proposed in RONO to adaptively distinguish clean and noisy samples for respectively providing them with positive and negative optimization directions, thus mitigating the negative impact of noisy labels. Besides, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information inside the noisy data by minimizing the cross-modal and semantic discrepancy between common space and label space simultaneously. Comprehensive mathematical analyses are given to theoretically prove the noise tolerance of the proposed method. Furthermore, we conduct extensive experiments on four 3D-model multimodal datasets to verify the effectiveness of our method by comparing it with 15 state-of-the-art methods. Code is available at https://github.com/penghu-cs/RONO." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.731, + 0.21, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Point-cloud retrieval (PCR) is fundamental and crucial for processing and analyzing 3D data [14], which could provide the direct technical support of the 3D data search engine, thus embracing compelling application prospects and practical value in the fields of robotics [7, 32], autonomous driving [23, 31], virtual/augmented reality [9], and medicine [29], etc. Different from 2D images, 3D point clouds could depict the internal architecture and ex" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.892, + 0.339 + ], + "angle": 0, + "content": "ternal appearance of objects from distinct views/modalities. Hence, PCR is often accompanied by retrieving across diverse modalities, termed 2D-3D cross-modal retrieval [19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.893, + 0.506 + ], + "angle": 0, + "content": "On the other hand, it is extremely expensive and labor-intensive to label such a huge amount of data points [17, 41], not to mention the additional challenges of the missing color and texture of the point clouds. In order to reduce the labeling cost, we could utilize open source or low-cost annotation tools (e.g., point-cloud-annotation-tool [18], LabelHub, etc.), hence it will inevitably introduce label noise due to the non-expert annotation. However, almost all existing works excessively rely on well-labeled data [19, 20, 44], thus making them vulnerable to noisy labels and leading to unavoidable performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.895, + 0.644 + ], + "angle": 0, + "content": "To address the aforementioned issues, we propose a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data as shown in Figure 1. Our RONO framework consists of two mechanisms: 1) a novel Robust Discriminative Center Learning mechanism (RDCL) to robustly and discriminatively tackle clean and noisy samples, and 2) a Shared Space Consistency Learning mechanism (SSCL) to alleviate and even eliminate the heterogeneity and semantic gaps across different modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.902 + ], + "angle": 0, + "content": "More specifically, RDCL is presented to adaptively divide the noisy data into clean and noisy samples based on the memorization effect of deep neural networks (DNNs) [3], and then endowing them with positive and negative optimization directions, respectively. In brief, RDCL could compact the clean points to the corresponding category centers while scattering the noisy ones apart away from the noisy centers in the common space, thus alleviating the interference of noisy labels. In addition, our SSCL aims at mitigating the inherent gaps in the common space, i.e., the heterogeneity and semantic gaps. On the one hand, to bridge the heterogeneity gap across different modalities, our SSCL enforces modality-specific samples from the same instance collapse into a single point in the common space, thus producing modality-invariant representations. On the other hand, our SSCL narrows the gap between the representation space and shared label space to explicitly elimi" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.411, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: Peng Hu (penghu.ml@gmail.com)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11610" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.138, + 0.088, + 0.833, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.895, + 0.455 + ], + "angle": 0, + "content": "Figure 1. The pipeline of our robust 2D-3D retrieval framework (RONO). First, modality-specific extractors project different modalities \\(\\{\\mathcal{X}_j,\\mathcal{Y}_j\\}_{j = 1}^M\\) into a common space. Second, our Robust Discriminative Center Learning mechanism (RDCL) is conducted in the common space to divide the clean and noisy data while rectifying the optimization direction of noisy ones, leading to robustness against noisy labels. Finally, RONO employs a Shared Space Consistency Learning mechanism (SSCL) to bridge the intrinsic gaps between common space and label space. To be specific, SSCL narrows the cross-modal gap by a Multimodal Gap loss (MG) while minimizing the semantic discrepancy between the common space and label space using a Common Representations Classification loss (CRC) \\(\\mathcal{L}_{\\mathrm{rc}}\\) , thus endowing representations with modality-invariant discrimination." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.471, + 0.526 + ], + "angle": 0, + "content": "nate the semantic discrepancy, thus encapsulating common discrimination into common representations. Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.537, + 0.47, + 0.628 + ], + "angle": 0, + "content": "- We propose a robust 2D-3D cross-modal retrieval framework (RONO) to robustly learn the common discriminative and modality-invariant representations from noisy labels. To the best of our knowledge, this work could be one of the first attempts to learn with noisy labels for 2D-3D cross-modal retrieval." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.638, + 0.47, + 0.715 + ], + "angle": 0, + "content": "- To mitigate the impact of noisy labels, a novel Robust Discriminative Center Learning mechanism (RDCL) is proposed to adaptively distinguish clean and noisy samples, and then provide them with positive and negative optimization directions, respectively." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.724, + 0.47, + 0.801 + ], + "angle": 0, + "content": "- To construct discriminative and modality-invariant representations, a Shared Space Consistency Learning mechanism (SSCL) is presented to alleviate the intrinsic gaps across heterogeneity, representation, and label spaces." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "- We theoretically and experimentally demonstrate the robustness of the proposed method under both synthetic symmetric/asymmetric and real-world noisy labels. Our RONO remarkably outperforms the state-of-the-art methods on 3D object benchmarks of different scales with noisy labels without bells and whistles." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.537, + 0.471, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.479, + 0.642, + 0.495 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.71, + 0.521 + ], + "angle": 0, + "content": "2.1. Cross-modal Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.892, + 0.833 + ], + "angle": 0, + "content": "In recent years, cross-modal retrieval has attracted more and more attention from academia and industry due to its flexible search [17, 39, 40]. The most popular solution is to project multimodal data into a common space, resulting in retrieving related content in the space across different modalities. They could be roughly classified into unsupervised and supervised methods. More specifically, 1) one typical kind of unsupervised method is Canonical Correlation Analysis (CCA) and its variants [1, 35, 45]. They aim to map multimodal inputs into a common space by maximizing the correlation across different modalities. 2) With the help of label information, supervised methods could encapsulate the discrimination into the shared space, thus suiting the downstream retrieval task better. To learn discriminative representations, some shallow methods utilize Fisher criterion [6] to project different modalities into a latent common space [20, 30]. To capture the high nonlinearity in multimodal data, Deep Neural Networks (DNNs) are introduced to learn discriminative and modality-invariant representations [28, 34, 44]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.75, + 0.863 + ], + "angle": 0, + "content": "2.2. Learning with Noisy Labels" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To tackle the ubiquitous imperfect annotations in the training data, numerous methods have been presented to im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11611" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.395 + ], + "angle": 0, + "content": "prove the robustness of DNNs against noisy labels. The existing works could be grouped into three main categories: 1) Architecture-based methods focus on modifying the DNN architecture to model the noise transition matrix [5, 8, 11]. However, it is still an open issue to accurately estimate noise transition due to the unpredictable and complex noise. 2) Samples-based methods generally learn from clean samples while weakening the adverse impact of noisy ones by re-weighting samples and refurbishing the labels [2, 25]. However, they require some additional well-labeled data, which is difficult and even impossible to satisfy in real-world applications. To address the problem, some methods adaptively divide the training data into clean and noisy sets based on the memorization effect of DNNs [3] for robust DNN training [13, 24]. 3) Loss-based methods mainly focus on designing robust optimization objectives to guide DNNs learning from noisy labels [10, 16, 26, 37, 43]. Although these robust loss functions could alleviate DNNs overfitting on noisy labels, they may lead DNNs to underfit the clean and hard samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.289, + 0.426 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.434, + 0.281, + 0.449 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.599 + ], + "angle": 0, + "content": "First, some notations are defined for a clear presentation. Boldface lowercase \\( \\pmb{x} \\) and plain letters \\( M, N \\) represent column vectors and scalars, respectively. Give a \\( K \\)-category multimodal dataset \\( \\mathcal{D} = \\{\\mathcal{M}_j\\}_{j=1}^M = \\{\\mathcal{X}_j, \\mathcal{Y}_j\\}_{j=1}^M \\), where \\( M \\) is the number of modalities, \\( N \\) is the number of samples in one modality, \\( \\mathcal{M}_j = \\{(x_i^j, y_i^j)\\}_{i=1}^N \\) is the \\( j \\)-th modality, \\( x_i^j \\in \\mathbb{R}^{d_j} \\) is the \\( i \\)-th sample from the \\( j \\)-th modality, \\( d_j \\) is the dimension of the \\( j \\)-th modality and \\( y_i^j \\) is the corresponding label of \\( x_i^j \\) that may be incorrect." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.47, + 0.736 + ], + "angle": 0, + "content": "To alleviate the influence of corrupted labels, a robust 2D-3D retrieval framework (RONO) is proposed to robustly learn discrimination from noisy labels while bridging the cross-modal gap. In the framework, we present a Robust Discriminative Center Learning mechanism (RDCL) to reduce the negative impact of unreliable labels, and a Shared Space Consistency Learning mechanism (SSCL) to simultaneously narrow the semantic and heterogeneity gaps. The overall objective function is shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.749, + 0.47, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\underbrace {\\mathcal {L} _ {r d c}} _ {R D C L} + \\underbrace {\\beta_ {m g} \\mathcal {L} _ {m g} + \\beta_ {c r c} \\mathcal {L} _ {c r c}} _ {S S C L}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rdc}\\) is the loss function adopted by RDCL (see Equation (4)), \\(\\mathcal{L}_{mg}\\) and \\(\\mathcal{L}_{crc}\\) are the loss functions employed by SSCL (see Equations (5) and (6)), and \\(\\beta_{mg}\\) and \\(\\beta_{crc}\\) are the trade-off parameters. Our RONO could be optimized by descending Equation (1) with stochastic gradient descent. In the following sections, we will elaborate on each component of our RONO." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.842, + 0.108 + ], + "angle": 0, + "content": "3.2. Robust Discriminative Center Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.219 + ], + "angle": 0, + "content": "To encapsulate the discrimination into the common space, we enforce the samples with the same category compact to the shared clustering centers, while escaping from other centering centers. First, we formulate a contrastive center error \\( t \\) to measure the semantic difference between the estimated representations and the clustering centers as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.223, + 0.892, + 0.265 + ], + "angle": 0, + "content": "\\[\nt _ {i} ^ {j} = \\frac {\\sum_ {k} ^ {K} e ^ {\\left(\\mathbf {c} _ {k \\neq y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}}{K - 1} - e ^ {\\left(\\mathbf {c} _ {k = y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.893, + 0.442 + ], + "angle": 0, + "content": "where \\(z_{i}^{j} = f_{j}(\\pmb{x}_{i}^{j})\\in \\mathbb{R}^{d_{c}}\\) is the \\(d_{c}\\)-D common representation of the \\(\\pmb{x}_i^j\\), \\(f_{j}:\\mathbb{R}^{d_{j}}\\to \\mathbb{R}^{d_{c}}\\) is the input space to common space mapping function, \\(\\pmb {c}_i = \\frac{1}{|\\mathcal{Z}_i|}\\sum_{\\pmb {z}\\in \\mathcal{Z}_i}\\pmb {z}\\) is the center of \\(i\\)-th category, and \\(\\mathcal{Z}_i\\) is the set of the \\(i\\)-th category in the common space. In Equation (2), the dot product is exploited to measure the similarity between a given point and a clustering center in the common space. Obviously, minimizing Equation (2) could maximize the within-class similarities while minimizing the between-class ones, thus endowing the common representations with discrimination. Thus, we could formulate a vanilla loss of RDCL as below:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.453, + 0.892, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r d c} ^ {\\prime} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} t _ {i} ^ {j}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.559 + ], + "angle": 0, + "content": "However, such a learning paradigm of Equation (3) will utilize all samples to train networks indiscriminately, thus leading to overfitting on corrupted labels like traditional supervision methods, especially under high noise rates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.893, + 0.816 + ], + "angle": 0, + "content": "To investigate the impact of noisy labels on \\(\\mathcal{L}_{rdc}^{\\prime}\\), we conduct some visualized experiments on noisy labels and true labels as shown in Figure 2. From the figure, one could observe that although \\(\\mathcal{L}_{rdc}^{\\prime}\\) makes the networks overfitting to corrupted labels (see Figures 2b and 2f), it could capture the correct discrimination to compact the samples with corrupted labels to the correct clusters in the early training stage (see Figures 2c and 2g), which is well known as the memorization effect of DNNs [3]. That is to say, the similarities between points and the assigned clusters could be markedly distinguishable after a short training period for the samples with correct and corrupt labels. Inspired by the observation, we propose a Robust Discriminative Center loss (RDC) to adaptively discriminate the clean and noisy samples according to \\(t\\), and then apply a bias to endow them with positive and negative optimization direction. Thus, we rewrite Equation (3) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.821, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r d c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} \\left[ (1 - v) t _ {i} ^ {j} - v | t _ {i} ^ {j} + \\alpha | \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(v\\in [0,1]\\) is a dynamically increasing balanced parameter increasing from 0 to 1 with the number of epoch lin" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11612" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.278, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.209, + 0.223, + 0.222 + ], + "angle": 0, + "content": "(a) Baseline [19]" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.482, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.209, + 0.408, + 0.223 + ], + "angle": 0, + "content": "(b) \\(\\mathcal{L}_{rdc}^{\\prime}\\)" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.089, + 0.688, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.209, + 0.65, + 0.223 + ], + "angle": 0, + "content": "(c) \\(\\mathcal{L}_{rdc}^{\\prime}\\) after 5 epochs" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.09, + 0.891, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.21, + 0.817, + 0.222 + ], + "angle": 0, + "content": "(d) \\(\\mathcal{L}_{rdc}\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.224, + 0.276, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.342, + 0.223, + 0.354 + ], + "angle": 0, + "content": "(e) Baseline [19]" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.224, + 0.481, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.341, + 0.406, + 0.356 + ], + "angle": 0, + "content": "(f) \\(\\mathcal{L}_{rdc}^{\\prime}\\)" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.224, + 0.686, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.342, + 0.65, + 0.356 + ], + "angle": 0, + "content": "(g) \\(\\mathcal{L}_{rdc}^{\\prime}\\) after 5 epochs" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.224, + 0.891, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.342, + 0.817, + 0.355 + ], + "angle": 0, + "content": "(h) \\(\\mathcal{L}_{rdc}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.894, + 0.478 + ], + "angle": 0, + "content": "Figure 2. (a), (b), (c) and (d) show the density vs. the similarity between common representations and noisy centers, and (e), (f), (g) and (h) show the density vs. the similarity between common representations and clean centers for the test set after the training under 0.4 symmetric noise. Moreover, (a) and (e) are trained with the Cross-Modal Center loss (CMC) [19], (b) and (f) are trained with vanilla RDCL loss \\(\\mathcal{L}_{rdc}^{\\prime}\\) of Equation (3), (c) and (g) are trained for only 5 epochs with \\(\\mathcal{L}_{rdc}^{\\prime}\\) and (d) and (h) are trained with the proposed Robust Discriminative Center loss (RDC). It can be found that after short training periods with vanilla RDCL loss, both true and false labeled samples are compacted to their real category centers, and false labeled samples are not similar to their mislabeled category centers. Adopting RDC for training could maintain and reinforce the robustness of the results, which makes the samples in noisy set adaptively avoid being similar to the mislabeled category centers and maintain their similarity to the real category centers, while CMC could hardly achieve." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.686 + ], + "angle": 0, + "content": "early within up to 30 epochs, and \\(\\alpha \\in [-e,e]\\) is a threshold for clean-noise separation. In our training stage, \\(v\\) gradually increases from 0 to 1. More specifically, our RDC will focus on learning simple patterns before fitting on the corrupted labels in the early stage. With further training, our RDC will make the second item dominant to explicitly separate samples into clean and noisy sets, and assign them with correct optimization directions. Surprisingly, our RDC could accurately cluster noisy samples into their correct centers regardless of the corrupted supervision as shown in the visualization results of Figures 2d and 2h, thus embracing robustness against noisy labels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.389, + 0.713 + ], + "angle": 0, + "content": "3.3. Shared Space Consistency Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Although our RDCL could achieve robustness against noisy labels, the cross-modal learning paradigm is frequently affected by the inherent gaps across different modalities. More specifically, due to the randomness of the category centers caused by the random initialization of DNNs, blindly increasing the discrimination between points and centers would lead to losing the intrinsic information inside the data, thus degrading the retrieval performance. To handle the problem, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information by narrowing the heterogeneity and semantic gaps simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.579 + ], + "angle": 0, + "content": "First, in order to further alleviate or even eliminate the inherent gap across different modalities, we adopt a Multimodal Gap loss (MG) to maximize the mutual information between different modalities from the instance-based perspective [16], which could be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.585, + 0.892, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m g} = - \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} l o g \\left(\\frac {\\sum_ {k} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {i} ^ {k}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}{\\sum_ {l} ^ {N} \\sum_ {m} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {l} ^ {m}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.693 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature parameter. By minimizing Equation (5), the discrepancy across different modalities could be reduced to project cross-modal samples into a common space, thus narrowing the heterogeneity gap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.693, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Second, in addition to the heterogeneity gap, the semantic discrepancy will also degrade the performance since distinct modalities intrinsically belong to the same label space. To eliminate the discrepancy, we propose a Common Representations Classification loss (CRC) to narrow the gap between the common space and label space. Specifically, a shared classifier is employed to bridge the common space and label space, and then minimize the difference between classification predictions and labels. To alleviate the influence of noisy labels, the robust MAE loss is utilized to minimize the difference as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.861, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c r c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} | g \\left(\\boldsymbol {z} _ {i} ^ {j}, \\Gamma\\right) - y _ {i} ^ {j} |, \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11613" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.122 + ], + "angle": 0, + "content": "where \\( g(z_i^j, \\Gamma) \\) is a common classifier with parameters \\( \\Gamma \\) shared by all modalities." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.13, + 0.3, + 0.146 + ], + "angle": 0, + "content": "3.4. Theoretical Justification" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.153, + 0.469, + 0.244 + ], + "angle": 0, + "content": "Following previous works [10, 26], we could indicate that our joint loss function \\(\\mathcal{L}\\) is robust against both symmetric and asymmetric label noise. Since DNNs are noise tolerant in the early training stage [3], we only discuss the robustness of our method during the latter training stage as \\(v\\) has dynamically increased to 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.255, + 0.351, + 0.271 + ], + "angle": 0, + "content": "Property 1 \\(\\exists \\alpha \\in [-e,e],RDC\\) satisfies:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.28, + 0.485, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\sum_ {i = 1} ^ {K} \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), i) = (K - 1) \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), y ^ {*}) + C \\quad \\boldsymbol {x} \\in \\mathcal {X}, \\forall f, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.469, + 0.38 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rdc}(f(\\pmb{x}), y^{*})\\) is the loss function to compute \\(\\mathcal{L}_{rdc}\\) with the common representations \\(f(\\pmb{x})\\) and \\(K\\)-category true label \\(y^{*}\\), and \\(C\\) is a constant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.39, + 0.469, + 0.421 + ], + "angle": 0, + "content": "Property 2 There exist upper and lower definite boundaries for \\(\\mathcal{L}_{rdc}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.469, + 0.477 + ], + "angle": 0, + "content": "Lemma 1 If the above properties are satisfied, RDC with appropriate \\(\\alpha\\) is noise tolerant against symmetric (or uniform) and asymmetric (or class conditional) noisy labels." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.469, + 0.622 + ], + "angle": 0, + "content": "Lemma 2 [10] When symmetric noise rate \\(\\eta < 1 - \\frac{1}{K}\\), MAE is robust against symmetric (or uniform) noisy labels. Defining the risk of the classifier is \\(R_{\\mathcal{L}_{mae}}(f)\\), \\(f^{*}\\) is the global minimizers of \\(R_{\\mathcal{L}_{mae}}(f)\\), \\(\\mathcal{L}_{mae}(f(\\pmb{x}),y)\\) is the calculation of MAE, when \\(R_{\\mathcal{L}_{mae}}(f^{*}) = 0\\), \\(0 \\leq \\mathcal{L}_{mae}(f(\\pmb{x}),i) \\leq \\frac{C}{K-1} = 2, \\forall i\\) and any category-wide noise rate is less than the rate of being clean \\(\\eta_{ij} \\leq 1 - \\eta_y\\), MAE is robust against asymmetric (or class conditional) noisy labels." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.634, + 0.469, + 0.681 + ], + "angle": 0, + "content": "Lemma 3 [21, 26] Assuming there are \\(n\\) noise tolerant loss functions \\(\\{\\mathcal{L}_i\\}_{i=1}^n\\), and \\(n\\) trade-off hyperparameters \\(\\{\\gamma_i\\}_{i=1}^n\\), then \\(\\mathcal{L} = \\sum_{i=1}^n \\gamma_i \\mathcal{L}_i\\) is noise tolerant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.69, + 0.469, + 0.87 + ], + "angle": 0, + "content": "The elaborate proofs for Property 1, Property 2, and Lemma 1 can be found in our Complementary Materials. Property 1 and Property 2 can be obtained by mathematical derivation. For Lemma 1, we denote the risk of representation extractor \\( f \\) with clean data \\( \\{x, y^*\\} \\) on our RDC as \\( R(f) = \\mathbb{E}_{x, y^*} \\mathcal{L}_{rdc} \\), and the risk with noisy labels as \\( R^\\eta(f) = \\mathbb{E}_{x, y} \\mathcal{L}_{rdc} \\). If \\( f^* \\) and \\( f_\\eta^* \\) are respectively the global minimizers of \\( R(f) \\) and \\( R^\\eta(f) \\), we require to prove \\( f^* \\) is also a global minimizer of noisy risk \\( R^\\eta(f) \\) for \\( \\mathcal{L}_{rdc} \\) that is robust against noisy labels. For Lemma 2 and Lemma 3, the theoretical proofs are provided in [10] and [21, 26], respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "According to Lemma 1 and Lemma 2, our RDC and CRC are theoretically robust against both symmetric and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "asymmetric noisy labels. Moreover, our MG is also noise tolerant with noisy labels since it is unsupervised and independent of labels. Therefore, according to Lemma 3, we could draw the conclusion that our joint loss function \\(\\mathcal{L}\\) is noise tolerant against noisy labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.634, + 0.197 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.892, + 0.266 + ], + "angle": 0, + "content": "To evaluate our RONO, we conduct extensive comparison experiments on four 3D multimodal datasets with different scales, i.e., 3D MNIST [38], RGB-D object [22], ModelNet10 [36] and ModelNet40 [36] datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.274, + 0.707, + 0.29 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.386 + ], + "angle": 0, + "content": "In this work, our RONO is implemented in PyTorch and its optimization process could be found in our Complementary Materials. All the experiments are carried out on GeForce RTX 1080Ti GPUs. Four widely-used 3D multimodal datasets are utilized for evaluation, which are briefly introduced below:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.463 + ], + "angle": 0, + "content": "3D MNIST [38]: It is a small-scale 3D model dataset collected in Kaggle which contains 6000 image-point cloud pairs. The point cloud samples are generated from the MNIST dataset. We divide the dataset into 2 subsets: 5000 and 1000 pairs for training and testing sets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.553 + ], + "angle": 0, + "content": "RGB-D object [22]: It is a large-scale dataset containing 300 common family objects belonging to 51 categories. The dataset has 207,621 image-point cloud pairs, which of each has a \\(640 \\times 480\\) image and a point-cloud object with 1000 to 5000 points. We split the dataset into 200,000 and 7,621 pairs for training and testing sets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.599 + ], + "angle": 0, + "content": "ModelNet10 [36]: It is a 10-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 2,468 and 908 for training and testing sets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.644 + ], + "angle": 0, + "content": "ModelNet40 [36]: It is a 40-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 9,840 and 3,991 for training and testing sets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.765 + ], + "angle": 0, + "content": "In our experiments, we compare our RONO with 15 state-of-the-art methods that include 5 unsupervised methods (i.e., CCA [15], DCCA [1], DCCAE [35], UCCH [17] and DGCPN [42]) and 10 supervised ones (i.e., GMA [30], MvDA [20], AGAH [12], DADH [4], DAGNN [28], ALGCN [27], DSCMR [44], MRL [16], CLF [19] and CLF [19] + MAE [10]). Note that, CLF+MAE is a variant of CLF [19] with a robust MAE [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Most of the experiments are conducted on bimodal settings to evaluate two cross-modal tasks: using images as queries to retrieve the point-cloud samples (Image \\(\\rightarrow\\) Point Cloud), using point-cloud samples as queries to retrieve the images (Point Cloud \\(\\rightarrow\\) Image). Without loss of generality, several experiments are conducted across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40. We use the widely-used mean Average Precision (mAP) score to evaluate the retrieval performance. We" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11614" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.362 + ], + "angle": 0, + "content": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.4150.4150.4150.4150.4140.4140.4140.4140.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.4490.4380.4260.4150.4370.4320.4230.4140.0900.0850.0880.0890.0870.0830.0870.086
MvDA [20]0.4810.4610.4320.3280.4820.4610.4310.3230.1330.1320.1280.1120.1320.1330.1090.102
AGAH [12]0.6880.5570.1280.1080.6800.5480.1220.1160.6080.3790.1950.0900.6010.3800.1940.090
DADH [4]0.7350.6320.4030.2900.7270.6140.3820.2860.6260.3340.1360.0620.6180.3260.1350.062
DAGNN [28]0.8830.8500.7490.4450.8790.8450.7430.4350.7070.6370.5200.3150.7150.6350.5130.313
ALGCN [27]0.8740.8400.7570.4010.8680.8310.7480.3850.6730.5010.3980.2040.6700.5010.4140.200
DSCMR [44]0.9080.8120.5120.2190.8960.8110.4720.1400.7270.6710.5320.2900.7310.6730.5230.275
MRL [16]0.9550.9370.9180.7850.9440.9310.9050.7910.7110.6460.6100.4980.7090.6230.5980.487
CLF [19]0.8900.8110.4600.1240.8720.7930.4260.1200.7230.6610.3460.1110.7030.6340.3430.106
CLF [19]+MAE [10]0.8100.8120.5010.1220.8090.8110.4830.1220.7050.6260.4260.1870.7030.6240.3990.167
Ours0.9620.9520.9310.8310.9480.9340.9150.8280.7740.7370.7360.7060.7710.7300.7290.700
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.373, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Table 1. Performance comparison in terms of mAP under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.415, + 0.889, + 0.69 + ], + "angle": 0, + "content": "
MethodModelNet10 [36]ModelNet40 [36]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.6250.6250.6250.6250.6270.6270.6270.6270.5320.5320.5320.5320.5310.5310.5310.531
DCCA [1]0.6840.6840.6840.6840.6770.6770.6770.6770.5840.5840.5840.5840.5690.5690.5690.569
DCCAE [35]0.7030.7030.7030.7030.6930.6930.6930.6930.5930.5930.5930.5930.5720.5720.5720.572
DGCPN [42]0.7650.7650.7650.7650.7590.7590.7590.7590.7050.7050.7050.7050.6970.6970.6970.697
UCCH [17]0.7710.7710.7710.7710.7700.7700.7700.7700.7550.7550.7550.7550.7390.7390.7390.739
GMA [30]0.6500.6170.5850.5210.6460.5790.5500.4970.5250.4850.4660.4480.5150.4870.4590.437
MvDA [20]0.4940.4580.4490.3900.4640.4280.4060.3280.4200.3730.3290.3160.4120.3700.3000.271
AGAH [12]0.8530.7360.5830.4250.8370.6990.5490.4080.8090.7320.6870.5680.7830.7360.6640.554
DADH [4]0.8600.7720.6700.5540.8380.7680.6580.5530.8180.7430.6760.5810.7820.7480.6570.586
DAGNN [28]0.8440.8000.7540.4220.8360.8100.7630.4480.8020.7230.6350.4020.7980.7280.6430.412
ALGCN [27]0.7880.5970.4260.2820.7970.5890.4400.2690.7660.5380.4260.2980.7630.5370.4030.279
DSCMR [44]0.8490.7580.6660.3240.8360.7320.6370.3070.8240.7880.6870.3280.8110.7850.6940.339
MRL [16]0.8760.8700.8630.8320.8610.8570.8480.8230.8330.8290.8280.8180.8240.8260.8200.817
CLF [19]0.8490.7820.6200.3650.8380.7640.5950.3870.8220.7780.6240.3150.8150.7710.5870.295
CLF [19]+MAE[10]0.8530.7520.6790.3430.8380.7160.6590.3730.8270.7580.6510.3840.8160.7490.6400.372
Ours0.8920.8770.8700.8360.8900.8750.8610.8300.8770.8580.8380.8230.8720.8540.8380.821
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.699, + 0.893, + 0.73 + ], + "angle": 0, + "content": "Table 2. Performance comparison under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the ModelNet10 and ModelNet40 datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.471, + 0.876 + ], + "angle": 0, + "content": "conduct the comparison experiments under both synthetic symmetric and asymmetric label noise for comprehensive evaluation. Due to the space limitation, we only evaluate the robustness against asymmetric label noise on 3D MNIST and RGB-D object datasets. More extra experimental results could be found in our Complementary Materials. For a comprehensive evaluation, the symmetric noise rates are set as 0.2, 0.4, 0.6, and 0.8, and the asymmetric ones are set as 0.1, 0.2, and 0.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.833, + 0.757 + ], + "angle": 0, + "content": "4.2. Comparison with the State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.87 + ], + "angle": 0, + "content": "We apply 2D-3D cross-modal retrieval on four 3D model multimodal datasets to evaluate the robustness of our RONO and the baselines. The experimental results under symmetric noise are reported in Tables 1 and 2, and ones under asymmetric noise are reported in Table 3. From these experimental results, we could obtain the following observations:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "- Noisy labels could remarkably reduce the retrieval per" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11615" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.364 + ], + "angle": 0, + "content": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
00.10.20.400.10.20.400.10.20.400.10.20.4
CCA [15]0.4150.4150.4150.4150.4150.4150.4150.4150.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.5140.4440.4360.4150.5000.4350.4170.3960.1260.0890.0850.0730.1210.0850.0810.069
MvDA [20]0.5300.4720.4070.3700.5080.4720.3970.3520.1880.1880.1590.1420.1990.1680.1390.124
AGAH [12]0.9670.7300.6110.5190.9610.7290.5890.5120.6520.6030.4440.3560.6280.5590.4360.361
DADH [4]0.9710.8480.7180.5700.9690.8250.7010.5720.7720.7230.5890.5240.7610.7030.5720.511
DAGNN [28]0.9270.8940.8710.6840.9270.8930.8640.6910.7410.7040.6460.5630.7240.6890.6310.554
ALGCN [27]0.9080.8760.8600.6350.9000.8710.8520.6410.7170.6850.6170.5260.6910.6780.5980.531
DSCMR [44]0.9630.9140.8690.7110.9450.9060.8620.7040.7740.7550.7110.6730.7680.7380.7000.659
MRL [16]0.9630.9590.9440.7920.9450.9400.9220.7620.7230.6550.6350.6020.7190.6520.6360.599
CLF [19]0.9830.9450.9240.8090.9580.9320.9200.8020.7720.7710.7340.6740.7660.7590.7210.659
CLF [19]+MAE[10]0.9710.9420.9210.7960.9510.9300.9180.7830.7520.7580.7200.6510.7410.7500.7120.637
Ours0.9830.9610.9580.9120.9680.9470.9380.8970.7790.7730.7280.6810.7710.7560.7210.669
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.374, + 0.89, + 0.404 + ], + "angle": 0, + "content": "Table 3. Performance comparison under the asymmetric noise rates of 0, 0.1, 0.2, and 0.4 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.429, + 0.47, + 0.504 + ], + "angle": 0, + "content": "formance of supervised methods. Their performance will be degraded rapidly as the noise rate increases. Especially, when the noise rate is high, supervised methods tend to perform worse than unsupervised ones, or even fail to fit the data." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.513, + 0.47, + 0.635 + ], + "angle": 0, + "content": "- For the symmetric noise, our RONO achieves remarkably better results than supervised (e.g., CLF, DAGNN, DSCMR, etc.), which demonstrates the robustness of our method against noisy labels. Besides, our RONO could utilize noisy labels to overcome the unsupervised methods (e.g., UCCH, DGCPN, etc.), thus indicating that additional label information could improve performance even if it contains noise." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.644, + 0.47, + 0.751 + ], + "angle": 0, + "content": "- Our RONO is superior to a strong baseline (i.e., MRL) that is a noise-tolerate cross-modal method. Especially, our method could achieve 0.703 in terms of mAP under 0.8 noise on the large-scale RGB-D object dataset, which is higher than MRL (0.493) by 0.210, thus demonstrating the effectiveness of our adaptive optimization strategy for clean and noisy data." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.759, + 0.47, + 0.821 + ], + "angle": 0, + "content": "- For asymmetric noise, the extremely perplexing class conditional noise will degrade the performance of the memorization effect of DNNs, however, our RONO still achieves superior robustness against noisy labels." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.829, + 0.47, + 0.89 + ], + "angle": 0, + "content": "- Our RONO shows superiority even without the addition of synthetic label noise, demonstrating that well-annotated datasets also contain noise impacting the performance of each non-robust method." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.513, + 0.47, + 0.89 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.426, + 0.895, + 0.582 + ], + "angle": 0, + "content": "
RDCLSSCL3D MNIST [38]ModelNet40 [36]
LrdcLmgLcrcImg→PntPnt→ImgImg→PntPnt→Img
0.40.80.40.80.40.8
✓✓✓0.9520.8310.9340.8280.8580.824
L′rdc✓✓0.8910.3420.8990.3140.8150.670
✓✓0.8410.6750.8320.6710.8210.777
✓✓0.9290.6150.9270.5640.7930.551
✓✓0.9300.7090.9140.7060.8040.673
✓0.6410.4230.6350.4290.7350.608
✓0.6610.6610.6600.6600.4440.444
✓0.5270.3480.5370.2750.7250.484
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.592, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Table 4. Ablation studies for RONO on the 3D MNIST and ModelNet40 datasets with 0.4 symmetric noise. \\( \\checkmark \\) stands for use." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.644, + 0.655, + 0.661 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we investigate the contribution of each proposed component (i.e., loss \\(\\mathcal{L}_{rdc}\\), \\(\\mathcal{L}_{mg}\\) and \\(\\mathcal{L}_{crc}\\)) to 2D-3D retrieval with noisy labels. For a comprehensive comparison, we ablate each component from the framework and conduct the variants with the same experimental settings on two distinct datasets (i.e., 3D MNIST and ModelNet40). The results are shown in Table 4. From the table, one could draw the following observation: 1) RONO with/without any component will improve/drop retrieval performance, which indicates that each component contributes to our framework. 2) Replacing RCD (i.e., \\(\\mathcal{L}_{rdc}\\)) with the vanilla loss of RDCL (i.e., \\(\\mathcal{L}_{rdc}^{\\prime}\\)) will result in remarkable performance degradation, thus demonstrating the effectiveness of differentiated optimization for clean and noisy data, especially for high noise rates." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11616" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.282 + ], + "angle": 0, + "content": "
ηQryImgMshPnt
RetrvImgMshPntImgMshPntImgMshPnt
0CLF0.9030.8980.8830.8910.8730.8820.8870.8830.881
Ours0.9110.9010.8910.8990.9010.8830.8910.8940.891
0.2CLF0.8250.8300.8250.8310.8500.8480.8290.8500.851
Ours0.8740.8720.8810.8830.8910.8890.8750.8840.890
0.4CLF0.6830.7490.7610.7370.8160.8290.7460.8280.848
Ours0.8580.8760.8630.8620.8810.8750.8590.8750.875
0.6CLF0.5600.5890.6270.5690.6810.7290.6040.7250.794
Ours0.8420.8530.8510.8570.8570.8620.8430.8680.872
0.8CLF0.3110.3160.3610.3230.3920.4000.3650.3850.559
Ours0.8280.8420.8420.8420.8680.8660.8410.8640.868
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.291, + 0.471, + 0.375 + ], + "angle": 0, + "content": "Table 5. Performance comparison of CLF [19] and our RONO under the symmetric noise rates of 0, 0.2, 0.4, 0.6 and 0.8 on trimodal ModelNet40 dataset [36]. The highest mAPs are shown in bold. For a convenience presentation, we abbreviate Image, Mesh, Point cloud, Query, and Retrieval to Img, Msh, Pnt, Qry, and Retrv, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.353, + 0.417 + ], + "angle": 0, + "content": "4.4. Further Comparison with CLF" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.558 + ], + "angle": 0, + "content": "To comprehensively evaluate our RONO, we conduct various 2D-3D cross-modal retrieval and visualization experiments across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40 [36], by comparing RONO with state-of-the-art CLF [19]. The comparison results are shown in Table 5 and Figures 3 and 4. Due to space limitation, more cross-modal and in-domain comparison results could be found in our Complementary Materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.471, + 0.697 + ], + "angle": 0, + "content": "From the experimental results, one could observe that: 1) Regardless of noise rates, our RONO show stronger robustness against noisy labels across three modalities. 2) Our RONO could obtain more discriminative clusters compared to CLR, which demonstrates the robustness of our RONO. 3) Our RONO could achieve more correct retrieved results while CLF fails on the same queries, indicating that our method has stronger robustness and is consistent with our quantitative results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.196, + 0.725 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a novel 2D-3D cross-modal retrieval framework to robustly learn discriminative and modality-invariant representations with noisy labels, termed RONO. To be specific, our RONO employs a novel Robust Discriminative Center Learning mechanism (RDCL) to endow clean and noisy samples with correct optimization directions, while a Shared Space Consistency Learning mechanism (SSCL) to guarantee the cross-modal and semantic consistency across different modalities in the common space. Comprehensive mathematical analyses are provided to theoretically prove the noise tolerance of our RONO." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.693, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.236, + 0.619, + 0.248 + ], + "angle": 0, + "content": "(a) CLF" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.089, + 0.892, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.236, + 0.821, + 0.248 + ], + "angle": 0, + "content": "(b) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.26, + 0.894, + 0.33 + ], + "angle": 0, + "content": "Figure 3. The representation visualization on the testing set of ModelNet40 by using t-SNE method [33]. CLF and our RONO are trained under 0.4 symmetric label noise. Samples from the same category are rendered with the same color, and ones from the same modality are rendered with the same marker." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.345, + 0.895, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.563, + 0.892, + 0.605 + ], + "angle": 0, + "content": "Figure 4. Top-5 retrieved results of CLF and our RONO under 0.4 label noise on the tri-modal ModelNet40 dataset. Green boxes indicate correct retrieval, while red boxes indicate wrong retrieval." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.633, + 0.892, + 0.694 + ], + "angle": 0, + "content": "Furthermore, we conduct extensive experiments compared to 15 state-of-the-art methods on four 3D model multimodal datasets to demonstrate the robustness of the proposed method against synthetic and real label noise." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.71, + 0.66, + 0.726 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work is supported by the National Key R&D Program of China under Grant 2020YFB1406702, the National Natural Science Foundation of China (Grants No. 62102274, 62176171, and U19A2078), Sichuan Science and Technology Planning Project (Grants No. 2021YFS0389, 2021YFG0317, 2021YFG0301, 2022YFQ0014, and 2022YFH0021), Fundamental Research Funds for the Central Universities, A\\*STAR AME Programmatic Funding A18A2b0046, RobotHTPO Seed Fund under Project C211518008 and EDB Space Technology Development Grant under Project S22-19016-STDP." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11617" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Galen Andrew, Raman Arora, Jeff Bilmes, and Karen Livescu. 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IEEE transactions on neural networks, 17(1):233-238, 2006. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11619" + } + ] +] \ No newline at end of file diff --git a/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_origin.pdf b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..403ba8cb73aa4c66d304ecbcdcc7ce9d65892a24 --- /dev/null +++ b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/27b72c7c-b71d-416b-9de2-a59860d5ddfe_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:76b78101c2835c4a1248912f107af272c6482da7823b6a97cefc996e86a9d137 +size 1346985 diff --git a/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/full.md b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e6052e851bb4ff2ca3299b59065b44467d9dfb27 --- /dev/null +++ b/2023/RONO_ Robust Discriminative Learning With Noisy Labels for 2D-3D Cross-Modal Retrieval/full.md @@ -0,0 +1,303 @@ +# RONO: Robust Discriminative Learning with Noisy Labels for 2D-3D Cross-Modal Retrieval + +Yanglin Feng + +Hongyuan Zhu + +1College of Computer Science, Sichuan University +3Sichuan Zhiqian Technology Co., Ltd + +Dezhong Peng $^{1,3,4}$ + +Xi Peng1 + +Peng Hu1* + +$^{2}$ Institute for Infocomm Research (I²R), A*STAR, Singapore + $^{4}$ Chengdu Ruibei Yingle Information Technology Co., Ltd + +# Abstract + +Recently, with the advent of Metaverse and AI Generated Content, cross-modal retrieval becomes popular with a burst of 2D and 3D data. However, this problem is challenging given the heterogeneous structure and semantic discrepancies. Moreover, imperfect annotations are ubiquitous given the ambiguous 2D and 3D content, thus inevitably producing noisy labels to degrade the learning performance. To tackle the problem, this paper proposes a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data. Specifically, one novel Robust Discriminative Center Learning mechanism (RDCL) is proposed in RONO to adaptively distinguish clean and noisy samples for respectively providing them with positive and negative optimization directions, thus mitigating the negative impact of noisy labels. Besides, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information inside the noisy data by minimizing the cross-modal and semantic discrepancy between common space and label space simultaneously. Comprehensive mathematical analyses are given to theoretically prove the noise tolerance of the proposed method. Furthermore, we conduct extensive experiments on four 3D-model multimodal datasets to verify the effectiveness of our method by comparing it with 15 state-of-the-art methods. Code is available at https://github.com/penghu-cs/RONO. + +# 1. Introduction + +Point-cloud retrieval (PCR) is fundamental and crucial for processing and analyzing 3D data [14], which could provide the direct technical support of the 3D data search engine, thus embracing compelling application prospects and practical value in the fields of robotics [7, 32], autonomous driving [23, 31], virtual/augmented reality [9], and medicine [29], etc. Different from 2D images, 3D point clouds could depict the internal architecture and ex + +ternal appearance of objects from distinct views/modalities. Hence, PCR is often accompanied by retrieving across diverse modalities, termed 2D-3D cross-modal retrieval [19]. + +On the other hand, it is extremely expensive and labor-intensive to label such a huge amount of data points [17, 41], not to mention the additional challenges of the missing color and texture of the point clouds. In order to reduce the labeling cost, we could utilize open source or low-cost annotation tools (e.g., point-cloud-annotation-tool [18], LabelHub, etc.), hence it will inevitably introduce label noise due to the non-expert annotation. However, almost all existing works excessively rely on well-labeled data [19, 20, 44], thus making them vulnerable to noisy labels and leading to unavoidable performance degradation. + +To address the aforementioned issues, we propose a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data as shown in Figure 1. Our RONO framework consists of two mechanisms: 1) a novel Robust Discriminative Center Learning mechanism (RDCL) to robustly and discriminatively tackle clean and noisy samples, and 2) a Shared Space Consistency Learning mechanism (SSCL) to alleviate and even eliminate the heterogeneity and semantic gaps across different modalities. + +More specifically, RDCL is presented to adaptively divide the noisy data into clean and noisy samples based on the memorization effect of deep neural networks (DNNs) [3], and then endowing them with positive and negative optimization directions, respectively. In brief, RDCL could compact the clean points to the corresponding category centers while scattering the noisy ones apart away from the noisy centers in the common space, thus alleviating the interference of noisy labels. In addition, our SSCL aims at mitigating the inherent gaps in the common space, i.e., the heterogeneity and semantic gaps. On the one hand, to bridge the heterogeneity gap across different modalities, our SSCL enforces modality-specific samples from the same instance collapse into a single point in the common space, thus producing modality-invariant representations. On the other hand, our SSCL narrows the gap between the representation space and shared label space to explicitly elimi + +![](images/5f3682d314260462355518a027708f5981e88e88bf5604391393e969f377bf84.jpg) +Figure 1. The pipeline of our robust 2D-3D retrieval framework (RONO). First, modality-specific extractors project different modalities $\{\mathcal{X}_j,\mathcal{Y}_j\}_{j = 1}^M$ into a common space. Second, our Robust Discriminative Center Learning mechanism (RDCL) is conducted in the common space to divide the clean and noisy data while rectifying the optimization direction of noisy ones, leading to robustness against noisy labels. Finally, RONO employs a Shared Space Consistency Learning mechanism (SSCL) to bridge the intrinsic gaps between common space and label space. To be specific, SSCL narrows the cross-modal gap by a Multimodal Gap loss (MG) while minimizing the semantic discrepancy between the common space and label space using a Common Representations Classification loss (CRC) $\mathcal{L}_{\mathrm{rc}}$ , thus endowing representations with modality-invariant discrimination. + +nate the semantic discrepancy, thus encapsulating common discrimination into common representations. Our main contributions can be summarized as follows: + +- We propose a robust 2D-3D cross-modal retrieval framework (RONO) to robustly learn the common discriminative and modality-invariant representations from noisy labels. To the best of our knowledge, this work could be one of the first attempts to learn with noisy labels for 2D-3D cross-modal retrieval. +- To mitigate the impact of noisy labels, a novel Robust Discriminative Center Learning mechanism (RDCL) is proposed to adaptively distinguish clean and noisy samples, and then provide them with positive and negative optimization directions, respectively. +- To construct discriminative and modality-invariant representations, a Shared Space Consistency Learning mechanism (SSCL) is presented to alleviate the intrinsic gaps across heterogeneity, representation, and label spaces. +- We theoretically and experimentally demonstrate the robustness of the proposed method under both synthetic symmetric/asymmetric and real-world noisy labels. Our RONO remarkably outperforms the state-of-the-art methods on 3D object benchmarks of different scales with noisy labels without bells and whistles. + +# 2. Related Work + +# 2.1. Cross-modal Retrieval + +In recent years, cross-modal retrieval has attracted more and more attention from academia and industry due to its flexible search [17, 39, 40]. The most popular solution is to project multimodal data into a common space, resulting in retrieving related content in the space across different modalities. They could be roughly classified into unsupervised and supervised methods. More specifically, 1) one typical kind of unsupervised method is Canonical Correlation Analysis (CCA) and its variants [1, 35, 45]. They aim to map multimodal inputs into a common space by maximizing the correlation across different modalities. 2) With the help of label information, supervised methods could encapsulate the discrimination into the shared space, thus suiting the downstream retrieval task better. To learn discriminative representations, some shallow methods utilize Fisher criterion [6] to project different modalities into a latent common space [20, 30]. To capture the high nonlinearity in multimodal data, Deep Neural Networks (DNNs) are introduced to learn discriminative and modality-invariant representations [28, 34, 44]. + +# 2.2. Learning with Noisy Labels + +To tackle the ubiquitous imperfect annotations in the training data, numerous methods have been presented to im + +prove the robustness of DNNs against noisy labels. The existing works could be grouped into three main categories: 1) Architecture-based methods focus on modifying the DNN architecture to model the noise transition matrix [5, 8, 11]. However, it is still an open issue to accurately estimate noise transition due to the unpredictable and complex noise. 2) Samples-based methods generally learn from clean samples while weakening the adverse impact of noisy ones by re-weighting samples and refurbishing the labels [2, 25]. However, they require some additional well-labeled data, which is difficult and even impossible to satisfy in real-world applications. To address the problem, some methods adaptively divide the training data into clean and noisy sets based on the memorization effect of DNNs [3] for robust DNN training [13, 24]. 3) Loss-based methods mainly focus on designing robust optimization objectives to guide DNNs learning from noisy labels [10, 16, 26, 37, 43]. Although these robust loss functions could alleviate DNNs overfitting on noisy labels, they may lead DNNs to underfit the clean and hard samples. + +# 3. The Proposed Method + +# 3.1. Problem Formulation + +First, some notations are defined for a clear presentation. Boldface lowercase $\pmb{x}$ and plain letters $M, N$ represent column vectors and scalars, respectively. Give a $K$ -category multimodal dataset $\mathcal{D} = \{\mathcal{M}_j\}_{j=1}^M = \{\mathcal{X}_j, \mathcal{Y}_j\}_{j=1}^M$ , where $M$ is the number of modalities, $N$ is the number of samples in one modality, $\mathcal{M}_j = \{(x_i^j, y_i^j)\}_{i=1}^N$ is the $j$ -th modality, $x_i^j \in \mathbb{R}^{d_j}$ is the $i$ -th sample from the $j$ -th modality, $d_j$ is the dimension of the $j$ -th modality and $y_i^j$ is the corresponding label of $x_i^j$ that may be incorrect. + +To alleviate the influence of corrupted labels, a robust 2D-3D retrieval framework (RONO) is proposed to robustly learn discrimination from noisy labels while bridging the cross-modal gap. In the framework, we present a Robust Discriminative Center Learning mechanism (RDCL) to reduce the negative impact of unreliable labels, and a Shared Space Consistency Learning mechanism (SSCL) to simultaneously narrow the semantic and heterogeneity gaps. The overall objective function is shown as follows: + +$$ +\mathcal {L} = \underbrace {\mathcal {L} _ {r d c}} _ {R D C L} + \underbrace {\beta_ {m g} \mathcal {L} _ {m g} + \beta_ {c r c} \mathcal {L} _ {c r c}} _ {S S C L}, \tag {1} +$$ + +where $\mathcal{L}_{rdc}$ is the loss function adopted by RDCL (see Equation (4)), $\mathcal{L}_{mg}$ and $\mathcal{L}_{crc}$ are the loss functions employed by SSCL (see Equations (5) and (6)), and $\beta_{mg}$ and $\beta_{crc}$ are the trade-off parameters. Our RONO could be optimized by descending Equation (1) with stochastic gradient descent. In the following sections, we will elaborate on each component of our RONO. + +# 3.2. Robust Discriminative Center Learning + +To encapsulate the discrimination into the common space, we enforce the samples with the same category compact to the shared clustering centers, while escaping from other centering centers. First, we formulate a contrastive center error $t$ to measure the semantic difference between the estimated representations and the clustering centers as follows: + +$$ +t _ {i} ^ {j} = \frac {\sum_ {k} ^ {K} e ^ {\left(\mathbf {c} _ {k \neq y _ {i} ^ {j}}\right) ^ {T} \mathbf {z} _ {i} ^ {j}}}{K - 1} - e ^ {\left(\mathbf {c} _ {k = y _ {i} ^ {j}}\right) ^ {T} \mathbf {z} _ {i} ^ {j}}, \tag {2} +$$ + +where $z_{i}^{j} = f_{j}(\pmb{x}_{i}^{j})\in \mathbb{R}^{d_{c}}$ is the $d_{c}$ -D common representation of the $\pmb{x}_i^j$ , $f_{j}:\mathbb{R}^{d_{j}}\to \mathbb{R}^{d_{c}}$ is the input space to common space mapping function, $\pmb {c}_i = \frac{1}{|\mathcal{Z}_i|}\sum_{\pmb {z}\in \mathcal{Z}_i}\pmb {z}$ is the center of $i$ -th category, and $\mathcal{Z}_i$ is the set of the $i$ -th category in the common space. In Equation (2), the dot product is exploited to measure the similarity between a given point and a clustering center in the common space. Obviously, minimizing Equation (2) could maximize the within-class similarities while minimizing the between-class ones, thus endowing the common representations with discrimination. Thus, we could formulate a vanilla loss of RDCL as below: + +$$ +\mathcal {L} _ {r d c} ^ {\prime} = \frac {1}{M N} \sum_ {i} ^ {N} \sum_ {j} ^ {M} t _ {i} ^ {j}, \tag {3} +$$ + +However, such a learning paradigm of Equation (3) will utilize all samples to train networks indiscriminately, thus leading to overfitting on corrupted labels like traditional supervision methods, especially under high noise rates. + +To investigate the impact of noisy labels on $\mathcal{L}_{rdc}^{\prime}$ , we conduct some visualized experiments on noisy labels and true labels as shown in Figure 2. From the figure, one could observe that although $\mathcal{L}_{rdc}^{\prime}$ makes the networks overfitting to corrupted labels (see Figures 2b and 2f), it could capture the correct discrimination to compact the samples with corrupted labels to the correct clusters in the early training stage (see Figures 2c and 2g), which is well known as the memorization effect of DNNs [3]. That is to say, the similarities between points and the assigned clusters could be markedly distinguishable after a short training period for the samples with correct and corrupt labels. Inspired by the observation, we propose a Robust Discriminative Center loss (RDC) to adaptively discriminate the clean and noisy samples according to $t$ , and then apply a bias to endow them with positive and negative optimization direction. Thus, we rewrite Equation (3) as follows: + +$$ +\mathcal {L} _ {r d c} = \frac {1}{M N} \sum_ {i} ^ {N} \sum_ {j} ^ {M} \left[ (1 - v) t _ {i} ^ {j} - v | t _ {i} ^ {j} + \alpha | \right], \tag {4} +$$ + +where $v\in [0,1]$ is a dynamically increasing balanced parameter increasing from 0 to 1 with the number of epoch lin + +![](images/5169172ff861dae6b230b3aaa4f914022b4260109cbe3d22239ac6f4b0fff69a.jpg) +(a) Baseline [19] + +![](images/8df2a74aa902c3c2958ed749a29086a7c5ac8c5f597fff6b6d7eee6aa58dee9e.jpg) + +![](images/5d94271e5e17b82514d19a4edebdf636df67ebc22bdf0e7faa71c4dc8f61a8c3.jpg) + +![](images/bc198c729bad7e083dc3d1243b38dc5279e7f486e11d50750d5c6637d8efad4a.jpg) + +![](images/d60a308fbf943c58d2145e1c517d13b85c3d0edcbff469cd43d360f6f08ee595.jpg) +(e) Baseline [19] + +![](images/610d9e26c1e39d36d70969c01d504ed947b9207c80d406ca0dedd974427dd8c5.jpg) +(b) $\mathcal{L}_{rdc}^{\prime}$ +(f) $\mathcal{L}_{rdc}^{\prime}$ + +![](images/f3652a3696cdbf5fc8bede1314c4b52d1e9039b3908d4f5829c7772b48daf320.jpg) +(c) $\mathcal{L}_{rdc}^{\prime}$ after 5 epochs +(g) $\mathcal{L}_{rdc}^{\prime}$ after 5 epochs +Figure 2. (a), (b), (c) and (d) show the density vs. the similarity between common representations and noisy centers, and (e), (f), (g) and (h) show the density vs. the similarity between common representations and clean centers for the test set after the training under 0.4 symmetric noise. Moreover, (a) and (e) are trained with the Cross-Modal Center loss (CMC) [19], (b) and (f) are trained with vanilla RDCL loss $\mathcal{L}_{rdc}^{\prime}$ of Equation (3), (c) and (g) are trained for only 5 epochs with $\mathcal{L}_{rdc}^{\prime}$ and (d) and (h) are trained with the proposed Robust Discriminative Center loss (RDC). It can be found that after short training periods with vanilla RDCL loss, both true and false labeled samples are compacted to their real category centers, and false labeled samples are not similar to their mislabeled category centers. Adopting RDC for training could maintain and reinforce the robustness of the results, which makes the samples in noisy set adaptively avoid being similar to the mislabeled category centers and maintain their similarity to the real category centers, while CMC could hardly achieve. + +![](images/5fbe530347785e29565210d77dca011f599632315ef58d628b343fcfdf231367.jpg) +(d) $\mathcal{L}_{rdc}$ +(h) $\mathcal{L}_{rdc}$ + +early within up to 30 epochs, and $\alpha \in [-e,e]$ is a threshold for clean-noise separation. In our training stage, $v$ gradually increases from 0 to 1. More specifically, our RDC will focus on learning simple patterns before fitting on the corrupted labels in the early stage. With further training, our RDC will make the second item dominant to explicitly separate samples into clean and noisy sets, and assign them with correct optimization directions. Surprisingly, our RDC could accurately cluster noisy samples into their correct centers regardless of the corrupted supervision as shown in the visualization results of Figures 2d and 2h, thus embracing robustness against noisy labels. + +# 3.3. Shared Space Consistency Learning + +Although our RDCL could achieve robustness against noisy labels, the cross-modal learning paradigm is frequently affected by the inherent gaps across different modalities. More specifically, due to the randomness of the category centers caused by the random initialization of DNNs, blindly increasing the discrimination between points and centers would lead to losing the intrinsic information inside the data, thus degrading the retrieval performance. To handle the problem, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information by narrowing the heterogeneity and semantic gaps simultaneously. + +First, in order to further alleviate or even eliminate the inherent gap across different modalities, we adopt a Multimodal Gap loss (MG) to maximize the mutual information between different modalities from the instance-based perspective [16], which could be formulated as: + +$$ +\mathcal {L} _ {m g} = - \frac {1}{M N} \sum_ {i} ^ {N} \sum_ {j} ^ {M} l o g \left(\frac {\sum_ {k} ^ {M} e ^ {\frac {1}{\tau} \left(\boldsymbol {z} _ {i} ^ {k}\right) ^ {T} \boldsymbol {z} _ {i} ^ {j}}}{\sum_ {l} ^ {N} \sum_ {m} ^ {M} e ^ {\frac {1}{\tau} \left(\boldsymbol {z} _ {l} ^ {m}\right) ^ {T} \boldsymbol {z} _ {i} ^ {j}}}\right), \tag {5} +$$ + +where $\tau$ is a temperature parameter. By minimizing Equation (5), the discrepancy across different modalities could be reduced to project cross-modal samples into a common space, thus narrowing the heterogeneity gap. + +Second, in addition to the heterogeneity gap, the semantic discrepancy will also degrade the performance since distinct modalities intrinsically belong to the same label space. To eliminate the discrepancy, we propose a Common Representations Classification loss (CRC) to narrow the gap between the common space and label space. Specifically, a shared classifier is employed to bridge the common space and label space, and then minimize the difference between classification predictions and labels. To alleviate the influence of noisy labels, the robust MAE loss is utilized to minimize the difference as follows: + +$$ +\mathcal {L} _ {c r c} = \frac {1}{M N} \sum_ {i} ^ {N} \sum_ {j} ^ {M} | g \left(\boldsymbol {z} _ {i} ^ {j}, \Gamma\right) - y _ {i} ^ {j} |, \tag {6} +$$ + +where $g(z_i^j, \Gamma)$ is a common classifier with parameters $\Gamma$ shared by all modalities. + +# 3.4. Theoretical Justification + +Following previous works [10, 26], we could indicate that our joint loss function $\mathcal{L}$ is robust against both symmetric and asymmetric label noise. Since DNNs are noise tolerant in the early training stage [3], we only discuss the robustness of our method during the latter training stage as $v$ has dynamically increased to 1. + +Property 1 $\exists \alpha \in [-e,e],RDC$ satisfies: + +$$ +\sum_ {i = 1} ^ {K} \mathcal {L} _ {r d c} (f (\boldsymbol {x}), i) = (K - 1) \mathcal {L} _ {r d c} (f (\boldsymbol {x}), y ^ {*}) + C \quad \boldsymbol {x} \in \mathcal {X}, \forall f, \tag {7} +$$ + +where $\mathcal{L}_{rdc}(f(\pmb{x}), y^{*})$ is the loss function to compute $\mathcal{L}_{rdc}$ with the common representations $f(\pmb{x})$ and $K$ -category true label $y^{*}$ , and $C$ is a constant. + +Property 2 There exist upper and lower definite boundaries for $\mathcal{L}_{rdc}$ . + +Lemma 1 If the above properties are satisfied, RDC with appropriate $\alpha$ is noise tolerant against symmetric (or uniform) and asymmetric (or class conditional) noisy labels. + +Lemma 2 [10] When symmetric noise rate $\eta < 1 - \frac{1}{K}$ , MAE is robust against symmetric (or uniform) noisy labels. Defining the risk of the classifier is $R_{\mathcal{L}_{mae}}(f)$ , $f^{*}$ is the global minimizers of $R_{\mathcal{L}_{mae}}(f)$ , $\mathcal{L}_{mae}(f(\pmb{x}),y)$ is the calculation of MAE, when $R_{\mathcal{L}_{mae}}(f^{*}) = 0$ , $0 \leq \mathcal{L}_{mae}(f(\pmb{x}),i) \leq \frac{C}{K-1} = 2, \forall i$ and any category-wide noise rate is less than the rate of being clean $\eta_{ij} \leq 1 - \eta_y$ , MAE is robust against asymmetric (or class conditional) noisy labels. + +Lemma 3 [21, 26] Assuming there are $n$ noise tolerant loss functions $\{\mathcal{L}_i\}_{i=1}^n$ , and $n$ trade-off hyperparameters $\{\gamma_i\}_{i=1}^n$ , then $\mathcal{L} = \sum_{i=1}^n \gamma_i \mathcal{L}_i$ is noise tolerant. + +The elaborate proofs for Property 1, Property 2, and Lemma 1 can be found in our Complementary Materials. Property 1 and Property 2 can be obtained by mathematical derivation. For Lemma 1, we denote the risk of representation extractor $f$ with clean data $\{x, y^*\}$ on our RDC as $R(f) = \mathbb{E}_{x, y^*} \mathcal{L}_{rdc}$ , and the risk with noisy labels as $R^\eta(f) = \mathbb{E}_{x, y} \mathcal{L}_{rdc}$ . If $f^*$ and $f_\eta^*$ are respectively the global minimizers of $R(f)$ and $R^\eta(f)$ , we require to prove $f^*$ is also a global minimizer of noisy risk $R^\eta(f)$ for $\mathcal{L}_{rdc}$ that is robust against noisy labels. For Lemma 2 and Lemma 3, the theoretical proofs are provided in [10] and [21, 26], respectively. + +According to Lemma 1 and Lemma 2, our RDC and CRC are theoretically robust against both symmetric and + +asymmetric noisy labels. Moreover, our MG is also noise tolerant with noisy labels since it is unsupervised and independent of labels. Therefore, according to Lemma 3, we could draw the conclusion that our joint loss function $\mathcal{L}$ is noise tolerant against noisy labels. + +# 4. Experiments + +To evaluate our RONO, we conduct extensive comparison experiments on four 3D multimodal datasets with different scales, i.e., 3D MNIST [38], RGB-D object [22], ModelNet10 [36] and ModelNet40 [36] datasets. + +# 4.1. Experimental Settings + +In this work, our RONO is implemented in PyTorch and its optimization process could be found in our Complementary Materials. All the experiments are carried out on GeForce RTX 1080Ti GPUs. Four widely-used 3D multimodal datasets are utilized for evaluation, which are briefly introduced below: + +3D MNIST [38]: It is a small-scale 3D model dataset collected in Kaggle which contains 6000 image-point cloud pairs. The point cloud samples are generated from the MNIST dataset. We divide the dataset into 2 subsets: 5000 and 1000 pairs for training and testing sets, respectively. + +RGB-D object [22]: It is a large-scale dataset containing 300 common family objects belonging to 51 categories. The dataset has 207,621 image-point cloud pairs, which of each has a $640 \times 480$ image and a point-cloud object with 1000 to 5000 points. We split the dataset into 200,000 and 7,621 pairs for training and testing sets, respectively. + +ModelNet10 [36]: It is a 10-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 2,468 and 908 for training and testing sets, respectively. + +ModelNet40 [36]: It is a 40-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 9,840 and 3,991 for training and testing sets, respectively. + +In our experiments, we compare our RONO with 15 state-of-the-art methods that include 5 unsupervised methods (i.e., CCA [15], DCCA [1], DCCAE [35], UCCH [17] and DGCPN [42]) and 10 supervised ones (i.e., GMA [30], MvDA [20], AGAH [12], DADH [4], DAGNN [28], ALGCN [27], DSCMR [44], MRL [16], CLF [19] and CLF [19] + MAE [10]). Note that, CLF+MAE is a variant of CLF [19] with a robust MAE [10]. + +Most of the experiments are conducted on bimodal settings to evaluate two cross-modal tasks: using images as queries to retrieve the point-cloud samples (Image $\rightarrow$ Point Cloud), using point-cloud samples as queries to retrieve the images (Point Cloud $\rightarrow$ Image). Without loss of generality, several experiments are conducted across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40. We use the widely-used mean Average Precision (mAP) score to evaluate the retrieval performance. We + +
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.4150.4150.4150.4150.4140.4140.4140.4140.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.4490.4380.4260.4150.4370.4320.4230.4140.0900.0850.0880.0890.0870.0830.0870.086
MvDA [20]0.4810.4610.4320.3280.4820.4610.4310.3230.1330.1320.1280.1120.1320.1330.1090.102
AGAH [12]0.6880.5570.1280.1080.6800.5480.1220.1160.6080.3790.1950.0900.6010.3800.1940.090
DADH [4]0.7350.6320.4030.2900.7270.6140.3820.2860.6260.3340.1360.0620.6180.3260.1350.062
DAGNN [28]0.8830.8500.7490.4450.8790.8450.7430.4350.7070.6370.5200.3150.7150.6350.5130.313
ALGCN [27]0.8740.8400.7570.4010.8680.8310.7480.3850.6730.5010.3980.2040.6700.5010.4140.200
DSCMR [44]0.9080.8120.5120.2190.8960.8110.4720.1400.7270.6710.5320.2900.7310.6730.5230.275
MRL [16]0.9550.9370.9180.7850.9440.9310.9050.7910.7110.6460.6100.4980.7090.6230.5980.487
CLF [19]0.8900.8110.4600.1240.8720.7930.4260.1200.7230.6610.3460.1110.7030.6340.3430.106
CLF [19]+MAE [10]0.8100.8120.5010.1220.8090.8110.4830.1220.7050.6260.4260.1870.7030.6240.3990.167
Ours0.9620.9520.9310.8310.9480.9340.9150.8280.7740.7370.7360.7060.7710.7300.7290.700
+ +Table 1. Performance comparison in terms of mAP under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined. + +
MethodModelNet10 [36]ModelNet40 [36]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.6250.6250.6250.6250.6270.6270.6270.6270.5320.5320.5320.5320.5310.5310.5310.531
DCCA [1]0.6840.6840.6840.6840.6770.6770.6770.6770.5840.5840.5840.5840.5690.5690.5690.569
DCCAE [35]0.7030.7030.7030.7030.6930.6930.6930.6930.5930.5930.5930.5930.5720.5720.5720.572
DGCPN [42]0.7650.7650.7650.7650.7590.7590.7590.7590.7050.7050.7050.7050.6970.6970.6970.697
UCCH [17]0.7710.7710.7710.7710.7700.7700.7700.7700.7550.7550.7550.7550.7390.7390.7390.739
GMA [30]0.6500.6170.5850.5210.6460.5790.5500.4970.5250.4850.4660.4480.5150.4870.4590.437
MvDA [20]0.4940.4580.4490.3900.4640.4280.4060.3280.4200.3730.3290.3160.4120.3700.3000.271
AGAH [12]0.8530.7360.5830.4250.8370.6990.5490.4080.8090.7320.6870.5680.7830.7360.6640.554
DADH [4]0.8600.7720.6700.5540.8380.7680.6580.5530.8180.7430.6760.5810.7820.7480.6570.586
DAGNN [28]0.8440.8000.7540.4220.8360.8100.7630.4480.8020.7230.6350.4020.7980.7280.6430.412
ALGCN [27]0.7880.5970.4260.2820.7970.5890.4400.2690.7660.5380.4260.2980.7630.5370.4030.279
DSCMR [44]0.8490.7580.6660.3240.8360.7320.6370.3070.8240.7880.6870.3280.8110.7850.6940.339
MRL [16]0.8760.8700.8630.8320.8610.8570.8480.8230.8330.8290.8280.8180.8240.8260.8200.817
CLF [19]0.8490.7820.6200.3650.8380.7640.5950.3870.8220.7780.6240.3150.8150.7710.5870.295
CLF [19]+MAE[10]0.8530.7520.6790.3430.8380.7160.6590.3730.8270.7580.6510.3840.8160.7490.6400.372
Ours0.8920.8770.8700.8360.8900.8750.8610.8300.8770.8580.8380.8230.8720.8540.8380.821
+ +Table 2. Performance comparison under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the ModelNet10 and ModelNet40 datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined. + +conduct the comparison experiments under both synthetic symmetric and asymmetric label noise for comprehensive evaluation. Due to the space limitation, we only evaluate the robustness against asymmetric label noise on 3D MNIST and RGB-D object datasets. More extra experimental results could be found in our Complementary Materials. For a comprehensive evaluation, the symmetric noise rates are set as 0.2, 0.4, 0.6, and 0.8, and the asymmetric ones are set as 0.1, 0.2, and 0.4. + +# 4.2. Comparison with the State-of-the-Arts + +We apply 2D-3D cross-modal retrieval on four 3D model multimodal datasets to evaluate the robustness of our RONO and the baselines. The experimental results under symmetric noise are reported in Tables 1 and 2, and ones under asymmetric noise are reported in Table 3. From these experimental results, we could obtain the following observations: + +- Noisy labels could remarkably reduce the retrieval per + +
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
00.10.20.400.10.20.400.10.20.400.10.20.4
CCA [15]0.4150.4150.4150.4150.4150.4150.4150.4150.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.5140.4440.4360.4150.5000.4350.4170.3960.1260.0890.0850.0730.1210.0850.0810.069
MvDA [20]0.5300.4720.4070.3700.5080.4720.3970.3520.1880.1880.1590.1420.1990.1680.1390.124
AGAH [12]0.9670.7300.6110.5190.9610.7290.5890.5120.6520.6030.4440.3560.6280.5590.4360.361
DADH [4]0.9710.8480.7180.5700.9690.8250.7010.5720.7720.7230.5890.5240.7610.7030.5720.511
DAGNN [28]0.9270.8940.8710.6840.9270.8930.8640.6910.7410.7040.6460.5630.7240.6890.6310.554
ALGCN [27]0.9080.8760.8600.6350.9000.8710.8520.6410.7170.6850.6170.5260.6910.6780.5980.531
DSCMR [44]0.9630.9140.8690.7110.9450.9060.8620.7040.7740.7550.7110.6730.7680.7380.7000.659
MRL [16]0.9630.9590.9440.7920.9450.9400.9220.7620.7230.6550.6350.6020.7190.6520.6360.599
CLF [19]0.9830.9450.9240.8090.9580.9320.9200.8020.7720.7710.7340.6740.7660.7590.7210.659
CLF [19]+MAE[10]0.9710.9420.9210.7960.9510.9300.9180.7830.7520.7580.7200.6510.7410.7500.7120.637
Ours0.9830.9610.9580.9120.9680.9470.9380.8970.7790.7730.7280.6810.7710.7560.7210.669
+ +formance of supervised methods. Their performance will be degraded rapidly as the noise rate increases. Especially, when the noise rate is high, supervised methods tend to perform worse than unsupervised ones, or even fail to fit the data. + +- For the symmetric noise, our RONO achieves remarkably better results than supervised (e.g., CLF, DAGNN, DSCMR, etc.), which demonstrates the robustness of our method against noisy labels. Besides, our RONO could utilize noisy labels to overcome the unsupervised methods (e.g., UCCH, DGCPN, etc.), thus indicating that additional label information could improve performance even if it contains noise. +- Our RONO is superior to a strong baseline (i.e., MRL) that is a noise-tolerate cross-modal method. Especially, our method could achieve 0.703 in terms of mAP under 0.8 noise on the large-scale RGB-D object dataset, which is higher than MRL (0.493) by 0.210, thus demonstrating the effectiveness of our adaptive optimization strategy for clean and noisy data. +- For asymmetric noise, the extremely perplexing class conditional noise will degrade the performance of the memorization effect of DNNs, however, our RONO still achieves superior robustness against noisy labels. +- Our RONO shows superiority even without the addition of synthetic label noise, demonstrating that well-annotated datasets also contain noise impacting the performance of each non-robust method. + +Table 3. Performance comparison under the asymmetric noise rates of 0, 0.1, 0.2, and 0.4 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined. + +
RDCLSSCL3D MNIST [38]ModelNet40 [36]
LrdcLmgLcrcImg→PntPnt→ImgImg→PntPnt→Img
0.40.80.40.80.40.8
✓✓✓0.9520.8310.9340.8280.8580.824
L′rdc✓✓0.8910.3420.8990.3140.8150.670
✓✓0.8410.6750.8320.6710.8210.777
✓✓0.9290.6150.9270.5640.7930.551
✓✓0.9300.7090.9140.7060.8040.673
✓0.6410.4230.6350.4290.7350.608
✓0.6610.6610.6600.6600.4440.444
✓0.5270.3480.5370.2750.7250.484
+ +Table 4. Ablation studies for RONO on the 3D MNIST and ModelNet40 datasets with 0.4 symmetric noise. $\checkmark$ stands for use. + +# 4.3. Ablation Study + +In this section, we investigate the contribution of each proposed component (i.e., loss $\mathcal{L}_{rdc}$ , $\mathcal{L}_{mg}$ and $\mathcal{L}_{crc}$ ) to 2D-3D retrieval with noisy labels. For a comprehensive comparison, we ablate each component from the framework and conduct the variants with the same experimental settings on two distinct datasets (i.e., 3D MNIST and ModelNet40). The results are shown in Table 4. From the table, one could draw the following observation: 1) RONO with/without any component will improve/drop retrieval performance, which indicates that each component contributes to our framework. 2) Replacing RCD (i.e., $\mathcal{L}_{rdc}$ ) with the vanilla loss of RDCL (i.e., $\mathcal{L}_{rdc}^{\prime}$ ) will result in remarkable performance degradation, thus demonstrating the effectiveness of differentiated optimization for clean and noisy data, especially for high noise rates. + +
ηQryImgMshPnt
RetrvImgMshPntImgMshPntImgMshPnt
0CLF0.9030.8980.8830.8910.8730.8820.8870.8830.881
Ours0.9110.9010.8910.8990.9010.8830.8910.8940.891
0.2CLF0.8250.8300.8250.8310.8500.8480.8290.8500.851
Ours0.8740.8720.8810.8830.8910.8890.8750.8840.890
0.4CLF0.6830.7490.7610.7370.8160.8290.7460.8280.848
Ours0.8580.8760.8630.8620.8810.8750.8590.8750.875
0.6CLF0.5600.5890.6270.5690.6810.7290.6040.7250.794
Ours0.8420.8530.8510.8570.8570.8620.8430.8680.872
0.8CLF0.3110.3160.3610.3230.3920.4000.3650.3850.559
Ours0.8280.8420.8420.8420.8680.8660.8410.8640.868
+ +Table 5. Performance comparison of CLF [19] and our RONO under the symmetric noise rates of 0, 0.2, 0.4, 0.6 and 0.8 on trimodal ModelNet40 dataset [36]. The highest mAPs are shown in bold. For a convenience presentation, we abbreviate Image, Mesh, Point cloud, Query, and Retrieval to Img, Msh, Pnt, Qry, and Retrv, respectively. + +# 4.4. Further Comparison with CLF + +To comprehensively evaluate our RONO, we conduct various 2D-3D cross-modal retrieval and visualization experiments across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40 [36], by comparing RONO with state-of-the-art CLF [19]. The comparison results are shown in Table 5 and Figures 3 and 4. Due to space limitation, more cross-modal and in-domain comparison results could be found in our Complementary Materials. + +From the experimental results, one could observe that: 1) Regardless of noise rates, our RONO show stronger robustness against noisy labels across three modalities. 2) Our RONO could obtain more discriminative clusters compared to CLR, which demonstrates the robustness of our RONO. 3) Our RONO could achieve more correct retrieved results while CLF fails on the same queries, indicating that our method has stronger robustness and is consistent with our quantitative results. + +# 5. Conclusion + +In this paper, we propose a novel 2D-3D cross-modal retrieval framework to robustly learn discriminative and modality-invariant representations with noisy labels, termed RONO. To be specific, our RONO employs a novel Robust Discriminative Center Learning mechanism (RDCL) to endow clean and noisy samples with correct optimization directions, while a Shared Space Consistency Learning mechanism (SSCL) to guarantee the cross-modal and semantic consistency across different modalities in the common space. Comprehensive mathematical analyses are provided to theoretically prove the noise tolerance of our RONO. + +![](images/21613b3f5dd1a7b6559c054f6f67ba3e5289f33f80b5f85d0295ffd0a4a40cda.jpg) +(a) CLF + +![](images/665871952dda2bec5c2cbe80bb7f55401a3ac9ac0ac67b5ee99d73ed16512f08.jpg) +(b) Ours + +![](images/028306bbaa728e64ce89842ab1eb5bc118e300b2ec13f246bfe1d17cbb365687.jpg) +Figure 3. The representation visualization on the testing set of ModelNet40 by using t-SNE method [33]. CLF and our RONO are trained under 0.4 symmetric label noise. Samples from the same category are rendered with the same color, and ones from the same modality are rendered with the same marker. +Figure 4. Top-5 retrieved results of CLF and our RONO under 0.4 label noise on the tri-modal ModelNet40 dataset. Green boxes indicate correct retrieval, while red boxes indicate wrong retrieval. + +Furthermore, we conduct extensive experiments compared to 15 state-of-the-art methods on four 3D model multimodal datasets to demonstrate the robustness of the proposed method against synthetic and real label noise. + +# Acknowledgments + +This work is supported by the National Key R&D Program of China under Grant 2020YFB1406702, the National Natural Science Foundation of China (Grants No. 62102274, 62176171, and U19A2078), Sichuan Science and Technology Planning Project (Grants No. 2021YFS0389, 2021YFG0317, 2021YFG0301, 2022YFQ0014, and 2022YFH0021), Fundamental Research Funds for the Central Universities, A\*STAR AME Programmatic Funding A18A2b0046, RobotHTPO Seed Fund under Project C211518008 and EDB Space Technology Development Grant under Project S22-19016-STDP. + +# References + +[1] Galen Andrew, Raman Arora, Jeff Bilmes, and Karen Livescu. Deep canonical correlation analysis. 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However, this problem is challenging given the heterogeneous structure and semantic discrepancies. Moreover, imperfect annotations are ubiquitous given the ambiguous 2D and 3D content, thus inevitably producing noisy labels to degrade the learning performance. To tackle the problem, this paper proposes a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data. Specifically, one novel Robust Discriminative Center Learning mechanism (RDCL) is proposed in RONO to adaptively distinguish clean and noisy samples for respectively providing them with positive and negative optimization directions, thus mitigating the negative impact of noisy labels. Besides, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information inside the noisy data by minimizing the cross-modal and semantic discrepancy between common space and label space simultaneously. Comprehensive mathematical analyses are given to theoretically prove the noise tolerance of the proposed method. Furthermore, we conduct extensive experiments on four 3D-model multimodal datasets to verify the effectiveness of our method by comparing it with 15 state-of-the-art methods. Code is available at https://github.com/penghu-cs/RONO." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 598, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 696 + ], + "type": "text", + "content": "Point-cloud retrieval (PCR) is fundamental and crucial for processing and analyzing 3D data [14], which could provide the direct technical support of the 3D data search engine, thus embracing compelling application prospects and practical value in the fields of robotics [7, 32], autonomous driving [23, 31], virtual/augmented reality [9], and medicine [29], etc. Different from 2D images, 3D point clouds could depict the internal architecture and ex" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 232, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 545, + 268 + ], + "type": "text", + "content": "ternal appearance of objects from distinct views/modalities. Hence, PCR is often accompanied by retrieving across diverse modalities, termed 2D-3D cross-modal retrieval [19]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 269, + 546, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 546, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 546, + 400 + ], + "type": "text", + "content": "On the other hand, it is extremely expensive and labor-intensive to label such a huge amount of data points [17, 41], not to mention the additional challenges of the missing color and texture of the point clouds. In order to reduce the labeling cost, we could utilize open source or low-cost annotation tools (e.g., point-cloud-annotation-tool [18], LabelHub, etc.), hence it will inevitably introduce label noise due to the non-expert annotation. However, almost all existing works excessively rely on well-labeled data [19, 20, 44], thus making them vulnerable to noisy labels and leading to unavoidable performance degradation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 402, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 510 + ], + "type": "text", + "content": "To address the aforementioned issues, we propose a robust 2D-3D retrieval framework (RONO) to robustly learn from noisy multimodal data as shown in Figure 1. Our RONO framework consists of two mechanisms: 1) a novel Robust Discriminative Center Learning mechanism (RDCL) to robustly and discriminatively tackle clean and noisy samples, and 2) a Shared Space Consistency Learning mechanism (SSCL) to alleviate and even eliminate the heterogeneity and semantic gaps across different modalities." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "More specifically, RDCL is presented to adaptively divide the noisy data into clean and noisy samples based on the memorization effect of deep neural networks (DNNs) [3], and then endowing them with positive and negative optimization directions, respectively. In brief, RDCL could compact the clean points to the corresponding category centers while scattering the noisy ones apart away from the noisy centers in the common space, thus alleviating the interference of noisy labels. In addition, our SSCL aims at mitigating the inherent gaps in the common space, i.e., the heterogeneity and semantic gaps. On the one hand, to bridge the heterogeneity gap across different modalities, our SSCL enforces modality-specific samples from the same instance collapse into a single point in the common space, thus producing modality-invariant representations. On the other hand, our SSCL narrows the gap between the representation space and shared label space to explicitly elimi" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 251, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 251, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 251, + 713 + ], + "type": "text", + "content": "*Corresponding author: Peng Hu (penghu.ml@gmail.com)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11610" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 84, + 69, + 509, + 276 + ], + "blocks": [ + { + "bbox": [ + 84, + 69, + 509, + 276 + ], + "lines": [ + { + "bbox": [ + 84, + 69, + 509, + 276 + ], + "spans": [ + { + "bbox": [ + 84, + 69, + 509, + 276 + ], + "type": "image", + "image_path": "5f3682d314260462355518a027708f5981e88e88bf5604391393e969f377bf84.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "type": "text", + "content": "Figure 1. The pipeline of our robust 2D-3D retrieval framework (RONO). First, modality-specific extractors project different modalities " + }, + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{X}_j,\\mathcal{Y}_j\\}_{j = 1}^M" + }, + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "type": "text", + "content": " into a common space. Second, our Robust Discriminative Center Learning mechanism (RDCL) is conducted in the common space to divide the clean and noisy data while rectifying the optimization direction of noisy ones, leading to robustness against noisy labels. Finally, RONO employs a Shared Space Consistency Learning mechanism (SSCL) to bridge the intrinsic gaps between common space and label space. To be specific, SSCL narrows the cross-modal gap by a Multimodal Gap loss (MG) while minimizing the semantic discrepancy between the common space and label space using a Common Representations Classification loss (CRC) " + }, + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rc}}" + }, + { + "bbox": [ + 46, + 282, + 547, + 360 + ], + "type": "text", + "content": " , thus endowing representations with modality-invariant discrimination." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 380, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 288, + 416 + ], + "type": "text", + "content": "nate the semantic discrepancy, thus encapsulating common discrimination into common representations. Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 425, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 425, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 425, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 58, + 425, + 287, + 497 + ], + "type": "text", + "content": "- We propose a robust 2D-3D cross-modal retrieval framework (RONO) to robustly learn the common discriminative and modality-invariant representations from noisy labels. To the best of our knowledge, this work could be one of the first attempts to learn with noisy labels for 2D-3D cross-modal retrieval." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 505, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 505, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 58, + 505, + 287, + 566 + ], + "type": "text", + "content": "- To mitigate the impact of noisy labels, a novel Robust Discriminative Center Learning mechanism (RDCL) is proposed to adaptively distinguish clean and noisy samples, and then provide them with positive and negative optimization directions, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 573, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 573, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 58, + 573, + 287, + 634 + ], + "type": "text", + "content": "- To construct discriminative and modality-invariant representations, a Shared Space Consistency Learning mechanism (SSCL) is presented to alleviate the intrinsic gaps across heterogeneity, representation, and label spaces." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 641, + 288, + 713 + ], + "type": "text", + "content": "- We theoretically and experimentally demonstrate the robustness of the proposed method under both synthetic symmetric/asymmetric and real-world noisy labels. Our RONO remarkably outperforms the state-of-the-art methods on 3D object benchmarks of different scales with noisy labels without bells and whistles." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 379, + 392, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 379, + 392, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 379, + 392, + 392 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 400, + 434, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 434, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 434, + 412 + ], + "type": "text", + "content": "2.1. Cross-modal Retrieval" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 419, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 659 + ], + "type": "text", + "content": "In recent years, cross-modal retrieval has attracted more and more attention from academia and industry due to its flexible search [17, 39, 40]. The most popular solution is to project multimodal data into a common space, resulting in retrieving related content in the space across different modalities. They could be roughly classified into unsupervised and supervised methods. More specifically, 1) one typical kind of unsupervised method is Canonical Correlation Analysis (CCA) and its variants [1, 35, 45]. They aim to map multimodal inputs into a common space by maximizing the correlation across different modalities. 2) With the help of label information, supervised methods could encapsulate the discrimination into the shared space, thus suiting the downstream retrieval task better. To learn discriminative representations, some shallow methods utilize Fisher criterion [6] to project different modalities into a latent common space [20, 30]. To capture the high nonlinearity in multimodal data, Deep Neural Networks (DNNs) are introduced to learn discriminative and modality-invariant representations [28, 34, 44]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 670, + 459, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 459, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 459, + 683 + ], + "type": "text", + "content": "2.2. Learning with Noisy Labels" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "To tackle the ubiquitous imperfect annotations in the training data, numerous methods have been presented to im" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11611" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "content": "prove the robustness of DNNs against noisy labels. The existing works could be grouped into three main categories: 1) Architecture-based methods focus on modifying the DNN architecture to model the noise transition matrix [5, 8, 11]. However, it is still an open issue to accurately estimate noise transition due to the unpredictable and complex noise. 2) Samples-based methods generally learn from clean samples while weakening the adverse impact of noisy ones by re-weighting samples and refurbishing the labels [2, 25]. However, they require some additional well-labeled data, which is difficult and even impossible to satisfy in real-world applications. To address the problem, some methods adaptively divide the training data into clean and noisy sets based on the memorization effect of DNNs [3] for robust DNN training [13, 24]. 3) Loss-based methods mainly focus on designing robust optimization objectives to guide DNNs learning from noisy labels [10, 16, 26, 37, 43]. Although these robust loss functions could alleviate DNNs overfitting on noisy labels, they may lead DNNs to underfit the clean and hard samples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 176, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 176, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 176, + 337 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 343, + 171, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 343, + 171, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 171, + 355 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "First, some notations are defined for a clear presentation. Boldface lowercase " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " and plain letters " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "M, N" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " represent column vectors and scalars, respectively. Give a " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "-category multimodal dataset " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathcal{M}_j\\}_{j=1}^M = \\{\\mathcal{X}_j, \\mathcal{Y}_j\\}_{j=1}^M" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the number of modalities, " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the number of samples in one modality, " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_j = \\{(x_i^j, y_i^j)\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "-th modality, " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "x_i^j \\in \\mathbb{R}^{d_j}" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "-th sample from the " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "-th modality, " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "d_j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the dimension of the " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": "-th modality and " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "y_i^j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " is the corresponding label of " + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "inline_equation", + "content": "x_i^j" + }, + { + "bbox": [ + 46, + 363, + 287, + 474 + ], + "type": "text", + "content": " that may be incorrect." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 475, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 582 + ], + "type": "text", + "content": "To alleviate the influence of corrupted labels, a robust 2D-3D retrieval framework (RONO) is proposed to robustly learn discrimination from noisy labels while bridging the cross-modal gap. In the framework, we present a Robust Discriminative Center Learning mechanism (RDCL) to reduce the negative impact of unreliable labels, and a Shared Space Consistency Learning mechanism (SSCL) to simultaneously narrow the semantic and heterogeneity gaps. The overall objective function is shown as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 593, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 593, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 77, + 593, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\underbrace {\\mathcal {L} _ {r d c}} _ {R D C L} + \\underbrace {\\beta_ {m g} \\mathcal {L} _ {m g} + \\beta_ {c r c} \\mathcal {L} _ {c r c}} _ {S S C L}, \\tag {1}", + "image_path": "ff5684fa253be6f196354105b5f18b3dd8d41255e70590dfaf30eb05ba229c22.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " is the loss function adopted by RDCL (see Equation (4)), " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mg}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{crc}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " are the loss functions employed by SSCL (see Equations (5) and (6)), and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{mg}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{crc}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " are the trade-off parameters. Our RONO could be optimized by descending Equation (1) with stochastic gradient descent. In the following sections, we will elaborate on each component of our RONO." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 515, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 515, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 515, + 85 + ], + "type": "text", + "content": "3.2. Robust Discriminative Center Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 547, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 173 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 173 + ], + "type": "text", + "content": "To encapsulate the discrimination into the common space, we enforce the samples with the same category compact to the shared clustering centers, while escaping from other centering centers. First, we formulate a contrastive center error " + }, + { + "bbox": [ + 304, + 90, + 547, + 173 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 90, + 547, + 173 + ], + "type": "text", + "content": " to measure the semantic difference between the estimated representations and the clustering centers as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 345, + 176, + 545, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 176, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 345, + 176, + 545, + 209 + ], + "type": "interline_equation", + "content": "t _ {i} ^ {j} = \\frac {\\sum_ {k} ^ {K} e ^ {\\left(\\mathbf {c} _ {k \\neq y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}}{K - 1} - e ^ {\\left(\\mathbf {c} _ {k = y _ {i} ^ {j}}\\right) ^ {T} \\mathbf {z} _ {i} ^ {j}}, \\tag {2}", + "image_path": "db9cafded3ac2512d2d265b260abf7a2fb6f86899137933d2dd5f81246831fae.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "z_{i}^{j} = f_{j}(\\pmb{x}_{i}^{j})\\in \\mathbb{R}^{d_{c}}" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "d_{c}" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": "-D common representation of the " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i^j" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "f_{j}:\\mathbb{R}^{d_{j}}\\to \\mathbb{R}^{d_{c}}" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": " is the input space to common space mapping function, " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "\\pmb {c}_i = \\frac{1}{|\\mathcal{Z}_i|}\\sum_{\\pmb {z}\\in \\mathcal{Z}_i}\\pmb {z}" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": " is the center of " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": "-th category, and " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": " is the set of the " + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 215, + 546, + 350 + ], + "type": "text", + "content": "-th category in the common space. In Equation (2), the dot product is exploited to measure the similarity between a given point and a clustering center in the common space. Obviously, minimizing Equation (2) could maximize the within-class similarities while minimizing the between-class ones, thus endowing the common representations with discrimination. Thus, we could formulate a vanilla loss of RDCL as below:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 358, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 358, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 375, + 358, + 545, + 392 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r d c} ^ {\\prime} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} t _ {i} ^ {j}, \\tag {3}", + "image_path": "78b364e1287037f41060f6a2c341a78b47bd6cf5a371066231e7fc73350bbd6a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 395, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 442 + ], + "type": "text", + "content": "However, such a learning paradigm of Equation (3) will utilize all samples to train networks indiscriminately, thus leading to overfitting on corrupted labels like traditional supervision methods, especially under high noise rates." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "text", + "content": "To investigate the impact of noisy labels on " + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "text", + "content": ", we conduct some visualized experiments on noisy labels and true labels as shown in Figure 2. From the figure, one could observe that although " + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "text", + "content": " makes the networks overfitting to corrupted labels (see Figures 2b and 2f), it could capture the correct discrimination to compact the samples with corrupted labels to the correct clusters in the early training stage (see Figures 2c and 2g), which is well known as the memorization effect of DNNs [3]. That is to say, the similarities between points and the assigned clusters could be markedly distinguishable after a short training period for the samples with correct and corrupt labels. Inspired by the observation, we propose a Robust Discriminative Center loss (RDC) to adaptively discriminate the clean and noisy samples according to " + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 443, + 546, + 646 + ], + "type": "text", + "content": ", and then apply a bias to endow them with positive and negative optimization direction. Thus, we rewrite Equation (3) as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 650, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 650, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 321, + 650, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r d c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} \\left[ (1 - v) t _ {i} ^ {j} - v | t _ {i} ^ {j} + \\alpha | \\right], \\tag {4}", + "image_path": "e4b9455c7ec85d888d07d71703fd22fca04e2f6572d1f1df58f6e3c3db12af12.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "v\\in [0,1]" + }, + { + "bbox": [ + 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"\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 321, + 270, + 397, + 281 + ], + "type": "text", + "content": " after 5 epochs" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "type": "text", + "content": "Figure 2. (a), (b), (c) and (d) show the density vs. the similarity between common representations and noisy centers, and (e), (f), (g) and (h) show the density vs. the similarity between common representations and clean centers for the test set after the training under 0.4 symmetric noise. Moreover, (a) and (e) are trained with the Cross-Modal Center loss (CMC) [19], (b) and (f) are trained with vanilla RDCL loss " + }, + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "type": "text", + "content": " of Equation (3), (c) and (g) are trained for only 5 epochs with " + }, + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 46, + 289, + 547, + 378 + ], + "type": "text", + "content": " and (d) and (h) are trained with the proposed Robust Discriminative Center loss (RDC). It can be found that after short training periods with vanilla RDCL loss, both true and false labeled samples are compacted to their real category centers, and false labeled samples are not similar to their mislabeled category centers. Adopting RDC for training could maintain and reinforce the robustness of the results, which makes the samples in noisy set adaptively avoid being similar to the mislabeled category centers and maintain their similarity to the real category centers, while CMC could hardly achieve." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 425, + 177, + 545, + 267 + ], + "blocks": [ + { + "bbox": [ + 470, + 166, + 500, + 175 + ], + "lines": [ + { + "bbox": [ + 470, + 166, + 500, + 175 + ], + "spans": [ + { + "bbox": [ + 470, + 166, + 500, + 175 + ], + "type": "text", + "content": "(d) " + }, + { + "bbox": [ + 470, + 166, + 500, + 175 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 425, + 177, + 545, + 267 + ], + "lines": [ + { + "bbox": [ + 425, + 177, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 425, + 177, + 545, + 267 + ], + "type": "image", + "image_path": "5fbe530347785e29565210d77dca011f599632315ef58d628b343fcfdf231367.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 270, + 500, + 281 + ], + "lines": [ + { + "bbox": [ + 470, + 270, + 500, + 281 + ], + "spans": [ + { + "bbox": [ + 470, + 270, + 500, + 281 + ], + "type": "text", + "content": "(h) " + }, + { + "bbox": [ + 470, + 270, + 500, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "content": "early within up to 30 epochs, and " + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "inline_equation", + "content": "\\alpha \\in [-e,e]" + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "content": " is a threshold for clean-noise separation. In our training stage, " + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "content": " gradually increases from 0 to 1. More specifically, our RDC will focus on learning simple patterns before fitting on the corrupted labels in the early stage. With further training, our RDC will make the second item dominant to explicitly separate samples into clean and noisy sets, and assign them with correct optimization directions. Surprisingly, our RDC could accurately cluster noisy samples into their correct centers regardless of the corrupted supervision as shown in the visualization results of Figures 2d and 2h, thus embracing robustness against noisy labels." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 551, + 238, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 238, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 238, + 564 + ], + "type": "text", + "content": "3.3. Shared Space Consistency Learning" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "Although our RDCL could achieve robustness against noisy labels, the cross-modal learning paradigm is frequently affected by the inherent gaps across different modalities. More specifically, due to the randomness of the category centers caused by the random initialization of DNNs, blindly increasing the discrimination between points and centers would lead to losing the intrinsic information inside the data, thus degrading the retrieval performance. To handle the problem, we present a Shared Space Consistency Learning mechanism (SSCL) to capture the intrinsic information by narrowing the heterogeneity and semantic gaps simultaneously." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 399, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 458 + ], + "type": "text", + "content": "First, in order to further alleviate or even eliminate the inherent gap across different modalities, we adopt a Multimodal Gap loss (MG) to maximize the mutual information between different modalities from the instance-based perspective [16], which could be formulated as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 312, + 463, + 545, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 463, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 312, + 463, + 545, + 497 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m g} = - \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} l o g \\left(\\frac {\\sum_ {k} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {i} ^ {k}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}{\\sum_ {l} ^ {N} \\sum_ {m} ^ {M} e ^ {\\frac {1}{\\tau} \\left(\\boldsymbol {z} _ {l} ^ {m}\\right) ^ {T} \\boldsymbol {z} _ {i} ^ {j}}}\\right), \\tag {5}", + "image_path": "d4a99408ef0947c77efa43db0f43ef6a9dbab61c22729cb074417fa43eca9cf0.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 500, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 545, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 500, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 500, + 545, + 548 + ], + "type": "text", + "content": " is a temperature parameter. By minimizing Equation (5), the discrepancy across different modalities could be reduced to project cross-modal samples into a common space, thus narrowing the heterogeneity gap." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 548, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 679 + ], + "type": "text", + "content": "Second, in addition to the heterogeneity gap, the semantic discrepancy will also degrade the performance since distinct modalities intrinsically belong to the same label space. To eliminate the discrepancy, we propose a Common Representations Classification loss (CRC) to narrow the gap between the common space and label space. Specifically, a shared classifier is employed to bridge the common space and label space, and then minimize the difference between classification predictions and labels. To alleviate the influence of noisy labels, the robust MAE loss is utilized to minimize the difference as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 348, + 681, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 681, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 348, + 681, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c r c} = \\frac {1}{M N} \\sum_ {i} ^ {N} \\sum_ {j} ^ {M} | g \\left(\\boldsymbol {z} _ {i} ^ {j}, \\Gamma\\right) - y _ {i} ^ {j} |, \\tag {6}", + "image_path": "beb724fbb8de655f114c1a4b5b4fe7b40578175d6cb4810453bbcf51baf6f98c.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11613" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "inline_equation", + "content": "g(z_i^j, \\Gamma)" + }, + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "text", + "content": " is a common classifier with parameters " + }, + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 47, + 71, + 287, + 96 + ], + "type": "text", + "content": " shared by all modalities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 102, + 183, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 183, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 183, + 115 + ], + "type": "text", + "content": "3.4. Theoretical Justification" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "text", + "content": "Following previous works [10, 26], we could indicate that our joint loss function " + }, + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "text", + "content": " is robust against both symmetric and asymmetric label noise. Since DNNs are noise tolerant in the early training stage [3], we only discuss the robustness of our method during the latter training stage as " + }, + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 121, + 287, + 193 + ], + "type": "text", + "content": " has dynamically increased to 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 201, + 214, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 201, + 214, + 214 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 214, + 214 + ], + "type": "text", + "content": "Property 1 " + }, + { + "bbox": [ + 47, + 201, + 214, + 214 + ], + "type": "inline_equation", + "content": "\\exists \\alpha \\in [-e,e],RDC" + }, + { + "bbox": [ + 47, + 201, + 214, + 214 + ], + "type": "text", + "content": " satisfies:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 221, + 296, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 296, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 296, + 264 + ], + "type": "interline_equation", + "content": "\\sum_ {i = 1} ^ {K} \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), i) = (K - 1) \\mathcal {L} _ {r d c} (f (\\boldsymbol {x}), y ^ {*}) + C \\quad \\boldsymbol {x} \\in \\mathcal {X}, \\forall f, \\tag {7}", + "image_path": "0696ce6ec6eb342f5af9fd38e8254e110435927a32c9b860a0f03b169bbb3fdd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}(f(\\pmb{x}), y^{*})" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": " is the loss function to compute " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": " with the common representations " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "f(\\pmb{x})" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": "-category true label " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "y^{*}" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 264, + 287, + 300 + ], + "type": "text", + "content": " is a constant." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 308, + 287, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 287, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 287, + 333 + ], + "type": "text", + "content": "Property 2 There exist upper and lower definite boundaries for " + }, + { + "bbox": [ + 47, + 308, + 287, + 333 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 47, + 308, + 287, + 333 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 341, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 377 + ], + "type": "text", + "content": "Lemma 1 If the above properties are satisfied, RDC with appropriate " + }, + { + "bbox": [ + 46, + 341, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 341, + 287, + 377 + ], + "type": "text", + "content": " is noise tolerant against symmetric (or uniform) and asymmetric (or class conditional) noisy labels." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": "Lemma 2 [10] When symmetric noise rate " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\eta < 1 - \\frac{1}{K}" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": ", MAE is robust against symmetric (or uniform) noisy labels. Defining the risk of the classifier is " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "R_{\\mathcal{L}_{mae}}(f)" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "f^{*}" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": " is the global minimizers of " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "R_{\\mathcal{L}_{mae}}(f)" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mae}(f(\\pmb{x}),y)" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": " is the calculation of MAE, when " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "R_{\\mathcal{L}_{mae}}(f^{*}) = 0" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "0 \\leq \\mathcal{L}_{mae}(f(\\pmb{x}),i) \\leq \\frac{C}{K-1} = 2, \\forall i" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": " and any category-wide noise rate is less than the rate of being clean " + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\eta_{ij} \\leq 1 - \\eta_y" + }, + { + "bbox": [ + 47, + 384, + 287, + 492 + ], + "type": "text", + "content": ", MAE is robust against asymmetric (or class conditional) noisy labels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": "Lemma 3 [21, 26] Assuming there are " + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": " noise tolerant loss functions " + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{L}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": " trade-off hyperparameters " + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\{\\gamma_i\\}_{i=1}^n" + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\sum_{i=1}^n \\gamma_i \\mathcal{L}_i" + }, + { + "bbox": [ + 47, + 502, + 287, + 539 + ], + "type": "text", + "content": " is noise tolerant." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": "The elaborate proofs for Property 1, Property 2, and Lemma 1 can be found in our Complementary Materials. Property 1 and Property 2 can be obtained by mathematical derivation. For Lemma 1, we denote the risk of representation extractor " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " with clean data " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\{x, y^*\\}" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " on our RDC as " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "R(f) = \\mathbb{E}_{x, y^*} \\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": ", and the risk with noisy labels as " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "R^\\eta(f) = \\mathbb{E}_{x, y} \\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "f^*" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "f_\\eta^*" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " are respectively the global minimizers of " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "R(f)" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "R^\\eta(f)" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": ", we require to prove " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "f^*" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " is also a global minimizer of noisy risk " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "R^\\eta(f)" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 47, + 546, + 287, + 689 + ], + "type": "text", + "content": " that is robust against noisy labels. For Lemma 2 and Lemma 3, the theoretical proofs are provided in [10] and [21, 26], respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "According to Lemma 1 and Lemma 2, our RDC and CRC are theoretically robust against both symmetric and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "asymmetric noisy labels. Moreover, our MG is also noise tolerant with noisy labels since it is unsupervised and independent of labels. Therefore, according to Lemma 3, we could draw the conclusion that our joint loss function " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " is noise tolerant against noisy labels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 142, + 388, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 388, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 388, + 156 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 162, + 545, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 545, + 210 + ], + "type": "text", + "content": "To evaluate our RONO, we conduct extensive comparison experiments on four 3D multimodal datasets with different scales, i.e., 3D MNIST [38], RGB-D object [22], ModelNet10 [36] and ModelNet40 [36] datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 217, + 432, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 432, + 229 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 432, + 229 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 235, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 305 + ], + "type": "text", + "content": "In this work, our RONO is implemented in PyTorch and its optimization process could be found in our Complementary Materials. All the experiments are carried out on GeForce RTX 1080Ti GPUs. Four widely-used 3D multimodal datasets are utilized for evaluation, which are briefly introduced below:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 307, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 366 + ], + "type": "text", + "content": "3D MNIST [38]: It is a small-scale 3D model dataset collected in Kaggle which contains 6000 image-point cloud pairs. The point cloud samples are generated from the MNIST dataset. We divide the dataset into 2 subsets: 5000 and 1000 pairs for training and testing sets, respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": "RGB-D object [22]: It is a large-scale dataset containing 300 common family objects belonging to 51 categories. The dataset has 207,621 image-point cloud pairs, which of each has a " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " image and a point-cloud object with 1000 to 5000 points. We split the dataset into 200,000 and 7,621 pairs for training and testing sets, respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 438, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 474 + ], + "type": "text", + "content": "ModelNet10 [36]: It is a 10-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 2,468 and 908 for training and testing sets, respectively." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "type": "text", + "content": "ModelNet40 [36]: It is a 40-categories 3D CAD object benchmark. We divide the dataset into 2 subsets: 9,840 and 3,991 for training and testing sets, respectively." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 510, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 605 + ], + "type": "text", + "content": "In our experiments, we compare our RONO with 15 state-of-the-art methods that include 5 unsupervised methods (i.e., CCA [15], DCCA [1], DCCAE [35], UCCH [17] and DGCPN [42]) and 10 supervised ones (i.e., GMA [30], MvDA [20], AGAH [12], DADH [4], DAGNN [28], ALGCN [27], DSCMR [44], MRL [16], CLF [19] and CLF [19] + MAE [10]). Note that, CLF+MAE is a variant of CLF [19] with a robust MAE [10]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Most of the experiments are conducted on bimodal settings to evaluate two cross-modal tasks: using images as queries to retrieve the point-cloud samples (Image " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " Point Cloud), using point-cloud samples as queries to retrieve the images (Point Cloud " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " Image). Without loss of generality, several experiments are conducted across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40. We use the widely-used mean Average Precision (mAP) score to evaluate the retrieval performance. We" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11614" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 286 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 286 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 286 + ], + "type": "table", + "html": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.4150.4150.4150.4150.4140.4140.4140.4140.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.4490.4380.4260.4150.4370.4320.4230.4140.0900.0850.0880.0890.0870.0830.0870.086
MvDA [20]0.4810.4610.4320.3280.4820.4610.4310.3230.1330.1320.1280.1120.1320.1330.1090.102
AGAH [12]0.6880.5570.1280.1080.6800.5480.1220.1160.6080.3790.1950.0900.6010.3800.1940.090
DADH [4]0.7350.6320.4030.2900.7270.6140.3820.2860.6260.3340.1360.0620.6180.3260.1350.062
DAGNN [28]0.8830.8500.7490.4450.8790.8450.7430.4350.7070.6370.5200.3150.7150.6350.5130.313
ALGCN [27]0.8740.8400.7570.4010.8680.8310.7480.3850.6730.5010.3980.2040.6700.5010.4140.200
DSCMR [44]0.9080.8120.5120.2190.8960.8110.4720.1400.7270.6710.5320.2900.7310.6730.5230.275
MRL [16]0.9550.9370.9180.7850.9440.9310.9050.7910.7110.6460.6100.4980.7090.6230.5980.487
CLF [19]0.8900.8110.4600.1240.8720.7930.4260.1200.7230.6610.3460.1110.7030.6340.3430.106
CLF [19]+MAE [10]0.8100.8120.5010.1220.8090.8110.4830.1220.7050.6260.4260.1870.7030.6240.3990.167
Ours0.9620.9520.9310.8310.9480.9340.9150.8280.7740.7370.7360.7060.7710.7300.7290.700
", + "image_path": "7c571f4108fd03f2311cd98dd1df7cb960364006fb323a59a7725d9109ec719a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 328, + 544, + 546 + ], + "blocks": [ + { + "bbox": [ + 47, + 295, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 47, + 295, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 295, + 546, + 319 + ], + "type": "text", + "content": "Table 1. Performance comparison in terms of mAP under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 328, + 544, + 546 + ], + "lines": [ + { + "bbox": [ + 50, + 328, + 544, + 546 + ], + "spans": [ + { + "bbox": [ + 50, + 328, + 544, + 546 + ], + "type": "table", + "html": "
MethodModelNet10 [36]ModelNet40 [36]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8
CCA [15]0.6250.6250.6250.6250.6270.6270.6270.6270.5320.5320.5320.5320.5310.5310.5310.531
DCCA [1]0.6840.6840.6840.6840.6770.6770.6770.6770.5840.5840.5840.5840.5690.5690.5690.569
DCCAE [35]0.7030.7030.7030.7030.6930.6930.6930.6930.5930.5930.5930.5930.5720.5720.5720.572
DGCPN [42]0.7650.7650.7650.7650.7590.7590.7590.7590.7050.7050.7050.7050.6970.6970.6970.697
UCCH [17]0.7710.7710.7710.7710.7700.7700.7700.7700.7550.7550.7550.7550.7390.7390.7390.739
GMA [30]0.6500.6170.5850.5210.6460.5790.5500.4970.5250.4850.4660.4480.5150.4870.4590.437
MvDA [20]0.4940.4580.4490.3900.4640.4280.4060.3280.4200.3730.3290.3160.4120.3700.3000.271
AGAH [12]0.8530.7360.5830.4250.8370.6990.5490.4080.8090.7320.6870.5680.7830.7360.6640.554
DADH [4]0.8600.7720.6700.5540.8380.7680.6580.5530.8180.7430.6760.5810.7820.7480.6570.586
DAGNN [28]0.8440.8000.7540.4220.8360.8100.7630.4480.8020.7230.6350.4020.7980.7280.6430.412
ALGCN [27]0.7880.5970.4260.2820.7970.5890.4400.2690.7660.5380.4260.2980.7630.5370.4030.279
DSCMR [44]0.8490.7580.6660.3240.8360.7320.6370.3070.8240.7880.6870.3280.8110.7850.6940.339
MRL [16]0.8760.8700.8630.8320.8610.8570.8480.8230.8330.8290.8280.8180.8240.8260.8200.817
CLF [19]0.8490.7820.6200.3650.8380.7640.5950.3870.8220.7780.6240.3150.8150.7710.5870.295
CLF [19]+MAE[10]0.8530.7520.6790.3430.8380.7160.6590.3730.8270.7580.6510.3840.8160.7490.6400.372
Ours0.8920.8770.8700.8360.8900.8750.8610.8300.8770.8580.8380.8230.8720.8540.8380.821
", + "image_path": "6b407398999444ad7647a2b7425621bf316b470d1cdaf511b6ee29751f59bf5c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 553, + 546, + 578 + ], + "lines": [ + { + "bbox": [ + 47, + 553, + 546, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 546, + 578 + ], + "type": "text", + "content": "Table 2. Performance comparison under the symmetric noise rates of 0.2, 0.4, 0.6, and 0.8 on the ModelNet10 and ModelNet40 datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "type": "text", + "content": "conduct the comparison experiments under both synthetic symmetric and asymmetric label noise for comprehensive evaluation. Due to the space limitation, we only evaluate the robustness against asymmetric label noise on 3D MNIST and RGB-D object datasets. More extra experimental results could be found in our Complementary Materials. For a comprehensive evaluation, the symmetric noise rates are set as 0.2, 0.4, 0.6, and 0.8, and the asymmetric ones are set as 0.1, 0.2, and 0.4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 586, + 509, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 509, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 509, + 599 + ], + "type": "text", + "content": "4.2. Comparison with the State-of-the-Arts" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "We apply 2D-3D cross-modal retrieval on four 3D model multimodal datasets to evaluate the robustness of our RONO and the baselines. The experimental results under symmetric noise are reported in Tables 1 and 2, and ones under asymmetric noise are reported in Table 3. From these experimental results, we could obtain the following observations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "- Noisy labels could remarkably reduce the retrieval per" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "11615" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 288 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 288 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 288 + ], + "type": "table", + "html": "
Method3D MNIST [38]RGB-D object [22]
Image→Point CloudPoint Cloud→ImageImage→Point CloudPoint Cloud→Image
00.10.20.400.10.20.400.10.20.400.10.20.4
CCA [15]0.4150.4150.4150.4150.4150.4150.4150.4150.1350.1350.1350.1350.1330.1330.1330.133
DCCA [1]0.5950.5950.5950.5950.5930.5930.5930.5930.2110.2110.2110.2110.2150.2150.2150.215
DCCAE [35]0.6000.6000.6000.6000.6000.6000.6000.6000.2170.2170.2170.2170.2180.2180.2180.218
DGCPN [42]0.7920.7920.7920.7920.7830.7830.7830.7830.1380.1380.1380.1380.1420.1420.1420.142
UCCH [17]0.7910.7910.7910.7910.7900.7900.7900.7900.3090.3090.3090.3090.3070.3070.3070.307
GMA [30]0.5140.4440.4360.4150.5000.4350.4170.3960.1260.0890.0850.0730.1210.0850.0810.069
MvDA [20]0.5300.4720.4070.3700.5080.4720.3970.3520.1880.1880.1590.1420.1990.1680.1390.124
AGAH [12]0.9670.7300.6110.5190.9610.7290.5890.5120.6520.6030.4440.3560.6280.5590.4360.361
DADH [4]0.9710.8480.7180.5700.9690.8250.7010.5720.7720.7230.5890.5240.7610.7030.5720.511
DAGNN [28]0.9270.8940.8710.6840.9270.8930.8640.6910.7410.7040.6460.5630.7240.6890.6310.554
ALGCN [27]0.9080.8760.8600.6350.9000.8710.8520.6410.7170.6850.6170.5260.6910.6780.5980.531
DSCMR [44]0.9630.9140.8690.7110.9450.9060.8620.7040.7740.7550.7110.6730.7680.7380.7000.659
MRL [16]0.9630.9590.9440.7920.9450.9400.9220.7620.7230.6550.6350.6020.7190.6520.6360.599
CLF [19]0.9830.9450.9240.8090.9580.9320.9200.8020.7720.7710.7340.6740.7660.7590.7210.659
CLF [19]+MAE[10]0.9710.9420.9210.7960.9510.9300.9180.7830.7520.7580.7200.6510.7410.7500.7120.637
Ours0.9830.9610.9580.9120.9680.9470.9380.8970.7790.7730.7280.6810.7710.7560.7210.669
", + "image_path": "e8c1e01763170a6e841bed905717321129e2924b286a5432e7752afce408d78f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 66, + 339, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 339, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 66, + 339, + 287, + 399 + ], + "type": "text", + "content": "formance of supervised methods. Their performance will be degraded rapidly as the noise rate increases. Especially, when the noise rate is high, supervised methods tend to perform worse than unsupervised ones, or even fail to fit the data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 406, + 287, + 704 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 406, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 406, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 58, + 406, + 287, + 502 + ], + "type": "text", + "content": "- For the symmetric noise, our RONO achieves remarkably better results than supervised (e.g., CLF, DAGNN, DSCMR, etc.), which demonstrates the robustness of our method against noisy labels. Besides, our RONO could utilize noisy labels to overcome the unsupervised methods (e.g., UCCH, DGCPN, etc.), thus indicating that additional label information could improve performance even if it contains noise." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 510, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 510, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 58, + 510, + 287, + 594 + ], + "type": "text", + "content": "- Our RONO is superior to a strong baseline (i.e., MRL) that is a noise-tolerate cross-modal method. Especially, our method could achieve 0.703 in terms of mAP under 0.8 noise on the large-scale RGB-D object dataset, which is higher than MRL (0.493) by 0.210, thus demonstrating the effectiveness of our adaptive optimization strategy for clean and noisy data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 601, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 601, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 58, + 601, + 287, + 650 + ], + "type": "text", + "content": "- For asymmetric noise, the extremely perplexing class conditional noise will degrade the performance of the memorization effect of DNNs, however, our RONO still achieves superior robustness against noisy labels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 656, + 287, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 656, + 287, + 704 + ], + "spans": [ + { + "bbox": [ + 58, + 656, + 287, + 704 + ], + "type": "text", + "content": "- Our RONO shows superiority even without the addition of synthetic label noise, demonstrating that well-annotated datasets also contain noise impacting the performance of each non-robust method." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 309, + 337, + 547, + 460 + ], + "blocks": [ + { + "bbox": [ + 47, + 296, + 544, + 319 + ], + "lines": [ + { + "bbox": [ + 47, + 296, + 544, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 296, + 544, + 319 + ], + "type": "text", + "content": "Table 3. Performance comparison under the asymmetric noise rates of 0, 0.1, 0.2, and 0.4 on the 3D MNIST and RGB-D object datasets. The highest mAPs are shown in bold and the second highest mAPs are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 337, + 547, + 460 + ], + "lines": [ + { + "bbox": [ + 309, + 337, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 309, + 337, + 547, + 460 + ], + "type": "table", + "html": "
RDCLSSCL3D MNIST [38]ModelNet40 [36]
LrdcLmgLcrcImg→PntPnt→ImgImg→PntPnt→Img
0.40.80.40.80.40.8
✓✓✓0.9520.8310.9340.8280.8580.824
L′rdc✓✓0.8910.3420.8990.3140.8150.670
✓✓0.8410.6750.8320.6710.8210.777
✓✓0.9290.6150.9270.5640.7930.551
✓✓0.9300.7090.9140.7060.8040.673
✓0.6410.4230.6350.4290.7350.608
✓0.6610.6610.6600.6600.4440.444
✓0.5270.3480.5370.2750.7250.484
", + "image_path": "4495a42d427a8a810147b12b84f6c5413f903994667d2b13e7423d0c80531dba.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 468, + 545, + 491 + ], + "lines": [ + { + "bbox": [ + 305, + 468, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 468, + 545, + 491 + ], + "type": "text", + "content": "Table 4. Ablation studies for RONO on the 3D MNIST and ModelNet40 datasets with 0.4 symmetric noise. " + }, + { + "bbox": [ + 305, + 468, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 305, + 468, + 545, + 491 + ], + "type": "text", + "content": " stands for use." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 510, + 400, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 400, + 523 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 400, + 523 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "In this section, we investigate the contribution of each proposed component (i.e., loss " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mg}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{crc}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ") to 2D-3D retrieval with noisy labels. For a comprehensive comparison, we ablate each component from the framework and conduct the variants with the same experimental settings on two distinct datasets (i.e., 3D MNIST and ModelNet40). The results are shown in Table 4. From the table, one could draw the following observation: 1) RONO with/without any component will improve/drop retrieval performance, which indicates that each component contributes to our framework. 2) Replacing RCD (i.e., " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ") with the vanilla loss of RDCL (i.e., " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rdc}^{\\prime}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ") will result in remarkable performance degradation, thus demonstrating the effectiveness of differentiated optimization for clean and noisy data, especially for high noise rates." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11616" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 289, + 223 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 223 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 223 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 223 + ], + "type": "table", + "html": "
ηQryImgMshPnt
RetrvImgMshPntImgMshPntImgMshPnt
0CLF0.9030.8980.8830.8910.8730.8820.8870.8830.881
Ours0.9110.9010.8910.8990.9010.8830.8910.8940.891
0.2CLF0.8250.8300.8250.8310.8500.8480.8290.8500.851
Ours0.8740.8720.8810.8830.8910.8890.8750.8840.890
0.4CLF0.6830.7490.7610.7370.8160.8290.7460.8280.848
Ours0.8580.8760.8630.8620.8810.8750.8590.8750.875
0.6CLF0.5600.5890.6270.5690.6810.7290.6040.7250.794
Ours0.8420.8530.8510.8570.8570.8620.8430.8680.872
0.8CLF0.3110.3160.3610.3230.3920.4000.3650.3850.559
Ours0.8280.8420.8420.8420.8680.8660.8410.8640.868
", + "image_path": "6f35e736dfa907279016eacec918404f0e382b7bb53130f3111d4a68a30fe70b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 288, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 288, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 288, + 297 + ], + "type": "text", + "content": "Table 5. Performance comparison of CLF [19] and our RONO under the symmetric noise rates of 0, 0.2, 0.4, 0.6 and 0.8 on trimodal ModelNet40 dataset [36]. The highest mAPs are shown in bold. For a convenience presentation, we abbreviate Image, Mesh, Point cloud, Query, and Retrieval to Img, Msh, Pnt, Qry, and Retrv, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 317, + 216, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 216, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 216, + 330 + ], + "type": "text", + "content": "4.4. Further Comparison with CLF" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": "To comprehensively evaluate our RONO, we conduct various 2D-3D cross-modal retrieval and visualization experiments across three modalities (i.e., Image, Mesh, and Point cloud) on ModelNet10 and ModelNet40 [36], by comparing RONO with state-of-the-art CLF [19]. The comparison results are shown in Table 5 and Figures 3 and 4. Due to space limitation, more cross-modal and in-domain comparison results could be found in our Complementary Materials." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 444, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 288, + 552 + ], + "type": "text", + "content": "From the experimental results, one could observe that: 1) Regardless of noise rates, our RONO show stronger robustness against noisy labels across three modalities. 2) Our RONO could obtain more discriminative clusters compared to CLR, which demonstrates the robustness of our RONO. 3) Our RONO could achieve more correct retrieved results while CLF fails on the same queries, indicating that our method has stronger robustness and is consistent with our quantitative results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 119, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 119, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 119, + 574 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we propose a novel 2D-3D cross-modal retrieval framework to robustly learn discriminative and modality-invariant representations with noisy labels, termed RONO. To be specific, our RONO employs a novel Robust Discriminative Center Learning mechanism (RDCL) to endow clean and noisy samples with correct optimization directions, while a Shared Space Consistency Learning mechanism (SSCL) to guarantee the cross-modal and semantic consistency across different modalities in the common space. Comprehensive mathematical analyses are provided to theoretically prove the noise tolerance of our RONO." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 424, + 184 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 424, + 184 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 424, + 184 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 424, + 184 + ], + "type": "image", + "image_path": "21613b3f5dd1a7b6559c054f6f67ba3e5289f33f80b5f85d0295ffd0a4a40cda.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 186, + 378, + 196 + ], + "lines": [ + { + "bbox": [ + 351, + 186, + 378, + 196 + ], + "spans": [ + { + "bbox": [ + 351, + 186, + 378, + 196 + ], + "type": "text", + "content": "(a) CLF" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 430, + 70, + 545, + 184 + ], + "blocks": [ + { + "bbox": [ + 430, + 70, + 545, + 184 + ], + "lines": [ + { + "bbox": [ + 430, + 70, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 430, + 70, + 545, + 184 + ], + "type": "image", + "image_path": "665871952dda2bec5c2cbe80bb7f55401a3ac9ac0ac67b5ee99d73ed16512f08.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 186, + 502, + 196 + ], + "lines": [ + { + "bbox": [ + 473, + 186, + 502, + 196 + ], + "spans": [ + { + "bbox": [ + 473, + 186, + 502, + 196 + ], + "type": "text", + "content": "(b) Ours" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 273, + 547, + 439 + ], + "blocks": [ + { + "bbox": [ + 305, + 205, + 547, + 261 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 547, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 547, + 261 + ], + "type": "text", + "content": "Figure 3. The representation visualization on the testing set of ModelNet40 by using t-SNE method [33]. CLF and our RONO are trained under 0.4 symmetric label noise. Samples from the same category are rendered with the same color, and ones from the same modality are rendered with the same marker." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 273, + 547, + 439 + ], + "lines": [ + { + "bbox": [ + 307, + 273, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 307, + 273, + 547, + 439 + ], + "type": "image", + "image_path": "028306bbaa728e64ce89842ab1eb5bc118e300b2ec13f246bfe1d17cbb365687.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "type": "text", + "content": "Figure 4. Top-5 retrieved results of CLF and our RONO under 0.4 label noise on the tri-modal ModelNet40 dataset. Green boxes indicate correct retrieval, while red boxes indicate wrong retrieval." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 501, + 545, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 501, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 305, + 501, + 545, + 549 + ], + "type": "text", + "content": "Furthermore, we conduct extensive experiments compared to 15 state-of-the-art methods on four 3D model multimodal datasets to demonstrate the robustness of the proposed method against synthetic and real label noise." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 562, + 403, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 403, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 403, + 574 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 582, + 545, + 713 + ], + "type": "text", + "content": "This work is supported by the National Key R&D Program of China under Grant 2020YFB1406702, the National Natural Science Foundation of China (Grants No. 62102274, 62176171, and U19A2078), Sichuan Science and Technology Planning Project (Grants No. 2021YFS0389, 2021YFG0317, 2021YFG0301, 2022YFQ0014, and 2022YFH0021), Fundamental Research Funds for the Central Universities, A\\*STAR AME Programmatic Funding A18A2b0046, RobotHTPO Seed Fund under Project C211518008 and EDB Space Technology Development Grant under Project S22-19016-STDP." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11617" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Galen Andrew, Raman Arora, Jeff Bilmes, and Karen Livescu. 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IEEE transactions on neural networks, 17(1):233-238, 2006. 2" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11619" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_content_list.json b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4ce9c385f8985d9c35024ae1e8b96459910ac95d --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_content_list.json @@ -0,0 +1,1537 @@ +[ + { + "type": "text", + "text": "RUST: Latent Neural Scene Representations from Unposed Imagery", + "text_level": 1, + "bbox": [ + 140, + 130, + 828, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mehdi S. M. Sajjadi* Aravindh Mahendran Thomas Kipf \nEtienne Pot Daniel Duckworth Mario Lucic Klaus Greff \nGoogle Research, Brain Team", + "bbox": [ + 232, + 180, + 736, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 272, + 312, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inferring the structure of 3D scenes from 2D observations is a fundamental challenge in computer vision. Recently popularized approaches based on neural scene representations have achieved tremendous impact and have been applied across a variety of applications. One of the major remaining challenges in this space is training a single model which can provide latent representations which effectively generalize beyond a single scene. Scene Representation Transformer (SRT) has shown promise in this direction, but scaling it to a larger set of diverse scenes is challenging and necessitates accurately posed ground truth data. To address this problem, we propose RUST (Really Unposed Scene representation Transformer), a pose-free approach to novel view synthesis trained on RGB images alone. Our main insight is that one can train a Pose Encoder that peeks at the target image and learns a latent pose embedding which is used by the decoder for view synthesis. We perform an empirical investigation into the learned latent pose structure and show that it allows meaningful test-time camera transformations and accurate explicit pose readouts. Perhaps surprisingly, RUST achieves similar quality as methods which have access to perfect camera pose, thereby unlocking the potential for large-scale training of amortized neural scene representations.", + "bbox": [ + 75, + 303, + 473, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 672, + 207, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Implicit neural representations have shown remarkable ability in capturing the 3D structure of complex real-world scenes while circumventing many of the downsides of mesh based, point cloud based, and voxel grid based representations [24]. Apart from visually pleasing novel view syn", + "bbox": [ + 75, + 694, + 470, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "*Correspondence: rust@msajjadi.com. Project page: rust-paper.github.io. Contributions: MS: Conception, model design, implementation lead, analysis, infrastructure, experiments, writing, project lead. AM: Conception, model design, implementation, code reviews, experiments-MSN, analysis-MSN, writing. TK: RUST explicit pose estimation, model figures, scoping, advising, writing. EP: GNeRF experiments, Street View dataset, interactive visualization for embedding inspection. DD: COLMAP experiments, evaluation. ML: Team buy-in, scoping, writing. KG: Conception, early MSN analysis, analysis-SV, data-collection and analysis, dataset generation, visualizations, scoping, advising, writing.", + "bbox": [ + 78, + 779, + 472, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c673c66ce640bc1a85087c89504175e2e2a7eeb5c2b247ea590577936502a6bd.jpg", + "image_caption": [ + "Figure 1. Model overview - RUST produces 3D-centric scene representations through novel view synthesis purely from RGB images without requiring any camera poses. For training, a novel Pose Estimator module glimpses at the target view and passes a low-dimensional latent pose feature to the decoder." + ], + "image_footnote": [], + "bbox": [ + 506, + 272, + 890, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thesis [14, 16], such representations have shown potential for semantics [25], object decomposition [21], and physics simulation [2] which makes them promising candidates for applications in augmented reality and robotics. However, to be useful in such applications, they need to (1) provide meaningful representations when conditioned on a very limited number of views, (2) have low latency for real-time rendering, and (3) produce scene representations that facilitate generalization of knowledge to novel views and scenes. The recently proposed Scene Representation Transformer (SRT) [22] exhibits most of these properties. It achieves state-of-the-art novel view synthesis in the regime when only a handful of posed input views are available, and produces representations that are well-suited for later segmentation at both semantic [22] and instance level [21]. A major challenge in scaling methods such as SRT, however, is the difficulty in obtaining accurately posed real world data which precludes the training of the models. We posit that it should be possible to train truly pose-free models from RGB images alone without requiring any ground truth pose information.", + "bbox": [ + 496, + 518, + 893, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose RUST (Really Unposed Scene representation Transformer), a novel method for neural scene representation learning through novel view synthesis that does not require pose information: neither for training, nor for inference; neither for input views, nor for target views. While at first", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17297", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "glance it may seem unlikely that such a model could be trained, our key insight is that a sneak-peek at the target view at training can be used to infer an implicit latent pose, thereby allowing the rendering of the correct view. We find that our model not only learns meaningful, controllable latent pose spaces, but the quality of its novel views are even comparable to the quality of posed methods.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key contributions are as follows:", + "bbox": [ + 76, + 204, + 323, + 218 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose RUST, a novel method that learns latent 3D scene representations through novel view synthesis on very complex synthetic and real datasets without any pose information.", + "- Our model strongly outperforms prior methods in settings with noisy camera poses while matching their performance when accurate pose information is available to the baselines.", + "- We provide an investigation into the structure of the learned latent pose spaces and demonstrate that meaningful camera transformations naturally emerge in a fully unsupervised fashion.", + "- Finally, we demonstrate that the representations learned by the model allow explicit pose readout and dense semantic segmentation." + ], + "bbox": [ + 76, + 222, + 468, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Method", + "text_level": 1, + "bbox": [ + 76, + 467, + 166, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The model pipeline is shown in Fig. 1. A data point consists of an unordered set of $N$ input views $x = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\}$ of a scene. Unlike SRT [22], they only consist of RGB images since RUST does not use explicit poses. Given these input views, the training objective is to predict a novel target view $y \\in \\mathbb{R}^{H \\times W \\times 3}$ of the same scene.", + "bbox": [ + 75, + 492, + 468, + 583 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, the input views $x$ are first encoded using a combination of a CNN and a transformer, resulting in the Set-Latent Scene Representation (SLSR) $S$ which captures the contents of the scene. The target view $y$ is then rendered by a transformer-based decoder that attends into the SLSR $S$ to retrieve relevant information about the scene for novel view synthesis. In addition, the decoder must be conditioned on some form of a query that identifies the desired view. Existing methods, including SRT [22], often use the explicit relative camera pose $p$ between one of the input views and the target view for this purpose. This imbues an explicit notion of 3D space into the model, which introduces a burdensome requirement for accurate camera poses, especially for training such models. RUST resolves this fundamental limitation by learning its own notion of implicit poses.", + "bbox": [ + 75, + 584, + 470, + 811 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit poses. Instead of querying the decoder with explicit poses, we allow the model to learn its own implicit space of camera poses through a learned Pose Estimator module. For training, the Pose Estimator sees parts of the target view $y$ and the SLSR $S$ and extracts a low-dimensional", + "bbox": [ + 75, + 825, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e649bcbc2335249797efc3bc0bfca311f23bb0ddc49eb71edd9115b4a62e5251.jpg", + "image_caption": [ + "Figure 2. Pose estimator model - A randomly chosen half of the target image is encoded into a latent pose. The model mainly consists of a CNN encoder followed by alternating cross- and self-attention layers. The final output is projected to 8 dimensions to encourage an easily controllable latent representation." + ], + "image_footnote": [], + "bbox": [ + 555, + 92, + 830, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "latent pose feature $\\tilde{p}$ . The decoder transformer then uses $\\tilde{p}$ as a query to cross-attend into the SLSR to ultimately render the full novel view $\\tilde{y}$ . This form of self supervision allows the model to be trained with standard reconstruction losses without requiring any pose information. At test time, latent poses can be computed on the input views and subsequently modified for novel view synthesis, see Sec. 4.2.", + "bbox": [ + 496, + 422, + 893, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Model components", + "text_level": 1, + "bbox": [ + 500, + 539, + 683, + 555 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Input view encoder. The encoder consists of a convolutional neural network (CNN) followed by a transformer. Each input image $x_{i}$ is encoded independently by the shared CNN which consists of 3 downsampling blocks, each of which halves the image height and width. As a result, each spatial output feature corresponds to an $8\\times 8$ patch in the original input image.", + "bbox": [ + 496, + 561, + 893, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We add the same learned position embeddings to all spatial feature maps to mark their spatial 2D position in the images. We further add another learned embedding only to the features of the first input image $x_{1}$ to allow the model to distinguish them from the others. This is relevant for the Pose Estimator module, as explained below. Finally, we flatten all spatial feature maps and combine them across input views into a single set of tokens. The encoder transformer then performs self-attention on this set of tokens, thereby exchanging information between the patch features. This results in the SLSR $S$ which captures the scene content as a bag of tokens.", + "bbox": [ + 496, + 669, + 893, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pose estimator. The model architecture of the Pose Estimator is shown in Fig. 2. A randomly chosen half of the target", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17298", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "view $y$ (i.e., either the left or the right half of the image) is first embedded into a set of tokens using a CNN similar to the input view encoder. A transformer then alternates between cross-attending from the target view tokens into a specific subset $\\tilde{S} \\subset S$ of the SLSR and self-attending between the target view tokens. The intuition behind cross-attending into $\\tilde{S}$ is that the latent pose $\\tilde{p}$ should be relative to the scene. We allow the Pose Estimator to only attend into SLSR tokens belonging to the (arbitrarily chosen) first input view after empirical findings that this leads to better-structured latent pose spaces. It is important to note that $\\tilde{S}$ contains information about all input views due to the self-attention in the preceding encoder transformer.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, we apply global mean pooling on the transformer's output and linearly project it down to an 8-dimensional latent pose $\\tilde{p}$ . It is important to note that we call $\\tilde{p}$ the estimated \"pose\" since it primarily serves the purpose of informing the decoder of the target camera pose. However, we do not enforce any explicit constraints on the latent, instead allowing the model to freely choose the structure of the latent poses. Nevertheless, we find that the model learns to model meaningful camera poses, see Sec. 4.2.", + "bbox": [ + 75, + 287, + 472, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Decoder transformer. Similar to SRT, each pixel is decoded independently by a decoder transformer that cross-attends from a query into the SLSR $S$ , thereby aggregating relevant information from the scene representation to establish the appearance of the novel view point. We initialize the query by concatenating the latent pose $\\tilde{p}$ with the spatial 2D position of the pixel in the target image and passing it through a small query MLP. The output of the decoder is the single RGB value of the target pixel.", + "bbox": [ + 75, + 436, + 472, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Training procedure", + "text_level": 1, + "bbox": [ + 76, + 584, + 264, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For each data point during training, we use 5 input views and 3 novel target views. The training objective is to render the target views by minimizing the mean-squared error between the predicted output and the target view: $||\\tilde{y} - y||_2^2$ . The entire model is trained end-to-end using the Adam optimizer [9]. In practice, we found the model to perform better when gradients flowing to and through the Pose Estimator module are scaled down by 0.2 which is inspired by spatial transformer networks [7].", + "bbox": [ + 75, + 607, + 470, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Related works", + "text_level": 1, + "bbox": [ + 76, + 753, + 222, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural rendering. The field of neural rendering is vast and the introduction of Neural Radiance Fields (NeRF) [16] has led to a surge of recent follow-up works. NeRF optimizes an MLP to map 3D positions of the scene to radiance and density values, which are used through a differentiable volumetric rendering equation to reconstruct the provided posed images of the scene. We refer the reader to surveys on neural rendering [24] and NeRF [4] for recent overviews.", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRF without pose. Most methods based on NeRF assume the availability of perfect camera pose. There exist a number of works extending NeRF for pose estimation or to no-pose settings. INeRF [28] uses pre-trained NeRFs to estimate the camera pose of novel views of the same scene. However, posed imagery is required for each scene in order to obtain the original NeRF models. NeRF-- [27] jointly optimizes the NeRF MLP along with the camera poses for the images. BARF [13] adds a progressive position encoding scheme for improved gradients. Both methods only succeed for forward-facing datasets while failing for more complex camera distributions unless noisy initial poses are given. GNeRF [15] works for scenes with more complex camera distributions, however, the prior distribution must be known for sampling. VMRF [30] extends this to settings where the prior distribution is unknown.", + "bbox": [ + 496, + 90, + 893, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All methods above require a comparably large number of images of the same scene, since NeRF tends to fail with few observations even with perfect pose [29]. While methods exist that optimize NeRFs from fewer observations [8, 18], they have limitations in terms of scene complexity [22] and to the best of our knowledge, no NeRF-based method has been demonstrated to work with few unposed images.", + "bbox": [ + 496, + 332, + 893, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent 3D scene representations. In the right setup, NeRF produces high-quality novel views, though it does so without providing tangible scene representations that could be readily used for downstream tasks. The line of research focusing on latent 3D scene representations includes NeRF-VAE [12] which uses a variational autoencoder [10] to learn a generative model of NeRF's for synthetic scenes, and GQN [3] which adds per-image latent representations to compute a global scene representation that is used by a recurrent latent variable model for novel view synthesis. A recent extension [19] of GQN performs pose estimation for novel target views by optimizing, at inference time, the posterior probability over poses as estimated by the generative model. All the methods above require ground truth poses for training and inference. GIRAFFE [17] requires no poses for training, but a prior distribution of camera views for the specific dataset. It uses a purely generative mechanism, without the ability to render novel views for given scenes.", + "bbox": [ + 496, + 450, + 895, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Posed and \"unposed\" SRT. The current most scalable latent method for neural scene representations is the Scene Representation Transformer (SRT) [22]. It uses a transformer-based encoder-decoder architecture for novel view synthesis, thereby scaling to much more complex scenes than prior work. Its scene representation, the SLSR, has been shown to be useful for 3D-centric supervised and unsupervised semantic downstream tasks [21, 22].", + "bbox": [ + 496, + 734, + 893, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While SRT requires posed imagery, the \"unposed\" variant UpSRT has been proposed as well in the original work [22]. Similar to RUST, it does not require posed input views. How-", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17299", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/a3e4563b430e57741a9bfebe1e823a8867affb57fa1a0f6ee660b9fad3fee7f5.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Quantitative results on MSN – Left: Comparison with prior work in various settings: perfect $(p_x, p_y)$ , noisy $(\\hat{p}_x, \\hat{p}_y)$ and lack of $(p_x, p_y)$ input and target poses. We report SRT both as proposed [22], and with our improved architecture $(\\mathrm{SRT}^\\dagger, \\mathrm{UpSRT}^\\dagger)$ . Despite requiring no poses, RUST matches the performance of SRT and $\\mathrm{UpSRT}^\\dagger$ while strongly outperforming all methods when target pose is noisy $\\hat{p}_y$ . Right: Model ablations, see Sec. 4.1.1." + ], + "table_body": "
MethodPosePSNRAblationPSNR
SRT [22]px, py23.31Right-half PE23.88
SRT†px, py24.40Stop grad.23.16
SRT†hatx, py23.81No SLSR20.83
UpSRT†px, py23.03No self-attn22.97
SRT†hatx, haty18.653-dim. p20.40
UpSRT†px, pγ18.6464-dim. p23.40
RUSTpx, pγ23.49768-dim. p23.11
", + "bbox": [ + 81, + 88, + 467, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ever, training an UpSRT model requires exact pose information for the target views to specify to the decoder which exact view of the scene to render. This restricts the application of UpSRT to settings where accurate pose information is available for the entire training dataset. We analyze further implications of this in Sec. 4.1.", + "bbox": [ + 75, + 359, + 470, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using targets as inputs for training. UViM [11] encodes targets such as panoptic segmentation maps into short latent codes during training to allow a single model architecture to perform well across several tasks. A bottleneck is enforced on the so-called guiding codes through discretization. Recent work on inferring protein conformations and poses [20] trains a VAE model in order to encode Cryo-EM images into latent distributions over poses and protein conformations. Unlike RUST, their method requires a base scene representation that is fixed a priori and uses an explicit differentiable rendered and explicit geometry in the architecture.", + "bbox": [ + 75, + 468, + 470, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 648, + 209, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We begin our experiments on the MultiShapeNet (MSN) dataset (version from [21]), a very challenging test bed for 3D-centric neural scene representation learning [22]. It consists of synthetically generated 3D scenes [6] that contain 16-32 ShapeNet objects [1] scattered in random orientations, and with photo-realistic backgrounds. Importantly, the set of ShapeNet objects is split for the training and test datasets, meaning that all objects encountered in the test scenes are not only in novel arrangements and orientations, but the model has never seen them in the training dataset. Camera positions are sampled from a half-sphere with varying distances to the scene. In all experiments, we follow prior work [22] by using 5 input views, and all quantitative metrics are computed on the right halves of the target views, since the left halves are used for pose estimation in RUST.", + "bbox": [ + 75, + 672, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/13ba1017c67287406b240b4d5b3b1d0426ac2e925b2e31f882776946b05d84ee.jpg", + "image_caption": [ + "Figure 3. Robustness to camera noise – Sajjadi et al. [22] evaluate SRT and UpSRT on (A) perfect pose, and (B) noisy input pose. In the more realistic setting (C) where input & target pose is noisy, both methods fail as they rely on accurate target camera pose for training. RUST needs no pose, so its performance is constant." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 885, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Novel view synthesis", + "text_level": 1, + "bbox": [ + 500, + 332, + 692, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core contribution of RUST is its ability to model 3D scenes without posed imagery. While camera poses in synthetic environments such as MSN are perfectly accurate, practical applications must often rely on noisy sensor data or inaccurate estimated poses. We therefore begin our investigations by measuring the quality of synthesized novel views in new scenes under various assumptions on the accuracy and availability of camera pose information during training. To simulate the real world, we follow prior work [13, 22] and perturb the training camera poses with additive noise for a relatively mild amount of $\\sigma = 0.1$ . We visualize the effect of this noise in Fig. 14 (appendix) to provide context for its scale. This leads to three possible settings for both input poses and target poses: perfect $(p_x, p_y)$ , noisy $(\\hat{p}_x, \\hat{p}_y)$ and lack of $(p_x, p_y)$ input and target cameras poses, respectively. Note that for the posed baselines, we always use perfect target poses for evaluation, i.e. the target poses are only perturbed during training.", + "bbox": [ + 496, + 354, + 893, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tab. 1 (left) shows our quantitative evaluation on the MSN dataset. We first compare SRT as proposed [22] with our improved architecture $\\mathrm{SRT}^{\\dagger}$ , both using perfect pose. We observe that our modifications to the architecture lead to significant improvements in PSNR (+1.09 db). Continuing with the improved architecture, perturbing the input views leads to a loss in 0.59 db ( $\\mathrm{SRT}^{\\dagger}$ , $\\hat{p}_x$ , $p_y$ ) while the lack thereof leads to a drop of 1.37 db ( $\\mathrm{UpSRT}^{\\dagger}$ , $p_x$ , $p_y$ ).", + "bbox": [ + 496, + 628, + 893, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Crucially, the most realistic setting where all poses are equally noisy leads to a dramatic decline in performance for prior work $(\\mathrm{SRT}^{\\dagger}$ and $\\mathrm{UpSRT}^{\\dagger},\\hat{p}_y)$ . RUST meanwhile outperforms the baselines by $+4.84$ db in this setting without any poses, while matching the performance of SRT [22] with perfect pose. We highlight the difference between only perturbing input poses (following prior work [22]) or all camera poses (more realistic setting) in Fig. 3. It is evident from the plot that RUST is the only model that is applicable when camera poses are noisy or even unavailable.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17300", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/becbde5e3e5976c2daa73c9881377ac6b06e1fab4d264628702484ffe4b0b10d.jpg", + "image_caption": [ + "Figure 4. Qualitative results on MSN - We compare RUSTo SRT [22] as proposed, and with the respective models using our improved architecture $(\\mathrm{SRT}^{\\dagger}, \\mathrm{UpSRT}^{\\dagger})$ . Different models support perfect $(p_x, p_y)$ , noisy $(\\hat{p}_x, \\hat{p}_y)$ , or a lack of $(\\mathcal{P}, \\mathcal{P})$ input and target poses, respectively. $\\mathrm{SRT}^{\\dagger}$ shows a mild drop in quality for perturbed input poses and achieves a similar reconstruction quality as $\\mathrm{UpSRT}^{\\dagger}$ with perfect target poses. In the realistic setting where the target poses are also perturbed $(\\hat{p}_y)$ , both methods fail entirely to render sharp images (only $\\mathrm{UpSRT}^{\\dagger}$ shown here, see appendix for $\\mathrm{SRT}^{\\dagger}$ ). RUST, without any camera poses, produces similar-quality renders as the baselines with perfect pose information, and even visibly outperforms the original SRT model [22] with perfect pose information." + ], + "image_footnote": [], + "bbox": [ + 76, + 97, + 890, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 4 shows qualitative results for a selection of these models. Notably, $\\mathrm{UpSRT}^{\\dagger}$ produces extremely blurry views of the scene when the target poses are mildly inaccurate, while RUST produces similar-looking results as $\\mathrm{UpSRT}^{\\dagger}$ with perfect target poses. Further qualitative results including videos are provided in the supplementary material.", + "bbox": [ + 75, + 433, + 470, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the remainder of the experimental section, we only compare RUST to the stronger $\\mathrm{SRT}^{\\dagger}$ and $\\mathrm{UpSRT}^{\\dagger}$ baselines and refer to these as SRT and UpSRT for ease of notation.", + "bbox": [ + 75, + 525, + 470, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Ablations", + "text_level": 1, + "bbox": [ + 76, + 589, + 199, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We investigate the effect of a selection of our design choices for RUST. The results are summarized in Tab. 1 (right). Metrics are computed only on the right half of each target image, since the left half is used for pose estimation by RUST. While we see a lot of evidence that the model is encoding a form of camera pose in the latent space (see Sec. 4.2), it is still possible that the model uses parts of the latent pose feature to encode content information about the target view. We therefore now evaluate the exact same RUST model (with identical weights), but now use the right halves of the target images in the Pose Estimator. We observe that this scheme only outperforms the left-half encoding scheme by $+0.39$ db, thereby showing that the latent pose primarily serves as a proxy for the camera position rather than directly informing the model about the target view content.", + "bbox": [ + 75, + 612, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our default model, we allow gradients to flow from the latent pose back into the encoder, though they are effectively scaled down by a factor of 0.2 (see Sec. 2.2). Cutting the gradients fully implies that the the Pose Estimator cannot", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "directly affect the encoder anymore through the SLSR during training. This variant leads to a drop of 0.33 db in PSNR.", + "bbox": [ + 496, + 433, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As described in Sec. 2.1, the Pose Estimator cross-attends into parts of the SLSR to allow it to anchor the target poses relative to the input views. Removing this cross-attention module makes it much harder for the model to estimate the target pose and pass it to the decoder. The performance therefore drops by a significant 2.66 db in PSNR. Removing the self-attention between the target image tokens from the Pose Estimator module has a less dramatic effect of 0.52 db.", + "bbox": [ + 496, + 465, + 892, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we investigate different choices for the size of the latent pose feature $\\tilde{p}$ . We found empirically that smaller sizes such as 3 dimensions would lead to significantly worse results (-3.09 db in PSNR). This is likely only a result of worse training dynamics, as the pose space in the MSN dataset can in theory be fully described with 3 degrees of freedom. Using significantly larger latent pose sizes (64, 768) on the other hand leads to a less controllable latent pose space, while rendering quality remains comparable.", + "bbox": [ + 496, + 588, + 893, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Latent pose investigations", + "text_level": 1, + "bbox": [ + 500, + 739, + 735, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to analyze the structure of the learned latent pose space, we use principal component analysis (PCA). Specifically, we collect latent poses $\\tilde{p}$ for three target views per scene from 4k test scenes of the MSN dataset and inspect the major PCA components of the resulting 8-dimensional pose distribution. We visualize the first three PCA components in Fig. 5 (left) and color-code the points such that hue encodes rotation relative to the first input view's camera and intensity encodes camera height. We find that the points", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17301", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/762ca78b0f2184e99b72daeba8c47abe40f5742d3ec6df027d1da0ac6ec4399c.jpg", + "image_caption": [ + "Figure 5. Latent pose investigations on MSN – Left: The first three PCA components of the latent poses across many scenes roughly constitute a cylinder. Points are coloured such that intensity represents camera height and hue represents their rotation around the scene's z-axis relative to the first input camera, modulo $120^{\\circ}$ . That means a single rotation around the scene maps to three rotations around this circle, with the $0^{\\circ}$ position mapping to the first input camera. We found that components 5 and 6 roughly capture one full 360 degree rotation, resolving the ambiguity. We elaborate on this in Appendix A.2. Right: Intuitive camera movement induced by traversals in PCA space." + ], + "image_footnote": [], + "bbox": [ + 83, + 93, + 289, + 271 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8de80d6482c94956385bc9e773cdf77a0eb284bd64a033ccbd7bab13a6dcbaae.jpg", + "image_caption": [ + "Height" + ], + "image_footnote": [], + "bbox": [ + 299, + 116, + 491, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/25514bebd89f1a870ca367696c952463be532b62e56c4dd42fd6341117ce61cc.jpg", + "image_caption": [ + "Rotation" + ], + "image_footnote": [], + "bbox": [ + 491, + 116, + 684, + 267 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1b11730a38fc2c9755a117d9e9b2c72e3119b9fcb3ab6173d22c26605f1e7e9d.jpg", + "image_caption": [ + "Distance" + ], + "image_footnote": [], + "bbox": [ + 684, + 116, + 877, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "form a cylinder whose axis is aligned with the first principal component. This axis correlates strongly with camera height with a Pearson's $r = 0.94$ . The qualitative effect of moving along this dimension is shown in Fig. 5 (Height). Similarly, rotating around the cylinder causes the camera to rotate around the scene in 3D as shown in Fig. 5 (Rotation), although only a third of the rotation is completed by a full traversal along the cylinder. Note that rotations in the latent space are encoded relative to the position of the first input camera, likely because the Pose Estimator only consumes the SLSR tokens $\\tilde{S}$ corresponding to the first input view.", + "bbox": [ + 75, + 383, + 470, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The cylinder-shaped latent pose distribution is sensible, considering that the camera poses in the MSN dataset are distributed along a dome and always point at the scene origin. At the pole of this dome is hence a discontinuity as the camera flips when crossing that point. The cylinder is therefore akin to this dome that is opened up at its pole to eliminate the discontinuity. The remaining PCA components are visualized in Appendix A.2. The fourth component captures the distance of the camera from the scene center $(r = 0.94)$ . We show traversals along this axis in Fig. 5 (Distance). We further find that components 5 and 6, capture a 360 degree absolute rotation in scene coordinates. This surprising finding is further investigated in Appendix A.2.", + "bbox": [ + 75, + 550, + 468, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is notable that the model has learned this meaningful structure in the latent pose space without any form of camera pose supervision. Furthermore, this shows that test-time camera control is feasible directly in the latent space.", + "bbox": [ + 75, + 746, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Explicit pose estimation", + "text_level": 1, + "bbox": [ + 76, + 819, + 297, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate to what extent information about the camera pose is retained in the small latent pose $\\tilde{p}$ of RUST, we perform an explicit pose estimation (EPE) experiment. As there is no canonical frame of reference, we choose to predict relative", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ea09933ef34bc7fbbcdacdf44ef969519076127d7cd6be22f6d6187e84de2984.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method# ViewsMSER2(%)Success (%)
RUST EPE70.0899.9[100]
COLMAP100.00100.04.2
COLMAP800.0799.729.5
COLMAP1600.3899.158.9
GNeRF1229.3946.7[100]
GNeRF1509.2483.1[100]
GNeRF-FG1504.0592.7[100]
", + "bbox": [ + 501, + 387, + 895, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Explicit pose estimation on MSN - RUST EPE recovers relative camera poses nearly perfectly from the SLSR (5 input views) and the pair of latent target poses. COLMAP [23] requires a much larger number of images, and still has a significantly lower success rate for registration. Similarly, GNeRF [15] requires many views of the scene, and fails to estimate accurate poses even when the background pixels are removed from the data (GNeRF-FG).", + "bbox": [ + 496, + 547, + 893, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "poses between two separate target views. Since all cameras on the MSN dataset are pointed at the center of the scene, we only estimate the relative camera position.", + "bbox": [ + 496, + 672, + 893, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our EPE module is trained on top of a (frozen) pre-trained RUST model. It takes the SLSR $S$ and the latent pose features $\\tilde{p}_1$ and $\\tilde{p}_2$ for the two target views and follows the design of the RUST decoder: the concatenation of the two latent poses acts as the query for a transformer which cross-attends into the SLSR $S$ . We found that this cross-attention step is necessary as the latent pose vectors $\\tilde{p}$ partially carry pose information that is relative to the SLSR (e.g., rotation, see Sec. 4.2). Finally, the result is passed through an MLP which is tasked to predict the explicit relative pose between the target views. We train the model using the L2 loss.", + "bbox": [ + 496, + 719, + 893, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results in terms of mean-squared error (MSE)", + "bbox": [ + 517, + 885, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17302", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 313, + 104, + 387, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/22a1af557c0f8b5dfee2f4798c1d4136a81792a379e6cb6f71567e09dffef199.jpg", + "image_caption": [ + "150 FG", + "15.71" + ], + "image_footnote": [], + "bbox": [ + 388, + 104, + 465, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/25a834131f2fd64f90db835231a5e7fb64229f3c06d5089c1bc937568dd434de.jpg", + "image_caption": [ + "Target", + "PSNR" + ], + "image_footnote": [], + "bbox": [ + 102, + 104, + 153, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce3c7cf203ae0b86f080a0c429724516ff0b41cb853c7f3d12bc6de7022257b0.jpg", + "image_caption": [ + "150 w/ pose", + "21.49" + ], + "image_footnote": [], + "bbox": [ + 156, + 104, + 232, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cab78656dfeb0f4cbf711612df85bd90d066535b8ddb18b2a8450bebd71a96ba.jpg", + "image_caption": [ + "12 w/ pose", + "13.41" + ], + "image_footnote": [], + "bbox": [ + 235, + 104, + 310, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c827fe0f45e3436ee820ac4d7b2c687eebb4118843cd8847bf804bfe7241c099.jpg", + "image_caption": [ + "150", + "14.42" + ], + "image_footnote": [], + "bbox": [ + 312, + 104, + 387, + 162 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and $R^2$ scores over 95 MSN test scenes are shown in Tab. 2. EPE recovers relative camera positions nearly perfectly on novel test scenes $(R^2 = 99.9\\%)$ using only the SLSR (derived from 5 input views) and the pair of latent pose vectors.", + "bbox": [ + 75, + 296, + 470, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Photogrammetry. To demonstrate the difficulty of the task, we apply COLMAP [23] to 95 newly generated MSN test scenes with up to 160 views (otherwise using the same parameters as the MSN test set). COLMAP uses correspondences between detected keypoints to estimate camera poses. While RUST EPE successfully recovers camera positions from just 7 total views, COLMAP struggles when only given access to a small number of views ( $e.g., < 10$ ) and needs up to 160 views to successfully register most views and estimate their camera poses. As COLMAP may pose only a subset of the provided images, we report metrics for a predetermined, arbitrarily chosen camera pair per scene. If COLMAP fails to pose either of these cameras, we consider pose estimation to have failed and exclude this camera pair from evaluation. We find an optimal rigid transformation that maps estimated camera positions to ground-truth positions before evaluating MSE and $R^2$ to be able to compare with RUST EPE.", + "bbox": [ + 75, + 373, + 470, + 630 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "NeRF-based methods. We evaluate GNeRF [15] as a strong representative for unsupervised NeRF-based pose estimation approaches on a single MSN scene using the implementation provided by the authors. GNeRF assumes knowledge of the camera intrinsics and that all cameras are pointed at the origin, i.e. only the 3-dimensional camera positions are estimated. Further, a prior for the camera pose initializations is given to the model. Using only 12 views, GNeRF fails to capture the scene. When using 150 views to train GNeRF, it still performs significantly worse than RUST EPE on explicit pose estimation, demonstrating the benefit of learning a generalizable pose representation across scenes, see Tab. 2. We show qualitative and quantitative results for novel view synthesis in Fig. 6. Training on perfect poses significantly improves NVS performance for GNeRF, showing that even with 150 views, GNeRF fails to accurately register the camera poses. As GNeRF expects the scene to be", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fabc321ebe442eea66ab4918c00b3adec995d7d984d8c5d66bc2e30978d27312.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 547, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/32202c08f6adb74b61017033a52d0209f6d6facb9ac5bd8da708a8d58616e11e.jpg", + "image_caption": [ + "Target View" + ], + "image_footnote": [], + "bbox": [ + 549, + 90, + 614, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4eb78dee20e303e2ede526f7bcf34712f6cf5419b424ce18a5e1f81eaa3e3389.jpg", + "image_caption": [ + "SRT" + ], + "image_footnote": [], + "bbox": [ + 617, + 90, + 684, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d0bc1116d4d401c74b5ad0caa61dcc507094739465002ceaddc63beeb287a479.jpg", + "image_caption": [ + "UpSRT" + ], + "image_footnote": [], + "bbox": [ + 686, + 90, + 753, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3ec292612f0a4b7a75bfb644dae38ef2556d1435ea0f3965780403125983e79e.jpg", + "image_caption": [ + "RUST" + ], + "image_footnote": [], + "bbox": [ + 754, + 90, + 821, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eef903e7133fdd90bc277afa4efc2b18ab94ef554be26708feb66ba4c6535c76.jpg", + "image_caption": [ + "RUST (Semantic)" + ], + "image_footnote": [], + "bbox": [ + 825, + 94, + 890, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/14e37e38872243ebf8e6685cb4416f23988c164ce511b064be41c4b2d9195d1e.jpg", + "image_caption": [ + "Figure 6. Qualitative results for GNeRF [15] - When trained with many posed views (150), results have high fidelity. Reducing the number of images to 12 leads to worse reconstruction and strong artifacts. When no pose is available, the model produces worse quality. Removing the backgrounds from the training dataset helps improve reconstruction accuracy. PSNR computed on 50 views.", + "Figure 7. Qualitative results on SV - Comparison of RUST with prior work using accurate camera pose. RUST outperforms our improved UpSRT variant, while producing similar quality as the fully posed improved SRT model. We further train a dense semantic segmentation decoder on top of the frozen RUST scene representation, showing that it retains semantic information about the scene." + ], + "image_footnote": [], + "bbox": [ + 501, + 159, + 547, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9875783e1bcfad454929eaffae4da2ec06c049b4fc7769d05a66d7580286e1c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 549, + 159, + 614, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/620eff8cb199af863e6331ac69c7bd2d01d0622e23b9b0a4ad37b30184b58c47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 159, + 684, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/154718f06a5821d592d2407674530e1edfa1edecc7b5a687a731339fef7e9c7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 159, + 753, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05bcca04c99f1c178debf3b97103c73056c2214baedf73287e8104d96beb77ae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 159, + 821, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/af45f91f6e2a23041a3c467219faa7aabef870dba67b7b6b55d4320ab552380c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 823, + 159, + 890, + 222 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "contained within a given bounding box, we also try training it only on the foreground (FG) objects in the scene, dropping all background pixels during optimization. We empirically find that this only leads to slightly improved pose accuracy.", + "bbox": [ + 496, + 356, + 890, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Application to real-world dataset", + "text_level": 1, + "bbox": [ + 498, + 425, + 789, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To answer the question whether RUST can learn to represent the 3D structure of complex real-world scenes, we apply it to the Street View (SV) dataset. We have received access to SV through private communication with the authors [5]. It contains 5M dynamic street scenes of San Francisco with moving objects, changes in exposure and white balance, and highly challenging camera positions, often with minimal visual overlap. Following Sajjadi et al. [22], we train and test the model using 5 randomly selected input views for each scene.", + "bbox": [ + 496, + 448, + 892, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Novel view synthesis. We first evaluate the novel view synthesis performance of RUST, and again find that its performance of 22.50 db in PSNR is comparable to that of SRT (22.72) and that it falls in-between that of our improved SRT (23.63) and UpSRT (21.25). Qualitatively, we find that novel views generated by RUST correctly capture the 3D structure of the scenes and, remarkably, the model seems to be more robust than UpSRT, see Fig. 7. This happens especially often when the reference view is far away from the target view.", + "bbox": [ + 496, + 613, + 892, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Latent pose space. In SV scenes, the camera positions mainly vary along the single forward-dimension of the street while horizontal rotations mainly move in discrete steps of $60^{\\circ}$ due to the spatial configuration of the six fixed cameras. This distribution of camera poses is very different from MSN, and we should thus expect the learned pose space to differ significantly as well. Similar to before, we compute a PCA decomposition on target views of 4k test-scenes and visualize the first three components in Fig. 8. Surprisingly,", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17303", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6852fb8958ffc6ecdac97f5c5f26fd30727c4aa3fe391ef716f97952598b1d81.jpg", + "image_caption": [ + "Figure 8. Latent pose investigations on SV - Left: Scatterplot showing the first three PCA components of the latent pose $\\tilde{p}$ distribution for $12\\mathrm{k}$ target views from 4k scenes. The color of each point indicates by which of the 6 cameras the image was taken, as shown on the color wheel. The first principal axis of these ellipsoids, marked by the long arrow, corresponds to movement along the street. Right: We found that specific linear directions in the latent space correspond to meaningful camera motions. Videos are provided in the supplementary material." + ], + "image_footnote": [], + "bbox": [ + 96, + 112, + 369, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5071d97be61d1f47e17112cf1573e0b525625cdb6cd581b733e7fdb35f18e5a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 388, + 104, + 542, + 286 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/84baa1812ed037f6e9536c614d7b9c0b1c0458d870d47962477acf4cb91f5f30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 549, + 104, + 702, + 286 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75bfa47ced88f918b1a2ed67360777d5e2b2a625e40f4dc50971fa9914872458.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 104, + 862, + 286 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we find only three (rather than six) ellipsoid clusters that each correspond to an opposing pair of cameras. This suggests that the model has learned to represent rotation in an absolute (scene-centric) coordinate frame with the direction of the street as a reference, and that opposing cameras are less well-distinguished due to the streets' approximate mirror symmetries, see Fig. 10 (appendix) for more details. We further find that movement along the street corresponds well to the long axis of these ellipsoids, which depending on the camera can correspond to either a forward/backward or a sideways motion in image space.", + "bbox": [ + 75, + 393, + 472, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Traversals. In Fig. 8, we show linear latent pose traversals that correspond to movement along the street, pitch and tilt of the camera. We find that these dimensions are mapped into the pose space predictably, contiguously and smoothly. The correct parallax effect observed in the forward movement in particular demonstrates that the model has correctly estimated the depth of the scene. These results indicate that RUST can learn to capture the 3D structure of complex real-world scenes from a handful of images, without access to any pose information. The learned latent pose space covers the training distribution of camera poses and enables traversals and novel view synthesis within distribution.", + "bbox": [ + 75, + 571, + 470, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 76, + 768, + 199, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RUST shares most strengths and limitations with other latent methods, especially with the SRT model [22] that it is based on. Resolution and quality of synthesized views do not reach the performance of NeRF [16], though it is important to note that NeRF does not yield latent scene representations, and it generally requires a large number of similar views of the scene. As has been demonstrated [22], even special-", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ized NeRF variants for sparse input view settings [8] fail to produce meaningful results on the challenging SV dataset, despite having access to accurate pose information.", + "bbox": [ + 496, + 393, + 893, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Secs. 4.2 and 4.3, RUST learns to effectively model the camera pose distribution of the datasets it is trained on. While this is desirable in many applications, it can limit generalization of the model to new poses that lie outside of the original distribution. For example, we may not find latent poses for which RUST would render views that do not point at the center of the scene in MSN, or represent movement orthogonal to the street in SV. It is notable that all learned methods suffer from such limitations to varying degrees, including light field parametrizations [22] and even volumetric models, especially when given few input images [18]. Nonetheless, more explicit methods tend to generalize better to out-of-distribution poses due to hardcoded assumptions such as explicit camera parametrizations or the volumetric rendering equation. Finally, we empirically found RUST to show higher variance in terms of PSNR compared to SRT. Over independent training runs with 3 random seeds, we observed a standard error of 0.19.", + "bbox": [ + 496, + 439, + 895, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 724, + 619, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose RUST, a novel method for latent neural scene representation learning that can be trained without any explicit pose information. RUST matches the quality of prior methods that require pose information while scaling to very complex real-world scenes. We further demonstrate that the model learns meaningful latent pose spaces that afford smooth 3D motion within the distribution of camera poses in the training data. We believe that this method is a major milestone towards applying implicit neural scene representations to large uncurated datasets.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17304", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. ShapeNet: An Information-Rich 3D Model Repository. arXiv preprint arXiv:1512.03012, 2015. 4", + "[2] Danny Driess, Zhiao Huang, Yunzhu Li, Russ Tedrake, and Marc Toussaint. Learning Multi-Object dynamics with compositional neural radiance fields. 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In ACM MM, 2022. 3", + "[31] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 13" + ], + "bbox": [ + 78, + 90, + 470, + 381 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17306", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_model.json b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_model.json new file mode 100644 index 0000000000000000000000000000000000000000..df778a49265ec157466de9da04ba3705dc56992b --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_model.json @@ -0,0 +1,2068 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.131, + 0.83, + 0.154 + ], + "angle": 0, + "content": "RUST: Latent Neural Scene Representations from Unposed Imagery" + }, + { + "type": "text", + "bbox": [ + 0.233, + 0.181, + 0.738, + 0.242 + ], + "angle": 0, + "content": "Mehdi S. M. Sajjadi* Aravindh Mahendran Thomas Kipf \nEtienne Pot Daniel Duckworth Mario Lucic Klaus Greff \nGoogle Research, Brain Team" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.273, + 0.313, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.474, + 0.653 + ], + "angle": 0, + "content": "Inferring the structure of 3D scenes from 2D observations is a fundamental challenge in computer vision. Recently popularized approaches based on neural scene representations have achieved tremendous impact and have been applied across a variety of applications. One of the major remaining challenges in this space is training a single model which can provide latent representations which effectively generalize beyond a single scene. Scene Representation Transformer (SRT) has shown promise in this direction, but scaling it to a larger set of diverse scenes is challenging and necessitates accurately posed ground truth data. To address this problem, we propose RUST (Really Unposed Scene representation Transformer), a pose-free approach to novel view synthesis trained on RGB images alone. Our main insight is that one can train a Pose Encoder that peeks at the target image and learns a latent pose embedding which is used by the decoder for view synthesis. We perform an empirical investigation into the learned latent pose structure and show that it allows meaningful test-time camera transformations and accurate explicit pose readouts. Perhaps surprisingly, RUST achieves similar quality as methods which have access to perfect camera pose, thereby unlocking the potential for large-scale training of amortized neural scene representations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.673, + 0.208, + 0.689 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.471, + 0.773 + ], + "angle": 0, + "content": "Implicit neural representations have shown remarkable ability in capturing the 3D structure of complex real-world scenes while circumventing many of the downsides of mesh based, point cloud based, and voxel grid based representations [24]. Apart from visually pleasing novel view syn" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.78, + 0.473, + 0.902 + ], + "angle": 0, + "content": "*Correspondence: rust@msajjadi.com. Project page: rust-paper.github.io. Contributions: MS: Conception, model design, implementation lead, analysis, infrastructure, experiments, writing, project lead. AM: Conception, model design, implementation, code reviews, experiments-MSN, analysis-MSN, writing. TK: RUST explicit pose estimation, model figures, scoping, advising, writing. EP: GNeRF experiments, Street View dataset, interactive visualization for embedding inspection. DD: COLMAP experiments, evaluation. ML: Team buy-in, scoping, writing. KG: Conception, early MSN analysis, analysis-SV, data-collection and analysis, dataset generation, visualizations, scoping, advising, writing." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.273, + 0.891, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.43, + 0.895, + 0.501 + ], + "angle": 0, + "content": "Figure 1. Model overview - RUST produces 3D-centric scene representations through novel view synthesis purely from RGB images without requiring any camera poses. For training, a novel Pose Estimator module glimpses at the target view and passes a low-dimensional latent pose feature to the decoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.895, + 0.822 + ], + "angle": 0, + "content": "thesis [14, 16], such representations have shown potential for semantics [25], object decomposition [21], and physics simulation [2] which makes them promising candidates for applications in augmented reality and robotics. However, to be useful in such applications, they need to (1) provide meaningful representations when conditioned on a very limited number of views, (2) have low latency for real-time rendering, and (3) produce scene representations that facilitate generalization of knowledge to novel views and scenes. The recently proposed Scene Representation Transformer (SRT) [22] exhibits most of these properties. It achieves state-of-the-art novel view synthesis in the regime when only a handful of posed input views are available, and produces representations that are well-suited for later segmentation at both semantic [22] and instance level [21]. A major challenge in scaling methods such as SRT, however, is the difficulty in obtaining accurately posed real world data which precludes the training of the models. We posit that it should be possible to train truly pose-free models from RGB images alone without requiring any ground truth pose information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We propose RUST (Really Unposed Scene representation Transformer), a novel method for neural scene representation learning through novel view synthesis that does not require pose information: neither for training, nor for inference; neither for input views, nor for target views. While at first" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17297" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "glance it may seem unlikely that such a model could be trained, our key insight is that a sneak-peek at the target view at training can be used to infer an implicit latent pose, thereby allowing the rendering of the correct view. We find that our model not only learns meaningful, controllable latent pose spaces, but the quality of its novel views are even comparable to the quality of posed methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.205, + 0.325, + 0.219 + ], + "angle": 0, + "content": "Our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.223, + 0.469, + 0.282 + ], + "angle": 0, + "content": "- We propose RUST, a novel method that learns latent 3D scene representations through novel view synthesis on very complex synthetic and real datasets without any pose information." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.285, + 0.47, + 0.344 + ], + "angle": 0, + "content": "- Our model strongly outperforms prior methods in settings with noisy camera poses while matching their performance when accurate pose information is available to the baselines." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.347, + 0.47, + 0.407 + ], + "angle": 0, + "content": "- We provide an investigation into the structure of the learned latent pose spaces and demonstrate that meaningful camera transformations naturally emerge in a fully unsupervised fashion." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.409, + 0.469, + 0.455 + ], + "angle": 0, + "content": "- Finally, we demonstrate that the representations learned by the model allow explicit pose readout and dense semantic segmentation." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.223, + 0.47, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.468, + 0.168, + 0.483 + ], + "angle": 0, + "content": "2. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.584 + ], + "angle": 0, + "content": "The model pipeline is shown in Fig. 1. A data point consists of an unordered set of \\( N \\) input views \\( x = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\} \\) of a scene. Unlike SRT [22], they only consist of RGB images since RUST does not use explicit poses. Given these input views, the training objective is to predict a novel target view \\( y \\in \\mathbb{R}^{H \\times W \\times 3} \\) of the same scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.471, + 0.812 + ], + "angle": 0, + "content": "To this end, the input views \\( x \\) are first encoded using a combination of a CNN and a transformer, resulting in the Set-Latent Scene Representation (SLSR) \\( S \\) which captures the contents of the scene. The target view \\( y \\) is then rendered by a transformer-based decoder that attends into the SLSR \\( S \\) to retrieve relevant information about the scene for novel view synthesis. In addition, the decoder must be conditioned on some form of a query that identifies the desired view. Existing methods, including SRT [22], often use the explicit relative camera pose \\( p \\) between one of the input views and the target view for this purpose. This imbues an explicit notion of 3D space into the model, which introduces a burdensome requirement for accurate camera poses, especially for training such models. RUST resolves this fundamental limitation by learning its own notion of implicit poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Implicit poses. Instead of querying the decoder with explicit poses, we allow the model to learn its own implicit space of camera poses through a learned Pose Estimator module. For training, the Pose Estimator sees parts of the target view \\( y \\) and the SLSR \\( S \\) and extracts a low-dimensional" + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.093, + 0.831, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.337, + 0.895, + 0.407 + ], + "angle": 0, + "content": "Figure 2. Pose estimator model - A randomly chosen half of the target image is encoded into a latent pose. The model mainly consists of a CNN encoder followed by alternating cross- and self-attention layers. The final output is projected to 8 dimensions to encourage an easily controllable latent representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.53 + ], + "angle": 0, + "content": "latent pose feature \\(\\tilde{p}\\). The decoder transformer then uses \\(\\tilde{p}\\) as a query to cross-attend into the SLSR to ultimately render the full novel view \\(\\tilde{y}\\). This form of self supervision allows the model to be trained with standard reconstruction losses without requiring any pose information. At test time, latent poses can be computed on the input views and subsequently modified for novel view synthesis, see Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.684, + 0.556 + ], + "angle": 0, + "content": "2.1. Model components" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.895, + 0.669 + ], + "angle": 0, + "content": "Input view encoder. The encoder consists of a convolutional neural network (CNN) followed by a transformer. Each input image \\( x_{i} \\) is encoded independently by the shared CNN which consists of 3 downsampling blocks, each of which halves the image height and width. As a result, each spatial output feature corresponds to an \\( 8\\times 8 \\) patch in the original input image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.895, + 0.851 + ], + "angle": 0, + "content": "We add the same learned position embeddings to all spatial feature maps to mark their spatial 2D position in the images. We further add another learned embedding only to the features of the first input image \\( x_{1} \\) to allow the model to distinguish them from the others. This is relevant for the Pose Estimator module, as explained below. Finally, we flatten all spatial feature maps and combine them across input views into a single set of tokens. The encoder transformer then performs self-attention on this set of tokens, thereby exchanging information between the patch features. This results in the SLSR \\( S \\) which captures the scene content as a bag of tokens." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Pose estimator. The model architecture of the Pose Estimator is shown in Fig. 2. A randomly chosen half of the target" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17298" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "view \\(y\\) (i.e., either the left or the right half of the image) is first embedded into a set of tokens using a CNN similar to the input view encoder. A transformer then alternates between cross-attending from the target view tokens into a specific subset \\(\\tilde{S} \\subset S\\) of the SLSR and self-attending between the target view tokens. The intuition behind cross-attending into \\(\\tilde{S}\\) is that the latent pose \\(\\tilde{p}\\) should be relative to the scene. We allow the Pose Estimator to only attend into SLSR tokens belonging to the (arbitrarily chosen) first input view after empirical findings that this leads to better-structured latent pose spaces. It is important to note that \\(\\tilde{S}\\) contains information about all input views due to the self-attention in the preceding encoder transformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.424 + ], + "angle": 0, + "content": "Finally, we apply global mean pooling on the transformer's output and linearly project it down to an 8-dimensional latent pose \\(\\tilde{p}\\). It is important to note that we call \\(\\tilde{p}\\) the estimated \"pose\" since it primarily serves the purpose of informing the decoder of the target camera pose. However, we do not enforce any explicit constraints on the latent, instead allowing the model to freely choose the structure of the latent poses. Nevertheless, we find that the model learns to model meaningful camera poses, see Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.473, + 0.575 + ], + "angle": 0, + "content": "Decoder transformer. Similar to SRT, each pixel is decoded independently by a decoder transformer that cross-attends from a query into the SLSR \\(S\\), thereby aggregating relevant information from the scene representation to establish the appearance of the novel view point. We initialize the query by concatenating the latent pose \\(\\tilde{p}\\) with the spatial 2D position of the pixel in the target image and passing it through a small query MLP. The output of the decoder is the single RGB value of the target pixel." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.585, + 0.265, + 0.601 + ], + "angle": 0, + "content": "2.2. Training procedure" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.472, + 0.744 + ], + "angle": 0, + "content": "For each data point during training, we use 5 input views and 3 novel target views. The training objective is to render the target views by minimizing the mean-squared error between the predicted output and the target view: \\( ||\\tilde{y} - y||_2^2 \\). The entire model is trained end-to-end using the Adam optimizer [9]. In practice, we found the model to perform better when gradients flowing to and through the Pose Estimator module are scaled down by 0.2 which is inspired by spatial transformer networks [7]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.223, + 0.77 + ], + "angle": 0, + "content": "3. Related works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Neural rendering. The field of neural rendering is vast and the introduction of Neural Radiance Fields (NeRF) [16] has led to a surge of recent follow-up works. NeRF optimizes an MLP to map 3D positions of the scene to radiance and density values, which are used through a differentiable volumetric rendering equation to reconstruct the provided posed images of the scene. We refer the reader to surveys on neural rendering [24] and NeRF [4] for recent overviews." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.333 + ], + "angle": 0, + "content": "NeRF without pose. Most methods based on NeRF assume the availability of perfect camera pose. There exist a number of works extending NeRF for pose estimation or to no-pose settings. INeRF [28] uses pre-trained NeRFs to estimate the camera pose of novel views of the same scene. However, posed imagery is required for each scene in order to obtain the original NeRF models. NeRF-- [27] jointly optimizes the NeRF MLP along with the camera poses for the images. BARF [13] adds a progressive position encoding scheme for improved gradients. Both methods only succeed for forward-facing datasets while failing for more complex camera distributions unless noisy initial poses are given. GNeRF [15] works for scenes with more complex camera distributions, however, the prior distribution must be known for sampling. VMRF [30] extends this to settings where the prior distribution is unknown." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.895, + 0.44 + ], + "angle": 0, + "content": "All methods above require a comparably large number of images of the same scene, since NeRF tends to fail with few observations even with perfect pose [29]. While methods exist that optimize NeRFs from fewer observations [8, 18], they have limitations in terms of scene complexity [22] and to the best of our knowledge, no NeRF-based method has been demonstrated to work with few unposed images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.897, + 0.724 + ], + "angle": 0, + "content": "Latent 3D scene representations. In the right setup, NeRF produces high-quality novel views, though it does so without providing tangible scene representations that could be readily used for downstream tasks. The line of research focusing on latent 3D scene representations includes NeRF-VAE [12] which uses a variational autoencoder [10] to learn a generative model of NeRF's for synthetic scenes, and GQN [3] which adds per-image latent representations to compute a global scene representation that is used by a recurrent latent variable model for novel view synthesis. A recent extension [19] of GQN performs pose estimation for novel target views by optimizing, at inference time, the posterior probability over poses as estimated by the generative model. All the methods above require ground truth poses for training and inference. GIRAFFE [17] requires no poses for training, but a prior distribution of camera views for the specific dataset. It uses a purely generative mechanism, without the ability to render novel views for given scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.856 + ], + "angle": 0, + "content": "Posed and \"unposed\" SRT. The current most scalable latent method for neural scene representations is the Scene Representation Transformer (SRT) [22]. It uses a transformer-based encoder-decoder architecture for novel view synthesis, thereby scaling to much more complex scenes than prior work. Its scene representation, the SLSR, has been shown to be useful for 3D-centric supervised and unsupervised semantic downstream tasks [21, 22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "While SRT requires posed imagery, the \"unposed\" variant UpSRT has been proposed as well in the original work [22]. Similar to RUST, it does not require posed input views. How-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17299" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.228 + ], + "angle": 0, + "content": "
MethodPosePSNRAblationPSNR
SRT [22]px, py23.31Right-half PE23.88
SRT†px, py24.40Stop grad.23.16
SRT†hatx, py23.81No SLSR20.83
UpSRT†px, py23.03No self-attn22.97
SRT†hatx, haty18.653-dim. p20.40
UpSRT†px, pγ18.6464-dim. p23.40
RUSTpx, pγ23.49768-dim. p23.11
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.237, + 0.472, + 0.336 + ], + "angle": 0, + "content": "Table 1. Quantitative results on MSN – Left: Comparison with prior work in various settings: perfect \\((p_x, p_y)\\), noisy \\((\\hat{p}_x, \\hat{p}_y)\\) and lack of \\((p_x, p_y)\\) input and target poses. We report SRT both as proposed [22], and with our improved architecture \\((\\mathrm{SRT}^\\dagger, \\mathrm{UpSRT}^\\dagger)\\). Despite requiring no poses, RUST matches the performance of SRT and \\(\\mathrm{UpSRT}^\\dagger\\) while strongly outperforming all methods when target pose is noisy \\(\\hat{p}_y\\). Right: Model ablations, see Sec. 4.1.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.472, + 0.452 + ], + "angle": 0, + "content": "ever, training an UpSRT model requires exact pose information for the target views to specify to the decoder which exact view of the scene to render. This restricts the application of UpSRT to settings where accurate pose information is available for the entire training dataset. We analyze further implications of this in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.472, + 0.637 + ], + "angle": 0, + "content": "Using targets as inputs for training. UViM [11] encodes targets such as panoptic segmentation maps into short latent codes during training to allow a single model architecture to perform well across several tasks. A bottleneck is enforced on the so-called guiding codes through discretization. Recent work on inferring protein conformations and poses [20] trains a VAE model in order to encode Cryo-EM images into latent distributions over poses and protein conformations. Unlike RUST, their method requires a base scene representation that is fixed a priori and uses an explicit differentiable rendered and explicit geometry in the architecture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.21, + 0.667 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.472, + 0.901 + ], + "angle": 0, + "content": "We begin our experiments on the MultiShapeNet (MSN) dataset (version from [21]), a very challenging test bed for 3D-centric neural scene representation learning [22]. It consists of synthetically generated 3D scenes [6] that contain 16-32 ShapeNet objects [1] scattered in random orientations, and with photo-realistic backgrounds. Importantly, the set of ShapeNet objects is split for the training and test datasets, meaning that all objects encountered in the test scenes are not only in novel arrangements and orientations, but the model has never seen them in the training dataset. Camera positions are sampled from a half-sphere with varying distances to the scene. In all experiments, we follow prior work [22] by using 5 input views, and all quantitative metrics are computed on the right halves of the target views, since the left halves are used for pose estimation in RUST." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.236, + 0.895, + 0.307 + ], + "angle": 0, + "content": "Figure 3. Robustness to camera noise – Sajjadi et al. [22] evaluate SRT and UpSRT on (A) perfect pose, and (B) noisy input pose. In the more realistic setting (C) where input & target pose is noisy, both methods fail as they rely on accurate target camera pose for training. RUST needs no pose, so its performance is constant." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.333, + 0.693, + 0.349 + ], + "angle": 0, + "content": "4.1. Novel view synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.895, + 0.629 + ], + "angle": 0, + "content": "The core contribution of RUST is its ability to model 3D scenes without posed imagery. While camera poses in synthetic environments such as MSN are perfectly accurate, practical applications must often rely on noisy sensor data or inaccurate estimated poses. We therefore begin our investigations by measuring the quality of synthesized novel views in new scenes under various assumptions on the accuracy and availability of camera pose information during training. To simulate the real world, we follow prior work [13, 22] and perturb the training camera poses with additive noise for a relatively mild amount of \\(\\sigma = 0.1\\). We visualize the effect of this noise in Fig. 14 (appendix) to provide context for its scale. This leads to three possible settings for both input poses and target poses: perfect \\((p_x, p_y)\\), noisy \\((\\hat{p}_x, \\hat{p}_y)\\) and lack of \\((p_x, p_y)\\) input and target cameras poses, respectively. Note that for the posed baselines, we always use perfect target poses for evaluation, i.e. the target poses are only perturbed during training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.751 + ], + "angle": 0, + "content": "Tab. 1 (left) shows our quantitative evaluation on the MSN dataset. We first compare SRT as proposed [22] with our improved architecture \\(\\mathrm{SRT}^{\\dagger}\\), both using perfect pose. We observe that our modifications to the architecture lead to significant improvements in PSNR (+1.09 db). Continuing with the improved architecture, perturbing the input views leads to a loss in 0.59 db (\\(\\mathrm{SRT}^{\\dagger}\\), \\(\\hat{p}_x\\), \\(p_y\\)) while the lack thereof leads to a drop of 1.37 db (\\(\\mathrm{UpSRT}^{\\dagger}\\), \\(p_x\\), \\(p_y\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Crucially, the most realistic setting where all poses are equally noisy leads to a dramatic decline in performance for prior work \\((\\mathrm{SRT}^{\\dagger}\\) and \\(\\mathrm{UpSRT}^{\\dagger},\\hat{p}_y)\\). RUST meanwhile outperforms the baselines by \\(+4.84\\) db in this setting without any poses, while matching the performance of SRT [22] with perfect pose. We highlight the difference between only perturbing input poses (following prior work [22]) or all camera poses (more realistic setting) in Fig. 3. It is evident from the plot that RUST is the only model that is applicable when camera poses are noisy or even unavailable." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17300" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.098, + 0.891, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.323, + 0.896, + 0.41 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on MSN - We compare RUSTo SRT [22] as proposed, and with the respective models using our improved architecture \\((\\mathrm{SRT}^{\\dagger}, \\mathrm{UpSRT}^{\\dagger})\\). Different models support perfect \\((p_x, p_y)\\), noisy \\((\\hat{p}_x, \\hat{p}_y)\\), or a lack of \\((\\mathcal{P}, \\mathcal{P})\\) input and target poses, respectively. \\(\\mathrm{SRT}^{\\dagger}\\) shows a mild drop in quality for perturbed input poses and achieves a similar reconstruction quality as \\(\\mathrm{UpSRT}^{\\dagger}\\) with perfect target poses. In the realistic setting where the target poses are also perturbed \\((\\hat{p}_y)\\), both methods fail entirely to render sharp images (only \\(\\mathrm{UpSRT}^{\\dagger}\\) shown here, see appendix for \\(\\mathrm{SRT}^{\\dagger}\\)). RUST, without any camera poses, produces similar-quality renders as the baselines with perfect pose information, and even visibly outperforms the original SRT model [22] with perfect pose information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.471, + 0.525 + ], + "angle": 0, + "content": "Fig. 4 shows qualitative results for a selection of these models. Notably, \\(\\mathrm{UpSRT}^{\\dagger}\\) produces extremely blurry views of the scene when the target poses are mildly inaccurate, while RUST produces similar-looking results as \\(\\mathrm{UpSRT}^{\\dagger}\\) with perfect target poses. Further qualitative results including videos are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.471, + 0.573 + ], + "angle": 0, + "content": "For the remainder of the experimental section, we only compare RUST to the stronger \\(\\mathrm{SRT}^{\\dagger}\\) and \\(\\mathrm{UpSRT}^{\\dagger}\\) baselines and refer to these as SRT and UpSRT for ease of notation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.59, + 0.2, + 0.605 + ], + "angle": 0, + "content": "4.1.1 Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.839 + ], + "angle": 0, + "content": "We investigate the effect of a selection of our design choices for RUST. The results are summarized in Tab. 1 (right). Metrics are computed only on the right half of each target image, since the left half is used for pose estimation by RUST. While we see a lot of evidence that the model is encoding a form of camera pose in the latent space (see Sec. 4.2), it is still possible that the model uses parts of the latent pose feature to encode content information about the target view. We therefore now evaluate the exact same RUST model (with identical weights), but now use the right halves of the target images in the Pose Estimator. We observe that this scheme only outperforms the left-half encoding scheme by \\(+0.39\\) db, thereby showing that the latent pose primarily serves as a proxy for the camera position rather than directly informing the model about the target view content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In our default model, we allow gradients to flow from the latent pose back into the encoder, though they are effectively scaled down by a factor of 0.2 (see Sec. 2.2). Cutting the gradients fully implies that the the Pose Estimator cannot" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.464 + ], + "angle": 0, + "content": "directly affect the encoder anymore through the SLSR during training. This variant leads to a drop of 0.33 db in PSNR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.893, + 0.587 + ], + "angle": 0, + "content": "As described in Sec. 2.1, the Pose Estimator cross-attends into parts of the SLSR to allow it to anchor the target poses relative to the input views. Removing this cross-attention module makes it much harder for the model to estimate the target pose and pass it to the decoder. The performance therefore drops by a significant 2.66 db in PSNR. Removing the self-attention between the target image tokens from the Pose Estimator module has a less dramatic effect of 0.52 db." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.895, + 0.726 + ], + "angle": 0, + "content": "Finally, we investigate different choices for the size of the latent pose feature \\(\\tilde{p}\\). We found empirically that smaller sizes such as 3 dimensions would lead to significantly worse results (-3.09 db in PSNR). This is likely only a result of worse training dynamics, as the pose space in the MSN dataset can in theory be fully described with 3 degrees of freedom. Using significantly larger latent pose sizes (64, 768) on the other hand leads to a less controllable latent pose space, while rendering quality remains comparable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.736, + 0.756 + ], + "angle": 0, + "content": "4.2. Latent pose investigations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In order to analyze the structure of the learned latent pose space, we use principal component analysis (PCA). Specifically, we collect latent poses \\(\\tilde{p}\\) for three target views per scene from 4k test scenes of the MSN dataset and inspect the major PCA components of the resulting 8-dimensional pose distribution. We visualize the first three PCA components in Fig. 5 (left) and color-code the points such that hue encodes rotation relative to the first input view's camera and intensity encodes camera height. We find that the points" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17301" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.094, + 0.29, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.101, + 0.422, + 0.114 + ], + "angle": 0, + "content": "Height" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.117, + 0.493, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.101, + 0.621, + 0.113 + ], + "angle": 0, + "content": "Rotation" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.117, + 0.685, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.101, + 0.812, + 0.113 + ], + "angle": 0, + "content": "Distance" + }, + { + "type": "image", + "bbox": [ + 0.686, + 0.117, + 0.878, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.895, + 0.359 + ], + "angle": 0, + "content": "Figure 5. Latent pose investigations on MSN – Left: The first three PCA components of the latent poses across many scenes roughly constitute a cylinder. Points are coloured such that intensity represents camera height and hue represents their rotation around the scene's z-axis relative to the first input camera, modulo \\(120^{\\circ}\\). That means a single rotation around the scene maps to three rotations around this circle, with the \\(0^{\\circ}\\) position mapping to the first input camera. We found that components 5 and 6 roughly capture one full 360 degree rotation, resolving the ambiguity. We elaborate on this in Appendix A.2. Right: Intuitive camera movement induced by traversals in PCA space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.55 + ], + "angle": 0, + "content": "form a cylinder whose axis is aligned with the first principal component. This axis correlates strongly with camera height with a Pearson's \\( r = 0.94 \\). The qualitative effect of moving along this dimension is shown in Fig. 5 (Height). Similarly, rotating around the cylinder causes the camera to rotate around the scene in 3D as shown in Fig. 5 (Rotation), although only a third of the rotation is completed by a full traversal along the cylinder. Note that rotations in the latent space are encoded relative to the position of the first input camera, likely because the Pose Estimator only consumes the SLSR tokens \\( \\tilde{S} \\) corresponding to the first input view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.746 + ], + "angle": 0, + "content": "The cylinder-shaped latent pose distribution is sensible, considering that the camera poses in the MSN dataset are distributed along a dome and always point at the scene origin. At the pole of this dome is hence a discontinuity as the camera flips when crossing that point. The cylinder is therefore akin to this dome that is opened up at its pole to eliminate the discontinuity. The remaining PCA components are visualized in Appendix A.2. The fourth component captures the distance of the camera from the scene center \\((r = 0.94)\\). We show traversals along this axis in Fig. 5 (Distance). We further find that components 5 and 6, capture a 360 degree absolute rotation in scene coordinates. This surprising finding is further investigated in Appendix A.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.807 + ], + "angle": 0, + "content": "It is notable that the model has learned this meaningful structure in the latent pose space without any form of camera pose supervision. Furthermore, this shows that test-time camera control is feasible directly in the latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.82, + 0.299, + 0.835 + ], + "angle": 0, + "content": "4.2.1 Explicit pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To validate to what extent information about the camera pose is retained in the small latent pose \\(\\tilde{p}\\) of RUST, we perform an explicit pose estimation (EPE) experiment. As there is no canonical frame of reference, we choose to predict relative" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.388, + 0.897, + 0.539 + ], + "angle": 0, + "content": "
Method# ViewsMSER2(%)Success (%)
RUST EPE70.0899.9[100]
COLMAP100.00100.04.2
COLMAP800.0799.729.5
COLMAP1600.3899.158.9
GNeRF1229.3946.7[100]
GNeRF1509.2483.1[100]
GNeRF-FG1504.0592.7[100]
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.549, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Table 2. Explicit pose estimation on MSN - RUST EPE recovers relative camera poses nearly perfectly from the SLSR (5 input views) and the pair of latent target poses. COLMAP [23] requires a much larger number of images, and still has a significantly lower success rate for registration. Similarly, GNeRF [15] requires many views of the scene, and fails to estimate accurate poses even when the background pixels are removed from the data (GNeRF-FG)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.894, + 0.719 + ], + "angle": 0, + "content": "poses between two separate target views. Since all cameras on the MSN dataset are pointed at the center of the scene, we only estimate the relative camera position." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.885 + ], + "angle": 0, + "content": "Our EPE module is trained on top of a (frozen) pre-trained RUST model. It takes the SLSR \\(S\\) and the latent pose features \\(\\tilde{p}_1\\) and \\(\\tilde{p}_2\\) for the two target views and follows the design of the RUST decoder: the concatenation of the two latent poses acts as the query for a transformer which cross-attends into the SLSR \\(S\\). We found that this cross-attention step is necessary as the latent pose vectors \\(\\tilde{p}\\) partially carry pose information that is relative to the SLSR (e.g., rotation, see Sec. 4.2). Finally, the result is passed through an MLP which is tasked to predict the explicit relative pose between the target views. We train the model using the L2 loss." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Quantitative results in terms of mean-squared error (MSE)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17302" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.09, + 0.14, + 0.103 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.091, + 0.233, + 0.103 + ], + "angle": 0, + "content": "150 w/ pose" + }, + { + "type": "image_caption", + "bbox": [ + 0.242, + 0.091, + 0.308, + 0.103 + ], + "angle": 0, + "content": "12 w/ pose" + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.091, + 0.364, + 0.102 + ], + "angle": 0, + "content": "150" + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.105, + 0.388, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.408, + 0.091, + 0.453, + 0.102 + ], + "angle": 0, + "content": "150 FG" + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.105, + 0.466, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.105, + 0.155, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.167, + 0.138, + 0.179 + ], + "angle": 0, + "content": "PSNR" + }, + { + "type": "image", + "bbox": [ + 0.157, + 0.105, + 0.233, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.167, + 0.214, + 0.179 + ], + "angle": 0, + "content": "21.49" + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.105, + 0.311, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.167, + 0.291, + 0.179 + ], + "angle": 0, + "content": "13.41" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.105, + 0.388, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.167, + 0.369, + 0.179 + ], + "angle": 0, + "content": "14.42" + }, + { + "type": "image_caption", + "bbox": [ + 0.413, + 0.167, + 0.446, + 0.179 + ], + "angle": 0, + "content": "15.71" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.193, + 0.471, + 0.276 + ], + "angle": 0, + "content": "Figure 6. Qualitative results for GNeRF [15] - When trained with many posed views (150), results have high fidelity. Reducing the number of images to 12 leads to worse reconstruction and strong artifacts. When no pose is available, the model produces worse quality. Removing the backgrounds from the training dataset helps improve reconstruction accuracy. PSNR computed on 50 views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.472, + 0.358 + ], + "angle": 0, + "content": "and \\(R^2\\) scores over 95 MSN test scenes are shown in Tab. 2. EPE recovers relative camera positions nearly perfectly on novel test scenes \\((R^2 = 99.9\\%)\\) using only the SLSR (derived from 5 input views) and the pair of latent pose vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.471, + 0.631 + ], + "angle": 0, + "content": "Photogrammetry. To demonstrate the difficulty of the task, we apply COLMAP [23] to 95 newly generated MSN test scenes with up to 160 views (otherwise using the same parameters as the MSN test set). COLMAP uses correspondences between detected keypoints to estimate camera poses. While RUST EPE successfully recovers camera positions from just 7 total views, COLMAP struggles when only given access to a small number of views (\\(e.g., < 10\\)) and needs up to 160 views to successfully register most views and estimate their camera poses. As COLMAP may pose only a subset of the provided images, we report metrics for a predetermined, arbitrarily chosen camera pair per scene. If COLMAP fails to pose either of these cameras, we consider pose estimation to have failed and exclude this camera pair from evaluation. We find an optimal rigid transformation that maps estimated camera positions to ground-truth positions before evaluating MSE and \\(R^2\\) to be able to compare with RUST EPE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.901 + ], + "angle": 0, + "content": "NeRF-based methods. We evaluate GNeRF [15] as a strong representative for unsupervised NeRF-based pose estimation approaches on a single MSN scene using the implementation provided by the authors. GNeRF assumes knowledge of the camera intrinsics and that all cameras are pointed at the origin, i.e. only the 3-dimensional camera positions are estimated. Further, a prior for the camera pose initializations is given to the model. Using only 12 views, GNeRF fails to capture the scene. When using 150 views to train GNeRF, it still performs significantly worse than RUST EPE on explicit pose estimation, demonstrating the benefit of learning a generalizable pose representation across scenes, see Tab. 2. We show qualitative and quantitative results for novel view synthesis in Fig. 6. Training on perfect poses significantly improves NVS performance for GNeRF, showing that even with 150 views, GNeRF fails to accurately register the camera poses. As GNeRF expects the scene to be" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.548, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.559, + 0.089, + 0.609, + 0.097 + ], + "angle": 0, + "content": "Target View" + }, + { + "type": "image", + "bbox": [ + 0.55, + 0.091, + 0.616, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.644, + 0.089, + 0.661, + 0.097 + ], + "angle": 0, + "content": "SRT" + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.091, + 0.685, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.089, + 0.735, + 0.097 + ], + "angle": 0, + "content": "UpSRT" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.091, + 0.754, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.089, + 0.801, + 0.097 + ], + "angle": 0, + "content": "RUST" + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.091, + 0.822, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.825, + 0.089, + 0.892, + 0.096 + ], + "angle": 0, + "content": "RUST (Semantic)" + }, + { + "type": "image", + "bbox": [ + 0.826, + 0.095, + 0.892, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.16, + 0.548, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.55, + 0.16, + 0.616, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.16, + 0.685, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.16, + 0.754, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.16, + 0.823, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.16, + 0.892, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.234, + 0.892, + 0.33 + ], + "angle": 0, + "content": "Figure 7. Qualitative results on SV - Comparison of RUST with prior work using accurate camera pose. RUST outperforms our improved UpSRT variant, while producing similar quality as the fully posed improved SRT model. We further train a dense semantic segmentation decoder on top of the frozen RUST scene representation, showing that it retains semantic information about the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.418 + ], + "angle": 0, + "content": "contained within a given bounding box, we also try training it only on the foreground (FG) objects in the scene, dropping all background pixels during optimization. We empirically find that this only leads to slightly improved pose accuracy." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.426, + 0.79, + 0.442 + ], + "angle": 0, + "content": "4.3. Application to real-world dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.893, + 0.6 + ], + "angle": 0, + "content": "To answer the question whether RUST can learn to represent the 3D structure of complex real-world scenes, we apply it to the Street View (SV) dataset. We have received access to SV through private communication with the authors [5]. It contains 5M dynamic street scenes of San Francisco with moving objects, changes in exposure and white balance, and highly challenging camera positions, often with minimal visual overlap. Following Sajjadi et al. [22], we train and test the model using 5 randomly selected input views for each scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.751 + ], + "angle": 0, + "content": "Novel view synthesis. We first evaluate the novel view synthesis performance of RUST, and again find that its performance of 22.50 db in PSNR is comparable to that of SRT (22.72) and that it falls in-between that of our improved SRT (23.63) and UpSRT (21.25). Qualitatively, we find that novel views generated by RUST correctly capture the 3D structure of the scenes and, remarkably, the model seems to be more robust than UpSRT, see Fig. 7. This happens especially often when the reference view is far away from the target view." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Latent pose space. In SV scenes, the camera positions mainly vary along the single forward-dimension of the street while horizontal rotations mainly move in discrete steps of \\(60^{\\circ}\\) due to the spatial configuration of the six fixed cameras. This distribution of camera poses is very different from MSN, and we should thus expect the learned pose space to differ significantly as well. Similar to before, we compute a PCA decomposition on target views of 4k test-scenes and visualize the first three components in Fig. 8. Surprisingly," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17303" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.113, + 0.37, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.106, + 0.544, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.55, + 0.106, + 0.703, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.106, + 0.864, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.37 + ], + "angle": 0, + "content": "Figure 8. Latent pose investigations on SV - Left: Scatterplot showing the first three PCA components of the latent pose \\(\\tilde{p}\\) distribution for \\(12\\mathrm{k}\\) target views from 4k scenes. The color of each point indicates by which of the 6 cameras the image was taken, as shown on the color wheel. The first principal axis of these ellipsoids, marked by the long arrow, corresponds to movement along the street. Right: We found that specific linear directions in the latent space correspond to meaningful camera motions. Videos are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.473, + 0.56 + ], + "angle": 0, + "content": "we find only three (rather than six) ellipsoid clusters that each correspond to an opposing pair of cameras. This suggests that the model has learned to represent rotation in an absolute (scene-centric) coordinate frame with the direction of the street as a reference, and that opposing cameras are less well-distinguished due to the streets' approximate mirror symmetries, see Fig. 10 (appendix) for more details. We further find that movement along the street corresponds well to the long axis of these ellipsoids, which depending on the camera can correspond to either a forward/backward or a sideways motion in image space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.472, + 0.753 + ], + "angle": 0, + "content": "Traversals. In Fig. 8, we show linear latent pose traversals that correspond to movement along the street, pitch and tilt of the camera. We find that these dimensions are mapped into the pose space predictably, contiguously and smoothly. The correct parallax effect observed in the forward movement in particular demonstrates that the model has correctly estimated the depth of the scene. These results indicate that RUST can learn to capture the 3D structure of complex real-world scenes from a handful of images, without access to any pose information. The learned latent pose space covers the training distribution of camera poses and enables traversals and novel view synthesis within distribution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.2, + 0.785 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.903 + ], + "angle": 0, + "content": "RUST shares most strengths and limitations with other latent methods, especially with the SRT model [22] that it is based on. Resolution and quality of synthesized views do not reach the performance of NeRF [16], though it is important to note that NeRF does not yield latent scene representations, and it generally requires a large number of similar views of the scene. As has been demonstrated [22], even special-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.895, + 0.44 + ], + "angle": 0, + "content": "ized NeRF variants for sparse input view settings [8] fail to produce meaningful results on the challenging SV dataset, despite having access to accurate pose information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.897, + 0.711 + ], + "angle": 0, + "content": "As shown in Secs. 4.2 and 4.3, RUST learns to effectively model the camera pose distribution of the datasets it is trained on. While this is desirable in many applications, it can limit generalization of the model to new poses that lie outside of the original distribution. For example, we may not find latent poses for which RUST would render views that do not point at the center of the scene in MSN, or represent movement orthogonal to the street in SV. It is notable that all learned methods suffer from such limitations to varying degrees, including light field parametrizations [22] and even volumetric models, especially when given few input images [18]. Nonetheless, more explicit methods tend to generalize better to out-of-distribution poses due to hardcoded assumptions such as explicit camera parametrizations or the volumetric rendering equation. Finally, we empirically found RUST to show higher variance in terms of PSNR compared to SRT. Over independent training runs with 3 random seeds, we observed a standard error of 0.19." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.62, + 0.74 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We propose RUST, a novel method for latent neural scene representation learning that can be trained without any explicit pose information. RUST matches the quality of prior methods that require pose information while scaling to very complex real-world scenes. We further demonstrate that the model learns meaningful latent pose spaces that afford smooth 3D motion within the distribution of camera poses in the training data. We believe that this method is a major milestone towards applying implicit neural scene representations to large uncurated datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17304" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.185 + ], + "angle": 0, + "content": "[1] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. ShapeNet: An Information-Rich 3D Model Repository. arXiv preprint arXiv:1512.03012, 2015. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.195, + 0.472, + 0.236 + ], + "angle": 0, + "content": "[2] Danny Driess, Zhiao Huang, Yunzhu Li, Russ Tedrake, and Marc Toussaint. Learning Multi-Object dynamics with compositional neural radiance fields. 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In CVPR, 2018. 13" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17306" + } + ] +] \ No newline at end of file diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_origin.pdf b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9278f597f2341cd12251af19036163d43322afbc --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/07e323fd-0ee1-490f-90cd-f65d4d015578_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:de2bb547709f33ac8618368070af186d745f525a01d39cea7cbba14309a293e7 +size 1262530 diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/full.md b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e52998725de9e993ad5a245eee52fda922787016 --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/full.md @@ -0,0 +1,282 @@ +# RUST: Latent Neural Scene Representations from Unposed Imagery + +Mehdi S. M. Sajjadi* Aravindh Mahendran Thomas Kipf +Etienne Pot Daniel Duckworth Mario Lucic Klaus Greff +Google Research, Brain Team + +# Abstract + +Inferring the structure of 3D scenes from 2D observations is a fundamental challenge in computer vision. Recently popularized approaches based on neural scene representations have achieved tremendous impact and have been applied across a variety of applications. One of the major remaining challenges in this space is training a single model which can provide latent representations which effectively generalize beyond a single scene. Scene Representation Transformer (SRT) has shown promise in this direction, but scaling it to a larger set of diverse scenes is challenging and necessitates accurately posed ground truth data. To address this problem, we propose RUST (Really Unposed Scene representation Transformer), a pose-free approach to novel view synthesis trained on RGB images alone. Our main insight is that one can train a Pose Encoder that peeks at the target image and learns a latent pose embedding which is used by the decoder for view synthesis. We perform an empirical investigation into the learned latent pose structure and show that it allows meaningful test-time camera transformations and accurate explicit pose readouts. Perhaps surprisingly, RUST achieves similar quality as methods which have access to perfect camera pose, thereby unlocking the potential for large-scale training of amortized neural scene representations. + +# 1. Introduction + +Implicit neural representations have shown remarkable ability in capturing the 3D structure of complex real-world scenes while circumventing many of the downsides of mesh based, point cloud based, and voxel grid based representations [24]. Apart from visually pleasing novel view syn + +*Correspondence: rust@msajjadi.com. Project page: rust-paper.github.io. Contributions: MS: Conception, model design, implementation lead, analysis, infrastructure, experiments, writing, project lead. AM: Conception, model design, implementation, code reviews, experiments-MSN, analysis-MSN, writing. TK: RUST explicit pose estimation, model figures, scoping, advising, writing. EP: GNeRF experiments, Street View dataset, interactive visualization for embedding inspection. DD: COLMAP experiments, evaluation. ML: Team buy-in, scoping, writing. KG: Conception, early MSN analysis, analysis-SV, data-collection and analysis, dataset generation, visualizations, scoping, advising, writing. + +![](images/c673c66ce640bc1a85087c89504175e2e2a7eeb5c2b247ea590577936502a6bd.jpg) +Figure 1. Model overview - RUST produces 3D-centric scene representations through novel view synthesis purely from RGB images without requiring any camera poses. For training, a novel Pose Estimator module glimpses at the target view and passes a low-dimensional latent pose feature to the decoder. + +thesis [14, 16], such representations have shown potential for semantics [25], object decomposition [21], and physics simulation [2] which makes them promising candidates for applications in augmented reality and robotics. However, to be useful in such applications, they need to (1) provide meaningful representations when conditioned on a very limited number of views, (2) have low latency for real-time rendering, and (3) produce scene representations that facilitate generalization of knowledge to novel views and scenes. The recently proposed Scene Representation Transformer (SRT) [22] exhibits most of these properties. It achieves state-of-the-art novel view synthesis in the regime when only a handful of posed input views are available, and produces representations that are well-suited for later segmentation at both semantic [22] and instance level [21]. A major challenge in scaling methods such as SRT, however, is the difficulty in obtaining accurately posed real world data which precludes the training of the models. We posit that it should be possible to train truly pose-free models from RGB images alone without requiring any ground truth pose information. + +We propose RUST (Really Unposed Scene representation Transformer), a novel method for neural scene representation learning through novel view synthesis that does not require pose information: neither for training, nor for inference; neither for input views, nor for target views. While at first + +glance it may seem unlikely that such a model could be trained, our key insight is that a sneak-peek at the target view at training can be used to infer an implicit latent pose, thereby allowing the rendering of the correct view. We find that our model not only learns meaningful, controllable latent pose spaces, but the quality of its novel views are even comparable to the quality of posed methods. + +Our key contributions are as follows: + +- We propose RUST, a novel method that learns latent 3D scene representations through novel view synthesis on very complex synthetic and real datasets without any pose information. +- Our model strongly outperforms prior methods in settings with noisy camera poses while matching their performance when accurate pose information is available to the baselines. +- We provide an investigation into the structure of the learned latent pose spaces and demonstrate that meaningful camera transformations naturally emerge in a fully unsupervised fashion. +- Finally, we demonstrate that the representations learned by the model allow explicit pose readout and dense semantic segmentation. + +# 2. Method + +The model pipeline is shown in Fig. 1. A data point consists of an unordered set of $N$ input views $x = \{x_{i} \in \mathbb{R}^{H \times W \times 3}\}$ of a scene. Unlike SRT [22], they only consist of RGB images since RUST does not use explicit poses. Given these input views, the training objective is to predict a novel target view $y \in \mathbb{R}^{H \times W \times 3}$ of the same scene. + +To this end, the input views $x$ are first encoded using a combination of a CNN and a transformer, resulting in the Set-Latent Scene Representation (SLSR) $S$ which captures the contents of the scene. The target view $y$ is then rendered by a transformer-based decoder that attends into the SLSR $S$ to retrieve relevant information about the scene for novel view synthesis. In addition, the decoder must be conditioned on some form of a query that identifies the desired view. Existing methods, including SRT [22], often use the explicit relative camera pose $p$ between one of the input views and the target view for this purpose. This imbues an explicit notion of 3D space into the model, which introduces a burdensome requirement for accurate camera poses, especially for training such models. RUST resolves this fundamental limitation by learning its own notion of implicit poses. + +Implicit poses. Instead of querying the decoder with explicit poses, we allow the model to learn its own implicit space of camera poses through a learned Pose Estimator module. For training, the Pose Estimator sees parts of the target view $y$ and the SLSR $S$ and extracts a low-dimensional + +![](images/e649bcbc2335249797efc3bc0bfca311f23bb0ddc49eb71edd9115b4a62e5251.jpg) +Figure 2. Pose estimator model - A randomly chosen half of the target image is encoded into a latent pose. The model mainly consists of a CNN encoder followed by alternating cross- and self-attention layers. The final output is projected to 8 dimensions to encourage an easily controllable latent representation. + +latent pose feature $\tilde{p}$ . The decoder transformer then uses $\tilde{p}$ as a query to cross-attend into the SLSR to ultimately render the full novel view $\tilde{y}$ . This form of self supervision allows the model to be trained with standard reconstruction losses without requiring any pose information. At test time, latent poses can be computed on the input views and subsequently modified for novel view synthesis, see Sec. 4.2. + +# 2.1. Model components + +Input view encoder. The encoder consists of a convolutional neural network (CNN) followed by a transformer. Each input image $x_{i}$ is encoded independently by the shared CNN which consists of 3 downsampling blocks, each of which halves the image height and width. As a result, each spatial output feature corresponds to an $8\times 8$ patch in the original input image. + +We add the same learned position embeddings to all spatial feature maps to mark their spatial 2D position in the images. We further add another learned embedding only to the features of the first input image $x_{1}$ to allow the model to distinguish them from the others. This is relevant for the Pose Estimator module, as explained below. Finally, we flatten all spatial feature maps and combine them across input views into a single set of tokens. The encoder transformer then performs self-attention on this set of tokens, thereby exchanging information between the patch features. This results in the SLSR $S$ which captures the scene content as a bag of tokens. + +Pose estimator. The model architecture of the Pose Estimator is shown in Fig. 2. A randomly chosen half of the target + +view $y$ (i.e., either the left or the right half of the image) is first embedded into a set of tokens using a CNN similar to the input view encoder. A transformer then alternates between cross-attending from the target view tokens into a specific subset $\tilde{S} \subset S$ of the SLSR and self-attending between the target view tokens. The intuition behind cross-attending into $\tilde{S}$ is that the latent pose $\tilde{p}$ should be relative to the scene. We allow the Pose Estimator to only attend into SLSR tokens belonging to the (arbitrarily chosen) first input view after empirical findings that this leads to better-structured latent pose spaces. It is important to note that $\tilde{S}$ contains information about all input views due to the self-attention in the preceding encoder transformer. + +Finally, we apply global mean pooling on the transformer's output and linearly project it down to an 8-dimensional latent pose $\tilde{p}$ . It is important to note that we call $\tilde{p}$ the estimated "pose" since it primarily serves the purpose of informing the decoder of the target camera pose. However, we do not enforce any explicit constraints on the latent, instead allowing the model to freely choose the structure of the latent poses. Nevertheless, we find that the model learns to model meaningful camera poses, see Sec. 4.2. + +Decoder transformer. Similar to SRT, each pixel is decoded independently by a decoder transformer that cross-attends from a query into the SLSR $S$ , thereby aggregating relevant information from the scene representation to establish the appearance of the novel view point. We initialize the query by concatenating the latent pose $\tilde{p}$ with the spatial 2D position of the pixel in the target image and passing it through a small query MLP. The output of the decoder is the single RGB value of the target pixel. + +# 2.2. Training procedure + +For each data point during training, we use 5 input views and 3 novel target views. The training objective is to render the target views by minimizing the mean-squared error between the predicted output and the target view: $||\tilde{y} - y||_2^2$ . The entire model is trained end-to-end using the Adam optimizer [9]. In practice, we found the model to perform better when gradients flowing to and through the Pose Estimator module are scaled down by 0.2 which is inspired by spatial transformer networks [7]. + +# 3. Related works + +Neural rendering. The field of neural rendering is vast and the introduction of Neural Radiance Fields (NeRF) [16] has led to a surge of recent follow-up works. NeRF optimizes an MLP to map 3D positions of the scene to radiance and density values, which are used through a differentiable volumetric rendering equation to reconstruct the provided posed images of the scene. We refer the reader to surveys on neural rendering [24] and NeRF [4] for recent overviews. + +NeRF without pose. Most methods based on NeRF assume the availability of perfect camera pose. There exist a number of works extending NeRF for pose estimation or to no-pose settings. INeRF [28] uses pre-trained NeRFs to estimate the camera pose of novel views of the same scene. However, posed imagery is required for each scene in order to obtain the original NeRF models. NeRF-- [27] jointly optimizes the NeRF MLP along with the camera poses for the images. BARF [13] adds a progressive position encoding scheme for improved gradients. Both methods only succeed for forward-facing datasets while failing for more complex camera distributions unless noisy initial poses are given. GNeRF [15] works for scenes with more complex camera distributions, however, the prior distribution must be known for sampling. VMRF [30] extends this to settings where the prior distribution is unknown. + +All methods above require a comparably large number of images of the same scene, since NeRF tends to fail with few observations even with perfect pose [29]. While methods exist that optimize NeRFs from fewer observations [8, 18], they have limitations in terms of scene complexity [22] and to the best of our knowledge, no NeRF-based method has been demonstrated to work with few unposed images. + +Latent 3D scene representations. In the right setup, NeRF produces high-quality novel views, though it does so without providing tangible scene representations that could be readily used for downstream tasks. The line of research focusing on latent 3D scene representations includes NeRF-VAE [12] which uses a variational autoencoder [10] to learn a generative model of NeRF's for synthetic scenes, and GQN [3] which adds per-image latent representations to compute a global scene representation that is used by a recurrent latent variable model for novel view synthesis. A recent extension [19] of GQN performs pose estimation for novel target views by optimizing, at inference time, the posterior probability over poses as estimated by the generative model. All the methods above require ground truth poses for training and inference. GIRAFFE [17] requires no poses for training, but a prior distribution of camera views for the specific dataset. It uses a purely generative mechanism, without the ability to render novel views for given scenes. + +Posed and "unposed" SRT. The current most scalable latent method for neural scene representations is the Scene Representation Transformer (SRT) [22]. It uses a transformer-based encoder-decoder architecture for novel view synthesis, thereby scaling to much more complex scenes than prior work. Its scene representation, the SLSR, has been shown to be useful for 3D-centric supervised and unsupervised semantic downstream tasks [21, 22]. + +While SRT requires posed imagery, the "unposed" variant UpSRT has been proposed as well in the original work [22]. Similar to RUST, it does not require posed input views. How- + +
MethodPosePSNRAblationPSNR
SRT [22]px, py23.31Right-half PE23.88
SRT†px, py24.40Stop grad.23.16
SRT†hatx, py23.81No SLSR20.83
UpSRT†px, py23.03No self-attn22.97
SRT†hatx, haty18.653-dim. p20.40
UpSRT†px, pγ18.6464-dim. p23.40
RUSTpx, pγ23.49768-dim. p23.11
+ +Table 1. Quantitative results on MSN – Left: Comparison with prior work in various settings: perfect $(p_x, p_y)$ , noisy $(\hat{p}_x, \hat{p}_y)$ and lack of $(p_x, p_y)$ input and target poses. We report SRT both as proposed [22], and with our improved architecture $(\mathrm{SRT}^\dagger, \mathrm{UpSRT}^\dagger)$ . Despite requiring no poses, RUST matches the performance of SRT and $\mathrm{UpSRT}^\dagger$ while strongly outperforming all methods when target pose is noisy $\hat{p}_y$ . Right: Model ablations, see Sec. 4.1.1. + +ever, training an UpSRT model requires exact pose information for the target views to specify to the decoder which exact view of the scene to render. This restricts the application of UpSRT to settings where accurate pose information is available for the entire training dataset. We analyze further implications of this in Sec. 4.1. + +Using targets as inputs for training. UViM [11] encodes targets such as panoptic segmentation maps into short latent codes during training to allow a single model architecture to perform well across several tasks. A bottleneck is enforced on the so-called guiding codes through discretization. Recent work on inferring protein conformations and poses [20] trains a VAE model in order to encode Cryo-EM images into latent distributions over poses and protein conformations. Unlike RUST, their method requires a base scene representation that is fixed a priori and uses an explicit differentiable rendered and explicit geometry in the architecture. + +# 4. Experiments + +We begin our experiments on the MultiShapeNet (MSN) dataset (version from [21]), a very challenging test bed for 3D-centric neural scene representation learning [22]. It consists of synthetically generated 3D scenes [6] that contain 16-32 ShapeNet objects [1] scattered in random orientations, and with photo-realistic backgrounds. Importantly, the set of ShapeNet objects is split for the training and test datasets, meaning that all objects encountered in the test scenes are not only in novel arrangements and orientations, but the model has never seen them in the training dataset. Camera positions are sampled from a half-sphere with varying distances to the scene. In all experiments, we follow prior work [22] by using 5 input views, and all quantitative metrics are computed on the right halves of the target views, since the left halves are used for pose estimation in RUST. + +![](images/13ba1017c67287406b240b4d5b3b1d0426ac2e925b2e31f882776946b05d84ee.jpg) +Figure 3. Robustness to camera noise – Sajjadi et al. [22] evaluate SRT and UpSRT on (A) perfect pose, and (B) noisy input pose. In the more realistic setting (C) where input & target pose is noisy, both methods fail as they rely on accurate target camera pose for training. RUST needs no pose, so its performance is constant. + +# 4.1. Novel view synthesis + +The core contribution of RUST is its ability to model 3D scenes without posed imagery. While camera poses in synthetic environments such as MSN are perfectly accurate, practical applications must often rely on noisy sensor data or inaccurate estimated poses. We therefore begin our investigations by measuring the quality of synthesized novel views in new scenes under various assumptions on the accuracy and availability of camera pose information during training. To simulate the real world, we follow prior work [13, 22] and perturb the training camera poses with additive noise for a relatively mild amount of $\sigma = 0.1$ . We visualize the effect of this noise in Fig. 14 (appendix) to provide context for its scale. This leads to three possible settings for both input poses and target poses: perfect $(p_x, p_y)$ , noisy $(\hat{p}_x, \hat{p}_y)$ and lack of $(p_x, p_y)$ input and target cameras poses, respectively. Note that for the posed baselines, we always use perfect target poses for evaluation, i.e. the target poses are only perturbed during training. + +Tab. 1 (left) shows our quantitative evaluation on the MSN dataset. We first compare SRT as proposed [22] with our improved architecture $\mathrm{SRT}^{\dagger}$ , both using perfect pose. We observe that our modifications to the architecture lead to significant improvements in PSNR (+1.09 db). Continuing with the improved architecture, perturbing the input views leads to a loss in 0.59 db ( $\mathrm{SRT}^{\dagger}$ , $\hat{p}_x$ , $p_y$ ) while the lack thereof leads to a drop of 1.37 db ( $\mathrm{UpSRT}^{\dagger}$ , $p_x$ , $p_y$ ). + +Crucially, the most realistic setting where all poses are equally noisy leads to a dramatic decline in performance for prior work $(\mathrm{SRT}^{\dagger}$ and $\mathrm{UpSRT}^{\dagger},\hat{p}_y)$ . RUST meanwhile outperforms the baselines by $+4.84$ db in this setting without any poses, while matching the performance of SRT [22] with perfect pose. We highlight the difference between only perturbing input poses (following prior work [22]) or all camera poses (more realistic setting) in Fig. 3. It is evident from the plot that RUST is the only model that is applicable when camera poses are noisy or even unavailable. + +![](images/becbde5e3e5976c2daa73c9881377ac6b06e1fab4d264628702484ffe4b0b10d.jpg) +Figure 4. Qualitative results on MSN - We compare RUSTo SRT [22] as proposed, and with the respective models using our improved architecture $(\mathrm{SRT}^{\dagger}, \mathrm{UpSRT}^{\dagger})$ . Different models support perfect $(p_x, p_y)$ , noisy $(\hat{p}_x, \hat{p}_y)$ , or a lack of $(\mathcal{P}, \mathcal{P})$ input and target poses, respectively. $\mathrm{SRT}^{\dagger}$ shows a mild drop in quality for perturbed input poses and achieves a similar reconstruction quality as $\mathrm{UpSRT}^{\dagger}$ with perfect target poses. In the realistic setting where the target poses are also perturbed $(\hat{p}_y)$ , both methods fail entirely to render sharp images (only $\mathrm{UpSRT}^{\dagger}$ shown here, see appendix for $\mathrm{SRT}^{\dagger}$ ). RUST, without any camera poses, produces similar-quality renders as the baselines with perfect pose information, and even visibly outperforms the original SRT model [22] with perfect pose information. + +Fig. 4 shows qualitative results for a selection of these models. Notably, $\mathrm{UpSRT}^{\dagger}$ produces extremely blurry views of the scene when the target poses are mildly inaccurate, while RUST produces similar-looking results as $\mathrm{UpSRT}^{\dagger}$ with perfect target poses. Further qualitative results including videos are provided in the supplementary material. + +For the remainder of the experimental section, we only compare RUST to the stronger $\mathrm{SRT}^{\dagger}$ and $\mathrm{UpSRT}^{\dagger}$ baselines and refer to these as SRT and UpSRT for ease of notation. + +# 4.1.1 Ablations + +We investigate the effect of a selection of our design choices for RUST. The results are summarized in Tab. 1 (right). Metrics are computed only on the right half of each target image, since the left half is used for pose estimation by RUST. While we see a lot of evidence that the model is encoding a form of camera pose in the latent space (see Sec. 4.2), it is still possible that the model uses parts of the latent pose feature to encode content information about the target view. We therefore now evaluate the exact same RUST model (with identical weights), but now use the right halves of the target images in the Pose Estimator. We observe that this scheme only outperforms the left-half encoding scheme by $+0.39$ db, thereby showing that the latent pose primarily serves as a proxy for the camera position rather than directly informing the model about the target view content. + +In our default model, we allow gradients to flow from the latent pose back into the encoder, though they are effectively scaled down by a factor of 0.2 (see Sec. 2.2). Cutting the gradients fully implies that the the Pose Estimator cannot + +directly affect the encoder anymore through the SLSR during training. This variant leads to a drop of 0.33 db in PSNR. + +As described in Sec. 2.1, the Pose Estimator cross-attends into parts of the SLSR to allow it to anchor the target poses relative to the input views. Removing this cross-attention module makes it much harder for the model to estimate the target pose and pass it to the decoder. The performance therefore drops by a significant 2.66 db in PSNR. Removing the self-attention between the target image tokens from the Pose Estimator module has a less dramatic effect of 0.52 db. + +Finally, we investigate different choices for the size of the latent pose feature $\tilde{p}$ . We found empirically that smaller sizes such as 3 dimensions would lead to significantly worse results (-3.09 db in PSNR). This is likely only a result of worse training dynamics, as the pose space in the MSN dataset can in theory be fully described with 3 degrees of freedom. Using significantly larger latent pose sizes (64, 768) on the other hand leads to a less controllable latent pose space, while rendering quality remains comparable. + +# 4.2. Latent pose investigations + +In order to analyze the structure of the learned latent pose space, we use principal component analysis (PCA). Specifically, we collect latent poses $\tilde{p}$ for three target views per scene from 4k test scenes of the MSN dataset and inspect the major PCA components of the resulting 8-dimensional pose distribution. We visualize the first three PCA components in Fig. 5 (left) and color-code the points such that hue encodes rotation relative to the first input view's camera and intensity encodes camera height. We find that the points + +![](images/762ca78b0f2184e99b72daeba8c47abe40f5742d3ec6df027d1da0ac6ec4399c.jpg) +Figure 5. Latent pose investigations on MSN – Left: The first three PCA components of the latent poses across many scenes roughly constitute a cylinder. Points are coloured such that intensity represents camera height and hue represents their rotation around the scene's z-axis relative to the first input camera, modulo $120^{\circ}$ . That means a single rotation around the scene maps to three rotations around this circle, with the $0^{\circ}$ position mapping to the first input camera. We found that components 5 and 6 roughly capture one full 360 degree rotation, resolving the ambiguity. We elaborate on this in Appendix A.2. Right: Intuitive camera movement induced by traversals in PCA space. + +![](images/8de80d6482c94956385bc9e773cdf77a0eb284bd64a033ccbd7bab13a6dcbaae.jpg) +Height + +![](images/25514bebd89f1a870ca367696c952463be532b62e56c4dd42fd6341117ce61cc.jpg) +Rotation + +![](images/1b11730a38fc2c9755a117d9e9b2c72e3119b9fcb3ab6173d22c26605f1e7e9d.jpg) +Distance + +form a cylinder whose axis is aligned with the first principal component. This axis correlates strongly with camera height with a Pearson's $r = 0.94$ . The qualitative effect of moving along this dimension is shown in Fig. 5 (Height). Similarly, rotating around the cylinder causes the camera to rotate around the scene in 3D as shown in Fig. 5 (Rotation), although only a third of the rotation is completed by a full traversal along the cylinder. Note that rotations in the latent space are encoded relative to the position of the first input camera, likely because the Pose Estimator only consumes the SLSR tokens $\tilde{S}$ corresponding to the first input view. + +The cylinder-shaped latent pose distribution is sensible, considering that the camera poses in the MSN dataset are distributed along a dome and always point at the scene origin. At the pole of this dome is hence a discontinuity as the camera flips when crossing that point. The cylinder is therefore akin to this dome that is opened up at its pole to eliminate the discontinuity. The remaining PCA components are visualized in Appendix A.2. The fourth component captures the distance of the camera from the scene center $(r = 0.94)$ . We show traversals along this axis in Fig. 5 (Distance). We further find that components 5 and 6, capture a 360 degree absolute rotation in scene coordinates. This surprising finding is further investigated in Appendix A.2. + +It is notable that the model has learned this meaningful structure in the latent pose space without any form of camera pose supervision. Furthermore, this shows that test-time camera control is feasible directly in the latent space. + +# 4.2.1 Explicit pose estimation + +To validate to what extent information about the camera pose is retained in the small latent pose $\tilde{p}$ of RUST, we perform an explicit pose estimation (EPE) experiment. As there is no canonical frame of reference, we choose to predict relative + +
Method# ViewsMSER2(%)Success (%)
RUST EPE70.0899.9[100]
COLMAP100.00100.04.2
COLMAP800.0799.729.5
COLMAP1600.3899.158.9
GNeRF1229.3946.7[100]
GNeRF1509.2483.1[100]
GNeRF-FG1504.0592.7[100]
+ +Table 2. Explicit pose estimation on MSN - RUST EPE recovers relative camera poses nearly perfectly from the SLSR (5 input views) and the pair of latent target poses. COLMAP [23] requires a much larger number of images, and still has a significantly lower success rate for registration. Similarly, GNeRF [15] requires many views of the scene, and fails to estimate accurate poses even when the background pixels are removed from the data (GNeRF-FG). + +poses between two separate target views. Since all cameras on the MSN dataset are pointed at the center of the scene, we only estimate the relative camera position. + +Our EPE module is trained on top of a (frozen) pre-trained RUST model. It takes the SLSR $S$ and the latent pose features $\tilde{p}_1$ and $\tilde{p}_2$ for the two target views and follows the design of the RUST decoder: the concatenation of the two latent poses acts as the query for a transformer which cross-attends into the SLSR $S$ . We found that this cross-attention step is necessary as the latent pose vectors $\tilde{p}$ partially carry pose information that is relative to the SLSR (e.g., rotation, see Sec. 4.2). Finally, the result is passed through an MLP which is tasked to predict the explicit relative pose between the target views. We train the model using the L2 loss. + +Quantitative results in terms of mean-squared error (MSE) + +![](images/22a1af557c0f8b5dfee2f4798c1d4136a81792a379e6cb6f71567e09dffef199.jpg) +150 FG +15.71 + +![](images/25a834131f2fd64f90db835231a5e7fb64229f3c06d5089c1bc937568dd434de.jpg) +Target +PSNR + +![](images/ce3c7cf203ae0b86f080a0c429724516ff0b41cb853c7f3d12bc6de7022257b0.jpg) +150 w/ pose +21.49 + +![](images/cab78656dfeb0f4cbf711612df85bd90d066535b8ddb18b2a8450bebd71a96ba.jpg) +12 w/ pose +13.41 + +![](images/c827fe0f45e3436ee820ac4d7b2c687eebb4118843cd8847bf804bfe7241c099.jpg) +150 +14.42 + +and $R^2$ scores over 95 MSN test scenes are shown in Tab. 2. EPE recovers relative camera positions nearly perfectly on novel test scenes $(R^2 = 99.9\%)$ using only the SLSR (derived from 5 input views) and the pair of latent pose vectors. + +Photogrammetry. To demonstrate the difficulty of the task, we apply COLMAP [23] to 95 newly generated MSN test scenes with up to 160 views (otherwise using the same parameters as the MSN test set). COLMAP uses correspondences between detected keypoints to estimate camera poses. While RUST EPE successfully recovers camera positions from just 7 total views, COLMAP struggles when only given access to a small number of views ( $e.g., < 10$ ) and needs up to 160 views to successfully register most views and estimate their camera poses. As COLMAP may pose only a subset of the provided images, we report metrics for a predetermined, arbitrarily chosen camera pair per scene. If COLMAP fails to pose either of these cameras, we consider pose estimation to have failed and exclude this camera pair from evaluation. We find an optimal rigid transformation that maps estimated camera positions to ground-truth positions before evaluating MSE and $R^2$ to be able to compare with RUST EPE. + +NeRF-based methods. We evaluate GNeRF [15] as a strong representative for unsupervised NeRF-based pose estimation approaches on a single MSN scene using the implementation provided by the authors. GNeRF assumes knowledge of the camera intrinsics and that all cameras are pointed at the origin, i.e. only the 3-dimensional camera positions are estimated. Further, a prior for the camera pose initializations is given to the model. Using only 12 views, GNeRF fails to capture the scene. When using 150 views to train GNeRF, it still performs significantly worse than RUST EPE on explicit pose estimation, demonstrating the benefit of learning a generalizable pose representation across scenes, see Tab. 2. We show qualitative and quantitative results for novel view synthesis in Fig. 6. Training on perfect poses significantly improves NVS performance for GNeRF, showing that even with 150 views, GNeRF fails to accurately register the camera poses. As GNeRF expects the scene to be + +![](images/fabc321ebe442eea66ab4918c00b3adec995d7d984d8c5d66bc2e30978d27312.jpg) + +![](images/32202c08f6adb74b61017033a52d0209f6d6facb9ac5bd8da708a8d58616e11e.jpg) +Target View + +![](images/4eb78dee20e303e2ede526f7bcf34712f6cf5419b424ce18a5e1f81eaa3e3389.jpg) +SRT + +![](images/d0bc1116d4d401c74b5ad0caa61dcc507094739465002ceaddc63beeb287a479.jpg) +UpSRT + +![](images/3ec292612f0a4b7a75bfb644dae38ef2556d1435ea0f3965780403125983e79e.jpg) +RUST + +![](images/eef903e7133fdd90bc277afa4efc2b18ab94ef554be26708feb66ba4c6535c76.jpg) +RUST (Semantic) + +![](images/14e37e38872243ebf8e6685cb4416f23988c164ce511b064be41c4b2d9195d1e.jpg) +Figure 6. Qualitative results for GNeRF [15] - When trained with many posed views (150), results have high fidelity. Reducing the number of images to 12 leads to worse reconstruction and strong artifacts. When no pose is available, the model produces worse quality. Removing the backgrounds from the training dataset helps improve reconstruction accuracy. PSNR computed on 50 views. +Figure 7. Qualitative results on SV - Comparison of RUST with prior work using accurate camera pose. RUST outperforms our improved UpSRT variant, while producing similar quality as the fully posed improved SRT model. We further train a dense semantic segmentation decoder on top of the frozen RUST scene representation, showing that it retains semantic information about the scene. + +![](images/9875783e1bcfad454929eaffae4da2ec06c049b4fc7769d05a66d7580286e1c0.jpg) + +![](images/620eff8cb199af863e6331ac69c7bd2d01d0622e23b9b0a4ad37b30184b58c47.jpg) + +![](images/154718f06a5821d592d2407674530e1edfa1edecc7b5a687a731339fef7e9c7d.jpg) + +![](images/05bcca04c99f1c178debf3b97103c73056c2214baedf73287e8104d96beb77ae.jpg) + +![](images/af45f91f6e2a23041a3c467219faa7aabef870dba67b7b6b55d4320ab552380c.jpg) + +contained within a given bounding box, we also try training it only on the foreground (FG) objects in the scene, dropping all background pixels during optimization. We empirically find that this only leads to slightly improved pose accuracy. + +# 4.3. Application to real-world dataset + +To answer the question whether RUST can learn to represent the 3D structure of complex real-world scenes, we apply it to the Street View (SV) dataset. We have received access to SV through private communication with the authors [5]. It contains 5M dynamic street scenes of San Francisco with moving objects, changes in exposure and white balance, and highly challenging camera positions, often with minimal visual overlap. Following Sajjadi et al. [22], we train and test the model using 5 randomly selected input views for each scene. + +Novel view synthesis. We first evaluate the novel view synthesis performance of RUST, and again find that its performance of 22.50 db in PSNR is comparable to that of SRT (22.72) and that it falls in-between that of our improved SRT (23.63) and UpSRT (21.25). Qualitatively, we find that novel views generated by RUST correctly capture the 3D structure of the scenes and, remarkably, the model seems to be more robust than UpSRT, see Fig. 7. This happens especially often when the reference view is far away from the target view. + +Latent pose space. In SV scenes, the camera positions mainly vary along the single forward-dimension of the street while horizontal rotations mainly move in discrete steps of $60^{\circ}$ due to the spatial configuration of the six fixed cameras. This distribution of camera poses is very different from MSN, and we should thus expect the learned pose space to differ significantly as well. Similar to before, we compute a PCA decomposition on target views of 4k test-scenes and visualize the first three components in Fig. 8. Surprisingly, + +![](images/6852fb8958ffc6ecdac97f5c5f26fd30727c4aa3fe391ef716f97952598b1d81.jpg) +Figure 8. Latent pose investigations on SV - Left: Scatterplot showing the first three PCA components of the latent pose $\tilde{p}$ distribution for $12\mathrm{k}$ target views from 4k scenes. The color of each point indicates by which of the 6 cameras the image was taken, as shown on the color wheel. The first principal axis of these ellipsoids, marked by the long arrow, corresponds to movement along the street. Right: We found that specific linear directions in the latent space correspond to meaningful camera motions. Videos are provided in the supplementary material. + +![](images/5071d97be61d1f47e17112cf1573e0b525625cdb6cd581b733e7fdb35f18e5a4.jpg) + +![](images/84baa1812ed037f6e9536c614d7b9c0b1c0458d870d47962477acf4cb91f5f30.jpg) + +![](images/75bfa47ced88f918b1a2ed67360777d5e2b2a625e40f4dc50971fa9914872458.jpg) + +we find only three (rather than six) ellipsoid clusters that each correspond to an opposing pair of cameras. This suggests that the model has learned to represent rotation in an absolute (scene-centric) coordinate frame with the direction of the street as a reference, and that opposing cameras are less well-distinguished due to the streets' approximate mirror symmetries, see Fig. 10 (appendix) for more details. We further find that movement along the street corresponds well to the long axis of these ellipsoids, which depending on the camera can correspond to either a forward/backward or a sideways motion in image space. + +Traversals. In Fig. 8, we show linear latent pose traversals that correspond to movement along the street, pitch and tilt of the camera. We find that these dimensions are mapped into the pose space predictably, contiguously and smoothly. The correct parallax effect observed in the forward movement in particular demonstrates that the model has correctly estimated the depth of the scene. These results indicate that RUST can learn to capture the 3D structure of complex real-world scenes from a handful of images, without access to any pose information. The learned latent pose space covers the training distribution of camera poses and enables traversals and novel view synthesis within distribution. + +# 5. Limitations + +RUST shares most strengths and limitations with other latent methods, especially with the SRT model [22] that it is based on. Resolution and quality of synthesized views do not reach the performance of NeRF [16], though it is important to note that NeRF does not yield latent scene representations, and it generally requires a large number of similar views of the scene. As has been demonstrated [22], even special- + +ized NeRF variants for sparse input view settings [8] fail to produce meaningful results on the challenging SV dataset, despite having access to accurate pose information. + +As shown in Secs. 4.2 and 4.3, RUST learns to effectively model the camera pose distribution of the datasets it is trained on. While this is desirable in many applications, it can limit generalization of the model to new poses that lie outside of the original distribution. For example, we may not find latent poses for which RUST would render views that do not point at the center of the scene in MSN, or represent movement orthogonal to the street in SV. It is notable that all learned methods suffer from such limitations to varying degrees, including light field parametrizations [22] and even volumetric models, especially when given few input images [18]. Nonetheless, more explicit methods tend to generalize better to out-of-distribution poses due to hardcoded assumptions such as explicit camera parametrizations or the volumetric rendering equation. Finally, we empirically found RUST to show higher variance in terms of PSNR compared to SRT. Over independent training runs with 3 random seeds, we observed a standard error of 0.19. + +# 6. Conclusion + +We propose RUST, a novel method for latent neural scene representation learning that can be trained without any explicit pose information. RUST matches the quality of prior methods that require pose information while scaling to very complex real-world scenes. We further demonstrate that the model learns meaningful latent pose spaces that afford smooth 3D motion within the distribution of camera poses in the training data. We believe that this method is a major milestone towards applying implicit neural scene representations to large uncurated datasets. + +# References + +[1] Angel X. 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In CVPR, 2021. 3 +[18] Michael Niemeyer, Jonathan T Barron, Ben Mildenhall, Mehdi SM Sajjadi, Andreas Geiger, and Noha Radwan. Reg-NeRF: Regularizing neural radiance fields for view synthesis from sparse inputs. In CVPR, 2022. 3, 8 +[19] Dan Rosenbaum, Frederic Besse, Fabio Viola, Danilo Jimenez Rezende, and S M Ali Eslami. Learning models for visual 3d localization with implicit mapping. NeurIPS workshop on Bayesian Deep Learning, 2018. 3 +[20] Dan Rosenbaum, Marta Garnelo, Michal Zielinski, Charlie Beattie, Ellen Clancy, Andrea Huber, Pushmeet Kohli, Andrew W. Senior, John Jumper, Carl Doersch, et al. Inferring a continuous distribution of atom coordinates from cryo-EM images using VAEs. NeurIPS workshop on Machine Learning in Structural Biology, 2021. 4 +[21] Mehdi S. M. Sajjadi, Daniel Duckworth, Aravindh Mahendran, Sjoerd van Steenkiste, Filip Pavetic, Mario Lucic, Leonidas J. Guibas, Klaus Greff, and Thomas Kipf. Object Scene Representation Transformer. In NeurIPS, 2022. 1, 3, 4, 11 +[22] Mehdi S. M. Sajjadi, Henning Meyer, Etienne Pot, Urs Bergmann, Klaus Greff, Noha Radwan, Suhani Vora, Mario Lucic, Daniel Duckworth, Alexey Dosovitskiy, et al. Scene Representation Transformer: Geometry-Free Novel View Synthesis Through Set-Latent Scene Representations. In CVPR, 2022. 1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 18 +[23] Johannes Lutz Schonberger and Jan-Michael Frahm. Structure-from-Motion Revisited. In CVPR, 2016. 6, 7, 12 +[24] Ayush Tewari, Justus Thies, Ben Mildenhall, Pratul Srinivasan, Edgar Tretschk, Yifan Wang, Christoph Lassner, Vincent Sitzmann, Ricardo Martin-Brualla, Stephen Lombardi, et al. Advances in neural rendering. Computer Graphics Forum, 41(2), 2022. 1, 3 +[25] Suhani Vora, Noha Radwan, Klaus Greff, Henning Meyer, Kyle Genova, Mehdi SM Sajjadi, Etienne Pot, Andrea Tagliasacchi, and Daniel Duckworth. NeSF: Neural semantic fields for generalizable semantic segmentation of 3d scenes. TMLR, 2022. 1 +[26] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. In IEEE TIP, 2004. 13 + +[27] Zirui Wang, Shangzhe Wu, Weidi Xie, Min Chen, and Victor Adrian Prisacariu. NeRF--: Neural radiance fields without known camera parameters. arXiv preprint arXiv:2102.07064, 2021.3 +[28] Lin Yen-Chen, Pete Florence, Jonathan Barron, Alberto Rodriguez, Phillip Isola, and Tsung-Yi Lin. iNeRF: Inverting Neural Radiance Fields for Pose Estimation. In IROS, 2021. 3 +[29] Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelNeRF: Neural Radiance Fields from One or Few Images. In CVPR, 2021. 3 +[30] Jiahui Zhang, Fangneng Zhan, Rongliang Wu, Yingchen Yu, Wenqing Zhang, Bai Song, Xiaoqin Zhang, and Shijian Lu. VMRF: View matching neural radiance fields. In ACM MM, 2022. 3 +[31] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 13 \ No newline at end of file diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/images.zip b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fbce23ae4b0358af481513e687412a6b4035a58a --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3ece931f68ca6f89b36fcc709edbddb0f52b123de29cffd2e32df6e190aff893 +size 453056 diff --git a/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/layout.json b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..38b35b48e7b7054d913dcd4f2e6c4736d92227db --- /dev/null +++ b/2023/RUST_ Latent Neural Scene Representations From Unposed Imagery/layout.json @@ -0,0 +1,8172 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 86, + 103, + 507, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 103, + 507, + 121 + ], + "spans": [ + { + "bbox": [ + 86, + 103, + 507, + 121 + ], + "type": "text", + "content": "RUST: Latent Neural Scene Representations from Unposed Imagery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 142, + 143, + 451, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 143, + 451, + 191 + ], + "spans": [ + { + "bbox": [ + 142, + 143, + 451, + 191 + ], + "type": "text", + "content": "Mehdi S. M. Sajjadi* Aravindh Mahendran Thomas Kipf \nEtienne Pot Daniel Duckworth Mario Lucic Klaus Greff \nGoogle Research, Brain Team" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 216, + 191, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 216, + 191, + 228 + ], + "spans": [ + { + "bbox": [ + 143, + 216, + 191, + 228 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 240, + 290, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 290, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 290, + 517 + ], + "type": "text", + "content": "Inferring the structure of 3D scenes from 2D observations is a fundamental challenge in computer vision. Recently popularized approaches based on neural scene representations have achieved tremendous impact and have been applied across a variety of applications. One of the major remaining challenges in this space is training a single model which can provide latent representations which effectively generalize beyond a single scene. Scene Representation Transformer (SRT) has shown promise in this direction, but scaling it to a larger set of diverse scenes is challenging and necessitates accurately posed ground truth data. To address this problem, we propose RUST (Really Unposed Scene representation Transformer), a pose-free approach to novel view synthesis trained on RGB images alone. Our main insight is that one can train a Pose Encoder that peeks at the target image and learns a latent pose embedding which is used by the decoder for view synthesis. We perform an empirical investigation into the learned latent pose structure and show that it allows meaningful test-time camera transformations and accurate explicit pose readouts. Perhaps surprisingly, RUST achieves similar quality as methods which have access to perfect camera pose, thereby unlocking the potential for large-scale training of amortized neural scene representations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 127, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 127, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 127, + 545 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 550, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 288, + 612 + ], + "type": "text", + "content": "Implicit neural representations have shown remarkable ability in capturing the 3D structure of complex real-world scenes while circumventing many of the downsides of mesh based, point cloud based, and voxel grid based representations [24]. Apart from visually pleasing novel view syn" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 617, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 617, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 48, + 617, + 289, + 714 + ], + "type": "text", + "content": "*Correspondence: rust@msajjadi.com. Project page: rust-paper.github.io. Contributions: MS: Conception, model design, implementation lead, analysis, infrastructure, experiments, writing, project lead. AM: Conception, model design, implementation, code reviews, experiments-MSN, analysis-MSN, writing. TK: RUST explicit pose estimation, model figures, scoping, advising, writing. EP: GNeRF experiments, Street View dataset, interactive visualization for embedding inspection. DD: COLMAP experiments, evaluation. ML: Team buy-in, scoping, writing. KG: Conception, early MSN analysis, analysis-SV, data-collection and analysis, dataset generation, visualizations, scoping, advising, writing." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 216, + 545, + 331 + ], + "blocks": [ + { + "bbox": [ + 310, + 216, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 310, + 216, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 310, + 216, + 545, + 331 + ], + "type": "image", + "image_path": "c673c66ce640bc1a85087c89504175e2e2a7eeb5c2b247ea590577936502a6bd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 340, + 547, + 396 + ], + "lines": [ + { + "bbox": [ + 304, + 340, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 547, + 396 + ], + "type": "text", + "content": "Figure 1. Model overview - RUST produces 3D-centric scene representations through novel view synthesis purely from RGB images without requiring any camera poses. For training, a novel Pose Estimator module glimpses at the target view and passes a low-dimensional latent pose feature to the decoder." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 411, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 651 + ], + "type": "text", + "content": "thesis [14, 16], such representations have shown potential for semantics [25], object decomposition [21], and physics simulation [2] which makes them promising candidates for applications in augmented reality and robotics. However, to be useful in such applications, they need to (1) provide meaningful representations when conditioned on a very limited number of views, (2) have low latency for real-time rendering, and (3) produce scene representations that facilitate generalization of knowledge to novel views and scenes. The recently proposed Scene Representation Transformer (SRT) [22] exhibits most of these properties. It achieves state-of-the-art novel view synthesis in the regime when only a handful of posed input views are available, and produces representations that are well-suited for later segmentation at both semantic [22] and instance level [21]. A major challenge in scaling methods such as SRT, however, is the difficulty in obtaining accurately posed real world data which precludes the training of the models. We posit that it should be possible to train truly pose-free models from RGB images alone without requiring any ground truth pose information." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "We propose RUST (Really Unposed Scene representation Transformer), a novel method for neural scene representation learning through novel view synthesis that does not require pose information: neither for training, nor for inference; neither for input views, nor for target views. While at first" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17297" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "glance it may seem unlikely that such a model could be trained, our key insight is that a sneak-peek at the target view at training can be used to infer an implicit latent pose, thereby allowing the rendering of the correct view. We find that our model not only learns meaningful, controllable latent pose spaces, but the quality of its novel views are even comparable to the quality of posed methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 162, + 198, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 162, + 198, + 173 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 198, + 173 + ], + "type": "text", + "content": "Our key contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 176, + 287, + 360 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 176, + 287, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 176, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 287, + 223 + ], + "type": "text", + "content": "- We propose RUST, a novel method that learns latent 3D scene representations through novel view synthesis on very complex synthetic and real datasets without any pose information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 225, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 225, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 225, + 287, + 272 + ], + "type": "text", + "content": "- Our model strongly outperforms prior methods in settings with noisy camera poses while matching their performance when accurate pose information is available to the baselines." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 274, + 287, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 287, + 322 + ], + "type": "text", + "content": "- We provide an investigation into the structure of the learned latent pose spaces and demonstrate that meaningful camera transformations naturally emerge in a fully unsupervised fashion." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 323, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 360 + ], + "type": "text", + "content": "- Finally, we demonstrate that the representations learned by the model allow explicit pose readout and dense semantic segmentation." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 370, + 102, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 102, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 102, + 382 + ], + "type": "text", + "content": "2. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": "The model pipeline is shown in Fig. 1. A data point consists of an unordered set of " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " input views " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "x = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\}" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " of a scene. Unlike SRT [22], they only consist of RGB images since RUST does not use explicit poses. Given these input views, the training objective is to predict a novel target view " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " of the same scene." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": "To this end, the input views " + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": " are first encoded using a combination of a CNN and a transformer, resulting in the Set-Latent Scene Representation (SLSR) " + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": " which captures the contents of the scene. The target view " + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": " is then rendered by a transformer-based decoder that attends into the SLSR " + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": " to retrieve relevant information about the scene for novel view synthesis. In addition, the decoder must be conditioned on some form of a query that identifies the desired view. Existing methods, including SRT [22], often use the explicit relative camera pose " + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 463, + 288, + 643 + ], + "type": "text", + "content": " between one of the input views and the target view for this purpose. This imbues an explicit notion of 3D space into the model, which introduces a burdensome requirement for accurate camera poses, especially for training such models. RUST resolves this fundamental limitation by learning its own notion of implicit poses." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": "Implicit poses. Instead of querying the decoder with explicit poses, we allow the model to learn its own implicit space of camera poses through a learned Pose Estimator module. For training, the Pose Estimator sees parts of the target view " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": " and the SLSR " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": " and extracts a low-dimensional" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 340, + 73, + 508, + 255 + ], + "blocks": [ + { + "bbox": [ + 340, + 73, + 508, + 255 + ], + "lines": [ + { + "bbox": [ + 340, + 73, + 508, + 255 + ], + "spans": [ + { + "bbox": [ + 340, + 73, + 508, + 255 + ], + "type": "image", + "image_path": "e649bcbc2335249797efc3bc0bfca311f23bb0ddc49eb71edd9115b4a62e5251.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 266, + 547, + 322 + ], + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 322 + ], + "type": "text", + "content": "Figure 2. Pose estimator model - A randomly chosen half of the target image is encoded into a latent pose. The model mainly consists of a CNN encoder followed by alternating cross- and self-attention layers. The final output is projected to 8 dimensions to encourage an easily controllable latent representation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "text", + "content": "latent pose feature " + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "text", + "content": ". The decoder transformer then uses " + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "text", + "content": " as a query to cross-attend into the SLSR to ultimately render the full novel view " + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "inline_equation", + "content": "\\tilde{y}" + }, + { + "bbox": [ + 304, + 335, + 547, + 419 + ], + "type": "text", + "content": ". This form of self supervision allows the model to be trained with standard reconstruction losses without requiring any pose information. At test time, latent poses can be computed on the input views and subsequently modified for novel view synthesis, see Sec. 4.2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 427, + 418, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 418, + 440 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 418, + 440 + ], + "type": "text", + "content": "2.1. Model components" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "text", + "content": "Input view encoder. The encoder consists of a convolutional neural network (CNN) followed by a transformer. Each input image " + }, + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "text", + "content": " is encoded independently by the shared CNN which consists of 3 downsampling blocks, each of which halves the image height and width. As a result, each spatial output feature corresponds to an " + }, + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "inline_equation", + "content": "8\\times 8" + }, + { + "bbox": [ + 304, + 445, + 547, + 529 + ], + "type": "text", + "content": " patch in the original input image." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "text", + "content": "We add the same learned position embeddings to all spatial feature maps to mark their spatial 2D position in the images. We further add another learned embedding only to the features of the first input image " + }, + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "text", + "content": " to allow the model to distinguish them from the others. This is relevant for the Pose Estimator module, as explained below. Finally, we flatten all spatial feature maps and combine them across input views into a single set of tokens. The encoder transformer then performs self-attention on this set of tokens, thereby exchanging information between the patch features. This results in the SLSR " + }, + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 530, + 547, + 673 + ], + "type": "text", + "content": " which captures the scene content as a bag of tokens." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Pose estimator. The model architecture of the Pose Estimator is shown in Fig. 2. A randomly chosen half of the target" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17298" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "view " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " (i.e., either the left or the right half of the image) is first embedded into a set of tokens using a CNN similar to the input view encoder. A transformer then alternates between cross-attending from the target view tokens into a specific subset " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{S} \\subset S" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " of the SLSR and self-attending between the target view tokens. The intuition behind cross-attending into " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{S}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " is that the latent pose " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " should be relative to the scene. We allow the Pose Estimator to only attend into SLSR tokens belonging to the (arbitrarily chosen) first input view after empirical findings that this leads to better-structured latent pose spaces. It is important to note that " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{S}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " contains information about all input views due to the self-attention in the preceding encoder transformer." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "content": "Finally, we apply global mean pooling on the transformer's output and linearly project it down to an 8-dimensional latent pose " + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "content": ". It is important to note that we call " + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "content": " the estimated \"pose\" since it primarily serves the purpose of informing the decoder of the target camera pose. However, we do not enforce any explicit constraints on the latent, instead allowing the model to freely choose the structure of the latent poses. Nevertheless, we find that the model learns to model meaningful camera poses, see Sec. 4.2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "text", + "content": "Decoder transformer. Similar to SRT, each pixel is decoded independently by a decoder transformer that cross-attends from a query into the SLSR " + }, + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "text", + "content": ", thereby aggregating relevant information from the scene representation to establish the appearance of the novel view point. We initialize the query by concatenating the latent pose " + }, + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 346, + 289, + 455 + ], + "type": "text", + "content": " with the spatial 2D position of the pixel in the target image and passing it through a small query MLP. The output of the decoder is the single RGB value of the target pixel." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 463, + 162, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 162, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 162, + 475 + ], + "type": "text", + "content": "2.2. Training procedure" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 481, + 288, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 288, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 288, + 589 + ], + "type": "text", + "content": "For each data point during training, we use 5 input views and 3 novel target views. The training objective is to render the target views by minimizing the mean-squared error between the predicted output and the target view: " + }, + { + "bbox": [ + 46, + 481, + 288, + 589 + ], + "type": "inline_equation", + "content": "||\\tilde{y} - y||_2^2" + }, + { + "bbox": [ + 46, + 481, + 288, + 589 + ], + "type": "text", + "content": ". The entire model is trained end-to-end using the Adam optimizer [9]. In practice, we found the model to perform better when gradients flowing to and through the Pose Estimator module are scaled down by 0.2 which is inspired by spatial transformer networks [7]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 136, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 136, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 136, + 609 + ], + "type": "text", + "content": "3. Related works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Neural rendering. The field of neural rendering is vast and the introduction of Neural Radiance Fields (NeRF) [16] has led to a surge of recent follow-up works. NeRF optimizes an MLP to map 3D positions of the scene to radiance and density values, which are used through a differentiable volumetric rendering equation to reconstruct the provided posed images of the scene. We refer the reader to surveys on neural rendering [24] and NeRF [4] for recent overviews." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "type": "text", + "content": "NeRF without pose. Most methods based on NeRF assume the availability of perfect camera pose. There exist a number of works extending NeRF for pose estimation or to no-pose settings. INeRF [28] uses pre-trained NeRFs to estimate the camera pose of novel views of the same scene. However, posed imagery is required for each scene in order to obtain the original NeRF models. NeRF-- [27] jointly optimizes the NeRF MLP along with the camera poses for the images. BARF [13] adds a progressive position encoding scheme for improved gradients. Both methods only succeed for forward-facing datasets while failing for more complex camera distributions unless noisy initial poses are given. GNeRF [15] works for scenes with more complex camera distributions, however, the prior distribution must be known for sampling. VMRF [30] extends this to settings where the prior distribution is unknown." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 263, + 547, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 547, + 348 + ], + "type": "text", + "content": "All methods above require a comparably large number of images of the same scene, since NeRF tends to fail with few observations even with perfect pose [29]. While methods exist that optimize NeRFs from fewer observations [8, 18], they have limitations in terms of scene complexity [22] and to the best of our knowledge, no NeRF-based method has been demonstrated to work with few unposed images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 357, + 548, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 548, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 548, + 573 + ], + "type": "text", + "content": "Latent 3D scene representations. In the right setup, NeRF produces high-quality novel views, though it does so without providing tangible scene representations that could be readily used for downstream tasks. The line of research focusing on latent 3D scene representations includes NeRF-VAE [12] which uses a variational autoencoder [10] to learn a generative model of NeRF's for synthetic scenes, and GQN [3] which adds per-image latent representations to compute a global scene representation that is used by a recurrent latent variable model for novel view synthesis. A recent extension [19] of GQN performs pose estimation for novel target views by optimizing, at inference time, the posterior probability over poses as estimated by the generative model. All the methods above require ground truth poses for training and inference. GIRAFFE [17] requires no poses for training, but a prior distribution of camera views for the specific dataset. It uses a purely generative mechanism, without the ability to render novel views for given scenes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "content": "Posed and \"unposed\" SRT. The current most scalable latent method for neural scene representations is the Scene Representation Transformer (SRT) [22]. It uses a transformer-based encoder-decoder architecture for novel view synthesis, thereby scaling to much more complex scenes than prior work. Its scene representation, the SLSR, has been shown to be useful for 3D-centric supervised and unsupervised semantic downstream tasks [21, 22]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "While SRT requires posed imagery, the \"unposed\" variant UpSRT has been proposed as well in the original work [22]. Similar to RUST, it does not require posed input views. How-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17299" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 180 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 180 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 180 + ], + "type": "table", + "html": "
MethodPosePSNRAblationPSNR
SRT [22]px, py23.31Right-half PE23.88
SRT†px, py24.40Stop grad.23.16
SRT†hatx, py23.81No SLSR20.83
UpSRT†px, py23.03No self-attn22.97
SRT†hatx, haty18.653-dim. p20.40
UpSRT†px, pγ18.6464-dim. p23.40
RUSTpx, pγ23.49768-dim. p23.11
", + "image_path": "a3e4563b430e57741a9bfebe1e823a8867affb57fa1a0f6ee660b9fad3fee7f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": "Table 1. Quantitative results on MSN – Left: Comparison with prior work in various settings: perfect " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "(p_x, p_y)" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": ", noisy " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "(\\hat{p}_x, \\hat{p}_y)" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": " and lack of " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "(p_x, p_y)" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": " input and target poses. We report SRT both as proposed [22], and with our improved architecture " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "(\\mathrm{SRT}^\\dagger, \\mathrm{UpSRT}^\\dagger)" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": ". Despite requiring no poses, RUST matches the performance of SRT and " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^\\dagger" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": " while strongly outperforming all methods when target pose is noisy " + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\hat{p}_y" + }, + { + "bbox": [ + 46, + 187, + 288, + 266 + ], + "type": "text", + "content": ". Right: Model ablations, see Sec. 4.1.1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 288, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 288, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 288, + 357 + ], + "type": "text", + "content": "ever, training an UpSRT model requires exact pose information for the target views to specify to the decoder which exact view of the scene to render. This restricts the application of UpSRT to settings where accurate pose information is available for the entire training dataset. We analyze further implications of this in Sec. 4.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 371, + 288, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 288, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 288, + 504 + ], + "type": "text", + "content": "Using targets as inputs for training. UViM [11] encodes targets such as panoptic segmentation maps into short latent codes during training to allow a single model architecture to perform well across several tasks. A bottleneck is enforced on the so-called guiding codes through discretization. Recent work on inferring protein conformations and poses [20] trains a VAE model in order to encode Cryo-EM images into latent distributions over poses and protein conformations. Unlike RUST, their method requires a base scene representation that is fixed a priori and uses an explicit differentiable rendered and explicit geometry in the architecture." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 514, + 128, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 128, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 128, + 528 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 713 + ], + "type": "text", + "content": "We begin our experiments on the MultiShapeNet (MSN) dataset (version from [21]), a very challenging test bed for 3D-centric neural scene representation learning [22]. It consists of synthetically generated 3D scenes [6] that contain 16-32 ShapeNet objects [1] scattered in random orientations, and with photo-realistic backgrounds. Importantly, the set of ShapeNet objects is split for the training and test datasets, meaning that all objects encountered in the test scenes are not only in novel arrangements and orientations, but the model has never seen them in the training dataset. Camera positions are sampled from a half-sphere with varying distances to the scene. In all experiments, we follow prior work [22] by using 5 input views, and all quantitative metrics are computed on the right halves of the target views, since the left halves are used for pose estimation in RUST." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 542, + 178 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 542, + 178 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 542, + 178 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 542, + 178 + ], + "type": "image", + "image_path": "13ba1017c67287406b240b4d5b3b1d0426ac2e925b2e31f882776946b05d84ee.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 186, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 304, + 186, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 547, + 243 + ], + "type": "text", + "content": "Figure 3. Robustness to camera noise – Sajjadi et al. [22] evaluate SRT and UpSRT on (A) perfect pose, and (B) noisy input pose. In the more realistic setting (C) where input & target pose is noisy, both methods fail as they rely on accurate target camera pose for training. RUST needs no pose, so its performance is constant." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 263, + 424, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 263, + 424, + 276 + ], + "spans": [ + { + "bbox": [ + 306, + 263, + 424, + 276 + ], + "type": "text", + "content": "4.1. Novel view synthesis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "content": "The core contribution of RUST is its ability to model 3D scenes without posed imagery. While camera poses in synthetic environments such as MSN are perfectly accurate, practical applications must often rely on noisy sensor data or inaccurate estimated poses. We therefore begin our investigations by measuring the quality of synthesized novel views in new scenes under various assumptions on the accuracy and availability of camera pose information during training. To simulate the real world, we follow prior work [13, 22] and perturb the training camera poses with additive noise for a relatively mild amount of " + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\sigma = 0.1" + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "content": ". We visualize the effect of this noise in Fig. 14 (appendix) to provide context for its scale. This leads to three possible settings for both input poses and target poses: perfect " + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "inline_equation", + "content": "(p_x, p_y)" + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "content": ", noisy " + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "inline_equation", + "content": "(\\hat{p}_x, \\hat{p}_y)" + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "content": " and lack of " + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "inline_equation", + "content": "(p_x, p_y)" + }, + { + "bbox": [ + 304, + 281, + 547, + 498 + ], + "type": "text", + "content": " input and target cameras poses, respectively. Note that for the posed baselines, we always use perfect target poses for evaluation, i.e. the target poses are only perturbed during training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": "Tab. 1 (left) shows our quantitative evaluation on the MSN dataset. We first compare SRT as proposed [22] with our improved architecture " + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ", both using perfect pose. We observe that our modifications to the architecture lead to significant improvements in PSNR (+1.09 db). Continuing with the improved architecture, perturbing the input views leads to a loss in 0.59 db (" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\hat{p}_x" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "p_y" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ") while the lack thereof leads to a drop of 1.37 db (" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "p_x" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "inline_equation", + "content": "p_y" + }, + { + "bbox": [ + 304, + 498, + 547, + 594 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Crucially, the most realistic setting where all poses are equally noisy leads to a dramatic decline in performance for prior work " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "(\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger},\\hat{p}_y)" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": ". RUST meanwhile outperforms the baselines by " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "+4.84" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " db in this setting without any poses, while matching the performance of SRT [22] with perfect pose. We highlight the difference between only perturbing input poses (following prior work [22]) or all camera poses (more realistic setting) in Fig. 3. It is evident from the plot that RUST is the only model that is applicable when camera poses are noisy or even unavailable." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17300" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 77, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 47, + 77, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 47, + 77, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 77, + 545, + 250 + ], + "type": "image", + "image_path": "becbde5e3e5976c2daa73c9881377ac6b06e1fab4d264628702484ffe4b0b10d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": "Figure 4. Qualitative results on MSN - We compare RUSTo SRT [22] as proposed, and with the respective models using our improved architecture " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "(\\mathrm{SRT}^{\\dagger}, \\mathrm{UpSRT}^{\\dagger})" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": ". Different models support perfect " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "(p_x, p_y)" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": ", noisy " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "(\\hat{p}_x, \\hat{p}_y)" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": ", or a lack of " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "(\\mathcal{P}, \\mathcal{P})" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": " input and target poses, respectively. " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": " shows a mild drop in quality for perturbed input poses and achieves a similar reconstruction quality as " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": " with perfect target poses. In the realistic setting where the target poses are also perturbed " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "(\\hat{p}_y)" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": ", both methods fail entirely to render sharp images (only " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": " shown here, see appendix for " + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 255, + 548, + 324 + ], + "type": "text", + "content": "). RUST, without any camera poses, produces similar-quality renders as the baselines with perfect pose information, and even visibly outperforms the original SRT model [22] with perfect pose information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "text", + "content": "Fig. 4 shows qualitative results for a selection of these models. Notably, " + }, + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "text", + "content": " produces extremely blurry views of the scene when the target poses are mildly inaccurate, while RUST produces similar-looking results as " + }, + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 343, + 288, + 415 + ], + "type": "text", + "content": " with perfect target poses. Further qualitative results including videos are provided in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "text", + "content": "For the remainder of the experimental section, we only compare RUST to the stronger " + }, + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathrm{SRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathrm{UpSRT}^{\\dagger}" + }, + { + "bbox": [ + 46, + 416, + 288, + 453 + ], + "type": "text", + "content": " baselines and refer to these as SRT and UpSRT for ease of notation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 467, + 122, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 122, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 122, + 479 + ], + "type": "text", + "content": "4.1.1 Ablations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 664 + ], + "type": "text", + "content": "We investigate the effect of a selection of our design choices for RUST. The results are summarized in Tab. 1 (right). Metrics are computed only on the right half of each target image, since the left half is used for pose estimation by RUST. While we see a lot of evidence that the model is encoding a form of camera pose in the latent space (see Sec. 4.2), it is still possible that the model uses parts of the latent pose feature to encode content information about the target view. We therefore now evaluate the exact same RUST model (with identical weights), but now use the right halves of the target images in the Pose Estimator. We observe that this scheme only outperforms the left-half encoding scheme by " + }, + { + "bbox": [ + 46, + 485, + 287, + 664 + ], + "type": "inline_equation", + "content": "+0.39" + }, + { + "bbox": [ + 46, + 485, + 287, + 664 + ], + "type": "text", + "content": " db, thereby showing that the latent pose primarily serves as a proxy for the camera position rather than directly informing the model about the target view content." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In our default model, we allow gradients to flow from the latent pose back into the encoder, though they are effectively scaled down by a factor of 0.2 (see Sec. 2.2). Cutting the gradients fully implies that the the Pose Estimator cannot" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 343, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 367 + ], + "type": "text", + "content": "directly affect the encoder anymore through the SLSR during training. This variant leads to a drop of 0.33 db in PSNR." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 369, + 546, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 546, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 546, + 464 + ], + "type": "text", + "content": "As described in Sec. 2.1, the Pose Estimator cross-attends into parts of the SLSR to allow it to anchor the target poses relative to the input views. Removing this cross-attention module makes it much harder for the model to estimate the target pose and pass it to the decoder. The performance therefore drops by a significant 2.66 db in PSNR. Removing the self-attention between the target image tokens from the Pose Estimator module has a less dramatic effect of 0.52 db." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "text", + "content": "Finally, we investigate different choices for the size of the latent pose feature " + }, + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 304, + 466, + 547, + 574 + ], + "type": "text", + "content": ". We found empirically that smaller sizes such as 3 dimensions would lead to significantly worse results (-3.09 db in PSNR). This is likely only a result of worse training dynamics, as the pose space in the MSN dataset can in theory be fully described with 3 degrees of freedom. Using significantly larger latent pose sizes (64, 768) on the other hand leads to a less controllable latent pose space, while rendering quality remains comparable." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 586, + 450, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 450, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 450, + 598 + ], + "type": "text", + "content": "4.2. Latent pose investigations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "In order to analyze the structure of the learned latent pose space, we use principal component analysis (PCA). Specifically, we collect latent poses " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " for three target views per scene from 4k test scenes of the MSN dataset and inspect the major PCA components of the resulting 8-dimensional pose distribution. We visualize the first three PCA components in Fig. 5 (left) and color-code the points such that hue encodes rotation relative to the first input view's camera and intensity encodes camera height. We find that the points" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17301" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 74, + 177, + 215 + ], + "blocks": [ + { + "bbox": [ + 51, + 74, + 177, + 215 + ], + "lines": [ + { + "bbox": [ + 51, + 74, + 177, + 215 + ], + "spans": [ + { + "bbox": [ + 51, + 74, + 177, + 215 + ], + "type": "image", + "image_path": "762ca78b0f2184e99b72daeba8c47abe40f5742d3ec6df027d1da0ac6ec4399c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "type": "text", + "content": "Figure 5. Latent pose investigations on MSN – Left: The first three PCA components of the latent poses across many scenes roughly constitute a cylinder. Points are coloured such that intensity represents camera height and hue represents their rotation around the scene's z-axis relative to the first input camera, modulo " + }, + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "type": "inline_equation", + "content": "120^{\\circ}" + }, + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "type": "text", + "content": ". That means a single rotation around the scene maps to three rotations around this circle, with the " + }, + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 46, + 228, + 547, + 284 + ], + "type": "text", + "content": " position mapping to the first input camera. We found that components 5 and 6 roughly capture one full 360 degree rotation, resolving the ambiguity. We elaborate on this in Appendix A.2. Right: Intuitive camera movement induced by traversals in PCA space." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 183, + 92, + 301, + 213 + ], + "blocks": [ + { + "bbox": [ + 229, + 79, + 258, + 90 + ], + "lines": [ + { + "bbox": [ + 229, + 79, + 258, + 90 + ], + "spans": [ + { + "bbox": [ + 229, + 79, + 258, + 90 + ], + "type": "text", + "content": "Height" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 183, + 92, + 301, + 213 + ], + "lines": [ + { + "bbox": [ + 183, + 92, + 301, + 213 + ], + "spans": [ + { + "bbox": [ + 183, + 92, + 301, + 213 + ], + "type": "image", + "image_path": "8de80d6482c94956385bc9e773cdf77a0eb284bd64a033ccbd7bab13a6dcbaae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 92, + 419, + 212 + ], + "blocks": [ + { + "bbox": [ + 343, + 79, + 380, + 89 + ], + "lines": [ + { + "bbox": [ + 343, + 79, + 380, + 89 + ], + "spans": [ + { + "bbox": [ + 343, + 79, + 380, + 89 + ], + "type": "text", + "content": "Rotation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 301, + 92, + 419, + 212 + ], + "lines": [ + { + "bbox": [ + 301, + 92, + 419, + 212 + ], + "spans": [ + { + "bbox": [ + 301, + 92, + 419, + 212 + ], + "type": "image", + "image_path": "25514bebd89f1a870ca367696c952463be532b62e56c4dd42fd6341117ce61cc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 419, + 92, + 537, + 213 + ], + "blocks": [ + { + "bbox": [ + 460, + 79, + 496, + 89 + ], + "lines": [ + { + "bbox": [ + 460, + 79, + 496, + 89 + ], + "spans": [ + { + "bbox": [ + 460, + 79, + 496, + 89 + ], + "type": "text", + "content": "Distance" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 419, + 92, + 537, + 213 + ], + "lines": [ + { + "bbox": [ + 419, + 92, + 537, + 213 + ], + "spans": [ + { + "bbox": [ + 419, + 92, + 537, + 213 + ], + "type": "image", + "image_path": "1b11730a38fc2c9755a117d9e9b2c72e3119b9fcb3ab6173d22c26605f1e7e9d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "text", + "content": "form a cylinder whose axis is aligned with the first principal component. This axis correlates strongly with camera height with a Pearson's " + }, + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "inline_equation", + "content": "r = 0.94" + }, + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "text", + "content": ". The qualitative effect of moving along this dimension is shown in Fig. 5 (Height). Similarly, rotating around the cylinder causes the camera to rotate around the scene in 3D as shown in Fig. 5 (Rotation), although only a third of the rotation is completed by a full traversal along the cylinder. Note that rotations in the latent space are encoded relative to the position of the first input camera, likely because the Pose Estimator only consumes the SLSR tokens " + }, + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "inline_equation", + "content": "\\tilde{S}" + }, + { + "bbox": [ + 46, + 304, + 288, + 435 + ], + "type": "text", + "content": " corresponding to the first input view." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 436, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 590 + ], + "type": "text", + "content": "The cylinder-shaped latent pose distribution is sensible, considering that the camera poses in the MSN dataset are distributed along a dome and always point at the scene origin. At the pole of this dome is hence a discontinuity as the camera flips when crossing that point. The cylinder is therefore akin to this dome that is opened up at its pole to eliminate the discontinuity. The remaining PCA components are visualized in Appendix A.2. The fourth component captures the distance of the camera from the scene center " + }, + { + "bbox": [ + 46, + 436, + 287, + 590 + ], + "type": "inline_equation", + "content": "(r = 0.94)" + }, + { + "bbox": [ + 46, + 436, + 287, + 590 + ], + "type": "text", + "content": ". We show traversals along this axis in Fig. 5 (Distance). We further find that components 5 and 6, capture a 360 degree absolute rotation in scene coordinates. This surprising finding is further investigated in Appendix A.2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 591, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 639 + ], + "type": "text", + "content": "It is notable that the model has learned this meaningful structure in the latent pose space without any form of camera pose supervision. Furthermore, this shows that test-time camera control is feasible directly in the latent space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 649, + 182, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 649, + 182, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 649, + 182, + 661 + ], + "type": "text", + "content": "4.2.1 Explicit pose estimation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "To validate to what extent information about the camera pose is retained in the small latent pose " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " of RUST, we perform an explicit pose estimation (EPE) experiment. As there is no canonical frame of reference, we choose to predict relative" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 307, + 307, + 548, + 426 + ], + "blocks": [ + { + "bbox": [ + 307, + 307, + 548, + 426 + ], + "lines": [ + { + "bbox": [ + 307, + 307, + 548, + 426 + ], + "spans": [ + { + "bbox": [ + 307, + 307, + 548, + 426 + ], + "type": "table", + "html": "
Method# ViewsMSER2(%)Success (%)
RUST EPE70.0899.9[100]
COLMAP100.00100.04.2
COLMAP800.0799.729.5
COLMAP1600.3899.158.9
GNeRF1229.3946.7[100]
GNeRF1509.2483.1[100]
GNeRF-FG1504.0592.7[100]
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Similarly, GNeRF [15] requires many views of the scene, and fails to estimate accurate poses even when the background pixels are removed from the data (GNeRF-FG)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 533, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 569 + ], + "type": "text", + "content": "poses between two separate target views. Since all cameras on the MSN dataset are pointed at the center of the scene, we only estimate the relative camera position." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": "Our EPE module is trained on top of a (frozen) pre-trained RUST model. It takes the SLSR " + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": " and the latent pose features " + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\tilde{p}_1" + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\tilde{p}_2" + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": " for the two target views and follows the design of the RUST decoder: the concatenation of the two latent poses acts as the query for a transformer which cross-attends into the SLSR " + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": ". We found that this cross-attention step is necessary as the latent pose vectors " + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": " partially carry pose information that is relative to the SLSR (e.g., rotation, see Sec. 4.2). Finally, the result is passed through an MLP which is tasked to predict the explicit relative pose between the target views. 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"spans": [ + { + "bbox": [ + 205, + 132, + 225, + 141 + ], + "type": "text", + "content": "14.42" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "text", + "content": " scores over 95 MSN test scenes are shown in Tab. 2. EPE recovers relative camera positions nearly perfectly on novel test scenes " + }, + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "inline_equation", + "content": "(R^2 = 99.9\\%)" + }, + { + "bbox": [ + 46, + 235, + 288, + 283 + ], + "type": "text", + "content": " using only the SLSR (derived from 5 input views) and the pair of latent pose vectors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "text", + "content": "Photogrammetry. To demonstrate the difficulty of the task, we apply COLMAP [23] to 95 newly generated MSN test scenes with up to 160 views (otherwise using the same parameters as the MSN test set). COLMAP uses correspondences between detected keypoints to estimate camera poses. While RUST EPE successfully recovers camera positions from just 7 total views, COLMAP struggles when only given access to a small number of views (" + }, + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "inline_equation", + "content": "e.g., < 10" + }, + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "text", + "content": ") and needs up to 160 views to successfully register most views and estimate their camera poses. As COLMAP may pose only a subset of the provided images, we report metrics for a predetermined, arbitrarily chosen camera pair per scene. If COLMAP fails to pose either of these cameras, we consider pose estimation to have failed and exclude this camera pair from evaluation. We find an optimal rigid transformation that maps estimated camera positions to ground-truth positions before evaluating MSE and " + }, + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 296, + 288, + 499 + ], + "type": "text", + "content": " to be able to compare with RUST EPE." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "NeRF-based methods. We evaluate GNeRF [15] as a strong representative for unsupervised NeRF-based pose estimation approaches on a single MSN scene using the implementation provided by the authors. GNeRF assumes knowledge of the camera intrinsics and that all cameras are pointed at the origin, i.e. only the 3-dimensional camera positions are estimated. Further, a prior for the camera pose initializations is given to the model. Using only 12 views, GNeRF fails to capture the scene. When using 150 views to train GNeRF, it still performs significantly worse than RUST EPE on explicit pose estimation, demonstrating the benefit of learning a generalizable pose representation across scenes, see Tab. 2. We show qualitative and quantitative results for novel view synthesis in Fig. 6. Training on perfect poses significantly improves NVS performance for GNeRF, showing that even with 150 views, GNeRF fails to accurately register the camera poses. As GNeRF expects the scene to be" + } + ] + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 335, + 125 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 335, + 125 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 335, + 125 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 335, + 125 + ], + "type": "image", + "image_path": "fabc321ebe442eea66ab4918c00b3adec995d7d984d8c5d66bc2e30978d27312.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 336, + 72, + 376, + 125 + ], + "blocks": [ + { + "bbox": [ + 342, + 70, + 372, + 76 + ], + "lines": [ + { + "bbox": [ + 342, + 70, + 372, + 76 + ], + "spans": [ + { + "bbox": [ + 342, + 70, + 372, + 76 + ], + "type": "text", + "content": "Target View" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 336, + 72, + 376, + 125 + ], + "lines": [ + { + "bbox": [ + 336, + 72, + 376, + 125 + ], + "spans": [ + { + "bbox": [ + 336, + 72, + 376, + 125 + ], + "type": "image", + "image_path": "32202c08f6adb74b61017033a52d0209f6d6facb9ac5bd8da708a8d58616e11e.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 378, + 72, + 419, + 125 + ], + "blocks": [ + { + "bbox": [ + 394, + 70, + 404, + 76 + ], + "lines": [ + { + "bbox": [ + 394, + 70, + 404, + 76 + ], + "spans": [ + { + "bbox": [ + 394, + 70, + 404, + 76 + ], + "type": "text", + "content": "SRT" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 378, + 72, + 419, + 125 + ], + "lines": [ + { + "bbox": [ + 378, + 72, + 419, + 125 + ], + "spans": [ + { + "bbox": [ + 378, + 72, + 419, + 125 + ], + "type": "image", + "image_path": "4eb78dee20e303e2ede526f7bcf34712f6cf5419b424ce18a5e1f81eaa3e3389.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 420, + 72, + 461, + 125 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 449, + 76 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 449, + 76 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 449, + 76 + ], + "type": "text", + "content": "UpSRT" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 420, + 72, + 461, + 125 + ], + "lines": [ + { + "bbox": [ + 420, + 72, + 461, + 125 + ], + "spans": [ + { + "bbox": [ + 420, + 72, + 461, + 125 + ], + "type": "image", + "image_path": "d0bc1116d4d401c74b5ad0caa61dcc507094739465002ceaddc63beeb287a479.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 462, + 72, + 503, + 125 + ], + "blocks": [ + { + "bbox": [ + 476, + 70, + 490, + 76 + ], + "lines": [ + { + "bbox": [ + 476, + 70, + 490, + 76 + ], + "spans": [ + { + "bbox": [ + 476, + 70, + 490, + 76 + ], + "type": "text", + "content": "RUST" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 462, + 72, + 503, + 125 + ], + "lines": [ + { + "bbox": [ + 462, + 72, + 503, + 125 + ], + "spans": [ + { + "bbox": [ + 462, + 72, + 503, + 125 + ], + "type": "image", + "image_path": "3ec292612f0a4b7a75bfb644dae38ef2556d1435ea0f3965780403125983e79e.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 505, + 75, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 504, + 70, + 545, + 76 + ], + "lines": [ + { + "bbox": [ + 504, + 70, + 545, + 76 + ], + "spans": [ + { + "bbox": [ + 504, + 70, + 545, + 76 + ], + "type": "text", + "content": "RUST (Semantic)" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 505, + 75, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 505, + 75, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 505, + 75, + 545, + 125 + ], + "type": "image", + "image_path": "eef903e7133fdd90bc277afa4efc2b18ab94ef554be26708feb66ba4c6535c76.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 307, + 126, + 335, + 176 + ], + "blocks": [ + { + "bbox": [ + 46, + 152, + 288, + 218 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 288, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 288, + 218 + ], + "type": "text", + "content": "Figure 6. Qualitative results for GNeRF [15] - When trained with many posed views (150), results have high fidelity. Reducing the number of images to 12 leads to worse reconstruction and strong artifacts. When no pose is available, the model produces worse quality. Removing the backgrounds from the training dataset helps improve reconstruction accuracy. PSNR computed on 50 views." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 126, + 335, + 176 + ], + "lines": [ + { + "bbox": [ + 307, + 126, + 335, + 176 + ], + "spans": [ + { + "bbox": [ + 307, + 126, + 335, + 176 + ], + "type": "image", + "image_path": "14e37e38872243ebf8e6685cb4416f23988c164ce511b064be41c4b2d9195d1e.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 185, + 545, + 261 + ], + "lines": [ + { + "bbox": [ + 304, + 185, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 545, + 261 + ], + "type": "text", + "content": "Figure 7. Qualitative results on SV - Comparison of RUST with prior work using accurate camera pose. RUST outperforms our improved UpSRT variant, while producing similar quality as the fully posed improved SRT model. We further train a dense semantic segmentation decoder on top of the frozen RUST scene representation, showing that it retains semantic information about the scene." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 336, + 126, + 376, + 176 + ], + "blocks": [ + { + "bbox": [ + 336, + 126, + 376, + 176 + ], + "lines": [ + { + "bbox": [ + 336, + 126, + 376, + 176 + ], + "spans": [ + { + "bbox": [ + 336, + 126, + 376, + 176 + ], + "type": "image", + "image_path": "9875783e1bcfad454929eaffae4da2ec06c049b4fc7769d05a66d7580286e1c0.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 378, + 126, + 419, + 176 + ], + "blocks": [ + { + "bbox": [ + 378, + 126, + 419, + 176 + ], + "lines": [ + { + "bbox": [ + 378, + 126, + 419, + 176 + ], + "spans": [ + { + "bbox": [ + 378, + 126, + 419, + 176 + ], + "type": "image", + "image_path": "620eff8cb199af863e6331ac69c7bd2d01d0622e23b9b0a4ad37b30184b58c47.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 420, + 126, + 461, + 176 + ], + "blocks": [ + { + "bbox": [ + 420, + 126, + 461, + 176 + ], + "lines": [ + { + "bbox": [ + 420, + 126, + 461, + 176 + ], + "spans": [ + { + "bbox": [ + 420, + 126, + 461, + 176 + ], + "type": "image", + "image_path": "154718f06a5821d592d2407674530e1edfa1edecc7b5a687a731339fef7e9c7d.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 462, + 126, + 503, + 176 + ], + "blocks": [ + { + "bbox": [ + 462, + 126, + 503, + 176 + ], + "lines": [ + { + "bbox": [ + 462, + 126, + 503, + 176 + ], + "spans": [ + { + "bbox": [ + 462, + 126, + 503, + 176 + ], + "type": "image", + "image_path": "05bcca04c99f1c178debf3b97103c73056c2214baedf73287e8104d96beb77ae.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 504, + 126, + 545, + 176 + ], + "blocks": [ + { + "bbox": [ + 504, + 126, + 545, + 176 + ], + "lines": [ + { + "bbox": [ + 504, + 126, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 504, + 126, + 545, + 176 + ], + "type": "image", + "image_path": "af45f91f6e2a23041a3c467219faa7aabef870dba67b7b6b55d4320ab552380c.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 282, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 331 + ], + "type": "text", + "content": "contained within a given bounding box, we also try training it only on the foreground (FG) objects in the scene, dropping all background pixels during optimization. We empirically find that this only leads to slightly improved pose accuracy." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 305, + 337, + 483, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 483, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 483, + 350 + ], + "type": "text", + "content": "4.3. Application to real-world dataset" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 355, + 546, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 546, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 546, + 475 + ], + "type": "text", + "content": "To answer the question whether RUST can learn to represent the 3D structure of complex real-world scenes, we apply it to the Street View (SV) dataset. We have received access to SV through private communication with the authors [5]. It contains 5M dynamic street scenes of San Francisco with moving objects, changes in exposure and white balance, and highly challenging camera positions, often with minimal visual overlap. Following Sajjadi et al. [22], we train and test the model using 5 randomly selected input views for each scene." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 486, + 546, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 594 + ], + "type": "text", + "content": "Novel view synthesis. We first evaluate the novel view synthesis performance of RUST, and again find that its performance of 22.50 db in PSNR is comparable to that of SRT (22.72) and that it falls in-between that of our improved SRT (23.63) and UpSRT (21.25). Qualitatively, we find that novel views generated by RUST correctly capture the 3D structure of the scenes and, remarkably, the model seems to be more robust than UpSRT, see Fig. 7. This happens especially often when the reference view is far away from the target view." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "Latent pose space. In SV scenes, the camera positions mainly vary along the single forward-dimension of the street while horizontal rotations mainly move in discrete steps of " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "60^{\\circ}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " due to the spatial configuration of the six fixed cameras. This distribution of camera poses is very different from MSN, and we should thus expect the learned pose space to differ significantly as well. Similar to before, we compute a PCA decomposition on target views of 4k test-scenes and visualize the first three components in Fig. 8. Surprisingly," + } + ] + } + ], + "index": 42 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17303" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 89, + 226, + 239 + ], + "blocks": [ + { + "bbox": [ + 59, + 89, + 226, + 239 + ], + "lines": [ + { + "bbox": [ + 59, + 89, + 226, + 239 + ], + "spans": [ + { + "bbox": [ + 59, + 89, + 226, + 239 + ], + "type": "image", + "image_path": "6852fb8958ffc6ecdac97f5c5f26fd30727c4aa3fe391ef716f97952598b1d81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": "Figure 8. Latent pose investigations on SV - Left: Scatterplot showing the first three PCA components of the latent pose " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "\\tilde{p}" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " distribution for " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "12\\mathrm{k}" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " target views from 4k scenes. The color of each point indicates by which of the 6 cameras the image was taken, as shown on the color wheel. The first principal axis of these ellipsoids, marked by the long arrow, corresponds to movement along the street. Right: We found that specific linear directions in the latent space correspond to meaningful camera motions. Videos are provided in the supplementary material." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 83, + 332, + 227 + ], + "blocks": [ + { + "bbox": [ + 238, + 83, + 332, + 227 + ], + "lines": [ + { + "bbox": [ + 238, + 83, + 332, + 227 + ], + "spans": [ + { + "bbox": [ + 238, + 83, + 332, + 227 + ], + "type": "image", + "image_path": "5071d97be61d1f47e17112cf1573e0b525625cdb6cd581b733e7fdb35f18e5a4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 336, + 83, + 430, + 227 + ], + "blocks": [ + { + "bbox": [ + 336, + 83, + 430, + 227 + ], + "lines": [ + { + "bbox": [ + 336, + 83, + 430, + 227 + ], + "spans": [ + { + "bbox": [ + 336, + 83, + 430, + 227 + ], + "type": "image", + "image_path": "84baa1812ed037f6e9536c614d7b9c0b1c0458d870d47962477acf4cb91f5f30.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 434, + 83, + 528, + 227 + ], + "blocks": [ + { + "bbox": [ + 434, + 83, + 528, + 227 + ], + "lines": [ + { + "bbox": [ + 434, + 83, + 528, + 227 + ], + "spans": [ + { + "bbox": [ + 434, + 83, + 528, + 227 + ], + "type": "image", + "image_path": "75bfa47ced88f918b1a2ed67360777d5e2b2a625e40f4dc50971fa9914872458.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "type": "text", + "content": "we find only three (rather than six) ellipsoid clusters that each correspond to an opposing pair of cameras. This suggests that the model has learned to represent rotation in an absolute (scene-centric) coordinate frame with the direction of the street as a reference, and that opposing cameras are less well-distinguished due to the streets' approximate mirror symmetries, see Fig. 10 (appendix) for more details. We further find that movement along the street corresponds well to the long axis of these ellipsoids, which depending on the camera can correspond to either a forward/backward or a sideways motion in image space." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 453, + 288, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 288, + 596 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 288, + 596 + ], + "type": "text", + "content": "Traversals. In Fig. 8, we show linear latent pose traversals that correspond to movement along the street, pitch and tilt of the camera. We find that these dimensions are mapped into the pose space predictably, contiguously and smoothly. The correct parallax effect observed in the forward movement in particular demonstrates that the model has correctly estimated the depth of the scene. These results indicate that RUST can learn to capture the 3D structure of complex real-world scenes from a handful of images, without access to any pose information. The learned latent pose space covers the training distribution of camera poses and enables traversals and novel view synthesis within distribution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 122, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 122, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 122, + 621 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "RUST shares most strengths and limitations with other latent methods, especially with the SRT model [22] that it is based on. Resolution and quality of synthesized views do not reach the performance of NeRF [16], though it is important to note that NeRF does not yield latent scene representations, and it generally requires a large number of similar views of the scene. As has been demonstrated [22], even special-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 312, + 547, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 348 + ], + "type": "text", + "content": "ized NeRF variants for sparse input view settings [8] fail to produce meaningful results on the challenging SV dataset, despite having access to accurate pose information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 348, + 548, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 548, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 548, + 563 + ], + "type": "text", + "content": "As shown in Secs. 4.2 and 4.3, RUST learns to effectively model the camera pose distribution of the datasets it is trained on. While this is desirable in many applications, it can limit generalization of the model to new poses that lie outside of the original distribution. For example, we may not find latent poses for which RUST would render views that do not point at the center of the scene in MSN, or represent movement orthogonal to the street in SV. It is notable that all learned methods suffer from such limitations to varying degrees, including light field parametrizations [22] and even volumetric models, especially when given few input images [18]. Nonetheless, more explicit methods tend to generalize better to out-of-distribution poses due to hardcoded assumptions such as explicit camera parametrizations or the volumetric rendering equation. Finally, we empirically found RUST to show higher variance in terms of PSNR compared to SRT. Over independent training runs with 3 random seeds, we observed a standard error of 0.19." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "We propose RUST, a novel method for latent neural scene representation learning that can be trained without any explicit pose information. RUST matches the quality of prior methods that require pose information while scaling to very complex real-world scenes. We further demonstrate that the model learns meaningful latent pose spaces that afford smooth 3D motion within the distribution of camera poses in the training data. 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In CVPR, 2018. 13" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "17306" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_content_list.json b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a49cd6ca2e93643f1c60c70e5d51956c6b9e9238 --- /dev/null +++ b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_content_list.json @@ -0,0 +1,2029 @@ +[ + { + "type": "text", + "text": "RWSC-Fusion: Region-Wise Style-Controlled Fusion Network for the Prohibited X-ray Security Image Synthesis", + "text_level": 1, + "bbox": [ + 122, + 137, + 919, + 177 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Luwen Duan $^{1,2}$ Min Wu $^{1}$ Lijian Mao $^{1}$ Jun Yin $^{1}$ Jianping Xiong $^{1*}$ Xi Li $^{2*}$", + "bbox": [ + 156, + 200, + 865, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Zhejiang Dahua Technology Co., Ltd., $^{2}$ Zhejiang University", + "bbox": [ + 226, + 218, + 749, + 235 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 268, + 263, + 346, + 278 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic prohibited item detection in security inspection X-ray images is necessary for transportation. The abundance and diversity of the X-ray security images with prohibited item, termed as prohibited X-ray security images, are essential for training the detection model. In order to solve the data insufficiency, we propose a Region-Wise Style-Controlled Fusion (RWSC-Fusion) network, which superimposes the prohibited items onto the normal X-ray security images, to synthesize the prohibited X-ray security images. The proposed RWSC-Fusion innovates both network structure and loss functions to generate more realistic X-ray security images. Specifically, a RWSC-Fusion module is designed to enable the region-wise fusion by controlling the appearance of the overlapping region with novel modulation parameters. In addition, an Edge-Attention (EA) module is proposed to effectively improve the sharpness of the synthetic images. As for the unsupervised loss function, we propose the Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD), to optimize the fused X-ray security images in terms of luminance and saturation. We evaluate the authenticity and the training effect of the synthetic X-ray security images on private and public SIXray dataset. The results confirm that our synthetic images are reliable enough to augment the prohibited X-ray security images.", + "bbox": [ + 110, + 293, + 502, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 112, + 655, + 243, + 668 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "X-ray imagery security inspection is a fundamental part in station/airport, for detecting prohibited items in baggage or suitcase images.", + "bbox": [ + 110, + 673, + 500, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, computer vision methods particularly deep learning [15, 33] have brought benefits to prohibited item detection [1, 16, 18, 25, 37]. The performance of these automated detection models relies heavily on a mass of annotated images. However, real X-ray security images usually are arduous and time-consuming to collect, and the occurrence rate of prohibited items is very low. Moreover, very few of public X-ray security image datasets contain large amounts of prohibited items. Existing datasets are", + "bbox": [ + 110, + 714, + 500, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Original baggage", + "bbox": [ + 546, + 275, + 606, + 285 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92c1ecd982a2388ca1da1534236755a219c251565f1d4170e968f57bb585f788.jpg", + "image_caption": [ + "Prohibited items" + ], + "image_footnote": [], + "bbox": [ + 613, + 267, + 687, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0ed3566f5043cba9025a1ba490c797804fcde93d7fd2acd90791061becbfe31f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 695, + 269, + 757, + 307 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/463d726f4b1981b1dd8e1d01d062fab885d241e4165a26222adfafb6b1b5baae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 268, + 831, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1a948a7d8e6321f7d03776d6d8236b85bbd1f2766e4d78d8aed87102eb82f0e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 843, + 268, + 917, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f8f43abfb9168ddbfbab2373a5e68f802c7517431d58bb22ac9a7bdcd82b145f.jpg", + "image_caption": [ + "II" + ], + "image_footnote": [], + "bbox": [ + 638, + 316, + 660, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6cfce0a2a4d11eb21d501fb6b8a6cb5caa96ced032fdbade154582fbf7c42bff.jpg", + "image_caption": [ + "1" + ], + "image_footnote": [], + "bbox": [ + 712, + 316, + 736, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5231baeae6b7f5c7b003b58529e331ac0edbea461084e3f0e7f55b19cec86774.jpg", + "image_caption": [ + "II" + ], + "image_footnote": [], + "bbox": [ + 794, + 316, + 808, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ea7bfdbdd15f260b74a7cccdd2aef93c20cf9902b1f63b697144615e2574f8e.jpg", + "image_caption": [ + "1" + ], + "image_footnote": [], + "bbox": [ + 873, + 316, + 889, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/01e6232e756f97b3fd7b20cf8d62a348a1c98349699df92446c65c6b999f2685.jpg", + "image_caption": [ + "Synthesized image" + ], + "image_footnote": [], + "bbox": [ + 613, + 360, + 687, + 403 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4b02f379f944a4212f86c76a0c781380da0e213cb90e916c898300a091775516.jpg", + "image_caption": [ + "Figure 1. Our RWSC-Fusion allows to superimpose prohibited items onto baggage images, to synthesize prohibited X-ray images. The composite prohibited items are marked with red box." + ], + "image_footnote": [], + "bbox": [ + 695, + 360, + 757, + 403 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb5dc5a937ec3b547a1d3d818377affadc1114d519862e16e5874d68498491f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 360, + 831, + 403 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5d9c133da100fd39912dbb803e7449ec711f6389397fd6bf997678bcbfc2d7f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 843, + 361, + 917, + 403 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mainly: (1) GDXray: The GDXray dataset [24] contains only three kinds of prohibited items: guns, shurikens, and razor blades. Besides, GDXray only involves grayscale images where backgrounds are too simple to conform with the real color X-ray security images; (2) OPIXray: The OPIXray dataset [36], which is especially designed for the cutter detection, contains 8885 synthetic X-ray security images with five kinds of cutters, and most images contain only one cutter; (3) SIXray: The SIXray dataset [26] contains 1, 059, 231 X-ray security images, but only 8929 images include prohibited items: guns, knives, wrenches, pliers, scissors, and hammers. Given the above, existing public datasets haven't been up to the standard of training.", + "bbox": [ + 537, + 458, + 927, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome the lack of training samples, traditional offline enhancement strategies such as rotation, re-scaling and mixing are applied to the augmentation of training samples [32, 42]. However, unlike natural images and other X-ray scans, X-ray security images usually involve randomly stacked objects [6, 11, 12, 22]. In addition, according to the imaging principle of X-ray security, objects overlap with each other in a translucent state, and appear differently for different materials and thickness. These traditional augmentation methods cannot improve the diversity and complexity for the inter-occlusion between prohibited items [31]. Therefore, it is very necessary to synthesize realistic X-ray security images, so as to enrich the prohibited items in pose, scale and position.", + "bbox": [ + 537, + 632, + 927, + 818 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A few researchers studied to directly generate prohibited", + "bbox": [ + 554, + 818, + 927, + 832 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 8, + 171, + 45 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 228, + 5, + 816, + 19 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 317, + 20, + 731, + 33 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 285, + 34, + 759, + 48 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: xilizju@zju.edu.cn, xiongp362204@163.com", + "bbox": [ + 112, + 845, + 489, + 859 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22398", + "bbox": [ + 465, + 883, + 504, + 894 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "X-ray security images by learning deep synthesis models. Inspired by the success of GANs in image synthesis [10, 34], Zhao et al. proposed X-ray Image-Synthesis-GAN [41] to generate the prohibited items from a noise region on the background images. Li et al. [17] synthesized the X-ray security images from the semantic label maps based on GANs. Yang et al. [40] enhanced the training of GANs to learn higher-quality X-ray security images. However, they synthesized only one prohibited item rather than stacked and overlapped ones in one image, which thus are not realistic enough for the complex X-ray security images in a real-world scenario. Isaac-Medina et al. [14] used the paired X-ray energy maps (high, low, effective-Z maps) to synthesize the pseudo-color images which however only served as a small amount of testing samples. Bhowmik et al. [3] developed a Synthetically Composed (SC) data augmentation strategy based on the Threat Image Projection (TIP) method [8], to fuse the prohibited items with the baggage images for generating images with stacked and cluttered prohibited items. However, the SC need adjust the parameters for each image to meet the various colors of different materials, and thus lacks automation, robustness and versatility.", + "bbox": [ + 110, + 124, + 504, + 430 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to synthesize the prohibited X-ray security images automatically, we propose a color X-ray security images fusion model, to superimpose the prohibited items onto baggage or suitcase images, as shown in Figure 1. In this way, we synthesize prohibited X-ray security images and obtain annotation automatically, thus avoiding the collection of the annotated prohibited X-ray security images for training the prohibited item detection model.", + "bbox": [ + 110, + 430, + 500, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The experimental results prove the advantage of our fusion model over other fusion methods in the field of X-ray security image. In addition, we also compare the prohibited item detection model trained with real and synthetic images. The results verify that our synthetic images are efficient to supplement the prohibited X-ray security images in downstream detection task.", + "bbox": [ + 110, + 537, + 502, + 629 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of our work are as follows:", + "bbox": [ + 129, + 630, + 468, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. We propose an unsupervised color X-ray security image fusion model. Due to the imaging particularity, existing fusion loss functions are inapplicable to X-ray security images. We design Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD) based on the principle of X-ray imaging and Threat image projection (TIP). The LL and CSD optimize the comprehensive luminance-saturation fusion between the foreground item and background image. Thus, we extend TIP to composite color X-ray security images.", + "bbox": [ + 110, + 643, + 500, + 775 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. We propose a Region-Wise Style-Controlled Fusion module, to control the fused appearance by learning the shifting and scaling modulation parameters pertinently. Moreover, the RWSC-Fusion module can adaptively modulate the local region of interest, i.e., the overlapping region of the prohibited items and baggage images.", + "bbox": [ + 110, + 776, + 502, + 857 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3. We develop an Edge-Attention module, which inhibits irrelevant information and enhances texture information, to improve the sharpness of generated images.", + "4. Our RWSC-Fusion and Edge-Attention modules are both universal and plug-and-play to other image fusion or synthesis models for generating high-quality images." + ], + "bbox": [ + 537, + 124, + 927, + 205 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 537, + 219, + 680, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Threat Image Projection", + "text_level": 1, + "bbox": [ + 537, + 248, + 766, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Plenty of prohibited X-ray security images are the precondition for automatic prohibited item detection models [27, 35]. However, prohibited items are a very small minority on X-ray security images in a real-world scenario. Therefore, threat image projection (TIP) method has been proposed to increase the occurrence of prohibited items [29]. TIP is a process that superimposes isolated prohibited items onto normal images, thus generating composite, yet realistic prohibited X-ray security images.", + "bbox": [ + 537, + 269, + 927, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The X-ray penetrates through objects to form X-ray image. The image intensity is related to the X-ray energy, object material, object thickness [21], simply expressed as:", + "bbox": [ + 537, + 388, + 927, + 429 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nI = I _ {0} e ^ {- \\mu h} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 685, + 432, + 922, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $I_0$ is the X-ray beam intensity, $\\mu$ is the absorption coefficient and $h$ is the thickness of the objects.", + "bbox": [ + 537, + 455, + 927, + 481 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accordingly, the prohibited item X-ray image $I_{f}$ , and background image $I_{b}$ , e.g. a baggage, can be expressed as:", + "bbox": [ + 537, + 482, + 927, + 511 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nI _ {f} = I _ {0} e ^ {- \\mu_ {f} h _ {f}}, \\quad I _ {b} = I _ {0} e ^ {- \\mu_ {b} h _ {b}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 514, + 924, + 533 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mu_{f}$ and $\\mu_{b}$ are the respective absorption coefficients, $h_f$ and $h_b$ are the respective thickness.", + "bbox": [ + 537, + 539, + 927, + 570 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When superimposing the prohibited items $I_{f}$ onto the baggage image $I_{b}$ , the fused X-ray image $I_{fb}$ could be:", + "bbox": [ + 537, + 571, + 927, + 601 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nI _ {f b} = I _ {0} e ^ {- \\mu_ {f} h _ {f} - \\mu_ {b} h _ {b}} = I _ {0} e ^ {- \\mu_ {f} h _ {f}} e ^ {- \\mu_ {b} h _ {b}} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 605, + 924, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thus, we can get:", + "bbox": [ + 556, + 630, + 677, + 643 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nI _ {f b} = \\frac {I _ {f} \\cdot I _ {b}}{I _ {0}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 673, + 644, + 924, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, the prohibited item can be projected into baggage images through multiplication, which is just the principle of TIP. Rogers et al. [30] applied TIP and exploit the approximate multiplicative property of X-ray imagery, to project threat items onto cargo transmission images. Mery et al. [23] replaced the multiplication with the addition of logarithmic, giving access to linear strategy for superimposing the prohibited items onto images. The TIP is almost exclusively applicable to grayscale X- ray images. However, X-ray security images in a real-world scenario are mostly rendered with pseudo-color. In this work, we will extend TIP principle to color X-ray images, to develop a prohibited X-ray security images synthesis model.", + "bbox": [ + 537, + 680, + 929, + 854 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22399", + "bbox": [ + 465, + 883, + 505, + 894 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/446eac864415596bd551580ea2d6e7b6fc57fdbddd9e39960c0499950c035c98.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed RWSC-Fusion." + ], + "image_footnote": [], + "bbox": [ + 218, + 123, + 828, + 250 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ad5c3bd015f9bd887327dbbed07261bbf8d47ed6f7c0c2117686678dd499f626.jpg", + "image_caption": [ + "Figure 3. EA-Dense Block with Edge-Attention module." + ], + "image_footnote": [], + "bbox": [ + 213, + 275, + 425, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Color X-ray Security Images Rendering", + "text_level": 1, + "bbox": [ + 112, + 491, + 458, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As mentioned above, real X-ray security images are rendered with pseudo-colors according to certain rules [5]. The most common rule is based on the three components: Hue (H), Saturation (S) and Value (V) in the HSV color space, which approximates the way human perceives and interprets color. First, the H component of pseudo-color is assigned according to the material category of the object, which depends on the dual energy responses. e.g., organic materials are usually shown in red, inorganic materials are in blue, and mixtures are in green. Next, the V component of the three is a normalized nonlinear mapping, while the S component is mostly correlated linearly with the single energy or dual energy responses. As a consequence, the colors of objects in X-ray security image (see examples in the supplementary material), vary differently according to the materials, thickness, viewpoint and background.", + "bbox": [ + 110, + 512, + 502, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Related work", + "text_level": 1, + "bbox": [ + 112, + 740, + 252, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of RWSC-Fusion is shown in Figure 2. The prohibited item image (foreground: $I_{f}$ ) and baggage image (background: $I_{b}$ ) are inputted separately into two branches, and are reconstructed through convolution layers and Edge-Attention Dense (EA-Dense) blocks to be $\\tilde{I}_{f}$ and $\\tilde{I}_{b}$ respectively. They share weights in parallel to encode respective features $F_{f}$ and $F_{b}$ . The two encoding features", + "bbox": [ + 110, + 758, + 500, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are inputted together into a RWSC-Fusion module, which fuses the two in a region-wise style-controlled manner, and then are reconstructed to be the composite image $I_{fb}$ .", + "bbox": [ + 537, + 278, + 929, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Edge-Attention Dense Block", + "text_level": 1, + "bbox": [ + 537, + 335, + 794, + 350 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Edge-Attention Dense (EA-Dense) block in our RWSC-Fusion is shown in Figure 3(a). The dense block is composed of four convolutional blocks, each taking the feature maps of all preceding blocks as input. To reinforce the information representation, we design and add an Edge-Attention (EA) module (shown in Figure 3(b)) into the top convolutional block before flowing into subsequent blocks.", + "bbox": [ + 537, + 356, + 927, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the low-level feature $F$ of the top block, we first employ $3 \\times 3$ average pooling layer with the stride of 1 to obtain the local mean feature. We subtract the local mean feature maps from the original feature maps to explore the structural texture, similar to Laplacian sharpening which is robust to noise for edge information extraction. Next, we calculate the mean responses along the channel dimension to reduce the channel number to 1, and obtain the edge-aware activation map $w$ by using the sigmoid function. At last, the edge-enhanced feature $\\widetilde{F}$ are acquired through the multiplication between the weight $w$ and feature $F$ . The whole process of EA module can be expressed as:", + "bbox": [ + 537, + 450, + 929, + 609 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw = \\sigma (M (\\left| A P 2 D (F) - F \\right|)) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 614, + 927, + 632 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {F} = _ {W} \\odot F \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 673, + 637, + 927, + 653 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $AP2D$ denotes 2D average pooling, $M$ denotes the mean value along the channel dimension, $\\sigma$ denotes the sigmoid activation, $\\odot$ denotes pixel-wise multiplication.", + "bbox": [ + 537, + 656, + 927, + 697 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the weight $w$ can activate and enhance the edge and texture information through sharpening operation, the resulting feature $\\widetilde{F}$ take advantage of both global and local texture information of the feature $F$ . Therefore, in our EA-Dense block, each convolutional block takes as input the feature of all preceding block and the edge-enhanced feature $\\widetilde{F}$ , and thus sharpen the image quality.", + "bbox": [ + 537, + 699, + 929, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Region-Wise Style-Controlled Fusion Module", + "text_level": 1, + "bbox": [ + 537, + 808, + 927, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Common image fusion methods usually fuse the features of two source images in a simple manner, such as addition,", + "bbox": [ + 537, + 829, + 929, + 857 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22400", + "bbox": [ + 465, + 883, + 505, + 895 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a21b9d8073ab04d71fd29fbc62c517e5f7595472ef29a9752c2893a7471f396.jpg", + "image_caption": [ + "Figure 4. Details of mask average pooling layer." + ], + "image_footnote": [], + "bbox": [ + 144, + 120, + 475, + 225 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ecb45371fd9e6ab703bfb075cd6619d69cbda043b2e699484304cfff5441fe4f.jpg", + "image_caption": [ + "Figure 5. Details of RWSC-Fusion module." + ], + "image_footnote": [], + "bbox": [ + 115, + 250, + 505, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "maximum or concatenation. However, for the fusion of the prohibited item and the baggage image, we focus more on the appearance fusion of the overlapping region rather than the global information fusion. Therefore, we propose a RWSC-Fusion module to fuse the features of prohibited item $F_{f}$ and the baggage image $F_{b}$ in a region-wise style-controlled manner. The RWSC-Fusion module modulates the appearance of the overlapping region between the two images by applying region-wise normalization.", + "bbox": [ + 110, + 413, + 500, + 533 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The traditional region-wise normalization [28] is:", + "bbox": [ + 129, + 533, + 457, + 548 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma_ {c, h, w} \\left(\\frac {b _ {n , c , h , w} - \\mu_ {c} (x)}{\\sigma_ {c} (x)}\\right) + \\beta_ {c, h, w} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 208, + 552, + 500, + 586 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{c,h,w}$ and $\\beta_{c,h,w}$ represent pixel-wise scaling and shifting parameters. Some researchers [7] learn $\\gamma_{c,h,w}$ and $\\beta_{c,h,w}$ from the style maps by using mask average pooling, which is shown in Figure 4. However, such parameters have less potential for realizing rich and fine style-control.", + "bbox": [ + 110, + 592, + 500, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By contrast, the region-wise normalization in RWSC-Fusion module innovate in two respects: (1) It learns the shifting and scaling parameters separately based on the mask average pooling and the deviation maps to modulate the mean and standard deviation; (2) It normalizes the local region adaptively with pixel-wise modulation parameters, to control the appearance of the region of interest.", + "bbox": [ + 110, + 667, + 500, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The RWSC-Fusion module is detailed in Figure 5. On one branch, the features $F_{f}$ and $F_{b}$ of two images are first sent jointly to one convolution layer. Then, the resulting features $F_{fb}$ with auxiliary mask of prohibited item are fed into the mask average pooling layer, where the average feature vectors are extracted and broadcast to create the mean maps $F_{fb}^{m}$ . Next, we subtract the mean maps $F_{fb}^{m}$ from", + "bbox": [ + 110, + 760, + 500, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the initial features $F_{fb}$ to get the local standard deviation maps $F_{fb}^{d}$ . Lastly, the deviation maps $F_{fb}^{d}$ and the mean maps $F_{fb}^{m}$ pass through two separate convolution layers to generate the pixel-wise scaling and shifting parameters $\\gamma_{c,h,w}^{fb}$ and $\\beta_{c,h,w}^{fb}$ . Meanwhile, on the other branch, we obtain parameters $\\gamma_{c,h,w}$ and $\\beta_{c,h,w}$ by doing the same operations on the feature $F_{b}$ of the single baggage image.", + "bbox": [ + 537, + 124, + 927, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We design the region-specific modulation parameters through the region-wise merging, and thus the final modulation parameters are expressed as:", + "bbox": [ + 537, + 233, + 927, + 273 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma_ {c, h, w} = M ^ {+} \\odot \\gamma_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\gamma_ {c, h, w} ^ {b} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 275, + 927, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {c, h, w} = M ^ {+} \\odot \\beta_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\beta_ {c, h, w} ^ {b} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 618, + 303, + 927, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M^{+}$ denotes the mask of prohibited item, while $1 - M^{+}$ denotes the complementary mask. The appearance of the overlapping region within the mask is modulated jointly by the prohibited item and baggage image, while the non-overlapping region is modulated by the single baggage image, avoiding the interference of prohibited item image.", + "bbox": [ + 537, + 325, + 927, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our region-adaptive normalization learns appropriate shifting and scaling parameters separately based on the mean maps and the deviation maps instead of single mask mean maps, so as to modulate the mean and standard deviation specifically and pointedly. Thus, it allows for fine control to generate rich stylization by considering the local information from the deviation maps. Hence, the RWSC-Fusion module enables the region-wise normal-appearing fusion of the prohibited item and baggage image to synthesize the prohibited X-ray security image.", + "bbox": [ + 537, + 407, + 927, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Loss Function", + "text_level": 1, + "bbox": [ + 539, + 554, + 685, + 567 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing unsupervised image fusion models usually maximize the similarity of fused image with source images instead of ground-truth, by using loss function as follows:", + "bbox": [ + 537, + 575, + 927, + 615 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = 1 - \\left[ w _ {1} \\bullet \\ell \\left(x _ {1}, y\\right) + w _ {2} \\bullet \\ell \\left(x _ {2}, y\\right) \\right] \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 623, + 619, + 931, + 634 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\ell(x, y)$ denotes the similarity metrics, such as SSD or SSIM. The weights $w_1$ and $w_2$ represent the information preservation degree of two source images. However, these functions are inapplicable to X-ray security image, for two reasons: (1) they produce global fusion, including the non-overlapping region, which instead should remain intact; (2) the addition strategy of these functions does not conform to the attenuation character of X-ray security imagery.", + "bbox": [ + 537, + 639, + 927, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As mentioned in Sec.2.1, when fusing the prohibited items $I_{f}$ with the baggage image $I_{b}$ by using the weights $w_{1}$ and $w_{2}$ , the fused X-ray image $I_{fb}$ could be:", + "bbox": [ + 537, + 746, + 927, + 789 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {f b} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f} - w _ {2} \\mu_ {b} h _ {b}} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f}} e ^ {- w _ {2} \\mu_ {b} h _ {b}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 794, + 924, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {f b} = \\frac {I _ {f} ^ {w _ {1}} \\cdot I _ {b} ^ {w _ {2}}}{I _ {0} ^ {w _ {1} + w _ {2} - 1}} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 657, + 818, + 924, + 850 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22401", + "bbox": [ + 465, + 883, + 502, + 894 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/6013f30057bc03f874d97be28a81be2a2814ebcf3613f3178c87809a8cf5d3e0.jpg", + "table_caption": [ + "Table 1. Quantitative evaluations for image quality of the models with and without the EA modules." + ], + "table_footnote": [], + "table_body": "
Modelwithout EA modulewith EA module
MAE2.0911.938
PSNR38.40239.084
", + "bbox": [ + 112, + 147, + 500, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the fused X-ray image $I_{fb}$ is approximatively correlated with the multiplication rather than addition of the prohibited item $I_{f}$ and the baggage image $I_{b}$ .", + "bbox": [ + 110, + 196, + 502, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this case, we adjust Eq. (10) by using the logarithmic form, giving access to multiplication relationship in linear form. Finally, we develop a Luminance loss in Logarithmic form $(LL)\\mathcal{L}_{LL}$ as follows:", + "bbox": [ + 110, + 239, + 500, + 294 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L L} = 1 - \\left[ w _ {1} \\bullet \\log \\ell \\left(I _ {f}, I _ {f b}\\right) + w _ {2} \\bullet \\log \\ell \\left(I _ {b}, I _ {f b}\\right) \\right] \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 296, + 500, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We put $w_{1}$ and $w_{2}$ inside the metric formula to develop a new similarity metric $\\ell(x, y, w)$ , and thus $\\mathcal{L}_{LL}$ turns into:", + "bbox": [ + 112, + 323, + 502, + 351 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L L} = 1 - \\left[ \\log \\ell \\left(I _ {f}, I _ {f b}, w _ {1}\\right) + \\log \\ell \\left(I _ {b}, I _ {f b}, w _ {2}\\right) \\right] \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 149, + 353, + 500, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\ell (x,y,w) = \\frac{2\\mu_x\\mu_y + \\varepsilon}{\\mu_x^{4w} + \\mu_y^2 + \\varepsilon}$ , and thus the local mean of", + "bbox": [ + 112, + 382, + 502, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "fused image $\\mu_{fb}$ is expected to converge to $\\mu_f^{w_1} \\cdot \\mu_b^{w_2}$ . The details and deduce are in the supplementary materials.", + "bbox": [ + 112, + 417, + 500, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We automatically estimate the weights $w_{1}$ and $w_{2}$ from the feature of R, G and B component of the prohibited item and the baggage image respectively, to get different power weights $w_{1}$ and $w_{2}$ for R, G and B component, and the sum of $w_{1}$ and $w_{2}$ is adjusted to 2.", + "bbox": [ + 110, + 449, + 500, + 514 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the other hand, considering that the saturation $(S)$ component of color X-ray security image is mostly correlated linearly with the energy responses, we assume that the $S$ component of the fused image is correlated linearly with the multiplication of the $S$ component of the two images. Therefore, the difference between the $S$ component of the prohibited item $(S_{f})$ and the fused image $(S_{fb})$ comes almost from the $S$ component of the baggage image $(S_{b})$ . Similarly, the difference between the $S_{b}$ and $S_{fb}$ comes almost from $S_{f}$ . We develop an another loss term Correlation Loss of Saturation Difference (CSD) $\\mathcal{L}_{CSD}$ :", + "bbox": [ + 112, + 514, + 502, + 668 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D _ {b} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {f}\\right) \\\\ D _ {f} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {b}\\right) (15) \\\\ \\mathcal {L} _ {C S D} = 1 - \\left[ C C \\left(D _ {f}, 1 - S _ {f}\\right) + C C \\left(D _ {b}, 1 - S _ {b}\\right) \\right] / 2 (16) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 134, + 669, + 500, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $CC$ is the normalized correlation coefficient.", + "bbox": [ + 112, + 731, + 453, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, a third loss term is the reconstruction loss $\\mathcal{L}_{\\text{recon}}$ of two source images $\\tilde{I}_f$ and $\\tilde{I}_b$ as follows:", + "bbox": [ + 112, + 744, + 500, + 772 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} = \\left\\| I _ {f}, \\tilde {I} _ {f} \\right\\| + \\left\\| I _ {b}, \\tilde {I} _ {b} \\right\\| \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 775, + 500, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In conclusion, the total loss function is:", + "bbox": [ + 129, + 799, + 393, + 812 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {L L} + \\mathcal {L} _ {C S D} + \\mathcal {L} _ {\\text {r e c o n}} \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 816, + 500, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment Results", + "text_level": 1, + "bbox": [ + 539, + 126, + 734, + 141 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 539, + 155, + 642, + 168 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Private data: We have collected millions of X-ray security images from urban rail transit, railway, highway and other real-world daily security inspection scenario. There are more than 40 kinds of manually-annotated prohibited items.", + "bbox": [ + 537, + 175, + 929, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Public data: The SIXray dataset [26] and OPIXray dataset [36], which have been introduced in Sec.1.", + "bbox": [ + 539, + 230, + 927, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 539, + 269, + 757, + 285 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training data are 12000 groups randomly composed by 12000 baggage images and 60 individual prohibited items of 15 categories. During training, all baggage images are resized to a resolution of $256 \\times 256$ , and all prohibited item images are randomly padded with [255,255,255] to share the same size. It is important to note that the random padding of the prohibited item images is regulated by utilizing the activation maps of the baggage images, in order to enable realistic and appropriate location of the prohibited item in the internal region of the baggage.", + "bbox": [ + 537, + 291, + 927, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 539, + 439, + 692, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3.1. Edge-Attention module", + "text_level": 1, + "bbox": [ + 542, + 458, + 752, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to the sparse texture of X-ray security images and the information loss in deep neural network, the generated images often suffer from low sharpness. We design EA module in the dense blocks to extract and recover the texture information for the fused image. In this section, we evaluate the efficacy of the proposed EA module.", + "bbox": [ + 537, + 473, + 927, + 552 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We quantitatively calculate the reconstruction loss of the non-overlapping regions between 6000 pairs of the fused images and the source images in terms of the Mean Absolute Error (MAE) and Peak Signal to-Noise Ratio (PSNR). The lower the MAE and the higher the PSNR, the closer the non-overlapping regions is to the source image and the higher the quality of fused images. The results are shown in Table 1. The model with EA modules produces lower MAE and higher PSNR than that without the EA modules. It indicates that the EA modules can effectively preserve the source information more completely in the resulting non-overlapping regions and improve the definition and sharpness of the synthesized images.", + "bbox": [ + 537, + 552, + 927, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We visualize the synthesized images from the models with and without the EA modules in Figure 6. Comparing the regions within the purple ROI which are magnified into view at the top-right corner, the X-ray security images generated by the model without EA modules are blurred and miss details, such as the zipper in the second row and the shoe sole texture in the fourth row. On the contrast, the model with EA modules can activate and enhance texture and edge information by using the attention map shown in Figure 7. Thus it can alleviate the shortage of texture and", + "bbox": [ + 537, + 726, + 927, + 859 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22402", + "bbox": [ + 465, + 883, + 505, + 895 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c902eb39c0d3237d4ead70513276f7eab1b69cd954475fbd36606bcfb24a16f9.jpg", + "image_caption": [ + "Figure 6. The generated images from the models with and without the EA modules. From left to right are: (a) original baggage image; (b) the synthesized images from the model without EA modules; (c) the synthesized images from the model with EA modules." + ], + "image_footnote": [], + "bbox": [ + 147, + 122, + 463, + 405 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3eee46c9f4c0fbdf74ec6a49d2791b08423cedb67c44d781ed115a96c193509a.jpg", + "image_caption": [ + "Figure 7. The edge attention maps of the X-ray security images in Figure 6. The first row shows the original images, and the second row shows the edge attention maps extracted by the EA module." + ], + "image_footnote": [], + "bbox": [ + 117, + 464, + 495, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "offer clearer appearance. It further follows that the EA module can indeed provide high-quality images with sharp textures via the Edge Attention mechanism.", + "bbox": [ + 112, + 667, + 502, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.2. Region-wise normalization", + "text_level": 1, + "bbox": [ + 112, + 720, + 346, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Existing region-adaptive normalization methods learn the shifting and scaling parameters both based on the mask mean maps [7, 28]. On the contrast, we learn the shifting and scaling parameters separately based on the mask mean maps and deviation maps, so as to modulate the mean and standard deviation pointedly. In this section, we evaluate the efficacy of our normalization mechanism.", + "bbox": [ + 112, + 734, + 500, + 826 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We visualize the generated X-ray security images from the fusion module with only mask average pooling layer", + "bbox": [ + 112, + 827, + 502, + 854 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/93ae644de86168c15f3c66298258655c3f42b40e4f813cf2a69dba7cd18ae8f3.jpg", + "image_caption": [ + "Figure 8. The generated images from the fusion module with only mask average pooling layer and our RWSC-Fusion module. From left to right are: (a) prohibited items; (b) original baggage image; (c) the synthesized images from the model with only mask average pooling layer; (d) the synthesized images from our model." + ], + "image_footnote": [], + "bbox": [ + 571, + 122, + 890, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and our RWSC-Fusion module in Figure 8. By comparing the prohibited items within the red ROI, the prohibited items synthesized by the model with only mask average pooling layer are fuzzy due to a lack of texture details, while the prohibited items from our model are more clear. It proves that our region-adaptive normalization method allows for fine control to provide rich stylization.", + "bbox": [ + 537, + 480, + 927, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 537, + 588, + 905, + 602 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare our RWSC-Fusion with four state-of-the-art image fusion methods: U2Fusion [38], FusionGAN [19], DeepFuse [13] and MEFNet [20], to evaluate the performance of X-ray security image fusion for the prohibited X-ray security image synthesis.", + "bbox": [ + 537, + 608, + 927, + 675 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The synthesized images from different methods are shown in Figure 9. It can be seen that compared with U2Fusion, FusionGAN and DeepFuse, RWSC-Fusion alleviates the problem of global fusion and successfully preserves the original appearance of the non-overlapping regions in the baggage images. The overlapping regions marked by the red box from the competitors, especially MEFNet, noticeably deviate from our desired appearance that can match the real X-ray security images in terms of hue, saturation and sharpness. Overall, our model achieves superior visual performance than these four competitors. These well demonstrate that our fusion model is better suited to the X-ray security image, and can synthesize more ideal and realistic prohibited X-ray security images.", + "bbox": [ + 537, + 675, + 929, + 863 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22403", + "bbox": [ + 465, + 883, + 504, + 895 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7f105d7316869ce7218fba506e1e1d9f3b4490da41690f7eccc4786e18ee9882.jpg", + "image_caption": [ + "Figure 9. The X-ray baggage images fused with the prohibited item by four other fusion methods and the proposed RWSC-Fusion." + ], + "image_footnote": [], + "bbox": [ + 184, + 123, + 836, + 338 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/827ee848f20a97b098940a105a37d5702bd3a2461863a5e40483c0fc4ffbcbc0.jpg", + "table_caption": [ + "Table 2. Quantitative comparison with state-of-the-art methods." + ], + "table_footnote": [], + "table_body": "
MetricQEQabfEIPSNR
U2Fusion [38]0.56350.346748.819016.7155
FusionGAN [19]0.56400.592478.093413.8471
DeepFuse [13]0.61570.181441.626616.8173
MEFNet [20]0.75090.609085.040317.7364
Ours0.83390.647281.380718.6455
", + "bbox": [ + 112, + 373, + 500, + 442 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The quantitative comparisons are performed on the 6000 image pairs. Four metrics, namely, QE [9], Qabf [39], Edge Intensity (EI) [2], and PSNR are used for evaluation. For all four metrics, larger values indicate better performance. The comparative results of four metrics are shown in Table 2. Our RWSC-Fusion ranks first on QE, Qabf and PSNR, proving that our method can synthesize images with richer textures and details. Although our RWSC-Fusion ranks second on EI, it also achieves comparable results. The promising outcomes show that our model keeps high fidelity with less distortion and noise.", + "bbox": [ + 110, + 455, + 500, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Supplement to Private Dataset", + "text_level": 1, + "bbox": [ + 112, + 615, + 384, + 630 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we synthesize the prohibited X-ray security images on our private dataset.", + "bbox": [ + 110, + 637, + 500, + 663 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "First, we conduct subjective evaluation experiment, which is detailed in the supplementary material. This result demonstrates that our synthetic prohibited X-ray security images are realistic enough to fool the inspectors.", + "bbox": [ + 110, + 664, + 500, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To analyze the efficacy of supplementing the training samples, we compare the performance of prohibited item detection model under the training of real and synthetic images. We use the YOLOv4 as the detector [4] to detect the five kinds of prohibited items: plastic bottles, cutters, scissors, thermos cups and glass bottles.", + "bbox": [ + 110, + 715, + 500, + 796 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The real training dataset contains 40000 samples (DataR: with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles). Besides, we train the detector with the following dataset: (1) DataR1/2: We remove 20000 samples from DataR,", + "bbox": [ + 110, + 796, + 500, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "resulting in 20000 training samples with 13127 plastic bottles, 17055 cutters, 5117 scissors, 2518 thermos cups and 8710 glass bottles.", + "bbox": [ + 566, + 362, + 927, + 401 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(2) DataRS: We synthesize and supplement the prohibited items into DataR1/2, resulting in 20000 samples with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles, with the same number of prohibited items as the DataR. (Note: since there are no extra 20000 negative samples excluding all five kinds of prohibited items, we cannot achieve the pure synthesis of 20000 samples, to be perfectly aligned with DataR)", + "(3) DataRS+: We synthesize prohibited items into other 20000 samples, and merge new synthetic samples with 20000 samples in DataR, resulting in 40000 samples with total 38983 plastic bottles, 51956 cutters, 15597 scissors, 7522 thermos cups and 26034 glass bottles." + ], + "bbox": [ + 539, + 401, + 927, + 587 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The detection results on the 9954 testing samples of YOLOv4 trained with above datasets are listed in Table 3.", + "bbox": [ + 539, + 587, + 927, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As compared with DataR1/2, the DataRS provides a considerable increase of more than $3\\%$ in mAP after we synthesize prohibited items in DataR1/2. This proves that our synthetic prohibited items are indeed beneficial to training the detection model. Moreover, since the results of DataRS can be comparable with or even better than those of DataR, it demonstrates the authenticity and reliability of our synthetic prohibited items for replacing the real ones. Accordingly, with the addition and the contribution of synthetic prohibited items, DataRS+ also has a remarkable advantage over DataR.", + "bbox": [ + 537, + 614, + 927, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Supplement to SIXray and OPIXray Dataset", + "text_level": 1, + "bbox": [ + 537, + 775, + 919, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we evaluate on public SIXray [26] and OPIXray dataset [36]. We fuse our private prohibited items with the negative samples in SIXray and OPIXray dataset. Moreover, we directly apply the model trained by our private dataset without any additional parameter tuning.", + "bbox": [ + 537, + 796, + 927, + 863 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22404", + "bbox": [ + 465, + 883, + 504, + 894 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b2a282c4e699f116564ca1ddf5a05294f74f7a14ef77cdd458d2f1ec0e15ad2.jpg", + "table_caption": [ + "Table 3 Detection results of YOLOv4 trained with different data on private dataset (recall and precision at confidence level of 0.5)." + ], + "table_footnote": [], + "table_body": "
Training DataDataRDataR1/2DataRSDataRS+
Plastic bottleRecall69.4964.8270.4674.15
Precision85.3683.2988.1485.13
AP69.5071.1671.0076.97
CutterRecall86.1774.0481.7084.50
Precision92.6287.6091.8193.45
AP86.9679.9883.4987.70
ScissorRecall71.2258.0370.8772.97
Precision90.6089.3488.3788.23
AP74.2866.8172.8378.29
Therm os cupRecall88.8688.8691.5992.76
Precision93.5290.1391.3892.54
AP85.5286.1788.9890.25
Glass bottleRecall56.4948.7458.7158.82
Precision86.7980.9784.0288.15
AP56.3153.7658.1361.87
mAP74.5271.5874.8879.02
", + "bbox": [ + 114, + 149, + 507, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For SIXRay dataset, it contains six kinds of prohibited items. We don't use the hammer class since it involves merely 60 samples. The SIXRay10 dataset contains 13412 testing samples, and 74960 training samples (SIXR:7496 positive samples with 4322 guns, 2758 knives, 2816 wrenches, 4624 pliers and 918 scissors). Moreover, we also train YOLOv4 by using following 74960 training samples:", + "bbox": [ + 110, + 351, + 500, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(1) SIXR1/2: We remove half the (3748) positive samples from SIXR, and supplement the other 3748 negative samples into SIXR.", + "bbox": [ + 112, + 445, + 500, + 485 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(2) SIXRS: We synthesize the prohibited items into the newly-added 3748 negative samples in SIXR1/2, to supplement the positive samples, resulting in mixed 7496 true/pseudo positive samples with the same number of prohibited items as SIXR.", + "bbox": [ + 112, + 485, + 500, + 552 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(3) SIXRS+: We synthesize prohibited items into other new 3748 negative samples, and replace 3748 negative samples in the SIXR, resulting in mixed 11244 true/pseudo positive samples, with 6469 guns, 4154 knives, 4195 wrenches, 6933 pliers and 1398 scissors.", + "bbox": [ + 112, + 552, + 500, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For OPIXray dataset, it contains 7109 training and 1776 testing images for cutter detection. The training datasets are: (1) OPIR: All the original 7109 images; (2) OPIRS: 3555 images supplemented with synthesized cutter, with the same number of cutter as OPIR; (3) OPIRS+: 7109 images supplemented with half the synthesized cutter.", + "bbox": [ + 110, + 619, + 502, + 697 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The detection results on SIXray and OPIXray dataset are respectively listed in Table 4 and Table 5.", + "bbox": [ + 110, + 699, + 500, + 725 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By comparing the models trained by SIXRS and SIXR1/2, SIXRS recover the degraded performance of SIXR1/2 by supplementing the synthetic positive samples effectively. Moreover, compared to SIXR, SIXRS can achieve higher mAP, and overall higher AP except for the scissor class. The comparison of OPIRS and OPIR also well verifies that our synthetic cutters are real enough to supplement the missing samples. The SIXRS achieves higher precision but lower recall for the scissor class, because our private scissor item database does not cover", + "bbox": [ + 110, + 725, + 500, + 858 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1864128a4a621b4834632a417b4e4f0191660db871af183fcd2e3fa155cd4a70.jpg", + "table_caption": [ + "Table 4 Detection results of YOLOv4 trained with different data on SIXray dataset." + ], + "table_footnote": [], + "table_body": "
Training DataSIXRSIXR1/2SIXRSSIXRS+
GunRecall79.7373.0283.2383.69
Precision96.3291.7697.3397.17
AP78.7175.2182.1982.74
KnifeRecall58.8845.6264.1766.04
Precision92.6586.3992.7993.39
AP62.8447.8866.6469.17
WrenchRecall55.9724.2559.3366.04
Precision87.7260.7583.6883.49
AP65.9326.3066.8268.88
PlierRecall66.3550.0771.4576.14
Precision85.4972.3486.8185.16
AP74.2057.6375.8479.53
ScissorRecall63.6225.7052.8067.76
Precision91.1666.2791.8785.80
AP72.1139.0862.9473.60
mAP70.7649.2270.8974.78
", + "bbox": [ + 539, + 149, + 927, + 340 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/70f86669a2033318214b8a270530c875ff400f4687dd18f147df565a53dac1ea.jpg", + "table_caption": [ + "Table 5 Detection results of different training data on OPIXray." + ], + "table_footnote": [], + "table_body": "
Training dataOPIXray dataset
RecallPrecisionAP
OPIR71.0875.8567.47
OPIRS71.1476.6072.20
OPIRS+80.4690.1384.80
", + "bbox": [ + 544, + 365, + 921, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "all the scissor type of SIXRay dataset, such as nail clipper set, to simulate the SIXRay samples. The recall and AP of the scissor class could be improved furthermore if the prohibited items that are more similar to SIXRay dataset are used for fusion. The comparison results between the SIXR and SIXRS+, OPIR and OPIRS+ also both can indicate that our synthetic positive images are beneficial in augmenting the training dataset to further improve the performance of the detection model.", + "bbox": [ + 537, + 434, + 929, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 537, + 569, + 658, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a RWSC-Fusion model, which fuses the prohibited items with baggage image in a Region-Wise Style-Controlled manner, for synthesizing the prohibited X-ray security images. The RWSC-Fusion learns the fused X-ray security images unsupervisedly based on novel loss functions: LL and CSD. Moreover, to generate more high-quality realistic and images, we innovate style-controlled mechanism and Edge-Attention module. The ablation studies verify the efficacy of the RWSC-Fusion and Edge-Attention module in achieving superior perceptual quality. The comparative experimental results illustrate that our method outperforms the state-of-the-arts in the field of X-ray security image. The performance comparison of the detector training demonstrates the authenticity and reliability of the synthetic images in promoting downstream tasks. In future work, we will generalize RWSC-Fusion to solve multiple fusion problems.", + "bbox": [ + 537, + 588, + 927, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by Zhejiang Dahua Technology Co., Ltd. and Zhejiang University.", + "bbox": [ + 537, + 828, + 927, + 854 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22405", + "bbox": [ + 465, + 883, + 504, + 895 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 114, + 126, + 208, + 139 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samet Akcay, Toby P. Breckon. Towards Automatic Threat Detection: A Survey of Advances of Deep Learning within X-ray Security Imaging. Pattern Recognition, 2022.", + "[2] Rajalingam Balakrishnan, Rainy Priya, Hybrid multimodality medical image fusion technique for feature enhancement in medical diagnosis, Int. J. Eng. Sci. 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In Proceedings of European Conference on Computer Vision (ECCV), 2016." + ], + "bbox": [ + 114, + 124, + 502, + 652 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22407", + "bbox": [ + 465, + 883, + 504, + 895 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_model.json b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..50261c588cc35e3b17fc1263f5189211ce503bb9 --- /dev/null +++ b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_model.json @@ -0,0 +1,2596 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.009, + 0.172, + 0.046 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.23, + 0.006, + 0.818, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.319, + 0.021, + 0.732, + 0.034 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.287, + 0.035, + 0.761, + 0.049 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.138, + 0.92, + 0.178 + ], + "angle": 0, + "content": "RWSC-Fusion: Region-Wise Style-Controlled Fusion Network for the Prohibited X-ray Security Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.201, + 0.866, + 0.219 + ], + "angle": 0, + "content": "Luwen Duan\\(^{1,2}\\) Min Wu\\(^{1}\\) Lijian Mao\\(^{1}\\) Jun Yin\\(^{1}\\) Jianping Xiong\\(^{1*}\\) Xi Li\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.219, + 0.75, + 0.236 + ], + "angle": 0, + "content": "\\(^{1}\\)Zhejiang Dahua Technology Co., Ltd., \\(^{2}\\)Zhejiang University" + }, + { + "type": "title", + "bbox": [ + 0.269, + 0.264, + 0.347, + 0.279 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.294, + 0.504, + 0.641 + ], + "angle": 0, + "content": "Automatic prohibited item detection in security inspection X-ray images is necessary for transportation. The abundance and diversity of the X-ray security images with prohibited item, termed as prohibited X-ray security images, are essential for training the detection model. In order to solve the data insufficiency, we propose a Region-Wise Style-Controlled Fusion (RWSC-Fusion) network, which superimposes the prohibited items onto the normal X-ray security images, to synthesize the prohibited X-ray security images. The proposed RWSC-Fusion innovates both network structure and loss functions to generate more realistic X-ray security images. Specifically, a RWSC-Fusion module is designed to enable the region-wise fusion by controlling the appearance of the overlapping region with novel modulation parameters. In addition, an Edge-Attention (EA) module is proposed to effectively improve the sharpness of the synthetic images. As for the unsupervised loss function, we propose the Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD), to optimize the fused X-ray security images in terms of luminance and saturation. We evaluate the authenticity and the training effect of the synthetic X-ray security images on private and public SIXray dataset. The results confirm that our synthetic images are reliable enough to augment the prohibited X-ray security images." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.656, + 0.245, + 0.669 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.674, + 0.501, + 0.715 + ], + "angle": 0, + "content": "X-ray imagery security inspection is a fundamental part in station/airport, for detecting prohibited items in baggage or suitcase images." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.715, + 0.502, + 0.835 + ], + "angle": 0, + "content": "Recently, computer vision methods particularly deep learning [15, 33] have brought benefits to prohibited item detection [1, 16, 18, 25, 37]. The performance of these automated detection models relies heavily on a mass of annotated images. However, real X-ray security images usually are arduous and time-consuming to collect, and the occurrence rate of prohibited items is very low. Moreover, very few of public X-ray security image datasets contain large amounts of prohibited items. Existing datasets are" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.277, + 0.608, + 0.286 + ], + "angle": 0, + "content": "Original baggage" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.268, + 0.688, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.27, + 0.759, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.269, + 0.833, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.845, + 0.269, + 0.919, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.331, + 0.604, + 0.339 + ], + "angle": 0, + "content": "Prohibited items" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.317, + 0.661, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.646, + 0.346, + 0.658, + 0.355 + ], + "angle": 0, + "content": "II" + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.317, + 0.737, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.346, + 0.731, + 0.355 + ], + "angle": 0, + "content": "1" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.317, + 0.809, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.346, + 0.807, + 0.355 + ], + "angle": 0, + "content": "II" + }, + { + "type": "image", + "bbox": [ + 0.875, + 0.317, + 0.89, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.875, + 0.346, + 0.885, + 0.355 + ], + "angle": 0, + "content": "1" + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.38, + 0.607, + 0.388 + ], + "angle": 0, + "content": "Synthesized image" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.361, + 0.688, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.361, + 0.759, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.361, + 0.833, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.845, + 0.362, + 0.919, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.41, + 0.928, + 0.448 + ], + "angle": 0, + "content": "Figure 1. Our RWSC-Fusion allows to superimpose prohibited items onto baggage images, to synthesize prohibited X-ray images. The composite prohibited items are marked with red box." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.459, + 0.929, + 0.633 + ], + "angle": 0, + "content": "mainly: (1) GDXray: The GDXray dataset [24] contains only three kinds of prohibited items: guns, shurikens, and razor blades. Besides, GDXray only involves grayscale images where backgrounds are too simple to conform with the real color X-ray security images; (2) OPIXray: The OPIXray dataset [36], which is especially designed for the cutter detection, contains 8885 synthetic X-ray security images with five kinds of cutters, and most images contain only one cutter; (3) SIXray: The SIXray dataset [26] contains 1, 059, 231 X-ray security images, but only 8929 images include prohibited items: guns, knives, wrenches, pliers, scissors, and hammers. Given the above, existing public datasets haven't been up to the standard of training." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.633, + 0.929, + 0.819 + ], + "angle": 0, + "content": "To overcome the lack of training samples, traditional offline enhancement strategies such as rotation, re-scaling and mixing are applied to the augmentation of training samples [32, 42]. However, unlike natural images and other X-ray scans, X-ray security images usually involve randomly stacked objects [6, 11, 12, 22]. In addition, according to the imaging principle of X-ray security, objects overlap with each other in a translucent state, and appear differently for different materials and thickness. These traditional augmentation methods cannot improve the diversity and complexity for the inter-occlusion between prohibited items [31]. Therefore, it is very necessary to synthesize realistic X-ray security images, so as to enrich the prohibited items in pose, scale and position." + }, + { + "type": "text", + "bbox": [ + 0.556, + 0.819, + 0.928, + 0.833 + ], + "angle": 0, + "content": "A few researchers studied to directly generate prohibited" + }, + { + "type": "page_footnote", + "bbox": [ + 0.113, + 0.846, + 0.49, + 0.86 + ], + "angle": 0, + "content": "*Corresponding author: xilizju@zju.edu.cn, xiongp362204@163.com" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.505, + 0.895 + ], + "angle": 0, + "content": "22398" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.125, + 0.505, + 0.431 + ], + "angle": 0, + "content": "X-ray security images by learning deep synthesis models. Inspired by the success of GANs in image synthesis [10, 34], Zhao et al. proposed X-ray Image-Synthesis-GAN [41] to generate the prohibited items from a noise region on the background images. Li et al. [17] synthesized the X-ray security images from the semantic label maps based on GANs. Yang et al. [40] enhanced the training of GANs to learn higher-quality X-ray security images. However, they synthesized only one prohibited item rather than stacked and overlapped ones in one image, which thus are not realistic enough for the complex X-ray security images in a real-world scenario. Isaac-Medina et al. [14] used the paired X-ray energy maps (high, low, effective-Z maps) to synthesize the pseudo-color images which however only served as a small amount of testing samples. Bhowmik et al. [3] developed a Synthetically Composed (SC) data augmentation strategy based on the Threat Image Projection (TIP) method [8], to fuse the prohibited items with the baggage images for generating images with stacked and cluttered prohibited items. However, the SC need adjust the parameters for each image to meet the various colors of different materials, and thus lacks automation, robustness and versatility." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.431, + 0.502, + 0.538 + ], + "angle": 0, + "content": "In order to synthesize the prohibited X-ray security images automatically, we propose a color X-ray security images fusion model, to superimpose the prohibited items onto baggage or suitcase images, as shown in Figure 1. In this way, we synthesize prohibited X-ray security images and obtain annotation automatically, thus avoiding the collection of the annotated prohibited X-ray security images for training the prohibited item detection model." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.538, + 0.504, + 0.63 + ], + "angle": 0, + "content": "The experimental results prove the advantage of our fusion model over other fusion methods in the field of X-ray security image. In addition, we also compare the prohibited item detection model trained with real and synthetic images. The results verify that our synthetic images are efficient to supplement the prohibited X-ray security images in downstream detection task." + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.631, + 0.47, + 0.643 + ], + "angle": 0, + "content": "The main contributions of our work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.644, + 0.502, + 0.776 + ], + "angle": 0, + "content": "1. We propose an unsupervised color X-ray security image fusion model. Due to the imaging particularity, existing fusion loss functions are inapplicable to X-ray security images. We design Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD) based on the principle of X-ray imaging and Threat image projection (TIP). The LL and CSD optimize the comprehensive luminance-saturation fusion between the foreground item and background image. Thus, we extend TIP to composite color X-ray security images." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.777, + 0.503, + 0.858 + ], + "angle": 0, + "content": "2. We propose a Region-Wise Style-Controlled Fusion module, to control the fused appearance by learning the shifting and scaling modulation parameters pertinently. Moreover, the RWSC-Fusion module can adaptively modulate the local region of interest, i.e., the overlapping region of the prohibited items and baggage images." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.125, + 0.928, + 0.165 + ], + "angle": 0, + "content": "3. We develop an Edge-Attention module, which inhibits irrelevant information and enhances texture information, to improve the sharpness of generated images." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.165, + 0.928, + 0.206 + ], + "angle": 0, + "content": "4. Our RWSC-Fusion and Edge-Attention modules are both universal and plug-and-play to other image fusion or synthesis models for generating high-quality images." + }, + { + "type": "list", + "bbox": [ + 0.538, + 0.125, + 0.928, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.22, + 0.681, + 0.235 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.249, + 0.768, + 0.264 + ], + "angle": 0, + "content": "2.1. Threat Image Projection" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.27, + 0.929, + 0.39 + ], + "angle": 0, + "content": "Plenty of prohibited X-ray security images are the precondition for automatic prohibited item detection models [27, 35]. However, prohibited items are a very small minority on X-ray security images in a real-world scenario. Therefore, threat image projection (TIP) method has been proposed to increase the occurrence of prohibited items [29]. TIP is a process that superimposes isolated prohibited items onto normal images, thus generating composite, yet realistic prohibited X-ray security images." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.39, + 0.928, + 0.43 + ], + "angle": 0, + "content": "The X-ray penetrates through objects to form X-ray image. The image intensity is related to the X-ray energy, object material, object thickness [21], simply expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.687, + 0.434, + 0.923, + 0.451 + ], + "angle": 0, + "content": "\\[\nI = I _ {0} e ^ {- \\mu h} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.456, + 0.928, + 0.482 + ], + "angle": 0, + "content": "where \\(I_0\\) is the X-ray beam intensity, \\(\\mu\\) is the absorption coefficient and \\(h\\) is the thickness of the objects." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.483, + 0.928, + 0.512 + ], + "angle": 0, + "content": "Accordingly, the prohibited item X-ray image \\(I_{f}\\), and background image \\(I_{b}\\), e.g. a baggage, can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.515, + 0.925, + 0.535 + ], + "angle": 0, + "content": "\\[\nI _ {f} = I _ {0} e ^ {- \\mu_ {f} h _ {f}}, \\quad I _ {b} = I _ {0} e ^ {- \\mu_ {b} h _ {b}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.54, + 0.928, + 0.571 + ], + "angle": 0, + "content": "where \\(\\mu_{f}\\) and \\(\\mu_{b}\\) are the respective absorption coefficients, \\(h_f\\) and \\(h_b\\) are the respective thickness." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.572, + 0.929, + 0.602 + ], + "angle": 0, + "content": "When superimposing the prohibited items \\( I_{f} \\) onto the baggage image \\( I_{b} \\), the fused X-ray image \\( I_{fb} \\) could be:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.606, + 0.926, + 0.626 + ], + "angle": 0, + "content": "\\[\nI _ {f b} = I _ {0} e ^ {- \\mu_ {f} h _ {f} - \\mu_ {b} h _ {b}} = I _ {0} e ^ {- \\mu_ {f} h _ {f}} e ^ {- \\mu_ {b} h _ {b}} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.557, + 0.631, + 0.678, + 0.644 + ], + "angle": 0, + "content": "Thus, we can get:" + }, + { + "type": "equation", + "bbox": [ + 0.674, + 0.645, + 0.925, + 0.68 + ], + "angle": 0, + "content": "\\[\nI _ {f b} = \\frac {I _ {f} \\cdot I _ {b}}{I _ {0}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.681, + 0.93, + 0.855 + ], + "angle": 0, + "content": "Therefore, the prohibited item can be projected into baggage images through multiplication, which is just the principle of TIP. Rogers et al. [30] applied TIP and exploit the approximate multiplicative property of X-ray imagery, to project threat items onto cargo transmission images. Mery et al. [23] replaced the multiplication with the addition of logarithmic, giving access to linear strategy for superimposing the prohibited items onto images. The TIP is almost exclusively applicable to grayscale X- ray images. However, X-ray security images in a real-world scenario are mostly rendered with pseudo-color. In this work, we will extend TIP principle to color X-ray images, to develop a prohibited X-ray security images synthesis model." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.506, + 0.895 + ], + "angle": 0, + "content": "22399" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.219, + 0.124, + 0.829, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.363, + 0.254, + 0.673, + 0.267 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed RWSC-Fusion." + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.277, + 0.426, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.465, + 0.466, + 0.479 + ], + "angle": 0, + "content": "Figure 3. EA-Dense Block with Edge-Attention module." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.492, + 0.459, + 0.508 + ], + "angle": 0, + "content": "2.2. Color X-ray Security Images Rendering" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.513, + 0.504, + 0.727 + ], + "angle": 0, + "content": "As mentioned above, real X-ray security images are rendered with pseudo-colors according to certain rules [5]. The most common rule is based on the three components: Hue (H), Saturation (S) and Value (V) in the HSV color space, which approximates the way human perceives and interprets color. First, the H component of pseudo-color is assigned according to the material category of the object, which depends on the dual energy responses. e.g., organic materials are usually shown in red, inorganic materials are in blue, and mixtures are in green. Next, the V component of the three is a normalized nonlinear mapping, while the S component is mostly correlated linearly with the single energy or dual energy responses. As a consequence, the colors of objects in X-ray security image (see examples in the supplementary material), vary differently according to the materials, thickness, viewpoint and background." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.741, + 0.253, + 0.755 + ], + "angle": 0, + "content": "3. Related work" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.759, + 0.502, + 0.86 + ], + "angle": 0, + "content": "The overview of RWSC-Fusion is shown in Figure 2. The prohibited item image (foreground: \\( I_{f} \\)) and baggage image (background: \\( I_{b} \\)) are inputted separately into two branches, and are reconstructed through convolution layers and Edge-Attention Dense (EA-Dense) blocks to be \\( \\tilde{I}_{f} \\) and \\( \\tilde{I}_{b} \\) respectively. They share weights in parallel to encode respective features \\( F_{f} \\) and \\( F_{b} \\). The two encoding features" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.279, + 0.93, + 0.322 + ], + "angle": 0, + "content": "are inputted together into a RWSC-Fusion module, which fuses the two in a region-wise style-controlled manner, and then are reconstructed to be the composite image \\( I_{fb} \\)." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.336, + 0.796, + 0.351 + ], + "angle": 0, + "content": "3.1. Edge-Attention Dense Block" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.357, + 0.929, + 0.45 + ], + "angle": 0, + "content": "The Edge-Attention Dense (EA-Dense) block in our RWSC-Fusion is shown in Figure 3(a). The dense block is composed of four convolutional blocks, each taking the feature maps of all preceding blocks as input. To reinforce the information representation, we design and add an Edge-Attention (EA) module (shown in Figure 3(b)) into the top convolutional block before flowing into subsequent blocks." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.451, + 0.93, + 0.611 + ], + "angle": 0, + "content": "Given the low-level feature \\( F \\) of the top block, we first employ \\( 3 \\times 3 \\) average pooling layer with the stride of 1 to obtain the local mean feature. We subtract the local mean feature maps from the original feature maps to explore the structural texture, similar to Laplacian sharpening which is robust to noise for edge information extraction. Next, we calculate the mean responses along the channel dimension to reduce the channel number to 1, and obtain the edge-aware activation map \\( w \\) by using the sigmoid function. At last, the edge-enhanced feature \\( \\widetilde{F} \\) are acquired through the multiplication between the weight \\( w \\) and feature \\( F \\). The whole process of EA module can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.615, + 0.929, + 0.633 + ], + "angle": 0, + "content": "\\[\nw = \\sigma (M (\\left| A P 2 D (F) - F \\right|)) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.675, + 0.638, + 0.929, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\tilde {F} = _ {W} \\odot F \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.657, + 0.928, + 0.699 + ], + "angle": 0, + "content": "where \\(AP2D\\) denotes 2D average pooling, \\(M\\) denotes the mean value along the channel dimension, \\(\\sigma\\) denotes the sigmoid activation, \\(\\odot\\) denotes pixel-wise multiplication." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.7, + 0.931, + 0.796 + ], + "angle": 0, + "content": "Since the weight \\( w \\) can activate and enhance the edge and texture information through sharpening operation, the resulting feature \\( \\widetilde{F} \\) take advantage of both global and local texture information of the feature \\( F \\). Therefore, in our EA-Dense block, each convolutional block takes as input the feature of all preceding block and the edge-enhanced feature \\( \\widetilde{F} \\), and thus sharpen the image quality." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.809, + 0.928, + 0.825 + ], + "angle": 0, + "content": "3.2. Region-Wise Style-Controlled Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.83, + 0.93, + 0.858 + ], + "angle": 0, + "content": "Common image fusion methods usually fuse the features of two source images in a simple manner, such as addition," + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.506, + 0.896 + ], + "angle": 0, + "content": "22400" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.146, + 0.121, + 0.476, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.228, + 0.446, + 0.241 + ], + "angle": 0, + "content": "Figure 4. Details of mask average pooling layer." + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.251, + 0.506, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.389, + 0.419, + 0.402 + ], + "angle": 0, + "content": "Figure 5. Details of RWSC-Fusion module." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.414, + 0.502, + 0.535 + ], + "angle": 0, + "content": "maximum or concatenation. However, for the fusion of the prohibited item and the baggage image, we focus more on the appearance fusion of the overlapping region rather than the global information fusion. Therefore, we propose a RWSC-Fusion module to fuse the features of prohibited item \\( F_{f} \\) and the baggage image \\( F_{b} \\) in a region-wise style-controlled manner. The RWSC-Fusion module modulates the appearance of the overlapping region between the two images by applying region-wise normalization." + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.535, + 0.458, + 0.549 + ], + "angle": 0, + "content": "The traditional region-wise normalization [28] is:" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.553, + 0.502, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\gamma_ {c, h, w} \\left(\\frac {b _ {n , c , h , w} - \\mu_ {c} (x)}{\\sigma_ {c} (x)}\\right) + \\beta_ {c, h, w} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.593, + 0.501, + 0.667 + ], + "angle": 0, + "content": "where \\(\\gamma_{c,h,w}\\) and \\(\\beta_{c,h,w}\\) represent pixel-wise scaling and shifting parameters. Some researchers [7] learn \\(\\gamma_{c,h,w}\\) and \\(\\beta_{c,h,w}\\) from the style maps by using mask average pooling, which is shown in Figure 4. However, such parameters have less potential for realizing rich and fine style-control." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.668, + 0.501, + 0.761 + ], + "angle": 0, + "content": "By contrast, the region-wise normalization in RWSC-Fusion module innovate in two respects: (1) It learns the shifting and scaling parameters separately based on the mask average pooling and the deviation maps to modulate the mean and standard deviation; (2) It normalizes the local region adaptively with pixel-wise modulation parameters, to control the appearance of the region of interest." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.761, + 0.502, + 0.859 + ], + "angle": 0, + "content": "The RWSC-Fusion module is detailed in Figure 5. On one branch, the features \\( F_{f} \\) and \\( F_{b} \\) of two images are first sent jointly to one convolution layer. Then, the resulting features \\( F_{fb} \\) with auxiliary mask of prohibited item are fed into the mask average pooling layer, where the average feature vectors are extracted and broadcast to create the mean maps \\( F_{fb}^{m} \\). Next, we subtract the mean maps \\( F_{fb}^{m} \\) from" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.125, + 0.928, + 0.234 + ], + "angle": 0, + "content": "the initial features \\(F_{fb}\\) to get the local standard deviation maps \\(F_{fb}^{d}\\). Lastly, the deviation maps \\(F_{fb}^{d}\\) and the mean maps \\(F_{fb}^{m}\\) pass through two separate convolution layers to generate the pixel-wise scaling and shifting parameters \\(\\gamma_{c,h,w}^{fb}\\) and \\(\\beta_{c,h,w}^{fb}\\). Meanwhile, on the other branch, we obtain parameters \\(\\gamma_{c,h,w}\\) and \\(\\beta_{c,h,w}\\) by doing the same operations on the feature \\(F_{b}\\) of the single baggage image." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.234, + 0.928, + 0.274 + ], + "angle": 0, + "content": "We design the region-specific modulation parameters through the region-wise merging, and thus the final modulation parameters are expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.277, + 0.928, + 0.295 + ], + "angle": 0, + "content": "\\[\n\\gamma_ {c, h, w} = M ^ {+} \\odot \\gamma_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\gamma_ {c, h, w} ^ {b} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.304, + 0.928, + 0.321 + ], + "angle": 0, + "content": "\\[\n\\beta_ {c, h, w} = M ^ {+} \\odot \\beta_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\beta_ {c, h, w} ^ {b} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.326, + 0.928, + 0.407 + ], + "angle": 0, + "content": "where \\(M^{+}\\) denotes the mask of prohibited item, while \\(1 - M^{+}\\) denotes the complementary mask. The appearance of the overlapping region within the mask is modulated jointly by the prohibited item and baggage image, while the non-overlapping region is modulated by the single baggage image, avoiding the interference of prohibited item image." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.408, + 0.928, + 0.541 + ], + "angle": 0, + "content": "Our region-adaptive normalization learns appropriate shifting and scaling parameters separately based on the mean maps and the deviation maps instead of single mask mean maps, so as to modulate the mean and standard deviation specifically and pointedly. Thus, it allows for fine control to generate rich stylization by considering the local information from the deviation maps. Hence, the RWSC-Fusion module enables the region-wise normal-appearing fusion of the prohibited item and baggage image to synthesize the prohibited X-ray security image." + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.555, + 0.686, + 0.568 + ], + "angle": 0, + "content": "3.3. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.576, + 0.928, + 0.616 + ], + "angle": 0, + "content": "Existing unsupervised image fusion models usually maximize the similarity of fused image with source images instead of ground-truth, by using loss function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.62, + 0.932, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = 1 - \\left[ w _ {1} \\bullet \\ell \\left(x _ {1}, y\\right) + w _ {2} \\bullet \\ell \\left(x _ {2}, y\\right) \\right] \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.64, + 0.928, + 0.747 + ], + "angle": 0, + "content": "where \\(\\ell(x, y)\\) denotes the similarity metrics, such as SSD or SSIM. The weights \\(w_1\\) and \\(w_2\\) represent the information preservation degree of two source images. However, these functions are inapplicable to X-ray security image, for two reasons: (1) they produce global fusion, including the non-overlapping region, which instead should remain intact; (2) the addition strategy of these functions does not conform to the attenuation character of X-ray security imagery." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.747, + 0.928, + 0.79 + ], + "angle": 0, + "content": "As mentioned in Sec.2.1, when fusing the prohibited items \\( I_{f} \\) with the baggage image \\( I_{b} \\) by using the weights \\( w_{1} \\) and \\( w_{2} \\), the fused X-ray image \\( I_{fb} \\) could be:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.795, + 0.925, + 0.815 + ], + "angle": 0, + "content": "\\[\nI _ {f b} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f} - w _ {2} \\mu_ {b} h _ {b}} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f}} e ^ {- w _ {2} \\mu_ {b} h _ {b}} \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.819, + 0.926, + 0.851 + ], + "angle": 0, + "content": "\\[\nI _ {f b} = \\frac {I _ {f} ^ {w _ {1}} \\cdot I _ {b} ^ {w _ {2}}}{I _ {0} ^ {w _ {1} + w _ {2} - 1}} \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.504, + 0.895 + ], + "angle": 0, + "content": "22401" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.125, + 0.502, + 0.147 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluations for image quality of the models with and without the EA modules." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.148, + 0.501, + 0.185 + ], + "angle": 0, + "content": "
Modelwithout EA modulewith EA module
MAE2.0911.938
PSNR38.40239.084
" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.197, + 0.503, + 0.24 + ], + "angle": 0, + "content": "Therefore, the fused X-ray image \\( I_{fb} \\) is approximatively correlated with the multiplication rather than addition of the prohibited item \\( I_{f} \\) and the baggage image \\( I_{b} \\)." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.24, + 0.502, + 0.295 + ], + "angle": 0, + "content": "In this case, we adjust Eq. (10) by using the logarithmic form, giving access to multiplication relationship in linear form. Finally, we develop a Luminance loss in Logarithmic form \\((LL)\\mathcal{L}_{LL}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.297, + 0.501, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L L} = 1 - \\left[ w _ {1} \\bullet \\log \\ell \\left(I _ {f}, I _ {f b}\\right) + w _ {2} \\bullet \\log \\ell \\left(I _ {b}, I _ {f b}\\right) \\right] \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.324, + 0.503, + 0.352 + ], + "angle": 0, + "content": "We put \\( w_{1} \\) and \\( w_{2} \\) inside the metric formula to develop a new similarity metric \\( \\ell(x, y, w) \\), and thus \\( \\mathcal{L}_{LL} \\) turns into:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.354, + 0.501, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L L} = 1 - \\left[ \\log \\ell \\left(I _ {f}, I _ {f b}, w _ {1}\\right) + \\log \\ell \\left(I _ {b}, I _ {f b}, w _ {2}\\right) \\right] \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.383, + 0.504, + 0.413 + ], + "angle": 0, + "content": "where \\(\\ell (x,y,w) = \\frac{2\\mu_x\\mu_y + \\varepsilon}{\\mu_x^{4w} + \\mu_y^2 + \\varepsilon}\\), and thus the local mean of" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.418, + 0.502, + 0.449 + ], + "angle": 0, + "content": "fused image \\(\\mu_{fb}\\) is expected to converge to \\(\\mu_f^{w_1} \\cdot \\mu_b^{w_2}\\). The details and deduce are in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.45, + 0.502, + 0.516 + ], + "angle": 0, + "content": "We automatically estimate the weights \\( w_{1} \\) and \\( w_{2} \\) from the feature of R, G and B component of the prohibited item and the baggage image respectively, to get different power weights \\( w_{1} \\) and \\( w_{2} \\) for R, G and B component, and the sum of \\( w_{1} \\) and \\( w_{2} \\) is adjusted to 2." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.516, + 0.504, + 0.669 + ], + "angle": 0, + "content": "On the other hand, considering that the saturation \\((S)\\) component of color X-ray security image is mostly correlated linearly with the energy responses, we assume that the \\(S\\) component of the fused image is correlated linearly with the multiplication of the \\(S\\) component of the two images. Therefore, the difference between the \\(S\\) component of the prohibited item \\((S_{f})\\) and the fused image \\((S_{fb})\\) comes almost from the \\(S\\) component of the baggage image \\((S_{b})\\). Similarly, the difference between the \\(S_{b}\\) and \\(S_{fb}\\) comes almost from \\(S_{f}\\). We develop an another loss term Correlation Loss of Saturation Difference (CSD) \\(\\mathcal{L}_{CSD}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.67, + 0.501, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D _ {b} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {f}\\right) \\\\ D _ {f} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {b}\\right) (15) \\\\ \\mathcal {L} _ {C S D} = 1 - \\left[ C C \\left(D _ {f}, 1 - S _ {f}\\right) + C C \\left(D _ {b}, 1 - S _ {b}\\right) \\right] / 2 (16) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.732, + 0.454, + 0.744 + ], + "angle": 0, + "content": "where \\( CC \\) is the normalized correlation coefficient." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.745, + 0.501, + 0.773 + ], + "angle": 0, + "content": "In addition, a third loss term is the reconstruction loss \\(\\mathcal{L}_{\\text{recon}}\\) of two source images \\(\\tilde{I}_f\\) and \\(\\tilde{I}_b\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.776, + 0.501, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c o n}} = \\left\\| I _ {f}, \\tilde {I} _ {f} \\right\\| + \\left\\| I _ {b}, \\tilde {I} _ {b} \\right\\| \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.8, + 0.394, + 0.813 + ], + "angle": 0, + "content": "In conclusion, the total loss function is:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.817, + 0.501, + 0.835 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {L L} + \\mathcal {L} _ {C S D} + \\mathcal {L} _ {\\text {r e c o n}} \\tag {18}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.127, + 0.735, + 0.142 + ], + "angle": 0, + "content": "4. Experiment Results" + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.156, + 0.643, + 0.169 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.176, + 0.93, + 0.23 + ], + "angle": 0, + "content": "Private data: We have collected millions of X-ray security images from urban rail transit, railway, highway and other real-world daily security inspection scenario. There are more than 40 kinds of manually-annotated prohibited items." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.231, + 0.929, + 0.257 + ], + "angle": 0, + "content": "Public data: The SIXray dataset [26] and OPIXray dataset [36], which have been introduced in Sec.1." + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.271, + 0.758, + 0.286 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.292, + 0.929, + 0.426 + ], + "angle": 0, + "content": "The training data are 12000 groups randomly composed by 12000 baggage images and 60 individual prohibited items of 15 categories. During training, all baggage images are resized to a resolution of \\(256 \\times 256\\), and all prohibited item images are randomly padded with [255,255,255] to share the same size. It is important to note that the random padding of the prohibited item images is regulated by utilizing the activation maps of the baggage images, in order to enable realistic and appropriate location of the prohibited item in the internal region of the baggage." + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.44, + 0.694, + 0.455 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.543, + 0.46, + 0.754, + 0.473 + ], + "angle": 0, + "content": "4.3.1. Edge-Attention module" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.474, + 0.928, + 0.553 + ], + "angle": 0, + "content": "Due to the sparse texture of X-ray security images and the information loss in deep neural network, the generated images often suffer from low sharpness. We design EA module in the dense blocks to extract and recover the texture information for the fused image. In this section, we evaluate the efficacy of the proposed EA module." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.553, + 0.929, + 0.727 + ], + "angle": 0, + "content": "We quantitatively calculate the reconstruction loss of the non-overlapping regions between 6000 pairs of the fused images and the source images in terms of the Mean Absolute Error (MAE) and Peak Signal to-Noise Ratio (PSNR). The lower the MAE and the higher the PSNR, the closer the non-overlapping regions is to the source image and the higher the quality of fused images. The results are shown in Table 1. The model with EA modules produces lower MAE and higher PSNR than that without the EA modules. It indicates that the EA modules can effectively preserve the source information more completely in the resulting non-overlapping regions and improve the definition and sharpness of the synthesized images." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.727, + 0.929, + 0.86 + ], + "angle": 0, + "content": "We visualize the synthesized images from the models with and without the EA modules in Figure 6. Comparing the regions within the purple ROI which are magnified into view at the top-right corner, the X-ray security images generated by the model without EA modules are blurred and miss details, such as the zipper in the second row and the shoe sole texture in the fourth row. On the contrast, the model with EA modules can activate and enhance texture and edge information by using the attention map shown in Figure 7. Thus it can alleviate the shortage of texture and" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.506, + 0.896 + ], + "angle": 0, + "content": "22402" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.149, + 0.123, + 0.465, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.408, + 0.505, + 0.457 + ], + "angle": 0, + "content": "Figure 6. The generated images from the models with and without the EA modules. From left to right are: (a) original baggage image; (b) the synthesized images from the model without EA modules; (c) the synthesized images from the model with EA modules." + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.465, + 0.496, + 0.619 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.62, + 0.501, + 0.656 + ], + "angle": 0, + "content": "Figure 7. The edge attention maps of the X-ray security images in Figure 6. The first row shows the original images, and the second row shows the edge attention maps extracted by the EA module." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.668, + 0.503, + 0.709 + ], + "angle": 0, + "content": "offer clearer appearance. It further follows that the EA module can indeed provide high-quality images with sharp textures via the Edge Attention mechanism." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.721, + 0.347, + 0.735 + ], + "angle": 0, + "content": "4.3.2. Region-wise normalization" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.735, + 0.501, + 0.827 + ], + "angle": 0, + "content": "Existing region-adaptive normalization methods learn the shifting and scaling parameters both based on the mask mean maps [7, 28]. On the contrast, we learn the shifting and scaling parameters separately based on the mask mean maps and deviation maps, so as to modulate the mean and standard deviation pointedly. In this section, we evaluate the efficacy of our normalization mechanism." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.828, + 0.503, + 0.855 + ], + "angle": 0, + "content": "We visualize the generated X-ray security images from the fusion module with only mask average pooling layer" + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.123, + 0.892, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.408, + 0.93, + 0.469 + ], + "angle": 0, + "content": "Figure 8. The generated images from the fusion module with only mask average pooling layer and our RWSC-Fusion module. From left to right are: (a) prohibited items; (b) original baggage image; (c) the synthesized images from the model with only mask average pooling layer; (d) the synthesized images from our model." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.481, + 0.929, + 0.575 + ], + "angle": 0, + "content": "and our RWSC-Fusion module in Figure 8. By comparing the prohibited items within the red ROI, the prohibited items synthesized by the model with only mask average pooling layer are fuzzy due to a lack of texture details, while the prohibited items from our model are more clear. It proves that our region-adaptive normalization method allows for fine control to provide rich stylization." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.589, + 0.907, + 0.604 + ], + "angle": 0, + "content": "4.4. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.609, + 0.928, + 0.676 + ], + "angle": 0, + "content": "In this section, we compare our RWSC-Fusion with four state-of-the-art image fusion methods: U2Fusion [38], FusionGAN [19], DeepFuse [13] and MEFNet [20], to evaluate the performance of X-ray security image fusion for the prohibited X-ray security image synthesis." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.676, + 0.93, + 0.864 + ], + "angle": 0, + "content": "The synthesized images from different methods are shown in Figure 9. It can be seen that compared with U2Fusion, FusionGAN and DeepFuse, RWSC-Fusion alleviates the problem of global fusion and successfully preserves the original appearance of the non-overlapping regions in the baggage images. The overlapping regions marked by the red box from the competitors, especially MEFNet, noticeably deviate from our desired appearance that can match the real X-ray security images in terms of hue, saturation and sharpness. Overall, our model achieves superior visual performance than these four competitors. These well demonstrate that our fusion model is better suited to the X-ray security image, and can synthesize more ideal and realistic prohibited X-ray security images." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.505, + 0.896 + ], + "angle": 0, + "content": "22403" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.186, + 0.124, + 0.837, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.339, + 0.888, + 0.352 + ], + "angle": 0, + "content": "Figure 9. The X-ray baggage images fused with the prohibited item by four other fusion methods and the proposed RWSC-Fusion." + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.363, + 0.492, + 0.374 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with state-of-the-art methods." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.374, + 0.501, + 0.443 + ], + "angle": 0, + "content": "
MetricQEQabfEIPSNR
U2Fusion [38]0.56350.346748.819016.7155
FusionGAN [19]0.56400.592478.093413.8471
DeepFuse [13]0.61570.181441.626616.8173
MEFNet [20]0.75090.609085.040317.7364
Ours0.83390.647281.380718.6455
" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.456, + 0.502, + 0.603 + ], + "angle": 0, + "content": "The quantitative comparisons are performed on the 6000 image pairs. Four metrics, namely, QE [9], Qabf [39], Edge Intensity (EI) [2], and PSNR are used for evaluation. For all four metrics, larger values indicate better performance. The comparative results of four metrics are shown in Table 2. Our RWSC-Fusion ranks first on QE, Qabf and PSNR, proving that our method can synthesize images with richer textures and details. Although our RWSC-Fusion ranks second on EI, it also achieves comparable results. The promising outcomes show that our model keeps high fidelity with less distortion and noise." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.617, + 0.385, + 0.631 + ], + "angle": 0, + "content": "4.5. Supplement to Private Dataset" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.638, + 0.501, + 0.664 + ], + "angle": 0, + "content": "In this section, we synthesize the prohibited X-ray security images on our private dataset." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.665, + 0.501, + 0.717 + ], + "angle": 0, + "content": "First, we conduct subjective evaluation experiment, which is detailed in the supplementary material. This result demonstrates that our synthetic prohibited X-ray security images are realistic enough to fool the inspectors." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.717, + 0.501, + 0.797 + ], + "angle": 0, + "content": "To analyze the efficacy of supplementing the training samples, we compare the performance of prohibited item detection model under the training of real and synthetic images. We use the YOLOv4 as the detector [4] to detect the five kinds of prohibited items: plastic bottles, cutters, scissors, thermos cups and glass bottles." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.797, + 0.502, + 0.864 + ], + "angle": 0, + "content": "The real training dataset contains 40000 samples (DataR: with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles). Besides, we train the detector with the following dataset: (1) DataR1/2: We remove 20000 samples from DataR," + }, + { + "type": "text", + "bbox": [ + 0.568, + 0.363, + 0.928, + 0.402 + ], + "angle": 0, + "content": "resulting in 20000 training samples with 13127 plastic bottles, 17055 cutters, 5117 scissors, 2518 thermos cups and 8710 glass bottles." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.402, + 0.929, + 0.522 + ], + "angle": 0, + "content": "(2) DataRS: We synthesize and supplement the prohibited items into DataR1/2, resulting in 20000 samples with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles, with the same number of prohibited items as the DataR. (Note: since there are no extra 20000 negative samples excluding all five kinds of prohibited items, we cannot achieve the pure synthesis of 20000 samples, to be perfectly aligned with DataR)" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.522, + 0.928, + 0.588 + ], + "angle": 0, + "content": "(3) DataRS+: We synthesize prohibited items into other 20000 samples, and merge new synthetic samples with 20000 samples in DataR, resulting in 40000 samples with total 38983 plastic bottles, 51956 cutters, 15597 scissors, 7522 thermos cups and 26034 glass bottles." + }, + { + "type": "list", + "bbox": [ + 0.54, + 0.402, + 0.929, + 0.588 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.588, + 0.929, + 0.614 + ], + "angle": 0, + "content": "The detection results on the 9954 testing samples of YOLOv4 trained with above datasets are listed in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.615, + 0.929, + 0.761 + ], + "angle": 0, + "content": "As compared with DataR1/2, the DataRS provides a considerable increase of more than \\(3\\%\\) in mAP after we synthesize prohibited items in DataR1/2. This proves that our synthetic prohibited items are indeed beneficial to training the detection model. Moreover, since the results of DataRS can be comparable with or even better than those of DataR, it demonstrates the authenticity and reliability of our synthetic prohibited items for replacing the real ones. Accordingly, with the addition and the contribution of synthetic prohibited items, DataRS+ also has a remarkable advantage over DataR." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.776, + 0.921, + 0.791 + ], + "angle": 0, + "content": "4.6. Supplement to SIXray and OPIXray Dataset" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.797, + 0.928, + 0.864 + ], + "angle": 0, + "content": "In this section, we evaluate on public SIXray [26] and OPIXray dataset [36]. We fuse our private prohibited items with the negative samples in SIXray and OPIXray dataset. Moreover, we directly apply the model trained by our private dataset without any additional parameter tuning." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.505, + 0.895 + ], + "angle": 0, + "content": "22404" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.125, + 0.501, + 0.148 + ], + "angle": 0, + "content": "Table 3 Detection results of YOLOv4 trained with different data on private dataset (recall and precision at confidence level of 0.5)." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.15, + 0.508, + 0.341 + ], + "angle": 0, + "content": "
Training DataDataRDataR1/2DataRSDataRS+
Plastic bottleRecall69.4964.8270.4674.15
Precision85.3683.2988.1485.13
AP69.5071.1671.0076.97
CutterRecall86.1774.0481.7084.50
Precision92.6287.6091.8193.45
AP86.9679.9883.4987.70
ScissorRecall71.2258.0370.8772.97
Precision90.6089.3488.3788.23
AP74.2866.8172.8378.29
Therm os cupRecall88.8688.8691.5992.76
Precision93.5290.1391.3892.54
AP85.5286.1788.9890.25
Glass bottleRecall56.4948.7458.7158.82
Precision86.7980.9784.0288.15
AP56.3153.7658.1361.87
mAP74.5271.5874.8879.02
" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.353, + 0.502, + 0.447 + ], + "angle": 0, + "content": "For SIXRay dataset, it contains six kinds of prohibited items. We don't use the hammer class since it involves merely 60 samples. The SIXRay10 dataset contains 13412 testing samples, and 74960 training samples (SIXR:7496 positive samples with 4322 guns, 2758 knives, 2816 wrenches, 4624 pliers and 918 scissors). Moreover, we also train YOLOv4 by using following 74960 training samples:" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.447, + 0.501, + 0.486 + ], + "angle": 0, + "content": "(1) SIXR1/2: We remove half the (3748) positive samples from SIXR, and supplement the other 3748 negative samples into SIXR." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.486, + 0.502, + 0.553 + ], + "angle": 0, + "content": "(2) SIXRS: We synthesize the prohibited items into the newly-added 3748 negative samples in SIXR1/2, to supplement the positive samples, resulting in mixed 7496 true/pseudo positive samples with the same number of prohibited items as SIXR." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.553, + 0.501, + 0.62 + ], + "angle": 0, + "content": "(3) SIXRS+: We synthesize prohibited items into other new 3748 negative samples, and replace 3748 negative samples in the SIXR, resulting in mixed 11244 true/pseudo positive samples, with 6469 guns, 4154 knives, 4195 wrenches, 6933 pliers and 1398 scissors." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.62, + 0.504, + 0.699 + ], + "angle": 0, + "content": "For OPIXray dataset, it contains 7109 training and 1776 testing images for cutter detection. The training datasets are: (1) OPIR: All the original 7109 images; (2) OPIRS: 3555 images supplemented with synthesized cutter, with the same number of cutter as OPIR; (3) OPIRS+: 7109 images supplemented with half the synthesized cutter." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.7, + 0.501, + 0.726 + ], + "angle": 0, + "content": "The detection results on SIXray and OPIXray dataset are respectively listed in Table 4 and Table 5." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.726, + 0.502, + 0.859 + ], + "angle": 0, + "content": "By comparing the models trained by SIXRS and SIXR1/2, SIXRS recover the degraded performance of SIXR1/2 by supplementing the synthetic positive samples effectively. Moreover, compared to SIXR, SIXRS can achieve higher mAP, and overall higher AP except for the scissor class. The comparison of OPIRS and OPIR also well verifies that our synthetic cutters are real enough to supplement the missing samples. The SIXRS achieves higher precision but lower recall for the scissor class, because our private scissor item database does not cover" + }, + { + "type": "table_caption", + "bbox": [ + 0.539, + 0.125, + 0.928, + 0.149 + ], + "angle": 0, + "content": "Table 4 Detection results of YOLOv4 trained with different data on SIXray dataset." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.15, + 0.929, + 0.341 + ], + "angle": 0, + "content": "
Training DataSIXRSIXR1/2SIXRSSIXRS+
GunRecall79.7373.0283.2383.69
Precision96.3291.7697.3397.17
AP78.7175.2182.1982.74
KnifeRecall58.8845.6264.1766.04
Precision92.6586.3992.7993.39
AP62.8447.8866.6469.17
WrenchRecall55.9724.2559.3366.04
Precision87.7260.7583.6883.49
AP65.9326.3066.8268.88
PlierRecall66.3550.0771.4576.14
Precision85.4972.3486.8185.16
AP74.2057.6375.8479.53
ScissorRecall63.6225.7052.8067.76
Precision91.1666.2791.8785.80
AP72.1139.0862.9473.60
mAP70.7649.2270.8974.78
" + }, + { + "type": "table_caption", + "bbox": [ + 0.541, + 0.354, + 0.92, + 0.366 + ], + "angle": 0, + "content": "Table 5 Detection results of different training data on OPIXray." + }, + { + "type": "table", + "bbox": [ + 0.546, + 0.366, + 0.922, + 0.423 + ], + "angle": 0, + "content": "
Training dataOPIXray dataset
RecallPrecisionAP
OPIR71.0875.8567.47
OPIRS71.1476.6072.20
OPIRS+80.4690.1384.80
" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.435, + 0.93, + 0.555 + ], + "angle": 0, + "content": "all the scissor type of SIXRay dataset, such as nail clipper set, to simulate the SIXRay samples. The recall and AP of the scissor class could be improved furthermore if the prohibited items that are more similar to SIXRay dataset are used for fusion. The comparison results between the SIXR and SIXRS+, OPIR and OPIRS+ also both can indicate that our synthetic positive images are beneficial in augmenting the training dataset to further improve the performance of the detection model." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.57, + 0.66, + 0.584 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.589, + 0.929, + 0.817 + ], + "angle": 0, + "content": "We propose a RWSC-Fusion model, which fuses the prohibited items with baggage image in a Region-Wise Style-Controlled manner, for synthesizing the prohibited X-ray security images. The RWSC-Fusion learns the fused X-ray security images unsupervisedly based on novel loss functions: LL and CSD. Moreover, to generate more high-quality realistic and images, we innovate style-controlled mechanism and Edge-Attention module. The ablation studies verify the efficacy of the RWSC-Fusion and Edge-Attention module in achieving superior perceptual quality. The comparative experimental results illustrate that our method outperforms the state-of-the-arts in the field of X-ray security image. The performance comparison of the detector training demonstrates the authenticity and reliability of the synthetic images in promoting downstream tasks. In future work, we will generalize RWSC-Fusion to solve multiple fusion problems." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.829, + 0.928, + 0.856 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by Zhejiang Dahua Technology Co., Ltd. and Zhejiang University." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.505, + 0.896 + ], + "angle": 0, + "content": "22405" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.115, + 0.127, + 0.21, + 0.14 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.116, + 0.146, + 0.502, + 0.182 + ], + "angle": 0, + "content": "[1] Samet Akcay, Toby P. Breckon. Towards Automatic Threat Detection: A Survey of Advances of Deep Learning within X-ray Security Imaging. 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In Proceedings of European Conference on Computer Vision (ECCV), 2016." + }, + { + "type": "list", + "bbox": [ + 0.115, + 0.125, + 0.504, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.884, + 0.505, + 0.896 + ], + "angle": 0, + "content": "22407" + } + ] +] \ No newline at end of file diff --git a/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_origin.pdf b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..29c9f1482b201a92d52ca0e60f5d8ce6986b1701 --- /dev/null +++ b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/4229304a-c9a9-4e95-92bc-4ee682221af2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1d63465e2d22c19d06bb18dfbf6913ddafaddea20343bfd8970ec1d3b1e5d1b0 +size 8151659 diff --git a/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/full.md b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..139661071a65859253f0d492ca2b5393bf6f4abe --- /dev/null +++ b/2023/RWSC-Fusion_ Region-Wise Style-Controlled Fusion Network for the Prohibited X-Ray Security Image Synthesis/full.md @@ -0,0 +1,404 @@ +# RWSC-Fusion: Region-Wise Style-Controlled Fusion Network for the Prohibited X-ray Security Image Synthesis + +Luwen Duan $^{1,2}$ Min Wu $^{1}$ Lijian Mao $^{1}$ Jun Yin $^{1}$ Jianping Xiong $^{1*}$ Xi Li $^{2*}$ + +$^{1}$ Zhejiang Dahua Technology Co., Ltd., $^{2}$ Zhejiang University + +# Abstract + +Automatic prohibited item detection in security inspection X-ray images is necessary for transportation. The abundance and diversity of the X-ray security images with prohibited item, termed as prohibited X-ray security images, are essential for training the detection model. In order to solve the data insufficiency, we propose a Region-Wise Style-Controlled Fusion (RWSC-Fusion) network, which superimposes the prohibited items onto the normal X-ray security images, to synthesize the prohibited X-ray security images. The proposed RWSC-Fusion innovates both network structure and loss functions to generate more realistic X-ray security images. Specifically, a RWSC-Fusion module is designed to enable the region-wise fusion by controlling the appearance of the overlapping region with novel modulation parameters. In addition, an Edge-Attention (EA) module is proposed to effectively improve the sharpness of the synthetic images. As for the unsupervised loss function, we propose the Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD), to optimize the fused X-ray security images in terms of luminance and saturation. We evaluate the authenticity and the training effect of the synthetic X-ray security images on private and public SIXray dataset. The results confirm that our synthetic images are reliable enough to augment the prohibited X-ray security images. + +# 1. Introduction + +X-ray imagery security inspection is a fundamental part in station/airport, for detecting prohibited items in baggage or suitcase images. + +Recently, computer vision methods particularly deep learning [15, 33] have brought benefits to prohibited item detection [1, 16, 18, 25, 37]. The performance of these automated detection models relies heavily on a mass of annotated images. However, real X-ray security images usually are arduous and time-consuming to collect, and the occurrence rate of prohibited items is very low. Moreover, very few of public X-ray security image datasets contain large amounts of prohibited items. Existing datasets are + +Original baggage + +![](images/92c1ecd982a2388ca1da1534236755a219c251565f1d4170e968f57bb585f788.jpg) +Prohibited items + +![](images/0ed3566f5043cba9025a1ba490c797804fcde93d7fd2acd90791061becbfe31f.jpg) + +![](images/463d726f4b1981b1dd8e1d01d062fab885d241e4165a26222adfafb6b1b5baae.jpg) + +![](images/1a948a7d8e6321f7d03776d6d8236b85bbd1f2766e4d78d8aed87102eb82f0e7.jpg) + +![](images/f8f43abfb9168ddbfbab2373a5e68f802c7517431d58bb22ac9a7bdcd82b145f.jpg) +II + +![](images/6cfce0a2a4d11eb21d501fb6b8a6cb5caa96ced032fdbade154582fbf7c42bff.jpg) +1 + +![](images/5231baeae6b7f5c7b003b58529e331ac0edbea461084e3f0e7f55b19cec86774.jpg) +II + +![](images/1ea7bfdbdd15f260b74a7cccdd2aef93c20cf9902b1f63b697144615e2574f8e.jpg) +1 + +![](images/01e6232e756f97b3fd7b20cf8d62a348a1c98349699df92446c65c6b999f2685.jpg) +Synthesized image + +![](images/4b02f379f944a4212f86c76a0c781380da0e213cb90e916c898300a091775516.jpg) +Figure 1. Our RWSC-Fusion allows to superimpose prohibited items onto baggage images, to synthesize prohibited X-ray images. The composite prohibited items are marked with red box. + +![](images/bb5dc5a937ec3b547a1d3d818377affadc1114d519862e16e5874d68498491f2.jpg) + +![](images/5d9c133da100fd39912dbb803e7449ec711f6389397fd6bf997678bcbfc2d7f2.jpg) + +mainly: (1) GDXray: The GDXray dataset [24] contains only three kinds of prohibited items: guns, shurikens, and razor blades. Besides, GDXray only involves grayscale images where backgrounds are too simple to conform with the real color X-ray security images; (2) OPIXray: The OPIXray dataset [36], which is especially designed for the cutter detection, contains 8885 synthetic X-ray security images with five kinds of cutters, and most images contain only one cutter; (3) SIXray: The SIXray dataset [26] contains 1, 059, 231 X-ray security images, but only 8929 images include prohibited items: guns, knives, wrenches, pliers, scissors, and hammers. Given the above, existing public datasets haven't been up to the standard of training. + +To overcome the lack of training samples, traditional offline enhancement strategies such as rotation, re-scaling and mixing are applied to the augmentation of training samples [32, 42]. However, unlike natural images and other X-ray scans, X-ray security images usually involve randomly stacked objects [6, 11, 12, 22]. In addition, according to the imaging principle of X-ray security, objects overlap with each other in a translucent state, and appear differently for different materials and thickness. These traditional augmentation methods cannot improve the diversity and complexity for the inter-occlusion between prohibited items [31]. Therefore, it is very necessary to synthesize realistic X-ray security images, so as to enrich the prohibited items in pose, scale and position. + +A few researchers studied to directly generate prohibited + +X-ray security images by learning deep synthesis models. Inspired by the success of GANs in image synthesis [10, 34], Zhao et al. proposed X-ray Image-Synthesis-GAN [41] to generate the prohibited items from a noise region on the background images. Li et al. [17] synthesized the X-ray security images from the semantic label maps based on GANs. Yang et al. [40] enhanced the training of GANs to learn higher-quality X-ray security images. However, they synthesized only one prohibited item rather than stacked and overlapped ones in one image, which thus are not realistic enough for the complex X-ray security images in a real-world scenario. Isaac-Medina et al. [14] used the paired X-ray energy maps (high, low, effective-Z maps) to synthesize the pseudo-color images which however only served as a small amount of testing samples. Bhowmik et al. [3] developed a Synthetically Composed (SC) data augmentation strategy based on the Threat Image Projection (TIP) method [8], to fuse the prohibited items with the baggage images for generating images with stacked and cluttered prohibited items. However, the SC need adjust the parameters for each image to meet the various colors of different materials, and thus lacks automation, robustness and versatility. + +In order to synthesize the prohibited X-ray security images automatically, we propose a color X-ray security images fusion model, to superimpose the prohibited items onto baggage or suitcase images, as shown in Figure 1. In this way, we synthesize prohibited X-ray security images and obtain annotation automatically, thus avoiding the collection of the annotated prohibited X-ray security images for training the prohibited item detection model. + +The experimental results prove the advantage of our fusion model over other fusion methods in the field of X-ray security image. In addition, we also compare the prohibited item detection model trained with real and synthetic images. The results verify that our synthetic images are efficient to supplement the prohibited X-ray security images in downstream detection task. + +The main contributions of our work are as follows: + +1. We propose an unsupervised color X-ray security image fusion model. Due to the imaging particularity, existing fusion loss functions are inapplicable to X-ray security images. We design Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD) based on the principle of X-ray imaging and Threat image projection (TIP). The LL and CSD optimize the comprehensive luminance-saturation fusion between the foreground item and background image. Thus, we extend TIP to composite color X-ray security images. + +2. We propose a Region-Wise Style-Controlled Fusion module, to control the fused appearance by learning the shifting and scaling modulation parameters pertinently. Moreover, the RWSC-Fusion module can adaptively modulate the local region of interest, i.e., the overlapping region of the prohibited items and baggage images. + +3. We develop an Edge-Attention module, which inhibits irrelevant information and enhances texture information, to improve the sharpness of generated images. +4. Our RWSC-Fusion and Edge-Attention modules are both universal and plug-and-play to other image fusion or synthesis models for generating high-quality images. + +# 2. Related work + +# 2.1. Threat Image Projection + +Plenty of prohibited X-ray security images are the precondition for automatic prohibited item detection models [27, 35]. However, prohibited items are a very small minority on X-ray security images in a real-world scenario. Therefore, threat image projection (TIP) method has been proposed to increase the occurrence of prohibited items [29]. TIP is a process that superimposes isolated prohibited items onto normal images, thus generating composite, yet realistic prohibited X-ray security images. + +The X-ray penetrates through objects to form X-ray image. The image intensity is related to the X-ray energy, object material, object thickness [21], simply expressed as: + +$$ +I = I _ {0} e ^ {- \mu h} \tag {1} +$$ + +where $I_0$ is the X-ray beam intensity, $\mu$ is the absorption coefficient and $h$ is the thickness of the objects. + +Accordingly, the prohibited item X-ray image $I_{f}$ , and background image $I_{b}$ , e.g. a baggage, can be expressed as: + +$$ +I _ {f} = I _ {0} e ^ {- \mu_ {f} h _ {f}}, \quad I _ {b} = I _ {0} e ^ {- \mu_ {b} h _ {b}} \tag {2} +$$ + +where $\mu_{f}$ and $\mu_{b}$ are the respective absorption coefficients, $h_f$ and $h_b$ are the respective thickness. + +When superimposing the prohibited items $I_{f}$ onto the baggage image $I_{b}$ , the fused X-ray image $I_{fb}$ could be: + +$$ +I _ {f b} = I _ {0} e ^ {- \mu_ {f} h _ {f} - \mu_ {b} h _ {b}} = I _ {0} e ^ {- \mu_ {f} h _ {f}} e ^ {- \mu_ {b} h _ {b}} \tag {3} +$$ + +Thus, we can get: + +$$ +I _ {f b} = \frac {I _ {f} \cdot I _ {b}}{I _ {0}} \tag {4} +$$ + +Therefore, the prohibited item can be projected into baggage images through multiplication, which is just the principle of TIP. Rogers et al. [30] applied TIP and exploit the approximate multiplicative property of X-ray imagery, to project threat items onto cargo transmission images. Mery et al. [23] replaced the multiplication with the addition of logarithmic, giving access to linear strategy for superimposing the prohibited items onto images. The TIP is almost exclusively applicable to grayscale X- ray images. However, X-ray security images in a real-world scenario are mostly rendered with pseudo-color. In this work, we will extend TIP principle to color X-ray images, to develop a prohibited X-ray security images synthesis model. + +![](images/446eac864415596bd551580ea2d6e7b6fc57fdbddd9e39960c0499950c035c98.jpg) +Figure 2. Overview of the proposed RWSC-Fusion. + +![](images/ad5c3bd015f9bd887327dbbed07261bbf8d47ed6f7c0c2117686678dd499f626.jpg) +Figure 3. EA-Dense Block with Edge-Attention module. + +# 2.2. Color X-ray Security Images Rendering + +As mentioned above, real X-ray security images are rendered with pseudo-colors according to certain rules [5]. The most common rule is based on the three components: Hue (H), Saturation (S) and Value (V) in the HSV color space, which approximates the way human perceives and interprets color. First, the H component of pseudo-color is assigned according to the material category of the object, which depends on the dual energy responses. e.g., organic materials are usually shown in red, inorganic materials are in blue, and mixtures are in green. Next, the V component of the three is a normalized nonlinear mapping, while the S component is mostly correlated linearly with the single energy or dual energy responses. As a consequence, the colors of objects in X-ray security image (see examples in the supplementary material), vary differently according to the materials, thickness, viewpoint and background. + +# 3. Related work + +The overview of RWSC-Fusion is shown in Figure 2. The prohibited item image (foreground: $I_{f}$ ) and baggage image (background: $I_{b}$ ) are inputted separately into two branches, and are reconstructed through convolution layers and Edge-Attention Dense (EA-Dense) blocks to be $\tilde{I}_{f}$ and $\tilde{I}_{b}$ respectively. They share weights in parallel to encode respective features $F_{f}$ and $F_{b}$ . The two encoding features + +are inputted together into a RWSC-Fusion module, which fuses the two in a region-wise style-controlled manner, and then are reconstructed to be the composite image $I_{fb}$ . + +# 3.1. Edge-Attention Dense Block + +The Edge-Attention Dense (EA-Dense) block in our RWSC-Fusion is shown in Figure 3(a). The dense block is composed of four convolutional blocks, each taking the feature maps of all preceding blocks as input. To reinforce the information representation, we design and add an Edge-Attention (EA) module (shown in Figure 3(b)) into the top convolutional block before flowing into subsequent blocks. + +Given the low-level feature $F$ of the top block, we first employ $3 \times 3$ average pooling layer with the stride of 1 to obtain the local mean feature. We subtract the local mean feature maps from the original feature maps to explore the structural texture, similar to Laplacian sharpening which is robust to noise for edge information extraction. Next, we calculate the mean responses along the channel dimension to reduce the channel number to 1, and obtain the edge-aware activation map $w$ by using the sigmoid function. At last, the edge-enhanced feature $\widetilde{F}$ are acquired through the multiplication between the weight $w$ and feature $F$ . The whole process of EA module can be expressed as: + +$$ +w = \sigma (M (\left| A P 2 D (F) - F \right|)) \tag {5} +$$ + +$$ +\tilde {F} = _ {W} \odot F \tag {6} +$$ + +where $AP2D$ denotes 2D average pooling, $M$ denotes the mean value along the channel dimension, $\sigma$ denotes the sigmoid activation, $\odot$ denotes pixel-wise multiplication. + +Since the weight $w$ can activate and enhance the edge and texture information through sharpening operation, the resulting feature $\widetilde{F}$ take advantage of both global and local texture information of the feature $F$ . Therefore, in our EA-Dense block, each convolutional block takes as input the feature of all preceding block and the edge-enhanced feature $\widetilde{F}$ , and thus sharpen the image quality. + +# 3.2. Region-Wise Style-Controlled Fusion Module + +Common image fusion methods usually fuse the features of two source images in a simple manner, such as addition, + +![](images/7a21b9d8073ab04d71fd29fbc62c517e5f7595472ef29a9752c2893a7471f396.jpg) +Figure 4. Details of mask average pooling layer. + +![](images/ecb45371fd9e6ab703bfb075cd6619d69cbda043b2e699484304cfff5441fe4f.jpg) +Figure 5. Details of RWSC-Fusion module. + +maximum or concatenation. However, for the fusion of the prohibited item and the baggage image, we focus more on the appearance fusion of the overlapping region rather than the global information fusion. Therefore, we propose a RWSC-Fusion module to fuse the features of prohibited item $F_{f}$ and the baggage image $F_{b}$ in a region-wise style-controlled manner. The RWSC-Fusion module modulates the appearance of the overlapping region between the two images by applying region-wise normalization. + +The traditional region-wise normalization [28] is: + +$$ +\gamma_ {c, h, w} \left(\frac {b _ {n , c , h , w} - \mu_ {c} (x)}{\sigma_ {c} (x)}\right) + \beta_ {c, h, w} \tag {7} +$$ + +where $\gamma_{c,h,w}$ and $\beta_{c,h,w}$ represent pixel-wise scaling and shifting parameters. Some researchers [7] learn $\gamma_{c,h,w}$ and $\beta_{c,h,w}$ from the style maps by using mask average pooling, which is shown in Figure 4. However, such parameters have less potential for realizing rich and fine style-control. + +By contrast, the region-wise normalization in RWSC-Fusion module innovate in two respects: (1) It learns the shifting and scaling parameters separately based on the mask average pooling and the deviation maps to modulate the mean and standard deviation; (2) It normalizes the local region adaptively with pixel-wise modulation parameters, to control the appearance of the region of interest. + +The RWSC-Fusion module is detailed in Figure 5. On one branch, the features $F_{f}$ and $F_{b}$ of two images are first sent jointly to one convolution layer. Then, the resulting features $F_{fb}$ with auxiliary mask of prohibited item are fed into the mask average pooling layer, where the average feature vectors are extracted and broadcast to create the mean maps $F_{fb}^{m}$ . Next, we subtract the mean maps $F_{fb}^{m}$ from + +the initial features $F_{fb}$ to get the local standard deviation maps $F_{fb}^{d}$ . Lastly, the deviation maps $F_{fb}^{d}$ and the mean maps $F_{fb}^{m}$ pass through two separate convolution layers to generate the pixel-wise scaling and shifting parameters $\gamma_{c,h,w}^{fb}$ and $\beta_{c,h,w}^{fb}$ . Meanwhile, on the other branch, we obtain parameters $\gamma_{c,h,w}$ and $\beta_{c,h,w}$ by doing the same operations on the feature $F_{b}$ of the single baggage image. + +We design the region-specific modulation parameters through the region-wise merging, and thus the final modulation parameters are expressed as: + +$$ +\gamma_ {c, h, w} = M ^ {+} \odot \gamma_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \odot \gamma_ {c, h, w} ^ {b} \tag {8} +$$ + +$$ +\beta_ {c, h, w} = M ^ {+} \odot \beta_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \odot \beta_ {c, h, w} ^ {b} \tag {9} +$$ + +where $M^{+}$ denotes the mask of prohibited item, while $1 - M^{+}$ denotes the complementary mask. The appearance of the overlapping region within the mask is modulated jointly by the prohibited item and baggage image, while the non-overlapping region is modulated by the single baggage image, avoiding the interference of prohibited item image. + +Our region-adaptive normalization learns appropriate shifting and scaling parameters separately based on the mean maps and the deviation maps instead of single mask mean maps, so as to modulate the mean and standard deviation specifically and pointedly. Thus, it allows for fine control to generate rich stylization by considering the local information from the deviation maps. Hence, the RWSC-Fusion module enables the region-wise normal-appearing fusion of the prohibited item and baggage image to synthesize the prohibited X-ray security image. + +# 3.3. Loss Function + +Existing unsupervised image fusion models usually maximize the similarity of fused image with source images instead of ground-truth, by using loss function as follows: + +$$ +\mathcal {L} = 1 - \left[ w _ {1} \bullet \ell \left(x _ {1}, y\right) + w _ {2} \bullet \ell \left(x _ {2}, y\right) \right] \tag {10} +$$ + +where $\ell(x, y)$ denotes the similarity metrics, such as SSD or SSIM. The weights $w_1$ and $w_2$ represent the information preservation degree of two source images. However, these functions are inapplicable to X-ray security image, for two reasons: (1) they produce global fusion, including the non-overlapping region, which instead should remain intact; (2) the addition strategy of these functions does not conform to the attenuation character of X-ray security imagery. + +As mentioned in Sec.2.1, when fusing the prohibited items $I_{f}$ with the baggage image $I_{b}$ by using the weights $w_{1}$ and $w_{2}$ , the fused X-ray image $I_{fb}$ could be: + +$$ +I _ {f b} = I _ {0} e ^ {- w _ {1} \mu_ {f} h _ {f} - w _ {2} \mu_ {b} h _ {b}} = I _ {0} e ^ {- w _ {1} \mu_ {f} h _ {f}} e ^ {- w _ {2} \mu_ {b} h _ {b}} \tag {11} +$$ + +$$ +I _ {f b} = \frac {I _ {f} ^ {w _ {1}} \cdot I _ {b} ^ {w _ {2}}}{I _ {0} ^ {w _ {1} + w _ {2} - 1}} \tag {12} +$$ + +Table 1. Quantitative evaluations for image quality of the models with and without the EA modules. + +
Modelwithout EA modulewith EA module
MAE2.0911.938
PSNR38.40239.084
+ +Therefore, the fused X-ray image $I_{fb}$ is approximatively correlated with the multiplication rather than addition of the prohibited item $I_{f}$ and the baggage image $I_{b}$ . + +In this case, we adjust Eq. (10) by using the logarithmic form, giving access to multiplication relationship in linear form. Finally, we develop a Luminance loss in Logarithmic form $(LL)\mathcal{L}_{LL}$ as follows: + +$$ +\mathcal {L} _ {L L} = 1 - \left[ w _ {1} \bullet \log \ell \left(I _ {f}, I _ {f b}\right) + w _ {2} \bullet \log \ell \left(I _ {b}, I _ {f b}\right) \right] \tag {13} +$$ + +We put $w_{1}$ and $w_{2}$ inside the metric formula to develop a new similarity metric $\ell(x, y, w)$ , and thus $\mathcal{L}_{LL}$ turns into: + +$$ +\mathcal {L} _ {L L} = 1 - \left[ \log \ell \left(I _ {f}, I _ {f b}, w _ {1}\right) + \log \ell \left(I _ {b}, I _ {f b}, w _ {2}\right) \right] \tag {14} +$$ + +where $\ell (x,y,w) = \frac{2\mu_x\mu_y + \varepsilon}{\mu_x^{4w} + \mu_y^2 + \varepsilon}$ , and thus the local mean of + +fused image $\mu_{fb}$ is expected to converge to $\mu_f^{w_1} \cdot \mu_b^{w_2}$ . The details and deduce are in the supplementary materials. + +We automatically estimate the weights $w_{1}$ and $w_{2}$ from the feature of R, G and B component of the prohibited item and the baggage image respectively, to get different power weights $w_{1}$ and $w_{2}$ for R, G and B component, and the sum of $w_{1}$ and $w_{2}$ is adjusted to 2. + +On the other hand, considering that the saturation $(S)$ component of color X-ray security image is mostly correlated linearly with the energy responses, we assume that the $S$ component of the fused image is correlated linearly with the multiplication of the $S$ component of the two images. Therefore, the difference between the $S$ component of the prohibited item $(S_{f})$ and the fused image $(S_{fb})$ comes almost from the $S$ component of the baggage image $(S_{b})$ . Similarly, the difference between the $S_{b}$ and $S_{fb}$ comes almost from $S_{f}$ . We develop an another loss term Correlation Loss of Saturation Difference (CSD) $\mathcal{L}_{CSD}$ : + +$$ +\begin{array}{l} D _ {b} = \left(1 - S _ {f b}\right) / \left(1 - S _ {f}\right) \\ D _ {f} = \left(1 - S _ {f b}\right) / \left(1 - S _ {b}\right) (15) \\ \mathcal {L} _ {C S D} = 1 - \left[ C C \left(D _ {f}, 1 - S _ {f}\right) + C C \left(D _ {b}, 1 - S _ {b}\right) \right] / 2 (16) \\ \end{array} +$$ + +where $CC$ is the normalized correlation coefficient. + +In addition, a third loss term is the reconstruction loss $\mathcal{L}_{\text{recon}}$ of two source images $\tilde{I}_f$ and $\tilde{I}_b$ as follows: + +$$ +\mathcal {L} _ {\text {r e c o n}} = \left\| I _ {f}, \tilde {I} _ {f} \right\| + \left\| I _ {b}, \tilde {I} _ {b} \right\| \tag {17} +$$ + +In conclusion, the total loss function is: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {L L} + \mathcal {L} _ {C S D} + \mathcal {L} _ {\text {r e c o n}} \tag {18} +$$ + +# 4. Experiment Results + +# 4.1. Datasets + +Private data: We have collected millions of X-ray security images from urban rail transit, railway, highway and other real-world daily security inspection scenario. There are more than 40 kinds of manually-annotated prohibited items. + +Public data: The SIXray dataset [26] and OPIXray dataset [36], which have been introduced in Sec.1. + +# 4.2. Implementation Details + +The training data are 12000 groups randomly composed by 12000 baggage images and 60 individual prohibited items of 15 categories. During training, all baggage images are resized to a resolution of $256 \times 256$ , and all prohibited item images are randomly padded with [255,255,255] to share the same size. It is important to note that the random padding of the prohibited item images is regulated by utilizing the activation maps of the baggage images, in order to enable realistic and appropriate location of the prohibited item in the internal region of the baggage. + +# 4.3. Ablation Study + +# 4.3.1. Edge-Attention module + +Due to the sparse texture of X-ray security images and the information loss in deep neural network, the generated images often suffer from low sharpness. We design EA module in the dense blocks to extract and recover the texture information for the fused image. In this section, we evaluate the efficacy of the proposed EA module. + +We quantitatively calculate the reconstruction loss of the non-overlapping regions between 6000 pairs of the fused images and the source images in terms of the Mean Absolute Error (MAE) and Peak Signal to-Noise Ratio (PSNR). The lower the MAE and the higher the PSNR, the closer the non-overlapping regions is to the source image and the higher the quality of fused images. The results are shown in Table 1. The model with EA modules produces lower MAE and higher PSNR than that without the EA modules. It indicates that the EA modules can effectively preserve the source information more completely in the resulting non-overlapping regions and improve the definition and sharpness of the synthesized images. + +We visualize the synthesized images from the models with and without the EA modules in Figure 6. Comparing the regions within the purple ROI which are magnified into view at the top-right corner, the X-ray security images generated by the model without EA modules are blurred and miss details, such as the zipper in the second row and the shoe sole texture in the fourth row. On the contrast, the model with EA modules can activate and enhance texture and edge information by using the attention map shown in Figure 7. Thus it can alleviate the shortage of texture and + +![](images/c902eb39c0d3237d4ead70513276f7eab1b69cd954475fbd36606bcfb24a16f9.jpg) +Figure 6. The generated images from the models with and without the EA modules. From left to right are: (a) original baggage image; (b) the synthesized images from the model without EA modules; (c) the synthesized images from the model with EA modules. + +![](images/3eee46c9f4c0fbdf74ec6a49d2791b08423cedb67c44d781ed115a96c193509a.jpg) +Figure 7. The edge attention maps of the X-ray security images in Figure 6. The first row shows the original images, and the second row shows the edge attention maps extracted by the EA module. + +offer clearer appearance. It further follows that the EA module can indeed provide high-quality images with sharp textures via the Edge Attention mechanism. + +# 4.3.2. Region-wise normalization + +Existing region-adaptive normalization methods learn the shifting and scaling parameters both based on the mask mean maps [7, 28]. On the contrast, we learn the shifting and scaling parameters separately based on the mask mean maps and deviation maps, so as to modulate the mean and standard deviation pointedly. In this section, we evaluate the efficacy of our normalization mechanism. + +We visualize the generated X-ray security images from the fusion module with only mask average pooling layer + +![](images/93ae644de86168c15f3c66298258655c3f42b40e4f813cf2a69dba7cd18ae8f3.jpg) +Figure 8. The generated images from the fusion module with only mask average pooling layer and our RWSC-Fusion module. From left to right are: (a) prohibited items; (b) original baggage image; (c) the synthesized images from the model with only mask average pooling layer; (d) the synthesized images from our model. + +and our RWSC-Fusion module in Figure 8. By comparing the prohibited items within the red ROI, the prohibited items synthesized by the model with only mask average pooling layer are fuzzy due to a lack of texture details, while the prohibited items from our model are more clear. It proves that our region-adaptive normalization method allows for fine control to provide rich stylization. + +# 4.4. Comparison with State-of-the-art Methods + +In this section, we compare our RWSC-Fusion with four state-of-the-art image fusion methods: U2Fusion [38], FusionGAN [19], DeepFuse [13] and MEFNet [20], to evaluate the performance of X-ray security image fusion for the prohibited X-ray security image synthesis. + +The synthesized images from different methods are shown in Figure 9. It can be seen that compared with U2Fusion, FusionGAN and DeepFuse, RWSC-Fusion alleviates the problem of global fusion and successfully preserves the original appearance of the non-overlapping regions in the baggage images. The overlapping regions marked by the red box from the competitors, especially MEFNet, noticeably deviate from our desired appearance that can match the real X-ray security images in terms of hue, saturation and sharpness. Overall, our model achieves superior visual performance than these four competitors. These well demonstrate that our fusion model is better suited to the X-ray security image, and can synthesize more ideal and realistic prohibited X-ray security images. + +![](images/7f105d7316869ce7218fba506e1e1d9f3b4490da41690f7eccc4786e18ee9882.jpg) +Figure 9. The X-ray baggage images fused with the prohibited item by four other fusion methods and the proposed RWSC-Fusion. + +Table 2. Quantitative comparison with state-of-the-art methods. + +
MetricQEQabfEIPSNR
U2Fusion [38]0.56350.346748.819016.7155
FusionGAN [19]0.56400.592478.093413.8471
DeepFuse [13]0.61570.181441.626616.8173
MEFNet [20]0.75090.609085.040317.7364
Ours0.83390.647281.380718.6455
+ +The quantitative comparisons are performed on the 6000 image pairs. Four metrics, namely, QE [9], Qabf [39], Edge Intensity (EI) [2], and PSNR are used for evaluation. For all four metrics, larger values indicate better performance. The comparative results of four metrics are shown in Table 2. Our RWSC-Fusion ranks first on QE, Qabf and PSNR, proving that our method can synthesize images with richer textures and details. Although our RWSC-Fusion ranks second on EI, it also achieves comparable results. The promising outcomes show that our model keeps high fidelity with less distortion and noise. + +# 4.5. Supplement to Private Dataset + +In this section, we synthesize the prohibited X-ray security images on our private dataset. + +First, we conduct subjective evaluation experiment, which is detailed in the supplementary material. This result demonstrates that our synthetic prohibited X-ray security images are realistic enough to fool the inspectors. + +To analyze the efficacy of supplementing the training samples, we compare the performance of prohibited item detection model under the training of real and synthetic images. We use the YOLOv4 as the detector [4] to detect the five kinds of prohibited items: plastic bottles, cutters, scissors, thermos cups and glass bottles. + +The real training dataset contains 40000 samples (DataR: with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles). Besides, we train the detector with the following dataset: (1) DataR1/2: We remove 20000 samples from DataR, + +resulting in 20000 training samples with 13127 plastic bottles, 17055 cutters, 5117 scissors, 2518 thermos cups and 8710 glass bottles. + +(2) DataRS: We synthesize and supplement the prohibited items into DataR1/2, resulting in 20000 samples with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles, with the same number of prohibited items as the DataR. (Note: since there are no extra 20000 negative samples excluding all five kinds of prohibited items, we cannot achieve the pure synthesis of 20000 samples, to be perfectly aligned with DataR) +(3) DataRS+: We synthesize prohibited items into other 20000 samples, and merge new synthetic samples with 20000 samples in DataR, resulting in 40000 samples with total 38983 plastic bottles, 51956 cutters, 15597 scissors, 7522 thermos cups and 26034 glass bottles. + +The detection results on the 9954 testing samples of YOLOv4 trained with above datasets are listed in Table 3. + +As compared with DataR1/2, the DataRS provides a considerable increase of more than $3\%$ in mAP after we synthesize prohibited items in DataR1/2. This proves that our synthetic prohibited items are indeed beneficial to training the detection model. Moreover, since the results of DataRS can be comparable with or even better than those of DataR, it demonstrates the authenticity and reliability of our synthetic prohibited items for replacing the real ones. Accordingly, with the addition and the contribution of synthetic prohibited items, DataRS+ also has a remarkable advantage over DataR. + +# 4.6. Supplement to SIXray and OPIXray Dataset + +In this section, we evaluate on public SIXray [26] and OPIXray dataset [36]. We fuse our private prohibited items with the negative samples in SIXray and OPIXray dataset. Moreover, we directly apply the model trained by our private dataset without any additional parameter tuning. + +Table 3 Detection results of YOLOv4 trained with different data on private dataset (recall and precision at confidence level of 0.5). + +
Training DataDataRDataR1/2DataRSDataRS+
Plastic bottleRecall69.4964.8270.4674.15
Precision85.3683.2988.1485.13
AP69.5071.1671.0076.97
CutterRecall86.1774.0481.7084.50
Precision92.6287.6091.8193.45
AP86.9679.9883.4987.70
ScissorRecall71.2258.0370.8772.97
Precision90.6089.3488.3788.23
AP74.2866.8172.8378.29
Therm os cupRecall88.8688.8691.5992.76
Precision93.5290.1391.3892.54
AP85.5286.1788.9890.25
Glass bottleRecall56.4948.7458.7158.82
Precision86.7980.9784.0288.15
AP56.3153.7658.1361.87
mAP74.5271.5874.8879.02
+ +For SIXRay dataset, it contains six kinds of prohibited items. We don't use the hammer class since it involves merely 60 samples. The SIXRay10 dataset contains 13412 testing samples, and 74960 training samples (SIXR:7496 positive samples with 4322 guns, 2758 knives, 2816 wrenches, 4624 pliers and 918 scissors). Moreover, we also train YOLOv4 by using following 74960 training samples: + +(1) SIXR1/2: We remove half the (3748) positive samples from SIXR, and supplement the other 3748 negative samples into SIXR. + +(2) SIXRS: We synthesize the prohibited items into the newly-added 3748 negative samples in SIXR1/2, to supplement the positive samples, resulting in mixed 7496 true/pseudo positive samples with the same number of prohibited items as SIXR. + +(3) SIXRS+: We synthesize prohibited items into other new 3748 negative samples, and replace 3748 negative samples in the SIXR, resulting in mixed 11244 true/pseudo positive samples, with 6469 guns, 4154 knives, 4195 wrenches, 6933 pliers and 1398 scissors. + +For OPIXray dataset, it contains 7109 training and 1776 testing images for cutter detection. The training datasets are: (1) OPIR: All the original 7109 images; (2) OPIRS: 3555 images supplemented with synthesized cutter, with the same number of cutter as OPIR; (3) OPIRS+: 7109 images supplemented with half the synthesized cutter. + +The detection results on SIXray and OPIXray dataset are respectively listed in Table 4 and Table 5. + +By comparing the models trained by SIXRS and SIXR1/2, SIXRS recover the degraded performance of SIXR1/2 by supplementing the synthetic positive samples effectively. Moreover, compared to SIXR, SIXRS can achieve higher mAP, and overall higher AP except for the scissor class. The comparison of OPIRS and OPIR also well verifies that our synthetic cutters are real enough to supplement the missing samples. The SIXRS achieves higher precision but lower recall for the scissor class, because our private scissor item database does not cover + +Table 4 Detection results of YOLOv4 trained with different data on SIXray dataset. + +
Training DataSIXRSIXR1/2SIXRSSIXRS+
GunRecall79.7373.0283.2383.69
Precision96.3291.7697.3397.17
AP78.7175.2182.1982.74
KnifeRecall58.8845.6264.1766.04
Precision92.6586.3992.7993.39
AP62.8447.8866.6469.17
WrenchRecall55.9724.2559.3366.04
Precision87.7260.7583.6883.49
AP65.9326.3066.8268.88
PlierRecall66.3550.0771.4576.14
Precision85.4972.3486.8185.16
AP74.2057.6375.8479.53
ScissorRecall63.6225.7052.8067.76
Precision91.1666.2791.8785.80
AP72.1139.0862.9473.60
mAP70.7649.2270.8974.78
+ +Table 5 Detection results of different training data on OPIXray. + +
Training dataOPIXray dataset
RecallPrecisionAP
OPIR71.0875.8567.47
OPIRS71.1476.6072.20
OPIRS+80.4690.1384.80
+ +all the scissor type of SIXRay dataset, such as nail clipper set, to simulate the SIXRay samples. The recall and AP of the scissor class could be improved furthermore if the prohibited items that are more similar to SIXRay dataset are used for fusion. The comparison results between the SIXR and SIXRS+, OPIR and OPIRS+ also both can indicate that our synthetic positive images are beneficial in augmenting the training dataset to further improve the performance of the detection model. + +# 5. Conclusion + +We propose a RWSC-Fusion model, which fuses the prohibited items with baggage image in a Region-Wise Style-Controlled manner, for synthesizing the prohibited X-ray security images. The RWSC-Fusion learns the fused X-ray security images unsupervisedly based on novel loss functions: LL and CSD. Moreover, to generate more high-quality realistic and images, we innovate style-controlled mechanism and Edge-Attention module. The ablation studies verify the efficacy of the RWSC-Fusion and Edge-Attention module in achieving superior perceptual quality. The comparative experimental results illustrate that our method outperforms the state-of-the-arts in the field of X-ray security image. The performance comparison of the detector training demonstrates the authenticity and reliability of the synthetic images in promoting downstream tasks. In future work, we will generalize RWSC-Fusion to solve multiple fusion problems. + +Acknowledgements. This work is supported by Zhejiang Dahua Technology Co., Ltd. and Zhejiang University. + +# References + +[1] Samet Akcay, Toby P. Breckon. Towards Automatic Threat Detection: A Survey of Advances of Deep Learning within X-ray Security Imaging. Pattern Recognition, 2022. +[2] Rajalingam Balakrishnan, Rainy Priya, Hybrid multimodality medical image fusion technique for feature enhancement in medical diagnosis, Int. J. Eng. Sci. 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The abundance and diversity of the X-ray security images with prohibited item, termed as prohibited X-ray security images, are essential for training the detection model. In order to solve the data insufficiency, we propose a Region-Wise Style-Controlled Fusion (RWSC-Fusion) network, which superimposes the prohibited items onto the normal X-ray security images, to synthesize the prohibited X-ray security images. The proposed RWSC-Fusion innovates both network structure and loss functions to generate more realistic X-ray security images. Specifically, a RWSC-Fusion module is designed to enable the region-wise fusion by controlling the appearance of the overlapping region with novel modulation parameters. In addition, an Edge-Attention (EA) module is proposed to effectively improve the sharpness of the synthetic images. As for the unsupervised loss function, we propose the Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD), to optimize the fused X-ray security images in terms of luminance and saturation. We evaluate the authenticity and the training effect of the synthetic X-ray security images on private and public SIXray dataset. The results confirm that our synthetic images are reliable enough to augment the prohibited X-ray security images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 551, + 145, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 551, + 145, + 562 + ], + "spans": [ + { + "bbox": [ + 67, + 551, + 145, + 562 + ], + "type": "text", + "content": "1. 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Our RWSC-Fusion allows to superimpose prohibited items onto baggage images, to synthesize prohibited X-ray images. The composite prohibited items are marked with red box." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 458, + 303, + 495, + 339 + ], + "blocks": [ + { + "bbox": [ + 458, + 303, + 495, + 339 + ], + "lines": [ + { + "bbox": [ + 458, + 303, + 495, + 339 + ], + "spans": [ + { + "bbox": [ + 458, + 303, + 495, + 339 + ], + "type": "image", + "image_path": "bb5dc5a937ec3b547a1d3d818377affadc1114d519862e16e5874d68498491f2.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 502, + 304, + 546, + 339 + ], + "blocks": [ + { + "bbox": [ + 502, + 304, + 546, + 339 + ], + "lines": [ + { + "bbox": [ + 502, + 304, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 502, + 304, + 546, + 339 + ], + "type": "image", + "image_path": "5d9c133da100fd39912dbb803e7449ec711f6389397fd6bf997678bcbfc2d7f2.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + } + ], + "index": 30 + }, + { + "bbox": [ + 320, + 386, + 552, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 386, + 552, + 532 + ], + "spans": [ + { + "bbox": [ + 320, + 386, + 552, + 532 + ], + "type": "text", + "content": "mainly: (1) GDXray: The GDXray dataset [24] contains only three kinds of prohibited items: guns, shurikens, and razor blades. Besides, GDXray only involves grayscale images where backgrounds are too simple to conform with the real color X-ray security images; (2) OPIXray: The OPIXray dataset [36], which is especially designed for the cutter detection, contains 8885 synthetic X-ray security images with five kinds of cutters, and most images contain only one cutter; (3) SIXray: The SIXray dataset [26] contains 1, 059, 231 X-ray security images, but only 8929 images include prohibited items: guns, knives, wrenches, pliers, scissors, and hammers. Given the above, existing public datasets haven't been up to the standard of training." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 320, + 532, + 552, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 532, + 552, + 688 + ], + "spans": [ + { + "bbox": [ + 320, + 532, + 552, + 688 + ], + "type": "text", + "content": "To overcome the lack of training samples, traditional offline enhancement strategies such as rotation, re-scaling and mixing are applied to the augmentation of training samples [32, 42]. However, unlike natural images and other X-ray scans, X-ray security images usually involve randomly stacked objects [6, 11, 12, 22]. In addition, according to the imaging principle of X-ray security, objects overlap with each other in a translucent state, and appear differently for different materials and thickness. These traditional augmentation methods cannot improve the diversity and complexity for the inter-occlusion between prohibited items [31]. Therefore, it is very necessary to synthesize realistic X-ray security images, so as to enrich the prohibited items in pose, scale and position." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 330, + 688, + 552, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 688, + 552, + 700 + ], + "spans": [ + { + "bbox": [ + 330, + 688, + 552, + 700 + ], + "type": "text", + "content": "A few researchers studied to directly generate prohibited" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "spans": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 5, + 486, + 16 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 5, + 486, + 16 + ], + "spans": [ + { + "bbox": [ + 136, + 5, + 486, + 16 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 189, + 17, + 435, + 28 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 17, + 435, + 28 + ], + "spans": [ + { + "bbox": [ + 189, + 17, + 435, + 28 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 170, + 29, + 452, + 41 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 170, + 29, + 452, + 41 + ], + "spans": [ + { + "bbox": [ + 170, + 29, + 452, + 41 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 711, + 291, + 723 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 711, + 291, + 723 + ], + "spans": [ + { + "bbox": [ + 67, + 711, + 291, + 723 + ], + "type": "text", + "content": "*Corresponding author: xilizju@zju.edu.cn, xiongp362204@163.com" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "type": "text", + "content": "22398" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 105, + 300, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 105, + 300, + 362 + ], + "spans": [ + { + "bbox": [ + 66, + 105, + 300, + 362 + ], + "type": "text", + "content": "X-ray security images by learning deep synthesis models. Inspired by the success of GANs in image synthesis [10, 34], Zhao et al. proposed X-ray Image-Synthesis-GAN [41] to generate the prohibited items from a noise region on the background images. Li et al. [17] synthesized the X-ray security images from the semantic label maps based on GANs. Yang et al. [40] enhanced the training of GANs to learn higher-quality X-ray security images. However, they synthesized only one prohibited item rather than stacked and overlapped ones in one image, which thus are not realistic enough for the complex X-ray security images in a real-world scenario. Isaac-Medina et al. [14] used the paired X-ray energy maps (high, low, effective-Z maps) to synthesize the pseudo-color images which however only served as a small amount of testing samples. Bhowmik et al. [3] developed a Synthetically Composed (SC) data augmentation strategy based on the Threat Image Projection (TIP) method [8], to fuse the prohibited items with the baggage images for generating images with stacked and cluttered prohibited items. However, the SC need adjust the parameters for each image to meet the various colors of different materials, and thus lacks automation, robustness and versatility." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 66, + 362, + 298, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 362, + 298, + 452 + ], + "spans": [ + { + "bbox": [ + 66, + 362, + 298, + 452 + ], + "type": "text", + "content": "In order to synthesize the prohibited X-ray security images automatically, we propose a color X-ray security images fusion model, to superimpose the prohibited items onto baggage or suitcase images, as shown in Figure 1. In this way, we synthesize prohibited X-ray security images and obtain annotation automatically, thus avoiding the collection of the annotated prohibited X-ray security images for training the prohibited item detection model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 452, + 299, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 452, + 299, + 529 + ], + "spans": [ + { + "bbox": [ + 66, + 452, + 299, + 529 + ], + "type": "text", + "content": "The experimental results prove the advantage of our fusion model over other fusion methods in the field of X-ray security image. In addition, we also compare the prohibited item detection model trained with real and synthetic images. The results verify that our synthetic images are efficient to supplement the prohibited X-ray security images in downstream detection task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 530, + 279, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 530, + 279, + 540 + ], + "spans": [ + { + "bbox": [ + 77, + 530, + 279, + 540 + ], + "type": "text", + "content": "The main contributions of our work are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 541, + 298, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 541, + 298, + 652 + ], + "spans": [ + { + "bbox": [ + 66, + 541, + 298, + 652 + ], + "type": "text", + "content": "1. We propose an unsupervised color X-ray security image fusion model. Due to the imaging particularity, existing fusion loss functions are inapplicable to X-ray security images. We design Luminance loss in Logarithmic form (LL) and Correlation loss of Saturation Difference (CSD) based on the principle of X-ray imaging and Threat image projection (TIP). The LL and CSD optimize the comprehensive luminance-saturation fusion between the foreground item and background image. Thus, we extend TIP to composite color X-ray security images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 66, + 653, + 299, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 653, + 299, + 721 + ], + "spans": [ + { + "bbox": [ + 66, + 653, + 299, + 721 + ], + "type": "text", + "content": "2. We propose a Region-Wise Style-Controlled Fusion module, to control the fused appearance by learning the shifting and scaling modulation parameters pertinently. Moreover, the RWSC-Fusion module can adaptively modulate the local region of interest, i.e., the overlapping region of the prohibited items and baggage images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 320, + 105, + 552, + 173 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 320, + 105, + 552, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 105, + 552, + 138 + ], + "spans": [ + { + "bbox": [ + 320, + 105, + 552, + 138 + ], + "type": "text", + "content": "3. We develop an Edge-Attention module, which inhibits irrelevant information and enhances texture information, to improve the sharpness of generated images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 320, + 138, + 552, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 138, + 552, + 173 + ], + "spans": [ + { + "bbox": [ + 320, + 138, + 552, + 173 + ], + "type": "text", + "content": "4. Our RWSC-Fusion and Edge-Attention modules are both universal and plug-and-play to other image fusion or synthesis models for generating high-quality images." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 320, + 185, + 405, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 185, + 405, + 197 + ], + "spans": [ + { + "bbox": [ + 320, + 185, + 405, + 197 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 320, + 209, + 456, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 209, + 456, + 222 + ], + "spans": [ + { + "bbox": [ + 320, + 209, + 456, + 222 + ], + "type": "text", + "content": "2.1. Threat Image Projection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 227, + 552, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 227, + 552, + 327 + ], + "spans": [ + { + "bbox": [ + 320, + 227, + 552, + 327 + ], + "type": "text", + "content": "Plenty of prohibited X-ray security images are the precondition for automatic prohibited item detection models [27, 35]. However, prohibited items are a very small minority on X-ray security images in a real-world scenario. Therefore, threat image projection (TIP) method has been proposed to increase the occurrence of prohibited items [29]. TIP is a process that superimposes isolated prohibited items onto normal images, thus generating composite, yet realistic prohibited X-ray security images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 327, + 552, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 327, + 552, + 361 + ], + "spans": [ + { + "bbox": [ + 320, + 327, + 552, + 361 + ], + "type": "text", + "content": "The X-ray penetrates through objects to form X-ray image. The image intensity is related to the X-ray energy, object material, object thickness [21], simply expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 408, + 364, + 549, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 364, + 549, + 379 + ], + "spans": [ + { + "bbox": [ + 408, + 364, + 549, + 379 + ], + "type": "interline_equation", + "content": "I = I _ {0} e ^ {- \\mu h} \\tag {1}", + "image_path": "96308ab82200becdcbefa930f5b5aad0482e5fbee9beb8654d364e8d30451c29.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "spans": [ + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "text", + "content": " is the X-ray beam intensity, " + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "text", + "content": " is the absorption coefficient and " + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 320, + 383, + 552, + 405 + ], + "type": "text", + "content": " is the thickness of the objects." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "spans": [ + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "text", + "content": "Accordingly, the prohibited item X-ray image " + }, + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "text", + "content": ", and background image " + }, + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 320, + 406, + 552, + 430 + ], + "type": "text", + "content": ", e.g. a baggage, can be expressed as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 381, + 433, + 550, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 433, + 550, + 449 + ], + "spans": [ + { + "bbox": [ + 381, + 433, + 550, + 449 + ], + "type": "interline_equation", + "content": "I _ {f} = I _ {0} e ^ {- \\mu_ {f} h _ {f}}, \\quad I _ {b} = I _ {0} e ^ {- \\mu_ {b} h _ {b}} \\tag {2}", + "image_path": "abd0f450497815b8850815cbc21de450d66baa476c6a4ab0eb7c5563d4580ca8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "spans": [ + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "inline_equation", + "content": "\\mu_{f}" + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "inline_equation", + "content": "\\mu_{b}" + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "content": " are the respective absorption coefficients, " + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "inline_equation", + "content": "h_f" + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "inline_equation", + "content": "h_b" + }, + { + "bbox": [ + 320, + 454, + 552, + 480 + ], + "type": "text", + "content": " are the respective thickness." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "spans": [ + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "text", + "content": "When superimposing the prohibited items " + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "text", + "content": " onto the baggage image " + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "text", + "content": ", the fused X-ray image " + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "inline_equation", + "content": "I_{fb}" + }, + { + "bbox": [ + 320, + 481, + 552, + 506 + ], + "type": "text", + "content": " could be:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 352, + 509, + 550, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 509, + 550, + 526 + ], + "spans": [ + { + "bbox": [ + 352, + 509, + 550, + 526 + ], + "type": "interline_equation", + "content": "I _ {f b} = I _ {0} e ^ {- \\mu_ {f} h _ {f} - \\mu_ {b} h _ {b}} = I _ {0} e ^ {- \\mu_ {f} h _ {f}} e ^ {- \\mu_ {b} h _ {b}} \\tag {3}", + "image_path": "6cbcd81fd6119214cf47a78c424649ac4ae177372827e28f0b3f86157fd50393.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 530, + 403, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 530, + 403, + 541 + ], + "spans": [ + { + "bbox": [ + 331, + 530, + 403, + 541 + ], + "type": "text", + "content": "Thus, we can get:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 401, + 542, + 550, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 401, + 542, + 550, + 571 + ], + "spans": [ + { + "bbox": [ + 401, + 542, + 550, + 571 + ], + "type": "interline_equation", + "content": "I _ {f b} = \\frac {I _ {f} \\cdot I _ {b}}{I _ {0}} \\tag {4}", + "image_path": "16877ae13a0b931b46723e8c2c82d7a22af872f82c7bd34a97265a77b5de4eda.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 320, + 572, + 553, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 572, + 553, + 719 + ], + "spans": [ + { + "bbox": [ + 320, + 572, + 553, + 719 + ], + "type": "text", + "content": "Therefore, the prohibited item can be projected into baggage images through multiplication, which is just the principle of TIP. Rogers et al. [30] applied TIP and exploit the approximate multiplicative property of X-ray imagery, to project threat items onto cargo transmission images. Mery et al. [23] replaced the multiplication with the addition of logarithmic, giving access to linear strategy for superimposing the prohibited items onto images. The TIP is almost exclusively applicable to grayscale X- ray images. However, X-ray security images in a real-world scenario are mostly rendered with pseudo-color. In this work, we will extend TIP principle to color X-ray images, to develop a prohibited X-ray security images synthesis model." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 301, + 752 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 301, + 752 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 301, + 752 + ], + "type": "text", + "content": "22399" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 104, + 493, + 211 + ], + "blocks": [ + { + "bbox": [ + 130, + 104, + 493, + 211 + ], + "lines": [ + { + "bbox": [ + 130, + 104, + 493, + 211 + ], + "spans": [ + { + "bbox": [ + 130, + 104, + 493, + 211 + ], + "type": "image", + "image_path": "446eac864415596bd551580ea2d6e7b6fc57fdbddd9e39960c0499950c035c98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 215, + 213, + 400, + 224 + ], + "lines": [ + { + "bbox": [ + 215, + 213, + 400, + 224 + ], + "spans": [ + { + "bbox": [ + 215, + 213, + 400, + 224 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed RWSC-Fusion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 127, + 232, + 253, + 389 + ], + "blocks": [ + { + "bbox": [ + 127, + 232, + 253, + 389 + ], + "lines": [ + { + "bbox": [ + 127, + 232, + 253, + 389 + ], + "spans": [ + { + "bbox": [ + 127, + 232, + 253, + 389 + ], + "type": "image", + "image_path": "ad5c3bd015f9bd887327dbbed07261bbf8d47ed6f7c0c2117686678dd499f626.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 391, + 277, + 402 + ], + "lines": [ + { + "bbox": [ + 76, + 391, + 277, + 402 + ], + "spans": [ + { + "bbox": [ + 76, + 391, + 277, + 402 + ], + "type": "text", + "content": "Figure 3. EA-Dense Block with Edge-Attention module." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 413, + 273, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 413, + 273, + 427 + ], + "spans": [ + { + "bbox": [ + 67, + 413, + 273, + 427 + ], + "type": "text", + "content": "2.2. Color X-ray Security Images Rendering" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 66, + 431, + 299, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 431, + 299, + 611 + ], + "spans": [ + { + "bbox": [ + 66, + 431, + 299, + 611 + ], + "type": "text", + "content": "As mentioned above, real X-ray security images are rendered with pseudo-colors according to certain rules [5]. The most common rule is based on the three components: Hue (H), Saturation (S) and Value (V) in the HSV color space, which approximates the way human perceives and interprets color. First, the H component of pseudo-color is assigned according to the material category of the object, which depends on the dual energy responses. e.g., organic materials are usually shown in red, inorganic materials are in blue, and mixtures are in green. Next, the V component of the three is a normalized nonlinear mapping, while the S component is mostly correlated linearly with the single energy or dual energy responses. As a consequence, the colors of objects in X-ray security image (see examples in the supplementary material), vary differently according to the materials, thickness, viewpoint and background." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 623, + 150, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 623, + 150, + 634 + ], + "spans": [ + { + "bbox": [ + 67, + 623, + 150, + 634 + ], + "type": "text", + "content": "3. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "spans": [ + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": "The overview of RWSC-Fusion is shown in Figure 2. The prohibited item image (foreground: " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": ") and baggage image (background: " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": ") are inputted separately into two branches, and are reconstructed through convolution layers and Edge-Attention Dense (EA-Dense) blocks to be " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "\\tilde{I}_{f}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "\\tilde{I}_{b}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": " respectively. They share weights in parallel to encode respective features " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "F_{f}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 66, + 638, + 298, + 723 + ], + "type": "text", + "content": ". The two encoding features" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 320, + 234, + 553, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 234, + 553, + 270 + ], + "spans": [ + { + "bbox": [ + 320, + 234, + 553, + 270 + ], + "type": "text", + "content": "are inputted together into a RWSC-Fusion module, which fuses the two in a region-wise style-controlled manner, and then are reconstructed to be the composite image " + }, + { + "bbox": [ + 320, + 234, + 553, + 270 + ], + "type": "inline_equation", + "content": "I_{fb}" + }, + { + "bbox": [ + 320, + 234, + 553, + 270 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 320, + 282, + 473, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 282, + 473, + 295 + ], + "spans": [ + { + "bbox": [ + 320, + 282, + 473, + 295 + ], + "type": "text", + "content": "3.1. Edge-Attention Dense Block" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 320, + 300, + 552, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 300, + 552, + 378 + ], + "spans": [ + { + "bbox": [ + 320, + 300, + 552, + 378 + ], + "type": "text", + "content": "The Edge-Attention Dense (EA-Dense) block in our RWSC-Fusion is shown in Figure 3(a). The dense block is composed of four convolutional blocks, each taking the feature maps of all preceding blocks as input. To reinforce the information representation, we design and add an Edge-Attention (EA) module (shown in Figure 3(b)) into the top convolutional block before flowing into subsequent blocks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "spans": [ + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": "Given the low-level feature " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": " of the top block, we first employ " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": " average pooling layer with the stride of 1 to obtain the local mean feature. We subtract the local mean feature maps from the original feature maps to explore the structural texture, similar to Laplacian sharpening which is robust to noise for edge information extraction. Next, we calculate the mean responses along the channel dimension to reduce the channel number to 1, and obtain the edge-aware activation map " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": " by using the sigmoid function. At last, the edge-enhanced feature " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "\\widetilde{F}" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": " are acquired through the multiplication between the weight " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": " and feature " + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 320, + 379, + 553, + 513 + ], + "type": "text", + "content": ". The whole process of EA module can be expressed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 361, + 517, + 552, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 517, + 552, + 532 + ], + "spans": [ + { + "bbox": [ + 361, + 517, + 552, + 532 + ], + "type": "interline_equation", + "content": "w = \\sigma (M (\\left| A P 2 D (F) - F \\right|)) \\tag {5}", + "image_path": "5ace665f31e253370d9d9960f0a1de955340a706cb81b0a7517ce6405d8b8e50.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 401, + 536, + 552, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 401, + 536, + 552, + 550 + ], + "spans": [ + { + "bbox": [ + 401, + 536, + 552, + 550 + ], + "type": "interline_equation", + "content": "\\tilde {F} = _ {W} \\odot F \\tag {6}", + "image_path": "9cdde7c310d0cc050189453617e3552c8582fdde43ec369338773234e286a9d7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "spans": [ + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "inline_equation", + "content": "AP2D" + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "content": " denotes 2D average pooling, " + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "content": " denotes the mean value along the channel dimension, " + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "content": " denotes the sigmoid activation, " + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 320, + 552, + 552, + 587 + ], + "type": "text", + "content": " denotes pixel-wise multiplication." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "spans": [ + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "content": "Since the weight " + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "content": " can activate and enhance the edge and texture information through sharpening operation, the resulting feature " + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "inline_equation", + "content": "\\widetilde{F}" + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "content": " take advantage of both global and local texture information of the feature " + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "content": ". Therefore, in our EA-Dense block, each convolutional block takes as input the feature of all preceding block and the edge-enhanced feature " + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "inline_equation", + "content": "\\widetilde{F}" + }, + { + "bbox": [ + 320, + 588, + 553, + 669 + ], + "type": "text", + "content": ", and thus sharpen the image quality." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 320, + 680, + 552, + 693 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 680, + 552, + 693 + ], + "spans": [ + { + "bbox": [ + 320, + 680, + 552, + 693 + ], + "type": "text", + "content": "3.2. Region-Wise Style-Controlled Fusion Module" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 698, + 553, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 698, + 553, + 721 + ], + "spans": [ + { + "bbox": [ + 320, + 698, + 553, + 721 + ], + "type": "text", + "content": "Common image fusion methods usually fuse the features of two source images in a simple manner, such as addition," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "type": "text", + "content": "22400" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 101, + 283, + 190 + ], + "blocks": [ + { + "bbox": [ + 86, + 101, + 283, + 190 + ], + "lines": [ + { + "bbox": [ + 86, + 101, + 283, + 190 + ], + "spans": [ + { + "bbox": [ + 86, + 101, + 283, + 190 + ], + "type": "image", + "image_path": "7a21b9d8073ab04d71fd29fbc62c517e5f7595472ef29a9752c2893a7471f396.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 93, + 191, + 265, + 202 + ], + "lines": [ + { + "bbox": [ + 93, + 191, + 265, + 202 + ], + "spans": [ + { + "bbox": [ + 93, + 191, + 265, + 202 + ], + "type": "text", + "content": "Figure 4. Details of mask average pooling layer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 211, + 301, + 324 + ], + "blocks": [ + { + "bbox": [ + 69, + 211, + 301, + 324 + ], + "lines": [ + { + "bbox": [ + 69, + 211, + 301, + 324 + ], + "spans": [ + { + "bbox": [ + 69, + 211, + 301, + 324 + ], + "type": "image", + "image_path": "ecb45371fd9e6ab703bfb075cd6619d69cbda043b2e699484304cfff5441fe4f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 93, + 327, + 249, + 338 + ], + "lines": [ + { + "bbox": [ + 93, + 327, + 249, + 338 + ], + "spans": [ + { + "bbox": [ + 93, + 327, + 249, + 338 + ], + "type": "text", + "content": "Figure 5. Details of RWSC-Fusion module." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "spans": [ + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "text", + "content": "maximum or concatenation. However, for the fusion of the prohibited item and the baggage image, we focus more on the appearance fusion of the overlapping region rather than the global information fusion. Therefore, we propose a RWSC-Fusion module to fuse the features of prohibited item " + }, + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "inline_equation", + "content": "F_{f}" + }, + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "text", + "content": " and the baggage image " + }, + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 66, + 348, + 298, + 449 + ], + "type": "text", + "content": " in a region-wise style-controlled manner. The RWSC-Fusion module modulates the appearance of the overlapping region between the two images by applying region-wise normalization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 449, + 272, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 449, + 272, + 461 + ], + "spans": [ + { + "bbox": [ + 77, + 449, + 272, + 461 + ], + "type": "text", + "content": "The traditional region-wise normalization [28] is:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 124, + 465, + 298, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 465, + 298, + 493 + ], + "spans": [ + { + "bbox": [ + 124, + 465, + 298, + 493 + ], + "type": "interline_equation", + "content": "\\gamma_ {c, h, w} \\left(\\frac {b _ {n , c , h , w} - \\mu_ {c} (x)}{\\sigma_ {c} (x)}\\right) + \\beta_ {c, h, w} \\tag {7}", + "image_path": "46763c2a025735551439d88b6067c1ecccbe6baebe473f54f6c07e0f4892c64f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "spans": [ + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "inline_equation", + "content": "\\gamma_{c,h,w}" + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "inline_equation", + "content": "\\beta_{c,h,w}" + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "content": " represent pixel-wise scaling and shifting parameters. Some researchers [7] learn " + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "inline_equation", + "content": "\\gamma_{c,h,w}" + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "inline_equation", + "content": "\\beta_{c,h,w}" + }, + { + "bbox": [ + 66, + 498, + 298, + 560 + ], + "type": "text", + "content": " from the style maps by using mask average pooling, which is shown in Figure 4. However, such parameters have less potential for realizing rich and fine style-control." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 561, + 298, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 561, + 298, + 640 + ], + "spans": [ + { + "bbox": [ + 66, + 561, + 298, + 640 + ], + "type": "text", + "content": "By contrast, the region-wise normalization in RWSC-Fusion module innovate in two respects: (1) It learns the shifting and scaling parameters separately based on the mask average pooling and the deviation maps to modulate the mean and standard deviation; (2) It normalizes the local region adaptively with pixel-wise modulation parameters, to control the appearance of the region of interest." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "spans": [ + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": "The RWSC-Fusion module is detailed in Figure 5. On one branch, the features " + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "inline_equation", + "content": "F_{f}" + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": " of two images are first sent jointly to one convolution layer. Then, the resulting features " + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "inline_equation", + "content": "F_{fb}" + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": " with auxiliary mask of prohibited item are fed into the mask average pooling layer, where the average feature vectors are extracted and broadcast to create the mean maps " + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "inline_equation", + "content": "F_{fb}^{m}" + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": ". Next, we subtract the mean maps " + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "inline_equation", + "content": "F_{fb}^{m}" + }, + { + "bbox": [ + 66, + 640, + 298, + 722 + ], + "type": "text", + "content": " from" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "spans": [ + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": "the initial features " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "F_{fb}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " to get the local standard deviation maps " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "F_{fb}^{d}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": ". Lastly, the deviation maps " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "F_{fb}^{d}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " and the mean maps " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "F_{fb}^{m}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " pass through two separate convolution layers to generate the pixel-wise scaling and shifting parameters " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "\\gamma_{c,h,w}^{fb}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "\\beta_{c,h,w}^{fb}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": ". Meanwhile, on the other branch, we obtain parameters " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "\\gamma_{c,h,w}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "\\beta_{c,h,w}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " by doing the same operations on the feature " + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 320, + 105, + 552, + 196 + ], + "type": "text", + "content": " of the single baggage image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 196, + 552, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 196, + 552, + 230 + ], + "spans": [ + { + "bbox": [ + 320, + 196, + 552, + 230 + ], + "type": "text", + "content": "We design the region-specific modulation parameters through the region-wise merging, and thus the final modulation parameters are expressed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 367, + 232, + 552, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 232, + 552, + 248 + ], + "spans": [ + { + "bbox": [ + 367, + 232, + 552, + 248 + ], + "type": "interline_equation", + "content": "\\gamma_ {c, h, w} = M ^ {+} \\odot \\gamma_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\gamma_ {c, h, w} ^ {b} \\tag {8}", + "image_path": "bfe003de27291a1581d2ffd76d671a6edadad1694a35dc9b09a4c64c621cd2b3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 368, + 255, + 552, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 255, + 552, + 269 + ], + "spans": [ + { + "bbox": [ + 368, + 255, + 552, + 269 + ], + "type": "interline_equation", + "content": "\\beta_ {c, h, w} = M ^ {+} \\odot \\beta_ {c, h, w} ^ {f b} + (1 - M ^ {+}) \\odot \\beta_ {c, h, w} ^ {b} \\tag {9}", + "image_path": "b01d7648a09a4335bc3a75ab7343784c403ec7a318de3f238588c76f1e115b35.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "spans": [ + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "inline_equation", + "content": "M^{+}" + }, + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "text", + "content": " denotes the mask of prohibited item, while " + }, + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "inline_equation", + "content": "1 - M^{+}" + }, + { + "bbox": [ + 320, + 274, + 552, + 342 + ], + "type": "text", + "content": " denotes the complementary mask. The appearance of the overlapping region within the mask is modulated jointly by the prohibited item and baggage image, while the non-overlapping region is modulated by the single baggage image, avoiding the interference of prohibited item image." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 343, + 552, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 343, + 552, + 454 + ], + "spans": [ + { + "bbox": [ + 320, + 343, + 552, + 454 + ], + "type": "text", + "content": "Our region-adaptive normalization learns appropriate shifting and scaling parameters separately based on the mean maps and the deviation maps instead of single mask mean maps, so as to modulate the mean and standard deviation specifically and pointedly. Thus, it allows for fine control to generate rich stylization by considering the local information from the deviation maps. Hence, the RWSC-Fusion module enables the region-wise normal-appearing fusion of the prohibited item and baggage image to synthesize the prohibited X-ray security image." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 321, + 466, + 408, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 466, + 408, + 477 + ], + "spans": [ + { + "bbox": [ + 321, + 466, + 408, + 477 + ], + "type": "text", + "content": "3.3. Loss Function" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 484, + 552, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 484, + 552, + 518 + ], + "spans": [ + { + "bbox": [ + 320, + 484, + 552, + 518 + ], + "type": "text", + "content": "Existing unsupervised image fusion models usually maximize the similarity of fused image with source images instead of ground-truth, by using loss function as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 371, + 521, + 554, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 521, + 554, + 534 + ], + "spans": [ + { + "bbox": [ + 371, + 521, + 554, + 534 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = 1 - \\left[ w _ {1} \\bullet \\ell \\left(x _ {1}, y\\right) + w _ {2} \\bullet \\ell \\left(x _ {2}, y\\right) \\right] \\tag {10}", + "image_path": "12a236ec7a4d5c2e7c266a408968a0bf9a63d3b80126bebdeaf6664dac3fcc52.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "spans": [ + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "inline_equation", + "content": "\\ell(x, y)" + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "text", + "content": " denotes the similarity metrics, such as SSD or SSIM. The weights " + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "inline_equation", + "content": "w_1" + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "inline_equation", + "content": "w_2" + }, + { + "bbox": [ + 320, + 538, + 552, + 628 + ], + "type": "text", + "content": " represent the information preservation degree of two source images. However, these functions are inapplicable to X-ray security image, for two reasons: (1) they produce global fusion, including the non-overlapping region, which instead should remain intact; (2) the addition strategy of these functions does not conform to the attenuation character of X-ray security imagery." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "spans": [ + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": "As mentioned in Sec.2.1, when fusing the prohibited items " + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": " with the baggage image " + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": " by using the weights " + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": ", the fused X-ray image " + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "inline_equation", + "content": "I_{fb}" + }, + { + "bbox": [ + 320, + 628, + 552, + 664 + ], + "type": "text", + "content": " could be:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 327, + 668, + 550, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 668, + 550, + 685 + ], + "spans": [ + { + "bbox": [ + 327, + 668, + 550, + 685 + ], + "type": "interline_equation", + "content": "I _ {f b} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f} - w _ {2} \\mu_ {b} h _ {b}} = I _ {0} e ^ {- w _ {1} \\mu_ {f} h _ {f}} e ^ {- w _ {2} \\mu_ {b} h _ {b}} \\tag {11}", + "image_path": "3d1097439676affe52b45840f48fc0da5fc4b0420f324651d7c3eccc00b2cfe0.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 391, + 688, + 550, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 688, + 550, + 715 + ], + "spans": [ + { + "bbox": [ + 391, + 688, + 550, + 715 + ], + "type": "interline_equation", + "content": "I _ {f b} = \\frac {I _ {f} ^ {w _ {1}} \\cdot I _ {b} ^ {w _ {2}}}{I _ {0} ^ {w _ {1} + w _ {2} - 1}} \\tag {12}", + "image_path": "78b0dff2271e5041e6f65bf980fd177495340e504fd7dc58ac17131e8bd2216a.jpg" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 299, + 752 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 299, + 752 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 299, + 752 + ], + "type": "text", + "content": "22401" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 124, + 298, + 155 + ], + "blocks": [ + { + "bbox": [ + 67, + 105, + 298, + 123 + ], + "lines": [ + { + "bbox": [ + 67, + 105, + 298, + 123 + ], + "spans": [ + { + "bbox": [ + 67, + 105, + 298, + 123 + ], + "type": "text", + "content": "Table 1. Quantitative evaluations for image quality of the models with and without the EA modules." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 124, + 298, + 155 + ], + "lines": [ + { + "bbox": [ + 67, + 124, + 298, + 155 + ], + "spans": [ + { + "bbox": [ + 67, + 124, + 298, + 155 + ], + "type": "table", + "html": "
Modelwithout EA modulewith EA module
MAE2.0911.938
PSNR38.40239.084
", + "image_path": "6013f30057bc03f874d97be28a81be2a2814ebcf3613f3178c87809a8cf5d3e0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "spans": [ + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "text", + "content": "Therefore, the fused X-ray image " + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "inline_equation", + "content": "I_{fb}" + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "text", + "content": " is approximatively correlated with the multiplication rather than addition of the prohibited item " + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "text", + "content": " and the baggage image " + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 66, + 165, + 299, + 201 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 201, + 298, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 201, + 298, + 248 + ], + "spans": [ + { + "bbox": [ + 66, + 201, + 298, + 248 + ], + "type": "text", + "content": "In this case, we adjust Eq. (10) by using the logarithmic form, giving access to multiplication relationship in linear form. Finally, we develop a Luminance loss in Logarithmic form " + }, + { + "bbox": [ + 66, + 201, + 298, + 248 + ], + "type": "inline_equation", + "content": "(LL)\\mathcal{L}_{LL}" + }, + { + "bbox": [ + 66, + 201, + 298, + 248 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 79, + 249, + 298, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 249, + 298, + 269 + ], + "spans": [ + { + "bbox": [ + 79, + 249, + 298, + 269 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L L} = 1 - \\left[ w _ {1} \\bullet \\log \\ell \\left(I _ {f}, I _ {f b}\\right) + w _ {2} \\bullet \\log \\ell \\left(I _ {b}, I _ {f b}\\right) \\right] \\tag {13}", + "image_path": "4e380c694121cdfed33d3f3ed3a0d69c1c5bdc4e7688454e942b635e5537aa3b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "spans": [ + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "content": "We put " + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "content": " inside the metric formula to develop a new similarity metric " + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "inline_equation", + "content": "\\ell(x, y, w)" + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "content": ", and thus " + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LL}" + }, + { + "bbox": [ + 67, + 272, + 299, + 296 + ], + "type": "text", + "content": " turns into:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 89, + 297, + 298, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 297, + 298, + 317 + ], + "spans": [ + { + "bbox": [ + 89, + 297, + 298, + 317 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L L} = 1 - \\left[ \\log \\ell \\left(I _ {f}, I _ {f b}, w _ {1}\\right) + \\log \\ell \\left(I _ {b}, I _ {f b}, w _ {2}\\right) \\right] \\tag {14}", + "image_path": "579343047b2f6530eebe8b1a2b40720a3c6df63ba527149adebb633452f43caa.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 322, + 299, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 322, + 299, + 347 + ], + "spans": [ + { + "bbox": [ + 67, + 322, + 299, + 347 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 67, + 322, + 299, + 347 + ], + "type": "inline_equation", + "content": "\\ell (x,y,w) = \\frac{2\\mu_x\\mu_y + \\varepsilon}{\\mu_x^{4w} + \\mu_y^2 + \\varepsilon}" + }, + { + "bbox": [ + 67, + 322, + 299, + 347 + ], + "type": "text", + "content": ", and thus the local mean of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "spans": [ + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "text", + "content": "fused image " + }, + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "inline_equation", + "content": "\\mu_{fb}" + }, + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "text", + "content": " is expected to converge to " + }, + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "inline_equation", + "content": "\\mu_f^{w_1} \\cdot \\mu_b^{w_2}" + }, + { + "bbox": [ + 67, + 351, + 298, + 377 + ], + "type": "text", + "content": ". The details and deduce are in the supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "spans": [ + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": "We automatically estimate the weights " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " from the feature of R, G and B component of the prohibited item and the baggage image respectively, to get different power weights " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " for R, G and B component, and the sum of " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 66, + 378, + 298, + 433 + ], + "type": "text", + "content": " is adjusted to 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "spans": [ + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": "On the other hand, considering that the saturation " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "(S)" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " component of color X-ray security image is mostly correlated linearly with the energy responses, we assume that the " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " component of the fused image is correlated linearly with the multiplication of the " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " component of the two images. Therefore, the difference between the " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " component of the prohibited item " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "(S_{f})" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " and the fused image " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "(S_{fb})" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " comes almost from the " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " component of the baggage image " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "(S_{b})" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": ". Similarly, the difference between the " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S_{b}" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S_{fb}" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": " comes almost from " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "S_{f}" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": ". We develop an another loss term Correlation Loss of Saturation Difference (CSD) " + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CSD}" + }, + { + "bbox": [ + 67, + 433, + 299, + 562 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 80, + 563, + 298, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 563, + 298, + 613 + ], + "spans": [ + { + "bbox": [ + 80, + 563, + 298, + 613 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D _ {b} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {f}\\right) \\\\ D _ {f} = \\left(1 - S _ {f b}\\right) / \\left(1 - S _ {b}\\right) (15) \\\\ \\mathcal {L} _ {C S D} = 1 - \\left[ C C \\left(D _ {f}, 1 - S _ {f}\\right) + C C \\left(D _ {b}, 1 - S _ {b}\\right) \\right] / 2 (16) \\\\ \\end{array}", + "image_path": "7e43bcec6a7cf96fd9493a8ab4824f7a0e073d28ff54f0af71114d225cf377cc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 67, + 615, + 270, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 615, + 270, + 625 + ], + "spans": [ + { + "bbox": [ + 67, + 615, + 270, + 625 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 67, + 615, + 270, + 625 + ], + "type": "inline_equation", + "content": "CC" + }, + { + "bbox": [ + 67, + 615, + 270, + 625 + ], + "type": "text", + "content": " is the normalized correlation coefficient." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "spans": [ + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "text", + "content": "In addition, a third loss term is the reconstruction loss " + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{recon}}" + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "text", + "content": " of two source images " + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "inline_equation", + "content": "\\tilde{I}_f" + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "inline_equation", + "content": "\\tilde{I}_b" + }, + { + "bbox": [ + 67, + 626, + 298, + 650 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 113, + 652, + 298, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 652, + 298, + 670 + ], + "spans": [ + { + "bbox": [ + 113, + 652, + 298, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c o n}} = \\left\\| I _ {f}, \\tilde {I} _ {f} \\right\\| + \\left\\| I _ {b}, \\tilde {I} _ {b} \\right\\| \\tag {17}", + "image_path": "fa5854019fefa66db7bd75fc516584837813f430aee1cd9960985b79d143f6da.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 77, + 672, + 234, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 672, + 234, + 683 + ], + "spans": [ + { + "bbox": [ + 77, + 672, + 234, + 683 + ], + "type": "text", + "content": "In conclusion, the total loss function is:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 113, + 687, + 298, + 702 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 687, + 298, + 702 + ], + "spans": [ + { + "bbox": [ + 113, + 687, + 298, + 702 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {L L} + \\mathcal {L} _ {C S D} + \\mathcal {L} _ {\\text {r e c o n}} \\tag {18}", + "image_path": "7859b7624e151f5376566afcb675d89a802db46beb4e05b52df74d13a5cd55bc.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 321, + 106, + 437, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 106, + 437, + 119 + ], + "spans": [ + { + "bbox": [ + 321, + 106, + 437, + 119 + ], + "type": "text", + "content": "4. Experiment Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 321, + 131, + 382, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 131, + 382, + 142 + ], + "spans": [ + { + "bbox": [ + 321, + 131, + 382, + 142 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 320, + 148, + 553, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 148, + 553, + 193 + ], + "spans": [ + { + "bbox": [ + 320, + 148, + 553, + 193 + ], + "type": "text", + "content": "Private data: We have collected millions of X-ray security images from urban rail transit, railway, highway and other real-world daily security inspection scenario. There are more than 40 kinds of manually-annotated prohibited items." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 194, + 552, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 194, + 552, + 216 + ], + "spans": [ + { + "bbox": [ + 321, + 194, + 552, + 216 + ], + "type": "text", + "content": "Public data: The SIXray dataset [26] and OPIXray dataset [36], which have been introduced in Sec.1." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 321, + 227, + 451, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 227, + 451, + 240 + ], + "spans": [ + { + "bbox": [ + 321, + 227, + 451, + 240 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 320, + 245, + 552, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 245, + 552, + 358 + ], + "spans": [ + { + "bbox": [ + 320, + 245, + 552, + 358 + ], + "type": "text", + "content": "The training data are 12000 groups randomly composed by 12000 baggage images and 60 individual prohibited items of 15 categories. During training, all baggage images are resized to a resolution of " + }, + { + "bbox": [ + 320, + 245, + 552, + 358 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 320, + 245, + 552, + 358 + ], + "type": "text", + "content": ", and all prohibited item images are randomly padded with [255,255,255] to share the same size. It is important to note that the random padding of the prohibited item images is regulated by utilizing the activation maps of the baggage images, in order to enable realistic and appropriate location of the prohibited item in the internal region of the baggage." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 321, + 370, + 412, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 370, + 412, + 382 + ], + "spans": [ + { + "bbox": [ + 321, + 370, + 412, + 382 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 323, + 386, + 448, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 386, + 448, + 397 + ], + "spans": [ + { + "bbox": [ + 323, + 386, + 448, + 397 + ], + "type": "text", + "content": "4.3.1. Edge-Attention module" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 320, + 398, + 552, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 398, + 552, + 465 + ], + "spans": [ + { + "bbox": [ + 320, + 398, + 552, + 465 + ], + "type": "text", + "content": "Due to the sparse texture of X-ray security images and the information loss in deep neural network, the generated images often suffer from low sharpness. We design EA module in the dense blocks to extract and recover the texture information for the fused image. In this section, we evaluate the efficacy of the proposed EA module." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 320, + 465, + 552, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 465, + 552, + 611 + ], + "spans": [ + { + "bbox": [ + 320, + 465, + 552, + 611 + ], + "type": "text", + "content": "We quantitatively calculate the reconstruction loss of the non-overlapping regions between 6000 pairs of the fused images and the source images in terms of the Mean Absolute Error (MAE) and Peak Signal to-Noise Ratio (PSNR). The lower the MAE and the higher the PSNR, the closer the non-overlapping regions is to the source image and the higher the quality of fused images. The results are shown in Table 1. The model with EA modules produces lower MAE and higher PSNR than that without the EA modules. It indicates that the EA modules can effectively preserve the source information more completely in the resulting non-overlapping regions and improve the definition and sharpness of the synthesized images." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 320, + 611, + 552, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 611, + 552, + 723 + ], + "spans": [ + { + "bbox": [ + 320, + 611, + 552, + 723 + ], + "type": "text", + "content": "We visualize the synthesized images from the models with and without the EA modules in Figure 6. Comparing the regions within the purple ROI which are magnified into view at the top-right corner, the X-ray security images generated by the model without EA modules are blurred and miss details, such as the zipper in the second row and the shoe sole texture in the fourth row. On the contrast, the model with EA modules can activate and enhance texture and edge information by using the attention map shown in Figure 7. Thus it can alleviate the shortage of texture and" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 301, + 753 + ], + "type": "text", + "content": "22402" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 88, + 103, + 276, + 341 + ], + "blocks": [ + { + "bbox": [ + 88, + 103, + 276, + 341 + ], + "lines": [ + { + "bbox": [ + 88, + 103, + 276, + 341 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 276, + 341 + ], + "type": "image", + "image_path": "c902eb39c0d3237d4ead70513276f7eab1b69cd954475fbd36606bcfb24a16f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 343, + 300, + 384 + ], + "lines": [ + { + "bbox": [ + 67, + 343, + 300, + 384 + ], + "spans": [ + { + "bbox": [ + 67, + 343, + 300, + 384 + ], + "type": "text", + "content": "Figure 6. The generated images from the models with and without the EA modules. From left to right are: (a) original baggage image; (b) the synthesized images from the model without EA modules; (c) the synthesized images from the model with EA modules." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 70, + 391, + 295, + 520 + ], + "blocks": [ + { + "bbox": [ + 70, + 391, + 295, + 520 + ], + "lines": [ + { + "bbox": [ + 70, + 391, + 295, + 520 + ], + "spans": [ + { + "bbox": [ + 70, + 391, + 295, + 520 + ], + "type": "image", + "image_path": "3eee46c9f4c0fbdf74ec6a49d2791b08423cedb67c44d781ed115a96c193509a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 521, + 298, + 551 + ], + "lines": [ + { + "bbox": [ + 67, + 521, + 298, + 551 + ], + "spans": [ + { + "bbox": [ + 67, + 521, + 298, + 551 + ], + "type": "text", + "content": "Figure 7. The edge attention maps of the X-ray security images in Figure 6. The first row shows the original images, and the second row shows the edge attention maps extracted by the EA module." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 561, + 299, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 561, + 299, + 596 + ], + "spans": [ + { + "bbox": [ + 67, + 561, + 299, + 596 + ], + "type": "text", + "content": "offer clearer appearance. It further follows that the EA module can indeed provide high-quality images with sharp textures via the Edge Attention mechanism." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 606, + 206, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 606, + 206, + 618 + ], + "spans": [ + { + "bbox": [ + 67, + 606, + 206, + 618 + ], + "type": "text", + "content": "4.3.2. Region-wise normalization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 618, + 298, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 618, + 298, + 695 + ], + "spans": [ + { + "bbox": [ + 67, + 618, + 298, + 695 + ], + "type": "text", + "content": "Existing region-adaptive normalization methods learn the shifting and scaling parameters both based on the mask mean maps [7, 28]. On the contrast, we learn the shifting and scaling parameters separately based on the mask mean maps and deviation maps, so as to modulate the mean and standard deviation pointedly. In this section, we evaluate the efficacy of our normalization mechanism." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 696, + 299, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 696, + 299, + 719 + ], + "spans": [ + { + "bbox": [ + 67, + 696, + 299, + 719 + ], + "type": "text", + "content": "We visualize the generated X-ray security images from the fusion module with only mask average pooling layer" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 340, + 103, + 530, + 342 + ], + "blocks": [ + { + "bbox": [ + 340, + 103, + 530, + 342 + ], + "lines": [ + { + "bbox": [ + 340, + 103, + 530, + 342 + ], + "spans": [ + { + "bbox": [ + 340, + 103, + 530, + 342 + ], + "type": "image", + "image_path": "93ae644de86168c15f3c66298258655c3f42b40e4f813cf2a69dba7cd18ae8f3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 343, + 553, + 394 + ], + "lines": [ + { + "bbox": [ + 320, + 343, + 553, + 394 + ], + "spans": [ + { + "bbox": [ + 320, + 343, + 553, + 394 + ], + "type": "text", + "content": "Figure 8. The generated images from the fusion module with only mask average pooling layer and our RWSC-Fusion module. From left to right are: (a) prohibited items; (b) original baggage image; (c) the synthesized images from the model with only mask average pooling layer; (d) the synthesized images from our model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 320, + 404, + 552, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 404, + 552, + 483 + ], + "spans": [ + { + "bbox": [ + 320, + 404, + 552, + 483 + ], + "type": "text", + "content": "and our RWSC-Fusion module in Figure 8. By comparing the prohibited items within the red ROI, the prohibited items synthesized by the model with only mask average pooling layer are fuzzy due to a lack of texture details, while the prohibited items from our model are more clear. It proves that our region-adaptive normalization method allows for fine control to provide rich stylization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 495, + 539, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 495, + 539, + 507 + ], + "spans": [ + { + "bbox": [ + 320, + 495, + 539, + 507 + ], + "type": "text", + "content": "4.4. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 512, + 552, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 512, + 552, + 568 + ], + "spans": [ + { + "bbox": [ + 320, + 512, + 552, + 568 + ], + "type": "text", + "content": "In this section, we compare our RWSC-Fusion with four state-of-the-art image fusion methods: U2Fusion [38], FusionGAN [19], DeepFuse [13] and MEFNet [20], to evaluate the performance of X-ray security image fusion for the prohibited X-ray security image synthesis." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 320, + 568, + 553, + 726 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 568, + 553, + 726 + ], + "spans": [ + { + "bbox": [ + 320, + 568, + 553, + 726 + ], + "type": "text", + "content": "The synthesized images from different methods are shown in Figure 9. It can be seen that compared with U2Fusion, FusionGAN and DeepFuse, RWSC-Fusion alleviates the problem of global fusion and successfully preserves the original appearance of the non-overlapping regions in the baggage images. The overlapping regions marked by the red box from the competitors, especially MEFNet, noticeably deviate from our desired appearance that can match the real X-ray security images in terms of hue, saturation and sharpness. Overall, our model achieves superior visual performance than these four competitors. These well demonstrate that our fusion model is better suited to the X-ray security image, and can synthesize more ideal and realistic prohibited X-ray security images." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "text", + "content": "22403" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 104, + 498, + 285 + ], + "blocks": [ + { + "bbox": [ + 110, + 104, + 498, + 285 + ], + "lines": [ + { + "bbox": [ + 110, + 104, + 498, + 285 + ], + "spans": [ + { + "bbox": [ + 110, + 104, + 498, + 285 + ], + "type": "image", + "image_path": "7f105d7316869ce7218fba506e1e1d9f3b4490da41690f7eccc4786e18ee9882.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 285, + 528, + 296 + ], + "lines": [ + { + "bbox": [ + 67, + 285, + 528, + 296 + ], + "spans": [ + { + "bbox": [ + 67, + 285, + 528, + 296 + ], + "type": "text", + "content": "Figure 9. The X-ray baggage images fused with the prohibited item by four other fusion methods and the proposed RWSC-Fusion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 67, + 314, + 298, + 372 + ], + "blocks": [ + { + "bbox": [ + 67, + 305, + 292, + 314 + ], + "lines": [ + { + "bbox": [ + 67, + 305, + 292, + 314 + ], + "spans": [ + { + "bbox": [ + 67, + 305, + 292, + 314 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with state-of-the-art methods." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 314, + 298, + 372 + ], + "lines": [ + { + "bbox": [ + 67, + 314, + 298, + 372 + ], + "spans": [ + { + "bbox": [ + 67, + 314, + 298, + 372 + ], + "type": "table", + "html": "
MetricQEQabfEIPSNR
U2Fusion [38]0.56350.346748.819016.7155
FusionGAN [19]0.56400.592478.093413.8471
DeepFuse [13]0.61570.181441.626616.8173
MEFNet [20]0.75090.609085.040317.7364
Ours0.83390.647281.380718.6455
", + "image_path": "827ee848f20a97b098940a105a37d5702bd3a2461863a5e40483c0fc4ffbcbc0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 383, + 298, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 383, + 298, + 507 + ], + "spans": [ + { + "bbox": [ + 66, + 383, + 298, + 507 + ], + "type": "text", + "content": "The quantitative comparisons are performed on the 6000 image pairs. Four metrics, namely, QE [9], Qabf [39], Edge Intensity (EI) [2], and PSNR are used for evaluation. For all four metrics, larger values indicate better performance. The comparative results of four metrics are shown in Table 2. Our RWSC-Fusion ranks first on QE, Qabf and PSNR, proving that our method can synthesize images with richer textures and details. Although our RWSC-Fusion ranks second on EI, it also achieves comparable results. The promising outcomes show that our model keeps high fidelity with less distortion and noise." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 518, + 229, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 518, + 229, + 530 + ], + "spans": [ + { + "bbox": [ + 67, + 518, + 229, + 530 + ], + "type": "text", + "content": "4.5. Supplement to Private Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 66, + 536, + 298, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 536, + 298, + 558 + ], + "spans": [ + { + "bbox": [ + 66, + 536, + 298, + 558 + ], + "type": "text", + "content": "In this section, we synthesize the prohibited X-ray security images on our private dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 559, + 298, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 559, + 298, + 602 + ], + "spans": [ + { + "bbox": [ + 66, + 559, + 298, + 602 + ], + "type": "text", + "content": "First, we conduct subjective evaluation experiment, which is detailed in the supplementary material. This result demonstrates that our synthetic prohibited X-ray security images are realistic enough to fool the inspectors." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 602, + 298, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 602, + 298, + 670 + ], + "spans": [ + { + "bbox": [ + 66, + 602, + 298, + 670 + ], + "type": "text", + "content": "To analyze the efficacy of supplementing the training samples, we compare the performance of prohibited item detection model under the training of real and synthetic images. We use the YOLOv4 as the detector [4] to detect the five kinds of prohibited items: plastic bottles, cutters, scissors, thermos cups and glass bottles." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 66, + 670, + 298, + 726 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 670, + 298, + 726 + ], + "spans": [ + { + "bbox": [ + 66, + 670, + 298, + 726 + ], + "type": "text", + "content": "The real training dataset contains 40000 samples (DataR: with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles). Besides, we train the detector with the following dataset: (1) DataR1/2: We remove 20000 samples from DataR," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 337, + 305, + 552, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 305, + 552, + 338 + ], + "spans": [ + { + "bbox": [ + 337, + 305, + 552, + 338 + ], + "type": "text", + "content": "resulting in 20000 training samples with 13127 plastic bottles, 17055 cutters, 5117 scissors, 2518 thermos cups and 8710 glass bottles." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 338, + 552, + 494 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 321, + 338, + 552, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 338, + 552, + 439 + ], + "spans": [ + { + "bbox": [ + 321, + 338, + 552, + 439 + ], + "type": "text", + "content": "(2) DataRS: We synthesize and supplement the prohibited items into DataR1/2, resulting in 20000 samples with 26048 plastic bottles, 34856 cutters, 10391 scissors, 4968 thermos cups and 17526 glass bottles, with the same number of prohibited items as the DataR. (Note: since there are no extra 20000 negative samples excluding all five kinds of prohibited items, we cannot achieve the pure synthesis of 20000 samples, to be perfectly aligned with DataR)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 321, + 439, + 552, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 439, + 552, + 494 + ], + "spans": [ + { + "bbox": [ + 321, + 439, + 552, + 494 + ], + "type": "text", + "content": "(3) DataRS+: We synthesize prohibited items into other 20000 samples, and merge new synthetic samples with 20000 samples in DataR, resulting in 40000 samples with total 38983 plastic bottles, 51956 cutters, 15597 scissors, 7522 thermos cups and 26034 glass bottles." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 321, + 494, + 552, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 494, + 552, + 516 + ], + "spans": [ + { + "bbox": [ + 321, + 494, + 552, + 516 + ], + "type": "text", + "content": "The detection results on the 9954 testing samples of YOLOv4 trained with above datasets are listed in Table 3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 517, + 552, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 517, + 552, + 640 + ], + "spans": [ + { + "bbox": [ + 320, + 517, + 552, + 640 + ], + "type": "text", + "content": "As compared with DataR1/2, the DataRS provides a considerable increase of more than " + }, + { + "bbox": [ + 320, + 517, + 552, + 640 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 320, + 517, + 552, + 640 + ], + "type": "text", + "content": " in mAP after we synthesize prohibited items in DataR1/2. This proves that our synthetic prohibited items are indeed beneficial to training the detection model. Moreover, since the results of DataRS can be comparable with or even better than those of DataR, it demonstrates the authenticity and reliability of our synthetic prohibited items for replacing the real ones. Accordingly, with the addition and the contribution of synthetic prohibited items, DataRS+ also has a remarkable advantage over DataR." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 320, + 652, + 547, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 652, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 320, + 652, + 547, + 665 + ], + "type": "text", + "content": "4.6. Supplement to SIXray and OPIXray Dataset" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 670, + 552, + 726 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 670, + 552, + 726 + ], + "spans": [ + { + "bbox": [ + 320, + 670, + 552, + 726 + ], + "type": "text", + "content": "In this section, we evaluate on public SIXray [26] and OPIXray dataset [36]. We fuse our private prohibited items with the negative samples in SIXray and OPIXray dataset. Moreover, we directly apply the model trained by our private dataset without any additional parameter tuning." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 300, + 752 + ], + "type": "text", + "content": "22404" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 68, + 126, + 302, + 286 + ], + "blocks": [ + { + "bbox": [ + 67, + 105, + 298, + 124 + ], + "lines": [ + { + "bbox": [ + 67, + 105, + 298, + 124 + ], + "spans": [ + { + "bbox": [ + 67, + 105, + 298, + 124 + ], + "type": "text", + "content": "Table 3 Detection results of YOLOv4 trained with different data on private dataset (recall and precision at confidence level of 0.5)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 68, + 126, + 302, + 286 + ], + "lines": [ + { + "bbox": [ + 68, + 126, + 302, + 286 + ], + "spans": [ + { + "bbox": [ + 68, + 126, + 302, + 286 + ], + "type": "table", + "html": "
Training DataDataRDataR1/2DataRSDataRS+
Plastic bottleRecall69.4964.8270.4674.15
Precision85.3683.2988.1485.13
AP69.5071.1671.0076.97
CutterRecall86.1774.0481.7084.50
Precision92.6287.6091.8193.45
AP86.9679.9883.4987.70
ScissorRecall71.2258.0370.8772.97
Precision90.6089.3488.3788.23
AP74.2866.8172.8378.29
Therm os cupRecall88.8688.8691.5992.76
Precision93.5290.1391.3892.54
AP85.5286.1788.9890.25
Glass bottleRecall56.4948.7458.7158.82
Precision86.7980.9784.0288.15
AP56.3153.7658.1361.87
mAP74.5271.5874.8879.02
", + "image_path": "4b2a282c4e699f116564ca1ddf5a05294f74f7a14ef77cdd458d2f1ec0e15ad2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 296, + 298, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 296, + 298, + 375 + ], + "spans": [ + { + "bbox": [ + 66, + 296, + 298, + 375 + ], + "type": "text", + "content": "For SIXRay dataset, it contains six kinds of prohibited items. We don't use the hammer class since it involves merely 60 samples. The SIXRay10 dataset contains 13412 testing samples, and 74960 training samples (SIXR:7496 positive samples with 4322 guns, 2758 knives, 2816 wrenches, 4624 pliers and 918 scissors). Moreover, we also train YOLOv4 by using following 74960 training samples:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 375, + 298, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 375, + 298, + 408 + ], + "spans": [ + { + "bbox": [ + 67, + 375, + 298, + 408 + ], + "type": "text", + "content": "(1) SIXR1/2: We remove half the (3748) positive samples from SIXR, and supplement the other 3748 negative samples into SIXR." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 408, + 298, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 408, + 298, + 465 + ], + "spans": [ + { + "bbox": [ + 67, + 408, + 298, + 465 + ], + "type": "text", + "content": "(2) SIXRS: We synthesize the prohibited items into the newly-added 3748 negative samples in SIXR1/2, to supplement the positive samples, resulting in mixed 7496 true/pseudo positive samples with the same number of prohibited items as SIXR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 465, + 298, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 465, + 298, + 521 + ], + "spans": [ + { + "bbox": [ + 67, + 465, + 298, + 521 + ], + "type": "text", + "content": "(3) SIXRS+: We synthesize prohibited items into other new 3748 negative samples, and replace 3748 negative samples in the SIXR, resulting in mixed 11244 true/pseudo positive samples, with 6469 guns, 4154 knives, 4195 wrenches, 6933 pliers and 1398 scissors." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 66, + 521, + 299, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 521, + 299, + 587 + ], + "spans": [ + { + "bbox": [ + 66, + 521, + 299, + 587 + ], + "type": "text", + "content": "For OPIXray dataset, it contains 7109 training and 1776 testing images for cutter detection. The training datasets are: (1) OPIR: All the original 7109 images; (2) OPIRS: 3555 images supplemented with synthesized cutter, with the same number of cutter as OPIR; (3) OPIRS+: 7109 images supplemented with half the synthesized cutter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 588, + 298, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 588, + 298, + 610 + ], + "spans": [ + { + "bbox": [ + 66, + 588, + 298, + 610 + ], + "type": "text", + "content": "The detection results on SIXray and OPIXray dataset are respectively listed in Table 4 and Table 5." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 610, + 298, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 610, + 298, + 722 + ], + "spans": [ + { + "bbox": [ + 66, + 610, + 298, + 722 + ], + "type": "text", + "content": "By comparing the models trained by SIXRS and SIXR1/2, SIXRS recover the degraded performance of SIXR1/2 by supplementing the synthetic positive samples effectively. Moreover, compared to SIXR, SIXRS can achieve higher mAP, and overall higher AP except for the scissor class. The comparison of OPIRS and OPIR also well verifies that our synthetic cutters are real enough to supplement the missing samples. The SIXRS achieves higher precision but lower recall for the scissor class, because our private scissor item database does not cover" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 321, + 126, + 552, + 286 + ], + "blocks": [ + { + "bbox": [ + 320, + 105, + 552, + 125 + ], + "lines": [ + { + "bbox": [ + 320, + 105, + 552, + 125 + ], + "spans": [ + { + "bbox": [ + 320, + 105, + 552, + 125 + ], + "type": "text", + "content": "Table 4 Detection results of YOLOv4 trained with different data on SIXray dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 126, + 552, + 286 + ], + "lines": [ + { + "bbox": [ + 321, + 126, + 552, + 286 + ], + "spans": [ + { + "bbox": [ + 321, + 126, + 552, + 286 + ], + "type": "table", + "html": "
Training DataSIXRSIXR1/2SIXRSSIXRS+
GunRecall79.7373.0283.2383.69
Precision96.3291.7697.3397.17
AP78.7175.2182.1982.74
KnifeRecall58.8845.6264.1766.04
Precision92.6586.3992.7993.39
AP62.8447.8866.6469.17
WrenchRecall55.9724.2559.3366.04
Precision87.7260.7583.6883.49
AP65.9326.3066.8268.88
PlierRecall66.3550.0771.4576.14
Precision85.4972.3486.8185.16
AP74.2057.6375.8479.53
ScissorRecall63.6225.7052.8067.76
Precision91.1666.2791.8785.80
AP72.1139.0862.9473.60
mAP70.7649.2270.8974.78
", + "image_path": "1864128a4a621b4834632a417b4e4f0191660db871af183fcd2e3fa155cd4a70.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 324, + 307, + 548, + 355 + ], + "blocks": [ + { + "bbox": [ + 321, + 297, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 321, + 297, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 321, + 297, + 547, + 307 + ], + "type": "text", + "content": "Table 5 Detection results of different training data on OPIXray." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 307, + 548, + 355 + ], + "lines": [ + { + "bbox": [ + 324, + 307, + 548, + 355 + ], + "spans": [ + { + "bbox": [ + 324, + 307, + 548, + 355 + ], + "type": "table", + "html": "
Training dataOPIXray dataset
RecallPrecisionAP
OPIR71.0875.8567.47
OPIRS71.1476.6072.20
OPIRS+80.4690.1384.80
", + "image_path": "70f86669a2033318214b8a270530c875ff400f4687dd18f147df565a53dac1ea.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 320, + 365, + 553, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 365, + 553, + 466 + ], + "spans": [ + { + "bbox": [ + 320, + 365, + 553, + 466 + ], + "type": "text", + "content": "all the scissor type of SIXRay dataset, such as nail clipper set, to simulate the SIXRay samples. The recall and AP of the scissor class could be improved furthermore if the prohibited items that are more similar to SIXRay dataset are used for fusion. The comparison results between the SIXR and SIXRS+, OPIR and OPIRS+ also both can indicate that our synthetic positive images are beneficial in augmenting the training dataset to further improve the performance of the detection model." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 320, + 479, + 392, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 479, + 392, + 491 + ], + "spans": [ + { + "bbox": [ + 320, + 479, + 392, + 491 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 495, + 552, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 495, + 552, + 687 + ], + "spans": [ + { + "bbox": [ + 320, + 495, + 552, + 687 + ], + "type": "text", + "content": "We propose a RWSC-Fusion model, which fuses the prohibited items with baggage image in a Region-Wise Style-Controlled manner, for synthesizing the prohibited X-ray security images. The RWSC-Fusion learns the fused X-ray security images unsupervisedly based on novel loss functions: LL and CSD. Moreover, to generate more high-quality realistic and images, we innovate style-controlled mechanism and Edge-Attention module. The ablation studies verify the efficacy of the RWSC-Fusion and Edge-Attention module in achieving superior perceptual quality. The comparative experimental results illustrate that our method outperforms the state-of-the-arts in the field of X-ray security image. The performance comparison of the detector training demonstrates the authenticity and reliability of the synthetic images in promoting downstream tasks. In future work, we will generalize RWSC-Fusion to solve multiple fusion problems." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 320, + 697, + 552, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 697, + 552, + 719 + ], + "spans": [ + { + "bbox": [ + 320, + 697, + 552, + 719 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by Zhejiang Dahua Technology Co., Ltd. and Zhejiang University." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "text", + "content": "22405" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 106, + 124, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 106, + 124, + 117 + ], + "spans": [ + { + "bbox": [ + 68, + 106, + 124, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 122, + 299, + 717 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 69, + 122, + 298, + 153 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 122, + 298, + 153 + ], + "spans": [ + { + "bbox": [ + 69, + 122, + 298, + 153 + ], + "type": "text", + "content": "[1] Samet Akcay, Toby P. 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In Proceedings of European Conference on Computer Vision (ECCV), 2016." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "spans": [ + { + "bbox": [ + 277, + 743, + 300, + 753 + ], + "type": "text", + "content": "22407" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_content_list.json b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..117c72edac0706a1f907054f8badce00290ddac1 --- /dev/null +++ b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_content_list.json @@ -0,0 +1,1696 @@ +[ + { + "type": "text", + "text": "RaBit: Parametric Modeling of 3D Biped Cartoon Characters with a Topological-consistent Dataset", + "text_level": 1, + "bbox": [ + 174, + 130, + 794, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhongjin Luo $^{1*}$ Shengcai Cai $^{1,3*}$ Jinguo Dong $^{1}$ Ruibo Ming $^{1,4}$ Liangdong Qiu $^{2,1}$ Xiaohang Zhan $^{3}$ Xiaoguang Han $^{1,2\\dagger}$", + "bbox": [ + 181, + 200, + 781, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ SSE, CUHKSZ $^{2}$ FNii, CUHKSZ $^{3}$ Huawei Technologies Co., Ltd. $^{4}$ Tsinghua University", + "bbox": [ + 99, + 253, + 864, + 277 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0ef10dedb6165916e913eebc0822dd69d3664f972002d09472ed23390db7439d.jpg", + "image_caption": [ + "Figure 1. We present 3DBiCar, the first large-scale repository of 3D biped cartoon characters. It contains 1,500 topologically consistent, textured, and skinned 3D high-quality meshes manually created by professional artists, covering 15 species. Further, we propose RaBit, the first cartoon character parametric model simultaneously parameterizing shape, pose, and texture." + ], + "image_footnote": [], + "bbox": [ + 98, + 305, + 870, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 580, + 313, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Assisting people in efficiently producing visually plausible 3D characters has always been a fundamental research topic in computer vision and computer graphics. Recent learning-based approaches have achieved unprecedented accuracy and efficiency in the area of 3D real human digitization. However, none of the prior works focus on modeling 3D biped cartoon characters, which are also in great demand in gaming and filming. In this paper, we introduce 3DBiCar, the first large-scale dataset of 3D biped cartoon characters, and RaBit, the corresponding parametric model. Our dataset contains 1,500 topologically consistent high-quality 3D textured models which are manually crafted by professional artists. Built upon the data, RaBit is thus designed with a SMPL-like linear blend shape model and a StyleGAN-based neural UV-texture generator, simultaneously expressing the shape, pose, and texture. To demonstrate the practicality", + "bbox": [ + 75, + 614, + 473, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of 3DBiCar and RaBit, various applications are conducted, including single-view reconstruction, sketch-based modeling, and 3D cartoon animation. For the single-view reconstruction setting, we find a straightforward global mapping from input images to the output UV-based texture maps tends to lose detailed appearances of some local parts (e.g., nose, ears). Thus, a part-sensitive texture reasoner is adopted to make all important local areas perceived. Experiments further demonstrate the effectiveness of our method both qualitatively and quantitatively. 3DBiCar and RaBit are available at gaplab.cuhk.edu.cn/projects/RaBit.", + "bbox": [ + 500, + 582, + 895, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 767, + 632, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid development of digitization, creating high-quality 3D articulated characters is highly demanded in game platforms, film industries, and metaverse scenarios. However, even for expert artists, creating a 3D character is labor-intensive and time-consuming. Therefore, reducing the cost of producing visually plausible 3D characters is essential in the field of computer vision and graphics.", + "bbox": [ + 496, + 794, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Z. Luo and S. Cai contribute equally.", + "bbox": [ + 76, + 875, + 279, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 80, + 887, + 204, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12825", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, researchers have made great progress in digitizing realistic human characters. The emergence and popularity of various 3D sensing devices make capturing 3D data from the real world convenient, prompting a growing number of 3D real-people scanned datasets [3,7,12,43,45,53,54,56]. Based on these large-scale datasets, several powerful parametric models [5,12,35,39] have been developed to facilitate the reconstruction and analysis of human shapes, actions, and interactions. With the help of parametric models, deep learning techniques have shown the potential to efficiently infer accurate 3D digital humans from single-view images [26,39] or even sparse sketches [9,24,48]. Most recently, there are some works [36,41] that devote to exploring the intelligent generation of cartoon-like character heads. However, none of the prior works focuses on the modeling of 3D full-body biped cartoon characters, which are also in great demand in the area of gaming (e.g., Animal Crossing), filming (e.g., Zootopia), and virtualizing (e.g., Metaverse). In this work, we raise a new problem to the community: How to quickly produce 3D biped cartoon characters from easy-to-obtain inputs (e.g., a single image)?", + "bbox": [ + 76, + 90, + 472, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Revisiting the road map of realistic human digitization, the first step to tackling the above problem is building a high-quality 3D biped cartoon characters dataset. We thus introduce 3DBiCar, the first large-scale publicly available 3D biped cartoon character dataset following three criteria: 1) Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models covering 15 species, as shown in the Fig. 3. 2) Richness. Each model in 3DBiCar owns not only a detailed shape but also a texture UV-map, which are matched with a reference image. Additionally, each character is attached with two models, one with T-pose and another with the reference pose. 3) Topological-consistency. Each 3D model is created by carefully deforming a pre-defined template mesh. All 3D characters in 3DBiCar are unified in topology, paving the way to learn a skinned parametric model. Fig. 1 shows some representative models of the proposed dataset.", + "bbox": [ + 76, + 411, + 472, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on 3DBiCar, we further propose a generative model, dubbed RaBit, for 3D biped cartoon character generation. It combines a linear blend shape model with a neural texture generator and simultaneously parameterizes the shape, pose, and texture to a low-dimensional parametric space. For shape and pose modeling, numerous methods have shown principal component analysis's (PCA's) advantage in building decent statistical shape models [5, 12, 32, 39]. Inspired by SMPL [35], we utilize the traditional PCA technique to parameterize shape. Due to the variety and complexity of cartoon texture, directly adopting PCA for texture modeling fails to reconstruct details and falls into blurry results. We tackle this problem by introducing a StyleGAN-based generator.", + "bbox": [ + 76, + 670, + 472, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To explore the practical usage of 3DBiCar and RaBit, we", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "first conduct the application of single-view reconstruction. Considering prior works for SMPL-based human geometry generation from single-view images [6, 26, 30], we build a baseline method with our dataset and the parametric model. We select one regression-based method for pose and shape inference. For texture inference, we find directly applying a global texture-generator tends to make the results lose detailed appearances, especially for some local but important regions (e.g., nose and ears). Thus a part-sensitive reasoner is utilized to deal with different local regions. We term our baseline method for single-view reconstruction as BiCarNet. Moreover, two further applications, i.e., sketch-based modeling and 3D character animation, are also explored. Experimental results on these applications demonstrate that it is already able to generate reasonable outputs.", + "bbox": [ + 496, + 90, + 893, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions include:", + "bbox": [ + 519, + 318, + 792, + 332 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 high-quality textured 3D models with a consistent mesh topology.", + "- We propose RaBit, the first 3D full-body cartoon parametric model for biped character modeling. We will release both 3DBiCar and RaBit for future research.", + "- We build BiCarNet, the baseline method to reconstruct 3D biped cartoon characters from a single-view image. A part-sensitive reasoner is adopted for detailed texture generation.", + "- Two other applications, i.e., sketch-based modeling and 3D character animation, are also conducted to demonstrate the promising potential of 3DBiCar and RaBit." + ], + "bbox": [ + 519, + 343, + 893, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 588, + 640, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Character Datasets. In general, 3D character datasets could be categorized as real-captured and computer-designed datasets. For capturing character data from the real world, the availability of 3D scanning devices has enabled researchers to collect many scanned 3D human-related datasets, mainly focusing on human faces [10] and bodies [13]. For human faces, FaceWarehouse [12] collects large-scale 3d faces with high diversity in age, ethnicity, and expression. FaceScape [53] further builds a large-scale detailed 3D face dataset with high resolution in texture and mesh. For human bodies, CAESAR dataset [43] opens up the learning of the human body and is widely used for body shape modeling for its shape diversity and satisfying resolution of meshes. Many following works [3,7,45,54,56] extend [43] in shape, pose, and texture, on quantity and quality. Although these real-captured datasets are widely used in realistic human digitalization, they are unsuitable for imaginary character generation.", + "bbox": [ + 496, + 613, + 893, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For designing character data with computers, researchers try to perform deformation on real 3D human faces or bodies", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12826", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to construct exaggerated shapes programmatically [11,24,46, 51]. Their results lack diversity and are far from satisfactory. To address this, 3DCaricShop [41] proposes a large-scale 3D exaggerated faces dataset. SimpModeling [36] constructs a large man-made animalmorphic head dataset. Although using 3DCaricShop and SimpModeling could facilitate the generation of unreal character heads, it still remains a problem to synthesize full-body cartoon characters due to the lack of corresponding body data. In our work, we tackle this problem by introducing a large 3D biped cartoon character dataset, 3DBiCar.", + "bbox": [ + 75, + 90, + 472, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parametric Shape Modeling. Parametric models of shapes are widely used in 3D digitizations. Blanz et al. [5] pioneer parametric modeling using PCA and release a 3D statistical morphable face model (3DMM). Their parameterization models textured faces and provides a set of controls for intuitively manipulating shapes, expressions, and textures. Since then, PCA-based parameterizing has gradually dominated the area of statistical shape modeling over the past decades. Following 3DMM, researchers model the whole head to represent the neck region and 3D head rotations [12, 32]. Allen et al. [2] open up the study of full body parameterization. However, they focus only on body shape and omit the body pose. SCAPE [3] represents body shape and pose in terms of triangle deformations, while SMPL [35] models a whole range of natural shapes and poses based on vertex displacements. SMPL-X [39] integrates SMPL [35] with FLAME [32] head model and the MANO [44] hand model for expressive capturing of bodies, hands and faces together. With recent advances in deep learning, researchers turn to explore nonlinear shape models using neural networks [1, 4, 8, 42, 52, 57]. However, since these non-linear modeling methods are inferior in simplicity, robustness and availability, PCA-based methods remain prevalent in the research community. In this paper, we also adopt PCA into RaBit to model the geometry of 3D biped cartoon characters.", + "bbox": [ + 75, + 261, + 472, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the above parametric models, researchers have made remarkable progress in human digitization, such as reconstruction from simple inputs (e.g., a single image or sparse sketches) [6, 15, 24, 26, 40] and real-time pose retargeting [14, 29, 50]. For instance, SMPLify [6] estimates 3D body shape and pose parameters automatically from 2D joints with multiple ellipsoids. HMR [26] proposes an end-to-end framework for reconstructing a full 3D mesh of a human body from a single RGB image. DeepSketch2Face [24] proposes a sketch-based system for inferring 3D face models from 2D sketches with the help of parametric models and CNN-based deep regression networks. TCMR [14] presents a temporally consistent mesh recovery system for recovering smooth 3D human motion from monocular videos. To probe the capability of RaBit to downstream applications, we conduct various utilization, such as single-view cartoon character reconstruction, sketch-based character modeling,", + "bbox": [ + 75, + 643, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and 3D cartoon animation. Experimental results demonstrate the practicality of 3DBiCar and RaBit.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parametric Texture Modeling. Traditionally, textures are modeled as a linear subspace using the similar idea of body blendshape models. Blanz et al. [5] represent the face appearance in per-vertex colors and parameterize texture as a linear model based on PCA. Dai et al. [16] store texture information in a UV space where the texture resolution is unconstrained by mesh resolution. Moschoglou et al. [37] formulate a robust matrix factorization problem to learn the parametric representation of facial UV maps from a collection of training textures. However, these linear texture models may lead to a sub-optimal appearance output [18, 23] due to the weak assumption of Gaussian and tend to produce blurry results.", + "bbox": [ + 496, + 121, + 893, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With recent advances in deep learning, researchers turn to utilize deep neural networks to model texture. A number of deep generative models [17, 19-22, 31, 38, 47] have been proposed to parameterize texture into a latent space. For example, GANFIT [21] utilizes GAN-based neural networks to train a generator of facial texture in UV space for 3D face reconstruction. StylePeople [22] incorporates neural texture synthesis, mesh rendering, and neural rendering into the joint generation process to train a neural texture generator for the task of single-view human reconstruction. GET3D [20] introduces a texture-field generative model that directly generates explicit textured 3D meshes, ranging from cars, chairs, animals, motorbikes, and human characters to buildings. These methods have shown the promising capacity of neural generators to represent texture. In our work, we adopt a GAN-based neural texture generator into RaBit to provide high-quality texture modeling.", + "bbox": [ + 496, + 316, + 895, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dataset", + "text_level": 1, + "bbox": [ + 500, + 588, + 588, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considerable progress has been made in digitizing realistic and articulated human characters. However, efficiently creating visually plausible biped cartoon characters remains demanding and challenging, mainly due to the lack of data. In this work, we propose to fill this gap by introducing 3DBiCar, the first large-scale full-body 3D biped character data. We build 3DBiCar following three rules:", + "bbox": [ + 496, + 613, + 893, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models. First, we carefully collect images of 2D full-body biped cartoon characters with diverse identities, shape, and textural styles from the Internet, resulting in 15 character species and 4 image styles, as shown in Fig. 3. Then we recruit six professional artists to create 3D corresponding character models according to the collected reference images. The modeling result is required to be matched with the reference images as much as possible. The representative image-model pairs sampled from our dataset are shown in Fig. 2.", + "bbox": [ + 496, + 719, + 893, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Topological-consistency. The key to building a linear", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12827", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e68fb4cb185abdc6e22d9dae796615591554ac9c68d47c27925eb5598da69136.jpg", + "image_caption": [ + "Figure 2. The gallery of the representative examples sampled from 3DBiCar. Each collected reference image is followed by the T-pose model and the posed model, created by professional artists. 3DBiCar contains 1,500 topologically consistent, textured and skinned 3D high-quality models with paired 2D images, which covers 15 species and 4 image styles." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 883, + 410 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9ffcc41dce4b8f33739dc01ae3a938315c4c9f4b0c00835d7da31c9d07b5bac6.jpg", + "image_caption": [ + "Figure 3. Data distribution. Chart (a) illustrates the number of 15 species of bipedal cartoon characters in 3DBiCar. Chart (b) shows the number of four styles of reference images collected in our dataset." + ], + "image_footnote": [], + "bbox": [ + 86, + 484, + 455, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "parametric shape model is keeping a unified mesh topology. Traditional human parametric models utilize a template mesh to register different human body scans with 3D landmarks to keep topologically uniform. Inspired by this, we first create a template mesh with several 3D colored landmarks as shown in Fig. 4. All six artists are required to craft 3D models by deforming the above-predefined template under the constraints of these obvious landmarks. We set up a review committee of 10 to check these models based on the landmarks, ensuring the consistency of mesh topology. The landmarks could also be used to compute the position of models' joints for body posing or character animation. The topological consistency", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/699dca7352e06eb10e8a0e2dd22341ba864528dc33897f66ffa4ca36f79b4a98.jpg", + "image_caption": [ + "Figure 4. Template. The models in the center are the predefined template mesh with landmarks. It can be seen that we refine the structure on specific regions, where a complex nose or tail may exist. The colored regions and delineated lines denote the landmarks. These landmarks represent specific components of the character's body, such as elbow and eye socket. During model crafting, artists are required to deform the template model while keeping the landmarks in the position where the original body components are." + ], + "image_footnote": [], + "bbox": [ + 509, + 487, + 888, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of 3DBiCar paves the way to learn a skinned parametric model, which we will discuss in Sec. 4.", + "bbox": [ + 496, + 809, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Richness. We provide various forms of data for each character. There are not only the 3D shape meshes and UV-space textures carefully crafted by artists but also collected reference images. For each character, artists are asked first", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12828", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to create a T-pose mesh and then deform it to match the reference pose. Furthermore, all the models are rigged and skinned using a predefined skeleton and skinning weight matrix, which enables further animation production for characters. In addition, each character contains two separate eyeballs specifically designed for facial animation. The body mesh of each character comprises 38,726 vertices and 77,448 faces, while each eyeball consists of 1,025 vertices and 2,046 faces.", + "bbox": [ + 75, + 90, + 472, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Parametric Modeling", + "text_level": 1, + "bbox": [ + 76, + 239, + 282, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose the first parametric model of 3D biped cartoon characters (RaBit), which contains a linear blend model for shapes and a neural generator for textures. RaBit simultaneously parameterizes the shape, pose, and texture of 3D biped characters. Specifically, we decompose the parametric space into identity-related body parameter $B$ (Sec. 4.1), non-rigid pose-related parameter $\\Theta$ (Sec. 4.2) and texture-related parameter $T$ (Sec. 4.3). Overall, a 3D biped character is parameterized as follows,", + "bbox": [ + 75, + 263, + 473, + 400 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} M = F (B, \\Theta , T) \\\\ = F _ {T} \\left(F _ {P} \\left(F _ {S} (B), \\Theta\\right), T\\right), \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 407, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{S}, F_{P}$ , and $F_{T}$ are the parametric functions to generate shape, pose, and texture respectively. The following sections will elaborate on the details of RaBit.", + "bbox": [ + 75, + 449, + 472, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Shape Modeling", + "text_level": 1, + "bbox": [ + 76, + 502, + 238, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recently, linear shape models dominate the representation of statistical 3D model. Numerous methods [5, 12, 32, 39] have shown PCA's ability in modeling the human body and face. Inspired by [35], we parameterize our character shape linearly with the following equation,", + "bbox": [ + 75, + 525, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {S} = F _ {S} (B) = \\bar {M} _ {S} + \\sum_ {i} ^ {| B |} \\beta_ {i} s _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 607, + 472, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{M}_S$ denotes the mean shape and $M_S$ is the reconstructed shape. The coefficients of linear shape are $\\beta_i \\in B$ . $|B|$ is the number of shape parameters and is set to 100 in our implementation. $s_i \\in \\mathbb{R}^{3 \\times N}$ denotes the orthogonal principal components of vertex displacements that capture shape variations in different character identities. The shape model of RaBit is learned from 1,050 characters of 3DBiCar using PCA [35]. RaBit's eyeballs can be computed based on the predefined landmarks shown in Fig. 4. Please refer to the Supplementary for more details.", + "bbox": [ + 75, + 657, + 472, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Pose Modeling", + "text_level": 1, + "bbox": [ + 76, + 816, + 227, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RaBit employs a standard vertex-based linear blend skinning technique, which uses the predefined skeleton and skinning weight matrix provided by 3DBiCar. The pose parameter $\\Theta$ defines a set of angles as $\\Theta = [\\theta_{1},\\theta_{2},\\dots,\\theta_{K}]\\in \\mathbb{R}^{69}$", + "bbox": [ + 75, + 839, + 473, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\theta_{k} \\in \\mathbb{R}^{3}$ denotes the axis-angle representation of the relative rotation of joint $k$ with respect to its parent and $K = 23$ represents the number of joints. $\\theta_{k}$ can be converted to the rotation matrix format $R(\\theta_k)$ using Rodrigues' formula [35]. The following equations demonstrate how the pose function $F_{P}$ changes vertex $v_{i} \\in M_{S}$ to its corresponding position $v_{i}' \\in M_{P}$ ,", + "bbox": [ + 496, + 90, + 893, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i} ^ {\\prime} = \\sum_ {k = 1} ^ {K} w _ {k, i} G _ {k} ^ {\\prime} (\\Theta , J) v _ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 205, + 893, + 247 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {k} ^ {\\prime} (\\Theta , J) = G _ {k} (\\Theta , J) G _ {k} (\\Theta^ {\\prime}, J) ^ {- 1}, \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 258, + 893, + 277 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {k} (\\Theta , J) = \\prod_ {j \\in A (k)} \\left[ \\begin{array}{c c} R \\left(\\theta_ {j}\\right) & J _ {j} \\\\ 0 & 1 \\end{array} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 291, + 892, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{k,i}$ is the $k$ -th element of the linear blend matrix $W$ for the $i$ -th vertex. $G_{k}(\\Theta, J)$ is the global transformation of joint $k$ , while $G_{k}'(\\Theta, J)$ is the global transformation of joint $k$ after removing the transformation of rest pose $\\Theta'$ . $A(k)$ denotes a set including all the ancestors of joint $k$ , and $J_{j}$ represents the location of the $j$ -th joint, which is located at the bounding box center of a specific body landmark. Thus given the T-posed mesh $M_{S}$ and specific pose $\\Theta$ , we can generate the corresponding posed mesh $M_{P}$ by $F_{P}$ ,", + "bbox": [ + 496, + 335, + 893, + 472 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {P} = F _ {P} \\left(M _ {S}, \\Theta\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 479, + 892, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Texture Modeling", + "text_level": 1, + "bbox": [ + 500, + 505, + 671, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although traditional linear PCA is capable of building a decent statistical shape model, it fails to represent high-frequency details in textures and can produce blurry results due to its weak Gaussian assumption. Recently, GAN-based architectures [19, 21, 22, 27, 28, 49] have shown the notable capability of generating high-fidelity images. Thus, we resort to StyleGAN2-based techniques for UV texture maps generation, but with a coherent UV unfolding (as shown in Fig. 5) to facilitate the learning of texture compared with [22]. Specifically, the neural texture generator in RaBit translates a latent code to a texture map, which could be formulated as follows,", + "bbox": [ + 496, + 527, + 893, + 707 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG (T): \\mathbb {R} ^ {Z} \\rightarrow \\mathbb {R} ^ {H \\times W \\times C}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 707, + 892, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $G(T)$ takes a Z-dimensional parameter vector as input and synthesizes a $H \\times W \\times C$ texture map. Thus given a posed mesh $M_P$ and a specific texture code $T$ , we can generate a textured mesh $M$ with the following equation,", + "bbox": [ + 496, + 729, + 892, + 792 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM = F _ {T} \\left(M _ {P}, T\\right) = H \\left(M _ {P}, G (T)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 799, + 892, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H$ means the process of applying the texture map to the mesh model. In our implementation, the generator follows the architecture of StyleGAN2 [28], while taking a 512-dimensional parameter vector as input and generating a $1024 \\times 1024 \\times 3$ texture map.", + "bbox": [ + 496, + 825, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12829", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Single-View Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 89, + 331, + 106 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a5b474f2ebf92843e6bf4c5df25696b4fd25e079f10a1edcfe5d62b40d1d4c3.jpg", + "image_caption": [ + "Figure 5. BiCarNet. Given a masked image, we first map it to the parametric vectors. The vectors are then fed to our RaBit to generate a posed body mesh, two eyeballs, and a global UV texture. A part-sensitive reasoner is utilized to perceive local regions and generate the detailed UV texture map. Finally, a vivid 3D cartoon character is obtained with our BiCarNet." + ], + "image_footnote": [], + "bbox": [ + 86, + 128, + 460, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Single-view reconstruction (SVR) is one of the most popular tasks of efficient 3D content generation, and recent work has made noticeable progress on human reconstruction based on parametric model of human characters (e.g., SMPL). To verify the practicality of our proposed 3DBiCar and RaBit, we conduct SVR for bipled cartoon characters. A baseline learning-based method is presented, which is termed as BiCarNet.", + "bbox": [ + 75, + 486, + 470, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. BiCarNet", + "text_level": 1, + "bbox": [ + 76, + 619, + 178, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Given a single masked image of cartoon characters, our BiCarNet aims to reconstruct the corresponding 3D shape, pose, and texture. The key problem is to build an encoder to map the input image to the parametric space of Rabbit. As shown in the upper part of Fig. 5, we adopt the learning block in HMR [26] as our Encoder. Once these parametric vectors are learned, we can feed them to our RaBit model to generate a posed body mesh, two eyeballs, and a UV texture (we name it global for convenience to introduce the following method description).", + "bbox": [ + 75, + 642, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During our preliminary experiments, we find that the shape reconstruction of characters, i.e. the eyes and body, is satisfactory, while the inferred UV tends to lose detailed appearances of some small yet significant areas, such as the nose and ears. We thus adopt a part-sensitive texture reasoner (PSR) to address the above issue, as the lower part of Fig. 5 shows. Specifically, we design five individual UV-mappings", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for these significant parts of the nose, ears, horns, eyes, and mouth. Five lightweight encoder-decoder branches are next introduced to learn the appearances of these local regions from the input image, respectively. The learned part UVs could be remapped to the corresponding area on the global UV map to produce a blended texture. However, a direct blending tends to cause seam artifacts. Thus we further adopt a Fuser to address the artifacts as Fig. 5 illustrates. Please refer to the Supplementary for thorough implementations of BiCarNet.", + "bbox": [ + 496, + 90, + 893, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Experiments", + "text_level": 1, + "bbox": [ + 500, + 252, + 633, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data preparation. We first split 3DBiCar into a training set (1,050 image-model pairs) and a testing set (450 pairs). To support a stable training of BiCarNet, we next generate a large number of synthetic paired data with the help of RaBit, which are highly diversified in shape, posture, and texture. To be specific, a lot of 3D textured models are first sampled from the RaBit space, which are then rendered into images from different camera views. This finally produces 13,650 pairs for training. Note that, BiCarNet takes an image with foreground masked as input. All synthetic images naturally have no background. For real images, all the foreground masks are manually annotated.", + "bbox": [ + 496, + 275, + 893, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Result gallery. Fig. 6 shows representative results generated by BiCarNet. As illustrated, our BiCarNet can generate vivid 3D cartoon characters loyal to individual cartoon images in shape, pose, and texture. We believe that our work opens the door to producing 3D biped cartoon characters from easy-to-obtain inputs.", + "bbox": [ + 496, + 457, + 893, + 547 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c7709e7bf28a9c0d328d3c8dca64f0e7891490f57cbdc6f59ad8861954b31d1b.jpg", + "image_caption": [ + "Figure 6. Result gallery of BiCarNet. Our BiCarNet is capable of generating vivid 3D cartoon characters with only single-view image input." + ], + "image_footnote": [], + "bbox": [ + 506, + 560, + 883, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Shape Reconstruction. As mentioned above, BiCarNet utilizes HMR-like blocks and RaBit for shape and pose learning. Currently, other reconstruction methods could also be used for topology-consistent geometry inference, such as GCNN-based methods [34] and UV-based methods [55]. We choose two representative methods for comparison, i.e., Mesh-Graphormer [33, 34] and DecoMR [55].", + "bbox": [ + 496, + 794, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12830", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mesh-Graphormer combines graph convolutions and self-attention in a transformer for 3D human reconstruction from a single image. DecoMR reconstructs 3D human mesh from single images by regressing a UV-based location map. Tab. 1 shows the quantitative comparisons of the above three methods on MPVE, MPJPE, and PA-MPJPE. We also provide qualitative comparisons in Fig. 7. Both quantitative and qualitative results demonstrate that the HMR-like method achieves the highest performance on geometry inference and provides more accurate reconstructions closer to ground truths. As noted, both Mesh-Graphormer and DecoMR outperform HMR for SMPL-based human reconstruction. It is interestingly found that they perform worse in our settings. One possible reason is that our biped cartoon meshes own an extremely larger amount of vertices than SMPL to model more complex geometry. This greatly increases the challenge of vertices regression in Mesh-Graphormer and DecoMR. Thus, in our setting, directly regressing the low-dimension parameters performs better.", + "bbox": [ + 75, + 90, + 472, + 378 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f4812255aef19f31f7879972ae00f7164adbcebb6e2765c9e34a4bb715e8b053.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMPVE ↓MPJPE ↓PA-MPJPE ↓
DecoMR [55]85.7481.2347.23
Mesh-Graphormer [34]63.3147.1534.12
Ours (HMR [26] + RaBit)51.4637.8025.97
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Qualitative comparisons on texture inference. The input image (a) is followed by the textured models from (b) PCA, (c) BiCarNet w/o PSR, (d) BiCarNet and (e) the ground truth. Note that we use the same shape and focus on the difference of textures." + ], + "image_footnote": [], + "bbox": [ + 387, + 609, + 449, + 678 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3f1052541792184b74ba3b915263952a2a034ea238feacb2122a2bfdcb760f4.jpg", + "image_caption": [ + "(e)", + "Figure 7. Qualitative results of shape reconstruction. From left to right, each row contains (a) the input image, reconstructed meshes of (b) Mesh Graphormer, (c) DecoMR, (d) our method, and (e) the GT mesh." + ], + "image_footnote": [], + "bbox": [ + 390, + 679, + 450, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Texture Inference. To demonstrate the capability of our proposed GAN-based texture generator, we first compare our RaBit-based texture inference (i.e., BiCarNet) with PCA-based inference. Specifically, for PCA-based", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method, we utilize the same learning architecture to map the input image into the PCA-based texture space. Furthermore, to evaluate the effectiveness of the proposed texture inference modules, we also conduct ablative analysis on BiCarNet without Fuser and BiCarNet without Part-sensitive Reasoner (PSR). Table 2 shows the quantitative results of different texture inference methods on MSE, PSNR and FID and our proposed method achieves the highest scores compared with all other methods. Moreover, Fig. 8 illustrates the qualitative results of these methods for texture inference. Fig. 9 shows the results without and with Fuser, which demonstrates our fusion module can deal with unnatural seam-like artifacts. We can observe that the part-sensitive texture reasoner and the Fuser help to capture the local regions of characters and recover their detailed appearances.", + "bbox": [ + 496, + 90, + 893, + 319 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d374ee176ba59f9aba5f3ff808b0894cc582b1f46a47142d820f81a72ed6e26b.jpg", + "table_caption": [ + "Table 1. Quantitative results of shape reconstruction. Our method achieves the best results in terms of MPVE, MPJPE and PA-MPJPE. Note that all metrics are measured in a unit $10^{-3}\\mathrm{m}$ ." + ], + "table_footnote": [], + "table_body": "
MethodMSE(×10-1)↓PSNR(×102) ↑FID ↓
PCA0.23090.22540.4642
BiCarNet0.10930.24580.1133
BiCarNet w/o Fuser0.11080.23970.1407
BiCarNet w/o PSR0.13460.23610.4024
", + "bbox": [ + 514, + 330, + 879, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative results on texture inference. PCA denotes linear modeling method for texture and the last two rows indicate the results of BiCarNet respectively without two designed module. Our BiCarNet outperforms others methods in all metrics.", + "bbox": [ + 496, + 436, + 893, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d8e1e8825a5bc0bc1d42c748ceb33b5ad6d98b5c514c1f0a689f9d74780bafa.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 514, + 516, + 589, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/052ca78664419d639f5bb84c0bd8c997c457b74d8d67bcf2a2b6d58ec3ebff97.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 591, + 517, + 660, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4432f4ab0d1177de93dd1ccef11dcd48b330cabd8a4c82b70e6384c9e7f6987.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 661, + 517, + 730, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bed1bed8810eb75b6f64a6158e546b4fc34d1ad2a9025f83a9b8a3859dd23e02.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 738, + 517, + 807, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/891ed9d6878e2c81efcf84a57d65fd39bc81f3055a299a53b8e34bca4cd6eac7.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 808, + 517, + 883, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. More Applications", + "text_level": 1, + "bbox": [ + 500, + 806, + 679, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Sketch-based Modeling", + "text_level": 1, + "bbox": [ + 500, + 830, + 717, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Customizing 3D biped cartoon characters usually requires a heavy workload with commercial tools, even for experienced artists. Sketch-based modeling enables amateur users", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12831", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3879b5c7063dfadc9b68417b4b38052e3c3fa9e2158a1bc8646cf34b0af01b1e.jpg", + "image_caption": [ + "Figure 9. Qualitative ablation on Fuser in Texture inference. Left: BiCarNet w/o Fuser. Right: BiCarNet with Fuser." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 459, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to get involved in 3D shape customization in a simple and intuitive fashion. We build a sketch-based modeling application with the help of 3DBiCar and RaBit.", + "bbox": [ + 75, + 266, + 470, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first sample a series of shape vectors randomly and feed them to RaBit to generate 3D cartoon characters with diversified shapes, resulting in 12,000 T-pose models. Then we apply suggestive contour [24] to render the front-view sketches with different abstraction levels and obtain 108,000 sketch-model pairs. Given a sketch as input, we employ ResNet-50 and three MLPs as the encoder and decoder to map the input sketch to 100-dimensional shape parameters. The generated shape parameters are next fed to RaBit to reconstruct the corresponding 3D model. Please refer to the Supplemental materials for more details. Note that users only need to depict a 3D character with T-pose on a 2D canvas while the output characters of our method are animation-ready and can be directly applied to other commercial tools. Fig. 10 displays the sketches created by users with little knowledge of modeling as well as the corresponding models generated by our system. It can be seen that our sketch-based modeling system offers a smart approach for amateur users to create 3D biped cartoon characters with diversified shapes. We will further explore the support of shape reconstruction from sketches with arbitrary poses, and texture painting in the future.", + "bbox": [ + 75, + 311, + 472, + 643 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/703250f15da0f568e27f0cde40a2619d3f7411f8b49794c7f5480e6dd08a5d17.jpg", + "image_caption": [ + "Figure 10. Result gallery of sketch-based modelling. The sketches created by amateur users denotes on the left and the generated models on the right." + ], + "image_footnote": [], + "bbox": [ + 81, + 655, + 460, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2.3D Character Animation", + "text_level": 1, + "bbox": [ + 76, + 830, + 305, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Following the recent advance of human recovering method and parametric model [35, 39, 50], we extract the human from input video frames and adopt a temporal-aware", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "encoder to recover the sequence of human poses [50]. Then, a motion retargeting method [25] is used to convert the poses on the human skeleton to the motion of our cartoon characters. As shown in Fig. 11, animation-ready characters generated by our RaBit can be directly applied to 3D animation. Please refer to the supplementary for animation video.", + "bbox": [ + 496, + 90, + 895, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8364d3aab17aab34f315f27f08fc340fff185b35b96b0d8cfc85c04cc726ab4e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 517, + 191, + 563, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/582f04a20b6412aafddf321bd03c246f87d10fedefde744c43b38ff9c1aef993.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 566, + 194, + 651, + 367 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/96b33770258c949485812b55b50d88c15a37326dcb333a6ed34d30e55b012901.jpg", + "image_caption": [ + "(c)", + "Figure 11. Transferring motion of a human video to animate characters. (a) denotes the input frames. (b), (c), and (d) indicate three corresponding posed cartoon characters." + ], + "image_footnote": [], + "bbox": [ + 663, + 195, + 763, + 366 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04f0740bc80e80c4d28d670767861f3723922c7039efa4dfa09e4bee2ba3bc14.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 774, + 195, + 875, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 452, + 619, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 textured and skinned models with a consistent mesh topology. Based on 3DBiCar, we propose the first 3D full-body cartoon parametric model RaBit for biped character modeling. Furthermore, we build a baseline method BiCarNet for reconstructing 3D textured models from a single image with cartoon characters. Experimental results demonstrate the capability of 3DBiCar and RaBit as well as the effectiveness of BiCarNet. Last but not least, two further applications, i.e., sketch-based modeling and 3D character animation, demonstrate the usability and practicality of our dataset and parametric model. We hope that our work will contribute to the development of 3D biped cartoon character modeling and inspire future works in this area.", + "bbox": [ + 496, + 477, + 895, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No. JCYJ20220530143604010, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055).", + "bbox": [ + 496, + 704, + 895, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12832", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Victoria Fernández Abrevaya, Stefanie Wuhrer, and Edmond Boyer. Multilinear autoencoder for 3d face model learning. 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Embodied hands: Modeling and capturing hands and bodies together. ACM Transactions on Graphics, (Proc. SIGGRAPH Asia), 36(6), Nov. 2017. 3", + "[45] Alexandre Saint, Eman Ahmed, Abd El Rahman Shabayek, Kseniya Cherenkova, Gleb Gusev, Djamila Aouada, and Bjorn Ottersten. 3dbodytex: Textured 3d body dataset. In 2018 International Conference on 3D Vision (3DV), pages 495-504, 2018. 2", + "[46] Matan Sela, Yonathan Aflalo, and Ron Kimmel. Computational caricaturization of surfaces. Computer Vision and Image Understanding, 141:1-17, 2015. 3", + "[47] Ron Slossberg, Gil Shamai, and Ron Kimmel. High quality facial surface and texture synthesis via generative adversarial networks. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 3", + "[48] Gizem Unlu, Mohamed Sayed, and Gabriel Brostow. Interactive sketching of mannequin poses. arXiv preprint arXiv:2212.07098, 2022. 2", + "[49] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. High-resolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. 5", + "[50] Zhouping Wang and Sarah Ostadabbas. Live stream temporally embedded 3d human body pose and shape estimation. arXiv preprint arXiv:2207.12537, 2022. 3, 8", + "[51] Qianyi Wu, Juyong Zhang, Yu-Kun Lai, Jianmin Zheng, and Jianfei Cai. Alive caricature from 2d to 3d. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7336-7345, 2018. 3", + "[52] Hongyi Xu, Eduard Gabriel Bazavan, Andrei Zanfir, William T Freeman, Rahul Sukthankar, and Cristian Sminchisescu. Ghum & ghuml: Generative 3d human shape and" + ], + "bbox": [ + 501, + 92, + 893, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12834", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "articulated pose models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6184-6193, 2020. 3", + "[53] H. Yang, H. Zhu, Y. Wang, M. Huang, Q. Shen, R. Yang, and X. Cao. Facescape: A large-scale high quality 3d face dataset and detailed riggable 3d face prediction. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 598-607, Los Alamitos, CA, USA, jun 2020. IEEE Computer Society. 2", + "[54] Yipin Yang, Yao Yu, Yu Zhou, Sidan Du, James Davis, and Ruigang Yang. Semantic parametric reshaping of human body models. 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Advances in Neural Information Processing Systems, 33:9251-9262, 2020. 3" + ], + "bbox": [ + 78, + 90, + 470, + 470 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12835", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_model.json b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..89a694d2e3e1c5bae400a05a4a823da2c13c82ab --- /dev/null +++ b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_model.json @@ -0,0 +1,2488 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.131, + 0.795, + 0.177 + ], + "angle": 0, + "content": "RaBit: Parametric Modeling of 3D Biped Cartoon Characters with a Topological-consistent Dataset" + }, + { + "type": "text", + "bbox": [ + 0.183, + 0.202, + 0.782, + 0.242 + ], + "angle": 0, + "content": "Zhongjin Luo\\(^{1*}\\) Shengcai Cai\\(^{1,3*}\\) Jinguo Dong\\(^{1}\\) Ruibo Ming\\(^{1,4}\\) Liangdong Qiu\\(^{2,1}\\) Xiaohang Zhan\\(^{3}\\) Xiaoguang Han\\(^{1,2\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.255, + 0.866, + 0.278 + ], + "angle": 0, + "content": "\\(^{1}\\)SSE, CUHKSZ \\(^{2}\\)FNii, CUHKSZ \\(^{3}\\)Huawei Technologies Co., Ltd. \\(^{4}\\)Tsinghua University" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.306, + 0.872, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.516, + 0.896, + 0.56 + ], + "angle": 0, + "content": "Figure 1. We present 3DBiCar, the first large-scale repository of 3D biped cartoon characters. It contains 1,500 topologically consistent, textured, and skinned 3D high-quality meshes manually created by professional artists, covering 15 species. Further, we propose RaBit, the first cartoon character parametric model simultaneously parameterizing shape, pose, and texture." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.581, + 0.314, + 0.599 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.475, + 0.859 + ], + "angle": 0, + "content": "Assisting people in efficiently producing visually plausible 3D characters has always been a fundamental research topic in computer vision and computer graphics. Recent learning-based approaches have achieved unprecedented accuracy and efficiency in the area of 3D real human digitization. However, none of the prior works focus on modeling 3D biped cartoon characters, which are also in great demand in gaming and filming. In this paper, we introduce 3DBiCar, the first large-scale dataset of 3D biped cartoon characters, and RaBit, the corresponding parametric model. Our dataset contains 1,500 topologically consistent high-quality 3D textured models which are manually crafted by professional artists. Built upon the data, RaBit is thus designed with a SMPL-like linear blend shape model and a StyleGAN-based neural UV-texture generator, simultaneously expressing the shape, pose, and texture. To demonstrate the practicality" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.583, + 0.896, + 0.751 + ], + "angle": 0, + "content": "of 3DBiCar and RaBit, various applications are conducted, including single-view reconstruction, sketch-based modeling, and 3D cartoon animation. For the single-view reconstruction setting, we find a straightforward global mapping from input images to the output UV-based texture maps tends to lose detailed appearances of some local parts (e.g., nose, ears). Thus, a part-sensitive texture reasoner is adopted to make all important local areas perceived. Experiments further demonstrate the effectiveness of our method both qualitatively and quantitatively. 3DBiCar and RaBit are available at gaplab.cuhk.edu.cn/projects/RaBit." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.768, + 0.633, + 0.784 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.896, + 0.903 + ], + "angle": 0, + "content": "With the rapid development of digitization, creating high-quality 3D articulated characters is highly demanded in game platforms, film industries, and metaverse scenarios. However, even for expert artists, creating a 3D character is labor-intensive and time-consuming. Therefore, reducing the cost of producing visually plausible 3D characters is essential in the field of computer vision and graphics." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.281, + 0.888 + ], + "angle": 0, + "content": "*Z. Luo and S. Cai contribute equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.081, + 0.888, + 0.205, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.875, + 0.281, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12825" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.41 + ], + "angle": 0, + "content": "Recently, researchers have made great progress in digitizing realistic human characters. The emergence and popularity of various 3D sensing devices make capturing 3D data from the real world convenient, prompting a growing number of 3D real-people scanned datasets [3,7,12,43,45,53,54,56]. Based on these large-scale datasets, several powerful parametric models [5,12,35,39] have been developed to facilitate the reconstruction and analysis of human shapes, actions, and interactions. With the help of parametric models, deep learning techniques have shown the potential to efficiently infer accurate 3D digital humans from single-view images [26,39] or even sparse sketches [9,24,48]. Most recently, there are some works [36,41] that devote to exploring the intelligent generation of cartoon-like character heads. However, none of the prior works focuses on the modeling of 3D full-body biped cartoon characters, which are also in great demand in the area of gaming (e.g., Animal Crossing), filming (e.g., Zootopia), and virtualizing (e.g., Metaverse). In this work, we raise a new problem to the community: How to quickly produce 3D biped cartoon characters from easy-to-obtain inputs (e.g., a single image)?" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.473, + 0.669 + ], + "angle": 0, + "content": "Revisiting the road map of realistic human digitization, the first step to tackling the above problem is building a high-quality 3D biped cartoon characters dataset. We thus introduce 3DBiCar, the first large-scale publicly available 3D biped cartoon character dataset following three criteria: 1) Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models covering 15 species, as shown in the Fig. 3. 2) Richness. Each model in 3DBiCar owns not only a detailed shape but also a texture UV-map, which are matched with a reference image. Additionally, each character is attached with two models, one with T-pose and another with the reference pose. 3) Topological-consistency. Each 3D model is created by carefully deforming a pre-defined template mesh. All 3D characters in 3DBiCar are unified in topology, paving the way to learn a skinned parametric model. Fig. 1 shows some representative models of the proposed dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.671, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Based on 3DBiCar, we further propose a generative model, dubbed RaBit, for 3D biped cartoon character generation. It combines a linear blend shape model with a neural texture generator and simultaneously parameterizes the shape, pose, and texture to a low-dimensional parametric space. For shape and pose modeling, numerous methods have shown principal component analysis's (PCA's) advantage in building decent statistical shape models [5, 12, 32, 39]. Inspired by SMPL [35], we utilize the traditional PCA technique to parameterize shape. Due to the variety and complexity of cartoon texture, directly adopting PCA for texture modeling fails to reconstruct details and falls into blurry results. We tackle this problem by introducing a StyleGAN-based generator." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To explore the practical usage of 3DBiCar and RaBit, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.318 + ], + "angle": 0, + "content": "first conduct the application of single-view reconstruction. Considering prior works for SMPL-based human geometry generation from single-view images [6, 26, 30], we build a baseline method with our dataset and the parametric model. We select one regression-based method for pose and shape inference. For texture inference, we find directly applying a global texture-generator tends to make the results lose detailed appearances, especially for some local but important regions (e.g., nose and ears). Thus a part-sensitive reasoner is utilized to deal with different local regions. We term our baseline method for single-view reconstruction as BiCarNet. Moreover, two further applications, i.e., sketch-based modeling and 3D character animation, are also explored. Experimental results on these applications demonstrate that it is already able to generate reasonable outputs." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.319, + 0.794, + 0.333 + ], + "angle": 0, + "content": "To summarize, our contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.344, + 0.892, + 0.39 + ], + "angle": 0, + "content": "- We introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 high-quality textured 3D models with a consistent mesh topology." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.401, + 0.894, + 0.445 + ], + "angle": 0, + "content": "- We propose RaBit, the first 3D full-body cartoon parametric model for biped character modeling. We will release both 3DBiCar and RaBit for future research." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.457, + 0.894, + 0.517 + ], + "angle": 0, + "content": "- We build BiCarNet, the baseline method to reconstruct 3D biped cartoon characters from a single-view image. A part-sensitive reasoner is adopted for detailed texture generation." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.529, + 0.894, + 0.573 + ], + "angle": 0, + "content": "- Two other applications, i.e., sketch-based modeling and 3D character animation, are also conducted to demonstrate the promising potential of 3DBiCar and RaBit." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.344, + 0.894, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.642, + 0.605 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.87 + ], + "angle": 0, + "content": "3D Character Datasets. In general, 3D character datasets could be categorized as real-captured and computer-designed datasets. For capturing character data from the real world, the availability of 3D scanning devices has enabled researchers to collect many scanned 3D human-related datasets, mainly focusing on human faces [10] and bodies [13]. For human faces, FaceWarehouse [12] collects large-scale 3d faces with high diversity in age, ethnicity, and expression. FaceScape [53] further builds a large-scale detailed 3D face dataset with high resolution in texture and mesh. For human bodies, CAESAR dataset [43] opens up the learning of the human body and is widely used for body shape modeling for its shape diversity and satisfying resolution of meshes. Many following works [3,7,45,54,56] extend [43] in shape, pose, and texture, on quantity and quality. Although these real-captured datasets are widely used in realistic human digitalization, they are unsuitable for imaginary character generation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "For designing character data with computers, researchers try to perform deformation on real 3D human faces or bodies" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12826" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.257 + ], + "angle": 0, + "content": "to construct exaggerated shapes programmatically [11,24,46, 51]. Their results lack diversity and are far from satisfactory. To address this, 3DCaricShop [41] proposes a large-scale 3D exaggerated faces dataset. SimpModeling [36] constructs a large man-made animalmorphic head dataset. Although using 3DCaricShop and SimpModeling could facilitate the generation of unreal character heads, it still remains a problem to synthesize full-body cartoon characters due to the lack of corresponding body data. In our work, we tackle this problem by introducing a large 3D biped cartoon character dataset, 3DBiCar." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.473, + 0.64 + ], + "angle": 0, + "content": "Parametric Shape Modeling. Parametric models of shapes are widely used in 3D digitizations. Blanz et al. [5] pioneer parametric modeling using PCA and release a 3D statistical morphable face model (3DMM). Their parameterization models textured faces and provides a set of controls for intuitively manipulating shapes, expressions, and textures. Since then, PCA-based parameterizing has gradually dominated the area of statistical shape modeling over the past decades. Following 3DMM, researchers model the whole head to represent the neck region and 3D head rotations [12, 32]. Allen et al. [2] open up the study of full body parameterization. However, they focus only on body shape and omit the body pose. SCAPE [3] represents body shape and pose in terms of triangle deformations, while SMPL [35] models a whole range of natural shapes and poses based on vertex displacements. SMPL-X [39] integrates SMPL [35] with FLAME [32] head model and the MANO [44] hand model for expressive capturing of bodies, hands and faces together. With recent advances in deep learning, researchers turn to explore nonlinear shape models using neural networks [1, 4, 8, 42, 52, 57]. However, since these non-linear modeling methods are inferior in simplicity, robustness and availability, PCA-based methods remain prevalent in the research community. In this paper, we also adopt PCA into RaBit to model the geometry of 3D biped cartoon characters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Based on the above parametric models, researchers have made remarkable progress in human digitization, such as reconstruction from simple inputs (e.g., a single image or sparse sketches) [6, 15, 24, 26, 40] and real-time pose retargeting [14, 29, 50]. For instance, SMPLify [6] estimates 3D body shape and pose parameters automatically from 2D joints with multiple ellipsoids. HMR [26] proposes an end-to-end framework for reconstructing a full 3D mesh of a human body from a single RGB image. DeepSketch2Face [24] proposes a sketch-based system for inferring 3D face models from 2D sketches with the help of parametric models and CNN-based deep regression networks. TCMR [14] presents a temporally consistent mesh recovery system for recovering smooth 3D human motion from monocular videos. To probe the capability of RaBit to downstream applications, we conduct various utilization, such as single-view cartoon character reconstruction, sketch-based character modeling," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "and 3D cartoon animation. Experimental results demonstrate the practicality of 3DBiCar and RaBit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Parametric Texture Modeling. Traditionally, textures are modeled as a linear subspace using the similar idea of body blendshape models. Blanz et al. [5] represent the face appearance in per-vertex colors and parameterize texture as a linear model based on PCA. Dai et al. [16] store texture information in a UV space where the texture resolution is unconstrained by mesh resolution. Moschoglou et al. [37] formulate a robust matrix factorization problem to learn the parametric representation of facial UV maps from a collection of training textures. However, these linear texture models may lead to a sub-optimal appearance output [18, 23] due to the weak assumption of Gaussian and tend to produce blurry results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.897, + 0.576 + ], + "angle": 0, + "content": "With recent advances in deep learning, researchers turn to utilize deep neural networks to model texture. A number of deep generative models [17, 19-22, 31, 38, 47] have been proposed to parameterize texture into a latent space. For example, GANFIT [21] utilizes GAN-based neural networks to train a generator of facial texture in UV space for 3D face reconstruction. StylePeople [22] incorporates neural texture synthesis, mesh rendering, and neural rendering into the joint generation process to train a neural texture generator for the task of single-view human reconstruction. GET3D [20] introduces a texture-field generative model that directly generates explicit textured 3D meshes, ranging from cars, chairs, animals, motorbikes, and human characters to buildings. These methods have shown the promising capacity of neural generators to represent texture. In our work, we adopt a GAN-based neural texture generator into RaBit to provide high-quality texture modeling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.589, + 0.604 + ], + "angle": 0, + "content": "3. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.719 + ], + "angle": 0, + "content": "Considerable progress has been made in digitizing realistic and articulated human characters. However, efficiently creating visually plausible biped cartoon characters remains demanding and challenging, mainly due to the lack of data. In this work, we propose to fill this gap by introducing 3DBiCar, the first large-scale full-body 3D biped character data. We build 3DBiCar following three rules:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.885 + ], + "angle": 0, + "content": "Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models. First, we carefully collect images of 2D full-body biped cartoon characters with diverse identities, shape, and textural styles from the Internet, resulting in 15 character species and 4 image styles, as shown in Fig. 3. Then we recruit six professional artists to create 3D corresponding character models according to the collected reference images. The modeling result is required to be matched with the reference images as much as possible. The representative image-model pairs sampled from our dataset are shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Topological-consistency. The key to building a linear" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12827" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.885, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.42, + 0.893, + 0.464 + ], + "angle": 0, + "content": "Figure 2. The gallery of the representative examples sampled from 3DBiCar. Each collected reference image is followed by the T-pose model and the posed model, created by professional artists. 3DBiCar contains 1,500 topologically consistent, textured and skinned 3D high-quality models with paired 2D images, which covers 15 species and 4 image styles." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.486, + 0.456, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.634, + 0.471, + 0.689 + ], + "angle": 0, + "content": "Figure 3. Data distribution. Chart (a) illustrates the number of 15 species of bipedal cartoon characters in 3DBiCar. Chart (b) shows the number of four styles of reference images collected in our dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "parametric shape model is keeping a unified mesh topology. Traditional human parametric models utilize a template mesh to register different human body scans with 3D landmarks to keep topologically uniform. Inspired by this, we first create a template mesh with several 3D colored landmarks as shown in Fig. 4. All six artists are required to craft 3D models by deforming the above-predefined template under the constraints of these obvious landmarks. We set up a review committee of 10 to check these models based on the landmarks, ensuring the consistency of mesh topology. The landmarks could also be used to compute the position of models' joints for body posing or character animation. The topological consistency" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.488, + 0.889, + 0.665 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.682, + 0.895, + 0.794 + ], + "angle": 0, + "content": "Figure 4. Template. The models in the center are the predefined template mesh with landmarks. It can be seen that we refine the structure on specific regions, where a complex nose or tail may exist. The colored regions and delineated lines denote the landmarks. These landmarks represent specific components of the character's body, such as elbow and eye socket. During model crafting, artists are required to deform the template model while keeping the landmarks in the position where the original body components are." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.891, + 0.839 + ], + "angle": 0, + "content": "of 3DBiCar paves the way to learn a skinned parametric model, which we will discuss in Sec. 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Richness. We provide various forms of data for each character. There are not only the 3D shape meshes and UV-space textures carefully crafted by artists but also collected reference images. For each character, artists are asked first" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12828" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.226 + ], + "angle": 0, + "content": "to create a T-pose mesh and then deform it to match the reference pose. Furthermore, all the models are rigged and skinned using a predefined skeleton and skinning weight matrix, which enables further animation production for characters. In addition, each character contains two separate eyeballs specifically designed for facial animation. The body mesh of each character comprises 38,726 vertices and 77,448 faces, while each eyeball consists of 1,025 vertices and 2,046 faces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.24, + 0.283, + 0.258 + ], + "angle": 0, + "content": "4. Parametric Modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.265, + 0.474, + 0.401 + ], + "angle": 0, + "content": "We propose the first parametric model of 3D biped cartoon characters (RaBit), which contains a linear blend model for shapes and a neural generator for textures. RaBit simultaneously parameterizes the shape, pose, and texture of 3D biped characters. Specifically, we decompose the parametric space into identity-related body parameter \\( B \\) (Sec. 4.1), non-rigid pose-related parameter \\( \\Theta \\) (Sec. 4.2) and texture-related parameter \\( T \\) (Sec. 4.3). Overall, a 3D biped character is parameterized as follows," + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.408, + 0.47, + 0.443 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} M = F (B, \\Theta , T) \\\\ = F _ {T} \\left(F _ {P} \\left(F _ {S} (B), \\Theta\\right), T\\right), \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.473, + 0.495 + ], + "angle": 0, + "content": "where \\( F_{S}, F_{P} \\), and \\( F_{T} \\) are the parametric functions to generate shape, pose, and texture respectively. The following sections will elaborate on the details of RaBit." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.503, + 0.24, + 0.519 + ], + "angle": 0, + "content": "4.1. Shape Modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Recently, linear shape models dominate the representation of statistical 3D model. Numerous methods [5, 12, 32, 39] have shown PCA's ability in modeling the human body and face. Inspired by [35], we parameterize our character shape linearly with the following equation," + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.608, + 0.473, + 0.651 + ], + "angle": 0, + "content": "\\[\nM _ {S} = F _ {S} (B) = \\bar {M} _ {S} + \\sum_ {i} ^ {| B |} \\beta_ {i} s _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.473, + 0.81 + ], + "angle": 0, + "content": "where \\( \\bar{M}_S \\) denotes the mean shape and \\( M_S \\) is the reconstructed shape. The coefficients of linear shape are \\( \\beta_i \\in B \\). \\( |B| \\) is the number of shape parameters and is set to 100 in our implementation. \\( s_i \\in \\mathbb{R}^{3 \\times N} \\) denotes the orthogonal principal components of vertex displacements that capture shape variations in different character identities. The shape model of RaBit is learned from 1,050 characters of 3DBiCar using PCA [35]. RaBit's eyeballs can be computed based on the predefined landmarks shown in Fig. 4. Please refer to the Supplementary for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.228, + 0.833 + ], + "angle": 0, + "content": "4.2. Pose Modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.474, + 0.903 + ], + "angle": 0, + "content": "RaBit employs a standard vertex-based linear blend skinning technique, which uses the predefined skeleton and skinning weight matrix provided by 3DBiCar. The pose parameter \\(\\Theta\\) defines a set of angles as \\(\\Theta = [\\theta_{1},\\theta_{2},\\dots,\\theta_{K}]\\in \\mathbb{R}^{69}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.199 + ], + "angle": 0, + "content": "where \\(\\theta_{k} \\in \\mathbb{R}^{3}\\) denotes the axis-angle representation of the relative rotation of joint \\(k\\) with respect to its parent and \\(K = 23\\) represents the number of joints. \\(\\theta_{k}\\) can be converted to the rotation matrix format \\(R(\\theta_k)\\) using Rodrigues' formula [35]. The following equations demonstrate how the pose function \\(F_{P}\\) changes vertex \\(v_{i} \\in M_{S}\\) to its corresponding position \\(v_{i}' \\in M_{P}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.206, + 0.895, + 0.248 + ], + "angle": 0, + "content": "\\[\nv _ {i} ^ {\\prime} = \\sum_ {k = 1} ^ {K} w _ {k, i} G _ {k} ^ {\\prime} (\\Theta , J) v _ {i}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.259, + 0.895, + 0.278 + ], + "angle": 0, + "content": "\\[\nG _ {k} ^ {\\prime} (\\Theta , J) = G _ {k} (\\Theta , J) G _ {k} (\\Theta^ {\\prime}, J) ^ {- 1}, \\qquad (4)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.292, + 0.893, + 0.332 + ], + "angle": 0, + "content": "\\[\nG _ {k} (\\Theta , J) = \\prod_ {j \\in A (k)} \\left[ \\begin{array}{c c} R \\left(\\theta_ {j}\\right) & J _ {j} \\\\ 0 & 1 \\end{array} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.895, + 0.473 + ], + "angle": 0, + "content": "where \\(w_{k,i}\\) is the \\(k\\)-th element of the linear blend matrix \\(W\\) for the \\(i\\)-th vertex. \\(G_{k}(\\Theta, J)\\) is the global transformation of joint \\(k\\), while \\(G_{k}'(\\Theta, J)\\) is the global transformation of joint \\(k\\) after removing the transformation of rest pose \\(\\Theta'\\). \\(A(k)\\) denotes a set including all the ancestors of joint \\(k\\), and \\(J_{j}\\) represents the location of the \\(j\\)-th joint, which is located at the bounding box center of a specific body landmark. Thus given the T-posed mesh \\(M_{S}\\) and specific pose \\(\\Theta\\), we can generate the corresponding posed mesh \\(M_{P}\\) by \\(F_{P}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.481, + 0.893, + 0.498 + ], + "angle": 0, + "content": "\\[\nM _ {P} = F _ {P} \\left(M _ {S}, \\Theta\\right). \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.673, + 0.523 + ], + "angle": 0, + "content": "4.3. Texture Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.708 + ], + "angle": 0, + "content": "Although traditional linear PCA is capable of building a decent statistical shape model, it fails to represent high-frequency details in textures and can produce blurry results due to its weak Gaussian assumption. Recently, GAN-based architectures [19, 21, 22, 27, 28, 49] have shown the notable capability of generating high-fidelity images. Thus, we resort to StyleGAN2-based techniques for UV texture maps generation, but with a coherent UV unfolding (as shown in Fig. 5) to facilitate the learning of texture compared with [22]. Specifically, the neural texture generator in RaBit translates a latent code to a texture map, which could be formulated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.708, + 0.893, + 0.727 + ], + "angle": 0, + "content": "\\[\nG (T): \\mathbb {R} ^ {Z} \\rightarrow \\mathbb {R} ^ {H \\times W \\times C}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.893, + 0.793 + ], + "angle": 0, + "content": "where \\( G(T) \\) takes a Z-dimensional parameter vector as input and synthesizes a \\( H \\times W \\times C \\) texture map. Thus given a posed mesh \\( M_P \\) and a specific texture code \\( T \\), we can generate a textured mesh \\( M \\) with the following equation," + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.8, + 0.893, + 0.817 + ], + "angle": 0, + "content": "\\[\nM = F _ {T} \\left(M _ {P}, T\\right) = H \\left(M _ {P}, G (T)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.902 + ], + "angle": 0, + "content": "where \\( H \\) means the process of applying the texture map to the mesh model. In our implementation, the generator follows the architecture of StyleGAN2 [28], while taking a 512-dimensional parameter vector as input and generating a \\( 1024 \\times 1024 \\times 3 \\) texture map." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12829" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.333, + 0.107 + ], + "angle": 0, + "content": "5. Single-View Reconstruction" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.13, + 0.462, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.386, + 0.472, + 0.469 + ], + "angle": 0, + "content": "Figure 5. BiCarNet. Given a masked image, we first map it to the parametric vectors. The vectors are then fed to our RaBit to generate a posed body mesh, two eyeballs, and a global UV texture. A part-sensitive reasoner is utilized to perceive local regions and generate the detailed UV texture map. Finally, a vivid 3D cartoon character is obtained with our BiCarNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.472, + 0.607 + ], + "angle": 0, + "content": "Single-view reconstruction (SVR) is one of the most popular tasks of efficient 3D content generation, and recent work has made noticeable progress on human reconstruction based on parametric model of human characters (e.g., SMPL). To verify the practicality of our proposed 3DBiCar and RaBit, we conduct SVR for bipled cartoon characters. A baseline learning-based method is presented, which is termed as BiCarNet." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.62, + 0.179, + 0.635 + ], + "angle": 0, + "content": "5.1. BiCarNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Given a single masked image of cartoon characters, our BiCarNet aims to reconstruct the corresponding 3D shape, pose, and texture. The key problem is to build an encoder to map the input image to the parametric space of Rabbit. As shown in the upper part of Fig. 5, we adopt the learning block in HMR [26] as our Encoder. Once these parametric vectors are learned, we can feed them to our RaBit model to generate a posed body mesh, two eyeballs, and a UV texture (we name it global for convenience to introduce the following method description)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "During our preliminary experiments, we find that the shape reconstruction of characters, i.e. the eyes and body, is satisfactory, while the inferred UV tends to lose detailed appearances of some small yet significant areas, such as the nose and ears. We thus adopt a part-sensitive texture reasoner (PSR) to address the above issue, as the lower part of Fig. 5 shows. Specifically, we design five individual UV-mappings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.243 + ], + "angle": 0, + "content": "for these significant parts of the nose, ears, horns, eyes, and mouth. Five lightweight encoder-decoder branches are next introduced to learn the appearances of these local regions from the input image, respectively. The learned part UVs could be remapped to the corresponding area on the global UV map to produce a blended texture. However, a direct blending tends to cause seam artifacts. Thus we further adopt a Fuser to address the artifacts as Fig. 5 illustrates. Please refer to the Supplementary for thorough implementations of BiCarNet." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.253, + 0.635, + 0.269 + ], + "angle": 0, + "content": "5.2. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.895, + 0.457 + ], + "angle": 0, + "content": "Data preparation. We first split 3DBiCar into a training set (1,050 image-model pairs) and a testing set (450 pairs). To support a stable training of BiCarNet, we next generate a large number of synthetic paired data with the help of RaBit, which are highly diversified in shape, posture, and texture. To be specific, a lot of 3D textured models are first sampled from the RaBit space, which are then rendered into images from different camera views. This finally produces 13,650 pairs for training. Note that, BiCarNet takes an image with foreground masked as input. All synthetic images naturally have no background. For real images, all the foreground masks are manually annotated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.895, + 0.548 + ], + "angle": 0, + "content": "Result gallery. Fig. 6 shows representative results generated by BiCarNet. As illustrated, our BiCarNet can generate vivid 3D cartoon characters loyal to individual cartoon images in shape, pose, and texture. We believe that our work opens the door to producing 3D biped cartoon characters from easy-to-obtain inputs." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.561, + 0.885, + 0.727 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.736, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Figure 6. Result gallery of BiCarNet. Our BiCarNet is capable of generating vivid 3D cartoon characters with only single-view image input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Results on Shape Reconstruction. As mentioned above, BiCarNet utilizes HMR-like blocks and RaBit for shape and pose learning. Currently, other reconstruction methods could also be used for topology-consistent geometry inference, such as GCNN-based methods [34] and UV-based methods [55]. We choose two representative methods for comparison, i.e., Mesh-Graphormer [33, 34] and DecoMR [55]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12830" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.38 + ], + "angle": 0, + "content": "Mesh-Graphormer combines graph convolutions and self-attention in a transformer for 3D human reconstruction from a single image. DecoMR reconstructs 3D human mesh from single images by regressing a UV-based location map. Tab. 1 shows the quantitative comparisons of the above three methods on MPVE, MPJPE, and PA-MPJPE. We also provide qualitative comparisons in Fig. 7. Both quantitative and qualitative results demonstrate that the HMR-like method achieves the highest performance on geometry inference and provides more accurate reconstructions closer to ground truths. As noted, both Mesh-Graphormer and DecoMR outperform HMR for SMPL-based human reconstruction. It is interestingly found that they perform worse in our settings. One possible reason is that our biped cartoon meshes own an extremely larger amount of vertices than SMPL to model more complex geometry. This greatly increases the challenge of vertices regression in Mesh-Graphormer and DecoMR. Thus, in our setting, directly regressing the low-dimension parameters performs better." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.391, + 0.468, + 0.472 + ], + "angle": 0, + "content": "
MethodMPVE ↓MPJPE ↓PA-MPJPE ↓
DecoMR [55]85.7481.2347.23
Mesh-Graphormer [34]63.3147.1534.12
Ours (HMR [26] + RaBit)51.4637.8025.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.482, + 0.472, + 0.525 + ], + "angle": 0, + "content": "Table 1. Quantitative results of shape reconstruction. Our method achieves the best results in terms of MPVE, MPJPE and PA-MPJPE. Note that all metrics are measured in a unit \\(10^{-3}\\mathrm{m}\\)." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.545, + 0.174, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.611, + 0.168, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.681, + 0.174, + 0.745 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.127, + 0.749, + 0.145, + 0.761 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.546, + 0.231, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.61, + 0.243, + 0.679 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.681, + 0.237, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.749, + 0.223, + 0.761 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.546, + 0.309, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.61, + 0.311, + 0.678 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.68, + 0.301, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.749, + 0.29, + 0.761 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.305, + 0.547, + 0.388, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.304, + 0.61, + 0.38, + 0.678 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.319, + 0.68, + 0.373, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.338, + 0.749, + 0.358, + 0.761 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.547, + 0.455, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.61, + 0.45, + 0.679 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.68, + 0.452, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.416, + 0.749, + 0.435, + 0.761 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.772, + 0.47, + 0.829 + ], + "angle": 0, + "content": "Figure 7. Qualitative results of shape reconstruction. From left to right, each row contains (a) the input image, reconstructed meshes of (b) Mesh Graphormer, (c) DecoMR, (d) our method, and (e) the GT mesh." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Results on Texture Inference. To demonstrate the capability of our proposed GAN-based texture generator, we first compare our RaBit-based texture inference (i.e., BiCarNet) with PCA-based inference. Specifically, for PCA-based" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.32 + ], + "angle": 0, + "content": "method, we utilize the same learning architecture to map the input image into the PCA-based texture space. Furthermore, to evaluate the effectiveness of the proposed texture inference modules, we also conduct ablative analysis on BiCarNet without Fuser and BiCarNet without Part-sensitive Reasoner (PSR). Table 2 shows the quantitative results of different texture inference methods on MSE, PSNR and FID and our proposed method achieves the highest scores compared with all other methods. Moreover, Fig. 8 illustrates the qualitative results of these methods for texture inference. Fig. 9 shows the results without and with Fuser, which demonstrates our fusion module can deal with unnatural seam-like artifacts. We can observe that the part-sensitive texture reasoner and the Fuser help to capture the local regions of characters and recover their detailed appearances." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.331, + 0.88, + 0.428 + ], + "angle": 0, + "content": "
MethodMSE(×10-1)↓PSNR(×102) ↑FID ↓
PCA0.23090.22540.4642
BiCarNet0.10930.24580.1133
BiCarNet w/o Fuser0.11080.23970.1407
BiCarNet w/o PSR0.13460.23610.4024
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.438, + 0.895, + 0.495 + ], + "angle": 0, + "content": "Table 2. Quantitative results on texture inference. PCA denotes linear modeling method for texture and the last two rows indicate the results of BiCarNet respectively without two designed module. Our BiCarNet outperforms others methods in all metrics." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.517, + 0.591, + 0.693 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.696, + 0.562, + 0.708 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.518, + 0.661, + 0.693 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.616, + 0.696, + 0.636, + 0.708 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.518, + 0.731, + 0.693 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.696, + 0.709, + 0.708 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.518, + 0.808, + 0.693 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.696, + 0.785, + 0.708 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.518, + 0.885, + 0.694 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.839, + 0.696, + 0.858, + 0.708 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.777 + ], + "angle": 0, + "content": "Figure 8. Qualitative comparisons on texture inference. The input image (a) is followed by the textured models from (b) PCA, (c) BiCarNet w/o PSR, (d) BiCarNet and (e) the ground truth. Note that we use the same shape and focus on the difference of textures." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.807, + 0.681, + 0.825 + ], + "angle": 0, + "content": "6. More Applications" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.718, + 0.849 + ], + "angle": 0, + "content": "6.1. Sketch-based Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Customizing 3D biped cartoon characters usually requires a heavy workload with commercial tools, even for experienced artists. Sketch-based modeling enables amateur users" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12831" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.092, + 0.46, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.211, + 0.472, + 0.24 + ], + "angle": 0, + "content": "Figure 9. Qualitative ablation on Fuser in Texture inference. Left: BiCarNet w/o Fuser. Right: BiCarNet with Fuser." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.471, + 0.312 + ], + "angle": 0, + "content": "to get involved in 3D shape customization in a simple and intuitive fashion. We build a sketch-based modeling application with the help of 3DBiCar and RaBit." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.473, + 0.645 + ], + "angle": 0, + "content": "We first sample a series of shape vectors randomly and feed them to RaBit to generate 3D cartoon characters with diversified shapes, resulting in 12,000 T-pose models. Then we apply suggestive contour [24] to render the front-view sketches with different abstraction levels and obtain 108,000 sketch-model pairs. Given a sketch as input, we employ ResNet-50 and three MLPs as the encoder and decoder to map the input sketch to 100-dimensional shape parameters. The generated shape parameters are next fed to RaBit to reconstruct the corresponding 3D model. Please refer to the Supplemental materials for more details. Note that users only need to depict a 3D character with T-pose on a 2D canvas while the output characters of our method are animation-ready and can be directly applied to other commercial tools. Fig. 10 displays the sketches created by users with little knowledge of modeling as well as the corresponding models generated by our system. It can be seen that our sketch-based modeling system offers a smart approach for amateur users to create 3D biped cartoon characters with diversified shapes. We will further explore the support of shape reconstruction from sketches with arbitrary poses, and texture painting in the future." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.656, + 0.462, + 0.768 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.778, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Figure 10. Result gallery of sketch-based modelling. The sketches created by amateur users denotes on the left and the generated models on the right." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.307, + 0.848 + ], + "angle": 0, + "content": "6.2.3D Character Animation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Following the recent advance of human recovering method and parametric model [35, 39, 50], we extract the human from input video frames and adopt a temporal-aware" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.896, + 0.184 + ], + "angle": 0, + "content": "encoder to recover the sequence of human poses [50]. Then, a motion retargeting method [25] is used to convert the poses on the human skeleton to the motion of our cartoon characters. As shown in Fig. 11, animation-ready characters generated by our RaBit can be directly applied to 3D animation. Please refer to the supplementary for animation video." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.193, + 0.564, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.37, + 0.553, + 0.382 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.195, + 0.652, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.37, + 0.627, + 0.382 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.196, + 0.764, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.369, + 0.73, + 0.382 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.196, + 0.877, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.827, + 0.369, + 0.846, + 0.382 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.393, + 0.894, + 0.437 + ], + "angle": 0, + "content": "Figure 11. Transferring motion of a human video to animate characters. (a) denotes the input frames. (b), (c), and (d) indicate three corresponding posed cartoon characters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.62, + 0.469 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.896, + 0.704 + ], + "angle": 0, + "content": "In this work, we introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 textured and skinned models with a consistent mesh topology. Based on 3DBiCar, we propose the first 3D full-body cartoon parametric model RaBit for biped character modeling. Furthermore, we build a baseline method BiCarNet for reconstructing 3D textured models from a single image with cartoon characters. Experimental results demonstrate the capability of 3DBiCar and RaBit as well as the effectiveness of BiCarNet. Last but not least, two further applications, i.e., sketch-based modeling and 3D character animation, demonstrate the usability and practicality of our dataset and parametric model. We hope that our work will contribute to the development of 3D biped cartoon character modeling and inspire future works in this area." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No. JCYJ20220530143604010, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12832" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Victoria Fernández Abrevaya, Stefanie Wuhrer, and Edmond Boyer. Multilinear autoencoder for 3d face model learning. 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Advances in Neural Information Processing Systems, 33:9251-9262, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "12835" + } + ] +] \ No newline at end of file diff --git a/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_origin.pdf b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e2a87c01405b829d683d281954070ad4bac95497 --- /dev/null +++ b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/1e9c4a16-13c2-47a3-ab7f-6611c669588a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:de13d56f2cb2279871a1be0683a74bd81d7ce160e027c527a2d5a1712e2cb14f +size 8754501 diff --git a/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/full.md b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/full.md new file mode 100644 index 0000000000000000000000000000000000000000..be28e8f5e0ce7630935d75beb7ddc7782e4bbf36 --- /dev/null +++ b/2023/RaBit_ Parametric Modeling of 3D Biped Cartoon Characters With a Topological-Consistent Dataset/full.md @@ -0,0 +1,337 @@ +# RaBit: Parametric Modeling of 3D Biped Cartoon Characters with a Topological-consistent Dataset + +Zhongjin Luo $^{1*}$ Shengcai Cai $^{1,3*}$ Jinguo Dong $^{1}$ Ruibo Ming $^{1,4}$ Liangdong Qiu $^{2,1}$ Xiaohang Zhan $^{3}$ Xiaoguang Han $^{1,2\dagger}$ + +$^{1}$ SSE, CUHKSZ $^{2}$ FNii, CUHKSZ $^{3}$ Huawei Technologies Co., Ltd. $^{4}$ Tsinghua University + +![](images/0ef10dedb6165916e913eebc0822dd69d3664f972002d09472ed23390db7439d.jpg) +Figure 1. We present 3DBiCar, the first large-scale repository of 3D biped cartoon characters. It contains 1,500 topologically consistent, textured, and skinned 3D high-quality meshes manually created by professional artists, covering 15 species. Further, we propose RaBit, the first cartoon character parametric model simultaneously parameterizing shape, pose, and texture. + +# Abstract + +Assisting people in efficiently producing visually plausible 3D characters has always been a fundamental research topic in computer vision and computer graphics. Recent learning-based approaches have achieved unprecedented accuracy and efficiency in the area of 3D real human digitization. However, none of the prior works focus on modeling 3D biped cartoon characters, which are also in great demand in gaming and filming. In this paper, we introduce 3DBiCar, the first large-scale dataset of 3D biped cartoon characters, and RaBit, the corresponding parametric model. Our dataset contains 1,500 topologically consistent high-quality 3D textured models which are manually crafted by professional artists. Built upon the data, RaBit is thus designed with a SMPL-like linear blend shape model and a StyleGAN-based neural UV-texture generator, simultaneously expressing the shape, pose, and texture. To demonstrate the practicality + +of 3DBiCar and RaBit, various applications are conducted, including single-view reconstruction, sketch-based modeling, and 3D cartoon animation. For the single-view reconstruction setting, we find a straightforward global mapping from input images to the output UV-based texture maps tends to lose detailed appearances of some local parts (e.g., nose, ears). Thus, a part-sensitive texture reasoner is adopted to make all important local areas perceived. Experiments further demonstrate the effectiveness of our method both qualitatively and quantitatively. 3DBiCar and RaBit are available at gaplab.cuhk.edu.cn/projects/RaBit. + +# 1. Introduction + +With the rapid development of digitization, creating high-quality 3D articulated characters is highly demanded in game platforms, film industries, and metaverse scenarios. However, even for expert artists, creating a 3D character is labor-intensive and time-consuming. Therefore, reducing the cost of producing visually plausible 3D characters is essential in the field of computer vision and graphics. + +Recently, researchers have made great progress in digitizing realistic human characters. The emergence and popularity of various 3D sensing devices make capturing 3D data from the real world convenient, prompting a growing number of 3D real-people scanned datasets [3,7,12,43,45,53,54,56]. Based on these large-scale datasets, several powerful parametric models [5,12,35,39] have been developed to facilitate the reconstruction and analysis of human shapes, actions, and interactions. With the help of parametric models, deep learning techniques have shown the potential to efficiently infer accurate 3D digital humans from single-view images [26,39] or even sparse sketches [9,24,48]. Most recently, there are some works [36,41] that devote to exploring the intelligent generation of cartoon-like character heads. However, none of the prior works focuses on the modeling of 3D full-body biped cartoon characters, which are also in great demand in the area of gaming (e.g., Animal Crossing), filming (e.g., Zootopia), and virtualizing (e.g., Metaverse). In this work, we raise a new problem to the community: How to quickly produce 3D biped cartoon characters from easy-to-obtain inputs (e.g., a single image)? + +Revisiting the road map of realistic human digitization, the first step to tackling the above problem is building a high-quality 3D biped cartoon characters dataset. We thus introduce 3DBiCar, the first large-scale publicly available 3D biped cartoon character dataset following three criteria: 1) Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models covering 15 species, as shown in the Fig. 3. 2) Richness. Each model in 3DBiCar owns not only a detailed shape but also a texture UV-map, which are matched with a reference image. Additionally, each character is attached with two models, one with T-pose and another with the reference pose. 3) Topological-consistency. Each 3D model is created by carefully deforming a pre-defined template mesh. All 3D characters in 3DBiCar are unified in topology, paving the way to learn a skinned parametric model. Fig. 1 shows some representative models of the proposed dataset. + +Based on 3DBiCar, we further propose a generative model, dubbed RaBit, for 3D biped cartoon character generation. It combines a linear blend shape model with a neural texture generator and simultaneously parameterizes the shape, pose, and texture to a low-dimensional parametric space. For shape and pose modeling, numerous methods have shown principal component analysis's (PCA's) advantage in building decent statistical shape models [5, 12, 32, 39]. Inspired by SMPL [35], we utilize the traditional PCA technique to parameterize shape. Due to the variety and complexity of cartoon texture, directly adopting PCA for texture modeling fails to reconstruct details and falls into blurry results. We tackle this problem by introducing a StyleGAN-based generator. + +To explore the practical usage of 3DBiCar and RaBit, we + +first conduct the application of single-view reconstruction. Considering prior works for SMPL-based human geometry generation from single-view images [6, 26, 30], we build a baseline method with our dataset and the parametric model. We select one regression-based method for pose and shape inference. For texture inference, we find directly applying a global texture-generator tends to make the results lose detailed appearances, especially for some local but important regions (e.g., nose and ears). Thus a part-sensitive reasoner is utilized to deal with different local regions. We term our baseline method for single-view reconstruction as BiCarNet. Moreover, two further applications, i.e., sketch-based modeling and 3D character animation, are also explored. Experimental results on these applications demonstrate that it is already able to generate reasonable outputs. + +To summarize, our contributions include: + +- We introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 high-quality textured 3D models with a consistent mesh topology. +- We propose RaBit, the first 3D full-body cartoon parametric model for biped character modeling. We will release both 3DBiCar and RaBit for future research. +- We build BiCarNet, the baseline method to reconstruct 3D biped cartoon characters from a single-view image. A part-sensitive reasoner is adopted for detailed texture generation. +- Two other applications, i.e., sketch-based modeling and 3D character animation, are also conducted to demonstrate the promising potential of 3DBiCar and RaBit. + +# 2. Related Work + +3D Character Datasets. In general, 3D character datasets could be categorized as real-captured and computer-designed datasets. For capturing character data from the real world, the availability of 3D scanning devices has enabled researchers to collect many scanned 3D human-related datasets, mainly focusing on human faces [10] and bodies [13]. For human faces, FaceWarehouse [12] collects large-scale 3d faces with high diversity in age, ethnicity, and expression. FaceScape [53] further builds a large-scale detailed 3D face dataset with high resolution in texture and mesh. For human bodies, CAESAR dataset [43] opens up the learning of the human body and is widely used for body shape modeling for its shape diversity and satisfying resolution of meshes. Many following works [3,7,45,54,56] extend [43] in shape, pose, and texture, on quantity and quality. Although these real-captured datasets are widely used in realistic human digitalization, they are unsuitable for imaginary character generation. + +For designing character data with computers, researchers try to perform deformation on real 3D human faces or bodies + +to construct exaggerated shapes programmatically [11,24,46, 51]. Their results lack diversity and are far from satisfactory. To address this, 3DCaricShop [41] proposes a large-scale 3D exaggerated faces dataset. SimpModeling [36] constructs a large man-made animalmorphic head dataset. Although using 3DCaricShop and SimpModeling could facilitate the generation of unreal character heads, it still remains a problem to synthesize full-body cartoon characters due to the lack of corresponding body data. In our work, we tackle this problem by introducing a large 3D biped cartoon character dataset, 3DBiCar. + +Parametric Shape Modeling. Parametric models of shapes are widely used in 3D digitizations. Blanz et al. [5] pioneer parametric modeling using PCA and release a 3D statistical morphable face model (3DMM). Their parameterization models textured faces and provides a set of controls for intuitively manipulating shapes, expressions, and textures. Since then, PCA-based parameterizing has gradually dominated the area of statistical shape modeling over the past decades. Following 3DMM, researchers model the whole head to represent the neck region and 3D head rotations [12, 32]. Allen et al. [2] open up the study of full body parameterization. However, they focus only on body shape and omit the body pose. SCAPE [3] represents body shape and pose in terms of triangle deformations, while SMPL [35] models a whole range of natural shapes and poses based on vertex displacements. SMPL-X [39] integrates SMPL [35] with FLAME [32] head model and the MANO [44] hand model for expressive capturing of bodies, hands and faces together. With recent advances in deep learning, researchers turn to explore nonlinear shape models using neural networks [1, 4, 8, 42, 52, 57]. However, since these non-linear modeling methods are inferior in simplicity, robustness and availability, PCA-based methods remain prevalent in the research community. In this paper, we also adopt PCA into RaBit to model the geometry of 3D biped cartoon characters. + +Based on the above parametric models, researchers have made remarkable progress in human digitization, such as reconstruction from simple inputs (e.g., a single image or sparse sketches) [6, 15, 24, 26, 40] and real-time pose retargeting [14, 29, 50]. For instance, SMPLify [6] estimates 3D body shape and pose parameters automatically from 2D joints with multiple ellipsoids. HMR [26] proposes an end-to-end framework for reconstructing a full 3D mesh of a human body from a single RGB image. DeepSketch2Face [24] proposes a sketch-based system for inferring 3D face models from 2D sketches with the help of parametric models and CNN-based deep regression networks. TCMR [14] presents a temporally consistent mesh recovery system for recovering smooth 3D human motion from monocular videos. To probe the capability of RaBit to downstream applications, we conduct various utilization, such as single-view cartoon character reconstruction, sketch-based character modeling, + +and 3D cartoon animation. Experimental results demonstrate the practicality of 3DBiCar and RaBit. + +Parametric Texture Modeling. Traditionally, textures are modeled as a linear subspace using the similar idea of body blendshape models. Blanz et al. [5] represent the face appearance in per-vertex colors and parameterize texture as a linear model based on PCA. Dai et al. [16] store texture information in a UV space where the texture resolution is unconstrained by mesh resolution. Moschoglou et al. [37] formulate a robust matrix factorization problem to learn the parametric representation of facial UV maps from a collection of training textures. However, these linear texture models may lead to a sub-optimal appearance output [18, 23] due to the weak assumption of Gaussian and tend to produce blurry results. + +With recent advances in deep learning, researchers turn to utilize deep neural networks to model texture. A number of deep generative models [17, 19-22, 31, 38, 47] have been proposed to parameterize texture into a latent space. For example, GANFIT [21] utilizes GAN-based neural networks to train a generator of facial texture in UV space for 3D face reconstruction. StylePeople [22] incorporates neural texture synthesis, mesh rendering, and neural rendering into the joint generation process to train a neural texture generator for the task of single-view human reconstruction. GET3D [20] introduces a texture-field generative model that directly generates explicit textured 3D meshes, ranging from cars, chairs, animals, motorbikes, and human characters to buildings. These methods have shown the promising capacity of neural generators to represent texture. In our work, we adopt a GAN-based neural texture generator into RaBit to provide high-quality texture modeling. + +# 3. Dataset + +Considerable progress has been made in digitizing realistic and articulated human characters. However, efficiently creating visually plausible biped cartoon characters remains demanding and challenging, mainly due to the lack of data. In this work, we propose to fill this gap by introducing 3DBiCar, the first large-scale full-body 3D biped character data. We build 3DBiCar following three rules: + +Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models. First, we carefully collect images of 2D full-body biped cartoon characters with diverse identities, shape, and textural styles from the Internet, resulting in 15 character species and 4 image styles, as shown in Fig. 3. Then we recruit six professional artists to create 3D corresponding character models according to the collected reference images. The modeling result is required to be matched with the reference images as much as possible. The representative image-model pairs sampled from our dataset are shown in Fig. 2. + +Topological-consistency. The key to building a linear + +![](images/e68fb4cb185abdc6e22d9dae796615591554ac9c68d47c27925eb5598da69136.jpg) +Figure 2. The gallery of the representative examples sampled from 3DBiCar. Each collected reference image is followed by the T-pose model and the posed model, created by professional artists. 3DBiCar contains 1,500 topologically consistent, textured and skinned 3D high-quality models with paired 2D images, which covers 15 species and 4 image styles. + +![](images/9ffcc41dce4b8f33739dc01ae3a938315c4c9f4b0c00835d7da31c9d07b5bac6.jpg) +Figure 3. Data distribution. Chart (a) illustrates the number of 15 species of bipedal cartoon characters in 3DBiCar. Chart (b) shows the number of four styles of reference images collected in our dataset. + +parametric shape model is keeping a unified mesh topology. Traditional human parametric models utilize a template mesh to register different human body scans with 3D landmarks to keep topologically uniform. Inspired by this, we first create a template mesh with several 3D colored landmarks as shown in Fig. 4. All six artists are required to craft 3D models by deforming the above-predefined template under the constraints of these obvious landmarks. We set up a review committee of 10 to check these models based on the landmarks, ensuring the consistency of mesh topology. The landmarks could also be used to compute the position of models' joints for body posing or character animation. The topological consistency + +![](images/699dca7352e06eb10e8a0e2dd22341ba864528dc33897f66ffa4ca36f79b4a98.jpg) +Figure 4. Template. The models in the center are the predefined template mesh with landmarks. It can be seen that we refine the structure on specific regions, where a complex nose or tail may exist. The colored regions and delineated lines denote the landmarks. These landmarks represent specific components of the character's body, such as elbow and eye socket. During model crafting, artists are required to deform the template model while keeping the landmarks in the position where the original body components are. + +of 3DBiCar paves the way to learn a skinned parametric model, which we will discuss in Sec. 4. + +Richness. We provide various forms of data for each character. There are not only the 3D shape meshes and UV-space textures carefully crafted by artists but also collected reference images. For each character, artists are asked first + +to create a T-pose mesh and then deform it to match the reference pose. Furthermore, all the models are rigged and skinned using a predefined skeleton and skinning weight matrix, which enables further animation production for characters. In addition, each character contains two separate eyeballs specifically designed for facial animation. The body mesh of each character comprises 38,726 vertices and 77,448 faces, while each eyeball consists of 1,025 vertices and 2,046 faces. + +# 4. Parametric Modeling + +We propose the first parametric model of 3D biped cartoon characters (RaBit), which contains a linear blend model for shapes and a neural generator for textures. RaBit simultaneously parameterizes the shape, pose, and texture of 3D biped characters. Specifically, we decompose the parametric space into identity-related body parameter $B$ (Sec. 4.1), non-rigid pose-related parameter $\Theta$ (Sec. 4.2) and texture-related parameter $T$ (Sec. 4.3). Overall, a 3D biped character is parameterized as follows, + +$$ +\begin{array}{l} M = F (B, \Theta , T) \\ = F _ {T} \left(F _ {P} \left(F _ {S} (B), \Theta\right), T\right), \tag {1} \\ \end{array} +$$ + +where $F_{S}, F_{P}$ , and $F_{T}$ are the parametric functions to generate shape, pose, and texture respectively. The following sections will elaborate on the details of RaBit. + +# 4.1. Shape Modeling + +Recently, linear shape models dominate the representation of statistical 3D model. Numerous methods [5, 12, 32, 39] have shown PCA's ability in modeling the human body and face. Inspired by [35], we parameterize our character shape linearly with the following equation, + +$$ +M _ {S} = F _ {S} (B) = \bar {M} _ {S} + \sum_ {i} ^ {| B |} \beta_ {i} s _ {i}, \tag {2} +$$ + +where $\bar{M}_S$ denotes the mean shape and $M_S$ is the reconstructed shape. The coefficients of linear shape are $\beta_i \in B$ . $|B|$ is the number of shape parameters and is set to 100 in our implementation. $s_i \in \mathbb{R}^{3 \times N}$ denotes the orthogonal principal components of vertex displacements that capture shape variations in different character identities. The shape model of RaBit is learned from 1,050 characters of 3DBiCar using PCA [35]. RaBit's eyeballs can be computed based on the predefined landmarks shown in Fig. 4. Please refer to the Supplementary for more details. + +# 4.2. Pose Modeling + +RaBit employs a standard vertex-based linear blend skinning technique, which uses the predefined skeleton and skinning weight matrix provided by 3DBiCar. The pose parameter $\Theta$ defines a set of angles as $\Theta = [\theta_{1},\theta_{2},\dots,\theta_{K}]\in \mathbb{R}^{69}$ + +where $\theta_{k} \in \mathbb{R}^{3}$ denotes the axis-angle representation of the relative rotation of joint $k$ with respect to its parent and $K = 23$ represents the number of joints. $\theta_{k}$ can be converted to the rotation matrix format $R(\theta_k)$ using Rodrigues' formula [35]. The following equations demonstrate how the pose function $F_{P}$ changes vertex $v_{i} \in M_{S}$ to its corresponding position $v_{i}' \in M_{P}$ , + +$$ +v _ {i} ^ {\prime} = \sum_ {k = 1} ^ {K} w _ {k, i} G _ {k} ^ {\prime} (\Theta , J) v _ {i}, \tag {3} +$$ + +$$ +G _ {k} ^ {\prime} (\Theta , J) = G _ {k} (\Theta , J) G _ {k} (\Theta^ {\prime}, J) ^ {- 1}, \qquad (4) +$$ + +$$ +G _ {k} (\Theta , J) = \prod_ {j \in A (k)} \left[ \begin{array}{c c} R \left(\theta_ {j}\right) & J _ {j} \\ 0 & 1 \end{array} \right], \tag {5} +$$ + +where $w_{k,i}$ is the $k$ -th element of the linear blend matrix $W$ for the $i$ -th vertex. $G_{k}(\Theta, J)$ is the global transformation of joint $k$ , while $G_{k}'(\Theta, J)$ is the global transformation of joint $k$ after removing the transformation of rest pose $\Theta'$ . $A(k)$ denotes a set including all the ancestors of joint $k$ , and $J_{j}$ represents the location of the $j$ -th joint, which is located at the bounding box center of a specific body landmark. Thus given the T-posed mesh $M_{S}$ and specific pose $\Theta$ , we can generate the corresponding posed mesh $M_{P}$ by $F_{P}$ , + +$$ +M _ {P} = F _ {P} \left(M _ {S}, \Theta\right). \tag {6} +$$ + +# 4.3. Texture Modeling + +Although traditional linear PCA is capable of building a decent statistical shape model, it fails to represent high-frequency details in textures and can produce blurry results due to its weak Gaussian assumption. Recently, GAN-based architectures [19, 21, 22, 27, 28, 49] have shown the notable capability of generating high-fidelity images. Thus, we resort to StyleGAN2-based techniques for UV texture maps generation, but with a coherent UV unfolding (as shown in Fig. 5) to facilitate the learning of texture compared with [22]. Specifically, the neural texture generator in RaBit translates a latent code to a texture map, which could be formulated as follows, + +$$ +G (T): \mathbb {R} ^ {Z} \rightarrow \mathbb {R} ^ {H \times W \times C}, \tag {7} +$$ + +where $G(T)$ takes a Z-dimensional parameter vector as input and synthesizes a $H \times W \times C$ texture map. Thus given a posed mesh $M_P$ and a specific texture code $T$ , we can generate a textured mesh $M$ with the following equation, + +$$ +M = F _ {T} \left(M _ {P}, T\right) = H \left(M _ {P}, G (T)\right), \tag {8} +$$ + +where $H$ means the process of applying the texture map to the mesh model. In our implementation, the generator follows the architecture of StyleGAN2 [28], while taking a 512-dimensional parameter vector as input and generating a $1024 \times 1024 \times 3$ texture map. + +# 5. Single-View Reconstruction + +![](images/1a5b474f2ebf92843e6bf4c5df25696b4fd25e079f10a1edcfe5d62b40d1d4c3.jpg) +Figure 5. BiCarNet. Given a masked image, we first map it to the parametric vectors. The vectors are then fed to our RaBit to generate a posed body mesh, two eyeballs, and a global UV texture. A part-sensitive reasoner is utilized to perceive local regions and generate the detailed UV texture map. Finally, a vivid 3D cartoon character is obtained with our BiCarNet. + +Single-view reconstruction (SVR) is one of the most popular tasks of efficient 3D content generation, and recent work has made noticeable progress on human reconstruction based on parametric model of human characters (e.g., SMPL). To verify the practicality of our proposed 3DBiCar and RaBit, we conduct SVR for bipled cartoon characters. A baseline learning-based method is presented, which is termed as BiCarNet. + +# 5.1. BiCarNet + +Given a single masked image of cartoon characters, our BiCarNet aims to reconstruct the corresponding 3D shape, pose, and texture. The key problem is to build an encoder to map the input image to the parametric space of Rabbit. As shown in the upper part of Fig. 5, we adopt the learning block in HMR [26] as our Encoder. Once these parametric vectors are learned, we can feed them to our RaBit model to generate a posed body mesh, two eyeballs, and a UV texture (we name it global for convenience to introduce the following method description). + +During our preliminary experiments, we find that the shape reconstruction of characters, i.e. the eyes and body, is satisfactory, while the inferred UV tends to lose detailed appearances of some small yet significant areas, such as the nose and ears. We thus adopt a part-sensitive texture reasoner (PSR) to address the above issue, as the lower part of Fig. 5 shows. Specifically, we design five individual UV-mappings + +for these significant parts of the nose, ears, horns, eyes, and mouth. Five lightweight encoder-decoder branches are next introduced to learn the appearances of these local regions from the input image, respectively. The learned part UVs could be remapped to the corresponding area on the global UV map to produce a blended texture. However, a direct blending tends to cause seam artifacts. Thus we further adopt a Fuser to address the artifacts as Fig. 5 illustrates. Please refer to the Supplementary for thorough implementations of BiCarNet. + +# 5.2. Experiments + +Data preparation. We first split 3DBiCar into a training set (1,050 image-model pairs) and a testing set (450 pairs). To support a stable training of BiCarNet, we next generate a large number of synthetic paired data with the help of RaBit, which are highly diversified in shape, posture, and texture. To be specific, a lot of 3D textured models are first sampled from the RaBit space, which are then rendered into images from different camera views. This finally produces 13,650 pairs for training. Note that, BiCarNet takes an image with foreground masked as input. All synthetic images naturally have no background. For real images, all the foreground masks are manually annotated. + +Result gallery. Fig. 6 shows representative results generated by BiCarNet. As illustrated, our BiCarNet can generate vivid 3D cartoon characters loyal to individual cartoon images in shape, pose, and texture. We believe that our work opens the door to producing 3D biped cartoon characters from easy-to-obtain inputs. + +![](images/c7709e7bf28a9c0d328d3c8dca64f0e7891490f57cbdc6f59ad8861954b31d1b.jpg) +Figure 6. Result gallery of BiCarNet. Our BiCarNet is capable of generating vivid 3D cartoon characters with only single-view image input. + +Results on Shape Reconstruction. As mentioned above, BiCarNet utilizes HMR-like blocks and RaBit for shape and pose learning. Currently, other reconstruction methods could also be used for topology-consistent geometry inference, such as GCNN-based methods [34] and UV-based methods [55]. We choose two representative methods for comparison, i.e., Mesh-Graphormer [33, 34] and DecoMR [55]. + +Mesh-Graphormer combines graph convolutions and self-attention in a transformer for 3D human reconstruction from a single image. DecoMR reconstructs 3D human mesh from single images by regressing a UV-based location map. Tab. 1 shows the quantitative comparisons of the above three methods on MPVE, MPJPE, and PA-MPJPE. We also provide qualitative comparisons in Fig. 7. Both quantitative and qualitative results demonstrate that the HMR-like method achieves the highest performance on geometry inference and provides more accurate reconstructions closer to ground truths. As noted, both Mesh-Graphormer and DecoMR outperform HMR for SMPL-based human reconstruction. It is interestingly found that they perform worse in our settings. One possible reason is that our biped cartoon meshes own an extremely larger amount of vertices than SMPL to model more complex geometry. This greatly increases the challenge of vertices regression in Mesh-Graphormer and DecoMR. Thus, in our setting, directly regressing the low-dimension parameters performs better. + +
MethodMPVE ↓MPJPE ↓PA-MPJPE ↓
DecoMR [55]85.7481.2347.23
Mesh-Graphormer [34]63.3147.1534.12
Ours (HMR [26] + RaBit)51.4637.8025.97
+ +![](images/9107f83c46abcd4846b8e03e8503fccb6f3133b5d0fe42fd254abbb0e781283d.jpg) + +![](images/9079c87cf03db7e8227da1d5ce2b676a6fc0cc35b28384457371ea560d08f26e.jpg) + +![](images/d8434b973035beb7acfdb3b36e7a9520aedbe3cb4162c6f458e6a00c25d382ff.jpg) +(a) + +![](images/009e3a53630deab0474efb1c9c717b2e84c66f080abf6bd7acdc223b2552ec5a.jpg) + +![](images/d1877d513ddc54ecba16906fbfd887aa72d1249fa34c2b7fe5c7da87d85ad9f9.jpg) + +![](images/06f6f37d85cee28387eccecfc4faa49577613e5b4efdf87b0a81a3c44eb8119e.jpg) +(b) + +![](images/6028568fb9e12fec56a29ab1d5277e66d3eabe296ccd792d7863aed496b7c1a7.jpg) + +![](images/5ab1c78a842f98e78f885a32456e26a3c7b55469ff1a18d975dbaa0619566ffe.jpg) + +![](images/b5f9a4b4f69bfa46a0f8a0c2939a88893746733bb9e705c8c1f4c1809a34297e.jpg) +(c) + +![](images/4f72609089e2bcea644ecca6e1cdd7ee10e7d613a3922c582a520a5a5cbe471a.jpg) + +![](images/5b02d7cba9b5d2524dd770e8341a83b6dc19192a8d56a135f18fe139eac6a529.jpg) + +![](images/952ad0a9b4f81c4dc4fa901aceb1ec0e8af48c4fd6aba0a3b3f63f00e13971b9.jpg) +(d) + +![](images/40dbeaa989259097db4a2bb73056564276d104271a18ea4287d51e0540f28354.jpg) + +![](images/4cd5786bdf05fdc6eb438a16fd9d3902246ac556f1b8d7984886f2a9539d5922.jpg) +Figure 8. Qualitative comparisons on texture inference. The input image (a) is followed by the textured models from (b) PCA, (c) BiCarNet w/o PSR, (d) BiCarNet and (e) the ground truth. Note that we use the same shape and focus on the difference of textures. + +![](images/e3f1052541792184b74ba3b915263952a2a034ea238feacb2122a2bfdcb760f4.jpg) +(e) +Figure 7. Qualitative results of shape reconstruction. From left to right, each row contains (a) the input image, reconstructed meshes of (b) Mesh Graphormer, (c) DecoMR, (d) our method, and (e) the GT mesh. + +Results on Texture Inference. To demonstrate the capability of our proposed GAN-based texture generator, we first compare our RaBit-based texture inference (i.e., BiCarNet) with PCA-based inference. Specifically, for PCA-based + +method, we utilize the same learning architecture to map the input image into the PCA-based texture space. Furthermore, to evaluate the effectiveness of the proposed texture inference modules, we also conduct ablative analysis on BiCarNet without Fuser and BiCarNet without Part-sensitive Reasoner (PSR). Table 2 shows the quantitative results of different texture inference methods on MSE, PSNR and FID and our proposed method achieves the highest scores compared with all other methods. Moreover, Fig. 8 illustrates the qualitative results of these methods for texture inference. Fig. 9 shows the results without and with Fuser, which demonstrates our fusion module can deal with unnatural seam-like artifacts. We can observe that the part-sensitive texture reasoner and the Fuser help to capture the local regions of characters and recover their detailed appearances. + +Table 1. Quantitative results of shape reconstruction. Our method achieves the best results in terms of MPVE, MPJPE and PA-MPJPE. Note that all metrics are measured in a unit $10^{-3}\mathrm{m}$ . + +
MethodMSE(×10-1)↓PSNR(×102) ↑FID ↓
PCA0.23090.22540.4642
BiCarNet0.10930.24580.1133
BiCarNet w/o Fuser0.11080.23970.1407
BiCarNet w/o PSR0.13460.23610.4024
+ +Table 2. Quantitative results on texture inference. PCA denotes linear modeling method for texture and the last two rows indicate the results of BiCarNet respectively without two designed module. Our BiCarNet outperforms others methods in all metrics. + +![](images/2d8e1e8825a5bc0bc1d42c748ceb33b5ad6d98b5c514c1f0a689f9d74780bafa.jpg) +(a) + +![](images/052ca78664419d639f5bb84c0bd8c997c457b74d8d67bcf2a2b6d58ec3ebff97.jpg) +(b) + +![](images/d4432f4ab0d1177de93dd1ccef11dcd48b330cabd8a4c82b70e6384c9e7f6987.jpg) +(c) + +![](images/bed1bed8810eb75b6f64a6158e546b4fc34d1ad2a9025f83a9b8a3859dd23e02.jpg) +(d) + +![](images/891ed9d6878e2c81efcf84a57d65fd39bc81f3055a299a53b8e34bca4cd6eac7.jpg) +(e) + +# 6. More Applications + +# 6.1. Sketch-based Modeling + +Customizing 3D biped cartoon characters usually requires a heavy workload with commercial tools, even for experienced artists. Sketch-based modeling enables amateur users + +![](images/3879b5c7063dfadc9b68417b4b38052e3c3fa9e2158a1bc8646cf34b0af01b1e.jpg) +Figure 9. Qualitative ablation on Fuser in Texture inference. Left: BiCarNet w/o Fuser. Right: BiCarNet with Fuser. + +to get involved in 3D shape customization in a simple and intuitive fashion. We build a sketch-based modeling application with the help of 3DBiCar and RaBit. + +We first sample a series of shape vectors randomly and feed them to RaBit to generate 3D cartoon characters with diversified shapes, resulting in 12,000 T-pose models. Then we apply suggestive contour [24] to render the front-view sketches with different abstraction levels and obtain 108,000 sketch-model pairs. Given a sketch as input, we employ ResNet-50 and three MLPs as the encoder and decoder to map the input sketch to 100-dimensional shape parameters. The generated shape parameters are next fed to RaBit to reconstruct the corresponding 3D model. Please refer to the Supplemental materials for more details. Note that users only need to depict a 3D character with T-pose on a 2D canvas while the output characters of our method are animation-ready and can be directly applied to other commercial tools. Fig. 10 displays the sketches created by users with little knowledge of modeling as well as the corresponding models generated by our system. It can be seen that our sketch-based modeling system offers a smart approach for amateur users to create 3D biped cartoon characters with diversified shapes. We will further explore the support of shape reconstruction from sketches with arbitrary poses, and texture painting in the future. + +![](images/703250f15da0f568e27f0cde40a2619d3f7411f8b49794c7f5480e6dd08a5d17.jpg) +Figure 10. Result gallery of sketch-based modelling. The sketches created by amateur users denotes on the left and the generated models on the right. + +# 6.2.3D Character Animation + +Following the recent advance of human recovering method and parametric model [35, 39, 50], we extract the human from input video frames and adopt a temporal-aware + +encoder to recover the sequence of human poses [50]. Then, a motion retargeting method [25] is used to convert the poses on the human skeleton to the motion of our cartoon characters. As shown in Fig. 11, animation-ready characters generated by our RaBit can be directly applied to 3D animation. Please refer to the supplementary for animation video. + +![](images/8364d3aab17aab34f315f27f08fc340fff185b35b96b0d8cfc85c04cc726ab4e.jpg) +(a) + +![](images/582f04a20b6412aafddf321bd03c246f87d10fedefde744c43b38ff9c1aef993.jpg) +(b) + +![](images/96b33770258c949485812b55b50d88c15a37326dcb333a6ed34d30e55b012901.jpg) +(c) +Figure 11. Transferring motion of a human video to animate characters. (a) denotes the input frames. (b), (c), and (d) indicate three corresponding posed cartoon characters. + +![](images/04f0740bc80e80c4d28d670767861f3723922c7039efa4dfa09e4bee2ba3bc14.jpg) +(d) + +# 7. Conclusion + +In this work, we introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 textured and skinned models with a consistent mesh topology. Based on 3DBiCar, we propose the first 3D full-body cartoon parametric model RaBit for biped character modeling. Furthermore, we build a baseline method BiCarNet for reconstructing 3D textured models from a single image with cartoon characters. Experimental results demonstrate the capability of 3DBiCar and RaBit as well as the effectiveness of BiCarNet. Last but not least, two further applications, i.e., sketch-based modeling and 3D character animation, demonstrate the usability and practicality of our dataset and parametric model. We hope that our work will contribute to the development of 3D biped cartoon character modeling and inspire future works in this area. + +Acknowledgements. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No. JCYJ20220530143604010, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055). + +# References + +[1] Victoria Fernández Abrevaya, Stefanie Wuhrer, and Edmond Boyer. Multilinear autoencoder for 3d face model learning. 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Embodied hands: Modeling and capturing hands and bodies together. ACM Transactions on Graphics, (Proc. SIGGRAPH Asia), 36(6), Nov. 2017. 3 +[45] Alexandre Saint, Eman Ahmed, Abd El Rahman Shabayek, Kseniya Cherenkova, Gleb Gusev, Djamila Aouada, and Bjorn Ottersten. 3dbodytex: Textured 3d body dataset. In 2018 International Conference on 3D Vision (3DV), pages 495-504, 2018. 2 +[46] Matan Sela, Yonathan Aflalo, and Ron Kimmel. Computational caricaturization of surfaces. Computer Vision and Image Understanding, 141:1-17, 2015. 3 +[47] Ron Slossberg, Gil Shamai, and Ron Kimmel. High quality facial surface and texture synthesis via generative adversarial networks. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 3 +[48] Gizem Unlu, Mohamed Sayed, and Gabriel Brostow. Interactive sketching of mannequin poses. arXiv preprint arXiv:2212.07098, 2022. 2 +[49] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. High-resolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. 5 +[50] Zhouping Wang and Sarah Ostadabbas. Live stream temporally embedded 3d human body pose and shape estimation. arXiv preprint arXiv:2207.12537, 2022. 3, 8 +[51] Qianyi Wu, Juyong Zhang, Yu-Kun Lai, Jianmin Zheng, and Jianfei Cai. Alive caricature from 2d to 3d. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7336-7345, 2018. 3 +[52] Hongyi Xu, Eduard Gabriel Bazavan, Andrei Zanfir, William T Freeman, Rahul Sukthankar, and Cristian Sminchisescu. Ghum & ghuml: Generative 3d human shape and + +articulated pose models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6184-6193, 2020. 3 +[53] H. Yang, H. Zhu, Y. Wang, M. Huang, Q. Shen, R. Yang, and X. Cao. Facescape: A large-scale high quality 3d face dataset and detailed riggable 3d face prediction. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 598-607, Los Alamitos, CA, USA, jun 2020. IEEE Computer Society. 2 +[54] Yipin Yang, Yao Yu, Yu Zhou, Sidan Du, James Davis, and Ruigang Yang. Semantic parametric reshaping of human body models. In 2014 2nd International Conference on 3D Vision, volume 2, pages 41-48, 2014. 2 +[55] Wang Zeng, Wanli Ouyang, Ping Luo, Wentao Liu, and Xiaogang Wang. 3d human mesh regression with dense correspondence. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7054-7063, 2020. 6, 7 +[56] Zerong Zheng, Tao Yu, Yixuan Wei, Qionghai Dai, and Yebin Liu. Deephuman: 3d human reconstruction from a single image. In The IEEE International Conference on Computer Vision (ICCV), October 2019. 2 +[57] Yi Zhou, Chenglei Wu, Zimo Li, Chen Cao, Yuting Ye, Jason Saragih, Hao Li, and Yaser Sheikh. Fully convolutional mesh autoencoder using efficient spatially varying kernels. 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It contains 1,500 topologically consistent, textured, and skinned 3D high-quality meshes manually created by professional artists, covering 15 species. Further, we propose RaBit, the first cartoon character parametric model simultaneously parameterizing shape, pose, and texture." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 460, + 192, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 460, + 192, + 474 + ], + "spans": [ + { + "bbox": [ + 143, + 460, + 192, + 474 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 487, + 290, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 290, + 680 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 290, + 680 + ], + "type": "text", + "content": "Assisting people in efficiently producing visually plausible 3D characters has always been a fundamental research topic in computer vision and computer graphics. Recent learning-based approaches have achieved unprecedented accuracy and efficiency in the area of 3D real human digitization. However, none of the prior works focus on modeling 3D biped cartoon characters, which are also in great demand in gaming and filming. In this paper, we introduce 3DBiCar, the first large-scale dataset of 3D biped cartoon characters, and RaBit, the corresponding parametric model. Our dataset contains 1,500 topologically consistent high-quality 3D textured models which are manually crafted by professional artists. Built upon the data, RaBit is thus designed with a SMPL-like linear blend shape model and a StyleGAN-based neural UV-texture generator, simultaneously expressing the shape, pose, and texture. To demonstrate the practicality" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 461, + 548, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 548, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 548, + 594 + ], + "type": "text", + "content": "of 3DBiCar and RaBit, various applications are conducted, including single-view reconstruction, sketch-based modeling, and 3D cartoon animation. For the single-view reconstruction setting, we find a straightforward global mapping from input images to the output UV-based texture maps tends to lose detailed appearances of some local parts (e.g., nose, ears). Thus, a part-sensitive texture reasoner is adopted to make all important local areas perceived. Experiments further demonstrate the effectiveness of our method both qualitatively and quantitatively. 3DBiCar and RaBit are available at gaplab.cuhk.edu.cn/projects/RaBit." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 608, + 387, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 387, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 387, + 620 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": "With the rapid development of digitization, creating high-quality 3D articulated characters is highly demanded in game platforms, film industries, and metaverse scenarios. However, even for expert artists, creating a 3D character is labor-intensive and time-consuming. Therefore, reducing the cost of producing visually plausible 3D characters is essential in the field of computer vision and graphics." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 171, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 171, + 703 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 171, + 703 + ], + "type": "text", + "content": "*Z. Luo and S. Cai contribute equally." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 49, + 703, + 125, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 703, + 125, + 713 + ], + "spans": [ + { + "bbox": [ + 49, + 703, + 125, + 713 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12825" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "content": "Recently, researchers have made great progress in digitizing realistic human characters. The emergence and popularity of various 3D sensing devices make capturing 3D data from the real world convenient, prompting a growing number of 3D real-people scanned datasets [3,7,12,43,45,53,54,56]. Based on these large-scale datasets, several powerful parametric models [5,12,35,39] have been developed to facilitate the reconstruction and analysis of human shapes, actions, and interactions. With the help of parametric models, deep learning techniques have shown the potential to efficiently infer accurate 3D digital humans from single-view images [26,39] or even sparse sketches [9,24,48]. Most recently, there are some works [36,41] that devote to exploring the intelligent generation of cartoon-like character heads. However, none of the prior works focuses on the modeling of 3D full-body biped cartoon characters, which are also in great demand in the area of gaming (e.g., Animal Crossing), filming (e.g., Zootopia), and virtualizing (e.g., Metaverse). In this work, we raise a new problem to the community: How to quickly produce 3D biped cartoon characters from easy-to-obtain inputs (e.g., a single image)?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 326, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 289, + 529 + ], + "type": "text", + "content": "Revisiting the road map of realistic human digitization, the first step to tackling the above problem is building a high-quality 3D biped cartoon characters dataset. We thus introduce 3DBiCar, the first large-scale publicly available 3D biped cartoon character dataset following three criteria: 1) Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models covering 15 species, as shown in the Fig. 3. 2) Richness. Each model in 3DBiCar owns not only a detailed shape but also a texture UV-map, which are matched with a reference image. Additionally, each character is attached with two models, one with T-pose and another with the reference pose. 3) Topological-consistency. Each 3D model is created by carefully deforming a pre-defined template mesh. All 3D characters in 3DBiCar are unified in topology, paving the way to learn a skinned parametric model. Fig. 1 shows some representative models of the proposed dataset." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 531, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 289, + 700 + ], + "type": "text", + "content": "Based on 3DBiCar, we further propose a generative model, dubbed RaBit, for 3D biped cartoon character generation. It combines a linear blend shape model with a neural texture generator and simultaneously parameterizes the shape, pose, and texture to a low-dimensional parametric space. For shape and pose modeling, numerous methods have shown principal component analysis's (PCA's) advantage in building decent statistical shape models [5, 12, 32, 39]. Inspired by SMPL [35], we utilize the traditional PCA technique to parameterize shape. Due to the variety and complexity of cartoon texture, directly adopting PCA for texture modeling fails to reconstruct details and falls into blurry results. We tackle this problem by introducing a StyleGAN-based generator." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "To explore the practical usage of 3DBiCar and RaBit, we" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "type": "text", + "content": "first conduct the application of single-view reconstruction. Considering prior works for SMPL-based human geometry generation from single-view images [6, 26, 30], we build a baseline method with our dataset and the parametric model. We select one regression-based method for pose and shape inference. For texture inference, we find directly applying a global texture-generator tends to make the results lose detailed appearances, especially for some local but important regions (e.g., nose and ears). Thus a part-sensitive reasoner is utilized to deal with different local regions. We term our baseline method for single-view reconstruction as BiCarNet. Moreover, two further applications, i.e., sketch-based modeling and 3D character animation, are also explored. Experimental results on these applications demonstrate that it is already able to generate reasonable outputs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 318, + 252, + 485, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 252, + 485, + 263 + ], + "spans": [ + { + "bbox": [ + 318, + 252, + 485, + 263 + ], + "type": "text", + "content": "To summarize, our contributions include:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 272, + 547, + 453 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 318, + 272, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 272, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 318, + 272, + 545, + 308 + ], + "type": "text", + "content": "- We introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 high-quality textured 3D models with a consistent mesh topology." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 317, + 547, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 317, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 318, + 317, + 547, + 352 + ], + "type": "text", + "content": "- We propose RaBit, the first 3D full-body cartoon parametric model for biped character modeling. We will release both 3DBiCar and RaBit for future research." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 361, + 547, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 361, + 547, + 409 + ], + "spans": [ + { + "bbox": [ + 318, + 361, + 547, + 409 + ], + "type": "text", + "content": "- We build BiCarNet, the baseline method to reconstruct 3D biped cartoon characters from a single-view image. A part-sensitive reasoner is adopted for detailed texture generation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 418, + 547, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 418, + 547, + 453 + ], + "spans": [ + { + "bbox": [ + 318, + 418, + 547, + 453 + ], + "type": "text", + "content": "- Two other applications, i.e., sketch-based modeling and 3D character animation, are also conducted to demonstrate the promising potential of 3DBiCar and RaBit." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 486, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 689 + ], + "type": "text", + "content": "3D Character Datasets. In general, 3D character datasets could be categorized as real-captured and computer-designed datasets. For capturing character data from the real world, the availability of 3D scanning devices has enabled researchers to collect many scanned 3D human-related datasets, mainly focusing on human faces [10] and bodies [13]. For human faces, FaceWarehouse [12] collects large-scale 3d faces with high diversity in age, ethnicity, and expression. FaceScape [53] further builds a large-scale detailed 3D face dataset with high resolution in texture and mesh. For human bodies, CAESAR dataset [43] opens up the learning of the human body and is widely used for body shape modeling for its shape diversity and satisfying resolution of meshes. Many following works [3,7,45,54,56] extend [43] in shape, pose, and texture, on quantity and quality. Although these real-captured datasets are widely used in realistic human digitalization, they are unsuitable for imaginary character generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "For designing character data with computers, researchers try to perform deformation on real 3D human faces or bodies" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12826" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": "to construct exaggerated shapes programmatically [11,24,46, 51]. Their results lack diversity and are far from satisfactory. To address this, 3DCaricShop [41] proposes a large-scale 3D exaggerated faces dataset. SimpModeling [36] constructs a large man-made animalmorphic head dataset. Although using 3DCaricShop and SimpModeling could facilitate the generation of unreal character heads, it still remains a problem to synthesize full-body cartoon characters due to the lack of corresponding body data. In our work, we tackle this problem by introducing a large 3D biped cartoon character dataset, 3DBiCar." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 289, + 506 + ], + "type": "text", + "content": "Parametric Shape Modeling. Parametric models of shapes are widely used in 3D digitizations. Blanz et al. [5] pioneer parametric modeling using PCA and release a 3D statistical morphable face model (3DMM). Their parameterization models textured faces and provides a set of controls for intuitively manipulating shapes, expressions, and textures. Since then, PCA-based parameterizing has gradually dominated the area of statistical shape modeling over the past decades. Following 3DMM, researchers model the whole head to represent the neck region and 3D head rotations [12, 32]. Allen et al. [2] open up the study of full body parameterization. However, they focus only on body shape and omit the body pose. SCAPE [3] represents body shape and pose in terms of triangle deformations, while SMPL [35] models a whole range of natural shapes and poses based on vertex displacements. SMPL-X [39] integrates SMPL [35] with FLAME [32] head model and the MANO [44] hand model for expressive capturing of bodies, hands and faces together. With recent advances in deep learning, researchers turn to explore nonlinear shape models using neural networks [1, 4, 8, 42, 52, 57]. However, since these non-linear modeling methods are inferior in simplicity, robustness and availability, PCA-based methods remain prevalent in the research community. In this paper, we also adopt PCA into RaBit to model the geometry of 3D biped cartoon characters." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": "Based on the above parametric models, researchers have made remarkable progress in human digitization, such as reconstruction from simple inputs (e.g., a single image or sparse sketches) [6, 15, 24, 26, 40] and real-time pose retargeting [14, 29, 50]. For instance, SMPLify [6] estimates 3D body shape and pose parameters automatically from 2D joints with multiple ellipsoids. HMR [26] proposes an end-to-end framework for reconstructing a full 3D mesh of a human body from a single RGB image. DeepSketch2Face [24] proposes a sketch-based system for inferring 3D face models from 2D sketches with the help of parametric models and CNN-based deep regression networks. TCMR [14] presents a temporally consistent mesh recovery system for recovering smooth 3D human motion from monocular videos. To probe the capability of RaBit to downstream applications, we conduct various utilization, such as single-view cartoon character reconstruction, sketch-based character modeling," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "and 3D cartoon animation. Experimental results demonstrate the practicality of 3DBiCar and RaBit." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 96, + 547, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 251 + ], + "type": "text", + "content": "Parametric Texture Modeling. Traditionally, textures are modeled as a linear subspace using the similar idea of body blendshape models. Blanz et al. [5] represent the face appearance in per-vertex colors and parameterize texture as a linear model based on PCA. Dai et al. [16] store texture information in a UV space where the texture resolution is unconstrained by mesh resolution. Moschoglou et al. [37] formulate a robust matrix factorization problem to learn the parametric representation of facial UV maps from a collection of training textures. However, these linear texture models may lead to a sub-optimal appearance output [18, 23] due to the weak assumption of Gaussian and tend to produce blurry results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 251, + 548, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 548, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 548, + 456 + ], + "type": "text", + "content": "With recent advances in deep learning, researchers turn to utilize deep neural networks to model texture. A number of deep generative models [17, 19-22, 31, 38, 47] have been proposed to parameterize texture into a latent space. For example, GANFIT [21] utilizes GAN-based neural networks to train a generator of facial texture in UV space for 3D face reconstruction. StylePeople [22] incorporates neural texture synthesis, mesh rendering, and neural rendering into the joint generation process to train a neural texture generator for the task of single-view human reconstruction. GET3D [20] introduces a texture-field generative model that directly generates explicit textured 3D meshes, ranging from cars, chairs, animals, motorbikes, and human characters to buildings. These methods have shown the promising capacity of neural generators to represent texture. In our work, we adopt a GAN-based neural texture generator into RaBit to provide high-quality texture modeling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 466, + 360, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 360, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 360, + 478 + ], + "type": "text", + "content": "3. Dataset" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 486, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 569 + ], + "type": "text", + "content": "Considerable progress has been made in digitizing realistic and articulated human characters. However, efficiently creating visually plausible biped cartoon characters remains demanding and challenging, mainly due to the lack of data. In this work, we propose to fill this gap by introducing 3DBiCar, the first large-scale full-body 3D biped character data. We build 3DBiCar following three rules:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 700 + ], + "type": "text", + "content": "Diversity. 3DBiCar spans a wide range of 3D biped cartoon characters, containing 1,500 high-quality 3D models. First, we carefully collect images of 2D full-body biped cartoon characters with diverse identities, shape, and textural styles from the Internet, resulting in 15 character species and 4 image styles, as shown in Fig. 3. Then we recruit six professional artists to create 3D corresponding character models according to the collected reference images. The modeling result is required to be matched with the reference images as much as possible. The representative image-model pairs sampled from our dataset are shown in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "Topological-consistency. The key to building a linear" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12827" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 541, + 325 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 541, + 325 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 541, + 325 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 541, + 325 + ], + "type": "image", + "image_path": "e68fb4cb185abdc6e22d9dae796615591554ac9c68d47c27925eb5598da69136.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 332, + 546, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 332, + 546, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 546, + 367 + ], + "type": "text", + "content": "Figure 2. The gallery of the representative examples sampled from 3DBiCar. Each collected reference image is followed by the T-pose model and the posed model, created by professional artists. 3DBiCar contains 1,500 topologically consistent, textured and skinned 3D high-quality models with paired 2D images, which covers 15 species and 4 image styles." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 384, + 279, + 493 + ], + "blocks": [ + { + "bbox": [ + 53, + 384, + 279, + 493 + ], + "lines": [ + { + "bbox": [ + 53, + 384, + 279, + 493 + ], + "spans": [ + { + "bbox": [ + 53, + 384, + 279, + 493 + ], + "type": "image", + "image_path": "9ffcc41dce4b8f33739dc01ae3a938315c4c9f4b0c00835d7da31c9d07b5bac6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 502, + 288, + 545 + ], + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 545 + ], + "type": "text", + "content": "Figure 3. Data distribution. Chart (a) illustrates the number of 15 species of bipedal cartoon characters in 3DBiCar. Chart (b) shows the number of four styles of reference images collected in our dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "parametric shape model is keeping a unified mesh topology. Traditional human parametric models utilize a template mesh to register different human body scans with 3D landmarks to keep topologically uniform. Inspired by this, we first create a template mesh with several 3D colored landmarks as shown in Fig. 4. All six artists are required to craft 3D models by deforming the above-predefined template under the constraints of these obvious landmarks. We set up a review committee of 10 to check these models based on the landmarks, ensuring the consistency of mesh topology. The landmarks could also be used to compute the position of models' joints for body posing or character animation. The topological consistency" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 312, + 386, + 544, + 526 + ], + "blocks": [ + { + "bbox": [ + 312, + 386, + 544, + 526 + ], + "lines": [ + { + "bbox": [ + 312, + 386, + 544, + 526 + ], + "spans": [ + { + "bbox": [ + 312, + 386, + 544, + 526 + ], + "type": "image", + "image_path": "699dca7352e06eb10e8a0e2dd22341ba864528dc33897f66ffa4ca36f79b4a98.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 540, + 547, + 628 + ], + "lines": [ + { + "bbox": [ + 304, + 540, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 547, + 628 + ], + "type": "text", + "content": "Figure 4. Template. The models in the center are the predefined template mesh with landmarks. It can be seen that we refine the structure on specific regions, where a complex nose or tail may exist. The colored regions and delineated lines denote the landmarks. These landmarks represent specific components of the character's body, such as elbow and eye socket. During model crafting, artists are required to deform the template model while keeping the landmarks in the position where the original body components are." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 641, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 664 + ], + "type": "text", + "content": "of 3DBiCar paves the way to learn a skinned parametric model, which we will discuss in Sec. 4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Richness. We provide various forms of data for each character. There are not only the 3D shape meshes and UV-space textures carefully crafted by artists but also collected reference images. For each character, artists are asked first" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12828" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "content": "to create a T-pose mesh and then deform it to match the reference pose. Furthermore, all the models are rigged and skinned using a predefined skeleton and skinning weight matrix, which enables further animation production for characters. In addition, each character contains two separate eyeballs specifically designed for facial animation. The body mesh of each character comprises 38,726 vertices and 77,448 faces, while each eyeball consists of 1,025 vertices and 2,046 faces." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 190, + 173, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 190, + 173, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 173, + 204 + ], + "type": "text", + "content": "4. Parametric Modeling" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "text", + "content": "We propose the first parametric model of 3D biped cartoon characters (RaBit), which contains a linear blend model for shapes and a neural generator for textures. RaBit simultaneously parameterizes the shape, pose, and texture of 3D biped characters. Specifically, we decompose the parametric space into identity-related body parameter " + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "text", + "content": " (Sec. 4.1), non-rigid pose-related parameter " + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "text", + "content": " (Sec. 4.2) and texture-related parameter " + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 209, + 290, + 317 + ], + "type": "text", + "content": " (Sec. 4.3). Overall, a 3D biped character is parameterized as follows," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 323, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 323, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 107, + 323, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} M = F (B, \\Theta , T) \\\\ = F _ {T} \\left(F _ {P} \\left(F _ {S} (B), \\Theta\\right), T\\right), \\tag {1} \\\\ \\end{array}", + "image_path": "98ffcbadcb41903a25969a7df97835761f5d86d3882af1bca4964fa1b14b6e0b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "inline_equation", + "content": "F_{S}, F_{P}" + }, + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "inline_equation", + "content": "F_{T}" + }, + { + "bbox": [ + 46, + 356, + 289, + 392 + ], + "type": "text", + "content": " are the parametric functions to generate shape, pose, and texture respectively. The following sections will elaborate on the details of RaBit." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 398, + 146, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 398, + 146, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 398, + 146, + 411 + ], + "type": "text", + "content": "4.1. Shape Modeling" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 416, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 477 + ], + "type": "text", + "content": "Recently, linear shape models dominate the representation of statistical 3D model. Numerous methods [5, 12, 32, 39] have shown PCA's ability in modeling the human body and face. Inspired by [35], we parameterize our character shape linearly with the following equation," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 98, + 481, + 289, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 481, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 98, + 481, + 289, + 515 + ], + "type": "interline_equation", + "content": "M _ {S} = F _ {S} (B) = \\bar {M} _ {S} + \\sum_ {i} ^ {| B |} \\beta_ {i} s _ {i}, \\tag {2}", + "image_path": "3167af5e28255f751c17ac3408d65dddaef248776cb8f1f7fda649e67553bbd6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\bar{M}_S" + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": " denotes the mean shape and " + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "inline_equation", + "content": "M_S" + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": " is the reconstructed shape. The coefficients of linear shape are " + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\beta_i \\in B" + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "inline_equation", + "content": "|B|" + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": " is the number of shape parameters and is set to 100 in our implementation. " + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "inline_equation", + "content": "s_i \\in \\mathbb{R}^{3 \\times N}" + }, + { + "bbox": [ + 46, + 521, + 289, + 641 + ], + "type": "text", + "content": " denotes the orthogonal principal components of vertex displacements that capture shape variations in different character identities. The shape model of RaBit is learned from 1,050 characters of 3DBiCar using PCA [35]. RaBit's eyeballs can be computed based on the predefined landmarks shown in Fig. 4. Please refer to the Supplementary for more details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 647, + 139, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 139, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 139, + 659 + ], + "type": "text", + "content": "4.2. Pose Modeling" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "type": "text", + "content": "RaBit employs a standard vertex-based linear blend skinning technique, which uses the predefined skeleton and skinning weight matrix provided by 3DBiCar. The pose parameter " + }, + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "type": "text", + "content": " defines a set of angles as " + }, + { + "bbox": [ + 46, + 665, + 290, + 715 + ], + "type": "inline_equation", + "content": "\\Theta = [\\theta_{1},\\theta_{2},\\dots,\\theta_{K}]\\in \\mathbb{R}^{69}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "\\theta_{k} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " denotes the axis-angle representation of the relative rotation of joint " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " with respect to its parent and " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "K = 23" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " represents the number of joints. " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " can be converted to the rotation matrix format " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "R(\\theta_k)" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " using Rodrigues' formula [35]. The following equations demonstrate how the pose function " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "F_{P}" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " changes vertex " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "v_{i} \\in M_{S}" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": " to its corresponding position " + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "inline_equation", + "content": "v_{i}' \\in M_{P}" + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 370, + 163, + 547, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 163, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 370, + 163, + 547, + 196 + ], + "type": "interline_equation", + "content": "v _ {i} ^ {\\prime} = \\sum_ {k = 1} ^ {K} w _ {k, i} G _ {k} ^ {\\prime} (\\Theta , J) v _ {i}, \\tag {3}", + "image_path": "c5601b911db8407e49a42540584dbbb883253164b76ca9704875829015599402.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 350, + 205, + 547, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 205, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 350, + 205, + 547, + 220 + ], + "type": "interline_equation", + "content": "G _ {k} ^ {\\prime} (\\Theta , J) = G _ {k} (\\Theta , J) G _ {k} (\\Theta^ {\\prime}, J) ^ {- 1}, \\qquad (4)", + "image_path": "54ceb6c57270f05352ebd198d3645b6f28409079669903649fb4c0b508d81f10.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 231, + 546, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 231, + 546, + 262 + ], + "spans": [ + { + "bbox": [ + 349, + 231, + 546, + 262 + ], + "type": "interline_equation", + "content": "G _ {k} (\\Theta , J) = \\prod_ {j \\in A (k)} \\left[ \\begin{array}{c c} R \\left(\\theta_ {j}\\right) & J _ {j} \\\\ 0 & 1 \\end{array} \\right], \\tag {5}", + "image_path": "d1b77b116c86ec2ca05e376af76f51f2a4d9a6372b54a91e50e34e94cc20237a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "w_{k,i}" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": "-th element of the linear blend matrix " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": "-th vertex. " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "G_{k}(\\Theta, J)" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " is the global transformation of joint " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "G_{k}'(\\Theta, J)" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " is the global transformation of joint " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " after removing the transformation of rest pose " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "\\Theta'" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "A(k)" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " denotes a set including all the ancestors of joint " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "J_{j}" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " represents the location of the " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": "-th joint, which is located at the bounding box center of a specific body landmark. Thus given the T-posed mesh " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "M_{S}" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " and specific pose " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": ", we can generate the corresponding posed mesh " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "M_{P}" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "inline_equation", + "content": "F_{P}" + }, + { + "bbox": [ + 304, + 266, + 547, + 374 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 383, + 380, + 546, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 380, + 546, + 394 + ], + "spans": [ + { + "bbox": [ + 383, + 380, + 546, + 394 + ], + "type": "interline_equation", + "content": "M _ {P} = F _ {P} \\left(M _ {S}, \\Theta\\right). \\tag {6}", + "image_path": "7445ca687e44970dd29d2813233b5f9b08c3933fa497b22f53998b38713769b8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 400, + 411, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 411, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 411, + 414 + ], + "type": "text", + "content": "4.3. Texture Modeling" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 418, + 547, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 560 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 560 + ], + "type": "text", + "content": "Although traditional linear PCA is capable of building a decent statistical shape model, it fails to represent high-frequency details in textures and can produce blurry results due to its weak Gaussian assumption. Recently, GAN-based architectures [19, 21, 22, 27, 28, 49] have shown the notable capability of generating high-fidelity images. Thus, we resort to StyleGAN2-based techniques for UV texture maps generation, but with a coherent UV unfolding (as shown in Fig. 5) to facilitate the learning of texture compared with [22]. Specifically, the neural texture generator in RaBit translates a latent code to a texture map, which could be formulated as follows," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 370, + 560, + 546, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 560, + 546, + 575 + ], + "spans": [ + { + "bbox": [ + 370, + 560, + 546, + 575 + ], + "type": "interline_equation", + "content": "G (T): \\mathbb {R} ^ {Z} \\rightarrow \\mathbb {R} ^ {H \\times W \\times C}, \\tag {7}", + "image_path": "293e788176da8259e9cf6bcc6e142a2c38f16e3c05912394f3cef110693e1283.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "inline_equation", + "content": "G(T)" + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": " takes a Z-dimensional parameter vector as input and synthesizes a " + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "inline_equation", + "content": "H \\times W \\times C" + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": " texture map. Thus given a posed mesh " + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "inline_equation", + "content": "M_P" + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": " and a specific texture code " + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": ", we can generate a textured mesh " + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 578, + 546, + 628 + ], + "type": "text", + "content": " with the following equation," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 349, + 633, + 546, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 633, + 546, + 647 + ], + "spans": [ + { + "bbox": [ + 349, + 633, + 546, + 647 + ], + "type": "interline_equation", + "content": "M = F _ {T} \\left(M _ {P}, T\\right) = H \\left(M _ {P}, G (T)\\right), \\tag {8}", + "image_path": "bc9284e974ca0a496b35b27a087b8308fa4d3d5ff7c848d84ba74132df863002.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": " means the process of applying the texture map to the mesh model. In our implementation, the generator follows the architecture of StyleGAN2 [28], while taking a 512-dimensional parameter vector as input and generating a " + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "inline_equation", + "content": "1024 \\times 1024 \\times 3" + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": " texture map." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12829" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 203, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 203, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 203, + 84 + ], + "type": "text", + "content": "5. Single-View Reconstruction" + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 102, + 282, + 297 + ], + "blocks": [ + { + "bbox": [ + 53, + 102, + 282, + 297 + ], + "lines": [ + { + "bbox": [ + 53, + 102, + 282, + 297 + ], + "spans": [ + { + "bbox": [ + 53, + 102, + 282, + 297 + ], + "type": "image", + "image_path": "1a5b474f2ebf92843e6bf4c5df25696b4fd25e079f10a1edcfe5d62b40d1d4c3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 305, + 288, + 371 + ], + "lines": [ + { + "bbox": [ + 46, + 305, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 288, + 371 + ], + "type": "text", + "content": "Figure 5. BiCarNet. Given a masked image, we first map it to the parametric vectors. The vectors are then fed to our RaBit to generate a posed body mesh, two eyeballs, and a global UV texture. A part-sensitive reasoner is utilized to perceive local regions and generate the detailed UV texture map. Finally, a vivid 3D cartoon character is obtained with our BiCarNet." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 385, + 288, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 288, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 288, + 480 + ], + "type": "text", + "content": "Single-view reconstruction (SVR) is one of the most popular tasks of efficient 3D content generation, and recent work has made noticeable progress on human reconstruction based on parametric model of human characters (e.g., SMPL). To verify the practicality of our proposed 3DBiCar and RaBit, we conduct SVR for bipled cartoon characters. A baseline learning-based method is presented, which is termed as BiCarNet." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 109, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 109, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 109, + 502 + ], + "type": "text", + "content": "5.1. BiCarNet" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "type": "text", + "content": "Given a single masked image of cartoon characters, our BiCarNet aims to reconstruct the corresponding 3D shape, pose, and texture. The key problem is to build an encoder to map the input image to the parametric space of Rabbit. As shown in the upper part of Fig. 5, we adopt the learning block in HMR [26] as our Encoder. Once these parametric vectors are learned, we can feed them to our RaBit model to generate a posed body mesh, two eyeballs, and a UV texture (we name it global for convenience to introduce the following method description)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "During our preliminary experiments, we find that the shape reconstruction of characters, i.e. the eyes and body, is satisfactory, while the inferred UV tends to lose detailed appearances of some small yet significant areas, such as the nose and ears. We thus adopt a part-sensitive texture reasoner (PSR) to address the above issue, as the lower part of Fig. 5 shows. Specifically, we design five individual UV-mappings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": "for these significant parts of the nose, ears, horns, eyes, and mouth. Five lightweight encoder-decoder branches are next introduced to learn the appearances of these local regions from the input image, respectively. The learned part UVs could be remapped to the corresponding area on the global UV map to produce a blended texture. However, a direct blending tends to cause seam artifacts. Thus we further adopt a Fuser to address the artifacts as Fig. 5 illustrates. Please refer to the Supplementary for thorough implementations of BiCarNet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 200, + 388, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 388, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 388, + 213 + ], + "type": "text", + "content": "5.2. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 218, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 547, + 361 + ], + "type": "text", + "content": "Data preparation. We first split 3DBiCar into a training set (1,050 image-model pairs) and a testing set (450 pairs). To support a stable training of BiCarNet, we next generate a large number of synthetic paired data with the help of RaBit, which are highly diversified in shape, posture, and texture. To be specific, a lot of 3D textured models are first sampled from the RaBit space, which are then rendered into images from different camera views. This finally produces 13,650 pairs for training. Note that, BiCarNet takes an image with foreground masked as input. All synthetic images naturally have no background. For real images, all the foreground masks are manually annotated." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 362, + 547, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 547, + 434 + ], + "type": "text", + "content": "Result gallery. Fig. 6 shows representative results generated by BiCarNet. As illustrated, our BiCarNet can generate vivid 3D cartoon characters loyal to individual cartoon images in shape, pose, and texture. We believe that our work opens the door to producing 3D biped cartoon characters from easy-to-obtain inputs." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 444, + 541, + 575 + ], + "blocks": [ + { + "bbox": [ + 310, + 444, + 541, + 575 + ], + "lines": [ + { + "bbox": [ + 310, + 444, + 541, + 575 + ], + "spans": [ + { + "bbox": [ + 310, + 444, + 541, + 575 + ], + "type": "image", + "image_path": "c7709e7bf28a9c0d328d3c8dca64f0e7891490f57cbdc6f59ad8861954b31d1b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 582, + 545, + 616 + ], + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 616 + ], + "type": "text", + "content": "Figure 6. Result gallery of BiCarNet. Our BiCarNet is capable of generating vivid 3D cartoon characters with only single-view image input." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": "Results on Shape Reconstruction. As mentioned above, BiCarNet utilizes HMR-like blocks and RaBit for shape and pose learning. Currently, other reconstruction methods could also be used for topology-consistent geometry inference, such as GCNN-based methods [34] and UV-based methods [55]. We choose two representative methods for comparison, i.e., Mesh-Graphormer [33, 34] and DecoMR [55]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12830" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": "Mesh-Graphormer combines graph convolutions and self-attention in a transformer for 3D human reconstruction from a single image. DecoMR reconstructs 3D human mesh from single images by regressing a UV-based location map. Tab. 1 shows the quantitative comparisons of the above three methods on MPVE, MPJPE, and PA-MPJPE. We also provide qualitative comparisons in Fig. 7. Both quantitative and qualitative results demonstrate that the HMR-like method achieves the highest performance on geometry inference and provides more accurate reconstructions closer to ground truths. As noted, both Mesh-Graphormer and DecoMR outperform HMR for SMPL-based human reconstruction. It is interestingly found that they perform worse in our settings. One possible reason is that our biped cartoon meshes own an extremely larger amount of vertices than SMPL to model more complex geometry. This greatly increases the challenge of vertices regression in Mesh-Graphormer and DecoMR. Thus, in our setting, directly regressing the low-dimension parameters performs better." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 309, + 286, + 373 + ], + "blocks": [ + { + "bbox": [ + 50, + 309, + 286, + 373 + ], + "lines": [ + { + "bbox": [ + 50, + 309, + 286, + 373 + ], + "spans": [ + { + "bbox": [ + 50, + 309, + 286, + 373 + ], + "type": "table", + "html": "
MethodMPVE ↓MPJPE ↓PA-MPJPE ↓
DecoMR [55]85.7481.2347.23
Mesh-Graphormer [34]63.3147.1534.12
Ours (HMR [26] + RaBit)51.4637.8025.97
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Qualitative comparisons on texture inference. The input image (a) is followed by the textured models from (b) PCA, (c) BiCarNet w/o PSR, (d) BiCarNet and (e) the ground truth. Note that we use the same shape and focus on the difference of textures." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 239, + 538, + 276, + 590 + ], + "blocks": [ + { + "bbox": [ + 239, + 538, + 276, + 590 + ], + "lines": [ + { + "bbox": [ + 239, + 538, + 276, + 590 + ], + "spans": [ + { + "bbox": [ + 239, + 538, + 276, + 590 + ], + "type": "image", + "image_path": "e3f1052541792184b74ba3b915263952a2a034ea238feacb2122a2bfdcb760f4.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 254, + 593, + 266, + 602 + ], + "lines": [ + { + "bbox": [ + 254, + 593, + 266, + 602 + ], + "spans": [ + { + "bbox": [ + 254, + 593, + 266, + 602 + ], + "type": "text", + "content": "(e)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 611, + 287, + 656 + ], + "lines": [ + { + "bbox": [ + 46, + 611, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 611, + 287, + 656 + ], + "type": "text", + "content": "Figure 7. Qualitative results of shape reconstruction. From left to right, each row contains (a) the input image, reconstructed meshes of (b) Mesh Graphormer, (c) DecoMR, (d) our method, and (e) the GT mesh." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": "Results on Texture Inference. To demonstrate the capability of our proposed GAN-based texture generator, we first compare our RaBit-based texture inference (i.e., BiCarNet) with PCA-based inference. Specifically, for PCA-based" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": "method, we utilize the same learning architecture to map the input image into the PCA-based texture space. Furthermore, to evaluate the effectiveness of the proposed texture inference modules, we also conduct ablative analysis on BiCarNet without Fuser and BiCarNet without Part-sensitive Reasoner (PSR). Table 2 shows the quantitative results of different texture inference methods on MSE, PSNR and FID and our proposed method achieves the highest scores compared with all other methods. Moreover, Fig. 8 illustrates the qualitative results of these methods for texture inference. Fig. 9 shows the results without and with Fuser, which demonstrates our fusion module can deal with unnatural seam-like artifacts. We can observe that the part-sensitive texture reasoner and the Fuser help to capture the local regions of characters and recover their detailed appearances." + } + ] + } + ], + "index": 25 + }, + { + "type": "table", + "bbox": [ + 315, + 262, + 538, + 338 + ], + "blocks": [ + { + "bbox": [ + 46, + 381, + 288, + 415 + ], + "lines": [ + { + "bbox": [ + 46, + 381, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 288, + 415 + ], + "type": "text", + "content": "Table 1. Quantitative results of shape reconstruction. Our method achieves the best results in terms of MPVE, MPJPE and PA-MPJPE. Note that all metrics are measured in a unit " + }, + { + "bbox": [ + 46, + 381, + 288, + 415 + ], + "type": "inline_equation", + "content": "10^{-3}\\mathrm{m}" + }, + { + "bbox": [ + 46, + 381, + 288, + 415 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 262, + 538, + 338 + ], + "lines": [ + { + "bbox": [ + 315, + 262, + 538, + 338 + ], + "spans": [ + { + "bbox": [ + 315, + 262, + 538, + 338 + ], + "type": "table", + "html": "
MethodMSE(×10-1)↓PSNR(×102) ↑FID ↓
PCA0.23090.22540.4642
BiCarNet0.10930.24580.1133
BiCarNet w/o Fuser0.11080.23970.1407
BiCarNet w/o PSR0.13460.23610.4024
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Our BiCarNet outperforms others methods in all metrics." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 315, + 409, + 361, + 548 + ], + "blocks": [ + { + "bbox": [ + 315, + 409, + 361, + 548 + ], + "lines": [ + { + "bbox": [ + 315, + 409, + 361, + 548 + ], + "spans": [ + { + "bbox": [ + 315, + 409, + 361, + 548 + ], + "type": "image", + "image_path": "2d8e1e8825a5bc0bc1d42c748ceb33b5ad6d98b5c514c1f0a689f9d74780bafa.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 551, + 343, + 560 + ], + "lines": [ + { + "bbox": [ + 332, + 551, + 343, + 560 + ], + "spans": [ + { + "bbox": [ + 332, + 551, + 343, + 560 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 362, + 410, + 404, + 548 + ], + "blocks": [ + { + "bbox": [ + 362, + 410, + 404, + 548 + ], + "lines": [ + { + "bbox": [ + 362, + 410, + 404, + 548 + ], + "spans": [ + { + "bbox": [ + 362, + 410, + 404, + 548 + ], + "type": "image", + "image_path": "052ca78664419d639f5bb84c0bd8c997c457b74d8d67bcf2a2b6d58ec3ebff97.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 376, + 551, + 389, + 560 + ], + "lines": [ + { + "bbox": [ + 376, + 551, + 389, + 560 + ], + "spans": [ + { + "bbox": [ + 376, + 551, + 389, + 560 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 405, + 410, + 447, + 548 + ], + "blocks": [ + { + "bbox": [ + 405, + 410, + 447, + 548 + ], + "lines": [ + { + "bbox": [ + 405, + 410, + 447, + 548 + ], + "spans": [ + { + "bbox": [ + 405, + 410, + 447, + 548 + ], + "type": "image", + "image_path": "d4432f4ab0d1177de93dd1ccef11dcd48b330cabd8a4c82b70e6384c9e7f6987.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 551, + 433, + 560 + ], + "lines": [ + { + "bbox": [ + 422, + 551, + 433, + 560 + ], + "spans": [ + { + "bbox": [ + 422, + 551, + 433, + 560 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 452, + 410, + 494, + 548 + ], + "blocks": [ + { + "bbox": [ + 452, + 410, + 494, + 548 + ], + "lines": [ + { + "bbox": [ + 452, + 410, + 494, + 548 + ], + "spans": [ + { + "bbox": [ + 452, + 410, + 494, + 548 + ], + "type": "image", + "image_path": "bed1bed8810eb75b6f64a6158e546b4fc34d1ad2a9025f83a9b8a3859dd23e02.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 551, + 480, + 560 + ], + "lines": [ + { + "bbox": [ + 468, + 551, + 480, + 560 + ], + "spans": [ + { + "bbox": [ + 468, + 551, + 480, + 560 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 495, + 410, + 541, + 549 + ], + "blocks": [ + { + "bbox": [ + 495, + 410, + 541, + 549 + ], + "lines": [ + { + "bbox": [ + 495, + 410, + 541, + 549 + ], + "spans": [ + { + "bbox": [ + 495, + 410, + 541, + 549 + ], + "type": "image", + "image_path": "891ed9d6878e2c81efcf84a57d65fd39bc81f3055a299a53b8e34bca4cd6eac7.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 513, + 551, + 525, + 560 + ], + "lines": [ + { + "bbox": [ + 513, + 551, + 525, + 560 + ], + "spans": [ + { + "bbox": [ + 513, + 551, + 525, + 560 + ], + "type": "text", + "content": "(e)" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 639, + 416, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 416, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 416, + 653 + ], + "type": "text", + "content": "6. More Applications" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 658, + 439, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 439, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 439, + 672 + ], + "type": "text", + "content": "6.1. Sketch-based Modeling" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Customizing 3D biped cartoon characters usually requires a heavy workload with commercial tools, even for experienced artists. Sketch-based modeling enables amateur users" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12831" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 281, + 156 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 281, + 156 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 281, + 156 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 281, + 156 + ], + "type": "image", + "image_path": "3879b5c7063dfadc9b68417b4b38052e3c3fa9e2158a1bc8646cf34b0af01b1e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 167, + 288, + 190 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 288, + 190 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 288, + 190 + ], + "type": "text", + "content": "Figure 9. Qualitative ablation on Fuser in Texture inference. Left: BiCarNet w/o Fuser. Right: BiCarNet with Fuser." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 211, + 288, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 288, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 288, + 247 + ], + "type": "text", + "content": "to get involved in 3D shape customization in a simple and intuitive fashion. We build a sketch-based modeling application with the help of 3DBiCar and RaBit." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 289, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 510 + ], + "type": "text", + "content": "We first sample a series of shape vectors randomly and feed them to RaBit to generate 3D cartoon characters with diversified shapes, resulting in 12,000 T-pose models. Then we apply suggestive contour [24] to render the front-view sketches with different abstraction levels and obtain 108,000 sketch-model pairs. Given a sketch as input, we employ ResNet-50 and three MLPs as the encoder and decoder to map the input sketch to 100-dimensional shape parameters. The generated shape parameters are next fed to RaBit to reconstruct the corresponding 3D model. Please refer to the Supplemental materials for more details. Note that users only need to depict a 3D character with T-pose on a 2D canvas while the output characters of our method are animation-ready and can be directly applied to other commercial tools. Fig. 10 displays the sketches created by users with little knowledge of modeling as well as the corresponding models generated by our system. It can be seen that our sketch-based modeling system offers a smart approach for amateur users to create 3D biped cartoon characters with diversified shapes. We will further explore the support of shape reconstruction from sketches with arbitrary poses, and texture painting in the future." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 519, + 282, + 608 + ], + "blocks": [ + { + "bbox": [ + 50, + 519, + 282, + 608 + ], + "lines": [ + { + "bbox": [ + 50, + 519, + 282, + 608 + ], + "spans": [ + { + "bbox": [ + 50, + 519, + 282, + 608 + ], + "type": "image", + "image_path": "703250f15da0f568e27f0cde40a2619d3f7411f8b49794c7f5480e6dd08a5d17.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 616, + 287, + 649 + ], + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 649 + ], + "type": "text", + "content": "Figure 10. Result gallery of sketch-based modelling. The sketches created by amateur users denotes on the left and the generated models on the right." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 187, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 187, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 187, + 671 + ], + "type": "text", + "content": "6.2.3D Character Animation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Following the recent advance of human recovering method and parametric model [35, 39, 50], we extract the human from input video frames and adopt a temporal-aware" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 548, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 548, + 145 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 548, + 145 + ], + "type": "text", + "content": "encoder to recover the sequence of human poses [50]. Then, a motion retargeting method [25] is used to convert the poses on the human skeleton to the motion of our cartoon characters. As shown in Fig. 11, animation-ready characters generated by our RaBit can be directly applied to 3D animation. Please refer to the supplementary for animation video." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 152, + 345, + 293 + ], + "blocks": [ + { + "bbox": [ + 317, + 152, + 345, + 293 + ], + "lines": [ + { + "bbox": [ + 317, + 152, + 345, + 293 + ], + "spans": [ + { + "bbox": [ + 317, + 152, + 345, + 293 + ], + "type": "image", + "image_path": "8364d3aab17aab34f315f27f08fc340fff185b35b96b0d8cfc85c04cc726ab4e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 293, + 338, + 302 + ], + "lines": [ + { + "bbox": [ + 325, + 293, + 338, + 302 + ], + "spans": [ + { + "bbox": [ + 325, + 293, + 338, + 302 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 347, + 154, + 399, + 291 + ], + "blocks": [ + { + "bbox": [ + 347, + 154, + 399, + 291 + ], + "lines": [ + { + "bbox": [ + 347, + 154, + 399, + 291 + ], + "spans": [ + { + "bbox": [ + 347, + 154, + 399, + 291 + ], + "type": "image", + "image_path": "582f04a20b6412aafddf321bd03c246f87d10fedefde744c43b38ff9c1aef993.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 293, + 383, + 302 + ], + "lines": [ + { + "bbox": [ + 371, + 293, + 383, + 302 + ], + "spans": [ + { + "bbox": [ + 371, + 293, + 383, + 302 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 406, + 155, + 467, + 290 + ], + "blocks": [ + { + "bbox": [ + 406, + 155, + 467, + 290 + ], + "lines": [ + { + "bbox": [ + 406, + 155, + 467, + 290 + ], + "spans": [ + { + "bbox": [ + 406, + 155, + 467, + 290 + ], + "type": "image", + "image_path": "96b33770258c949485812b55b50d88c15a37326dcb333a6ed34d30e55b012901.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 434, + 292, + 446, + 302 + ], + "lines": [ + { + "bbox": [ + 434, + 292, + 446, + 302 + ], + "spans": [ + { + "bbox": [ + 434, + 292, + 446, + 302 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 311, + 547, + 346 + ], + "lines": [ + { + "bbox": [ + 304, + 311, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 547, + 346 + ], + "type": "text", + "content": "Figure 11. Transferring motion of a human video to animate characters. (a) denotes the input frames. (b), (c), and (d) indicate three corresponding posed cartoon characters." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 474, + 155, + 536, + 290 + ], + "blocks": [ + { + "bbox": [ + 474, + 155, + 536, + 290 + ], + "lines": [ + { + "bbox": [ + 474, + 155, + 536, + 290 + ], + "spans": [ + { + "bbox": [ + 474, + 155, + 536, + 290 + ], + "type": "image", + "image_path": "04f0740bc80e80c4d28d670767861f3723922c7039efa4dfa09e4bee2ba3bc14.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 506, + 292, + 517, + 302 + ], + "lines": [ + { + "bbox": [ + 506, + 292, + 517, + 302 + ], + "spans": [ + { + "bbox": [ + 506, + 292, + 517, + 302 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 358, + 379, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 379, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 379, + 371 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 378, + 548, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 548, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 548, + 557 + ], + "type": "text", + "content": "In this work, we introduce 3DBiCar, the first large-scale 3D biped cartoon character dataset. It contains 1,500 textured and skinned models with a consistent mesh topology. Based on 3DBiCar, we propose the first 3D full-body cartoon parametric model RaBit for biped character modeling. Furthermore, we build a baseline method BiCarNet for reconstructing 3D textured models from a single image with cartoon characters. Experimental results demonstrate the capability of 3DBiCar and RaBit as well as the effectiveness of BiCarNet. Last but not least, two further applications, i.e., sketch-based modeling and 3D character animation, demonstrate the usability and practicality of our dataset and parametric model. We hope that our work will contribute to the development of 3D biped cartoon character modeling and inspire future works in this area." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 558, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 548, + 713 + ], + "type": "text", + "content": "Acknowledgements. The work was supported in part by NSFC with Grant No. 62293482, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by Shenzhen General Project with No. JCYJ20220530143604010, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12832" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Victoria Fernández Abrevaya, Stefanie Wuhrer, and Edmond Boyer. 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Advances in Neural Information Processing Systems, 33:9251-9262, 2020. 3" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12835" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_content_list.json b/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..60b72bcb889c91321440fe4ab5ea74e3416b948d --- /dev/null +++ b/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_content_list.json @@ -0,0 +1,1614 @@ +[ + { + "type": "text", + "text": "Randomized Adversarial Training via Taylor Expansion", + "text_level": 1, + "bbox": [ + 200, + 130, + 769, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gaojie Jin $^{1,2}$ , Xinping Yi $^{2\\boxtimes}$ , Dengyu Wu $^{2}$ , Ronghui Mu $^{3}$ , Xiaowei Huang $^{2\\boxtimes}$", + "bbox": [ + 184, + 191, + 782, + 213 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China", + "bbox": [ + 138, + 222, + 831, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ University of Liverpool, Liverpool, UK", + "bbox": [ + 325, + 241, + 645, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Lancaster University, Lancaster, UK", + "bbox": [ + 336, + 258, + 632, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{g.jin3, xinping.yi, xiaowei.huang} $@$ liverpool.ac.uk", + "bbox": [ + 277, + 276, + 692, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Corresponding Author", + "bbox": [ + 385, + 294, + 584, + 311 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 357, + 313, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, there has been an explosion of research into developing more robust deep neural networks against adversarial examples. Adversarial training appears as one of the most successful methods. To deal with both the robustness against adversarial examples and the accuracy over clean examples, many works develop enhanced adversarial training methods to achieve various trade-offs between them [19,38,80]. Leveraging over the studies [8,32] that smoothed update on weights during training may help find flat minima and improve generalization, we suggest reconciling the robustness-accuracy trade-off from another perspective, i.e., by adding random noise into deterministic weights. The randomized weights enable our design of a novel adversarial training method via Taylor expansion of a small Gaussian noise, and we show that the new adversarial training method can flatten loss landscape and find flat minima. With PGD, CW, and Auto Attacks, an extensive set of experiments demonstrate that our method enhances the state-of-the-art adversarial training methods, boosting both robustness and clean accuracy. The code is available at https://github.com/Alexkael/RandomizedAdversarial-Training.", + "bbox": [ + 75, + 391, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Trade-off between adversarial robustness and clean accuracy has recently been intensively studied [63, 68, 80] and demonstrated to exist [34, 58, 70, 77]. Many different techniques have been developed to alleviate the loss of clean accuracy when improving robustness, including data augmentation [1, 5, 29], early-stopping [60, 81], instance reweighting [3, 82], and various adversarial training methods [11, 36, 42, 74, 80]. Adversarial training is believed to be the most effective defense method against adversarial at", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tacks, and is usually formulated as a minimax optimization problem where the network weights are assumed deterministic in each alternating iteration. Given the fact that both clean and adversarial examples are drawn from unknown distributions which interact with one another through the network weights, it is reasonable to relax the assumption that neural networks are simply deterministic models where weights are scalar values. This paper is based on a view, illustrated in Fig. 1, that randomized models enable the training optimization to consider multiple directions within a small area and may achieve smoothed weights update – in a way different from checkpoint averaging [8, 32] – and obtain robust models against new clean/adversarial examples.", + "bbox": [ + 496, + 358, + 893, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building upon the above view, we find a way, drastically different from most existing studies in adversarial training, to balance robustness and clean accuracy, that is, embedding neural network weights with random noise. Whilst the randomized weights framework is not new in statistical learning theory, where it has been used in many previous works for e.g., generalization analysis [18, 52, 75], we hope to advance the empirical understanding of the robustness-accuracy trade-off problem in adversarial training by leveraging the rich tool sets in statistical learning. Remarkably, it turns out adversarial training with the optimization over randomized weights can improve the state-of-the-art adversarial training methods over both the adversarial robustness and clean accuracy.", + "bbox": [ + 496, + 561, + 895, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By modeling weights as randomized variables with an artificially injected weight perturbation, we start with an empirical analysis of flatness of loss landscape in Sec. 3. We show that our method can flatten loss landscape and find flatter minima in adversarial training, which is generally regarded as an indicator of good generalization ability. After the flatness analysis, we show how to optimize with randomized weights during adversarial training in Sec. 4. A", + "bbox": [ + 496, + 779, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16447", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ea5ab0f5cb6db2441f9378efa1b585c85f54698caadae2a309d911dade437244.jpg", + "image_caption": [ + "(a) Adversarial Training of TRADES" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 411, + 228 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7839665f5571fd764e6626cb5b965e80dfba536e074c00d423c7276f3704a34e.jpg", + "image_caption": [ + "(b) Our Method", + "Figure 1. A conceptual illustration of decision boundaries learned via (a) adversarial training of TRADES and (b) our method. (a) shows that TRADES considers a deterministic model and optimizes the distance of adversarial data and boundary only through one direction. Our method in (b) takes into account randomized weights (perturbed boundaries) and optimizes the distance of adversarial data and boundary via multi directions in a small area. The boundary learned by our method can be smoother and more robust against new data." + ], + "image_footnote": [], + "bbox": [ + 413, + 88, + 890, + 229 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "novel adversarial training method based on TRADES [80] is proposed to reconcile adversarial robustness with clean accuracy by closing the gap between clean latent space and adversarial latent space over randomized weights. Specifically, we utilize Taylor series to expand the objective function over weights, in such a way that we can deconstruct the function into Taylor series (e.g., zeroth term, first term, second term, etc). From an algorithmic viewpoint, these Taylor terms can thus replace the objective function effectively and time-efficiently. As Fig. 1 shows, since our method takes randomized models into consideration during training, the learned boundary is smoother and the learned model is more robust in a small perturbed area.", + "bbox": [ + 75, + 310, + 468, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We validate the effectiveness of our optimization method with the first and the second derivative terms of Taylor series. In consideration of training complexity and efficiency, we omit the third and higher derivative terms. Through an extensive set of experiments on a wide range of datasets (CIFAR-10 [40], CIFAR-100, SVHN [51]) and model architectures (ResNet [27], WideResNet [78], VGG [65], MobileNetV2 [62]), we find that our method can further enhance the state-of-the-art adversarial training methods on both adversarial robustness and clean accuracy, consistently across the datasets and the model architectures. Overall, this paper makes the following contributions:", + "bbox": [ + 75, + 506, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We conduct a pilot study of the trade-off between adversarial robustness and clean accuracy with randomized weights, and offer a new insight on the smoothed weights update and the flat minima during adversarial training (Sec. 3).", + "- We propose a novel adversarial training method under a randomized model to smooth the weights. The key enabler is the Taylor series expansion (in Sec. 4) of the robustness loss function over randomized weights (deterministic weights with random noise), so that the optimization can be simultaneously done over the zeroth, first, and second orders of Taylor series. In doing so, the proposed method can effectively enhance adversarial robustness without a significant compromise" + ], + "bbox": [ + 94, + 688, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "on clean accuracy.", + "bbox": [ + 531, + 311, + 656, + 325 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- An extensive set of empirical results are provided to demonstrate that our method can improve both robustness and clean accuracy consistently across different datasets and different network architectures (Sec. 5).", + "bbox": [ + 517, + 325, + 890, + 385 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 398, + 637, + 414 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Basic Notation. Consider the classification task with the training set $S = \\{\\mathbf{s}_1,\\dots ,\\mathbf{s}_m\\}$ where $m$ samples are drawn from the data distribution $\\mathcal{D}$ . For notational convenience, we omit the label $y$ of sample $\\mathbf{s}$ . The adversarial example $\\mathbf{s}'$ is generally not in the natural dataset $S$ , such that $\\| \\mathbf{s}' - \\mathbf{s}\\|_p \\leq \\epsilon$ where $\\| \\cdot \\|_p$ is by default the $\\ell_p$ -norm. Let $f_{\\mathbf{w}}(\\cdot)$ be a learning model parameterized by $\\mathbf{w}$ , where $\\mathbf{w}$ is the vectorization of weight matrix $\\mathbf{W}$ . $\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}), y)$ is the cross-entropy loss between $f_{\\mathbf{w}}(\\mathbf{s})$ and $y$ with normalization. Define $\\mathcal{L}(f_{\\mathbf{w}}(\\mathcal{S}), \\mathcal{Y}) \\coloneqq \\mathbb{E}_{\\mathbf{s} \\in \\mathcal{S}}[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}), y)]$ .", + "bbox": [ + 498, + 422, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vanilla Adversarial Training. Adversarial training can be formulated as a minimax optimization problem [45]", + "bbox": [ + 498, + 575, + 890, + 604 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w}} \\left\\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\max _ {\\mathbf {s} ^ {\\prime}: \\| \\mathbf {s} ^ {\\prime} - \\mathbf {s} \\| _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w}} \\left(\\mathbf {s} ^ {\\prime}\\right), y\\right) \\right] \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 606, + 890, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{s}'$ is an adversarial example causing the largest loss within an $\\epsilon$ -ball centered at a clean example $s$ with respect to a norm distance. Adversarial training aims to learn a model with the loss of adversarial examples minimized, without caring about the loss of the clean examples.", + "bbox": [ + 496, + 638, + 890, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "TRADES-like Adversarial Training. Advanced adversarial training methods, such as TRADES [80], strike a trade-off between clean accuracy and adversarial robustness, by optimizing the following problem", + "bbox": [ + 496, + 712, + 890, + 768 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w}} \\Big \\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), y) + \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), f _ {\\mathbf {w}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right] \\Big \\},\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 775, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where the first term contributes to clean accuracy, and the second term with hyperparameter $\\lambda$ can be seen as a regularization for adversarial robustness that balances the outputs of clean and adversarial examples.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Nevertheless, each adversarial example $\\mathbf{s}'$ is generated from a clean example $\\mathbf{s}$ based on a specific weight $\\mathbf{w}$ , and", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16448", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3db41d602e62f5c04d90811c33897fcd840ef059e40cc5f314795b4810c63014.jpg", + "image_caption": [ + "Figure 2. Comparison of loss landscapes of TRADES trained model (the first row) and $\\mathrm{TRADES} + 1_{st} + 2_{nd}$ (our method, the second row) trained model. Loss plots in each column are generated from the same original image randomly chosen from the CIFAR-10 test dataset. Following the settings in [20], the $z$ axis represents the loss, the $x$ and $y$ axes represent the magnitude of the perturbation added in the directions of $\\mathrm{sign}\\nabla_{\\mathbf{s}}f(\\mathbf{s})$ and Rademacher(0.5) respectively. We provide more empirical results in Appendix A." + ], + "image_footnote": [], + "bbox": [ + 155, + 88, + 803, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the weight $\\mathbf{w}$ is obtained by optimizing both clean and adversarial data with SGD. This is a chick-and-egg problem. A not-very-well-trained model $\\mathbf{w}$ may generate some misleading adversarial data samples, which in turn drive the training process away from the optimum.", + "bbox": [ + 75, + 380, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by the idea of model smoothing, we believe that the introduction of noise term into the training process may smooth the update of weights and thus robustify the models. To elaborate on this, we introduce our method from the perspective of flatness of loss landscape in Sec. 3. This is followed by a formalization in Sec. 4, where a noise term is injected to network weight $\\mathbf{w}$ during adversarial training to transform deterministic weights into randomized weights.", + "bbox": [ + 75, + 455, + 470, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Motivation", + "text_level": 1, + "bbox": [ + 76, + 590, + 194, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Flatness is commonly thought to be a metric of standard generalization: the loss surface at the final learnt weights for well-generalizing models is generally \"flat\" [18,21,35,52]. Moreover, [73] believed that a flatter adversarial loss landscape reduces the generalization gap in robustness. This aligns with [28], where the authors demonstrated that the local Lipschitz constant can be used to explicitly quantify the robustness of machine learning models. Many empirical defensive approaches, such as hessian/curvature-based regularization [48], gradient magnitude penalty [71], smoothening with random noise [44], or entropy regularization [33], have echoed the flatness performance of a robust model. However, all the above approaches require significant computational or memory resources, and many of them, such as hessian/curvature-based solutions, may suffer from standard accuracy decreases [26].", + "bbox": [ + 75, + 612, + 468, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stochastic weight averaging (SWA) [32] is known to find solutions that are far flatter than SGD, is incredibly simple to implement, enhances standard generalization, and", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "has almost no computational overhead. It was developed to guarantee weight smoothness by simply averaging various checkpoints throughout the training trajectory. SWA has been applied to semi-supervised learning, Bayesian inference, and low-precision training. Especially, [8] used SWA for the first time in adversarial training in order to smooth the weights and locate flatter minima, and showed that it enhances the adversarial generalization.", + "bbox": [ + 496, + 380, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from SWA, we propose a novel method (with details provided in Sec. 4) via Taylor expansion of a small Gaussian noise to smooth the update of weights. This method regards the TRADES [80], a state-of-the-art adversarial training method, as a special case with only zero-th term, and is able to locate flatter minima. To demonstrate the latter, we visualize the loss landscape with respect to both input and weight spaces. As shown in Fig. 2, compared to the TRADES, our method significantly flattens the rugged landscape. In addition, it is worth noting that our empirical results (in Sec. 5) demonstrate that our method can further improve not only clean accuracy but also adversarial accuracy compared with other SOTA (includes SWA from [8]).", + "bbox": [ + 496, + 501, + 892, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 500, + 723, + 635, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a deterministic model of weight $\\mathbf{w}$ , we consider an additive small Gaussian noise $\\mathbf{u}$ to smooth $\\mathbf{w}$ . Based on TRADES [80], we propose that the robust optimization problem can be further enhanced by", + "bbox": [ + 496, + 744, + 890, + 805 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), y\\right)\\right) \\right. \\tag {2} \\\\ \\left. + \\mathbb {E} _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathrm {K L} (f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}) | | f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 809, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the first term contributes to clean accuracy, and the second term with hyperparameter $\\lambda$ can be seen as a regu", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16449", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Adversarial training with randomized weights" + ], + "code_body": "Input: minibatch $\\{\\mathbf{s}_i\\}_{i = 1}^n$ , network architecture parametrized by w, learning rate $\\eta_{l}$ , step size $\\eta_{s}$ , hyper-parameters $\\eta$ , $\\lambda$ zero mean Gaussian u, number of iterations $K$ in inner optimization. \nOutput: Robust network $f_{\\mathbf{w}}$ \nRandomly initialize network $f_{\\mathrm{w}}$ , or initialize network with pre-trained configuration \nrepeat Generate adversarial examples: Sample u from u for $i = 1$ to n do $\\mathbf{s}_i^\\prime \\gets \\mathbf{s}_i + 0.001\\cdot \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ for $k = 1$ to $K$ do $\\mathbf{s}_i^\\prime \\leftarrow \\Pi (\\eta_s\\mathrm{sign}(\\nabla_{\\mathbf{s}_i^\\prime}\\mathcal{L}(f_{\\mathbf{w} + u}(\\mathbf{s}_i),f_{\\mathbf{w} + u}(\\mathbf{s}_i^\\prime))) + \\mathbf{s}_i^\\prime)$ , subject to $||\\mathbf{s}_i - \\mathbf{s}_i^\\prime ||_p\\leq \\epsilon$ , where II is the projection operator. end for end for Optimization: w $\\leftarrow$ w- $\\eta_l\\frac{1}{n}\\sum_{i = 1}^{n}\\nabla_{\\mathbf{w}}\\Big[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}_i),y_i)$ (zeroth term) $+L(g_{\\mathbf{s}_i}(\\mathbf{w}),g_{\\mathbf{s}_i'}(\\mathbf{w})) / \\lambda$ (first term) $+ \\eta \\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( g _ { \\textup { s } _ { i } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } , g _ { \\textup { s } _ { i } ^ { \\prime } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } ) \\big )$ (second term) $+ \\frac {\\eta}{2}\\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } , \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } ^ { \\prime \\prime } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } ) \\big ) ]$ where various optimization methods can be applied: zeroth term optimization (TRADES), zeroth + first terms opti- mization and zeroth + first + second terms optimization. until training converged", + "bbox": [ + 84, + 108, + 885, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "larization for adversarial robustness with weights $\\mathbf{w}$ and a small Gaussian noise $\\mathbf{u}$ .", + "bbox": [ + 75, + 469, + 468, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following [17, 35], we let the Gaussian $\\mathbf{u}$ be small enough to maintain the generalization performance on clean data. Then, we can extend Eq. (2) by replacing $\\mathrm{KL}(\\cdot ||\\cdot)$ with a multi-class calibrated loss $\\mathcal{L}(\\cdot ,\\cdot)$ [80]:", + "bbox": [ + 75, + 500, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} \\underset {\\mathbf {w}} {\\min } & \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right)\\right) \\right. \\\\ & \\left. + \\mathbb {E} _ {\\mathbf {s}} \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\end{array} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 566, + 468, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As the minimax optimization is entangled with expectation of randomized weights, it is challenging to solve such optimization problem directly. Instead, we propose to solve this problem in an alternating manner between the inner maximization and outer minimization.", + "bbox": [ + 75, + 630, + 468, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the inner maximization, with a given model weight $\\mathbf{w}$ , we solve it by adopting the commonly used gradient-based approach (e.g., PGD) to generate the adversarial perturbation. That is, at the $t$ -th iteration, the adversarial perturbation is produced iteratively by letting", + "bbox": [ + 75, + 705, + 468, + 781 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} _ {t + 1} ^ {\\prime} \\leftarrow \\Pi \\left(\\mathbf {s} _ {t} ^ {\\prime} + \\eta_ {s} \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {s} _ {t} ^ {\\prime}} \\mathcal {L} \\left(f _ {\\mathbf {w} + u} (\\mathbf {s}), f _ {\\mathbf {w} + u} \\left(\\mathbf {s} _ {t} ^ {\\prime}\\right)\\right)\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 786, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "until the maximum allowed iterations are reached, where $\\Pi$ is the projection operator, $\\eta_{s}$ is the step size and $u$ is a sample of $\\mathbf{u}$ . To reduce complexity, we only use one sample $u$ to generate adversarial example for each minibatch. Nevertheless, sufficient samples of $\\mathbf{u}$ can still be produced in one", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "epoch as there are many minibatches. As Fig. 1 shows, the adversarial example is generated by one model (boundary), then the optimization with randomized weights in multiple directions can be executed through the following minimization method.", + "bbox": [ + 496, + 469, + 890, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the outer minimization, when the optimal perturbed sample $\\mathbf{s}'$ is generated by the inner maximization, we solve the following problem", + "bbox": [ + 496, + 545, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {s}} \\left[ \\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right) + \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 595, + 890, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This optimization problem is challenging due to the entanglement between the deterministic weight $\\mathbf{w}$ and the random perturbation $\\mathbf{u}$ , which makes gradient updating much involved.", + "bbox": [ + 496, + 637, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To resolve this issue, we decompose the two components in such a way that gradient updating and model averaging can be done separately. Let $f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}) = g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u})$ , by Taylor expansion of $g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u})$ at $\\mathbf{w}$ , we have", + "bbox": [ + 496, + 696, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} g _ {\\mathbf {s}} (\\mathbf {w} + \\mathbf {u}) = g _ {\\mathbf {s}} (\\mathbf {w}) + g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u} + \\mathbf {u} ^ {T} \\frac {g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w})}{2 !} \\mathbf {u} \\tag {6} \\\\ + \\mathcal {O} _ {\\mathbf {s}} (| | \\mathbf {u} | | ^ {2}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 763, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g_{\\mathbf{s}}^{\\prime}(\\mathbf{w}) = \\frac{\\partial g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}}\\in \\mathbb{R}^{d\\times 1}$ and $g_{\\mathbf{s}}^{\\prime \\prime}(\\mathbf{w}) = \\frac{\\partial^{2}g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}\\partial\\mathbf{w}}\\in$ $\\mathbb{R}^{d\\times d}$ are the first and second derivative of the function $g_{\\mathrm{s}}(\\mathbf{w})$ versus the weight w, respectively, and $\\mathcal{O}_{\\mathbf{s}}(||\\mathbf{u}||^{2})$ tends to be zero with respect to $||\\mathbf{u}||^2$ . By such approximation, the gradient computation will be solely done on the", + "bbox": [ + 496, + 820, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16450", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "deterministic part $\\mathbf{w}$ , and model smoothing with averaged random variable $\\mathbf{u}$ is done independently.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The intuition behind is the following. For the randomized model $\\mathbf{w} + \\mathbf{u}$ with a specific input $\\mathbf{s}$ , the Taylor approximation explicitly takes into account the deterministic model $g_{\\mathbf{s}}(\\mathbf{w})$ , the projection of its gradient onto the random direction $g_{\\mathbf{s}}^{\\prime}(\\mathbf{w})^{T}\\mathbf{u}$ , and the projection of its curvature onto the subspace spanned by $\\mathbf{u}^{T}\\frac{g_{\\mathbf{s}}^{\\prime\\prime}(\\mathbf{w})}{2!}\\mathbf{u}$ , capturing higher-order information of the loss function with respect to $\\mathbf{u}$ .", + "bbox": [ + 75, + 121, + 467, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further simplify the computation, we minimize an upper bound of Eq. (5) instead. Due to the local convexity of loss landscape, by Jensen's inequality, we conclude that", + "bbox": [ + 75, + 229, + 468, + 275 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\sum_ {i} x _ {i}, \\sum_ {i} y _ {i}\\right) \\leq \\sum_ {i} \\mathcal {L} \\left(x _ {i}, y _ {i}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 282, + 468, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the second term in Eq. (5) can be upper bounded by", + "bbox": [ + 75, + 320, + 468, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})\\right) \\\\ \\leq \\mathcal {L} \\left(g _ {\\mathbf {s}} (\\mathbf {w}), g _ {\\mathbf {s} ^ {\\prime}} (\\mathbf {w})\\right) + \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}, g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}\\right)\\right) \\\\ + \\frac {1}{2} \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(\\mathbf {u} ^ {T} g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}, \\mathbf {u} ^ {T} g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}\\right)\\right), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 351, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the terms on the right-hand side are referred to as the zeroth, first, and second order Taylor expressions. Instead of minimizing Eq. (5) directly, we minimize the upper bound in Eq. (8), which is easier to compute in practical models. Details of the optimization are given in Appendix D.", + "bbox": [ + 75, + 431, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The pseudo-code of the proposed adversarial training method is presented in Algorithm 1. Note that the zeroth term optimization in Algorithm 1 is almost the same as TRADES [80], thus we use TRADES and AWP-TRADES [74] as (zeroth term optimization) baselines in our experiments in Sec. 5, and verify how much first and second terms optimization can improve. Note that we perform both AWP and our method through applying randomized weight perturbations on AWP updated weights.", + "bbox": [ + 75, + 523, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all of our experiments, we limit the noise variance of $\\mathbf{u}$ to be small enough [17, 35] to maintain the training, e.g., $\\sigma = 0.01$ . For the zeroth term hyper-parameter $1 / \\lambda$ in Algorithm 1, we set $1 / \\lambda = 6$ for all of our experiments, which is a widely-used setting for TRADES [53, 74, 80]. The number of inner optimization iterations $K$ is set to 10 as usual. To make our method more flexible, we set $\\eta$ and $\\frac{\\eta}{2}$ as the first term and second term hyper-parameters, respectively, and analyze the sensitivity of $\\eta$ in Sec. 5.1.", + "bbox": [ + 75, + 659, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The main novelty of our proposed method is two-fold: (1) Instead of considering a single model with a deterministic weight $\\mathbf{w}$ , we consider a model ensemble with $\\mathbf{w} + \\mathbf{u}$ to smooth the update of weights. By averaging these models during adversarial training, we come up with a robust model with smoothed classification boundary tolerant to potential adversarial weight perturbation. (2) When averaging", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "over the ensemble of randomized models during training, we disentangle gradient from random weight perturbation so that the gradient updating can be computed efficiently. In particular, we apply Taylor expansion at the mean weight $\\mathbf{w}$ (i.e., the deterministic component) and approximate the cross-entropy loss function with the zeroth, first, and second Taylor terms. In doing so, the deterministic and statistical components of $\\mathbf{w} + \\mathbf{u}$ can be decomposed and then computed independently.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Empirical results", + "text_level": 1, + "bbox": [ + 498, + 239, + 668, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first discuss the hyper-parameter sensitivity of our method, and then evaluate the robustness on benchmark datasets against various white-box, black-box attacks and Auto Attack with $\\ell_2$ and $\\ell_{\\infty}$ threat models.", + "bbox": [ + 496, + 266, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adversarial Training Setting. We train PreAct ResNet-18 [27] for $\\ell_{\\infty}$ and $\\ell_2$ threat models on CIFAR-10/100 [40] and SVHN [51]. In addition, we also train WideResNet-34-10 [78] for CIFAR-10/100, VGG16 and MobileNetV2 for CIFAR-10, with $\\ell_{\\infty}$ threat model. We adopt the widely used adversarial training setting [60]: for the $\\ell_{\\infty}$ threat model, $\\epsilon = 8 / 255$ and step size $2 / 255$ ; for the $\\ell_2$ threat model, $\\epsilon = 128 / 255$ and step size $15 / 255$ . For normal adversarial training, the training examples are generated with 10 steps. All models (except SVHN) are trained for 200 epochs using SGD with momentum 0.9, batchsize 128, weight decay $5\\times 10^{-4}$ , and an initial learning rate of 0.1 that is divided by 10 at the 100th and 150th epochs. Except for setting the starting learning rate to 0.01 for SVHN, we utilize the same other settings. Simple data augmentations are used, such as $32\\times 32$ random crop with 4-pixel padding and random horizontal flip. We report the highest robustness that ever achieved at different checkpoints for each dataset and report the clean accuracy on the model which gets the highest PGD-20 accuracy. We omit the standard deviations of 3 runs as they are very small ( $< 0.40\\%$ ) and implement all models on NVIDIA A100.", + "bbox": [ + 496, + 327, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Setting. We evaluate the robustness with white-box attacks, black-box attacks and auto attack. For white-box attacks, we adopt PGD-20 [45] and CW-20 [4] (the $\\ell_{\\infty}$ version of CW loss optimized by PGD-20) to evaluate trained models. For black-box attacks, we generate adversarial perturbations by attacking a surrogate normal adversarial training model (with same setting) [55], and then apply these adversarial examples to the defense model and evaluate the performances. The attacking methods for black-box attacks we have used are PGD-20 and CW-20. For Auto Attack (AA) [10], one of the strongest attack methods, we adopt it through a mixture of different parameter-free attacks which include three white-box attacks (APGD-CE [10], APGD-DLR [10], and FAB [9]) and one black-box attack (Square Attack [2]). We provide more details about the experimental setups in Appendix B.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16451", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0a2543801b8305233831ffdfd055c3b65b0f3392a19fc082854a60f954c8cac9.jpg", + "table_caption": [ + "Table 1. First and Second Derivative terms optimization on CIFAR-10 with $\\ell_{\\infty}$ threat model for PreAct ResNet18. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack with different hyper-parameters $\\eta = 0.05, 0.1, 0.2, 0.3, 0.4$ . We highlight the best results in bold." + ], + "table_footnote": [], + "table_body": "
MethodCleanPGD-20CW-20AAMethodCleanPGD-20CW-20AA
1st(0.05)83.1953.9852.1248.21st+2nd(0.05)83.2554.0751.9348.4
1st(0.1)82.8654.2952.2449.31st+2nd(0.1)83.4754.4252.2849.7
1st(0.2)83.5554.8652.6548.81st+2nd(0.2)84.1354.9152.5350.3
1st(0.3)83.9655.0552.5449.71st+2nd(0.3)84.2754.3651.8048.9
1st(0.4)83.9354.6552.2348.61st+2nd(0.4)84.1454.3851.5649.6
", + "bbox": [ + 125, + 132, + 841, + 231 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/03644a382a8861f49a3c68a9c251af92c2cb5deabbcf6f1300eea0d094fc6880.jpg", + "table_caption": [ + "Table 2. First and Second Derivative terms optimization on CIFAR-10/CIFAR-100 with $\\ell_{\\infty}$ threat model for WideResNet, compared with current state-of-the-art. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack ( $\\epsilon = 0.031$ ) and Auto Attack $(\\epsilon = 8/255)$ . The results of our methods are in **bold**. Note that * is under PGD-40 attack and ** is under PGD-10 attack." + ], + "table_footnote": [], + "table_body": "
DatasetMethodArchitectureCleanPGD-20CW-20AA
CIFAR-10 ℓ∞Lee et al. (2020) [42]WRN-34-1092.5659.7554.5339.70
Wang et al. (2020) [72]WRN-34-1083.5158.3154.3351.10
Rice et al. (2020) [60]WRN-34-2085.34--53.42
Zhang et al. (2020) [81]WRN-34-1084.52--53.51
Pang et al. (2021) [54]WRN-34-2086.4357.91**-54.39
Jin et al. (2022) [36]WRN-34-2086.0161.1257.9355.90
Gowal et al. (2020) [24]WRN-70-1685.2958.22*-57.20
Zhang et al. (2019) [80] (0th)WRN-34-1084.6556.6854.4953.0
+ Ours (1st)WRN-34-1085.5158.3456.0654.0
+ Ours (1st+2nd)WRN-34-1085.9858.4756.1354.2
Wu et al. (2020) [74] (0th)WRN-34-1085.1759.6457.3356.2
+ Ours (1st)WRN-34-1086.1061.4758.0957.1
+ Ours (1st+2nd)WRN-34-1086.1261.4558.2257.4
CIFAR-100 ℓ∞Cui et al. (2021) [11]WRN-34-1060.4335.5031.5029.34
Gowal et al. (2020) [24]WRN-70-1660.8631.47*-30.03
Zhang et al. (2019) [80] (0th)WRN-34-1060.2232.1128.9326.9
+ Ours (1st)WRN-34-1063.0133.2629.4428.1
+ Ours (1st+2nd)WRN-34-1062.9333.3629.6127.9
Wu et al. (2020) [74] (0th)WRN-34-1060.3834.0930.7828.6
+ Ours (1st)WRN-34-1063.9835.3631.6329.8
+ Ours (1st+2nd)WRN-34-1064.7135.7331.4130.2
", + "bbox": [ + 138, + 277, + 828, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Sensitivity of hyper-parameter", + "text_level": 1, + "bbox": [ + 76, + 633, + 346, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our proposed algorithm, the regularization hyperparameter $\\eta$ is crucial. We use numerical experiments on CIFAR-10 with PreAct ResNet-18 to illustrate how the regularization hyper-parameter influences the performance of our robust classifiers. To develop robust classifiers for multi-class tasks, we use the gradient descent update formula in Algorithm 1, with $\\mathcal{L}$ as the cross-entropy loss. Note that, for the zeroth term hyper-parameter $1 / \\lambda$ in Algorithm 1, we set $1 / \\lambda = 6$ for all of our experiments, which is a widely used setting for TRADES. We train the models with $\\eta = 0.05$ , 0.1, 0.2, 0.3, 0.4 respectively. All models are trained with 200 epochs and 128 batchsize.", + "bbox": [ + 75, + 657, + 468, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tab. 1, we observe that as the regularization parameter $\\eta$ increases, the clean accuracy and robust accuracy almost both go up first and then down. In particular, the accuracy under Auto Attack is sensitive to the regularization", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "hyper-parameter $\\eta$ . Considering both robustness accuracy and clean accuracy, it is not difficult to find that $\\eta = 0.3$ is the best for first term optimization and $\\eta = 0.2$ is the best for first + second terms optimization. Thus in the following experiments, we set $\\eta = 0.3$ for first term optimization and $\\eta = 0.2$ for first + second terms optimization as default.", + "bbox": [ + 496, + 635, + 890, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with SOTA on WideResNet", + "text_level": 1, + "bbox": [ + 498, + 738, + 843, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tab. 2, we compare our method with state-of-the-art on WideResNet with CIFAR-10 and CIFAR-100. For zeroth term optimization, we use TRADES [80] and AWPTRADES [74] as baselines with $1 / \\lambda = 6$ . We also report other state-of-the-art, include AVMixup [42], MART [72], [60], [81], [54], TRADES+LBGAT [11] and [24].", + "bbox": [ + 496, + 763, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results in Tab. 2 demonstrate that our method can both improve clean accuracy and robustness accuracy consistently over different datasets and models. Especially for", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16452", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5faed2e2605f873a29fbc81f9fc07d44da7f6dd7da8966ea499441867cb93032.jpg", + "table_caption": [ + "Table 3. Adversarial training across datasets on PreAct ResNet18 with ${\\ell }_{2}$ threat model. Classification accuracy (%) on clean images and under PGD-20 attack and Auto Attack. The results of our methods are in bold." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDAACleanPGDAACleanPGDAA
Wu et al. (2020) [74](0th)87.0572.0871.662.8745.1141.892.8672.4563.8
+ Ours (1st+2nd)88.4172.8572.065.5946.8842.493.9873.0764.5
", + "bbox": [ + 102, + 119, + 862, + 186 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6ef290fbaf300bbc0409f168844b006bc9d93008a2c921aefa9756d30a33ccfe.jpg", + "table_caption": [ + "Table 4. Adversarial training across datasets on PreAct ResNet18 with $\\ell_{\\infty}$ threat model. Classification accuracy (%) on clean images and black-box attacks. Black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. The results of our methods are in bold." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDCWCleanPGDCWCleanPGDCW
Wu et al. (2020) [74](0th)82.7861.7959.4258.3338.5536.7093.7763.8059.54
+ Ours (1st+2nd)84.2762.5660.5861.0839.8237.8495.1166.1663.59
", + "bbox": [ + 91, + 234, + 874, + 303 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/67c3a747cd7565ffbdba38591dbc81c21bc62fdc4342f4a8cbb56374dc4ae4a4.jpg", + "table_caption": [ + "Table 5. Adversarial training across VGG16, MobileNetV2 on CIFAR-10 with $\\ell_{\\infty}$ threat model. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack. The results of our methods are in bold." + ], + "table_footnote": [], + "table_body": "
MethodVGG16MobileNetV2
CleanPGD-20CW-20AACleanPGD-20CW-20AA
Zhang et al. (2019) [80] (0th)79.7849.8846.9544.379.7351.4148.4346.4
+ Ours (1st+2nd)80.9950.1347.0944.481.8653.3449.9347.8
Wu et al. (2020) [74] (0th)78.4651.1947.4146.379.8653.5650.1147.7
+ Ours (1st+2nd)80.3152.7148.3846.581.9555.3751.5549.4
", + "bbox": [ + 98, + 339, + 867, + 439 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/518b6e1cbc5039fcd7c5600832588ed2efd53c8a297fd19b4e3f6760a0cedd63.jpg", + "table_caption": [ + "Table 6. Time consumption and GPU memory usage for WideRes-Net on CIFAR-10 with $\\ell_{\\infty}$ threat model. We deploy each model on a single NVIDIA A100 with batchsize 128. The results of our methods are in bold." + ], + "table_footnote": [], + "table_body": "
MethodWideResNet-34-10
Time/EpochGPU Memory
Zhang et al. (2019) [80] (0th)1666s12875MB
+ Ours (1st)2161s20629MB
+ Ours (1st+2nd)2362s26409MB
", + "bbox": [ + 80, + 506, + 467, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Auto Attack, our method can get $57.4\\%$ on CIFAR-10 and $30.2\\%$ on CIFAR-100 with WRN-34-10, even surpass the performance of WRN-70-16 from [24].", + "bbox": [ + 75, + 590, + 468, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Other empirical results", + "text_level": 1, + "bbox": [ + 76, + 647, + 292, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adversarial training with $\\ell_2$ threat model. For the experiments with $\\ell_2$ threat model on CIFAR-10, CIFAR-100 and SVHN in Tab. 3, the results still support that our method can enhance the performance under clean data, PGD-20 attack and Auto Attack. For CIFAR-100, it can even increase about $3\\%$ on clean accuracy.", + "bbox": [ + 75, + 671, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness under black-box attacks. We train PreAct ResNet18 for $\\ell_{\\infty}$ threat model on CIFAR-10, CIFAR-100 and SVHN. The black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. Tab. 4 shows our method is also effective under black-box attacks. For SVHN, ours can even obtain a significant improvement over the existing ones.", + "bbox": [ + 75, + 763, + 470, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness on other architectures. We train VGG16", + "bbox": [ + 96, + 885, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and MobileNetV2 for $\\ell_{\\infty}$ threat model on CIFAR-10. Our results in Tab. 5 show a comprehensive improvement under clean data and robustness accuracy. Particularly, for MobileNetV2, ours can achieve an improvement greater than $1\\%$ and $2\\%$ under Auto Attack and clean data, respectively.", + "bbox": [ + 496, + 450, + 890, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with SWA from [8]. The best PGD-20 accuracy and AA accuracy on CIFAR-10 for ResNet-18 from [8] are $52.14\\%$ and $49.44\\%$ respectively, whereas ours are $55.13\\%$ and $50.8\\%$ in Tab. 1 (with $1_{st} + 2_{nd}$ (0.2)).", + "bbox": [ + 496, + 527, + 890, + 587 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "More empirical results are given in Appendix E.", + "bbox": [ + 517, + 588, + 839, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Limitations and future work", + "text_level": 1, + "bbox": [ + 500, + 614, + 756, + 630 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use some approximation methods, e.g., Eq. (8), to reduce the complexity of our adversarial training method. The results in Tab. 6 show that though our method with WideResNet-34-10 can work on a single NVIDIA A100, the growth of training time and GPU memory still cannot be ignored. In the future work, we plan to further reduce the complexity of our algorithm and apply the first and second terms optimization on larger datasets.", + "bbox": [ + 496, + 638, + 890, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Related work", + "text_level": 1, + "bbox": [ + 500, + 775, + 637, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Adversarial training", + "text_level": 1, + "bbox": [ + 500, + 800, + 694, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adversarial training methods can generally be divided into three groups. In the first group, Eq. (1) is translated into an equivalent, (or approximate, expression), which is mainly used to narrow the distance between $f_{\\mathbf{w}}(\\mathbf{s})$ and $f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})$ . For example, ALP [19, 38] estimates the similar-", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16453", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ity between $f_{\\mathbf{w}}(\\mathbf{s})$ and $f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})$ , and maximizes this similarity in the objective function. MMA [13] proposes each correctly classified instance $\\mathbf{s}$ to leave sufficiently the decision boundary, through making the size of shortest successful perturbation as large as possible. TRADES [80] looks for the adversarial example $\\mathbf{s}^{\\prime}$ which can obtain the largest KL divergence between $f_{\\mathbf{w}}(\\mathbf{s})$ and $f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})$ , then trains with these adversarial examples. Besides, [84] adopts the similarity between local distributions of natural and adversarial example, [67] measures the similarity of local distributions with Wasserstein distance, and [15, 16, 46, 54] try to optimize with the distribution over a series of adversarial examples for a single input.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the second group, adversarial examples are preprocessed before being used for training rather than being directly generated by attack algorithms. For example, label smoothing [8, 69] replaces the hard label $y$ with the soft label $\\tilde{y}$ , where $\\tilde{y}$ is a combination of the hard label $y$ and uniform distribution. A further empirical exploration with of how label smoothing works is provided in [49]. AVMixup [42, 83] defines a virtual sample in the adversarial direction based on these. Through linear interpolation of the virtual sample and the clean sample, it extends the training distribution with soft labels. Instead of smoothing labels, [79] perturbs the local neighborhoods with an unsupervised way to produce adversarial examples. In addition, data augmentation [25, 59] is also shown to be an invaluable aid for adversarial training.", + "bbox": [ + 75, + 287, + 472, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The above two groups merely adjust the component parts of the min-max formalism. With AWP [74], one more maximization is performed to find a weight perturbation based on the generated adversarial examples. The altered weights [12] are then used in the outer minimization function to reduce the loss caused by the adversarial cases.", + "bbox": [ + 76, + 516, + 468, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different from previous work, this paper optimizes the distance between $f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s})$ and $f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}')$ through randomized weights, and therefore, effectively, it considers the optimization problem where the decision boundary is smoothed by these randomized models.", + "bbox": [ + 76, + 607, + 468, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2. Randomized weights", + "text_level": 1, + "bbox": [ + 76, + 695, + 274, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the previous work to study generalization or robustness, modeling neural network weights as random variables has been frequently used. For example, [50,75] estimate the mutual information between random weights and dataset, provide the expected generalization bound over weight distribution. Another example of random weights is on the PAC-Bayesian framework, a well-known theoretical tool to bound the generalization error of machine learning models [41,47,56,64]. In the recent years, PAC-Bayes is also developed to bound the generalization error or robustness error of deep neural networks [18,21,35,52]. In addition, [23] draws random noise into deterministic weights, to measure", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the mutual information between input dataset and activations under information bottleneck theory.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While we also consider randomized weights, a major difference from previous theoretical works is that randomized weights are applied to robustness, from which we find an insight to design a novel adversarial training method which decomposes objective function (parameterized with randomized weights) with Taylor series.", + "bbox": [ + 496, + 121, + 893, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Flatness", + "text_level": 1, + "bbox": [ + 500, + 220, + 601, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The generalization performance of machine learning models is believed to be correlated with the flatness of loss curve [30, 31], especially for deep neural networks [6, 14, 37, 43, 76]. For instance, in pioneering research [30, 31], the minimum description length (MDL) [61] was used to demonstrate that the flatness of the minimum is a reasonable generalization metric to consider. [39] investigated the cause of the decrease in generalization for large-batch networks and demonstrated that large-batch algorithms tend to converge to sharp minima, resulting in worse generalization. [35] undertook a large-scale empirical study and found that flatness-based measurements correlate with generalization more strongly than weight norms and (margin and optimization)-based measures. [22] introduced Sharpness-Aware Minimization (SAM) to locate parameters that lie in neighborhoods with consistently low loss. Moreover, [8] used SWA [32] in adversarial training to smooth the weights and find flatter minima, and showed that this can improve adversarial generalization.", + "bbox": [ + 496, + 244, + 893, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different from previous work, this paper uses Taylor expansion of the injected Gaussian to smooth the update of weights and search for flat minima during adversarial training. Our empirical results show the effectiveness of our method to flatten loss landscape and improve both robustness and clean accuracy.", + "bbox": [ + 496, + 531, + 893, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 635, + 619, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work studies the trade-off between robustness and clean accuracy through the lens of randomized weights. Through empirical analysis of loss landscape, algorithmic design (via Taylor expansion) on training optimization, and extensive experiments, we demonstrate that optimizing over randomized weights can consistently outperform the state-of-the-art adversarial training methods not only in clean accuracy but also in robustness.", + "bbox": [ + 496, + 660, + 893, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. GJ is supported by the CAS Project for Young Scientists in Basic Research, Grant No.YSBR040. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956123, and is also supported by the U.K. EPSRC through End-to-End Conceptual Guarding of Neural Architectures [EP/T026995/1].", + "bbox": [ + 496, + 789, + 893, + 896 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16454", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jonathan Uesato, Po-Sen Huang, Alhussein Fawzi, Robert Stanforth, and Pushmeet Kohli. Are labels required for improving adversarial robustness? In NeurIPS, 2019. 1", + "[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. 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In AAAI, 2019. 8" + ], + "bbox": [ + 78, + 92, + 467, + 703 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16457", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_model.json b/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9f3171ef1e8a320961549475da9249440420882a --- /dev/null +++ b/2023/Randomized Adversarial Training via Taylor Expansion/67c6de64-e0fe-4f60-a88b-da38f54fe451_model.json @@ -0,0 +1,2532 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.202, + 0.131, + 0.77, + 0.154 + ], + "angle": 0, + "content": "Randomized Adversarial Training via Taylor Expansion" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.192, + 0.783, + 0.214 + ], + "angle": 0, + "content": "Gaojie Jin\\(^{1,2}\\), Xinping Yi\\(^{2\\boxtimes}\\), Dengyu Wu\\(^{2}\\), Ronghui Mu\\(^{3}\\), Xiaowei Huang\\(^{2\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.223, + 0.832, + 0.242 + ], + "angle": 0, + "content": "1State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.326, + 0.242, + 0.646, + 0.259 + ], + "angle": 0, + "content": "\\(^{2}\\)University of Liverpool, Liverpool, UK" + }, + { + "type": "text", + "bbox": [ + 0.338, + 0.259, + 0.633, + 0.277 + ], + "angle": 0, + "content": "\\(^{3}\\)Lancaster University, Lancaster, UK" + }, + { + "type": "text", + "bbox": [ + 0.278, + 0.277, + 0.693, + 0.295 + ], + "angle": 0, + "content": "{g.jin3, xinping.yi, xiaowei.huang} \\(@\\) liverpool.ac.uk" + }, + { + "type": "text", + "bbox": [ + 0.387, + 0.295, + 0.585, + 0.312 + ], + "angle": 0, + "content": "Corresponding Author" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.358, + 0.314, + 0.373 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.474, + 0.725 + ], + "angle": 0, + "content": "In recent years, there has been an explosion of research into developing more robust deep neural networks against adversarial examples. Adversarial training appears as one of the most successful methods. To deal with both the robustness against adversarial examples and the accuracy over clean examples, many works develop enhanced adversarial training methods to achieve various trade-offs between them [19,38,80]. Leveraging over the studies [8,32] that smoothed update on weights during training may help find flat minima and improve generalization, we suggest reconciling the robustness-accuracy trade-off from another perspective, i.e., by adding random noise into deterministic weights. The randomized weights enable our design of a novel adversarial training method via Taylor expansion of a small Gaussian noise, and we show that the new adversarial training method can flatten loss landscape and find flat minima. With PGD, CW, and Auto Attacks, an extensive set of experiments demonstrate that our method enhances the state-of-the-art adversarial training methods, boosting both robustness and clean accuracy. The code is available at https://github.com/Alexkael/RandomizedAdversarial-Training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.745, + 0.21, + 0.76 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Trade-off between adversarial robustness and clean accuracy has recently been intensively studied [63, 68, 80] and demonstrated to exist [34, 58, 70, 77]. Many different techniques have been developed to alleviate the loss of clean accuracy when improving robustness, including data augmentation [1, 5, 29], early-stopping [60, 81], instance reweighting [3, 82], and various adversarial training methods [11, 36, 42, 74, 80]. Adversarial training is believed to be the most effective defense method against adversarial at" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.895, + 0.557 + ], + "angle": 0, + "content": "tacks, and is usually formulated as a minimax optimization problem where the network weights are assumed deterministic in each alternating iteration. Given the fact that both clean and adversarial examples are drawn from unknown distributions which interact with one another through the network weights, it is reasonable to relax the assumption that neural networks are simply deterministic models where weights are scalar values. This paper is based on a view, illustrated in Fig. 1, that randomized models enable the training optimization to consider multiple directions within a small area and may achieve smoothed weights update – in a way different from checkpoint averaging [8, 32] – and obtain robust models against new clean/adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.896, + 0.775 + ], + "angle": 0, + "content": "Building upon the above view, we find a way, drastically different from most existing studies in adversarial training, to balance robustness and clean accuracy, that is, embedding neural network weights with random noise. Whilst the randomized weights framework is not new in statistical learning theory, where it has been used in many previous works for e.g., generalization analysis [18, 52, 75], we hope to advance the empirical understanding of the robustness-accuracy trade-off problem in adversarial training by leveraging the rich tool sets in statistical learning. Remarkably, it turns out adversarial training with the optimization over randomized weights can improve the state-of-the-art adversarial training methods over both the adversarial robustness and clean accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.903 + ], + "angle": 0, + "content": "By modeling weights as randomized variables with an artificially injected weight perturbation, we start with an empirical analysis of flatness of loss landscape in Sec. 3. We show that our method can flatten loss landscape and find flatter minima in adversarial training, which is generally regarded as an indicator of good generalization ability. After the flatness analysis, we show how to optimize with randomized weights during adversarial training in Sec. 4. A" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16447" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.413, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.23, + 0.288, + 0.242 + ], + "angle": 0, + "content": "(a) Adversarial Training of TRADES" + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.089, + 0.892, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.415, + 0.23, + 0.505, + 0.242 + ], + "angle": 0, + "content": "(b) Our Method" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.894, + 0.302 + ], + "angle": 0, + "content": "Figure 1. A conceptual illustration of decision boundaries learned via (a) adversarial training of TRADES and (b) our method. (a) shows that TRADES considers a deterministic model and optimizes the distance of adversarial data and boundary only through one direction. Our method in (b) takes into account randomized weights (perturbed boundaries) and optimizes the distance of adversarial data and boundary via multi directions in a small area. The boundary learned by our method can be smoother and more robust against new data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.506 + ], + "angle": 0, + "content": "novel adversarial training method based on TRADES [80] is proposed to reconcile adversarial robustness with clean accuracy by closing the gap between clean latent space and adversarial latent space over randomized weights. Specifically, we utilize Taylor series to expand the objective function over weights, in such a way that we can deconstruct the function into Taylor series (e.g., zeroth term, first term, second term, etc). From an algorithmic viewpoint, these Taylor terms can thus replace the objective function effectively and time-efficiently. As Fig. 1 shows, since our method takes randomized models into consideration during training, the learned boundary is smoother and the learned model is more robust in a small perturbed area." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.688 + ], + "angle": 0, + "content": "We validate the effectiveness of our optimization method with the first and the second derivative terms of Taylor series. In consideration of training complexity and efficiency, we omit the third and higher derivative terms. Through an extensive set of experiments on a wide range of datasets (CIFAR-10 [40], CIFAR-100, SVHN [51]) and model architectures (ResNet [27], WideResNet [78], VGG [65], MobileNetV2 [62]), we find that our method can further enhance the state-of-the-art adversarial training methods on both adversarial robustness and clean accuracy, consistently across the datasets and the model architectures. Overall, this paper makes the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.689, + 0.469, + 0.764 + ], + "angle": 0, + "content": "- We conduct a pilot study of the trade-off between adversarial robustness and clean accuracy with randomized weights, and offer a new insight on the smoothed weights update and the flat minima during adversarial training (Sec. 3)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- We propose a novel adversarial training method under a randomized model to smooth the weights. The key enabler is the Taylor series expansion (in Sec. 4) of the robustness loss function over randomized weights (deterministic weights with random noise), so that the optimization can be simultaneously done over the zeroth, first, and second orders of Taylor series. In doing so, the proposed method can effectively enhance adversarial robustness without a significant compromise" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.689, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.312, + 0.658, + 0.326 + ], + "angle": 0, + "content": "on clean accuracy." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.326, + 0.892, + 0.386 + ], + "angle": 0, + "content": "- An extensive set of empirical results are provided to demonstrate that our method can improve both robustness and clean accuracy consistently across different datasets and different network architectures (Sec. 5)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.638, + 0.415 + ], + "angle": 0, + "content": "2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.424, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Basic Notation. Consider the classification task with the training set \\(S = \\{\\mathbf{s}_1,\\dots ,\\mathbf{s}_m\\}\\) where \\(m\\) samples are drawn from the data distribution \\(\\mathcal{D}\\). For notational convenience, we omit the label \\(y\\) of sample \\(\\mathbf{s}\\). The adversarial example \\(\\mathbf{s}'\\) is generally not in the natural dataset \\(S\\), such that \\(\\| \\mathbf{s}' - \\mathbf{s}\\|_p \\leq \\epsilon\\) where \\(\\| \\cdot \\|_p\\) is by default the \\(\\ell_p\\)-norm. Let \\(f_{\\mathbf{w}}(\\cdot)\\) be a learning model parameterized by \\(\\mathbf{w}\\), where \\(\\mathbf{w}\\) is the vectorization of weight matrix \\(\\mathbf{W}\\). \\(\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}), y)\\) is the cross-entropy loss between \\(f_{\\mathbf{w}}(\\mathbf{s})\\) and \\(y\\) with normalization. Define \\(\\mathcal{L}(f_{\\mathbf{w}}(\\mathcal{S}), \\mathcal{Y}) \\coloneqq \\mathbb{E}_{\\mathbf{s} \\in \\mathcal{S}}[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}), y)]\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.576, + 0.891, + 0.606 + ], + "angle": 0, + "content": "Vanilla Adversarial Training. Adversarial training can be formulated as a minimax optimization problem [45]" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.607, + 0.891, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w}} \\left\\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\max _ {\\mathbf {s} ^ {\\prime}: \\| \\mathbf {s} ^ {\\prime} - \\mathbf {s} \\| _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w}} \\left(\\mathbf {s} ^ {\\prime}\\right), y\\right) \\right] \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.713 + ], + "angle": 0, + "content": "where \\( \\mathbf{s}' \\) is an adversarial example causing the largest loss within an \\( \\epsilon \\)-ball centered at a clean example \\( s \\) with respect to a norm distance. Adversarial training aims to learn a model with the loss of adversarial examples minimized, without caring about the loss of the clean examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.77 + ], + "angle": 0, + "content": "TRADES-like Adversarial Training. Advanced adversarial training methods, such as TRADES [80], strike a trade-off between clean accuracy and adversarial robustness, by optimizing the following problem" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.776, + 0.891, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w}} \\Big \\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), y) + \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), f _ {\\mathbf {w}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right] \\Big \\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.891, + 0.87 + ], + "angle": 0, + "content": "where the first term contributes to clean accuracy, and the second term with hyperparameter \\(\\lambda\\) can be seen as a regularization for adversarial robustness that balances the outputs of clean and adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Nevertheless, each adversarial example \\(\\mathbf{s}'\\) is generated from a clean example \\(\\mathbf{s}\\) based on a specific weight \\(\\mathbf{w}\\), and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16448" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.089, + 0.805, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.313, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Figure 2. Comparison of loss landscapes of TRADES trained model (the first row) and \\(\\mathrm{TRADES} + 1_{st} + 2_{nd}\\) (our method, the second row) trained model. Loss plots in each column are generated from the same original image randomly chosen from the CIFAR-10 test dataset. Following the settings in [20], the \\(z\\) axis represents the loss, the \\(x\\) and \\(y\\) axes represent the magnitude of the perturbation added in the directions of \\(\\mathrm{sign}\\nabla_{\\mathbf{s}}f(\\mathbf{s})\\) and Rademacher(0.5) respectively. We provide more empirical results in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.456 + ], + "angle": 0, + "content": "the weight \\(\\mathbf{w}\\) is obtained by optimizing both clean and adversarial data with SGD. This is a chick-and-egg problem. A not-very-well-trained model \\(\\mathbf{w}\\) may generate some misleading adversarial data samples, which in turn drive the training process away from the optimum." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.471, + 0.579 + ], + "angle": 0, + "content": "Inspired by the idea of model smoothing, we believe that the introduction of noise term into the training process may smooth the update of weights and thus robustify the models. To elaborate on this, we introduce our method from the perspective of flatness of loss landscape in Sec. 3. This is followed by a formalization in Sec. 4, where a noise term is injected to network weight \\(\\mathbf{w}\\) during adversarial training to transform deterministic weights into randomized weights." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.196, + 0.607 + ], + "angle": 0, + "content": "3. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Flatness is commonly thought to be a metric of standard generalization: the loss surface at the final learnt weights for well-generalizing models is generally \"flat\" [18,21,35,52]. Moreover, [73] believed that a flatter adversarial loss landscape reduces the generalization gap in robustness. This aligns with [28], where the authors demonstrated that the local Lipschitz constant can be used to explicitly quantify the robustness of machine learning models. Many empirical defensive approaches, such as hessian/curvature-based regularization [48], gradient magnitude penalty [71], smoothening with random noise [44], or entropy regularization [33], have echoed the flatness performance of a robust model. However, all the above approaches require significant computational or memory resources, and many of them, such as hessian/curvature-based solutions, may suffer from standard accuracy decreases [26]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Stochastic weight averaging (SWA) [32] is known to find solutions that are far flatter than SGD, is incredibly simple to implement, enhances standard generalization, and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.501 + ], + "angle": 0, + "content": "has almost no computational overhead. It was developed to guarantee weight smoothness by simply averaging various checkpoints throughout the training trajectory. SWA has been applied to semi-supervised learning, Bayesian inference, and low-precision training. Especially, [8] used SWA for the first time in adversarial training in order to smooth the weights and locate flatter minima, and showed that it enhances the adversarial generalization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.713 + ], + "angle": 0, + "content": "Different from SWA, we propose a novel method (with details provided in Sec. 4) via Taylor expansion of a small Gaussian noise to smooth the update of weights. This method regards the TRADES [80], a state-of-the-art adversarial training method, as a special case with only zero-th term, and is able to locate flatter minima. To demonstrate the latter, we visualize the loss landscape with respect to both input and weight spaces. As shown in Fig. 2, compared to the TRADES, our method significantly flattens the rugged landscape. In addition, it is worth noting that our empirical results (in Sec. 5) demonstrate that our method can further improve not only clean accuracy but also adversarial accuracy compared with other SOTA (includes SWA from [8])." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.636, + 0.741 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Given a deterministic model of weight \\(\\mathbf{w}\\), we consider an additive small Gaussian noise \\(\\mathbf{u}\\) to smooth \\(\\mathbf{w}\\). Based on TRADES [80], we propose that the robust optimization problem can be further enhanced by" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.81, + 0.892, + 0.867 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), y\\right)\\right) \\right. \\tag {2} \\\\ \\left. + \\mathbb {E} _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathrm {K L} (f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}) | | f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where the first term contributes to clean accuracy, and the second term with hyperparameter \\(\\lambda\\) can be seen as a regu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16449" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.081, + 0.092, + 0.471, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Adversarial training with randomized weights" + }, + { + "type": "algorithm", + "bbox": [ + 0.086, + 0.109, + 0.887, + 0.445 + ], + "angle": 0, + "content": "Input: minibatch \\(\\{\\mathbf{s}_i\\}_{i = 1}^n\\) , network architecture parametrized by w, learning rate \\(\\eta_{l}\\) , step size \\(\\eta_{s}\\) , hyper-parameters \\(\\eta\\) , \\(\\lambda\\) zero mean Gaussian u, number of iterations \\(K\\) in inner optimization. \nOutput: Robust network \\(f_{\\mathbf{w}}\\) \nRandomly initialize network \\(f_{\\mathrm{w}}\\) , or initialize network with pre-trained configuration \nrepeat Generate adversarial examples: Sample u from u for \\(i = 1\\) to n do \\(\\mathbf{s}_i^\\prime \\gets \\mathbf{s}_i + 0.001\\cdot \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) for \\(k = 1\\) to \\(K\\) do \\(\\mathbf{s}_i^\\prime \\leftarrow \\Pi (\\eta_s\\mathrm{sign}(\\nabla_{\\mathbf{s}_i^\\prime}\\mathcal{L}(f_{\\mathbf{w} + u}(\\mathbf{s}_i),f_{\\mathbf{w} + u}(\\mathbf{s}_i^\\prime))) + \\mathbf{s}_i^\\prime)\\) , subject to \\(||\\mathbf{s}_i - \\mathbf{s}_i^\\prime ||_p\\leq \\epsilon\\) , where II is the projection operator. end for end for Optimization: w \\(\\leftarrow\\) w- \\(\\eta_l\\frac{1}{n}\\sum_{i = 1}^{n}\\nabla_{\\mathbf{w}}\\Big[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}_i),y_i)\\) (zeroth term) \\(+L(g_{\\mathbf{s}_i}(\\mathbf{w}),g_{\\mathbf{s}_i'}(\\mathbf{w})) / \\lambda\\) (first term) \\(+ \\eta \\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( g _ { \\textup { s } _ { i } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } , g _ { \\textup { s } _ { i } ^ { \\prime } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } ) \\big )\\) (second term) \\(+ \\frac {\\eta}{2}\\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } , \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } ^ { \\prime \\prime } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } ) \\big ) ]\\) where various optimization methods can be applied: zeroth term optimization (TRADES), zeroth + first terms opti- mization and zeroth + first + second terms optimization. until training converged" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.499 + ], + "angle": 0, + "content": "larization for adversarial robustness with weights \\(\\mathbf{w}\\) and a small Gaussian noise \\(\\mathbf{u}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.562 + ], + "angle": 0, + "content": "Following [17, 35], we let the Gaussian \\(\\mathbf{u}\\) be small enough to maintain the generalization performance on clean data. Then, we can extend Eq. (2) by replacing \\(\\mathrm{KL}(\\cdot ||\\cdot)\\) with a multi-class calibrated loss \\(\\mathcal{L}(\\cdot ,\\cdot)\\) [80]:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.567, + 0.47, + 0.626 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} \\underset {\\mathbf {w}} {\\min } & \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right)\\right) \\right. \\\\ & \\left. + \\mathbb {E} _ {\\mathbf {s}} \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\end{array} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.705 + ], + "angle": 0, + "content": "As the minimax optimization is entangled with expectation of randomized weights, it is challenging to solve such optimization problem directly. Instead, we propose to solve this problem in an alternating manner between the inner maximization and outer minimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.47, + 0.782 + ], + "angle": 0, + "content": "For the inner maximization, with a given model weight \\(\\mathbf{w}\\), we solve it by adopting the commonly used gradient-based approach (e.g., PGD) to generate the adversarial perturbation. That is, at the \\(t\\)-th iteration, the adversarial perturbation is produced iteratively by letting" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.787, + 0.469, + 0.825 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} _ {t + 1} ^ {\\prime} \\leftarrow \\Pi \\left(\\mathbf {s} _ {t} ^ {\\prime} + \\eta_ {s} \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {s} _ {t} ^ {\\prime}} \\mathcal {L} \\left(f _ {\\mathbf {w} + u} (\\mathbf {s}), f _ {\\mathbf {w} + u} \\left(\\mathbf {s} _ {t} ^ {\\prime}\\right)\\right)\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": "until the maximum allowed iterations are reached, where \\(\\Pi\\) is the projection operator, \\(\\eta_{s}\\) is the step size and \\(u\\) is a sample of \\(\\mathbf{u}\\). To reduce complexity, we only use one sample \\(u\\) to generate adversarial example for each minibatch. Nevertheless, sufficient samples of \\(\\mathbf{u}\\) can still be produced in one" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.545 + ], + "angle": 0, + "content": "epoch as there are many minibatches. As Fig. 1 shows, the adversarial example is generated by one model (boundary), then the optimization with randomized weights in multiple directions can be executed through the following minimization method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.892, + 0.592 + ], + "angle": 0, + "content": "For the outer minimization, when the optimal perturbed sample \\(\\mathbf{s}'\\) is generated by the inner maximization, we solve the following problem" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.597, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {s}} \\left[ \\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right) + \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.695 + ], + "angle": 0, + "content": "This optimization problem is challenging due to the entanglement between the deterministic weight \\(\\mathbf{w}\\) and the random perturbation \\(\\mathbf{u}\\), which makes gradient updating much involved." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.759 + ], + "angle": 0, + "content": "To resolve this issue, we decompose the two components in such a way that gradient updating and model averaging can be done separately. Let \\( f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}) = g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u}) \\), by Taylor expansion of \\( g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u}) \\) at \\( \\mathbf{w} \\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.764, + 0.892, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} g _ {\\mathbf {s}} (\\mathbf {w} + \\mathbf {u}) = g _ {\\mathbf {s}} (\\mathbf {w}) + g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u} + \\mathbf {u} ^ {T} \\frac {g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w})}{2 !} \\mathbf {u} \\tag {6} \\\\ + \\mathcal {O} _ {\\mathbf {s}} (| | \\mathbf {u} | | ^ {2}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.821, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(g_{\\mathbf{s}}^{\\prime}(\\mathbf{w}) = \\frac{\\partial g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}}\\in \\mathbb{R}^{d\\times 1}\\) and \\(g_{\\mathbf{s}}^{\\prime \\prime}(\\mathbf{w}) = \\frac{\\partial^{2}g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}\\partial\\mathbf{w}}\\in\\) \\(\\mathbb{R}^{d\\times d}\\) are the first and second derivative of the function \\(g_{\\mathrm{s}}(\\mathbf{w})\\) versus the weight w, respectively, and \\(\\mathcal{O}_{\\mathbf{s}}(||\\mathbf{u}||^{2})\\) tends to be zero with respect to \\(||\\mathbf{u}||^2\\) . By such approximation, the gradient computation will be solely done on the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16450" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "deterministic part \\(\\mathbf{w}\\), and model smoothing with averaged random variable \\(\\mathbf{u}\\) is done independently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.23 + ], + "angle": 0, + "content": "The intuition behind is the following. For the randomized model \\(\\mathbf{w} + \\mathbf{u}\\) with a specific input \\(\\mathbf{s}\\), the Taylor approximation explicitly takes into account the deterministic model \\(g_{\\mathbf{s}}(\\mathbf{w})\\), the projection of its gradient onto the random direction \\(g_{\\mathbf{s}}^{\\prime}(\\mathbf{w})^{T}\\mathbf{u}\\), and the projection of its curvature onto the subspace spanned by \\(\\mathbf{u}^{T}\\frac{g_{\\mathbf{s}}^{\\prime\\prime}(\\mathbf{w})}{2!}\\mathbf{u}\\), capturing higher-order information of the loss function with respect to \\(\\mathbf{u}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.469, + 0.276 + ], + "angle": 0, + "content": "To further simplify the computation, we minimize an upper bound of Eq. (5) instead. Due to the local convexity of loss landscape, by Jensen's inequality, we conclude that" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.283, + 0.469, + 0.315 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\sum_ {i} x _ {i}, \\sum_ {i} y _ {i}\\right) \\leq \\sum_ {i} \\mathcal {L} \\left(x _ {i}, y _ {i}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.469, + 0.351 + ], + "angle": 0, + "content": "Therefore, the second term in Eq. (5) can be upper bounded by" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.352, + 0.469, + 0.432 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})\\right) \\\\ \\leq \\mathcal {L} \\left(g _ {\\mathbf {s}} (\\mathbf {w}), g _ {\\mathbf {s} ^ {\\prime}} (\\mathbf {w})\\right) + \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}, g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}\\right)\\right) \\\\ + \\frac {1}{2} \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(\\mathbf {u} ^ {T} g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}, \\mathbf {u} ^ {T} g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}\\right)\\right), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.469, + 0.522 + ], + "angle": 0, + "content": "where the terms on the right-hand side are referred to as the zeroth, first, and second order Taylor expressions. Instead of minimizing Eq. (5) directly, we minimize the upper bound in Eq. (8), which is easier to compute in practical models. Details of the optimization are given in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.469, + 0.659 + ], + "angle": 0, + "content": "The pseudo-code of the proposed adversarial training method is presented in Algorithm 1. Note that the zeroth term optimization in Algorithm 1 is almost the same as TRADES [80], thus we use TRADES and AWP-TRADES [74] as (zeroth term optimization) baselines in our experiments in Sec. 5, and verify how much first and second terms optimization can improve. Note that we perform both AWP and our method through applying randomized weight perturbations on AWP updated weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.795 + ], + "angle": 0, + "content": "For all of our experiments, we limit the noise variance of \\(\\mathbf{u}\\) to be small enough [17, 35] to maintain the training, e.g., \\(\\sigma = 0.01\\). For the zeroth term hyper-parameter \\(1 / \\lambda\\) in Algorithm 1, we set \\(1 / \\lambda = 6\\) for all of our experiments, which is a widely-used setting for TRADES [53, 74, 80]. The number of inner optimization iterations \\(K\\) is set to 10 as usual. To make our method more flexible, we set \\(\\eta\\) and \\(\\frac{\\eta}{2}\\) as the first term and second term hyper-parameters, respectively, and analyze the sensitivity of \\(\\eta\\) in Sec. 5.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The main novelty of our proposed method is two-fold: (1) Instead of considering a single model with a deterministic weight \\(\\mathbf{w}\\), we consider a model ensemble with \\(\\mathbf{w} + \\mathbf{u}\\) to smooth the update of weights. By averaging these models during adversarial training, we come up with a robust model with smoothed classification boundary tolerant to potential adversarial weight perturbation. (2) When averaging" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "over the ensemble of randomized models during training, we disentangle gradient from random weight perturbation so that the gradient updating can be computed efficiently. In particular, we apply Taylor expansion at the mean weight \\(\\mathbf{w}\\) (i.e., the deterministic component) and approximate the cross-entropy loss function with the zeroth, first, and second Taylor terms. In doing so, the deterministic and statistical components of \\(\\mathbf{w} + \\mathbf{u}\\) can be decomposed and then computed independently." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.241, + 0.669, + 0.259 + ], + "angle": 0, + "content": "5. Empirical results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.327 + ], + "angle": 0, + "content": "In this section, we first discuss the hyper-parameter sensitivity of our method, and then evaluate the robustness on benchmark datasets against various white-box, black-box attacks and Auto Attack with \\(\\ell_2\\) and \\(\\ell_{\\infty}\\) threat models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Adversarial Training Setting. We train PreAct ResNet-18 [27] for \\(\\ell_{\\infty}\\) and \\(\\ell_2\\) threat models on CIFAR-10/100 [40] and SVHN [51]. In addition, we also train WideResNet-34-10 [78] for CIFAR-10/100, VGG16 and MobileNetV2 for CIFAR-10, with \\(\\ell_{\\infty}\\) threat model. We adopt the widely used adversarial training setting [60]: for the \\(\\ell_{\\infty}\\) threat model, \\(\\epsilon = 8 / 255\\) and step size \\(2 / 255\\); for the \\(\\ell_2\\) threat model, \\(\\epsilon = 128 / 255\\) and step size \\(15 / 255\\). For normal adversarial training, the training examples are generated with 10 steps. All models (except SVHN) are trained for 200 epochs using SGD with momentum 0.9, batchsize 128, weight decay \\(5\\times 10^{-4}\\), and an initial learning rate of 0.1 that is divided by 10 at the 100th and 150th epochs. Except for setting the starting learning rate to 0.01 for SVHN, we utilize the same other settings. Simple data augmentations are used, such as \\(32\\times 32\\) random crop with 4-pixel padding and random horizontal flip. We report the highest robustness that ever achieved at different checkpoints for each dataset and report the clean accuracy on the model which gets the highest PGD-20 accuracy. We omit the standard deviations of 3 runs as they are very small (\\(< 0.40\\%\\)) and implement all models on NVIDIA A100." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation Setting. We evaluate the robustness with white-box attacks, black-box attacks and auto attack. For white-box attacks, we adopt PGD-20 [45] and CW-20 [4] (the \\(\\ell_{\\infty}\\) version of CW loss optimized by PGD-20) to evaluate trained models. For black-box attacks, we generate adversarial perturbations by attacking a surrogate normal adversarial training model (with same setting) [55], and then apply these adversarial examples to the defense model and evaluate the performances. The attacking methods for black-box attacks we have used are PGD-20 and CW-20. For Auto Attack (AA) [10], one of the strongest attack methods, we adopt it through a mixture of different parameter-free attacks which include three white-box attacks (APGD-CE [10], APGD-DLR [10], and FAB [9]) and one black-box attack (Square Attack [2]). We provide more details about the experimental setups in Appendix B." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16451" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.131 + ], + "angle": 0, + "content": "Table 1. First and Second Derivative terms optimization on CIFAR-10 with \\( \\ell_{\\infty} \\) threat model for PreAct ResNet18. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack with different hyper-parameters \\( \\eta = 0.05, 0.1, 0.2, 0.3, 0.4 \\). We highlight the best results in bold." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.133, + 0.842, + 0.232 + ], + "angle": 0, + "content": "
MethodCleanPGD-20CW-20AAMethodCleanPGD-20CW-20AA
1st(0.05)83.1953.9852.1248.21st+2nd(0.05)83.2554.0751.9348.4
1st(0.1)82.8654.2952.2449.31st+2nd(0.1)83.4754.4252.2849.7
1st(0.2)83.5554.8652.6548.81st+2nd(0.2)84.1354.9152.5350.3
1st(0.3)83.9655.0552.5449.71st+2nd(0.3)84.2754.3651.8048.9
1st(0.4)83.9354.6552.2348.61st+2nd(0.4)84.1454.3851.5649.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.235, + 0.895, + 0.278 + ], + "angle": 0, + "content": "Table 2. First and Second Derivative terms optimization on CIFAR-10/CIFAR-100 with \\( \\ell_{\\infty} \\) threat model for WideResNet, compared with current state-of-the-art. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack ( \\( \\epsilon = 0.031 \\)) and Auto Attack \\( (\\epsilon = 8/255) \\). The results of our methods are in **bold**. Note that * is under PGD-40 attack and ** is under PGD-10 attack." + }, + { + "type": "table", + "bbox": [ + 0.139, + 0.279, + 0.83, + 0.621 + ], + "angle": 0, + "content": "
DatasetMethodArchitectureCleanPGD-20CW-20AA
CIFAR-10 ℓ∞Lee et al. (2020) [42]WRN-34-1092.5659.7554.5339.70
Wang et al. (2020) [72]WRN-34-1083.5158.3154.3351.10
Rice et al. (2020) [60]WRN-34-2085.34--53.42
Zhang et al. (2020) [81]WRN-34-1084.52--53.51
Pang et al. (2021) [54]WRN-34-2086.4357.91**-54.39
Jin et al. (2022) [36]WRN-34-2086.0161.1257.9355.90
Gowal et al. (2020) [24]WRN-70-1685.2958.22*-57.20
Zhang et al. (2019) [80] (0th)WRN-34-1084.6556.6854.4953.0
+ Ours (1st)WRN-34-1085.5158.3456.0654.0
+ Ours (1st+2nd)WRN-34-1085.9858.4756.1354.2
Wu et al. (2020) [74] (0th)WRN-34-1085.1759.6457.3356.2
+ Ours (1st)WRN-34-1086.1061.4758.0957.1
+ Ours (1st+2nd)WRN-34-1086.1261.4558.2257.4
CIFAR-100 ℓ∞Cui et al. (2021) [11]WRN-34-1060.4335.5031.5029.34
Gowal et al. (2020) [24]WRN-70-1660.8631.47*-30.03
Zhang et al. (2019) [80] (0th)WRN-34-1060.2232.1128.9326.9
+ Ours (1st)WRN-34-1063.0133.2629.4428.1
+ Ours (1st+2nd)WRN-34-1062.9333.3629.6127.9
Wu et al. (2020) [74] (0th)WRN-34-1060.3834.0930.7828.6
+ Ours (1st)WRN-34-1063.9835.3631.6329.8
+ Ours (1st+2nd)WRN-34-1064.7135.7331.4130.2
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.348, + 0.652 + ], + "angle": 0, + "content": "5.1. Sensitivity of hyper-parameter" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In our proposed algorithm, the regularization hyperparameter \\(\\eta\\) is crucial. We use numerical experiments on CIFAR-10 with PreAct ResNet-18 to illustrate how the regularization hyper-parameter influences the performance of our robust classifiers. To develop robust classifiers for multi-class tasks, we use the gradient descent update formula in Algorithm 1, with \\(\\mathcal{L}\\) as the cross-entropy loss. Note that, for the zeroth term hyper-parameter \\(1 / \\lambda\\) in Algorithm 1, we set \\(1 / \\lambda = 6\\) for all of our experiments, which is a widely used setting for TRADES. We train the models with \\(\\eta = 0.05\\), 0.1, 0.2, 0.3, 0.4 respectively. All models are trained with 200 epochs and 128 batchsize." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In Tab. 1, we observe that as the regularization parameter \\(\\eta\\) increases, the clean accuracy and robust accuracy almost both go up first and then down. In particular, the accuracy under Auto Attack is sensitive to the regularization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.727 + ], + "angle": 0, + "content": "hyper-parameter \\(\\eta\\). Considering both robustness accuracy and clean accuracy, it is not difficult to find that \\(\\eta = 0.3\\) is the best for first term optimization and \\(\\eta = 0.2\\) is the best for first + second terms optimization. Thus in the following experiments, we set \\(\\eta = 0.3\\) for first term optimization and \\(\\eta = 0.2\\) for first + second terms optimization as default." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.739, + 0.844, + 0.756 + ], + "angle": 0, + "content": "5.2. Comparison with SOTA on WideResNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.854 + ], + "angle": 0, + "content": "In Tab. 2, we compare our method with state-of-the-art on WideResNet with CIFAR-10 and CIFAR-100. For zeroth term optimization, we use TRADES [80] and AWPTRADES [74] as baselines with \\(1 / \\lambda = 6\\). We also report other state-of-the-art, include AVMixup [42], MART [72], [60], [81], [54], TRADES+LBGAT [11] and [24]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The results in Tab. 2 demonstrate that our method can both improve clean accuracy and robustness accuracy consistently over different datasets and models. Especially for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16452" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.117 + ], + "angle": 0, + "content": "Table 3. Adversarial training across datasets on PreAct ResNet18 with \\( {\\ell }_{2} \\) threat model. Classification accuracy (%) on clean images and under PGD-20 attack and Auto Attack. The results of our methods are in bold." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.12, + 0.864, + 0.188 + ], + "angle": 0, + "content": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDAACleanPGDAACleanPGDAA
Wu et al. (2020) [74](0th)87.0572.0871.662.8745.1141.892.8672.4563.8
+ Ours (1st+2nd)88.4172.8572.065.5946.8842.493.9873.0764.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.191, + 0.895, + 0.233 + ], + "angle": 0, + "content": "Table 4. Adversarial training across datasets on PreAct ResNet18 with \\( \\ell_{\\infty} \\) threat model. Classification accuracy (%) on clean images and black-box attacks. Black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. The results of our methods are in bold." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.235, + 0.875, + 0.304 + ], + "angle": 0, + "content": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDCWCleanPGDCWCleanPGDCW
Wu et al. (2020) [74](0th)82.7861.7959.4258.3338.5536.7093.7763.8059.54
+ Ours (1st+2nd)84.2762.5660.5861.0839.8237.8495.1166.1663.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.307, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Table 5. Adversarial training across VGG16, MobileNetV2 on CIFAR-10 with \\( \\ell_{\\infty} \\) threat model. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack. The results of our methods are in bold." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.34, + 0.868, + 0.44 + ], + "angle": 0, + "content": "
MethodVGG16MobileNetV2
CleanPGD-20CW-20AACleanPGD-20CW-20AA
Zhang et al. (2019) [80] (0th)79.7849.8846.9544.379.7351.4148.4346.4
+ Ours (1st+2nd)80.9950.1347.0944.481.8653.3449.9347.8
Wu et al. (2020) [74] (0th)78.4651.1947.4146.379.8653.5650.1147.7
+ Ours (1st+2nd)80.3152.7148.3846.581.9555.3751.5549.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Table 6. Time consumption and GPU memory usage for WideRes-Net on CIFAR-10 with \\( \\ell_{\\infty} \\) threat model. We deploy each model on a single NVIDIA A100 with batchsize 128. The results of our methods are in bold." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.507, + 0.468, + 0.576 + ], + "angle": 0, + "content": "
MethodWideResNet-34-10
Time/EpochGPU Memory
Zhang et al. (2019) [80] (0th)1666s12875MB
+ Ours (1st)2161s20629MB
+ Ours (1st+2nd)2362s26409MB
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.47, + 0.637 + ], + "angle": 0, + "content": "Auto Attack, our method can get \\(57.4\\%\\) on CIFAR-10 and \\(30.2\\%\\) on CIFAR-100 with WRN-34-10, even surpass the performance of WRN-70-16 from [24]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.648, + 0.294, + 0.665 + ], + "angle": 0, + "content": "5.3. Other empirical results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Adversarial training with \\(\\ell_2\\) threat model. For the experiments with \\(\\ell_2\\) threat model on CIFAR-10, CIFAR-100 and SVHN in Tab. 3, the results still support that our method can enhance the performance under clean data, PGD-20 attack and Auto Attack. For CIFAR-100, it can even increase about \\(3\\%\\) on clean accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.471, + 0.884 + ], + "angle": 0, + "content": "Robustness under black-box attacks. We train PreAct ResNet18 for \\(\\ell_{\\infty}\\) threat model on CIFAR-10, CIFAR-100 and SVHN. The black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. Tab. 4 shows our method is also effective under black-box attacks. For SVHN, ours can even obtain a significant improvement over the existing ones." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Robustness on other architectures. We train VGG16" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.892, + 0.527 + ], + "angle": 0, + "content": "and MobileNetV2 for \\(\\ell_{\\infty}\\) threat model on CIFAR-10. Our results in Tab. 5 show a comprehensive improvement under clean data and robustness accuracy. Particularly, for MobileNetV2, ours can achieve an improvement greater than \\(1\\%\\) and \\(2\\%\\) under Auto Attack and clean data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.588 + ], + "angle": 0, + "content": "Comparison with SWA from [8]. The best PGD-20 accuracy and AA accuracy on CIFAR-10 for ResNet-18 from [8] are \\(52.14\\%\\) and \\(49.44\\%\\) respectively, whereas ours are \\(55.13\\%\\) and \\(50.8\\%\\) in Tab. 1 (with \\(1_{st} + 2_{nd}\\) (0.2))." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.589, + 0.84, + 0.605 + ], + "angle": 0, + "content": "More empirical results are given in Appendix E." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.757, + 0.631 + ], + "angle": 0, + "content": "5.4. Limitations and future work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.761 + ], + "angle": 0, + "content": "We use some approximation methods, e.g., Eq. (8), to reduce the complexity of our adversarial training method. The results in Tab. 6 show that though our method with WideResNet-34-10 can work on a single NVIDIA A100, the growth of training time and GPU memory still cannot be ignored. In the future work, we plan to further reduce the complexity of our algorithm and apply the first and second terms optimization on larger datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.776, + 0.638, + 0.791 + ], + "angle": 0, + "content": "6. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.695, + 0.818 + ], + "angle": 0, + "content": "6.1. Adversarial training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Adversarial training methods can generally be divided into three groups. In the first group, Eq. (1) is translated into an equivalent, (or approximate, expression), which is mainly used to narrow the distance between \\( f_{\\mathbf{w}}(\\mathbf{s}) \\) and \\( f_{\\mathbf{w}}(\\mathbf{s}^{\\prime}) \\). For example, ALP [19, 38] estimates the similar-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16453" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "ity between \\( f_{\\mathbf{w}}(\\mathbf{s}) \\) and \\( f_{\\mathbf{w}}(\\mathbf{s}^{\\prime}) \\), and maximizes this similarity in the objective function. MMA [13] proposes each correctly classified instance \\( \\mathbf{s} \\) to leave sufficiently the decision boundary, through making the size of shortest successful perturbation as large as possible. TRADES [80] looks for the adversarial example \\( \\mathbf{s}^{\\prime} \\) which can obtain the largest KL divergence between \\( f_{\\mathbf{w}}(\\mathbf{s}) \\) and \\( f_{\\mathbf{w}}(\\mathbf{s}^{\\prime}) \\), then trains with these adversarial examples. Besides, [84] adopts the similarity between local distributions of natural and adversarial example, [67] measures the similarity of local distributions with Wasserstein distance, and [15, 16, 46, 54] try to optimize with the distribution over a series of adversarial examples for a single input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.515 + ], + "angle": 0, + "content": "In the second group, adversarial examples are preprocessed before being used for training rather than being directly generated by attack algorithms. For example, label smoothing [8, 69] replaces the hard label \\( y \\) with the soft label \\( \\tilde{y} \\), where \\( \\tilde{y} \\) is a combination of the hard label \\( y \\) and uniform distribution. A further empirical exploration with of how label smoothing works is provided in [49]. AVMixup [42, 83] defines a virtual sample in the adversarial direction based on these. Through linear interpolation of the virtual sample and the clean sample, it extends the training distribution with soft labels. Instead of smoothing labels, [79] perturbs the local neighborhoods with an unsupervised way to produce adversarial examples. In addition, data augmentation [25, 59] is also shown to be an invaluable aid for adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.517, + 0.47, + 0.607 + ], + "angle": 0, + "content": "The above two groups merely adjust the component parts of the min-max formalism. With AWP [74], one more maximization is performed to find a weight perturbation based on the generated adversarial examples. The altered weights [12] are then used in the outer minimization function to reduce the loss caused by the adversarial cases." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.608, + 0.47, + 0.683 + ], + "angle": 0, + "content": "Different from previous work, this paper optimizes the distance between \\( f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}) \\) and \\( f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}') \\) through randomized weights, and therefore, effectively, it considers the optimization problem where the decision boundary is smoothed by these randomized models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.275, + 0.712 + ], + "angle": 0, + "content": "6.2. Randomized weights" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In the previous work to study generalization or robustness, modeling neural network weights as random variables has been frequently used. For example, [50,75] estimate the mutual information between random weights and dataset, provide the expected generalization bound over weight distribution. Another example of random weights is on the PAC-Bayesian framework, a well-known theoretical tool to bound the generalization error of machine learning models [41,47,56,64]. In the recent years, PAC-Bayes is also developed to bound the generalization error or robustness error of deep neural networks [18,21,35,52]. In addition, [23] draws random noise into deterministic weights, to measure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "the mutual information between input dataset and activations under information bottleneck theory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.213 + ], + "angle": 0, + "content": "While we also consider randomized weights, a major difference from previous theoretical works is that randomized weights are applied to robustness, from which we find an insight to design a novel adversarial training method which decomposes objective function (parameterized with randomized weights) with Taylor series." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.222, + 0.602, + 0.236 + ], + "angle": 0, + "content": "6.3. Flatness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.895, + 0.532 + ], + "angle": 0, + "content": "The generalization performance of machine learning models is believed to be correlated with the flatness of loss curve [30, 31], especially for deep neural networks [6, 14, 37, 43, 76]. For instance, in pioneering research [30, 31], the minimum description length (MDL) [61] was used to demonstrate that the flatness of the minimum is a reasonable generalization metric to consider. [39] investigated the cause of the decrease in generalization for large-batch networks and demonstrated that large-batch algorithms tend to converge to sharp minima, resulting in worse generalization. [35] undertook a large-scale empirical study and found that flatness-based measurements correlate with generalization more strongly than weight norms and (margin and optimization)-based measures. [22] introduced Sharpness-Aware Minimization (SAM) to locate parameters that lie in neighborhoods with consistently low loss. Moreover, [8] used SWA [32] in adversarial training to smooth the weights and find flatter minima, and showed that this can improve adversarial generalization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.894, + 0.623 + ], + "angle": 0, + "content": "Different from previous work, this paper uses Taylor expansion of the injected Gaussian to smooth the update of weights and search for flat minima during adversarial training. Our empirical results show the effectiveness of our method to flatten loss landscape and improve both robustness and clean accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.62, + 0.652 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.894, + 0.782 + ], + "angle": 0, + "content": "This work studies the trade-off between robustness and clean accuracy through the lens of randomized weights. Through empirical analysis of loss landscape, algorithmic design (via Taylor expansion) on training optimization, and extensive experiments, we demonstrate that optimizing over randomized weights can consistently outperform the state-of-the-art adversarial training methods not only in clean accuracy but also in robustness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.894, + 0.897 + ], + "angle": 0, + "content": "Acknowledgment. GJ is supported by the CAS Project for Young Scientists in Basic Research, Grant No.YSBR040. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956123, and is also supported by the U.K. EPSRC through End-to-End Conceptual Guarding of Neural Architectures [EP/T026995/1]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "16454" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jonathan Uesato, Po-Sen Huang, Alhussein Fawzi, Robert Stanforth, and Pushmeet Kohli. Are labels required for improving adversarial robustness? 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Adversarial training appears as one of the most successful methods. To deal with both the robustness against adversarial examples and the accuracy over clean examples, many works develop enhanced adversarial training methods to achieve various trade-offs between them [19,38,80]. Leveraging over the studies [8,32] that smoothed update on weights during training may help find flat minima and improve generalization, we suggest reconciling the robustness-accuracy trade-off from another perspective, i.e., by adding random noise into deterministic weights. The randomized weights enable our design of a novel adversarial training method via Taylor expansion of a small Gaussian noise, and we show that the new adversarial training method can flatten loss landscape and find flat minima. With PGD, CW, and Auto Attacks, an extensive set of experiments demonstrate that our method enhances the state-of-the-art adversarial training methods, boosting both robustness and clean accuracy. The code is available at https://github.com/Alexkael/RandomizedAdversarial-Training. + +# 1. Introduction + +Trade-off between adversarial robustness and clean accuracy has recently been intensively studied [63, 68, 80] and demonstrated to exist [34, 58, 70, 77]. Many different techniques have been developed to alleviate the loss of clean accuracy when improving robustness, including data augmentation [1, 5, 29], early-stopping [60, 81], instance reweighting [3, 82], and various adversarial training methods [11, 36, 42, 74, 80]. Adversarial training is believed to be the most effective defense method against adversarial at + +tacks, and is usually formulated as a minimax optimization problem where the network weights are assumed deterministic in each alternating iteration. Given the fact that both clean and adversarial examples are drawn from unknown distributions which interact with one another through the network weights, it is reasonable to relax the assumption that neural networks are simply deterministic models where weights are scalar values. This paper is based on a view, illustrated in Fig. 1, that randomized models enable the training optimization to consider multiple directions within a small area and may achieve smoothed weights update – in a way different from checkpoint averaging [8, 32] – and obtain robust models against new clean/adversarial examples. + +Building upon the above view, we find a way, drastically different from most existing studies in adversarial training, to balance robustness and clean accuracy, that is, embedding neural network weights with random noise. Whilst the randomized weights framework is not new in statistical learning theory, where it has been used in many previous works for e.g., generalization analysis [18, 52, 75], we hope to advance the empirical understanding of the robustness-accuracy trade-off problem in adversarial training by leveraging the rich tool sets in statistical learning. Remarkably, it turns out adversarial training with the optimization over randomized weights can improve the state-of-the-art adversarial training methods over both the adversarial robustness and clean accuracy. + +By modeling weights as randomized variables with an artificially injected weight perturbation, we start with an empirical analysis of flatness of loss landscape in Sec. 3. We show that our method can flatten loss landscape and find flatter minima in adversarial training, which is generally regarded as an indicator of good generalization ability. After the flatness analysis, we show how to optimize with randomized weights during adversarial training in Sec. 4. A + +![](images/ea5ab0f5cb6db2441f9378efa1b585c85f54698caadae2a309d911dade437244.jpg) +(a) Adversarial Training of TRADES + +![](images/7839665f5571fd764e6626cb5b965e80dfba536e074c00d423c7276f3704a34e.jpg) +(b) Our Method +Figure 1. A conceptual illustration of decision boundaries learned via (a) adversarial training of TRADES and (b) our method. (a) shows that TRADES considers a deterministic model and optimizes the distance of adversarial data and boundary only through one direction. Our method in (b) takes into account randomized weights (perturbed boundaries) and optimizes the distance of adversarial data and boundary via multi directions in a small area. The boundary learned by our method can be smoother and more robust against new data. + +novel adversarial training method based on TRADES [80] is proposed to reconcile adversarial robustness with clean accuracy by closing the gap between clean latent space and adversarial latent space over randomized weights. Specifically, we utilize Taylor series to expand the objective function over weights, in such a way that we can deconstruct the function into Taylor series (e.g., zeroth term, first term, second term, etc). From an algorithmic viewpoint, these Taylor terms can thus replace the objective function effectively and time-efficiently. As Fig. 1 shows, since our method takes randomized models into consideration during training, the learned boundary is smoother and the learned model is more robust in a small perturbed area. + +We validate the effectiveness of our optimization method with the first and the second derivative terms of Taylor series. In consideration of training complexity and efficiency, we omit the third and higher derivative terms. Through an extensive set of experiments on a wide range of datasets (CIFAR-10 [40], CIFAR-100, SVHN [51]) and model architectures (ResNet [27], WideResNet [78], VGG [65], MobileNetV2 [62]), we find that our method can further enhance the state-of-the-art adversarial training methods on both adversarial robustness and clean accuracy, consistently across the datasets and the model architectures. Overall, this paper makes the following contributions: + +- We conduct a pilot study of the trade-off between adversarial robustness and clean accuracy with randomized weights, and offer a new insight on the smoothed weights update and the flat minima during adversarial training (Sec. 3). +- We propose a novel adversarial training method under a randomized model to smooth the weights. The key enabler is the Taylor series expansion (in Sec. 4) of the robustness loss function over randomized weights (deterministic weights with random noise), so that the optimization can be simultaneously done over the zeroth, first, and second orders of Taylor series. In doing so, the proposed method can effectively enhance adversarial robustness without a significant compromise + +on clean accuracy. + +- An extensive set of empirical results are provided to demonstrate that our method can improve both robustness and clean accuracy consistently across different datasets and different network architectures (Sec. 5). + +# 2. Preliminaries + +Basic Notation. Consider the classification task with the training set $S = \{\mathbf{s}_1,\dots ,\mathbf{s}_m\}$ where $m$ samples are drawn from the data distribution $\mathcal{D}$ . For notational convenience, we omit the label $y$ of sample $\mathbf{s}$ . The adversarial example $\mathbf{s}'$ is generally not in the natural dataset $S$ , such that $\| \mathbf{s}' - \mathbf{s}\|_p \leq \epsilon$ where $\| \cdot \|_p$ is by default the $\ell_p$ -norm. Let $f_{\mathbf{w}}(\cdot)$ be a learning model parameterized by $\mathbf{w}$ , where $\mathbf{w}$ is the vectorization of weight matrix $\mathbf{W}$ . $\mathcal{L}(f_{\mathbf{w}}(\mathbf{s}), y)$ is the cross-entropy loss between $f_{\mathbf{w}}(\mathbf{s})$ and $y$ with normalization. Define $\mathcal{L}(f_{\mathbf{w}}(\mathcal{S}), \mathcal{Y}) \coloneqq \mathbb{E}_{\mathbf{s} \in \mathcal{S}}[\mathcal{L}(f_{\mathbf{w}}(\mathbf{s}), y)]$ . + +Vanilla Adversarial Training. Adversarial training can be formulated as a minimax optimization problem [45] + +$$ +\min _ {\mathbf {w}} \left\{\underset {\mathbf {s} \sim \mathcal {D}} {\mathbb {E}} \left[ \max _ {\mathbf {s} ^ {\prime}: \| \mathbf {s} ^ {\prime} - \mathbf {s} \| _ {p} \leq \epsilon} \mathcal {L} \left(f _ {\mathbf {w}} \left(\mathbf {s} ^ {\prime}\right), y\right) \right] \right\}, \tag {1} +$$ + +where $\mathbf{s}'$ is an adversarial example causing the largest loss within an $\epsilon$ -ball centered at a clean example $s$ with respect to a norm distance. Adversarial training aims to learn a model with the loss of adversarial examples minimized, without caring about the loss of the clean examples. + +TRADES-like Adversarial Training. Advanced adversarial training methods, such as TRADES [80], strike a trade-off between clean accuracy and adversarial robustness, by optimizing the following problem + +$$ +\min _ {\mathbf {w}} \Big \{\underset {\mathbf {s} \sim \mathcal {D}} {\mathbb {E}} \left[ \mathcal {L} (f _ {\mathbf {w}} (\mathbf {s}), y) + \max _ {\mathbf {s} ^ {\prime}: | | \mathbf {s} ^ {\prime} - \mathbf {s} | | _ {p} \leq \epsilon} \mathcal {L} (f _ {\mathbf {w}} (\mathbf {s}), f _ {\mathbf {w}} (\mathbf {s} ^ {\prime})) / \lambda \right] \Big \}, +$$ + +where the first term contributes to clean accuracy, and the second term with hyperparameter $\lambda$ can be seen as a regularization for adversarial robustness that balances the outputs of clean and adversarial examples. + +Nevertheless, each adversarial example $\mathbf{s}'$ is generated from a clean example $\mathbf{s}$ based on a specific weight $\mathbf{w}$ , and + +![](images/3db41d602e62f5c04d90811c33897fcd840ef059e40cc5f314795b4810c63014.jpg) +Figure 2. Comparison of loss landscapes of TRADES trained model (the first row) and $\mathrm{TRADES} + 1_{st} + 2_{nd}$ (our method, the second row) trained model. Loss plots in each column are generated from the same original image randomly chosen from the CIFAR-10 test dataset. Following the settings in [20], the $z$ axis represents the loss, the $x$ and $y$ axes represent the magnitude of the perturbation added in the directions of $\mathrm{sign}\nabla_{\mathbf{s}}f(\mathbf{s})$ and Rademacher(0.5) respectively. We provide more empirical results in Appendix A. + +the weight $\mathbf{w}$ is obtained by optimizing both clean and adversarial data with SGD. This is a chick-and-egg problem. A not-very-well-trained model $\mathbf{w}$ may generate some misleading adversarial data samples, which in turn drive the training process away from the optimum. + +Inspired by the idea of model smoothing, we believe that the introduction of noise term into the training process may smooth the update of weights and thus robustify the models. To elaborate on this, we introduce our method from the perspective of flatness of loss landscape in Sec. 3. This is followed by a formalization in Sec. 4, where a noise term is injected to network weight $\mathbf{w}$ during adversarial training to transform deterministic weights into randomized weights. + +# 3. Motivation + +Flatness is commonly thought to be a metric of standard generalization: the loss surface at the final learnt weights for well-generalizing models is generally "flat" [18,21,35,52]. Moreover, [73] believed that a flatter adversarial loss landscape reduces the generalization gap in robustness. This aligns with [28], where the authors demonstrated that the local Lipschitz constant can be used to explicitly quantify the robustness of machine learning models. Many empirical defensive approaches, such as hessian/curvature-based regularization [48], gradient magnitude penalty [71], smoothening with random noise [44], or entropy regularization [33], have echoed the flatness performance of a robust model. However, all the above approaches require significant computational or memory resources, and many of them, such as hessian/curvature-based solutions, may suffer from standard accuracy decreases [26]. + +Stochastic weight averaging (SWA) [32] is known to find solutions that are far flatter than SGD, is incredibly simple to implement, enhances standard generalization, and + +has almost no computational overhead. It was developed to guarantee weight smoothness by simply averaging various checkpoints throughout the training trajectory. SWA has been applied to semi-supervised learning, Bayesian inference, and low-precision training. Especially, [8] used SWA for the first time in adversarial training in order to smooth the weights and locate flatter minima, and showed that it enhances the adversarial generalization. + +Different from SWA, we propose a novel method (with details provided in Sec. 4) via Taylor expansion of a small Gaussian noise to smooth the update of weights. This method regards the TRADES [80], a state-of-the-art adversarial training method, as a special case with only zero-th term, and is able to locate flatter minima. To demonstrate the latter, we visualize the loss landscape with respect to both input and weight spaces. As shown in Fig. 2, compared to the TRADES, our method significantly flattens the rugged landscape. In addition, it is worth noting that our empirical results (in Sec. 5) demonstrate that our method can further improve not only clean accuracy but also adversarial accuracy compared with other SOTA (includes SWA from [8]). + +# 4. Methodology + +Given a deterministic model of weight $\mathbf{w}$ , we consider an additive small Gaussian noise $\mathbf{u}$ to smooth $\mathbf{w}$ . Based on TRADES [80], we propose that the robust optimization problem can be further enhanced by + +$$ +\begin{array}{l} \min _ {\mathbf {w}} \mathbb {E} _ {\mathbf {u}} \left[ \mathbb {E} _ {\mathbf {s}} \left(\mathcal {L} \left(f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s}), y\right)\right) \right. \tag {2} \\ \left. + \mathbb {E} _ {\mathbf {s} ^ {\prime}: | | \mathbf {s} ^ {\prime} - \mathbf {s} | | _ {p} \leq \epsilon} \mathrm {K L} (f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s}) | | f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s} ^ {\prime})) / \lambda \right], \\ \end{array} +$$ + +where the first term contributes to clean accuracy, and the second term with hyperparameter $\lambda$ can be seen as a regu + +Algorithm 1 Adversarial training with randomized weights +Input: minibatch $\{\mathbf{s}_i\}_{i = 1}^n$ , network architecture parametrized by w, learning rate $\eta_{l}$ , step size $\eta_{s}$ , hyper-parameters $\eta$ , $\lambda$ zero mean Gaussian u, number of iterations $K$ in inner optimization. +Output: Robust network $f_{\mathbf{w}}$ +Randomly initialize network $f_{\mathrm{w}}$ , or initialize network with pre-trained configuration +repeat Generate adversarial examples: Sample u from u for $i = 1$ to n do $\mathbf{s}_i^\prime \gets \mathbf{s}_i + 0.001\cdot \mathcal{N}(\mathbf{0},\mathbf{I})$ for $k = 1$ to $K$ do $\mathbf{s}_i^\prime \leftarrow \Pi (\eta_s\mathrm{sign}(\nabla_{\mathbf{s}_i^\prime}\mathcal{L}(f_{\mathbf{w} + u}(\mathbf{s}_i),f_{\mathbf{w} + u}(\mathbf{s}_i^\prime))) + \mathbf{s}_i^\prime)$ , subject to $||\mathbf{s}_i - \mathbf{s}_i^\prime ||_p\leq \epsilon$ , where II is the projection operator. end for end for Optimization: w $\leftarrow$ w- $\eta_l\frac{1}{n}\sum_{i = 1}^{n}\nabla_{\mathbf{w}}\Big[\mathcal{L}(f_{\mathbf{w}}(\mathbf{s}_i),y_i)$ (zeroth term) $+L(g_{\mathbf{s}_i}(\mathbf{w}),g_{\mathbf{s}_i'}(\mathbf{w})) / \lambda$ (first term) $+ \eta \mathbb { E } _ { \textup { u } } \big ( \mathcal { L } ( g _ { \textup { s } _ { i } } ^ { \prime } ( \mathbf { w } ) ^ { T } \mathbf { u } , g _ { \textup { s } _ { i } ^ { \prime } } ^ { \prime } ( \mathbf { w } ) ^ { T } \mathbf { u } ) \big )$ (second term) $+ \frac {\eta}{2}\mathbb { E } _ { \textup { u } } \big ( \mathcal { L } ( \mathbf { u } ^ { T } g _ { \textup { s } _ { i } } ^ { \prime \prime } ( \mathbf { w } ) \mathbf { u } , \mathbf { u } ^ { T } g _ { \textup { s } _ { i } ^ { \prime \prime } } ^ { \prime \prime } ( \mathbf { w } ) \mathbf { u } ) \big ) ]$ where various optimization methods can be applied: zeroth term optimization (TRADES), zeroth + first terms opti- mization and zeroth + first + second terms optimization. until training converged + +larization for adversarial robustness with weights $\mathbf{w}$ and a small Gaussian noise $\mathbf{u}$ . + +Following [17, 35], we let the Gaussian $\mathbf{u}$ be small enough to maintain the generalization performance on clean data. Then, we can extend Eq. (2) by replacing $\mathrm{KL}(\cdot ||\cdot)$ with a multi-class calibrated loss $\mathcal{L}(\cdot ,\cdot)$ [80]: + +$$ +\begin{array}{r l} \underset {\mathbf {w}} {\min } & \mathbb {E} _ {\mathbf {u}} \left[ \mathbb {E} _ {\mathbf {s}} \left(\mathcal {L} \left(f _ {\mathbf {w}} (\mathbf {s}), y\right)\right) \right. \\ & \left. + \mathbb {E} _ {\mathbf {s}} \max _ {\mathbf {s} ^ {\prime}: | | \mathbf {s} ^ {\prime} - \mathbf {s} | | _ {p} \leq \epsilon} \mathcal {L} \left(f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s}), f _ {\mathbf {w} + \mathbf {u}} \left(\mathbf {s} ^ {\prime}\right)\right) / \lambda \right]. \end{array} \tag {3} +$$ + +As the minimax optimization is entangled with expectation of randomized weights, it is challenging to solve such optimization problem directly. Instead, we propose to solve this problem in an alternating manner between the inner maximization and outer minimization. + +For the inner maximization, with a given model weight $\mathbf{w}$ , we solve it by adopting the commonly used gradient-based approach (e.g., PGD) to generate the adversarial perturbation. That is, at the $t$ -th iteration, the adversarial perturbation is produced iteratively by letting + +$$ +\mathbf {s} _ {t + 1} ^ {\prime} \leftarrow \Pi \left(\mathbf {s} _ {t} ^ {\prime} + \eta_ {s} \operatorname {s i g n} \left(\nabla_ {\mathbf {s} _ {t} ^ {\prime}} \mathcal {L} \left(f _ {\mathbf {w} + u} (\mathbf {s}), f _ {\mathbf {w} + u} \left(\mathbf {s} _ {t} ^ {\prime}\right)\right)\right)\right) \tag {4} +$$ + +until the maximum allowed iterations are reached, where $\Pi$ is the projection operator, $\eta_{s}$ is the step size and $u$ is a sample of $\mathbf{u}$ . To reduce complexity, we only use one sample $u$ to generate adversarial example for each minibatch. Nevertheless, sufficient samples of $\mathbf{u}$ can still be produced in one + +epoch as there are many minibatches. As Fig. 1 shows, the adversarial example is generated by one model (boundary), then the optimization with randomized weights in multiple directions can be executed through the following minimization method. + +For the outer minimization, when the optimal perturbed sample $\mathbf{s}'$ is generated by the inner maximization, we solve the following problem + +$$ +\min _ {\mathbf {w}} \mathbb {E} _ {\mathbf {s}} \left[ \mathcal {L} \left(f _ {\mathbf {w}} (\mathbf {s}), y\right) + \mathbb {E} _ {\mathbf {u}} \mathcal {L} \left(f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s}), f _ {\mathbf {w} + \mathbf {u}} \left(\mathbf {s} ^ {\prime}\right)\right) / \lambda \right]. \tag {5} +$$ + +This optimization problem is challenging due to the entanglement between the deterministic weight $\mathbf{w}$ and the random perturbation $\mathbf{u}$ , which makes gradient updating much involved. + +To resolve this issue, we decompose the two components in such a way that gradient updating and model averaging can be done separately. Let $f_{\mathbf{w} + \mathbf{u}}(\mathbf{s}) = g_{\mathbf{s}}(\mathbf{w} + \mathbf{u})$ , by Taylor expansion of $g_{\mathbf{s}}(\mathbf{w} + \mathbf{u})$ at $\mathbf{w}$ , we have + +$$ +\begin{array}{l} g _ {\mathbf {s}} (\mathbf {w} + \mathbf {u}) = g _ {\mathbf {s}} (\mathbf {w}) + g _ {\mathbf {s}} ^ {\prime} (\mathbf {w}) ^ {T} \mathbf {u} + \mathbf {u} ^ {T} \frac {g _ {\mathbf {s}} ^ {\prime \prime} (\mathbf {w})}{2 !} \mathbf {u} \tag {6} \\ + \mathcal {O} _ {\mathbf {s}} (| | \mathbf {u} | | ^ {2}), \\ \end{array} +$$ + +where $g_{\mathbf{s}}^{\prime}(\mathbf{w}) = \frac{\partial g_{\mathbf{s}}(\mathbf{w})}{\partial\mathbf{w}}\in \mathbb{R}^{d\times 1}$ and $g_{\mathbf{s}}^{\prime \prime}(\mathbf{w}) = \frac{\partial^{2}g_{\mathbf{s}}(\mathbf{w})}{\partial\mathbf{w}\partial\mathbf{w}}\in$ $\mathbb{R}^{d\times d}$ are the first and second derivative of the function $g_{\mathrm{s}}(\mathbf{w})$ versus the weight w, respectively, and $\mathcal{O}_{\mathbf{s}}(||\mathbf{u}||^{2})$ tends to be zero with respect to $||\mathbf{u}||^2$ . By such approximation, the gradient computation will be solely done on the + +deterministic part $\mathbf{w}$ , and model smoothing with averaged random variable $\mathbf{u}$ is done independently. + +The intuition behind is the following. For the randomized model $\mathbf{w} + \mathbf{u}$ with a specific input $\mathbf{s}$ , the Taylor approximation explicitly takes into account the deterministic model $g_{\mathbf{s}}(\mathbf{w})$ , the projection of its gradient onto the random direction $g_{\mathbf{s}}^{\prime}(\mathbf{w})^{T}\mathbf{u}$ , and the projection of its curvature onto the subspace spanned by $\mathbf{u}^{T}\frac{g_{\mathbf{s}}^{\prime\prime}(\mathbf{w})}{2!}\mathbf{u}$ , capturing higher-order information of the loss function with respect to $\mathbf{u}$ . + +To further simplify the computation, we minimize an upper bound of Eq. (5) instead. Due to the local convexity of loss landscape, by Jensen's inequality, we conclude that + +$$ +\mathcal {L} \left(\sum_ {i} x _ {i}, \sum_ {i} y _ {i}\right) \leq \sum_ {i} \mathcal {L} \left(x _ {i}, y _ {i}\right). \tag {7} +$$ + +Therefore, the second term in Eq. (5) can be upper bounded by + +$$ +\begin{array}{l} \mathbb {E} _ {\mathbf {u}} \mathcal {L} \left(f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s}), f _ {\mathbf {w} + \mathbf {u}} (\mathbf {s} ^ {\prime})\right) \\ \leq \mathcal {L} \left(g _ {\mathbf {s}} (\mathbf {w}), g _ {\mathbf {s} ^ {\prime}} (\mathbf {w})\right) + \mathbb {E} _ {\mathbf {u}} \left(\mathcal {L} \left(g _ {\mathbf {s}} ^ {\prime} (\mathbf {w}) ^ {T} \mathbf {u}, g _ {\mathbf {s} ^ {\prime}} ^ {\prime} (\mathbf {w}) ^ {T} \mathbf {u}\right)\right) \\ + \frac {1}{2} \mathbb {E} _ {\mathbf {u}} \left(\mathcal {L} \left(\mathbf {u} ^ {T} g _ {\mathbf {s}} ^ {\prime \prime} (\mathbf {w}) \mathbf {u}, \mathbf {u} ^ {T} g _ {\mathbf {s} ^ {\prime}} ^ {\prime \prime} (\mathbf {w}) \mathbf {u}\right)\right), \tag {8} \\ \end{array} +$$ + +where the terms on the right-hand side are referred to as the zeroth, first, and second order Taylor expressions. Instead of minimizing Eq. (5) directly, we minimize the upper bound in Eq. (8), which is easier to compute in practical models. Details of the optimization are given in Appendix D. + +The pseudo-code of the proposed adversarial training method is presented in Algorithm 1. Note that the zeroth term optimization in Algorithm 1 is almost the same as TRADES [80], thus we use TRADES and AWP-TRADES [74] as (zeroth term optimization) baselines in our experiments in Sec. 5, and verify how much first and second terms optimization can improve. Note that we perform both AWP and our method through applying randomized weight perturbations on AWP updated weights. + +For all of our experiments, we limit the noise variance of $\mathbf{u}$ to be small enough [17, 35] to maintain the training, e.g., $\sigma = 0.01$ . For the zeroth term hyper-parameter $1 / \lambda$ in Algorithm 1, we set $1 / \lambda = 6$ for all of our experiments, which is a widely-used setting for TRADES [53, 74, 80]. The number of inner optimization iterations $K$ is set to 10 as usual. To make our method more flexible, we set $\eta$ and $\frac{\eta}{2}$ as the first term and second term hyper-parameters, respectively, and analyze the sensitivity of $\eta$ in Sec. 5.1. + +The main novelty of our proposed method is two-fold: (1) Instead of considering a single model with a deterministic weight $\mathbf{w}$ , we consider a model ensemble with $\mathbf{w} + \mathbf{u}$ to smooth the update of weights. By averaging these models during adversarial training, we come up with a robust model with smoothed classification boundary tolerant to potential adversarial weight perturbation. (2) When averaging + +over the ensemble of randomized models during training, we disentangle gradient from random weight perturbation so that the gradient updating can be computed efficiently. In particular, we apply Taylor expansion at the mean weight $\mathbf{w}$ (i.e., the deterministic component) and approximate the cross-entropy loss function with the zeroth, first, and second Taylor terms. In doing so, the deterministic and statistical components of $\mathbf{w} + \mathbf{u}$ can be decomposed and then computed independently. + +# 5. Empirical results + +In this section, we first discuss the hyper-parameter sensitivity of our method, and then evaluate the robustness on benchmark datasets against various white-box, black-box attacks and Auto Attack with $\ell_2$ and $\ell_{\infty}$ threat models. + +Adversarial Training Setting. We train PreAct ResNet-18 [27] for $\ell_{\infty}$ and $\ell_2$ threat models on CIFAR-10/100 [40] and SVHN [51]. In addition, we also train WideResNet-34-10 [78] for CIFAR-10/100, VGG16 and MobileNetV2 for CIFAR-10, with $\ell_{\infty}$ threat model. We adopt the widely used adversarial training setting [60]: for the $\ell_{\infty}$ threat model, $\epsilon = 8 / 255$ and step size $2 / 255$ ; for the $\ell_2$ threat model, $\epsilon = 128 / 255$ and step size $15 / 255$ . For normal adversarial training, the training examples are generated with 10 steps. All models (except SVHN) are trained for 200 epochs using SGD with momentum 0.9, batchsize 128, weight decay $5\times 10^{-4}$ , and an initial learning rate of 0.1 that is divided by 10 at the 100th and 150th epochs. Except for setting the starting learning rate to 0.01 for SVHN, we utilize the same other settings. Simple data augmentations are used, such as $32\times 32$ random crop with 4-pixel padding and random horizontal flip. We report the highest robustness that ever achieved at different checkpoints for each dataset and report the clean accuracy on the model which gets the highest PGD-20 accuracy. We omit the standard deviations of 3 runs as they are very small ( $< 0.40\%$ ) and implement all models on NVIDIA A100. + +Evaluation Setting. We evaluate the robustness with white-box attacks, black-box attacks and auto attack. For white-box attacks, we adopt PGD-20 [45] and CW-20 [4] (the $\ell_{\infty}$ version of CW loss optimized by PGD-20) to evaluate trained models. For black-box attacks, we generate adversarial perturbations by attacking a surrogate normal adversarial training model (with same setting) [55], and then apply these adversarial examples to the defense model and evaluate the performances. The attacking methods for black-box attacks we have used are PGD-20 and CW-20. For Auto Attack (AA) [10], one of the strongest attack methods, we adopt it through a mixture of different parameter-free attacks which include three white-box attacks (APGD-CE [10], APGD-DLR [10], and FAB [9]) and one black-box attack (Square Attack [2]). We provide more details about the experimental setups in Appendix B. + +Table 1. First and Second Derivative terms optimization on CIFAR-10 with $\ell_{\infty}$ threat model for PreAct ResNet18. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack with different hyper-parameters $\eta = 0.05, 0.1, 0.2, 0.3, 0.4$ . We highlight the best results in bold. + +
MethodCleanPGD-20CW-20AAMethodCleanPGD-20CW-20AA
1st(0.05)83.1953.9852.1248.21st+2nd(0.05)83.2554.0751.9348.4
1st(0.1)82.8654.2952.2449.31st+2nd(0.1)83.4754.4252.2849.7
1st(0.2)83.5554.8652.6548.81st+2nd(0.2)84.1354.9152.5350.3
1st(0.3)83.9655.0552.5449.71st+2nd(0.3)84.2754.3651.8048.9
1st(0.4)83.9354.6552.2348.61st+2nd(0.4)84.1454.3851.5649.6
+ +Table 2. First and Second Derivative terms optimization on CIFAR-10/CIFAR-100 with $\ell_{\infty}$ threat model for WideResNet, compared with current state-of-the-art. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack ( $\epsilon = 0.031$ ) and Auto Attack $(\epsilon = 8/255)$ . The results of our methods are in **bold**. Note that * is under PGD-40 attack and ** is under PGD-10 attack. + +
DatasetMethodArchitectureCleanPGD-20CW-20AA
CIFAR-10 ℓ∞Lee et al. (2020) [42]WRN-34-1092.5659.7554.5339.70
Wang et al. (2020) [72]WRN-34-1083.5158.3154.3351.10
Rice et al. (2020) [60]WRN-34-2085.34--53.42
Zhang et al. (2020) [81]WRN-34-1084.52--53.51
Pang et al. (2021) [54]WRN-34-2086.4357.91**-54.39
Jin et al. (2022) [36]WRN-34-2086.0161.1257.9355.90
Gowal et al. (2020) [24]WRN-70-1685.2958.22*-57.20
Zhang et al. (2019) [80] (0th)WRN-34-1084.6556.6854.4953.0
+ Ours (1st)WRN-34-1085.5158.3456.0654.0
+ Ours (1st+2nd)WRN-34-1085.9858.4756.1354.2
Wu et al. (2020) [74] (0th)WRN-34-1085.1759.6457.3356.2
+ Ours (1st)WRN-34-1086.1061.4758.0957.1
+ Ours (1st+2nd)WRN-34-1086.1261.4558.2257.4
CIFAR-100 ℓ∞Cui et al. (2021) [11]WRN-34-1060.4335.5031.5029.34
Gowal et al. (2020) [24]WRN-70-1660.8631.47*-30.03
Zhang et al. (2019) [80] (0th)WRN-34-1060.2232.1128.9326.9
+ Ours (1st)WRN-34-1063.0133.2629.4428.1
+ Ours (1st+2nd)WRN-34-1062.9333.3629.6127.9
Wu et al. (2020) [74] (0th)WRN-34-1060.3834.0930.7828.6
+ Ours (1st)WRN-34-1063.9835.3631.6329.8
+ Ours (1st+2nd)WRN-34-1064.7135.7331.4130.2
+ +# 5.1. Sensitivity of hyper-parameter + +In our proposed algorithm, the regularization hyperparameter $\eta$ is crucial. We use numerical experiments on CIFAR-10 with PreAct ResNet-18 to illustrate how the regularization hyper-parameter influences the performance of our robust classifiers. To develop robust classifiers for multi-class tasks, we use the gradient descent update formula in Algorithm 1, with $\mathcal{L}$ as the cross-entropy loss. Note that, for the zeroth term hyper-parameter $1 / \lambda$ in Algorithm 1, we set $1 / \lambda = 6$ for all of our experiments, which is a widely used setting for TRADES. We train the models with $\eta = 0.05$ , 0.1, 0.2, 0.3, 0.4 respectively. All models are trained with 200 epochs and 128 batchsize. + +In Tab. 1, we observe that as the regularization parameter $\eta$ increases, the clean accuracy and robust accuracy almost both go up first and then down. In particular, the accuracy under Auto Attack is sensitive to the regularization + +hyper-parameter $\eta$ . Considering both robustness accuracy and clean accuracy, it is not difficult to find that $\eta = 0.3$ is the best for first term optimization and $\eta = 0.2$ is the best for first + second terms optimization. Thus in the following experiments, we set $\eta = 0.3$ for first term optimization and $\eta = 0.2$ for first + second terms optimization as default. + +# 5.2. Comparison with SOTA on WideResNet + +In Tab. 2, we compare our method with state-of-the-art on WideResNet with CIFAR-10 and CIFAR-100. For zeroth term optimization, we use TRADES [80] and AWPTRADES [74] as baselines with $1 / \lambda = 6$ . We also report other state-of-the-art, include AVMixup [42], MART [72], [60], [81], [54], TRADES+LBGAT [11] and [24]. + +The results in Tab. 2 demonstrate that our method can both improve clean accuracy and robustness accuracy consistently over different datasets and models. Especially for + +Table 3. Adversarial training across datasets on PreAct ResNet18 with ${\ell }_{2}$ threat model. Classification accuracy (%) on clean images and under PGD-20 attack and Auto Attack. The results of our methods are in bold. + +
MethodCIFAR-10CIFAR-100SVHN
CleanPGDAACleanPGDAACleanPGDAA
Wu et al. (2020) [74](0th)87.0572.0871.662.8745.1141.892.8672.4563.8
+ Ours (1st+2nd)88.4172.8572.065.5946.8842.493.9873.0764.5
+ +Table 4. Adversarial training across datasets on PreAct ResNet18 with $\ell_{\infty}$ threat model. Classification accuracy (%) on clean images and black-box attacks. Black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. The results of our methods are in bold. + +
MethodCIFAR-10CIFAR-100SVHN
CleanPGDCWCleanPGDCWCleanPGDCW
Wu et al. (2020) [74](0th)82.7861.7959.4258.3338.5536.7093.7763.8059.54
+ Ours (1st+2nd)84.2762.5660.5861.0839.8237.8495.1166.1663.59
+ +Table 5. Adversarial training across VGG16, MobileNetV2 on CIFAR-10 with $\ell_{\infty}$ threat model. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack. The results of our methods are in bold. + +
MethodVGG16MobileNetV2
CleanPGD-20CW-20AACleanPGD-20CW-20AA
Zhang et al. (2019) [80] (0th)79.7849.8846.9544.379.7351.4148.4346.4
+ Ours (1st+2nd)80.9950.1347.0944.481.8653.3449.9347.8
Wu et al. (2020) [74] (0th)78.4651.1947.4146.379.8653.5650.1147.7
+ Ours (1st+2nd)80.3152.7148.3846.581.9555.3751.5549.4
+ +Table 6. Time consumption and GPU memory usage for WideRes-Net on CIFAR-10 with $\ell_{\infty}$ threat model. We deploy each model on a single NVIDIA A100 with batchsize 128. The results of our methods are in bold. + +
MethodWideResNet-34-10
Time/EpochGPU Memory
Zhang et al. (2019) [80] (0th)1666s12875MB
+ Ours (1st)2161s20629MB
+ Ours (1st+2nd)2362s26409MB
+ +Auto Attack, our method can get $57.4\%$ on CIFAR-10 and $30.2\%$ on CIFAR-100 with WRN-34-10, even surpass the performance of WRN-70-16 from [24]. + +# 5.3. Other empirical results + +Adversarial training with $\ell_2$ threat model. For the experiments with $\ell_2$ threat model on CIFAR-10, CIFAR-100 and SVHN in Tab. 3, the results still support that our method can enhance the performance under clean data, PGD-20 attack and Auto Attack. For CIFAR-100, it can even increase about $3\%$ on clean accuracy. + +Robustness under black-box attacks. We train PreAct ResNet18 for $\ell_{\infty}$ threat model on CIFAR-10, CIFAR-100 and SVHN. The black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. Tab. 4 shows our method is also effective under black-box attacks. For SVHN, ours can even obtain a significant improvement over the existing ones. + +Robustness on other architectures. We train VGG16 + +and MobileNetV2 for $\ell_{\infty}$ threat model on CIFAR-10. Our results in Tab. 5 show a comprehensive improvement under clean data and robustness accuracy. Particularly, for MobileNetV2, ours can achieve an improvement greater than $1\%$ and $2\%$ under Auto Attack and clean data, respectively. + +Comparison with SWA from [8]. The best PGD-20 accuracy and AA accuracy on CIFAR-10 for ResNet-18 from [8] are $52.14\%$ and $49.44\%$ respectively, whereas ours are $55.13\%$ and $50.8\%$ in Tab. 1 (with $1_{st} + 2_{nd}$ (0.2)). + +More empirical results are given in Appendix E. + +# 5.4. Limitations and future work + +We use some approximation methods, e.g., Eq. (8), to reduce the complexity of our adversarial training method. The results in Tab. 6 show that though our method with WideResNet-34-10 can work on a single NVIDIA A100, the growth of training time and GPU memory still cannot be ignored. In the future work, we plan to further reduce the complexity of our algorithm and apply the first and second terms optimization on larger datasets. + +# 6. Related work + +# 6.1. Adversarial training + +Adversarial training methods can generally be divided into three groups. In the first group, Eq. (1) is translated into an equivalent, (or approximate, expression), which is mainly used to narrow the distance between $f_{\mathbf{w}}(\mathbf{s})$ and $f_{\mathbf{w}}(\mathbf{s}^{\prime})$ . For example, ALP [19, 38] estimates the similar- + +ity between $f_{\mathbf{w}}(\mathbf{s})$ and $f_{\mathbf{w}}(\mathbf{s}^{\prime})$ , and maximizes this similarity in the objective function. MMA [13] proposes each correctly classified instance $\mathbf{s}$ to leave sufficiently the decision boundary, through making the size of shortest successful perturbation as large as possible. TRADES [80] looks for the adversarial example $\mathbf{s}^{\prime}$ which can obtain the largest KL divergence between $f_{\mathbf{w}}(\mathbf{s})$ and $f_{\mathbf{w}}(\mathbf{s}^{\prime})$ , then trains with these adversarial examples. Besides, [84] adopts the similarity between local distributions of natural and adversarial example, [67] measures the similarity of local distributions with Wasserstein distance, and [15, 16, 46, 54] try to optimize with the distribution over a series of adversarial examples for a single input. + +In the second group, adversarial examples are preprocessed before being used for training rather than being directly generated by attack algorithms. For example, label smoothing [8, 69] replaces the hard label $y$ with the soft label $\tilde{y}$ , where $\tilde{y}$ is a combination of the hard label $y$ and uniform distribution. A further empirical exploration with of how label smoothing works is provided in [49]. AVMixup [42, 83] defines a virtual sample in the adversarial direction based on these. Through linear interpolation of the virtual sample and the clean sample, it extends the training distribution with soft labels. Instead of smoothing labels, [79] perturbs the local neighborhoods with an unsupervised way to produce adversarial examples. In addition, data augmentation [25, 59] is also shown to be an invaluable aid for adversarial training. + +The above two groups merely adjust the component parts of the min-max formalism. With AWP [74], one more maximization is performed to find a weight perturbation based on the generated adversarial examples. The altered weights [12] are then used in the outer minimization function to reduce the loss caused by the adversarial cases. + +Different from previous work, this paper optimizes the distance between $f_{\mathbf{w} + \mathbf{u}}(\mathbf{s})$ and $f_{\mathbf{w} + \mathbf{u}}(\mathbf{s}')$ through randomized weights, and therefore, effectively, it considers the optimization problem where the decision boundary is smoothed by these randomized models. + +# 6.2. Randomized weights + +In the previous work to study generalization or robustness, modeling neural network weights as random variables has been frequently used. For example, [50,75] estimate the mutual information between random weights and dataset, provide the expected generalization bound over weight distribution. Another example of random weights is on the PAC-Bayesian framework, a well-known theoretical tool to bound the generalization error of machine learning models [41,47,56,64]. In the recent years, PAC-Bayes is also developed to bound the generalization error or robustness error of deep neural networks [18,21,35,52]. In addition, [23] draws random noise into deterministic weights, to measure + +the mutual information between input dataset and activations under information bottleneck theory. + +While we also consider randomized weights, a major difference from previous theoretical works is that randomized weights are applied to robustness, from which we find an insight to design a novel adversarial training method which decomposes objective function (parameterized with randomized weights) with Taylor series. + +# 6.3. Flatness + +The generalization performance of machine learning models is believed to be correlated with the flatness of loss curve [30, 31], especially for deep neural networks [6, 14, 37, 43, 76]. For instance, in pioneering research [30, 31], the minimum description length (MDL) [61] was used to demonstrate that the flatness of the minimum is a reasonable generalization metric to consider. [39] investigated the cause of the decrease in generalization for large-batch networks and demonstrated that large-batch algorithms tend to converge to sharp minima, resulting in worse generalization. [35] undertook a large-scale empirical study and found that flatness-based measurements correlate with generalization more strongly than weight norms and (margin and optimization)-based measures. [22] introduced Sharpness-Aware Minimization (SAM) to locate parameters that lie in neighborhoods with consistently low loss. Moreover, [8] used SWA [32] in adversarial training to smooth the weights and find flatter minima, and showed that this can improve adversarial generalization. + +Different from previous work, this paper uses Taylor expansion of the injected Gaussian to smooth the update of weights and search for flat minima during adversarial training. Our empirical results show the effectiveness of our method to flatten loss landscape and improve both robustness and clean accuracy. + +# 7. Conclusion + +This work studies the trade-off between robustness and clean accuracy through the lens of randomized weights. Through empirical analysis of loss landscape, algorithmic design (via Taylor expansion) on training optimization, and extensive experiments, we demonstrate that optimizing over randomized weights can consistently outperform the state-of-the-art adversarial training methods not only in clean accuracy but also in robustness. + +Acknowledgment. GJ is supported by the CAS Project for Young Scientists in Basic Research, Grant No.YSBR040. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956123, and is also supported by the U.K. EPSRC through End-to-End Conceptual Guarding of Neural Architectures [EP/T026995/1]. + +# References + +[1] Jean-Baptiste Alayrac, Jonathan Uesato, Po-Sen Huang, Alhussein Fawzi, Robert Stanforth, and Pushmeet Kohli. Are labels required for improving adversarial robustness? In NeurIPS, 2019. 1 +[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In ECCV, 2020. 5 +[3] Yogesh Balaji, Tom Goldstein, and Judy Hoffman. Instance adaptive adversarial training: Improved accuracy tradeoffs in neural nets. CoRR, 2019. 1 +[4] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. 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years, there has been an explosion of research into developing more robust deep neural networks against adversarial examples. Adversarial training appears as one of the most successful methods. To deal with both the robustness against adversarial examples and the accuracy over clean examples, many works develop enhanced adversarial training methods to achieve various trade-offs between them [19,38,80]. Leveraging over the studies [8,32] that smoothed update on weights during training may help find flat minima and improve generalization, we suggest reconciling the robustness-accuracy trade-off from another perspective, i.e., by adding random noise into deterministic weights. The randomized weights enable our design of a novel adversarial training method via Taylor expansion of a small Gaussian noise, and we show that the new adversarial training method can flatten loss landscape and find flat minima. With PGD, CW, and Auto Attacks, an extensive set of experiments demonstrate that our method enhances the state-of-the-art adversarial training methods, boosting both robustness and clean accuracy. The code is available at https://github.com/Alexkael/RandomizedAdversarial-Training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 590, + 128, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 128, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 128, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Trade-off between adversarial robustness and clean accuracy has recently been intensively studied [63, 68, 80] and demonstrated to exist [34, 58, 70, 77]. Many different techniques have been developed to alleviate the loss of clean accuracy when improving robustness, including data augmentation [1, 5, 29], early-stopping [60, 81], instance reweighting [3, 82], and various adversarial training methods [11, 36, 42, 74, 80]. Adversarial training is believed to be the most effective defense method against adversarial at" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 284, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 547, + 441 + ], + "type": "text", + "content": "tacks, and is usually formulated as a minimax optimization problem where the network weights are assumed deterministic in each alternating iteration. Given the fact that both clean and adversarial examples are drawn from unknown distributions which interact with one another through the network weights, it is reasonable to relax the assumption that neural networks are simply deterministic models where weights are scalar values. This paper is based on a view, illustrated in Fig. 1, that randomized models enable the training optimization to consider multiple directions within a small area and may achieve smoothed weights update – in a way different from checkpoint averaging [8, 32] – and obtain robust models against new clean/adversarial examples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 445, + 548, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 548, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 548, + 613 + ], + "type": "text", + "content": "Building upon the above view, we find a way, drastically different from most existing studies in adversarial training, to balance robustness and clean accuracy, that is, embedding neural network weights with random noise. Whilst the randomized weights framework is not new in statistical learning theory, where it has been used in many previous works for e.g., generalization analysis [18, 52, 75], we hope to advance the empirical understanding of the robustness-accuracy trade-off problem in adversarial training by leveraging the rich tool sets in statistical learning. Remarkably, it turns out adversarial training with the optimization over randomized weights can improve the state-of-the-art adversarial training methods over both the adversarial robustness and clean accuracy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "content": "By modeling weights as randomized variables with an artificially injected weight perturbation, we start with an empirical analysis of flatness of loss landscape in Sec. 3. We show that our method can flatten loss landscape and find flatter minima in adversarial training, which is generally regarded as an indicator of good generalization ability. After the flatness analysis, we show how to optimize with randomized weights during adversarial training in Sec. 4. A" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16447" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 252, + 181 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 252, + 181 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 252, + 181 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 252, + 181 + ], + "type": "image", + "image_path": "ea5ab0f5cb6db2441f9378efa1b585c85f54698caadae2a309d911dade437244.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 182, + 176, + 191 + ], + "lines": [ + { + "bbox": [ + 48, + 182, + 176, + 191 + ], + "spans": [ + { + "bbox": [ + 48, + 182, + 176, + 191 + ], + "type": "text", + "content": "(a) Adversarial Training of TRADES" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 253, + 70, + 545, + 182 + ], + "blocks": [ + { + "bbox": [ + 253, + 70, + 545, + 182 + ], + "lines": [ + { + "bbox": [ + 253, + 70, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 253, + 70, + 545, + 182 + ], + "type": "image", + "image_path": "7839665f5571fd764e6626cb5b965e80dfba536e074c00d423c7276f3704a34e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 253, + 182, + 309, + 191 + ], + "lines": [ + { + "bbox": [ + 253, + 182, + 309, + 191 + ], + "spans": [ + { + "bbox": [ + 253, + 182, + 309, + 191 + ], + "type": "text", + "content": "(b) Our Method" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 194, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 547, + 239 + ], + "type": "text", + "content": "Figure 1. A conceptual illustration of decision boundaries learned via (a) adversarial training of TRADES and (b) our method. (a) shows that TRADES considers a deterministic model and optimizes the distance of adversarial data and boundary only through one direction. Our method in (b) takes into account randomized weights (perturbed boundaries) and optimizes the distance of adversarial data and boundary via multi directions in a small area. The boundary learned by our method can be smoother and more robust against new data." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 246, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 400 + ], + "type": "text", + "content": "novel adversarial training method based on TRADES [80] is proposed to reconcile adversarial robustness with clean accuracy by closing the gap between clean latent space and adversarial latent space over randomized weights. Specifically, we utilize Taylor series to expand the objective function over weights, in such a way that we can deconstruct the function into Taylor series (e.g., zeroth term, first term, second term, etc). From an algorithmic viewpoint, these Taylor terms can thus replace the objective function effectively and time-efficiently. As Fig. 1 shows, since our method takes randomized models into consideration during training, the learned boundary is smoother and the learned model is more robust in a small perturbed area." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": "We validate the effectiveness of our optimization method with the first and the second derivative terms of Taylor series. In consideration of training complexity and efficiency, we omit the third and higher derivative terms. Through an extensive set of experiments on a wide range of datasets (CIFAR-10 [40], CIFAR-100, SVHN [51]) and model architectures (ResNet [27], WideResNet [78], VGG [65], MobileNetV2 [62]), we find that our method can further enhance the state-of-the-art adversarial training methods on both adversarial robustness and clean accuracy, consistently across the datasets and the model architectures. Overall, this paper makes the following contributions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 545, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 58, + 545, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 545, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 58, + 545, + 287, + 605 + ], + "type": "text", + "content": "- We conduct a pilot study of the trade-off between adversarial robustness and clean accuracy with randomized weights, and offer a new insight on the smoothed weights update and the flat minima during adversarial training (Sec. 3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "type": "text", + "content": "- We propose a novel adversarial training method under a randomized model to smooth the weights. The key enabler is the Taylor series expansion (in Sec. 4) of the robustness loss function over randomized weights (deterministic weights with random noise), so that the optimization can be simultaneously done over the zeroth, first, and second orders of Taylor series. In doing so, the proposed method can effectively enhance adversarial robustness without a significant compromise" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 247, + 402, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 247, + 402, + 258 + ], + "spans": [ + { + "bbox": [ + 325, + 247, + 402, + 258 + ], + "type": "text", + "content": "on clean accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 258, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 258, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 317, + 258, + 545, + 305 + ], + "type": "text", + "content": "- An extensive set of empirical results are provided to demonstrate that our method can improve both robustness and clean accuracy consistently across different datasets and different network architectures (Sec. 5)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 316, + 390, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 390, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 390, + 328 + ], + "type": "text", + "content": "2. Preliminaries" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": "Basic Notation. Consider the classification task with the training set " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "S = \\{\\mathbf{s}_1,\\dots ,\\mathbf{s}_m\\}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " samples are drawn from the data distribution " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": ". For notational convenience, we omit the label " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " of sample " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": ". The adversarial example " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{s}'" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " is generally not in the natural dataset " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{s}' - \\mathbf{s}\\|_p \\leq \\epsilon" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_p" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " is by default the " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": "-norm. Let " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\cdot)" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " be a learning model parameterized by " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": " is the vectorization of weight matrix " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": ". 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Define " + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\mathbf{w}}(\\mathcal{S}), \\mathcal{Y}) \\coloneqq \\mathbb{E}_{\\mathbf{s} \\in \\mathcal{S}}[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}), y)]" + }, + { + "bbox": [ + 305, + 335, + 545, + 456 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 456, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 479 + ], + "type": "text", + "content": "Vanilla Adversarial Training. Adversarial training can be formulated as a minimax optimization problem [45]" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 480, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 480, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 340, + 480, + 545, + 503 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w}} \\left\\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\max _ {\\mathbf {s} ^ {\\prime}: \\| \\mathbf {s} ^ {\\prime} - \\mathbf {s} \\| _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w}} \\left(\\mathbf {s} ^ {\\prime}\\right), y\\right) \\right] \\right\\}, \\tag {1}", + "image_path": "f0fa1ef038935d0d07e41c6db30065fb3fac49cdf5f37e9774649862df98a1ec.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{s}'" + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": " is an adversarial example causing the largest loss within an " + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": "-ball centered at a clean example " + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 506, + 545, + 564 + ], + "type": "text", + "content": " with respect to a norm distance. Adversarial training aims to learn a model with the loss of adversarial examples minimized, without caring about the loss of the clean examples." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 564, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 609 + ], + "type": "text", + "content": "TRADES-like Adversarial Training. Advanced adversarial training methods, such as TRADES [80], strike a trade-off between clean accuracy and adversarial robustness, by optimizing the following problem" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 614, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 614, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 614, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w}} \\Big \\{\\underset {\\mathbf {s} \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), y) + \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} (f _ {\\mathbf {w}} (\\mathbf {s}), f _ {\\mathbf {w}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right] \\Big \\},", + "image_path": "3f01acb50e36de3c16e831e11e5f8deb37dbe209f2d1a6f419b9690ddd6a2c17.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "where the first term contributes to clean accuracy, and the second term with hyperparameter " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " can be seen as a regularization for adversarial robustness that balances the outputs of clean and adversarial examples." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Nevertheless, each adversarial example " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{s}'" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " is generated from a clean example " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " based on a specific weight " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16448" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 70, + 492, + 247 + ], + "blocks": [ + { + "bbox": [ + 95, + 70, + 492, + 247 + ], + "lines": [ + { + "bbox": [ + 95, + 70, + 492, + 247 + ], + "spans": [ + { + "bbox": [ + 95, + 70, + 492, + 247 + ], + "type": "image", + "image_path": "3db41d602e62f5c04d90811c33897fcd840ef059e40cc5f314795b4810c63014.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": "Figure 2. Comparison of loss landscapes of TRADES trained model (the first row) and " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{TRADES} + 1_{st} + 2_{nd}" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " (our method, the second row) trained model. Loss plots in each column are generated from the same original image randomly chosen from the CIFAR-10 test dataset. Following the settings in [20], the " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " axis represents the loss, the " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " axes represent the magnitude of the perturbation added in the directions of " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}\\nabla_{\\mathbf{s}}f(\\mathbf{s})" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " and Rademacher(0.5) respectively. We provide more empirical results in Appendix A." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "content": "the weight " + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "content": " is obtained by optimizing both clean and adversarial data with SGD. This is a chick-and-egg problem. A not-very-well-trained model " + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "content": " may generate some misleading adversarial data samples, which in turn drive the training process away from the optimum." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 288, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 458 + ], + "type": "text", + "content": "Inspired by the idea of model smoothing, we believe that the introduction of noise term into the training process may smooth the update of weights and thus robustify the models. To elaborate on this, we introduce our method from the perspective of flatness of loss landscape in Sec. 3. This is followed by a formalization in Sec. 4, where a noise term is injected to network weight " + }, + { + "bbox": [ + 46, + 361, + 288, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 361, + 288, + 458 + ], + "type": "text", + "content": " during adversarial training to transform deterministic weights into randomized weights." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 468, + 119, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 119, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 119, + 480 + ], + "type": "text", + "content": "3. Motivation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 676 + ], + "type": "text", + "content": "Flatness is commonly thought to be a metric of standard generalization: the loss surface at the final learnt weights for well-generalizing models is generally \"flat\" [18,21,35,52]. Moreover, [73] believed that a flatter adversarial loss landscape reduces the generalization gap in robustness. This aligns with [28], where the authors demonstrated that the local Lipschitz constant can be used to explicitly quantify the robustness of machine learning models. Many empirical defensive approaches, such as hessian/curvature-based regularization [48], gradient magnitude penalty [71], smoothening with random noise [44], or entropy regularization [33], have echoed the flatness performance of a robust model. However, all the above approaches require significant computational or memory resources, and many of them, such as hessian/curvature-based solutions, may suffer from standard accuracy decreases [26]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Stochastic weight averaging (SWA) [32] is known to find solutions that are far flatter than SGD, is incredibly simple to implement, enhances standard generalization, and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 301, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 396 + ], + "type": "text", + "content": "has almost no computational overhead. It was developed to guarantee weight smoothness by simply averaging various checkpoints throughout the training trajectory. SWA has been applied to semi-supervised learning, Bayesian inference, and low-precision training. Especially, [8] used SWA for the first time in adversarial training in order to smooth the weights and locate flatter minima, and showed that it enhances the adversarial generalization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "text", + "content": "Different from SWA, we propose a novel method (with details provided in Sec. 4) via Taylor expansion of a small Gaussian noise to smooth the update of weights. This method regards the TRADES [80], a state-of-the-art adversarial training method, as a special case with only zero-th term, and is able to locate flatter minima. To demonstrate the latter, we visualize the loss landscape with respect to both input and weight spaces. As shown in Fig. 2, compared to the TRADES, our method significantly flattens the rugged landscape. In addition, it is worth noting that our empirical results (in Sec. 5) demonstrate that our method can further improve not only clean accuracy but also adversarial accuracy compared with other SOTA (includes SWA from [8])." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 573, + 389, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 389, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 389, + 586 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": "Given a deterministic model of weight " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": ", we consider an additive small Gaussian noise " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": " to smooth " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": ". Based on TRADES [80], we propose that the robust optimization problem can be further enhanced by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 641, + 545, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 641, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 312, + 641, + 545, + 686 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), y\\right)\\right) \\right. \\tag {2} \\\\ \\left. + \\mathbb {E} _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathrm {K L} (f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}) | | f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})) / \\lambda \\right], \\\\ \\end{array}", + "image_path": "88fd3dbb988680f4a91e588ce7d4069471baa1499ebf17c9c153cf22fefc406b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where the first term contributes to clean accuracy, and the second term with hyperparameter " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " can be seen as a regu" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16449" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 52, + 86, + 542, + 352 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 288, + 84 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 288, + 84 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 288, + 84 + ], + "type": "text", + "content": "Algorithm 1 Adversarial training with randomized weights" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "lines": [ + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "spans": [ + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": "Input: minibatch " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i = 1}^n" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , network architecture parametrized by w, learning rate " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\eta_{l}" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , step size " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\eta_{s}" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , hyper-parameters " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " zero mean Gaussian u, number of iterations " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " in inner optimization. \nOutput: Robust network " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " \nRandomly initialize network " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{w}}" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , or initialize network with pre-trained configuration \nrepeat Generate adversarial examples: Sample u from u for " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " to n do " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i^\\prime \\gets \\mathbf{s}_i + 0.001\\cdot \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " do " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i^\\prime \\leftarrow \\Pi (\\eta_s\\mathrm{sign}(\\nabla_{\\mathbf{s}_i^\\prime}\\mathcal{L}(f_{\\mathbf{w} + u}(\\mathbf{s}_i),f_{\\mathbf{w} + u}(\\mathbf{s}_i^\\prime))) + \\mathbf{s}_i^\\prime)" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , subject to " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "||\\mathbf{s}_i - \\mathbf{s}_i^\\prime ||_p\\leq \\epsilon" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " , where II is the projection operator. end for end for Optimization: w " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " w- " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "\\eta_l\\frac{1}{n}\\sum_{i = 1}^{n}\\nabla_{\\mathbf{w}}\\Big[\\mathcal{L}(f_{\\mathbf{w}}(\\mathbf{s}_i),y_i)" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " (zeroth term) " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "+L(g_{\\mathbf{s}_i}(\\mathbf{w}),g_{\\mathbf{s}_i'}(\\mathbf{w})) / \\lambda" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " (first term) " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "+ \\eta \\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( g _ { \\textup { s } _ { i } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } , g _ { \\textup { s } _ { i } ^ { \\prime } } ^ { \\prime } ( \\mathbf { w } ) ^ { T } \\mathbf { u } ) \\big )" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " (second term) " + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "inline_equation", + "content": "+ \\frac {\\eta}{2}\\mathbb { E } _ { \\textup { u } } \\big ( \\mathcal { L } ( \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } , \\mathbf { u } ^ { T } g _ { \\textup { s } _ { i } ^ { \\prime \\prime } } ^ { \\prime \\prime } ( \\mathbf { w } ) \\mathbf { u } ) \\big ) ]" + }, + { + "bbox": [ + 52, + 86, + 542, + 352 + ], + "type": "text", + "content": " where various optimization methods can be applied: zeroth term optimization (TRADES), zeroth + first terms opti- mization and zeroth + first + second terms optimization. until training converged" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "text", + "content": "larization for adversarial robustness with weights " + }, + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "text", + "content": " and a small Gaussian noise " + }, + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 372, + 287, + 395 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "text", + "content": "Following [17, 35], we let the Gaussian " + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "text", + "content": " be small enough to maintain the generalization performance on clean data. Then, we can extend Eq. (2) by replacing " + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(\\cdot ||\\cdot)" + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "text", + "content": " with a multi-class calibrated loss " + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 396, + 287, + 445 + ], + "type": "text", + "content": " [80]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 449, + 287, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 449, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 56, + 449, + 287, + 495 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} \\underset {\\mathbf {w}} {\\min } & \\mathbb {E} _ {\\mathbf {u}} \\left[ \\mathbb {E} _ {\\mathbf {s}} \\left(\\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right)\\right) \\right. \\\\ & \\left. + \\mathbb {E} _ {\\mathbf {s}} \\max _ {\\mathbf {s} ^ {\\prime}: | | \\mathbf {s} ^ {\\prime} - \\mathbf {s} | | _ {p} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\end{array} \\tag {3}", + "image_path": "37f43f95d488ab0e57b07001f11511b13efe5c569e06e88c5cccab1f90da300f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 499, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 558 + ], + "type": "text", + "content": "As the minimax optimization is entangled with expectation of randomized weights, it is challenging to solve such optimization problem directly. Instead, we propose to solve this problem in an alternating manner between the inner maximization and outer minimization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "text", + "content": "For the inner maximization, with a given model weight " + }, + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "text", + "content": ", we solve it by adopting the commonly used gradient-based approach (e.g., PGD) to generate the adversarial perturbation. That is, at the " + }, + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 559, + 287, + 619 + ], + "type": "text", + "content": "-th iteration, the adversarial perturbation is produced iteratively by letting" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 623, + 287, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 623, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 55, + 623, + 287, + 653 + ], + "type": "interline_equation", + "content": "\\mathbf {s} _ {t + 1} ^ {\\prime} \\leftarrow \\Pi \\left(\\mathbf {s} _ {t} ^ {\\prime} + \\eta_ {s} \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {s} _ {t} ^ {\\prime}} \\mathcal {L} \\left(f _ {\\mathbf {w} + u} (\\mathbf {s}), f _ {\\mathbf {w} + u} \\left(\\mathbf {s} _ {t} ^ {\\prime}\\right)\\right)\\right)\\right) \\tag {4}", + "image_path": "d199e770514eb0e6612ba2ad48e74a0413afb049883f68595ff08d804086155f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "until the maximum allowed iterations are reached, where " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " is the projection operator, " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\eta_{s}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " is the step size and " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " is a sample of " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ". To reduce complexity, we only use one sample " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " to generate adversarial example for each minibatch. Nevertheless, sufficient samples of " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " can still be produced in one" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "content": "epoch as there are many minibatches. As Fig. 1 shows, the adversarial example is generated by one model (boundary), then the optimization with randomized weights in multiple directions can be executed through the following minimization method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 432, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 545, + 468 + ], + "type": "text", + "content": "For the outer minimization, when the optimal perturbed sample " + }, + { + "bbox": [ + 304, + 432, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{s}'" + }, + { + "bbox": [ + 304, + 432, + 545, + 468 + ], + "type": "text", + "content": " is generated by the inner maximization, we solve the following problem" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 472, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 472, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 313, + 472, + 545, + 503 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w}} \\mathbb {E} _ {\\mathbf {s}} \\left[ \\mathcal {L} \\left(f _ {\\mathbf {w}} (\\mathbf {s}), y\\right) + \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} \\left(\\mathbf {s} ^ {\\prime}\\right)\\right) / \\lambda \\right]. \\tag {5}", + "image_path": "70ede7387b12341ff9852cb3701cf96370dd3b3d9b620ad172c34074883a4c59.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "text", + "content": "This optimization problem is challenging due to the entanglement between the deterministic weight " + }, + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "text", + "content": " and the random perturbation " + }, + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 304, + 505, + 545, + 550 + ], + "type": "text", + "content": ", which makes gradient updating much involved." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "text", + "content": "To resolve this issue, we decompose the two components in such a way that gradient updating and model averaging can be done separately. Let " + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}) = g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u})" + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "text", + "content": ", by Taylor expansion of " + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "inline_equation", + "content": "g_{\\mathbf{s}}(\\mathbf{w} + \\mathbf{u})" + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 552, + 545, + 601 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 605, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 605, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 321, + 605, + 545, + 644 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} g _ {\\mathbf {s}} (\\mathbf {w} + \\mathbf {u}) = g _ {\\mathbf {s}} (\\mathbf {w}) + g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u} + \\mathbf {u} ^ {T} \\frac {g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w})}{2 !} \\mathbf {u} \\tag {6} \\\\ + \\mathcal {O} _ {\\mathbf {s}} (| | \\mathbf {u} | | ^ {2}), \\\\ \\end{array}", + "image_path": "ad2edf23a83b6af53611db5b4d3703e91bac30a4dfd540edc3fd2628722a2731.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathbf{s}}^{\\prime}(\\mathbf{w}) = \\frac{\\partial g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}}\\in \\mathbb{R}^{d\\times 1}" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathbf{s}}^{\\prime \\prime}(\\mathbf{w}) = \\frac{\\partial^{2}g_{\\mathbf{s}}(\\mathbf{w})}{\\partial\\mathbf{w}\\partial\\mathbf{w}}\\in" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{d\\times d}" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": " are the first and second derivative of the function " + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{s}}(\\mathbf{w})" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": " versus the weight w, respectively, and " + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{\\mathbf{s}}(||\\mathbf{u}||^{2})" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": " tends to be zero with respect to " + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "inline_equation", + "content": "||\\mathbf{u}||^2" + }, + { + "bbox": [ + 304, + 650, + 545, + 713 + ], + "type": "text", + "content": " . By such approximation, the gradient computation will be solely done on the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16450" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "deterministic part " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": ", and model smoothing with averaged random variable " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is done independently." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": "The intuition behind is the following. For the randomized model " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{w} + \\mathbf{u}" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": " with a specific input " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": ", the Taylor approximation explicitly takes into account the deterministic model " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "g_{\\mathbf{s}}(\\mathbf{w})" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": ", the projection of its gradient onto the random direction " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "g_{\\mathbf{s}}^{\\prime}(\\mathbf{w})^{T}\\mathbf{u}" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": ", and the projection of its curvature onto the subspace spanned by " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{u}^{T}\\frac{g_{\\mathbf{s}}^{\\prime\\prime}(\\mathbf{w})}{2!}\\mathbf{u}" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": ", capturing higher-order information of the loss function with respect to " + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 96, + 286, + 182 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 287, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 218 + ], + "type": "text", + "content": "To further simplify the computation, we minimize an upper bound of Eq. (5) instead. Due to the local convexity of loss landscape, by Jensen's inequality, we conclude that" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 95, + 224, + 287, + 249 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 224, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 95, + 224, + 287, + 249 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\sum_ {i} x _ {i}, \\sum_ {i} y _ {i}\\right) \\leq \\sum_ {i} \\mathcal {L} \\left(x _ {i}, y _ {i}\\right). \\tag {7}", + "image_path": "1f23ea2d51d41bdf1ce6869ca4a3d376ebbe98eb4a06774e62ca98771516a574.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 254, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 277 + ], + "type": "text", + "content": "Therefore, the second term in Eq. (5) can be upper bounded by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 278, + 287, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 278, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 59, + 278, + 287, + 342 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\mathbf {u}} \\mathcal {L} \\left(f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s}), f _ {\\mathbf {w} + \\mathbf {u}} (\\mathbf {s} ^ {\\prime})\\right) \\\\ \\leq \\mathcal {L} \\left(g _ {\\mathbf {s}} (\\mathbf {w}), g _ {\\mathbf {s} ^ {\\prime}} (\\mathbf {w})\\right) + \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(g _ {\\mathbf {s}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}, g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime} (\\mathbf {w}) ^ {T} \\mathbf {u}\\right)\\right) \\\\ + \\frac {1}{2} \\mathbb {E} _ {\\mathbf {u}} \\left(\\mathcal {L} \\left(\\mathbf {u} ^ {T} g _ {\\mathbf {s}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}, \\mathbf {u} ^ {T} g _ {\\mathbf {s} ^ {\\prime}} ^ {\\prime \\prime} (\\mathbf {w}) \\mathbf {u}\\right)\\right), \\tag {8} \\\\ \\end{array}", + "image_path": "d16226771f226edb776a1ec36a8dc1d2789be45904e8dd625ddbb8d18d971e0c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 342, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 413 + ], + "type": "text", + "content": "where the terms on the right-hand side are referred to as the zeroth, first, and second order Taylor expressions. Instead of minimizing Eq. (5) directly, we minimize the upper bound in Eq. (8), which is easier to compute in practical models. Details of the optimization are given in Appendix D." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 415, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 521 + ], + "type": "text", + "content": "The pseudo-code of the proposed adversarial training method is presented in Algorithm 1. Note that the zeroth term optimization in Algorithm 1 is almost the same as TRADES [80], thus we use TRADES and AWP-TRADES [74] as (zeroth term optimization) baselines in our experiments in Sec. 5, and verify how much first and second terms optimization can improve. Note that we perform both AWP and our method through applying randomized weight perturbations on AWP updated weights." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": "For all of our experiments, we limit the noise variance of " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " to be small enough [17, 35] to maintain the training, e.g., " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\sigma = 0.01" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": ". For the zeroth term hyper-parameter " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "1 / \\lambda" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " in Algorithm 1, we set " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "1 / \\lambda = 6" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " for all of our experiments, which is a widely-used setting for TRADES [53, 74, 80]. The number of inner optimization iterations " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " is set to 10 as usual. To make our method more flexible, we set " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\frac{\\eta}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " as the first term and second term hyper-parameters, respectively, and analyze the sensitivity of " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " in Sec. 5.1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "The main novelty of our proposed method is two-fold: (1) Instead of considering a single model with a deterministic weight " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": ", we consider a model ensemble with " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w} + \\mathbf{u}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " to smooth the update of weights. By averaging these models during adversarial training, we come up with a robust model with smoothed classification boundary tolerant to potential adversarial weight perturbation. (2) When averaging" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "over the ensemble of randomized models during training, we disentangle gradient from random weight perturbation so that the gradient updating can be computed efficiently. In particular, we apply Taylor expansion at the mean weight " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " (i.e., the deterministic component) and approximate the cross-entropy loss function with the zeroth, first, and second Taylor terms. In doing so, the deterministic and statistical components of " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{w} + \\mathbf{u}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " can be decomposed and then computed independently." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 190, + 409, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 409, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 409, + 205 + ], + "type": "text", + "content": "5. Empirical results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "content": "In this section, we first discuss the hyper-parameter sensitivity of our method, and then evaluate the robustness on benchmark datasets against various white-box, black-box attacks and Auto Attack with " + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "content": " threat models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": "Adversarial Training Setting. We train PreAct ResNet-18 [27] for " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " threat models on CIFAR-10/100 [40] and SVHN [51]. In addition, we also train WideResNet-34-10 [78] for CIFAR-10/100, VGG16 and MobileNetV2 for CIFAR-10, with " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " threat model. We adopt the widely used adversarial training setting [60]: for the " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " threat model, " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\epsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " and step size " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "2 / 255" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": "; for the " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " threat model, " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\epsilon = 128 / 255" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " and step size " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "15 / 255" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": ". For normal adversarial training, the training examples are generated with 10 steps. All models (except SVHN) are trained for 200 epochs using SGD with momentum 0.9, batchsize 128, weight decay " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "5\\times 10^{-4}" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": ", and an initial learning rate of 0.1 that is divided by 10 at the 100th and 150th epochs. Except for setting the starting learning rate to 0.01 for SVHN, we utilize the same other settings. Simple data augmentations are used, such as " + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "32\\times 32" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": " random crop with 4-pixel padding and random horizontal flip. We report the highest robustness that ever achieved at different checkpoints for each dataset and report the clean accuracy on the model which gets the highest PGD-20 accuracy. We omit the standard deviations of 3 runs as they are very small (" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "inline_equation", + "content": "< 0.40\\%" + }, + { + "bbox": [ + 304, + 259, + 545, + 521 + ], + "type": "text", + "content": ") and implement all models on NVIDIA A100." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Evaluation Setting. We evaluate the robustness with white-box attacks, black-box attacks and auto attack. For white-box attacks, we adopt PGD-20 [45] and CW-20 [4] (the " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " version of CW loss optimized by PGD-20) to evaluate trained models. For black-box attacks, we generate adversarial perturbations by attacking a surrogate normal adversarial training model (with same setting) [55], and then apply these adversarial examples to the defense model and evaluate the performances. The attacking methods for black-box attacks we have used are PGD-20 and CW-20. For Auto Attack (AA) [10], one of the strongest attack methods, we adopt it through a mixture of different parameter-free attacks which include three white-box attacks (APGD-CE [10], APGD-DLR [10], and FAB [9]) and one black-box attack (Square Attack [2]). We provide more details about the experimental setups in Appendix B." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16451" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 105, + 515, + 183 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "type": "text", + "content": "Table 1. First and Second Derivative terms optimization on CIFAR-10 with " + }, + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "type": "text", + "content": " threat model for PreAct ResNet18. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack with different hyper-parameters " + }, + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "type": "inline_equation", + "content": "\\eta = 0.05, 0.1, 0.2, 0.3, 0.4" + }, + { + "bbox": [ + 46, + 70, + 545, + 103 + ], + "type": "text", + "content": ". We highlight the best results in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 105, + 515, + 183 + ], + "lines": [ + { + "bbox": [ + 77, + 105, + 515, + 183 + ], + "spans": [ + { + "bbox": [ + 77, + 105, + 515, + 183 + ], + "type": "table", + "html": "
MethodCleanPGD-20CW-20AAMethodCleanPGD-20CW-20AA
1st(0.05)83.1953.9852.1248.21st+2nd(0.05)83.2554.0751.9348.4
1st(0.1)82.8654.2952.2449.31st+2nd(0.1)83.4754.4252.2849.7
1st(0.2)83.5554.8652.6548.81st+2nd(0.2)84.1354.9152.5350.3
1st(0.3)83.9655.0552.5449.71st+2nd(0.3)84.2754.3651.8048.9
1st(0.4)83.9354.6552.2348.61st+2nd(0.4)84.1454.3851.5649.6
", + "image_path": "0a2543801b8305233831ffdfd055c3b65b0f3392a19fc082854a60f954c8cac9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 85, + 220, + 507, + 491 + ], + "blocks": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": "Table 2. First and Second Derivative terms optimization on CIFAR-10/CIFAR-100 with " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " threat model for WideResNet, compared with current state-of-the-art. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack ( " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.031" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": ") and Auto Attack " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "(\\epsilon = 8/255)" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": ". The results of our methods are in **bold**. Note that * is under PGD-40 attack and ** is under PGD-10 attack." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 220, + 507, + 491 + ], + "lines": [ + { + "bbox": [ + 85, + 220, + 507, + 491 + ], + "spans": [ + { + "bbox": [ + 85, + 220, + 507, + 491 + ], + "type": "table", + "html": "
DatasetMethodArchitectureCleanPGD-20CW-20AA
CIFAR-10 ℓ∞Lee et al. (2020) [42]WRN-34-1092.5659.7554.5339.70
Wang et al. (2020) [72]WRN-34-1083.5158.3154.3351.10
Rice et al. (2020) [60]WRN-34-2085.34--53.42
Zhang et al. (2020) [81]WRN-34-1084.52--53.51
Pang et al. (2021) [54]WRN-34-2086.4357.91**-54.39
Jin et al. (2022) [36]WRN-34-2086.0161.1257.9355.90
Gowal et al. (2020) [24]WRN-70-1685.2958.22*-57.20
Zhang et al. (2019) [80] (0th)WRN-34-1084.6556.6854.4953.0
+ Ours (1st)WRN-34-1085.5158.3456.0654.0
+ Ours (1st+2nd)WRN-34-1085.9858.4756.1354.2
Wu et al. (2020) [74] (0th)WRN-34-1085.1759.6457.3356.2
+ Ours (1st)WRN-34-1086.1061.4758.0957.1
+ Ours (1st+2nd)WRN-34-1086.1261.4558.2257.4
CIFAR-100 ℓ∞Cui et al. (2021) [11]WRN-34-1060.4335.5031.5029.34
Gowal et al. (2020) [24]WRN-70-1660.8631.47*-30.03
Zhang et al. (2019) [80] (0th)WRN-34-1060.2232.1128.9326.9
+ Ours (1st)WRN-34-1063.0133.2629.4428.1
+ Ours (1st+2nd)WRN-34-1062.9333.3629.6127.9
Wu et al. (2020) [74] (0th)WRN-34-1060.3834.0930.7828.6
+ Ours (1st)WRN-34-1063.9835.3631.6329.8
+ Ours (1st+2nd)WRN-34-1064.7135.7331.4130.2
", + "image_path": "03644a382a8861f49a3c68a9c251af92c2cb5deabbcf6f1300eea0d094fc6880.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 212, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 212, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 212, + 516 + ], + "type": "text", + "content": "5.1. Sensitivity of hyper-parameter" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": "In our proposed algorithm, the regularization hyperparameter " + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": " is crucial. We use numerical experiments on CIFAR-10 with PreAct ResNet-18 to illustrate how the regularization hyper-parameter influences the performance of our robust classifiers. To develop robust classifiers for multi-class tasks, we use the gradient descent update formula in Algorithm 1, with " + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": " as the cross-entropy loss. Note that, for the zeroth term hyper-parameter " + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "inline_equation", + "content": "1 / \\lambda" + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": " in Algorithm 1, we set " + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "inline_equation", + "content": "1 / \\lambda = 6" + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": " for all of our experiments, which is a widely used setting for TRADES. We train the models with " + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\eta = 0.05" + }, + { + "bbox": [ + 46, + 521, + 287, + 664 + ], + "type": "text", + "content": ", 0.1, 0.2, 0.3, 0.4 respectively. All models are trained with 200 epochs and 128 batchsize." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "In Tab. 1, we observe that as the regularization parameter " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " increases, the clean accuracy and robust accuracy almost both go up first and then down. In particular, the accuracy under Auto Attack is sensitive to the regularization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": "hyper-parameter " + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": ". Considering both robustness accuracy and clean accuracy, it is not difficult to find that " + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\eta = 0.3" + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": " is the best for first term optimization and " + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\eta = 0.2" + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": " is the best for first + second terms optimization. Thus in the following experiments, we set " + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\eta = 0.3" + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": " for first term optimization and " + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\eta = 0.2" + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": " for first + second terms optimization as default." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 585, + 516, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 585, + 516, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 585, + 516, + 598 + ], + "type": "text", + "content": "5.2. Comparison with SOTA on WideResNet" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "In Tab. 2, we compare our method with state-of-the-art on WideResNet with CIFAR-10 and CIFAR-100. For zeroth term optimization, we use TRADES [80] and AWPTRADES [74] as baselines with " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "1 / \\lambda = 6" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": ". We also report other state-of-the-art, include AVMixup [42], MART [72], [60], [81], [54], TRADES+LBGAT [11] and [24]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "The results in Tab. 2 demonstrate that our method can both improve clean accuracy and robustness accuracy consistently over different datasets and models. Especially for" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16452" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 95, + 528, + 148 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "type": "text", + "content": "Table 3. Adversarial training across datasets on PreAct ResNet18 with " + }, + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "type": "inline_equation", + "content": "{\\ell }_{2}" + }, + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "type": "text", + "content": " threat model. Classification accuracy (%) on clean images and under PGD-20 attack and Auto Attack. The results of our methods are in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 95, + 528, + 148 + ], + "lines": [ + { + "bbox": [ + 63, + 95, + 528, + 148 + ], + "spans": [ + { + "bbox": [ + 63, + 95, + 528, + 148 + ], + "type": "table", + "html": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDAACleanPGDAACleanPGDAA
Wu et al. (2020) [74](0th)87.0572.0871.662.8745.1141.892.8672.4563.8
+ Ours (1st+2nd)88.4172.8572.065.5946.8842.493.9873.0764.5
", + "image_path": "5faed2e2605f873a29fbc81f9fc07d44da7f6dd7da8966ea499441867cb93032.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 56, + 186, + 535, + 240 + ], + "blocks": [ + { + "bbox": [ + 46, + 151, + 547, + 184 + ], + "lines": [ + { + "bbox": [ + 46, + 151, + 547, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 151, + 547, + 184 + ], + "type": "text", + "content": "Table 4. Adversarial training across datasets on PreAct ResNet18 with " + }, + { + "bbox": [ + 46, + 151, + 547, + 184 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 151, + 547, + 184 + ], + "type": "text", + "content": " threat model. Classification accuracy (%) on clean images and black-box attacks. Black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. The results of our methods are in bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 186, + 535, + 240 + ], + "lines": [ + { + "bbox": [ + 56, + 186, + 535, + 240 + ], + "spans": [ + { + "bbox": [ + 56, + 186, + 535, + 240 + ], + "type": "table", + "html": "
MethodCIFAR-10CIFAR-100SVHN
CleanPGDCWCleanPGDCWCleanPGDCW
Wu et al. (2020) [74](0th)82.7861.7959.4258.3338.5536.7093.7763.8059.54
+ Ours (1st+2nd)84.2762.5660.5861.0839.8237.8495.1166.1663.59
", + "image_path": "6ef290fbaf300bbc0409f168844b006bc9d93008a2c921aefa9756d30a33ccfe.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 60, + 269, + 531, + 348 + ], + "blocks": [ + { + "bbox": [ + 46, + 243, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 545, + 266 + ], + "type": "text", + "content": "Table 5. Adversarial training across VGG16, MobileNetV2 on CIFAR-10 with " + }, + { + "bbox": [ + 46, + 243, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 243, + 545, + 266 + ], + "type": "text", + "content": " threat model. Classification accuracy (%) on clean images and under PGD-20 attack, CW-20 attack and Auto Attack. The results of our methods are in bold." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 269, + 531, + 348 + ], + "lines": [ + { + "bbox": [ + 60, + 269, + 531, + 348 + ], + "spans": [ + { + "bbox": [ + 60, + 269, + 531, + 348 + ], + "type": "table", + "html": "
MethodVGG16MobileNetV2
CleanPGD-20CW-20AACleanPGD-20CW-20AA
Zhang et al. (2019) [80] (0th)79.7849.8846.9544.379.7351.4148.4346.4
+ Ours (1st+2nd)80.9950.1347.0944.481.8653.3449.9347.8
Wu et al. (2020) [74] (0th)78.4651.1947.4146.379.8653.5650.1147.7
+ Ours (1st+2nd)80.3152.7148.3846.581.9555.3751.5549.4
", + "image_path": "67c3a747cd7565ffbdba38591dbc81c21bc62fdc4342f4a8cbb56374dc4ae4a4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 49, + 401, + 286, + 456 + ], + "blocks": [ + { + "bbox": [ + 46, + 355, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 399 + ], + "type": "text", + "content": "Table 6. Time consumption and GPU memory usage for WideRes-Net on CIFAR-10 with " + }, + { + "bbox": [ + 46, + 355, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 355, + 287, + 399 + ], + "type": "text", + "content": " threat model. We deploy each model on a single NVIDIA A100 with batchsize 128. The results of our methods are in bold." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 401, + 286, + 456 + ], + "lines": [ + { + "bbox": [ + 49, + 401, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 49, + 401, + 286, + 456 + ], + "type": "table", + "html": "
MethodWideResNet-34-10
Time/EpochGPU Memory
Zhang et al. (2019) [80] (0th)1666s12875MB
+ Ours (1st)2161s20629MB
+ Ours (1st+2nd)2362s26409MB
", + "image_path": "518b6e1cbc5039fcd7c5600832588ed2efd53c8a297fd19b4e3f6760a0cedd63.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "text", + "content": "Auto Attack, our method can get " + }, + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "inline_equation", + "content": "57.4\\%" + }, + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "text", + "content": " on CIFAR-10 and " + }, + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "inline_equation", + "content": "30.2\\%" + }, + { + "bbox": [ + 46, + 468, + 287, + 504 + ], + "type": "text", + "content": " on CIFAR-100 with WRN-34-10, even surpass the performance of WRN-70-16 from [24]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 513, + 179, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 179, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 179, + 526 + ], + "type": "text", + "content": "5.3. Other empirical results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "text", + "content": "Adversarial training with " + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "text", + "content": " threat model. For the experiments with " + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "text", + "content": " threat model on CIFAR-10, CIFAR-100 and SVHN in Tab. 3, the results still support that our method can enhance the performance under clean data, PGD-20 attack and Auto Attack. For CIFAR-100, it can even increase about " + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 532, + 287, + 604 + ], + "type": "text", + "content": " on clean accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 700 + ], + "type": "text", + "content": "Robustness under black-box attacks. We train PreAct ResNet18 for " + }, + { + "bbox": [ + 46, + 605, + 288, + 700 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 605, + 288, + 700 + ], + "type": "text", + "content": " threat model on CIFAR-10, CIFAR-100 and SVHN. The black-box adversarial examples are generated by a surrogate normal adversarial training model (of same setting) with PGD-20 attack and CW-20 attack. Tab. 4 shows our method is also effective under black-box attacks. For SVHN, ours can even obtain a significant improvement over the existing ones." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "type": "text", + "content": "Robustness on other architectures. We train VGG16" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "text", + "content": "and MobileNetV2 for " + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "text", + "content": " threat model on CIFAR-10. Our results in Tab. 5 show a comprehensive improvement under clean data and robustness accuracy. Particularly, for MobileNetV2, ours can achieve an improvement greater than " + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 357, + 545, + 417 + ], + "type": "text", + "content": " under Auto Attack and clean data, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": "Comparison with SWA from [8]. The best PGD-20 accuracy and AA accuracy on CIFAR-10 for ResNet-18 from [8] are " + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "inline_equation", + "content": "52.14\\%" + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "inline_equation", + "content": "49.44\\%" + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": " respectively, whereas ours are " + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "inline_equation", + "content": "55.13\\%" + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "inline_equation", + "content": "50.8\\%" + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": " in Tab. 1 (with " + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "inline_equation", + "content": "1_{st} + 2_{nd}" + }, + { + "bbox": [ + 304, + 418, + 545, + 465 + ], + "type": "text", + "content": " (0.2))." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 466, + 514, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 466, + 514, + 479 + ], + "spans": [ + { + "bbox": [ + 317, + 466, + 514, + 479 + ], + "type": "text", + "content": "More empirical results are given in Appendix E." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 487, + 463, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 463, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 463, + 499 + ], + "type": "text", + "content": "5.4. Limitations and future work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 506, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 602 + ], + "type": "text", + "content": "We use some approximation methods, e.g., Eq. (8), to reduce the complexity of our adversarial training method. The results in Tab. 6 show that though our method with WideResNet-34-10 can work on a single NVIDIA A100, the growth of training time and GPU memory still cannot be ignored. In the future work, we plan to further reduce the complexity of our algorithm and apply the first and second terms optimization on larger datasets." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 614, + 390, + 626 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 614, + 390, + 626 + ], + "spans": [ + { + "bbox": [ + 306, + 614, + 390, + 626 + ], + "type": "text", + "content": "6. Related work" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 634, + 425, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 425, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 425, + 647 + ], + "type": "text", + "content": "6.1. Adversarial training" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Adversarial training methods can generally be divided into three groups. In the first group, Eq. (1) is translated into an equivalent, (or approximate, expression), which is mainly used to narrow the distance between " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s})" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ". For example, ALP [19, 38] estimates the similar-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16453" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "ity between " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s})" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", and maximizes this similarity in the objective function. MMA [13] proposes each correctly classified instance " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " to leave sufficiently the decision boundary, through making the size of shortest successful perturbation as large as possible. TRADES [80] looks for the adversarial example " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^{\\prime}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " which can obtain the largest KL divergence between " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s})" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w}}(\\mathbf{s}^{\\prime})" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", then trains with these adversarial examples. Besides, [84] adopts the similarity between local distributions of natural and adversarial example, [67] measures the similarity of local distributions with Wasserstein distance, and [15, 16, 46, 54] try to optimize with the distribution over a series of adversarial examples for a single input." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "content": "In the second group, adversarial examples are preprocessed before being used for training rather than being directly generated by attack algorithms. For example, label smoothing [8, 69] replaces the hard label " + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "content": " with the soft label " + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{y}" + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{y}" + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "content": " is a combination of the hard label " + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 228, + 289, + 407 + ], + "type": "text", + "content": " and uniform distribution. A further empirical exploration with of how label smoothing works is provided in [49]. AVMixup [42, 83] defines a virtual sample in the adversarial direction based on these. Through linear interpolation of the virtual sample and the clean sample, it extends the training distribution with soft labels. Instead of smoothing labels, [79] perturbs the local neighborhoods with an unsupervised way to produce adversarial examples. In addition, data augmentation [25, 59] is also shown to be an invaluable aid for adversarial training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 409, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 409, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 409, + 287, + 480 + ], + "type": "text", + "content": "The above two groups merely adjust the component parts of the min-max formalism. With AWP [74], one more maximization is performed to find a weight perturbation based on the generated adversarial examples. The altered weights [12] are then used in the outer minimization function to reduce the loss caused by the adversarial cases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "text", + "content": "Different from previous work, this paper optimizes the distance between " + }, + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s})" + }, + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{w} + \\mathbf{u}}(\\mathbf{s}')" + }, + { + "bbox": [ + 47, + 481, + 287, + 540 + ], + "type": "text", + "content": " through randomized weights, and therefore, effectively, it considers the optimization problem where the decision boundary is smoothed by these randomized models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 551, + 168, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 168, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 168, + 563 + ], + "type": "text", + "content": "6.2. Randomized weights" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "In the previous work to study generalization or robustness, modeling neural network weights as random variables has been frequently used. For example, [50,75] estimate the mutual information between random weights and dataset, provide the expected generalization bound over weight distribution. Another example of random weights is on the PAC-Bayesian framework, a well-known theoretical tool to bound the generalization error of machine learning models [41,47,56,64]. In the recent years, PAC-Bayes is also developed to bound the generalization error or robustness error of deep neural networks [18,21,35,52]. In addition, [23] draws random noise into deterministic weights, to measure" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "the mutual information between input dataset and activations under information bottleneck theory." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "type": "text", + "content": "While we also consider randomized weights, a major difference from previous theoretical works is that randomized weights are applied to robustness, from which we find an insight to design a novel adversarial training method which decomposes objective function (parameterized with randomized weights) with Taylor series." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 175, + 368, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 368, + 186 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 368, + 186 + ], + "type": "text", + "content": "6.3. Flatness" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 194, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 421 + ], + "type": "text", + "content": "The generalization performance of machine learning models is believed to be correlated with the flatness of loss curve [30, 31], especially for deep neural networks [6, 14, 37, 43, 76]. For instance, in pioneering research [30, 31], the minimum description length (MDL) [61] was used to demonstrate that the flatness of the minimum is a reasonable generalization metric to consider. [39] investigated the cause of the decrease in generalization for large-batch networks and demonstrated that large-batch algorithms tend to converge to sharp minima, resulting in worse generalization. [35] undertook a large-scale empirical study and found that flatness-based measurements correlate with generalization more strongly than weight norms and (margin and optimization)-based measures. [22] introduced Sharpness-Aware Minimization (SAM) to locate parameters that lie in neighborhoods with consistently low loss. Moreover, [8] used SWA [32] in adversarial training to smooth the weights and find flatter minima, and showed that this can improve adversarial generalization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 421, + 547, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 493 + ], + "type": "text", + "content": "Different from previous work, this paper uses Taylor expansion of the injected Gaussian to smooth the update of weights and search for flat minima during adversarial training. Our empirical results show the effectiveness of our method to flatten loss landscape and improve both robustness and clean accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 503, + 379, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 379, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 379, + 516 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 523, + 547, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 547, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 547, + 619 + ], + "type": "text", + "content": "This work studies the trade-off between robustness and clean accuracy through the lens of randomized weights. Through empirical analysis of loss landscape, algorithmic design (via Taylor expansion) on training optimization, and extensive experiments, we demonstrate that optimizing over randomized weights can consistently outperform the state-of-the-art adversarial training methods not only in clean accuracy but also in robustness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 625, + 547, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 547, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 547, + 710 + ], + "type": "text", + "content": "Acknowledgment. GJ is supported by the CAS Project for Young Scientists in Basic Research, Grant No.YSBR040. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956123, and is also supported by the U.K. EPSRC through End-to-End Conceptual Guarding of Neural Architectures [EP/T026995/1]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16454" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jonathan Uesato, Po-Sen Huang, Alhussein Fawzi, Robert Stanforth, and Pushmeet Kohli. 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Ren $^{2,3}$ , Shunqing Ren $^{1,\\boxtimes}$ , Harbin Institute of Technology, Harbin, China \n $^{2}$ SenseTime Research and Tetras.AI, Beijing, China \n $^{3}$ Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China", + "bbox": [ + 84, + 178, + 924, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 285, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continuous-time video frame interpolation is a fundamental technique in computer vision for its flexibility in synthesizing motion trajectories and novel video frames at arbitrary intermediate time steps. Yet, how to infer accurate intermediate motion and synthesize high-quality video frames are two critical challenges. In this paper, we present a novel VFI framework with improved treatment for these challenges. To address the former, we propose focalized trajectory fitting, which performs confidence-aware motion trajectory estimation by learning to pay focus to reliable optical flow candidates while suppressing the outliers. The second is range-nullspace synthesis, a novel frame renderer cast as solving an ill-posed problem addressed by learning decoupled components in orthogonal subspaces. The proposed framework sets new records on 7 of 10 public VFI benchmarks.", + "bbox": [ + 73, + 319, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 593, + 209, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continuous-time Video Frame Interpolation (VFI) aims at upsampling the temporal resolution of low frame-rate videos steplessly by synthesizing the missing frames at arbitrary time steps. It is a fundamental technology for various downstream video applications such as streaming [34], stabilization [5], and compression [35].", + "bbox": [ + 75, + 619, + 468, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key challenge of this task is to find a continuous mapping from arbitrary time step to the latent scene motion to correctly render the target frame, observing the low frame-rate video. Typically, it was realized via two stages: motion trajectory fitting and frame synthesis, e.g. [1,3,4,10,13,17, 21,29,36,38,39]. In the former, a parametric trajectory model is fitted from the optical flows extracted from input frames, which can be resampled at any time step to get intermediate motion. For representing such a motion model,", + "bbox": [ + 75, + 712, + 468, + 849 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ecf815a0db0a124efcd9890b3b0e2f50f4f23dbc770c4d6db55d184054461f3f.jpg", + "image_caption": [ + "Figure 1. Motivation of the proposed method. Given input frames and extracted optical flows (a), common VFI pipeline (b) is to fit a continuous motion trajectory model, resample flows at the target time step, based on which rendering rays are predicted to synthesize the intermediate frame by reorganizing pixels from the input frames. Our pipeline (c) proposes improved treatment in two aspects: 1) our focalized motion estimation assigns dynamic weights to the extracted optical flows to suppress the outlier flows and improve fitting accuracy, and the novel range-nullspace solver treats intermediate frame synthesis as an inverse problem instead of direct rendering. Please see text for more details." + ], + "image_footnote": [], + "bbox": [ + 504, + 284, + 890, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the Taylor polynomial is often adopted with different orders [4, 13, 36]. However, fitting trajectory models are prone to optical flow errors, which are inevitable due to occlusion.", + "bbox": [ + 496, + 744, + 892, + 790 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Besides motion fitting, the frame synthesis step faces the challenges of correctly inferring scene geometry. Particularly, the intermediate flows resampled from the continuous motion model only depict partial correspondences between the intermediate frame with input frames, while existing methods predict complete rendering rays in a data-driven manner to facilitate full rendering, as shown in Fig. 1 (b).", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* This work is done during Zhiyang's internship at SenseTime.", + "bbox": [ + 88, + 862, + 423, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Correspondence should be addressed to Yu Zhang (zhangyulb@gmail.com) and Shunqing Ren (renshunqing@hit.edu.cn).", + "bbox": [ + 78, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22159", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Though powerful architectures [15] and rendering mechanisms [10] were proposed, it requires the network to fully encode the scene geometry to predict correct rays, which may raise the difficulty of architecture design and the burden of learning.", + "bbox": [ + 75, + 90, + 467, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome these issues, we propose a novel framework with improved motion fitting and frame synthesis components. As shown in Fig. 1 (c), the first is focalized trajectory fitting, which extracts a set of optical flow candidates from the input video and assigns learned confidence weights to them. Confidence-aware, differentiable trajectory fitting is then followed, focalizing only the confident flows and producing improved parametric motion models. Such models, when resampled at the target time step, can produce accurate flows even at the occlusion boundary. For the latter, we follow the fact that intermediate frame synthesis is an ill-posed task and propose a deep solver based on the range nullspace theory [2]. Our solver decomposes the latent intermediate frame into several orthogonal image components and adopts different networks to learn each of them. Such physics-guided design encourages learning decoupled subtasks for each network, relieving the burden of encoding scene geometry and benefiting the use of lightweight models. In particular, our framework sets new records on 7 out of 10 public VFI benchmarks while being parameter-efficient.", + "bbox": [ + 75, + 167, + 468, + 481 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize the contributions of this paper as follows. 1) A novel lightweight VFI framework is proposed, which refreshes the records of 7 out of 10 public VFI benchmarks. 2) The idea of focalized trajectory fitting, which improves parametric motion estimation in VFI and generates better resampling quality of intermediate flows. 3) A new perspective that treats intermediate frame synthesis as an ill-posed problem, solved with a deep range nullspace solver that decouples frame synthesis into several orthogonal tasks.", + "bbox": [ + 75, + 483, + 467, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 76, + 633, + 220, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video frame interpolation requires estimating the motion of intermediate frames before synthesizing them. Such motion could be directly predicted as image correspondences in a data-driven manner [11, 15], or evaluated from parameterized motion trajectories fitted with optical flows extracted from input frames. Typically the latter one is more flexible to do frame interpolation at any time step. For representing the motion model, linear motion is mostly assumed [1, 3, 10, 13, 21, 29], while quadratic [17, 36, 38, 39] and cubic [4] models were proposed and show improved performance with higher orders of freedom. Frame synthesis was then carried out by warping the information from input frames, guided by the estimated motion. This involves synthesis techniques of backward warping [13, 17, 29, 36] or forward splatting [10, 21], depending on the direction of intermediate flows. High-quality synthesis poses the de", + "bbox": [ + 75, + 659, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mand of reasoning occlusion, which was implemented explicitly with scene depth [1] or implicitly via powerful post-processing architectures [11, 17]. VFI can also be implemented in a highly data-driven manner [14], abstracting out all the above steps with neural networks.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There was also an important track of VFI that only synthesizes the middle frame of a pair of input frames. Without the need of representing motion continuously and interpolating arbitrary time steps, sophisticated components can be designed to optimally fit this task. For example, intermediate frame synthesis was solved with bilateral cost volumes [23], asymmetric bilateral volumes [24], expanded flows [8], and deformable convolutions [7]. There was also kernel-based method [22], with enhanced variants [3,16,27] that introduce more freedom into standard kernels with learned offsets and weights. Recent advances of deep learning architectures, like transformer [28] and channel attention modules [6], are also beneficial.", + "bbox": [ + 496, + 167, + 890, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Range-nullspace learning provides a solver for inverse problems where the forward degeneration is a known linear operator [26]. It finds applications in solving superresolution [2], denoising [33] and compressed sensing [19]. Treating video frame interpolation as an inverse problem was first performed by [39], which developed iterative solvers based on learned gradients under the Bayesian inference framework. In this work, we adapt the range-nullspace theory to VFI and propose a non-iterative solver that learns orthogonally decomposed image components to relieve the entanglement of learned representations.", + "bbox": [ + 496, + 363, + 890, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. The Proposed Framework", + "text_level": 1, + "bbox": [ + 500, + 542, + 743, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 566, + 609, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following the routine of previous works [17, 36, 38, 39], our framework takes 4 adjacent input video frames $\\mathbf{I}_{-1},\\mathbf{I}_0,\\mathbf{I}_1,\\mathbf{I}_2\\in [-1,1]^{H\\times W\\times 3}$ and generates intermediate frame $\\mathbf{I}_t$ for any given time $t\\in (0,1)$ . As shown in Fig. 2, our pipeline starts by extracting appearance features for each input frame with a contextual network $\\mathcal{C}$ :", + "bbox": [ + 496, + 590, + 890, + 679 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {i} = \\mathcal {C} (\\mathbf {I} _ {i}), i \\in \\{- 1, 0, 1, 2 \\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 691, + 890, + 707 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the meantime, optical flows starting from $\\mathbf{I}_0$ , $\\mathbf{I}_1$ to other neighbours are computed. This yields 6 optical flow maps $\\mathbf{F}_{i\\rightarrow j}\\in \\mathbb{R}^{H\\times W\\times 2}$ , where $i\\in \\{0,1\\}$ and $j\\neq i$ .", + "bbox": [ + 496, + 717, + 890, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Focalized Motion Estimation (FME) in Fig. 2 consumes optical flows and contextual features. It consists of three steps: flow confidence estimation, focalized trajectory fitting, motion resampling and refinement, and outputs motion specifications at a given time $t$ . Bi-directional motions are inferred, regarding both time 0 and 1:", + "bbox": [ + 496, + 763, + 890, + 853 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l}\\hat {\\mathbf {F}} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathrm {F M E} (t, \\left\\{\\mathbf {F} _ {0 \\rightarrow j} \\right\\} _ {j \\neq 0}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),\\\\\\hat {\\quad}\\end{array}\\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 864, + 890, + 888 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {1 \\rightarrow t}, \\mathbf {M} _ {1 \\rightarrow t} = \\operatorname {F M E} (1 - t, \\left\\{\\mathbf {F} _ {1 \\rightarrow j} \\right\\} _ {j \\neq 1}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 887, + 849, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22160", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fc0842946a3993d3585174f59ea509007795e798f5df177aee937bfbb8be7baa.jpg", + "image_caption": [ + "Figure 2. Pipeline of our proposed method including contextual feature extraction, flow estimation, focalized motion estimation (FME), and range-nullsapce synthesis (RNS). Detailed descriptions of FME (middle) can be found in Sect. 3.2, and RNS (right) is elaborated in Sect. 3.3. For the details of mathematical symbols, please refer to the text." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 890, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $\\hat{\\mathbf{F}}_{i\\rightarrow t}$ and $\\mathbf{M}_{i\\rightarrow t}$ , $i\\in \\{0,1\\}$ are the resampled flows and occlusion relation masks to be explained in Sect. 3.2. Finally, we feed these motion specifications at time $t$ and contextual features of input frames $\\mathbf{I}_0$ , $\\mathbf{I}_1$ into the Range-Nullspace Synthesis (RNS) module,", + "bbox": [ + 75, + 412, + 468, + 491 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {t} ^ {*} = \\operatorname {R N S} \\left(\\left\\{\\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}, \\mathbf {C} _ {i} \\right\\} _ {i \\in \\{0, 1 \\}}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 500, + 468, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we will elaborate technical details of the proposed FTE and RNS modules.", + "bbox": [ + 76, + 537, + 468, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Focalized Motion Estimation (FME)", + "text_level": 1, + "bbox": [ + 76, + 578, + 390, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the sake of conciseness, only the direction $0 \\to t$ in Eq. (2) is considered here, as $1 \\to t$ follows the similar process. Given contextual features $\\mathbf{C}_i$ and candidate flows $\\{\\mathbf{F}_{0 \\to j}\\}_{j \\neq 0}$ , the confidence estimation step dynamically weights optical flow candidates. To this end, the contextual features $\\mathbf{C}_i$ are half split along the channel dimension, yielding $[\\mathbf{C}_i^a, \\mathbf{C}_i^b]$ , and the confidence estimation only works with the right half $\\mathbf{C}_i^b$ to save calculation and leave the representation ability of remaining features untouched. The following warping residual is computed:", + "bbox": [ + 75, + 602, + 468, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} _ {i} = \\mathbf {C} _ {0} ^ {b} - \\phi_ {\\mathcal {B}} (\\mathbf {C} _ {i} ^ {b}, \\mathbf {F} _ {0 \\rightarrow i}), i \\in \\{- 1, 1, 2 \\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 765, + 468, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi_{\\mathcal{B}}$ represents the bilinear warping function [12] that projects features $\\mathbf{C}_i^b$ to time 0 with backward warping. Intuitively, the residuals $\\mathbf{R}_i$ conveys rich information of appearance warping errors induced by flows. We map such residuals to confidence weights via a network $\\mathcal{W}$ :", + "bbox": [ + 75, + 796, + 468, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} _ {- 1}, \\mathbf {W} _ {1}, \\mathbf {W} _ {2} = \\mathcal {W} (\\mathbf {R} _ {- 1}, \\mathbf {R} _ {1}, \\mathbf {R} _ {2}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 883, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_i\\in (0,1)^{H\\times W\\times 1}$ and $\\sum_{i\\in \\{-1,1,2\\}}\\mathbf{W}_i = 1$ Higher value of $\\mathbf{W}_i$ indicates higher confidence of the flow values in $\\mathbf{F}_{0\\rightarrow i}$ , which deserves more focus for fitting parametric motion trajectory models.", + "bbox": [ + 498, + 410, + 890, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Focalized trajectory fitting. We suppose that, in a short time interval around each pixel of $\\mathbf{I}_0$ , the motion trajectory is approximated with 2nd-order Taylor polynomial:", + "bbox": [ + 498, + 473, + 890, + 518 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\tau ; \\mathbf {A}, \\mathbf {B}) = \\mathbf {A} \\tau^ {2} + \\mathbf {B} \\tau , \\mathbf {A}, \\mathbf {B} \\in \\mathbb {R} ^ {H \\times W \\times 2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 527, + 890, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{A}$ and $\\mathbf{B}$ are model coefficients to fit, and $\\tau \\in [-1,2]$ is the temporal distance w.r.t. time 0. Solving $\\mathbf{A}$ and $\\mathbf{B}$ can be formulated with the following weighted least squares:", + "bbox": [ + 498, + 554, + 890, + 599 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {A}, \\mathbf {B}} \\sum_ {i \\in \\{- 1, 1, 2 \\}} \\| \\sqrt {\\mathbf {W} _ {i}} \\odot (\\mathbf {F} _ {0 \\rightarrow i} - f (i; \\mathbf {A}, \\mathbf {B})) \\| _ {2} ^ {2}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 609, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\odot$ denotes element-wise product (with broadcasting along channel dimension). The optimal solution of this weighted least squares has the analytical form", + "bbox": [ + 498, + 652, + 890, + 696 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {\\Theta}} _ {x, y, z} = \\left(\\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {X} ^ {T}\\right) ^ {- 1} \\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {F} _ {x, y, z}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 705, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x, y$ and $z$ index the vertical, horizontal and channel dimensions of tensors, $\\hat{\\Theta}_{x,y,z} = \\left(\\hat{\\mathbf{A}}(x,y,z),\\hat{\\mathbf{B}}(x,y,z)\\right)^{\\mathrm{T}}$ is the solved coefficients. Other matrices are:", + "bbox": [ + 498, + 733, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l}\\mathbf {W} _ {x, y} = \\left[\\begin{array}{c c c}\\mathbf {W} _ {- 1} (x, y, 0)&&\\\\&\\mathbf {W} _ {1} (x, y, 0)&\\\\&&\\mathbf {W} _ {2} (x, y, 0) (x, y)\\end{array}\\right],\\\\\\mathbf {X} = \\left[\\begin{array}{c c c}1&1&4\\\\- 1&1&2\\end{array}\\right], \\mathbf {F} _ {x, y, z} = \\left[\\begin{array}{c}\\mathbf {F} _ {0 \\rightarrow - 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 2} (x, y, z)\\end{array}\\right].\\end{array}\\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 792, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All the calculations of Eq. (8) are fast to compute, including the $2 \\times 2$ matrix inverse which is closed-form. This", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22161", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1341e4edc0f420d74e6b7ef4b918f95818cc7c3774064ce5a8c1482232b23c46.jpg", + "image_caption": [ + "Figure 3. A toy 1-D example comparing different trajectory fitting methods. Linear model [13] is not adequate to approximate curved trajectory. Due to noisy measurements, quadratic models [17, 36] do not approximate the real curve well with fixed optical flow weighting. The cubic model [4] performs even worse due to the outlier at $t = 2$ , which deteriorates high-order polynomial regression. The proposed FTF achieves best approximation by dynamically weighting the contributions of measurements. In Sect. 4.4, we show benefits of this idea on real VFI samples." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 472, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "renders the solver an efficient layer when integrated into the whole architecture.", + "bbox": [ + 75, + 428, + 468, + 457 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motion resampling and refinement. After model fitting, we can resample the intermediate flows $\\mathbf{F}_{0\\rightarrow t}$ by evaluating $f(t;\\hat{\\mathbf{A}},\\hat{\\mathbf{B}})$ . Similar with previous works [10, 21], we also learn to refine the resampled flows to get benefits from end-to-end training, and infer the visibility masks indicating occlusion relations at time $t$ . This is achieved with a refinement network $\\mathcal{M}$ :", + "bbox": [ + 75, + 459, + 472, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathcal {M} \\left(\\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {C} _ {0}, \\bar {\\mathbf {C}} _ {1 \\rightarrow 0}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 575, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{C}}_{1\\rightarrow 0} = \\phi_{\\mathcal{B}}(\\mathbf{C}_1,\\mathbf{F}_{0\\rightarrow 1})$ is the warped features from time 1 to 0. The refined intermediate flows are $\\hat{\\mathbf{F}}_{0\\rightarrow t} = \\mathbf{F}_{0\\rightarrow t} + \\Delta \\mathbf{F}_{0\\rightarrow t}$ , with a soft mask $\\mathbf{M}_{0\\rightarrow t}\\in (0,1)^{H\\times W\\times 1}$ indicating the occlusion order of pixels used for soft splating [21], which are to be used in Sect. 3.3.", + "bbox": [ + 75, + 601, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Range-nullspace Synthesis (RNS)", + "text_level": 1, + "bbox": [ + 76, + 686, + 369, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The rest pipeline aims to synthesize the target frame at time $t$ . Arguably, rendering cannot be fully performed with the resampled flows $\\hat{\\mathbf{F}}_{0\\rightarrow t}$ and $\\hat{\\mathbf{F}}_{1\\rightarrow t}$ , which only depict partial correspondences from $\\mathbf{I}_0$ or $\\mathbf{I}_1$ to $\\mathbf{I}_t$ , and do not account for occluded pixels in $\\mathbf{I}_0$ and $\\mathbf{I}_1$ . Instead of predicting full correspondences, we treat frame synthesis as an inverse problem and solve it with a theory developed for it.", + "bbox": [ + 75, + 710, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our starting point is that given the unknown $\\mathbf{I}_t$ and forward flows $\\hat{\\mathbf{F}}_{0\\rightarrow t}$ and $\\hat{\\mathbf{F}}_{1\\rightarrow t}$ , we can relate these terms with the observations $\\mathbf{I}_0$ and $\\mathbf{I}_1$ as follows:", + "bbox": [ + 75, + 816, + 468, + 862 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right] = \\left[\\begin{array}{l}\\mathbf {H} _ {0 \\rightarrow t}\\\\\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right] \\mathbf {I} _ {t} + \\left[\\begin{array}{l}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 869, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With slight abuse of notation, $\\mathbf{I}_0$ , $\\mathbf{I}_1$ and $\\mathbf{I}_t$ now denote with vectorized and raster scanned images in $[-1,1]^N$ , where $N = H \\times W \\times C$ , $C = 3$ is the total number of pixels. In this case, flow-based warping with $\\hat{\\mathbf{F}}_{0 \\to t}$ and $\\hat{\\mathbf{F}}_{1 \\to t}$ can be reorganized as matrix multiplication with $\\mathbf{H}_{0 \\to t}, \\mathbf{H}_{1 \\to t} \\in \\mathbb{R}^{N \\times N}$ . The additive residuals $\\boldsymbol{\\Upsilon}_t$ represent image components that cannot be modelled by warping, e.g. occluded image content and lost high-frequencies caused by warping operator.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Taking $\\mathbf{I}_t$ in (11) as the latent to restore and $\\mathbf{I}_y$ as the measurements, we can treat (11) as an inverse problem with linear forward operator $\\mathbf{H}_t$ . Solving general linear inverse problems is not trivial, especially when the distributions of the residuals $\\Upsilon_t$ and the latent $\\mathbf{I}_t$ are complex. Replacing the former with simple analytical distributions can lead to classical Bayesian solvers, which are usually iterative even with learned gradients [39]. In this paper, we instead embrace a non-iterative and fast alternative, based on the deep range-nullspace solvers [2].", + "bbox": [ + 496, + 227, + 890, + 377 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Range nullspace learning. Range-nullspace theory states that if a forward operator $\\mathbf{H}$ has right inverse $\\mathbf{H}^+$ that satisfies $\\mathbf{HH}^{+} = \\mathbf{I}_{d}$ where $\\mathbf{I}_d$ is the identity matrix, it is possible to define two orthogonal projections $\\mathcal{R}$ and $\\mathcal{N}$ :", + "bbox": [ + 496, + 378, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} (\\boldsymbol {x}) \\triangleq \\mathbf {H} ^ {+} \\mathbf {H} \\boldsymbol {x}, \\mathcal {N} (\\boldsymbol {x}) \\triangleq \\left(\\mathbf {I} _ {d} - \\mathbf {H} ^ {+} \\mathbf {H}\\right) \\boldsymbol {x}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 446, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is easy to verify that $\\pmb{x} = \\mathcal{R}(\\pmb{x}) + \\mathcal{N}(\\pmb{x})$ for any $\\pmb{x}$ , and $\\mathcal{R}(\\pmb{x})^{\\mathrm{T}}\\mathcal{N}(\\pmb{y}) = 0$ for any $\\pmb{x}$ and $\\pmb{y}$ . $\\mathcal{R}(\\pmb{x})$ and $\\mathcal{N}(\\pmb{x})$ are called range- and null-space projections, respectively. Particularly, $\\mathcal{N}(\\pmb{x})$ satisfies", + "bbox": [ + 496, + 473, + 890, + 534 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} (\\boldsymbol {x}) \\in \\left\\{\\boldsymbol {u} \\in \\mathbb {R} ^ {N \\times 3} | \\mathbf {H} \\boldsymbol {u} = \\boldsymbol {0} \\right\\}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 542, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding our problem (11), unfortunately, the forward operator $[\\mathbf{H}_{0\\rightarrow t}^{\\mathrm{T}},\\mathbf{H}_{1\\rightarrow t}^{\\mathrm{T}}]^{\\mathrm{T}}$ has no right inverse (we refer interested readers to the supplementary material for derivations). However, it has the following equivalent form:", + "bbox": [ + 496, + 570, + 890, + 631 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right]} _ {\\mathbf {I} _ {y}} = \\underbrace {\\left[\\begin{array}{c c}\\mathbf {H} _ {0 \\rightarrow t}&\\mathbf {0}\\\\\\mathbf {0}&\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\mathbf {H} _ {t}} \\tilde {\\mathbf {I}} _ {t} + \\underbrace {\\left[\\begin{array}{c}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\boldsymbol {\\Upsilon} _ {t}}, \\text {s . t .} \\mathbf {C} \\tilde {\\mathbf {I}} _ {t} = \\mathbf {0}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 637, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{\\mathbf{I}}_t$ is divided into the top and bottom half, i.e. $\\tilde{\\mathbf{I}}_t = [\\tilde{\\mathbf{I}}_{t,1}^{\\mathrm{T}},\\tilde{\\mathbf{I}}_{t,2}^{\\mathrm{T}}]^{\\mathrm{T}}$ , and $\\mathbf{C} = [\\mathbf{I}_d, - \\mathbf{I}_d]$ . The constraint simply confines that $\\mathbf{I}_{t,1}^{\\mathrm{T}} = \\mathbf{I}_{t,2}^{\\mathrm{T}}$ . Our strategy is to first solve $\\tilde{\\mathbf{I}}_t$ without the constraint. In this case, $\\mathbf{H}_t$ in Eq. (14) can be right reversed. To meet the constraint, we find a projection of the result into the constraint set $\\{\\pmb {u}\\in \\mathbb{R}^{2N}|\\mathbf{C}\\pmb {u} = \\mathbf{0}\\}$ .", + "bbox": [ + 496, + 704, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The appealing property of nullspace projection (13) can be used to construct the following solver:", + "bbox": [ + 496, + 801, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right) + \\mathcal {N} (g (\\cdot)), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 840, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g(\\cdot)$ is arbitrary vector-to-vector function. The interesting fact of (15) is, by this construction, $\\tilde{\\mathbf{I}}_t^*$ always satisfies", + "bbox": [ + 496, + 868, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22162", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* +\\Upsilon_t$ for any $g(\\cdot)$ . Different $g(\\cdot)$ s lead to different reconstructions, revealing the ill-posedness of inverse problems. To get results that fall onto natural images, we implement $g(\\cdot)$ with a neural network trained to minimize the empirical errors on a dataset.", + "bbox": [ + 75, + 89, + 468, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Solving (15) is left to know the residuals $\\Upsilon_{t}$ . Though following complex, structured distributions, $\\Upsilon_{t}$ is mostly sparse and universally bounded ( $|\\Upsilon_{t}| \\leq 2$ ), which can be approximated well with neural networks. Inspired by [2], we use another network $r(\\cdot)$ to directly approximate $\\mathbf{H}_t^+\\mathbf{\\Upsilon}_t$ which is also bounded. When ideal convergence is reached after training, $|r(\\cdot) - \\mathbf{H}_t^+\\mathbf{\\Upsilon}_t| \\to 0$ , then the data consistency $\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* + \\Upsilon_t$ can be met by (15).", + "bbox": [ + 75, + 166, + 468, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After yielding the result $\\tilde{\\mathbf{I}}_t$ , projection onto $\\mathbf{C}\\tilde{\\mathbf{I}}_t = \\mathbf{0}$ is performed by minimizing", + "bbox": [ + 76, + 290, + 468, + 321 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} ^ {*} = \\arg \\min _ {\\boldsymbol {y} \\in \\mathbb {R} ^ {2 N}} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 328, + 468, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_{\\mathcal{C}}(\\boldsymbol{y}) = (\\mathbf{I}_d - \\mathbf{C}^{\\pm}\\mathbf{C})\\boldsymbol{y}$ is the nullspace projection of $\\mathbf{C}$ , $\\mathbf{C}^{\\pm}$ is the pseudo inverse, and $\\boldsymbol{\\Sigma} \\in [0,1]^{2N \\times 2N}$ defines the distance metric. The projected result is $\\mathbf{I}_t^* = \\mathcal{N}_{\\mathcal{C}}(\\mathbf{y}^*)$ . If $\\boldsymbol{\\Sigma} = \\mathbf{I}_d$ , it is easy to show $\\mathbf{I}_t^*$ is simply the average of the top and bottom half of $\\tilde{\\mathbf{I}}_t^*$ , $\\mathbf{I}_t^* = (\\tilde{\\mathbf{I}}_{t,1}^* + \\tilde{\\mathbf{I}}_{t,2}^*) / 2$ (see supplementary material for details). Instead, we benefit from end-to-end training and predict a dynamic blending mask as a diagonal matrix $\\boldsymbol{\\Lambda} \\in [0,1]^{N \\times N}$ , and obtain the result by $\\mathbf{I}_t^* = \\boldsymbol{\\Lambda}\\tilde{\\mathbf{I}}_{t,1}^* + (\\mathbf{I}_d - \\boldsymbol{\\Lambda})\\tilde{\\mathbf{I}}_{t,2}^*$ . It corresponds to learned distance matrix in (16), where $\\boldsymbol{\\Sigma} = \\mathrm{diag}([\\boldsymbol{\\Lambda},\\mathbf{I}_d - \\boldsymbol{\\Lambda}])$ .", + "bbox": [ + 75, + 369, + 468, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The decomposition learning (15) amortizes the difficulty of frame synthesis by several decoupled components. The term $\\mathbf{H}_t^+\\mathbf{I}_y$ , where $\\mathbf{H}_t^+ = \\mathrm{diag}([\\mathbf{H}_{0\\to t}^+, \\mathbf{H}_{1\\to t}^+])$ , can be intuitively thought of warping $\\mathbf{I}_0$ and $\\mathbf{I}_1$ to time $t$ , yielding physics-guided synthesis results. The network $r(\\cdot)$ learns to correct the error of physics-based warping, as the $\\mathcal{R}$ operator first back-projects the network output to time 0 and 1, and then does the same forward warping. The network $g(\\cdot)$ inpaints image content that cannot be addressed by forward warping, which are often occluded layer. In Sect. 4.4, we provide a visual analysis of the learned components.", + "bbox": [ + 75, + 525, + 468, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation. The network $r(\\cdot)$ and $g(\\cdot)$ have many design choices, not limited to the following one we use:", + "bbox": [ + 76, + 691, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {f}, \\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t} = r \\left(\\left\\{\\phi_ {\\mathcal {F}} (\\mathbf {C} _ {i}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}) \\right\\} _ {i \\in \\{0, 1 \\}}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 729, + 429, + 762 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Lambda}, \\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}} = g \\left(\\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right), \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y}, \\boldsymbol {f}\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 763, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} (\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}) + \\mathcal {N} (\\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}}),\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 787, + 383, + 809 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {t} ^ {*} = [ \\boldsymbol {\\Lambda}, \\mathbf {I} _ {d} - \\boldsymbol {\\Lambda} ] \\tilde {\\mathbf {I}} _ {t} ^ {*}.\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 811, + 272, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note $r(\\cdot)$ and $g(\\cdot)$ form casaded structure, where the estimation result of $r(\\cdot)$ is the input of $g(\\cdot)$ . We also pass through intermediate features $\\pmb{f}$ in this casade as unobstructed information flow. Matrix multiplications with $\\mathbf{H}_t$ and $\\mathbf{H}_t^+$ are all", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "implemented via warping operations. Multiplications with $\\mathbf{H}_{0\\rightarrow t}$ or $\\mathbf{H}_{1\\rightarrow t}$ can be done via backward warping, while with their inverse we use softmax splatting [21]:", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {i \\rightarrow t} \\boldsymbol {x} = \\phi_ {\\mathcal {B}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 148, + 890, + 174 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {i \\rightarrow t} ^ {+} \\boldsymbol {x} \\approx \\phi_ {\\mathcal {F}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}),\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 170, + 802, + 188 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{F}}_{i\\rightarrow t}$ and $\\mathbf{M}_{i\\rightarrow t}$ are the corresponding flows and masks defined in (10). Note this only slightly breaks the right inverse constraint but improves efficiency and flexibility. The overall working flow of steps (17) is referred to Fig. 2. Due to space limit, the detailed network configurations are referred to the supplementary material.", + "bbox": [ + 496, + 202, + 890, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss functions. Our loss function is defined as follows", + "bbox": [ + 517, + 294, + 883, + 309 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t o t a l} = \\log \\left(\\left\\| \\mathbf {I} _ {t} ^ {*} - \\mathbf {I} _ {t} ^ {g t} \\right\\| _ {2} ^ {2} + \\epsilon\\right) + \\alpha \\left\\| \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} - \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} ^ {g t} \\right\\| _ {1}, \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 320, + 890, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first one is a variant of standard $\\ell_2$ error. In the supplementary material we show this loss mitigates the diminishing gradient issue of $\\ell_2$ loss and yields improved performance. We set $\\epsilon = 10^{-8}$ to avoid numeric issues. The second loss enables that $r(\\cdot)$ approximates the true residual, where $\\mathbf{Y}_t^{gt} = \\mathbf{I}_y - \\mathbf{H}_t\\mathbf{I}_t^{gt}$ . Empirically, we set $\\alpha = 0.02$ .", + "bbox": [ + 496, + 353, + 890, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 458, + 710, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 483, + 601, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$8 \\times$ VFI. We test our method on three public 8x VFI datasets: GoPro [20], X4K1000FPS [29] and Adobe240 [31]. For GoPro, we follow [14, 39] and train our method on the official train split of GoPro and evaluate it on its test split at a resolution of $1280 \\times 720$ . We extract training samples according to the strategy applied in [14] and [39], yielding 22128 samples, each having 25 frames. In each sample, the $1^{st}$ , $9^{th}$ , $17^{th}$ and $25^{th}$ frames are used as input, while $10^{th}$ to $16^{th}$ frames serve as the supervision. The test set of GoPro is sampled similarly, resulting into 1500 non-overlapped samples. To verify the generalization capability, our model pre-trained on GoPro is also evaluated on a subset of Adobe240 [31] dataset including 630 samples, sampled with the strategy of [39], as well as the official test set of X4K1000FPS [29]. For fair comparisons on X4K1000FPS dataset, we also retrain and evaluate our method following its benchmarking protocol [29] strictly.", + "bbox": [ + 496, + 507, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Single-frame $(2\\times)$ VFI. Though our method is not designed for $2\\times$ VFI, we also evaluate on seven $2\\times$ VFI datasets for completeness. For training our method, since 4 input frames are required, we use the training split of the septuble set of Vince-90k [37], which contains 64612 samples at resolution $256\\times 448$ . In each septuplet, we take the $1^{st}$ , $3^{rd}$ , $5^{th}$ , $7^{th}$ frames as input and the $4^{th}$ frame as the supervision. For evaluation, we use 7824 samples from the test split of Vince-90k septuplet set, 100 samples", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22163", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b650dcab1396ff9d5a22eb9cbfb91649a685167a3f8727748e4d814d63759f4f.jpg", + "image_caption": [ + "Figure 4. Visual comparisons on X4K1000FPS (top 2 rows), and Adobe240 (bottom 2 rows) datasets, where each row corresponds to a scene. We overlay the nearest 2 input frames to illustrate the input motion. More results can be found in the supplementary material." + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 885, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from UCF101 [30], 2849 samples from DAVIS [25], and 310 samples from the easy, medium, hard and extreme subsets of SNU-FILM [6]. Note that these are the same evaluation protocols also adopted in [14, 28, 39].", + "bbox": [ + 75, + 494, + 470, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental settings", + "text_level": 1, + "bbox": [ + 76, + 566, + 282, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$8 \\times$ VFI. On each benchmark, we train the network for 120 epochs with batch size 32 and patch size $512 \\times 512$ , which is optimized by the AdamW [18] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ and weight decay $= 1 \\times 10^{-3}$ . At each iteration, the learning rate is decayed from $5 \\times 10^{-4}$ to $1 \\times 10^{-6}$ gradually via cosine annealing with warm steps $= 2000$ . During the training process, we adopt random cropping, flipping, and color jittering for data augmentation.", + "bbox": [ + 75, + 590, + 468, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Single-frame $(2\\times)$ VFI. The network is trained for 200 epochs with batch size 48 and patch size $256\\times 256$ , leaving the remaining settings the same as above.", + "bbox": [ + 75, + 712, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In all the benchmarks, we use two common metrics, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for quantitative evaluation, which is averaged across all the generated frames. Besides that, we use [32] for computing optical flows among input frames.", + "bbox": [ + 75, + 758, + 468, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparisons with State-of-the-Art models", + "text_level": 1, + "bbox": [ + 76, + 845, + 441, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$8 \\times$ VFI trained on GoPro. We compare our method with 11 competitive VFI methods that supports $8 \\times$ VFI:", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative results of $8 \\times$ VFI in terms of PSNR/SSIM and the number of parameters, evaluated on GoPro, Adobe240 and X4K1000FPS datasets. The best performed model is highlighted in red and the second best is colored in blue.", + "bbox": [ + 498, + 492, + 893, + 547 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/664577851b63ed1ac81b63a57457a6ed04f67b600c3bb50dfad7546974b2b351.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GoProAdobe240X4K1000FPSParam(M)
SloMo [13]29.71/0.92429.63/0.92725.07/0.79539.61
QVI [36]30.52/0.94131.41/0.95528.06/0.85529.23
EQVI [17]30.81/0.94232.13/0.95926.96/0.84328.07
DAIN [1]29.53/0.92030.53/0.93927.28/0.83524.03
EDSC [3]29.20/0.91629.87/0.93125.30/0.8118.95
FLAVR [14]31.10/0.94230.92/0.93824.50/0.79142.06
XVFI [29]29.80/0.92529.74/0.93028.42/0.8815.61
M2M [10]30.52/0.93329.93/0.93130.04/0.9057.61
IFRNet [15]30.00/0.92829.62/0.92523.77/0.79319.69
RIFEm [11]29.79/0.92529.81/0.93028.70/0.88010.71
DBVI [39]31.73/0.94733.28/0.96531.10/0.92815.18
Ours32.31/0.95133.32/0.96431.97/0.93210.10
", + "bbox": [ + 503, + 559, + 888, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SloMo [13], QVI [36], EQVI [17], DAIN [1], XVFI [29], M2M [10], DBVI [39], EDSC [3], FLAVR [14], IFRNet [15] and RIFE [11]. Note our evaluating settings are identical with [39], and for methods that do not follow the unified protocol proposed in [39], including EQVI, M2M, IFRNet and RIFE, we retrain them using the same protocol on GoPro and report the results. The quantitative results on GoPro, Adobe240 and X4K1000FPS are reported in Ta", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22164", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/81dbb7e14b567a690d6f7120da74affd46da5c220f4a71edaff0262c41d1a72a.jpg", + "table_caption": [ + "Table 2. Quantitative results of $8\\times$ VFI on X4K1000FPS dataset. following the benchmark protocol of [29]." + ], + "table_footnote": [], + "table_body": "
AdaCoF [16]FeFlow [9]SloMoQVIEQVIDAINFLAVRXVFIM2MIFRNetRIFEmDBVIOurs
PSNR25.8125.1627.7729.9628.2727.5227.9230.1230.8428.3630.7532.8933.88
SSIM0.7720.7830.8490.8920.8600.8210.8530.8700.9160.8700.9140.9390.946
", + "bbox": [ + 81, + 114, + 893, + 171 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f08622b0afcda9cdc568ff6fc32e437865d782605ad9207fcd76c88a2b3ff575.jpg", + "table_caption": [ + "Table 3. Quantitative results on $2\\times$ interpolation in terms of PSNR/SSIM with number of parameters and flops. All the methods are trained on the training set of Vimeo-90K (septulets)." + ], + "table_footnote": [], + "table_body": "
Vimeo-90K (septulets)UCF101DAVISSNU-FILMParam(M)
EasyMediumHardExtreme
SloMo [13]34.43/0.96932.45/0.96726.10/0.86236.12/0.98433.44/0.97229.17/0.92824.14/0.84339.61
QVI [36]34.98/0.97032.87/0.96627.20/0.87439.53/0.99036.43/0.98331.07/0.94724.96/0.85629.23
EQVI [17]35.16/0.97332.99/0.97027.51/0.89137.44/0.97835.19/0.98130.72/0.94625.42/0.86828.07
XVFI [29]35.21/0.97032.68/0.96826.89/0.86839.21/0.98934.96/0.97729.43/0.92824.02/0.8415.61
DAIN [1]33.57/0.96431.65/0.96326.61/0.86738.53/0.98834.34/0.97429.50/0.93024.54/0.85124.03
BMBC [23]34.76/0.96532.61/0.95526.42/0.86839.90/0.99135.34/0.97829.34/0.92723.65/0.83711.01
ABME [24]35.67/0.97232.81/0.96927.00/0.86839.59/0.99035.77/0.97730.58/0.93625.42/0.86418.1
EDSC [3]34.52/0.96732.67/0.96826.28/0.84940.01/0.99035.37/0.97829.59/0.92624.39/0.8438.95
GDConv [27]35.58/0.97233.11/0.96927.02/0.87040.36/0.99136.14/0.98230.25/0.94024.82/0.8605.14
CAIN [6]34.69/0.96932.40/0.96627.12/0.87239.33/0.98935.34/0.97730.15/0.93324.88/0.85542.78
FLAVR [14]36.30/0.97533.33/0.97127.44/0.87340.44/0.99136.37/0.98130.87/0.94225.18/0.86242.06
M2M [10]35.56/0.97332.70/0.96927.57/0.88739.35/0.98935.23/0.97729.99/0.93424.83/0.8577.60
IFRNet [15]36.37/0.97632.87/0.96927.94/0.89039.68/0.99035.57/0.97930.21/0.93824.71/0.85519.69
Softsplat [21]35.76/0.97232.89/0.97027.42/0.878----12.46
RIFEm [11]35.87/0.97432.64/0.96927.75/0.88639.50/0.99035.46/0.97830.17/0.93624.79/0.85410.71
VFIT-B [28]36.96/0.97833.44/0.97128.17/0.88940.57/0.99136.54/0.98231.04/0.94525.50/0.86729.1
ST-MFNet [8]36.46/0.97633.46/0.97128.30/0.89640.78/0.99237.12/0.98431.61/0.95125.78/0.87421.03
DBVI [39]36.17/0.97633.01/0.97028.61/0.90540.46/0.99136.95/0.98531.68/0.95325.90/0.87621.69
Ours36.33/0.97533.25/0.97028.84/0.90540.67/0.99137.36/0.98532.21/0.95526.22/0.87710.10
", + "bbox": [ + 80, + 224, + 890, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ble 1, with the model size in terms of the number of parameters. Our approach achieves the best results across all the datasets, achieving at least 0.58dB improvement on GoPro and 0.87dB on X4K1000FPS. Compared with the state-of-the-art model DBVI, our model has only two-thirds parameters. For those with less parameters than ours (e.g. M2M), we achieve nearly 1.19dB improvements at least. $8 \\times$ VFI on X4K1000FPS dataset, following the protocol of [29]. We following the training and testing protocol of [29] to report fair benchmarking results on X4K1000FPS dataset. For fair comparison, we also retrain several methods (M2M, IFRNet, RIFE, EQVI) on the official training split and compare with the results already available from $[29,39]^1$ . As summarized in Table 2, our approach achieves 0.99dB improvement than previous leading method DBVI. As shown in Fig. 4, our approach outperforms existing methods especially in several hard cases, like occluded or high frequency area. More visual results can be found in our supplementary material.", + "bbox": [ + 75, + 579, + 472, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Single-frame $(2\\times)$ VFI. Finally, we report the results on $2\\times$ VFI for completeness. Though our method is not dedicatedly designed for single-frame interpolation, we compare with 18 strong existing models and report the results in 3. Note that results of ABME, BMBC and CAIN have been reported in [39], while we extend this benchmarking with ST-MFNet $^{2}$ , VFIT, GD-Conv, as well as multiframe VFI models. All the additional models are trained on the train split of Video-90K (setptulets set). Our approach achieves the best results on 4 of 7 datasets. Slightly worse performance is observed on low resolution datasets Video-90K, UCF101 and the easy subset of SNU-FILM, whose motion is slight. On more challenging datasets like DAVIS and other subsets of SUN-FILM, the proposed method shows better generalizability.", + "bbox": [ + 496, + 579, + 893, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Performance Analysis", + "text_level": 1, + "bbox": [ + 500, + 818, + 705, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation analysis of motion trajectory fitting and range-nullspace learning. We have designed a series of", + "bbox": [ + 500, + 843, + 893, + 873 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1The results of AdaCoF [16] and FeFlow [9] are adopted from [29], which were trained and evaluated under the same settings.", + "bbox": [ + 76, + 875, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2The retrained model of ST-MFNet is kindly provided by the authors.", + "bbox": [ + 514, + 886, + 885, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22165", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a363b2810158efbe2356e9de9cbbd1f150cc79a44bcf8dedfd13f2beed79a6e8.jpg", + "image_caption": [ + "Figure 5. Analyzing the effectiveness of focalized trajectory fitting. Given the input frames (left), we show in the middle optical flow errors as the error maps of warping the frames $\\mathbf{I}_{-1}$ , $\\mathbf{I}_1$ and $\\mathbf{I}_2$ to time 0, and the corresponding weight maps of optical flows. Red denotes higher error/weight values, and blue represents lower values. Note a pixel is highlighted in green showing that higher optical flow error leads to lower weight. On the right, we show the warped result of $\\mathbf{I}_0$ using the intermediate flows $\\mathbf{F}_{0\\rightarrow t}$ resampled from different trajectory models. Note the warping results are overlayed with groundtruth, thus sharper result means more accurate warping. We also illustrate the position of a pixel at the boundary of hula hoop after warped to time $t$ by the intermediate flows (yellow cross), and the groundtruth position (red point)." + ], + "image_footnote": [], + "bbox": [ + 88, + 88, + 279, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/18d909dfe65f9959aa44230736e6646bddbc12c9b14a242f47ea2715c952c31f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 89, + 424, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2528b6d21d71f094c0aabe989cab0803006c0d85162858a57f2a1dbf6ed961fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 426, + 90, + 571, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/492f42c5453bda2789b55a850a90b5199d46c6461a04c8ee056f9d75d4c79f84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 90, + 717, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f687e40d2970ab0f239d964bbf5812c1dc54e7d589ba7943f043b0b182a8eb24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 90, + 803, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/49dd9896bc6553dc4a6f0522a6413dd82b1fea168cdaf740e6c14c15453b0a61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 90, + 887, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e63e920a51b7e097b3509ad5d1ef741fcafa1aa7d60eb35d4831a9e2ddab62a9.jpg", + "image_caption": [ + "$\\pmb{H}_{t}^{\\dagger}\\pmb{I}_{0}$" + ], + "image_footnote": [], + "bbox": [ + 81, + 344, + 215, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a5649a8840d915cf719522f7ac7d600bf2783afcfd2485e5ff78842b19cf670.jpg", + "image_caption": [ + "- $\\mathcal{R}(H_t^\\dagger Y_t)$" + ], + "image_footnote": [], + "bbox": [ + 218, + 344, + 346, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e8ffc1b1efcce64f592a662c9bb2654bcacc86821a39d387db2ae8bc158f288b.jpg", + "image_caption": [ + "HtI0-R(HtYt)" + ], + "image_footnote": [], + "bbox": [ + 349, + 344, + 482, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc2e092a14af74370a68bffbf471b10f502682daf54565d8e51852768192a977.jpg", + "image_caption": [ + "$\\tilde{I}_t^N$", + "Figure 6. Visualization of the learned range-null space image components. From left to right: 1) forward warping result of $\\mathbf{I}_0$ by intermediate flows $\\hat{\\mathbf{F}}_{0\\rightarrow t}$ , 2) range space component, 3) range compensated result, 4) nullspace component, 5) full result, and 6) ground truth." + ], + "image_footnote": [], + "bbox": [ + 485, + 344, + 616, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19a5cf09d99b21d59935295aea6803c3ebdc8a4f3e43a8471ba66d38a5f1c51c.jpg", + "image_caption": [ + "HtI0-RCHTy)+" + ], + "image_footnote": [], + "bbox": [ + 619, + 344, + 750, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3362dd55dcd57a5fa16fc6c356cc76f6567bfddc9996958971a3b73cab452b0.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 753, + 344, + 883, + 404 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c7e126f33309c16ceaba63473a312ff42932bd0382b21a28a562c8f1d0d6e75a.jpg", + "table_caption": [ + "Table 4. Ablation analysis on the GoPro and Adobe240 datasets." + ], + "table_footnote": [], + "table_body": "
TrajectoryRendererGoProAdobe
Linear [10]R + N31.10/0.93731.13/0.942
Quadratic [36]R + N32.07/0.94933.20/0.963
Quadratic [17]R + N31.81/0.94633.02/0.962
Cubic [4]R + N32.01/0.94933.09/0.962
FTFR32.13/0.95032.99/0.962
FTFN32.17/0.95032.99/0.962
FTFUnet32.17/0.95133.15/0.963
FTFR + N32.31/0.95133.32/0.964
", + "bbox": [ + 84, + 496, + 459, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ablation study experiments in Table 4. We report results on the test set of GoPro and Adobe240 datasets with $8 \\times$ VFI setting. First, we replace our focalized trajectory fitting with conventional linear, quadratic and cubic trajectory models without flow confidence learning (i.e., estimating the trajectory parameters $\\Theta$ in (8) with conventional models). As shown in the 1-4 rows in Table 4, using linear, quadratic and cubic models without focalized fitting mechanism will degrade the performance at different levels (linear model performs worst, as expected). We also verify the contributions of learning range and null space image components. Here, presence of $\\mathcal{R}$ or $\\mathcal{N}$ represent that the corresponding network outputs are included to constitute final reconstruction. By rows 5 and 6, We observe that removing either component would degrade the performance. In the 7th row, we also implement a baseline using a UNet with similar pa", + "bbox": [ + 75, + 659, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rameter size to replace the proposed RNS module, which achieves worse performance and demonstrate the effectiveness of RNS architecture.", + "bbox": [ + 496, + 473, + 890, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizing the effectiveness of focalized trajectory fitting. In Fig. 5, we show with one example the optical flow errors, learned weight maps, and quality of flow resampling. As can be seen, low weights are assigned to optical flows with high matching errors. Particularly, our approach yields more accurate correspondence along the occlusion boundary (as shown in Fig. 5 right).", + "bbox": [ + 496, + 518, + 890, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizing the range and nullspace components. In Fig. 6 we visualize the learned range and nullspace image components of one example. As it stands, the rangespace component fixes the errors of warping neighbouring frames (note the front wheel and wheel arches), while the nullspace component addresses image content that cannot be created by warping, i.e. inpainting the occluded content.", + "bbox": [ + 496, + 625, + 890, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 743, + 617, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes two improved treatments towards video frame interpolation. The first is focalized trajectory fitting, which improves motion estimation by suppressing low-quality optical flows. Another is range nullspace synthesis, that formulates intermediate frame synthesis as an ill-posed problem, solved by learning orthogonally decomposed image components. The proposed model achieves leading results on various public VFI datasets.", + "bbox": [ + 496, + 768, + 890, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22166", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. Depth-aware video frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 3703-3712, 2019. 1, 2, 6, 7", + "[2] Dongdong Chen and Mike E Davies. Deep decomposition learning for inverse imaging problems. In Proc. Eur. Conf. Comput. Vis., pages 510-526, 2020. 2, 4, 5", + "[3] Xianhang Cheng and Zhenzhong Chen. Multiple video frame interpolation via enhanced deformable separable convolution. IEEE Trans. Pattern Anal. Mach. 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Vis., pages 144-160, 2022. 1, 2, 4, 5, 6, 7" + ], + "bbox": [ + 501, + 92, + 892, + 318 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22168", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_model.json b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fcc3f0b6343554cbc41d8543740287ceb1851f84 --- /dev/null +++ b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_model.json @@ -0,0 +1,2255 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.131, + 0.88, + 0.152 + ], + "angle": 0, + "content": "Range-nullspace Video Frame Interpolation with Focalized Motion Estimation" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.179, + 0.925, + 0.253 + ], + "angle": 0, + "content": "Zhiyang Yu\\(^{1,\\ast}\\), Yu Zhang\\(^{2,\\boxtimes}\\), Dongqing Zou\\(^{2,3}\\), Xijun Chen\\(^{1}\\), Jimmy S. Ren\\(^{2,3}\\), Shunqing Ren\\(^{1,\\boxtimes}\\), Harbin Institute of Technology, Harbin, China \n\\(^{2}\\) SenseTime Research and Tetras.AI, Beijing, China \n\\(^{3}\\) Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.32, + 0.474, + 0.562 + ], + "angle": 0, + "content": "Continuous-time video frame interpolation is a fundamental technique in computer vision for its flexibility in synthesizing motion trajectories and novel video frames at arbitrary intermediate time steps. Yet, how to infer accurate intermediate motion and synthesize high-quality video frames are two critical challenges. In this paper, we present a novel VFI framework with improved treatment for these challenges. To address the former, we propose focalized trajectory fitting, which performs confidence-aware motion trajectory estimation by learning to pay focus to reliable optical flow candidates while suppressing the outliers. The second is range-nullspace synthesis, a novel frame renderer cast as solving an ill-posed problem addressed by learning decoupled components in orthogonal subspaces. The proposed framework sets new records on 7 of 10 public VFI benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.594, + 0.21, + 0.609 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.47, + 0.711 + ], + "angle": 0, + "content": "Continuous-time Video Frame Interpolation (VFI) aims at upsampling the temporal resolution of low frame-rate videos steplessly by synthesizing the missing frames at arbitrary time steps. It is a fundamental technology for various downstream video applications such as streaming [34], stabilization [5], and compression [35]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.85 + ], + "angle": 0, + "content": "A key challenge of this task is to find a continuous mapping from arbitrary time step to the latent scene motion to correctly render the target frame, observing the low frame-rate video. Typically, it was realized via two stages: motion trajectory fitting and frame synthesis, e.g. [1,3,4,10,13,17, 21,29,36,38,39]. In the former, a parametric trajectory model is fitted from the optical flows extracted from input frames, which can be resampled at any time step to get intermediate motion. For representing such a motion model," + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.285, + 0.891, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.556, + 0.894, + 0.709 + ], + "angle": 0, + "content": "Figure 1. Motivation of the proposed method. Given input frames and extracted optical flows (a), common VFI pipeline (b) is to fit a continuous motion trajectory model, resample flows at the target time step, based on which rendering rays are predicted to synthesize the intermediate frame by reorganizing pixels from the input frames. Our pipeline (c) proposes improved treatment in two aspects: 1) our focalized motion estimation assigns dynamic weights to the extracted optical flows to suppress the outlier flows and improve fitting accuracy, and the novel range-nullspace solver treats intermediate frame synthesis as an inverse problem instead of direct rendering. Please see text for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.893, + 0.791 + ], + "angle": 0, + "content": "the Taylor polynomial is often adopted with different orders [4, 13, 36]. However, fitting trajectory models are prone to optical flow errors, which are inevitable due to occlusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Besides motion fitting, the frame synthesis step faces the challenges of correctly inferring scene geometry. Particularly, the intermediate flows resampled from the continuous motion model only depict partial correspondences between the intermediate frame with input frames, while existing methods predict complete rendering rays in a data-driven manner to facilitate full rendering, as shown in Fig. 1 (b)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.089, + 0.863, + 0.424, + 0.876 + ], + "angle": 0, + "content": "* This work is done during Zhiyang's internship at SenseTime." + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.876, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Correspondence should be addressed to Yu Zhang (zhangyulb@gmail.com) and Shunqing Ren (renshunqing@hit.edu.cn)." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22159" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.166 + ], + "angle": 0, + "content": "Though powerful architectures [15] and rendering mechanisms [10] were proposed, it requires the network to fully encode the scene geometry to predict correct rays, which may raise the difficulty of architecture design and the burden of learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.47, + 0.482 + ], + "angle": 0, + "content": "To overcome these issues, we propose a novel framework with improved motion fitting and frame synthesis components. As shown in Fig. 1 (c), the first is focalized trajectory fitting, which extracts a set of optical flow candidates from the input video and assigns learned confidence weights to them. Confidence-aware, differentiable trajectory fitting is then followed, focalizing only the confident flows and producing improved parametric motion models. Such models, when resampled at the target time step, can produce accurate flows even at the occlusion boundary. For the latter, we follow the fact that intermediate frame synthesis is an ill-posed task and propose a deep solver based on the range nullspace theory [2]. Our solver decomposes the latent intermediate frame into several orthogonal image components and adopts different networks to learn each of them. Such physics-guided design encourages learning decoupled subtasks for each network, relieving the burden of encoding scene geometry and benefiting the use of lightweight models. In particular, our framework sets new records on 7 out of 10 public VFI benchmarks while being parameter-efficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.468, + 0.62 + ], + "angle": 0, + "content": "We summarize the contributions of this paper as follows. 1) A novel lightweight VFI framework is proposed, which refreshes the records of 7 out of 10 public VFI benchmarks. 2) The idea of focalized trajectory fitting, which improves parametric motion estimation in VFI and generates better resampling quality of intermediate flows. 3) A new perspective that treats intermediate frame synthesis as an ill-posed problem, solved with a deep range nullspace solver that decouples frame synthesis into several orthogonal tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.634, + 0.222, + 0.649 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Video frame interpolation requires estimating the motion of intermediate frames before synthesizing them. Such motion could be directly predicted as image correspondences in a data-driven manner [11, 15], or evaluated from parameterized motion trajectories fitted with optical flows extracted from input frames. Typically the latter one is more flexible to do frame interpolation at any time step. For representing the motion model, linear motion is mostly assumed [1, 3, 10, 13, 21, 29], while quadratic [17, 36, 38, 39] and cubic [4] models were proposed and show improved performance with higher orders of freedom. Frame synthesis was then carried out by warping the information from input frames, guided by the estimated motion. This involves synthesis techniques of backward warping [13, 17, 29, 36] or forward splatting [10, 21], depending on the direction of intermediate flows. High-quality synthesis poses the de" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.891, + 0.166 + ], + "angle": 0, + "content": "mand of reasoning occlusion, which was implemented explicitly with scene depth [1] or implicitly via powerful post-processing architectures [11, 17]. VFI can also be implemented in a highly data-driven manner [14], abstracting out all the above steps with neural networks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.362 + ], + "angle": 0, + "content": "There was also an important track of VFI that only synthesizes the middle frame of a pair of input frames. Without the need of representing motion continuously and interpolating arbitrary time steps, sophisticated components can be designed to optimally fit this task. For example, intermediate frame synthesis was solved with bilateral cost volumes [23], asymmetric bilateral volumes [24], expanded flows [8], and deformable convolutions [7]. There was also kernel-based method [22], with enhanced variants [3,16,27] that introduce more freedom into standard kernels with learned offsets and weights. Recent advances of deep learning architectures, like transformer [28] and channel attention modules [6], are also beneficial." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Range-nullspace learning provides a solver for inverse problems where the forward degeneration is a known linear operator [26]. It finds applications in solving superresolution [2], denoising [33] and compressed sensing [19]. Treating video frame interpolation as an inverse problem was first performed by [39], which developed iterative solvers based on learned gradients under the Bayesian inference framework. In this work, we adapt the range-nullspace theory to VFI and propose a non-iterative solver that learns orthogonally decomposed image components to relieve the entanglement of learned representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.744, + 0.559 + ], + "angle": 0, + "content": "3. The Proposed Framework" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.567, + 0.61, + 0.581 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.891, + 0.68 + ], + "angle": 0, + "content": "Following the routine of previous works [17, 36, 38, 39], our framework takes 4 adjacent input video frames \\(\\mathbf{I}_{-1},\\mathbf{I}_0,\\mathbf{I}_1,\\mathbf{I}_2\\in [-1,1]^{H\\times W\\times 3}\\) and generates intermediate frame \\(\\mathbf{I}_t\\) for any given time \\(t\\in (0,1)\\). As shown in Fig. 2, our pipeline starts by extracting appearance features for each input frame with a contextual network \\(\\mathcal{C}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.692, + 0.891, + 0.708 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {i} = \\mathcal {C} (\\mathbf {I} _ {i}), i \\in \\{- 1, 0, 1, 2 \\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.891, + 0.763 + ], + "angle": 0, + "content": "In the meantime, optical flows starting from \\(\\mathbf{I}_0\\), \\(\\mathbf{I}_1\\) to other neighbours are computed. This yields 6 optical flow maps \\(\\mathbf{F}_{i\\rightarrow j}\\in \\mathbb{R}^{H\\times W\\times 2}\\), where \\(i\\in \\{0,1\\}\\) and \\(j\\neq i\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.854 + ], + "angle": 0, + "content": "The Focalized Motion Estimation (FME) in Fig. 2 consumes optical flows and contextual features. It consists of three steps: flow confidence estimation, focalized trajectory fitting, motion resampling and refinement, and outputs motion specifications at a given time \\( t \\). Bi-directional motions are inferred, regarding both time 0 and 1:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.865, + 0.891, + 0.89 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l}\\hat {\\mathbf {F}} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathrm {F M E} (t, \\left\\{\\mathbf {F} _ {0 \\rightarrow j} \\right\\} _ {j \\neq 0}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),\\\\\\hat {\\quad}\\end{array}\\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.888, + 0.85, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {1 \\rightarrow t}, \\mathbf {M} _ {1 \\rightarrow t} = \\operatorname {F M E} (1 - t, \\left\\{\\mathbf {F} _ {1 \\rightarrow j} \\right\\} _ {j \\neq 1}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22160" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.891, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.893, + 0.388 + ], + "angle": 0, + "content": "Figure 2. Pipeline of our proposed method including contextual feature extraction, flow estimation, focalized motion estimation (FME), and range-nullsapce synthesis (RNS). Detailed descriptions of FME (middle) can be found in Sect. 3.2, and RNS (right) is elaborated in Sect. 3.3. For the details of mathematical symbols, please refer to the text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Here, \\(\\hat{\\mathbf{F}}_{i\\rightarrow t}\\) and \\(\\mathbf{M}_{i\\rightarrow t}\\), \\(i\\in \\{0,1\\}\\) are the resampled flows and occlusion relation masks to be explained in Sect. 3.2. Finally, we feed these motion specifications at time \\(t\\) and contextual features of input frames \\(\\mathbf{I}_0\\), \\(\\mathbf{I}_1\\) into the Range-Nullspace Synthesis (RNS) module," + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.501, + 0.47, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {t} ^ {*} = \\operatorname {R N S} \\left(\\left\\{\\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}, \\mathbf {C} _ {i} \\right\\} _ {i \\in \\{0, 1 \\}}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.538, + 0.47, + 0.569 + ], + "angle": 0, + "content": "In the following, we will elaborate technical details of the proposed FTE and RNS modules." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.579, + 0.391, + 0.595 + ], + "angle": 0, + "content": "3.2. Focalized Motion Estimation (FME)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.755 + ], + "angle": 0, + "content": "For the sake of conciseness, only the direction \\(0 \\to t\\) in Eq. (2) is considered here, as \\(1 \\to t\\) follows the similar process. Given contextual features \\(\\mathbf{C}_i\\) and candidate flows \\(\\{\\mathbf{F}_{0 \\to j}\\}_{j \\neq 0}\\), the confidence estimation step dynamically weights optical flow candidates. To this end, the contextual features \\(\\mathbf{C}_i\\) are half split along the channel dimension, yielding \\([\\mathbf{C}_i^a, \\mathbf{C}_i^b]\\), and the confidence estimation only works with the right half \\(\\mathbf{C}_i^b\\) to save calculation and leave the representation ability of remaining features untouched. The following warping residual is computed:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.766, + 0.469, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} _ {i} = \\mathbf {C} _ {0} ^ {b} - \\phi_ {\\mathcal {B}} (\\mathbf {C} _ {i} ^ {b}, \\mathbf {F} _ {0 \\rightarrow i}), i \\in \\{- 1, 1, 2 \\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.469, + 0.873 + ], + "angle": 0, + "content": "where \\(\\phi_{\\mathcal{B}}\\) represents the bilinear warping function [12] that projects features \\(\\mathbf{C}_i^b\\) to time 0 with backward warping. Intuitively, the residuals \\(\\mathbf{R}_i\\) conveys rich information of appearance warping errors induced by flows. We map such residuals to confidence weights via a network \\(\\mathcal{W}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.885, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} _ {- 1}, \\mathbf {W} _ {1}, \\mathbf {W} _ {2} = \\mathcal {W} (\\mathbf {R} _ {- 1}, \\mathbf {R} _ {1}, \\mathbf {R} _ {2}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.891, + 0.474 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_i\\in (0,1)^{H\\times W\\times 1}\\) and \\(\\sum_{i\\in \\{-1,1,2\\}}\\mathbf{W}_i = 1\\) Higher value of \\(\\mathbf{W}_i\\) indicates higher confidence of the flow values in \\(\\mathbf{F}_{0\\rightarrow i}\\), which deserves more focus for fitting parametric motion trajectory models." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.474, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Focalized trajectory fitting. We suppose that, in a short time interval around each pixel of \\(\\mathbf{I}_0\\), the motion trajectory is approximated with 2nd-order Taylor polynomial:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.528, + 0.891, + 0.546 + ], + "angle": 0, + "content": "\\[\nf (\\tau ; \\mathbf {A}, \\mathbf {B}) = \\mathbf {A} \\tau^ {2} + \\mathbf {B} \\tau , \\mathbf {A}, \\mathbf {B} \\in \\mathbb {R} ^ {H \\times W \\times 2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.891, + 0.601 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}\\) and \\(\\mathbf{B}\\) are model coefficients to fit, and \\(\\tau \\in [-1,2]\\) is the temporal distance w.r.t. time 0. Solving \\(\\mathbf{A}\\) and \\(\\mathbf{B}\\) can be formulated with the following weighted least squares:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.61, + 0.891, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {A}, \\mathbf {B}} \\sum_ {i \\in \\{- 1, 1, 2 \\}} \\| \\sqrt {\\mathbf {W} _ {i}} \\odot (\\mathbf {F} _ {0 \\rightarrow i} - f (i; \\mathbf {A}, \\mathbf {B})) \\| _ {2} ^ {2}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.653, + 0.891, + 0.698 + ], + "angle": 0, + "content": "in which \\(\\odot\\) denotes element-wise product (with broadcasting along channel dimension). The optimal solution of this weighted least squares has the analytical form" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.706, + 0.891, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {\\Theta}} _ {x, y, z} = \\left(\\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {X} ^ {T}\\right) ^ {- 1} \\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {F} _ {x, y, z}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.734, + 0.891, + 0.788 + ], + "angle": 0, + "content": "where \\(x, y\\) and \\(z\\) index the vertical, horizontal and channel dimensions of tensors, \\(\\hat{\\Theta}_{x,y,z} = \\left(\\hat{\\mathbf{A}}(x,y,z),\\hat{\\mathbf{B}}(x,y,z)\\right)^{\\mathrm{T}}\\) is the solved coefficients. Other matrices are:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.793, + 0.891, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l}\\mathbf {W} _ {x, y} = \\left[\\begin{array}{c c c}\\mathbf {W} _ {- 1} (x, y, 0)&&\\\\&\\mathbf {W} _ {1} (x, y, 0)&\\\\&&\\mathbf {W} _ {2} (x, y, 0) (x, y)\\end{array}\\right],\\\\\\mathbf {X} = \\left[\\begin{array}{c c c}1&1&4\\\\- 1&1&2\\end{array}\\right], \\mathbf {F} _ {x, y, z} = \\left[\\begin{array}{c}\\mathbf {F} _ {0 \\rightarrow - 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 2} (x, y, z)\\end{array}\\right].\\end{array}\\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "All the calculations of Eq. (8) are fast to compute, including the \\(2 \\times 2\\) matrix inverse which is closed-form. This" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "22161" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.473, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.473, + 0.404 + ], + "angle": 0, + "content": "Figure 3. A toy 1-D example comparing different trajectory fitting methods. Linear model [13] is not adequate to approximate curved trajectory. Due to noisy measurements, quadratic models [17, 36] do not approximate the real curve well with fixed optical flow weighting. The cubic model [4] performs even worse due to the outlier at \\( t = 2 \\), which deteriorates high-order polynomial regression. The proposed FTF achieves best approximation by dynamically weighting the contributions of measurements. In Sect. 4.4, we show benefits of this idea on real VFI samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.458 + ], + "angle": 0, + "content": "renders the solver an efficient layer when integrated into the whole architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.565 + ], + "angle": 0, + "content": "Motion resampling and refinement. After model fitting, we can resample the intermediate flows \\(\\mathbf{F}_{0\\rightarrow t}\\) by evaluating \\(f(t;\\hat{\\mathbf{A}},\\hat{\\mathbf{B}})\\). Similar with previous works [10, 21], we also learn to refine the resampled flows to get benefits from end-to-end training, and infer the visibility masks indicating occlusion relations at time \\(t\\). This is achieved with a refinement network \\(\\mathcal{M}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.576, + 0.47, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\Delta \\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathcal {M} \\left(\\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {C} _ {0}, \\bar {\\mathbf {C}} _ {1 \\rightarrow 0}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.47, + 0.68 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{C}}_{1\\rightarrow 0} = \\phi_{\\mathcal{B}}(\\mathbf{C}_1,\\mathbf{F}_{0\\rightarrow 1})\\) is the warped features from time 1 to 0. The refined intermediate flows are \\(\\hat{\\mathbf{F}}_{0\\rightarrow t} = \\mathbf{F}_{0\\rightarrow t} + \\Delta \\mathbf{F}_{0\\rightarrow t}\\), with a soft mask \\(\\mathbf{M}_{0\\rightarrow t}\\in (0,1)^{H\\times W\\times 1}\\) indicating the occlusion order of pixels used for soft splating [21], which are to be used in Sect. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.688, + 0.37, + 0.705 + ], + "angle": 0, + "content": "3.3. Range-nullspace Synthesis (RNS)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.817 + ], + "angle": 0, + "content": "The rest pipeline aims to synthesize the target frame at time \\( t \\). Arguably, rendering cannot be fully performed with the resampled flows \\( \\hat{\\mathbf{F}}_{0\\rightarrow t} \\) and \\( \\hat{\\mathbf{F}}_{1\\rightarrow t} \\), which only depict partial correspondences from \\( \\mathbf{I}_0 \\) or \\( \\mathbf{I}_1 \\) to \\( \\mathbf{I}_t \\), and do not account for occluded pixels in \\( \\mathbf{I}_0 \\) and \\( \\mathbf{I}_1 \\). Instead of predicting full correspondences, we treat frame synthesis as an inverse problem and solve it with a theory developed for it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.818, + 0.47, + 0.863 + ], + "angle": 0, + "content": "Our starting point is that given the unknown \\(\\mathbf{I}_t\\) and forward flows \\(\\hat{\\mathbf{F}}_{0\\rightarrow t}\\) and \\(\\hat{\\mathbf{F}}_{1\\rightarrow t}\\), we can relate these terms with the observations \\(\\mathbf{I}_0\\) and \\(\\mathbf{I}_1\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.871, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right] = \\left[\\begin{array}{l}\\mathbf {H} _ {0 \\rightarrow t}\\\\\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right] \\mathbf {I} _ {t} + \\left[\\begin{array}{l}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "With slight abuse of notation, \\(\\mathbf{I}_0\\), \\(\\mathbf{I}_1\\) and \\(\\mathbf{I}_t\\) now denote with vectorized and raster scanned images in \\([-1,1]^N\\), where \\(N = H \\times W \\times C\\), \\(C = 3\\) is the total number of pixels. In this case, flow-based warping with \\(\\hat{\\mathbf{F}}_{0 \\to t}\\) and \\(\\hat{\\mathbf{F}}_{1 \\to t}\\) can be reorganized as matrix multiplication with \\(\\mathbf{H}_{0 \\to t}, \\mathbf{H}_{1 \\to t} \\in \\mathbb{R}^{N \\times N}\\). The additive residuals \\(\\boldsymbol{\\Upsilon}_t\\) represent image components that cannot be modelled by warping, e.g. occluded image content and lost high-frequencies caused by warping operator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.378 + ], + "angle": 0, + "content": "Taking \\(\\mathbf{I}_t\\) in (11) as the latent to restore and \\(\\mathbf{I}_y\\) as the measurements, we can treat (11) as an inverse problem with linear forward operator \\(\\mathbf{H}_t\\). Solving general linear inverse problems is not trivial, especially when the distributions of the residuals \\(\\Upsilon_t\\) and the latent \\(\\mathbf{I}_t\\) are complex. Replacing the former with simple analytical distributions can lead to classical Bayesian solvers, which are usually iterative even with learned gradients [39]. In this paper, we instead embrace a non-iterative and fast alternative, based on the deep range-nullspace solvers [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Range nullspace learning. Range-nullspace theory states that if a forward operator \\(\\mathbf{H}\\) has right inverse \\(\\mathbf{H}^+\\) that satisfies \\(\\mathbf{HH}^{+} = \\mathbf{I}_{d}\\) where \\(\\mathbf{I}_d\\) is the identity matrix, it is possible to define two orthogonal projections \\(\\mathcal{R}\\) and \\(\\mathcal{N}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.447, + 0.892, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} (\\boldsymbol {x}) \\triangleq \\mathbf {H} ^ {+} \\mathbf {H} \\boldsymbol {x}, \\mathcal {N} (\\boldsymbol {x}) \\triangleq \\left(\\mathbf {I} _ {d} - \\mathbf {H} ^ {+} \\mathbf {H}\\right) \\boldsymbol {x}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.535 + ], + "angle": 0, + "content": "It is easy to verify that \\(\\pmb{x} = \\mathcal{R}(\\pmb{x}) + \\mathcal{N}(\\pmb{x})\\) for any \\(\\pmb{x}\\), and \\(\\mathcal{R}(\\pmb{x})^{\\mathrm{T}}\\mathcal{N}(\\pmb{y}) = 0\\) for any \\(\\pmb{x}\\) and \\(\\pmb{y}\\). \\(\\mathcal{R}(\\pmb{x})\\) and \\(\\mathcal{N}(\\pmb{x})\\) are called range- and null-space projections, respectively. Particularly, \\(\\mathcal{N}(\\pmb{x})\\) satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.543, + 0.892, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} (\\boldsymbol {x}) \\in \\left\\{\\boldsymbol {u} \\in \\mathbb {R} ^ {N \\times 3} | \\mathbf {H} \\boldsymbol {u} = \\boldsymbol {0} \\right\\}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.632 + ], + "angle": 0, + "content": "Regarding our problem (11), unfortunately, the forward operator \\([\\mathbf{H}_{0\\rightarrow t}^{\\mathrm{T}},\\mathbf{H}_{1\\rightarrow t}^{\\mathrm{T}}]^{\\mathrm{T}}\\) has no right inverse (we refer interested readers to the supplementary material for derivations). However, it has the following equivalent form:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.638, + 0.892, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\underbrace {\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right]} _ {\\mathbf {I} _ {y}} = \\underbrace {\\left[\\begin{array}{c c}\\mathbf {H} _ {0 \\rightarrow t}&\\mathbf {0}\\\\\\mathbf {0}&\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\mathbf {H} _ {t}} \\tilde {\\mathbf {I}} _ {t} + \\underbrace {\\left[\\begin{array}{c}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\boldsymbol {\\Upsilon} _ {t}}, \\text {s . t .} \\mathbf {C} \\tilde {\\mathbf {I}} _ {t} = \\mathbf {0}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.802 + ], + "angle": 0, + "content": "where \\(\\tilde{\\mathbf{I}}_t\\) is divided into the top and bottom half, i.e. \\(\\tilde{\\mathbf{I}}_t = [\\tilde{\\mathbf{I}}_{t,1}^{\\mathrm{T}},\\tilde{\\mathbf{I}}_{t,2}^{\\mathrm{T}}]^{\\mathrm{T}}\\), and \\(\\mathbf{C} = [\\mathbf{I}_d, - \\mathbf{I}_d]\\). The constraint simply confines that \\(\\mathbf{I}_{t,1}^{\\mathrm{T}} = \\mathbf{I}_{t,2}^{\\mathrm{T}}\\). Our strategy is to first solve \\(\\tilde{\\mathbf{I}}_t\\) without the constraint. In this case, \\(\\mathbf{H}_t\\) in Eq. (14) can be right reversed. To meet the constraint, we find a projection of the result into the constraint set \\(\\{\\pmb {u}\\in \\mathbb{R}^{2N}|\\mathbf{C}\\pmb {u} = \\mathbf{0}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.802, + 0.892, + 0.832 + ], + "angle": 0, + "content": "The appealing property of nullspace projection (13) can be used to construct the following solver:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.841, + 0.892, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right) + \\mathcal {N} (g (\\cdot)), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.869, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(g(\\cdot)\\) is arbitrary vector-to-vector function. The interesting fact of (15) is, by this construction, \\(\\tilde{\\mathbf{I}}_t^*\\) always satisfies" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22162" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.47, + 0.166 + ], + "angle": 0, + "content": "\\(\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* +\\Upsilon_t\\) for any \\(g(\\cdot)\\). Different \\(g(\\cdot)\\)s lead to different reconstructions, revealing the ill-posedness of inverse problems. To get results that fall onto natural images, we implement \\(g(\\cdot)\\) with a neural network trained to minimize the empirical errors on a dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.167, + 0.469, + 0.29 + ], + "angle": 0, + "content": "Solving (15) is left to know the residuals \\(\\Upsilon_{t}\\). Though following complex, structured distributions, \\(\\Upsilon_{t}\\) is mostly sparse and universally bounded (\\(|\\Upsilon_{t}| \\leq 2\\)), which can be approximated well with neural networks. Inspired by [2], we use another network \\(r(\\cdot)\\) to directly approximate \\(\\mathbf{H}_t^+\\mathbf{\\Upsilon}_t\\) which is also bounded. When ideal convergence is reached after training, \\(|r(\\cdot) - \\mathbf{H}_t^+\\mathbf{\\Upsilon}_t| \\to 0\\), then the data consistency \\(\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* + \\Upsilon_t\\) can be met by (15)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.291, + 0.47, + 0.323 + ], + "angle": 0, + "content": "After yielding the result \\(\\tilde{\\mathbf{I}}_t\\), projection onto \\(\\mathbf{C}\\tilde{\\mathbf{I}}_t = \\mathbf{0}\\) is performed by minimizing" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.329, + 0.47, + 0.36 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} ^ {*} = \\arg \\min _ {\\boldsymbol {y} \\in \\mathbb {R} ^ {2 N}} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.526 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_{\\mathcal{C}}(\\boldsymbol{y}) = (\\mathbf{I}_d - \\mathbf{C}^{\\pm}\\mathbf{C})\\boldsymbol{y}\\) is the nullspace projection of \\(\\mathbf{C}\\), \\(\\mathbf{C}^{\\pm}\\) is the pseudo inverse, and \\(\\boldsymbol{\\Sigma} \\in [0,1]^{2N \\times 2N}\\) defines the distance metric. The projected result is \\(\\mathbf{I}_t^* = \\mathcal{N}_{\\mathcal{C}}(\\mathbf{y}^*)\\). If \\(\\boldsymbol{\\Sigma} = \\mathbf{I}_d\\), it is easy to show \\(\\mathbf{I}_t^*\\) is simply the average of the top and bottom half of \\(\\tilde{\\mathbf{I}}_t^*\\), \\(\\mathbf{I}_t^* = (\\tilde{\\mathbf{I}}_{t,1}^* + \\tilde{\\mathbf{I}}_{t,2}^*) / 2\\) (see supplementary material for details). Instead, we benefit from end-to-end training and predict a dynamic blending mask as a diagonal matrix \\(\\boldsymbol{\\Lambda} \\in [0,1]^{N \\times N}\\), and obtain the result by \\(\\mathbf{I}_t^* = \\boldsymbol{\\Lambda}\\tilde{\\mathbf{I}}_{t,1}^* + (\\mathbf{I}_d - \\boldsymbol{\\Lambda})\\tilde{\\mathbf{I}}_{t,2}^*\\). It corresponds to learned distance matrix in (16), where \\(\\boldsymbol{\\Sigma} = \\mathrm{diag}([\\boldsymbol{\\Lambda},\\mathbf{I}_d - \\boldsymbol{\\Lambda}])\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.469, + 0.691 + ], + "angle": 0, + "content": "The decomposition learning (15) amortizes the difficulty of frame synthesis by several decoupled components. The term \\(\\mathbf{H}_t^+\\mathbf{I}_y\\), where \\(\\mathbf{H}_t^+ = \\mathrm{diag}([\\mathbf{H}_{0\\to t}^+, \\mathbf{H}_{1\\to t}^+])\\), can be intuitively thought of warping \\(\\mathbf{I}_0\\) and \\(\\mathbf{I}_1\\) to time \\(t\\), yielding physics-guided synthesis results. The network \\(r(\\cdot)\\) learns to correct the error of physics-based warping, as the \\(\\mathcal{R}\\) operator first back-projects the network output to time 0 and 1, and then does the same forward warping. The network \\(g(\\cdot)\\) inpaints image content that cannot be addressed by forward warping, which are often occluded layer. In Sect. 4.4, we provide a visual analysis of the learned components." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.692, + 0.469, + 0.722 + ], + "angle": 0, + "content": "Implementation. The network \\( r(\\cdot) \\) and \\( g(\\cdot) \\) have many design choices, not limited to the following one we use:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.73, + 0.43, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {f}, \\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t} = r \\left(\\left\\{\\phi_ {\\mathcal {F}} (\\mathbf {C} _ {i}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}) \\right\\} _ {i \\in \\{0, 1 \\}}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.765, + 0.469, + 0.788 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Lambda}, \\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}} = g \\left(\\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right), \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y}, \\boldsymbol {f}\\right), \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.789, + 0.384, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} (\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}) + \\mathcal {N} (\\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.813, + 0.274, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {t} ^ {*} = [ \\boldsymbol {\\Lambda}, \\mathbf {I} _ {d} - \\boldsymbol {\\Lambda} ] \\tilde {\\mathbf {I}} _ {t} ^ {*}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Note \\( r(\\cdot) \\) and \\( g(\\cdot) \\) form casaded structure, where the estimation result of \\( r(\\cdot) \\) is the input of \\( g(\\cdot) \\). We also pass through intermediate features \\( \\pmb{f} \\) in this casade as unobstructed information flow. Matrix multiplications with \\( \\mathbf{H}_t \\) and \\( \\mathbf{H}_t^+ \\) are all" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "implemented via warping operations. Multiplications with \\(\\mathbf{H}_{0\\rightarrow t}\\) or \\(\\mathbf{H}_{1\\rightarrow t}\\) can be done via backward warping, while with their inverse we use softmax splatting [21]:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.15, + 0.892, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {i \\rightarrow t} \\boldsymbol {x} = \\phi_ {\\mathcal {B}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}), \\tag {18}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.171, + 0.803, + 0.189 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {i \\rightarrow t} ^ {+} \\boldsymbol {x} \\approx \\phi_ {\\mathcal {F}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.203, + 0.892, + 0.295 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{F}}_{i\\rightarrow t}\\) and \\(\\mathbf{M}_{i\\rightarrow t}\\) are the corresponding flows and masks defined in (10). Note this only slightly breaks the right inverse constraint but improves efficiency and flexibility. The overall working flow of steps (17) is referred to Fig. 2. Due to space limit, the detailed network configurations are referred to the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.295, + 0.885, + 0.31 + ], + "angle": 0, + "content": "Loss functions. Our loss function is defined as follows" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.321, + 0.891, + 0.353 + ], + "angle": 0, + "content": "\\[\nL _ {t o t a l} = \\log \\left(\\left\\| \\mathbf {I} _ {t} ^ {*} - \\mathbf {I} _ {t} ^ {g t} \\right\\| _ {2} ^ {2} + \\epsilon\\right) + \\alpha \\left\\| \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} - \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} ^ {g t} \\right\\| _ {1}, \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.445 + ], + "angle": 0, + "content": "where the first one is a variant of standard \\(\\ell_2\\) error. In the supplementary material we show this loss mitigates the diminishing gradient issue of \\(\\ell_2\\) loss and yields improved performance. We set \\(\\epsilon = 10^{-8}\\) to avoid numeric issues. The second loss enables that \\(r(\\cdot)\\) approximates the true residual, where \\(\\mathbf{Y}_t^{gt} = \\mathbf{I}_y - \\mathbf{H}_t\\mathbf{I}_t^{gt}\\). Empirically, we set \\(\\alpha = 0.02\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.459, + 0.712, + 0.476 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.602, + 0.498 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\(8 \\times\\) VFI. We test our method on three public 8x VFI datasets: GoPro [20], X4K1000FPS [29] and Adobe240 [31]. For GoPro, we follow [14, 39] and train our method on the official train split of GoPro and evaluate it on its test split at a resolution of \\(1280 \\times 720\\). We extract training samples according to the strategy applied in [14] and [39], yielding 22128 samples, each having 25 frames. In each sample, the \\(1^{st}\\), \\(9^{th}\\), \\(17^{th}\\) and \\(25^{th}\\) frames are used as input, while \\(10^{th}\\) to \\(16^{th}\\) frames serve as the supervision. The test set of GoPro is sampled similarly, resulting into 1500 non-overlapped samples. To verify the generalization capability, our model pre-trained on GoPro is also evaluated on a subset of Adobe240 [31] dataset including 630 samples, sampled with the strategy of [39], as well as the official test set of X4K1000FPS [29]. For fair comparisons on X4K1000FPS dataset, we also retrain and evaluate our method following its benchmarking protocol [29] strictly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Single-frame \\((2\\times)\\) VFI. Though our method is not designed for \\(2\\times\\) VFI, we also evaluate on seven \\(2\\times\\) VFI datasets for completeness. For training our method, since 4 input frames are required, we use the training split of the septuble set of Vince-90k [37], which contains 64612 samples at resolution \\(256\\times 448\\). In each septuplet, we take the \\(1^{st}\\), \\(3^{rd}\\), \\(5^{th}\\), \\(7^{th}\\) frames as input and the \\(4^{th}\\) frame as the supervision. For evaluation, we use 7824 samples from the test split of Vince-90k septuplet set, 100 samples" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22163" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.887, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.895, + 0.471 + ], + "angle": 0, + "content": "Figure 4. Visual comparisons on X4K1000FPS (top 2 rows), and Adobe240 (bottom 2 rows) datasets, where each row corresponds to a scene. We overlay the nearest 2 input frames to illustrate the input motion. More results can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.471, + 0.556 + ], + "angle": 0, + "content": "from UCF101 [30], 2849 samples from DAVIS [25], and 310 samples from the easy, medium, hard and extreme subsets of SNU-FILM [6]. Note that these are the same evaluation protocols also adopted in [14, 28, 39]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.568, + 0.283, + 0.584 + ], + "angle": 0, + "content": "4.2. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.713 + ], + "angle": 0, + "content": "\\(8 \\times\\) VFI. On each benchmark, we train the network for 120 epochs with batch size 32 and patch size \\(512 \\times 512\\), which is optimized by the AdamW [18] with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\) and weight decay \\(= 1 \\times 10^{-3}\\). At each iteration, the learning rate is decayed from \\(5 \\times 10^{-4}\\) to \\(1 \\times 10^{-6}\\) gradually via cosine annealing with warm steps \\(= 2000\\). During the training process, we adopt random cropping, flipping, and color jittering for data augmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Single-frame \\((2\\times)\\) VFI. The network is trained for 200 epochs with batch size 48 and patch size \\(256\\times 256\\), leaving the remaining settings the same as above." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.47, + 0.837 + ], + "angle": 0, + "content": "In all the benchmarks, we use two common metrics, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for quantitative evaluation, which is averaged across all the generated frames. Besides that, we use [32] for computing optical flows among input frames." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.442, + 0.863 + ], + "angle": 0, + "content": "4.3. Comparisons with State-of-the-Art models" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "\\(8 \\times\\) VFI trained on GoPro. We compare our method with 11 competitive VFI methods that supports \\(8 \\times\\) VFI:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.493, + 0.895, + 0.549 + ], + "angle": 0, + "content": "Table 1. Quantitative results of \\(8 \\times\\) VFI in terms of PSNR/SSIM and the number of parameters, evaluated on GoPro, Adobe240 and X4K1000FPS datasets. The best performed model is highlighted in red and the second best is colored in blue." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.56, + 0.89, + 0.746 + ], + "angle": 0, + "content": "
GoProAdobe240X4K1000FPSParam(M)
SloMo [13]29.71/0.92429.63/0.92725.07/0.79539.61
QVI [36]30.52/0.94131.41/0.95528.06/0.85529.23
EQVI [17]30.81/0.94232.13/0.95926.96/0.84328.07
DAIN [1]29.53/0.92030.53/0.93927.28/0.83524.03
EDSC [3]29.20/0.91629.87/0.93125.30/0.8118.95
FLAVR [14]31.10/0.94230.92/0.93824.50/0.79142.06
XVFI [29]29.80/0.92529.74/0.93028.42/0.8815.61
M2M [10]30.52/0.93329.93/0.93130.04/0.9057.61
IFRNet [15]30.00/0.92829.62/0.92523.77/0.79319.69
RIFEm [11]29.79/0.92529.81/0.93028.70/0.88010.71
DBVI [39]31.73/0.94733.28/0.96531.10/0.92815.18
Ours32.31/0.95133.32/0.96431.97/0.93210.10
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SloMo [13], QVI [36], EQVI [17], DAIN [1], XVFI [29], M2M [10], DBVI [39], EDSC [3], FLAVR [14], IFRNet [15] and RIFE [11]. Note our evaluating settings are identical with [39], and for methods that do not follow the unified protocol proposed in [39], including EQVI, M2M, IFRNet and RIFE, we retrain them using the same protocol on GoPro and report the results. The quantitative results on GoPro, Adobe240 and X4K1000FPS are reported in Ta" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22164" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.164, + 0.089, + 0.807, + 0.105 + ], + "angle": 0, + "content": "Table 2. Quantitative results of \\(8\\times\\) VFI on X4K1000FPS dataset. following the benchmark protocol of [29]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.895, + 0.172 + ], + "angle": 0, + "content": "
AdaCoF [16]FeFlow [9]SloMoQVIEQVIDAINFLAVRXVFIM2MIFRNetRIFEmDBVIOurs
PSNR25.8125.1627.7729.9628.2727.5227.9230.1230.8428.3630.7532.8933.88
SSIM0.7720.7830.8490.8920.8600.8210.8530.8700.9160.8700.9140.9390.946
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.185, + 0.895, + 0.214 + ], + "angle": 0, + "content": "Table 3. Quantitative results on \\(2\\times\\) interpolation in terms of PSNR/SSIM with number of parameters and flops. All the methods are trained on the training set of Vimeo-90K (septulets)." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.226, + 0.891, + 0.561 + ], + "angle": 0, + "content": "
Vimeo-90K (septulets)UCF101DAVISSNU-FILMParam(M)
EasyMediumHardExtreme
SloMo [13]34.43/0.96932.45/0.96726.10/0.86236.12/0.98433.44/0.97229.17/0.92824.14/0.84339.61
QVI [36]34.98/0.97032.87/0.96627.20/0.87439.53/0.99036.43/0.98331.07/0.94724.96/0.85629.23
EQVI [17]35.16/0.97332.99/0.97027.51/0.89137.44/0.97835.19/0.98130.72/0.94625.42/0.86828.07
XVFI [29]35.21/0.97032.68/0.96826.89/0.86839.21/0.98934.96/0.97729.43/0.92824.02/0.8415.61
DAIN [1]33.57/0.96431.65/0.96326.61/0.86738.53/0.98834.34/0.97429.50/0.93024.54/0.85124.03
BMBC [23]34.76/0.96532.61/0.95526.42/0.86839.90/0.99135.34/0.97829.34/0.92723.65/0.83711.01
ABME [24]35.67/0.97232.81/0.96927.00/0.86839.59/0.99035.77/0.97730.58/0.93625.42/0.86418.1
EDSC [3]34.52/0.96732.67/0.96826.28/0.84940.01/0.99035.37/0.97829.59/0.92624.39/0.8438.95
GDConv [27]35.58/0.97233.11/0.96927.02/0.87040.36/0.99136.14/0.98230.25/0.94024.82/0.8605.14
CAIN [6]34.69/0.96932.40/0.96627.12/0.87239.33/0.98935.34/0.97730.15/0.93324.88/0.85542.78
FLAVR [14]36.30/0.97533.33/0.97127.44/0.87340.44/0.99136.37/0.98130.87/0.94225.18/0.86242.06
M2M [10]35.56/0.97332.70/0.96927.57/0.88739.35/0.98935.23/0.97729.99/0.93424.83/0.8577.60
IFRNet [15]36.37/0.97632.87/0.96927.94/0.89039.68/0.99035.57/0.97930.21/0.93824.71/0.85519.69
Softsplat [21]35.76/0.97232.89/0.97027.42/0.878----12.46
RIFEm [11]35.87/0.97432.64/0.96927.75/0.88639.50/0.99035.46/0.97830.17/0.93624.79/0.85410.71
VFIT-B [28]36.96/0.97833.44/0.97128.17/0.88940.57/0.99136.54/0.98231.04/0.94525.50/0.86729.1
ST-MFNet [8]36.46/0.97633.46/0.97128.30/0.89640.78/0.99237.12/0.98431.61/0.95125.78/0.87421.03
DBVI [39]36.17/0.97633.01/0.97028.61/0.90540.46/0.99136.95/0.98531.68/0.95325.90/0.87621.69
Ours36.33/0.97533.25/0.97028.84/0.90540.67/0.99137.36/0.98532.21/0.95526.22/0.87710.10
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.473, + 0.866 + ], + "angle": 0, + "content": "ble 1, with the model size in terms of the number of parameters. Our approach achieves the best results across all the datasets, achieving at least 0.58dB improvement on GoPro and 0.87dB on X4K1000FPS. Compared with the state-of-the-art model DBVI, our model has only two-thirds parameters. For those with less parameters than ours (e.g. M2M), we achieve nearly 1.19dB improvements at least. \\(8 \\times\\) VFI on X4K1000FPS dataset, following the protocol of [29]. We following the training and testing protocol of [29] to report fair benchmarking results on X4K1000FPS dataset. For fair comparison, we also retrain several methods (M2M, IFRNet, RIFE, EQVI) on the official training split and compare with the results already available from \\([29,39]^1\\). As summarized in Table 2, our approach achieves 0.99dB improvement than previous leading method DBVI. As shown in Fig. 4, our approach outperforms existing methods especially in several hard cases, like occluded or high frequency area. More visual results can be found in our supplementary material." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.903 + ], + "angle": 0, + "content": "1The results of AdaCoF [16] and FeFlow [9] are adopted from [29], which were trained and evaluated under the same settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.807 + ], + "angle": 0, + "content": "Single-frame \\((2\\times)\\) VFI. Finally, we report the results on \\(2\\times\\) VFI for completeness. Though our method is not dedicatedly designed for single-frame interpolation, we compare with 18 strong existing models and report the results in 3. Note that results of ABME, BMBC and CAIN have been reported in [39], while we extend this benchmarking with ST-MFNet\\(^{2}\\), VFIT, GD-Conv, as well as multiframe VFI models. All the additional models are trained on the train split of Video-90K (setptulets set). Our approach achieves the best results on 4 of 7 datasets. Slightly worse performance is observed on low resolution datasets Video-90K, UCF101 and the easy subset of SNU-FILM, whose motion is slight. On more challenging datasets like DAVIS and other subsets of SUN-FILM, the proposed method shows better generalizability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.819, + 0.707, + 0.836 + ], + "angle": 0, + "content": "4.4. Performance Analysis" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.844, + 0.895, + 0.874 + ], + "angle": 0, + "content": "Ablation analysis of motion trajectory fitting and range-nullspace learning. We have designed a series of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.886, + 0.902 + ], + "angle": 0, + "content": "2The retrained model of ST-MFNet is kindly provided by the authors." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22165" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.089, + 0.28, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.09, + 0.426, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.091, + 0.572, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.091, + 0.718, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.091, + 0.805, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.091, + 0.888, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 5. Analyzing the effectiveness of focalized trajectory fitting. Given the input frames (left), we show in the middle optical flow errors as the error maps of warping the frames \\(\\mathbf{I}_{-1}\\), \\(\\mathbf{I}_1\\) and \\(\\mathbf{I}_2\\) to time 0, and the corresponding weight maps of optical flows. Red denotes higher error/weight values, and blue represents lower values. Note a pixel is highlighted in green showing that higher optical flow error leads to lower weight. On the right, we show the warped result of \\(\\mathbf{I}_0\\) using the intermediate flows \\(\\mathbf{F}_{0\\rightarrow t}\\) resampled from different trajectory models. Note the warping results are overlayed with groundtruth, thus sharper result means more accurate warping. We also illustrate the position of a pixel at the boundary of hula hoop after warped to time \\(t\\) by the intermediate flows (yellow cross), and the groundtruth position (red point)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.345, + 0.216, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.408, + 0.164, + 0.421 + ], + "angle": 0, + "content": "\\(\\pmb{H}_{t}^{\\dagger}\\pmb{I}_{0}\\)" + }, + { + "type": "image", + "bbox": [ + 0.219, + 0.345, + 0.348, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.408, + 0.315, + 0.421 + ], + "angle": 0, + "content": "- \\(\\mathcal{R}(H_t^\\dagger Y_t)\\)" + }, + { + "type": "image", + "bbox": [ + 0.351, + 0.345, + 0.483, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.374, + 0.407, + 0.464, + 0.422 + ], + "angle": 0, + "content": "HtI0-R(HtYt)" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.345, + 0.617, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.407, + 0.559, + 0.42 + ], + "angle": 0, + "content": "\\(\\tilde{I}_t^N\\)" + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.345, + 0.751, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.407, + 0.741, + 0.422 + ], + "angle": 0, + "content": "HtI0-RCHTy)+" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.345, + 0.885, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.408, + 0.857, + 0.419 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.433, + 0.89, + 0.462 + ], + "angle": 0, + "content": "Figure 6. Visualization of the learned range-null space image components. From left to right: 1) forward warping result of \\(\\mathbf{I}_0\\) by intermediate flows \\(\\hat{\\mathbf{F}}_{0\\rightarrow t}\\), 2) range space component, 3) range compensated result, 4) nullspace component, 5) full result, and 6) ground truth." + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.472, + 0.465, + 0.485 + ], + "angle": 0, + "content": "Table 4. Ablation analysis on the GoPro and Adobe240 datasets." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.497, + 0.46, + 0.629 + ], + "angle": 0, + "content": "
TrajectoryRendererGoProAdobe
Linear [10]R + N31.10/0.93731.13/0.942
Quadratic [36]R + N32.07/0.94933.20/0.963
Quadratic [17]R + N31.81/0.94633.02/0.962
Cubic [4]R + N32.01/0.94933.09/0.962
FTFR32.13/0.95032.99/0.962
FTFN32.17/0.95032.99/0.962
FTFUnet32.17/0.95133.15/0.963
FTFR + N32.31/0.95133.32/0.964
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.901 + ], + "angle": 0, + "content": "ablation study experiments in Table 4. We report results on the test set of GoPro and Adobe240 datasets with \\(8 \\times\\) VFI setting. First, we replace our focalized trajectory fitting with conventional linear, quadratic and cubic trajectory models without flow confidence learning (i.e., estimating the trajectory parameters \\(\\Theta\\) in (8) with conventional models). As shown in the 1-4 rows in Table 4, using linear, quadratic and cubic models without focalized fitting mechanism will degrade the performance at different levels (linear model performs worst, as expected). We also verify the contributions of learning range and null space image components. Here, presence of \\(\\mathcal{R}\\) or \\(\\mathcal{N}\\) represent that the corresponding network outputs are included to constitute final reconstruction. By rows 5 and 6, We observe that removing either component would degrade the performance. In the 7th row, we also implement a baseline using a UNet with similar pa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.891, + 0.518 + ], + "angle": 0, + "content": "rameter size to replace the proposed RNS module, which achieves worse performance and demonstrate the effectiveness of RNS architecture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.625 + ], + "angle": 0, + "content": "Visualizing the effectiveness of focalized trajectory fitting. In Fig. 5, we show with one example the optical flow errors, learned weight maps, and quality of flow resampling. As can be seen, low weights are assigned to optical flows with high matching errors. Particularly, our approach yields more accurate correspondence along the occlusion boundary (as shown in Fig. 5 right)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Visualizing the range and nullspace components. In Fig. 6 we visualize the learned range and nullspace image components of one example. As it stands, the rangespace component fixes the errors of warping neighbouring frames (note the front wheel and wheel arches), while the nullspace component addresses image content that cannot be created by warping, i.e. inpainting the occluded content." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.744, + 0.619, + 0.759 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.89 + ], + "angle": 0, + "content": "This paper proposes two improved treatments towards video frame interpolation. The first is focalized trajectory fitting, which improves motion estimation by suppressing low-quality optical flows. Another is range nullspace synthesis, that formulates intermediate frame synthesis as an ill-posed problem, solved by learning orthogonally decomposed image components. The proposed model achieves leading results on various public VFI datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22166" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. Depth-aware video frame interpolation. In Proc. IEEE Conf. Comput. Vis. 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Vis., pages 144-160, 2022. 1, 2, 4, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22168" + } + ] +] \ No newline at end of file diff --git a/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_origin.pdf b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b991f6730179c5dc72644675248a1101e1ec3e5f --- /dev/null +++ b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/fb8c4ec0-3368-4408-98c9-491162515b01_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d0b65e8e030befc2075199bf53ab5fa0c862b34e99d5179b2a2e8afdf39ac190 +size 6807259 diff --git a/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/full.md b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ad428ecf7357a8a9cb8e21b3edc8af3a970156b1 --- /dev/null +++ b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/full.md @@ -0,0 +1,364 @@ +# Range-nullspace Video Frame Interpolation with Focalized Motion Estimation + +Zhiyang Yu $^{1,\ast}$ , Yu Zhang $^{2,\boxtimes}$ , Dongqing Zou $^{2,3}$ , Xijun Chen $^{1}$ , Jimmy S. Ren $^{2,3}$ , Shunqing Ren $^{1,\boxtimes}$ , Harbin Institute of Technology, Harbin, China + $^{2}$ SenseTime Research and Tetras.AI, Beijing, China + $^{3}$ Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China + +# Abstract + +Continuous-time video frame interpolation is a fundamental technique in computer vision for its flexibility in synthesizing motion trajectories and novel video frames at arbitrary intermediate time steps. Yet, how to infer accurate intermediate motion and synthesize high-quality video frames are two critical challenges. In this paper, we present a novel VFI framework with improved treatment for these challenges. To address the former, we propose focalized trajectory fitting, which performs confidence-aware motion trajectory estimation by learning to pay focus to reliable optical flow candidates while suppressing the outliers. The second is range-nullspace synthesis, a novel frame renderer cast as solving an ill-posed problem addressed by learning decoupled components in orthogonal subspaces. The proposed framework sets new records on 7 of 10 public VFI benchmarks. + +# 1. Introduction + +Continuous-time Video Frame Interpolation (VFI) aims at upsampling the temporal resolution of low frame-rate videos steplessly by synthesizing the missing frames at arbitrary time steps. It is a fundamental technology for various downstream video applications such as streaming [34], stabilization [5], and compression [35]. + +A key challenge of this task is to find a continuous mapping from arbitrary time step to the latent scene motion to correctly render the target frame, observing the low frame-rate video. Typically, it was realized via two stages: motion trajectory fitting and frame synthesis, e.g. [1,3,4,10,13,17, 21,29,36,38,39]. In the former, a parametric trajectory model is fitted from the optical flows extracted from input frames, which can be resampled at any time step to get intermediate motion. For representing such a motion model, + +![](images/ecf815a0db0a124efcd9890b3b0e2f50f4f23dbc770c4d6db55d184054461f3f.jpg) +Figure 1. Motivation of the proposed method. Given input frames and extracted optical flows (a), common VFI pipeline (b) is to fit a continuous motion trajectory model, resample flows at the target time step, based on which rendering rays are predicted to synthesize the intermediate frame by reorganizing pixels from the input frames. Our pipeline (c) proposes improved treatment in two aspects: 1) our focalized motion estimation assigns dynamic weights to the extracted optical flows to suppress the outlier flows and improve fitting accuracy, and the novel range-nullspace solver treats intermediate frame synthesis as an inverse problem instead of direct rendering. Please see text for more details. + +the Taylor polynomial is often adopted with different orders [4, 13, 36]. However, fitting trajectory models are prone to optical flow errors, which are inevitable due to occlusion. + +Besides motion fitting, the frame synthesis step faces the challenges of correctly inferring scene geometry. Particularly, the intermediate flows resampled from the continuous motion model only depict partial correspondences between the intermediate frame with input frames, while existing methods predict complete rendering rays in a data-driven manner to facilitate full rendering, as shown in Fig. 1 (b). + +Though powerful architectures [15] and rendering mechanisms [10] were proposed, it requires the network to fully encode the scene geometry to predict correct rays, which may raise the difficulty of architecture design and the burden of learning. + +To overcome these issues, we propose a novel framework with improved motion fitting and frame synthesis components. As shown in Fig. 1 (c), the first is focalized trajectory fitting, which extracts a set of optical flow candidates from the input video and assigns learned confidence weights to them. Confidence-aware, differentiable trajectory fitting is then followed, focalizing only the confident flows and producing improved parametric motion models. Such models, when resampled at the target time step, can produce accurate flows even at the occlusion boundary. For the latter, we follow the fact that intermediate frame synthesis is an ill-posed task and propose a deep solver based on the range nullspace theory [2]. Our solver decomposes the latent intermediate frame into several orthogonal image components and adopts different networks to learn each of them. Such physics-guided design encourages learning decoupled subtasks for each network, relieving the burden of encoding scene geometry and benefiting the use of lightweight models. In particular, our framework sets new records on 7 out of 10 public VFI benchmarks while being parameter-efficient. + +We summarize the contributions of this paper as follows. 1) A novel lightweight VFI framework is proposed, which refreshes the records of 7 out of 10 public VFI benchmarks. 2) The idea of focalized trajectory fitting, which improves parametric motion estimation in VFI and generates better resampling quality of intermediate flows. 3) A new perspective that treats intermediate frame synthesis as an ill-posed problem, solved with a deep range nullspace solver that decouples frame synthesis into several orthogonal tasks. + +# 2. Related works + +Video frame interpolation requires estimating the motion of intermediate frames before synthesizing them. Such motion could be directly predicted as image correspondences in a data-driven manner [11, 15], or evaluated from parameterized motion trajectories fitted with optical flows extracted from input frames. Typically the latter one is more flexible to do frame interpolation at any time step. For representing the motion model, linear motion is mostly assumed [1, 3, 10, 13, 21, 29], while quadratic [17, 36, 38, 39] and cubic [4] models were proposed and show improved performance with higher orders of freedom. Frame synthesis was then carried out by warping the information from input frames, guided by the estimated motion. This involves synthesis techniques of backward warping [13, 17, 29, 36] or forward splatting [10, 21], depending on the direction of intermediate flows. High-quality synthesis poses the de + +mand of reasoning occlusion, which was implemented explicitly with scene depth [1] or implicitly via powerful post-processing architectures [11, 17]. VFI can also be implemented in a highly data-driven manner [14], abstracting out all the above steps with neural networks. + +There was also an important track of VFI that only synthesizes the middle frame of a pair of input frames. Without the need of representing motion continuously and interpolating arbitrary time steps, sophisticated components can be designed to optimally fit this task. For example, intermediate frame synthesis was solved with bilateral cost volumes [23], asymmetric bilateral volumes [24], expanded flows [8], and deformable convolutions [7]. There was also kernel-based method [22], with enhanced variants [3,16,27] that introduce more freedom into standard kernels with learned offsets and weights. Recent advances of deep learning architectures, like transformer [28] and channel attention modules [6], are also beneficial. + +Range-nullspace learning provides a solver for inverse problems where the forward degeneration is a known linear operator [26]. It finds applications in solving superresolution [2], denoising [33] and compressed sensing [19]. Treating video frame interpolation as an inverse problem was first performed by [39], which developed iterative solvers based on learned gradients under the Bayesian inference framework. In this work, we adapt the range-nullspace theory to VFI and propose a non-iterative solver that learns orthogonally decomposed image components to relieve the entanglement of learned representations. + +# 3. The Proposed Framework + +# 3.1. Overview + +Following the routine of previous works [17, 36, 38, 39], our framework takes 4 adjacent input video frames $\mathbf{I}_{-1},\mathbf{I}_0,\mathbf{I}_1,\mathbf{I}_2\in [-1,1]^{H\times W\times 3}$ and generates intermediate frame $\mathbf{I}_t$ for any given time $t\in (0,1)$ . As shown in Fig. 2, our pipeline starts by extracting appearance features for each input frame with a contextual network $\mathcal{C}$ : + +$$ +\mathbf {C} _ {i} = \mathcal {C} (\mathbf {I} _ {i}), i \in \{- 1, 0, 1, 2 \}. \tag {1} +$$ + +In the meantime, optical flows starting from $\mathbf{I}_0$ , $\mathbf{I}_1$ to other neighbours are computed. This yields 6 optical flow maps $\mathbf{F}_{i\rightarrow j}\in \mathbb{R}^{H\times W\times 2}$ , where $i\in \{0,1\}$ and $j\neq i$ . + +The Focalized Motion Estimation (FME) in Fig. 2 consumes optical flows and contextual features. It consists of three steps: flow confidence estimation, focalized trajectory fitting, motion resampling and refinement, and outputs motion specifications at a given time $t$ . Bi-directional motions are inferred, regarding both time 0 and 1: + +$$ +\begin{array}{l}\hat {\mathbf {F}} _ {0 \rightarrow t}, \mathbf {M} _ {0 \rightarrow t} = \mathrm {F M E} (t, \left\{\mathbf {F} _ {0 \rightarrow j} \right\} _ {j \neq 0}, \left\{\mathbf {C} _ {i} \right\} _ {\forall i}),\\\hat {\quad}\end{array}\tag {2} +$$ + +$$ +\mathbf {F} _ {1 \rightarrow t}, \mathbf {M} _ {1 \rightarrow t} = \operatorname {F M E} (1 - t, \left\{\mathbf {F} _ {1 \rightarrow j} \right\} _ {j \neq 1}, \left\{\mathbf {C} _ {i} \right\} _ {\forall i}), +$$ + +![](images/fc0842946a3993d3585174f59ea509007795e798f5df177aee937bfbb8be7baa.jpg) +Figure 2. Pipeline of our proposed method including contextual feature extraction, flow estimation, focalized motion estimation (FME), and range-nullsapce synthesis (RNS). Detailed descriptions of FME (middle) can be found in Sect. 3.2, and RNS (right) is elaborated in Sect. 3.3. For the details of mathematical symbols, please refer to the text. + +Here, $\hat{\mathbf{F}}_{i\rightarrow t}$ and $\mathbf{M}_{i\rightarrow t}$ , $i\in \{0,1\}$ are the resampled flows and occlusion relation masks to be explained in Sect. 3.2. Finally, we feed these motion specifications at time $t$ and contextual features of input frames $\mathbf{I}_0$ , $\mathbf{I}_1$ into the Range-Nullspace Synthesis (RNS) module, + +$$ +\mathbf {I} _ {t} ^ {*} = \operatorname {R N S} \left(\left\{\hat {\mathbf {F}} _ {i \rightarrow t}, \mathbf {M} _ {i \rightarrow t}, \mathbf {C} _ {i} \right\} _ {i \in \{0, 1 \}}\right). \tag {3} +$$ + +In the following, we will elaborate technical details of the proposed FTE and RNS modules. + +# 3.2. Focalized Motion Estimation (FME) + +For the sake of conciseness, only the direction $0 \to t$ in Eq. (2) is considered here, as $1 \to t$ follows the similar process. Given contextual features $\mathbf{C}_i$ and candidate flows $\{\mathbf{F}_{0 \to j}\}_{j \neq 0}$ , the confidence estimation step dynamically weights optical flow candidates. To this end, the contextual features $\mathbf{C}_i$ are half split along the channel dimension, yielding $[\mathbf{C}_i^a, \mathbf{C}_i^b]$ , and the confidence estimation only works with the right half $\mathbf{C}_i^b$ to save calculation and leave the representation ability of remaining features untouched. The following warping residual is computed: + +$$ +\mathbf {R} _ {i} = \mathbf {C} _ {0} ^ {b} - \phi_ {\mathcal {B}} (\mathbf {C} _ {i} ^ {b}, \mathbf {F} _ {0 \rightarrow i}), i \in \{- 1, 1, 2 \}, \tag {4} +$$ + +where $\phi_{\mathcal{B}}$ represents the bilinear warping function [12] that projects features $\mathbf{C}_i^b$ to time 0 with backward warping. Intuitively, the residuals $\mathbf{R}_i$ conveys rich information of appearance warping errors induced by flows. We map such residuals to confidence weights via a network $\mathcal{W}$ : + +$$ +\mathbf {W} _ {- 1}, \mathbf {W} _ {1}, \mathbf {W} _ {2} = \mathcal {W} (\mathbf {R} _ {- 1}, \mathbf {R} _ {1}, \mathbf {R} _ {2}), \tag {5} +$$ + +where $\mathbf{W}_i\in (0,1)^{H\times W\times 1}$ and $\sum_{i\in \{-1,1,2\}}\mathbf{W}_i = 1$ Higher value of $\mathbf{W}_i$ indicates higher confidence of the flow values in $\mathbf{F}_{0\rightarrow i}$ , which deserves more focus for fitting parametric motion trajectory models. + +Focalized trajectory fitting. We suppose that, in a short time interval around each pixel of $\mathbf{I}_0$ , the motion trajectory is approximated with 2nd-order Taylor polynomial: + +$$ +f (\tau ; \mathbf {A}, \mathbf {B}) = \mathbf {A} \tau^ {2} + \mathbf {B} \tau , \mathbf {A}, \mathbf {B} \in \mathbb {R} ^ {H \times W \times 2}, \tag {6} +$$ + +where $\mathbf{A}$ and $\mathbf{B}$ are model coefficients to fit, and $\tau \in [-1,2]$ is the temporal distance w.r.t. time 0. Solving $\mathbf{A}$ and $\mathbf{B}$ can be formulated with the following weighted least squares: + +$$ +\min _ {\mathbf {A}, \mathbf {B}} \sum_ {i \in \{- 1, 1, 2 \}} \| \sqrt {\mathbf {W} _ {i}} \odot (\mathbf {F} _ {0 \rightarrow i} - f (i; \mathbf {A}, \mathbf {B})) \| _ {2} ^ {2}, \tag {7} +$$ + +in which $\odot$ denotes element-wise product (with broadcasting along channel dimension). The optimal solution of this weighted least squares has the analytical form + +$$ +\hat {\boldsymbol {\Theta}} _ {x, y, z} = \left(\mathbf {X} \mathbf {W} _ {x, y} \mathbf {X} ^ {T}\right) ^ {- 1} \mathbf {X} \mathbf {W} _ {x, y} \mathbf {F} _ {x, y, z}, \tag {8} +$$ + +where $x, y$ and $z$ index the vertical, horizontal and channel dimensions of tensors, $\hat{\Theta}_{x,y,z} = \left(\hat{\mathbf{A}}(x,y,z),\hat{\mathbf{B}}(x,y,z)\right)^{\mathrm{T}}$ is the solved coefficients. Other matrices are: + +$$ +\begin{array}{l}\mathbf {W} _ {x, y} = \left[\begin{array}{c c c}\mathbf {W} _ {- 1} (x, y, 0)&&\\&\mathbf {W} _ {1} (x, y, 0)&\\&&\mathbf {W} _ {2} (x, y, 0) (x, y)\end{array}\right],\\\mathbf {X} = \left[\begin{array}{c c c}1&1&4\\- 1&1&2\end{array}\right], \mathbf {F} _ {x, y, z} = \left[\begin{array}{c}\mathbf {F} _ {0 \rightarrow - 1} (x, y, z)\\\mathbf {F} _ {0 \rightarrow 1} (x, y, z)\\\mathbf {F} _ {0 \rightarrow 2} (x, y, z)\end{array}\right].\end{array}\tag {9} +$$ + +All the calculations of Eq. (8) are fast to compute, including the $2 \times 2$ matrix inverse which is closed-form. This + +![](images/1341e4edc0f420d74e6b7ef4b918f95818cc7c3774064ce5a8c1482232b23c46.jpg) +Figure 3. A toy 1-D example comparing different trajectory fitting methods. Linear model [13] is not adequate to approximate curved trajectory. Due to noisy measurements, quadratic models [17, 36] do not approximate the real curve well with fixed optical flow weighting. The cubic model [4] performs even worse due to the outlier at $t = 2$ , which deteriorates high-order polynomial regression. The proposed FTF achieves best approximation by dynamically weighting the contributions of measurements. In Sect. 4.4, we show benefits of this idea on real VFI samples. + +renders the solver an efficient layer when integrated into the whole architecture. + +Motion resampling and refinement. After model fitting, we can resample the intermediate flows $\mathbf{F}_{0\rightarrow t}$ by evaluating $f(t;\hat{\mathbf{A}},\hat{\mathbf{B}})$ . Similar with previous works [10, 21], we also learn to refine the resampled flows to get benefits from end-to-end training, and infer the visibility masks indicating occlusion relations at time $t$ . This is achieved with a refinement network $\mathcal{M}$ : + +$$ +\Delta \mathbf {F} _ {0 \rightarrow t}, \mathbf {M} _ {0 \rightarrow t} = \mathcal {M} \left(\mathbf {F} _ {0 \rightarrow t}, \mathbf {C} _ {0}, \bar {\mathbf {C}} _ {1 \rightarrow 0}\right), \tag {10} +$$ + +where $\bar{\mathbf{C}}_{1\rightarrow 0} = \phi_{\mathcal{B}}(\mathbf{C}_1,\mathbf{F}_{0\rightarrow 1})$ is the warped features from time 1 to 0. The refined intermediate flows are $\hat{\mathbf{F}}_{0\rightarrow t} = \mathbf{F}_{0\rightarrow t} + \Delta \mathbf{F}_{0\rightarrow t}$ , with a soft mask $\mathbf{M}_{0\rightarrow t}\in (0,1)^{H\times W\times 1}$ indicating the occlusion order of pixels used for soft splating [21], which are to be used in Sect. 3.3. + +# 3.3. Range-nullspace Synthesis (RNS) + +The rest pipeline aims to synthesize the target frame at time $t$ . Arguably, rendering cannot be fully performed with the resampled flows $\hat{\mathbf{F}}_{0\rightarrow t}$ and $\hat{\mathbf{F}}_{1\rightarrow t}$ , which only depict partial correspondences from $\mathbf{I}_0$ or $\mathbf{I}_1$ to $\mathbf{I}_t$ , and do not account for occluded pixels in $\mathbf{I}_0$ and $\mathbf{I}_1$ . Instead of predicting full correspondences, we treat frame synthesis as an inverse problem and solve it with a theory developed for it. + +Our starting point is that given the unknown $\mathbf{I}_t$ and forward flows $\hat{\mathbf{F}}_{0\rightarrow t}$ and $\hat{\mathbf{F}}_{1\rightarrow t}$ , we can relate these terms with the observations $\mathbf{I}_0$ and $\mathbf{I}_1$ as follows: + +$$ +\left[\begin{array}{l}\mathbf {I} _ {0}\\\mathbf {I} _ {1}\end{array}\right] = \left[\begin{array}{l}\mathbf {H} _ {0 \rightarrow t}\\\mathbf {H} _ {1 \rightarrow t}\end{array}\right] \mathbf {I} _ {t} + \left[\begin{array}{l}\boldsymbol {\Upsilon} _ {0 \rightarrow t}\\\boldsymbol {\Upsilon} _ {1 \rightarrow t}\end{array}\right]. \tag {11} +$$ + +With slight abuse of notation, $\mathbf{I}_0$ , $\mathbf{I}_1$ and $\mathbf{I}_t$ now denote with vectorized and raster scanned images in $[-1,1]^N$ , where $N = H \times W \times C$ , $C = 3$ is the total number of pixels. In this case, flow-based warping with $\hat{\mathbf{F}}_{0 \to t}$ and $\hat{\mathbf{F}}_{1 \to t}$ can be reorganized as matrix multiplication with $\mathbf{H}_{0 \to t}, \mathbf{H}_{1 \to t} \in \mathbb{R}^{N \times N}$ . The additive residuals $\boldsymbol{\Upsilon}_t$ represent image components that cannot be modelled by warping, e.g. occluded image content and lost high-frequencies caused by warping operator. + +Taking $\mathbf{I}_t$ in (11) as the latent to restore and $\mathbf{I}_y$ as the measurements, we can treat (11) as an inverse problem with linear forward operator $\mathbf{H}_t$ . Solving general linear inverse problems is not trivial, especially when the distributions of the residuals $\Upsilon_t$ and the latent $\mathbf{I}_t$ are complex. Replacing the former with simple analytical distributions can lead to classical Bayesian solvers, which are usually iterative even with learned gradients [39]. In this paper, we instead embrace a non-iterative and fast alternative, based on the deep range-nullspace solvers [2]. + +Range nullspace learning. Range-nullspace theory states that if a forward operator $\mathbf{H}$ has right inverse $\mathbf{H}^+$ that satisfies $\mathbf{HH}^{+} = \mathbf{I}_{d}$ where $\mathbf{I}_d$ is the identity matrix, it is possible to define two orthogonal projections $\mathcal{R}$ and $\mathcal{N}$ : + +$$ +\mathcal {R} (\boldsymbol {x}) \triangleq \mathbf {H} ^ {+} \mathbf {H} \boldsymbol {x}, \mathcal {N} (\boldsymbol {x}) \triangleq \left(\mathbf {I} _ {d} - \mathbf {H} ^ {+} \mathbf {H}\right) \boldsymbol {x}. \tag {12} +$$ + +It is easy to verify that $\pmb{x} = \mathcal{R}(\pmb{x}) + \mathcal{N}(\pmb{x})$ for any $\pmb{x}$ , and $\mathcal{R}(\pmb{x})^{\mathrm{T}}\mathcal{N}(\pmb{y}) = 0$ for any $\pmb{x}$ and $\pmb{y}$ . $\mathcal{R}(\pmb{x})$ and $\mathcal{N}(\pmb{x})$ are called range- and null-space projections, respectively. Particularly, $\mathcal{N}(\pmb{x})$ satisfies + +$$ +\mathcal {N} (\boldsymbol {x}) \in \left\{\boldsymbol {u} \in \mathbb {R} ^ {N \times 3} | \mathbf {H} \boldsymbol {u} = \boldsymbol {0} \right\}. \tag {13} +$$ + +Regarding our problem (11), unfortunately, the forward operator $[\mathbf{H}_{0\rightarrow t}^{\mathrm{T}},\mathbf{H}_{1\rightarrow t}^{\mathrm{T}}]^{\mathrm{T}}$ has no right inverse (we refer interested readers to the supplementary material for derivations). However, it has the following equivalent form: + +$$ +\underbrace {\left[\begin{array}{l}\mathbf {I} _ {0}\\\mathbf {I} _ {1}\end{array}\right]} _ {\mathbf {I} _ {y}} = \underbrace {\left[\begin{array}{c c}\mathbf {H} _ {0 \rightarrow t}&\mathbf {0}\\\mathbf {0}&\mathbf {H} _ {1 \rightarrow t}\end{array}\right]} _ {\mathbf {H} _ {t}} \tilde {\mathbf {I}} _ {t} + \underbrace {\left[\begin{array}{c}\boldsymbol {\Upsilon} _ {0 \rightarrow t}\\\boldsymbol {\Upsilon} _ {1 \rightarrow t}\end{array}\right]} _ {\boldsymbol {\Upsilon} _ {t}}, \text {s . t .} \mathbf {C} \tilde {\mathbf {I}} _ {t} = \mathbf {0}, \tag {14} +$$ + +where $\tilde{\mathbf{I}}_t$ is divided into the top and bottom half, i.e. $\tilde{\mathbf{I}}_t = [\tilde{\mathbf{I}}_{t,1}^{\mathrm{T}},\tilde{\mathbf{I}}_{t,2}^{\mathrm{T}}]^{\mathrm{T}}$ , and $\mathbf{C} = [\mathbf{I}_d, - \mathbf{I}_d]$ . The constraint simply confines that $\mathbf{I}_{t,1}^{\mathrm{T}} = \mathbf{I}_{t,2}^{\mathrm{T}}$ . Our strategy is to first solve $\tilde{\mathbf{I}}_t$ without the constraint. In this case, $\mathbf{H}_t$ in Eq. (14) can be right reversed. To meet the constraint, we find a projection of the result into the constraint set $\{\pmb {u}\in \mathbb{R}^{2N}|\mathbf{C}\pmb {u} = \mathbf{0}\}$ . + +The appealing property of nullspace projection (13) can be used to construct the following solver: + +$$ +\tilde {\mathbf {I}} _ {t} ^ {*} = \mathbf {H} _ {t} ^ {+} \mathbf {I} _ {y} - \mathcal {R} \left(\mathbf {H} _ {t} ^ {+} \boldsymbol {\Upsilon} _ {t}\right) + \mathcal {N} (g (\cdot)), \tag {15} +$$ + +where $g(\cdot)$ is arbitrary vector-to-vector function. The interesting fact of (15) is, by this construction, $\tilde{\mathbf{I}}_t^*$ always satisfies + +$\mathbf{I}_y = \mathbf{H}_t\tilde{\mathbf{I}}_t^* +\Upsilon_t$ for any $g(\cdot)$ . Different $g(\cdot)$ s lead to different reconstructions, revealing the ill-posedness of inverse problems. To get results that fall onto natural images, we implement $g(\cdot)$ with a neural network trained to minimize the empirical errors on a dataset. + +Solving (15) is left to know the residuals $\Upsilon_{t}$ . Though following complex, structured distributions, $\Upsilon_{t}$ is mostly sparse and universally bounded ( $|\Upsilon_{t}| \leq 2$ ), which can be approximated well with neural networks. Inspired by [2], we use another network $r(\cdot)$ to directly approximate $\mathbf{H}_t^+\mathbf{\Upsilon}_t$ which is also bounded. When ideal convergence is reached after training, $|r(\cdot) - \mathbf{H}_t^+\mathbf{\Upsilon}_t| \to 0$ , then the data consistency $\mathbf{I}_y = \mathbf{H}_t\tilde{\mathbf{I}}_t^* + \Upsilon_t$ can be met by (15). + +After yielding the result $\tilde{\mathbf{I}}_t$ , projection onto $\mathbf{C}\tilde{\mathbf{I}}_t = \mathbf{0}$ is performed by minimizing + +$$ +\boldsymbol {y} ^ {*} = \arg \min _ {\boldsymbol {y} \in \mathbb {R} ^ {2 N}} \left(\mathcal {N} _ {\mathcal {C}} (\boldsymbol {y}) - \tilde {\mathbf {I}} _ {t}\right) ^ {\mathrm {T}} \boldsymbol {\Sigma} \left(\mathcal {N} _ {\mathcal {C}} (\boldsymbol {y}) - \tilde {\mathbf {I}} _ {t}\right), \tag {16} +$$ + +where $\mathcal{N}_{\mathcal{C}}(\boldsymbol{y}) = (\mathbf{I}_d - \mathbf{C}^{\pm}\mathbf{C})\boldsymbol{y}$ is the nullspace projection of $\mathbf{C}$ , $\mathbf{C}^{\pm}$ is the pseudo inverse, and $\boldsymbol{\Sigma} \in [0,1]^{2N \times 2N}$ defines the distance metric. The projected result is $\mathbf{I}_t^* = \mathcal{N}_{\mathcal{C}}(\mathbf{y}^*)$ . If $\boldsymbol{\Sigma} = \mathbf{I}_d$ , it is easy to show $\mathbf{I}_t^*$ is simply the average of the top and bottom half of $\tilde{\mathbf{I}}_t^*$ , $\mathbf{I}_t^* = (\tilde{\mathbf{I}}_{t,1}^* + \tilde{\mathbf{I}}_{t,2}^*) / 2$ (see supplementary material for details). Instead, we benefit from end-to-end training and predict a dynamic blending mask as a diagonal matrix $\boldsymbol{\Lambda} \in [0,1]^{N \times N}$ , and obtain the result by $\mathbf{I}_t^* = \boldsymbol{\Lambda}\tilde{\mathbf{I}}_{t,1}^* + (\mathbf{I}_d - \boldsymbol{\Lambda})\tilde{\mathbf{I}}_{t,2}^*$ . It corresponds to learned distance matrix in (16), where $\boldsymbol{\Sigma} = \mathrm{diag}([\boldsymbol{\Lambda},\mathbf{I}_d - \boldsymbol{\Lambda}])$ . + +The decomposition learning (15) amortizes the difficulty of frame synthesis by several decoupled components. The term $\mathbf{H}_t^+\mathbf{I}_y$ , where $\mathbf{H}_t^+ = \mathrm{diag}([\mathbf{H}_{0\to t}^+, \mathbf{H}_{1\to t}^+])$ , can be intuitively thought of warping $\mathbf{I}_0$ and $\mathbf{I}_1$ to time $t$ , yielding physics-guided synthesis results. The network $r(\cdot)$ learns to correct the error of physics-based warping, as the $\mathcal{R}$ operator first back-projects the network output to time 0 and 1, and then does the same forward warping. The network $g(\cdot)$ inpaints image content that cannot be addressed by forward warping, which are often occluded layer. In Sect. 4.4, we provide a visual analysis of the learned components. + +Implementation. The network $r(\cdot)$ and $g(\cdot)$ have many design choices, not limited to the following one we use: + +$$ +\boldsymbol {f}, \mathbf {H} _ {t} ^ {+} \boldsymbol {\Upsilon} _ {t} = r \left(\left\{\phi_ {\mathcal {F}} (\mathbf {C} _ {i}; \hat {\mathbf {F}} _ {i \rightarrow t}, \mathbf {M} _ {i \rightarrow t}) \right\} _ {i \in \{0, 1 \}}\right), +$$ + +$$ +\boldsymbol {\Lambda}, \tilde {\mathbf {I}} _ {t} ^ {\mathcal {N}} = g \left(\mathbf {H} _ {t} ^ {+} \mathbf {I} _ {y} - \mathcal {R} \left(\mathbf {H} _ {t} ^ {+} \boldsymbol {\Upsilon} _ {t}\right), \mathbf {H} _ {t} ^ {+} \mathbf {I} _ {y}, \boldsymbol {f}\right), \tag {17} +$$ + +$$ +\tilde {\mathbf {I}} _ {t} ^ {*} = \mathbf {H} _ {t} ^ {+} \mathbf {I} _ {y} - \mathcal {R} (\mathbf {H} _ {t} ^ {+} \boldsymbol {\Upsilon} _ {t}) + \mathcal {N} (\tilde {\mathbf {I}} _ {t} ^ {\mathcal {N}}), +$$ + +$$ +\mathbf {I} _ {t} ^ {*} = [ \boldsymbol {\Lambda}, \mathbf {I} _ {d} - \boldsymbol {\Lambda} ] \tilde {\mathbf {I}} _ {t} ^ {*}. +$$ + +Note $r(\cdot)$ and $g(\cdot)$ form casaded structure, where the estimation result of $r(\cdot)$ is the input of $g(\cdot)$ . We also pass through intermediate features $\pmb{f}$ in this casade as unobstructed information flow. Matrix multiplications with $\mathbf{H}_t$ and $\mathbf{H}_t^+$ are all + +implemented via warping operations. Multiplications with $\mathbf{H}_{0\rightarrow t}$ or $\mathbf{H}_{1\rightarrow t}$ can be done via backward warping, while with their inverse we use softmax splatting [21]: + +$$ +\mathbf {H} _ {i \rightarrow t} \boldsymbol {x} = \phi_ {\mathcal {B}} (\boldsymbol {x}; \hat {\mathbf {F}} _ {i \rightarrow t}), \tag {18} +$$ + +$$ +\mathbf {H} _ {i \rightarrow t} ^ {+} \boldsymbol {x} \approx \phi_ {\mathcal {F}} (\boldsymbol {x}; \hat {\mathbf {F}} _ {i \rightarrow t}, \mathbf {M} _ {i \rightarrow t}), +$$ + +where $\hat{\mathbf{F}}_{i\rightarrow t}$ and $\mathbf{M}_{i\rightarrow t}$ are the corresponding flows and masks defined in (10). Note this only slightly breaks the right inverse constraint but improves efficiency and flexibility. The overall working flow of steps (17) is referred to Fig. 2. Due to space limit, the detailed network configurations are referred to the supplementary material. + +Loss functions. Our loss function is defined as follows + +$$ +L _ {t o t a l} = \log \left(\left\| \mathbf {I} _ {t} ^ {*} - \mathbf {I} _ {t} ^ {g t} \right\| _ {2} ^ {2} + \epsilon\right) + \alpha \left\| \mathbf {H} ^ {+} \boldsymbol {\Upsilon} _ {t} - \mathbf {H} ^ {+} \boldsymbol {\Upsilon} _ {t} ^ {g t} \right\| _ {1}, \tag {19} +$$ + +where the first one is a variant of standard $\ell_2$ error. In the supplementary material we show this loss mitigates the diminishing gradient issue of $\ell_2$ loss and yields improved performance. We set $\epsilon = 10^{-8}$ to avoid numeric issues. The second loss enables that $r(\cdot)$ approximates the true residual, where $\mathbf{Y}_t^{gt} = \mathbf{I}_y - \mathbf{H}_t\mathbf{I}_t^{gt}$ . Empirically, we set $\alpha = 0.02$ . + +# 4. Experimental Results + +# 4.1. Datasets + +$8 \times$ VFI. We test our method on three public 8x VFI datasets: GoPro [20], X4K1000FPS [29] and Adobe240 [31]. For GoPro, we follow [14, 39] and train our method on the official train split of GoPro and evaluate it on its test split at a resolution of $1280 \times 720$ . We extract training samples according to the strategy applied in [14] and [39], yielding 22128 samples, each having 25 frames. In each sample, the $1^{st}$ , $9^{th}$ , $17^{th}$ and $25^{th}$ frames are used as input, while $10^{th}$ to $16^{th}$ frames serve as the supervision. The test set of GoPro is sampled similarly, resulting into 1500 non-overlapped samples. To verify the generalization capability, our model pre-trained on GoPro is also evaluated on a subset of Adobe240 [31] dataset including 630 samples, sampled with the strategy of [39], as well as the official test set of X4K1000FPS [29]. For fair comparisons on X4K1000FPS dataset, we also retrain and evaluate our method following its benchmarking protocol [29] strictly. + +Single-frame $(2\times)$ VFI. Though our method is not designed for $2\times$ VFI, we also evaluate on seven $2\times$ VFI datasets for completeness. For training our method, since 4 input frames are required, we use the training split of the septuble set of Vince-90k [37], which contains 64612 samples at resolution $256\times 448$ . In each septuplet, we take the $1^{st}$ , $3^{rd}$ , $5^{th}$ , $7^{th}$ frames as input and the $4^{th}$ frame as the supervision. For evaluation, we use 7824 samples from the test split of Vince-90k septuplet set, 100 samples + +![](images/b650dcab1396ff9d5a22eb9cbfb91649a685167a3f8727748e4d814d63759f4f.jpg) +Figure 4. Visual comparisons on X4K1000FPS (top 2 rows), and Adobe240 (bottom 2 rows) datasets, where each row corresponds to a scene. We overlay the nearest 2 input frames to illustrate the input motion. More results can be found in the supplementary material. + +from UCF101 [30], 2849 samples from DAVIS [25], and 310 samples from the easy, medium, hard and extreme subsets of SNU-FILM [6]. Note that these are the same evaluation protocols also adopted in [14, 28, 39]. + +# 4.2. Experimental settings + +$8 \times$ VFI. On each benchmark, we train the network for 120 epochs with batch size 32 and patch size $512 \times 512$ , which is optimized by the AdamW [18] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ and weight decay $= 1 \times 10^{-3}$ . At each iteration, the learning rate is decayed from $5 \times 10^{-4}$ to $1 \times 10^{-6}$ gradually via cosine annealing with warm steps $= 2000$ . During the training process, we adopt random cropping, flipping, and color jittering for data augmentation. + +Single-frame $(2\times)$ VFI. The network is trained for 200 epochs with batch size 48 and patch size $256\times 256$ , leaving the remaining settings the same as above. + +In all the benchmarks, we use two common metrics, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for quantitative evaluation, which is averaged across all the generated frames. Besides that, we use [32] for computing optical flows among input frames. + +# 4.3. Comparisons with State-of-the-Art models + +$8 \times$ VFI trained on GoPro. We compare our method with 11 competitive VFI methods that supports $8 \times$ VFI: + +Table 1. Quantitative results of $8 \times$ VFI in terms of PSNR/SSIM and the number of parameters, evaluated on GoPro, Adobe240 and X4K1000FPS datasets. The best performed model is highlighted in red and the second best is colored in blue. + +
GoProAdobe240X4K1000FPSParam(M)
SloMo [13]29.71/0.92429.63/0.92725.07/0.79539.61
QVI [36]30.52/0.94131.41/0.95528.06/0.85529.23
EQVI [17]30.81/0.94232.13/0.95926.96/0.84328.07
DAIN [1]29.53/0.92030.53/0.93927.28/0.83524.03
EDSC [3]29.20/0.91629.87/0.93125.30/0.8118.95
FLAVR [14]31.10/0.94230.92/0.93824.50/0.79142.06
XVFI [29]29.80/0.92529.74/0.93028.42/0.8815.61
M2M [10]30.52/0.93329.93/0.93130.04/0.9057.61
IFRNet [15]30.00/0.92829.62/0.92523.77/0.79319.69
RIFEm [11]29.79/0.92529.81/0.93028.70/0.88010.71
DBVI [39]31.73/0.94733.28/0.96531.10/0.92815.18
Ours32.31/0.95133.32/0.96431.97/0.93210.10
+ +SloMo [13], QVI [36], EQVI [17], DAIN [1], XVFI [29], M2M [10], DBVI [39], EDSC [3], FLAVR [14], IFRNet [15] and RIFE [11]. Note our evaluating settings are identical with [39], and for methods that do not follow the unified protocol proposed in [39], including EQVI, M2M, IFRNet and RIFE, we retrain them using the same protocol on GoPro and report the results. The quantitative results on GoPro, Adobe240 and X4K1000FPS are reported in Ta + +Table 2. Quantitative results of $8\times$ VFI on X4K1000FPS dataset. following the benchmark protocol of [29]. + +
AdaCoF [16]FeFlow [9]SloMoQVIEQVIDAINFLAVRXVFIM2MIFRNetRIFEmDBVIOurs
PSNR25.8125.1627.7729.9628.2727.5227.9230.1230.8428.3630.7532.8933.88
SSIM0.7720.7830.8490.8920.8600.8210.8530.8700.9160.8700.9140.9390.946
+ +Table 3. Quantitative results on $2\times$ interpolation in terms of PSNR/SSIM with number of parameters and flops. All the methods are trained on the training set of Vimeo-90K (septulets). + +
Vimeo-90K (septulets)UCF101DAVISSNU-FILMParam(M)
EasyMediumHardExtreme
SloMo [13]34.43/0.96932.45/0.96726.10/0.86236.12/0.98433.44/0.97229.17/0.92824.14/0.84339.61
QVI [36]34.98/0.97032.87/0.96627.20/0.87439.53/0.99036.43/0.98331.07/0.94724.96/0.85629.23
EQVI [17]35.16/0.97332.99/0.97027.51/0.89137.44/0.97835.19/0.98130.72/0.94625.42/0.86828.07
XVFI [29]35.21/0.97032.68/0.96826.89/0.86839.21/0.98934.96/0.97729.43/0.92824.02/0.8415.61
DAIN [1]33.57/0.96431.65/0.96326.61/0.86738.53/0.98834.34/0.97429.50/0.93024.54/0.85124.03
BMBC [23]34.76/0.96532.61/0.95526.42/0.86839.90/0.99135.34/0.97829.34/0.92723.65/0.83711.01
ABME [24]35.67/0.97232.81/0.96927.00/0.86839.59/0.99035.77/0.97730.58/0.93625.42/0.86418.1
EDSC [3]34.52/0.96732.67/0.96826.28/0.84940.01/0.99035.37/0.97829.59/0.92624.39/0.8438.95
GDConv [27]35.58/0.97233.11/0.96927.02/0.87040.36/0.99136.14/0.98230.25/0.94024.82/0.8605.14
CAIN [6]34.69/0.96932.40/0.96627.12/0.87239.33/0.98935.34/0.97730.15/0.93324.88/0.85542.78
FLAVR [14]36.30/0.97533.33/0.97127.44/0.87340.44/0.99136.37/0.98130.87/0.94225.18/0.86242.06
M2M [10]35.56/0.97332.70/0.96927.57/0.88739.35/0.98935.23/0.97729.99/0.93424.83/0.8577.60
IFRNet [15]36.37/0.97632.87/0.96927.94/0.89039.68/0.99035.57/0.97930.21/0.93824.71/0.85519.69
Softsplat [21]35.76/0.97232.89/0.97027.42/0.878----12.46
RIFEm [11]35.87/0.97432.64/0.96927.75/0.88639.50/0.99035.46/0.97830.17/0.93624.79/0.85410.71
VFIT-B [28]36.96/0.97833.44/0.97128.17/0.88940.57/0.99136.54/0.98231.04/0.94525.50/0.86729.1
ST-MFNet [8]36.46/0.97633.46/0.97128.30/0.89640.78/0.99237.12/0.98431.61/0.95125.78/0.87421.03
DBVI [39]36.17/0.97633.01/0.97028.61/0.90540.46/0.99136.95/0.98531.68/0.95325.90/0.87621.69
Ours36.33/0.97533.25/0.97028.84/0.90540.67/0.99137.36/0.98532.21/0.95526.22/0.87710.10
+ +ble 1, with the model size in terms of the number of parameters. Our approach achieves the best results across all the datasets, achieving at least 0.58dB improvement on GoPro and 0.87dB on X4K1000FPS. Compared with the state-of-the-art model DBVI, our model has only two-thirds parameters. For those with less parameters than ours (e.g. M2M), we achieve nearly 1.19dB improvements at least. $8 \times$ VFI on X4K1000FPS dataset, following the protocol of [29]. We following the training and testing protocol of [29] to report fair benchmarking results on X4K1000FPS dataset. For fair comparison, we also retrain several methods (M2M, IFRNet, RIFE, EQVI) on the official training split and compare with the results already available from $[29,39]^1$ . As summarized in Table 2, our approach achieves 0.99dB improvement than previous leading method DBVI. As shown in Fig. 4, our approach outperforms existing methods especially in several hard cases, like occluded or high frequency area. More visual results can be found in our supplementary material. + +Single-frame $(2\times)$ VFI. Finally, we report the results on $2\times$ VFI for completeness. Though our method is not dedicatedly designed for single-frame interpolation, we compare with 18 strong existing models and report the results in 3. Note that results of ABME, BMBC and CAIN have been reported in [39], while we extend this benchmarking with ST-MFNet $^{2}$ , VFIT, GD-Conv, as well as multiframe VFI models. All the additional models are trained on the train split of Video-90K (setptulets set). Our approach achieves the best results on 4 of 7 datasets. Slightly worse performance is observed on low resolution datasets Video-90K, UCF101 and the easy subset of SNU-FILM, whose motion is slight. On more challenging datasets like DAVIS and other subsets of SUN-FILM, the proposed method shows better generalizability. + +# 4.4. Performance Analysis + +Ablation analysis of motion trajectory fitting and range-nullspace learning. We have designed a series of + +![](images/a363b2810158efbe2356e9de9cbbd1f150cc79a44bcf8dedfd13f2beed79a6e8.jpg) +Figure 5. Analyzing the effectiveness of focalized trajectory fitting. Given the input frames (left), we show in the middle optical flow errors as the error maps of warping the frames $\mathbf{I}_{-1}$ , $\mathbf{I}_1$ and $\mathbf{I}_2$ to time 0, and the corresponding weight maps of optical flows. Red denotes higher error/weight values, and blue represents lower values. Note a pixel is highlighted in green showing that higher optical flow error leads to lower weight. On the right, we show the warped result of $\mathbf{I}_0$ using the intermediate flows $\mathbf{F}_{0\rightarrow t}$ resampled from different trajectory models. Note the warping results are overlayed with groundtruth, thus sharper result means more accurate warping. We also illustrate the position of a pixel at the boundary of hula hoop after warped to time $t$ by the intermediate flows (yellow cross), and the groundtruth position (red point). + +![](images/18d909dfe65f9959aa44230736e6646bddbc12c9b14a242f47ea2715c952c31f.jpg) + +![](images/2528b6d21d71f094c0aabe989cab0803006c0d85162858a57f2a1dbf6ed961fe.jpg) + +![](images/492f42c5453bda2789b55a850a90b5199d46c6461a04c8ee056f9d75d4c79f84.jpg) + +![](images/f687e40d2970ab0f239d964bbf5812c1dc54e7d589ba7943f043b0b182a8eb24.jpg) + +![](images/49dd9896bc6553dc4a6f0522a6413dd82b1fea168cdaf740e6c14c15453b0a61.jpg) + +![](images/e63e920a51b7e097b3509ad5d1ef741fcafa1aa7d60eb35d4831a9e2ddab62a9.jpg) +$\pmb{H}_{t}^{\dagger}\pmb{I}_{0}$ + +![](images/8a5649a8840d915cf719522f7ac7d600bf2783afcfd2485e5ff78842b19cf670.jpg) +- $\mathcal{R}(H_t^\dagger Y_t)$ + +![](images/e8ffc1b1efcce64f592a662c9bb2654bcacc86821a39d387db2ae8bc158f288b.jpg) +HtI0-R(HtYt) + +![](images/dc2e092a14af74370a68bffbf471b10f502682daf54565d8e51852768192a977.jpg) +$\tilde{I}_t^N$ +Figure 6. Visualization of the learned range-null space image components. From left to right: 1) forward warping result of $\mathbf{I}_0$ by intermediate flows $\hat{\mathbf{F}}_{0\rightarrow t}$ , 2) range space component, 3) range compensated result, 4) nullspace component, 5) full result, and 6) ground truth. + +![](images/19a5cf09d99b21d59935295aea6803c3ebdc8a4f3e43a8471ba66d38a5f1c51c.jpg) +HtI0-RCHTy)+ + +![](images/d3362dd55dcd57a5fa16fc6c356cc76f6567bfddc9996958971a3b73cab452b0.jpg) +Ground Truth + +Table 4. Ablation analysis on the GoPro and Adobe240 datasets. + +
TrajectoryRendererGoProAdobe
Linear [10]R + N31.10/0.93731.13/0.942
Quadratic [36]R + N32.07/0.94933.20/0.963
Quadratic [17]R + N31.81/0.94633.02/0.962
Cubic [4]R + N32.01/0.94933.09/0.962
FTFR32.13/0.95032.99/0.962
FTFN32.17/0.95032.99/0.962
FTFUnet32.17/0.95133.15/0.963
FTFR + N32.31/0.95133.32/0.964
+ +ablation study experiments in Table 4. We report results on the test set of GoPro and Adobe240 datasets with $8 \times$ VFI setting. First, we replace our focalized trajectory fitting with conventional linear, quadratic and cubic trajectory models without flow confidence learning (i.e., estimating the trajectory parameters $\Theta$ in (8) with conventional models). As shown in the 1-4 rows in Table 4, using linear, quadratic and cubic models without focalized fitting mechanism will degrade the performance at different levels (linear model performs worst, as expected). We also verify the contributions of learning range and null space image components. Here, presence of $\mathcal{R}$ or $\mathcal{N}$ represent that the corresponding network outputs are included to constitute final reconstruction. By rows 5 and 6, We observe that removing either component would degrade the performance. In the 7th row, we also implement a baseline using a UNet with similar pa + +rameter size to replace the proposed RNS module, which achieves worse performance and demonstrate the effectiveness of RNS architecture. + +Visualizing the effectiveness of focalized trajectory fitting. In Fig. 5, we show with one example the optical flow errors, learned weight maps, and quality of flow resampling. As can be seen, low weights are assigned to optical flows with high matching errors. Particularly, our approach yields more accurate correspondence along the occlusion boundary (as shown in Fig. 5 right). + +Visualizing the range and nullspace components. In Fig. 6 we visualize the learned range and nullspace image components of one example. As it stands, the rangespace component fixes the errors of warping neighbouring frames (note the front wheel and wheel arches), while the nullspace component addresses image content that cannot be created by warping, i.e. inpainting the occluded content. + +# 5. Conclusion + +This paper proposes two improved treatments towards video frame interpolation. The first is focalized trajectory fitting, which improves motion estimation by suppressing low-quality optical flows. Another is range nullspace synthesis, that formulates intermediate frame synthesis as an ill-posed problem, solved by learning orthogonally decomposed image components. The proposed model achieves leading results on various public VFI datasets. + +# References + +[1] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. Depth-aware video frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 3703-3712, 2019. 1, 2, 6, 7 +[2] Dongdong Chen and Mike E Davies. Deep decomposition learning for inverse imaging problems. In Proc. Eur. Conf. Comput. Vis., pages 510-526, 2020. 2, 4, 5 +[3] Xianhang Cheng and Zhenzhong Chen. Multiple video frame interpolation via enhanced deformable separable convolution. IEEE Trans. Pattern Anal. Mach. Intell., pages 1-1, 2021. 1, 2, 6, 7 +[4] Z. Chi, R. M. Nasiri, Z. Liu, J. Lu, J. Tang, and K. N. Plataniotis. All at once: Temporally adaptive multi-frame interpolation with advanced motion modeling. In Proc. Eur. Conf. Comput. Vis., pages 107-123, 2020. 1, 2, 4, 8 +[5] Jinsoo Choi and In So Kweon. Deep iterative frame interpolation for full-frame video stabilization. ACM Trans. Graph., 39(1):1-9, 2020. 1 +[6] Myungsub Choi, Heewon Kim, Bohyung Han, Ning Xu, and Kyoung Mu Lee. Channel attention is all you need for video frame interpolation. In Proc. Assoc. Adv. Artif. Intell., volume 34, pages 10663-10671, 2020. 2, 6, 7 +[7] Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen Wei. Deformable convolutional networks. In Proc. IEEE Int. Conf. Comput. Vis., pages 764-773, 2017. 2 +[8] Duolikun Danier, Fan Zhang, and David Bull. ST-MFNet: A spatio-temporal multi-flow network for frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 3521-3531, June 2022. 2, 7 +[9] Shurui Gui, Chaoyue Wang, Qihua Chen, and Dacheng Tao. Featureflow: Robust video interpolation via structure-to-texture generation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 14004-14013, 2020. 7 +[10] Ping Hu, Simon Niklaus, Stan Sclaroff, and Kate Saenko. Many-to-many splatting for efficient video frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 3553-3562, 2022. 1, 2, 4, 6, 7, 8 +[11] Zhewei Huang, Tianyuan Zhang, Wen Heng, Boxin Shi, and Shuchang Zhou. Real-time intermediate flow estimation for video frame interpolation. In Proc. Eur. Conf. Comput. Vis., 2022. 2, 6, 7 +[12] M. Jaderberg, K. Simonyan, A. Zisserman, and K. Kavukcuoglu. Spatial transformer networks. In Proc. Adv. Neural Inf. Process. Syst., pages 2017-2025, 2015. 3 +[13] H. Jiang, D. Sun, V. Jampani, M.-H. Yang, E. G. Learned-Miller, and J. Kautz. Super SloMo: High quality estimation of multiple intermediate frames for video interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 9000-9008, 2018. 1, 2, 4, 6, 7 +[14] Tarun Kalluri, Deepak Pathak, Manmohan Chandraker, and Du Tran. Flavr: Flow-agnostic video representations for fast frame interpolation. arXiv:2012.08512, 2020. 2, 5, 6, 7 +[15] Lingtong Kong, Boyuan Jiang, Donghao Luo, Wenqing Chu, Xiaoming Huang, Ying Tai, Chengjie Wang, and Jie Yang. + +Ifrnnet: Intermediate feature refine network for efficient frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 1969-1978, 2022. 2, 6, 7 +[16] Hyeongmin Lee, Taeoh Kim, Tae-young Chung, Daehyun Pak, Yuseok Ban, and Sangyoun Lee. Adacof: Adaptive collaboration of flows for video frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 5316-5325, 2020. 2, 7 +[17] Yihao Liu, Liangbin Xie, Li Siyao, Wenxiu Sun, Yu Qiao, and Chao Dong. Enhanced quadratic video interpolation. In Proc. Eur. Conf. Comput. Vis. Workshops, pages 41-56, 2020. 1, 2, 4, 6, 7, 8 +[18] Ilya Loshchilov and Frank Hutter. Fixing weight decay regularization in adam. arXiv:1711.05101, 2018. 6 +[19] Mahsa Lotfi and Mathukumalli Vidyasagar. Compressed sensing using binary matrices of nearly optimal dimensions. IEEE Trans. Signal Process, 68:3008-3021, 2020. 2 +[20] Seungjun Nah, Tae Hyun Kim, and Kyoung Mu Lee. Deep multi-scale convolutional neural network for dynamic scene deblurring. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 3883-3891, 2017. 5 +[21] Simon Niklaus and Feng Liu. Softmax splatting for video frame interpolation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 5437-5446, 2020. 1, 2, 4, 5, 7 +[22] Simon Niklaus, Long Mai, and Feng Liu. Video frame interpolation via adaptive convolution. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 2270-2279, 2017. 2 +[23] J. Park, K. Ko, C. Lee, and C.-S. Kim. BMBC: bilateral motion estimation with bilateral cost volume for video interpolation. In Proc. Eur. Conf. Comput. Vis., pages 109-125, 2020. 2, 7 +[24] Junheum Park, Chul Lee, and Chang-Su Kim. Asymmetric bilateral motion estimation for video frame interpolation. In Proc. IEEE Int. Conf. Comput. Vis., pages 14539-14548, 2021. 2, 7 +[25] Federico Perazzi, Jordi Pont-Tuset, Brian McWilliams, Luc Van Gool, Markus Gross, and Alexander Sorkine-Hornung. A benchmark dataset and evaluation methodology for video object segmentation. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 724-732, 2016. 6 +[26] Johannes Schwab, Stephan Antholzer, and Markus Haltmeier. Deep null space learning for inverse problems: convergence analysis and rates. Inverse Problems, 35(2):025008, 2019. 2 +[27] Zhihao Shi, Xiaohong Liu, Kangdi Shi, Linhui Dai, and Jun Chen. Video frame interpolation via generalized deformable convolution. IEEE Trans. Multimedia, 24:426-439, 2021. 2, 7 +[28] Zhihao Shi, Xiangyu Xu, Xiaohong Liu, Jun Chen, and Ming-Hsuan Yang. Video frame interpolation transformer. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 17482-17491, 2022. 2, 6, 7 +[29] Hyeunjun Sim, Jihyong Oh, and Munchurl Kim. XVFI: Extreme video frame interpolation. In Proc. IEEE Int. Conf. Comput. Vis., pages 14489-14498, 2021. 1, 2, 5, 6, 7 +[30] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah. Ucf101: A dataset of 101 human actions classes from videos in the wild. arXiv:1212.0402, 2012. 6 + +[31] Shuochen Su, Maurizio Delbracio, Jue Wang, Guillermo Sapiro, Wolfgang Heidrich, and Oliver Wang. Deep video deblurring for hand-held cameras. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 1279-1288, 2017. 5 +[32] Zachary Teed and Jia Deng. Raft: Recurrent all-pairs field transforms for optical flow. In Proc. Eur. Conf. Comput. Vis., volume 12347, pages 402-419, 2020. 6 +[33] Tom Tirer and Raja Giryes. Image restoration by iterative denoising and backward projections. IEEE Trans. Image Process, 28(3):1220-1234, 2018. 2 +[34] Muhammad Usman, Xiangjian He, Kin-Man Lam, Min Xu, Syed Mohsin Matloob Bokhari, and Jinjun Chen. Frame interpolation for cloud-based mobile video streaming. IEEE Trans. Multimedia, 18(5):831-839, 2016. 1 +[35] Chao-Yuan Wu, Nayan Singhal, and Philipp Krahenbuhl. Video compression through image interpolation. In Proc. + +Eur. Conf. Comput. Vis., pages 416-431, 2018. 1 +[36] Xiangyu Xu, Li Siyao, Wenxiu Sun, Qian Yin, and Ming-Hsuan Yang. Quadratic video interpolation. In Proc. Adv. Neural Inf. Process. Syst., pages 1645-1654, 2019. 1, 2, 4, 6, 7, 8 +[37] Tianfan Xue, Baian Chen, Jiajun Wu, Donglai Wei, and William T Freeman. Video enhancement with task-oriented flow. Int. J. Comput. Vis., 127(8):1106-1125, 2019. 5 +[38] Zhiyang Yu, Yu Zhang, Deyuan Liu, Dongqing Zou, Xijun Chen, Yebin Liu, and Jimmy Ren. Training weakly supervised video frame interpolation with events. In Proc. IEEE Int. Conf. Comput. Vis., pages 14569-14578, 2021. 1, 2 +[39] Zhiyang Yu, Yu Zhang, Xujie Xiang, Dongqing Zou, Xijun Chen, and Jimmy S. Ren. Deep bayesian video frame interpolation. In Proc. Eur. Conf. Comput. Vis., pages 144-160, 2022. 1, 2, 4, 5, 6, 7 \ No newline at end of file diff --git a/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/images.zip b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0dab47b2ffafba1c95cb7270b2e247b40999de2f --- /dev/null +++ b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bd8e7e30ca1adf84110756c6a1444337fa3dea48ec5e876ae7885fe954a4ed3e +size 1066364 diff --git a/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/layout.json b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2ae577b7c98525b02c276658d3152509775c1c33 --- /dev/null +++ b/2023/Range-Nullspace Video Frame Interpolation With Focalized Motion Estimation/layout.json @@ -0,0 +1,11164 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 55, + 103, + 538, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 103, + 538, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 103, + 538, + 120 + ], + "type": "text", + "content": "Range-nullspace Video Frame Interpolation with Focalized Motion Estimation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "spans": [ + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": "Zhiyang Yu" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Yu Zhang" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{2,\\boxtimes}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Dongqing Zou" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Xijun Chen" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Jimmy S. Ren" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Shunqing Ren" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{1,\\boxtimes}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": ", Harbin Institute of Technology, Harbin, China \n" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": " SenseTime Research and Tetras.AI, Beijing, China \n" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 52, + 141, + 566, + 200 + ], + "type": "text", + "content": " Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 226, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 253, + 290, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 253, + 290, + 445 + ], + "spans": [ + { + "bbox": [ + 45, + 253, + 290, + 445 + ], + "type": "text", + "content": "Continuous-time video frame interpolation is a fundamental technique in computer vision for its flexibility in synthesizing motion trajectories and novel video frames at arbitrary intermediate time steps. Yet, how to infer accurate intermediate motion and synthesize high-quality video frames are two critical challenges. In this paper, we present a novel VFI framework with improved treatment for these challenges. To address the former, we propose focalized trajectory fitting, which performs confidence-aware motion trajectory estimation by learning to pay focus to reliable optical flow candidates while suppressing the outliers. The second is range-nullspace synthesis, a novel frame renderer cast as solving an ill-posed problem addressed by learning decoupled components in orthogonal subspaces. The proposed framework sets new records on 7 of 10 public VFI benchmarks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 470, + 128, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 128, + 482 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 128, + 482 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": "Continuous-time Video Frame Interpolation (VFI) aims at upsampling the temporal resolution of low frame-rate videos steplessly by synthesizing the missing frames at arbitrary time steps. It is a fundamental technology for various downstream video applications such as streaming [34], stabilization [5], and compression [35]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 564, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 673 + ], + "type": "text", + "content": "A key challenge of this task is to find a continuous mapping from arbitrary time step to the latent scene motion to correctly render the target frame, observing the low frame-rate video. Typically, it was realized via two stages: motion trajectory fitting and frame synthesis, e.g. [1,3,4,10,13,17, 21,29,36,38,39]. In the former, a parametric trajectory model is fitted from the optical flows extracted from input frames, which can be resampled at any time step to get intermediate motion. For representing such a motion model," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 225, + 545, + 432 + ], + "blocks": [ + { + "bbox": [ + 309, + 225, + 545, + 432 + ], + "lines": [ + { + "bbox": [ + 309, + 225, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 309, + 225, + 545, + 432 + ], + "type": "image", + "image_path": "ecf815a0db0a124efcd9890b3b0e2f50f4f23dbc770c4d6db55d184054461f3f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 440, + 547, + 561 + ], + "lines": [ + { + "bbox": [ + 305, + 440, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 305, + 440, + 547, + 561 + ], + "type": "text", + "content": "Figure 1. Motivation of the proposed method. Given input frames and extracted optical flows (a), common VFI pipeline (b) is to fit a continuous motion trajectory model, resample flows at the target time step, based on which rendering rays are predicted to synthesize the intermediate frame by reorganizing pixels from the input frames. Our pipeline (c) proposes improved treatment in two aspects: 1) our focalized motion estimation assigns dynamic weights to the extracted optical flows to suppress the outlier flows and improve fitting accuracy, and the novel range-nullspace solver treats intermediate frame synthesis as an inverse problem instead of direct rendering. Please see text for more details." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 590, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 546, + 626 + ], + "type": "text", + "content": "the Taylor polynomial is often adopted with different orders [4, 13, 36]. However, fitting trajectory models are prone to optical flow errors, which are inevitable due to occlusion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Besides motion fitting, the frame synthesis step faces the challenges of correctly inferring scene geometry. Particularly, the intermediate flows resampled from the continuous motion model only depict partial correspondences between the intermediate frame with input frames, while existing methods predict complete rendering rays in a data-driven manner to facilitate full rendering, as shown in Fig. 1 (b)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 683, + 259, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 683, + 259, + 693 + ], + "spans": [ + { + "bbox": [ + 54, + 683, + 259, + 693 + ], + "type": "text", + "content": "* This work is done during Zhiyang's internship at SenseTime." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "type": "text", + "content": "Correspondence should be addressed to Yu Zhang (zhangyulb@gmail.com) and Shunqing Ren (renshunqing@hit.edu.cn)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22159" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "content": "Though powerful architectures [15] and rendering mechanisms [10] were proposed, it requires the network to fully encode the scene geometry to predict correct rays, which may raise the difficulty of architecture design and the burden of learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 287, + 381 + ], + "type": "text", + "content": "To overcome these issues, we propose a novel framework with improved motion fitting and frame synthesis components. As shown in Fig. 1 (c), the first is focalized trajectory fitting, which extracts a set of optical flow candidates from the input video and assigns learned confidence weights to them. Confidence-aware, differentiable trajectory fitting is then followed, focalizing only the confident flows and producing improved parametric motion models. Such models, when resampled at the target time step, can produce accurate flows even at the occlusion boundary. For the latter, we follow the fact that intermediate frame synthesis is an ill-posed task and propose a deep solver based on the range nullspace theory [2]. Our solver decomposes the latent intermediate frame into several orthogonal image components and adopts different networks to learn each of them. Such physics-guided design encourages learning decoupled subtasks for each network, relieving the burden of encoding scene geometry and benefiting the use of lightweight models. In particular, our framework sets new records on 7 out of 10 public VFI benchmarks while being parameter-efficient." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 383, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 286, + 491 + ], + "type": "text", + "content": "We summarize the contributions of this paper as follows. 1) A novel lightweight VFI framework is proposed, which refreshes the records of 7 out of 10 public VFI benchmarks. 2) The idea of focalized trajectory fitting, which improves parametric motion estimation in VFI and generates better resampling quality of intermediate flows. 3) A new perspective that treats intermediate frame synthesis as an ill-posed problem, solved with a deep range nullspace solver that decouples frame synthesis into several orthogonal tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 502, + 135, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 135, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 135, + 514 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": "Video frame interpolation requires estimating the motion of intermediate frames before synthesizing them. Such motion could be directly predicted as image correspondences in a data-driven manner [11, 15], or evaluated from parameterized motion trajectories fitted with optical flows extracted from input frames. Typically the latter one is more flexible to do frame interpolation at any time step. For representing the motion model, linear motion is mostly assumed [1, 3, 10, 13, 21, 29], while quadratic [17, 36, 38, 39] and cubic [4] models were proposed and show improved performance with higher orders of freedom. Frame synthesis was then carried out by warping the information from input frames, guided by the estimated motion. This involves synthesis techniques of backward warping [13, 17, 29, 36] or forward splatting [10, 21], depending on the direction of intermediate flows. High-quality synthesis poses the de" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "mand of reasoning occlusion, which was implemented explicitly with scene depth [1] or implicitly via powerful post-processing architectures [11, 17]. VFI can also be implemented in a highly data-driven manner [14], abstracting out all the above steps with neural networks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 133, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 286 + ], + "type": "text", + "content": "There was also an important track of VFI that only synthesizes the middle frame of a pair of input frames. Without the need of representing motion continuously and interpolating arbitrary time steps, sophisticated components can be designed to optimally fit this task. For example, intermediate frame synthesis was solved with bilateral cost volumes [23], asymmetric bilateral volumes [24], expanded flows [8], and deformable convolutions [7]. There was also kernel-based method [22], with enhanced variants [3,16,27] that introduce more freedom into standard kernels with learned offsets and weights. Recent advances of deep learning architectures, like transformer [28] and channel attention modules [6], are also beneficial." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 288, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 419 + ], + "type": "text", + "content": "Range-nullspace learning provides a solver for inverse problems where the forward degeneration is a known linear operator [26]. It finds applications in solving superresolution [2], denoising [33] and compressed sensing [19]. Treating video frame interpolation as an inverse problem was first performed by [39], which developed iterative solvers based on learned gradients under the Bayesian inference framework. In this work, we adapt the range-nullspace theory to VFI and propose a non-iterative solver that learns orthogonally decomposed image components to relieve the entanglement of learned representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 430, + 455, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 455, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 455, + 442 + ], + "type": "text", + "content": "3. The Proposed Framework" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 449, + 373, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 373, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 373, + 460 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "content": "Following the routine of previous works [17, 36, 38, 39], our framework takes 4 adjacent input video frames " + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{-1},\\mathbf{I}_0,\\mathbf{I}_1,\\mathbf{I}_2\\in [-1,1]^{H\\times W\\times 3}" + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "content": " and generates intermediate frame " + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "content": " for any given time " + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "inline_equation", + "content": "t\\in (0,1)" + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "content": ". As shown in Fig. 2, our pipeline starts by extracting appearance features for each input frame with a contextual network " + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 468, + 545, + 538 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 548, + 545, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 548, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 364, + 548, + 545, + 560 + ], + "type": "interline_equation", + "content": "\\mathbf {C} _ {i} = \\mathcal {C} (\\mathbf {I} _ {i}), i \\in \\{- 1, 0, 1, 2 \\}. \\tag {1}", + "image_path": "14269d22a5ea84aaba813858e3856051e85999fd0b1e653216c5ef24a3fd9bba.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": "In the meantime, optical flows starting from " + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": " to other neighbours are computed. This yields 6 optical flow maps " + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{i\\rightarrow j}\\in \\mathbb{R}^{H\\times W\\times 2}" + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "inline_equation", + "content": "i\\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "inline_equation", + "content": "j\\neq i" + }, + { + "bbox": [ + 304, + 568, + 545, + 604 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "The Focalized Motion Estimation (FME) in Fig. 2 consumes optical flows and contextual features. It consists of three steps: flow confidence estimation, focalized trajectory fitting, motion resampling and refinement, and outputs motion specifications at a given time " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": ". Bi-directional motions are inferred, regarding both time 0 and 1:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 685, + 545, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 685, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 317, + 685, + 545, + 704 + ], + "type": "interline_equation", + "content": "\\begin{array}{l}\\hat {\\mathbf {F}} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathrm {F M E} (t, \\left\\{\\mathbf {F} _ {0 \\rightarrow j} \\right\\} _ {j \\neq 0}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),\\\\\\hat {\\quad}\\end{array}\\tag {2}", + "image_path": "f21f1ac5c1e80f69e6ee73d6a634cfe6753fb8f04fca108d6df6af78e2050615.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 319, + 703, + 520, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 703, + 520, + 715 + ], + "spans": [ + { + "bbox": [ + 319, + 703, + 520, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {1 \\rightarrow t}, \\mathbf {M} _ {1 \\rightarrow t} = \\operatorname {F M E} (1 - t, \\left\\{\\mathbf {F} _ {1 \\rightarrow j} \\right\\} _ {j \\neq 1}, \\left\\{\\mathbf {C} _ {i} \\right\\} _ {\\forall i}),", + "image_path": "54a7c28a2a9b04f3f1b82c54ae032ca0524925257416560ba946f4c30f0073f1.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22160" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 545, + 262 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 545, + 262 + ], + "type": "image", + "image_path": "fc0842946a3993d3585174f59ea509007795e798f5df177aee937bfbb8be7baa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 546, + 307 + ], + "type": "text", + "content": "Figure 2. Pipeline of our proposed method including contextual feature extraction, flow estimation, focalized motion estimation (FME), and range-nullsapce synthesis (RNS). Detailed descriptions of FME (middle) can be found in Sect. 3.2, and RNS (right) is elaborated in Sect. 3.3. For the details of mathematical symbols, please refer to the text." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{i\\rightarrow t}" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{i\\rightarrow t}" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "i\\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": " are the resampled flows and occlusion relation masks to be explained in Sect. 3.2. Finally, we feed these motion specifications at time " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": " and contextual features of input frames " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 327, + 287, + 389 + ], + "type": "text", + "content": " into the Range-Nullspace Synthesis (RNS) module," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 84, + 396, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 396, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 84, + 396, + 287, + 417 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {t} ^ {*} = \\operatorname {R N S} \\left(\\left\\{\\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}, \\mathbf {C} _ {i} \\right\\} _ {i \\in \\{0, 1 \\}}\\right). \\tag {3}", + "image_path": "1a6ba3d85c1adf72519e9fdc40418d1d6af78b920975e21821234ed3e1029219.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "type": "text", + "content": "In the following, we will elaborate technical details of the proposed FTE and RNS modules." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 458, + 239, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 239, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 239, + 471 + ], + "type": "text", + "content": "3.2. Focalized Motion Estimation (FME)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": "For the sake of conciseness, only the direction " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "0 \\to t" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": " in Eq. (2) is considered here, as " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "1 \\to t" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": " follows the similar process. Given contextual features " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": " and candidate flows " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_{0 \\to j}\\}_{j \\neq 0}" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": ", the confidence estimation step dynamically weights optical flow candidates. To this end, the contextual features " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": " are half split along the channel dimension, yielding " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "[\\mathbf{C}_i^a, \\mathbf{C}_i^b]" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": ", and the confidence estimation only works with the right half " + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i^b" + }, + { + "bbox": [ + 46, + 477, + 287, + 597 + ], + "type": "text", + "content": " to save calculation and leave the representation ability of remaining features untouched. The following warping residual is computed:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 77, + 606, + 287, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 606, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 77, + 606, + 287, + 622 + ], + "type": "interline_equation", + "content": "\\mathbf {R} _ {i} = \\mathbf {C} _ {0} ^ {b} - \\phi_ {\\mathcal {B}} (\\mathbf {C} _ {i} ^ {b}, \\mathbf {F} _ {0 \\rightarrow i}), i \\in \\{- 1, 1, 2 \\}, \\tag {4}", + "image_path": "2e8c66b12d5c335a3bb78a22f83ac3ac21de1872a3f81af9164036d55c6df55b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathcal{B}}" + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "content": " represents the bilinear warping function [12] that projects features " + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i^b" + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "content": " to time 0 with backward warping. Intuitively, the residuals " + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_i" + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "content": " conveys rich information of appearance warping errors induced by flows. We map such residuals to confidence weights via a network " + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 631, + 287, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 88, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {W} _ {- 1}, \\mathbf {W} _ {1}, \\mathbf {W} _ {2} = \\mathcal {W} (\\mathbf {R} _ {- 1}, \\mathbf {R} _ {1}, \\mathbf {R} _ {2}), \\tag {5}", + "image_path": "2445970e542dc18f4c606d2ce43b361dadfdc86a91f6e3afb38658f5379bd68a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_i\\in (0,1)^{H\\times W\\times 1}" + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\sum_{i\\in \\{-1,1,2\\}}\\mathbf{W}_i = 1" + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "content": " Higher value of " + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_i" + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "content": " indicates higher confidence of the flow values in " + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{0\\rightarrow i}" + }, + { + "bbox": [ + 305, + 325, + 545, + 375 + ], + "type": "text", + "content": ", which deserves more focus for fitting parametric motion trajectory models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 375, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 375, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 545, + 411 + ], + "type": "text", + "content": "Focalized trajectory fitting. We suppose that, in a short time interval around each pixel of " + }, + { + "bbox": [ + 305, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 305, + 375, + 545, + 411 + ], + "type": "text", + "content": ", the motion trajectory is approximated with 2nd-order Taylor polynomial:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 418, + 545, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 418, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 331, + 418, + 545, + 432 + ], + "type": "interline_equation", + "content": "f (\\tau ; \\mathbf {A}, \\mathbf {B}) = \\mathbf {A} \\tau^ {2} + \\mathbf {B} \\tau , \\mathbf {A}, \\mathbf {B} \\in \\mathbb {R} ^ {H \\times W \\times 2}, \\tag {6}", + "image_path": "3fe94e22a32f1aa62b253c211c264e83aeefbbdfafc694d8b6bfe71226680ba8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": " are model coefficients to fit, and " + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\tau \\in [-1,2]" + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": " is the temporal distance w.r.t. time 0. Solving " + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 305, + 439, + 545, + 475 + ], + "type": "text", + "content": " can be formulated with the following weighted least squares:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 483, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 483, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 318, + 483, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {A}, \\mathbf {B}} \\sum_ {i \\in \\{- 1, 1, 2 \\}} \\| \\sqrt {\\mathbf {W} _ {i}} \\odot (\\mathbf {F} _ {0 \\rightarrow i} - f (i; \\mathbf {A}, \\mathbf {B})) \\| _ {2} ^ {2}, \\tag {7}", + "image_path": "98eee6a4446949ed36c9f813bce102849adc295bc323baa38e4d17fda66d4810.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 517, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 517, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 517, + 545, + 552 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 305, + 517, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 305, + 517, + 545, + 552 + ], + "type": "text", + "content": " denotes element-wise product (with broadcasting along channel dimension). The optimal solution of this weighted least squares has the analytical form" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 340, + 559, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 559, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 340, + 559, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {\\Theta}} _ {x, y, z} = \\left(\\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {X} ^ {T}\\right) ^ {- 1} \\mathbf {X} \\mathbf {W} _ {x, y} \\mathbf {F} _ {x, y, z}, \\tag {8}", + "image_path": "24cf68d354907b44a29ff793354bc2f60bc608c84db060a8de7c2444b7a2f0f7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "inline_equation", + "content": "x, y" + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "text", + "content": " index the vertical, horizontal and channel dimensions of tensors, " + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\hat{\\Theta}_{x,y,z} = \\left(\\hat{\\mathbf{A}}(x,y,z),\\hat{\\mathbf{B}}(x,y,z)\\right)^{\\mathrm{T}}" + }, + { + "bbox": [ + 305, + 581, + 545, + 624 + ], + "type": "text", + "content": " is the solved coefficients. Other matrices are:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 319, + 628, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 628, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 319, + 628, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\begin{array}{l}\\mathbf {W} _ {x, y} = \\left[\\begin{array}{c c c}\\mathbf {W} _ {- 1} (x, y, 0)&&\\\\&\\mathbf {W} _ {1} (x, y, 0)&\\\\&&\\mathbf {W} _ {2} (x, y, 0) (x, y)\\end{array}\\right],\\\\\\mathbf {X} = \\left[\\begin{array}{c c c}1&1&4\\\\- 1&1&2\\end{array}\\right], \\mathbf {F} _ {x, y, z} = \\left[\\begin{array}{c}\\mathbf {F} _ {0 \\rightarrow - 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 1} (x, y, z)\\\\\\mathbf {F} _ {0 \\rightarrow 2} (x, y, z)\\end{array}\\right].\\end{array}\\tag {9}", + "image_path": "d7590ca173d437b9c7c2911627ce36815b287353b10b22fe8b163c535c14a45e.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "All the calculations of Eq. (8) are fast to compute, including the " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " matrix inverse which is closed-form. This" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22161" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 289, + 212 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 289, + 212 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 289, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 289, + 212 + ], + "type": "image", + "image_path": "1341e4edc0f420d74e6b7ef4b918f95818cc7c3774064ce5a8c1482232b23c46.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 289, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 289, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 289, + 319 + ], + "type": "text", + "content": "Figure 3. A toy 1-D example comparing different trajectory fitting methods. Linear model [13] is not adequate to approximate curved trajectory. Due to noisy measurements, quadratic models [17, 36] do not approximate the real curve well with fixed optical flow weighting. The cubic model [4] performs even worse due to the outlier at " + }, + { + "bbox": [ + 46, + 220, + 289, + 319 + ], + "type": "inline_equation", + "content": "t = 2" + }, + { + "bbox": [ + 46, + 220, + 289, + 319 + ], + "type": "text", + "content": ", which deteriorates high-order polynomial regression. The proposed FTF achieves best approximation by dynamically weighting the contributions of measurements. In Sect. 4.4, we show benefits of this idea on real VFI samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 339, + 287, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 362 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 362 + ], + "type": "text", + "content": "renders the solver an efficient layer when integrated into the whole architecture." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "content": "Motion resampling and refinement. After model fitting, we can resample the intermediate flows " + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "content": " by evaluating " + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "inline_equation", + "content": "f(t;\\hat{\\mathbf{A}},\\hat{\\mathbf{B}})" + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "content": ". Similar with previous works [10, 21], we also learn to refine the resampled flows to get benefits from end-to-end training, and infer the visibility masks indicating occlusion relations at time " + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "content": ". This is achieved with a refinement network " + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 364, + 289, + 447 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 81, + 456, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 456, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 81, + 456, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\Delta \\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {M} _ {0 \\rightarrow t} = \\mathcal {M} \\left(\\mathbf {F} _ {0 \\rightarrow t}, \\mathbf {C} _ {0}, \\bar {\\mathbf {C}} _ {1 \\rightarrow 0}\\right), \\tag {10}", + "image_path": "fcef41d2e9ec3d946a117e458a54cc34114dab984b92152ff0b0a45df59f4cfe.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{C}}_{1\\rightarrow 0} = \\phi_{\\mathcal{B}}(\\mathbf{C}_1,\\mathbf{F}_{0\\rightarrow 1})" + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "text", + "content": " is the warped features from time 1 to 0. The refined intermediate flows are " + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{0\\rightarrow t} = \\mathbf{F}_{0\\rightarrow t} + \\Delta \\mathbf{F}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "text", + "content": ", with a soft mask " + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{0\\rightarrow t}\\in (0,1)^{H\\times W\\times 1}" + }, + { + "bbox": [ + 46, + 476, + 287, + 538 + ], + "type": "text", + "content": " indicating the occlusion order of pixels used for soft splating [21], which are to be used in Sect. 3.3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 544, + 226, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 226, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 226, + 558 + ], + "type": "text", + "content": "3.3. Range-nullspace Synthesis (RNS)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": "The rest pipeline aims to synthesize the target frame at time " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": ". Arguably, rendering cannot be fully performed with the resampled flows " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{1\\rightarrow t}" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": ", which only depict partial correspondences from " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": ", and do not account for occluded pixels in " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 563, + 287, + 647 + ], + "type": "text", + "content": ". Instead of predicting full correspondences, we treat frame synthesis as an inverse problem and solve it with a theory developed for it." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": "Our starting point is that given the unknown " + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": " and forward flows " + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{1\\rightarrow t}" + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": ", we can relate these terms with the observations " + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 647, + 287, + 683 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 102, + 689, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 689, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 102, + 689, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right] = \\left[\\begin{array}{l}\\mathbf {H} _ {0 \\rightarrow t}\\\\\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right] \\mathbf {I} _ {t} + \\left[\\begin{array}{l}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]. \\tag {11}", + "image_path": "170bf5e944a2272b4faa9a4be399c94ca7c82282ca762aa12c3ba56852697d76.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "With slight abuse of notation, " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " now denote with vectorized and raster scanned images in " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "[-1,1]^N" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "N = H \\times W \\times C" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "C = 3" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " is the total number of pixels. In this case, flow-based warping with " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{0 \\to t}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{1 \\to t}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " can be reorganized as matrix multiplication with " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{0 \\to t}, \\mathbf{H}_{1 \\to t} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ". The additive residuals " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Upsilon}_t" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " represent image components that cannot be modelled by warping, e.g. occluded image content and lost high-frequencies caused by warping operator." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": "Taking " + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": " in (11) as the latent to restore and " + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_y" + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": " as the measurements, we can treat (11) as an inverse problem with linear forward operator " + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t" + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": ". Solving general linear inverse problems is not trivial, especially when the distributions of the residuals " + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\Upsilon_t" + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": " and the latent " + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t" + }, + { + "bbox": [ + 304, + 180, + 545, + 299 + ], + "type": "text", + "content": " are complex. Replacing the former with simple analytical distributions can lead to classical Bayesian solvers, which are usually iterative even with learned gradients [39]. In this paper, we instead embrace a non-iterative and fast alternative, based on the deep range-nullspace solvers [2]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": "Range nullspace learning. Range-nullspace theory states that if a forward operator " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": " has right inverse " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^+" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": " that satisfies " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{HH}^{+} = \\mathbf{I}_{d}" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_d" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": " is the identity matrix, it is possible to define two orthogonal projections " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 304, + 300, + 545, + 348 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 327, + 354, + 545, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 354, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 327, + 354, + 545, + 368 + ], + "type": "interline_equation", + "content": "\\mathcal {R} (\\boldsymbol {x}) \\triangleq \\mathbf {H} ^ {+} \\mathbf {H} \\boldsymbol {x}, \\mathcal {N} (\\boldsymbol {x}) \\triangleq \\left(\\mathbf {I} _ {d} - \\mathbf {H} ^ {+} \\mathbf {H}\\right) \\boldsymbol {x}. \\tag {12}", + "image_path": "9fb0a9911e2b42c560594db6022ec3dbd35a7f11f17db837998ceca90b9fd981.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": "It is easy to verify that " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\pmb{x} = \\mathcal{R}(\\pmb{x}) + \\mathcal{N}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\pmb{x})^{\\mathrm{T}}\\mathcal{N}(\\pmb{y}) = 0" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " are called range- and null-space projections, respectively. Particularly, " + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 375, + 545, + 423 + ], + "type": "text", + "content": " satisfies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 430, + 545, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 430, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 358, + 430, + 545, + 444 + ], + "type": "interline_equation", + "content": "\\mathcal {N} (\\boldsymbol {x}) \\in \\left\\{\\boldsymbol {u} \\in \\mathbb {R} ^ {N \\times 3} | \\mathbf {H} \\boldsymbol {u} = \\boldsymbol {0} \\right\\}. \\tag {13}", + "image_path": "b6b15d68e3db116dc5da483a4d6389a3ed7eba9b5259b816b0d88dc55060dfc4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 452, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 500 + ], + "type": "text", + "content": "Regarding our problem (11), unfortunately, the forward operator " + }, + { + "bbox": [ + 304, + 452, + 545, + 500 + ], + "type": "inline_equation", + "content": "[\\mathbf{H}_{0\\rightarrow t}^{\\mathrm{T}},\\mathbf{H}_{1\\rightarrow t}^{\\mathrm{T}}]^{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 452, + 545, + 500 + ], + "type": "text", + "content": " has no right inverse (we refer interested readers to the supplementary material for derivations). However, it has the following equivalent form:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 505, + 545, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 505, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 314, + 505, + 545, + 557 + ], + "type": "interline_equation", + "content": "\\underbrace {\\left[\\begin{array}{l}\\mathbf {I} _ {0}\\\\\\mathbf {I} _ {1}\\end{array}\\right]} _ {\\mathbf {I} _ {y}} = \\underbrace {\\left[\\begin{array}{c c}\\mathbf {H} _ {0 \\rightarrow t}&\\mathbf {0}\\\\\\mathbf {0}&\\mathbf {H} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\mathbf {H} _ {t}} \\tilde {\\mathbf {I}} _ {t} + \\underbrace {\\left[\\begin{array}{c}\\boldsymbol {\\Upsilon} _ {0 \\rightarrow t}\\\\\\boldsymbol {\\Upsilon} _ {1 \\rightarrow t}\\end{array}\\right]} _ {\\boldsymbol {\\Upsilon} _ {t}}, \\text {s . t .} \\mathbf {C} \\tilde {\\mathbf {I}} _ {t} = \\mathbf {0}, \\tag {14}", + "image_path": "9ff1ade002b27438778014d78c9a102d2797147ca4fa073b4ffa5ec72f6e69fd.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": " is divided into the top and bottom half, i.e. " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t = [\\tilde{\\mathbf{I}}_{t,1}^{\\mathrm{T}},\\tilde{\\mathbf{I}}_{t,2}^{\\mathrm{T}}]^{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = [\\mathbf{I}_d, - \\mathbf{I}_d]" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": ". The constraint simply confines that " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{t,1}^{\\mathrm{T}} = \\mathbf{I}_{t,2}^{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": ". Our strategy is to first solve " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": " without the constraint. In this case, " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": " in Eq. (14) can be right reversed. To meet the constraint, we find a projection of the result into the constraint set " + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\{\\pmb {u}\\in \\mathbb{R}^{2N}|\\mathbf{C}\\pmb {u} = \\mathbf{0}\\}" + }, + { + "bbox": [ + 304, + 558, + 545, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 635, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 658 + ], + "type": "text", + "content": "The appealing property of nullspace projection (13) can be used to construct the following solver:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 347, + 666, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 666, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 347, + 666, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right) + \\mathcal {N} (g (\\cdot)), \\tag {15}", + "image_path": "0820b8d44696a521fc4dca88728f8ef26ed0f45f1cdbffbfce133b8d1948456a.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "text", + "content": " is arbitrary vector-to-vector function. The interesting fact of (15) is, by this construction, " + }, + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t^*" + }, + { + "bbox": [ + 304, + 688, + 545, + 714 + ], + "type": "text", + "content": " always satisfies" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22162" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* +\\Upsilon_t" + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "text", + "content": ". Different " + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "text", + "content": "s lead to different reconstructions, revealing the ill-posedness of inverse problems. To get results that fall onto natural images, we implement " + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 71, + 287, + 131 + ], + "type": "text", + "content": " with a neural network trained to minimize the empirical errors on a dataset." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": "Solving (15) is left to know the residuals " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\Upsilon_{t}" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": ". Though following complex, structured distributions, " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\Upsilon_{t}" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": " is mostly sparse and universally bounded (" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "|\\Upsilon_{t}| \\leq 2" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": "), which can be approximated well with neural networks. Inspired by [2], we use another network " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": " to directly approximate " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t^+\\mathbf{\\Upsilon}_t" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": " which is also bounded. When ideal convergence is reached after training, " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "|r(\\cdot) - \\mathbf{H}_t^+\\mathbf{\\Upsilon}_t| \\to 0" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": ", then the data consistency " + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_y = \\mathbf{H}_t\\tilde{\\mathbf{I}}_t^* + \\Upsilon_t" + }, + { + "bbox": [ + 46, + 132, + 287, + 229 + ], + "type": "text", + "content": " can be met by (15)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "text", + "content": "After yielding the result " + }, + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t" + }, + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "text", + "content": ", projection onto " + }, + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{C}\\tilde{\\mathbf{I}}_t = \\mathbf{0}" + }, + { + "bbox": [ + 47, + 230, + 287, + 255 + ], + "type": "text", + "content": " is performed by minimizing" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 260, + 287, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 260, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 52, + 260, + 287, + 285 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} ^ {*} = \\arg \\min _ {\\boldsymbol {y} \\in \\mathbb {R} ^ {2 N}} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} \\left(\\mathcal {N} _ {\\mathcal {C}} (\\boldsymbol {y}) - \\tilde {\\mathbf {I}} _ {t}\\right), \\tag {16}", + "image_path": "6ca88c852490daf4ca1d1ea7b1b5fc60c653be3625f7faff2b21d63d508a23a4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{C}}(\\boldsymbol{y}) = (\\mathbf{I}_d - \\mathbf{C}^{\\pm}\\mathbf{C})\\boldsymbol{y}" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": " is the nullspace projection of " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\pm}" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": " is the pseudo inverse, and " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma} \\in [0,1]^{2N \\times 2N}" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": " defines the distance metric. The projected result is " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^* = \\mathcal{N}_{\\mathcal{C}}(\\mathbf{y}^*)" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma} = \\mathbf{I}_d" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ", it is easy to show " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^*" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": " is simply the average of the top and bottom half of " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}_t^*" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^* = (\\tilde{\\mathbf{I}}_{t,1}^* + \\tilde{\\mathbf{I}}_{t,2}^*) / 2" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": " (see supplementary material for details). Instead, we benefit from end-to-end training and predict a dynamic blending mask as a diagonal matrix " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Lambda} \\in [0,1]^{N \\times N}" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ", and obtain the result by " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^* = \\boldsymbol{\\Lambda}\\tilde{\\mathbf{I}}_{t,1}^* + (\\mathbf{I}_d - \\boldsymbol{\\Lambda})\\tilde{\\mathbf{I}}_{t,2}^*" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": ". It corresponds to learned distance matrix in (16), where " + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma} = \\mathrm{diag}([\\boldsymbol{\\Lambda},\\mathbf{I}_d - \\boldsymbol{\\Lambda}])" + }, + { + "bbox": [ + 46, + 293, + 287, + 416 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": "The decomposition learning (15) amortizes the difficulty of frame synthesis by several decoupled components. The term " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t^+\\mathbf{I}_y" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t^+ = \\mathrm{diag}([\\mathbf{H}_{0\\to t}^+, \\mathbf{H}_{1\\to t}^+])" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": ", can be intuitively thought of warping " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": " to time " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": ", yielding physics-guided synthesis results. The network " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": " learns to correct the error of physics-based warping, as the " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": " operator first back-projects the network output to time 0 and 1, and then does the same forward warping. The network " + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 416, + 287, + 547 + ], + "type": "text", + "content": " inpaints image content that cannot be addressed by forward warping, which are often occluded layer. In Sect. 4.4, we provide a visual analysis of the learned components." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "content": "Implementation. The network " + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "content": " have many design choices, not limited to the following one we use:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 578, + 263, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 578, + 263, + 604 + ], + "spans": [ + { + "bbox": [ + 53, + 578, + 263, + 604 + ], + "type": "interline_equation", + "content": "\\boldsymbol {f}, \\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t} = r \\left(\\left\\{\\phi_ {\\mathcal {F}} (\\mathbf {C} _ {i}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}) \\right\\} _ {i \\in \\{0, 1 \\}}\\right),", + "image_path": "f4a587b40127a5a32ad6b9955046c8d081cabba153d5d7a8d6c5d699c32d7010.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 605, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 605, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 69, + 605, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Lambda}, \\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}} = g \\left(\\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} \\left(\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}\\right), \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y}, \\boldsymbol {f}\\right), \\tag {17}", + "image_path": "cca973f86c33df59f6ac9ca8c24fe0adba3fa3cba6868cd8f46b8878f718fdc0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 624, + 235, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 624, + 235, + 641 + ], + "spans": [ + { + "bbox": [ + 85, + 624, + 235, + 641 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {I}} _ {t} ^ {*} = \\mathbf {H} _ {t} ^ {+} \\mathbf {I} _ {y} - \\mathcal {R} (\\mathbf {H} _ {t} ^ {+} \\boldsymbol {\\Upsilon} _ {t}) + \\mathcal {N} (\\tilde {\\mathbf {I}} _ {t} ^ {\\mathcal {N}}),", + "image_path": "4cf765e10d031f636f5fdd15d5e77d38ec7090045661839ca4158e356bf2ecf9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 85, + 643, + 167, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 643, + 167, + 658 + ], + "spans": [ + { + "bbox": [ + 85, + 643, + 167, + 658 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {t} ^ {*} = [ \\boldsymbol {\\Lambda}, \\mathbf {I} _ {d} - \\boldsymbol {\\Lambda} ] \\tilde {\\mathbf {I}} _ {t} ^ {*}.", + "image_path": "518b36bd433c7f018af4fe4186a62f9c9fd4dcfb642e8dabbc8b82568168dd14.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Note " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " form casaded structure, where the estimation result of " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is the input of " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": ". We also pass through intermediate features " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " in this casade as unobstructed information flow. Matrix multiplications with " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_t^+" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " are all" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "implemented via warping operations. Multiplications with " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{0\\rightarrow t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{1\\rightarrow t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " can be done via backward warping, while with their inverse we use softmax splatting [21]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 118, + 545, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 118, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 359, + 118, + 545, + 138 + ], + "type": "interline_equation", + "content": "\\mathbf {H} _ {i \\rightarrow t} \\boldsymbol {x} = \\phi_ {\\mathcal {B}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}), \\tag {18}", + "image_path": "c1b82a73a95750145821e69f979f7be2cb2a0d6ab2db768e380253d61a89929e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 361, + 135, + 491, + 149 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 135, + 491, + 149 + ], + "spans": [ + { + "bbox": [ + 361, + 135, + 491, + 149 + ], + "type": "interline_equation", + "content": "\\mathbf {H} _ {i \\rightarrow t} ^ {+} \\boldsymbol {x} \\approx \\phi_ {\\mathcal {F}} (\\boldsymbol {x}; \\hat {\\mathbf {F}} _ {i \\rightarrow t}, \\mathbf {M} _ {i \\rightarrow t}),", + "image_path": "adfdbcfa3b2463147db89f9be570c6d2328fa30b989f24f5fc342471017f1c1a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{i\\rightarrow t}" + }, + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{i\\rightarrow t}" + }, + { + "bbox": [ + 304, + 160, + 545, + 233 + ], + "type": "text", + "content": " are the corresponding flows and masks defined in (10). Note this only slightly breaks the right inverse constraint but improves efficiency and flexibility. The overall working flow of steps (17) is referred to Fig. 2. Due to space limit, the detailed network configurations are referred to the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 233, + 541, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 233, + 541, + 245 + ], + "spans": [ + { + "bbox": [ + 317, + 233, + 541, + 245 + ], + "type": "text", + "content": "Loss functions. Our loss function is defined as follows" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 309, + 254, + 545, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 254, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 309, + 254, + 545, + 279 + ], + "type": "interline_equation", + "content": "L _ {t o t a l} = \\log \\left(\\left\\| \\mathbf {I} _ {t} ^ {*} - \\mathbf {I} _ {t} ^ {g t} \\right\\| _ {2} ^ {2} + \\epsilon\\right) + \\alpha \\left\\| \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} - \\mathbf {H} ^ {+} \\boldsymbol {\\Upsilon} _ {t} ^ {g t} \\right\\| _ {1}, \\tag {19}", + "image_path": "7309daf72ac307a2bd7d785cbfa33aa691c8e0b5ef5051be7f8a24aac43e2ed2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": "where the first one is a variant of standard " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": " error. In the supplementary material we show this loss mitigates the diminishing gradient issue of " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": " loss and yields improved performance. We set " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-8}" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": " to avoid numeric issues. The second loss enables that " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "r(\\cdot)" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": " approximates the true residual, where " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_t^{gt} = \\mathbf{I}_y - \\mathbf{H}_t\\mathbf{I}_t^{gt}" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": ". Empirically, we set " + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\alpha = 0.02" + }, + { + "bbox": [ + 304, + 280, + 545, + 352 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 363, + 435, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 435, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 435, + 376 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": " VFI. We test our method on three public 8x VFI datasets: GoPro [20], X4K1000FPS [29] and Adobe240 [31]. For GoPro, we follow [14, 39] and train our method on the official train split of GoPro and evaluate it on its test split at a resolution of " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": ". We extract training samples according to the strategy applied in [14] and [39], yielding 22128 samples, each having 25 frames. In each sample, the " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "9^{th}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "17^{th}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "25^{th}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": " frames are used as input, while " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "10^{th}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "inline_equation", + "content": "16^{th}" + }, + { + "bbox": [ + 304, + 402, + 545, + 605 + ], + "type": "text", + "content": " frames serve as the supervision. The test set of GoPro is sampled similarly, resulting into 1500 non-overlapped samples. To verify the generalization capability, our model pre-trained on GoPro is also evaluated on a subset of Adobe240 [31] dataset including 630 samples, sampled with the strategy of [39], as well as the official test set of X4K1000FPS [29]. For fair comparisons on X4K1000FPS dataset, we also retrain and evaluate our method following its benchmarking protocol [29] strictly." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Single-frame " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "(2\\times)" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " VFI. Though our method is not designed for " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " VFI, we also evaluate on seven " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " VFI datasets for completeness. For training our method, since 4 input frames are required, we use the training split of the septuble set of Vince-90k [37], which contains 64612 samples at resolution " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "256\\times 448" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ". In each septuplet, we take the " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "5^{th}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "7^{th}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " frames as input and the " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " frame as the supervision. For evaluation, we use 7824 samples from the test split of Vince-90k septuplet set, 100 samples" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22163" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 542, + 339 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 542, + 339 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 542, + 339 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 542, + 339 + ], + "type": "image", + "image_path": "b650dcab1396ff9d5a22eb9cbfb91649a685167a3f8727748e4d814d63759f4f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 348, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 348, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 547, + 373 + ], + "type": "text", + "content": "Figure 4. Visual comparisons on X4K1000FPS (top 2 rows), and Adobe240 (bottom 2 rows) datasets, where each row corresponds to a scene. We overlay the nearest 2 input frames to illustrate the input motion. More results can be found in the supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 392, + 288, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 440 + ], + "type": "text", + "content": "from UCF101 [30], 2849 samples from DAVIS [25], and 310 samples from the easy, medium, hard and extreme subsets of SNU-FILM [6]. Note that these are the same evaluation protocols also adopted in [14, 28, 39]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 449, + 173, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 173, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 173, + 462 + ], + "type": "text", + "content": "4.2. Experimental settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": " VFI. On each benchmark, we train the network for 120 epochs with batch size 32 and patch size " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": ", which is optimized by the AdamW [18] with " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": " and weight decay " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "= 1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": ". At each iteration, the learning rate is decayed from " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": " gradually via cosine annealing with warm steps " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "= 2000" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": ". During the training process, we adopt random cropping, flipping, and color jittering for data augmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "text", + "content": "Single-frame " + }, + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "inline_equation", + "content": "(2\\times)" + }, + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "text", + "content": " VFI. The network is trained for 200 epochs with batch size 48 and patch size " + }, + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 46, + 564, + 287, + 601 + ], + "type": "text", + "content": ", leaving the remaining settings the same as above." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": "In all the benchmarks, we use two common metrics, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for quantitative evaluation, which is averaged across all the generated frames. Besides that, we use [32] for computing optical flows among input frames." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 670, + 270, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 270, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 270, + 683 + ], + "type": "text", + "content": "4.3. Comparisons with State-of-the-Art models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " VFI trained on GoPro. We compare our method with 11 competitive VFI methods that supports " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " VFI:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 390, + 547, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 547, + 434 + ], + "type": "text", + "content": "Table 1. Quantitative results of " + }, + { + "bbox": [ + 305, + 390, + 547, + 434 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 305, + 390, + 547, + 434 + ], + "type": "text", + "content": " VFI in terms of PSNR/SSIM and the number of parameters, evaluated on GoPro, Adobe240 and X4K1000FPS datasets. The best performed model is highlighted in red and the second best is colored in blue." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 443, + 544, + 590 + ], + "blocks": [ + { + "bbox": [ + 308, + 443, + 544, + 590 + ], + "lines": [ + { + "bbox": [ + 308, + 443, + 544, + 590 + ], + "spans": [ + { + "bbox": [ + 308, + 443, + 544, + 590 + ], + "type": "table", + "html": "
GoProAdobe240X4K1000FPSParam(M)
SloMo [13]29.71/0.92429.63/0.92725.07/0.79539.61
QVI [36]30.52/0.94131.41/0.95528.06/0.85529.23
EQVI [17]30.81/0.94232.13/0.95926.96/0.84328.07
DAIN [1]29.53/0.92030.53/0.93927.28/0.83524.03
EDSC [3]29.20/0.91629.87/0.93125.30/0.8118.95
FLAVR [14]31.10/0.94230.92/0.93824.50/0.79142.06
XVFI [29]29.80/0.92529.74/0.93028.42/0.8815.61
M2M [10]30.52/0.93329.93/0.93130.04/0.9057.61
IFRNet [15]30.00/0.92829.62/0.92523.77/0.79319.69
RIFEm [11]29.79/0.92529.81/0.93028.70/0.88010.71
DBVI [39]31.73/0.94733.28/0.96531.10/0.92815.18
Ours32.31/0.95133.32/0.96431.97/0.93210.10
", + "image_path": "664577851b63ed1ac81b63a57457a6ed04f67b600c3bb50dfad7546974b2b351.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "SloMo [13], QVI [36], EQVI [17], DAIN [1], XVFI [29], M2M [10], DBVI [39], EDSC [3], FLAVR [14], IFRNet [15] and RIFE [11]. Note our evaluating settings are identical with [39], and for methods that do not follow the unified protocol proposed in [39], including EQVI, M2M, IFRNet and RIFE, we retrain them using the same protocol on GoPro and report the results. The quantitative results on GoPro, Adobe240 and X4K1000FPS are reported in Ta" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22164" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 547, + 136 + ], + "blocks": [ + { + "bbox": [ + 100, + 70, + 493, + 83 + ], + "lines": [ + { + "bbox": [ + 100, + 70, + 493, + 83 + ], + "spans": [ + { + "bbox": [ + 100, + 70, + 493, + 83 + ], + "type": "text", + "content": "Table 2. Quantitative results of " + }, + { + "bbox": [ + 100, + 70, + 493, + 83 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 100, + 70, + 493, + 83 + ], + "type": "text", + "content": " VFI on X4K1000FPS dataset. following the benchmark protocol of [29]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 547, + 136 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 547, + 136 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 547, + 136 + ], + "type": "table", + "html": "
AdaCoF [16]FeFlow [9]SloMoQVIEQVIDAINFLAVRXVFIM2MIFRNetRIFEmDBVIOurs
PSNR25.8125.1627.7729.9628.2727.5227.9230.1230.8428.3630.7532.8933.88
SSIM0.7720.7830.8490.8920.8600.8210.8530.8700.9160.8700.9140.9390.946
", + "image_path": "81dbb7e14b567a690d6f7120da74affd46da5c220f4a71edaff0262c41d1a72a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 178, + 545, + 444 + ], + "blocks": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "lines": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "type": "text", + "content": "Table 3. Quantitative results on " + }, + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "type": "text", + "content": " interpolation in terms of PSNR/SSIM with number of parameters and flops. All the methods are trained on the training set of Vimeo-90K (septulets)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 178, + 545, + 444 + ], + "lines": [ + { + "bbox": [ + 49, + 178, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 49, + 178, + 545, + 444 + ], + "type": "table", + "html": "
Vimeo-90K (septulets)UCF101DAVISSNU-FILMParam(M)
EasyMediumHardExtreme
SloMo [13]34.43/0.96932.45/0.96726.10/0.86236.12/0.98433.44/0.97229.17/0.92824.14/0.84339.61
QVI [36]34.98/0.97032.87/0.96627.20/0.87439.53/0.99036.43/0.98331.07/0.94724.96/0.85629.23
EQVI [17]35.16/0.97332.99/0.97027.51/0.89137.44/0.97835.19/0.98130.72/0.94625.42/0.86828.07
XVFI [29]35.21/0.97032.68/0.96826.89/0.86839.21/0.98934.96/0.97729.43/0.92824.02/0.8415.61
DAIN [1]33.57/0.96431.65/0.96326.61/0.86738.53/0.98834.34/0.97429.50/0.93024.54/0.85124.03
BMBC [23]34.76/0.96532.61/0.95526.42/0.86839.90/0.99135.34/0.97829.34/0.92723.65/0.83711.01
ABME [24]35.67/0.97232.81/0.96927.00/0.86839.59/0.99035.77/0.97730.58/0.93625.42/0.86418.1
EDSC [3]34.52/0.96732.67/0.96826.28/0.84940.01/0.99035.37/0.97829.59/0.92624.39/0.8438.95
GDConv [27]35.58/0.97233.11/0.96927.02/0.87040.36/0.99136.14/0.98230.25/0.94024.82/0.8605.14
CAIN [6]34.69/0.96932.40/0.96627.12/0.87239.33/0.98935.34/0.97730.15/0.93324.88/0.85542.78
FLAVR [14]36.30/0.97533.33/0.97127.44/0.87340.44/0.99136.37/0.98130.87/0.94225.18/0.86242.06
M2M [10]35.56/0.97332.70/0.96927.57/0.88739.35/0.98935.23/0.97729.99/0.93424.83/0.8577.60
IFRNet [15]36.37/0.97632.87/0.96927.94/0.89039.68/0.99035.57/0.97930.21/0.93824.71/0.85519.69
Softsplat [21]35.76/0.97232.89/0.97027.42/0.878----12.46
RIFEm [11]35.87/0.97432.64/0.96927.75/0.88639.50/0.99035.46/0.97830.17/0.93624.79/0.85410.71
VFIT-B [28]36.96/0.97833.44/0.97128.17/0.88940.57/0.99136.54/0.98231.04/0.94525.50/0.86729.1
ST-MFNet [8]36.46/0.97633.46/0.97128.30/0.89640.78/0.99237.12/0.98431.61/0.95125.78/0.87421.03
DBVI [39]36.17/0.97633.01/0.97028.61/0.90540.46/0.99136.95/0.98531.68/0.95325.90/0.87621.69
Ours36.33/0.97533.25/0.97028.84/0.90540.67/0.99137.36/0.98532.21/0.95526.22/0.87710.10
", + "image_path": "f08622b0afcda9cdc568ff6fc32e437865d782605ad9207fcd76c88a2b3ff575.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "text", + "content": "ble 1, with the model size in terms of the number of parameters. Our approach achieves the best results across all the datasets, achieving at least 0.58dB improvement on GoPro and 0.87dB on X4K1000FPS. Compared with the state-of-the-art model DBVI, our model has only two-thirds parameters. For those with less parameters than ours (e.g. M2M), we achieve nearly 1.19dB improvements at least. " + }, + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "text", + "content": " VFI on X4K1000FPS dataset, following the protocol of [29]. We following the training and testing protocol of [29] to report fair benchmarking results on X4K1000FPS dataset. For fair comparison, we also retrain several methods (M2M, IFRNet, RIFE, EQVI) on the official training split and compare with the results already available from " + }, + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "inline_equation", + "content": "[29,39]^1" + }, + { + "bbox": [ + 46, + 459, + 289, + 685 + ], + "type": "text", + "content": ". As summarized in Table 2, our approach achieves 0.99dB improvement than previous leading method DBVI. As shown in Fig. 4, our approach outperforms existing methods especially in several hard cases, like occluded or high frequency area. More visual results can be found in our supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "text", + "content": "Single-frame " + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "inline_equation", + "content": "(2\\times)" + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "text", + "content": " VFI. Finally, we report the results on " + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "text", + "content": " VFI for completeness. Though our method is not dedicatedly designed for single-frame interpolation, we compare with 18 strong existing models and report the results in 3. Note that results of ABME, BMBC and CAIN have been reported in [39], while we extend this benchmarking with ST-MFNet" + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 304, + 459, + 547, + 639 + ], + "type": "text", + "content": ", VFIT, GD-Conv, as well as multiframe VFI models. All the additional models are trained on the train split of Video-90K (setptulets set). Our approach achieves the best results on 4 of 7 datasets. Slightly worse performance is observed on low resolution datasets Video-90K, UCF101 and the easy subset of SNU-FILM, whose motion is slight. On more challenging datasets like DAVIS and other subsets of SUN-FILM, the proposed method shows better generalizability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 648, + 432, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 648, + 432, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 648, + 432, + 662 + ], + "type": "text", + "content": "4.4. Performance Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 668, + 547, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 547, + 692 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 547, + 692 + ], + "type": "text", + "content": "Ablation analysis of motion trajectory fitting and range-nullspace learning. We have designed a series of" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "text", + "content": "1The results of AdaCoF [16] and FeFlow [9] are adopted from [29], which were trained and evaluated under the same settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 702, + 542, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 542, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 542, + 714 + ], + "type": "text", + "content": "2The retrained model of ST-MFNet is kindly provided by the authors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22165" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 70, + 171, + 173 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 171, + 173 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 171, + 173 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 171, + 173 + ], + "type": "image", + "image_path": "a363b2810158efbe2356e9de9cbbd1f150cc79a44bcf8dedfd13f2beed79a6e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": "Figure 5. Analyzing the effectiveness of focalized trajectory fitting. Given the input frames (left), we show in the middle optical flow errors as the error maps of warping the frames " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{-1}" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_1" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_2" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": " to time 0, and the corresponding weight maps of optical flows. Red denotes higher error/weight values, and blue represents lower values. Note a pixel is highlighted in green showing that higher optical flow error leads to lower weight. On the right, we show the warped result of " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": " using the intermediate flows " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": " resampled from different trajectory models. Note the warping results are overlayed with groundtruth, thus sharper result means more accurate warping. We also illustrate the position of a pixel at the boundary of hula hoop after warped to time " + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 182, + 545, + 258 + ], + "type": "text", + "content": " by the intermediate flows (yellow cross), and the groundtruth position (red point)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 71, + 260, + 172 + ], + "blocks": [ + { + "bbox": [ + 173, + 71, + 260, + 172 + ], + "lines": [ + { + "bbox": [ + 173, + 71, + 260, + 172 + ], + "spans": [ + { + "bbox": [ + 173, + 71, + 260, + 172 + ], + "type": "image", + "image_path": "18d909dfe65f9959aa44230736e6646bddbc12c9b14a242f47ea2715c952c31f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 261, + 72, + 350, + 172 + ], + "blocks": [ + { + 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], + "type": "text", + "content": "Figure 6. Visualization of the learned range-null space image components. From left to right: 1) forward warping result of " + }, + { + "bbox": [ + 46, + 342, + 544, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 46, + 342, + 544, + 365 + ], + "type": "text", + "content": " by intermediate flows " + }, + { + "bbox": [ + 46, + 342, + 544, + 365 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{0\\rightarrow t}" + }, + { + "bbox": [ + 46, + 342, + 544, + 365 + ], + "type": "text", + "content": ", 2) range space component, 3) range compensated result, 4) nullspace component, 5) full result, and 6) ground truth." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 379, + 273, + 459, + 320 + ], + "blocks": [ + { + "bbox": [ + 379, + 273, + 459, + 320 + ], + "lines": [ + { + "bbox": [ + 379, + 273, + 459, + 320 + ], + "spans": [ + { + "bbox": [ + 379, + 273, + 459, + 320 + ], + "type": "image", + "image_path": "19a5cf09d99b21d59935295aea6803c3ebdc8a4f3e43a8471ba66d38a5f1c51c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 322, + 453, + 334 + ], + "lines": [ + { + "bbox": [ + 383, + 322, + 453, + 334 + ], + "spans": [ + { + "bbox": [ + 383, + 322, + 453, + 334 + ], + "type": "text", + "content": "HtI0-RCHTy)+" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 461, + 273, + 541, + 320 + ], + "blocks": [ + { + "bbox": [ + 461, + 273, + 541, + 320 + ], + "lines": [ + { + "bbox": [ + 461, + 273, + 541, + 320 + ], + "spans": [ + { + "bbox": [ + 461, + 273, + 541, + 320 + ], + "type": "image", + "image_path": "d3362dd55dcd57a5fa16fc6c356cc76f6567bfddc9996958971a3b73cab452b0.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 323, + 524, + 331 + ], + "lines": [ + { + "bbox": [ + 474, + 323, + 524, + 331 + ], + "spans": [ + { + "bbox": [ + 474, + 323, + 524, + 331 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 52, + 393, + 281, + 498 + ], + "blocks": [ + { + "bbox": [ + 49, + 373, + 284, + 384 + ], + "lines": [ + { + "bbox": [ + 49, + 373, + 284, + 384 + ], + "spans": [ + { + "bbox": [ + 49, + 373, + 284, + 384 + ], + "type": "text", + "content": "Table 4. Ablation analysis on the GoPro and Adobe240 datasets." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 393, + 281, + 498 + ], + "lines": [ + { + "bbox": [ + 52, + 393, + 281, + 498 + ], + "spans": [ + { + "bbox": [ + 52, + 393, + 281, + 498 + ], + "type": "table", + "html": "
TrajectoryRendererGoProAdobe
Linear [10]R + N31.10/0.93731.13/0.942
Quadratic [36]R + N32.07/0.94933.20/0.963
Quadratic [17]R + N31.81/0.94633.02/0.962
Cubic [4]R + N32.01/0.94933.09/0.962
FTFR32.13/0.95032.99/0.962
FTFN32.17/0.95032.99/0.962
FTFUnet32.17/0.95133.15/0.963
FTFR + N32.31/0.95133.32/0.964
", + "image_path": "c7e126f33309c16ceaba63473a312ff42932bd0382b21a28a562c8f1d0d6e75a.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": "ablation study experiments in Table 4. We report results on the test set of GoPro and Adobe240 datasets with " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " VFI setting. First, we replace our focalized trajectory fitting with conventional linear, quadratic and cubic trajectory models without flow confidence learning (i.e., estimating the trajectory parameters " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " in (8) with conventional models). As shown in the 1-4 rows in Table 4, using linear, quadratic and cubic models without focalized fitting mechanism will degrade the performance at different levels (linear model performs worst, as expected). We also verify the contributions of learning range and null space image components. Here, presence of " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " represent that the corresponding network outputs are included to constitute final reconstruction. By rows 5 and 6, We observe that removing either component would degrade the performance. In the 7th row, we also implement a baseline using a UNet with similar pa" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 375, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 410 + ], + "type": "text", + "content": "rameter size to replace the proposed RNS module, which achieves worse performance and demonstrate the effectiveness of RNS architecture." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 411, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 495 + ], + "type": "text", + "content": "Visualizing the effectiveness of focalized trajectory fitting. In Fig. 5, we show with one example the optical flow errors, learned weight maps, and quality of flow resampling. As can be seen, low weights are assigned to optical flows with high matching errors. Particularly, our approach yields more accurate correspondence along the occlusion boundary (as shown in Fig. 5 right)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 495, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 578 + ], + "type": "text", + "content": "Visualizing the range and nullspace components. In Fig. 6 we visualize the learned range and nullspace image components of one example. As it stands, the rangespace component fixes the errors of warping neighbouring frames (note the front wheel and wheel arches), while the nullspace component addresses image content that cannot be created by warping, i.e. inpainting the occluded content." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 589, + 378, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 589, + 378, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 589, + 378, + 601 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 609, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 545, + 704 + ], + "type": "text", + "content": "This paper proposes two improved treatments towards video frame interpolation. The first is focalized trajectory fitting, which improves motion estimation by suppressing low-quality optical flows. Another is range nullspace synthesis, that formulates intermediate frame synthesis as an ill-posed problem, solved by learning orthogonally decomposed image components. The proposed model achieves leading results on various public VFI datasets." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22166" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. 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Vis., pages 144-160, 2022. 1, 2, 4, 5, 6, 7" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22168" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_content_list.json b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2395ccfd1a0dc922de85039b589548d7194e1186 --- /dev/null +++ b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_content_list.json @@ -0,0 +1,1542 @@ +[ + { + "type": "text", + "text": "RangeViT: Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving", + "text_level": 1, + "bbox": [ + 207, + 130, + 759, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Angelika Ando $^{1,2,*}$ , Spyros Gidaris $^{1}$ , Andrei Bursuc $^{1}$ , Gilles Puy $^{1}$ , Alexandre Boulch $^{1}$ , Renaud Marlet $^{1,3}$", + "bbox": [ + 86, + 202, + 910, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Valeo.ai, Paris, France $^{2}$ Centre for Robotics, Mines Paris, Université PSL, Paris, France $^{3}$ LIGM, Ecole des Ponts, Univ. Gustave Eiffel, CNRS, Marne-la-Vallee, France", + "bbox": [ + 133, + 232, + 867, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Casting semantic segmentation of outdoor LiDAR point clouds as a 2D problem, e.g., via range projection, is an effective and popular approach. These projection-based methods usually benefit from fast computations and, when combined with techniques which use other point cloud representations, achieve state-of-the-art results. Today, projection-based methods leverage 2D CNNs but recent advances in computer vision show that vision transformers (ViTs) have achieved state-of-the-art results in many image-based benchmarks. In this work, we question if projection-based methods for 3D semantic segmentation can benefit from these latest improvements on ViTs. We answer positively but only after combining them with three key ingredients: (a) ViTs are notoriously hard to train and require a lot of training data to learn powerful representations. By preserving the same backbone architecture as for RGB images, we can exploit the knowledge from long training on large image collections that are much cheaper to acquire and annotate than point clouds. We reach our best results with pre-trained ViTs on large image datasets. (b) We compensate ViTs' lack of inductive bias by substituting a tailored convolutional stem for the classical linear embedding layer. (c) We refine pixel-wise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grained features of the convolutional stem with the high-level but coarse predictions of the ViT encoder. With these ingredients, we show that our method, called RangeViT, outperforms existing projection-based methods on nuScenes and SemanticKITTI. The code is available at https://github.com/valeoai/rangevit.", + "bbox": [ + 75, + 329, + 473, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 824, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation of LiDAR point clouds permits vehicles to perceive their surrounding 3D environment in", + "bbox": [ + 76, + 849, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a241e668366c1a33e1da31893471b878938707211cee6c192bc32670ee4a57f9.jpg", + "image_caption": [ + "Figure 1. Exploiting vision transformer (ViT) architectures and weights for LiDAR point cloud semantic segmentation. We leverage the flexibility of transformer-based architectures to re-purpose them with minimal changes for processing sparse point clouds in autonomous driving tasks. The common ViT backbone across modalities allows to effectively transfer weights pre-trained on large image repositories towards improving point cloud segmentation performance with fine-tuning." + ], + "image_footnote": [], + "bbox": [ + 503, + 305, + 890, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dependently of the lighting condition, providing useful information to build safe and reliable vehicles. A common approach to segment large scale LiDAR point clouds is to project the points on a 2D surface and then to use regular CNNs, originally designed for images, to process the projected point clouds [1, 11, 26, 36, 60, 66]. Recently, Vision Transformers (ViTs) were introduced as an alternative to convolutional neural networks for processing images [14]: images are divided into patches which are linearly embedded into a high-dimensional space to create a sequence of visual tokens; these tokens are then consumed by a pure transformer architecture [51] to output deep visual representations of each token. Despite the absence of almost any domain-specific inductive bias apart from the image tokenization process, ViTs have a strong representation learning capacity [14] and achieve excellent results on various", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This project was done during an internship at Valeo.ai.", + "bbox": [ + 94, + 886, + 388, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5240", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "image perception tasks, such as image classification [14], object detection [8] or semantic segmentation [45].", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by this success of ViTs for image understanding, we propose to implement projection-based LiDAR semantic segmentation with a pure vision transformer architecture at its core. Our goals are threefold in doing so: (1) Exploit the strong representation learning capacity of vision transformer for LiDAR semantic segmentation; (2) Work towards unifying network architectures used for processing LiDAR point clouds or images so that any advance in one domain benefits to both; (3) Show that one can leverage ViTs pre-trained on large-size natural image datasets for LiDAR point cloud segmentation. The last goal is crucial because the downside of having few inductive biases in ViTs is that they underperform when trained from scratch on small or medium-size datasets and that, for now, the only well-performing pre-trained ViTs [9, 14, 45] publicly available are trained on large collections of images that can be acquired, annotated and stored easier than point clouds.", + "bbox": [ + 75, + 123, + 472, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this context, our main contribution is a ViT-based Li-DAR segmentation approach that compensates ViTs' lack of inductive biases on our data and that achieves state-of-the-art results among projection-based methods. To the best of our knowledge, although works using ViT architectures on dense indoor point clouds already exist [63, 67], this is the first solution using ViTs for the LiDAR point clouds of autonomous driving datasets, which are significantly sparser and noisier than the dense depth-map-based points clouds found in indoor datasets. Our solution, RangeViT, starts with a classical range projection to obtain a 2D representation of the point cloud [11, 26, 36, 60]. Then, we extract patch-based visual tokens from this 2D map and feed them to a plain ViT encoder [14] to get deep patch representations. These representations are decoded using a lightweight network to obtain pixel-wise label predictions, which are projected back to the 3D point cloud.", + "bbox": [ + 75, + 382, + 472, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our finding is that this ViT architecture needs three key ingredients to reach its peak performance. First, we leverage ViT models pre-trained on large natural image datasets for LiDAR segmentation and demonstrate that our method benefits from them despite the fact that natural images display little resemblance with range-projection images. Second, we further compensate for ViTs' lack of inductive bias by substituting the classical linear embedding layer with a multi-layer convolutional stem. Finally, we refine pixelwise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grain features of the convolutional stem with the high-level but coarse predictions of the ViT encoder.", + "bbox": [ + 75, + 641, + 472, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are the following: (1) To the best of our knowledge, we are the first to exploit the strong representation learning capacity of vision transformers architectures for 3D semantic segmentation from", + "bbox": [ + 75, + 839, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR point clouds. By revisiting, in the context of our problem, the tokenization process of the ViT's encoder and adding a light-weight convolutional decoder for refining the coarse patch-wise ViT representations, we derive a simple but effective projection-based LiDAR segmentation approach, which we call RangeViT. (2) Furthermore, as shown in Fig. 1, the proposed approach allows one to harness ViT models pre-trained on the RGB image domain for the LiDAR segmentation problem. Indeed, despite the large gap between the two domains, we empirically demonstrate that using such pre-training strategies improves segmentation performance. (3) Finally, our RangeViT approach, despite its simplicity, achieves state-of-the-art results among project-based segmentation methods.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 315, + 638, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. CNNs for Point Cloud Segmentation", + "text_level": 1, + "bbox": [ + 500, + 339, + 815, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2D Methods Several works [3,11,24,26,28,36,42,47,50, 60,64,66,70] project the 3D point cloud into the 2D space with range, perspective or bird's-eye-view (BEV) projection and process the projected images with 2D CNNs. For instance, PolarNet [66] employs bird's-eye-view projection to polar coordinates and then processes the bird-eye-view features with a Ring CNN. DarkNetSeg [3], SalsaNext [11], KPRNet [26], RangeNet++ [36], Lite-HDSeg [42] and SqueezeSegV3 [60] use range projection and then process the input images with a U-Net-like architecture. PMF [70], a multi-modal segmentation approach for point clouds and RGB images [2,29,53,65,70], projects the 3D points onto 2D camera frames and processes them together with the RGB images using a dual-stream CNN network.", + "bbox": [ + 496, + 366, + 893, + 579 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Methods Instead of the 2D space, voxel-based approaches [20,22,35,46] process the point clouds in their 3D space by first dividing the 3D space into voxels using cartesian coordinates and then applying 3D convolutions. Cylinder3D [69] show that dividing the 3D space into voxels using cylindrical coordinates instead of cartesian improves the segmentation performance. Although voxel-based methods consider the geometric properties of the 3D space, their drawback is that they are computationally expensive.", + "bbox": [ + 496, + 580, + 893, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Also, for indoor-scene point cloud segmentation there are many methods [15, 37, 47, 52, 54, 56, 58, 62] relying on PointNet-inspired architectures [38] that directly process raw 3D points. However, these approaches cannot be easily adapted to outdoor-scene point cloud segmentation, which we consider in this work, as the large quantity of points cause computational difficulties.", + "bbox": [ + 496, + 718, + 893, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. ViTs for Point Cloud Segmentation", + "text_level": 1, + "bbox": [ + 500, + 832, + 807, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recent rise to prominence of ViT architectures in computer vision has inspired a series of works for indoor point cloud segmentation [31, 57, 63, 67, 68].", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5241", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Processing point clouds with a ViT model can be challenging and computationally expensive due to the large number of points. Point-BERT [63] uses farthest point sampling [39] and the K-NN algorithm to define input tokens for the transformer. Also, it proposes a self-supervised pretraining strategy for point data inspired by the masked token modeling approaches in the RGB image [23] and text [13] domains. Point Transformer [67] has a U-Net-like architecture but without convolutional layers and it integrates self-attention mechanism in all of its blocks. Finally, Bridged Transformer [57] jointly processes point clouds and RGB images with a fully transformer-based architecture.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using a transformer-based architecture for the semantic segmentation task on outdoor LiDAR point clouds remains challenging. To the best of our knowledge, there has been no work published yet about outdoor LiDAR point cloud semantic segmentation with a ViT-based architecture.", + "bbox": [ + 75, + 272, + 470, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Transfer Learning from Images to Point Clouds", + "text_level": 1, + "bbox": [ + 76, + 354, + 468, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ViT models have the capacity to learn powerful representations, but require vast amounts of training data for it. However, large LiDAR point cloud datasets are less common due to the costly and time consuming annotation procedure. Recent works [21,32,40,43,55,61] explore transfer learning of 2D image pre-trained models to 3D point clouds.", + "bbox": [ + 75, + 378, + 468, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image2Point [61] converts a 2D CNN into a 3D sparse CNN [61] by inflating 2D convolutions into 3D convolutions, which is done by repeating the 2D kernel along the third dimension. SLidR [43] is a self-supervised pretraining method on LiDAR data. It uses a student-teacher architecture, where the 2D teacher network pre-trained on images transfers information into the 3D student network. Pix4Point [40] and Simple3D-Former [55] study transfer learning from images to indoor point clouds with fully transformer-based architectures. They adapt the tokenizer and the head layer to be specialized for 3D point cloud data. Pix4Point [40] applies farthest point sampling [39], the K-NN algorithm and then a graph convolution on the aggregated neighborhoods to extract input tokens for the ViT encoder. Simple3D-Former [55] memorizes the ImageNet [12] representation of 2D image classification by incorporating a KL divergence term in the loss between its 2D image classification predictions and those obtained from a fixed ImageNet [12] pre-trained ViT network.", + "bbox": [ + 75, + 469, + 472, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. RangeViT", + "text_level": 1, + "bbox": [ + 76, + 768, + 187, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we describe our ViT-based LiDAR semantic segmentation approach, for which we provide an overview in Fig. 2.", + "bbox": [ + 75, + 792, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. General architecture", + "text_level": 1, + "bbox": [ + 76, + 847, + 272, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We represent a LiDAR point cloud of $N$ points with a matrix $\\mathbf{P} \\in \\mathbb{R}^{N \\times 4}$ . Each point $p = (x, y, z, i) \\in \\mathbf{P}$ has", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Cartesian coordinates denoted by $(x,y,z)$ and LiDAR intensity denoted by $i$ , and is annotated with a label $\\ell \\in \\{1,\\dots ,K\\}$ encoding one of the $K$ semantic classes.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Range projection. The input of our RangeViT backbone is a 2D representation of the input point cloud. We use the well-known range projection [36]. Each point $\\mathbf{p} \\in \\mathbf{P}$ with coordinates $(x, y, z)$ is projected on a range image of size $H \\times W$ . The projected 2D coordinates satisfies", + "bbox": [ + 498, + 160, + 890, + 236 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\binom {h} {w} = \\left( \\begin{array}{c} \\frac {1}{2} (1 - \\arctan (y, x) \\pi^ {- 1}) W \\\\ (1 - (\\arcsin (z, r ^ {- 1}) + | f _ {\\text {d o w n}} |) f _ {v} ^ {- 1}) H \\end{array} \\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 247, + 890, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f_{v} = |f_{\\mathrm{down}}| + |f_{\\mathrm{up}}|$ is the vertical field-of-view of the LiDAR sensor. We associate $C = 5$ low-level features $(r, x, y, z, i)$ to each projected point, where $r = \\sqrt{x^2 + y^2 + z^2}$ is the range of the corresponding point (i.e., its distance from the LiDAR sensor), to create the range image $\\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W}$ . Note that if more than one point is projected onto the same pixel, then only the feature with the smallest range is kept. Pixels with no point projected on them have their features filled with zeros.", + "bbox": [ + 498, + 294, + 892, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Convolutional stem. In a standard ViT, the image is divided into $M$ patches of size $P_{H} \\times P_{W}$ , which are linearly embedded to provide $D$ -dimensional visual tokens. Yet, our empirical study in Sec. 4.2 shows that this tokenization process of standard ViTs is far from optimal on both our task and datasets of interest. In order to bridge this potential domain gap between range images and standard ViTs, we replace the embedding layer with a non-linear convolutional stem [59]. Non-linear convolutional stems have been shown to increase optimization stability and predictive performance of ViTs [59], whereas we leverage them primarily for steering range images towards ViT-like inputs.", + "bbox": [ + 496, + 455, + 890, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first part of the convolutional stem consists of the first 4 residual blocks of SalsaNext [11], called context module. This context module captures short-range dependencies of the 3D points projected in the range image and produces pixel-wise features with $D_{\\mathrm{h}}$ channels at the same resolution of the input range image, hence the tensor of context features $\\mathbf{t}_{\\mathrm{c}}$ has size $D_{\\mathrm{h}} \\times H \\times W$ . Then, in order to produce tokens compatible with the input of a ViT, we use an average pooling layer that reduces the spatial dimensions of the context features $\\mathbf{t}_{\\mathrm{c}}$ from $H \\times W$ to $(H / P_{H}) \\times (W / P_{W})$ , and use a final $1 \\times 1$ convolutional layer with $D$ output channels. The convolutional stem thus yields $M = (HW) / (P_{H}P_{W})$ visual tokens $\\mathbf{v}_1, \\ldots, \\mathbf{v}_M$ of dimension $D$ , i.e., matching the input dimension and number of tokens of a traditional ViT.", + "bbox": [ + 496, + 638, + 892, + 864 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "The first 3 residual layers actually have $D_{\\mathrm{in}} = 32$ channels, which is typically smaller than $D_{\\mathrm{h}}$ .", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5242", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f3ed7b63a2d18fd90a53982053b4d2f9c4724f5da59e27ee9c0167984e7f0a8c.jpg", + "image_caption": [ + "Figure 2. Overview of RangeViT architecture. First, the point cloud is projected in a 2D space with range projection. Then, the produced range image is processed by the convolutional stem, the ViT encoder and the decoder to obtain a 2D feature map. It is then processed by a 3D refiner layer for 3D point-wise predictions. Note that there is a single skip connection between the convolutional stem and the decoder." + ], + "image_footnote": [], + "bbox": [ + 98, + 90, + 880, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ViT encoder. The output of the convolutional stem can be fed directly to a ViT [14]. The input $\\mathbf{t}_0$ to our ViT encoder is prepared by stacking all the visual tokens $\\mathbf{v}_1, \\ldots, \\mathbf{v}_M$ and a classification token $\\mathbf{v}_{\\mathrm{class}} \\in \\mathbb{R}^D$ , to which we add the positional embeddings $\\mathbf{E}_{\\mathrm{pos}} \\in \\mathbb{R}^{(M + 1) \\times D}$ :", + "bbox": [ + 75, + 332, + 470, + 409 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {t} _ {0} = \\left[ \\mathbf {v} _ {\\text {c l a s s}}, \\mathbf {v} _ {1}, \\dots , \\mathbf {v} _ {M} \\right] + \\mathbf {E} _ {\\text {p o s}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 417, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The input tokens are then transformed by the ViT encoder to obtain an updated sequence of tokens $\\mathbf{t}_L\\in \\mathbb{R}^{(M + 1)\\times D}$ where $L$ denotes the number of transformer blocks. Then, we remove the classification token from $\\mathbf{t}_L$ to keep only the deep patch representations $\\mathbf{t}_L^{\\prime}\\in \\mathbb{R}^{M\\times D}$ .", + "bbox": [ + 75, + 441, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder. The representations $\\mathbf{t}_L^{\\prime}$ provided by the ViT encoder are patch representations which are unfortunately too coarse to obtain good point predictions. Therefore, we use a decoder to refine these coarse patch representations. First, $\\mathbf{t}_L^{\\prime}$ is reshaped in form of a 2D feature map of size $D\\times H / P_H\\times W / P_W$ . Our convolutional decoder consists of a $1\\times 1$ convolution layer with $D_{\\mathrm{h}}P_{H}P_{W}$ output channels, followed by a Pixel Shuffle layer [44] which yields feature maps with shape $D_{\\mathrm{h}}\\times H\\times W$ , i.e., with the same resolution as the original range image. While the convolutional decoder can still produce coarse features or decoding artifacts, the Pixel Shuffle is particularly effective in recovering fine information from features. Then, we concatenate these features with the context features $\\mathbf{t}_{\\mathrm{c}}$ from the convolutional stem and use a series of two convolutional layers with $3\\times 3$ and $1\\times 1$ kernels respectively, each of them followed by Leaky ReLU and batch normalisation, to obtain the refined feature map $\\mathbf{t}_{\\mathrm{dec}}\\in \\mathbb{R}^{D_{\\mathrm{h}}\\times H\\times W}$ .", + "bbox": [ + 75, + 535, + 470, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D refiner. Ultimately, we need to convert the pixel-wise features from the range image space into point-wise predictions in the 3D space. Most prior range-projection based methods first make pixel-wise class predictions and then unproject them to the 3D space, where at inference time often", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "there is a post-processing step relying, e.g., on K-NN [36] or CRFs [27]. The purpose of the latter post-processing step is to fix segmentation mistakes related to the projection and processing of 3D points in a 2D space (e.g., multiple 3D points being projected on the same pixel, or 2D boundary prediction errors for points that are actually far away in the 3D space). Instead, we follow the approach of KPRNet [26] that proposes an end-to-end approach that learns this post-processing step with a KPConv [47] layer.", + "bbox": [ + 496, + 332, + 890, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "KPConv [47] is a point convolution technique which works directly on the original 3D points. It permits to leverage the underlying geometry of the 3D point clouds to refine features at the point level. So, in our network, we project the 2D feature maps $\\mathbf{t}_{\\mathrm{dec}}$ of the 2D decoder back to original 3D points by bilinear upsampling, thus obtaining point-wise features with shape $N\\times D_{\\mathrm{h}}$ , where $N$ is the number of 3D points. Then, these point features are given to the KPConv layer as input along with the 3D coordinates of the corresponding points, which outputs $D_{\\mathrm{h}}$ -dimensional point features. Finally, the logits $\\mathbf{s}\\in \\mathbb{R}^{N\\times K}$ are obtained by applying a BatchNorm, a ReLU and a final point-wise linear layer on these point features.", + "bbox": [ + 496, + 468, + 892, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 674, + 714, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training loss We use the sum of the multi-class focal loss [30] and the Lovász-softmax loss [4]. The focal loss is a scaled version of the cross-entropy loss [19] adapting its penalty to the hardness of the samples, making it suited for datasets with class imbalance, such as semantic segmentation. The Lovász-softmax is developed specifically for semantic segmentation and built to optimize the mIoU.", + "bbox": [ + 496, + 700, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference As in [45], we use a sliding-window method during inference. The network actually never sees the entire range images during training but only crops extracted from it. At inference, the range image is divided into overlapping crops of the same size as those used during training. The corresponding 2D features at the output of the decoder are", + "bbox": [ + 496, + 809, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5243", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/a007923cdc2f18e6a2305a8f5a7b12ac288b883c3ba0c508b5399f365bdc22aa.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Model ablations. Results on the nuScenes validation set with $D_{\\mathrm{h}} = 192$ . The linear stem refers to the linear patch embedding layer. When the 3D refiner layer (Refiner column) is not used, we use the K-NN post-processing technique [36]." + ], + "table_body": "
StemDecoderRefinermIoU (%)#Params
LinearLinear65.5222.0M
ConvLinear69.8222.8M
ConvUpConv73.8324.6M
ConvUpConv✓74.6025.2M
", + "bbox": [ + 124, + 88, + 419, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "then averaged to reconstruct the entire feature map, which is then processed by our 3D refinement layer.", + "bbox": [ + 75, + 238, + 468, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 282, + 209, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 306, + 266, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and metrics. We validate our approach for 3D point cloud semantic segmentation on two different commonly used datasets: nuScenes [7] and SemanticKITTI [3]. We conduct most of our ablation studies on nuScenes and compare against previous works on both nuScenes and SemanticKITTI. As evaluation metric, we use the mean Intersection over Union (mIoU) [16].", + "bbox": [ + 75, + 333, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NuScenes [7] consists of 1,000 scenes of 20 seconds in Boston and Singapore with various urban scenarios, lighting and weather conditions. The LiDAR sensor has 32 laser beams. Furthermore, there are 16 annotated semantic classes and the dataset is split into 28,130 training and 6,019 validation point cloud scans.", + "bbox": [ + 75, + 439, + 468, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SemanticKITTI [3] is created from the KITTI Vision Odometry Benchmark [17] and consists of urban scenes collected in Germany. Sequences 00-10 are used for training, except sequence 08 which is used for validation. There are 19,130 training and 4,071 validation scans. Sequences 11-21 are used for test and they contain 20,351 scans. The LiDAR sensor has 64 laser beams and there are 19 annotated semantic classes.", + "bbox": [ + 75, + 530, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model and pre-trained weights. For all experiments, we use the ViT-S/16 model [14] as the encoder. It has $L = 12$ layers, 6 attention heads and $D = 384$ channels, amounting to approximately 21M parameters. Unless otherwise stated, (a) this ViT encoder is initialized with weights pre-trained on ImageNet21k [12] for classification and then fine-tuned on Cityscapes [10] for semantic image segmentation [45]; (b) the stem, decoder and 3D refiner layers, which are always randomly initialized, use $D_{\\mathrm{h}} = 256$ feature channels.", + "bbox": [ + 75, + 654, + 468, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization. We use the AdamW optimizer [34] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ and weight decay 0.01. The batch-size is 32 and 16 for nuScenes and SemanticKITTI, respectively. For the learning rate $lr$ , we use a linear warm-up from 0 to its peak value for 10 epochs and then we decrease it over the remaining training epochs to 0 with a cosine annealing schedule [33]. In SemanticKITTI, we use 60 train-", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/59dd71ffbcc59e4a604b8b1f803d47c316b61c3644cd27ae46806dea91fce9a5.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Impact of the channel size $D_{\\mathrm{h}}$ used in the stem, decoder, and 3D refiner layers. Results on the nuScenes and the SemanticKITTI validation sets." + ], + "table_body": "
Dh size64128192256
#Params22.7M23.7M25.2M27.1M
nuScenes mIoU (%)74.0074.1274.6075.21
SemanticKITTI mIoU (%)58.4860.7360.4560.55
", + "bbox": [ + 516, + 88, + 874, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ing epochs and the peak $lr$ is $4 \\times 10^{-4}$ . In nuScenes, we use 150 epochs and the peak $lr$ is $8 \\times 10^{-4}$ when training from Cityscapes, ImageNet21k and random initializations, and $2 \\times 10^{-4}$ when training from DINO initialization.", + "bbox": [ + 496, + 219, + 890, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data augmentations. As point cloud augmentations we use: (a) flips over the $y$ axis (the vertical axis on the range image), (b) random translations, and (c) random rotations between $\\pm 5^{\\circ}$ (using the roll, pitch and yaw angles). All augmentations are applied randomly with probability 0.5. Finally, after range projection, we take a random image crop with a fixed size of $32 \\times 384$ for nuScenes and $64 \\times 384$ for SemanticKITTI. Note that the full size of a range image is $32 \\times 2048$ for nuScenes and $64 \\times 2048$ for SemanticKITTI.", + "bbox": [ + 496, + 284, + 890, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. What makes a ViT architecture for 3D semantic segmentation?", + "text_level": 1, + "bbox": [ + 498, + 431, + 890, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our aim is to adapt to LiDAR point clouds with the fewest possible modifications of the standard ViT architecture [14], which already follows faithfully the original self-attention Transformer design [51]. Differently from ViT that performs classification on images, RangeViT performs semantic segmentation of point cloud-derived range images. We study here the possible choices for the input processing and decoder layers using the nuScenes dataset.", + "bbox": [ + 496, + 469, + 890, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stem and decoder. In Tab. 1, we study the impact of the convolutional stem and the UpConv decoder. To that end, we report results using a linear patch embedding [14] as a stem and a linear decoder. Starting from a model with linear stem and linear decoder, introducing the proposed convolutional stem leads to a significant mIoU boost $(65.52\\rightarrow 69.82)$ . This highlights the importance of having a non-linear network component for producing appropriate input token features for the ViT backbone. In addition, when using image pre-trained ViTs (Sec. 4.3) the convolutional stem can effectively steer the distribution of input range images towards the image-based feature distribution the ViT has been pre-trained on, leading to smoother fine-tuning. Then, also replacing the linear decoder with the proposed UpConv decoder leads to another notable improvement on mIoU $(69.8\\rightarrow 73.83)$ , validating this design choice. Finally, replacing the K-NN refinement [36] with", + "bbox": [ + 496, + 595, + 892, + 852 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2The linear decoder consists of a simple $1\\times 1$ conv. layer, which predicts patch-wise classification scores, and a bilinear upsampling to reach the input image resolution.", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5244", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/41b12a6e43487944d2e015a309181131a97632a72c4581eb00483222c6c486fe.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Patch size ablations. Results on the nuScenes validation set. The mIoU scores are in increasing order. The train time is relative to the $16 \\times 16$ patch size case." + ], + "table_body": "
Patch size16 × 168 × 84 × 164 × 84 × 42 × 162 × 8
mIoU (%)68.4572.0472.7273.3073.7073.8875.21
Tokens49193193385769385769
Train time×1×1.02×1.02×1.13×1.43×1.13×1.43
", + "bbox": [ + 80, + 89, + 467, + 152 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the KPCov layer (in the 3D refiner layer), leads to a small but non-trivial mIoU increase $(73.83\\rightarrow 74.60)$", + "bbox": [ + 75, + 213, + 468, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tab. 2, we study what is the impact, on the mIoU, of changing the number of feature channels $D_{\\mathrm{h}}$ on the stem, decoder and 3D refiner layer. On nuScenes, we observe that the results gradually increase when increasing the dimension $D_{\\mathrm{h}}$ . In the SemanticKITTI case, $D_{\\mathrm{h}} = 128$ gives the best results and further increasing $D_{\\mathrm{h}}$ does not help. Note that the size of the ViT's embeddings is fixed at $D = 384$ , regardless of the $D_{\\mathrm{h}}$ size.", + "bbox": [ + 75, + 244, + 468, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "What patch-size for range image \"tokenization\"? The size of the input patch tokens is an essential factor for controlling the trade-off between speed and accuracy performance without changing the number of parameters in the model. Intuitively, reducing the patch-size results in a finer representation, but also a longer input sequence that takes longer to process. Conversely, larger patches lead to a coarser representation, yet faster inference. The performance impact of the patch-size can sometimes match the one of model size [45]. For simplicity, standard ViT models use square patches of size 32, 16 or 8, as they are typically trained on square images. In contrast, range images have a much different aspect ratio (high width) and different layout of the content in the image (rows of points corresponding to LiDAR beams). With this insight, we revisit the practice of using square patches and look into rectangular patches with different aspect ratio (1:2, 1:4, 1:8) that would better capture the specific local patterns of the range images.", + "bbox": [ + 75, + 368, + 468, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 3 shows the mIoU scores for different patch sizes for dividing the range image to patch tokens. Note that the convolutional stem first produces pixel-wise features and then, given a patch-size $(P_{H}, P_{W})$ , reduces the spatial dimensions of these features to $(H / P_{H}, W / P_{W})$ using local average pooling. We observe that smaller patch area is better but not necessarily with a square patch, commonly used for ViT models. The wide range images benefit more from rectangular patches ( $2 \\times 8$ performing best). The smaller patches enable the extraction of more fine-grained information leading to more precise predictions for smaller and thinner objects and points at object boundaries.", + "bbox": [ + 75, + 641, + 470, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Exploiting image pre-trained ViTs", + "text_level": 1, + "bbox": [ + 76, + 830, + 377, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "So far, we have studied the architectural choices necessary for using ViT models for point cloud semantic segmentation. The final RangeViT model preserves the ViT back", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ecf98f4225e2577772b50605c51a1187a83030e8cd158169c3a04f33a710cba3.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. ViT pre-training on RGB images. Comparison of different weight initializations of the ViT encoder on the nuScenes validation set. Rand: randomly initialized. The positional embeddings are initialized with the corresponding pre-trained weights or randomly when training from scratch. The convolutional stem, the decoder and the 3D refiner layer are randomly initialized." + ], + "table_body": "
Pre-trainingRandDINOIN21kCS
mIoU (%)72.3773.3374.7775.21
", + "bbox": [ + 563, + 89, + 825, + 127 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21d54f0f69d04676d212384aa4c7475d7334992dbc49cc5a6177b61daa146996.jpg", + "image_caption": [ + "Figure 3. Training efficiency with image-pretrained ViTs. Comparison of the validation mIoU curves for different weight initialisations of the ViT encoder on the nuScenes validation set." + ], + "image_footnote": [], + "bbox": [ + 513, + 232, + 854, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "bone intact allowing us to initialize it with weights from models pre-trained on large datasets. We study now whether using such an initialization helps or not and what fine-tuning strategies would be more suitable in this context.", + "bbox": [ + 498, + 483, + 890, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Is pre-training on RGB images beneficial? In Tab. 4, we study the effect of transferring to our task ViT models pre-trained on natural RGB images. In particular, we explore initializing RangeViT's backbone with ViTs pretrained: (a) on supervised ImageNet21k classification [14] (entry IN21k), (b) on supervised image segmentation on Cityscapes with Segmenter [45] (entry CS), which in its turn was pre-trained with IN21k, and (c) with the DINO [9] self-supervised approach on ImageNet1k (entry DINO).", + "bbox": [ + 496, + 551, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe that, despite the large domain gap, using ViT models pre-trained on RGB images is always better than training from scratch on LiDAR data (entry Rand). For instance, using the IN21k and CS pretrained ViTs leads to improving the mIoU scores by 2.4 and 2.8 points respectively. Additionally, as we see in Fig. 3, which plots the nuScenes validation mIoU as a function of the training epochs, using such pre-trained ViTs leads to faster training convergence of the LiDAR segmentation model. We argue that this is a highly interesting finding. It means that our RangeViT approach, by being able to use off-the-shelf pre-trained ViT models, can directly benefit from current and future advances on the training ViT models with natural RGB images, a very active and rapidly growing re", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5245", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/69fb7ee3a5503d64ca887b03b89f1fb080d81ebce8c8854d35649f19cd090ce9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelFine-tuningIN21k mIoU (%)CS (%)
LNATTNFFN
(a)✓✓✓74.7975.21
(b)67.8868.03
(c)✓69.0869.31
(d)✓✓73.5672.77
(e)✓✓75.1175.47
", + "bbox": [ + 145, + 88, + 398, + 193 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/45a96316cd44a844f9051f316ee996782ae9d780cea22166275927ebf78c5e90.jpg", + "table_caption": [ + "Table 5. Partial ViT fine-tuning. We use a ViT encoder pretrained on ImageNet21k (IN21k) or Cityscapes (CS) and partially fine-tune RangeViT on the nuScenes training set. The convolutional stem, the positional embeddings and the UpConv decoder are always fine-tuned. LN: fine-tuning the LayerNorm layers of the ViT encoder. ATTN: fine-tuning the multi-head attention layers of the ViT encoder. FFN: fine-tuning the feed-forward network layers of the ViT encoder. Model (a) is full fine-tuning of the network. The results are reported on the nuScenes validation set." + ], + "table_footnote": [], + "table_body": "
EncoderViT-S†ViT-SRN50†RN50Identity
mIoU (%)67.8874.7760.4872.3053.73
", + "bbox": [ + 112, + 335, + 431, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablating encoder backbones. ViT-S and RN50 are pretrained on IN21k. †: the encoder remains frozen during training.", + "bbox": [ + 76, + 378, + 467, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "search field [23, 41, 48, 49]. Furthermore, from the small difference between the mIoU scores with the IN21k and CS pre-trainings, we infer that the pre-training can lead to consistent performance improvements even if it is not on the strongly-supervised image segmentation task, which requires expensive-to-announce datasets.", + "bbox": [ + 75, + 425, + 467, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Which ViT layers is better to fine-tune? In the image domain, several practices have emerged for fine-tuning a pre-trained convolutional network on a downstream dataset. Taking into consideration the domain gap between the pretraining and downstream data and the amount of labeled data available, the entire network can be fine-tuned or only a part of it. Here the domain gap between RGB images and range images is major and we would expect a full fine-tuning of the network to be better. To understand how much prior knowledge of the image pre-trained ViT is useful for point clouds, we study different fine-tuning strategies: fine-tuning all layers, only the attention (ATTN) layers or only the feedforward network (FFN) layers.", + "bbox": [ + 75, + 522, + 467, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Tab. 5, we show results with these different fine-tuning strategies. Interestingly, the best results are not achieved with full fine-tuning (model (a)) but when the attention layers are kept frozen (model (e)). This suggests that the pretrained ATTN layers are already well learnt and ready to generalize to range images. With CS pre-training ATTN layers may capture the layout of the scenes more easily without much fine-tuning, as the LiDAR scans have been also acquired from urban road scenes. Fine-tuning FFN may have more impact due to the different specifics of the LiDAR data compared to RGB images. In addition, FFN layers are in practice easier and more stable to optimize", + "bbox": [ + 75, + 719, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3f4bfeec95ddebeea5829bd608e032d1eea1a9cb706f8ca2196db50652e4ebb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 93, + 696, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4e47f997373b436e55588c460ef2f0a9b5c73937ad2262b8fe93f658df1dc358.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 93, + 885, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ee2ec0996ec4bef98540715cc64f2244fcbfdcd264d2850d55f4fe5a2396a42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 202, + 696, + 296 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a29d83b88d26ebbc6b1144144ae545feabb437abb83e345504a8d5b656f6a8b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 202, + 885, + 296 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc874d517e74daf814b62fc76531ad8220fcf0e48cde744b519b9bcdb10c9ae7.jpg", + "image_caption": [ + "Figure 4. Visualizing the segmentation accuracy. Left: ground truth segmentation of validation point clouds of nuScenes, coloured based on their label. Right: segmentation accuracy of RangeViT - good predictions are in blue and the bad ones in red." + ], + "image_footnote": [], + "bbox": [ + 508, + 297, + 696, + 392 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e41c718e61e6e33f5d3265459323d2081142b8aa72a5416bc668503cebdc353.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 297, + 885, + 392 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(they are essentially fully-connected and normalization layers) than ATTN layers that usually require more careful hyper-parameter selection. These findings align with recent ones from the image domain [48], confirming that the convolutional stems do steer the input LiDAR data to behave like image data once on in the ViT backbone.", + "bbox": [ + 496, + 479, + 890, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablating encoder backbones. In Tab. 6, we replace the ViT-S encoder backbone of RangeViT with a ResNet-50 (RN50) encoder or the identity function (i.e., the decoder follows directly the stem). Both ViT-S and RN50 are pretrained on IN21k. We see that switching from ViT-S to RN50 decreases the mIoU from $74.77\\%$ to $72.30\\%$ . Furthermore, when the backbones remain frozen $(\\mathrm{ViT - S}^{\\dagger}$ and $\\mathrm{RN50\\dagger}$ models), we reach $67.88\\%$ with ViT-S and $60.48\\%$ with RN50, demonstrating that ViT features are more appropriate for transfer learning to LiDAR data than CNNs. Finally, with the Identity backbone, we achieve $53.73\\%$ , which is more than 14 points worse than the $\\mathrm{ViT - S}^{\\dagger}$ model that has the same number of learnable parameters.", + "bbox": [ + 496, + 577, + 890, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison to the state of the art", + "text_level": 1, + "bbox": [ + 500, + 786, + 794, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 7 and 8 report the final comparison on the nuScenes validation set and on the SemanticKITTI test set including class-wise IoU scores. We observe that our model achieves superior mIoU performance compared to prior 2D-projection based methods on both datasets, reducing the gap with the strong voxel-based Cylinder3D [69] method.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5246", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f4ed65877f72332205bffe7e34b0d15b237fa3c282d055e748d0a7eef70cdeee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdriveableother flatsidewalkterrainmammadevegetationmIoU (%)
Voxel-based Cylinder3D [69]76.440.391.393.851.378.078.964.962.184.496.871.676.475.490.587.476.1
2D Projection-based
RangeNet++ [36]66.021.377.280.930.266.869.652.154.272.394.166.663.570.183.179.865.5
PolarNet [66]74.728.285.390.935.177.571.358.857.476.196.571.174.774.087.385.771.0
SalsaNext [11]74.834.185.988.442.272.472.263.161.376.596.070.871.271.586.784.472.2
RangeViT-IN21k (ours)75.139.090.288.448.079.277.266.465.176.796.371.173.773.988.987.174.8
RangeViT-CS (ours)75.540.788.390.149.379.377.266.365.280.096.471.473.873.889.987.275.2
", + "bbox": [ + 81, + 88, + 890, + 253 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cc0a604be481b91d686815195f15c8806039a85031eb46ad01eeac9a614a1ea1.jpg", + "table_caption": [ + "Table 7. nuScenes validation set comparison with state-of-the-art methods. The best results are bold and the second best results are blue." + ], + "table_footnote": [], + "table_body": "
Methodcarbicyclemotorcycletruckother vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother groundbuildingfencevegetationtrunkterrainpoletraffic signmIoU (%)
Voxel-based Cylinder3D [69]97.167.664.059.058.673.967.936.091.465.175.532.391.066.585.471.868.562.665.667.8
2D Projection-based
RangeNet++ [36]91.425.734.425.723.038.338.84.891.865.075.227.887.458.680.555.164.647.955.952.2
PolarNet [66]93.840.330.122.928.543.240.25.690.861.774.421.790.061.384.065.567.851.857.554.3
SqueezeSegV3 [60]92.538.736.529.633.045.646.220.191.763.474.826.489.059.482.058.765.449.658.955.9
SalsaNext [11]91.948.338.638.931.960.259.019.491.763.775.829.190.264.281.863.666.554.362.159.5
KPRNet [26]95.554.147.923.642.665.965.016.593.273.980.630.291.768.485.769.871.258.764.163.1
Lite-HDSeg [42]92.340.055.437.739.659.271.654.193.068.278.329.391.565.078.265.865.159.567.763.8
RangeViT-CS (ours)95.455.843.529.842.163.958.238.193.170.280.032.592.069.085.370.671.260.864.764.0
", + "bbox": [ + 81, + 276, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. SemanticKITTI test set comparison with state-of-the-art methods. The best results are bold and the second best results are blue.", + "bbox": [ + 80, + 467, + 890, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Class-wise IoU result analysis. In Tab. 7 and 8, we can see that RangeViT often achieves the best or the second best class-wise IoU scores. In both datasets, the classes are imbalanced and due to the sparsity and varying density of Li-DAR point clouds, some classes (e.g., bicycle, pedestrian) are represented with few, not necessarily structured points per scene, so it is difficult to recognize them. This problem could possibly be reduced by jointly processing point clouds and RGB images, since RGB images might provide extra cues about the outline and the shape of these objects.", + "bbox": [ + 75, + 498, + 468, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 657, + 259, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the 3D point clouds with the ground truth semantic labels as well as the predictions with CloudCompare [18]. Fig. 4 shows the predictions of RangeViT on three validation point clouds of nuScenes. We notice minor errors such as man-made objects predicted as sidewalk and imperfect borders for the vegetation. We also remark difficulties in recognizing pedestrians and confusion between the driveable surface and the sidewalk for few points.", + "bbox": [ + 75, + 681, + 468, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 815, + 194, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We studied the feasibility of leveraging (pre-trained) ViTs for LiDAR 3D semantic segmentation with projection-based methods. We discover that in spite of the significant domain gap between RGB images and range images and", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "their high requirements of training data, ViTs can be successfully used without any changes in the original transformer backbone. We achieve this thanks to an adapted tokenization and pre-processing for the ViT encoder and a simple convolutional decoder. We show that ViTs pre-trained on large image datasets can be effectively repurposed for LiDAR segmentation towards reaching state-of-the-art performance among 2D projection methods. We release the code for our implementation and hope that it could be used as a testbed for evaluating the ability of ViT image \"foundation\" models [6] to generalize on different domains.", + "bbox": [ + 496, + 498, + 890, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future work. Although the results are promising, there is still room for improvement. For instance, we identified the tokenization of LiDAR data as a crucial factor for success. As future work, we could further improve this process, e.g., with FlexiViT [5] (random patch sizes) or Perceiver IO [25] (learning to extract tokens), and consider tokenizing raw 3D data instead of the 2D projections.", + "bbox": [ + 496, + 667, + 890, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. We would like to express our gratitude to Matthieu Cord and Hugo Touvron for their insightful comments, Robin Strudel et al. 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In ICCV, 2021. 2" + ], + "bbox": [ + 501, + 90, + 890, + 214 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5250", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_model.json b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d2f3cecb235ef9d679dee542f9c0680d4bd07d42 --- /dev/null +++ b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_model.json @@ -0,0 +1,2290 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.209, + 0.131, + 0.761, + 0.177 + ], + "angle": 0, + "content": "RangeViT: Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.203, + 0.911, + 0.223 + ], + "angle": 0, + "content": "Angelika Ando\\(^{1,2,*}\\), Spyros Gidaris\\(^{1}\\), Andrei Bursuc\\(^{1}\\), Gilles Puy\\(^{1}\\), Alexandre Boulch\\(^{1}\\), Renaud Marlet\\(^{1,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.233, + 0.868, + 0.27 + ], + "angle": 0, + "content": "\\(^{1}\\)Valeo.ai, Paris, France \\(^{2}\\)Centre for Robotics, Mines Paris, Université PSL, Paris, France \\(^{3}\\)LIGM, Ecole des Ponts, Univ. Gustave Eiffel, CNRS, Marne-la-Vallee, France" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.474, + 0.799 + ], + "angle": 0, + "content": "Casting semantic segmentation of outdoor LiDAR point clouds as a 2D problem, e.g., via range projection, is an effective and popular approach. These projection-based methods usually benefit from fast computations and, when combined with techniques which use other point cloud representations, achieve state-of-the-art results. Today, projection-based methods leverage 2D CNNs but recent advances in computer vision show that vision transformers (ViTs) have achieved state-of-the-art results in many image-based benchmarks. In this work, we question if projection-based methods for 3D semantic segmentation can benefit from these latest improvements on ViTs. We answer positively but only after combining them with three key ingredients: (a) ViTs are notoriously hard to train and require a lot of training data to learn powerful representations. By preserving the same backbone architecture as for RGB images, we can exploit the knowledge from long training on large image collections that are much cheaper to acquire and annotate than point clouds. We reach our best results with pre-trained ViTs on large image datasets. (b) We compensate ViTs' lack of inductive bias by substituting a tailored convolutional stem for the classical linear embedding layer. (c) We refine pixel-wise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grained features of the convolutional stem with the high-level but coarse predictions of the ViT encoder. With these ingredients, we show that our method, called RangeViT, outperforms existing projection-based methods on nuScenes and SemanticKITTI. The code is available at https://github.com/valeoai/rangevit." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.825, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Semantic segmentation of LiDAR point clouds permits vehicles to perceive their surrounding 3D environment in" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.306, + 0.891, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.634 + ], + "angle": 0, + "content": "Figure 1. Exploiting vision transformer (ViT) architectures and weights for LiDAR point cloud semantic segmentation. We leverage the flexibility of transformer-based architectures to re-purpose them with minimal changes for processing sparse point clouds in autonomous driving tasks. The common ViT backbone across modalities allows to effectively transfer weights pre-trained on large image repositories towards improving point cloud segmentation performance with fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "dependently of the lighting condition, providing useful information to build safe and reliable vehicles. A common approach to segment large scale LiDAR point clouds is to project the points on a 2D surface and then to use regular CNNs, originally designed for images, to process the projected point clouds [1, 11, 26, 36, 60, 66]. Recently, Vision Transformers (ViTs) were introduced as an alternative to convolutional neural networks for processing images [14]: images are divided into patches which are linearly embedded into a high-dimensional space to create a sequence of visual tokens; these tokens are then consumed by a pure transformer architecture [51] to output deep visual representations of each token. Despite the absence of almost any domain-specific inductive bias apart from the image tokenization process, ViTs have a strong representation learning capacity [14] and achieve excellent results on various" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.39, + 0.901 + ], + "angle": 0, + "content": "*This project was done during an internship at Valeo.ai." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5240" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "image perception tasks, such as image classification [14], object detection [8] or semantic segmentation [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.124, + 0.473, + 0.382 + ], + "angle": 0, + "content": "Inspired by this success of ViTs for image understanding, we propose to implement projection-based LiDAR semantic segmentation with a pure vision transformer architecture at its core. Our goals are threefold in doing so: (1) Exploit the strong representation learning capacity of vision transformer for LiDAR semantic segmentation; (2) Work towards unifying network architectures used for processing LiDAR point clouds or images so that any advance in one domain benefits to both; (3) Show that one can leverage ViTs pre-trained on large-size natural image datasets for LiDAR point cloud segmentation. The last goal is crucial because the downside of having few inductive biases in ViTs is that they underperform when trained from scratch on small or medium-size datasets and that, for now, the only well-performing pre-trained ViTs [9, 14, 45] publicly available are trained on large collections of images that can be acquired, annotated and stored easier than point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.473, + 0.64 + ], + "angle": 0, + "content": "In this context, our main contribution is a ViT-based Li-DAR segmentation approach that compensates ViTs' lack of inductive biases on our data and that achieves state-of-the-art results among projection-based methods. To the best of our knowledge, although works using ViT architectures on dense indoor point clouds already exist [63, 67], this is the first solution using ViTs for the LiDAR point clouds of autonomous driving datasets, which are significantly sparser and noisier than the dense depth-map-based points clouds found in indoor datasets. Our solution, RangeViT, starts with a classical range projection to obtain a 2D representation of the point cloud [11, 26, 36, 60]. Then, we extract patch-based visual tokens from this 2D map and feed them to a plain ViT encoder [14] to get deep patch representations. These representations are decoded using a lightweight network to obtain pixel-wise label predictions, which are projected back to the 3D point cloud." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.473, + 0.839 + ], + "angle": 0, + "content": "Our finding is that this ViT architecture needs three key ingredients to reach its peak performance. First, we leverage ViT models pre-trained on large natural image datasets for LiDAR segmentation and demonstrate that our method benefits from them despite the fact that natural images display little resemblance with range-projection images. Second, we further compensate for ViTs' lack of inductive bias by substituting the classical linear embedding layer with a multi-layer convolutional stem. Finally, we refine pixelwise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grain features of the convolutional stem with the high-level but coarse predictions of the ViT encoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In summary, our contributions are the following: (1) To the best of our knowledge, we are the first to exploit the strong representation learning capacity of vision transformers architectures for 3D semantic segmentation from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "LiDAR point clouds. By revisiting, in the context of our problem, the tokenization process of the ViT's encoder and adding a light-weight convolutional decoder for refining the coarse patch-wise ViT representations, we derive a simple but effective projection-based LiDAR segmentation approach, which we call RangeViT. (2) Furthermore, as shown in Fig. 1, the proposed approach allows one to harness ViT models pre-trained on the RGB image domain for the LiDAR segmentation problem. Indeed, despite the large gap between the two domains, we empirically demonstrate that using such pre-training strategies improves segmentation performance. (3) Finally, our RangeViT approach, despite its simplicity, achieves state-of-the-art results among project-based segmentation methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.316, + 0.64, + 0.332 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.34, + 0.816, + 0.358 + ], + "angle": 0, + "content": "2.1. CNNs for Point Cloud Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.895, + 0.58 + ], + "angle": 0, + "content": "2D Methods Several works [3,11,24,26,28,36,42,47,50, 60,64,66,70] project the 3D point cloud into the 2D space with range, perspective or bird's-eye-view (BEV) projection and process the projected images with 2D CNNs. For instance, PolarNet [66] employs bird's-eye-view projection to polar coordinates and then processes the bird-eye-view features with a Ring CNN. DarkNetSeg [3], SalsaNext [11], KPRNet [26], RangeNet++ [36], Lite-HDSeg [42] and SqueezeSegV3 [60] use range projection and then process the input images with a U-Net-like architecture. PMF [70], a multi-modal segmentation approach for point clouds and RGB images [2,29,53,65,70], projects the 3D points onto 2D camera frames and processes them together with the RGB images using a dual-stream CNN network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.718 + ], + "angle": 0, + "content": "3D Methods Instead of the 2D space, voxel-based approaches [20,22,35,46] process the point clouds in their 3D space by first dividing the 3D space into voxels using cartesian coordinates and then applying 3D convolutions. Cylinder3D [69] show that dividing the 3D space into voxels using cylindrical coordinates instead of cartesian improves the segmentation performance. Although voxel-based methods consider the geometric properties of the 3D space, their drawback is that they are computationally expensive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.895, + 0.825 + ], + "angle": 0, + "content": "Also, for indoor-scene point cloud segmentation there are many methods [15, 37, 47, 52, 54, 56, 58, 62] relying on PointNet-inspired architectures [38] that directly process raw 3D points. However, these approaches cannot be easily adapted to outdoor-scene point cloud segmentation, which we consider in this work, as the large quantity of points cause computational difficulties." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.808, + 0.849 + ], + "angle": 0, + "content": "2.2. ViTs for Point Cloud Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The recent rise to prominence of ViT architectures in computer vision has inspired a series of works for indoor point cloud segmentation [31, 57, 63, 67, 68]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.958 + ], + "angle": 0, + "content": "5241" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "Processing point clouds with a ViT model can be challenging and computationally expensive due to the large number of points. Point-BERT [63] uses farthest point sampling [39] and the K-NN algorithm to define input tokens for the transformer. Also, it proposes a self-supervised pretraining strategy for point data inspired by the masked token modeling approaches in the RGB image [23] and text [13] domains. Point Transformer [67] has a U-Net-like architecture but without convolutional layers and it integrates self-attention mechanism in all of its blocks. Finally, Bridged Transformer [57] jointly processes point clouds and RGB images with a fully transformer-based architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.472, + 0.349 + ], + "angle": 0, + "content": "Using a transformer-based architecture for the semantic segmentation task on outdoor LiDAR point clouds remains challenging. To the best of our knowledge, there has been no work published yet about outdoor LiDAR point cloud semantic segmentation with a ViT-based architecture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.356, + 0.47, + 0.373 + ], + "angle": 0, + "content": "2.3. Transfer Learning from Images to Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.47 + ], + "angle": 0, + "content": "ViT models have the capacity to learn powerful representations, but require vast amounts of training data for it. However, large LiDAR point cloud datasets are less common due to the costly and time consuming annotation procedure. Recent works [21,32,40,43,55,61] explore transfer learning of 2D image pre-trained models to 3D point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.473, + 0.759 + ], + "angle": 0, + "content": "Image2Point [61] converts a 2D CNN into a 3D sparse CNN [61] by inflating 2D convolutions into 3D convolutions, which is done by repeating the 2D kernel along the third dimension. SLidR [43] is a self-supervised pretraining method on LiDAR data. It uses a student-teacher architecture, where the 2D teacher network pre-trained on images transfers information into the 3D student network. Pix4Point [40] and Simple3D-Former [55] study transfer learning from images to indoor point clouds with fully transformer-based architectures. They adapt the tokenizer and the head layer to be specialized for 3D point cloud data. Pix4Point [40] applies farthest point sampling [39], the K-NN algorithm and then a graph convolution on the aggregated neighborhoods to extract input tokens for the ViT encoder. Simple3D-Former [55] memorizes the ImageNet [12] representation of 2D image classification by incorporating a KL divergence term in the loss between its 2D image classification predictions and those obtained from a fixed ImageNet [12] pre-trained ViT network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.188, + 0.787 + ], + "angle": 0, + "content": "3. RangeViT" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.47, + 0.84 + ], + "angle": 0, + "content": "In this section, we describe our ViT-based LiDAR semantic segmentation approach, for which we provide an overview in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.274, + 0.862 + ], + "angle": 0, + "content": "3.1. General architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We represent a LiDAR point cloud of \\(N\\) points with a matrix \\(\\mathbf{P} \\in \\mathbb{R}^{N \\times 4}\\). Each point \\(p = (x, y, z, i) \\in \\mathbf{P}\\) has" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Cartesian coordinates denoted by \\((x,y,z)\\) and LiDAR intensity denoted by \\(i\\), and is annotated with a label \\(\\ell \\in \\{1,\\dots ,K\\}\\) encoding one of the \\(K\\) semantic classes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.161, + 0.892, + 0.237 + ], + "angle": 0, + "content": "Range projection. The input of our RangeViT backbone is a 2D representation of the input point cloud. We use the well-known range projection [36]. Each point \\(\\mathbf{p} \\in \\mathbf{P}\\) with coordinates \\((x, y, z)\\) is projected on a range image of size \\(H \\times W\\). The projected 2D coordinates satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.248, + 0.892, + 0.283 + ], + "angle": 0, + "content": "\\[\n\\binom {h} {w} = \\left( \\begin{array}{c} \\frac {1}{2} (1 - \\arctan (y, x) \\pi^ {- 1}) W \\\\ (1 - (\\arcsin (z, r ^ {- 1}) + | f _ {\\text {d o w n}} |) f _ {v} ^ {- 1}) H \\end{array} \\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.295, + 0.893, + 0.432 + ], + "angle": 0, + "content": "where \\( f_{v} = |f_{\\mathrm{down}}| + |f_{\\mathrm{up}}| \\) is the vertical field-of-view of the LiDAR sensor. We associate \\( C = 5 \\) low-level features \\( (r, x, y, z, i) \\) to each projected point, where \\( r = \\sqrt{x^2 + y^2 + z^2} \\) is the range of the corresponding point (i.e., its distance from the LiDAR sensor), to create the range image \\( \\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W} \\). Note that if more than one point is projected onto the same pixel, then only the feature with the smallest range is kept. Pixels with no point projected on them have their features filled with zeros." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Convolutional stem. In a standard ViT, the image is divided into \\(M\\) patches of size \\(P_{H} \\times P_{W}\\), which are linearly embedded to provide \\(D\\)-dimensional visual tokens. Yet, our empirical study in Sec. 4.2 shows that this tokenization process of standard ViTs is far from optimal on both our task and datasets of interest. In order to bridge this potential domain gap between range images and standard ViTs, we replace the embedding layer with a non-linear convolutional stem [59]. Non-linear convolutional stems have been shown to increase optimization stability and predictive performance of ViTs [59], whereas we leverage them primarily for steering range images towards ViT-like inputs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.893, + 0.865 + ], + "angle": 0, + "content": "The first part of the convolutional stem consists of the first 4 residual blocks of SalsaNext [11], called context module. This context module captures short-range dependencies of the 3D points projected in the range image and produces pixel-wise features with \\( D_{\\mathrm{h}} \\) channels at the same resolution of the input range image, hence the tensor of context features \\( \\mathbf{t}_{\\mathrm{c}} \\) has size \\( D_{\\mathrm{h}} \\times H \\times W \\). Then, in order to produce tokens compatible with the input of a ViT, we use an average pooling layer that reduces the spatial dimensions of the context features \\( \\mathbf{t}_{\\mathrm{c}} \\) from \\( H \\times W \\) to \\( (H / P_{H}) \\times (W / P_{W}) \\), and use a final \\( 1 \\times 1 \\) convolutional layer with \\( D \\) output channels. The convolutional stem thus yields \\( M = (HW) / (P_{H}P_{W}) \\) visual tokens \\( \\mathbf{v}_1, \\ldots, \\mathbf{v}_M \\) of dimension \\( D \\), i.e., matching the input dimension and number of tokens of a traditional ViT." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The first 3 residual layers actually have \\( D_{\\mathrm{in}} = 32 \\) channels, which is typically smaller than \\( D_{\\mathrm{h}} \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5242" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.092, + 0.881, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.894, + 0.308 + ], + "angle": 0, + "content": "Figure 2. Overview of RangeViT architecture. First, the point cloud is projected in a 2D space with range projection. Then, the produced range image is processed by the convolutional stem, the ViT encoder and the decoder to obtain a 2D feature map. It is then processed by a 3D refiner layer for 3D point-wise predictions. Note that there is a single skip connection between the convolutional stem and the decoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.471, + 0.41 + ], + "angle": 0, + "content": "ViT encoder. The output of the convolutional stem can be fed directly to a ViT [14]. The input \\(\\mathbf{t}_0\\) to our ViT encoder is prepared by stacking all the visual tokens \\(\\mathbf{v}_1, \\ldots, \\mathbf{v}_M\\) and a classification token \\(\\mathbf{v}_{\\mathrm{class}} \\in \\mathbb{R}^D\\), to which we add the positional embeddings \\(\\mathbf{E}_{\\mathrm{pos}} \\in \\mathbb{R}^{(M + 1) \\times D}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.418, + 0.469, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\mathbf {t} _ {0} = \\left[ \\mathbf {v} _ {\\text {c l a s s}}, \\mathbf {v} _ {1}, \\dots , \\mathbf {v} _ {M} \\right] + \\mathbf {E} _ {\\text {p o s}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.52 + ], + "angle": 0, + "content": "The input tokens are then transformed by the ViT encoder to obtain an updated sequence of tokens \\(\\mathbf{t}_L\\in \\mathbb{R}^{(M + 1)\\times D}\\) where \\(L\\) denotes the number of transformer blocks. Then, we remove the classification token from \\(\\mathbf{t}_L\\) to keep only the deep patch representations \\(\\mathbf{t}_L^{\\prime}\\in \\mathbb{R}^{M\\times D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.471, + 0.809 + ], + "angle": 0, + "content": "Decoder. The representations \\(\\mathbf{t}_L^{\\prime}\\) provided by the ViT encoder are patch representations which are unfortunately too coarse to obtain good point predictions. Therefore, we use a decoder to refine these coarse patch representations. First, \\(\\mathbf{t}_L^{\\prime}\\) is reshaped in form of a 2D feature map of size \\(D\\times H / P_H\\times W / P_W\\). Our convolutional decoder consists of a \\(1\\times 1\\) convolution layer with \\(D_{\\mathrm{h}}P_{H}P_{W}\\) output channels, followed by a Pixel Shuffle layer [44] which yields feature maps with shape \\(D_{\\mathrm{h}}\\times H\\times W\\), i.e., with the same resolution as the original range image. While the convolutional decoder can still produce coarse features or decoding artifacts, the Pixel Shuffle is particularly effective in recovering fine information from features. Then, we concatenate these features with the context features \\(\\mathbf{t}_{\\mathrm{c}}\\) from the convolutional stem and use a series of two convolutional layers with \\(3\\times 3\\) and \\(1\\times 1\\) kernels respectively, each of them followed by Leaky ReLU and batch normalisation, to obtain the refined feature map \\(\\mathbf{t}_{\\mathrm{dec}}\\in \\mathbb{R}^{D_{\\mathrm{h}}\\times H\\times W}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "3D refiner. Ultimately, we need to convert the pixel-wise features from the range image space into point-wise predictions in the 3D space. Most prior range-projection based methods first make pixel-wise class predictions and then unproject them to the 3D space, where at inference time often" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.892, + 0.469 + ], + "angle": 0, + "content": "there is a post-processing step relying, e.g., on K-NN [36] or CRFs [27]. The purpose of the latter post-processing step is to fix segmentation mistakes related to the projection and processing of 3D points in a 2D space (e.g., multiple 3D points being projected on the same pixel, or 2D boundary prediction errors for points that are actually far away in the 3D space). Instead, we follow the approach of KPRNet [26] that proposes an end-to-end approach that learns this post-processing step with a KPConv [47] layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.893, + 0.667 + ], + "angle": 0, + "content": "KPConv [47] is a point convolution technique which works directly on the original 3D points. It permits to leverage the underlying geometry of the 3D point clouds to refine features at the point level. So, in our network, we project the 2D feature maps \\(\\mathbf{t}_{\\mathrm{dec}}\\) of the 2D decoder back to original 3D points by bilinear upsampling, thus obtaining point-wise features with shape \\(N\\times D_{\\mathrm{h}}\\), where \\(N\\) is the number of 3D points. Then, these point features are given to the KPConv layer as input along with the 3D coordinates of the corresponding points, which outputs \\(D_{\\mathrm{h}}\\)-dimensional point features. Finally, the logits \\(\\mathbf{s}\\in \\mathbb{R}^{N\\times K}\\) are obtained by applying a BatchNorm, a ReLU and a final point-wise linear layer on these point features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.675, + 0.715, + 0.69 + ], + "angle": 0, + "content": "3.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Training loss We use the sum of the multi-class focal loss [30] and the Lovász-softmax loss [4]. The focal loss is a scaled version of the cross-entropy loss [19] adapting its penalty to the hardness of the samples, making it suited for datasets with class imbalance, such as semantic segmentation. The Lovász-softmax is developed specifically for semantic segmentation and built to optimize the mIoU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Inference As in [45], we use a sliding-window method during inference. The network actually never sees the entire range images during training but only crops extracted from it. At inference, the range image is divided into overlapping crops of the same size as those used during training. The corresponding 2D features at the output of the decoder are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5243" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.125, + 0.089, + 0.421, + 0.166 + ], + "angle": 0, + "content": "
StemDecoderRefinermIoU (%)#Params
LinearLinear65.5222.0M
ConvLinear69.8222.8M
ConvUpConv73.8324.6M
ConvUpConv✓74.6025.2M
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.166, + 0.47, + 0.222 + ], + "angle": 0, + "content": "Table 1. Model ablations. Results on the nuScenes validation set with \\( D_{\\mathrm{h}} = 192 \\). The linear stem refers to the linear patch embedding layer. When the 3D refiner layer (Refiner column) is not used, we use the K-NN post-processing technique [36]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.239, + 0.469, + 0.269 + ], + "angle": 0, + "content": "then averaged to reconstruct the entire feature map, which is then processed by our 3D refinement layer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.283, + 0.21, + 0.3 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.308, + 0.267, + 0.325 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.469, + 0.44 + ], + "angle": 0, + "content": "Datasets and metrics. We validate our approach for 3D point cloud semantic segmentation on two different commonly used datasets: nuScenes [7] and SemanticKITTI [3]. We conduct most of our ablation studies on nuScenes and compare against previous works on both nuScenes and SemanticKITTI. As evaluation metric, we use the mean Intersection over Union (mIoU) [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.469, + 0.53 + ], + "angle": 0, + "content": "NuScenes [7] consists of 1,000 scenes of 20 seconds in Boston and Singapore with various urban scenarios, lighting and weather conditions. The LiDAR sensor has 32 laser beams. Furthermore, there are 16 annotated semantic classes and the dataset is split into 28,130 training and 6,019 validation point cloud scans." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.469, + 0.65 + ], + "angle": 0, + "content": "SemanticKITTI [3] is created from the KITTI Vision Odometry Benchmark [17] and consists of urban scenes collected in Germany. Sequences 00-10 are used for training, except sequence 08 which is used for validation. There are 19,130 training and 4,071 validation scans. Sequences 11-21 are used for test and they contain 20,351 scans. The LiDAR sensor has 64 laser beams and there are 19 annotated semantic classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.792 + ], + "angle": 0, + "content": "Model and pre-trained weights. For all experiments, we use the ViT-S/16 model [14] as the encoder. It has \\( L = 12 \\) layers, 6 attention heads and \\( D = 384 \\) channels, amounting to approximately 21M parameters. Unless otherwise stated, (a) this ViT encoder is initialized with weights pre-trained on ImageNet21k [12] for classification and then fine-tuned on Cityscapes [10] for semantic image segmentation [45]; (b) the stem, decoder and 3D refiner layers, which are always randomly initialized, use \\( D_{\\mathrm{h}} = 256 \\) feature channels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Optimization. We use the AdamW optimizer [34] with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\) and weight decay 0.01. The batch-size is 32 and 16 for nuScenes and SemanticKITTI, respectively. For the learning rate \\(lr\\), we use a linear warm-up from 0 to its peak value for 10 epochs and then we decrease it over the remaining training epochs to 0 with a cosine annealing schedule [33]. In SemanticKITTI, we use 60 train-" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.875, + 0.159 + ], + "angle": 0, + "content": "
Dh size64128192256
#Params22.7M23.7M25.2M27.1M
nuScenes mIoU (%)74.0074.1274.6075.21
SemanticKITTI mIoU (%)58.4860.7360.4560.55
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.16, + 0.892, + 0.201 + ], + "angle": 0, + "content": "Table 2. Impact of the channel size \\( D_{\\mathrm{h}} \\) used in the stem, decoder, and 3D refiner layers. Results on the nuScenes and the SemanticKITTI validation sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.892, + 0.28 + ], + "angle": 0, + "content": "ing epochs and the peak \\( lr \\) is \\( 4 \\times 10^{-4} \\). In nuScenes, we use 150 epochs and the peak \\( lr \\) is \\( 8 \\times 10^{-4} \\) when training from Cityscapes, ImageNet21k and random initializations, and \\( 2 \\times 10^{-4} \\) when training from DINO initialization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.892, + 0.421 + ], + "angle": 0, + "content": "Data augmentations. As point cloud augmentations we use: (a) flips over the \\(y\\) axis (the vertical axis on the range image), (b) random translations, and (c) random rotations between \\(\\pm 5^{\\circ}\\) (using the roll, pitch and yaw angles). All augmentations are applied randomly with probability 0.5. Finally, after range projection, we take a random image crop with a fixed size of \\(32 \\times 384\\) for nuScenes and \\(64 \\times 384\\) for SemanticKITTI. Note that the full size of a range image is \\(32 \\times 2048\\) for nuScenes and \\(64 \\times 2048\\) for SemanticKITTI." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.463 + ], + "angle": 0, + "content": "4.2. What makes a ViT architecture for 3D semantic segmentation?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.592 + ], + "angle": 0, + "content": "Our aim is to adapt to LiDAR point clouds with the fewest possible modifications of the standard ViT architecture [14], which already follows faithfully the original self-attention Transformer design [51]. Differently from ViT that performs classification on images, RangeViT performs semantic segmentation of point cloud-derived range images. We study here the possible choices for the input processing and decoder layers using the nuScenes dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.853 + ], + "angle": 0, + "content": "Stem and decoder. In Tab. 1, we study the impact of the convolutional stem and the UpConv decoder. To that end, we report results using a linear patch embedding [14] as a stem and a linear decoder. Starting from a model with linear stem and linear decoder, introducing the proposed convolutional stem leads to a significant mIoU boost \\((65.52\\rightarrow 69.82)\\). This highlights the importance of having a non-linear network component for producing appropriate input token features for the ViT backbone. In addition, when using image pre-trained ViTs (Sec. 4.3) the convolutional stem can effectively steer the distribution of input range images towards the image-based feature distribution the ViT has been pre-trained on, leading to smoother fine-tuning. Then, also replacing the linear decoder with the proposed UpConv decoder leads to another notable improvement on mIoU \\((69.8\\rightarrow 73.83)\\), validating this design choice. Finally, replacing the K-NN refinement [36] with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2The linear decoder consists of a simple \\(1\\times 1\\) conv. layer, which predicts patch-wise classification scores, and a bilinear upsampling to reach the input image resolution." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5244" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.153 + ], + "angle": 0, + "content": "
Patch size16 × 168 × 84 × 164 × 84 × 42 × 162 × 8
mIoU (%)68.4572.0472.7273.3073.7073.8875.21
Tokens49193193385769385769
Train time×1×1.02×1.02×1.13×1.43×1.13×1.43
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.155, + 0.47, + 0.198 + ], + "angle": 0, + "content": "Table 3. Patch size ablations. Results on the nuScenes validation set. The mIoU scores are in increasing order. The train time is relative to the \\(16 \\times 16\\) patch size case." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.469, + 0.244 + ], + "angle": 0, + "content": "the KPCov layer (in the 3D refiner layer), leads to a small but non-trivial mIoU increase \\((73.83\\rightarrow 74.60)\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.47, + 0.365 + ], + "angle": 0, + "content": "In Tab. 2, we study what is the impact, on the mIoU, of changing the number of feature channels \\( D_{\\mathrm{h}} \\) on the stem, decoder and 3D refiner layer. On nuScenes, we observe that the results gradually increase when increasing the dimension \\( D_{\\mathrm{h}} \\). In the SemanticKITTI case, \\( D_{\\mathrm{h}} = 128 \\) gives the best results and further increasing \\( D_{\\mathrm{h}} \\) does not help. Note that the size of the ViT's embeddings is fixed at \\( D = 384 \\), regardless of the \\( D_{\\mathrm{h}} \\) size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.641 + ], + "angle": 0, + "content": "What patch-size for range image \"tokenization\"? The size of the input patch tokens is an essential factor for controlling the trade-off between speed and accuracy performance without changing the number of parameters in the model. Intuitively, reducing the patch-size results in a finer representation, but also a longer input sequence that takes longer to process. Conversely, larger patches lead to a coarser representation, yet faster inference. The performance impact of the patch-size can sometimes match the one of model size [45]. For simplicity, standard ViT models use square patches of size 32, 16 or 8, as they are typically trained on square images. In contrast, range images have a much different aspect ratio (high width) and different layout of the content in the image (rows of points corresponding to LiDAR beams). With this insight, we revisit the practice of using square patches and look into rectangular patches with different aspect ratio (1:2, 1:4, 1:8) that would better capture the specific local patterns of the range images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.471, + 0.822 + ], + "angle": 0, + "content": "Tab. 3 shows the mIoU scores for different patch sizes for dividing the range image to patch tokens. Note that the convolutional stem first produces pixel-wise features and then, given a patch-size \\((P_{H}, P_{W})\\), reduces the spatial dimensions of these features to \\((H / P_{H}, W / P_{W})\\) using local average pooling. We observe that smaller patch area is better but not necessarily with a square patch, commonly used for ViT models. The wide range images benefit more from rectangular patches (\\(2 \\times 8\\) performing best). The smaller patches enable the extraction of more fine-grained information leading to more precise predictions for smaller and thinner objects and points at object boundaries." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.379, + 0.849 + ], + "angle": 0, + "content": "4.3. Exploiting image pre-trained ViTs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "So far, we have studied the architectural choices necessary for using ViT models for point cloud semantic segmentation. The final RangeViT model preserves the ViT back" + }, + { + "type": "table", + "bbox": [ + 0.565, + 0.09, + 0.826, + 0.128 + ], + "angle": 0, + "content": "
Pre-trainingRandDINOIN21kCS
mIoU (%)72.3773.3374.7775.21
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.13, + 0.892, + 0.214 + ], + "angle": 0, + "content": "Table 4. ViT pre-training on RGB images. Comparison of different weight initializations of the ViT encoder on the nuScenes validation set. Rand: randomly initialized. The positional embeddings are initialized with the corresponding pre-trained weights or randomly when training from scratch. The convolutional stem, the decoder and the 3D refiner layer are randomly initialized." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.233, + 0.856, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.465 + ], + "angle": 0, + "content": "Figure 3. Training efficiency with image-pretrained ViTs. Comparison of the validation mIoU curves for different weight initialisations of the ViT encoder on the nuScenes validation set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.484, + 0.892, + 0.545 + ], + "angle": 0, + "content": "bone intact allowing us to initialize it with weights from models pre-trained on large datasets. We study now whether using such an initialization helps or not and what fine-tuning strategies would be more suitable in this context." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Is pre-training on RGB images beneficial? In Tab. 4, we study the effect of transferring to our task ViT models pre-trained on natural RGB images. In particular, we explore initializing RangeViT's backbone with ViTs pretrained: (a) on supervised ImageNet21k classification [14] (entry IN21k), (b) on supervised image segmentation on Cityscapes with Segmenter [45] (entry CS), which in its turn was pre-trained with IN21k, and (c) with the DINO [9] self-supervised approach on ImageNet1k (entry DINO)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We observe that, despite the large domain gap, using ViT models pre-trained on RGB images is always better than training from scratch on LiDAR data (entry Rand). For instance, using the IN21k and CS pretrained ViTs leads to improving the mIoU scores by 2.4 and 2.8 points respectively. Additionally, as we see in Fig. 3, which plots the nuScenes validation mIoU as a function of the training epochs, using such pre-trained ViTs leads to faster training convergence of the LiDAR segmentation model. We argue that this is a highly interesting finding. It means that our RangeViT approach, by being able to use off-the-shelf pre-trained ViT models, can directly benefit from current and future advances on the training ViT models with natural RGB images, a very active and rapidly growing re" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5245" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.146, + 0.089, + 0.4, + 0.194 + ], + "angle": 0, + "content": "
ModelFine-tuningIN21k mIoU (%)CS (%)
LNATTNFFN
(a)✓✓✓74.7975.21
(b)67.8868.03
(c)✓69.0869.31
(d)✓✓73.5672.77
(e)✓✓75.1175.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.197, + 0.47, + 0.321 + ], + "angle": 0, + "content": "Table 5. Partial ViT fine-tuning. We use a ViT encoder pretrained on ImageNet21k (IN21k) or Cityscapes (CS) and partially fine-tune RangeViT on the nuScenes training set. The convolutional stem, the positional embeddings and the UpConv decoder are always fine-tuned. LN: fine-tuning the LayerNorm layers of the ViT encoder. ATTN: fine-tuning the multi-head attention layers of the ViT encoder. FFN: fine-tuning the feed-forward network layers of the ViT encoder. Model (a) is full fine-tuning of the network. The results are reported on the nuScenes validation set." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.337, + 0.432, + 0.378 + ], + "angle": 0, + "content": "
EncoderViT-S†ViT-SRN50†RN50Identity
mIoU (%)67.8874.7760.4872.3053.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.468, + 0.407 + ], + "angle": 0, + "content": "Table 6. Ablating encoder backbones. ViT-S and RN50 are pretrained on IN21k. †: the encoder remains frozen during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.468, + 0.516 + ], + "angle": 0, + "content": "search field [23, 41, 48, 49]. Furthermore, from the small difference between the mIoU scores with the IN21k and CS pre-trainings, we infer that the pre-training can lead to consistent performance improvements even if it is not on the strongly-supervised image segmentation task, which requires expensive-to-announce datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.718 + ], + "angle": 0, + "content": "Which ViT layers is better to fine-tune? In the image domain, several practices have emerged for fine-tuning a pre-trained convolutional network on a downstream dataset. Taking into consideration the domain gap between the pretraining and downstream data and the amount of labeled data available, the entire network can be fine-tuned or only a part of it. Here the domain gap between RGB images and range images is major and we would expect a full fine-tuning of the network to be better. To understand how much prior knowledge of the image pre-trained ViT is useful for point clouds, we study different fine-tuning strategies: fine-tuning all layers, only the attention (ATTN) layers or only the feedforward network (FFN) layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In Tab. 5, we show results with these different fine-tuning strategies. Interestingly, the best results are not achieved with full fine-tuning (model (a)) but when the attention layers are kept frozen (model (e)). This suggests that the pretrained ATTN layers are already well learnt and ready to generalize to range images. With CS pre-training ATTN layers may capture the layout of the scenes more easily without much fine-tuning, as the LiDAR scans have been also acquired from urban road scenes. Fine-tuning FFN may have more impact due to the different specifics of the LiDAR data compared to RGB images. In addition, FFN layers are in practice easier and more stable to optimize" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.094, + 0.697, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.094, + 0.886, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.203, + 0.697, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.203, + 0.886, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.299, + 0.697, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.299, + 0.886, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.397, + 0.892, + 0.453 + ], + "angle": 0, + "content": "Figure 4. Visualizing the segmentation accuracy. Left: ground truth segmentation of validation point clouds of nuScenes, coloured based on their label. Right: segmentation accuracy of RangeViT - good predictions are in blue and the bad ones in red." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.571 + ], + "angle": 0, + "content": "(they are essentially fully-connected and normalization layers) than ATTN layers that usually require more careful hyper-parameter selection. These findings align with recent ones from the image domain [48], confirming that the convolutional stems do steer the input LiDAR data to behave like image data once on in the ViT backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.774 + ], + "angle": 0, + "content": "Ablating encoder backbones. In Tab. 6, we replace the ViT-S encoder backbone of RangeViT with a ResNet-50 (RN50) encoder or the identity function (i.e., the decoder follows directly the stem). Both ViT-S and RN50 are pretrained on IN21k. We see that switching from ViT-S to RN50 decreases the mIoU from \\(74.77\\%\\) to \\(72.30\\%\\). Furthermore, when the backbones remain frozen \\((\\mathrm{ViT - S}^{\\dagger}\\) and \\(\\mathrm{RN50\\dagger}\\) models), we reach \\(67.88\\%\\) with ViT-S and \\(60.48\\%\\) with RN50, demonstrating that ViT features are more appropriate for transfer learning to LiDAR data than CNNs. Finally, with the Identity backbone, we achieve \\(53.73\\%\\), which is more than 14 points worse than the \\(\\mathrm{ViT - S}^{\\dagger}\\) model that has the same number of learnable parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.795, + 0.802 + ], + "angle": 0, + "content": "4.4. Comparison to the state of the art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tab. 7 and 8 report the final comparison on the nuScenes validation set and on the SemanticKITTI test set including class-wise IoU scores. We observe that our model achieves superior mIoU performance compared to prior 2D-projection based methods on both datasets, reducing the gap with the strong voxel-based Cylinder3D [69] method." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5246" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.254 + ], + "angle": 0, + "content": "
Methodbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdriveableother flatsidewalkterrainmammadevegetationmIoU (%)
Voxel-based Cylinder3D [69]76.440.391.393.851.378.078.964.962.184.496.871.676.475.490.587.476.1
2D Projection-based
RangeNet++ [36]66.021.377.280.930.266.869.652.154.272.394.166.663.570.183.179.865.5
PolarNet [66]74.728.285.390.935.177.571.358.857.476.196.571.174.774.087.385.771.0
SalsaNext [11]74.834.185.988.442.272.472.263.161.376.596.070.871.271.586.784.472.2
RangeViT-IN21k (ours)75.139.090.288.448.079.277.266.465.176.796.371.173.773.988.987.174.8
RangeViT-CS (ours)75.540.788.390.149.379.377.266.365.280.096.471.473.873.889.987.275.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.256, + 0.891, + 0.269 + ], + "angle": 0, + "content": "Table 7. nuScenes validation set comparison with state-of-the-art methods. The best results are bold and the second best results are blue." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.277, + 0.891, + 0.467 + ], + "angle": 0, + "content": "
Methodcarbicyclemotorcycletruckother vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother groundbuildingfencevegetationtrunkterrainpoletraffic signmIoU (%)
Voxel-based Cylinder3D [69]97.167.664.059.058.673.967.936.091.465.175.532.391.066.585.471.868.562.665.667.8
2D Projection-based
RangeNet++ [36]91.425.734.425.723.038.338.84.891.865.075.227.887.458.680.555.164.647.955.952.2
PolarNet [66]93.840.330.122.928.543.240.25.690.861.774.421.790.061.384.065.567.851.857.554.3
SqueezeSegV3 [60]92.538.736.529.633.045.646.220.191.763.474.826.489.059.482.058.765.449.658.955.9
SalsaNext [11]91.948.338.638.931.960.259.019.491.763.775.829.190.264.281.863.666.554.362.159.5
KPRNet [26]95.554.147.923.642.665.965.016.593.273.980.630.291.768.485.769.871.258.764.163.1
Lite-HDSeg [42]92.340.055.437.739.659.271.654.193.068.278.329.391.565.078.265.865.159.567.763.8
RangeViT-CS (ours)95.455.843.529.842.163.958.238.193.170.280.032.592.069.085.370.671.260.864.764.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.468, + 0.891, + 0.481 + ], + "angle": 0, + "content": "Table 8. SemanticKITTI test set comparison with state-of-the-art methods. The best results are bold and the second best results are blue." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Class-wise IoU result analysis. In Tab. 7 and 8, we can see that RangeViT often achieves the best or the second best class-wise IoU scores. In both datasets, the classes are imbalanced and due to the sparsity and varying density of Li-DAR point clouds, some classes (e.g., bicycle, pedestrian) are represented with few, not necessarily structured points per scene, so it is difficult to recognize them. This problem could possibly be reduced by jointly processing point clouds and RGB images, since RGB images might provide extra cues about the outline and the shape of these objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.659, + 0.26, + 0.674 + ], + "angle": 0, + "content": "4.5. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.47, + 0.803 + ], + "angle": 0, + "content": "We visualize the 3D point clouds with the ground truth semantic labels as well as the predictions with CloudCompare [18]. Fig. 4 shows the predictions of RangeViT on three validation point clouds of nuScenes. We notice minor errors such as man-made objects predicted as sidewalk and imperfect borders for the vegetation. We also remark difficulties in recognizing pedestrians and confusion between the driveable surface and the sidewalk for few points." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.195, + 0.831 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We studied the feasibility of leveraging (pre-trained) ViTs for LiDAR 3D semantic segmentation with projection-based methods. We discover that in spite of the significant domain gap between RGB images and range images and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.665 + ], + "angle": 0, + "content": "their high requirements of training data, ViTs can be successfully used without any changes in the original transformer backbone. We achieve this thanks to an adapted tokenization and pre-processing for the ViT encoder and a simple convolutional decoder. We show that ViTs pre-trained on large image datasets can be effectively repurposed for LiDAR segmentation towards reaching state-of-the-art performance among 2D projection methods. We release the code for our implementation and hope that it could be used as a testbed for evaluating the ability of ViT image \"foundation\" models [6] to generalize on different domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.775 + ], + "angle": 0, + "content": "Future work. Although the results are promising, there is still room for improvement. For instance, we identified the tokenization of LiDAR data as a crucial factor for success. As future work, we could further improve this process, e.g., with FlexiViT [5] (random patch sizes) or Perceiver IO [25] (learning to extract tokens), and consider tokenizing raw 3D data instead of the 2D projections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.782, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. We would like to express our gratitude to Matthieu Cord and Hugo Touvron for their insightful comments, Robin Strudel et al. [45] for kindly providing ViT-S pre-trained on Cityscapes, and Oriane Simeoni for her valuable contribution to certain experiments. This work was performed using HPC resources from GENCI-IDRIS (Grants 2022-AD011012884R1, 2022-AD011013413 and 2022-AD011013701). The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-21-CE23-0032 (project MultiTrans)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5247" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Eren Erdal Aksoy, Saimir Baci, and Selcuk Cavidar. SalsaNet: Fast road and vehicle segmentation in LiDAR point clouds for autonomous driving. 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Perception-aware multi-sensor fusion for 3D LiDAR semantic segmentation. In ICCV, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5250" + } + ] +] \ No newline at end of file diff --git a/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_origin.pdf b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c1cea28e07e92568240c29bba4f31e70bcd69485 --- /dev/null +++ b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/94b91fe6-a01e-4a69-8957-2c035de25886_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e47d9ff91d6d142fbdc4912be0afa8f0c859f80307618ffe7327b53821ee149d +size 1160889 diff --git a/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/full.md b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1195b2011a48f1d2ff4318a102e91c6503fbebe0 --- /dev/null +++ b/2023/RangeViT_ Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving/full.md @@ -0,0 +1,302 @@ +# RangeViT: Towards Vision Transformers for 3D Semantic Segmentation in Autonomous Driving + +Angelika Ando $^{1,2,*}$ , Spyros Gidaris $^{1}$ , Andrei Bursuc $^{1}$ , Gilles Puy $^{1}$ , Alexandre Boulch $^{1}$ , Renaud Marlet $^{1,3}$ + +$^{1}$ Valeo.ai, Paris, France $^{2}$ Centre for Robotics, Mines Paris, Université PSL, Paris, France $^{3}$ LIGM, Ecole des Ponts, Univ. Gustave Eiffel, CNRS, Marne-la-Vallee, France + +# Abstract + +Casting semantic segmentation of outdoor LiDAR point clouds as a 2D problem, e.g., via range projection, is an effective and popular approach. These projection-based methods usually benefit from fast computations and, when combined with techniques which use other point cloud representations, achieve state-of-the-art results. Today, projection-based methods leverage 2D CNNs but recent advances in computer vision show that vision transformers (ViTs) have achieved state-of-the-art results in many image-based benchmarks. In this work, we question if projection-based methods for 3D semantic segmentation can benefit from these latest improvements on ViTs. We answer positively but only after combining them with three key ingredients: (a) ViTs are notoriously hard to train and require a lot of training data to learn powerful representations. By preserving the same backbone architecture as for RGB images, we can exploit the knowledge from long training on large image collections that are much cheaper to acquire and annotate than point clouds. We reach our best results with pre-trained ViTs on large image datasets. (b) We compensate ViTs' lack of inductive bias by substituting a tailored convolutional stem for the classical linear embedding layer. (c) We refine pixel-wise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grained features of the convolutional stem with the high-level but coarse predictions of the ViT encoder. With these ingredients, we show that our method, called RangeViT, outperforms existing projection-based methods on nuScenes and SemanticKITTI. The code is available at https://github.com/valeoai/rangevit. + +# 1. Introduction + +Semantic segmentation of LiDAR point clouds permits vehicles to perceive their surrounding 3D environment in + +![](images/a241e668366c1a33e1da31893471b878938707211cee6c192bc32670ee4a57f9.jpg) +Figure 1. Exploiting vision transformer (ViT) architectures and weights for LiDAR point cloud semantic segmentation. We leverage the flexibility of transformer-based architectures to re-purpose them with minimal changes for processing sparse point clouds in autonomous driving tasks. The common ViT backbone across modalities allows to effectively transfer weights pre-trained on large image repositories towards improving point cloud segmentation performance with fine-tuning. + +dependently of the lighting condition, providing useful information to build safe and reliable vehicles. A common approach to segment large scale LiDAR point clouds is to project the points on a 2D surface and then to use regular CNNs, originally designed for images, to process the projected point clouds [1, 11, 26, 36, 60, 66]. Recently, Vision Transformers (ViTs) were introduced as an alternative to convolutional neural networks for processing images [14]: images are divided into patches which are linearly embedded into a high-dimensional space to create a sequence of visual tokens; these tokens are then consumed by a pure transformer architecture [51] to output deep visual representations of each token. Despite the absence of almost any domain-specific inductive bias apart from the image tokenization process, ViTs have a strong representation learning capacity [14] and achieve excellent results on various + +image perception tasks, such as image classification [14], object detection [8] or semantic segmentation [45]. + +Inspired by this success of ViTs for image understanding, we propose to implement projection-based LiDAR semantic segmentation with a pure vision transformer architecture at its core. Our goals are threefold in doing so: (1) Exploit the strong representation learning capacity of vision transformer for LiDAR semantic segmentation; (2) Work towards unifying network architectures used for processing LiDAR point clouds or images so that any advance in one domain benefits to both; (3) Show that one can leverage ViTs pre-trained on large-size natural image datasets for LiDAR point cloud segmentation. The last goal is crucial because the downside of having few inductive biases in ViTs is that they underperform when trained from scratch on small or medium-size datasets and that, for now, the only well-performing pre-trained ViTs [9, 14, 45] publicly available are trained on large collections of images that can be acquired, annotated and stored easier than point clouds. + +In this context, our main contribution is a ViT-based Li-DAR segmentation approach that compensates ViTs' lack of inductive biases on our data and that achieves state-of-the-art results among projection-based methods. To the best of our knowledge, although works using ViT architectures on dense indoor point clouds already exist [63, 67], this is the first solution using ViTs for the LiDAR point clouds of autonomous driving datasets, which are significantly sparser and noisier than the dense depth-map-based points clouds found in indoor datasets. Our solution, RangeViT, starts with a classical range projection to obtain a 2D representation of the point cloud [11, 26, 36, 60]. Then, we extract patch-based visual tokens from this 2D map and feed them to a plain ViT encoder [14] to get deep patch representations. These representations are decoded using a lightweight network to obtain pixel-wise label predictions, which are projected back to the 3D point cloud. + +Our finding is that this ViT architecture needs three key ingredients to reach its peak performance. First, we leverage ViT models pre-trained on large natural image datasets for LiDAR segmentation and demonstrate that our method benefits from them despite the fact that natural images display little resemblance with range-projection images. Second, we further compensate for ViTs' lack of inductive bias by substituting the classical linear embedding layer with a multi-layer convolutional stem. Finally, we refine pixelwise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grain features of the convolutional stem with the high-level but coarse predictions of the ViT encoder. + +In summary, our contributions are the following: (1) To the best of our knowledge, we are the first to exploit the strong representation learning capacity of vision transformers architectures for 3D semantic segmentation from + +LiDAR point clouds. By revisiting, in the context of our problem, the tokenization process of the ViT's encoder and adding a light-weight convolutional decoder for refining the coarse patch-wise ViT representations, we derive a simple but effective projection-based LiDAR segmentation approach, which we call RangeViT. (2) Furthermore, as shown in Fig. 1, the proposed approach allows one to harness ViT models pre-trained on the RGB image domain for the LiDAR segmentation problem. Indeed, despite the large gap between the two domains, we empirically demonstrate that using such pre-training strategies improves segmentation performance. (3) Finally, our RangeViT approach, despite its simplicity, achieves state-of-the-art results among project-based segmentation methods. + +# 2. Related work + +# 2.1. CNNs for Point Cloud Segmentation + +2D Methods Several works [3,11,24,26,28,36,42,47,50, 60,64,66,70] project the 3D point cloud into the 2D space with range, perspective or bird's-eye-view (BEV) projection and process the projected images with 2D CNNs. For instance, PolarNet [66] employs bird's-eye-view projection to polar coordinates and then processes the bird-eye-view features with a Ring CNN. DarkNetSeg [3], SalsaNext [11], KPRNet [26], RangeNet++ [36], Lite-HDSeg [42] and SqueezeSegV3 [60] use range projection and then process the input images with a U-Net-like architecture. PMF [70], a multi-modal segmentation approach for point clouds and RGB images [2,29,53,65,70], projects the 3D points onto 2D camera frames and processes them together with the RGB images using a dual-stream CNN network. + +3D Methods Instead of the 2D space, voxel-based approaches [20,22,35,46] process the point clouds in their 3D space by first dividing the 3D space into voxels using cartesian coordinates and then applying 3D convolutions. Cylinder3D [69] show that dividing the 3D space into voxels using cylindrical coordinates instead of cartesian improves the segmentation performance. Although voxel-based methods consider the geometric properties of the 3D space, their drawback is that they are computationally expensive. + +Also, for indoor-scene point cloud segmentation there are many methods [15, 37, 47, 52, 54, 56, 58, 62] relying on PointNet-inspired architectures [38] that directly process raw 3D points. However, these approaches cannot be easily adapted to outdoor-scene point cloud segmentation, which we consider in this work, as the large quantity of points cause computational difficulties. + +# 2.2. ViTs for Point Cloud Segmentation + +The recent rise to prominence of ViT architectures in computer vision has inspired a series of works for indoor point cloud segmentation [31, 57, 63, 67, 68]. + +Processing point clouds with a ViT model can be challenging and computationally expensive due to the large number of points. Point-BERT [63] uses farthest point sampling [39] and the K-NN algorithm to define input tokens for the transformer. Also, it proposes a self-supervised pretraining strategy for point data inspired by the masked token modeling approaches in the RGB image [23] and text [13] domains. Point Transformer [67] has a U-Net-like architecture but without convolutional layers and it integrates self-attention mechanism in all of its blocks. Finally, Bridged Transformer [57] jointly processes point clouds and RGB images with a fully transformer-based architecture. + +Using a transformer-based architecture for the semantic segmentation task on outdoor LiDAR point clouds remains challenging. To the best of our knowledge, there has been no work published yet about outdoor LiDAR point cloud semantic segmentation with a ViT-based architecture. + +# 2.3. Transfer Learning from Images to Point Clouds + +ViT models have the capacity to learn powerful representations, but require vast amounts of training data for it. However, large LiDAR point cloud datasets are less common due to the costly and time consuming annotation procedure. Recent works [21,32,40,43,55,61] explore transfer learning of 2D image pre-trained models to 3D point clouds. + +Image2Point [61] converts a 2D CNN into a 3D sparse CNN [61] by inflating 2D convolutions into 3D convolutions, which is done by repeating the 2D kernel along the third dimension. SLidR [43] is a self-supervised pretraining method on LiDAR data. It uses a student-teacher architecture, where the 2D teacher network pre-trained on images transfers information into the 3D student network. Pix4Point [40] and Simple3D-Former [55] study transfer learning from images to indoor point clouds with fully transformer-based architectures. They adapt the tokenizer and the head layer to be specialized for 3D point cloud data. Pix4Point [40] applies farthest point sampling [39], the K-NN algorithm and then a graph convolution on the aggregated neighborhoods to extract input tokens for the ViT encoder. Simple3D-Former [55] memorizes the ImageNet [12] representation of 2D image classification by incorporating a KL divergence term in the loss between its 2D image classification predictions and those obtained from a fixed ImageNet [12] pre-trained ViT network. + +# 3. RangeViT + +In this section, we describe our ViT-based LiDAR semantic segmentation approach, for which we provide an overview in Fig. 2. + +# 3.1. General architecture + +We represent a LiDAR point cloud of $N$ points with a matrix $\mathbf{P} \in \mathbb{R}^{N \times 4}$ . Each point $p = (x, y, z, i) \in \mathbf{P}$ has + +Cartesian coordinates denoted by $(x,y,z)$ and LiDAR intensity denoted by $i$ , and is annotated with a label $\ell \in \{1,\dots ,K\}$ encoding one of the $K$ semantic classes. + +Range projection. The input of our RangeViT backbone is a 2D representation of the input point cloud. We use the well-known range projection [36]. Each point $\mathbf{p} \in \mathbf{P}$ with coordinates $(x, y, z)$ is projected on a range image of size $H \times W$ . The projected 2D coordinates satisfies + +$$ +\binom {h} {w} = \left( \begin{array}{c} \frac {1}{2} (1 - \arctan (y, x) \pi^ {- 1}) W \\ (1 - (\arcsin (z, r ^ {- 1}) + | f _ {\text {d o w n}} |) f _ {v} ^ {- 1}) H \end{array} \right), \tag {1} +$$ + +where $f_{v} = |f_{\mathrm{down}}| + |f_{\mathrm{up}}|$ is the vertical field-of-view of the LiDAR sensor. We associate $C = 5$ low-level features $(r, x, y, z, i)$ to each projected point, where $r = \sqrt{x^2 + y^2 + z^2}$ is the range of the corresponding point (i.e., its distance from the LiDAR sensor), to create the range image $\mathbf{I} \in \mathbb{R}^{C \times H \times W}$ . Note that if more than one point is projected onto the same pixel, then only the feature with the smallest range is kept. Pixels with no point projected on them have their features filled with zeros. + +Convolutional stem. In a standard ViT, the image is divided into $M$ patches of size $P_{H} \times P_{W}$ , which are linearly embedded to provide $D$ -dimensional visual tokens. Yet, our empirical study in Sec. 4.2 shows that this tokenization process of standard ViTs is far from optimal on both our task and datasets of interest. In order to bridge this potential domain gap between range images and standard ViTs, we replace the embedding layer with a non-linear convolutional stem [59]. Non-linear convolutional stems have been shown to increase optimization stability and predictive performance of ViTs [59], whereas we leverage them primarily for steering range images towards ViT-like inputs. + +The first part of the convolutional stem consists of the first 4 residual blocks of SalsaNext [11], called context module. This context module captures short-range dependencies of the 3D points projected in the range image and produces pixel-wise features with $D_{\mathrm{h}}$ channels at the same resolution of the input range image, hence the tensor of context features $\mathbf{t}_{\mathrm{c}}$ has size $D_{\mathrm{h}} \times H \times W$ . Then, in order to produce tokens compatible with the input of a ViT, we use an average pooling layer that reduces the spatial dimensions of the context features $\mathbf{t}_{\mathrm{c}}$ from $H \times W$ to $(H / P_{H}) \times (W / P_{W})$ , and use a final $1 \times 1$ convolutional layer with $D$ output channels. The convolutional stem thus yields $M = (HW) / (P_{H}P_{W})$ visual tokens $\mathbf{v}_1, \ldots, \mathbf{v}_M$ of dimension $D$ , i.e., matching the input dimension and number of tokens of a traditional ViT. + +![](images/f3ed7b63a2d18fd90a53982053b4d2f9c4724f5da59e27ee9c0167984e7f0a8c.jpg) +Figure 2. Overview of RangeViT architecture. First, the point cloud is projected in a 2D space with range projection. Then, the produced range image is processed by the convolutional stem, the ViT encoder and the decoder to obtain a 2D feature map. It is then processed by a 3D refiner layer for 3D point-wise predictions. Note that there is a single skip connection between the convolutional stem and the decoder. + +ViT encoder. The output of the convolutional stem can be fed directly to a ViT [14]. The input $\mathbf{t}_0$ to our ViT encoder is prepared by stacking all the visual tokens $\mathbf{v}_1, \ldots, \mathbf{v}_M$ and a classification token $\mathbf{v}_{\mathrm{class}} \in \mathbb{R}^D$ , to which we add the positional embeddings $\mathbf{E}_{\mathrm{pos}} \in \mathbb{R}^{(M + 1) \times D}$ : + +$$ +\mathbf {t} _ {0} = \left[ \mathbf {v} _ {\text {c l a s s}}, \mathbf {v} _ {1}, \dots , \mathbf {v} _ {M} \right] + \mathbf {E} _ {\text {p o s}}. \tag {2} +$$ + +The input tokens are then transformed by the ViT encoder to obtain an updated sequence of tokens $\mathbf{t}_L\in \mathbb{R}^{(M + 1)\times D}$ where $L$ denotes the number of transformer blocks. Then, we remove the classification token from $\mathbf{t}_L$ to keep only the deep patch representations $\mathbf{t}_L^{\prime}\in \mathbb{R}^{M\times D}$ . + +Decoder. The representations $\mathbf{t}_L^{\prime}$ provided by the ViT encoder are patch representations which are unfortunately too coarse to obtain good point predictions. Therefore, we use a decoder to refine these coarse patch representations. First, $\mathbf{t}_L^{\prime}$ is reshaped in form of a 2D feature map of size $D\times H / P_H\times W / P_W$ . Our convolutional decoder consists of a $1\times 1$ convolution layer with $D_{\mathrm{h}}P_{H}P_{W}$ output channels, followed by a Pixel Shuffle layer [44] which yields feature maps with shape $D_{\mathrm{h}}\times H\times W$ , i.e., with the same resolution as the original range image. While the convolutional decoder can still produce coarse features or decoding artifacts, the Pixel Shuffle is particularly effective in recovering fine information from features. Then, we concatenate these features with the context features $\mathbf{t}_{\mathrm{c}}$ from the convolutional stem and use a series of two convolutional layers with $3\times 3$ and $1\times 1$ kernels respectively, each of them followed by Leaky ReLU and batch normalisation, to obtain the refined feature map $\mathbf{t}_{\mathrm{dec}}\in \mathbb{R}^{D_{\mathrm{h}}\times H\times W}$ . + +3D refiner. Ultimately, we need to convert the pixel-wise features from the range image space into point-wise predictions in the 3D space. Most prior range-projection based methods first make pixel-wise class predictions and then unproject them to the 3D space, where at inference time often + +there is a post-processing step relying, e.g., on K-NN [36] or CRFs [27]. The purpose of the latter post-processing step is to fix segmentation mistakes related to the projection and processing of 3D points in a 2D space (e.g., multiple 3D points being projected on the same pixel, or 2D boundary prediction errors for points that are actually far away in the 3D space). Instead, we follow the approach of KPRNet [26] that proposes an end-to-end approach that learns this post-processing step with a KPConv [47] layer. + +KPConv [47] is a point convolution technique which works directly on the original 3D points. It permits to leverage the underlying geometry of the 3D point clouds to refine features at the point level. So, in our network, we project the 2D feature maps $\mathbf{t}_{\mathrm{dec}}$ of the 2D decoder back to original 3D points by bilinear upsampling, thus obtaining point-wise features with shape $N\times D_{\mathrm{h}}$ , where $N$ is the number of 3D points. Then, these point features are given to the KPConv layer as input along with the 3D coordinates of the corresponding points, which outputs $D_{\mathrm{h}}$ -dimensional point features. Finally, the logits $\mathbf{s}\in \mathbb{R}^{N\times K}$ are obtained by applying a BatchNorm, a ReLU and a final point-wise linear layer on these point features. + +# 3.2. Implementation details + +Training loss We use the sum of the multi-class focal loss [30] and the Lovász-softmax loss [4]. The focal loss is a scaled version of the cross-entropy loss [19] adapting its penalty to the hardness of the samples, making it suited for datasets with class imbalance, such as semantic segmentation. The Lovász-softmax is developed specifically for semantic segmentation and built to optimize the mIoU. + +Inference As in [45], we use a sliding-window method during inference. The network actually never sees the entire range images during training but only crops extracted from it. At inference, the range image is divided into overlapping crops of the same size as those used during training. The corresponding 2D features at the output of the decoder are + +
StemDecoderRefinermIoU (%)#Params
LinearLinear65.5222.0M
ConvLinear69.8222.8M
ConvUpConv73.8324.6M
ConvUpConv✓74.6025.2M
+ +Table 1. Model ablations. Results on the nuScenes validation set with $D_{\mathrm{h}} = 192$ . The linear stem refers to the linear patch embedding layer. When the 3D refiner layer (Refiner column) is not used, we use the K-NN post-processing technique [36]. + +then averaged to reconstruct the entire feature map, which is then processed by our 3D refinement layer. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and metrics. We validate our approach for 3D point cloud semantic segmentation on two different commonly used datasets: nuScenes [7] and SemanticKITTI [3]. We conduct most of our ablation studies on nuScenes and compare against previous works on both nuScenes and SemanticKITTI. As evaluation metric, we use the mean Intersection over Union (mIoU) [16]. + +NuScenes [7] consists of 1,000 scenes of 20 seconds in Boston and Singapore with various urban scenarios, lighting and weather conditions. The LiDAR sensor has 32 laser beams. Furthermore, there are 16 annotated semantic classes and the dataset is split into 28,130 training and 6,019 validation point cloud scans. + +SemanticKITTI [3] is created from the KITTI Vision Odometry Benchmark [17] and consists of urban scenes collected in Germany. Sequences 00-10 are used for training, except sequence 08 which is used for validation. There are 19,130 training and 4,071 validation scans. Sequences 11-21 are used for test and they contain 20,351 scans. The LiDAR sensor has 64 laser beams and there are 19 annotated semantic classes. + +Model and pre-trained weights. For all experiments, we use the ViT-S/16 model [14] as the encoder. It has $L = 12$ layers, 6 attention heads and $D = 384$ channels, amounting to approximately 21M parameters. Unless otherwise stated, (a) this ViT encoder is initialized with weights pre-trained on ImageNet21k [12] for classification and then fine-tuned on Cityscapes [10] for semantic image segmentation [45]; (b) the stem, decoder and 3D refiner layers, which are always randomly initialized, use $D_{\mathrm{h}} = 256$ feature channels. + +Optimization. We use the AdamW optimizer [34] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ and weight decay 0.01. The batch-size is 32 and 16 for nuScenes and SemanticKITTI, respectively. For the learning rate $lr$ , we use a linear warm-up from 0 to its peak value for 10 epochs and then we decrease it over the remaining training epochs to 0 with a cosine annealing schedule [33]. In SemanticKITTI, we use 60 train- + +
Dh size64128192256
#Params22.7M23.7M25.2M27.1M
nuScenes mIoU (%)74.0074.1274.6075.21
SemanticKITTI mIoU (%)58.4860.7360.4560.55
+ +Table 2. Impact of the channel size $D_{\mathrm{h}}$ used in the stem, decoder, and 3D refiner layers. Results on the nuScenes and the SemanticKITTI validation sets. + +ing epochs and the peak $lr$ is $4 \times 10^{-4}$ . In nuScenes, we use 150 epochs and the peak $lr$ is $8 \times 10^{-4}$ when training from Cityscapes, ImageNet21k and random initializations, and $2 \times 10^{-4}$ when training from DINO initialization. + +Data augmentations. As point cloud augmentations we use: (a) flips over the $y$ axis (the vertical axis on the range image), (b) random translations, and (c) random rotations between $\pm 5^{\circ}$ (using the roll, pitch and yaw angles). All augmentations are applied randomly with probability 0.5. Finally, after range projection, we take a random image crop with a fixed size of $32 \times 384$ for nuScenes and $64 \times 384$ for SemanticKITTI. Note that the full size of a range image is $32 \times 2048$ for nuScenes and $64 \times 2048$ for SemanticKITTI. + +# 4.2. What makes a ViT architecture for 3D semantic segmentation? + +Our aim is to adapt to LiDAR point clouds with the fewest possible modifications of the standard ViT architecture [14], which already follows faithfully the original self-attention Transformer design [51]. Differently from ViT that performs classification on images, RangeViT performs semantic segmentation of point cloud-derived range images. We study here the possible choices for the input processing and decoder layers using the nuScenes dataset. + +Stem and decoder. In Tab. 1, we study the impact of the convolutional stem and the UpConv decoder. To that end, we report results using a linear patch embedding [14] as a stem and a linear decoder. Starting from a model with linear stem and linear decoder, introducing the proposed convolutional stem leads to a significant mIoU boost $(65.52\rightarrow 69.82)$ . This highlights the importance of having a non-linear network component for producing appropriate input token features for the ViT backbone. In addition, when using image pre-trained ViTs (Sec. 4.3) the convolutional stem can effectively steer the distribution of input range images towards the image-based feature distribution the ViT has been pre-trained on, leading to smoother fine-tuning. Then, also replacing the linear decoder with the proposed UpConv decoder leads to another notable improvement on mIoU $(69.8\rightarrow 73.83)$ , validating this design choice. Finally, replacing the K-NN refinement [36] with + +
Patch size16 × 168 × 84 × 164 × 84 × 42 × 162 × 8
mIoU (%)68.4572.0472.7273.3073.7073.8875.21
Tokens49193193385769385769
Train time×1×1.02×1.02×1.13×1.43×1.13×1.43
+ +Table 3. Patch size ablations. Results on the nuScenes validation set. The mIoU scores are in increasing order. The train time is relative to the $16 \times 16$ patch size case. + +the KPCov layer (in the 3D refiner layer), leads to a small but non-trivial mIoU increase $(73.83\rightarrow 74.60)$ + +In Tab. 2, we study what is the impact, on the mIoU, of changing the number of feature channels $D_{\mathrm{h}}$ on the stem, decoder and 3D refiner layer. On nuScenes, we observe that the results gradually increase when increasing the dimension $D_{\mathrm{h}}$ . In the SemanticKITTI case, $D_{\mathrm{h}} = 128$ gives the best results and further increasing $D_{\mathrm{h}}$ does not help. Note that the size of the ViT's embeddings is fixed at $D = 384$ , regardless of the $D_{\mathrm{h}}$ size. + +What patch-size for range image "tokenization"? The size of the input patch tokens is an essential factor for controlling the trade-off between speed and accuracy performance without changing the number of parameters in the model. Intuitively, reducing the patch-size results in a finer representation, but also a longer input sequence that takes longer to process. Conversely, larger patches lead to a coarser representation, yet faster inference. The performance impact of the patch-size can sometimes match the one of model size [45]. For simplicity, standard ViT models use square patches of size 32, 16 or 8, as they are typically trained on square images. In contrast, range images have a much different aspect ratio (high width) and different layout of the content in the image (rows of points corresponding to LiDAR beams). With this insight, we revisit the practice of using square patches and look into rectangular patches with different aspect ratio (1:2, 1:4, 1:8) that would better capture the specific local patterns of the range images. + +Tab. 3 shows the mIoU scores for different patch sizes for dividing the range image to patch tokens. Note that the convolutional stem first produces pixel-wise features and then, given a patch-size $(P_{H}, P_{W})$ , reduces the spatial dimensions of these features to $(H / P_{H}, W / P_{W})$ using local average pooling. We observe that smaller patch area is better but not necessarily with a square patch, commonly used for ViT models. The wide range images benefit more from rectangular patches ( $2 \times 8$ performing best). The smaller patches enable the extraction of more fine-grained information leading to more precise predictions for smaller and thinner objects and points at object boundaries. + +# 4.3. Exploiting image pre-trained ViTs + +So far, we have studied the architectural choices necessary for using ViT models for point cloud semantic segmentation. The final RangeViT model preserves the ViT back + +
Pre-trainingRandDINOIN21kCS
mIoU (%)72.3773.3374.7775.21
+ +Table 4. ViT pre-training on RGB images. Comparison of different weight initializations of the ViT encoder on the nuScenes validation set. Rand: randomly initialized. The positional embeddings are initialized with the corresponding pre-trained weights or randomly when training from scratch. The convolutional stem, the decoder and the 3D refiner layer are randomly initialized. + +![](images/21d54f0f69d04676d212384aa4c7475d7334992dbc49cc5a6177b61daa146996.jpg) +Figure 3. Training efficiency with image-pretrained ViTs. Comparison of the validation mIoU curves for different weight initialisations of the ViT encoder on the nuScenes validation set. + +bone intact allowing us to initialize it with weights from models pre-trained on large datasets. We study now whether using such an initialization helps or not and what fine-tuning strategies would be more suitable in this context. + +Is pre-training on RGB images beneficial? In Tab. 4, we study the effect of transferring to our task ViT models pre-trained on natural RGB images. In particular, we explore initializing RangeViT's backbone with ViTs pretrained: (a) on supervised ImageNet21k classification [14] (entry IN21k), (b) on supervised image segmentation on Cityscapes with Segmenter [45] (entry CS), which in its turn was pre-trained with IN21k, and (c) with the DINO [9] self-supervised approach on ImageNet1k (entry DINO). + +We observe that, despite the large domain gap, using ViT models pre-trained on RGB images is always better than training from scratch on LiDAR data (entry Rand). For instance, using the IN21k and CS pretrained ViTs leads to improving the mIoU scores by 2.4 and 2.8 points respectively. Additionally, as we see in Fig. 3, which plots the nuScenes validation mIoU as a function of the training epochs, using such pre-trained ViTs leads to faster training convergence of the LiDAR segmentation model. We argue that this is a highly interesting finding. It means that our RangeViT approach, by being able to use off-the-shelf pre-trained ViT models, can directly benefit from current and future advances on the training ViT models with natural RGB images, a very active and rapidly growing re + +
ModelFine-tuningIN21k mIoU (%)CS (%)
LNATTNFFN
(a)✓✓✓74.7975.21
(b)67.8868.03
(c)✓69.0869.31
(d)✓✓73.5672.77
(e)✓✓75.1175.47
+ +Table 5. Partial ViT fine-tuning. We use a ViT encoder pretrained on ImageNet21k (IN21k) or Cityscapes (CS) and partially fine-tune RangeViT on the nuScenes training set. The convolutional stem, the positional embeddings and the UpConv decoder are always fine-tuned. LN: fine-tuning the LayerNorm layers of the ViT encoder. ATTN: fine-tuning the multi-head attention layers of the ViT encoder. FFN: fine-tuning the feed-forward network layers of the ViT encoder. Model (a) is full fine-tuning of the network. The results are reported on the nuScenes validation set. + +
EncoderViT-S†ViT-SRN50†RN50Identity
mIoU (%)67.8874.7760.4872.3053.73
+ +Table 6. Ablating encoder backbones. ViT-S and RN50 are pretrained on IN21k. †: the encoder remains frozen during training. + +search field [23, 41, 48, 49]. Furthermore, from the small difference between the mIoU scores with the IN21k and CS pre-trainings, we infer that the pre-training can lead to consistent performance improvements even if it is not on the strongly-supervised image segmentation task, which requires expensive-to-announce datasets. + +Which ViT layers is better to fine-tune? In the image domain, several practices have emerged for fine-tuning a pre-trained convolutional network on a downstream dataset. Taking into consideration the domain gap between the pretraining and downstream data and the amount of labeled data available, the entire network can be fine-tuned or only a part of it. Here the domain gap between RGB images and range images is major and we would expect a full fine-tuning of the network to be better. To understand how much prior knowledge of the image pre-trained ViT is useful for point clouds, we study different fine-tuning strategies: fine-tuning all layers, only the attention (ATTN) layers or only the feedforward network (FFN) layers. + +In Tab. 5, we show results with these different fine-tuning strategies. Interestingly, the best results are not achieved with full fine-tuning (model (a)) but when the attention layers are kept frozen (model (e)). This suggests that the pretrained ATTN layers are already well learnt and ready to generalize to range images. With CS pre-training ATTN layers may capture the layout of the scenes more easily without much fine-tuning, as the LiDAR scans have been also acquired from urban road scenes. Fine-tuning FFN may have more impact due to the different specifics of the LiDAR data compared to RGB images. In addition, FFN layers are in practice easier and more stable to optimize + +![](images/3f4bfeec95ddebeea5829bd608e032d1eea1a9cb706f8ca2196db50652e4ebb6.jpg) + +![](images/4e47f997373b436e55588c460ef2f0a9b5c73937ad2262b8fe93f658df1dc358.jpg) + +![](images/2ee2ec0996ec4bef98540715cc64f2244fcbfdcd264d2850d55f4fe5a2396a42.jpg) + +![](images/a29d83b88d26ebbc6b1144144ae545feabb437abb83e345504a8d5b656f6a8b1.jpg) + +![](images/bc874d517e74daf814b62fc76531ad8220fcf0e48cde744b519b9bcdb10c9ae7.jpg) +Figure 4. Visualizing the segmentation accuracy. Left: ground truth segmentation of validation point clouds of nuScenes, coloured based on their label. Right: segmentation accuracy of RangeViT - good predictions are in blue and the bad ones in red. + +![](images/6e41c718e61e6e33f5d3265459323d2081142b8aa72a5416bc668503cebdc353.jpg) + +(they are essentially fully-connected and normalization layers) than ATTN layers that usually require more careful hyper-parameter selection. These findings align with recent ones from the image domain [48], confirming that the convolutional stems do steer the input LiDAR data to behave like image data once on in the ViT backbone. + +Ablating encoder backbones. In Tab. 6, we replace the ViT-S encoder backbone of RangeViT with a ResNet-50 (RN50) encoder or the identity function (i.e., the decoder follows directly the stem). Both ViT-S and RN50 are pretrained on IN21k. We see that switching from ViT-S to RN50 decreases the mIoU from $74.77\%$ to $72.30\%$ . Furthermore, when the backbones remain frozen $(\mathrm{ViT - S}^{\dagger}$ and $\mathrm{RN50\dagger}$ models), we reach $67.88\%$ with ViT-S and $60.48\%$ with RN50, demonstrating that ViT features are more appropriate for transfer learning to LiDAR data than CNNs. Finally, with the Identity backbone, we achieve $53.73\%$ , which is more than 14 points worse than the $\mathrm{ViT - S}^{\dagger}$ model that has the same number of learnable parameters. + +# 4.4. Comparison to the state of the art + +Tab. 7 and 8 report the final comparison on the nuScenes validation set and on the SemanticKITTI test set including class-wise IoU scores. We observe that our model achieves superior mIoU performance compared to prior 2D-projection based methods on both datasets, reducing the gap with the strong voxel-based Cylinder3D [69] method. + +
Methodbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdriveableother flatsidewalkterrainmammadevegetationmIoU (%)
Voxel-based Cylinder3D [69]76.440.391.393.851.378.078.964.962.184.496.871.676.475.490.587.476.1
2D Projection-based
RangeNet++ [36]66.021.377.280.930.266.869.652.154.272.394.166.663.570.183.179.865.5
PolarNet [66]74.728.285.390.935.177.571.358.857.476.196.571.174.774.087.385.771.0
SalsaNext [11]74.834.185.988.442.272.472.263.161.376.596.070.871.271.586.784.472.2
RangeViT-IN21k (ours)75.139.090.288.448.079.277.266.465.176.796.371.173.773.988.987.174.8
RangeViT-CS (ours)75.540.788.390.149.379.377.266.365.280.096.471.473.873.889.987.275.2
+ +Table 7. nuScenes validation set comparison with state-of-the-art methods. The best results are bold and the second best results are blue. + +
Methodcarbicyclemotorcycletruckother vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother groundbuildingfencevegetationtrunkterrainpoletraffic signmIoU (%)
Voxel-based Cylinder3D [69]97.167.664.059.058.673.967.936.091.465.175.532.391.066.585.471.868.562.665.667.8
2D Projection-based
RangeNet++ [36]91.425.734.425.723.038.338.84.891.865.075.227.887.458.680.555.164.647.955.952.2
PolarNet [66]93.840.330.122.928.543.240.25.690.861.774.421.790.061.384.065.567.851.857.554.3
SqueezeSegV3 [60]92.538.736.529.633.045.646.220.191.763.474.826.489.059.482.058.765.449.658.955.9
SalsaNext [11]91.948.338.638.931.960.259.019.491.763.775.829.190.264.281.863.666.554.362.159.5
KPRNet [26]95.554.147.923.642.665.965.016.593.273.980.630.291.768.485.769.871.258.764.163.1
Lite-HDSeg [42]92.340.055.437.739.659.271.654.193.068.278.329.391.565.078.265.865.159.567.763.8
RangeViT-CS (ours)95.455.843.529.842.163.958.238.193.170.280.032.592.069.085.370.671.260.864.764.0
+ +Table 8. SemanticKITTI test set comparison with state-of-the-art methods. The best results are bold and the second best results are blue. + +Class-wise IoU result analysis. In Tab. 7 and 8, we can see that RangeViT often achieves the best or the second best class-wise IoU scores. In both datasets, the classes are imbalanced and due to the sparsity and varying density of Li-DAR point clouds, some classes (e.g., bicycle, pedestrian) are represented with few, not necessarily structured points per scene, so it is difficult to recognize them. This problem could possibly be reduced by jointly processing point clouds and RGB images, since RGB images might provide extra cues about the outline and the shape of these objects. + +# 4.5. Qualitative Results + +We visualize the 3D point clouds with the ground truth semantic labels as well as the predictions with CloudCompare [18]. Fig. 4 shows the predictions of RangeViT on three validation point clouds of nuScenes. We notice minor errors such as man-made objects predicted as sidewalk and imperfect borders for the vegetation. We also remark difficulties in recognizing pedestrians and confusion between the driveable surface and the sidewalk for few points. + +# 5. Conclusion + +We studied the feasibility of leveraging (pre-trained) ViTs for LiDAR 3D semantic segmentation with projection-based methods. We discover that in spite of the significant domain gap between RGB images and range images and + +their high requirements of training data, ViTs can be successfully used without any changes in the original transformer backbone. We achieve this thanks to an adapted tokenization and pre-processing for the ViT encoder and a simple convolutional decoder. We show that ViTs pre-trained on large image datasets can be effectively repurposed for LiDAR segmentation towards reaching state-of-the-art performance among 2D projection methods. We release the code for our implementation and hope that it could be used as a testbed for evaluating the ability of ViT image "foundation" models [6] to generalize on different domains. + +Future work. Although the results are promising, there is still room for improvement. For instance, we identified the tokenization of LiDAR data as a crucial factor for success. As future work, we could further improve this process, e.g., with FlexiViT [5] (random patch sizes) or Perceiver IO [25] (learning to extract tokens), and consider tokenizing raw 3D data instead of the 2D projections. + +Acknowledgements. We would like to express our gratitude to Matthieu Cord and Hugo Touvron for their insightful comments, Robin Strudel et al. [45] for kindly providing ViT-S pre-trained on Cityscapes, and Oriane Simeoni for her valuable contribution to certain experiments. This work was performed using HPC resources from GENCI-IDRIS (Grants 2022-AD011012884R1, 2022-AD011013413 and 2022-AD011013701). 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Early convolutions help transformers see better. In NeurIPS, 2021. 3 +[60] Chenfeng Xu, Bichen Wu, Zining Wang, Wei Zhan, Peter Vajda, Kurt Keutzer, and Masayoshi Tomizuka. SqueezeSegV3: Spatially-adaptive convolution for efficient pointcloud segmentation. In ECCV, 2020. 1, 2, 8 +[61] Chenfeng Xu, Shijia Yang, Bohan Zhai, Bichen Wu, Xiangyu Yue, Wei Zhan, Peter Vajda, Kurt Keutzer, and Masayoshi Tomizuka. Image2Point: 3D point-cloud understanding with pretrained 2D convnets. In arXiv, 2021. 3 +[62] Xu Yan, Chaoda Zheng, Zhen Li, Sheng Wang, and Shuguang Cui. PointASNL: Robust point clouds processing using nonlocal neural networks with adaptive sampling. In CVPR, 2020. 2 +[63] Xumin Yu, Lulu Tang, Yongming Rao, Tiejun Huang, Jie Zhou, and Jiwen Lu. Point-BERT: Pre-training 3D point cloud transformers with masked point modeling. In CVPR, 2022. 2, 3 +[64] Feihu Zhang, Jin Fang, Benjamin Wah, and Philip Torr. Deep FusionNet for point cloud semantic segmentation. In ECCV, 2020. 2 +[65] Yanan Zhang, Jiaxin Chen, and Di Huang. CAT-Det: Contrastively augmented transformer for multi-modal 3D object detection. In CVPR, 2022. 2 + +[66] Yang Zhang, Zixiang Zhou, Philip David, Xiangyu Yue, Zerong Xi, Boqing Gong, and Hassan Foroosh. PolarNet: An improved grid representation for online LiDAR point clouds semantic segmentation. In CVPR, 2020. 1, 2, 8 +[67] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip HS Torr, and Vladlen Koltun. Point Transformer. In ICCV, 2021. 2, 3 +[68] Junsheng Zhou, Xin Wen, Yu-Shen Liu, Yi Fang, and Zhizhong Han. Self-supervised point cloud representation learning with occlusion auto-encoder. In arXiv, 2022. 2 + +[69] Xinge Zhu, Hui Zhou, Tai Wang, Fangzhou Hong, Wei Li, Yuexin Ma, Hongsheng Li, Ruigang Yang, and Dahua Lin. Cylindrical and asymmetrical 3D convolution networks for LiDAR-based perception. In CVPR, 2021. 2, 7, 8 +[70] Zhuangwei Zhuang, Rong Li, Kui Jia, Qicheng Wang, Yuanqing Li, and Mingkui Tan. Perception-aware multi-sensor fusion for 3D LiDAR semantic segmentation. 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Gustave Eiffel, CNRS, Marne-la-Vallee, France" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 261, + 290, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 290, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 290, + 632 + ], + "type": "text", + "content": "Casting semantic segmentation of outdoor LiDAR point clouds as a 2D problem, e.g., via range projection, is an effective and popular approach. These projection-based methods usually benefit from fast computations and, when combined with techniques which use other point cloud representations, achieve state-of-the-art results. Today, projection-based methods leverage 2D CNNs but recent advances in computer vision show that vision transformers (ViTs) have achieved state-of-the-art results in many image-based benchmarks. In this work, we question if projection-based methods for 3D semantic segmentation can benefit from these latest improvements on ViTs. We answer positively but only after combining them with three key ingredients: (a) ViTs are notoriously hard to train and require a lot of training data to learn powerful representations. By preserving the same backbone architecture as for RGB images, we can exploit the knowledge from long training on large image collections that are much cheaper to acquire and annotate than point clouds. We reach our best results with pre-trained ViTs on large image datasets. (b) We compensate ViTs' lack of inductive bias by substituting a tailored convolutional stem for the classical linear embedding layer. (c) We refine pixel-wise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grained features of the convolutional stem with the high-level but coarse predictions of the ViT encoder. With these ingredients, we show that our method, called RangeViT, outperforms existing projection-based methods on nuScenes and SemanticKITTI. The code is available at https://github.com/valeoai/rangevit." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "content": "Semantic segmentation of LiDAR point clouds permits vehicles to perceive their surrounding 3D environment in" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 242, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 308, + 242, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 308, + 242, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 308, + 242, + 545, + 406 + ], + "type": "image", + "image_path": "a241e668366c1a33e1da31893471b878938707211cee6c192bc32670ee4a57f9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 412, + 547, + 502 + ], + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 502 + ], + "type": "text", + "content": "Figure 1. Exploiting vision transformer (ViT) architectures and weights for LiDAR point cloud semantic segmentation. We leverage the flexibility of transformer-based architectures to re-purpose them with minimal changes for processing sparse point clouds in autonomous driving tasks. The common ViT backbone across modalities allows to effectively transfer weights pre-trained on large image repositories towards improving point cloud segmentation performance with fine-tuning." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "dependently of the lighting condition, providing useful information to build safe and reliable vehicles. A common approach to segment large scale LiDAR point clouds is to project the points on a 2D surface and then to use regular CNNs, originally designed for images, to process the projected point clouds [1, 11, 26, 36, 60, 66]. Recently, Vision Transformers (ViTs) were introduced as an alternative to convolutional neural networks for processing images [14]: images are divided into patches which are linearly embedded into a high-dimensional space to create a sequence of visual tokens; these tokens are then consumed by a pure transformer architecture [51] to output deep visual representations of each token. Despite the absence of almost any domain-specific inductive bias apart from the image tokenization process, ViTs have a strong representation learning capacity [14] and achieve excellent results on various" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "type": "text", + "content": "*This project was done during an internship at Valeo.ai." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5240" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "image perception tasks, such as image classification [14], object detection [8] or semantic segmentation [45]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 98, + 289, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 98, + 289, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 98, + 289, + 302 + ], + "type": "text", + "content": "Inspired by this success of ViTs for image understanding, we propose to implement projection-based LiDAR semantic segmentation with a pure vision transformer architecture at its core. Our goals are threefold in doing so: (1) Exploit the strong representation learning capacity of vision transformer for LiDAR semantic segmentation; (2) Work towards unifying network architectures used for processing LiDAR point clouds or images so that any advance in one domain benefits to both; (3) Show that one can leverage ViTs pre-trained on large-size natural image datasets for LiDAR point cloud segmentation. The last goal is crucial because the downside of having few inductive biases in ViTs is that they underperform when trained from scratch on small or medium-size datasets and that, for now, the only well-performing pre-trained ViTs [9, 14, 45] publicly available are trained on large collections of images that can be acquired, annotated and stored easier than point clouds." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 303, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 289, + 506 + ], + "type": "text", + "content": "In this context, our main contribution is a ViT-based Li-DAR segmentation approach that compensates ViTs' lack of inductive biases on our data and that achieves state-of-the-art results among projection-based methods. To the best of our knowledge, although works using ViT architectures on dense indoor point clouds already exist [63, 67], this is the first solution using ViTs for the LiDAR point clouds of autonomous driving datasets, which are significantly sparser and noisier than the dense depth-map-based points clouds found in indoor datasets. Our solution, RangeViT, starts with a classical range projection to obtain a 2D representation of the point cloud [11, 26, 36, 60]. Then, we extract patch-based visual tokens from this 2D map and feed them to a plain ViT encoder [14] to get deep patch representations. These representations are decoded using a lightweight network to obtain pixel-wise label predictions, which are projected back to the 3D point cloud." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 508, + 289, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 289, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 289, + 664 + ], + "type": "text", + "content": "Our finding is that this ViT architecture needs three key ingredients to reach its peak performance. First, we leverage ViT models pre-trained on large natural image datasets for LiDAR segmentation and demonstrate that our method benefits from them despite the fact that natural images display little resemblance with range-projection images. Second, we further compensate for ViTs' lack of inductive bias by substituting the classical linear embedding layer with a multi-layer convolutional stem. Finally, we refine pixelwise predictions with a convolutional decoder and a skip connection from the convolutional stem to combine low-level but fine-grain features of the convolutional stem with the high-level but coarse predictions of the ViT encoder." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": "In summary, our contributions are the following: (1) To the best of our knowledge, we are the first to exploit the strong representation learning capacity of vision transformers architectures for 3D semantic segmentation from" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "LiDAR point clouds. By revisiting, in the context of our problem, the tokenization process of the ViT's encoder and adding a light-weight convolutional decoder for refining the coarse patch-wise ViT representations, we derive a simple but effective projection-based LiDAR segmentation approach, which we call RangeViT. (2) Furthermore, as shown in Fig. 1, the proposed approach allows one to harness ViT models pre-trained on the RGB image domain for the LiDAR segmentation problem. Indeed, despite the large gap between the two domains, we empirically demonstrate that using such pre-training strategies improves segmentation performance. (3) Finally, our RangeViT approach, despite its simplicity, achieves state-of-the-art results among project-based segmentation methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 250, + 391, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 250, + 391, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 250, + 391, + 262 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 269, + 499, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 269, + 499, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 269, + 499, + 283 + ], + "type": "text", + "content": "2.1. CNNs for Point Cloud Segmentation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 290, + 547, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 547, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 547, + 459 + ], + "type": "text", + "content": "2D Methods Several works [3,11,24,26,28,36,42,47,50, 60,64,66,70] project the 3D point cloud into the 2D space with range, perspective or bird's-eye-view (BEV) projection and process the projected images with 2D CNNs. For instance, PolarNet [66] employs bird's-eye-view projection to polar coordinates and then processes the bird-eye-view features with a Ring CNN. DarkNetSeg [3], SalsaNext [11], KPRNet [26], RangeNet++ [36], Lite-HDSeg [42] and SqueezeSegV3 [60] use range projection and then process the input images with a U-Net-like architecture. PMF [70], a multi-modal segmentation approach for point clouds and RGB images [2,29,53,65,70], projects the 3D points onto 2D camera frames and processes them together with the RGB images using a dual-stream CNN network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 460, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 568 + ], + "type": "text", + "content": "3D Methods Instead of the 2D space, voxel-based approaches [20,22,35,46] process the point clouds in their 3D space by first dividing the 3D space into voxels using cartesian coordinates and then applying 3D convolutions. Cylinder3D [69] show that dividing the 3D space into voxels using cylindrical coordinates instead of cartesian improves the segmentation performance. Although voxel-based methods consider the geometric properties of the 3D space, their drawback is that they are computationally expensive." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 569, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 653 + ], + "type": "text", + "content": "Also, for indoor-scene point cloud segmentation there are many methods [15, 37, 47, 52, 54, 56, 58, 62] relying on PointNet-inspired architectures [38] that directly process raw 3D points. However, these approaches cannot be easily adapted to outdoor-scene point cloud segmentation, which we consider in this work, as the large quantity of points cause computational difficulties." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 659, + 494, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 494, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 494, + 672 + ], + "type": "text", + "content": "2.2. ViTs for Point Cloud Segmentation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "The recent rise to prominence of ViT architectures in computer vision has inspired a series of works for indoor point cloud segmentation [31, 57, 63, 67, 68]." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "5241" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "Processing point clouds with a ViT model can be challenging and computationally expensive due to the large number of points. Point-BERT [63] uses farthest point sampling [39] and the K-NN algorithm to define input tokens for the transformer. Also, it proposes a self-supervised pretraining strategy for point data inspired by the masked token modeling approaches in the RGB image [23] and text [13] domains. Point Transformer [67] has a U-Net-like architecture but without convolutional layers and it integrates self-attention mechanism in all of its blocks. Finally, Bridged Transformer [57] jointly processes point clouds and RGB images with a fully transformer-based architecture." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 288, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 276 + ], + "type": "text", + "content": "Using a transformer-based architecture for the semantic segmentation task on outdoor LiDAR point clouds remains challenging. To the best of our knowledge, there has been no work published yet about outdoor LiDAR point cloud semantic segmentation with a ViT-based architecture." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 281, + 287, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 295 + ], + "type": "text", + "content": "2.3. Transfer Learning from Images to Point Clouds" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 287, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 372 + ], + "type": "text", + "content": "ViT models have the capacity to learn powerful representations, but require vast amounts of training data for it. However, large LiDAR point cloud datasets are less common due to the costly and time consuming annotation procedure. Recent works [21,32,40,43,55,61] explore transfer learning of 2D image pre-trained models to 3D point clouds." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 372, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 289, + 601 + ], + "type": "text", + "content": "Image2Point [61] converts a 2D CNN into a 3D sparse CNN [61] by inflating 2D convolutions into 3D convolutions, which is done by repeating the 2D kernel along the third dimension. SLidR [43] is a self-supervised pretraining method on LiDAR data. It uses a student-teacher architecture, where the 2D teacher network pre-trained on images transfers information into the 3D student network. Pix4Point [40] and Simple3D-Former [55] study transfer learning from images to indoor point clouds with fully transformer-based architectures. They adapt the tokenizer and the head layer to be specialized for 3D point cloud data. Pix4Point [40] applies farthest point sampling [39], the K-NN algorithm and then a graph convolution on the aggregated neighborhoods to extract input tokens for the ViT encoder. Simple3D-Former [55] memorizes the ImageNet [12] representation of 2D image classification by incorporating a KL divergence term in the loss between its 2D image classification predictions and those obtained from a fixed ImageNet [12] pre-trained ViT network." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 609, + 115, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 115, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 115, + 623 + ], + "type": "text", + "content": "3. RangeViT" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "type": "text", + "content": "In this section, we describe our ViT-based LiDAR semantic segmentation approach, for which we provide an overview in Fig. 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 167, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 167, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 167, + 682 + ], + "type": "text", + "content": "3.1. General architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "We represent a LiDAR point cloud of " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " points with a matrix " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{N \\times 4}" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": ". Each point " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "p = (x, y, z, i) \\in \\mathbf{P}" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " has" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "Cartesian coordinates denoted by " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and LiDAR intensity denoted by " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", and is annotated with a label " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\ell \\in \\{1,\\dots ,K\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " encoding one of the " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " semantic classes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "text", + "content": "Range projection. The input of our RangeViT backbone is a 2D representation of the input point cloud. We use the well-known range projection [36]. Each point " + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbf{P}" + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "text", + "content": " with coordinates " + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "inline_equation", + "content": "(x, y, z)" + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "text", + "content": " is projected on a range image of size " + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 305, + 127, + 545, + 187 + ], + "type": "text", + "content": ". The projected 2D coordinates satisfies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 196, + 545, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 196, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 196, + 545, + 224 + ], + "type": "interline_equation", + "content": "\\binom {h} {w} = \\left( \\begin{array}{c} \\frac {1}{2} (1 - \\arctan (y, x) \\pi^ {- 1}) W \\\\ (1 - (\\arcsin (z, r ^ {- 1}) + | f _ {\\text {d o w n}} |) f _ {v} ^ {- 1}) H \\end{array} \\right), \\tag {1}", + "image_path": "c2b8b82fd8416d2fd00cbc9e055df795c53d8439635b380f252fe4d7d0f64777.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "inline_equation", + "content": "f_{v} = |f_{\\mathrm{down}}| + |f_{\\mathrm{up}}|" + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": " is the vertical field-of-view of the LiDAR sensor. We associate " + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "inline_equation", + "content": "C = 5" + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": " low-level features " + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "inline_equation", + "content": "(r, x, y, z, i)" + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": " to each projected point, where " + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "inline_equation", + "content": "r = \\sqrt{x^2 + y^2 + z^2}" + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": " is the range of the corresponding point (i.e., its distance from the LiDAR sensor), to create the range image " + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{C \\times H \\times W}" + }, + { + "bbox": [ + 305, + 233, + 546, + 342 + ], + "type": "text", + "content": ". Note that if more than one point is projected onto the same pixel, then only the feature with the smallest range is kept. Pixels with no point projected on them have their features filled with zeros." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "text", + "content": "Convolutional stem. In a standard ViT, the image is divided into " + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "text", + "content": " patches of size " + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "inline_equation", + "content": "P_{H} \\times P_{W}" + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "text", + "content": ", which are linearly embedded to provide " + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 361, + 545, + 504 + ], + "type": "text", + "content": "-dimensional visual tokens. Yet, our empirical study in Sec. 4.2 shows that this tokenization process of standard ViTs is far from optimal on both our task and datasets of interest. In order to bridge this potential domain gap between range images and standard ViTs, we replace the embedding layer with a non-linear convolutional stem [59]. Non-linear convolutional stems have been shown to increase optimization stability and predictive performance of ViTs [59], whereas we leverage them primarily for steering range images towards ViT-like inputs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": "The first part of the convolutional stem consists of the first 4 residual blocks of SalsaNext [11], called context module. This context module captures short-range dependencies of the 3D points projected in the range image and produces pixel-wise features with " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " channels at the same resolution of the input range image, hence the tensor of context features " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{c}}" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " has size " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}} \\times H \\times W" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": ". Then, in order to produce tokens compatible with the input of a ViT, we use an average pooling layer that reduces the spatial dimensions of the context features " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{c}}" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "(H / P_{H}) \\times (W / P_{W})" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": ", and use a final " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " convolutional layer with " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " output channels. The convolutional stem thus yields " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "M = (HW) / (P_{H}P_{W})" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " visual tokens " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_1, \\ldots, \\mathbf{v}_M" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": " of dimension " + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 506, + 546, + 685 + ], + "type": "text", + "content": ", i.e., matching the input dimension and number of tokens of a traditional ViT." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "The first 3 residual layers actually have " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{in}} = 32" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " channels, which is typically smaller than " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5242" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 72, + 539, + 201 + ], + "blocks": [ + { + "bbox": [ + 60, + 72, + 539, + 201 + ], + "lines": [ + { + "bbox": [ + 60, + 72, + 539, + 201 + ], + "spans": [ + { + "bbox": [ + 60, + 72, + 539, + 201 + ], + "type": "image", + "image_path": "f3ed7b63a2d18fd90a53982053b4d2f9c4724f5da59e27ee9c0167984e7f0a8c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "type": "text", + "content": "Figure 2. Overview of RangeViT architecture. First, the point cloud is projected in a 2D space with range projection. Then, the produced range image is processed by the convolutional stem, the ViT encoder and the decoder to obtain a 2D feature map. It is then processed by a 3D refiner layer for 3D point-wise predictions. Note that there is a single skip connection between the convolutional stem and the decoder." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "content": "ViT encoder. The output of the convolutional stem can be fed directly to a ViT [14]. The input " + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_0" + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "content": " to our ViT encoder is prepared by stacking all the visual tokens " + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_1, \\ldots, \\mathbf{v}_M" + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "content": " and a classification token " + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{class}} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "content": ", to which we add the positional embeddings " + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathrm{pos}} \\in \\mathbb{R}^{(M + 1) \\times D}" + }, + { + "bbox": [ + 46, + 263, + 288, + 324 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 98, + 331, + 287, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 331, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 98, + 331, + 287, + 344 + ], + "type": "interline_equation", + "content": "\\mathbf {t} _ {0} = \\left[ \\mathbf {v} _ {\\text {c l a s s}}, \\mathbf {v} _ {1}, \\dots , \\mathbf {v} _ {M} \\right] + \\mathbf {E} _ {\\text {p o s}}. \\tag {2}", + "image_path": "be1f86b6f02e15133d477f9cdbeecfa101ff01693077875338d4180f2a8e34e7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "content": "The input tokens are then transformed by the ViT encoder to obtain an updated sequence of tokens " + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_L\\in \\mathbb{R}^{(M + 1)\\times D}" + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "content": " denotes the number of transformer blocks. Then, we remove the classification token from " + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_L" + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "content": " to keep only the deep patch representations " + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_L^{\\prime}\\in \\mathbb{R}^{M\\times D}" + }, + { + "bbox": [ + 46, + 350, + 287, + 411 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": "Decoder. The representations " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_L^{\\prime}" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " provided by the ViT encoder are patch representations which are unfortunately too coarse to obtain good point predictions. Therefore, we use a decoder to refine these coarse patch representations. First, " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_L^{\\prime}" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " is reshaped in form of a 2D feature map of size " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "D\\times H / P_H\\times W / P_W" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": ". Our convolutional decoder consists of a " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " convolution layer with " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}P_{H}P_{W}" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " output channels, followed by a Pixel Shuffle layer [44] which yields feature maps with shape " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}\\times H\\times W" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": ", i.e., with the same resolution as the original range image. While the convolutional decoder can still produce coarse features or decoding artifacts, the Pixel Shuffle is particularly effective in recovering fine information from features. Then, we concatenate these features with the context features " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{c}}" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " from the convolutional stem and use a series of two convolutional layers with " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": " kernels respectively, each of them followed by Leaky ReLU and batch normalisation, to obtain the refined feature map " + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{dec}}\\in \\mathbb{R}^{D_{\\mathrm{h}}\\times H\\times W}" + }, + { + "bbox": [ + 46, + 424, + 288, + 640 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "3D refiner. Ultimately, we need to convert the pixel-wise features from the range image space into point-wise predictions in the 3D space. Most prior range-projection based methods first make pixel-wise class predictions and then unproject them to the 3D space, where at inference time often" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 263, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 545, + 371 + ], + "type": "text", + "content": "there is a post-processing step relying, e.g., on K-NN [36] or CRFs [27]. The purpose of the latter post-processing step is to fix segmentation mistakes related to the projection and processing of 3D points in a 2D space (e.g., multiple 3D points being projected on the same pixel, or 2D boundary prediction errors for points that are actually far away in the 3D space). Instead, we follow the approach of KPRNet [26] that proposes an end-to-end approach that learns this post-processing step with a KPConv [47] layer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": "KPConv [47] is a point convolution technique which works directly on the original 3D points. It permits to leverage the underlying geometry of the 3D point clouds to refine features at the point level. So, in our network, we project the 2D feature maps " + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{dec}}" + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": " of the 2D decoder back to original 3D points by bilinear upsampling, thus obtaining point-wise features with shape " + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "inline_equation", + "content": "N\\times D_{\\mathrm{h}}" + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": " is the number of 3D points. Then, these point features are given to the KPConv layer as input along with the 3D coordinates of the corresponding points, which outputs " + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": "-dimensional point features. Finally, the logits " + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "inline_equation", + "content": "\\mathbf{s}\\in \\mathbb{R}^{N\\times K}" + }, + { + "bbox": [ + 304, + 371, + 546, + 528 + ], + "type": "text", + "content": " are obtained by applying a BatchNorm, a ReLU and a final point-wise linear layer on these point features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 534, + 437, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 437, + 546 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 437, + 546 + ], + "type": "text", + "content": "3.2. Implementation details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 555, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 639 + ], + "type": "text", + "content": "Training loss We use the sum of the multi-class focal loss [30] and the Lovász-softmax loss [4]. The focal loss is a scaled version of the cross-entropy loss [19] adapting its penalty to the hardness of the samples, making it suited for datasets with class imbalance, such as semantic segmentation. The Lovász-softmax is developed specifically for semantic segmentation and built to optimize the mIoU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": "Inference As in [45], we use a sliding-window method during inference. The network actually never sees the entire range images during training but only crops extracted from it. At inference, the range image is divided into overlapping crops of the same size as those used during training. The corresponding 2D features at the output of the decoder are" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5243" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 76, + 70, + 257, + 131 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 257, + 131 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 257, + 131 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 257, + 131 + ], + "type": "table", + "html": "
StemDecoderRefinermIoU (%)#Params
LinearLinear65.5222.0M
ConvLinear69.8222.8M
ConvUpConv73.8324.6M
ConvUpConv✓74.6025.2M
", + "image_path": "a007923cdc2f18e6a2305a8f5a7b12ac288b883c3ba0c508b5399f365bdc22aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 131, + 287, + 175 + ], + "lines": [ + { + "bbox": [ + 46, + 131, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 131, + 287, + 175 + ], + "type": "text", + "content": "Table 1. Model ablations. Results on the nuScenes validation set with " + }, + { + "bbox": [ + 46, + 131, + 287, + 175 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}} = 192" + }, + { + "bbox": [ + 46, + 131, + 287, + 175 + ], + "type": "text", + "content": ". The linear stem refers to the linear patch embedding layer. When the 3D refiner layer (Refiner column) is not used, we use the K-NN post-processing technique [36]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 189, + 287, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 189, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 287, + 213 + ], + "type": "text", + "content": "then averaged to reconstruct the entire feature map, which is then processed by our 3D refinement layer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 224, + 128, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 128, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 128, + 237 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 243, + 163, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 163, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 163, + 257 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "type": "text", + "content": "Datasets and metrics. We validate our approach for 3D point cloud semantic segmentation on two different commonly used datasets: nuScenes [7] and SemanticKITTI [3]. We conduct most of our ablation studies on nuScenes and compare against previous works on both nuScenes and SemanticKITTI. As evaluation metric, we use the mean Intersection over Union (mIoU) [16]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 348, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 419 + ], + "type": "text", + "content": "NuScenes [7] consists of 1,000 scenes of 20 seconds in Boston and Singapore with various urban scenarios, lighting and weather conditions. The LiDAR sensor has 32 laser beams. Furthermore, there are 16 annotated semantic classes and the dataset is split into 28,130 training and 6,019 validation point cloud scans." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 420, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 514 + ], + "type": "text", + "content": "SemanticKITTI [3] is created from the KITTI Vision Odometry Benchmark [17] and consists of urban scenes collected in Germany. Sequences 00-10 are used for training, except sequence 08 which is used for validation. There are 19,130 training and 4,071 validation scans. Sequences 11-21 are used for test and they contain 20,351 scans. The LiDAR sensor has 64 laser beams and there are 19 annotated semantic classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "text", + "content": "Model and pre-trained weights. For all experiments, we use the ViT-S/16 model [14] as the encoder. It has " + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "inline_equation", + "content": "L = 12" + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "text", + "content": " layers, 6 attention heads and " + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "inline_equation", + "content": "D = 384" + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "text", + "content": " channels, amounting to approximately 21M parameters. Unless otherwise stated, (a) this ViT encoder is initialized with weights pre-trained on ImageNet21k [12] for classification and then fine-tuned on Cityscapes [10] for semantic image segmentation [45]; (b) the stem, decoder and 3D refiner layers, which are always randomly initialized, use " + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}} = 256" + }, + { + "bbox": [ + 46, + 518, + 287, + 627 + ], + "type": "text", + "content": " feature channels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Optimization. We use the AdamW optimizer [34] with " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and weight decay 0.01. The batch-size is 32 and 16 for nuScenes and SemanticKITTI, respectively. For the learning rate " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", we use a linear warm-up from 0 to its peak value for 10 epochs and then we decrease it over the remaining training epochs to 0 with a cosine annealing schedule [33]. In SemanticKITTI, we use 60 train-" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 535, + 125 + ], + "blocks": [ + { + "bbox": [ + 316, + 70, + 535, + 125 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 535, + 125 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 535, + 125 + ], + "type": "table", + "html": "
Dh size64128192256
#Params22.7M23.7M25.2M27.1M
nuScenes mIoU (%)74.0074.1274.6075.21
SemanticKITTI mIoU (%)58.4860.7360.4560.55
", + "image_path": "59dd71ffbcc59e4a604b8b1f803d47c316b61c3644cd27ae46806dea91fce9a5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 126, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 305, + 126, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 126, + 545, + 159 + ], + "type": "text", + "content": "Table 2. Impact of the channel size " + }, + { + "bbox": [ + 305, + 126, + 545, + 159 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 305, + 126, + 545, + 159 + ], + "type": "text", + "content": " used in the stem, decoder, and 3D refiner layers. Results on the nuScenes and the SemanticKITTI validation sets." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": "ing epochs and the peak " + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "4 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": ". In nuScenes, we use 150 epochs and the peak " + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "8 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": " when training from Cityscapes, ImageNet21k and random initializations, and " + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 174, + 545, + 221 + ], + "type": "text", + "content": " when training from DINO initialization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": "Data augmentations. As point cloud augmentations we use: (a) flips over the " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " axis (the vertical axis on the range image), (b) random translations, and (c) random rotations between " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "\\pm 5^{\\circ}" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " (using the roll, pitch and yaw angles). All augmentations are applied randomly with probability 0.5. Finally, after range projection, we take a random image crop with a fixed size of " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "32 \\times 384" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " for nuScenes and " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "64 \\times 384" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " for SemanticKITTI. Note that the full size of a range image is " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "32 \\times 2048" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " for nuScenes and " + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "inline_equation", + "content": "64 \\times 2048" + }, + { + "bbox": [ + 304, + 225, + 545, + 333 + ], + "type": "text", + "content": " for SemanticKITTI." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 342, + 545, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 366 + ], + "type": "text", + "content": "4.2. What makes a ViT architecture for 3D semantic segmentation?" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "text", + "content": "Our aim is to adapt to LiDAR point clouds with the fewest possible modifications of the standard ViT architecture [14], which already follows faithfully the original self-attention Transformer design [51]. Differently from ViT that performs classification on images, RangeViT performs semantic segmentation of point cloud-derived range images. We study here the possible choices for the input processing and decoder layers using the nuScenes dataset." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "content": "Stem and decoder. In Tab. 1, we study the impact of the convolutional stem and the UpConv decoder. To that end, we report results using a linear patch embedding [14] as a stem and a linear decoder. Starting from a model with linear stem and linear decoder, introducing the proposed convolutional stem leads to a significant mIoU boost " + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "inline_equation", + "content": "(65.52\\rightarrow 69.82)" + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "content": ". This highlights the importance of having a non-linear network component for producing appropriate input token features for the ViT backbone. In addition, when using image pre-trained ViTs (Sec. 4.3) the convolutional stem can effectively steer the distribution of input range images towards the image-based feature distribution the ViT has been pre-trained on, leading to smoother fine-tuning. Then, also replacing the linear decoder with the proposed UpConv decoder leads to another notable improvement on mIoU " + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "inline_equation", + "content": "(69.8\\rightarrow 73.83)" + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "content": ", validating this design choice. Finally, replacing the K-NN refinement [36] with" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "2The linear decoder consists of a simple " + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": " conv. layer, which predicts patch-wise classification scores, and a bilinear upsampling to reach the input image resolution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5244" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 286, + 121 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "type": "table", + "html": "
Patch size16 × 168 × 84 × 164 × 84 × 42 × 162 × 8
mIoU (%)68.4572.0472.7273.3073.7073.8875.21
Tokens49193193385769385769
Train time×1×1.02×1.02×1.13×1.43×1.13×1.43
", + "image_path": "41b12a6e43487944d2e015a309181131a97632a72c4581eb00483222c6c486fe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 122, + 287, + 156 + ], + "lines": [ + { + "bbox": [ + 47, + 122, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 287, + 156 + ], + "type": "text", + "content": "Table 3. Patch size ablations. Results on the nuScenes validation set. The mIoU scores are in increasing order. The train time is relative to the " + }, + { + "bbox": [ + 47, + 122, + 287, + 156 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 47, + 122, + 287, + 156 + ], + "type": "text", + "content": " patch size case." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 287, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 287, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 287, + 193 + ], + "type": "text", + "content": "the KPCov layer (in the 3D refiner layer), leads to a small but non-trivial mIoU increase " + }, + { + "bbox": [ + 46, + 169, + 287, + 193 + ], + "type": "inline_equation", + "content": "(73.83\\rightarrow 74.60)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": "In Tab. 2, we study what is the impact, on the mIoU, of changing the number of feature channels " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": " on the stem, decoder and 3D refiner layer. On nuScenes, we observe that the results gradually increase when increasing the dimension " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": ". In the SemanticKITTI case, " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}} = 128" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": " gives the best results and further increasing " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": " does not help. Note that the size of the ViT's embeddings is fixed at " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D = 384" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": ", regardless of the " + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{h}}" + }, + { + "bbox": [ + 46, + 194, + 287, + 289 + ], + "type": "text", + "content": " size." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 292, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 507 + ], + "type": "text", + "content": "What patch-size for range image \"tokenization\"? The size of the input patch tokens is an essential factor for controlling the trade-off between speed and accuracy performance without changing the number of parameters in the model. Intuitively, reducing the patch-size results in a finer representation, but also a longer input sequence that takes longer to process. Conversely, larger patches lead to a coarser representation, yet faster inference. The performance impact of the patch-size can sometimes match the one of model size [45]. For simplicity, standard ViT models use square patches of size 32, 16 or 8, as they are typically trained on square images. In contrast, range images have a much different aspect ratio (high width) and different layout of the content in the image (rows of points corresponding to LiDAR beams). With this insight, we revisit the practice of using square patches and look into rectangular patches with different aspect ratio (1:2, 1:4, 1:8) that would better capture the specific local patterns of the range images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "text", + "content": "Tab. 3 shows the mIoU scores for different patch sizes for dividing the range image to patch tokens. Note that the convolutional stem first produces pixel-wise features and then, given a patch-size " + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "inline_equation", + "content": "(P_{H}, P_{W})" + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "text", + "content": ", reduces the spatial dimensions of these features to " + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "inline_equation", + "content": "(H / P_{H}, W / P_{W})" + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "text", + "content": " using local average pooling. We observe that smaller patch area is better but not necessarily with a square patch, commonly used for ViT models. The wide range images benefit more from rectangular patches (" + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "inline_equation", + "content": "2 \\times 8" + }, + { + "bbox": [ + 46, + 508, + 288, + 651 + ], + "type": "text", + "content": " performing best). The smaller patches enable the extraction of more fine-grained information leading to more precise predictions for smaller and thinner objects and points at object boundaries." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 231, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 231, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 231, + 672 + ], + "type": "text", + "content": "4.3. Exploiting image pre-trained ViTs" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "So far, we have studied the architectural choices necessary for using ViT models for point cloud semantic segmentation. The final RangeViT model preserves the ViT back" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 345, + 71, + 505, + 101 + ], + "blocks": [ + { + "bbox": [ + 345, + 71, + 505, + 101 + ], + "lines": [ + { + "bbox": [ + 345, + 71, + 505, + 101 + ], + "spans": [ + { + "bbox": [ + 345, + 71, + 505, + 101 + ], + "type": "table", + "html": "
Pre-trainingRandDINOIN21kCS
mIoU (%)72.3773.3374.7775.21
", + "image_path": "ecf98f4225e2577772b50605c51a1187a83030e8cd158169c3a04f33a710cba3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 102, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 305, + 102, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 305, + 102, + 545, + 169 + ], + "type": "text", + "content": "Table 4. ViT pre-training on RGB images. Comparison of different weight initializations of the ViT encoder on the nuScenes validation set. Rand: randomly initialized. The positional embeddings are initialized with the corresponding pre-trained weights or randomly when training from scratch. The convolutional stem, the decoder and the 3D refiner layer are randomly initialized." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 314, + 184, + 523, + 332 + ], + "blocks": [ + { + "bbox": [ + 314, + 184, + 523, + 332 + ], + "lines": [ + { + "bbox": [ + 314, + 184, + 523, + 332 + ], + "spans": [ + { + "bbox": [ + 314, + 184, + 523, + 332 + ], + "type": "image", + "image_path": "21d54f0f69d04676d212384aa4c7475d7334992dbc49cc5a6177b61daa146996.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 335, + 545, + 368 + ], + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 368 + ], + "type": "text", + "content": "Figure 3. Training efficiency with image-pretrained ViTs. Comparison of the validation mIoU curves for different weight initialisations of the ViT encoder on the nuScenes validation set." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 383, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 431 + ], + "type": "text", + "content": "bone intact allowing us to initialize it with weights from models pre-trained on large datasets. We study now whether using such an initialization helps or not and what fine-tuning strategies would be more suitable in this context." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": "Is pre-training on RGB images beneficial? In Tab. 4, we study the effect of transferring to our task ViT models pre-trained on natural RGB images. In particular, we explore initializing RangeViT's backbone with ViTs pretrained: (a) on supervised ImageNet21k classification [14] (entry IN21k), (b) on supervised image segmentation on Cityscapes with Segmenter [45] (entry CS), which in its turn was pre-trained with IN21k, and (c) with the DINO [9] self-supervised approach on ImageNet1k (entry DINO)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "We observe that, despite the large domain gap, using ViT models pre-trained on RGB images is always better than training from scratch on LiDAR data (entry Rand). For instance, using the IN21k and CS pretrained ViTs leads to improving the mIoU scores by 2.4 and 2.8 points respectively. Additionally, as we see in Fig. 3, which plots the nuScenes validation mIoU as a function of the training epochs, using such pre-trained ViTs leads to faster training convergence of the LiDAR segmentation model. We argue that this is a highly interesting finding. It means that our RangeViT approach, by being able to use off-the-shelf pre-trained ViT models, can directly benefit from current and future advances on the training ViT models with natural RGB images, a very active and rapidly growing re" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5245" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 89, + 70, + 244, + 153 + ], + "blocks": [ + { + "bbox": [ + 89, + 70, + 244, + 153 + ], + "lines": [ + { + "bbox": [ + 89, + 70, + 244, + 153 + ], + "spans": [ + { + "bbox": [ + 89, + 70, + 244, + 153 + ], + "type": "table", + "html": "
ModelFine-tuningIN21k mIoU (%)CS (%)
LNATTNFFN
(a)✓✓✓74.7975.21
(b)67.8868.03
(c)✓69.0869.31
(d)✓✓73.5672.77
(e)✓✓75.1175.47
", + "image_path": "69fb7ee3a5503d64ca887b03b89f1fb080d81ebce8c8854d35649f19cd090ce9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 266, + 264, + 299 + ], + "blocks": [ + { + "bbox": [ + 46, + 156, + 287, + 254 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 254 + ], + "type": "text", + "content": "Table 5. Partial ViT fine-tuning. We use a ViT encoder pretrained on ImageNet21k (IN21k) or Cityscapes (CS) and partially fine-tune RangeViT on the nuScenes training set. The convolutional stem, the positional embeddings and the UpConv decoder are always fine-tuned. LN: fine-tuning the LayerNorm layers of the ViT encoder. ATTN: fine-tuning the multi-head attention layers of the ViT encoder. FFN: fine-tuning the feed-forward network layers of the ViT encoder. Model (a) is full fine-tuning of the network. The results are reported on the nuScenes validation set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 266, + 264, + 299 + ], + "lines": [ + { + "bbox": [ + 69, + 266, + 264, + 299 + ], + "spans": [ + { + "bbox": [ + 69, + 266, + 264, + 299 + ], + "type": "table", + "html": "
EncoderViT-S†ViT-SRN50†RN50Identity
mIoU (%)67.8874.7760.4872.3053.73
", + "image_path": "45a96316cd44a844f9051f316ee996782ae9d780cea22166275927ebf78c5e90.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 300, + 286, + 322 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 286, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 286, + 322 + ], + "type": "text", + "content": "Table 6. Ablating encoder backbones. ViT-S and RN50 are pretrained on IN21k. †: the encoder remains frozen during training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 337, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 286, + 408 + ], + "type": "text", + "content": "search field [23, 41, 48, 49]. Furthermore, from the small difference between the mIoU scores with the IN21k and CS pre-trainings, we infer that the pre-training can lead to consistent performance improvements even if it is not on the strongly-supervised image segmentation task, which requires expensive-to-announce datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 414, + 286, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 568 + ], + "type": "text", + "content": "Which ViT layers is better to fine-tune? In the image domain, several practices have emerged for fine-tuning a pre-trained convolutional network on a downstream dataset. Taking into consideration the domain gap between the pretraining and downstream data and the amount of labeled data available, the entire network can be fine-tuned or only a part of it. Here the domain gap between RGB images and range images is major and we would expect a full fine-tuning of the network to be better. To understand how much prior knowledge of the image pre-trained ViT is useful for point clouds, we study different fine-tuning strategies: fine-tuning all layers, only the attention (ATTN) layers or only the feedforward network (FFN) layers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "content": "In Tab. 5, we show results with these different fine-tuning strategies. Interestingly, the best results are not achieved with full fine-tuning (model (a)) but when the attention layers are kept frozen (model (e)). This suggests that the pretrained ATTN layers are already well learnt and ready to generalize to range images. With CS pre-training ATTN layers may capture the layout of the scenes more easily without much fine-tuning, as the LiDAR scans have been also acquired from urban road scenes. Fine-tuning FFN may have more impact due to the different specifics of the LiDAR data compared to RGB images. In addition, FFN layers are in practice easier and more stable to optimize" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 74, + 426, + 159 + ], + "blocks": [ + { + "bbox": [ + 310, + 74, + 426, + 159 + ], + "lines": [ + { + "bbox": [ + 310, + 74, + 426, + 159 + ], + "spans": [ + { + "bbox": [ + 310, + 74, + 426, + 159 + ], + "type": "image", + "image_path": "3f4bfeec95ddebeea5829bd608e032d1eea1a9cb706f8ca2196db50652e4ebb6.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 432, + 74, + 542, + 159 + ], + "blocks": [ + { + "bbox": [ + 432, + 74, + 542, + 159 + ], + "lines": [ + { + "bbox": [ + 432, + 74, + 542, + 159 + ], + "spans": [ + { + "bbox": [ + 432, + 74, + 542, + 159 + ], + "type": "image", + "image_path": "4e47f997373b436e55588c460ef2f0a9b5c73937ad2262b8fe93f658df1dc358.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 311, + 160, + 426, + 235 + ], + "blocks": [ + { + "bbox": [ + 311, + 160, + 426, + 235 + ], + "lines": [ + { + "bbox": [ + 311, + 160, + 426, + 235 + ], + "spans": [ + { + "bbox": [ + 311, + 160, + 426, + 235 + ], + "type": "image", + "image_path": "2ee2ec0996ec4bef98540715cc64f2244fcbfdcd264d2850d55f4fe5a2396a42.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 160, + 542, + 235 + ], + "blocks": [ + { + "bbox": [ + 427, + 160, + 542, + 235 + ], + "lines": [ + { + "bbox": [ + 427, + 160, + 542, + 235 + ], + "spans": [ + { + "bbox": [ + 427, + 160, + 542, + 235 + ], + "type": "image", + "image_path": "a29d83b88d26ebbc6b1144144ae545feabb437abb83e345504a8d5b656f6a8b1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 311, + 236, + 426, + 311 + ], + "blocks": [ + { + "bbox": [ + 311, + 236, + 426, + 311 + ], + "lines": [ + { + "bbox": [ + 311, + 236, + 426, + 311 + ], + "spans": [ + { + "bbox": [ + 311, + 236, + 426, + 311 + ], + "type": "image", + "image_path": "bc874d517e74daf814b62fc76531ad8220fcf0e48cde744b519b9bcdb10c9ae7.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 314, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 306, + 314, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 545, + 358 + ], + "type": "text", + "content": "Figure 4. Visualizing the segmentation accuracy. Left: ground truth segmentation of validation point clouds of nuScenes, coloured based on their label. Right: segmentation accuracy of RangeViT - good predictions are in blue and the bad ones in red." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 236, + 542, + 311 + ], + "blocks": [ + { + "bbox": [ + 427, + 236, + 542, + 311 + ], + "lines": [ + { + "bbox": [ + 427, + 236, + 542, + 311 + ], + "spans": [ + { + "bbox": [ + 427, + 236, + 542, + 311 + ], + "type": "image", + "image_path": "6e41c718e61e6e33f5d3265459323d2081142b8aa72a5416bc668503cebdc353.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 380, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 452 + ], + "type": "text", + "content": "(they are essentially fully-connected and normalization layers) than ATTN layers that usually require more careful hyper-parameter selection. These findings align with recent ones from the image domain [48], confirming that the convolutional stems do steer the input LiDAR data to behave like image data once on in the ViT backbone." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": "Ablating encoder backbones. In Tab. 6, we replace the ViT-S encoder backbone of RangeViT with a ResNet-50 (RN50) encoder or the identity function (i.e., the decoder follows directly the stem). Both ViT-S and RN50 are pretrained on IN21k. We see that switching from ViT-S to RN50 decreases the mIoU from " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "74.77\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "72.30\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": ". Furthermore, when the backbones remain frozen " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "(\\mathrm{ViT - S}^{\\dagger}" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathrm{RN50\\dagger}" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " models), we reach " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "67.88\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " with ViT-S and " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "60.48\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " with RN50, demonstrating that ViT features are more appropriate for transfer learning to LiDAR data than CNNs. Finally, with the Identity backbone, we achieve " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "53.73\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": ", which is more than 14 points worse than the " + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathrm{ViT - S}^{\\dagger}" + }, + { + "bbox": [ + 304, + 457, + 545, + 613 + ], + "type": "text", + "content": " model that has the same number of learnable parameters." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 623, + 486, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 486, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 486, + 635 + ], + "type": "text", + "content": "4.4. Comparison to the state of the art" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Tab. 7 and 8 report the final comparison on the nuScenes validation set and on the SemanticKITTI test set including class-wise IoU scores. We observe that our model achieves superior mIoU performance compared to prior 2D-projection based methods on both datasets, reducing the gap with the strong voxel-based Cylinder3D [69] method." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5246" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 201 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "type": "table", + "html": "
Methodbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdriveableother flatsidewalkterrainmammadevegetationmIoU (%)
Voxel-based Cylinder3D [69]76.440.391.393.851.378.078.964.962.184.496.871.676.475.490.587.476.1
2D Projection-based
RangeNet++ [36]66.021.377.280.930.266.869.652.154.272.394.166.663.570.183.179.865.5
PolarNet [66]74.728.285.390.935.177.571.358.857.476.196.571.174.774.087.385.771.0
SalsaNext [11]74.834.185.988.442.272.472.263.161.376.596.070.871.271.586.784.472.2
RangeViT-IN21k (ours)75.139.090.288.448.079.277.266.465.176.796.371.173.773.988.987.174.8
RangeViT-CS (ours)75.540.788.390.149.379.377.266.365.280.096.471.473.873.889.987.275.2
", + "image_path": "f4ed65877f72332205bffe7e34b0d15b237fa3c282d055e748d0a7eef70cdeee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 219, + 545, + 369 + ], + "blocks": [ + { + "bbox": [ + 49, + 202, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 49, + 202, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 49, + 202, + 545, + 213 + ], + "type": "text", + "content": "Table 7. nuScenes validation set comparison with state-of-the-art methods. The best results are bold and the second best results are blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 219, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 50, + 219, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 50, + 219, + 545, + 369 + ], + "type": "table", + "html": "
Methodcarbicyclemotorcycletruckother vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother groundbuildingfencevegetationtrunkterrainpoletraffic signmIoU (%)
Voxel-based Cylinder3D [69]97.167.664.059.058.673.967.936.091.465.175.532.391.066.585.471.868.562.665.667.8
2D Projection-based
RangeNet++ [36]91.425.734.425.723.038.338.84.891.865.075.227.887.458.680.555.164.647.955.952.2
PolarNet [66]93.840.330.122.928.543.240.25.690.861.774.421.790.061.384.065.567.851.857.554.3
SqueezeSegV3 [60]92.538.736.529.633.045.646.220.191.763.474.826.489.059.482.058.765.449.658.955.9
SalsaNext [11]91.948.338.638.931.960.259.019.491.763.775.829.190.264.281.863.666.554.362.159.5
KPRNet [26]95.554.147.923.642.665.965.016.593.273.980.630.291.768.485.769.871.258.764.163.1
Lite-HDSeg [42]92.340.055.437.739.659.271.654.193.068.278.329.391.565.078.265.865.159.567.763.8
RangeViT-CS (ours)95.455.843.529.842.163.958.238.193.170.280.032.592.069.085.370.671.260.864.764.0
", + "image_path": "cc0a604be481b91d686815195f15c8806039a85031eb46ad01eeac9a614a1ea1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 370, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 49, + 370, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 49, + 370, + 545, + 380 + ], + "type": "text", + "content": "Table 8. SemanticKITTI test set comparison with state-of-the-art methods. The best results are bold and the second best results are blue." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "content": "Class-wise IoU result analysis. In Tab. 7 and 8, we can see that RangeViT often achieves the best or the second best class-wise IoU scores. In both datasets, the classes are imbalanced and due to the sparsity and varying density of Li-DAR point clouds, some classes (e.g., bicycle, pedestrian) are represented with few, not necessarily structured points per scene, so it is difficult to recognize them. This problem could possibly be reduced by jointly processing point clouds and RGB images, since RGB images might provide extra cues about the outline and the shape of these objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 521, + 159, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 159, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 159, + 533 + ], + "type": "text", + "content": "4.5. Qualitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "type": "text", + "content": "We visualize the 3D point clouds with the ground truth semantic labels as well as the predictions with CloudCompare [18]. Fig. 4 shows the predictions of RangeViT on three validation point clouds of nuScenes. We notice minor errors such as man-made objects predicted as sidewalk and imperfect borders for the vegetation. We also remark difficulties in recognizing pedestrians and confusion between the driveable surface and the sidewalk for few points." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "We studied the feasibility of leveraging (pre-trained) ViTs for LiDAR 3D semantic segmentation with projection-based methods. We discover that in spite of the significant domain gap between RGB images and range images and" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 395, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 526 + ], + "type": "text", + "content": "their high requirements of training data, ViTs can be successfully used without any changes in the original transformer backbone. We achieve this thanks to an adapted tokenization and pre-processing for the ViT encoder and a simple convolutional decoder. We show that ViTs pre-trained on large image datasets can be effectively repurposed for LiDAR segmentation towards reaching state-of-the-art performance among 2D projection methods. We release the code for our implementation and hope that it could be used as a testbed for evaluating the ability of ViT image \"foundation\" models [6] to generalize on different domains." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 529, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 613 + ], + "type": "text", + "content": "Future work. Although the results are promising, there is still room for improvement. For instance, we identified the tokenization of LiDAR data as a crucial factor for success. As future work, we could further improve this process, e.g., with FlexiViT [5] (random patch sizes) or Perceiver IO [25] (learning to extract tokens), and consider tokenizing raw 3D data instead of the 2D projections." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 619, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 619, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 619, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. We would like to express our gratitude to Matthieu Cord and Hugo Touvron for their insightful comments, Robin Strudel et al. [45] for kindly providing ViT-S pre-trained on Cityscapes, and Oriane Simeoni for her valuable contribution to certain experiments. This work was performed using HPC resources from GENCI-IDRIS (Grants 2022-AD011012884R1, 2022-AD011013413 and 2022-AD011013701). The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-21-CE23-0032 (project MultiTrans)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5247" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Eren Erdal Aksoy, Saimir Baci, and Selcuk Cavidar. 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The WSI datasets are also imbalanced in categories. These unique characteristics, significantly different from the ones in natural images, pose the challenge of classifying WSI images as a kind of weakly supervise learning problems. In this study, we propose, RankMix, a data augmentation method of mixing ranked features in a pair of WSIs. RankMix introduces the concepts of pseudo labeling and ranking in order to extract key WSI regions in contributing to the WSI classification task. A two-stage training is further proposed to boost stable training and model performance.", + "bbox": [ + 75, + 323, + 472, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To our knowledge, the study of weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories is relatively unexplored.", + "bbox": [ + 75, + 505, + 472, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 609, + 209, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1.1. Background", + "text_level": 1, + "bbox": [ + 76, + 635, + 209, + 651 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Natural image processing tasks, including image classification and object detection, have been widely solved using deep learning models and obtain astounding results. In this study, we investigate how medical imaging can also benefit from deep learning with focus on whole slide images (WSIs). WSI scanning is commonly used in disease diagnosis [12, 34]. The demand of computer aided assessment makes deep learning widely adopted in this field [1]. Because WSI is a gigapixel image and lacks pixel-level annotations, multiple instance learning (MIL) [31, 32] is an exact solution to this weakly supervised learning problem [2]. In MIL, a WSI is often cropped into tens of thousands of patches and then an aggregator will make a prediction based on integrating these patches. Most recent works [5,9,10,25,28,30,37,38,44] focus on aggregator architecture design and improving feature extraction of the patches.", + "bbox": [ + 75, + 657, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, because WSI is difficult to collect and share, we explore the possibility of data augmentation in WSI classification to increase training samples and mitigate the problem of class imbalance [19, 26, 33, 48] that WSI may have due to rare diseases (versus common diseases). In addition, patch feature extractor is often trained by self-supervised learning [24, 28] or comes from pre-trained models (such as pre-trained in ImageNet [30, 37] or WSI datasets [5, 11]). Therefore, for universality and portability, our work will focus on studying the feature domain instead of pixel domain of patches.", + "bbox": [ + 496, + 292, + 893, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditionally, mixup methods [18, 48] are employed to mix photos of the same aspect ratio or vectors of the same dimension. Nevertheless, this is not the case for WSI as WSI intrinsically has a different number of patches, ranging from hundreds to hundred of thousands. This is because the generation of a WSI, caused by the tissue placement and the tissue size, will make WSIs of varying aspect ratios and sizes.", + "bbox": [ + 496, + 458, + 893, + 578 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition, because a WSI tends to be a very large size (equivalent to tens of thousands of $224 \\times 224$ patches or even larger) and the background often occupies a large part, it is better to use data pre-processing to remove unimportant background parts in order to save computation time and avoid possible unnecessary information [21, 39] (such as noise and artifacts). That is, the pre-processing step of cropping a WSI into patches, as shown in Fig. 1, will remove most of the background patches. The resultant WSI patches, however, will lose their absolute positions.", + "bbox": [ + 496, + 580, + 895, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1.2. Challenges", + "text_level": 1, + "bbox": [ + 500, + 741, + 620, + 757 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The above characteristics of WSI lead to the difficulty of directly employing the traditional mixup methods. We cannot simply resize two WSIs to have the same size for the sake of performing mixup. This is because all WSIs are scanned at the same magnification (e.g., $20\\mathrm{x}$ ), the physical meanings will be lost if they are rescaled casually. More importantly, due to loss of absolute positions among the patches after removing the WSI background, resizing patches actually do not solve this problem.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23936", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another commonly used techniques for data augmentation are based on cutting, including Cutout [14] and Cutmix [47]. The core of cutting aims at obtaining or removing parts of an images. However, the key difference between WSI images and natural images is that the main objects can occupy a major part of a natural image, but it is not the case in WSIs. For example, the tumor slide of Camelyon16 dataset [16] only has a small area of tumor (approximately $< 10\\%$ of tissue area). Therefore, if a random cut is made, there is a non-negligible probability that the tumor slide will not contain any tumor patches.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose a novel mixup method, called RankMix, for augmentation of whole slide images with diverse sizes and imbalanced categories. RankMix introduces the concepts of instance-level pseudo labeling and ranking in order to obtain meaningful WSI regions that can contribute to the WSI classification task. In order to further enhance model performance, two-stage training is proposed in that the first step is to train a stable score function by general MIL, and then the score function and mixup technique are jointly used in the second stage of training.", + "bbox": [ + 75, + 257, + 472, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1.3. Our Contributions", + "text_level": 1, + "bbox": [ + 76, + 433, + 259, + 448 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 96, + 455, + 398, + 470 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To our knowledge, MIL currently focuses on improving feature extraction and aggregator-based classification. It is relatively ignored in investigating weakly supervised learning from the perspective of data augmentation. Our proposed method can be applied to WSI classification problems and can be easily incorporated to existing MIL methods.", + "- In contrast to the existing mixup methods that aim at mixing natural images of the same size, our method can mix images (e.g., WSIs) of different sizes.", + "- Because of rare diseases and the difficulty of medical image collection, the WSI classification problem is apt to suffer from lack of training data and imbalance of categories. Our proposed method is demonstrated to be feasible in addressing these challenges." + ], + "bbox": [ + 94, + 481, + 468, + 728 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 751, + 217, + 767 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly introduce the techniques that are relevant to our work.", + "bbox": [ + 76, + 777, + 468, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Data Augmentation", + "text_level": 1, + "bbox": [ + 76, + 816, + 264, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data augmentation can improve the generalization and has been widely used in training neural networks. Mixup [48] fuses information from two images by convex combination. CutMix [47] inpaints the masking area (produced by", + "bbox": [ + 76, + 840, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "random occlusion) with another image content at the same location. Recently, Part et al. [35] proposed how the majority can help the minority with re-balancing distribution of each sub-class. In addition to mixing in the pixel domain, Manifold Mixup [42] and PatchUp [18] proposed mixing the features of two images. Despite promising, the aforementioned methods are not presented for medical images.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For medical imaging, Galdran et al. [19] mixed two medical images sampled from different distributions, including instance-based sampling and class-based sampling. By increasing the sampling probability of the minority class, the class imbalance problem that usually occurs in medical imaging can be properly alleviated. In histopathology studies, the datasets often suffer from stain color variation because of different stain approaches, procedures, and slide scanner. To address this problem, Chang et al. [4] mixed two stain color matrices from stained images in order to increase the generalization of unseen colors. Chen et al. proposed Flow-Mixup [6] to regularize medical images with corrupted multi-labels because the annotations of medical images are costing and automatic annotation often provides corrupted labels. Gazda et al. [20] used the mixup technique to improve model performance for medical image segmentation. In ReMix [46], Yang et al. proposed using latent-space data augmentation to deal with WSI classification. However, ReMix only mixed instance prototypes of slides from the same class by $K$ -Means while maintaining the original labels. From this perspective, ReMix acts like a kind of feature augmentation instead of general mixup.", + "bbox": [ + 496, + 198, + 892, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As shown in Tab. 1, although the previous researches on medical images are diverse, their data augmentations are not feasible for WSIs with large gaps in size.", + "bbox": [ + 496, + 531, + 893, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Multiple Instance Learning (MIL)", + "text_level": 1, + "bbox": [ + 500, + 589, + 799, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent MIL studies, the patches of a WSI are transformed into the features of fixed size by a feature extractor and then the patch features will be aggregated to get a final slide-level prediction. To leverage patch features, MIL-RNN [2] uses the recurrent neural network (RNN) [36] to encode position information. Because RNNs are apt to suffer from information loss over long distances, the follow-up works proposed attention-based MIL [25, 30] to calculate the contributions of instance-level features by learnable neural networks. Thanks to the success of Transformer [15, 41], self-attention based MIL methods [10, 28, 37] receive considerable attention in WSI classifications. Li et al. [28] proposed the non-local attention mechanism to calculate the relation between the critical feature and remaining features, but ignored the position relationship between patches. To address this problem, Shao et al. proposed TransMIL [37], which emphasizes the benefits of Pyramid Position Encoding Generator (PPEG), to encode spatial information by group convolution. Recently, Chikontwe et", + "bbox": [ + 496, + 613, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23937", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/875479b6c4bda4608bf876875b01e6eb9e1415f4a7a30ecbdd774ff13af9d88f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingImage typeMixup inputMixup outputLarge size gap between 2 inputs
Mixup [48]Natural imageImagevx
Manifold Mixup [42]Natural imageImage, Hidden statevx
Balanced-MixUp [19]Retinal image, Gastro-intestinal imageImagevx
Stain Mix-up [4]Patches of WSIStain matrixvx
Flow-Mixup [6]Chest X-ray, ECGHidden statevx
Mixup for KiTS [20]CT imageImagevx
ReMix [46]WSIInstance prototypexv
RankMix (Ours)WSIImage featurevv
", + "bbox": [ + 114, + 88, + 859, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Comparisons among mixup methods. Our method, RankMix, deals with mixing of not only two images with large gap in size in the feature domain but also their labels.", + "bbox": [ + 75, + 263, + 893, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "al. [10] proposed combining the critical feature [28] with PPEG [37], treating the tumor slides as a kind of out-of-distribution compared to normal slides, and re-calibrating the patch features of a slide according to the magnitudes of critical feature and slide label.", + "bbox": [ + 75, + 318, + 470, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Self-Training and Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 405, + 428, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge distillation [23,40] uses soft labels instead of hard labels (which are the maximum of class probabilities) from the teacher model to train the student model. The student model, aiming for model compression, is a smaller one to mimic the output of its teacher model. Instead of compressing models, Xie et al. [45] integrated self-training with knowledge distillation to improve the image classification task with unlabeled data. The authors propagated pseudo soft labels of unlabeled data from the teacher model to the student model. The researches [3,8,17] further used self-training and knowledge distillation to deal with the self-supervised learning problem.", + "bbox": [ + 75, + 429, + 468, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To sum up, our work, RankMix, has similar concepts with previous works, but we study how the general MIL model can be adopted as the teacher model. This makes RankMix act like a post-processing of traditional MIL, as illustrated in Fig. 2, and can be simply plugged into the exist approaches.", + "bbox": [ + 75, + 611, + 468, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 717, + 204, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the classification problem of WSIs, as well as some baseline techniques and notations, to make this paper self-contained.", + "bbox": [ + 75, + 744, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 800, + 279, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the WSI classification problem, we have a series of WSIs $X = \\{X_{1},X_{2},\\ldots ,X_{n}\\}$ and corresponding slide labels $Y = \\{Y_{1},Y_{2},\\dots ,Y_{n}\\}$ as dataset $\\mathcal{D} = \\{(X_i,Y_i),\\quad i = 1,\\ldots ,n\\}$ . Our goal is to train an NN model based on dataset $\\mathcal{D}$ for binary slide label $Y_{i}\\in \\{0,1\\}$", + "bbox": [ + 76, + 824, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "prediction of an incoming WSI image $X_{i}$ . In MIL, a WSI can be treated as a bag (slide) containing the instances (patches) as $X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m(i)}\\}$ . Note that the WSI $X_{i}$ 's have different numbers $m(i)$ 's of instances and the instance-level labels $\\{y_{i,1}, y_{i,2}, \\ldots, y_{i,m(i)}\\}$ are unknown. Without loss of generality, we will mostly use $m$ in place of $m(i)$ for notation simplicity. The slide label $Y_{i}$ of a WSI $X_{i}$ is defined to be negative ( $Y_{i} = 0$ ) when all instances in a bag are negative (without tumors), i.e., $y_{i,j} = 0$ for all $j$ . If at least one instance in $X_{i}$ is positive (with tumor), its slide label will be positive ( $Y_{i} = 1$ ). The slide label of WSI $X_{i}$ is defined as:", + "bbox": [ + 496, + 318, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nY _ {i} = \\left\\{ \\begin{array}{l} 0, \\text {i f f} \\sum y _ {i, j} = 0 \\\\ 1, \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 507, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. MIL as Baseline Model", + "text_level": 1, + "bbox": [ + 500, + 555, + 714, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In MIL, as shown in Fig. 1, the slide $X_{i}$ will first be cut into many instances (patches) as $X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m}\\}$ and then passed through an instance feature extractor $G_{\\theta}$ to get the so-called features (embeddings) $H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}$ via Eq. (2) as:", + "bbox": [ + 498, + 578, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i, j} = G _ {\\theta} \\left(x _ {i, j}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 662, + 890, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d$ denotes the length of a feature vector and $m$ denotes the number of features. As mentioned before, different WSIs will have different numbers of features but feature length $d$ is the same. Finally, the aggregator will output a slide label prediction $\\hat{Y}_i$ by Eq. (3) as:", + "bbox": [ + 496, + 686, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {Y} _ {i} = \\text {a g g r e g a t o r} \\left(h _ {i, 1}, h _ {i, 2}, \\dots , h _ {i, m}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 768, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we use DSMIL [28] and FRMIL [10] as the backbone models to represent SOTA permutation-variant and permutation-invariant MIL models, respectively, where the former only considers the relationship between each embedding and does not consider relative positions, and the latter uses the pooling multi-head self-attention (PMSA) module and positional encoding module (PEM) to fuse relative", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23938", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7e5abbd55991213a74cd4fba628fa26ee4ddfad6af111eb40c615a62ccb39aaa.jpg", + "image_caption": [ + "Figure 1. The workflow of general MIL." + ], + "image_footnote": [], + "bbox": [ + 179, + 85, + 781, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "spatial information. We study the impact of RankMix on these two models and demonstrate that our method can be plugged into the current MIL methods. The general loss function of an MIL model can be formulated as:", + "bbox": [ + 75, + 311, + 470, + 371 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {M I L}} = w _ {1} * \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {i}, Y _ {i}\\right) + \\sum_ {\\ell} w _ {\\ell} * \\mathcal {L} _ {\\ell}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 378, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{bag}$ is a binary cross-entropy (BCE) loss, $\\mathcal{L}_{\\ell}$ is other loss term that depends on different MIL models, and $w_{\\ell}$ 's are the corresponding balance weights.", + "bbox": [ + 75, + 420, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Mixup", + "text_level": 1, + "bbox": [ + 76, + 474, + 165, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mixup technique was first proposed in [48] as:", + "bbox": [ + 96, + 498, + 431, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {m x p} = \\lambda x _ {1} + (1 - \\lambda) x _ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 525, + 468, + 541 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {m x p} = \\lambda y _ {1} + (1 - \\lambda) y _ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 551, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the input sample $x_{i}$ ( $i = 1,2$ ) is drawn from the training dataset, the label corresponding to the input sample $x_{i}$ is $y_{i}$ , and $\\lambda \\in [0,1]$ is sampled from $\\sim \\mathrm{Beta}(\\alpha, \\alpha)$ .", + "bbox": [ + 75, + 573, + 468, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The main goal of mixup is to make linear combinations of inputs and outputs, respectively, and to ensure that the mapping of the mixed input and mixed output can maintain linear constraints. Therefore, the mixup technique is able to boost the generalization and robustness of an NN model. In addition, mixup can improve the performance of a model encountering the class imbalance problem [19].", + "bbox": [ + 75, + 619, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proposed Method: RankMix", + "text_level": 1, + "bbox": [ + 76, + 737, + 341, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "RankMix is mainly composed of pseudo labeling, ranking, mixing ranked features, and self-training, as illustrated in Fig. 2. We will describe the motivation of our method and the role of each component in RankMix.", + "bbox": [ + 75, + 762, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Motivation", + "text_level": 1, + "bbox": [ + 76, + 832, + 197, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A WSI is usually composed of normal tissue and special areas, as shown in Fig. 3a. Special areas can be tumors or defects, etc. If a pathologist obtains a WSI that contains", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tumors, his/her expertise is sufficient to make a correct decision of determining whether there is a tumor inside it. Based on this premise, even a pathologist obtains a partial image of the same WSI that contains most of the tumor areas, as shown in Fig. 3b, it suffices to determine that the image contains tumors. By contrast, if an entire WSI or a partial WSI contains only normal tissues, it can be easily determined that the WSI is normal, as shown in Figs. 3c and 3d, respectively.", + "bbox": [ + 496, + 311, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, the hypothesis here is that cropping a WSI into patches will not affect tumor detection, not to mention the fact that dealing with the entire WSI as a whole is indeed impractical when computing power and memory consumption are taken into consideration.", + "bbox": [ + 496, + 446, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moreover, based on the problem introduced in Sec. 1.2, it is easy to lose physical meaning from picking patches and resizing them to have the same size. If we can select the areas of arbitrary sizes to represent the original slide, we can prepare two partial but representative slides of the same size for use in the mixup technologies. Nevertheless, the prerequisite is based on the fact that we can know which parts of the slide are sufficient to represent the original slide. This conflicts with the scenario that we only have the label of entire slide and do not have the instance-level labels corresponding to patches in the slide, as described in Sec. 3.1.", + "bbox": [ + 496, + 523, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In view of the above challenges, we will explain in following subsections how to pick out fragments that are sufficient to represent a slide without instance-level labels. We will demonstrate how to get the pseudo instance-level labels in Sec. 4.2, how to select representative features in Sec. 4.3, and how to combine representative features with a mixup mechanism in Sec. 4.4. The module of pseudo labeling and ranking in RankMix (Fig. 2) is further detailed in Fig. 4.", + "bbox": [ + 496, + 689, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Pseudo Labeling", + "text_level": 1, + "bbox": [ + 500, + 816, + 663, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}$ from a WSI $X_{i}$ by Eq. (2), the pseudo patch-level labels will be predicted to determine which patches are useful for mixup later. Specifically, if we have a score function $f \\in \\mathbb{R}^{d \\times 1}$", + "bbox": [ + 496, + 838, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23939", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/10b8d30a9dfaf6f031c17bd08ca6e0acd29bc931f2a498ae45ca20c4d5fe86dc.jpg", + "image_caption": [ + "Figure 2. The flowchart of MIL with RankMix. We train the general MIL model with the training set $X$ in the first stage (Top), and then the score function $f$ obtained in the first stage is used to make pseudo labels for $\\{X_{a}, X_{b}\\}$ and train the MIL model with mixup mechanism in the second stage (Bottom). The dashed arrows indicate the patch scores that may be used by the aggregator depending on the MIL method." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 880, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "implemented by a multilayer perceptron (MLP) as:", + "bbox": [ + 76, + 440, + 413, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i, j} = \\operatorname {s c o r e} _ {i, j} = f \\left(h _ {i, j}\\right), \\quad \\forall i = 1, \\dots , n \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 463, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we can define a loss function $\\mathcal{L}_{max}$ as:", + "bbox": [ + 76, + 487, + 334, + 502 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\max } = \\operatorname {B C E} \\left(\\hat {y} _ {i, j ^ {*}}, Y _ {i}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 510, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $j^{*} = \\arg \\max_{j}(\\hat{y}_{i,j})$ and $Y_{i}$ is obtained from Eq. (1). Note that the score function here can be calculated indi", + "bbox": [ + 76, + 534, + 468, + 563 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/18d122e61359faba2bb3743a5896a48eba1786bc885b9560692bb2bc0a277093.jpg", + "image_caption": [ + "(a) Example of tumor slide from Camelyon16." + ], + "image_footnote": [], + "bbox": [ + 107, + 580, + 272, + 672 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/94b4507f4bdaf563af87d478d80287095f088b1d5ef0b0e2beba823d51e96133.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 580, + 439, + 672 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9842474857879fc7ed3a23a94c4641a1e3a6bb950c19d857cde0e1d560ac6323.jpg", + "image_caption": [ + "(b) Partial slide (in red bounding box) selected from (a).", + "Figure 3. Illustration of judging if a whole slide or partial slide contains tumors or not. The green annotation indicates the tumor regions and red bounding box indicates the partial region of WSI that is considered to have the same label as the original WSI." + ], + "image_footnote": [], + "bbox": [ + 107, + 699, + 272, + 801 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3bbe4a93255dae9b40e3ffee4bb89e1a3f71d41953c8899890a030da8eb11dfd.jpg", + "image_caption": [ + "(c) Example of normal slide from Camelyon16.", + "(d) Partial slide (in red bounding box) selected from (c)." + ], + "image_footnote": [], + "bbox": [ + 274, + 698, + 439, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "vidually to deal with the multi-class classification problems (e.g., TCGA-Lung dataset in Sec. 5.1) and can be replaced by any similar mechanisms of MIL, which calculates the importance of each patch to yield a final slide-level prediction (e.g., attention mechanism [25, 28, 30] or the distance between clusters [9, 38, 44]). So far, we can get the class probability of every patch in a WSI by the score function $f$ .", + "bbox": [ + 496, + 440, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Ranking", + "text_level": 1, + "bbox": [ + 500, + 561, + 602, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the score function $f$ , we already have the basic ability to achieve the motivation mentioned in Sec. 4.1. If we want to obtain a representative portion that can represent the original WSI, we need to score each feature $\\{\\hat{y}_{i,1},\\dots ,\\hat{y}_{i,m}\\} \\in \\mathbb{R}^{m\\times 1}$ in the WSI and then sort the patch scores as:", + "bbox": [ + 496, + 587, + 890, + 679 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Z _ {i} = \\left\\{z _ {i, 1}, z _ {i, 2}, \\dots , z _ {i, m} \\right\\} \\\\ \\text {s . t .} \\hat {y} _ {i, z _ {i, 1}} > \\hat {y} _ {i, z _ {i, 2}} > \\dots > \\hat {y} _ {i, z _ {i, m}} \\quad \\forall i = 1, \\dots , n. \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 694, + 890, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to the number $k$ ( $k$ is an arbitrary positive integer) of features we need, we can obtain the desired features $\\bar{H}_i\\in \\mathbb{R}^{k\\times d}$ from the original features $H_{i}\\in \\mathbb{R}^{m\\times d}$ as:", + "bbox": [ + 500, + 743, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {H} _ {i} = \\left\\{h _ {i, z _ {i, 1}}, h _ {i, z _ {i, 2}}, \\dots , h _ {i, z _ {i, k}} \\right\\}. \\tag {10} \\\\ \\text {f o r} k \\leq m, \\forall i = 1, \\dots , n \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 804, + 890, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, in order to maintain the relative position information among patches, the features in $\\bar{H}_i$ are rearranged in the original order to get the final representative features", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23940", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6771ffb035a01549345b89a0b0c735c55edd7b31d79e0ffa52307a8bc5e60bd0.jpg", + "image_caption": [ + "Figure 4. Illustration of the pseudo labeling and ranking mechanism." + ], + "image_footnote": [], + "bbox": [ + 174, + 85, + 803, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$H_{i}^{\\prime}\\in \\mathbb{R}^{k\\times d}$ as:", + "bbox": [ + 76, + 292, + 181, + 310 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nH _ {i} ^ {\\prime} = \\left\\{h _ {i, z _ {i, 1} ^ {\\prime}}, h _ {i, z _ {i, 2} ^ {\\prime}}, \\dots , h _ {i, z _ {i, k} ^ {\\prime}} \\right\\}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 316, + 468, + 340 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ns. t. z _ {i, 1} ^ {\\prime} < z _ {i, 2} ^ {\\prime} < \\dots < z _ {i, k} ^ {\\prime} \\quad \\forall i = 1, \\dots , n\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 339, + 413, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $H_{i}^{\\prime}$ indicates the $k$ features selected from the original $i^{th}$ slide with the order preserved.", + "bbox": [ + 76, + 364, + 468, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Mixup in Ranked Features", + "text_level": 1, + "bbox": [ + 76, + 402, + 318, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to Eq. (5) and Eq. (6), we can formulate the mixup of features from two examples, $(X_{a},Y_{a})$ and $(X_{b},Y_{b})$ , sampled from the dataset $\\mathcal{D}$ , as follows:", + "bbox": [ + 76, + 426, + 468, + 470 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nH _ {m x p} = \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 479, + 468, + 497 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nY _ {m x p} = \\lambda Y _ {a} + (1 - \\lambda) Y _ {b}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 503, + 468, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $H_{a}^{\\prime}\\in \\mathbb{R}^{k\\times d}$ and $H_{b}^{\\prime}\\in \\mathbb{R}^{k\\times d}$ are obtained from $H_{a}\\in \\mathbb{R}^{m(a)\\times d}$ and $H_{b}\\in \\mathbb{R}^{m(b)\\times d}$ , respectively, by Eq. (9)~Eq. (11), and $m(a)$ and $m(b)$ denote the numbers of features obtained from $X_{a}$ and $X_{b}$ , respectively. Different from the existing mixup techniques, we conduct mixup in ranked features.", + "bbox": [ + 76, + 523, + 468, + 613 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. MIL Model with RankMix", + "text_level": 1, + "bbox": [ + 76, + 623, + 318, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As described in Sec. 3.2 and Sec. 4.2, RankMix can be applied to MIL models with the total loss being defined as:", + "bbox": [ + 76, + 647, + 468, + 676 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = w _ {1} \\mathcal {L} _ {m a x} \\left(\\hat {y} _ {m x p, j ^ {*}}, Y _ {m x p}\\right) + w _ {2} \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {m x p}, Y _ {m x p}\\right) \\\\ + \\sum_ {\\ell} w _ {\\ell} \\mathcal {L} _ {\\ell}, \\tag {14} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 696, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the first term comes from Eq. (8) and the remaining terms come from Eq. (4). So far, we have explained how to accomplish the middle component of RankMix in MIL in Fig. 2, i.e., the first stage of training.", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.6. Self-Training: Second Stage of Training", + "text_level": 1, + "bbox": [ + 76, + 830, + 419, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "WSI classification faces the tough problem that each WSI is only given a slide-level label; that is, tens of thousands of patches correspond to one label. This kind of", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "weakly supervised learning is more difficult to train than supervised learning. If the RankMix proposed so far is used, unstable training will be encountered. However, if the score function is more reliable (i.e., can distinguish patch labels) at the beginning, then RankMix is found to achieve better results. We can imagine that the score function acts like expert annotations, and higher quality annotations will naturally result in better performance.", + "bbox": [ + 496, + 292, + 890, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inspired by self-training [40,45] and BERT-based model [13, 27, 29], we design a score function by learning from a pre-trained task in advance (i.e., can output the class probability distribution of a patch) as:", + "bbox": [ + 496, + 416, + 890, + 477 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\hat {Y} _ {i} \\mid H _ {i}\\right) = \\text {a g g r e g a t o r} \\left(H _ {i}\\right) = p \\left(\\hat {Y} _ {i} \\mid h _ {i, 1}, \\dots , h _ {i, m}\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 508, + 888, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, by using the concept of self-training, the stronger model is used as a teacher to extract the area that can represent the original WSI via score function for the student model to mixup ranked features as:", + "bbox": [ + 496, + 541, + 890, + 601 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {Y} _ {m x p} = p \\left(Y _ {m x p} \\mid H _ {m x p}\\right) = p \\left(Y _ {m x p} \\mid h _ {m x p, 1}, \\dots , h _ {m x p, k}\\right) \\\\ = p \\left(Y _ {m x p} | \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right) \\\\ = \\text {a g g r e g a t o r} \\left(\\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right). \\tag {16} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 631, + 890, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From the perspective of BERT-based models, we use the teacher model to learn the WSI classification problem (also known as the pretext task) as pretraining, and treat the mixup of ranked features as the downstream task to further improve the performance. Please see Fig. 2 for the illustration of two-stage training procedure.", + "bbox": [ + 496, + 702, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments and Results", + "text_level": 1, + "bbox": [ + 500, + 811, + 733, + 829 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we will describe the datasets used for experiments in Sec. 5.1, experimental setting and performance metrics in Sec. 5.2, main results in Sec. 5.3, and ablation studies in Sec. 8.1 (Appendix).", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23941", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/92b215bd456e8be8c494845a226fed3791c41c5b7ad2a4431a3048c451a04b66.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method/DatasetCamelyon16WSI-usabilityTCGA-Lung
ACCAUCAUPRCACCAUCAUPRCACCAUCAUPRC
DSMIL [28]86.82%93.32%92.68%76.11%86.60%24.51%93.81%97.89%97.75%
+ ReMix [46]82.17%86.89%83.86%83.19%85.83%25.59%94.29%97.62%97.29%
+ RankMix w/o self-training87.60%92.07%92.43%90.27%87.07%25.66%94.29%98.00%97.76%
+ RankMix89.92%93.47%92.74%90.27%88.16%28.41%94.29%98.04%97.79%
FRMIL [10]89.15%94.57%93.66%83.19%87.69%45.99%90.95%95.38%94.96%
+ ReMix [46]82.59%87.29%87.35%89.25%80.63%33.09%92.22%96.99%97.04%
+ RankMix w/o self-training90.70%94.11%93.68%80.53%84.27%38.55%93.33%95.84%97.01%
+ RankMix91.47%94.59%93.99%93.81%93.61%47.65%93.33%97.00%97.04%
", + "bbox": [ + 135, + 88, + 834, + 237 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of WSI classification between RankMix and vanilla models under three datasets.", + "bbox": [ + 181, + 247, + 785, + 261 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 287, + 179, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We introduce the WSI datasets used for experiments here, and a pre-processing setting was adopted to extract patches from each WSI. Each WSI was cropped into different numbers of $224 \\times 224$ patches at $20\\mathrm{x}$ magnification without overlapping. We follow [10,28] to discard the background patches with tissue entropy less than $15\\%$ of a WSI.", + "bbox": [ + 75, + 311, + 468, + 401 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Camelyon16 [16] is a public and well-known dataset proposed for metastasis detection in breast cancer. The dataset contains 270 training slides and 130 testing slides, and roughly has 4.1 million patches at $20\\mathrm{x}$ magnification with the maximum of 44000 patches per WSI and a minimum of 1200 patches per WSI in our pre-processing setting. If a WSI contains at least one tumor region, it is regarded as a positive slide. On the contrary, if the entire area of a WSI is normal, it is negative. In Camelyon16, the tumor area only accounts for approximately less than $10\\%$ of the tissue area in the positive slide.", + "bbox": [ + 75, + 401, + 468, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "TCGA-Lung is a public dataset that has two types of lung cancer, Lung Adenocarcinoma (TCGA-LUAD) and Lung Squamous Cell Carcinoma (TCGA-LUSC), from the Caner Genome Atlas (TCGA). Please refer to https://pubmed.ncbi.nlm.nih.gov/25691825/ for details. There are in total 1046 diagnostic WSIs, including 534 TCGA-LUAD and 512 TCGA-LUSC, were split into 836 training slides and 210 testing slides. After pre-processing, TCGA-Lung roughly has a minimum of 50 patches per slide and a maximum of 12700 patches per slide, with a total of 3.2 million patches.", + "bbox": [ + 75, + 568, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "WSI-usability is a private dataset used for distinguishing whether a WSI is usable or not. The purpose of this dataset is used for evaluating automatic quality control (QC). In order to have sufficient practicality, two pathologist experts each annotated 250 WSIs from TCGA, of which 50 WSIs were redundant, resulting in 450 WSIs in total. If it is a bad (labeled as positive) slide, it means that the WSI is not usable; otherwise, it is a good WSI and annotated as a negative slide. WSI-usability has only 23 positive slides, so it possesses a severe class imbalance problem. After preprocessing, WSI-usability roughly has a minimum of 700", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "patches per slide and a maximum of 120000 patches per slide, with a total of 5.7 million patches.", + "bbox": [ + 498, + 287, + 890, + 318 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Summing up the above, the adopted datasets cover the imbalance/balanced classes, unbalanced/balanced bags, and single/multiple-class problem. Among them, WSI-usability has majority and minority categories with a huge gap, which indicates the rare diseases and other costly data. For the positive slides in Camelyon16, tumors occupy quite smaller areas than normal tissues, while the negative slide is all filled with normal tissues. Different from the other two datasets, TCGA-Lung has two types of positive slides, namely TCGA-LUSD and TCGA-LUSC, leading to a multi-class classification problem.", + "bbox": [ + 496, + 319, + 892, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Experimental Setup and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 497, + 872, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet18 [22] was adopted as our backbone model that was trained by SimCLR [7] and Adam optimizer to obtain feature extractor $G_{\\theta}$ with a mini-batch size of 512, learning rate of $1e - 4$ , and weight decay of $1e - 5$ . For Camelyon16, we used the weights of ResNet18 trained by Lee et al. [28], as described in [10]. Then, the embeddings $H_{i} \\in \\mathbb{R}^{m(i) \\times 512}$ of a WSI $X_{i}$ were obtained from the global average pooling layer of feature extractor $G_{\\theta}$ .", + "bbox": [ + 496, + 521, + 890, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For training aggregator, we used the Adam optimizer for 200 epochs with the mini-batch size of 1 (bag), learning rate of $2e - 4$ , and weight decay of $5e - 3$ . Note that the minibatch for performing mixup of ranked features was 2, where the sampling methods of DSMIL and FRMIL followed [19] and [10], respectively. The number $k$ of features used in RankMix was set to $\\min(m(a), m(b))$ for two WSIs $X_a$ and $X_b$ .", + "bbox": [ + 496, + 642, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For two-stage training, we trained teacher models by the general MIL (i.e., DSMIL and FR-MIL). Then, the teacher models were used to guide the training of student models by RankMix. The structures of both the teacher model and student model are the same, which can be considered as a kind of self-distillation mechanism. The temperature parameter $\\tau$ commonly used in knowledge distillation was set to 1.0 (see Eq. (20) later).", + "bbox": [ + 496, + 763, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The classification performance was evaluated in terms of", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23942", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e20bab4103c7540234f0bb3bba8455fc027004ac251e96e824d78874e0733c08.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method/DatasetCamelyon16WSI-UsabilityTCGA-Lung
AccuracyAUCAccuracyAUCAccuracyAUC
DSMIL [28]86.82%93.32%76.11%86.60%93.81%97.89%
DSMIL + Direct Mixup84.50%90.51%89.38%71.18%94.29%98.03%
DSMIL + Shrink Mixup86.05%92.42%88.50%69.94%93.81%97.95%
DSMIL + Duplicate Mixup84.50%91.96%89.38%72.43%93.81%97.99%
DSMIL + Random Mixup87.60%91.89%88.50%83.33%94.29%97.99%
DSMIL + RankMix89.92%93.47%90.27%88.16%94.29%98.04%
FRMIL [10]89.15%94.57%83.19%87.69%90.95%95.38%
FRMIL + Direct Mixup88.37%92.50%59.29%80.37%92.38%95.96%
FRMIL + Shrink Mixup89.92%93.16%68.14%57.09%92.86%96.88%
FRMIL + Duplicate Mixup87.60%92.78%86.73%74.77%92.38%96.73%
FRMIL + Random Mixup90.70%94.23%77.88%80.69%93.33%96.98%
FRMIL + RankMix91.47%94.59%93.81%93.61%93.33%97.00%
", + "bbox": [ + 202, + 88, + 767, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Comparisons between RankMix and four custom mixup techniques.", + "bbox": [ + 256, + 297, + 712, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the accuracy and area under the curve (AUC).", + "bbox": [ + 76, + 339, + 379, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 362, + 215, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, we applied the proposed method, RankMix, to two baseline models, DSMIL [28] and FRMIL [10], and compared the performance with the vanilla models in Tab. 2. We can observe that self-training indeed boosts the overall model performance, as described in Sec. 4.6. Without self-training (i.e., mixup in the model without being derived from a teacher model), RankMix can sometimes achieve slightly better results, but as the model and dataset vary, it can be seen that the performance is slightly degraded in few cases. On the contrary, when self-training is introduced, the performance can be improved further. A recent work, ReMix [46], which is a SOTA augmentation method in WSI, was included for comparison. It can be found that RankMix outperforms ReMix remarkably.", + "bbox": [ + 75, + 385, + 468, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Second, we compared our method with the general mixup techniques under different custom settings in Tab. 3. This is because the existing mixup researches, to our knowledge, were conducted on the same feature number, they cannot be readily employed to be compared with our method under the scenario that two features of different numbers were mixed. Here, we discuss four situations for mixing up two WSIs $(H_{a}$ and $H_{b})$ with different numbers $(m(a)$ and $m(b))$ of features in the following.", + "bbox": [ + 75, + 597, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1) Direct Mixup: Perform mixup directly regardless of feature numbers $(m(a)$ and $m(b))$ , where the feature with a smaller number is padded with zeros. So, the feature number after mixing is defined as:", + "bbox": [ + 76, + 733, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nk _ {d} = \\max (m (a), m (b)). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 801, + 468, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "2) Shrink Mixup: Extract the same number $k_{s}$ of features for mixing up by", + "bbox": [ + 76, + 825, + 468, + 856 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nk _ {s} = \\left\\{ \\begin{array}{l} m (b), \\text {i f f} m (a) > m (b) \\\\ m (a), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 863, + 468, + 904 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3) Duplicate Mixup: Duplicate the feature with a smaller number to have the same size $k_{du}$ as the larger feature as:", + "bbox": [ + 498, + 339, + 890, + 382 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nk _ {d u} = \\left\\{ \\begin{array}{l} m (a), \\text {i f f} m (a) > m (b) \\\\ m (b), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 381, + 890, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4) Random Mixup: By randomly performing both the duplicate and shrink mixups.", + "bbox": [ + 498, + 426, + 890, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared with the above four straightforward cases, it can be seen from Tab. 3 that RankMix is a sophisticated design according to the characteristics of WSI, described in Sec. 1.2, and generally performs better than others.", + "bbox": [ + 496, + 455, + 890, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we conduct ablation studies to further evaluate RankMix in two aspects. On the one hand, we examine how the score functions learned under different pre-trained models, as described in Sec. 4.6, affect RankMix. On the other hand, we examine how different knowledge transfer techniques affect the student model performance in WSI classification. Please refer to Sec. 8.1 in Appendix for details.", + "bbox": [ + 496, + 517, + 890, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 636, + 617, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we investigate weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories. A new data augmentation method, RankMix, of is proposed to mix ranked features in a pair of WSIs with different sizes. RankMix is composed of pseudo labeling and ranking for extracting key WSI regions, and two-stage training for boosting stable training and model performance.", + "bbox": [ + 496, + 661, + 890, + 797 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 811, + 679, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the Ministry of Science and Technology of Taiwan, ROC, under Grant MOST 110-2634-F-006-022.", + "bbox": [ + 498, + 835, + 890, + 880 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23943", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sugata Banerji and Sushmita Mitra. Deep learning in histopathology: A review. 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In International Conference on Learning Representations, 2018. 1, 2, 3, 4" + ], + "bbox": [ + 503, + 92, + 890, + 895 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23945", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_model.json b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8626fe8a162474a1dedc790bc544a712b3ac57 --- /dev/null +++ b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_model.json @@ -0,0 +1,2409 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.13, + 0.88, + 0.177 + ], + "angle": 0, + "content": "RankMix: Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images with Diverse Sizes and Imbalanced Categories" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.205, + 0.462, + 0.258 + ], + "angle": 0, + "content": "Yuan-Chih Chen \nIIS, Academia Sinica, Taiwan, ROC \nwillpower057@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.205, + 0.8, + 0.257 + ], + "angle": 0, + "content": "Chun-Shien Lu \nIIS, Academia Sinica, Taiwan, ROC \nlcs@iis.sinica.edu.tw" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.505 + ], + "angle": 0, + "content": "Whole Slide Images (WSIs) are usually gigapixel in size and lack pixel-level annotations. The WSI datasets are also imbalanced in categories. These unique characteristics, significantly different from the ones in natural images, pose the challenge of classifying WSI images as a kind of weakly supervise learning problems. In this study, we propose, RankMix, a data augmentation method of mixing ranked features in a pair of WSIs. RankMix introduces the concepts of pseudo labeling and ranking in order to extract key WSI regions in contributing to the WSI classification task. A two-stage training is further proposed to boost stable training and model performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.582 + ], + "angle": 0, + "content": "To our knowledge, the study of weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories is relatively unexplored." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.611, + 0.21, + 0.627 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.636, + 0.21, + 0.652 + ], + "angle": 0, + "content": "1.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Natural image processing tasks, including image classification and object detection, have been widely solved using deep learning models and obtain astounding results. In this study, we investigate how medical imaging can also benefit from deep learning with focus on whole slide images (WSIs). WSI scanning is commonly used in disease diagnosis [12, 34]. The demand of computer aided assessment makes deep learning widely adopted in this field [1]. Because WSI is a gigapixel image and lacks pixel-level annotations, multiple instance learning (MIL) [31, 32] is an exact solution to this weakly supervised learning problem [2]. In MIL, a WSI is often cropped into tens of thousands of patches and then an aggregator will make a prediction based on integrating these patches. Most recent works [5,9,10,25,28,30,37,38,44] focus on aggregator architecture design and improving feature extraction of the patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.895, + 0.459 + ], + "angle": 0, + "content": "However, because WSI is difficult to collect and share, we explore the possibility of data augmentation in WSI classification to increase training samples and mitigate the problem of class imbalance [19, 26, 33, 48] that WSI may have due to rare diseases (versus common diseases). In addition, patch feature extractor is often trained by self-supervised learning [24, 28] or comes from pre-trained models (such as pre-trained in ImageNet [30, 37] or WSI datasets [5, 11]). Therefore, for universality and portability, our work will focus on studying the feature domain instead of pixel domain of patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.579 + ], + "angle": 0, + "content": "Traditionally, mixup methods [18, 48] are employed to mix photos of the same aspect ratio or vectors of the same dimension. Nevertheless, this is not the case for WSI as WSI intrinsically has a different number of patches, ranging from hundreds to hundred of thousands. This is because the generation of a WSI, caused by the tissue placement and the tissue size, will make WSIs of varying aspect ratios and sizes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.896, + 0.732 + ], + "angle": 0, + "content": "In addition, because a WSI tends to be a very large size (equivalent to tens of thousands of \\(224 \\times 224\\) patches or even larger) and the background often occupies a large part, it is better to use data pre-processing to remove unimportant background parts in order to save computation time and avoid possible unnecessary information [21, 39] (such as noise and artifacts). That is, the pre-processing step of cropping a WSI into patches, as shown in Fig. 1, will remove most of the background patches. The resultant WSI patches, however, will lose their absolute positions." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.742, + 0.622, + 0.758 + ], + "angle": 0, + "content": "1.2. Challenges" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The above characteristics of WSI lead to the difficulty of directly employing the traditional mixup methods. We cannot simply resize two WSIs to have the same size for the sake of performing mixup. This is because all WSIs are scanned at the same magnification (e.g., \\(20\\mathrm{x}\\)), the physical meanings will be lost if they are rescaled casually. More importantly, due to loss of absolute positions among the patches after removing the WSI background, resizing patches actually do not solve this problem." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23936" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "Another commonly used techniques for data augmentation are based on cutting, including Cutout [14] and Cutmix [47]. The core of cutting aims at obtaining or removing parts of an images. However, the key difference between WSI images and natural images is that the main objects can occupy a major part of a natural image, but it is not the case in WSIs. For example, the tumor slide of Camelyon16 dataset [16] only has a small area of tumor (approximately \\(< 10\\%\\) of tissue area). Therefore, if a random cut is made, there is a non-negligible probability that the tumor slide will not contain any tumor patches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.424 + ], + "angle": 0, + "content": "To address these challenges, we propose a novel mixup method, called RankMix, for augmentation of whole slide images with diverse sizes and imbalanced categories. RankMix introduces the concepts of instance-level pseudo labeling and ranking in order to obtain meaningful WSI regions that can contribute to the WSI classification task. In order to further enhance model performance, two-stage training is proposed in that the first step is to train a stable score function by general MIL, and then the score function and mixup technique are jointly used in the second stage of training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.434, + 0.26, + 0.449 + ], + "angle": 0, + "content": "1.3. Our Contributions" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.457, + 0.4, + 0.471 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.482, + 0.47, + 0.588 + ], + "angle": 0, + "content": "- To our knowledge, MIL currently focuses on improving feature extraction and aggregator-based classification. It is relatively ignored in investigating weakly supervised learning from the perspective of data augmentation. Our proposed method can be applied to WSI classification problems and can be easily incorporated to existing MIL methods." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.598, + 0.47, + 0.643 + ], + "angle": 0, + "content": "- In contrast to the existing mixup methods that aim at mixing natural images of the same size, our method can mix images (e.g., WSIs) of different sizes." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.653, + 0.47, + 0.729 + ], + "angle": 0, + "content": "- Because of rare diseases and the difficulty of medical image collection, the WSI classification problem is apt to suffer from lack of training data and imbalance of categories. Our proposed method is demonstrated to be feasible in addressing these challenges." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.482, + 0.47, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.752, + 0.218, + 0.768 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.778, + 0.47, + 0.808 + ], + "angle": 0, + "content": "In this section, we briefly introduce the techniques that are relevant to our work." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.266, + 0.833 + ], + "angle": 0, + "content": "2.1. Data Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Data augmentation can improve the generalization and has been widely used in training neural networks. Mixup [48] fuses information from two images by convex combination. CutMix [47] inpaints the masking area (produced by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "random occlusion) with another image content at the same location. Recently, Part et al. [35] proposed how the majority can help the minority with re-balancing distribution of each sub-class. In addition to mixing in the pixel domain, Manifold Mixup [42] and PatchUp [18] proposed mixing the features of two images. Despite promising, the aforementioned methods are not presented for medical images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.893, + 0.531 + ], + "angle": 0, + "content": "For medical imaging, Galdran et al. [19] mixed two medical images sampled from different distributions, including instance-based sampling and class-based sampling. By increasing the sampling probability of the minority class, the class imbalance problem that usually occurs in medical imaging can be properly alleviated. In histopathology studies, the datasets often suffer from stain color variation because of different stain approaches, procedures, and slide scanner. To address this problem, Chang et al. [4] mixed two stain color matrices from stained images in order to increase the generalization of unseen colors. Chen et al. proposed Flow-Mixup [6] to regularize medical images with corrupted multi-labels because the annotations of medical images are costing and automatic annotation often provides corrupted labels. Gazda et al. [20] used the mixup technique to improve model performance for medical image segmentation. In ReMix [46], Yang et al. proposed using latent-space data augmentation to deal with WSI classification. However, ReMix only mixed instance prototypes of slides from the same class by \\( K \\)-Means while maintaining the original labels. From this perspective, ReMix acts like a kind of feature augmentation instead of general mixup." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.894, + 0.577 + ], + "angle": 0, + "content": "As shown in Tab. 1, although the previous researches on medical images are diverse, their data augmentations are not feasible for WSIs with large gaps in size." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.8, + 0.607 + ], + "angle": 0, + "content": "2.2. Multiple Instance Learning (MIL)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In recent MIL studies, the patches of a WSI are transformed into the features of fixed size by a feature extractor and then the patch features will be aggregated to get a final slide-level prediction. To leverage patch features, MIL-RNN [2] uses the recurrent neural network (RNN) [36] to encode position information. Because RNNs are apt to suffer from information loss over long distances, the follow-up works proposed attention-based MIL [25, 30] to calculate the contributions of instance-level features by learnable neural networks. Thanks to the success of Transformer [15, 41], self-attention based MIL methods [10, 28, 37] receive considerable attention in WSI classifications. Li et al. [28] proposed the non-local attention mechanism to calculate the relation between the critical feature and remaining features, but ignored the position relationship between patches. To address this problem, Shao et al. proposed TransMIL [37], which emphasizes the benefits of Pyramid Position Encoding Generator (PPEG), to encode spatial information by group convolution. Recently, Chikontwe et" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23937" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.089, + 0.861, + 0.255 + ], + "angle": 0, + "content": "
SettingImage typeMixup inputMixup outputLarge size gap between 2 inputs
Mixup [48]Natural imageImagevx
Manifold Mixup [42]Natural imageImage, Hidden statevx
Balanced-MixUp [19]Retinal image, Gastro-intestinal imageImagevx
Stain Mix-up [4]Patches of WSIStain matrixvx
Flow-Mixup [6]Chest X-ray, ECGHidden statevx
Mixup for KiTS [20]CT imageImagevx
ReMix [46]WSIInstance prototypexv
RankMix (Ours)WSIImage featurevv
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.265, + 0.895, + 0.294 + ], + "angle": 0, + "content": "Table 1. Comparisons among mixup methods. Our method, RankMix, deals with mixing of not only two images with large gap in size in the feature domain but also their labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.471, + 0.395 + ], + "angle": 0, + "content": "al. [10] proposed combining the critical feature [28] with PPEG [37], treating the tumor slides as a kind of out-of-distribution compared to normal slides, and re-calibrating the patch features of a slide according to the magnitudes of critical feature and slide label." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.406, + 0.429, + 0.423 + ], + "angle": 0, + "content": "2.3. Self-Training and Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Knowledge distillation [23,40] uses soft labels instead of hard labels (which are the maximum of class probabilities) from the teacher model to train the student model. The student model, aiming for model compression, is a smaller one to mimic the output of its teacher model. Instead of compressing models, Xie et al. [45] integrated self-training with knowledge distillation to improve the image classification task with unlabeled data. The authors propagated pseudo soft labels of unlabeled data from the teacher model to the student model. The researches [3,8,17] further used self-training and knowledge distillation to deal with the self-supervised learning problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.704 + ], + "angle": 0, + "content": "To sum up, our work, RankMix, has similar concepts with previous works, but we study how the general MIL model can be adopted as the teacher model. This makes RankMix act like a post-processing of traditional MIL, as illustrated in Fig. 2, and can be simply plugged into the exist approaches." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.718, + 0.205, + 0.736 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.469, + 0.79 + ], + "angle": 0, + "content": "In this section, we introduce the classification problem of WSIs, as well as some baseline techniques and notations, to make this paper self-contained." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.281, + 0.817 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.903 + ], + "angle": 0, + "content": "In the WSI classification problem, we have a series of WSIs \\( X = \\{X_{1},X_{2},\\ldots ,X_{n}\\} \\) and corresponding slide labels \\( Y = \\{Y_{1},Y_{2},\\dots ,Y_{n}\\} \\) as dataset \\( \\mathcal{D} = \\{(X_i,Y_i),\\quad i = 1,\\ldots ,n\\} \\). Our goal is to train an NN model based on dataset \\( \\mathcal{D} \\) for binary slide label \\( Y_{i}\\in \\{0,1\\} \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.501 + ], + "angle": 0, + "content": "prediction of an incoming WSI image \\( X_{i} \\). In MIL, a WSI can be treated as a bag (slide) containing the instances (patches) as \\( X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m(i)}\\} \\). Note that the WSI \\( X_{i} \\)'s have different numbers \\( m(i) \\)'s of instances and the instance-level labels \\( \\{y_{i,1}, y_{i,2}, \\ldots, y_{i,m(i)}\\} \\) are unknown. Without loss of generality, we will mostly use \\( m \\) in place of \\( m(i) \\) for notation simplicity. The slide label \\( Y_{i} \\) of a WSI \\( X_{i} \\) is defined to be negative (\\( Y_{i} = 0 \\)) when all instances in a bag are negative (without tumors), i.e., \\( y_{i,j} = 0 \\) for all \\( j \\). If at least one instance in \\( X_{i} \\) is positive (with tumor), its slide label will be positive (\\( Y_{i} = 1 \\)). The slide label of WSI \\( X_{i} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.508, + 0.892, + 0.549 + ], + "angle": 0, + "content": "\\[\nY _ {i} = \\left\\{ \\begin{array}{l} 0, \\text {i f f} \\sum y _ {i, j} = 0 \\\\ 1, \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.556, + 0.715, + 0.571 + ], + "angle": 0, + "content": "3.2. MIL as Baseline Model" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.579, + 0.892, + 0.657 + ], + "angle": 0, + "content": "In MIL, as shown in Fig. 1, the slide \\(X_{i}\\) will first be cut into many instances (patches) as \\(X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m}\\}\\) and then passed through an instance feature extractor \\(G_{\\theta}\\) to get the so-called features (embeddings) \\(H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}\\) via Eq. (2) as:" + }, + { + "type": "equation", + "bbox": [ + 0.639, + 0.663, + 0.891, + 0.681 + ], + "angle": 0, + "content": "\\[\nh _ {i, j} = G _ {\\theta} \\left(x _ {i, j}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.764 + ], + "angle": 0, + "content": "where \\(d\\) denotes the length of a feature vector and \\(m\\) denotes the number of features. As mentioned before, different WSIs will have different numbers of features but feature length \\(d\\) is the same. Finally, the aggregator will output a slide label prediction \\(\\hat{Y}_i\\) by Eq. (3) as:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.77, + 0.891, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\hat {Y} _ {i} = \\text {a g g r e g a t o r} \\left(h _ {i, 1}, h _ {i, 2}, \\dots , h _ {i, m}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we use DSMIL [28] and FRMIL [10] as the backbone models to represent SOTA permutation-variant and permutation-invariant MIL models, respectively, where the former only considers the relationship between each embedding and does not consider relative positions, and the latter uses the pooling multi-head self-attention (PMSA) module and positional encoding module (PEM) to fuse relative" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23938" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.18, + 0.087, + 0.782, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.363, + 0.271, + 0.605, + 0.285 + ], + "angle": 0, + "content": "Figure 1. The workflow of general MIL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.471, + 0.372 + ], + "angle": 0, + "content": "spatial information. We study the impact of RankMix on these two models and demonstrate that our method can be plugged into the current MIL methods. The general loss function of an MIL model can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.38, + 0.47, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {M I L}} = w _ {1} * \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {i}, Y _ {i}\\right) + \\sum_ {\\ell} w _ {\\ell} * \\mathcal {L} _ {\\ell}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.47, + 0.468 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{bag}\\) is a binary cross-entropy (BCE) loss, \\(\\mathcal{L}_{\\ell}\\) is other loss term that depends on different MIL models, and \\(w_{\\ell}\\)'s are the corresponding balance weights." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.476, + 0.166, + 0.492 + ], + "angle": 0, + "content": "3.3. Mixup" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.499, + 0.433, + 0.515 + ], + "angle": 0, + "content": "The mixup technique was first proposed in [48] as:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.526, + 0.469, + 0.542 + ], + "angle": 0, + "content": "\\[\nx _ {m x p} = \\lambda x _ {1} + (1 - \\lambda) x _ {2} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.552, + 0.469, + 0.568 + ], + "angle": 0, + "content": "\\[\ny _ {m x p} = \\lambda y _ {1} + (1 - \\lambda) y _ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.469, + 0.619 + ], + "angle": 0, + "content": "where the input sample \\( x_{i} \\) (\\( i = 1,2 \\)) is drawn from the training dataset, the label corresponding to the input sample \\( x_{i} \\) is \\( y_{i} \\), and \\( \\lambda \\in [0,1] \\) is sampled from \\( \\sim \\mathrm{Beta}(\\alpha, \\alpha) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.469, + 0.725 + ], + "angle": 0, + "content": "The main goal of mixup is to make linear combinations of inputs and outputs, respectively, and to ensure that the mapping of the mixed input and mixed output can maintain linear constraints. Therefore, the mixup technique is able to boost the generalization and robustness of an NN model. In addition, mixup can improve the performance of a model encountering the class imbalance problem [19]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.738, + 0.342, + 0.755 + ], + "angle": 0, + "content": "4. Proposed Method: RankMix" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.469, + 0.824 + ], + "angle": 0, + "content": "RankMix is mainly composed of pseudo labeling, ranking, mixing ranked features, and self-training, as illustrated in Fig. 2. We will describe the motivation of our method and the role of each component in RankMix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.199, + 0.847 + ], + "angle": 0, + "content": "4.1. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "A WSI is usually composed of normal tissue and special areas, as shown in Fig. 3a. Special areas can be tumors or defects, etc. If a pathologist obtains a WSI that contains" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.447 + ], + "angle": 0, + "content": "tumors, his/her expertise is sufficient to make a correct decision of determining whether there is a tumor inside it. Based on this premise, even a pathologist obtains a partial image of the same WSI that contains most of the tumor areas, as shown in Fig. 3b, it suffices to determine that the image contains tumors. By contrast, if an entire WSI or a partial WSI contains only normal tissues, it can be easily determined that the WSI is normal, as shown in Figs. 3c and 3d, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Therefore, the hypothesis here is that cropping a WSI into patches will not affect tumor detection, not to mention the fact that dealing with the entire WSI as a whole is indeed impractical when computing power and memory consumption are taken into consideration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Moreover, based on the problem introduced in Sec. 1.2, it is easy to lose physical meaning from picking patches and resizing them to have the same size. If we can select the areas of arbitrary sizes to represent the original slide, we can prepare two partial but representative slides of the same size for use in the mixup technologies. Nevertheless, the prerequisite is based on the fact that we can know which parts of the slide are sufficient to represent the original slide. This conflicts with the scenario that we only have the label of entire slide and do not have the instance-level labels corresponding to patches in the slide, as described in Sec. 3.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.81 + ], + "angle": 0, + "content": "In view of the above challenges, we will explain in following subsections how to pick out fragments that are sufficient to represent a slide without instance-level labels. We will demonstrate how to get the pseudo instance-level labels in Sec. 4.2, how to select representative features in Sec. 4.3, and how to combine representative features with a mixup mechanism in Sec. 4.4. The module of pseudo labeling and ranking in RankMix (Fig. 2) is further detailed in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.665, + 0.833 + ], + "angle": 0, + "content": "4.2. Pseudo Labeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.839, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given \\(H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}\\) from a WSI \\(X_{i}\\) by Eq. (2), the pseudo patch-level labels will be predicted to determine which patches are useful for mixup later. Specifically, if we have a score function \\(f \\in \\mathbb{R}^{d \\times 1}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23939" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.881, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.416 + ], + "angle": 0, + "content": "Figure 2. The flowchart of MIL with RankMix. We train the general MIL model with the training set \\( X \\) in the first stage (Top), and then the score function \\( f \\) obtained in the first stage is used to make pseudo labels for \\( \\{X_{a}, X_{b}\\} \\) and train the MIL model with mixup mechanism in the second stage (Bottom). The dashed arrows indicate the patch scores that may be used by the aggregator depending on the MIL method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.441, + 0.415, + 0.457 + ], + "angle": 0, + "content": "implemented by a multilayer perceptron (MLP) as:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.464, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i, j} = \\operatorname {s c o r e} _ {i, j} = f \\left(h _ {i, j}\\right), \\quad \\forall i = 1, \\dots , n \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.488, + 0.336, + 0.503 + ], + "angle": 0, + "content": "we can define a loss function \\(\\mathcal{L}_{max}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.511, + 0.469, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\max } = \\operatorname {B C E} \\left(\\hat {y} _ {i, j ^ {*}}, Y _ {i}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.469, + 0.564 + ], + "angle": 0, + "content": "where \\(j^{*} = \\arg \\max_{j}(\\hat{y}_{i,j})\\) and \\(Y_{i}\\) is obtained from Eq. (1). Note that the score function here can be calculated indi" + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.581, + 0.273, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.675, + 0.272, + 0.698 + ], + "angle": 0, + "content": "(a) Example of tumor slide from Camelyon16." + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.581, + 0.44, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.675, + 0.439, + 0.698 + ], + "angle": 0, + "content": "(b) Partial slide (in red bounding box) selected from (a)." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.7, + 0.274, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.805, + 0.273, + 0.829 + ], + "angle": 0, + "content": "(c) Example of normal slide from Camelyon16." + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.699, + 0.44, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.805, + 0.439, + 0.83 + ], + "angle": 0, + "content": "(d) Partial slide (in red bounding box) selected from (c)." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.897 + ], + "angle": 0, + "content": "Figure 3. Illustration of judging if a whole slide or partial slide contains tumors or not. The green annotation indicates the tumor regions and red bounding box indicates the partial region of WSI that is considered to have the same label as the original WSI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.548 + ], + "angle": 0, + "content": "vidually to deal with the multi-class classification problems (e.g., TCGA-Lung dataset in Sec. 5.1) and can be replaced by any similar mechanisms of MIL, which calculates the importance of each patch to yield a final slide-level prediction (e.g., attention mechanism [25, 28, 30] or the distance between clusters [9, 38, 44]). So far, we can get the class probability of every patch in a WSI by the score function \\( f \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.562, + 0.604, + 0.579 + ], + "angle": 0, + "content": "4.3. Ranking" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.68 + ], + "angle": 0, + "content": "After obtaining the score function \\( f \\), we already have the basic ability to achieve the motivation mentioned in Sec. 4.1. If we want to obtain a representative portion that can represent the original WSI, we need to score each feature \\( \\{\\hat{y}_{i,1},\\dots ,\\hat{y}_{i,m}\\} \\in \\mathbb{R}^{m\\times 1} \\) in the WSI and then sort the patch scores as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.695, + 0.892, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Z _ {i} = \\left\\{z _ {i, 1}, z _ {i, 2}, \\dots , z _ {i, m} \\right\\} \\\\ \\text {s . t .} \\hat {y} _ {i, z _ {i, 1}} > \\hat {y} _ {i, z _ {i, 2}} > \\dots > \\hat {y} _ {i, z _ {i, m}} \\quad \\forall i = 1, \\dots , n. \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.744, + 0.892, + 0.789 + ], + "angle": 0, + "content": "According to the number \\(k\\) (\\(k\\) is an arbitrary positive integer) of features we need, we can obtain the desired features \\(\\bar{H}_i\\in \\mathbb{R}^{k\\times d}\\) from the original features \\(H_{i}\\in \\mathbb{R}^{m\\times d}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.805, + 0.892, + 0.839 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {H} _ {i} = \\left\\{h _ {i, z _ {i, 1}}, h _ {i, z _ {i, 2}}, \\dots , h _ {i, z _ {i, k}} \\right\\}. \\tag {10} \\\\ \\text {f o r} k \\leq m, \\forall i = 1, \\dots , n \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Finally, in order to maintain the relative position information among patches, the features in \\(\\bar{H}_i\\) are rearranged in the original order to get the final representative features" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23940" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.175, + 0.087, + 0.805, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.28, + 0.253, + 0.687, + 0.267 + ], + "angle": 0, + "content": "Figure 4. Illustration of the pseudo labeling and ranking mechanism." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.293, + 0.182, + 0.311 + ], + "angle": 0, + "content": "\\(H_{i}^{\\prime}\\in \\mathbb{R}^{k\\times d}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.317, + 0.469, + 0.342 + ], + "angle": 0, + "content": "\\[\nH _ {i} ^ {\\prime} = \\left\\{h _ {i, z _ {i, 1} ^ {\\prime}}, h _ {i, z _ {i, 2} ^ {\\prime}}, \\dots , h _ {i, z _ {i, k} ^ {\\prime}} \\right\\}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.34, + 0.414, + 0.358 + ], + "angle": 0, + "content": "\\[\ns. t. z _ {i, 1} ^ {\\prime} < z _ {i, 2} ^ {\\prime} < \\dots < z _ {i, k} ^ {\\prime} \\quad \\forall i = 1, \\dots , n\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.469, + 0.396 + ], + "angle": 0, + "content": "where \\(H_{i}^{\\prime}\\) indicates the \\(k\\) features selected from the original \\(i^{th}\\) slide with the order preserved." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.403, + 0.319, + 0.42 + ], + "angle": 0, + "content": "4.4. Mixup in Ranked Features" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.427, + 0.469, + 0.472 + ], + "angle": 0, + "content": "According to Eq. (5) and Eq. (6), we can formulate the mixup of features from two examples, \\((X_{a},Y_{a})\\) and \\((X_{b},Y_{b})\\), sampled from the dataset \\(\\mathcal{D}\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.48, + 0.469, + 0.498 + ], + "angle": 0, + "content": "\\[\nH _ {m x p} = \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime} \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.505, + 0.469, + 0.521 + ], + "angle": 0, + "content": "\\[\nY _ {m x p} = \\lambda Y _ {a} + (1 - \\lambda) Y _ {b}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.525, + 0.469, + 0.614 + ], + "angle": 0, + "content": "where \\(H_{a}^{\\prime}\\in \\mathbb{R}^{k\\times d}\\) and \\(H_{b}^{\\prime}\\in \\mathbb{R}^{k\\times d}\\) are obtained from \\(H_{a}\\in \\mathbb{R}^{m(a)\\times d}\\) and \\(H_{b}\\in \\mathbb{R}^{m(b)\\times d}\\), respectively, by Eq. (9)~Eq. (11), and \\(m(a)\\) and \\(m(b)\\) denote the numbers of features obtained from \\(X_{a}\\) and \\(X_{b}\\), respectively. Different from the existing mixup techniques, we conduct mixup in ranked features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.624, + 0.319, + 0.639 + ], + "angle": 0, + "content": "4.5. MIL Model with RankMix" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.469, + 0.678 + ], + "angle": 0, + "content": "As described in Sec. 3.2 and Sec. 4.2, RankMix can be applied to MIL models with the total loss being defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.697, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = w _ {1} \\mathcal {L} _ {m a x} \\left(\\hat {y} _ {m x p, j ^ {*}}, Y _ {m x p}\\right) + w _ {2} \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {m x p}, Y _ {m x p}\\right) \\\\ + \\sum_ {\\ell} w _ {\\ell} \\mathcal {L} _ {\\ell}, \\tag {14} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.825 + ], + "angle": 0, + "content": "where the first term comes from Eq. (8) and the remaining terms come from Eq. (4). So far, we have explained how to accomplish the middle component of RankMix in MIL in Fig. 2, i.e., the first stage of training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.42, + 0.85 + ], + "angle": 0, + "content": "4.6. Self-Training: Second Stage of Training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "WSI classification faces the tough problem that each WSI is only given a slide-level label; that is, tens of thousands of patches correspond to one label. This kind of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.892, + 0.415 + ], + "angle": 0, + "content": "weakly supervised learning is more difficult to train than supervised learning. If the RankMix proposed so far is used, unstable training will be encountered. However, if the score function is more reliable (i.e., can distinguish patch labels) at the beginning, then RankMix is found to achieve better results. We can imagine that the score function acts like expert annotations, and higher quality annotations will naturally result in better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.478 + ], + "angle": 0, + "content": "Inspired by self-training [40,45] and BERT-based model [13, 27, 29], we design a score function by learning from a pre-trained task in advance (i.e., can output the class probability distribution of a patch) as:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.51, + 0.89, + 0.541 + ], + "angle": 0, + "content": "\\[\np \\left(\\hat {Y} _ {i} \\mid H _ {i}\\right) = \\text {a g g r e g a t o r} \\left(H _ {i}\\right) = p \\left(\\hat {Y} _ {i} \\mid h _ {i, 1}, \\dots , h _ {i, m}\\right). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Then, by using the concept of self-training, the stronger model is used as a teacher to extract the area that can represent the original WSI via score function for the student model to mixup ranked features as:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.632, + 0.891, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {Y} _ {m x p} = p \\left(Y _ {m x p} \\mid H _ {m x p}\\right) = p \\left(Y _ {m x p} \\mid h _ {m x p, 1}, \\dots , h _ {m x p, k}\\right) \\\\ = p \\left(Y _ {m x p} | \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right) \\\\ = \\text {a g g r e g a t o r} \\left(\\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right). \\tag {16} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.794 + ], + "angle": 0, + "content": "From the perspective of BERT-based models, we use the teacher model to learn the WSI classification problem (also known as the pretext task) as pretraining, and treat the mixup of ranked features as the downstream task to further improve the performance. Please see Fig. 2 for the illustration of two-stage training procedure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.734, + 0.83 + ], + "angle": 0, + "content": "5. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we will describe the datasets used for experiments in Sec. 5.1, experimental setting and performance metrics in Sec. 5.2, main results in Sec. 5.3, and ablation studies in Sec. 8.1 (Appendix)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23941" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.137, + 0.089, + 0.835, + 0.238 + ], + "angle": 0, + "content": "
Method/DatasetCamelyon16WSI-usabilityTCGA-Lung
ACCAUCAUPRCACCAUCAUPRCACCAUCAUPRC
DSMIL [28]86.82%93.32%92.68%76.11%86.60%24.51%93.81%97.89%97.75%
+ ReMix [46]82.17%86.89%83.86%83.19%85.83%25.59%94.29%97.62%97.29%
+ RankMix w/o self-training87.60%92.07%92.43%90.27%87.07%25.66%94.29%98.00%97.76%
+ RankMix89.92%93.47%92.74%90.27%88.16%28.41%94.29%98.04%97.79%
FRMIL [10]89.15%94.57%93.66%83.19%87.69%45.99%90.95%95.38%94.96%
+ ReMix [46]82.59%87.29%87.35%89.25%80.63%33.09%92.22%96.99%97.04%
+ RankMix w/o self-training90.70%94.11%93.68%80.53%84.27%38.55%93.33%95.84%97.01%
+ RankMix91.47%94.59%93.99%93.81%93.61%47.65%93.33%97.00%97.04%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.182, + 0.248, + 0.786, + 0.262 + ], + "angle": 0, + "content": "Table 2. Comparison of WSI classification between RankMix and vanilla models under three datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.288, + 0.18, + 0.303 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.469, + 0.402 + ], + "angle": 0, + "content": "We introduce the WSI datasets used for experiments here, and a pre-processing setting was adopted to extract patches from each WSI. Each WSI was cropped into different numbers of \\(224 \\times 224\\) patches at \\(20\\mathrm{x}\\) magnification without overlapping. We follow [10,28] to discard the background patches with tissue entropy less than \\(15\\%\\) of a WSI." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.469, + 0.568 + ], + "angle": 0, + "content": "Camelyon16 [16] is a public and well-known dataset proposed for metastasis detection in breast cancer. The dataset contains 270 training slides and 130 testing slides, and roughly has 4.1 million patches at \\(20\\mathrm{x}\\) magnification with the maximum of 44000 patches per WSI and a minimum of 1200 patches per WSI in our pre-processing setting. If a WSI contains at least one tumor region, it is regarded as a positive slide. On the contrary, if the entire area of a WSI is normal, it is negative. In Camelyon16, the tumor area only accounts for approximately less than \\(10\\%\\) of the tissue area in the positive slide." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.734 + ], + "angle": 0, + "content": "TCGA-Lung is a public dataset that has two types of lung cancer, Lung Adenocarcinoma (TCGA-LUAD) and Lung Squamous Cell Carcinoma (TCGA-LUSC), from the Caner Genome Atlas (TCGA). Please refer to https://pubmed.ncbi.nlm.nih.gov/25691825/ for details. There are in total 1046 diagnostic WSIs, including 534 TCGA-LUAD and 512 TCGA-LUSC, were split into 836 training slides and 210 testing slides. After pre-processing, TCGA-Lung roughly has a minimum of 50 patches per slide and a maximum of 12700 patches per slide, with a total of 3.2 million patches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "WSI-usability is a private dataset used for distinguishing whether a WSI is usable or not. The purpose of this dataset is used for evaluating automatic quality control (QC). In order to have sufficient practicality, two pathologist experts each annotated 250 WSIs from TCGA, of which 50 WSIs were redundant, resulting in 450 WSIs in total. If it is a bad (labeled as positive) slide, it means that the WSI is not usable; otherwise, it is a good WSI and annotated as a negative slide. WSI-usability has only 23 positive slides, so it possesses a severe class imbalance problem. After preprocessing, WSI-usability roughly has a minimum of 700" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.319 + ], + "angle": 0, + "content": "patches per slide and a maximum of 120000 patches per slide, with a total of 5.7 million patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Summing up the above, the adopted datasets cover the imbalance/balanced classes, unbalanced/balanced bags, and single/multiple-class problem. Among them, WSI-usability has majority and minority categories with a huge gap, which indicates the rare diseases and other costly data. For the positive slides in Camelyon16, tumors occupy quite smaller areas than normal tissues, while the negative slide is all filled with normal tissues. Different from the other two datasets, TCGA-Lung has two types of positive slides, namely TCGA-LUSD and TCGA-LUSC, leading to a multi-class classification problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.874, + 0.514 + ], + "angle": 0, + "content": "5.2. Experimental Setup and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.643 + ], + "angle": 0, + "content": "ResNet18 [22] was adopted as our backbone model that was trained by SimCLR [7] and Adam optimizer to obtain feature extractor \\( G_{\\theta} \\) with a mini-batch size of 512, learning rate of \\( 1e - 4 \\), and weight decay of \\( 1e - 5 \\). For Camelyon16, we used the weights of ResNet18 trained by Lee et al. [28], as described in [10]. Then, the embeddings \\( H_{i} \\in \\mathbb{R}^{m(i) \\times 512} \\) of a WSI \\( X_{i} \\) were obtained from the global average pooling layer of feature extractor \\( G_{\\theta} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.763 + ], + "angle": 0, + "content": "For training aggregator, we used the Adam optimizer for 200 epochs with the mini-batch size of 1 (bag), learning rate of \\(2e - 4\\), and weight decay of \\(5e - 3\\). Note that the minibatch for performing mixup of ranked features was 2, where the sampling methods of DSMIL and FRMIL followed [19] and [10], respectively. The number \\(k\\) of features used in RankMix was set to \\(\\min(m(a), m(b))\\) for two WSIs \\(X_a\\) and \\(X_b\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.884 + ], + "angle": 0, + "content": "For two-stage training, we trained teacher models by the general MIL (i.e., DSMIL and FR-MIL). Then, the teacher models were used to guide the training of student models by RankMix. The structures of both the teacher model and student model are the same, which can be considered as a kind of self-distillation mechanism. The temperature parameter \\(\\tau\\) commonly used in knowledge distillation was set to 1.0 (see Eq. (20) later)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The classification performance was evaluated in terms of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23942" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.203, + 0.089, + 0.768, + 0.289 + ], + "angle": 0, + "content": "
Method/DatasetCamelyon16WSI-UsabilityTCGA-Lung
AccuracyAUCAccuracyAUCAccuracyAUC
DSMIL [28]86.82%93.32%76.11%86.60%93.81%97.89%
DSMIL + Direct Mixup84.50%90.51%89.38%71.18%94.29%98.03%
DSMIL + Shrink Mixup86.05%92.42%88.50%69.94%93.81%97.95%
DSMIL + Duplicate Mixup84.50%91.96%89.38%72.43%93.81%97.99%
DSMIL + Random Mixup87.60%91.89%88.50%83.33%94.29%97.99%
DSMIL + RankMix89.92%93.47%90.27%88.16%94.29%98.04%
FRMIL [10]89.15%94.57%83.19%87.69%90.95%95.38%
FRMIL + Direct Mixup88.37%92.50%59.29%80.37%92.38%95.96%
FRMIL + Shrink Mixup89.92%93.16%68.14%57.09%92.86%96.88%
FRMIL + Duplicate Mixup87.60%92.78%86.73%74.77%92.38%96.73%
FRMIL + Random Mixup90.70%94.23%77.88%80.69%93.33%96.98%
FRMIL + RankMix91.47%94.59%93.81%93.61%93.33%97.00%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.257, + 0.299, + 0.713, + 0.313 + ], + "angle": 0, + "content": "Table 3. Comparisons between RankMix and four custom mixup techniques." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.34, + 0.38, + 0.355 + ], + "angle": 0, + "content": "the accuracy and area under the curve (AUC)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.363, + 0.216, + 0.377 + ], + "angle": 0, + "content": "5.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.597 + ], + "angle": 0, + "content": "First, we applied the proposed method, RankMix, to two baseline models, DSMIL [28] and FRMIL [10], and compared the performance with the vanilla models in Tab. 2. We can observe that self-training indeed boosts the overall model performance, as described in Sec. 4.6. Without self-training (i.e., mixup in the model without being derived from a teacher model), RankMix can sometimes achieve slightly better results, but as the model and dataset vary, it can be seen that the performance is slightly degraded in few cases. On the contrary, when self-training is introduced, the performance can be improved further. A recent work, ReMix [46], which is a SOTA augmentation method in WSI, was included for comparison. It can be found that RankMix outperforms ReMix remarkably." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Second, we compared our method with the general mixup techniques under different custom settings in Tab. 3. This is because the existing mixup researches, to our knowledge, were conducted on the same feature number, they cannot be readily employed to be compared with our method under the scenario that two features of different numbers were mixed. Here, we discuss four situations for mixing up two WSIs \\((H_{a}\\) and \\(H_{b})\\) with different numbers \\((m(a)\\) and \\(m(b))\\) of features in the following." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.734, + 0.47, + 0.795 + ], + "angle": 0, + "content": "1) Direct Mixup: Perform mixup directly regardless of feature numbers \\((m(a)\\) and \\(m(b))\\), where the feature with a smaller number is padded with zeros. So, the feature number after mixing is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.803, + 0.469, + 0.819 + ], + "angle": 0, + "content": "\\[\nk _ {d} = \\max (m (a), m (b)). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.827, + 0.469, + 0.857 + ], + "angle": 0, + "content": "2) Shrink Mixup: Extract the same number \\( k_{s} \\) of features for mixing up by" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.864, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\nk _ {s} = \\left\\{ \\begin{array}{l} m (b), \\text {i f f} m (a) > m (b) \\\\ m (a), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.34, + 0.892, + 0.383 + ], + "angle": 0, + "content": "3) Duplicate Mixup: Duplicate the feature with a smaller number to have the same size \\( k_{du} \\) as the larger feature as:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.382, + 0.891, + 0.422 + ], + "angle": 0, + "content": "\\[\nk _ {d u} = \\left\\{ \\begin{array}{l} m (a), \\text {i f f} m (a) > m (b) \\\\ m (b), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.427, + 0.891, + 0.457 + ], + "angle": 0, + "content": "4) Random Mixup: By randomly performing both the duplicate and shrink mixups." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.517 + ], + "angle": 0, + "content": "Compared with the above four straightforward cases, it can be seen from Tab. 3 that RankMix is a sophisticated design according to the characteristics of WSI, described in Sec. 1.2, and generally performs better than others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Finally, we conduct ablation studies to further evaluate RankMix in two aspects. On the one hand, we examine how the score functions learned under different pre-trained models, as described in Sec. 4.6, affect RankMix. On the other hand, we examine how different knowledge transfer techniques affect the student model performance in WSI classification. Please refer to Sec. 8.1 in Appendix for details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.637, + 0.619, + 0.652 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.798 + ], + "angle": 0, + "content": "In this work, we investigate weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories. A new data augmentation method, RankMix, of is proposed to mix ranked features in a pair of WSIs with different sizes. RankMix is composed of pseudo labeling and ranking for extracting key WSI regions, and two-stage training for boosting stable training and model performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.812, + 0.681, + 0.829 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.837, + 0.892, + 0.881 + ], + "angle": 0, + "content": "This work was supported in part by the Ministry of Science and Technology of Taiwan, ROC, under Grant MOST 110-2634-F-006-022." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23943" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.469, + 0.16 + ], + "angle": 0, + "content": "[1] Sugata Banerji and Sushmita Mitra. Deep learning in histopathology: A review. 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In International Conference on Learning Representations, 2018. 1, 2, 3, 4" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.896 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23945" + } + ] +] \ No newline at end of file diff --git a/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_origin.pdf b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..209b095f6793c6fec22fdc2c0a928c9e2faea4e9 --- /dev/null +++ b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/9892a862-63a2-48f4-8e5a-1651be4bb51a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c192efd605aafc2fc370332c192966d0f1c17e20cb73775947702e6ee4dda4ca +size 9127340 diff --git a/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/full.md b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/full.md new file mode 100644 index 0000000000000000000000000000000000000000..40d2934b502dc18e2d317f0119fd9cb8c77db26f --- /dev/null +++ b/2023/RankMix_ Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images With Diverse Sizes and Imbalanced Categories/full.md @@ -0,0 +1,388 @@ +# RankMix: Data Augmentation for Weakly Supervised Learning of Classifying Whole Slide Images with Diverse Sizes and Imbalanced Categories + +Yuan-Chih Chen +IIS, Academia Sinica, Taiwan, ROC +willpower057@gmail.com + +Chun-Shien Lu +IIS, Academia Sinica, Taiwan, ROC +lcs@iis.sinica.edu.tw + +# Abstract + +Whole Slide Images (WSIs) are usually gigapixel in size and lack pixel-level annotations. The WSI datasets are also imbalanced in categories. These unique characteristics, significantly different from the ones in natural images, pose the challenge of classifying WSI images as a kind of weakly supervise learning problems. In this study, we propose, RankMix, a data augmentation method of mixing ranked features in a pair of WSIs. RankMix introduces the concepts of pseudo labeling and ranking in order to extract key WSI regions in contributing to the WSI classification task. A two-stage training is further proposed to boost stable training and model performance. + +To our knowledge, the study of weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories is relatively unexplored. + +# 1. Introduction + +# 1.1. Background + +Natural image processing tasks, including image classification and object detection, have been widely solved using deep learning models and obtain astounding results. In this study, we investigate how medical imaging can also benefit from deep learning with focus on whole slide images (WSIs). WSI scanning is commonly used in disease diagnosis [12, 34]. The demand of computer aided assessment makes deep learning widely adopted in this field [1]. Because WSI is a gigapixel image and lacks pixel-level annotations, multiple instance learning (MIL) [31, 32] is an exact solution to this weakly supervised learning problem [2]. In MIL, a WSI is often cropped into tens of thousands of patches and then an aggregator will make a prediction based on integrating these patches. Most recent works [5,9,10,25,28,30,37,38,44] focus on aggregator architecture design and improving feature extraction of the patches. + +However, because WSI is difficult to collect and share, we explore the possibility of data augmentation in WSI classification to increase training samples and mitigate the problem of class imbalance [19, 26, 33, 48] that WSI may have due to rare diseases (versus common diseases). In addition, patch feature extractor is often trained by self-supervised learning [24, 28] or comes from pre-trained models (such as pre-trained in ImageNet [30, 37] or WSI datasets [5, 11]). Therefore, for universality and portability, our work will focus on studying the feature domain instead of pixel domain of patches. + +Traditionally, mixup methods [18, 48] are employed to mix photos of the same aspect ratio or vectors of the same dimension. Nevertheless, this is not the case for WSI as WSI intrinsically has a different number of patches, ranging from hundreds to hundred of thousands. This is because the generation of a WSI, caused by the tissue placement and the tissue size, will make WSIs of varying aspect ratios and sizes. + +In addition, because a WSI tends to be a very large size (equivalent to tens of thousands of $224 \times 224$ patches or even larger) and the background often occupies a large part, it is better to use data pre-processing to remove unimportant background parts in order to save computation time and avoid possible unnecessary information [21, 39] (such as noise and artifacts). That is, the pre-processing step of cropping a WSI into patches, as shown in Fig. 1, will remove most of the background patches. The resultant WSI patches, however, will lose their absolute positions. + +# 1.2. Challenges + +The above characteristics of WSI lead to the difficulty of directly employing the traditional mixup methods. We cannot simply resize two WSIs to have the same size for the sake of performing mixup. This is because all WSIs are scanned at the same magnification (e.g., $20\mathrm{x}$ ), the physical meanings will be lost if they are rescaled casually. More importantly, due to loss of absolute positions among the patches after removing the WSI background, resizing patches actually do not solve this problem. + +Another commonly used techniques for data augmentation are based on cutting, including Cutout [14] and Cutmix [47]. The core of cutting aims at obtaining or removing parts of an images. However, the key difference between WSI images and natural images is that the main objects can occupy a major part of a natural image, but it is not the case in WSIs. For example, the tumor slide of Camelyon16 dataset [16] only has a small area of tumor (approximately $< 10\%$ of tissue area). Therefore, if a random cut is made, there is a non-negligible probability that the tumor slide will not contain any tumor patches. + +To address these challenges, we propose a novel mixup method, called RankMix, for augmentation of whole slide images with diverse sizes and imbalanced categories. RankMix introduces the concepts of instance-level pseudo labeling and ranking in order to obtain meaningful WSI regions that can contribute to the WSI classification task. In order to further enhance model performance, two-stage training is proposed in that the first step is to train a stable score function by general MIL, and then the score function and mixup technique are jointly used in the second stage of training. + +# 1.3. Our Contributions + +Our contributions are summarized as follows: + +- To our knowledge, MIL currently focuses on improving feature extraction and aggregator-based classification. It is relatively ignored in investigating weakly supervised learning from the perspective of data augmentation. Our proposed method can be applied to WSI classification problems and can be easily incorporated to existing MIL methods. +- In contrast to the existing mixup methods that aim at mixing natural images of the same size, our method can mix images (e.g., WSIs) of different sizes. +- Because of rare diseases and the difficulty of medical image collection, the WSI classification problem is apt to suffer from lack of training data and imbalance of categories. Our proposed method is demonstrated to be feasible in addressing these challenges. + +# 2. Related Work + +In this section, we briefly introduce the techniques that are relevant to our work. + +# 2.1. Data Augmentation + +Data augmentation can improve the generalization and has been widely used in training neural networks. Mixup [48] fuses information from two images by convex combination. CutMix [47] inpaints the masking area (produced by + +random occlusion) with another image content at the same location. Recently, Part et al. [35] proposed how the majority can help the minority with re-balancing distribution of each sub-class. In addition to mixing in the pixel domain, Manifold Mixup [42] and PatchUp [18] proposed mixing the features of two images. Despite promising, the aforementioned methods are not presented for medical images. + +For medical imaging, Galdran et al. [19] mixed two medical images sampled from different distributions, including instance-based sampling and class-based sampling. By increasing the sampling probability of the minority class, the class imbalance problem that usually occurs in medical imaging can be properly alleviated. In histopathology studies, the datasets often suffer from stain color variation because of different stain approaches, procedures, and slide scanner. To address this problem, Chang et al. [4] mixed two stain color matrices from stained images in order to increase the generalization of unseen colors. Chen et al. proposed Flow-Mixup [6] to regularize medical images with corrupted multi-labels because the annotations of medical images are costing and automatic annotation often provides corrupted labels. Gazda et al. [20] used the mixup technique to improve model performance for medical image segmentation. In ReMix [46], Yang et al. proposed using latent-space data augmentation to deal with WSI classification. However, ReMix only mixed instance prototypes of slides from the same class by $K$ -Means while maintaining the original labels. From this perspective, ReMix acts like a kind of feature augmentation instead of general mixup. + +As shown in Tab. 1, although the previous researches on medical images are diverse, their data augmentations are not feasible for WSIs with large gaps in size. + +# 2.2. Multiple Instance Learning (MIL) + +In recent MIL studies, the patches of a WSI are transformed into the features of fixed size by a feature extractor and then the patch features will be aggregated to get a final slide-level prediction. To leverage patch features, MIL-RNN [2] uses the recurrent neural network (RNN) [36] to encode position information. Because RNNs are apt to suffer from information loss over long distances, the follow-up works proposed attention-based MIL [25, 30] to calculate the contributions of instance-level features by learnable neural networks. Thanks to the success of Transformer [15, 41], self-attention based MIL methods [10, 28, 37] receive considerable attention in WSI classifications. Li et al. [28] proposed the non-local attention mechanism to calculate the relation between the critical feature and remaining features, but ignored the position relationship between patches. To address this problem, Shao et al. proposed TransMIL [37], which emphasizes the benefits of Pyramid Position Encoding Generator (PPEG), to encode spatial information by group convolution. Recently, Chikontwe et + +
SettingImage typeMixup inputMixup outputLarge size gap between 2 inputs
Mixup [48]Natural imageImagevx
Manifold Mixup [42]Natural imageImage, Hidden statevx
Balanced-MixUp [19]Retinal image, Gastro-intestinal imageImagevx
Stain Mix-up [4]Patches of WSIStain matrixvx
Flow-Mixup [6]Chest X-ray, ECGHidden statevx
Mixup for KiTS [20]CT imageImagevx
ReMix [46]WSIInstance prototypexv
RankMix (Ours)WSIImage featurevv
+ +Table 1. Comparisons among mixup methods. Our method, RankMix, deals with mixing of not only two images with large gap in size in the feature domain but also their labels. + +al. [10] proposed combining the critical feature [28] with PPEG [37], treating the tumor slides as a kind of out-of-distribution compared to normal slides, and re-calibrating the patch features of a slide according to the magnitudes of critical feature and slide label. + +# 2.3. Self-Training and Knowledge Distillation + +Knowledge distillation [23,40] uses soft labels instead of hard labels (which are the maximum of class probabilities) from the teacher model to train the student model. The student model, aiming for model compression, is a smaller one to mimic the output of its teacher model. Instead of compressing models, Xie et al. [45] integrated self-training with knowledge distillation to improve the image classification task with unlabeled data. The authors propagated pseudo soft labels of unlabeled data from the teacher model to the student model. The researches [3,8,17] further used self-training and knowledge distillation to deal with the self-supervised learning problem. + +To sum up, our work, RankMix, has similar concepts with previous works, but we study how the general MIL model can be adopted as the teacher model. This makes RankMix act like a post-processing of traditional MIL, as illustrated in Fig. 2, and can be simply plugged into the exist approaches. + +# 3. Preliminary + +In this section, we introduce the classification problem of WSIs, as well as some baseline techniques and notations, to make this paper self-contained. + +# 3.1. Problem Formulation + +In the WSI classification problem, we have a series of WSIs $X = \{X_{1},X_{2},\ldots ,X_{n}\}$ and corresponding slide labels $Y = \{Y_{1},Y_{2},\dots ,Y_{n}\}$ as dataset $\mathcal{D} = \{(X_i,Y_i),\quad i = 1,\ldots ,n\}$ . Our goal is to train an NN model based on dataset $\mathcal{D}$ for binary slide label $Y_{i}\in \{0,1\}$ + +prediction of an incoming WSI image $X_{i}$ . In MIL, a WSI can be treated as a bag (slide) containing the instances (patches) as $X_{i} = \{x_{i,1}, x_{i,2}, \ldots, x_{i,m(i)}\}$ . Note that the WSI $X_{i}$ 's have different numbers $m(i)$ 's of instances and the instance-level labels $\{y_{i,1}, y_{i,2}, \ldots, y_{i,m(i)}\}$ are unknown. Without loss of generality, we will mostly use $m$ in place of $m(i)$ for notation simplicity. The slide label $Y_{i}$ of a WSI $X_{i}$ is defined to be negative ( $Y_{i} = 0$ ) when all instances in a bag are negative (without tumors), i.e., $y_{i,j} = 0$ for all $j$ . If at least one instance in $X_{i}$ is positive (with tumor), its slide label will be positive ( $Y_{i} = 1$ ). The slide label of WSI $X_{i}$ is defined as: + +$$ +Y _ {i} = \left\{ \begin{array}{l} 0, \text {i f f} \sum y _ {i, j} = 0 \\ 1, \text {o t h e r w i s e} \end{array} . \right. \tag {1} +$$ + +# 3.2. MIL as Baseline Model + +In MIL, as shown in Fig. 1, the slide $X_{i}$ will first be cut into many instances (patches) as $X_{i} = \{x_{i,1}, x_{i,2}, \ldots, x_{i,m}\}$ and then passed through an instance feature extractor $G_{\theta}$ to get the so-called features (embeddings) $H_{i} = \{h_{i,1}, h_{i,2}, \ldots, h_{i,m}\} \in \mathbb{R}^{m \times d}$ via Eq. (2) as: + +$$ +h _ {i, j} = G _ {\theta} \left(x _ {i, j}\right), \tag {2} +$$ + +where $d$ denotes the length of a feature vector and $m$ denotes the number of features. As mentioned before, different WSIs will have different numbers of features but feature length $d$ is the same. Finally, the aggregator will output a slide label prediction $\hat{Y}_i$ by Eq. (3) as: + +$$ +\hat {Y} _ {i} = \text {a g g r e g a t o r} \left(h _ {i, 1}, h _ {i, 2}, \dots , h _ {i, m}\right). \tag {3} +$$ + +In this work, we use DSMIL [28] and FRMIL [10] as the backbone models to represent SOTA permutation-variant and permutation-invariant MIL models, respectively, where the former only considers the relationship between each embedding and does not consider relative positions, and the latter uses the pooling multi-head self-attention (PMSA) module and positional encoding module (PEM) to fuse relative + +![](images/7e5abbd55991213a74cd4fba628fa26ee4ddfad6af111eb40c615a62ccb39aaa.jpg) +Figure 1. The workflow of general MIL. + +spatial information. We study the impact of RankMix on these two models and demonstrate that our method can be plugged into the current MIL methods. The general loss function of an MIL model can be formulated as: + +$$ +\mathcal {L} _ {\mathcal {M I L}} = w _ {1} * \mathcal {L} _ {b a g} \left(\hat {Y} _ {i}, Y _ {i}\right) + \sum_ {\ell} w _ {\ell} * \mathcal {L} _ {\ell}, \tag {4} +$$ + +where $\mathcal{L}_{bag}$ is a binary cross-entropy (BCE) loss, $\mathcal{L}_{\ell}$ is other loss term that depends on different MIL models, and $w_{\ell}$ 's are the corresponding balance weights. + +# 3.3. Mixup + +The mixup technique was first proposed in [48] as: + +$$ +x _ {m x p} = \lambda x _ {1} + (1 - \lambda) x _ {2} \tag {5} +$$ + +$$ +y _ {m x p} = \lambda y _ {1} + (1 - \lambda) y _ {2}, \tag {6} +$$ + +where the input sample $x_{i}$ ( $i = 1,2$ ) is drawn from the training dataset, the label corresponding to the input sample $x_{i}$ is $y_{i}$ , and $\lambda \in [0,1]$ is sampled from $\sim \mathrm{Beta}(\alpha, \alpha)$ . + +The main goal of mixup is to make linear combinations of inputs and outputs, respectively, and to ensure that the mapping of the mixed input and mixed output can maintain linear constraints. Therefore, the mixup technique is able to boost the generalization and robustness of an NN model. In addition, mixup can improve the performance of a model encountering the class imbalance problem [19]. + +# 4. Proposed Method: RankMix + +RankMix is mainly composed of pseudo labeling, ranking, mixing ranked features, and self-training, as illustrated in Fig. 2. We will describe the motivation of our method and the role of each component in RankMix. + +# 4.1. Motivation + +A WSI is usually composed of normal tissue and special areas, as shown in Fig. 3a. Special areas can be tumors or defects, etc. If a pathologist obtains a WSI that contains + +tumors, his/her expertise is sufficient to make a correct decision of determining whether there is a tumor inside it. Based on this premise, even a pathologist obtains a partial image of the same WSI that contains most of the tumor areas, as shown in Fig. 3b, it suffices to determine that the image contains tumors. By contrast, if an entire WSI or a partial WSI contains only normal tissues, it can be easily determined that the WSI is normal, as shown in Figs. 3c and 3d, respectively. + +Therefore, the hypothesis here is that cropping a WSI into patches will not affect tumor detection, not to mention the fact that dealing with the entire WSI as a whole is indeed impractical when computing power and memory consumption are taken into consideration. + +Moreover, based on the problem introduced in Sec. 1.2, it is easy to lose physical meaning from picking patches and resizing them to have the same size. If we can select the areas of arbitrary sizes to represent the original slide, we can prepare two partial but representative slides of the same size for use in the mixup technologies. Nevertheless, the prerequisite is based on the fact that we can know which parts of the slide are sufficient to represent the original slide. This conflicts with the scenario that we only have the label of entire slide and do not have the instance-level labels corresponding to patches in the slide, as described in Sec. 3.1. + +In view of the above challenges, we will explain in following subsections how to pick out fragments that are sufficient to represent a slide without instance-level labels. We will demonstrate how to get the pseudo instance-level labels in Sec. 4.2, how to select representative features in Sec. 4.3, and how to combine representative features with a mixup mechanism in Sec. 4.4. The module of pseudo labeling and ranking in RankMix (Fig. 2) is further detailed in Fig. 4. + +# 4.2. Pseudo Labeling + +Given $H_{i} = \{h_{i,1}, h_{i,2}, \ldots, h_{i,m}\} \in \mathbb{R}^{m \times d}$ from a WSI $X_{i}$ by Eq. (2), the pseudo patch-level labels will be predicted to determine which patches are useful for mixup later. Specifically, if we have a score function $f \in \mathbb{R}^{d \times 1}$ + +![](images/10b8d30a9dfaf6f031c17bd08ca6e0acd29bc931f2a498ae45ca20c4d5fe86dc.jpg) +Figure 2. The flowchart of MIL with RankMix. We train the general MIL model with the training set $X$ in the first stage (Top), and then the score function $f$ obtained in the first stage is used to make pseudo labels for $\{X_{a}, X_{b}\}$ and train the MIL model with mixup mechanism in the second stage (Bottom). The dashed arrows indicate the patch scores that may be used by the aggregator depending on the MIL method. + +implemented by a multilayer perceptron (MLP) as: + +$$ +\hat {y} _ {i, j} = \operatorname {s c o r e} _ {i, j} = f \left(h _ {i, j}\right), \quad \forall i = 1, \dots , n \tag {7} +$$ + +we can define a loss function $\mathcal{L}_{max}$ as: + +$$ +\mathcal {L} _ {\max } = \operatorname {B C E} \left(\hat {y} _ {i, j ^ {*}}, Y _ {i}\right), \tag {8} +$$ + +where $j^{*} = \arg \max_{j}(\hat{y}_{i,j})$ and $Y_{i}$ is obtained from Eq. (1). Note that the score function here can be calculated indi + +![](images/18d122e61359faba2bb3743a5896a48eba1786bc885b9560692bb2bc0a277093.jpg) +(a) Example of tumor slide from Camelyon16. + +![](images/94b4507f4bdaf563af87d478d80287095f088b1d5ef0b0e2beba823d51e96133.jpg) + +![](images/9842474857879fc7ed3a23a94c4641a1e3a6bb950c19d857cde0e1d560ac6323.jpg) +(b) Partial slide (in red bounding box) selected from (a). +Figure 3. Illustration of judging if a whole slide or partial slide contains tumors or not. The green annotation indicates the tumor regions and red bounding box indicates the partial region of WSI that is considered to have the same label as the original WSI. + +![](images/3bbe4a93255dae9b40e3ffee4bb89e1a3f71d41953c8899890a030da8eb11dfd.jpg) +(c) Example of normal slide from Camelyon16. +(d) Partial slide (in red bounding box) selected from (c). + +vidually to deal with the multi-class classification problems (e.g., TCGA-Lung dataset in Sec. 5.1) and can be replaced by any similar mechanisms of MIL, which calculates the importance of each patch to yield a final slide-level prediction (e.g., attention mechanism [25, 28, 30] or the distance between clusters [9, 38, 44]). So far, we can get the class probability of every patch in a WSI by the score function $f$ . + +# 4.3. Ranking + +After obtaining the score function $f$ , we already have the basic ability to achieve the motivation mentioned in Sec. 4.1. If we want to obtain a representative portion that can represent the original WSI, we need to score each feature $\{\hat{y}_{i,1},\dots ,\hat{y}_{i,m}\} \in \mathbb{R}^{m\times 1}$ in the WSI and then sort the patch scores as: + +$$ +\begin{array}{l} Z _ {i} = \left\{z _ {i, 1}, z _ {i, 2}, \dots , z _ {i, m} \right\} \\ \text {s . t .} \hat {y} _ {i, z _ {i, 1}} > \hat {y} _ {i, z _ {i, 2}} > \dots > \hat {y} _ {i, z _ {i, m}} \quad \forall i = 1, \dots , n. \tag {9} \\ \end{array} +$$ + +According to the number $k$ ( $k$ is an arbitrary positive integer) of features we need, we can obtain the desired features $\bar{H}_i\in \mathbb{R}^{k\times d}$ from the original features $H_{i}\in \mathbb{R}^{m\times d}$ as: + +$$ +\begin{array}{l} \bar {H} _ {i} = \left\{h _ {i, z _ {i, 1}}, h _ {i, z _ {i, 2}}, \dots , h _ {i, z _ {i, k}} \right\}. \tag {10} \\ \text {f o r} k \leq m, \forall i = 1, \dots , n \\ \end{array} +$$ + +Finally, in order to maintain the relative position information among patches, the features in $\bar{H}_i$ are rearranged in the original order to get the final representative features + +![](images/6771ffb035a01549345b89a0b0c735c55edd7b31d79e0ffa52307a8bc5e60bd0.jpg) +Figure 4. Illustration of the pseudo labeling and ranking mechanism. + +$H_{i}^{\prime}\in \mathbb{R}^{k\times d}$ as: + +$$ +H _ {i} ^ {\prime} = \left\{h _ {i, z _ {i, 1} ^ {\prime}}, h _ {i, z _ {i, 2} ^ {\prime}}, \dots , h _ {i, z _ {i, k} ^ {\prime}} \right\}, \tag {11} +$$ + +$$ +s. t. z _ {i, 1} ^ {\prime} < z _ {i, 2} ^ {\prime} < \dots < z _ {i, k} ^ {\prime} \quad \forall i = 1, \dots , n +$$ + +where $H_{i}^{\prime}$ indicates the $k$ features selected from the original $i^{th}$ slide with the order preserved. + +# 4.4. Mixup in Ranked Features + +According to Eq. (5) and Eq. (6), we can formulate the mixup of features from two examples, $(X_{a},Y_{a})$ and $(X_{b},Y_{b})$ , sampled from the dataset $\mathcal{D}$ , as follows: + +$$ +H _ {m x p} = \lambda H _ {a} ^ {\prime} + (1 - \lambda) H _ {b} ^ {\prime} \tag {12} +$$ + +$$ +Y _ {m x p} = \lambda Y _ {a} + (1 - \lambda) Y _ {b}, \tag {13} +$$ + +where $H_{a}^{\prime}\in \mathbb{R}^{k\times d}$ and $H_{b}^{\prime}\in \mathbb{R}^{k\times d}$ are obtained from $H_{a}\in \mathbb{R}^{m(a)\times d}$ and $H_{b}\in \mathbb{R}^{m(b)\times d}$ , respectively, by Eq. (9)~Eq. (11), and $m(a)$ and $m(b)$ denote the numbers of features obtained from $X_{a}$ and $X_{b}$ , respectively. Different from the existing mixup techniques, we conduct mixup in ranked features. + +# 4.5. MIL Model with RankMix + +As described in Sec. 3.2 and Sec. 4.2, RankMix can be applied to MIL models with the total loss being defined as: + +$$ +\begin{array}{l} \mathcal {L} = w _ {1} \mathcal {L} _ {m a x} \left(\hat {y} _ {m x p, j ^ {*}}, Y _ {m x p}\right) + w _ {2} \mathcal {L} _ {b a g} \left(\hat {Y} _ {m x p}, Y _ {m x p}\right) \\ + \sum_ {\ell} w _ {\ell} \mathcal {L} _ {\ell}, \tag {14} \\ \end{array} +$$ + +where the first term comes from Eq. (8) and the remaining terms come from Eq. (4). So far, we have explained how to accomplish the middle component of RankMix in MIL in Fig. 2, i.e., the first stage of training. + +# 4.6. Self-Training: Second Stage of Training + +WSI classification faces the tough problem that each WSI is only given a slide-level label; that is, tens of thousands of patches correspond to one label. This kind of + +weakly supervised learning is more difficult to train than supervised learning. If the RankMix proposed so far is used, unstable training will be encountered. However, if the score function is more reliable (i.e., can distinguish patch labels) at the beginning, then RankMix is found to achieve better results. We can imagine that the score function acts like expert annotations, and higher quality annotations will naturally result in better performance. + +Inspired by self-training [40,45] and BERT-based model [13, 27, 29], we design a score function by learning from a pre-trained task in advance (i.e., can output the class probability distribution of a patch) as: + +$$ +p \left(\hat {Y} _ {i} \mid H _ {i}\right) = \text {a g g r e g a t o r} \left(H _ {i}\right) = p \left(\hat {Y} _ {i} \mid h _ {i, 1}, \dots , h _ {i, m}\right). \tag {15} +$$ + +Then, by using the concept of self-training, the stronger model is used as a teacher to extract the area that can represent the original WSI via score function for the student model to mixup ranked features as: + +$$ +\begin{array}{l} \hat {Y} _ {m x p} = p \left(Y _ {m x p} \mid H _ {m x p}\right) = p \left(Y _ {m x p} \mid h _ {m x p, 1}, \dots , h _ {m x p, k}\right) \\ = p \left(Y _ {m x p} | \lambda H _ {a} ^ {\prime} + (1 - \lambda) H _ {b} ^ {\prime}\right) \\ = \text {a g g r e g a t o r} \left(\lambda H _ {a} ^ {\prime} + (1 - \lambda) H _ {b} ^ {\prime}\right). \tag {16} \\ \end{array} +$$ + +From the perspective of BERT-based models, we use the teacher model to learn the WSI classification problem (also known as the pretext task) as pretraining, and treat the mixup of ranked features as the downstream task to further improve the performance. Please see Fig. 2 for the illustration of two-stage training procedure. + +# 5. Experiments and Results + +In this section, we will describe the datasets used for experiments in Sec. 5.1, experimental setting and performance metrics in Sec. 5.2, main results in Sec. 5.3, and ablation studies in Sec. 8.1 (Appendix). + +
Method/DatasetCamelyon16WSI-usabilityTCGA-Lung
ACCAUCAUPRCACCAUCAUPRCACCAUCAUPRC
DSMIL [28]86.82%93.32%92.68%76.11%86.60%24.51%93.81%97.89%97.75%
+ ReMix [46]82.17%86.89%83.86%83.19%85.83%25.59%94.29%97.62%97.29%
+ RankMix w/o self-training87.60%92.07%92.43%90.27%87.07%25.66%94.29%98.00%97.76%
+ RankMix89.92%93.47%92.74%90.27%88.16%28.41%94.29%98.04%97.79%
FRMIL [10]89.15%94.57%93.66%83.19%87.69%45.99%90.95%95.38%94.96%
+ ReMix [46]82.59%87.29%87.35%89.25%80.63%33.09%92.22%96.99%97.04%
+ RankMix w/o self-training90.70%94.11%93.68%80.53%84.27%38.55%93.33%95.84%97.01%
+ RankMix91.47%94.59%93.99%93.81%93.61%47.65%93.33%97.00%97.04%
+ +Table 2. Comparison of WSI classification between RankMix and vanilla models under three datasets. + +# 5.1. Datasets + +We introduce the WSI datasets used for experiments here, and a pre-processing setting was adopted to extract patches from each WSI. Each WSI was cropped into different numbers of $224 \times 224$ patches at $20\mathrm{x}$ magnification without overlapping. We follow [10,28] to discard the background patches with tissue entropy less than $15\%$ of a WSI. + +Camelyon16 [16] is a public and well-known dataset proposed for metastasis detection in breast cancer. The dataset contains 270 training slides and 130 testing slides, and roughly has 4.1 million patches at $20\mathrm{x}$ magnification with the maximum of 44000 patches per WSI and a minimum of 1200 patches per WSI in our pre-processing setting. If a WSI contains at least one tumor region, it is regarded as a positive slide. On the contrary, if the entire area of a WSI is normal, it is negative. In Camelyon16, the tumor area only accounts for approximately less than $10\%$ of the tissue area in the positive slide. + +TCGA-Lung is a public dataset that has two types of lung cancer, Lung Adenocarcinoma (TCGA-LUAD) and Lung Squamous Cell Carcinoma (TCGA-LUSC), from the Caner Genome Atlas (TCGA). Please refer to https://pubmed.ncbi.nlm.nih.gov/25691825/ for details. There are in total 1046 diagnostic WSIs, including 534 TCGA-LUAD and 512 TCGA-LUSC, were split into 836 training slides and 210 testing slides. After pre-processing, TCGA-Lung roughly has a minimum of 50 patches per slide and a maximum of 12700 patches per slide, with a total of 3.2 million patches. + +WSI-usability is a private dataset used for distinguishing whether a WSI is usable or not. The purpose of this dataset is used for evaluating automatic quality control (QC). In order to have sufficient practicality, two pathologist experts each annotated 250 WSIs from TCGA, of which 50 WSIs were redundant, resulting in 450 WSIs in total. If it is a bad (labeled as positive) slide, it means that the WSI is not usable; otherwise, it is a good WSI and annotated as a negative slide. WSI-usability has only 23 positive slides, so it possesses a severe class imbalance problem. After preprocessing, WSI-usability roughly has a minimum of 700 + +patches per slide and a maximum of 120000 patches per slide, with a total of 5.7 million patches. + +Summing up the above, the adopted datasets cover the imbalance/balanced classes, unbalanced/balanced bags, and single/multiple-class problem. Among them, WSI-usability has majority and minority categories with a huge gap, which indicates the rare diseases and other costly data. For the positive slides in Camelyon16, tumors occupy quite smaller areas than normal tissues, while the negative slide is all filled with normal tissues. Different from the other two datasets, TCGA-Lung has two types of positive slides, namely TCGA-LUSD and TCGA-LUSC, leading to a multi-class classification problem. + +# 5.2. Experimental Setup and Evaluation Metrics + +ResNet18 [22] was adopted as our backbone model that was trained by SimCLR [7] and Adam optimizer to obtain feature extractor $G_{\theta}$ with a mini-batch size of 512, learning rate of $1e - 4$ , and weight decay of $1e - 5$ . For Camelyon16, we used the weights of ResNet18 trained by Lee et al. [28], as described in [10]. Then, the embeddings $H_{i} \in \mathbb{R}^{m(i) \times 512}$ of a WSI $X_{i}$ were obtained from the global average pooling layer of feature extractor $G_{\theta}$ . + +For training aggregator, we used the Adam optimizer for 200 epochs with the mini-batch size of 1 (bag), learning rate of $2e - 4$ , and weight decay of $5e - 3$ . Note that the minibatch for performing mixup of ranked features was 2, where the sampling methods of DSMIL and FRMIL followed [19] and [10], respectively. The number $k$ of features used in RankMix was set to $\min(m(a), m(b))$ for two WSIs $X_a$ and $X_b$ . + +For two-stage training, we trained teacher models by the general MIL (i.e., DSMIL and FR-MIL). Then, the teacher models were used to guide the training of student models by RankMix. The structures of both the teacher model and student model are the same, which can be considered as a kind of self-distillation mechanism. The temperature parameter $\tau$ commonly used in knowledge distillation was set to 1.0 (see Eq. (20) later). + +The classification performance was evaluated in terms of + +
Method/DatasetCamelyon16WSI-UsabilityTCGA-Lung
AccuracyAUCAccuracyAUCAccuracyAUC
DSMIL [28]86.82%93.32%76.11%86.60%93.81%97.89%
DSMIL + Direct Mixup84.50%90.51%89.38%71.18%94.29%98.03%
DSMIL + Shrink Mixup86.05%92.42%88.50%69.94%93.81%97.95%
DSMIL + Duplicate Mixup84.50%91.96%89.38%72.43%93.81%97.99%
DSMIL + Random Mixup87.60%91.89%88.50%83.33%94.29%97.99%
DSMIL + RankMix89.92%93.47%90.27%88.16%94.29%98.04%
FRMIL [10]89.15%94.57%83.19%87.69%90.95%95.38%
FRMIL + Direct Mixup88.37%92.50%59.29%80.37%92.38%95.96%
FRMIL + Shrink Mixup89.92%93.16%68.14%57.09%92.86%96.88%
FRMIL + Duplicate Mixup87.60%92.78%86.73%74.77%92.38%96.73%
FRMIL + Random Mixup90.70%94.23%77.88%80.69%93.33%96.98%
FRMIL + RankMix91.47%94.59%93.81%93.61%93.33%97.00%
+ +Table 3. Comparisons between RankMix and four custom mixup techniques. + +the accuracy and area under the curve (AUC). + +# 5.3. Main Results + +First, we applied the proposed method, RankMix, to two baseline models, DSMIL [28] and FRMIL [10], and compared the performance with the vanilla models in Tab. 2. We can observe that self-training indeed boosts the overall model performance, as described in Sec. 4.6. Without self-training (i.e., mixup in the model without being derived from a teacher model), RankMix can sometimes achieve slightly better results, but as the model and dataset vary, it can be seen that the performance is slightly degraded in few cases. On the contrary, when self-training is introduced, the performance can be improved further. A recent work, ReMix [46], which is a SOTA augmentation method in WSI, was included for comparison. It can be found that RankMix outperforms ReMix remarkably. + +Second, we compared our method with the general mixup techniques under different custom settings in Tab. 3. This is because the existing mixup researches, to our knowledge, were conducted on the same feature number, they cannot be readily employed to be compared with our method under the scenario that two features of different numbers were mixed. Here, we discuss four situations for mixing up two WSIs $(H_{a}$ and $H_{b})$ with different numbers $(m(a)$ and $m(b))$ of features in the following. + +1) Direct Mixup: Perform mixup directly regardless of feature numbers $(m(a)$ and $m(b))$ , where the feature with a smaller number is padded with zeros. So, the feature number after mixing is defined as: + +$$ +k _ {d} = \max (m (a), m (b)). \tag {17} +$$ + +2) Shrink Mixup: Extract the same number $k_{s}$ of features for mixing up by + +$$ +k _ {s} = \left\{ \begin{array}{l} m (b), \text {i f f} m (a) > m (b) \\ m (a), \text {o t h e r w i s e} \end{array} . \right. \tag {18} +$$ + +3) Duplicate Mixup: Duplicate the feature with a smaller number to have the same size $k_{du}$ as the larger feature as: + +$$ +k _ {d u} = \left\{ \begin{array}{l} m (a), \text {i f f} m (a) > m (b) \\ m (b), \text {o t h e r w i s e} \end{array} . \right. \tag {19} +$$ + +4) Random Mixup: By randomly performing both the duplicate and shrink mixups. + +Compared with the above four straightforward cases, it can be seen from Tab. 3 that RankMix is a sophisticated design according to the characteristics of WSI, described in Sec. 1.2, and generally performs better than others. + +Finally, we conduct ablation studies to further evaluate RankMix in two aspects. On the one hand, we examine how the score functions learned under different pre-trained models, as described in Sec. 4.6, affect RankMix. On the other hand, we examine how different knowledge transfer techniques affect the student model performance in WSI classification. Please refer to Sec. 8.1 in Appendix for details. + +# 6. Conclusion + +In this work, we investigate weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories. A new data augmentation method, RankMix, of is proposed to mix ranked features in a pair of WSIs with different sizes. RankMix is composed of pseudo labeling and ranking for extracting key WSI regions, and two-stage training for boosting stable training and model performance. + +# 7. Acknowledgement + +This work was supported in part by the Ministry of Science and Technology of Taiwan, ROC, under Grant MOST 110-2634-F-006-022. + +# References + +[1] Sugata Banerji and Sushmita Mitra. Deep learning in histopathology: A review. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 12(1), 2022. 1 +[2] Gabriele Campanella, Matthew G Hanna, Luke Geneslaw, Allen Miraflor, Vitor Werneck Krauss Silva, Klaus J Busam, Edi Brogi, Victor E Reuter, David S Klimstra, and Thomas J Fuchs. Clinical-grade computational pathology using weakly supervised deep learning on whole slide images. Nature medicine, 25(8):1301-1309, 2019. 1, 2 +[3] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. 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The WSI datasets are also imbalanced in categories. These unique characteristics, significantly different from the ones in natural images, pose the challenge of classifying WSI images as a kind of weakly supervise learning problems. In this study, we propose, RankMix, a data augmentation method of mixing ranked features in a pair of WSIs. RankMix introduces the concepts of pseudo labeling and ranking in order to extract key WSI regions in contributing to the WSI classification task. A two-stage training is further proposed to boost stable training and model performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 400, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 460 + ], + "type": "text", + "content": "To our knowledge, the study of weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories is relatively unexplored." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 483, + 128, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 128, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 128, + 496 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 503, + 128, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 128, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 128, + 516 + ], + "type": "text", + "content": "1.1. Background" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "content": "Natural image processing tasks, including image classification and object detection, have been widely solved using deep learning models and obtain astounding results. In this study, we investigate how medical imaging can also benefit from deep learning with focus on whole slide images (WSIs). WSI scanning is commonly used in disease diagnosis [12, 34]. The demand of computer aided assessment makes deep learning widely adopted in this field [1]. Because WSI is a gigapixel image and lacks pixel-level annotations, multiple instance learning (MIL) [31, 32] is an exact solution to this weakly supervised learning problem [2]. In MIL, a WSI is often cropped into tens of thousands of patches and then an aggregator will make a prediction based on integrating these patches. Most recent works [5,9,10,25,28,30,37,38,44] focus on aggregator architecture design and improving feature extraction of the patches." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 232, + 547, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 363 + ], + "type": "text", + "content": "However, because WSI is difficult to collect and share, we explore the possibility of data augmentation in WSI classification to increase training samples and mitigate the problem of class imbalance [19, 26, 33, 48] that WSI may have due to rare diseases (versus common diseases). In addition, patch feature extractor is often trained by self-supervised learning [24, 28] or comes from pre-trained models (such as pre-trained in ImageNet [30, 37] or WSI datasets [5, 11]). Therefore, for universality and portability, our work will focus on studying the feature domain instead of pixel domain of patches." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 363, + 547, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 458 + ], + "type": "text", + "content": "Traditionally, mixup methods [18, 48] are employed to mix photos of the same aspect ratio or vectors of the same dimension. Nevertheless, this is not the case for WSI as WSI intrinsically has a different number of patches, ranging from hundreds to hundred of thousands. This is because the generation of a WSI, caused by the tissue placement and the tissue size, will make WSIs of varying aspect ratios and sizes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 548, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 548, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 548, + 579 + ], + "type": "text", + "content": "In addition, because a WSI tends to be a very large size (equivalent to tens of thousands of " + }, + { + "bbox": [ + 304, + 460, + 548, + 579 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 460, + 548, + 579 + ], + "type": "text", + "content": " patches or even larger) and the background often occupies a large part, it is better to use data pre-processing to remove unimportant background parts in order to save computation time and avoid possible unnecessary information [21, 39] (such as noise and artifacts). That is, the pre-processing step of cropping a WSI into patches, as shown in Fig. 1, will remove most of the background patches. The resultant WSI patches, however, will lose their absolute positions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 587, + 380, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 380, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 380, + 600 + ], + "type": "text", + "content": "1.2. Challenges" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "The above characteristics of WSI lead to the difficulty of directly employing the traditional mixup methods. We cannot simply resize two WSIs to have the same size for the sake of performing mixup. This is because all WSIs are scanned at the same magnification (e.g., " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "20\\mathrm{x}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "), the physical meanings will be lost if they are rescaled casually. More importantly, due to loss of absolute positions among the patches after removing the WSI background, resizing patches actually do not solve this problem." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "23936" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "Another commonly used techniques for data augmentation are based on cutting, including Cutout [14] and Cutmix [47]. The core of cutting aims at obtaining or removing parts of an images. However, the key difference between WSI images and natural images is that the main objects can occupy a major part of a natural image, but it is not the case in WSIs. For example, the tumor slide of Camelyon16 dataset [16] only has a small area of tumor (approximately " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "< 10\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " of tissue area). Therefore, if a random cut is made, there is a non-negligible probability that the tumor slide will not contain any tumor patches." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 335 + ], + "type": "text", + "content": "To address these challenges, we propose a novel mixup method, called RankMix, for augmentation of whole slide images with diverse sizes and imbalanced categories. RankMix introduces the concepts of instance-level pseudo labeling and ranking in order to obtain meaningful WSI regions that can contribute to the WSI classification task. In order to further enhance model performance, two-stage training is proposed in that the first step is to train a stable score function by general MIL, and then the score function and mixup technique are jointly used in the second stage of training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 343, + 159, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 343, + 159, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 159, + 355 + ], + "type": "text", + "content": "1.3. Our Contributions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 361, + 244, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 361, + 244, + 373 + ], + "spans": [ + { + "bbox": [ + 59, + 361, + 244, + 373 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 381, + 287, + 577 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 381, + 287, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 381, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 58, + 381, + 287, + 465 + ], + "type": "text", + "content": "- To our knowledge, MIL currently focuses on improving feature extraction and aggregator-based classification. It is relatively ignored in investigating weakly supervised learning from the perspective of data augmentation. Our proposed method can be applied to WSI classification problems and can be easily incorporated to existing MIL methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 473, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 473, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 58, + 473, + 287, + 509 + ], + "type": "text", + "content": "- In contrast to the existing mixup methods that aim at mixing natural images of the same size, our method can mix images (e.g., WSIs) of different sizes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 517, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 517, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 58, + 517, + 287, + 577 + ], + "type": "text", + "content": "- Because of rare diseases and the difficulty of medical image collection, the WSI classification problem is apt to suffer from lack of training data and imbalance of categories. Our proposed method is demonstrated to be feasible in addressing these challenges." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 595, + 133, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 133, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 133, + 608 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 616, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 287, + 639 + ], + "type": "text", + "content": "In this section, we briefly introduce the techniques that are relevant to our work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 162, + 659 + ], + "type": "text", + "content": "2.1. Data Augmentation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "text", + "content": "Data augmentation can improve the generalization and has been widely used in training neural networks. Mixup [48] fuses information from two images by convex combination. CutMix [47] inpaints the masking area (produced by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "random occlusion) with another image content at the same location. Recently, Part et al. [35] proposed how the majority can help the minority with re-balancing distribution of each sub-class. In addition to mixing in the pixel domain, Manifold Mixup [42] and PatchUp [18] proposed mixing the features of two images. Despite promising, the aforementioned methods are not presented for medical images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 157, + 546, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 546, + 420 + ], + "type": "text", + "content": "For medical imaging, Galdran et al. [19] mixed two medical images sampled from different distributions, including instance-based sampling and class-based sampling. By increasing the sampling probability of the minority class, the class imbalance problem that usually occurs in medical imaging can be properly alleviated. In histopathology studies, the datasets often suffer from stain color variation because of different stain approaches, procedures, and slide scanner. To address this problem, Chang et al. [4] mixed two stain color matrices from stained images in order to increase the generalization of unseen colors. Chen et al. proposed Flow-Mixup [6] to regularize medical images with corrupted multi-labels because the annotations of medical images are costing and automatic annotation often provides corrupted labels. Gazda et al. [20] used the mixup technique to improve model performance for medical image segmentation. In ReMix [46], Yang et al. proposed using latent-space data augmentation to deal with WSI classification. However, ReMix only mixed instance prototypes of slides from the same class by " + }, + { + "bbox": [ + 304, + 157, + 546, + 420 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 157, + 546, + 420 + ], + "type": "text", + "content": "-Means while maintaining the original labels. From this perspective, ReMix acts like a kind of feature augmentation instead of general mixup." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 421, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 456 + ], + "type": "text", + "content": "As shown in Tab. 1, although the previous researches on medical images are diverse, their data augmentations are not feasible for WSIs with large gaps in size." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 467, + 489, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 489, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 489, + 480 + ], + "type": "text", + "content": "2.2. Multiple Instance Learning (MIL)" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": "In recent MIL studies, the patches of a WSI are transformed into the features of fixed size by a feature extractor and then the patch features will be aggregated to get a final slide-level prediction. To leverage patch features, MIL-RNN [2] uses the recurrent neural network (RNN) [36] to encode position information. Because RNNs are apt to suffer from information loss over long distances, the follow-up works proposed attention-based MIL [25, 30] to calculate the contributions of instance-level features by learnable neural networks. Thanks to the success of Transformer [15, 41], self-attention based MIL methods [10, 28, 37] receive considerable attention in WSI classifications. Li et al. [28] proposed the non-local attention mechanism to calculate the relation between the critical feature and remaining features, but ignored the position relationship between patches. To address this problem, Shao et al. proposed TransMIL [37], which emphasizes the benefits of Pyramid Position Encoding Generator (PPEG), to encode spatial information by group convolution. Recently, Chikontwe et" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23937" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 526, + 201 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 526, + 201 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 526, + 201 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 526, + 201 + ], + "type": "table", + "html": "
SettingImage typeMixup inputMixup outputLarge size gap between 2 inputs
Mixup [48]Natural imageImagevx
Manifold Mixup [42]Natural imageImage, Hidden statevx
Balanced-MixUp [19]Retinal image, Gastro-intestinal imageImagevx
Stain Mix-up [4]Patches of WSIStain matrixvx
Flow-Mixup [6]Chest X-ray, ECGHidden statevx
Mixup for KiTS [20]CT imageImagevx
ReMix [46]WSIInstance prototypexv
RankMix (Ours)WSIImage featurevv
", + "image_path": "875479b6c4bda4608bf876875b01e6eb9e1415f4a7a30ecbdd774ff13af9d88f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 209, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 232 + ], + "type": "text", + "content": "Table 1. Comparisons among mixup methods. Our method, RankMix, deals with mixing of not only two images with large gap in size in the feature domain but also their labels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 252, + 288, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 288, + 312 + ], + "type": "text", + "content": "al. [10] proposed combining the critical feature [28] with PPEG [37], treating the tumor slides as a kind of out-of-distribution compared to normal slides, and re-calibrating the patch features of a slide according to the magnitudes of critical feature and slide label." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 321, + 262, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 321, + 262, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 262, + 335 + ], + "type": "text", + "content": "2.3. Self-Training and Knowledge Distillation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 340, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 484 + ], + "type": "text", + "content": "Knowledge distillation [23,40] uses soft labels instead of hard labels (which are the maximum of class probabilities) from the teacher model to train the student model. The student model, aiming for model compression, is a smaller one to mimic the output of its teacher model. Instead of compressing models, Xie et al. [45] integrated self-training with knowledge distillation to improve the image classification task with unlabeled data. The authors propagated pseudo soft labels of unlabeled data from the teacher model to the student model. The researches [3,8,17] further used self-training and knowledge distillation to deal with the self-supervised learning problem." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 557 + ], + "type": "text", + "content": "To sum up, our work, RankMix, has similar concepts with previous works, but we study how the general MIL model can be adopted as the teacher model. This makes RankMix act like a post-processing of traditional MIL, as illustrated in Fig. 2, and can be simply plugged into the exist approaches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 568, + 125, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 125, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 125, + 582 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 625 + ], + "type": "text", + "content": "In this section, we introduce the classification problem of WSIs, as well as some baseline techniques and notations, to make this paper self-contained." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 634, + 171, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 171, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 171, + 647 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": "In the WSI classification problem, we have a series of WSIs " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "X = \\{X_{1},X_{2},\\ldots ,X_{n}\\}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " and corresponding slide labels " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "Y = \\{Y_{1},Y_{2},\\dots ,Y_{n}\\}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " as dataset " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(X_i,Y_i),\\quad i = 1,\\ldots ,n\\}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": ". Our goal is to train an NN model based on dataset " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " for binary slide label " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "Y_{i}\\in \\{0,1\\}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": "prediction of an incoming WSI image " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": ". In MIL, a WSI can be treated as a bag (slide) containing the instances (patches) as " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m(i)}\\}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": ". Note that the WSI " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": "'s have different numbers " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "m(i)" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": "'s of instances and the instance-level labels " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\{y_{i,1}, y_{i,2}, \\ldots, y_{i,m(i)}\\}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " are unknown. Without loss of generality, we will mostly use " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " in place of " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "m(i)" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " for notation simplicity. The slide label " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "Y_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " of a WSI " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " is defined to be negative (" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "Y_{i} = 0" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": ") when all instances in a bag are negative (without tumors), i.e., " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "y_{i,j} = 0" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": ". If at least one instance in " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " is positive (with tumor), its slide label will be positive (" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "Y_{i} = 1" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": "). The slide label of WSI " + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 252, + 545, + 396 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 370, + 402, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 402, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 370, + 402, + 545, + 434 + ], + "type": "interline_equation", + "content": "Y _ {i} = \\left\\{ \\begin{array}{l} 0, \\text {i f f} \\sum y _ {i, j} = 0 \\\\ 1, \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {1}", + "image_path": "e11e7956cbe352b60425e00c2d9e51a597e214607893cd1f3cac12704b7489e9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 440, + 437, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 440, + 437, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 440, + 437, + 452 + ], + "type": "text", + "content": "3.2. MIL as Baseline Model" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "content": "In MIL, as shown in Fig. 1, the slide " + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "content": " will first be cut into many instances (patches) as " + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "inline_equation", + "content": "X_{i} = \\{x_{i,1}, x_{i,2}, \\ldots, x_{i,m}\\}" + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "content": " and then passed through an instance feature extractor " + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "content": " to get the so-called features (embeddings) " + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "inline_equation", + "content": "H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}" + }, + { + "bbox": [ + 305, + 458, + 545, + 520 + ], + "type": "text", + "content": " via Eq. (2) as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 391, + 525, + 545, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 525, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 391, + 525, + 545, + 539 + ], + "type": "interline_equation", + "content": "h _ {i, j} = G _ {\\theta} \\left(x _ {i, j}\\right), \\tag {2}", + "image_path": "cdc80c0bee7f447cc57e7f6553a347cd476b7bc0f603fd46b0b272f8d1ed4ae7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " denotes the length of a feature vector and " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " denotes the number of features. As mentioned before, different WSIs will have different numbers of features but feature length " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " is the same. Finally, the aggregator will output a slide label prediction " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\hat{Y}_i" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " by Eq. (3) as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 609, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 609, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 345, + 609, + 545, + 624 + ], + "type": "interline_equation", + "content": "\\hat {Y} _ {i} = \\text {a g g r e g a t o r} \\left(h _ {i, 1}, h _ {i, 2}, \\dots , h _ {i, m}\\right). \\tag {3}", + "image_path": "b1bba94816c0f20cbc62bb5bc4a7f7a16d322d0809c53bd0676c7272cab9c319.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this work, we use DSMIL [28] and FRMIL [10] as the backbone models to represent SOTA permutation-variant and permutation-invariant MIL models, respectively, where the former only considers the relationship between each embedding and does not consider relative positions, and the latter uses the pooling multi-head self-attention (PMSA) module and positional encoding module (PEM) to fuse relative" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23938" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 68, + 478, + 208 + ], + "blocks": [ + { + "bbox": [ + 110, + 68, + 478, + 208 + ], + "lines": [ + { + "bbox": [ + 110, + 68, + 478, + 208 + ], + "spans": [ + { + "bbox": [ + 110, + 68, + 478, + 208 + ], + "type": "image", + "image_path": "7e5abbd55991213a74cd4fba628fa26ee4ddfad6af111eb40c615a62ccb39aaa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 214, + 370, + 225 + ], + "lines": [ + { + "bbox": [ + 222, + 214, + 370, + 225 + ], + "spans": [ + { + "bbox": [ + 222, + 214, + 370, + 225 + ], + "type": "text", + "content": "Figure 1. The workflow of general MIL." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 247, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 294 + ], + "type": "text", + "content": "spatial information. We study the impact of RankMix on these two models and demonstrate that our method can be plugged into the current MIL methods. The general loss function of an MIL model can be formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 300, + 287, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 300, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 78, + 300, + 287, + 326 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {M I L}} = w _ {1} * \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {i}, Y _ {i}\\right) + \\sum_ {\\ell} w _ {\\ell} * \\mathcal {L} _ {\\ell}, \\tag {4}", + "image_path": "f6c1d75667031bc7cb346026b64e3aaf3eaba669bf1e3ac0156fc0af8b97a8a1.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bag}" + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "text", + "content": " is a binary cross-entropy (BCE) loss, " + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\ell}" + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "text", + "content": " is other loss term that depends on different MIL models, and " + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "inline_equation", + "content": "w_{\\ell}" + }, + { + "bbox": [ + 46, + 333, + 287, + 370 + ], + "type": "text", + "content": "'s are the corresponding balance weights." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 376, + 101, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 101, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 101, + 389 + ], + "type": "text", + "content": "3.3. Mixup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 395, + 264, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 395, + 264, + 407 + ], + "spans": [ + { + "bbox": [ + 59, + 395, + 264, + 407 + ], + "type": "text", + "content": "The mixup technique was first proposed in [48] as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 112, + 416, + 287, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 416, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 112, + 416, + 287, + 429 + ], + "type": "interline_equation", + "content": "x _ {m x p} = \\lambda x _ {1} + (1 - \\lambda) x _ {2} \\tag {5}", + "image_path": "3dcb0c6ab7a0dce96eeb655ffa0e222eb8f8bb9a2e6351265a0b5128046f7e48.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 437, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 437, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 113, + 437, + 287, + 449 + ], + "type": "interline_equation", + "content": "y _ {m x p} = \\lambda y _ {1} + (1 - \\lambda) y _ {2}, \\tag {6}", + "image_path": "735ca2c0e0067a81e4e05c74ac88c1e51d5535117f1a858ad03f3f24d618db9d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": "where the input sample " + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "i = 1,2" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": ") is drawn from the training dataset, the label corresponding to the input sample " + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\lambda \\in [0,1]" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": " is sampled from " + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\sim \\mathrm{Beta}(\\alpha, \\alpha)" + }, + { + "bbox": [ + 46, + 454, + 287, + 490 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 491, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 574 + ], + "type": "text", + "content": "The main goal of mixup is to make linear combinations of inputs and outputs, respectively, and to ensure that the mapping of the mixed input and mixed output can maintain linear constraints. Therefore, the mixup technique is able to boost the generalization and robustness of an NN model. In addition, mixup can improve the performance of a model encountering the class imbalance problem [19]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 584, + 209, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 209, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 209, + 597 + ], + "type": "text", + "content": "4. Proposed Method: RankMix" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 604, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 652 + ], + "type": "text", + "content": "RankMix is mainly composed of pseudo labeling, ranking, mixing ranked features, and self-training, as illustrated in Fig. 2. We will describe the motivation of our method and the role of each component in RankMix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 659, + 121, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 121, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 121, + 670 + ], + "type": "text", + "content": "4.1. Motivation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "A WSI is usually composed of normal tissue and special areas, as shown in Fig. 3a. Special areas can be tumors or defects, etc. If a pathologist obtains a WSI that contains" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 247, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 354 + ], + "type": "text", + "content": "tumors, his/her expertise is sufficient to make a correct decision of determining whether there is a tumor inside it. Based on this premise, even a pathologist obtains a partial image of the same WSI that contains most of the tumor areas, as shown in Fig. 3b, it suffices to determine that the image contains tumors. By contrast, if an entire WSI or a partial WSI contains only normal tissues, it can be easily determined that the WSI is normal, as shown in Figs. 3c and 3d, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 354, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 413 + ], + "type": "text", + "content": "Therefore, the hypothesis here is that cropping a WSI into patches will not affect tumor detection, not to mention the fact that dealing with the entire WSI as a whole is indeed impractical when computing power and memory consumption are taken into consideration." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 415, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 545 + ], + "type": "text", + "content": "Moreover, based on the problem introduced in Sec. 1.2, it is easy to lose physical meaning from picking patches and resizing them to have the same size. If we can select the areas of arbitrary sizes to represent the original slide, we can prepare two partial but representative slides of the same size for use in the mixup technologies. Nevertheless, the prerequisite is based on the fact that we can know which parts of the slide are sufficient to represent the original slide. This conflicts with the scenario that we only have the label of entire slide and do not have the instance-level labels corresponding to patches in the slide, as described in Sec. 3.1." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": "In view of the above challenges, we will explain in following subsections how to pick out fragments that are sufficient to represent a slide without instance-level labels. We will demonstrate how to get the pseudo instance-level labels in Sec. 4.2, how to select representative features in Sec. 4.3, and how to combine representative features with a mixup mechanism in Sec. 4.4. The module of pseudo labeling and ranking in RankMix (Fig. 2) is further detailed in Fig. 4." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 406, + 659 + ], + "type": "text", + "content": "4.2. Pseudo Labeling" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "H_{i} = \\{h_{i,1}, h_{i,2}, \\ldots, h_{i,m}\\} \\in \\mathbb{R}^{m \\times d}" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " from a WSI " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " by Eq. (2), the pseudo patch-level labels will be predicted to determine which patches are useful for mixup later. Specifically, if we have a score function " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{d \\times 1}" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23939" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 539, + 284 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 539, + 284 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 539, + 284 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 539, + 284 + ], + "type": "image", + "image_path": "10b8d30a9dfaf6f031c17bd08ca6e0acd29bc931f2a498ae45ca20c4d5fe86dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "text", + "content": "Figure 2. The flowchart of MIL with RankMix. We train the general MIL model with the training set " + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "text", + "content": " in the first stage (Top), and then the score function " + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "text", + "content": " obtained in the first stage is used to make pseudo labels for " + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "inline_equation", + "content": "\\{X_{a}, X_{b}\\}" + }, + { + "bbox": [ + 46, + 294, + 547, + 329 + ], + "type": "text", + "content": " and train the MIL model with mixup mechanism in the second stage (Bottom). The dashed arrows indicate the patch scores that may be used by the aggregator depending on the MIL method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 349, + 253, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 253, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 253, + 361 + ], + "type": "text", + "content": "implemented by a multilayer perceptron (MLP) as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 367, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 367, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 78, + 367, + 287, + 380 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i, j} = \\operatorname {s c o r e} _ {i, j} = f \\left(h _ {i, j}\\right), \\quad \\forall i = 1, \\dots , n \\tag {7}", + "image_path": "3497fc696084254c79752e30a450a975c9ad59839bfca0568021d7ed593614e2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 386, + 205, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 205, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 205, + 398 + ], + "type": "text", + "content": "we can define a loss function " + }, + { + "bbox": [ + 47, + 386, + 205, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{max}" + }, + { + "bbox": [ + 47, + 386, + 205, + 398 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 404, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 404, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 116, + 404, + 287, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\max } = \\operatorname {B C E} \\left(\\hat {y} _ {i, j ^ {*}}, Y _ {i}\\right), \\tag {8}", + "image_path": "e257d0530cbecf1a1ea376e82747bda845c1ff2128e7aa903e5062a587fb8e22.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "inline_equation", + "content": "j^{*} = \\arg \\max_{j}(\\hat{y}_{i,j})" + }, + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "inline_equation", + "content": "Y_{i}" + }, + { + "bbox": [ + 47, + 423, + 287, + 446 + ], + "type": "text", + "content": " is obtained from Eq. (1). Note that the score function here can be calculated indi" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 66, + 460, + 167, + 533 + ], + "blocks": [ + { + "bbox": [ + 66, + 460, + 167, + 533 + ], + "lines": [ + { + "bbox": [ + 66, + 460, + 167, + 533 + ], + "spans": [ + { + "bbox": [ + 66, + 460, + 167, + 533 + ], + "type": "image", + "image_path": "18d122e61359faba2bb3743a5896a48eba1786bc885b9560692bb2bc0a277093.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 534, + 166, + 552 + ], + "lines": [ + { + "bbox": [ + 66, + 534, + 166, + 552 + ], + "spans": [ + { + "bbox": [ + 66, + 534, + 166, + 552 + ], + "type": "text", + "content": "(a) Example of tumor slide from Camelyon16." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 167, + 460, + 269, + 533 + ], + "blocks": [ + { + "bbox": [ + 167, + 460, + 269, + 533 + ], + "lines": [ + { + "bbox": [ + 167, + 460, + 269, + 533 + ], + "spans": [ + { + "bbox": [ + 167, + 460, + 269, + 533 + ], + "type": "image", + "image_path": "94b4507f4bdaf563af87d478d80287095f088b1d5ef0b0e2beba823d51e96133.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 66, + 554, + 167, + 635 + ], + "blocks": [ + { + "bbox": [ + 167, + 534, + 268, + 552 + ], + "lines": [ + { + "bbox": [ + 167, + 534, + 268, + 552 + ], + "spans": [ + { + "bbox": [ + 167, + 534, + 268, + 552 + ], + "type": "text", + "content": "(b) Partial slide (in red bounding box) selected from (a)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 66, + 554, + 167, + 635 + ], + "lines": [ + { + "bbox": [ + 66, + 554, + 167, + 635 + ], + "spans": [ + { + "bbox": [ + 66, + 554, + 167, + 635 + ], + "type": "image", + "image_path": "9842474857879fc7ed3a23a94c4641a1e3a6bb950c19d857cde0e1d560ac6323.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 666, + 288, + 710 + ], + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 710 + ], + "type": "text", + "content": "Figure 3. Illustration of judging if a whole slide or partial slide contains tumors or not. The green annotation indicates the tumor regions and red bounding box indicates the partial region of WSI that is considered to have the same label as the original WSI." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 168, + 553, + 269, + 635 + ], + "blocks": [ + { + "bbox": [ + 66, + 637, + 167, + 656 + ], + "lines": [ + { + "bbox": [ + 66, + 637, + 167, + 656 + ], + "spans": [ + { + "bbox": [ + 66, + 637, + 167, + 656 + ], + "type": "text", + "content": "(c) Example of normal slide from Camelyon16." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 168, + 553, + 269, + 635 + ], + "lines": [ + { + "bbox": [ + 168, + 553, + 269, + 635 + ], + "spans": [ + { + "bbox": [ + 168, + 553, + 269, + 635 + ], + "type": "image", + "image_path": "3bbe4a93255dae9b40e3ffee4bb89e1a3f71d41953c8899890a030da8eb11dfd.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 168, + 637, + 268, + 657 + ], + "lines": [ + { + "bbox": [ + 168, + 637, + 268, + 657 + ], + "spans": [ + { + "bbox": [ + 168, + 637, + 268, + 657 + ], + "type": "text", + "content": "(d) Partial slide (in red bounding box) selected from (c)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 349, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 434 + ], + "type": "text", + "content": "vidually to deal with the multi-class classification problems (e.g., TCGA-Lung dataset in Sec. 5.1) and can be replaced by any similar mechanisms of MIL, which calculates the importance of each patch to yield a final slide-level prediction (e.g., attention mechanism [25, 28, 30] or the distance between clusters [9, 38, 44]). So far, we can get the class probability of every patch in a WSI by the score function " + }, + { + "bbox": [ + 304, + 349, + 545, + 434 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 349, + 545, + 434 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 445, + 369, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 369, + 458 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 369, + 458 + ], + "type": "text", + "content": "4.3. Ranking" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "text", + "content": "After obtaining the score function " + }, + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "text", + "content": ", we already have the basic ability to achieve the motivation mentioned in Sec. 4.1. If we want to obtain a representative portion that can represent the original WSI, we need to score each feature " + }, + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\{\\hat{y}_{i,1},\\dots ,\\hat{y}_{i,m}\\} \\in \\mathbb{R}^{m\\times 1}" + }, + { + "bbox": [ + 304, + 465, + 545, + 538 + ], + "type": "text", + "content": " in the WSI and then sort the patch scores as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 550, + 545, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 550, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 315, + 550, + 545, + 588 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Z _ {i} = \\left\\{z _ {i, 1}, z _ {i, 2}, \\dots , z _ {i, m} \\right\\} \\\\ \\text {s . t .} \\hat {y} _ {i, z _ {i, 1}} > \\hat {y} _ {i, z _ {i, 2}} > \\dots > \\hat {y} _ {i, z _ {i, m}} \\quad \\forall i = 1, \\dots , n. \\tag {9} \\\\ \\end{array}", + "image_path": "d3c81b931fa842baa0ec5970f429ad59cdb26e40eb31b8e10cc189044cb3d4c9.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "content": "According to the number " + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "content": " is an arbitrary positive integer) of features we need, we can obtain the desired features " + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\bar{H}_i\\in \\mathbb{R}^{k\\times d}" + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "content": " from the original features " + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "inline_equation", + "content": "H_{i}\\in \\mathbb{R}^{m\\times d}" + }, + { + "bbox": [ + 306, + 589, + 545, + 624 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 355, + 637, + 545, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 637, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 355, + 637, + 545, + 664 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {H} _ {i} = \\left\\{h _ {i, z _ {i, 1}}, h _ {i, z _ {i, 2}}, \\dots , h _ {i, z _ {i, k}} \\right\\}. \\tag {10} \\\\ \\text {f o r} k \\leq m, \\forall i = 1, \\dots , n \\\\ \\end{array}", + "image_path": "96dd64adf65e9211ac8586c0758ce822f62b6ef345a54931e226cdb12e47df63.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Finally, in order to maintain the relative position information among patches, the features in " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{H}_i" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " are rearranged in the original order to get the final representative features" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23940" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 68, + 492, + 194 + ], + "blocks": [ + { + "bbox": [ + 107, + 68, + 492, + 194 + ], + "lines": [ + { + "bbox": [ + 107, + 68, + 492, + 194 + ], + "spans": [ + { + "bbox": [ + 107, + 68, + 492, + 194 + ], + "type": "image", + "image_path": "6771ffb035a01549345b89a0b0c735c55edd7b31d79e0ffa52307a8bc5e60bd0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 171, + 200, + 420, + 211 + ], + "lines": [ + { + "bbox": [ + 171, + 200, + 420, + 211 + ], + "spans": [ + { + "bbox": [ + 171, + 200, + 420, + 211 + ], + "type": "text", + "content": "Figure 4. Illustration of the pseudo labeling and ranking mechanism." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 232, + 111, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 111, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 111, + 246 + ], + "type": "inline_equation", + "content": "H_{i}^{\\prime}\\in \\mathbb{R}^{k\\times d}" + }, + { + "bbox": [ + 47, + 232, + 111, + 246 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 251, + 287, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 251, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 64, + 251, + 287, + 270 + ], + "type": "interline_equation", + "content": "H _ {i} ^ {\\prime} = \\left\\{h _ {i, z _ {i, 1} ^ {\\prime}}, h _ {i, z _ {i, 2} ^ {\\prime}}, \\dots , h _ {i, z _ {i, k} ^ {\\prime}} \\right\\}, \\tag {11}", + "image_path": "47c37b4c681ef68e8e29c0e83d433077ab8e439f391ad5fdb29693adaaa448ca.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 269, + 253, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 269, + 253, + 283 + ], + "spans": [ + { + "bbox": [ + 77, + 269, + 253, + 283 + ], + "type": "interline_equation", + "content": "s. t. z _ {i, 1} ^ {\\prime} < z _ {i, 2} ^ {\\prime} < \\dots < z _ {i, k} ^ {\\prime} \\quad \\forall i = 1, \\dots , n", + "image_path": "e516e935b05e52e3f974a0832a9c3cb1b4e98d6a3a93a46c7aaf4f23b6609f59.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "inline_equation", + "content": "H_{i}^{\\prime}" + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "text", + "content": " features selected from the original " + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 47, + 289, + 287, + 313 + ], + "type": "text", + "content": " slide with the order preserved." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 319, + 195, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 195, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 195, + 332 + ], + "type": "text", + "content": "4.4. Mixup in Ranked Features" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "text", + "content": "According to Eq. (5) and Eq. (6), we can formulate the mixup of features from two examples, " + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "inline_equation", + "content": "(X_{a},Y_{a})" + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "inline_equation", + "content": "(X_{b},Y_{b})" + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "text", + "content": ", sampled from the dataset " + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 338, + 287, + 373 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 110, + 380, + 287, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 380, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 110, + 380, + 287, + 394 + ], + "type": "interline_equation", + "content": "H _ {m x p} = \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime} \\tag {12}", + "image_path": "e40b610047581d4c417aa437693f052bc76130d1800d5d8cce457e1198686846.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 399, + 287, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 399, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 111, + 399, + 287, + 412 + ], + "type": "interline_equation", + "content": "Y _ {m x p} = \\lambda Y _ {a} + (1 - \\lambda) Y _ {b}, \\tag {13}", + "image_path": "f4c4468cd0799f1255cb1cf2ea2263e3e78b08ce21d19feb2497cb41400a3086.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "H_{a}^{\\prime}\\in \\mathbb{R}^{k\\times d}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "H_{b}^{\\prime}\\in \\mathbb{R}^{k\\times d}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " are obtained from " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "H_{a}\\in \\mathbb{R}^{m(a)\\times d}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "H_{b}\\in \\mathbb{R}^{m(b)\\times d}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": ", respectively, by Eq. (9)~Eq. (11), and " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "m(a)" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "m(b)" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " denote the numbers of features obtained from " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "X_{a}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 47, + 415, + 287, + 486 + ], + "type": "text", + "content": ", respectively. Different from the existing mixup techniques, we conduct mixup in ranked features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 494, + 195, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 195, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 195, + 506 + ], + "type": "text", + "content": "4.5. MIL Model with RankMix" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "content": "As described in Sec. 3.2 and Sec. 4.2, RankMix can be applied to MIL models with the total loss being defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 56, + 552, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 552, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 56, + 552, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = w _ {1} \\mathcal {L} _ {m a x} \\left(\\hat {y} _ {m x p, j ^ {*}}, Y _ {m x p}\\right) + w _ {2} \\mathcal {L} _ {b a g} \\left(\\hat {Y} _ {m x p}, Y _ {m x p}\\right) \\\\ + \\sum_ {\\ell} w _ {\\ell} \\mathcal {L} _ {\\ell}, \\tag {14} \\\\ \\end{array}", + "image_path": "7454c751edf4e0fd87e269737112a0f1ca680797bb8f8ef1ca83addbdca5f7c9.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "where the first term comes from Eq. (8) and the remaining terms come from Eq. (4). So far, we have explained how to accomplish the middle component of RankMix in MIL in Fig. 2, i.e., the first stage of training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 658, + 257, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 257, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 257, + 673 + ], + "type": "text", + "content": "4.6. Self-Training: Second Stage of Training" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "WSI classification faces the tough problem that each WSI is only given a slide-level label; that is, tens of thousands of patches correspond to one label. This kind of" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 232, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 328 + ], + "type": "text", + "content": "weakly supervised learning is more difficult to train than supervised learning. If the RankMix proposed so far is used, unstable training will be encountered. However, if the score function is more reliable (i.e., can distinguish patch labels) at the beginning, then RankMix is found to achieve better results. We can imagine that the score function acts like expert annotations, and higher quality annotations will naturally result in better performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 330, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 378 + ], + "type": "text", + "content": "Inspired by self-training [40,45] and BERT-based model [13, 27, 29], we design a score function by learning from a pre-trained task in advance (i.e., can output the class probability distribution of a patch) as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 316, + 403, + 544, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 403, + 544, + 428 + ], + "spans": [ + { + "bbox": [ + 316, + 403, + 544, + 428 + ], + "type": "interline_equation", + "content": "p \\left(\\hat {Y} _ {i} \\mid H _ {i}\\right) = \\text {a g g r e g a t o r} \\left(H _ {i}\\right) = p \\left(\\hat {Y} _ {i} \\mid h _ {i, 1}, \\dots , h _ {i, m}\\right). \\tag {15}", + "image_path": "1a3859ca80073171ff83103050d04c31b945a17c5690f23f75efbfc0bc5504be.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "content": "Then, by using the concept of self-training, the stronger model is used as a teacher to extract the area that can represent the original WSI via score function for the student model to mixup ranked features as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 310, + 500, + 545, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 500, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 310, + 500, + 545, + 554 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {Y} _ {m x p} = p \\left(Y _ {m x p} \\mid H _ {m x p}\\right) = p \\left(Y _ {m x p} \\mid h _ {m x p, 1}, \\dots , h _ {m x p, k}\\right) \\\\ = p \\left(Y _ {m x p} | \\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right) \\\\ = \\text {a g g r e g a t o r} \\left(\\lambda H _ {a} ^ {\\prime} + (1 - \\lambda) H _ {b} ^ {\\prime}\\right). \\tag {16} \\\\ \\end{array}", + "image_path": "350482f1e18357ceceab60f4b1057bb71b9c700308abeef0a71b048880a5620b.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": "From the perspective of BERT-based models, we use the teacher model to learn the WSI classification problem (also known as the pretext task) as pretraining, and treat the mixup of ranked features as the downstream task to further improve the performance. Please see Fig. 2 for the illustration of two-stage training procedure." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 643, + 449, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 449, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 449, + 657 + ], + "type": "text", + "content": "5. Experiments and Results" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "In this section, we will describe the datasets used for experiments in Sec. 5.1, experimental setting and performance metrics in Sec. 5.2, main results in Sec. 5.3, and ablation studies in Sec. 8.1 (Appendix)." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23941" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 70, + 511, + 188 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 511, + 188 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 511, + 188 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 511, + 188 + ], + "type": "table", + "html": "
Method/DatasetCamelyon16WSI-usabilityTCGA-Lung
ACCAUCAUPRCACCAUCAUPRCACCAUCAUPRC
DSMIL [28]86.82%93.32%92.68%76.11%86.60%24.51%93.81%97.89%97.75%
+ ReMix [46]82.17%86.89%83.86%83.19%85.83%25.59%94.29%97.62%97.29%
+ RankMix w/o self-training87.60%92.07%92.43%90.27%87.07%25.66%94.29%98.00%97.76%
+ RankMix89.92%93.47%92.74%90.27%88.16%28.41%94.29%98.04%97.79%
FRMIL [10]89.15%94.57%93.66%83.19%87.69%45.99%90.95%95.38%94.96%
+ ReMix [46]82.59%87.29%87.35%89.25%80.63%33.09%92.22%96.99%97.04%
+ RankMix w/o self-training90.70%94.11%93.68%80.53%84.27%38.55%93.33%95.84%97.01%
+ RankMix91.47%94.59%93.99%93.81%93.61%47.65%93.33%97.00%97.04%
", + "image_path": "92b215bd456e8be8c494845a226fed3791c41c5b7ad2a4431a3048c451a04b66.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 111, + 196, + 481, + 207 + ], + "lines": [ + { + "bbox": [ + 111, + 196, + 481, + 207 + ], + "spans": [ + { + "bbox": [ + 111, + 196, + 481, + 207 + ], + "type": "text", + "content": "Table 2. Comparison of WSI classification between RankMix and vanilla models under three datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 228, + 110, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 110, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 110, + 239 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "text", + "content": "We introduce the WSI datasets used for experiments here, and a pre-processing setting was adopted to extract patches from each WSI. Each WSI was cropped into different numbers of " + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "text", + "content": " patches at " + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "inline_equation", + "content": "20\\mathrm{x}" + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "text", + "content": " magnification without overlapping. We follow [10,28] to discard the background patches with tissue entropy less than " + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 247, + 287, + 318 + ], + "type": "text", + "content": " of a WSI." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "text", + "content": "Camelyon16 [16] is a public and well-known dataset proposed for metastasis detection in breast cancer. The dataset contains 270 training slides and 130 testing slides, and roughly has 4.1 million patches at " + }, + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "inline_equation", + "content": "20\\mathrm{x}" + }, + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "text", + "content": " magnification with the maximum of 44000 patches per WSI and a minimum of 1200 patches per WSI in our pre-processing setting. If a WSI contains at least one tumor region, it is regarded as a positive slide. On the contrary, if the entire area of a WSI is normal, it is negative. In Camelyon16, the tumor area only accounts for approximately less than " + }, + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 318, + 287, + 449 + ], + "type": "text", + "content": " of the tissue area in the positive slide." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": "TCGA-Lung is a public dataset that has two types of lung cancer, Lung Adenocarcinoma (TCGA-LUAD) and Lung Squamous Cell Carcinoma (TCGA-LUSC), from the Caner Genome Atlas (TCGA). Please refer to https://pubmed.ncbi.nlm.nih.gov/25691825/ for details. There are in total 1046 diagnostic WSIs, including 534 TCGA-LUAD and 512 TCGA-LUSC, were split into 836 training slides and 210 testing slides. After pre-processing, TCGA-Lung roughly has a minimum of 50 patches per slide and a maximum of 12700 patches per slide, with a total of 3.2 million patches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "WSI-usability is a private dataset used for distinguishing whether a WSI is usable or not. The purpose of this dataset is used for evaluating automatic quality control (QC). In order to have sufficient practicality, two pathologist experts each annotated 250 WSIs from TCGA, of which 50 WSIs were redundant, resulting in 450 WSIs in total. If it is a bad (labeled as positive) slide, it means that the WSI is not usable; otherwise, it is a good WSI and annotated as a negative slide. WSI-usability has only 23 positive slides, so it possesses a severe class imbalance problem. After preprocessing, WSI-usability roughly has a minimum of 700" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 228, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 252 + ], + "type": "text", + "content": "patches per slide and a maximum of 120000 patches per slide, with a total of 5.7 million patches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 253, + 546, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 546, + 384 + ], + "type": "text", + "content": "Summing up the above, the adopted datasets cover the imbalance/balanced classes, unbalanced/balanced bags, and single/multiple-class problem. Among them, WSI-usability has majority and minority categories with a huge gap, which indicates the rare diseases and other costly data. For the positive slides in Camelyon16, tumors occupy quite smaller areas than normal tissues, while the negative slide is all filled with normal tissues. Different from the other two datasets, TCGA-Lung has two types of positive slides, namely TCGA-LUSD and TCGA-LUSC, leading to a multi-class classification problem." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 394, + 534, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 534, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 534, + 407 + ], + "type": "text", + "content": "5.2. Experimental Setup and Evaluation Metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": "ResNet18 [22] was adopted as our backbone model that was trained by SimCLR [7] and Adam optimizer to obtain feature extractor " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": " with a mini-batch size of 512, learning rate of " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": ", and weight decay of " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "1e - 5" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": ". For Camelyon16, we used the weights of ResNet18 trained by Lee et al. [28], as described in [10]. Then, the embeddings " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "H_{i} \\in \\mathbb{R}^{m(i) \\times 512}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": " of a WSI " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "X_{i}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": " were obtained from the global average pooling layer of feature extractor " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": "For training aggregator, we used the Adam optimizer for 200 epochs with the mini-batch size of 1 (bag), learning rate of " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "2e - 4" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": ", and weight decay of " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "5e - 3" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": ". Note that the minibatch for performing mixup of ranked features was 2, where the sampling methods of DSMIL and FRMIL followed [19] and [10], respectively. The number " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " of features used in RankMix was set to " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\min(m(a), m(b))" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " for two WSIs " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "X_a" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "X_b" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "content": "For two-stage training, we trained teacher models by the general MIL (i.e., DSMIL and FR-MIL). Then, the teacher models were used to guide the training of student models by RankMix. The structures of both the teacher model and student model are the same, which can be considered as a kind of self-distillation mechanism. The temperature parameter " + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "content": " commonly used in knowledge distillation was set to 1.0 (see Eq. (20) later)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "The classification performance was evaluated in terms of" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23942" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 70, + 470, + 228 + ], + "blocks": [ + { + "bbox": [ + 124, + 70, + 470, + 228 + ], + "lines": [ + { + "bbox": [ + 124, + 70, + 470, + 228 + ], + "spans": [ + { + "bbox": [ + 124, + 70, + 470, + 228 + ], + "type": "table", + "html": "
Method/DatasetCamelyon16WSI-UsabilityTCGA-Lung
AccuracyAUCAccuracyAUCAccuracyAUC
DSMIL [28]86.82%93.32%76.11%86.60%93.81%97.89%
DSMIL + Direct Mixup84.50%90.51%89.38%71.18%94.29%98.03%
DSMIL + Shrink Mixup86.05%92.42%88.50%69.94%93.81%97.95%
DSMIL + Duplicate Mixup84.50%91.96%89.38%72.43%93.81%97.99%
DSMIL + Random Mixup87.60%91.89%88.50%83.33%94.29%97.99%
DSMIL + RankMix89.92%93.47%90.27%88.16%94.29%98.04%
FRMIL [10]89.15%94.57%83.19%87.69%90.95%95.38%
FRMIL + Direct Mixup88.37%92.50%59.29%80.37%92.38%95.96%
FRMIL + Shrink Mixup89.92%93.16%68.14%57.09%92.86%96.88%
FRMIL + Duplicate Mixup87.60%92.78%86.73%74.77%92.38%96.73%
FRMIL + Random Mixup90.70%94.23%77.88%80.69%93.33%96.98%
FRMIL + RankMix91.47%94.59%93.81%93.61%93.33%97.00%
", + "image_path": "e20bab4103c7540234f0bb3bba8455fc027004ac251e96e824d78874e0733c08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 157, + 236, + 436, + 247 + ], + "lines": [ + { + "bbox": [ + 157, + 236, + 436, + 247 + ], + "spans": [ + { + "bbox": [ + 157, + 236, + 436, + 247 + ], + "type": "text", + "content": "Table 3. Comparisons between RankMix and four custom mixup techniques." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 269, + 232, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 269, + 232, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 269, + 232, + 281 + ], + "type": "text", + "content": "the accuracy and area under the curve (AUC)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 287, + 132, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 287, + 132, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 132, + 298 + ], + "type": "text", + "content": "5.3. Main Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 305, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 472 + ], + "type": "text", + "content": "First, we applied the proposed method, RankMix, to two baseline models, DSMIL [28] and FRMIL [10], and compared the performance with the vanilla models in Tab. 2. We can observe that self-training indeed boosts the overall model performance, as described in Sec. 4.6. Without self-training (i.e., mixup in the model without being derived from a teacher model), RankMix can sometimes achieve slightly better results, but as the model and dataset vary, it can be seen that the performance is slightly degraded in few cases. On the contrary, when self-training is introduced, the performance can be improved further. A recent work, ReMix [46], which is a SOTA augmentation method in WSI, was included for comparison. It can be found that RankMix outperforms ReMix remarkably." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": "Second, we compared our method with the general mixup techniques under different custom settings in Tab. 3. This is because the existing mixup researches, to our knowledge, were conducted on the same feature number, they cannot be readily employed to be compared with our method under the scenario that two features of different numbers were mixed. Here, we discuss four situations for mixing up two WSIs " + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "inline_equation", + "content": "(H_{a}" + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "inline_equation", + "content": "H_{b})" + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": " with different numbers " + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "inline_equation", + "content": "(m(a)" + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "inline_equation", + "content": "m(b))" + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": " of features in the following." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "text", + "content": "1) Direct Mixup: Perform mixup directly regardless of feature numbers " + }, + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "inline_equation", + "content": "(m(a)" + }, + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "inline_equation", + "content": "m(b))" + }, + { + "bbox": [ + 47, + 581, + 287, + 629 + ], + "type": "text", + "content": ", where the feature with a smaller number is padded with zeros. So, the feature number after mixing is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 635, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 635, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 115, + 635, + 287, + 648 + ], + "type": "interline_equation", + "content": "k _ {d} = \\max (m (a), m (b)). \\tag {17}", + "image_path": "a7303070c243082a97e955dba7d4522391c03a57818a06d0bb6807d24c7d5bb1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": "2) Shrink Mixup: Extract the same number " + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "inline_equation", + "content": "k_{s}" + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": " of features for mixing up by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 101, + 684, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 684, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 101, + 684, + 287, + 716 + ], + "type": "interline_equation", + "content": "k _ {s} = \\left\\{ \\begin{array}{l} m (b), \\text {i f f} m (a) > m (b) \\\\ m (a), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {18}", + "image_path": "0447ae093cb75b18d15f23933c3aa211840740e145db34683923c81ecb443e99.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 269, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 269, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 545, + 303 + ], + "type": "text", + "content": "3) Duplicate Mixup: Duplicate the feature with a smaller number to have the same size " + }, + { + "bbox": [ + 305, + 269, + 545, + 303 + ], + "type": "inline_equation", + "content": "k_{du}" + }, + { + "bbox": [ + 305, + 269, + 545, + 303 + ], + "type": "text", + "content": " as the larger feature as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 357, + 302, + 545, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 302, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 357, + 302, + 545, + 334 + ], + "type": "interline_equation", + "content": "k _ {d u} = \\left\\{ \\begin{array}{l} m (a), \\text {i f f} m (a) > m (b) \\\\ m (b), \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {19}", + "image_path": "a5487fe97b22dab8cde5c486f9737760f2f2deea8b06e1ad42f67252b53bc49a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 338, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 545, + 361 + ], + "type": "text", + "content": "4) Random Mixup: By randomly performing both the duplicate and shrink mixups." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 361, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 409 + ], + "type": "text", + "content": "Compared with the above four straightforward cases, it can be seen from Tab. 3 that RankMix is a sophisticated design according to the characteristics of WSI, described in Sec. 1.2, and generally performs better than others." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 410, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 494 + ], + "type": "text", + "content": "Finally, we conduct ablation studies to further evaluate RankMix in two aspects. On the one hand, we examine how the score functions learned under different pre-trained models, as described in Sec. 4.6, affect RankMix. On the other hand, we examine how different knowledge transfer techniques affect the student model performance in WSI classification. Please refer to Sec. 8.1 in Appendix for details." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 504, + 378, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 504, + 378, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 504, + 378, + 516 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 524, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 632 + ], + "type": "text", + "content": "In this work, we investigate weakly supervised learning from the perspective of data augmentation to deal with the WSI classification problem that suffers from lack of training data and imbalance of categories. A new data augmentation method, RankMix, of is proposed to mix ranked features in a pair of WSIs with different sizes. RankMix is composed of pseudo labeling and ranking for extracting key WSI regions, and two-stage training for boosting stable training and model performance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 643, + 416, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 416, + 656 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 416, + 656 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 662, + 545, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 662, + 545, + 697 + ], + "spans": [ + { + "bbox": [ + 305, + 662, + 545, + 697 + ], + "type": "text", + "content": "This work was supported in part by the Ministry of Science and Technology of Taiwan, ROC, under Grant MOST 110-2634-F-006-022." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23943" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 126 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 126 + ], + "type": "text", + "content": "[1] Sugata Banerji and Sushmita Mitra. 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In International Conference on Learning Representations, 2018. 1, 2, 3, 4" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23945" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_content_list.json b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..78e20563d5dffd68a1b4b282299691f5123c24d7 --- /dev/null +++ b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_content_list.json @@ -0,0 +1,1406 @@ +[ + { + "type": "text", + "text": "Ranking Regularization for Critical Rare Classes: Minimizing False Positives at a High True Positive Rate", + "text_level": 1, + "bbox": [ + 84, + 128, + 885, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kiarash Mohammadi $^{1,2*}$ He Zhao $^{1}$ Mengyao Zhai $^{1}$ Frederick Tung $^{1}$ $^{1}$ Borealis AI $^{2}$ Mila, Université de Montréal", + "bbox": [ + 189, + 202, + 776, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "kiarash.mohammadi@mila.quebec, {he.zhao, mengyao.zhai, frederick.tung}@borealisai.com", + "bbox": [ + 104, + 241, + 857, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In many real-world settings, the critical class is rare and a missed detection carries a disproportionately high cost. For example, tumors are rare and a false negative diagnosis could have severe consequences on treatment outcomes; fraudulent banking transactions are rare and an undetected occurrence could result in significant losses or legal penalties. In such contexts, systems are often operated at a high true positive rate, which may require tolerating high false positives. In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. We propose a ranking-based regularization (RankReg) approach that is easy to implement, and show empirically that it not only effectively reduces false positives, but also complements conventional imbalanced learning losses. With this novel technique in hand, we conduct a series of experiments on three broadly explored datasets (CIFAR-10&100 and Melanoma) and show that our approach lifts the previous state-of-the-art performance by notable margins.", + "bbox": [ + 73, + 321, + 473, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 638, + 209, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The cost of error is often asymmetric in real-world systems that involve rare classes or events. For example, in medical imaging, incorrectly diagnosing a tumor as benign (a false negative) could lead to cancer being detected later at a more advanced stage, when survival rates are much worse. This would be a higher cost of error than incorrectly diagnosing a benign tumour as potentially cancerous (a false positive). In banking, misclassifying a fraudulent transaction as legitimate may be more costly in terms of financial losses or legal penalties than misclassifying a legitimate transaction as fraudulent (a false positive). In both of these examples, the critical class is rare, and a missed detection carries a disproportionately high cost. In such situations, systems are often operated at high true positive rates,", + "bbox": [ + 75, + 664, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1455e6fd0fff84112716f02a09d76edc07f477d2778396d5a86e99222e3dad70.jpg", + "image_caption": [ + "Figure 1. Which optimization option is preferred in operational contexts with critical positives? We propose a novel regularizer for systems that need to operate at a high true positive rate (TPR). Our approach prioritizes reducing false positives at a high TPR when presented with different options that equally improve the base objective, e.g. area under the ROC curve (AUC). In this toy example, option 2 is preferred because, with a suitable threshold depicted by the dashed line, all positives can be detected (100% TPR) with only one false positive (i.e., 25% FPR at 100% TPR), better than option 1 where two false positives need to be tolerated. Our regularizer is consistent with this preference: $\\ell_{reg}$ is lower for option 2 than option 1 (i.e., 13 vs. 17)." + ], + "image_footnote": [], + "bbox": [ + 519, + 292, + 877, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "even though this may require tolerating high false positive rates. Unfortunately, false positives can undermine user confidence in the system and responding to them could incur other costs (e.g. additional medical imaging tests).", + "bbox": [ + 496, + 794, + 890, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. Surprisingly, this", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Borealis AI", + "bbox": [ + 94, + 886, + 346, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15783", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "high-stakes operational setting has rarely been studied by the research community. In contrast to conventional imbalanced classification methods, we propose a general method for inducing a deep neural network to prioritize the reduction of false positives at a high true positive rate. To remain as broadly applicable as possible, we make minimal assumptions on the architecture and optimization details of the deep neural network. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play solution adds a simple yet effective ranking-based regularization term to the usual neural network training objective. The regularization term places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores, which works to push up the scores of the hardest positives.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. The main contributions of this paper are as follows:", + "bbox": [ + 76, + 333, + 468, + 362 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel plug-and-play regularization term that induces a deep neural network to prioritize the reduction of false positives in operational contexts where a high true positive rate is required.", + "- Our regularizer is generic and can be easily combined with other methods for imbalanced learning.", + "- We conduct extensive experiments on three public benchmarks to show how the proposed regularization term is complementary to conventional imbalanced learning losses, and achieves state-of-the-art performance in the high true positive rate operational setting." + ], + "bbox": [ + 96, + 373, + 468, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 573, + 215, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Imbalanced classification. Class imbalance poses a challenge in training real-world neural network models. Without intervention, the optimization of a classification network becomes dominated by the common classes at the expense of the rare classes. Performing robust and efficient classification on imbalanced data is of practical importance and has seen much recent progress. In general, existing methods for imbalanced classification can be summarized into three major groups: cost function based, model output based, and data based. In the first group, various auxiliary optimization objectives are used during training, with a special attention to increase (or balance) the impact of under-represented classes. One such effort used weighted binary cross entropy (WBCE) [35], where the losses of minority samples are multiplied by a scaling factor (typically larger than one) to introduce more cost. Other cost function based approaches include symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], class-balanced BCE (CB-BCE) [8] and label distribution aware", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "margin (LDAM) [4]. The second group of work tackles the problem by post-processing the model outputs. One simple approach divides the output scores with class cooccurrence frequencies [1, 15]. Similarly, other work adjusts the outputs by re-balancing the probabilities based on minority classes [28]. The third group of work focuses on data re-sampling or augmentation. Re-sampling or oversampling the minority classes has shown solid benefits [6]. Enhancing samples from rare classes via augmentation also has received much consideration in recent years. Some representative examples are UnMix [31], ReMix [7] and MixUp [36]. Though approaching the same problem differently, all aforementioned methods have been used in a variety of vision tasks, e.g., image classification [1,2,6,12], object detection [5,16] and image/video segmentation [14,32], where class imbalance is severe.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work falls into the first group (i.e. cost function based). We show in the experiments that our ranking-based regularization term is complementary to a wide range of established cost function based approaches (see Sec. 4). Importantly, in contrast to conventional imbalanced classification methods, we prioritize the reduction of false positives at a high true positive rate.", + "bbox": [ + 496, + 335, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differentiable ranking. Our regularization objective requires ranking the critical positive samples higher than the negative samples. This task is challenging as ranking operations are piece-wise constant functions, which have zero gradient almost everywhere [11]. Learning ranking directly through backprop is not feasible. To this end, many alternative solutions have been explored. For instance, an earlier effort considered using the expectation of the ranking as soft-ranker [27]. Some recent work used dynamic programming, instead of backprop, for weights update [26], while others achieved this purpose using a differentiable relaxation of histogram binning [3, 13, 21]. Other work has reformulated it as an optimal transport problem [9]. Our work relies on a recent advance that recasts the ranking operation as the minimizer of a linear combinatorial objective [29], which can be sovled elegantly by a blackbox combinatorial solvers [30] that can provide informative gradients from a continuous interpolation.", + "bbox": [ + 496, + 444, + 890, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep AUC optimization. Our work can be considered (and will be demonstrated in Section 4) as an optimizer for maximizing the AUC score, cf. [10,19,33,34]. Nonetheless, none of them are designed to favor low false positive rates given a high true positive rate requirement. The work most similarly motivated to ours is ALM [24], which recently advocated yielding higher score (i.e. probability) for critical positives than non-critical negatives, thus improving the AUC. ALM formulates the problem from a constrained optimization perspective and achieves strong empirical results. We provide comprehensive comparisons with this state-of-the-art baseline in our experiments.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15784", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9b8c773e8f5b2405a77a9c8ac453b7f680f24f324b6fa13adc249c32183b56bf.jpg", + "image_caption": [ + "Figure 2. An illustration of the regularization term by example. Given a batch of inputs and a buffer (i.e., external memory) of positive samples, we collect the probability scores from the classifier, $f_{\\theta}$ , and apply the ranking function, $rk(\\cdot)$ , to obtain a vector $r$ of rank values. The rank values associated with the positive samples (i.e., numbers in green boxes) are then used to compute the ranking-based regularization loss, $\\ell_{reg}$ , using Eq. 4; we drop the normalization in this figure for simplicity of presentation. Note that $f_{\\theta}$ can be an arbitrary classification architecture and RankReg does not rely on the specifics of that approach." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 472, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Technical approach", + "text_level": 1, + "bbox": [ + 76, + 491, + 266, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present a novel, plug-and-play regularization loss as a generic method for inducing a neural network to prioritize minimizing false positives at a high true positive rate. First, we formulate the imbalanced binary classification task with critical positives in Sec. 3.1. Second, to obtain a solution that is tailored asymmetrically to the high true positive rate setting, we introduce a ranking-based regularization term that encourages models to rank the critical positives higher than the non-critical negatives, while prioritizing reducing the false positive rate at high true positive rate thresholds. Third, we discuss the used optimization solution in Sec. 3.4, as the ranking operation is challenging to optimize with back-propagation due to its non-differentiable nature.", + "bbox": [ + 75, + 517, + 472, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem formulation", + "text_level": 1, + "bbox": [ + 76, + 724, + 274, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We seek to predict the correct label over a highly imbalanced binary classification dataset $D = \\{(x_{1},y_{1}),(x_{2},y_{2}),\\ldots ,(x_{n},y_{n}),y_{i}\\in \\{0,1\\} \\}$ where $x_{i}$ are data samples, $y_{i}$ are labels, and the critical data samples (positive class, labelled 1) appear much less frequently than the non-critical data samples (negative class, labelled 0). For example, medical images with cancerous tumors may be critical positives, while images with benign tumors or no tumors may be negatives. It is assumed that the cost of missing the positive class (a false", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "negative) carries a disproportionately high cost, and that the system is required to operate at a high true positive rate.", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to produce a general method for inducing a deep neural network (DNN) classifier $f_{\\theta} : \\mathbb{R}^{d} \\rightarrow \\mathbb{R}$ , mapping $d$ -dimensional inputs to output scores, to prioritize the reduction of false positives at a high true positive rate [24]. To be as general as possible, the method should make minimal assumptions on the architecture and optimization details of $f_{\\theta}$ .", + "bbox": [ + 496, + 122, + 893, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 237, + 629, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a novel ranking-based [11, 29] regularizer that fulfills the above desiderata. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play approach adds a regularization term to the usual DNN training objective, making our solution complementary to a wide range of base objective functions, from conventional binary cross-entropy to more sophisticated imbalanced losses such as asymmetric focal loss [17]. In other words, we modify the DNN training objective to be:", + "bbox": [ + 496, + 260, + 893, + 426 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\ell_ {\\text {b a s e}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) + \\lambda \\ell_ {\\text {r e g}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 439, + 890, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\ell_{base}$ is the base objective function, $\\ell_{reg}$ is the new regularization term, and $\\lambda$ is a balancing hyperparameter with value empirically set to 1.", + "bbox": [ + 496, + 467, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Ranking regularizer", + "text_level": 1, + "bbox": [ + 500, + 523, + 692, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denote by $r_k(\\cdot)$ the ranking function that takes a vector of real values $\\pmb{a}$ and outputs the rank of each element in the sorted vector. In other words, the $i$ th element in $r_k(a)$ is given by", + "bbox": [ + 496, + 561, + 890, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) _ {i} = 1 + | \\left\\{j: \\boldsymbol {a} _ {j} > \\boldsymbol {a} _ {i} \\right\\} |. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 623, + 890, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, we devise a regularization term that is computed as the normalized sum over the squared rank values of the positive samples:", + "bbox": [ + 496, + 646, + 890, + 691 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {r} = \\boldsymbol {r} \\boldsymbol {k} \\left(\\left[ f _ {\\theta} \\left(\\boldsymbol {x} _ {1}\\right), f _ {\\theta} \\left(\\boldsymbol {x} _ {2}\\right), \\dots , f _ {\\theta} \\left(\\boldsymbol {x} _ {B}\\right) \\right]\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 704, + 890, + 720 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {r e g} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\frac {1}{| P |} \\sum_ {i = 1} ^ {B} \\boldsymbol {r} _ {i} ^ {2} \\cdot \\mathbb {1} \\left[ y _ {i} = 1 \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 724, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $|P| = \\sum_{i=1}^{B} \\mathbb{1}[y_i = 1]$ is the number of positive samples in the batch of $B$ samples. In practice, since positive samples may be severely under-represented in the dataset, we compute the regularization term over the union of the batch and an external memory that caches previous positive samples; we will revisit the implementation details of this buffer in Section 3.5. We also normalize the rank values $r$ to be between 0 and 1.", + "bbox": [ + 496, + 777, + 893, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15785", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To see how this regularization term prioritizes the reduction of false positives at a high true positive rate, let us consider the toy example in Figure 1. Suppose that the classifier $f_{\\theta}$ currently produces the sorted ordering shown in the left column. The ground-truth critical positives are represented by green plus icons and the ground-truth negatives are represented by grey minus icons. The positive examples induce the second and fourth highest classification scores (higher is better for positives). To achieve a high true positive rate of $100\\%$ on these two positives, we would have to accept at least two false positives, obtaining a false positive rate of $50\\%$ . Now, suppose that in the next training iteration, the optimizer has two options, shown in the middle and right columns, that would equally improve the training objective; here, we illustrate with the area under the ROC curve (AUC), a common retrieval-based objective. While equally preferable by the training objective, the right column is better aligned with our goal of reducing false positives at a high true positive rate: with a suitable threshold (depicted by the dashed line), we can obtain a false positive rate of $33\\%$ at a true positive rate of $100\\%$ . On the other hand, the middle column can at best achieve a false positive rate of $50\\%$ at a true positive rate of $100\\%$ .", + "bbox": [ + 76, + 90, + 472, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed regularization term distinguishes between the middle and right columns, and assigns a higher loss to the middle column. In the middle column, the positives have the first and fourth highest classification scores, producing a regularization loss of $1^{2} + 4^{2} = 17$ (we drop the normalization terms here for simplicity of presentation). In the right column, the positives have the second and third highest classification scores, producing a regularization loss of $2^{2} + 3^{2} = 13$ . The proposed regularization therefore favors the right column, as desired. Note that if we use the ranks directly instead of squaring, the regularization loss would be 5 in both cases $(1 + 4 = 2 + 3 = 5)$ . Squaring places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's output scores, which works to push up the scores of the least confident positive samples.", + "bbox": [ + 76, + 441, + 472, + 685 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Optimization on ranking operations", + "text_level": 1, + "bbox": [ + 76, + 705, + 388, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rank-based objectives often arise in computer vision [13, 25, 27] and are typically challenging to optimize due to the non-differentiability of the ranking function. The ranking function is piece-wise constant, i.e., perturbing the input would most likely not change the output. Thus, we cannot obtain informative gradients (i.e., gradients are zero almost everywhere). We adopt the optimization approach of [22], which frames the ranking function as a combinatorial solver and relies on an elegant way of backpropagating through blackbox combinatorial solvers [29]. The combinatorial objective version of computing the ranking function is given", + "bbox": [ + 76, + 734, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by", + "bbox": [ + 500, + 92, + 521, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) = \\underset {\\pi \\in \\Pi_ {n}} {\\arg \\min } \\boldsymbol {a} \\cdot \\boldsymbol {\\pi}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 106, + 890, + 131 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for an arbitrary vector $\\mathbf{a}$ of real values (see Eq. 2), where $\\Pi_{n}$ is a set that contains all the permutations of $\\{1,2,\\dots ,n\\}$ . This reframing enables us to leverage [29] to differentiate through a blackbox combinatorial solver: [29] proposes a family of piecewise affine continuous interpolation functions parameterized by a single hyperparameter that controls the tradeoff between faithfulness to the true function and informativeness of the gradient. In brief, we compute and return the gradient of the continuous interpolation: $\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{a}} = -\\frac{1}{\\gamma} (\\mathbf{r}\\mathbf{k}(\\mathbf{a}) - \\mathbf{r}\\mathbf{k}(\\mathbf{a}_{\\gamma}))$ where $\\mathbf{a}_{\\gamma}$ is a perturbed input derived from the incoming gradient information $\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}$ via $\\mathbf{a}_{\\gamma} = \\mathbf{a} + \\gamma \\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}$ . We refer the interested reader to [22] for further details.", + "bbox": [ + 496, + 136, + 893, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Buffer of positive samples", + "text_level": 1, + "bbox": [ + 500, + 347, + 733, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During training, we maintain a buffer (i.e., an external memory) of positive samples to enable the regularization term to be computed per batch even in datasets with severe imbalance ratios, as a batch may contain few (or no) positive samples. The whole buffer is always appended to the batch. We implement the buffer as a priority queue and it works as follows. At the start of training, positive samples are accumulated from the incoming batches and added to the buffer up to a fixed maximum capacity. Afterwards, as batches are processed, new positive samples replace the samples in the buffer for which the model is the most certain, i.e., the buffered samples with the maximum $f_{\\theta}$ responses. This replacement strategy keeps the hard positives in the buffer and removes positives for which the classifier is already confident. We consider the alternative replacement strategies of first-in-first-out (FIFO) and minimum $f_{\\theta}$ responses in the ablation studies. The complete pipeline, including the buffer of positive samples, is illustrated by example in Figure 2 (without normalization for simplicity of presentation).", + "bbox": [ + 496, + 369, + 893, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Empirical evaluation", + "text_level": 1, + "bbox": [ + 500, + 686, + 699, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 710, + 609, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of RankReg, extensive experiments are conducted on three public image-based benchmarks: binary imbalanced CIFAR-10, binary imbalanced CIFAR-100, and Melanoma. To adapt CIFAR-10 and CIFAR-100 to the critical positives setting, we follow the same experimental protocol as the state-of-the-art baseline [24]. As we do not have access to the private medical imaging dataset used in [24], we performed experiments on a publicly available medical imaging dataset (i.e., Melanoma). In this section, we first describe the benchmarks, baselines, and training details. We then present ex", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15786", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/e88cf2e921209da2ff94e28640e1c1944ab35681e92945b4915ed73e45513ccd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsBinary CIFAR10, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRAUC ↑
BCE56.045.029.091.2
+ALM52.034.021.093.1
+RankReg47.126.220.694.3
S-ML59.040.026.091.7
+ALM50.037.024.092.5
+RankReg45.631.429.793.9
S-FL59.040.027.091.7
+ALM55.039.025.091.5
+RankReg53.335.420.792.8
A-ML54.036.023.092.4
+ALM45.035.023.092.8
+RankReg47.828.921.494.1
A-FL50.038.024.092.3
+ALM49.037.023.092.8
+RankReg50.528.720.994.3
CB-BCE89.072.059.078.0
+ALM67.051.036.088.1
+RankReg48.829.924.693.2
W-BCE69.052.037.087.4
+ALM66.048.031.089.3
+RankReg60.039.429.692.1
LDAM65.048.034.089.0
+ALM60.042.031.091.0
+RankReg42.825.623.895.0
Avg. Δ6.09.72.82.3
", + "bbox": [ + 89, + 88, + 459, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "perimental results on the three benchmarks, showing how the proposed regularizer is complementary to conventional imbalanced learning losses and achieves state-of-the-art results. We conclude with ablations and analyses of design choices.", + "bbox": [ + 75, + 642, + 468, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Datasets and evaluation protocol", + "text_level": 1, + "bbox": [ + 76, + 726, + 364, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Binary imbalanced CIFARs. For a fair comparison, we adopt the same binary imbalanced versions of CIFAR-10 and 100 as curated by the authors of the state-of-the-art method [24]. In brief, binary imbalanced CIFAR-10 is constructed by randomly designating two classes as positives and negatives. All training samples from the negative class are used, while training samples from the positive class are subsampled. Binary imbalanced CIFAR-100 is constructed by designating one super-class as the negative class and a sub-class of a different super-class as the positive class.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ba35c090dd76396a9243b83c440b9448f552bf9273d561be5002e77506f4357c.jpg", + "table_caption": [ + "Table 1. Comparison results for binary imbalanced CIFAR-10 showing FPRs at $\\{98\\%, 95\\%, 92\\%\\}$ TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + ], + "table_footnote": [], + "table_body": "
MethodsBinary CIFAR100, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓90%TPRAUC ↑
BCE93.063.047.081.8
+ALM91.049.039.082.7
+RankReg85.242.428.785.5
S-ML89.065.043.082.7
+ALM88.069.041.081.7
+RankReg64.044.834.585.4
S-FL89.062.044.082.6
+ALM88.060.042.081.7
+RankReg84.649.238.484.7
A-ML91.063.044.081.8
+ALM89.055.037.082.7
+RankReg81.643.432.685.5
A-FL88.063.045.082.8
+ALM86.062.040.083.2
+RankReg70.053.435.884.6
CB-BCE93.075.052.078.8
+ALM89.059.036.083.8
+RankReg89.848.633.484.1
W-BCE88.059.041.079.7
+ALM87.053.039.083.2
+RankReg84.060.041.182.9
LDAM84.070.042.082.3
+ALM80.059.040.083.2
+RankReg70.351.635.084.7
Avg. Δ8.68.64.31.9
", + "bbox": [ + 511, + 88, + 880, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Comparison results for binary imbalanced CIFAR-100 showing FPRs at $\\{98\\%, 95\\%, 90\\%\\}$ TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively.", + "bbox": [ + 498, + 559, + 893, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Again, all training samples from the negative class are used, while training samples from the positive class are subsampled. We refer the interested reader to [24] for the construction details. Following the evaluation protocol in [24], we experiment with 1:100 and 1:200 imbalance ratios (1 critical positive to 100 or 200 negatives), set aside 100 and 50 samples per class to form the validation set for hyperparameter selection for CIFAR-10 and 100 respectively, and evaluate on a class-balanced test set.", + "bbox": [ + 496, + 642, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Melanoma. The Kaggle Melanoma dataset is a medical image classification dataset that was first proposed on a competition for identifying melanoma (a common form of skin cancer) in imaging scans of skin lesion [23]. It is composed of 33,126 images collected from patients in large variance, where only 584 out of the entire set are malignant (i.e., positive) melanoma; therefore, the dataset has a 1:176 imbalance ratio. It is split into training, validation, and test sets", + "bbox": [ + 496, + 779, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15787", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with ratios of $70\\%$ , $10\\%$ , and $20\\%$ , respectively. The original resolutions of images in Melanoma are too high (e.g., [6000, 4000] or [1920, 1080]) to fit in the backbone network (i.e., ResNet-18). We resize them into [256, 256] for the convenience of computational resources, cf. [34]. Since Melanoma is naturally imbalanced, no further curation is needed for our study.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We evaluate the performance using the false positive rate (FPR) against several increasingly strict true positive rates (TPR), i.e., FPR@{β}TPR and $\\beta \\in$ $\\{90\\%, 92\\%, 95\\%, 98\\% \\}$ . For completeness, we also evaluate using the area under curve metric (AUC) to reveal the overall classification performance, as typically seen in related work [10, 19, 33, 34].", + "bbox": [ + 75, + 196, + 468, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Baseline methods.** Following previous method [24], we consider applying our proposed regularizer with several different existing loss functions, most of which have been designed to handle class imbalance: binary cross-entropy (BCE), symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], cost-weighted BCE (WBCE) [35], class-balanced BCE (CB-BCE) [8], and label distribution aware margin (LDAM) [4].", + "bbox": [ + 75, + 303, + 470, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 452, + 290, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Backbone architectures. For the binary imbalanced CIFAR datasets, we adopt the ResNet-10 architecture up to the second last layer as feature extractor and append a multi-layer perceptron (MLP) with shape $[512\\to 2]$ as the classifier. For Melanoma, we adopt the richer architecture of ResNet-18 and repeat the same step to create the classifier.", + "bbox": [ + 75, + 476, + 468, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Buffer usage. The buffer of positive samples can have a rebalancing effect when used to compute the base loss in addition to the usual batch samples. We leverage this effect when training models on the binary imbalanced CIFAR-10 and CIFAR-100, which have balanced test sets following the protocol in [24]. Since all splits in the Melanoma dataset follow the data's natural class imbalance, when training the Melanoma models we compute the base loss using the batch samples only. Throughout our experiments, we set the batch size to 64 when training other methods (including base methods and ALM). When training RankReg models, we use a buffer size of 32 and reduce the batch size to 32.", + "bbox": [ + 75, + 566, + 470, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyper-parameter search. For CIFAR-10 and CIFAR-100, which we have in common with [24], we use the same hyper-parameters on all base loss functions, for the sake of fair comparison. For Melanoma dataset, we tune the hyperparameters as follows. The more general parameters like learning rate and batch size are chosen and fixed to work with the BCE loss. For ALM [24], a two step grid-search is performed. In the first step, we perform a grid-search over $\\rho$ and $\\mu^{(0)}$ . We choose $\\rho$ from the set $\\{2,3\\}$ and $\\mu^{(0)}$ from the set $\\{10^{-2},10^{-3},10^{-4},10^{-5},10^{-6},10^{-7},10^{-8},10^{-9}\\}$", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5393ae8f05a66509cd06778b2359c28e767ebc866f3819e26d4c12ed4d8e22e8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsMelanoma, imb. 1:170
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRFPR@ ↓90%TPRAUC ↑
BCE49.845.938.635.585.7
+ALM49.941.840.037.785.6
+RankReg49.437.933.931.686.8
S-ML46.642.838.437.485.3
+ALM51.340.539.836.283.5
+RankReg54.642.436.134.486.3
S-FL59.047.344.439.583.8
+ALM47.842.739.238.184.0
+RankReg56.637.831.229.886.1
A-ML47.542.940.436.685.4
+ALM51.041.537.537.183.7
+RankReg58.340.836.733.986.2
A-FL55.645.042.741.284.4
+ALM49.042.440.138.183.6
+RankReg48.036.230.728.886.3
CB-BCE67.259.535.733.282.6
+ALM60.859.546.345.881.5
+RankReg57.844.935.734.783.7
W-BCE69.052.037.032.187.4
+ALM66.048.031.030.789.3
+RankReg56.441.133.030.590.9
LDAM59.748.246.239.083.4
+ALM62.747.743.340.781.5
+RankReg65.647.545.743.981.7
", + "bbox": [ + 498, + 88, + 890, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison results for Melanoma dataset showing FPRs at $\\{98\\%, 95\\%, 92\\%, 90\\% \\}$ TPRs. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively.", + "bbox": [ + 498, + 484, + 890, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(note that this is a slightly more thorough grid-search than the original paper). When these two are fixed, we search for the best $\\delta$ from the set $\\{0.1, 0.25, 0.5, 1.0\\}$ . These parameters are tuned based on the AUC on the validation set.", + "bbox": [ + 496, + 566, + 890, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model ensembling. For CIFAR-10 and CIFAR-100 where the datasets are rather small, we report results from 10 ensembling models for higher reliability and to diminish dataset-dependant biases, matching the protocol in [24]. In detail, 10 random stratified splits of the dataset are created and a model is trained on each. Finally, these models are ensembled by averaging their outputs in the logit space. We do not perform ensembling on Melanoma, as it is larger and has a standard data split.", + "bbox": [ + 496, + 626, + 890, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Comparison to alternative approaches", + "text_level": 1, + "bbox": [ + 498, + 771, + 828, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Binary imbalanced CIFAR-10. Table 1 compares the performance of using RankReg as well as the previous state-of-the-art method ALM [24] together with eight base losses on CIFAR-10 dataset, curated with a imbalance ratio of 1:100 (see Sec. 4.2). We group the empirical results by base loss (BCE, S-ML, S-FL, etc.). Within each group, we first show the results obtained by applying the base method as well as", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15788", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/81ff1fbb6501bf21befbfceda1b72f43ae789fc7ef961e31be38453fbf22e2f8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Ranks52.135.224.093.686.352.843.083.2
Squared ranks47.126.220.694.385.242.428.785.5
Cubed ranks45.531.923.093.784.253.850.483.7
Exponential of ranks44.534.024.393.683.648.839.484.9
", + "bbox": [ + 78, + 88, + 467, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the previous state-of-the-art approach. Then, we show our results. For each FPR and overall AUC, the best result is either underlined or highlighted in red text.", + "bbox": [ + 75, + 233, + 468, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is clear that our results are consistently better on most metrics, except for three FPR values at S-ML, A-FL and A-ML baselines, where RankReg is the second best approach. The performance improvement is especially striking when coupling RankReg with CB-BCE: RangReg reduces the FPR at the strictest TPR ratio by $18\\%$ , i.e., from 67.0 to 48.8 in FPR@98%TPR. The best overall results are obtained by fusing RankReg with the LDAM baseline, where we achieve the highest AUC score (i.e., 95.0) as well as the lowest FPR@98%TPR value (i.e., 42.8) across all experimental results.", + "bbox": [ + 75, + 279, + 468, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Even though our goal is not to have higher AUC scores, our approach obtains the new state-of-the-art AUC performance on all baselines. The bottom row in Table 1 shows the improvements on FPRs using RankReg compared to previous best results, averaged across all baselines. It is notable that our approach obtains larger gains at higher TPRs. For instance, our approach achieves 6.0 and 9.7 FPR improvements at $98\\%$ and $95\\%$ TPRs, respectively, compared to 2.8 at $92\\%$ TPR, which is favored by our goal (see Sec. 3.3).", + "bbox": [ + 75, + 446, + 468, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Binary imbalanced CIFAR-100. To show the capability of our method to scale, we evaluate our method on the curated CIFAR-100 dataset. The results in Table 2 are consistent with our results on CIFAR-10. Once again, our approach is the top performer across most metrics. However, this time, both the BCE and A-ML baselines achieve the highest AUC score using RankReg. Moreover, it is notable that on the highest TPR (i.e., $98\\%$ ), our approach outperforms the previous state-of-the-art with the margin $>10\\%$ on 5 different baselines (i.e., A-FL, S-ML, BCE, LDAM and S-FL). Such notable gains are only observed twice in previous experiments (i.e., LDAM and CB-BCE in Table 1).", + "bbox": [ + 75, + 598, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Melanoma. We demonstrate the application of RankReg on imbalanced cancer classification using the Melanoma benchmark and show results in Table 3. As we are the first to perform FPR vs. TPR study on such a large-scale dataset, there is a lack of comparison methods. Therefore, we provide results for all baselines as well as their combination with ALM by running experiments ourselves. It can be seen that, across all baselines, RankReg achieves state-", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bc7b13a117df3e5972612b597c6da4939f3a410b78638b474d0860aa02396630.jpg", + "table_caption": [ + "Table 4. Ablation study of different ranking penalty choices on imbalanced CIFAR-10 and 100 datasets." + ], + "table_footnote": [], + "table_body": "
FPR@βTPRCIFAR100Melanoma
98%95%92%AUC98%95%92%AUC
Dequeue Max85.242.428.785.549.437.933.986.8
FIFO86.844.231.285.259.247.640.583.1
Dequeue Min88.255.944.883.2
", + "bbox": [ + 500, + 88, + 890, + 161 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/968576addccbe183f059aa936e9030d5ef2b428e740019bd91c4dff89715bbb6.jpg", + "table_caption": [ + "Table 5. Ablation study on buffer update strategy. Swapping out the most confident sample with incoming ones (i.e., Dequeue Max) performs better than other alternatives." + ], + "table_footnote": [], + "table_body": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Buffer = 058.843.630.290.493.448.437.483.1
Buffer = 553.042.428.792.686.657.239.082.5
Buffer = 1048.126.926.294.585.250.228.784.6
Buffer = 2047.626.222.093.885.250.029.884.9
Buffer = 3247.126.220.694.385.242.428.785.5
Buffer = 4846.124.323.293.985.242.127.685.5
", + "bbox": [ + 500, + 227, + 890, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Illustration of the impact of the positive buffer. We report false positive rate results at high true positive rates for various buffer sizes.", + "bbox": [ + 498, + 345, + 890, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of-the-art performance in the majority of metrics, with a minor setback on LDAM, where both ours and ALM achieve one best metric. These results verify the effectiveness of RankReg on a real-world dataset with critical positives.", + "bbox": [ + 496, + 414, + 890, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Discussion. We attribute the performance lift obtained by RankReg to its more direct approach in ordering the critical positives ahead of the negatives, which is accomplished indirectly through margins in the previous state-of-the-art method ALM [24]. The FPR at a given TPR depends only on how samples are ranked relative to each other, and not on the magnitude of the classification scores. Furthermore, the FPR at a high TPR is determined by the ranking of the least confident positives. Our regularizer places an increasing penalty on positive samples the lower they are ranked, which works to push up the scores of the hardest positives.", + "bbox": [ + 496, + 474, + 890, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablations and additional analyses", + "text_level": 1, + "bbox": [ + 500, + 650, + 794, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we examine the impact of used components as well as provide additional evaluation to reveal our system's pros and cons. For these additional studies, unless otherwise indicated, we present results from using our approach with BCE as the base function.", + "bbox": [ + 496, + 674, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Rank penalty ablation. Table 4 shows an ablation study on different choices for the rank penalty in Eq. 4, including raw rank values $r$ , squared rank values $r^2$ , cubed rank values $r^3$ , and the exponential of rank values $e^r$ . Squared rank provides the best overall result while being simple.", + "bbox": [ + 496, + 750, + 890, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of buffer maintenance strategy. Our approach uses a buffer of critical positive samples to have meaningful ranking regularization signals at each batch of training. We evaluate the role of buffer by considering three kinds of maintenance strategies: (1) remove the most confident", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15789", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/18e3e07d3ddd6c054f3893aee28629f10790597e5cf4a8cc028ee8d1f1aeb60d.jpg", + "image_caption": [ + "Figure 3. Evaluation of ROC results produced by our approach vs. others on the CIFAR10 dataset (in 1:100 imbalance ratio)." + ], + "image_footnote": [], + "bbox": [ + 107, + 90, + 433, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sample while adding new positive samples from a incoming batch (i.e., Dequeue Max), (2) first-in-first-out (i.e., FIFO), and (3) remove the least confident sample (i.e., Dequeue Min). The results in Table 5 show that feeding sufficient amount of low-ranking positives to the model is useful, as evidenced by the increased performance across all metrics.", + "bbox": [ + 75, + 338, + 468, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of buffer size. Throughout the empirical results in Sec. 4.4, we use a buffer size of 32. Next, we ablate the size of the buffer by allowing the model to use more buffered positive samples during training. Table 6 shows that the buffer plays an important role in our approach. Indeed, excluding the buffer component yields worse results; and performance (especially FPR@98TPR) improves quickly as buffer size increases. 32 seems to be an improving plateau.", + "bbox": [ + 75, + 429, + 468, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of ROCs. To further estimate the effectiveness of our approach to reduce false positive rates at high true positive rates, we visualize our ROC curves as well as comparison methods, as shown in Figure 3. The top two curves (i.e., ours and ALM) significantly surpass that of the BCE baseline on FPRs at earlier TPRs, i.e., starting from $30\\%$ TPR and onward. Importantly, our approach performs on par with ALM up until $\\sim 75\\%$ TPR, and then consistently yields lower FPR values ever since to almost $100\\%$ TPR.", + "bbox": [ + 75, + 551, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness to label noise. Real-world datasets often contain unlabeled data. To evaluate the robustness of our approach in the presence of label noise, we perform additional experiments in which we incrementally flip a proportion $\\eta$ of training labels. Figure 4 shows how FPR@{98, 95, 92}\\%TPR (left to right) degrade as a function of $\\eta$ in the range of [0, 0.5], using BCE as base loss. These results suggest that RankReg is as robust to label noise as the state-of-the-art approach [24].", + "bbox": [ + 75, + 686, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1:200 imbalance ratio. We also test our model on more imbalanced situations, e.g., 1:200 imbalance ratio. To this end, we use the same data curation pipeline as introduced in Sec. 4.2 and build binary imbalanced CIFAR-10 and 100 datasets with a 1:200 imbalance ratio. We defer the full re", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/05340314c3ec620fce41eadbf0feb29abf90f2774c7bba40fe98bceb8adbf6ce.jpg", + "image_caption": [ + "Figure 4. Label noise experiments using BCE as base loss on CIFAR10. We report FPR@{98, 95, 92}\\%TPR (left to right) with varied noise ratios." + ], + "image_footnote": [], + "bbox": [ + 511, + 89, + 629, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6535ba8c3ebdd2a16663da9c8dc16616cfe2da8c651bae9d363f8db28b9b2e4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 90, + 754, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c33ada88a7f0506518b065fad3bb0e692d5a160d69de9aba11284b711da07d52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 90, + 879, + 162 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/afc8d07afec700c232b7b0d067f13114662ec89ffc2de7023efd0521be97acb1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Error@β%TPR ↓LT-CIFAR10imb. 100LT-CIFAR10imb. 200
80%90%Acc.80%90%Acc
CE29.834.770.437.842.464.0
CE+ALM28.933.970.936.139.965.1
CE+RankReg26.729.371.636.737.865.0
", + "bbox": [ + 500, + 234, + 888, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Multi-class experiments using long-tailed CIFAR-10. Baseline numbers are quoted from ALM [24].", + "bbox": [ + 500, + 321, + 890, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sult tables to the supplementary material for space reasons. Looking at the averaged improvements (i.e., $\\mathrm{Avg}.\\Delta$ ) in the bottom row, our approach leads by a large margin.", + "bbox": [ + 498, + 381, + 890, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Multi-class extension. RankReg can be used in multiclass settings by ranking the critical samples higher than others based on the output probability for each class. Table 7 shows additional results in the multi-class setting using long-tailed CIFAR-10 following the experiment protocol in [24]. We report the average error rate of other classes after setting thresholds for $\\{80,90\\}\\%$ TPR on the critical class [24]. Our method performs better than [24] under the 1:100 imbalance ratio setting and comparably under the 1:200 setting.", + "bbox": [ + 498, + 429, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 601, + 617, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The problem setting of critical rare positives has been surprisingly under-studied in the research community. This paper introduces a general method for inducing a neural network to prioritize the reduction of false positives when the operational context calls for a high true positive rate. Motivated by the observation that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network, we formulated a ranking-based regularizer that places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores. Experimental results show how our regularizer can be combined with a wide range of conventional losses and achieves state-of-the-art results in standard evaluations. We hope that our findings will inspire broader interest in this important problem setting, as well as provide practitioners a simple yet effective method to train better neural network models for critical rare classes.", + "bbox": [ + 498, + 628, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15790", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mateusz Buda, Atsuto Maki, and Maciej A Mazurowski. A systematic study of the class imbalance problem in convolutional neural networks. Neural networks, 106:249-259, 2018. 2", + "[2] Jonathon Byrd and Zachary Chase Lipton. What is the effect of importance weighting in deep learning? In ICML, 2019. 2", + "[3] Fatih Cakir, Kun He, Xide Xia, Brian Kulis, and Stan Sclaroff. 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In ICLR, 2018. 2" + ], + "bbox": [ + 78, + 90, + 468, + 176 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15792", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_model.json b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_model.json new file mode 100644 index 0000000000000000000000000000000000000000..41e7cf4d503f9aac207ba5851ba2cb6dbb741d43 --- /dev/null +++ b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/b62e2938-5b12-4774-98d6-2d9d2cd9fe90_model.json @@ -0,0 +1,1815 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.085, + 0.13, + 0.887, + 0.175 + ], + "angle": 0, + "content": "Ranking Regularization for Critical Rare Classes: Minimizing False Positives at a High True Positive Rate" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.203, + 0.777, + 0.238 + ], + "angle": 0, + "content": "Kiarash Mohammadi\\(^{1,2*}\\) He Zhao\\(^{1}\\) Mengyao Zhai\\(^{1}\\) Frederick Tung\\(^{1}\\) \n\\(^{1}\\)Borealis AI \\(^{2}\\) Mila, Université de Montréal" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.242, + 0.858, + 0.258 + ], + "angle": 0, + "content": "kiarash.mohammadi@mila.quebec, {he.zhao, mengyao.zhai, frederick.tung}@borealisai.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.323, + 0.474, + 0.611 + ], + "angle": 0, + "content": "In many real-world settings, the critical class is rare and a missed detection carries a disproportionately high cost. For example, tumors are rare and a false negative diagnosis could have severe consequences on treatment outcomes; fraudulent banking transactions are rare and an undetected occurrence could result in significant losses or legal penalties. In such contexts, systems are often operated at a high true positive rate, which may require tolerating high false positives. In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. We propose a ranking-based regularization (RankReg) approach that is easy to implement, and show empirically that it not only effectively reduces false positives, but also complements conventional imbalanced learning losses. With this novel technique in hand, we conduct a series of experiments on three broadly explored datasets (CIFAR-10&100 and Melanoma) and show that our approach lifts the previous state-of-the-art performance by notable margins." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.64, + 0.21, + 0.657 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.47, + 0.878 + ], + "angle": 0, + "content": "The cost of error is often asymmetric in real-world systems that involve rare classes or events. For example, in medical imaging, incorrectly diagnosing a tumor as benign (a false negative) could lead to cancer being detected later at a more advanced stage, when survival rates are much worse. This would be a higher cost of error than incorrectly diagnosing a benign tumour as potentially cancerous (a false positive). In banking, misclassifying a fraudulent transaction as legitimate may be more costly in terms of financial losses or legal penalties than misclassifying a legitimate transaction as fraudulent (a false positive). In both of these examples, the critical class is rare, and a missed detection carries a disproportionately high cost. In such situations, systems are often operated at high true positive rates," + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.294, + 0.878, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.601, + 0.895, + 0.768 + ], + "angle": 0, + "content": "Figure 1. Which optimization option is preferred in operational contexts with critical positives? We propose a novel regularizer for systems that need to operate at a high true positive rate (TPR). Our approach prioritizes reducing false positives at a high TPR when presented with different options that equally improve the base objective, e.g. area under the ROC curve (AUC). In this toy example, option 2 is preferred because, with a suitable threshold depicted by the dashed line, all positives can be detected (100% TPR) with only one false positive (i.e., 25% FPR at 100% TPR), better than option 1 where two false positives need to be tolerated. Our regularizer is consistent with this preference: \\(\\ell_{reg}\\) is lower for option 2 than option 1 (i.e., 13 vs. 17)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.856 + ], + "angle": 0, + "content": "even though this may require tolerating high false positive rates. Unfortunately, false positives can undermine user confidence in the system and responding to them could incur other costs (e.g. additional medical imaging tests)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. Surprisingly, this" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.348, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at Borealis AI" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15783" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "high-stakes operational setting has rarely been studied by the research community. In contrast to conventional imbalanced classification methods, we propose a general method for inducing a deep neural network to prioritize the reduction of false positives at a high true positive rate. To remain as broadly applicable as possible, we make minimal assumptions on the architecture and optimization details of the deep neural network. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play solution adds a simple yet effective ranking-based regularization term to the usual neural network training objective. The regularization term places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores, which works to push up the scores of the hardest positives." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.47, + 0.363 + ], + "angle": 0, + "content": "Contributions. The main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.374, + 0.469, + 0.435 + ], + "angle": 0, + "content": "- We present a novel plug-and-play regularization term that induces a deep neural network to prioritize the reduction of false positives in operational contexts where a high true positive rate is required." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.444, + 0.469, + 0.474 + ], + "angle": 0, + "content": "- Our regularizer is generic and can be easily combined with other methods for imbalanced learning." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.484, + 0.469, + 0.56 + ], + "angle": 0, + "content": "- We conduct extensive experiments on three public benchmarks to show how the proposed regularization term is complementary to conventional imbalanced learning losses, and achieves state-of-the-art performance in the high true positive rate operational setting." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.374, + 0.469, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.216, + 0.589 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Imbalanced classification. Class imbalance poses a challenge in training real-world neural network models. Without intervention, the optimization of a classification network becomes dominated by the common classes at the expense of the rare classes. Performing robust and efficient classification on imbalanced data is of practical importance and has seen much recent progress. In general, existing methods for imbalanced classification can be summarized into three major groups: cost function based, model output based, and data based. In the first group, various auxiliary optimization objectives are used during training, with a special attention to increase (or balance) the impact of under-represented classes. One such effort used weighted binary cross entropy (WBCE) [35], where the losses of minority samples are multiplied by a scaling factor (typically larger than one) to introduce more cost. Other cost function based approaches include symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], class-balanced BCE (CB-BCE) [8] and label distribution aware" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "margin (LDAM) [4]. The second group of work tackles the problem by post-processing the model outputs. One simple approach divides the output scores with class cooccurrence frequencies [1, 15]. Similarly, other work adjusts the outputs by re-balancing the probabilities based on minority classes [28]. The third group of work focuses on data re-sampling or augmentation. Re-sampling or oversampling the minority classes has shown solid benefits [6]. Enhancing samples from rare classes via augmentation also has received much consideration in recent years. Some representative examples are UnMix [31], ReMix [7] and MixUp [36]. Though approaching the same problem differently, all aforementioned methods have been used in a variety of vision tasks, e.g., image classification [1,2,6,12], object detection [5,16] and image/video segmentation [14,32], where class imbalance is severe." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Our work falls into the first group (i.e. cost function based). We show in the experiments that our ranking-based regularization term is complementary to a wide range of established cost function based approaches (see Sec. 4). Importantly, in contrast to conventional imbalanced classification methods, we prioritize the reduction of false positives at a high true positive rate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.717 + ], + "angle": 0, + "content": "Differentiable ranking. Our regularization objective requires ranking the critical positive samples higher than the negative samples. This task is challenging as ranking operations are piece-wise constant functions, which have zero gradient almost everywhere [11]. Learning ranking directly through backprop is not feasible. To this end, many alternative solutions have been explored. For instance, an earlier effort considered using the expectation of the ranking as soft-ranker [27]. Some recent work used dynamic programming, instead of backprop, for weights update [26], while others achieved this purpose using a differentiable relaxation of histogram binning [3, 13, 21]. Other work has reformulated it as an optimal transport problem [9]. Our work relies on a recent advance that recasts the ranking operation as the minimizer of a linear combinatorial objective [29], which can be sovled elegantly by a blackbox combinatorial solvers [30] that can provide informative gradients from a continuous interpolation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Deep AUC optimization. Our work can be considered (and will be demonstrated in Section 4) as an optimizer for maximizing the AUC score, cf. [10,19,33,34]. Nonetheless, none of them are designed to favor low false positive rates given a high true positive rate requirement. The work most similarly motivated to ours is ALM [24], which recently advocated yielding higher score (i.e. probability) for critical positives than non-critical negatives, thus improving the AUC. ALM formulates the problem from a constrained optimization perspective and achieves strong empirical results. We provide comprehensive comparisons with this state-of-the-art baseline in our experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15784" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.473, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.466 + ], + "angle": 0, + "content": "Figure 2. An illustration of the regularization term by example. Given a batch of inputs and a buffer (i.e., external memory) of positive samples, we collect the probability scores from the classifier, \\( f_{\\theta} \\), and apply the ranking function, \\( rk(\\cdot) \\), to obtain a vector \\( r \\) of rank values. The rank values associated with the positive samples (i.e., numbers in green boxes) are then used to compute the ranking-based regularization loss, \\( \\ell_{reg} \\), using Eq. 4; we drop the normalization in this figure for simplicity of presentation. Note that \\( f_{\\theta} \\) can be an arbitrary classification architecture and RankReg does not rely on the specifics of that approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.492, + 0.267, + 0.51 + ], + "angle": 0, + "content": "3. Technical approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.473, + 0.716 + ], + "angle": 0, + "content": "We present a novel, plug-and-play regularization loss as a generic method for inducing a neural network to prioritize minimizing false positives at a high true positive rate. First, we formulate the imbalanced binary classification task with critical positives in Sec. 3.1. Second, to obtain a solution that is tailored asymmetrically to the high true positive rate setting, we introduce a ranking-based regularization term that encourages models to rank the critical positives higher than the non-critical negatives, while prioritizing reducing the false positive rate at high true positive rate thresholds. Third, we discuss the used optimization solution in Sec. 3.4, as the ranking operation is challenging to optimize with back-propagation due to its non-differentiable nature." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.276, + 0.74 + ], + "angle": 0, + "content": "3.1. Problem formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "We seek to predict the correct label over a highly imbalanced binary classification dataset \\(D = \\{(x_{1},y_{1}),(x_{2},y_{2}),\\ldots ,(x_{n},y_{n}),y_{i}\\in \\{0,1\\} \\}\\) where \\(x_{i}\\) are data samples, \\(y_{i}\\) are labels, and the critical data samples (positive class, labelled 1) appear much less frequently than the non-critical data samples (negative class, labelled 0). For example, medical images with cancerous tumors may be critical positives, while images with benign tumors or no tumors may be negatives. It is assumed that the cost of missing the positive class (a false" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "negative) carries a disproportionately high cost, and that the system is required to operate at a high true positive rate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.894, + 0.228 + ], + "angle": 0, + "content": "Our goal is to produce a general method for inducing a deep neural network (DNN) classifier \\( f_{\\theta} : \\mathbb{R}^{d} \\rightarrow \\mathbb{R} \\), mapping \\( d \\)-dimensional inputs to output scores, to prioritize the reduction of false positives at a high true positive rate [24]. To be as general as possible, the method should make minimal assumptions on the architecture and optimization details of \\( f_{\\theta} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.63, + 0.254 + ], + "angle": 0, + "content": "3.2. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.428 + ], + "angle": 0, + "content": "We propose a novel ranking-based [11, 29] regularizer that fulfills the above desiderata. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play approach adds a regularization term to the usual DNN training objective, making our solution complementary to a wide range of base objective functions, from conventional binary cross-entropy to more sophisticated imbalanced losses such as asymmetric focal loss [17]. In other words, we modify the DNN training objective to be:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.44, + 0.892, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\ell \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\ell_ {\\text {b a s e}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) + \\lambda \\ell_ {\\text {r e g}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.514 + ], + "angle": 0, + "content": "where \\(\\ell_{base}\\) is the base objective function, \\(\\ell_{reg}\\) is the new regularization term, and \\(\\lambda\\) is a balancing hyperparameter with value empirically set to 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.524, + 0.693, + 0.54 + ], + "angle": 0, + "content": "3.3. Ranking regularizer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Denote by \\(r_k(\\cdot)\\) the ranking function that takes a vector of real values \\(\\pmb{a}\\) and outputs the rank of each element in the sorted vector. In other words, the \\(i\\)th element in \\(r_k(a)\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.624, + 0.891, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) _ {i} = 1 + | \\left\\{j: \\boldsymbol {a} _ {j} > \\boldsymbol {a} _ {i} \\right\\} |. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.647, + 0.892, + 0.692 + ], + "angle": 0, + "content": "Then, we devise a regularization term that is computed as the normalized sum over the squared rank values of the positive samples:" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.705, + 0.891, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {r} = \\boldsymbol {r} \\boldsymbol {k} \\left(\\left[ f _ {\\theta} \\left(\\boldsymbol {x} _ {1}\\right), f _ {\\theta} \\left(\\boldsymbol {x} _ {2}\\right), \\dots , f _ {\\theta} \\left(\\boldsymbol {x} _ {B}\\right) \\right]\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.725, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\ell_ {r e g} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\frac {1}{| P |} \\sum_ {i = 1} ^ {B} \\boldsymbol {r} _ {i} ^ {2} \\cdot \\mathbb {1} \\left[ y _ {i} = 1 \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.895, + 0.9 + ], + "angle": 0, + "content": "where \\( |P| = \\sum_{i=1}^{B} \\mathbb{1}[y_i = 1] \\) is the number of positive samples in the batch of \\( B \\) samples. In practice, since positive samples may be severely under-represented in the dataset, we compute the regularization term over the union of the batch and an external memory that caches previous positive samples; we will revisit the implementation details of this buffer in Section 3.5. We also normalize the rank values \\( r \\) to be between 0 and 1." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15785" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.439 + ], + "angle": 0, + "content": "To see how this regularization term prioritizes the reduction of false positives at a high true positive rate, let us consider the toy example in Figure 1. Suppose that the classifier \\( f_{\\theta} \\) currently produces the sorted ordering shown in the left column. The ground-truth critical positives are represented by green plus icons and the ground-truth negatives are represented by grey minus icons. The positive examples induce the second and fourth highest classification scores (higher is better for positives). To achieve a high true positive rate of \\( 100\\% \\) on these two positives, we would have to accept at least two false positives, obtaining a false positive rate of \\( 50\\% \\). Now, suppose that in the next training iteration, the optimizer has two options, shown in the middle and right columns, that would equally improve the training objective; here, we illustrate with the area under the ROC curve (AUC), a common retrieval-based objective. While equally preferable by the training objective, the right column is better aligned with our goal of reducing false positives at a high true positive rate: with a suitable threshold (depicted by the dashed line), we can obtain a false positive rate of \\( 33\\% \\) at a true positive rate of \\( 100\\% \\). On the other hand, the middle column can at best achieve a false positive rate of \\( 50\\% \\) at a true positive rate of \\( 100\\% \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.473, + 0.686 + ], + "angle": 0, + "content": "The proposed regularization term distinguishes between the middle and right columns, and assigns a higher loss to the middle column. In the middle column, the positives have the first and fourth highest classification scores, producing a regularization loss of \\( 1^{2} + 4^{2} = 17 \\) (we drop the normalization terms here for simplicity of presentation). In the right column, the positives have the second and third highest classification scores, producing a regularization loss of \\( 2^{2} + 3^{2} = 13 \\). The proposed regularization therefore favors the right column, as desired. Note that if we use the ranks directly instead of squaring, the regularization loss would be 5 in both cases \\( (1 + 4 = 2 + 3 = 5) \\). Squaring places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's output scores, which works to push up the scores of the least confident positive samples." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.707, + 0.39, + 0.723 + ], + "angle": 0, + "content": "3.4. Optimization on ranking operations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Rank-based objectives often arise in computer vision [13, 25, 27] and are typically challenging to optimize due to the non-differentiability of the ranking function. The ranking function is piece-wise constant, i.e., perturbing the input would most likely not change the output. Thus, we cannot obtain informative gradients (i.e., gradients are zero almost everywhere). We adopt the optimization approach of [22], which frames the ranking function as a combinatorial solver and relies on an elegant way of backpropagating through blackbox combinatorial solvers [29]. The combinatorial objective version of computing the ranking function is given" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.093, + 0.522, + 0.107 + ], + "angle": 0, + "content": "by" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.107, + 0.892, + 0.132 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) = \\underset {\\pi \\in \\Pi_ {n}} {\\arg \\min } \\boldsymbol {a} \\cdot \\boldsymbol {\\pi}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.895, + 0.337 + ], + "angle": 0, + "content": "for an arbitrary vector \\(\\mathbf{a}\\) of real values (see Eq. 2), where \\(\\Pi_{n}\\) is a set that contains all the permutations of \\(\\{1,2,\\dots ,n\\}\\). This reframing enables us to leverage [29] to differentiate through a blackbox combinatorial solver: [29] proposes a family of piecewise affine continuous interpolation functions parameterized by a single hyperparameter that controls the tradeoff between faithfulness to the true function and informativeness of the gradient. In brief, we compute and return the gradient of the continuous interpolation: \\(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{a}} = -\\frac{1}{\\gamma} (\\mathbf{r}\\mathbf{k}(\\mathbf{a}) - \\mathbf{r}\\mathbf{k}(\\mathbf{a}_{\\gamma}))\\) where \\(\\mathbf{a}_{\\gamma}\\) is a perturbed input derived from the incoming gradient information \\(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}\\) via \\(\\mathbf{a}_{\\gamma} = \\mathbf{a} + \\gamma \\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}\\). We refer the interested reader to [22] for further details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.348, + 0.734, + 0.365 + ], + "angle": 0, + "content": "3.5. Buffer of positive samples" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.895, + 0.675 + ], + "angle": 0, + "content": "During training, we maintain a buffer (i.e., an external memory) of positive samples to enable the regularization term to be computed per batch even in datasets with severe imbalance ratios, as a batch may contain few (or no) positive samples. The whole buffer is always appended to the batch. We implement the buffer as a priority queue and it works as follows. At the start of training, positive samples are accumulated from the incoming batches and added to the buffer up to a fixed maximum capacity. Afterwards, as batches are processed, new positive samples replace the samples in the buffer for which the model is the most certain, i.e., the buffered samples with the maximum \\( f_{\\theta} \\) responses. This replacement strategy keeps the hard positives in the buffer and removes positives for which the classifier is already confident. We consider the alternative replacement strategies of first-in-first-out (FIFO) and minimum \\( f_{\\theta} \\) responses in the ablation studies. The complete pipeline, including the buffer of positive samples, is illustrated by example in Figure 2 (without normalization for simplicity of presentation)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.687, + 0.7, + 0.704 + ], + "angle": 0, + "content": "4. Empirical evaluation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.611, + 0.727 + ], + "angle": 0, + "content": "4.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of RankReg, extensive experiments are conducted on three public image-based benchmarks: binary imbalanced CIFAR-10, binary imbalanced CIFAR-100, and Melanoma. To adapt CIFAR-10 and CIFAR-100 to the critical positives setting, we follow the same experimental protocol as the state-of-the-art baseline [24]. As we do not have access to the private medical imaging dataset used in [24], we performed experiments on a publicly available medical imaging dataset (i.e., Melanoma). In this section, we first describe the benchmarks, baselines, and training details. We then present ex" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15786" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.46, + 0.55 + ], + "angle": 0, + "content": "
MethodsBinary CIFAR10, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRAUC ↑
BCE56.045.029.091.2
+ALM52.034.021.093.1
+RankReg47.126.220.694.3
S-ML59.040.026.091.7
+ALM50.037.024.092.5
+RankReg45.631.429.793.9
S-FL59.040.027.091.7
+ALM55.039.025.091.5
+RankReg53.335.420.792.8
A-ML54.036.023.092.4
+ALM45.035.023.092.8
+RankReg47.828.921.494.1
A-FL50.038.024.092.3
+ALM49.037.023.092.8
+RankReg50.528.720.994.3
CB-BCE89.072.059.078.0
+ALM67.051.036.088.1
+RankReg48.829.924.693.2
W-BCE69.052.037.087.4
+ALM66.048.031.089.3
+RankReg60.039.429.692.1
LDAM65.048.034.089.0
+ALM60.042.031.091.0
+RankReg42.825.623.895.0
Avg. Δ6.09.72.82.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.56, + 0.472, + 0.618 + ], + "angle": 0, + "content": "Table 1. Comparison results for binary imbalanced CIFAR-10 showing FPRs at \\(\\{98\\%, 95\\%, 92\\%\\}\\) TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.718 + ], + "angle": 0, + "content": "perimental results on the three benchmarks, showing how the proposed regularizer is complementary to conventional imbalanced learning losses and achieves state-of-the-art results. We conclude with ablations and analyses of design choices." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.365, + 0.743 + ], + "angle": 0, + "content": "4.2. Datasets and evaluation protocol" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Binary imbalanced CIFARs. For a fair comparison, we adopt the same binary imbalanced versions of CIFAR-10 and 100 as curated by the authors of the state-of-the-art method [24]. In brief, binary imbalanced CIFAR-10 is constructed by randomly designating two classes as positives and negatives. All training samples from the negative class are used, while training samples from the positive class are subsampled. Binary imbalanced CIFAR-100 is constructed by designating one super-class as the negative class and a sub-class of a different super-class as the positive class." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.089, + 0.882, + 0.55 + ], + "angle": 0, + "content": "
MethodsBinary CIFAR100, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓90%TPRAUC ↑
BCE93.063.047.081.8
+ALM91.049.039.082.7
+RankReg85.242.428.785.5
S-ML89.065.043.082.7
+ALM88.069.041.081.7
+RankReg64.044.834.585.4
S-FL89.062.044.082.6
+ALM88.060.042.081.7
+RankReg84.649.238.484.7
A-ML91.063.044.081.8
+ALM89.055.037.082.7
+RankReg81.643.432.685.5
A-FL88.063.045.082.8
+ALM86.062.040.083.2
+RankReg70.053.435.884.6
CB-BCE93.075.052.078.8
+ALM89.059.036.083.8
+RankReg89.848.633.484.1
W-BCE88.059.041.079.7
+ALM87.053.039.083.2
+RankReg84.060.041.182.9
LDAM84.070.042.082.3
+ALM80.059.040.083.2
+RankReg70.351.635.084.7
Avg. Δ8.68.64.31.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.56, + 0.894, + 0.618 + ], + "angle": 0, + "content": "Table 2. Comparison results for binary imbalanced CIFAR-100 showing FPRs at \\(\\{98\\%, 95\\%, 90\\%\\}\\) TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Again, all training samples from the negative class are used, while training samples from the positive class are subsampled. We refer the interested reader to [24] for the construction details. Following the evaluation protocol in [24], we experiment with 1:100 and 1:200 imbalance ratios (1 critical positive to 100 or 200 negatives), set aside 100 and 50 samples per class to form the validation set for hyperparameter selection for CIFAR-10 and 100 respectively, and evaluate on a class-balanced test set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Melanoma. The Kaggle Melanoma dataset is a medical image classification dataset that was first proposed on a competition for identifying melanoma (a common form of skin cancer) in imaging scans of skin lesion [23]. It is composed of 33,126 images collected from patients in large variance, where only 584 out of the entire set are malignant (i.e., positive) melanoma; therefore, the dataset has a 1:176 imbalance ratio. It is split into training, validation, and test sets" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15787" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "with ratios of \\(70\\%\\), \\(10\\%\\), and \\(20\\%\\), respectively. The original resolutions of images in Melanoma are too high (e.g., [6000, 4000] or [1920, 1080]) to fit in the backbone network (i.e., ResNet-18). We resize them into [256, 256] for the convenience of computational resources, cf. [34]. Since Melanoma is naturally imbalanced, no further curation is needed for our study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Metrics. We evaluate the performance using the false positive rate (FPR) against several increasingly strict true positive rates (TPR), i.e., FPR@{β}TPR and \\(\\beta \\in\\) \\(\\{90\\%, 92\\%, 95\\%, 98\\% \\}\\). For completeness, we also evaluate using the area under curve metric (AUC) to reveal the overall classification performance, as typically seen in related work [10, 19, 33, 34]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.471, + 0.442 + ], + "angle": 0, + "content": "**Baseline methods.** Following previous method [24], we consider applying our proposed regularizer with several different existing loss functions, most of which have been designed to handle class imbalance: binary cross-entropy (BCE), symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], cost-weighted BCE (WBCE) [35], class-balanced BCE (CB-BCE) [8], and label distribution aware margin (LDAM) [4]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.292, + 0.469 + ], + "angle": 0, + "content": "4.3. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.568 + ], + "angle": 0, + "content": "Backbone architectures. For the binary imbalanced CIFAR datasets, we adopt the ResNet-10 architecture up to the second last layer as feature extractor and append a multi-layer perceptron (MLP) with shape \\([512\\to 2]\\) as the classifier. For Melanoma, we adopt the richer architecture of ResNet-18 and repeat the same step to create the classifier." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.471, + 0.749 + ], + "angle": 0, + "content": "Buffer usage. The buffer of positive samples can have a rebalancing effect when used to compute the base loss in addition to the usual batch samples. We leverage this effect when training models on the binary imbalanced CIFAR-10 and CIFAR-100, which have balanced test sets following the protocol in [24]. Since all splits in the Melanoma dataset follow the data's natural class imbalance, when training the Melanoma models we compute the base loss using the batch samples only. Throughout our experiments, we set the batch size to 64 when training other methods (including base methods and ALM). When training RankReg models, we use a buffer size of 32 and reduce the batch size to 32." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Hyper-parameter search. For CIFAR-10 and CIFAR-100, which we have in common with [24], we use the same hyper-parameters on all base loss functions, for the sake of fair comparison. For Melanoma dataset, we tune the hyperparameters as follows. The more general parameters like learning rate and batch size are chosen and fixed to work with the BCE loss. For ALM [24], a two step grid-search is performed. In the first step, we perform a grid-search over \\(\\rho\\) and \\(\\mu^{(0)}\\). We choose \\(\\rho\\) from the set \\(\\{2,3\\}\\) and \\(\\mu^{(0)}\\) from the set \\(\\{10^{-2},10^{-3},10^{-4},10^{-5},10^{-6},10^{-7},10^{-8},10^{-9}\\}\\)" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.891, + 0.476 + ], + "angle": 0, + "content": "
MethodsMelanoma, imb. 1:170
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRFPR@ ↓90%TPRAUC ↑
BCE49.845.938.635.585.7
+ALM49.941.840.037.785.6
+RankReg49.437.933.931.686.8
S-ML46.642.838.437.485.3
+ALM51.340.539.836.283.5
+RankReg54.642.436.134.486.3
S-FL59.047.344.439.583.8
+ALM47.842.739.238.184.0
+RankReg56.637.831.229.886.1
A-ML47.542.940.436.685.4
+ALM51.041.537.537.183.7
+RankReg58.340.836.733.986.2
A-FL55.645.042.741.284.4
+ALM49.042.440.138.183.6
+RankReg48.036.230.728.886.3
CB-BCE67.259.535.733.282.6
+ALM60.859.546.345.881.5
+RankReg57.844.935.734.783.7
W-BCE69.052.037.032.187.4
+ALM66.048.031.030.789.3
+RankReg56.441.133.030.590.9
LDAM59.748.246.239.083.4
+ALM62.747.743.340.781.5
+RankReg65.647.545.743.981.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.485, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Table 3. Comparison results for Melanoma dataset showing FPRs at \\(\\{98\\%, 95\\%, 92\\%, 90\\% \\}\\) TPRs. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.627 + ], + "angle": 0, + "content": "(note that this is a slightly more thorough grid-search than the original paper). When these two are fixed, we search for the best \\(\\delta\\) from the set \\(\\{0.1, 0.25, 0.5, 1.0\\}\\). These parameters are tuned based on the AUC on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Model ensembling. For CIFAR-10 and CIFAR-100 where the datasets are rather small, we report results from 10 ensembling models for higher reliability and to diminish dataset-dependant biases, matching the protocol in [24]. In detail, 10 random stratified splits of the dataset are created and a model is trained on each. Finally, these models are ensembled by averaging their outputs in the logit space. We do not perform ensembling on Melanoma, as it is larger and has a standard data split." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.83, + 0.789 + ], + "angle": 0, + "content": "4.4. Comparison to alternative approaches" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Binary imbalanced CIFAR-10. Table 1 compares the performance of using RankReg as well as the previous state-of-the-art method ALM [24] together with eight base losses on CIFAR-10 dataset, curated with a imbalance ratio of 1:100 (see Sec. 4.2). We group the empirical results by base loss (BCE, S-ML, S-FL, etc.). Within each group, we first show the results obtained by applying the base method as well as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15788" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.468, + 0.168 + ], + "angle": 0, + "content": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Ranks52.135.224.093.686.352.843.083.2
Squared ranks47.126.220.694.385.242.428.785.5
Cubed ranks45.531.923.093.784.253.850.483.7
Exponential of ranks44.534.024.393.683.648.839.484.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.178, + 0.47, + 0.205 + ], + "angle": 0, + "content": "Table 4. Ablation study of different ranking penalty choices on imbalanced CIFAR-10 and 100 datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.469, + 0.279 + ], + "angle": 0, + "content": "the previous state-of-the-art approach. Then, we show our results. For each FPR and overall AUC, the best result is either underlined or highlighted in red text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.469, + 0.446 + ], + "angle": 0, + "content": "It is clear that our results are consistently better on most metrics, except for three FPR values at S-ML, A-FL and A-ML baselines, where RankReg is the second best approach. The performance improvement is especially striking when coupling RankReg with CB-BCE: RangReg reduces the FPR at the strictest TPR ratio by \\(18\\%\\), i.e., from 67.0 to 48.8 in FPR@98%TPR. The best overall results are obtained by fusing RankReg with the LDAM baseline, where we achieve the highest AUC score (i.e., 95.0) as well as the lowest FPR@98%TPR value (i.e., 42.8) across all experimental results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.469, + 0.597 + ], + "angle": 0, + "content": "Even though our goal is not to have higher AUC scores, our approach obtains the new state-of-the-art AUC performance on all baselines. The bottom row in Table 1 shows the improvements on FPRs using RankReg compared to previous best results, averaged across all baselines. It is notable that our approach obtains larger gains at higher TPRs. For instance, our approach achieves 6.0 and 9.7 FPR improvements at \\(98\\%\\) and \\(95\\%\\) TPRs, respectively, compared to 2.8 at \\(92\\%\\) TPR, which is favored by our goal (see Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Binary imbalanced CIFAR-100. To show the capability of our method to scale, we evaluate our method on the curated CIFAR-100 dataset. The results in Table 2 are consistent with our results on CIFAR-10. Once again, our approach is the top performer across most metrics. However, this time, both the BCE and A-ML baselines achieve the highest AUC score using RankReg. Moreover, it is notable that on the highest TPR (i.e., \\(98\\%\\)), our approach outperforms the previous state-of-the-art with the margin \\(>10\\%\\) on 5 different baselines (i.e., A-FL, S-ML, BCE, LDAM and S-FL). Such notable gains are only observed twice in previous experiments (i.e., LDAM and CB-BCE in Table 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Melanoma. We demonstrate the application of RankReg on imbalanced cancer classification using the Melanoma benchmark and show results in Table 3. As we are the first to perform FPR vs. TPR study on such a large-scale dataset, there is a lack of comparison methods. Therefore, we provide results for all baselines as well as their combination with ALM by running experiments ourselves. It can be seen that, across all baselines, RankReg achieves state-" + }, + { + "type": "table", + "bbox": [ + 0.5, + 0.089, + 0.891, + 0.162 + ], + "angle": 0, + "content": "
FPR@βTPRCIFAR100Melanoma
98%95%92%AUC98%95%92%AUC
Dequeue Max85.242.428.785.549.437.933.986.8
FIFO86.844.231.285.259.247.640.583.1
Dequeue Min88.255.944.883.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.173, + 0.892, + 0.215 + ], + "angle": 0, + "content": "Table 5. Ablation study on buffer update strategy. Swapping out the most confident sample with incoming ones (i.e., Dequeue Max) performs better than other alternatives." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.228, + 0.891, + 0.336 + ], + "angle": 0, + "content": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Buffer = 058.843.630.290.493.448.437.483.1
Buffer = 553.042.428.792.686.657.239.082.5
Buffer = 1048.126.926.294.585.250.228.784.6
Buffer = 2047.626.222.093.885.250.029.884.9
Buffer = 3247.126.220.694.385.242.428.785.5
Buffer = 4846.124.323.293.985.242.127.685.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.346, + 0.892, + 0.387 + ], + "angle": 0, + "content": "Table 6. Illustration of the impact of the positive buffer. We report false positive rate results at high true positive rates for various buffer sizes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.476 + ], + "angle": 0, + "content": "of-the-art performance in the majority of metrics, with a minor setback on LDAM, where both ours and ALM achieve one best metric. These results verify the effectiveness of RankReg on a real-world dataset with critical positives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.642 + ], + "angle": 0, + "content": "Discussion. We attribute the performance lift obtained by RankReg to its more direct approach in ordering the critical positives ahead of the negatives, which is accomplished indirectly through margins in the previous state-of-the-art method ALM [24]. The FPR at a given TPR depends only on how samples are ranked relative to each other, and not on the magnitude of the classification scores. Furthermore, the FPR at a high TPR is determined by the ranking of the least confident positives. Our regularizer places an increasing penalty on positive samples the lower they are ranked, which works to push up the scores of the hardest positives." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.795, + 0.667 + ], + "angle": 0, + "content": "4.5. Ablations and additional analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.749 + ], + "angle": 0, + "content": "In this section, we examine the impact of used components as well as provide additional evaluation to reveal our system's pros and cons. For these additional studies, unless otherwise indicated, we present results from using our approach with BCE as the base function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.826 + ], + "angle": 0, + "content": "Rank penalty ablation. Table 4 shows an ablation study on different choices for the rank penalty in Eq. 4, including raw rank values \\( r \\), squared rank values \\( r^2 \\), cubed rank values \\( r^3 \\), and the exponential of rank values \\( e^r \\). Squared rank provides the best overall result while being simple." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Impact of buffer maintenance strategy. Our approach uses a buffer of critical positive samples to have meaningful ranking regularization signals at each batch of training. We evaluate the role of buffer by considering three kinds of maintenance strategies: (1) remove the most confident" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15789" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.091, + 0.434, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.47, + 0.311 + ], + "angle": 0, + "content": "Figure 3. Evaluation of ROC results produced by our approach vs. others on the CIFAR10 dataset (in 1:100 imbalance ratio)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.47, + 0.429 + ], + "angle": 0, + "content": "sample while adding new positive samples from a incoming batch (i.e., Dequeue Max), (2) first-in-first-out (i.e., FIFO), and (3) remove the least confident sample (i.e., Dequeue Min). The results in Table 5 show that feeding sufficient amount of low-ranking positives to the model is useful, as evidenced by the increased performance across all metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.55 + ], + "angle": 0, + "content": "Impact of buffer size. Throughout the empirical results in Sec. 4.4, we use a buffer size of 32. Next, we ablate the size of the buffer by allowing the model to use more buffered positive samples during training. Table 6 shows that the buffer plays an important role in our approach. Indeed, excluding the buffer component yields worse results; and performance (especially FPR@98TPR) improves quickly as buffer size increases. 32 seems to be an improving plateau." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Visualization of ROCs. To further estimate the effectiveness of our approach to reduce false positive rates at high true positive rates, we visualize our ROC curves as well as comparison methods, as shown in Figure 3. The top two curves (i.e., ours and ALM) significantly surpass that of the BCE baseline on FPRs at earlier TPRs, i.e., starting from \\(30\\%\\) TPR and onward. Importantly, our approach performs on par with ALM up until \\(\\sim 75\\%\\) TPR, and then consistently yields lower FPR values ever since to almost \\(100\\%\\) TPR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Robustness to label noise. Real-world datasets often contain unlabeled data. To evaluate the robustness of our approach in the presence of label noise, we perform additional experiments in which we incrementally flip a proportion \\(\\eta\\) of training labels. Figure 4 shows how FPR@{98, 95, 92}\\%TPR (left to right) degrade as a function of \\(\\eta\\) in the range of [0, 0.5], using BCE as base loss. These results suggest that RankReg is as robust to label noise as the state-of-the-art approach [24]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.9 + ], + "angle": 0, + "content": "1:200 imbalance ratio. We also test our model on more imbalanced situations, e.g., 1:200 imbalance ratio. To this end, we use the same data curation pipeline as introduced in Sec. 4.2 and build binary imbalanced CIFAR-10 and 100 datasets with a 1:200 imbalance ratio. We defer the full re" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.09, + 0.63, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.091, + 0.755, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.091, + 0.88, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.175, + 0.892, + 0.216 + ], + "angle": 0, + "content": "Figure 4. Label noise experiments using BCE as base loss on CIFAR10. We report FPR@{98, 95, 92}\\%TPR (left to right) with varied noise ratios." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.236, + 0.89, + 0.313 + ], + "angle": 0, + "content": "
Error@β%TPR ↓LT-CIFAR10imb. 100LT-CIFAR10imb. 200
80%90%Acc.80%90%Acc
CE29.834.770.437.842.464.0
CE+ALM28.933.970.936.139.965.1
CE+RankReg26.729.371.636.737.865.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.323, + 0.892, + 0.351 + ], + "angle": 0, + "content": "Table 7. Multi-class experiments using long-tailed CIFAR-10. Baseline numbers are quoted from ALM [24]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.891, + 0.428 + ], + "angle": 0, + "content": "sult tables to the supplementary material for space reasons. Looking at the averaged improvements (i.e., \\(\\mathrm{Avg}.\\Delta\\)) in the bottom row, our approach leads by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Multi-class extension. RankReg can be used in multiclass settings by ranking the critical samples higher than others based on the output probability for each class. Table 7 shows additional results in the multi-class setting using long-tailed CIFAR-10 following the experiment protocol in [24]. We report the average error rate of other classes after setting thresholds for \\(\\{80,90\\}\\%\\) TPR on the critical class [24]. Our method performs better than [24] under the 1:100 imbalance ratio setting and comparably under the 1:200 setting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.619, + 0.617 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.9 + ], + "angle": 0, + "content": "The problem setting of critical rare positives has been surprisingly under-studied in the research community. This paper introduces a general method for inducing a neural network to prioritize the reduction of false positives when the operational context calls for a high true positive rate. Motivated by the observation that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network, we formulated a ranking-based regularizer that places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores. Experimental results show how our regularizer can be combined with a wide range of conventional losses and achieves state-of-the-art results in standard evaluations. We hope that our findings will inspire broader interest in this important problem setting, as well as provide practitioners a simple yet effective method to train better neural network models for critical rare classes." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15790" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Mateusz Buda, Atsuto Maki, and Maciej A Mazurowski. A systematic study of the class imbalance problem in convolutional neural networks. Neural networks, 106:249-259, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.174, + 0.472, + 0.214 + ], + "angle": 0, + "content": "[2] Jonathon Byrd and Zachary Chase Lipton. What is the effect of importance weighting in deep learning? 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For example, tumors are rare and a false negative diagnosis could have severe consequences on treatment outcomes; fraudulent banking transactions are rare and an undetected occurrence could result in significant losses or legal penalties. In such contexts, systems are often operated at a high true positive rate, which may require tolerating high false positives. In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. We propose a ranking-based regularization (RankReg) approach that is easy to implement, and show empirically that it not only effectively reduces false positives, but also complements conventional imbalanced learning losses. With this novel technique in hand, we conduct a series of experiments on three broadly explored datasets (CIFAR-10&100 and Melanoma) and show that our approach lifts the previous state-of-the-art performance by notable margins. + +# 1. Introduction + +The cost of error is often asymmetric in real-world systems that involve rare classes or events. For example, in medical imaging, incorrectly diagnosing a tumor as benign (a false negative) could lead to cancer being detected later at a more advanced stage, when survival rates are much worse. This would be a higher cost of error than incorrectly diagnosing a benign tumour as potentially cancerous (a false positive). In banking, misclassifying a fraudulent transaction as legitimate may be more costly in terms of financial losses or legal penalties than misclassifying a legitimate transaction as fraudulent (a false positive). In both of these examples, the critical class is rare, and a missed detection carries a disproportionately high cost. In such situations, systems are often operated at high true positive rates, + +![](images/1455e6fd0fff84112716f02a09d76edc07f477d2778396d5a86e99222e3dad70.jpg) +Figure 1. Which optimization option is preferred in operational contexts with critical positives? We propose a novel regularizer for systems that need to operate at a high true positive rate (TPR). Our approach prioritizes reducing false positives at a high TPR when presented with different options that equally improve the base objective, e.g. area under the ROC curve (AUC). In this toy example, option 2 is preferred because, with a suitable threshold depicted by the dashed line, all positives can be detected (100% TPR) with only one false positive (i.e., 25% FPR at 100% TPR), better than option 1 where two false positives need to be tolerated. Our regularizer is consistent with this preference: $\ell_{reg}$ is lower for option 2 than option 1 (i.e., 13 vs. 17). + +even though this may require tolerating high false positive rates. Unfortunately, false positives can undermine user confidence in the system and responding to them could incur other costs (e.g. additional medical imaging tests). + +In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. Surprisingly, this + +high-stakes operational setting has rarely been studied by the research community. In contrast to conventional imbalanced classification methods, we propose a general method for inducing a deep neural network to prioritize the reduction of false positives at a high true positive rate. To remain as broadly applicable as possible, we make minimal assumptions on the architecture and optimization details of the deep neural network. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play solution adds a simple yet effective ranking-based regularization term to the usual neural network training objective. The regularization term places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores, which works to push up the scores of the hardest positives. + +Contributions. The main contributions of this paper are as follows: + +- We present a novel plug-and-play regularization term that induces a deep neural network to prioritize the reduction of false positives in operational contexts where a high true positive rate is required. +- Our regularizer is generic and can be easily combined with other methods for imbalanced learning. +- We conduct extensive experiments on three public benchmarks to show how the proposed regularization term is complementary to conventional imbalanced learning losses, and achieves state-of-the-art performance in the high true positive rate operational setting. + +# 2. Related work + +Imbalanced classification. Class imbalance poses a challenge in training real-world neural network models. Without intervention, the optimization of a classification network becomes dominated by the common classes at the expense of the rare classes. Performing robust and efficient classification on imbalanced data is of practical importance and has seen much recent progress. In general, existing methods for imbalanced classification can be summarized into three major groups: cost function based, model output based, and data based. In the first group, various auxiliary optimization objectives are used during training, with a special attention to increase (or balance) the impact of under-represented classes. One such effort used weighted binary cross entropy (WBCE) [35], where the losses of minority samples are multiplied by a scaling factor (typically larger than one) to introduce more cost. Other cost function based approaches include symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], class-balanced BCE (CB-BCE) [8] and label distribution aware + +margin (LDAM) [4]. The second group of work tackles the problem by post-processing the model outputs. One simple approach divides the output scores with class cooccurrence frequencies [1, 15]. Similarly, other work adjusts the outputs by re-balancing the probabilities based on minority classes [28]. The third group of work focuses on data re-sampling or augmentation. Re-sampling or oversampling the minority classes has shown solid benefits [6]. Enhancing samples from rare classes via augmentation also has received much consideration in recent years. Some representative examples are UnMix [31], ReMix [7] and MixUp [36]. Though approaching the same problem differently, all aforementioned methods have been used in a variety of vision tasks, e.g., image classification [1,2,6,12], object detection [5,16] and image/video segmentation [14,32], where class imbalance is severe. + +Our work falls into the first group (i.e. cost function based). We show in the experiments that our ranking-based regularization term is complementary to a wide range of established cost function based approaches (see Sec. 4). Importantly, in contrast to conventional imbalanced classification methods, we prioritize the reduction of false positives at a high true positive rate. + +Differentiable ranking. Our regularization objective requires ranking the critical positive samples higher than the negative samples. This task is challenging as ranking operations are piece-wise constant functions, which have zero gradient almost everywhere [11]. Learning ranking directly through backprop is not feasible. To this end, many alternative solutions have been explored. For instance, an earlier effort considered using the expectation of the ranking as soft-ranker [27]. Some recent work used dynamic programming, instead of backprop, for weights update [26], while others achieved this purpose using a differentiable relaxation of histogram binning [3, 13, 21]. Other work has reformulated it as an optimal transport problem [9]. Our work relies on a recent advance that recasts the ranking operation as the minimizer of a linear combinatorial objective [29], which can be sovled elegantly by a blackbox combinatorial solvers [30] that can provide informative gradients from a continuous interpolation. + +Deep AUC optimization. Our work can be considered (and will be demonstrated in Section 4) as an optimizer for maximizing the AUC score, cf. [10,19,33,34]. Nonetheless, none of them are designed to favor low false positive rates given a high true positive rate requirement. The work most similarly motivated to ours is ALM [24], which recently advocated yielding higher score (i.e. probability) for critical positives than non-critical negatives, thus improving the AUC. ALM formulates the problem from a constrained optimization perspective and achieves strong empirical results. We provide comprehensive comparisons with this state-of-the-art baseline in our experiments. + +![](images/9b8c773e8f5b2405a77a9c8ac453b7f680f24f324b6fa13adc249c32183b56bf.jpg) +Figure 2. An illustration of the regularization term by example. Given a batch of inputs and a buffer (i.e., external memory) of positive samples, we collect the probability scores from the classifier, $f_{\theta}$ , and apply the ranking function, $rk(\cdot)$ , to obtain a vector $r$ of rank values. The rank values associated with the positive samples (i.e., numbers in green boxes) are then used to compute the ranking-based regularization loss, $\ell_{reg}$ , using Eq. 4; we drop the normalization in this figure for simplicity of presentation. Note that $f_{\theta}$ can be an arbitrary classification architecture and RankReg does not rely on the specifics of that approach. + +# 3. Technical approach + +We present a novel, plug-and-play regularization loss as a generic method for inducing a neural network to prioritize minimizing false positives at a high true positive rate. First, we formulate the imbalanced binary classification task with critical positives in Sec. 3.1. Second, to obtain a solution that is tailored asymmetrically to the high true positive rate setting, we introduce a ranking-based regularization term that encourages models to rank the critical positives higher than the non-critical negatives, while prioritizing reducing the false positive rate at high true positive rate thresholds. Third, we discuss the used optimization solution in Sec. 3.4, as the ranking operation is challenging to optimize with back-propagation due to its non-differentiable nature. + +# 3.1. Problem formulation + +We seek to predict the correct label over a highly imbalanced binary classification dataset $D = \{(x_{1},y_{1}),(x_{2},y_{2}),\ldots ,(x_{n},y_{n}),y_{i}\in \{0,1\} \}$ where $x_{i}$ are data samples, $y_{i}$ are labels, and the critical data samples (positive class, labelled 1) appear much less frequently than the non-critical data samples (negative class, labelled 0). For example, medical images with cancerous tumors may be critical positives, while images with benign tumors or no tumors may be negatives. It is assumed that the cost of missing the positive class (a false + +negative) carries a disproportionately high cost, and that the system is required to operate at a high true positive rate. + +Our goal is to produce a general method for inducing a deep neural network (DNN) classifier $f_{\theta} : \mathbb{R}^{d} \rightarrow \mathbb{R}$ , mapping $d$ -dimensional inputs to output scores, to prioritize the reduction of false positives at a high true positive rate [24]. To be as general as possible, the method should make minimal assumptions on the architecture and optimization details of $f_{\theta}$ . + +# 3.2. Preliminary + +We propose a novel ranking-based [11, 29] regularizer that fulfills the above desiderata. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play approach adds a regularization term to the usual DNN training objective, making our solution complementary to a wide range of base objective functions, from conventional binary cross-entropy to more sophisticated imbalanced losses such as asymmetric focal loss [17]. In other words, we modify the DNN training objective to be: + +$$ +\ell \left(f _ {\theta} (\boldsymbol {x}), \boldsymbol {y}\right) = \ell_ {\text {b a s e}} \left(f _ {\theta} (\boldsymbol {x}), \boldsymbol {y}\right) + \lambda \ell_ {\text {r e g}} \left(f _ {\theta} (\boldsymbol {x}), \boldsymbol {y}\right), \tag {1} +$$ + +where $\ell_{base}$ is the base objective function, $\ell_{reg}$ is the new regularization term, and $\lambda$ is a balancing hyperparameter with value empirically set to 1. + +# 3.3. Ranking regularizer + +Denote by $r_k(\cdot)$ the ranking function that takes a vector of real values $\pmb{a}$ and outputs the rank of each element in the sorted vector. In other words, the $i$ th element in $r_k(a)$ is given by + +$$ +\boldsymbol {r} \boldsymbol {k} (\boldsymbol {a}) _ {i} = 1 + | \left\{j: \boldsymbol {a} _ {j} > \boldsymbol {a} _ {i} \right\} |. \tag {2} +$$ + +Then, we devise a regularization term that is computed as the normalized sum over the squared rank values of the positive samples: + +$$ +\boldsymbol {r} = \boldsymbol {r} \boldsymbol {k} \left(\left[ f _ {\theta} \left(\boldsymbol {x} _ {1}\right), f _ {\theta} \left(\boldsymbol {x} _ {2}\right), \dots , f _ {\theta} \left(\boldsymbol {x} _ {B}\right) \right]\right), \tag {3} +$$ + +$$ +\ell_ {r e g} \left(f _ {\theta} (\boldsymbol {x}), \boldsymbol {y}\right) = \frac {1}{| P |} \sum_ {i = 1} ^ {B} \boldsymbol {r} _ {i} ^ {2} \cdot \mathbb {1} \left[ y _ {i} = 1 \right], \tag {4} +$$ + +where $|P| = \sum_{i=1}^{B} \mathbb{1}[y_i = 1]$ is the number of positive samples in the batch of $B$ samples. In practice, since positive samples may be severely under-represented in the dataset, we compute the regularization term over the union of the batch and an external memory that caches previous positive samples; we will revisit the implementation details of this buffer in Section 3.5. We also normalize the rank values $r$ to be between 0 and 1. + +To see how this regularization term prioritizes the reduction of false positives at a high true positive rate, let us consider the toy example in Figure 1. Suppose that the classifier $f_{\theta}$ currently produces the sorted ordering shown in the left column. The ground-truth critical positives are represented by green plus icons and the ground-truth negatives are represented by grey minus icons. The positive examples induce the second and fourth highest classification scores (higher is better for positives). To achieve a high true positive rate of $100\%$ on these two positives, we would have to accept at least two false positives, obtaining a false positive rate of $50\%$ . Now, suppose that in the next training iteration, the optimizer has two options, shown in the middle and right columns, that would equally improve the training objective; here, we illustrate with the area under the ROC curve (AUC), a common retrieval-based objective. While equally preferable by the training objective, the right column is better aligned with our goal of reducing false positives at a high true positive rate: with a suitable threshold (depicted by the dashed line), we can obtain a false positive rate of $33\%$ at a true positive rate of $100\%$ . On the other hand, the middle column can at best achieve a false positive rate of $50\%$ at a true positive rate of $100\%$ . + +The proposed regularization term distinguishes between the middle and right columns, and assigns a higher loss to the middle column. In the middle column, the positives have the first and fourth highest classification scores, producing a regularization loss of $1^{2} + 4^{2} = 17$ (we drop the normalization terms here for simplicity of presentation). In the right column, the positives have the second and third highest classification scores, producing a regularization loss of $2^{2} + 3^{2} = 13$ . The proposed regularization therefore favors the right column, as desired. Note that if we use the ranks directly instead of squaring, the regularization loss would be 5 in both cases $(1 + 4 = 2 + 3 = 5)$ . Squaring places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's output scores, which works to push up the scores of the least confident positive samples. + +# 3.4. Optimization on ranking operations + +Rank-based objectives often arise in computer vision [13, 25, 27] and are typically challenging to optimize due to the non-differentiability of the ranking function. The ranking function is piece-wise constant, i.e., perturbing the input would most likely not change the output. Thus, we cannot obtain informative gradients (i.e., gradients are zero almost everywhere). We adopt the optimization approach of [22], which frames the ranking function as a combinatorial solver and relies on an elegant way of backpropagating through blackbox combinatorial solvers [29]. The combinatorial objective version of computing the ranking function is given + +by + +$$ +\boldsymbol {r} \boldsymbol {k} (\boldsymbol {a}) = \underset {\pi \in \Pi_ {n}} {\arg \min } \boldsymbol {a} \cdot \boldsymbol {\pi}, \tag {5} +$$ + +for an arbitrary vector $\mathbf{a}$ of real values (see Eq. 2), where $\Pi_{n}$ is a set that contains all the permutations of $\{1,2,\dots ,n\}$ . This reframing enables us to leverage [29] to differentiate through a blackbox combinatorial solver: [29] proposes a family of piecewise affine continuous interpolation functions parameterized by a single hyperparameter that controls the tradeoff between faithfulness to the true function and informativeness of the gradient. In brief, we compute and return the gradient of the continuous interpolation: $\frac{\partial\mathcal{L}}{\partial\mathbf{a}} = -\frac{1}{\gamma} (\mathbf{r}\mathbf{k}(\mathbf{a}) - \mathbf{r}\mathbf{k}(\mathbf{a}_{\gamma}))$ where $\mathbf{a}_{\gamma}$ is a perturbed input derived from the incoming gradient information $\frac{\partial\mathcal{L}}{\partial\mathbf{rk}}$ via $\mathbf{a}_{\gamma} = \mathbf{a} + \gamma \frac{\partial\mathcal{L}}{\partial\mathbf{rk}}$ . We refer the interested reader to [22] for further details. + +# 3.5. Buffer of positive samples + +During training, we maintain a buffer (i.e., an external memory) of positive samples to enable the regularization term to be computed per batch even in datasets with severe imbalance ratios, as a batch may contain few (or no) positive samples. The whole buffer is always appended to the batch. We implement the buffer as a priority queue and it works as follows. At the start of training, positive samples are accumulated from the incoming batches and added to the buffer up to a fixed maximum capacity. Afterwards, as batches are processed, new positive samples replace the samples in the buffer for which the model is the most certain, i.e., the buffered samples with the maximum $f_{\theta}$ responses. This replacement strategy keeps the hard positives in the buffer and removes positives for which the classifier is already confident. We consider the alternative replacement strategies of first-in-first-out (FIFO) and minimum $f_{\theta}$ responses in the ablation studies. The complete pipeline, including the buffer of positive samples, is illustrated by example in Figure 2 (without normalization for simplicity of presentation). + +# 4. Empirical evaluation + +# 4.1. Overview + +To demonstrate the effectiveness of RankReg, extensive experiments are conducted on three public image-based benchmarks: binary imbalanced CIFAR-10, binary imbalanced CIFAR-100, and Melanoma. To adapt CIFAR-10 and CIFAR-100 to the critical positives setting, we follow the same experimental protocol as the state-of-the-art baseline [24]. As we do not have access to the private medical imaging dataset used in [24], we performed experiments on a publicly available medical imaging dataset (i.e., Melanoma). In this section, we first describe the benchmarks, baselines, and training details. We then present ex + +
MethodsBinary CIFAR10, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRAUC ↑
BCE56.045.029.091.2
+ALM52.034.021.093.1
+RankReg47.126.220.694.3
S-ML59.040.026.091.7
+ALM50.037.024.092.5
+RankReg45.631.429.793.9
S-FL59.040.027.091.7
+ALM55.039.025.091.5
+RankReg53.335.420.792.8
A-ML54.036.023.092.4
+ALM45.035.023.092.8
+RankReg47.828.921.494.1
A-FL50.038.024.092.3
+ALM49.037.023.092.8
+RankReg50.528.720.994.3
CB-BCE89.072.059.078.0
+ALM67.051.036.088.1
+RankReg48.829.924.693.2
W-BCE69.052.037.087.4
+ALM66.048.031.089.3
+RankReg60.039.429.692.1
LDAM65.048.034.089.0
+ALM60.042.031.091.0
+RankReg42.825.623.895.0
Avg. Δ6.09.72.82.3
+ +perimental results on the three benchmarks, showing how the proposed regularizer is complementary to conventional imbalanced learning losses and achieves state-of-the-art results. We conclude with ablations and analyses of design choices. + +# 4.2. Datasets and evaluation protocol + +Binary imbalanced CIFARs. For a fair comparison, we adopt the same binary imbalanced versions of CIFAR-10 and 100 as curated by the authors of the state-of-the-art method [24]. In brief, binary imbalanced CIFAR-10 is constructed by randomly designating two classes as positives and negatives. All training samples from the negative class are used, while training samples from the positive class are subsampled. Binary imbalanced CIFAR-100 is constructed by designating one super-class as the negative class and a sub-class of a different super-class as the positive class. + +Table 1. Comparison results for binary imbalanced CIFAR-10 showing FPRs at $\{98\%, 95\%, 92\%\}$ TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively. + +
MethodsBinary CIFAR100, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓90%TPRAUC ↑
BCE93.063.047.081.8
+ALM91.049.039.082.7
+RankReg85.242.428.785.5
S-ML89.065.043.082.7
+ALM88.069.041.081.7
+RankReg64.044.834.585.4
S-FL89.062.044.082.6
+ALM88.060.042.081.7
+RankReg84.649.238.484.7
A-ML91.063.044.081.8
+ALM89.055.037.082.7
+RankReg81.643.432.685.5
A-FL88.063.045.082.8
+ALM86.062.040.083.2
+RankReg70.053.435.884.6
CB-BCE93.075.052.078.8
+ALM89.059.036.083.8
+RankReg89.848.633.484.1
W-BCE88.059.041.079.7
+ALM87.053.039.083.2
+RankReg84.060.041.182.9
LDAM84.070.042.082.3
+ALM80.059.040.083.2
+RankReg70.351.635.084.7
Avg. Δ8.68.64.31.9
+ +Table 2. Comparison results for binary imbalanced CIFAR-100 showing FPRs at $\{98\%, 95\%, 90\%\}$ TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively. + +Again, all training samples from the negative class are used, while training samples from the positive class are subsampled. We refer the interested reader to [24] for the construction details. Following the evaluation protocol in [24], we experiment with 1:100 and 1:200 imbalance ratios (1 critical positive to 100 or 200 negatives), set aside 100 and 50 samples per class to form the validation set for hyperparameter selection for CIFAR-10 and 100 respectively, and evaluate on a class-balanced test set. + +Melanoma. The Kaggle Melanoma dataset is a medical image classification dataset that was first proposed on a competition for identifying melanoma (a common form of skin cancer) in imaging scans of skin lesion [23]. It is composed of 33,126 images collected from patients in large variance, where only 584 out of the entire set are malignant (i.e., positive) melanoma; therefore, the dataset has a 1:176 imbalance ratio. It is split into training, validation, and test sets + +with ratios of $70\%$ , $10\%$ , and $20\%$ , respectively. The original resolutions of images in Melanoma are too high (e.g., [6000, 4000] or [1920, 1080]) to fit in the backbone network (i.e., ResNet-18). We resize them into [256, 256] for the convenience of computational resources, cf. [34]. Since Melanoma is naturally imbalanced, no further curation is needed for our study. + +Metrics. We evaluate the performance using the false positive rate (FPR) against several increasingly strict true positive rates (TPR), i.e., FPR@{β}TPR and $\beta \in$ $\{90\%, 92\%, 95\%, 98\% \}$ . For completeness, we also evaluate using the area under curve metric (AUC) to reveal the overall classification performance, as typically seen in related work [10, 19, 33, 34]. + +**Baseline methods.** Following previous method [24], we consider applying our proposed regularizer with several different existing loss functions, most of which have been designed to handle class imbalance: binary cross-entropy (BCE), symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], cost-weighted BCE (WBCE) [35], class-balanced BCE (CB-BCE) [8], and label distribution aware margin (LDAM) [4]. + +# 4.3. Implementation details + +Backbone architectures. For the binary imbalanced CIFAR datasets, we adopt the ResNet-10 architecture up to the second last layer as feature extractor and append a multi-layer perceptron (MLP) with shape $[512\to 2]$ as the classifier. For Melanoma, we adopt the richer architecture of ResNet-18 and repeat the same step to create the classifier. + +Buffer usage. The buffer of positive samples can have a rebalancing effect when used to compute the base loss in addition to the usual batch samples. We leverage this effect when training models on the binary imbalanced CIFAR-10 and CIFAR-100, which have balanced test sets following the protocol in [24]. Since all splits in the Melanoma dataset follow the data's natural class imbalance, when training the Melanoma models we compute the base loss using the batch samples only. Throughout our experiments, we set the batch size to 64 when training other methods (including base methods and ALM). When training RankReg models, we use a buffer size of 32 and reduce the batch size to 32. + +Hyper-parameter search. For CIFAR-10 and CIFAR-100, which we have in common with [24], we use the same hyper-parameters on all base loss functions, for the sake of fair comparison. For Melanoma dataset, we tune the hyperparameters as follows. The more general parameters like learning rate and batch size are chosen and fixed to work with the BCE loss. For ALM [24], a two step grid-search is performed. In the first step, we perform a grid-search over $\rho$ and $\mu^{(0)}$ . We choose $\rho$ from the set $\{2,3\}$ and $\mu^{(0)}$ from the set $\{10^{-2},10^{-3},10^{-4},10^{-5},10^{-6},10^{-7},10^{-8},10^{-9}\}$ + +
MethodsMelanoma, imb. 1:170
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRFPR@ ↓90%TPRAUC ↑
BCE49.845.938.635.585.7
+ALM49.941.840.037.785.6
+RankReg49.437.933.931.686.8
S-ML46.642.838.437.485.3
+ALM51.340.539.836.283.5
+RankReg54.642.436.134.486.3
S-FL59.047.344.439.583.8
+ALM47.842.739.238.184.0
+RankReg56.637.831.229.886.1
A-ML47.542.940.436.685.4
+ALM51.041.537.537.183.7
+RankReg58.340.836.733.986.2
A-FL55.645.042.741.284.4
+ALM49.042.440.138.183.6
+RankReg48.036.230.728.886.3
CB-BCE67.259.535.733.282.6
+ALM60.859.546.345.881.5
+RankReg57.844.935.734.783.7
W-BCE69.052.037.032.187.4
+ALM66.048.031.030.789.3
+RankReg56.441.133.030.590.9
LDAM59.748.246.239.083.4
+ALM62.747.743.340.781.5
+RankReg65.647.545.743.981.7
+ +Table 3. Comparison results for Melanoma dataset showing FPRs at $\{98\%, 95\%, 92\%, 90\% \}$ TPRs. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively. + +(note that this is a slightly more thorough grid-search than the original paper). When these two are fixed, we search for the best $\delta$ from the set $\{0.1, 0.25, 0.5, 1.0\}$ . These parameters are tuned based on the AUC on the validation set. + +Model ensembling. For CIFAR-10 and CIFAR-100 where the datasets are rather small, we report results from 10 ensembling models for higher reliability and to diminish dataset-dependant biases, matching the protocol in [24]. In detail, 10 random stratified splits of the dataset are created and a model is trained on each. Finally, these models are ensembled by averaging their outputs in the logit space. We do not perform ensembling on Melanoma, as it is larger and has a standard data split. + +# 4.4. Comparison to alternative approaches + +Binary imbalanced CIFAR-10. Table 1 compares the performance of using RankReg as well as the previous state-of-the-art method ALM [24] together with eight base losses on CIFAR-10 dataset, curated with a imbalance ratio of 1:100 (see Sec. 4.2). We group the empirical results by base loss (BCE, S-ML, S-FL, etc.). Within each group, we first show the results obtained by applying the base method as well as + +
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Ranks52.135.224.093.686.352.843.083.2
Squared ranks47.126.220.694.385.242.428.785.5
Cubed ranks45.531.923.093.784.253.850.483.7
Exponential of ranks44.534.024.393.683.648.839.484.9
+ +the previous state-of-the-art approach. Then, we show our results. For each FPR and overall AUC, the best result is either underlined or highlighted in red text. + +It is clear that our results are consistently better on most metrics, except for three FPR values at S-ML, A-FL and A-ML baselines, where RankReg is the second best approach. The performance improvement is especially striking when coupling RankReg with CB-BCE: RangReg reduces the FPR at the strictest TPR ratio by $18\%$ , i.e., from 67.0 to 48.8 in FPR@98%TPR. The best overall results are obtained by fusing RankReg with the LDAM baseline, where we achieve the highest AUC score (i.e., 95.0) as well as the lowest FPR@98%TPR value (i.e., 42.8) across all experimental results. + +Even though our goal is not to have higher AUC scores, our approach obtains the new state-of-the-art AUC performance on all baselines. The bottom row in Table 1 shows the improvements on FPRs using RankReg compared to previous best results, averaged across all baselines. It is notable that our approach obtains larger gains at higher TPRs. For instance, our approach achieves 6.0 and 9.7 FPR improvements at $98\%$ and $95\%$ TPRs, respectively, compared to 2.8 at $92\%$ TPR, which is favored by our goal (see Sec. 3.3). + +Binary imbalanced CIFAR-100. To show the capability of our method to scale, we evaluate our method on the curated CIFAR-100 dataset. The results in Table 2 are consistent with our results on CIFAR-10. Once again, our approach is the top performer across most metrics. However, this time, both the BCE and A-ML baselines achieve the highest AUC score using RankReg. Moreover, it is notable that on the highest TPR (i.e., $98\%$ ), our approach outperforms the previous state-of-the-art with the margin $>10\%$ on 5 different baselines (i.e., A-FL, S-ML, BCE, LDAM and S-FL). Such notable gains are only observed twice in previous experiments (i.e., LDAM and CB-BCE in Table 1). + +Melanoma. We demonstrate the application of RankReg on imbalanced cancer classification using the Melanoma benchmark and show results in Table 3. As we are the first to perform FPR vs. TPR study on such a large-scale dataset, there is a lack of comparison methods. Therefore, we provide results for all baselines as well as their combination with ALM by running experiments ourselves. It can be seen that, across all baselines, RankReg achieves state- + +Table 4. Ablation study of different ranking penalty choices on imbalanced CIFAR-10 and 100 datasets. + +
FPR@βTPRCIFAR100Melanoma
98%95%92%AUC98%95%92%AUC
Dequeue Max85.242.428.785.549.437.933.986.8
FIFO86.844.231.285.259.247.640.583.1
Dequeue Min88.255.944.883.2
+ +Table 5. Ablation study on buffer update strategy. Swapping out the most confident sample with incoming ones (i.e., Dequeue Max) performs better than other alternatives. + +
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Buffer = 058.843.630.290.493.448.437.483.1
Buffer = 553.042.428.792.686.657.239.082.5
Buffer = 1048.126.926.294.585.250.228.784.6
Buffer = 2047.626.222.093.885.250.029.884.9
Buffer = 3247.126.220.694.385.242.428.785.5
Buffer = 4846.124.323.293.985.242.127.685.5
+ +Table 6. Illustration of the impact of the positive buffer. We report false positive rate results at high true positive rates for various buffer sizes. + +of-the-art performance in the majority of metrics, with a minor setback on LDAM, where both ours and ALM achieve one best metric. These results verify the effectiveness of RankReg on a real-world dataset with critical positives. + +Discussion. We attribute the performance lift obtained by RankReg to its more direct approach in ordering the critical positives ahead of the negatives, which is accomplished indirectly through margins in the previous state-of-the-art method ALM [24]. The FPR at a given TPR depends only on how samples are ranked relative to each other, and not on the magnitude of the classification scores. Furthermore, the FPR at a high TPR is determined by the ranking of the least confident positives. Our regularizer places an increasing penalty on positive samples the lower they are ranked, which works to push up the scores of the hardest positives. + +# 4.5. Ablations and additional analyses + +In this section, we examine the impact of used components as well as provide additional evaluation to reveal our system's pros and cons. For these additional studies, unless otherwise indicated, we present results from using our approach with BCE as the base function. + +Rank penalty ablation. Table 4 shows an ablation study on different choices for the rank penalty in Eq. 4, including raw rank values $r$ , squared rank values $r^2$ , cubed rank values $r^3$ , and the exponential of rank values $e^r$ . Squared rank provides the best overall result while being simple. + +Impact of buffer maintenance strategy. Our approach uses a buffer of critical positive samples to have meaningful ranking regularization signals at each batch of training. We evaluate the role of buffer by considering three kinds of maintenance strategies: (1) remove the most confident + +![](images/18e3e07d3ddd6c054f3893aee28629f10790597e5cf4a8cc028ee8d1f1aeb60d.jpg) +Figure 3. Evaluation of ROC results produced by our approach vs. others on the CIFAR10 dataset (in 1:100 imbalance ratio). + +sample while adding new positive samples from a incoming batch (i.e., Dequeue Max), (2) first-in-first-out (i.e., FIFO), and (3) remove the least confident sample (i.e., Dequeue Min). The results in Table 5 show that feeding sufficient amount of low-ranking positives to the model is useful, as evidenced by the increased performance across all metrics. + +Impact of buffer size. Throughout the empirical results in Sec. 4.4, we use a buffer size of 32. Next, we ablate the size of the buffer by allowing the model to use more buffered positive samples during training. Table 6 shows that the buffer plays an important role in our approach. Indeed, excluding the buffer component yields worse results; and performance (especially FPR@98TPR) improves quickly as buffer size increases. 32 seems to be an improving plateau. + +Visualization of ROCs. To further estimate the effectiveness of our approach to reduce false positive rates at high true positive rates, we visualize our ROC curves as well as comparison methods, as shown in Figure 3. The top two curves (i.e., ours and ALM) significantly surpass that of the BCE baseline on FPRs at earlier TPRs, i.e., starting from $30\%$ TPR and onward. Importantly, our approach performs on par with ALM up until $\sim 75\%$ TPR, and then consistently yields lower FPR values ever since to almost $100\%$ TPR. + +Robustness to label noise. Real-world datasets often contain unlabeled data. To evaluate the robustness of our approach in the presence of label noise, we perform additional experiments in which we incrementally flip a proportion $\eta$ of training labels. Figure 4 shows how FPR@{98, 95, 92}\%TPR (left to right) degrade as a function of $\eta$ in the range of [0, 0.5], using BCE as base loss. These results suggest that RankReg is as robust to label noise as the state-of-the-art approach [24]. + +1:200 imbalance ratio. We also test our model on more imbalanced situations, e.g., 1:200 imbalance ratio. To this end, we use the same data curation pipeline as introduced in Sec. 4.2 and build binary imbalanced CIFAR-10 and 100 datasets with a 1:200 imbalance ratio. We defer the full re + +![](images/05340314c3ec620fce41eadbf0feb29abf90f2774c7bba40fe98bceb8adbf6ce.jpg) +Figure 4. Label noise experiments using BCE as base loss on CIFAR10. We report FPR@{98, 95, 92}\%TPR (left to right) with varied noise ratios. + +![](images/6535ba8c3ebdd2a16663da9c8dc16616cfe2da8c651bae9d363f8db28b9b2e4f.jpg) + +![](images/c33ada88a7f0506518b065fad3bb0e692d5a160d69de9aba11284b711da07d52.jpg) + +
Error@β%TPR ↓LT-CIFAR10imb. 100LT-CIFAR10imb. 200
80%90%Acc.80%90%Acc
CE29.834.770.437.842.464.0
CE+ALM28.933.970.936.139.965.1
CE+RankReg26.729.371.636.737.865.0
+ +Table 7. Multi-class experiments using long-tailed CIFAR-10. Baseline numbers are quoted from ALM [24]. + +sult tables to the supplementary material for space reasons. Looking at the averaged improvements (i.e., $\mathrm{Avg}.\Delta$ ) in the bottom row, our approach leads by a large margin. + +Multi-class extension. RankReg can be used in multiclass settings by ranking the critical samples higher than others based on the output probability for each class. Table 7 shows additional results in the multi-class setting using long-tailed CIFAR-10 following the experiment protocol in [24]. We report the average error rate of other classes after setting thresholds for $\{80,90\}\%$ TPR on the critical class [24]. Our method performs better than [24] under the 1:100 imbalance ratio setting and comparably under the 1:200 setting. + +# 5. Conclusion + +The problem setting of critical rare positives has been surprisingly under-studied in the research community. This paper introduces a general method for inducing a neural network to prioritize the reduction of false positives when the operational context calls for a high true positive rate. Motivated by the observation that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network, we formulated a ranking-based regularizer that places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores. Experimental results show how our regularizer can be combined with a wide range of conventional losses and achieves state-of-the-art results in standard evaluations. We hope that our findings will inspire broader interest in this important problem setting, as well as provide practitioners a simple yet effective method to train better neural network models for critical rare classes. + +# References + +[1] Mateusz Buda, Atsuto Maki, and Maciej A Mazurowski. 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Peter Soyer. https://arxiv.org/abs/2008.07360. 5 +[24] Sara Sangalli, Ertunc Erdil, Andreas Hoetker, Olivio Donati, and Ender Konukoglu. Constrained optimization to train neural networks on critical and under-represented classes. In NeurIPS, 2021. 2, 3, 4, 5, 6, 7, 8 +[25] Yang Song, Alexander Schwing, Raquel Urtasun, et al. Training deep neural networks via direct loss minimization. In ICML, 2016. 4 +[26] Yang Song, Alexander G. Schwing, Richard S. Zemel, and Raquel Urtasun. Training deep neural networks via direct loss minimization. In ICML, 2016. 2 +[27] Michael Taylor, John Guiver, Stephen Robertson, and Tom Minka. SoftRank: Optimizing non-smooth rank metrics. In ICWDM, 2008. 2, 4 +[28] Junjiao Tian, Yen-Cheng Liu, Nathaniel Glaser, Yen-Chang Hsu, and Zsolt Kira. Posterior re-calibration for imbalanced datasets. In NeurIPS, 2020. 2 +[29] Marin Vlastelica, Anselm Paulus, Vít Musil, Georg Martius, and Michal Rolínek. Differentiation of blackbox combinatorial solvers. In ICLR, 2020. 2, 3, 4 +[30] Marin Vlastelica, Anselm Paulus, Vít Musil, Georg Martius, and Michal Rolínek. Differentiation of blackbox combinatorial solvers. In ICLR, 2020. 2 +[31] Zhengzhuo Xu, Zenghao Chai, and Chun Yuan. Towards calibrated model for long-tailed visual recognition from prior perspective. In NeurIPS, 2021. 2 +[32] Michael Yeung, Evis Sala, Carola-Bibiane Schonlieb, and Leonardo Rundo. Unified focal loss: Generalising dice and cross entropy-based losses to handle class imbalanced medical image segmentation. Computerized Medical Imaging and Graphics, 95:102026, 2022. 2 +[33] Yiming Ying, Longyin Wen, and Siwei Lyu. Stochastic online AUC maximization. In NeurIPS, 2016. 2, 6 +[34] Zhuoning Yuan, Yan Yan, Milan Sonka, and Tianbao Yang. Large-scale robust deep AUC maximization: A new surrogate loss and empirical studies on medical image classification. In CVPR, 2021. 2, 6 + +[35] Bianca Zadrozny, John Langford, and Naoki Abe. 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In ICLR, 2018. 2 \ No newline at end of file diff --git a/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/images.zip b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3b2f2f134e0f1006d57298fbbe1b4a4c21edb616 --- /dev/null +++ b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:158becbdb1abac38b14a461ad8ef484f0d469b4ff7f2789dd8b1aaedc3dce01d +size 478790 diff --git a/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/layout.json b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..03485ad1601536f0a9323eecc5dd7730be5396ea --- /dev/null +++ b/2023/Ranking Regularization for Critical Rare Classes_ Minimizing False Positives at a High True Positive Rate/layout.json @@ -0,0 +1,7177 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 52, + 102, + 542, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 102, + 542, + 138 + ], + "spans": [ + { + "bbox": [ + 52, + 102, + 542, + 138 + ], + "type": "text", + "content": "Ranking Regularization for Critical Rare Classes: Minimizing False Positives at a High True Positive Rate" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "spans": [ + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": "Kiarash Mohammadi" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": " He Zhao" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": " Mengyao Zhai" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": " Frederick Tung" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": "Borealis AI " + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 116, + 160, + 475, + 188 + ], + "type": "text", + "content": " Mila, Université de Montréal" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 191, + 525, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 191, + 525, + 204 + ], + "spans": [ + { + "bbox": [ + 64, + 191, + 525, + 204 + ], + "type": "text", + "content": "kiarash.mohammadi@mila.quebec, {he.zhao, mengyao.zhai, frederick.tung}@borealisai.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 255, + 290, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 255, + 290, + 483 + ], + "spans": [ + { + "bbox": [ + 45, + 255, + 290, + 483 + ], + "type": "text", + "content": "In many real-world settings, the critical class is rare and a missed detection carries a disproportionately high cost. For example, tumors are rare and a false negative diagnosis could have severe consequences on treatment outcomes; fraudulent banking transactions are rare and an undetected occurrence could result in significant losses or legal penalties. In such contexts, systems are often operated at a high true positive rate, which may require tolerating high false positives. In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. We propose a ranking-based regularization (RankReg) approach that is easy to implement, and show empirically that it not only effectively reduces false positives, but also complements conventional imbalanced learning losses. With this novel technique in hand, we conduct a series of experiments on three broadly explored datasets (CIFAR-10&100 and Melanoma) and show that our approach lifts the previous state-of-the-art performance by notable margins." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 506, + 128, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 128, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 128, + 520 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 526, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 526, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 526, + 287, + 695 + ], + "type": "text", + "content": "The cost of error is often asymmetric in real-world systems that involve rare classes or events. For example, in medical imaging, incorrectly diagnosing a tumor as benign (a false negative) could lead to cancer being detected later at a more advanced stage, when survival rates are much worse. This would be a higher cost of error than incorrectly diagnosing a benign tumour as potentially cancerous (a false positive). In banking, misclassifying a fraudulent transaction as legitimate may be more costly in terms of financial losses or legal penalties than misclassifying a legitimate transaction as fraudulent (a false positive). In both of these examples, the critical class is rare, and a missed detection carries a disproportionately high cost. In such situations, systems are often operated at high true positive rates," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 318, + 232, + 537, + 459 + ], + "blocks": [ + { + "bbox": [ + 318, + 232, + 537, + 459 + ], + "lines": [ + { + "bbox": [ + 318, + 232, + 537, + 459 + ], + "spans": [ + { + "bbox": [ + 318, + 232, + 537, + 459 + ], + "type": "image", + "image_path": "1455e6fd0fff84112716f02a09d76edc07f477d2778396d5a86e99222e3dad70.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "type": "text", + "content": "Figure 1. Which optimization option is preferred in operational contexts with critical positives? We propose a novel regularizer for systems that need to operate at a high true positive rate (TPR). Our approach prioritizes reducing false positives at a high TPR when presented with different options that equally improve the base objective, e.g. area under the ROC curve (AUC). In this toy example, option 2 is preferred because, with a suitable threshold depicted by the dashed line, all positives can be detected (100% TPR) with only one false positive (i.e., 25% FPR at 100% TPR), better than option 1 where two false positives need to be tolerated. Our regularizer is consistent with this preference: " + }, + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "type": "inline_equation", + "content": "\\ell_{reg}" + }, + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "type": "text", + "content": " is lower for option 2 than option 1 (i.e., 13 vs. 17)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 677 + ], + "type": "text", + "content": "even though this may require tolerating high false positive rates. Unfortunately, false positives can undermine user confidence in the system and responding to them could incur other costs (e.g. additional medical imaging tests)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. Surprisingly, this" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 212, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 212, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 212, + 712 + ], + "type": "text", + "content": "*Work done during an internship at Borealis AI" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15783" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "high-stakes operational setting has rarely been studied by the research community. In contrast to conventional imbalanced classification methods, we propose a general method for inducing a deep neural network to prioritize the reduction of false positives at a high true positive rate. To remain as broadly applicable as possible, we make minimal assumptions on the architecture and optimization details of the deep neural network. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play solution adds a simple yet effective ranking-based regularization term to the usual neural network training objective. The regularization term places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores, which works to push up the scores of the hardest positives." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "type": "text", + "content": "Contributions. The main contributions of this paper are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 296, + 287, + 443 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 296, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 296, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 59, + 296, + 287, + 344 + ], + "type": "text", + "content": "- We present a novel plug-and-play regularization term that induces a deep neural network to prioritize the reduction of false positives in operational contexts where a high true positive rate is required." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 351, + 287, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 351, + 287, + 375 + ], + "spans": [ + { + "bbox": [ + 59, + 351, + 287, + 375 + ], + "type": "text", + "content": "- Our regularizer is generic and can be easily combined with other methods for imbalanced learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 383, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 383, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 59, + 383, + 287, + 443 + ], + "type": "text", + "content": "- We conduct extensive experiments on three public benchmarks to show how the proposed regularization term is complementary to conventional imbalanced learning losses, and achieves state-of-the-art performance in the high true positive rate operational setting." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 454, + 132, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 132, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 132, + 466 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "Imbalanced classification. Class imbalance poses a challenge in training real-world neural network models. Without intervention, the optimization of a classification network becomes dominated by the common classes at the expense of the rare classes. Performing robust and efficient classification on imbalanced data is of practical importance and has seen much recent progress. In general, existing methods for imbalanced classification can be summarized into three major groups: cost function based, model output based, and data based. In the first group, various auxiliary optimization objectives are used during training, with a special attention to increase (or balance) the impact of under-represented classes. One such effort used weighted binary cross entropy (WBCE) [35], where the losses of minority samples are multiplied by a scaling factor (typically larger than one) to introduce more cost. Other cost function based approaches include symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], class-balanced BCE (CB-BCE) [8] and label distribution aware" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "margin (LDAM) [4]. The second group of work tackles the problem by post-processing the model outputs. One simple approach divides the output scores with class cooccurrence frequencies [1, 15]. Similarly, other work adjusts the outputs by re-balancing the probabilities based on minority classes [28]. The third group of work focuses on data re-sampling or augmentation. Re-sampling or oversampling the minority classes has shown solid benefits [6]. Enhancing samples from rare classes via augmentation also has received much consideration in recent years. Some representative examples are UnMix [31], ReMix [7] and MixUp [36]. Though approaching the same problem differently, all aforementioned methods have been used in a variety of vision tasks, e.g., image classification [1,2,6,12], object detection [5,16] and image/video segmentation [14,32], where class imbalance is severe." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "type": "text", + "content": "Our work falls into the first group (i.e. cost function based). We show in the experiments that our ranking-based regularization term is complementary to a wide range of established cost function based approaches (see Sec. 4). Importantly, in contrast to conventional imbalanced classification methods, we prioritize the reduction of false positives at a high true positive rate." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 352, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 567 + ], + "type": "text", + "content": "Differentiable ranking. Our regularization objective requires ranking the critical positive samples higher than the negative samples. This task is challenging as ranking operations are piece-wise constant functions, which have zero gradient almost everywhere [11]. Learning ranking directly through backprop is not feasible. To this end, many alternative solutions have been explored. For instance, an earlier effort considered using the expectation of the ranking as soft-ranker [27]. Some recent work used dynamic programming, instead of backprop, for weights update [26], while others achieved this purpose using a differentiable relaxation of histogram binning [3, 13, 21]. Other work has reformulated it as an optimal transport problem [9]. Our work relies on a recent advance that recasts the ranking operation as the minimizer of a linear combinatorial objective [29], which can be sovled elegantly by a blackbox combinatorial solvers [30] that can provide informative gradients from a continuous interpolation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Deep AUC optimization. Our work can be considered (and will be demonstrated in Section 4) as an optimizer for maximizing the AUC score, cf. [10,19,33,34]. Nonetheless, none of them are designed to favor low false positive rates given a high true positive rate requirement. The work most similarly motivated to ours is ALM [24], which recently advocated yielding higher score (i.e. probability) for critical positives than non-critical negatives, thus improving the AUC. ALM formulates the problem from a constrained optimization perspective and achieves strong empirical results. We provide comprehensive comparisons with this state-of-the-art baseline in our experiments." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15784" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 289, + 238 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 289, + 238 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 289, + 238 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 289, + 238 + ], + "type": "image", + "image_path": "9b8c773e8f5b2405a77a9c8ac453b7f680f24f324b6fa13adc249c32183b56bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": "Figure 2. An illustration of the regularization term by example. Given a batch of inputs and a buffer (i.e., external memory) of positive samples, we collect the probability scores from the classifier, " + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": ", and apply the ranking function, " + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "inline_equation", + "content": "rk(\\cdot)" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": ", to obtain a vector " + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": " of rank values. The rank values associated with the positive samples (i.e., numbers in green boxes) are then used to compute the ranking-based regularization loss, " + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "inline_equation", + "content": "\\ell_{reg}" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": ", using Eq. 4; we drop the normalization in this figure for simplicity of presentation. Note that " + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 258, + 290, + 369 + ], + "type": "text", + "content": " can be an arbitrary classification architecture and RankReg does not rely on the specifics of that approach." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 389, + 163, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 163, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 163, + 403 + ], + "type": "text", + "content": "3. Technical approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 410, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 289, + 567 + ], + "type": "text", + "content": "We present a novel, plug-and-play regularization loss as a generic method for inducing a neural network to prioritize minimizing false positives at a high true positive rate. First, we formulate the imbalanced binary classification task with critical positives in Sec. 3.1. Second, to obtain a solution that is tailored asymmetrically to the high true positive rate setting, we introduce a ranking-based regularization term that encourages models to rank the critical positives higher than the non-critical negatives, while prioritizing reducing the false positive rate at high true positive rate thresholds. Third, we discuss the used optimization solution in Sec. 3.4, as the ranking operation is challenging to optimize with back-propagation due to its non-differentiable nature." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 168, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 168, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 168, + 586 + ], + "type": "text", + "content": "3.1. Problem formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "We seek to predict the correct label over a highly imbalanced binary classification dataset " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "D = \\{(x_{1},y_{1}),(x_{2},y_{2}),\\ldots ,(x_{n},y_{n}),y_{i}\\in \\{0,1\\} \\}" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " are data samples, " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " are labels, and the critical data samples (positive class, labelled 1) appear much less frequently than the non-critical data samples (negative class, labelled 0). For example, medical images with cancerous tumors may be critical positives, while images with benign tumors or no tumors may be negatives. It is assumed that the cost of missing the positive class (a false" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "negative) carries a disproportionately high cost, and that the system is required to operate at a high true positive rate." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "text", + "content": "Our goal is to produce a general method for inducing a deep neural network (DNN) classifier " + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "inline_equation", + "content": "f_{\\theta} : \\mathbb{R}^{d} \\rightarrow \\mathbb{R}" + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "text", + "content": ", mapping " + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "text", + "content": "-dimensional inputs to output scores, to prioritize the reduction of false positives at a high true positive rate [24]. To be as general as possible, the method should make minimal assumptions on the architecture and optimization details of " + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 97, + 547, + 180 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 188, + 385, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 385, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 385, + 201 + ], + "type": "text", + "content": "3.2. Preliminary" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 206, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 338 + ], + "type": "text", + "content": "We propose a novel ranking-based [11, 29] regularizer that fulfills the above desiderata. Our key insight is that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network. Our plug-and-play approach adds a regularization term to the usual DNN training objective, making our solution complementary to a wide range of base objective functions, from conventional binary cross-entropy to more sophisticated imbalanced losses such as asymmetric focal loss [17]. In other words, we modify the DNN training objective to be:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 348, + 545, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 348, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 316, + 348, + 545, + 361 + ], + "type": "interline_equation", + "content": "\\ell \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\ell_ {\\text {b a s e}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) + \\lambda \\ell_ {\\text {r e g}} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right), \\tag {1}", + "image_path": "6dfa4d9fbba9803ff1c1ec937aa8f91457569a217b5b5cc267662588193b6475.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\ell_{base}" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " is the base objective function, " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\ell_{reg}" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " is the new regularization term, and " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " is a balancing hyperparameter with value empirically set to 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 415, + 424, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 424, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 424, + 427 + ], + "type": "text", + "content": "3.3. Ranking regularizer" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "content": "Denote by " + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "inline_equation", + "content": "r_k(\\cdot)" + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "content": " the ranking function that takes a vector of real values " + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{a}" + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "content": " and outputs the rank of each element in the sorted vector. In other words, the " + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "content": "th element in " + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "inline_equation", + "content": "r_k(a)" + }, + { + "bbox": [ + 304, + 445, + 545, + 492 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 361, + 494, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 494, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 361, + 494, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) _ {i} = 1 + | \\left\\{j: \\boldsymbol {a} _ {j} > \\boldsymbol {a} _ {i} \\right\\} |. \\tag {2}", + "image_path": "890fca0c4f3da9972cbaee5595ac19c7dc85e51a07842fa2a8f9c4a90b2498b8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 512, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 512, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 512, + 545, + 548 + ], + "type": "text", + "content": "Then, we devise a regularization term that is computed as the normalized sum over the squared rank values of the positive samples:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 342, + 558, + 545, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 558, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 342, + 558, + 545, + 571 + ], + "type": "interline_equation", + "content": "\\boldsymbol {r} = \\boldsymbol {r} \\boldsymbol {k} \\left(\\left[ f _ {\\theta} \\left(\\boldsymbol {x} _ {1}\\right), f _ {\\theta} \\left(\\boldsymbol {x} _ {2}\\right), \\dots , f _ {\\theta} \\left(\\boldsymbol {x} _ {B}\\right) \\right]\\right), \\tag {3}", + "image_path": "afb886db3590e49b30fb9542247fda5c9c1274cc0f6002a268666dad56a2e998.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 342, + 574, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 574, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 342, + 574, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\ell_ {r e g} \\left(f _ {\\theta} (\\boldsymbol {x}), \\boldsymbol {y}\\right) = \\frac {1}{| P |} \\sum_ {i = 1} ^ {B} \\boldsymbol {r} _ {i} ^ {2} \\cdot \\mathbb {1} \\left[ y _ {i} = 1 \\right], \\tag {4}", + "image_path": "031cbde40eb532f4ffe90c5cca7b2e2e1af69e15b3e21529601abd7a299563c2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "inline_equation", + "content": "|P| = \\sum_{i=1}^{B} \\mathbb{1}[y_i = 1]" + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "text", + "content": " is the number of positive samples in the batch of " + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "text", + "content": " samples. In practice, since positive samples may be severely under-represented in the dataset, we compute the regularization term over the union of the batch and an external memory that caches previous positive samples; we will revisit the implementation details of this buffer in Section 3.5. We also normalize the rank values " + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 616, + 547, + 712 + ], + "type": "text", + "content": " to be between 0 and 1." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15785" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": "To see how this regularization term prioritizes the reduction of false positives at a high true positive rate, let us consider the toy example in Figure 1. Suppose that the classifier " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": " currently produces the sorted ordering shown in the left column. The ground-truth critical positives are represented by green plus icons and the ground-truth negatives are represented by grey minus icons. The positive examples induce the second and fourth highest classification scores (higher is better for positives). To achieve a high true positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": " on these two positives, we would have to accept at least two false positives, obtaining a false positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": ". Now, suppose that in the next training iteration, the optimizer has two options, shown in the middle and right columns, that would equally improve the training objective; here, we illustrate with the area under the ROC curve (AUC), a common retrieval-based objective. While equally preferable by the training objective, the right column is better aligned with our goal of reducing false positives at a high true positive rate: with a suitable threshold (depicted by the dashed line), we can obtain a false positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": " at a true positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": ". On the other hand, the middle column can at best achieve a false positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": " at a true positive rate of " + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 347 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "text", + "content": "The proposed regularization term distinguishes between the middle and right columns, and assigns a higher loss to the middle column. In the middle column, the positives have the first and fourth highest classification scores, producing a regularization loss of " + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "inline_equation", + "content": "1^{2} + 4^{2} = 17" + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "text", + "content": " (we drop the normalization terms here for simplicity of presentation). In the right column, the positives have the second and third highest classification scores, producing a regularization loss of " + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "inline_equation", + "content": "2^{2} + 3^{2} = 13" + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "text", + "content": ". The proposed regularization therefore favors the right column, as desired. Note that if we use the ranks directly instead of squaring, the regularization loss would be 5 in both cases " + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "inline_equation", + "content": "(1 + 4 = 2 + 3 = 5)" + }, + { + "bbox": [ + 47, + 350, + 289, + 543 + ], + "type": "text", + "content": ". Squaring places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's output scores, which works to push up the scores of the least confident positive samples." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 559, + 238, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 238, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 238, + 572 + ], + "type": "text", + "content": "3.4. Optimization on ranking operations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 289, + 715 + ], + "type": "text", + "content": "Rank-based objectives often arise in computer vision [13, 25, 27] and are typically challenging to optimize due to the non-differentiability of the ranking function. The ranking function is piece-wise constant, i.e., perturbing the input would most likely not change the output. Thus, we cannot obtain informative gradients (i.e., gradients are zero almost everywhere). We adopt the optimization approach of [22], which frames the ranking function as a combinatorial solver and relies on an elegant way of backpropagating through blackbox combinatorial solvers [29]. The combinatorial objective version of computing the ranking function is given" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 73, + 319, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 73, + 319, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 73, + 319, + 84 + ], + "type": "text", + "content": "by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 375, + 84, + 545, + 104 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 84, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 375, + 84, + 545, + 104 + ], + "type": "interline_equation", + "content": "\\boldsymbol {r} \\boldsymbol {k} (\\boldsymbol {a}) = \\underset {\\pi \\in \\Pi_ {n}} {\\arg \\min } \\boldsymbol {a} \\cdot \\boldsymbol {\\pi}, \\tag {5}", + "image_path": "ed9b37e0df556246dc363f18a293d1157e371aad262ea8188a1192a124b16df2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": "for an arbitrary vector " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": " of real values (see Eq. 2), where " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\Pi_{n}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": " is a set that contains all the permutations of " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\{1,2,\\dots ,n\\}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": ". This reframing enables us to leverage [29] to differentiate through a blackbox combinatorial solver: [29] proposes a family of piecewise affine continuous interpolation functions parameterized by a single hyperparameter that controls the tradeoff between faithfulness to the true function and informativeness of the gradient. In brief, we compute and return the gradient of the continuous interpolation: " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{a}} = -\\frac{1}{\\gamma} (\\mathbf{r}\\mathbf{k}(\\mathbf{a}) - \\mathbf{r}\\mathbf{k}(\\mathbf{a}_{\\gamma}))" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\gamma}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": " is a perturbed input derived from the incoming gradient information " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\gamma} = \\mathbf{a} + \\gamma \\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{rk}}" + }, + { + "bbox": [ + 304, + 108, + 547, + 266 + ], + "type": "text", + "content": ". We refer the interested reader to [22] for further details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 275, + 449, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 275, + 449, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 275, + 449, + 289 + ], + "type": "text", + "content": "3.5. Buffer of positive samples" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "text", + "content": "During training, we maintain a buffer (i.e., an external memory) of positive samples to enable the regularization term to be computed per batch even in datasets with severe imbalance ratios, as a batch may contain few (or no) positive samples. The whole buffer is always appended to the batch. We implement the buffer as a priority queue and it works as follows. At the start of training, positive samples are accumulated from the incoming batches and added to the buffer up to a fixed maximum capacity. Afterwards, as batches are processed, new positive samples replace the samples in the buffer for which the model is the most certain, i.e., the buffered samples with the maximum " + }, + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "text", + "content": " responses. This replacement strategy keeps the hard positives in the buffer and removes positives for which the classifier is already confident. We consider the alternative replacement strategies of first-in-first-out (FIFO) and minimum " + }, + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 293, + 547, + 534 + ], + "type": "text", + "content": " responses in the ablation studies. The complete pipeline, including the buffer of positive samples, is illustrated by example in Figure 2 (without normalization for simplicity of presentation)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 544, + 428, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 428, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 428, + 557 + ], + "type": "text", + "content": "4. Empirical evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 563, + 373, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 373, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 373, + 575 + ], + "type": "text", + "content": "4.1. Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "To demonstrate the effectiveness of RankReg, extensive experiments are conducted on three public image-based benchmarks: binary imbalanced CIFAR-10, binary imbalanced CIFAR-100, and Melanoma. To adapt CIFAR-10 and CIFAR-100 to the critical positives setting, we follow the same experimental protocol as the state-of-the-art baseline [24]. As we do not have access to the private medical imaging dataset used in [24], we performed experiments on a publicly available medical imaging dataset (i.e., Melanoma). In this section, we first describe the benchmarks, baselines, and training details. We then present ex" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15786" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 281, + 435 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 281, + 435 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 281, + 435 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 281, + 435 + ], + "type": "table", + "html": "
MethodsBinary CIFAR10, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRAUC ↑
BCE56.045.029.091.2
+ALM52.034.021.093.1
+RankReg47.126.220.694.3
S-ML59.040.026.091.7
+ALM50.037.024.092.5
+RankReg45.631.429.793.9
S-FL59.040.027.091.7
+ALM55.039.025.091.5
+RankReg53.335.420.792.8
A-ML54.036.023.092.4
+ALM45.035.023.092.8
+RankReg47.828.921.494.1
A-FL50.038.024.092.3
+ALM49.037.023.092.8
+RankReg50.528.720.994.3
CB-BCE89.072.059.078.0
+ALM67.051.036.088.1
+RankReg48.829.924.693.2
W-BCE69.052.037.087.4
+ALM66.048.031.089.3
+RankReg60.039.429.692.1
LDAM65.048.034.089.0
+ALM60.042.031.091.0
+RankReg42.825.623.895.0
Avg. Δ6.09.72.82.3
", + "image_path": "e88cf2e921209da2ff94e28640e1c1944ab35681e92945b4915ed73e45513ccd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": "perimental results on the three benchmarks, showing how the proposed regularizer is complementary to conventional imbalanced learning losses and achieves state-of-the-art results. We conclude with ablations and analyses of design choices." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 575, + 223, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 223, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 223, + 588 + ], + "type": "text", + "content": "4.2. Datasets and evaluation protocol" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Binary imbalanced CIFARs. For a fair comparison, we adopt the same binary imbalanced versions of CIFAR-10 and 100 as curated by the authors of the state-of-the-art method [24]. In brief, binary imbalanced CIFAR-10 is constructed by randomly designating two classes as positives and negatives. All training samples from the negative class are used, while training samples from the positive class are subsampled. Binary imbalanced CIFAR-100 is constructed by designating one super-class as the negative class and a sub-class of a different super-class as the positive class." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 313, + 70, + 539, + 435 + ], + "blocks": [ + { + "bbox": [ + 46, + 443, + 288, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 443, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 288, + 489 + ], + "type": "text", + "content": "Table 1. Comparison results for binary imbalanced CIFAR-10 showing FPRs at " + }, + { + "bbox": [ + 46, + 443, + 288, + 489 + ], + "type": "inline_equation", + "content": "\\{98\\%, 95\\%, 92\\%\\}" + }, + { + "bbox": [ + 46, + 443, + 288, + 489 + ], + "type": "text", + "content": " TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 70, + 539, + 435 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 539, + 435 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 539, + 435 + ], + "type": "table", + "html": "
MethodsBinary CIFAR100, imb. 1:100
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓90%TPRAUC ↑
BCE93.063.047.081.8
+ALM91.049.039.082.7
+RankReg85.242.428.785.5
S-ML89.065.043.082.7
+ALM88.069.041.081.7
+RankReg64.044.834.585.4
S-FL89.062.044.082.6
+ALM88.060.042.081.7
+RankReg84.649.238.484.7
A-ML91.063.044.081.8
+ALM89.055.037.082.7
+RankReg81.643.432.685.5
A-FL88.063.045.082.8
+ALM86.062.040.083.2
+RankReg70.053.435.884.6
CB-BCE93.075.052.078.8
+ALM89.059.036.083.8
+RankReg89.848.633.484.1
W-BCE88.059.041.079.7
+ALM87.053.039.083.2
+RankReg84.060.041.182.9
LDAM84.070.042.082.3
+ALM80.059.040.083.2
+RankReg70.351.635.084.7
Avg. Δ8.68.64.31.9
", + "image_path": "ba35c090dd76396a9243b83c440b9448f552bf9273d561be5002e77506f4357c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 443, + 547, + 489 + ], + "lines": [ + { + "bbox": [ + 305, + 443, + 547, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 547, + 489 + ], + "type": "text", + "content": "Table 2. Comparison results for binary imbalanced CIFAR-100 showing FPRs at " + }, + { + "bbox": [ + 305, + 443, + 547, + 489 + ], + "type": "inline_equation", + "content": "\\{98\\%, 95\\%, 90\\%\\}" + }, + { + "bbox": [ + 305, + 443, + 547, + 489 + ], + "type": "text", + "content": " TPRs. Baseline numbers are quoted from ALM [24]. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "text", + "content": "Again, all training samples from the negative class are used, while training samples from the positive class are subsampled. We refer the interested reader to [24] for the construction details. Following the evaluation protocol in [24], we experiment with 1:100 and 1:200 imbalance ratios (1 critical positive to 100 or 200 negatives), set aside 100 and 50 samples per class to form the validation set for hyperparameter selection for CIFAR-10 and 100 respectively, and evaluate on a class-balanced test set." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "type": "text", + "content": "Melanoma. The Kaggle Melanoma dataset is a medical image classification dataset that was first proposed on a competition for identifying melanoma (a common form of skin cancer) in imaging scans of skin lesion [23]. It is composed of 33,126 images collected from patients in large variance, where only 584 out of the entire set are malignant (i.e., positive) melanoma; therefore, the dataset has a 1:176 imbalance ratio. It is split into training, validation, and test sets" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15787" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "with ratios of " + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": ", respectively. The original resolutions of images in Melanoma are too high (e.g., [6000, 4000] or [1920, 1080]) to fit in the backbone network (i.e., ResNet-18). We resize them into [256, 256] for the convenience of computational resources, cf. [34]. Since Melanoma is naturally imbalanced, no further curation is needed for our study." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "type": "text", + "content": "Metrics. We evaluate the performance using the false positive rate (FPR) against several increasingly strict true positive rates (TPR), i.e., FPR@{β}TPR and " + }, + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\beta \\in" + }, + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\{90\\%, 92\\%, 95\\%, 98\\% \\}" + }, + { + "bbox": [ + 46, + 156, + 287, + 240 + ], + "type": "text", + "content": ". For completeness, we also evaluate using the area under curve metric (AUC) to reveal the overall classification performance, as typically seen in related work [10, 19, 33, 34]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 288, + 350 + ], + "type": "text", + "content": "**Baseline methods.** Following previous method [24], we consider applying our proposed regularizer with several different existing loss functions, most of which have been designed to handle class imbalance: binary cross-entropy (BCE), symmetric margin loss (S-ML) [20], symmetric focal loss (S-FL) [18], asymmetric margin loss (A-ML) and focal loss (A-FL) [17], cost-weighted BCE (WBCE) [35], class-balanced BCE (CB-BCE) [8], and label distribution aware margin (LDAM) [4]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 358, + 178, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 178, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 178, + 371 + ], + "type": "text", + "content": "4.3. Implementation details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "content": "Backbone architectures. For the binary imbalanced CIFAR datasets, we adopt the ResNet-10 architecture up to the second last layer as feature extractor and append a multi-layer perceptron (MLP) with shape " + }, + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "inline_equation", + "content": "[512\\to 2]" + }, + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "content": " as the classifier. For Melanoma, we adopt the richer architecture of ResNet-18 and repeat the same step to create the classifier." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 593 + ], + "type": "text", + "content": "Buffer usage. The buffer of positive samples can have a rebalancing effect when used to compute the base loss in addition to the usual batch samples. We leverage this effect when training models on the binary imbalanced CIFAR-10 and CIFAR-100, which have balanced test sets following the protocol in [24]. Since all splits in the Melanoma dataset follow the data's natural class imbalance, when training the Melanoma models we compute the base loss using the batch samples only. Throughout our experiments, we set the batch size to 64 when training other methods (including base methods and ALM). When training RankReg models, we use a buffer size of 32 and reduce the batch size to 32." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Hyper-parameter search. For CIFAR-10 and CIFAR-100, which we have in common with [24], we use the same hyper-parameters on all base loss functions, for the sake of fair comparison. For Melanoma dataset, we tune the hyperparameters as follows. The more general parameters like learning rate and batch size are chosen and fixed to work with the BCE loss. For ALM [24], a two step grid-search is performed. In the first step, we perform a grid-search over " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mu^{(0)}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ". We choose " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " from the set " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{2,3\\}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mu^{(0)}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " from the set " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{10^{-2},10^{-3},10^{-4},10^{-5},10^{-6},10^{-7},10^{-8},10^{-9}\\}" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 545, + 376 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 376 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 376 + ], + "type": "table", + "html": "
MethodsMelanoma, imb. 1:170
FPR@ ↓98%TPRFPR@ ↓95%TPRFPR@ ↓92%TPRFPR@ ↓90%TPRAUC ↑
BCE49.845.938.635.585.7
+ALM49.941.840.037.785.6
+RankReg49.437.933.931.686.8
S-ML46.642.838.437.485.3
+ALM51.340.539.836.283.5
+RankReg54.642.436.134.486.3
S-FL59.047.344.439.583.8
+ALM47.842.739.238.184.0
+RankReg56.637.831.229.886.1
A-ML47.542.940.436.685.4
+ALM51.041.537.537.183.7
+RankReg58.340.836.733.986.2
A-FL55.645.042.741.284.4
+ALM49.042.440.138.183.6
+RankReg48.036.230.728.886.3
CB-BCE67.259.535.733.282.6
+ALM60.859.546.345.881.5
+RankReg57.844.935.734.783.7
W-BCE69.052.037.032.187.4
+ALM66.048.031.030.789.3
+RankReg56.441.133.030.590.9
LDAM59.748.246.239.083.4
+ALM62.747.743.340.781.5
+RankReg65.647.545.743.981.7
", + "image_path": "5393ae8f05a66509cd06778b2359c28e767ebc866f3819e26d4c12ed4d8e22e8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 384, + 545, + 430 + ], + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 430 + ], + "type": "text", + "content": "Table 3. Comparison results for Melanoma dataset showing FPRs at " + }, + { + "bbox": [ + 305, + 384, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\{98\\%, 95\\%, 92\\%, 90\\% \\}" + }, + { + "bbox": [ + 305, + 384, + 545, + 430 + ], + "type": "text", + "content": " TPRs. “+ALM” and “+RankReg” are shorthand for BaseLoss+ALM and BaseLoss+RankReg, respectively." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": "(note that this is a slightly more thorough grid-search than the original paper). When these two are fixed, we search for the best " + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": " from the set " + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\{0.1, 0.25, 0.5, 1.0\\}" + }, + { + "bbox": [ + 304, + 449, + 545, + 496 + ], + "type": "text", + "content": ". These parameters are tuned based on the AUC on the validation set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 605 + ], + "type": "text", + "content": "Model ensembling. For CIFAR-10 and CIFAR-100 where the datasets are rather small, we report results from 10 ensembling models for higher reliability and to diminish dataset-dependant biases, matching the protocol in [24]. In detail, 10 random stratified splits of the dataset are created and a model is trained on each. Finally, these models are ensembled by averaging their outputs in the logit space. We do not perform ensembling on Melanoma, as it is larger and has a standard data split." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 611, + 507, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 507, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 507, + 624 + ], + "type": "text", + "content": "4.4. Comparison to alternative approaches" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "Binary imbalanced CIFAR-10. Table 1 compares the performance of using RankReg as well as the previous state-of-the-art method ALM [24] together with eight base losses on CIFAR-10 dataset, curated with a imbalance ratio of 1:100 (see Sec. 4.2). We group the empirical results by base loss (BCE, S-ML, S-FL, etc.). Within each group, we first show the results obtained by applying the base method as well as" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15788" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 133 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 133 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 133 + ], + "type": "table", + "html": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Ranks52.135.224.093.686.352.843.083.2
Squared ranks47.126.220.694.385.242.428.785.5
Cubed ranks45.531.923.093.784.253.850.483.7
Exponential of ranks44.534.024.393.683.648.839.484.9
", + "image_path": "81ff1fbb6501bf21befbfceda1b72f43ae789fc7ef961e31be38453fbf22e2f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 287, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 287, + 220 + ], + "type": "text", + "content": "the previous state-of-the-art approach. Then, we show our results. For each FPR and overall AUC, the best result is either underlined or highlighted in red text." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 221, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 353 + ], + "type": "text", + "content": "It is clear that our results are consistently better on most metrics, except for three FPR values at S-ML, A-FL and A-ML baselines, where RankReg is the second best approach. The performance improvement is especially striking when coupling RankReg with CB-BCE: RangReg reduces the FPR at the strictest TPR ratio by " + }, + { + "bbox": [ + 46, + 221, + 287, + 353 + ], + "type": "inline_equation", + "content": "18\\%" + }, + { + "bbox": [ + 46, + 221, + 287, + 353 + ], + "type": "text", + "content": ", i.e., from 67.0 to 48.8 in FPR@98%TPR. The best overall results are obtained by fusing RankReg with the LDAM baseline, where we achieve the highest AUC score (i.e., 95.0) as well as the lowest FPR@98%TPR value (i.e., 42.8) across all experimental results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "text", + "content": "Even though our goal is not to have higher AUC scores, our approach obtains the new state-of-the-art AUC performance on all baselines. The bottom row in Table 1 shows the improvements on FPRs using RankReg compared to previous best results, averaged across all baselines. It is notable that our approach obtains larger gains at higher TPRs. For instance, our approach achieves 6.0 and 9.7 FPR improvements at " + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "text", + "content": " TPRs, respectively, compared to 2.8 at " + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "inline_equation", + "content": "92\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 472 + ], + "type": "text", + "content": " TPR, which is favored by our goal (see Sec. 3.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "content": "Binary imbalanced CIFAR-100. To show the capability of our method to scale, we evaluate our method on the curated CIFAR-100 dataset. The results in Table 2 are consistent with our results on CIFAR-10. Once again, our approach is the top performer across most metrics. However, this time, both the BCE and A-ML baselines achieve the highest AUC score using RankReg. Moreover, it is notable that on the highest TPR (i.e., " + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "content": "), our approach outperforms the previous state-of-the-art with the margin " + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "inline_equation", + "content": ">10\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "content": " on 5 different baselines (i.e., A-FL, S-ML, BCE, LDAM and S-FL). Such notable gains are only observed twice in previous experiments (i.e., LDAM and CB-BCE in Table 1)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Melanoma. We demonstrate the application of RankReg on imbalanced cancer classification using the Melanoma benchmark and show results in Table 3. As we are the first to perform FPR vs. TPR study on such a large-scale dataset, there is a lack of comparison methods. Therefore, we provide results for all baselines as well as their combination with ALM by running experiments ourselves. It can be seen that, across all baselines, RankReg achieves state-" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 545, + 128 + ], + "blocks": [ + { + "bbox": [ + 47, + 140, + 287, + 162 + ], + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 162 + ], + "type": "text", + "content": "Table 4. Ablation study of different ranking penalty choices on imbalanced CIFAR-10 and 100 datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 70, + 545, + 128 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 128 + ], + "type": "table", + "html": "
FPR@βTPRCIFAR100Melanoma
98%95%92%AUC98%95%92%AUC
Dequeue Max85.242.428.785.549.437.933.986.8
FIFO86.844.231.285.259.247.640.583.1
Dequeue Min88.255.944.883.2
", + "image_path": "bc7b13a117df3e5972612b597c6da4939f3a410b78638b474d0860aa02396630.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 306, + 180, + 545, + 266 + ], + "blocks": [ + { + "bbox": [ + 305, + 137, + 545, + 170 + ], + "lines": [ + { + "bbox": [ + 305, + 137, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 305, + 137, + 545, + 170 + ], + "type": "text", + "content": "Table 5. Ablation study on buffer update strategy. Swapping out the most confident sample with incoming ones (i.e., Dequeue Max) performs better than other alternatives." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 180, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 306, + 180, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 545, + 266 + ], + "type": "table", + "html": "
FPR@βTPRCIFAR10CIFAR100
98%95%92%AUC98%95%90%AUC
Buffer = 058.843.630.290.493.448.437.483.1
Buffer = 553.042.428.792.686.657.239.082.5
Buffer = 1048.126.926.294.585.250.228.784.6
Buffer = 2047.626.222.093.885.250.029.884.9
Buffer = 3247.126.220.694.385.242.428.785.5
Buffer = 4846.124.323.293.985.242.127.685.5
", + "image_path": "968576addccbe183f059aa936e9030d5ef2b428e740019bd91c4dff89715bbb6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 274, + 545, + 306 + ], + "lines": [ + { + "bbox": [ + 305, + 274, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 545, + 306 + ], + "type": "text", + "content": "Table 6. Illustration of the impact of the positive buffer. We report false positive rate results at high true positive rates for various buffer sizes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "type": "text", + "content": "of-the-art performance in the majority of metrics, with a minor setback on LDAM, where both ours and ALM achieve one best metric. These results verify the effectiveness of RankReg on a real-world dataset with critical positives." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 376, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 508 + ], + "type": "text", + "content": "Discussion. We attribute the performance lift obtained by RankReg to its more direct approach in ordering the critical positives ahead of the negatives, which is accomplished indirectly through margins in the previous state-of-the-art method ALM [24]. The FPR at a given TPR depends only on how samples are ranked relative to each other, and not on the magnitude of the classification scores. Furthermore, the FPR at a high TPR is determined by the ranking of the least confident positives. Our regularizer places an increasing penalty on positive samples the lower they are ranked, which works to push up the scores of the hardest positives." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 515, + 486, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 486, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 486, + 528 + ], + "type": "text", + "content": "4.5. Ablations and additional analyses" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 593 + ], + "type": "text", + "content": "In this section, we examine the impact of used components as well as provide additional evaluation to reveal our system's pros and cons. For these additional studies, unless otherwise indicated, we present results from using our approach with BCE as the base function." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": "Rank penalty ablation. Table 4 shows an ablation study on different choices for the rank penalty in Eq. 4, including raw rank values " + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": ", squared rank values " + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "inline_equation", + "content": "r^2" + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": ", cubed rank values " + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "inline_equation", + "content": "r^3" + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": ", and the exponential of rank values " + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "inline_equation", + "content": "e^r" + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": ". Squared rank provides the best overall result while being simple." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Impact of buffer maintenance strategy. Our approach uses a buffer of critical positive samples to have meaningful ranking regularization signals at each batch of training. We evaluate the role of buffer by considering three kinds of maintenance strategies: (1) remove the most confident" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15789" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 72, + 265, + 205 + ], + "blocks": [ + { + "bbox": [ + 66, + 72, + 265, + 205 + ], + "lines": [ + { + "bbox": [ + 66, + 72, + 265, + 205 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 265, + 205 + ], + "type": "image", + "image_path": "18e3e07d3ddd6c054f3893aee28629f10790597e5cf4a8cc028ee8d1f1aeb60d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 223, + 287, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 287, + 246 + ], + "type": "text", + "content": "Figure 3. Evaluation of ROC results produced by our approach vs. others on the CIFAR10 dataset (in 1:100 imbalance ratio)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 268, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 339 + ], + "type": "text", + "content": "sample while adding new positive samples from a incoming batch (i.e., Dequeue Max), (2) first-in-first-out (i.e., FIFO), and (3) remove the least confident sample (i.e., Dequeue Min). The results in Table 5 show that feeding sufficient amount of low-ranking positives to the model is useful, as evidenced by the increased performance across all metrics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": "Impact of buffer size. Throughout the empirical results in Sec. 4.4, we use a buffer size of 32. Next, we ablate the size of the buffer by allowing the model to use more buffered positive samples during training. Table 6 shows that the buffer plays an important role in our approach. Indeed, excluding the buffer component yields worse results; and performance (especially FPR@98TPR) improves quickly as buffer size increases. 32 seems to be an improving plateau." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "text", + "content": "Visualization of ROCs. To further estimate the effectiveness of our approach to reduce false positive rates at high true positive rates, we visualize our ROC curves as well as comparison methods, as shown in Figure 3. The top two curves (i.e., ours and ALM) significantly surpass that of the BCE baseline on FPRs at earlier TPRs, i.e., starting from " + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "text", + "content": " TPR and onward. Importantly, our approach performs on par with ALM up until " + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\sim 75\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "text", + "content": " TPR, and then consistently yields lower FPR values ever since to almost " + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 544 + ], + "type": "text", + "content": " TPR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": "Robustness to label noise. Real-world datasets often contain unlabeled data. To evaluate the robustness of our approach in the presence of label noise, we perform additional experiments in which we incrementally flip a proportion " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " of training labels. Figure 4 shows how FPR@{98, 95, 92}\\%TPR (left to right) degrade as a function of " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " in the range of [0, 0.5], using BCE as base loss. These results suggest that RankReg is as robust to label noise as the state-of-the-art approach [24]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "1:200 imbalance ratio. We also test our model on more imbalanced situations, e.g., 1:200 imbalance ratio. To this end, we use the same data curation pipeline as introduced in Sec. 4.2 and build binary imbalanced CIFAR-10 and 100 datasets with a 1:200 imbalance ratio. We defer the full re" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 313, + 71, + 385, + 129 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 385, + 129 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 385, + 129 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 385, + 129 + ], + "type": "image", + "image_path": "05340314c3ec620fce41eadbf0feb29abf90f2774c7bba40fe98bceb8adbf6ce.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 138, + 545, + 171 + ], + "lines": [ + { + "bbox": [ + 306, + 138, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 545, + 171 + ], + "type": "text", + "content": "Figure 4. Label noise experiments using BCE as base loss on CIFAR10. We report FPR@{98, 95, 92}\\%TPR (left to right) with varied noise ratios." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 390, + 72, + 462, + 129 + ], + "blocks": [ + { + "bbox": [ + 390, + 72, + 462, + 129 + ], + "lines": [ + { + "bbox": [ + 390, + 72, + 462, + 129 + ], + "spans": [ + { + "bbox": [ + 390, + 72, + 462, + 129 + ], + "type": "image", + "image_path": "6535ba8c3ebdd2a16663da9c8dc16616cfe2da8c651bae9d363f8db28b9b2e4f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 467, + 72, + 538, + 129 + ], + "blocks": [ + { + "bbox": [ + 467, + 72, + 538, + 129 + ], + "lines": [ + { + "bbox": [ + 467, + 72, + 538, + 129 + ], + "spans": [ + { + "bbox": [ + 467, + 72, + 538, + 129 + ], + "type": "image", + "image_path": "c33ada88a7f0506518b065fad3bb0e692d5a160d69de9aba11284b711da07d52.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 306, + 186, + 544, + 247 + ], + "blocks": [ + { + "bbox": [ + 306, + 186, + 544, + 247 + ], + "lines": [ + { + "bbox": [ + 306, + 186, + 544, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 544, + 247 + ], + "type": "table", + "html": "
Error@β%TPR ↓LT-CIFAR10imb. 100LT-CIFAR10imb. 200
80%90%Acc.80%90%Acc
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", + "image_path": "afc8d07afec700c232b7b0d067f13114662ec89ffc2de7023efd0521be97acb1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 255, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 306, + 255, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 545, + 277 + ], + "type": "text", + "content": "Table 7. Multi-class experiments using long-tailed CIFAR-10. Baseline numbers are quoted from ALM [24]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "text", + "content": "sult tables to the supplementary material for space reasons. Looking at the averaged improvements (i.e., " + }, + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{Avg}.\\Delta" + }, + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "text", + "content": ") in the bottom row, our approach leads by a large margin." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 340, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 460 + ], + "type": "text", + "content": "Multi-class extension. RankReg can be used in multiclass settings by ranking the critical samples higher than others based on the output probability for each class. Table 7 shows additional results in the multi-class setting using long-tailed CIFAR-10 following the experiment protocol in [24]. We report the average error rate of other classes after setting thresholds for " + }, + { + "bbox": [ + 305, + 340, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\{80,90\\}\\%" + }, + { + "bbox": [ + 305, + 340, + 545, + 460 + ], + "type": "text", + "content": " TPR on the critical class [24]. Our method performs better than [24] under the 1:100 imbalance ratio setting and comparably under the 1:200 setting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 476, + 378, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 378, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 378, + 488 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 498, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 712 + ], + "type": "text", + "content": "The problem setting of critical rare positives has been surprisingly under-studied in the research community. This paper introduces a general method for inducing a neural network to prioritize the reduction of false positives when the operational context calls for a high true positive rate. Motivated by the observation that the false positive rate at a high true positive rate is determined by how the least confident positives are ranked by the network, we formulated a ranking-based regularizer that places an increasing penalty on positive samples the lower they are ranked in a sorted list of the network's classification scores. Experimental results show how our regularizer can be combined with a wide range of conventional losses and achieves state-of-the-art results in standard evaluations. We hope that our findings will inspire broader interest in this important problem setting, as well as provide practitioners a simple yet effective method to train better neural network models for critical rare classes." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15790" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Mateusz Buda, Atsuto Maki, and Maciej A Mazurowski. 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In ICLR, 2018. 2" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15792" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_content_list.json b/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bed707f7c91a326ecb2ff694c81a3f1170326953 --- /dev/null +++ b/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_content_list.json @@ -0,0 +1,1807 @@ +[ + { + "type": "text", + "text": "Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks", + "text_level": 1, + "bbox": [ + 94, + 128, + 875, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tong Bu, Jianhao Ding, Zecheng Hao, Zhaofei Yu* Peking University", + "bbox": [ + 282, + 180, + 684, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "putong30@pku.edu.cn，djh01998@stu.pku.edu.cn，{zechenghao，yuzf12}@pku.edu.cn", + "bbox": [ + 140, + 219, + 821, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 263, + 268, + 343, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spiking Neural Networks (SNNs) have attracted significant attention due to their energy-efficient properties and potential application on neuromorphic hardware. State-of-the-art SNNs are typically composed of simple Leaky Integrate-and-Fire (LIF) neurons and have become comparable to ANNs in image classification tasks on large-scale datasets. However, the robustness of these deep SNNs has not yet been fully uncovered. In this paper, we first experimentally observe that layers in these SNNs mostly communicate by rate coding. Based on this rate coding property, we develop a novel rate coding SNN-specified attack method, Rate Gradient Approximation Attack (RGA). We generalize the RGA attack to SNNs composed of LIF neurons with different leaky parameters and input encoding by designing surrogate gradients. In addition, we develop the time-extended enhancement to generate more effective adversarial examples. The experiment results indicate that our proposed RGA attack is more effective than the previous attack and is less sensitive to neuron hyperparameters. We also conclude from the experiment that rate-coded SNN composed of LIF neurons is not secure, which calls for exploring training methods for SNNs composed of complex neurons and other neuronal codings. Code is available at https://github.com/putshua/SNN_attack_RGA", + "bbox": [ + 76, + 300, + 472, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 695, + 209, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As the third generation of artificial neural networks [47], Spiking Neural Networks (SNNs) have gained more attraction due to their spatio-temporal, discrete representation, and event-driven properties. These bio-inspired neural networks borrow the characteristics of spiking representations and neuronal dynamics from biological brains [23, 75]. Unlike traditional Analog Neural Networks (ANNs), SNNs utilize spiking neurons as their essential components, which accumulate current over time, emit spikes when the membrane potential exceeds the threshold, and pass on informa", + "bbox": [ + 76, + 720, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion through spike trains. The natural sparsity of the spike trains leads to the low power consumption of SNNs [59,69].", + "bbox": [ + 500, + 268, + 890, + 300 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SNNs are competitive in real-world vision applications. The development of neuromorphic computing [10, 11, 20, 54, 56, 76] has further magnified the advantages of low-power consumption properties of SNNs, so that they can be deployed in power-limited scenarios [8, 64], such as edge computing or mobile application. However, the training algorithms of SNNs are also improving. The most practical training methods are ANN-SNN conversion [7], supervised training [72], and hybrid training [57, 58].", + "bbox": [ + 496, + 303, + 892, + 440 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When SNNs are applied to safety-critical systems, the reliability of SNNs should be a major concern. The adversarial attack is one of the most significant categories that threatens model security [24, 68]. Similar to ANNs, SNNs can also be fooled by crafting adversarial examples that are imperceptible to human eyes from gradient-based backpropagation [62], which may lead to catastrophic consequences when SNNs are deployed in safety-related scenarios. Nevertheless, SNNs are still considered to be more robust than ANNs. This robustness comes from inherent neural dynamics, such as forgetting historical information and discrete spikes [63]. Besides, the robustness of SNNs can be improved through special structural enhancements [9] or training techniques [37, 45, 71].", + "bbox": [ + 496, + 443, + 893, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Effective attack examples of ANNs can be crafted from well-defined gradients on the activation functions [68]. For SNNs, a common way to construct gradient-based attacks is by backpropagating through a surrogate function over discrete spikes. In this way, the gradient may suffer from explosion and vanishment in temporal and layer-by-layer communication [72]; at the same time, the membrane potential of all historical time steps needs to be saved when backpropagation, which requires a large amount of memory. Currently, high-performance SNNs typically combine leaky integrate-and-fire models and rate-encoded inputs. While the rate coding scheme brings excellent performance to SNN, it also exposes shortcomings. If the rate coding nature in SNN is considered, can we construct a more powerful attack? After all, the activation functions of many ANNs are inspired by the firing rate of biological neurons [52].", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author", + "bbox": [ + 101, + 886, + 228, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7896", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we develop a novel Rate Gradient Approximation Attack (RGA) based on components of rate coding in high-performance SNNs. RGA attack is more effective than previously used attacks as it makes better use of the rate coding feature. We expect our work to provide benchmarks for SNN defense against adversarial attacks and inspire future research for SNNs. The main contributions of this paper are:", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We observe that layers in SNN are mainly communicated by rate coding, either for converted SNN or for surrogate-trained SNN.", + "- We develop the Rate Gradient Approximation Attack based on rate coding and apply it to SNNs composed of different types of neurons and input codings. We further propose a time-extended variant to get more effective adversarial examples.", + "- Experiments prove that the RGA attack outperforms the STBP attack and is less sensitive to neuron hyperparameters. Based on the proposed attack, we compare the robustness of SNNs using different leaky parameters with that of ANNs and manifest that the SNNs composed of LIF neurons cannot provide strong enough security. This conclusion inspires further research on networks with more complex neurons." + ], + "bbox": [ + 94, + 224, + 467, + 464 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 481, + 225, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning of SNNs. The most efficient and commonly used SNNs training methods are ANN-SNN conversion [7] and Spatio-temporal Backpropagation (STBP) [72]. The core idea of ANN-SNN conversion is mapping the weights of a pre-trained ANN into an SNN. Researchers found that adjusting the weights or threshold in the SNN can balance the trade between inference time-steps and performance after conversion [12, 14, 16, 25, 28, 50, 61]. Some recent works quantized the source ANN to boost the performance of converted SNNs using ultra-low time-steps [5, 41, 43, 74]. ANN-SNN conversion is the most practical training method to train SNNs on large-scale datasets, and the converted SNNs always have outstanding performance [6, 26, 27, 34]. The temporal characteristics of the spiking neuron make it similar to a Recurrent Neural Network (RNN). Based on this, Wu et al. [72] borrowed the idea of Back Propagation Through Time [70] and proposed the supervised learning way of STBP. As the firing of neurons is a non-differentiable Heaviside function, the surrogate gradient approximation is proposed to smooth the gradient [19, 21, 40, 53, 65, 67, 77]. Nowadays, the performance of SNNs trained with backpropagation is comparable to that of ANNs [13, 17, 22, 29, 33, 35, 39, 73, 80]. Time-based backpropagation is another supervised learning method that can maintain the sparsity of the gradient. However, these works can only extend to shallow networks [3, 51, 78, 79, 81].", + "bbox": [ + 75, + 507, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The robustness of SNN. SNNs are vulnerable to adversarial attacks as ANNs by adopting the gradient scheme in training. Firstly, SNNs obtained from ANN-SNN conversion can be attacked by the source ANNs with shared weights [62]. Besides, end-to-end trained SNNs suffer from the attack constructed from STBP. Sharmin et al. [62] summarized the two types of attacks as ANN-crafted and SNN-crafted attacks and revealed that attacks based on STBP are believed to be more powerful than those based on ANNs. Moreover, Liang et al. [44] exploited spike-compatible gradient to perform bit-flip attacks on SNN. Considering that SNNs are suitable for event-based tasks, various attacks on the event data of neuromorphic sensors are also explored [46, 49]. In these attacks, the STBP gradients are merged into sparse event data to construct attacks.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the performance of SNNs can be degraded by such a variety of attack schemes, SNNs are still considered to have additional robustness compared to ANNs [15]. This is because more encodings are supported in SNNs. Compared to direct coding, Poisson coding is believed to process more inherent robustness as it introduces a noisy discretization to SNNs [37, 63]. Even so, how strong an attack Poisson coding can withstand still remains unknown. Another key robustness component of SNNs is the leaky parameter [63]. The leaky parameter controls the forgetting of historical information in LIF neurons. El-Allami et al. [18] achieved improved robustness by only searching in the space of leaky parameters. The current understanding of the robustness of SNNs is mainly focused on rate coding, and LIF neurons are also thought to perform the same coding. Therefore, gaining new insights into the robustness of rate coding is crucial for the practical application of SNNs.", + "bbox": [ + 496, + 316, + 892, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 589, + 637, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Neuron Model for SNNs", + "text_level": 1, + "bbox": [ + 500, + 613, + 720, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we consider the commonly used Leaky-Integrate-and-Fire (LIF) model and Integrate-and-Fire (IF) model [23, 31], the dynamics of membrane potential under firing threshold can be described by the following equations, respectively.", + "bbox": [ + 496, + 637, + 890, + 714 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = - (u (t) - u _ {\\text {r e s t}}) + R I (t), \\quad (\\mathbf {L I F}) (1) \\\\ \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = R I (t). \\quad (\\mathbf {I F}) (2) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 723, + 890, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Here $\\tau_{m}$ and $R$ denote the membrane time constant and the membrane resistance constant, respectively. $u(t)$ and $I(t)$ represent the membrane potential and input current at time $t$ , respectively. Once the membrane potential reaches the firing threshold $\\theta$ , the neuron will fire, and then the membrane potential will reset to the resting potential $u_{rest} < \\theta$ . Without loss of generality, to simulate the network of LIF", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7897", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "neurons on a computer with a Von Neumann architecture, the above process can be simplified and discretized to another set of equations [4].", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} (t) = \\lambda u _ {i} (t - 1) + w _ {i j} s _ {j} (t) + b _ {i} + \\eta_ {i} (t), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 150, + 468, + 167 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} (t) = \\left\\{ \\begin{array}{l l} 1, & t = t _ {i} ^ {(f)} \\\\ 0, & t \\neq t _ {i} ^ {(f)} \\end{array} , \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 170, + 468, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $j$ and $i$ indicate presynaptic and postsynaptic neurons, $w_{ij}$ represents the connection strength between the two neurons, and $b_{i}$ is an extra constant input current to neuron $i$ . $s_i(t)$ describes whether neuron $i$ fires at time-step $t$ , and the trigger is membrane potential $u_{i}(t)$ reaches the firing threshold $\\theta$ . We also mark the firing time-step of neuron $i$ as $t_i^{(f)}$ , $f = 1,2,\\ldots,\\lambda$ is the membrane leaky constant corresponding to the membrane time constant in Eq. (1). Note that if we explicitly $\\lambda$ to 1, this LIF neuron model will degenerate to the none-leaky IF model. Also, we add a reset term $\\eta_i(t)$ on Eq. (3) to describe the neuron reset behavior. Despite the hard-reset function that resets the neuron membrane potential to resting potential (Eq. (5)), we also consider the soft-reset function (Eq. (6)) that directly subtracts the membrane potential by the threshold $\\theta$ [25, 60].", + "bbox": [ + 75, + 224, + 468, + 454 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\eta_ {i} ^ {\\text {h a r d}} (t) = \\left\\{ \\begin{array}{l l} - \\left(u _ {i} \\left(t _ {i} ^ {(f)}\\right) - u _ {\\text {r e s t}}\\right) & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}. \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 465, + 468, + 508 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\eta_ {i} ^ {\\text {s o f t}} (t) = \\left\\{ \\begin{array}{l l} - \\theta & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}, \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 511, + 468, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Supervised Training of SNNs with STBP", + "text_level": 1, + "bbox": [ + 76, + 566, + 423, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Equation (3) implies that the LIF neuron has a function similar to that of an RNN. Thus, SNNs can be trained in the same way as RNNs with Back Propagation Through Time. STBP uses this idea to unroll the SNN over time-steps and accumulate gradient at each time-step [53, 72]. As illustrated in Fig. 1, the gradient of the loss function $\\mathcal{L}$ with respect to the output spikes $s_j(t)$ is:", + "bbox": [ + 75, + 590, + 468, + 698 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t)} = \\frac {\\partial \\mathcal {L}}{\\partial s _ {i} (t)} \\frac {\\partial s _ {i} (t)}{\\partial u _ {i} (t)} \\frac {\\partial u _ {i} (t)}{\\partial s _ {j} (t)} + \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 710, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t + 1)} \\frac {\\partial s _ {j} (t + 1)}{\\partial u _ {j} (t + 1)} \\frac {\\partial u _ {j} (t + 1)}{\\partial u _ {j} (t)} \\frac {\\partial u _ {j} (t)}{\\partial s _ {j} (t)}.\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 746, + 437, + 780 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that as the derivative of spike with respect to the membrane potential $\\frac{\\partial s_i(t)}{\\partial u_i(t)}$ is nondifferentiable, the surrogate gradient [53] is often used in backpropagation.", + "bbox": [ + 75, + 790, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the STBP method enables supervised training of SNNs, this method can also generate gradient-based adversarial examples [62]. Therefore, we will use STBP as the baseline gradient obtain method.", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1eba3d9a86b1099e2eb2fafa7458b3f16bd4d43d1cb1b01f7f9e8ca665b7db49.jpg", + "image_caption": [ + "Figure 1. Forward pass and backward pass for STBP. The pink line shows that surrogate functions are applied in the non-differentiable process of neuron firing to obtain approximate gradients." + ], + "image_footnote": [], + "bbox": [ + 513, + 90, + 880, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 315, + 689, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial attack is a method to generate imperceptible perturbations that can fool neural networks, which can be formulated as an optimization problem:", + "bbox": [ + 498, + 340, + 890, + 386 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\max _ {\\delta} \\mathcal {L} (f (\\boldsymbol {x} + \\delta), y) \\quad s. t. \\| \\delta \\| _ {p} \\leq \\epsilon , \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 401, + 890, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is the loss function, $f$ is the network under attack, and $\\pmb{x},\\pmb{y}$ are the input images and output target of the given network, respectively. $\\delta$ is the adversarial perturbation we want to optimize. $\\| \\cdot \\| _p$ is the $L_{p}$ -norm, and parameter $\\epsilon$ limits the strength of the perturbation to a level that is indistinguishable to the human eye. Here we consider two classic adversarial attack algorithms: Fast Gradient Sign Method (FGSM) [24] and Projected Gradient Descent (PGD) [38]. FGSM is a simple but effective attack method, which perturbs the data $\\pmb{x}$ along the sign of the gradient to increase the perturbed linear output, that is", + "bbox": [ + 498, + 436, + 890, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {x}} = \\boldsymbol {x} + \\epsilon \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x}, y))\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 621, + 890, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PGD is an iterative variant of FGSM. By iteratively optimizing the perturbation, PGD offers a more powerful attack [48]. The iteration can be summarized as:", + "bbox": [ + 498, + 654, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {x}} ^ {k} = \\Pi_ {\\epsilon} \\left\\{\\boldsymbol {x} ^ {k - 1} + \\alpha \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x} ^ {k - 1}, y))\\right) \\right\\}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 714, + 890, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k$ is the number of the iteration step, and $\\alpha$ is the step size of each iteration. $\\Pi_{\\epsilon}$ constrains the data in each iteration and projects it onto the space of the $\\epsilon - l_{p}$ neighborhood of $x$ .", + "bbox": [ + 498, + 747, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For all attack methods, we consider two different attack scenarios, white-box attack, and black-box attack. The white-box attack is the case that the hacker has complete access to the model topology, model parameters, and gradients, while the black-box attack is the case the hacker can only get the basic information of the model.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7898", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f7e2d6b8770838dd8f56cae59096c7792317487bd449075fdd13a4cb44fe89e7.jpg", + "image_caption": [ + "Figure 2. Experimental scheme of spike shuffle" + ], + "image_footnote": [], + "bbox": [ + 171, + 104, + 377, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Methods", + "text_level": 1, + "bbox": [ + 76, + 329, + 174, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we first show that the current high-performance SNNs for image classification tasks are encoded by firing rate and do not contain timing information, whether they are trained by STBP and ANN-SNN conversion. Based on this, we propose rate gradient approximation, a new attack method against SNNs, and apply it to SNNs composed of different types of neurons and input encodings. Finally, we propose the time-extended attack as an attack enhancement method.", + "bbox": [ + 75, + 354, + 468, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Does well-trained SNNs contain timing information?", + "text_level": 1, + "bbox": [ + 76, + 498, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here we design an experiment and test whether the well-trained SNNs are rate coded and whether they contain timing information. The definition of firing rate refers to the temporal average of the spikes. As illustrated in Eq. (11), the firing rate of one given neuron $i$ is the total spike count in an interval of time-steps $T$ divided by the duration $T$ .", + "bbox": [ + 75, + 537, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i} = \\frac {\\sum_ {t = 1} ^ {T} s _ {i}}{T}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 648, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed experimental scheme is shown in Fig. 2. We add a random number generator to shuffle each neuron's output spike firing order so that the spike trains will never contain temporal information. We apply this design to the pre-trained SNN models and test accuracy change before and after the spike shuffle.", + "bbox": [ + 75, + 688, + 468, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The experiment is implemented on the CIFAR-10 dataset with VGG-11 network architecture. To test different SNNs, we choose combinations of different training methods, leakage parameters, and reset functions. We pre-train SNN for each combination and then substitute all the spiking neurons with shuffled neurons.", + "bbox": [ + 75, + 779, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tab. 1 reports the average performance of 10 runs, from which we find that the accuracy after spike shuffle is slightly", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2b79240be88cd2554dfd6aac299e95e5e87dc0a38ae98ccfe67619a67760c6da.jpg", + "image_caption": [ + "Figure 3. Forward pass and backward pass for RGA attack. The pink line shows that surrogate functions are applied to the approximation of the derivative for firing rate and input current." + ], + "image_footnote": [], + "bbox": [ + 522, + 90, + 870, + 241 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/885edf3c820fec6bceca527468b164139ec36498efa3e50e537e29b08b1a05fe.jpg", + "table_caption": [ + "Table 1. Performance before and after the spike shuffle" + ], + "table_footnote": [], + "table_body": "
DatasetTraining MethodTλResetClean Acc.Shuffled Acc.Rate
CIFAR-10ANNSNN161.0soft93.2593.358✓
CIFAR-10STBP81.0soft92.7592.086✓
CIFAR-10STBP81.0hard93.0692.214✓
CIFAR-10STBP80.9hard93.0392.545✓
CIFAR-10STBP80.5hard91.4891.225✓
CIFAR10-DVSSTBP100.9hard77.0075.400✓
", + "bbox": [ + 501, + 335, + 887, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "different from the clean accuracy for all SNNs. For the model converted from ANNs, the model performance after the spike shuffle is slightly improved. The performance after spike shuffle is slightly reduced for other models obtained by supervised STBP training. In fact, even for models trained on the DVS dataset, the performance gap before and after shuffling is small, which proves that models trained on the DVS dataset contain very little timing information. Therefore, we assert that firing rates encode major information in these SNNs.", + "bbox": [ + 496, + 489, + 890, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Rate Gradient Approximation Attack", + "text_level": 1, + "bbox": [ + 500, + 650, + 823, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section proposes the Rate Gradient Approximation (RGA) attack for spike count rate coding SNNs. In the above section, we have shown that the well-trained SNNs are all rate-encoded at each layer. Thus, we can approximate the backward pass of SNNs using only the average firing rate over time-steps to generate effective gradients. Specifically, we introduce an intermediate variable $I_{i}$ to denote the average input current of neuron $i$ in Eq. (3), which is defined by:", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {i} = \\sum_ {t = 1} ^ {T} w _ {i j} s _ {j} (t) + b _ {i} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 820, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that $I_{i}$ also represents the weighted firing rate from the previous layer. Fig. 3 illustrates how the gradient propa", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7899", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6b8f2f78355b2c06aa6cea9c153344b38718142308cce5bbfb48152f7f2234b0.jpg", + "image_caption": [ + "(a) IF R-I curve" + ], + "image_footnote": [], + "bbox": [ + 94, + 89, + 271, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4f38aed04c487e50ff7c793b02c45ba51675b00be061bead40db4d2f17dec888.jpg", + "image_caption": [ + "(b) Derivative of IF R-I curve" + ], + "image_footnote": [], + "bbox": [ + 276, + 88, + 452, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "gates between two adjacent neurons $i$ and $j$ with the defined weighted firing rate. The gradient propagation starts from the firing rate $r_i$ of the $i$ -th neuron, passes to the input current $I_i$ , and finally arrives at the firing rate $r_j$ of the $j$ -th neuron, that is", + "bbox": [ + 75, + 281, + 468, + 356 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial r _ {j}} = \\frac {\\partial \\mathcal {L}}{\\partial r _ {i}} \\frac {\\partial r _ {i}}{\\partial I _ {i}} \\frac {\\partial I _ {i}}{\\partial r _ {j}}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 362, + 468, + 397 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This result can be generalized to the network with the chain rule. If we use vectors $\\boldsymbol{r}^l$ and $\\boldsymbol{I}^l$ to denote the firing rates and average input currents of all neurons in layer $l$ , respectively, and use vector $\\boldsymbol{r}^0$ to denote the input image. The gradient propagates from the loss function to the input image is formulated as:", + "bbox": [ + 75, + 404, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {0}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {L}} \\left(\\prod_ {l = 1} ^ {L} \\frac {\\partial \\boldsymbol {r} ^ {l}}{\\partial \\boldsymbol {I} ^ {l}} \\frac {\\partial \\boldsymbol {I} ^ {l}}{\\partial \\boldsymbol {r} ^ {l - 1}}\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 503, + 468, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. RGA Attack with Surrogate Gradient", + "text_level": 1, + "bbox": [ + 76, + 551, + 403, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to Eq. (11) and (12), one can compute the gradient $\\frac{\\partial I_i}{\\partial r_j}$ , the only part we cannot directly calculate the gradient in Eq. (13) is $\\frac{\\partial r_i}{\\partial I_i}$ . To get a proper approximation for $\\frac{\\partial r_i}{\\partial I_i}$ , we need to use a differentiable surrogate function $f(\\cdot)$ to approximate the relationship between output firing rate $r_i$ and input current $I_i$ . Here, we propose to use the static R-I curve, which refers to the relationship between the input current and output firing rate when the input is constant, as the approximation function. We discuss the cases of IF neurons and LIF neurons separately.", + "bbox": [ + 75, + 575, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RGA Attack the Integrate-and-Fire Neuron", + "text_level": 1, + "bbox": [ + 76, + 734, + 385, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For IF neurons, the static R-I curve is the clipped ReLU function [7, 14], which is presented in Fig. 4a by the blue line. We also sampled from a pre-trained VGG-11 network to obtain the actual distribution of average input current and average output firing rate (more details are in the Appendix), which is represented by the light blue scatter in the figure. We find that if we simply set the static RI curve as the surrogate gradient, many data points would be wrongly assigned to zero derivatives. To avoid the derivatives being all zero in the interval $[\\theta, +\\infty]$ , we propose a", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e4adde9d367ad481d47e9e95ffb229341395e1d33ae559eec46ae6bf14aa2628.jpg", + "image_caption": [ + "Figure 4. Surrogate function and gradient for IF neuron", + "(a) LIF R-I curve", + "Figure 5. Surrogate function and gradient for LIF neuron" + ], + "image_footnote": [], + "bbox": [ + 517, + 89, + 694, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dd5dfb0a92ae19947171b4b003774a5e55b4cf325e28aee1c354da7bc97846fb.jpg", + "image_caption": [ + "(b) Derivative of LIF R-I curve" + ], + "image_footnote": [], + "bbox": [ + 699, + 89, + 875, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "modified R-I curve function as the final surrogate function (green line in Fig. 4a). We introduce a relaxation parameter $\\beta \\in [1, +\\infty]$ to keep the derivatives to be none-zero between $[0, \\beta \\theta]$ . Then its corresponding derivative (surrogate gradient) is:", + "bbox": [ + 498, + 282, + 890, + 358 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} 1 / (\\beta \\theta), & 0 \\leqslant I _ {i} \\leqslant \\beta \\theta \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} . \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 369, + 890, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the formula for backpropagation and the derivatives of intermediate nodes, we can calculate the derivatives that are ultimately passed to the input image.", + "bbox": [ + 498, + 420, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RGA Attack the Leaky-Integrate-and-Fire Neuron", + "text_level": 1, + "bbox": [ + 500, + 465, + 856, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to the RGA Attack for IF neurons, the surrogate function for LIF neurons is inspired by the static R-I curve. Following the work of [23, 30], we derive the R-I curve function for the LIF neurons. Supposing that a LIF neuron receives a constant input $I_{i}$ and $u_{rest} = 0$ , the LIF neuron (Eq. (3)) can be simplified to:", + "bbox": [ + 498, + 481, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} (t) = \\lambda u _ {i} (t - 1) + I _ {i}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 583, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then iterate this recursive formula to get the neuron membrane potential as a function of time.", + "bbox": [ + 498, + 612, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} (t) = \\frac {I _ {i}}{\\lambda - 1} \\lambda^ {t} - \\frac {I _ {i}}{\\lambda - 1} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 652, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From the formula above, we can calculate the time required for the neuron to accumulate from 0 to $\\theta$ , and finally obtain the firing rate by inverse the calculated time interval.", + "bbox": [ + 498, + 691, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i} = \\left\\lceil \\log_ {\\lambda} \\frac {I _ {i} + \\theta (\\lambda - 1)}{I _ {i}} \\right\\rceil^ {- 1} \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 750, + 890, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 5a, the light blue scatter represents the actual distribution of average input current and average output firing rate from a pre-trained VGG-11 network with LIF neurons. Although the static RI curve matches the actual situation, the static RI curve (blue curve) contains the non-derivable equation. The derivative is always zero when $x < (1 - \\lambda)\\theta$ or $x > \\theta$ . Meanwhile, as $\\lim_{x\\to (1 - \\lambda)\\theta^{+}}$ , the", + "bbox": [ + 498, + 794, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7900", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "derivative of the function approaches infinity. This will lead to gradient vanishing and exploding problems in backpropagation. Therefore, it is impractical to calculate the derivatives directly from the static R-I curve.", + "bbox": [ + 75, + 90, + 468, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to the characteristics of this static R-I curve, we segment it at the position of $(1 - \\lambda)\\theta$ and then separately perform piecewise linear interpolation at $x\\in [0,(1 - \\lambda)\\theta ]$ and $x\\in [(1 - \\lambda)\\theta ,\\beta \\theta ]$ , where $\\beta$ is a relaxation parameter to control the end point of interpolation. Thus, we obtain two straight lines (green line in Fig. 5a). In order to avoid zero derivatives over the interval $[0,(1 - \\lambda)\\theta ]$ , we also add a hyperparameter $\\gamma$ which is the derivative of the first half of the linear function. In conclusion, the first part of the linear interpolation start at data point $(0,0)$ and end at $((1-$ $\\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)$ . The second part of the interpolation start at $((1 - \\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)$ and end at $(\\beta \\theta ,1)$ .", + "bbox": [ + 75, + 151, + 470, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, the final surrogate gradient can be written as", + "bbox": [ + 96, + 333, + 468, + 347 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} \\gamma , & 0 \\leqslant I _ {i} \\leqslant (1 - \\lambda) \\theta \\\\ \\frac {1 - \\gamma \\theta + \\gamma \\theta \\lambda}{(\\beta + \\lambda - 1) \\theta}, & (1 - \\lambda) \\theta < I _ {i} \\leqslant \\beta \\theta . \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} \\right. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 368, + 468, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The derivative of this surrogate gradient function is $\\gamma$ in the first interval and $(1 - \\gamma \\theta +\\gamma \\theta \\lambda) / ((\\beta +\\lambda -1)\\theta)$ in the second interval. Note that when we set the leaky parameter $\\lambda = 1$ , this function degenerates into the same form as the surrogate function for the IF neuron (Eq. (15)). Thus, this function can apply to both types of neurons.", + "bbox": [ + 75, + 448, + 468, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The hyperparameter $\\beta$ and $\\gamma$ are mainly smoothing terms to prevent the gradient from disappearing. We set $\\beta$ to 2 and $\\gamma$ to 0.2 in the rest of this paper. More ablation experiments of the hyperparameters are provided in the Appendix.", + "bbox": [ + 75, + 539, + 468, + 599 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. RGA Attack the Poisson Encoding", + "text_level": 1, + "bbox": [ + 76, + 607, + 377, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our proposed method can generalize to SNNs that receive spike inputs. For Poisson input SNN, we can regard it as a combined structure of a Poisson encoder and an end-to-end SNN receives spike input. Therefore, we also need to attack the Poisson encoder rather than only perturbing the network. We can consider the Poisson encoder as a random transformation and use a straight through estimator [2] to attack this random transformation [1]. The gradient can be written as:", + "bbox": [ + 75, + 631, + 468, + 765 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\text {P o i s s o n} (x)}{\\partial x} \\approx \\frac {\\partial \\mathbb {E} _ {x} (\\text {P o i s s o n} (x))}{\\partial x} = 1. \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 772, + 468, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Adversarial example generation methodology proposed by Sharmin et al. [63] also includes the attack on Poisson encoded attack. Note that although our attack on the Poisson encoder is implemented differently from theirs, it is mathematically equivalent, and the generated adversarial examples are the same.", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89f808ec16b6f15483062c3726551abb70e158a831360b0cb75a20294ce97b6c.jpg", + "image_caption": [ + "Figure 6. The attack success rate change with respect to the attack strength for VGG-11 model on the CIFAR-10 dataset. Here WB stands for white box attack while BB stands for black box attack. The blue and purple bar display the attack success rates $(\\%)$ for RGA-FGSM and STBP-FGSM, respectively." + ], + "image_footnote": [], + "bbox": [ + 535, + 92, + 859, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Time Extended RGA Attack", + "text_level": 1, + "bbox": [ + 500, + 579, + 754, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here we introduce an SNN-specific attack enhancement method. When generating attack samples, we expect to generate more effective adversarial samples by increasing the inference time of SNNs. We call this method as Time Extended attack. When we apply this time-extended enhancement with RGA attack, the effects of randomness can be reduced by increasing the simulation time of attacking, resulting in a more accurate estimation of the firing rate. Therefore, the time-extended enhancement is generally more suitable for RGA-based attacks and is more effective for attacking against SNNs with Poisson inputs.", + "bbox": [ + 496, + 603, + 890, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 784, + 632, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct various experiments to evaluate the effectiveness of the proposed methods [32, 55]. We first test our attack method on the CIFAR-10, CIFAR-100 dataset [36] and CIFAR10-DVS dataset [42] with the VGG-11 [66] and ResNet-17 architecture [80]. We implement both non-iterative attack FGSM and iterative attack PGD", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7901", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/db8a2547f9c3c5f43893a959cc9ed7da1f0bac1b527df858bb2d9afc22e1433c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ArchitectureDatasetInputTλTEAttackClean Acc.White Box AttackBlack Box Attack
ASR. (STBP)ASR. (RGA)ASR. (STBP)ASR. (RGA)
VGG-11CIFAR-10Direct81.0-FGSM93.0686.277793.735268.031473.2646
VGG-11CIFAR-10Direct81.02×FGSM93.0686.073594.734664.839973.6192
VGG-11CIFAR-10Direct81.0-PGD93.0699.494999.828186.460487.1266
VGG-11CIFAR-10Direct161.0-FGSM93.0385.327392.421865.796073.1269
VGG-11CIFAR-10Direct161.0-PGD93.0399.365899.838885.585387.4234
VGG-11CIFAR-10Poisson161.0-FGSM86.7254.979858.032840.867344.2259
VGG-11CIFAR-10Poisson161.02×FGSM86.7256.810660.529642.844046.9085
VGG-11CIFAR-10Poisson161.0-PGD86.7251.902257.141237.091741.1887
VGG-11CIFAR-10Direct80.5-FGSM91.4891.714093.627077.765679.6458
VGG-11CIFAR-10Direct80.5-PGD91.4899.825199.770493.681793.0367
VGG-11CIFAR-10Direct80.9-FGSM93.0389.906594.410473.449477.2761
VGG-11CIFAR-10Direct80.9-PGD93.0399.731399.828091.766191.3899
ResNet-17CIFAR-10Direct80.9-FGSM93.0484.243392.927867.110980.1053
ResNet-17CIFAR-10Direct80.9-PGD93.0499.9248100.00092.003497.5172
VGG-11CIFAR-100Direct80.9-FGSM73.2892.876694.718980.895284.2658
VGG-11CIFAR-100Direct80.9-PGD73.2899.754499.849992.235392.0579
ResNet-17CIFAR-100Direct80.9-FGSM72.0585.662792.061174.295681.1936
ResNet-17CIFAR-100Direct80.9-PGD72.0599.583699.889087.633695.2949
VGG-11CIFAR10-DVSFrame100.9-FGSM77.0059.508459.560748.496747.9275
", + "bbox": [ + 81, + 88, + 885, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Results of RGA based attack and STBP based attack on different type of SNNs. The seven columns on the left describes the parameter settings of the attack object, including architecture, datasets, input coding, simulation time-steps, leaky parameters, time extant (TE), and attack method. ASR. is short for attack success rate. For clarity, the better of the two attack results is bolded.", + "bbox": [ + 78, + 420, + 890, + 462 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and combine them with the proposed RGA attack and compare the results with STBP-based attacks. Note that when attacking DVS-related models, we directly generate and add adversarial examples on the preprocessed frames.", + "bbox": [ + 80, + 488, + 467, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As for training methods, since the ANN-SNN conversion method is proved insecure [63], we only consider SNNs obtained by supervised STBP training. We used the attack success rate as our metric for each attack, which is the proportion of samples that fool the network into misclassification. The details of the training configurations for pretrained networks are provided in the Appendix.", + "bbox": [ + 78, + 550, + 467, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Effectiveness of the RGA Attack", + "text_level": 1, + "bbox": [ + 80, + 665, + 359, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here we test the effectiveness of the proposed RGA attack. We choose the STBP attack as a baseline and compare the attack success rate. To compare the effectiveness of the attack on various neuron settings, we select SNNs composed of LIF neurons with a leaky parameter of 0.9 and none-leaky IF neurons with a leaky parameter of 1.0. Also, the inference time-steps vary from 8 to 16.", + "bbox": [ + 78, + 689, + 467, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 6, we find that the attack success rate of our RGA attack method surpasses the previously commonly used STBP attack in most cases. When the attack strength is small, the attack success rate of the RGA attack and STBP attack is not much different. However, when the attack strength gradually increases to 8/255, the attack success rate of the RGA attack will be much higher than that", + "bbox": [ + 78, + 795, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "obtained by the STBP attack. These results demonstrate that the RGA attack is more effective than the STBP attack for different SNN settings.", + "bbox": [ + 503, + 488, + 890, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Effectiveness of Time Extended Attack", + "text_level": 1, + "bbox": [ + 503, + 542, + 830, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of the time-extended attack, we pre-train two SNNs with different neurons and input encoding. We then double and triple the inference time-steps to attack these SNNs while keeping the origin inference time-steps for evaluation. The SNN configuration and the final results are shown in Fig. 7. The combination of the time-extended enhancement and RGA-based attack can achieve better attack performance since the attack effectiveness increases as the simulation time-step increases. However, applying the time-extended enhancement attack on the STBP-based attack cannot improve the attack. Meanwhile, we also find that the time-extended enhancement method is more effective for the Poisson input model.", + "bbox": [ + 503, + 566, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Generalizability of the RGA Attacks", + "text_level": 1, + "bbox": [ + 503, + 771, + 813, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To discuss the generalizability of RGA attacks across different SNNs, we conduct further experiments across various SNNs. Tab. 2 reports the detailed comparison of RGA attack and STBP attack over various SNN neurons, architecture, and dataset settings. In this experiment, we set the attack strength $\\epsilon$ to 8/255 for CIFAR-10/100 dataset and 0.02 for the CIFAR10-DVS dataset. Also, the step size and", + "bbox": [ + 503, + 795, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7902", + "bbox": [ + 483, + 946, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/854b3ee48d07dce26f39646e9ff4c90bbe2c27481ca98b1fd644ac7386a5eac6.jpg", + "image_caption": [ + "(a) $\\lambda = 0.9$ $\\mathrm{T} = 8$ ,Direct Input" + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 271, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0c149b985393f6aef8ba52d2ecf24ded16e74cbd8bfc722324a9410690085bcf.jpg", + "image_caption": [ + "(b) $\\lambda = 1$ $\\mathrm{T} = 16$ Poisson Input", + "Figure 7. White box attack results of the time-extended attack with different settings. The $1 \\times$ represents the baseline attack, while $2 \\times$ and $3 \\times$ represent double or triple the simulation time when attacked. The model under attack is VGG-11 composed of LIF neurons on the CIFAR-10 dataset." + ], + "image_footnote": [], + "bbox": [ + 276, + 88, + 454, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the number of steps for the PGD attack are set to 2/255 and 5, respectively.", + "bbox": [ + 75, + 315, + 468, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From Tab. 2, one can find that all RGA-based attacks outperform STBP-based attacks when conducting single-step attacks. In attacks cases without time-extended enhancement, the largest performance gap exceeds $8.6\\%$ and $13\\%$ in ResNet-17 for white box and black box attacks, respectively. When conducting multi-step attacks, the proposed RGA-based attack achieves better performance than the STBP-based attack in most cases and gets comparable performance for the rest of the cases. In attack cases with time-extended enhancement, the performance of the RGA attack not only exceeds the STBP attack, but also exceeds the performance of RGA attack without time-extended enhancement. Even in attacks on the CIFAR10-DVS dataset, the RGA-based attack gets comparable performance as the STBP-based attack.", + "bbox": [ + 75, + 347, + 468, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, the proposed RGA attack can produce stronger adversarial examples in most cases. The RGA attack is also insensitive to neuron hyperparameters. Currently, high-performance SNNs are mainly applied in tasks related to static images or DVS datasets. We have proved through experiments that those SNNs contain very limited temporal information and they are vulnerable to the designed RGA-based attack. This demonstrates the importance and generalizability of the RGA-based attack method.", + "bbox": [ + 75, + 575, + 468, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. LIF Neuron is not that Robust", + "text_level": 1, + "bbox": [ + 76, + 724, + 344, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Previous research suggested that the VGG5 SNNs trained with LIF neurons are more robust than the ones trained with IF neurons [63]. Here, we test whether this conclusion can be generalized to deeper networks with RGA-based attacks. We train multiple networks with the same architecture, including one quantized ANN and six SNNs with leaky parameters ranging from 0.5 to 1. We select VGG-11 as the model architecture and CIFAR-10 as the evaluation dataset. Then, we apply the white box FGSM attack to the quantized ANN and both RGA-FGSM", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2db5701c771ff4f4c5e2b3edad8c32f10f239b7439417e939dc30603142cbaea.jpg", + "image_caption": [ + "Figure 8. The white box attack success rate changes with respect to the leaky parameter of the spiking neuron. The red line represents the RGA attack, while the green line represents the STBP attack. The blue dashed line illustrates the attack success rate of a quantized ANN under the FGSM attack. The selected leaky parameters range from 0.5 to 1.0. This experiment is conducted on the CIFAR-10 dataset with VGG-11 architecture." + ], + "image_footnote": [], + "bbox": [ + 513, + 90, + 882, + 214 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and STBP-FGSM attacks to the six SNNs.", + "bbox": [ + 500, + 353, + 781, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 8 demonstrates the results. The blue dashed line represents the attack success rate of ANN being attacked by FGSM. The red and green lines represent the attack success rate of the RGA-FGSM and STBP-FGSM, respectively. According to this figure, one can find that compared to the STBP attack (green line), the RGA attack (red line) is more stable. Meanwhile, the red line is always above the green line, indicating that the RGA attack can not only generate stronger adversarial examples, but is also less sensitive to neuron leakage parameters.", + "bbox": [ + 496, + 369, + 890, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, the performance of all types of SNNs under STBP-based attacks fluctuates around the baseline, while the RGA attack success rate is always higher than the baseline. Therefore, we found that SNN composed of LIF neurons with different leakage parameters has no advantage over ANNs in terms of adversarial robustness.", + "bbox": [ + 496, + 520, + 890, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 626, + 617, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a new attack method for SNNs that outperforms previous methods. Our approach can serve as a benchmark for future research on SNN adversarial robustness. In addition, considering the strength of this attack method and the lower time cost compared to the STBP attack, we also look forward to the research on adversarial training based on this attack method. Our findings show that the rate-coded SNN composed of LIF neurons is not secure against stronger adversarial attacks, highlighting the need for exploring training methods for SNNs utilizing complex neurons and other neuronal codings.", + "bbox": [ + 496, + 652, + 890, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 833, + 679, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is funded by STI2030Project (2021ZD0200300), and the National Natural Science Foundation of China (621 76003, 62088102).", + "bbox": [ + 500, + 857, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7903", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In International Conference on Machine Learning, 2018. 6", + "[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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In Advances in Neural Information Processing Systems, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 753 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7906", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_model.json b/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..df44dac498c7489f6d6f755379d789dcde4e3801 --- /dev/null +++ b/2023/Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks/5607e0f0-af41-4d3b-ab58-e27bce5086e1_model.json @@ -0,0 +1,2741 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.13, + 0.877, + 0.154 + ], + "angle": 0, + "content": "Rate Gradient Approximation Attack Threats Deep Spiking Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.181, + 0.686, + 0.218 + ], + "angle": 0, + "content": "Tong Bu, Jianhao Ding, Zecheng Hao, Zhaofei Yu* Peking University" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.22, + 0.822, + 0.234 + ], + "angle": 0, + "content": "putong30@pku.edu.cn，djh01998@stu.pku.edu.cn，{zechenghao，yuzf12}@pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.264, + 0.269, + 0.344, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.473, + 0.664 + ], + "angle": 0, + "content": "Spiking Neural Networks (SNNs) have attracted significant attention due to their energy-efficient properties and potential application on neuromorphic hardware. State-of-the-art SNNs are typically composed of simple Leaky Integrate-and-Fire (LIF) neurons and have become comparable to ANNs in image classification tasks on large-scale datasets. However, the robustness of these deep SNNs has not yet been fully uncovered. In this paper, we first experimentally observe that layers in these SNNs mostly communicate by rate coding. Based on this rate coding property, we develop a novel rate coding SNN-specified attack method, Rate Gradient Approximation Attack (RGA). We generalize the RGA attack to SNNs composed of LIF neurons with different leaky parameters and input encoding by designing surrogate gradients. In addition, we develop the time-extended enhancement to generate more effective adversarial examples. The experiment results indicate that our proposed RGA attack is more effective than the previous attack and is less sensitive to neuron hyperparameters. We also conclude from the experiment that rate-coded SNN composed of LIF neurons is not secure, which calls for exploring training methods for SNNs composed of complex neurons and other neuronal codings. Code is available at https://github.com/putshua/SNN_attack_RGA" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.696, + 0.21, + 0.712 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.722, + 0.47, + 0.875 + ], + "angle": 0, + "content": "As the third generation of artificial neural networks [47], Spiking Neural Networks (SNNs) have gained more attraction due to their spatio-temporal, discrete representation, and event-driven properties. These bio-inspired neural networks borrow the characteristics of spiking representations and neuronal dynamics from biological brains [23, 75]. Unlike traditional Analog Neural Networks (ANNs), SNNs utilize spiking neurons as their essential components, which accumulate current over time, emit spikes when the membrane potential exceeds the threshold, and pass on informa" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.892, + 0.301 + ], + "angle": 0, + "content": "tion through spike trains. The natural sparsity of the spike trains leads to the low power consumption of SNNs [59,69]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.893, + 0.441 + ], + "angle": 0, + "content": "SNNs are competitive in real-world vision applications. The development of neuromorphic computing [10, 11, 20, 54, 56, 76] has further magnified the advantages of low-power consumption properties of SNNs, so that they can be deployed in power-limited scenarios [8, 64], such as edge computing or mobile application. However, the training algorithms of SNNs are also improving. The most practical training methods are ANN-SNN conversion [7], supervised training [72], and hybrid training [57, 58]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.895, + 0.656 + ], + "angle": 0, + "content": "When SNNs are applied to safety-critical systems, the reliability of SNNs should be a major concern. The adversarial attack is one of the most significant categories that threatens model security [24, 68]. Similar to ANNs, SNNs can also be fooled by crafting adversarial examples that are imperceptible to human eyes from gradient-based backpropagation [62], which may lead to catastrophic consequences when SNNs are deployed in safety-related scenarios. Nevertheless, SNNs are still considered to be more robust than ANNs. This robustness comes from inherent neural dynamics, such as forgetting historical information and discrete spikes [63]. Besides, the robustness of SNNs can be improved through special structural enhancements [9] or training techniques [37, 45, 71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Effective attack examples of ANNs can be crafted from well-defined gradients on the activation functions [68]. For SNNs, a common way to construct gradient-based attacks is by backpropagating through a surrogate function over discrete spikes. In this way, the gradient may suffer from explosion and vanishment in temporal and layer-by-layer communication [72]; at the same time, the membrane potential of all historical time steps needs to be saved when backpropagation, which requires a large amount of memory. Currently, high-performance SNNs typically combine leaky integrate-and-fire models and rate-encoded inputs. While the rate coding scheme brings excellent performance to SNN, it also exposes shortcomings. If the rate coding nature in SNN is considered, can we construct a more powerful attack? After all, the activation functions of many ANNs are inspired by the firing rate of biological neurons [52]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.887, + 0.23, + 0.901 + ], + "angle": 0, + "content": "* Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7896" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "In this paper, we develop a novel Rate Gradient Approximation Attack (RGA) based on components of rate coding in high-performance SNNs. RGA attack is more effective than previously used attacks as it makes better use of the rate coding feature. We expect our work to provide benchmarks for SNN defense against adversarial attacks and inspire future research for SNNs. The main contributions of this paper are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.225, + 0.468, + 0.268 + ], + "angle": 0, + "content": "- We observe that layers in SNN are mainly communicated by rate coding, either for converted SNN or for surrogate-trained SNN." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.271, + 0.468, + 0.343 + ], + "angle": 0, + "content": "- We develop the Rate Gradient Approximation Attack based on rate coding and apply it to SNNs composed of different types of neurons and input codings. We further propose a time-extended variant to get more effective adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.346, + 0.468, + 0.465 + ], + "angle": 0, + "content": "- Experiments prove that the RGA attack outperforms the STBP attack and is less sensitive to neuron hyperparameters. Based on the proposed attack, we compare the robustness of SNNs using different leaky parameters with that of ANNs and manifest that the SNNs composed of LIF neurons cannot provide strong enough security. This conclusion inspires further research on networks with more complex neurons." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.225, + 0.468, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.482, + 0.227, + 0.497 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Learning of SNNs. The most efficient and commonly used SNNs training methods are ANN-SNN conversion [7] and Spatio-temporal Backpropagation (STBP) [72]. The core idea of ANN-SNN conversion is mapping the weights of a pre-trained ANN into an SNN. Researchers found that adjusting the weights or threshold in the SNN can balance the trade between inference time-steps and performance after conversion [12, 14, 16, 25, 28, 50, 61]. Some recent works quantized the source ANN to boost the performance of converted SNNs using ultra-low time-steps [5, 41, 43, 74]. ANN-SNN conversion is the most practical training method to train SNNs on large-scale datasets, and the converted SNNs always have outstanding performance [6, 26, 27, 34]. The temporal characteristics of the spiking neuron make it similar to a Recurrent Neural Network (RNN). Based on this, Wu et al. [72] borrowed the idea of Back Propagation Through Time [70] and proposed the supervised learning way of STBP. As the firing of neurons is a non-differentiable Heaviside function, the surrogate gradient approximation is proposed to smooth the gradient [19, 21, 40, 53, 65, 67, 77]. Nowadays, the performance of SNNs trained with backpropagation is comparable to that of ANNs [13, 17, 22, 29, 33, 35, 39, 73, 80]. Time-based backpropagation is another supervised learning method that can maintain the sparsity of the gradient. However, these works can only extend to shallow networks [3, 51, 78, 79, 81]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "The robustness of SNN. SNNs are vulnerable to adversarial attacks as ANNs by adopting the gradient scheme in training. Firstly, SNNs obtained from ANN-SNN conversion can be attacked by the source ANNs with shared weights [62]. Besides, end-to-end trained SNNs suffer from the attack constructed from STBP. Sharmin et al. [62] summarized the two types of attacks as ANN-crafted and SNN-crafted attacks and revealed that attacks based on STBP are believed to be more powerful than those based on ANNs. Moreover, Liang et al. [44] exploited spike-compatible gradient to perform bit-flip attacks on SNN. Considering that SNNs are suitable for event-based tasks, various attacks on the event data of neuromorphic sensors are also explored [46, 49]. In these attacks, the STBP gradients are merged into sparse event data to construct attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.893, + 0.576 + ], + "angle": 0, + "content": "Although the performance of SNNs can be degraded by such a variety of attack schemes, SNNs are still considered to have additional robustness compared to ANNs [15]. This is because more encodings are supported in SNNs. Compared to direct coding, Poisson coding is believed to process more inherent robustness as it introduces a noisy discretization to SNNs [37, 63]. Even so, how strong an attack Poisson coding can withstand still remains unknown. Another key robustness component of SNNs is the leaky parameter [63]. The leaky parameter controls the forgetting of historical information in LIF neurons. El-Allami et al. [18] achieved improved robustness by only searching in the space of leaky parameters. The current understanding of the robustness of SNNs is mainly focused on rate coding, and LIF neurons are also thought to perform the same coding. Therefore, gaining new insights into the robustness of rate coding is crucial for the practical application of SNNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.638, + 0.605 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.614, + 0.722, + 0.63 + ], + "angle": 0, + "content": "3.1. Neuron Model for SNNs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.715 + ], + "angle": 0, + "content": "In this paper, we consider the commonly used Leaky-Integrate-and-Fire (LIF) model and Integrate-and-Fire (IF) model [23, 31], the dynamics of membrane potential under firing threshold can be described by the following equations, respectively." + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.724, + 0.891, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = - (u (t) - u _ {\\text {r e s t}}) + R I (t), \\quad (\\mathbf {L I F}) (1) \\\\ \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = R I (t). \\quad (\\mathbf {I F}) (2) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Here \\(\\tau_{m}\\) and \\(R\\) denote the membrane time constant and the membrane resistance constant, respectively. \\(u(t)\\) and \\(I(t)\\) represent the membrane potential and input current at time \\(t\\), respectively. Once the membrane potential reaches the firing threshold \\(\\theta\\), the neuron will fire, and then the membrane potential will reset to the resting potential \\(u_{rest} < \\theta\\). Without loss of generality, to simulate the network of LIF" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7897" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "neurons on a computer with a Von Neumann architecture, the above process can be simplified and discretized to another set of equations [4]." + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.151, + 0.469, + 0.168 + ], + "angle": 0, + "content": "\\[\nu _ {i} (t) = \\lambda u _ {i} (t - 1) + w _ {i j} s _ {j} (t) + b _ {i} + \\eta_ {i} (t), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.171, + 0.469, + 0.213 + ], + "angle": 0, + "content": "\\[\ns _ {i} (t) = \\left\\{ \\begin{array}{l l} 1, & t = t _ {i} ^ {(f)} \\\\ 0, & t \\neq t _ {i} ^ {(f)} \\end{array} , \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.226, + 0.47, + 0.455 + ], + "angle": 0, + "content": "where \\(j\\) and \\(i\\) indicate presynaptic and postsynaptic neurons, \\(w_{ij}\\) represents the connection strength between the two neurons, and \\(b_{i}\\) is an extra constant input current to neuron \\(i\\). \\(s_i(t)\\) describes whether neuron \\(i\\) fires at time-step \\(t\\), and the trigger is membrane potential \\(u_{i}(t)\\) reaches the firing threshold \\(\\theta\\). We also mark the firing time-step of neuron \\(i\\) as \\(t_i^{(f)}\\), \\(f = 1,2,\\ldots,\\lambda\\) is the membrane leaky constant corresponding to the membrane time constant in Eq. (1). Note that if we explicitly \\(\\lambda\\) to 1, this LIF neuron model will degenerate to the none-leaky IF model. Also, we add a reset term \\(\\eta_i(t)\\) on Eq. (3) to describe the neuron reset behavior. Despite the hard-reset function that resets the neuron membrane potential to resting potential (Eq. (5)), we also consider the soft-reset function (Eq. (6)) that directly subtracts the membrane potential by the threshold \\(\\theta\\) [25, 60]." + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.466, + 0.469, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\eta_ {i} ^ {\\text {h a r d}} (t) = \\left\\{ \\begin{array}{l l} - \\left(u _ {i} \\left(t _ {i} ^ {(f)}\\right) - u _ {\\text {r e s t}}\\right) & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}. \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.512, + 0.469, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\eta_ {i} ^ {\\text {s o f t}} (t) = \\left\\{ \\begin{array}{l l} - \\theta & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}, \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.568, + 0.424, + 0.584 + ], + "angle": 0, + "content": "3.2. Supervised Training of SNNs with STBP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.469, + 0.699 + ], + "angle": 0, + "content": "Equation (3) implies that the LIF neuron has a function similar to that of an RNN. Thus, SNNs can be trained in the same way as RNNs with Back Propagation Through Time. STBP uses this idea to unroll the SNN over time-steps and accumulate gradient at each time-step [53, 72]. As illustrated in Fig. 1, the gradient of the loss function \\(\\mathcal{L}\\) with respect to the output spikes \\(s_j(t)\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.711, + 0.469, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t)} = \\frac {\\partial \\mathcal {L}}{\\partial s _ {i} (t)} \\frac {\\partial s _ {i} (t)}{\\partial u _ {i} (t)} \\frac {\\partial u _ {i} (t)}{\\partial s _ {j} (t)} + \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.747, + 0.439, + 0.781 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t + 1)} \\frac {\\partial s _ {j} (t + 1)}{\\partial u _ {j} (t + 1)} \\frac {\\partial u _ {j} (t + 1)}{\\partial u _ {j} (t)} \\frac {\\partial u _ {j} (t)}{\\partial s _ {j} (t)}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.791, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Note that as the derivative of spike with respect to the membrane potential \\(\\frac{\\partial s_i(t)}{\\partial u_i(t)}\\) is nondifferentiable, the surrogate gradient [53] is often used in backpropagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Since the STBP method enables supervised training of SNNs, this method can also generate gradient-based adversarial examples [62]. Therefore, we will use STBP as the baseline gradient obtain method." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.092, + 0.882, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.244, + 0.892, + 0.287 + ], + "angle": 0, + "content": "Figure 1. Forward pass and backward pass for STBP. The pink line shows that surrogate functions are applied in the non-differentiable process of neuron firing to obtain approximate gradients." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.316, + 0.691, + 0.33 + ], + "angle": 0, + "content": "3.3. Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.341, + 0.892, + 0.387 + ], + "angle": 0, + "content": "Adversarial attack is a method to generate imperceptible perturbations that can fool neural networks, which can be formulated as an optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.402, + 0.891, + 0.424 + ], + "angle": 0, + "content": "\\[\n\\arg \\max _ {\\delta} \\mathcal {L} (f (\\boldsymbol {x} + \\delta), y) \\quad s. t. \\| \\delta \\| _ {p} \\leq \\epsilon , \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.438, + 0.892, + 0.606 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is the loss function, \\(f\\) is the network under attack, and \\(\\pmb{x},\\pmb{y}\\) are the input images and output target of the given network, respectively. \\(\\delta\\) is the adversarial perturbation we want to optimize. \\(\\| \\cdot \\| _p\\) is the \\(L_{p}\\)-norm, and parameter \\(\\epsilon\\) limits the strength of the perturbation to a level that is indistinguishable to the human eye. Here we consider two classic adversarial attack algorithms: Fast Gradient Sign Method (FGSM) [24] and Projected Gradient Descent (PGD) [38]. FGSM is a simple but effective attack method, which perturbs the data \\(\\pmb{x}\\) along the sign of the gradient to increase the perturbed linear output, that is" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.622, + 0.891, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {x}} = \\boldsymbol {x} + \\epsilon \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x}, y))\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.655, + 0.891, + 0.701 + ], + "angle": 0, + "content": "PGD is an iterative variant of FGSM. By iteratively optimizing the perturbation, PGD offers a more powerful attack [48]. The iteration can be summarized as:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.715, + 0.891, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {x}} ^ {k} = \\Pi_ {\\epsilon} \\left\\{\\boldsymbol {x} ^ {k - 1} + \\alpha \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x} ^ {k - 1}, y))\\right) \\right\\}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.748, + 0.891, + 0.807 + ], + "angle": 0, + "content": "where \\( k \\) is the number of the iteration step, and \\( \\alpha \\) is the step size of each iteration. \\( \\Pi_{\\epsilon} \\) constrains the data in each iteration and projects it onto the space of the \\( \\epsilon - l_{p} \\) neighborhood of \\( x \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For all attack methods, we consider two different attack scenarios, white-box attack, and black-box attack. The white-box attack is the case that the hacker has complete access to the model topology, model parameters, and gradients, while the black-box attack is the case the hacker can only get the basic information of the model." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7898" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.173, + 0.106, + 0.378, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.292, + 0.414, + 0.307 + ], + "angle": 0, + "content": "Figure 2. Experimental scheme of spike shuffle" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.176, + 0.345 + ], + "angle": 0, + "content": "4. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.491 + ], + "angle": 0, + "content": "In this section, we first show that the current high-performance SNNs for image classification tasks are encoded by firing rate and do not contain timing information, whether they are trained by STBP and ANN-SNN conversion. Based on this, we propose rate gradient approximation, a new attack method against SNNs, and apply it to SNNs composed of different types of neurons and input encodings. Finally, we propose the time-extended attack as an attack enhancement method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.499, + 0.469, + 0.53 + ], + "angle": 0, + "content": "4.1. Does well-trained SNNs contain timing information?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.469, + 0.629 + ], + "angle": 0, + "content": "Here we design an experiment and test whether the well-trained SNNs are rate coded and whether they contain timing information. The definition of firing rate refers to the temporal average of the spikes. As illustrated in Eq. (11), the firing rate of one given neuron \\( i \\) is the total spike count in an interval of time-steps \\( T \\) divided by the duration \\( T \\)." + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.649, + 0.469, + 0.682 + ], + "angle": 0, + "content": "\\[\nr _ {i} = \\frac {\\sum_ {t = 1} ^ {T} s _ {i}}{T}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.779 + ], + "angle": 0, + "content": "The detailed experimental scheme is shown in Fig. 2. We add a random number generator to shuffle each neuron's output spike firing order so that the spike trains will never contain temporal information. We apply this design to the pre-trained SNN models and test accuracy change before and after the spike shuffle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.869 + ], + "angle": 0, + "content": "The experiment is implemented on the CIFAR-10 dataset with VGG-11 network architecture. To test different SNNs, we choose combinations of different training methods, leakage parameters, and reset functions. We pre-train SNN for each combination and then substitute all the spiking neurons with shuffled neurons." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 reports the average performance of 10 runs, from which we find that the accuracy after spike shuffle is slightly" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.092, + 0.872, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.255, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Figure 3. Forward pass and backward pass for RGA attack. The pink line shows that surrogate functions are applied to the approximation of the derivative for firing rate and input current." + }, + { + "type": "table_caption", + "bbox": [ + 0.532, + 0.312, + 0.86, + 0.326 + ], + "angle": 0, + "content": "Table 1. Performance before and after the spike shuffle" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.337, + 0.888, + 0.466 + ], + "angle": 0, + "content": "
DatasetTraining MethodTλResetClean Acc.Shuffled Acc.Rate
CIFAR-10ANNSNN161.0soft93.2593.358✓
CIFAR-10STBP81.0soft92.7592.086✓
CIFAR-10STBP81.0hard93.0692.214✓
CIFAR-10STBP80.9hard93.0392.545✓
CIFAR-10STBP80.5hard91.4891.225✓
CIFAR10-DVSSTBP100.9hard77.0075.400✓
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.641 + ], + "angle": 0, + "content": "different from the clean accuracy for all SNNs. For the model converted from ANNs, the model performance after the spike shuffle is slightly improved. The performance after spike shuffle is slightly reduced for other models obtained by supervised STBP training. In fact, even for models trained on the DVS dataset, the performance gap before and after shuffling is small, which proves that models trained on the DVS dataset contain very little timing information. Therefore, we assert that firing rates encode major information in these SNNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.825, + 0.667 + ], + "angle": 0, + "content": "4.2. Rate Gradient Approximation Attack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.809 + ], + "angle": 0, + "content": "This section proposes the Rate Gradient Approximation (RGA) attack for spike count rate coding SNNs. In the above section, we have shown that the well-trained SNNs are all rate-encoded at each layer. Thus, we can approximate the backward pass of SNNs using only the average firing rate over time-steps to generate effective gradients. Specifically, we introduce an intermediate variable \\( I_{i} \\) to denote the average input current of neuron \\( i \\) in Eq. (3), which is defined by:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.821, + 0.891, + 0.861 + ], + "angle": 0, + "content": "\\[\nI _ {i} = \\sum_ {t = 1} ^ {T} w _ {i j} s _ {j} (t) + b _ {i} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Note that \\( I_{i} \\) also represents the weighted firing rate from the previous layer. Fig. 3 illustrates how the gradient propa" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7899" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.09, + 0.272, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.219, + 0.226, + 0.231 + ], + "angle": 0, + "content": "(a) IF R-I curve" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.089, + 0.454, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.219, + 0.444, + 0.231 + ], + "angle": 0, + "content": "(b) Derivative of IF R-I curve" + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.243, + 0.438, + 0.258 + ], + "angle": 0, + "content": "Figure 4. Surrogate function and gradient for IF neuron" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.47, + 0.357 + ], + "angle": 0, + "content": "gates between two adjacent neurons \\(i\\) and \\(j\\) with the defined weighted firing rate. The gradient propagation starts from the firing rate \\(r_i\\) of the \\(i\\)-th neuron, passes to the input current \\(I_i\\), and finally arrives at the firing rate \\(r_j\\) of the \\(j\\)-th neuron, that is" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.363, + 0.47, + 0.398 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial r _ {j}} = \\frac {\\partial \\mathcal {L}}{\\partial r _ {i}} \\frac {\\partial r _ {i}}{\\partial I _ {i}} \\frac {\\partial I _ {i}}{\\partial r _ {j}}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.469, + 0.495 + ], + "angle": 0, + "content": "This result can be generalized to the network with the chain rule. If we use vectors \\( \\boldsymbol{r}^l \\) and \\( \\boldsymbol{I}^l \\) to denote the firing rates and average input currents of all neurons in layer \\( l \\), respectively, and use vector \\( \\boldsymbol{r}^0 \\) to denote the input image. The gradient propagates from the loss function to the input image is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.504, + 0.469, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {0}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {L}} \\left(\\prod_ {l = 1} ^ {L} \\frac {\\partial \\boldsymbol {r} ^ {l}}{\\partial \\boldsymbol {I} ^ {l}} \\frac {\\partial \\boldsymbol {I} ^ {l}}{\\partial \\boldsymbol {r} ^ {l - 1}}\\right). \\tag {14}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.553, + 0.405, + 0.57 + ], + "angle": 0, + "content": "4.3. RGA Attack with Surrogate Gradient" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.469, + 0.734 + ], + "angle": 0, + "content": "According to Eq. (11) and (12), one can compute the gradient \\(\\frac{\\partial I_i}{\\partial r_j}\\), the only part we cannot directly calculate the gradient in Eq. (13) is \\(\\frac{\\partial r_i}{\\partial I_i}\\). To get a proper approximation for \\(\\frac{\\partial r_i}{\\partial I_i}\\), we need to use a differentiable surrogate function \\(f(\\cdot)\\) to approximate the relationship between output firing rate \\(r_i\\) and input current \\(I_i\\). Here, we propose to use the static R-I curve, which refers to the relationship between the input current and output firing rate when the input is constant, as the approximation function. We discuss the cases of IF neurons and LIF neurons separately." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.387, + 0.749 + ], + "angle": 0, + "content": "RGA Attack the Integrate-and-Fire Neuron" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "For IF neurons, the static R-I curve is the clipped ReLU function [7, 14], which is presented in Fig. 4a by the blue line. We also sampled from a pre-trained VGG-11 network to obtain the actual distribution of average input current and average output firing rate (more details are in the Appendix), which is represented by the light blue scatter in the figure. We find that if we simply set the static RI curve as the surrogate gradient, many data points would be wrongly assigned to zero derivatives. To avoid the derivatives being all zero in the interval \\([\\theta, +\\infty]\\), we propose a" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.09, + 0.695, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.559, + 0.219, + 0.653, + 0.231 + ], + "angle": 0, + "content": "(a) LIF R-I curve" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.09, + 0.877, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.218, + 0.871, + 0.231 + ], + "angle": 0, + "content": "(b) Derivative of LIF R-I curve" + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.243, + 0.866, + 0.258 + ], + "angle": 0, + "content": "Figure 5. Surrogate function and gradient for LIF neuron" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.284, + 0.892, + 0.359 + ], + "angle": 0, + "content": "modified R-I curve function as the final surrogate function (green line in Fig. 4a). We introduce a relaxation parameter \\(\\beta \\in [1, +\\infty]\\) to keep the derivatives to be none-zero between \\([0, \\beta \\theta]\\). Then its corresponding derivative (surrogate gradient) is:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.37, + 0.891, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} 1 / (\\beta \\theta), & 0 \\leqslant I _ {i} \\leqslant \\beta \\theta \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} . \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.421, + 0.892, + 0.466 + ], + "angle": 0, + "content": "With the formula for backpropagation and the derivatives of intermediate nodes, we can calculate the derivatives that are ultimately passed to the input image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.467, + 0.857, + 0.481 + ], + "angle": 0, + "content": "RGA Attack the Leaky-Integrate-and-Fire Neuron" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.482, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Similar to the RGA Attack for IF neurons, the surrogate function for LIF neurons is inspired by the static R-I curve. Following the work of [23, 30], we derive the R-I curve function for the LIF neurons. Supposing that a LIF neuron receives a constant input \\( I_{i} \\) and \\( u_{rest} = 0 \\), the LIF neuron (Eq. (3)) can be simplified to:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.584, + 0.891, + 0.601 + ], + "angle": 0, + "content": "\\[\nu _ {i} (t) = \\lambda u _ {i} (t - 1) + I _ {i}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.613, + 0.891, + 0.643 + ], + "angle": 0, + "content": "We then iterate this recursive formula to get the neuron membrane potential as a function of time." + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.653, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\nu _ {i} (t) = \\frac {I _ {i}}{\\lambda - 1} \\lambda^ {t} - \\frac {I _ {i}}{\\lambda - 1} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.693, + 0.891, + 0.739 + ], + "angle": 0, + "content": "From the formula above, we can calculate the time required for the neuron to accumulate from 0 to \\(\\theta\\), and finally obtain the firing rate by inverse the calculated time interval." + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.75, + 0.891, + 0.786 + ], + "angle": 0, + "content": "\\[\nr _ {i} = \\left\\lceil \\log_ {\\lambda} \\frac {I _ {i} + \\theta (\\lambda - 1)}{I _ {i}} \\right\\rceil^ {- 1} \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 5a, the light blue scatter represents the actual distribution of average input current and average output firing rate from a pre-trained VGG-11 network with LIF neurons. Although the static RI curve matches the actual situation, the static RI curve (blue curve) contains the non-derivable equation. The derivative is always zero when \\( x < (1 - \\lambda)\\theta \\) or \\( x > \\theta \\). Meanwhile, as \\( \\lim_{x\\to (1 - \\lambda)\\theta^{+}} \\), the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7900" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.151 + ], + "angle": 0, + "content": "derivative of the function approaches infinity. This will lead to gradient vanishing and exploding problems in backpropagation. Therefore, it is impractical to calculate the derivatives directly from the static R-I curve." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.333 + ], + "angle": 0, + "content": "According to the characteristics of this static R-I curve, we segment it at the position of \\((1 - \\lambda)\\theta\\) and then separately perform piecewise linear interpolation at \\(x\\in [0,(1 - \\lambda)\\theta ]\\) and \\(x\\in [(1 - \\lambda)\\theta ,\\beta \\theta ]\\), where \\(\\beta\\) is a relaxation parameter to control the end point of interpolation. Thus, we obtain two straight lines (green line in Fig. 5a). In order to avoid zero derivatives over the interval \\([0,(1 - \\lambda)\\theta ]\\), we also add a hyperparameter \\(\\gamma\\) which is the derivative of the first half of the linear function. In conclusion, the first part of the linear interpolation start at data point \\((0,0)\\) and end at \\(((1-\\) \\(\\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)\\). The second part of the interpolation start at \\(((1 - \\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)\\) and end at \\((\\beta \\theta ,1)\\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.334, + 0.469, + 0.348 + ], + "angle": 0, + "content": "Therefore, the final surrogate gradient can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.369, + 0.47, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} \\gamma , & 0 \\leqslant I _ {i} \\leqslant (1 - \\lambda) \\theta \\\\ \\frac {1 - \\gamma \\theta + \\gamma \\theta \\lambda}{(\\beta + \\lambda - 1) \\theta}, & (1 - \\lambda) \\theta < I _ {i} \\leqslant \\beta \\theta . \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} \\right. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.54 + ], + "angle": 0, + "content": "The derivative of this surrogate gradient function is \\(\\gamma\\) in the first interval and \\((1 - \\gamma \\theta +\\gamma \\theta \\lambda) / ((\\beta +\\lambda -1)\\theta)\\) in the second interval. Note that when we set the leaky parameter \\(\\lambda = 1\\), this function degenerates into the same form as the surrogate function for the IF neuron (Eq. (15)). Thus, this function can apply to both types of neurons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.601 + ], + "angle": 0, + "content": "The hyperparameter \\(\\beta\\) and \\(\\gamma\\) are mainly smoothing terms to prevent the gradient from disappearing. We set \\(\\beta\\) to 2 and \\(\\gamma\\) to 0.2 in the rest of this paper. More ablation experiments of the hyperparameters are provided in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.608, + 0.379, + 0.625 + ], + "angle": 0, + "content": "4.4. RGA Attack the Poisson Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.766 + ], + "angle": 0, + "content": "Our proposed method can generalize to SNNs that receive spike inputs. For Poisson input SNN, we can regard it as a combined structure of a Poisson encoder and an end-to-end SNN receives spike input. Therefore, we also need to attack the Poisson encoder rather than only perturbing the network. We can consider the Poisson encoder as a random transformation and use a straight through estimator [2] to attack this random transformation [1]. The gradient can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.773, + 0.469, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\text {P o i s s o n} (x)}{\\partial x} \\approx \\frac {\\partial \\mathbb {E} _ {x} (\\text {P o i s s o n} (x))}{\\partial x} = 1. \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The Adversarial example generation methodology proposed by Sharmin et al. [63] also includes the attack on Poisson encoded attack. Note that although our attack on the Poisson encoder is implemented differently from theirs, it is mathematically equivalent, and the generated adversarial examples are the same." + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.093, + 0.86, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.484, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Figure 6. The attack success rate change with respect to the attack strength for VGG-11 model on the CIFAR-10 dataset. Here WB stands for white box attack while BB stands for black box attack. The blue and purple bar display the attack success rates \\((\\%)\\) for RGA-FGSM and STBP-FGSM, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.755, + 0.594 + ], + "angle": 0, + "content": "4.5. Time Extended RGA Attack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.77 + ], + "angle": 0, + "content": "Here we introduce an SNN-specific attack enhancement method. When generating attack samples, we expect to generate more effective adversarial samples by increasing the inference time of SNNs. We call this method as Time Extended attack. When we apply this time-extended enhancement with RGA attack, the effects of randomness can be reduced by increasing the simulation time of attacking, resulting in a more accurate estimation of the firing rate. Therefore, the time-extended enhancement is generally more suitable for RGA-based attacks and is more effective for attacking against SNNs with Poisson inputs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.633, + 0.802 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this section, we conduct various experiments to evaluate the effectiveness of the proposed methods [32, 55]. We first test our attack method on the CIFAR-10, CIFAR-100 dataset [36] and CIFAR10-DVS dataset [42] with the VGG-11 [66] and ResNet-17 architecture [80]. We implement both non-iterative attack FGSM and iterative attack PGD" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7901" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.887, + 0.41 + ], + "angle": 0, + "content": "
ArchitectureDatasetInputTλTEAttackClean Acc.White Box AttackBlack Box Attack
ASR. (STBP)ASR. (RGA)ASR. (STBP)ASR. (RGA)
VGG-11CIFAR-10Direct81.0-FGSM93.0686.277793.735268.031473.2646
VGG-11CIFAR-10Direct81.02×FGSM93.0686.073594.734664.839973.6192
VGG-11CIFAR-10Direct81.0-PGD93.0699.494999.828186.460487.1266
VGG-11CIFAR-10Direct161.0-FGSM93.0385.327392.421865.796073.1269
VGG-11CIFAR-10Direct161.0-PGD93.0399.365899.838885.585387.4234
VGG-11CIFAR-10Poisson161.0-FGSM86.7254.979858.032840.867344.2259
VGG-11CIFAR-10Poisson161.02×FGSM86.7256.810660.529642.844046.9085
VGG-11CIFAR-10Poisson161.0-PGD86.7251.902257.141237.091741.1887
VGG-11CIFAR-10Direct80.5-FGSM91.4891.714093.627077.765679.6458
VGG-11CIFAR-10Direct80.5-PGD91.4899.825199.770493.681793.0367
VGG-11CIFAR-10Direct80.9-FGSM93.0389.906594.410473.449477.2761
VGG-11CIFAR-10Direct80.9-PGD93.0399.731399.828091.766191.3899
ResNet-17CIFAR-10Direct80.9-FGSM93.0484.243392.927867.110980.1053
ResNet-17CIFAR-10Direct80.9-PGD93.0499.9248100.00092.003497.5172
VGG-11CIFAR-100Direct80.9-FGSM73.2892.876694.718980.895284.2658
VGG-11CIFAR-100Direct80.9-PGD73.2899.754499.849992.235392.0579
ResNet-17CIFAR-100Direct80.9-FGSM72.0585.662792.061174.295681.1936
ResNet-17CIFAR-100Direct80.9-PGD72.0599.583699.889087.633695.2949
VGG-11CIFAR10-DVSFrame100.9-FGSM77.0059.508459.560748.496747.9275
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.421, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Table 2. Results of RGA based attack and STBP based attack on different type of SNNs. The seven columns on the left describes the parameter settings of the attack object, including architecture, datasets, input coding, simulation time-steps, leaky parameters, time extant (TE), and attack method. ASR. is short for attack success rate. For clarity, the better of the two attack results is bolded." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.489, + 0.468, + 0.55 + ], + "angle": 0, + "content": "and combine them with the proposed RGA attack and compare the results with STBP-based attacks. Note that when attacking DVS-related models, we directly generate and add adversarial examples on the preprocessed frames." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.551, + 0.468, + 0.656 + ], + "angle": 0, + "content": "As for training methods, since the ANN-SNN conversion method is proved insecure [63], we only consider SNNs obtained by supervised STBP training. We used the attack success rate as our metric for each attack, which is the proportion of samples that fool the network into misclassification. The details of the training configurations for pretrained networks are provided in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.666, + 0.36, + 0.681 + ], + "angle": 0, + "content": "5.1. Effectiveness of the RGA Attack" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.69, + 0.468, + 0.795 + ], + "angle": 0, + "content": "Here we test the effectiveness of the proposed RGA attack. We choose the STBP attack as a baseline and compare the attack success rate. To compare the effectiveness of the attack on various neuron settings, we select SNNs composed of LIF neurons with a leaky parameter of 0.9 and none-leaky IF neurons with a leaky parameter of 1.0. Also, the inference time-steps vary from 8 to 16." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.796, + 0.468, + 0.9 + ], + "angle": 0, + "content": "As shown in Fig. 6, we find that the attack success rate of our RGA attack method surpasses the previously commonly used STBP attack in most cases. When the attack strength is small, the attack success rate of the RGA attack and STBP attack is not much different. However, when the attack strength gradually increases to 8/255, the attack success rate of the RGA attack will be much higher than that" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.489, + 0.891, + 0.535 + ], + "angle": 0, + "content": "obtained by the STBP attack. These results demonstrate that the RGA attack is more effective than the STBP attack for different SNN settings." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.544, + 0.831, + 0.559 + ], + "angle": 0, + "content": "5.2. Effectiveness of Time Extended Attack" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.567, + 0.891, + 0.763 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of the time-extended attack, we pre-train two SNNs with different neurons and input encoding. We then double and triple the inference time-steps to attack these SNNs while keeping the origin inference time-steps for evaluation. The SNN configuration and the final results are shown in Fig. 7. The combination of the time-extended enhancement and RGA-based attack can achieve better attack performance since the attack effectiveness increases as the simulation time-step increases. However, applying the time-extended enhancement attack on the STBP-based attack cannot improve the attack. Meanwhile, we also find that the time-extended enhancement method is more effective for the Poisson input model." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.772, + 0.815, + 0.787 + ], + "angle": 0, + "content": "5.3. Generalizability of the RGA Attacks" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.796, + 0.891, + 0.9 + ], + "angle": 0, + "content": "To discuss the generalizability of RGA attacks across different SNNs, we conduct further experiments across various SNNs. Tab. 2 reports the detailed comparison of RGA attack and STBP attack over various SNN neurons, architecture, and dataset settings. In this experiment, we set the attack strength \\(\\epsilon\\) to 8/255 for CIFAR-10/100 dataset and 0.02 for the CIFAR10-DVS dataset. Also, the step size and" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.515, + 0.957 + ], + "angle": 0, + "content": "7902" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.272, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.192, + 0.258, + 0.204 + ], + "angle": 0, + "content": "(a) \\(\\lambda = 0.9\\) \\(\\mathrm{T} = 8\\) ,Direct Input" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.089, + 0.455, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.192, + 0.443, + 0.205 + ], + "angle": 0, + "content": "(b) \\(\\lambda = 1\\) \\(\\mathrm{T} = 16\\) Poisson Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.216, + 0.47, + 0.286 + ], + "angle": 0, + "content": "Figure 7. White box attack results of the time-extended attack with different settings. The \\(1 \\times\\) represents the baseline attack, while \\(2 \\times\\) and \\(3 \\times\\) represent double or triple the simulation time when attacked. The model under attack is VGG-11 composed of LIF neurons on the CIFAR-10 dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.316, + 0.469, + 0.346 + ], + "angle": 0, + "content": "the number of steps for the PGD attack are set to 2/255 and 5, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.469, + 0.573 + ], + "angle": 0, + "content": "From Tab. 2, one can find that all RGA-based attacks outperform STBP-based attacks when conducting single-step attacks. In attacks cases without time-extended enhancement, the largest performance gap exceeds \\(8.6\\%\\) and \\(13\\%\\) in ResNet-17 for white box and black box attacks, respectively. When conducting multi-step attacks, the proposed RGA-based attack achieves better performance than the STBP-based attack in most cases and gets comparable performance for the rest of the cases. In attack cases with time-extended enhancement, the performance of the RGA attack not only exceeds the STBP attack, but also exceeds the performance of RGA attack without time-extended enhancement. Even in attacks on the CIFAR10-DVS dataset, the RGA-based attack gets comparable performance as the STBP-based attack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.469, + 0.711 + ], + "angle": 0, + "content": "In conclusion, the proposed RGA attack can produce stronger adversarial examples in most cases. The RGA attack is also insensitive to neuron hyperparameters. Currently, high-performance SNNs are mainly applied in tasks related to static images or DVS datasets. We have proved through experiments that those SNNs contain very limited temporal information and they are vulnerable to the designed RGA-based attack. This demonstrates the importance and generalizability of the RGA-based attack method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.345, + 0.74 + ], + "angle": 0, + "content": "5.4. LIF Neuron is not that Robust" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Previous research suggested that the VGG5 SNNs trained with LIF neurons are more robust than the ones trained with IF neurons [63]. Here, we test whether this conclusion can be generalized to deeper networks with RGA-based attacks. We train multiple networks with the same architecture, including one quantized ANN and six SNNs with leaky parameters ranging from 0.5 to 1. We select VGG-11 as the model architecture and CIFAR-10 as the evaluation dataset. Then, we apply the white box FGSM attack to the quantized ANN and both RGA-FGSM" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.092, + 0.883, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.326 + ], + "angle": 0, + "content": "Figure 8. The white box attack success rate changes with respect to the leaky parameter of the spiking neuron. The red line represents the RGA attack, while the green line represents the STBP attack. The blue dashed line illustrates the attack success rate of a quantized ANN under the FGSM attack. The selected leaky parameters range from 0.5 to 1.0. This experiment is conducted on the CIFAR-10 dataset with VGG-11 architecture." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.354, + 0.782, + 0.368 + ], + "angle": 0, + "content": "and STBP-FGSM attacks to the six SNNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Fig. 8 demonstrates the results. The blue dashed line represents the attack success rate of ANN being attacked by FGSM. The red and green lines represent the attack success rate of the RGA-FGSM and STBP-FGSM, respectively. According to this figure, one can find that compared to the STBP attack (green line), the RGA attack (red line) is more stable. Meanwhile, the red line is always above the green line, indicating that the RGA attack can not only generate stronger adversarial examples, but is also less sensitive to neuron leakage parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.611 + ], + "angle": 0, + "content": "In addition, the performance of all types of SNNs under STBP-based attacks fluctuates around the baseline, while the RGA attack success rate is always higher than the baseline. Therefore, we found that SNN composed of LIF neurons with different leakage parameters has no advantage over ANNs in terms of adversarial robustness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.619, + 0.642 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.819 + ], + "angle": 0, + "content": "In this paper, we propose a new attack method for SNNs that outperforms previous methods. Our approach can serve as a benchmark for future research on SNN adversarial robustness. In addition, considering the strength of this attack method and the lower time cost compared to the STBP attack, we also look forward to the research on adversarial training based on this attack method. Our findings show that the rate-coded SNN composed of LIF neurons is not secure against stronger adversarial attacks, highlighting the need for exploring training methods for SNNs utilizing complex neurons and other neuronal codings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.834, + 0.68, + 0.851 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.858, + 0.891, + 0.901 + ], + "angle": 0, + "content": "This work is funded by STI2030Project (2021ZD0200300), and the National Natural Science Foundation of China (621 76003, 62088102)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7903" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In International Conference on Machine Learning, 2018. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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State-of-the-art SNNs are typically composed of simple Leaky Integrate-and-Fire (LIF) neurons and have become comparable to ANNs in image classification tasks on large-scale datasets. However, the robustness of these deep SNNs has not yet been fully uncovered. In this paper, we first experimentally observe that layers in these SNNs mostly communicate by rate coding. Based on this rate coding property, we develop a novel rate coding SNN-specified attack method, Rate Gradient Approximation Attack (RGA). We generalize the RGA attack to SNNs composed of LIF neurons with different leaky parameters and input encoding by designing surrogate gradients. In addition, we develop the time-extended enhancement to generate more effective adversarial examples. The experiment results indicate that our proposed RGA attack is more effective than the previous attack and is less sensitive to neuron hyperparameters. We also conclude from the experiment that rate-coded SNN composed of LIF neurons is not secure, which calls for exploring training methods for SNNs composed of complex neurons and other neuronal codings. Code is available at https://github.com/putshua/SNN_attack_RGA + +# 1. Introduction + +As the third generation of artificial neural networks [47], Spiking Neural Networks (SNNs) have gained more attraction due to their spatio-temporal, discrete representation, and event-driven properties. These bio-inspired neural networks borrow the characteristics of spiking representations and neuronal dynamics from biological brains [23, 75]. Unlike traditional Analog Neural Networks (ANNs), SNNs utilize spiking neurons as their essential components, which accumulate current over time, emit spikes when the membrane potential exceeds the threshold, and pass on informa + +tion through spike trains. The natural sparsity of the spike trains leads to the low power consumption of SNNs [59,69]. + +SNNs are competitive in real-world vision applications. The development of neuromorphic computing [10, 11, 20, 54, 56, 76] has further magnified the advantages of low-power consumption properties of SNNs, so that they can be deployed in power-limited scenarios [8, 64], such as edge computing or mobile application. However, the training algorithms of SNNs are also improving. The most practical training methods are ANN-SNN conversion [7], supervised training [72], and hybrid training [57, 58]. + +When SNNs are applied to safety-critical systems, the reliability of SNNs should be a major concern. The adversarial attack is one of the most significant categories that threatens model security [24, 68]. Similar to ANNs, SNNs can also be fooled by crafting adversarial examples that are imperceptible to human eyes from gradient-based backpropagation [62], which may lead to catastrophic consequences when SNNs are deployed in safety-related scenarios. Nevertheless, SNNs are still considered to be more robust than ANNs. This robustness comes from inherent neural dynamics, such as forgetting historical information and discrete spikes [63]. Besides, the robustness of SNNs can be improved through special structural enhancements [9] or training techniques [37, 45, 71]. + +Effective attack examples of ANNs can be crafted from well-defined gradients on the activation functions [68]. For SNNs, a common way to construct gradient-based attacks is by backpropagating through a surrogate function over discrete spikes. In this way, the gradient may suffer from explosion and vanishment in temporal and layer-by-layer communication [72]; at the same time, the membrane potential of all historical time steps needs to be saved when backpropagation, which requires a large amount of memory. Currently, high-performance SNNs typically combine leaky integrate-and-fire models and rate-encoded inputs. While the rate coding scheme brings excellent performance to SNN, it also exposes shortcomings. If the rate coding nature in SNN is considered, can we construct a more powerful attack? After all, the activation functions of many ANNs are inspired by the firing rate of biological neurons [52]. + +In this paper, we develop a novel Rate Gradient Approximation Attack (RGA) based on components of rate coding in high-performance SNNs. RGA attack is more effective than previously used attacks as it makes better use of the rate coding feature. We expect our work to provide benchmarks for SNN defense against adversarial attacks and inspire future research for SNNs. The main contributions of this paper are: + +- We observe that layers in SNN are mainly communicated by rate coding, either for converted SNN or for surrogate-trained SNN. +- We develop the Rate Gradient Approximation Attack based on rate coding and apply it to SNNs composed of different types of neurons and input codings. We further propose a time-extended variant to get more effective adversarial examples. +- Experiments prove that the RGA attack outperforms the STBP attack and is less sensitive to neuron hyperparameters. Based on the proposed attack, we compare the robustness of SNNs using different leaky parameters with that of ANNs and manifest that the SNNs composed of LIF neurons cannot provide strong enough security. This conclusion inspires further research on networks with more complex neurons. + +# 2. Related Works + +Learning of SNNs. The most efficient and commonly used SNNs training methods are ANN-SNN conversion [7] and Spatio-temporal Backpropagation (STBP) [72]. The core idea of ANN-SNN conversion is mapping the weights of a pre-trained ANN into an SNN. Researchers found that adjusting the weights or threshold in the SNN can balance the trade between inference time-steps and performance after conversion [12, 14, 16, 25, 28, 50, 61]. Some recent works quantized the source ANN to boost the performance of converted SNNs using ultra-low time-steps [5, 41, 43, 74]. ANN-SNN conversion is the most practical training method to train SNNs on large-scale datasets, and the converted SNNs always have outstanding performance [6, 26, 27, 34]. The temporal characteristics of the spiking neuron make it similar to a Recurrent Neural Network (RNN). Based on this, Wu et al. [72] borrowed the idea of Back Propagation Through Time [70] and proposed the supervised learning way of STBP. As the firing of neurons is a non-differentiable Heaviside function, the surrogate gradient approximation is proposed to smooth the gradient [19, 21, 40, 53, 65, 67, 77]. Nowadays, the performance of SNNs trained with backpropagation is comparable to that of ANNs [13, 17, 22, 29, 33, 35, 39, 73, 80]. Time-based backpropagation is another supervised learning method that can maintain the sparsity of the gradient. However, these works can only extend to shallow networks [3, 51, 78, 79, 81]. + +The robustness of SNN. SNNs are vulnerable to adversarial attacks as ANNs by adopting the gradient scheme in training. Firstly, SNNs obtained from ANN-SNN conversion can be attacked by the source ANNs with shared weights [62]. Besides, end-to-end trained SNNs suffer from the attack constructed from STBP. Sharmin et al. [62] summarized the two types of attacks as ANN-crafted and SNN-crafted attacks and revealed that attacks based on STBP are believed to be more powerful than those based on ANNs. Moreover, Liang et al. [44] exploited spike-compatible gradient to perform bit-flip attacks on SNN. Considering that SNNs are suitable for event-based tasks, various attacks on the event data of neuromorphic sensors are also explored [46, 49]. In these attacks, the STBP gradients are merged into sparse event data to construct attacks. + +Although the performance of SNNs can be degraded by such a variety of attack schemes, SNNs are still considered to have additional robustness compared to ANNs [15]. This is because more encodings are supported in SNNs. Compared to direct coding, Poisson coding is believed to process more inherent robustness as it introduces a noisy discretization to SNNs [37, 63]. Even so, how strong an attack Poisson coding can withstand still remains unknown. Another key robustness component of SNNs is the leaky parameter [63]. The leaky parameter controls the forgetting of historical information in LIF neurons. El-Allami et al. [18] achieved improved robustness by only searching in the space of leaky parameters. The current understanding of the robustness of SNNs is mainly focused on rate coding, and LIF neurons are also thought to perform the same coding. Therefore, gaining new insights into the robustness of rate coding is crucial for the practical application of SNNs. + +# 3. Preliminaries + +# 3.1. Neuron Model for SNNs + +In this paper, we consider the commonly used Leaky-Integrate-and-Fire (LIF) model and Integrate-and-Fire (IF) model [23, 31], the dynamics of membrane potential under firing threshold can be described by the following equations, respectively. + +$$ +\begin{array}{l} \tau_ {m} \frac {\mathrm {d} u}{\mathrm {d} t} = - (u (t) - u _ {\text {r e s t}}) + R I (t), \quad (\mathbf {L I F}) (1) \\ \tau_ {m} \frac {\mathrm {d} u}{\mathrm {d} t} = R I (t). \quad (\mathbf {I F}) (2) \\ \end{array} +$$ + +Here $\tau_{m}$ and $R$ denote the membrane time constant and the membrane resistance constant, respectively. $u(t)$ and $I(t)$ represent the membrane potential and input current at time $t$ , respectively. Once the membrane potential reaches the firing threshold $\theta$ , the neuron will fire, and then the membrane potential will reset to the resting potential $u_{rest} < \theta$ . Without loss of generality, to simulate the network of LIF + +neurons on a computer with a Von Neumann architecture, the above process can be simplified and discretized to another set of equations [4]. + +$$ +u _ {i} (t) = \lambda u _ {i} (t - 1) + w _ {i j} s _ {j} (t) + b _ {i} + \eta_ {i} (t), \tag {3} +$$ + +$$ +s _ {i} (t) = \left\{ \begin{array}{l l} 1, & t = t _ {i} ^ {(f)} \\ 0, & t \neq t _ {i} ^ {(f)} \end{array} , \right. \tag {4} +$$ + +where $j$ and $i$ indicate presynaptic and postsynaptic neurons, $w_{ij}$ represents the connection strength between the two neurons, and $b_{i}$ is an extra constant input current to neuron $i$ . $s_i(t)$ describes whether neuron $i$ fires at time-step $t$ , and the trigger is membrane potential $u_{i}(t)$ reaches the firing threshold $\theta$ . We also mark the firing time-step of neuron $i$ as $t_i^{(f)}$ , $f = 1,2,\ldots,\lambda$ is the membrane leaky constant corresponding to the membrane time constant in Eq. (1). Note that if we explicitly $\lambda$ to 1, this LIF neuron model will degenerate to the none-leaky IF model. Also, we add a reset term $\eta_i(t)$ on Eq. (3) to describe the neuron reset behavior. Despite the hard-reset function that resets the neuron membrane potential to resting potential (Eq. (5)), we also consider the soft-reset function (Eq. (6)) that directly subtracts the membrane potential by the threshold $\theta$ [25, 60]. + +$$ +\eta_ {i} ^ {\text {h a r d}} (t) = \left\{ \begin{array}{l l} - \left(u _ {i} \left(t _ {i} ^ {(f)}\right) - u _ {\text {r e s t}}\right) & , t = t _ {i} ^ {(f)} \\ 0 & , t \neq t _ {i} ^ {(f)}. \end{array} \right. \tag {5} +$$ + +$$ +\eta_ {i} ^ {\text {s o f t}} (t) = \left\{ \begin{array}{l l} - \theta & , t = t _ {i} ^ {(f)} \\ 0 & , t \neq t _ {i} ^ {(f)}, \end{array} \right. \tag {6} +$$ + +# 3.2. Supervised Training of SNNs with STBP + +Equation (3) implies that the LIF neuron has a function similar to that of an RNN. Thus, SNNs can be trained in the same way as RNNs with Back Propagation Through Time. STBP uses this idea to unroll the SNN over time-steps and accumulate gradient at each time-step [53, 72]. As illustrated in Fig. 1, the gradient of the loss function $\mathcal{L}$ with respect to the output spikes $s_j(t)$ is: + +$$ +\frac {\partial \mathcal {L}}{\partial s _ {j} (t)} = \frac {\partial \mathcal {L}}{\partial s _ {i} (t)} \frac {\partial s _ {i} (t)}{\partial u _ {i} (t)} \frac {\partial u _ {i} (t)}{\partial s _ {j} (t)} + \tag {7} +$$ + +$$ +\frac {\partial \mathcal {L}}{\partial s _ {j} (t + 1)} \frac {\partial s _ {j} (t + 1)}{\partial u _ {j} (t + 1)} \frac {\partial u _ {j} (t + 1)}{\partial u _ {j} (t)} \frac {\partial u _ {j} (t)}{\partial s _ {j} (t)}. +$$ + +Note that as the derivative of spike with respect to the membrane potential $\frac{\partial s_i(t)}{\partial u_i(t)}$ is nondifferentiable, the surrogate gradient [53] is often used in backpropagation. + +Since the STBP method enables supervised training of SNNs, this method can also generate gradient-based adversarial examples [62]. Therefore, we will use STBP as the baseline gradient obtain method. + +![](images/1eba3d9a86b1099e2eb2fafa7458b3f16bd4d43d1cb1b01f7f9e8ca665b7db49.jpg) +Figure 1. Forward pass and backward pass for STBP. The pink line shows that surrogate functions are applied in the non-differentiable process of neuron firing to obtain approximate gradients. + +# 3.3. Adversarial Attacks + +Adversarial attack is a method to generate imperceptible perturbations that can fool neural networks, which can be formulated as an optimization problem: + +$$ +\arg \max _ {\delta} \mathcal {L} (f (\boldsymbol {x} + \delta), y) \quad s. t. \| \delta \| _ {p} \leq \epsilon , \tag {8} +$$ + +where $\mathcal{L}$ is the loss function, $f$ is the network under attack, and $\pmb{x},\pmb{y}$ are the input images and output target of the given network, respectively. $\delta$ is the adversarial perturbation we want to optimize. $\| \cdot \| _p$ is the $L_{p}$ -norm, and parameter $\epsilon$ limits the strength of the perturbation to a level that is indistinguishable to the human eye. Here we consider two classic adversarial attack algorithms: Fast Gradient Sign Method (FGSM) [24] and Projected Gradient Descent (PGD) [38]. FGSM is a simple but effective attack method, which perturbs the data $\pmb{x}$ along the sign of the gradient to increase the perturbed linear output, that is + +$$ +\hat {\boldsymbol {x}} = \boldsymbol {x} + \epsilon \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} (f (\boldsymbol {x}, y))\right). \tag {9} +$$ + +PGD is an iterative variant of FGSM. By iteratively optimizing the perturbation, PGD offers a more powerful attack [48]. The iteration can be summarized as: + +$$ +\hat {\boldsymbol {x}} ^ {k} = \Pi_ {\epsilon} \left\{\boldsymbol {x} ^ {k - 1} + \alpha \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} (f (\boldsymbol {x} ^ {k - 1}, y))\right) \right\}, \tag {10} +$$ + +where $k$ is the number of the iteration step, and $\alpha$ is the step size of each iteration. $\Pi_{\epsilon}$ constrains the data in each iteration and projects it onto the space of the $\epsilon - l_{p}$ neighborhood of $x$ . + +For all attack methods, we consider two different attack scenarios, white-box attack, and black-box attack. The white-box attack is the case that the hacker has complete access to the model topology, model parameters, and gradients, while the black-box attack is the case the hacker can only get the basic information of the model. + +![](images/f7e2d6b8770838dd8f56cae59096c7792317487bd449075fdd13a4cb44fe89e7.jpg) +Figure 2. Experimental scheme of spike shuffle + +# 4. Methods + +In this section, we first show that the current high-performance SNNs for image classification tasks are encoded by firing rate and do not contain timing information, whether they are trained by STBP and ANN-SNN conversion. Based on this, we propose rate gradient approximation, a new attack method against SNNs, and apply it to SNNs composed of different types of neurons and input encodings. Finally, we propose the time-extended attack as an attack enhancement method. + +# 4.1. Does well-trained SNNs contain timing information? + +Here we design an experiment and test whether the well-trained SNNs are rate coded and whether they contain timing information. The definition of firing rate refers to the temporal average of the spikes. As illustrated in Eq. (11), the firing rate of one given neuron $i$ is the total spike count in an interval of time-steps $T$ divided by the duration $T$ . + +$$ +r _ {i} = \frac {\sum_ {t = 1} ^ {T} s _ {i}}{T}. \tag {11} +$$ + +The detailed experimental scheme is shown in Fig. 2. We add a random number generator to shuffle each neuron's output spike firing order so that the spike trains will never contain temporal information. We apply this design to the pre-trained SNN models and test accuracy change before and after the spike shuffle. + +The experiment is implemented on the CIFAR-10 dataset with VGG-11 network architecture. To test different SNNs, we choose combinations of different training methods, leakage parameters, and reset functions. We pre-train SNN for each combination and then substitute all the spiking neurons with shuffled neurons. + +Tab. 1 reports the average performance of 10 runs, from which we find that the accuracy after spike shuffle is slightly + +![](images/2b79240be88cd2554dfd6aac299e95e5e87dc0a38ae98ccfe67619a67760c6da.jpg) +Figure 3. Forward pass and backward pass for RGA attack. The pink line shows that surrogate functions are applied to the approximation of the derivative for firing rate and input current. + +Table 1. Performance before and after the spike shuffle + +
DatasetTraining MethodTλResetClean Acc.Shuffled Acc.Rate
CIFAR-10ANNSNN161.0soft93.2593.358✓
CIFAR-10STBP81.0soft92.7592.086✓
CIFAR-10STBP81.0hard93.0692.214✓
CIFAR-10STBP80.9hard93.0392.545✓
CIFAR-10STBP80.5hard91.4891.225✓
CIFAR10-DVSSTBP100.9hard77.0075.400✓
+ +different from the clean accuracy for all SNNs. For the model converted from ANNs, the model performance after the spike shuffle is slightly improved. The performance after spike shuffle is slightly reduced for other models obtained by supervised STBP training. In fact, even for models trained on the DVS dataset, the performance gap before and after shuffling is small, which proves that models trained on the DVS dataset contain very little timing information. Therefore, we assert that firing rates encode major information in these SNNs. + +# 4.2. Rate Gradient Approximation Attack + +This section proposes the Rate Gradient Approximation (RGA) attack for spike count rate coding SNNs. In the above section, we have shown that the well-trained SNNs are all rate-encoded at each layer. Thus, we can approximate the backward pass of SNNs using only the average firing rate over time-steps to generate effective gradients. Specifically, we introduce an intermediate variable $I_{i}$ to denote the average input current of neuron $i$ in Eq. (3), which is defined by: + +$$ +I _ {i} = \sum_ {t = 1} ^ {T} w _ {i j} s _ {j} (t) + b _ {i} \tag {12} +$$ + +Note that $I_{i}$ also represents the weighted firing rate from the previous layer. Fig. 3 illustrates how the gradient propa + +![](images/6b8f2f78355b2c06aa6cea9c153344b38718142308cce5bbfb48152f7f2234b0.jpg) +(a) IF R-I curve + +![](images/4f38aed04c487e50ff7c793b02c45ba51675b00be061bead40db4d2f17dec888.jpg) +(b) Derivative of IF R-I curve + +gates between two adjacent neurons $i$ and $j$ with the defined weighted firing rate. The gradient propagation starts from the firing rate $r_i$ of the $i$ -th neuron, passes to the input current $I_i$ , and finally arrives at the firing rate $r_j$ of the $j$ -th neuron, that is + +$$ +\frac {\partial \mathcal {L}}{\partial r _ {j}} = \frac {\partial \mathcal {L}}{\partial r _ {i}} \frac {\partial r _ {i}}{\partial I _ {i}} \frac {\partial I _ {i}}{\partial r _ {j}}. \tag {13} +$$ + +This result can be generalized to the network with the chain rule. If we use vectors $\boldsymbol{r}^l$ and $\boldsymbol{I}^l$ to denote the firing rates and average input currents of all neurons in layer $l$ , respectively, and use vector $\boldsymbol{r}^0$ to denote the input image. The gradient propagates from the loss function to the input image is formulated as: + +$$ +\frac {\partial \mathcal {L}}{\partial \boldsymbol {r} ^ {0}} = \frac {\partial \mathcal {L}}{\partial \boldsymbol {r} ^ {L}} \left(\prod_ {l = 1} ^ {L} \frac {\partial \boldsymbol {r} ^ {l}}{\partial \boldsymbol {I} ^ {l}} \frac {\partial \boldsymbol {I} ^ {l}}{\partial \boldsymbol {r} ^ {l - 1}}\right). \tag {14} +$$ + +# 4.3. RGA Attack with Surrogate Gradient + +According to Eq. (11) and (12), one can compute the gradient $\frac{\partial I_i}{\partial r_j}$ , the only part we cannot directly calculate the gradient in Eq. (13) is $\frac{\partial r_i}{\partial I_i}$ . To get a proper approximation for $\frac{\partial r_i}{\partial I_i}$ , we need to use a differentiable surrogate function $f(\cdot)$ to approximate the relationship between output firing rate $r_i$ and input current $I_i$ . Here, we propose to use the static R-I curve, which refers to the relationship between the input current and output firing rate when the input is constant, as the approximation function. We discuss the cases of IF neurons and LIF neurons separately. + +# RGA Attack the Integrate-and-Fire Neuron + +For IF neurons, the static R-I curve is the clipped ReLU function [7, 14], which is presented in Fig. 4a by the blue line. We also sampled from a pre-trained VGG-11 network to obtain the actual distribution of average input current and average output firing rate (more details are in the Appendix), which is represented by the light blue scatter in the figure. We find that if we simply set the static RI curve as the surrogate gradient, many data points would be wrongly assigned to zero derivatives. To avoid the derivatives being all zero in the interval $[\theta, +\infty]$ , we propose a + +![](images/e4adde9d367ad481d47e9e95ffb229341395e1d33ae559eec46ae6bf14aa2628.jpg) +Figure 4. Surrogate function and gradient for IF neuron +(a) LIF R-I curve +Figure 5. Surrogate function and gradient for LIF neuron + +![](images/dd5dfb0a92ae19947171b4b003774a5e55b4cf325e28aee1c354da7bc97846fb.jpg) +(b) Derivative of LIF R-I curve + +modified R-I curve function as the final surrogate function (green line in Fig. 4a). We introduce a relaxation parameter $\beta \in [1, +\infty]$ to keep the derivatives to be none-zero between $[0, \beta \theta]$ . Then its corresponding derivative (surrogate gradient) is: + +$$ +\frac {\partial r _ {i}}{\partial I _ {i}} = \left\{ \begin{array}{l l} 1 / (\beta \theta), & 0 \leqslant I _ {i} \leqslant \beta \theta \\ 0, & I _ {i} > \beta \theta \text {o r} I _ {i} < 0 \end{array} . \right. \tag {15} +$$ + +With the formula for backpropagation and the derivatives of intermediate nodes, we can calculate the derivatives that are ultimately passed to the input image. + +# RGA Attack the Leaky-Integrate-and-Fire Neuron + +Similar to the RGA Attack for IF neurons, the surrogate function for LIF neurons is inspired by the static R-I curve. Following the work of [23, 30], we derive the R-I curve function for the LIF neurons. Supposing that a LIF neuron receives a constant input $I_{i}$ and $u_{rest} = 0$ , the LIF neuron (Eq. (3)) can be simplified to: + +$$ +u _ {i} (t) = \lambda u _ {i} (t - 1) + I _ {i}. \tag {16} +$$ + +We then iterate this recursive formula to get the neuron membrane potential as a function of time. + +$$ +u _ {i} (t) = \frac {I _ {i}}{\lambda - 1} \lambda^ {t} - \frac {I _ {i}}{\lambda - 1} \tag {17} +$$ + +From the formula above, we can calculate the time required for the neuron to accumulate from 0 to $\theta$ , and finally obtain the firing rate by inverse the calculated time interval. + +$$ +r _ {i} = \left\lceil \log_ {\lambda} \frac {I _ {i} + \theta (\lambda - 1)}{I _ {i}} \right\rceil^ {- 1} \tag {18} +$$ + +As shown in Fig. 5a, the light blue scatter represents the actual distribution of average input current and average output firing rate from a pre-trained VGG-11 network with LIF neurons. Although the static RI curve matches the actual situation, the static RI curve (blue curve) contains the non-derivable equation. The derivative is always zero when $x < (1 - \lambda)\theta$ or $x > \theta$ . Meanwhile, as $\lim_{x\to (1 - \lambda)\theta^{+}}$ , the + +derivative of the function approaches infinity. This will lead to gradient vanishing and exploding problems in backpropagation. Therefore, it is impractical to calculate the derivatives directly from the static R-I curve. + +According to the characteristics of this static R-I curve, we segment it at the position of $(1 - \lambda)\theta$ and then separately perform piecewise linear interpolation at $x\in [0,(1 - \lambda)\theta ]$ and $x\in [(1 - \lambda)\theta ,\beta \theta ]$ , where $\beta$ is a relaxation parameter to control the end point of interpolation. Thus, we obtain two straight lines (green line in Fig. 5a). In order to avoid zero derivatives over the interval $[0,(1 - \lambda)\theta ]$ , we also add a hyperparameter $\gamma$ which is the derivative of the first half of the linear function. In conclusion, the first part of the linear interpolation start at data point $(0,0)$ and end at $((1-$ $\lambda)\theta ,(1 - \lambda)\theta \gamma)$ . The second part of the interpolation start at $((1 - \lambda)\theta ,(1 - \lambda)\theta \gamma)$ and end at $(\beta \theta ,1)$ . + +Therefore, the final surrogate gradient can be written as + +$$ +\frac {\partial r _ {i}}{\partial I _ {i}} = \left\{ \begin{array}{l l} \gamma , & 0 \leqslant I _ {i} \leqslant (1 - \lambda) \theta \\ \frac {1 - \gamma \theta + \gamma \theta \lambda}{(\beta + \lambda - 1) \theta}, & (1 - \lambda) \theta < I _ {i} \leqslant \beta \theta . \\ 0, & I _ {i} > \beta \theta \text {o r} I _ {i} < 0 \end{array} \right. \tag {19} +$$ + +The derivative of this surrogate gradient function is $\gamma$ in the first interval and $(1 - \gamma \theta +\gamma \theta \lambda) / ((\beta +\lambda -1)\theta)$ in the second interval. Note that when we set the leaky parameter $\lambda = 1$ , this function degenerates into the same form as the surrogate function for the IF neuron (Eq. (15)). Thus, this function can apply to both types of neurons. + +The hyperparameter $\beta$ and $\gamma$ are mainly smoothing terms to prevent the gradient from disappearing. We set $\beta$ to 2 and $\gamma$ to 0.2 in the rest of this paper. More ablation experiments of the hyperparameters are provided in the Appendix. + +# 4.4. RGA Attack the Poisson Encoding + +Our proposed method can generalize to SNNs that receive spike inputs. For Poisson input SNN, we can regard it as a combined structure of a Poisson encoder and an end-to-end SNN receives spike input. Therefore, we also need to attack the Poisson encoder rather than only perturbing the network. We can consider the Poisson encoder as a random transformation and use a straight through estimator [2] to attack this random transformation [1]. The gradient can be written as: + +$$ +\frac {\partial \text {P o i s s o n} (x)}{\partial x} \approx \frac {\partial \mathbb {E} _ {x} (\text {P o i s s o n} (x))}{\partial x} = 1. \tag {20} +$$ + +The Adversarial example generation methodology proposed by Sharmin et al. [63] also includes the attack on Poisson encoded attack. Note that although our attack on the Poisson encoder is implemented differently from theirs, it is mathematically equivalent, and the generated adversarial examples are the same. + +![](images/89f808ec16b6f15483062c3726551abb70e158a831360b0cb75a20294ce97b6c.jpg) +Figure 6. The attack success rate change with respect to the attack strength for VGG-11 model on the CIFAR-10 dataset. Here WB stands for white box attack while BB stands for black box attack. The blue and purple bar display the attack success rates $(\%)$ for RGA-FGSM and STBP-FGSM, respectively. + +# 4.5. Time Extended RGA Attack + +Here we introduce an SNN-specific attack enhancement method. When generating attack samples, we expect to generate more effective adversarial samples by increasing the inference time of SNNs. We call this method as Time Extended attack. When we apply this time-extended enhancement with RGA attack, the effects of randomness can be reduced by increasing the simulation time of attacking, resulting in a more accurate estimation of the firing rate. Therefore, the time-extended enhancement is generally more suitable for RGA-based attacks and is more effective for attacking against SNNs with Poisson inputs. + +# 5. Experiments + +In this section, we conduct various experiments to evaluate the effectiveness of the proposed methods [32, 55]. We first test our attack method on the CIFAR-10, CIFAR-100 dataset [36] and CIFAR10-DVS dataset [42] with the VGG-11 [66] and ResNet-17 architecture [80]. We implement both non-iterative attack FGSM and iterative attack PGD + +
ArchitectureDatasetInputTλTEAttackClean Acc.White Box AttackBlack Box Attack
ASR. (STBP)ASR. (RGA)ASR. (STBP)ASR. (RGA)
VGG-11CIFAR-10Direct81.0-FGSM93.0686.277793.735268.031473.2646
VGG-11CIFAR-10Direct81.02×FGSM93.0686.073594.734664.839973.6192
VGG-11CIFAR-10Direct81.0-PGD93.0699.494999.828186.460487.1266
VGG-11CIFAR-10Direct161.0-FGSM93.0385.327392.421865.796073.1269
VGG-11CIFAR-10Direct161.0-PGD93.0399.365899.838885.585387.4234
VGG-11CIFAR-10Poisson161.0-FGSM86.7254.979858.032840.867344.2259
VGG-11CIFAR-10Poisson161.02×FGSM86.7256.810660.529642.844046.9085
VGG-11CIFAR-10Poisson161.0-PGD86.7251.902257.141237.091741.1887
VGG-11CIFAR-10Direct80.5-FGSM91.4891.714093.627077.765679.6458
VGG-11CIFAR-10Direct80.5-PGD91.4899.825199.770493.681793.0367
VGG-11CIFAR-10Direct80.9-FGSM93.0389.906594.410473.449477.2761
VGG-11CIFAR-10Direct80.9-PGD93.0399.731399.828091.766191.3899
ResNet-17CIFAR-10Direct80.9-FGSM93.0484.243392.927867.110980.1053
ResNet-17CIFAR-10Direct80.9-PGD93.0499.9248100.00092.003497.5172
VGG-11CIFAR-100Direct80.9-FGSM73.2892.876694.718980.895284.2658
VGG-11CIFAR-100Direct80.9-PGD73.2899.754499.849992.235392.0579
ResNet-17CIFAR-100Direct80.9-FGSM72.0585.662792.061174.295681.1936
ResNet-17CIFAR-100Direct80.9-PGD72.0599.583699.889087.633695.2949
VGG-11CIFAR10-DVSFrame100.9-FGSM77.0059.508459.560748.496747.9275
+ +Table 2. Results of RGA based attack and STBP based attack on different type of SNNs. The seven columns on the left describes the parameter settings of the attack object, including architecture, datasets, input coding, simulation time-steps, leaky parameters, time extant (TE), and attack method. ASR. is short for attack success rate. For clarity, the better of the two attack results is bolded. + +and combine them with the proposed RGA attack and compare the results with STBP-based attacks. Note that when attacking DVS-related models, we directly generate and add adversarial examples on the preprocessed frames. + +As for training methods, since the ANN-SNN conversion method is proved insecure [63], we only consider SNNs obtained by supervised STBP training. We used the attack success rate as our metric for each attack, which is the proportion of samples that fool the network into misclassification. The details of the training configurations for pretrained networks are provided in the Appendix. + +# 5.1. Effectiveness of the RGA Attack + +Here we test the effectiveness of the proposed RGA attack. We choose the STBP attack as a baseline and compare the attack success rate. To compare the effectiveness of the attack on various neuron settings, we select SNNs composed of LIF neurons with a leaky parameter of 0.9 and none-leaky IF neurons with a leaky parameter of 1.0. Also, the inference time-steps vary from 8 to 16. + +As shown in Fig. 6, we find that the attack success rate of our RGA attack method surpasses the previously commonly used STBP attack in most cases. When the attack strength is small, the attack success rate of the RGA attack and STBP attack is not much different. However, when the attack strength gradually increases to 8/255, the attack success rate of the RGA attack will be much higher than that + +obtained by the STBP attack. These results demonstrate that the RGA attack is more effective than the STBP attack for different SNN settings. + +# 5.2. Effectiveness of Time Extended Attack + +To demonstrate the effectiveness of the time-extended attack, we pre-train two SNNs with different neurons and input encoding. We then double and triple the inference time-steps to attack these SNNs while keeping the origin inference time-steps for evaluation. The SNN configuration and the final results are shown in Fig. 7. The combination of the time-extended enhancement and RGA-based attack can achieve better attack performance since the attack effectiveness increases as the simulation time-step increases. However, applying the time-extended enhancement attack on the STBP-based attack cannot improve the attack. Meanwhile, we also find that the time-extended enhancement method is more effective for the Poisson input model. + +# 5.3. Generalizability of the RGA Attacks + +To discuss the generalizability of RGA attacks across different SNNs, we conduct further experiments across various SNNs. Tab. 2 reports the detailed comparison of RGA attack and STBP attack over various SNN neurons, architecture, and dataset settings. In this experiment, we set the attack strength $\epsilon$ to 8/255 for CIFAR-10/100 dataset and 0.02 for the CIFAR10-DVS dataset. Also, the step size and + +![](images/854b3ee48d07dce26f39646e9ff4c90bbe2c27481ca98b1fd644ac7386a5eac6.jpg) +(a) $\lambda = 0.9$ $\mathrm{T} = 8$ ,Direct Input + +![](images/0c149b985393f6aef8ba52d2ecf24ded16e74cbd8bfc722324a9410690085bcf.jpg) +(b) $\lambda = 1$ $\mathrm{T} = 16$ Poisson Input +Figure 7. White box attack results of the time-extended attack with different settings. The $1 \times$ represents the baseline attack, while $2 \times$ and $3 \times$ represent double or triple the simulation time when attacked. The model under attack is VGG-11 composed of LIF neurons on the CIFAR-10 dataset. + +the number of steps for the PGD attack are set to 2/255 and 5, respectively. + +From Tab. 2, one can find that all RGA-based attacks outperform STBP-based attacks when conducting single-step attacks. In attacks cases without time-extended enhancement, the largest performance gap exceeds $8.6\%$ and $13\%$ in ResNet-17 for white box and black box attacks, respectively. When conducting multi-step attacks, the proposed RGA-based attack achieves better performance than the STBP-based attack in most cases and gets comparable performance for the rest of the cases. In attack cases with time-extended enhancement, the performance of the RGA attack not only exceeds the STBP attack, but also exceeds the performance of RGA attack without time-extended enhancement. Even in attacks on the CIFAR10-DVS dataset, the RGA-based attack gets comparable performance as the STBP-based attack. + +In conclusion, the proposed RGA attack can produce stronger adversarial examples in most cases. The RGA attack is also insensitive to neuron hyperparameters. Currently, high-performance SNNs are mainly applied in tasks related to static images or DVS datasets. We have proved through experiments that those SNNs contain very limited temporal information and they are vulnerable to the designed RGA-based attack. This demonstrates the importance and generalizability of the RGA-based attack method. + +# 5.4. LIF Neuron is not that Robust + +Previous research suggested that the VGG5 SNNs trained with LIF neurons are more robust than the ones trained with IF neurons [63]. Here, we test whether this conclusion can be generalized to deeper networks with RGA-based attacks. We train multiple networks with the same architecture, including one quantized ANN and six SNNs with leaky parameters ranging from 0.5 to 1. We select VGG-11 as the model architecture and CIFAR-10 as the evaluation dataset. Then, we apply the white box FGSM attack to the quantized ANN and both RGA-FGSM + +![](images/2db5701c771ff4f4c5e2b3edad8c32f10f239b7439417e939dc30603142cbaea.jpg) +Figure 8. The white box attack success rate changes with respect to the leaky parameter of the spiking neuron. The red line represents the RGA attack, while the green line represents the STBP attack. The blue dashed line illustrates the attack success rate of a quantized ANN under the FGSM attack. The selected leaky parameters range from 0.5 to 1.0. This experiment is conducted on the CIFAR-10 dataset with VGG-11 architecture. + +and STBP-FGSM attacks to the six SNNs. + +Fig. 8 demonstrates the results. The blue dashed line represents the attack success rate of ANN being attacked by FGSM. The red and green lines represent the attack success rate of the RGA-FGSM and STBP-FGSM, respectively. According to this figure, one can find that compared to the STBP attack (green line), the RGA attack (red line) is more stable. Meanwhile, the red line is always above the green line, indicating that the RGA attack can not only generate stronger adversarial examples, but is also less sensitive to neuron leakage parameters. + +In addition, the performance of all types of SNNs under STBP-based attacks fluctuates around the baseline, while the RGA attack success rate is always higher than the baseline. Therefore, we found that SNN composed of LIF neurons with different leakage parameters has no advantage over ANNs in terms of adversarial robustness. + +# 6. Conclusion + +In this paper, we propose a new attack method for SNNs that outperforms previous methods. Our approach can serve as a benchmark for future research on SNN adversarial robustness. In addition, considering the strength of this attack method and the lower time cost compared to the STBP attack, we also look forward to the research on adversarial training based on this attack method. Our findings show that the rate-coded SNN composed of LIF neurons is not secure against stronger adversarial attacks, highlighting the need for exploring training methods for SNNs utilizing complex neurons and other neuronal codings. + +# 7. Acknowledgement + +This work is funded by STI2030Project (2021ZD0200300), and the National Natural Science Foundation of China (621 76003, 62088102). + +# References + +[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In International Conference on Machine Learning, 2018. 6 +[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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State-of-the-art SNNs are typically composed of simple Leaky Integrate-and-Fire (LIF) neurons and have become comparable to ANNs in image classification tasks on large-scale datasets. However, the robustness of these deep SNNs has not yet been fully uncovered. In this paper, we first experimentally observe that layers in these SNNs mostly communicate by rate coding. Based on this rate coding property, we develop a novel rate coding SNN-specified attack method, Rate Gradient Approximation Attack (RGA). We generalize the RGA attack to SNNs composed of LIF neurons with different leaky parameters and input encoding by designing surrogate gradients. In addition, we develop the time-extended enhancement to generate more effective adversarial examples. The experiment results indicate that our proposed RGA attack is more effective than the previous attack and is less sensitive to neuron hyperparameters. We also conclude from the experiment that rate-coded SNN composed of LIF neurons is not secure, which calls for exploring training methods for SNNs composed of complex neurons and other neuronal codings. Code is available at https://github.com/putshua/SNN_attack_RGA" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 287, + 693 + ], + "type": "text", + "content": "As the third generation of artificial neural networks [47], Spiking Neural Networks (SNNs) have gained more attraction due to their spatio-temporal, discrete representation, and event-driven properties. These bio-inspired neural networks borrow the characteristics of spiking representations and neuronal dynamics from biological brains [23, 75]. Unlike traditional Analog Neural Networks (ANNs), SNNs utilize spiking neurons as their essential components, which accumulate current over time, emit spikes when the membrane potential exceeds the threshold, and pass on informa" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 213, + 545, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 238 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 238 + ], + "type": "text", + "content": "tion through spike trains. The natural sparsity of the spike trains leads to the low power consumption of SNNs [59,69]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 240, + 546, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 546, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 546, + 349 + ], + "type": "text", + "content": "SNNs are competitive in real-world vision applications. The development of neuromorphic computing [10, 11, 20, 54, 56, 76] has further magnified the advantages of low-power consumption properties of SNNs, so that they can be deployed in power-limited scenarios [8, 64], such as edge computing or mobile application. However, the training algorithms of SNNs are also improving. The most practical training methods are ANN-SNN conversion [7], supervised training [72], and hybrid training [57, 58]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 351, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 547, + 519 + ], + "type": "text", + "content": "When SNNs are applied to safety-critical systems, the reliability of SNNs should be a major concern. The adversarial attack is one of the most significant categories that threatens model security [24, 68]. Similar to ANNs, SNNs can also be fooled by crafting adversarial examples that are imperceptible to human eyes from gradient-based backpropagation [62], which may lead to catastrophic consequences when SNNs are deployed in safety-related scenarios. Nevertheless, SNNs are still considered to be more robust than ANNs. This robustness comes from inherent neural dynamics, such as forgetting historical information and discrete spikes [63]. Besides, the robustness of SNNs can be improved through special structural enhancements [9] or training techniques [37, 45, 71]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "Effective attack examples of ANNs can be crafted from well-defined gradients on the activation functions [68]. For SNNs, a common way to construct gradient-based attacks is by backpropagating through a surrogate function over discrete spikes. In this way, the gradient may suffer from explosion and vanishment in temporal and layer-by-layer communication [72]; at the same time, the membrane potential of all historical time steps needs to be saved when backpropagation, which requires a large amount of memory. Currently, high-performance SNNs typically combine leaky integrate-and-fire models and rate-encoded inputs. While the rate coding scheme brings excellent performance to SNN, it also exposes shortcomings. If the rate coding nature in SNN is considered, can we construct a more powerful attack? After all, the activation functions of many ANNs are inspired by the firing rate of biological neurons [52]." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 702, + 140, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 702, + 140, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 702, + 140, + 713 + ], + "type": "text", + "content": "* Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7896" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "In this paper, we develop a novel Rate Gradient Approximation Attack (RGA) based on components of rate coding in high-performance SNNs. RGA attack is more effective than previously used attacks as it makes better use of the rate coding feature. We expect our work to provide benchmarks for SNN defense against adversarial attacks and inspire future research for SNNs. The main contributions of this paper are:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 178, + 286, + 368 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 58, + 178, + 286, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 178, + 286, + 212 + ], + "spans": [ + { + "bbox": [ + 58, + 178, + 286, + 212 + ], + "type": "text", + "content": "- We observe that layers in SNN are mainly communicated by rate coding, either for converted SNN or for surrogate-trained SNN." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 214, + 286, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 214, + 286, + 271 + ], + "spans": [ + { + "bbox": [ + 58, + 214, + 286, + 271 + ], + "type": "text", + "content": "- We develop the Rate Gradient Approximation Attack based on rate coding and apply it to SNNs composed of different types of neurons and input codings. We further propose a time-extended variant to get more effective adversarial examples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 274, + 286, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 274, + 286, + 368 + ], + "spans": [ + { + "bbox": [ + 58, + 274, + 286, + 368 + ], + "type": "text", + "content": "- Experiments prove that the RGA attack outperforms the STBP attack and is less sensitive to neuron hyperparameters. Based on the proposed attack, we compare the robustness of SNNs using different leaky parameters with that of ANNs and manifest that the SNNs composed of LIF neurons cannot provide strong enough security. This conclusion inspires further research on networks with more complex neurons." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 381, + 138, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 138, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 138, + 393 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": "Learning of SNNs. The most efficient and commonly used SNNs training methods are ANN-SNN conversion [7] and Spatio-temporal Backpropagation (STBP) [72]. The core idea of ANN-SNN conversion is mapping the weights of a pre-trained ANN into an SNN. Researchers found that adjusting the weights or threshold in the SNN can balance the trade between inference time-steps and performance after conversion [12, 14, 16, 25, 28, 50, 61]. Some recent works quantized the source ANN to boost the performance of converted SNNs using ultra-low time-steps [5, 41, 43, 74]. ANN-SNN conversion is the most practical training method to train SNNs on large-scale datasets, and the converted SNNs always have outstanding performance [6, 26, 27, 34]. The temporal characteristics of the spiking neuron make it similar to a Recurrent Neural Network (RNN). Based on this, Wu et al. [72] borrowed the idea of Back Propagation Through Time [70] and proposed the supervised learning way of STBP. As the firing of neurons is a non-differentiable Heaviside function, the surrogate gradient approximation is proposed to smooth the gradient [19, 21, 40, 53, 65, 67, 77]. Nowadays, the performance of SNNs trained with backpropagation is comparable to that of ANNs [13, 17, 22, 29, 33, 35, 39, 73, 80]. Time-based backpropagation is another supervised learning method that can maintain the sparsity of the gradient. However, these works can only extend to shallow networks [3, 51, 78, 79, 81]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "The robustness of SNN. SNNs are vulnerable to adversarial attacks as ANNs by adopting the gradient scheme in training. Firstly, SNNs obtained from ANN-SNN conversion can be attacked by the source ANNs with shared weights [62]. Besides, end-to-end trained SNNs suffer from the attack constructed from STBP. Sharmin et al. [62] summarized the two types of attacks as ANN-crafted and SNN-crafted attacks and revealed that attacks based on STBP are believed to be more powerful than those based on ANNs. Moreover, Liang et al. [44] exploited spike-compatible gradient to perform bit-flip attacks on SNN. Considering that SNNs are suitable for event-based tasks, various attacks on the event data of neuromorphic sensors are also explored [46, 49]. In these attacks, the STBP gradients are merged into sparse event data to construct attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 251, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 456 + ], + "type": "text", + "content": "Although the performance of SNNs can be degraded by such a variety of attack schemes, SNNs are still considered to have additional robustness compared to ANNs [15]. This is because more encodings are supported in SNNs. Compared to direct coding, Poisson coding is believed to process more inherent robustness as it introduces a noisy discretization to SNNs [37, 63]. Even so, how strong an attack Poisson coding can withstand still remains unknown. Another key robustness component of SNNs is the leaky parameter [63]. The leaky parameter controls the forgetting of historical information in LIF neurons. El-Allami et al. [18] achieved improved robustness by only searching in the space of leaky parameters. The current understanding of the robustness of SNNs is mainly focused on rate coding, and LIF neurons are also thought to perform the same coding. Therefore, gaining new insights into the robustness of rate coding is crucial for the practical application of SNNs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 486, + 441, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 486, + 441, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 486, + 441, + 498 + ], + "type": "text", + "content": "3.1. Neuron Model for SNNs" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 505, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 566 + ], + "type": "text", + "content": "In this paper, we consider the commonly used Leaky-Integrate-and-Fire (LIF) model and Integrate-and-Fire (IF) model [23, 31], the dynamics of membrane potential under firing threshold can be described by the following equations, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 335, + 573, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 573, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 335, + 573, + 545, + 622 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = - (u (t) - u _ {\\text {r e s t}}) + R I (t), \\quad (\\mathbf {L I F}) (1) \\\\ \\tau_ {m} \\frac {\\mathrm {d} u}{\\mathrm {d} t} = R I (t). \\quad (\\mathbf {I F}) (2) \\\\ \\end{array}", + "image_path": "cfecdffdf6fc2ed26b5b8261e521cdb136979ffba717e9c919247b0f8476c550.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{m}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " denote the membrane time constant and the membrane resistance constant, respectively. " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "u(t)" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "I(t)" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " represent the membrane potential and input current at time " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", respectively. Once the membrane potential reaches the firing threshold " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", the neuron will fire, and then the membrane potential will reset to the resting potential " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "u_{rest} < \\theta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ". Without loss of generality, to simulate the network of LIF" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7897" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "neurons on a computer with a Von Neumann architecture, the above process can be simplified and discretized to another set of equations [4]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 77, + 119, + 287, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 119, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 77, + 119, + 287, + 133 + ], + "type": "interline_equation", + "content": "u _ {i} (t) = \\lambda u _ {i} (t - 1) + w _ {i j} s _ {j} (t) + b _ {i} + \\eta_ {i} (t), \\tag {3}", + "image_path": "5fc270e0a96fbdd67b58d4ffcc584c306d8f6a481cb7b414652520c4d586fb16.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 77, + 135, + 287, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 135, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 77, + 135, + 287, + 168 + ], + "type": "interline_equation", + "content": "s _ {i} (t) = \\left\\{ \\begin{array}{l l} 1, & t = t _ {i} ^ {(f)} \\\\ 0, & t \\neq t _ {i} ^ {(f)} \\end{array} , \\right. \\tag {4}", + "image_path": "403a57148a0fd99ed3ff342f8b7e17777f9197f0a651612ed51a0b2e88ef2ecc.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " indicate presynaptic and postsynaptic neurons, " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "w_{ij}" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " represents the connection strength between the two neurons, and " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " is an extra constant input current to neuron " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "s_i(t)" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " describes whether neuron " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " fires at time-step " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": ", and the trigger is membrane potential " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "u_{i}(t)" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " reaches the firing threshold " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": ". We also mark the firing time-step of neuron " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "t_i^{(f)}" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "f = 1,2,\\ldots,\\lambda" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " is the membrane leaky constant corresponding to the membrane time constant in Eq. (1). Note that if we explicitly " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " to 1, this LIF neuron model will degenerate to the none-leaky IF model. Also, we add a reset term " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "\\eta_i(t)" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " on Eq. (3) to describe the neuron reset behavior. Despite the hard-reset function that resets the neuron membrane potential to resting potential (Eq. (5)), we also consider the soft-reset function (Eq. (6)) that directly subtracts the membrane potential by the threshold " + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 178, + 287, + 360 + ], + "type": "text", + "content": " [25, 60]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 369, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 369, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 63, + 369, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\eta_ {i} ^ {\\text {h a r d}} (t) = \\left\\{ \\begin{array}{l l} - \\left(u _ {i} \\left(t _ {i} ^ {(f)}\\right) - u _ {\\text {r e s t}}\\right) & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}. \\end{array} \\right. \\tag {5}", + "image_path": "99c276519e94fc844079a96a1380c387c8f612ce6bd62939160597d857e6b311.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 63, + 405, + 287, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 405, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 63, + 405, + 287, + 439 + ], + "type": "interline_equation", + "content": "\\eta_ {i} ^ {\\text {s o f t}} (t) = \\left\\{ \\begin{array}{l l} - \\theta & , t = t _ {i} ^ {(f)} \\\\ 0 & , t \\neq t _ {i} ^ {(f)}, \\end{array} \\right. \\tag {6}", + "image_path": "df73454108fadf7ce3936d291ea31d10008793390bd48f775dd0d8a65485996b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 449, + 259, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 259, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 259, + 462 + ], + "type": "text", + "content": "3.2. Supervised Training of SNNs with STBP" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "text", + "content": "Equation (3) implies that the LIF neuron has a function similar to that of an RNN. Thus, SNNs can be trained in the same way as RNNs with Back Propagation Through Time. STBP uses this idea to unroll the SNN over time-steps and accumulate gradient at each time-step [53, 72]. As illustrated in Fig. 1, the gradient of the loss function " + }, + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "text", + "content": " with respect to the output spikes " + }, + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "inline_equation", + "content": "s_j(t)" + }, + { + "bbox": [ + 46, + 468, + 287, + 553 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 563, + 287, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 563, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 66, + 563, + 287, + 590 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t)} = \\frac {\\partial \\mathcal {L}}{\\partial s _ {i} (t)} \\frac {\\partial s _ {i} (t)}{\\partial u _ {i} (t)} \\frac {\\partial u _ {i} (t)}{\\partial s _ {j} (t)} + \\tag {7}", + "image_path": "7f7c8744c02e893653e2b88d6171c0fe4b18d8e91a3f08241df299bd1fd09a47.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 95, + 591, + 268, + 618 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 591, + 268, + 618 + ], + "spans": [ + { + "bbox": [ + 95, + 591, + 268, + 618 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial s _ {j} (t + 1)} \\frac {\\partial s _ {j} (t + 1)}{\\partial u _ {j} (t + 1)} \\frac {\\partial u _ {j} (t + 1)}{\\partial u _ {j} (t)} \\frac {\\partial u _ {j} (t)}{\\partial s _ {j} (t)}.", + "image_path": "2e7d708630cfce53204512c17a75b4266ac9cf0483ad01ec905fad80daec1d14.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 626, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 626, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 626, + 287, + 665 + ], + "type": "text", + "content": "Note that as the derivative of spike with respect to the membrane potential " + }, + { + "bbox": [ + 46, + 626, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\frac{\\partial s_i(t)}{\\partial u_i(t)}" + }, + { + "bbox": [ + 46, + 626, + 287, + 665 + ], + "type": "text", + "content": " is nondifferentiable, the surrogate gradient [53] is often used in backpropagation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Since the STBP method enables supervised training of SNNs, this method can also generate gradient-based adversarial examples [62]. Therefore, we will use STBP as the baseline gradient obtain method." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 314, + 72, + 539, + 182 + ], + "blocks": [ + { + "bbox": [ + 314, + 72, + 539, + 182 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 539, + 182 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 539, + 182 + ], + "type": "image", + "image_path": "1eba3d9a86b1099e2eb2fafa7458b3f16bd4d43d1cb1b01f7f9e8ca665b7db49.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 193, + 545, + 227 + ], + "lines": [ + { + "bbox": [ + 305, + 193, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 193, + 545, + 227 + ], + "type": "text", + "content": "Figure 1. Forward pass and backward pass for STBP. The pink line shows that surrogate functions are applied in the non-differentiable process of neuron firing to obtain approximate gradients." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 250, + 422, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 250, + 422, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 250, + 422, + 261 + ], + "type": "text", + "content": "3.3. Adversarial Attacks" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 270, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 306 + ], + "type": "text", + "content": "Adversarial attack is a method to generate imperceptible perturbations that can fool neural networks, which can be formulated as an optimization problem:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 340, + 318, + 545, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 318, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 340, + 318, + 545, + 335 + ], + "type": "interline_equation", + "content": "\\arg \\max _ {\\delta} \\mathcal {L} (f (\\boldsymbol {x} + \\delta), y) \\quad s. t. \\| \\delta \\| _ {p} \\leq \\epsilon , \\tag {8}", + "image_path": "c19ea69043819478c62a88ef6b8fe81b92c7837ffa3fc720d1c8b9d76eb56a69.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " is the loss function, " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " is the network under attack, and " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\pmb{x},\\pmb{y}" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " are the input images and output target of the given network, respectively. " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " is the adversarial perturbation we want to optimize. " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _p" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "L_{p}" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": "-norm, and parameter " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " limits the strength of the perturbation to a level that is indistinguishable to the human eye. Here we consider two classic adversarial attack algorithms: Fast Gradient Sign Method (FGSM) [24] and Projected Gradient Descent (PGD) [38]. FGSM is a simple but effective attack method, which perturbs the data " + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 346, + 545, + 479 + ], + "type": "text", + "content": " along the sign of the gradient to increase the perturbed linear output, that is" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 358, + 492, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 492, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 358, + 492, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {x}} = \\boldsymbol {x} + \\epsilon \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x}, y))\\right). \\tag {9}", + "image_path": "ec6bc8ff626f049f18c9fd8a1d85c443f705416646d47eb34189915c54b28fc0.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 518, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 518, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 518, + 545, + 555 + ], + "type": "text", + "content": "PGD is an iterative variant of FGSM. By iteratively optimizing the perturbation, PGD offers a more powerful attack [48]. The iteration can be summarized as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 320, + 566, + 545, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 566, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 320, + 566, + 545, + 580 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {x}} ^ {k} = \\Pi_ {\\epsilon} \\left\\{\\boldsymbol {x} ^ {k - 1} + \\alpha \\operatorname {s i g n} \\left(\\nabla_ {\\boldsymbol {x}} \\mathcal {L} (f (\\boldsymbol {x} ^ {k - 1}, y))\\right) \\right\\}, \\tag {10}", + "image_path": "aacaea0813cdd174d32fc9c56e23a78dcbeb04cb5fa2da2babe05fd9eb96976c.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": " is the number of the iteration step, and " + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": " is the step size of each iteration. " + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\Pi_{\\epsilon}" + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": " constrains the data in each iteration and projects it onto the space of the " + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\epsilon - l_{p}" + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": " neighborhood of " + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 592, + 545, + 639 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "For all attack methods, we consider two different attack scenarios, white-box attack, and black-box attack. The white-box attack is the case that the hacker has complete access to the model topology, model parameters, and gradients, while the black-box attack is the case the hacker can only get the basic information of the model." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7898" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 105, + 83, + 231, + 209 + ], + "blocks": [ + { + "bbox": [ + 105, + 83, + 231, + 209 + ], + "lines": [ + { + "bbox": [ + 105, + 83, + 231, + 209 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 231, + 209 + ], + "type": "image", + "image_path": "f7e2d6b8770838dd8f56cae59096c7792317487bd449075fdd13a4cb44fe89e7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 231, + 253, + 243 + ], + "lines": [ + { + "bbox": [ + 80, + 231, + 253, + 243 + ], + "spans": [ + { + "bbox": [ + 80, + 231, + 253, + 243 + ], + "type": "text", + "content": "Figure 2. Experimental scheme of spike shuffle" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 261, + 107, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 107, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 107, + 273 + ], + "type": "text", + "content": "4. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": "In this section, we first show that the current high-performance SNNs for image classification tasks are encoded by firing rate and do not contain timing information, whether they are trained by STBP and ANN-SNN conversion. Based on this, we propose rate gradient approximation, a new attack method against SNNs, and apply it to SNNs composed of different types of neurons and input encodings. Finally, we propose the time-extended attack as an attack enhancement method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 395, + 287, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 287, + 419 + ], + "type": "text", + "content": "4.1. Does well-trained SNNs contain timing information?" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "text", + "content": "Here we design an experiment and test whether the well-trained SNNs are rate coded and whether they contain timing information. The definition of firing rate refers to the temporal average of the spikes. As illustrated in Eq. (11), the firing rate of one given neuron " + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "text", + "content": " is the total spike count in an interval of time-steps " + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "text", + "content": " divided by the duration " + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 426, + 287, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 134, + 514, + 287, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 514, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 134, + 514, + 287, + 540 + ], + "type": "interline_equation", + "content": "r _ {i} = \\frac {\\sum_ {t = 1} ^ {T} s _ {i}}{T}. \\tag {11}", + "image_path": "66203c3228828c6e2443f73acab8f5925026b4a7ec51a09829ebbb86c65fc569.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 616 + ], + "type": "text", + "content": "The detailed experimental scheme is shown in Fig. 2. We add a random number generator to shuffle each neuron's output spike firing order so that the spike trains will never contain temporal information. We apply this design to the pre-trained SNN models and test accuracy change before and after the spike shuffle." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "type": "text", + "content": "The experiment is implemented on the CIFAR-10 dataset with VGG-11 network architecture. To test different SNNs, we choose combinations of different training methods, leakage parameters, and reset functions. We pre-train SNN for each combination and then substitute all the spiking neurons with shuffled neurons." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Tab. 1 reports the average performance of 10 runs, from which we find that the accuracy after spike shuffle is slightly" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 320, + 72, + 533, + 191 + ], + "blocks": [ + { + "bbox": [ + 320, + 72, + 533, + 191 + ], + "lines": [ + { + "bbox": [ + 320, + 72, + 533, + 191 + ], + "spans": [ + { + "bbox": [ + 320, + 72, + 533, + 191 + ], + "type": "image", + "image_path": "2b79240be88cd2554dfd6aac299e95e5e87dc0a38ae98ccfe67619a67760c6da.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": "Figure 3. Forward pass and backward pass for RGA attack. The pink line shows that surrogate functions are applied to the approximation of the derivative for firing rate and input current." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 266, + 543, + 369 + ], + "blocks": [ + { + "bbox": [ + 325, + 247, + 526, + 258 + ], + "lines": [ + { + "bbox": [ + 325, + 247, + 526, + 258 + ], + "spans": [ + { + "bbox": [ + 325, + 247, + 526, + 258 + ], + "type": "text", + "content": "Table 1. Performance before and after the spike shuffle" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 266, + 543, + 369 + ], + "lines": [ + { + "bbox": [ + 307, + 266, + 543, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 266, + 543, + 369 + ], + "type": "table", + "html": "
DatasetTraining MethodTλResetClean Acc.Shuffled Acc.Rate
CIFAR-10ANNSNN161.0soft93.2593.358✓
CIFAR-10STBP81.0soft92.7592.086✓
CIFAR-10STBP81.0hard93.0692.214✓
CIFAR-10STBP80.9hard93.0392.545✓
CIFAR-10STBP80.5hard91.4891.225✓
CIFAR10-DVSSTBP100.9hard77.0075.400✓
", + "image_path": "885edf3c820fec6bceca527468b164139ec36498efa3e50e537e29b08b1a05fe.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 388, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 507 + ], + "type": "text", + "content": "different from the clean accuracy for all SNNs. For the model converted from ANNs, the model performance after the spike shuffle is slightly improved. The performance after spike shuffle is slightly reduced for other models obtained by supervised STBP training. In fact, even for models trained on the DVS dataset, the performance gap before and after shuffling is small, which proves that models trained on the DVS dataset contain very little timing information. Therefore, we assert that firing rates encode major information in these SNNs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 515, + 504, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 504, + 528 + ], + "type": "text", + "content": "4.2. Rate Gradient Approximation Attack" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "This section proposes the Rate Gradient Approximation (RGA) attack for spike count rate coding SNNs. In the above section, we have shown that the well-trained SNNs are all rate-encoded at each layer. Thus, we can approximate the backward pass of SNNs using only the average firing rate over time-steps to generate effective gradients. Specifically, we introduce an intermediate variable " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " to denote the average input current of neuron " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " in Eq. (3), which is defined by:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 378, + 650, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 650, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 378, + 650, + 545, + 681 + ], + "type": "interline_equation", + "content": "I _ {i} = \\sum_ {t = 1} ^ {T} w _ {i j} s _ {j} (t) + b _ {i} \\tag {12}", + "image_path": "f86ea65621d4b56745240b86d3781a00d1e28c1deba74842ed929267f8ae2a83.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " also represents the weighted firing rate from the previous layer. Fig. 3 illustrates how the gradient propa" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7899" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 71, + 166, + 169 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 166, + 169 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 166, + 169 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 166, + 169 + ], + "type": "image", + "image_path": "6b8f2f78355b2c06aa6cea9c153344b38718142308cce5bbfb48152f7f2234b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 85, + 173, + 138, + 182 + ], + "lines": [ + { + "bbox": [ + 85, + 173, + 138, + 182 + ], + "spans": [ + { + "bbox": [ + 85, + 173, + 138, + 182 + ], + "type": "text", + "content": "(a) IF R-I curve" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 70, + 277, + 169 + ], + "blocks": [ + { + "bbox": [ + 169, + 70, + 277, + 169 + ], + "lines": [ + { + "bbox": [ + 169, + 70, + 277, + 169 + ], + "spans": [ + { + "bbox": [ + 169, + 70, + 277, + 169 + ], + "type": "image", + "image_path": "4f38aed04c487e50ff7c793b02c45ba51675b00be061bead40db4d2f17dec888.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 173, + 271, + 182 + ], + "lines": [ + { + "bbox": [ + 175, + 173, + 271, + 182 + ], + "spans": [ + { + "bbox": [ + 175, + 173, + 271, + 182 + ], + "type": "text", + "content": "(b) Derivative of IF R-I curve" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": "gates between two adjacent neurons " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": " with the defined weighted firing rate. The gradient propagation starts from the firing rate " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": "-th neuron, passes to the input current " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": ", and finally arrives at the firing rate " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "r_j" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 223, + 287, + 282 + ], + "type": "text", + "content": "-th neuron, that is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 124, + 287, + 287, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 287, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 124, + 287, + 287, + 315 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial r _ {j}} = \\frac {\\partial \\mathcal {L}}{\\partial r _ {i}} \\frac {\\partial r _ {i}}{\\partial I _ {i}} \\frac {\\partial I _ {i}}{\\partial r _ {j}}. \\tag {13}", + "image_path": "c198bebf76ed14c100430ccffe4d107cd67e20018c453ff3e63595921a2e7fe0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "content": "This result can be generalized to the network with the chain rule. If we use vectors " + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}^l" + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\boldsymbol{I}^l" + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "content": " to denote the firing rates and average input currents of all neurons in layer " + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "content": ", respectively, and use vector " + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}^0" + }, + { + "bbox": [ + 46, + 320, + 287, + 392 + ], + "type": "text", + "content": " to denote the input image. The gradient propagates from the loss function to the input image is formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 99, + 399, + 287, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 399, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 99, + 399, + 287, + 431 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {0}} = \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {r} ^ {L}} \\left(\\prod_ {l = 1} ^ {L} \\frac {\\partial \\boldsymbol {r} ^ {l}}{\\partial \\boldsymbol {I} ^ {l}} \\frac {\\partial \\boldsymbol {I} ^ {l}}{\\partial \\boldsymbol {r} ^ {l - 1}}\\right). \\tag {14}", + "image_path": "ebc7c7b64a69193803d2596a7d95f31ed9c8dd60baf87ef692b015ea35bab8ee.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 437, + 247, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 247, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 247, + 451 + ], + "type": "text", + "content": "4.3. RGA Attack with Surrogate Gradient" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": "According to Eq. (11) and (12), one can compute the gradient " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\frac{\\partial I_i}{\\partial r_j}" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": ", the only part we cannot directly calculate the gradient in Eq. (13) is " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\frac{\\partial r_i}{\\partial I_i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": ". To get a proper approximation for " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\frac{\\partial r_i}{\\partial I_i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": ", we need to use a differentiable surrogate function " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": " to approximate the relationship between output firing rate " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": " and input current " + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 46, + 456, + 287, + 581 + ], + "type": "text", + "content": ". Here, we propose to use the static R-I curve, which refers to the relationship between the input current and output firing rate when the input is constant, as the approximation function. We discuss the cases of IF neurons and LIF neurons separately." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 582, + 236, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 236, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 236, + 593 + ], + "type": "text", + "content": "RGA Attack the Integrate-and-Fire Neuron" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "For IF neurons, the static R-I curve is the clipped ReLU function [7, 14], which is presented in Fig. 4a by the blue line. We also sampled from a pre-trained VGG-11 network to obtain the actual distribution of average input current and average output firing rate (more details are in the Appendix), which is represented by the light blue scatter in the figure. We find that if we simply set the static RI curve as the surrogate gradient, many data points would be wrongly assigned to zero derivatives. To avoid the derivatives being all zero in the interval " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "[\\theta, +\\infty]" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": ", we propose a" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 71, + 425, + 169 + ], + "blocks": [ + { + "bbox": [ + 65, + 192, + 268, + 204 + ], + "lines": [ + { + "bbox": [ + 65, + 192, + 268, + 204 + ], + "spans": [ + { + "bbox": [ + 65, + 192, + 268, + 204 + ], + "type": "text", + "content": "Figure 4. Surrogate function and gradient for IF neuron" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 71, + 425, + 169 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 425, + 169 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 425, + 169 + ], + "type": "image", + "image_path": "e4adde9d367ad481d47e9e95ffb229341395e1d33ae559eec46ae6bf14aa2628.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 342, + 173, + 399, + 182 + ], + "lines": [ + { + "bbox": [ + 342, + 173, + 399, + 182 + ], + "spans": [ + { + "bbox": [ + 342, + 173, + 399, + 182 + ], + "type": "text", + "content": "(a) LIF R-I curve" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 321, + 192, + 529, + 204 + ], + "lines": [ + { + "bbox": [ + 321, + 192, + 529, + 204 + ], + "spans": [ + { + "bbox": [ + 321, + 192, + 529, + 204 + ], + "type": "text", + "content": "Figure 5. Surrogate function and gradient for LIF neuron" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 428, + 71, + 536, + 169 + ], + "blocks": [ + { + "bbox": [ + 428, + 71, + 536, + 169 + ], + "lines": [ + { + "bbox": [ + 428, + 71, + 536, + 169 + ], + "spans": [ + { + "bbox": [ + 428, + 71, + 536, + 169 + ], + "type": "image", + "image_path": "dd5dfb0a92ae19947171b4b003774a5e55b4cf325e28aee1c354da7bc97846fb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 172, + 533, + 182 + ], + "lines": [ + { + "bbox": [ + 431, + 172, + 533, + 182 + ], + "spans": [ + { + "bbox": [ + 431, + 172, + 533, + 182 + ], + "type": "text", + "content": "(b) Derivative of LIF R-I curve" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "text", + "content": "modified R-I curve function as the final surrogate function (green line in Fig. 4a). We introduce a relaxation parameter " + }, + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\beta \\in [1, +\\infty]" + }, + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "text", + "content": " to keep the derivatives to be none-zero between " + }, + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "inline_equation", + "content": "[0, \\beta \\theta]" + }, + { + "bbox": [ + 305, + 224, + 545, + 284 + ], + "type": "text", + "content": ". Then its corresponding derivative (surrogate gradient) is:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 341, + 293, + 545, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 293, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 341, + 293, + 545, + 326 + ], + "type": "interline_equation", + "content": "\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} 1 / (\\beta \\theta), & 0 \\leqslant I _ {i} \\leqslant \\beta \\theta \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} . \\right. \\tag {15}", + "image_path": "66711e71efe55af6c83e2da6a7522909a6a639307b2e3d7551d59235adb468e0.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 333, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 333, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 333, + 545, + 369 + ], + "type": "text", + "content": "With the formula for backpropagation and the derivatives of intermediate nodes, we can calculate the derivatives that are ultimately passed to the input image." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 369, + 524, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 524, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 524, + 380 + ], + "type": "text", + "content": "RGA Attack the Leaky-Integrate-and-Fire Neuron" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "text", + "content": "Similar to the RGA Attack for IF neurons, the surrogate function for LIF neurons is inspired by the static R-I curve. Following the work of [23, 30], we derive the R-I curve function for the LIF neurons. Supposing that a LIF neuron receives a constant input " + }, + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "inline_equation", + "content": "u_{rest} = 0" + }, + { + "bbox": [ + 305, + 381, + 545, + 453 + ], + "type": "text", + "content": ", the LIF neuron (Eq. (3)) can be simplified to:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 374, + 462, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 462, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 374, + 462, + 545, + 475 + ], + "type": "interline_equation", + "content": "u _ {i} (t) = \\lambda u _ {i} (t - 1) + I _ {i}. \\tag {16}", + "image_path": "68fe58ae3b2bfeb82fbc355d6d991b662f48def01019a44347472354b8347a5e.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "content": "We then iterate this recursive formula to get the neuron membrane potential as a function of time." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 371, + 517, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 517, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 371, + 517, + 545, + 541 + ], + "type": "interline_equation", + "content": "u _ {i} (t) = \\frac {I _ {i}}{\\lambda - 1} \\lambda^ {t} - \\frac {I _ {i}}{\\lambda - 1} \\tag {17}", + "image_path": "542739522aca3f47fd93287c95c8a186a6275a020bd7feb0d9ace263e646b273.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "content": "From the formula above, we can calculate the time required for the neuron to accumulate from 0 to " + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "content": ", and finally obtain the firing rate by inverse the calculated time interval." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 362, + 594, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 594, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 362, + 594, + 545, + 622 + ], + "type": "interline_equation", + "content": "r _ {i} = \\left\\lceil \\log_ {\\lambda} \\frac {I _ {i} + \\theta (\\lambda - 1)}{I _ {i}} \\right\\rceil^ {- 1} \\tag {18}", + "image_path": "ab8f2ca71e43a54d9f7342069544e9326e43cf55c5cf68ce09a613e07dfff2c4.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": "As shown in Fig. 5a, the light blue scatter represents the actual distribution of average input current and average output firing rate from a pre-trained VGG-11 network with LIF neurons. Although the static RI curve matches the actual situation, the static RI curve (blue curve) contains the non-derivable equation. The derivative is always zero when " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "x < (1 - \\lambda)\\theta" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "x > \\theta" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": ". Meanwhile, as " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\lim_{x\\to (1 - \\lambda)\\theta^{+}}" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": ", the" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7900" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "content": "derivative of the function approaches infinity. This will lead to gradient vanishing and exploding problems in backpropagation. Therefore, it is impractical to calculate the derivatives directly from the static R-I curve." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": "According to the characteristics of this static R-I curve, we segment it at the position of " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "(1 - \\lambda)\\theta" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " and then separately perform piecewise linear interpolation at " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "x\\in [0,(1 - \\lambda)\\theta ]" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "x\\in [(1 - \\lambda)\\theta ,\\beta \\theta ]" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " is a relaxation parameter to control the end point of interpolation. Thus, we obtain two straight lines (green line in Fig. 5a). In order to avoid zero derivatives over the interval " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "[0,(1 - \\lambda)\\theta ]" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": ", we also add a hyperparameter " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " which is the derivative of the first half of the linear function. In conclusion, the first part of the linear interpolation start at data point " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "(0,0)" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " and end at " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "((1-" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "\\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": ". The second part of the interpolation start at " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "((1 - \\lambda)\\theta ,(1 - \\lambda)\\theta \\gamma)" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": " and end at " + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "inline_equation", + "content": "(\\beta \\theta ,1)" + }, + { + "bbox": [ + 46, + 120, + 288, + 263 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 264, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 264, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 59, + 264, + 287, + 275 + ], + "type": "text", + "content": "Therefore, the final surrogate gradient can be written as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 292, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 292, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 59, + 292, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\frac {\\partial r _ {i}}{\\partial I _ {i}} = \\left\\{ \\begin{array}{l l} \\gamma , & 0 \\leqslant I _ {i} \\leqslant (1 - \\lambda) \\theta \\\\ \\frac {1 - \\gamma \\theta + \\gamma \\theta \\lambda}{(\\beta + \\lambda - 1) \\theta}, & (1 - \\lambda) \\theta < I _ {i} \\leqslant \\beta \\theta . \\\\ 0, & I _ {i} > \\beta \\theta \\text {o r} I _ {i} < 0 \\end{array} \\right. \\tag {19}", + "image_path": "8cac4876bb4a3f5b2e792ccf43026a1379d3010a37e1d447095ca9ebeae6f84d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "content": "The derivative of this surrogate gradient function is " + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "content": " in the first interval and " + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "inline_equation", + "content": "(1 - \\gamma \\theta +\\gamma \\theta \\lambda) / ((\\beta +\\lambda -1)\\theta)" + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "content": " in the second interval. Note that when we set the leaky parameter " + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "content": ", this function degenerates into the same form as the surrogate function for the IF neuron (Eq. (15)). Thus, this function can apply to both types of neurons." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "content": "The hyperparameter " + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "content": " are mainly smoothing terms to prevent the gradient from disappearing. We set " + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "content": " to 2 and " + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 427, + 287, + 475 + ], + "type": "text", + "content": " to 0.2 in the rest of this paper. More ablation experiments of the hyperparameters are provided in the Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 481, + 231, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 231, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 231, + 495 + ], + "type": "text", + "content": "4.4. RGA Attack the Poisson Encoding" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 500, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 606 + ], + "type": "text", + "content": "Our proposed method can generalize to SNNs that receive spike inputs. For Poisson input SNN, we can regard it as a combined structure of a Poisson encoder and an end-to-end SNN receives spike input. Therefore, we also need to attack the Poisson encoder rather than only perturbing the network. We can consider the Poisson encoder as a random transformation and use a straight through estimator [2] to attack this random transformation [1]. The gradient can be written as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 612, + 287, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 612, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 85, + 612, + 287, + 637 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\text {P o i s s o n} (x)}{\\partial x} \\approx \\frac {\\partial \\mathbb {E} _ {x} (\\text {P o i s s o n} (x))}{\\partial x} = 1. \\tag {20}", + "image_path": "08fd6f8ccd260ce7b2786e30962e19f965abb57c84042e36218046ec9fbcf281.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "The Adversarial example generation methodology proposed by Sharmin et al. [63] also includes the attack on Poisson encoded attack. Note that although our attack on the Poisson encoder is implemented differently from theirs, it is mathematically equivalent, and the generated adversarial examples are the same." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 328, + 73, + 526, + 375 + ], + "blocks": [ + { + "bbox": [ + 328, + 73, + 526, + 375 + ], + "lines": [ + { + "bbox": [ + 328, + 73, + 526, + 375 + ], + "spans": [ + { + "bbox": [ + 328, + 73, + 526, + 375 + ], + "type": "image", + "image_path": "89f808ec16b6f15483062c3726551abb70e158a831360b0cb75a20294ce97b6c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 383, + 545, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 437 + ], + "type": "text", + "content": "Figure 6. The attack success rate change with respect to the attack strength for VGG-11 model on the CIFAR-10 dataset. Here WB stands for white box attack while BB stands for black box attack. The blue and purple bar display the attack success rates " + }, + { + "bbox": [ + 305, + 383, + 545, + 437 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 383, + 545, + 437 + ], + "type": "text", + "content": " for RGA-FGSM and STBP-FGSM, respectively." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 459, + 462, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 462, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 462, + 470 + ], + "type": "text", + "content": "4.5. Time Extended RGA Attack" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 478, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 545, + 609 + ], + "type": "text", + "content": "Here we introduce an SNN-specific attack enhancement method. When generating attack samples, we expect to generate more effective adversarial samples by increasing the inference time of SNNs. We call this method as Time Extended attack. When we apply this time-extended enhancement with RGA attack, the effects of randomness can be reduced by increasing the simulation time of attacking, resulting in a more accurate estimation of the firing rate. Therefore, the time-extended enhancement is generally more suitable for RGA-based attacks and is more effective for attacking against SNNs with Poisson inputs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 387, + 635 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "In this section, we conduct various experiments to evaluate the effectiveness of the proposed methods [32, 55]. We first test our attack method on the CIFAR-10, CIFAR-100 dataset [36] and CIFAR10-DVS dataset [42] with the VGG-11 [66] and ResNet-17 architecture [80]. We implement both non-iterative attack FGSM and iterative attack PGD" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7901" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 542, + 324 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 542, + 324 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 542, + 324 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 542, + 324 + ], + "type": "table", + "html": "
ArchitectureDatasetInputTλTEAttackClean Acc.White Box AttackBlack Box Attack
ASR. (STBP)ASR. (RGA)ASR. (STBP)ASR. (RGA)
VGG-11CIFAR-10Direct81.0-FGSM93.0686.277793.735268.031473.2646
VGG-11CIFAR-10Direct81.02×FGSM93.0686.073594.734664.839973.6192
VGG-11CIFAR-10Direct81.0-PGD93.0699.494999.828186.460487.1266
VGG-11CIFAR-10Direct161.0-FGSM93.0385.327392.421865.796073.1269
VGG-11CIFAR-10Direct161.0-PGD93.0399.365899.838885.585387.4234
VGG-11CIFAR-10Poisson161.0-FGSM86.7254.979858.032840.867344.2259
VGG-11CIFAR-10Poisson161.02×FGSM86.7256.810660.529642.844046.9085
VGG-11CIFAR-10Poisson161.0-PGD86.7251.902257.141237.091741.1887
VGG-11CIFAR-10Direct80.5-FGSM91.4891.714093.627077.765679.6458
VGG-11CIFAR-10Direct80.5-PGD91.4899.825199.770493.681793.0367
VGG-11CIFAR-10Direct80.9-FGSM93.0389.906594.410473.449477.2761
VGG-11CIFAR-10Direct80.9-PGD93.0399.731399.828091.766191.3899
ResNet-17CIFAR-10Direct80.9-FGSM93.0484.243392.927867.110980.1053
ResNet-17CIFAR-10Direct80.9-PGD93.0499.9248100.00092.003497.5172
VGG-11CIFAR-100Direct80.9-FGSM73.2892.876694.718980.895284.2658
VGG-11CIFAR-100Direct80.9-PGD73.2899.754499.849992.235392.0579
ResNet-17CIFAR-100Direct80.9-FGSM72.0585.662792.061174.295681.1936
ResNet-17CIFAR-100Direct80.9-PGD72.0599.583699.889087.633695.2949
VGG-11CIFAR10-DVSFrame100.9-FGSM77.0059.508459.560748.496747.9275
", + "image_path": "db8a2547f9c3c5f43893a959cc9ed7da1f0bac1b527df858bb2d9afc22e1433c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 333, + 545, + 366 + ], + "lines": [ + { + "bbox": [ + 48, + 333, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 48, + 333, + 545, + 366 + ], + "type": "text", + "content": "Table 2. Results of RGA based attack and STBP based attack on different type of SNNs. The seven columns on the left describes the parameter settings of the attack object, including architecture, datasets, input coding, simulation time-steps, leaky parameters, time extant (TE), and attack method. ASR. is short for attack success rate. For clarity, the better of the two attack results is bolded." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 49, + 387, + 286, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 387, + 286, + 435 + ], + "spans": [ + { + "bbox": [ + 49, + 387, + 286, + 435 + ], + "type": "text", + "content": "and combine them with the proposed RGA attack and compare the results with STBP-based attacks. Note that when attacking DVS-related models, we directly generate and add adversarial examples on the preprocessed frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 436, + 286, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 436, + 286, + 519 + ], + "spans": [ + { + "bbox": [ + 48, + 436, + 286, + 519 + ], + "type": "text", + "content": "As for training methods, since the ANN-SNN conversion method is proved insecure [63], we only consider SNNs obtained by supervised STBP training. We used the attack success rate as our metric for each attack, which is the proportion of samples that fool the network into misclassification. The details of the training configurations for pretrained networks are provided in the Appendix." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 527, + 220, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 527, + 220, + 539 + ], + "spans": [ + { + "bbox": [ + 49, + 527, + 220, + 539 + ], + "type": "text", + "content": "5.1. Effectiveness of the RGA Attack" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 546, + 286, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 546, + 286, + 629 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 629 + ], + "type": "text", + "content": "Here we test the effectiveness of the proposed RGA attack. We choose the STBP attack as a baseline and compare the attack success rate. To compare the effectiveness of the attack on various neuron settings, we select SNNs composed of LIF neurons with a leaky parameter of 0.9 and none-leaky IF neurons with a leaky parameter of 1.0. Also, the inference time-steps vary from 8 to 16." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "content": "As shown in Fig. 6, we find that the attack success rate of our RGA attack method surpasses the previously commonly used STBP attack in most cases. When the attack strength is small, the attack success rate of the RGA attack and STBP attack is not much different. However, when the attack strength gradually increases to 8/255, the attack success rate of the RGA attack will be much higher than that" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 387, + 545, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 387, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 308, + 387, + 545, + 423 + ], + "type": "text", + "content": "obtained by the STBP attack. These results demonstrate that the RGA attack is more effective than the STBP attack for different SNN settings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 430, + 508, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 430, + 508, + 442 + ], + "spans": [ + { + "bbox": [ + 308, + 430, + 508, + 442 + ], + "type": "text", + "content": "5.2. Effectiveness of Time Extended Attack" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 449, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 449, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 308, + 449, + 545, + 604 + ], + "type": "text", + "content": "To demonstrate the effectiveness of the time-extended attack, we pre-train two SNNs with different neurons and input encoding. We then double and triple the inference time-steps to attack these SNNs while keeping the origin inference time-steps for evaluation. The SNN configuration and the final results are shown in Fig. 7. The combination of the time-extended enhancement and RGA-based attack can achieve better attack performance since the attack effectiveness increases as the simulation time-step increases. However, applying the time-extended enhancement attack on the STBP-based attack cannot improve the attack. Meanwhile, we also find that the time-extended enhancement method is more effective for the Poisson input model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 611, + 498, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 611, + 498, + 623 + ], + "spans": [ + { + "bbox": [ + 308, + 611, + 498, + 623 + ], + "type": "text", + "content": "5.3. Generalizability of the RGA Attacks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 630, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 630, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 630, + 545, + 712 + ], + "type": "text", + "content": "To discuss the generalizability of RGA attacks across different SNNs, we conduct further experiments across various SNNs. Tab. 2 reports the detailed comparison of RGA attack and STBP attack over various SNN neurons, architecture, and dataset settings. In this experiment, we set the attack strength " + }, + { + "bbox": [ + 308, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 308, + 630, + 545, + 712 + ], + "type": "text", + "content": " to 8/255 for CIFAR-10/100 dataset and 0.02 for the CIFAR10-DVS dataset. Also, the step size and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "type": "text", + "content": "7902" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 166, + 148 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 166, + 148 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 166, + 148 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 166, + 148 + ], + "type": "image", + "image_path": "854b3ee48d07dce26f39646e9ff4c90bbe2c27481ca98b1fd644ac7386a5eac6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "lines": [ + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "spans": [ + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "type": "inline_equation", + "content": "\\lambda = 0.9" + }, + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 8" + }, + { + "bbox": [ + 65, + 152, + 157, + 161 + ], + "type": "text", + "content": " ,Direct Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 70, + 278, + 148 + ], + "blocks": [ + { + "bbox": [ + 169, + 70, + 278, + 148 + ], + "lines": [ + { + "bbox": [ + 169, + 70, + 278, + 148 + ], + "spans": [ + { + "bbox": [ + 169, + 70, + 278, + 148 + ], + "type": "image", + "image_path": "0c149b985393f6aef8ba52d2ecf24ded16e74cbd8bfc722324a9410690085bcf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "lines": [ + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "spans": [ + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 16" + }, + { + "bbox": [ + 175, + 152, + 271, + 162 + ], + "type": "text", + "content": " Poisson Input" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": "Figure 7. White box attack results of the time-extended attack with different settings. The " + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": " represents the baseline attack, while " + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": " represent double or triple the simulation time when attacked. The model under attack is VGG-11 composed of LIF neurons on the CIFAR-10 dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 250, + 287, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 250, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 287, + 274 + ], + "type": "text", + "content": "the number of steps for the PGD attack are set to 2/255 and 5, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "content": "From Tab. 2, one can find that all RGA-based attacks outperform STBP-based attacks when conducting single-step attacks. In attacks cases without time-extended enhancement, the largest performance gap exceeds " + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "inline_equation", + "content": "8.6\\%" + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "content": " in ResNet-17 for white box and black box attacks, respectively. When conducting multi-step attacks, the proposed RGA-based attack achieves better performance than the STBP-based attack in most cases and gets comparable performance for the rest of the cases. In attack cases with time-extended enhancement, the performance of the RGA attack not only exceeds the STBP attack, but also exceeds the performance of RGA attack without time-extended enhancement. Even in attacks on the CIFAR10-DVS dataset, the RGA-based attack gets comparable performance as the STBP-based attack." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 456, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 563 + ], + "type": "text", + "content": "In conclusion, the proposed RGA attack can produce stronger adversarial examples in most cases. The RGA attack is also insensitive to neuron hyperparameters. Currently, high-performance SNNs are mainly applied in tasks related to static images or DVS datasets. We have proved through experiments that those SNNs contain very limited temporal information and they are vulnerable to the designed RGA-based attack. This demonstrates the importance and generalizability of the RGA-based attack method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 574, + 211, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 211, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 211, + 586 + ], + "type": "text", + "content": "5.4. LIF Neuron is not that Robust" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "Previous research suggested that the VGG5 SNNs trained with LIF neurons are more robust than the ones trained with IF neurons [63]. Here, we test whether this conclusion can be generalized to deeper networks with RGA-based attacks. We train multiple networks with the same architecture, including one quantized ANN and six SNNs with leaky parameters ranging from 0.5 to 1. We select VGG-11 as the model architecture and CIFAR-10 as the evaluation dataset. Then, we apply the white box FGSM attack to the quantized ANN and both RGA-FGSM" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 314, + 72, + 540, + 170 + ], + "blocks": [ + { + "bbox": [ + 314, + 72, + 540, + 170 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 540, + 170 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 540, + 170 + ], + "type": "image", + "image_path": "2db5701c771ff4f4c5e2b3edad8c32f10f239b7439417e939dc30603142cbaea.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 182, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 258 + ], + "type": "text", + "content": "Figure 8. The white box attack success rate changes with respect to the leaky parameter of the spiking neuron. The red line represents the RGA attack, while the green line represents the STBP attack. The blue dashed line illustrates the attack success rate of a quantized ANN under the FGSM attack. The selected leaky parameters range from 0.5 to 1.0. This experiment is conducted on the CIFAR-10 dataset with VGG-11 architecture." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 280, + 478, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 280, + 478, + 291 + ], + "spans": [ + { + "bbox": [ + 306, + 280, + 478, + 291 + ], + "type": "text", + "content": "and STBP-FGSM attacks to the six SNNs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 293, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 411 + ], + "type": "text", + "content": "Fig. 8 demonstrates the results. The blue dashed line represents the attack success rate of ANN being attacked by FGSM. The red and green lines represent the attack success rate of the RGA-FGSM and STBP-FGSM, respectively. According to this figure, one can find that compared to the STBP attack (green line), the RGA attack (red line) is more stable. Meanwhile, the red line is always above the green line, indicating that the RGA attack can not only generate stronger adversarial examples, but is also less sensitive to neuron leakage parameters." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 412, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 483 + ], + "type": "text", + "content": "In addition, the performance of all types of SNNs under STBP-based attacks fluctuates around the baseline, while the RGA attack success rate is always higher than the baseline. Therefore, we found that SNN composed of LIF neurons with different leakage parameters has no advantage over ANNs in terms of adversarial robustness." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 496, + 378, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 378, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 378, + 508 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 517, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 648 + ], + "type": "text", + "content": "In this paper, we propose a new attack method for SNNs that outperforms previous methods. Our approach can serve as a benchmark for future research on SNN adversarial robustness. In addition, considering the strength of this attack method and the lower time cost compared to the STBP attack, we also look forward to the research on adversarial training based on this attack method. Our findings show that the rate-coded SNN composed of LIF neurons is not secure against stronger adversarial attacks, highlighting the need for exploring training methods for SNNs utilizing complex neurons and other neuronal codings." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 660, + 416, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 660, + 416, + 673 + ], + "spans": [ + { + "bbox": [ + 306, + 660, + 416, + 673 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 679, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 679, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 679, + 545, + 713 + ], + "type": "text", + "content": "This work is funded by STI2030Project (2021ZD0200300), and the National Natural Science Foundation of China (621 76003, 62088102)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7903" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Anish Athalye, Nicholas Carlini, and David Wagner. 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In Advances in Neural Information Processing Systems, 2022. 2" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7906" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_content_list.json b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fd497119388937fb513a752e83b67be70aa9bb80 --- /dev/null +++ b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_content_list.json @@ -0,0 +1,1690 @@ +[ + { + "type": "text", + "text": "Raw Image Reconstruction with Learned Compact Metadata", + "text_level": 1, + "bbox": [ + 176, + 130, + 794, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yufei Wang $^{1}$ , Yi Yu $^{1}$ , Wenhan Yang $^{2}$ , Lanqing Guo $^{1}$ , Lap-Pui Chau $^{3}$ , Alex C. Kot $^{1}$ , Bihan Wen $^{1*}$ $^{1}$ Nanyang Technological University \n $^{2}$ Peng Cheng Laboratory \n $^{3}$ The Hong Kong Polytechnic University", + "bbox": [ + 104, + 179, + 870, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yufei001, yuyi0010, lanqing001, eackot, bihan.wen}@ntu.edu.sg", + "bbox": [ + 210, + 234, + 759, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yangwh@pcl.ac.cn lap-pui.chau@polyu.edu.hk", + "bbox": [ + 285, + 253, + 676, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While raw images exhibit advantages over sRGB images (e.g., linearity and fine-grained quantization level), they are not widely used by common users due to the large storage requirements. Very recent works propose to compress raw images by designing the sampling masks in the raw image pixel space, leading to suboptimal image representations and redundant metadata. In this paper, we propose a novel framework to learn a compact representation in the latent space serving as the metadata in an end-to-end manner. Furthermore, we propose a novel sRGB-guided context model with the improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed. We illustrate how the proposed raw image compression scheme can adaptively allocate more bits to image regions that are important from a global perspective. The experimental results show that the proposed method can achieve superior raw image reconstruction results using a smaller size of the metadata on both uncompressed sRGB images and JPEG images. The code will be released at https://github.com/wyf0912/R2LCM.", + "bbox": [ + 75, + 335, + 473, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 672, + 209, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As an unprocessed and uncompressed data format directly obtained from camera sensors, raw images has unique advantages for computer vision tasks in practice. For example, it is easier to model the distribution of real image noise in raw space, which enables generalized deep real denoising networks [1,40]; As pixel values in raw images have a linear relationship with scene radiance, they own benefits to recover shadows and highlights without bringing in the grainy noise usually associated with high ISO [12, 16, 33, 35], which greatly contributes to the low-light image enhancement. Besides, with richer colors, raw images offer more room for correction and artistic manipulation.", + "bbox": [ + 75, + 698, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ba3ce45feacda37d7c46a445c47cc965acc505f254328e4a6d2cef573350f91.jpg", + "image_caption": [ + "(a) Previous SOTA methods sample in the raw space [26, 30]." + ], + "image_footnote": [], + "bbox": [ + 506, + 303, + 885, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be417a1597ce76872e07da88f1ef2779c506bca9c36a223f77cd2fd1278d3e12.jpg", + "image_caption": [ + "(b) The proposed method samples in the latent space." + ], + "image_footnote": [], + "bbox": [ + 506, + 396, + 885, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. The comparison between the previous SOTA methods (in blue) and our proposed method (in green). Different from the previous work where the sampling strategy is hand-crafted or learned by a pre-defined sampling loss, we learn the sampling and reconstruction process in a unified end-to-end manner. In addition, the sampling of previous works is in the raw pixel space, which in fact still includes a large amount of spatial redundancy and precision redundancy. Instead, we conduct sampling in the feature space, and more compact metadata is obtained for pixels in the feature space via the adaptive allocation. The saved metadata is annotated in dashed box.", + "bbox": [ + 496, + 497, + 893, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite of these merits, raw images are not widely adopted by common users due to large file sizes. In addition, since raw images are unprocessed, additional post processing steps, e.g., demosaicing and denoising, are always needed before displaying them. For fast image rendering in practice, a copy of JPEG image is usually saved along with its raw data [2]. To improve the storage efficiency, raw-image reconstruction problem attracts more and more attention, i.e., how to minimize the amount of metadata required for de-rendering sRGB images back to raw space. Classic metadata-based raw image reconstruction methods model the workflow of image signal processing (ISP) pipeline and save the required parameters in ISP as metadata [27]. To further reduce the storage and computational complexity towards a lightweight and flexible reverse ISP reconstruction,", + "bbox": [ + 496, + 674, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18206", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6c4055c8791f7ac5d002cb91741e1216a6d035d3dc61eba554623ff011ac87d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 88, + 467, + 132 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/46f820130ab0abbf0b59180c4aae05343d8b6c3024aca9e89d667c1626cea62d.jpg", + "image_caption": [ + "(b) Processed Raw" + ], + "image_footnote": [], + "bbox": [ + 81, + 150, + 199, + 217 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d6d7eeaa2d632c09770a23ba20aff2f8e1857323924ea7bb4f45e1b2e01207dc.jpg", + "image_caption": [ + "(a) Simplified ISP adopted from [21]", + "(c) Quantized sRGB" + ], + "image_footnote": [], + "bbox": [ + 200, + 148, + 318, + 217 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/94cfe272ad593a581a0f268c50141af633cc82273d3c585356a8a7ed05060984.jpg", + "image_caption": [ + "(d) Quantization error map", + "Figure 2. An illustration of the information loss caused by the ISP. (a) A simplified ISP suffers from the information loss caused by nonlinear transformations. (b) Raw image after process to better display the details. (c) Quantized sRGB image after ISP which suffers information loss, e.g., the red bounding box area. (d) The quantization error map. As we can see from the above figures, the information loss caused by the quantization is non-uniformly distributed in both over-exposed areas and normally-exposed areas." + ], + "image_footnote": [], + "bbox": [ + 320, + 148, + 439, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "very recent methods focus on sparse sampling of raw image pixels [26, 30]. Specifically, in [30], a uniform sampling strategy is proposed to combine with an interpolation algorithm that solves systems of linear equations. The work in [26] proposes a sampling network and approximates the reconstruction process by deep learning to further improve the sampling strategy.", + "bbox": [ + 75, + 371, + 468, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Though lots of progress has been made, existing sparse sampling based raw image reconstruction methods still face limitations in terms of coding efficiency and image reconstruction quality. Specifically, the bit allocation should be adaptive and globally optimized for the image contents, given the non-linear transformation and quantization steps in ISP as shown in Fig. 2. For example, the smooth regions of an image can be well reconstructed with much sparser samples, comparing to the texture-rich regions which deserve denser sampling. In constraint, in existing practices, even for the state-of-the-art method [26] where the sampling is enforced to be locally non-uniform, it is still almost uniform from the global perspective, which causes metadata redundancy and limits the reconstruction performance. In addition, very recent works [26, 30] sample in a fixed sampling space, i.e., raw image space, with a fixed bit depth of sampled pixels, leading to limited representation ability and precision redundancy.", + "bbox": [ + 75, + 478, + 468, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above issues, instead of adopting a predefined sampling strategy or sampling loss, e.g., super-pixel loss [37], we propose a novel end-to-end learned raw image reconstruction framework based on encoded latent features. Specifically, the latent features are obtained by minimizing the reconstruction loss and its bitstream cost simultaneously. To further improve the rate-distortion performance, we propose an sRGB-guided context model based on a learnable order prediction network. Different from the commonly used auto-regressive models [9, 24] which en", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "code/decode the latent features pixel-by-pixel in a sequential way, the proposed sRGB-guided context requires much fewer steps (reduce by more than $10^{6}$ -fold) with the aid of a learned order mask, which makes the computational cost feasible while maintaining comparable performance. Fig. 1 compares the proposed raw image reconstruction method with the previous strategies [9,24].", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows,", + "bbox": [ + 517, + 196, + 821, + 210 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose the first end-to-end deep encoding framework for raw image reconstruction, by fully optimizing the use of stored metadata.", + "2. A novel sRGB-guided context model is proposed by introducing two improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed.", + "3. We evaluate our method over popular raw image datasets. The experimental results demonstrate that we can achieve better reconstruction quality with less metadata required comparing with SOTA methods." + ], + "bbox": [ + 511, + 220, + 890, + 386 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 398, + 640, + 415 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Raw image reconstruction", + "text_level": 1, + "bbox": [ + 500, + 424, + 736, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The current raw image reconstruction works can be categorized into two categories: blind raw reconstruction and raw reconstruction with metadata.", + "bbox": [ + 496, + 448, + 890, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Blind raw reconstruction. Blind raw reconstruction aims to reconstruct the raw image only based on the rendered sRGB image [32, 41]. Early works aim to recover the linearity of the image by radiometric calibration [10]. More complex models [7, 11, 18] are subsequently proposed to better describe the workflows of the ISP pipeline. With the development of the deep-learning, deep-learning based models are rapidly developing. For example, [22] directly learns a mapping from LDR (low dynamic range) to HDR (high dynamic range). [21] uses three specialized CNNs to reserve the proposed subdivided pipeline from HDR to LDR. Recently, [36] proposes to use an invertible network to learn the mapping between sRGB space and raw space and vice versa. Though great progress has been done, due to the information loss during the ISP pipeline, e.g., quantization, the fidelity of the reconstructed ones is inevitably constrained.", + "bbox": [ + 496, + 493, + 892, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Raw reconstruction with metadata. To further improve the fidelity of the raw image reconstruction, an alternative way is to save additional metadata to assist the reconstruction [26, 29, 39]. For instance, the work in [39] proposes to save a low resolution raw file to model the tone mapping curve. The works in [27, 28] propose to save the estimated parameters of the simplified ISP pipeline. The work in [30] proposes a spatial aware algorithm that estimates the parameters of interpolation during the test time based on saved uniformly sampled raw image pixels. A recent", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18207", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/77af6617d0f25af56630cbcdca88824d7a11af61c5ebddf6a3856346001db1a8.jpg", + "image_caption": [ + "Figure 3. The overall framework of our method includes three parts: (a) The encoding/decoding process maps the raw image into the latent space and vice versa. (b) The sRGB-guided context model, which is based on the iterative Gaussian entropy model, encodes/decodes the latent variable $\\hat{\\mathbf{z}}$ into/from bitstream. (c) The hyper-prior model encodes/decodes the auxiliary variable $\\hat{\\mathbf{v}}$ into/from the bitstream based on the saved channel-mean value $m(\\hat{\\mathbf{v}})$ . The blue blocks with white text represent the saved metadata, and layers in gray represent that the sRGB image is additionally concatenated to their inputs." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 890, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "work [26] improves the sampling strategy by sampling representative raw pixels based on the superpixel. Besides, a UNet is adopted [26] to further speed-up the inference process. However, the training of the sampling network is based a pre-defined loss which leads to suboptimal sampling strategy and affects the restoration performance. Different from previous works that usually save discrete pixels of raw images, we propose an end-to-end network that can learn to extract necessary metadata in the latent space.", + "bbox": [ + 75, + 465, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Learned image compression", + "text_level": 1, + "bbox": [ + 76, + 618, + 328, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, a great number of deep learning based image compression methods [4, 15, 20, 38] have been proposed and achieve promising results. End-to-end training is made possible thanks to the development of differential quantization and rate estimation [3, 4, 31]. Besides, the introduction of the contextual model [19, 24] greatly improves the compression rate of learned compression models and attracts more and more attention recently. Specifically, the works in [19, 24] propose to utilize an autoregressive model to utilize the information that already decompressed from the bitstream. However, due to the nature of the context model, both compress and decompress processes are extremely slow for the image with high resolution. To minimize the serial processing, [25] proposes a channel-conditioning and [13] proposes a checkerboard context model. Besides, though the learning-based image compression exhibits very promising results on the low bpp", + "bbox": [ + 75, + 643, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(bit per pixel) scenarios, the network architecture needs to be carefully designed for the settings that require high fidelity as shown in [14, 23].", + "bbox": [ + 498, + 465, + 892, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 530, + 633, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Motivation", + "text_level": 1, + "bbox": [ + 500, + 556, + 620, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to reconstruct the raw image $\\mathbf{x}$ which has a linear relationship with the scene radiance based on the sRGB image $\\mathbf{y}$ after the ISP pipeline. Due to the operations like quantization and tone mapping, the process from the raw image to sRGB image is non-linear and the information loss is spatially non-uniform as shown in Fig. 2. Different from the previous works that uniformly/approximately uniformly save the sparse raw-pixel values with a fixed number of bits, we propose to learn the coding of information in the latent space with an adaptively allocated number of bits for each pixel in an end-to-end manner.", + "bbox": [ + 496, + 582, + 890, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 3, our method aims to obtain a compact representation $\\hat{\\mathbf{z}}$ of the image conditioned on the corresponding sRGB image. The latent feature $\\hat{\\mathbf{z}}$ is expected to have necessary information to reconstruct the raw image with high fidelity and its code-length shall be as small as possible. To this end, we propose an sRGB-guided context model which can make better use of decoded information and greatly improve computational efficiency. Besides, an improved hyper-prior is proposed to further improve the coding efficiency and reconstruction quality.", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18208", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d622ea9c6fb513fcfd093d474c9e760d284dc96a3fec35354daa73d5ba731caf.jpg", + "image_caption": [ + "Figure 4. An illustration of a step of the proposed iterative Gaussian entropy model. We model the distribution of $\\hat{\\mathbf{z}}^{i + 1}$ based on the existing information $\\sum_{j = 0}^{i}\\hat{\\mathbf{z}}^{j}$ and $h_s(\\hat{\\mathbf{v}})$ where $\\hat{\\mathbf{v}}$ is the auxiliary variable from the hyper-prior. Then arithmetic coding is used to compress/decompress the latent code $\\hat{\\mathbf{z}}^{i + 1}$ losslessly. The dashed arrows represent the following step." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 885, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. The overall of entropy-based coding", + "text_level": 1, + "bbox": [ + 76, + 327, + 390, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, our framework can be formulated by", + "bbox": [ + 96, + 351, + 424, + 367 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} = g _ {a} (\\mathbf {x}, \\mathbf {y}; \\phi)\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 377, + 326, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} = Q (\\mathbf {z}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 396, + 468, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = g _ {s} (\\hat {\\mathbf {z}}, \\mathbf {y}; \\theta),\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 415, + 326, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}$ and $\\hat{\\mathbf{z}}$ are latent codes w/o and w/ quantization. $g_{a}$ and $g_{s}$ are the analysis and synthesis transforms. $\\phi$ and $\\theta$ represent the parameters of these two transforms respectively. $Q$ is the quantization operation. We further introduce hyperprior [5] to model spatial dependencies in $\\mathbf{z}$ as follows", + "bbox": [ + 76, + 441, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} = h _ {a} (\\mathbf {z}, \\mathbf {y}; \\phi_ {h})\n$$\n", + "text_format": "latex", + "bbox": [ + 250, + 527, + 367, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {v}} = Q (\\mathbf {v}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 251, + 547, + 468, + 563 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\leftarrow h _ {s} (\\hat {\\mathbf {v}}, \\mathbf {y}; \\theta_ {h}),\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 565, + 375, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h_a$ and $h_s$ represent the auxiliary analysis and synthesis transforms respectively, and $\\phi_h$ and $\\theta_h$ are the learned parameters of them. The optimization objective that simultaneously minimizes the raw image reconstruction loss and the codelength of latent codes is defined as follows", + "bbox": [ + 75, + 592, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\underbrace {\\mathcal {R} (\\hat {\\mathbf {z}}) + \\mathcal {R} (\\hat {\\mathbf {v}})} _ {\\text {r a t e}} + \\lambda \\cdot \\underbrace {\\mathcal {D} (\\hat {\\mathbf {x}} , \\mathbf {x})} _ {\\text {d i s t o r t i o n}} \\\\ = \\mathbb {E} \\left[ - \\log_ {2} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\right] \\tag {3} \\\\ + \\mathbb {E} [ - \\log_ {2} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) ] + \\lambda \\cdot \\mathcal {D} (\\hat {\\mathbf {x}}, \\mathbf {x}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 678, + 468, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m(\\mathbf{v})$ represents the mean value of different channels, and $\\mathcal{D}$ is the mean square error to measure the reconstruction loss. The details of the likelihood estimations of different latent codes will be introduced below.", + "bbox": [ + 75, + 762, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. The estimation of the likelihood", + "text_level": 1, + "bbox": [ + 76, + 830, + 356, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As revealed by the cross entropy $H(p,q) = H(p) + \\mathcal{D}_{KL}(p||q)$ that measures the number of extra bits to code the desired distribution $p$ using an estimated one $q$ , the key", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of reducing the code length is to accurately model the distribution of latent codes. To this end, we propose to model the distribution of different latent variables with different strategies since they depend on different information.", + "bbox": [ + 496, + 328, + 890, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following a similar way of previous works [5,9], we use a non-parametric, fully factorized density model to encode the auxiliary latent codes $\\mathbf{v}$ . However, due to the limitation of the network design, e.g., the domain of the hyper-prior model must be univariate and the network must be monotonic increasing [5], we find that there is still lots of redundant information in the auxiliary latent codes $v$ as shown in Fig. 5. To further improve the coding efficiency, we propose to additionally save the mean value of each channel $m(\\mathbf{v})$ to the metadata to reduce the redundancy. Specifically, we model the conditional distribution $q_{\\hat{\\mathbf{v}} | m(\\mathbf{v})}$ as follows", + "bbox": [ + 496, + 388, + 892, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) = \\\\ \\prod_ {i} \\left[ \\left(q _ {v _ {i} | m (\\mathbf {v})} \\left(\\psi^ {(i)}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) \\left(\\hat {\\mathbf {v}} - m (\\mathbf {v})\\right) _ {i} \\right], \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 564, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\psi^i$ is the parameters of each univariate conditional distribution $p_{v_i|m(\\mathbf{v})}$ , and $i$ is the position index.", + "bbox": [ + 496, + 628, + 890, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the encoding of $\\hat{\\mathbf{z}}$ , previous works show great improvement by introducing the context model, i.e., the already decompressed pixels can help to predict the pixels which are not decompressed yet to further improve the coding efficiency. However, due to its serialization property, the autoregressive model incurs a significant computational cost which is unacceptable in the raw image reconstruction since its high-resolution, e.g., $4000 \\times 6000$ . To improve the computational efficiency while preserve the advantages of the autoregressive model, we propose a novel sRGB-guided context model. More specifically, our proposed context model includes two parts: a learnable order prediction network $g_{m}$ as shown in Fig. 3, and an iterative Gaussian entropy model as shown in Fig. 4.", + "bbox": [ + 496, + 659, + 892, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The learnable order prediction network. As the prerequisite of our proposed context model, the order masks of com", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18209", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3f7fc52ee075ede0f073eb47f8ba811340ada6809ec03bda7859d14ac2b75ded.jpg", + "image_caption": [ + "Figure 5. Visualization of a channel of the auxiliary latent features $\\mathbf{v}$ and its value distribution." + ], + "image_footnote": [], + "bbox": [ + 106, + 103, + 460, + 199 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4bcd1bf4196e1202a7b34bf1a203baef9f97eec521e5a93b93e409d9790ffb08.jpg", + "image_caption": [ + "Figure 6. The proposed masked deconvolution layer." + ], + "image_footnote": [], + "bbox": [ + 174, + 258, + 356, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pression/decompression play a significant role. To make sampling order masks learnable, we propose a training strategy that makes end-to-end training of the whole framework feasible. Specifically, we utilize Gumbel-softmax [17] to make the binary mask derivable for training as follows", + "bbox": [ + 76, + 405, + 468, + 481 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {i, j} ^ {k} = \\frac {\\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {k}\\right) + g _ {i , j} ^ {k}\\right) / \\tau\\right)}{\\sum_ {t = 1} ^ {N} \\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {t}\\right) + g _ {i , j} ^ {t}\\right) / \\tau\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 492, + 468, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $k$ is the index of sampling masks, $N$ is the number of iterations, $\\mathbf{g} \\in \\mathbb{R}^{N \\times h \\times w}$ is a random matrix i.i.d sampled from Gumbel(0,1) distribution, $\\tau$ is a temperature hyper-parameter, and $\\mathbf{m} \\in \\mathbb{R}^{N \\times h \\times w}$ denotes unnormalized log probabilities predicted by a subnetwork. For inference, to make sure that we have exactly the same random vector $\\mathbf{g}$ during compress/decompress processes, we add a registered buffer to the model to save a pre-sampled $\\mathbf{g}$ . The pre-sampled $\\mathbf{g}$ is then cropped to the same size as the $\\mathbf{m}$ to generate a set of sparsely sampled $\\mathbf{M}^k$ .", + "bbox": [ + 75, + 542, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we find that the vanilla convolutional layer cannot well utilize the information from the randomly sparsely sampled features (can refer to the sampling mask in Fig. 9). Therefore, we further propose a new masked deconvolution layer that can alleviate negative impacts from the randomness and sparsity as shown in Fig. 6. For an input feature $\\hat{\\mathbf{z}}$ and its corresponding mask $\\mathbf{M}^c = \\sum_{i=0}^{k} \\mathbf{M}^k$ which records the positions of all already decoded ones, the output $\\hat{\\mathbf{z}}'$ is as follows", + "bbox": [ + 75, + 694, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} ^ {\\prime} = \\frac {\\operatorname {D e c o n v} (\\mathbf {z})}{\\max \\left(1 , \\operatorname {D e c o n v} _ {\\mathbf {1}} \\left(\\mathbf {M} ^ {c}\\right)\\right)}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 842, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where Deconv and $\\mathrm{Conv}_{\\mathbf{1}}$ are deconvolution layers with", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "stride of 1. Besides, $\\mathrm{Deconv}_1$ is a fixed layer that the weights are all one and the bias is zero.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The iterative Gaussian entropy model. After obtaining the predicted order mask, we can iteratively compress/decompress the information as shown in Fig 4. Specifically, we use information from the auxiliary latent variable $\\hat{\\mathbf{v}}$ and already encoded/decoded partial of $\\hat{\\mathbf{z}}$ to predict the distribution of the to-be-processed part of $\\hat{\\mathbf{z}}$ as follows", + "bbox": [ + 496, + 121, + 893, + 224 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} ^ {i + 1}, \\boldsymbol {\\sigma} ^ {i + 1} = g _ {c} \\left(g _ {z} \\left(\\left(\\sum_ {k = 0} ^ {i} \\mathbf {M} ^ {i}\\right) \\odot \\hat {\\mathbf {z}}, y\\right), h _ {s} (\\hat {\\mathbf {v}})\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 234, + 890, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ is a pixel-wise multiplication, $g_{z}$ is the masked decoder, and $g_{c}$ is the Gaussian prior module to predict the distribution of $\\hat{\\mathbf{z}}^{i + 1}$ that are not encoded. Then, the likelihood of $\\hat{\\mathbf{z}}$ is formulated as", + "bbox": [ + 496, + 285, + 890, + 345 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {z} _ {i} | \\hat {\\mathbf {v}}, \\mathbf {y}) = \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) (\\hat {z} _ {i}) \\tag {8} \\\\ = c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} + 0. 5) - c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} - 0. 5), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 352, + 890, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the subscript $i$ is the index of the pixel position, $k_{i}$ is the index of parameter groups defined in Eq. 7, and $c_{\\mu_i^{k_i},\\sigma_i^{k_i}}(\\cdot)$ is its corresponding cumulative function.", + "bbox": [ + 498, + 414, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 474, + 633, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental settings", + "text_level": 1, + "bbox": [ + 500, + 500, + 702, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We utilize two widely-used datasets, NUS dataset [8] and AdobeFiveK dataset [6], to evaluate the effectiveness of our proposed methods. These datasets are all natural images collected from different scenarios and devices. Following previous work [26,30], we use the raw image after demosaic and render sRGB images using a software ISP. Specifically, AdobeFiveK dataset [6] includes 5000 photographs taken by different photographers and devices so that it covers a wide range of scenes and lighting conditions. We randomly split the whole dataset into training set and validation set which include 4900 and 100 images respectively. For the NUS dataset [8], we select the same subsets of devices with the previous work [26].", + "bbox": [ + 496, + 523, + 890, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compared the proposed method with several SOTA methods, including InvISP [36], SAM [30], and Nam et al. [26]. Specifically, InvISP [36] is a SOTA raw image reconstruction model that utilizes a single invertible network to learn the mapping from sRGB image to raw image and vice versa. SAM [30] is a test-time adaptation model that saves the uniformly sampled raw pixels as metadata. Nam et al. [26] learn the sampling process and reconstruction process using two separate neural networks [37].", + "bbox": [ + 496, + 719, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. All the code will be released after acceptance. For training, we use a batch size of 1 and patch size of 1024 to reduce the I/O time. Adam is used as the", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18210", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b3aeebc80826d618a09ea9d7c0da9c2760b2a443d4b904571242a55d72c59ddc.jpg", + "image_caption": [ + "(a) Input (8 bit sRGB image)" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 209, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/54e6e6f207f9bdf45624c1056f6febf276658379b749208dd34e56f998710111.jpg", + "image_caption": [ + "(b) InvISP [36] (bpp: N/A)" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 338, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4103b1b9b2b66ff315dfcf6821e160d98aa7ba225e66ce403f6ce3103d41195a.jpg", + "image_caption": [ + "(c) SAM [30] (bpp: 9.52e-3)" + ], + "image_footnote": [], + "bbox": [ + 339, + 88, + 467, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e584220e4d45ade221477d58b2bdfc411075d833d5f60b35aaf27570dba40b8f.jpg", + "image_caption": [ + "(d) Nam et al. [26] (bpp: 8.44e-1)" + ], + "image_footnote": [], + "bbox": [ + 468, + 88, + 596, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bc68f48e29b92693dbd8b02cb38d310822bfd52dec00b4bba914cefc87fe7366.jpg", + "image_caption": [ + "(e) Ours (bpp: 4.90e-4)", + "Figure 7. Qualitative comparison of the raw image reconstruction results. We visualize the maximum value of the error among three channels on the pixel level. For better visualization, we apply gamma correction to the raw image to increase the visibility." + ], + "image_footnote": [], + "bbox": [ + 598, + 88, + 727, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/555805f683f9cdb2a4918579fa805f2d112d86b61e7bbe98ad2fccdaeb225018.jpg", + "image_caption": [ + "(f) Raw image (After gamma correction)" + ], + "image_footnote": [], + "bbox": [ + 733, + 88, + 890, + 359 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2b85ae320bae705717fc858763fa26c29835b154a3905d829bf8fe59aa60544e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodbppPSNRSSIM
InvISP [36]N/A52.690.99938
SAM [30]9.566e-449.610.99874
SAM [30]9.5219-354.760.99945
Nam et al. [26]8.438e-156.720.99958
Ours (w/o metadata)N/A53.030.99926
Ours4.901e-458.140.99969
", + "bbox": [ + 112, + 435, + 434, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative evaluation on AdobeFiveK dataset.", + "bbox": [ + 104, + 554, + 439, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "optimizer with a learning rate of 1e-4. We train the models for 100 epochs for AdobeFiveK dataset and 200 epochs for NUS dataset. We reduce the learning rate by a factor of 0.1 if there is no improvement in terms of the loss after every 20 epochs. For the sRGB-guided context model, we set $N = 2$ for the model conditioned on uncompressed sRGB images and $N = 4$ for the compressed JPEG data.", + "bbox": [ + 75, + 584, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental results", + "text_level": 1, + "bbox": [ + 76, + 699, + 272, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the evaluation metrics, we utilize PSNR and SSIM [34] which are widely used to evaluate the reconstruction quality with the reference image. We also utilize bpp (bit per pixel) to evaluate the coding efficiency of the model.", + "bbox": [ + 75, + 722, + 468, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Results on uncompressed sRGB data.", + "text_level": 1, + "bbox": [ + 75, + 801, + 390, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on AdobeFiveK dataset. We report the quantitative evaluation results in Table 1. As we can see in the table, raw image reconstruction models with metadata can achieve better performance than SOTA raw image reconstruction model without metadata [36]. Besides, compared", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with previous metadata-based SOTA methods [26, 30], our method achieves better reconstruction quality with lower storage overhead. Besides, to exclude the effect of network structure, we retrain and evaluate the performance of the model without the help of metadata using the same architecture as ours. Specifically, we set the original input of the raw image to zero, and remove the quantization step and code length loss. We find that its reconstruction quality is much lower than the results obtained from the same network with meta-data, which demonstrates the effectiveness of the saved metadata. Visual comparisons can be found in Fig. 7.", + "bbox": [ + 496, + 438, + 890, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on NUS dataset. We also evaluate the performance of models on NUS dataset following a similar evaluation paradigm with Nam et al. [26]. The results are reported in Table 2. As can be seen in the table, we achieve huge performance improvement compared with SOTA method Nam et al. [26] (even compared with the test-time optimization version). In addition, the number of bits we need to save as metadata is less than $0.1\\%$ of [26].", + "bbox": [ + 496, + 604, + 890, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Results on compressed sRGB data.", + "text_level": 1, + "bbox": [ + 500, + 753, + 795, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further consider a more challenging and realistic setting that we reconstruct the raw image based on compressed JPEG image. To evaluate the robustness of our method, we train a single model across different devices and JPEG quality factors. The results are reported in Table 3. As we can see, our method can adaptively allocate different bpp to JPEG images with different quality factors, i.e., assigning higher bpp to the image with worse JPEG quality. Our", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18211", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c8670a225a27f9213c699d4f85084a239c39d28f4b86eb7322b02477aaba0339.jpg", + "table_caption": [], + "table_footnote": [ + "1 The reason that the bpp of SAM [30] and Nam et al. [26] is slightly different is that Nam et al. [26] need extra bits to save the locations of sampled raw pixels as shown in Fig. 8.", + "2 For the experiments in the gray area, we use a five-fold cross validation, and report the mean and std in the table." + ], + "table_body": "
Methodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
RIR [27]3.253e-245.660.993948.420.992451.260.9982
SAM [30]7.500e-147.030.996249.350.997850.440.9982
Nam et al. [26]18.438e-148.080.996850.710.997550.490.9973
[26] w/ fine-tuning8.438e-149.570.997551.540.998053.110.9985
Ours2.887e-457.84±0.890.9997±0.0059.08±0.950.9998±0.0058.76±0.950.9997±0.00
", + "bbox": [ + 106, + 88, + 864, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. The quantitative results of NUS dataset [8] conditioned on sRGB images.", + "bbox": [ + 238, + 244, + 727, + 258 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method achieves the best reconstruction quality with the least metadata compared with previous SOTA methods.", + "bbox": [ + 75, + 280, + 468, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 318, + 227, + 334 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The comparison of bits allocation. One of the main advantages of the proposed method is that we could learn the bits allocation in an end-to-end manner. As shown in Fig. 2, the information loss is non-uniform so a good bits allocation algorithm is the core of raw image reconstruction algorithms. To this end, we visualize the bits allocation of both current SOTA methods and the proposed method in Fig. 8. In [30], the metadata are uniformly sampled in the raw pixel space, which leads to redundancy. Although Nam et al. [26] propose a superpixel based sampling network, the training of reconstruction and sampling networks are separated into two phases. In addition, even if its sampling is locally non-uniform, it still remains uniform globally, which limits the coding efficiency and reconstruction quality. As we can see in the figure, our method can adaptively allocate different bits to different areas. Specifically, for the flat area, e.g. flat area in the blue bounding box, our methods utilize few bits to encode. While for the area with more complicated context, e.g. boundary area in the blue bounding box, our method allocates relatively more bits. Besides, even for areas where we allocate bits, the need of bits is much lower than methods that sample in the raw pixel space.", + "bbox": [ + 75, + 340, + 472, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The hand-crafted metadata of v. To verify the effectiveness of our proposed modeling of the hyper-prior variable $\\hat{\\mathbf{v}}$ . We compare the models trained w/ and w/o the hand-crafted metadata $m(\\mathbf{v})$ . We keep other settings the same as in Table 3 and evaluate the models on a fold of NUS dataset. The results are reported in Table 4. As we can see in the table, there are improvements in terms of both the bpp and the reconstruction quality that benefited from the more accurate value of v and alleviated redundancy.", + "bbox": [ + 75, + 674, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The sRGB-guided context model. To better understand how the proposed context model works, we visualize each step of encoding/decoding $\\mathbf{z}$ in Fig. 9 (a). As we can see, the order of the compress/decompress process is highly-related to the context of the image, which demonstrates that our proposed context model can well utilize the information", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2985194b5b93a264e96f6f47eac8c64243e3e6255321f8f06d081900c9661fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 277, + 586, + 420 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d57e1ba5bfab709fb3de5cb165aee8e07e2ff1d5f08e3524b616aa8c820fca29.jpg", + "image_caption": [ + "Figure 8. The comparison of the bits allocation. (a) The input 8-bit sRGB image. (b)-(d) The bits allocation maps of the red bounding box area (the first row) and the blue area (the second row). For better visualization, we enlarge the size of sampled pixels in (b). It is worth noting that for (b)-(c), each sampled raw pixel needs 48 bits to save. Best zoom in for more details." + ], + "image_footnote": [], + "bbox": [ + 586, + 277, + 660, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3e80bc8fc398a0b31dacdb0cdfbb66c8fec486306ad8ac83b6cb7db107cf3dea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 660, + 277, + 764, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5bccb9866209270729fb124f16a3ce658ad808003b6bf63a8dc7f107ae1a7607.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 277, + 888, + 439 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce0d359f445ef8b88ca82a19478e3f00544cde57a03580db430f05884e260e41.jpg", + "image_caption": [ + "Figure 9. The visualization of each step of the sRGB-guided context model (a) The sampling masks from $\\mathbf{M}^0$ to $\\mathbf{M}^3$ respectively. The sampling rate and the bytes of the encoded string are displayed on the right side of the mask. (b) The bpp maps of the latent variable $z$ based on the already decoded information. Specifically, the $i_{th}$ (range from 0 to 3) bpp map is estimated using the information of $\\sum_{k = -1}^{i - 1}\\mathbf{M}^k\\odot \\hat{\\mathbf{z}}$ , where $\\mathbf{M}^{-1}$ is an all zero mask." + ], + "image_footnote": [], + "bbox": [ + 500, + 534, + 694, + 611 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b14542cf771e01709b8c32e08426eae5a6fc82df3656bb1bb57210ab84f8fe6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 535, + 794, + 609 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dcf0d68d5e98e85ee7f51b0b31ae9d0890a540fc4387ede64205e75603b03594.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 535, + 893, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from the sRGB image. The sparse sampling mask can help a model better predict the distribution of the adjacent pixels that have not been compressed/decompressed. In addition, our method gradually increases the number of sampled pixels in the latent space as more and more pixels are available to help to predict the distribution of the unseen ones, which leads to better coding efficiency. As shown in Fig. 9 (b), we can get more accurate estimation of the likelihood (i.e., smaller bpp) of $\\mathbf{z}$ with the help of already decoded $\\hat{\\mathbf{z}}$ . We also quantitatively evaluate the effectiveness of our proposed sRGB-guided context model as shown in Fig. 10. We", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18212", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/405640db28d23941d12b9f8fa006d9192a9e7b89df17d6d1da83c9be902131dc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
QualityMethodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
10InvISPN/A26.620.883629.120.898029.120.9002
SAM9.556e-424.420.894625.240.909425.560.9110
SAM9.522e-327.940.923428.220.937627.830.9374
Nam et al.8.438e-133.060.937334.030.947734.290.9506
Ours7.736e-433.130.938634.040.948234.310.9515
30InvISPN/A28.719.931631.760.942130.890.9459
SAM9.556e-428.880.934430.210.946529.650.9458
SAM9.522e-334.240.955335.870.964836.120.9677
Nam et al.8.438e-137.210.963038.700.972339.060.9750
Ours3.613e-437.400.964038.810.972939.180.9757
50InvISPN/A30.020.941632.910.952932.970.9579
SAM9.556e-430.780.944832.410.955932.050.9567
SAM9.522e-336.320.962937.770.970538.240.9739
Nam et al.8.438e-138.340.968640.070.976740.040.9797
Ours3.368e-438.670.969940.330.977640.730.9806
70InvISPN/A30.860.945832.910.955332.970.9592
SAM9.556e-432.080.952934.140.962033.900.9637
SAM9.522e-337.420.968438.960.974539.380.9780
Nam et al.8.438e-139.130.972441.010.976941.420.9825
Ours3.210e-439.590.974241.360.980741.750.9836
90InvISPN/A31.550.947633.740.959833.680.9643
SAM9.556e-434.370.966336.600.971236.780.9747
SAM9.522e-339.170.978740.790.981241.200.9843
Nam et al.8.438e-140.320.978242.330.983842.820.9864
Ours2.944e-441.190.982142.980.985643.430.9882
", + "bbox": [ + 119, + 88, + 848, + 479 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e021c91c7e3808986bea5b7152f4f80d183c97b5911955c6e3e1aa23366e9219.jpg", + "table_caption": [ + "Table 3. The quantitative results of NUS dataset [8] conditioned on the compressed JPEG image with different quality factors." + ], + "table_footnote": [], + "table_body": "
Ours w/o m(v)Ours
bpp ↓PSNRSSIMbpp ↓PSNRSSIM
Samsung2.92e-457.500.99972.88e-457.790.9997
Olympus2.93e-458.930.99972.90e-459.350.9997
Sony2.90e-459.050.99972.89e-459.240.9997
Mean2.92e-458.660.99962.89e-458.790.9997
", + "bbox": [ + 81, + 516, + 460, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. The ablation study on the proposed modeling of $\\widehat{\\mathbf{v}}$ .", + "bbox": [ + 94, + 606, + 449, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "compare our proposed sRGB-guided context model with He et al. [13] which proposes an improved context model to obtain faster speed. For a fair comparison, we directly replace our proposed context model (Fig. 3 (b)) with the checkboard one in He et al. [13] and keep other settings the same. As we can see, all models achieve very similar reconstruction quality and our method achieves much lower bpp.", + "bbox": [ + 75, + 635, + 468, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 753, + 194, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a novel approach to reconstructing raw images using compact metadata. We introduce end-to-end coding techniques that encode the metadata in the latent space using an adaptive bits allocation strategy, resulting in improved reconstruction quality and higher coding efficiency. Additionally, our proposed sRGB-guided context model leads to better reconstruction quality, smaller metadata size, and faster processing speed. We evaluate", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8ff7cd2843c5e50bbbf2ef1cd375190f443fb81c1dee22bbbd65041597968a9.jpg", + "image_caption": [ + "Figure 10. A comparison of models trained with different steps of the proposed sRGB-guided context model and He et al. [13]. The models are evaluated using JPEG images with varying quality factors (10, 30, 50, 70, 90). For all models, PSNR and SSIM decrease monotonously, with the lowering of the conditioned JPEG quality." + ], + "image_footnote": [], + "bbox": [ + 509, + 520, + 692, + 621 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f0ccca19c39ee785f2e46a55bf1e798b915ca98ab220ecf207d667a2c27a6320.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 518, + 875, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our method on widely-used datasets and the results demonstrate that our method significantly improves performance over prior methods, i.e., we achieve better reconstruction quality and smaller size of metadata.", + "bbox": [ + 496, + 703, + 890, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was done at Rapid-Rich Object Search (ROSE) Lab, Nanyang Technological University. This research is supported in part by the NTUPKU Joint Research Institute (a collaboration between the Nanyang Technological University and Peking University that is sponsored by a donation from the Ng Teng Fong Charitable Foundation), the Basic and Frontier Research Project of PCL, the Major Key Project of PCL, and the MOE AcRF Tier 1 (RG61/22) and Start-Up Grant.", + "bbox": [ + 496, + 763, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18213", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Marcus A Brubaker, and Michael S Brown. Noise flow: Noise modeling with conditional normalizing flows. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3165-3173, 2019. 1", + "[2] Adobe. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4449-4458, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 190 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18215", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_model.json b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..60ab63f045fe8dc70c422e2a8a690f9806c1220c --- /dev/null +++ b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_model.json @@ -0,0 +1,2299 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.131, + 0.795, + 0.154 + ], + "angle": 0, + "content": "Raw Image Reconstruction with Learned Compact Metadata" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.18, + 0.871, + 0.234 + ], + "angle": 0, + "content": "Yufei Wang\\(^{1}\\), Yi Yu\\(^{1}\\), Wenhan Yang\\(^{2}\\), Lanqing Guo\\(^{1}\\), Lap-Pui Chau\\(^{3}\\), Alex C. Kot\\(^{1}\\), Bihan Wen\\(^{1*}\\) \n\\(^{1}\\)Nanyang Technological University \n\\(^{2}\\)Peng Cheng Laboratory \n\\(^{3}\\)The Hong Kong Polytechnic University" + }, + { + "type": "text", + "bbox": [ + 0.211, + 0.236, + 0.76, + 0.253 + ], + "angle": 0, + "content": "{yufei001, yuyi0010, lanqing001, eackot, bihan.wen}@ntu.edu.sg" + }, + { + "type": "text", + "bbox": [ + 0.287, + 0.255, + 0.678, + 0.27 + ], + "angle": 0, + "content": "yangwh@pcl.ac.cn lap-pui.chau@polyu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.474, + 0.653 + ], + "angle": 0, + "content": "While raw images exhibit advantages over sRGB images (e.g., linearity and fine-grained quantization level), they are not widely used by common users due to the large storage requirements. Very recent works propose to compress raw images by designing the sampling masks in the raw image pixel space, leading to suboptimal image representations and redundant metadata. In this paper, we propose a novel framework to learn a compact representation in the latent space serving as the metadata in an end-to-end manner. Furthermore, we propose a novel sRGB-guided context model with the improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed. We illustrate how the proposed raw image compression scheme can adaptively allocate more bits to image regions that are important from a global perspective. The experimental results show that the proposed method can achieve superior raw image reconstruction results using a smaller size of the metadata on both uncompressed sRGB images and JPEG images. The code will be released at https://github.com/wyf0912/R2LCM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.674, + 0.21, + 0.689 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.88 + ], + "angle": 0, + "content": "As an unprocessed and uncompressed data format directly obtained from camera sensors, raw images has unique advantages for computer vision tasks in practice. For example, it is easier to model the distribution of real image noise in raw space, which enables generalized deep real denoising networks [1,40]; As pixel values in raw images have a linear relationship with scene radiance, they own benefits to recover shadows and highlights without bringing in the grainy noise usually associated with high ISO [12, 16, 33, 35], which greatly contributes to the low-light image enhancement. Besides, with richer colors, raw images offer more room for correction and artistic manipulation." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.304, + 0.887, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.382, + 0.858, + 0.395 + ], + "angle": 0, + "content": "(a) Previous SOTA methods sample in the raw space [26, 30]." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.397, + 0.887, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.474, + 0.837, + 0.487 + ], + "angle": 0, + "content": "(b) The proposed method samples in the latent space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.895, + 0.651 + ], + "angle": 0, + "content": "Figure 1. The comparison between the previous SOTA methods (in blue) and our proposed method (in green). Different from the previous work where the sampling strategy is hand-crafted or learned by a pre-defined sampling loss, we learn the sampling and reconstruction process in a unified end-to-end manner. In addition, the sampling of previous works is in the raw pixel space, which in fact still includes a large amount of spatial redundancy and precision redundancy. Instead, we conduct sampling in the feature space, and more compact metadata is obtained for pixels in the feature space via the adaptive allocation. The saved metadata is annotated in dashed box." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite of these merits, raw images are not widely adopted by common users due to large file sizes. In addition, since raw images are unprocessed, additional post processing steps, e.g., demosaicing and denoising, are always needed before displaying them. For fast image rendering in practice, a copy of JPEG image is usually saved along with its raw data [2]. To improve the storage efficiency, raw-image reconstruction problem attracts more and more attention, i.e., how to minimize the amount of metadata required for de-rendering sRGB images back to raw space. Classic metadata-based raw image reconstruction methods model the workflow of image signal processing (ISP) pipeline and save the required parameters in ISP as metadata [27]. To further reduce the storage and computational complexity towards a lightweight and flexible reverse ISP reconstruction," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18206" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.133 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.136, + 0.373, + 0.149 + ], + "angle": 0, + "content": "(a) Simplified ISP adopted from [21]" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.151, + 0.2, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.22, + 0.192, + 0.232 + ], + "angle": 0, + "content": "(b) Processed Raw" + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.15, + 0.32, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.206, + 0.22, + 0.314, + 0.232 + ], + "angle": 0, + "content": "(c) Quantized sRGB" + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.15, + 0.44, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.22, + 0.466, + 0.233 + ], + "angle": 0, + "content": "(d) Quantization error map" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.241, + 0.47, + 0.352 + ], + "angle": 0, + "content": "Figure 2. An illustration of the information loss caused by the ISP. (a) A simplified ISP suffers from the information loss caused by nonlinear transformations. (b) Raw image after process to better display the details. (c) Quantized sRGB image after ISP which suffers information loss, e.g., the red bounding box area. (d) The quantization error map. As we can see from the above figures, the information loss caused by the quantization is non-uniformly distributed in both over-exposed areas and normally-exposed areas." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.469, + 0.478 + ], + "angle": 0, + "content": "very recent methods focus on sparse sampling of raw image pixels [26, 30]. Specifically, in [30], a uniform sampling strategy is proposed to combine with an interpolation algorithm that solves systems of linear equations. The work in [26] proposes a sampling network and approximates the reconstruction process by deep learning to further improve the sampling strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Though lots of progress has been made, existing sparse sampling based raw image reconstruction methods still face limitations in terms of coding efficiency and image reconstruction quality. Specifically, the bit allocation should be adaptive and globally optimized for the image contents, given the non-linear transformation and quantization steps in ISP as shown in Fig. 2. For example, the smooth regions of an image can be well reconstructed with much sparser samples, comparing to the texture-rich regions which deserve denser sampling. In constraint, in existing practices, even for the state-of-the-art method [26] where the sampling is enforced to be locally non-uniform, it is still almost uniform from the global perspective, which causes metadata redundancy and limits the reconstruction performance. In addition, very recent works [26, 30] sample in a fixed sampling space, i.e., raw image space, with a fixed bit depth of sampled pixels, leading to limited representation ability and precision redundancy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To address the above issues, instead of adopting a predefined sampling strategy or sampling loss, e.g., super-pixel loss [37], we propose a novel end-to-end learned raw image reconstruction framework based on encoded latent features. Specifically, the latent features are obtained by minimizing the reconstruction loss and its bitstream cost simultaneously. To further improve the rate-distortion performance, we propose an sRGB-guided context model based on a learnable order prediction network. Different from the commonly used auto-regressive models [9, 24] which en" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.197 + ], + "angle": 0, + "content": "code/decode the latent features pixel-by-pixel in a sequential way, the proposed sRGB-guided context requires much fewer steps (reduce by more than \\(10^{6}\\)-fold) with the aid of a learned order mask, which makes the computational cost feasible while maintaining comparable performance. Fig. 1 compares the proposed raw image reconstruction method with the previous strategies [9,24]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.198, + 0.822, + 0.212 + ], + "angle": 0, + "content": "Our contributions are summarized as follows," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.221, + 0.891, + 0.265 + ], + "angle": 0, + "content": "1. We propose the first end-to-end deep encoding framework for raw image reconstruction, by fully optimizing the use of stored metadata." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.266, + 0.892, + 0.327 + ], + "angle": 0, + "content": "2. A novel sRGB-guided context model is proposed by introducing two improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.327, + 0.892, + 0.387 + ], + "angle": 0, + "content": "3. We evaluate our method over popular raw image datasets. The experimental results demonstrate that we can achieve better reconstruction quality with less metadata required comparing with SOTA methods." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.221, + 0.892, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.4, + 0.642, + 0.416 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.425, + 0.738, + 0.44 + ], + "angle": 0, + "content": "2.1. Raw image reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.492 + ], + "angle": 0, + "content": "The current raw image reconstruction works can be categorized into two categories: blind raw reconstruction and raw reconstruction with metadata." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.893, + 0.749 + ], + "angle": 0, + "content": "Blind raw reconstruction. Blind raw reconstruction aims to reconstruct the raw image only based on the rendered sRGB image [32, 41]. Early works aim to recover the linearity of the image by radiometric calibration [10]. More complex models [7, 11, 18] are subsequently proposed to better describe the workflows of the ISP pipeline. With the development of the deep-learning, deep-learning based models are rapidly developing. For example, [22] directly learns a mapping from LDR (low dynamic range) to HDR (high dynamic range). [21] uses three specialized CNNs to reserve the proposed subdivided pipeline from HDR to LDR. Recently, [36] proposes to use an invertible network to learn the mapping between sRGB space and raw space and vice versa. Though great progress has been done, due to the information loss during the ISP pipeline, e.g., quantization, the fidelity of the reconstructed ones is inevitably constrained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Raw reconstruction with metadata. To further improve the fidelity of the raw image reconstruction, an alternative way is to save additional metadata to assist the reconstruction [26, 29, 39]. For instance, the work in [39] proposes to save a low resolution raw file to model the tone mapping curve. The works in [27, 28] propose to save the estimated parameters of the simplified ISP pipeline. The work in [30] proposes a spatial aware algorithm that estimates the parameters of interpolation during the test time based on saved uniformly sampled raw image pixels. A recent" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18207" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.891, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.377, + 0.893, + 0.447 + ], + "angle": 0, + "content": "Figure 3. The overall framework of our method includes three parts: (a) The encoding/decoding process maps the raw image into the latent space and vice versa. (b) The sRGB-guided context model, which is based on the iterative Gaussian entropy model, encodes/decodes the latent variable \\(\\hat{\\mathbf{z}}\\) into/from bitstream. (c) The hyper-prior model encodes/decodes the auxiliary variable \\(\\hat{\\mathbf{v}}\\) into/from the bitstream based on the saved channel-mean value \\(m(\\hat{\\mathbf{v}})\\). The blue blocks with white text represent the saved metadata, and layers in gray represent that the sRGB image is additionally concatenated to their inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.603 + ], + "angle": 0, + "content": "work [26] improves the sampling strategy by sampling representative raw pixels based on the superpixel. Besides, a UNet is adopted [26] to further speed-up the inference process. However, the training of the sampling network is based a pre-defined loss which leads to suboptimal sampling strategy and affects the restoration performance. Different from previous works that usually save discrete pixels of raw images, we propose an end-to-end network that can learn to extract necessary metadata in the latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.33, + 0.635 + ], + "angle": 0, + "content": "2.2. Learned image compression" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Recently, a great number of deep learning based image compression methods [4, 15, 20, 38] have been proposed and achieve promising results. End-to-end training is made possible thanks to the development of differential quantization and rate estimation [3, 4, 31]. Besides, the introduction of the contextual model [19, 24] greatly improves the compression rate of learned compression models and attracts more and more attention recently. Specifically, the works in [19, 24] propose to utilize an autoregressive model to utilize the information that already decompressed from the bitstream. However, due to the nature of the context model, both compress and decompress processes are extremely slow for the image with high resolution. To minimize the serial processing, [25] proposes a channel-conditioning and [13] proposes a checkerboard context model. Besides, though the learning-based image compression exhibits very promising results on the low bpp" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.466, + 0.893, + 0.512 + ], + "angle": 0, + "content": "(bit per pixel) scenarios, the network architecture needs to be carefully designed for the settings that require high fidelity as shown in [14, 23]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.634, + 0.548 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.622, + 0.572 + ], + "angle": 0, + "content": "3.1. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Our goal is to reconstruct the raw image \\( \\mathbf{x} \\) which has a linear relationship with the scene radiance based on the sRGB image \\( \\mathbf{y} \\) after the ISP pipeline. Due to the operations like quantization and tone mapping, the process from the raw image to sRGB image is non-linear and the information loss is spatially non-uniform as shown in Fig. 2. Different from the previous works that uniformly/approximately uniformly save the sparse raw-pixel values with a fixed number of bits, we propose to learn the coding of information in the latent space with an adaptively allocated number of bits for each pixel in an end-to-end manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 3, our method aims to obtain a compact representation \\(\\hat{\\mathbf{z}}\\) of the image conditioned on the corresponding sRGB image. The latent feature \\(\\hat{\\mathbf{z}}\\) is expected to have necessary information to reconstruct the raw image with high fidelity and its code-length shall be as small as possible. To this end, we propose an sRGB-guided context model which can make better use of decoded information and greatly improve computational efficiency. Besides, an improved hyper-prior is proposed to further improve the coding efficiency and reconstruction quality." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18208" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.887, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 4. An illustration of a step of the proposed iterative Gaussian entropy model. We model the distribution of \\(\\hat{\\mathbf{z}}^{i + 1}\\) based on the existing information \\(\\sum_{j = 0}^{i}\\hat{\\mathbf{z}}^{j}\\) and \\(h_s(\\hat{\\mathbf{v}})\\) where \\(\\hat{\\mathbf{v}}\\) is the auxiliary variable from the hyper-prior. Then arithmetic coding is used to compress/decompress the latent code \\(\\hat{\\mathbf{z}}^{i + 1}\\) losslessly. The dashed arrows represent the following step." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.328, + 0.391, + 0.344 + ], + "angle": 0, + "content": "3.2. The overall of entropy-based coding" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.352, + 0.426, + 0.368 + ], + "angle": 0, + "content": "Specifically, our framework can be formulated by" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.378, + 0.327, + 0.394 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} = g _ {a} (\\mathbf {x}, \\mathbf {y}; \\phi)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.397, + 0.469, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} = Q (\\mathbf {z}) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.416, + 0.328, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = g _ {s} (\\hat {\\mathbf {z}}, \\mathbf {y}; \\theta),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.469, + 0.518 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}\\) and \\(\\hat{\\mathbf{z}}\\) are latent codes w/o and w/ quantization. \\(g_{a}\\) and \\(g_{s}\\) are the analysis and synthesis transforms. \\(\\phi\\) and \\(\\theta\\) represent the parameters of these two transforms respectively. \\(Q\\) is the quantization operation. We further introduce hyperprior [5] to model spatial dependencies in \\(\\mathbf{z}\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.251, + 0.529, + 0.369, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} = h _ {a} (\\mathbf {z}, \\mathbf {y}; \\phi_ {h})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.253, + 0.548, + 0.469, + 0.564 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {v}} = Q (\\mathbf {v}) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.566, + 0.376, + 0.584 + ], + "angle": 0, + "content": "\\[\nq _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\leftarrow h _ {s} (\\hat {\\mathbf {v}}, \\mathbf {y}; \\theta_ {h}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.669 + ], + "angle": 0, + "content": "where \\( h_a \\) and \\( h_s \\) represent the auxiliary analysis and synthesis transforms respectively, and \\( \\phi_h \\) and \\( \\theta_h \\) are the learned parameters of them. The optimization objective that simultaneously minimizes the raw image reconstruction loss and the codelength of latent codes is defined as follows" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.679, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\underbrace {\\mathcal {R} (\\hat {\\mathbf {z}}) + \\mathcal {R} (\\hat {\\mathbf {v}})} _ {\\text {r a t e}} + \\lambda \\cdot \\underbrace {\\mathcal {D} (\\hat {\\mathbf {x}} , \\mathbf {x})} _ {\\text {d i s t o r t i o n}} \\\\ = \\mathbb {E} \\left[ - \\log_ {2} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\right] \\tag {3} \\\\ + \\mathbb {E} [ - \\log_ {2} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) ] + \\lambda \\cdot \\mathcal {D} (\\hat {\\mathbf {x}}, \\mathbf {x}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.823 + ], + "angle": 0, + "content": "where \\(m(\\mathbf{v})\\) represents the mean value of different channels, and \\(\\mathcal{D}\\) is the mean square error to measure the reconstruction loss. The details of the likelihood estimations of different latent codes will be introduced below." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.357, + 0.848 + ], + "angle": 0, + "content": "3.3. The estimation of the likelihood" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "As revealed by the cross entropy \\( H(p,q) = H(p) + \\mathcal{D}_{KL}(p||q) \\) that measures the number of extra bits to code the desired distribution \\( p \\) using an estimated one \\( q \\), the key" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.389 + ], + "angle": 0, + "content": "of reducing the code length is to accurately model the distribution of latent codes. To this end, we propose to model the distribution of different latent variables with different strategies since they depend on different information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.893, + 0.557 + ], + "angle": 0, + "content": "Following a similar way of previous works [5,9], we use a non-parametric, fully factorized density model to encode the auxiliary latent codes \\(\\mathbf{v}\\). However, due to the limitation of the network design, e.g., the domain of the hyper-prior model must be univariate and the network must be monotonic increasing [5], we find that there is still lots of redundant information in the auxiliary latent codes \\(v\\) as shown in Fig. 5. To further improve the coding efficiency, we propose to additionally save the mean value of each channel \\(m(\\mathbf{v})\\) to the metadata to reduce the redundancy. Specifically, we model the conditional distribution \\(q_{\\hat{\\mathbf{v}} | m(\\mathbf{v})}\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.565, + 0.891, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) = \\\\ \\prod_ {i} \\left[ \\left(q _ {v _ {i} | m (\\mathbf {v})} \\left(\\psi^ {(i)}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) \\left(\\hat {\\mathbf {v}} - m (\\mathbf {v})\\right) _ {i} \\right], \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.66 + ], + "angle": 0, + "content": "where \\(\\psi^i\\) is the parameters of each univariate conditional distribution \\(p_{v_i|m(\\mathbf{v})}\\), and \\(i\\) is the position index." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.87 + ], + "angle": 0, + "content": "For the encoding of \\(\\hat{\\mathbf{z}}\\), previous works show great improvement by introducing the context model, i.e., the already decompressed pixels can help to predict the pixels which are not decompressed yet to further improve the coding efficiency. However, due to its serialization property, the autoregressive model incurs a significant computational cost which is unacceptable in the raw image reconstruction since its high-resolution, e.g., \\(4000 \\times 6000\\). To improve the computational efficiency while preserve the advantages of the autoregressive model, we propose a novel sRGB-guided context model. More specifically, our proposed context model includes two parts: a learnable order prediction network \\(g_{m}\\) as shown in Fig. 3, and an iterative Gaussian entropy model as shown in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The learnable order prediction network. As the prerequisite of our proposed context model, the order masks of com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18209" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.104, + 0.462, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.214, + 0.47, + 0.242 + ], + "angle": 0, + "content": "Figure 5. Visualization of a channel of the auxiliary latent features \\(\\mathbf{v}\\) and its value distribution." + }, + { + "type": "image", + "bbox": [ + 0.175, + 0.259, + 0.357, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.381, + 0.43, + 0.396 + ], + "angle": 0, + "content": "Figure 6. The proposed masked deconvolution layer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.406, + 0.47, + 0.482 + ], + "angle": 0, + "content": "pression/decompression play a significant role. To make sampling order masks learnable, we propose a training strategy that makes end-to-end training of the whole framework feasible. Specifically, we utilize Gumbel-softmax [17] to make the binary mask derivable for training as follows" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.493, + 0.47, + 0.534 + ], + "angle": 0, + "content": "\\[\nM _ {i, j} ^ {k} = \\frac {\\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {k}\\right) + g _ {i , j} ^ {k}\\right) / \\tau\\right)}{\\sum_ {t = 1} ^ {N} \\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {t}\\right) + g _ {i , j} ^ {t}\\right) / \\tau\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.469, + 0.693 + ], + "angle": 0, + "content": "where \\( k \\) is the index of sampling masks, \\( N \\) is the number of iterations, \\( \\mathbf{g} \\in \\mathbb{R}^{N \\times h \\times w} \\) is a random matrix i.i.d sampled from Gumbel(0,1) distribution, \\( \\tau \\) is a temperature hyper-parameter, and \\( \\mathbf{m} \\in \\mathbb{R}^{N \\times h \\times w} \\) denotes unnormalized log probabilities predicted by a subnetwork. For inference, to make sure that we have exactly the same random vector \\( \\mathbf{g} \\) during compress/decompress processes, we add a registered buffer to the model to save a pre-sampled \\( \\mathbf{g} \\). The pre-sampled \\( \\mathbf{g} \\) is then cropped to the same size as the \\( \\mathbf{m} \\) to generate a set of sparsely sampled \\( \\mathbf{M}^k \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.469, + 0.831 + ], + "angle": 0, + "content": "In addition, we find that the vanilla convolutional layer cannot well utilize the information from the randomly sparsely sampled features (can refer to the sampling mask in Fig. 9). Therefore, we further propose a new masked deconvolution layer that can alleviate negative impacts from the randomness and sparsity as shown in Fig. 6. For an input feature \\(\\hat{\\mathbf{z}}\\) and its corresponding mask \\(\\mathbf{M}^c = \\sum_{i=0}^{k} \\mathbf{M}^k\\) which records the positions of all already decoded ones, the output \\(\\hat{\\mathbf{z}}'\\) is as follows" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.843, + 0.469, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} ^ {\\prime} = \\frac {\\operatorname {D e c o n v} (\\mathbf {z})}{\\max \\left(1 , \\operatorname {D e c o n v} _ {\\mathbf {1}} \\left(\\mathbf {M} ^ {c}\\right)\\right)}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where Deconv and \\(\\mathrm{Conv}_{\\mathbf{1}}\\) are deconvolution layers with" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "stride of 1. Besides, \\(\\mathrm{Deconv}_1\\) is a fixed layer that the weights are all one and the bias is zero." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.226 + ], + "angle": 0, + "content": "The iterative Gaussian entropy model. After obtaining the predicted order mask, we can iteratively compress/decompress the information as shown in Fig 4. Specifically, we use information from the auxiliary latent variable \\(\\hat{\\mathbf{v}}\\) and already encoded/decoded partial of \\(\\hat{\\mathbf{z}}\\) to predict the distribution of the to-be-processed part of \\(\\hat{\\mathbf{z}}\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.236, + 0.892, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} ^ {i + 1}, \\boldsymbol {\\sigma} ^ {i + 1} = g _ {c} \\left(g _ {z} \\left(\\left(\\sum_ {k = 0} ^ {i} \\mathbf {M} ^ {i}\\right) \\odot \\hat {\\mathbf {z}}, y\\right), h _ {s} (\\hat {\\mathbf {v}})\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.286, + 0.892, + 0.346 + ], + "angle": 0, + "content": "where \\(\\odot\\) is a pixel-wise multiplication, \\(g_{z}\\) is the masked decoder, and \\(g_{c}\\) is the Gaussian prior module to predict the distribution of \\(\\hat{\\mathbf{z}}^{i + 1}\\) that are not encoded. Then, the likelihood of \\(\\hat{\\mathbf{z}}\\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.353, + 0.892, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {z} _ {i} | \\hat {\\mathbf {v}}, \\mathbf {y}) = \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) (\\hat {z} _ {i}) \\tag {8} \\\\ = c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} + 0. 5) - c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} - 0. 5), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.415, + 0.892, + 0.466 + ], + "angle": 0, + "content": "where the subscript \\(i\\) is the index of the pixel position, \\(k_{i}\\) is the index of parameter groups defined in Eq. 7, and \\(c_{\\mu_i^{k_i},\\sigma_i^{k_i}}(\\cdot)\\) is its corresponding cumulative function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.476, + 0.634, + 0.493 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.704, + 0.517 + ], + "angle": 0, + "content": "4.1. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Datasets. We utilize two widely-used datasets, NUS dataset [8] and AdobeFiveK dataset [6], to evaluate the effectiveness of our proposed methods. These datasets are all natural images collected from different scenarios and devices. Following previous work [26,30], we use the raw image after demosaic and render sRGB images using a software ISP. Specifically, AdobeFiveK dataset [6] includes 5000 photographs taken by different photographers and devices so that it covers a wide range of scenes and lighting conditions. We randomly split the whole dataset into training set and validation set which include 4900 and 100 images respectively. For the NUS dataset [8], we select the same subsets of devices with the previous work [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Baselines. We compared the proposed method with several SOTA methods, including InvISP [36], SAM [30], and Nam et al. [26]. Specifically, InvISP [36] is a SOTA raw image reconstruction model that utilizes a single invertible network to learn the mapping from sRGB image to raw image and vice versa. SAM [30] is a test-time adaptation model that saves the uniformly sampled raw pixels as metadata. Nam et al. [26] learn the sampling process and reconstruction process using two separate neural networks [37]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Implementation details. All the code will be released after acceptance. For training, we use a batch size of 1 and patch size of 1024 to reduce the I/O time. Adam is used as the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18210" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.21, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.362, + 0.191, + 0.384 + ], + "angle": 0, + "content": "(a) Input (8 bit sRGB image)" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.339, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.362, + 0.31, + 0.383 + ], + "angle": 0, + "content": "(b) InvISP [36] (bpp: N/A)" + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.089, + 0.468, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.362, + 0.435, + 0.383 + ], + "angle": 0, + "content": "(c) SAM [30] (bpp: 9.52e-3)" + }, + { + "type": "image", + "bbox": [ + 0.47, + 0.089, + 0.598, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.488, + 0.362, + 0.575, + 0.383 + ], + "angle": 0, + "content": "(d) Nam et al. [26] (bpp: 8.44e-1)" + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.089, + 0.728, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.628, + 0.362, + 0.696, + 0.383 + ], + "angle": 0, + "content": "(e) Ours (bpp: 4.90e-4)" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.089, + 0.892, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.362, + 0.883, + 0.383 + ], + "angle": 0, + "content": "(f) Raw image (After gamma correction)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.395, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison of the raw image reconstruction results. We visualize the maximum value of the error among three channels on the pixel level. For better visualization, we apply gamma correction to the raw image to increase the visibility." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.436, + 0.436, + 0.544 + ], + "angle": 0, + "content": "
MethodbppPSNRSSIM
InvISP [36]N/A52.690.99938
SAM [30]9.566e-449.610.99874
SAM [30]9.5219-354.760.99945
Nam et al. [26]8.438e-156.720.99958
Ours (w/o metadata)N/A53.030.99926
Ours4.901e-458.140.99969
" + }, + { + "type": "table_caption", + "bbox": [ + 0.105, + 0.555, + 0.441, + 0.568 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation on AdobeFiveK dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.47, + 0.692 + ], + "angle": 0, + "content": "optimizer with a learning rate of 1e-4. We train the models for 100 epochs for AdobeFiveK dataset and 200 epochs for NUS dataset. We reduce the learning rate by a factor of 0.1 if there is no improvement in terms of the loss after every 20 epochs. For the sRGB-guided context model, we set \\(N = 2\\) for the model conditioned on uncompressed sRGB images and \\(N = 4\\) for the compressed JPEG data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.7, + 0.274, + 0.716 + ], + "angle": 0, + "content": "4.2. Experimental results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.47, + 0.785 + ], + "angle": 0, + "content": "For the evaluation metrics, we utilize PSNR and SSIM [34] which are widely used to evaluate the reconstruction quality with the reference image. We also utilize bpp (bit per pixel) to evaluate the coding efficiency of the model." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.802, + 0.391, + 0.817 + ], + "angle": 0, + "content": "4.2.1 Results on uncompressed sRGB data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Results on AdobeFiveK dataset. We report the quantitative evaluation results in Table 1. As we can see in the table, raw image reconstruction models with metadata can achieve better performance than SOTA raw image reconstruction model without metadata [36]. Besides, compared" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.605 + ], + "angle": 0, + "content": "with previous metadata-based SOTA methods [26, 30], our method achieves better reconstruction quality with lower storage overhead. Besides, to exclude the effect of network structure, we retrain and evaluate the performance of the model without the help of metadata using the same architecture as ours. Specifically, we set the original input of the raw image to zero, and remove the quantization step and code length loss. We find that its reconstruction quality is much lower than the results obtained from the same network with meta-data, which demonstrates the effectiveness of the saved metadata. Visual comparisons can be found in Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Results on NUS dataset. We also evaluate the performance of models on NUS dataset following a similar evaluation paradigm with Nam et al. [26]. The results are reported in Table 2. As can be seen in the table, we achieve huge performance improvement compared with SOTA method Nam et al. [26] (even compared with the test-time optimization version). In addition, the number of bits we need to save as metadata is less than \\(0.1\\%\\) of [26]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.754, + 0.796, + 0.769 + ], + "angle": 0, + "content": "4.2.2 Results on compressed sRGB data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We further consider a more challenging and realistic setting that we reconstruct the raw image based on compressed JPEG image. To evaluate the robustness of our method, we train a single model across different devices and JPEG quality factors. The results are reported in Table 3. As we can see, our method can adaptively allocate different bpp to JPEG images with different quality factors, i.e., assigning higher bpp to the image with worse JPEG quality. Our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18211" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.865, + 0.198 + ], + "angle": 0, + "content": "
Methodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
RIR [27]3.253e-245.660.993948.420.992451.260.9982
SAM [30]7.500e-147.030.996249.350.997850.440.9982
Nam et al. [26]18.438e-148.080.996850.710.997550.490.9973
[26] w/ fine-tuning8.438e-149.570.997551.540.998053.110.9985
Ours2.887e-457.84±0.890.9997±0.0059.08±0.950.9998±0.0058.76±0.950.9997±0.00
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.115, + 0.199, + 0.861, + 0.228 + ], + "angle": 0, + "content": "1 The reason that the bpp of SAM [30] and Nam et al. [26] is slightly different is that Nam et al. [26] need extra bits to save the locations of sampled raw pixels as shown in Fig. 8." + }, + { + "type": "table_footnote", + "bbox": [ + 0.115, + 0.228, + 0.813, + 0.242 + ], + "angle": 0, + "content": "2 For the experiments in the gray area, we use a five-fold cross validation, and report the mean and std in the table." + }, + { + "type": "list", + "bbox": [ + 0.115, + 0.199, + 0.861, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.24, + 0.245, + 0.728, + 0.26 + ], + "angle": 0, + "content": "Table 2. The quantitative results of NUS dataset [8] conditioned on sRGB images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.47, + 0.312 + ], + "angle": 0, + "content": "method achieves the best reconstruction quality with the least metadata compared with previous SOTA methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.319, + 0.228, + 0.335 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.675 + ], + "angle": 0, + "content": "The comparison of bits allocation. One of the main advantages of the proposed method is that we could learn the bits allocation in an end-to-end manner. As shown in Fig. 2, the information loss is non-uniform so a good bits allocation algorithm is the core of raw image reconstruction algorithms. To this end, we visualize the bits allocation of both current SOTA methods and the proposed method in Fig. 8. In [30], the metadata are uniformly sampled in the raw pixel space, which leads to redundancy. Although Nam et al. [26] propose a superpixel based sampling network, the training of reconstruction and sampling networks are separated into two phases. In addition, even if its sampling is locally non-uniform, it still remains uniform globally, which limits the coding efficiency and reconstruction quality. As we can see in the figure, our method can adaptively allocate different bits to different areas. Specifically, for the flat area, e.g. flat area in the blue bounding box, our methods utilize few bits to encode. While for the area with more complicated context, e.g. boundary area in the blue bounding box, our method allocates relatively more bits. Besides, even for areas where we allocate bits, the need of bits is much lower than methods that sample in the raw pixel space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.81 + ], + "angle": 0, + "content": "The hand-crafted metadata of v. To verify the effectiveness of our proposed modeling of the hyper-prior variable \\(\\hat{\\mathbf{v}}\\). We compare the models trained w/ and w/o the hand-crafted metadata \\(m(\\mathbf{v})\\). We keep other settings the same as in Table 3 and evaluate the models on a fold of NUS dataset. The results are reported in Table 4. As we can see in the table, there are improvements in terms of both the bpp and the reconstruction quality that benefited from the more accurate value of v and alleviated redundancy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The sRGB-guided context model. To better understand how the proposed context model works, we visualize each step of encoding/decoding \\(\\mathbf{z}\\) in Fig. 9 (a). As we can see, the order of the compress/decompress process is highly-related to the context of the image, which demonstrates that our proposed context model can well utilize the information" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.279, + 0.587, + 0.421 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.588, + 0.279, + 0.661, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.279, + 0.765, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.279, + 0.889, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.445, + 0.895, + 0.529 + ], + "angle": 0, + "content": "Figure 8. The comparison of the bits allocation. (a) The input 8-bit sRGB image. (b)-(d) The bits allocation maps of the red bounding box area (the first row) and the blue area (the second row). For better visualization, we enlarge the size of sampled pixels in (b). It is worth noting that for (b)-(c), each sampled raw pixel needs 48 bits to save. Best zoom in for more details." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.535, + 0.695, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.536, + 0.795, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.536, + 0.895, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.719 + ], + "angle": 0, + "content": "Figure 9. The visualization of each step of the sRGB-guided context model (a) The sampling masks from \\(\\mathbf{M}^0\\) to \\(\\mathbf{M}^3\\) respectively. The sampling rate and the bytes of the encoded string are displayed on the right side of the mask. (b) The bpp maps of the latent variable \\(z\\) based on the already decoded information. Specifically, the \\(i_{th}\\) (range from 0 to 3) bpp map is estimated using the information of \\(\\sum_{k = -1}^{i - 1}\\mathbf{M}^k\\odot \\hat{\\mathbf{z}}\\), where \\(\\mathbf{M}^{-1}\\) is an all zero mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "from the sRGB image. The sparse sampling mask can help a model better predict the distribution of the adjacent pixels that have not been compressed/decompressed. In addition, our method gradually increases the number of sampled pixels in the latent space as more and more pixels are available to help to predict the distribution of the unseen ones, which leads to better coding efficiency. As shown in Fig. 9 (b), we can get more accurate estimation of the likelihood (i.e., smaller bpp) of \\(\\mathbf{z}\\) with the help of already decoded \\(\\hat{\\mathbf{z}}\\). We also quantitatively evaluate the effectiveness of our proposed sRGB-guided context model as shown in Fig. 10. We" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18212" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.849, + 0.48 + ], + "angle": 0, + "content": "
QualityMethodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
10InvISPN/A26.620.883629.120.898029.120.9002
SAM9.556e-424.420.894625.240.909425.560.9110
SAM9.522e-327.940.923428.220.937627.830.9374
Nam et al.8.438e-133.060.937334.030.947734.290.9506
Ours7.736e-433.130.938634.040.948234.310.9515
30InvISPN/A28.719.931631.760.942130.890.9459
SAM9.556e-428.880.934430.210.946529.650.9458
SAM9.522e-334.240.955335.870.964836.120.9677
Nam et al.8.438e-137.210.963038.700.972339.060.9750
Ours3.613e-437.400.964038.810.972939.180.9757
50InvISPN/A30.020.941632.910.952932.970.9579
SAM9.556e-430.780.944832.410.955932.050.9567
SAM9.522e-336.320.962937.770.970538.240.9739
Nam et al.8.438e-138.340.968640.070.976740.040.9797
Ours3.368e-438.670.969940.330.977640.730.9806
70InvISPN/A30.860.945832.910.955332.970.9592
SAM9.556e-432.080.952934.140.962033.900.9637
SAM9.522e-337.420.968438.960.974539.380.9780
Nam et al.8.438e-139.130.972441.010.976941.420.9825
Ours3.210e-439.590.974241.360.980741.750.9836
90InvISPN/A31.550.947633.740.959833.680.9643
SAM9.556e-434.370.966336.600.971236.780.9747
SAM9.522e-339.170.978740.790.981241.200.9843
Nam et al.8.438e-140.320.978242.330.983842.820.9864
Ours2.944e-441.190.982142.980.985643.430.9882
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.485, + 0.856, + 0.5 + ], + "angle": 0, + "content": "Table 3. The quantitative results of NUS dataset [8] conditioned on the compressed JPEG image with different quality factors." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.517, + 0.462, + 0.603 + ], + "angle": 0, + "content": "
Ours w/o m(v)Ours
bpp ↓PSNRSSIMbpp ↓PSNRSSIM
Samsung2.92e-457.500.99972.88e-457.790.9997
Olympus2.93e-458.930.99972.90e-459.350.9997
Sony2.90e-459.050.99972.89e-459.240.9997
Mean2.92e-458.660.99962.89e-458.790.9997
" + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.607, + 0.45, + 0.621 + ], + "angle": 0, + "content": "Table 4. The ablation study on the proposed modeling of \\( \\widehat{\\mathbf{v}} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.743 + ], + "angle": 0, + "content": "compare our proposed sRGB-guided context model with He et al. [13] which proposes an improved context model to obtain faster speed. For a fair comparison, we directly replace our proposed context model (Fig. 3 (b)) with the checkboard one in He et al. [13] and keep other settings the same. As we can see, all models achieve very similar reconstruction quality and our method achieves much lower bpp." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.196, + 0.77 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present a novel approach to reconstructing raw images using compact metadata. We introduce end-to-end coding techniques that encode the metadata in the latent space using an adaptive bits allocation strategy, resulting in improved reconstruction quality and higher coding efficiency. Additionally, our proposed sRGB-guided context model leads to better reconstruction quality, smaller metadata size, and faster processing speed. We evaluate" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.521, + 0.693, + 0.622 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.52, + 0.876, + 0.622 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.625, + 0.894, + 0.696 + ], + "angle": 0, + "content": "Figure 10. A comparison of models trained with different steps of the proposed sRGB-guided context model and He et al. [13]. The models are evaluated using JPEG images with varying quality factors (10, 30, 50, 70, 90). For all models, PSNR and SSIM decrease monotonously, with the lowering of the conditioned JPEG quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.763 + ], + "angle": 0, + "content": "our method on widely-used datasets and the results demonstrate that our method significantly improves performance over prior methods, i.e., we achieve better reconstruction quality and smaller size of metadata." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was done at Rapid-Rich Object Search (ROSE) Lab, Nanyang Technological University. This research is supported in part by the NTUPKU Joint Research Institute (a collaboration between the Nanyang Technological University and Peking University that is sponsored by a donation from the Ng Teng Fong Charitable Foundation), the Basic and Frontier Research Project of PCL, the Major Key Project of PCL, and the MOE AcRF Tier 1 (RG61/22) and Start-Up Grant." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18213" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Marcus A Brubaker, and Michael S Brown. Noise flow: Noise modeling with conditional normalizing flows. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4449-4458, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18215" + } + ] +] \ No newline at end of file diff --git a/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_origin.pdf b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5026f44c9ca8acb9a08b12b4754eb8b671ccfd80 --- /dev/null +++ b/2023/Raw Image Reconstruction With Learned Compact Metadata/8175d738-aa28-456a-99d1-d591bc04940f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9f4a766433270ff9cf8eb65a6019957267569d40647b976a8dd200cf39e2d0e1 +size 5105152 diff --git a/2023/Raw Image Reconstruction With Learned Compact Metadata/full.md b/2023/Raw Image Reconstruction With Learned Compact Metadata/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f358e29f9a284955926f014a3c80341ace7b7a76 --- /dev/null +++ b/2023/Raw Image Reconstruction With Learned Compact Metadata/full.md @@ -0,0 +1,338 @@ +# Raw Image Reconstruction with Learned Compact Metadata + +Yufei Wang $^{1}$ , Yi Yu $^{1}$ , Wenhan Yang $^{2}$ , Lanqing Guo $^{1}$ , Lap-Pui Chau $^{3}$ , Alex C. Kot $^{1}$ , Bihan Wen $^{1*}$ $^{1}$ Nanyang Technological University + $^{2}$ Peng Cheng Laboratory + $^{3}$ The Hong Kong Polytechnic University + +{yufei001, yuyi0010, lanqing001, eackot, bihan.wen}@ntu.edu.sg + +yangwh@pcl.ac.cn lap-pui.chau@polyu.edu.hk + +# Abstract + +While raw images exhibit advantages over sRGB images (e.g., linearity and fine-grained quantization level), they are not widely used by common users due to the large storage requirements. Very recent works propose to compress raw images by designing the sampling masks in the raw image pixel space, leading to suboptimal image representations and redundant metadata. In this paper, we propose a novel framework to learn a compact representation in the latent space serving as the metadata in an end-to-end manner. Furthermore, we propose a novel sRGB-guided context model with the improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed. We illustrate how the proposed raw image compression scheme can adaptively allocate more bits to image regions that are important from a global perspective. The experimental results show that the proposed method can achieve superior raw image reconstruction results using a smaller size of the metadata on both uncompressed sRGB images and JPEG images. The code will be released at https://github.com/wyf0912/R2LCM. + +# 1. Introduction + +As an unprocessed and uncompressed data format directly obtained from camera sensors, raw images has unique advantages for computer vision tasks in practice. For example, it is easier to model the distribution of real image noise in raw space, which enables generalized deep real denoising networks [1,40]; As pixel values in raw images have a linear relationship with scene radiance, they own benefits to recover shadows and highlights without bringing in the grainy noise usually associated with high ISO [12, 16, 33, 35], which greatly contributes to the low-light image enhancement. Besides, with richer colors, raw images offer more room for correction and artistic manipulation. + +![](images/6ba3ce45feacda37d7c46a445c47cc965acc505f254328e4a6d2cef573350f91.jpg) +(a) Previous SOTA methods sample in the raw space [26, 30]. + +![](images/be417a1597ce76872e07da88f1ef2779c506bca9c36a223f77cd2fd1278d3e12.jpg) +(b) The proposed method samples in the latent space. + +Figure 1. The comparison between the previous SOTA methods (in blue) and our proposed method (in green). Different from the previous work where the sampling strategy is hand-crafted or learned by a pre-defined sampling loss, we learn the sampling and reconstruction process in a unified end-to-end manner. In addition, the sampling of previous works is in the raw pixel space, which in fact still includes a large amount of spatial redundancy and precision redundancy. Instead, we conduct sampling in the feature space, and more compact metadata is obtained for pixels in the feature space via the adaptive allocation. The saved metadata is annotated in dashed box. + +Despite of these merits, raw images are not widely adopted by common users due to large file sizes. In addition, since raw images are unprocessed, additional post processing steps, e.g., demosaicing and denoising, are always needed before displaying them. For fast image rendering in practice, a copy of JPEG image is usually saved along with its raw data [2]. To improve the storage efficiency, raw-image reconstruction problem attracts more and more attention, i.e., how to minimize the amount of metadata required for de-rendering sRGB images back to raw space. Classic metadata-based raw image reconstruction methods model the workflow of image signal processing (ISP) pipeline and save the required parameters in ISP as metadata [27]. To further reduce the storage and computational complexity towards a lightweight and flexible reverse ISP reconstruction, + +![](images/6c4055c8791f7ac5d002cb91741e1216a6d035d3dc61eba554623ff011ac87d4.jpg) + +![](images/46f820130ab0abbf0b59180c4aae05343d8b6c3024aca9e89d667c1626cea62d.jpg) +(b) Processed Raw + +![](images/d6d7eeaa2d632c09770a23ba20aff2f8e1857323924ea7bb4f45e1b2e01207dc.jpg) +(a) Simplified ISP adopted from [21] +(c) Quantized sRGB + +![](images/94cfe272ad593a581a0f268c50141af633cc82273d3c585356a8a7ed05060984.jpg) +(d) Quantization error map +Figure 2. An illustration of the information loss caused by the ISP. (a) A simplified ISP suffers from the information loss caused by nonlinear transformations. (b) Raw image after process to better display the details. (c) Quantized sRGB image after ISP which suffers information loss, e.g., the red bounding box area. (d) The quantization error map. As we can see from the above figures, the information loss caused by the quantization is non-uniformly distributed in both over-exposed areas and normally-exposed areas. + +very recent methods focus on sparse sampling of raw image pixels [26, 30]. Specifically, in [30], a uniform sampling strategy is proposed to combine with an interpolation algorithm that solves systems of linear equations. The work in [26] proposes a sampling network and approximates the reconstruction process by deep learning to further improve the sampling strategy. + +Though lots of progress has been made, existing sparse sampling based raw image reconstruction methods still face limitations in terms of coding efficiency and image reconstruction quality. Specifically, the bit allocation should be adaptive and globally optimized for the image contents, given the non-linear transformation and quantization steps in ISP as shown in Fig. 2. For example, the smooth regions of an image can be well reconstructed with much sparser samples, comparing to the texture-rich regions which deserve denser sampling. In constraint, in existing practices, even for the state-of-the-art method [26] where the sampling is enforced to be locally non-uniform, it is still almost uniform from the global perspective, which causes metadata redundancy and limits the reconstruction performance. In addition, very recent works [26, 30] sample in a fixed sampling space, i.e., raw image space, with a fixed bit depth of sampled pixels, leading to limited representation ability and precision redundancy. + +To address the above issues, instead of adopting a predefined sampling strategy or sampling loss, e.g., super-pixel loss [37], we propose a novel end-to-end learned raw image reconstruction framework based on encoded latent features. Specifically, the latent features are obtained by minimizing the reconstruction loss and its bitstream cost simultaneously. To further improve the rate-distortion performance, we propose an sRGB-guided context model based on a learnable order prediction network. Different from the commonly used auto-regressive models [9, 24] which en + +code/decode the latent features pixel-by-pixel in a sequential way, the proposed sRGB-guided context requires much fewer steps (reduce by more than $10^{6}$ -fold) with the aid of a learned order mask, which makes the computational cost feasible while maintaining comparable performance. Fig. 1 compares the proposed raw image reconstruction method with the previous strategies [9,24]. + +Our contributions are summarized as follows, + +1. We propose the first end-to-end deep encoding framework for raw image reconstruction, by fully optimizing the use of stored metadata. +2. A novel sRGB-guided context model is proposed by introducing two improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed. +3. We evaluate our method over popular raw image datasets. The experimental results demonstrate that we can achieve better reconstruction quality with less metadata required comparing with SOTA methods. + +# 2. Related Work + +# 2.1. Raw image reconstruction + +The current raw image reconstruction works can be categorized into two categories: blind raw reconstruction and raw reconstruction with metadata. + +Blind raw reconstruction. Blind raw reconstruction aims to reconstruct the raw image only based on the rendered sRGB image [32, 41]. Early works aim to recover the linearity of the image by radiometric calibration [10]. More complex models [7, 11, 18] are subsequently proposed to better describe the workflows of the ISP pipeline. With the development of the deep-learning, deep-learning based models are rapidly developing. For example, [22] directly learns a mapping from LDR (low dynamic range) to HDR (high dynamic range). [21] uses three specialized CNNs to reserve the proposed subdivided pipeline from HDR to LDR. Recently, [36] proposes to use an invertible network to learn the mapping between sRGB space and raw space and vice versa. Though great progress has been done, due to the information loss during the ISP pipeline, e.g., quantization, the fidelity of the reconstructed ones is inevitably constrained. + +Raw reconstruction with metadata. To further improve the fidelity of the raw image reconstruction, an alternative way is to save additional metadata to assist the reconstruction [26, 29, 39]. For instance, the work in [39] proposes to save a low resolution raw file to model the tone mapping curve. The works in [27, 28] propose to save the estimated parameters of the simplified ISP pipeline. The work in [30] proposes a spatial aware algorithm that estimates the parameters of interpolation during the test time based on saved uniformly sampled raw image pixels. A recent + +![](images/77af6617d0f25af56630cbcdca88824d7a11af61c5ebddf6a3856346001db1a8.jpg) +Figure 3. The overall framework of our method includes three parts: (a) The encoding/decoding process maps the raw image into the latent space and vice versa. (b) The sRGB-guided context model, which is based on the iterative Gaussian entropy model, encodes/decodes the latent variable $\hat{\mathbf{z}}$ into/from bitstream. (c) The hyper-prior model encodes/decodes the auxiliary variable $\hat{\mathbf{v}}$ into/from the bitstream based on the saved channel-mean value $m(\hat{\mathbf{v}})$ . The blue blocks with white text represent the saved metadata, and layers in gray represent that the sRGB image is additionally concatenated to their inputs. + +work [26] improves the sampling strategy by sampling representative raw pixels based on the superpixel. Besides, a UNet is adopted [26] to further speed-up the inference process. However, the training of the sampling network is based a pre-defined loss which leads to suboptimal sampling strategy and affects the restoration performance. Different from previous works that usually save discrete pixels of raw images, we propose an end-to-end network that can learn to extract necessary metadata in the latent space. + +# 2.2. Learned image compression + +Recently, a great number of deep learning based image compression methods [4, 15, 20, 38] have been proposed and achieve promising results. End-to-end training is made possible thanks to the development of differential quantization and rate estimation [3, 4, 31]. Besides, the introduction of the contextual model [19, 24] greatly improves the compression rate of learned compression models and attracts more and more attention recently. Specifically, the works in [19, 24] propose to utilize an autoregressive model to utilize the information that already decompressed from the bitstream. However, due to the nature of the context model, both compress and decompress processes are extremely slow for the image with high resolution. To minimize the serial processing, [25] proposes a channel-conditioning and [13] proposes a checkerboard context model. Besides, though the learning-based image compression exhibits very promising results on the low bpp + +(bit per pixel) scenarios, the network architecture needs to be carefully designed for the settings that require high fidelity as shown in [14, 23]. + +# 3. Methodology + +# 3.1. Motivation + +Our goal is to reconstruct the raw image $\mathbf{x}$ which has a linear relationship with the scene radiance based on the sRGB image $\mathbf{y}$ after the ISP pipeline. Due to the operations like quantization and tone mapping, the process from the raw image to sRGB image is non-linear and the information loss is spatially non-uniform as shown in Fig. 2. Different from the previous works that uniformly/approximately uniformly save the sparse raw-pixel values with a fixed number of bits, we propose to learn the coding of information in the latent space with an adaptively allocated number of bits for each pixel in an end-to-end manner. + +As shown in Fig. 3, our method aims to obtain a compact representation $\hat{\mathbf{z}}$ of the image conditioned on the corresponding sRGB image. The latent feature $\hat{\mathbf{z}}$ is expected to have necessary information to reconstruct the raw image with high fidelity and its code-length shall be as small as possible. To this end, we propose an sRGB-guided context model which can make better use of decoded information and greatly improve computational efficiency. Besides, an improved hyper-prior is proposed to further improve the coding efficiency and reconstruction quality. + +![](images/d622ea9c6fb513fcfd093d474c9e760d284dc96a3fec35354daa73d5ba731caf.jpg) +Figure 4. An illustration of a step of the proposed iterative Gaussian entropy model. We model the distribution of $\hat{\mathbf{z}}^{i + 1}$ based on the existing information $\sum_{j = 0}^{i}\hat{\mathbf{z}}^{j}$ and $h_s(\hat{\mathbf{v}})$ where $\hat{\mathbf{v}}$ is the auxiliary variable from the hyper-prior. Then arithmetic coding is used to compress/decompress the latent code $\hat{\mathbf{z}}^{i + 1}$ losslessly. The dashed arrows represent the following step. + +# 3.2. The overall of entropy-based coding + +Specifically, our framework can be formulated by + +$$ +\mathbf {z} = g _ {a} (\mathbf {x}, \mathbf {y}; \phi) +$$ + +$$ +\hat {\mathbf {z}} = Q (\mathbf {z}) \tag {1} +$$ + +$$ +\hat {\mathbf {x}} = g _ {s} (\hat {\mathbf {z}}, \mathbf {y}; \theta), +$$ + +where $\mathbf{z}$ and $\hat{\mathbf{z}}$ are latent codes w/o and w/ quantization. $g_{a}$ and $g_{s}$ are the analysis and synthesis transforms. $\phi$ and $\theta$ represent the parameters of these two transforms respectively. $Q$ is the quantization operation. We further introduce hyperprior [5] to model spatial dependencies in $\mathbf{z}$ as follows + +$$ +\mathbf {v} = h _ {a} (\mathbf {z}, \mathbf {y}; \phi_ {h}) +$$ + +$$ +\hat {\mathbf {v}} = Q (\mathbf {v}) \tag {2} +$$ + +$$ +q _ {\hat {\mathbf {z}} | \hat {\mathbf {v}}, \mathbf {y}} (\hat {\mathbf {z}} | \hat {\mathbf {v}}, \mathbf {y}) \leftarrow h _ {s} (\hat {\mathbf {v}}, \mathbf {y}; \theta_ {h}), +$$ + +where $h_a$ and $h_s$ represent the auxiliary analysis and synthesis transforms respectively, and $\phi_h$ and $\theta_h$ are the learned parameters of them. The optimization objective that simultaneously minimizes the raw image reconstruction loss and the codelength of latent codes is defined as follows + +$$ +\begin{array}{l} \mathcal {L} = \underbrace {\mathcal {R} (\hat {\mathbf {z}}) + \mathcal {R} (\hat {\mathbf {v}})} _ {\text {r a t e}} + \lambda \cdot \underbrace {\mathcal {D} (\hat {\mathbf {x}} , \mathbf {x})} _ {\text {d i s t o r t i o n}} \\ = \mathbb {E} \left[ - \log_ {2} q _ {\hat {\mathbf {z}} | \hat {\mathbf {v}}, \mathbf {y}} (\hat {\mathbf {z}} | \hat {\mathbf {v}}, \mathbf {y}) \right] \tag {3} \\ + \mathbb {E} [ - \log_ {2} q _ {\hat {\mathbf {v}} | m (\mathbf {v})} (\hat {\mathbf {v}} | m (\mathbf {v})) ] + \lambda \cdot \mathcal {D} (\hat {\mathbf {x}}, \mathbf {x}), \\ \end{array} +$$ + +where $m(\mathbf{v})$ represents the mean value of different channels, and $\mathcal{D}$ is the mean square error to measure the reconstruction loss. The details of the likelihood estimations of different latent codes will be introduced below. + +# 3.3. The estimation of the likelihood + +As revealed by the cross entropy $H(p,q) = H(p) + \mathcal{D}_{KL}(p||q)$ that measures the number of extra bits to code the desired distribution $p$ using an estimated one $q$ , the key + +of reducing the code length is to accurately model the distribution of latent codes. To this end, we propose to model the distribution of different latent variables with different strategies since they depend on different information. + +Following a similar way of previous works [5,9], we use a non-parametric, fully factorized density model to encode the auxiliary latent codes $\mathbf{v}$ . However, due to the limitation of the network design, e.g., the domain of the hyper-prior model must be univariate and the network must be monotonic increasing [5], we find that there is still lots of redundant information in the auxiliary latent codes $v$ as shown in Fig. 5. To further improve the coding efficiency, we propose to additionally save the mean value of each channel $m(\mathbf{v})$ to the metadata to reduce the redundancy. Specifically, we model the conditional distribution $q_{\hat{\mathbf{v}} | m(\mathbf{v})}$ as follows + +$$ +\begin{array}{l} q _ {\hat {\mathbf {v}} | m (\mathbf {v})} (\hat {\mathbf {v}} | m (\mathbf {v})) = \\ \prod_ {i} \left[ \left(q _ {v _ {i} | m (\mathbf {v})} \left(\psi^ {(i)}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right)\right) \left(\hat {\mathbf {v}} - m (\mathbf {v})\right) _ {i} \right], \tag {4} \\ \end{array} +$$ + +where $\psi^i$ is the parameters of each univariate conditional distribution $p_{v_i|m(\mathbf{v})}$ , and $i$ is the position index. + +For the encoding of $\hat{\mathbf{z}}$ , previous works show great improvement by introducing the context model, i.e., the already decompressed pixels can help to predict the pixels which are not decompressed yet to further improve the coding efficiency. However, due to its serialization property, the autoregressive model incurs a significant computational cost which is unacceptable in the raw image reconstruction since its high-resolution, e.g., $4000 \times 6000$ . To improve the computational efficiency while preserve the advantages of the autoregressive model, we propose a novel sRGB-guided context model. More specifically, our proposed context model includes two parts: a learnable order prediction network $g_{m}$ as shown in Fig. 3, and an iterative Gaussian entropy model as shown in Fig. 4. + +The learnable order prediction network. As the prerequisite of our proposed context model, the order masks of com + +![](images/3f7fc52ee075ede0f073eb47f8ba811340ada6809ec03bda7859d14ac2b75ded.jpg) +Figure 5. Visualization of a channel of the auxiliary latent features $\mathbf{v}$ and its value distribution. + +![](images/4bcd1bf4196e1202a7b34bf1a203baef9f97eec521e5a93b93e409d9790ffb08.jpg) +Figure 6. The proposed masked deconvolution layer. + +pression/decompression play a significant role. To make sampling order masks learnable, we propose a training strategy that makes end-to-end training of the whole framework feasible. Specifically, we utilize Gumbel-softmax [17] to make the binary mask derivable for training as follows + +$$ +M _ {i, j} ^ {k} = \frac {\exp \left(\left(\log \left(m _ {i , j} ^ {k}\right) + g _ {i , j} ^ {k}\right) / \tau\right)}{\sum_ {t = 1} ^ {N} \exp \left(\left(\log \left(m _ {i , j} ^ {t}\right) + g _ {i , j} ^ {t}\right) / \tau\right)}, \tag {5} +$$ + +where $k$ is the index of sampling masks, $N$ is the number of iterations, $\mathbf{g} \in \mathbb{R}^{N \times h \times w}$ is a random matrix i.i.d sampled from Gumbel(0,1) distribution, $\tau$ is a temperature hyper-parameter, and $\mathbf{m} \in \mathbb{R}^{N \times h \times w}$ denotes unnormalized log probabilities predicted by a subnetwork. For inference, to make sure that we have exactly the same random vector $\mathbf{g}$ during compress/decompress processes, we add a registered buffer to the model to save a pre-sampled $\mathbf{g}$ . The pre-sampled $\mathbf{g}$ is then cropped to the same size as the $\mathbf{m}$ to generate a set of sparsely sampled $\mathbf{M}^k$ . + +In addition, we find that the vanilla convolutional layer cannot well utilize the information from the randomly sparsely sampled features (can refer to the sampling mask in Fig. 9). Therefore, we further propose a new masked deconvolution layer that can alleviate negative impacts from the randomness and sparsity as shown in Fig. 6. For an input feature $\hat{\mathbf{z}}$ and its corresponding mask $\mathbf{M}^c = \sum_{i=0}^{k} \mathbf{M}^k$ which records the positions of all already decoded ones, the output $\hat{\mathbf{z}}'$ is as follows + +$$ +\hat {\mathbf {z}} ^ {\prime} = \frac {\operatorname {D e c o n v} (\mathbf {z})}{\max \left(1 , \operatorname {D e c o n v} _ {\mathbf {1}} \left(\mathbf {M} ^ {c}\right)\right)}, \tag {6} +$$ + +where Deconv and $\mathrm{Conv}_{\mathbf{1}}$ are deconvolution layers with + +stride of 1. Besides, $\mathrm{Deconv}_1$ is a fixed layer that the weights are all one and the bias is zero. + +The iterative Gaussian entropy model. After obtaining the predicted order mask, we can iteratively compress/decompress the information as shown in Fig 4. Specifically, we use information from the auxiliary latent variable $\hat{\mathbf{v}}$ and already encoded/decoded partial of $\hat{\mathbf{z}}$ to predict the distribution of the to-be-processed part of $\hat{\mathbf{z}}$ as follows + +$$ +\boldsymbol {\mu} ^ {i + 1}, \boldsymbol {\sigma} ^ {i + 1} = g _ {c} \left(g _ {z} \left(\left(\sum_ {k = 0} ^ {i} \mathbf {M} ^ {i}\right) \odot \hat {\mathbf {z}}, y\right), h _ {s} (\hat {\mathbf {v}})\right), \tag {7} +$$ + +where $\odot$ is a pixel-wise multiplication, $g_{z}$ is the masked decoder, and $g_{c}$ is the Gaussian prior module to predict the distribution of $\hat{\mathbf{z}}^{i + 1}$ that are not encoded. Then, the likelihood of $\hat{\mathbf{z}}$ is formulated as + +$$ +\begin{array}{l} q _ {\hat {\mathbf {z}} | \hat {\mathbf {v}}, \mathbf {y}} (\hat {z} _ {i} | \hat {\mathbf {v}}, \mathbf {y}) = \left(\mathcal {N} \left(\mu_ {i} ^ {k _ {i}}, \sigma_ {i} ^ {k _ {i}}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right)\right) (\hat {z} _ {i}) \tag {8} \\ = c _ {\mu_ {i} ^ {k _ {i}}, \sigma_ {i} ^ {k _ {i}}} (\hat {z} _ {i} + 0. 5) - c _ {\mu_ {i} ^ {k _ {i}}, \sigma_ {i} ^ {k _ {i}}} (\hat {z} _ {i} - 0. 5), \\ \end{array} +$$ + +where the subscript $i$ is the index of the pixel position, $k_{i}$ is the index of parameter groups defined in Eq. 7, and $c_{\mu_i^{k_i},\sigma_i^{k_i}}(\cdot)$ is its corresponding cumulative function. + +# 4. Experiments + +# 4.1. Experimental settings + +Datasets. We utilize two widely-used datasets, NUS dataset [8] and AdobeFiveK dataset [6], to evaluate the effectiveness of our proposed methods. These datasets are all natural images collected from different scenarios and devices. Following previous work [26,30], we use the raw image after demosaic and render sRGB images using a software ISP. Specifically, AdobeFiveK dataset [6] includes 5000 photographs taken by different photographers and devices so that it covers a wide range of scenes and lighting conditions. We randomly split the whole dataset into training set and validation set which include 4900 and 100 images respectively. For the NUS dataset [8], we select the same subsets of devices with the previous work [26]. + +Baselines. We compared the proposed method with several SOTA methods, including InvISP [36], SAM [30], and Nam et al. [26]. Specifically, InvISP [36] is a SOTA raw image reconstruction model that utilizes a single invertible network to learn the mapping from sRGB image to raw image and vice versa. SAM [30] is a test-time adaptation model that saves the uniformly sampled raw pixels as metadata. Nam et al. [26] learn the sampling process and reconstruction process using two separate neural networks [37]. + +Implementation details. All the code will be released after acceptance. For training, we use a batch size of 1 and patch size of 1024 to reduce the I/O time. Adam is used as the + +![](images/b3aeebc80826d618a09ea9d7c0da9c2760b2a443d4b904571242a55d72c59ddc.jpg) +(a) Input (8 bit sRGB image) + +![](images/54e6e6f207f9bdf45624c1056f6febf276658379b749208dd34e56f998710111.jpg) +(b) InvISP [36] (bpp: N/A) + +![](images/4103b1b9b2b66ff315dfcf6821e160d98aa7ba225e66ce403f6ce3103d41195a.jpg) +(c) SAM [30] (bpp: 9.52e-3) + +![](images/e584220e4d45ade221477d58b2bdfc411075d833d5f60b35aaf27570dba40b8f.jpg) +(d) Nam et al. [26] (bpp: 8.44e-1) + +![](images/bc68f48e29b92693dbd8b02cb38d310822bfd52dec00b4bba914cefc87fe7366.jpg) +(e) Ours (bpp: 4.90e-4) +Figure 7. Qualitative comparison of the raw image reconstruction results. We visualize the maximum value of the error among three channels on the pixel level. For better visualization, we apply gamma correction to the raw image to increase the visibility. + +![](images/555805f683f9cdb2a4918579fa805f2d112d86b61e7bbe98ad2fccdaeb225018.jpg) +(f) Raw image (After gamma correction) + +
MethodbppPSNRSSIM
InvISP [36]N/A52.690.99938
SAM [30]9.566e-449.610.99874
SAM [30]9.5219-354.760.99945
Nam et al. [26]8.438e-156.720.99958
Ours (w/o metadata)N/A53.030.99926
Ours4.901e-458.140.99969
+ +Table 1. Quantitative evaluation on AdobeFiveK dataset. + +optimizer with a learning rate of 1e-4. We train the models for 100 epochs for AdobeFiveK dataset and 200 epochs for NUS dataset. We reduce the learning rate by a factor of 0.1 if there is no improvement in terms of the loss after every 20 epochs. For the sRGB-guided context model, we set $N = 2$ for the model conditioned on uncompressed sRGB images and $N = 4$ for the compressed JPEG data. + +# 4.2. Experimental results + +For the evaluation metrics, we utilize PSNR and SSIM [34] which are widely used to evaluate the reconstruction quality with the reference image. We also utilize bpp (bit per pixel) to evaluate the coding efficiency of the model. + +# 4.2.1 Results on uncompressed sRGB data. + +Results on AdobeFiveK dataset. We report the quantitative evaluation results in Table 1. As we can see in the table, raw image reconstruction models with metadata can achieve better performance than SOTA raw image reconstruction model without metadata [36]. Besides, compared + +with previous metadata-based SOTA methods [26, 30], our method achieves better reconstruction quality with lower storage overhead. Besides, to exclude the effect of network structure, we retrain and evaluate the performance of the model without the help of metadata using the same architecture as ours. Specifically, we set the original input of the raw image to zero, and remove the quantization step and code length loss. We find that its reconstruction quality is much lower than the results obtained from the same network with meta-data, which demonstrates the effectiveness of the saved metadata. Visual comparisons can be found in Fig. 7. + +Results on NUS dataset. We also evaluate the performance of models on NUS dataset following a similar evaluation paradigm with Nam et al. [26]. The results are reported in Table 2. As can be seen in the table, we achieve huge performance improvement compared with SOTA method Nam et al. [26] (even compared with the test-time optimization version). In addition, the number of bits we need to save as metadata is less than $0.1\%$ of [26]. + +# 4.2.2 Results on compressed sRGB data. + +We further consider a more challenging and realistic setting that we reconstruct the raw image based on compressed JPEG image. To evaluate the robustness of our method, we train a single model across different devices and JPEG quality factors. The results are reported in Table 3. As we can see, our method can adaptively allocate different bpp to JPEG images with different quality factors, i.e., assigning higher bpp to the image with worse JPEG quality. Our + +
Methodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
RIR [27]3.253e-245.660.993948.420.992451.260.9982
SAM [30]7.500e-147.030.996249.350.997850.440.9982
Nam et al. [26]18.438e-148.080.996850.710.997550.490.9973
[26] w/ fine-tuning8.438e-149.570.997551.540.998053.110.9985
Ours2.887e-457.84±0.890.9997±0.0059.08±0.950.9998±0.0058.76±0.950.9997±0.00
+ +1 The reason that the bpp of SAM [30] and Nam et al. [26] is slightly different is that Nam et al. [26] need extra bits to save the locations of sampled raw pixels as shown in Fig. 8. +2 For the experiments in the gray area, we use a five-fold cross validation, and report the mean and std in the table. + +Table 2. The quantitative results of NUS dataset [8] conditioned on sRGB images. + +method achieves the best reconstruction quality with the least metadata compared with previous SOTA methods. + +# 4.3. Ablation study + +The comparison of bits allocation. One of the main advantages of the proposed method is that we could learn the bits allocation in an end-to-end manner. As shown in Fig. 2, the information loss is non-uniform so a good bits allocation algorithm is the core of raw image reconstruction algorithms. To this end, we visualize the bits allocation of both current SOTA methods and the proposed method in Fig. 8. In [30], the metadata are uniformly sampled in the raw pixel space, which leads to redundancy. Although Nam et al. [26] propose a superpixel based sampling network, the training of reconstruction and sampling networks are separated into two phases. In addition, even if its sampling is locally non-uniform, it still remains uniform globally, which limits the coding efficiency and reconstruction quality. As we can see in the figure, our method can adaptively allocate different bits to different areas. Specifically, for the flat area, e.g. flat area in the blue bounding box, our methods utilize few bits to encode. While for the area with more complicated context, e.g. boundary area in the blue bounding box, our method allocates relatively more bits. Besides, even for areas where we allocate bits, the need of bits is much lower than methods that sample in the raw pixel space. + +The hand-crafted metadata of v. To verify the effectiveness of our proposed modeling of the hyper-prior variable $\hat{\mathbf{v}}$ . We compare the models trained w/ and w/o the hand-crafted metadata $m(\mathbf{v})$ . We keep other settings the same as in Table 3 and evaluate the models on a fold of NUS dataset. The results are reported in Table 4. As we can see in the table, there are improvements in terms of both the bpp and the reconstruction quality that benefited from the more accurate value of v and alleviated redundancy. + +The sRGB-guided context model. To better understand how the proposed context model works, we visualize each step of encoding/decoding $\mathbf{z}$ in Fig. 9 (a). As we can see, the order of the compress/decompress process is highly-related to the context of the image, which demonstrates that our proposed context model can well utilize the information + +![](images/b2985194b5b93a264e96f6f47eac8c64243e3e6255321f8f06d081900c9661fd.jpg) + +![](images/d57e1ba5bfab709fb3de5cb165aee8e07e2ff1d5f08e3524b616aa8c820fca29.jpg) +Figure 8. The comparison of the bits allocation. (a) The input 8-bit sRGB image. (b)-(d) The bits allocation maps of the red bounding box area (the first row) and the blue area (the second row). For better visualization, we enlarge the size of sampled pixels in (b). It is worth noting that for (b)-(c), each sampled raw pixel needs 48 bits to save. Best zoom in for more details. + +![](images/3e80bc8fc398a0b31dacdb0cdfbb66c8fec486306ad8ac83b6cb7db107cf3dea.jpg) + +![](images/5bccb9866209270729fb124f16a3ce658ad808003b6bf63a8dc7f107ae1a7607.jpg) + +![](images/ce0d359f445ef8b88ca82a19478e3f00544cde57a03580db430f05884e260e41.jpg) +Figure 9. The visualization of each step of the sRGB-guided context model (a) The sampling masks from $\mathbf{M}^0$ to $\mathbf{M}^3$ respectively. The sampling rate and the bytes of the encoded string are displayed on the right side of the mask. (b) The bpp maps of the latent variable $z$ based on the already decoded information. Specifically, the $i_{th}$ (range from 0 to 3) bpp map is estimated using the information of $\sum_{k = -1}^{i - 1}\mathbf{M}^k\odot \hat{\mathbf{z}}$ , where $\mathbf{M}^{-1}$ is an all zero mask. + +![](images/4b14542cf771e01709b8c32e08426eae5a6fc82df3656bb1bb57210ab84f8fe6.jpg) + +![](images/dcf0d68d5e98e85ee7f51b0b31ae9d0890a540fc4387ede64205e75603b03594.jpg) + +from the sRGB image. The sparse sampling mask can help a model better predict the distribution of the adjacent pixels that have not been compressed/decompressed. In addition, our method gradually increases the number of sampled pixels in the latent space as more and more pixels are available to help to predict the distribution of the unseen ones, which leads to better coding efficiency. As shown in Fig. 9 (b), we can get more accurate estimation of the likelihood (i.e., smaller bpp) of $\mathbf{z}$ with the help of already decoded $\hat{\mathbf{z}}$ . We also quantitatively evaluate the effectiveness of our proposed sRGB-guided context model as shown in Fig. 10. We + +
QualityMethodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
10InvISPN/A26.620.883629.120.898029.120.9002
SAM9.556e-424.420.894625.240.909425.560.9110
SAM9.522e-327.940.923428.220.937627.830.9374
Nam et al.8.438e-133.060.937334.030.947734.290.9506
Ours7.736e-433.130.938634.040.948234.310.9515
30InvISPN/A28.719.931631.760.942130.890.9459
SAM9.556e-428.880.934430.210.946529.650.9458
SAM9.522e-334.240.955335.870.964836.120.9677
Nam et al.8.438e-137.210.963038.700.972339.060.9750
Ours3.613e-437.400.964038.810.972939.180.9757
50InvISPN/A30.020.941632.910.952932.970.9579
SAM9.556e-430.780.944832.410.955932.050.9567
SAM9.522e-336.320.962937.770.970538.240.9739
Nam et al.8.438e-138.340.968640.070.976740.040.9797
Ours3.368e-438.670.969940.330.977640.730.9806
70InvISPN/A30.860.945832.910.955332.970.9592
SAM9.556e-432.080.952934.140.962033.900.9637
SAM9.522e-337.420.968438.960.974539.380.9780
Nam et al.8.438e-139.130.972441.010.976941.420.9825
Ours3.210e-439.590.974241.360.980741.750.9836
90InvISPN/A31.550.947633.740.959833.680.9643
SAM9.556e-434.370.966336.600.971236.780.9747
SAM9.522e-339.170.978740.790.981241.200.9843
Nam et al.8.438e-140.320.978242.330.983842.820.9864
Ours2.944e-441.190.982142.980.985643.430.9882
+ +Table 3. The quantitative results of NUS dataset [8] conditioned on the compressed JPEG image with different quality factors. + +
Ours w/o m(v)Ours
bpp ↓PSNRSSIMbpp ↓PSNRSSIM
Samsung2.92e-457.500.99972.88e-457.790.9997
Olympus2.93e-458.930.99972.90e-459.350.9997
Sony2.90e-459.050.99972.89e-459.240.9997
Mean2.92e-458.660.99962.89e-458.790.9997
+ +Table 4. The ablation study on the proposed modeling of $\widehat{\mathbf{v}}$ . + +compare our proposed sRGB-guided context model with He et al. [13] which proposes an improved context model to obtain faster speed. For a fair comparison, we directly replace our proposed context model (Fig. 3 (b)) with the checkboard one in He et al. [13] and keep other settings the same. As we can see, all models achieve very similar reconstruction quality and our method achieves much lower bpp. + +# 5. Conclusion + +In this paper, we present a novel approach to reconstructing raw images using compact metadata. We introduce end-to-end coding techniques that encode the metadata in the latent space using an adaptive bits allocation strategy, resulting in improved reconstruction quality and higher coding efficiency. Additionally, our proposed sRGB-guided context model leads to better reconstruction quality, smaller metadata size, and faster processing speed. We evaluate + +![](images/a8ff7cd2843c5e50bbbf2ef1cd375190f443fb81c1dee22bbbd65041597968a9.jpg) +Figure 10. A comparison of models trained with different steps of the proposed sRGB-guided context model and He et al. [13]. The models are evaluated using JPEG images with varying quality factors (10, 30, 50, 70, 90). For all models, PSNR and SSIM decrease monotonously, with the lowering of the conditioned JPEG quality. + +![](images/f0ccca19c39ee785f2e46a55bf1e798b915ca98ab220ecf207d667a2c27a6320.jpg) + +our method on widely-used datasets and the results demonstrate that our method significantly improves performance over prior methods, i.e., we achieve better reconstruction quality and smaller size of metadata. + +Acknowledgement. This work was done at Rapid-Rich Object Search (ROSE) Lab, Nanyang Technological University. This research is supported in part by the NTUPKU Joint Research Institute (a collaboration between the Nanyang Technological University and Peking University that is sponsored by a donation from the Ng Teng Fong Charitable Foundation), the Basic and Frontier Research Project of PCL, the Major Key Project of PCL, and the MOE AcRF Tier 1 (RG61/22) and Start-Up Grant. + +# References + +[1] Abdelrahman Abdelhamed, Marcus A Brubaker, and Michael S Brown. Noise flow: Noise modeling with conditional normalizing flows. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3165-3173, 2019. 1 +[2] Adobe. Digital negative (png) specification. https:// www.kronometric.org/phot/processing/DNG/ dng_spec_1.4.0.0.pdf. 1 +[3] Eirikur Agustsson, Fabian Mentzer, Michael Tschannen, Lukas Cavigelli, Radu Timofte, Luca Benini, and Luc V Gool. Soft-to-hard vector quantization for end-to-end learning compressible representations. 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Very recent works propose to compress raw images by designing the sampling masks in the raw image pixel space, leading to suboptimal image representations and redundant metadata. In this paper, we propose a novel framework to learn a compact representation in the latent space serving as the metadata in an end-to-end manner. Furthermore, we propose a novel sRGB-guided context model with the improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed. We illustrate how the proposed raw image compression scheme can adaptively allocate more bits to image regions that are important from a global perspective. The experimental results show that the proposed method can achieve superior raw image reconstruction results using a smaller size of the metadata on both uncompressed sRGB images and JPEG images. The code will be released at https://github.com/wyf0912/R2LCM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "type": "text", + "content": "As an unprocessed and uncompressed data format directly obtained from camera sensors, raw images has unique advantages for computer vision tasks in practice. For example, it is easier to model the distribution of real image noise in raw space, which enables generalized deep real denoising networks [1,40]; As pixel values in raw images have a linear relationship with scene radiance, they own benefits to recover shadows and highlights without bringing in the grainy noise usually associated with high ISO [12, 16, 33, 35], which greatly contributes to the low-light image enhancement. Besides, with richer colors, raw images offer more room for correction and artistic manipulation." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 240, + 542, + 300 + ], + "blocks": [ + { + "bbox": [ + 310, + 240, + 542, + 300 + ], + "lines": [ + { + "bbox": [ + 310, + 240, + 542, + 300 + ], + "spans": [ + { + "bbox": [ + 310, + 240, + 542, + 300 + ], + "type": "image", + "image_path": "6ba3ce45feacda37d7c46a445c47cc965acc505f254328e4a6d2cef573350f91.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 302, + 525, + 312 + ], + "lines": [ + { + "bbox": [ + 326, + 302, + 525, + 312 + ], + "spans": [ + { + "bbox": [ + 326, + 302, + 525, + 312 + ], + "type": "text", + "content": "(a) Previous SOTA methods sample in the raw space [26, 30]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 314, + 542, + 370 + ], + "blocks": [ + { + "bbox": [ + 310, + 314, + 542, + 370 + ], + "lines": [ + { + "bbox": [ + 310, + 314, + 542, + 370 + ], + "spans": [ + { + "bbox": [ + 310, + 314, + 542, + 370 + ], + "type": "image", + "image_path": "be417a1597ce76872e07da88f1ef2779c506bca9c36a223f77cd2fd1278d3e12.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 375, + 512, + 385 + ], + "lines": [ + { + "bbox": [ + 339, + 375, + 512, + 385 + ], + "spans": [ + { + "bbox": [ + 339, + 375, + 512, + 385 + ], + "type": "text", + "content": "(b) The proposed method samples in the latent space." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 394, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 547, + 515 + ], + "type": "text", + "content": "Figure 1. The comparison between the previous SOTA methods (in blue) and our proposed method (in green). Different from the previous work where the sampling strategy is hand-crafted or learned by a pre-defined sampling loss, we learn the sampling and reconstruction process in a unified end-to-end manner. In addition, the sampling of previous works is in the raw pixel space, which in fact still includes a large amount of spatial redundancy and precision redundancy. Instead, we conduct sampling in the feature space, and more compact metadata is obtained for pixels in the feature space via the adaptive allocation. The saved metadata is annotated in dashed box." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": "Despite of these merits, raw images are not widely adopted by common users due to large file sizes. In addition, since raw images are unprocessed, additional post processing steps, e.g., demosaicing and denoising, are always needed before displaying them. For fast image rendering in practice, a copy of JPEG image is usually saved along with its raw data [2]. To improve the storage efficiency, raw-image reconstruction problem attracts more and more attention, i.e., how to minimize the amount of metadata required for de-rendering sRGB images back to raw space. Classic metadata-based raw image reconstruction methods model the workflow of image signal processing (ISP) pipeline and save the required parameters in ISP as metadata [27]. To further reduce the storage and computational complexity towards a lightweight and flexible reverse ISP reconstruction," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18206" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 286, + 105 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 105 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 105 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 105 + ], + "type": "image", + "image_path": "6c4055c8791f7ac5d002cb91741e1216a6d035d3dc61eba554623ff011ac87d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 119, + 122, + 172 + ], + "blocks": [ + { + "bbox": [ + 50, + 119, + 122, + 172 + ], + "lines": [ + { + "bbox": [ + 50, + 119, + 122, + 172 + ], + "spans": [ + { + "bbox": [ + 50, + 119, + 122, + 172 + ], + "type": "image", + "image_path": "46f820130ab0abbf0b59180c4aae05343d8b6c3024aca9e89d667c1626cea62d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 174, + 117, + 183 + ], + "lines": [ + { + "bbox": [ + 55, + 174, + 117, + 183 + ], + "spans": [ + { + "bbox": [ + 55, + 174, + 117, + 183 + ], + "type": "text", + "content": "(b) Processed Raw" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 123, + 118, + 195, + 172 + ], + "blocks": [ + { + "bbox": [ + 107, + 107, + 228, + 118 + ], + "lines": [ + { + "bbox": [ + 107, + 107, + 228, + 118 + ], + "spans": [ + { + "bbox": [ + 107, + 107, + 228, + 118 + ], + "type": "text", + "content": "(a) Simplified ISP adopted from [21]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 123, + 118, + 195, + 172 + ], + "lines": [ + { + "bbox": [ + 123, + 118, + 195, + 172 + ], + "spans": [ + { + "bbox": [ + 123, + 118, + 195, + 172 + ], + "type": "image", + "image_path": "d6d7eeaa2d632c09770a23ba20aff2f8e1857323924ea7bb4f45e1b2e01207dc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 126, + 174, + 192, + 183 + ], + "lines": [ + { + "bbox": [ + 126, + 174, + 192, + 183 + ], + "spans": [ + { + "bbox": [ + 126, + 174, + 192, + 183 + ], + "type": "text", + "content": "(c) Quantized sRGB" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 196, + 118, + 269, + 173 + ], + "blocks": [ + { + "bbox": [ + 196, + 118, + 269, + 173 + ], + "lines": [ + { + "bbox": [ + 196, + 118, + 269, + 173 + ], + "spans": [ + { + "bbox": [ + 196, + 118, + 269, + 173 + ], + "type": "image", + "image_path": "94cfe272ad593a581a0f268c50141af633cc82273d3c585356a8a7ed05060984.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 197, + 174, + 285, + 184 + ], + "lines": [ + { + "bbox": [ + 197, + 174, + 285, + 184 + ], + "spans": [ + { + "bbox": [ + 197, + 174, + 285, + 184 + ], + "type": "text", + "content": "(d) Quantization error map" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "type": "text", + "content": "Figure 2. An illustration of the information loss caused by the ISP. (a) A simplified ISP suffers from the information loss caused by nonlinear transformations. (b) Raw image after process to better display the details. (c) Quantized sRGB image after ISP which suffers information loss, e.g., the red bounding box area. (d) The quantization error map. As we can see from the above figures, the information loss caused by the quantization is non-uniformly distributed in both over-exposed areas and normally-exposed areas." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 294, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 378 + ], + "type": "text", + "content": "very recent methods focus on sparse sampling of raw image pixels [26, 30]. Specifically, in [30], a uniform sampling strategy is proposed to combine with an interpolation algorithm that solves systems of linear equations. The work in [26] proposes a sampling network and approximates the reconstruction process by deep learning to further improve the sampling strategy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 379, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 594 + ], + "type": "text", + "content": "Though lots of progress has been made, existing sparse sampling based raw image reconstruction methods still face limitations in terms of coding efficiency and image reconstruction quality. Specifically, the bit allocation should be adaptive and globally optimized for the image contents, given the non-linear transformation and quantization steps in ISP as shown in Fig. 2. For example, the smooth regions of an image can be well reconstructed with much sparser samples, comparing to the texture-rich regions which deserve denser sampling. In constraint, in existing practices, even for the state-of-the-art method [26] where the sampling is enforced to be locally non-uniform, it is still almost uniform from the global perspective, which causes metadata redundancy and limits the reconstruction performance. In addition, very recent works [26, 30] sample in a fixed sampling space, i.e., raw image space, with a fixed bit depth of sampled pixels, leading to limited representation ability and precision redundancy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "To address the above issues, instead of adopting a predefined sampling strategy or sampling loss, e.g., super-pixel loss [37], we propose a novel end-to-end learned raw image reconstruction framework based on encoded latent features. Specifically, the latent features are obtained by minimizing the reconstruction loss and its bitstream cost simultaneously. To further improve the rate-distortion performance, we propose an sRGB-guided context model based on a learnable order prediction network. Different from the commonly used auto-regressive models [9, 24] which en" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "code/decode the latent features pixel-by-pixel in a sequential way, the proposed sRGB-guided context requires much fewer steps (reduce by more than " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "10^{6}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "-fold) with the aid of a learned order mask, which makes the computational cost feasible while maintaining comparable performance. Fig. 1 compares the proposed raw image reconstruction method with the previous strategies [9,24]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 156, + 503, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 156, + 503, + 167 + ], + "spans": [ + { + "bbox": [ + 317, + 156, + 503, + 167 + ], + "type": "text", + "content": "Our contributions are summarized as follows," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 175, + 545, + 306 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 313, + 175, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 175, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 545, + 209 + ], + "type": "text", + "content": "1. We propose the first end-to-end deep encoding framework for raw image reconstruction, by fully optimizing the use of stored metadata." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 210, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 210, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 313, + 210, + 545, + 258 + ], + "type": "text", + "content": "2. A novel sRGB-guided context model is proposed by introducing two improved entropy estimation strategies, which leads to better reconstruction quality, smaller size of metadata, and faster speed." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 258, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 258, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 545, + 306 + ], + "type": "text", + "content": "3. We evaluate our method over popular raw image datasets. The experimental results demonstrate that we can achieve better reconstruction quality with less metadata required comparing with SOTA methods." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 336, + 451, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 336, + 451, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 451, + 348 + ], + "type": "text", + "content": "2.1. Raw image reconstruction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 355, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 389 + ], + "type": "text", + "content": "The current raw image reconstruction works can be categorized into two categories: blind raw reconstruction and raw reconstruction with metadata." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 391, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 546, + 593 + ], + "type": "text", + "content": "Blind raw reconstruction. Blind raw reconstruction aims to reconstruct the raw image only based on the rendered sRGB image [32, 41]. Early works aim to recover the linearity of the image by radiometric calibration [10]. More complex models [7, 11, 18] are subsequently proposed to better describe the workflows of the ISP pipeline. With the development of the deep-learning, deep-learning based models are rapidly developing. For example, [22] directly learns a mapping from LDR (low dynamic range) to HDR (high dynamic range). [21] uses three specialized CNNs to reserve the proposed subdivided pipeline from HDR to LDR. Recently, [36] proposes to use an invertible network to learn the mapping between sRGB space and raw space and vice versa. Though great progress has been done, due to the information loss during the ISP pipeline, e.g., quantization, the fidelity of the reconstructed ones is inevitably constrained." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Raw reconstruction with metadata. To further improve the fidelity of the raw image reconstruction, an alternative way is to save additional metadata to assist the reconstruction [26, 29, 39]. For instance, the work in [39] proposes to save a low resolution raw file to model the tone mapping curve. The works in [27, 28] propose to save the estimated parameters of the simplified ISP pipeline. The work in [30] proposes a spatial aware algorithm that estimates the parameters of interpolation during the test time based on saved uniformly sampled raw image pixels. A recent" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18207" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 545, + 289 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 545, + 289 + ], + "type": "image", + "image_path": "77af6617d0f25af56630cbcdca88824d7a11af61c5ebddf6a3856346001db1a8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "text", + "content": "Figure 3. The overall framework of our method includes three parts: (a) The encoding/decoding process maps the raw image into the latent space and vice versa. (b) The sRGB-guided context model, which is based on the iterative Gaussian entropy model, encodes/decodes the latent variable " + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "text", + "content": " into/from bitstream. (c) The hyper-prior model encodes/decodes the auxiliary variable " + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}" + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "text", + "content": " into/from the bitstream based on the saved channel-mean value " + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "inline_equation", + "content": "m(\\hat{\\mathbf{v}})" + }, + { + "bbox": [ + 46, + 298, + 546, + 354 + ], + "type": "text", + "content": ". The blue blocks with white text represent the saved metadata, and layers in gray represent that the sRGB image is additionally concatenated to their inputs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 477 + ], + "type": "text", + "content": "work [26] improves the sampling strategy by sampling representative raw pixels based on the superpixel. Besides, a UNet is adopted [26] to further speed-up the inference process. However, the training of the sampling network is based a pre-defined loss which leads to suboptimal sampling strategy and affects the restoration performance. Different from previous works that usually save discrete pixels of raw images, we propose an end-to-end network that can learn to extract necessary metadata in the latent space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 490, + 201, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 201, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 201, + 502 + ], + "type": "text", + "content": "2.2. Learned image compression" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": "Recently, a great number of deep learning based image compression methods [4, 15, 20, 38] have been proposed and achieve promising results. End-to-end training is made possible thanks to the development of differential quantization and rate estimation [3, 4, 31]. Besides, the introduction of the contextual model [19, 24] greatly improves the compression rate of learned compression models and attracts more and more attention recently. Specifically, the works in [19, 24] propose to utilize an autoregressive model to utilize the information that already decompressed from the bitstream. However, due to the nature of the context model, both compress and decompress processes are extremely slow for the image with high resolution. To minimize the serial processing, [25] proposes a channel-conditioning and [13] proposes a checkerboard context model. Besides, though the learning-based image compression exhibits very promising results on the low bpp" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "content": "(bit per pixel) scenarios, the network architecture needs to be carefully designed for the settings that require high fidelity as shown in [14, 23]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 420, + 388, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 388, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 388, + 434 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 441, + 380, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 380, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 380, + 453 + ], + "type": "text", + "content": "3.1. Motivation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "text", + "content": "Our goal is to reconstruct the raw image " + }, + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "text", + "content": " which has a linear relationship with the scene radiance based on the sRGB image " + }, + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 461, + 545, + 592 + ], + "type": "text", + "content": " after the ISP pipeline. Due to the operations like quantization and tone mapping, the process from the raw image to sRGB image is non-linear and the information loss is spatially non-uniform as shown in Fig. 2. Different from the previous works that uniformly/approximately uniformly save the sparse raw-pixel values with a fixed number of bits, we propose to learn the coding of information in the latent space with an adaptively allocated number of bits for each pixel in an end-to-end manner." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "As shown in Fig. 3, our method aims to obtain a compact representation " + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": " of the image conditioned on the corresponding sRGB image. The latent feature " + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": " is expected to have necessary information to reconstruct the raw image with high fidelity and its code-length shall be as small as possible. To this end, we propose an sRGB-guided context model which can make better use of decoded information and greatly improve computational efficiency. Besides, an improved hyper-prior is proposed to further improve the coding efficiency and reconstruction quality." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18208" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 542, + 190 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 542, + 190 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 542, + 190 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 542, + 190 + ], + "type": "image", + "image_path": "d622ea9c6fb513fcfd093d474c9e760d284dc96a3fec35354daa73d5ba731caf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": "Figure 4. An illustration of a step of the proposed iterative Gaussian entropy model. We model the distribution of " + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{i + 1}" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": " based on the existing information " + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\sum_{j = 0}^{i}\\hat{\\mathbf{z}}^{j}" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "inline_equation", + "content": "h_s(\\hat{\\mathbf{v}})" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": " is the auxiliary variable from the hyper-prior. Then arithmetic coding is used to compress/decompress the latent code " + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{i + 1}" + }, + { + "bbox": [ + 46, + 204, + 547, + 240 + ], + "type": "text", + "content": " losslessly. The dashed arrows represent the following step." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 259, + 239, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 239, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 239, + 272 + ], + "type": "text", + "content": "3.2. The overall of entropy-based coding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 278, + 260, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 278, + 260, + 291 + ], + "spans": [ + { + "bbox": [ + 59, + 278, + 260, + 291 + ], + "type": "text", + "content": "Specifically, our framework can be formulated by" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 299, + 200, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 299, + 200, + 312 + ], + "spans": [ + { + "bbox": [ + 133, + 299, + 200, + 312 + ], + "type": "interline_equation", + "content": "\\mathbf {z} = g _ {a} (\\mathbf {x}, \\mathbf {y}; \\phi)", + "image_path": "df499bcb5b0e9e82cf3ad9a3321a38cf445710be9473cd4f118105abc83d352d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 314, + 287, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 314, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 134, + 314, + 287, + 327 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} = Q (\\mathbf {z}) \\tag {1}", + "image_path": "172f312827b55e6bd438a44531415a35c4c515c36b70981e424fcb14427b7fd5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 133, + 329, + 200, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 329, + 200, + 342 + ], + "spans": [ + { + "bbox": [ + 133, + 329, + 200, + 342 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = g _ {s} (\\hat {\\mathbf {z}}, \\mathbf {y}; \\theta),", + "image_path": "0629e738188aa0a305cde17c4a5fe32ad9d1136dc3251d5d7b947ecbfa5b7a20.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " are latent codes w/o and w/ quantization. " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "g_{a}" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "g_{s}" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " are the analysis and synthesis transforms. " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " represent the parameters of these two transforms respectively. " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " is the quantization operation. We further introduce hyperprior [5] to model spatial dependencies in " + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 350, + 287, + 410 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 153, + 418, + 225, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 418, + 225, + 431 + ], + "spans": [ + { + "bbox": [ + 153, + 418, + 225, + 431 + ], + "type": "interline_equation", + "content": "\\mathbf {v} = h _ {a} (\\mathbf {z}, \\mathbf {y}; \\phi_ {h})", + "image_path": "d2ba31e4f418fc59b8f4a542fe6cf02e79e0ba21428e93107a148a876fc37c5d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 154, + 434, + 287, + 446 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 154, + 434, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 154, + 434, + 287, + 446 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {v}} = Q (\\mathbf {v}) \\tag {2}", + "image_path": "9834fbd3aae0adda8f553ffd07d7cfb03eb397cef9db05441e1051c14e87d381.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 448, + 230, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 448, + 230, + 462 + ], + "spans": [ + { + "bbox": [ + 104, + 448, + 230, + 462 + ], + "type": "interline_equation", + "content": "q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\leftarrow h _ {s} (\\hat {\\mathbf {v}}, \\mathbf {y}; \\theta_ {h}),", + "image_path": "628e59cc9f80589abb8a73c6637b6587146a5ea5ec0dd03a7adf1fda53dc610e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "inline_equation", + "content": "h_a" + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "inline_equation", + "content": "h_s" + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": " represent the auxiliary analysis and synthesis transforms respectively, and " + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\phi_h" + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": " are the learned parameters of them. The optimization objective that simultaneously minimizes the raw image reconstruction loss and the codelength of latent codes is defined as follows" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 70, + 537, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 537, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 70, + 537, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\underbrace {\\mathcal {R} (\\hat {\\mathbf {z}}) + \\mathcal {R} (\\hat {\\mathbf {v}})} _ {\\text {r a t e}} + \\lambda \\cdot \\underbrace {\\mathcal {D} (\\hat {\\mathbf {x}} , \\mathbf {x})} _ {\\text {d i s t o r t i o n}} \\\\ = \\mathbb {E} \\left[ - \\log_ {2} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}) \\right] \\tag {3} \\\\ + \\mathbb {E} [ - \\log_ {2} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) ] + \\lambda \\cdot \\mathcal {D} (\\hat {\\mathbf {x}}, \\mathbf {x}), \\\\ \\end{array}", + "image_path": "49638f4c46c3812a76d24f18b64a8b998beb1bf1e0aa2899d164b5c2a5acd1db.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "inline_equation", + "content": "m(\\mathbf{v})" + }, + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "text", + "content": " represents the mean value of different channels, and " + }, + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 604, + 287, + 651 + ], + "type": "text", + "content": " is the mean square error to measure the reconstruction loss. The details of the likelihood estimations of different latent codes will be introduced below." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 658, + 218, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 218, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 218, + 671 + ], + "type": "text", + "content": "3.3. The estimation of the likelihood" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "As revealed by the cross entropy " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "H(p,q) = H(p) + \\mathcal{D}_{KL}(p||q)" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " that measures the number of extra bits to code the desired distribution " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " using an estimated one " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": ", the key" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "content": "of reducing the code length is to accurately model the distribution of latent codes. To this end, we propose to model the distribution of different latent variables with different strategies since they depend on different information." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "content": "Following a similar way of previous works [5,9], we use a non-parametric, fully factorized density model to encode the auxiliary latent codes " + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "content": ". However, due to the limitation of the network design, e.g., the domain of the hyper-prior model must be univariate and the network must be monotonic increasing [5], we find that there is still lots of redundant information in the auxiliary latent codes " + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "content": " as shown in Fig. 5. To further improve the coding efficiency, we propose to additionally save the mean value of each channel " + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "inline_equation", + "content": "m(\\mathbf{v})" + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "content": " to the metadata to reduce the redundancy. Specifically, we model the conditional distribution " + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "inline_equation", + "content": "q_{\\hat{\\mathbf{v}} | m(\\mathbf{v})}" + }, + { + "bbox": [ + 304, + 308, + 546, + 441 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 322, + 447, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 447, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 322, + 447, + 545, + 491 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q _ {\\hat {\\mathbf {v}} | m (\\mathbf {v})} (\\hat {\\mathbf {v}} | m (\\mathbf {v})) = \\\\ \\prod_ {i} \\left[ \\left(q _ {v _ {i} | m (\\mathbf {v})} \\left(\\psi^ {(i)}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) \\left(\\hat {\\mathbf {v}} - m (\\mathbf {v})\\right) _ {i} \\right], \\tag {4} \\\\ \\end{array}", + "image_path": "f054070171975d3fbaabb5fa9f624b0e8096df9c585dec2952b59a668dcedeaf.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "inline_equation", + "content": "\\psi^i" + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "content": " is the parameters of each univariate conditional distribution " + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "inline_equation", + "content": "p_{v_i|m(\\mathbf{v})}" + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "content": " is the position index." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "text", + "content": "For the encoding of " + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "text", + "content": ", previous works show great improvement by introducing the context model, i.e., the already decompressed pixels can help to predict the pixels which are not decompressed yet to further improve the coding efficiency. However, due to its serialization property, the autoregressive model incurs a significant computational cost which is unacceptable in the raw image reconstruction since its high-resolution, e.g., " + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "inline_equation", + "content": "4000 \\times 6000" + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "text", + "content": ". To improve the computational efficiency while preserve the advantages of the autoregressive model, we propose a novel sRGB-guided context model. More specifically, our proposed context model includes two parts: a learnable order prediction network " + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "inline_equation", + "content": "g_{m}" + }, + { + "bbox": [ + 304, + 522, + 546, + 689 + ], + "type": "text", + "content": " as shown in Fig. 3, and an iterative Gaussian entropy model as shown in Fig. 4." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "The learnable order prediction network. As the prerequisite of our proposed context model, the order masks of com" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18209" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 82, + 282, + 158 + ], + "blocks": [ + { + "bbox": [ + 65, + 82, + 282, + 158 + ], + "lines": [ + { + "bbox": [ + 65, + 82, + 282, + 158 + ], + "spans": [ + { + "bbox": [ + 65, + 82, + 282, + 158 + ], + "type": "image", + "image_path": "3f7fc52ee075ede0f073eb47f8ba811340ada6809ec03bda7859d14ac2b75ded.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 169, + 287, + 191 + ], + "lines": [ + { + "bbox": [ + 47, + 169, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 169, + 287, + 191 + ], + "type": "text", + "content": "Figure 5. Visualization of a channel of the auxiliary latent features " + }, + { + "bbox": [ + 47, + 169, + 287, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 169, + 287, + 191 + ], + "type": "text", + "content": " and its value distribution." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 107, + 205, + 218, + 293 + ], + "blocks": [ + { + "bbox": [ + 107, + 205, + 218, + 293 + ], + "lines": [ + { + "bbox": [ + 107, + 205, + 218, + 293 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 218, + 293 + ], + "type": "image", + "image_path": "4bcd1bf4196e1202a7b34bf1a203baef9f97eec521e5a93b93e409d9790ffb08.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 301, + 263, + 313 + ], + "lines": [ + { + "bbox": [ + 70, + 301, + 263, + 313 + ], + "spans": [ + { + "bbox": [ + 70, + 301, + 263, + 313 + ], + "type": "text", + "content": "Figure 6. The proposed masked deconvolution layer." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 321, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 321, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 287, + 381 + ], + "type": "text", + "content": "pression/decompression play a significant role. To make sampling order masks learnable, we propose a training strategy that makes end-to-end training of the whole framework feasible. Specifically, we utilize Gumbel-softmax [17] to make the binary mask derivable for training as follows" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 390, + 287, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 390, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 80, + 390, + 287, + 422 + ], + "type": "interline_equation", + "content": "M _ {i, j} ^ {k} = \\frac {\\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {k}\\right) + g _ {i , j} ^ {k}\\right) / \\tau\\right)}{\\sum_ {t = 1} ^ {N} \\exp \\left(\\left(\\log \\left(m _ {i , j} ^ {t}\\right) + g _ {i , j} ^ {t}\\right) / \\tau\\right)}, \\tag {5}", + "image_path": "ad79befc2c2464cacc6268776bf72cb313ce36b1bfd73d3a32b1116ad7f8880f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " is the index of sampling masks, " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " is the number of iterations, " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{g} \\in \\mathbb{R}^{N \\times h \\times w}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " is a random matrix i.i.d sampled from Gumbel(0,1) distribution, " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " is a temperature hyper-parameter, and " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{m} \\in \\mathbb{R}^{N \\times h \\times w}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " denotes unnormalized log probabilities predicted by a subnetwork. For inference, to make sure that we have exactly the same random vector " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " during compress/decompress processes, we add a registered buffer to the model to save a pre-sampled " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": ". The pre-sampled " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " is then cropped to the same size as the " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": " to generate a set of sparsely sampled " + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^k" + }, + { + "bbox": [ + 46, + 430, + 287, + 548 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "text", + "content": "In addition, we find that the vanilla convolutional layer cannot well utilize the information from the randomly sparsely sampled features (can refer to the sampling mask in Fig. 9). Therefore, we further propose a new masked deconvolution layer that can alleviate negative impacts from the randomness and sparsity as shown in Fig. 6. For an input feature " + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "text", + "content": " and its corresponding mask " + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^c = \\sum_{i=0}^{k} \\mathbf{M}^k" + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "text", + "content": " which records the positions of all already decoded ones, the output " + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}'" + }, + { + "bbox": [ + 46, + 550, + 287, + 658 + ], + "type": "text", + "content": " is as follows" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 667, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 667, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 104, + 667, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} ^ {\\prime} = \\frac {\\operatorname {D e c o n v} (\\mathbf {z})}{\\max \\left(1 , \\operatorname {D e c o n v} _ {\\mathbf {1}} \\left(\\mathbf {M} ^ {c}\\right)\\right)}, \\tag {6}", + "image_path": "d8e7fbb790573f7544bdba34dba9d7c7ff68e9b957453d50af74d9169391bd12.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "where Deconv and " + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{\\mathbf{1}}" + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": " are deconvolution layers with" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "stride of 1. Besides, " + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\mathrm{Deconv}_1" + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": " is a fixed layer that the weights are all one and the bias is zero." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "text", + "content": "The iterative Gaussian entropy model. After obtaining the predicted order mask, we can iteratively compress/decompress the information as shown in Fig 4. Specifically, we use information from the auxiliary latent variable " + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}" + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "text", + "content": " and already encoded/decoded partial of " + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "text", + "content": " to predict the distribution of the to-be-processed part of " + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 96, + 547, + 178 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 186, + 545, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 186, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 329, + 186, + 545, + 219 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} ^ {i + 1}, \\boldsymbol {\\sigma} ^ {i + 1} = g _ {c} \\left(g _ {z} \\left(\\left(\\sum_ {k = 0} ^ {i} \\mathbf {M} ^ {i}\\right) \\odot \\hat {\\mathbf {z}}, y\\right), h _ {s} (\\hat {\\mathbf {v}})\\right), \\tag {7}", + "image_path": "7887a2e856da16489f68a8e715ece02f3a449f740407e061f2bfe76f30dcb795.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": " is a pixel-wise multiplication, " + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "inline_equation", + "content": "g_{z}" + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": " is the masked decoder, and " + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "inline_equation", + "content": "g_{c}" + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": " is the Gaussian prior module to predict the distribution of " + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{i + 1}" + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": " that are not encoded. Then, the likelihood of " + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 226, + 545, + 274 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 319, + 279, + 545, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 279, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 319, + 279, + 545, + 321 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q _ {\\hat {\\mathbf {z}} | \\hat {\\mathbf {v}}, \\mathbf {y}} (\\hat {z} _ {i} | \\hat {\\mathbf {v}}, \\mathbf {y}) = \\left(\\mathcal {N} \\left(\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}\\right) * \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right)\\right) (\\hat {z} _ {i}) \\tag {8} \\\\ = c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} + 0. 5) - c _ {\\mu_ {i} ^ {k _ {i}}, \\sigma_ {i} ^ {k _ {i}}} (\\hat {z} _ {i} - 0. 5), \\\\ \\end{array}", + "image_path": "c1690b351651d2d012236f3cf861fd91dd39663c8265a6affea53b9c53210154.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "text", + "content": "where the subscript " + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "text", + "content": " is the index of the pixel position, " + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "text", + "content": " is the index of parameter groups defined in Eq. 7, and " + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "inline_equation", + "content": "c_{\\mu_i^{k_i},\\sigma_i^{k_i}}(\\cdot)" + }, + { + "bbox": [ + 305, + 328, + 545, + 369 + ], + "type": "text", + "content": " is its corresponding cumulative function." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 376, + 388, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 388, + 390 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 388, + 390 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 396, + 430, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 430, + 409 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 430, + 409 + ], + "type": "text", + "content": "4.1. Experimental settings" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": "Datasets. We utilize two widely-used datasets, NUS dataset [8] and AdobeFiveK dataset [6], to evaluate the effectiveness of our proposed methods. These datasets are all natural images collected from different scenarios and devices. Following previous work [26,30], we use the raw image after demosaic and render sRGB images using a software ISP. Specifically, AdobeFiveK dataset [6] includes 5000 photographs taken by different photographers and devices so that it covers a wide range of scenes and lighting conditions. We randomly split the whole dataset into training set and validation set which include 4900 and 100 images respectively. For the NUS dataset [8], we select the same subsets of devices with the previous work [26]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": "Baselines. We compared the proposed method with several SOTA methods, including InvISP [36], SAM [30], and Nam et al. [26]. Specifically, InvISP [36] is a SOTA raw image reconstruction model that utilizes a single invertible network to learn the mapping from sRGB image to raw image and vice versa. SAM [30] is a test-time adaptation model that saves the uniformly sampled raw pixels as metadata. Nam et al. [26] learn the sampling process and reconstruction process using two separate neural networks [37]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Implementation details. All the code will be released after acceptance. For training, we use a batch size of 1 and patch size of 1024 to reduce the I/O time. Adam is used as the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18210" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 128, + 285 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 128, + 285 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 128, + 285 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 128, + 285 + ], + "type": "image", + "image_path": "b3aeebc80826d618a09ea9d7c0da9c2760b2a443d4b904571242a55d72c59ddc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 286, + 116, + 304 + ], + "lines": [ + { + "bbox": [ + 60, + 286, + 116, + 304 + ], + "spans": [ + { + "bbox": [ + 60, + 286, + 116, + 304 + ], + "type": "text", + "content": "(a) Input (8 bit sRGB image)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 207, + 285 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 207, + 285 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 207, + 285 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 207, + 285 + ], + "type": "image", + "image_path": "54e6e6f207f9bdf45624c1056f6febf276658379b749208dd34e56f998710111.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 146, + 286, + 189, + 303 + ], + "lines": [ + { + "bbox": [ + 146, + 286, + 189, + 303 + ], + "spans": [ + { + "bbox": [ + 146, + 286, + 189, + 303 + ], + "type": "text", + "content": "(b) InvISP [36] (bpp: N/A)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 208, + 70, + 286, + 285 + ], + "blocks": [ + { + "bbox": [ + 208, + 70, + 286, + 285 + ], + "lines": [ + { + "bbox": [ + 208, + 70, + 286, + 285 + ], + "spans": [ + { + "bbox": [ + 208, + 70, + 286, + 285 + ], + "type": "image", + "image_path": "4103b1b9b2b66ff315dfcf6821e160d98aa7ba225e66ce403f6ce3103d41195a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 225, + 286, + 266, + 303 + ], + "lines": [ + { + "bbox": [ + 225, + 286, + 266, + 303 + ], + "spans": [ + { + "bbox": [ + 225, + 286, + 266, + 303 + ], + "type": "text", + "content": "(c) SAM [30] (bpp: 9.52e-3)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 287, + 70, + 365, + 285 + ], + "blocks": [ + { + "bbox": [ + 287, + 70, + 365, + 285 + ], + "lines": [ + { + "bbox": [ + 287, + 70, + 365, + 285 + ], + "spans": [ + { + "bbox": [ + 287, + 70, + 365, + 285 + ], + "type": "image", + "image_path": "e584220e4d45ade221477d58b2bdfc411075d833d5f60b35aaf27570dba40b8f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 298, + 286, + 351, + 303 + ], + "lines": [ + { + "bbox": [ + 298, + 286, + 351, + 303 + ], + "spans": [ + { + "bbox": [ + 298, + 286, + 351, + 303 + ], + "type": "text", + "content": "(d) Nam et al. [26] (bpp: 8.44e-1)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 366, + 70, + 445, + 285 + ], + "blocks": [ + { + "bbox": [ + 366, + 70, + 445, + 285 + ], + "lines": [ + { + "bbox": [ + 366, + 70, + 445, + 285 + ], + "spans": [ + { + "bbox": [ + 366, + 70, + 445, + 285 + ], + "type": "image", + "image_path": "bc68f48e29b92693dbd8b02cb38d310822bfd52dec00b4bba914cefc87fe7366.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 384, + 286, + 425, + 303 + ], + "lines": [ + { + "bbox": [ + 384, + 286, + 425, + 303 + ], + "spans": [ + { + "bbox": [ + 384, + 286, + 425, + 303 + ], + "type": "text", + "content": "(e) Ours (bpp: 4.90e-4)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 312, + 546, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 546, + 335 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison of the raw image reconstruction results. We visualize the maximum value of the error among three channels on the pixel level. For better visualization, we apply gamma correction to the raw image to increase the visibility." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 449, + 70, + 545, + 285 + ], + "blocks": [ + { + "bbox": [ + 449, + 70, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 449, + 70, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 449, + 70, + 545, + 285 + ], + "type": "image", + "image_path": "555805f683f9cdb2a4918579fa805f2d112d86b61e7bbe98ad2fccdaeb225018.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 286, + 540, + 303 + ], + "lines": [ + { + "bbox": [ + 468, + 286, + 540, + 303 + ], + "spans": [ + { + "bbox": [ + 468, + 286, + 540, + 303 + ], + "type": "text", + "content": "(f) Raw image (After gamma correction)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 69, + 345, + 266, + 430 + ], + "blocks": [ + { + "bbox": [ + 69, + 345, + 266, + 430 + ], + "lines": [ + { + "bbox": [ + 69, + 345, + 266, + 430 + ], + "spans": [ + { + "bbox": [ + 69, + 345, + 266, + 430 + ], + "type": "table", + "html": "
MethodbppPSNRSSIM
InvISP [36]N/A52.690.99938
SAM [30]9.566e-449.610.99874
SAM [30]9.5219-354.760.99945
Nam et al. [26]8.438e-156.720.99958
Ours (w/o metadata)N/A53.030.99926
Ours4.901e-458.140.99969
", + "image_path": "2b85ae320bae705717fc858763fa26c29835b154a3905d829bf8fe59aa60544e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 64, + 439, + 269, + 449 + ], + "lines": [ + { + "bbox": [ + 64, + 439, + 269, + 449 + ], + "spans": [ + { + "bbox": [ + 64, + 439, + 269, + 449 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation on AdobeFiveK dataset." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "text", + "content": "optimizer with a learning rate of 1e-4. We train the models for 100 epochs for AdobeFiveK dataset and 200 epochs for NUS dataset. We reduce the learning rate by a factor of 0.1 if there is no improvement in terms of the loss after every 20 epochs. For the sRGB-guided context model, we set " + }, + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "inline_equation", + "content": "N = 2" + }, + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "text", + "content": " for the model conditioned on uncompressed sRGB images and " + }, + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "inline_equation", + "content": "N = 4" + }, + { + "bbox": [ + 46, + 463, + 287, + 548 + ], + "type": "text", + "content": " for the compressed JPEG data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 554, + 167, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 167, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 167, + 567 + ], + "type": "text", + "content": "4.2. Experimental results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 572, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 621 + ], + "type": "text", + "content": "For the evaluation metrics, we utilize PSNR and SSIM [34] which are widely used to evaluate the reconstruction quality with the reference image. We also utilize bpp (bit per pixel) to evaluate the coding efficiency of the model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 635, + 239, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 239, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 239, + 647 + ], + "type": "text", + "content": "4.2.1 Results on uncompressed sRGB data." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Results on AdobeFiveK dataset. We report the quantitative evaluation results in Table 1. As we can see in the table, raw image reconstruction models with metadata can achieve better performance than SOTA raw image reconstruction model without metadata [36]. Besides, compared" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 347, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 479 + ], + "type": "text", + "content": "with previous metadata-based SOTA methods [26, 30], our method achieves better reconstruction quality with lower storage overhead. Besides, to exclude the effect of network structure, we retrain and evaluate the performance of the model without the help of metadata using the same architecture as ours. Specifically, we set the original input of the raw image to zero, and remove the quantization step and code length loss. We find that its reconstruction quality is much lower than the results obtained from the same network with meta-data, which demonstrates the effectiveness of the saved metadata. Visual comparisons can be found in Fig. 7." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 479, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 576 + ], + "type": "text", + "content": "Results on NUS dataset. We also evaluate the performance of models on NUS dataset following a similar evaluation paradigm with Nam et al. [26]. The results are reported in Table 2. As can be seen in the table, we achieve huge performance improvement compared with SOTA method Nam et al. [26] (even compared with the test-time optimization version). In addition, the number of bits we need to save as metadata is less than " + }, + { + "bbox": [ + 304, + 479, + 545, + 576 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 304, + 479, + 545, + 576 + ], + "type": "text", + "content": " of [26]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 597, + 487, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 487, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 487, + 609 + ], + "type": "text", + "content": "4.2.2 Results on compressed sRGB data." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "We further consider a more challenging and realistic setting that we reconstruct the raw image based on compressed JPEG image. To evaluate the robustness of our method, we train a single model across different devices and JPEG quality factors. The results are reported in Table 3. As we can see, our method can adaptively allocate different bpp to JPEG images with different quality factors, i.e., assigning higher bpp to the image with worse JPEG quality. Our" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18211" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 529, + 156 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 529, + 156 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 529, + 156 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 529, + 156 + ], + "type": "table", + "html": "
Methodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
RIR [27]3.253e-245.660.993948.420.992451.260.9982
SAM [30]7.500e-147.030.996249.350.997850.440.9982
Nam et al. [26]18.438e-148.080.996850.710.997550.490.9973
[26] w/ fine-tuning8.438e-149.570.997551.540.998053.110.9985
Ours2.887e-457.84±0.890.9997±0.0059.08±0.950.9998±0.0058.76±0.950.9997±0.00
", + "image_path": "c8670a225a27f9213c699d4f85084a239c39d28f4b86eb7322b02477aaba0339.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 70, + 157, + 526, + 180 + ], + "lines": [ + { + "bbox": [ + 70, + 157, + 526, + 180 + ], + "spans": [ + { + "bbox": [ + 70, + 157, + 526, + 180 + ], + "type": "text", + "content": "1 The reason that the bpp of SAM [30] and Nam et al. [26] is slightly different is that Nam et al. [26] need extra bits to save the locations of sampled raw pixels as shown in Fig. 8." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 70, + 180, + 497, + 191 + ], + "lines": [ + { + "bbox": [ + 70, + 180, + 497, + 191 + ], + "spans": [ + { + "bbox": [ + 70, + 180, + 497, + 191 + ], + "type": "text", + "content": "2 For the experiments in the gray area, we use a five-fold cross validation, and report the mean and std in the table." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 194, + 445, + 205 + ], + "lines": [ + { + "bbox": [ + 146, + 194, + 445, + 205 + ], + "spans": [ + { + "bbox": [ + 146, + 194, + 445, + 205 + ], + "type": "text", + "content": "Table 2. The quantitative results of NUS dataset [8] conditioned on sRGB images." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "content": "method achieves the best reconstruction quality with the least metadata compared with previous SOTA methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 252, + 139, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 139, + 265 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 139, + 265 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 270, + 289, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 534 + ], + "type": "text", + "content": "The comparison of bits allocation. One of the main advantages of the proposed method is that we could learn the bits allocation in an end-to-end manner. As shown in Fig. 2, the information loss is non-uniform so a good bits allocation algorithm is the core of raw image reconstruction algorithms. To this end, we visualize the bits allocation of both current SOTA methods and the proposed method in Fig. 8. In [30], the metadata are uniformly sampled in the raw pixel space, which leads to redundancy. Although Nam et al. [26] propose a superpixel based sampling network, the training of reconstruction and sampling networks are separated into two phases. In addition, even if its sampling is locally non-uniform, it still remains uniform globally, which limits the coding efficiency and reconstruction quality. As we can see in the figure, our method can adaptively allocate different bits to different areas. Specifically, for the flat area, e.g. flat area in the blue bounding box, our methods utilize few bits to encode. While for the area with more complicated context, e.g. boundary area in the blue bounding box, our method allocates relatively more bits. Besides, even for areas where we allocate bits, the need of bits is much lower than methods that sample in the raw pixel space." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": "The hand-crafted metadata of v. To verify the effectiveness of our proposed modeling of the hyper-prior variable " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{v}}" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ". We compare the models trained w/ and w/o the hand-crafted metadata " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "m(\\mathbf{v})" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ". We keep other settings the same as in Table 3 and evaluate the models on a fold of NUS dataset. The results are reported in Table 4. As we can see in the table, there are improvements in terms of both the bpp and the reconstruction quality that benefited from the more accurate value of v and alleviated redundancy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "The sRGB-guided context model. To better understand how the proposed context model works, we visualize each step of encoding/decoding " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " in Fig. 9 (a). As we can see, the order of the compress/decompress process is highly-related to the context of the image, which demonstrates that our proposed context model can well utilize the information" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 220, + 359, + 333 + ], + "blocks": [ + { + "bbox": [ + 309, + 220, + 359, + 333 + ], + "lines": [ + { + "bbox": [ + 309, + 220, + 359, + 333 + ], + "spans": [ + { + "bbox": [ + 309, + 220, + 359, + 333 + ], + "type": "image", + "image_path": "b2985194b5b93a264e96f6f47eac8c64243e3e6255321f8f06d081900c9661fd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 359, + 220, + 404, + 347 + ], + "blocks": [ + { + "bbox": [ + 359, + 220, + 404, + 347 + ], + "lines": [ + { + "bbox": [ + 359, + 220, + 404, + 347 + ], + "spans": [ + { + "bbox": [ + 359, + 220, + 404, + 347 + ], + "type": "image", + "image_path": "d57e1ba5bfab709fb3de5cb165aee8e07e2ff1d5f08e3524b616aa8c820fca29.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 352, + 547, + 418 + ], + "lines": [ + { + "bbox": [ + 304, + 352, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 547, + 418 + ], + "type": "text", + "content": "Figure 8. The comparison of the bits allocation. (a) The input 8-bit sRGB image. (b)-(d) The bits allocation maps of the red bounding box area (the first row) and the blue area (the second row). For better visualization, we enlarge the size of sampled pixels in (b). It is worth noting that for (b)-(c), each sampled raw pixel needs 48 bits to save. Best zoom in for more details." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 404, + 220, + 468, + 347 + ], + "blocks": [ + { + "bbox": [ + 404, + 220, + 468, + 347 + ], + "lines": [ + { + "bbox": [ + 404, + 220, + 468, + 347 + ], + "spans": [ + { + "bbox": [ + 404, + 220, + 468, + 347 + ], + "type": "image", + "image_path": "3e80bc8fc398a0b31dacdb0cdfbb66c8fec486306ad8ac83b6cb7db107cf3dea.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 468, + 220, + 544, + 348 + ], + "blocks": [ + { + "bbox": [ + 468, + 220, + 544, + 348 + ], + "lines": [ + { + "bbox": [ + 468, + 220, + 544, + 348 + ], + "spans": [ + { + "bbox": [ + 468, + 220, + 544, + 348 + ], + "type": "image", + "image_path": "5bccb9866209270729fb124f16a3ce658ad808003b6bf63a8dc7f107ae1a7607.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 423, + 425, + 484 + ], + "blocks": [ + { + "bbox": [ + 306, + 423, + 425, + 484 + ], + "lines": [ + { + "bbox": [ + 306, + 423, + 425, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 425, + 484 + ], + "type": "image", + "image_path": "ce0d359f445ef8b88ca82a19478e3f00544cde57a03580db430f05884e260e41.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": "Figure 9. The visualization of each step of the sRGB-guided context model (a) The sampling masks from " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^0" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^3" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": " respectively. The sampling rate and the bytes of the encoded string are displayed on the right side of the mask. (b) The bpp maps of the latent variable " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": " based on the already decoded information. Specifically, the " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": " (range from 0 to 3) bpp map is estimated using the information of " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "\\sum_{k = -1}^{i - 1}\\mathbf{M}^k\\odot \\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{-1}" + }, + { + "bbox": [ + 304, + 491, + 547, + 569 + ], + "type": "text", + "content": " is an all zero mask." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 427, + 424, + 486, + 483 + ], + "blocks": [ + { + "bbox": [ + 427, + 424, + 486, + 483 + ], + "lines": [ + { + "bbox": [ + 427, + 424, + 486, + 483 + ], + "spans": [ + { + "bbox": [ + 427, + 424, + 486, + 483 + ], + "type": "image", + "image_path": "4b14542cf771e01709b8c32e08426eae5a6fc82df3656bb1bb57210ab84f8fe6.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 488, + 424, + 547, + 483 + ], + "blocks": [ + { + "bbox": [ + 488, + 424, + 547, + 483 + ], + "lines": [ + { + "bbox": [ + 488, + 424, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 488, + 424, + 547, + 483 + ], + "type": "image", + "image_path": "dcf0d68d5e98e85ee7f51b0b31ae9d0890a540fc4387ede64205e75603b03594.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "from the sRGB image. The sparse sampling mask can help a model better predict the distribution of the adjacent pixels that have not been compressed/decompressed. In addition, our method gradually increases the number of sampled pixels in the latent space as more and more pixels are available to help to predict the distribution of the unseen ones, which leads to better coding efficiency. As shown in Fig. 9 (b), we can get more accurate estimation of the likelihood (i.e., smaller bpp) of " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " with the help of already decoded " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ". We also quantitatively evaluate the effectiveness of our proposed sRGB-guided context model as shown in Fig. 10. We" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18212" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 519, + 380 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 519, + 380 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 519, + 380 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 519, + 380 + ], + "type": "table", + "html": "
QualityMethodbpp ↓Samsung NX2000Olympus E-PL6Sony SLT-A57
PSNR ↑SSIM ↑PSNR ↑SSIM ↑PSNR ↑SSIM ↑
10InvISPN/A26.620.883629.120.898029.120.9002
SAM9.556e-424.420.894625.240.909425.560.9110
SAM9.522e-327.940.923428.220.937627.830.9374
Nam et al.8.438e-133.060.937334.030.947734.290.9506
Ours7.736e-433.130.938634.040.948234.310.9515
30InvISPN/A28.719.931631.760.942130.890.9459
SAM9.556e-428.880.934430.210.946529.650.9458
SAM9.522e-334.240.955335.870.964836.120.9677
Nam et al.8.438e-137.210.963038.700.972339.060.9750
Ours3.613e-437.400.964038.810.972939.180.9757
50InvISPN/A30.020.941632.910.952932.970.9579
SAM9.556e-430.780.944832.410.955932.050.9567
SAM9.522e-336.320.962937.770.970538.240.9739
Nam et al.8.438e-138.340.968640.070.976740.040.9797
Ours3.368e-438.670.969940.330.977640.730.9806
70InvISPN/A30.860.945832.910.955332.970.9592
SAM9.556e-432.080.952934.140.962033.900.9637
SAM9.522e-337.420.968438.960.974539.380.9780
Nam et al.8.438e-139.130.972441.010.976941.420.9825
Ours3.210e-439.590.974241.360.980741.750.9836
90InvISPN/A31.550.947633.740.959833.680.9643
SAM9.556e-434.370.966336.600.971236.780.9747
SAM9.522e-339.170.978740.790.981241.200.9843
Nam et al.8.438e-140.320.978242.330.983842.820.9864
Ours2.944e-441.190.982142.980.985643.430.9882
", + "image_path": "405640db28d23941d12b9f8fa006d9192a9e7b89df17d6d1da83c9be902131dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 409, + 282, + 477 + ], + "blocks": [ + { + "bbox": [ + 69, + 384, + 523, + 396 + ], + "lines": [ + { + "bbox": [ + 69, + 384, + 523, + 396 + ], + "spans": [ + { + "bbox": [ + 69, + 384, + 523, + 396 + ], + "type": "text", + "content": "Table 3. The quantitative results of NUS dataset [8] conditioned on the compressed JPEG image with different quality factors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 409, + 282, + 477 + ], + "lines": [ + { + "bbox": [ + 50, + 409, + 282, + 477 + ], + "spans": [ + { + "bbox": [ + 50, + 409, + 282, + 477 + ], + "type": "table", + "html": "
Ours w/o m(v)Ours
bpp ↓PSNRSSIMbpp ↓PSNRSSIM
Samsung2.92e-457.500.99972.88e-457.790.9997
Olympus2.93e-458.930.99972.90e-459.350.9997
Sony2.90e-459.050.99972.89e-459.240.9997
Mean2.92e-458.660.99962.89e-458.790.9997
", + "image_path": "e021c91c7e3808986bea5b7152f4f80d183c97b5911955c6e3e1aa23366e9219.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 480, + 275, + 491 + ], + "lines": [ + { + "bbox": [ + 58, + 480, + 275, + 491 + ], + "spans": [ + { + "bbox": [ + 58, + 480, + 275, + 491 + ], + "type": "text", + "content": "Table 4. The ablation study on the proposed modeling of " + }, + { + "bbox": [ + 58, + 480, + 275, + 491 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{v}}" + }, + { + "bbox": [ + 58, + 480, + 275, + 491 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 503, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 588 + ], + "type": "text", + "content": "compare our proposed sRGB-guided context model with He et al. [13] which proposes an improved context model to obtain faster speed. For a fair comparison, we directly replace our proposed context model (Fig. 3 (b)) with the checkboard one in He et al. [13] and keep other settings the same. As we can see, all models achieve very similar reconstruction quality and our method achieves much lower bpp." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we present a novel approach to reconstructing raw images using compact metadata. We introduce end-to-end coding techniques that encode the metadata in the latent space using an adaptive bits allocation strategy, resulting in improved reconstruction quality and higher coding efficiency. Additionally, our proposed sRGB-guided context model leads to better reconstruction quality, smaller metadata size, and faster processing speed. We evaluate" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 312, + 412, + 424, + 492 + ], + "blocks": [ + { + "bbox": [ + 312, + 412, + 424, + 492 + ], + "lines": [ + { + "bbox": [ + 312, + 412, + 424, + 492 + ], + "spans": [ + { + "bbox": [ + 312, + 412, + 424, + 492 + ], + "type": "image", + "image_path": "a8ff7cd2843c5e50bbbf2ef1cd375190f443fb81c1dee22bbbd65041597968a9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "text", + "content": "Figure 10. A comparison of models trained with different steps of the proposed sRGB-guided context model and He et al. [13]. The models are evaluated using JPEG images with varying quality factors (10, 30, 50, 70, 90). For all models, PSNR and SSIM decrease monotonously, with the lowering of the conditioned JPEG quality." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 424, + 411, + 536, + 492 + ], + "blocks": [ + { + "bbox": [ + 424, + 411, + 536, + 492 + ], + "lines": [ + { + "bbox": [ + 424, + 411, + 536, + 492 + ], + "spans": [ + { + "bbox": [ + 424, + 411, + 536, + 492 + ], + "type": "image", + "image_path": "f0ccca19c39ee785f2e46a55bf1e798b915ca98ab220ecf207d667a2c27a6320.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 604 + ], + "type": "text", + "content": "our method on widely-used datasets and the results demonstrate that our method significantly improves performance over prior methods, i.e., we achieve better reconstruction quality and smaller size of metadata." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was done at Rapid-Rich Object Search (ROSE) Lab, Nanyang Technological University. This research is supported in part by the NTUPKU Joint Research Institute (a collaboration between the Nanyang Technological University and Peking University that is sponsored by a donation from the Ng Teng Fong Charitable Foundation), the Basic and Frontier Research Project of PCL, the Major Key Project of PCL, and the MOE AcRF Tier 1 (RG61/22) and Start-Up Grant." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18213" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Marcus A Brubaker, and Michael S Brown. 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However, creating training datasets for such environments is expensive and hard due to the difficulties of data collection and annotation. It is desirable if we could get a robust model without the need for hard-to-obtain datasets. One simple approach is to apply data augmentation such as color jitter and blur to standard RGB (sRGB) images in simple scenes. Unfortunately, this approach struggles to yield realistic images in terms of pixel intensity and noise distribution due to not considering the non-linearity of Image Signal Processors (ISPs) and noise characteristics of image sensors. Instead, we propose a noise-accounted RAW image augmentation method. In essence, color jitter and blur augmentation are applied to a RAW image before applying non-linear ISP, resulting in realistic intensity. Furthermore, we introduce a noise amount alignment method that calibrates the domain gap in the noise property caused by the augmentation. We show that our proposed noise-accounted RAW augmentation method doubles the image recognition accuracy in challenging environments only with simple training data.", + "bbox": [ + 75, + 325, + 473, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 691, + 209, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although image recognition has been actively studied, its performance in challenging environments still needs improvement [15]. Sensitive applications such as mobility sensing and head-mounted wearables need to be robust to various kinds of difficulties, including low light, high dynamic range (HDR) illuminance, motion blur, and camera shake. One possible solution is to use image enhancement and restoration methods. A lot of DNN-based low-light image enhancement [12, 20, 29, 30, 46, 54], denoising [32, 43, 53], and deblurring [43, 48, 52] methods are proposed to improve the pre-captured sRGB image quality. While they are useful for improving pre-captured image", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/351d84d8f1681024bff9913736f1574c90d26716b2bf205d3faf71d26897e693.jpg", + "image_caption": [ + "(a) Usual training pipeline" + ], + "image_footnote": [], + "bbox": [ + 504, + 290, + 897, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4a50bea20f0307b6407b5e90354fb075ca70aae9daf1f79f1fdd6f828766e288.jpg", + "image_caption": [ + "(b) Noise-accounted RAW augmentation pipeline", + "Figure 1. The concept of the proposed noise-accounted RAW augmentation. Conventional augmentation (a) is applied to the output of an ISP; due to the nonlinear operations in the ISP, it produces images that cannot be captured at any ambient light intensities. Instead, ours (b) applies augmentation before an ISP. It generates realistic pixel intensity distribution that can be captured when the light intensity is different. Moreover, the noise amount is also corrected to minimize the domain gap between real and augmented ones." + ], + "image_footnote": [], + "bbox": [ + 503, + 391, + 887, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "quality, a recent work [15] shows that using them as preprocessing for image recognition models has limited accuracy gains since they already lost some information, and restoring the lost information is difficult.", + "bbox": [ + 496, + 657, + 890, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another possible solution is to prepare a dataset for difficult environments [3, 33]. However, these datasets only cover one or a few difficulties, and creating datasets in various environments is too expensive. Especially, manual annotation of challenging scenes is difficult and time-consuming. For example, we can see almost nothing in usual sRGB images under extremely low-light environments due to heavy noise. In addition, some regions in HDR scenes suffer from halation or blocked-up shadows because the 8-bit range of usual sRGB images cannot fully preserve the real world, which is 0.000001 $[cd / m^2]$ under starlight and 1.6 billion $[cd / m^2]$ under direct sunlight [37]. Heavy", + "bbox": [ + 496, + 719, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14007", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "motion blur and camera shake also make annotation difficult. Some works capture paired short-exposure and long-exposure images, and the clean long-exposure images are used for annotation or ground truth [15-17, 19]. The limitation is that the target scene needs to be motionless if the pairs are taken sequentially with one camera [15], and positional calibration is required if the pairs are taken with synchronized cameras [16,17]. Some works use a beam splitter to capture challenging images and their references without calibration [19, 45]. However, they are difficult to apply in dark scenes. Moreover, HDR images cannot be taken in the same way because some regions become overexposed or underexposed in both cameras.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we aim to train image recognition models that work in various environments only using a training dataset in simple environments like bright, low dynamic range, and blurless. In this case, image augmentation or domain adaptation is important to overcome the domain gap between easy training data and difficult test data. However, we believe usual augmentations on sRGB space are ineffective because it does not take into account the nonlinear mapping of ISPs. In particular, tone mapping significantly changes the RAW image values, which are roughly proportional to physical brightness [44]. Contrast, brightness, and hue augmentation on sRGB space result in unrealistic images that cannot be captured under any ambient light intensity as shown in Fig. 1(a). In contrast, we propose augmentation on RAW images. In other words, augmentation is applied before ISPs to diminish the domain shift as shown in Fig. 1(b).", + "bbox": [ + 75, + 287, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Oher possible sources of the domain gap are differences in noise amount and noise distribution. To tackle these problems, we propose a method to align both light intensity and noise domains. Recent works show that adding physics-based realistic noise improves the performance of DNN-based denoisers [2, 44, 47, 50] and dark image recognition [4, 15]. Although their proposed sensor noise modelings are accurate, they assume that the original bright images are noise free. In contrast, we propose to modify the noise amount after contrast, brightness, and hue conversion considering the noise amount in the original images. It enables a more accurate alignment of the noise domain. Even bright images may have dark areas due to shadows or object colors, and their prior noise cannot be ignored. Another merit of our method is that it is possible to take dark images that already contain a lot of noise as input. In addition to noise alignment after color jitter augmentation, we show the importance of noise alignment after blur augmentation, which is proposed for the first time in this paper.", + "bbox": [ + 75, + 545, + 472, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are as follows:", + "bbox": [ + 96, + 830, + 315, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- It is the first work to emphasize the importance of augmentation before ISP for image recognition to the best of our knowledge.", + "bbox": [ + 94, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Noise amount alignment method is proposed to reduce the noise domain gap after RAW image augmentation. In contrast to previous works, our proposed method takes into account prior noise in the input image. It enables more accurate alignment and use of any strength of augmentation and even already noisy input.", + "bbox": [ + 517, + 90, + 890, + 183 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We show qualitative analysis for the validity of our sensor noise modeling and corresponding noise-accounted augmentation. We prove that our proposed noise-accounted RAW augmentation has the edge over the previous methods.", + "bbox": [ + 517, + 205, + 893, + 282 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 306, + 648, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Recognition in Difficult Environment", + "text_level": 1, + "bbox": [ + 500, + 334, + 820, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many works have tackled image recognition in difficult environments. For low-light environments, several works improve the accuracy by replacing a traditional ISP with a powerful DNN-based ISP to create clean images for downstream image recognition models [5, 25, 33]. Even though these methods are promising because there is no information loss, the computational cost is the problem. Another approach is direct RAW image recognition without ISP [15, 39]. Their image recognition models benefit from the richest information and improve accuracy under low-light environments. However, several works report ISPs, especially tone mapping, are helpful for machine vision [13, 49]. Direct RAW image recognition may works well if the images have a low dynamic range. Another approach is domain adaptation or related methods which support low-light recognition with bright images [4, 15, 38].", + "bbox": [ + 496, + 361, + 890, + 602 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For HDR environments, some works propose DNN-based auto-exposure control [35, 42] to improve downstream recognition. Also, multi-frame HDR synthesis methods [1, 6] can be used as a preprocessing, although camera motion makes them challenging. A luminance normalization method is also introduced to improve recognition performance under varying illumination conditions [18].", + "bbox": [ + 496, + 606, + 890, + 728 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For blurry environments, deblurring methods are actively studied [48,51]. These DNN-based methods successfully restore clear images from heavily blurred images.", + "bbox": [ + 496, + 731, + 890, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differing from the above, we aim to do image recognition under all the above difficulties using simple scene training data with our proposed augmentation method. We do not use domain adaptation methods since these methods are usually used in a setting where the target domain is equal to or smaller than the source domain [10]. On the contrary, in our setting, the distribution of the target domain is much wider than that of the source domain.", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14008", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Image Conversion on RAW", + "text_level": 1, + "bbox": [ + 76, + 90, + 321, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, several methods [2,4,29] convert bright sRGB images into realistic dark images by the following procedures. First, they invert an ISP pipeline to generate RAW-like images followed by illumination change on the RAW data space with plausible sensor noise. Afterward, degraded sRGB is generated by applying the forward ISP pipeline. This operation avoids the nonlinear mappings in the ISP and simulates short exposures and dark environments. With a similar intention, we propose to apply augmentation before ISPs to train image recognition models.", + "bbox": [ + 75, + 113, + 468, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Noise Modeling and Noise Amount Alignment", + "text_level": 1, + "bbox": [ + 76, + 275, + 465, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the electronic imaging sensor community, detailed noise modelings based on electric current and circuit have been studied [7, 11, 23, 41]. They are precise but difficult to be applied to the image-to-image conversion. Thus, in the machine vision community, simplified pixel value-based noise modelings are proposed based on electric noise modelings [2, 44, 47]. Although the noise model of [47] is well designed with a high degree of freedom Tukey lambda distribution [21], we are based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50] because it is still well fitted to real sensor noise and we can consider prior noise in original images which will be explained later.", + "bbox": [ + 75, + 297, + 468, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, adding realistic model-based sensor noise to the ground truth clean images is proved to be helpful to train DNN-based denoiser [2,44,47,50] and low-light object detection models [4, 15]. Although they use highly consistent noise models, they regard original images as noise-free. In contrast, we propose to modify the noise amount after image conversion considering the noise amount of the original images. It enables a more accurate alignment of the noise domain and enables the use of any intensity of augmentation and already noisy images as input.", + "bbox": [ + 75, + 479, + 468, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 645, + 210, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce our noise model, calibration procedure, and proposed noise-accounted RAW augmentation.", + "bbox": [ + 75, + 670, + 468, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Noise Model", + "text_level": 1, + "bbox": [ + 76, + 726, + 209, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we briefly introduce our noise model for later explanation although it is based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50]. The number of photons $u$ hitting the photodiode of each pixel is converted to a voltage with quantum efficiency $\\alpha$ . Some processing is then performed to read out the voltage, in which noise $n_d$ is inevitably mixed. Next, analog gain $g$ is multiplied to amplify the value. Lastly, the voltage is converted to a digital value. We simplify and summarize the noise after analog gain as $n_r$ . Since it is common to use analog gain which", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "has a better signal-to-noise ratio (SNR), we omit the digital gain term in our noise model. To sum up, the photon-to-RAW pixel value conversion can be formulated as,", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx = g \\left(\\alpha u + n _ {d}\\right) + n _ {r}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 146, + 890, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We approximate $n_d$ and $n_r$ as Gaussian noise $\\mathcal{N}\\left(0,\\sigma_d^2\\right)$ $\\mathcal{N}\\left(0,\\sigma_r^2\\right)$ and the number of photons $u$ itself obeys the Poisson distribution $\\mathcal{P}(\\bar{u})$ where $\\bar{u}$ is the expected number of photons. If $\\bar{u}$ is large enough, we can approximate as $\\mathcal{P}(\\bar{u})\\doteq \\mathcal{N}(\\bar{u},\\bar{u})$ [9]. Thus, our noise model is as follows;", + "bbox": [ + 498, + 169, + 890, + 248 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx \\sim g (\\alpha \\mathcal {N} (\\bar {u}, \\bar {u}) + \\mathcal {N} (0, \\sigma_ {d} ^ {2})) + \\mathcal {N} (0, \\sigma_ {r} ^ {2}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 255, + 890, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We show the validity of the Gaussian approximation of $n_d$ , $n_r$ , and $\\mathcal{P}(\\bar{u})$ in the Section 4.3. We don't follow the further development of the formula in [9] for our purpose.", + "bbox": [ + 498, + 281, + 890, + 327 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gaussian distribution has the following convenient natures;", + "bbox": [ + 498, + 327, + 890, + 354 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} X \\sim \\mathcal {N} \\left(\\mu_ {X}, \\sigma_ {X} ^ {2}\\right) \\\\ Y \\sim \\mathcal {N} \\left(\\mu_ {Y}, \\sigma_ {Y} ^ {2}\\right) \\\\ X + Y \\sim \\mathcal {N} \\left(\\mu_ {X} + \\mu_ {Y}, \\sigma_ {X} ^ {2} + \\sigma_ {Y} ^ {2}\\right) \\\\ c X \\sim \\mathcal {N} \\left(c \\mu_ {X}, c ^ {2} \\sigma_ {X} ^ {2}\\right) \\end{array} , \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 369, + 890, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "if $X$ and $Y$ are independent, and that's why we choose the simple Gaussian approximation instead of the recently proposed more expressive noise model [47]. These natures enable the proposed noise-accounted RAW augmentation to account for prior noise in input images. Furthermore, they further simplify our noise model as,", + "bbox": [ + 496, + 446, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx \\sim \\mathcal {N} \\left(g \\alpha \\bar {u}, g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 544, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Because the expected number of photon $\\bar{u}$ is inconvenient to use in image-to-image conversion, we replace it with the expected pixel value $\\mu_{x} = g\\alpha \\bar{u}$ , and our final noise model is defined as,", + "bbox": [ + 498, + 571, + 890, + 631 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx \\sim \\mathcal {N} \\left(\\mu_ {x}, \\sigma_ {x} ^ {2} = g \\alpha \\mu_ {x} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 638, + 890, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Noise Model Calibration", + "text_level": 1, + "bbox": [ + 500, + 665, + 725, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our sensor noise model shown in Eq. (5) has three parameters, $\\alpha$ , $\\sigma_d^2$ , and $\\sigma_r^2$ , which have to be calibrated per target sensor. We capture a series of RAW images of a color checker as shown in Fig. 2(a). We then calculate the mean $\\mu_x$ and variance $\\sigma_x^2$ along the time direction of each pixel position. We calculate them along the time direction instead of the spatial direction as performed in [44] since lens distortion changes the luminance of the same color patch. These operations are performed several times by changing the analog gain and exposure time. Eventually, we get various sets of $\\{\\mu_x,\\sigma_x^2\\}$ for each analog gain. Note that we calculate mean and variance without separating RGB channels because there is no significant difference in noise properties.", + "bbox": [ + 496, + 689, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14009", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f6754d2cb8cc1c712127bd0957030dde6d37d0ad6c8e2fde568d6b910ad68317.jpg", + "image_caption": [ + "(a) burst capture with several analog gains" + ], + "image_footnote": [], + "bbox": [ + 130, + 88, + 377, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/29679e824bad8593e5a747a5686314997862211727f27eef1e91a6c4db69b758.jpg", + "image_caption": [ + "(b) estimate linear relationship of the mean and variance", + "(c) estimate the sensor specific parameters", + "Figure 2. Our noise model calibration procedures to a target sensor. It just needs to capture burst RAW images and does not need special devices." + ], + "image_footnote": [], + "bbox": [ + 388, + 88, + 808, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (5), $\\mu_{x}$ and $\\sigma_x^2$ have a linear relationship per analog gain $g_{n}$ ;", + "bbox": [ + 76, + 305, + 468, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {x} ^ {2} = a _ {g _ {n}} \\mu_ {x} + b _ {g _ {n}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 337, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we solve linear regression to estimate $a_{g_n}$ and $b_{g_n}$ per gain like Fig. 2(b). In addition, we use RANSAC [8] to robustly take care of outlier $\\{\\mu_x, \\sigma_x^2\\}$ pairs.", + "bbox": [ + 76, + 364, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we estimate $\\alpha$ , $\\sigma_d^2$ , and $\\sigma_r^2$ from the following redundant simultaneous equations by least-squares method,", + "bbox": [ + 76, + 411, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{c} a _ {g _ {1}} = g _ {1} \\alpha \\\\ \\vdots \\\\ a _ {g _ {n}} = g _ {n} \\alpha \\end{array} , \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 455, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} b _ {g _ {1}} = g _ {1} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\\\ \\vdots \\\\ b _ {g _ {n}} = g _ {n} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\end{array} . \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 535, + 468, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The procedure above enables calibration of the sensor noise model without special devices. We later show that our sensor model and the calibration method represent the real sensor noise with enough preciseness.", + "bbox": [ + 76, + 606, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Noise-Accounted RAW Augmentation", + "text_level": 1, + "bbox": [ + 76, + 679, + 401, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose augmentation before ISP instead of the usual augmentation after ISP to generate realistic images. Furthermore, we improve the reality of the augmented images by considering the sensor noise model. Unlike the previous works [2,4,15,44,47,50], ours takes the prior noise amount of input images into account. It generates more realistic noise since even bright images have some extent of noise. Especially, dark parts due to shadow or the color of objects might have a non-negligible amount of noise. Moreover, it allows any brightness of input images different from previous works. Specifically, we introduce how to adjust noise amount after contrast, brightness, hue, and blur augmentation.", + "bbox": [ + 75, + 703, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Color Jitter Augmentation", + "text_level": 1, + "bbox": [ + 500, + 305, + 738, + 320 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Contrast, brightness, and hue augmentation simulate different exposure times, light intensities, and analog gain. Hence, we first assume to multiply the exposure time, light intensity, and analog gain by $p_e$ , $p_i$ , and $p_g$ respectively. Because $p_e$ and $p_i$ equally change the number of photon $u$ in the case of our noise model, we rewrite them as $p_u = p_e p_i$ . Then, images in the above environment settings $x_{new}$ can be rewritten as,", + "bbox": [ + 496, + 328, + 890, + 448 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {n e w} \\sim \\mathcal {N} \\binom {(p _ {g} g) \\alpha \\left(p _ {u} \\bar {u}\\right),} {\\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 458, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on Eq. (3), it can be expanded as", + "bbox": [ + 500, + 507, + 763, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\left(p _ {g} p _ {u}\\right) \\alpha g \\bar {u}, \\left(p _ {g} p _ {u}\\right) ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - (p _ {g} p _ {u}) ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {10} \\\\ + \\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 531, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By inserting $\\mu_{x} = g\\alpha \\bar{u}$ and original pixel value, $x_{pre} \\sim \\mathcal{N}\\left(\\mu_x, g\\alpha \\mu_x + g^2\\sigma_d^2 + \\sigma_r^2\\right)$ , it can be expressed with a pixel value-based equation as follows;", + "bbox": [ + 498, + 601, + 890, + 646 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} x _ {n e w} \\sim p _ {u} p _ {g} x _ {p r e} + \\\\ \\mathcal {N} \\left(0, p _ {u} \\left(1 - p _ {u}\\right) p _ {g} ^ {2} g \\alpha \\mu_ {x} \\right. \\tag {11} \\\\ + \\left(1 - p _ {u} ^ {2}\\right) p _ {g} ^ {2} g ^ {2} \\sigma_ {d} ^ {2} + \\left(1 - p _ {u} ^ {2} p _ {g} ^ {2}\\right) \\sigma_ {r} ^ {2}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 659, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because the expected original pixel value $\\mu_{x}$ in the Gaussian term is impossible to obtain, we approximate it as $\\mu_{x} = x_{pre}$ . Based on this equation, we can precisely simulate as if exposure time, light intensity, and analog gain were $p_{e}, p_{i}$ , and $p_{g}$ times. Then, let's come back to contrast, brightness, and hue augmentation. When contrast is multiplied by $p_{c}$ and brightness is changed by $p_{b}$ , it can be expressed as,", + "bbox": [ + 496, + 724, + 890, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {n e w} = p _ {c} x _ {p r e} + p _ {b}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 845, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This function is represented as multiplication by $\\frac{(p_c x_{pre} + p_b)}{x_{pre}}$ . Therefore, noise-accounted contrast and", + "bbox": [ + 500, + 868, + 890, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14010", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "brightness augmentation is finally defined as,", + "bbox": [ + 76, + 90, + 375, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\text {r a n d o m} p _ {c}, p _ {b} \\\\ \\text {r a n d o m} p _ {u}, p _ {g} (\\text {w h e r e} p _ {u} p _ {g} = \\frac {\\left(p _ {c} x _ {p r e} + p _ {b}\\right)}{x _ {p r e}}, p _ {u}, p _ {g} > 0) \\\\ E q. (1 1) \\left(\\mu_ {x} \\leftarrow x _ {p r e}\\right) \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 114, + 473, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We can also convert hue by changing $p_c$ and $p_b$ per color filter position in the RAW bayer.", + "bbox": [ + 76, + 184, + 468, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Blur Augmentation", + "text_level": 1, + "bbox": [ + 76, + 232, + 266, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we introduce noise-accounted blur augmentation. Usual blur augmentation makes noise smaller than actual blur because the noise $n_d$ and $n_r$ are smoothed out although their noise amounts, in reality, are not related to how fast you shake a camera or how fast objects move. Only the photon number-related noise is smoothed out in actual motion blur. The actual blurred pixel is expressed as,", + "bbox": [ + 75, + 255, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {n e w} \\sim \\mathcal {N} \\left(g \\alpha \\sum_ {k} w _ {k} \\bar {u} _ {k}, g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 368, + 473, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sum_{k}w_{k} = 1$ is the blur kernel. With similar equation manipulation from Eq. (9) to Eq. (11), noise-accounted blur augmentation is", + "bbox": [ + 76, + 421, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\sum_ {k} w _ {k} g \\alpha \\bar {u} _ {k}, \\sum_ {k} w _ {k} ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - \\sum_ {k} w _ {k} ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u _ {k}} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\\\ + g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {15} \\\\ = \\sum_ {k} w _ {k} x _ {p r e} + \\mathcal {N} (0, g \\alpha \\sum_ {k} (1 - w _ {k}) w _ {k} x _ {p r e, k} \\\\ + (1 - \\sum_ {k} w _ {k} ^ {2}) (g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2})). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 474, + 472, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We account for prior noise but not for prior blur amounts because most images in usual datasets are not very blurry. Furthermore, it is difficult to estimate the prior blur amount.", + "bbox": [ + 76, + 659, + 468, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, please note that augmentation to make images clean (make them brighter and deblurred) is inevitably difficult with noise-accounted RAW augmentation. Clipping noise variance in Eq. (11) to zero forcibly enables brightening, but brightening too much causes a mismatch of noise domain.", + "bbox": [ + 75, + 705, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 806, + 192, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 832, + 171, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although our method can be applied to any computer vision task, we choose a human detection task as a target because of its wide usage. We prepared a RAW image dataset", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for human detection task captured with an internally developed sensor. As mentioned earlier, our objective is to train image recognition models that work in various environments only using a training dataset in simple environments. So, most training images are taken under normal light conditions with fixed camera positions in several environments. Note that moderately dark and HDR images are also included to some extent in the training dataset. The analog gain is set to 6dB outdoors, 12dB indoors, and 32dB at night in moderate darkness to generate realistic easy images without auto-exposure. Test images, on the other hand, are taken in HDR or extremely dark environments. In addition, about $50\\%$ of them are captured with a strong camera shake. Moreover, the analog gain is chosen from 3dB, 6dB, 12dB, and 24dB regardless of the environment. Both datasets are captured with around 1 fps to increase diversity among images.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We manually annotate the human bounding boxes of both training and test data. Because precise annotation of test data on sRGB is impossible due to the noise and blur, we apply an offline ISP to each image and then annotate the bounding boxes. We manually set adequate ISP parameters per image and had to change the parameters several times to grasp the entire image. To avoid annotating large training datasets in this time-consuming way, it is desirable to train the model with a simple dataset. In total, 18,880 images are collected for training and 2,800 for testing. The examples are shown in Fig. 3.", + "bbox": [ + 496, + 348, + 892, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 527, + 718, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We mainly test with TTFNet [27] whose backbone is ResNet18 [14]. The network is trained for 48 epochs from scratch using Adam optimizer [22] and a cosine decay learning rate scheduler with a linear warmup [28] for the first 1,000 iterations whose maximum and minimum learning rates are 1e-3 and 1e-4. As to an ISP, a simple software ISP consisting of only a gamma tone mapping is implemented. In detail, two types of gamma tone mapping are implemented. One is the simplest gamma tone mapping, $y = x^{\\frac{1}{\\gamma}}$ ( $0 \\leq x \\leq 1$ ). The $\\gamma$ is set to 5 after tuning with a rough grid search manner. The other is a gamma tone mapping parameterized with three parameters [34]. Because the grid search for three parameters is time-consuming, we tuned the parameters with backpropagation together with the detector's weights as performed in [35, 49]. Other ISP functions are not used because they are known to have less impact on image recognition compared with tone mapping [13]. We also prepare an elaborated black-box ISP consisting of many functions in addition to a tone mapping function. The parameters are tuned for human perceptual quality by experts. We only use the elaborated black-box ISP under the conventional training pipeline. In other words, experiments are performed un", + "bbox": [ + 496, + 551, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14011", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/118b7e4a94c8f9f5e39038e4fe3b6707882b125088db2d22dfd117811f20647d.jpg", + "image_caption": [ + "Figure 3. Examples of the introduced dataset. The upper row shows the training dataset collected in simple environments while the lower row shows the challenging test dataset collected in various environments from dark to bright, HDR, and with or without handshake blur." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 851, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "der ISP-augmentation-detection order with the elaborated black-box ISP due to the hardware limitation. If contrast augmentation is used, the hue is also changed with a probability of $50\\%$ . In detail, the contrast factor per color channel $p_{c,h} = \\{R,G,B\\}$ is randomized from the base contrast factor $p_{c,\\text{base}}$ by $(0.8p_{c,\\text{base}}, 1.2p_{c,\\text{base}})$ after $p_{c,\\text{base}}$ is randomly decided. If blur augmentation is used, a random-sized blur kernel with a probability of $50\\%$ is used. Random shift and random scale augmentation whose maximum transformations are $10\\%$ and $3\\%$ of the input size are also applied with a probability of $80\\%$ before color jitter augmentation. The input size to the detector is (576, 352, 3). The performance of the detector is evaluated with average precision (AP@0.5:0.95) [24].", + "bbox": [ + 75, + 328, + 472, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Calibration of the Noise Model", + "text_level": 1, + "bbox": [ + 76, + 555, + 349, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each analog gain of 6dB, 12dB, and 24dB, two burst sequences are captured with different illumination. Each sequence consists of 100 images. $24 \\times 24$ Bayer pixels are sampled from each of the 24 color patches to calculate the mean and variance. In total $2 \\times 24 \\times 24 \\times 24$ pairs of mean and variance sets are obtained per analog gain to estimate the noise model. Thanks to the various color filters, exposure values, and color patches, two sequences are enough to ensure diversity. The lines in Fig. 4 show the estimated linear relationship in Eq. (6). The coefficients of determination, $R^2$ , for these line estimations are 0.9833, 0.9884, 0.9862 for 6, 12, and 24dB respectively. High values of $R^2$ indicate that the noise intensity is well modeled with respect to illumination intensity. Also, $R^2$ of the Eq. (7) and Eq. (8) are 1.0000 and 0.9984. This means the noise intensity is well modeled with respect to the analog gain. Based on the above, our noise model and the calibration method are well suited to the sensor in terms of noise intensity.", + "bbox": [ + 75, + 580, + 468, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we check the validity of the shape of the distribution. All noises were assumed to follow a Gaussian distribution. Especially, it is unclear whether the approximation", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/68d420a429e890c4e5d1e2b376d6f1be39e789c794e2f2c55fb6bf96d27e3c51.jpg", + "image_caption": [ + "Figure 4. Sensor noise model calibration result. The dots in the left graph are the mean and variance pairs for each pixel, and the lines are the estimated linear relationship for each analog gain. Since large numbers of dots are plotted, they seem to be widely spread. On the other hand, the histogram plot per analog gain (right) shows a clear difference between them." + ], + "image_footnote": [], + "bbox": [ + 498, + 325, + 893, + 441 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0fcbc7210852d82eb9a5b3376309771e5ff5d01eb992c44003809f001fd351df.jpg", + "image_caption": [ + "Figure 5. The result of the Shapiro-Wilk [40] test for each expected pixel value. When testing whether the 100 pixel values at each location correspond to a Gaussian distribution, most p-values are larger than 0.05 (a). The right (b) shows the cases where $\\mathfrak{p} < 0.05$ . It indicates the small p-values come from sparsity, not skew." + ], + "image_footnote": [], + "bbox": [ + 503, + 550, + 893, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathcal{P}(\\bar{u}) \\doteq \\mathcal{N}(\\bar{u}, \\bar{u})$ [9] is true. Therefore, the Shapiro-Wilk test [40] is performed. If the p-value of the test is higher than 0.05, it indicates that we cannot reject the null hypothesis that the data are normally distributed with more than a $95\\%$ confidence interval. Fig. 5(a) shows that most of them are higher than 0.05, but some results for dark pixels are less than 0.05. However, the distributions of the dark pixels are like Fig. 5(b). It is not very skewed and the sparsity causes the small p-value. Therefore, we conclude that all the noise", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14012", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4068d637165831208ae3384d04a2e8c49758ad212de0156ddfb9382b84e12e1a.jpg", + "image_caption": [ + "Figure 6. The statistical validation of the noise alignment. The green dots represent real image data, and the others are converted from it. The conversions are $\\times 0.1$ and $\\times 0.5$ contrast conversion with several methods. The (a) is a dark-to-extreme-dark conversion, and the (b) is a bright-to-dark conversion." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 472, + 215 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sources can be regarded as Gaussian noise.", + "bbox": [ + 76, + 315, + 361, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Based on the above, our sensor noise model and the calibration method represent the sensor noise well in terms of both intensity and distribution.", + "bbox": [ + 75, + 330, + 468, + 376 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Statistical Validation of the Noise Alignment", + "text_level": 1, + "bbox": [ + 76, + 387, + 452, + 404 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Before confirming the effectiveness of the proposed noise-accounted RAW augmentation to computer vision applications, the statistical validity is evaluated one more time by utilizing the series of color checker images. The evaluation method is as follows. First, the contrast of the sequential images is changed with or without noise consideration. Second, mean and variance pairs along the sequential dimension are computed. Third, the distributions of real and converted pairs are examined. If the real and converted pairs matched well, it means the converted images have the same noise amount as the original real images.", + "bbox": [ + 75, + 411, + 468, + 577 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Three different noise alignment methods are compared, i.e., no noise consideration, the usual noise-accounted method that disregards prior noise in the input [4,15,44,47], and our proposed noise alignment method. Fig. 6 shows the comparison result. It indicates that prior noise consideration is unnecessary if pixels are darkened considerably. However, a small contrast factor caused a noise domain gap even if the input is bright like Fig. 6 (right). In contrast, our noise-accounted conversion always converted images with realistic noise. It implies that our proposed method is suited for various strengths of augmentation. If prior noise is not accounted for, the inputs always have to be darkened considerably and already dark images are difficult to use.", + "bbox": [ + 75, + 579, + 468, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Augmentation Parameters Tuning", + "text_level": 1, + "bbox": [ + 76, + 786, + 375, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The optimal augmentation parameters should be different between augmentation before and after ISP. To make a fair comparison, we roughly tune both of the augmentation parameters. The strategy is as follows. First, we search the appropriate range of contrast factor $p_c$ and brightness perturbation $p_b$ successively. To be robust to any illumination", + "bbox": [ + 75, + 810, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of inputs, we re-parameterize $p_b$ as $p_b = \\hat{p}_b \\min(x)$ and randomize the $\\hat{p}_b$ instead of $p_b$ . Lastly, we search for the appropriate max blur distance $p_d$ . In these experiments, we do not account for sensor noise. We use the elaborated black-box ISP for the augmentation after ISP setting and the simplest gamma function for the augmentation before ISP setting.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results are shown in Table 1. The best parameter settings are used in the next section.", + "bbox": [ + 498, + 181, + 890, + 213 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Evaluation of the Noise-Accounted RAW Augmentation", + "text_level": 1, + "bbox": [ + 498, + 224, + 890, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, the proposed noise-accounted RAW augmentation is evaluated on training image recognition models. First, as Table 2 shows, augmentation before ISP drastically improves the accuracy with the simplest ISP. It suggests the realistic pixel intensity distribution achieved by augmentation before ISP is the key to improving the accuracy in wide environments. In the color jitter augmentation only setting, the accuracy is improved from the general noise alignment method [2,4,9,15,26,31,36,47,50] by considering prior noise. In the color jitter and blur augmentation setting, noise-accounted color jitter augmentation plus normal blur augmentation does not improve much from no noise-accounted settings. Instead, noise alignment in both color jitter and blur augmentation improves the accuracy. It indicates that random noise is not effective and realistic noise is important. Comparing the accuracy under the same simplest gamma tone mapping setting, our proposed noise-accounted RAW augmentation doubles the accuracy of conventional augmentation after ISP. Furthermore, when parameterized gamma tone mapping is used as our simple ISP, the accuracy is even superior to the elaborated black-box ISP consisting of many functions in addition to a tone mapping function. As the visualization results in the supplementary material show, the elaborated black-box ISP outputs more perceivable images. It suggests that minimizing the domain gap caused by augmentation is more important than the superiority of the ISP. We might improve the accuracy more by an elaborated ISP and the proposed augmentation.", + "bbox": [ + 496, + 265, + 892, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As mentioned earlier, there are noise dealing works in noise-related fields like denoising. We compare ours with these methods in the detection task. One is the K-Sigma transform [44], a kind of noise domain generalization. It normalizes images so that the pixel value and the standard deviation of the noise are linearly correlated. The other is noise amount notification with a concatenation of the noise variance map [2]. To follow the previous setup, direct RAW input without an ISP is also compared. Color jitter and blur augmentation are also applied to the methods different from the previous papers for a fair comparison. Table 3 shows the comparison results. As to the K-Sigma transform, simply applying \"aug.\" before or after the K-Sigma", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14013", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aac2416aa842f053ac14b742de618de4be2fe2c15b50a8ee3e59c8b6750d159d.jpg", + "table_caption": [ + "Table 1. The augmentation hyperparameter tuning for a fair comparison between before and after ISP augmentation. The range of contrast, brightness, and blur distance are tuned one by one, taking over the previous best parameters." + ], + "table_footnote": [], + "table_body": "
augmentation after ISP (tuned for the black-box ISP)augmentation before ISP (tuned for the simplest ISP)
contrastrange0.2-10.1-10.2-50.1-100.05-200.1-10.02-10.01-10.005-10.01-1.1
AP@0.5:0.95 [%]41.941.843.245.144.536.939.840.435.838.9
brightnessrange0-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.70-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.7
AP@0.5:0.95 [%]45.144.544.545.244.740.440.939.939.439.4
blur distancerange0-00-30-50-90-130-00-30-50-90-13
AP@0.5:0.95 [%]45.246.845.745.937.940.939.839.640.643.3
", + "bbox": [ + 81, + 127, + 893, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f75ffe1d232f5dca2d8ae3406c4570a3bd3d8af484725943d9f8e12ebef631a2.jpg", + "table_caption": [ + "Table 2. Evaluation of the noise-accounted RAW augmentation. The color augmentation contains default hue augmentation plus tuned contrast and brightness augmentation. The w/o prior means the prior input noise is disregarded like many of the previous noise-accounted image conversion methods [2,4,9,15,26,31,36, 47, 50]. Because we adopt the well-established heteroscedastic Gaussian model Eq. (2), it is identical to the noise alignment of [2,9,36,50]. In this experiment, we also use the parameterized gamma tone mapping as the simple ISP, although it can't be used in the augmentation after ISP settings because the gradient from the detection loss is needed to tune." + ], + "table_footnote": [ + "†: The noise alignment is only applied to the color jitter augmentation." + ], + "table_body": "
augmentationnoisemAP@0.5:0.95 [%]
black-box ESPsimple ESP
simplestparameterized
Colorafter-45.219.3-
before (ours)--40.944.4
w/o prior-43.547.7
ours-44.648.1
Color + Blurafter-46.820.4-
before (ours)--43.343.8
ours†-43.447.9
ours-45.348.3
", + "bbox": [ + 81, + 410, + 468, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "transforms gives a better result. However, there is a theoretical problem in both cases. If \"aug.\" is applied after the transform, the linear relation between pixel value and noise amount is retained but pixel intensity becomes inconsistent. On the other hand, applying \"aug.\" before the transform makes the noise amount unrealistic. Changing the augmentation to \"our aug.\" makes the intensity and noise realistic and improves the accuracy. From the experiment, we find the proposed augmentation boosts previous noise-dealing methods if ISPs are used. However, if ISPs are not used, noise accounted augmentation slightly deteriorated the accuracy. We argue that it is because the intensity distributions of RAW images are too difficult and unrealistic clean images might help training. However, the overall accuracy is lower than with ISPs. Also, for the detection task, only our proposed method is enough. It might be because, unlike the denoising task which should focus on noise, it is important to make the detector focus on pixel intensity distribution for the detection task.", + "bbox": [ + 75, + 613, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ddcb609c51bbf6eea2ca253deba7c18ccb66b5922d344dd6511fa757ba44219d.jpg", + "table_caption": [ + "Table 3. The comparison results with other noise-dealing techniques. The \"aug.\" means contrast and blur augmentation without noise-accounted and \"our aug.\" means with noise-accounted. We use the simplest gamma function in the ISP." + ], + "table_footnote": [], + "table_body": "
methodAP@0.5:0.95 [%]
w/o ISPw/ ISP
concat [2]16.521.5
aug. + concat [2]35.031.6
our aug. + concat [2]33.740.4
K-Sigma [44]14.327.5
K-Sigma [44] + aug.25.034.1
aug. + K-Sigma [44]26.642.1
our aug. + K-Sigma [44]26.344.0
our aug.32.845.3
", + "bbox": [ + 535, + 313, + 859, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 500, + 619, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a noise-accounted RAW augmentation method in which augmentation is applied before ISP to minimize the luminance domain gap and a sensor noise model is taken into account to minimize the noise domain gap. Unlike previous noise-accounted methods, ours takes the prior input noise into account. It minimizes the domain gap more and enables the use of already noisy images as training data. Thanks to the realistic augmentation, our method improves the detection accuracy in difficult scenes compared to the conventional methods. In the future, we would like to investigate whether the proposed augmentation with an elaborate ISP improves computer vision performance even further. Also, we would like to check the effectiveness against other image recognition tasks, such as classification or segmentation, by preparing datasets. We believe it is effective because our method is task-independent. Lastly, we are glad if this work sheds light on the importance of RAW images.", + "bbox": [ + 496, + 527, + 893, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 804, + 596, + 819 + ], + "page_idx": 7 + }, + { + "type": "ref_text", + "text": "[1] Goutam Bhat, Martin Danelljan, Fisher Yu, Luc Van Gool, and Radu Timofte. Deep reparametrization of multi-frame super-resolution and denoising. 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In Proceedings of the 27th ACM international conference on multimedia, pages 1632-1640, 2019. 1" + ], + "bbox": [ + 78, + 90, + 470, + 289 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14017", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Rawgment_ Noise-Accounted RAW Augmentation Enables Recognition in a Wide Variety of Environments/98100afc-c86e-439b-98cd-4768d6e60a6a_model.json b/2023/Rawgment_ Noise-Accounted RAW Augmentation Enables Recognition in a Wide Variety of Environments/98100afc-c86e-439b-98cd-4768d6e60a6a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e3cf3f0d665681b81ba931ca83d99dd82e52f046 --- /dev/null +++ b/2023/Rawgment_ Noise-Accounted RAW Augmentation Enables Recognition in a Wide Variety of Environments/98100afc-c86e-439b-98cd-4768d6e60a6a_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.13, + 0.868, + 0.177 + ], + "angle": 0, + "content": "Rawgment: Noise-Accounted RAW Augmentation Enables Recognition in a Wide Variety of Environments" + }, + { + "type": "text", + "bbox": [ + 0.213, + 0.204, + 0.757, + 0.24 + ], + "angle": 0, + "content": "Masakazu Yoshimura Junji Otsuka Atsushi Irie Takeshi Ohashi Sony Group Corporation" + }, + { + "type": "text", + "bbox": [ + 0.154, + 0.242, + 0.816, + 0.258 + ], + "angle": 0, + "content": "{masakazu.yoshimura, junji.otsuka, atsushi.irie, takeshi.a.ohashi}@sony.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.658 + ], + "angle": 0, + "content": "Image recognition models that work in challenging environments (e.g., extremely dark, blurry, or high dynamic range conditions) must be useful. However, creating training datasets for such environments is expensive and hard due to the difficulties of data collection and annotation. It is desirable if we could get a robust model without the need for hard-to-obtain datasets. One simple approach is to apply data augmentation such as color jitter and blur to standard RGB (sRGB) images in simple scenes. Unfortunately, this approach struggles to yield realistic images in terms of pixel intensity and noise distribution due to not considering the non-linearity of Image Signal Processors (ISPs) and noise characteristics of image sensors. Instead, we propose a noise-accounted RAW image augmentation method. In essence, color jitter and blur augmentation are applied to a RAW image before applying non-linear ISP, resulting in realistic intensity. Furthermore, we introduce a noise amount alignment method that calibrates the domain gap in the noise property caused by the augmentation. We show that our proposed noise-accounted RAW augmentation method doubles the image recognition accuracy in challenging environments only with simple training data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.692, + 0.21, + 0.709 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Although image recognition has been actively studied, its performance in challenging environments still needs improvement [15]. Sensitive applications such as mobility sensing and head-mounted wearables need to be robust to various kinds of difficulties, including low light, high dynamic range (HDR) illuminance, motion blur, and camera shake. One possible solution is to use image enhancement and restoration methods. A lot of DNN-based low-light image enhancement [12, 20, 29, 30, 46, 54], denoising [32, 43, 53], and deblurring [43, 48, 52] methods are proposed to improve the pre-captured sRGB image quality. While they are useful for improving pre-captured image" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.291, + 0.898, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.63, + 0.372, + 0.754, + 0.384 + ], + "angle": 0, + "content": "(a) Usual training pipeline" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.392, + 0.888, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.583, + 0.483, + 0.813, + 0.495 + ], + "angle": 0, + "content": "(b) Noise-accounted RAW augmentation pipeline" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.63 + ], + "angle": 0, + "content": "Figure 1. The concept of the proposed noise-accounted RAW augmentation. Conventional augmentation (a) is applied to the output of an ISP; due to the nonlinear operations in the ISP, it produces images that cannot be captured at any ambient light intensities. Instead, ours (b) applies augmentation before an ISP. It generates realistic pixel intensity distribution that can be captured when the light intensity is different. Moreover, the noise amount is also corrected to minimize the domain gap between real and augmented ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.718 + ], + "angle": 0, + "content": "quality, a recent work [15] shows that using them as preprocessing for image recognition models has limited accuracy gains since they already lost some information, and restoring the lost information is difficult." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Another possible solution is to prepare a dataset for difficult environments [3, 33]. However, these datasets only cover one or a few difficulties, and creating datasets in various environments is too expensive. Especially, manual annotation of challenging scenes is difficult and time-consuming. For example, we can see almost nothing in usual sRGB images under extremely low-light environments due to heavy noise. In addition, some regions in HDR scenes suffer from halation or blocked-up shadows because the 8-bit range of usual sRGB images cannot fully preserve the real world, which is 0.000001 \\([cd / m^2]\\) under starlight and 1.6 billion \\([cd / m^2]\\) under direct sunlight [37]. Heavy" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14007" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "motion blur and camera shake also make annotation difficult. Some works capture paired short-exposure and long-exposure images, and the clean long-exposure images are used for annotation or ground truth [15-17, 19]. The limitation is that the target scene needs to be motionless if the pairs are taken sequentially with one camera [15], and positional calibration is required if the pairs are taken with synchronized cameras [16,17]. Some works use a beam splitter to capture challenging images and their references without calibration [19, 45]. However, they are difficult to apply in dark scenes. Moreover, HDR images cannot be taken in the same way because some regions become overexposed or underexposed in both cameras." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.544 + ], + "angle": 0, + "content": "To this end, we aim to train image recognition models that work in various environments only using a training dataset in simple environments like bright, low dynamic range, and blurless. In this case, image augmentation or domain adaptation is important to overcome the domain gap between easy training data and difficult test data. However, we believe usual augmentations on sRGB space are ineffective because it does not take into account the nonlinear mapping of ISPs. In particular, tone mapping significantly changes the RAW image values, which are roughly proportional to physical brightness [44]. Contrast, brightness, and hue augmentation on sRGB space result in unrealistic images that cannot be captured under any ambient light intensity as shown in Fig. 1(a). In contrast, we propose augmentation on RAW images. In other words, augmentation is applied before ISPs to diminish the domain shift as shown in Fig. 1(b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.473, + 0.831 + ], + "angle": 0, + "content": "Oher possible sources of the domain gap are differences in noise amount and noise distribution. To tackle these problems, we propose a method to align both light intensity and noise domains. Recent works show that adding physics-based realistic noise improves the performance of DNN-based denoisers [2, 44, 47, 50] and dark image recognition [4, 15]. Although their proposed sensor noise modelings are accurate, they assume that the original bright images are noise free. In contrast, we propose to modify the noise amount after contrast, brightness, and hue conversion considering the noise amount in the original images. It enables a more accurate alignment of the noise domain. Even bright images may have dark areas due to shadows or object colors, and their prior noise cannot be ignored. Another merit of our method is that it is possible to take dark images that already contain a lot of noise as input. In addition to noise alignment after color jitter augmentation, we show the importance of noise alignment after blur augmentation, which is proposed for the first time in this paper." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.832, + 0.316, + 0.845 + ], + "angle": 0, + "content": "Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- It is the first work to emphasize the importance of augmentation before ISP for image recognition to the best of our knowledge." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.184 + ], + "angle": 0, + "content": "- Noise amount alignment method is proposed to reduce the noise domain gap after RAW image augmentation. In contrast to previous works, our proposed method takes into account prior noise in the input image. It enables more accurate alignment and use of any strength of augmentation and even already noisy input." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.207, + 0.894, + 0.283 + ], + "angle": 0, + "content": "- We show qualitative analysis for the validity of our sensor noise modeling and corresponding noise-accounted augmentation. We prove that our proposed noise-accounted RAW augmentation has the edge over the previous methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.307, + 0.65, + 0.323 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.335, + 0.821, + 0.351 + ], + "angle": 0, + "content": "2.1. Recognition in Difficult Environment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Many works have tackled image recognition in difficult environments. For low-light environments, several works improve the accuracy by replacing a traditional ISP with a powerful DNN-based ISP to create clean images for downstream image recognition models [5, 25, 33]. Even though these methods are promising because there is no information loss, the computational cost is the problem. Another approach is direct RAW image recognition without ISP [15, 39]. Their image recognition models benefit from the richest information and improve accuracy under low-light environments. However, several works report ISPs, especially tone mapping, are helpful for machine vision [13, 49]. Direct RAW image recognition may works well if the images have a low dynamic range. Another approach is domain adaptation or related methods which support low-light recognition with bright images [4, 15, 38]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.729 + ], + "angle": 0, + "content": "For HDR environments, some works propose DNN-based auto-exposure control [35, 42] to improve downstream recognition. Also, multi-frame HDR synthesis methods [1, 6] can be used as a preprocessing, although camera motion makes them challenging. A luminance normalization method is also introduced to improve recognition performance under varying illumination conditions [18]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.777 + ], + "angle": 0, + "content": "For blurry environments, deblurring methods are actively studied [48,51]. These DNN-based methods successfully restore clear images from heavily blurred images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Differing from the above, we aim to do image recognition under all the above difficulties using simple scene training data with our proposed augmentation method. We do not use domain adaptation methods since these methods are usually used in a setting where the target domain is equal to or smaller than the source domain [10]. On the contrary, in our setting, the distribution of the target domain is much wider than that of the source domain." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14008" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.323, + 0.107 + ], + "angle": 0, + "content": "2.2. Image Conversion on RAW" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.266 + ], + "angle": 0, + "content": "Recently, several methods [2,4,29] convert bright sRGB images into realistic dark images by the following procedures. First, they invert an ISP pipeline to generate RAW-like images followed by illumination change on the RAW data space with plausible sensor noise. Afterward, degraded sRGB is generated by applying the forward ISP pipeline. This operation avoids the nonlinear mappings in the ISP and simulates short exposures and dark environments. With a similar intention, we propose to apply augmentation before ISPs to train image recognition models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.276, + 0.466, + 0.292 + ], + "angle": 0, + "content": "2.3. Noise Modeling and Noise Amount Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.469, + 0.48 + ], + "angle": 0, + "content": "In the electronic imaging sensor community, detailed noise modelings based on electric current and circuit have been studied [7, 11, 23, 41]. They are precise but difficult to be applied to the image-to-image conversion. Thus, in the machine vision community, simplified pixel value-based noise modelings are proposed based on electric noise modelings [2, 44, 47]. Although the noise model of [47] is well designed with a high degree of freedom Tukey lambda distribution [21], we are based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50] because it is still well fitted to real sensor noise and we can consider prior noise in original images which will be explained later." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.469, + 0.632 + ], + "angle": 0, + "content": "Recently, adding realistic model-based sensor noise to the ground truth clean images is proved to be helpful to train DNN-based denoiser [2,44,47,50] and low-light object detection models [4, 15]. Although they use highly consistent noise models, they regard original images as noise-free. In contrast, we propose to modify the noise amount after image conversion considering the noise amount of the original images. It enables a more accurate alignment of the noise domain and enables the use of any intensity of augmentation and already noisy images as input." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.212, + 0.663 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.469, + 0.716 + ], + "angle": 0, + "content": "In this section, we introduce our noise model, calibration procedure, and proposed noise-accounted RAW augmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.21, + 0.74 + ], + "angle": 0, + "content": "3.1. Noise Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "First, we briefly introduce our noise model for later explanation although it is based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50]. The number of photons \\( u \\) hitting the photodiode of each pixel is converted to a voltage with quantum efficiency \\( \\alpha \\). Some processing is then performed to read out the voltage, in which noise \\( n_d \\) is inevitably mixed. Next, analog gain \\( g \\) is multiplied to amplify the value. Lastly, the voltage is converted to a digital value. We simplify and summarize the noise after analog gain as \\( n_r \\). Since it is common to use analog gain which" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "has a better signal-to-noise ratio (SNR), we omit the digital gain term in our noise model. To sum up, the photon-to-RAW pixel value conversion can be formulated as," + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.147, + 0.892, + 0.163 + ], + "angle": 0, + "content": "\\[\nx = g \\left(\\alpha u + n _ {d}\\right) + n _ {r}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.17, + 0.892, + 0.249 + ], + "angle": 0, + "content": "We approximate \\(n_d\\) and \\(n_r\\) as Gaussian noise \\(\\mathcal{N}\\left(0,\\sigma_d^2\\right)\\) \\(\\mathcal{N}\\left(0,\\sigma_r^2\\right)\\) and the number of photons \\(u\\) itself obeys the Poisson distribution \\(\\mathcal{P}(\\bar{u})\\) where \\(\\bar{u}\\) is the expected number of photons. If \\(\\bar{u}\\) is large enough, we can approximate as \\(\\mathcal{P}(\\bar{u})\\doteq \\mathcal{N}(\\bar{u},\\bar{u})\\) [9]. Thus, our noise model is as follows;" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.256, + 0.892, + 0.275 + ], + "angle": 0, + "content": "\\[\nx \\sim g (\\alpha \\mathcal {N} (\\bar {u}, \\bar {u}) + \\mathcal {N} (0, \\sigma_ {d} ^ {2})) + \\mathcal {N} (0, \\sigma_ {r} ^ {2}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.282, + 0.892, + 0.328 + ], + "angle": 0, + "content": "We show the validity of the Gaussian approximation of \\( n_d \\), \\( n_r \\), and \\( \\mathcal{P}(\\bar{u}) \\) in the Section 4.3. We don't follow the further development of the formula in [9] for our purpose." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.328, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Gaussian distribution has the following convenient natures;" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.37, + 0.892, + 0.444 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} X \\sim \\mathcal {N} \\left(\\mu_ {X}, \\sigma_ {X} ^ {2}\\right) \\\\ Y \\sim \\mathcal {N} \\left(\\mu_ {Y}, \\sigma_ {Y} ^ {2}\\right) \\\\ X + Y \\sim \\mathcal {N} \\left(\\mu_ {X} + \\mu_ {Y}, \\sigma_ {X} ^ {2} + \\sigma_ {Y} ^ {2}\\right) \\\\ c X \\sim \\mathcal {N} \\left(c \\mu_ {X}, c ^ {2} \\sigma_ {X} ^ {2}\\right) \\end{array} , \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.538 + ], + "angle": 0, + "content": "if \\( X \\) and \\( Y \\) are independent, and that's why we choose the simple Gaussian approximation instead of the recently proposed more expressive noise model [47]. These natures enable the proposed noise-accounted RAW augmentation to account for prior noise in input images. Furthermore, they further simplify our noise model as," + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.545, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nx \\sim \\mathcal {N} \\left(g \\alpha \\bar {u}, g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.632 + ], + "angle": 0, + "content": "Because the expected number of photon \\(\\bar{u}\\) is inconvenient to use in image-to-image conversion, we replace it with the expected pixel value \\(\\mu_{x} = g\\alpha \\bar{u}\\), and our final noise model is defined as," + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.64, + 0.892, + 0.66 + ], + "angle": 0, + "content": "\\[\nx \\sim \\mathcal {N} \\left(\\mu_ {x}, \\sigma_ {x} ^ {2} = g \\alpha \\mu_ {x} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.726, + 0.681 + ], + "angle": 0, + "content": "3.2. Noise Model Calibration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Our sensor noise model shown in Eq. (5) has three parameters, \\(\\alpha\\), \\(\\sigma_d^2\\), and \\(\\sigma_r^2\\), which have to be calibrated per target sensor. We capture a series of RAW images of a color checker as shown in Fig. 2(a). We then calculate the mean \\(\\mu_x\\) and variance \\(\\sigma_x^2\\) along the time direction of each pixel position. We calculate them along the time direction instead of the spatial direction as performed in [44] since lens distortion changes the luminance of the same color patch. These operations are performed several times by changing the analog gain and exposure time. Eventually, we get various sets of \\(\\{\\mu_x,\\sigma_x^2\\}\\) for each analog gain. Note that we calculate mean and variance without separating RGB channels because there is no significant difference in noise properties." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14009" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.089, + 0.379, + 0.225 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.228, + 0.334, + 0.24 + ], + "angle": 0, + "content": "(a) burst capture with several analog gains" + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.089, + 0.81, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.39, + 0.228, + 0.65, + 0.24 + ], + "angle": 0, + "content": "(b) estimate linear relationship of the mean and variance" + }, + { + "type": "image_caption", + "bbox": [ + 0.672, + 0.228, + 0.868, + 0.24 + ], + "angle": 0, + "content": "(c) estimate the sensor specific parameters" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.89, + 0.278 + ], + "angle": 0, + "content": "Figure 2. Our noise model calibration procedures to a target sensor. It just needs to capture burst RAW images and does not need special devices." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.306, + 0.469, + 0.336 + ], + "angle": 0, + "content": "In Eq. (5), \\(\\mu_{x}\\) and \\(\\sigma_x^2\\) have a linear relationship per analog gain \\(g_{n}\\);" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.338, + 0.469, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {x} ^ {2} = a _ {g _ {n}} \\mu_ {x} + b _ {g _ {n}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.366, + 0.469, + 0.412 + ], + "angle": 0, + "content": "Therefore, we solve linear regression to estimate \\( a_{g_n} \\) and \\( b_{g_n} \\) per gain like Fig. 2(b). In addition, we use RANSAC [8] to robustly take care of outlier \\( \\{\\mu_x, \\sigma_x^2\\} \\) pairs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.469, + 0.442 + ], + "angle": 0, + "content": "Finally, we estimate \\(\\alpha\\), \\(\\sigma_d^2\\), and \\(\\sigma_r^2\\) from the following redundant simultaneous equations by least-squares method," + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.457, + 0.469, + 0.52 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{c} a _ {g _ {1}} = g _ {1} \\alpha \\\\ \\vdots \\\\ a _ {g _ {n}} = g _ {n} \\alpha \\end{array} , \\right. \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.536, + 0.469, + 0.599 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} b _ {g _ {1}} = g _ {1} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\\\ \\vdots \\\\ b _ {g _ {n}} = g _ {n} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\end{array} . \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.607, + 0.469, + 0.668 + ], + "angle": 0, + "content": "The procedure above enables calibration of the sensor noise model without special devices. We later show that our sensor model and the calibration method represent the real sensor noise with enough preciseness." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.402, + 0.696 + ], + "angle": 0, + "content": "3.3. Noise-Accounted RAW Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.9 + ], + "angle": 0, + "content": "We propose augmentation before ISP instead of the usual augmentation after ISP to generate realistic images. Furthermore, we improve the reality of the augmented images by considering the sensor noise model. Unlike the previous works [2,4,15,44,47,50], ours takes the prior noise amount of input images into account. It generates more realistic noise since even bright images have some extent of noise. Especially, dark parts due to shadow or the color of objects might have a non-negligible amount of noise. Moreover, it allows any brightness of input images different from previous works. Specifically, we introduce how to adjust noise amount after contrast, brightness, hue, and blur augmentation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.306, + 0.739, + 0.321 + ], + "angle": 0, + "content": "3.3.1 Color Jitter Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.449 + ], + "angle": 0, + "content": "Contrast, brightness, and hue augmentation simulate different exposure times, light intensities, and analog gain. Hence, we first assume to multiply the exposure time, light intensity, and analog gain by \\( p_e \\), \\( p_i \\), and \\( p_g \\) respectively. Because \\( p_e \\) and \\( p_i \\) equally change the number of photon \\( u \\) in the case of our noise model, we rewrite them as \\( p_u = p_e p_i \\). Then, images in the above environment settings \\( x_{new} \\) can be rewritten as," + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.459, + 0.891, + 0.501 + ], + "angle": 0, + "content": "\\[\nx _ {n e w} \\sim \\mathcal {N} \\binom {(p _ {g} g) \\alpha \\left(p _ {u} \\bar {u}\\right),} {\\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.508, + 0.764, + 0.524 + ], + "angle": 0, + "content": "Based on Eq. (3), it can be expanded as" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.532, + 0.892, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\left(p _ {g} p _ {u}\\right) \\alpha g \\bar {u}, \\left(p _ {g} p _ {u}\\right) ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - (p _ {g} p _ {u}) ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {10} \\\\ + \\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.602, + 0.891, + 0.647 + ], + "angle": 0, + "content": "By inserting \\(\\mu_{x} = g\\alpha \\bar{u}\\) and original pixel value, \\(x_{pre} \\sim \\mathcal{N}\\left(\\mu_x, g\\alpha \\mu_x + g^2\\sigma_d^2 + \\sigma_r^2\\right)\\), it can be expressed with a pixel value-based equation as follows;" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.66, + 0.891, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} x _ {n e w} \\sim p _ {u} p _ {g} x _ {p r e} + \\\\ \\mathcal {N} \\left(0, p _ {u} \\left(1 - p _ {u}\\right) p _ {g} ^ {2} g \\alpha \\mu_ {x} \\right. \\tag {11} \\\\ + \\left(1 - p _ {u} ^ {2}\\right) p _ {g} ^ {2} g ^ {2} \\sigma_ {d} ^ {2} + \\left(1 - p _ {u} ^ {2} p _ {g} ^ {2}\\right) \\sigma_ {r} ^ {2}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.846 + ], + "angle": 0, + "content": "Because the expected original pixel value \\(\\mu_{x}\\) in the Gaussian term is impossible to obtain, we approximate it as \\(\\mu_{x} = x_{pre}\\). Based on this equation, we can precisely simulate as if exposure time, light intensity, and analog gain were \\(p_{e}, p_{i}\\), and \\(p_{g}\\) times. Then, let's come back to contrast, brightness, and hue augmentation. When contrast is multiplied by \\(p_{c}\\) and brightness is changed by \\(p_{b}\\), it can be expressed as," + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.847, + 0.891, + 0.863 + ], + "angle": 0, + "content": "\\[\nx _ {n e w} = p _ {c} x _ {p r e} + p _ {b}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.869, + 0.892, + 0.905 + ], + "angle": 0, + "content": "This function is represented as multiplication by \\(\\frac{(p_c x_{pre} + p_b)}{x_{pre}}\\). Therefore, noise-accounted contrast and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14010" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.377, + 0.107 + ], + "angle": 0, + "content": "brightness augmentation is finally defined as," + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.116, + 0.474, + 0.184 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\text {r a n d o m} p _ {c}, p _ {b} \\\\ \\text {r a n d o m} p _ {u}, p _ {g} (\\text {w h e r e} p _ {u} p _ {g} = \\frac {\\left(p _ {c} x _ {p r e} + p _ {b}\\right)}{x _ {p r e}}, p _ {u}, p _ {g} > 0) \\\\ E q. (1 1) \\left(\\mu_ {x} \\leftarrow x _ {p r e}\\right) \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.185, + 0.47, + 0.216 + ], + "angle": 0, + "content": "We can also convert hue by changing \\( p_c \\) and \\( p_b \\) per color filter position in the RAW bayer." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.233, + 0.267, + 0.248 + ], + "angle": 0, + "content": "3.3.2 Blur Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.256, + 0.47, + 0.362 + ], + "angle": 0, + "content": "Next, we introduce noise-accounted blur augmentation. Usual blur augmentation makes noise smaller than actual blur because the noise \\( n_d \\) and \\( n_r \\) are smoothed out although their noise amounts, in reality, are not related to how fast you shake a camera or how fast objects move. Only the photon number-related noise is smoothed out in actual motion blur. The actual blurred pixel is expressed as," + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.369, + 0.474, + 0.422 + ], + "angle": 0, + "content": "\\[\nx _ {n e w} \\sim \\mathcal {N} \\left(g \\alpha \\sum_ {k} w _ {k} \\bar {u} _ {k}, g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.47, + 0.468 + ], + "angle": 0, + "content": "where \\(\\sum_{k}w_{k} = 1\\) is the blur kernel. With similar equation manipulation from Eq. (9) to Eq. (11), noise-accounted blur augmentation is" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.475, + 0.473, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\sum_ {k} w _ {k} g \\alpha \\bar {u} _ {k}, \\sum_ {k} w _ {k} ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - \\sum_ {k} w _ {k} ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u _ {k}} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\\\ + g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {15} \\\\ = \\sum_ {k} w _ {k} x _ {p r e} + \\mathcal {N} (0, g \\alpha \\sum_ {k} (1 - w _ {k}) w _ {k} x _ {p r e, k} \\\\ + (1 - \\sum_ {k} w _ {k} ^ {2}) (g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2})). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.66, + 0.469, + 0.705 + ], + "angle": 0, + "content": "We account for prior noise but not for prior blur amounts because most images in usual datasets are not very blurry. Furthermore, it is difficult to estimate the prior blur amount." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.469, + 0.795 + ], + "angle": 0, + "content": "In addition, please note that augmentation to make images clean (make them brighter and deblurred) is inevitably difficult with noise-accounted RAW augmentation. Clipping noise variance in Eq. (11) to zero forcibly enables brightening, but brightening too much causes a mismatch of noise domain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.808, + 0.194, + 0.823 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.833, + 0.173, + 0.847 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Although our method can be applied to any computer vision task, we choose a human detection task as a target because of its wide usage. We prepared a RAW image dataset" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "for human detection task captured with an internally developed sensor. As mentioned earlier, our objective is to train image recognition models that work in various environments only using a training dataset in simple environments. So, most training images are taken under normal light conditions with fixed camera positions in several environments. Note that moderately dark and HDR images are also included to some extent in the training dataset. The analog gain is set to 6dB outdoors, 12dB indoors, and 32dB at night in moderate darkness to generate realistic easy images without auto-exposure. Test images, on the other hand, are taken in HDR or extremely dark environments. In addition, about \\(50\\%\\) of them are captured with a strong camera shake. Moreover, the analog gain is chosen from 3dB, 6dB, 12dB, and 24dB regardless of the environment. Both datasets are captured with around 1 fps to increase diversity among images." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.349, + 0.893, + 0.516 + ], + "angle": 0, + "content": "We manually annotate the human bounding boxes of both training and test data. Because precise annotation of test data on sRGB is impossible due to the noise and blur, we apply an offline ISP to each image and then annotate the bounding boxes. We manually set adequate ISP parameters per image and had to change the parameters several times to grasp the entire image. To avoid annotating large training datasets in this time-consuming way, it is desirable to train the model with a simple dataset. In total, 18,880 images are collected for training and 2,800 for testing. The examples are shown in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.719, + 0.543 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.552, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We mainly test with TTFNet [27] whose backbone is ResNet18 [14]. The network is trained for 48 epochs from scratch using Adam optimizer [22] and a cosine decay learning rate scheduler with a linear warmup [28] for the first 1,000 iterations whose maximum and minimum learning rates are 1e-3 and 1e-4. As to an ISP, a simple software ISP consisting of only a gamma tone mapping is implemented. In detail, two types of gamma tone mapping are implemented. One is the simplest gamma tone mapping, \\( y = x^{\\frac{1}{\\gamma}} \\) (\\( 0 \\leq x \\leq 1 \\)). The \\( \\gamma \\) is set to 5 after tuning with a rough grid search manner. The other is a gamma tone mapping parameterized with three parameters [34]. Because the grid search for three parameters is time-consuming, we tuned the parameters with backpropagation together with the detector's weights as performed in [35, 49]. Other ISP functions are not used because they are known to have less impact on image recognition compared with tone mapping [13]. We also prepare an elaborated black-box ISP consisting of many functions in addition to a tone mapping function. The parameters are tuned for human perceptual quality by experts. We only use the elaborated black-box ISP under the conventional training pipeline. In other words, experiments are performed un" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14011" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.089, + 0.852, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 3. Examples of the introduced dataset. The upper row shows the training dataset collected in simple environments while the lower row shows the challenging test dataset collected in various environments from dark to bright, HDR, and with or without handshake blur." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.473, + 0.542 + ], + "angle": 0, + "content": "der ISP-augmentation-detection order with the elaborated black-box ISP due to the hardware limitation. If contrast augmentation is used, the hue is also changed with a probability of \\(50\\%\\). In detail, the contrast factor per color channel \\(p_{c,h} = \\{R,G,B\\}\\) is randomized from the base contrast factor \\(p_{c,\\text{base}}\\) by \\((0.8p_{c,\\text{base}}, 1.2p_{c,\\text{base}})\\) after \\(p_{c,\\text{base}}\\) is randomly decided. If blur augmentation is used, a random-sized blur kernel with a probability of \\(50\\%\\) is used. Random shift and random scale augmentation whose maximum transformations are \\(10\\%\\) and \\(3\\%\\) of the input size are also applied with a probability of \\(80\\%\\) before color jitter augmentation. The input size to the detector is (576, 352, 3). The performance of the detector is evaluated with average precision (AP@0.5:0.95) [24]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.556, + 0.351, + 0.572 + ], + "angle": 0, + "content": "4.3. Calibration of the Noise Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.853 + ], + "angle": 0, + "content": "For each analog gain of 6dB, 12dB, and 24dB, two burst sequences are captured with different illumination. Each sequence consists of 100 images. \\(24 \\times 24\\) Bayer pixels are sampled from each of the 24 color patches to calculate the mean and variance. In total \\(2 \\times 24 \\times 24 \\times 24\\) pairs of mean and variance sets are obtained per analog gain to estimate the noise model. Thanks to the various color filters, exposure values, and color patches, two sequences are enough to ensure diversity. The lines in Fig. 4 show the estimated linear relationship in Eq. (6). The coefficients of determination, \\(R^2\\), for these line estimations are 0.9833, 0.9884, 0.9862 for 6, 12, and 24dB respectively. High values of \\(R^2\\) indicate that the noise intensity is well modeled with respect to illumination intensity. Also, \\(R^2\\) of the Eq. (7) and Eq. (8) are 1.0000 and 0.9984. This means the noise intensity is well modeled with respect to the analog gain. Based on the above, our noise model and the calibration method are well suited to the sensor in terms of noise intensity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Next, we check the validity of the shape of the distribution. All noises were assumed to follow a Gaussian distribution. Especially, it is unclear whether the approximation" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.326, + 0.895, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.45, + 0.895, + 0.534 + ], + "angle": 0, + "content": "Figure 4. Sensor noise model calibration result. The dots in the left graph are the mean and variance pairs for each pixel, and the lines are the estimated linear relationship for each analog gain. Since large numbers of dots are plotted, they seem to be widely spread. On the other hand, the histogram plot per analog gain (right) shows a clear difference between them." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.551, + 0.895, + 0.656 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.665, + 0.895, + 0.737 + ], + "angle": 0, + "content": "Figure 5. The result of the Shapiro-Wilk [40] test for each expected pixel value. When testing whether the 100 pixel values at each location correspond to a Gaussian distribution, most p-values are larger than 0.05 (a). The right (b) shows the cases where \\( \\mathfrak{p} < 0.05 \\). It indicates the small p-values come from sparsity, not skew." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.895, + 0.903 + ], + "angle": 0, + "content": "\\(\\mathcal{P}(\\bar{u}) \\doteq \\mathcal{N}(\\bar{u}, \\bar{u})\\) [9] is true. Therefore, the Shapiro-Wilk test [40] is performed. If the p-value of the test is higher than 0.05, it indicates that we cannot reject the null hypothesis that the data are normally distributed with more than a \\(95\\%\\) confidence interval. Fig. 5(a) shows that most of them are higher than 0.05, but some results for dark pixels are less than 0.05. However, the distributions of the dark pixels are like Fig. 5(b). It is not very skewed and the sparsity causes the small p-value. Therefore, we conclude that all the noise" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14012" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.473, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.47, + 0.288 + ], + "angle": 0, + "content": "Figure 6. The statistical validation of the noise alignment. The green dots represent real image data, and the others are converted from it. The conversions are \\(\\times 0.1\\) and \\(\\times 0.5\\) contrast conversion with several methods. The (a) is a dark-to-extreme-dark conversion, and the (b) is a bright-to-dark conversion." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.316, + 0.362, + 0.331 + ], + "angle": 0, + "content": "sources can be regarded as Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.331, + 0.47, + 0.377 + ], + "angle": 0, + "content": "Based on the above, our sensor noise model and the calibration method represent the sensor noise well in terms of both intensity and distribution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.388, + 0.453, + 0.405 + ], + "angle": 0, + "content": "4.4. Statistical Validation of the Noise Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.47, + 0.578 + ], + "angle": 0, + "content": "Before confirming the effectiveness of the proposed noise-accounted RAW augmentation to computer vision applications, the statistical validity is evaluated one more time by utilizing the series of color checker images. The evaluation method is as follows. First, the contrast of the sequential images is changed with or without noise consideration. Second, mean and variance pairs along the sequential dimension are computed. Third, the distributions of real and converted pairs are examined. If the real and converted pairs matched well, it means the converted images have the same noise amount as the original real images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.777 + ], + "angle": 0, + "content": "Three different noise alignment methods are compared, i.e., no noise consideration, the usual noise-accounted method that disregards prior noise in the input [4,15,44,47], and our proposed noise alignment method. Fig. 6 shows the comparison result. It indicates that prior noise consideration is unnecessary if pixels are darkened considerably. However, a small contrast factor caused a noise domain gap even if the input is bright like Fig. 6 (right). In contrast, our noise-accounted conversion always converted images with realistic noise. It implies that our proposed method is suited for various strengths of augmentation. If prior noise is not accounted for, the inputs always have to be darkened considerably and already dark images are difficult to use." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.376, + 0.803 + ], + "angle": 0, + "content": "4.5. Augmentation Parameters Tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The optimal augmentation parameters should be different between augmentation before and after ISP. To make a fair comparison, we roughly tune both of the augmentation parameters. The strategy is as follows. First, we search the appropriate range of contrast factor \\( p_c \\) and brightness perturbation \\( p_b \\) successively. To be robust to any illumination" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "of inputs, we re-parameterize \\( p_b \\) as \\( p_b = \\hat{p}_b \\min(x) \\) and randomize the \\( \\hat{p}_b \\) instead of \\( p_b \\). Lastly, we search for the appropriate max blur distance \\( p_d \\). In these experiments, we do not account for sensor noise. We use the elaborated black-box ISP for the augmentation after ISP setting and the simplest gamma function for the augmentation before ISP setting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.183, + 0.892, + 0.214 + ], + "angle": 0, + "content": "The results are shown in Table 1. The best parameter settings are used in the next section." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.256 + ], + "angle": 0, + "content": "4.6. Evaluation of the Noise-Accounted RAW Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.893, + 0.702 + ], + "angle": 0, + "content": "In this section, the proposed noise-accounted RAW augmentation is evaluated on training image recognition models. First, as Table 2 shows, augmentation before ISP drastically improves the accuracy with the simplest ISP. It suggests the realistic pixel intensity distribution achieved by augmentation before ISP is the key to improving the accuracy in wide environments. In the color jitter augmentation only setting, the accuracy is improved from the general noise alignment method [2,4,9,15,26,31,36,47,50] by considering prior noise. In the color jitter and blur augmentation setting, noise-accounted color jitter augmentation plus normal blur augmentation does not improve much from no noise-accounted settings. Instead, noise alignment in both color jitter and blur augmentation improves the accuracy. It indicates that random noise is not effective and realistic noise is important. Comparing the accuracy under the same simplest gamma tone mapping setting, our proposed noise-accounted RAW augmentation doubles the accuracy of conventional augmentation after ISP. Furthermore, when parameterized gamma tone mapping is used as our simple ISP, the accuracy is even superior to the elaborated black-box ISP consisting of many functions in addition to a tone mapping function. As the visualization results in the supplementary material show, the elaborated black-box ISP outputs more perceivable images. It suggests that minimizing the domain gap caused by augmentation is more important than the superiority of the ISP. We might improve the accuracy more by an elaborated ISP and the proposed augmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.894, + 0.902 + ], + "angle": 0, + "content": "As mentioned earlier, there are noise dealing works in noise-related fields like denoising. We compare ours with these methods in the detection task. One is the K-Sigma transform [44], a kind of noise domain generalization. It normalizes images so that the pixel value and the standard deviation of the noise are linearly correlated. The other is noise amount notification with a concatenation of the noise variance map [2]. To follow the previous setup, direct RAW input without an ISP is also compared. Color jitter and blur augmentation are also applied to the methods different from the previous papers for a fair comparison. Table 3 shows the comparison results. As to the K-Sigma transform, simply applying \"aug.\" before or after the K-Sigma" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14013" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1. The augmentation hyperparameter tuning for a fair comparison between before and after ISP augmentation. The range of contrast, brightness, and blur distance are tuned one by one, taking over the previous best parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.128, + 0.894, + 0.226 + ], + "angle": 0, + "content": "
augmentation after ISP (tuned for the black-box ISP)augmentation before ISP (tuned for the simplest ISP)
contrastrange0.2-10.1-10.2-50.1-100.05-200.1-10.02-10.01-10.005-10.01-1.1
AP@0.5:0.95 [%]41.941.843.245.144.536.939.840.435.838.9
brightnessrange0-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.70-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.7
AP@0.5:0.95 [%]45.144.544.545.244.740.440.939.939.439.4
blur distancerange0-00-30-50-90-130-00-30-50-90-13
AP@0.5:0.95 [%]45.246.845.745.937.940.939.839.640.643.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.247, + 0.473, + 0.4 + ], + "angle": 0, + "content": "Table 2. Evaluation of the noise-accounted RAW augmentation. The color augmentation contains default hue augmentation plus tuned contrast and brightness augmentation. The w/o prior means the prior input noise is disregarded like many of the previous noise-accounted image conversion methods [2,4,9,15,26,31,36, 47, 50]. Because we adopt the well-established heteroscedastic Gaussian model Eq. (2), it is identical to the noise alignment of [2,9,36,50]. In this experiment, we also use the parameterized gamma tone mapping as the simple ISP, although it can't be used in the augmentation after ISP settings because the gradient from the detection loss is needed to tune." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.411, + 0.469, + 0.542 + ], + "angle": 0, + "content": "
augmentationnoisemAP@0.5:0.95 [%]
black-box ESPsimple ESP
simplestparameterized
Colorafter-45.219.3-
before (ours)--40.944.4
w/o prior-43.547.7
ours-44.648.1
Color + Blurafter-46.820.4-
before (ours)--43.343.8
ours†-43.447.9
ours-45.348.3
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.099, + 0.542, + 0.446, + 0.552 + ], + "angle": 0, + "content": "†: The noise alignment is only applied to the color jitter augmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.901 + ], + "angle": 0, + "content": "transforms gives a better result. However, there is a theoretical problem in both cases. If \"aug.\" is applied after the transform, the linear relation between pixel value and noise amount is retained but pixel intensity becomes inconsistent. On the other hand, applying \"aug.\" before the transform makes the noise amount unrealistic. Changing the augmentation to \"our aug.\" makes the intensity and noise realistic and improves the accuracy. From the experiment, we find the proposed augmentation boosts previous noise-dealing methods if ISPs are used. However, if ISPs are not used, noise accounted augmentation slightly deteriorated the accuracy. We argue that it is because the intensity distributions of RAW images are too difficult and unrealistic clean images might help training. However, the overall accuracy is lower than with ISPs. Also, for the detection task, only our proposed method is enough. It might be because, unlike the denoising task which should focus on noise, it is important to make the detector focus on pixel intensity distribution for the detection task." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.247, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Table 3. The comparison results with other noise-dealing techniques. The \"aug.\" means contrast and blur augmentation without noise-accounted and \"our aug.\" means with noise-accounted. We use the simplest gamma function in the ISP." + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.314, + 0.86, + 0.473 + ], + "angle": 0, + "content": "
methodAP@0.5:0.95 [%]
w/o ISPw/ ISP
concat [2]16.521.5
aug. + concat [2]35.031.6
our aug. + concat [2]33.740.4
K-Sigma [44]14.327.5
K-Sigma [44] + aug.25.034.1
aug. + K-Sigma [44]26.642.1
our aug. + K-Sigma [44]26.344.0
our aug.32.845.3
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.62, + 0.516 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.895, + 0.786 + ], + "angle": 0, + "content": "We propose a noise-accounted RAW augmentation method in which augmentation is applied before ISP to minimize the luminance domain gap and a sensor noise model is taken into account to minimize the noise domain gap. Unlike previous noise-accounted methods, ours takes the prior input noise into account. It minimizes the domain gap more and enables the use of already noisy images as training data. Thanks to the realistic augmentation, our method improves the detection accuracy in difficult scenes compared to the conventional methods. In the future, we would like to investigate whether the proposed augmentation with an elaborate ISP improves computer vision performance even further. Also, we would like to check the effectiveness against other image recognition tasks, such as classification or segmentation, by preparing datasets. We believe it is effective because our method is task-independent. Lastly, we are glad if this work sheds light on the importance of RAW images." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.805, + 0.597, + 0.82 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.831, + 0.894, + 0.903 + ], + "angle": 0, + "content": "[1] Goutam Bhat, Martin Danelljan, Fisher Yu, Luc Van Gool, and Radu Timofte. Deep reparametrization of multi-frame super-resolution and denoising. 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However, creating training datasets for such environments is expensive and hard due to the difficulties of data collection and annotation. It is desirable if we could get a robust model without the need for hard-to-obtain datasets. One simple approach is to apply data augmentation such as color jitter and blur to standard RGB (sRGB) images in simple scenes. Unfortunately, this approach struggles to yield realistic images in terms of pixel intensity and noise distribution due to not considering the non-linearity of Image Signal Processors (ISPs) and noise characteristics of image sensors. Instead, we propose a noise-accounted RAW image augmentation method. In essence, color jitter and blur augmentation are applied to a RAW image before applying non-linear ISP, resulting in realistic intensity. Furthermore, we introduce a noise amount alignment method that calibrates the domain gap in the noise property caused by the augmentation. We show that our proposed noise-accounted RAW augmentation method doubles the image recognition accuracy in challenging environments only with simple training data. + +# 1. Introduction + +Although image recognition has been actively studied, its performance in challenging environments still needs improvement [15]. Sensitive applications such as mobility sensing and head-mounted wearables need to be robust to various kinds of difficulties, including low light, high dynamic range (HDR) illuminance, motion blur, and camera shake. One possible solution is to use image enhancement and restoration methods. A lot of DNN-based low-light image enhancement [12, 20, 29, 30, 46, 54], denoising [32, 43, 53], and deblurring [43, 48, 52] methods are proposed to improve the pre-captured sRGB image quality. While they are useful for improving pre-captured image + +![](images/351d84d8f1681024bff9913736f1574c90d26716b2bf205d3faf71d26897e693.jpg) +(a) Usual training pipeline + +![](images/4a50bea20f0307b6407b5e90354fb075ca70aae9daf1f79f1fdd6f828766e288.jpg) +(b) Noise-accounted RAW augmentation pipeline +Figure 1. The concept of the proposed noise-accounted RAW augmentation. Conventional augmentation (a) is applied to the output of an ISP; due to the nonlinear operations in the ISP, it produces images that cannot be captured at any ambient light intensities. Instead, ours (b) applies augmentation before an ISP. It generates realistic pixel intensity distribution that can be captured when the light intensity is different. Moreover, the noise amount is also corrected to minimize the domain gap between real and augmented ones. + +quality, a recent work [15] shows that using them as preprocessing for image recognition models has limited accuracy gains since they already lost some information, and restoring the lost information is difficult. + +Another possible solution is to prepare a dataset for difficult environments [3, 33]. However, these datasets only cover one or a few difficulties, and creating datasets in various environments is too expensive. Especially, manual annotation of challenging scenes is difficult and time-consuming. For example, we can see almost nothing in usual sRGB images under extremely low-light environments due to heavy noise. In addition, some regions in HDR scenes suffer from halation or blocked-up shadows because the 8-bit range of usual sRGB images cannot fully preserve the real world, which is 0.000001 $[cd / m^2]$ under starlight and 1.6 billion $[cd / m^2]$ under direct sunlight [37]. Heavy + +motion blur and camera shake also make annotation difficult. Some works capture paired short-exposure and long-exposure images, and the clean long-exposure images are used for annotation or ground truth [15-17, 19]. The limitation is that the target scene needs to be motionless if the pairs are taken sequentially with one camera [15], and positional calibration is required if the pairs are taken with synchronized cameras [16,17]. Some works use a beam splitter to capture challenging images and their references without calibration [19, 45]. However, they are difficult to apply in dark scenes. Moreover, HDR images cannot be taken in the same way because some regions become overexposed or underexposed in both cameras. + +To this end, we aim to train image recognition models that work in various environments only using a training dataset in simple environments like bright, low dynamic range, and blurless. In this case, image augmentation or domain adaptation is important to overcome the domain gap between easy training data and difficult test data. However, we believe usual augmentations on sRGB space are ineffective because it does not take into account the nonlinear mapping of ISPs. In particular, tone mapping significantly changes the RAW image values, which are roughly proportional to physical brightness [44]. Contrast, brightness, and hue augmentation on sRGB space result in unrealistic images that cannot be captured under any ambient light intensity as shown in Fig. 1(a). In contrast, we propose augmentation on RAW images. In other words, augmentation is applied before ISPs to diminish the domain shift as shown in Fig. 1(b). + +Oher possible sources of the domain gap are differences in noise amount and noise distribution. To tackle these problems, we propose a method to align both light intensity and noise domains. Recent works show that adding physics-based realistic noise improves the performance of DNN-based denoisers [2, 44, 47, 50] and dark image recognition [4, 15]. Although their proposed sensor noise modelings are accurate, they assume that the original bright images are noise free. In contrast, we propose to modify the noise amount after contrast, brightness, and hue conversion considering the noise amount in the original images. It enables a more accurate alignment of the noise domain. Even bright images may have dark areas due to shadows or object colors, and their prior noise cannot be ignored. Another merit of our method is that it is possible to take dark images that already contain a lot of noise as input. In addition to noise alignment after color jitter augmentation, we show the importance of noise alignment after blur augmentation, which is proposed for the first time in this paper. + +Our contributions are as follows: + +- It is the first work to emphasize the importance of augmentation before ISP for image recognition to the best of our knowledge. + +- Noise amount alignment method is proposed to reduce the noise domain gap after RAW image augmentation. In contrast to previous works, our proposed method takes into account prior noise in the input image. It enables more accurate alignment and use of any strength of augmentation and even already noisy input. + +- We show qualitative analysis for the validity of our sensor noise modeling and corresponding noise-accounted augmentation. We prove that our proposed noise-accounted RAW augmentation has the edge over the previous methods. + +# 2. Related Works + +# 2.1. Recognition in Difficult Environment + +Many works have tackled image recognition in difficult environments. For low-light environments, several works improve the accuracy by replacing a traditional ISP with a powerful DNN-based ISP to create clean images for downstream image recognition models [5, 25, 33]. Even though these methods are promising because there is no information loss, the computational cost is the problem. Another approach is direct RAW image recognition without ISP [15, 39]. Their image recognition models benefit from the richest information and improve accuracy under low-light environments. However, several works report ISPs, especially tone mapping, are helpful for machine vision [13, 49]. Direct RAW image recognition may works well if the images have a low dynamic range. Another approach is domain adaptation or related methods which support low-light recognition with bright images [4, 15, 38]. + +For HDR environments, some works propose DNN-based auto-exposure control [35, 42] to improve downstream recognition. Also, multi-frame HDR synthesis methods [1, 6] can be used as a preprocessing, although camera motion makes them challenging. A luminance normalization method is also introduced to improve recognition performance under varying illumination conditions [18]. + +For blurry environments, deblurring methods are actively studied [48,51]. These DNN-based methods successfully restore clear images from heavily blurred images. + +Differing from the above, we aim to do image recognition under all the above difficulties using simple scene training data with our proposed augmentation method. We do not use domain adaptation methods since these methods are usually used in a setting where the target domain is equal to or smaller than the source domain [10]. On the contrary, in our setting, the distribution of the target domain is much wider than that of the source domain. + +# 2.2. Image Conversion on RAW + +Recently, several methods [2,4,29] convert bright sRGB images into realistic dark images by the following procedures. First, they invert an ISP pipeline to generate RAW-like images followed by illumination change on the RAW data space with plausible sensor noise. Afterward, degraded sRGB is generated by applying the forward ISP pipeline. This operation avoids the nonlinear mappings in the ISP and simulates short exposures and dark environments. With a similar intention, we propose to apply augmentation before ISPs to train image recognition models. + +# 2.3. Noise Modeling and Noise Amount Alignment + +In the electronic imaging sensor community, detailed noise modelings based on electric current and circuit have been studied [7, 11, 23, 41]. They are precise but difficult to be applied to the image-to-image conversion. Thus, in the machine vision community, simplified pixel value-based noise modelings are proposed based on electric noise modelings [2, 44, 47]. Although the noise model of [47] is well designed with a high degree of freedom Tukey lambda distribution [21], we are based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50] because it is still well fitted to real sensor noise and we can consider prior noise in original images which will be explained later. + +Recently, adding realistic model-based sensor noise to the ground truth clean images is proved to be helpful to train DNN-based denoiser [2,44,47,50] and low-light object detection models [4, 15]. Although they use highly consistent noise models, they regard original images as noise-free. In contrast, we propose to modify the noise amount after image conversion considering the noise amount of the original images. It enables a more accurate alignment of the noise domain and enables the use of any intensity of augmentation and already noisy images as input. + +# 3. Methodology + +In this section, we introduce our noise model, calibration procedure, and proposed noise-accounted RAW augmentation. + +# 3.1. Noise Model + +First, we briefly introduce our noise model for later explanation although it is based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50]. The number of photons $u$ hitting the photodiode of each pixel is converted to a voltage with quantum efficiency $\alpha$ . Some processing is then performed to read out the voltage, in which noise $n_d$ is inevitably mixed. Next, analog gain $g$ is multiplied to amplify the value. Lastly, the voltage is converted to a digital value. We simplify and summarize the noise after analog gain as $n_r$ . Since it is common to use analog gain which + +has a better signal-to-noise ratio (SNR), we omit the digital gain term in our noise model. To sum up, the photon-to-RAW pixel value conversion can be formulated as, + +$$ +x = g \left(\alpha u + n _ {d}\right) + n _ {r}. \tag {1} +$$ + +We approximate $n_d$ and $n_r$ as Gaussian noise $\mathcal{N}\left(0,\sigma_d^2\right)$ $\mathcal{N}\left(0,\sigma_r^2\right)$ and the number of photons $u$ itself obeys the Poisson distribution $\mathcal{P}(\bar{u})$ where $\bar{u}$ is the expected number of photons. If $\bar{u}$ is large enough, we can approximate as $\mathcal{P}(\bar{u})\doteq \mathcal{N}(\bar{u},\bar{u})$ [9]. Thus, our noise model is as follows; + +$$ +x \sim g (\alpha \mathcal {N} (\bar {u}, \bar {u}) + \mathcal {N} (0, \sigma_ {d} ^ {2})) + \mathcal {N} (0, \sigma_ {r} ^ {2}). \tag {2} +$$ + +We show the validity of the Gaussian approximation of $n_d$ , $n_r$ , and $\mathcal{P}(\bar{u})$ in the Section 4.3. We don't follow the further development of the formula in [9] for our purpose. + +Gaussian distribution has the following convenient natures; + +$$ +\left\{ \begin{array}{l} X \sim \mathcal {N} \left(\mu_ {X}, \sigma_ {X} ^ {2}\right) \\ Y \sim \mathcal {N} \left(\mu_ {Y}, \sigma_ {Y} ^ {2}\right) \\ X + Y \sim \mathcal {N} \left(\mu_ {X} + \mu_ {Y}, \sigma_ {X} ^ {2} + \sigma_ {Y} ^ {2}\right) \\ c X \sim \mathcal {N} \left(c \mu_ {X}, c ^ {2} \sigma_ {X} ^ {2}\right) \end{array} , \right. \tag {3} +$$ + +if $X$ and $Y$ are independent, and that's why we choose the simple Gaussian approximation instead of the recently proposed more expressive noise model [47]. These natures enable the proposed noise-accounted RAW augmentation to account for prior noise in input images. Furthermore, they further simplify our noise model as, + +$$ +x \sim \mathcal {N} \left(g \alpha \bar {u}, g ^ {2} \alpha^ {2} \bar {u} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}\right). \tag {4} +$$ + +Because the expected number of photon $\bar{u}$ is inconvenient to use in image-to-image conversion, we replace it with the expected pixel value $\mu_{x} = g\alpha \bar{u}$ , and our final noise model is defined as, + +$$ +x \sim \mathcal {N} \left(\mu_ {x}, \sigma_ {x} ^ {2} = g \alpha \mu_ {x} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}\right). \tag {5} +$$ + +# 3.2. Noise Model Calibration + +Our sensor noise model shown in Eq. (5) has three parameters, $\alpha$ , $\sigma_d^2$ , and $\sigma_r^2$ , which have to be calibrated per target sensor. We capture a series of RAW images of a color checker as shown in Fig. 2(a). We then calculate the mean $\mu_x$ and variance $\sigma_x^2$ along the time direction of each pixel position. We calculate them along the time direction instead of the spatial direction as performed in [44] since lens distortion changes the luminance of the same color patch. These operations are performed several times by changing the analog gain and exposure time. Eventually, we get various sets of $\{\mu_x,\sigma_x^2\}$ for each analog gain. Note that we calculate mean and variance without separating RGB channels because there is no significant difference in noise properties. + +![](images/f6754d2cb8cc1c712127bd0957030dde6d37d0ad6c8e2fde568d6b910ad68317.jpg) +(a) burst capture with several analog gains + +![](images/29679e824bad8593e5a747a5686314997862211727f27eef1e91a6c4db69b758.jpg) +(b) estimate linear relationship of the mean and variance +(c) estimate the sensor specific parameters +Figure 2. Our noise model calibration procedures to a target sensor. It just needs to capture burst RAW images and does not need special devices. + +In Eq. (5), $\mu_{x}$ and $\sigma_x^2$ have a linear relationship per analog gain $g_{n}$ ; + +$$ +\sigma_ {x} ^ {2} = a _ {g _ {n}} \mu_ {x} + b _ {g _ {n}}. \tag {6} +$$ + +Therefore, we solve linear regression to estimate $a_{g_n}$ and $b_{g_n}$ per gain like Fig. 2(b). In addition, we use RANSAC [8] to robustly take care of outlier $\{\mu_x, \sigma_x^2\}$ pairs. + +Finally, we estimate $\alpha$ , $\sigma_d^2$ , and $\sigma_r^2$ from the following redundant simultaneous equations by least-squares method, + +$$ +\left\{ \begin{array}{c} a _ {g _ {1}} = g _ {1} \alpha \\ \vdots \\ a _ {g _ {n}} = g _ {n} \alpha \end{array} , \right. \tag {7} +$$ + +$$ +\left\{ \begin{array}{l} b _ {g _ {1}} = g _ {1} ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2} \\ \vdots \\ b _ {g _ {n}} = g _ {n} ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2} \end{array} . \right. \tag {8} +$$ + +The procedure above enables calibration of the sensor noise model without special devices. We later show that our sensor model and the calibration method represent the real sensor noise with enough preciseness. + +# 3.3. Noise-Accounted RAW Augmentation + +We propose augmentation before ISP instead of the usual augmentation after ISP to generate realistic images. Furthermore, we improve the reality of the augmented images by considering the sensor noise model. Unlike the previous works [2,4,15,44,47,50], ours takes the prior noise amount of input images into account. It generates more realistic noise since even bright images have some extent of noise. Especially, dark parts due to shadow or the color of objects might have a non-negligible amount of noise. Moreover, it allows any brightness of input images different from previous works. Specifically, we introduce how to adjust noise amount after contrast, brightness, hue, and blur augmentation. + +# 3.3.1 Color Jitter Augmentation + +Contrast, brightness, and hue augmentation simulate different exposure times, light intensities, and analog gain. Hence, we first assume to multiply the exposure time, light intensity, and analog gain by $p_e$ , $p_i$ , and $p_g$ respectively. Because $p_e$ and $p_i$ equally change the number of photon $u$ in the case of our noise model, we rewrite them as $p_u = p_e p_i$ . Then, images in the above environment settings $x_{new}$ can be rewritten as, + +$$ +x _ {n e w} \sim \mathcal {N} \binom {(p _ {g} g) \alpha \left(p _ {u} \bar {u}\right),} {\left(p _ {g} g\right) ^ {2} \alpha^ {2} \left(p _ {u} \bar {u}\right) + \left(p _ {g} g\right) ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}}. \tag {9} +$$ + +Based on Eq. (3), it can be expanded as + +$$ +\begin{array}{l} x _ {n e w} \sim \mathcal {N} \left(\left(p _ {g} p _ {u}\right) \alpha g \bar {u}, \left(p _ {g} p _ {u}\right) ^ {2} \left(g ^ {2} \alpha^ {2} \bar {u} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}\right)\right) \\ + \mathcal {N} (0, - (p _ {g} p _ {u}) ^ {2} (g ^ {2} \alpha^ {2} \bar {u} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}) \tag {10} \\ + \left(p _ {g} g\right) ^ {2} \alpha^ {2} \left(p _ {u} \bar {u}\right) + \left(p _ {g} g\right) ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}). \\ \end{array} +$$ + +By inserting $\mu_{x} = g\alpha \bar{u}$ and original pixel value, $x_{pre} \sim \mathcal{N}\left(\mu_x, g\alpha \mu_x + g^2\sigma_d^2 + \sigma_r^2\right)$ , it can be expressed with a pixel value-based equation as follows; + +$$ +\begin{array}{l} x _ {n e w} \sim p _ {u} p _ {g} x _ {p r e} + \\ \mathcal {N} \left(0, p _ {u} \left(1 - p _ {u}\right) p _ {g} ^ {2} g \alpha \mu_ {x} \right. \tag {11} \\ + \left(1 - p _ {u} ^ {2}\right) p _ {g} ^ {2} g ^ {2} \sigma_ {d} ^ {2} + \left(1 - p _ {u} ^ {2} p _ {g} ^ {2}\right) \sigma_ {r} ^ {2}). \\ \end{array} +$$ + +Because the expected original pixel value $\mu_{x}$ in the Gaussian term is impossible to obtain, we approximate it as $\mu_{x} = x_{pre}$ . Based on this equation, we can precisely simulate as if exposure time, light intensity, and analog gain were $p_{e}, p_{i}$ , and $p_{g}$ times. Then, let's come back to contrast, brightness, and hue augmentation. When contrast is multiplied by $p_{c}$ and brightness is changed by $p_{b}$ , it can be expressed as, + +$$ +x _ {n e w} = p _ {c} x _ {p r e} + p _ {b}. \tag {12} +$$ + +This function is represented as multiplication by $\frac{(p_c x_{pre} + p_b)}{x_{pre}}$ . Therefore, noise-accounted contrast and + +brightness augmentation is finally defined as, + +$$ +\left\{ \begin{array}{l} \text {r a n d o m} p _ {c}, p _ {b} \\ \text {r a n d o m} p _ {u}, p _ {g} (\text {w h e r e} p _ {u} p _ {g} = \frac {\left(p _ {c} x _ {p r e} + p _ {b}\right)}{x _ {p r e}}, p _ {u}, p _ {g} > 0) \\ E q. (1 1) \left(\mu_ {x} \leftarrow x _ {p r e}\right) \end{array} \right. \tag {13} +$$ + +We can also convert hue by changing $p_c$ and $p_b$ per color filter position in the RAW bayer. + +# 3.3.2 Blur Augmentation + +Next, we introduce noise-accounted blur augmentation. Usual blur augmentation makes noise smaller than actual blur because the noise $n_d$ and $n_r$ are smoothed out although their noise amounts, in reality, are not related to how fast you shake a camera or how fast objects move. Only the photon number-related noise is smoothed out in actual motion blur. The actual blurred pixel is expressed as, + +$$ +x _ {n e w} \sim \mathcal {N} \left(g \alpha \sum_ {k} w _ {k} \bar {u} _ {k}, g ^ {2} \alpha^ {2} \sum_ {k} w _ {k} \bar {u} _ {k} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}\right), \tag {14} +$$ + +where $\sum_{k}w_{k} = 1$ is the blur kernel. With similar equation manipulation from Eq. (9) to Eq. (11), noise-accounted blur augmentation is + +$$ +\begin{array}{l} x _ {n e w} \sim \mathcal {N} \left(\sum_ {k} w _ {k} g \alpha \bar {u} _ {k}, \sum_ {k} w _ {k} ^ {2} \left(g ^ {2} \alpha^ {2} \bar {u} _ {k} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}\right)\right) \\ + \mathcal {N} (0, - \sum_ {k} w _ {k} ^ {2} (g ^ {2} \alpha^ {2} \bar {u _ {k}} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}) \\ + g ^ {2} \alpha^ {2} \sum_ {k} w _ {k} \bar {u} _ {k} + g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2}) \tag {15} \\ = \sum_ {k} w _ {k} x _ {p r e} + \mathcal {N} (0, g \alpha \sum_ {k} (1 - w _ {k}) w _ {k} x _ {p r e, k} \\ + (1 - \sum_ {k} w _ {k} ^ {2}) (g ^ {2} \sigma_ {d} ^ {2} + \sigma_ {r} ^ {2})). \\ \end{array} +$$ + +We account for prior noise but not for prior blur amounts because most images in usual datasets are not very blurry. Furthermore, it is difficult to estimate the prior blur amount. + +In addition, please note that augmentation to make images clean (make them brighter and deblurred) is inevitably difficult with noise-accounted RAW augmentation. Clipping noise variance in Eq. (11) to zero forcibly enables brightening, but brightening too much causes a mismatch of noise domain. + +# 4. Evaluation + +# 4.1. Dataset + +Although our method can be applied to any computer vision task, we choose a human detection task as a target because of its wide usage. We prepared a RAW image dataset + +for human detection task captured with an internally developed sensor. As mentioned earlier, our objective is to train image recognition models that work in various environments only using a training dataset in simple environments. So, most training images are taken under normal light conditions with fixed camera positions in several environments. Note that moderately dark and HDR images are also included to some extent in the training dataset. The analog gain is set to 6dB outdoors, 12dB indoors, and 32dB at night in moderate darkness to generate realistic easy images without auto-exposure. Test images, on the other hand, are taken in HDR or extremely dark environments. In addition, about $50\%$ of them are captured with a strong camera shake. Moreover, the analog gain is chosen from 3dB, 6dB, 12dB, and 24dB regardless of the environment. Both datasets are captured with around 1 fps to increase diversity among images. + +We manually annotate the human bounding boxes of both training and test data. Because precise annotation of test data on sRGB is impossible due to the noise and blur, we apply an offline ISP to each image and then annotate the bounding boxes. We manually set adequate ISP parameters per image and had to change the parameters several times to grasp the entire image. To avoid annotating large training datasets in this time-consuming way, it is desirable to train the model with a simple dataset. In total, 18,880 images are collected for training and 2,800 for testing. The examples are shown in Fig. 3. + +# 4.2. Implementation Details + +We mainly test with TTFNet [27] whose backbone is ResNet18 [14]. The network is trained for 48 epochs from scratch using Adam optimizer [22] and a cosine decay learning rate scheduler with a linear warmup [28] for the first 1,000 iterations whose maximum and minimum learning rates are 1e-3 and 1e-4. As to an ISP, a simple software ISP consisting of only a gamma tone mapping is implemented. In detail, two types of gamma tone mapping are implemented. One is the simplest gamma tone mapping, $y = x^{\frac{1}{\gamma}}$ ( $0 \leq x \leq 1$ ). The $\gamma$ is set to 5 after tuning with a rough grid search manner. The other is a gamma tone mapping parameterized with three parameters [34]. Because the grid search for three parameters is time-consuming, we tuned the parameters with backpropagation together with the detector's weights as performed in [35, 49]. Other ISP functions are not used because they are known to have less impact on image recognition compared with tone mapping [13]. We also prepare an elaborated black-box ISP consisting of many functions in addition to a tone mapping function. The parameters are tuned for human perceptual quality by experts. We only use the elaborated black-box ISP under the conventional training pipeline. In other words, experiments are performed un + +![](images/118b7e4a94c8f9f5e39038e4fe3b6707882b125088db2d22dfd117811f20647d.jpg) +Figure 3. Examples of the introduced dataset. The upper row shows the training dataset collected in simple environments while the lower row shows the challenging test dataset collected in various environments from dark to bright, HDR, and with or without handshake blur. + +der ISP-augmentation-detection order with the elaborated black-box ISP due to the hardware limitation. If contrast augmentation is used, the hue is also changed with a probability of $50\%$ . In detail, the contrast factor per color channel $p_{c,h} = \{R,G,B\}$ is randomized from the base contrast factor $p_{c,\text{base}}$ by $(0.8p_{c,\text{base}}, 1.2p_{c,\text{base}})$ after $p_{c,\text{base}}$ is randomly decided. If blur augmentation is used, a random-sized blur kernel with a probability of $50\%$ is used. Random shift and random scale augmentation whose maximum transformations are $10\%$ and $3\%$ of the input size are also applied with a probability of $80\%$ before color jitter augmentation. The input size to the detector is (576, 352, 3). The performance of the detector is evaluated with average precision (AP@0.5:0.95) [24]. + +# 4.3. Calibration of the Noise Model + +For each analog gain of 6dB, 12dB, and 24dB, two burst sequences are captured with different illumination. Each sequence consists of 100 images. $24 \times 24$ Bayer pixels are sampled from each of the 24 color patches to calculate the mean and variance. In total $2 \times 24 \times 24 \times 24$ pairs of mean and variance sets are obtained per analog gain to estimate the noise model. Thanks to the various color filters, exposure values, and color patches, two sequences are enough to ensure diversity. The lines in Fig. 4 show the estimated linear relationship in Eq. (6). The coefficients of determination, $R^2$ , for these line estimations are 0.9833, 0.9884, 0.9862 for 6, 12, and 24dB respectively. High values of $R^2$ indicate that the noise intensity is well modeled with respect to illumination intensity. Also, $R^2$ of the Eq. (7) and Eq. (8) are 1.0000 and 0.9984. This means the noise intensity is well modeled with respect to the analog gain. Based on the above, our noise model and the calibration method are well suited to the sensor in terms of noise intensity. + +Next, we check the validity of the shape of the distribution. All noises were assumed to follow a Gaussian distribution. Especially, it is unclear whether the approximation + +![](images/68d420a429e890c4e5d1e2b376d6f1be39e789c794e2f2c55fb6bf96d27e3c51.jpg) +Figure 4. Sensor noise model calibration result. The dots in the left graph are the mean and variance pairs for each pixel, and the lines are the estimated linear relationship for each analog gain. Since large numbers of dots are plotted, they seem to be widely spread. On the other hand, the histogram plot per analog gain (right) shows a clear difference between them. + +![](images/0fcbc7210852d82eb9a5b3376309771e5ff5d01eb992c44003809f001fd351df.jpg) +Figure 5. The result of the Shapiro-Wilk [40] test for each expected pixel value. When testing whether the 100 pixel values at each location correspond to a Gaussian distribution, most p-values are larger than 0.05 (a). The right (b) shows the cases where $\mathfrak{p} < 0.05$ . It indicates the small p-values come from sparsity, not skew. + +$\mathcal{P}(\bar{u}) \doteq \mathcal{N}(\bar{u}, \bar{u})$ [9] is true. Therefore, the Shapiro-Wilk test [40] is performed. If the p-value of the test is higher than 0.05, it indicates that we cannot reject the null hypothesis that the data are normally distributed with more than a $95\%$ confidence interval. Fig. 5(a) shows that most of them are higher than 0.05, but some results for dark pixels are less than 0.05. However, the distributions of the dark pixels are like Fig. 5(b). It is not very skewed and the sparsity causes the small p-value. Therefore, we conclude that all the noise + +![](images/4068d637165831208ae3384d04a2e8c49758ad212de0156ddfb9382b84e12e1a.jpg) +Figure 6. The statistical validation of the noise alignment. The green dots represent real image data, and the others are converted from it. The conversions are $\times 0.1$ and $\times 0.5$ contrast conversion with several methods. The (a) is a dark-to-extreme-dark conversion, and the (b) is a bright-to-dark conversion. + +sources can be regarded as Gaussian noise. + +Based on the above, our sensor noise model and the calibration method represent the sensor noise well in terms of both intensity and distribution. + +# 4.4. Statistical Validation of the Noise Alignment + +Before confirming the effectiveness of the proposed noise-accounted RAW augmentation to computer vision applications, the statistical validity is evaluated one more time by utilizing the series of color checker images. The evaluation method is as follows. First, the contrast of the sequential images is changed with or without noise consideration. Second, mean and variance pairs along the sequential dimension are computed. Third, the distributions of real and converted pairs are examined. If the real and converted pairs matched well, it means the converted images have the same noise amount as the original real images. + +Three different noise alignment methods are compared, i.e., no noise consideration, the usual noise-accounted method that disregards prior noise in the input [4,15,44,47], and our proposed noise alignment method. Fig. 6 shows the comparison result. It indicates that prior noise consideration is unnecessary if pixels are darkened considerably. However, a small contrast factor caused a noise domain gap even if the input is bright like Fig. 6 (right). In contrast, our noise-accounted conversion always converted images with realistic noise. It implies that our proposed method is suited for various strengths of augmentation. If prior noise is not accounted for, the inputs always have to be darkened considerably and already dark images are difficult to use. + +# 4.5. Augmentation Parameters Tuning + +The optimal augmentation parameters should be different between augmentation before and after ISP. To make a fair comparison, we roughly tune both of the augmentation parameters. The strategy is as follows. First, we search the appropriate range of contrast factor $p_c$ and brightness perturbation $p_b$ successively. To be robust to any illumination + +of inputs, we re-parameterize $p_b$ as $p_b = \hat{p}_b \min(x)$ and randomize the $\hat{p}_b$ instead of $p_b$ . Lastly, we search for the appropriate max blur distance $p_d$ . In these experiments, we do not account for sensor noise. We use the elaborated black-box ISP for the augmentation after ISP setting and the simplest gamma function for the augmentation before ISP setting. + +The results are shown in Table 1. The best parameter settings are used in the next section. + +# 4.6. Evaluation of the Noise-Accounted RAW Augmentation + +In this section, the proposed noise-accounted RAW augmentation is evaluated on training image recognition models. First, as Table 2 shows, augmentation before ISP drastically improves the accuracy with the simplest ISP. It suggests the realistic pixel intensity distribution achieved by augmentation before ISP is the key to improving the accuracy in wide environments. In the color jitter augmentation only setting, the accuracy is improved from the general noise alignment method [2,4,9,15,26,31,36,47,50] by considering prior noise. In the color jitter and blur augmentation setting, noise-accounted color jitter augmentation plus normal blur augmentation does not improve much from no noise-accounted settings. Instead, noise alignment in both color jitter and blur augmentation improves the accuracy. It indicates that random noise is not effective and realistic noise is important. Comparing the accuracy under the same simplest gamma tone mapping setting, our proposed noise-accounted RAW augmentation doubles the accuracy of conventional augmentation after ISP. Furthermore, when parameterized gamma tone mapping is used as our simple ISP, the accuracy is even superior to the elaborated black-box ISP consisting of many functions in addition to a tone mapping function. As the visualization results in the supplementary material show, the elaborated black-box ISP outputs more perceivable images. It suggests that minimizing the domain gap caused by augmentation is more important than the superiority of the ISP. We might improve the accuracy more by an elaborated ISP and the proposed augmentation. + +As mentioned earlier, there are noise dealing works in noise-related fields like denoising. We compare ours with these methods in the detection task. One is the K-Sigma transform [44], a kind of noise domain generalization. It normalizes images so that the pixel value and the standard deviation of the noise are linearly correlated. The other is noise amount notification with a concatenation of the noise variance map [2]. To follow the previous setup, direct RAW input without an ISP is also compared. Color jitter and blur augmentation are also applied to the methods different from the previous papers for a fair comparison. Table 3 shows the comparison results. As to the K-Sigma transform, simply applying "aug." before or after the K-Sigma + +Table 1. The augmentation hyperparameter tuning for a fair comparison between before and after ISP augmentation. The range of contrast, brightness, and blur distance are tuned one by one, taking over the previous best parameters. + +
augmentation after ISP (tuned for the black-box ISP)augmentation before ISP (tuned for the simplest ISP)
contrastrange0.2-10.1-10.2-50.1-100.05-200.1-10.02-10.01-10.005-10.01-1.1
AP@0.5:0.95 [%]41.941.843.245.144.536.939.840.435.838.9
brightnessrange0-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.70-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.7
AP@0.5:0.95 [%]45.144.544.545.244.740.440.939.939.439.4
blur distancerange0-00-30-50-90-130-00-30-50-90-13
AP@0.5:0.95 [%]45.246.845.745.937.940.939.839.640.643.3
+ +Table 2. Evaluation of the noise-accounted RAW augmentation. The color augmentation contains default hue augmentation plus tuned contrast and brightness augmentation. The w/o prior means the prior input noise is disregarded like many of the previous noise-accounted image conversion methods [2,4,9,15,26,31,36, 47, 50]. Because we adopt the well-established heteroscedastic Gaussian model Eq. (2), it is identical to the noise alignment of [2,9,36,50]. In this experiment, we also use the parameterized gamma tone mapping as the simple ISP, although it can't be used in the augmentation after ISP settings because the gradient from the detection loss is needed to tune. + +
augmentationnoisemAP@0.5:0.95 [%]
black-box ESPsimple ESP
simplestparameterized
Colorafter-45.219.3-
before (ours)--40.944.4
w/o prior-43.547.7
ours-44.648.1
Color + Blurafter-46.820.4-
before (ours)--43.343.8
ours†-43.447.9
ours-45.348.3
+ +†: The noise alignment is only applied to the color jitter augmentation. + +transforms gives a better result. However, there is a theoretical problem in both cases. If "aug." is applied after the transform, the linear relation between pixel value and noise amount is retained but pixel intensity becomes inconsistent. On the other hand, applying "aug." before the transform makes the noise amount unrealistic. Changing the augmentation to "our aug." makes the intensity and noise realistic and improves the accuracy. From the experiment, we find the proposed augmentation boosts previous noise-dealing methods if ISPs are used. However, if ISPs are not used, noise accounted augmentation slightly deteriorated the accuracy. We argue that it is because the intensity distributions of RAW images are too difficult and unrealistic clean images might help training. However, the overall accuracy is lower than with ISPs. Also, for the detection task, only our proposed method is enough. It might be because, unlike the denoising task which should focus on noise, it is important to make the detector focus on pixel intensity distribution for the detection task. + +Table 3. The comparison results with other noise-dealing techniques. The "aug." means contrast and blur augmentation without noise-accounted and "our aug." means with noise-accounted. We use the simplest gamma function in the ISP. + +
methodAP@0.5:0.95 [%]
w/o ISPw/ ISP
concat [2]16.521.5
aug. + concat [2]35.031.6
our aug. + concat [2]33.740.4
K-Sigma [44]14.327.5
K-Sigma [44] + aug.25.034.1
aug. + K-Sigma [44]26.642.1
our aug. + K-Sigma [44]26.344.0
our aug.32.845.3
+ +# 5. Conclusion + +We propose a noise-accounted RAW augmentation method in which augmentation is applied before ISP to minimize the luminance domain gap and a sensor noise model is taken into account to minimize the noise domain gap. Unlike previous noise-accounted methods, ours takes the prior input noise into account. It minimizes the domain gap more and enables the use of already noisy images as training data. Thanks to the realistic augmentation, our method improves the detection accuracy in difficult scenes compared to the conventional methods. In the future, we would like to investigate whether the proposed augmentation with an elaborate ISP improves computer vision performance even further. Also, we would like to check the effectiveness against other image recognition tasks, such as classification or segmentation, by preparing datasets. We believe it is effective because our method is task-independent. 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However, creating training datasets for such environments is expensive and hard due to the difficulties of data collection and annotation. It is desirable if we could get a robust model without the need for hard-to-obtain datasets. One simple approach is to apply data augmentation such as color jitter and blur to standard RGB (sRGB) images in simple scenes. Unfortunately, this approach struggles to yield realistic images in terms of pixel intensity and noise distribution due to not considering the non-linearity of Image Signal Processors (ISPs) and noise characteristics of image sensors. Instead, we propose a noise-accounted RAW image augmentation method. In essence, color jitter and blur augmentation are applied to a RAW image before applying non-linear ISP, resulting in realistic intensity. Furthermore, we introduce a noise amount alignment method that calibrates the domain gap in the noise property caused by the augmentation. 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The concept of the proposed noise-accounted RAW augmentation. Conventional augmentation (a) is applied to the output of an ISP; due to the nonlinear operations in the ISP, it produces images that cannot be captured at any ambient light intensities. Instead, ours (b) applies augmentation before an ISP. It generates realistic pixel intensity distribution that can be captured when the light intensity is different. 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Heavy" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14007" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "motion blur and camera shake also make annotation difficult. Some works capture paired short-exposure and long-exposure images, and the clean long-exposure images are used for annotation or ground truth [15-17, 19]. The limitation is that the target scene needs to be motionless if the pairs are taken sequentially with one camera [15], and positional calibration is required if the pairs are taken with synchronized cameras [16,17]. Some works use a beam splitter to capture challenging images and their references without calibration [19, 45]. However, they are difficult to apply in dark scenes. Moreover, HDR images cannot be taken in the same way because some regions become overexposed or underexposed in both cameras." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 430 + ], + "type": "text", + "content": "To this end, we aim to train image recognition models that work in various environments only using a training dataset in simple environments like bright, low dynamic range, and blurless. In this case, image augmentation or domain adaptation is important to overcome the domain gap between easy training data and difficult test data. However, we believe usual augmentations on sRGB space are ineffective because it does not take into account the nonlinear mapping of ISPs. In particular, tone mapping significantly changes the RAW image values, which are roughly proportional to physical brightness [44]. Contrast, brightness, and hue augmentation on sRGB space result in unrealistic images that cannot be captured under any ambient light intensity as shown in Fig. 1(a). In contrast, we propose augmentation on RAW images. In other words, augmentation is applied before ISPs to diminish the domain shift as shown in Fig. 1(b)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 432, + 289, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 289, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 289, + 658 + ], + "type": "text", + "content": "Oher possible sources of the domain gap are differences in noise amount and noise distribution. To tackle these problems, we propose a method to align both light intensity and noise domains. Recent works show that adding physics-based realistic noise improves the performance of DNN-based denoisers [2, 44, 47, 50] and dark image recognition [4, 15]. Although their proposed sensor noise modelings are accurate, they assume that the original bright images are noise free. In contrast, we propose to modify the noise amount after contrast, brightness, and hue conversion considering the noise amount in the original images. It enables a more accurate alignment of the noise domain. Even bright images may have dark areas due to shadows or object colors, and their prior noise cannot be ignored. Another merit of our method is that it is possible to take dark images that already contain a lot of noise as input. In addition to noise alignment after color jitter augmentation, we show the importance of noise alignment after blur augmentation, which is proposed for the first time in this paper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 658, + 193, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 658, + 193, + 669 + ], + "spans": [ + { + "bbox": [ + 59, + 658, + 193, + 669 + ], + "type": "text", + "content": "Our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "type": "text", + "content": "- It is the first work to emphasize the importance of augmentation before ISP for image recognition to the best of our knowledge." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 72, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 145 + ], + "type": "text", + "content": "- Noise amount alignment method is proposed to reduce the noise domain gap after RAW image augmentation. In contrast to previous works, our proposed method takes into account prior noise in the input image. It enables more accurate alignment and use of any strength of augmentation and even already noisy input." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 163, + 547, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 163, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 317, + 163, + 547, + 224 + ], + "type": "text", + "content": "- We show qualitative analysis for the validity of our sensor noise modeling and corresponding noise-accounted augmentation. We prove that our proposed noise-accounted RAW augmentation has the edge over the previous methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 243, + 397, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 243, + 397, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 397, + 255 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 265, + 502, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 265, + 502, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 265, + 502, + 277 + ], + "type": "text", + "content": "2.1. Recognition in Difficult Environment" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 286, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 545, + 477 + ], + "type": "text", + "content": "Many works have tackled image recognition in difficult environments. For low-light environments, several works improve the accuracy by replacing a traditional ISP with a powerful DNN-based ISP to create clean images for downstream image recognition models [5, 25, 33]. Even though these methods are promising because there is no information loss, the computational cost is the problem. Another approach is direct RAW image recognition without ISP [15, 39]. Their image recognition models benefit from the richest information and improve accuracy under low-light environments. However, several works report ISPs, especially tone mapping, are helpful for machine vision [13, 49]. Direct RAW image recognition may works well if the images have a low dynamic range. Another approach is domain adaptation or related methods which support low-light recognition with bright images [4, 15, 38]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 480, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 577 + ], + "type": "text", + "content": "For HDR environments, some works propose DNN-based auto-exposure control [35, 42] to improve downstream recognition. Also, multi-frame HDR synthesis methods [1, 6] can be used as a preprocessing, although camera motion makes them challenging. A luminance normalization method is also introduced to improve recognition performance under varying illumination conditions [18]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 579, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 615 + ], + "type": "text", + "content": "For blurry environments, deblurring methods are actively studied [48,51]. These DNN-based methods successfully restore clear images from heavily blurred images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "Differing from the above, we aim to do image recognition under all the above difficulties using simple scene training data with our proposed augmentation method. We do not use domain adaptation methods since these methods are usually used in a setting where the target domain is equal to or smaller than the source domain [10]. On the contrary, in our setting, the distribution of the target domain is much wider than that of the source domain." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14008" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 197, + 84 + ], + "type": "text", + "content": "2.2. Image Conversion on RAW" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 210 + ], + "type": "text", + "content": "Recently, several methods [2,4,29] convert bright sRGB images into realistic dark images by the following procedures. First, they invert an ISP pipeline to generate RAW-like images followed by illumination change on the RAW data space with plausible sensor noise. Afterward, degraded sRGB is generated by applying the forward ISP pipeline. This operation avoids the nonlinear mappings in the ISP and simulates short exposures and dark environments. With a similar intention, we propose to apply augmentation before ISPs to train image recognition models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 218, + 285, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 285, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 285, + 231 + ], + "type": "text", + "content": "2.3. Noise Modeling and Noise Amount Alignment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 236, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 380 + ], + "type": "text", + "content": "In the electronic imaging sensor community, detailed noise modelings based on electric current and circuit have been studied [7, 11, 23, 41]. They are precise but difficult to be applied to the image-to-image conversion. Thus, in the machine vision community, simplified pixel value-based noise modelings are proposed based on electric noise modelings [2, 44, 47]. Although the noise model of [47] is well designed with a high degree of freedom Tukey lambda distribution [21], we are based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50] because it is still well fitted to real sensor noise and we can consider prior noise in original images which will be explained later." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 287, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 500 + ], + "type": "text", + "content": "Recently, adding realistic model-based sensor noise to the ground truth clean images is proved to be helpful to train DNN-based denoiser [2,44,47,50] and low-light object detection models [4, 15]. Although they use highly consistent noise models, they regard original images as noise-free. In contrast, we propose to modify the noise amount after image conversion considering the noise amount of the original images. It enables a more accurate alignment of the noise domain and enables the use of any intensity of augmentation and already noisy images as input." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 511, + 129, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 129, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 129, + 525 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 531, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 567 + ], + "type": "text", + "content": "In this section, we introduce our noise model, calibration procedure, and proposed noise-accounted RAW augmentation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 575, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 128, + 586 + ], + "type": "text", + "content": "3.1. Noise Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "First, we briefly introduce our noise model for later explanation although it is based on the well-established heteroscedastic Gaussian model [2, 9, 36, 50]. The number of photons " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " hitting the photodiode of each pixel is converted to a voltage with quantum efficiency " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": ". Some processing is then performed to read out the voltage, in which noise " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "n_d" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " is inevitably mixed. Next, analog gain " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " is multiplied to amplify the value. Lastly, the voltage is converted to a digital value. We simplify and summarize the noise after analog gain as " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "n_r" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": ". Since it is common to use analog gain which" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "has a better signal-to-noise ratio (SNR), we omit the digital gain term in our noise model. To sum up, the photon-to-RAW pixel value conversion can be formulated as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 376, + 116, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 116, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 376, + 116, + 545, + 129 + ], + "type": "interline_equation", + "content": "x = g \\left(\\alpha u + n _ {d}\\right) + n _ {r}. \\tag {1}", + "image_path": "663875975ae6a311b3dc4705e80ccd80733b211fc001f90c7ee5165f3bc226c4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": "We approximate " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "n_d" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "n_r" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " as Gaussian noise " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\mathcal{N}\\left(0,\\sigma_d^2\\right)" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\mathcal{N}\\left(0,\\sigma_r^2\\right)" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " and the number of photons " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " itself obeys the Poisson distribution " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\bar{u})" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\bar{u}" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " is the expected number of photons. If " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\bar{u}" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " is large enough, we can approximate as " + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\bar{u})\\doteq \\mathcal{N}(\\bar{u},\\bar{u})" + }, + { + "bbox": [ + 305, + 134, + 545, + 197 + ], + "type": "text", + "content": " [9]. Thus, our noise model is as follows;" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 202, + 545, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 202, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 331, + 202, + 545, + 217 + ], + "type": "interline_equation", + "content": "x \\sim g (\\alpha \\mathcal {N} (\\bar {u}, \\bar {u}) + \\mathcal {N} (0, \\sigma_ {d} ^ {2})) + \\mathcal {N} (0, \\sigma_ {r} ^ {2}). \\tag {2}", + "image_path": "771f15f4a2031e594290da216278da3e227477629054d7cd32ff2a567be3b0a9.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "text", + "content": "We show the validity of the Gaussian approximation of " + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "inline_equation", + "content": "n_d" + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "inline_equation", + "content": "n_r" + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\bar{u})" + }, + { + "bbox": [ + 305, + 223, + 545, + 259 + ], + "type": "text", + "content": " in the Section 4.3. We don't follow the further development of the formula in [9] for our purpose." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 259, + 545, + 281 + ], + "type": "text", + "content": "Gaussian distribution has the following convenient natures;" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 293, + 545, + 351 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 293, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 340, + 293, + 545, + 351 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} X \\sim \\mathcal {N} \\left(\\mu_ {X}, \\sigma_ {X} ^ {2}\\right) \\\\ Y \\sim \\mathcal {N} \\left(\\mu_ {Y}, \\sigma_ {Y} ^ {2}\\right) \\\\ X + Y \\sim \\mathcal {N} \\left(\\mu_ {X} + \\mu_ {Y}, \\sigma_ {X} ^ {2} + \\sigma_ {Y} ^ {2}\\right) \\\\ c X \\sim \\mathcal {N} \\left(c \\mu_ {X}, c ^ {2} \\sigma_ {X} ^ {2}\\right) \\end{array} , \\right. \\tag {3}", + "image_path": "3664f9c64cc9861fc39da64d2495fec95b998b52a850545c6e30982d2513152c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "content": "if " + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "content": " are independent, and that's why we choose the simple Gaussian approximation instead of the recently proposed more expressive noise model [47]. These natures enable the proposed noise-accounted RAW augmentation to account for prior noise in input images. Furthermore, they further simplify our noise model as," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 350, + 431, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 431, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 350, + 431, + 545, + 447 + ], + "type": "interline_equation", + "content": "x \\sim \\mathcal {N} \\left(g \\alpha \\bar {u}, g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {4}", + "image_path": "97b51fe34c7c629b30c03bf0c89574ddf7dd4454781f5658a557b4e41f0cd941.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "text", + "content": "Because the expected number of photon " + }, + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "inline_equation", + "content": "\\bar{u}" + }, + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "text", + "content": " is inconvenient to use in image-to-image conversion, we replace it with the expected pixel value " + }, + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "inline_equation", + "content": "\\mu_{x} = g\\alpha \\bar{u}" + }, + { + "bbox": [ + 305, + 453, + 545, + 500 + ], + "type": "text", + "content": ", and our final noise model is defined as," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 343, + 506, + 545, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 506, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 343, + 506, + 545, + 522 + ], + "type": "interline_equation", + "content": "x \\sim \\mathcal {N} \\left(\\mu_ {x}, \\sigma_ {x} ^ {2} = g \\alpha \\mu_ {x} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right). \\tag {5}", + "image_path": "d7e090e095a397caeb4ebb896737778415999f8feff7b54122e1cb089d709737.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 527, + 444, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 444, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 444, + 539 + ], + "type": "text", + "content": "3.2. Noise Model Calibration" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": "Our sensor noise model shown in Eq. (5) has three parameters, " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\sigma_d^2" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\sigma_r^2" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": ", which have to be calibrated per target sensor. We capture a series of RAW images of a color checker as shown in Fig. 2(a). We then calculate the mean " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mu_x" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\sigma_x^2" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": " along the time direction of each pixel position. We calculate them along the time direction instead of the spatial direction as performed in [44] since lens distortion changes the luminance of the same color patch. These operations are performed several times by changing the analog gain and exposure time. Eventually, we get various sets of " + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\{\\mu_x,\\sigma_x^2\\}" + }, + { + "bbox": [ + 304, + 546, + 545, + 712 + ], + "type": "text", + "content": " for each analog gain. Note that we calculate mean and variance without separating RGB channels because there is no significant difference in noise properties." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14009" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 70, + 231, + 178 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 231, + 178 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 231, + 178 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 231, + 178 + ], + "type": "image", + "image_path": "f6754d2cb8cc1c712127bd0957030dde6d37d0ad6c8e2fde568d6b910ad68317.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 180, + 204, + 190 + ], + "lines": [ + { + "bbox": [ + 84, + 180, + 204, + 190 + ], + "spans": [ + { + "bbox": [ + 84, + 180, + 204, + 190 + ], + "type": "text", + "content": "(a) burst capture with several analog gains" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 70, + 495, + 176 + ], + "blocks": [ + { + "bbox": [ + 238, + 70, + 495, + 176 + ], + "lines": [ + { + "bbox": [ + 238, + 70, + 495, + 176 + ], + "spans": [ + { + "bbox": [ + 238, + 70, + 495, + 176 + ], + "type": "image", + "image_path": "29679e824bad8593e5a747a5686314997862211727f27eef1e91a6c4db69b758.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 180, + 397, + 190 + ], + "lines": [ + { + "bbox": [ + 238, + 180, + 397, + 190 + ], + "spans": [ + { + "bbox": [ + 238, + 180, + 397, + 190 + ], + "type": "text", + "content": "(b) estimate linear relationship of the mean and variance" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 411, + 180, + 531, + 190 + ], + "lines": [ + { + "bbox": [ + 411, + 180, + 531, + 190 + ], + "spans": [ + { + "bbox": [ + 411, + 180, + 531, + 190 + ], + "type": "text", + "content": "(c) estimate the sensor specific parameters" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 198, + 544, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 544, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 544, + 220 + ], + "type": "text", + "content": "Figure 2. Our noise model calibration procedures to a target sensor. It just needs to capture burst RAW images and does not need special devices." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "text", + "content": "In Eq. (5), " + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mu_{x}" + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\sigma_x^2" + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "text", + "content": " have a linear relationship per analog gain " + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "inline_equation", + "content": "g_{n}" + }, + { + "bbox": [ + 47, + 242, + 287, + 266 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 126, + 267, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 267, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 126, + 267, + 287, + 281 + ], + "type": "interline_equation", + "content": "\\sigma_ {x} ^ {2} = a _ {g _ {n}} \\mu_ {x} + b _ {g _ {n}}. \\tag {6}", + "image_path": "2846064db80d6f8023588e16619025b7eadf539f8d8739acb1e237d6bd70a289.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "text", + "content": "Therefore, we solve linear regression to estimate " + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "inline_equation", + "content": "a_{g_n}" + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "inline_equation", + "content": "b_{g_n}" + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "text", + "content": " per gain like Fig. 2(b). In addition, we use RANSAC [8] to robustly take care of outlier " + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\{\\mu_x, \\sigma_x^2\\}" + }, + { + "bbox": [ + 47, + 289, + 287, + 326 + ], + "type": "text", + "content": " pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "content": "Finally, we estimate " + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\sigma_d^2" + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\sigma_r^2" + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "content": " from the following redundant simultaneous equations by least-squares method," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 132, + 361, + 287, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 361, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 132, + 361, + 287, + 411 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{c} a _ {g _ {1}} = g _ {1} \\alpha \\\\ \\vdots \\\\ a _ {g _ {n}} = g _ {n} \\alpha \\end{array} , \\right. \\tag {7}", + "image_path": "0f6c57169f3cfbad9d1c3ba36e04762ee8daee1c556a711f94bbee25b482a9d5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 119, + 424, + 287, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 424, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 119, + 424, + 287, + 474 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} b _ {g _ {1}} = g _ {1} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\\\ \\vdots \\\\ b _ {g _ {n}} = g _ {n} ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2} \\end{array} . \\right. \\tag {8}", + "image_path": "e5ed51d7f0ddc036e3faf45bdc43fa941ea97fdabb1b13fc845a3f65b696f182.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 480, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 287, + 529 + ], + "type": "text", + "content": "The procedure above enables calibration of the sensor noise model without special devices. We later show that our sensor model and the calibration method represent the real sensor noise with enough preciseness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 538, + 246, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 246, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 246, + 551 + ], + "type": "text", + "content": "3.3. Noise-Accounted RAW Augmentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 557, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 712 + ], + "type": "text", + "content": "We propose augmentation before ISP instead of the usual augmentation after ISP to generate realistic images. Furthermore, we improve the reality of the augmented images by considering the sensor noise model. Unlike the previous works [2,4,15,44,47,50], ours takes the prior noise amount of input images into account. It generates more realistic noise since even bright images have some extent of noise. Especially, dark parts due to shadow or the color of objects might have a non-negligible amount of noise. Moreover, it allows any brightness of input images different from previous works. Specifically, we introduce how to adjust noise amount after contrast, brightness, hue, and blur augmentation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 242, + 452, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 452, + 254 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 452, + 254 + ], + "type": "text", + "content": "3.3.1 Color Jitter Augmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": "Contrast, brightness, and hue augmentation simulate different exposure times, light intensities, and analog gain. Hence, we first assume to multiply the exposure time, light intensity, and analog gain by " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_e" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_g" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": " respectively. Because " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_e" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": " equally change the number of photon " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": " in the case of our noise model, we rewrite them as " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "p_u = p_e p_i" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": ". Then, images in the above environment settings " + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "inline_equation", + "content": "x_{new}" + }, + { + "bbox": [ + 304, + 260, + 545, + 355 + ], + "type": "text", + "content": " can be rewritten as," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 363, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 363, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 318, + 363, + 545, + 396 + ], + "type": "interline_equation", + "content": "x _ {n e w} \\sim \\mathcal {N} \\binom {(p _ {g} g) \\alpha \\left(p _ {u} \\bar {u}\\right),} {\\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}}. \\tag {9}", + "image_path": "b4ac51ce5db950f87eb31c68d3b0b0bdb3ab9cf38f9a414e7a46eec500647def.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 402, + 467, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 467, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 467, + 415 + ], + "type": "text", + "content": "Based on Eq. (3), it can be expanded as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 421, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 421, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 315, + 421, + 545, + 468 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\left(p _ {g} p _ {u}\\right) \\alpha g \\bar {u}, \\left(p _ {g} p _ {u}\\right) ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - (p _ {g} p _ {u}) ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {10} \\\\ + \\left(p _ {g} g\\right) ^ {2} \\alpha^ {2} \\left(p _ {u} \\bar {u}\\right) + \\left(p _ {g} g\\right) ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}). \\\\ \\end{array}", + "image_path": "301ed2e507b32786dd07aab49638f46fc9deb09f9170e77adb97545df91f47b7.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "text", + "content": "By inserting " + }, + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\mu_{x} = g\\alpha \\bar{u}" + }, + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "text", + "content": " and original pixel value, " + }, + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "inline_equation", + "content": "x_{pre} \\sim \\mathcal{N}\\left(\\mu_x, g\\alpha \\mu_x + g^2\\sigma_d^2 + \\sigma_r^2\\right)" + }, + { + "bbox": [ + 305, + 476, + 545, + 512 + ], + "type": "text", + "content": ", it can be expressed with a pixel value-based equation as follows;" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 321, + 522, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 522, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 321, + 522, + 545, + 567 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} x _ {n e w} \\sim p _ {u} p _ {g} x _ {p r e} + \\\\ \\mathcal {N} \\left(0, p _ {u} \\left(1 - p _ {u}\\right) p _ {g} ^ {2} g \\alpha \\mu_ {x} \\right. \\tag {11} \\\\ + \\left(1 - p _ {u} ^ {2}\\right) p _ {g} ^ {2} g ^ {2} \\sigma_ {d} ^ {2} + \\left(1 - p _ {u} ^ {2} p _ {g} ^ {2}\\right) \\sigma_ {r} ^ {2}). \\\\ \\end{array}", + "image_path": "f11c9f5e11be9b885e6670ddff9611554bfe5940c06ec74fa2b14899066d5f70.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": "Because the expected original pixel value " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mu_{x}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": " in the Gaussian term is impossible to obtain, we approximate it as " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "\\mu_{x} = x_{pre}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": ". Based on this equation, we can precisely simulate as if exposure time, light intensity, and analog gain were " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "p_{e}, p_{i}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "p_{g}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": " times. Then, let's come back to contrast, brightness, and hue augmentation. When contrast is multiplied by " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "p_{c}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": " and brightness is changed by " + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "inline_equation", + "content": "p_{b}" + }, + { + "bbox": [ + 304, + 574, + 545, + 670 + ], + "type": "text", + "content": ", it can be expressed as," + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 381, + 670, + 545, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 670, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 381, + 670, + 545, + 683 + ], + "type": "interline_equation", + "content": "x _ {n e w} = p _ {c} x _ {p r e} + p _ {b}. \\tag {12}", + "image_path": "2b1870084c9ee80ad10d14717ee3069f7ddb2b953c0c5009991beb30f79fa0d0.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 688, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 688, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 306, + 688, + 545, + 716 + ], + "type": "text", + "content": "This function is represented as multiplication by " + }, + { + "bbox": [ + 306, + 688, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\frac{(p_c x_{pre} + p_b)}{x_{pre}}" + }, + { + "bbox": [ + 306, + 688, + 545, + 716 + ], + "type": "text", + "content": ". Therefore, noise-accounted contrast and" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14010" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 230, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 230, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 230, + 84 + ], + "type": "text", + "content": "brightness augmentation is finally defined as," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 290, + 145 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 91, + 290, + 145 + ], + "spans": [ + { + "bbox": [ + 48, + 91, + 290, + 145 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\text {r a n d o m} p _ {c}, p _ {b} \\\\ \\text {r a n d o m} p _ {u}, p _ {g} (\\text {w h e r e} p _ {u} p _ {g} = \\frac {\\left(p _ {c} x _ {p r e} + p _ {b}\\right)}{x _ {p r e}}, p _ {u}, p _ {g} > 0) \\\\ E q. (1 1) \\left(\\mu_ {x} \\leftarrow x _ {p r e}\\right) \\end{array} \\right. \\tag {13}", + "image_path": "72d329fb813f4ead30c3759ff8ef6912ec6176c6af70bbddccfa2e112c282ba4.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": "We can also convert hue by changing " + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": " per color filter position in the RAW bayer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 184, + 163, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 184, + 163, + 196 + ], + "spans": [ + { + "bbox": [ + 47, + 184, + 163, + 196 + ], + "type": "text", + "content": "3.3.2 Blur Augmentation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "text", + "content": "Next, we introduce noise-accounted blur augmentation. Usual blur augmentation makes noise smaller than actual blur because the noise " + }, + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "inline_equation", + "content": "n_d" + }, + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "inline_equation", + "content": "n_r" + }, + { + "bbox": [ + 46, + 202, + 287, + 286 + ], + "type": "text", + "content": " are smoothed out although their noise amounts, in reality, are not related to how fast you shake a camera or how fast objects move. Only the photon number-related noise is smoothed out in actual motion blur. The actual blurred pixel is expressed as," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 292, + 290, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 290, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 290, + 334 + ], + "type": "interline_equation", + "content": "x _ {n e w} \\sim \\mathcal {N} \\left(g \\alpha \\sum_ {k} w _ {k} \\bar {u} _ {k}, g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right), \\tag {14}", + "image_path": "7aed160781b79416cda1f34f45b4dbca8f00587a81da8c2f1ec7eb2a963ee50f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 334, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 287, + 370 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 334, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\sum_{k}w_{k} = 1" + }, + { + "bbox": [ + 47, + 334, + 287, + 370 + ], + "type": "text", + "content": " is the blur kernel. With similar equation manipulation from Eq. (9) to Eq. (11), noise-accounted blur augmentation is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 376, + 289, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 289, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 289, + 517 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} x _ {n e w} \\sim \\mathcal {N} \\left(\\sum_ {k} w _ {k} g \\alpha \\bar {u} _ {k}, \\sum_ {k} w _ {k} ^ {2} \\left(g ^ {2} \\alpha^ {2} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}\\right)\\right) \\\\ + \\mathcal {N} (0, - \\sum_ {k} w _ {k} ^ {2} (g ^ {2} \\alpha^ {2} \\bar {u _ {k}} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\\\ + g ^ {2} \\alpha^ {2} \\sum_ {k} w _ {k} \\bar {u} _ {k} + g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2}) \\tag {15} \\\\ = \\sum_ {k} w _ {k} x _ {p r e} + \\mathcal {N} (0, g \\alpha \\sum_ {k} (1 - w _ {k}) w _ {k} x _ {p r e, k} \\\\ + (1 - \\sum_ {k} w _ {k} ^ {2}) (g ^ {2} \\sigma_ {d} ^ {2} + \\sigma_ {r} ^ {2})). \\\\ \\end{array}", + "image_path": "c3a787811799cc9e81e9459409992998b5b8e48ef9d246e2c763f3695f5a6bba.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 522, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 287, + 558 + ], + "type": "text", + "content": "We account for prior noise but not for prior blur amounts because most images in usual datasets are not very blurry. Furthermore, it is difficult to estimate the prior blur amount." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 559, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 559, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 559, + 287, + 629 + ], + "type": "text", + "content": "In addition, please note that augmentation to make images clean (make them brighter and deblurred) is inevitably difficult with noise-accounted RAW augmentation. Clipping noise variance in Eq. (11) to zero forcibly enables brightening, but brightening too much causes a mismatch of noise domain." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 639, + 118, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 118, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 118, + 651 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 659, + 105, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 105, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 105, + 670 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Although our method can be applied to any computer vision task, we choose a human detection task as a target because of its wide usage. We prepared a RAW image dataset" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "for human detection task captured with an internally developed sensor. As mentioned earlier, our objective is to train image recognition models that work in various environments only using a training dataset in simple environments. So, most training images are taken under normal light conditions with fixed camera positions in several environments. Note that moderately dark and HDR images are also included to some extent in the training dataset. The analog gain is set to 6dB outdoors, 12dB indoors, and 32dB at night in moderate darkness to generate realistic easy images without auto-exposure. Test images, on the other hand, are taken in HDR or extremely dark environments. In addition, about " + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": " of them are captured with a strong camera shake. Moreover, the analog gain is chosen from 3dB, 6dB, 12dB, and 24dB regardless of the environment. Both datasets are captured with around 1 fps to increase diversity among images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 276, + 546, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 546, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 546, + 408 + ], + "type": "text", + "content": "We manually annotate the human bounding boxes of both training and test data. Because precise annotation of test data on sRGB is impossible due to the noise and blur, we apply an offline ISP to each image and then annotate the bounding boxes. We manually set adequate ISP parameters per image and had to change the parameters several times to grasp the entire image. To avoid annotating large training datasets in this time-consuming way, it is desirable to train the model with a simple dataset. In total, 18,880 images are collected for training and 2,800 for testing. The examples are shown in Fig. 3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 418, + 440, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 440, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 440, + 430 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "text", + "content": "We mainly test with TTFNet [27] whose backbone is ResNet18 [14]. The network is trained for 48 epochs from scratch using Adam optimizer [22] and a cosine decay learning rate scheduler with a linear warmup [28] for the first 1,000 iterations whose maximum and minimum learning rates are 1e-3 and 1e-4. As to an ISP, a simple software ISP consisting of only a gamma tone mapping is implemented. In detail, two types of gamma tone mapping are implemented. One is the simplest gamma tone mapping, " + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "inline_equation", + "content": "y = x^{\\frac{1}{\\gamma}}" + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "inline_equation", + "content": "0 \\leq x \\leq 1" + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "text", + "content": "). The " + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 437, + 545, + 715 + ], + "type": "text", + "content": " is set to 5 after tuning with a rough grid search manner. The other is a gamma tone mapping parameterized with three parameters [34]. Because the grid search for three parameters is time-consuming, we tuned the parameters with backpropagation together with the detector's weights as performed in [35, 49]. Other ISP functions are not used because they are known to have less impact on image recognition compared with tone mapping [13]. We also prepare an elaborated black-box ISP consisting of many functions in addition to a tone mapping function. The parameters are tuned for human perceptual quality by experts. We only use the elaborated black-box ISP under the conventional training pipeline. In other words, experiments are performed un" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14011" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 521, + 208 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 521, + 208 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 521, + 208 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 521, + 208 + ], + "type": "image", + "image_path": "118b7e4a94c8f9f5e39038e4fe3b6707882b125088db2d22dfd117811f20647d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 547, + 240 + ], + "type": "text", + "content": "Figure 3. Examples of the introduced dataset. The upper row shows the training dataset collected in simple environments while the lower row shows the challenging test dataset collected in various environments from dark to bright, HDR, and with or without handshake blur." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": "der ISP-augmentation-detection order with the elaborated black-box ISP due to the hardware limitation. If contrast augmentation is used, the hue is also changed with a probability of " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": ". In detail, the contrast factor per color channel " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "p_{c,h} = \\{R,G,B\\}" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " is randomized from the base contrast factor " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "p_{c,\\text{base}}" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "(0.8p_{c,\\text{base}}, 1.2p_{c,\\text{base}})" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "p_{c,\\text{base}}" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " is randomly decided. If blur augmentation is used, a random-sized blur kernel with a probability of " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " is used. Random shift and random scale augmentation whose maximum transformations are " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " of the input size are also applied with a probability of " + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 260, + 289, + 429 + ], + "type": "text", + "content": " before color jitter augmentation. The input size to the detector is (576, 352, 3). The performance of the detector is evaluated with average precision (AP@0.5:0.95) [24]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 440, + 214, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 214, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 214, + 453 + ], + "type": "text", + "content": "4.3. Calibration of the Noise Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": "For each analog gain of 6dB, 12dB, and 24dB, two burst sequences are captured with different illumination. Each sequence consists of 100 images. " + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "inline_equation", + "content": "24 \\times 24" + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": " Bayer pixels are sampled from each of the 24 color patches to calculate the mean and variance. In total " + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "inline_equation", + "content": "2 \\times 24 \\times 24 \\times 24" + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": " pairs of mean and variance sets are obtained per analog gain to estimate the noise model. Thanks to the various color filters, exposure values, and color patches, two sequences are enough to ensure diversity. The lines in Fig. 4 show the estimated linear relationship in Eq. (6). The coefficients of determination, " + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": ", for these line estimations are 0.9833, 0.9884, 0.9862 for 6, 12, and 24dB respectively. High values of " + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": " indicate that the noise intensity is well modeled with respect to illumination intensity. Also, " + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 46, + 460, + 287, + 675 + ], + "type": "text", + "content": " of the Eq. (7) and Eq. (8) are 1.0000 and 0.9984. This means the noise intensity is well modeled with respect to the analog gain. Based on the above, our noise model and the calibration method are well suited to the sensor in terms of noise intensity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Next, we check the validity of the shape of the distribution. All noises were assumed to follow a Gaussian distribution. Especially, it is unclear whether the approximation" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 305, + 258, + 547, + 350 + ], + "blocks": [ + { + "bbox": [ + 305, + 258, + 547, + 350 + ], + "lines": [ + { + "bbox": [ + 305, + 258, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 547, + 350 + ], + "type": "image", + "image_path": "68d420a429e890c4e5d1e2b376d6f1be39e789c794e2f2c55fb6bf96d27e3c51.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 356, + 547, + 422 + ], + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 422 + ], + "type": "text", + "content": "Figure 4. Sensor noise model calibration result. The dots in the left graph are the mean and variance pairs for each pixel, and the lines are the estimated linear relationship for each analog gain. Since large numbers of dots are plotted, they seem to be widely spread. On the other hand, the histogram plot per analog gain (right) shows a clear difference between them." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 308, + 436, + 547, + 519 + ], + "blocks": [ + { + "bbox": [ + 308, + 436, + 547, + 519 + ], + "lines": [ + { + "bbox": [ + 308, + 436, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 308, + 436, + 547, + 519 + ], + "type": "image", + "image_path": "0fcbc7210852d82eb9a5b3376309771e5ff5d01eb992c44003809f001fd351df.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 526, + 547, + 583 + ], + "lines": [ + { + "bbox": [ + 304, + 526, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 547, + 583 + ], + "type": "text", + "content": "Figure 5. The result of the Shapiro-Wilk [40] test for each expected pixel value. When testing whether the 100 pixel values at each location correspond to a Gaussian distribution, most p-values are larger than 0.05 (a). The right (b) shows the cases where " + }, + { + "bbox": [ + 304, + 526, + 547, + 583 + ], + "type": "inline_equation", + "content": "\\mathfrak{p} < 0.05" + }, + { + "bbox": [ + 304, + 526, + 547, + 583 + ], + "type": "text", + "content": ". It indicates the small p-values come from sparsity, not skew." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\bar{u}) \\doteq \\mathcal{N}(\\bar{u}, \\bar{u})" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " [9] is true. Therefore, the Shapiro-Wilk test [40] is performed. If the p-value of the test is higher than 0.05, it indicates that we cannot reject the null hypothesis that the data are normally distributed with more than a " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " confidence interval. Fig. 5(a) shows that most of them are higher than 0.05, but some results for dark pixels are less than 0.05. However, the distributions of the dark pixels are like Fig. 5(b). It is not very skewed and the sparsity causes the small p-value. Therefore, we conclude that all the noise" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14012" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 289, + 171 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 289, + 171 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 289, + 171 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 289, + 171 + ], + "type": "image", + "image_path": "4068d637165831208ae3384d04a2e8c49758ad212de0156ddfb9382b84e12e1a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "type": "text", + "content": "Figure 6. The statistical validation of the noise alignment. The green dots represent real image data, and the others are converted from it. The conversions are " + }, + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\times 0.1" + }, + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\times 0.5" + }, + { + "bbox": [ + 46, + 172, + 287, + 228 + ], + "type": "text", + "content": " contrast conversion with several methods. The (a) is a dark-to-extreme-dark conversion, and the (b) is a bright-to-dark conversion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 250, + 221, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 250, + 221, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 221, + 262 + ], + "type": "text", + "content": "sources can be regarded as Gaussian noise." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 262, + 287, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 298 + ], + "type": "text", + "content": "Based on the above, our sensor noise model and the calibration method represent the sensor noise well in terms of both intensity and distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 307, + 277, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 307, + 277, + 320 + ], + "spans": [ + { + "bbox": [ + 47, + 307, + 277, + 320 + ], + "type": "text", + "content": "4.4. Statistical Validation of the Noise Alignment" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 326, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 457 + ], + "type": "text", + "content": "Before confirming the effectiveness of the proposed noise-accounted RAW augmentation to computer vision applications, the statistical validity is evaluated one more time by utilizing the series of color checker images. The evaluation method is as follows. First, the contrast of the sequential images is changed with or without noise consideration. Second, mean and variance pairs along the sequential dimension are computed. Third, the distributions of real and converted pairs are examined. If the real and converted pairs matched well, it means the converted images have the same noise amount as the original real images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 459, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 615 + ], + "type": "text", + "content": "Three different noise alignment methods are compared, i.e., no noise consideration, the usual noise-accounted method that disregards prior noise in the input [4,15,44,47], and our proposed noise alignment method. Fig. 6 shows the comparison result. It indicates that prior noise consideration is unnecessary if pixels are darkened considerably. However, a small contrast factor caused a noise domain gap even if the input is bright like Fig. 6 (right). In contrast, our noise-accounted conversion always converted images with realistic noise. It implies that our proposed method is suited for various strengths of augmentation. If prior noise is not accounted for, the inputs always have to be darkened considerably and already dark images are difficult to use." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 623, + 230, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 230, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 230, + 635 + ], + "type": "text", + "content": "4.5. Augmentation Parameters Tuning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "content": "The optimal augmentation parameters should be different between augmentation before and after ISP. To make a fair comparison, we roughly tune both of the augmentation parameters. The strategy is as follows. First, we search the appropriate range of contrast factor " + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "content": " and brightness perturbation " + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 46, + 642, + 287, + 715 + ], + "type": "text", + "content": " successively. To be robust to any illumination" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "of inputs, we re-parameterize " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "p_b = \\hat{p}_b \\min(x)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " and randomize the " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\hat{p}_b" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". Lastly, we search for the appropriate max blur distance " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "p_d" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". In these experiments, we do not account for sensor noise. We use the elaborated black-box ISP for the augmentation after ISP setting and the simplest gamma function for the augmentation before ISP setting." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 144, + 545, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 144, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 305, + 144, + 545, + 169 + ], + "type": "text", + "content": "The results are shown in Table 1. The best parameter settings are used in the next section." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 178, + 545, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 202 + ], + "type": "text", + "content": "4.6. Evaluation of the Noise-Accounted RAW Augmentation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 210, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 210, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 546, + 555 + ], + "type": "text", + "content": "In this section, the proposed noise-accounted RAW augmentation is evaluated on training image recognition models. First, as Table 2 shows, augmentation before ISP drastically improves the accuracy with the simplest ISP. It suggests the realistic pixel intensity distribution achieved by augmentation before ISP is the key to improving the accuracy in wide environments. In the color jitter augmentation only setting, the accuracy is improved from the general noise alignment method [2,4,9,15,26,31,36,47,50] by considering prior noise. In the color jitter and blur augmentation setting, noise-accounted color jitter augmentation plus normal blur augmentation does not improve much from no noise-accounted settings. Instead, noise alignment in both color jitter and blur augmentation improves the accuracy. It indicates that random noise is not effective and realistic noise is important. Comparing the accuracy under the same simplest gamma tone mapping setting, our proposed noise-accounted RAW augmentation doubles the accuracy of conventional augmentation after ISP. Furthermore, when parameterized gamma tone mapping is used as our simple ISP, the accuracy is even superior to the elaborated black-box ISP consisting of many functions in addition to a tone mapping function. As the visualization results in the supplementary material show, the elaborated black-box ISP outputs more perceivable images. It suggests that minimizing the domain gap caused by augmentation is more important than the superiority of the ISP. We might improve the accuracy more by an elaborated ISP and the proposed augmentation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "As mentioned earlier, there are noise dealing works in noise-related fields like denoising. We compare ours with these methods in the detection task. One is the K-Sigma transform [44], a kind of noise domain generalization. It normalizes images so that the pixel value and the standard deviation of the noise are linearly correlated. The other is noise amount notification with a concatenation of the noise variance map [2]. To follow the previous setup, direct RAW input without an ISP is also compared. Color jitter and blur augmentation are also applied to the methods different from the previous papers for a fair comparison. Table 3 shows the comparison results. As to the K-Sigma transform, simply applying \"aug.\" before or after the K-Sigma" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14013" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 101, + 547, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1. The augmentation hyperparameter tuning for a fair comparison between before and after ISP augmentation. The range of contrast, brightness, and blur distance are tuned one by one, taking over the previous best parameters." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 101, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 101, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 101, + 547, + 178 + ], + "type": "table", + "html": "
augmentation after ISP (tuned for the black-box ISP)augmentation before ISP (tuned for the simplest ISP)
contrastrange0.2-10.1-10.2-50.1-100.05-200.1-10.02-10.01-10.005-10.01-1.1
AP@0.5:0.95 [%]41.941.843.245.144.536.939.840.435.838.9
brightnessrange0-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.70-0-0.1-0.1-0.2-0.2-0.5-0.5-0.7-0.7
AP@0.5:0.95 [%]45.144.544.545.244.740.440.939.939.439.4
blur distancerange0-00-30-50-90-130-00-30-50-90-13
AP@0.5:0.95 [%]45.246.845.745.937.940.939.839.640.643.3
", + "image_path": "aac2416aa842f053ac14b742de618de4be2fe2c15b50a8ee3e59c8b6750d159d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 325, + 287, + 429 + ], + "blocks": [ + { + "bbox": [ + 46, + 195, + 289, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 195, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 289, + 316 + ], + "type": "text", + "content": "Table 2. Evaluation of the noise-accounted RAW augmentation. The color augmentation contains default hue augmentation plus tuned contrast and brightness augmentation. The w/o prior means the prior input noise is disregarded like many of the previous noise-accounted image conversion methods [2,4,9,15,26,31,36, 47, 50]. Because we adopt the well-established heteroscedastic Gaussian model Eq. (2), it is identical to the noise alignment of [2,9,36,50]. In this experiment, we also use the parameterized gamma tone mapping as the simple ISP, although it can't be used in the augmentation after ISP settings because the gradient from the detection loss is needed to tune." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 325, + 287, + 429 + ], + "lines": [ + { + "bbox": [ + 50, + 325, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 50, + 325, + 287, + 429 + ], + "type": "table", + "html": "
augmentationnoisemAP@0.5:0.95 [%]
black-box ESPsimple ESP
simplestparameterized
Colorafter-45.219.3-
before (ours)--40.944.4
w/o prior-43.547.7
ours-44.648.1
Color + Blurafter-46.820.4-
before (ours)--43.343.8
ours†-43.447.9
ours-45.348.3
", + "image_path": "f75ffe1d232f5dca2d8ae3406c4570a3bd3d8af484725943d9f8e12ebef631a2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 60, + 429, + 272, + 437 + ], + "lines": [ + { + "bbox": [ + 60, + 429, + 272, + 437 + ], + "spans": [ + { + "bbox": [ + 60, + 429, + 272, + 437 + ], + "type": "text", + "content": "†: The noise alignment is only applied to the color jitter augmentation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": "transforms gives a better result. However, there is a theoretical problem in both cases. If \"aug.\" is applied after the transform, the linear relation between pixel value and noise amount is retained but pixel intensity becomes inconsistent. On the other hand, applying \"aug.\" before the transform makes the noise amount unrealistic. Changing the augmentation to \"our aug.\" makes the intensity and noise realistic and improves the accuracy. From the experiment, we find the proposed augmentation boosts previous noise-dealing methods if ISPs are used. However, if ISPs are not used, noise accounted augmentation slightly deteriorated the accuracy. We argue that it is because the intensity distributions of RAW images are too difficult and unrealistic clean images might help training. However, the overall accuracy is lower than with ISPs. Also, for the detection task, only our proposed method is enough. It might be because, unlike the denoising task which should focus on noise, it is important to make the detector focus on pixel intensity distribution for the detection task." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 328, + 248, + 526, + 374 + ], + "blocks": [ + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "text", + "content": "Table 3. The comparison results with other noise-dealing techniques. The \"aug.\" means contrast and blur augmentation without noise-accounted and \"our aug.\" means with noise-accounted. We use the simplest gamma function in the ISP." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 248, + 526, + 374 + ], + "lines": [ + { + "bbox": [ + 328, + 248, + 526, + 374 + ], + "spans": [ + { + "bbox": [ + 328, + 248, + 526, + 374 + ], + "type": "table", + "html": "
methodAP@0.5:0.95 [%]
w/o ISPw/ ISP
concat [2]16.521.5
aug. + concat [2]35.031.6
our aug. + concat [2]33.740.4
K-Sigma [44]14.327.5
K-Sigma [44] + aug.25.034.1
aug. + K-Sigma [44]26.642.1
our aug. + K-Sigma [44]26.344.0
our aug.32.845.3
", + "image_path": "ddcb609c51bbf6eea2ca253deba7c18ccb66b5922d344dd6511fa757ba44219d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 396, + 379, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 379, + 408 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 379, + 408 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 418, + 547, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 622 + ], + "type": "text", + "content": "We propose a noise-accounted RAW augmentation method in which augmentation is applied before ISP to minimize the luminance domain gap and a sensor noise model is taken into account to minimize the noise domain gap. Unlike previous noise-accounted methods, ours takes the prior input noise into account. It minimizes the domain gap more and enables the use of already noisy images as training data. Thanks to the realistic augmentation, our method improves the detection accuracy in difficult scenes compared to the conventional methods. In the future, we would like to investigate whether the proposed augmentation with an elaborate ISP improves computer vision performance even further. Also, we would like to check the effectiveness against other image recognition tasks, such as classification or segmentation, by preparing datasets. We believe it is effective because our method is task-independent. 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Guerrero Peña", + "bbox": [ + 200, + 181, + 388, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fidel-alejandro.guerrero-pena@etsmtl.ca", + "bbox": [ + 122, + 202, + 468, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thomas Dubail", + "bbox": [ + 241, + 224, + 366, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thomas.dubail.1@ens.etsmtl.ca", + "bbox": [ + 173, + 244, + 431, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Eric Granger", + "bbox": [ + 289, + 267, + 395, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "eric.granger@etsmtl.ca", + "bbox": [ + 243, + 287, + 439, + 300 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Heitor Rapela Medeiros", + "bbox": [ + 581, + 181, + 774, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "heitor.rapela-medeiros.1@ens.etsmtl.ca", + "bbox": [ + 509, + 202, + 846, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Masih Aminbeidokhti", + "bbox": [ + 550, + 224, + 727, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "masih.aminbeidokhti.1@ens.etsmtl.ca", + "bbox": [ + 482, + 244, + 794, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Marco Pedersoli", + "bbox": [ + 547, + 267, + 679, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "marco.pedersoli@etsmtl.ca", + "bbox": [ + 501, + 287, + 725, + 300 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LIVIA, Dept. of Systems Engineering ETS Montreal, Canada", + "bbox": [ + 331, + 309, + 635, + 344 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 378, + 312, + 395 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces and some promising properties like mode connectivity. However, finding the permutation that minimizes some objectives is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to suboptimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature under several conditions for both optimal transport and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with the state-of-art. The source code is provided at https://github.com/fagp/sinkhorn-rebasin.", + "bbox": [ + 75, + 411, + 472, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 800, + 209, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the success of deep learning (DL) across many application domains, the loss surfaces of neural networks (NNs) are not well understood. Even for shallow NNs, the number of saddle points and local optima can increase exponentially with the number of parameters [4, 13]. The permu", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/20e36d8f1c619bc8acadec912ce8bb714772433fb7caea446cf928d7005fe2f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 563, + 411, + 830, + 573 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a126f321aaecf2f8c3e0a61b76db2604b7512c70a292a853412537003debdd0d.jpg", + "image_caption": [ + "(a)", + "(b)", + "Figure 1. (a) Loss landscape for the polynomial approximation task [27]. $\\theta_{A}$ and $\\theta_{B}$ are models found by SGD. LMC suggests that re-basin the model $\\theta_{B}$ would result in a functionally equivalent model $\\pi_{\\mathcal{P}}(\\theta_B)$ , with no barrier on its linear interpolation $(1 - \\lambda)\\theta_{A} + \\lambda \\pi_{\\mathcal{P}}(\\theta_{B})$ . (b) Comparison of the cost in the linear path along $\\lambda$ before and after re-basin using weight matching (WM) [2] and our Sinkhorn. The dashed line in the figures corresponds with the naive path, and the solid line is the path after the proposed Sinkhorn re-basin. The blue line represents WM path." + ], + "image_footnote": [], + "bbox": [ + 519, + 585, + 803, + 744 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20237", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tation symmetry of neurons in each layer allows the same function to be represented with many different parameter values of the same network. Symmetries imposed by these invariances help us to better understand the structure of the loss landscape [6, 11, 13].", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous studies establish that minima found by Stochastic Gradient Descent (SGD) are not only connected in the network parameter's space by a path of non-increasing loss, but also permutation symmetries may allow us to connect those points linearly with no detriment to the loss [9, 11-13, 15, 24]. This phenomenon is often referred to as linear mode connectivity (LMC) [24]. For instance, Fig. 1a shows a portion of the loss landscape for the polynomial approximation task [27] using the method proposed by Li et al. [16]. $\\theta_{A}$ and $\\theta_{B}$ are two minima found by SGD in different basins with an energy barrier between the pair. LMC suggests that if one considers permutation invariance, we can teleport solutions into a single basin where there is almost no loss barrier between different solutions [2, 11]. In literature, this mechanism is called re-basin [2]. However, efficiently searching for permutation symmetries that bring all solutions to one basin is a challenging problem [11]. Three main approaches for matching units between two NNs have been explored in the literature [2]. Some studies propose a data-dependent algorithm that associates units across two NNs by matching their activations [2, 26]. Since activation-based matching is data dependent, it helps to adjust permutations to certain desired kinds of classes or domains [26]. Instead of associating units by their activations, one could align the weights of the model itself [2, 26], which is independent of the dataset, and therefore the computational cost is much lower. Finally, the third approach is to iteratively adjust the permutation of weights. In particular, Ainsworth et al. [2] have proposed alternating between models alignment and barrier minimization using a Straight-Through Estimator. Unfortunately, the proposed approaches so far are either non-differentiable [2, 11, 26] or computationally expensive [2], making the solution difficult to be extended to other applications, with a different objective. For instance, adapting those methods for incremental learning by including the algorithm for weight matching between two models trained on different domains is not trivial because of the difficulties in optimizing new objectives.", + "bbox": [ + 75, + 169, + 472, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, inspired by [21], we relax the permutation matrix with the Sinkhorn operator [1], and use it to solve the re-basin problem in a differentiable fashion. To avoid the high cost for computing gradients in the proposal of Mena et al. [21], we use the implicit differentiation algorithm proposed in [10], which has been shown to be more cost-effective. Our re-basin formulation allows defining any differentiable objective as a loss function.", + "bbox": [ + 75, + 746, + 468, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A direct application of re-basin is the merger of diverse models without significantly degrading their performance", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[2, 5, 12, 13, 28]. Applications like federate learning [2], ensembling [12], or model initialization [5] exploit such a merger by selecting a model in the line connecting the models to be combined. To show the effectiveness of our approach, we propose a new continual learning algorithm that combines models trained on different domains. Our continual learning algorithm differs from previous state-of-art approaches [22] because it directly estimates a model at the intersection of previous and new knowledge, by exploiting the LMC property observed in SGD-based solutions.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contribution can be summarized as follows:", + "bbox": [ + 517, + 242, + 872, + 256 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Solving the re-basin for optimal transportation using implicit Sinkhorn differentiation, enabling better differentiable solutions that can be integrated on any loss.", + "(2) A powerful way to use our re-basin method based on the Sinkhorn operator for incremental learning by considering it as a model merging problem and leveraging LMC.", + "(3) An extensive set of experiments that validate our method for: (i) finding the optimal permutation to transform a model to another one equivalent; (ii) linear mode connectivity, to linearly connect two models such that their loss is almost identical along the entire connecting line in the weights space; and (iii) learning new domains and tasks incrementally while not forgetting the previous ones." + ], + "bbox": [ + 496, + 257, + 890, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 467, + 637, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Re-basin. Recently, in the NN community, re-basin has been demonstrating useful properties. The main goal of such re-basin approaches is to obtain functionally equivalent models in a different region of the weight space following some pre-defined objective. Permutation symmetries are a well-known example of transformations that allows performing re-basin. In particular, Entezari et al. [11] show that the invariances of NNs using random permutations on SGD solutions are likely to have almost zero barriers, and therefore the randomness in terms of permutations does not impact the quality of the final training result of the model. A simulated annealing-based algorithm was proposed for doing a re-basin with an elevated computational cost, making it impractical to use, especially for bigger models. Ainsworth et al. [2] proposed three new re-basin algorithms that rely on solving linear assignment problems to find permutation matrices that satisfy their encoded objective. The methods showed to perform well, especially in achieving linear mode connectivity. On the downside, new objectives are difficult to plug into their framework. Their solution uses greedy algorithms that do not guarantee finding the optimal solution, as shown in our experiments. Using a similar approach, Benzing et al. [5] found strong evidence that two random initialization of a NN after permutation can lead to a good performance, showing that the random initialization is already in the same loss valley during the initialization. Finally, [3] uses the concepts of", + "bbox": [ + 496, + 493, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20238", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Wasserstein barycenter and Gromov-Wasserstein barycenter, offering a NN model fusion framework with insights about linear mode connectivity of SGD solutions. Even though the previous works presented solutions to perform re-basin by solving linear assignment problems, their approach fails to generalize well for other objectives. Using gradient descent-based algorithms seems to be a more suitable approach.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mode connectivity. Mode connectivity is the task of finding low-barrier paths connecting models within the weight space. In their work, Garipov et al. [13] found that the local optima of deep learning models are connected by simple curves. The fast geometric ensembling method was proposed as an application for their proposal. Almost at the same time, [9] proposed a nudged elastic band-based method to construct continuous paths between minima of NN architectures. Finally, Frankle et al. [12] studied the sensitivity of different levels of SGD noise on NNs. These pioneering works are the basis for applications of mode connectivity, like [2, 22] and ours.", + "bbox": [ + 75, + 215, + 472, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Incremental learning. Continual or incremental learning (IL) allows adapting models incrementally based on new training data without forgetting previous knowledge. Catastrophic forgetting [19,25] occurs when a previously trained model that is fine-tuned on a new task loses information learned to perform well on previous datasets. To address this issue, Kirkpatrick et al. [14] proposes elastic weight consolidation (EWC), which reduces catastrophic forgetting by regularizing NN parameters with respect to the importance of the weights concerning the previous and actual tasks. Chaudhry et al. [8] proposed using a small number of samples for replay. Their experience replay (ER) helps to perform IL such that the performance on classification tasks is improved, even with a tiny episodic memory. Closer to our work, [22] proposes an LMC-based method with replay. Its solution is called mode connectivity SGD (MC-SGD), which relies on the assumption that there is always an existing solution that solves all seen tasks incrementally, and they are connected by a low-barrier and linear path. Furthermore, MC-SGD utilizes a replay buffer to remember previous tasks for IL. Its efficiency relies on exploring the linear path of low loss to constrain learning, thereby outperforming competitors like EWC when less data is available. However, such an approach has a high computational cost since it requires training independent models for the new task and merging them as a separate step with the model for previous knowledge. Also, the method has been shown to be difficult to reproduce or adapt to new benchmarks [20]. A compelling scenario for continual learning is using a linear mode connectivity path to keep learning and adapt the model without forgetting the previous knowledge. The trade-off between flatness of the LMC path and direction to adapt the loss can be tuned in a way that brings more", + "bbox": [ + 75, + 401, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "stability or plasticity depending on the target final solution.", + "bbox": [ + 498, + 90, + 885, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Re-basin via the Sinkhorn operator", + "text_level": 1, + "bbox": [ + 498, + 119, + 821, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $f_{\\theta}(.)$ be a parameterized mapping where $\\theta$ represents a vector of parameters within the solution space $\\Theta \\subset \\mathbb{R}^d$ , where $d$ is the number of parameters in $\\theta$ . In the deep learning context, $f$ can be seen as a NN architecture, and $f_{\\theta}$ is a model with weights $\\theta$ . Here, we refer to $\\theta$ as a model for simplicity. Consequently, the cost (or error) of a model for a given task can be defined as $\\mathcal{C}(\\theta) = \\frac{1}{|\\mathbb{T}|}\\sum_{(x,y)\\in \\mathbb{T}}\\mathcal{L}(f_{\\theta}(x),y)$ , where $(x,y)\\in \\mathbb{T}$ are input and expect output in the training set $\\mathbb{T}$ , and $\\mathcal{L}$ is an appropriate supervised loss function.", + "bbox": [ + 496, + 145, + 890, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A function $f$ is invariant to a transformation if and only if the obtained transformed function is functionally equivalent to the original mapping. Note that such invariances can also be found between two functions within the family of parametric functions $\\{f_{\\theta}\\}_{\\theta \\in \\Theta}$ . The permutation of neurons is a well-known example of such transformations applied to NNs that allow obtaining functionally equivalent models, i.e., $f_{\\theta_A}(x) = f_{\\theta_B}(x), \\forall x$ . These invariant models are obtained via the permutation transformation or re-basin function, here defined as $\\pi \\colon \\Theta \\to \\Theta$ , which shifts a model to a symmetric region of the loss landscape, $\\mathcal{C}(\\theta) = \\mathcal{C}(\\pi_{\\mathcal{P}}(\\theta))$ . In this work $\\mathcal{P} = (P_1, \\dots, P_h)$ is a transportation plan with $P_i$ contained in the transportation polytope,", + "bbox": [ + 496, + 297, + 892, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Pi = \\left\\{P \\in \\mathbb {R} _ {+} ^ {m \\times n} | P \\mathbf {1} _ {m} = \\mathbf {1} _ {n}, P ^ {T} \\mathbf {1} _ {n} = \\mathbf {1} _ {m} \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 503, + 890, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbb{1}_d = (1,\\dots,1)^d$ . Without loss of generality, let $f_{\\theta}(x) = (\\ell_h\\circ \\ldots \\circ \\ell_1)(x)$ be a NN defined as the composition of $h$ layers such that $\\ell_i(z) = \\sigma (W_iz + b_i)$ . Here, the weights $W_{i}$ and biases $b_{i}$ are the parameters of the network, $\\theta = \\{W_i,b_i\\}_{i = 1}^h$ , and $\\sigma$ is a non-linear activation function. Then, the re-based model $\\pi_{\\mathcal{P}}(\\theta)$ can be written as the functionally equivalent mapping:", + "bbox": [ + 496, + 532, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {i} ^ {\\prime} (z) = \\sigma \\left(P _ {i} W _ {i} P _ {i - 1} ^ {T} z + P _ {i} b _ {i}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 650, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $P_{i}\\in \\Pi$ is a valid permutation matrix, and $P_{h} = P_{0}^{T} = I$ is the identity matrix.", + "bbox": [ + 498, + 679, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With regards to permutation invariance, Entezari et al. [11] conjectured that re-based SGD solutions are likely to have a low barrier within their linear interpolation $B(\\theta_A, \\theta_B) \\approx 0$ , where $B(.)$ is defined as:", + "bbox": [ + 498, + 709, + 890, + 771 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nB \\left(\\theta_ {A}, \\theta_ {B}\\right) = \\sup _ {\\lambda} \\left[ \\left. \\mathcal {C} ((1 - \\lambda) \\theta_ {A} + \\lambda \\theta_ {B}) \\right] - \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 781, + 841, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ (1 - \\lambda) \\mathcal {C} (\\theta_ {A}) + \\lambda \\mathcal {C} (\\theta_ {B}) ] ], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 816, + 890, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and $\\lambda \\in (0,1)$ . This phenomenon is known as LMC [12], and it is a particular case of the widely studied mode connectivity [9, 13]. Notably, Ainsworth et al. [2] proposed three approaches that ratify the conjecture in [11] by finding", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "footer", + "text": "20239", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a re-based model $\\pi_{\\mathcal{P}}(\\theta_B)$ with LMC to a target model $\\theta_A$ . Fig. 1 depicts the goal of such re-basin approaches. This figure shows two solutions for the task, $\\theta_A$ and $\\theta_B$ , found through SGD. As shown in Fig. 1b, the naive path between $\\theta_A$ and $\\theta_B$ has higher values of the barrier within the line $(1 - \\lambda)\\theta_A + \\lambda \\theta_B, \\lambda \\in (0,1)$ . On the other hand, and consistently with the results in [2,11], our re-based model $\\pi_{\\mathcal{P}}(\\theta_B)$ achieves LMC by successfully finding a transportation plan $\\mathcal{P}$ that shifts model $\\theta_B$ to the same basin of model $\\theta_A$ .", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the seminal work by Ainsworth et al. [2] proposed a highly efficient approach for finding a permutation that minimizes the distances between models, their nondifferentiable approach provides solutions that are difficult to be extended to other applications with a different objective. Specifically, their algorithms use a formulation based on the linear assignment problem (LAP) to find suitable permutations, meaning any new objective needs to be cast as a LAP which is a hard task in itself.", + "bbox": [ + 75, + 227, + 470, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This work proposes a differentiable approach to perform a re-basin that defines any differentiable objective as a loss function. Here, we relax the rigid constraint of having a binary permutation matrix $P$ , and consequently add an entropy regularizer $h(P) = -\\sum P(\\log P)$ to the original LAP as proposed by [21]. The final equation is then defined as:", + "bbox": [ + 75, + 364, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\tau} (X) = \\underset {P \\in \\Pi} {\\arg \\max } \\langle P, X \\rangle_ {F} + \\tau h (P), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 472, + 468, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where is $\\tau$ a factor that weights the strengths of the entropy regularization term.", + "bbox": [ + 75, + 506, + 468, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The formulation in Eq. (4) is known as the Sinkhorn operator and can be efficiently approximated by:", + "bbox": [ + 75, + 537, + 468, + 568 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\tau} ^ {(0)} (X) = \\exp \\left(\\frac {X}{\\tau}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 580, + 351, + 614 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\tau} ^ {(t + 1)} (X) = \\mathcal {T} _ {c} \\left(\\mathcal {T} _ {r} \\left(S _ {\\tau} ^ {(t)} (X)\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 628, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X \\in \\mathbb{R}^{m \\times n}$ is a soft version of the permutation matrix, $\\mathcal{T}_c(X) = X \\oslash (\\mathbb{1}_m\\mathbb{1}_m^T X)$ and $\\mathcal{T}_r(X) = X \\oslash (X\\mathbb{1}_n\\mathbb{1}_n^T)$ are respectively the re-normalization of columns and rows of $X$ , and $\\oslash$ is the element-wise division. In their work, Mena et al. [21] proved that Eq. (5) converges to Eq. (4) when $t \\to \\infty$ . However, in practice, only a finite number of iterations are needed to produce a suitable approximation.", + "bbox": [ + 75, + 657, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the Sinkhorn operator is reasonably easy to implement within the NN layers, a significant drawback arises when considering the efficiency of its differentiation. We use the implicit differentiation algorithm proposed by Eisenberger et al. [10] to mitigate such an increase in the computational cost. Their method significantly increases the efficiency and also stability of the training process. The marginals of the generic formulation in [10] are defined as $\\pmb{a} = \\mathbb{1}_m / m$ and $\\pmb{b} = \\mathbb{1}_n / n$ to match the re-basin task.", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, our proposed Sinkhorn re-basin re-writes the original re-basin mapping in Eq. (2) as:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {i} ^ {\\prime} (z) = \\sigma (S _ {\\tau} (P _ {i}) W _ {i} S _ {\\tau} (P _ {i - 1} ^ {T}) z + S _ {\\tau} (P _ {i}) b _ {i}). \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 128, + 890, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{i}\\in \\mathbb{R}^{m\\times n}$ is a differentiable permutation matrix.", + "bbox": [ + 498, + 156, + 877, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To show the ability of our proposed Sinkhorn re-basin to minimize any differentiable objective, we provide three examples of cost functions that are minimized without changing the formulation in Eq. (6). These cost functions are used in the SGD framework to compute the gradient of the weights in our Sinkhorn re-basin network, and finally update the permutation matrices to minimize the objective. First, for a data-free objective like Weights Matching [2], we directly minimize the squared L2 distance defined as:", + "bbox": [ + 496, + 171, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {L 2} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\left\\| \\theta_ {A} - \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right) \\right\\| ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 315, + 890, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the ability of our method to use differentiable objectives, we introduce two other data-driven cost functions. Inspired by the Straight-Through Estimator in [2], we propose a differentiable midpoint cost function to minimize the barrier,", + "bbox": [ + 496, + 342, + 890, + 416 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {M i d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left(\\frac {\\theta_ {A} + \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right)}{2}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 424, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since minimizing the midpoint can lead to a multimodal cost path, i.e., lower cost value for $\\lambda = 0.5$ , and higher cost values elsewhere, we propose a cost function that minimizes the cost at random points within the line:", + "bbox": [ + 496, + 465, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {R n d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left((1 - \\lambda) \\theta_ {A} + \\lambda \\pi_ {\\mathcal {P}} (\\theta_ {B})\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 535, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\lambda$ uniformly sampled at each iteration, $\\lambda \\sim U(0,1)$", + "bbox": [ + 500, + 560, + 874, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Re-basin incremental learning", + "text_level": 1, + "bbox": [ + 500, + 588, + 777, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A critical application of re-basin approaches is the ability to merge models without a significant performance reduction. Such merging is usually done by selecting a model in their connecting line. Applications like federate learning [2], ensembling [12], or model initialization [5] have been explored recently for merging models trained on the same task. Here we consider merging based on re-basin by proposing a new incremental learning approach that combines models trained on different domains or classes. Our proposed approach relies on a stability-plasticity hyperparameter $\\alpha$ , allowing the user to choose the balance between forgetting and incorporating new knowledge.", + "bbox": [ + 496, + 613, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\theta_0$ be an initial model trained over dataset $\\mathbb{T}_0$ , and $\\mathcal{T} = \\{\\mathbb{T}_1, \\mathbb{T}_2, \\ldots\\}$ be a stream of data, where $\\mathbb{T}_i = \\{(x_{ij}, y_{ij}) | x_{ij} \\in \\mathbb{X}_i, y_{ij} \\in \\mathbb{Y}_i\\}, 1 \\leq i \\leq N_i$ , is a supervised dataset with input $\\mathbb{X}_i$ , output $\\mathbb{Y}_i$ , and $N_i$ data points. Note that the sets $\\mathbb{T}_i$ are also known in incremental learning literature as tasks, but these are not limited to task incremental learning scenarios, and also include domain and", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "20240", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/99bcb0ad798cfc3ddcfb512b966fde136a28bf7d66d337b9bbee7fd5b250f421.jpg", + "image_caption": [ + "Figure 2. Graphical representation of the intersection of low curvature regions of the loss landscape for task $\\mathbb{T}_i$ (red) and $\\mathbb{T}_{i + 1}$ (blue). The goal of our method is to find a re-basin $\\pi_{\\mathcal{P}_i}(\\theta_i)$ that transverses the multitask region using LMC. The final model $\\theta_{i + 1}$ (Eq. (12)) is found in the surroundings of the line by adding a learnable residual $\\delta_{i}$ ." + ], + "image_footnote": [], + "bbox": [ + 135, + 87, + 369, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "class incremental learning. Incremental or continual learning seeks to incorporate the new knowledge $\\mathbb{T}_{i + 1}$ into the model $\\theta_{i}$ without forgetting how to perform correctly in previous datasets $\\mathbb{T}_0,\\dots,\\mathbb{T}_i$ . To this end, the continual learning community has proposed approaches that exploit the fact that multitask low curvature regions usually appear at the intersection of low curvature regions for individual tasks [14, 22] (see Fig. 2 for a visual reference). In particular, the Mirzadeh et al. [22] approach uses a two steps training, where the model $\\theta_{i + 1}$ is first trained over dataset $\\mathbb{T}_{i + 1}$ , and then a mode connectivity-based merging finds the model with low loss value on both new and previous knowledge.", + "bbox": [ + 75, + 382, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In contrast with [22], our approach directly estimates a model at the intersection of previous and new knowledge by exploiting our differentiable method to obtain the LMC observed in SGD-based solutions. Similarly to approaches introduced in the last section, our method looks for a rebasin of the given model that minimizes a given objective. For continual learning purposes, a new cost function is introduced such that, like in Eq. (8), the cost of the model in the middle of the line $(1 - \\lambda)\\theta_{i} + \\lambda \\pi_{\\mathcal{P}_{i}}(\\theta_{i}), \\lambda \\in (0,1)$ , is minimized for dataset $\\mathbb{T}_{i+1}$ (see Fig. 2). In such a continual learning scenario, the middle point is the furthest model in the line from high stability points $\\theta_{i}$ and $\\pi_{\\mathcal{P}_{i}}(\\theta_{i})$ , noting that the endpoints are solutions for previous tasks, but not for the new one. The smooth nature of the loss landscape implies that neighboring models have similar costs for all tasks, thus it is important to select the farthest model from the extremes. However, constraining the solution space to models within the line yields a solution that performs well on the previous task, but does not allow optimal performance on the new task, thus affecting the training plasticity. Similarly to Kirkpatrick et al. [14], we find well-behaved models for $\\mathbb{T}_{i+1}$ in the neighborhood of our optimization", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "target. This is done by adding a regularization term that minimizes the $l_{2}$ norm of the residual vector $\\delta_{i}$ . Finally, the proposed cost is calculated as:", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right) = \\mathcal {C} \\left(\\frac {\\theta_ {i} + \\pi \\mathcal {P} _ {i} \\left(\\theta_ {i}\\right)}{2} + \\delta_ {i}\\right) + \\beta \\| \\delta_ {i} \\| ^ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 145, + 890, + 180 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the learning phase, the underlying optimization problem finds:", + "bbox": [ + 498, + 186, + 890, + 217 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i} ^ {*}, \\mathcal {P} _ {i} ^ {*} = \\underset {\\delta_ {i}, \\mathcal {P} _ {i}} {\\arg \\min } \\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 228, + 890, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta_i^*$ and $\\mathcal{P}_i^*$ are found at the same time. Note that the cost in Eq. (10) can be computed over any knowledge dataset. This work uses a replay method by taking the average of Eq. (10) for current and previous datasets.", + "bbox": [ + 496, + 263, + 890, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Combining a model with a balance between previous and new knowledge should be obtained after minimizing the cost in Eq. (10). Here, the incremented model at episode $i + 1$ is defined as:", + "bbox": [ + 496, + 324, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {i + 1} = (1 - \\alpha) \\theta_ {i} + \\alpha \\pi_ {\\mathcal {P} _ {i}} (\\theta_ {i}) + \\delta_ {i}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 395, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyper-parameter controlling the balance between plasticity and stability. Note that values of $\\alpha$ near 0.5 favor higher plasticity, while values around 0.0 and 1.0 give more importance to previous knowledge.", + "bbox": [ + 496, + 422, + 890, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental results and analysis", + "text_level": 1, + "bbox": [ + 498, + 494, + 805, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The experimental procedure for comparing re-basin approaches follows the same one used by Ainsworth et al. [2], while the continual learning experiments follow the standard experimental procedure in incremental learning literature [22]. For all experiments, the mean and standard deviation of results is reported and obtained over independent runs with different seeds. We used the original implementation provided by the authors in all cases. The effect of re-basin is studied for both classification and regression tasks. Mnist and Cifar10 datasets were used for image classification, while the polynomial approximation problems from [27] were used for regression. Feedforward NNs with 2 to 8 layers were explored as backbone architectures. In all our experiments, $t = 20$ and $\\tau = 1.0$ were used, as proposed in [21] for the Sinkhorn operator. Furthermore, the corresponding performance measures and hyper-parameters are summarized in each subsection. Additional details on the experimental methodology, e.g., dataset, protocol, and performance measures, as well as other experimental settings, i.e., convolutional architectures, are provided in the supplementary materials.", + "bbox": [ + 496, + 521, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Finding the optimal transport", + "text_level": 1, + "bbox": [ + 500, + 847, + 766, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this experiment, we measure the ability of both Weights Matching (WM) [2] and our Sinkhorn re-basin to", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20241", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b8a7eff706677dff374c4d50dc060e3da8f862f48389a4103d28bf367f59717c.jpg", + "image_caption": [ + "Figure 3. Estimated permutation matrices via weight matching (WM) [2] and the proposed Sinkhorn re-basin. $P_{i}$ refers to the expected $10 \\times 10$ permutation matrix with ones represented in black and zeros in white. The estimated permutations matrix $\\hat{P}_{i}$ shows matching permutations as blue squares and miss-matchings in red and yellow. The permutation matrices $P_{i} \\in \\mathbb{R}^{10 \\times 10}$ correspond with transportation plans of layer $i$ , with each layer containing 10 neurons. These matrices correspond with actual permutation matrices from the experiment with random initialization and 2 hidden layers." + ], + "image_footnote": [], + "bbox": [ + 117, + 85, + 854, + 220 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "find the optimal permutation. Similar to our $\\mathcal{C}_{L2}$ , the WM method minimizes the distance between the re-based and target models by solving a LAP. The cost function used for our re-basin is the squared L2 distance between models (Eq. (7)). Note that the objectives are not data-driven, and therefore we only measure the ability of each algorithm to reach the global minima without any context. Each method received a model and a randomly permuted version of it to find the permutation matrices that originated the target re-basin.", + "bbox": [ + 75, + 325, + 470, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For our purposes, 9 datasets are created, each one containing 50 models and a random re-basin, $\\mathbb{T}_i = \\{(\\theta_{ij},\\pi_{\\mathcal{P}}(\\theta_{ij}))\\mid P_k\\sim \\mathrm{U}(\\Pi),\\forall P_k\\in \\mathcal{P}\\}$ , where $1\\leq j\\leq 50$ is the index of the model within dataset $\\mathbb{T}_i$ and $1\\le k\\le h$ is the number of hidden layers in the NN. Note that we select random permutation matrices following a uniform distribution, $\\mathrm{U}(\\Pi)$ . NNs with two, four, and eight hidden layers were used as base architecture. Additionally, we tested three types of initializations - random initialization with weights following a normal distribution $\\mathcal{N}(0,1)$ , hereafter called Rnd, and models trained in a third and first-degree polynomial approximation problem, named Pol3 and Poll1 respectively. The 9 data set configurations lie within the combination $\\{\\mathrm{Rnd},\\mathrm{Pol3},\\mathrm{Pol1}\\} \\times \\{2$ hidden, 4 hidden, 8 hidden\\}.", + "bbox": [ + 75, + 477, + 468, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Sinkhorn re-basin model was updated using the Adam optimizer with an initial learning rate of 0.1, and for a maximum of 5 iterations, using early stopping in case of convergence. Tab. 1 summarizes the L1 norm between weights after re-basin, $|\\pi_{\\hat{P}}(\\theta) - \\pi_{\\mathcal{P}}(\\theta)|$ , where $\\hat{\\mathcal{P}}$ and $\\mathcal{P}$ are the estimated and optimal transportation plan, respectively. As expected, our proposal always finds the optimal permutation thanks to its ability to simultaneously look at all permutation matrices. In contrast, the WM results fall short for some scenarios. It is worth mentioning that these results match the ones obtained by Ainsworth et al. in [2]. In general, the WM algorithm seems to be affected by random initialization, while increasing the network's capacity", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "improves its ability to reach the global minimum. We hypothesize that this is an effect of using a greedy algorithm that optimizes the objective for different layers at each iteration. A deeper inspection of the estimated permutation matrices shows that WM reaches local minima close to the expected re-basin, with only a few misplaced permutations (see Fig. 3). A more challenging alignment scenario and convergence analysis are shown in supplementary material.", + "bbox": [ + 496, + 325, + 893, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Linear mode connectivity", + "text_level": 1, + "bbox": [ + 500, + 460, + 732, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We measure the ability of our method to find linear connectivity between SGD modes after re-basin one of them. For this experiment, four datasets are employed - first and third-degree polynomial regression tasks [27], along with the classical classification benchmarks, Mnist and Cifar10. Our experiment follows a similar setup to the one described by [2], i.e., two networks were trained over the same dataset, and we performed the re-basin of one of them, hoping to reach the same basin as the unchanged model. The experiment was repeated 50 times for every dataset, and each method saw the same two networks. To measure the ability of the different approaches to find LMC, we use the Barrier [12] (Eq. (3)) and Area Under the Curve (AUC) over", + "bbox": [ + 496, + 486, + 890, + 684 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3c9d3d4735bd7c59636f06d25824da59f73c826744cd71ad6a34b52d4463d0bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInit2 hidden ↓4 hidden ↓8 hidden ↓
WM [2]Rnd6.05±9.174.12±6.580.50±1.55
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol30.57±2.840.07±0.460.01±0.10
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol10.27±0.940.00±0.000.00±0.00
CL2(Ours)0.00±0.000.00±0.000.00±0.00
", + "bbox": [ + 504, + 708, + 888, + 844 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. L1 distance between the estimated and expected re-basin with different network initializations and depths. Distances are scaled $\\times 10^{3}$ .", + "bbox": [ + 496, + 854, + 893, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20242", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e719ab64003c4d3aaff3b69a326cd9b7d1e5644bebbfb6e25934427c272765ec.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFirst degree polynomialThird degree polynomialMnistCifar10
AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓
Naive0.31±0.380.62±0.710.25±0.150.58±0.330.34±0.081.07±0.210.73±0.121.23±0.18
WM [2]0.16±0.150.32±0.280.19±0.260.41±0.570.01±0.000.03±0.010.13±0.020.27±0.04
\\( \\mathcal{C}_{L2} \\) (Ours)0.05±0.060.10±0.120.05±0.060.12±0.120.01±0.000.02±0.000.09±0.020.19±0.03
STE [2]0.11±0.100.23±0.220.09±0.070.24±0.230.01±0.000.01±0.010.08±0.010.15±0.02
\\( \\mathcal{C}_{Mid} \\) (Ours)0.03±0.020.07±0.050.05±0.040.17±0.170.00±0.000.00±0.000.02±0.010.05±0.01
\\( \\mathcal{C}_{Rnd} \\) (Ours)0.01±0.010.03±0.020.01±0.010.03±0.030.00±0.000.01±0.000.02±0.010.06±0.01
", + "bbox": [ + 81, + 88, + 890, + 233 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. AUC and loss Barrier results of linear mode connectivity for regression datasets (first and third-degree polynomial approximation), and classification datasets (Mnist and Cifar10). The WM method and our Sinkhorn with $\\mathcal{C}_{L2}$ belong to the data-free category, while STE, Sinkhorn with $\\mathcal{C}_{Mid}$ and $\\mathcal{C}_{Rnd}$ are data-driven.", + "bbox": [ + 75, + 242, + 892, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e959dd6bb08ef08e3280277a5220928a90ec41c69ec8d8848fc78619abab60e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 297, + 349, + 439 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a4a8cf1cabd388ff10db4b5f5a2ef931fe7582838312cb8fb3f5c3dc193a67e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 297, + 602, + 439 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7104a10cd6d1a97054df46052afc0321e30c9c50a687471dea04d2d838399b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 297, + 854, + 439 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d91f4bbeee736758429907b85e1d48aeaffe96102a063af82201fa7424185b60.jpg", + "image_caption": [ + "Figure 4. Example of linear mode connectivity achieved by WM [2], STE [2], and our Sinkhorn re-basin with $\\mathcal{C}_{L2}$ , $\\mathcal{C}_{Mid}$ , and $\\mathcal{C}_{Rnd}$ costs for a NN with two hidden layers. Accuracy and loss are shown for the Mnist and Cifar10 classification, while only the L2 loss is shown for the regression tasks. For Mnist, we include an amplified version of the loss and accuracy for better comparison." + ], + "image_footnote": [], + "bbox": [ + 116, + 443, + 352, + 595 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89113635364e208bcf8b94847dc56932f927173a30f4ba70c9aa92805c8e958b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 443, + 601, + 595 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/87db02a7507515e33d172ea1c332b5ced77549d1e456d56f33b519ae42537cde.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 443, + 851, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the estimated cost curve within the linear path. Both measures achieve the best performance when a method provides a low value, with a lower bound of 0.", + "bbox": [ + 75, + 675, + 468, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our approach with different objectives – L2 (Eq. (7)), Middle point (Eq. (8)), and Random point (Eq. (9)) with the recently introduced WM and Straight-Through Estimator (STE) [2]. Tab. 2 summarizes the performance of the methods for each dataset. All experiments used a NN with two hidden layers. The table shows that our methods outperform state-of-art methods with (the first three rows) and without considering the data (last three rows) during the re-basin. Specifically, our $\\mathcal{C}_{L2}$ method exceeded WM for both AUC and Barrier measures for all datasets, except Mnist, where no significant differences", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "were observed. Our other proposals outperform the state-of-art STE approach for AUC and Barrier in the data-driven category. In particular, our $\\mathcal{C}_{Rnd}$ loss showed the best results, comparable to our $\\mathcal{C}_{Mid}$ for more challenging scenarios like Cifar10. Note that STE and our $\\mathcal{C}_{Mid}$ have the same objective, and their difference in performance lies in the solver. Additionally, our $\\mathcal{C}_{L2},\\mathcal{C}_{Mid}$ , and $\\mathcal{C}_{Rnd}$ share the same architecture but with various loss functions, and their discrepancy in performance lies in the objective. As a general point, all methods significantly improve the naive path.", + "bbox": [ + 496, + 675, + 890, + 828 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the obtained loss and accuracy curves over the linear path before doing a re-basin (naive) and after applying WM, STE, and Sinkhorn with $\\mathcal{C}_{L2}$ , $\\mathcal{C}_{Mid}$ , and $\\mathcal{C}_{Rnd}$ methods in Fig. 4. Please note that our method can also", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20243", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b0ff6cc63eeb0b4956233a50696bc64fadea76b5fcdeae8d674841c2daeacb42.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRotated MnistSplit Cifar100
Accuracy ↑Forgetting ↓Accuracy ↑Forgetting ↓
Finetune46.28±1.010.52±0.0135.41±0.950.49±0.01
EWC [14]59.92±1.710.34±0.0250.50±1.330.24±0.02
LwF [17]61.86±3.660.29±0.0641.43±4.060.51±0.01
A-GEM [7]68.47±0.900.28±0.0144.42±1.460.36±0.01
Rebasin /w replay (Ours)78.14±0.500.12±0.0151.34±0.740.07±0.02
Joint training90.84±4.300.0060.48±0.540.00
", + "bbox": [ + 197, + 88, + 771, + 232 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Performance of our proposed and state-of-art methods on the continual learning benchmark datasets over 20 episodes.", + "bbox": [ + 109, + 242, + 857, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "perform re-basin of convolutional architectures with residual connections, as shown in supplementary materials.", + "bbox": [ + 75, + 284, + 468, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Incremental learning application", + "text_level": 1, + "bbox": [ + 76, + 327, + 366, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This experiment seeks to compare our method with other well-known continual learning approaches from the literature. Since our proposal can fit the regularization techniques that use replay, we compare it with different algorithms within this category. In particular, we compared 3 regularization-based approaches - elastic weight consolidation (EWC) [14], learning without forgetting (LwF) [17], and average gradient episodic memory (A-GEM) [7]. The average accuracy was calculated to measure the overall performance of model $\\theta_{i}$ in the first episodes $\\mathbb{T}_j$ . In addition, the forgetting measure averages the forgetting in terms of accuracy for each domain or task in the episode.", + "bbox": [ + 75, + 352, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Given the variety of libraries and implementations, we limited our comparison to reproducible methods that could be used in the Avalanche environment [18]. All measurements, benchmarks, networks, and algorithms, including our own, were implemented using the framework. While we attempted to incorporate other recent approaches like MC-SGD [22] and Stable SGD [23] into Avalanche, a high discrepancy was observed w.r.t. their reported results and, therefore, we did not include them into our study. Difficulties in adapting MC-SGD to new conditions have also been observed by other authors [20].", + "bbox": [ + 75, + 535, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We focused our experiments on low episodic memory scenarios, using only five examples per class for both benchmarks in methods that rely on memory replay (A-GEM and our method). We used a NN with one hidden layer and 256 neurons for the Rotated Mnist benchmark. For the Split Cifar100 benchmark, a multi-head ResNet18 was used following the settings in [22, 23]. In this experiment, we only apply the re-basin to linear layers.", + "bbox": [ + 75, + 702, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 shows methods' accuracy and forgetting performance on the benchmarks Rotated Mnist and Split Cifar100 datasets using 20 episodes. Our method outperforms the others and still performs better or comparable to those reported in [23]. The reader should pay special attention", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to the low values of forgetting achieved using our re-basin approach. This is a consequence of setting the value of $\\alpha = 0.8$ when fusing the models (Eq. (12)). A-GEM is ranked second in accuracy and forgetting for Rotated Mnist. LwF showed a similar forgetting to A-GEM in this benchmark. On Split Cifar100, EWC ranked second for both measures. Despite having similar accuracy to our approach, the high forgetting value suggests stability issues. In general, the method showed to be robust to the values $\\alpha$ and $\\beta$ . We included the corresponding ablation in supplementary materials.", + "bbox": [ + 496, + 282, + 893, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 463, + 619, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work proposes a new method based on the Sinkhorn operator to estimate permutation matrices that make two neural network models equivalent. With respect to previous work, such as weight matching, our method is (i) more flexible because it is differentiable and can be applied with any loss, (ii) estimates the permutations for all layers at the same time, avoiding getting stuck in local minima, (iii) more accurate, as shown in our experimental evaluation on well-known benchmarks. First, our experiments yielded perfect results when our approach was evaluated to produce the optimal permutation between a model and its artificially permuted transformation. We have also used our approach for linear mode connectivity, showing better connectivity (lower loss barrier) than weight matching. Finally, we showed that our efficient and differentiable approach for re-basin can easily be applied to the challenging task of continual learning, producing results comparable to, or better than state-of-art approaches. As a limitation to our work, we observed from our experiments and analysis of the literature that linear assignment problems solved with greedy Hungarian-based approaches are generally more efficient in terms of memory than the Sinkhorn operator.", + "bbox": [ + 496, + 488, + 893, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by Distech Controls Inc., the Natural Sciences and Engineering Research Council of Canada, and the Digital Research Alliance of Canada.", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20244", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ryan Prescott Adams and Richard S Zemel. 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Catastrophic interference in connectionist networks: The sequential learning problem. In *Psychology of learning and motivation*, volume 24, pages 109–165. Elsevier, 1989. 3", + "[20] Sanket Vaibhav Mehta, Darshan Patil, Sarath Chandar, and Emma Strubell. An empirical investigation of the role of pre-training in lifelong learning. arXiv preprint arXiv:2112.09153, 2021. 3, 8", + "[21] Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with Gumbel-Sinkhorn Networks. In International Conference on Learning Representations, 2018. 2, 4, 5", + "[22] Seyed Iman Mirzadeh, Mehrdad Farajtabar, Dilan Gorur, Razvan Pascanu, and Hassan Ghasemzadeh. Linear Mode Connectivity in Multitask and Continual Learning. In International Conference on Learning Representations, 2021. 2, 3, 5, 8", + "[23] Seyed Iman Mirzadeh, Mehrdad Farajtabar, Razvan Pascanu, and Hassan Ghasemzadeh. Understanding the role of training regimes in continual learning. 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In International Conference on Learning Representations, 2020. 1, 2, 5, 6", + "[28] Hongyi Wang, Mikhail Yurochkin, Yuekai Sun, Dimitris Papailiopoulos, and Yasaman Khazaeni. Federated learning with matched averaging. arXiv preprint arXiv:2002.06440, 2020. 2" + ], + "bbox": [ + 78, + 90, + 468, + 244 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20246", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_model.json b/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c47bb1aafb798ab9cd6065de5b2b8f72edd4c217 --- /dev/null +++ b/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_model.json @@ -0,0 +1,1881 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.255, + 0.131, + 0.717, + 0.154 + ], + "angle": 0, + "content": "Re-basin via implicit Sinkhorn differentiation" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.182, + 0.39, + 0.198 + ], + "angle": 0, + "content": "Fidel A. Guerrero Peña" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.203, + 0.469, + 0.216 + ], + "angle": 0, + "content": "fidel-alejandro.guerrero-pena@etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.242, + 0.225, + 0.367, + 0.24 + ], + "angle": 0, + "content": "Thomas Dubail" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.246, + 0.433, + 0.258 + ], + "angle": 0, + "content": "thomas.dubail.1@ens.etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.268, + 0.396, + 0.285 + ], + "angle": 0, + "content": "Eric Granger" + }, + { + "type": "text", + "bbox": [ + 0.244, + 0.289, + 0.441, + 0.301 + ], + "angle": 0, + "content": "eric.granger@etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.582, + 0.182, + 0.776, + 0.199 + ], + "angle": 0, + "content": "Heitor Rapela Medeiros" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.203, + 0.847, + 0.216 + ], + "angle": 0, + "content": "heitor.rapela-medeiros.1@ens.etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.225, + 0.728, + 0.24 + ], + "angle": 0, + "content": "Masih Aminbeidokhti" + }, + { + "type": "text", + "bbox": [ + 0.483, + 0.246, + 0.795, + 0.258 + ], + "angle": 0, + "content": "masih.aminbeidokhti.1@ens.etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.548, + 0.268, + 0.681, + 0.283 + ], + "angle": 0, + "content": "Marco Pedersoli" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.289, + 0.726, + 0.301 + ], + "angle": 0, + "content": "marco.pedersoli@etsmtl.ca" + }, + { + "type": "text", + "bbox": [ + 0.333, + 0.31, + 0.637, + 0.345 + ], + "angle": 0, + "content": "LIVIA, Dept. of Systems Engineering ETS Montreal, Canada" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.38, + 0.313, + 0.396 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.473, + 0.775 + ], + "angle": 0, + "content": "The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces and some promising properties like mode connectivity. However, finding the permutation that minimizes some objectives is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to suboptimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature under several conditions for both optimal transport and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with the state-of-art. The source code is provided at https://github.com/fagp/sinkhorn-rebasin." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.801, + 0.21, + 0.816 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Despite the success of deep learning (DL) across many application domains, the loss surfaces of neural networks (NNs) are not well understood. Even for shallow NNs, the number of saddle points and local optima can increase exponentially with the number of parameters [4, 13]. The permu" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.412, + 0.831, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.577, + 0.706, + 0.587 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.587, + 0.804, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.748, + 0.682, + 0.759 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.772, + 0.895, + 0.898 + ], + "angle": 0, + "content": "Figure 1. (a) Loss landscape for the polynomial approximation task [27]. \\(\\theta_{A}\\) and \\(\\theta_{B}\\) are models found by SGD. LMC suggests that re-basin the model \\(\\theta_{B}\\) would result in a functionally equivalent model \\(\\pi_{\\mathcal{P}}(\\theta_B)\\), with no barrier on its linear interpolation \\((1 - \\lambda)\\theta_{A} + \\lambda \\pi_{\\mathcal{P}}(\\theta_{B})\\). (b) Comparison of the cost in the linear path along \\(\\lambda\\) before and after re-basin using weight matching (WM) [2] and our Sinkhorn. The dashed line in the figures corresponds with the naive path, and the solid line is the path after the proposed Sinkhorn re-basin. The blue line represents WM path." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20237" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "tation symmetry of neurons in each layer allows the same function to be represented with many different parameter values of the same network. Symmetries imposed by these invariances help us to better understand the structure of the loss landscape [6, 11, 13]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.473, + 0.744 + ], + "angle": 0, + "content": "Previous studies establish that minima found by Stochastic Gradient Descent (SGD) are not only connected in the network parameter's space by a path of non-increasing loss, but also permutation symmetries may allow us to connect those points linearly with no detriment to the loss [9, 11-13, 15, 24]. This phenomenon is often referred to as linear mode connectivity (LMC) [24]. For instance, Fig. 1a shows a portion of the loss landscape for the polynomial approximation task [27] using the method proposed by Li et al. [16]. \\(\\theta_{A}\\) and \\(\\theta_{B}\\) are two minima found by SGD in different basins with an energy barrier between the pair. LMC suggests that if one considers permutation invariance, we can teleport solutions into a single basin where there is almost no loss barrier between different solutions [2, 11]. In literature, this mechanism is called re-basin [2]. However, efficiently searching for permutation symmetries that bring all solutions to one basin is a challenging problem [11]. Three main approaches for matching units between two NNs have been explored in the literature [2]. Some studies propose a data-dependent algorithm that associates units across two NNs by matching their activations [2, 26]. Since activation-based matching is data dependent, it helps to adjust permutations to certain desired kinds of classes or domains [26]. Instead of associating units by their activations, one could align the weights of the model itself [2, 26], which is independent of the dataset, and therefore the computational cost is much lower. Finally, the third approach is to iteratively adjust the permutation of weights. In particular, Ainsworth et al. [2] have proposed alternating between models alignment and barrier minimization using a Straight-Through Estimator. Unfortunately, the proposed approaches so far are either non-differentiable [2, 11, 26] or computationally expensive [2], making the solution difficult to be extended to other applications, with a different objective. For instance, adapting those methods for incremental learning by including the algorithm for weight matching between two models trained on different domains is not trivial because of the difficulties in optimizing new objectives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In this work, inspired by [21], we relax the permutation matrix with the Sinkhorn operator [1], and use it to solve the re-basin problem in a differentiable fashion. To avoid the high cost for computing gradients in the proposal of Mena et al. [21], we use the implicit differentiation algorithm proposed in [10], which has been shown to be more cost-effective. Our re-basin formulation allows defining any differentiable objective as a loss function." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "A direct application of re-basin is the merger of diverse models without significantly degrading their performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "[2, 5, 12, 13, 28]. Applications like federate learning [2], ensembling [12], or model initialization [5] exploit such a merger by selecting a model in the line connecting the models to be combined. To show the effectiveness of our approach, we propose a new continual learning algorithm that combines models trained on different domains. Our continual learning algorithm differs from previous state-of-art approaches [22] because it directly estimates a model at the intersection of previous and new knowledge, by exploiting the LMC property observed in SGD-based solutions." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.243, + 0.874, + 0.257 + ], + "angle": 0, + "content": "Our main contribution can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.303 + ], + "angle": 0, + "content": "(1) Solving the re-basin for optimal transportation using implicit Sinkhorn differentiation, enabling better differentiable solutions that can be integrated on any loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.348 + ], + "angle": 0, + "content": "(2) A powerful way to use our re-basin method based on the Sinkhorn operator for incremental learning by considering it as a model merging problem and leveraging LMC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.455 + ], + "angle": 0, + "content": "(3) An extensive set of experiments that validate our method for: (i) finding the optimal permutation to transform a model to another one equivalent; (ii) linear mode connectivity, to linearly connect two models such that their loss is almost identical along the entire connecting line in the weights space; and (iii) learning new domains and tasks incrementally while not forgetting the previous ones." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.638, + 0.484 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Re-basin. Recently, in the NN community, re-basin has been demonstrating useful properties. The main goal of such re-basin approaches is to obtain functionally equivalent models in a different region of the weight space following some pre-defined objective. Permutation symmetries are a well-known example of transformations that allows performing re-basin. In particular, Entezari et al. [11] show that the invariances of NNs using random permutations on SGD solutions are likely to have almost zero barriers, and therefore the randomness in terms of permutations does not impact the quality of the final training result of the model. A simulated annealing-based algorithm was proposed for doing a re-basin with an elevated computational cost, making it impractical to use, especially for bigger models. Ainsworth et al. [2] proposed three new re-basin algorithms that rely on solving linear assignment problems to find permutation matrices that satisfy their encoded objective. The methods showed to perform well, especially in achieving linear mode connectivity. On the downside, new objectives are difficult to plug into their framework. Their solution uses greedy algorithms that do not guarantee finding the optimal solution, as shown in our experiments. Using a similar approach, Benzing et al. [5] found strong evidence that two random initialization of a NN after permutation can lead to a good performance, showing that the random initialization is already in the same loss valley during the initialization. Finally, [3] uses the concepts of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20238" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "Wasserstein barycenter and Gromov-Wasserstein barycenter, offering a NN model fusion framework with insights about linear mode connectivity of SGD solutions. Even though the previous works presented solutions to perform re-basin by solving linear assignment problems, their approach fails to generalize well for other objectives. Using gradient descent-based algorithms seems to be a more suitable approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.473, + 0.399 + ], + "angle": 0, + "content": "Mode connectivity. Mode connectivity is the task of finding low-barrier paths connecting models within the weight space. In their work, Garipov et al. [13] found that the local optima of deep learning models are connected by simple curves. The fast geometric ensembling method was proposed as an application for their proposal. Almost at the same time, [9] proposed a nudged elastic band-based method to construct continuous paths between minima of NN architectures. Finally, Frankle et al. [12] studied the sensitivity of different levels of SGD noise on NNs. These pioneering works are the basis for applications of mode connectivity, like [2, 22] and ours." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Incremental learning. Continual or incremental learning (IL) allows adapting models incrementally based on new training data without forgetting previous knowledge. Catastrophic forgetting [19,25] occurs when a previously trained model that is fine-tuned on a new task loses information learned to perform well on previous datasets. To address this issue, Kirkpatrick et al. [14] proposes elastic weight consolidation (EWC), which reduces catastrophic forgetting by regularizing NN parameters with respect to the importance of the weights concerning the previous and actual tasks. Chaudhry et al. [8] proposed using a small number of samples for replay. Their experience replay (ER) helps to perform IL such that the performance on classification tasks is improved, even with a tiny episodic memory. Closer to our work, [22] proposes an LMC-based method with replay. Its solution is called mode connectivity SGD (MC-SGD), which relies on the assumption that there is always an existing solution that solves all seen tasks incrementally, and they are connected by a low-barrier and linear path. Furthermore, MC-SGD utilizes a replay buffer to remember previous tasks for IL. Its efficiency relies on exploring the linear path of low loss to constrain learning, thereby outperforming competitors like EWC when less data is available. However, such an approach has a high computational cost since it requires training independent models for the new task and merging them as a separate step with the model for previous knowledge. Also, the method has been shown to be difficult to reproduce or adapt to new benchmarks [20]. A compelling scenario for continual learning is using a linear mode connectivity path to keep learning and adapt the model without forgetting the previous knowledge. The trade-off between flatness of the LMC path and direction to adapt the loss can be tuned in a way that brings more" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.887, + 0.108 + ], + "angle": 0, + "content": "stability or plasticity depending on the target final solution." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.12, + 0.822, + 0.138 + ], + "angle": 0, + "content": "3. Re-basin via the Sinkhorn operator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.146, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Let \\( f_{\\theta}(.) \\) be a parameterized mapping where \\( \\theta \\) represents a vector of parameters within the solution space \\( \\Theta \\subset \\mathbb{R}^d \\), where \\( d \\) is the number of parameters in \\( \\theta \\). In the deep learning context, \\( f \\) can be seen as a NN architecture, and \\( f_{\\theta} \\) is a model with weights \\( \\theta \\). Here, we refer to \\( \\theta \\) as a model for simplicity. Consequently, the cost (or error) of a model for a given task can be defined as \\( \\mathcal{C}(\\theta) = \\frac{1}{|\\mathbb{T}|}\\sum_{(x,y)\\in \\mathbb{T}}\\mathcal{L}(f_{\\theta}(x),y) \\), where \\( (x,y)\\in \\mathbb{T} \\) are input and expect output in the training set \\( \\mathbb{T} \\), and \\( \\mathcal{L} \\) is an appropriate supervised loss function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.893, + 0.495 + ], + "angle": 0, + "content": "A function \\( f \\) is invariant to a transformation if and only if the obtained transformed function is functionally equivalent to the original mapping. Note that such invariances can also be found between two functions within the family of parametric functions \\( \\{f_{\\theta}\\}_{\\theta \\in \\Theta} \\). The permutation of neurons is a well-known example of such transformations applied to NNs that allow obtaining functionally equivalent models, i.e., \\( f_{\\theta_A}(x) = f_{\\theta_B}(x), \\forall x \\). These invariant models are obtained via the permutation transformation or re-basin function, here defined as \\( \\pi \\colon \\Theta \\to \\Theta \\), which shifts a model to a symmetric region of the loss landscape, \\( \\mathcal{C}(\\theta) = \\mathcal{C}(\\pi_{\\mathcal{P}}(\\theta)) \\). In this work \\( \\mathcal{P} = (P_1, \\dots, P_h) \\) is a transportation plan with \\( P_i \\) contained in the transportation polytope," + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.505, + 0.892, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\Pi = \\left\\{P \\in \\mathbb {R} _ {+} ^ {m \\times n} | P \\mathbf {1} _ {m} = \\mathbf {1} _ {n}, P ^ {T} \\mathbf {1} _ {n} = \\mathbf {1} _ {m} \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.641 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}_d = (1,\\dots,1)^d\\). Without loss of generality, let \\(f_{\\theta}(x) = (\\ell_h\\circ \\ldots \\circ \\ell_1)(x)\\) be a NN defined as the composition of \\(h\\) layers such that \\(\\ell_i(z) = \\sigma (W_iz + b_i)\\). Here, the weights \\(W_{i}\\) and biases \\(b_{i}\\) are the parameters of the network, \\(\\theta = \\{W_i,b_i\\}_{i = 1}^h\\), and \\(\\sigma\\) is a non-linear activation function. Then, the re-based model \\(\\pi_{\\mathcal{P}}(\\theta)\\) can be written as the functionally equivalent mapping:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.651, + 0.891, + 0.669 + ], + "angle": 0, + "content": "\\[\n\\ell_ {i} ^ {\\prime} (z) = \\sigma \\left(P _ {i} W _ {i} P _ {i - 1} ^ {T} z + P _ {i} b _ {i}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.68, + 0.892, + 0.71 + ], + "angle": 0, + "content": "where \\(P_{i}\\in \\Pi\\) is a valid permutation matrix, and \\(P_{h} = P_{0}^{T} = I\\) is the identity matrix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.71, + 0.892, + 0.772 + ], + "angle": 0, + "content": "With regards to permutation invariance, Entezari et al. [11] conjectured that re-based SGD solutions are likely to have a low barrier within their linear interpolation \\( B(\\theta_A, \\theta_B) \\approx 0 \\), where \\( B(.) \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.782, + 0.842, + 0.808 + ], + "angle": 0, + "content": "\\[\nB \\left(\\theta_ {A}, \\theta_ {B}\\right) = \\sup _ {\\lambda} \\left[ \\left. \\mathcal {C} ((1 - \\lambda) \\theta_ {A} + \\lambda \\theta_ {B}) \\right] - \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.817, + 0.892, + 0.835 + ], + "angle": 0, + "content": "\\[\n[ (1 - \\lambda) \\mathcal {C} (\\theta_ {A}) + \\lambda \\mathcal {C} (\\theta_ {B}) ] ], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "and \\(\\lambda \\in (0,1)\\). This phenomenon is known as LMC [12], and it is a particular case of the widely studied mode connectivity [9, 13]. Notably, Ainsworth et al. [2] proposed three approaches that ratify the conjecture in [11] by finding" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20239" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "a re-based model \\(\\pi_{\\mathcal{P}}(\\theta_B)\\) with LMC to a target model \\(\\theta_A\\). Fig. 1 depicts the goal of such re-basin approaches. This figure shows two solutions for the task, \\(\\theta_A\\) and \\(\\theta_B\\), found through SGD. As shown in Fig. 1b, the naive path between \\(\\theta_A\\) and \\(\\theta_B\\) has higher values of the barrier within the line \\((1 - \\lambda)\\theta_A + \\lambda \\theta_B, \\lambda \\in (0,1)\\). On the other hand, and consistently with the results in [2,11], our re-based model \\(\\pi_{\\mathcal{P}}(\\theta_B)\\) achieves LMC by successfully finding a transportation plan \\(\\mathcal{P}\\) that shifts model \\(\\theta_B\\) to the same basin of model \\(\\theta_A\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.363 + ], + "angle": 0, + "content": "Although the seminal work by Ainsworth et al. [2] proposed a highly efficient approach for finding a permutation that minimizes the distances between models, their nondifferentiable approach provides solutions that are difficult to be extended to other applications with a different objective. Specifically, their algorithms use a formulation based on the linear assignment problem (LAP) to find suitable permutations, meaning any new objective needs to be cast as a LAP which is a hard task in itself." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.469 + ], + "angle": 0, + "content": "This work proposes a differentiable approach to perform a re-basin that defines any differentiable objective as a loss function. Here, we relax the rigid constraint of having a binary permutation matrix \\( P \\), and consequently add an entropy regularizer \\( h(P) = -\\sum P(\\log P) \\) to the original LAP as proposed by [21]. The final equation is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.473, + 0.469, + 0.498 + ], + "angle": 0, + "content": "\\[\nS _ {\\tau} (X) = \\underset {P \\in \\Pi} {\\arg \\max } \\langle P, X \\rangle_ {F} + \\tau h (P), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.469, + 0.537 + ], + "angle": 0, + "content": "where is \\(\\tau\\) a factor that weights the strengths of the entropy regularization term." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.469, + 0.569 + ], + "angle": 0, + "content": "The formulation in Eq. (4) is known as the Sinkhorn operator and can be efficiently approximated by:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.581, + 0.352, + 0.615 + ], + "angle": 0, + "content": "\\[\nS _ {\\tau} ^ {(0)} (X) = \\exp \\left(\\frac {X}{\\tau}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.63, + 0.469, + 0.65 + ], + "angle": 0, + "content": "\\[\nS _ {\\tau} ^ {(t + 1)} (X) = \\mathcal {T} _ {c} \\left(\\mathcal {T} _ {r} \\left(S _ {\\tau} ^ {(t)} (X)\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.764 + ], + "angle": 0, + "content": "where \\(X \\in \\mathbb{R}^{m \\times n}\\) is a soft version of the permutation matrix, \\(\\mathcal{T}_c(X) = X \\oslash (\\mathbb{1}_m\\mathbb{1}_m^T X)\\) and \\(\\mathcal{T}_r(X) = X \\oslash (X\\mathbb{1}_n\\mathbb{1}_n^T)\\) are respectively the re-normalization of columns and rows of \\(X\\), and \\(\\oslash\\) is the element-wise division. In their work, Mena et al. [21] proved that Eq. (5) converges to Eq. (4) when \\(t \\to \\infty\\). However, in practice, only a finite number of iterations are needed to produce a suitable approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Although the Sinkhorn operator is reasonably easy to implement within the NN layers, a significant drawback arises when considering the efficiency of its differentiation. We use the implicit differentiation algorithm proposed by Eisenberger et al. [10] to mitigate such an increase in the computational cost. Their method significantly increases the efficiency and also stability of the training process. The marginals of the generic formulation in [10] are defined as \\( \\pmb{a} = \\mathbb{1}_m / m \\) and \\( \\pmb{b} = \\mathbb{1}_n / n \\) to match the re-basin task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "Finally, our proposed Sinkhorn re-basin re-writes the original re-basin mapping in Eq. (2) as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.13, + 0.892, + 0.149 + ], + "angle": 0, + "content": "\\[\n\\ell_ {i} ^ {\\prime} (z) = \\sigma (S _ {\\tau} (P _ {i}) W _ {i} S _ {\\tau} (P _ {i - 1} ^ {T}) z + S _ {\\tau} (P _ {i}) b _ {i}). \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.157, + 0.878, + 0.171 + ], + "angle": 0, + "content": "where \\(P_{i}\\in \\mathbb{R}^{m\\times n}\\) is a differentiable permutation matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.172, + 0.892, + 0.308 + ], + "angle": 0, + "content": "To show the ability of our proposed Sinkhorn re-basin to minimize any differentiable objective, we provide three examples of cost functions that are minimized without changing the formulation in Eq. (6). These cost functions are used in the SGD framework to compute the gradient of the weights in our Sinkhorn re-basin network, and finally update the permutation matrices to minimize the objective. First, for a data-free objective like Weights Matching [2], we directly minimize the squared L2 distance defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.316, + 0.892, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {L 2} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\left\\| \\theta_ {A} - \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right) \\right\\| ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.417 + ], + "angle": 0, + "content": "Given the ability of our method to use differentiable objectives, we introduce two other data-driven cost functions. Inspired by the Straight-Through Estimator in [2], we propose a differentiable midpoint cost function to minimize the barrier," + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.425, + 0.892, + 0.459 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {M i d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left(\\frac {\\theta_ {A} + \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right)}{2}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Since minimizing the midpoint can lead to a multimodal cost path, i.e., lower cost value for \\(\\lambda = 0.5\\), and higher cost values elsewhere, we propose a cost function that minimizes the cost at random points within the line:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.536, + 0.892, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {R n d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left((1 - \\lambda) \\theta_ {A} + \\lambda \\pi_ {\\mathcal {P}} (\\theta_ {B})\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.561, + 0.875, + 0.577 + ], + "angle": 0, + "content": "with \\(\\lambda\\) uniformly sampled at each iteration, \\(\\lambda \\sim U(0,1)\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.779, + 0.607 + ], + "angle": 0, + "content": "4. Re-basin incremental learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.795 + ], + "angle": 0, + "content": "A critical application of re-basin approaches is the ability to merge models without a significant performance reduction. Such merging is usually done by selecting a model in their connecting line. Applications like federate learning [2], ensembling [12], or model initialization [5] have been explored recently for merging models trained on the same task. Here we consider merging based on re-basin by proposing a new incremental learning approach that combines models trained on different domains or classes. Our proposed approach relies on a stability-plasticity hyperparameter \\(\\alpha\\), allowing the user to choose the balance between forgetting and incorporating new knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Let \\(\\theta_0\\) be an initial model trained over dataset \\(\\mathbb{T}_0\\), and \\(\\mathcal{T} = \\{\\mathbb{T}_1, \\mathbb{T}_2, \\ldots\\}\\) be a stream of data, where \\(\\mathbb{T}_i = \\{(x_{ij}, y_{ij}) | x_{ij} \\in \\mathbb{X}_i, y_{ij} \\in \\mathbb{Y}_i\\}, 1 \\leq i \\leq N_i\\), is a supervised dataset with input \\(\\mathbb{X}_i\\), output \\(\\mathbb{Y}_i\\), and \\(N_i\\) data points. Note that the sets \\(\\mathbb{T}_i\\) are also known in incremental learning literature as tasks, but these are not limited to task incremental learning scenarios, and also include domain and" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20240" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.088, + 0.37, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.473, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Graphical representation of the intersection of low curvature regions of the loss landscape for task \\(\\mathbb{T}_i\\) (red) and \\(\\mathbb{T}_{i + 1}\\) (blue). The goal of our method is to find a re-basin \\(\\pi_{\\mathcal{P}_i}(\\theta_i)\\) that transverses the multitask region using LMC. The final model \\(\\theta_{i + 1}\\) (Eq. (12)) is found in the surroundings of the line by adding a learnable residual \\(\\delta_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.566 + ], + "angle": 0, + "content": "class incremental learning. Incremental or continual learning seeks to incorporate the new knowledge \\(\\mathbb{T}_{i + 1}\\) into the model \\(\\theta_{i}\\) without forgetting how to perform correctly in previous datasets \\(\\mathbb{T}_0,\\dots,\\mathbb{T}_i\\). To this end, the continual learning community has proposed approaches that exploit the fact that multitask low curvature regions usually appear at the intersection of low curvature regions for individual tasks [14, 22] (see Fig. 2 for a visual reference). In particular, the Mirzadeh et al. [22] approach uses a two steps training, where the model \\(\\theta_{i + 1}\\) is first trained over dataset \\(\\mathbb{T}_{i + 1}\\), and then a mode connectivity-based merging finds the model with low loss value on both new and previous knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In contrast with [22], our approach directly estimates a model at the intersection of previous and new knowledge by exploiting our differentiable method to obtain the LMC observed in SGD-based solutions. Similarly to approaches introduced in the last section, our method looks for a rebasin of the given model that minimizes a given objective. For continual learning purposes, a new cost function is introduced such that, like in Eq. (8), the cost of the model in the middle of the line \\((1 - \\lambda)\\theta_{i} + \\lambda \\pi_{\\mathcal{P}_{i}}(\\theta_{i}), \\lambda \\in (0,1)\\), is minimized for dataset \\(\\mathbb{T}_{i+1}\\) (see Fig. 2). In such a continual learning scenario, the middle point is the furthest model in the line from high stability points \\(\\theta_{i}\\) and \\(\\pi_{\\mathcal{P}_{i}}(\\theta_{i})\\), noting that the endpoints are solutions for previous tasks, but not for the new one. The smooth nature of the loss landscape implies that neighboring models have similar costs for all tasks, thus it is important to select the farthest model from the extremes. However, constraining the solution space to models within the line yields a solution that performs well on the previous task, but does not allow optimal performance on the new task, thus affecting the training plasticity. Similarly to Kirkpatrick et al. [14], we find well-behaved models for \\(\\mathbb{T}_{i+1}\\) in the neighborhood of our optimization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "target. This is done by adding a regularization term that minimizes the \\(l_{2}\\) norm of the residual vector \\(\\delta_{i}\\). Finally, the proposed cost is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.146, + 0.892, + 0.181 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right) = \\mathcal {C} \\left(\\frac {\\theta_ {i} + \\pi \\mathcal {P} _ {i} \\left(\\theta_ {i}\\right)}{2} + \\delta_ {i}\\right) + \\beta \\| \\delta_ {i} \\| ^ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.188, + 0.892, + 0.218 + ], + "angle": 0, + "content": "During the learning phase, the underlying optimization problem finds:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.229, + 0.892, + 0.255 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i} ^ {*}, \\mathcal {P} _ {i} ^ {*} = \\underset {\\delta_ {i}, \\mathcal {P} _ {i}} {\\arg \\min } \\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.325 + ], + "angle": 0, + "content": "where \\(\\delta_i^*\\) and \\(\\mathcal{P}_i^*\\) are found at the same time. Note that the cost in Eq. (10) can be computed over any knowledge dataset. This work uses a replay method by taking the average of Eq. (10) for current and previous datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.384 + ], + "angle": 0, + "content": "Combining a model with a balance between previous and new knowledge should be obtained after minimizing the cost in Eq. (10). Here, the incremented model at episode \\( i + 1 \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.396, + 0.892, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\theta_ {i + 1} = (1 - \\alpha) \\theta_ {i} + \\alpha \\pi_ {\\mathcal {P} _ {i}} (\\theta_ {i}) + \\delta_ {i}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.892, + 0.484 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyper-parameter controlling the balance between plasticity and stability. Note that values of \\(\\alpha\\) near 0.5 favor higher plasticity, while values around 0.0 and 1.0 give more importance to previous knowledge." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.496, + 0.807, + 0.514 + ], + "angle": 0, + "content": "5. Experimental results and analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.84 + ], + "angle": 0, + "content": "The experimental procedure for comparing re-basin approaches follows the same one used by Ainsworth et al. [2], while the continual learning experiments follow the standard experimental procedure in incremental learning literature [22]. For all experiments, the mean and standard deviation of results is reported and obtained over independent runs with different seeds. We used the original implementation provided by the authors in all cases. The effect of re-basin is studied for both classification and regression tasks. Mnist and Cifar10 datasets were used for image classification, while the polynomial approximation problems from [27] were used for regression. Feedforward NNs with 2 to 8 layers were explored as backbone architectures. In all our experiments, \\( t = 20 \\) and \\( \\tau = 1.0 \\) were used, as proposed in [21] for the Sinkhorn operator. Furthermore, the corresponding performance measures and hyper-parameters are summarized in each subsection. Additional details on the experimental methodology, e.g., dataset, protocol, and performance measures, as well as other experimental settings, i.e., convolutional architectures, are provided in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.767, + 0.864 + ], + "angle": 0, + "content": "5.1. Finding the optimal transport" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this experiment, we measure the ability of both Weights Matching (WM) [2] and our Sinkhorn re-basin to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20241" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.087, + 0.855, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.894, + 0.3 + ], + "angle": 0, + "content": "Figure 3. Estimated permutation matrices via weight matching (WM) [2] and the proposed Sinkhorn re-basin. \\( P_{i} \\) refers to the expected \\( 10 \\times 10 \\) permutation matrix with ones represented in black and zeros in white. The estimated permutations matrix \\( \\hat{P}_{i} \\) shows matching permutations as blue squares and miss-matchings in red and yellow. The permutation matrices \\( P_{i} \\in \\mathbb{R}^{10 \\times 10} \\) correspond with transportation plans of layer \\( i \\), with each layer containing 10 neurons. These matrices correspond with actual permutation matrices from the experiment with random initialization and 2 hidden layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.471, + 0.476 + ], + "angle": 0, + "content": "find the optimal permutation. Similar to our \\(\\mathcal{C}_{L2}\\), the WM method minimizes the distance between the re-based and target models by solving a LAP. The cost function used for our re-basin is the squared L2 distance between models (Eq. (7)). Note that the objectives are not data-driven, and therefore we only measure the ability of each algorithm to reach the global minima without any context. Each method received a model and a randomly permuted version of it to find the permutation matrices that originated the target re-basin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.704 + ], + "angle": 0, + "content": "For our purposes, 9 datasets are created, each one containing 50 models and a random re-basin, \\(\\mathbb{T}_i = \\{(\\theta_{ij},\\pi_{\\mathcal{P}}(\\theta_{ij}))\\mid P_k\\sim \\mathrm{U}(\\Pi),\\forall P_k\\in \\mathcal{P}\\}\\), where \\(1\\leq j\\leq 50\\) is the index of the model within dataset \\(\\mathbb{T}_i\\) and \\(1\\le k\\le h\\) is the number of hidden layers in the NN. Note that we select random permutation matrices following a uniform distribution, \\(\\mathrm{U}(\\Pi)\\). NNs with two, four, and eight hidden layers were used as base architecture. Additionally, we tested three types of initializations - random initialization with weights following a normal distribution \\(\\mathcal{N}(0,1)\\), hereafter called Rnd, and models trained in a third and first-degree polynomial approximation problem, named Pol3 and Poll1 respectively. The 9 data set configurations lie within the combination \\(\\{\\mathrm{Rnd},\\mathrm{Pol3},\\mathrm{Pol1}\\} \\times \\{2\\) hidden, 4 hidden, 8 hidden\\}." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The Sinkhorn re-basin model was updated using the Adam optimizer with an initial learning rate of 0.1, and for a maximum of 5 iterations, using early stopping in case of convergence. Tab. 1 summarizes the L1 norm between weights after re-basin, \\( |\\pi_{\\hat{P}}(\\theta) - \\pi_{\\mathcal{P}}(\\theta)| \\), where \\( \\hat{\\mathcal{P}} \\) and \\( \\mathcal{P} \\) are the estimated and optimal transportation plan, respectively. As expected, our proposal always finds the optimal permutation thanks to its ability to simultaneously look at all permutation matrices. In contrast, the WM results fall short for some scenarios. It is worth mentioning that these results match the ones obtained by Ainsworth et al. in [2]. In general, the WM algorithm seems to be affected by random initialization, while increasing the network's capacity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.895, + 0.449 + ], + "angle": 0, + "content": "improves its ability to reach the global minimum. We hypothesize that this is an effect of using a greedy algorithm that optimizes the objective for different layers at each iteration. A deeper inspection of the estimated permutation matrices shows that WM reaches local minima close to the expected re-basin, with only a few misplaced permutations (see Fig. 3). A more challenging alignment scenario and convergence analysis are shown in supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.733, + 0.478 + ], + "angle": 0, + "content": "5.2. Linear mode connectivity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.685 + ], + "angle": 0, + "content": "We measure the ability of our method to find linear connectivity between SGD modes after re-basin one of them. For this experiment, four datasets are employed - first and third-degree polynomial regression tasks [27], along with the classical classification benchmarks, Mnist and Cifar10. Our experiment follows a similar setup to the one described by [2], i.e., two networks were trained over the same dataset, and we performed the re-basin of one of them, hoping to reach the same basin as the unchanged model. The experiment was repeated 50 times for every dataset, and each method saw the same two networks. To measure the ability of the different approaches to find LMC, we use the Barrier [12] (Eq. (3)) and Area Under the Curve (AUC) over" + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.709, + 0.89, + 0.845 + ], + "angle": 0, + "content": "
MethodInit2 hidden ↓4 hidden ↓8 hidden ↓
WM [2]Rnd6.05±9.174.12±6.580.50±1.55
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol30.57±2.840.07±0.460.01±0.10
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol10.27±0.940.00±0.000.00±0.00
CL2(Ours)0.00±0.000.00±0.000.00±0.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.855, + 0.895, + 0.898 + ], + "angle": 0, + "content": "Table 1. L1 distance between the estimated and expected re-basin with different network initializations and depths. Distances are scaled \\(\\times 10^{3}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20242" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.234 + ], + "angle": 0, + "content": "
MethodFirst degree polynomialThird degree polynomialMnistCifar10
AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓
Naive0.31±0.380.62±0.710.25±0.150.58±0.330.34±0.081.07±0.210.73±0.121.23±0.18
WM [2]0.16±0.150.32±0.280.19±0.260.41±0.570.01±0.000.03±0.010.13±0.020.27±0.04
\\( \\mathcal{C}_{L2} \\) (Ours)0.05±0.060.10±0.120.05±0.060.12±0.120.01±0.000.02±0.000.09±0.020.19±0.03
STE [2]0.11±0.100.23±0.220.09±0.070.24±0.230.01±0.000.01±0.010.08±0.010.15±0.02
\\( \\mathcal{C}_{Mid} \\) (Ours)0.03±0.020.07±0.050.05±0.040.17±0.170.00±0.000.00±0.000.02±0.010.05±0.01
\\( \\mathcal{C}_{Rnd} \\) (Ours)0.01±0.010.03±0.020.01±0.010.03±0.030.00±0.000.01±0.000.02±0.010.06±0.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.243, + 0.893, + 0.286 + ], + "angle": 0, + "content": "Table 2. AUC and loss Barrier results of linear mode connectivity for regression datasets (first and third-degree polynomial approximation), and classification datasets (Mnist and Cifar10). The WM method and our Sinkhorn with \\( \\mathcal{C}_{L2} \\) belong to the data-free category, while STE, Sinkhorn with \\( \\mathcal{C}_{Mid} \\) and \\( \\mathcal{C}_{Rnd} \\) are data-driven." + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.298, + 0.351, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.298, + 0.603, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.298, + 0.856, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.444, + 0.353, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.444, + 0.602, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.444, + 0.852, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.607, + 0.893, + 0.649 + ], + "angle": 0, + "content": "Figure 4. Example of linear mode connectivity achieved by WM [2], STE [2], and our Sinkhorn re-basin with \\( \\mathcal{C}_{L2} \\), \\( \\mathcal{C}_{Mid} \\), and \\( \\mathcal{C}_{Rnd} \\) costs for a NN with two hidden layers. Accuracy and loss are shown for the Mnist and Cifar10 classification, while only the L2 loss is shown for the regression tasks. For Mnist, we include an amplified version of the loss and accuracy for better comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.47, + 0.721 + ], + "angle": 0, + "content": "the estimated cost curve within the linear path. Both measures achieve the best performance when a method provides a low value, with a lower bound of 0." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We compare our approach with different objectives – L2 (Eq. (7)), Middle point (Eq. (8)), and Random point (Eq. (9)) with the recently introduced WM and Straight-Through Estimator (STE) [2]. Tab. 2 summarizes the performance of the methods for each dataset. All experiments used a NN with two hidden layers. The table shows that our methods outperform state-of-art methods with (the first three rows) and without considering the data (last three rows) during the re-basin. Specifically, our \\(\\mathcal{C}_{L2}\\) method exceeded WM for both AUC and Barrier measures for all datasets, except Mnist, where no significant differences" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.892, + 0.829 + ], + "angle": 0, + "content": "were observed. Our other proposals outperform the state-of-art STE approach for AUC and Barrier in the data-driven category. In particular, our \\(\\mathcal{C}_{Rnd}\\) loss showed the best results, comparable to our \\(\\mathcal{C}_{Mid}\\) for more challenging scenarios like Cifar10. Note that STE and our \\(\\mathcal{C}_{Mid}\\) have the same objective, and their difference in performance lies in the solver. Additionally, our \\(\\mathcal{C}_{L2},\\mathcal{C}_{Mid}\\), and \\(\\mathcal{C}_{Rnd}\\) share the same architecture but with various loss functions, and their discrepancy in performance lies in the objective. As a general point, all methods significantly improve the naive path." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We show the obtained loss and accuracy curves over the linear path before doing a re-basin (naive) and after applying WM, STE, and Sinkhorn with \\( \\mathcal{C}_{L2} \\), \\( \\mathcal{C}_{Mid} \\), and \\( \\mathcal{C}_{Rnd} \\) methods in Fig. 4. Please note that our method can also" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20243" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.199, + 0.089, + 0.772, + 0.233 + ], + "angle": 0, + "content": "
MethodRotated MnistSplit Cifar100
Accuracy ↑Forgetting ↓Accuracy ↑Forgetting ↓
Finetune46.28±1.010.52±0.0135.41±0.950.49±0.01
EWC [14]59.92±1.710.34±0.0250.50±1.330.24±0.02
LwF [17]61.86±3.660.29±0.0641.43±4.060.51±0.01
A-GEM [7]68.47±0.900.28±0.0144.42±1.460.36±0.01
Rebasin /w replay (Ours)78.14±0.500.12±0.0151.34±0.740.07±0.02
Joint training90.84±4.300.0060.48±0.540.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.11, + 0.243, + 0.859, + 0.258 + ], + "angle": 0, + "content": "Table 3. Performance of our proposed and state-of-art methods on the continual learning benchmark datasets over 20 episodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.47, + 0.316 + ], + "angle": 0, + "content": "perform re-basin of convolutional architectures with residual connections, as shown in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.328, + 0.367, + 0.346 + ], + "angle": 0, + "content": "5.3. Incremental learning application" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.534 + ], + "angle": 0, + "content": "This experiment seeks to compare our method with other well-known continual learning approaches from the literature. Since our proposal can fit the regularization techniques that use replay, we compare it with different algorithms within this category. In particular, we compared 3 regularization-based approaches - elastic weight consolidation (EWC) [14], learning without forgetting (LwF) [17], and average gradient episodic memory (A-GEM) [7]. The average accuracy was calculated to measure the overall performance of model \\(\\theta_{i}\\) in the first episodes \\(\\mathbb{T}_j\\). In addition, the forgetting measure averages the forgetting in terms of accuracy for each domain or task in the episode." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.702 + ], + "angle": 0, + "content": "Given the variety of libraries and implementations, we limited our comparison to reproducible methods that could be used in the Avalanche environment [18]. All measurements, benchmarks, networks, and algorithms, including our own, were implemented using the framework. While we attempted to incorporate other recent approaches like MC-SGD [22] and Stable SGD [23] into Avalanche, a high discrepancy was observed w.r.t. their reported results and, therefore, we did not include them into our study. Difficulties in adapting MC-SGD to new conditions have also been observed by other authors [20]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We focused our experiments on low episodic memory scenarios, using only five examples per class for both benchmarks in methods that rely on memory replay (A-GEM and our method). We used a NN with one hidden layer and 256 neurons for the Rotated Mnist benchmark. For the Split Cifar100 benchmark, a multi-head ResNet18 was used following the settings in [22, 23]. In this experiment, we only apply the re-basin to linear layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Tab. 3 shows methods' accuracy and forgetting performance on the benchmarks Rotated Mnist and Split Cifar100 datasets using 20 episodes. Our method outperforms the others and still performs better or comparable to those reported in [23]. The reader should pay special attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.895, + 0.451 + ], + "angle": 0, + "content": "to the low values of forgetting achieved using our re-basin approach. This is a consequence of setting the value of \\(\\alpha = 0.8\\) when fusing the models (Eq. (12)). A-GEM is ranked second in accuracy and forgetting for Rotated Mnist. LwF showed a similar forgetting to A-GEM in this benchmark. On Split Cifar100, EWC ranked second for both measures. Despite having similar accuracy to our approach, the high forgetting value suggests stability issues. In general, the method showed to be robust to the values \\(\\alpha\\) and \\(\\beta\\). We included the corresponding ablation in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.464, + 0.62, + 0.48 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.823 + ], + "angle": 0, + "content": "This work proposes a new method based on the Sinkhorn operator to estimate permutation matrices that make two neural network models equivalent. With respect to previous work, such as weight matching, our method is (i) more flexible because it is differentiable and can be applied with any loss, (ii) estimates the permutations for all layers at the same time, avoiding getting stuck in local minima, (iii) more accurate, as shown in our experimental evaluation on well-known benchmarks. First, our experiments yielded perfect results when our approach was evaluated to produce the optimal permutation between a model and its artificially permuted transformation. We have also used our approach for linear mode connectivity, showing better connectivity (lower loss barrier) than weight matching. Finally, we showed that our efficient and differentiable approach for re-basin can easily be applied to the challenging task of continual learning, producing results comparable to, or better than state-of-art approaches. As a limitation to our work, we observed from our experiments and analysis of the literature that linear assignment problems solved with greedy Hungarian-based approaches are generally more efficient in terms of memory than the Sinkhorn operator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by Distech Controls Inc., the Natural Sciences and Engineering Research Council of Canada, and the Digital Research Alliance of Canada." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20244" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Ryan Prescott Adams and Richard S Zemel. 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Federated learning with matched averaging. arXiv preprint arXiv:2002.06440, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20246" + } + ] +] \ No newline at end of file diff --git a/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_origin.pdf b/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e86de16b9fee1971a1ddc661a575b0ab761883ce --- /dev/null +++ b/2023/Re-Basin via Implicit Sinkhorn Differentiation/dc7a818b-aa01-4c23-bb8a-90b1d6f90212_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd5e6edd2a570cca0431225e602809c15228b1065cb96f460d14991cd7397e12 +size 439136 diff --git a/2023/Re-Basin via Implicit Sinkhorn Differentiation/full.md b/2023/Re-Basin via Implicit Sinkhorn Differentiation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e813e419ead40d75ad4d01b7974aae012372172a --- /dev/null +++ b/2023/Re-Basin via Implicit Sinkhorn Differentiation/full.md @@ -0,0 +1,299 @@ +# Re-basin via implicit Sinkhorn differentiation + +Fidel A. Guerrero Peña + +fidel-alejandro.guerrero-pena@etsmtl.ca + +Thomas Dubail + +thomas.dubail.1@ens.etsmtl.ca + +Eric Granger + +eric.granger@etsmtl.ca + +Heitor Rapela Medeiros + +heitor.rapela-medeiros.1@ens.etsmtl.ca + +Masih Aminbeidokhti + +masih.aminbeidokhti.1@ens.etsmtl.ca + +Marco Pedersoli + +marco.pedersoli@etsmtl.ca + +LIVIA, Dept. of Systems Engineering ETS Montreal, Canada + +# Abstract + +The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces and some promising properties like mode connectivity. However, finding the permutation that minimizes some objectives is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to suboptimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature under several conditions for both optimal transport and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with the state-of-art. The source code is provided at https://github.com/fagp/sinkhorn-rebasin. + +# 1. Introduction + +Despite the success of deep learning (DL) across many application domains, the loss surfaces of neural networks (NNs) are not well understood. Even for shallow NNs, the number of saddle points and local optima can increase exponentially with the number of parameters [4, 13]. The permu + +![](images/20e36d8f1c619bc8acadec912ce8bb714772433fb7caea446cf928d7005fe2f1.jpg) + +![](images/a126f321aaecf2f8c3e0a61b76db2604b7512c70a292a853412537003debdd0d.jpg) +(a) +(b) +Figure 1. (a) Loss landscape for the polynomial approximation task [27]. $\theta_{A}$ and $\theta_{B}$ are models found by SGD. LMC suggests that re-basin the model $\theta_{B}$ would result in a functionally equivalent model $\pi_{\mathcal{P}}(\theta_B)$ , with no barrier on its linear interpolation $(1 - \lambda)\theta_{A} + \lambda \pi_{\mathcal{P}}(\theta_{B})$ . (b) Comparison of the cost in the linear path along $\lambda$ before and after re-basin using weight matching (WM) [2] and our Sinkhorn. The dashed line in the figures corresponds with the naive path, and the solid line is the path after the proposed Sinkhorn re-basin. The blue line represents WM path. + +tation symmetry of neurons in each layer allows the same function to be represented with many different parameter values of the same network. Symmetries imposed by these invariances help us to better understand the structure of the loss landscape [6, 11, 13]. + +Previous studies establish that minima found by Stochastic Gradient Descent (SGD) are not only connected in the network parameter's space by a path of non-increasing loss, but also permutation symmetries may allow us to connect those points linearly with no detriment to the loss [9, 11-13, 15, 24]. This phenomenon is often referred to as linear mode connectivity (LMC) [24]. For instance, Fig. 1a shows a portion of the loss landscape for the polynomial approximation task [27] using the method proposed by Li et al. [16]. $\theta_{A}$ and $\theta_{B}$ are two minima found by SGD in different basins with an energy barrier between the pair. LMC suggests that if one considers permutation invariance, we can teleport solutions into a single basin where there is almost no loss barrier between different solutions [2, 11]. In literature, this mechanism is called re-basin [2]. However, efficiently searching for permutation symmetries that bring all solutions to one basin is a challenging problem [11]. Three main approaches for matching units between two NNs have been explored in the literature [2]. Some studies propose a data-dependent algorithm that associates units across two NNs by matching their activations [2, 26]. Since activation-based matching is data dependent, it helps to adjust permutations to certain desired kinds of classes or domains [26]. Instead of associating units by their activations, one could align the weights of the model itself [2, 26], which is independent of the dataset, and therefore the computational cost is much lower. Finally, the third approach is to iteratively adjust the permutation of weights. In particular, Ainsworth et al. [2] have proposed alternating between models alignment and barrier minimization using a Straight-Through Estimator. Unfortunately, the proposed approaches so far are either non-differentiable [2, 11, 26] or computationally expensive [2], making the solution difficult to be extended to other applications, with a different objective. For instance, adapting those methods for incremental learning by including the algorithm for weight matching between two models trained on different domains is not trivial because of the difficulties in optimizing new objectives. + +In this work, inspired by [21], we relax the permutation matrix with the Sinkhorn operator [1], and use it to solve the re-basin problem in a differentiable fashion. To avoid the high cost for computing gradients in the proposal of Mena et al. [21], we use the implicit differentiation algorithm proposed in [10], which has been shown to be more cost-effective. Our re-basin formulation allows defining any differentiable objective as a loss function. + +A direct application of re-basin is the merger of diverse models without significantly degrading their performance + +[2, 5, 12, 13, 28]. Applications like federate learning [2], ensembling [12], or model initialization [5] exploit such a merger by selecting a model in the line connecting the models to be combined. To show the effectiveness of our approach, we propose a new continual learning algorithm that combines models trained on different domains. Our continual learning algorithm differs from previous state-of-art approaches [22] because it directly estimates a model at the intersection of previous and new knowledge, by exploiting the LMC property observed in SGD-based solutions. + +Our main contribution can be summarized as follows: + +(1) Solving the re-basin for optimal transportation using implicit Sinkhorn differentiation, enabling better differentiable solutions that can be integrated on any loss. +(2) A powerful way to use our re-basin method based on the Sinkhorn operator for incremental learning by considering it as a model merging problem and leveraging LMC. +(3) An extensive set of experiments that validate our method for: (i) finding the optimal permutation to transform a model to another one equivalent; (ii) linear mode connectivity, to linearly connect two models such that their loss is almost identical along the entire connecting line in the weights space; and (iii) learning new domains and tasks incrementally while not forgetting the previous ones. + +# 2. Related work + +Re-basin. Recently, in the NN community, re-basin has been demonstrating useful properties. The main goal of such re-basin approaches is to obtain functionally equivalent models in a different region of the weight space following some pre-defined objective. Permutation symmetries are a well-known example of transformations that allows performing re-basin. In particular, Entezari et al. [11] show that the invariances of NNs using random permutations on SGD solutions are likely to have almost zero barriers, and therefore the randomness in terms of permutations does not impact the quality of the final training result of the model. A simulated annealing-based algorithm was proposed for doing a re-basin with an elevated computational cost, making it impractical to use, especially for bigger models. Ainsworth et al. [2] proposed three new re-basin algorithms that rely on solving linear assignment problems to find permutation matrices that satisfy their encoded objective. The methods showed to perform well, especially in achieving linear mode connectivity. On the downside, new objectives are difficult to plug into their framework. Their solution uses greedy algorithms that do not guarantee finding the optimal solution, as shown in our experiments. Using a similar approach, Benzing et al. [5] found strong evidence that two random initialization of a NN after permutation can lead to a good performance, showing that the random initialization is already in the same loss valley during the initialization. Finally, [3] uses the concepts of + +Wasserstein barycenter and Gromov-Wasserstein barycenter, offering a NN model fusion framework with insights about linear mode connectivity of SGD solutions. Even though the previous works presented solutions to perform re-basin by solving linear assignment problems, their approach fails to generalize well for other objectives. Using gradient descent-based algorithms seems to be a more suitable approach. + +Mode connectivity. Mode connectivity is the task of finding low-barrier paths connecting models within the weight space. In their work, Garipov et al. [13] found that the local optima of deep learning models are connected by simple curves. The fast geometric ensembling method was proposed as an application for their proposal. Almost at the same time, [9] proposed a nudged elastic band-based method to construct continuous paths between minima of NN architectures. Finally, Frankle et al. [12] studied the sensitivity of different levels of SGD noise on NNs. These pioneering works are the basis for applications of mode connectivity, like [2, 22] and ours. + +Incremental learning. Continual or incremental learning (IL) allows adapting models incrementally based on new training data without forgetting previous knowledge. Catastrophic forgetting [19,25] occurs when a previously trained model that is fine-tuned on a new task loses information learned to perform well on previous datasets. To address this issue, Kirkpatrick et al. [14] proposes elastic weight consolidation (EWC), which reduces catastrophic forgetting by regularizing NN parameters with respect to the importance of the weights concerning the previous and actual tasks. Chaudhry et al. [8] proposed using a small number of samples for replay. Their experience replay (ER) helps to perform IL such that the performance on classification tasks is improved, even with a tiny episodic memory. Closer to our work, [22] proposes an LMC-based method with replay. Its solution is called mode connectivity SGD (MC-SGD), which relies on the assumption that there is always an existing solution that solves all seen tasks incrementally, and they are connected by a low-barrier and linear path. Furthermore, MC-SGD utilizes a replay buffer to remember previous tasks for IL. Its efficiency relies on exploring the linear path of low loss to constrain learning, thereby outperforming competitors like EWC when less data is available. However, such an approach has a high computational cost since it requires training independent models for the new task and merging them as a separate step with the model for previous knowledge. Also, the method has been shown to be difficult to reproduce or adapt to new benchmarks [20]. A compelling scenario for continual learning is using a linear mode connectivity path to keep learning and adapt the model without forgetting the previous knowledge. The trade-off between flatness of the LMC path and direction to adapt the loss can be tuned in a way that brings more + +stability or plasticity depending on the target final solution. + +# 3. Re-basin via the Sinkhorn operator + +Let $f_{\theta}(.)$ be a parameterized mapping where $\theta$ represents a vector of parameters within the solution space $\Theta \subset \mathbb{R}^d$ , where $d$ is the number of parameters in $\theta$ . In the deep learning context, $f$ can be seen as a NN architecture, and $f_{\theta}$ is a model with weights $\theta$ . Here, we refer to $\theta$ as a model for simplicity. Consequently, the cost (or error) of a model for a given task can be defined as $\mathcal{C}(\theta) = \frac{1}{|\mathbb{T}|}\sum_{(x,y)\in \mathbb{T}}\mathcal{L}(f_{\theta}(x),y)$ , where $(x,y)\in \mathbb{T}$ are input and expect output in the training set $\mathbb{T}$ , and $\mathcal{L}$ is an appropriate supervised loss function. + +A function $f$ is invariant to a transformation if and only if the obtained transformed function is functionally equivalent to the original mapping. Note that such invariances can also be found between two functions within the family of parametric functions $\{f_{\theta}\}_{\theta \in \Theta}$ . The permutation of neurons is a well-known example of such transformations applied to NNs that allow obtaining functionally equivalent models, i.e., $f_{\theta_A}(x) = f_{\theta_B}(x), \forall x$ . These invariant models are obtained via the permutation transformation or re-basin function, here defined as $\pi \colon \Theta \to \Theta$ , which shifts a model to a symmetric region of the loss landscape, $\mathcal{C}(\theta) = \mathcal{C}(\pi_{\mathcal{P}}(\theta))$ . In this work $\mathcal{P} = (P_1, \dots, P_h)$ is a transportation plan with $P_i$ contained in the transportation polytope, + +$$ +\Pi = \left\{P \in \mathbb {R} _ {+} ^ {m \times n} | P \mathbf {1} _ {m} = \mathbf {1} _ {n}, P ^ {T} \mathbf {1} _ {n} = \mathbf {1} _ {m} \right\}, \tag {1} +$$ + +where $\mathbb{1}_d = (1,\dots,1)^d$ . Without loss of generality, let $f_{\theta}(x) = (\ell_h\circ \ldots \circ \ell_1)(x)$ be a NN defined as the composition of $h$ layers such that $\ell_i(z) = \sigma (W_iz + b_i)$ . Here, the weights $W_{i}$ and biases $b_{i}$ are the parameters of the network, $\theta = \{W_i,b_i\}_{i = 1}^h$ , and $\sigma$ is a non-linear activation function. Then, the re-based model $\pi_{\mathcal{P}}(\theta)$ can be written as the functionally equivalent mapping: + +$$ +\ell_ {i} ^ {\prime} (z) = \sigma \left(P _ {i} W _ {i} P _ {i - 1} ^ {T} z + P _ {i} b _ {i}\right), \tag {2} +$$ + +where $P_{i}\in \Pi$ is a valid permutation matrix, and $P_{h} = P_{0}^{T} = I$ is the identity matrix. + +With regards to permutation invariance, Entezari et al. [11] conjectured that re-based SGD solutions are likely to have a low barrier within their linear interpolation $B(\theta_A, \theta_B) \approx 0$ , where $B(.)$ is defined as: + +$$ +B \left(\theta_ {A}, \theta_ {B}\right) = \sup _ {\lambda} \left[ \left. \mathcal {C} ((1 - \lambda) \theta_ {A} + \lambda \theta_ {B}) \right] - \right. +$$ + +$$ +[ (1 - \lambda) \mathcal {C} (\theta_ {A}) + \lambda \mathcal {C} (\theta_ {B}) ] ], \tag {3} +$$ + +and $\lambda \in (0,1)$ . This phenomenon is known as LMC [12], and it is a particular case of the widely studied mode connectivity [9, 13]. Notably, Ainsworth et al. [2] proposed three approaches that ratify the conjecture in [11] by finding + +a re-based model $\pi_{\mathcal{P}}(\theta_B)$ with LMC to a target model $\theta_A$ . Fig. 1 depicts the goal of such re-basin approaches. This figure shows two solutions for the task, $\theta_A$ and $\theta_B$ , found through SGD. As shown in Fig. 1b, the naive path between $\theta_A$ and $\theta_B$ has higher values of the barrier within the line $(1 - \lambda)\theta_A + \lambda \theta_B, \lambda \in (0,1)$ . On the other hand, and consistently with the results in [2,11], our re-based model $\pi_{\mathcal{P}}(\theta_B)$ achieves LMC by successfully finding a transportation plan $\mathcal{P}$ that shifts model $\theta_B$ to the same basin of model $\theta_A$ . + +Although the seminal work by Ainsworth et al. [2] proposed a highly efficient approach for finding a permutation that minimizes the distances between models, their nondifferentiable approach provides solutions that are difficult to be extended to other applications with a different objective. Specifically, their algorithms use a formulation based on the linear assignment problem (LAP) to find suitable permutations, meaning any new objective needs to be cast as a LAP which is a hard task in itself. + +This work proposes a differentiable approach to perform a re-basin that defines any differentiable objective as a loss function. Here, we relax the rigid constraint of having a binary permutation matrix $P$ , and consequently add an entropy regularizer $h(P) = -\sum P(\log P)$ to the original LAP as proposed by [21]. The final equation is then defined as: + +$$ +S _ {\tau} (X) = \underset {P \in \Pi} {\arg \max } \langle P, X \rangle_ {F} + \tau h (P), \tag {4} +$$ + +where is $\tau$ a factor that weights the strengths of the entropy regularization term. + +The formulation in Eq. (4) is known as the Sinkhorn operator and can be efficiently approximated by: + +$$ +S _ {\tau} ^ {(0)} (X) = \exp \left(\frac {X}{\tau}\right), +$$ + +$$ +S _ {\tau} ^ {(t + 1)} (X) = \mathcal {T} _ {c} \left(\mathcal {T} _ {r} \left(S _ {\tau} ^ {(t)} (X)\right)\right). \tag {5} +$$ + +where $X \in \mathbb{R}^{m \times n}$ is a soft version of the permutation matrix, $\mathcal{T}_c(X) = X \oslash (\mathbb{1}_m\mathbb{1}_m^T X)$ and $\mathcal{T}_r(X) = X \oslash (X\mathbb{1}_n\mathbb{1}_n^T)$ are respectively the re-normalization of columns and rows of $X$ , and $\oslash$ is the element-wise division. In their work, Mena et al. [21] proved that Eq. (5) converges to Eq. (4) when $t \to \infty$ . However, in practice, only a finite number of iterations are needed to produce a suitable approximation. + +Although the Sinkhorn operator is reasonably easy to implement within the NN layers, a significant drawback arises when considering the efficiency of its differentiation. We use the implicit differentiation algorithm proposed by Eisenberger et al. [10] to mitigate such an increase in the computational cost. Their method significantly increases the efficiency and also stability of the training process. The marginals of the generic formulation in [10] are defined as $\pmb{a} = \mathbb{1}_m / m$ and $\pmb{b} = \mathbb{1}_n / n$ to match the re-basin task. + +Finally, our proposed Sinkhorn re-basin re-writes the original re-basin mapping in Eq. (2) as: + +$$ +\ell_ {i} ^ {\prime} (z) = \sigma (S _ {\tau} (P _ {i}) W _ {i} S _ {\tau} (P _ {i - 1} ^ {T}) z + S _ {\tau} (P _ {i}) b _ {i}). \qquad (6) +$$ + +where $P_{i}\in \mathbb{R}^{m\times n}$ is a differentiable permutation matrix. + +To show the ability of our proposed Sinkhorn re-basin to minimize any differentiable objective, we provide three examples of cost functions that are minimized without changing the formulation in Eq. (6). These cost functions are used in the SGD framework to compute the gradient of the weights in our Sinkhorn re-basin network, and finally update the permutation matrices to minimize the objective. First, for a data-free objective like Weights Matching [2], we directly minimize the squared L2 distance defined as: + +$$ +\mathcal {C} _ {L 2} (\mathcal {P}; \theta_ {A}, \theta_ {B}) = \left\| \theta_ {A} - \pi_ {\mathcal {P}} \left(\theta_ {B}\right) \right\| ^ {2}. \tag {7} +$$ + +Given the ability of our method to use differentiable objectives, we introduce two other data-driven cost functions. Inspired by the Straight-Through Estimator in [2], we propose a differentiable midpoint cost function to minimize the barrier, + +$$ +\mathcal {C} _ {M i d} (\mathcal {P}; \theta_ {A}, \theta_ {B}) = \mathcal {C} \left(\frac {\theta_ {A} + \pi_ {\mathcal {P}} \left(\theta_ {B}\right)}{2}\right). \tag {8} +$$ + +Since minimizing the midpoint can lead to a multimodal cost path, i.e., lower cost value for $\lambda = 0.5$ , and higher cost values elsewhere, we propose a cost function that minimizes the cost at random points within the line: + +$$ +\mathcal {C} _ {R n d} (\mathcal {P}; \theta_ {A}, \theta_ {B}) = \mathcal {C} \left((1 - \lambda) \theta_ {A} + \lambda \pi_ {\mathcal {P}} (\theta_ {B})\right), \tag {9} +$$ + +with $\lambda$ uniformly sampled at each iteration, $\lambda \sim U(0,1)$ + +# 4. Re-basin incremental learning + +A critical application of re-basin approaches is the ability to merge models without a significant performance reduction. Such merging is usually done by selecting a model in their connecting line. Applications like federate learning [2], ensembling [12], or model initialization [5] have been explored recently for merging models trained on the same task. Here we consider merging based on re-basin by proposing a new incremental learning approach that combines models trained on different domains or classes. Our proposed approach relies on a stability-plasticity hyperparameter $\alpha$ , allowing the user to choose the balance between forgetting and incorporating new knowledge. + +Let $\theta_0$ be an initial model trained over dataset $\mathbb{T}_0$ , and $\mathcal{T} = \{\mathbb{T}_1, \mathbb{T}_2, \ldots\}$ be a stream of data, where $\mathbb{T}_i = \{(x_{ij}, y_{ij}) | x_{ij} \in \mathbb{X}_i, y_{ij} \in \mathbb{Y}_i\}, 1 \leq i \leq N_i$ , is a supervised dataset with input $\mathbb{X}_i$ , output $\mathbb{Y}_i$ , and $N_i$ data points. Note that the sets $\mathbb{T}_i$ are also known in incremental learning literature as tasks, but these are not limited to task incremental learning scenarios, and also include domain and + +![](images/99bcb0ad798cfc3ddcfb512b966fde136a28bf7d66d337b9bbee7fd5b250f421.jpg) +Figure 2. Graphical representation of the intersection of low curvature regions of the loss landscape for task $\mathbb{T}_i$ (red) and $\mathbb{T}_{i + 1}$ (blue). The goal of our method is to find a re-basin $\pi_{\mathcal{P}_i}(\theta_i)$ that transverses the multitask region using LMC. The final model $\theta_{i + 1}$ (Eq. (12)) is found in the surroundings of the line by adding a learnable residual $\delta_{i}$ . + +class incremental learning. Incremental or continual learning seeks to incorporate the new knowledge $\mathbb{T}_{i + 1}$ into the model $\theta_{i}$ without forgetting how to perform correctly in previous datasets $\mathbb{T}_0,\dots,\mathbb{T}_i$ . To this end, the continual learning community has proposed approaches that exploit the fact that multitask low curvature regions usually appear at the intersection of low curvature regions for individual tasks [14, 22] (see Fig. 2 for a visual reference). In particular, the Mirzadeh et al. [22] approach uses a two steps training, where the model $\theta_{i + 1}$ is first trained over dataset $\mathbb{T}_{i + 1}$ , and then a mode connectivity-based merging finds the model with low loss value on both new and previous knowledge. + +In contrast with [22], our approach directly estimates a model at the intersection of previous and new knowledge by exploiting our differentiable method to obtain the LMC observed in SGD-based solutions. Similarly to approaches introduced in the last section, our method looks for a rebasin of the given model that minimizes a given objective. For continual learning purposes, a new cost function is introduced such that, like in Eq. (8), the cost of the model in the middle of the line $(1 - \lambda)\theta_{i} + \lambda \pi_{\mathcal{P}_{i}}(\theta_{i}), \lambda \in (0,1)$ , is minimized for dataset $\mathbb{T}_{i+1}$ (see Fig. 2). In such a continual learning scenario, the middle point is the furthest model in the line from high stability points $\theta_{i}$ and $\pi_{\mathcal{P}_{i}}(\theta_{i})$ , noting that the endpoints are solutions for previous tasks, but not for the new one. The smooth nature of the loss landscape implies that neighboring models have similar costs for all tasks, thus it is important to select the farthest model from the extremes. However, constraining the solution space to models within the line yields a solution that performs well on the previous task, but does not allow optimal performance on the new task, thus affecting the training plasticity. Similarly to Kirkpatrick et al. [14], we find well-behaved models for $\mathbb{T}_{i+1}$ in the neighborhood of our optimization + +target. This is done by adding a regularization term that minimizes the $l_{2}$ norm of the residual vector $\delta_{i}$ . Finally, the proposed cost is calculated as: + +$$ +\mathcal {C} _ {C L} \left(\delta_ {i}, \mathcal {P} _ {i}; \theta_ {i}\right) = \mathcal {C} \left(\frac {\theta_ {i} + \pi \mathcal {P} _ {i} \left(\theta_ {i}\right)}{2} + \delta_ {i}\right) + \beta \| \delta_ {i} \| ^ {2}. \tag {10} +$$ + +During the learning phase, the underlying optimization problem finds: + +$$ +\delta_ {i} ^ {*}, \mathcal {P} _ {i} ^ {*} = \underset {\delta_ {i}, \mathcal {P} _ {i}} {\arg \min } \mathcal {C} _ {C L} \left(\delta_ {i}, \mathcal {P} _ {i}; \theta_ {i}\right), \tag {11} +$$ + +where $\delta_i^*$ and $\mathcal{P}_i^*$ are found at the same time. Note that the cost in Eq. (10) can be computed over any knowledge dataset. This work uses a replay method by taking the average of Eq. (10) for current and previous datasets. + +Combining a model with a balance between previous and new knowledge should be obtained after minimizing the cost in Eq. (10). Here, the incremented model at episode $i + 1$ is defined as: + +$$ +\theta_ {i + 1} = (1 - \alpha) \theta_ {i} + \alpha \pi_ {\mathcal {P} _ {i}} (\theta_ {i}) + \delta_ {i}, \tag {12} +$$ + +where $\alpha$ is a hyper-parameter controlling the balance between plasticity and stability. Note that values of $\alpha$ near 0.5 favor higher plasticity, while values around 0.0 and 1.0 give more importance to previous knowledge. + +# 5. Experimental results and analysis + +The experimental procedure for comparing re-basin approaches follows the same one used by Ainsworth et al. [2], while the continual learning experiments follow the standard experimental procedure in incremental learning literature [22]. For all experiments, the mean and standard deviation of results is reported and obtained over independent runs with different seeds. We used the original implementation provided by the authors in all cases. The effect of re-basin is studied for both classification and regression tasks. Mnist and Cifar10 datasets were used for image classification, while the polynomial approximation problems from [27] were used for regression. Feedforward NNs with 2 to 8 layers were explored as backbone architectures. In all our experiments, $t = 20$ and $\tau = 1.0$ were used, as proposed in [21] for the Sinkhorn operator. Furthermore, the corresponding performance measures and hyper-parameters are summarized in each subsection. Additional details on the experimental methodology, e.g., dataset, protocol, and performance measures, as well as other experimental settings, i.e., convolutional architectures, are provided in the supplementary materials. + +# 5.1. Finding the optimal transport + +In this experiment, we measure the ability of both Weights Matching (WM) [2] and our Sinkhorn re-basin to + +![](images/b8a7eff706677dff374c4d50dc060e3da8f862f48389a4103d28bf367f59717c.jpg) +Figure 3. Estimated permutation matrices via weight matching (WM) [2] and the proposed Sinkhorn re-basin. $P_{i}$ refers to the expected $10 \times 10$ permutation matrix with ones represented in black and zeros in white. The estimated permutations matrix $\hat{P}_{i}$ shows matching permutations as blue squares and miss-matchings in red and yellow. The permutation matrices $P_{i} \in \mathbb{R}^{10 \times 10}$ correspond with transportation plans of layer $i$ , with each layer containing 10 neurons. These matrices correspond with actual permutation matrices from the experiment with random initialization and 2 hidden layers. + +find the optimal permutation. Similar to our $\mathcal{C}_{L2}$ , the WM method minimizes the distance between the re-based and target models by solving a LAP. The cost function used for our re-basin is the squared L2 distance between models (Eq. (7)). Note that the objectives are not data-driven, and therefore we only measure the ability of each algorithm to reach the global minima without any context. Each method received a model and a randomly permuted version of it to find the permutation matrices that originated the target re-basin. + +For our purposes, 9 datasets are created, each one containing 50 models and a random re-basin, $\mathbb{T}_i = \{(\theta_{ij},\pi_{\mathcal{P}}(\theta_{ij}))\mid P_k\sim \mathrm{U}(\Pi),\forall P_k\in \mathcal{P}\}$ , where $1\leq j\leq 50$ is the index of the model within dataset $\mathbb{T}_i$ and $1\le k\le h$ is the number of hidden layers in the NN. Note that we select random permutation matrices following a uniform distribution, $\mathrm{U}(\Pi)$ . NNs with two, four, and eight hidden layers were used as base architecture. Additionally, we tested three types of initializations - random initialization with weights following a normal distribution $\mathcal{N}(0,1)$ , hereafter called Rnd, and models trained in a third and first-degree polynomial approximation problem, named Pol3 and Poll1 respectively. The 9 data set configurations lie within the combination $\{\mathrm{Rnd},\mathrm{Pol3},\mathrm{Pol1}\} \times \{2$ hidden, 4 hidden, 8 hidden\}. + +The Sinkhorn re-basin model was updated using the Adam optimizer with an initial learning rate of 0.1, and for a maximum of 5 iterations, using early stopping in case of convergence. Tab. 1 summarizes the L1 norm between weights after re-basin, $|\pi_{\hat{P}}(\theta) - \pi_{\mathcal{P}}(\theta)|$ , where $\hat{\mathcal{P}}$ and $\mathcal{P}$ are the estimated and optimal transportation plan, respectively. As expected, our proposal always finds the optimal permutation thanks to its ability to simultaneously look at all permutation matrices. In contrast, the WM results fall short for some scenarios. It is worth mentioning that these results match the ones obtained by Ainsworth et al. in [2]. In general, the WM algorithm seems to be affected by random initialization, while increasing the network's capacity + +improves its ability to reach the global minimum. We hypothesize that this is an effect of using a greedy algorithm that optimizes the objective for different layers at each iteration. A deeper inspection of the estimated permutation matrices shows that WM reaches local minima close to the expected re-basin, with only a few misplaced permutations (see Fig. 3). A more challenging alignment scenario and convergence analysis are shown in supplementary material. + +# 5.2. Linear mode connectivity + +We measure the ability of our method to find linear connectivity between SGD modes after re-basin one of them. For this experiment, four datasets are employed - first and third-degree polynomial regression tasks [27], along with the classical classification benchmarks, Mnist and Cifar10. Our experiment follows a similar setup to the one described by [2], i.e., two networks were trained over the same dataset, and we performed the re-basin of one of them, hoping to reach the same basin as the unchanged model. The experiment was repeated 50 times for every dataset, and each method saw the same two networks. To measure the ability of the different approaches to find LMC, we use the Barrier [12] (Eq. (3)) and Area Under the Curve (AUC) over + +
MethodInit2 hidden ↓4 hidden ↓8 hidden ↓
WM [2]Rnd6.05±9.174.12±6.580.50±1.55
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol30.57±2.840.07±0.460.01±0.10
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol10.27±0.940.00±0.000.00±0.00
CL2(Ours)0.00±0.000.00±0.000.00±0.00
+ +Table 1. L1 distance between the estimated and expected re-basin with different network initializations and depths. Distances are scaled $\times 10^{3}$ . + +
MethodFirst degree polynomialThird degree polynomialMnistCifar10
AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓
Naive0.31±0.380.62±0.710.25±0.150.58±0.330.34±0.081.07±0.210.73±0.121.23±0.18
WM [2]0.16±0.150.32±0.280.19±0.260.41±0.570.01±0.000.03±0.010.13±0.020.27±0.04
\( \mathcal{C}_{L2} \) (Ours)0.05±0.060.10±0.120.05±0.060.12±0.120.01±0.000.02±0.000.09±0.020.19±0.03
STE [2]0.11±0.100.23±0.220.09±0.070.24±0.230.01±0.000.01±0.010.08±0.010.15±0.02
\( \mathcal{C}_{Mid} \) (Ours)0.03±0.020.07±0.050.05±0.040.17±0.170.00±0.000.00±0.000.02±0.010.05±0.01
\( \mathcal{C}_{Rnd} \) (Ours)0.01±0.010.03±0.020.01±0.010.03±0.030.00±0.000.01±0.000.02±0.010.06±0.01
+ +Table 2. AUC and loss Barrier results of linear mode connectivity for regression datasets (first and third-degree polynomial approximation), and classification datasets (Mnist and Cifar10). The WM method and our Sinkhorn with $\mathcal{C}_{L2}$ belong to the data-free category, while STE, Sinkhorn with $\mathcal{C}_{Mid}$ and $\mathcal{C}_{Rnd}$ are data-driven. + +![](images/e959dd6bb08ef08e3280277a5220928a90ec41c69ec8d8848fc78619abab60e1.jpg) + +![](images/a4a8cf1cabd388ff10db4b5f5a2ef931fe7582838312cb8fb3f5c3dc193a67e5.jpg) + +![](images/a7104a10cd6d1a97054df46052afc0321e30c9c50a687471dea04d2d838399b4.jpg) + +![](images/d91f4bbeee736758429907b85e1d48aeaffe96102a063af82201fa7424185b60.jpg) +Figure 4. Example of linear mode connectivity achieved by WM [2], STE [2], and our Sinkhorn re-basin with $\mathcal{C}_{L2}$ , $\mathcal{C}_{Mid}$ , and $\mathcal{C}_{Rnd}$ costs for a NN with two hidden layers. Accuracy and loss are shown for the Mnist and Cifar10 classification, while only the L2 loss is shown for the regression tasks. For Mnist, we include an amplified version of the loss and accuracy for better comparison. + +![](images/89113635364e208bcf8b94847dc56932f927173a30f4ba70c9aa92805c8e958b.jpg) + +![](images/87db02a7507515e33d172ea1c332b5ced77549d1e456d56f33b519ae42537cde.jpg) + +the estimated cost curve within the linear path. Both measures achieve the best performance when a method provides a low value, with a lower bound of 0. + +We compare our approach with different objectives – L2 (Eq. (7)), Middle point (Eq. (8)), and Random point (Eq. (9)) with the recently introduced WM and Straight-Through Estimator (STE) [2]. Tab. 2 summarizes the performance of the methods for each dataset. All experiments used a NN with two hidden layers. The table shows that our methods outperform state-of-art methods with (the first three rows) and without considering the data (last three rows) during the re-basin. Specifically, our $\mathcal{C}_{L2}$ method exceeded WM for both AUC and Barrier measures for all datasets, except Mnist, where no significant differences + +were observed. Our other proposals outperform the state-of-art STE approach for AUC and Barrier in the data-driven category. In particular, our $\mathcal{C}_{Rnd}$ loss showed the best results, comparable to our $\mathcal{C}_{Mid}$ for more challenging scenarios like Cifar10. Note that STE and our $\mathcal{C}_{Mid}$ have the same objective, and their difference in performance lies in the solver. Additionally, our $\mathcal{C}_{L2},\mathcal{C}_{Mid}$ , and $\mathcal{C}_{Rnd}$ share the same architecture but with various loss functions, and their discrepancy in performance lies in the objective. As a general point, all methods significantly improve the naive path. + +We show the obtained loss and accuracy curves over the linear path before doing a re-basin (naive) and after applying WM, STE, and Sinkhorn with $\mathcal{C}_{L2}$ , $\mathcal{C}_{Mid}$ , and $\mathcal{C}_{Rnd}$ methods in Fig. 4. Please note that our method can also + +
MethodRotated MnistSplit Cifar100
Accuracy ↑Forgetting ↓Accuracy ↑Forgetting ↓
Finetune46.28±1.010.52±0.0135.41±0.950.49±0.01
EWC [14]59.92±1.710.34±0.0250.50±1.330.24±0.02
LwF [17]61.86±3.660.29±0.0641.43±4.060.51±0.01
A-GEM [7]68.47±0.900.28±0.0144.42±1.460.36±0.01
Rebasin /w replay (Ours)78.14±0.500.12±0.0151.34±0.740.07±0.02
Joint training90.84±4.300.0060.48±0.540.00
+ +Table 3. Performance of our proposed and state-of-art methods on the continual learning benchmark datasets over 20 episodes. + +perform re-basin of convolutional architectures with residual connections, as shown in supplementary materials. + +# 5.3. Incremental learning application + +This experiment seeks to compare our method with other well-known continual learning approaches from the literature. Since our proposal can fit the regularization techniques that use replay, we compare it with different algorithms within this category. In particular, we compared 3 regularization-based approaches - elastic weight consolidation (EWC) [14], learning without forgetting (LwF) [17], and average gradient episodic memory (A-GEM) [7]. The average accuracy was calculated to measure the overall performance of model $\theta_{i}$ in the first episodes $\mathbb{T}_j$ . In addition, the forgetting measure averages the forgetting in terms of accuracy for each domain or task in the episode. + +Given the variety of libraries and implementations, we limited our comparison to reproducible methods that could be used in the Avalanche environment [18]. All measurements, benchmarks, networks, and algorithms, including our own, were implemented using the framework. While we attempted to incorporate other recent approaches like MC-SGD [22] and Stable SGD [23] into Avalanche, a high discrepancy was observed w.r.t. their reported results and, therefore, we did not include them into our study. Difficulties in adapting MC-SGD to new conditions have also been observed by other authors [20]. + +We focused our experiments on low episodic memory scenarios, using only five examples per class for both benchmarks in methods that rely on memory replay (A-GEM and our method). We used a NN with one hidden layer and 256 neurons for the Rotated Mnist benchmark. For the Split Cifar100 benchmark, a multi-head ResNet18 was used following the settings in [22, 23]. In this experiment, we only apply the re-basin to linear layers. + +Tab. 3 shows methods' accuracy and forgetting performance on the benchmarks Rotated Mnist and Split Cifar100 datasets using 20 episodes. Our method outperforms the others and still performs better or comparable to those reported in [23]. The reader should pay special attention + +to the low values of forgetting achieved using our re-basin approach. This is a consequence of setting the value of $\alpha = 0.8$ when fusing the models (Eq. (12)). A-GEM is ranked second in accuracy and forgetting for Rotated Mnist. LwF showed a similar forgetting to A-GEM in this benchmark. On Split Cifar100, EWC ranked second for both measures. Despite having similar accuracy to our approach, the high forgetting value suggests stability issues. In general, the method showed to be robust to the values $\alpha$ and $\beta$ . We included the corresponding ablation in supplementary materials. + +# 6. Conclusion + +This work proposes a new method based on the Sinkhorn operator to estimate permutation matrices that make two neural network models equivalent. With respect to previous work, such as weight matching, our method is (i) more flexible because it is differentiable and can be applied with any loss, (ii) estimates the permutations for all layers at the same time, avoiding getting stuck in local minima, (iii) more accurate, as shown in our experimental evaluation on well-known benchmarks. First, our experiments yielded perfect results when our approach was evaluated to produce the optimal permutation between a model and its artificially permuted transformation. We have also used our approach for linear mode connectivity, showing better connectivity (lower loss barrier) than weight matching. Finally, we showed that our efficient and differentiable approach for re-basin can easily be applied to the challenging task of continual learning, producing results comparable to, or better than state-of-art approaches. As a limitation to our work, we observed from our experiments and analysis of the literature that linear assignment problems solved with greedy Hungarian-based approaches are generally more efficient in terms of memory than the Sinkhorn operator. + +Acknowledgements: This work was supported by Distech Controls Inc., the Natural Sciences and Engineering Research Council of Canada, and the Digital Research Alliance of Canada. + +# References + +[1] Ryan Prescott Adams and Richard S Zemel. Ranking via sinkhorn propagation. arXiv preprint arXiv:1106.1925, 2011. 2 +[2] Samuel K Ainsworth, Jonathan Hayase, and Siddhartha Srinivasa. 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Overcoming catastrophic forgetting in neural networks. Proceedings of the National Academy of Sciences, 114(13):3521-3526, 2017. 3, 5, 8 +[15] Rohith Kuditipudi, Xiang Wang, Holden Lee, Yi Zhang, Zhiyuan Li, Wei Hu, Rong Ge, and Sanjeev Arora. Explaining landscape connectivity of low-cost solutions for multilayer nets. Advances in Neural Information Processing Systems, 32, 2019. 2 +[16] Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein. Visualizing the loss landscape of neural nets. In Advances in Neural Information Processing Systems, 2018. 2 +[17] Zhizhong Li and Derek Hoiem. Learning without forgetting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(12):2935-2947, 2017. 8 +[18] Vincenzo Lomonaco, Lorenzo Pellegrini, Andrea Cossu, Antonio Carta, Gabriele Graffieti, Tyler L. Hayes, Matthias De Lange, Marc Masana, Jary Pomponi, Gido van de Ven, Martin Mundt, Qi She, Keiland Cooper, Jeremy Forest, Eden Belouadah, Simone Calderara, German I. Parisi, Fabio Cuzzolin, Andreas Tobias, Simone Scardapane, Luca Antiga, Subutai Amhad, Adrian Popescu, Christopher Kanan, Joost van de Weijer, Tinne Tuytelaars, Davide Bacciu, and Davide Maltoni. Avalanche: an End-to-End Library for Continual Learning. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2nd Continual Learning in Computer Vision Workshop, 2021. 8 +[19] Michael McCloskey and Neal J Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. In *Psychology of learning and motivation*, volume 24, pages 109–165. Elsevier, 1989. 3 +[20] Sanket Vaibhav Mehta, Darshan Patil, Sarath Chandar, and Emma Strubell. An empirical investigation of the role of pre-training in lifelong learning. arXiv preprint arXiv:2112.09153, 2021. 3, 8 +[21] Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with Gumbel-Sinkhorn Networks. In International Conference on Learning Representations, 2018. 2, 4, 5 +[22] Seyed Iman Mirzadeh, Mehrdad Farajtabar, Dilan Gorur, Razvan Pascanu, and Hassan Ghasemzadeh. Linear Mode Connectivity in Multitask and Continual Learning. In International Conference on Learning Representations, 2021. 2, 3, 5, 8 +[23] Seyed Iman Mirzadeh, Mehrdad Farajtabar, Razvan Pascanu, and Hassan Ghasemzadeh. Understanding the role of training regimes in continual learning. Advances in Neural Information Processing Systems, 33:7308-7320, 2020. 8 +[24] Vaishnavh Nagarajan and J Zico Kolter. Uniform convergence may be unable to explain generalization in deep learning. Advances in Neural Information Processing Systems, 32, 2019. 2 +[25] Roger Ratcliff. Connectionist models of recognition memory: constraints imposed by learning and forgetting functions. Psychological review, 97(2):285, 1990. 3 + +[26] Sidak Pal Singh and Martin Jaggi. Model fusion via optimal transport. 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However, finding the permutation that minimizes some objectives is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to suboptimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature under several conditions for both optimal transport and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with the state-of-art. The source code is provided at https://github.com/fagp/sinkhorn-rebasin." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Despite the success of deep learning (DL) across many application domains, the loss surfaces of neural networks (NNs) are not well understood. Even for shallow NNs, the number of saddle points and local optima can increase exponentially with the number of parameters [4, 13]. The permu" + } + ] + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 345, + 326, + 508, + 454 + ], + "blocks": [ + { + "bbox": [ + 345, + 326, + 508, + 454 + ], + "lines": [ + { + "bbox": [ + 345, + 326, + 508, + 454 + ], + "spans": [ + { + "bbox": [ + 345, + 326, + 508, + 454 + ], + "type": "image", + "image_path": "20e36d8f1c619bc8acadec912ce8bb714772433fb7caea446cf928d7005fe2f1.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 318, + 464, + 492, + 590 + ], + "blocks": [ + { + "bbox": [ + 421, + 456, + 432, + 464 + ], + "lines": [ + { + "bbox": [ + 421, + 456, + 432, + 464 + ], + "spans": [ + { + "bbox": [ + 421, + 456, + 432, + 464 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 318, + 464, + 492, + 590 + ], + "lines": [ + { + "bbox": [ + 318, + 464, + 492, + 590 + ], + "spans": [ + { + "bbox": [ + 318, + 464, + 492, + 590 + ], + "type": "image", + "image_path": "a126f321aaecf2f8c3e0a61b76db2604b7512c70a292a853412537003debdd0d.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 592, + 417, + 601 + ], + "lines": [ + { + "bbox": [ + 406, + 592, + 417, + 601 + ], + "spans": [ + { + "bbox": [ + 406, + 592, + 417, + 601 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "lines": [ + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": "Figure 1. (a) Loss landscape for the polynomial approximation task [27]. " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\theta_{A}" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\theta_{B}" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": " are models found by SGD. LMC suggests that re-basin the model " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\theta_{B}" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": " would result in a functionally equivalent model " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}}(\\theta_B)" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": ", with no barrier on its linear interpolation " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "(1 - \\lambda)\\theta_{A} + \\lambda \\pi_{\\mathcal{P}}(\\theta_{B})" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": ". (b) Comparison of the cost in the linear path along " + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 611, + 547, + 711 + ], + "type": "text", + "content": " before and after re-basin using weight matching (WM) [2] and our Sinkhorn. The dashed line in the figures corresponds with the naive path, and the solid line is the path after the proposed Sinkhorn re-basin. The blue line represents WM path." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20237" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "tation symmetry of neurons in each layer allows the same function to be represented with many different parameter values of the same network. Symmetries imposed by these invariances help us to better understand the structure of the loss landscape [6, 11, 13]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "text", + "content": "Previous studies establish that minima found by Stochastic Gradient Descent (SGD) are not only connected in the network parameter's space by a path of non-increasing loss, but also permutation symmetries may allow us to connect those points linearly with no detriment to the loss [9, 11-13, 15, 24]. This phenomenon is often referred to as linear mode connectivity (LMC) [24]. For instance, Fig. 1a shows a portion of the loss landscape for the polynomial approximation task [27] using the method proposed by Li et al. [16]. " + }, + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{A}" + }, + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{B}" + }, + { + "bbox": [ + 46, + 134, + 289, + 589 + ], + "type": "text", + "content": " are two minima found by SGD in different basins with an energy barrier between the pair. LMC suggests that if one considers permutation invariance, we can teleport solutions into a single basin where there is almost no loss barrier between different solutions [2, 11]. In literature, this mechanism is called re-basin [2]. However, efficiently searching for permutation symmetries that bring all solutions to one basin is a challenging problem [11]. Three main approaches for matching units between two NNs have been explored in the literature [2]. Some studies propose a data-dependent algorithm that associates units across two NNs by matching their activations [2, 26]. Since activation-based matching is data dependent, it helps to adjust permutations to certain desired kinds of classes or domains [26]. Instead of associating units by their activations, one could align the weights of the model itself [2, 26], which is independent of the dataset, and therefore the computational cost is much lower. Finally, the third approach is to iteratively adjust the permutation of weights. In particular, Ainsworth et al. [2] have proposed alternating between models alignment and barrier minimization using a Straight-Through Estimator. Unfortunately, the proposed approaches so far are either non-differentiable [2, 11, 26] or computationally expensive [2], making the solution difficult to be extended to other applications, with a different objective. For instance, adapting those methods for incremental learning by including the algorithm for weight matching between two models trained on different domains is not trivial because of the difficulties in optimizing new objectives." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 687 + ], + "type": "text", + "content": "In this work, inspired by [21], we relax the permutation matrix with the Sinkhorn operator [1], and use it to solve the re-basin problem in a differentiable fashion. To avoid the high cost for computing gradients in the proposal of Mena et al. [21], we use the implicit differentiation algorithm proposed in [10], which has been shown to be more cost-effective. Our re-basin formulation allows defining any differentiable objective as a loss function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "A direct application of re-basin is the merger of diverse models without significantly degrading their performance" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "[2, 5, 12, 13, 28]. Applications like federate learning [2], ensembling [12], or model initialization [5] exploit such a merger by selecting a model in the line connecting the models to be combined. To show the effectiveness of our approach, we propose a new continual learning algorithm that combines models trained on different domains. Our continual learning algorithm differs from previous state-of-art approaches [22] because it directly estimates a model at the intersection of previous and new knowledge, by exploiting the LMC property observed in SGD-based solutions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 192, + 534, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 192, + 534, + 203 + ], + "spans": [ + { + "bbox": [ + 317, + 192, + 534, + 203 + ], + "type": "text", + "content": "Our main contribution can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 204, + 545, + 360 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 304, + 204, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 239 + ], + "type": "text", + "content": "(1) Solving the re-basin for optimal transportation using implicit Sinkhorn differentiation, enabling better differentiable solutions that can be integrated on any loss." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "content": "(2) A powerful way to use our re-basin method based on the Sinkhorn operator for incremental learning by considering it as a model merging problem and leveraging LMC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 276, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 360 + ], + "type": "text", + "content": "(3) An extensive set of experiments that validate our method for: (i) finding the optimal permutation to transform a model to another one equivalent; (ii) linear mode connectivity, to linearly connect two models such that their loss is almost identical along the entire connecting line in the weights space; and (iii) learning new domains and tasks incrementally while not forgetting the previous ones." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 370, + 390, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 390, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 390, + 383 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 391, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 713 + ], + "type": "text", + "content": "Re-basin. Recently, in the NN community, re-basin has been demonstrating useful properties. The main goal of such re-basin approaches is to obtain functionally equivalent models in a different region of the weight space following some pre-defined objective. Permutation symmetries are a well-known example of transformations that allows performing re-basin. In particular, Entezari et al. [11] show that the invariances of NNs using random permutations on SGD solutions are likely to have almost zero barriers, and therefore the randomness in terms of permutations does not impact the quality of the final training result of the model. A simulated annealing-based algorithm was proposed for doing a re-basin with an elevated computational cost, making it impractical to use, especially for bigger models. Ainsworth et al. [2] proposed three new re-basin algorithms that rely on solving linear assignment problems to find permutation matrices that satisfy their encoded objective. The methods showed to perform well, especially in achieving linear mode connectivity. On the downside, new objectives are difficult to plug into their framework. Their solution uses greedy algorithms that do not guarantee finding the optimal solution, as shown in our experiments. Using a similar approach, Benzing et al. [5] found strong evidence that two random initialization of a NN after permutation can lead to a good performance, showing that the random initialization is already in the same loss valley during the initialization. Finally, [3] uses the concepts of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20238" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "Wasserstein barycenter and Gromov-Wasserstein barycenter, offering a NN model fusion framework with insights about linear mode connectivity of SGD solutions. Even though the previous works presented solutions to perform re-basin by solving linear assignment problems, their approach fails to generalize well for other objectives. Using gradient descent-based algorithms seems to be a more suitable approach." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 289, + 316 + ], + "type": "text", + "content": "Mode connectivity. Mode connectivity is the task of finding low-barrier paths connecting models within the weight space. In their work, Garipov et al. [13] found that the local optima of deep learning models are connected by simple curves. The fast geometric ensembling method was proposed as an application for their proposal. Almost at the same time, [9] proposed a nudged elastic band-based method to construct continuous paths between minima of NN architectures. Finally, Frankle et al. [12] studied the sensitivity of different levels of SGD noise on NNs. These pioneering works are the basis for applications of mode connectivity, like [2, 22] and ours." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 289, + 714 + ], + "type": "text", + "content": "Incremental learning. Continual or incremental learning (IL) allows adapting models incrementally based on new training data without forgetting previous knowledge. Catastrophic forgetting [19,25] occurs when a previously trained model that is fine-tuned on a new task loses information learned to perform well on previous datasets. To address this issue, Kirkpatrick et al. [14] proposes elastic weight consolidation (EWC), which reduces catastrophic forgetting by regularizing NN parameters with respect to the importance of the weights concerning the previous and actual tasks. Chaudhry et al. [8] proposed using a small number of samples for replay. Their experience replay (ER) helps to perform IL such that the performance on classification tasks is improved, even with a tiny episodic memory. Closer to our work, [22] proposes an LMC-based method with replay. Its solution is called mode connectivity SGD (MC-SGD), which relies on the assumption that there is always an existing solution that solves all seen tasks incrementally, and they are connected by a low-barrier and linear path. Furthermore, MC-SGD utilizes a replay buffer to remember previous tasks for IL. Its efficiency relies on exploring the linear path of low loss to constrain learning, thereby outperforming competitors like EWC when less data is available. However, such an approach has a high computational cost since it requires training independent models for the new task and merging them as a separate step with the model for previous knowledge. Also, the method has been shown to be difficult to reproduce or adapt to new benchmarks [20]. A compelling scenario for continual learning is using a linear mode connectivity path to keep learning and adapt the model without forgetting the previous knowledge. The trade-off between flatness of the LMC path and direction to adapt the loss can be tuned in a way that brings more" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 542, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 542, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 542, + 85 + ], + "type": "text", + "content": "stability or plasticity depending on the target final solution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 95, + 503, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 95, + 503, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 95, + 503, + 109 + ], + "type": "text", + "content": "3. Re-basin via the Sinkhorn operator" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "f_{\\theta}(.)" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " be a parameterized mapping where " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " represents a vector of parameters within the solution space " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\Theta \\subset \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " is the number of parameters in " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": ". In the deep learning context, " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " can be seen as a NN architecture, and " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " is a model with weights " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": ". Here, we refer to " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " as a model for simplicity. Consequently, the cost (or error) of a model for a given task can be defined as " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\theta) = \\frac{1}{|\\mathbb{T}|}\\sum_{(x,y)\\in \\mathbb{T}}\\mathcal{L}(f_{\\theta}(x),y)" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "(x,y)\\in \\mathbb{T}" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " are input and expect output in the training set " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\mathbb{T}" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 115, + 545, + 236 + ], + "type": "text", + "content": " is an appropriate supervised loss function." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": "A function " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": " is invariant to a transformation if and only if the obtained transformed function is functionally equivalent to the original mapping. Note that such invariances can also be found between two functions within the family of parametric functions " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "\\{f_{\\theta}\\}_{\\theta \\in \\Theta}" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": ". The permutation of neurons is a well-known example of such transformations applied to NNs that allow obtaining functionally equivalent models, i.e., " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "f_{\\theta_A}(x) = f_{\\theta_B}(x), \\forall x" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": ". These invariant models are obtained via the permutation transformation or re-basin function, here defined as " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "\\pi \\colon \\Theta \\to \\Theta" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": ", which shifts a model to a symmetric region of the loss landscape, " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\theta) = \\mathcal{C}(\\pi_{\\mathcal{P}}(\\theta))" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": ". In this work " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = (P_1, \\dots, P_h)" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": " is a transportation plan with " + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 304, + 236, + 546, + 392 + ], + "type": "text", + "content": " contained in the transportation polytope," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 331, + 399, + 545, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 399, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 331, + 399, + 545, + 414 + ], + "type": "interline_equation", + "content": "\\Pi = \\left\\{P \\in \\mathbb {R} _ {+} ^ {m \\times n} | P \\mathbf {1} _ {m} = \\mathbf {1} _ {n}, P ^ {T} \\mathbf {1} _ {n} = \\mathbf {1} _ {m} \\right\\}, \\tag {1}", + "image_path": "8c31f76daeb271632996a33f5763d1b7de902d27d4b1e5322a593f53580dc711.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_d = (1,\\dots,1)^d" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": ". Without loss of generality, let " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x) = (\\ell_h\\circ \\ldots \\circ \\ell_1)(x)" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " be a NN defined as the composition of " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " layers such that " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\ell_i(z) = \\sigma (W_iz + b_i)" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": ". Here, the weights " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "W_{i}" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " and biases " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " are the parameters of the network, " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\theta = \\{W_i,b_i\\}_{i = 1}^h" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " is a non-linear activation function. Then, the re-based model " + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}}(\\theta)" + }, + { + "bbox": [ + 304, + 422, + 545, + 507 + ], + "type": "text", + "content": " can be written as the functionally equivalent mapping:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 359, + 515, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 515, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 359, + 515, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\ell_ {i} ^ {\\prime} (z) = \\sigma \\left(P _ {i} W _ {i} P _ {i - 1} ^ {T} z + P _ {i} b _ {i}\\right), \\tag {2}", + "image_path": "b2f4949f2617479dace280f1d0140226a143ba65d8ccb8c0f953202d3061cb15.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "inline_equation", + "content": "P_{i}\\in \\Pi" + }, + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "text", + "content": " is a valid permutation matrix, and " + }, + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "inline_equation", + "content": "P_{h} = P_{0}^{T} = I" + }, + { + "bbox": [ + 305, + 538, + 545, + 562 + ], + "type": "text", + "content": " is the identity matrix." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "text", + "content": "With regards to permutation invariance, Entezari et al. [11] conjectured that re-based SGD solutions are likely to have a low barrier within their linear interpolation " + }, + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "inline_equation", + "content": "B(\\theta_A, \\theta_B) \\approx 0" + }, + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "inline_equation", + "content": "B(.)" + }, + { + "bbox": [ + 305, + 562, + 545, + 611 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 336, + 619, + 515, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 619, + 515, + 639 + ], + "spans": [ + { + "bbox": [ + 336, + 619, + 515, + 639 + ], + "type": "interline_equation", + "content": "B \\left(\\theta_ {A}, \\theta_ {B}\\right) = \\sup _ {\\lambda} \\left[ \\left. \\mathcal {C} ((1 - \\lambda) \\theta_ {A} + \\lambda \\theta_ {B}) \\right] - \\right.", + "image_path": "2769f5efbc3eda2a4e7957bd9c420bc8fb2fec1e6fbe70e50c104406006072fc.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 368, + 647, + 545, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 647, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 368, + 647, + 545, + 661 + ], + "type": "interline_equation", + "content": "[ (1 - \\lambda) \\mathcal {C} (\\theta_ {A}) + \\lambda \\mathcal {C} (\\theta_ {B}) ] ], \\tag {3}", + "image_path": "439338bf920f8f8a20a7cdc9c4b389b887bd0c3f8ad6dab5cc3b91b2f0ccb327.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda \\in (0,1)" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ". This phenomenon is known as LMC [12], and it is a particular case of the widely studied mode connectivity [9, 13]. Notably, Ainsworth et al. [2] proposed three approaches that ratify the conjecture in [11] by finding" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20239" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "a re-based model " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}}(\\theta_B)" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " with LMC to a target model " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_A" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": ". Fig. 1 depicts the goal of such re-basin approaches. This figure shows two solutions for the task, " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_A" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_B" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": ", found through SGD. As shown in Fig. 1b, the naive path between " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_A" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_B" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " has higher values of the barrier within the line " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "(1 - \\lambda)\\theta_A + \\lambda \\theta_B, \\lambda \\in (0,1)" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": ". On the other hand, and consistently with the results in [2,11], our re-based model " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}}(\\theta_B)" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " achieves LMC by successfully finding a transportation plan " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " that shifts model " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_B" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " to the same basin of model " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\theta_A" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 287 + ], + "type": "text", + "content": "Although the seminal work by Ainsworth et al. [2] proposed a highly efficient approach for finding a permutation that minimizes the distances between models, their nondifferentiable approach provides solutions that are difficult to be extended to other applications with a different objective. Specifically, their algorithms use a formulation based on the linear assignment problem (LAP) to find suitable permutations, meaning any new objective needs to be cast as a LAP which is a hard task in itself." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "text", + "content": "This work proposes a differentiable approach to perform a re-basin that defines any differentiable objective as a loss function. Here, we relax the rigid constraint of having a binary permutation matrix " + }, + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "text", + "content": ", and consequently add an entropy regularizer " + }, + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "inline_equation", + "content": "h(P) = -\\sum P(\\log P)" + }, + { + "bbox": [ + 46, + 289, + 287, + 371 + ], + "type": "text", + "content": " to the original LAP as proposed by [21]. The final equation is then defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 374, + 287, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 374, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 89, + 374, + 287, + 394 + ], + "type": "interline_equation", + "content": "S _ {\\tau} (X) = \\underset {P \\in \\Pi} {\\arg \\max } \\langle P, X \\rangle_ {F} + \\tau h (P), \\tag {4}", + "image_path": "de0534a6e7cac4d272ba86aab8d87c4c07de395017bc42964cf82171c9fed051.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": "where is " + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 401, + 287, + 425 + ], + "type": "text", + "content": " a factor that weights the strengths of the entropy regularization term." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 450 + ], + "type": "text", + "content": "The formulation in Eq. (4) is known as the Sinkhorn operator and can be efficiently approximated by:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 460, + 215, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 460, + 215, + 487 + ], + "spans": [ + { + "bbox": [ + 117, + 460, + 215, + 487 + ], + "type": "interline_equation", + "content": "S _ {\\tau} ^ {(0)} (X) = \\exp \\left(\\frac {X}{\\tau}\\right),", + "image_path": "2d7ac93f2903ff1f72a2ace7dbddaaf3f4d60fd2dcbc43d9e182b38e97ed807c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 498, + 287, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 498, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 102, + 498, + 287, + 514 + ], + "type": "interline_equation", + "content": "S _ {\\tau} ^ {(t + 1)} (X) = \\mathcal {T} _ {c} \\left(\\mathcal {T} _ {r} \\left(S _ {\\tau} ^ {(t)} (X)\\right)\\right). \\tag {5}", + "image_path": "39ab13011446a6f98dd2d7431358144fa159365cbb7133b13b5ef6e415f2fa4b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{m \\times n}" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " is a soft version of the permutation matrix, " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_c(X) = X \\oslash (\\mathbb{1}_m\\mathbb{1}_m^T X)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_r(X) = X \\oslash (X\\mathbb{1}_n\\mathbb{1}_n^T)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " are respectively the re-normalization of columns and rows of " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\oslash" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " is the element-wise division. In their work, Mena et al. [21] proved that Eq. (5) converges to Eq. (4) when " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "t \\to \\infty" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ". However, in practice, only a finite number of iterations are needed to produce a suitable approximation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Although the Sinkhorn operator is reasonably easy to implement within the NN layers, a significant drawback arises when considering the efficiency of its differentiation. We use the implicit differentiation algorithm proposed by Eisenberger et al. [10] to mitigate such an increase in the computational cost. Their method significantly increases the efficiency and also stability of the training process. The marginals of the generic formulation in [10] are defined as " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{a} = \\mathbb{1}_m / m" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{b} = \\mathbb{1}_n / n" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " to match the re-basin task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "Finally, our proposed Sinkhorn re-basin re-writes the original re-basin mapping in Eq. (2) as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 332, + 102, + 545, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 102, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 332, + 102, + 545, + 118 + ], + "type": "interline_equation", + "content": "\\ell_ {i} ^ {\\prime} (z) = \\sigma (S _ {\\tau} (P _ {i}) W _ {i} S _ {\\tau} (P _ {i - 1} ^ {T}) z + S _ {\\tau} (P _ {i}) b _ {i}). \\qquad (6)", + "image_path": "fa2bd3913c05978b7b0a160fb2b0e7ce687d5b0e978956d7f06690cc74d3c632.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 124, + 537, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 124, + 537, + 135 + ], + "spans": [ + { + "bbox": [ + 305, + 124, + 537, + 135 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 124, + 537, + 135 + ], + "type": "inline_equation", + "content": "P_{i}\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 305, + 124, + 537, + 135 + ], + "type": "text", + "content": " is a differentiable permutation matrix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 136, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 136, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 545, + 243 + ], + "type": "text", + "content": "To show the ability of our proposed Sinkhorn re-basin to minimize any differentiable objective, we provide three examples of cost functions that are minimized without changing the formulation in Eq. (6). These cost functions are used in the SGD framework to compute the gradient of the weights in our Sinkhorn re-basin network, and finally update the permutation matrices to minimize the objective. First, for a data-free objective like Weights Matching [2], we directly minimize the squared L2 distance defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 250, + 545, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 250, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 349, + 250, + 545, + 264 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {L 2} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\left\\| \\theta_ {A} - \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right) \\right\\| ^ {2}. \\tag {7}", + "image_path": "c678fa2369dd2330b1dfc97ff36bb6b6ea2e0a22566ce26e3c064050719c2157.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 271, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 330 + ], + "type": "text", + "content": "Given the ability of our method to use differentiable objectives, we introduce two other data-driven cost functions. Inspired by the Straight-Through Estimator in [2], we propose a differentiable midpoint cost function to minimize the barrier," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 340, + 336, + 545, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 336, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 340, + 336, + 545, + 363 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {M i d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left(\\frac {\\theta_ {A} + \\pi_ {\\mathcal {P}} \\left(\\theta_ {B}\\right)}{2}\\right). \\tag {8}", + "image_path": "7d56d6aa1bc5b105f4e42a6dda1d45c14ad474eee131b2a60407b660be161064.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 369, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 417 + ], + "type": "text", + "content": "Since minimizing the midpoint can lead to a multimodal cost path, i.e., lower cost value for " + }, + { + "bbox": [ + 304, + 369, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\lambda = 0.5" + }, + { + "bbox": [ + 304, + 369, + 545, + 417 + ], + "type": "text", + "content": ", and higher cost values elsewhere, we propose a cost function that minimizes the cost at random points within the line:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 321, + 424, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 424, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 321, + 424, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {R n d} (\\mathcal {P}; \\theta_ {A}, \\theta_ {B}) = \\mathcal {C} \\left((1 - \\lambda) \\theta_ {A} + \\lambda \\pi_ {\\mathcal {P}} (\\theta_ {B})\\right), \\tag {9}", + "image_path": "a309510813847824f08ccf7e185aa9e94889055b17c7ceba1f0bb26b074f2e1e.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "type": "text", + "content": " uniformly sampled at each iteration, " + }, + { + "bbox": [ + 306, + 444, + 535, + 456 + ], + "type": "inline_equation", + "content": "\\lambda \\sim U(0,1)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 466, + 476, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 476, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 476, + 480 + ], + "type": "text", + "content": "4. Re-basin incremental learning" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 486, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 629 + ], + "type": "text", + "content": "A critical application of re-basin approaches is the ability to merge models without a significant performance reduction. Such merging is usually done by selecting a model in their connecting line. Applications like federate learning [2], ensembling [12], or model initialization [5] have been explored recently for merging models trained on the same task. Here we consider merging based on re-basin by proposing a new incremental learning approach that combines models trained on different domains or classes. Our proposed approach relies on a stability-plasticity hyperparameter " + }, + { + "bbox": [ + 304, + 486, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 486, + 545, + 629 + ], + "type": "text", + "content": ", allowing the user to choose the balance between forgetting and incorporating new knowledge." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta_0" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " be an initial model trained over dataset " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_0" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\mathbb{T}_1, \\mathbb{T}_2, \\ldots\\}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " be a stream of data, where " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_i = \\{(x_{ij}, y_{ij}) | x_{ij} \\in \\mathbb{X}_i, y_{ij} \\in \\mathbb{Y}_i\\}, 1 \\leq i \\leq N_i" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", is a supervised dataset with input " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_i" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", output " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{Y}_i" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_i" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " data points. Note that the sets " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_i" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " are also known in incremental learning literature as tasks, but these are not limited to task incremental learning scenarios, and also include domain and" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20240" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 69, + 226, + 201 + ], + "blocks": [ + { + "bbox": [ + 83, + 69, + 226, + 201 + ], + "lines": [ + { + "bbox": [ + 83, + 69, + 226, + 201 + ], + "spans": [ + { + "bbox": [ + 83, + 69, + 226, + 201 + ], + "type": "image", + "image_path": "99bcb0ad798cfc3ddcfb512b966fde136a28bf7d66d337b9bbee7fd5b250f421.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": "Figure 2. Graphical representation of the intersection of low curvature regions of the loss landscape for task " + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_i" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": " (red) and " + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_{i + 1}" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": " (blue). The goal of our method is to find a re-basin " + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}_i}(\\theta_i)" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": " that transverses the multitask region using LMC. The final model " + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\theta_{i + 1}" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": " (Eq. (12)) is found in the surroundings of the line by adding a learnable residual " + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 46, + 208, + 289, + 275 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": "class incremental learning. Incremental or continual learning seeks to incorporate the new knowledge " + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_{i + 1}" + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": " into the model " + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": " without forgetting how to perform correctly in previous datasets " + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_0,\\dots,\\mathbb{T}_i" + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": ". To this end, the continual learning community has proposed approaches that exploit the fact that multitask low curvature regions usually appear at the intersection of low curvature regions for individual tasks [14, 22] (see Fig. 2 for a visual reference). In particular, the Mirzadeh et al. [22] approach uses a two steps training, where the model " + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\theta_{i + 1}" + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": " is first trained over dataset " + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_{i + 1}" + }, + { + "bbox": [ + 46, + 303, + 287, + 448 + ], + "type": "text", + "content": ", and then a mode connectivity-based merging finds the model with low loss value on both new and previous knowledge." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": "In contrast with [22], our approach directly estimates a model at the intersection of previous and new knowledge by exploiting our differentiable method to obtain the LMC observed in SGD-based solutions. Similarly to approaches introduced in the last section, our method looks for a rebasin of the given model that minimizes a given objective. For continual learning purposes, a new cost function is introduced such that, like in Eq. (8), the cost of the model in the middle of the line " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "(1 - \\lambda)\\theta_{i} + \\lambda \\pi_{\\mathcal{P}_{i}}(\\theta_{i}), \\lambda \\in (0,1)" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": ", is minimized for dataset " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_{i+1}" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " (see Fig. 2). In such a continual learning scenario, the middle point is the furthest model in the line from high stability points " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathcal{P}_{i}}(\\theta_{i})" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": ", noting that the endpoints are solutions for previous tasks, but not for the new one. The smooth nature of the loss landscape implies that neighboring models have similar costs for all tasks, thus it is important to select the farthest model from the extremes. However, constraining the solution space to models within the line yields a solution that performs well on the previous task, but does not allow optimal performance on the new task, thus affecting the training plasticity. Similarly to Kirkpatrick et al. [14], we find well-behaved models for " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_{i+1}" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " in the neighborhood of our optimization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "target. This is done by adding a regularization term that minimizes the " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " norm of the residual vector " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ". Finally, the proposed cost is calculated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 310, + 115, + 545, + 143 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 115, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 310, + 115, + 545, + 143 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right) = \\mathcal {C} \\left(\\frac {\\theta_ {i} + \\pi \\mathcal {P} _ {i} \\left(\\theta_ {i}\\right)}{2} + \\delta_ {i}\\right) + \\beta \\| \\delta_ {i} \\| ^ {2}. \\tag {10}", + "image_path": "5cfede7a0a998d660cb6ccdb310fa424724b2ee169c73db2c5b7333369c5e6db.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 148, + 545, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 148, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 545, + 172 + ], + "type": "text", + "content": "During the learning phase, the underlying optimization problem finds:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 355, + 181, + 545, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 181, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 355, + 181, + 545, + 201 + ], + "type": "interline_equation", + "content": "\\delta_ {i} ^ {*}, \\mathcal {P} _ {i} ^ {*} = \\underset {\\delta_ {i}, \\mathcal {P} _ {i}} {\\arg \\min } \\mathcal {C} _ {C L} \\left(\\delta_ {i}, \\mathcal {P} _ {i}; \\theta_ {i}\\right), \\tag {11}", + "image_path": "85993fca93c207516af0cbc173e8504a88d915ea8b4954033e4f1f14e111dc43.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\delta_i^*" + }, + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^*" + }, + { + "bbox": [ + 304, + 209, + 545, + 257 + ], + "type": "text", + "content": " are found at the same time. Note that the cost in Eq. (10) can be computed over any knowledge dataset. This work uses a replay method by taking the average of Eq. (10) for current and previous datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 257, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 304 + ], + "type": "text", + "content": "Combining a model with a balance between previous and new knowledge should be obtained after minimizing the cost in Eq. (10). Here, the incremented model at episode " + }, + { + "bbox": [ + 304, + 257, + 545, + 304 + ], + "type": "inline_equation", + "content": "i + 1" + }, + { + "bbox": [ + 304, + 257, + 545, + 304 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 351, + 313, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 313, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 351, + 313, + 545, + 327 + ], + "type": "interline_equation", + "content": "\\theta_ {i + 1} = (1 - \\alpha) \\theta_ {i} + \\alpha \\pi_ {\\mathcal {P} _ {i}} (\\theta_ {i}) + \\delta_ {i}, \\tag {12}", + "image_path": "433e3e85c637bbd2f15ddde90133095836f7869ee095e590a51d26b4eb1b0423.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "text", + "content": " is a hyper-parameter controlling the balance between plasticity and stability. Note that values of " + }, + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 335, + 545, + 383 + ], + "type": "text", + "content": " near 0.5 favor higher plasticity, while values around 0.0 and 1.0 give more importance to previous knowledge." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 392, + 493, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 392, + 493, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 493, + 407 + ], + "type": "text", + "content": "5. Experimental results and analysis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "text", + "content": "The experimental procedure for comparing re-basin approaches follows the same one used by Ainsworth et al. [2], while the continual learning experiments follow the standard experimental procedure in incremental learning literature [22]. For all experiments, the mean and standard deviation of results is reported and obtained over independent runs with different seeds. We used the original implementation provided by the authors in all cases. The effect of re-basin is studied for both classification and regression tasks. Mnist and Cifar10 datasets were used for image classification, while the polynomial approximation problems from [27] were used for regression. Feedforward NNs with 2 to 8 layers were explored as backbone architectures. In all our experiments, " + }, + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "inline_equation", + "content": "t = 20" + }, + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\tau = 1.0" + }, + { + "bbox": [ + 304, + 413, + 545, + 665 + ], + "type": "text", + "content": " were used, as proposed in [21] for the Sinkhorn operator. Furthermore, the corresponding performance measures and hyper-parameters are summarized in each subsection. Additional details on the experimental methodology, e.g., dataset, protocol, and performance measures, as well as other experimental settings, i.e., convolutional architectures, are provided in the supplementary materials." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 469, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 469, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 469, + 684 + ], + "type": "text", + "content": "5.1. Finding the optimal transport" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "In this experiment, we measure the ability of both Weights Matching (WM) [2] and our Sinkhorn re-basin to" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20241" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 68, + 523, + 175 + ], + "blocks": [ + { + "bbox": [ + 72, + 68, + 523, + 175 + ], + "lines": [ + { + "bbox": [ + 72, + 68, + 523, + 175 + ], + "spans": [ + { + "bbox": [ + 72, + 68, + 523, + 175 + ], + "type": "image", + "image_path": "b8a7eff706677dff374c4d50dc060e3da8f862f48389a4103d28bf367f59717c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": "Figure 3. Estimated permutation matrices via weight matching (WM) [2] and the proposed Sinkhorn re-basin. " + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": " refers to the expected " + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "inline_equation", + "content": "10 \\times 10" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": " permutation matrix with ones represented in black and zeros in white. The estimated permutations matrix " + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "inline_equation", + "content": "\\hat{P}_{i}" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": " shows matching permutations as blue squares and miss-matchings in red and yellow. The permutation matrices " + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "inline_equation", + "content": "P_{i} \\in \\mathbb{R}^{10 \\times 10}" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": " correspond with transportation plans of layer " + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 182, + 547, + 237 + ], + "type": "text", + "content": ", with each layer containing 10 neurons. These matrices correspond with actual permutation matrices from the experiment with random initialization and 2 hidden layers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 376 + ], + "type": "text", + "content": "find the optimal permutation. Similar to our " + }, + { + "bbox": [ + 46, + 258, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2}" + }, + { + "bbox": [ + 46, + 258, + 288, + 376 + ], + "type": "text", + "content": ", the WM method minimizes the distance between the re-based and target models by solving a LAP. The cost function used for our re-basin is the squared L2 distance between models (Eq. (7)). Note that the objectives are not data-driven, and therefore we only measure the ability of each algorithm to reach the global minima without any context. Each method received a model and a randomly permuted version of it to find the permutation matrices that originated the target re-basin." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": "For our purposes, 9 datasets are created, each one containing 50 models and a random re-basin, " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_i = \\{(\\theta_{ij},\\pi_{\\mathcal{P}}(\\theta_{ij}))\\mid P_k\\sim \\mathrm{U}(\\Pi),\\forall P_k\\in \\mathcal{P}\\}" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "1\\leq j\\leq 50" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": " is the index of the model within dataset " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_i" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "1\\le k\\le h" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": " is the number of hidden layers in the NN. Note that we select random permutation matrices following a uniform distribution, " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{U}(\\Pi)" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": ". NNs with two, four, and eight hidden layers were used as base architecture. Additionally, we tested three types of initializations - random initialization with weights following a normal distribution " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,1)" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": ", hereafter called Rnd, and models trained in a third and first-degree polynomial approximation problem, named Pol3 and Poll1 respectively. The 9 data set configurations lie within the combination " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{Rnd},\\mathrm{Pol3},\\mathrm{Pol1}\\} \\times \\{2" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": " hidden, 4 hidden, 8 hidden\\}." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "The Sinkhorn re-basin model was updated using the Adam optimizer with an initial learning rate of 0.1, and for a maximum of 5 iterations, using early stopping in case of convergence. Tab. 1 summarizes the L1 norm between weights after re-basin, " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "|\\pi_{\\hat{P}}(\\theta) - \\pi_{\\mathcal{P}}(\\theta)|" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " are the estimated and optimal transportation plan, respectively. As expected, our proposal always finds the optimal permutation thanks to its ability to simultaneously look at all permutation matrices. In contrast, the WM results fall short for some scenarios. It is worth mentioning that these results match the ones obtained by Ainsworth et al. in [2]. In general, the WM algorithm seems to be affected by random initialization, while increasing the network's capacity" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 258, + 547, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 355 + ], + "type": "text", + "content": "improves its ability to reach the global minimum. We hypothesize that this is an effect of using a greedy algorithm that optimizes the objective for different layers at each iteration. A deeper inspection of the estimated permutation matrices shows that WM reaches local minima close to the expected re-basin, with only a few misplaced permutations (see Fig. 3). A more challenging alignment scenario and convergence analysis are shown in supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 365, + 448, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 448, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 448, + 378 + ], + "type": "text", + "content": "5.2. Linear mode connectivity" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 385, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 542 + ], + "type": "text", + "content": "We measure the ability of our method to find linear connectivity between SGD modes after re-basin one of them. For this experiment, four datasets are employed - first and third-degree polynomial regression tasks [27], along with the classical classification benchmarks, Mnist and Cifar10. Our experiment follows a similar setup to the one described by [2], i.e., two networks were trained over the same dataset, and we performed the re-basin of one of them, hoping to reach the same basin as the unchanged model. The experiment was repeated 50 times for every dataset, and each method saw the same two networks. To measure the ability of the different approaches to find LMC, we use the Barrier [12] (Eq. (3)) and Area Under the Curve (AUC) over" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 561, + 544, + 669 + ], + "blocks": [ + { + "bbox": [ + 309, + 561, + 544, + 669 + ], + "lines": [ + { + "bbox": [ + 309, + 561, + 544, + 669 + ], + "spans": [ + { + "bbox": [ + 309, + 561, + 544, + 669 + ], + "type": "table", + "html": "
MethodInit2 hidden ↓4 hidden ↓8 hidden ↓
WM [2]Rnd6.05±9.174.12±6.580.50±1.55
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol30.57±2.840.07±0.460.01±0.10
CL2(Ours)0.00±0.000.00±0.000.00±0.00
WM [2]Pol10.27±0.940.00±0.000.00±0.00
CL2(Ours)0.00±0.000.00±0.000.00±0.00
", + "image_path": "3c9d3d4735bd7c59636f06d25824da59f73c826744cd71ad6a34b52d4463d0bc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 547, + 711 + ], + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 711 + ], + "type": "text", + "content": "Table 1. L1 distance between the estimated and expected re-basin with different network initializations and depths. Distances are scaled " + }, + { + "bbox": [ + 304, + 677, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\times 10^{3}" + }, + { + "bbox": [ + 304, + 677, + 547, + 711 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20242" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 185 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 185 + ], + "type": "table", + "html": "
MethodFirst degree polynomialThird degree polynomialMnistCifar10
AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓AUC ↓Barrier ↓
Naive0.31±0.380.62±0.710.25±0.150.58±0.330.34±0.081.07±0.210.73±0.121.23±0.18
WM [2]0.16±0.150.32±0.280.19±0.260.41±0.570.01±0.000.03±0.010.13±0.020.27±0.04
\\( \\mathcal{C}_{L2} \\) (Ours)0.05±0.060.10±0.120.05±0.060.12±0.120.01±0.000.02±0.000.09±0.020.19±0.03
STE [2]0.11±0.100.23±0.220.09±0.070.24±0.230.01±0.000.01±0.010.08±0.010.15±0.02
\\( \\mathcal{C}_{Mid} \\) (Ours)0.03±0.020.07±0.050.05±0.040.17±0.170.00±0.000.00±0.000.02±0.010.05±0.01
\\( \\mathcal{C}_{Rnd} \\) (Ours)0.01±0.010.03±0.020.01±0.010.03±0.030.00±0.000.01±0.000.02±0.010.06±0.01
", + "image_path": "e719ab64003c4d3aaff3b69a326cd9b7d1e5644bebbfb6e25934427c272765ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "text", + "content": "Table 2. AUC and loss Barrier results of linear mode connectivity for regression datasets (first and third-degree polynomial approximation), and classification datasets (Mnist and Cifar10). The WM method and our Sinkhorn with " + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2}" + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "text", + "content": " belong to the data-free category, while STE, Sinkhorn with " + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Rnd}" + }, + { + "bbox": [ + 46, + 192, + 546, + 226 + ], + "type": "text", + "content": " are data-driven." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 72, + 236, + 214, + 348 + ], + "blocks": [ + { + "bbox": [ + 72, + 236, + 214, + 348 + ], + "lines": [ + { + "bbox": [ + 72, + 236, + 214, + 348 + ], + "spans": [ + { + "bbox": [ + 72, + 236, + 214, + 348 + ], + "type": "image", + "image_path": "e959dd6bb08ef08e3280277a5220928a90ec41c69ec8d8848fc78619abab60e1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 228, + 236, + 369, + 348 + ], + "blocks": [ + { + "bbox": [ + 228, + 236, + 369, + 348 + ], + "lines": [ + { + "bbox": [ + 228, + 236, + 369, + 348 + ], + "spans": [ + { + "bbox": [ + 228, + 236, + 369, + 348 + ], + "type": "image", + "image_path": "a4a8cf1cabd388ff10db4b5f5a2ef931fe7582838312cb8fb3f5c3dc193a67e5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 378, + 236, + 523, + 348 + ], + "blocks": [ + { + "bbox": [ + 378, + 236, + 523, + 348 + ], + "lines": [ + { + "bbox": [ + 378, + 236, + 523, + 348 + ], + "spans": [ + { + "bbox": [ + 378, + 236, + 523, + 348 + ], + "type": "image", + "image_path": "a7104a10cd6d1a97054df46052afc0321e30c9c50a687471dea04d2d838399b4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 71, + 351, + 216, + 472 + ], + "blocks": [ + { + "bbox": [ + 71, + 351, + 216, + 472 + ], + "lines": [ + { + "bbox": [ + 71, + 351, + 216, + 472 + ], + "spans": [ + { + "bbox": [ + 71, + 351, + 216, + 472 + ], + "type": "image", + "image_path": "d91f4bbeee736758429907b85e1d48aeaffe96102a063af82201fa7424185b60.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "lines": [ + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "spans": [ + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "text", + "content": "Figure 4. Example of linear mode connectivity achieved by WM [2], STE [2], and our Sinkhorn re-basin with " + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2}" + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Rnd}" + }, + { + "bbox": [ + 45, + 480, + 546, + 514 + ], + "type": "text", + "content": " costs for a NN with two hidden layers. Accuracy and loss are shown for the Mnist and Cifar10 classification, while only the L2 loss is shown for the regression tasks. For Mnist, we include an amplified version of the loss and accuracy for better comparison." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 228, + 351, + 368, + 472 + ], + "blocks": [ + { + "bbox": [ + 228, + 351, + 368, + 472 + ], + "lines": [ + { + "bbox": [ + 228, + 351, + 368, + 472 + ], + "spans": [ + { + "bbox": [ + 228, + 351, + 368, + 472 + ], + "type": "image", + "image_path": "89113635364e208bcf8b94847dc56932f927173a30f4ba70c9aa92805c8e958b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 381, + 351, + 521, + 472 + ], + "blocks": [ + { + "bbox": [ + 381, + 351, + 521, + 472 + ], + "lines": [ + { + "bbox": [ + 381, + 351, + 521, + 472 + ], + "spans": [ + { + "bbox": [ + 381, + 351, + 521, + 472 + ], + "type": "image", + "image_path": "87db02a7507515e33d172ea1c332b5ced77549d1e456d56f33b519ae42537cde.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 535, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 287, + 571 + ], + "type": "text", + "content": "the estimated cost curve within the linear path. Both measures achieve the best performance when a method provides a low value, with a lower bound of 0." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "We compare our approach with different objectives – L2 (Eq. (7)), Middle point (Eq. (8)), and Random point (Eq. (9)) with the recently introduced WM and Straight-Through Estimator (STE) [2]. Tab. 2 summarizes the performance of the methods for each dataset. All experiments used a NN with two hidden layers. The table shows that our methods outperform state-of-art methods with (the first three rows) and without considering the data (last three rows) during the re-basin. Specifically, our " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " method exceeded WM for both AUC and Barrier measures for all datasets, except Mnist, where no significant differences" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": "were observed. Our other proposals outperform the state-of-art STE approach for AUC and Barrier in the data-driven category. In particular, our " + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Rnd}" + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": " loss showed the best results, comparable to our " + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": " for more challenging scenarios like Cifar10. Note that STE and our " + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": " have the same objective, and their difference in performance lies in the solver. Additionally, our " + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2},\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Rnd}" + }, + { + "bbox": [ + 304, + 535, + 545, + 656 + ], + "type": "text", + "content": " share the same architecture but with various loss functions, and their discrepancy in performance lies in the objective. As a general point, all methods significantly improve the naive path." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "We show the obtained loss and accuracy curves over the linear path before doing a re-basin (naive) and after applying WM, STE, and Sinkhorn with " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{L2}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Mid}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{Rnd}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " methods in Fig. 4. Please note that our method can also" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20243" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 121, + 70, + 472, + 184 + ], + "blocks": [ + { + "bbox": [ + 121, + 70, + 472, + 184 + ], + "lines": [ + { + "bbox": [ + 121, + 70, + 472, + 184 + ], + "spans": [ + { + "bbox": [ + 121, + 70, + 472, + 184 + ], + "type": "table", + "html": "
MethodRotated MnistSplit Cifar100
Accuracy ↑Forgetting ↓Accuracy ↑Forgetting ↓
Finetune46.28±1.010.52±0.0135.41±0.950.49±0.01
EWC [14]59.92±1.710.34±0.0250.50±1.330.24±0.02
LwF [17]61.86±3.660.29±0.0641.43±4.060.51±0.01
A-GEM [7]68.47±0.900.28±0.0144.42±1.460.36±0.01
Rebasin /w replay (Ours)78.14±0.500.12±0.0151.34±0.740.07±0.02
Joint training90.84±4.300.0060.48±0.540.00
", + "image_path": "b0ff6cc63eeb0b4956233a50696bc64fadea76b5fcdeae8d674841c2daeacb42.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 192, + 525, + 204 + ], + "lines": [ + { + "bbox": [ + 67, + 192, + 525, + 204 + ], + "spans": [ + { + "bbox": [ + 67, + 192, + 525, + 204 + ], + "type": "text", + "content": "Table 3. Performance of our proposed and state-of-art methods on the continual learning benchmark datasets over 20 episodes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 225, + 287, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 287, + 250 + ], + "type": "text", + "content": "perform re-basin of convolutional architectures with residual connections, as shown in supplementary materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 259, + 224, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 224, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 224, + 274 + ], + "type": "text", + "content": "5.3. Incremental learning application" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "text", + "content": "This experiment seeks to compare our method with other well-known continual learning approaches from the literature. Since our proposal can fit the regularization techniques that use replay, we compare it with different algorithms within this category. In particular, we compared 3 regularization-based approaches - elastic weight consolidation (EWC) [14], learning without forgetting (LwF) [17], and average gradient episodic memory (A-GEM) [7]. The average accuracy was calculated to measure the overall performance of model " + }, + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "text", + "content": " in the first episodes " + }, + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "inline_equation", + "content": "\\mathbb{T}_j" + }, + { + "bbox": [ + 46, + 279, + 287, + 422 + ], + "type": "text", + "content": ". In addition, the forgetting measure averages the forgetting in terms of accuracy for each domain or task in the episode." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "type": "text", + "content": "Given the variety of libraries and implementations, we limited our comparison to reproducible methods that could be used in the Avalanche environment [18]. All measurements, benchmarks, networks, and algorithms, including our own, were implemented using the framework. While we attempted to incorporate other recent approaches like MC-SGD [22] and Stable SGD [23] into Avalanche, a high discrepancy was observed w.r.t. their reported results and, therefore, we did not include them into our study. Difficulties in adapting MC-SGD to new conditions have also been observed by other authors [20]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 556, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 653 + ], + "type": "text", + "content": "We focused our experiments on low episodic memory scenarios, using only five examples per class for both benchmarks in methods that rely on memory replay (A-GEM and our method). We used a NN with one hidden layer and 256 neurons for the Rotated Mnist benchmark. For the Split Cifar100 benchmark, a multi-head ResNet18 was used following the settings in [22, 23]. In this experiment, we only apply the re-basin to linear layers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Tab. 3 shows methods' accuracy and forgetting performance on the benchmarks Rotated Mnist and Split Cifar100 datasets using 20 episodes. Our method outperforms the others and still performs better or comparable to those reported in [23]. The reader should pay special attention" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "text", + "content": "to the low values of forgetting achieved using our re-basin approach. This is a consequence of setting the value of " + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "inline_equation", + "content": "\\alpha = 0.8" + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "text", + "content": " when fusing the models (Eq. (12)). A-GEM is ranked second in accuracy and forgetting for Rotated Mnist. LwF showed a similar forgetting to A-GEM in this benchmark. On Split Cifar100, EWC ranked second for both measures. Despite having similar accuracy to our approach, the high forgetting value suggests stability issues. In general, the method showed to be robust to the values " + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 224, + 547, + 357 + ], + "type": "text", + "content": ". We included the corresponding ablation in supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 367, + 379, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 367, + 379, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 367, + 379, + 380 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 387, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 651 + ], + "type": "text", + "content": "This work proposes a new method based on the Sinkhorn operator to estimate permutation matrices that make two neural network models equivalent. With respect to previous work, such as weight matching, our method is (i) more flexible because it is differentiable and can be applied with any loss, (ii) estimates the permutations for all layers at the same time, avoiding getting stuck in local minima, (iii) more accurate, as shown in our experimental evaluation on well-known benchmarks. First, our experiments yielded perfect results when our approach was evaluated to produce the optimal permutation between a model and its artificially permuted transformation. We have also used our approach for linear mode connectivity, showing better connectivity (lower loss barrier) than weight matching. Finally, we showed that our efficient and differentiable approach for re-basin can easily be applied to the challenging task of continual learning, producing results comparable to, or better than state-of-art approaches. As a limitation to our work, we observed from our experiments and analysis of the literature that linear assignment problems solved with greedy Hungarian-based approaches are generally more efficient in terms of memory than the Sinkhorn operator." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by Distech Controls Inc., the Natural Sciences and Engineering Research Council of Canada, and the Digital Research Alliance of Canada." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20244" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Ryan Prescott Adams and Richard S Zemel. 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(left) Image generation trained on multiple few-shot generation datasets, such as 100-shot Obama [1], Panda [1], and Animal Face-Cat (A-Cat) [2]; (right) FID scores vs. CIFAR-10 [3] training set size with training cost, FLOPs. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 511, + 287, + 864, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 267, + 551, + 346, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Training Generative Adversarial Networks (GANs) on high-fidelity images usually requires a vast number of training images. Recent research on GAN tickets reveals that dense GANs models contain sparse sub-networks or \"lottery tickets\" that, when trained separately, yield better results under limited data. However, finding GANs tickets requires an expensive process of train-prune-retrain. In this paper, we propose Re-GAN, a data-efficient GANs training that dynamically reconfigures GANs architecture during training to explore different sub-network structures in training time. Our method repeatedly prunes unimportant connections to regularize GANs network and regrows them to reduce the risk of prematurely pruning important connections. Re-GAN stabilizes the GANs models with less data and offers an alternative to the existing GANs tickets and progressive growing methods. We demonstrate that Re-GAN is a generic training methodology which achieves stability on datasets of varying sizes, domains, and resolutions (CIFAR-10, TinyImageNet, and multiple few-shot generation datasets) as well as different GANs architectures (SNGAN, ProGAN,", + "bbox": [ + 111, + 585, + 503, + 891 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "StyleGAN2 and AutoGAN). Re-GAN also improves performance when combined with the recent augmentation approaches. Moreover, Re-GAN requires fewer floating-point operations (FLOPs) and less training time by removing the unimportant connections during GANs training while maintaining comparable or even generating higher-quality samples. When compared to state-of-the-art StyleGAN2, our method outperforms without requiring any additional fine-tuning step. Code can be found at this link: https://github.com/IntellicentAI-Lab/Re-GAN", + "bbox": [ + 537, + 537, + 929, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 539, + 714, + 671, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, Generative adversarial networks (GANs) [4]–[7] have made great strides in generating high-fidelity images. The GANs models serve as the backbone of several vision applications, such as data augmentation [5], [8], [9], domain adaptation [10], [11], and image-to-image translation [14]–[16].", + "bbox": [ + 537, + 734, + 928, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of the GANs methods largely depends on a massive quantity of diverse training data, which is often time-consuming and challenging to collect [17]. Figure 1 shows how the performance of the StyleGAN2 [18] model drastically declines under the limited training data. As a", + "bbox": [ + 537, + 823, + 928, + 896 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16230", + "bbox": [ + 480, + 941, + 519, + 954 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "result, various new methods [1], [19], [20] have emerged to deal with the problem of insufficient data. Dynamic data-augmentation [1], [19]-[21] fills in the gap and stabilizes GANs training with less data. Very recently, [22], [23] introduced the lottery ticket hypothesis (LTH) in GANs (called \"GANs tickets\"), a complementary to the existing augmentation techniques. LTH identifies sparse sub-networks (called \"winning tickets\") that can be trained in isolation to match or even surpass the performance of unpruned models. [24] demonstrated that an identified GANs ticket can be used as a sparse structural prior to alleviate the problem of limited data in GANs. However, identifying these winning tickets requires many iterations of a time-consuming and computationally expensive train-prune-retrain process. This results in high training time and a number of floating-point operations (FLOPs) than training a dense GANs models, such as StyleGAN2 [18] and BigGAN [5]. In addition, these methods train a full-scale model before pruning, and then, after the pruning process, they engage in an extra fine-tuning to improve the performance. Given this perspective, we ask:", + "bbox": [ + 109, + 89, + 501, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Is there any way to achieve training efficiency w.r.to both data and computation in GANs while preserving or even improving its performance?", + "bbox": [ + 111, + 402, + 503, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One potential solution is network pruning during training, which can allow the exploration of different subnetwork structures in training-time. Network structure exploration during training has shown to be effective in a variety of domains [25], [26], and its properties have been the subject of a significant amount of research [27], [28]. However, network pruning is never introduced to GANs training; as a result, the investigation of different subnetwork structures exploration during GANs training remains mysterious.", + "bbox": [ + 109, + 453, + 500, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this gap in the literature, we investigate and introduce the network pruning, i.e., connections, in GANs training by dynamically reconfiguring GANs architecture to allow the exploration of different sub-network structures in training time, dubbed as Re-GAN. However, on the other hand, it is common knowledge that the learning capabilities of the two competing networks—a generator (G) and a discriminator (D), need to be carefully maintained equilibrium in their respective capabilities for learning. Hence to build Re-GAN, the first question is: how to explore different network structures during GANs training? Network pruning during training regularizes the G to allow a robust gradient flow through G. This stabilizes the GANs models under limited training data and improves training efficiency. Re-GAN repeatedly prunes and grows the connections during the training process to reduce the risk of pruning important connections prematurely and prevent the model from losing its representational capabilities early in the training process. As a result, network growing provides a second opportunity to", + "bbox": [ + 109, + 599, + 503, + 891 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "reinitialize pruned connections by reusing information from previously explored sub-network structures.", + "bbox": [ + 537, + 90, + 926, + 119 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/29248e15189d4b11f0c6d202b6ea763d8e930e1f78433910e03ccf70cac89735.jpg", + "image_caption": [ + "Figure 2: Conventional GANs training has fixed connectivity space. Re-GAN uses network pruning and growing during training to make connectivity space flexible that helps in the propagation of robust gradients. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 550, + 128, + 916, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second question is: how to explore different subnetwork structures in $G$ and $D$ simultaneously? On the one hand, if we employ a pretrained $D$ (or $G$ ) and prune solely for $G$ (or $D$ ), it can quickly incur an imbalance between the capabilities of $D$ or $G$ (particularly in the early stage of training), resulting in slow convergence. While it is possible to prune for $G$ and $D$ simultaneously, empirical experiments show that doing so significantly degrades the initial unstable GANs training, resulting in highly fluctuating training curves and, in many cases, a failure to converge. As a trade-off, we propose expanding $D$ as per standard GANs training while applying pruning exclusively to $G$ 's architecture.", + "bbox": [ + 537, + 337, + 928, + 526 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, our method is robust, working well with a wide range of GANs architectures (ProGANs [29], SNGAN [30], StyleGAN2, and AutoGAN [31], [32]) and datasets (CIFAR-10 [3], Tiny-ImageNet [33], Flickr Faces HQ [34], and many few-shot generation datasets). We find that exploring different sub-network structures during training accounts for a significant decrease in FID score compared to the vanilla DCGAN [35] architecture without a pre-trained model or fine-tuning the pruned model (see Figure 2). Our method delivers higher performance in less training time to state-of-the-art (SOTA) methods on most available datasets without additional hyperparameters that progressive growing method introduces, such as training schedules and learning rates for different generation stages (resolutions). This robustness allows the Re-GAN to be easily generalized on unseen datasets.", + "bbox": [ + 537, + 526, + 928, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To the best of our knowledge, Re-GAN is the first attempt to incorporate network pruning during GANs training. Our technical innovations are as follows:", + "bbox": [ + 537, + 758, + 926, + 801 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We conduct the first in-depth study on taking a unified approach of incorporating pruning in GANs training without pre-training a large model or fine-tuning the pruned model.", + "- Our method repeatedly prunes and grows the connections during training to reduce the possibility of" + ], + "bbox": [ + 539, + 803, + 928, + 891 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16231", + "bbox": [ + 480, + 941, + 517, + 954 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pruning important connections and helps the model to maintain its representation ability early in training. Thus, network growing gives another chance to reinitialize pruned connections from the explored network sub-structures.", + "bbox": [ + 140, + 90, + 501, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- Extensive experiments are conducted across a wide range of GANs architectures and demonstrated that Re-GAN could be easily applied on these GANs architectures to improve their performances, both in regular and low-data regime setups. For example, for the identified winning GANs ticket, ProGAN and StyleGAN2 on full CIFAR-10, we achieve $70.23\\%$ , $18.81\\%$ , and $19\\%$ training FLOPs savings, respectively, while improved generated sample quality for both full and $10\\%$ training data. Re-GAN presents a viable alternative to the GANs tickets and progressive growing techniques. Additionally, the performance of Re-GAN is enhanced when integrated with recent augmentation techniques.", + "bbox": [ + 112, + 162, + 501, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 112, + 382, + 264, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stabilize the GANs training. In recent years, different loss functions [4], [36], [37], regularization [30], [38], and architectural designs [39], [40] have all been proposed as ways to enhance GANs [6]. Our efforts are in the category of network architecture design. Recently, state-of-the-art (SOTA) models like StyleGAN2 and BigGAN have suggested making networks deeper and wider. They have also shown that training deep GANs networks usually leads to better generalization. However, a deeper model with more convolution layers results in a longer training time for GANs. This is because a deeper model contains a greater number of model parameters and a weaker gradient flow via G [29], [41], [42]. The findings of Progressive GAN (ProGAN) [29] show that gradually growing and training both networks together from a lower resolution, stabilizes the training and enhances the generation quality. MSG-GAN [39] introduced a solution to the gradient flow issue in which G gets feedback from a number of different resolutions simultaneously. Nevertheless, these methods further add to the computational cost, necessitating an even high amount of GPU memory and more training time.", + "bbox": [ + 116, + 404, + 500, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GANs compression. GANs, like other deep neural networks, excel in image generation and translation tasks [29], [43]–[45], but suffer from high computational complexity and memory requirements. Han et al. [46] introduced a co-evolutionary pruning technique for GANs compression, while Wang et al. [47] proposed quantizing GANs to 1 or 2 bits. Li et al. [48] used distillation to improve compressed D with a pre-trained GANs model, and Wang et al. [49] combined these three techniques into one framework. Although impressive results were achieved in training compressed G with a pre-trained D [50], existing GANs compression approaches require pre", + "bbox": [ + 111, + 710, + 501, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "training an over-parameterized model, limiting training efficiency. Meanwhile, [51] proposed dynamic network size modification during training, but design space exploration is constrained by network augmentation. Our approach injects sparsity during training to enhance generalization, stabilize GANs with limited data, and improve training efficiency, distinguishing it from these inference-focused techniques.", + "bbox": [ + 537, + 90, + 928, + 205 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lottery Ticket Hypothesis (LTH). Recently, [22]–[24] have shown the existence of winning tickets in the min-max game beyond minimization by extending LTH to GANs. [52] claims the existence of independently trainable sparse sub-networks capable of performing at the same level as dense networks and in some instances, even better. While [53], [54] scaled up LTH by rewinding [55], [56]. However, these methods do not restore key connections that have been prematurely pruned, which restricts the model's capacity. In contrast, the proposed method can restore connections that have been prematurely pruned and can better preserve the capacity of the model.", + "bbox": [ + 537, + 207, + 928, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the other hand, the total number of FLOPs necessary to locate and train a winning ticket at a sparsity level of $80\\%$ is more than four times as many as the number of FLOPs necessary to train a dense model [57]. As the size of SOTA models have grown (e.g., BigGAN and StyleGAN2), such huge resource needs would cause financial and environmental problems [58]–[60]. Being unique and orthogonal efforts from ours, these methods do not focus on the training efficiency yet.", + "bbox": [ + 537, + 381, + 929, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 537, + 527, + 676, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Design motivation", + "text_level": 1, + "bbox": [ + 537, + 564, + 718, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The synaptic connection topology of the brain is very dynamic, yet the brain still maintains a stable and efficient computing function [61], [62]. It has been shown that the underlying process of synaptic rewiring plays a crucial part in learning [63]. We consider the training of GANs to be akin to such biological learning processes and combine it with different training objectives under sparsity constraint.", + "bbox": [ + 537, + 587, + 928, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to conventional GANs training with predefined static connectivity, we prune and grow the connections during the GANs training. We conduct a thorough investigation to find that introducing network pruning and growing into GANs training yields desirable results on many fronts, specifically: (1) stabilizes GANs across various datasets, resolutions, domains, and architectures; (2) maintaining comparable or even generating higher-quality samples; and (3) enhancing the GANs training efficiency w.r.t both data and computation by removing the unimportant connections.", + "bbox": [ + 537, + 690, + 928, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the next sub-section, we review the traditional GANs models, then describe in detail our proposed GANs training methodology via architectural reconfiguration.", + "bbox": [ + 537, + 848, + 928, + 893 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16232", + "bbox": [ + 480, + 941, + 519, + 954 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/25cbf60c2f4de0e574847ff9931a1e632675b888eb828f2b5a9d111fa0c703a9.jpg", + "image_caption": [ + "Figure 3: Architecture of Re-GAN, shown here on the base model proposed in GANs [6]. The key feature of Re-GAN is that it provides sparse-dense model pairs at the end of the training process. This is beneficial in practice, as it may be desired to deploy compressed variant in resource-constrained environments without redoing the full training process." + ], + "image_footnote": [], + "bbox": [ + 155, + 88, + 885, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Generative Adversarial Networks", + "text_level": 1, + "bbox": [ + 112, + 410, + 408, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A GANs model consists of a discriminator $\\mathrm{D}$ and a generator $\\mathrm{G}$ . The training objectives of the $\\mathrm{D}$ and $\\mathrm{G}$ can be represented as $\\theta_{D}$ and $\\theta_{G}$ , respectively. The GANs framework can be as follows:", + "bbox": [ + 111, + 433, + 501, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x)) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z))) ] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 498, + 500, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D (G (z))\\right) \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 537, + 500, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_{z}$ is the prior distribution (e.g., $N(0, I)$ ) and $p_{data}$ is the real training data used to approximate the data distribution. The notations $f_{D}, f_{G}$ , and $g_{G}$ in Eq. (1) and (2) represent the mapping functions from which various GANs losses can be derived [64].", + "bbox": [ + 111, + 568, + 501, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. GANs training with architectural reconfiguration", + "text_level": 1, + "bbox": [ + 112, + 656, + 408, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A network's topology is equivalent to a directed acyclic graph with a predetermined order of nodes. Each node $X_{\\mathrm{in}}$ serves as an input feature, and each edge functions as a computation cell with hyperparameters. We parameterize architectural space by associating a mask variable $m \\in \\{0,1\\}$ with each computation cell to enable training time pruning ( $m = 1 \\rightarrow 0$ ) and growing ( $m = 0 \\rightarrow 1$ ). We consider a single-level configuration space for GANs architecture that enables dynamic pruning and growing networks width-wise.", + "bbox": [ + 111, + 695, + 500, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Revisiting GANs training. Re-GAN reconfigures G's architecture to explore different sub-network structures during training. As shown in Algorithm 1, we start the", + "bbox": [ + 111, + 840, + 501, + 886 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "GANs training on the dense network for several iterations, warm-up phase, and learn the connection weights to know their importance. To achieve the sparse structure, we prune the least important weights based on the pre-defined pruning criterion. We then activate the pruned connections to further grow the network after a series of iterative optimizations. Once the network topology has been changed from sparse to dense, it will train the new network until the next connectivity update. The overview of ReGAN is shown in Figure 3. The main factors of Re-GAN training are as follows: 1) sparsity distribution, 2) update schedule, 3) pruning, and 4) grow.", + "bbox": [ + 537, + 393, + 928, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "GANs sub-networks exploration. We prune the low-weight connections by using unstructured magnitude pruning [65], [66] by using the binary masks $m_{g}$ and $m_{d}$ . The pruning ratio $\\rho$ determines the amount of weights removed during the pruning phase. We use $\\rho = 10\\%$ in all experiments except StyleGAN2 for FFHQ $(\\rho = 30\\%)$ . We use the same sparsity across all layers, i.e., uniform sparsity distribution. First, we sort the weights and produced a binary mask to exclude weights smaller than $\\lambda$ . If the mask of each layer that has to be regularized is calculated, then the mask of the whole parameter space, $M$ , can be obtained for both G and D. Consequently, Eq. 1 and 2 here become:", + "bbox": [ + 537, + 569, + 928, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x, \\theta_ {D} \\odot M _ {D})) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z, \\theta_ {G} \\odot M _ {G}))) ] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 752, + 954, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D \\left(G (z, \\theta_ {G} \\odot M _ {G})\\right)\\right) \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 805, + 924, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_{G}, M_{G}, \\theta_{D}$ and $M_{D}$ are the corresponding weights and masks for G and D, $\\odot$ stands for Hadamard product.", + "bbox": [ + 537, + 835, + 926, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The update schedule contains two key factors, (i) the update interval (g) is the number of training iterations", + "bbox": [ + 537, + 866, + 926, + 895 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16233", + "bbox": [ + 480, + 941, + 517, + 953 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "between the pruning and growing phase and vice versa; (ii) the learning rate, we set 1/10 the initial learning rate during the network growing phase. Other hyperparameters remained the same as per the given GANs network architecture.", + "bbox": [ + 109, + 90, + 501, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During each connectivity update, we use the weight magnitude as the indicator for pruning and make the following state transitions: if an indicator changes from 1 to 0, we remove the corresponding connection from the computational graph; During the network growing, all the pruned connections return to 1, indicating that the network will be grown back, initialized weights with 0 and trained. The network growing phase boosts the network's model capacity and makes it easier to get a better local minimum than with a sparse network topology. Similarly, growing new connections in G allows for the search for optimal connectivity and escape from undesired local minima. In addition, by deleting the least significant connections, our method considerably reduces both the training memory cost and the training time, hence enhancing training efficiency. We experiment with three distinct loss functions for the $\\mathrm{d}_{\\mathrm{crit}}$ function namely, WGAN-GP [67] which is used by ProGAN, hinge loss is used by SNGAN and non-saturating GAN loss with 1-sided GP [6] which is used by StyleGAN2.", + "bbox": [ + 109, + 162, + 503, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 112, + 469, + 318, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we perform experiments on various datasets that contain a wide range of content categories. We evaluate CIFAR-10 and Tiny-ImageNet at $64 \\times 64$ resolution, based on unconditional ProGAN [29][68], SNGAN [30][69], and SOTA StyleGAN2 [18][70]. We use the widely adopted evaluation metrics, such as the Fréchet Inception Distance (FID) [71] and Inception Score (IS) [4], and also provide the number of real images (#RI (in Millions (M)) [29][30]. If model $A$ is taking less number of real images and is achieving comparable or better results than model $B$ , it shows that model $A$ is efficient. Note that higher performing GANs models are indicated by lower FID ( $\\downarrow$ ), and larger IS ( $\\uparrow$ ). We further extend our study on $256^2$ resolution, we test on Animal-Face Dog and Cat [2], 100-Shot-Obama [1], Panda [1], and Grumpy-cat [1], and Oxford-flowers [72]. On $1024^2$ resolution, we test on 1k, 5k, 10k and 70k Flickr-Face-HQ (FFHQ) [34]. We also perform extensive ablation study to analyze the effectiveness of each component in Re-GAN.", + "bbox": [ + 109, + 491, + 503, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 112, + 782, + 328, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For ProGAN and StyleGAN2, for each dataset, we use the same 512-dimensional initial latent space, derived from a standard normal distribution $N(0, l)$ , followed by hypersphere normalization [29]. For SNGAN, the latent variable dimension is 128 for all datasets. For all experiments, we use the same hyperparameter settings.", + "bbox": [ + 109, + 805, + 501, + 893 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, we reduce the learning rate ten times during network growing phase for better learning. We initialize parameters using standard normal distribution $N(0,1)$ .", + "bbox": [ + 537, + 90, + 926, + 133 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We trained all models ourselves and used the same hardware to provide fair comparisons of the training times for the corresponding set of experiments. We use NVIDIA RTX 3090 GPU with 24 GB for all $64 \\times 64$ , and $256 \\times 256$ experiments, and NVIDIA Quadro RTX 8000 GPU with 48 GB for all $1024 \\times 1024$ experiments. We train for the same number of iterations predefined by the baseline models. We save the checkpoints every 10k iterations during training and report the best FID as well as the time it took to obtain that score from the checkpoints (e.g., happens at least after 15 hours of training for StyleGAN2).", + "bbox": [ + 537, + 133, + 929, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm1 Re-GAN training", + "text_level": 1, + "bbox": [ + 545, + 305, + 710, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: An L-layer GANs model; target sparsity k; total training iterations $\\mathrm{T}_{\\text{total}}$ ; training iterations between two consecutive steps, update interval $g$ ; training set $S$ ; learning rate $\\alpha$ ; \nOutput: Converged $G$ and $D$", + "bbox": [ + 544, + 321, + 926, + 369 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Randomly initialize all model weights $\\theta_{G} \\in \\mathbb{R}^{N}, \\theta_{D} \\in \\mathbb{R}^{N}$ ;", + "2. Train the weights $\\theta_{G}$ and $\\theta_{D}$ for $\\Delta_W$ epochs // warm-up phase", + "3. while each training iteration $t \\in [\\mathrm{T}_{\\mathrm{total}}]$ do", + "4. if mod $(\\mathrm{t},\\mathrm{g}) = 0$ then" + ], + "bbox": [ + 562, + 371, + 908, + 419 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "// entered a pruning phase", + "5. $\\theta_{G}\\gets T_{k}(\\theta_{G},k)$ //Apply compression(top-k)-", + "6. $\\theta_{D} \\gets T_{k}(\\theta_{D}, k) \\quad //$ operations on weights", + "7. $m_{G}, m_{D} \\gets 1[\\theta_{i} \\neq 0] // Create masks$", + "8. else", + "// entered a growing phase", + "9. $\\alpha = \\alpha * 0.1$ // reduce the learning rate by 10", + "10. $m_{G}, m_{D} \\gets 1_{N}$ // reset all masks", + "11. end if", + "12. Sample a mini-batch from $S$ ;", + "13. $\\theta_{G},\\theta_{D}\\gets \\theta_{G}\\odot m_{G},\\theta_{D}\\odot m_{D} / / \\mathrm{Update}\\theta_{G},\\theta_{D}$ by Eq. (3)", + "14. end while // and (4), respectively" + ], + "bbox": [ + 563, + 371, + 903, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For StyleGAN2, we find that using default settings is hardly to converge on CIFAR-10 and Tiny-/ImageNet, so we follow the settings in [4] for CIFAR-10, in which both path length regularization and lazy regularization are not used, the coefficient for R1 regularization $\\gamma$ is set to 0.1 for CIFAR-10, the output channel at final size level is 128 instead of 512 and doubled at each coarser level with a maximum 512. We use a similar setting for Tiny-/ImageNet except setting $\\gamma$ to 1. For few-shot learning, FFHQ experiments, we set $\\gamma$ to 10. We note a discrepancy between the results the author described scores and what we could able to accomplish using the author's provided code. This could be the result of subtle hardware variations or variations between runs.", + "bbox": [ + 537, + 580, + 929, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparison to state-of-the-art", + "text_level": 1, + "bbox": [ + 537, + 801, + 812, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the best-performing model ProGAN and StyleGAN2 and perform experiments at $64 \\times 64$ resolution on CIFAR-10 and Tiny-ImageNet. We evaluate our method with $100\\%$ data available and with $10\\%$ , $20\\%$ and $50\\%$ data available, with the findings summarized in Table", + "bbox": [ + 537, + 824, + 928, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16234", + "bbox": [ + 480, + 941, + 519, + 954 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1 and 2, respectively.", + "bbox": [ + 112, + 90, + 256, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The following observations can be drawn: First, Re-ProGAN and Re-StyleGAN2 can achieve consistently improved performance for all training cases, from complete data to limited data. In particular, likely to gain more when there is less training data available (e.g., $10\\%$ ), which is consistent with our design principle. With only $10\\%$ training data available, Re-ProGAN and Re-StyleGAN2 obtain massive gains of 29.33 FID/7.69 IS and 32.91 FID/7.35 IS on CIFAR-10, respectively, and 79.08", + "bbox": [ + 109, + 104, + 501, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FID/6.45 IS and 82.63 FID/6.47 IS on Tiny-ImageNet, respectively. Second, due to removing unimportant connections of low weights, Re-GAN consistently reduces the cost of computation associated with training and requires fewer total hours of GPU training time.", + "bbox": [ + 537, + 90, + 928, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results and precision-recall curve for Re-StyleGAN2 on CIFAR-10 is in the supplementary material. We also provide a study in the supplementary material to show that Re-GAN helps to alleviate mode collapse.", + "bbox": [ + 537, + 162, + 928, + 234 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a22f70ab59ec831f6a9119942ba1e3a70c7308b753a3e430fbad210c0193dfa0.jpg", + "table_caption": [ + "Table 1: FID comparison on few-shot datasets at $64\\times 64$ resolution. FID and IS are calculated using 10k randomly generated samples, with the test data (10k) serving as the reference distribution. The best performance is highlighted." + ], + "table_footnote": [], + "table_body": "
DatasetSizeMethods#Real Images (RI)(in M)Training Time (hour)FLOPs ×109IS↑FID↓
CIFAR-1050KProGAN19.511.612.978.05 ± 0.2026.14
Re-ProGAN15.99.810.538.22 ± 0.1921.17
StyleGAN217.714.25.08.76 ± 0.2213.19
Re-StyleGAN212.110.14.058.88 ± 0.2412.16
Tiny-ImageNet100KProGAN9.45327.479.44 ± 0.3140.27
Re-ProGAN8.748.922.189.57 ± 0.3537.47
StyleGAN219.252.521.0711.75 ± 0.2520.95
Re-StyleGAN217.846.717.0412.10 ± 0.2820.21
", + "bbox": [ + 129, + 268, + 913, + 409 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/94047b98934926f6c8fd70382bb1aba1b9118ba4fc6df2df3c512bd93bac96ea.jpg", + "table_caption": [ + "Table 2: Experiments on ${64} \\times {64}$ resolution ${50}\\% ,{20}\\%$ and ${10}\\%$ of training datasets. The best performance is highlighted." + ], + "table_footnote": [], + "table_body": "
DatasetMethods50% data20% data10% data
#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓
CIFAR-10ProGAN10.57.75±0.1928.337.27.51±0.1928.645.67.47±0.1630.08
Re-ProGAN9.47.97±0.1325.746.17.63±0.1827.194.97.69±0.2329.33
StyleGAN26.48.39±0.1517.224.17.36±0.2729.773.27.20±0.2436.45
Re-StyleGAN248.48±0.1616.093.87.46±0.2327.982.77.35±0.1332.91
Tiny-ImageNetProGAN9.68.71±0.274986.84±0.1277.867.76.38±0.1983.27
Re-ProGAN8.38.84±0.2546.787.76.92±0.1575.227.46.45±0.2279.08
StyleGAN214.511.02±0.2730.035.18.32±0.2465.263.26.32±0.1084.86
Re-StyleGAN213.211.25±0.3129.194.28.53±0.2962.341.36.47±0.1082.63
", + "bbox": [ + 101, + 431, + 939, + 583 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2452642c5fe74a61c88e2a57bb434cd470920498080a4342f21276ef8c130d4f.jpg", + "table_caption": [ + "Table 3: FID comparison to NAS-based GANs, i.e., AutoGAN for full CIFAR-10 dataset." + ], + "table_footnote": [], + "table_body": "
Methods#RI (M)Training time (hour)Flops (×1016)FID↓ Full data
AutoGAN (Top A)4.76.719M17.70
Re-AutoGAN (Top A)4.15.7216.5M17.61
AutoGAN (Top B)5.27.7523M18.08
Re-AutoGAN (Top B)4.25.9518M17.30
AutoGAN (Top C)5.78.1223M17.09
Re-AutoGAN (Top C)56.7320M16.61
", + "bbox": [ + 104, + 619, + 509, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We extend our method comparison with the NAS-based GANs method, i.e., AutoGAN (Top A, B and C architectures) [31], [32]. The result in Table 3 shows that Re-GAN not only improves the performance for human-designed networks (e.g., SNGAN, ProGAN, StyleGAN2) but also boosts the performance and reduces training time and FLOPs for automatically searched architecture, AutoGAN. It also minimizes training time and FLOPs for all top three searched GANs architectures.", + "bbox": [ + 109, + 758, + 501, + 891 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with GANs tickets", + "text_level": 1, + "bbox": [ + 537, + 611, + 816, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Recently, Iterative Magnitude Pruning (IMP), an unstructured magnitude pruning [24] have shown performing well in finding lottery tickets in GANs than other pruning methods [66], [73] to find GANs tickets [22], [23] [24]. We find GANs tickets using IMP at $20\\%$ and $46\\%$ pruning ratio for the full training dataset, named ST_SNGAN@20% and ST_SNGAN@46%, respectively. We also include growing with random initialization (RI), Re-SNGAN-RI in which weights are randomly initialized during the growing rather than zero initialization. Also, we set same learning rate for both dense and sparse phases, Re-SNGAN-lr. The results are summarized in Table 4. The results show that our proposed Re-SNGAN performs well w.r.t FID. Re-SNGAN-RI results in longer convergence times, as network has to explore more diverse weight configurations to find best solution. While, setting 1/10 learning rate during dense phase performs better than same learning rate in both phases as it promotes stability by", + "bbox": [ + 537, + 633, + 928, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16235", + "bbox": [ + 478, + 941, + 519, + 954 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "avoiding large, sudden weight updates. Also, finding GANs tickets is highly time consuming. While the training time for exploring different sub-network structures during training, even only at $10\\%$ pruning ratio, is comparable to the dense model; In addition, Re-SNGAN consumes less training FLOPs than the GANs tickets.", + "bbox": [ + 109, + 90, + 501, + 176 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/849f2af8ef23133d615479b249780a2d140d36d0ae25819419a351417731bf2b.jpg", + "table_caption": [ + "Table 4: Comparison to GANs tickets methods on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
Methods#RI (M)Training time (hour)Flops (×1017)FID↓ Full data
SNGAN@0%306.21.0120.12
ST_SNGAN@20%92.519.72.6018.96
ST_SNGAN@46%150323.4618.22
Re-SNGAN-Ir49.410.51.5719.06
Re-SNGAN-RI33.17.31.2519.71
Re-SNGAN31.56.61.0317.87
", + "bbox": [ + 107, + 196, + 506, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5ed4b2568be1786bd64434b963ca9af09ff63afbec5d095313bb6dc84fa7daf.jpg", + "image_caption": [ + "Figure 4: IS $(\\uparrow)$ and FID $(\\downarrow)$ results of SNGAN with $10\\%$ , $20\\%$ , $40\\%$ , $80\\%$ , and full training data of CIFAR-10. Four settings are evaluated: (i) SNGAN (unpruned SNGAN), (ii) ST_SNGAN (applied IMP for finding sparse GANs ticket at $20\\%$ pruning ratio), (iii) Sparse_Re-SNGAN (Re-GAN output is sparse), (iv) Dense_Re-SNGAN (Re-GAN output is dense). The main advantage is that it provides both a high-performing dense model and its compressed version at the end of the training." + ], + "image_footnote": [], + "bbox": [ + 542, + 89, + 732, + 198 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0965be78c124c3d504bc4653d223cd5d5e637fe66f75d5ba5a929ee05b06b18e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 89, + 924, + 198 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bb32b5c4c2aadd93655a5332f41865d27c56d0932455b4f7c11729ca8c4e9bc0.jpg", + "table_caption": [ + "Table 5: FID comparison on few-shot datasets at $256\\times 256$ resolution. FID and IS are calculated using 5k randomly generated samples, with the training data serving as the reference distribution. The best performance is highlighted." + ], + "table_footnote": [], + "table_body": "
MethodsObamaGrumpy CatPandaAnimal FaceOxford Flowers
CatDog
# of images1001001003891601000
ProGAN129.52135.89235.86289.73259.32224.70
Re-ProGAN110.46124.06205.82283.29227.59198.56
StyleGAN286.6751.395.0881.91157.63147.67
Re-StyleGAN272.9238.2378.4573.05133.4138.35
StyleGAN2 + APA68.7433.7218.2462.7181.1385.88
Re-StyleGAN2 + APA64.2831.7416.3360.2677.4482.19
StyleGAN2 + DiffAug46.3128.612.8942.8558.4746.21
Re-StyleGAN2 + DiffAug45.727.3612.642.1157.245.13
", + "bbox": [ + 140, + 354, + 900, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide another set of experiments of SNGAN training on CIFAR-10, with training data ranging from $10\\%$ to $100\\%$ . Figure 4 provides a summary of the key findings. The following observations can be drawn: First, at the same data availability (from $10\\%$ to even $100\\%$ ), exploring multiple sub-networks during training at only $10\\%$ pruning ratio is always preferable to training the dense model and sparse ticket; Second, sparse Re-GAN model is also performing consistently well than GANs tickets.", + "bbox": [ + 109, + 520, + 501, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Few-shot generation", + "text_level": 1, + "bbox": [ + 112, + 666, + 307, + 683 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Collecting a large number of image datasets can be prohibitively costly or perhaps impossible for a certain character or a topic. In this context, a data-efficient model for the image synthesis task will be highly important. In Table 5, we show that our method finds data-efficient GANs that can be trained from scratch with only 100 training image data (without any pre-training) and demonstrates consistently superior performance (See supplementary material for visualizations of few-shot generation and style interpolation). Results also show that proposed Re-GAN improve the generated sample quality of SOTA methods, such as Diffaug [1] and APA [21] for few-shot datasets. We further extend our study for high-resolution experiments (Table 6 and Figure 5) where the", + "bbox": [ + 109, + 689, + 503, + 893 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Re-StyleGAN2 model gets better FID scores on all 1k, 5k, 10k and 70k FFHQ datasets (see supplementary material for more details). To further demonstrate the effectiveness of our Re-GAN, we apply it to other recent methods, FastGAN [74] for several few-shot datasets. Results are shown in supplementary material.", + "bbox": [ + 537, + 520, + 928, + 608 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0cdb0e89561d0f763bb9a266dda36010470b7b2abf065e1bcac8f95864220759.jpg", + "table_caption": [ + "Table 6: FID comparison on few-shot datasets at $1024 \\times 1024$ resolution. FID and IS are calculated using 50k randomly generated samples, with the training data (70k) serving as the reference distribution." + ], + "table_footnote": [], + "table_body": "
MethodsFFHQ
70k10k5k1k
StyleGAN24.3513.0621.7640.24
Re-StyleGAN24.1911.2219.1336.3
", + "bbox": [ + 540, + 670, + 928, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation and analysis", + "text_level": 1, + "bbox": [ + 537, + 742, + 743, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Prune G/D: We study the impact of exploring different sub-network structures on G or D only, or on both G and D (represented as B) at $10\\%$ , $30\\%$ , and $50\\%$ pruning ratio (i.e., weight remaining ratio indicates the sparsity levels of explored sub-network structures during training) on CIFAR-10 full training dataset. Figure 6 shows a summary of the results. We notice that employing pruning on D or both G and D, achieves comparable or better performance than the base model. While for the same sparsity", + "bbox": [ + 537, + 765, + 929, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16236", + "bbox": [ + 478, + 941, + 519, + 954 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "distribution (i.e., pruning ratio), pruning only on G achieves significant performance improvement (i.e., largely reducing the FID). We also notice that update interval (g) 100 works well with only G.", + "bbox": [ + 112, + 90, + 501, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b504987451e00754a2b43be72e3217e14d989697e883039eb675bcd4cedd0fef.jpg", + "image_caption": [ + "Figure 5: Few-shot generalization results of Re-StyleGAN2 on 10k FFHQ (1024×1024). Samples are randomly drawn without cherry picking." + ], + "image_footnote": [], + "bbox": [ + 125, + 161, + 486, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness to learning rate. Previous research works [75]–[77] have observed that GANs convergence highly depends on the selection of hyperparameters, especially the learning rate, $\\alpha$ . As shown in Table 7, we validate our network by training it with five different $\\alpha$ values (0.0001, 0.0002, 0.0005, 0.0007, and 0.00001) for the CIFAR-10 dataset. Results show that for all different $\\alpha$ values, our models converged and achieved similar inception scores.", + "bbox": [ + 111, + 446, + 501, + 565 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/21232ef59f9a4b13640fdfd204e52278edb7a79450f045ec12d994ae052b828e.jpg", + "image_caption": [ + "Figure 6: FID with different pruning ratio and update interval (g) of Re-SNGAN (CIFAR-10)." + ], + "image_footnote": [], + "bbox": [ + 174, + 571, + 439, + 714 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47241a72b20693e231034cef6005ddf85d1a73082c140d706ab9764862ce781c.jpg", + "image_caption": [ + "Figure 7: Stability during training on the $10\\%$ CIFAR-10." + ], + "image_footnote": [], + "bbox": [ + 168, + 741, + 444, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Stability during training. To compare the stability of Re-SNGAN with SNGAN, we evaluate how the samples produced for the same set of latent points vary during training. As proposed in [30], we use the mean squared error (MSE) between two consecutive generated samples as a quantitative measure of training stability. Figure 7 shows the MSE between generated images from the same latent code in the midst of successive epochs on the $10\\%$ CIFAR-10 dataset. Results show that dense Re-SNGAN converges consistently over time, while SNGAN varies dramatically across epochs.", + "bbox": [ + 537, + 90, + 928, + 251 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1d0444c06eb26990e6114fa794dbbffd41a8a4e94a7ae9fe73908e39e2d13583.jpg", + "table_caption": [ + "Table 7: Robustness to learning rate." + ], + "table_footnote": [], + "table_body": "
MethodsLearning rateResults
ISFID
Real images-11.34-
SNGAN0.00028.07±0.1620.12
0.00077.93±0.3021.76
0.00058.03±0.2320.17
Re-SNGAN0.00028.16±0.1517.87
0.00018.03±0.1719.03
0.000018.01±0.2519.65
", + "bbox": [ + 568, + 273, + 898, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Discussion of Broader Impact", + "text_level": 1, + "bbox": [ + 537, + 412, + 883, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce a new perspective on data-efficient GANs by exploring different sub-network structures during training, which is a novel approach compared to existing methods. Extensive experiments on various GANs architectures, objectives, and datasets demonstrate the effectiveness and training efficiency of our proposed GANs training methodology, Re-GAN. In this work, we focus on unstructured sparsity to showcase the algorithm-level innovations of Re-GAN. However, only specific hardware supports sparse tensor cores for weight pruning. Future work could aim for a high pruning ratio and reconfigure network width and depth simultaneously during GANs training, addressing the limitations of the current approach.", + "bbox": [ + 537, + 452, + 928, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research aims to enhance generalization performance, stabilize GANs models under limited data, and improve training efficiency, which has practical implications for various applications and industries. However, these advancements might also exacerbate existing social risks associated with GANs. We plan to investigate whether the sparse structures affect issues like image generation bias in future work. The ability to generate images with less data could potentially be exploited for undesirable applications, such as DeepFakes.", + "bbox": [ + 537, + 655, + 928, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 539, + 816, + 697, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by PolyU Internal Start-up Fund (Grant no: P0038876), Research Impact Fund (No. R5034-18), and RGC Collaborative Research Fund (Grant no: C5026-18G).", + "bbox": [ + 537, + 838, + 928, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16237", + "bbox": [ + 480, + 941, + 517, + 954 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 130, + 90, + 210, + 103 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] S. Zhao, Z. Liu, J. Lin, J. Y. Zhu, and S. 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Available: http://arxiv.org/abs/1611.02163." + ], + "bbox": [ + 114, + 89, + 503, + 875 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16240", + "bbox": [ + 480, + 941, + 519, + 954 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Re-GAN_ Data-Efficient GANs Training via Architectural Reconfiguration/33c6c6a6-066b-4807-b712-d7b820960347_model.json b/2023/Re-GAN_ Data-Efficient GANs Training via Architectural Reconfiguration/33c6c6a6-066b-4807-b712-d7b820960347_model.json new file mode 100644 index 0000000000000000000000000000000000000000..35699e28d6c88e3fe5ab33f03d5468bf78848a96 --- /dev/null +++ b/2023/Re-GAN_ Data-Efficient GANs Training via Architectural Reconfiguration/33c6c6a6-066b-4807-b712-d7b820960347_model.json @@ -0,0 +1,2576 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.152, + 0.105, + 0.89, + 0.127 + ], + "angle": 0, + "content": "Re-GAN: Data-Efficient GANs Training via Architectural Reconfiguration" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.154, + 0.76, + 0.173 + ], + "angle": 0, + "content": "Divya Saxena, Jiannong Cao, Jiahao Xu, Tarun Kulshrestha" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.174, + 0.732, + 0.19 + ], + "angle": 0, + "content": "The Hong Kong Polytechnic University, Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.321, + 0.19, + 0.721, + 0.206 + ], + "angle": 0, + "content": "{divsaxen, csjcao}@comp.polyu.edu.hk," + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.206, + 0.804, + 0.221 + ], + "angle": 0, + "content": "jiahaoxxuu@gmail.com, tarun.kulshrestha@polyu.edu.hk" + }, + { + "type": "image_caption", + "bbox": [ + 0.246, + 0.258, + 0.434, + 0.273 + ], + "angle": 0, + "content": "Few-shot learning training set" + }, + { + "type": "image", + "bbox": [ + 0.175, + 0.274, + 0.506, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.288, + 0.866, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.471, + 0.92, + 0.524 + ], + "angle": 0, + "content": "Figure 1: Results of our proposed Re-GAN where dynamically GANs architecture is reconfigured to explore different GANs subnetwork structures during training time. (left) Image generation trained on multiple few-shot generation datasets, such as 100-shot Obama [1], Panda [1], and Animal Face-Cat (A-Cat) [2]; (right) FID scores vs. CIFAR-10 [3] training set size with training cost, FLOPs. Best viewed in color." + }, + { + "type": "title", + "bbox": [ + 0.269, + 0.553, + 0.347, + 0.569 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.586, + 0.504, + 0.892 + ], + "angle": 0, + "content": "Training Generative Adversarial Networks (GANs) on high-fidelity images usually requires a vast number of training images. Recent research on GAN tickets reveals that dense GANs models contain sparse sub-networks or \"lottery tickets\" that, when trained separately, yield better results under limited data. However, finding GANs tickets requires an expensive process of train-prune-retrain. In this paper, we propose Re-GAN, a data-efficient GANs training that dynamically reconfigures GANs architecture during training to explore different sub-network structures in training time. Our method repeatedly prunes unimportant connections to regularize GANs network and regrows them to reduce the risk of prematurely pruning important connections. Re-GAN stabilizes the GANs models with less data and offers an alternative to the existing GANs tickets and progressive growing methods. We demonstrate that Re-GAN is a generic training methodology which achieves stability on datasets of varying sizes, domains, and resolutions (CIFAR-10, TinyImageNet, and multiple few-shot generation datasets) as well as different GANs architectures (SNGAN, ProGAN," + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.538, + 0.93, + 0.685 + ], + "angle": 0, + "content": "StyleGAN2 and AutoGAN). Re-GAN also improves performance when combined with the recent augmentation approaches. Moreover, Re-GAN requires fewer floating-point operations (FLOPs) and less training time by removing the unimportant connections during GANs training while maintaining comparable or even generating higher-quality samples. When compared to state-of-the-art StyleGAN2, our method outperforms without requiring any additional fine-tuning step. Code can be found at this link: https://github.com/IntellicentAI-Lab/Re-GAN" + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.715, + 0.673, + 0.73 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.736, + 0.929, + 0.824 + ], + "angle": 0, + "content": "In recent years, Generative adversarial networks (GANs) [4]–[7] have made great strides in generating high-fidelity images. The GANs models serve as the backbone of several vision applications, such as data augmentation [5], [8], [9], domain adaptation [10], [11], and image-to-image translation [14]–[16]." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.824, + 0.929, + 0.897 + ], + "angle": 0, + "content": "The success of the GANs methods largely depends on a massive quantity of diverse training data, which is often time-consuming and challenging to collect [17]. Figure 1 shows how the performance of the StyleGAN2 [18] model drastically declines under the limited training data. As a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.942, + 0.52, + 0.955 + ], + "angle": 0, + "content": "16230" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.111, + 0.09, + 0.502, + 0.397 + ], + "angle": 0, + "content": "result, various new methods [1], [19], [20] have emerged to deal with the problem of insufficient data. Dynamic data-augmentation [1], [19]-[21] fills in the gap and stabilizes GANs training with less data. Very recently, [22], [23] introduced the lottery ticket hypothesis (LTH) in GANs (called \"GANs tickets\"), a complementary to the existing augmentation techniques. LTH identifies sparse sub-networks (called \"winning tickets\") that can be trained in isolation to match or even surpass the performance of unpruned models. [24] demonstrated that an identified GANs ticket can be used as a sparse structural prior to alleviate the problem of limited data in GANs. However, identifying these winning tickets requires many iterations of a time-consuming and computationally expensive train-prune-retrain process. This results in high training time and a number of floating-point operations (FLOPs) than training a dense GANs models, such as StyleGAN2 [18] and BigGAN [5]. In addition, these methods train a full-scale model before pruning, and then, after the pruning process, they engage in an extra fine-tuning to improve the performance. Given this perspective, we ask:" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.403, + 0.504, + 0.448 + ], + "angle": 0, + "content": "Is there any way to achieve training efficiency w.r.to both data and computation in GANs while preserving or even improving its performance?" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.454, + 0.501, + 0.599 + ], + "angle": 0, + "content": "One potential solution is network pruning during training, which can allow the exploration of different subnetwork structures in training-time. Network structure exploration during training has shown to be effective in a variety of domains [25], [26], and its properties have been the subject of a significant amount of research [27], [28]. However, network pruning is never introduced to GANs training; as a result, the investigation of different subnetwork structures exploration during GANs training remains mysterious." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.6, + 0.504, + 0.892 + ], + "angle": 0, + "content": "To address this gap in the literature, we investigate and introduce the network pruning, i.e., connections, in GANs training by dynamically reconfiguring GANs architecture to allow the exploration of different sub-network structures in training time, dubbed as Re-GAN. However, on the other hand, it is common knowledge that the learning capabilities of the two competing networks—a generator (G) and a discriminator (D), need to be carefully maintained equilibrium in their respective capabilities for learning. Hence to build Re-GAN, the first question is: how to explore different network structures during GANs training? Network pruning during training regularizes the G to allow a robust gradient flow through G. This stabilizes the GANs models under limited training data and improves training efficiency. Re-GAN repeatedly prunes and grows the connections during the training process to reduce the risk of pruning important connections prematurely and prevent the model from losing its representational capabilities early in the training process. As a result, network growing provides a second opportunity to" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.091, + 0.928, + 0.121 + ], + "angle": 0, + "content": "reinitialize pruned connections by reusing information from previously explored sub-network structures." + }, + { + "type": "image", + "bbox": [ + 0.551, + 0.129, + 0.917, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.279, + 0.92, + 0.332 + ], + "angle": 0, + "content": "Figure 2: Conventional GANs training has fixed connectivity space. Re-GAN uses network pruning and growing during training to make connectivity space flexible that helps in the propagation of robust gradients. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.338, + 0.929, + 0.527 + ], + "angle": 0, + "content": "The second question is: how to explore different subnetwork structures in \\( G \\) and \\( D \\) simultaneously? On the one hand, if we employ a pretrained \\( D \\) (or \\( G \\)) and prune solely for \\( G \\) (or \\( D \\)), it can quickly incur an imbalance between the capabilities of \\( D \\) or \\( G \\) (particularly in the early stage of training), resulting in slow convergence. While it is possible to prune for \\( G \\) and \\( D \\) simultaneously, empirical experiments show that doing so significantly degrades the initial unstable GANs training, resulting in highly fluctuating training curves and, in many cases, a failure to converge. As a trade-off, we propose expanding \\( D \\) as per standard GANs training while applying pruning exclusively to \\( G \\)'s architecture." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.527, + 0.929, + 0.759 + ], + "angle": 0, + "content": "Additionally, our method is robust, working well with a wide range of GANs architectures (ProGANs [29], SNGAN [30], StyleGAN2, and AutoGAN [31], [32]) and datasets (CIFAR-10 [3], Tiny-ImageNet [33], Flickr Faces HQ [34], and many few-shot generation datasets). We find that exploring different sub-network structures during training accounts for a significant decrease in FID score compared to the vanilla DCGAN [35] architecture without a pre-trained model or fine-tuning the pruned model (see Figure 2). Our method delivers higher performance in less training time to state-of-the-art (SOTA) methods on most available datasets without additional hyperparameters that progressive growing method introduces, such as training schedules and learning rates for different generation stages (resolutions). This robustness allows the Re-GAN to be easily generalized on unseen datasets." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.759, + 0.928, + 0.802 + ], + "angle": 0, + "content": "To the best of our knowledge, Re-GAN is the first attempt to incorporate network pruning during GANs training. Our technical innovations are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.804, + 0.928, + 0.861 + ], + "angle": 0, + "content": "- We conduct the first in-depth study on taking a unified approach of incorporating pruning in GANs training without pre-training a large model or fine-tuning the pruned model." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.863, + 0.929, + 0.892 + ], + "angle": 0, + "content": "- Our method repeatedly prunes and grows the connections during training to reduce the possibility of" + }, + { + "type": "list", + "bbox": [ + 0.54, + 0.804, + 0.929, + 0.892 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.943, + 0.518, + 0.955 + ], + "angle": 0, + "content": "16231" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.141, + 0.091, + 0.502, + 0.163 + ], + "angle": 0, + "content": "pruning important connections and helps the model to maintain its representation ability early in training. Thus, network growing gives another chance to reinitialize pruned connections from the explored network sub-structures." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.164, + 0.503, + 0.368 + ], + "angle": 0, + "content": "- Extensive experiments are conducted across a wide range of GANs architectures and demonstrated that Re-GAN could be easily applied on these GANs architectures to improve their performances, both in regular and low-data regime setups. For example, for the identified winning GANs ticket, ProGAN and StyleGAN2 on full CIFAR-10, we achieve \\(70.23\\%\\), \\(18.81\\%\\), and \\(19\\%\\) training FLOPs savings, respectively, while improved generated sample quality for both full and \\(10\\%\\) training data. Re-GAN presents a viable alternative to the GANs tickets and progressive growing techniques. Additionally, the performance of Re-GAN is enhanced when integrated with recent augmentation techniques." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.383, + 0.266, + 0.399 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.405, + 0.501, + 0.71 + ], + "angle": 0, + "content": "Stabilize the GANs training. In recent years, different loss functions [4], [36], [37], regularization [30], [38], and architectural designs [39], [40] have all been proposed as ways to enhance GANs [6]. Our efforts are in the category of network architecture design. Recently, state-of-the-art (SOTA) models like StyleGAN2 and BigGAN have suggested making networks deeper and wider. They have also shown that training deep GANs networks usually leads to better generalization. However, a deeper model with more convolution layers results in a longer training time for GANs. This is because a deeper model contains a greater number of model parameters and a weaker gradient flow via G [29], [41], [42]. The findings of Progressive GAN (ProGAN) [29] show that gradually growing and training both networks together from a lower resolution, stabilizes the training and enhances the generation quality. MSG-GAN [39] introduced a solution to the gradient flow issue in which G gets feedback from a number of different resolutions simultaneously. Nevertheless, these methods further add to the computational cost, necessitating an even high amount of GPU memory and more training time." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.711, + 0.503, + 0.886 + ], + "angle": 0, + "content": "GANs compression. GANs, like other deep neural networks, excel in image generation and translation tasks [29], [43]–[45], but suffer from high computational complexity and memory requirements. Han et al. [46] introduced a co-evolutionary pruning technique for GANs compression, while Wang et al. [47] proposed quantizing GANs to 1 or 2 bits. Li et al. [48] used distillation to improve compressed D with a pre-trained GANs model, and Wang et al. [49] combined these three techniques into one framework. Although impressive results were achieved in training compressed G with a pre-trained D [50], existing GANs compression approaches require pre" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.091, + 0.929, + 0.207 + ], + "angle": 0, + "content": "training an over-parameterized model, limiting training efficiency. Meanwhile, [51] proposed dynamic network size modification during training, but design space exploration is constrained by network augmentation. Our approach injects sparsity during training to enhance generalization, stabilize GANs with limited data, and improve training efficiency, distinguishing it from these inference-focused techniques." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.208, + 0.929, + 0.381 + ], + "angle": 0, + "content": "Lottery Ticket Hypothesis (LTH). Recently, [22]–[24] have shown the existence of winning tickets in the min-max game beyond minimization by extending LTH to GANs. [52] claims the existence of independently trainable sparse sub-networks capable of performing at the same level as dense networks and in some instances, even better. While [53], [54] scaled up LTH by rewinding [55], [56]. However, these methods do not restore key connections that have been prematurely pruned, which restricts the model's capacity. In contrast, the proposed method can restore connections that have been prematurely pruned and can better preserve the capacity of the model." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.382, + 0.93, + 0.513 + ], + "angle": 0, + "content": "On the other hand, the total number of FLOPs necessary to locate and train a winning ticket at a sparsity level of \\(80\\%\\) is more than four times as many as the number of FLOPs necessary to train a dense model [57]. As the size of SOTA models have grown (e.g., BigGAN and StyleGAN2), such huge resource needs would cause financial and environmental problems [58]–[60]. Being unique and orthogonal efforts from ours, these methods do not focus on the training efficiency yet." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.528, + 0.677, + 0.546 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.565, + 0.719, + 0.581 + ], + "angle": 0, + "content": "3.1. Design motivation" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.588, + 0.929, + 0.69 + ], + "angle": 0, + "content": "The synaptic connection topology of the brain is very dynamic, yet the brain still maintains a stable and efficient computing function [61], [62]. It has been shown that the underlying process of synaptic rewiring plays a crucial part in learning [63]. We consider the training of GANs to be akin to such biological learning processes and combine it with different training objectives under sparsity constraint." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.691, + 0.929, + 0.849 + ], + "angle": 0, + "content": "In contrast to conventional GANs training with predefined static connectivity, we prune and grow the connections during the GANs training. We conduct a thorough investigation to find that introducing network pruning and growing into GANs training yields desirable results on many fronts, specifically: (1) stabilizes GANs across various datasets, resolutions, domains, and architectures; (2) maintaining comparable or even generating higher-quality samples; and (3) enhancing the GANs training efficiency w.r.t both data and computation by removing the unimportant connections." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.849, + 0.929, + 0.895 + ], + "angle": 0, + "content": "In the next sub-section, we review the traditional GANs models, then describe in detail our proposed GANs training methodology via architectural reconfiguration." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.942, + 0.521, + 0.955 + ], + "angle": 0, + "content": "16232" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.089, + 0.887, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.348, + 0.93, + 0.389 + ], + "angle": 0, + "content": "Figure 3: Architecture of Re-GAN, shown here on the base model proposed in GANs [6]. The key feature of Re-GAN is that it provides sparse-dense model pairs at the end of the training process. This is beneficial in practice, as it may be desired to deploy compressed variant in resource-constrained environments without redoing the full training process." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.411, + 0.41, + 0.426 + ], + "angle": 0, + "content": "3.2. Generative Adversarial Networks" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.434, + 0.502, + 0.492 + ], + "angle": 0, + "content": "A GANs model consists of a discriminator \\( \\mathrm{D} \\) and a generator \\( \\mathrm{G} \\). The training objectives of the \\( \\mathrm{D} \\) and \\( \\mathrm{G} \\) can be represented as \\( \\theta_{D} \\) and \\( \\theta_{G} \\), respectively. The GANs framework can be as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.499, + 0.501, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x)) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z))) ] \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.538, + 0.501, + 0.564 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D (G (z))\\right) \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.569, + 0.503, + 0.643 + ], + "angle": 0, + "content": "where \\( p_{z} \\) is the prior distribution (e.g., \\( N(0, I) \\)) and \\( p_{data} \\) is the real training data used to approximate the data distribution. The notations \\( f_{D}, f_{G} \\), and \\( g_{G} \\) in Eq. (1) and (2) represent the mapping functions from which various GANs losses can be derived [64]." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.657, + 0.409, + 0.689 + ], + "angle": 0, + "content": "3.3. GANs training with architectural reconfiguration" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.696, + 0.501, + 0.841 + ], + "angle": 0, + "content": "A network's topology is equivalent to a directed acyclic graph with a predetermined order of nodes. Each node \\( X_{\\mathrm{in}} \\) serves as an input feature, and each edge functions as a computation cell with hyperparameters. We parameterize architectural space by associating a mask variable \\( m \\in \\{0,1\\} \\) with each computation cell to enable training time pruning (\\( m = 1 \\rightarrow 0 \\)) and growing (\\( m = 0 \\rightarrow 1 \\)). We consider a single-level configuration space for GANs architecture that enables dynamic pruning and growing networks width-wise." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.842, + 0.503, + 0.887 + ], + "angle": 0, + "content": "Revisiting GANs training. Re-GAN reconfigures G's architecture to explore different sub-network structures during training. As shown in Algorithm 1, we start the" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.395, + 0.929, + 0.57 + ], + "angle": 0, + "content": "GANs training on the dense network for several iterations, warm-up phase, and learn the connection weights to know their importance. To achieve the sparse structure, we prune the least important weights based on the pre-defined pruning criterion. We then activate the pruned connections to further grow the network after a series of iterative optimizations. Once the network topology has been changed from sparse to dense, it will train the new network until the next connectivity update. The overview of ReGAN is shown in Figure 3. The main factors of Re-GAN training are as follows: 1) sparsity distribution, 2) update schedule, 3) pruning, and 4) grow." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.57, + 0.929, + 0.747 + ], + "angle": 0, + "content": "GANs sub-networks exploration. We prune the low-weight connections by using unstructured magnitude pruning [65], [66] by using the binary masks \\( m_{g} \\) and \\( m_{d} \\). The pruning ratio \\( \\rho \\) determines the amount of weights removed during the pruning phase. We use \\( \\rho = 10\\% \\) in all experiments except StyleGAN2 for FFHQ \\( (\\rho = 30\\%) \\). We use the same sparsity across all layers, i.e., uniform sparsity distribution. First, we sort the weights and produced a binary mask to exclude weights smaller than \\( \\lambda \\). If the mask of each layer that has to be regularized is calculated, then the mask of the whole parameter space, \\( M \\), can be obtained for both G and D. Consequently, Eq. 1 and 2 here become:" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.753, + 0.955, + 0.791 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x, \\theta_ {D} \\odot M _ {D})) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z, \\theta_ {G} \\odot M _ {G}))) ] \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.806, + 0.925, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D \\left(G (z, \\theta_ {G} \\odot M _ {G})\\right)\\right) \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.837, + 0.928, + 0.866 + ], + "angle": 0, + "content": "where \\(\\theta_{G}, M_{G}, \\theta_{D}\\) and \\(M_{D}\\) are the corresponding weights and masks for G and D, \\(\\odot\\) stands for Hadamard product." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.867, + 0.928, + 0.896 + ], + "angle": 0, + "content": "The update schedule contains two key factors, (i) the update interval (g) is the number of training iterations" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.942, + 0.519, + 0.954 + ], + "angle": 0, + "content": "16233" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.111, + 0.091, + 0.502, + 0.163 + ], + "angle": 0, + "content": "between the pruning and growing phase and vice versa; (ii) the learning rate, we set 1/10 the initial learning rate during the network growing phase. Other hyperparameters remained the same as per the given GANs network architecture." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.164, + 0.504, + 0.455 + ], + "angle": 0, + "content": "During each connectivity update, we use the weight magnitude as the indicator for pruning and make the following state transitions: if an indicator changes from 1 to 0, we remove the corresponding connection from the computational graph; During the network growing, all the pruned connections return to 1, indicating that the network will be grown back, initialized weights with 0 and trained. The network growing phase boosts the network's model capacity and makes it easier to get a better local minimum than with a sparse network topology. Similarly, growing new connections in G allows for the search for optimal connectivity and escape from undesired local minima. In addition, by deleting the least significant connections, our method considerably reduces both the training memory cost and the training time, hence enhancing training efficiency. We experiment with three distinct loss functions for the \\( \\mathrm{d}_{\\mathrm{crit}} \\) function namely, WGAN-GP [67] which is used by ProGAN, hinge loss is used by SNGAN and non-saturating GAN loss with 1-sided GP [6] which is used by StyleGAN2." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.47, + 0.32, + 0.487 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.492, + 0.504, + 0.768 + ], + "angle": 0, + "content": "In this section, we perform experiments on various datasets that contain a wide range of content categories. We evaluate CIFAR-10 and Tiny-ImageNet at \\(64 \\times 64\\) resolution, based on unconditional ProGAN [29][68], SNGAN [30][69], and SOTA StyleGAN2 [18][70]. We use the widely adopted evaluation metrics, such as the Fréchet Inception Distance (FID) [71] and Inception Score (IS) [4], and also provide the number of real images (#RI (in Millions (M)) [29][30]. If model \\(A\\) is taking less number of real images and is achieving comparable or better results than model \\(B\\), it shows that model \\(A\\) is efficient. Note that higher performing GANs models are indicated by lower FID (\\(\\downarrow\\)), and larger IS (\\(\\uparrow\\)). We further extend our study on \\(256^2\\) resolution, we test on Animal-Face Dog and Cat [2], 100-Shot-Obama [1], Panda [1], and Grumpy-cat [1], and Oxford-flowers [72]. On \\(1024^2\\) resolution, we test on 1k, 5k, 10k and 70k Flickr-Face-HQ (FFHQ) [34]. We also perform extensive ablation study to analyze the effectiveness of each component in Re-GAN." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.783, + 0.33, + 0.8 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.806, + 0.502, + 0.895 + ], + "angle": 0, + "content": "For ProGAN and StyleGAN2, for each dataset, we use the same 512-dimensional initial latent space, derived from a standard normal distribution \\(N(0, l)\\), followed by hypersphere normalization [29]. For SNGAN, the latent variable dimension is 128 for all datasets. For all experiments, we use the same hyperparameter settings." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.091, + 0.928, + 0.135 + ], + "angle": 0, + "content": "However, we reduce the learning rate ten times during network growing phase for better learning. We initialize parameters using standard normal distribution \\(N(0,1)\\)." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.135, + 0.931, + 0.296 + ], + "angle": 0, + "content": "We trained all models ourselves and used the same hardware to provide fair comparisons of the training times for the corresponding set of experiments. We use NVIDIA RTX 3090 GPU with 24 GB for all \\(64 \\times 64\\), and \\(256 \\times 256\\) experiments, and NVIDIA Quadro RTX 8000 GPU with 48 GB for all \\(1024 \\times 1024\\) experiments. We train for the same number of iterations predefined by the baseline models. We save the checkpoints every 10k iterations during training and report the best FID as well as the time it took to obtain that score from the checkpoints (e.g., happens at least after 15 hours of training for StyleGAN2)." + }, + { + "type": "title", + "bbox": [ + 0.547, + 0.306, + 0.712, + 0.319 + ], + "angle": 0, + "content": "Algorithm1 Re-GAN training" + }, + { + "type": "text", + "bbox": [ + 0.545, + 0.323, + 0.928, + 0.371 + ], + "angle": 0, + "content": "Input: An L-layer GANs model; target sparsity k; total training iterations \\( \\mathrm{T}_{\\text{total}} \\); training iterations between two consecutive steps, update interval \\( g \\); training set \\( S \\); learning rate \\( \\alpha \\); \nOutput: Converged \\( G \\) and \\( D \\)" + }, + { + "type": "text", + "bbox": [ + 0.563, + 0.372, + 0.897, + 0.385 + ], + "angle": 0, + "content": "1. Randomly initialize all model weights \\(\\theta_{G} \\in \\mathbb{R}^{N}, \\theta_{D} \\in \\mathbb{R}^{N}\\);" + }, + { + "type": "text", + "bbox": [ + 0.563, + 0.385, + 0.909, + 0.396 + ], + "angle": 0, + "content": "2. Train the weights \\(\\theta_{G}\\) and \\(\\theta_{D}\\) for \\(\\Delta_W\\) epochs // warm-up phase" + }, + { + "type": "text", + "bbox": [ + 0.563, + 0.396, + 0.801, + 0.408 + ], + "angle": 0, + "content": "3. while each training iteration \\(t \\in [\\mathrm{T}_{\\mathrm{total}}]\\) do" + }, + { + "type": "text", + "bbox": [ + 0.563, + 0.408, + 0.708, + 0.42 + ], + "angle": 0, + "content": "4. if mod \\((\\mathrm{t},\\mathrm{g}) = 0\\) then" + }, + { + "type": "list", + "bbox": [ + 0.563, + 0.372, + 0.909, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.597, + 0.42, + 0.733, + 0.432 + ], + "angle": 0, + "content": "// entered a pruning phase" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.432, + 0.888, + 0.445 + ], + "angle": 0, + "content": "5. \\(\\theta_{G}\\gets T_{k}(\\theta_{G},k)\\) //Apply compression(top-k)-" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.445, + 0.859, + 0.457 + ], + "angle": 0, + "content": "6. \\(\\theta_{D} \\gets T_{k}(\\theta_{D}, k) \\quad //\\) operations on weights" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.457, + 0.814, + 0.469 + ], + "angle": 0, + "content": "7. \\(m_{G}, m_{D} \\gets 1[\\theta_{i} \\neq 0] // Create masks\\)" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.469, + 0.622, + 0.48 + ], + "angle": 0, + "content": "8. else" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.481, + 0.735, + 0.492 + ], + "angle": 0, + "content": "// entered a growing phase" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.492, + 0.894, + 0.504 + ], + "angle": 0, + "content": "9. \\(\\alpha = \\alpha * 0.1\\) // reduce the learning rate by 10" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.505, + 0.815, + 0.517 + ], + "angle": 0, + "content": "10. \\(m_{G}, m_{D} \\gets 1_{N}\\) // reset all masks" + }, + { + "type": "text", + "bbox": [ + 0.566, + 0.518, + 0.633, + 0.528 + ], + "angle": 0, + "content": "11. end if" + }, + { + "type": "text", + "bbox": [ + 0.566, + 0.529, + 0.747, + 0.54 + ], + "angle": 0, + "content": "12. Sample a mini-batch from \\( S \\);" + }, + { + "type": "text", + "bbox": [ + 0.566, + 0.54, + 0.904, + 0.552 + ], + "angle": 0, + "content": "13. \\(\\theta_{G},\\theta_{D}\\gets \\theta_{G}\\odot m_{G},\\theta_{D}\\odot m_{D} / / \\mathrm{Update}\\theta_{G},\\theta_{D}\\) by Eq. (3)" + }, + { + "type": "text", + "bbox": [ + 0.566, + 0.553, + 0.879, + 0.565 + ], + "angle": 0, + "content": "14. end while // and (4), respectively" + }, + { + "type": "list", + "bbox": [ + 0.565, + 0.372, + 0.904, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.582, + 0.93, + 0.786 + ], + "angle": 0, + "content": "For StyleGAN2, we find that using default settings is hardly to converge on CIFAR-10 and Tiny-/ImageNet, so we follow the settings in [4] for CIFAR-10, in which both path length regularization and lazy regularization are not used, the coefficient for R1 regularization \\(\\gamma\\) is set to 0.1 for CIFAR-10, the output channel at final size level is 128 instead of 512 and doubled at each coarser level with a maximum 512. We use a similar setting for Tiny-/ImageNet except setting \\(\\gamma\\) to 1. For few-shot learning, FFHQ experiments, we set \\(\\gamma\\) to 10. We note a discrepancy between the results the author described scores and what we could able to accomplish using the author's provided code. This could be the result of subtle hardware variations or variations between runs." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.802, + 0.813, + 0.818 + ], + "angle": 0, + "content": "4.2. Comparison to state-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.825, + 0.929, + 0.899 + ], + "angle": 0, + "content": "We use the best-performing model ProGAN and StyleGAN2 and perform experiments at \\(64 \\times 64\\) resolution on CIFAR-10 and Tiny-ImageNet. We evaluate our method with \\(100\\%\\) data available and with \\(10\\%\\), \\(20\\%\\) and \\(50\\%\\) data available, with the findings summarized in Table" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.942, + 0.52, + 0.955 + ], + "angle": 0, + "content": "16234" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.114, + 0.091, + 0.258, + 0.106 + ], + "angle": 0, + "content": "1 and 2, respectively." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.106, + 0.502, + 0.236 + ], + "angle": 0, + "content": "The following observations can be drawn: First, Re-ProGAN and Re-StyleGAN2 can achieve consistently improved performance for all training cases, from complete data to limited data. In particular, likely to gain more when there is less training data available (e.g., \\(10\\%\\)), which is consistent with our design principle. With only \\(10\\%\\) training data available, Re-ProGAN and Re-StyleGAN2 obtain massive gains of 29.33 FID/7.69 IS and 32.91 FID/7.35 IS on CIFAR-10, respectively, and 79.08" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.091, + 0.929, + 0.164 + ], + "angle": 0, + "content": "FID/6.45 IS and 82.63 FID/6.47 IS on Tiny-ImageNet, respectively. Second, due to removing unimportant connections of low weights, Re-GAN consistently reduces the cost of computation associated with training and requires fewer total hours of GPU training time." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.164, + 0.929, + 0.236 + ], + "angle": 0, + "content": "Qualitative results and precision-recall curve for Re-StyleGAN2 on CIFAR-10 is in the supplementary material. We also provide a study in the supplementary material to show that Re-GAN helps to alleviate mode collapse." + }, + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.243, + 0.928, + 0.27 + ], + "angle": 0, + "content": "Table 1: FID comparison on few-shot datasets at \\(64\\times 64\\) resolution. FID and IS are calculated using 10k randomly generated samples, with the test data (10k) serving as the reference distribution. The best performance is highlighted." + }, + { + "type": "table", + "bbox": [ + 0.13, + 0.27, + 0.915, + 0.41 + ], + "angle": 0, + "content": "
DatasetSizeMethods#Real Images (RI)(in M)Training Time (hour)FLOPs ×109IS↑FID↓
CIFAR-1050KProGAN19.511.612.978.05 ± 0.2026.14
Re-ProGAN15.99.810.538.22 ± 0.1921.17
StyleGAN217.714.25.08.76 ± 0.2213.19
Re-StyleGAN212.110.14.058.88 ± 0.2412.16
Tiny-ImageNet100KProGAN9.45327.479.44 ± 0.3140.27
Re-ProGAN8.748.922.189.57 ± 0.3537.47
StyleGAN219.252.521.0711.75 ± 0.2520.95
Re-StyleGAN217.846.717.0412.10 ± 0.2820.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.163, + 0.419, + 0.877, + 0.432 + ], + "angle": 0, + "content": "Table 2: Experiments on \\( {64} \\times {64} \\) resolution \\( {50}\\% ,{20}\\% \\) and \\( {10}\\% \\) of training datasets. The best performance is highlighted." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.432, + 0.941, + 0.584 + ], + "angle": 0, + "content": "
DatasetMethods50% data20% data10% data
#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓
CIFAR-10ProGAN10.57.75±0.1928.337.27.51±0.1928.645.67.47±0.1630.08
Re-ProGAN9.47.97±0.1325.746.17.63±0.1827.194.97.69±0.2329.33
StyleGAN26.48.39±0.1517.224.17.36±0.2729.773.27.20±0.2436.45
Re-StyleGAN248.48±0.1616.093.87.46±0.2327.982.77.35±0.1332.91
Tiny-ImageNetProGAN9.68.71±0.274986.84±0.1277.867.76.38±0.1983.27
Re-ProGAN8.38.84±0.2546.787.76.92±0.1575.227.46.45±0.2279.08
StyleGAN214.511.02±0.2730.035.18.32±0.2465.263.26.32±0.1084.86
Re-StyleGAN213.211.25±0.3129.194.28.53±0.2962.341.36.47±0.1082.63
" + }, + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.595, + 0.501, + 0.621 + ], + "angle": 0, + "content": "Table 3: FID comparison to NAS-based GANs, i.e., AutoGAN for full CIFAR-10 dataset." + }, + { + "type": "table", + "bbox": [ + 0.106, + 0.621, + 0.51, + 0.747 + ], + "angle": 0, + "content": "
Methods#RI (M)Training time (hour)Flops (×1016)FID↓ Full data
AutoGAN (Top A)4.76.719M17.70
Re-AutoGAN (Top A)4.15.7216.5M17.61
AutoGAN (Top B)5.27.7523M18.08
Re-AutoGAN (Top B)4.25.9518M17.30
AutoGAN (Top C)5.78.1223M17.09
Re-AutoGAN (Top C)56.7320M16.61
" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.76, + 0.503, + 0.892 + ], + "angle": 0, + "content": "We extend our method comparison with the NAS-based GANs method, i.e., AutoGAN (Top A, B and C architectures) [31], [32]. The result in Table 3 shows that Re-GAN not only improves the performance for human-designed networks (e.g., SNGAN, ProGAN, StyleGAN2) but also boosts the performance and reduces training time and FLOPs for automatically searched architecture, AutoGAN. It also minimizes training time and FLOPs for all top three searched GANs architectures." + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.612, + 0.818, + 0.629 + ], + "angle": 0, + "content": "4.3. Comparison with GANs tickets" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.635, + 0.929, + 0.898 + ], + "angle": 0, + "content": "Recently, Iterative Magnitude Pruning (IMP), an unstructured magnitude pruning [24] have shown performing well in finding lottery tickets in GANs than other pruning methods [66], [73] to find GANs tickets [22], [23] [24]. We find GANs tickets using IMP at \\(20\\%\\) and \\(46\\%\\) pruning ratio for the full training dataset, named ST_SNGAN@20% and ST_SNGAN@46%, respectively. We also include growing with random initialization (RI), Re-SNGAN-RI in which weights are randomly initialized during the growing rather than zero initialization. Also, we set same learning rate for both dense and sparse phases, Re-SNGAN-lr. The results are summarized in Table 4. The results show that our proposed Re-SNGAN performs well w.r.t FID. Re-SNGAN-RI results in longer convergence times, as network has to explore more diverse weight configurations to find best solution. While, setting 1/10 learning rate during dense phase performs better than same learning rate in both phases as it promotes stability by" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.942, + 0.521, + 0.955 + ], + "angle": 0, + "content": "16235" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.111, + 0.091, + 0.502, + 0.178 + ], + "angle": 0, + "content": "avoiding large, sudden weight updates. Also, finding GANs tickets is highly time consuming. While the training time for exploring different sub-network structures during training, even only at \\(10\\%\\) pruning ratio, is comparable to the dense model; In addition, Re-SNGAN consumes less training FLOPs than the GANs tickets." + }, + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.185, + 0.493, + 0.198 + ], + "angle": 0, + "content": "Table 4: Comparison to GANs tickets methods on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.198, + 0.508, + 0.322 + ], + "angle": 0, + "content": "
Methods#RI (M)Training time (hour)Flops (×1017)FID↓ Full data
SNGAN@0%306.21.0120.12
ST_SNGAN@20%92.519.72.6018.96
ST_SNGAN@46%150323.4618.22
Re-SNGAN-Ir49.410.51.5719.06
Re-SNGAN-RI33.17.31.2519.71
Re-SNGAN31.56.61.0317.87
" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.09, + 0.733, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.09, + 0.926, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.21, + 0.929, + 0.317 + ], + "angle": 0, + "content": "Figure 4: IS \\((\\uparrow)\\) and FID \\((\\downarrow)\\) results of SNGAN with \\(10\\%\\), \\(20\\%\\), \\(40\\%\\), \\(80\\%\\), and full training data of CIFAR-10. Four settings are evaluated: (i) SNGAN (unpruned SNGAN), (ii) ST_SNGAN (applied IMP for finding sparse GANs ticket at \\(20\\%\\) pruning ratio), (iii) Sparse_Re-SNGAN (Re-GAN output is sparse), (iv) Dense_Re-SNGAN (Re-GAN output is dense). The main advantage is that it provides both a high-performing dense model and its compressed version at the end of the training." + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.328, + 0.928, + 0.354 + ], + "angle": 0, + "content": "Table 5: FID comparison on few-shot datasets at \\(256\\times 256\\) resolution. FID and IS are calculated using 5k randomly generated samples, with the training data serving as the reference distribution. The best performance is highlighted." + }, + { + "type": "table", + "bbox": [ + 0.142, + 0.355, + 0.901, + 0.508 + ], + "angle": 0, + "content": "
MethodsObamaGrumpy CatPandaAnimal FaceOxford Flowers
CatDog
# of images1001001003891601000
ProGAN129.52135.89235.86289.73259.32224.70
Re-ProGAN110.46124.06205.82283.29227.59198.56
StyleGAN286.6751.395.0881.91157.63147.67
Re-StyleGAN272.9238.2378.4573.05133.4138.35
StyleGAN2 + APA68.7433.7218.2462.7181.1385.88
Re-StyleGAN2 + APA64.2831.7416.3360.2677.4482.19
StyleGAN2 + DiffAug46.3128.612.8942.8558.4746.21
Re-StyleGAN2 + DiffAug45.727.3612.642.1157.245.13
" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.521, + 0.502, + 0.653 + ], + "angle": 0, + "content": "We provide another set of experiments of SNGAN training on CIFAR-10, with training data ranging from \\(10\\%\\) to \\(100\\%\\). Figure 4 provides a summary of the key findings. The following observations can be drawn: First, at the same data availability (from \\(10\\%\\) to even \\(100\\%\\)), exploring multiple sub-networks during training at only \\(10\\%\\) pruning ratio is always preferable to training the dense model and sparse ticket; Second, sparse Re-GAN model is also performing consistently well than GANs tickets." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.667, + 0.308, + 0.684 + ], + "angle": 0, + "content": "4.4. Few-shot generation" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.69, + 0.504, + 0.895 + ], + "angle": 0, + "content": "Collecting a large number of image datasets can be prohibitively costly or perhaps impossible for a certain character or a topic. In this context, a data-efficient model for the image synthesis task will be highly important. In Table 5, we show that our method finds data-efficient GANs that can be trained from scratch with only 100 training image data (without any pre-training) and demonstrates consistently superior performance (See supplementary material for visualizations of few-shot generation and style interpolation). Results also show that proposed Re-GAN improve the generated sample quality of SOTA methods, such as Diffaug [1] and APA [21] for few-shot datasets. We further extend our study for high-resolution experiments (Table 6 and Figure 5) where the" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.521, + 0.929, + 0.609 + ], + "angle": 0, + "content": "Re-StyleGAN2 model gets better FID scores on all 1k, 5k, 10k and 70k FFHQ datasets (see supplementary material for more details). To further demonstrate the effectiveness of our Re-GAN, we apply it to other recent methods, FastGAN [74] for several few-shot datasets. Results are shown in supplementary material." + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.618, + 0.929, + 0.671 + ], + "angle": 0, + "content": "Table 6: FID comparison on few-shot datasets at \\(1024 \\times 1024\\) resolution. FID and IS are calculated using 50k randomly generated samples, with the training data (70k) serving as the reference distribution." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.671, + 0.929, + 0.73 + ], + "angle": 0, + "content": "
MethodsFFHQ
70k10k5k1k
StyleGAN24.3513.0621.7640.24
Re-StyleGAN24.1911.2219.1336.3
" + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.743, + 0.744, + 0.76 + ], + "angle": 0, + "content": "4.5. Ablation and analysis" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.766, + 0.931, + 0.9 + ], + "angle": 0, + "content": "Prune G/D: We study the impact of exploring different sub-network structures on G or D only, or on both G and D (represented as B) at \\(10\\%\\), \\(30\\%\\), and \\(50\\%\\) pruning ratio (i.e., weight remaining ratio indicates the sparsity levels of explored sub-network structures during training) on CIFAR-10 full training dataset. Figure 6 shows a summary of the results. We notice that employing pruning on D or both G and D, achieves comparable or better performance than the base model. While for the same sparsity" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.942, + 0.521, + 0.955 + ], + "angle": 0, + "content": "16236" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.091, + 0.502, + 0.15 + ], + "angle": 0, + "content": "distribution (i.e., pruning ratio), pruning only on G achieves significant performance improvement (i.e., largely reducing the FID). We also notice that update interval (g) 100 works well with only G." + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.162, + 0.488, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.395, + 0.503, + 0.435 + ], + "angle": 0, + "content": "Figure 5: Few-shot generalization results of Re-StyleGAN2 on 10k FFHQ (1024×1024). Samples are randomly drawn without cherry picking." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.447, + 0.503, + 0.566 + ], + "angle": 0, + "content": "Robustness to learning rate. Previous research works [75]–[77] have observed that GANs convergence highly depends on the selection of hyperparameters, especially the learning rate, \\(\\alpha\\). As shown in Table 7, we validate our network by training it with five different \\(\\alpha\\) values (0.0001, 0.0002, 0.0005, 0.0007, and 0.00001) for the CIFAR-10 dataset. Results show that for all different \\(\\alpha\\) values, our models converged and achieved similar inception scores." + }, + { + "type": "image", + "bbox": [ + 0.175, + 0.573, + 0.44, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.715, + 0.49, + 0.741 + ], + "angle": 0, + "content": "Figure 6: FID with different pruning ratio and update interval (g) of Re-SNGAN (CIFAR-10)." + }, + { + "type": "image", + "bbox": [ + 0.169, + 0.742, + 0.446, + 0.88 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.881, + 0.479, + 0.896 + ], + "angle": 0, + "content": "Figure 7: Stability during training on the \\(10\\%\\) CIFAR-10." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.091, + 0.929, + 0.252 + ], + "angle": 0, + "content": "Stability during training. To compare the stability of Re-SNGAN with SNGAN, we evaluate how the samples produced for the same set of latent points vary during training. As proposed in [30], we use the mean squared error (MSE) between two consecutive generated samples as a quantitative measure of training stability. Figure 7 shows the MSE between generated images from the same latent code in the midst of successive epochs on the \\(10\\%\\) CIFAR-10 dataset. Results show that dense Re-SNGAN converges consistently over time, while SNGAN varies dramatically across epochs." + }, + { + "type": "table_caption", + "bbox": [ + 0.624, + 0.262, + 0.843, + 0.274 + ], + "angle": 0, + "content": "Table 7: Robustness to learning rate." + }, + { + "type": "table", + "bbox": [ + 0.57, + 0.274, + 0.899, + 0.399 + ], + "angle": 0, + "content": "
MethodsLearning rateResults
ISFID
Real images-11.34-
SNGAN0.00028.07±0.1620.12
0.00077.93±0.3021.76
0.00058.03±0.2320.17
Re-SNGAN0.00028.16±0.1517.87
0.00018.03±0.1719.03
0.000018.01±0.2519.65
" + }, + { + "type": "title", + "bbox": [ + 0.539, + 0.413, + 0.885, + 0.449 + ], + "angle": 0, + "content": "5. Conclusion and Discussion of Broader Impact" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.453, + 0.929, + 0.656 + ], + "angle": 0, + "content": "We introduce a new perspective on data-efficient GANs by exploring different sub-network structures during training, which is a novel approach compared to existing methods. Extensive experiments on various GANs architectures, objectives, and datasets demonstrate the effectiveness and training efficiency of our proposed GANs training methodology, Re-GAN. In this work, we focus on unstructured sparsity to showcase the algorithm-level innovations of Re-GAN. However, only specific hardware supports sparse tensor cores for weight pruning. Future work could aim for a high pruning ratio and reconfigure network width and depth simultaneously during GANs training, addressing the limitations of the current approach." + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.656, + 0.929, + 0.803 + ], + "angle": 0, + "content": "This research aims to enhance generalization performance, stabilize GANs models under limited data, and improve training efficiency, which has practical implications for various applications and industries. However, these advancements might also exacerbate existing social risks associated with GANs. We plan to investigate whether the sparse structures affect issues like image generation bias in future work. The ability to generate images with less data could potentially be exploited for undesirable applications, such as DeepFakes." + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.818, + 0.699, + 0.835 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.839, + 0.929, + 0.898 + ], + "angle": 0, + "content": "This work is supported by PolyU Internal Start-up Fund (Grant no: P0038876), Research Impact Fund (No. R5034-18), and RGC Collaborative Research Fund (Grant no: C5026-18G)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.942, + 0.519, + 0.955 + ], + "angle": 0, + "content": "16237" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.131, + 0.092, + 0.212, + 0.104 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.116, + 0.106, + 0.502, + 0.158 + ], + "angle": 0, + "content": "[1] S. Zhao, Z. Liu, J. Lin, J. Y. Zhu, and S. 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(left) Image generation trained on multiple few-shot generation datasets, such as 100-shot Obama [1], Panda [1], and Animal Face-Cat (A-Cat) [2]; (right) FID scores vs. CIFAR-10 [3] training set size with training cost, FLOPs. Best viewed in color. + +# Abstract + +Training Generative Adversarial Networks (GANs) on high-fidelity images usually requires a vast number of training images. Recent research on GAN tickets reveals that dense GANs models contain sparse sub-networks or "lottery tickets" that, when trained separately, yield better results under limited data. However, finding GANs tickets requires an expensive process of train-prune-retrain. In this paper, we propose Re-GAN, a data-efficient GANs training that dynamically reconfigures GANs architecture during training to explore different sub-network structures in training time. Our method repeatedly prunes unimportant connections to regularize GANs network and regrows them to reduce the risk of prematurely pruning important connections. Re-GAN stabilizes the GANs models with less data and offers an alternative to the existing GANs tickets and progressive growing methods. We demonstrate that Re-GAN is a generic training methodology which achieves stability on datasets of varying sizes, domains, and resolutions (CIFAR-10, TinyImageNet, and multiple few-shot generation datasets) as well as different GANs architectures (SNGAN, ProGAN, + +StyleGAN2 and AutoGAN). Re-GAN also improves performance when combined with the recent augmentation approaches. Moreover, Re-GAN requires fewer floating-point operations (FLOPs) and less training time by removing the unimportant connections during GANs training while maintaining comparable or even generating higher-quality samples. When compared to state-of-the-art StyleGAN2, our method outperforms without requiring any additional fine-tuning step. Code can be found at this link: https://github.com/IntellicentAI-Lab/Re-GAN + +# 1. Introduction + +In recent years, Generative adversarial networks (GANs) [4]–[7] have made great strides in generating high-fidelity images. The GANs models serve as the backbone of several vision applications, such as data augmentation [5], [8], [9], domain adaptation [10], [11], and image-to-image translation [14]–[16]. + +The success of the GANs methods largely depends on a massive quantity of diverse training data, which is often time-consuming and challenging to collect [17]. Figure 1 shows how the performance of the StyleGAN2 [18] model drastically declines under the limited training data. As a + +result, various new methods [1], [19], [20] have emerged to deal with the problem of insufficient data. Dynamic data-augmentation [1], [19]-[21] fills in the gap and stabilizes GANs training with less data. Very recently, [22], [23] introduced the lottery ticket hypothesis (LTH) in GANs (called "GANs tickets"), a complementary to the existing augmentation techniques. LTH identifies sparse sub-networks (called "winning tickets") that can be trained in isolation to match or even surpass the performance of unpruned models. [24] demonstrated that an identified GANs ticket can be used as a sparse structural prior to alleviate the problem of limited data in GANs. However, identifying these winning tickets requires many iterations of a time-consuming and computationally expensive train-prune-retrain process. This results in high training time and a number of floating-point operations (FLOPs) than training a dense GANs models, such as StyleGAN2 [18] and BigGAN [5]. In addition, these methods train a full-scale model before pruning, and then, after the pruning process, they engage in an extra fine-tuning to improve the performance. Given this perspective, we ask: + +Is there any way to achieve training efficiency w.r.to both data and computation in GANs while preserving or even improving its performance? + +One potential solution is network pruning during training, which can allow the exploration of different subnetwork structures in training-time. Network structure exploration during training has shown to be effective in a variety of domains [25], [26], and its properties have been the subject of a significant amount of research [27], [28]. However, network pruning is never introduced to GANs training; as a result, the investigation of different subnetwork structures exploration during GANs training remains mysterious. + +To address this gap in the literature, we investigate and introduce the network pruning, i.e., connections, in GANs training by dynamically reconfiguring GANs architecture to allow the exploration of different sub-network structures in training time, dubbed as Re-GAN. However, on the other hand, it is common knowledge that the learning capabilities of the two competing networks—a generator (G) and a discriminator (D), need to be carefully maintained equilibrium in their respective capabilities for learning. Hence to build Re-GAN, the first question is: how to explore different network structures during GANs training? Network pruning during training regularizes the G to allow a robust gradient flow through G. This stabilizes the GANs models under limited training data and improves training efficiency. Re-GAN repeatedly prunes and grows the connections during the training process to reduce the risk of pruning important connections prematurely and prevent the model from losing its representational capabilities early in the training process. As a result, network growing provides a second opportunity to + +reinitialize pruned connections by reusing information from previously explored sub-network structures. + +![](images/29248e15189d4b11f0c6d202b6ea763d8e930e1f78433910e03ccf70cac89735.jpg) +Figure 2: Conventional GANs training has fixed connectivity space. Re-GAN uses network pruning and growing during training to make connectivity space flexible that helps in the propagation of robust gradients. Best viewed in color. + +The second question is: how to explore different subnetwork structures in $G$ and $D$ simultaneously? On the one hand, if we employ a pretrained $D$ (or $G$ ) and prune solely for $G$ (or $D$ ), it can quickly incur an imbalance between the capabilities of $D$ or $G$ (particularly in the early stage of training), resulting in slow convergence. While it is possible to prune for $G$ and $D$ simultaneously, empirical experiments show that doing so significantly degrades the initial unstable GANs training, resulting in highly fluctuating training curves and, in many cases, a failure to converge. As a trade-off, we propose expanding $D$ as per standard GANs training while applying pruning exclusively to $G$ 's architecture. + +Additionally, our method is robust, working well with a wide range of GANs architectures (ProGANs [29], SNGAN [30], StyleGAN2, and AutoGAN [31], [32]) and datasets (CIFAR-10 [3], Tiny-ImageNet [33], Flickr Faces HQ [34], and many few-shot generation datasets). We find that exploring different sub-network structures during training accounts for a significant decrease in FID score compared to the vanilla DCGAN [35] architecture without a pre-trained model or fine-tuning the pruned model (see Figure 2). Our method delivers higher performance in less training time to state-of-the-art (SOTA) methods on most available datasets without additional hyperparameters that progressive growing method introduces, such as training schedules and learning rates for different generation stages (resolutions). This robustness allows the Re-GAN to be easily generalized on unseen datasets. + +To the best of our knowledge, Re-GAN is the first attempt to incorporate network pruning during GANs training. Our technical innovations are as follows: + +- We conduct the first in-depth study on taking a unified approach of incorporating pruning in GANs training without pre-training a large model or fine-tuning the pruned model. +- Our method repeatedly prunes and grows the connections during training to reduce the possibility of + +pruning important connections and helps the model to maintain its representation ability early in training. Thus, network growing gives another chance to reinitialize pruned connections from the explored network sub-structures. + +- Extensive experiments are conducted across a wide range of GANs architectures and demonstrated that Re-GAN could be easily applied on these GANs architectures to improve their performances, both in regular and low-data regime setups. For example, for the identified winning GANs ticket, ProGAN and StyleGAN2 on full CIFAR-10, we achieve $70.23\%$ , $18.81\%$ , and $19\%$ training FLOPs savings, respectively, while improved generated sample quality for both full and $10\%$ training data. Re-GAN presents a viable alternative to the GANs tickets and progressive growing techniques. Additionally, the performance of Re-GAN is enhanced when integrated with recent augmentation techniques. + +# 2. Related Works + +Stabilize the GANs training. In recent years, different loss functions [4], [36], [37], regularization [30], [38], and architectural designs [39], [40] have all been proposed as ways to enhance GANs [6]. Our efforts are in the category of network architecture design. Recently, state-of-the-art (SOTA) models like StyleGAN2 and BigGAN have suggested making networks deeper and wider. They have also shown that training deep GANs networks usually leads to better generalization. However, a deeper model with more convolution layers results in a longer training time for GANs. This is because a deeper model contains a greater number of model parameters and a weaker gradient flow via G [29], [41], [42]. The findings of Progressive GAN (ProGAN) [29] show that gradually growing and training both networks together from a lower resolution, stabilizes the training and enhances the generation quality. MSG-GAN [39] introduced a solution to the gradient flow issue in which G gets feedback from a number of different resolutions simultaneously. Nevertheless, these methods further add to the computational cost, necessitating an even high amount of GPU memory and more training time. + +GANs compression. GANs, like other deep neural networks, excel in image generation and translation tasks [29], [43]–[45], but suffer from high computational complexity and memory requirements. Han et al. [46] introduced a co-evolutionary pruning technique for GANs compression, while Wang et al. [47] proposed quantizing GANs to 1 or 2 bits. Li et al. [48] used distillation to improve compressed D with a pre-trained GANs model, and Wang et al. [49] combined these three techniques into one framework. Although impressive results were achieved in training compressed G with a pre-trained D [50], existing GANs compression approaches require pre + +training an over-parameterized model, limiting training efficiency. Meanwhile, [51] proposed dynamic network size modification during training, but design space exploration is constrained by network augmentation. Our approach injects sparsity during training to enhance generalization, stabilize GANs with limited data, and improve training efficiency, distinguishing it from these inference-focused techniques. + +Lottery Ticket Hypothesis (LTH). Recently, [22]–[24] have shown the existence of winning tickets in the min-max game beyond minimization by extending LTH to GANs. [52] claims the existence of independently trainable sparse sub-networks capable of performing at the same level as dense networks and in some instances, even better. While [53], [54] scaled up LTH by rewinding [55], [56]. However, these methods do not restore key connections that have been prematurely pruned, which restricts the model's capacity. In contrast, the proposed method can restore connections that have been prematurely pruned and can better preserve the capacity of the model. + +On the other hand, the total number of FLOPs necessary to locate and train a winning ticket at a sparsity level of $80\%$ is more than four times as many as the number of FLOPs necessary to train a dense model [57]. As the size of SOTA models have grown (e.g., BigGAN and StyleGAN2), such huge resource needs would cause financial and environmental problems [58]–[60]. Being unique and orthogonal efforts from ours, these methods do not focus on the training efficiency yet. + +# 3. Methodology + +# 3.1. Design motivation + +The synaptic connection topology of the brain is very dynamic, yet the brain still maintains a stable and efficient computing function [61], [62]. It has been shown that the underlying process of synaptic rewiring plays a crucial part in learning [63]. We consider the training of GANs to be akin to such biological learning processes and combine it with different training objectives under sparsity constraint. + +In contrast to conventional GANs training with predefined static connectivity, we prune and grow the connections during the GANs training. We conduct a thorough investigation to find that introducing network pruning and growing into GANs training yields desirable results on many fronts, specifically: (1) stabilizes GANs across various datasets, resolutions, domains, and architectures; (2) maintaining comparable or even generating higher-quality samples; and (3) enhancing the GANs training efficiency w.r.t both data and computation by removing the unimportant connections. + +In the next sub-section, we review the traditional GANs models, then describe in detail our proposed GANs training methodology via architectural reconfiguration. + +![](images/25cbf60c2f4de0e574847ff9931a1e632675b888eb828f2b5a9d111fa0c703a9.jpg) +Figure 3: Architecture of Re-GAN, shown here on the base model proposed in GANs [6]. The key feature of Re-GAN is that it provides sparse-dense model pairs at the end of the training process. This is beneficial in practice, as it may be desired to deploy compressed variant in resource-constrained environments without redoing the full training process. + +# 3.2. Generative Adversarial Networks + +A GANs model consists of a discriminator $\mathrm{D}$ and a generator $\mathrm{G}$ . The training objectives of the $\mathrm{D}$ and $\mathrm{G}$ can be represented as $\theta_{D}$ and $\theta_{G}$ , respectively. The GANs framework can be as follows: + +$$ +\max _ {\theta_ {D}} \mathbb {E} _ {x \sim p _ {d a t a}} [ f _ {D} (D (x)) ] + \mathbb {E} _ {z \sim p _ {z}} [ f _ {G} (D (G (z))) ] \tag {1} +$$ + +$$ +\min _ {\theta_ {G}} \mathbb {E} _ {z \sim p _ {z}} \left[ g _ {G} \left(D (G (z))\right) \right], \tag {2} +$$ + +where $p_{z}$ is the prior distribution (e.g., $N(0, I)$ ) and $p_{data}$ is the real training data used to approximate the data distribution. The notations $f_{D}, f_{G}$ , and $g_{G}$ in Eq. (1) and (2) represent the mapping functions from which various GANs losses can be derived [64]. + +# 3.3. GANs training with architectural reconfiguration + +A network's topology is equivalent to a directed acyclic graph with a predetermined order of nodes. Each node $X_{\mathrm{in}}$ serves as an input feature, and each edge functions as a computation cell with hyperparameters. We parameterize architectural space by associating a mask variable $m \in \{0,1\}$ with each computation cell to enable training time pruning ( $m = 1 \rightarrow 0$ ) and growing ( $m = 0 \rightarrow 1$ ). We consider a single-level configuration space for GANs architecture that enables dynamic pruning and growing networks width-wise. + +Revisiting GANs training. Re-GAN reconfigures G's architecture to explore different sub-network structures during training. As shown in Algorithm 1, we start the + +GANs training on the dense network for several iterations, warm-up phase, and learn the connection weights to know their importance. To achieve the sparse structure, we prune the least important weights based on the pre-defined pruning criterion. We then activate the pruned connections to further grow the network after a series of iterative optimizations. Once the network topology has been changed from sparse to dense, it will train the new network until the next connectivity update. The overview of ReGAN is shown in Figure 3. The main factors of Re-GAN training are as follows: 1) sparsity distribution, 2) update schedule, 3) pruning, and 4) grow. + +GANs sub-networks exploration. We prune the low-weight connections by using unstructured magnitude pruning [65], [66] by using the binary masks $m_{g}$ and $m_{d}$ . The pruning ratio $\rho$ determines the amount of weights removed during the pruning phase. We use $\rho = 10\%$ in all experiments except StyleGAN2 for FFHQ $(\rho = 30\%)$ . We use the same sparsity across all layers, i.e., uniform sparsity distribution. First, we sort the weights and produced a binary mask to exclude weights smaller than $\lambda$ . If the mask of each layer that has to be regularized is calculated, then the mask of the whole parameter space, $M$ , can be obtained for both G and D. Consequently, Eq. 1 and 2 here become: + +$$ +\max _ {\theta_ {D}} \mathbb {E} _ {x \sim p _ {d a t a}} [ f _ {D} (D (x, \theta_ {D} \odot M _ {D})) ] + \mathbb {E} _ {z \sim p _ {z}} [ f _ {G} (D (G (z, \theta_ {G} \odot M _ {G}))) ] \tag {3} +$$ + +$$ +\min _ {\theta_ {G}} \mathbb {E} _ {z \sim p _ {z}} \left[ g _ {G} \left(D \left(G (z, \theta_ {G} \odot M _ {G})\right)\right) \right], \tag {4} +$$ + +where $\theta_{G}, M_{G}, \theta_{D}$ and $M_{D}$ are the corresponding weights and masks for G and D, $\odot$ stands for Hadamard product. + +The update schedule contains two key factors, (i) the update interval (g) is the number of training iterations + +between the pruning and growing phase and vice versa; (ii) the learning rate, we set 1/10 the initial learning rate during the network growing phase. Other hyperparameters remained the same as per the given GANs network architecture. + +During each connectivity update, we use the weight magnitude as the indicator for pruning and make the following state transitions: if an indicator changes from 1 to 0, we remove the corresponding connection from the computational graph; During the network growing, all the pruned connections return to 1, indicating that the network will be grown back, initialized weights with 0 and trained. The network growing phase boosts the network's model capacity and makes it easier to get a better local minimum than with a sparse network topology. Similarly, growing new connections in G allows for the search for optimal connectivity and escape from undesired local minima. In addition, by deleting the least significant connections, our method considerably reduces both the training memory cost and the training time, hence enhancing training efficiency. We experiment with three distinct loss functions for the $\mathrm{d}_{\mathrm{crit}}$ function namely, WGAN-GP [67] which is used by ProGAN, hinge loss is used by SNGAN and non-saturating GAN loss with 1-sided GP [6] which is used by StyleGAN2. + +# 4. Experimental Results + +In this section, we perform experiments on various datasets that contain a wide range of content categories. We evaluate CIFAR-10 and Tiny-ImageNet at $64 \times 64$ resolution, based on unconditional ProGAN [29][68], SNGAN [30][69], and SOTA StyleGAN2 [18][70]. We use the widely adopted evaluation metrics, such as the Fréchet Inception Distance (FID) [71] and Inception Score (IS) [4], and also provide the number of real images (#RI (in Millions (M)) [29][30]. If model $A$ is taking less number of real images and is achieving comparable or better results than model $B$ , it shows that model $A$ is efficient. Note that higher performing GANs models are indicated by lower FID ( $\downarrow$ ), and larger IS ( $\uparrow$ ). We further extend our study on $256^2$ resolution, we test on Animal-Face Dog and Cat [2], 100-Shot-Obama [1], Panda [1], and Grumpy-cat [1], and Oxford-flowers [72]. On $1024^2$ resolution, we test on 1k, 5k, 10k and 70k Flickr-Face-HQ (FFHQ) [34]. We also perform extensive ablation study to analyze the effectiveness of each component in Re-GAN. + +# 4.1. Implementation details + +For ProGAN and StyleGAN2, for each dataset, we use the same 512-dimensional initial latent space, derived from a standard normal distribution $N(0, l)$ , followed by hypersphere normalization [29]. For SNGAN, the latent variable dimension is 128 for all datasets. For all experiments, we use the same hyperparameter settings. + +However, we reduce the learning rate ten times during network growing phase for better learning. We initialize parameters using standard normal distribution $N(0,1)$ . + +We trained all models ourselves and used the same hardware to provide fair comparisons of the training times for the corresponding set of experiments. We use NVIDIA RTX 3090 GPU with 24 GB for all $64 \times 64$ , and $256 \times 256$ experiments, and NVIDIA Quadro RTX 8000 GPU with 48 GB for all $1024 \times 1024$ experiments. We train for the same number of iterations predefined by the baseline models. We save the checkpoints every 10k iterations during training and report the best FID as well as the time it took to obtain that score from the checkpoints (e.g., happens at least after 15 hours of training for StyleGAN2). + +# Algorithm1 Re-GAN training + +Input: An L-layer GANs model; target sparsity k; total training iterations $\mathrm{T}_{\text{total}}$ ; training iterations between two consecutive steps, update interval $g$ ; training set $S$ ; learning rate $\alpha$ ; +Output: Converged $G$ and $D$ + +1. Randomly initialize all model weights $\theta_{G} \in \mathbb{R}^{N}, \theta_{D} \in \mathbb{R}^{N}$ ; +2. Train the weights $\theta_{G}$ and $\theta_{D}$ for $\Delta_W$ epochs // warm-up phase +3. while each training iteration $t \in [\mathrm{T}_{\mathrm{total}}]$ do +4. if mod $(\mathrm{t},\mathrm{g}) = 0$ then + +// entered a pruning phase +5. $\theta_{G}\gets T_{k}(\theta_{G},k)$ //Apply compression(top-k)- +6. $\theta_{D} \gets T_{k}(\theta_{D}, k) \quad //$ operations on weights +7. $m_{G}, m_{D} \gets 1[\theta_{i} \neq 0] // Create masks$ +8. else +// entered a growing phase +9. $\alpha = \alpha * 0.1$ // reduce the learning rate by 10 +10. $m_{G}, m_{D} \gets 1_{N}$ // reset all masks +11. end if +12. Sample a mini-batch from $S$ ; +13. $\theta_{G},\theta_{D}\gets \theta_{G}\odot m_{G},\theta_{D}\odot m_{D} / / \mathrm{Update}\theta_{G},\theta_{D}$ by Eq. (3) +14. end while // and (4), respectively + +For StyleGAN2, we find that using default settings is hardly to converge on CIFAR-10 and Tiny-/ImageNet, so we follow the settings in [4] for CIFAR-10, in which both path length regularization and lazy regularization are not used, the coefficient for R1 regularization $\gamma$ is set to 0.1 for CIFAR-10, the output channel at final size level is 128 instead of 512 and doubled at each coarser level with a maximum 512. We use a similar setting for Tiny-/ImageNet except setting $\gamma$ to 1. For few-shot learning, FFHQ experiments, we set $\gamma$ to 10. We note a discrepancy between the results the author described scores and what we could able to accomplish using the author's provided code. This could be the result of subtle hardware variations or variations between runs. + +# 4.2. Comparison to state-of-the-art + +We use the best-performing model ProGAN and StyleGAN2 and perform experiments at $64 \times 64$ resolution on CIFAR-10 and Tiny-ImageNet. We evaluate our method with $100\%$ data available and with $10\%$ , $20\%$ and $50\%$ data available, with the findings summarized in Table + +1 and 2, respectively. + +The following observations can be drawn: First, Re-ProGAN and Re-StyleGAN2 can achieve consistently improved performance for all training cases, from complete data to limited data. In particular, likely to gain more when there is less training data available (e.g., $10\%$ ), which is consistent with our design principle. With only $10\%$ training data available, Re-ProGAN and Re-StyleGAN2 obtain massive gains of 29.33 FID/7.69 IS and 32.91 FID/7.35 IS on CIFAR-10, respectively, and 79.08 + +FID/6.45 IS and 82.63 FID/6.47 IS on Tiny-ImageNet, respectively. Second, due to removing unimportant connections of low weights, Re-GAN consistently reduces the cost of computation associated with training and requires fewer total hours of GPU training time. + +Qualitative results and precision-recall curve for Re-StyleGAN2 on CIFAR-10 is in the supplementary material. We also provide a study in the supplementary material to show that Re-GAN helps to alleviate mode collapse. + +Table 1: FID comparison on few-shot datasets at $64\times 64$ resolution. FID and IS are calculated using 10k randomly generated samples, with the test data (10k) serving as the reference distribution. The best performance is highlighted. + +
DatasetSizeMethods#Real Images (RI)(in M)Training Time (hour)FLOPs ×109IS↑FID↓
CIFAR-1050KProGAN19.511.612.978.05 ± 0.2026.14
Re-ProGAN15.99.810.538.22 ± 0.1921.17
StyleGAN217.714.25.08.76 ± 0.2213.19
Re-StyleGAN212.110.14.058.88 ± 0.2412.16
Tiny-ImageNet100KProGAN9.45327.479.44 ± 0.3140.27
Re-ProGAN8.748.922.189.57 ± 0.3537.47
StyleGAN219.252.521.0711.75 ± 0.2520.95
Re-StyleGAN217.846.717.0412.10 ± 0.2820.21
+ +Table 2: Experiments on ${64} \times {64}$ resolution ${50}\% ,{20}\%$ and ${10}\%$ of training datasets. The best performance is highlighted. + +
DatasetMethods50% data20% data10% data
#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓
CIFAR-10ProGAN10.57.75±0.1928.337.27.51±0.1928.645.67.47±0.1630.08
Re-ProGAN9.47.97±0.1325.746.17.63±0.1827.194.97.69±0.2329.33
StyleGAN26.48.39±0.1517.224.17.36±0.2729.773.27.20±0.2436.45
Re-StyleGAN248.48±0.1616.093.87.46±0.2327.982.77.35±0.1332.91
Tiny-ImageNetProGAN9.68.71±0.274986.84±0.1277.867.76.38±0.1983.27
Re-ProGAN8.38.84±0.2546.787.76.92±0.1575.227.46.45±0.2279.08
StyleGAN214.511.02±0.2730.035.18.32±0.2465.263.26.32±0.1084.86
Re-StyleGAN213.211.25±0.3129.194.28.53±0.2962.341.36.47±0.1082.63
+ +Table 3: FID comparison to NAS-based GANs, i.e., AutoGAN for full CIFAR-10 dataset. + +
Methods#RI (M)Training time (hour)Flops (×1016)FID↓ Full data
AutoGAN (Top A)4.76.719M17.70
Re-AutoGAN (Top A)4.15.7216.5M17.61
AutoGAN (Top B)5.27.7523M18.08
Re-AutoGAN (Top B)4.25.9518M17.30
AutoGAN (Top C)5.78.1223M17.09
Re-AutoGAN (Top C)56.7320M16.61
+ +We extend our method comparison with the NAS-based GANs method, i.e., AutoGAN (Top A, B and C architectures) [31], [32]. The result in Table 3 shows that Re-GAN not only improves the performance for human-designed networks (e.g., SNGAN, ProGAN, StyleGAN2) but also boosts the performance and reduces training time and FLOPs for automatically searched architecture, AutoGAN. It also minimizes training time and FLOPs for all top three searched GANs architectures. + +# 4.3. Comparison with GANs tickets + +Recently, Iterative Magnitude Pruning (IMP), an unstructured magnitude pruning [24] have shown performing well in finding lottery tickets in GANs than other pruning methods [66], [73] to find GANs tickets [22], [23] [24]. We find GANs tickets using IMP at $20\%$ and $46\%$ pruning ratio for the full training dataset, named ST_SNGAN@20% and ST_SNGAN@46%, respectively. We also include growing with random initialization (RI), Re-SNGAN-RI in which weights are randomly initialized during the growing rather than zero initialization. Also, we set same learning rate for both dense and sparse phases, Re-SNGAN-lr. The results are summarized in Table 4. The results show that our proposed Re-SNGAN performs well w.r.t FID. Re-SNGAN-RI results in longer convergence times, as network has to explore more diverse weight configurations to find best solution. While, setting 1/10 learning rate during dense phase performs better than same learning rate in both phases as it promotes stability by + +avoiding large, sudden weight updates. Also, finding GANs tickets is highly time consuming. While the training time for exploring different sub-network structures during training, even only at $10\%$ pruning ratio, is comparable to the dense model; In addition, Re-SNGAN consumes less training FLOPs than the GANs tickets. + +Table 4: Comparison to GANs tickets methods on CIFAR-10. + +
Methods#RI (M)Training time (hour)Flops (×1017)FID↓ Full data
SNGAN@0%306.21.0120.12
ST_SNGAN@20%92.519.72.6018.96
ST_SNGAN@46%150323.4618.22
Re-SNGAN-Ir49.410.51.5719.06
Re-SNGAN-RI33.17.31.2519.71
Re-SNGAN31.56.61.0317.87
+ +![](images/c5ed4b2568be1786bd64434b963ca9af09ff63afbec5d095313bb6dc84fa7daf.jpg) +Figure 4: IS $(\uparrow)$ and FID $(\downarrow)$ results of SNGAN with $10\%$ , $20\%$ , $40\%$ , $80\%$ , and full training data of CIFAR-10. Four settings are evaluated: (i) SNGAN (unpruned SNGAN), (ii) ST_SNGAN (applied IMP for finding sparse GANs ticket at $20\%$ pruning ratio), (iii) Sparse_Re-SNGAN (Re-GAN output is sparse), (iv) Dense_Re-SNGAN (Re-GAN output is dense). The main advantage is that it provides both a high-performing dense model and its compressed version at the end of the training. + +![](images/0965be78c124c3d504bc4653d223cd5d5e637fe66f75d5ba5a929ee05b06b18e.jpg) + +Table 5: FID comparison on few-shot datasets at $256\times 256$ resolution. FID and IS are calculated using 5k randomly generated samples, with the training data serving as the reference distribution. The best performance is highlighted. + +
MethodsObamaGrumpy CatPandaAnimal FaceOxford Flowers
CatDog
# of images1001001003891601000
ProGAN129.52135.89235.86289.73259.32224.70
Re-ProGAN110.46124.06205.82283.29227.59198.56
StyleGAN286.6751.395.0881.91157.63147.67
Re-StyleGAN272.9238.2378.4573.05133.4138.35
StyleGAN2 + APA68.7433.7218.2462.7181.1385.88
Re-StyleGAN2 + APA64.2831.7416.3360.2677.4482.19
StyleGAN2 + DiffAug46.3128.612.8942.8558.4746.21
Re-StyleGAN2 + DiffAug45.727.3612.642.1157.245.13
+ +We provide another set of experiments of SNGAN training on CIFAR-10, with training data ranging from $10\%$ to $100\%$ . Figure 4 provides a summary of the key findings. The following observations can be drawn: First, at the same data availability (from $10\%$ to even $100\%$ ), exploring multiple sub-networks during training at only $10\%$ pruning ratio is always preferable to training the dense model and sparse ticket; Second, sparse Re-GAN model is also performing consistently well than GANs tickets. + +# 4.4. Few-shot generation + +Collecting a large number of image datasets can be prohibitively costly or perhaps impossible for a certain character or a topic. In this context, a data-efficient model for the image synthesis task will be highly important. In Table 5, we show that our method finds data-efficient GANs that can be trained from scratch with only 100 training image data (without any pre-training) and demonstrates consistently superior performance (See supplementary material for visualizations of few-shot generation and style interpolation). Results also show that proposed Re-GAN improve the generated sample quality of SOTA methods, such as Diffaug [1] and APA [21] for few-shot datasets. We further extend our study for high-resolution experiments (Table 6 and Figure 5) where the + +Re-StyleGAN2 model gets better FID scores on all 1k, 5k, 10k and 70k FFHQ datasets (see supplementary material for more details). To further demonstrate the effectiveness of our Re-GAN, we apply it to other recent methods, FastGAN [74] for several few-shot datasets. Results are shown in supplementary material. + +Table 6: FID comparison on few-shot datasets at $1024 \times 1024$ resolution. FID and IS are calculated using 50k randomly generated samples, with the training data (70k) serving as the reference distribution. + +
MethodsFFHQ
70k10k5k1k
StyleGAN24.3513.0621.7640.24
Re-StyleGAN24.1911.2219.1336.3
+ +# 4.5. Ablation and analysis + +Prune G/D: We study the impact of exploring different sub-network structures on G or D only, or on both G and D (represented as B) at $10\%$ , $30\%$ , and $50\%$ pruning ratio (i.e., weight remaining ratio indicates the sparsity levels of explored sub-network structures during training) on CIFAR-10 full training dataset. Figure 6 shows a summary of the results. We notice that employing pruning on D or both G and D, achieves comparable or better performance than the base model. While for the same sparsity + +distribution (i.e., pruning ratio), pruning only on G achieves significant performance improvement (i.e., largely reducing the FID). We also notice that update interval (g) 100 works well with only G. + +![](images/b504987451e00754a2b43be72e3217e14d989697e883039eb675bcd4cedd0fef.jpg) +Figure 5: Few-shot generalization results of Re-StyleGAN2 on 10k FFHQ (1024×1024). Samples are randomly drawn without cherry picking. + +Robustness to learning rate. Previous research works [75]–[77] have observed that GANs convergence highly depends on the selection of hyperparameters, especially the learning rate, $\alpha$ . As shown in Table 7, we validate our network by training it with five different $\alpha$ values (0.0001, 0.0002, 0.0005, 0.0007, and 0.00001) for the CIFAR-10 dataset. Results show that for all different $\alpha$ values, our models converged and achieved similar inception scores. + +![](images/21232ef59f9a4b13640fdfd204e52278edb7a79450f045ec12d994ae052b828e.jpg) +Figure 6: FID with different pruning ratio and update interval (g) of Re-SNGAN (CIFAR-10). + +![](images/47241a72b20693e231034cef6005ddf85d1a73082c140d706ab9764862ce781c.jpg) +Figure 7: Stability during training on the $10\%$ CIFAR-10. + +Stability during training. To compare the stability of Re-SNGAN with SNGAN, we evaluate how the samples produced for the same set of latent points vary during training. As proposed in [30], we use the mean squared error (MSE) between two consecutive generated samples as a quantitative measure of training stability. Figure 7 shows the MSE between generated images from the same latent code in the midst of successive epochs on the $10\%$ CIFAR-10 dataset. Results show that dense Re-SNGAN converges consistently over time, while SNGAN varies dramatically across epochs. + +Table 7: Robustness to learning rate. + +
MethodsLearning rateResults
ISFID
Real images-11.34-
SNGAN0.00028.07±0.1620.12
0.00077.93±0.3021.76
0.00058.03±0.2320.17
Re-SNGAN0.00028.16±0.1517.87
0.00018.03±0.1719.03
0.000018.01±0.2519.65
+ +# 5. Conclusion and Discussion of Broader Impact + +We introduce a new perspective on data-efficient GANs by exploring different sub-network structures during training, which is a novel approach compared to existing methods. Extensive experiments on various GANs architectures, objectives, and datasets demonstrate the effectiveness and training efficiency of our proposed GANs training methodology, Re-GAN. In this work, we focus on unstructured sparsity to showcase the algorithm-level innovations of Re-GAN. However, only specific hardware supports sparse tensor cores for weight pruning. Future work could aim for a high pruning ratio and reconfigure network width and depth simultaneously during GANs training, addressing the limitations of the current approach. + +This research aims to enhance generalization performance, stabilize GANs models under limited data, and improve training efficiency, which has practical implications for various applications and industries. However, these advancements might also exacerbate existing social risks associated with GANs. We plan to investigate whether the sparse structures affect issues like image generation bias in future work. The ability to generate images with less data could potentially be exploited for undesirable applications, such as DeepFakes. + +# Acknowledgments + +This work is supported by PolyU Internal Start-up Fund (Grant no: P0038876), Research Impact Fund (No. R5034-18), and RGC Collaborative Research Fund (Grant no: C5026-18G). + +# References + +[1] S. Zhao, Z. Liu, J. Lin, J. Y. Zhu, and S. Han, "Differentiable augmentation for data-efficient GAN training," in Advances in Neural Information Processing Systems, 2020, pp. 7559-7570. +[2] Z. Si and S.-C. Zhu, "Learning hybrid image templates (HIT) by information projection," IEEE Trans. Pattern Anal. Mach. Intell., vol. 34, no. 7, pp. 1354-1367, 2011. +[3] A. 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(left) Image generation trained on multiple few-shot generation datasets, such as 100-shot Obama [1], Panda [1], and Animal Face-Cat (A-Cat) [2]; (right) FID scores vs. CIFAR-10 [3] training set size with training cost, FLOPs. Best viewed in color." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 164, + 437, + 212, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 437, + 212, + 450 + ], + "spans": [ + { + "bbox": [ + 164, + 437, + 212, + 450 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 68, + 464, + 308, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 464, + 308, + 706 + ], + "spans": [ + { + "bbox": [ + 68, + 464, + 308, + 706 + ], + "type": "text", + "content": "Training Generative Adversarial Networks (GANs) on high-fidelity images usually requires a vast number of training images. Recent research on GAN tickets reveals that dense GANs models contain sparse sub-networks or \"lottery tickets\" that, when trained separately, yield better results under limited data. However, finding GANs tickets requires an expensive process of train-prune-retrain. In this paper, we propose Re-GAN, a data-efficient GANs training that dynamically reconfigures GANs architecture during training to explore different sub-network structures in training time. Our method repeatedly prunes unimportant connections to regularize GANs network and regrows them to reduce the risk of prematurely pruning important connections. Re-GAN stabilizes the GANs models with less data and offers an alternative to the existing GANs tickets and progressive growing methods. We demonstrate that Re-GAN is a generic training methodology which achieves stability on datasets of varying sizes, domains, and resolutions (CIFAR-10, TinyImageNet, and multiple few-shot generation datasets) as well as different GANs architectures (SNGAN, ProGAN," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 426, + 569, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 426, + 569, + 542 + ], + "spans": [ + { + "bbox": [ + 329, + 426, + 569, + 542 + ], + "type": "text", + "content": "StyleGAN2 and AutoGAN). Re-GAN also improves performance when combined with the recent augmentation approaches. Moreover, Re-GAN requires fewer floating-point operations (FLOPs) and less training time by removing the unimportant connections during GANs training while maintaining comparable or even generating higher-quality samples. When compared to state-of-the-art StyleGAN2, our method outperforms without requiring any additional fine-tuning step. Code can be found at this link: https://github.com/IntellicentAI-Lab/Re-GAN" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 566, + 411, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 566, + 411, + 578 + ], + "spans": [ + { + "bbox": [ + 330, + 566, + 411, + 578 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 582, + 568, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 582, + 568, + 652 + ], + "spans": [ + { + "bbox": [ + 329, + 582, + 568, + 652 + ], + "type": "text", + "content": "In recent years, Generative adversarial networks (GANs) [4]–[7] have made great strides in generating high-fidelity images. The GANs models serve as the backbone of several vision applications, such as data augmentation [5], [8], [9], domain adaptation [10], [11], and image-to-image translation [14]–[16]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 329, + 652, + 568, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 652, + 568, + 710 + ], + "spans": [ + { + "bbox": [ + 329, + 652, + 568, + 710 + ], + "type": "text", + "content": "The success of the GANs methods largely depends on a massive quantity of diverse training data, which is often time-consuming and challenging to collect [17]. Figure 1 shows how the performance of the StyleGAN2 [18] model drastically declines under the limited training data. As a" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "text", + "content": "16230" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 71, + 307, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 71, + 307, + 314 + ], + "spans": [ + { + "bbox": [ + 67, + 71, + 307, + 314 + ], + "type": "text", + "content": "result, various new methods [1], [19], [20] have emerged to deal with the problem of insufficient data. Dynamic data-augmentation [1], [19]-[21] fills in the gap and stabilizes GANs training with less data. Very recently, [22], [23] introduced the lottery ticket hypothesis (LTH) in GANs (called \"GANs tickets\"), a complementary to the existing augmentation techniques. LTH identifies sparse sub-networks (called \"winning tickets\") that can be trained in isolation to match or even surpass the performance of unpruned models. [24] demonstrated that an identified GANs ticket can be used as a sparse structural prior to alleviate the problem of limited data in GANs. However, identifying these winning tickets requires many iterations of a time-consuming and computationally expensive train-prune-retrain process. This results in high training time and a number of floating-point operations (FLOPs) than training a dense GANs models, such as StyleGAN2 [18] and BigGAN [5]. In addition, these methods train a full-scale model before pruning, and then, after the pruning process, they engage in an extra fine-tuning to improve the performance. Given this perspective, we ask:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 319, + 308, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 319, + 308, + 354 + ], + "spans": [ + { + "bbox": [ + 68, + 319, + 308, + 354 + ], + "type": "text", + "content": "Is there any way to achieve training efficiency w.r.to both data and computation in GANs while preserving or even improving its performance?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 359, + 306, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 359, + 306, + 474 + ], + "spans": [ + { + "bbox": [ + 67, + 359, + 306, + 474 + ], + "type": "text", + "content": "One potential solution is network pruning during training, which can allow the exploration of different subnetwork structures in training-time. Network structure exploration during training has shown to be effective in a variety of domains [25], [26], and its properties have been the subject of a significant amount of research [27], [28]. However, network pruning is never introduced to GANs training; as a result, the investigation of different subnetwork structures exploration during GANs training remains mysterious." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 475, + 308, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 475, + 308, + 706 + ], + "spans": [ + { + "bbox": [ + 67, + 475, + 308, + 706 + ], + "type": "text", + "content": "To address this gap in the literature, we investigate and introduce the network pruning, i.e., connections, in GANs training by dynamically reconfiguring GANs architecture to allow the exploration of different sub-network structures in training time, dubbed as Re-GAN. However, on the other hand, it is common knowledge that the learning capabilities of the two competing networks—a generator (G) and a discriminator (D), need to be carefully maintained equilibrium in their respective capabilities for learning. Hence to build Re-GAN, the first question is: how to explore different network structures during GANs training? Network pruning during training regularizes the G to allow a robust gradient flow through G. This stabilizes the GANs models under limited training data and improves training efficiency. Re-GAN repeatedly prunes and grows the connections during the training process to reduce the risk of pruning important connections prematurely and prevent the model from losing its representational capabilities early in the training process. As a result, network growing provides a second opportunity to" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 329, + 72, + 567, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 72, + 567, + 95 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 567, + 95 + ], + "type": "text", + "content": "reinitialize pruned connections by reusing information from previously explored sub-network structures." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 337, + 102, + 561, + 220 + ], + "blocks": [ + { + "bbox": [ + 337, + 102, + 561, + 220 + ], + "lines": [ + { + "bbox": [ + 337, + 102, + 561, + 220 + ], + "spans": [ + { + "bbox": [ + 337, + 102, + 561, + 220 + ], + "type": "image", + "image_path": "29248e15189d4b11f0c6d202b6ea763d8e930e1f78433910e03ccf70cac89735.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 220, + 563, + 262 + ], + "lines": [ + { + "bbox": [ + 334, + 220, + 563, + 262 + ], + "spans": [ + { + "bbox": [ + 334, + 220, + 563, + 262 + ], + "type": "text", + "content": "Figure 2: Conventional GANs training has fixed connectivity space. Re-GAN uses network pruning and growing during training to make connectivity space flexible that helps in the propagation of robust gradients. Best viewed in color." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "spans": [ + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": "The second question is: how to explore different subnetwork structures in " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " simultaneously? On the one hand, if we employ a pretrained " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": ") and prune solely for " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": "), it can quickly incur an imbalance between the capabilities of " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " (particularly in the early stage of training), resulting in slow convergence. While it is possible to prune for " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " simultaneously, empirical experiments show that doing so significantly degrades the initial unstable GANs training, resulting in highly fluctuating training curves and, in many cases, a failure to converge. As a trade-off, we propose expanding " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": " as per standard GANs training while applying pruning exclusively to " + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 329, + 267, + 568, + 417 + ], + "type": "text", + "content": "'s architecture." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 329, + 417, + 568, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 417, + 568, + 601 + ], + "spans": [ + { + "bbox": [ + 329, + 417, + 568, + 601 + ], + "type": "text", + "content": "Additionally, our method is robust, working well with a wide range of GANs architectures (ProGANs [29], SNGAN [30], StyleGAN2, and AutoGAN [31], [32]) and datasets (CIFAR-10 [3], Tiny-ImageNet [33], Flickr Faces HQ [34], and many few-shot generation datasets). We find that exploring different sub-network structures during training accounts for a significant decrease in FID score compared to the vanilla DCGAN [35] architecture without a pre-trained model or fine-tuning the pruned model (see Figure 2). Our method delivers higher performance in less training time to state-of-the-art (SOTA) methods on most available datasets without additional hyperparameters that progressive growing method introduces, such as training schedules and learning rates for different generation stages (resolutions). This robustness allows the Re-GAN to be easily generalized on unseen datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 329, + 601, + 567, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 601, + 567, + 635 + ], + "spans": [ + { + "bbox": [ + 329, + 601, + 567, + 635 + ], + "type": "text", + "content": "To the best of our knowledge, Re-GAN is the first attempt to incorporate network pruning during GANs training. Our technical innovations are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 330, + 636, + 568, + 706 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 330, + 636, + 567, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 636, + 567, + 681 + ], + "spans": [ + { + "bbox": [ + 330, + 636, + 567, + 681 + ], + "type": "text", + "content": "- We conduct the first in-depth study on taking a unified approach of incorporating pruning in GANs training without pre-training a large model or fine-tuning the pruned model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 683, + 568, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 683, + 568, + 706 + ], + "spans": [ + { + "bbox": [ + 330, + 683, + 568, + 706 + ], + "type": "text", + "content": "- Our method repeatedly prunes and grows the connections during training to reduce the possibility of" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "type": "text", + "content": "16231" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 86, + 72, + 307, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 72, + 307, + 129 + ], + "spans": [ + { + "bbox": [ + 86, + 72, + 307, + 129 + ], + "type": "text", + "content": "pruning important connections and helps the model to maintain its representation ability early in training. Thus, network growing gives another chance to reinitialize pruned connections from the explored network sub-structures." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "spans": [ + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "content": "- Extensive experiments are conducted across a wide range of GANs architectures and demonstrated that Re-GAN could be easily applied on these GANs architectures to improve their performances, both in regular and low-data regime setups. For example, for the identified winning GANs ticket, ProGAN and StyleGAN2 on full CIFAR-10, we achieve " + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "inline_equation", + "content": "70.23\\%" + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "inline_equation", + "content": "18.81\\%" + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "inline_equation", + "content": "19\\%" + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "content": " training FLOPs savings, respectively, while improved generated sample quality for both full and " + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 69, + 129, + 307, + 291 + ], + "type": "text", + "content": " training data. Re-GAN presents a viable alternative to the GANs tickets and progressive growing techniques. Additionally, the performance of Re-GAN is enhanced when integrated with recent augmentation techniques." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 303, + 162, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 303, + 162, + 316 + ], + "spans": [ + { + "bbox": [ + 69, + 303, + 162, + 316 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 320, + 306, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 320, + 306, + 562 + ], + "spans": [ + { + "bbox": [ + 71, + 320, + 306, + 562 + ], + "type": "text", + "content": "Stabilize the GANs training. In recent years, different loss functions [4], [36], [37], regularization [30], [38], and architectural designs [39], [40] have all been proposed as ways to enhance GANs [6]. Our efforts are in the category of network architecture design. Recently, state-of-the-art (SOTA) models like StyleGAN2 and BigGAN have suggested making networks deeper and wider. They have also shown that training deep GANs networks usually leads to better generalization. However, a deeper model with more convolution layers results in a longer training time for GANs. This is because a deeper model contains a greater number of model parameters and a weaker gradient flow via G [29], [41], [42]. The findings of Progressive GAN (ProGAN) [29] show that gradually growing and training both networks together from a lower resolution, stabilizes the training and enhances the generation quality. MSG-GAN [39] introduced a solution to the gradient flow issue in which G gets feedback from a number of different resolutions simultaneously. Nevertheless, these methods further add to the computational cost, necessitating an even high amount of GPU memory and more training time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 563, + 307, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 563, + 307, + 701 + ], + "spans": [ + { + "bbox": [ + 68, + 563, + 307, + 701 + ], + "type": "text", + "content": "GANs compression. GANs, like other deep neural networks, excel in image generation and translation tasks [29], [43]–[45], but suffer from high computational complexity and memory requirements. Han et al. [46] introduced a co-evolutionary pruning technique for GANs compression, while Wang et al. [47] proposed quantizing GANs to 1 or 2 bits. Li et al. [48] used distillation to improve compressed D with a pre-trained GANs model, and Wang et al. [49] combined these three techniques into one framework. Although impressive results were achieved in training compressed G with a pre-trained D [50], existing GANs compression approaches require pre" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 329, + 72, + 568, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 72, + 568, + 163 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 568, + 163 + ], + "type": "text", + "content": "training an over-parameterized model, limiting training efficiency. Meanwhile, [51] proposed dynamic network size modification during training, but design space exploration is constrained by network augmentation. Our approach injects sparsity during training to enhance generalization, stabilize GANs with limited data, and improve training efficiency, distinguishing it from these inference-focused techniques." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 329, + 164, + 568, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 164, + 568, + 301 + ], + "spans": [ + { + "bbox": [ + 329, + 164, + 568, + 301 + ], + "type": "text", + "content": "Lottery Ticket Hypothesis (LTH). Recently, [22]–[24] have shown the existence of winning tickets in the min-max game beyond minimization by extending LTH to GANs. [52] claims the existence of independently trainable sparse sub-networks capable of performing at the same level as dense networks and in some instances, even better. While [53], [54] scaled up LTH by rewinding [55], [56]. However, these methods do not restore key connections that have been prematurely pruned, which restricts the model's capacity. In contrast, the proposed method can restore connections that have been prematurely pruned and can better preserve the capacity of the model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 329, + 302, + 569, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 302, + 569, + 406 + ], + "spans": [ + { + "bbox": [ + 329, + 302, + 569, + 406 + ], + "type": "text", + "content": "On the other hand, the total number of FLOPs necessary to locate and train a winning ticket at a sparsity level of " + }, + { + "bbox": [ + 329, + 302, + 569, + 406 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 329, + 302, + 569, + 406 + ], + "type": "text", + "content": " is more than four times as many as the number of FLOPs necessary to train a dense model [57]. As the size of SOTA models have grown (e.g., BigGAN and StyleGAN2), such huge resource needs would cause financial and environmental problems [58]–[60]. Being unique and orthogonal efforts from ours, these methods do not focus on the training efficiency yet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 329, + 418, + 414, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 418, + 414, + 432 + ], + "spans": [ + { + "bbox": [ + 329, + 418, + 414, + 432 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 329, + 447, + 440, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 447, + 440, + 460 + ], + "spans": [ + { + "bbox": [ + 329, + 447, + 440, + 460 + ], + "type": "text", + "content": "3.1. Design motivation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 329, + 465, + 568, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 465, + 568, + 546 + ], + "spans": [ + { + "bbox": [ + 329, + 465, + 568, + 546 + ], + "type": "text", + "content": "The synaptic connection topology of the brain is very dynamic, yet the brain still maintains a stable and efficient computing function [61], [62]. It has been shown that the underlying process of synaptic rewiring plays a crucial part in learning [63]. We consider the training of GANs to be akin to such biological learning processes and combine it with different training objectives under sparsity constraint." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 547, + 568, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 547, + 568, + 672 + ], + "spans": [ + { + "bbox": [ + 329, + 547, + 568, + 672 + ], + "type": "text", + "content": "In contrast to conventional GANs training with predefined static connectivity, we prune and grow the connections during the GANs training. We conduct a thorough investigation to find that introducing network pruning and growing into GANs training yields desirable results on many fronts, specifically: (1) stabilizes GANs across various datasets, resolutions, domains, and architectures; (2) maintaining comparable or even generating higher-quality samples; and (3) enhancing the GANs training efficiency w.r.t both data and computation by removing the unimportant connections." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 672, + 568, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 672, + 568, + 708 + ], + "spans": [ + { + "bbox": [ + 329, + 672, + 568, + 708 + ], + "type": "text", + "content": "In the next sub-section, we review the traditional GANs models, then describe in detail our proposed GANs training methodology via architectural reconfiguration." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "text", + "content": "16232" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 70, + 542, + 270 + ], + "blocks": [ + { + "bbox": [ + 95, + 70, + 542, + 270 + ], + "lines": [ + { + "bbox": [ + 95, + 70, + 542, + 270 + ], + "spans": [ + { + "bbox": [ + 95, + 70, + 542, + 270 + ], + "type": "image", + "image_path": "25cbf60c2f4de0e574847ff9931a1e632675b888eb828f2b5a9d111fa0c703a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 275, + 569, + 308 + ], + "lines": [ + { + "bbox": [ + 68, + 275, + 569, + 308 + ], + "spans": [ + { + "bbox": [ + 68, + 275, + 569, + 308 + ], + "type": "text", + "content": "Figure 3: Architecture of Re-GAN, shown here on the base model proposed in GANs [6]. The key feature of Re-GAN is that it provides sparse-dense model pairs at the end of the training process. This is beneficial in practice, as it may be desired to deploy compressed variant in resource-constrained environments without redoing the full training process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 325, + 250, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 325, + 250, + 337 + ], + "spans": [ + { + "bbox": [ + 69, + 325, + 250, + 337 + ], + "type": "text", + "content": "3.2. Generative Adversarial Networks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "spans": [ + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": "A GANs model consists of a discriminator " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{D}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": " and a generator " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{G}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": ". The training objectives of the " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{D}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{G}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": " can be represented as " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\theta_{D}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "inline_equation", + "content": "\\theta_{G}" + }, + { + "bbox": [ + 68, + 343, + 307, + 389 + ], + "type": "text", + "content": ", respectively. The GANs framework can be as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 87, + 395, + 306, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 395, + 306, + 416 + ], + "spans": [ + { + "bbox": [ + 87, + 395, + 306, + 416 + ], + "type": "interline_equation", + "content": "\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x)) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z))) ] \\tag {1}", + "image_path": "198e292738f6048e73c1d2a1beaa58eb4b77d85a9a18482f0f2fcf17be1a1d75.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 133, + 426, + 306, + 446 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 426, + 306, + 446 + ], + "spans": [ + { + "bbox": [ + 133, + 426, + 306, + 446 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D (G (z))\\right) \\right], \\tag {2}", + "image_path": "892d0a3cbb5196429b70bf4db26c3b472e8d6b1272f722f0d54cc857194fb486.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "spans": [ + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "inline_equation", + "content": "p_{z}" + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": " is the prior distribution (e.g., " + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "inline_equation", + "content": "N(0, I)" + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "inline_equation", + "content": "p_{data}" + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": " is the real training data used to approximate the data distribution. The notations " + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "inline_equation", + "content": "f_{D}, f_{G}" + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "inline_equation", + "content": "g_{G}" + }, + { + "bbox": [ + 68, + 450, + 307, + 509 + ], + "type": "text", + "content": " in Eq. (1) and (2) represent the mapping functions from which various GANs losses can be derived [64]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 520, + 250, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 520, + 250, + 545 + ], + "spans": [ + { + "bbox": [ + 69, + 520, + 250, + 545 + ], + "type": "text", + "content": "3.3. GANs training with architectural reconfiguration" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "spans": [ + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "content": "A network's topology is equivalent to a directed acyclic graph with a predetermined order of nodes. Each node " + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{in}}" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "content": " serves as an input feature, and each edge functions as a computation cell with hyperparameters. We parameterize architectural space by associating a mask variable " + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "inline_equation", + "content": "m \\in \\{0,1\\}" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "content": " with each computation cell to enable training time pruning (" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "inline_equation", + "content": "m = 1 \\rightarrow 0" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "content": ") and growing (" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "inline_equation", + "content": "m = 0 \\rightarrow 1" + }, + { + "bbox": [ + 68, + 551, + 306, + 666 + ], + "type": "text", + "content": "). We consider a single-level configuration space for GANs architecture that enables dynamic pruning and growing networks width-wise." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 666, + 307, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 666, + 307, + 702 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 307, + 702 + ], + "type": "text", + "content": "Revisiting GANs training. Re-GAN reconfigures G's architecture to explore different sub-network structures during training. As shown in Algorithm 1, we start the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 329, + 312, + 568, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 312, + 568, + 451 + ], + "spans": [ + { + "bbox": [ + 329, + 312, + 568, + 451 + ], + "type": "text", + "content": "GANs training on the dense network for several iterations, warm-up phase, and learn the connection weights to know their importance. To achieve the sparse structure, we prune the least important weights based on the pre-defined pruning criterion. We then activate the pruned connections to further grow the network after a series of iterative optimizations. Once the network topology has been changed from sparse to dense, it will train the new network until the next connectivity update. The overview of ReGAN is shown in Figure 3. The main factors of Re-GAN training are as follows: 1) sparsity distribution, 2) update schedule, 3) pruning, and 4) grow." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "spans": [ + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": "GANs sub-networks exploration. We prune the low-weight connections by using unstructured magnitude pruning [65], [66] by using the binary masks " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "m_{g}" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "m_{d}" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": ". The pruning ratio " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": " determines the amount of weights removed during the pruning phase. We use " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "\\rho = 10\\%" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": " in all experiments except StyleGAN2 for FFHQ " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "(\\rho = 30\\%)" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": ". We use the same sparsity across all layers, i.e., uniform sparsity distribution. First, we sort the weights and produced a binary mask to exclude weights smaller than " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": ". If the mask of each layer that has to be regularized is calculated, then the mask of the whole parameter space, " + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 329, + 451, + 568, + 591 + ], + "type": "text", + "content": ", can be obtained for both G and D. Consequently, Eq. 1 and 2 here become:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 596, + 584, + 626 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 596, + 584, + 626 + ], + "spans": [ + { + "bbox": [ + 329, + 596, + 584, + 626 + ], + "type": "interline_equation", + "content": "\\max _ {\\theta_ {D}} \\mathbb {E} _ {x \\sim p _ {d a t a}} [ f _ {D} (D (x, \\theta_ {D} \\odot M _ {D})) ] + \\mathbb {E} _ {z \\sim p _ {z}} [ f _ {G} (D (G (z, \\theta_ {G} \\odot M _ {G}))) ] \\tag {3}", + "image_path": "eaeac5e977f4f1c7beb5037ac1b8492174a84518e3c11393a9f99127bf29ea4c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 376, + 638, + 566, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 638, + 566, + 658 + ], + "spans": [ + { + "bbox": [ + 376, + 638, + 566, + 658 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta_ {G}} \\mathbb {E} _ {z \\sim p _ {z}} \\left[ g _ {G} \\left(D \\left(G (z, \\theta_ {G} \\odot M _ {G})\\right)\\right) \\right], \\tag {4}", + "image_path": "d062615b865e24d6604037189e1e0e46d03a894acd155858d352946335753aac.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "spans": [ + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "inline_equation", + "content": "\\theta_{G}, M_{G}, \\theta_{D}" + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "inline_equation", + "content": "M_{D}" + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "text", + "content": " are the corresponding weights and masks for G and D, " + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 329, + 662, + 567, + 685 + ], + "type": "text", + "content": " stands for Hadamard product." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 686, + 567, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 686, + 567, + 709 + ], + "spans": [ + { + "bbox": [ + 329, + 686, + 567, + 709 + ], + "type": "text", + "content": "The update schedule contains two key factors, (i) the update interval (g) is the number of training iterations" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 317, + 755 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 317, + 755 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 317, + 755 + ], + "type": "text", + "content": "16233" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 307, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 307, + 129 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 307, + 129 + ], + "type": "text", + "content": "between the pruning and growing phase and vice versa; (ii) the learning rate, we set 1/10 the initial learning rate during the network growing phase. Other hyperparameters remained the same as per the given GANs network architecture." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 129, + 308, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 129, + 308, + 360 + ], + "spans": [ + { + "bbox": [ + 67, + 129, + 308, + 360 + ], + "type": "text", + "content": "During each connectivity update, we use the weight magnitude as the indicator for pruning and make the following state transitions: if an indicator changes from 1 to 0, we remove the corresponding connection from the computational graph; During the network growing, all the pruned connections return to 1, indicating that the network will be grown back, initialized weights with 0 and trained. The network growing phase boosts the network's model capacity and makes it easier to get a better local minimum than with a sparse network topology. Similarly, growing new connections in G allows for the search for optimal connectivity and escape from undesired local minima. In addition, by deleting the least significant connections, our method considerably reduces both the training memory cost and the training time, hence enhancing training efficiency. We experiment with three distinct loss functions for the " + }, + { + "bbox": [ + 67, + 129, + 308, + 360 + ], + "type": "inline_equation", + "content": "\\mathrm{d}_{\\mathrm{crit}}" + }, + { + "bbox": [ + 67, + 129, + 308, + 360 + ], + "type": "text", + "content": " function namely, WGAN-GP [67] which is used by ProGAN, hinge loss is used by SNGAN and non-saturating GAN loss with 1-sided GP [6] which is used by StyleGAN2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 372, + 195, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 372, + 195, + 385 + ], + "spans": [ + { + "bbox": [ + 69, + 372, + 195, + 385 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "spans": [ + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": "In this section, we perform experiments on various datasets that contain a wide range of content categories. We evaluate CIFAR-10 and Tiny-ImageNet at " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": " resolution, based on unconditional ProGAN [29][68], SNGAN [30][69], and SOTA StyleGAN2 [18][70]. We use the widely adopted evaluation metrics, such as the Fréchet Inception Distance (FID) [71] and Inception Score (IS) [4], and also provide the number of real images (#RI (in Millions (M)) [29][30]. If model " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": " is taking less number of real images and is achieving comparable or better results than model " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": ", it shows that model " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": " is efficient. Note that higher performing GANs models are indicated by lower FID (" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": "), and larger IS (" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": "). We further extend our study on " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": " resolution, we test on Animal-Face Dog and Cat [2], 100-Shot-Obama [1], Panda [1], and Grumpy-cat [1], and Oxford-flowers [72]. On " + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 67, + 389, + 308, + 608 + ], + "type": "text", + "content": " resolution, we test on 1k, 5k, 10k and 70k Flickr-Face-HQ (FFHQ) [34]. We also perform extensive ablation study to analyze the effectiveness of each component in Re-GAN." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 620, + 201, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 620, + 201, + 633 + ], + "spans": [ + { + "bbox": [ + 69, + 620, + 201, + 633 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 638, + 307, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 638, + 307, + 708 + ], + "spans": [ + { + "bbox": [ + 67, + 638, + 307, + 708 + ], + "type": "text", + "content": "For ProGAN and StyleGAN2, for each dataset, we use the same 512-dimensional initial latent space, derived from a standard normal distribution " + }, + { + "bbox": [ + 67, + 638, + 307, + 708 + ], + "type": "inline_equation", + "content": "N(0, l)" + }, + { + "bbox": [ + 67, + 638, + 307, + 708 + ], + "type": "text", + "content": ", followed by hypersphere normalization [29]. For SNGAN, the latent variable dimension is 128 for all datasets. For all experiments, we use the same hyperparameter settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 329, + 72, + 567, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 72, + 567, + 106 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 567, + 106 + ], + "type": "text", + "content": "However, we reduce the learning rate ten times during network growing phase for better learning. We initialize parameters using standard normal distribution " + }, + { + "bbox": [ + 329, + 72, + 567, + 106 + ], + "type": "inline_equation", + "content": "N(0,1)" + }, + { + "bbox": [ + 329, + 72, + 567, + 106 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "spans": [ + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "text", + "content": "We trained all models ourselves and used the same hardware to provide fair comparisons of the training times for the corresponding set of experiments. We use NVIDIA RTX 3090 GPU with 24 GB for all " + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "text", + "content": " experiments, and NVIDIA Quadro RTX 8000 GPU with 48 GB for all " + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 329, + 106, + 569, + 234 + ], + "type": "text", + "content": " experiments. We train for the same number of iterations predefined by the baseline models. We save the checkpoints every 10k iterations during training and report the best FID as well as the time it took to obtain that score from the checkpoints (e.g., happens at least after 15 hours of training for StyleGAN2)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 334, + 242, + 435, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 242, + 435, + 252 + ], + "spans": [ + { + "bbox": [ + 334, + 242, + 435, + 252 + ], + "type": "text", + "content": "Algorithm1 Re-GAN training" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "spans": [ + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": "Input: An L-layer GANs model; target sparsity k; total training iterations " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_{\\text{total}}" + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": "; training iterations between two consecutive steps, update interval " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": "; training set " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": "; learning rate " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": "; \nOutput: Converged " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 333, + 255, + 567, + 293 + ], + "type": "inline_equation", + "content": "D" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 344, + 294, + 556, + 332 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 344, + 294, + 548, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 294, + 548, + 304 + ], + "spans": [ + { + "bbox": [ + 344, + 294, + 548, + 304 + ], + "type": "text", + "content": "1. Randomly initialize all model weights " + }, + { + "bbox": [ + 344, + 294, + 548, + 304 + ], + "type": "inline_equation", + "content": "\\theta_{G} \\in \\mathbb{R}^{N}, \\theta_{D} \\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 344, + 294, + 548, + 304 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "spans": [ + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "text", + "content": "2. Train the weights " + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "inline_equation", + "content": "\\theta_{G}" + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "inline_equation", + "content": "\\theta_{D}" + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "inline_equation", + "content": "\\Delta_W" + }, + { + "bbox": [ + 344, + 304, + 556, + 313 + ], + "type": "text", + "content": " epochs // warm-up phase" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 344, + 313, + 490, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 313, + 490, + 323 + ], + "spans": [ + { + "bbox": [ + 344, + 313, + 490, + 323 + ], + "type": "text", + "content": "3. while each training iteration " + }, + { + "bbox": [ + 344, + 313, + 490, + 323 + ], + "type": "inline_equation", + "content": "t \\in [\\mathrm{T}_{\\mathrm{total}}]" + }, + { + "bbox": [ + 344, + 313, + 490, + 323 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 344, + 323, + 433, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 323, + 433, + 332 + ], + "spans": [ + { + "bbox": [ + 344, + 323, + 433, + 332 + ], + "type": "text", + "content": "4. if mod " + }, + { + "bbox": [ + 344, + 323, + 433, + 332 + ], + "type": "inline_equation", + "content": "(\\mathrm{t},\\mathrm{g}) = 0" + }, + { + "bbox": [ + 344, + 323, + 433, + 332 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 345, + 294, + 553, + 447 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 365, + 332, + 448, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 332, + 448, + 342 + ], + "spans": [ + { + "bbox": [ + 365, + 332, + 448, + 342 + ], + "type": "text", + "content": "// entered a pruning phase" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 342, + 543, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 342, + 543, + 352 + ], + "spans": [ + { + "bbox": [ + 345, + 342, + 543, + 352 + ], + "type": "text", + "content": "5. " + }, + { + "bbox": [ + 345, + 342, + 543, + 352 + ], + "type": "inline_equation", + "content": "\\theta_{G}\\gets T_{k}(\\theta_{G},k)" + }, + { + "bbox": [ + 345, + 342, + 543, + 352 + ], + "type": "text", + "content": " //Apply compression(top-k)-" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 345, + 352, + 525, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 352, + 525, + 361 + ], + "spans": [ + { + "bbox": [ + 345, + 352, + 525, + 361 + ], + "type": "text", + "content": "6. " + }, + { + "bbox": [ + 345, + 352, + 525, + 361 + ], + "type": "inline_equation", + "content": "\\theta_{D} \\gets T_{k}(\\theta_{D}, k) \\quad //" + }, + { + "bbox": [ + 345, + 352, + 525, + 361 + ], + "type": "text", + "content": " operations on weights" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 345, + 361, + 498, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 361, + 498, + 371 + ], + "spans": [ + { + "bbox": [ + 345, + 361, + 498, + 371 + ], + "type": "text", + "content": "7. " + }, + { + "bbox": [ + 345, + 361, + 498, + 371 + ], + "type": "inline_equation", + "content": "m_{G}, m_{D} \\gets 1[\\theta_{i} \\neq 0] // Create masks" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 345, + 371, + 380, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 371, + 380, + 380 + ], + "spans": [ + { + "bbox": [ + 345, + 371, + 380, + 380 + ], + "type": "text", + "content": "8. else" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 345, + 380, + 449, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 380, + 449, + 389 + ], + "spans": [ + { + "bbox": [ + 345, + 380, + 449, + 389 + ], + "type": "text", + "content": "// entered a growing phase" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 345, + 389, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 389, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 345, + 389, + 547, + 399 + ], + "type": "text", + "content": "9. " + }, + { + "bbox": [ + 345, + 389, + 547, + 399 + ], + "type": "inline_equation", + "content": "\\alpha = \\alpha * 0.1" + }, + { + "bbox": [ + 345, + 389, + 547, + 399 + ], + "type": "text", + "content": " // reduce the learning rate by 10" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 345, + 399, + 498, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 399, + 498, + 409 + ], + "spans": [ + { + "bbox": [ + 345, + 399, + 498, + 409 + ], + "type": "text", + "content": "10. " + }, + { + "bbox": [ + 345, + 399, + 498, + 409 + ], + "type": "inline_equation", + "content": "m_{G}, m_{D} \\gets 1_{N}" + }, + { + "bbox": [ + 345, + 399, + 498, + 409 + ], + "type": "text", + "content": " // reset all masks" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 346, + 410, + 387, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 410, + 387, + 418 + ], + "spans": [ + { + "bbox": [ + 346, + 410, + 387, + 418 + ], + "type": "text", + "content": "11. end if" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 346, + 418, + 457, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 418, + 457, + 427 + ], + "spans": [ + { + "bbox": [ + 346, + 418, + 457, + 427 + ], + "type": "text", + "content": "12. Sample a mini-batch from " + }, + { + "bbox": [ + 346, + 418, + 457, + 427 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 346, + 418, + 457, + 427 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 346, + 427, + 553, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 427, + 553, + 437 + ], + "spans": [ + { + "bbox": [ + 346, + 427, + 553, + 437 + ], + "type": "text", + "content": "13. " + }, + { + "bbox": [ + 346, + 427, + 553, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{G},\\theta_{D}\\gets \\theta_{G}\\odot m_{G},\\theta_{D}\\odot m_{D} / / \\mathrm{Update}\\theta_{G},\\theta_{D}" + }, + { + "bbox": [ + 346, + 427, + 553, + 437 + ], + "type": "text", + "content": " by Eq. (3)" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 346, + 437, + 537, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 437, + 537, + 447 + ], + "spans": [ + { + "bbox": [ + 346, + 437, + 537, + 447 + ], + "type": "text", + "content": "14. end while // and (4), respectively" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "spans": [ + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "text", + "content": "For StyleGAN2, we find that using default settings is hardly to converge on CIFAR-10 and Tiny-/ImageNet, so we follow the settings in [4] for CIFAR-10, in which both path length regularization and lazy regularization are not used, the coefficient for R1 regularization " + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "text", + "content": " is set to 0.1 for CIFAR-10, the output channel at final size level is 128 instead of 512 and doubled at each coarser level with a maximum 512. We use a similar setting for Tiny-/ImageNet except setting " + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "text", + "content": " to 1. For few-shot learning, FFHQ experiments, we set " + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 329, + 460, + 569, + 622 + ], + "type": "text", + "content": " to 10. We note a discrepancy between the results the author described scores and what we could able to accomplish using the author's provided code. This could be the result of subtle hardware variations or variations between runs." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 329, + 635, + 497, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 635, + 497, + 647 + ], + "spans": [ + { + "bbox": [ + 329, + 635, + 497, + 647 + ], + "type": "text", + "content": "4.2. Comparison to state-of-the-art" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "spans": [ + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": "We use the best-performing model ProGAN and StyleGAN2 and perform experiments at " + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": " resolution on CIFAR-10 and Tiny-ImageNet. We evaluate our method with " + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": " data available and with " + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 329, + 653, + 568, + 712 + ], + "type": "text", + "content": " data available, with the findings summarized in Table" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 318, + 756 + ], + "type": "text", + "content": "16234" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 72, + 157, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 72, + 157, + 83 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 157, + 83 + ], + "type": "text", + "content": "1 and 2, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "spans": [ + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "text", + "content": "The following observations can be drawn: First, Re-ProGAN and Re-StyleGAN2 can achieve consistently improved performance for all training cases, from complete data to limited data. In particular, likely to gain more when there is less training data available (e.g., " + }, + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "text", + "content": "), which is consistent with our design principle. With only " + }, + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 67, + 83, + 307, + 186 + ], + "type": "text", + "content": " training data available, Re-ProGAN and Re-StyleGAN2 obtain massive gains of 29.33 FID/7.69 IS and 32.91 FID/7.35 IS on CIFAR-10, respectively, and 79.08" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 329, + 72, + 568, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 72, + 568, + 129 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 568, + 129 + ], + "type": "text", + "content": "FID/6.45 IS and 82.63 FID/6.47 IS on Tiny-ImageNet, respectively. Second, due to removing unimportant connections of low weights, Re-GAN consistently reduces the cost of computation associated with training and requires fewer total hours of GPU training time." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 329, + 129, + 568, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 129, + 568, + 186 + ], + "spans": [ + { + "bbox": [ + 329, + 129, + 568, + 186 + ], + "type": "text", + "content": "Qualitative results and precision-recall curve for Re-StyleGAN2 on CIFAR-10 is in the supplementary material. We also provide a study in the supplementary material to show that Re-GAN helps to alleviate mode collapse." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 79, + 213, + 559, + 324 + ], + "blocks": [ + { + "bbox": [ + 67, + 192, + 567, + 213 + ], + "lines": [ + { + "bbox": [ + 67, + 192, + 567, + 213 + ], + "spans": [ + { + "bbox": [ + 67, + 192, + 567, + 213 + ], + "type": "text", + "content": "Table 1: FID comparison on few-shot datasets at " + }, + { + "bbox": [ + 67, + 192, + 567, + 213 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 67, + 192, + 567, + 213 + ], + "type": "text", + "content": " resolution. FID and IS are calculated using 10k randomly generated samples, with the test data (10k) serving as the reference distribution. The best performance is highlighted." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 213, + 559, + 324 + ], + "lines": [ + { + "bbox": [ + 79, + 213, + 559, + 324 + ], + "spans": [ + { + "bbox": [ + 79, + 213, + 559, + 324 + ], + "type": "table", + "html": "
DatasetSizeMethods#Real Images (RI)(in M)Training Time (hour)FLOPs ×109IS↑FID↓
CIFAR-1050KProGAN19.511.612.978.05 ± 0.2026.14
Re-ProGAN15.99.810.538.22 ± 0.1921.17
StyleGAN217.714.25.08.76 ± 0.2213.19
Re-StyleGAN212.110.14.058.88 ± 0.2412.16
Tiny-ImageNet100KProGAN9.45327.479.44 ± 0.3140.27
Re-ProGAN8.748.922.189.57 ± 0.3537.47
StyleGAN219.252.521.0711.75 ± 0.2520.95
Re-StyleGAN217.846.717.0412.10 ± 0.2820.21
", + "image_path": "a22f70ab59ec831f6a9119942ba1e3a70c7308b753a3e430fbad210c0193dfa0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 62, + 342, + 575, + 462 + ], + "blocks": [ + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "lines": [ + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "spans": [ + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "text", + "content": "Table 2: Experiments on " + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "inline_equation", + "content": "{64} \\times {64}" + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "text", + "content": " resolution " + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "inline_equation", + "content": "{50}\\% ,{20}\\%" + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "inline_equation", + "content": "{10}\\%" + }, + { + "bbox": [ + 99, + 331, + 536, + 342 + ], + "type": "text", + "content": " of training datasets. The best performance is highlighted." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 342, + 575, + 462 + ], + "lines": [ + { + "bbox": [ + 62, + 342, + 575, + 462 + ], + "spans": [ + { + "bbox": [ + 62, + 342, + 575, + 462 + ], + "type": "table", + "html": "
DatasetMethods50% data20% data10% data
#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓#RI (in M)IS↑FID↓
CIFAR-10ProGAN10.57.75±0.1928.337.27.51±0.1928.645.67.47±0.1630.08
Re-ProGAN9.47.97±0.1325.746.17.63±0.1827.194.97.69±0.2329.33
StyleGAN26.48.39±0.1517.224.17.36±0.2729.773.27.20±0.2436.45
Re-StyleGAN248.48±0.1616.093.87.46±0.2327.982.77.35±0.1332.91
Tiny-ImageNetProGAN9.68.71±0.274986.84±0.1277.867.76.38±0.1983.27
Re-ProGAN8.38.84±0.2546.787.76.92±0.1575.227.46.45±0.2279.08
StyleGAN214.511.02±0.2730.035.18.32±0.2465.263.26.32±0.1084.86
Re-StyleGAN213.211.25±0.3129.194.28.53±0.2962.341.36.47±0.1082.63
", + "image_path": "94047b98934926f6c8fd70382bb1aba1b9118ba4fc6df2df3c512bd93bac96ea.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 64, + 491, + 312, + 591 + ], + "blocks": [ + { + "bbox": [ + 67, + 471, + 306, + 491 + ], + "lines": [ + { + "bbox": [ + 67, + 471, + 306, + 491 + ], + "spans": [ + { + "bbox": [ + 67, + 471, + 306, + 491 + ], + "type": "text", + "content": "Table 3: FID comparison to NAS-based GANs, i.e., AutoGAN for full CIFAR-10 dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 491, + 312, + 591 + ], + "lines": [ + { + "bbox": [ + 64, + 491, + 312, + 591 + ], + "spans": [ + { + "bbox": [ + 64, + 491, + 312, + 591 + ], + "type": "table", + "html": "
Methods#RI (M)Training time (hour)Flops (×1016)FID↓ Full data
AutoGAN (Top A)4.76.719M17.70
Re-AutoGAN (Top A)4.15.7216.5M17.61
AutoGAN (Top B)5.27.7523M18.08
Re-AutoGAN (Top B)4.25.9518M17.30
AutoGAN (Top C)5.78.1223M17.09
Re-AutoGAN (Top C)56.7320M16.61
", + "image_path": "2452642c5fe74a61c88e2a57bb434cd470920498080a4342f21276ef8c130d4f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 601, + 307, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 601, + 307, + 706 + ], + "spans": [ + { + "bbox": [ + 67, + 601, + 307, + 706 + ], + "type": "text", + "content": "We extend our method comparison with the NAS-based GANs method, i.e., AutoGAN (Top A, B and C architectures) [31], [32]. The result in Table 3 shows that Re-GAN not only improves the performance for human-designed networks (e.g., SNGAN, ProGAN, StyleGAN2) but also boosts the performance and reduces training time and FLOPs for automatically searched architecture, AutoGAN. It also minimizes training time and FLOPs for all top three searched GANs architectures." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 484, + 500, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 484, + 500, + 498 + ], + "spans": [ + { + "bbox": [ + 329, + 484, + 500, + 498 + ], + "type": "text", + "content": "4.3. Comparison with GANs tickets" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "spans": [ + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "text", + "content": "Recently, Iterative Magnitude Pruning (IMP), an unstructured magnitude pruning [24] have shown performing well in finding lottery tickets in GANs than other pruning methods [66], [73] to find GANs tickets [22], [23] [24]. We find GANs tickets using IMP at " + }, + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "inline_equation", + "content": "46\\%" + }, + { + "bbox": [ + 329, + 502, + 568, + 711 + ], + "type": "text", + "content": " pruning ratio for the full training dataset, named ST_SNGAN@20% and ST_SNGAN@46%, respectively. We also include growing with random initialization (RI), Re-SNGAN-RI in which weights are randomly initialized during the growing rather than zero initialization. Also, we set same learning rate for both dense and sparse phases, Re-SNGAN-lr. The results are summarized in Table 4. The results show that our proposed Re-SNGAN performs well w.r.t FID. Re-SNGAN-RI results in longer convergence times, as network has to explore more diverse weight configurations to find best solution. While, setting 1/10 learning rate during dense phase performs better than same learning rate in both phases as it promotes stability by" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "spans": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "type": "text", + "content": "16235" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 307, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 307, + 140 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 307, + 140 + ], + "type": "text", + "content": "avoiding large, sudden weight updates. Also, finding GANs tickets is highly time consuming. While the training time for exploring different sub-network structures during training, even only at " + }, + { + "bbox": [ + 67, + 72, + 307, + 140 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 67, + 72, + 307, + 140 + ], + "type": "text", + "content": " pruning ratio, is comparable to the dense model; In addition, Re-SNGAN consumes less training FLOPs than the GANs tickets." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 66, + 156, + 310, + 255 + ], + "blocks": [ + { + "bbox": [ + 75, + 146, + 301, + 156 + ], + "lines": [ + { + "bbox": [ + 75, + 146, + 301, + 156 + ], + "spans": [ + { + "bbox": [ + 75, + 146, + 301, + 156 + ], + "type": "text", + "content": "Table 4: Comparison to GANs tickets methods on CIFAR-10." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 156, + 310, + 255 + ], + "lines": [ + { + "bbox": [ + 66, + 156, + 310, + 255 + ], + "spans": [ + { + "bbox": [ + 66, + 156, + 310, + 255 + ], + "type": "table", + "html": "
Methods#RI (M)Training time (hour)Flops (×1017)FID↓ Full data
SNGAN@0%306.21.0120.12
ST_SNGAN@20%92.519.72.6018.96
ST_SNGAN@46%150323.4618.22
Re-SNGAN-Ir49.410.51.5719.06
Re-SNGAN-RI33.17.31.2519.71
Re-SNGAN31.56.61.0317.87
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MethodsObamaGrumpy CatPandaAnimal FaceOxford Flowers
CatDog
# of images1001001003891601000
ProGAN129.52135.89235.86289.73259.32224.70
Re-ProGAN110.46124.06205.82283.29227.59198.56
StyleGAN286.6751.395.0881.91157.63147.67
Re-StyleGAN272.9238.2378.4573.05133.4138.35
StyleGAN2 + APA68.7433.7218.2462.7181.1385.88
Re-StyleGAN2 + APA64.2831.7416.3360.2677.4482.19
StyleGAN2 + DiffAug46.3128.612.8942.8558.4746.21
Re-StyleGAN2 + DiffAug45.727.3612.642.1157.245.13
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MethodsFFHQ
70k10k5k1k
StyleGAN24.3513.0621.7640.24
Re-StyleGAN24.1911.2219.1336.3
", + "image_path": "0cdb0e89561d0f763bb9a266dda36010470b7b2abf065e1bcac8f95864220759.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 588, + 455, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 588, + 455, + 601 + ], + "spans": [ + { + "bbox": [ + 329, + 588, + 455, + 601 + ], + "type": "text", + "content": "4.5. Ablation and analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "spans": [ + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "text", + "content": "Prune G/D: We study the impact of exploring different sub-network structures on G or D only, or on both G and D (represented as B) at " + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 329, + 606, + 569, + 712 + ], + "type": "text", + "content": " pruning ratio (i.e., weight remaining ratio indicates the sparsity levels of explored sub-network structures during training) on CIFAR-10 full training dataset. Figure 6 shows a summary of the results. We notice that employing pruning on D or both G and D, achieves comparable or better performance than the base model. While for the same sparsity" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "spans": [ + { + "bbox": [ + 293, + 746, + 318, + 756 + ], + "type": "text", + "content": "16236" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 72, + 307, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 72, + 307, + 118 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 307, + 118 + ], + "type": "text", + "content": "distribution (i.e., pruning ratio), pruning only on G achieves significant performance improvement (i.e., largely reducing the FID). We also notice that update interval (g) 100 works well with only G." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 77, + 128, + 298, + 312 + ], + "blocks": [ + { + "bbox": [ + 77, + 128, + 298, + 312 + ], + "lines": [ + { + "bbox": [ + 77, + 128, + 298, + 312 + ], + "spans": [ + { + "bbox": [ + 77, + 128, + 298, + 312 + ], + "type": "image", + "image_path": "b504987451e00754a2b43be72e3217e14d989697e883039eb675bcd4cedd0fef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 312, + 307, + 344 + ], + "lines": [ + { + "bbox": [ + 69, + 312, + 307, + 344 + ], + "spans": [ + { + "bbox": [ + 69, + 312, + 307, + 344 + ], + "type": "text", + "content": "Figure 5: Few-shot generalization results of Re-StyleGAN2 on 10k FFHQ (1024×1024). Samples are randomly drawn without cherry picking." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "spans": [ + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "text", + "content": "Robustness to learning rate. Previous research works [75]–[77] have observed that GANs convergence highly depends on the selection of hyperparameters, especially the learning rate, " + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "text", + "content": ". As shown in Table 7, we validate our network by training it with five different " + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "text", + "content": " values (0.0001, 0.0002, 0.0005, 0.0007, and 0.00001) for the CIFAR-10 dataset. Results show that for all different " + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 68, + 354, + 307, + 448 + ], + "type": "text", + "content": " values, our models converged and achieved similar inception scores." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 107, + 453, + 269, + 566 + ], + "blocks": [ + { + "bbox": [ + 107, + 453, + 269, + 566 + ], + "lines": [ + { + "bbox": [ + 107, + 453, + 269, + 566 + ], + "spans": [ + { + "bbox": [ + 107, + 453, + 269, + 566 + ], + "type": "image", + "image_path": "21232ef59f9a4b13640fdfd204e52278edb7a79450f045ec12d994ae052b828e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 566, + 299, + 586 + ], + "lines": [ + { + "bbox": [ + 75, + 566, + 299, + 586 + ], + "spans": [ + { + "bbox": [ + 75, + 566, + 299, + 586 + ], + "type": "text", + "content": "Figure 6: FID with different pruning ratio and update interval (g) of Re-SNGAN (CIFAR-10)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 103, + 587, + 272, + 696 + ], + "blocks": [ + { + "bbox": [ + 103, + 587, + 272, + 696 + ], + "lines": [ + { + "bbox": [ + 103, + 587, + 272, + 696 + ], + "spans": [ + { + "bbox": [ + 103, + 587, + 272, + 696 + ], + "type": "image", + "image_path": "47241a72b20693e231034cef6005ddf85d1a73082c140d706ab9764862ce781c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 82, + 697, + 293, + 709 + ], + "lines": [ + { + "bbox": [ + 82, + 697, + 293, + 709 + ], + "spans": [ + { + "bbox": [ + 82, + 697, + 293, + 709 + ], + "type": "text", + "content": "Figure 7: Stability during training on the " + }, + { + "bbox": [ + 82, + 697, + 293, + 709 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 82, + 697, + 293, + 709 + ], + "type": "text", + "content": " CIFAR-10." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 329, + 72, + 568, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 72, + 568, + 199 + ], + "spans": [ + { + "bbox": [ + 329, + 72, + 568, + 199 + ], + "type": "text", + "content": "Stability during training. To compare the stability of Re-SNGAN with SNGAN, we evaluate how the samples produced for the same set of latent points vary during training. As proposed in [30], we use the mean squared error (MSE) between two consecutive generated samples as a quantitative measure of training stability. Figure 7 shows the MSE between generated images from the same latent code in the midst of successive epochs on the " + }, + { + "bbox": [ + 329, + 72, + 568, + 199 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 329, + 72, + 568, + 199 + ], + "type": "text", + "content": " CIFAR-10 dataset. Results show that dense Re-SNGAN converges consistently over time, while SNGAN varies dramatically across epochs." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 348, + 217, + 550, + 316 + ], + "blocks": [ + { + "bbox": [ + 381, + 207, + 515, + 217 + ], + "lines": [ + { + "bbox": [ + 381, + 207, + 515, + 217 + ], + "spans": [ + { + "bbox": [ + 381, + 207, + 515, + 217 + ], + "type": "text", + "content": "Table 7: Robustness to learning rate." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 348, + 217, + 550, + 316 + ], + "lines": [ + { + "bbox": [ + 348, + 217, + 550, + 316 + ], + "spans": [ + { + "bbox": [ + 348, + 217, + 550, + 316 + ], + "type": "table", + "html": "
MethodsLearning rateResults
ISFID
Real images-11.34-
SNGAN0.00028.07±0.1620.12
0.00077.93±0.3021.76
0.00058.03±0.2320.17
Re-SNGAN0.00028.16±0.1517.87
0.00018.03±0.1719.03
0.000018.01±0.2519.65
", + "image_path": "1d0444c06eb26990e6114fa794dbbffd41a8a4e94a7ae9fe73908e39e2d13583.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 327, + 541, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 327, + 541, + 355 + ], + "spans": [ + { + "bbox": [ + 329, + 327, + 541, + 355 + ], + "type": "text", + "content": "5. Conclusion and Discussion of Broader Impact" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 358, + 568, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 358, + 568, + 519 + ], + "spans": [ + { + "bbox": [ + 329, + 358, + 568, + 519 + ], + "type": "text", + "content": "We introduce a new perspective on data-efficient GANs by exploring different sub-network structures during training, which is a novel approach compared to existing methods. Extensive experiments on various GANs architectures, objectives, and datasets demonstrate the effectiveness and training efficiency of our proposed GANs training methodology, Re-GAN. In this work, we focus on unstructured sparsity to showcase the algorithm-level innovations of Re-GAN. However, only specific hardware supports sparse tensor cores for weight pruning. Future work could aim for a high pruning ratio and reconfigure network width and depth simultaneously during GANs training, addressing the limitations of the current approach." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 519, + 568, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 519, + 568, + 635 + ], + "spans": [ + { + "bbox": [ + 329, + 519, + 568, + 635 + ], + "type": "text", + "content": "This research aims to enhance generalization performance, stabilize GANs models under limited data, and improve training efficiency, which has practical implications for various applications and industries. However, these advancements might also exacerbate existing social risks associated with GANs. We plan to investigate whether the sparse structures affect issues like image generation bias in future work. The ability to generate images with less data could potentially be exploited for undesirable applications, such as DeepFakes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 647, + 427, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 647, + 427, + 661 + ], + "spans": [ + { + "bbox": [ + 330, + 647, + 427, + 661 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 664, + 568, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 664, + 568, + 711 + ], + "spans": [ + { + "bbox": [ + 329, + 664, + 568, + 711 + ], + "type": "text", + "content": "This work is supported by PolyU Internal Start-up Fund (Grant no: P0038876), Research Impact Fund (No. R5034-18), and RGC Collaborative Research Fund (Grant no: C5026-18G)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 317, + 756 + ], + "type": "text", + "content": "16237" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 80, + 72, + 129, + 82 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 72, + 129, + 82 + ], + "spans": [ + { + "bbox": [ + 80, + 72, + 129, + 82 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 83, + 307, + 704 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 70, + 83, + 307, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 83, + 307, + 125 + ], + "spans": [ + { + "bbox": [ + 70, + 83, + 307, + 125 + ], + "type": "text", + "content": "[1] S. 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Bovik", + "bbox": [ + 589, + 181, + 709, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Laboratory of Image and Video Engineering, The University of Texas at Austin", + "bbox": [ + 168, + 198, + 795, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 267 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic Perceptual Image Quality Assessment is a challenging problem that impacts billions of internet, and social media users daily. To advance research in this field, we propose a Mixture of Experts approach to train two separate encoders to learn high-level content and low-level image quality features in an unsupervised setting. The unique novelty of our approach is its ability to generate low-level representations of image quality that are complementary to high-level features representing image content. We refer to the framework used to train the two encoders as Re-IQA. For Image Quality Assessment in the Wild, we deploy the complementary low and high-level image representations obtained from the Re-IQA framework to train a linear regression model, which is used to map the image representations to the ground truth quality scores, refer Figure 1. Our method achieves state-of-the-art performance on multiple large-scale image quality assessment databases containing both real and synthetic distortions, demonstrating how deep neural networks can be trained in an unsupervised setting to produce perceptually relevant representations. We conclude from our experiments that the low and high-level features obtained are indeed complementary and positively impact the performance of the linear regressor. A public release of all the codes associated with this work will be made available on GitHub.", + "bbox": [ + 75, + 282, + 473, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 691, + 209, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Millions of digital images are shared daily on social media platforms such as Instagram, Snapchat, Flickr, etc. Making robust and accurate Image Quality Assessments (IQA) that correlate well with human perceptual judgments is essential to ensuring acceptable levels of visual experience. Social media platforms also use IQA metrics to decide parameter settings for post-upload processing of the images, such as resizing, compression, enhancement, etc.", + "bbox": [ + 75, + 717, + 468, + 839 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/927b61bce702303ec58042a7a37739a82cb1db8407d901a4d758d76129a4b53d.jpg", + "image_caption": [ + "Figure 1. IQA score prediction uses two encoders trained for complementary tasks of learning content and quality aware image representations. The encoders are frozen while the regressor learns to map image representations to quality predictions." + ], + "image_footnote": [], + "bbox": [ + 501, + 250, + 893, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition, predictions generated by IQA algorithms are often used as input to recommendation engines on social media platforms to generate user feeds and responses to search queries. Thus, accurately predicting the perceptual quality of digital images is a high-stakes endeavor affecting the way billions of images are stored, processed, and displayed to the public at large.", + "bbox": [ + 496, + 477, + 893, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "IQA metrics can be simply categorized into Full-Reference (FR) and No-Reference (NR) algorithms. FR-IQA algorithms like SSIM [35], FSIM [43], and LPIPS [44] require both reference (undistorted) and distorted version of an image to quantify the human-perceivable quality. This requirement limits their applicability for the \"Images in the Wild\" scenario, where the reference image is unavailable. On the contrary, NR-IQA algorithms like BRISQUE [19], PaQ-2-PiQ [40], and CONTRIQUE [16] do not require a reference image nor any knowledge about the kind of present distortions to quantify human-perceivable quality in a test image, paving the way for their use in \"Images in the Wild\" scenarios.", + "bbox": [ + 496, + 584, + 895, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "No-Reference IQA for \"Images in the Wild\" presents exciting challenges due to the complex interplay among the various kinds of distortions. Furthermore, due to the intricate nature of the human visual system, image content affects quality perception. In this work, we aim to learn low-level quality-aware image representations that are complementary to high-level features representative of image content. Figure 2 illustrates some of the challenges encountered", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution, Correspondence to Avinab Saha (avinab.saha@utexas.edu) & Sandeep Mishra (sandy.mishra@utexas.edu). This work was supported by the National Science Foundation AI Institute for Foundations of Machine Learning (IFML) under Grant 2019844.", + "bbox": [ + 75, + 849, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5846", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2d67359add27060242b72755c54702e031e1e3860cf0615278fad40538c86a02.jpg", + "image_caption": [ + "(a) JPEG Compressed : 1" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 274, + 202 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b47558248fde6129ef70f40d98f741bed4e974ea8c85d8012846dd0c2d742e23.jpg", + "image_caption": [ + "(b) JPEG Compressed: 2", + "Figure 2. Exemplar Synthetically and \"In the Wild\" distorted pictures. (a), (b) are two images captured on iPhone 13 Pro and then JPEG compressed using the same encoding parameters. (c), (d), were taken from KonIQ and AVA datasets respectively, and exhibit typical \"Images in the Wild\" distortions. Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 202 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/95a6246d297735de1a583555b9627a0a69b95e3f541183bf2ee7c748b555f488.jpg", + "image_caption": [ + "(c) Motion Blur - Camera Shake" + ], + "image_footnote": [], + "bbox": [ + 488, + 89, + 684, + 202 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9a6b5e7db40364c5b0b0961b009f803e205920dd7a9c003752354fb469cd9e0c.jpg", + "image_caption": [ + "(d) Overlaid Film Grain/ Noise" + ], + "image_footnote": [], + "bbox": [ + 694, + 89, + 890, + 202 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in the development of NR-IQA algorithms. Figures 2 (a-b) show two images captured by the authors on an iPhone 13 Pro and compressed using the same encoding parameters. While any distortions are almost negligible in Figure 2 (a), there are artifacts that are clearly visible in Figure 2 (b). As in these examples, it is well known that picture distortion perception is content dependent, and is heavily affected by content related perceptual processes like masking [1]. Figures 2 (c-d) illustrates a few distorted pictures \"In the Wild\". Figures 2 (c-d) show two exemplar distorted pictures, one impaired by motion blur (Figure 2 (c)) and the other by film grain noise (Figure 2 (d)). It is also well established that perceived quality does not correlate well with image metadata like resolution, file size, color profile, or compression ratio [36]. Because of all these factors and the essentially infinite diversity of picture distortions, accurate prediction of the perception of image quality remains a challenging task, despite its apparent simplicity, and hence research on this topic remains quite active [16, 17, 19, 28, 35, 39, 42-44].", + "bbox": [ + 75, + 297, + 468, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is inspired by the success of momentum contrastive learning methods [2, 7] in learning unsupervised representations for image classification. In this work, we engineer our models to learn content and quality-aware image representations for NR-IQA on real, authentically distorted pictures in an unsupervised setting. We adopt a Mixture of Experts approach to independently train two encoders, each of which accurately learns high-level content and low-level image quality features. We refer to the new framework as Re-IQA. The key contributions we make are as follows:", + "bbox": [ + 75, + 585, + 468, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose an unsupervised low-level image quality representation learning framework that generates features complementary to high-level representations of image content. We demonstrate how the \"Mixture\" of the two enables Re-IQA to produce image quality predictions that are highly competitive with existing state-of-the-art traditional, CNN, and Transformer based NR-IQA models, developed in both supervised and unsupervised settings across several databases.", + "bbox": [ + 94, + 763, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We demonstrate the superiority of high-level representations of image content for the NR-IQA task, obtained from the unsupervised pre-training of the ResNet-50 [8] encoder over the features obtained from supervised pre-trained ResNet-50 on the ImageNet database [3]. We learn these high-level representations of image content using the unsupervised training framework proposed in MoCo-v2 [2]", + "- Inspired by the principles of visual distortion perception we propose a novel Image Augmentation and Intra-Pair Image Swapping scheme to enable learning of low-level image quality representations. The dynamic nature of the image augmentation scheme prevents the learning of discrete distortion classes, since it is applied to both pristine and authentically distorted images, enforcing learning of perceptually relevant image-quality features." + ], + "bbox": [ + 517, + 297, + 890, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 573, + 640, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As discussed in Section 1, perceptual image quality prediction for \"Images in the Wild\" is a challenging task due to the complex distortions that arise, and the combinations of them, and how they are perceived when they affect different kinds of pictorial content. Over the last few decades, a great deal of effort has been invested in the development of NR-IQA models that are able to accurately predict human judgment of picture quality. In recent years, NR-IQA models have evolved from using hand-crafted perceptual features, feeding shallow learners, into Deep Learning based approaches trained on large subjective databases. Traditional NR-IQA models generally have two components: a feature extractor, which generates quality-relevant features, and a low-complexity regression model, which maps the extracted features to quality scores. Most prior models have focused on improving the feature extractor and, thus improving the performance of the overall IQA algorithm. A common practice in traditional NR-IQA methods is to model image artifacts using statistical information extracted from a test image. Natural Scene Statistics (NSS) mod", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5847", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/638e3180dbd370670447a4efbc29c7a51a949455d790672a09d1b83128007f08.jpg", + "image_caption": [ + "(a) Original Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 210, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/eadd61043c0ddc768f024309f05f939b52b641ab86db9df1b5a3e9c9e99fde61.jpg", + "image_caption": [ + "(b) Gaussian Blur" + ], + "image_footnote": [], + "bbox": [ + 215, + 88, + 346, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/77f6d6167742404bc6d63070991a84a8f140defa05616a0dec0c743e60c643aa.jpg", + "image_caption": [ + "(c) Saturate" + ], + "image_footnote": [], + "bbox": [ + 351, + 88, + 482, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/329518431690f2f25f2301c905578b9400db96d37e368c026ac9ed9d6fb2e748.jpg", + "image_caption": [ + "(d) Compression" + ], + "image_footnote": [], + "bbox": [ + 486, + 88, + 619, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dd1f467931c2eed83be6f0141db924954b76ec75040d2c7d2ac126553748b5c1.jpg", + "image_caption": [ + "(e) Gaussian Noise" + ], + "image_footnote": [], + "bbox": [ + 624, + 88, + 754, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/15170aee36d285180d129f2b20a6f674872c510683cb997d75ea40186a12ca97.jpg", + "image_caption": [ + "(f) Color Saturate" + ], + "image_footnote": [], + "bbox": [ + 759, + 88, + 890, + 190 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/70bc25dbd8bd785aaebf8c8e1c9f09ed6f930f600b96e4d4733715f0a74df53a.jpg", + "image_caption": [ + "(g) Pixelate" + ], + "image_footnote": [], + "bbox": [ + 80, + 205, + 210, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e52f843786be63c8c91b3193d6b3801448ceed47288d98cc3955ccd63d245bd9.jpg", + "image_caption": [ + "(h) Contrast" + ], + "image_footnote": [], + "bbox": [ + 215, + 205, + 346, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0841b3d20de5611931ee867472029460acb01a90d4ff6a9b8a581ffd96bf8e6c.jpg", + "image_caption": [ + "(i) Darken" + ], + "image_footnote": [], + "bbox": [ + 351, + 205, + 482, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/91536e2fe85d4732e33b714b98ec117f869edba56117aeda727358fb0da78dbc.jpg", + "image_caption": [ + "(j) Resizing", + "Figure 3. Some samples of distortions available in the Image Augmentation Scheme. There are a total of 25 distortions available in the bank, with 5 levels of distortion for each. More details are provided in Supplemental Material." + ], + "image_footnote": [], + "bbox": [ + 486, + 205, + 619, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/91197dff51fb83c56b05776f33cdce8f92b7769d33357e9498be59f5ecdbc6d4.jpg", + "image_caption": [ + "(k) Jitter" + ], + "image_footnote": [], + "bbox": [ + 624, + 205, + 754, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f20306f75853df0b261c0391db9edbc6487b7c5a861aa0a3df37c145af8fb1e0.jpg", + "image_caption": [ + "(1) Motion Blur" + ], + "image_footnote": [], + "bbox": [ + 759, + 205, + 890, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "els and distorted versions of them are popular, where features are extracted from transformed domains, on which statistical measurements of deviations due to distortions are used as features for NR-IQA. For example, the NSS-based BRISQUE [19] and NIQE [20] models obtain features that capture in a normalized bandpass space [26]. DIIVINE [21] uses steerable pyramids, and BLIINDS [27] uses DCT coefficients to measure statistical traces of distortions. Other methods like CORNIA [39] and HOSA [38] utilize codebooks constructed from local patches, which are applied to obtain quality-aware features. Most of the methods discussed above often obtain acceptable results when evaluated on synthetically distorted images, but their performances significantly degrade when applied to \"Images in the Wild\". This is because the above-discussed methods focus primarily on modeling the distortions present in a test image as statistical deviations from naturalness while completely ignoring the high-level content present in the image.", + "bbox": [ + 75, + 388, + 468, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The majority of deep learning approaches utilize pretrained CNN backbones as feature extractors. This is done since end-to-end supervised training of NR-IQA models is difficult given the limited sizes of existing perceptual quality databases. These models typically use CNN backbones trained for ImageNet classification to extract features, combining them with low-complexity regression models like Support Vector Regression or Linear Regression to map the features to human-labeled scores. A few models use labeled scores from IQA databases to fine-tune the CNN backbone. The authors of the RAPIQUE [32] show that features obtained from pretrained ResNet-50 [8] could effectively predict quality scores on \"In the Wild\" content. In DB-CNN [45], authors adopt a two-path technique, where one CNN branch generates distortion-class and distortion-level", + "bbox": [ + 75, + 661, + 470, + 887 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "features, while the other CNN branch provides high-level image content information. These are then combined using bilinear pooling. PQR [41] achieved faster convergence and better quality estimates by using the statistical distributions of subjective opinion scores instead of just scalar mean opinion scores (MOS) during training. BIECON [11] trains a CNN model on patches of distorted images, using proxy quality scores generated by FR-IQA models as labels. The authors of [30] proposed an adaptive hypernetwork architecture that considers content comprehension during perceptual quality prediction. Very recent works on NR-IQA include PaQ-2-PiQ [40], CONTRIQUE [16] and MUSIQ [10]. PaQ-2-PiQ benefits from a specially designed dataset wherein the authors not only collected subjective quality scores on whole pictures but also on a large number of image patches. The dataset is also large enough to train deep models in a supervised setting, and PaQ-2-PiQ achieves state-of-the-art performance. However, although the authors use patch-level and image-level quality information during training, the training process may be susceptible to dataset sampling errors since only a few patches were extracted from each image and annotated with quality scores. MUSIQ uses a transformer-based architecture [34] pre-trained on the ImageNet classification dataset. The method benefits significantly by using transformer architecture and fine-tuning the transformer backbone on the IQA test databases. CONTRIQUE is a closely related work that aims to learn quality-aware representations in a self-supervised setting. CONTRIQUE learns to group images with similar types and distortion degrees into classes on an independent dataset. In this way, it proposes to learn quality-aware image representations. However, the class labels used to define 'similar-quality' and 'different-quality'", + "bbox": [ + 496, + 388, + 890, + 888 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5848", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "samples in CONTRIQUE are in fact distortion labels instead of being true-quality labels. We address this shortcoming in our proposed framework. Our method, which is also completely unsupervised, does not learn representations based on distortion class labels, which can be inaccurate when asserted on \"In the Wild\" data. Instead, our model, which is inspired by the fundamental principles of visual distortion perception, proposes to independently learn high-level semantic image content and low-level image quality features. These image representation features are mapped directly to subjective scores using a low-complexity regression model without fine-tuning the deep neural networks. Here, we utilize ResNet-based architectures [8] throughout the Re-IQA framework. As our proposed framework is generalizable enough to be implemented using other CNN and transformer-based architectures, we plan to extend it to transformer-based architectures in the future.", + "bbox": [ + 75, + 90, + 472, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Rethinking-IQA", + "text_level": 1, + "bbox": [ + 76, + 375, + 238, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Re-IQA model framework is embodied in three processing phases. The first and second phases consist of training two ResNet50 encoders using contrastive learning of high-level and low-level image information. We then use the pre-trained encoders with frozen weights as image representation generation backbones, which supply features to a low-complexity regression model that is trained to conduct image quality prediction as shown in Figure 1.", + "bbox": [ + 75, + 400, + 468, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To learn high-level content-aware information we deploy MoCo-v2 [2] ImageNet pre-trained model and adopt the design considerations developed in the original paper. Further discussed in section 3.1. To learn quality-aware representations we develop a contrastive learning framework that deploys a novel augmentation protocol and an intra-pair image-swapping scheme to facilitate model convergence towards learning robust image quality-aware features. Further discussed in section 3.2.", + "bbox": [ + 75, + 521, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Re-IQA : Content Aware", + "text_level": 1, + "bbox": [ + 76, + 665, + 305, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The primary objective in the MoCo-v2 framework [2] is to assign a 'similar' label to two crops from a single image while assigning a 'different' label to two crops taken from two different images. Although, content aware Re-IQA based completely on the original MoCo-v2 framework performs well in the image quality prediction problem (refer Table 2), it still suffers from a critical design problem: two crops from a same image can be given significantly different quality scores by human viewers. Hence we only use, the original MoCo-v2 framework to generate content-aware image representations. We make appropriate changes, discussed next, to the MoCo-v2 framework to enable accurate learning of quality-aware representations that complement content-aware representations.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Re-IQA : Quality Aware", + "text_level": 1, + "bbox": [ + 500, + 90, + 723, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our quality-aware contrastive learning framework uses an Image Augmentation method and an Intra-pair image Swapping scheme to train a ResNet-50 encoder within the MoCo-v2 framework [2] with a goal of modeling a feature space wherein all images having similar degrees of perceptual quality fall closer to one another than to images having different perceptual qualities. The MoCo-v2 framework simultaneously processes a query image through the query encoder and a key image through the key encoder. In a single batch, a positive sample occurs when features are generated using any paired query and key, the pair being labeled 'similar.' A negative sample occurs when the query and the key do not belong to the same pair, hence they are marked 'different.'", + "bbox": [ + 496, + 114, + 890, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train a contrastive network we need paired images, such that for any sample index $k$ , we have image pairs $[i_1^k, i_2^k]$ that can be assigned the 'similar-quality' label, and for any $j, k$ ; where $k \\neq j$ we have image pairs $[i_1^k, i_2^j]$ that can be assigned the 'different-quality' label. From here on we shall refer to perceptual quality-aware features as PQAF. To define the decision boundary between 'similar-quality' and 'different-quality' labels, we assume the following three hypotheses to be true:", + "bbox": [ + 496, + 325, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "H1: PQAF varies within an image itself. If we assign PQAF to an image patch $x$ and denote it as $PQAF_x$ , then $PQAF_x$ varies only a small amount between neighboring patches. However, $PQAF_x$ may vary significantly between two distant patches.", + "H2: The PQAF of any two randomly selected images are 'different,' which assumes that the scenes depicted in the images to be different. However, this does not enforce any restrictions on the quality scores of the two images.", + "H3: Two different distorted versions of the same image have different PQAF." + ], + "bbox": [ + 496, + 460, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These hypotheses are further discussed in the Supplemental material §S.4.", + "bbox": [ + 496, + 627, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Quality-Aware Image Augmentation Scheme", + "text_level": 1, + "bbox": [ + 498, + 680, + 864, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To conduct quality-aware image feature extraction, we deploy a novel bank of image quality distortion augmentations, as elaborated in the Supplemental material §S.1. The augmentation bank is a collection of 25 distortion methods, each realized at 5 levels of severity. For any source image $i^k$ from the training set, where $k \\in \\{1, 2 \\dots K\\}$ and $K$ is the total number of images in the training data, a randomly chosen subset of the augmentations available in the bank are applied to each image resulting in a mini-batch of distorted images. We combine each source image with its distorted versions to form $chunk^k$ :", + "bbox": [ + 496, + 704, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc h u n k ^ {k} = \\left[ i ^ {k}, i _ {1} ^ {k}, i _ {2} ^ {k}, \\dots , i _ {n} ^ {k} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5849", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5c394efcb587a6c320a6ea2a2bfa23faf16686ddd32205fab7749a1a57cd767c.jpg", + "image_caption": [ + "Figure 4. Learning Quality Aware Representations: The OLA based cropping, Image Augmentation scheme and Half-swapping enable the generation of appropriate 'similar-quality' and 'different-quality' image pairs which can be used to learn quality-aware features. Note that $A_0$ has no augmentation, while $A_1..A_n$ are randomly sampled from the augmentation bank. During loss calculation, representations generated using the key encoder for the previous 65536 samples are also used as negative keys, following MoCo-V2 settings." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i_j^k$ is the $j^{th}$ distorted version of $i^k$ , and $n$ is the number of augmentations drawn from the bank. We then generate two random crops of $chunk^k$ , namely $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ , using an overlap area based smart cropping mechanism. We choose these crop locations such that the overlapping area (OLA) in the two crops falls within minimum and maximum bounds. We make sure that the crop location is the same over all images in each chunk and different between chunks, resulting in:", + "bbox": [ + 75, + 333, + 473, + 470 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {c h u n k} ^ {k _ {c 1}} = \\left[ i ^ {k _ {c 1}}, i _ {1} ^ {k _ {c 1}}, i _ {2} ^ {k _ {c 1}}, \\dots , i _ {n} ^ {k _ {c 1}} \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 491, + 403, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc h u n k ^ {k _ {c 2}} = \\left[ i ^ {k _ {c 2}}, i _ {1} ^ {k _ {c 2}}, i _ {2} ^ {k _ {c 2}}, \\dots , i _ {n} ^ {k _ {c 2}} \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 508, + 468, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When training, by choosing an augmented image $a_{th}$ from both $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ , form the pair $[i_a^{k_{c1}}, i_a^{k_{c2}}]$ . Image $i_a^{k_{c1}}$ and $i_a^{k_{c2}}$ are neighboring patches because of OLA-based cropping and hence are marked 'similar-quality' as stated in H1. Similarly, for any image $k$ and distortion $a, b$ where $a \\neq b$ , the pair $[i_a^{k_{c1}}, i_b^{k_{c2}}]$ are labelled as 'different-quality' as in H1. Finally, for any two different image samples $k, j$ , label the pair $[i\\_ k_{c1}, i\\_ j_{c2}]$ as 'different-quality', following H2.", + "bbox": [ + 75, + 540, + 472, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Intra-Pair Image Swapping Scheme", + "text_level": 1, + "bbox": [ + 76, + 693, + 382, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a spatial arrangement of $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ :", + "bbox": [ + 76, + 715, + 452, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 1}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 2}} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 752, + 460, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "form the following types of image-pairs and corresponding labels:", + "bbox": [ + 76, + 820, + 468, + 851 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} ] \\mapsto \\text {s i m i l a r - q u a l i t y}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 857, + 377, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{c} i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\end{array} \\right] \\mapsto d i f f e r e n t q u a l i t y\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 878, + 392, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then apply intra-pair image swapping on the generated chunks to obtain the following arrangement:", + "bbox": [ + 500, + 334, + 893, + 364 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 2}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 1}} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 393, + 885, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By swapping images within each pair over half the pairs, (referred to as Half Swap), the network is introduced to samples having the following configuration: $[i_a^{k_{c1}}, i_b^{k_{c1}}]$ where $a, b; a \\neq b$ are two different distortions. Note that the crops $[i_a^{k_{c1}}, i_b^{k_{c1}}]$ are exactly the same, except for the distortion applied, and thus contain the same essential visual content. Despite this, we mark such samples as 'different-quality' as stated in H3, thus forcing the network to look beyond content-dependent features. With this, we finally end up with the following image pairs and labels:", + "bbox": [ + 496, + 470, + 893, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} \\right] \\mapsto \\text {s i m i l a r - q u a l i t y}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 638, + 799, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\right] \\mapsto d i f f e r e n t - q u a l i t y\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 659, + 815, + 678 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 1}} \\right] \\mapsto d i f f e r e n t - q u a l i t y\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 680, + 815, + 699 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {j _ {c 2}} \\right] \\mapsto d i f f e r - q u a l i t y\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 702, + 815, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Quality-Aware Training", + "text_level": 1, + "bbox": [ + 500, + 751, + 723, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Define two identical encoders 1) Online Encoder (query encoder) and 2) Momentum Encoder (key encoder). Both encoders have ResNet-50 backbones and an MLP head to generate the final output embeddings from the ResNet features. Split the pairs designed in the previous step, passing the first image from each pair through the query encoder, and the other through the key encoder. To calculate the loss between the representation generated by the query and key", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5850", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "encoder, we use the InfoNCE [23] loss function:", + "bbox": [ + 76, + 90, + 398, + 107 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {q, k ^ {+}, \\{k ^ {-} \\}} = - \\log \\frac {\\exp (q . k ^ {+} / \\tau)}{\\exp (q . k ^ {+} / \\tau) + \\sum_ {k ^ {-}} \\exp (q . k ^ {-} / \\tau)} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 118, + 468, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here $q$ is the query image, $k^{+}$ is a positive sample (similar-quality), $k^{-}$ represent negative samples (different-quality), and $\\tau$ is a temperature hyper-parameter. This loss is then used to update the weights of the online encoder by back-propagation. The weights of the momentum encoder are updated using the weighted sum of its previous weights and the new weights of the online encoder. Formally denoting the parameters of the query encoder by $\\theta_{q}$ and the parameters of the key encoder as $\\theta_{k}$ , update $\\theta_{k}$ as:", + "bbox": [ + 75, + 179, + 472, + 316 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {k} \\leftarrow m \\theta_ {k} + (1 - m) \\theta_ {q} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 333, + 468, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here $m \\in [0,1)$ , is the momentum coefficient. Once the encoder pre-training has saturated the frozen ResNet-50 can be used as an encoder backbone for any downstream task associated with perceptual image quality.", + "bbox": [ + 75, + 359, + 468, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. IQA Regression", + "text_level": 1, + "bbox": [ + 76, + 431, + 235, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We concatenate the image representations obtained from the content and quality-aware encoders in the previous steps to train a regressor head to map the obtained features to the final perceptual image quality scores as shown in Figure 1. In our experiments, we use a single-layer perceptron as the regressor head. It is important to note that we train only the low-complexity regressor head while evaluating our Re-IQA framework across multiple databases. Our method does not require us to fine-tune the feature extraction backbone(s) separately for each evaluation database as required in MUSIQ.", + "bbox": [ + 75, + 455, + 468, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 638, + 282, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Training Datasets", + "text_level": 1, + "bbox": [ + 76, + 664, + 250, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the Re-IQA framework, two ResNet-50 encoders are trained to obtain high-level image content features and low-level image quality features. The encoder that learns high-level image content features was trained on a subset of the ImageNet database [3] containing approximately 1.28 million images across 1000 classes. When training the encoder in an unsupervised setting, we discard the class label information and only use images without labels during the training process.", + "bbox": [ + 75, + 688, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To learn the low-level image quality features, we use a combination of pristine images and authentically distorted images as training data. The augmentation scheme (applied to all images in the dataset) ensures that the network learns how to differentiate between distortions when the semantic", + "bbox": [ + 75, + 825, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "content in the image is the same. The presence of authentically distorted images in the dataset helps tune the model to accurately predict the quality of \"In the Wild\" pictures.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Pristine Images: We used the 140K pristine images in the KADIS dataset [13]. We do not use the 700K distorted images available in the same dataset. The authors of KADIS did not provide subjective quality scores for any image in the dataset.", + "- Arguably Distorted Images: We used the same combination of datasets as proposed in CONTRIQUE [16] to form our distorted image set: (a) AVA [22] - 255K images, (b) COCO [14] - 330K images, (c) CERTH-Blur [18] - 2450 images, d) VOC [4] - 33K images" + ], + "bbox": [ + 517, + 146, + 893, + 318 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8fcfb162d8db6ae78c1fcbfdbb178642247ed4443f31cfc333da487f7cc1f4dd.jpg", + "image_caption": [ + "(a) Re-IQA Quality-Aware" + ], + "image_footnote": [], + "bbox": [ + 583, + 354, + 802, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cebdb718ae18b2889ca34fa1f17c9d5d0e4ac8b62adb51472ef011606116f444.jpg", + "image_caption": [ + "(b) CONTRIQUE", + "Figure 5. Comparison of 2D TSNE Visualization of learned representations of 1016 images sampled from KonIQ (UGC - #150) and CSIQ (Synthetic Distortions - #866) between Re-IQA Quality Aware sub-module and CONTRIQUE. Best viewed zoomed in." + ], + "image_footnote": [], + "bbox": [ + 583, + 491, + 802, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Datasets", + "text_level": 1, + "bbox": [ + 500, + 710, + 689, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Many previous IQA methods used legacy databases like LIVE IQA [29], TID-2008 [25], TID-2013 [24], CSIQ-IQA [12], and KADID [13] for development and evaluation purposes. However, these datasets contain only a small number $(\\sim 25 - 100)$ of pristine images synthetically distorted by various levels and types of single distortions. Hence, these datasets lack diversity and realism of content and distortion. Recently many \"In the Wild\" datasets like KonIQ [9], CLIVE [6], FLIVE [40], and SPAQ [5] have been developed and used by visual quality researchers since they address the shortcomings of the legacy datasets. The newer breed of", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5851", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "perceptual quality datasets contain many authentically distorted images. KonIQ-10K dataset consists of 10K images selected from the publicly available multimedia large-scale YFCC100M database [31]. CLIVE contains 1162 authentically distorted images captured using various mobile devices. FLIVE, on the other hand, is comprised of 40,000 images sampled from open-source images and designed to emulate the feature distributions found in social media images statistically. Lastly, SPAQ consists of 11,000 images captured using 66 mobile devices, and each image is accompanied by various annotations such as brightness, content labels, and EXIF data. However, our experiments only utilize the image and its corresponding quality score.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also evaluated our method on four legacy synthetically distorted datasets: LIVE-IQA, TID-2013, CSIQ-IQA, and KADID. We provide short descriptions of each of the databases. The LIVE IQA dataset includes 779 images that have been synthetically distorted using five types of distortions at four different intensity levels. TID-2013, on the other hand, contains 3000 images that have been synthetically distorted using 24 different types of distortions at five different levels of intensity, with 25 reference images as the base. The CSIQ-IQA dataset comprises 866 images that have been synthetically distorted using six types of distortions on top of 30 reference images. Lastly, the KADID dataset comprises 10125 images synthetically distorted using 25 different distortions on 81 reference images.", + "bbox": [ + 75, + 287, + 472, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Training Configurations", + "text_level": 1, + "bbox": [ + 76, + 513, + 302, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our content-aware encoder is pre-trained on the ImageNet database following the configuration proposed in MoCo-v2. Due to time and resource constraints, we train the content-aware encoder for 200 epochs. For the quality-aware encoder, we used ResNet-50 as a feature extractor, and a 2-layer MLP head to regress contrastive features of dimension 128. The hidden dimension of the MLP head has 2048 neurons. In each forward pass, the OverLap Area (OLA) based cropping mechanism chooses two crops $(C_1$ and $C_2)$ from each image, such that the percentage of overlap between the crops is maintained within a minimum and a maximum bound. The performance variation of Re-IQA-QA (quality aware module only) and Re-IQA against percentage OverLap Area, patch-sizes, and the number of image distortion augmentations is depicted in Table 1. The optimal parameters are chosen based on the combined performance of the two modules in Re-IQA. We achieved the best performance using $10 - 30\\%$ percentage OverLap Area bound, patch size of 160, and 11 distortion augmentations.", + "bbox": [ + 75, + 537, + 472, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The processed chunks are passed through the query and key encoders respectively in the MoCo-v2 framework, followed by an adaptive pooling layer to compress the output of the ResNet-50 into a 1D feature vector. The generated feature vector is then fed to the MLP head to generate the", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "contrastive feature vectors required for loss computation. Our design of the Re-IQA model is inspired by previous works [16, 37] that use images both at their original and half-scale. Therefore, during the training phase of the Re-IQA model we use all images in a database both at original and half-scale, thereby doubling the training dataset.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "During training, the following hyper-parameters were fixed throughout all experiments: learning rate $= 0.6$ with cosine annealing [15] scheduler, InfoNCE temperature $\\tau = 0.2$ , and momentum coefficient $= 0.999$ . Our best-performing model required a batch size of 630 (effectively $630 \\times (n + 1)$ augmentations x (2) scales) during training and was trained for 25 epochs. Convergence occurs in a relatively shorter number of epochs as the effective dataset size increases drastically due to a large number of augmentations and processing of each image in the dataset at two scales. All the implementations were done in Python using the PyTorch deep learning framework. We trained the content and quality-aware encoders on a system configured with 18 Nvidia A100-40GB GPUs.", + "bbox": [ + 496, + 181, + 892, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Evaluation Protocol", + "text_level": 1, + "bbox": [ + 498, + 404, + 691, + 419 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We tested our Re-IQA model against other state-of-the-art models on all of the \"In the Wild\" and synthetically distorted IQA databases described in Section 4.2. Each of these datasets is a collection of images labeled by subjective opinions of picture quality in the form of the mean of the opinion scores (MOS). The single-layer regressor head in Re-IQA is trained by feeding the output of the pre-trained encoders and then comparing the output of the regressor, against the ground truth MOS using L2 loss. We use both Spearman's rank order correlation coefficient (SRCC) and Pearson's linear correlation coefficient (PLCC) as metrics to evaluate the trained model across IQA databases.", + "bbox": [ + 496, + 428, + 893, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following the evaluation protocol used in [16], each dataset was randomly divided into $70\\%$ , $10\\%$ and $20\\%$ corresponding to training, validation and test sets, respectively. We used the validation set to determine the regularization coefficient of the regressor head using a 1D grid search over values in the range $[10^{-3}, 10^{3}]$ . To avoid overlap of contents in datasets with synthetic distortions, splits were selected based on source images. We also prevented any bias towards the training set selection by repeating the train/test split operation 10 times and reporting the median performance. On FLIVE, due to the large dataset size, we follow the train-test split recommended by the authors in [40].", + "bbox": [ + 496, + 609, + 893, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Results", + "text_level": 1, + "bbox": [ + 500, + 801, + 591, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our \"Mixture of Experts\" approach in Re-IQA enables us to learn robust high-level image content and low-level quality aware representations independently, the benefit of which can be clearly observed in the performance values reported in Table 2. We compared the performance of Re-", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5852", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/756e4e83a4817d2e30703118b1926334ceae4e679489336ac90d4364c064db9b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelEvaluation Datasetn_augPatch SizeOLA bound (%)
251115231281601922242565-1510-3050-80No Bound
Re-IQA(Quality-Aware)KonIQ0.8550.8580.8610.8620.8600.8600.8610.8610.8600.8580.8560.8610.8570.858
SPAQ0.8900.8960.9000.9000.8970.8980.9000.9010.8980.8940.8890.9000.8860.890
CSIQ0.9280.9370.9440.9360.9300.9370.9440.9390.9300.9280.9370.9440.9310.938
Re-IQA(Quality-Aware +Content Aware)KonIQ0.8950.9010.9140.8980.8950.9100.9140.9110.9050.8970.9030.9140.8970.905
SPAQ0.9020.9130.9180.9100.9090.9160.9180.9140.9080.9030.9070.9180.9040.906
CSIQ0.9320.9410.9470.9370.9350.9400.9470.9420.9370.9320.9390.9470.9350.940
", + "bbox": [ + 78, + 88, + 893, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ba533ebb1b59ac8b6175d7277415208bfb1dea591b5ccff694390ea4be1871cc.jpg", + "table_caption": [ + "Table 1. SRCC performance comparison of Re-IQA-QA and Re-IQA while varying one hyper-parameter at a time. While varying $n_{aug}$ , we keep patch size 160 and OLA bound $10 - 30\\%$ . When varying patch size, $n_{aug}$ was fixed to 11 and OLA bound to $10 - 30\\%$ . When varying OLA bound, $n_{aug}$ was set to 11 and the patch size was set to 160." + ], + "table_footnote": [], + "table_body": "
MethodAuthentic Distortions a.k.a "Images in the Wild"Synthetic Distortions
KonIQCLIVEFLIVESPAQLIVE-IQACSIQ-IQATID-2013KADID
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
BRISQUE0.6650.6810.6080.6290.2880.3730.8090.8170.9390.9350.7460.8290.6040.6940.5280.567
CORNIA0.7800.7950.6290.671--0.7090.7250.9470.9500.6780.7760.6780.7680.5160.558
DB-CNN0.8750.8840.8510.8690.5540.6520.9110.9150.9680.9710.9460.9590.8160.8650.8510.856
PQR0.8800.8840.8570.882----0.9650.9710.8720.9010.7400.798--
PaQ-2-PiQ0.8700.8800.8400.8500.5710.623----------
HyperlQA0.9060.9170.8590.8820.5350.6230.9160.9190.9620.9660.9230.9420.8400.8580.8520.845
CONTRIQUE0.8940.9060.8450.8570.5800.6410.9140.9190.9600.9610.9420.9550.8430.8570.9340.937
MUSIQ0.9160.928--0.6460.7390.9170.921--------
ImageNet Pretrained (Supervised)0.8880.9040.7810.8090.5950.6480.9040.9090.9250.9310.8400.8480.6790.7290.7010.677
Re-IQA (content aware)0.8960.9120.8080.8440.5880.6990.9020.9080.8670.8580.7660.8240.6580.7360.6010.656
Re-IQA (quality aware)0.8610.8850.8060.8240.5840.5900.9000.9100.9710.9720.9440.9640.8440.8800.8850.892
Re-IQA (content + quality)0.9140.9230.8400.8540.6450.7330.9180.9250.9700.9710.9470.9600.8040.8610.8720.885
", + "bbox": [ + 78, + 250, + 892, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Performance comparison of Re-IQA against various NR-IQA models on IQA databases with authentic and synthetic distortions. The top 2 best performing models are in bold. Higher SRCC and PLCC imply better performance. MUSIQ results from [10]. Results of all other existing methods from [16].", + "bbox": [ + 75, + 416, + 892, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "IQA along with its sub-modules against other state-of-the-art models on IQA datasets containing authentic and synthetic distortions in Table 2. We used the features extracted from the Resnet-50 backbone for the supervised ImageNet pre-trained model. From the results, we conclude that Re-IQA achieves competitive performance across all tested databases.", + "bbox": [ + 75, + 484, + 468, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results from Table 2 highlight the impact of content and low-level image quality on the final NR-IQA task. We observe that high-level content-aware features dominate quality-aware features for authentically distorted images, while the quality-aware features dominate the high-level content-aware features for authentically distorted images. We can hypothesize the reason to be high variation in content in the \"Images in the Wild\" scenario. Training a simple linear regressor head that is fed with features from both the content and quality-aware encoders provides flexibility to adjust the final model based on the application dataset. This can be observed in the performance scores achieved by the combined model when compared to the individual sub-modules. The performance scores of the quality-aware sub-module do not beat other methods when considering the \"Images in the Wild\" scenario, primarily due to the heavy impact of content. Despite this, when evaluated on synthetic distortion datasets, the quality-aware sub-module of Re-IQA outperforms most of its competitors all by itself. Thus we conclude that our generated quality-aware", + "bbox": [ + 75, + 590, + 470, + 893 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "representations align very well with distortions present in an image. This is also conclusive from the t-SNE visualizations [33] depicted in Figure 5. Further details on t-SNE experiments are shared in Supplemental Material §S.3.", + "bbox": [ + 496, + 484, + 892, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Concluding Remarks", + "text_level": 1, + "bbox": [ + 498, + 558, + 705, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We developed a holistic approach to Image quality Assessment by individually targeting the impact of content and distortion on the overall image quality score. NR-IQA for \"Images in the Wild\" benefits significantly from content-aware image representations, especially when learned in an unsupervised setting. This work aims to demonstrate that complementary content and image quality-aware features can be learned and, when combined, achieve competitive performance across all evaluated IQA databases. We re-engineer the MoCo-v2 framework for learning quality-aware representations to include our proposed novel Image Augmentation, OLA-based smart cropping, and a Half-Swap scheme. The results of experiments on the eight IQA datasets demonstrate that Re-IQA can consistently achieve state-of-the-art performance. Our Re-IQA framework is flexible to changes in the design of encoder architectures and can be extended to other CNN architectures and Transformer based models like MUSIQ. Although developed for IQA tasks, Re-IQA can be extended as a spatial feature extraction module in Video Quality Assessment algorithms that currently use supervised pre-trained Resnet-50.", + "bbox": [ + 496, + 583, + 892, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5853", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alan Conrad Bovik. Automatic prediction of perceptual image and video quality. Proceedings of the IEEE, 101:2008-2024, 2013. 2", + "[2] Xinlei Chen, Haoqi Fan, Ross B. Girshick, and Kaiming He. Improved baselines with momentum contrastive learning. 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Blind image quality assessment using a deep bilinear convolutional neural network. IEEE Transactions on Circuits and Systems for Video Technology, 30(1):36-47, 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 202 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5855", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/90946db8-a492-4f97-b0fd-e3875b8d588a_model.json b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/90946db8-a492-4f97-b0fd-e3875b8d588a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9d1d35ce6abb09fab47f5485e28feaf0f07518f5 --- /dev/null +++ b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/90946db8-a492-4f97-b0fd-e3875b8d588a_model.json @@ -0,0 +1,2266 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Re-IQA: Unsupervised Learning for Image Quality Assessment in the Wild" + }, + { + "type": "text", + "bbox": [ + 0.26, + 0.181, + 0.374, + 0.198 + ], + "angle": 0, + "content": "Avinab Saha*" + }, + { + "type": "text", + "bbox": [ + 0.413, + 0.182, + 0.551, + 0.199 + ], + "angle": 0, + "content": "Sandeep Mishra*" + }, + { + "type": "text", + "bbox": [ + 0.591, + 0.182, + 0.71, + 0.198 + ], + "angle": 0, + "content": "Alan C. Bovik" + }, + { + "type": "text", + "bbox": [ + 0.169, + 0.199, + 0.796, + 0.218 + ], + "angle": 0, + "content": "Laboratory of Image and Video Engineering, The University of Texas at Austin" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.268 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.474, + 0.661 + ], + "angle": 0, + "content": "Automatic Perceptual Image Quality Assessment is a challenging problem that impacts billions of internet, and social media users daily. To advance research in this field, we propose a Mixture of Experts approach to train two separate encoders to learn high-level content and low-level image quality features in an unsupervised setting. The unique novelty of our approach is its ability to generate low-level representations of image quality that are complementary to high-level features representing image content. We refer to the framework used to train the two encoders as Re-IQA. For Image Quality Assessment in the Wild, we deploy the complementary low and high-level image representations obtained from the Re-IQA framework to train a linear regression model, which is used to map the image representations to the ground truth quality scores, refer Figure 1. Our method achieves state-of-the-art performance on multiple large-scale image quality assessment databases containing both real and synthetic distortions, demonstrating how deep neural networks can be trained in an unsupervised setting to produce perceptually relevant representations. We conclude from our experiments that the low and high-level features obtained are indeed complementary and positively impact the performance of the linear regressor. A public release of all the codes associated with this work will be made available on GitHub." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.692, + 0.21, + 0.709 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Millions of digital images are shared daily on social media platforms such as Instagram, Snapchat, Flickr, etc. Making robust and accurate Image Quality Assessments (IQA) that correlate well with human perceptual judgments is essential to ensuring acceptable levels of visual experience. Social media platforms also use IQA metrics to decide parameter settings for post-upload processing of the images, such as resizing, compression, enhancement, etc." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.251, + 0.895, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.391, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Figure 1. IQA score prediction uses two encoders trained for complementary tasks of learning content and quality aware image representations. The encoders are frozen while the regressor learns to map image representations to quality predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.895, + 0.584 + ], + "angle": 0, + "content": "In addition, predictions generated by IQA algorithms are often used as input to recommendation engines on social media platforms to generate user feeds and responses to search queries. Thus, accurately predicting the perceptual quality of digital images is a high-stakes endeavor affecting the way billions of images are stored, processed, and displayed to the public at large." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.896, + 0.779 + ], + "angle": 0, + "content": "IQA metrics can be simply categorized into Full-Reference (FR) and No-Reference (NR) algorithms. FR-IQA algorithms like SSIM [35], FSIM [43], and LPIPS [44] require both reference (undistorted) and distorted version of an image to quantify the human-perceivable quality. This requirement limits their applicability for the \"Images in the Wild\" scenario, where the reference image is unavailable. On the contrary, NR-IQA algorithms like BRISQUE [19], PaQ-2-PiQ [40], and CONTRIQUE [16] do not require a reference image nor any knowledge about the kind of present distortions to quantify human-perceivable quality in a test image, paving the way for their use in \"Images in the Wild\" scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.902 + ], + "angle": 0, + "content": "No-Reference IQA for \"Images in the Wild\" presents exciting challenges due to the complex interplay among the various kinds of distortions. Furthermore, due to the intricate nature of the human visual system, image content affects quality perception. In this work, we aim to learn low-level quality-aware image representations that are complementary to high-level features representative of image content. Figure 2 illustrates some of the challenges encountered" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*Equal Contribution, Correspondence to Avinab Saha (avinab.saha@utexas.edu) & Sandeep Mishra (sandy.mishra@utexas.edu). This work was supported by the National Science Foundation AI Institute for Foundations of Machine Learning (IFML) under Grant 2019844." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5846" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.276, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.206, + 0.245, + 0.218 + ], + "angle": 0, + "content": "(a) JPEG Compressed : 1" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.481, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.206, + 0.451, + 0.218 + ], + "angle": 0, + "content": "(b) JPEG Compressed: 2" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.09, + 0.686, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.502, + 0.206, + 0.674, + 0.217 + ], + "angle": 0, + "content": "(c) Motion Blur - Camera Shake" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.09, + 0.891, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.206, + 0.875, + 0.217 + ], + "angle": 0, + "content": "(d) Overlaid Film Grain/ Noise" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.893, + 0.272 + ], + "angle": 0, + "content": "Figure 2. Exemplar Synthetically and \"In the Wild\" distorted pictures. (a), (b) are two images captured on iPhone 13 Pro and then JPEG compressed using the same encoding parameters. (c), (d), were taken from KonIQ and AVA datasets respectively, and exhibit typical \"Images in the Wild\" distortions. Best viewed when zoomed in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.47, + 0.586 + ], + "angle": 0, + "content": "in the development of NR-IQA algorithms. Figures 2 (a-b) show two images captured by the authors on an iPhone 13 Pro and compressed using the same encoding parameters. While any distortions are almost negligible in Figure 2 (a), there are artifacts that are clearly visible in Figure 2 (b). As in these examples, it is well known that picture distortion perception is content dependent, and is heavily affected by content related perceptual processes like masking [1]. Figures 2 (c-d) illustrates a few distorted pictures \"In the Wild\". Figures 2 (c-d) show two exemplar distorted pictures, one impaired by motion blur (Figure 2 (c)) and the other by film grain noise (Figure 2 (d)). It is also well established that perceived quality does not correlate well with image metadata like resolution, file size, color profile, or compression ratio [36]. Because of all these factors and the essentially infinite diversity of picture distortions, accurate prediction of the perception of image quality remains a challenging task, despite its apparent simplicity, and hence research on this topic remains quite active [16, 17, 19, 28, 35, 39, 42-44]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.751 + ], + "angle": 0, + "content": "Our work is inspired by the success of momentum contrastive learning methods [2, 7] in learning unsupervised representations for image classification. In this work, we engineer our models to learn content and quality-aware image representations for NR-IQA on real, authentically distorted pictures in an unsupervised setting. We adopt a Mixture of Experts approach to independently train two encoders, each of which accurately learns high-level content and low-level image quality features. We refer to the new framework as Re-IQA. The key contributions we make are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We propose an unsupervised low-level image quality representation learning framework that generates features complementary to high-level representations of image content. We demonstrate how the \"Mixture\" of the two enables Re-IQA to produce image quality predictions that are highly competitive with existing state-of-the-art traditional, CNN, and Transformer based NR-IQA models, developed in both supervised and unsupervised settings across several databases." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.299, + 0.892, + 0.42 + ], + "angle": 0, + "content": "- We demonstrate the superiority of high-level representations of image content for the NR-IQA task, obtained from the unsupervised pre-training of the ResNet-50 [8] encoder over the features obtained from supervised pre-trained ResNet-50 on the ImageNet database [3]. We learn these high-level representations of image content using the unsupervised training framework proposed in MoCo-v2 [2]" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.425, + 0.892, + 0.561 + ], + "angle": 0, + "content": "- Inspired by the principles of visual distortion perception we propose a novel Image Augmentation and Intra-Pair Image Swapping scheme to enable learning of low-level image quality representations. The dynamic nature of the image augmentation scheme prevents the learning of discrete distortion classes, since it is applied to both pristine and authentically distorted images, enforcing learning of perceptually relevant image-quality features." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.299, + 0.892, + 0.561 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.642, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As discussed in Section 1, perceptual image quality prediction for \"Images in the Wild\" is a challenging task due to the complex distortions that arise, and the combinations of them, and how they are perceived when they affect different kinds of pictorial content. Over the last few decades, a great deal of effort has been invested in the development of NR-IQA models that are able to accurately predict human judgment of picture quality. In recent years, NR-IQA models have evolved from using hand-crafted perceptual features, feeding shallow learners, into Deep Learning based approaches trained on large subjective databases. Traditional NR-IQA models generally have two components: a feature extractor, which generates quality-relevant features, and a low-complexity regression model, which maps the extracted features to quality scores. Most prior models have focused on improving the feature extractor and, thus improving the performance of the overall IQA algorithm. A common practice in traditional NR-IQA methods is to model image artifacts using statistical information extracted from a test image. Natural Scene Statistics (NSS) mod" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5847" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.212, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.194, + 0.195, + 0.205 + ], + "angle": 0, + "content": "(a) Original Image" + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.089, + 0.348, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.194, + 0.33, + 0.205 + ], + "angle": 0, + "content": "(b) Gaussian Blur" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.089, + 0.483, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.388, + 0.194, + 0.449, + 0.205 + ], + "angle": 0, + "content": "(c) Saturate" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.089, + 0.62, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.194, + 0.598, + 0.205 + ], + "angle": 0, + "content": "(d) Compression" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.089, + 0.756, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.194, + 0.739, + 0.205 + ], + "angle": 0, + "content": "(e) Gaussian Noise" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.089, + 0.892, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.194, + 0.872, + 0.205 + ], + "angle": 0, + "content": "(f) Color Saturate" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.207, + 0.212, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.311, + 0.177, + 0.322 + ], + "angle": 0, + "content": "(g) Pixelate" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.207, + 0.348, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.25, + 0.311, + 0.314, + 0.322 + ], + "angle": 0, + "content": "(h) Contrast" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.207, + 0.483, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.311, + 0.445, + 0.322 + ], + "angle": 0, + "content": "(i) Darken" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.207, + 0.62, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.311, + 0.585, + 0.323 + ], + "angle": 0, + "content": "(j) Resizing" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.207, + 0.756, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.311, + 0.712, + 0.322 + ], + "angle": 0, + "content": "(k) Jitter" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.207, + 0.892, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.311, + 0.866, + 0.321 + ], + "angle": 0, + "content": "(1) Motion Blur" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.335, + 0.892, + 0.363 + ], + "angle": 0, + "content": "Figure 3. Some samples of distortions available in the Image Augmentation Scheme. There are a total of 25 distortions available in the bank, with 5 levels of distortion for each. More details are provided in Supplemental Material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.661 + ], + "angle": 0, + "content": "els and distorted versions of them are popular, where features are extracted from transformed domains, on which statistical measurements of deviations due to distortions are used as features for NR-IQA. For example, the NSS-based BRISQUE [19] and NIQE [20] models obtain features that capture in a normalized bandpass space [26]. DIIVINE [21] uses steerable pyramids, and BLIINDS [27] uses DCT coefficients to measure statistical traces of distortions. Other methods like CORNIA [39] and HOSA [38] utilize codebooks constructed from local patches, which are applied to obtain quality-aware features. Most of the methods discussed above often obtain acceptable results when evaluated on synthetically distorted images, but their performances significantly degrade when applied to \"Images in the Wild\". This is because the above-discussed methods focus primarily on modeling the distortions present in a test image as statistical deviations from naturalness while completely ignoring the high-level content present in the image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.471, + 0.888 + ], + "angle": 0, + "content": "The majority of deep learning approaches utilize pretrained CNN backbones as feature extractors. This is done since end-to-end supervised training of NR-IQA models is difficult given the limited sizes of existing perceptual quality databases. These models typically use CNN backbones trained for ImageNet classification to extract features, combining them with low-complexity regression models like Support Vector Regression or Linear Regression to map the features to human-labeled scores. A few models use labeled scores from IQA databases to fine-tune the CNN backbone. The authors of the RAPIQUE [32] show that features obtained from pretrained ResNet-50 [8] could effectively predict quality scores on \"In the Wild\" content. In DB-CNN [45], authors adopt a two-path technique, where one CNN branch generates distortion-class and distortion-level" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.892, + 0.889 + ], + "angle": 0, + "content": "features, while the other CNN branch provides high-level image content information. These are then combined using bilinear pooling. PQR [41] achieved faster convergence and better quality estimates by using the statistical distributions of subjective opinion scores instead of just scalar mean opinion scores (MOS) during training. BIECON [11] trains a CNN model on patches of distorted images, using proxy quality scores generated by FR-IQA models as labels. The authors of [30] proposed an adaptive hypernetwork architecture that considers content comprehension during perceptual quality prediction. Very recent works on NR-IQA include PaQ-2-PiQ [40], CONTRIQUE [16] and MUSIQ [10]. PaQ-2-PiQ benefits from a specially designed dataset wherein the authors not only collected subjective quality scores on whole pictures but also on a large number of image patches. The dataset is also large enough to train deep models in a supervised setting, and PaQ-2-PiQ achieves state-of-the-art performance. However, although the authors use patch-level and image-level quality information during training, the training process may be susceptible to dataset sampling errors since only a few patches were extracted from each image and annotated with quality scores. MUSIQ uses a transformer-based architecture [34] pre-trained on the ImageNet classification dataset. The method benefits significantly by using transformer architecture and fine-tuning the transformer backbone on the IQA test databases. CONTRIQUE is a closely related work that aims to learn quality-aware representations in a self-supervised setting. CONTRIQUE learns to group images with similar types and distortion degrees into classes on an independent dataset. In this way, it proposes to learn quality-aware image representations. However, the class labels used to define 'similar-quality' and 'different-quality'" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5848" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.364 + ], + "angle": 0, + "content": "samples in CONTRIQUE are in fact distortion labels instead of being true-quality labels. We address this shortcoming in our proposed framework. Our method, which is also completely unsupervised, does not learn representations based on distortion class labels, which can be inaccurate when asserted on \"In the Wild\" data. Instead, our model, which is inspired by the fundamental principles of visual distortion perception, proposes to independently learn high-level semantic image content and low-level image quality features. These image representation features are mapped directly to subjective scores using a low-complexity regression model without fine-tuning the deep neural networks. Here, we utilize ResNet-based architectures [8] throughout the Re-IQA framework. As our proposed framework is generalizable enough to be implemented using other CNN and transformer-based architectures, we plan to extend it to transformer-based architectures in the future." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.24, + 0.394 + ], + "angle": 0, + "content": "3. Rethinking-IQA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.47, + 0.522 + ], + "angle": 0, + "content": "The Re-IQA model framework is embodied in three processing phases. The first and second phases consist of training two ResNet50 encoders using contrastive learning of high-level and low-level image information. We then use the pre-trained encoders with frozen weights as image representation generation backbones, which supply features to a low-complexity regression model that is trained to conduct image quality prediction as shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.658 + ], + "angle": 0, + "content": "To learn high-level content-aware information we deploy MoCo-v2 [2] ImageNet pre-trained model and adopt the design considerations developed in the original paper. Further discussed in section 3.1. To learn quality-aware representations we develop a contrastive learning framework that deploys a novel augmentation protocol and an intra-pair image-swapping scheme to facilitate model convergence towards learning robust image quality-aware features. Further discussed in section 3.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.307, + 0.683 + ], + "angle": 0, + "content": "3.1. Re-IQA : Content Aware" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The primary objective in the MoCo-v2 framework [2] is to assign a 'similar' label to two crops from a single image while assigning a 'different' label to two crops taken from two different images. Although, content aware Re-IQA based completely on the original MoCo-v2 framework performs well in the image quality prediction problem (refer Table 2), it still suffers from a critical design problem: two crops from a same image can be given significantly different quality scores by human viewers. Hence we only use, the original MoCo-v2 framework to generate content-aware image representations. We make appropriate changes, discussed next, to the MoCo-v2 framework to enable accurate learning of quality-aware representations that complement content-aware representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.725, + 0.108 + ], + "angle": 0, + "content": "3.2. Re-IQA : Quality Aware" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.325 + ], + "angle": 0, + "content": "Our quality-aware contrastive learning framework uses an Image Augmentation method and an Intra-pair image Swapping scheme to train a ResNet-50 encoder within the MoCo-v2 framework [2] with a goal of modeling a feature space wherein all images having similar degrees of perceptual quality fall closer to one another than to images having different perceptual qualities. The MoCo-v2 framework simultaneously processes a query image through the query encoder and a key image through the key encoder. In a single batch, a positive sample occurs when features are generated using any paired query and key, the pair being labeled 'similar.' A negative sample occurs when the query and the key do not belong to the same pair, hence they are marked 'different.'" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.462 + ], + "angle": 0, + "content": "To train a contrastive network we need paired images, such that for any sample index \\( k \\), we have image pairs \\( [i_1^k, i_2^k] \\) that can be assigned the 'similar-quality' label, and for any \\( j, k \\); where \\( k \\neq j \\) we have image pairs \\( [i_1^k, i_2^j] \\) that can be assigned the 'different-quality' label. From here on we shall refer to perceptual quality-aware features as PQAF. To define the decision boundary between 'similar-quality' and 'different-quality' labels, we assume the following three hypotheses to be true:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.537 + ], + "angle": 0, + "content": "H1: PQAF varies within an image itself. If we assign PQAF to an image patch \\( x \\) and denote it as \\( PQAF_x \\), then \\( PQAF_x \\) varies only a small amount between neighboring patches. However, \\( PQAF_x \\) may vary significantly between two distant patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.598 + ], + "angle": 0, + "content": "H2: The PQAF of any two randomly selected images are 'different,' which assumes that the scenes depicted in the images to be different. However, this does not enforce any restrictions on the quality scores of the two images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.627 + ], + "angle": 0, + "content": "H3: Two different distorted versions of the same image have different PQAF." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.627 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.658 + ], + "angle": 0, + "content": "These hypotheses are further discussed in the Supplemental material §S.4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.681, + 0.866, + 0.697 + ], + "angle": 0, + "content": "3.2.1 Quality-Aware Image Augmentation Scheme" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.871 + ], + "angle": 0, + "content": "To conduct quality-aware image feature extraction, we deploy a novel bank of image quality distortion augmentations, as elaborated in the Supplemental material §S.1. The augmentation bank is a collection of 25 distortion methods, each realized at 5 levels of severity. For any source image \\( i^k \\) from the training set, where \\( k \\in \\{1, 2 \\dots K\\} \\) and \\( K \\) is the total number of images in the training data, a randomly chosen subset of the augmentations available in the bank are applied to each image resulting in a mini-batch of distorted images. We combine each source image with its distorted versions to form \\( chunk^k \\):" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nc h u n k ^ {k} = \\left[ i ^ {k}, i _ {1} ^ {k}, i _ {2} ^ {k}, \\dots , i _ {n} ^ {k} \\right] \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5849" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.895, + 0.312 + ], + "angle": 0, + "content": "Figure 4. Learning Quality Aware Representations: The OLA based cropping, Image Augmentation scheme and Half-swapping enable the generation of appropriate 'similar-quality' and 'different-quality' image pairs which can be used to learn quality-aware features. Note that \\( A_0 \\) has no augmentation, while \\( A_1..A_n \\) are randomly sampled from the augmentation bank. During loss calculation, representations generated using the key encoder for the previous 65536 samples are also used as negative keys, following MoCo-V2 settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.475, + 0.472 + ], + "angle": 0, + "content": "where \\( i_j^k \\) is the \\( j^{th} \\) distorted version of \\( i^k \\), and \\( n \\) is the number of augmentations drawn from the bank. We then generate two random crops of \\( chunk^k \\), namely \\( chunk^{k_{c1}} \\) and \\( chunk^{k_{c2}} \\), using an overlap area based smart cropping mechanism. We choose these crop locations such that the overlapping area (OLA) in the two crops falls within minimum and maximum bounds. We make sure that the crop location is the same over all images in each chunk and different between chunks, resulting in:" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.492, + 0.405, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\operatorname {c h u n k} ^ {k _ {c 1}} = \\left[ i ^ {k _ {c 1}}, i _ {1} ^ {k _ {c 1}}, i _ {2} ^ {k _ {c 1}}, \\dots , i _ {n} ^ {k _ {c 1}} \\right]\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.509, + 0.469, + 0.531 + ], + "angle": 0, + "content": "\\[\nc h u n k ^ {k _ {c 2}} = \\left[ i ^ {k _ {c 2}}, i _ {1} ^ {k _ {c 2}}, i _ {2} ^ {k _ {c 2}}, \\dots , i _ {n} ^ {k _ {c 2}} \\right] \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.473, + 0.678 + ], + "angle": 0, + "content": "When training, by choosing an augmented image \\( a_{th} \\) from both \\( chunk^{k_{c1}} \\) and \\( chunk^{k_{c2}} \\), form the pair \\( [i_a^{k_{c1}}, i_a^{k_{c2}}] \\). Image \\( i_a^{k_{c1}} \\) and \\( i_a^{k_{c2}} \\) are neighboring patches because of OLA-based cropping and hence are marked 'similar-quality' as stated in H1. Similarly, for any image \\( k \\) and distortion \\( a, b \\) where \\( a \\neq b \\), the pair \\( [i_a^{k_{c1}}, i_b^{k_{c2}}] \\) are labelled as 'different-quality' as in H1. Finally, for any two different image samples \\( k, j \\), label the pair \\( [i\\_ k_{c1}, i\\_ j_{c2}] \\) as 'different-quality', following H2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.383, + 0.71 + ], + "angle": 0, + "content": "3.2.2 Intra-Pair Image Swapping Scheme" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.717, + 0.454, + 0.734 + ], + "angle": 0, + "content": "Given a spatial arrangement of \\( chunk^{k_{c1}} \\) and \\( chunk^{k_{c2}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.753, + 0.462, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 1}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 2}} \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.821, + 0.47, + 0.852 + ], + "angle": 0, + "content": "form the following types of image-pairs and corresponding labels:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.858, + 0.378, + 0.877 + ], + "angle": 0, + "content": "\\[\n[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} ] \\mapsto \\text {s i m i l a r - q u a l i t y}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.879, + 0.393, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{c} i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\end{array} \\right] \\mapsto d i f f e r e n t q u a l i t y\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.335, + 0.894, + 0.366 + ], + "angle": 0, + "content": "Then apply intra-pair image swapping on the generated chunks to obtain the following arrangement:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.395, + 0.887, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 2}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 1}} \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.895, + 0.625 + ], + "angle": 0, + "content": "By swapping images within each pair over half the pairs, (referred to as Half Swap), the network is introduced to samples having the following configuration: \\([i_a^{k_{c1}}, i_b^{k_{c1}}]\\) where \\(a, b; a \\neq b\\) are two different distortions. Note that the crops \\([i_a^{k_{c1}}, i_b^{k_{c1}}]\\) are exactly the same, except for the distortion applied, and thus contain the same essential visual content. Despite this, we mark such samples as 'different-quality' as stated in H3, thus forcing the network to look beyond content-dependent features. With this, we finally end up with the following image pairs and labels:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.639, + 0.8, + 0.658 + ], + "angle": 0, + "content": "\\[\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} \\right] \\mapsto \\text {s i m i l a r - q u a l i t y}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.66, + 0.816, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\right] \\mapsto d i f f e r e n t - q u a l i t y\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.681, + 0.816, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 1}} \\right] \\mapsto d i f f e r e n t - q u a l i t y\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.703, + 0.816, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {j _ {c 2}} \\right] \\mapsto d i f f e r - q u a l i t y\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.752, + 0.724, + 0.768 + ], + "angle": 0, + "content": "3.2.3 Quality-Aware Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Define two identical encoders 1) Online Encoder (query encoder) and 2) Momentum Encoder (key encoder). Both encoders have ResNet-50 backbones and an MLP head to generate the final output embeddings from the ResNet features. Split the pairs designed in the previous step, passing the first image from each pair through the query encoder, and the other through the key encoder. To calculate the loss between the representation generated by the query and key" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5850" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.4, + 0.108 + ], + "angle": 0, + "content": "encoder, we use the InfoNCE [23] loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.119, + 0.47, + 0.164 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {q, k ^ {+}, \\{k ^ {-} \\}} = - \\log \\frac {\\exp (q . k ^ {+} / \\tau)}{\\exp (q . k ^ {+} / \\tau) + \\sum_ {k ^ {-}} \\exp (q . k ^ {-} / \\tau)} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.18, + 0.473, + 0.318 + ], + "angle": 0, + "content": "Here \\(q\\) is the query image, \\(k^{+}\\) is a positive sample (similar-quality), \\(k^{-}\\) represent negative samples (different-quality), and \\(\\tau\\) is a temperature hyper-parameter. This loss is then used to update the weights of the online encoder by back-propagation. The weights of the momentum encoder are updated using the weighted sum of its previous weights and the new weights of the online encoder. Formally denoting the parameters of the query encoder by \\(\\theta_{q}\\) and the parameters of the key encoder as \\(\\theta_{k}\\), update \\(\\theta_{k}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.334, + 0.47, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\theta_ {k} \\leftarrow m \\theta_ {k} + (1 - m) \\theta_ {q} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.47, + 0.422 + ], + "angle": 0, + "content": "Here \\(m \\in [0,1)\\), is the momentum coefficient. Once the encoder pre-training has saturated the frozen ResNet-50 can be used as an encoder backbone for any downstream task associated with perceptual image quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.433, + 0.236, + 0.449 + ], + "angle": 0, + "content": "3.3. IQA Regression" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.624 + ], + "angle": 0, + "content": "We concatenate the image representations obtained from the content and quality-aware encoders in the previous steps to train a regressor head to map the obtained features to the final perceptual image quality scores as shown in Figure 1. In our experiments, we use a single-layer perceptron as the regressor head. It is important to note that we train only the low-complexity regressor head while evaluating our Re-IQA framework across multiple databases. Our method does not require us to fine-tune the feature extraction backbone(s) separately for each evaluation database as required in MUSIQ." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.64, + 0.283, + 0.657 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.251, + 0.681 + ], + "angle": 0, + "content": "4.1. Training Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.825 + ], + "angle": 0, + "content": "In the Re-IQA framework, two ResNet-50 encoders are trained to obtain high-level image content features and low-level image quality features. The encoder that learns high-level image content features was trained on a subset of the ImageNet database [3] containing approximately 1.28 million images across 1000 classes. When training the encoder in an unsupervised setting, we discard the class label information and only use images without labels during the training process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.9 + ], + "angle": 0, + "content": "To learn the low-level image quality features, we use a combination of pristine images and authentically distorted images as training data. The augmentation scheme (applied to all images in the dataset) ensures that the network learns how to differentiate between distortions when the semantic" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "content in the image is the same. The presence of authentically distorted images in the dataset helps tune the model to accurately predict the quality of \"In the Wild\" pictures." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.147, + 0.892, + 0.223 + ], + "angle": 0, + "content": "- Pristine Images: We used the 140K pristine images in the KADIS dataset [13]. We do not use the 700K distorted images available in the same dataset. The authors of KADIS did not provide subjective quality scores for any image in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.228, + 0.894, + 0.319 + ], + "angle": 0, + "content": "- Arguably Distorted Images: We used the same combination of datasets as proposed in CONTRIQUE [16] to form our distorted image set: (a) AVA [22] - 255K images, (b) COCO [14] - 330K images, (c) CERTH-Blur [18] - 2450 images, d) VOC [4] - 33K images" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.147, + 0.894, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.355, + 0.803, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.467, + 0.769, + 0.48 + ], + "angle": 0, + "content": "(a) Re-IQA Quality-Aware" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.492, + 0.803, + 0.599 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.605, + 0.746, + 0.617 + ], + "angle": 0, + "content": "(b) CONTRIQUE" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.686 + ], + "angle": 0, + "content": "Figure 5. Comparison of 2D TSNE Visualization of learned representations of 1016 images sampled from KonIQ (UGC - #150) and CSIQ (Synthetic Distortions - #866) between Re-IQA Quality Aware sub-module and CONTRIQUE. Best viewed zoomed in." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.691, + 0.726 + ], + "angle": 0, + "content": "4.2. Evaluation Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Many previous IQA methods used legacy databases like LIVE IQA [29], TID-2008 [25], TID-2013 [24], CSIQ-IQA [12], and KADID [13] for development and evaluation purposes. However, these datasets contain only a small number \\((\\sim 25 - 100)\\) of pristine images synthetically distorted by various levels and types of single distortions. Hence, these datasets lack diversity and realism of content and distortion. Recently many \"In the Wild\" datasets like KonIQ [9], CLIVE [6], FLIVE [40], and SPAQ [5] have been developed and used by visual quality researchers since they address the shortcomings of the legacy datasets. The newer breed of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5851" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "perceptual quality datasets contain many authentically distorted images. KonIQ-10K dataset consists of 10K images selected from the publicly available multimedia large-scale YFCC100M database [31]. CLIVE contains 1162 authentically distorted images captured using various mobile devices. FLIVE, on the other hand, is comprised of 40,000 images sampled from open-source images and designed to emulate the feature distributions found in social media images statistically. Lastly, SPAQ consists of 11,000 images captured using 66 mobile devices, and each image is accompanied by various annotations such as brightness, content labels, and EXIF data. However, our experiments only utilize the image and its corresponding quality score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.502 + ], + "angle": 0, + "content": "We also evaluated our method on four legacy synthetically distorted datasets: LIVE-IQA, TID-2013, CSIQ-IQA, and KADID. We provide short descriptions of each of the databases. The LIVE IQA dataset includes 779 images that have been synthetically distorted using five types of distortions at four different intensity levels. TID-2013, on the other hand, contains 3000 images that have been synthetically distorted using 24 different types of distortions at five different levels of intensity, with 25 reference images as the base. The CSIQ-IQA dataset comprises 866 images that have been synthetically distorted using six types of distortions on top of 30 reference images. Lastly, the KADID dataset comprises 10125 images synthetically distorted using 25 different distortions on 81 reference images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.514, + 0.303, + 0.53 + ], + "angle": 0, + "content": "4.3. Training Configurations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.827 + ], + "angle": 0, + "content": "Our content-aware encoder is pre-trained on the ImageNet database following the configuration proposed in MoCo-v2. Due to time and resource constraints, we train the content-aware encoder for 200 epochs. For the quality-aware encoder, we used ResNet-50 as a feature extractor, and a 2-layer MLP head to regress contrastive features of dimension 128. The hidden dimension of the MLP head has 2048 neurons. In each forward pass, the OverLap Area (OLA) based cropping mechanism chooses two crops \\((C_1\\) and \\(C_2)\\) from each image, such that the percentage of overlap between the crops is maintained within a minimum and a maximum bound. The performance variation of Re-IQA-QA (quality aware module only) and Re-IQA against percentage OverLap Area, patch-sizes, and the number of image distortion augmentations is depicted in Table 1. The optimal parameters are chosen based on the combined performance of the two modules in Re-IQA. We achieved the best performance using \\(10 - 30\\%\\) percentage OverLap Area bound, patch size of 160, and 11 distortion augmentations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The processed chunks are passed through the query and key encoders respectively in the MoCo-v2 framework, followed by an adaptive pooling layer to compress the output of the ResNet-50 into a 1D feature vector. The generated feature vector is then fed to the MLP head to generate the" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "contrastive feature vectors required for loss computation. Our design of the Re-IQA model is inspired by previous works [16, 37] that use images both at their original and half-scale. Therefore, during the training phase of the Re-IQA model we use all images in a database both at original and half-scale, thereby doubling the training dataset." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.183, + 0.893, + 0.394 + ], + "angle": 0, + "content": "During training, the following hyper-parameters were fixed throughout all experiments: learning rate \\( = 0.6 \\) with cosine annealing [15] scheduler, InfoNCE temperature \\( \\tau = 0.2 \\), and momentum coefficient \\( = 0.999 \\). Our best-performing model required a batch size of 630 (effectively \\( 630 \\times (n + 1) \\) augmentations x (2) scales) during training and was trained for 25 epochs. Convergence occurs in a relatively shorter number of epochs as the effective dataset size increases drastically due to a large number of augmentations and processing of each image in the dataset at two scales. All the implementations were done in Python using the PyTorch deep learning framework. We trained the content and quality-aware encoders on a system configured with 18 Nvidia A100-40GB GPUs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.405, + 0.692, + 0.42 + ], + "angle": 0, + "content": "4.4. Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.429, + 0.895, + 0.609 + ], + "angle": 0, + "content": "We tested our Re-IQA model against other state-of-the-art models on all of the \"In the Wild\" and synthetically distorted IQA databases described in Section 4.2. Each of these datasets is a collection of images labeled by subjective opinions of picture quality in the form of the mean of the opinion scores (MOS). The single-layer regressor head in Re-IQA is trained by feeding the output of the pre-trained encoders and then comparing the output of the regressor, against the ground truth MOS using L2 loss. We use both Spearman's rank order correlation coefficient (SRCC) and Pearson's linear correlation coefficient (PLCC) as metrics to evaluate the trained model across IQA databases." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.61, + 0.895, + 0.791 + ], + "angle": 0, + "content": "Following the evaluation protocol used in [16], each dataset was randomly divided into \\(70\\%\\), \\(10\\%\\) and \\(20\\%\\) corresponding to training, validation and test sets, respectively. We used the validation set to determine the regularization coefficient of the regressor head using a 1D grid search over values in the range \\([10^{-3}, 10^{3}]\\). To avoid overlap of contents in datasets with synthetic distortions, splits were selected based on source images. We also prevented any bias towards the training set selection by repeating the train/test split operation 10 times and reporting the median performance. On FLIVE, due to the large dataset size, we follow the train-test split recommended by the authors in [40]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.593, + 0.817 + ], + "angle": 0, + "content": "4.5. Results" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Our \"Mixture of Experts\" approach in Re-IQA enables us to learn robust high-level image content and low-level quality aware representations independently, the benefit of which can be clearly observed in the performance values reported in Table 2. We compared the performance of Re-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5852" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.894, + 0.187 + ], + "angle": 0, + "content": "
ModelEvaluation Datasetn_augPatch SizeOLA bound (%)
251115231281601922242565-1510-3050-80No Bound
Re-IQA(Quality-Aware)KonIQ0.8550.8580.8610.8620.8600.8600.8610.8610.8600.8580.8560.8610.8570.858
SPAQ0.8900.8960.9000.9000.8970.8980.9000.9010.8980.8940.8890.9000.8860.890
CSIQ0.9280.9370.9440.9360.9300.9370.9440.9390.9300.9280.9370.9440.9310.938
Re-IQA(Quality-Aware +Content Aware)KonIQ0.8950.9010.9140.8980.8950.9100.9140.9110.9050.8970.9030.9140.8970.905
SPAQ0.9020.9130.9180.9100.9090.9160.9180.9140.9080.9030.9070.9180.9040.906
CSIQ0.9320.9410.9470.9370.9350.9400.9470.9420.9370.9320.9390.9470.9350.940
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.196, + 0.893, + 0.239 + ], + "angle": 0, + "content": "Table 1. SRCC performance comparison of Re-IQA-QA and Re-IQA while varying one hyper-parameter at a time. While varying \\( n_{aug} \\), we keep patch size 160 and OLA bound \\( 10 - 30\\% \\). When varying patch size, \\( n_{aug} \\) was fixed to 11 and OLA bound to \\( 10 - 30\\% \\). When varying OLA bound, \\( n_{aug} \\) was set to 11 and the patch size was set to 160." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.251, + 0.893, + 0.409 + ], + "angle": 0, + "content": "
MethodAuthentic Distortions a.k.a "Images in the Wild"Synthetic Distortions
KonIQCLIVEFLIVESPAQLIVE-IQACSIQ-IQATID-2013KADID
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
BRISQUE0.6650.6810.6080.6290.2880.3730.8090.8170.9390.9350.7460.8290.6040.6940.5280.567
CORNIA0.7800.7950.6290.671--0.7090.7250.9470.9500.6780.7760.6780.7680.5160.558
DB-CNN0.8750.8840.8510.8690.5540.6520.9110.9150.9680.9710.9460.9590.8160.8650.8510.856
PQR0.8800.8840.8570.882----0.9650.9710.8720.9010.7400.798--
PaQ-2-PiQ0.8700.8800.8400.8500.5710.623----------
HyperlQA0.9060.9170.8590.8820.5350.6230.9160.9190.9620.9660.9230.9420.8400.8580.8520.845
CONTRIQUE0.8940.9060.8450.8570.5800.6410.9140.9190.9600.9610.9420.9550.8430.8570.9340.937
MUSIQ0.9160.928--0.6460.7390.9170.921--------
ImageNet Pretrained (Supervised)0.8880.9040.7810.8090.5950.6480.9040.9090.9250.9310.8400.8480.6790.7290.7010.677
Re-IQA (content aware)0.8960.9120.8080.8440.5880.6990.9020.9080.8670.8580.7660.8240.6580.7360.6010.656
Re-IQA (quality aware)0.8610.8850.8060.8240.5840.5900.9000.9100.9710.9720.9440.9640.8440.8800.8850.892
Re-IQA (content + quality)0.9140.9230.8400.8540.6450.7330.9180.9250.9700.9710.9470.9600.8040.8610.8720.885
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.417, + 0.893, + 0.461 + ], + "angle": 0, + "content": "Table 2. Performance comparison of Re-IQA against various NR-IQA models on IQA databases with authentic and synthetic distortions. The top 2 best performing models are in bold. Higher SRCC and PLCC imply better performance. MUSIQ results from [10]. Results of all other existing methods from [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.59 + ], + "angle": 0, + "content": "IQA along with its sub-modules against other state-of-the-art models on IQA datasets containing authentic and synthetic distortions in Table 2. We used the features extracted from the Resnet-50 backbone for the supervised ImageNet pre-trained model. From the results, we conclude that Re-IQA achieves competitive performance across all tested databases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.471, + 0.894 + ], + "angle": 0, + "content": "Results from Table 2 highlight the impact of content and low-level image quality on the final NR-IQA task. We observe that high-level content-aware features dominate quality-aware features for authentically distorted images, while the quality-aware features dominate the high-level content-aware features for authentically distorted images. We can hypothesize the reason to be high variation in content in the \"Images in the Wild\" scenario. Training a simple linear regressor head that is fed with features from both the content and quality-aware encoders provides flexibility to adjust the final model based on the application dataset. This can be observed in the performance scores achieved by the combined model when compared to the individual sub-modules. The performance scores of the quality-aware sub-module do not beat other methods when considering the \"Images in the Wild\" scenario, primarily due to the heavy impact of content. Despite this, when evaluated on synthetic distortion datasets, the quality-aware sub-module of Re-IQA outperforms most of its competitors all by itself. Thus we conclude that our generated quality-aware" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.893, + 0.548 + ], + "angle": 0, + "content": "representations align very well with distortions present in an image. This is also conclusive from the t-SNE visualizations [33] depicted in Figure 5. Further details on t-SNE experiments are shared in Supplemental Material §S.3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.559, + 0.707, + 0.575 + ], + "angle": 0, + "content": "5. Concluding Remarks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.903 + ], + "angle": 0, + "content": "We developed a holistic approach to Image quality Assessment by individually targeting the impact of content and distortion on the overall image quality score. NR-IQA for \"Images in the Wild\" benefits significantly from content-aware image representations, especially when learned in an unsupervised setting. This work aims to demonstrate that complementary content and image quality-aware features can be learned and, when combined, achieve competitive performance across all evaluated IQA databases. We re-engineer the MoCo-v2 framework for learning quality-aware representations to include our proposed novel Image Augmentation, OLA-based smart cropping, and a Half-Swap scheme. The results of experiments on the eight IQA datasets demonstrate that Re-IQA can consistently achieve state-of-the-art performance. Our Re-IQA framework is flexible to changes in the design of encoder architectures and can be extended to other CNN architectures and Transformer based models like MUSIQ. Although developed for IQA tasks, Re-IQA can be extended as a spatial feature extraction module in Video Quality Assessment algorithms that currently use supervised pre-trained Resnet-50." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5853" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Alan Conrad Bovik. Automatic prediction of perceptual image and video quality. Proceedings of the IEEE, 101:2008-2024, 2013. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Xinlei Chen, Haoqi Fan, Ross B. 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Bovik + +Laboratory of Image and Video Engineering, The University of Texas at Austin + +# Abstract + +Automatic Perceptual Image Quality Assessment is a challenging problem that impacts billions of internet, and social media users daily. To advance research in this field, we propose a Mixture of Experts approach to train two separate encoders to learn high-level content and low-level image quality features in an unsupervised setting. The unique novelty of our approach is its ability to generate low-level representations of image quality that are complementary to high-level features representing image content. We refer to the framework used to train the two encoders as Re-IQA. For Image Quality Assessment in the Wild, we deploy the complementary low and high-level image representations obtained from the Re-IQA framework to train a linear regression model, which is used to map the image representations to the ground truth quality scores, refer Figure 1. Our method achieves state-of-the-art performance on multiple large-scale image quality assessment databases containing both real and synthetic distortions, demonstrating how deep neural networks can be trained in an unsupervised setting to produce perceptually relevant representations. We conclude from our experiments that the low and high-level features obtained are indeed complementary and positively impact the performance of the linear regressor. A public release of all the codes associated with this work will be made available on GitHub. + +# 1. Introduction + +Millions of digital images are shared daily on social media platforms such as Instagram, Snapchat, Flickr, etc. Making robust and accurate Image Quality Assessments (IQA) that correlate well with human perceptual judgments is essential to ensuring acceptable levels of visual experience. Social media platforms also use IQA metrics to decide parameter settings for post-upload processing of the images, such as resizing, compression, enhancement, etc. + +![](images/927b61bce702303ec58042a7a37739a82cb1db8407d901a4d758d76129a4b53d.jpg) +Figure 1. IQA score prediction uses two encoders trained for complementary tasks of learning content and quality aware image representations. The encoders are frozen while the regressor learns to map image representations to quality predictions. + +In addition, predictions generated by IQA algorithms are often used as input to recommendation engines on social media platforms to generate user feeds and responses to search queries. Thus, accurately predicting the perceptual quality of digital images is a high-stakes endeavor affecting the way billions of images are stored, processed, and displayed to the public at large. + +IQA metrics can be simply categorized into Full-Reference (FR) and No-Reference (NR) algorithms. FR-IQA algorithms like SSIM [35], FSIM [43], and LPIPS [44] require both reference (undistorted) and distorted version of an image to quantify the human-perceivable quality. This requirement limits their applicability for the "Images in the Wild" scenario, where the reference image is unavailable. On the contrary, NR-IQA algorithms like BRISQUE [19], PaQ-2-PiQ [40], and CONTRIQUE [16] do not require a reference image nor any knowledge about the kind of present distortions to quantify human-perceivable quality in a test image, paving the way for their use in "Images in the Wild" scenarios. + +No-Reference IQA for "Images in the Wild" presents exciting challenges due to the complex interplay among the various kinds of distortions. Furthermore, due to the intricate nature of the human visual system, image content affects quality perception. In this work, we aim to learn low-level quality-aware image representations that are complementary to high-level features representative of image content. Figure 2 illustrates some of the challenges encountered + +![](images/2d67359add27060242b72755c54702e031e1e3860cf0615278fad40538c86a02.jpg) +(a) JPEG Compressed : 1 + +![](images/b47558248fde6129ef70f40d98f741bed4e974ea8c85d8012846dd0c2d742e23.jpg) +(b) JPEG Compressed: 2 +Figure 2. Exemplar Synthetically and "In the Wild" distorted pictures. (a), (b) are two images captured on iPhone 13 Pro and then JPEG compressed using the same encoding parameters. (c), (d), were taken from KonIQ and AVA datasets respectively, and exhibit typical "Images in the Wild" distortions. Best viewed when zoomed in. + +![](images/95a6246d297735de1a583555b9627a0a69b95e3f541183bf2ee7c748b555f488.jpg) +(c) Motion Blur - Camera Shake + +![](images/9a6b5e7db40364c5b0b0961b009f803e205920dd7a9c003752354fb469cd9e0c.jpg) +(d) Overlaid Film Grain/ Noise + +in the development of NR-IQA algorithms. Figures 2 (a-b) show two images captured by the authors on an iPhone 13 Pro and compressed using the same encoding parameters. While any distortions are almost negligible in Figure 2 (a), there are artifacts that are clearly visible in Figure 2 (b). As in these examples, it is well known that picture distortion perception is content dependent, and is heavily affected by content related perceptual processes like masking [1]. Figures 2 (c-d) illustrates a few distorted pictures "In the Wild". Figures 2 (c-d) show two exemplar distorted pictures, one impaired by motion blur (Figure 2 (c)) and the other by film grain noise (Figure 2 (d)). It is also well established that perceived quality does not correlate well with image metadata like resolution, file size, color profile, or compression ratio [36]. Because of all these factors and the essentially infinite diversity of picture distortions, accurate prediction of the perception of image quality remains a challenging task, despite its apparent simplicity, and hence research on this topic remains quite active [16, 17, 19, 28, 35, 39, 42-44]. + +Our work is inspired by the success of momentum contrastive learning methods [2, 7] in learning unsupervised representations for image classification. In this work, we engineer our models to learn content and quality-aware image representations for NR-IQA on real, authentically distorted pictures in an unsupervised setting. We adopt a Mixture of Experts approach to independently train two encoders, each of which accurately learns high-level content and low-level image quality features. We refer to the new framework as Re-IQA. The key contributions we make are as follows: + +- We propose an unsupervised low-level image quality representation learning framework that generates features complementary to high-level representations of image content. We demonstrate how the "Mixture" of the two enables Re-IQA to produce image quality predictions that are highly competitive with existing state-of-the-art traditional, CNN, and Transformer based NR-IQA models, developed in both supervised and unsupervised settings across several databases. + +- We demonstrate the superiority of high-level representations of image content for the NR-IQA task, obtained from the unsupervised pre-training of the ResNet-50 [8] encoder over the features obtained from supervised pre-trained ResNet-50 on the ImageNet database [3]. We learn these high-level representations of image content using the unsupervised training framework proposed in MoCo-v2 [2] +- Inspired by the principles of visual distortion perception we propose a novel Image Augmentation and Intra-Pair Image Swapping scheme to enable learning of low-level image quality representations. The dynamic nature of the image augmentation scheme prevents the learning of discrete distortion classes, since it is applied to both pristine and authentically distorted images, enforcing learning of perceptually relevant image-quality features. + +# 2. Related Work + +As discussed in Section 1, perceptual image quality prediction for "Images in the Wild" is a challenging task due to the complex distortions that arise, and the combinations of them, and how they are perceived when they affect different kinds of pictorial content. Over the last few decades, a great deal of effort has been invested in the development of NR-IQA models that are able to accurately predict human judgment of picture quality. In recent years, NR-IQA models have evolved from using hand-crafted perceptual features, feeding shallow learners, into Deep Learning based approaches trained on large subjective databases. Traditional NR-IQA models generally have two components: a feature extractor, which generates quality-relevant features, and a low-complexity regression model, which maps the extracted features to quality scores. Most prior models have focused on improving the feature extractor and, thus improving the performance of the overall IQA algorithm. A common practice in traditional NR-IQA methods is to model image artifacts using statistical information extracted from a test image. Natural Scene Statistics (NSS) mod + +![](images/638e3180dbd370670447a4efbc29c7a51a949455d790672a09d1b83128007f08.jpg) +(a) Original Image + +![](images/eadd61043c0ddc768f024309f05f939b52b641ab86db9df1b5a3e9c9e99fde61.jpg) +(b) Gaussian Blur + +![](images/77f6d6167742404bc6d63070991a84a8f140defa05616a0dec0c743e60c643aa.jpg) +(c) Saturate + +![](images/329518431690f2f25f2301c905578b9400db96d37e368c026ac9ed9d6fb2e748.jpg) +(d) Compression + +![](images/dd1f467931c2eed83be6f0141db924954b76ec75040d2c7d2ac126553748b5c1.jpg) +(e) Gaussian Noise + +![](images/15170aee36d285180d129f2b20a6f674872c510683cb997d75ea40186a12ca97.jpg) +(f) Color Saturate + +![](images/70bc25dbd8bd785aaebf8c8e1c9f09ed6f930f600b96e4d4733715f0a74df53a.jpg) +(g) Pixelate + +![](images/e52f843786be63c8c91b3193d6b3801448ceed47288d98cc3955ccd63d245bd9.jpg) +(h) Contrast + +![](images/0841b3d20de5611931ee867472029460acb01a90d4ff6a9b8a581ffd96bf8e6c.jpg) +(i) Darken + +![](images/91536e2fe85d4732e33b714b98ec117f869edba56117aeda727358fb0da78dbc.jpg) +(j) Resizing +Figure 3. Some samples of distortions available in the Image Augmentation Scheme. There are a total of 25 distortions available in the bank, with 5 levels of distortion for each. More details are provided in Supplemental Material. + +![](images/91197dff51fb83c56b05776f33cdce8f92b7769d33357e9498be59f5ecdbc6d4.jpg) +(k) Jitter + +![](images/f20306f75853df0b261c0391db9edbc6487b7c5a861aa0a3df37c145af8fb1e0.jpg) +(1) Motion Blur + +els and distorted versions of them are popular, where features are extracted from transformed domains, on which statistical measurements of deviations due to distortions are used as features for NR-IQA. For example, the NSS-based BRISQUE [19] and NIQE [20] models obtain features that capture in a normalized bandpass space [26]. DIIVINE [21] uses steerable pyramids, and BLIINDS [27] uses DCT coefficients to measure statistical traces of distortions. Other methods like CORNIA [39] and HOSA [38] utilize codebooks constructed from local patches, which are applied to obtain quality-aware features. Most of the methods discussed above often obtain acceptable results when evaluated on synthetically distorted images, but their performances significantly degrade when applied to "Images in the Wild". This is because the above-discussed methods focus primarily on modeling the distortions present in a test image as statistical deviations from naturalness while completely ignoring the high-level content present in the image. + +The majority of deep learning approaches utilize pretrained CNN backbones as feature extractors. This is done since end-to-end supervised training of NR-IQA models is difficult given the limited sizes of existing perceptual quality databases. These models typically use CNN backbones trained for ImageNet classification to extract features, combining them with low-complexity regression models like Support Vector Regression or Linear Regression to map the features to human-labeled scores. A few models use labeled scores from IQA databases to fine-tune the CNN backbone. The authors of the RAPIQUE [32] show that features obtained from pretrained ResNet-50 [8] could effectively predict quality scores on "In the Wild" content. In DB-CNN [45], authors adopt a two-path technique, where one CNN branch generates distortion-class and distortion-level + +features, while the other CNN branch provides high-level image content information. These are then combined using bilinear pooling. PQR [41] achieved faster convergence and better quality estimates by using the statistical distributions of subjective opinion scores instead of just scalar mean opinion scores (MOS) during training. BIECON [11] trains a CNN model on patches of distorted images, using proxy quality scores generated by FR-IQA models as labels. The authors of [30] proposed an adaptive hypernetwork architecture that considers content comprehension during perceptual quality prediction. Very recent works on NR-IQA include PaQ-2-PiQ [40], CONTRIQUE [16] and MUSIQ [10]. PaQ-2-PiQ benefits from a specially designed dataset wherein the authors not only collected subjective quality scores on whole pictures but also on a large number of image patches. The dataset is also large enough to train deep models in a supervised setting, and PaQ-2-PiQ achieves state-of-the-art performance. However, although the authors use patch-level and image-level quality information during training, the training process may be susceptible to dataset sampling errors since only a few patches were extracted from each image and annotated with quality scores. MUSIQ uses a transformer-based architecture [34] pre-trained on the ImageNet classification dataset. The method benefits significantly by using transformer architecture and fine-tuning the transformer backbone on the IQA test databases. CONTRIQUE is a closely related work that aims to learn quality-aware representations in a self-supervised setting. CONTRIQUE learns to group images with similar types and distortion degrees into classes on an independent dataset. In this way, it proposes to learn quality-aware image representations. However, the class labels used to define 'similar-quality' and 'different-quality' + +samples in CONTRIQUE are in fact distortion labels instead of being true-quality labels. We address this shortcoming in our proposed framework. Our method, which is also completely unsupervised, does not learn representations based on distortion class labels, which can be inaccurate when asserted on "In the Wild" data. Instead, our model, which is inspired by the fundamental principles of visual distortion perception, proposes to independently learn high-level semantic image content and low-level image quality features. These image representation features are mapped directly to subjective scores using a low-complexity regression model without fine-tuning the deep neural networks. Here, we utilize ResNet-based architectures [8] throughout the Re-IQA framework. As our proposed framework is generalizable enough to be implemented using other CNN and transformer-based architectures, we plan to extend it to transformer-based architectures in the future. + +# 3. Rethinking-IQA + +The Re-IQA model framework is embodied in three processing phases. The first and second phases consist of training two ResNet50 encoders using contrastive learning of high-level and low-level image information. We then use the pre-trained encoders with frozen weights as image representation generation backbones, which supply features to a low-complexity regression model that is trained to conduct image quality prediction as shown in Figure 1. + +To learn high-level content-aware information we deploy MoCo-v2 [2] ImageNet pre-trained model and adopt the design considerations developed in the original paper. Further discussed in section 3.1. To learn quality-aware representations we develop a contrastive learning framework that deploys a novel augmentation protocol and an intra-pair image-swapping scheme to facilitate model convergence towards learning robust image quality-aware features. Further discussed in section 3.2. + +# 3.1. Re-IQA : Content Aware + +The primary objective in the MoCo-v2 framework [2] is to assign a 'similar' label to two crops from a single image while assigning a 'different' label to two crops taken from two different images. Although, content aware Re-IQA based completely on the original MoCo-v2 framework performs well in the image quality prediction problem (refer Table 2), it still suffers from a critical design problem: two crops from a same image can be given significantly different quality scores by human viewers. Hence we only use, the original MoCo-v2 framework to generate content-aware image representations. We make appropriate changes, discussed next, to the MoCo-v2 framework to enable accurate learning of quality-aware representations that complement content-aware representations. + +# 3.2. Re-IQA : Quality Aware + +Our quality-aware contrastive learning framework uses an Image Augmentation method and an Intra-pair image Swapping scheme to train a ResNet-50 encoder within the MoCo-v2 framework [2] with a goal of modeling a feature space wherein all images having similar degrees of perceptual quality fall closer to one another than to images having different perceptual qualities. The MoCo-v2 framework simultaneously processes a query image through the query encoder and a key image through the key encoder. In a single batch, a positive sample occurs when features are generated using any paired query and key, the pair being labeled 'similar.' A negative sample occurs when the query and the key do not belong to the same pair, hence they are marked 'different.' + +To train a contrastive network we need paired images, such that for any sample index $k$ , we have image pairs $[i_1^k, i_2^k]$ that can be assigned the 'similar-quality' label, and for any $j, k$ ; where $k \neq j$ we have image pairs $[i_1^k, i_2^j]$ that can be assigned the 'different-quality' label. From here on we shall refer to perceptual quality-aware features as PQAF. To define the decision boundary between 'similar-quality' and 'different-quality' labels, we assume the following three hypotheses to be true: + +H1: PQAF varies within an image itself. If we assign PQAF to an image patch $x$ and denote it as $PQAF_x$ , then $PQAF_x$ varies only a small amount between neighboring patches. However, $PQAF_x$ may vary significantly between two distant patches. +H2: The PQAF of any two randomly selected images are 'different,' which assumes that the scenes depicted in the images to be different. However, this does not enforce any restrictions on the quality scores of the two images. +H3: Two different distorted versions of the same image have different PQAF. + +These hypotheses are further discussed in the Supplemental material §S.4. + +# 3.2.1 Quality-Aware Image Augmentation Scheme + +To conduct quality-aware image feature extraction, we deploy a novel bank of image quality distortion augmentations, as elaborated in the Supplemental material §S.1. The augmentation bank is a collection of 25 distortion methods, each realized at 5 levels of severity. For any source image $i^k$ from the training set, where $k \in \{1, 2 \dots K\}$ and $K$ is the total number of images in the training data, a randomly chosen subset of the augmentations available in the bank are applied to each image resulting in a mini-batch of distorted images. We combine each source image with its distorted versions to form $chunk^k$ : + +$$ +c h u n k ^ {k} = \left[ i ^ {k}, i _ {1} ^ {k}, i _ {2} ^ {k}, \dots , i _ {n} ^ {k} \right] \tag {1} +$$ + +![](images/5c394efcb587a6c320a6ea2a2bfa23faf16686ddd32205fab7749a1a57cd767c.jpg) +Figure 4. Learning Quality Aware Representations: The OLA based cropping, Image Augmentation scheme and Half-swapping enable the generation of appropriate 'similar-quality' and 'different-quality' image pairs which can be used to learn quality-aware features. Note that $A_0$ has no augmentation, while $A_1..A_n$ are randomly sampled from the augmentation bank. During loss calculation, representations generated using the key encoder for the previous 65536 samples are also used as negative keys, following MoCo-V2 settings. + +where $i_j^k$ is the $j^{th}$ distorted version of $i^k$ , and $n$ is the number of augmentations drawn from the bank. We then generate two random crops of $chunk^k$ , namely $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ , using an overlap area based smart cropping mechanism. We choose these crop locations such that the overlapping area (OLA) in the two crops falls within minimum and maximum bounds. We make sure that the crop location is the same over all images in each chunk and different between chunks, resulting in: + +$$ +\operatorname {c h u n k} ^ {k _ {c 1}} = \left[ i ^ {k _ {c 1}}, i _ {1} ^ {k _ {c 1}}, i _ {2} ^ {k _ {c 1}}, \dots , i _ {n} ^ {k _ {c 1}} \right] +$$ + +$$ +c h u n k ^ {k _ {c 2}} = \left[ i ^ {k _ {c 2}}, i _ {1} ^ {k _ {c 2}}, i _ {2} ^ {k _ {c 2}}, \dots , i _ {n} ^ {k _ {c 2}} \right] \tag {2} +$$ + +When training, by choosing an augmented image $a_{th}$ from both $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ , form the pair $[i_a^{k_{c1}}, i_a^{k_{c2}}]$ . Image $i_a^{k_{c1}}$ and $i_a^{k_{c2}}$ are neighboring patches because of OLA-based cropping and hence are marked 'similar-quality' as stated in H1. Similarly, for any image $k$ and distortion $a, b$ where $a \neq b$ , the pair $[i_a^{k_{c1}}, i_b^{k_{c2}}]$ are labelled as 'different-quality' as in H1. Finally, for any two different image samples $k, j$ , label the pair $[i\_ k_{c1}, i\_ j_{c2}]$ as 'different-quality', following H2. + +# 3.2.2 Intra-Pair Image Swapping Scheme + +Given a spatial arrangement of $chunk^{k_{c1}}$ and $chunk^{k_{c2}}$ : + +$$ +\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 1}} \\ \updownarrow & \updownarrow & & \updownarrow & \updownarrow & & \updownarrow & \updownarrow \\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 2}} \end{array} +$$ + +form the following types of image-pairs and corresponding labels: + +$$ +[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} ] \mapsto \text {s i m i l a r - q u a l i t y} +$$ + +$$ +\left[ \begin{array}{c} i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \end{array} \right] \mapsto d i f f e r e n t q u a l i t y +$$ + +Then apply intra-pair image swapping on the generated chunks to obtain the following arrangement: + +$$ +\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 2}} \\ \updownarrow & \updownarrow & & \updownarrow & \updownarrow & & \updownarrow & \updownarrow \\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 1}} \end{array} +$$ + +By swapping images within each pair over half the pairs, (referred to as Half Swap), the network is introduced to samples having the following configuration: $[i_a^{k_{c1}}, i_b^{k_{c1}}]$ where $a, b; a \neq b$ are two different distortions. Note that the crops $[i_a^{k_{c1}}, i_b^{k_{c1}}]$ are exactly the same, except for the distortion applied, and thus contain the same essential visual content. Despite this, we mark such samples as 'different-quality' as stated in H3, thus forcing the network to look beyond content-dependent features. With this, we finally end up with the following image pairs and labels: + +$$ +\left[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} \right] \mapsto \text {s i m i l a r - q u a l i t y} +$$ + +$$ +\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \right] \mapsto d i f f e r e n t - q u a l i t y +$$ + +$$ +\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 1}} \right] \mapsto d i f f e r e n t - q u a l i t y +$$ + +$$ +\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {j _ {c 2}} \right] \mapsto d i f f e r - q u a l i t y +$$ + +# 3.2.3 Quality-Aware Training + +Define two identical encoders 1) Online Encoder (query encoder) and 2) Momentum Encoder (key encoder). Both encoders have ResNet-50 backbones and an MLP head to generate the final output embeddings from the ResNet features. Split the pairs designed in the previous step, passing the first image from each pair through the query encoder, and the other through the key encoder. To calculate the loss between the representation generated by the query and key + +encoder, we use the InfoNCE [23] loss function: + +$$ +\mathcal {L} _ {q, k ^ {+}, \{k ^ {-} \}} = - \log \frac {\exp (q . k ^ {+} / \tau)}{\exp (q . k ^ {+} / \tau) + \sum_ {k ^ {-}} \exp (q . k ^ {-} / \tau)} \tag {3} +$$ + +Here $q$ is the query image, $k^{+}$ is a positive sample (similar-quality), $k^{-}$ represent negative samples (different-quality), and $\tau$ is a temperature hyper-parameter. This loss is then used to update the weights of the online encoder by back-propagation. The weights of the momentum encoder are updated using the weighted sum of its previous weights and the new weights of the online encoder. Formally denoting the parameters of the query encoder by $\theta_{q}$ and the parameters of the key encoder as $\theta_{k}$ , update $\theta_{k}$ as: + +$$ +\theta_ {k} \leftarrow m \theta_ {k} + (1 - m) \theta_ {q} \tag {4} +$$ + +Here $m \in [0,1)$ , is the momentum coefficient. Once the encoder pre-training has saturated the frozen ResNet-50 can be used as an encoder backbone for any downstream task associated with perceptual image quality. + +# 3.3. IQA Regression + +We concatenate the image representations obtained from the content and quality-aware encoders in the previous steps to train a regressor head to map the obtained features to the final perceptual image quality scores as shown in Figure 1. In our experiments, we use a single-layer perceptron as the regressor head. It is important to note that we train only the low-complexity regressor head while evaluating our Re-IQA framework across multiple databases. Our method does not require us to fine-tune the feature extraction backbone(s) separately for each evaluation database as required in MUSIQ. + +# 4. Experimental Results + +# 4.1. Training Datasets + +In the Re-IQA framework, two ResNet-50 encoders are trained to obtain high-level image content features and low-level image quality features. The encoder that learns high-level image content features was trained on a subset of the ImageNet database [3] containing approximately 1.28 million images across 1000 classes. When training the encoder in an unsupervised setting, we discard the class label information and only use images without labels during the training process. + +To learn the low-level image quality features, we use a combination of pristine images and authentically distorted images as training data. The augmentation scheme (applied to all images in the dataset) ensures that the network learns how to differentiate between distortions when the semantic + +content in the image is the same. The presence of authentically distorted images in the dataset helps tune the model to accurately predict the quality of "In the Wild" pictures. + +- Pristine Images: We used the 140K pristine images in the KADIS dataset [13]. We do not use the 700K distorted images available in the same dataset. The authors of KADIS did not provide subjective quality scores for any image in the dataset. +- Arguably Distorted Images: We used the same combination of datasets as proposed in CONTRIQUE [16] to form our distorted image set: (a) AVA [22] - 255K images, (b) COCO [14] - 330K images, (c) CERTH-Blur [18] - 2450 images, d) VOC [4] - 33K images + +![](images/8fcfb162d8db6ae78c1fcbfdbb178642247ed4443f31cfc333da487f7cc1f4dd.jpg) +(a) Re-IQA Quality-Aware + +![](images/cebdb718ae18b2889ca34fa1f17c9d5d0e4ac8b62adb51472ef011606116f444.jpg) +(b) CONTRIQUE +Figure 5. Comparison of 2D TSNE Visualization of learned representations of 1016 images sampled from KonIQ (UGC - #150) and CSIQ (Synthetic Distortions - #866) between Re-IQA Quality Aware sub-module and CONTRIQUE. Best viewed zoomed in. + +# 4.2. Evaluation Datasets + +Many previous IQA methods used legacy databases like LIVE IQA [29], TID-2008 [25], TID-2013 [24], CSIQ-IQA [12], and KADID [13] for development and evaluation purposes. However, these datasets contain only a small number $(\sim 25 - 100)$ of pristine images synthetically distorted by various levels and types of single distortions. Hence, these datasets lack diversity and realism of content and distortion. Recently many "In the Wild" datasets like KonIQ [9], CLIVE [6], FLIVE [40], and SPAQ [5] have been developed and used by visual quality researchers since they address the shortcomings of the legacy datasets. The newer breed of + +perceptual quality datasets contain many authentically distorted images. KonIQ-10K dataset consists of 10K images selected from the publicly available multimedia large-scale YFCC100M database [31]. CLIVE contains 1162 authentically distorted images captured using various mobile devices. FLIVE, on the other hand, is comprised of 40,000 images sampled from open-source images and designed to emulate the feature distributions found in social media images statistically. Lastly, SPAQ consists of 11,000 images captured using 66 mobile devices, and each image is accompanied by various annotations such as brightness, content labels, and EXIF data. However, our experiments only utilize the image and its corresponding quality score. + +We also evaluated our method on four legacy synthetically distorted datasets: LIVE-IQA, TID-2013, CSIQ-IQA, and KADID. We provide short descriptions of each of the databases. The LIVE IQA dataset includes 779 images that have been synthetically distorted using five types of distortions at four different intensity levels. TID-2013, on the other hand, contains 3000 images that have been synthetically distorted using 24 different types of distortions at five different levels of intensity, with 25 reference images as the base. The CSIQ-IQA dataset comprises 866 images that have been synthetically distorted using six types of distortions on top of 30 reference images. Lastly, the KADID dataset comprises 10125 images synthetically distorted using 25 different distortions on 81 reference images. + +# 4.3. Training Configurations + +Our content-aware encoder is pre-trained on the ImageNet database following the configuration proposed in MoCo-v2. Due to time and resource constraints, we train the content-aware encoder for 200 epochs. For the quality-aware encoder, we used ResNet-50 as a feature extractor, and a 2-layer MLP head to regress contrastive features of dimension 128. The hidden dimension of the MLP head has 2048 neurons. In each forward pass, the OverLap Area (OLA) based cropping mechanism chooses two crops $(C_1$ and $C_2)$ from each image, such that the percentage of overlap between the crops is maintained within a minimum and a maximum bound. The performance variation of Re-IQA-QA (quality aware module only) and Re-IQA against percentage OverLap Area, patch-sizes, and the number of image distortion augmentations is depicted in Table 1. The optimal parameters are chosen based on the combined performance of the two modules in Re-IQA. We achieved the best performance using $10 - 30\%$ percentage OverLap Area bound, patch size of 160, and 11 distortion augmentations. + +The processed chunks are passed through the query and key encoders respectively in the MoCo-v2 framework, followed by an adaptive pooling layer to compress the output of the ResNet-50 into a 1D feature vector. The generated feature vector is then fed to the MLP head to generate the + +contrastive feature vectors required for loss computation. Our design of the Re-IQA model is inspired by previous works [16, 37] that use images both at their original and half-scale. Therefore, during the training phase of the Re-IQA model we use all images in a database both at original and half-scale, thereby doubling the training dataset. + +During training, the following hyper-parameters were fixed throughout all experiments: learning rate $= 0.6$ with cosine annealing [15] scheduler, InfoNCE temperature $\tau = 0.2$ , and momentum coefficient $= 0.999$ . Our best-performing model required a batch size of 630 (effectively $630 \times (n + 1)$ augmentations x (2) scales) during training and was trained for 25 epochs. Convergence occurs in a relatively shorter number of epochs as the effective dataset size increases drastically due to a large number of augmentations and processing of each image in the dataset at two scales. All the implementations were done in Python using the PyTorch deep learning framework. We trained the content and quality-aware encoders on a system configured with 18 Nvidia A100-40GB GPUs. + +# 4.4. Evaluation Protocol + +We tested our Re-IQA model against other state-of-the-art models on all of the "In the Wild" and synthetically distorted IQA databases described in Section 4.2. Each of these datasets is a collection of images labeled by subjective opinions of picture quality in the form of the mean of the opinion scores (MOS). The single-layer regressor head in Re-IQA is trained by feeding the output of the pre-trained encoders and then comparing the output of the regressor, against the ground truth MOS using L2 loss. We use both Spearman's rank order correlation coefficient (SRCC) and Pearson's linear correlation coefficient (PLCC) as metrics to evaluate the trained model across IQA databases. + +Following the evaluation protocol used in [16], each dataset was randomly divided into $70\%$ , $10\%$ and $20\%$ corresponding to training, validation and test sets, respectively. We used the validation set to determine the regularization coefficient of the regressor head using a 1D grid search over values in the range $[10^{-3}, 10^{3}]$ . To avoid overlap of contents in datasets with synthetic distortions, splits were selected based on source images. We also prevented any bias towards the training set selection by repeating the train/test split operation 10 times and reporting the median performance. On FLIVE, due to the large dataset size, we follow the train-test split recommended by the authors in [40]. + +# 4.5. Results + +Our "Mixture of Experts" approach in Re-IQA enables us to learn robust high-level image content and low-level quality aware representations independently, the benefit of which can be clearly observed in the performance values reported in Table 2. We compared the performance of Re- + +
ModelEvaluation Datasetn_augPatch SizeOLA bound (%)
251115231281601922242565-1510-3050-80No Bound
Re-IQA(Quality-Aware)KonIQ0.8550.8580.8610.8620.8600.8600.8610.8610.8600.8580.8560.8610.8570.858
SPAQ0.8900.8960.9000.9000.8970.8980.9000.9010.8980.8940.8890.9000.8860.890
CSIQ0.9280.9370.9440.9360.9300.9370.9440.9390.9300.9280.9370.9440.9310.938
Re-IQA(Quality-Aware +Content Aware)KonIQ0.8950.9010.9140.8980.8950.9100.9140.9110.9050.8970.9030.9140.8970.905
SPAQ0.9020.9130.9180.9100.9090.9160.9180.9140.9080.9030.9070.9180.9040.906
CSIQ0.9320.9410.9470.9370.9350.9400.9470.9420.9370.9320.9390.9470.9350.940
+ +Table 1. SRCC performance comparison of Re-IQA-QA and Re-IQA while varying one hyper-parameter at a time. While varying $n_{aug}$ , we keep patch size 160 and OLA bound $10 - 30\%$ . When varying patch size, $n_{aug}$ was fixed to 11 and OLA bound to $10 - 30\%$ . When varying OLA bound, $n_{aug}$ was set to 11 and the patch size was set to 160. + +
MethodAuthentic Distortions a.k.a "Images in the Wild"Synthetic Distortions
KonIQCLIVEFLIVESPAQLIVE-IQACSIQ-IQATID-2013KADID
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
BRISQUE0.6650.6810.6080.6290.2880.3730.8090.8170.9390.9350.7460.8290.6040.6940.5280.567
CORNIA0.7800.7950.6290.671--0.7090.7250.9470.9500.6780.7760.6780.7680.5160.558
DB-CNN0.8750.8840.8510.8690.5540.6520.9110.9150.9680.9710.9460.9590.8160.8650.8510.856
PQR0.8800.8840.8570.882----0.9650.9710.8720.9010.7400.798--
PaQ-2-PiQ0.8700.8800.8400.8500.5710.623----------
HyperlQA0.9060.9170.8590.8820.5350.6230.9160.9190.9620.9660.9230.9420.8400.8580.8520.845
CONTRIQUE0.8940.9060.8450.8570.5800.6410.9140.9190.9600.9610.9420.9550.8430.8570.9340.937
MUSIQ0.9160.928--0.6460.7390.9170.921--------
ImageNet Pretrained (Supervised)0.8880.9040.7810.8090.5950.6480.9040.9090.9250.9310.8400.8480.6790.7290.7010.677
Re-IQA (content aware)0.8960.9120.8080.8440.5880.6990.9020.9080.8670.8580.7660.8240.6580.7360.6010.656
Re-IQA (quality aware)0.8610.8850.8060.8240.5840.5900.9000.9100.9710.9720.9440.9640.8440.8800.8850.892
Re-IQA (content + quality)0.9140.9230.8400.8540.6450.7330.9180.9250.9700.9710.9470.9600.8040.8610.8720.885
+ +Table 2. Performance comparison of Re-IQA against various NR-IQA models on IQA databases with authentic and synthetic distortions. The top 2 best performing models are in bold. Higher SRCC and PLCC imply better performance. MUSIQ results from [10]. Results of all other existing methods from [16]. + +IQA along with its sub-modules against other state-of-the-art models on IQA datasets containing authentic and synthetic distortions in Table 2. We used the features extracted from the Resnet-50 backbone for the supervised ImageNet pre-trained model. From the results, we conclude that Re-IQA achieves competitive performance across all tested databases. + +Results from Table 2 highlight the impact of content and low-level image quality on the final NR-IQA task. We observe that high-level content-aware features dominate quality-aware features for authentically distorted images, while the quality-aware features dominate the high-level content-aware features for authentically distorted images. We can hypothesize the reason to be high variation in content in the "Images in the Wild" scenario. Training a simple linear regressor head that is fed with features from both the content and quality-aware encoders provides flexibility to adjust the final model based on the application dataset. This can be observed in the performance scores achieved by the combined model when compared to the individual sub-modules. The performance scores of the quality-aware sub-module do not beat other methods when considering the "Images in the Wild" scenario, primarily due to the heavy impact of content. Despite this, when evaluated on synthetic distortion datasets, the quality-aware sub-module of Re-IQA outperforms most of its competitors all by itself. Thus we conclude that our generated quality-aware + +representations align very well with distortions present in an image. This is also conclusive from the t-SNE visualizations [33] depicted in Figure 5. Further details on t-SNE experiments are shared in Supplemental Material §S.3. + +# 5. Concluding Remarks + +We developed a holistic approach to Image quality Assessment by individually targeting the impact of content and distortion on the overall image quality score. NR-IQA for "Images in the Wild" benefits significantly from content-aware image representations, especially when learned in an unsupervised setting. This work aims to demonstrate that complementary content and image quality-aware features can be learned and, when combined, achieve competitive performance across all evaluated IQA databases. We re-engineer the MoCo-v2 framework for learning quality-aware representations to include our proposed novel Image Augmentation, OLA-based smart cropping, and a Half-Swap scheme. 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IEEE, 2012. 2, 3 +[40] Zhenqiang Ying, Haoran Niu, Praful Gupta, Dhruv Mahajan, Deepti Ghadiyaram, and Alan C. Bovik. From patches to pictures (paq-2-piq): Mapping the perceptual space of picture quality. CoRR, abs/1912.10088, 2019. 1, 3, 6, 7 +[41] Hui Zeng, Lei Zhang, and Alan C Bovik. A probabilistic quality representation approach to deep blind image quality prediction. arXiv preprint arXiv:1708.08190, 2017. 3 +[42] Lin Zhang, Ying Shen, and Hongyu Li. Vsi: A visual saliency-induced index for perceptual image quality assessment. IEEE Transactions on Image Processing, 23(10):4270-4281, 2014. 2 +[43] Lin Zhang, Lei Zhang, Xuanqin Mou, and David Zhang. Fsim: A feature similarity index for image quality assessment. IEEE Transactions on Image Processing, 20(8):2378-2386, 2011. 1, 2 +[44] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of + +deep features as a perceptual metric. 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IEEE Transactions on Circuits and Systems for Video Technology, 30(1):36-47, 2018. 3 \ No newline at end of file diff --git a/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/images.zip b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3b3a3f6cd0b708928dc421d9fe04e180c1e1f91f --- /dev/null +++ b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b808405c3d8dc9e94dc9c0a003a10974d5f015c8088033c763069b155d82aa1e +size 547653 diff --git a/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/layout.json b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1a618ea51e1b2771689d25e7b765d6dba1727b83 --- /dev/null +++ b/2023/Re-IQA_ Unsupervised Learning for Image Quality Assessment in the Wild/layout.json @@ -0,0 +1,8274 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "spans": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "type": "text", + "content": "Re-IQA: Unsupervised Learning for Image Quality Assessment in the Wild" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 159, + 143, + 228, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 143, + 228, + 156 + ], + "spans": [ + { + "bbox": [ + 159, + 143, + 228, + 156 + ], + "type": "text", + "content": "Avinab Saha*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 252, + 144, + 337, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 252, + 144, + 337, + 157 + ], + "spans": [ + { + "bbox": [ + 252, + 144, + 337, + 157 + ], + "type": "text", + "content": "Sandeep Mishra*" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 361, + 144, + 434, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 144, + 434, + 156 + ], + "spans": [ + { + "bbox": [ + 361, + 144, + 434, + 156 + ], + "type": "text", + "content": "Alan C. Bovik" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 103, + 157, + 487, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 157, + 487, + 172 + ], + "spans": [ + { + "bbox": [ + 103, + 157, + 487, + 172 + ], + "type": "text", + "content": "Laboratory of Image and Video Engineering, The University of Texas at Austin" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 224, + 290, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 290, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 290, + 523 + ], + "type": "text", + "content": "Automatic Perceptual Image Quality Assessment is a challenging problem that impacts billions of internet, and social media users daily. To advance research in this field, we propose a Mixture of Experts approach to train two separate encoders to learn high-level content and low-level image quality features in an unsupervised setting. The unique novelty of our approach is its ability to generate low-level representations of image quality that are complementary to high-level features representing image content. We refer to the framework used to train the two encoders as Re-IQA. For Image Quality Assessment in the Wild, we deploy the complementary low and high-level image representations obtained from the Re-IQA framework to train a linear regression model, which is used to map the image representations to the ground truth quality scores, refer Figure 1. Our method achieves state-of-the-art performance on multiple large-scale image quality assessment databases containing both real and synthetic distortions, demonstrating how deep neural networks can be trained in an unsupervised setting to produce perceptually relevant representations. We conclude from our experiments that the low and high-level features obtained are indeed complementary and positively impact the performance of the linear regressor. A public release of all the codes associated with this work will be made available on GitHub." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 128, + 561 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 568, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 665 + ], + "type": "text", + "content": "Millions of digital images are shared daily on social media platforms such as Instagram, Snapchat, Flickr, etc. Making robust and accurate Image Quality Assessments (IQA) that correlate well with human perceptual judgments is essential to ensuring acceptable levels of visual experience. Social media platforms also use IQA metrics to decide parameter settings for post-upload processing of the images, such as resizing, compression, enhancement, etc." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 198, + 547, + 299 + ], + "blocks": [ + { + "bbox": [ + 307, + 198, + 547, + 299 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 547, + 299 + ], + "type": "image", + "image_path": "927b61bce702303ec58042a7a37739a82cb1db8407d901a4d758d76129a4b53d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 309, + 547, + 354 + ], + "lines": [ + { + "bbox": [ + 305, + 309, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 547, + 354 + ], + "type": "text", + "content": "Figure 1. IQA score prediction uses two encoders trained for complementary tasks of learning content and quality aware image representations. The encoders are frozen while the regressor learns to map image representations to quality predictions." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 378, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 547, + 462 + ], + "type": "text", + "content": "In addition, predictions generated by IQA algorithms are often used as input to recommendation engines on social media platforms to generate user feeds and responses to search queries. Thus, accurately predicting the perceptual quality of digital images is a high-stakes endeavor affecting the way billions of images are stored, processed, and displayed to the public at large." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 463, + 548, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 548, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 548, + 616 + ], + "type": "text", + "content": "IQA metrics can be simply categorized into Full-Reference (FR) and No-Reference (NR) algorithms. FR-IQA algorithms like SSIM [35], FSIM [43], and LPIPS [44] require both reference (undistorted) and distorted version of an image to quantify the human-perceivable quality. This requirement limits their applicability for the \"Images in the Wild\" scenario, where the reference image is unavailable. On the contrary, NR-IQA algorithms like BRISQUE [19], PaQ-2-PiQ [40], and CONTRIQUE [16] do not require a reference image nor any knowledge about the kind of present distortions to quantify human-perceivable quality in a test image, paving the way for their use in \"Images in the Wild\" scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "No-Reference IQA for \"Images in the Wild\" presents exciting challenges due to the complex interplay among the various kinds of distortions. Furthermore, due to the intricate nature of the human visual system, image content affects quality perception. In this work, we aim to learn low-level quality-aware image representations that are complementary to high-level features representative of image content. Figure 2 illustrates some of the challenges encountered" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "text", + "content": "*Equal Contribution, Correspondence to Avinab Saha (avinab.saha@utexas.edu) & Sandeep Mishra (sandy.mishra@utexas.edu). This work was supported by the National Science Foundation AI Institute for Foundations of Machine Learning (IFML) under Grant 2019844." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5846" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 168, + 160 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 168, + 160 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 168, + 160 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 168, + 160 + ], + "type": "image", + "image_path": "2d67359add27060242b72755c54702e031e1e3860cf0615278fad40538c86a02.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 163, + 149, + 172 + ], + "lines": [ + { + "bbox": [ + 67, + 163, + 149, + 172 + ], + "spans": [ + { + "bbox": [ + 67, + 163, + 149, + 172 + ], + "type": "text", + "content": "(a) JPEG Compressed : 1" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 294, + 160 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 294, + 160 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 294, + 160 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 294, + 160 + ], + "type": "image", + "image_path": "b47558248fde6129ef70f40d98f741bed4e974ea8c85d8012846dd0c2d742e23.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 163, + 276, + 172 + ], + "lines": [ + { + "bbox": [ + 192, + 163, + 276, + 172 + ], + "spans": [ + { + "bbox": [ + 192, + 163, + 276, + 172 + ], + "type": "text", + "content": "(b) JPEG Compressed: 2" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 182, + 546, + 215 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 546, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 546, + 215 + ], + "type": "text", + "content": "Figure 2. Exemplar Synthetically and \"In the Wild\" distorted pictures. (a), (b) are two images captured on iPhone 13 Pro and then JPEG compressed using the same encoding parameters. (c), (d), were taken from KonIQ and AVA datasets respectively, and exhibit typical \"Images in the Wild\" distortions. Best viewed when zoomed in." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 299, + 71, + 419, + 160 + ], + "blocks": [ + { + "bbox": [ + 299, + 71, + 419, + 160 + ], + "lines": [ + { + "bbox": [ + 299, + 71, + 419, + 160 + ], + "spans": [ + { + "bbox": [ + 299, + 71, + 419, + 160 + ], + "type": "image", + "image_path": "95a6246d297735de1a583555b9627a0a69b95e3f541183bf2ee7c748b555f488.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 163, + 412, + 171 + ], + "lines": [ + { + "bbox": [ + 307, + 163, + 412, + 171 + ], + "spans": [ + { + "bbox": [ + 307, + 163, + 412, + 171 + ], + "type": "text", + "content": "(c) Motion Blur - Camera Shake" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 425, + 71, + 545, + 160 + ], + "blocks": [ + { + "bbox": [ + 425, + 71, + 545, + 160 + ], + "lines": [ + { + "bbox": [ + 425, + 71, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 425, + 71, + 545, + 160 + ], + "type": "image", + "image_path": "9a6b5e7db40364c5b0b0961b009f803e205920dd7a9c003752354fb469cd9e0c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 163, + 535, + 171 + ], + "lines": [ + { + "bbox": [ + 435, + 163, + 535, + 171 + ], + "spans": [ + { + "bbox": [ + 435, + 163, + 535, + 171 + ], + "type": "text", + "content": "(d) Overlaid Film Grain/ Noise" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 236, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 464 + ], + "type": "text", + "content": "in the development of NR-IQA algorithms. Figures 2 (a-b) show two images captured by the authors on an iPhone 13 Pro and compressed using the same encoding parameters. While any distortions are almost negligible in Figure 2 (a), there are artifacts that are clearly visible in Figure 2 (b). As in these examples, it is well known that picture distortion perception is content dependent, and is heavily affected by content related perceptual processes like masking [1]. Figures 2 (c-d) illustrates a few distorted pictures \"In the Wild\". Figures 2 (c-d) show two exemplar distorted pictures, one impaired by motion blur (Figure 2 (c)) and the other by film grain noise (Figure 2 (d)). It is also well established that perceived quality does not correlate well with image metadata like resolution, file size, color profile, or compression ratio [36]. Because of all these factors and the essentially infinite diversity of picture distortions, accurate prediction of the perception of image quality remains a challenging task, despite its apparent simplicity, and hence research on this topic remains quite active [16, 17, 19, 28, 35, 39, 42-44]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 464, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 594 + ], + "type": "text", + "content": "Our work is inspired by the success of momentum contrastive learning methods [2, 7] in learning unsupervised representations for image classification. In this work, we engineer our models to learn content and quality-aware image representations for NR-IQA on real, authentically distorted pictures in an unsupervised setting. We adopt a Mixture of Experts approach to independently train two encoders, each of which accurately learns high-level content and low-level image quality features. We refer to the new framework as Re-IQA. The key contributions we make are as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 605, + 287, + 713 + ], + "type": "text", + "content": "- We propose an unsupervised low-level image quality representation learning framework that generates features complementary to high-level representations of image content. We demonstrate how the \"Mixture\" of the two enables Re-IQA to produce image quality predictions that are highly competitive with existing state-of-the-art traditional, CNN, and Transformer based NR-IQA models, developed in both supervised and unsupervised settings across several databases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 236, + 545, + 444 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 317, + 236, + 545, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 236, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 317, + 236, + 545, + 332 + ], + "type": "text", + "content": "- We demonstrate the superiority of high-level representations of image content for the NR-IQA task, obtained from the unsupervised pre-training of the ResNet-50 [8] encoder over the features obtained from supervised pre-trained ResNet-50 on the ImageNet database [3]. We learn these high-level representations of image content using the unsupervised training framework proposed in MoCo-v2 [2]" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 336, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 336, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 317, + 336, + 545, + 444 + ], + "type": "text", + "content": "- Inspired by the principles of visual distortion perception we propose a novel Image Augmentation and Intra-Pair Image Swapping scheme to enable learning of low-level image quality representations. The dynamic nature of the image augmentation scheme prevents the learning of discrete distortion classes, since it is applied to both pristine and authentically distorted images, enforcing learning of perceptually relevant image-quality features." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 392, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "As discussed in Section 1, perceptual image quality prediction for \"Images in the Wild\" is a challenging task due to the complex distortions that arise, and the combinations of them, and how they are perceived when they affect different kinds of pictorial content. Over the last few decades, a great deal of effort has been invested in the development of NR-IQA models that are able to accurately predict human judgment of picture quality. In recent years, NR-IQA models have evolved from using hand-crafted perceptual features, feeding shallow learners, into Deep Learning based approaches trained on large subjective databases. Traditional NR-IQA models generally have two components: a feature extractor, which generates quality-relevant features, and a low-complexity regression model, which maps the extracted features to quality scores. Most prior models have focused on improving the feature extractor and, thus improving the performance of the overall IQA algorithm. A common practice in traditional NR-IQA methods is to model image artifacts using statistical information extracted from a test image. Natural Scene Statistics (NSS) mod" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5847" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 129, + 151 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 129, + 151 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 129, + 151 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 129, + 151 + ], + "type": "image", + "image_path": "638e3180dbd370670447a4efbc29c7a51a949455d790672a09d1b83128007f08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 153, + 119, + 162 + ], + "lines": [ + { + "bbox": [ + 59, + 153, + 119, + 162 + ], + 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Some samples of distortions available in the Image Augmentation Scheme. There are a total of 25 distortions available in the bank, with 5 levels of distortion for each. More details are provided in Supplemental Material." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 382, + 163, + 462, + 243 + ], + "blocks": [ + { + "bbox": [ + 382, + 163, + 462, + 243 + ], + "lines": [ + { + "bbox": [ + 382, + 163, + 462, + 243 + ], + "spans": [ + { + "bbox": [ + 382, + 163, + 462, + 243 + ], + "type": "image", + "image_path": "91197dff51fb83c56b05776f33cdce8f92b7769d33357e9498be59f5ecdbc6d4.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 246, + 435, + 255 + ], + "lines": [ + { + "bbox": [ + 408, + 246, + 435, + 255 + ], + "spans": [ + { + "bbox": [ + 408, + 246, + 435, + 255 + ], + "type": "text", + "content": "(k) Jitter" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 465, + 163, + 545, + 243 + ], + "blocks": [ + { + "bbox": [ + 465, + 163, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 465, + 163, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 465, + 163, + 545, + 243 + ], + "type": "image", + "image_path": "f20306f75853df0b261c0391db9edbc6487b7c5a861aa0a3df37c145af8fb1e0.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 480, + 246, + 529, + 254 + ], + "lines": [ + { + "bbox": [ + 480, + 246, + 529, + 254 + ], + "spans": [ + { + "bbox": [ + 480, + 246, + 529, + 254 + ], + "type": "text", + "content": "(1) Motion Blur" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 308, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 523 + ], + "type": "text", + "content": "els and distorted versions of them are popular, where features are extracted from transformed domains, on which statistical measurements of deviations due to distortions are used as features for NR-IQA. For example, the NSS-based BRISQUE [19] and NIQE [20] models obtain features that capture in a normalized bandpass space [26]. DIIVINE [21] uses steerable pyramids, and BLIINDS [27] uses DCT coefficients to measure statistical traces of distortions. Other methods like CORNIA [39] and HOSA [38] utilize codebooks constructed from local patches, which are applied to obtain quality-aware features. Most of the methods discussed above often obtain acceptable results when evaluated on synthetically distorted images, but their performances significantly degrade when applied to \"Images in the Wild\". This is because the above-discussed methods focus primarily on modeling the distortions present in a test image as statistical deviations from naturalness while completely ignoring the high-level content present in the image." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 524, + 288, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 288, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 288, + 703 + ], + "type": "text", + "content": "The majority of deep learning approaches utilize pretrained CNN backbones as feature extractors. This is done since end-to-end supervised training of NR-IQA models is difficult given the limited sizes of existing perceptual quality databases. These models typically use CNN backbones trained for ImageNet classification to extract features, combining them with low-complexity regression models like Support Vector Regression or Linear Regression to map the features to human-labeled scores. A few models use labeled scores from IQA databases to fine-tune the CNN backbone. The authors of the RAPIQUE [32] show that features obtained from pretrained ResNet-50 [8] could effectively predict quality scores on \"In the Wild\" content. In DB-CNN [45], authors adopt a two-path technique, where one CNN branch generates distortion-class and distortion-level" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 308, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 704 + ], + "type": "text", + "content": "features, while the other CNN branch provides high-level image content information. These are then combined using bilinear pooling. PQR [41] achieved faster convergence and better quality estimates by using the statistical distributions of subjective opinion scores instead of just scalar mean opinion scores (MOS) during training. BIECON [11] trains a CNN model on patches of distorted images, using proxy quality scores generated by FR-IQA models as labels. The authors of [30] proposed an adaptive hypernetwork architecture that considers content comprehension during perceptual quality prediction. Very recent works on NR-IQA include PaQ-2-PiQ [40], CONTRIQUE [16] and MUSIQ [10]. PaQ-2-PiQ benefits from a specially designed dataset wherein the authors not only collected subjective quality scores on whole pictures but also on a large number of image patches. The dataset is also large enough to train deep models in a supervised setting, and PaQ-2-PiQ achieves state-of-the-art performance. However, although the authors use patch-level and image-level quality information during training, the training process may be susceptible to dataset sampling errors since only a few patches were extracted from each image and annotated with quality scores. MUSIQ uses a transformer-based architecture [34] pre-trained on the ImageNet classification dataset. The method benefits significantly by using transformer architecture and fine-tuning the transformer backbone on the IQA test databases. CONTRIQUE is a closely related work that aims to learn quality-aware representations in a self-supervised setting. CONTRIQUE learns to group images with similar types and distortion degrees into classes on an independent dataset. In this way, it proposes to learn quality-aware image representations. However, the class labels used to define 'similar-quality' and 'different-quality'" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5848" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": "samples in CONTRIQUE are in fact distortion labels instead of being true-quality labels. We address this shortcoming in our proposed framework. Our method, which is also completely unsupervised, does not learn representations based on distortion class labels, which can be inaccurate when asserted on \"In the Wild\" data. Instead, our model, which is inspired by the fundamental principles of visual distortion perception, proposes to independently learn high-level semantic image content and low-level image quality features. These image representation features are mapped directly to subjective scores using a low-complexity regression model without fine-tuning the deep neural networks. Here, we utilize ResNet-based architectures [8] throughout the Re-IQA framework. As our proposed framework is generalizable enough to be implemented using other CNN and transformer-based architectures, we plan to extend it to transformer-based architectures in the future." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 297, + 146, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 146, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 146, + 312 + ], + "type": "text", + "content": "3. Rethinking-IQA" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 317, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 413 + ], + "type": "text", + "content": "The Re-IQA model framework is embodied in three processing phases. The first and second phases consist of training two ResNet50 encoders using contrastive learning of high-level and low-level image information. We then use the pre-trained encoders with frozen weights as image representation generation backbones, which supply features to a low-complexity regression model that is trained to conduct image quality prediction as shown in Figure 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": "To learn high-level content-aware information we deploy MoCo-v2 [2] ImageNet pre-trained model and adopt the design considerations developed in the original paper. Further discussed in section 3.1. To learn quality-aware representations we develop a contrastive learning framework that deploys a novel augmentation protocol and an intra-pair image-swapping scheme to facilitate model convergence towards learning robust image quality-aware features. Further discussed in section 3.2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 527, + 187, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 187, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 187, + 540 + ], + "type": "text", + "content": "3.1. Re-IQA : Content Aware" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "The primary objective in the MoCo-v2 framework [2] is to assign a 'similar' label to two crops from a single image while assigning a 'different' label to two crops taken from two different images. Although, content aware Re-IQA based completely on the original MoCo-v2 framework performs well in the image quality prediction problem (refer Table 2), it still suffers from a critical design problem: two crops from a same image can be given significantly different quality scores by human viewers. Hence we only use, the original MoCo-v2 framework to generate content-aware image representations. We make appropriate changes, discussed next, to the MoCo-v2 framework to enable accurate learning of quality-aware representations that complement content-aware representations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "type": "text", + "content": "3.2. Re-IQA : Quality Aware" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 545, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 257 + ], + "type": "text", + "content": "Our quality-aware contrastive learning framework uses an Image Augmentation method and an Intra-pair image Swapping scheme to train a ResNet-50 encoder within the MoCo-v2 framework [2] with a goal of modeling a feature space wherein all images having similar degrees of perceptual quality fall closer to one another than to images having different perceptual qualities. The MoCo-v2 framework simultaneously processes a query image through the query encoder and a key image through the key encoder. In a single batch, a positive sample occurs when features are generated using any paired query and key, the pair being labeled 'similar.' A negative sample occurs when the query and the key do not belong to the same pair, hence they are marked 'different.'" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": "To train a contrastive network we need paired images, such that for any sample index " + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": ", we have image pairs " + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "inline_equation", + "content": "[i_1^k, i_2^k]" + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": " that can be assigned the 'similar-quality' label, and for any " + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "inline_equation", + "content": "j, k" + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": "; where " + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "inline_equation", + "content": "k \\neq j" + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": " we have image pairs " + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "inline_equation", + "content": "[i_1^k, i_2^j]" + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": " that can be assigned the 'different-quality' label. From here on we shall refer to perceptual quality-aware features as PQAF. To define the decision boundary between 'similar-quality' and 'different-quality' labels, we assume the following three hypotheses to be true:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 545, + 496 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": "H1: PQAF varies within an image itself. If we assign PQAF to an image patch " + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": " and denote it as " + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "inline_equation", + "content": "PQAF_x" + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "inline_equation", + "content": "PQAF_x" + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": " varies only a small amount between neighboring patches. However, " + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "inline_equation", + "content": "PQAF_x" + }, + { + "bbox": [ + 304, + 365, + 545, + 425 + ], + "type": "text", + "content": " may vary significantly between two distant patches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 473 + ], + "type": "text", + "content": "H2: The PQAF of any two randomly selected images are 'different,' which assumes that the scenes depicted in the images to be different. However, this does not enforce any restrictions on the quality scores of the two images." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 496 + ], + "type": "text", + "content": "H3: Two different distorted versions of the same image have different PQAF." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 497, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 521 + ], + "type": "text", + "content": "These hypotheses are further discussed in the Supplemental material §S.4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "type": "text", + "content": "3.2.1 Quality-Aware Image Augmentation Scheme" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": "To conduct quality-aware image feature extraction, we deploy a novel bank of image quality distortion augmentations, as elaborated in the Supplemental material §S.1. The augmentation bank is a collection of 25 distortion methods, each realized at 5 levels of severity. For any source image " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "i^k" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " from the training set, where " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "k \\in \\{1, 2 \\dots K\\}" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " is the total number of images in the training data, a randomly chosen subset of the augmentations available in the bank are applied to each image resulting in a mini-batch of distorted images. We combine each source image with its distorted versions to form " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "chunk^k" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 361, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 361, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "c h u n k ^ {k} = \\left[ i ^ {k}, i _ {1} ^ {k}, i _ {2} ^ {k}, \\dots , i _ {n} ^ {k} \\right] \\tag {1}", + "image_path": "886ef698a75dd4a3d966492fa2be13787f2ae8e282d193182556cbde6af37d7c.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5849" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 190 + ], + "type": "image", + "image_path": "5c394efcb587a6c320a6ea2a2bfa23faf16686ddd32205fab7749a1a57cd767c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "type": "text", + "content": "Figure 4. Learning Quality Aware Representations: The OLA based cropping, Image Augmentation scheme and Half-swapping enable the generation of appropriate 'similar-quality' and 'different-quality' image pairs which can be used to learn quality-aware features. Note that " + }, + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "type": "inline_equation", + "content": "A_0" + }, + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "type": "text", + "content": " has no augmentation, while " + }, + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "type": "inline_equation", + "content": "A_1..A_n" + }, + { + "bbox": [ + 46, + 199, + 547, + 247 + ], + "type": "text", + "content": " are randomly sampled from the augmentation bank. During loss calculation, representations generated using the key encoder for the previous 65536 samples are also used as negative keys, following MoCo-V2 settings." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "i_j^k" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": " distorted version of " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "i^k" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": " is the number of augmentations drawn from the bank. We then generate two random crops of " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "chunk^k" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": ", namely " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "chunk^{k_{c1}}" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "inline_equation", + "content": "chunk^{k_{c2}}" + }, + { + "bbox": [ + 46, + 264, + 290, + 373 + ], + "type": "text", + "content": ", using an overlap area based smart cropping mechanism. We choose these crop locations such that the overlapping area (OLA) in the two crops falls within minimum and maximum bounds. We make sure that the crop location is the same over all images in each chunk and different between chunks, resulting in:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 389, + 247, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 389, + 247, + 403 + ], + "spans": [ + { + "bbox": [ + 85, + 389, + 247, + 403 + ], + "type": "interline_equation", + "content": "\\operatorname {c h u n k} ^ {k _ {c 1}} = \\left[ i ^ {k _ {c 1}}, i _ {1} ^ {k _ {c 1}}, i _ {2} ^ {k _ {c 1}}, \\dots , i _ {n} ^ {k _ {c 1}} \\right]", + "image_path": "cc3170c2bee32d8d4a11f040f56c125446e27b0992b0bfaee4884677043dc0c4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 403, + 287, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 403, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 86, + 403, + 287, + 420 + ], + "type": "interline_equation", + "content": "c h u n k ^ {k _ {c 2}} = \\left[ i ^ {k _ {c 2}}, i _ {1} ^ {k _ {c 2}}, i _ {2} ^ {k _ {c 2}}, \\dots , i _ {n} ^ {k _ {c 2}} \\right] \\tag {2}", + "image_path": "a3fb7cae2d36173095888cac2808dde092afc62d799f86956e51b8a6d103dd74.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": "When training, by choosing an augmented image " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "a_{th}" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " from both " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "chunk^{k_{c1}}" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "chunk^{k_{c2}}" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": ", form the pair " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "[i_a^{k_{c1}}, i_a^{k_{c2}}]" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": ". Image " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "i_a^{k_{c1}}" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "i_a^{k_{c2}}" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " are neighboring patches because of OLA-based cropping and hence are marked 'similar-quality' as stated in H1. Similarly, for any image " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " and distortion " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "a, b" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "a \\neq b" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": ", the pair " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "[i_a^{k_{c1}}, i_b^{k_{c2}}]" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " are labelled as 'different-quality' as in H1. Finally, for any two different image samples " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "k, j" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": ", label the pair " + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "inline_equation", + "content": "[i\\_ k_{c1}, i\\_ j_{c2}]" + }, + { + "bbox": [ + 46, + 428, + 289, + 536 + ], + "type": "text", + "content": " as 'different-quality', following H2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 549, + 234, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 234, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 234, + 562 + ], + "type": "text", + "content": "3.2.2 Intra-Pair Image Swapping Scheme" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "text", + "content": "Given a spatial arrangement of " + }, + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "inline_equation", + "content": "chunk^{k_{c1}}" + }, + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "inline_equation", + "content": "chunk^{k_{c2}}" + }, + { + "bbox": [ + 47, + 567, + 277, + 581 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 596, + 282, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 596, + 282, + 643 + ], + "spans": [ + { + "bbox": [ + 50, + 596, + 282, + 643 + ], + "type": "interline_equation", + "content": "\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 1}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 2}} \\end{array}", + "image_path": "7bae9b0303f809590a80950812c8dfc176c5d21c0ddb8e814375a886a906b4e3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 650, + 287, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 287, + 674 + ], + "type": "text", + "content": "form the following types of image-pairs and corresponding labels:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 679, + 231, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 679, + 231, + 694 + ], + "spans": [ + { + "bbox": [ + 93, + 679, + 231, + 694 + ], + "type": "interline_equation", + "content": "[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} ] \\mapsto \\text {s i m i l a r - q u a l i t y}", + "image_path": "7f69f092f295ed164818228f26f4495c82684c8aff04ea1781f14e1bb04c2de2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 94, + 696, + 240, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 696, + 240, + 711 + ], + "spans": [ + { + "bbox": [ + 94, + 696, + 240, + 711 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{c} i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\end{array} \\right] \\mapsto d i f f e r e n t q u a l i t y", + "image_path": "9e1372eec6361d94eabca642ff5e9961a342eec7236f5d3548aad544a13bffed.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 265, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 265, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 265, + 547, + 289 + ], + "type": "text", + "content": "Then apply intra-pair image swapping on the generated chunks to obtain the following arrangement:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 312, + 542, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 312, + 542, + 360 + ], + "spans": [ + { + "bbox": [ + 309, + 312, + 542, + 360 + ], + "type": "interline_equation", + "content": "\\begin{array}{c c c c c c c c} i ^ {k _ {c 1}} & i _ {1} ^ {k _ {c 2}} & ... & i _ {m} ^ {k _ {c 1}} & i _ {m + 1} ^ {k _ {c 2}} & ... & i _ {n - 1} ^ {k _ {c 1}} & i _ {n} ^ {k _ {c 2}} \\\\ \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow & & \\updownarrow & \\updownarrow \\\\ i ^ {k _ {c 2}} & i _ {1} ^ {k _ {c 1}} & ... & i _ {m} ^ {k _ {c 2}} & i _ {m + 1} ^ {k _ {c 1}} & ... & i _ {n - 1} ^ {k _ {c 2}} & i _ {n} ^ {k _ {c 1}} \\end{array}", + "image_path": "9464dde9ddc68edbf8ce615eee3f2bd160c0bab84f405735e01dfee90b545bfd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "content": "By swapping images within each pair over half the pairs, (referred to as Half Swap), the network is introduced to samples having the following configuration: " + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "inline_equation", + "content": "[i_a^{k_{c1}}, i_b^{k_{c1}}]" + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "inline_equation", + "content": "a, b; a \\neq b" + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "content": " are two different distortions. Note that the crops " + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "inline_equation", + "content": "[i_a^{k_{c1}}, i_b^{k_{c1}}]" + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "content": " are exactly the same, except for the distortion applied, and thus contain the same essential visual content. Despite this, we mark such samples as 'different-quality' as stated in H3, thus forcing the network to look beyond content-dependent features. With this, we finally end up with the following image pairs and labels:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 506, + 489, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 506, + 489, + 521 + ], + "spans": [ + { + "bbox": [ + 351, + 506, + 489, + 521 + ], + "type": "interline_equation", + "content": "\\left[ i _ {m} ^ {k _ {c 1}}, i _ {m} ^ {k _ {c 2}} \\right] \\mapsto \\text {s i m i l a r - q u a l i t y}", + "image_path": "c79f24f75bb7948803974f260af5dd105b8893488082bbb9108a35b883eccb7c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 353, + 522, + 499, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 522, + 499, + 537 + ], + "spans": [ + { + "bbox": [ + 353, + 522, + 499, + 537 + ], + "type": "interline_equation", + "content": "\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 2}} \\right] \\mapsto d i f f e r e n t - q u a l i t y", + "image_path": "3f99532c001a2eefbce9279745fcff7b2226afd7963d4b6053a61b70565354a8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 354, + 539, + 499, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 539, + 499, + 554 + ], + "spans": [ + { + "bbox": [ + 354, + 539, + 499, + 554 + ], + "type": "interline_equation", + "content": "\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {k _ {c 1}} \\right] \\mapsto d i f f e r e n t - q u a l i t y", + "image_path": "407e9a6e1c2562771e04aef8ab6e0192ff32d5e5a448bdf703aad28311bb4249.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 354, + 556, + 499, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 556, + 499, + 571 + ], + "spans": [ + { + "bbox": [ + 354, + 556, + 499, + 571 + ], + "type": "interline_equation", + "content": "\\left[ i _ {m} ^ {k _ {c 1}}, i _ {l} ^ {j _ {c 2}} \\right] \\mapsto d i f f e r - q u a l i t y", + "image_path": "dac787ab23027dce4d7524b69bb6741ce4e58b10b9ed653d14ca9e20e6e0ca5c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 595, + 443, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 595, + 443, + 608 + ], + "spans": [ + { + "bbox": [ + 306, + 595, + 443, + 608 + ], + "type": "text", + "content": "3.2.3 Quality-Aware Training" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Define two identical encoders 1) Online Encoder (query encoder) and 2) Momentum Encoder (key encoder). Both encoders have ResNet-50 backbones and an MLP head to generate the final output embeddings from the ResNet features. Split the pairs designed in the previous step, passing the first image from each pair through the query encoder, and the other through the key encoder. To calculate the loss between the representation generated by the query and key" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5850" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 244, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 244, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 244, + 85 + ], + "type": "text", + "content": "encoder, we use the InfoNCE [23] loss function:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 94, + 287, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 94, + 287, + 129 + ], + "spans": [ + { + "bbox": [ + 49, + 94, + 287, + 129 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {q, k ^ {+}, \\{k ^ {-} \\}} = - \\log \\frac {\\exp (q . k ^ {+} / \\tau)}{\\exp (q . k ^ {+} / \\tau) + \\sum_ {k ^ {-}} \\exp (q . k ^ {-} / \\tau)} \\tag {3}", + "image_path": "cd591ced0e53e05901da594b0d81f332abec10c9ae7c0c572885dda8a4c67ecc.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " is the query image, " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "k^{+}" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " is a positive sample (similar-quality), " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "k^{-}" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " represent negative samples (different-quality), and " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " is a temperature hyper-parameter. This loss is then used to update the weights of the online encoder by back-propagation. The weights of the momentum encoder are updated using the weighted sum of its previous weights and the new weights of the online encoder. Formally denoting the parameters of the query encoder by " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\theta_{q}" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " and the parameters of the key encoder as " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": ", update " + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 46, + 142, + 289, + 251 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 264, + 287, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 264, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 116, + 264, + 287, + 277 + ], + "type": "interline_equation", + "content": "\\theta_ {k} \\leftarrow m \\theta_ {k} + (1 - m) \\theta_ {q} \\tag {4}", + "image_path": "b69f676379c085ffaab258c37b93c1360523ceebd7a26fb35b00c0d603d190d6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "inline_equation", + "content": "m \\in [0,1)" + }, + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "content": ", is the momentum coefficient. Once the encoder pre-training has saturated the frozen ResNet-50 can be used as an encoder backbone for any downstream task associated with perceptual image quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 342, + 144, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 144, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 144, + 355 + ], + "type": "text", + "content": "3.3. IQA Regression" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 361, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 494 + ], + "type": "text", + "content": "We concatenate the image representations obtained from the content and quality-aware encoders in the previous steps to train a regressor head to map the obtained features to the final perceptual image quality scores as shown in Figure 1. In our experiments, we use a single-layer perceptron as the regressor head. It is important to note that we train only the low-complexity regressor head while evaluating our Re-IQA framework across multiple databases. Our method does not require us to fine-tune the feature extraction backbone(s) separately for each evaluation database as required in MUSIQ." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 506, + 173, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 173, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 173, + 520 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 526, + 153, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 153, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 153, + 539 + ], + "type": "text", + "content": "4.1. Training Datasets" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": "In the Re-IQA framework, two ResNet-50 encoders are trained to obtain high-level image content features and low-level image quality features. The encoder that learns high-level image content features was trained on a subset of the ImageNet database [3] containing approximately 1.28 million images across 1000 classes. When training the encoder in an unsupervised setting, we discard the class label information and only use images without labels during the training process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "content": "To learn the low-level image quality features, we use a combination of pristine images and authentically distorted images as training data. The augmentation scheme (applied to all images in the dataset) ensures that the network learns how to differentiate between distortions when the semantic" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "content in the image is the same. The presence of authentically distorted images in the dataset helps tune the model to accurately predict the quality of \"In the Wild\" pictures." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 116, + 547, + 252 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 317, + 116, + 545, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 116, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 317, + 116, + 545, + 176 + ], + "type": "text", + "content": "- Pristine Images: We used the 140K pristine images in the KADIS dataset [13]. We do not use the 700K distorted images available in the same dataset. The authors of KADIS did not provide subjective quality scores for any image in the dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 180, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 180, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 317, + 180, + 547, + 252 + ], + "type": "text", + "content": "- Arguably Distorted Images: We used the same combination of datasets as proposed in CONTRIQUE [16] to form our distorted image set: (a) AVA [22] - 255K images, (b) COCO [14] - 330K images, (c) CERTH-Blur [18] - 2450 images, d) VOC [4] - 33K images" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 357, + 281, + 491, + 365 + ], + "blocks": [ + { + "bbox": [ + 357, + 281, + 491, + 365 + ], + "lines": [ + { + "bbox": [ + 357, + 281, + 491, + 365 + ], + "spans": [ + { + "bbox": [ + 357, + 281, + 491, + 365 + ], + "type": "image", + "image_path": "8fcfb162d8db6ae78c1fcbfdbb178642247ed4443f31cfc333da487f7cc1f4dd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 369, + 470, + 380 + ], + "lines": [ + { + "bbox": [ + 383, + 369, + 470, + 380 + ], + "spans": [ + { + "bbox": [ + 383, + 369, + 470, + 380 + ], + "type": "text", + "content": "(a) Re-IQA Quality-Aware" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 357, + 389, + 491, + 474 + ], + "blocks": [ + { + "bbox": [ + 357, + 389, + 491, + 474 + ], + "lines": [ + { + "bbox": [ + 357, + 389, + 491, + 474 + ], + "spans": [ + { + "bbox": [ + 357, + 389, + 491, + 474 + ], + "type": "image", + "image_path": "cebdb718ae18b2889ca34fa1f17c9d5d0e4ac8b62adb51472ef011606116f444.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 479, + 456, + 488 + ], + "lines": [ + { + "bbox": [ + 397, + 479, + 456, + 488 + ], + "spans": [ + { + "bbox": [ + 397, + 479, + 456, + 488 + ], + "type": "text", + "content": "(b) CONTRIQUE" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 498, + 545, + 543 + ], + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 543 + ], + "type": "text", + "content": "Figure 5. Comparison of 2D TSNE Visualization of learned representations of 1016 images sampled from KonIQ (UGC - #150) and CSIQ (Synthetic Distortions - #866) between Re-IQA Quality Aware sub-module and CONTRIQUE. Best viewed zoomed in." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 563, + 422, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 422, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 422, + 574 + ], + "type": "text", + "content": "4.2. Evaluation Datasets" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Many previous IQA methods used legacy databases like LIVE IQA [29], TID-2008 [25], TID-2013 [24], CSIQ-IQA [12], and KADID [13] for development and evaluation purposes. However, these datasets contain only a small number " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "(\\sim 25 - 100)" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " of pristine images synthetically distorted by various levels and types of single distortions. Hence, these datasets lack diversity and realism of content and distortion. Recently many \"In the Wild\" datasets like KonIQ [9], CLIVE [6], FLIVE [40], and SPAQ [5] have been developed and used by visual quality researchers since they address the shortcomings of the legacy datasets. The newer breed of" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5851" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "perceptual quality datasets contain many authentically distorted images. KonIQ-10K dataset consists of 10K images selected from the publicly available multimedia large-scale YFCC100M database [31]. CLIVE contains 1162 authentically distorted images captured using various mobile devices. FLIVE, on the other hand, is comprised of 40,000 images sampled from open-source images and designed to emulate the feature distributions found in social media images statistically. Lastly, SPAQ consists of 11,000 images captured using 66 mobile devices, and each image is accompanied by various annotations such as brightness, content labels, and EXIF data. However, our experiments only utilize the image and its corresponding quality score." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 397 + ], + "type": "text", + "content": "We also evaluated our method on four legacy synthetically distorted datasets: LIVE-IQA, TID-2013, CSIQ-IQA, and KADID. We provide short descriptions of each of the databases. The LIVE IQA dataset includes 779 images that have been synthetically distorted using five types of distortions at four different intensity levels. TID-2013, on the other hand, contains 3000 images that have been synthetically distorted using 24 different types of distortions at five different levels of intensity, with 25 reference images as the base. The CSIQ-IQA dataset comprises 866 images that have been synthetically distorted using six types of distortions on top of 30 reference images. Lastly, the KADID dataset comprises 10125 images synthetically distorted using 25 different distortions on 81 reference images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 407, + 185, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 185, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 185, + 419 + ], + "type": "text", + "content": "4.3. Training Configurations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "text", + "content": "Our content-aware encoder is pre-trained on the ImageNet database following the configuration proposed in MoCo-v2. Due to time and resource constraints, we train the content-aware encoder for 200 epochs. For the quality-aware encoder, we used ResNet-50 as a feature extractor, and a 2-layer MLP head to regress contrastive features of dimension 128. The hidden dimension of the MLP head has 2048 neurons. In each forward pass, the OverLap Area (OLA) based cropping mechanism chooses two crops " + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "inline_equation", + "content": "(C_1" + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "inline_equation", + "content": "C_2)" + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "text", + "content": " from each image, such that the percentage of overlap between the crops is maintained within a minimum and a maximum bound. The performance variation of Re-IQA-QA (quality aware module only) and Re-IQA against percentage OverLap Area, patch-sizes, and the number of image distortion augmentations is depicted in Table 1. The optimal parameters are chosen based on the combined performance of the two modules in Re-IQA. We achieved the best performance using " + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "inline_equation", + "content": "10 - 30\\%" + }, + { + "bbox": [ + 46, + 426, + 289, + 654 + ], + "type": "text", + "content": " percentage OverLap Area bound, patch size of 160, and 11 distortion augmentations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "The processed chunks are passed through the query and key encoders respectively in the MoCo-v2 framework, followed by an adaptive pooling layer to compress the output of the ResNet-50 into a 1D feature vector. The generated feature vector is then fed to the MLP head to generate the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "contrastive feature vectors required for loss computation. Our design of the Re-IQA model is inspired by previous works [16, 37] that use images both at their original and half-scale. Therefore, during the training phase of the Re-IQA model we use all images in a database both at original and half-scale, thereby doubling the training dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": "During training, the following hyper-parameters were fixed throughout all experiments: learning rate " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "= 0.6" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " with cosine annealing [15] scheduler, InfoNCE temperature " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "\\tau = 0.2" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": ", and momentum coefficient " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "= 0.999" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": ". Our best-performing model required a batch size of 630 (effectively " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "630 \\times (n + 1)" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " augmentations x (2) scales) during training and was trained for 25 epochs. Convergence occurs in a relatively shorter number of epochs as the effective dataset size increases drastically due to a large number of augmentations and processing of each image in the dataset at two scales. All the implementations were done in Python using the PyTorch deep learning framework. We trained the content and quality-aware encoders on a system configured with 18 Nvidia A100-40GB GPUs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 320, + 423, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 320, + 423, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 423, + 332 + ], + "type": "text", + "content": "4.4. Evaluation Protocol" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 339, + 547, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 482 + ], + "type": "text", + "content": "We tested our Re-IQA model against other state-of-the-art models on all of the \"In the Wild\" and synthetically distorted IQA databases described in Section 4.2. Each of these datasets is a collection of images labeled by subjective opinions of picture quality in the form of the mean of the opinion scores (MOS). The single-layer regressor head in Re-IQA is trained by feeding the output of the pre-trained encoders and then comparing the output of the regressor, against the ground truth MOS using L2 loss. We use both Spearman's rank order correlation coefficient (SRCC) and Pearson's linear correlation coefficient (PLCC) as metrics to evaluate the trained model across IQA databases." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "content": "Following the evaluation protocol used in [16], each dataset was randomly divided into " + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "content": " corresponding to training, validation and test sets, respectively. We used the validation set to determine the regularization coefficient of the regressor head using a 1D grid search over values in the range " + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "inline_equation", + "content": "[10^{-3}, 10^{3}]" + }, + { + "bbox": [ + 304, + 483, + 547, + 626 + ], + "type": "text", + "content": ". To avoid overlap of contents in datasets with synthetic distortions, splits were selected based on source images. We also prevented any bias towards the training set selection by repeating the train/test split operation 10 times and reporting the median performance. On FLIVE, due to the large dataset size, we follow the train-test split recommended by the authors in [40]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 635, + 362, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 362, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 362, + 647 + ], + "type": "text", + "content": "4.5. Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Our \"Mixture of Experts\" approach in Re-IQA enables us to learn robust high-level image content and low-level quality aware representations independently, the benefit of which can be clearly observed in the performance values reported in Table 2. We compared the performance of Re-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5852" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "type": "table", + "html": "
ModelEvaluation Datasetn_augPatch SizeOLA bound (%)
251115231281601922242565-1510-3050-80No Bound
Re-IQA(Quality-Aware)KonIQ0.8550.8580.8610.8620.8600.8600.8610.8610.8600.8580.8560.8610.8570.858
SPAQ0.8900.8960.9000.9000.8970.8980.9000.9010.8980.8940.8890.9000.8860.890
CSIQ0.9280.9370.9440.9360.9300.9370.9440.9390.9300.9280.9370.9440.9310.938
Re-IQA(Quality-Aware +Content Aware)KonIQ0.8950.9010.9140.8980.8950.9100.9140.9110.9050.8970.9030.9140.8970.905
SPAQ0.9020.9130.9180.9100.9090.9160.9180.9140.9080.9030.9070.9180.9040.906
CSIQ0.9320.9410.9470.9370.9350.9400.9470.9420.9370.9320.9390.9470.9350.940
", + "image_path": "756e4e83a4817d2e30703118b1926334ceae4e679489336ac90d4364c064db9b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 198, + 546, + 323 + ], + "blocks": [ + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "lines": [ + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "spans": [ + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": "Table 1. SRCC performance comparison of Re-IQA-QA and Re-IQA while varying one hyper-parameter at a time. While varying " + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "inline_equation", + "content": "n_{aug}" + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": ", we keep patch size 160 and OLA bound " + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "inline_equation", + "content": "10 - 30\\%" + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": ". When varying patch size, " + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "inline_equation", + "content": "n_{aug}" + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": " was fixed to 11 and OLA bound to " + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "inline_equation", + "content": "10 - 30\\%" + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": ". When varying OLA bound, " + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "inline_equation", + "content": "n_{aug}" + }, + { + "bbox": [ + 46, + 155, + 546, + 189 + ], + "type": "text", + "content": " was set to 11 and the patch size was set to 160." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 198, + 546, + 323 + ], + "lines": [ + { + "bbox": [ + 48, + 198, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 48, + 198, + 546, + 323 + ], + "type": "table", + "html": "
MethodAuthentic Distortions a.k.a "Images in the Wild"Synthetic Distortions
KonIQCLIVEFLIVESPAQLIVE-IQACSIQ-IQATID-2013KADID
SRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCCSRCCPLCC
BRISQUE0.6650.6810.6080.6290.2880.3730.8090.8170.9390.9350.7460.8290.6040.6940.5280.567
CORNIA0.7800.7950.6290.671--0.7090.7250.9470.9500.6780.7760.6780.7680.5160.558
DB-CNN0.8750.8840.8510.8690.5540.6520.9110.9150.9680.9710.9460.9590.8160.8650.8510.856
PQR0.8800.8840.8570.882----0.9650.9710.8720.9010.7400.798--
PaQ-2-PiQ0.8700.8800.8400.8500.5710.623----------
HyperlQA0.9060.9170.8590.8820.5350.6230.9160.9190.9620.9660.9230.9420.8400.8580.8520.845
CONTRIQUE0.8940.9060.8450.8570.5800.6410.9140.9190.9600.9610.9420.9550.8430.8570.9340.937
MUSIQ0.9160.928--0.6460.7390.9170.921--------
ImageNet Pretrained (Supervised)0.8880.9040.7810.8090.5950.6480.9040.9090.9250.9310.8400.8480.6790.7290.7010.677
Re-IQA (content aware)0.8960.9120.8080.8440.5880.6990.9020.9080.8670.8580.7660.8240.6580.7360.6010.656
Re-IQA (quality aware)0.8610.8850.8060.8240.5840.5900.9000.9100.9710.9720.9440.9640.8440.8800.8850.892
Re-IQA (content + quality)0.9140.9230.8400.8540.6450.7330.9180.9250.9700.9710.9470.9600.8040.8610.8720.885
", + "image_path": "ba533ebb1b59ac8b6175d7277415208bfb1dea591b5ccff694390ea4be1871cc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 546, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 330, + 546, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 546, + 365 + ], + "type": "text", + "content": "Table 2. Performance comparison of Re-IQA against various NR-IQA models on IQA databases with authentic and synthetic distortions. The top 2 best performing models are in bold. Higher SRCC and PLCC imply better performance. MUSIQ results from [10]. Results of all other existing methods from [16]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "type": "text", + "content": "IQA along with its sub-modules against other state-of-the-art models on IQA datasets containing authentic and synthetic distortions in Table 2. We used the features extracted from the Resnet-50 backbone for the supervised ImageNet pre-trained model. From the results, we conclude that Re-IQA achieves competitive performance across all tested databases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 288, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 288, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 288, + 708 + ], + "type": "text", + "content": "Results from Table 2 highlight the impact of content and low-level image quality on the final NR-IQA task. We observe that high-level content-aware features dominate quality-aware features for authentically distorted images, while the quality-aware features dominate the high-level content-aware features for authentically distorted images. We can hypothesize the reason to be high variation in content in the \"Images in the Wild\" scenario. Training a simple linear regressor head that is fed with features from both the content and quality-aware encoders provides flexibility to adjust the final model based on the application dataset. This can be observed in the performance scores achieved by the combined model when compared to the individual sub-modules. The performance scores of the quality-aware sub-module do not beat other methods when considering the \"Images in the Wild\" scenario, primarily due to the heavy impact of content. Despite this, when evaluated on synthetic distortion datasets, the quality-aware sub-module of Re-IQA outperforms most of its competitors all by itself. Thus we conclude that our generated quality-aware" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 384, + 546, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 546, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 546, + 434 + ], + "type": "text", + "content": "representations align very well with distortions present in an image. This is also conclusive from the t-SNE visualizations [33] depicted in Figure 5. Further details on t-SNE experiments are shared in Supplemental Material §S.3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 442, + 432, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 442, + 432, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 442, + 432, + 455 + ], + "type": "text", + "content": "5. Concluding Remarks" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": "We developed a holistic approach to Image quality Assessment by individually targeting the impact of content and distortion on the overall image quality score. NR-IQA for \"Images in the Wild\" benefits significantly from content-aware image representations, especially when learned in an unsupervised setting. This work aims to demonstrate that complementary content and image quality-aware features can be learned and, when combined, achieve competitive performance across all evaluated IQA databases. We re-engineer the MoCo-v2 framework for learning quality-aware representations to include our proposed novel Image Augmentation, OLA-based smart cropping, and a Half-Swap scheme. The results of experiments on the eight IQA datasets demonstrate that Re-IQA can consistently achieve state-of-the-art performance. Our Re-IQA framework is flexible to changes in the design of encoder architectures and can be extended to other CNN architectures and Transformer based models like MUSIQ. Although developed for IQA tasks, Re-IQA can be extended as a spatial feature extraction module in Video Quality Assessment algorithms that currently use supervised pre-trained Resnet-50." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5853" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Alan Conrad Bovik. 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IEEE Transactions on Circuits and Systems for Video Technology, 30(1):36-47, 2018. 3" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5855" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_content_list.json b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..969225138152d0f28745068e3d2b5efe86356eed --- /dev/null +++ b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_content_list.json @@ -0,0 +1,1606 @@ +[ + { + "type": "text", + "text": "Re-thinking Federated Active Learning based on Inter-class Diversity", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SangMook $\\mathrm{Kim}^{1*}$ Sangmin Bae $^{1*}$ Hwanjun Song $^{2\\dagger}$ Se-Young Yun $^{1\\dagger}$ $^{1}$ KAIST AI $^{2}$ NAVER AI LAB", + "bbox": [ + 166, + 179, + 803, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sangmook.kim, bsmn0223, yunseyoung}@kaist.ac.kr ghkswns91@gmail.com", + "bbox": [ + 166, + 220, + 797, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 271, + 313, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although federated learning has made awe-inspiring advances, most studies have assumed that the client's data are fully labeled. However, in a real-world scenario, every client may have a significant amount of unlabeled instances. Among the various approaches to utilizing unlabeled data, a federated active learning framework has emerged as a promising solution. In the decentralized setting, there are two types of available query selector models, namely 'global' and 'local-only' models, but little literature discusses their performance dominance and its causes. In this work, we first demonstrate that the superiority of two selector models depends on the global and local interclass diversity. Furthermore, we observe that the global and local-only models are the keys to resolving the imbalance of each side. Based on our findings, we propose LoGo, a FAL sampling strategy robust to varying local heterogeneity levels and global imbalance ratio, that integrates both models by two steps of active selection scheme. LoGo consistently outperforms six active learning strategies in the total number of 38 experimental settings. The code is available at: https://github.com/raymin0223/LoGo.", + "bbox": [ + 76, + 300, + 473, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 631, + 209, + 646 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated learning (FL) is a distributed framework that allows multiple parties to learn a unified deep learning model cooperatively with preserving the privacy of the local client [23,28,31]. Typically, FL has been actively studied in a standard supervised learning setting, where all the training instances are labeled, but it is more realistic for each client to contain both labeled and unlabeled data due to the high labeling cost [29, 48]. Here, active learning (AL) can be a promising solution to improve the performance of a cooperated model with the pool of unlabeled data. In practice, federated active learning (FAL) framework has recently attempted to bridge two different philosophies in FL and AL [3,4]. As illustrated in Figure 1-(a) FAL framework alternates an FL procedure (red line) of training a predictive", + "bbox": [ + 76, + 656, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "model collaboratively through local updates and aggregation phases, and an AL procedure (green line) of querying and annotating informative instances separately per client.", + "bbox": [ + 500, + 273, + 890, + 318 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although the overall framework just appears to be a straightforward fusion of two research fields, FL factors introduce two major challenges to the AL procedure. First, the class imbalance of the local dataset originates from heterogeneous distribution across local clients [15, 23, 28]. Hence, in the FAL framework, the active selection algorithm has to ensure inter-class diversity from both local and global perspectives. Second, there are two available types of query-selecting models, a global model, which is globally optimized through the FL pipeline, and a locally only model [9, 33], which can be separately trained only for each client. In the query selection phase, the global model can leverage the aggregated knowledge of all clients, while the local-only model is able to detect the most valuable instances for the local updates.", + "bbox": [ + 496, + 319, + 892, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior FAL literature [3, 4], which simply adapt conventional AL strategies, had little discussion on these challenges. As our first contribution, we found the significant performance gap between two types of query selector (see Figure 1-(b)), and it is the first study to solve a conundrum of dominance trend by introducing two indicators of interclass diversity1–local heterogeneity level $(\\alpha)$ and global imbalance ratio $(\\rho)$ . The first indicator $\\alpha$ is the concentration parameter of Dirichlet distribution, commonly seen in the FL literature [1, 15, 23], resulting in more locally imbalanced class distribution at lower values. Besides, $\\rho$ indicator is the ratio of class imbalance for the aggregated global data of all clients [7, 21]. We discovered three meaningful insights on selector dominance: (Obs. 1) Interestingly, the superiority of the two selectors varies depending on the two indicators of inter-class diversity, $\\alpha$ and $\\rho$ . (Obs. 2) When local heterogeneity is severe ( $\\alpha$ is low), a local-only model is preferred for weighing minority instances for each client, and (Obs. 3) when globally minor classes exist ( $\\rho$ is high), the knowledge of the entire data distribution, inherent in a global model, is more essential. > See Section 4", + "bbox": [ + 496, + 546, + 893, + 864 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1We use the term inter-class diversity interchangeably with class balance throughout the paper.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ corresponding authors", + "bbox": [ + 96, + 887, + 220, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3944", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6c5bd360ef6f5cc219fc361d220fac0de4f974b0533bd8cad8b6e6fcf3ea6686.jpg", + "image_caption": [ + "(a) Federated Active Learning framework." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 472, + 273 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2442e7078b55853afe6d550e68f031f06fd531ee22e100e0477beed69f4f464a.jpg", + "image_caption": [ + "(b) Superiority change of query selector.", + "Figure 1. Motivation: (a) The red and green lines correspond to the conventional FL and AL framework. We focus on a sampling strategy for FAL (green box) with the considerations of hierarchy structure and two available query-selecting models. (b) For a fixed querying strategy (Entropy sampling), the performance gap occurs only by changing the query selector. The y-axis is the gap in the winning rate in total active rounds (refer to Section 4). Closer to 1 indicates that global models outperforms than local-only models, and -1 is the opposite." + ], + "image_footnote": [], + "bbox": [ + 491, + 98, + 836, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a real FAL scenario, the superiority of two query models for a given dataset cannot be known in advance due to privacy preservation. Therefore, as our second contribution, we design a simple yet effective FAL querying approach, LoGo, that simultaneously leverages local-only and global models, to be robust to varying heterogeneity levels and global imbalance ratios. LoGo is a clustering-based sampling strategy, which is composed of macro and micro step exploiting local-only and global models, respectively. The rationale behind our method is that the optimal querying policy needs to evaluate the informativeness of instances with both models, which implicitly learn local and global data distribution, respectively. In a macro step, to improve the local inter-class diversity first, we perform $k$ -means clustering [30] in hallucinated gradient space generated from local-only models. Then, in a micro step, the final query set is determined via one step of the EM algorithm [10], making cluster boundaries using instances from macro step (E-step) and cluster-wise sampling with the global model (M-step). The proposed cluster-wise sampling conservatively guarantees the diversity information of the macro step, i.e., the local inter-class diversity obtained by local-only models, while also considering the global minority classes via the global model. $\\triangleright$ See Section 5", + "bbox": [ + 75, + 371, + 468, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As our third contribution, we conduct a total number of 38 experiments on five datasets using seven AL strategies including our LoGo algorithm. To verify the superiority of our method in real-world scenarios, we build comprehensive combinations of six categories, including query selector types (local-only vs. global models), local heterogeneity levels $(\\alpha \\in [0.1,\\infty))$ , global imbalance ratios $(\\rho \\in [1,58])$ , model architectures, budget sizes, and model initialization scheme. As a result, the experimental results empirically prove our three observations (Obs. 1-3). Besides, our method outperforms all other AL baselines and", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "naive implementations for an ensemble of two query selectors in extensive experimental settings. $\\triangleright$ See Section 6", + "bbox": [ + 500, + 371, + 888, + 401 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 414, + 640, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Federated Learning is a collaborative learning framework with multiple clients while maintaining the privacy of each client dataset. In this decentralized framework, FedAvg [31] is considered a de facto algorithm in which a server and clients communicate only model parameters efficiently. One of the main bottlenecks for FL is the statistical heterogeneity problem across the clients' dataset, as the weight divergence from heterogeneous distributions hinders convergence during the aggregation scheme. Hence, several algorithms have tackled the local heterogeneity through the alignment between the local-updated gradient and the aggregated gradient, as a form of correction term [15, 23], regularization loss [1, 28], or distillation-based loss [25, 26]. Furthermore, there are existing literature to alleviate the class imbalance on the local side and they eventually achieve the global balance via rebalancing datasets [11] or a weighted loss function with a monitoring scheme [43].", + "bbox": [ + 496, + 439, + 890, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Active Learning minimizes the labeling effort by querying the most informative instances from the unlabeled data pool. There are three major types of active learning strategies, namely uncertainty-based sampling, diversity-based sampling, and hybrid strategy. Uncertainty-based sampling queries the most uncertain instances that lie on the current decision boundary [12,14,35,41], while diversity-based sampling selects a set of unlabeled instances that represents the entire unlabeled data distribution [16, 37]. Recently, hybrid strategies simultaneously consider both uncertainty and diversity. BADGE [6] utilized the gradient embedding as the uncertainty measure and selected the diverse query set by a $k$ -means++ initialization scheme [5]. Several hybrid", + "bbox": [ + 496, + 703, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3945", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/f88fcc06e594659f2341c7f181d81acd5edb9b31236d920f9031e72865d73413.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Indices:
cIndex for a class (c ∈ {1, ..., C})
rIndex for AL round (r ∈ {1, ..., R} = [R])
kIndex for a client (k ∈ {1, ..., K} = [K])
Parameters:
BLabeling budget for each AL round r
αLocal heterogeneity level
ρGlobal imbalance ratio
Data:
Uk^rPool of unlabeled instances for a client k at round r
Lk^rA queried instance set from Uk^r at round r
Dk^rAn available labeled set at round r
Weights:
Θr*Aggregated weights via FL phases on Dr^r (global model)
Θk*Separately optimized weights on Dk^r (local-only model)
", + "bbox": [ + 81, + 88, + 472, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Summary of notations throughout the paper.", + "bbox": [ + 114, + 295, + 431, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "AL methods are based on a submodular data subset selection [44], pairwise contextual diversity [2], or feature mixing [34]. In addition to the three categories, model-based strategies have also been recently proposed to train additional networks for query selection, such as a VAE and discriminator [38] or a sequential graph neural network [8].", + "bbox": [ + 75, + 325, + 468, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Federated Active Learning has been recently studied to address a more realistic scenario, where clients have lots of the unlabeled instances [20, 47, 48]. However, previous works [3, 4] have not deeply discussed the challenges of FAL framework and naively applied existing AL strategies. Ahn et al. [4] have even considered the local-only query selector, but concluded that the global model is superior to the local-only model with limited experimental settings, three benchmarks and one heterogeneity level. In this work, we observe the counterparts in varying benchmarks and heterogeneity levels, which motivates us to design a novel sampling strategy by exploiting both global and local-only models. Our extensive analysis and experimental results encourage future research on the FAL problem.", + "bbox": [ + 75, + 421, + 472, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 645, + 204, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "AL Procedure. For the ease of understanding, we summarize notations in Table 1. At the first AL round (i.e., $r = 1$ ), each client $k$ randomly selects $B$ instances, $L_{k}^{1} = \\{x_{1},\\ldots ,x_{B}\\}$ , from $U_{k}^{1}$ , and oracles annotate them to obtain the initial labeled set $D_{k}^{1} = \\{(x_{1},y_{1}),\\ldots ,(x_{B},y_{B})\\}$ . For the next round ( $r\\geq 2$ ), based on the given querying strategy $\\mathcal{A}(\\cdot)$ and the model parameters $\\Theta$ , the query set of the $k$ -th client at round $r$ is sampled by", + "bbox": [ + 75, + 672, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k} ^ {r} = \\mathcal {A} \\left(U _ {k} ^ {r}, \\Theta , B\\right), \\text {w h e r e} U _ {k} ^ {r} = U _ {k} ^ {r - 1} \\backslash L _ {k} ^ {r - 1}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 799, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The querying function $\\mathcal{A}(\\cdot)$ in Eq. (1) depends on which AL algorithm is used. For example, Entropy sampling [41] queries the instances with the highest uncertainty like:", + "bbox": [ + 75, + 824, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (U, \\Theta , B) = \\underset {x _ {i} \\in L, | L | = B, L \\subseteq U} {\\arg \\max } H (p (y | x _ {i}; \\Theta)) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 876, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $H(p) = -\\sum_{c=1}^{C} p_c \\ln p_c$ , and $p$ is the predictive probability. The query set is annotated by the oracle and assembled to expand the available labeled set, i.e., $D_k^r = D_k^{r-1} \\cup \\{(x_i, y_i) | x_i \\in L_k^r\\}$ .", + "bbox": [ + 498, + 89, + 893, + 154 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FL Procedure. After each AL round, we perform the FL procedure of which the objective is to obtain the optimal parameter $\\Theta^{r*}$ such that it minimizes the target loss on the given labeled set for all clients, $D^{r} = \\cup_{k=1}^{K} D_{k}^{r}$ ,", + "bbox": [ + 498, + 166, + 893, + 228 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta^ {r *} = \\underset {\\Theta} {\\arg \\min } f \\left(\\Theta^ {r}\\right) = \\underset {\\Theta} {\\arg \\min } \\frac {1}{| D ^ {r} |} \\sum_ {i = 1} ^ {| D ^ {r} |} f _ {i} \\left(\\Theta^ {r}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 238, + 892, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f_{i}(\\Theta) = \\ell (x_{i},y_{i};\\Theta)$ and $\\ell (\\cdot)$ is the loss function determined by the network parameter $\\Theta$ . However, due to data privacy, the global model is optimized based on the reformulated update rule on the partitioned data over clients:", + "bbox": [ + 498, + 291, + 892, + 351 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\Theta^ {r}) = \\sum_ {k = 1} ^ {K} \\frac {| D _ {k} ^ {r} |}{| D ^ {r} |} F (\\Theta_ {k} ^ {r}),\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 362, + 787, + 402 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} F \\left(\\Theta_ {k} ^ {r}\\right) = \\frac {1}{\\left| D _ {k} ^ {r} \\right|} \\sum_ {\\left(x _ {i}, y _ {i}\\right) \\in D _ {k} ^ {r}} \\ell \\left(x _ {i}, y _ {i}; \\Theta_ {k} ^ {r}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 405, + 892, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model $\\Theta_k^r$ is updated locally on the client side for its local data $D_k^r$ , and then it is aggregated globally to generate a global model $\\Theta^r$ . The local update and model aggregation steps are alternated until the global model converges; this corresponds to the most popular FL training pipeline, FedAvg proposed by [31].", + "bbox": [ + 496, + 454, + 890, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The previous studies [3, 4] have typically used the converged global model $\\Theta^{r*}$ in the next AL round as the query selector of Eq. (2). However, considering the hierarchy structure in the FAL framework, it is also possible to use a separately optimized model on local partitioned data; replacing $D^r$ with $D_k^r$ in Eq. (3). It is often referred to as the local-only model [9, 33], and we denote it as $\\Theta_{k}^{r*}$ . In the following section, we investigate what these models are specialized in and when they are beneficial to use.", + "bbox": [ + 496, + 545, + 892, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Observation and Analysis", + "text_level": 1, + "bbox": [ + 498, + 694, + 740, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we analyze the performance trend between global and local-only models as the query selector, with respect to the degree of class imbalance in local and global data distribution. We synthetically adjust two indicators of inter-class diversity, $\\alpha \\in \\{0.1, 1.0, \\infty\\}$ and $\\rho \\in \\{1, 5, 10, 20\\}$ , on CIFAR-10 benchmark. As $\\alpha$ and $\\rho$ get lower and higher, the levels of local heterogeneity and global imbalance increase, respectively (refer to Appendix A for the detailed data distribution). For both query selectors, we use Entropy sampling [41] as an active learning algorithm, and the training set is progressively labeled with the query ratio of $10\\%$ in each AL round.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3946", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c6426a9f88fb96837819920e8d173831f06ffb72c1a3d112ccc2741ecd048e1b.jpg", + "image_caption": [ + "Figure 2. Gap between the winning rate of global and local-only models by varying global imbalance ratio $(\\rho)$ and local heterogeneity $(\\alpha)$ on CIFAR-10 benchmark. The experimental setups for (a)-(d) are also compatible with Figure 3 and Table 2." + ], + "image_footnote": [], + "bbox": [ + 91, + 93, + 441, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparison Metric. We evaluate the superiority over AL rounds through pairwise comparison [6, 34], widely used in conventional AL literature. We repeat each experimental setup, a pair of $\\alpha$ and $\\rho$ , with four different seeds and obtain a set of four accuracy results $a_{r} = \\{a_{r,1}, \\ldots, a_{r,4}\\}$ at each round $r$ . Then, we conduct a two-sided t-test, where $t$ -score is defined by Definition 1 for two given strategies $i$ and $j$ . Note that the strategy denotes the combination of the sampling strategy and the type of query selector.", + "bbox": [ + 75, + 334, + 472, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1. [36] Let $a_r^i$ and $a_r^j$ be the set of accuracies for two different FAL strategies $i$ and $j$ . Then, t-score at AL round $r$ is formulated as:", + "bbox": [ + 73, + 479, + 470, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {r} ^ {i j} = \\frac {\\sqrt {4} \\mu_ {r} ^ {i j}}{\\sigma_ {r} ^ {i j}}, \\text {w h e r e} \\mu_ {r} ^ {i j} = \\frac {1}{4} \\sum_ {l = 1} ^ {4} \\left(a _ {r, l} ^ {i} - a _ {r, l} ^ {j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 536, + 468, + 589 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {a n d} \\sigma_ {r} ^ {i j} = \\sqrt {\\frac {1}{3} \\sum_ {l = 1} ^ {4} \\left(\\left(a _ {r , l} ^ {i} - a _ {r , l} ^ {j}\\right) - \\mu_ {r} ^ {i j}\\right)}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 579, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, the strategy $i$ is considered to beat the strategy $j$ if $t_r^{ij} > 2.776$ . Therefore, the winning rate for all AL rounds is formulated as follows:", + "bbox": [ + 76, + 640, + 470, + 685 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {w i n} ^ {i j} = \\sum_ {r = 1} ^ {R} \\frac {1}{R} \\mathbb {1} _ {t _ {r} ^ {i j} > 2. 7 7 6}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 694, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The value of winning rate becomes 1 if the strategy $i$ beats the strategy $j$ over all AL rounds.", + "bbox": [ + 76, + 744, + 468, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation 1. The superiority of local-only and global query-selecting models varies according to the degree of local heterogeneity and global imbalance ratio.", + "bbox": [ + 76, + 784, + 470, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Figure 2, we summarize the performance gap between two query models depending on the local heterogeneity level (indicated by different shapes) and the global imbalance ratio (increased along x-axis). The y-axis represents", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the gap of the winning rate in Eq.(6) between global and local-only models; thus, the value becomes positive up to $+1$ if the global model beats the local-only model, otherwise negative up to -1. At a glance, there is a clear and consistent superiority of two query models according to $\\alpha$ and $\\rho$ , where the dominance has intensified toward both extremes (e.g., upper right and lower left). This observation contradicts the previous findings that the global model has always outperformed the local-only model as the query selector in a FAL framework [4]. We provide more in-depth analysis in following Obs. 2 and Obs. 3.", + "bbox": [ + 496, + 90, + 893, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation 2. As local heterogeneity increases $(\\alpha \\downarrow)$ , a local-only query selector is preferred due to the increased significance of local inter-class diversity.", + "bbox": [ + 498, + 282, + 893, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As the collapse of the local inter-class balance (i.e., lower $\\alpha$ ) incurs severe performance degradation due to a weight divergence [11, 31], addressing local imbalance can improve the learning stability and performance. Since the local-only models are separately trained on each client, in general, the local-only model has shown higher confidence for its own data distribution than the global model [9, 33]. In Figure 3, we visualized the number of class instances and the class-wise test accuracy in the first AL round (see the caption for details). Specifically, we confirmed a high correlation between counts and accuracy in Figure 3-(a), such that the local-only models have higher accuracy than the global model for major classes of their data distribution. Thus, by the nature of favoring low-confident instances in AL, the local-only model tends to select the instances with local minority classes as the query.", + "bbox": [ + 496, + 340, + 893, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More precisely, we verify that the local-only model indeed queries the locally balanced set using earth mover's distance (EMD) [46]. In Table 2, local EMD measures the mean of distance between class distribution of local query sets and a uniform distribution. The lower the value, the more balanced the locally queried instances. As shown in Table 2-(a) with high local heterogeneity, the local EMD of the local-only model (L) is lower than that of the global model (G). That is, the local-only model queries more diverse instances than the global model with respect to the local inter-class diversity.", + "bbox": [ + 496, + 583, + 893, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Meanwhile, in the case of (b), the global model, trained with more samples, has higher accuracy over the classes due to little distribution discrepancy. Although the more accurate model is likely to have the higher prediction confidence, it does not mean that it is better at identifying the required instances based on the current local dataset, which the global model had not directly learned. In practice, the local-only model still chose the more locally balanced query set (Table 2-(b)), and we supposed this contradiction makes no sizeable winning gap of the case (b) in Figure 2.", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3947", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/96d4bf458b987618e31012b91c5860d71e9f254853092a1bec52a6ed7efb978c.jpg", + "image_caption": [ + "of Instances" + ], + "image_footnote": [], + "bbox": [ + 91, + 98, + 279, + 252 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ca903081aebeabdc0c09f93e521ec24ef5cda3b9e4c18fe0680d5554a8aa4f17.jpg", + "image_caption": [ + "Test Accuracy" + ], + "image_footnote": [], + "bbox": [ + 290, + 98, + 464, + 252 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cfdd2df35d45c57a95a2d0f6715fa63b16deb0ec4cbfdd9dd4489302070ec52f.jpg", + "image_caption": [ + "(a) Low global imbalance $(\\rho = 1)$ and high heterogeneity $(\\alpha = 0.1)$ ." + ], + "image_footnote": [], + "bbox": [ + 88, + 270, + 276, + 424 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0143fb442e7822b2f21b43ae8aaf24b43800d7257c5382d8d9faa84e334e0432.jpg", + "image_caption": [ + "(c) High global imbalance $(\\rho = 20)$ and high heterogeneity $(\\alpha = 0.1)$ ." + ], + "image_footnote": [], + "bbox": [ + 287, + 270, + 460, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e6d2ae38b9a04d93322635e7cff4044da928ecfe46307031d8dffeac80502f52.jpg", + "image_caption": [ + "of Instances" + ], + "image_footnote": [], + "bbox": [ + 501, + 98, + 691, + 252 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3810551e75fde1b3a63bf1edf63e0baebf637d231141bb36e14591639bf79b17.jpg", + "image_caption": [ + "Test Accuracy" + ], + "image_footnote": [], + "bbox": [ + 702, + 98, + 875, + 252 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/099aa6526cee49d3ee96bfd1dfe1ab957a1dd3f13eed194289dda4660c32df5b.jpg", + "image_caption": [ + "(d) High global imbalance $(\\rho = 20)$ and low heterogeneity $(\\alpha = \\infty)$ .", + "Figure 3. Matrices of data count (left) and class-wise accuracy (right) for CIFAR-10, with four combinations of $\\rho = \\{1,20\\}$ and $\\alpha = \\{0.1,\\infty\\}$ . k1-10 denote ten clients, c1-10 are ten classes of CIFAR-10. There are two types of data counts, # of per-client local instances (1-10th rows) and aggregated instances over all clients (the last row). Similarly, the test accuracy is measured with local-only models (1-10th rows) and a global model (the last row). (a)-(d) setups correspond to those of Figure 2. See Appendix B.1 for the more cases." + ], + "image_footnote": [], + "bbox": [ + 501, + 270, + 689, + 424 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f498ac60f4e0bce0ab99389e8a5f0c9f11f6892835a979d0f588a360fa657470.jpg", + "image_caption": [ + "(b) Low global imbalance $(\\rho = 1)$ and low heterogeneity $(\\alpha = \\infty)$ ." + ], + "image_footnote": [], + "bbox": [ + 702, + 270, + 874, + 424 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/906ab47f098d29b17fce67e9da1986af18eb369ffaaea85c160faf5c06929660.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CaseModelObs. 2: Local EMD (↓)Obs. 3: Global EMD (↓)
10%20%30%40%10%20%30%40%
(a)G0.6320.6380.6410.6430.0190.0640.0860.095
L0.6320.5970.5920.5950.0190.0500.0500.046
(b)G0.0490.0770.0700.0840.0140.0700.0660.063
L0.0490.0420.0540.0590.0140.0250.0440.053
(c)G0.6920.6800.6760.6740.3770.3000.2940.294
L0.6920.6410.6330.6360.3770.3340.3260.321
(d)G0.3710.2980.2840.2740.3680.2940.2820.272
L0.3710.3130.2930.2900.3680.3090.2870.288
", + "bbox": [ + 81, + 518, + 468, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Local EMD and global EMD on CIFAR-10. We summarize the results of four AL rounds with the labeling budget of $10\\%$ per round. (a)-(d) setups correspond to those of Figure 2. See Appendix B.2 for EMDs of more cases.", + "bbox": [ + 75, + 652, + 468, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Observation 3. As the degree of global class imbalance increases ( $\\rho \\uparrow$ ), it is more advantageous to exploit a global model that alleviates the global class imbalance.", + "bbox": [ + 75, + 720, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Obs. 2, the local-only model should outperform the global model in the case (c), but there is no clear superiority between them with respect to the winning rate in the case (c) of Figure 2. The only answer for this conundrum is the presence of global minority classes due to the high global imbalance ratio. The local heterogeneity is obviously a crucial factor by Obs. 2, but global class imbalance is also another factor that significantly degrades the classification", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "performance in the FAL framework. Here, the major challenge is that neither the central server nor local clients cannot access any information of aggregated data due to privacy preservation. The only way to address this problem, we should utilize the global model that implicitly learns the knowledge of the entire data distribution through the aggregation phase in Eq. (4).", + "bbox": [ + 496, + 521, + 890, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We introduce an additional global EMD, the indicator of measuring the inter-class diversity of the aggregated queried set over all clients. As can be seen in Table 2-(c), where the global imbalance ratio is high, we confirm that the global query selector (G) favors to query global minority classes. The global EMD of the global model is lower than that of the local-only model, i.e. the more globally balanced query set, but the local EMD is the opposite.", + "bbox": [ + 496, + 628, + 892, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Meanwhile, in the case of (d), the minority classes are always the same from the global and local perspectives. It is different from the case (b), where the minority classes with respect to the accuracy differ in each client depending on the informativeness of instances despite the same instance number. Therefore, in this scenario, the global model has high confidence even in local datasets, leading to significantly overwhelming the local-only model in the case (d) of Figure 2. In conclusion, the global inter-class diversity is an essential factor when global imbalance exists.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3948", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 169, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From three observations in Section 4, we confirmed that FAL framework requires delicate consideration of local and global inter-class diversity. However, since clients are reluctant to share their data information, we should simultaneously utilize local-only and global models to ensure both sides of inter-class diversity. To this end, we propose a novel query sample strategy, named LoGo, that composed of macro and micro steps. Pseudo algorithm for LoGo is provided in Appendix C. Before describing details of each step, let us assume a scenario where $k$ -th client queries $B$ unlabeled instances at the round of $r$ .", + "bbox": [ + 75, + 114, + 472, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Macro Step: Clustering with Local-Only Model.", + "text_level": 1, + "bbox": [ + 76, + 286, + 418, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The ultimate goal of macro step is to satisfy local interclass diversity by primarily sampling the informative instances by the local-only model. In detail, we introduce $k$ -means clustering [30] on the hypothetical gradient embedding. Let $z$ be the embedding vector before forwarding to the last layer $W$ for $x \\in U_k^r$ . Here, we utilize the gradient of negative cross-entropy loss, induced by a pseudo label, with respect to the last layer of encoder as follows:", + "bbox": [ + 75, + 301, + 468, + 422 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ng _ {c} ^ {x} = - \\frac {\\partial}{\\partial W _ {c}} \\ell_ {C E} (x, \\hat {y}; \\Theta_ {k *} ^ {r}) = z \\cdot \\left(\\mathbb {1} _ {[ \\hat {y} = c ]} - p _ {c}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 426, + 468, + 457 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{y} = \\arg \\max_{c\\in [C]}p_c$ and $W_{c}$ is the weights connected to $c$ -th neuron of logits. Gradient embedding is widely used in conventional AL algorithm [6, 40], and we consider only the gradients corresponding to the pseudo label (i.e., $g_{\\hat{y}}^x$ ) for computation efficiency.", + "bbox": [ + 75, + 460, + 468, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, we calculate $B$ number of centroids on the hallucinated gradient space via EM algorithm [10] of $k$ -means clustering by minimizing", + "bbox": [ + 75, + 536, + 468, + 580 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nJ = \\sum_ {i = 1} ^ {N} \\sum_ {b = 1} ^ {B} w _ {i b} \\| g _ {\\hat {y}} ^ {x _ {i}} - \\mu_ {b} \\| ^ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 585, + 468, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $w_{ib}$ is an indicator function whether $g_{\\hat{y}}^{x_i}$ is assigned to $\\mu_b$ for E-step. Eq. (7) shows that the gradient embedding is a just scaling of feature embedding $z$ , especially with the scale of uncertainty. In other words, if an instance is uncertain to predict (low value of $p_{\\hat{y}}$ ), its gradient will be much highly scaled. In this sense, Eq. (8) can be regarded as a weighted $k$ -means clustering [13,39] on the feature embedding space by using the function of softmax response [17]. Hence, the macro step of LoGo enable the query set to contain both diversity in the embedding space and uncertainty from the perspective of local-only model.", + "bbox": [ + 75, + 631, + 468, + 799 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Micro Step: Cluster-wise Sampling with Global Model.", + "text_level": 1, + "bbox": [ + 76, + 803, + 465, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In micro step, the global model selects the final instances that results in the higher global inter-class diversity. Given $B$ selected instances from the macro step, the most uncertain instance is selected for each cluster:", + "bbox": [ + 76, + 818, + 468, + 878 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k} ^ {r} = \\left\\{\\mathcal {A} \\left(\\mathcal {C} _ {1}, \\Theta^ {r *}, 1\\right), \\dots , \\mathcal {A} \\left(\\mathcal {C} _ {B}, \\Theta^ {r *}, 1\\right) \\right\\} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 883, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$C_b$ denotes $b$ -th cluster, generated by the query set from the macro step. We simply used Entropy sampling for $\\mathcal{A}$ , but we should note that $\\mathcal{A}$ can be any AL sampling strategy.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The cluster-wise sampling in the micro step is a simple yet effective strategy to leverage the advantages of both query selector models, ensuring local and global inter-class diversity. Here, we discuss how LoGo can be a promising sampling strategy for the FAL framework.", + "bbox": [ + 496, + 136, + 890, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 1. The micro step is same with one step of EM algorithm. We first update cluster assignments with $B$ number of centroids from the macro step (E-step). Then, within each cluster, we select the most informative instance based on the uncertainty score. This can be regarded as one $M$ -step of the weighted $k$ -means clustering, using infinitely scaled weight function of uncertainty measure.", + "bbox": [ + 496, + 219, + 890, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, let $c_{b}$ be a centroid of $C_{b}$ and we define $M$ as follows:", + "bbox": [ + 500, + 333, + 890, + 349 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nM = \\sum_ {b = 1} ^ {B} \\| c _ {b} - \\tilde {x} _ {b} \\| ^ {2}, \\text {w h e r e} \\tilde {x} _ {b} = \\arg \\min _ {x} \\| c _ {b} - x \\| ^ {2} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 354, + 890, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $x \\in L_k^r$ (Eq. (9)) and $\\tilde{x}$ is one-to-one mapping with the minimal transport cost. The lower value of $M$ means that the final query set much consider the diversity in the macro step.", + "bbox": [ + 496, + 405, + 890, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 2. EM-based sampling in the micro step guarantees the diversity information of the macro step. Through sampling one instance per cluster, each $\\tilde{x}_b$ is disjointly assigned to one cluster. Therefore, LoGo conservatively ensures the local inter-class diversity from the macro step (i.e., lower $M$ value), comparing to any other strategy that query at least two instances for one cluster.", + "bbox": [ + 496, + 473, + 890, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Evaluation", + "text_level": 1, + "bbox": [ + 500, + 592, + 616, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Experimental Configuration", + "text_level": 1, + "bbox": [ + 500, + 617, + 754, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Settings. In a FAL framework, a central server should carefully consider the fairness of labeling and training costs between clients. Therefore, we assume that ten clients have the same size of unlabeled data pool and query the same number of instances per every AL round. Moreover, we focus on a cross-silo FL setting [22] where every client participates in every FL round.", + "bbox": [ + 496, + 640, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared LoGo with six active learning strategies on five benchmark dataset (CIFAR-10 [24], SVHN [32], PathMNIST, DermaMNIST, and OrganAMNIST [45]). We considered 38 comprehensive experimental settings combined into six categories (see Figure 4). Except for learning ablations of the architectures, labeling budgets, and initialization schemes, in default, we implemented four layers of CNN and trained the encoder from scratch with the labeling budget of $5\\%$ for every AL round. We repeat all experiments four times and report their averaged values. Refer to Appendix D for detailed experimental settings.", + "bbox": [ + 496, + 746, + 890, + 912 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3949", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/519afe232a9676d425d82dcb8033d8516799dc74d93d9455e300b7e64bda262a.jpg", + "image_caption": [ + "Figure 4. Winning percentage across six categories. We also added defeat percentage, the black hatched bar that represents the percentage at which LoGo has been defeated by each baseline. Among total experiments, only statistically reliable values ( $t$ -score $>2.776$ ) are considered. Thus, the lower value of the colored bar and the higher value of the black bar indicate a more comparable baseline." + ], + "image_footnote": [], + "bbox": [ + 84, + 71, + 872, + 198 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2556a42832e40d2c8dbf5d254cce44fae73794a3b5e8d7e82f254b80f8df9eea.jpg", + "image_caption": [ + "Figure 5. Pairwise penalty matrix over 38 experimental settings. The value $P_{ij}$ indicates the number of times that the $i$ -th strategy outperforms the $j$ -th strategy (i.e., sum of win $^{ij}$ in Eq.(6) over 38 settings). The last row is the average number of times the $j$ -th strategy is defeated by the rest strategies; the lower, the better." + ], + "image_footnote": [], + "bbox": [ + 107, + 263, + 433, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We considered six standard AL strategies. Random randomly samples the instances from the unlabeled pool. Entropy selects instances with the largest entropy [41]. CoreSet chooses the small subset that can represent the whole unlabeled set [37]. BADGE selects the diverse points with high magnitude in a hallucinated gradient space [6]. GCNAL adapts CoreSet on a sequential graph convolution network to measure the relation between labeled and unlabeled instances [8]. ALFA-Mix identifies the valuable instances by seeking inconsistencies in the prediction of mixing features [34]. We adopt these sampling strategies with either the global model or local-only model in FedAvg pipeline. Refer to Appendix E for the comparison of query selection cost. Besides, we summarized the results with various FL methods in Appendix F.", + "bbox": [ + 75, + 585, + 472, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Overall Comparison", + "text_level": 1, + "bbox": [ + 76, + 821, + 272, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2.1 Pairwise Penalty Matrix", + "text_level": 1, + "bbox": [ + 76, + 845, + 302, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We summarized the overall comparison results as a pairwise penalty matrix $P$ in Figure 5, following the recent", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "work [6, 34]. Each cell of the pairwise penalty matrix represents the summation of the winning rate of Eq. (6) calculated above for each of the 38 experimental sets. As the rows of the matrix $P_{i}$ indicate how many times $i$ -th algorithm outperforms the other algorithms, the brighter color means the better algorithm (conversely, the darker columns are the better). Note that we only considered statistically reliable results throughout the two-sided t-test.", + "bbox": [ + 496, + 267, + 890, + 387 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LoGo defeats all baselines in general (see 7-th row values) while under-performed only 0.9 out of 38 times on average (see 7-th column values in the last row). In particular, LoGo outperforms BADGE and Entropy sampling, which are top-2 baselines, with 13.7 and 12.0 out of 38 times, while LoGo only loses 2.4 and 1.9 out of 38 times, respectively. This results demonstrate the robust effectiveness of our LoGo algorithm in various experimental settings.", + "bbox": [ + 496, + 388, + 892, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2.2 Winning Rate Bar Plots", + "text_level": 1, + "bbox": [ + 500, + 518, + 720, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 4 summarizes the comparison results according to the six categories, which is the breakdown of Figure 5 on a more systematic categorization. For example, the colored bar of the overall category is calculated by dividing the total setting number of 38 in the 7-th row vector of Figure 5 (the black bar is from the 7-th column vector). The colored bar represents the average percentage at which LoGo defeats each baseline algorithm, and the higher bar means that LoGo has won more. Appendix G.1 provides the detailed comparison penalty values according to each category.", + "bbox": [ + 496, + 541, + 893, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Overall, LoGo consistently shows an overwhelming winning percentage toward any baseline against the defeat percentage. Interestingly, ALFA-Mix, the latest AL strategy, shows performance considerably varying depending on which query selector is selected (see the query selector in Figure 4). The reason would be that a local-only model, which is separately trained on the highly heterogeneous dataset, is not appropriate for the feature mixing or the sensitivity to lots of hyperparameters. Moreover, Coreset, which does not consider uncertainty, cannot resolve the local and global imbalance, showing similar performance as Random sampling. Thus, LoGo is a superior algorithm for a FAL framework in that it is robust to the type of query selector or most combinations of experimental settings.", + "bbox": [ + 496, + 691, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3950", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0f2d68565b45461c0dedb80097a5c7bd8362caafb17bc7ef0a6e1942d3fbc2a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodModelCIFAR-10SVHNPathMNISTDermaMNIST
20%40%60%80%20%30%40%50%20%30%40%50%20%30%40%50%
Random-64.1969.0771.6372.8180.9083.0784.2284.7768.4172.7073.7675.4971.7072.5772.6672.86
Entropy [41]G64.0269.1271.8773.3382.0884.6185.8886.3171.5474.3975.9176.6572.4972.6373.0273.20
L66.2971.4573.5174.0282.0984.5885.6986.1876.5278.2978.7179.1071.3872.0472.2272.65
Coreset [37]G64.6669.4371.7573.180.9482.7483.8184.4674.8476.2476.8576.8072.0272.1672.3472.74
L64.0668.7971.4973.2880.9482.9283.7884.4872.5376.0676.2876.8671.1371.4872.1572.38
BADGE [6]G65.1269.5772.1173.5382.8184.8285.8986.272.2174.3875.5376.9772.5973.0973.2373.45
L66.3271.2873.4174.2882.6984.6785.6186.176.4878.5178.4278.6871.3572.1372.2572.99
GCNAL [8]G65.4070.0572.4173.4282.0584.0785.0985.6175.5177.7978.1378.8172.0172.6073.0773.17
L65.6270.1872.3673.4281.9283.5884.5585.1074.8576.4677.1877.4571.9572.9172.9173.29
ALFA-Mix [34]G65.4569.8772.2473.2983.0284.9986.0586.3373.3474.8376.3177.4372.3973.1473.2773.10
L64.1468.7971.0372.681.0882.5583.6284.3371.1075.0175.8176.7071.5172.1872.9473.28
LoGo (ours)G,L66.5071.7073.8074.4983.4685.3186.0286.3876.3278.7279.5179.5872.6173.1873.3373.77
", + "bbox": [ + 81, + 88, + 893, + 290 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2.3 Under Query Selector Category", + "text_level": 1, + "bbox": [ + 76, + 359, + 352, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3 shows the test accuracy according to the increased labeling budgets over rounds on four datasets. Even with the same active learning strategy, a gap in test accuracy occurs depending on which query selector is used because the global imbalance varies by 1.0–58.7 across datasets. For example, in general, global models outperform local-only models for SVHN and DermaMNIST, while the opposite trend is observed for CIFAR-10 and PathMNIST. However, irrespective of the benchmarks and querying model types, our LoGo shows the best performance in most cases. Two-step selection strategy enables LoGo to be robust by utilizing both the benefits of global and local-only models. Because we cannot know the degree of local and global imbalance in advance, our proposed method has a strong advantage in providing data-agnostic performance improvements over all baselines. Appendix G.2 provides a detailed performance comparison between LoGo and baselines under various experimental settings.", + "bbox": [ + 75, + 383, + 470, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. LoGo vs. Simple Ensemble", + "text_level": 1, + "bbox": [ + 76, + 665, + 321, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To prove that LoGo is an effective way to leverage the advantages of both models, we compared LoGo with three naive implementation of ensemble methods for global and local-only models: (1) the average of logits (for Entropy sampling) or gradient embedding (for BADGE) from two models, (2) weighing the instances based on the selection ranks (i.e., more weights if it is selected from both models), and (3) fine-tuning the global model on local datasets.", + "bbox": [ + 75, + 688, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 4, LoGo consistently shows better classification accuracy over increasing labeling budgets than three counterparts. Compared with the results in both Tables 3 and 4, all three ensemble methods show lower performance than using a single superior query selector. That is, the naive ensemble suffers from a performance trade-off between two", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/674b819c429e136f744c9daec2e1a0684b5a60667f4202c28c8b8ecde20f4716.jpg", + "table_caption": [ + "Table 3. Comparison of test accuracy on four benchmarks with $\\alpha = 0.1$ . We reported the results with four random seeds. The baselines, except for Random sampling, are combined with two query selector models, $G$ and $L$ that stands for a global or local-only model, respectively. **Bold and underline mean Top-1 and Top-2**, respectively." + ], + "table_footnote": [], + "table_body": "
MethodStrategyCIFAR-10SVHN
20%40%60%80%20%30%40%
Ens. Logit+Entropy64.5370.3673.0274.2881.8184.6485.87
+BADGE65.5570.3172.8373.9782.7784.7685.90
Ens. Rank+Entropy65.9070.9273.3474.2082.1584.3885.64
+BADGE66.2170.9873.1574.0183.0285.0585.86
Fine-tuning+Entropy65.1070.7573.2174.2382.5385.0586.01
+BADGE65.8270.9572.9474.1282.5984.8985.82
LoGo (ours)-66.5071.7073.8074.4983.4685.3186.02
", + "bbox": [ + 503, + 356, + 890, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of test accuracy on two benchmarks $(\\alpha = 0.1)$ with baselines using both global and local information.", + "bbox": [ + 500, + 482, + 890, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "query selector models and, therefore, their results fall somewhere in the middle of using global and local models.", + "bbox": [ + 498, + 525, + 890, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 569, + 617, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We discovered the superiority of the two query selectors according to the local heterogeneity level and global imbalance ratio. Based on our findings, the local-only and global models are both crucial since global and local inter-class diversity affects their performance dominance. To this end, we propose LoGo algorithm that incorporates local-only and global models into macro and micro steps of cluster-based active learning. LoGo preferentially selects samples that simultaneously alleviate local and global imbalance as a query, making it robust to local and global imbalance. Our experiments verified that LoGo consistently outperforms six baselines under comprehensive settings of 38 combinations using six categories.", + "bbox": [ + 496, + 594, + 890, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3951", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263, 2021. 1, 2", + "[2] Sharat Agarwal, Himanshu Arora, Saket Anand, and Chetan Arora. 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Divergence-aware federated self-supervised learning. arXiv preprint arXiv:2204.04385, 2022. 1, 3" + ], + "bbox": [ + 78, + 90, + 468, + 873 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3953", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_model.json b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e934924822d3da19c786d76952a93feae784e2e9 --- /dev/null +++ b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Re-thinking Federated Active Learning based on Inter-class Diversity" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.18, + 0.804, + 0.22 + ], + "angle": 0, + "content": "SangMook \\(\\mathrm{Kim}^{1*}\\) Sangmin Bae\\(^{1*}\\) Hwanjun Song\\(^{2\\dagger}\\) Se-Young Yun\\(^{1\\dagger}\\) \n\\(^{1}\\)KAIST AI \\(^{2}\\)NAVER AI LAB" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.222, + 0.799, + 0.238 + ], + "angle": 0, + "content": "{sangmook.kim, bsmn0223, yunseyoung}@kaist.ac.kr ghkswns91@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.272, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.619 + ], + "angle": 0, + "content": "Although federated learning has made awe-inspiring advances, most studies have assumed that the client's data are fully labeled. However, in a real-world scenario, every client may have a significant amount of unlabeled instances. Among the various approaches to utilizing unlabeled data, a federated active learning framework has emerged as a promising solution. In the decentralized setting, there are two types of available query selector models, namely 'global' and 'local-only' models, but little literature discusses their performance dominance and its causes. In this work, we first demonstrate that the superiority of two selector models depends on the global and local interclass diversity. Furthermore, we observe that the global and local-only models are the keys to resolving the imbalance of each side. Based on our findings, we propose LoGo, a FAL sampling strategy robust to varying local heterogeneity levels and global imbalance ratio, that integrates both models by two steps of active selection scheme. LoGo consistently outperforms six active learning strategies in the total number of 38 experimental settings. The code is available at: https://github.com/raymin0223/LoGo." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.632, + 0.21, + 0.647 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.657, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Federated learning (FL) is a distributed framework that allows multiple parties to learn a unified deep learning model cooperatively with preserving the privacy of the local client [23,28,31]. Typically, FL has been actively studied in a standard supervised learning setting, where all the training instances are labeled, but it is more realistic for each client to contain both labeled and unlabeled data due to the high labeling cost [29, 48]. Here, active learning (AL) can be a promising solution to improve the performance of a cooperated model with the pool of unlabeled data. In practice, federated active learning (FAL) framework has recently attempted to bridge two different philosophies in FL and AL [3,4]. As illustrated in Figure 1-(a) FAL framework alternates an FL procedure (red line) of training a predictive" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.274, + 0.892, + 0.319 + ], + "angle": 0, + "content": "model collaboratively through local updates and aggregation phases, and an AL procedure (green line) of querying and annotating informative instances separately per client." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.893, + 0.546 + ], + "angle": 0, + "content": "Although the overall framework just appears to be a straightforward fusion of two research fields, FL factors introduce two major challenges to the AL procedure. First, the class imbalance of the local dataset originates from heterogeneous distribution across local clients [15, 23, 28]. Hence, in the FAL framework, the active selection algorithm has to ensure inter-class diversity from both local and global perspectives. Second, there are two available types of query-selecting models, a global model, which is globally optimized through the FL pipeline, and a locally only model [9, 33], which can be separately trained only for each client. In the query selection phase, the global model can leverage the aggregated knowledge of all clients, while the local-only model is able to detect the most valuable instances for the local updates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.895, + 0.865 + ], + "angle": 0, + "content": "Prior FAL literature [3, 4], which simply adapt conventional AL strategies, had little discussion on these challenges. As our first contribution, we found the significant performance gap between two types of query selector (see Figure 1-(b)), and it is the first study to solve a conundrum of dominance trend by introducing two indicators of interclass diversity1–local heterogeneity level \\((\\alpha)\\) and global imbalance ratio \\((\\rho)\\). The first indicator \\(\\alpha\\) is the concentration parameter of Dirichlet distribution, commonly seen in the FL literature [1, 15, 23], resulting in more locally imbalanced class distribution at lower values. Besides, \\(\\rho\\) indicator is the ratio of class imbalance for the aggregated global data of all clients [7, 21]. We discovered three meaningful insights on selector dominance: (Obs. 1) Interestingly, the superiority of the two selectors varies depending on the two indicators of inter-class diversity, \\(\\alpha\\) and \\(\\rho\\). (Obs. 2) When local heterogeneity is severe (\\(\\alpha\\) is low), a local-only model is preferred for weighing minority instances for each client, and (Obs. 3) when globally minor classes exist (\\(\\rho\\) is high), the knowledge of the entire data distribution, inherent in a global model, is more essential. > See Section 4" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1We use the term inter-class diversity interchangeably with class balance throughout the paper." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.203, + 0.888 + ], + "angle": 0, + "content": "*equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.222, + 0.901 + ], + "angle": 0, + "content": "\\(\\dagger\\) corresponding authors" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3944" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.473, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.276, + 0.419, + 0.288 + ], + "angle": 0, + "content": "(a) Federated Active Learning framework." + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.099, + 0.837, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.275, + 0.789, + 0.288 + ], + "angle": 0, + "content": "(b) Superiority change of query selector." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Figure 1. Motivation: (a) The red and green lines correspond to the conventional FL and AL framework. We focus on a sampling strategy for FAL (green box) with the considerations of hierarchy structure and two available query-selecting models. (b) For a fixed querying strategy (Entropy sampling), the performance gap occurs only by changing the query selector. The y-axis is the gap in the winning rate in total active rounds (refer to Section 4). Closer to 1 indicates that global models outperforms than local-only models, and -1 is the opposite." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.47, + 0.734 + ], + "angle": 0, + "content": "In a real FAL scenario, the superiority of two query models for a given dataset cannot be known in advance due to privacy preservation. Therefore, as our second contribution, we design a simple yet effective FAL querying approach, LoGo, that simultaneously leverages local-only and global models, to be robust to varying heterogeneity levels and global imbalance ratios. LoGo is a clustering-based sampling strategy, which is composed of macro and micro step exploiting local-only and global models, respectively. The rationale behind our method is that the optimal querying policy needs to evaluate the informativeness of instances with both models, which implicitly learn local and global data distribution, respectively. In a macro step, to improve the local inter-class diversity first, we perform \\( k \\)-means clustering [30] in hallucinated gradient space generated from local-only models. Then, in a micro step, the final query set is determined via one step of the EM algorithm [10], making cluster boundaries using instances from macro step (E-step) and cluster-wise sampling with the global model (M-step). The proposed cluster-wise sampling conservatively guarantees the diversity information of the macro step, i.e., the local inter-class diversity obtained by local-only models, while also considering the global minority classes via the global model. \\( \\triangleright \\) See Section 5" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "As our third contribution, we conduct a total number of 38 experiments on five datasets using seven AL strategies including our LoGo algorithm. To verify the superiority of our method in real-world scenarios, we build comprehensive combinations of six categories, including query selector types (local-only vs. global models), local heterogeneity levels \\((\\alpha \\in [0.1,\\infty))\\), global imbalance ratios \\((\\rho \\in [1,58])\\), model architectures, budget sizes, and model initialization scheme. As a result, the experimental results empirically prove our three observations (Obs. 1-3). Besides, our method outperforms all other AL baselines and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.372, + 0.89, + 0.402 + ], + "angle": 0, + "content": "naive implementations for an ensemble of two query selectors in extensive experimental settings. \\(\\triangleright\\) See Section 6" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.415, + 0.641, + 0.43 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.698 + ], + "angle": 0, + "content": "Federated Learning is a collaborative learning framework with multiple clients while maintaining the privacy of each client dataset. In this decentralized framework, FedAvg [31] is considered a de facto algorithm in which a server and clients communicate only model parameters efficiently. One of the main bottlenecks for FL is the statistical heterogeneity problem across the clients' dataset, as the weight divergence from heterogeneous distributions hinders convergence during the aggregation scheme. Hence, several algorithms have tackled the local heterogeneity through the alignment between the local-updated gradient and the aggregated gradient, as a form of correction term [15, 23], regularization loss [1, 28], or distillation-based loss [25, 26]. Furthermore, there are existing literature to alleviate the class imbalance on the local side and they eventually achieve the global balance via rebalancing datasets [11] or a weighted loss function with a monitoring scheme [43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Active Learning minimizes the labeling effort by querying the most informative instances from the unlabeled data pool. There are three major types of active learning strategies, namely uncertainty-based sampling, diversity-based sampling, and hybrid strategy. Uncertainty-based sampling queries the most uncertain instances that lie on the current decision boundary [12,14,35,41], while diversity-based sampling selects a set of unlabeled instances that represents the entire unlabeled data distribution [16, 37]. Recently, hybrid strategies simultaneously consider both uncertainty and diversity. BADGE [6] utilized the gradient embedding as the uncertainty measure and selected the diverse query set by a \\(k\\)-means++ initialization scheme [5]. Several hybrid" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3945" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.292 + ], + "angle": 0, + "content": "
Indices:
cIndex for a class (c ∈ {1, ..., C})
rIndex for AL round (r ∈ {1, ..., R} = [R])
kIndex for a client (k ∈ {1, ..., K} = [K])
Parameters:
BLabeling budget for each AL round r
αLocal heterogeneity level
ρGlobal imbalance ratio
Data:
Uk^rPool of unlabeled instances for a client k at round r
Lk^rA queried instance set from Uk^r at round r
Dk^rAn available labeled set at round r
Weights:
Θr*Aggregated weights via FL phases on Dr^r (global model)
Θk*Separately optimized weights on Dk^r (local-only model)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.296, + 0.432, + 0.31 + ], + "angle": 0, + "content": "Table 1. Summary of notations throughout the paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.418 + ], + "angle": 0, + "content": "AL methods are based on a submodular data subset selection [44], pairwise contextual diversity [2], or feature mixing [34]. In addition to the three categories, model-based strategies have also been recently proposed to train additional networks for query selection, such as a VAE and discriminator [38] or a sequential graph neural network [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.473, + 0.635 + ], + "angle": 0, + "content": "Federated Active Learning has been recently studied to address a more realistic scenario, where clients have lots of the unlabeled instances [20, 47, 48]. However, previous works [3, 4] have not deeply discussed the challenges of FAL framework and naively applied existing AL strategies. Ahn et al. [4] have even considered the local-only query selector, but concluded that the global model is superior to the local-only model with limited experimental settings, three benchmarks and one heterogeneity level. In this work, we observe the counterparts in varying benchmarks and heterogeneity levels, which motivates us to design a novel sampling strategy by exploiting both global and local-only models. Our extensive analysis and experimental results encourage future research on the FAL problem." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.205, + 0.663 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.795 + ], + "angle": 0, + "content": "AL Procedure. For the ease of understanding, we summarize notations in Table 1. At the first AL round (i.e., \\(r = 1\\)), each client \\(k\\) randomly selects \\(B\\) instances, \\(L_{k}^{1} = \\{x_{1},\\ldots ,x_{B}\\}\\), from \\(U_{k}^{1}\\), and oracles annotate them to obtain the initial labeled set \\(D_{k}^{1} = \\{(x_{1},y_{1}),\\ldots ,(x_{B},y_{B})\\}\\). For the next round (\\(r\\geq 2\\)), based on the given querying strategy \\(\\mathcal{A}(\\cdot)\\) and the model parameters \\(\\Theta\\), the query set of the \\(k\\)-th client at round \\(r\\) is sampled by" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.8, + 0.47, + 0.82 + ], + "angle": 0, + "content": "\\[\nL _ {k} ^ {r} = \\mathcal {A} \\left(U _ {k} ^ {r}, \\Theta , B\\right), \\text {w h e r e} U _ {k} ^ {r} = U _ {k} ^ {r - 1} \\backslash L _ {k} ^ {r - 1}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.871 + ], + "angle": 0, + "content": "The querying function \\(\\mathcal{A}(\\cdot)\\) in Eq. (1) depends on which AL algorithm is used. For example, Entropy sampling [41] queries the instances with the highest uncertainty like:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.877, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (U, \\Theta , B) = \\underset {x _ {i} \\in L, | L | = B, L \\subseteq U} {\\arg \\max } H (p (y | x _ {i}; \\Theta)) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.894, + 0.155 + ], + "angle": 0, + "content": "where \\( H(p) = -\\sum_{c=1}^{C} p_c \\ln p_c \\), and \\( p \\) is the predictive probability. The query set is annotated by the oracle and assembled to expand the available labeled set, i.e., \\( D_k^r = D_k^{r-1} \\cup \\{(x_i, y_i) | x_i \\in L_k^r\\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.167, + 0.894, + 0.229 + ], + "angle": 0, + "content": "FL Procedure. After each AL round, we perform the FL procedure of which the objective is to obtain the optimal parameter \\(\\Theta^{r*}\\) such that it minimizes the target loss on the given labeled set for all clients, \\(D^{r} = \\cup_{k=1}^{K} D_{k}^{r}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.239, + 0.893, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\Theta^ {r *} = \\underset {\\Theta} {\\arg \\min } f \\left(\\Theta^ {r}\\right) = \\underset {\\Theta} {\\arg \\min } \\frac {1}{| D ^ {r} |} \\sum_ {i = 1} ^ {| D ^ {r} |} f _ {i} \\left(\\Theta^ {r}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.292, + 0.893, + 0.352 + ], + "angle": 0, + "content": "where \\( f_{i}(\\Theta) = \\ell (x_{i},y_{i};\\Theta) \\) and \\( \\ell (\\cdot) \\) is the loss function determined by the network parameter \\( \\Theta \\). However, due to data privacy, the global model is optimized based on the reformulated update rule on the partitioned data over clients:" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.363, + 0.789, + 0.404 + ], + "angle": 0, + "content": "\\[\nf (\\Theta^ {r}) = \\sum_ {k = 1} ^ {K} \\frac {| D _ {k} ^ {r} |}{| D ^ {r} |} F (\\Theta_ {k} ^ {r}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.406, + 0.893, + 0.446 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} F \\left(\\Theta_ {k} ^ {r}\\right) = \\frac {1}{\\left| D _ {k} ^ {r} \\right|} \\sum_ {\\left(x _ {i}, y _ {i}\\right) \\in D _ {k} ^ {r}} \\ell \\left(x _ {i}, y _ {i}; \\Theta_ {k} ^ {r}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.546 + ], + "angle": 0, + "content": "The model \\(\\Theta_k^r\\) is updated locally on the client side for its local data \\(D_k^r\\), and then it is aggregated globally to generate a global model \\(\\Theta^r\\). The local update and model aggregation steps are alternated until the global model converges; this corresponds to the most popular FL training pipeline, FedAvg proposed by [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.893, + 0.682 + ], + "angle": 0, + "content": "The previous studies [3, 4] have typically used the converged global model \\(\\Theta^{r*}\\) in the next AL round as the query selector of Eq. (2). However, considering the hierarchy structure in the FAL framework, it is also possible to use a separately optimized model on local partitioned data; replacing \\(D^r\\) with \\(D_k^r\\) in Eq. (3). It is often referred to as the local-only model [9, 33], and we denote it as \\(\\Theta_{k}^{r*}\\). In the following section, we investigate what these models are specialized in and when they are beneficial to use." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.695, + 0.741, + 0.712 + ], + "angle": 0, + "content": "4. Observation and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In this section, we analyze the performance trend between global and local-only models as the query selector, with respect to the degree of class imbalance in local and global data distribution. We synthetically adjust two indicators of inter-class diversity, \\(\\alpha \\in \\{0.1, 1.0, \\infty\\}\\) and \\(\\rho \\in \\{1, 5, 10, 20\\}\\), on CIFAR-10 benchmark. As \\(\\alpha\\) and \\(\\rho\\) get lower and higher, the levels of local heterogeneity and global imbalance increase, respectively (refer to Appendix A for the detailed data distribution). For both query selectors, we use Entropy sampling [41] as an active learning algorithm, and the training set is progressively labeled with the query ratio of \\(10\\%\\) in each AL round." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3946" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.094, + 0.442, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.315 + ], + "angle": 0, + "content": "Figure 2. Gap between the winning rate of global and local-only models by varying global imbalance ratio \\((\\rho)\\) and local heterogeneity \\((\\alpha)\\) on CIFAR-10 benchmark. The experimental setups for (a)-(d) are also compatible with Figure 3 and Table 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Comparison Metric. We evaluate the superiority over AL rounds through pairwise comparison [6, 34], widely used in conventional AL literature. We repeat each experimental setup, a pair of \\(\\alpha\\) and \\(\\rho\\), with four different seeds and obtain a set of four accuracy results \\(a_{r} = \\{a_{r,1}, \\ldots, a_{r,4}\\}\\) at each round \\(r\\). Then, we conduct a two-sided t-test, where \\(t\\)-score is defined by Definition 1 for two given strategies \\(i\\) and \\(j\\). Note that the strategy denotes the combination of the sampling strategy and the type of query selector." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.48, + 0.471, + 0.526 + ], + "angle": 0, + "content": "Definition 1. [36] Let \\( a_r^i \\) and \\( a_r^j \\) be the set of accuracies for two different FAL strategies \\( i \\) and \\( j \\). Then, t-score at AL round \\( r \\) is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.537, + 0.47, + 0.59 + ], + "angle": 0, + "content": "\\[\nt _ {r} ^ {i j} = \\frac {\\sqrt {4} \\mu_ {r} ^ {i j}}{\\sigma_ {r} ^ {i j}}, \\text {w h e r e} \\mu_ {r} ^ {i j} = \\frac {1}{4} \\sum_ {l = 1} ^ {4} \\left(a _ {r, l} ^ {i} - a _ {r, l} ^ {j}\\right) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.58, + 0.47, + 0.63 + ], + "angle": 0, + "content": "\\[\n\\text {a n d} \\sigma_ {r} ^ {i j} = \\sqrt {\\frac {1}{3} \\sum_ {l = 1} ^ {4} \\left(\\left(a _ {r , l} ^ {i} - a _ {r , l} ^ {j}\\right) - \\mu_ {r} ^ {i j}\\right)}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.641, + 0.471, + 0.686 + ], + "angle": 0, + "content": "Here, the strategy \\( i \\) is considered to beat the strategy \\( j \\) if \\( t_r^{ij} > 2.776 \\). Therefore, the winning rate for all AL rounds is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.695, + 0.47, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\operatorname {w i n} ^ {i j} = \\sum_ {r = 1} ^ {R} \\frac {1}{R} \\mathbb {1} _ {t _ {r} ^ {i j} > 2. 7 7 6}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.745, + 0.47, + 0.777 + ], + "angle": 0, + "content": "The value of winning rate becomes 1 if the strategy \\( i \\) beats the strategy \\( j \\) over all AL rounds." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.471, + 0.832 + ], + "angle": 0, + "content": "Observation 1. The superiority of local-only and global query-selecting models varies according to the degree of local heterogeneity and global imbalance ratio." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In Figure 2, we summarize the performance gap between two query models depending on the local heterogeneity level (indicated by different shapes) and the global imbalance ratio (increased along x-axis). The y-axis represents" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.259 + ], + "angle": 0, + "content": "the gap of the winning rate in Eq.(6) between global and local-only models; thus, the value becomes positive up to \\(+1\\) if the global model beats the local-only model, otherwise negative up to -1. At a glance, there is a clear and consistent superiority of two query models according to \\(\\alpha\\) and \\(\\rho\\), where the dominance has intensified toward both extremes (e.g., upper right and lower left). This observation contradicts the previous findings that the global model has always outperformed the local-only model as the query selector in a FAL framework [4]. We provide more in-depth analysis in following Obs. 2 and Obs. 3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.895, + 0.33 + ], + "angle": 0, + "content": "Observation 2. As local heterogeneity increases \\((\\alpha \\downarrow)\\), a local-only query selector is preferred due to the increased significance of local inter-class diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.895, + 0.583 + ], + "angle": 0, + "content": "As the collapse of the local inter-class balance (i.e., lower \\(\\alpha\\)) incurs severe performance degradation due to a weight divergence [11, 31], addressing local imbalance can improve the learning stability and performance. Since the local-only models are separately trained on each client, in general, the local-only model has shown higher confidence for its own data distribution than the global model [9, 33]. In Figure 3, we visualized the number of class instances and the class-wise test accuracy in the first AL round (see the caption for details). Specifically, we confirmed a high correlation between counts and accuracy in Figure 3-(a), such that the local-only models have higher accuracy than the global model for major classes of their data distribution. Thus, by the nature of favoring low-confident instances in AL, the local-only model tends to select the instances with local minority classes as the query." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.749 + ], + "angle": 0, + "content": "More precisely, we verify that the local-only model indeed queries the locally balanced set using earth mover's distance (EMD) [46]. In Table 2, local EMD measures the mean of distance between class distribution of local query sets and a uniform distribution. The lower the value, the more balanced the locally queried instances. As shown in Table 2-(a) with high local heterogeneity, the local EMD of the local-only model (L) is lower than that of the global model (G). That is, the local-only model queries more diverse instances than the global model with respect to the local inter-class diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Meanwhile, in the case of (b), the global model, trained with more samples, has higher accuracy over the classes due to little distribution discrepancy. Although the more accurate model is likely to have the higher prediction confidence, it does not mean that it is better at identifying the required instances based on the current local dataset, which the global model had not directly learned. In practice, the local-only model still chose the more locally balanced query set (Table 2-(b)), and we supposed this contradiction makes no sizeable winning gap of the case (b) in Figure 2." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3947" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.163, + 0.089, + 0.229, + 0.098 + ], + "angle": 0, + "content": "of Instances" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.099, + 0.28, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.089, + 0.411, + 0.098 + ], + "angle": 0, + "content": "Test Accuracy" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.099, + 0.465, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.257, + 0.461, + 0.269 + ], + "angle": 0, + "content": "(a) Low global imbalance \\((\\rho = 1)\\) and high heterogeneity \\((\\alpha = 0.1)\\)." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.271, + 0.277, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.271, + 0.462, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.429, + 0.464, + 0.442 + ], + "angle": 0, + "content": "(c) High global imbalance \\((\\rho = 20)\\) and high heterogeneity \\((\\alpha = 0.1)\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.089, + 0.642, + 0.098 + ], + "angle": 0, + "content": "of Instances" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.099, + 0.692, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.089, + 0.824, + 0.098 + ], + "angle": 0, + "content": "Test Accuracy" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.099, + 0.877, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.256, + 0.87, + 0.269 + ], + "angle": 0, + "content": "(b) Low global imbalance \\((\\rho = 1)\\) and low heterogeneity \\((\\alpha = \\infty)\\)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.271, + 0.691, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.271, + 0.875, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.429, + 0.872, + 0.442 + ], + "angle": 0, + "content": "(d) High global imbalance \\((\\rho = 20)\\) and low heterogeneity \\((\\alpha = \\infty)\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.447, + 0.894, + 0.503 + ], + "angle": 0, + "content": "Figure 3. Matrices of data count (left) and class-wise accuracy (right) for CIFAR-10, with four combinations of \\(\\rho = \\{1,20\\}\\) and \\(\\alpha = \\{0.1,\\infty\\}\\). k1-10 denote ten clients, c1-10 are ten classes of CIFAR-10. There are two types of data counts, # of per-client local instances (1-10th rows) and aggregated instances over all clients (the last row). Similarly, the test accuracy is measured with local-only models (1-10th rows) and a global model (the last row). (a)-(d) setups correspond to those of Figure 2. See Appendix B.1 for the more cases." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.52, + 0.469, + 0.648 + ], + "angle": 0, + "content": "
CaseModelObs. 2: Local EMD (↓)Obs. 3: Global EMD (↓)
10%20%30%40%10%20%30%40%
(a)G0.6320.6380.6410.6430.0190.0640.0860.095
L0.6320.5970.5920.5950.0190.0500.0500.046
(b)G0.0490.0770.0700.0840.0140.0700.0660.063
L0.0490.0420.0540.0590.0140.0250.0440.053
(c)G0.6920.6800.6760.6740.3770.3000.2940.294
L0.6920.6410.6330.6360.3770.3340.3260.321
(d)G0.3710.2980.2840.2740.3680.2940.2820.272
L0.3710.3130.2930.2900.3680.3090.2870.288
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.653, + 0.47, + 0.709 + ], + "angle": 0, + "content": "Table 2. Local EMD and global EMD on CIFAR-10. We summarize the results of four AL rounds with the labeling budget of \\(10\\%\\) per round. (a)-(d) setups correspond to those of Figure 2. See Appendix B.2 for EMDs of more cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Observation 3. As the degree of global class imbalance increases (\\(\\rho \\uparrow\\)), it is more advantageous to exploit a global model that alleviates the global class imbalance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Based on Obs. 2, the local-only model should outperform the global model in the case (c), but there is no clear superiority between them with respect to the winning rate in the case (c) of Figure 2. The only answer for this conundrum is the presence of global minority classes due to the high global imbalance ratio. The local heterogeneity is obviously a crucial factor by Obs. 2, but global class imbalance is also another factor that significantly degrades the classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.628 + ], + "angle": 0, + "content": "performance in the FAL framework. Here, the major challenge is that neither the central server nor local clients cannot access any information of aggregated data due to privacy preservation. The only way to address this problem, we should utilize the global model that implicitly learns the knowledge of the entire data distribution through the aggregation phase in Eq. (4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.749 + ], + "angle": 0, + "content": "We introduce an additional global EMD, the indicator of measuring the inter-class diversity of the aggregated queried set over all clients. As can be seen in Table 2-(c), where the global imbalance ratio is high, we confirm that the global query selector (G) favors to query global minority classes. The global EMD of the global model is lower than that of the local-only model, i.e. the more globally balanced query set, but the local EMD is the opposite." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Meanwhile, in the case of (d), the minority classes are always the same from the global and local perspectives. It is different from the case (b), where the minority classes with respect to the accuracy differ in each client depending on the informativeness of instances despite the same instance number. Therefore, in this scenario, the global model has high confidence even in local datasets, leading to significantly overwhelming the local-only model in the case (d) of Figure 2. In conclusion, the global inter-class diversity is an essential factor when global imbalance exists." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3948" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.17, + 0.106 + ], + "angle": 0, + "content": "5. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.283 + ], + "angle": 0, + "content": "From three observations in Section 4, we confirmed that FAL framework requires delicate consideration of local and global inter-class diversity. However, since clients are reluctant to share their data information, we should simultaneously utilize local-only and global models to ensure both sides of inter-class diversity. To this end, we propose a novel query sample strategy, named LoGo, that composed of macro and micro steps. Pseudo algorithm for LoGo is provided in Appendix C. Before describing details of each step, let us assume a scenario where \\( k \\)-th client queries \\( B \\) unlabeled instances at the round of \\( r \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.287, + 0.419, + 0.302 + ], + "angle": 0, + "content": "Macro Step: Clustering with Local-Only Model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.47, + 0.424 + ], + "angle": 0, + "content": "The ultimate goal of macro step is to satisfy local interclass diversity by primarily sampling the informative instances by the local-only model. In detail, we introduce \\( k \\)-means clustering [30] on the hypothetical gradient embedding. Let \\( z \\) be the embedding vector before forwarding to the last layer \\( W \\) for \\( x \\in U_k^r \\). Here, we utilize the gradient of negative cross-entropy loss, induced by a pseudo label, with respect to the last layer of encoder as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.427, + 0.47, + 0.458 + ], + "angle": 0, + "content": "\\[\ng _ {c} ^ {x} = - \\frac {\\partial}{\\partial W _ {c}} \\ell_ {C E} (x, \\hat {y}; \\Theta_ {k *} ^ {r}) = z \\cdot \\left(\\mathbb {1} _ {[ \\hat {y} = c ]} - p _ {c}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.538 + ], + "angle": 0, + "content": "where \\(\\hat{y} = \\arg \\max_{c\\in [C]}p_c\\) and \\(W_{c}\\) is the weights connected to \\(c\\)-th neuron of logits. Gradient embedding is widely used in conventional AL algorithm [6, 40], and we consider only the gradients corresponding to the pseudo label (i.e., \\(g_{\\hat{y}}^x\\)) for computation efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Then, we calculate \\( B \\) number of centroids on the hallucinated gradient space via EM algorithm [10] of \\( k \\)-means clustering by minimizing" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.586, + 0.47, + 0.628 + ], + "angle": 0, + "content": "\\[\nJ = \\sum_ {i = 1} ^ {N} \\sum_ {b = 1} ^ {B} w _ {i b} \\| g _ {\\hat {y}} ^ {x _ {i}} - \\mu_ {b} \\| ^ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.8 + ], + "angle": 0, + "content": "where \\( w_{ib} \\) is an indicator function whether \\( g_{\\hat{y}}^{x_i} \\) is assigned to \\( \\mu_b \\) for E-step. Eq. (7) shows that the gradient embedding is a just scaling of feature embedding \\( z \\), especially with the scale of uncertainty. In other words, if an instance is uncertain to predict (low value of \\( p_{\\hat{y}} \\)), its gradient will be much highly scaled. In this sense, Eq. (8) can be regarded as a weighted \\( k \\)-means clustering [13,39] on the feature embedding space by using the function of softmax response [17]. Hence, the macro step of LoGo enable the query set to contain both diversity in the embedding space and uncertainty from the perspective of local-only model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.804, + 0.466, + 0.819 + ], + "angle": 0, + "content": "Micro Step: Cluster-wise Sampling with Global Model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.819, + 0.469, + 0.879 + ], + "angle": 0, + "content": "In micro step, the global model selects the final instances that results in the higher global inter-class diversity. Given \\( B \\) selected instances from the macro step, the most uncertain instance is selected for each cluster:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.885, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\nL _ {k} ^ {r} = \\left\\{\\mathcal {A} \\left(\\mathcal {C} _ {1}, \\Theta^ {r *}, 1\\right), \\dots , \\mathcal {A} \\left(\\mathcal {C} _ {B}, \\Theta^ {r *}, 1\\right) \\right\\} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "\\(C_b\\) denotes \\(b\\)-th cluster, generated by the query set from the macro step. We simply used Entropy sampling for \\(\\mathcal{A}\\), but we should note that \\(\\mathcal{A}\\) can be any AL sampling strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.213 + ], + "angle": 0, + "content": "The cluster-wise sampling in the micro step is a simple yet effective strategy to leverage the advantages of both query selector models, ensuring local and global inter-class diversity. Here, we discuss how LoGo can be a promising sampling strategy for the FAL framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Remark 1. The micro step is same with one step of EM algorithm. We first update cluster assignments with \\( B \\) number of centroids from the macro step (E-step). Then, within each cluster, we select the most informative instance based on the uncertainty score. This can be regarded as one \\( M \\)-step of the weighted \\( k \\)-means clustering, using infinitely scaled weight function of uncertainty measure." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.334, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Then, let \\( c_{b} \\) be a centroid of \\( C_{b} \\) and we define \\( M \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.356, + 0.892, + 0.399 + ], + "angle": 0, + "content": "\\[\nM = \\sum_ {b = 1} ^ {B} \\| c _ {b} - \\tilde {x} _ {b} \\| ^ {2}, \\text {w h e r e} \\tilde {x} _ {b} = \\arg \\min _ {x} \\| c _ {b} - x \\| ^ {2} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.467 + ], + "angle": 0, + "content": "where \\( x \\in L_k^r \\) (Eq. (9)) and \\( \\tilde{x} \\) is one-to-one mapping with the minimal transport cost. The lower value of \\( M \\) means that the final query set much consider the diversity in the macro step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Remark 2. EM-based sampling in the micro step guarantees the diversity information of the macro step. Through sampling one instance per cluster, each \\(\\tilde{x}_b\\) is disjointly assigned to one cluster. Therefore, LoGo conservatively ensures the local inter-class diversity from the macro step (i.e., lower \\(M\\) value), comparing to any other strategy that query at least two instances for one cluster." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.593, + 0.617, + 0.608 + ], + "angle": 0, + "content": "6. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.755, + 0.634 + ], + "angle": 0, + "content": "6.1. Experimental Configuration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Training Settings. In a FAL framework, a central server should carefully consider the fairness of labeling and training costs between clients. Therefore, we assume that ten clients have the same size of unlabeled data pool and query the same number of instances per every AL round. Moreover, we focus on a cross-silo FL setting [22] where every client participates in every FL round." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.892, + 0.913 + ], + "angle": 0, + "content": "We compared LoGo with six active learning strategies on five benchmark dataset (CIFAR-10 [24], SVHN [32], PathMNIST, DermaMNIST, and OrganAMNIST [45]). We considered 38 comprehensive experimental settings combined into six categories (see Figure 4). Except for learning ablations of the architectures, labeling budgets, and initialization schemes, in default, we implemented four layers of CNN and trained the encoder from scratch with the labeling budget of \\(5\\%\\) for every AL round. We repeat all experiments four times and report their averaged values. Refer to Appendix D for detailed experimental settings." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3949" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.073, + 0.873, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.203, + 0.894, + 0.245 + ], + "angle": 0, + "content": "Figure 4. Winning percentage across six categories. We also added defeat percentage, the black hatched bar that represents the percentage at which LoGo has been defeated by each baseline. Among total experiments, only statistically reliable values (\\(t\\)-score \\(>2.776\\)) are considered. Thus, the lower value of the colored bar and the higher value of the black bar indicate a more comparable baseline." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.264, + 0.434, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.571 + ], + "angle": 0, + "content": "Figure 5. Pairwise penalty matrix over 38 experimental settings. The value \\( P_{ij} \\) indicates the number of times that the \\( i \\)-th strategy outperforms the \\( j \\)-th strategy (i.e., sum of win\\(^{ij}\\) in Eq.(6) over 38 settings). The last row is the average number of times the \\( j \\)-th strategy is defeated by the rest strategies; the lower, the better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.473, + 0.816 + ], + "angle": 0, + "content": "Baselines. We considered six standard AL strategies. Random randomly samples the instances from the unlabeled pool. Entropy selects instances with the largest entropy [41]. CoreSet chooses the small subset that can represent the whole unlabeled set [37]. BADGE selects the diverse points with high magnitude in a hallucinated gradient space [6]. GCNAL adapts CoreSet on a sequential graph convolution network to measure the relation between labeled and unlabeled instances [8]. ALFA-Mix identifies the valuable instances by seeking inconsistencies in the prediction of mixing features [34]. We adopt these sampling strategies with either the global model or local-only model in FedAvg pipeline. Refer to Appendix E for the comparison of query selection cost. Besides, we summarized the results with various FL methods in Appendix F." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.823, + 0.273, + 0.839 + ], + "angle": 0, + "content": "6.2. Overall Comparison" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.303, + 0.862 + ], + "angle": 0, + "content": "6.2.1 Pairwise Penalty Matrix" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We summarized the overall comparison results as a pairwise penalty matrix \\( P \\) in Figure 5, following the recent" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.892, + 0.388 + ], + "angle": 0, + "content": "work [6, 34]. Each cell of the pairwise penalty matrix represents the summation of the winning rate of Eq. (6) calculated above for each of the 38 experimental sets. As the rows of the matrix \\( P_{i} \\) indicate how many times \\( i \\)-th algorithm outperforms the other algorithms, the brighter color means the better algorithm (conversely, the darker columns are the better). Note that we only considered statistically reliable results throughout the two-sided t-test." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.893, + 0.51 + ], + "angle": 0, + "content": "LoGo defeats all baselines in general (see 7-th row values) while under-performed only 0.9 out of 38 times on average (see 7-th column values in the last row). In particular, LoGo outperforms BADGE and Entropy sampling, which are top-2 baselines, with 13.7 and 12.0 out of 38 times, while LoGo only loses 2.4 and 1.9 out of 38 times, respectively. This results demonstrate the robust effectiveness of our LoGo algorithm in various experimental settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.519, + 0.722, + 0.535 + ], + "angle": 0, + "content": "6.2.2 Winning Rate Bar Plots" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.895, + 0.692 + ], + "angle": 0, + "content": "Figure 4 summarizes the comparison results according to the six categories, which is the breakdown of Figure 5 on a more systematic categorization. For example, the colored bar of the overall category is calculated by dividing the total setting number of 38 in the 7-th row vector of Figure 5 (the black bar is from the 7-th column vector). The colored bar represents the average percentage at which LoGo defeats each baseline algorithm, and the higher bar means that LoGo has won more. Appendix G.1 provides the detailed comparison penalty values according to each category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.693, + 0.896, + 0.904 + ], + "angle": 0, + "content": "Overall, LoGo consistently shows an overwhelming winning percentage toward any baseline against the defeat percentage. Interestingly, ALFA-Mix, the latest AL strategy, shows performance considerably varying depending on which query selector is selected (see the query selector in Figure 4). The reason would be that a local-only model, which is separately trained on the highly heterogeneous dataset, is not appropriate for the feature mixing or the sensitivity to lots of hyperparameters. Moreover, Coreset, which does not consider uncertainty, cannot resolve the local and global imbalance, showing similar performance as Random sampling. Thus, LoGo is a superior algorithm for a FAL framework in that it is robust to the type of query selector or most combinations of experimental settings." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3950" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.894, + 0.291 + ], + "angle": 0, + "content": "
MethodModelCIFAR-10SVHNPathMNISTDermaMNIST
20%40%60%80%20%30%40%50%20%30%40%50%20%30%40%50%
Random-64.1969.0771.6372.8180.9083.0784.2284.7768.4172.7073.7675.4971.7072.5772.6672.86
Entropy [41]G64.0269.1271.8773.3382.0884.6185.8886.3171.5474.3975.9176.6572.4972.6373.0273.20
L66.2971.4573.5174.0282.0984.5885.6986.1876.5278.2978.7179.1071.3872.0472.2272.65
Coreset [37]G64.6669.4371.7573.180.9482.7483.8184.4674.8476.2476.8576.8072.0272.1672.3472.74
L64.0668.7971.4973.2880.9482.9283.7884.4872.5376.0676.2876.8671.1371.4872.1572.38
BADGE [6]G65.1269.5772.1173.5382.8184.8285.8986.272.2174.3875.5376.9772.5973.0973.2373.45
L66.3271.2873.4174.2882.6984.6785.6186.176.4878.5178.4278.6871.3572.1372.2572.99
GCNAL [8]G65.4070.0572.4173.4282.0584.0785.0985.6175.5177.7978.1378.8172.0172.6073.0773.17
L65.6270.1872.3673.4281.9283.5884.5585.1074.8576.4677.1877.4571.9572.9172.9173.29
ALFA-Mix [34]G65.4569.8772.2473.2983.0284.9986.0586.3373.3474.8376.3177.4372.3973.1473.2773.10
L64.1468.7971.0372.681.0882.5583.6284.3371.1075.0175.8176.7071.5172.1872.9473.28
LoGo (ours)G,L66.5071.7073.8074.4983.4685.3186.0286.3876.3278.7279.5179.5872.6173.1873.3373.77
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.339 + ], + "angle": 0, + "content": "Table 3. Comparison of test accuracy on four benchmarks with \\( \\alpha = 0.1 \\). We reported the results with four random seeds. The baselines, except for Random sampling, are combined with two query selector models, \\( G \\) and \\( L \\) that stands for a global or local-only model, respectively. **Bold and underline mean Top-1 and Top-2**, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.36, + 0.353, + 0.377 + ], + "angle": 0, + "content": "6.2.3 Under Query Selector Category" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.471, + 0.656 + ], + "angle": 0, + "content": "Table 3 shows the test accuracy according to the increased labeling budgets over rounds on four datasets. Even with the same active learning strategy, a gap in test accuracy occurs depending on which query selector is used because the global imbalance varies by 1.0–58.7 across datasets. For example, in general, global models outperform local-only models for SVHN and DermaMNIST, while the opposite trend is observed for CIFAR-10 and PathMNIST. However, irrespective of the benchmarks and querying model types, our LoGo shows the best performance in most cases. Two-step selection strategy enables LoGo to be robust by utilizing both the benefits of global and local-only models. Because we cannot know the degree of local and global imbalance in advance, our proposed method has a strong advantage in providing data-agnostic performance improvements over all baselines. Appendix G.2 provides a detailed performance comparison between LoGo and baselines under various experimental settings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.322, + 0.683 + ], + "angle": 0, + "content": "6.3. LoGo vs. Simple Ensemble" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.81 + ], + "angle": 0, + "content": "To prove that LoGo is an effective way to leverage the advantages of both models, we compared LoGo with three naive implementation of ensemble methods for global and local-only models: (1) the average of logits (for Entropy sampling) or gradient embedding (for BADGE) from two models, (2) weighing the instances based on the selection ranks (i.e., more weights if it is selected from both models), and (3) fine-tuning the global model on local datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In Table 4, LoGo consistently shows better classification accuracy over increasing labeling budgets than three counterparts. Compared with the results in both Tables 3 and 4, all three ensemble methods show lower performance than using a single superior query selector. That is, the naive ensemble suffers from a performance trade-off between two" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.357, + 0.892, + 0.478 + ], + "angle": 0, + "content": "
MethodStrategyCIFAR-10SVHN
20%40%60%80%20%30%40%
Ens. Logit+Entropy64.5370.3673.0274.2881.8184.6485.87
+BADGE65.5570.3172.8373.9782.7784.7685.90
Ens. Rank+Entropy65.9070.9273.3474.2082.1584.3885.64
+BADGE66.2170.9873.1574.0183.0285.0585.86
Fine-tuning+Entropy65.1070.7573.2174.2382.5385.0586.01
+BADGE65.8270.9572.9474.1282.5984.8985.82
LoGo (ours)-66.5071.7073.8074.4983.4685.3186.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.483, + 0.892, + 0.512 + ], + "angle": 0, + "content": "Table 4. Comparison of test accuracy on two benchmarks \\((\\alpha = 0.1)\\) with baselines using both global and local information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.557 + ], + "angle": 0, + "content": "query selector models and, therefore, their results fall somewhere in the middle of using global and local models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.57, + 0.618, + 0.586 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.791 + ], + "angle": 0, + "content": "We discovered the superiority of the two query selectors according to the local heterogeneity level and global imbalance ratio. Based on our findings, the local-only and global models are both crucial since global and local inter-class diversity affects their performance dominance. To this end, we propose LoGo algorithm that incorporates local-only and global models into macro and micro steps of cluster-based active learning. LoGo preferentially selects samples that simultaneously alleviate local and global imbalance as a query, making it robust to local and global imbalance. Our experiments verified that LoGo consistently outperforms six baselines under comprehensive settings of 38 combinations using six categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3951" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. 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Divergence-aware federated self-supervised learning. arXiv preprint arXiv:2204.04385, 2022. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.874 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3953" + } + ] +] \ No newline at end of file diff --git a/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_origin.pdf b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3fce1788750a7972ee4fa7098f2bceedd9d1a9e8 --- /dev/null +++ b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/f3aeecdc-b140-4a20-9d11-a2f96511d465_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:524e23b3d821ebb7d47d0d8242aacc40eae3962e0d92039f49ce71029368edd3 +size 856500 diff --git a/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/full.md b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6740152f4a677a3958e2a54f0908e29c8f9e0da6 --- /dev/null +++ b/2023/Re-Thinking Federated Active Learning Based on Inter-Class Diversity/full.md @@ -0,0 +1,319 @@ +# Re-thinking Federated Active Learning based on Inter-class Diversity + +SangMook $\mathrm{Kim}^{1*}$ Sangmin Bae $^{1*}$ Hwanjun Song $^{2\dagger}$ Se-Young Yun $^{1\dagger}$ $^{1}$ KAIST AI $^{2}$ NAVER AI LAB + +{sangmook.kim, bsmn0223, yunseyoung}@kaist.ac.kr ghkswns91@gmail.com + +# Abstract + +Although federated learning has made awe-inspiring advances, most studies have assumed that the client's data are fully labeled. However, in a real-world scenario, every client may have a significant amount of unlabeled instances. Among the various approaches to utilizing unlabeled data, a federated active learning framework has emerged as a promising solution. In the decentralized setting, there are two types of available query selector models, namely 'global' and 'local-only' models, but little literature discusses their performance dominance and its causes. In this work, we first demonstrate that the superiority of two selector models depends on the global and local interclass diversity. Furthermore, we observe that the global and local-only models are the keys to resolving the imbalance of each side. Based on our findings, we propose LoGo, a FAL sampling strategy robust to varying local heterogeneity levels and global imbalance ratio, that integrates both models by two steps of active selection scheme. LoGo consistently outperforms six active learning strategies in the total number of 38 experimental settings. The code is available at: https://github.com/raymin0223/LoGo. + +# 1. Introduction + +Federated learning (FL) is a distributed framework that allows multiple parties to learn a unified deep learning model cooperatively with preserving the privacy of the local client [23,28,31]. Typically, FL has been actively studied in a standard supervised learning setting, where all the training instances are labeled, but it is more realistic for each client to contain both labeled and unlabeled data due to the high labeling cost [29, 48]. Here, active learning (AL) can be a promising solution to improve the performance of a cooperated model with the pool of unlabeled data. In practice, federated active learning (FAL) framework has recently attempted to bridge two different philosophies in FL and AL [3,4]. As illustrated in Figure 1-(a) FAL framework alternates an FL procedure (red line) of training a predictive + +model collaboratively through local updates and aggregation phases, and an AL procedure (green line) of querying and annotating informative instances separately per client. + +Although the overall framework just appears to be a straightforward fusion of two research fields, FL factors introduce two major challenges to the AL procedure. First, the class imbalance of the local dataset originates from heterogeneous distribution across local clients [15, 23, 28]. Hence, in the FAL framework, the active selection algorithm has to ensure inter-class diversity from both local and global perspectives. Second, there are two available types of query-selecting models, a global model, which is globally optimized through the FL pipeline, and a locally only model [9, 33], which can be separately trained only for each client. In the query selection phase, the global model can leverage the aggregated knowledge of all clients, while the local-only model is able to detect the most valuable instances for the local updates. + +Prior FAL literature [3, 4], which simply adapt conventional AL strategies, had little discussion on these challenges. As our first contribution, we found the significant performance gap between two types of query selector (see Figure 1-(b)), and it is the first study to solve a conundrum of dominance trend by introducing two indicators of interclass diversity1–local heterogeneity level $(\alpha)$ and global imbalance ratio $(\rho)$ . The first indicator $\alpha$ is the concentration parameter of Dirichlet distribution, commonly seen in the FL literature [1, 15, 23], resulting in more locally imbalanced class distribution at lower values. Besides, $\rho$ indicator is the ratio of class imbalance for the aggregated global data of all clients [7, 21]. We discovered three meaningful insights on selector dominance: (Obs. 1) Interestingly, the superiority of the two selectors varies depending on the two indicators of inter-class diversity, $\alpha$ and $\rho$ . (Obs. 2) When local heterogeneity is severe ( $\alpha$ is low), a local-only model is preferred for weighing minority instances for each client, and (Obs. 3) when globally minor classes exist ( $\rho$ is high), the knowledge of the entire data distribution, inherent in a global model, is more essential. > See Section 4 + +![](images/6c5bd360ef6f5cc219fc361d220fac0de4f974b0533bd8cad8b6e6fcf3ea6686.jpg) +(a) Federated Active Learning framework. + +![](images/2442e7078b55853afe6d550e68f031f06fd531ee22e100e0477beed69f4f464a.jpg) +(b) Superiority change of query selector. +Figure 1. Motivation: (a) The red and green lines correspond to the conventional FL and AL framework. We focus on a sampling strategy for FAL (green box) with the considerations of hierarchy structure and two available query-selecting models. (b) For a fixed querying strategy (Entropy sampling), the performance gap occurs only by changing the query selector. The y-axis is the gap in the winning rate in total active rounds (refer to Section 4). Closer to 1 indicates that global models outperforms than local-only models, and -1 is the opposite. + +In a real FAL scenario, the superiority of two query models for a given dataset cannot be known in advance due to privacy preservation. Therefore, as our second contribution, we design a simple yet effective FAL querying approach, LoGo, that simultaneously leverages local-only and global models, to be robust to varying heterogeneity levels and global imbalance ratios. LoGo is a clustering-based sampling strategy, which is composed of macro and micro step exploiting local-only and global models, respectively. The rationale behind our method is that the optimal querying policy needs to evaluate the informativeness of instances with both models, which implicitly learn local and global data distribution, respectively. In a macro step, to improve the local inter-class diversity first, we perform $k$ -means clustering [30] in hallucinated gradient space generated from local-only models. Then, in a micro step, the final query set is determined via one step of the EM algorithm [10], making cluster boundaries using instances from macro step (E-step) and cluster-wise sampling with the global model (M-step). The proposed cluster-wise sampling conservatively guarantees the diversity information of the macro step, i.e., the local inter-class diversity obtained by local-only models, while also considering the global minority classes via the global model. $\triangleright$ See Section 5 + +As our third contribution, we conduct a total number of 38 experiments on five datasets using seven AL strategies including our LoGo algorithm. To verify the superiority of our method in real-world scenarios, we build comprehensive combinations of six categories, including query selector types (local-only vs. global models), local heterogeneity levels $(\alpha \in [0.1,\infty))$ , global imbalance ratios $(\rho \in [1,58])$ , model architectures, budget sizes, and model initialization scheme. As a result, the experimental results empirically prove our three observations (Obs. 1-3). Besides, our method outperforms all other AL baselines and + +naive implementations for an ensemble of two query selectors in extensive experimental settings. $\triangleright$ See Section 6 + +# 2. Related Work + +Federated Learning is a collaborative learning framework with multiple clients while maintaining the privacy of each client dataset. In this decentralized framework, FedAvg [31] is considered a de facto algorithm in which a server and clients communicate only model parameters efficiently. One of the main bottlenecks for FL is the statistical heterogeneity problem across the clients' dataset, as the weight divergence from heterogeneous distributions hinders convergence during the aggregation scheme. Hence, several algorithms have tackled the local heterogeneity through the alignment between the local-updated gradient and the aggregated gradient, as a form of correction term [15, 23], regularization loss [1, 28], or distillation-based loss [25, 26]. Furthermore, there are existing literature to alleviate the class imbalance on the local side and they eventually achieve the global balance via rebalancing datasets [11] or a weighted loss function with a monitoring scheme [43]. + +Active Learning minimizes the labeling effort by querying the most informative instances from the unlabeled data pool. There are three major types of active learning strategies, namely uncertainty-based sampling, diversity-based sampling, and hybrid strategy. Uncertainty-based sampling queries the most uncertain instances that lie on the current decision boundary [12,14,35,41], while diversity-based sampling selects a set of unlabeled instances that represents the entire unlabeled data distribution [16, 37]. Recently, hybrid strategies simultaneously consider both uncertainty and diversity. BADGE [6] utilized the gradient embedding as the uncertainty measure and selected the diverse query set by a $k$ -means++ initialization scheme [5]. Several hybrid + +
Indices:
cIndex for a class (c ∈ {1, ..., C})
rIndex for AL round (r ∈ {1, ..., R} = [R])
kIndex for a client (k ∈ {1, ..., K} = [K])
Parameters:
BLabeling budget for each AL round r
αLocal heterogeneity level
ρGlobal imbalance ratio
Data:
Uk^rPool of unlabeled instances for a client k at round r
Lk^rA queried instance set from Uk^r at round r
Dk^rAn available labeled set at round r
Weights:
Θr*Aggregated weights via FL phases on Dr^r (global model)
Θk*Separately optimized weights on Dk^r (local-only model)
+ +Table 1. Summary of notations throughout the paper. + +AL methods are based on a submodular data subset selection [44], pairwise contextual diversity [2], or feature mixing [34]. In addition to the three categories, model-based strategies have also been recently proposed to train additional networks for query selection, such as a VAE and discriminator [38] or a sequential graph neural network [8]. + +Federated Active Learning has been recently studied to address a more realistic scenario, where clients have lots of the unlabeled instances [20, 47, 48]. However, previous works [3, 4] have not deeply discussed the challenges of FAL framework and naively applied existing AL strategies. Ahn et al. [4] have even considered the local-only query selector, but concluded that the global model is superior to the local-only model with limited experimental settings, three benchmarks and one heterogeneity level. In this work, we observe the counterparts in varying benchmarks and heterogeneity levels, which motivates us to design a novel sampling strategy by exploiting both global and local-only models. Our extensive analysis and experimental results encourage future research on the FAL problem. + +# 3. Preliminary + +AL Procedure. For the ease of understanding, we summarize notations in Table 1. At the first AL round (i.e., $r = 1$ ), each client $k$ randomly selects $B$ instances, $L_{k}^{1} = \{x_{1},\ldots ,x_{B}\}$ , from $U_{k}^{1}$ , and oracles annotate them to obtain the initial labeled set $D_{k}^{1} = \{(x_{1},y_{1}),\ldots ,(x_{B},y_{B})\}$ . For the next round ( $r\geq 2$ ), based on the given querying strategy $\mathcal{A}(\cdot)$ and the model parameters $\Theta$ , the query set of the $k$ -th client at round $r$ is sampled by + +$$ +L _ {k} ^ {r} = \mathcal {A} \left(U _ {k} ^ {r}, \Theta , B\right), \text {w h e r e} U _ {k} ^ {r} = U _ {k} ^ {r - 1} \backslash L _ {k} ^ {r - 1}. \tag {1} +$$ + +The querying function $\mathcal{A}(\cdot)$ in Eq. (1) depends on which AL algorithm is used. For example, Entropy sampling [41] queries the instances with the highest uncertainty like: + +$$ +\mathcal {A} (U, \Theta , B) = \underset {x _ {i} \in L, | L | = B, L \subseteq U} {\arg \max } H (p (y | x _ {i}; \Theta)) \tag {2} +$$ + +where $H(p) = -\sum_{c=1}^{C} p_c \ln p_c$ , and $p$ is the predictive probability. The query set is annotated by the oracle and assembled to expand the available labeled set, i.e., $D_k^r = D_k^{r-1} \cup \{(x_i, y_i) | x_i \in L_k^r\}$ . + +FL Procedure. After each AL round, we perform the FL procedure of which the objective is to obtain the optimal parameter $\Theta^{r*}$ such that it minimizes the target loss on the given labeled set for all clients, $D^{r} = \cup_{k=1}^{K} D_{k}^{r}$ , + +$$ +\Theta^ {r *} = \underset {\Theta} {\arg \min } f \left(\Theta^ {r}\right) = \underset {\Theta} {\arg \min } \frac {1}{| D ^ {r} |} \sum_ {i = 1} ^ {| D ^ {r} |} f _ {i} \left(\Theta^ {r}\right) \tag {3} +$$ + +where $f_{i}(\Theta) = \ell (x_{i},y_{i};\Theta)$ and $\ell (\cdot)$ is the loss function determined by the network parameter $\Theta$ . However, due to data privacy, the global model is optimized based on the reformulated update rule on the partitioned data over clients: + +$$ +f (\Theta^ {r}) = \sum_ {k = 1} ^ {K} \frac {| D _ {k} ^ {r} |}{| D ^ {r} |} F (\Theta_ {k} ^ {r}), +$$ + +$$ +\text {w h e r e} F \left(\Theta_ {k} ^ {r}\right) = \frac {1}{\left| D _ {k} ^ {r} \right|} \sum_ {\left(x _ {i}, y _ {i}\right) \in D _ {k} ^ {r}} \ell \left(x _ {i}, y _ {i}; \Theta_ {k} ^ {r}\right). \tag {4} +$$ + +The model $\Theta_k^r$ is updated locally on the client side for its local data $D_k^r$ , and then it is aggregated globally to generate a global model $\Theta^r$ . The local update and model aggregation steps are alternated until the global model converges; this corresponds to the most popular FL training pipeline, FedAvg proposed by [31]. + +The previous studies [3, 4] have typically used the converged global model $\Theta^{r*}$ in the next AL round as the query selector of Eq. (2). However, considering the hierarchy structure in the FAL framework, it is also possible to use a separately optimized model on local partitioned data; replacing $D^r$ with $D_k^r$ in Eq. (3). It is often referred to as the local-only model [9, 33], and we denote it as $\Theta_{k}^{r*}$ . In the following section, we investigate what these models are specialized in and when they are beneficial to use. + +# 4. Observation and Analysis + +In this section, we analyze the performance trend between global and local-only models as the query selector, with respect to the degree of class imbalance in local and global data distribution. We synthetically adjust two indicators of inter-class diversity, $\alpha \in \{0.1, 1.0, \infty\}$ and $\rho \in \{1, 5, 10, 20\}$ , on CIFAR-10 benchmark. As $\alpha$ and $\rho$ get lower and higher, the levels of local heterogeneity and global imbalance increase, respectively (refer to Appendix A for the detailed data distribution). For both query selectors, we use Entropy sampling [41] as an active learning algorithm, and the training set is progressively labeled with the query ratio of $10\%$ in each AL round. + +![](images/c6426a9f88fb96837819920e8d173831f06ffb72c1a3d112ccc2741ecd048e1b.jpg) +Figure 2. Gap between the winning rate of global and local-only models by varying global imbalance ratio $(\rho)$ and local heterogeneity $(\alpha)$ on CIFAR-10 benchmark. The experimental setups for (a)-(d) are also compatible with Figure 3 and Table 2. + +Comparison Metric. We evaluate the superiority over AL rounds through pairwise comparison [6, 34], widely used in conventional AL literature. We repeat each experimental setup, a pair of $\alpha$ and $\rho$ , with four different seeds and obtain a set of four accuracy results $a_{r} = \{a_{r,1}, \ldots, a_{r,4}\}$ at each round $r$ . Then, we conduct a two-sided t-test, where $t$ -score is defined by Definition 1 for two given strategies $i$ and $j$ . Note that the strategy denotes the combination of the sampling strategy and the type of query selector. + +Definition 1. [36] Let $a_r^i$ and $a_r^j$ be the set of accuracies for two different FAL strategies $i$ and $j$ . Then, t-score at AL round $r$ is formulated as: + +$$ +t _ {r} ^ {i j} = \frac {\sqrt {4} \mu_ {r} ^ {i j}}{\sigma_ {r} ^ {i j}}, \text {w h e r e} \mu_ {r} ^ {i j} = \frac {1}{4} \sum_ {l = 1} ^ {4} \left(a _ {r, l} ^ {i} - a _ {r, l} ^ {j}\right) \tag {5} +$$ + +$$ +\text {a n d} \sigma_ {r} ^ {i j} = \sqrt {\frac {1}{3} \sum_ {l = 1} ^ {4} \left(\left(a _ {r , l} ^ {i} - a _ {r , l} ^ {j}\right) - \mu_ {r} ^ {i j}\right)}. \tag {5} +$$ + +Here, the strategy $i$ is considered to beat the strategy $j$ if $t_r^{ij} > 2.776$ . Therefore, the winning rate for all AL rounds is formulated as follows: + +$$ +\operatorname {w i n} ^ {i j} = \sum_ {r = 1} ^ {R} \frac {1}{R} \mathbb {1} _ {t _ {r} ^ {i j} > 2. 7 7 6}. \tag {6} +$$ + +The value of winning rate becomes 1 if the strategy $i$ beats the strategy $j$ over all AL rounds. + +Observation 1. The superiority of local-only and global query-selecting models varies according to the degree of local heterogeneity and global imbalance ratio. + +In Figure 2, we summarize the performance gap between two query models depending on the local heterogeneity level (indicated by different shapes) and the global imbalance ratio (increased along x-axis). The y-axis represents + +the gap of the winning rate in Eq.(6) between global and local-only models; thus, the value becomes positive up to $+1$ if the global model beats the local-only model, otherwise negative up to -1. At a glance, there is a clear and consistent superiority of two query models according to $\alpha$ and $\rho$ , where the dominance has intensified toward both extremes (e.g., upper right and lower left). This observation contradicts the previous findings that the global model has always outperformed the local-only model as the query selector in a FAL framework [4]. We provide more in-depth analysis in following Obs. 2 and Obs. 3. + +Observation 2. As local heterogeneity increases $(\alpha \downarrow)$ , a local-only query selector is preferred due to the increased significance of local inter-class diversity. + +As the collapse of the local inter-class balance (i.e., lower $\alpha$ ) incurs severe performance degradation due to a weight divergence [11, 31], addressing local imbalance can improve the learning stability and performance. Since the local-only models are separately trained on each client, in general, the local-only model has shown higher confidence for its own data distribution than the global model [9, 33]. In Figure 3, we visualized the number of class instances and the class-wise test accuracy in the first AL round (see the caption for details). Specifically, we confirmed a high correlation between counts and accuracy in Figure 3-(a), such that the local-only models have higher accuracy than the global model for major classes of their data distribution. Thus, by the nature of favoring low-confident instances in AL, the local-only model tends to select the instances with local minority classes as the query. + +More precisely, we verify that the local-only model indeed queries the locally balanced set using earth mover's distance (EMD) [46]. In Table 2, local EMD measures the mean of distance between class distribution of local query sets and a uniform distribution. The lower the value, the more balanced the locally queried instances. As shown in Table 2-(a) with high local heterogeneity, the local EMD of the local-only model (L) is lower than that of the global model (G). That is, the local-only model queries more diverse instances than the global model with respect to the local inter-class diversity. + +Meanwhile, in the case of (b), the global model, trained with more samples, has higher accuracy over the classes due to little distribution discrepancy. Although the more accurate model is likely to have the higher prediction confidence, it does not mean that it is better at identifying the required instances based on the current local dataset, which the global model had not directly learned. In practice, the local-only model still chose the more locally balanced query set (Table 2-(b)), and we supposed this contradiction makes no sizeable winning gap of the case (b) in Figure 2. + +![](images/96d4bf458b987618e31012b91c5860d71e9f254853092a1bec52a6ed7efb978c.jpg) +of Instances + +![](images/ca903081aebeabdc0c09f93e521ec24ef5cda3b9e4c18fe0680d5554a8aa4f17.jpg) +Test Accuracy + +![](images/cfdd2df35d45c57a95a2d0f6715fa63b16deb0ec4cbfdd9dd4489302070ec52f.jpg) +(a) Low global imbalance $(\rho = 1)$ and high heterogeneity $(\alpha = 0.1)$ . + +![](images/0143fb442e7822b2f21b43ae8aaf24b43800d7257c5382d8d9faa84e334e0432.jpg) +(c) High global imbalance $(\rho = 20)$ and high heterogeneity $(\alpha = 0.1)$ . + +![](images/e6d2ae38b9a04d93322635e7cff4044da928ecfe46307031d8dffeac80502f52.jpg) +of Instances + +![](images/3810551e75fde1b3a63bf1edf63e0baebf637d231141bb36e14591639bf79b17.jpg) +Test Accuracy + +![](images/099aa6526cee49d3ee96bfd1dfe1ab957a1dd3f13eed194289dda4660c32df5b.jpg) +(d) High global imbalance $(\rho = 20)$ and low heterogeneity $(\alpha = \infty)$ . +Figure 3. Matrices of data count (left) and class-wise accuracy (right) for CIFAR-10, with four combinations of $\rho = \{1,20\}$ and $\alpha = \{0.1,\infty\}$ . k1-10 denote ten clients, c1-10 are ten classes of CIFAR-10. There are two types of data counts, # of per-client local instances (1-10th rows) and aggregated instances over all clients (the last row). Similarly, the test accuracy is measured with local-only models (1-10th rows) and a global model (the last row). (a)-(d) setups correspond to those of Figure 2. See Appendix B.1 for the more cases. + +![](images/f498ac60f4e0bce0ab99389e8a5f0c9f11f6892835a979d0f588a360fa657470.jpg) +(b) Low global imbalance $(\rho = 1)$ and low heterogeneity $(\alpha = \infty)$ . + +
CaseModelObs. 2: Local EMD (↓)Obs. 3: Global EMD (↓)
10%20%30%40%10%20%30%40%
(a)G0.6320.6380.6410.6430.0190.0640.0860.095
L0.6320.5970.5920.5950.0190.0500.0500.046
(b)G0.0490.0770.0700.0840.0140.0700.0660.063
L0.0490.0420.0540.0590.0140.0250.0440.053
(c)G0.6920.6800.6760.6740.3770.3000.2940.294
L0.6920.6410.6330.6360.3770.3340.3260.321
(d)G0.3710.2980.2840.2740.3680.2940.2820.272
L0.3710.3130.2930.2900.3680.3090.2870.288
+ +Table 2. Local EMD and global EMD on CIFAR-10. We summarize the results of four AL rounds with the labeling budget of $10\%$ per round. (a)-(d) setups correspond to those of Figure 2. See Appendix B.2 for EMDs of more cases. + +Observation 3. As the degree of global class imbalance increases ( $\rho \uparrow$ ), it is more advantageous to exploit a global model that alleviates the global class imbalance. + +Based on Obs. 2, the local-only model should outperform the global model in the case (c), but there is no clear superiority between them with respect to the winning rate in the case (c) of Figure 2. The only answer for this conundrum is the presence of global minority classes due to the high global imbalance ratio. The local heterogeneity is obviously a crucial factor by Obs. 2, but global class imbalance is also another factor that significantly degrades the classification + +performance in the FAL framework. Here, the major challenge is that neither the central server nor local clients cannot access any information of aggregated data due to privacy preservation. The only way to address this problem, we should utilize the global model that implicitly learns the knowledge of the entire data distribution through the aggregation phase in Eq. (4). + +We introduce an additional global EMD, the indicator of measuring the inter-class diversity of the aggregated queried set over all clients. As can be seen in Table 2-(c), where the global imbalance ratio is high, we confirm that the global query selector (G) favors to query global minority classes. The global EMD of the global model is lower than that of the local-only model, i.e. the more globally balanced query set, but the local EMD is the opposite. + +Meanwhile, in the case of (d), the minority classes are always the same from the global and local perspectives. It is different from the case (b), where the minority classes with respect to the accuracy differ in each client depending on the informativeness of instances despite the same instance number. Therefore, in this scenario, the global model has high confidence even in local datasets, leading to significantly overwhelming the local-only model in the case (d) of Figure 2. In conclusion, the global inter-class diversity is an essential factor when global imbalance exists. + +# 5. Method + +From three observations in Section 4, we confirmed that FAL framework requires delicate consideration of local and global inter-class diversity. However, since clients are reluctant to share their data information, we should simultaneously utilize local-only and global models to ensure both sides of inter-class diversity. To this end, we propose a novel query sample strategy, named LoGo, that composed of macro and micro steps. Pseudo algorithm for LoGo is provided in Appendix C. Before describing details of each step, let us assume a scenario where $k$ -th client queries $B$ unlabeled instances at the round of $r$ . + +# Macro Step: Clustering with Local-Only Model. + +The ultimate goal of macro step is to satisfy local interclass diversity by primarily sampling the informative instances by the local-only model. In detail, we introduce $k$ -means clustering [30] on the hypothetical gradient embedding. Let $z$ be the embedding vector before forwarding to the last layer $W$ for $x \in U_k^r$ . Here, we utilize the gradient of negative cross-entropy loss, induced by a pseudo label, with respect to the last layer of encoder as follows: + +$$ +g _ {c} ^ {x} = - \frac {\partial}{\partial W _ {c}} \ell_ {C E} (x, \hat {y}; \Theta_ {k *} ^ {r}) = z \cdot \left(\mathbb {1} _ {[ \hat {y} = c ]} - p _ {c}\right), \tag {7} +$$ + +where $\hat{y} = \arg \max_{c\in [C]}p_c$ and $W_{c}$ is the weights connected to $c$ -th neuron of logits. Gradient embedding is widely used in conventional AL algorithm [6, 40], and we consider only the gradients corresponding to the pseudo label (i.e., $g_{\hat{y}}^x$ ) for computation efficiency. + +Then, we calculate $B$ number of centroids on the hallucinated gradient space via EM algorithm [10] of $k$ -means clustering by minimizing + +$$ +J = \sum_ {i = 1} ^ {N} \sum_ {b = 1} ^ {B} w _ {i b} \| g _ {\hat {y}} ^ {x _ {i}} - \mu_ {b} \| ^ {2}, \tag {8} +$$ + +where $w_{ib}$ is an indicator function whether $g_{\hat{y}}^{x_i}$ is assigned to $\mu_b$ for E-step. Eq. (7) shows that the gradient embedding is a just scaling of feature embedding $z$ , especially with the scale of uncertainty. In other words, if an instance is uncertain to predict (low value of $p_{\hat{y}}$ ), its gradient will be much highly scaled. In this sense, Eq. (8) can be regarded as a weighted $k$ -means clustering [13,39] on the feature embedding space by using the function of softmax response [17]. Hence, the macro step of LoGo enable the query set to contain both diversity in the embedding space and uncertainty from the perspective of local-only model. + +# Micro Step: Cluster-wise Sampling with Global Model. + +In micro step, the global model selects the final instances that results in the higher global inter-class diversity. Given $B$ selected instances from the macro step, the most uncertain instance is selected for each cluster: + +$$ +L _ {k} ^ {r} = \left\{\mathcal {A} \left(\mathcal {C} _ {1}, \Theta^ {r *}, 1\right), \dots , \mathcal {A} \left(\mathcal {C} _ {B}, \Theta^ {r *}, 1\right) \right\} \tag {9} +$$ + +$C_b$ denotes $b$ -th cluster, generated by the query set from the macro step. We simply used Entropy sampling for $\mathcal{A}$ , but we should note that $\mathcal{A}$ can be any AL sampling strategy. + +The cluster-wise sampling in the micro step is a simple yet effective strategy to leverage the advantages of both query selector models, ensuring local and global inter-class diversity. Here, we discuss how LoGo can be a promising sampling strategy for the FAL framework. + +Remark 1. The micro step is same with one step of EM algorithm. We first update cluster assignments with $B$ number of centroids from the macro step (E-step). Then, within each cluster, we select the most informative instance based on the uncertainty score. This can be regarded as one $M$ -step of the weighted $k$ -means clustering, using infinitely scaled weight function of uncertainty measure. + +Then, let $c_{b}$ be a centroid of $C_{b}$ and we define $M$ as follows: + +$$ +M = \sum_ {b = 1} ^ {B} \| c _ {b} - \tilde {x} _ {b} \| ^ {2}, \text {w h e r e} \tilde {x} _ {b} = \arg \min _ {x} \| c _ {b} - x \| ^ {2} \tag {10} +$$ + +where $x \in L_k^r$ (Eq. (9)) and $\tilde{x}$ is one-to-one mapping with the minimal transport cost. The lower value of $M$ means that the final query set much consider the diversity in the macro step. + +Remark 2. EM-based sampling in the micro step guarantees the diversity information of the macro step. Through sampling one instance per cluster, each $\tilde{x}_b$ is disjointly assigned to one cluster. Therefore, LoGo conservatively ensures the local inter-class diversity from the macro step (i.e., lower $M$ value), comparing to any other strategy that query at least two instances for one cluster. + +# 6. Evaluation + +# 6.1. Experimental Configuration + +Training Settings. In a FAL framework, a central server should carefully consider the fairness of labeling and training costs between clients. Therefore, we assume that ten clients have the same size of unlabeled data pool and query the same number of instances per every AL round. Moreover, we focus on a cross-silo FL setting [22] where every client participates in every FL round. + +We compared LoGo with six active learning strategies on five benchmark dataset (CIFAR-10 [24], SVHN [32], PathMNIST, DermaMNIST, and OrganAMNIST [45]). We considered 38 comprehensive experimental settings combined into six categories (see Figure 4). Except for learning ablations of the architectures, labeling budgets, and initialization schemes, in default, we implemented four layers of CNN and trained the encoder from scratch with the labeling budget of $5\%$ for every AL round. We repeat all experiments four times and report their averaged values. Refer to Appendix D for detailed experimental settings. + +![](images/519afe232a9676d425d82dcb8033d8516799dc74d93d9455e300b7e64bda262a.jpg) +Figure 4. Winning percentage across six categories. We also added defeat percentage, the black hatched bar that represents the percentage at which LoGo has been defeated by each baseline. Among total experiments, only statistically reliable values ( $t$ -score $>2.776$ ) are considered. Thus, the lower value of the colored bar and the higher value of the black bar indicate a more comparable baseline. + +![](images/2556a42832e40d2c8dbf5d254cce44fae73794a3b5e8d7e82f254b80f8df9eea.jpg) +Figure 5. Pairwise penalty matrix over 38 experimental settings. The value $P_{ij}$ indicates the number of times that the $i$ -th strategy outperforms the $j$ -th strategy (i.e., sum of win $^{ij}$ in Eq.(6) over 38 settings). The last row is the average number of times the $j$ -th strategy is defeated by the rest strategies; the lower, the better. + +Baselines. We considered six standard AL strategies. Random randomly samples the instances from the unlabeled pool. Entropy selects instances with the largest entropy [41]. CoreSet chooses the small subset that can represent the whole unlabeled set [37]. BADGE selects the diverse points with high magnitude in a hallucinated gradient space [6]. GCNAL adapts CoreSet on a sequential graph convolution network to measure the relation between labeled and unlabeled instances [8]. ALFA-Mix identifies the valuable instances by seeking inconsistencies in the prediction of mixing features [34]. We adopt these sampling strategies with either the global model or local-only model in FedAvg pipeline. Refer to Appendix E for the comparison of query selection cost. Besides, we summarized the results with various FL methods in Appendix F. + +# 6.2. Overall Comparison + +# 6.2.1 Pairwise Penalty Matrix + +We summarized the overall comparison results as a pairwise penalty matrix $P$ in Figure 5, following the recent + +work [6, 34]. Each cell of the pairwise penalty matrix represents the summation of the winning rate of Eq. (6) calculated above for each of the 38 experimental sets. As the rows of the matrix $P_{i}$ indicate how many times $i$ -th algorithm outperforms the other algorithms, the brighter color means the better algorithm (conversely, the darker columns are the better). Note that we only considered statistically reliable results throughout the two-sided t-test. + +LoGo defeats all baselines in general (see 7-th row values) while under-performed only 0.9 out of 38 times on average (see 7-th column values in the last row). In particular, LoGo outperforms BADGE and Entropy sampling, which are top-2 baselines, with 13.7 and 12.0 out of 38 times, while LoGo only loses 2.4 and 1.9 out of 38 times, respectively. This results demonstrate the robust effectiveness of our LoGo algorithm in various experimental settings. + +# 6.2.2 Winning Rate Bar Plots + +Figure 4 summarizes the comparison results according to the six categories, which is the breakdown of Figure 5 on a more systematic categorization. For example, the colored bar of the overall category is calculated by dividing the total setting number of 38 in the 7-th row vector of Figure 5 (the black bar is from the 7-th column vector). The colored bar represents the average percentage at which LoGo defeats each baseline algorithm, and the higher bar means that LoGo has won more. Appendix G.1 provides the detailed comparison penalty values according to each category. + +Overall, LoGo consistently shows an overwhelming winning percentage toward any baseline against the defeat percentage. Interestingly, ALFA-Mix, the latest AL strategy, shows performance considerably varying depending on which query selector is selected (see the query selector in Figure 4). The reason would be that a local-only model, which is separately trained on the highly heterogeneous dataset, is not appropriate for the feature mixing or the sensitivity to lots of hyperparameters. Moreover, Coreset, which does not consider uncertainty, cannot resolve the local and global imbalance, showing similar performance as Random sampling. Thus, LoGo is a superior algorithm for a FAL framework in that it is robust to the type of query selector or most combinations of experimental settings. + +
MethodModelCIFAR-10SVHNPathMNISTDermaMNIST
20%40%60%80%20%30%40%50%20%30%40%50%20%30%40%50%
Random-64.1969.0771.6372.8180.9083.0784.2284.7768.4172.7073.7675.4971.7072.5772.6672.86
Entropy [41]G64.0269.1271.8773.3382.0884.6185.8886.3171.5474.3975.9176.6572.4972.6373.0273.20
L66.2971.4573.5174.0282.0984.5885.6986.1876.5278.2978.7179.1071.3872.0472.2272.65
Coreset [37]G64.6669.4371.7573.180.9482.7483.8184.4674.8476.2476.8576.8072.0272.1672.3472.74
L64.0668.7971.4973.2880.9482.9283.7884.4872.5376.0676.2876.8671.1371.4872.1572.38
BADGE [6]G65.1269.5772.1173.5382.8184.8285.8986.272.2174.3875.5376.9772.5973.0973.2373.45
L66.3271.2873.4174.2882.6984.6785.6186.176.4878.5178.4278.6871.3572.1372.2572.99
GCNAL [8]G65.4070.0572.4173.4282.0584.0785.0985.6175.5177.7978.1378.8172.0172.6073.0773.17
L65.6270.1872.3673.4281.9283.5884.5585.1074.8576.4677.1877.4571.9572.9172.9173.29
ALFA-Mix [34]G65.4569.8772.2473.2983.0284.9986.0586.3373.3474.8376.3177.4372.3973.1473.2773.10
L64.1468.7971.0372.681.0882.5583.6284.3371.1075.0175.8176.7071.5172.1872.9473.28
LoGo (ours)G,L66.5071.7073.8074.4983.4685.3186.0286.3876.3278.7279.5179.5872.6173.1873.3373.77
+ +# 6.2.3 Under Query Selector Category + +Table 3 shows the test accuracy according to the increased labeling budgets over rounds on four datasets. Even with the same active learning strategy, a gap in test accuracy occurs depending on which query selector is used because the global imbalance varies by 1.0–58.7 across datasets. For example, in general, global models outperform local-only models for SVHN and DermaMNIST, while the opposite trend is observed for CIFAR-10 and PathMNIST. However, irrespective of the benchmarks and querying model types, our LoGo shows the best performance in most cases. Two-step selection strategy enables LoGo to be robust by utilizing both the benefits of global and local-only models. Because we cannot know the degree of local and global imbalance in advance, our proposed method has a strong advantage in providing data-agnostic performance improvements over all baselines. Appendix G.2 provides a detailed performance comparison between LoGo and baselines under various experimental settings. + +# 6.3. LoGo vs. Simple Ensemble + +To prove that LoGo is an effective way to leverage the advantages of both models, we compared LoGo with three naive implementation of ensemble methods for global and local-only models: (1) the average of logits (for Entropy sampling) or gradient embedding (for BADGE) from two models, (2) weighing the instances based on the selection ranks (i.e., more weights if it is selected from both models), and (3) fine-tuning the global model on local datasets. + +In Table 4, LoGo consistently shows better classification accuracy over increasing labeling budgets than three counterparts. Compared with the results in both Tables 3 and 4, all three ensemble methods show lower performance than using a single superior query selector. That is, the naive ensemble suffers from a performance trade-off between two + +Table 3. Comparison of test accuracy on four benchmarks with $\alpha = 0.1$ . We reported the results with four random seeds. The baselines, except for Random sampling, are combined with two query selector models, $G$ and $L$ that stands for a global or local-only model, respectively. **Bold and underline mean Top-1 and Top-2**, respectively. + +
MethodStrategyCIFAR-10SVHN
20%40%60%80%20%30%40%
Ens. Logit+Entropy64.5370.3673.0274.2881.8184.6485.87
+BADGE65.5570.3172.8373.9782.7784.7685.90
Ens. Rank+Entropy65.9070.9273.3474.2082.1584.3885.64
+BADGE66.2170.9873.1574.0183.0285.0585.86
Fine-tuning+Entropy65.1070.7573.2174.2382.5385.0586.01
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+ +Table 4. Comparison of test accuracy on two benchmarks $(\alpha = 0.1)$ with baselines using both global and local information. + +query selector models and, therefore, their results fall somewhere in the middle of using global and local models. + +# 7. Conclusion + +We discovered the superiority of the two query selectors according to the local heterogeneity level and global imbalance ratio. Based on our findings, the local-only and global models are both crucial since global and local inter-class diversity affects their performance dominance. To this end, we propose LoGo algorithm that incorporates local-only and global models into macro and micro steps of cluster-based active learning. LoGo preferentially selects samples that simultaneously alleviate local and global imbalance as a query, making it robust to local and global imbalance. Our experiments verified that LoGo consistently outperforms six baselines under comprehensive settings of 38 combinations using six categories. + +Acknowledgement. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration). + +# References + +[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263, 2021. 1, 2 +[2] Sharat Agarwal, Himanshu Arora, Saket Anand, and Chetan Arora. Contextual diversity for active learning. In ECCV, pages 137-153, 2020. 3 +[3] Lulwa Ahmed, Kashif Ahmad, Naina Said, Basheer Qolomany, Junaid Qadir, and Ala Al-Fuqaha. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1We use the term inter-class diversity interchangeably with class balance throughout the paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*equal contribution" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 703, + 135, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 59, + 703, + 135, + 713 + ], + "type": "text", + "content": " corresponding authors" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3944" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 289, + 217 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 289, + 217 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 289, + 217 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 289, + 217 + ], + "type": "image", + "image_path": "6c5bd360ef6f5cc219fc361d220fac0de4f974b0533bd8cad8b6e6fcf3ea6686.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 218, + 256, + 228 + ], + "lines": [ + { + "bbox": [ + 104, + 218, + 256, + 228 + ], + "spans": [ + { + "bbox": [ + 104, + 218, + 256, + 228 + ], + "type": "text", + "content": "(a) Federated Active Learning framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 301, + 78, + 512, + 213 + ], + "blocks": [ + { + "bbox": [ + 301, + 78, + 512, + 213 + ], + "lines": [ + { + "bbox": [ + 301, + 78, + 512, + 213 + ], + "spans": [ + { + "bbox": [ + 301, + 78, + 512, + 213 + ], + "type": "image", + "image_path": "2442e7078b55853afe6d550e68f031f06fd531ee22e100e0477beed69f4f464a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 338, + 217, + 482, + 228 + ], + "lines": [ + { + "bbox": [ + 338, + 217, + 482, + 228 + ], + "spans": [ + { + "bbox": [ + 338, + 217, + 482, + 228 + ], + "type": "text", + "content": "(b) Superiority change of query selector." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 233, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 545, + 278 + ], + "type": "text", + "content": "Figure 1. Motivation: (a) The red and green lines correspond to the conventional FL and AL framework. We focus on a sampling strategy for FAL (green box) with the considerations of hierarchy structure and two available query-selecting models. (b) For a fixed querying strategy (Entropy sampling), the performance gap occurs only by changing the query selector. The y-axis is the gap in the winning rate in total active rounds (refer to Section 4). Closer to 1 indicates that global models outperforms than local-only models, and -1 is the opposite." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "text", + "content": "In a real FAL scenario, the superiority of two query models for a given dataset cannot be known in advance due to privacy preservation. Therefore, as our second contribution, we design a simple yet effective FAL querying approach, LoGo, that simultaneously leverages local-only and global models, to be robust to varying heterogeneity levels and global imbalance ratios. LoGo is a clustering-based sampling strategy, which is composed of macro and micro step exploiting local-only and global models, respectively. The rationale behind our method is that the optimal querying policy needs to evaluate the informativeness of instances with both models, which implicitly learn local and global data distribution, respectively. In a macro step, to improve the local inter-class diversity first, we perform " + }, + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "text", + "content": "-means clustering [30] in hallucinated gradient space generated from local-only models. Then, in a micro step, the final query set is determined via one step of the EM algorithm [10], making cluster boundaries using instances from macro step (E-step) and cluster-wise sampling with the global model (M-step). The proposed cluster-wise sampling conservatively guarantees the diversity information of the macro step, i.e., the local inter-class diversity obtained by local-only models, while also considering the global minority classes via the global model. " + }, + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 46, + 294, + 287, + 581 + ], + "type": "text", + "content": " See Section 5" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "As our third contribution, we conduct a total number of 38 experiments on five datasets using seven AL strategies including our LoGo algorithm. To verify the superiority of our method in real-world scenarios, we build comprehensive combinations of six categories, including query selector types (local-only vs. global models), local heterogeneity levels " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha \\in [0.1,\\infty))" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": ", global imbalance ratios " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\rho \\in [1,58])" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": ", model architectures, budget sizes, and model initialization scheme. As a result, the experimental results empirically prove our three observations (Obs. 1-3). Besides, our method outperforms all other AL baselines and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 294, + 544, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 294, + 544, + 318 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 544, + 318 + ], + "type": "text", + "content": "naive implementations for an ensemble of two query selectors in extensive experimental settings. " + }, + { + "bbox": [ + 306, + 294, + 544, + 318 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 306, + 294, + 544, + 318 + ], + "type": "text", + "content": " See Section 6" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 328, + 392, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 328, + 392, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 328, + 392, + 340 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 348, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 552 + ], + "type": "text", + "content": "Federated Learning is a collaborative learning framework with multiple clients while maintaining the privacy of each client dataset. In this decentralized framework, FedAvg [31] is considered a de facto algorithm in which a server and clients communicate only model parameters efficiently. One of the main bottlenecks for FL is the statistical heterogeneity problem across the clients' dataset, as the weight divergence from heterogeneous distributions hinders convergence during the aggregation scheme. Hence, several algorithms have tackled the local heterogeneity through the alignment between the local-updated gradient and the aggregated gradient, as a form of correction term [15, 23], regularization loss [1, 28], or distillation-based loss [25, 26]. Furthermore, there are existing literature to alleviate the class imbalance on the local side and they eventually achieve the global balance via rebalancing datasets [11] or a weighted loss function with a monitoring scheme [43]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "content": "Active Learning minimizes the labeling effort by querying the most informative instances from the unlabeled data pool. There are three major types of active learning strategies, namely uncertainty-based sampling, diversity-based sampling, and hybrid strategy. Uncertainty-based sampling queries the most uncertain instances that lie on the current decision boundary [12,14,35,41], while diversity-based sampling selects a set of unlabeled instances that represents the entire unlabeled data distribution [16, 37]. Recently, hybrid strategies simultaneously consider both uncertainty and diversity. BADGE [6] utilized the gradient embedding as the uncertainty measure and selected the diverse query set by a " + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "content": "-means++ initialization scheme [5]. Several hybrid" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3945" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 289, + 231 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 231 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 231 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 231 + ], + "type": "table", + "html": "
Indices:
cIndex for a class (c ∈ {1, ..., C})
rIndex for AL round (r ∈ {1, ..., R} = [R])
kIndex for a client (k ∈ {1, ..., K} = [K])
Parameters:
BLabeling budget for each AL round r
αLocal heterogeneity level
ρGlobal imbalance ratio
Data:
Uk^rPool of unlabeled instances for a client k at round r
Lk^rA queried instance set from Uk^r at round r
Dk^rAn available labeled set at round r
Weights:
Θr*Aggregated weights via FL phases on Dr^r (global model)
Θk*Separately optimized weights on Dk^r (local-only model)
", + "image_path": "f88fcc06e594659f2341c7f181d81acd5edb9b31236d920f9031e72865d73413.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 234, + 264, + 245 + ], + "lines": [ + { + "bbox": [ + 70, + 234, + 264, + 245 + ], + "spans": [ + { + "bbox": [ + 70, + 234, + 264, + 245 + ], + "type": "text", + "content": "Table 1. Summary of notations throughout the paper." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 258, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 331 + ], + "type": "text", + "content": "AL methods are based on a submodular data subset selection [44], pairwise contextual diversity [2], or feature mixing [34]. In addition to the three categories, model-based strategies have also been recently proposed to train additional networks for query selection, such as a VAE and discriminator [38] or a sequential graph neural network [8]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "content": "Federated Active Learning has been recently studied to address a more realistic scenario, where clients have lots of the unlabeled instances [20, 47, 48]. However, previous works [3, 4] have not deeply discussed the challenges of FAL framework and naively applied existing AL strategies. Ahn et al. [4] have even considered the local-only query selector, but concluded that the global model is superior to the local-only model with limited experimental settings, three benchmarks and one heterogeneity level. In this work, we observe the counterparts in varying benchmarks and heterogeneity levels, which motivates us to design a novel sampling strategy by exploiting both global and local-only models. Our extensive analysis and experimental results encourage future research on the FAL problem." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 511, + 125, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 125, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 125, + 525 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": "AL Procedure. For the ease of understanding, we summarize notations in Table 1. At the first AL round (i.e., " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "r = 1" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": "), each client " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": " randomly selects " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": " instances, " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "L_{k}^{1} = \\{x_{1},\\ldots ,x_{B}\\}" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": ", from " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "U_{k}^{1}" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": ", and oracles annotate them to obtain the initial labeled set " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "D_{k}^{1} = \\{(x_{1},y_{1}),\\ldots ,(x_{B},y_{B})\\}" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": ". For the next round (" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "r\\geq 2" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": "), based on the given querying strategy " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": " and the model parameters " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": ", the query set of the " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": "-th client at round " + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": " is sampled by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 633, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 633, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 59, + 633, + 287, + 649 + ], + "type": "interline_equation", + "content": "L _ {k} ^ {r} = \\mathcal {A} \\left(U _ {k} ^ {r}, \\Theta , B\\right), \\text {w h e r e} U _ {k} ^ {r} = U _ {k} ^ {r - 1} \\backslash L _ {k} ^ {r - 1}. \\tag {1}", + "image_path": "844d75da7b26538faed6d6ab952d116d11e33853c5ffce26fa9c13f48a27a524.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": "The querying function " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": " in Eq. (1) depends on which AL algorithm is used. For example, Entropy sampling [41] queries the instances with the highest uncertainty like:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 71, + 694, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 694, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 71, + 694, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (U, \\Theta , B) = \\underset {x _ {i} \\in L, | L | = B, L \\subseteq U} {\\arg \\max } H (p (y | x _ {i}; \\Theta)) \\tag {2}", + "image_path": "9b69fd955d9b3898cc8d3abf595b85644d3aeff2a7b7e95bce72c8ce53e5ea82.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "inline_equation", + "content": "H(p) = -\\sum_{c=1}^{C} p_c \\ln p_c" + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "text", + "content": " is the predictive probability. The query set is annotated by the oracle and assembled to expand the available labeled set, i.e., " + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "inline_equation", + "content": "D_k^r = D_k^{r-1} \\cup \\{(x_i, y_i) | x_i \\in L_k^r\\}" + }, + { + "bbox": [ + 305, + 71, + 547, + 122 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "spans": [ + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "text", + "content": "FL Procedure. After each AL round, we perform the FL procedure of which the objective is to obtain the optimal parameter " + }, + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "inline_equation", + "content": "\\Theta^{r*}" + }, + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "text", + "content": " such that it minimizes the target loss on the given labeled set for all clients, " + }, + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "inline_equation", + "content": "D^{r} = \\cup_{k=1}^{K} D_{k}^{r}" + }, + { + "bbox": [ + 305, + 132, + 547, + 181 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 189, + 546, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 189, + 546, + 223 + ], + "spans": [ + { + "bbox": [ + 315, + 189, + 546, + 223 + ], + "type": "interline_equation", + "content": "\\Theta^ {r *} = \\underset {\\Theta} {\\arg \\min } f \\left(\\Theta^ {r}\\right) = \\underset {\\Theta} {\\arg \\min } \\frac {1}{| D ^ {r} |} \\sum_ {i = 1} ^ {| D ^ {r} |} f _ {i} \\left(\\Theta^ {r}\\right) \\tag {3}", + "image_path": "02c5bc015719f19c38ef894322cbebd610e6bdd0a0bc067d5efac425bad3581b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "inline_equation", + "content": "f_{i}(\\Theta) = \\ell (x_{i},y_{i};\\Theta)" + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "inline_equation", + "content": "\\ell (\\cdot)" + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "text", + "content": " is the loss function determined by the network parameter " + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 231, + 546, + 278 + ], + "type": "text", + "content": ". However, due to data privacy, the global model is optimized based on the reformulated update rule on the partitioned data over clients:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 369, + 287, + 482, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 287, + 482, + 319 + ], + "spans": [ + { + "bbox": [ + 369, + 287, + 482, + 319 + ], + "type": "interline_equation", + "content": "f (\\Theta^ {r}) = \\sum_ {k = 1} ^ {K} \\frac {| D _ {k} ^ {r} |}{| D ^ {r} |} F (\\Theta_ {k} ^ {r}),", + "image_path": "31982371e3c5b014d3e3decaffe584c26a08bbc1731a69a1a111e3944f2868b5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 332, + 321, + 546, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 321, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 332, + 321, + 546, + 353 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} F \\left(\\Theta_ {k} ^ {r}\\right) = \\frac {1}{\\left| D _ {k} ^ {r} \\right|} \\sum_ {\\left(x _ {i}, y _ {i}\\right) \\in D _ {k} ^ {r}} \\ell \\left(x _ {i}, y _ {i}; \\Theta_ {k} ^ {r}\\right). \\tag {4}", + "image_path": "581c060f52e110514feac58a82b50165b94f1bcfff03300bbc08727c1aaae4ed.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "text", + "content": "The model " + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\Theta_k^r" + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "text", + "content": " is updated locally on the client side for its local data " + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "inline_equation", + "content": "D_k^r" + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "text", + "content": ", and then it is aggregated globally to generate a global model " + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\Theta^r" + }, + { + "bbox": [ + 304, + 360, + 545, + 432 + ], + "type": "text", + "content": ". The local update and model aggregation steps are alternated until the global model converges; this corresponds to the most popular FL training pipeline, FedAvg proposed by [31]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "content": "The previous studies [3, 4] have typically used the converged global model " + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\Theta^{r*}" + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "content": " in the next AL round as the query selector of Eq. (2). However, considering the hierarchy structure in the FAL framework, it is also possible to use a separately optimized model on local partitioned data; replacing " + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "inline_equation", + "content": "D^r" + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "inline_equation", + "content": "D_k^r" + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "content": " in Eq. (3). It is often referred to as the local-only model [9, 33], and we denote it as " + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\Theta_{k}^{r*}" + }, + { + "bbox": [ + 304, + 432, + 546, + 540 + ], + "type": "text", + "content": ". In the following section, we investigate what these models are specialized in and when they are beneficial to use." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 550, + 453, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 550, + 453, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 550, + 453, + 563 + ], + "type": "text", + "content": "4. Observation and Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "In this section, we analyze the performance trend between global and local-only models as the query selector, with respect to the degree of class imbalance in local and global data distribution. We synthetically adjust two indicators of inter-class diversity, " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\{0.1, 1.0, \\infty\\}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\rho \\in \\{1, 5, 10, 20\\}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", on CIFAR-10 benchmark. As " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " get lower and higher, the levels of local heterogeneity and global imbalance increase, respectively (refer to Appendix A for the detailed data distribution). For both query selectors, we use Entropy sampling [41] as an active learning algorithm, and the training set is progressively labeled with the query ratio of " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " in each AL round." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3946" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 74, + 270, + 201 + ], + "blocks": [ + { + "bbox": [ + 56, + 74, + 270, + 201 + ], + "lines": [ + { + "bbox": [ + 56, + 74, + 270, + 201 + ], + "spans": [ + { + "bbox": [ + 56, + 74, + 270, + 201 + ], + "type": "image", + "image_path": "c6426a9f88fb96837819920e8d173831f06ffb72c1a3d112ccc2741ecd048e1b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "type": "text", + "content": "Figure 2. Gap between the winning rate of global and local-only models by varying global imbalance ratio " + }, + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "type": "text", + "content": " and local heterogeneity " + }, + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "type": "inline_equation", + "content": "(\\alpha)" + }, + { + "bbox": [ + 46, + 204, + 289, + 249 + ], + "type": "text", + "content": " on CIFAR-10 benchmark. The experimental setups for (a)-(d) are also compatible with Figure 3 and Table 2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": "Comparison Metric. We evaluate the superiority over AL rounds through pairwise comparison [6, 34], widely used in conventional AL literature. We repeat each experimental setup, a pair of " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": ", with four different seeds and obtain a set of four accuracy results " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "a_{r} = \\{a_{r,1}, \\ldots, a_{r,4}\\}" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": " at each round " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": ". Then, we conduct a two-sided t-test, where " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": "-score is defined by Definition 1 for two given strategies " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 265, + 289, + 373 + ], + "type": "text", + "content": ". Note that the strategy denotes the combination of the sampling strategy and the type of query selector." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": "Definition 1. [36] Let " + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "inline_equation", + "content": "a_r^i" + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "inline_equation", + "content": "a_r^j" + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": " be the set of accuracies for two different FAL strategies " + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": ". Then, t-score at AL round " + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 380, + 288, + 416 + ], + "type": "text", + "content": " is formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 73, + 425, + 287, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 425, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 73, + 425, + 287, + 467 + ], + "type": "interline_equation", + "content": "t _ {r} ^ {i j} = \\frac {\\sqrt {4} \\mu_ {r} ^ {i j}}{\\sigma_ {r} ^ {i j}}, \\text {w h e r e} \\mu_ {r} ^ {i j} = \\frac {1}{4} \\sum_ {l = 1} ^ {4} \\left(a _ {r, l} ^ {i} - a _ {r, l} ^ {j}\\right) \\tag {5}", + "image_path": "e63997b57f689df5dd58387cca2da462159fed53a41558e81f127d734c16bbdb.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 79, + 459, + 287, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 459, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 79, + 459, + 287, + 498 + ], + "type": "interline_equation", + "content": "\\text {a n d} \\sigma_ {r} ^ {i j} = \\sqrt {\\frac {1}{3} \\sum_ {l = 1} ^ {4} \\left(\\left(a _ {r , l} ^ {i} - a _ {r , l} ^ {j}\\right) - \\mu_ {r} ^ {i j}\\right)}. \\tag {5}", + "image_path": "e64e11d9b9bb1eb1e547352acadfa0e4162a384a86b39f4921ca2628aa0de588.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "text", + "content": "Here, the strategy " + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "text", + "content": " is considered to beat the strategy " + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "inline_equation", + "content": "t_r^{ij} > 2.776" + }, + { + "bbox": [ + 47, + 507, + 288, + 543 + ], + "type": "text", + "content": ". Therefore, the winning rate for all AL rounds is formulated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 550, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 550, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 113, + 550, + 287, + 583 + ], + "type": "interline_equation", + "content": "\\operatorname {w i n} ^ {i j} = \\sum_ {r = 1} ^ {R} \\frac {1}{R} \\mathbb {1} _ {t _ {r} ^ {i j} > 2. 7 7 6}. \\tag {6}", + "image_path": "1535287ddd15167d38a6db2b6f51b56a817ffc30c8479e3e49ce1d6bee9f46a7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "text", + "content": "The value of winning rate becomes 1 if the strategy " + }, + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "text", + "content": " beats the strategy " + }, + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 590, + 287, + 615 + ], + "type": "text", + "content": " over all AL rounds." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "content": "Observation 1. The superiority of local-only and global query-selecting models varies according to the degree of local heterogeneity and global imbalance ratio." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "In Figure 2, we summarize the performance gap between two query models depending on the local heterogeneity level (indicated by different shapes) and the global imbalance ratio (increased along x-axis). The y-axis represents" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": "the gap of the winning rate in Eq.(6) between global and local-only models; thus, the value becomes positive up to " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "+1" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " if the global model beats the local-only model, otherwise negative up to -1. At a glance, there is a clear and consistent superiority of two query models according to " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ", where the dominance has intensified toward both extremes (e.g., upper right and lower left). This observation contradicts the previous findings that the global model has always outperformed the local-only model as the query selector in a FAL framework [4]. We provide more in-depth analysis in following Obs. 2 and Obs. 3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 224, + 547, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 547, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 547, + 261 + ], + "type": "text", + "content": "Observation 2. As local heterogeneity increases " + }, + { + "bbox": [ + 305, + 224, + 547, + 261 + ], + "type": "inline_equation", + "content": "(\\alpha \\downarrow)" + }, + { + "bbox": [ + 305, + 224, + 547, + 261 + ], + "type": "text", + "content": ", a local-only query selector is preferred due to the increased significance of local inter-class diversity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 270, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 461 + ], + "type": "text", + "content": "As the collapse of the local inter-class balance (i.e., lower " + }, + { + "bbox": [ + 304, + 270, + 547, + 461 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 270, + 547, + 461 + ], + "type": "text", + "content": ") incurs severe performance degradation due to a weight divergence [11, 31], addressing local imbalance can improve the learning stability and performance. Since the local-only models are separately trained on each client, in general, the local-only model has shown higher confidence for its own data distribution than the global model [9, 33]. In Figure 3, we visualized the number of class instances and the class-wise test accuracy in the first AL round (see the caption for details). Specifically, we confirmed a high correlation between counts and accuracy in Figure 3-(a), such that the local-only models have higher accuracy than the global model for major classes of their data distribution. Thus, by the nature of favoring low-confident instances in AL, the local-only model tends to select the instances with local minority classes as the query." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 593 + ], + "type": "text", + "content": "More precisely, we verify that the local-only model indeed queries the locally balanced set using earth mover's distance (EMD) [46]. In Table 2, local EMD measures the mean of distance between class distribution of local query sets and a uniform distribution. The lower the value, the more balanced the locally queried instances. As shown in Table 2-(a) with high local heterogeneity, the local EMD of the local-only model (L) is lower than that of the global model (G). That is, the local-only model queries more diverse instances than the global model with respect to the local inter-class diversity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "Meanwhile, in the case of (b), the global model, trained with more samples, has higher accuracy over the classes due to little distribution discrepancy. Although the more accurate model is likely to have the higher prediction confidence, it does not mean that it is better at identifying the required instances based on the current local dataset, which the global model had not directly learned. In practice, the local-only model still chose the more locally balanced query set (Table 2-(b)), and we supposed this contradiction makes no sizeable winning gap of the case (b) in Figure 2." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3947" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 78, + 171, + 200 + ], + "blocks": [ + { + "bbox": [ + 99, + 70, + 140, + 77 + ], + "lines": [ + { + "bbox": [ + 99, + 70, + 140, + 77 + ], + "spans": [ + { + "bbox": [ + 99, + 70, + 140, + 77 + ], + "type": "text", + "content": "of Instances" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ 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Matrices of data count (left) and class-wise accuracy (right) for CIFAR-10, with four combinations of " + }, + { + "bbox": [ + 47, + 354, + 547, + 398 + ], + "type": "inline_equation", + "content": "\\rho = \\{1,20\\}" + }, + { + "bbox": [ + 47, + 354, + 547, + 398 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 354, + 547, + 398 + ], + "type": "inline_equation", + "content": "\\alpha = \\{0.1,\\infty\\}" + }, + { + "bbox": [ + 47, + 354, + 547, + 398 + ], + "type": "text", + "content": ". k1-10 denote ten clients, c1-10 are ten classes of CIFAR-10. There are two types of data counts, # of per-client local instances (1-10th rows) and aggregated instances over all clients (the last row). Similarly, the test accuracy is measured with local-only models (1-10th rows) and a global model (the last row). (a)-(d) setups correspond to those of Figure 2. See Appendix B.1 for the more cases." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 430, + 214, + 535, + 336 + ], + "blocks": [ + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "lines": [ + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "spans": [ + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "type": "text", + "content": "(b) Low global imbalance " + }, + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "type": "inline_equation", + "content": "(\\rho = 1)" + }, + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "type": "text", + "content": " and low heterogeneity " + }, + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "type": "inline_equation", + "content": "(\\alpha = \\infty)" + }, + { + "bbox": [ + 313, + 202, + 532, + 213 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 430, + 214, + 535, + 336 + ], + "lines": [ + { + "bbox": [ + 430, + 214, + 535, + 336 + ], + "spans": [ + { + "bbox": [ + 430, + 214, + 535, + 336 + ], + "type": "image", + "image_path": "f498ac60f4e0bce0ab99389e8a5f0c9f11f6892835a979d0f588a360fa657470.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 50, + 411, + 287, + 513 + ], + "blocks": [ + { + "bbox": [ + 50, + 411, + 287, + 513 + ], + "lines": [ + { + "bbox": [ + 50, + 411, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 50, + 411, + 287, + 513 + ], + "type": "table", + "html": "
CaseModelObs. 2: Local EMD (↓)Obs. 3: Global EMD (↓)
10%20%30%40%10%20%30%40%
(a)G0.6320.6380.6410.6430.0190.0640.0860.095
L0.6320.5970.5920.5950.0190.0500.0500.046
(b)G0.0490.0770.0700.0840.0140.0700.0660.063
L0.0490.0420.0540.0590.0140.0250.0440.053
(c)G0.6920.6800.6760.6740.3770.3000.2940.294
L0.6920.6410.6330.6360.3770.3340.3260.321
(d)G0.3710.2980.2840.2740.3680.2940.2820.272
L0.3710.3130.2930.2900.3680.3090.2870.288
", + "image_path": "906ab47f098d29b17fce67e9da1986af18eb369ffaaea85c160faf5c06929660.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 517, + 287, + 561 + ], + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 561 + ], + "type": "text", + "content": "Table 2. Local EMD and global EMD on CIFAR-10. We summarize the results of four AL rounds with the labeling budget of " + }, + { + "bbox": [ + 46, + 517, + 287, + 561 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 517, + 287, + 561 + ], + "type": "text", + "content": " per round. (a)-(d) setups correspond to those of Figure 2. See Appendix B.2 for EMDs of more cases." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": "Observation 3. As the degree of global class imbalance increases (" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\rho \\uparrow" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": "), it is more advantageous to exploit a global model that alleviates the global class imbalance." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Based on Obs. 2, the local-only model should outperform the global model in the case (c), but there is no clear superiority between them with respect to the winning rate in the case (c) of Figure 2. The only answer for this conundrum is the presence of global minority classes due to the high global imbalance ratio. The local heterogeneity is obviously a crucial factor by Obs. 2, but global class imbalance is also another factor that significantly degrades the classification" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 413, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 497 + ], + "type": "text", + "content": "performance in the FAL framework. Here, the major challenge is that neither the central server nor local clients cannot access any information of aggregated data due to privacy preservation. The only way to address this problem, we should utilize the global model that implicitly learns the knowledge of the entire data distribution through the aggregation phase in Eq. (4)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 498, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 593 + ], + "type": "text", + "content": "We introduce an additional global EMD, the indicator of measuring the inter-class diversity of the aggregated queried set over all clients. As can be seen in Table 2-(c), where the global imbalance ratio is high, we confirm that the global query selector (G) favors to query global minority classes. The global EMD of the global model is lower than that of the local-only model, i.e. the more globally balanced query set, but the local EMD is the opposite." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Meanwhile, in the case of (d), the minority classes are always the same from the global and local perspectives. It is different from the case (b), where the minority classes with respect to the accuracy differ in each client depending on the informativeness of instances despite the same instance number. Therefore, in this scenario, the global model has high confidence even in local datasets, leading to significantly overwhelming the local-only model in the case (d) of Figure 2. In conclusion, the global inter-class diversity is an essential factor when global imbalance exists." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3948" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "text", + "content": "5. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "text", + "content": "From three observations in Section 4, we confirmed that FAL framework requires delicate consideration of local and global inter-class diversity. However, since clients are reluctant to share their data information, we should simultaneously utilize local-only and global models to ensure both sides of inter-class diversity. To this end, we propose a novel query sample strategy, named LoGo, that composed of macro and micro steps. Pseudo algorithm for LoGo is provided in Appendix C. Before describing details of each step, let us assume a scenario where " + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "text", + "content": "-th client queries " + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "text", + "content": " unlabeled instances at the round of " + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 91, + 289, + 224 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 227, + 256, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 256, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 256, + 239 + ], + "type": "text", + "content": "Macro Step: Clustering with Local-Only Model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": "The ultimate goal of macro step is to satisfy local interclass diversity by primarily sampling the informative instances by the local-only model. In detail, we introduce " + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": "-means clustering [30] on the hypothetical gradient embedding. Let " + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": " be the embedding vector before forwarding to the last layer " + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "inline_equation", + "content": "x \\in U_k^r" + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": ". Here, we utilize the gradient of negative cross-entropy loss, induced by a pseudo label, with respect to the last layer of encoder as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 338, + 287, + 362 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 338, + 287, + 362 + ], + "spans": [ + { + "bbox": [ + 62, + 338, + 287, + 362 + ], + "type": "interline_equation", + "content": "g _ {c} ^ {x} = - \\frac {\\partial}{\\partial W _ {c}} \\ell_ {C E} (x, \\hat {y}; \\Theta_ {k *} ^ {r}) = z \\cdot \\left(\\mathbb {1} _ {[ \\hat {y} = c ]} - p _ {c}\\right), \\tag {7}", + "image_path": "db9a4eeb5b8fc0f7d72ab3be281ef2abf83655eed24583bf5b6fff6dd8221435.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\arg \\max_{c\\in [C]}p_c" + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "W_{c}" + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "content": " is the weights connected to " + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "content": "-th neuron of logits. Gradient embedding is widely used in conventional AL algorithm [6, 40], and we consider only the gradients corresponding to the pseudo label (i.e., " + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "g_{\\hat{y}}^x" + }, + { + "bbox": [ + 46, + 365, + 287, + 426 + ], + "type": "text", + "content": ") for computation efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "content": "Then, we calculate " + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "content": " number of centroids on the hallucinated gradient space via EM algorithm [10] of " + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 425, + 287, + 460 + ], + "type": "text", + "content": "-means clustering by minimizing" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 464, + 287, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 464, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 287, + 497 + ], + "type": "interline_equation", + "content": "J = \\sum_ {i = 1} ^ {N} \\sum_ {b = 1} ^ {B} w _ {i b} \\| g _ {\\hat {y}} ^ {x _ {i}} - \\mu_ {b} \\| ^ {2}, \\tag {8}", + "image_path": "b702226d6f83be922deaf2b8d0757539b50c22ac95e955f4e4ff6c3fefe3213a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "w_{ib}" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": " is an indicator function whether " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "g_{\\hat{y}}^{x_i}" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": " is assigned to " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\mu_b" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": " for E-step. Eq. (7) shows that the gradient embedding is a just scaling of feature embedding " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": ", especially with the scale of uncertainty. In other words, if an instance is uncertain to predict (low value of " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "p_{\\hat{y}}" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": "), its gradient will be much highly scaled. In this sense, Eq. (8) can be regarded as a weighted " + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 500, + 287, + 633 + ], + "type": "text", + "content": "-means clustering [13,39] on the feature embedding space by using the function of softmax response [17]. Hence, the macro step of LoGo enable the query set to contain both diversity in the embedding space and uncertainty from the perspective of local-only model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 636, + 285, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 636, + 285, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 636, + 285, + 648 + ], + "type": "text", + "content": "Micro Step: Cluster-wise Sampling with Global Model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 648, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 648, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 648, + 287, + 696 + ], + "type": "text", + "content": "In micro step, the global model selects the final instances that results in the higher global inter-class diversity. Given " + }, + { + "bbox": [ + 47, + 648, + 287, + 696 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 648, + 287, + 696 + ], + "type": "text", + "content": " selected instances from the macro step, the most uncertain instance is selected for each cluster:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 82, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 82, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "L _ {k} ^ {r} = \\left\\{\\mathcal {A} \\left(\\mathcal {C} _ {1}, \\Theta^ {r *}, 1\\right), \\dots , \\mathcal {A} \\left(\\mathcal {C} _ {B}, \\Theta^ {r *}, 1\\right) \\right\\} \\tag {9}", + "image_path": "68adb21be0cc49803c44db027a9596d3e6cd9877014ed605a60d04e4e3fbdf12.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "C_b" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "-th cluster, generated by the query set from the macro step. We simply used Entropy sampling for " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": ", but we should note that " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " can be any AL sampling strategy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 108, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 168 + ], + "type": "text", + "content": "The cluster-wise sampling in the micro step is a simple yet effective strategy to leverage the advantages of both query selector models, ensuring local and global inter-class diversity. Here, we discuss how LoGo can be a promising sampling strategy for the FAL framework." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "text", + "content": "Remark 1. The micro step is same with one step of EM algorithm. We first update cluster assignments with " + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "text", + "content": " number of centroids from the macro step (E-step). Then, within each cluster, we select the most informative instance based on the uncertainty score. This can be regarded as one " + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "text", + "content": "-step of the weighted " + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 174, + 545, + 258 + ], + "type": "text", + "content": "-means clustering, using infinitely scaled weight function of uncertainty measure." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "text", + "content": "Then, let " + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "inline_equation", + "content": "c_{b}" + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "text", + "content": " be a centroid of " + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "inline_equation", + "content": "C_{b}" + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "text", + "content": " and we define " + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 264, + 545, + 277 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 281, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 281, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 310, + 281, + 545, + 316 + ], + "type": "interline_equation", + "content": "M = \\sum_ {b = 1} ^ {B} \\| c _ {b} - \\tilde {x} _ {b} \\| ^ {2}, \\text {w h e r e} \\tilde {x} _ {b} = \\arg \\min _ {x} \\| c _ {b} - x \\| ^ {2} \\tag {10}", + "image_path": "b51975f3ee1c38ea634605a34addfb31f611943288da3c7aca6e9e8de33f7f26.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "inline_equation", + "content": "x \\in L_k^r" + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "text", + "content": " (Eq. (9)) and " + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "text", + "content": " is one-to-one mapping with the minimal transport cost. The lower value of " + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 321, + 545, + 369 + ], + "type": "text", + "content": " means that the final query set much consider the diversity in the macro step." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "text", + "content": "Remark 2. EM-based sampling in the micro step guarantees the diversity information of the macro step. Through sampling one instance per cluster, each " + }, + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\tilde{x}_b" + }, + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "text", + "content": " is disjointly assigned to one cluster. Therefore, LoGo conservatively ensures the local inter-class diversity from the macro step (i.e., lower " + }, + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 375, + 545, + 460 + ], + "type": "text", + "content": " value), comparing to any other strategy that query at least two instances for one cluster." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 469, + 377, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 377, + 481 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 377, + 481 + ], + "type": "text", + "content": "6. Evaluation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 489, + 462, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 462, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 462, + 502 + ], + "type": "text", + "content": "6.1. Experimental Configuration" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "type": "text", + "content": "Training Settings. In a FAL framework, a central server should carefully consider the fairness of labeling and training costs between clients. Therefore, we assume that ten clients have the same size of unlabeled data pool and query the same number of instances per every AL round. Moreover, we focus on a cross-silo FL setting [22] where every client participates in every FL round." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 591, + 545, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 545, + 723 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 545, + 723 + ], + "type": "text", + "content": "We compared LoGo with six active learning strategies on five benchmark dataset (CIFAR-10 [24], SVHN [32], PathMNIST, DermaMNIST, and OrganAMNIST [45]). We considered 38 comprehensive experimental settings combined into six categories (see Figure 4). Except for learning ablations of the architectures, labeling budgets, and initialization schemes, in default, we implemented four layers of CNN and trained the encoder from scratch with the labeling budget of " + }, + { + "bbox": [ + 304, + 591, + 545, + 723 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 591, + 545, + 723 + ], + "type": "text", + "content": " for every AL round. We repeat all experiments four times and report their averaged values. Refer to Appendix D for detailed experimental settings." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3949" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 57, + 534, + 157 + ], + "blocks": [ + { + "bbox": [ + 52, + 57, + 534, + 157 + ], + "lines": [ + { + "bbox": [ + 52, + 57, + 534, + 157 + ], + "spans": [ + { + "bbox": [ + 52, + 57, + 534, + 157 + ], + "type": "image", + "image_path": "519afe232a9676d425d82dcb8033d8516799dc74d93d9455e300b7e64bda262a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "type": "text", + "content": "Figure 4. Winning percentage across six categories. We also added defeat percentage, the black hatched bar that represents the percentage at which LoGo has been defeated by each baseline. Among total experiments, only statistically reliable values (" + }, + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "type": "text", + "content": "-score " + }, + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "type": "inline_equation", + "content": ">2.776" + }, + { + "bbox": [ + 46, + 160, + 547, + 194 + ], + "type": "text", + "content": ") are considered. Thus, the lower value of the colored bar and the higher value of the black bar indicate a more comparable baseline." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 66, + 209, + 265, + 388 + ], + "blocks": [ + { + "bbox": [ + 66, + 209, + 265, + 388 + ], + "lines": [ + { + "bbox": [ + 66, + 209, + 265, + 388 + ], + "spans": [ + { + "bbox": [ + 66, + 209, + 265, + 388 + ], + "type": "image", + "image_path": "2556a42832e40d2c8dbf5d254cce44fae73794a3b5e8d7e82f254b80f8df9eea.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": "Figure 5. Pairwise penalty matrix over 38 experimental settings. The value " + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "P_{ij}" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": " indicates the number of times that the " + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": "-th strategy outperforms the " + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": "-th strategy (i.e., sum of win" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "^{ij}" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": " in Eq.(6) over 38 settings). The last row is the average number of times the " + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": "-th strategy is defeated by the rest strategies; the lower, the better." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 464, + 289, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 289, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 289, + 646 + ], + "type": "text", + "content": "Baselines. We considered six standard AL strategies. Random randomly samples the instances from the unlabeled pool. Entropy selects instances with the largest entropy [41]. CoreSet chooses the small subset that can represent the whole unlabeled set [37]. BADGE selects the diverse points with high magnitude in a hallucinated gradient space [6]. GCNAL adapts CoreSet on a sequential graph convolution network to measure the relation between labeled and unlabeled instances [8]. ALFA-Mix identifies the valuable instances by seeking inconsistencies in the prediction of mixing features [34]. We adopt these sampling strategies with either the global model or local-only model in FedAvg pipeline. Refer to Appendix E for the comparison of query selection cost. Besides, we summarized the results with various FL methods in Appendix F." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 651, + 167, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 167, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 167, + 664 + ], + "type": "text", + "content": "6.2. Overall Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 185, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 185, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 185, + 682 + ], + "type": "text", + "content": "6.2.1 Pairwise Penalty Matrix" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "We summarized the overall comparison results as a pairwise penalty matrix " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " in Figure 5, following the recent" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "text", + "content": "work [6, 34]. Each cell of the pairwise penalty matrix represents the summation of the winning rate of Eq. (6) calculated above for each of the 38 experimental sets. As the rows of the matrix " + }, + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "text", + "content": " indicate how many times " + }, + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 212, + 545, + 307 + ], + "type": "text", + "content": "-th algorithm outperforms the other algorithms, the brighter color means the better algorithm (conversely, the darker columns are the better). Note that we only considered statistically reliable results throughout the two-sided t-test." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 308, + 546, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 546, + 403 + ], + "type": "text", + "content": "LoGo defeats all baselines in general (see 7-th row values) while under-performed only 0.9 out of 38 times on average (see 7-th column values in the last row). In particular, LoGo outperforms BADGE and Entropy sampling, which are top-2 baselines, with 13.7 and 12.0 out of 38 times, while LoGo only loses 2.4 and 1.9 out of 38 times, respectively. This results demonstrate the robust effectiveness of our LoGo algorithm in various experimental settings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 411, + 441, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 441, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 441, + 423 + ], + "type": "text", + "content": "6.2.2 Winning Rate Bar Plots" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 429, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 547, + 548 + ], + "type": "text", + "content": "Figure 4 summarizes the comparison results according to the six categories, which is the breakdown of Figure 5 on a more systematic categorization. For example, the colored bar of the overall category is calculated by dividing the total setting number of 38 in the 7-th row vector of Figure 5 (the black bar is from the 7-th column vector). The colored bar represents the average percentage at which LoGo defeats each baseline algorithm, and the higher bar means that LoGo has won more. Appendix G.1 provides the detailed comparison penalty values according to each category." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 548, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 548, + 715 + ], + "type": "text", + "content": "Overall, LoGo consistently shows an overwhelming winning percentage toward any baseline against the defeat percentage. Interestingly, ALFA-Mix, the latest AL strategy, shows performance considerably varying depending on which query selector is selected (see the query selector in Figure 4). The reason would be that a local-only model, which is separately trained on the highly heterogeneous dataset, is not appropriate for the feature mixing or the sensitivity to lots of hyperparameters. Moreover, Coreset, which does not consider uncertainty, cannot resolve the local and global imbalance, showing similar performance as Random sampling. Thus, LoGo is a superior algorithm for a FAL framework in that it is robust to the type of query selector or most combinations of experimental settings." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3950" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 547, + 230 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 230 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 230 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 230 + ], + "type": "table", + "html": "
MethodModelCIFAR-10SVHNPathMNISTDermaMNIST
20%40%60%80%20%30%40%50%20%30%40%50%20%30%40%50%
Random-64.1969.0771.6372.8180.9083.0784.2284.7768.4172.7073.7675.4971.7072.5772.6672.86
Entropy [41]G64.0269.1271.8773.3382.0884.6185.8886.3171.5474.3975.9176.6572.4972.6373.0273.20
L66.2971.4573.5174.0282.0984.5885.6986.1876.5278.2978.7179.1071.3872.0472.2272.65
Coreset [37]G64.6669.4371.7573.180.9482.7483.8184.4674.8476.2476.8576.8072.0272.1672.3472.74
L64.0668.7971.4973.2880.9482.9283.7884.4872.5376.0676.2876.8671.1371.4872.1572.38
BADGE [6]G65.1269.5772.1173.5382.8184.8285.8986.272.2174.3875.5376.9772.5973.0973.2373.45
L66.3271.2873.4174.2882.6984.6785.6186.176.4878.5178.4278.6871.3572.1372.2572.99
GCNAL [8]G65.4070.0572.4173.4282.0584.0785.0985.6175.5177.7978.1378.8172.0172.6073.0773.17
L65.6270.1872.3673.4281.9283.5884.5585.1074.8576.4677.1877.4571.9572.9172.9173.29
ALFA-Mix [34]G65.4569.8772.2473.2983.0284.9986.0586.3373.3474.8376.3177.4372.3973.1473.2773.10
L64.1468.7971.0372.681.0882.5583.6284.3371.1075.0175.8176.7071.5172.1872.9473.28
LoGo (ours)G,L66.5071.7073.8074.4983.4685.3186.0286.3876.3278.7279.5179.5872.6173.1873.3373.77
", + "image_path": "e0f2d68565b45461c0dedb80097a5c7bd8362caafb17bc7ef0a6e1942d3fbc2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 285, + 216, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 216, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 216, + 298 + ], + "type": "text", + "content": "6.2.3 Under Query Selector Category" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 288, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 519 + ], + "type": "text", + "content": "Table 3 shows the test accuracy according to the increased labeling budgets over rounds on four datasets. Even with the same active learning strategy, a gap in test accuracy occurs depending on which query selector is used because the global imbalance varies by 1.0–58.7 across datasets. For example, in general, global models outperform local-only models for SVHN and DermaMNIST, while the opposite trend is observed for CIFAR-10 and PathMNIST. However, irrespective of the benchmarks and querying model types, our LoGo shows the best performance in most cases. Two-step selection strategy enables LoGo to be robust by utilizing both the benefits of global and local-only models. Because we cannot know the degree of local and global imbalance in advance, our proposed method has a strong advantage in providing data-agnostic performance improvements over all baselines. Appendix G.2 provides a detailed performance comparison between LoGo and baselines under various experimental settings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 527, + 197, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 197, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 197, + 540 + ], + "type": "text", + "content": "6.3. LoGo vs. Simple Ensemble" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "content": "To prove that LoGo is an effective way to leverage the advantages of both models, we compared LoGo with three naive implementation of ensemble methods for global and local-only models: (1) the average of logits (for Entropy sampling) or gradient embedding (for BADGE) from two models, (2) weighing the instances based on the selection ranks (i.e., more weights if it is selected from both models), and (3) fine-tuning the global model on local datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "In Table 4, LoGo consistently shows better classification accuracy over increasing labeling budgets than three counterparts. Compared with the results in both Tables 3 and 4, all three ensemble methods show lower performance than using a single superior query selector. That is, the naive ensemble suffers from a performance trade-off between two" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 282, + 545, + 378 + ], + "blocks": [ + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "text", + "content": "Table 3. Comparison of test accuracy on four benchmarks with " + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "text", + "content": ". We reported the results with four random seeds. The baselines, except for Random sampling, are combined with two query selector models, " + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "text", + "content": " that stands for a global or local-only model, respectively. **Bold and underline mean Top-1 and Top-2**, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 282, + 545, + 378 + ], + "lines": [ + { + "bbox": [ + 308, + 282, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 282, + 545, + 378 + ], + "type": "table", + "html": "
MethodStrategyCIFAR-10SVHN
20%40%60%80%20%30%40%
Ens. Logit+Entropy64.5370.3673.0274.2881.8184.6485.87
+BADGE65.5570.3172.8373.9782.7784.7685.90
Ens. Rank+Entropy65.9070.9273.3474.2082.1584.3885.64
+BADGE66.2170.9873.1574.0183.0285.0585.86
Fine-tuning+Entropy65.1070.7573.2174.2382.5385.0586.01
+BADGE65.8270.9572.9474.1282.5984.8985.82
LoGo (ours)-66.5071.7073.8074.4983.4685.3186.02
", + "image_path": "674b819c429e136f744c9daec2e1a0684b5a60667f4202c28c8b8ecde20f4716.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 382, + 545, + 405 + ], + "lines": [ + { + "bbox": [ + 306, + 382, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 545, + 405 + ], + "type": "text", + "content": "Table 4. Comparison of test accuracy on two benchmarks " + }, + { + "bbox": [ + 306, + 382, + 545, + 405 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.1)" + }, + { + "bbox": [ + 306, + 382, + 545, + 405 + ], + "type": "text", + "content": " with baselines using both global and local information." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "content": "query selector models and, therefore, their results fall somewhere in the middle of using global and local models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 451, + 378, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 451, + 378, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 451, + 378, + 464 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 471, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 626 + ], + "type": "text", + "content": "We discovered the superiority of the two query selectors according to the local heterogeneity level and global imbalance ratio. Based on our findings, the local-only and global models are both crucial since global and local inter-class diversity affects their performance dominance. To this end, we propose LoGo algorithm that incorporates local-only and global models into macro and micro steps of cluster-based active learning. LoGo preferentially selects samples that simultaneously alleviate local and global imbalance as a query, making it robust to local and global imbalance. Our experiments verified that LoGo consistently outperforms six baselines under comprehensive settings of 38 combinations using six categories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and No. 2022-0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3951" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. 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Divergence-aware federated self-supervised learning. arXiv preprint arXiv:2204.04385, 2022. 1, 3" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3953" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_content_list.json b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..720cb6a20dbd962e990dd8d8ea69fac4c8d7949a --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_content_list.json @@ -0,0 +1,1274 @@ +[ + { + "type": "text", + "text": "Re-thinking Model Inversion Attacks Against Deep Neural Networks", + "text_level": 1, + "bbox": [ + 138, + 130, + 831, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ngoc-Bao Nguyen* Keshigeyan Chandrasegaran* Milad Abdollahzadeh Ngai-Man Cheung† \nSingapore University of Technology and Design (SUTD)", + "bbox": [ + 104, + 180, + 890, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thibaongoc_nguyen@mymail.sutd.edu.sg,{keshigeyan,milad_abdollahzadeh,ngaiman_cheung}@sutd.edu.sg", + "bbox": [ + 66, + 219, + 903, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Model inversion (MI) attacks aim to infer and reconstruct private training data by abusing access to a model. MI attacks have raised concerns about the leaking of sensitive information (e.g. private face images used in training a face recognition system). Recently, several algorithms for MI have been proposed to improve the attack performance. In this work, we revisit MI, study two fundamental issues pertaining to all state-of-the-art (SOTA) MI algorithms, and propose solutions to these issues which lead to a significant boost in attack performance for all SOTA MI. In particular, our contributions are two-fold: 1) We analyze the optimization objective of SOTA MI algorithms, argue that the objective is sub-optimal for achieving MI, and propose an improved optimization objective that boosts attack performance significantly. 2) We analyze \"MI overfitting\", show that it would prevent reconstructed images from learning semantics of training data, and propose a novel \"model augmentation\" idea to overcome this issue. Our proposed solutions are simple and improve all SOTA MI attack accuracy significantly. E.g., in the standard CelebA benchmark, our solutions improve accuracy by $11.8\\%$ and achieve for the first time over $90\\%$ attack accuracy. Our findings demonstrate that there is a clear risk of leaking sensitive information from deep learning models. We urge serious consideration to be given to the privacy implications. Our code, demo, and models are available at https://ngoc-nguyen-0.github.io/re-thinking_model_inversion_attacks/.", + "bbox": [ + 75, + 301, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 756, + 209, + 771 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Privacy of deep neural networks (DNNs) has attracted considerable attention recently [2, 3, 23, 31, 32]. Today, DNNs are being applied in many domains involving private and sensitive datasets, e.g., healthcare, and security. There is a growing concern of privacy attacks to gain knowledge of confidential datasets used in training DNNs. One", + "bbox": [ + 75, + 782, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "important category of privacy attacks is Model Inversion (MI) [5, 8, 11, 12, 16, 36, 37, 39, 40] (Fig. 1). Given access to a model, MI attacks aim to infer and reconstruct features of the private dataset used in the training of the model. For example, a malicious user may attack a face recognition system to reconstruct sensitive face images used in training. Similar to previous work [5, 36, 39], we will use face recognition models as the running example.", + "bbox": [ + 500, + 268, + 893, + 393 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Related Work. MI attacks were first introduced in [12], where simple linear regression is the target of attack. Recently, there is a fair amount of interest to extend MI to complex DNNs. Most of these attacks [5, 36, 39] focus on the whitebox setting and the attacker is assumed to have complete knowledge of the model subject to attack. As many platforms provide downloading of entire trained DNNs for users [5, 39], whitebox attacks are important. [39] proposes Generative Model Inversion (GMI) attack, where generic public information is leveraged to learn a distributional prior via generative adversarial networks (GANs) [13, 35], and this prior is used to guide reconstruction of private training samples. [5] proposes Knowledge-Enriched Distributional Model Inversion (KEDMI), where an inversion-specific GAN is trained by leveraging knowledge provided by the target model. [36] proposes Variational Model Inversion (VMI), where a probabilistic interpretation of MI leads to a variational objective for the attack. KEDMI and VMI achieve SOTA attack performance (See Supplementary for further discussion of related work).", + "bbox": [ + 496, + 396, + 893, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we revisit SOTA MI, study two issues pertaining to all SOTA MI and propose solutions to these issues that are complementary and applicable to all SOTA MI (Fig. 1). In particular, despite the range of approaches proposed in recent works, common and central to all these approaches is an inversion step which formulates reconstruction of training samples as an optimization. The optimization objective in the inversion step involves the identity loss, which is the same for all SOTA MI and is formulated as the negative log-likelihood for the reconstructed samples under the model being attacked. While ideas have been proposed to advance other aspects of MI, effective design of the identity loss has not been studied.", + "bbox": [ + 496, + 703, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution † Corresponding Author", + "bbox": [ + 94, + 886, + 351, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16384", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/50b2f108036a08cd727c88a3ed237952084036bfe5b85a952ecb529180215f19.jpg", + "image_caption": [ + "Figure 1. Overview and our contributions. $①$ We consider the problem of the Model Inversion (MI) attack to reconstruct private training data based on model parameters. Our work makes two foundational contributions to MI attacks. $②$ First, we analyse the optimization objective of existing SOTA MI algorithms and show that they are sub-optimal. Further, we propose an improved optimization objective that boosts MI attack performance significantly (Sec 3.1). $③$ Second, we formalize the concept of \"MI overfitting\" showing that it prevents reconstructed images from learning identity semantics of training data. Further, we propose a novel \"model augmentation\" idea to overcome this issue (Sec 3.2). $④$ Our proposed method significantly boosts MI attack accuracy. $E.g.$ In the standard CelebA benchmark, our method boosts attack accuracy by $11.8\\%$ , achieving above $90\\%$ attack accuracy for the first time in contemporary MI literature." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 486, + 547 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/17fbbe929754bfc236ef4ddb17646e003d9f80e9ddca2635f94026b9c9eb7fc7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 90, + 875, + 352 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/56b293e499c8c72c281865399ea5f43c2425fec23c80e682b3a7092d648d0cae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 354, + 875, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this research gap, our work studies subtleties of identity loss in all SOTA MI, analyzes the issues and proposes improvements that boost the performance of all SOTA significantly. In summary, our contributions are as follows:", + "bbox": [ + 75, + 660, + 468, + 720 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We analyze existing identity loss, argue that it could be sub-optimal for MI, and propose an improved identity loss that aligns better with the goal of MI (Fig. 1 ②).", + "- We formalize the concept of MI overfitting, analyze its impact on MI and propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue (Fig. 1 ③).", + "- We conduct extensive experiments to demonstrate that" + ], + "bbox": [ + 76, + 731, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "our solutions can improve SOTA MI algorithms (GMI [39], KEDMI [5], VMI [36]) significantly. Our solutions achieve for the first time over $90\\%$ attack accuracy under standard CelebA benchmark (Fig. 1 $(4)$ ).", + "bbox": [ + 511, + 660, + 890, + 720 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work sounds alarm over the rising threats of MI attacks, and urges more attention on measures against the leaking of private information from DNNs.", + "bbox": [ + 498, + 737, + 890, + 782 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. General Framework of SOTA MI Attacks", + "text_level": 1, + "bbox": [ + 500, + 799, + 870, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Problem Setup. In MI, an attacker abuses access to a model $M$ trained on a private dataset $\\mathcal{D}_{priv}$ . The attacker can access $M$ , but $\\mathcal{D}_{priv}$ is not intended to be shared. The goal of MI is to infer information about private samples in $\\mathcal{D}_{priv}$ . In existing work, for the desired class (label) $y$ ,", + "bbox": [ + 498, + 825, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16385", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/056310ae6a62f95b9f0346c7b495c6c8d1338a44ab8f8cccab3fb91ff91065ef.jpg", + "table_caption": [ + "Table 1. Categorizing SOTA MI attacks based on their difference in latent code distribution and prior loss. $p_{\\mathrm{GAN}}(\\mathbf{z})$ is a GAN prior. $G$ and $D$ are generator and discriminator of a GAN." + ], + "table_footnote": [], + "table_body": "
MethodLatent distribution q(z)Prior loss Lprior
GMI [39]Point estimate δ(z - z0)-D(G(z))
KEDMI [5]Gaussian N(μ, Σ)- log D(G(z))
VMI [36]Gaussian N(μ, Σ) or Normalizing Flow [19]Distance w.r.t. GAN prior DKL(q(z)||pGAN(z))
", + "bbox": [ + 78, + 142, + 468, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MI is formulated as the reconstruction of an input $\\mathbf{x}$ which is most likely classified into $y$ by the model $M$ . For instance, if the problem involves inverting a facial recognition model, given the desired identity, MI is formulated as the reconstruction of facial images that are most likely to be recognized as the desired identity. The model subject to MI attacks is called target model. Following previous works [5, 36, 39], we focus on whitebox MI attack, where the attacker is assumed to have complete access to the target model. For high-dimensional data such as facial images, this reconstruction problem is ill-posed. Consequently, various SOTA MI methods have been proposed recently to constrain the search space to the manifold of meaningful and relevant images using a GAN: using a GAN trained on some public dataset $D_{pub}$ [39], using an inversion-specific GAN [5], and defining variational inference in latent space of GAN [36].", + "bbox": [ + 75, + 289, + 468, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite the differences in various SOTA MI, common and central to all these methods is an inversion step -called secret revelation in [39]-, which performs the following optimization:", + "bbox": [ + 75, + 547, + 468, + 608 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq ^ {*} (\\mathbf {z}) = \\underset {q (\\mathbf {z})} {\\arg \\min } \\mathbb {E} _ {\\mathbf {z} \\sim q (\\mathbf {z})} \\left\\{L _ {i d} (\\mathbf {z}; y, M) + \\lambda L _ {p r i o r} (\\mathbf {z}) \\right\\} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 619, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here $L_{id}(\\mathbf{z};y,M) = -\\log \\mathbb{P}_M(y|G(\\mathbf{z}))$ is referred to as identity loss in MI [39], which guides the reconstruction of $\\mathbf{x} = G(\\mathbf{z})$ that is most likely to be recognized by model $M$ as identity $y$ , and $L_{prior}$ is some prior loss, and $q^{*}(\\mathbf{z})$ is the optimal distribution of latent code used to generate inverted samples by GAN ( $\\mathbf{x} = G(\\mathbf{z})$ ; $\\mathbf{z} \\sim q^{*}(\\mathbf{z}))$ . Importantly, all SOTA MI methods use the same identity loss $L_{id}(\\mathbf{z};y,M)$ although they have different assumptions about $q(\\mathbf{z})$ and the prior loss $L_{prior}$ (see Table 1 and Supplementary for more details on each algorithm). While advances observed by improving $q(\\mathbf{z})$ and $L_{prior}$ , the design of more effective $L_{id}$ has been left unnoticed in all SOTA MI algorithms. Therefore, our work instead focuses on $L_{id}$ , analyzes issues, and proposes improvement for $L_{id}$ that can lead to a performance boost in all SOTA MI. To simplify notations, we denote $L_{id}(\\mathbf{z};y,M)$ by $L_{id}(\\mathbf{x};y)$ when appropriate, where", + "bbox": [ + 75, + 657, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbf{x} = G(\\mathbf{z})$ is the reconstructed image.", + "bbox": [ + 500, + 90, + 750, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. A Closer Look at Model Inversion Attacks", + "text_level": 1, + "bbox": [ + 500, + 123, + 879, + 138 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. An Improved Formulation of MI Identity Loss", + "text_level": 1, + "bbox": [ + 500, + 148, + 890, + 166 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we discuss our first contribution and take a closer look at the optimization objective of identity loss, $L_{id}(\\mathbf{x};y)$ . Existing SOTA MI methods, namely GMI [39], KEDMI [5] and VMI [36] formulate the identity loss as an optimization to minimize the negative log likelihood of an identity under model parameters (i.e. cross-entropy loss). Particularly, the $L_{id}(\\mathbf{x};y)$ introduced in Eqn. 1 for an inversion targeting class $k$ can be re-written as follows:", + "bbox": [ + 498, + 174, + 890, + 295 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i d} (\\mathbf {x}; y = k) = - \\log \\frac {\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right)}{\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right) + \\sum_ {j = 1 , j \\neq k} ^ {N} \\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {j}\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 300, + 901, + 351 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{p}$ refers to penultimate layer activations [4, 26] for sample $\\mathbf{x}$ and $\\mathbf{w}_i$ refers to the last layer weights for the $i^{th}$ class in target model $M$ .", + "bbox": [ + 498, + 352, + 890, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing identity loss (Eqn. 2) used in SOTA MI methods [5,36,39] is sub-optimal for MI (Fig. 1 ②). Although the optimization in Eqn. 2 accurately captures the essence of a classification problem (e.g. face recognition), we postulate that such formulation is sub-optimal for MI. We provide our intuition through the lens of penultimate layer activations, $\\mathbf{p}$ (Fig. 1 ②). In a classification setting, the main expectation for $\\mathbf{p}$ is to be sufficiently discriminative for class $k$ (e.g. recognize between 'Peter', 'Simon' and 'David'). This objective can be achieved by both maximizing $\\exp (\\mathbf{p}^T\\mathbf{w}_k)$ and/or minimizing $\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)$ in Eqn. 2. On the contrary, the goal of MI is to reconstruct training data. That is, in addition to $\\mathbf{p}$ being sufficiently discriminative for class $k$ , successful inversion also requires $\\mathbf{p}$ to be close to the training data representations for class $k$ represented by $\\mathbf{w}_k$ (i.e. an inversion targeting 'Simon' needs to reconstruct a sample close to the private training data of 'Simon'; Fig. 1 ②). Specifically, we argue that MI requires a lot more attention on maximizing $\\exp (\\mathbf{p}^T\\mathbf{w}_k)$ compared to minimizing $\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)$ in Eqn. 2.", + "bbox": [ + 496, + 405, + 892, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by this hypothesis, we conduct an analysis to investigate the proximity between private training data and reconstructed data in SOTA MI methods using penultimate layer representations [4, 25, 26, 29]. Particularly, our analysis using KEDMI [5] (SOTA) shows several instances where using Eqn. 2 for identity loss is unable to reconstruct data close to the private training data. We show this in Fig. 2 (top row). Consequently, our analysis motivates the search for an improved identity loss focusing on maximizing $\\exp (\\mathbf{p}^T\\mathbf{w}_k)$ for MI.", + "bbox": [ + 496, + 712, + 890, + 861 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "${}^{1}\\mathbf{p}$ is concatenated with 1 at the end to include bias as $\\mathbf{w}_i$ includes biases at the end.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16386", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9278f33ac2e3792433a38bab0d31b4b502276d201f1ff586d934f6d53e85f07e.jpg", + "image_caption": [ + "Figure 2. Visualization of the penultimate layer representations $(\\mathcal{D}_{priv} = \\text{CelebA}[24], \\mathcal{D}_{pub} = \\text{CelebA}[24], \\text{Target Model} = \\text{IR152}[5], \\text{Evaluation Model} = \\text{face.evoLve}[6], \\text{Inversion iterations} = 2400)$ for private training data and reconstructed data using KEDMI [5]. Following the exact evaluation protocol in [5], we use face.evoLve [6] to extract representations. We show results for 3 randomly chosen identities. We include KNN distance (for different iterations) and final attack accuracy following the protocol in [5]. For each identity, we also include randomly selected private training data and the closest reconstructed sample at iteration $= 2400$ . ① Identity loss in SOTA MI methods [5, 36, 39] (Eqn. 2) is sub-optimal for MI (Top). Using penultimate representations during inversion, we observe 2 instances (e.g. target identity 57 and 143) where KEDMI [5] (using Eqn. 2 for identity loss) is unable to reconstruct data close to private training data. Hence, private and reconstructed facial images are qualitatively different. ② Our proposed identity loss, $L_{id}^{\\text{logit}}$ (Eqn. 3), can effectively guide the reconstruction of data close to private training data (Bottom). This can be clearly observed using both penultimate layer representations and KNN distances for all 3 target classes 57, 143 and 252. We show similar results using additional MI algorithms (GMI [39], VMI [36]) and target classifiers (face.evoLve, VGG16) in Supplementary. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 93, + 90, + 879, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Logit Maximization as an improved MI identity loss. In light of our analysis / observations above, we propose to directly maximize the logit, $\\mathbf{p}^T\\mathbf{w}_k$ , instead of maximizing the log likelihood of class $k$ for MI. Our proposed identity loss objective is shown below:", + "bbox": [ + 75, + 569, + 470, + 645 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i d} ^ {\\text {l o g i t}} (\\mathbf {x}; y = k) = - \\log \\mathbf {p} ^ {T} \\mathbf {w} _ {k} + \\lambda | | \\mathbf {p} - \\mathbf {p} _ {r e g} | | _ {2} ^ {2} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 655, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda (>0)$ is a hyper-parameter and $\\mathbf{p}_{reg}$ is used for regularizing $\\mathbf{p}$ . Particularly, if the regularization in Eqn. 3 is omitted and hence $||\\mathbf{p}||$ is unbounded, a crude simplified way to solve Eqn. 3 is to maximize $||\\mathbf{p}||$ . Hence, we use $\\mathbf{p}_{reg}$ to regularize $\\mathbf{p}$ . Given that the attacker has no access to private training data, we estimate $\\mathbf{p}_{reg}$ by a simple method using public data (See Supplementary). We remark that $\\mathbf{p} = M^{\\mathrm{pen}}(\\mathbf{x})$ where $\\mathbf{x} = G(\\mathbf{z})$ and $M^{\\mathrm{pen}}()$ operator returns the penultimate layer representations for a given input.", + "bbox": [ + 75, + 686, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our analysis shows that our proposed identity loss, $L_{id}^{logit}$ (Eqn. 3), can significantly improve reconstruction of private training data compared to existing identity loss used in SOTA MI algorithms [5,36,39]. This can be clearly observed using both penultimate layer representations and", + "bbox": [ + 75, + 825, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "KNN distances in Fig. 2 (bottom row). Here KNN Dist refers to the shortest Euclidean feature distance from a reconstructed image to private training images for a given identity [5, 39]. Our proposed $L_{id}^{logit}$ can be easily plugged in to all existing SOTA MI algorithms by replacing $L_{id}$ with our proposed $L_{id}^{logit}$ in Eqn. 1 (in the inversion step) with minimal computational overhead.", + "bbox": [ + 496, + 569, + 893, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overcoming MI Overfitting in SOTA methods", + "text_level": 1, + "bbox": [ + 498, + 693, + 888, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we discuss our second contribution. In particular, we formalize a concept of MI overfitting, observe its considerable impacts even in SOTA MI methods [5,36,39], and propose a new, simple solution to overcome this issue (Fig. 1 ③). To better discuss our MI overfitting concept, we first review the conventional concept of overfitting in machine learning: Given the fixed training dataset and our goal of learning a model, conventionally, overfitting is defined as instances which during model learning (training stage), the model fits too closely to the training data and adapts to the random variation and noise of training data, failing to adequately learn the semantics of the train", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16387", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing data [1, 28, 34, 38, 41]. As the model lacks semantics of training data, it could be observed that the model performs poorly under unseen data (Fig. 1 ③ a).", + "bbox": [ + 75, + 90, + 470, + 137 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6d197a0e38f4790aa33f3775e3cbd12071567148a50328a1f115e2367ec07b2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 147, + 444, + 224 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5b3f6c822708cef5812907755138233199f329b072a6a19f172968b162748cf3.jpg", + "image_caption": [ + "Figure 3. Qualitative / Quantitative studies to demonstrate MI overfitting in SOTA methods. We demonstrate this observation using KEDMI [5]. We use $\\mathcal{D}_{pri} =$ CelebA [24], $\\mathcal{D}_{pub} =$ CelebA [24] and $M = \\mathrm{IR152}$ [5]. ① We show qualitative results to illustrate MI overfitting. We show 6 identities, top: private data, bottom: reconstructed data from $M$ . The reconstructed samples have fit too closely to $M$ during inversion resulting in samples with lack of identity semantics. Particularly, we remark that these samples have very low identity loss under the target model $M$ . ② Quantitative results validating the prevalence of MI overfitting in SOTA MI methods. We use an additional target classifier $M' =$ VGG16 released by [5, 39] to quantitatively verify the presence of MI overfitting using identity loss. For 1,500 reconstructed samples from $M$ , we visualize their identity loss w.r.t. $M$ and $M'$ in the scatter plot and respective histograms. Particularly, we find that there are $26.7\\%$ of samples with low identity loss under the target model $M$ , but large identity loss under unseen VGG16 model $M'$ , hinting that these samples might lack identity semantics. This result shows that MI overfitting is a considerable issue even in SOTA MI methods. Note that VGG16 is used here only for analysis and is not part of our solution, as private data is not available. ③ Model Augmentation to alleviate MI overfitting during inversion. We repeat the above analysis, with $M' = \\mathrm{VGG16}$ replaced by $M_{aug}$ = EfficientNet-B0. Importantly, $M_{aug}$ is trained by public data using knowledge distillation [15]. We similarly observe samples with large identity loss under $M_{aug}$ ." + ], + "image_footnote": [], + "bbox": [ + 86, + 226, + 271, + 375 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d4caea7b827282e5a73a2b3e5184d4ba91815018c0671436a413f6fb39817f24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 227, + 442, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overfitting in MI. We formalize the concept of overfitting in MI (Fig. 1 ③ ⑥). Given the fixed (target) model and our goal of learning reconstructed samples, we define MI overfitting as instances which during model inversion, the reconstructed samples fit too closely to the target model and adapt to the random variation and noise of the target model parameters, failing to adequately learn semantics of the identity. As these reconstructed samples lack identity semantics, it could be observed that they perform poorly under another unseen model.", + "bbox": [ + 75, + 750, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Analysis. In what follows, we discuss our analysis to demonstrate MI overfitting and understand its impact in SOTA. See Fig. 3 for analysis setups and results. In particular, in Fig. 3 (1), we show some reconstructed samples which achieve low identity loss under the target model $M$ , yet they lack identity semantics. In Fig. 3 (2), we show that for a considerable percentage of reconstructed samples from target model $M$ with low identity loss under $M$ , their identity loss under another unseen model $M'$ is large as shown in the scatter plot and histograms, hinting that these samples might have suffered from MI overfitting and lack identity semantics. We note that the identity loss under $M'$ is obtained by feeding the reconstructed sample into $M'$ in a forward pass. We also note that SOTA KEDMI [5] is used in this analysis but the issue persists in [36, 39].", + "bbox": [ + 496, + 90, + 890, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed solution to MI overfitting. We propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue. In particular, for conventional overfitting, augmenting the training dataset could alleviate the issue [21]. Therefore, we hypothesize that by augmenting the target model we can alleviate MI overfitting.", + "bbox": [ + 496, + 328, + 890, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we propose to apply knowledge distillation (KD) [15], with target model $M_{t}$ as the teacher, to train augmented models $M_{aug}^{(i)}$ . Importantly, as we do not have access to the private data, during KD, each $M_{aug}^{(i)}$ is trained on the public dataset to match its output to the output of $M_{t}$ . We select different network architectures for $M_{aug}^{(i)}$ and they are different from $M_{t}$ (Detailed discussion in the Supplementary). After performing KD, we apply $M_{aug}^{(i)}$ together with the target model $M_{t}$ in the inversion step and compute the identity loss (with model augmentation):", + "bbox": [ + 496, + 454, + 890, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {i d} ^ {a u g} (\\mathbf {x}; y) = \\gamma_ {t} \\cdot L _ {i d} (\\mathbf {x}; y, M _ {t}) \\\\ + \\gamma_ {a u g} \\cdot \\sum_ {i = 1} ^ {N _ {a u g}} L _ {i d} (\\mathbf {x}; y, M _ {a u g} ^ {(i)}) \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 633, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\gamma_{t}$ and $\\gamma_{aug}$ are two hyper-parameters. In particular, we use $\\gamma_{t} = \\gamma_{aug} = \\frac{1}{N_{aug} + 1}$ , where $N_{aug}$ is the number of augmented models. $L_{id}^{aug}$ in Eqn. 4 is used to replace $L_{id}$ in the inversion step in Eqn. 1. Furthermore, our proposed $L_{id}^{logit}$ in Eqn. 3 can be used in Eqn. 4 to combine the improvements. See details in Supplementary.", + "bbox": [ + 496, + 720, + 890, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Fig. 3 (3), we analyze the performance of $M_{\\text{aug}}^{(i)}$ . Similar to using the unseen model $M'$ , we observe samples with large identity loss under $M_{\\text{aug}}^{(i)}$ , suggesting that samples with MI overfitting perform poorly under $M_{\\text{aug}}^{(i)}$ as these samples lack identity semantic.", + "bbox": [ + 496, + 818, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16388", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/64c04daf82b1af8058552284150a592b23936535adbb121df6a9ff4c867c652f.jpg", + "table_caption": [ + "Table 2. We follow the exact the experiment setups in [5] for GMI [39] and KEDMI [5]. For VMI [36], we follow the exact experiment setups in [36]. In total, we conduct 72 experiments spanning 18 setups to demonstrate the effectiveness of our proposed method." + ], + "table_footnote": [], + "table_body": "
MethodPrivate DatasetPublic DatasetTarget modelEvaluation ModelModel Augmentation
GMI [39] / KEDMI [5]CelebA [24]CelebA / FFHQ [18]VGG16 [30] / IR152 [14] / face.evoLve [7]face.evoLveEfficientNet-B0 [33], EfficientNet-B1 [33], EfficientNet-B2 [33]
CIFAR-10 [20]CIFAR-10VGG16ResNet-18 [14]
MNIST [22]MNISTCNN(Conv3)CNN(Conv5)CNN(Conv2), CNN(Conv4)
VMI [36]CelebACelebAResNet-34 [14]IR-SE50 [10]EfficientNet-B0, EfficientNet-B1, EfficientNet-B2
MNISTEMNIST [9]ResNet-10ResNet-10CNN(Conv2), CNN(Conv4)
", + "bbox": [ + 127, + 127, + 834, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 287, + 209, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the performance of the proposed method in recovering a representative input from the target model, against current SOTA methods: GMI [39], VMI [36], and KEDMI [5]. More specifically, as our proposed method identifies two major limitations in current $L_{id}(\\mathbf{x};y)$ -used commonly in all SOTA MI approaches-- we will evaluate the improvement brought by our improved identity loss $L_{id}^{\\text{logit}}$ , and model augmentation $L_{id}^{\\text{aug}}$ for all SOTA MI approaches.", + "bbox": [ + 75, + 311, + 470, + 449 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 458, + 266, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to have a fair comparison, when evaluating our method against each SOTA MI approach, we follow the exactly same experimental setup of that approach. In what follows, we discuss the details of these setups.", + "bbox": [ + 75, + 481, + 468, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. Following previous works, we evaluate the proposed method on different tasks: face recognition and digit classification is used for comparison with all three SOTA approaches, and image classification is used for comparison with GMI [39], and KEDMI [5]. For the face recognition task, we use CelebA dataset [24] that includes celebrity images, and the FFHQ dataset [18] which contains images with larger variation in terms of background, ethnicity, and age. The MNIST handwritten digits dataset [22] is used for digit classification. We utilize the CIFAR-10 dataset [20] for image classification.", + "bbox": [ + 75, + 547, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data Preparation Protocol. Following previous SOTA approaches [5, 36, 39], we split each dataset into two disjoint parts: one part is used as private dataset $\\mathcal{D}_{priv}$ for training target model, and another part is used as a public dataset $\\mathcal{D}_{pub}$ to extract the prior information. Most importantly, throughout all experiments, public dataset $\\mathcal{D}_{pub}$ has no class intersection with private dataset $\\mathcal{D}_{priv}$ used for training target model. Note that this is essential to make sure that adversary uses $\\mathcal{D}_{pub}$ only to gain prior knowledge about features that are general to that task (i.e., face recognition), and does not have access to information about class-specific and private information used for training target model.", + "bbox": [ + 75, + 719, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Models. Following previous works, we implement several different models with varied complexities. As GMI [39] and KEDMI [5] use exactly similar model architecture in experiments, for comparison with these two algorithms, we use the same models. More specifically, for face recognition on CelebA and FFHQ, we use VGG16 [30], IR152 [14], and face.evoLve [7]–as SOTA face recognition model. For digit classification on MNIST, we use a CNN with 3 convolutional layers and 2 pooling layers. Finally, for image classification, following [5] we use VGG16 [30]. For a fair comparison with VMI, we follow its design in [36] and use ResNet-34 for face recognition CelebA, and ResNet-10 for digit classification on MNIST. The details of the target models, augmented models and datasets used in experiments are summarized in Table 2. We remark that when comparing our proposed method with each of the SOTA MI approaches, we use exactly the same target model and GAN for both SOTA and our approach.", + "bbox": [ + 496, + 287, + 893, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. To evaluate the performance of a MI attack, we need to assess whether the reconstructed image exposes private information about a target label/identity. In this work, following the literature, we conduct both qualitative evaluations by visual inspection, and quantitative evaluations using different metrics, including:", + "bbox": [ + 496, + 565, + 893, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- Attack Accuracy (Attack Acc). Following [5, 36, 39], we use an evaluation model that predicts the label/identity of the reconstructed image. Similar to previous works, the evaluation model is different from the target model (different structure/initialization seed), but it is trained on the same private dataset (see Table 2). Intuitively, considering a highly accurate evaluation model, it can be viewed as a proxy for human inspection [39]. Therefore, if the evaluation model infers high accuracy on reconstructed images, it means these images are exposing private information about the private dataset, i.e. high attack accuracy.", + "bbox": [ + 500, + 664, + 893, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- K-Nearest Neighbors Distance (KNN Dist). KNN Dist indicates the distance between the reconstructed image for a specific label/id and corresponding images in the private training dataset. More specifically, it measures the", + "bbox": [ + 500, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16389", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "shortest feature distance from the reconstructed image to the real images in the private dataset, given a class/id. It is measured as $l_{2}$ distance between two images in the feature space, i.e., the penultimate layer of the evaluation model.", + "bbox": [ + 89, + 90, + 468, + 151 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fb179728287c4ce1926f04c27541decf13be3f6a3f1eb932e22a2850d54ed29f.jpg", + "image_caption": [ + "Figure 4. Qualitative / Quantitative (Top1 Attack Acc., KNN Dist) results to demonstrate the efficacy of our proposed method. We use KEDMI [5] (SOTA), $\\mathcal{D}_{priv} = \\text{CelebA}$ [24], $\\mathcal{D}_{pub} = \\text{CelebA}$ [24] and $M = \\text{IR152}$ [14]. As one can observe, our proposed method achieves better reconstruction of private data both visually and quantitatively (validated by KNN results) resulting in a significant boost in attack performance." + ], + "image_footnote": [], + "bbox": [ + 86, + 154, + 457, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 446, + 279, + 463 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with previous state-of-the-art. We use GMI [39], KEDMI [5], and VMI [36] as SOTA MI baselines. We reproduce all baseline results using official public implementations. We report results for GMI and KEDMI for CelebA/ CelebA experiments in Table 3. We report VMI results for CelebA/ CelebA experiments in Table 4. For each baseline setup, we report results for 3 variants: $\\bullet$ LOM (Logit Maximization, Sec. 3.1), $\\bullet$ MA (Model Augmentation, Sec. 3.2), $\\bullet$ LOMMA (Logit Maximization + Model Augmentation). The details are as follows:", + "bbox": [ + 75, + 469, + 468, + 619 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. +LOM (Ours): We replace existing identity loss, $L_{id}$ with our improved identity loss $L_{id}^{logit}$ (Sec. 3.1).", + "2. + MA (Ours): We replace existing identity loss, $L_{id}$ with our proposed $L_{id}^{aug}$ (Sec. 3.2).", + "3. +LOMMA (Ours): We combine both $L_{id}^{logit}$ (Sec. 3.1) and $L_{id}^{aug}$ (Sec. 3.2) for model inversion." + ], + "bbox": [ + 88, + 628, + 468, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As one can clearly observe from Table 3 and Table 4, our proposed methods yield significant improvement in MI attack accuracy in all experiment setups showing the efficacy of our proposed methods. Further, by combining both our proposed methods, we significantly boost attack accuracy. The KNN results also clearly show that our proposed methods are able to reconstruct data close to the private training data compared to existing SOTA MI algorithms. Particularly, we improve the KEDMI baseline [5] attack accuracy by $12.4\\%$ under IR152 target classifier. We show private", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Following exact experiment setups in [5], here $\\mathcal{D}_{priv} =$ CelebA, $\\mathcal{D}_{pub} =$ CelebA, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we achieve new SOTA MI performance (face.evoLve: $81.40\\% \\rightarrow 93.20\\%$ ).", + "bbox": [ + 496, + 88, + 890, + 214 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c92c7543d8564fd19112271b44b9de5d8f94bd31055f148a6031022bbe2a03c2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/IR152
KEDMI80.53 ± 3.86-1247.28
+ LOM (Ours)92.47 ± 1.4111.941168.55
+ MA (Ours)84.73 ± 3.764.201220.23
+ LOMMA (Ours)92.93 ± 1.1512.401138.62
GMI30.60 ± 6.54-1609.29
+ LOM (Ours)78.53 ± 3.4147.931289.62
+ MA (Ours)61.20 ± 4.3430.601389.99
+ LOMMA (Ours)82.40± 4.3751.801254.32
", + "bbox": [ + 516, + 224, + 864, + 371 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aaaa07fcf9b7cca920537c7b6285deaf48f4d9a08be24022f9c26df89c0b9dae.jpg", + "table_caption": [ + "CelebA/CelebA/face.evoLve" + ], + "table_footnote": [], + "table_body": "
KEDMI81.40 ± 3.25-1248.32
+ LOM (Ours)92.53 ± 1.5111.131183.76
+ MA (Ours)85.07 ± 2.713.671222.02
+ LOMMA (Ours)93.20 ± 0.8511.801154.32
GMI27.07 ± 6.72-1635.87
+ LOM (Ours)61.67 ± 4.9234.601405.35
+ MA (Ours)74.13 ± 4.3247.061352.25
+ LOMMA (Ours)82.33 ± 3.5155.261257.50
", + "bbox": [ + 517, + 388, + 864, + 497 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5bc330dabadf1af0242c936e09f1725f274fd4c299d376f12646252f49a122a1.jpg", + "table_caption": [ + "CelebA/CelebA/VGG16" + ], + "table_footnote": [], + "table_body": "
KEDMI74.00 ± 3.10-1289.88
+ LOM (Ours)89.07 ± 1.4615.071218.46
+ MA (Ours)82.00 ± 3.858.001248.33
+ LOMMA (Ours)90.27 ± 1.3616.271147.41
GMI19.07 ± 4.47-1715.60
+ LOM (Ours)69.67 ± 4.8050.601363.81
+ MA (Ours)51.73 ± 6.0332.661467.68
+ LOMMA (Ours)77.60 ± 4.6458.531296.26
", + "bbox": [ + 517, + 512, + 864, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "training data and reconstructed samples for KEDMI [5] under IR152 target model including all 3 variants in Fig. 4. We remark that in the standard CelebA benchmark, our method boosts attack accuracy significantly thereby achieving more than $90\\%$ attack accuracy (Table 3) for the first time in contemporary MI literature. We also include CIFAR-10, MNIST and additional results in Supplementary.", + "bbox": [ + 496, + 636, + 890, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross-dataset. Following [5], we conduct a series of experiments to study the effect of distribution shift between public and private data on attack performance and KNN distance. We use FFHQ [18] as the public dataset. In particular, we use FFHQ as public data for CelebA experiments. We train GAN models and three model augmentations using the public data. We remark that such setups closely replicate real-world MI attack scenario. We report top 1 accuracy and KNN distance for IR152, face.evoLve, and VGG16 target classifiers in Table 6. It is well known that baseline", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16390", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a872274eee939835881cbcb744812fc3a581020c136abc343b8b45df75aa23a8.jpg", + "table_caption": [ + "Table 4. We follow exact the experiment setup of [36] for VMI experiments. Specifically, we use StyleGAN [17] and Flow model [19] to learn the distribution of $z$ . The best results are in **bold**. Following exact experiment setups in [36], here $\\mathcal{D}_{priv} = \\text{CelebA}$ , $\\mathcal{D}_{pub} = \\text{CelebA}$ , target model $= \\text{ResNet-34}$ , evaluation model $= \\text{IRSE50}$ . We report top 1 attack accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance (KNN Dist). The top 5 attack accuracies are included in the Supplementary. The best results are in **bold**. By alleviating both these major problems in MI algorithms, we improve the attack accuracy by $14.94\\%$ ( $59.96\\% \\rightarrow 74.90\\%$ )." + ], + "table_footnote": [], + "table_body": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/ResNet-34
VMI59.96 ± 0.27-1.144
+ LOM (Ours)68.34 ± 0.368.381.131
+ MA (Ours)64.16 ± 0.274.201.140
+ LOMMA (Ours)74.90 ± 0.3414.941.109
", + "bbox": [ + 96, + 252, + 439, + 345 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/44c86b3a3d4a1b0293472706b8ddad3c3cee9355aec6c3a945fa39d507583852.jpg", + "table_caption": [ + "Table 5. Results for SOTA defense model BiDO-HSIC [27]: Following exact experiment setups in BiDO-HSIC, $\\mathcal{D}_{priv} = \\mathrm{CelebA}$ , $\\mathcal{D}_{pub} = \\mathrm{CelebA}$ , evaluation model = face.evoLve, target model = BiDO-HSIC. We report top 1 attack accuracies (Attack Acc.), and KNN distance (KNN Dist)." + ], + "table_footnote": [], + "table_body": "
MethodGMIKEDMI
Attack Acc ↑KNN Dist ↓Attack Acc ↑KNN Dist ↓
No Def.19.07 ± 4.471715.6074.00 ± 3.101289.88
Def. Model5.20 ± 2.751962.5842.80 ± 5.021469.75
+ LOM (Ours)55.80 ± 3.641397.0564.33 ± 1.821360.57
+ MA (Ours)23.93 ± 5.501634.8449.27 ± 4.021413.81
+ LOMMA (Ours)62.13 ± 4.041358.5470.47 ± 2.361293.25
", + "bbox": [ + 78, + 422, + 468, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "attack performances will degrade due to distribution shift between public and private data [5]. But we remark that our proposed methods consistently improves the baseline SOTA attack performances. i.e. Our method boosts the attack accuracy of IR152 target model from $52.87\\% \\rightarrow 77.27\\%$ .", + "bbox": [ + 75, + 508, + 468, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MI under SOTA defense models. We further evaluate our method on SOTA MI defense models provided by BiDO-HSIC [27]. Specifically, we use the exact GAN and defense models provided by BiDO-HSIC which are trained on CelebA dataset. We then transfer knowledge from the defense model to $M_{\\text{aug}} = \\{\\text{Efficientnet-B0}, \\text{Efficientnet-B1}, \\text{Efficientnet-B2}\\}$ using $D_{pub}$ . Results using GMI and KEDMI are shown in Table 5. We observe that SOTA defense BiDO-HSIC is rather ineffective for our proposed MI.", + "bbox": [ + 75, + 589, + 468, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 739, + 191, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. We revisit SOTA MI and study two issues pertaining to all SOTA MI approaches. First, we analyze existing identity loss in SOTA and argue that it is sub-optimal for MI. We propose a new logit based identity loss that aligns better with the goal of MI. Second, we formalize the concept of MI overfitting and show that it has a considerable impact even in SOTA. Inspired by conventional data augmentation, we propose model augmentation to alleviate MI overfitting. Extensive experiments demonstrate that", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6140175d137d492267dc23474b549f7129c844fbe484f11293b2845175acf659.jpg", + "table_caption": [ + "Table 6. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Here $\\mathcal{D}_{priv} =$ CelebA, $\\mathcal{D}_{pub} =$ FFHQ, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we improve the attack accuracy $24.40\\%$ (IR152: $52.87\\% \\rightarrow 77.27\\%$ )." + ], + "table_footnote": [], + "table_body": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/FFHQ/IR152
KEDMI52.87 ± 4.96-1418.83
+ LOM (Ours)67.73 ± 2.2914.861325.28
+ MA (Ours)64.13 ± 4.4911.261373.42
+ LOMMA (Ours)77.27 ± 2.0124.401292.80
GMI17.20 ± 5.31-1701.76
+ LOM (Ours)56.00 ± 5.2038.801427.59
+ MA (Ours)50.80 ± 6.8933.601462.92
+ LOMMA (Ours)72.00 ± 6.6254.801338.35
CelebA/FFHQ/face.evoLve
KEDMI51.87 ± 3.88-1440.19
+ LOM (Ours)69.73 ± 2.4717.861379.73
+ MA (Ours)65.73 ± 3.5113.861379.09
+ LOMMA (Ours)73.20 ± 2.2421.331321.00
GMI14.27 ± 4.42-1744.47
+ LOM (Ours)47.93 ± 4.8733.661498.19
+ MA (Ours)46.07 ± 4.8831.801500.10
+ LOMMA (Ours)64.33 ± 4.6950.061386.33
CelebA/FFHQ/VGG16
KEDMI41.27 ± 3.50-1490.09
+ LOM (Ours)55.07 ± 1.8813.801438.72
+ MA (Ours)52.07 ± 2.9210.801428.77
+ LOMMA (Ours)62.67 ± 2.2921.401366.94
GMI10.93 ± 3.47-1766.27
+ LOM (Ours)44.40 ± 5.9633.471508.84
+ MA (Ours)34.93 ± 4.5224.001547.93
+ LOMMA (Ours)58.73 ± 6.1847.801415.06
", + "bbox": [ + 517, + 210, + 864, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our solutions can improve SOTA significantly, achieving for the first time over $90\\%$ attack accuracy under the standard benchmark. Our findings highlight rising threats based on MI and prompt serious consideration on privacy of machine learning.", + "bbox": [ + 496, + 592, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Ethical Concerns. We follow previous work in experimental setups. The scale of our experiments is comparable to previous works. Furthermore, extension of our methods for blackbox/ label-only attacks can be considered in future. While our improved MI methods could have negative societal impacts if it is used by malicious users, our work contributes to increased awareness about privacy attacks on DNNs.", + "bbox": [ + 496, + 671, + 892, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programmes (AISG Award No.: AISG2-RP-2021-021; AISG Award No.: AISG2-TC-2022-007). This project is also supported by SUTD project PIE-SGP-AI-2018-01. We thank reviewers for their valuable comments. We also thank Loo Yi and Kelly Kuo for helpful discussion.", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16391", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Milad Abdollahzadeh, Touba Malekzadeh, and Ngai-Man Cheung. Revisit multimodal meta-learning through the lens of multi-task learning. 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In" + ], + "bbox": [ + 78, + 90, + 468, + 898 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 682-692, 2021.", + "[41] Yunqing Zhao, Keshigeyan Chandrasegaran, Milad Abdollahzadeh, and Ngai-Man Cheung. Few-shot image generation via adaptation-aware kernel modulation. In Advances in Neural Information Processing Systems, 2022." + ], + "bbox": [ + 501, + 92, + 890, + 176 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16393", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_model.json b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_model.json new file mode 100644 index 0000000000000000000000000000000000000000..71cc1c17355388ba42cdff1b6f876d60b0b083ed --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_model.json @@ -0,0 +1,1815 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.139, + 0.131, + 0.833, + 0.154 + ], + "angle": 0, + "content": "Re-thinking Model Inversion Attacks Against Deep Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.181, + 0.892, + 0.218 + ], + "angle": 0, + "content": "Ngoc-Bao Nguyen* Keshigeyan Chandrasegaran* Milad Abdollahzadeh Ngai-Man Cheung† \nSingapore University of Technology and Design (SUTD)" + }, + { + "type": "text", + "bbox": [ + 0.068, + 0.22, + 0.905, + 0.235 + ], + "angle": 0, + "content": "thibaongoc_nguyen@mymail.sutd.edu.sg,{keshigeyan,milad_abdollahzadeh,ngaiman_cheung}@sutd.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Model inversion (MI) attacks aim to infer and reconstruct private training data by abusing access to a model. MI attacks have raised concerns about the leaking of sensitive information (e.g. private face images used in training a face recognition system). Recently, several algorithms for MI have been proposed to improve the attack performance. In this work, we revisit MI, study two fundamental issues pertaining to all state-of-the-art (SOTA) MI algorithms, and propose solutions to these issues which lead to a significant boost in attack performance for all SOTA MI. In particular, our contributions are two-fold: 1) We analyze the optimization objective of SOTA MI algorithms, argue that the objective is sub-optimal for achieving MI, and propose an improved optimization objective that boosts attack performance significantly. 2) We analyze \"MI overfitting\", show that it would prevent reconstructed images from learning semantics of training data, and propose a novel \"model augmentation\" idea to overcome this issue. Our proposed solutions are simple and improve all SOTA MI attack accuracy significantly. E.g., in the standard CelebA benchmark, our solutions improve accuracy by \\(11.8\\%\\) and achieve for the first time over \\(90\\%\\) attack accuracy. Our findings demonstrate that there is a clear risk of leaking sensitive information from deep learning models. We urge serious consideration to be given to the privacy implications. Our code, demo, and models are available at https://ngoc-nguyen-0.github.io/re-thinking_model_inversion_attacks/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.757, + 0.21, + 0.772 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.783, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Privacy of deep neural networks (DNNs) has attracted considerable attention recently [2, 3, 23, 31, 32]. Today, DNNs are being applied in many domains involving private and sensitive datasets, e.g., healthcare, and security. There is a growing concern of privacy attacks to gain knowledge of confidential datasets used in training DNNs. One" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.895, + 0.394 + ], + "angle": 0, + "content": "important category of privacy attacks is Model Inversion (MI) [5, 8, 11, 12, 16, 36, 37, 39, 40] (Fig. 1). Given access to a model, MI attacks aim to infer and reconstruct features of the private dataset used in the training of the model. For example, a malicious user may attack a face recognition system to reconstruct sensitive face images used in training. Similar to previous work [5, 36, 39], we will use face recognition models as the running example." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.895, + 0.7 + ], + "angle": 0, + "content": "Related Work. MI attacks were first introduced in [12], where simple linear regression is the target of attack. Recently, there is a fair amount of interest to extend MI to complex DNNs. Most of these attacks [5, 36, 39] focus on the whitebox setting and the attacker is assumed to have complete knowledge of the model subject to attack. As many platforms provide downloading of entire trained DNNs for users [5, 39], whitebox attacks are important. [39] proposes Generative Model Inversion (GMI) attack, where generic public information is leveraged to learn a distributional prior via generative adversarial networks (GANs) [13, 35], and this prior is used to guide reconstruction of private training samples. [5] proposes Knowledge-Enriched Distributional Model Inversion (KEDMI), where an inversion-specific GAN is trained by leveraging knowledge provided by the target model. [36] proposes Variational Model Inversion (VMI), where a probabilistic interpretation of MI leads to a variational objective for the attack. KEDMI and VMI achieve SOTA attack performance (See Supplementary for further discussion of related work)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.896, + 0.901 + ], + "angle": 0, + "content": "In this paper, we revisit SOTA MI, study two issues pertaining to all SOTA MI and propose solutions to these issues that are complementary and applicable to all SOTA MI (Fig. 1). In particular, despite the range of approaches proposed in recent works, common and central to all these approaches is an inversion step which formulates reconstruction of training samples as an optimization. The optimization objective in the inversion step involves the identity loss, which is the same for all SOTA MI and is formulated as the negative log-likelihood for the reconstructed samples under the model being attacked. While ideas have been proposed to advance other aspects of MI, effective design of the identity loss has not been studied." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.352, + 0.901 + ], + "angle": 0, + "content": "* Equal Contribution † Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16384" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.487, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.091, + 0.877, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.356, + 0.877, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.552, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Figure 1. Overview and our contributions. \\(①\\) We consider the problem of the Model Inversion (MI) attack to reconstruct private training data based on model parameters. Our work makes two foundational contributions to MI attacks. \\(②\\) First, we analyse the optimization objective of existing SOTA MI algorithms and show that they are sub-optimal. Further, we propose an improved optimization objective that boosts MI attack performance significantly (Sec 3.1). \\(③\\) Second, we formalize the concept of \"MI overfitting\" showing that it prevents reconstructed images from learning identity semantics of training data. Further, we propose a novel \"model augmentation\" idea to overcome this issue (Sec 3.2). \\(④\\) Our proposed method significantly boosts MI attack accuracy. \\(E.g.\\) In the standard CelebA benchmark, our method boosts attack accuracy by \\(11.8\\%\\) , achieving above \\(90\\%\\) attack accuracy for the first time in contemporary MI literature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.47, + 0.722 + ], + "angle": 0, + "content": "To address this research gap, our work studies subtleties of identity loss in all SOTA MI, analyzes the issues and proposes improvements that boost the performance of all SOTA significantly. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.732, + 0.47, + 0.778 + ], + "angle": 0, + "content": "- We analyze existing identity loss, argue that it could be sub-optimal for MI, and propose an improved identity loss that aligns better with the goal of MI (Fig. 1 ②)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.787, + 0.471, + 0.877 + ], + "angle": 0, + "content": "- We formalize the concept of MI overfitting, analyze its impact on MI and propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue (Fig. 1 ③)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.471, + 0.901 + ], + "angle": 0, + "content": "- We conduct extensive experiments to demonstrate that" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.732, + 0.471, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.661, + 0.892, + 0.722 + ], + "angle": 0, + "content": "our solutions can improve SOTA MI algorithms (GMI [39], KEDMI [5], VMI [36]) significantly. Our solutions achieve for the first time over \\(90\\%\\) attack accuracy under standard CelebA benchmark (Fig. 1 \\((4)\\))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.738, + 0.892, + 0.783 + ], + "angle": 0, + "content": "Our work sounds alarm over the rising threats of MI attacks, and urges more attention on measures against the leaking of private information from DNNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.872, + 0.815 + ], + "angle": 0, + "content": "2. General Framework of SOTA MI Attacks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Problem Setup. In MI, an attacker abuses access to a model \\(M\\) trained on a private dataset \\(\\mathcal{D}_{priv}\\). The attacker can access \\(M\\), but \\(\\mathcal{D}_{priv}\\) is not intended to be shared. The goal of MI is to infer information about private samples in \\(\\mathcal{D}_{priv}\\). In existing work, for the desired class (label) \\(y\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16385" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.132 + ], + "angle": 0, + "content": "Table 1. Categorizing SOTA MI attacks based on their difference in latent code distribution and prior loss. \\( p_{\\mathrm{GAN}}(\\mathbf{z}) \\) is a GAN prior. \\( G \\) and \\( D \\) are generator and discriminator of a GAN." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.143, + 0.47, + 0.264 + ], + "angle": 0, + "content": "
MethodLatent distribution q(z)Prior loss Lprior
GMI [39]Point estimate δ(z - z0)-D(G(z))
KEDMI [5]Gaussian N(μ, Σ)- log D(G(z))
VMI [36]Gaussian N(μ, Σ) or Normalizing Flow [19]Distance w.r.t. GAN prior DKL(q(z)||pGAN(z))
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.47, + 0.547 + ], + "angle": 0, + "content": "MI is formulated as the reconstruction of an input \\( \\mathbf{x} \\) which is most likely classified into \\( y \\) by the model \\( M \\). For instance, if the problem involves inverting a facial recognition model, given the desired identity, MI is formulated as the reconstruction of facial images that are most likely to be recognized as the desired identity. The model subject to MI attacks is called target model. Following previous works [5, 36, 39], we focus on whitebox MI attack, where the attacker is assumed to have complete access to the target model. For high-dimensional data such as facial images, this reconstruction problem is ill-posed. Consequently, various SOTA MI methods have been proposed recently to constrain the search space to the manifold of meaningful and relevant images using a GAN: using a GAN trained on some public dataset \\( D_{pub} \\) [39], using an inversion-specific GAN [5], and defining variational inference in latent space of GAN [36]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.609 + ], + "angle": 0, + "content": "Despite the differences in various SOTA MI, common and central to all these methods is an inversion step -called secret revelation in [39]-, which performs the following optimization:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.621, + 0.47, + 0.659 + ], + "angle": 0, + "content": "\\[\nq ^ {*} (\\mathbf {z}) = \\underset {q (\\mathbf {z})} {\\arg \\min } \\mathbb {E} _ {\\mathbf {z} \\sim q (\\mathbf {z})} \\left\\{L _ {i d} (\\mathbf {z}; y, M) + \\lambda L _ {p r i o r} (\\mathbf {z}) \\right\\} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Here \\(L_{id}(\\mathbf{z};y,M) = -\\log \\mathbb{P}_M(y|G(\\mathbf{z}))\\) is referred to as identity loss in MI [39], which guides the reconstruction of \\(\\mathbf{x} = G(\\mathbf{z})\\) that is most likely to be recognized by model \\(M\\) as identity \\(y\\), and \\(L_{prior}\\) is some prior loss, and \\(q^{*}(\\mathbf{z})\\) is the optimal distribution of latent code used to generate inverted samples by GAN (\\(\\mathbf{x} = G(\\mathbf{z})\\); \\(\\mathbf{z} \\sim q^{*}(\\mathbf{z}))\\). Importantly, all SOTA MI methods use the same identity loss \\(L_{id}(\\mathbf{z};y,M)\\) although they have different assumptions about \\(q(\\mathbf{z})\\) and the prior loss \\(L_{prior}\\) (see Table 1 and Supplementary for more details on each algorithm). While advances observed by improving \\(q(\\mathbf{z})\\) and \\(L_{prior}\\), the design of more effective \\(L_{id}\\) has been left unnoticed in all SOTA MI algorithms. Therefore, our work instead focuses on \\(L_{id}\\), analyzes issues, and proposes improvement for \\(L_{id}\\) that can lead to a performance boost in all SOTA MI. To simplify notations, we denote \\(L_{id}(\\mathbf{z};y,M)\\) by \\(L_{id}(\\mathbf{x};y)\\) when appropriate, where" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.75, + 0.108 + ], + "angle": 0, + "content": "\\(\\mathbf{x} = G(\\mathbf{z})\\) is the reconstructed image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.124, + 0.88, + 0.14 + ], + "angle": 0, + "content": "3. A Closer Look at Model Inversion Attacks" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.15, + 0.892, + 0.167 + ], + "angle": 0, + "content": "3.1. An Improved Formulation of MI Identity Loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.175, + 0.892, + 0.296 + ], + "angle": 0, + "content": "In this section, we discuss our first contribution and take a closer look at the optimization objective of identity loss, \\( L_{id}(\\mathbf{x};y) \\). Existing SOTA MI methods, namely GMI [39], KEDMI [5] and VMI [36] formulate the identity loss as an optimization to minimize the negative log likelihood of an identity under model parameters (i.e. cross-entropy loss). Particularly, the \\( L_{id}(\\mathbf{x};y) \\) introduced in Eqn. 1 for an inversion targeting class \\( k \\) can be re-written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.301, + 0.903, + 0.352 + ], + "angle": 0, + "content": "\\[\nL _ {i d} (\\mathbf {x}; y = k) = - \\log \\frac {\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right)}{\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right) + \\sum_ {j = 1 , j \\neq k} ^ {N} \\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {j}\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.353, + 0.892, + 0.398 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}\\) refers to penultimate layer activations [4, 26] for sample \\(\\mathbf{x}\\) and \\(\\mathbf{w}_i\\) refers to the last layer weights for the \\(i^{th}\\) class in target model \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.893, + 0.713 + ], + "angle": 0, + "content": "Existing identity loss (Eqn. 2) used in SOTA MI methods [5,36,39] is sub-optimal for MI (Fig. 1 ②). Although the optimization in Eqn. 2 accurately captures the essence of a classification problem (e.g. face recognition), we postulate that such formulation is sub-optimal for MI. We provide our intuition through the lens of penultimate layer activations, \\(\\mathbf{p}\\) (Fig. 1 ②). In a classification setting, the main expectation for \\(\\mathbf{p}\\) is to be sufficiently discriminative for class \\(k\\) (e.g. recognize between 'Peter', 'Simon' and 'David'). This objective can be achieved by both maximizing \\(\\exp (\\mathbf{p}^T\\mathbf{w}_k)\\) and/or minimizing \\(\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)\\) in Eqn. 2. On the contrary, the goal of MI is to reconstruct training data. That is, in addition to \\(\\mathbf{p}\\) being sufficiently discriminative for class \\(k\\), successful inversion also requires \\(\\mathbf{p}\\) to be close to the training data representations for class \\(k\\) represented by \\(\\mathbf{w}_k\\) (i.e. an inversion targeting 'Simon' needs to reconstruct a sample close to the private training data of 'Simon'; Fig. 1 ②). Specifically, we argue that MI requires a lot more attention on maximizing \\(\\exp (\\mathbf{p}^T\\mathbf{w}_k)\\) compared to minimizing \\(\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)\\) in Eqn. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.862 + ], + "angle": 0, + "content": "Motivated by this hypothesis, we conduct an analysis to investigate the proximity between private training data and reconstructed data in SOTA MI methods using penultimate layer representations [4, 25, 26, 29]. Particularly, our analysis using KEDMI [5] (SOTA) shows several instances where using Eqn. 2 for identity loss is unable to reconstruct data close to the private training data. We show this in Fig. 2 (top row). Consequently, our analysis motivates the search for an improved identity loss focusing on maximizing \\(\\exp (\\mathbf{p}^T\\mathbf{w}_k)\\) for MI." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "\\({}^{1}\\mathbf{p}\\) is concatenated with 1 at the end to include bias as \\(\\mathbf{w}_i\\) includes biases at the end." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16386" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.092, + 0.88, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.896, + 0.562 + ], + "angle": 0, + "content": "Figure 2. Visualization of the penultimate layer representations \\((\\mathcal{D}_{priv} = \\text{CelebA}[24], \\mathcal{D}_{pub} = \\text{CelebA}[24], \\text{Target Model} = \\text{IR152}[5], \\text{Evaluation Model} = \\text{face.evoLve}[6], \\text{Inversion iterations} = 2400)\\) for private training data and reconstructed data using KEDMI [5]. Following the exact evaluation protocol in [5], we use face.evoLve [6] to extract representations. We show results for 3 randomly chosen identities. We include KNN distance (for different iterations) and final attack accuracy following the protocol in [5]. For each identity, we also include randomly selected private training data and the closest reconstructed sample at iteration \\(= 2400\\). ① Identity loss in SOTA MI methods [5, 36, 39] (Eqn. 2) is sub-optimal for MI (Top). Using penultimate representations during inversion, we observe 2 instances (e.g. target identity 57 and 143) where KEDMI [5] (using Eqn. 2 for identity loss) is unable to reconstruct data close to private training data. Hence, private and reconstructed facial images are qualitatively different. ② Our proposed identity loss, \\(L_{id}^{\\text{logit}}\\) (Eqn. 3), can effectively guide the reconstruction of data close to private training data (Bottom). This can be clearly observed using both penultimate layer representations and KNN distances for all 3 target classes 57, 143 and 252. We show similar results using additional MI algorithms (GMI [39], VMI [36]) and target classifiers (face.evoLve, VGG16) in Supplementary. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.471, + 0.646 + ], + "angle": 0, + "content": "Logit Maximization as an improved MI identity loss. In light of our analysis / observations above, we propose to directly maximize the logit, \\(\\mathbf{p}^T\\mathbf{w}_k\\), instead of maximizing the log likelihood of class \\(k\\) for MI. Our proposed identity loss objective is shown below:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.656, + 0.47, + 0.677 + ], + "angle": 0, + "content": "\\[\nL _ {i d} ^ {\\text {l o g i t}} (\\mathbf {x}; y = k) = - \\log \\mathbf {p} ^ {T} \\mathbf {w} _ {k} + \\lambda | | \\mathbf {p} - \\mathbf {p} _ {r e g} | | _ {2} ^ {2} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\(\\lambda (>0)\\) is a hyper-parameter and \\(\\mathbf{p}_{reg}\\) is used for regularizing \\(\\mathbf{p}\\). Particularly, if the regularization in Eqn. 3 is omitted and hence \\(||\\mathbf{p}||\\) is unbounded, a crude simplified way to solve Eqn. 3 is to maximize \\(||\\mathbf{p}||\\). Hence, we use \\(\\mathbf{p}_{reg}\\) to regularize \\(\\mathbf{p}\\). Given that the attacker has no access to private training data, we estimate \\(\\mathbf{p}_{reg}\\) by a simple method using public data (See Supplementary). We remark that \\(\\mathbf{p} = M^{\\mathrm{pen}}(\\mathbf{x})\\) where \\(\\mathbf{x} = G(\\mathbf{z})\\) and \\(M^{\\mathrm{pen}}()\\) operator returns the penultimate layer representations for a given input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Our analysis shows that our proposed identity loss, \\( L_{id}^{logit} \\) (Eqn. 3), can significantly improve reconstruction of private training data compared to existing identity loss used in SOTA MI algorithms [5,36,39]. This can be clearly observed using both penultimate layer representations and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.678 + ], + "angle": 0, + "content": "KNN distances in Fig. 2 (bottom row). Here KNN Dist refers to the shortest Euclidean feature distance from a reconstructed image to private training images for a given identity [5, 39]. Our proposed \\( L_{id}^{logit} \\) can be easily plugged in to all existing SOTA MI algorithms by replacing \\( L_{id} \\) with our proposed \\( L_{id}^{logit} \\) in Eqn. 1 (in the inversion step) with minimal computational overhead." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.694, + 0.89, + 0.71 + ], + "angle": 0, + "content": "3.2. Overcoming MI Overfitting in SOTA methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this section, we discuss our second contribution. In particular, we formalize a concept of MI overfitting, observe its considerable impacts even in SOTA MI methods [5,36,39], and propose a new, simple solution to overcome this issue (Fig. 1 ③). To better discuss our MI overfitting concept, we first review the conventional concept of overfitting in machine learning: Given the fixed training dataset and our goal of learning a model, conventionally, overfitting is defined as instances which during model learning (training stage), the model fits too closely to the training data and adapts to the random variation and noise of training data, failing to adequately learn the semantics of the train" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16387" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.138 + ], + "angle": 0, + "content": "ing data [1, 28, 34, 38, 41]. As the model lacks semantics of training data, it could be observed that the model performs poorly under unseen data (Fig. 1 ③ a)." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.148, + 0.445, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.227, + 0.272, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.228, + 0.444, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.381, + 0.471, + 0.743 + ], + "angle": 0, + "content": "Figure 3. Qualitative / Quantitative studies to demonstrate MI overfitting in SOTA methods. We demonstrate this observation using KEDMI [5]. We use \\(\\mathcal{D}_{pri} =\\) CelebA [24], \\(\\mathcal{D}_{pub} =\\) CelebA [24] and \\(M = \\mathrm{IR152}\\) [5]. ① We show qualitative results to illustrate MI overfitting. We show 6 identities, top: private data, bottom: reconstructed data from \\(M\\). The reconstructed samples have fit too closely to \\(M\\) during inversion resulting in samples with lack of identity semantics. Particularly, we remark that these samples have very low identity loss under the target model \\(M\\). ② Quantitative results validating the prevalence of MI overfitting in SOTA MI methods. We use an additional target classifier \\(M' =\\) VGG16 released by [5, 39] to quantitatively verify the presence of MI overfitting using identity loss. For 1,500 reconstructed samples from \\(M\\), we visualize their identity loss w.r.t. \\(M\\) and \\(M'\\) in the scatter plot and respective histograms. Particularly, we find that there are \\(26.7\\%\\) of samples with low identity loss under the target model \\(M\\), but large identity loss under unseen VGG16 model \\(M'\\), hinting that these samples might lack identity semantics. This result shows that MI overfitting is a considerable issue even in SOTA MI methods. Note that VGG16 is used here only for analysis and is not part of our solution, as private data is not available. ③ Model Augmentation to alleviate MI overfitting during inversion. We repeat the above analysis, with \\(M' = \\mathrm{VGG16}\\) replaced by \\(M_{aug}\\) = EfficientNet-B0. Importantly, \\(M_{aug}\\) is trained by public data using knowledge distillation [15]. We similarly observe samples with large identity loss under \\(M_{aug}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Overfitting in MI. We formalize the concept of overfitting in MI (Fig. 1 ③ ⑥). Given the fixed (target) model and our goal of learning reconstructed samples, we define MI overfitting as instances which during model inversion, the reconstructed samples fit too closely to the target model and adapt to the random variation and noise of the target model parameters, failing to adequately learn semantics of the identity. As these reconstructed samples lack identity semantics, it could be observed that they perform poorly under another unseen model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Analysis. In what follows, we discuss our analysis to demonstrate MI overfitting and understand its impact in SOTA. See Fig. 3 for analysis setups and results. In particular, in Fig. 3 (1), we show some reconstructed samples which achieve low identity loss under the target model \\( M \\), yet they lack identity semantics. In Fig. 3 (2), we show that for a considerable percentage of reconstructed samples from target model \\( M \\) with low identity loss under \\( M \\), their identity loss under another unseen model \\( M' \\) is large as shown in the scatter plot and histograms, hinting that these samples might have suffered from MI overfitting and lack identity semantics. We note that the identity loss under \\( M' \\) is obtained by feeding the reconstructed sample into \\( M' \\) in a forward pass. We also note that SOTA KEDMI [5] is used in this analysis but the issue persists in [36, 39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.45 + ], + "angle": 0, + "content": "Our proposed solution to MI overfitting. We propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue. In particular, for conventional overfitting, augmenting the training dataset could alleviate the issue [21]. Therefore, we hypothesize that by augmenting the target model we can alleviate MI overfitting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Specifically, we propose to apply knowledge distillation (KD) [15], with target model \\( M_{t} \\) as the teacher, to train augmented models \\( M_{aug}^{(i)} \\). Importantly, as we do not have access to the private data, during KD, each \\( M_{aug}^{(i)} \\) is trained on the public dataset to match its output to the output of \\( M_{t} \\). We select different network architectures for \\( M_{aug}^{(i)} \\) and they are different from \\( M_{t} \\) (Detailed discussion in the Supplementary). After performing KD, we apply \\( M_{aug}^{(i)} \\) together with the target model \\( M_{t} \\) in the inversion step and compute the identity loss (with model augmentation):" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.635, + 0.892, + 0.699 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {i d} ^ {a u g} (\\mathbf {x}; y) = \\gamma_ {t} \\cdot L _ {i d} (\\mathbf {x}; y, M _ {t}) \\\\ + \\gamma_ {a u g} \\cdot \\sum_ {i = 1} ^ {N _ {a u g}} L _ {i d} (\\mathbf {x}; y, M _ {a u g} ^ {(i)}) \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.892, + 0.814 + ], + "angle": 0, + "content": "Here, \\(\\gamma_{t}\\) and \\(\\gamma_{aug}\\) are two hyper-parameters. In particular, we use \\(\\gamma_{t} = \\gamma_{aug} = \\frac{1}{N_{aug} + 1}\\), where \\(N_{aug}\\) is the number of augmented models. \\(L_{id}^{aug}\\) in Eqn. 4 is used to replace \\(L_{id}\\) in the inversion step in Eqn. 1. Furthermore, our proposed \\(L_{id}^{logit}\\) in Eqn. 3 can be used in Eqn. 4 to combine the improvements. See details in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.819, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Fig. 3 (3), we analyze the performance of \\( M_{\\text{aug}}^{(i)} \\). Similar to using the unseen model \\( M' \\), we observe samples with large identity loss under \\( M_{\\text{aug}}^{(i)} \\), suggesting that samples with MI overfitting perform poorly under \\( M_{\\text{aug}}^{(i)} \\) as these samples lack identity semantic." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16388" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.12 + ], + "angle": 0, + "content": "Table 2. We follow the exact the experiment setups in [5] for GMI [39] and KEDMI [5]. For VMI [36], we follow the exact experiment setups in [36]. In total, we conduct 72 experiments spanning 18 setups to demonstrate the effectiveness of our proposed method." + }, + { + "type": "table", + "bbox": [ + 0.129, + 0.128, + 0.835, + 0.265 + ], + "angle": 0, + "content": "
MethodPrivate DatasetPublic DatasetTarget modelEvaluation ModelModel Augmentation
GMI [39] / KEDMI [5]CelebA [24]CelebA / FFHQ [18]VGG16 [30] / IR152 [14] / face.evoLve [7]face.evoLveEfficientNet-B0 [33], EfficientNet-B1 [33], EfficientNet-B2 [33]
CIFAR-10 [20]CIFAR-10VGG16ResNet-18 [14]
MNIST [22]MNISTCNN(Conv3)CNN(Conv5)CNN(Conv2), CNN(Conv4)
VMI [36]CelebACelebAResNet-34 [14]IR-SE50 [10]EfficientNet-B0, EfficientNet-B1, EfficientNet-B2
MNISTEMNIST [9]ResNet-10ResNet-10CNN(Conv2), CNN(Conv4)
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.288, + 0.21, + 0.306 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.471, + 0.45 + ], + "angle": 0, + "content": "In this section, we evaluate the performance of the proposed method in recovering a representative input from the target model, against current SOTA methods: GMI [39], VMI [36], and KEDMI [5]. More specifically, as our proposed method identifies two major limitations in current \\( L_{id}(\\mathbf{x};y) \\) -used commonly in all SOTA MI approaches-- we will evaluate the improvement brought by our improved identity loss \\( L_{id}^{\\text{logit}} \\), and model augmentation \\( L_{id}^{\\text{aug}} \\) for all SOTA MI approaches." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.459, + 0.267, + 0.475 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.543 + ], + "angle": 0, + "content": "In order to have a fair comparison, when evaluating our method against each SOTA MI approach, we follow the exactly same experimental setup of that approach. In what follows, we discuss the details of these setups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Dataset. Following previous works, we evaluate the proposed method on different tasks: face recognition and digit classification is used for comparison with all three SOTA approaches, and image classification is used for comparison with GMI [39], and KEDMI [5]. For the face recognition task, we use CelebA dataset [24] that includes celebrity images, and the FFHQ dataset [18] which contains images with larger variation in terms of background, ethnicity, and age. The MNIST handwritten digits dataset [22] is used for digit classification. We utilize the CIFAR-10 dataset [20] for image classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Data Preparation Protocol. Following previous SOTA approaches [5, 36, 39], we split each dataset into two disjoint parts: one part is used as private dataset \\(\\mathcal{D}_{priv}\\) for training target model, and another part is used as a public dataset \\(\\mathcal{D}_{pub}\\) to extract the prior information. Most importantly, throughout all experiments, public dataset \\(\\mathcal{D}_{pub}\\) has no class intersection with private dataset \\(\\mathcal{D}_{priv}\\) used for training target model. Note that this is essential to make sure that adversary uses \\(\\mathcal{D}_{pub}\\) only to gain prior knowledge about features that are general to that task (i.e., face recognition), and does not have access to information about class-specific and private information used for training target model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.895, + 0.562 + ], + "angle": 0, + "content": "Models. Following previous works, we implement several different models with varied complexities. As GMI [39] and KEDMI [5] use exactly similar model architecture in experiments, for comparison with these two algorithms, we use the same models. More specifically, for face recognition on CelebA and FFHQ, we use VGG16 [30], IR152 [14], and face.evoLve [7]–as SOTA face recognition model. For digit classification on MNIST, we use a CNN with 3 convolutional layers and 2 pooling layers. Finally, for image classification, following [5] we use VGG16 [30]. For a fair comparison with VMI, we follow its design in [36] and use ResNet-34 for face recognition CelebA, and ResNet-10 for digit classification on MNIST. The details of the target models, augmented models and datasets used in experiments are summarized in Table 2. We remark that when comparing our proposed method with each of the SOTA MI approaches, we use exactly the same target model and GAN for both SOTA and our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.658 + ], + "angle": 0, + "content": "Evaluation Metrics. To evaluate the performance of a MI attack, we need to assess whether the reconstructed image exposes private information about a target label/identity. In this work, following the literature, we conduct both qualitative evaluations by visual inspection, and quantitative evaluations using different metrics, including:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.665, + 0.894, + 0.833 + ], + "angle": 0, + "content": "- Attack Accuracy (Attack Acc). Following [5, 36, 39], we use an evaluation model that predicts the label/identity of the reconstructed image. Similar to previous works, the evaluation model is different from the target model (different structure/initialization seed), but it is trained on the same private dataset (see Table 2). Intuitively, considering a highly accurate evaluation model, it can be viewed as a proxy for human inspection [39]. Therefore, if the evaluation model infers high accuracy on reconstructed images, it means these images are exposing private information about the private dataset, i.e. high attack accuracy." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "- K-Nearest Neighbors Distance (KNN Dist). KNN Dist indicates the distance between the reconstructed image for a specific label/id and corresponding images in the private training dataset. More specifically, it measures the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16389" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "shortest feature distance from the reconstructed image to the real images in the private dataset, given a class/id. It is measured as \\( l_{2} \\) distance between two images in the feature space, i.e., the penultimate layer of the evaluation model." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.155, + 0.458, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.471, + 0.435 + ], + "angle": 0, + "content": "Figure 4. Qualitative / Quantitative (Top1 Attack Acc., KNN Dist) results to demonstrate the efficacy of our proposed method. We use KEDMI [5] (SOTA), \\(\\mathcal{D}_{priv} = \\text{CelebA}\\) [24], \\(\\mathcal{D}_{pub} = \\text{CelebA}\\) [24] and \\(M = \\text{IR152}\\) [14]. As one can observe, our proposed method achieves better reconstruction of private data both visually and quantitatively (validated by KNN results) resulting in a significant boost in attack performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.447, + 0.281, + 0.464 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.621 + ], + "angle": 0, + "content": "Comparison with previous state-of-the-art. We use GMI [39], KEDMI [5], and VMI [36] as SOTA MI baselines. We reproduce all baseline results using official public implementations. We report results for GMI and KEDMI for CelebA/ CelebA experiments in Table 3. We report VMI results for CelebA/ CelebA experiments in Table 4. For each baseline setup, we report results for 3 variants: \\(\\bullet\\) LOM (Logit Maximization, Sec. 3.1), \\(\\bullet\\) MA (Model Augmentation, Sec. 3.2), \\(\\bullet\\) LOMMA (Logit Maximization + Model Augmentation). The details are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.63, + 0.47, + 0.663 + ], + "angle": 0, + "content": "1. +LOM (Ours): We replace existing identity loss, \\( L_{id} \\) with our improved identity loss \\( L_{id}^{logit} \\) (Sec. 3.1)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.669, + 0.47, + 0.702 + ], + "angle": 0, + "content": "2. + MA (Ours): We replace existing identity loss, \\( L_{id} \\) with our proposed \\( L_{id}^{aug} \\) (Sec. 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.71, + 0.469, + 0.743 + ], + "angle": 0, + "content": "3. +LOMMA (Ours): We combine both \\(L_{id}^{logit}\\) (Sec. 3.1) and \\(L_{id}^{aug}\\) (Sec. 3.2) for model inversion." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.63, + 0.47, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As one can clearly observe from Table 3 and Table 4, our proposed methods yield significant improvement in MI attack accuracy in all experiment setups showing the efficacy of our proposed methods. Further, by combining both our proposed methods, we significantly boost attack accuracy. The KNN results also clearly show that our proposed methods are able to reconstruct data close to the private training data compared to existing SOTA MI algorithms. Particularly, we improve the KEDMI baseline [5] attack accuracy by \\(12.4\\%\\) under IR152 target classifier. We show private" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.215 + ], + "angle": 0, + "content": "Table 3. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Following exact experiment setups in [5], here \\( \\mathcal{D}_{priv} = \\) CelebA, \\( \\mathcal{D}_{pub} = \\) CelebA, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we achieve new SOTA MI performance (face.evoLve: \\( 81.40\\% \\rightarrow 93.20\\% \\))." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.226, + 0.866, + 0.372 + ], + "angle": 0, + "content": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/IR152
KEDMI80.53 ± 3.86-1247.28
+ LOM (Ours)92.47 ± 1.4111.941168.55
+ MA (Ours)84.73 ± 3.764.201220.23
+ LOMMA (Ours)92.93 ± 1.1512.401138.62
GMI30.60 ± 6.54-1609.29
+ LOM (Ours)78.53 ± 3.4147.931289.62
+ MA (Ours)61.20 ± 4.3430.601389.99
+ LOMMA (Ours)82.40± 4.3751.801254.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.608, + 0.374, + 0.774, + 0.386 + ], + "angle": 0, + "content": "CelebA/CelebA/face.evoLve" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.389, + 0.865, + 0.498 + ], + "angle": 0, + "content": "
KEDMI81.40 ± 3.25-1248.32
+ LOM (Ours)92.53 ± 1.5111.131183.76
+ MA (Ours)85.07 ± 2.713.671222.02
+ LOMMA (Ours)93.20 ± 0.8511.801154.32
GMI27.07 ± 6.72-1635.87
+ LOM (Ours)61.67 ± 4.9234.601405.35
+ MA (Ours)74.13 ± 4.3247.061352.25
+ LOMMA (Ours)82.33 ± 3.5155.261257.50
" + }, + { + "type": "table_caption", + "bbox": [ + 0.619, + 0.499, + 0.764, + 0.511 + ], + "angle": 0, + "content": "CelebA/CelebA/VGG16" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.513, + 0.865, + 0.624 + ], + "angle": 0, + "content": "
KEDMI74.00 ± 3.10-1289.88
+ LOM (Ours)89.07 ± 1.4615.071218.46
+ MA (Ours)82.00 ± 3.858.001248.33
+ LOMMA (Ours)90.27 ± 1.3616.271147.41
GMI19.07 ± 4.47-1715.60
+ LOM (Ours)69.67 ± 4.8050.601363.81
+ MA (Ours)51.73 ± 6.0332.661467.68
+ LOMMA (Ours)77.60 ± 4.6458.531296.26
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.744 + ], + "angle": 0, + "content": "training data and reconstructed samples for KEDMI [5] under IR152 target model including all 3 variants in Fig. 4. We remark that in the standard CelebA benchmark, our method boosts attack accuracy significantly thereby achieving more than \\(90\\%\\) attack accuracy (Table 3) for the first time in contemporary MI literature. We also include CIFAR-10, MNIST and additional results in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross-dataset. Following [5], we conduct a series of experiments to study the effect of distribution shift between public and private data on attack performance and KNN distance. We use FFHQ [18] as the public dataset. In particular, we use FFHQ as public data for CelebA experiments. We train GAN models and three model augmentations using the public data. We remark that such setups closely replicate real-world MI attack scenario. We report top 1 accuracy and KNN distance for IR152, face.evoLve, and VGG16 target classifiers in Table 6. It is well known that baseline" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16390" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.243 + ], + "angle": 0, + "content": "Table 4. We follow exact the experiment setup of [36] for VMI experiments. Specifically, we use StyleGAN [17] and Flow model [19] to learn the distribution of \\( z \\). The best results are in **bold**. Following exact experiment setups in [36], here \\( \\mathcal{D}_{priv} = \\text{CelebA} \\), \\( \\mathcal{D}_{pub} = \\text{CelebA} \\), target model \\( = \\text{ResNet-34} \\), evaluation model \\( = \\text{IRSE50} \\). We report top 1 attack accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance (KNN Dist). The top 5 attack accuracies are included in the Supplementary. The best results are in **bold**. By alleviating both these major problems in MI algorithms, we improve the attack accuracy by \\( 14.94\\% \\) (\\( 59.96\\% \\rightarrow 74.90\\% \\))." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.253, + 0.44, + 0.346 + ], + "angle": 0, + "content": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/ResNet-34
VMI59.96 ± 0.27-1.144
+ LOM (Ours)68.34 ± 0.368.381.131
+ MA (Ours)64.16 ± 0.274.201.140
+ LOMMA (Ours)74.90 ± 0.3414.941.109
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.35, + 0.472, + 0.42 + ], + "angle": 0, + "content": "Table 5. Results for SOTA defense model BiDO-HSIC [27]: Following exact experiment setups in BiDO-HSIC, \\(\\mathcal{D}_{priv} = \\mathrm{CelebA}\\), \\(\\mathcal{D}_{pub} = \\mathrm{CelebA}\\), evaluation model = face.evoLve, target model = BiDO-HSIC. We report top 1 attack accuracies (Attack Acc.), and KNN distance (KNN Dist)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.424, + 0.469, + 0.503 + ], + "angle": 0, + "content": "
MethodGMIKEDMI
Attack Acc ↑KNN Dist ↓Attack Acc ↑KNN Dist ↓
No Def.19.07 ± 4.471715.6074.00 ± 3.101289.88
Def. Model5.20 ± 2.751962.5842.80 ± 5.021469.75
+ LOM (Ours)55.80 ± 3.641397.0564.33 ± 1.821360.57
+ MA (Ours)23.93 ± 5.501634.8449.27 ± 4.021413.81
+ LOMMA (Ours)62.13 ± 4.041358.5470.47 ± 2.361293.25
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.47, + 0.587 + ], + "angle": 0, + "content": "attack performances will degrade due to distribution shift between public and private data [5]. But we remark that our proposed methods consistently improves the baseline SOTA attack performances. i.e. Our method boosts the attack accuracy of IR152 target model from \\(52.87\\% \\rightarrow 77.27\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.727 + ], + "angle": 0, + "content": "MI under SOTA defense models. We further evaluate our method on SOTA MI defense models provided by BiDO-HSIC [27]. Specifically, we use the exact GAN and defense models provided by BiDO-HSIC which are trained on CelebA dataset. We then transfer knowledge from the defense model to \\( M_{\\text{aug}} = \\{\\text{Efficientnet-B0}, \\text{Efficientnet-B1}, \\text{Efficientnet-B2}\\} \\) using \\( D_{pub} \\). Results using GMI and KEDMI are shown in Table 5. We observe that SOTA defense BiDO-HSIC is rather ineffective for our proposed MI." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.192, + 0.755 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Conclusion. We revisit SOTA MI and study two issues pertaining to all SOTA MI approaches. First, we analyze existing identity loss in SOTA and argue that it is sub-optimal for MI. We propose a new logit based identity loss that aligns better with the goal of MI. Second, we formalize the concept of MI overfitting and show that it has a considerable impact even in SOTA. Inspired by conventional data augmentation, we propose model augmentation to alleviate MI overfitting. Extensive experiments demonstrate that" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.895, + 0.203 + ], + "angle": 0, + "content": "Table 6. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Here \\( \\mathcal{D}_{priv} = \\) CelebA, \\( \\mathcal{D}_{pub} = \\) FFHQ, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we improve the attack accuracy \\( 24.40\\% \\) (IR152: \\( 52.87\\% \\rightarrow 77.27\\% \\))." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.212, + 0.865, + 0.585 + ], + "angle": 0, + "content": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/FFHQ/IR152
KEDMI52.87 ± 4.96-1418.83
+ LOM (Ours)67.73 ± 2.2914.861325.28
+ MA (Ours)64.13 ± 4.4911.261373.42
+ LOMMA (Ours)77.27 ± 2.0124.401292.80
GMI17.20 ± 5.31-1701.76
+ LOM (Ours)56.00 ± 5.2038.801427.59
+ MA (Ours)50.80 ± 6.8933.601462.92
+ LOMMA (Ours)72.00 ± 6.6254.801338.35
CelebA/FFHQ/face.evoLve
KEDMI51.87 ± 3.88-1440.19
+ LOM (Ours)69.73 ± 2.4717.861379.73
+ MA (Ours)65.73 ± 3.5113.861379.09
+ LOMMA (Ours)73.20 ± 2.2421.331321.00
GMI14.27 ± 4.42-1744.47
+ LOM (Ours)47.93 ± 4.8733.661498.19
+ MA (Ours)46.07 ± 4.8831.801500.10
+ LOMMA (Ours)64.33 ± 4.6950.061386.33
CelebA/FFHQ/VGG16
KEDMI41.27 ± 3.50-1490.09
+ LOM (Ours)55.07 ± 1.8813.801438.72
+ MA (Ours)52.07 ± 2.9210.801428.77
+ LOMMA (Ours)62.67 ± 2.2921.401366.94
GMI10.93 ± 3.47-1766.27
+ LOM (Ours)44.40 ± 5.9633.471508.84
+ MA (Ours)34.93 ± 4.5224.001547.93
+ LOMMA (Ours)58.73 ± 6.1847.801415.06
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.669 + ], + "angle": 0, + "content": "our solutions can improve SOTA significantly, achieving for the first time over \\(90\\%\\) attack accuracy under the standard benchmark. Our findings highlight rising threats based on MI and prompt serious consideration on privacy of machine learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.793 + ], + "angle": 0, + "content": "Limitations and Ethical Concerns. We follow previous work in experimental setups. The scale of our experiments is comparable to previous works. Furthermore, extension of our methods for blackbox/ label-only attacks can be considered in future. While our improved MI methods could have negative societal impacts if it is used by malicious users, our work contributes to increased awareness about privacy attacks on DNNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programmes (AISG Award No.: AISG2-RP-2021-021; AISG Award No.: AISG2-TC-2022-007). This project is also supported by SUTD project PIE-SGP-AI-2018-01. We thank reviewers for their valuable comments. We also thank Loo Yi and Kelly Kuo for helpful discussion." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16391" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Milad Abdollahzadeh, Touba Malekzadeh, and Ngai-Man Cheung. Revisit multimodal meta-learning through the lens of multi-task learning. Advances in Neural Information Processing Systems, 34:14632-14644, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.242 + ], + "angle": 0, + "content": "[2] Brett K Beaulieu-Jones, Zhiwei Steven Wu, Chris Williams, Ran Lee, Sanjeev P Bhavnani, James Brian Byrd, and Casey S Greene. Privacy-preserving generative deep neural networks support clinical data sharing. 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In Advances in Neural Information Processing Systems, 2022." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16393" + } + ] +] \ No newline at end of file diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_origin.pdf b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e859ce50c38765324f49ebe9bd19f276e00c9763 --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/b89c7e51-fdb6-461b-acc1-402a12f4a254_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f28c8f3fd44c53f66e5f9530bce783a794b6237a97693b481ecabc7f720f5e22 +size 4279129 diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/full.md b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8406022b7f5f9b62337320cb3b2a88887d24aa26 --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/full.md @@ -0,0 +1,247 @@ +# Re-thinking Model Inversion Attacks Against Deep Neural Networks + +Ngoc-Bao Nguyen* Keshigeyan Chandrasegaran* Milad Abdollahzadeh Ngai-Man Cheung† +Singapore University of Technology and Design (SUTD) + +thibaongoc_nguyen@mymail.sutd.edu.sg,{keshigeyan,milad_abdollahzadeh,ngaiman_cheung}@sutd.edu.sg + +# Abstract + +Model inversion (MI) attacks aim to infer and reconstruct private training data by abusing access to a model. MI attacks have raised concerns about the leaking of sensitive information (e.g. private face images used in training a face recognition system). Recently, several algorithms for MI have been proposed to improve the attack performance. In this work, we revisit MI, study two fundamental issues pertaining to all state-of-the-art (SOTA) MI algorithms, and propose solutions to these issues which lead to a significant boost in attack performance for all SOTA MI. In particular, our contributions are two-fold: 1) We analyze the optimization objective of SOTA MI algorithms, argue that the objective is sub-optimal for achieving MI, and propose an improved optimization objective that boosts attack performance significantly. 2) We analyze "MI overfitting", show that it would prevent reconstructed images from learning semantics of training data, and propose a novel "model augmentation" idea to overcome this issue. Our proposed solutions are simple and improve all SOTA MI attack accuracy significantly. E.g., in the standard CelebA benchmark, our solutions improve accuracy by $11.8\%$ and achieve for the first time over $90\%$ attack accuracy. Our findings demonstrate that there is a clear risk of leaking sensitive information from deep learning models. We urge serious consideration to be given to the privacy implications. Our code, demo, and models are available at https://ngoc-nguyen-0.github.io/re-thinking_model_inversion_attacks/. + +# 1. Introduction + +Privacy of deep neural networks (DNNs) has attracted considerable attention recently [2, 3, 23, 31, 32]. Today, DNNs are being applied in many domains involving private and sensitive datasets, e.g., healthcare, and security. There is a growing concern of privacy attacks to gain knowledge of confidential datasets used in training DNNs. One + +important category of privacy attacks is Model Inversion (MI) [5, 8, 11, 12, 16, 36, 37, 39, 40] (Fig. 1). Given access to a model, MI attacks aim to infer and reconstruct features of the private dataset used in the training of the model. For example, a malicious user may attack a face recognition system to reconstruct sensitive face images used in training. Similar to previous work [5, 36, 39], we will use face recognition models as the running example. + +Related Work. MI attacks were first introduced in [12], where simple linear regression is the target of attack. Recently, there is a fair amount of interest to extend MI to complex DNNs. Most of these attacks [5, 36, 39] focus on the whitebox setting and the attacker is assumed to have complete knowledge of the model subject to attack. As many platforms provide downloading of entire trained DNNs for users [5, 39], whitebox attacks are important. [39] proposes Generative Model Inversion (GMI) attack, where generic public information is leveraged to learn a distributional prior via generative adversarial networks (GANs) [13, 35], and this prior is used to guide reconstruction of private training samples. [5] proposes Knowledge-Enriched Distributional Model Inversion (KEDMI), where an inversion-specific GAN is trained by leveraging knowledge provided by the target model. [36] proposes Variational Model Inversion (VMI), where a probabilistic interpretation of MI leads to a variational objective for the attack. KEDMI and VMI achieve SOTA attack performance (See Supplementary for further discussion of related work). + +In this paper, we revisit SOTA MI, study two issues pertaining to all SOTA MI and propose solutions to these issues that are complementary and applicable to all SOTA MI (Fig. 1). In particular, despite the range of approaches proposed in recent works, common and central to all these approaches is an inversion step which formulates reconstruction of training samples as an optimization. The optimization objective in the inversion step involves the identity loss, which is the same for all SOTA MI and is formulated as the negative log-likelihood for the reconstructed samples under the model being attacked. While ideas have been proposed to advance other aspects of MI, effective design of the identity loss has not been studied. + +![](images/50b2f108036a08cd727c88a3ed237952084036bfe5b85a952ecb529180215f19.jpg) +Figure 1. Overview and our contributions. $①$ We consider the problem of the Model Inversion (MI) attack to reconstruct private training data based on model parameters. Our work makes two foundational contributions to MI attacks. $②$ First, we analyse the optimization objective of existing SOTA MI algorithms and show that they are sub-optimal. Further, we propose an improved optimization objective that boosts MI attack performance significantly (Sec 3.1). $③$ Second, we formalize the concept of "MI overfitting" showing that it prevents reconstructed images from learning identity semantics of training data. Further, we propose a novel "model augmentation" idea to overcome this issue (Sec 3.2). $④$ Our proposed method significantly boosts MI attack accuracy. $E.g.$ In the standard CelebA benchmark, our method boosts attack accuracy by $11.8\%$ , achieving above $90\%$ attack accuracy for the first time in contemporary MI literature. + +![](images/17fbbe929754bfc236ef4ddb17646e003d9f80e9ddca2635f94026b9c9eb7fc7.jpg) + +![](images/56b293e499c8c72c281865399ea5f43c2425fec23c80e682b3a7092d648d0cae.jpg) + +To address this research gap, our work studies subtleties of identity loss in all SOTA MI, analyzes the issues and proposes improvements that boost the performance of all SOTA significantly. In summary, our contributions are as follows: + +- We analyze existing identity loss, argue that it could be sub-optimal for MI, and propose an improved identity loss that aligns better with the goal of MI (Fig. 1 ②). +- We formalize the concept of MI overfitting, analyze its impact on MI and propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue (Fig. 1 ③). +- We conduct extensive experiments to demonstrate that + +our solutions can improve SOTA MI algorithms (GMI [39], KEDMI [5], VMI [36]) significantly. Our solutions achieve for the first time over $90\%$ attack accuracy under standard CelebA benchmark (Fig. 1 $(4)$ ). + +Our work sounds alarm over the rising threats of MI attacks, and urges more attention on measures against the leaking of private information from DNNs. + +# 2. General Framework of SOTA MI Attacks + +Problem Setup. In MI, an attacker abuses access to a model $M$ trained on a private dataset $\mathcal{D}_{priv}$ . The attacker can access $M$ , but $\mathcal{D}_{priv}$ is not intended to be shared. The goal of MI is to infer information about private samples in $\mathcal{D}_{priv}$ . In existing work, for the desired class (label) $y$ , + +Table 1. Categorizing SOTA MI attacks based on their difference in latent code distribution and prior loss. $p_{\mathrm{GAN}}(\mathbf{z})$ is a GAN prior. $G$ and $D$ are generator and discriminator of a GAN. + +
MethodLatent distribution q(z)Prior loss Lprior
GMI [39]Point estimate δ(z - z0)-D(G(z))
KEDMI [5]Gaussian N(μ, Σ)- log D(G(z))
VMI [36]Gaussian N(μ, Σ) or Normalizing Flow [19]Distance w.r.t. GAN prior DKL(q(z)||pGAN(z))
+ +MI is formulated as the reconstruction of an input $\mathbf{x}$ which is most likely classified into $y$ by the model $M$ . For instance, if the problem involves inverting a facial recognition model, given the desired identity, MI is formulated as the reconstruction of facial images that are most likely to be recognized as the desired identity. The model subject to MI attacks is called target model. Following previous works [5, 36, 39], we focus on whitebox MI attack, where the attacker is assumed to have complete access to the target model. For high-dimensional data such as facial images, this reconstruction problem is ill-posed. Consequently, various SOTA MI methods have been proposed recently to constrain the search space to the manifold of meaningful and relevant images using a GAN: using a GAN trained on some public dataset $D_{pub}$ [39], using an inversion-specific GAN [5], and defining variational inference in latent space of GAN [36]. + +Despite the differences in various SOTA MI, common and central to all these methods is an inversion step -called secret revelation in [39]-, which performs the following optimization: + +$$ +q ^ {*} (\mathbf {z}) = \underset {q (\mathbf {z})} {\arg \min } \mathbb {E} _ {\mathbf {z} \sim q (\mathbf {z})} \left\{L _ {i d} (\mathbf {z}; y, M) + \lambda L _ {p r i o r} (\mathbf {z}) \right\} \tag {1} +$$ + +Here $L_{id}(\mathbf{z};y,M) = -\log \mathbb{P}_M(y|G(\mathbf{z}))$ is referred to as identity loss in MI [39], which guides the reconstruction of $\mathbf{x} = G(\mathbf{z})$ that is most likely to be recognized by model $M$ as identity $y$ , and $L_{prior}$ is some prior loss, and $q^{*}(\mathbf{z})$ is the optimal distribution of latent code used to generate inverted samples by GAN ( $\mathbf{x} = G(\mathbf{z})$ ; $\mathbf{z} \sim q^{*}(\mathbf{z}))$ . Importantly, all SOTA MI methods use the same identity loss $L_{id}(\mathbf{z};y,M)$ although they have different assumptions about $q(\mathbf{z})$ and the prior loss $L_{prior}$ (see Table 1 and Supplementary for more details on each algorithm). While advances observed by improving $q(\mathbf{z})$ and $L_{prior}$ , the design of more effective $L_{id}$ has been left unnoticed in all SOTA MI algorithms. Therefore, our work instead focuses on $L_{id}$ , analyzes issues, and proposes improvement for $L_{id}$ that can lead to a performance boost in all SOTA MI. To simplify notations, we denote $L_{id}(\mathbf{z};y,M)$ by $L_{id}(\mathbf{x};y)$ when appropriate, where + +$\mathbf{x} = G(\mathbf{z})$ is the reconstructed image. + +# 3. A Closer Look at Model Inversion Attacks + +# 3.1. An Improved Formulation of MI Identity Loss + +In this section, we discuss our first contribution and take a closer look at the optimization objective of identity loss, $L_{id}(\mathbf{x};y)$ . Existing SOTA MI methods, namely GMI [39], KEDMI [5] and VMI [36] formulate the identity loss as an optimization to minimize the negative log likelihood of an identity under model parameters (i.e. cross-entropy loss). Particularly, the $L_{id}(\mathbf{x};y)$ introduced in Eqn. 1 for an inversion targeting class $k$ can be re-written as follows: + +$$ +L _ {i d} (\mathbf {x}; y = k) = - \log \frac {\exp \left(\mathbf {p} ^ {T} \mathbf {w} _ {k}\right)}{\exp \left(\mathbf {p} ^ {T} \mathbf {w} _ {k}\right) + \sum_ {j = 1 , j \neq k} ^ {N} \exp \left(\mathbf {p} ^ {T} \mathbf {w} _ {j}\right)} \tag {2} +$$ + +where $\mathbf{p}$ refers to penultimate layer activations [4, 26] for sample $\mathbf{x}$ and $\mathbf{w}_i$ refers to the last layer weights for the $i^{th}$ class in target model $M$ . + +Existing identity loss (Eqn. 2) used in SOTA MI methods [5,36,39] is sub-optimal for MI (Fig. 1 ②). Although the optimization in Eqn. 2 accurately captures the essence of a classification problem (e.g. face recognition), we postulate that such formulation is sub-optimal for MI. We provide our intuition through the lens of penultimate layer activations, $\mathbf{p}$ (Fig. 1 ②). In a classification setting, the main expectation for $\mathbf{p}$ is to be sufficiently discriminative for class $k$ (e.g. recognize between 'Peter', 'Simon' and 'David'). This objective can be achieved by both maximizing $\exp (\mathbf{p}^T\mathbf{w}_k)$ and/or minimizing $\sum_{j = 1,j\neq k}^{N}\exp (\mathbf{p}^T\mathbf{w}_j)$ in Eqn. 2. On the contrary, the goal of MI is to reconstruct training data. That is, in addition to $\mathbf{p}$ being sufficiently discriminative for class $k$ , successful inversion also requires $\mathbf{p}$ to be close to the training data representations for class $k$ represented by $\mathbf{w}_k$ (i.e. an inversion targeting 'Simon' needs to reconstruct a sample close to the private training data of 'Simon'; Fig. 1 ②). Specifically, we argue that MI requires a lot more attention on maximizing $\exp (\mathbf{p}^T\mathbf{w}_k)$ compared to minimizing $\sum_{j = 1,j\neq k}^{N}\exp (\mathbf{p}^T\mathbf{w}_j)$ in Eqn. 2. + +Motivated by this hypothesis, we conduct an analysis to investigate the proximity between private training data and reconstructed data in SOTA MI methods using penultimate layer representations [4, 25, 26, 29]. Particularly, our analysis using KEDMI [5] (SOTA) shows several instances where using Eqn. 2 for identity loss is unable to reconstruct data close to the private training data. We show this in Fig. 2 (top row). Consequently, our analysis motivates the search for an improved identity loss focusing on maximizing $\exp (\mathbf{p}^T\mathbf{w}_k)$ for MI. + +![](images/9278f33ac2e3792433a38bab0d31b4b502276d201f1ff586d934f6d53e85f07e.jpg) +Figure 2. Visualization of the penultimate layer representations $(\mathcal{D}_{priv} = \text{CelebA}[24], \mathcal{D}_{pub} = \text{CelebA}[24], \text{Target Model} = \text{IR152}[5], \text{Evaluation Model} = \text{face.evoLve}[6], \text{Inversion iterations} = 2400)$ for private training data and reconstructed data using KEDMI [5]. Following the exact evaluation protocol in [5], we use face.evoLve [6] to extract representations. We show results for 3 randomly chosen identities. We include KNN distance (for different iterations) and final attack accuracy following the protocol in [5]. For each identity, we also include randomly selected private training data and the closest reconstructed sample at iteration $= 2400$ . ① Identity loss in SOTA MI methods [5, 36, 39] (Eqn. 2) is sub-optimal for MI (Top). Using penultimate representations during inversion, we observe 2 instances (e.g. target identity 57 and 143) where KEDMI [5] (using Eqn. 2 for identity loss) is unable to reconstruct data close to private training data. Hence, private and reconstructed facial images are qualitatively different. ② Our proposed identity loss, $L_{id}^{\text{logit}}$ (Eqn. 3), can effectively guide the reconstruction of data close to private training data (Bottom). This can be clearly observed using both penultimate layer representations and KNN distances for all 3 target classes 57, 143 and 252. We show similar results using additional MI algorithms (GMI [39], VMI [36]) and target classifiers (face.evoLve, VGG16) in Supplementary. Best viewed in color. + +Logit Maximization as an improved MI identity loss. In light of our analysis / observations above, we propose to directly maximize the logit, $\mathbf{p}^T\mathbf{w}_k$ , instead of maximizing the log likelihood of class $k$ for MI. Our proposed identity loss objective is shown below: + +$$ +L _ {i d} ^ {\text {l o g i t}} (\mathbf {x}; y = k) = - \log \mathbf {p} ^ {T} \mathbf {w} _ {k} + \lambda | | \mathbf {p} - \mathbf {p} _ {r e g} | | _ {2} ^ {2} \tag {3} +$$ + +where $\lambda (>0)$ is a hyper-parameter and $\mathbf{p}_{reg}$ is used for regularizing $\mathbf{p}$ . Particularly, if the regularization in Eqn. 3 is omitted and hence $||\mathbf{p}||$ is unbounded, a crude simplified way to solve Eqn. 3 is to maximize $||\mathbf{p}||$ . Hence, we use $\mathbf{p}_{reg}$ to regularize $\mathbf{p}$ . Given that the attacker has no access to private training data, we estimate $\mathbf{p}_{reg}$ by a simple method using public data (See Supplementary). We remark that $\mathbf{p} = M^{\mathrm{pen}}(\mathbf{x})$ where $\mathbf{x} = G(\mathbf{z})$ and $M^{\mathrm{pen}}()$ operator returns the penultimate layer representations for a given input. + +Our analysis shows that our proposed identity loss, $L_{id}^{logit}$ (Eqn. 3), can significantly improve reconstruction of private training data compared to existing identity loss used in SOTA MI algorithms [5,36,39]. This can be clearly observed using both penultimate layer representations and + +KNN distances in Fig. 2 (bottom row). Here KNN Dist refers to the shortest Euclidean feature distance from a reconstructed image to private training images for a given identity [5, 39]. Our proposed $L_{id}^{logit}$ can be easily plugged in to all existing SOTA MI algorithms by replacing $L_{id}$ with our proposed $L_{id}^{logit}$ in Eqn. 1 (in the inversion step) with minimal computational overhead. + +# 3.2. Overcoming MI Overfitting in SOTA methods + +In this section, we discuss our second contribution. In particular, we formalize a concept of MI overfitting, observe its considerable impacts even in SOTA MI methods [5,36,39], and propose a new, simple solution to overcome this issue (Fig. 1 ③). To better discuss our MI overfitting concept, we first review the conventional concept of overfitting in machine learning: Given the fixed training dataset and our goal of learning a model, conventionally, overfitting is defined as instances which during model learning (training stage), the model fits too closely to the training data and adapts to the random variation and noise of training data, failing to adequately learn the semantics of the train + +ing data [1, 28, 34, 38, 41]. As the model lacks semantics of training data, it could be observed that the model performs poorly under unseen data (Fig. 1 ③ a). + +![](images/6d197a0e38f4790aa33f3775e3cbd12071567148a50328a1f115e2367ec07b2a.jpg) + +![](images/5b3f6c822708cef5812907755138233199f329b072a6a19f172968b162748cf3.jpg) +Figure 3. Qualitative / Quantitative studies to demonstrate MI overfitting in SOTA methods. We demonstrate this observation using KEDMI [5]. We use $\mathcal{D}_{pri} =$ CelebA [24], $\mathcal{D}_{pub} =$ CelebA [24] and $M = \mathrm{IR152}$ [5]. ① We show qualitative results to illustrate MI overfitting. We show 6 identities, top: private data, bottom: reconstructed data from $M$ . The reconstructed samples have fit too closely to $M$ during inversion resulting in samples with lack of identity semantics. Particularly, we remark that these samples have very low identity loss under the target model $M$ . ② Quantitative results validating the prevalence of MI overfitting in SOTA MI methods. We use an additional target classifier $M' =$ VGG16 released by [5, 39] to quantitatively verify the presence of MI overfitting using identity loss. For 1,500 reconstructed samples from $M$ , we visualize their identity loss w.r.t. $M$ and $M'$ in the scatter plot and respective histograms. Particularly, we find that there are $26.7\%$ of samples with low identity loss under the target model $M$ , but large identity loss under unseen VGG16 model $M'$ , hinting that these samples might lack identity semantics. This result shows that MI overfitting is a considerable issue even in SOTA MI methods. Note that VGG16 is used here only for analysis and is not part of our solution, as private data is not available. ③ Model Augmentation to alleviate MI overfitting during inversion. We repeat the above analysis, with $M' = \mathrm{VGG16}$ replaced by $M_{aug}$ = EfficientNet-B0. Importantly, $M_{aug}$ is trained by public data using knowledge distillation [15]. We similarly observe samples with large identity loss under $M_{aug}$ . + +![](images/d4caea7b827282e5a73a2b3e5184d4ba91815018c0671436a413f6fb39817f24.jpg) + +Overfitting in MI. We formalize the concept of overfitting in MI (Fig. 1 ③ ⑥). Given the fixed (target) model and our goal of learning reconstructed samples, we define MI overfitting as instances which during model inversion, the reconstructed samples fit too closely to the target model and adapt to the random variation and noise of the target model parameters, failing to adequately learn semantics of the identity. As these reconstructed samples lack identity semantics, it could be observed that they perform poorly under another unseen model. + +Analysis. In what follows, we discuss our analysis to demonstrate MI overfitting and understand its impact in SOTA. See Fig. 3 for analysis setups and results. In particular, in Fig. 3 (1), we show some reconstructed samples which achieve low identity loss under the target model $M$ , yet they lack identity semantics. In Fig. 3 (2), we show that for a considerable percentage of reconstructed samples from target model $M$ with low identity loss under $M$ , their identity loss under another unseen model $M'$ is large as shown in the scatter plot and histograms, hinting that these samples might have suffered from MI overfitting and lack identity semantics. We note that the identity loss under $M'$ is obtained by feeding the reconstructed sample into $M'$ in a forward pass. We also note that SOTA KEDMI [5] is used in this analysis but the issue persists in [36, 39]. + +Our proposed solution to MI overfitting. We propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue. In particular, for conventional overfitting, augmenting the training dataset could alleviate the issue [21]. Therefore, we hypothesize that by augmenting the target model we can alleviate MI overfitting. + +Specifically, we propose to apply knowledge distillation (KD) [15], with target model $M_{t}$ as the teacher, to train augmented models $M_{aug}^{(i)}$ . Importantly, as we do not have access to the private data, during KD, each $M_{aug}^{(i)}$ is trained on the public dataset to match its output to the output of $M_{t}$ . We select different network architectures for $M_{aug}^{(i)}$ and they are different from $M_{t}$ (Detailed discussion in the Supplementary). After performing KD, we apply $M_{aug}^{(i)}$ together with the target model $M_{t}$ in the inversion step and compute the identity loss (with model augmentation): + +$$ +\begin{array}{l} L _ {i d} ^ {a u g} (\mathbf {x}; y) = \gamma_ {t} \cdot L _ {i d} (\mathbf {x}; y, M _ {t}) \\ + \gamma_ {a u g} \cdot \sum_ {i = 1} ^ {N _ {a u g}} L _ {i d} (\mathbf {x}; y, M _ {a u g} ^ {(i)}) \tag {4} \\ \end{array} +$$ + +Here, $\gamma_{t}$ and $\gamma_{aug}$ are two hyper-parameters. In particular, we use $\gamma_{t} = \gamma_{aug} = \frac{1}{N_{aug} + 1}$ , where $N_{aug}$ is the number of augmented models. $L_{id}^{aug}$ in Eqn. 4 is used to replace $L_{id}$ in the inversion step in Eqn. 1. Furthermore, our proposed $L_{id}^{logit}$ in Eqn. 3 can be used in Eqn. 4 to combine the improvements. See details in Supplementary. + +In Fig. 3 (3), we analyze the performance of $M_{\text{aug}}^{(i)}$ . Similar to using the unseen model $M'$ , we observe samples with large identity loss under $M_{\text{aug}}^{(i)}$ , suggesting that samples with MI overfitting perform poorly under $M_{\text{aug}}^{(i)}$ as these samples lack identity semantic. + +Table 2. We follow the exact the experiment setups in [5] for GMI [39] and KEDMI [5]. For VMI [36], we follow the exact experiment setups in [36]. In total, we conduct 72 experiments spanning 18 setups to demonstrate the effectiveness of our proposed method. + +
MethodPrivate DatasetPublic DatasetTarget modelEvaluation ModelModel Augmentation
GMI [39] / KEDMI [5]CelebA [24]CelebA / FFHQ [18]VGG16 [30] / IR152 [14] / face.evoLve [7]face.evoLveEfficientNet-B0 [33], EfficientNet-B1 [33], EfficientNet-B2 [33]
CIFAR-10 [20]CIFAR-10VGG16ResNet-18 [14]
MNIST [22]MNISTCNN(Conv3)CNN(Conv5)CNN(Conv2), CNN(Conv4)
VMI [36]CelebACelebAResNet-34 [14]IR-SE50 [10]EfficientNet-B0, EfficientNet-B1, EfficientNet-B2
MNISTEMNIST [9]ResNet-10ResNet-10CNN(Conv2), CNN(Conv4)
+ +# 4. Experiments + +In this section, we evaluate the performance of the proposed method in recovering a representative input from the target model, against current SOTA methods: GMI [39], VMI [36], and KEDMI [5]. More specifically, as our proposed method identifies two major limitations in current $L_{id}(\mathbf{x};y)$ -used commonly in all SOTA MI approaches-- we will evaluate the improvement brought by our improved identity loss $L_{id}^{\text{logit}}$ , and model augmentation $L_{id}^{\text{aug}}$ for all SOTA MI approaches. + +# 4.1. Experimental Setup + +In order to have a fair comparison, when evaluating our method against each SOTA MI approach, we follow the exactly same experimental setup of that approach. In what follows, we discuss the details of these setups. + +Dataset. Following previous works, we evaluate the proposed method on different tasks: face recognition and digit classification is used for comparison with all three SOTA approaches, and image classification is used for comparison with GMI [39], and KEDMI [5]. For the face recognition task, we use CelebA dataset [24] that includes celebrity images, and the FFHQ dataset [18] which contains images with larger variation in terms of background, ethnicity, and age. The MNIST handwritten digits dataset [22] is used for digit classification. We utilize the CIFAR-10 dataset [20] for image classification. + +Data Preparation Protocol. Following previous SOTA approaches [5, 36, 39], we split each dataset into two disjoint parts: one part is used as private dataset $\mathcal{D}_{priv}$ for training target model, and another part is used as a public dataset $\mathcal{D}_{pub}$ to extract the prior information. Most importantly, throughout all experiments, public dataset $\mathcal{D}_{pub}$ has no class intersection with private dataset $\mathcal{D}_{priv}$ used for training target model. Note that this is essential to make sure that adversary uses $\mathcal{D}_{pub}$ only to gain prior knowledge about features that are general to that task (i.e., face recognition), and does not have access to information about class-specific and private information used for training target model. + +Models. Following previous works, we implement several different models with varied complexities. As GMI [39] and KEDMI [5] use exactly similar model architecture in experiments, for comparison with these two algorithms, we use the same models. More specifically, for face recognition on CelebA and FFHQ, we use VGG16 [30], IR152 [14], and face.evoLve [7]–as SOTA face recognition model. For digit classification on MNIST, we use a CNN with 3 convolutional layers and 2 pooling layers. Finally, for image classification, following [5] we use VGG16 [30]. For a fair comparison with VMI, we follow its design in [36] and use ResNet-34 for face recognition CelebA, and ResNet-10 for digit classification on MNIST. The details of the target models, augmented models and datasets used in experiments are summarized in Table 2. We remark that when comparing our proposed method with each of the SOTA MI approaches, we use exactly the same target model and GAN for both SOTA and our approach. + +Evaluation Metrics. To evaluate the performance of a MI attack, we need to assess whether the reconstructed image exposes private information about a target label/identity. In this work, following the literature, we conduct both qualitative evaluations by visual inspection, and quantitative evaluations using different metrics, including: + +- Attack Accuracy (Attack Acc). Following [5, 36, 39], we use an evaluation model that predicts the label/identity of the reconstructed image. Similar to previous works, the evaluation model is different from the target model (different structure/initialization seed), but it is trained on the same private dataset (see Table 2). Intuitively, considering a highly accurate evaluation model, it can be viewed as a proxy for human inspection [39]. Therefore, if the evaluation model infers high accuracy on reconstructed images, it means these images are exposing private information about the private dataset, i.e. high attack accuracy. + +- K-Nearest Neighbors Distance (KNN Dist). KNN Dist indicates the distance between the reconstructed image for a specific label/id and corresponding images in the private training dataset. More specifically, it measures the + +shortest feature distance from the reconstructed image to the real images in the private dataset, given a class/id. It is measured as $l_{2}$ distance between two images in the feature space, i.e., the penultimate layer of the evaluation model. + +![](images/fb179728287c4ce1926f04c27541decf13be3f6a3f1eb932e22a2850d54ed29f.jpg) +Figure 4. Qualitative / Quantitative (Top1 Attack Acc., KNN Dist) results to demonstrate the efficacy of our proposed method. We use KEDMI [5] (SOTA), $\mathcal{D}_{priv} = \text{CelebA}$ [24], $\mathcal{D}_{pub} = \text{CelebA}$ [24] and $M = \text{IR152}$ [14]. As one can observe, our proposed method achieves better reconstruction of private data both visually and quantitatively (validated by KNN results) resulting in a significant boost in attack performance. + +# 4.2. Experimental Results + +Comparison with previous state-of-the-art. We use GMI [39], KEDMI [5], and VMI [36] as SOTA MI baselines. We reproduce all baseline results using official public implementations. We report results for GMI and KEDMI for CelebA/ CelebA experiments in Table 3. We report VMI results for CelebA/ CelebA experiments in Table 4. For each baseline setup, we report results for 3 variants: $\bullet$ LOM (Logit Maximization, Sec. 3.1), $\bullet$ MA (Model Augmentation, Sec. 3.2), $\bullet$ LOMMA (Logit Maximization + Model Augmentation). The details are as follows: + +1. +LOM (Ours): We replace existing identity loss, $L_{id}$ with our improved identity loss $L_{id}^{logit}$ (Sec. 3.1). +2. + MA (Ours): We replace existing identity loss, $L_{id}$ with our proposed $L_{id}^{aug}$ (Sec. 3.2). +3. +LOMMA (Ours): We combine both $L_{id}^{logit}$ (Sec. 3.1) and $L_{id}^{aug}$ (Sec. 3.2) for model inversion. + +As one can clearly observe from Table 3 and Table 4, our proposed methods yield significant improvement in MI attack accuracy in all experiment setups showing the efficacy of our proposed methods. Further, by combining both our proposed methods, we significantly boost attack accuracy. The KNN results also clearly show that our proposed methods are able to reconstruct data close to the private training data compared to existing SOTA MI algorithms. Particularly, we improve the KEDMI baseline [5] attack accuracy by $12.4\%$ under IR152 target classifier. We show private + +Table 3. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Following exact experiment setups in [5], here $\mathcal{D}_{priv} =$ CelebA, $\mathcal{D}_{pub} =$ CelebA, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we achieve new SOTA MI performance (face.evoLve: $81.40\% \rightarrow 93.20\%$ ). + +
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/IR152
KEDMI80.53 ± 3.86-1247.28
+ LOM (Ours)92.47 ± 1.4111.941168.55
+ MA (Ours)84.73 ± 3.764.201220.23
+ LOMMA (Ours)92.93 ± 1.1512.401138.62
GMI30.60 ± 6.54-1609.29
+ LOM (Ours)78.53 ± 3.4147.931289.62
+ MA (Ours)61.20 ± 4.3430.601389.99
+ LOMMA (Ours)82.40± 4.3751.801254.32
+ +CelebA/CelebA/face.evoLve + +
KEDMI81.40 ± 3.25-1248.32
+ LOM (Ours)92.53 ± 1.5111.131183.76
+ MA (Ours)85.07 ± 2.713.671222.02
+ LOMMA (Ours)93.20 ± 0.8511.801154.32
GMI27.07 ± 6.72-1635.87
+ LOM (Ours)61.67 ± 4.9234.601405.35
+ MA (Ours)74.13 ± 4.3247.061352.25
+ LOMMA (Ours)82.33 ± 3.5155.261257.50
+ +CelebA/CelebA/VGG16 + +
KEDMI74.00 ± 3.10-1289.88
+ LOM (Ours)89.07 ± 1.4615.071218.46
+ MA (Ours)82.00 ± 3.858.001248.33
+ LOMMA (Ours)90.27 ± 1.3616.271147.41
GMI19.07 ± 4.47-1715.60
+ LOM (Ours)69.67 ± 4.8050.601363.81
+ MA (Ours)51.73 ± 6.0332.661467.68
+ LOMMA (Ours)77.60 ± 4.6458.531296.26
+ +training data and reconstructed samples for KEDMI [5] under IR152 target model including all 3 variants in Fig. 4. We remark that in the standard CelebA benchmark, our method boosts attack accuracy significantly thereby achieving more than $90\%$ attack accuracy (Table 3) for the first time in contemporary MI literature. We also include CIFAR-10, MNIST and additional results in Supplementary. + +Cross-dataset. Following [5], we conduct a series of experiments to study the effect of distribution shift between public and private data on attack performance and KNN distance. We use FFHQ [18] as the public dataset. In particular, we use FFHQ as public data for CelebA experiments. We train GAN models and three model augmentations using the public data. We remark that such setups closely replicate real-world MI attack scenario. We report top 1 accuracy and KNN distance for IR152, face.evoLve, and VGG16 target classifiers in Table 6. It is well known that baseline + +Table 4. We follow exact the experiment setup of [36] for VMI experiments. Specifically, we use StyleGAN [17] and Flow model [19] to learn the distribution of $z$ . The best results are in **bold**. Following exact experiment setups in [36], here $\mathcal{D}_{priv} = \text{CelebA}$ , $\mathcal{D}_{pub} = \text{CelebA}$ , target model $= \text{ResNet-34}$ , evaluation model $= \text{IRSE50}$ . We report top 1 attack accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance (KNN Dist). The top 5 attack accuracies are included in the Supplementary. The best results are in **bold**. By alleviating both these major problems in MI algorithms, we improve the attack accuracy by $14.94\%$ ( $59.96\% \rightarrow 74.90\%$ ). + +
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/ResNet-34
VMI59.96 ± 0.27-1.144
+ LOM (Ours)68.34 ± 0.368.381.131
+ MA (Ours)64.16 ± 0.274.201.140
+ LOMMA (Ours)74.90 ± 0.3414.941.109
+ +Table 5. Results for SOTA defense model BiDO-HSIC [27]: Following exact experiment setups in BiDO-HSIC, $\mathcal{D}_{priv} = \mathrm{CelebA}$ , $\mathcal{D}_{pub} = \mathrm{CelebA}$ , evaluation model = face.evoLve, target model = BiDO-HSIC. We report top 1 attack accuracies (Attack Acc.), and KNN distance (KNN Dist). + +
MethodGMIKEDMI
Attack Acc ↑KNN Dist ↓Attack Acc ↑KNN Dist ↓
No Def.19.07 ± 4.471715.6074.00 ± 3.101289.88
Def. Model5.20 ± 2.751962.5842.80 ± 5.021469.75
+ LOM (Ours)55.80 ± 3.641397.0564.33 ± 1.821360.57
+ MA (Ours)23.93 ± 5.501634.8449.27 ± 4.021413.81
+ LOMMA (Ours)62.13 ± 4.041358.5470.47 ± 2.361293.25
+ +attack performances will degrade due to distribution shift between public and private data [5]. But we remark that our proposed methods consistently improves the baseline SOTA attack performances. i.e. Our method boosts the attack accuracy of IR152 target model from $52.87\% \rightarrow 77.27\%$ . + +MI under SOTA defense models. We further evaluate our method on SOTA MI defense models provided by BiDO-HSIC [27]. Specifically, we use the exact GAN and defense models provided by BiDO-HSIC which are trained on CelebA dataset. We then transfer knowledge from the defense model to $M_{\text{aug}} = \{\text{Efficientnet-B0}, \text{Efficientnet-B1}, \text{Efficientnet-B2}\}$ using $D_{pub}$ . Results using GMI and KEDMI are shown in Table 5. We observe that SOTA defense BiDO-HSIC is rather ineffective for our proposed MI. + +# 5. Discussion + +Conclusion. We revisit SOTA MI and study two issues pertaining to all SOTA MI approaches. First, we analyze existing identity loss in SOTA and argue that it is sub-optimal for MI. We propose a new logit based identity loss that aligns better with the goal of MI. Second, we formalize the concept of MI overfitting and show that it has a considerable impact even in SOTA. Inspired by conventional data augmentation, we propose model augmentation to alleviate MI overfitting. Extensive experiments demonstrate that + +Table 6. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Here $\mathcal{D}_{priv} =$ CelebA, $\mathcal{D}_{pub} =$ FFHQ, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we improve the attack accuracy $24.40\%$ (IR152: $52.87\% \rightarrow 77.27\%$ ). + +
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/FFHQ/IR152
KEDMI52.87 ± 4.96-1418.83
+ LOM (Ours)67.73 ± 2.2914.861325.28
+ MA (Ours)64.13 ± 4.4911.261373.42
+ LOMMA (Ours)77.27 ± 2.0124.401292.80
GMI17.20 ± 5.31-1701.76
+ LOM (Ours)56.00 ± 5.2038.801427.59
+ MA (Ours)50.80 ± 6.8933.601462.92
+ LOMMA (Ours)72.00 ± 6.6254.801338.35
CelebA/FFHQ/face.evoLve
KEDMI51.87 ± 3.88-1440.19
+ LOM (Ours)69.73 ± 2.4717.861379.73
+ MA (Ours)65.73 ± 3.5113.861379.09
+ LOMMA (Ours)73.20 ± 2.2421.331321.00
GMI14.27 ± 4.42-1744.47
+ LOM (Ours)47.93 ± 4.8733.661498.19
+ MA (Ours)46.07 ± 4.8831.801500.10
+ LOMMA (Ours)64.33 ± 4.6950.061386.33
CelebA/FFHQ/VGG16
KEDMI41.27 ± 3.50-1490.09
+ LOM (Ours)55.07 ± 1.8813.801438.72
+ MA (Ours)52.07 ± 2.9210.801428.77
+ LOMMA (Ours)62.67 ± 2.2921.401366.94
GMI10.93 ± 3.47-1766.27
+ LOM (Ours)44.40 ± 5.9633.471508.84
+ MA (Ours)34.93 ± 4.5224.001547.93
+ LOMMA (Ours)58.73 ± 6.1847.801415.06
+ +our solutions can improve SOTA significantly, achieving for the first time over $90\%$ attack accuracy under the standard benchmark. Our findings highlight rising threats based on MI and prompt serious consideration on privacy of machine learning. + +Limitations and Ethical Concerns. We follow previous work in experimental setups. The scale of our experiments is comparable to previous works. Furthermore, extension of our methods for blackbox/ label-only attacks can be considered in future. While our improved MI methods could have negative societal impacts if it is used by malicious users, our work contributes to increased awareness about privacy attacks on DNNs. + +Acknowledgements. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programmes (AISG Award No.: AISG2-RP-2021-021; AISG Award No.: AISG2-TC-2022-007). This project is also supported by SUTD project PIE-SGP-AI-2018-01. We thank reviewers for their valuable comments. 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In Advances in Neural Information Processing Systems, 2022. \ No newline at end of file diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/images.zip b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6cee7f3295a1c4d7000392ea4de7c38c262b746c --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ebb53c23f098d6af9ad772b4d3ed25835b294e5c8a12d0911de24788b7264f64 +size 798726 diff --git a/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/layout.json b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d88eac5a10b94ddf51d4967f0a2debbda1acf78b --- /dev/null +++ b/2023/Re-Thinking Model Inversion Attacks Against Deep Neural Networks/layout.json @@ -0,0 +1,8985 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 85, + 103, + 509, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 103, + 509, + 121 + ], + "spans": [ + { + "bbox": [ + 85, + 103, + 509, + 121 + ], + "type": "text", + "content": "Re-thinking Model Inversion Attacks Against Deep Neural Networks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 143, + 545, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 143, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 64, + 143, + 545, + 172 + ], + "type": "text", + "content": "Ngoc-Bao Nguyen* Keshigeyan Chandrasegaran* Milad Abdollahzadeh Ngai-Man Cheung† \nSingapore University of Technology and Design (SUTD)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 41, + 174, + 553, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 41, + 174, + 553, + 186 + ], + "spans": [ + { + "bbox": [ + 41, + 174, + 553, + 186 + ], + "type": "text", + "content": "thibaongoc_nguyen@mymail.sutd.edu.sg,{keshigeyan,milad_abdollahzadeh,ngaiman_cheung}@sutd.edu.sg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "text", + "content": "Model inversion (MI) attacks aim to infer and reconstruct private training data by abusing access to a model. MI attacks have raised concerns about the leaking of sensitive information (e.g. private face images used in training a face recognition system). Recently, several algorithms for MI have been proposed to improve the attack performance. In this work, we revisit MI, study two fundamental issues pertaining to all state-of-the-art (SOTA) MI algorithms, and propose solutions to these issues which lead to a significant boost in attack performance for all SOTA MI. In particular, our contributions are two-fold: 1) We analyze the optimization objective of SOTA MI algorithms, argue that the objective is sub-optimal for achieving MI, and propose an improved optimization objective that boosts attack performance significantly. 2) We analyze \"MI overfitting\", show that it would prevent reconstructed images from learning semantics of training data, and propose a novel \"model augmentation\" idea to overcome this issue. Our proposed solutions are simple and improve all SOTA MI attack accuracy significantly. E.g., in the standard CelebA benchmark, our solutions improve accuracy by " + }, + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "inline_equation", + "content": "11.8\\%" + }, + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "text", + "content": " and achieve for the first time over " + }, + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 239, + 290, + 574 + ], + "type": "text", + "content": " attack accuracy. Our findings demonstrate that there is a clear risk of leaking sensitive information from deep learning models. We urge serious consideration to be given to the privacy implications. Our code, demo, and models are available at https://ngoc-nguyen-0.github.io/re-thinking_model_inversion_attacks/." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "content": "Privacy of deep neural networks (DNNs) has attracted considerable attention recently [2, 3, 23, 31, 32]. Today, DNNs are being applied in many domains involving private and sensitive datasets, e.g., healthcare, and security. There is a growing concern of privacy attacks to gain knowledge of confidential datasets used in training DNNs. One" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 213, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 547, + 312 + ], + "type": "text", + "content": "important category of privacy attacks is Model Inversion (MI) [5, 8, 11, 12, 16, 36, 37, 39, 40] (Fig. 1). Given access to a model, MI attacks aim to infer and reconstruct features of the private dataset used in the training of the model. For example, a malicious user may attack a face recognition system to reconstruct sensitive face images used in training. Similar to previous work [5, 36, 39], we will use face recognition models as the running example." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 314, + 547, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 547, + 554 + ], + "type": "text", + "content": "Related Work. MI attacks were first introduced in [12], where simple linear regression is the target of attack. Recently, there is a fair amount of interest to extend MI to complex DNNs. Most of these attacks [5, 36, 39] focus on the whitebox setting and the attacker is assumed to have complete knowledge of the model subject to attack. As many platforms provide downloading of entire trained DNNs for users [5, 39], whitebox attacks are important. [39] proposes Generative Model Inversion (GMI) attack, where generic public information is leveraged to learn a distributional prior via generative adversarial networks (GANs) [13, 35], and this prior is used to guide reconstruction of private training samples. [5] proposes Knowledge-Enriched Distributional Model Inversion (KEDMI), where an inversion-specific GAN is trained by leveraging knowledge provided by the target model. [36] proposes Variational Model Inversion (VMI), where a probabilistic interpretation of MI leads to a variational objective for the attack. KEDMI and VMI achieve SOTA attack performance (See Supplementary for further discussion of related work)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "type": "text", + "content": "In this paper, we revisit SOTA MI, study two issues pertaining to all SOTA MI and propose solutions to these issues that are complementary and applicable to all SOTA MI (Fig. 1). In particular, despite the range of approaches proposed in recent works, common and central to all these approaches is an inversion step which formulates reconstruction of training samples as an optimization. The optimization objective in the inversion step involves the identity loss, which is the same for all SOTA MI and is formulated as the negative log-likelihood for the reconstructed samples under the model being attacked. While ideas have been proposed to advance other aspects of MI, effective design of the identity loss has not been studied." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "type": "text", + "content": "* Equal Contribution † Corresponding Author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16384" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 298, + 434 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 298, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 298, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 298, + 434 + ], + "type": "image", + "image_path": "50b2f108036a08cd727c88a3ed237952084036bfe5b85a952ecb529180215f19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "lines": [ + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": "Figure 1. Overview and our contributions. " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " We consider the problem of the Model Inversion (MI) attack to reconstruct private training data based on model parameters. Our work makes two foundational contributions to MI attacks. " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "②" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " First, we analyse the optimization objective of existing SOTA MI algorithms and show that they are sub-optimal. Further, we propose an improved optimization objective that boosts MI attack performance significantly (Sec 3.1). " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "③" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " Second, we formalize the concept of \"MI overfitting\" showing that it prevents reconstructed images from learning identity semantics of training data. Further, we propose a novel \"model augmentation\" idea to overcome this issue (Sec 3.2). " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "④" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " Our proposed method significantly boosts MI attack accuracy. " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "E.g." + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " In the standard CelebA benchmark, our method boosts attack accuracy by " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "11.8\\%" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " , achieving above " + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 437, + 545, + 514 + ], + "type": "text", + "content": " attack accuracy for the first time in contemporary MI literature." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 72, + 536, + 279 + ], + "blocks": [ + { + "bbox": [ + 299, + 72, + 536, + 279 + ], + "lines": [ + { + "bbox": [ + 299, + 72, + 536, + 279 + ], + "spans": [ + { + "bbox": [ + 299, + 72, + 536, + 279 + ], + "type": "image", + "image_path": "17fbbe929754bfc236ef4ddb17646e003d9f80e9ddca2635f94026b9c9eb7fc7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 281, + 536, + 434 + ], + "blocks": [ + { + "bbox": [ + 299, + 281, + 536, + 434 + ], + "lines": [ + { + "bbox": [ + 299, + 281, + 536, + 434 + ], + "spans": [ + { + "bbox": [ + 299, + 281, + 536, + 434 + ], + "type": "image", + "image_path": "56b293e499c8c72c281865399ea5f43c2425fec23c80e682b3a7092d648d0cae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 523, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 571 + ], + "type": "text", + "content": "To address this research gap, our work studies subtleties of identity loss in all SOTA MI, analyzes the issues and proposes improvements that boost the performance of all SOTA significantly. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 579, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 579, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 287, + 616 + ], + "type": "text", + "content": "- We analyze existing identity loss, argue that it could be sub-optimal for MI, and propose an improved identity loss that aligns better with the goal of MI (Fig. 1 ②)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 623, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 288, + 694 + ], + "type": "text", + "content": "- We formalize the concept of MI overfitting, analyze its impact on MI and propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue (Fig. 1 ③)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "content": "- We conduct extensive experiments to demonstrate that" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "text", + "content": "our solutions can improve SOTA MI algorithms (GMI [39], KEDMI [5], VMI [36]) significantly. Our solutions achieve for the first time over " + }, + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "text", + "content": " attack accuracy under standard CelebA benchmark (Fig. 1 " + }, + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "inline_equation", + "content": "(4)" + }, + { + "bbox": [ + 313, + 523, + 545, + 571 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 305, + 584, + 545, + 620 + ], + "type": "text", + "content": "Our work sounds alarm over the rising threats of MI attacks, and urges more attention on measures against the leaking of private information from DNNs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 633, + 533, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 533, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 533, + 645 + ], + "type": "text", + "content": "2. General Framework of SOTA MI Attacks" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": "Problem Setup. In MI, an attacker abuses access to a model " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": " trained on a private dataset " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv}" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": ". The attacker can access " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": ", but " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv}" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": " is not intended to be shared. The goal of MI is to infer information about private samples in " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv}" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": ". In existing work, for the desired class (label) " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16385" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 113, + 287, + 209 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "text", + "content": "Table 1. Categorizing SOTA MI attacks based on their difference in latent code distribution and prior loss. " + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{GAN}}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "text", + "content": " is a GAN prior. " + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 70, + 287, + 104 + ], + "type": "text", + "content": " are generator and discriminator of a GAN." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 113, + 287, + 209 + ], + "lines": [ + { + "bbox": [ + 48, + 113, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 48, + 113, + 287, + 209 + ], + "type": "table", + "html": "
MethodLatent distribution q(z)Prior loss Lprior
GMI [39]Point estimate δ(z - z0)-D(G(z))
KEDMI [5]Gaussian N(μ, Σ)- log D(G(z))
VMI [36]Gaussian N(μ, Σ) or Normalizing Flow [19]Distance w.r.t. GAN prior DKL(q(z)||pGAN(z))
", + "image_path": "056310ae6a62f95b9f0346c7b495c6c8d1338a44ab8f8cccab3fb91ff91065ef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "content": "MI is formulated as the reconstruction of an input " + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "content": " which is most likely classified into " + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "content": " by the model " + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "content": ". For instance, if the problem involves inverting a facial recognition model, given the desired identity, MI is formulated as the reconstruction of facial images that are most likely to be recognized as the desired identity. The model subject to MI attacks is called target model. Following previous works [5, 36, 39], we focus on whitebox MI attack, where the attacker is assumed to have complete access to the target model. For high-dimensional data such as facial images, this reconstruction problem is ill-posed. Consequently, various SOTA MI methods have been proposed recently to constrain the search space to the manifold of meaningful and relevant images using a GAN: using a GAN trained on some public dataset " + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "inline_equation", + "content": "D_{pub}" + }, + { + "bbox": [ + 46, + 229, + 287, + 433 + ], + "type": "text", + "content": " [39], using an inversion-specific GAN [5], and defining variational inference in latent space of GAN [36]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 434, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 482 + ], + "type": "text", + "content": "Despite the differences in various SOTA MI, common and central to all these methods is an inversion step -called secret revelation in [39]-, which performs the following optimization:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 491, + 287, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 491, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 55, + 491, + 287, + 521 + ], + "type": "interline_equation", + "content": "q ^ {*} (\\mathbf {z}) = \\underset {q (\\mathbf {z})} {\\arg \\min } \\mathbb {E} _ {\\mathbf {z} \\sim q (\\mathbf {z})} \\left\\{L _ {i d} (\\mathbf {z}; y, M) + \\lambda L _ {p r i o r} (\\mathbf {z}) \\right\\} \\tag {1}", + "image_path": "31789cc24f3425e607140ca10f05a2a73ff3cb6b41a5386c5254abfc2c8b2c40.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{z};y,M) = -\\log \\mathbb{P}_M(y|G(\\mathbf{z}))" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " is referred to as identity loss in MI [39], which guides the reconstruction of " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = G(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " that is most likely to be recognized by model " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " as identity " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{prior}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " is some prior loss, and " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "q^{*}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " is the optimal distribution of latent code used to generate inverted samples by GAN (" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = G(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\sim q^{*}(\\mathbf{z}))" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": ". Importantly, all SOTA MI methods use the same identity loss " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{z};y,M)" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " although they have different assumptions about " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "q(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " and the prior loss " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{prior}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " (see Table 1 and Supplementary for more details on each algorithm). While advances observed by improving " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "q(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{prior}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": ", the design of more effective " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " has been left unnoticed in all SOTA MI algorithms. Therefore, our work instead focuses on " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": ", analyzes issues, and proposes improvement for " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " that can lead to a performance boost in all SOTA MI. To simplify notations, we denote " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{z};y,M)" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{x};y)" + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": " when appropriate, where" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 459, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 459, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 459, + 85 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = G(\\mathbf{z})" + }, + { + "bbox": [ + 306, + 72, + 459, + 85 + ], + "type": "text", + "content": " is the reconstructed image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 98, + 538, + 110 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 98, + 538, + 110 + ], + "spans": [ + { + "bbox": [ + 306, + 98, + 538, + 110 + ], + "type": "text", + "content": "3. A Closer Look at Model Inversion Attacks" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 118, + 545, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 118, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 545, + 132 + ], + "type": "text", + "content": "3.1. An Improved Formulation of MI Identity Loss" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "text", + "content": "In this section, we discuss our first contribution and take a closer look at the optimization objective of identity loss, " + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{x};y)" + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "text", + "content": ". Existing SOTA MI methods, namely GMI [39], KEDMI [5] and VMI [36] formulate the identity loss as an optimization to minimize the negative log likelihood of an identity under model parameters (i.e. cross-entropy loss). Particularly, the " + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{x};y)" + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "text", + "content": " introduced in Eqn. 1 for an inversion targeting class " + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 138, + 545, + 234 + ], + "type": "text", + "content": " can be re-written as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 238, + 552, + 278 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 238, + 552, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 238, + 552, + 278 + ], + "type": "interline_equation", + "content": "L _ {i d} (\\mathbf {x}; y = k) = - \\log \\frac {\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right)}{\\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {k}\\right) + \\sum_ {j = 1 , j \\neq k} ^ {N} \\exp \\left(\\mathbf {p} ^ {T} \\mathbf {w} _ {j}\\right)} \\tag {2}", + "image_path": "11b042c1e3d2e78f58f46c1f28d05b26df69ac58605bdff3b67d2e9d9f02b350.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " refers to penultimate layer activations [4, 26] for sample " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " refers to the last layer weights for the " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " class in target model " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": "Existing identity loss (Eqn. 2) used in SOTA MI methods [5,36,39] is sub-optimal for MI (Fig. 1 ②). Although the optimization in Eqn. 2 accurately captures the essence of a classification problem (e.g. face recognition), we postulate that such formulation is sub-optimal for MI. We provide our intuition through the lens of penultimate layer activations, " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " (Fig. 1 ②). In a classification setting, the main expectation for " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " is to be sufficiently discriminative for class " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " (e.g. recognize between 'Peter', 'Simon' and 'David'). This objective can be achieved by both maximizing " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\exp (\\mathbf{p}^T\\mathbf{w}_k)" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " and/or minimizing " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " in Eqn. 2. On the contrary, the goal of MI is to reconstruct training data. That is, in addition to " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " being sufficiently discriminative for class " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": ", successful inversion also requires " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " to be close to the training data representations for class " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " represented by " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " (i.e. an inversion targeting 'Simon' needs to reconstruct a sample close to the private training data of 'Simon'; Fig. 1 ②). Specifically, we argue that MI requires a lot more attention on maximizing " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\exp (\\mathbf{p}^T\\mathbf{w}_k)" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " compared to minimizing " + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\sum_{j = 1,j\\neq k}^{N}\\exp (\\mathbf{p}^T\\mathbf{w}_j)" + }, + { + "bbox": [ + 304, + 321, + 546, + 564 + ], + "type": "text", + "content": " in Eqn. 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 564, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 682 + ], + "type": "text", + "content": "Motivated by this hypothesis, we conduct an analysis to investigate the proximity between private training data and reconstructed data in SOTA MI methods using penultimate layer representations [4, 25, 26, 29]. Particularly, our analysis using KEDMI [5] (SOTA) shows several instances where using Eqn. 2 for identity loss is unable to reconstruct data close to the private training data. We show this in Fig. 2 (top row). Consequently, our analysis motivates the search for an improved identity loss focusing on maximizing " + }, + { + "bbox": [ + 304, + 564, + 545, + 682 + ], + "type": "inline_equation", + "content": "\\exp (\\mathbf{p}^T\\mathbf{w}_k)" + }, + { + "bbox": [ + 304, + 564, + 545, + 682 + ], + "type": "text", + "content": " for MI." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "inline_equation", + "content": "{}^{1}\\mathbf{p}" + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": " is concatenated with 1 at the end to include bias as " + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": " includes biases at the end." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16386" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 72, + 538, + 321 + ], + "blocks": [ + { + "bbox": [ + 57, + 72, + 538, + 321 + ], + "lines": [ + { + "bbox": [ + 57, + 72, + 538, + 321 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 538, + 321 + ], + "type": "image", + "image_path": "9278f33ac2e3792433a38bab0d31b4b502276d201f1ff586d934f6d53e85f07e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "text", + "content": "Figure 2. Visualization of the penultimate layer representations " + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{priv} = \\text{CelebA}[24], \\mathcal{D}_{pub} = \\text{CelebA}[24], \\text{Target Model} = \\text{IR152}[5], \\text{Evaluation Model} = \\text{face.evoLve}[6], \\text{Inversion iterations} = 2400)" + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "text", + "content": " for private training data and reconstructed data using KEDMI [5]. Following the exact evaluation protocol in [5], we use face.evoLve [6] to extract representations. We show results for 3 randomly chosen identities. We include KNN distance (for different iterations) and final attack accuracy following the protocol in [5]. For each identity, we also include randomly selected private training data and the closest reconstructed sample at iteration " + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "inline_equation", + "content": "= 2400" + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "text", + "content": ". ① Identity loss in SOTA MI methods [5, 36, 39] (Eqn. 2) is sub-optimal for MI (Top). Using penultimate representations during inversion, we observe 2 instances (e.g. target identity 57 and 143) where KEDMI [5] (using Eqn. 2 for identity loss) is unable to reconstruct data close to private training data. Hence, private and reconstructed facial images are qualitatively different. ② Our proposed identity loss, " + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "inline_equation", + "content": "L_{id}^{\\text{logit}}" + }, + { + "bbox": [ + 46, + 323, + 548, + 445 + ], + "type": "text", + "content": " (Eqn. 3), can effectively guide the reconstruction of data close to private training data (Bottom). This can be clearly observed using both penultimate layer representations and KNN distances for all 3 target classes 57, 143 and 252. We show similar results using additional MI algorithms (GMI [39], VMI [36]) and target classifiers (face.evoLve, VGG16) in Supplementary. Best viewed in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "text", + "content": "Logit Maximization as an improved MI identity loss. In light of our analysis / observations above, we propose to directly maximize the logit, " + }, + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^T\\mathbf{w}_k" + }, + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "text", + "content": ", instead of maximizing the log likelihood of class " + }, + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 451, + 288, + 511 + ], + "type": "text", + "content": " for MI. Our proposed identity loss objective is shown below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 519, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 519, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 61, + 519, + 287, + 536 + ], + "type": "interline_equation", + "content": "L _ {i d} ^ {\\text {l o g i t}} (\\mathbf {x}; y = k) = - \\log \\mathbf {p} ^ {T} \\mathbf {w} _ {k} + \\lambda | | \\mathbf {p} - \\mathbf {p} _ {r e g} | | _ {2} ^ {2} \\tag {3}", + "image_path": "a3df266b131f76833232980b6545c84b728582b780eea5e8f9181b43064a6a8e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\lambda (>0)" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " is a hyper-parameter and " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{reg}" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " is used for regularizing " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": ". Particularly, if the regularization in Eqn. 3 is omitted and hence " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "||\\mathbf{p}||" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " is unbounded, a crude simplified way to solve Eqn. 3 is to maximize " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "||\\mathbf{p}||" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": ". Hence, we use " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{reg}" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " to regularize " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": ". Given that the attacker has no access to private training data, we estimate " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{reg}" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " by a simple method using public data (See Supplementary). We remark that " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = M^{\\mathrm{pen}}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = G(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{pen}}()" + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": " operator returns the penultimate layer representations for a given input." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": "Our analysis shows that our proposed identity loss, " + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": " (Eqn. 3), can significantly improve reconstruction of private training data compared to existing identity loss used in SOTA MI algorithms [5,36,39]. This can be clearly observed using both penultimate layer representations and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "text", + "content": "KNN distances in Fig. 2 (bottom row). Here KNN Dist refers to the shortest Euclidean feature distance from a reconstructed image to private training images for a given identity [5, 39]. Our proposed " + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "text", + "content": " can be easily plugged in to all existing SOTA MI algorithms by replacing " + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "text", + "content": " with our proposed " + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 304, + 451, + 547, + 536 + ], + "type": "text", + "content": " in Eqn. 1 (in the inversion step) with minimal computational overhead." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 549, + 544, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 549, + 544, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 549, + 544, + 562 + ], + "type": "text", + "content": "3.2. Overcoming MI Overfitting in SOTA methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "In this section, we discuss our second contribution. In particular, we formalize a concept of MI overfitting, observe its considerable impacts even in SOTA MI methods [5,36,39], and propose a new, simple solution to overcome this issue (Fig. 1 ③). To better discuss our MI overfitting concept, we first review the conventional concept of overfitting in machine learning: Given the fixed training dataset and our goal of learning a model, conventionally, overfitting is defined as instances which during model learning (training stage), the model fits too closely to the training data and adapts to the random variation and noise of training data, failing to adequately learn the semantics of the train" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16387" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "content": "ing data [1, 28, 34, 38, 41]. As the model lacks semantics of training data, it could be observed that the model performs poorly under unseen data (Fig. 1 ③ a)." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 117, + 272, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 117, + 272, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 117, + 272, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 117, + 272, + 178 + ], + "type": "image", + "image_path": "6d197a0e38f4790aa33f3775e3cbd12071567148a50328a1f115e2367ec07b2a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 179, + 166, + 297 + ], + "blocks": [ + { + "bbox": [ + 53, + 179, + 166, + 297 + ], + "lines": [ + { + "bbox": [ + 53, + 179, + 166, + 297 + ], + "spans": [ + { + "bbox": [ + 53, + 179, + 166, + 297 + ], + "type": "image", + "image_path": "5b3f6c822708cef5812907755138233199f329b072a6a19f172968b162748cf3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": "Figure 3. Qualitative / Quantitative studies to demonstrate MI overfitting in SOTA methods. We demonstrate this observation using KEDMI [5]. We use " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pri} =" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " CelebA [24], " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} =" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " CelebA [24] and " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M = \\mathrm{IR152}" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " [5]. ① We show qualitative results to illustrate MI overfitting. We show 6 identities, top: private data, bottom: reconstructed data from " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": ". The reconstructed samples have fit too closely to " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " during inversion resulting in samples with lack of identity semantics. Particularly, we remark that these samples have very low identity loss under the target model " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": ". ② Quantitative results validating the prevalence of MI overfitting in SOTA MI methods. We use an additional target classifier " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M' =" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " VGG16 released by [5, 39] to quantitatively verify the presence of MI overfitting using identity loss. For 1,500 reconstructed samples from " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": ", we visualize their identity loss w.r.t. " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " in the scatter plot and respective histograms. Particularly, we find that there are " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "26.7\\%" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " of samples with low identity loss under the target model " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": ", but large identity loss under unseen VGG16 model " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": ", hinting that these samples might lack identity semantics. This result shows that MI overfitting is a considerable issue even in SOTA MI methods. Note that VGG16 is used here only for analysis and is not part of our solution, as private data is not available. ③ Model Augmentation to alleviate MI overfitting during inversion. We repeat the above analysis, with " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M' = \\mathrm{VGG16}" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " replaced by " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M_{aug}" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " = EfficientNet-B0. Importantly, " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M_{aug}" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": " is trained by public data using knowledge distillation [15]. We similarly observe samples with large identity loss under " + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "inline_equation", + "content": "M_{aug}" + }, + { + "bbox": [ + 46, + 301, + 288, + 588 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 160, + 180, + 271, + 298 + ], + "blocks": [ + { + "bbox": [ + 160, + 180, + 271, + 298 + ], + "lines": [ + { + "bbox": [ + 160, + 180, + 271, + 298 + ], + "spans": [ + { + "bbox": [ + 160, + 180, + 271, + 298 + ], + "type": "image", + "image_path": "d4caea7b827282e5a73a2b3e5184d4ba91815018c0671436a413f6fb39817f24.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 712 + ], + "type": "text", + "content": "Overfitting in MI. We formalize the concept of overfitting in MI (Fig. 1 ③ ⑥). Given the fixed (target) model and our goal of learning reconstructed samples, we define MI overfitting as instances which during model inversion, the reconstructed samples fit too closely to the target model and adapt to the random variation and noise of the target model parameters, failing to adequately learn semantics of the identity. As these reconstructed samples lack identity semantics, it could be observed that they perform poorly under another unseen model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": "Analysis. In what follows, we discuss our analysis to demonstrate MI overfitting and understand its impact in SOTA. See Fig. 3 for analysis setups and results. In particular, in Fig. 3 (1), we show some reconstructed samples which achieve low identity loss under the target model " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ", yet they lack identity semantics. In Fig. 3 (2), we show that for a considerable percentage of reconstructed samples from target model " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " with low identity loss under " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ", their identity loss under another unseen model " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " is large as shown in the scatter plot and histograms, hinting that these samples might have suffered from MI overfitting and lack identity semantics. We note that the identity loss under " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " is obtained by feeding the reconstructed sample into " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " in a forward pass. We also note that SOTA KEDMI [5] is used in this analysis but the issue persists in [36, 39]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 260, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 356 + ], + "type": "text", + "content": "Our proposed solution to MI overfitting. We propose a novel solution based on model augmentation. Our idea is inspired by the conventional issue of overfitting in model training and data augmentation as a solution to alleviate the issue. In particular, for conventional overfitting, augmenting the training dataset could alleviate the issue [21]. Therefore, we hypothesize that by augmenting the target model we can alleviate MI overfitting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": "Specifically, we propose to apply knowledge distillation (KD) [15], with target model " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " as the teacher, to train augmented models " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{aug}^{(i)}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": ". Importantly, as we do not have access to the private data, during KD, each " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{aug}^{(i)}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " is trained on the public dataset to match its output to the output of " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": ". We select different network architectures for " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{aug}^{(i)}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " and they are different from " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " (Detailed discussion in the Supplementary). After performing KD, we apply " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{aug}^{(i)}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " together with the target model " + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 304, + 360, + 545, + 487 + ], + "type": "text", + "content": " in the inversion step and compute the identity loss (with model augmentation):" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 340, + 502, + 545, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 502, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 340, + 502, + 545, + 553 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {i d} ^ {a u g} (\\mathbf {x}; y) = \\gamma_ {t} \\cdot L _ {i d} (\\mathbf {x}; y, M _ {t}) \\\\ + \\gamma_ {a u g} \\cdot \\sum_ {i = 1} ^ {N _ {a u g}} L _ {i d} (\\mathbf {x}; y, M _ {a u g} ^ {(i)}) \\tag {4} \\\\ \\end{array}", + "image_path": "fcfe64da0a3f329bc3fe84112f3633d178fe43e20963197aa9c225d93afc261c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\gamma_{aug}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " are two hyper-parameters. In particular, we use " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\gamma_{t} = \\gamma_{aug} = \\frac{1}{N_{aug} + 1}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "N_{aug}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " is the number of augmented models. " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "L_{id}^{aug}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " in Eqn. 4 is used to replace " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " in the inversion step in Eqn. 1. Furthermore, our proposed " + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 304, + 571, + 545, + 644 + ], + "type": "text", + "content": " in Eqn. 3 can be used in Eqn. 4 to combine the improvements. See details in Supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "content": "In Fig. 3 (3), we analyze the performance of " + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\text{aug}}^{(i)}" + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "content": ". Similar to using the unseen model " + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "content": ", we observe samples with large identity loss under " + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\text{aug}}^{(i)}" + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "content": ", suggesting that samples with MI overfitting perform poorly under " + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\text{aug}}^{(i)}" + }, + { + "bbox": [ + 304, + 648, + 545, + 713 + ], + "type": "text", + "content": " as these samples lack identity semantic." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16388" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 101, + 511, + 209 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "Table 2. We follow the exact the experiment setups in [5] for GMI [39] and KEDMI [5]. For VMI [36], we follow the exact experiment setups in [36]. In total, we conduct 72 experiments spanning 18 setups to demonstrate the effectiveness of our proposed method." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 101, + 511, + 209 + ], + "lines": [ + { + "bbox": [ + 78, + 101, + 511, + 209 + ], + "spans": [ + { + "bbox": [ + 78, + 101, + 511, + 209 + ], + "type": "table", + "html": "
MethodPrivate DatasetPublic DatasetTarget modelEvaluation ModelModel Augmentation
GMI [39] / KEDMI [5]CelebA [24]CelebA / FFHQ [18]VGG16 [30] / IR152 [14] / face.evoLve [7]face.evoLveEfficientNet-B0 [33], EfficientNet-B1 [33], EfficientNet-B2 [33]
CIFAR-10 [20]CIFAR-10VGG16ResNet-18 [14]
MNIST [22]MNISTCNN(Conv3)CNN(Conv5)CNN(Conv2), CNN(Conv4)
VMI [36]CelebACelebAResNet-34 [14]IR-SE50 [10]EfficientNet-B0, EfficientNet-B1, EfficientNet-B2
MNISTEMNIST [9]ResNet-10ResNet-10CNN(Conv2), CNN(Conv4)
", + "image_path": "64c04daf82b1af8058552284150a592b23936535adbb121df6a9ff4c867c652f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 228, + 128, + 242 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 128, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 128, + 242 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "text", + "content": "In this section, we evaluate the performance of the proposed method in recovering a representative input from the target model, against current SOTA methods: GMI [39], VMI [36], and KEDMI [5]. More specifically, as our proposed method identifies two major limitations in current " + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "inline_equation", + "content": "L_{id}(\\mathbf{x};y)" + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "text", + "content": " -used commonly in all SOTA MI approaches-- we will evaluate the improvement brought by our improved identity loss " + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "inline_equation", + "content": "L_{id}^{\\text{logit}}" + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "text", + "content": ", and model augmentation " + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "inline_equation", + "content": "L_{id}^{\\text{aug}}" + }, + { + "bbox": [ + 46, + 247, + 288, + 356 + ], + "type": "text", + "content": " for all SOTA MI approaches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 363, + 163, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 163, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 163, + 376 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 381, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 430 + ], + "type": "text", + "content": "In order to have a fair comparison, when evaluating our method against each SOTA MI approach, we follow the exactly same experimental setup of that approach. In what follows, we discuss the details of these setups." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 434, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 567 + ], + "type": "text", + "content": "Dataset. Following previous works, we evaluate the proposed method on different tasks: face recognition and digit classification is used for comparison with all three SOTA approaches, and image classification is used for comparison with GMI [39], and KEDMI [5]. For the face recognition task, we use CelebA dataset [24] that includes celebrity images, and the FFHQ dataset [18] which contains images with larger variation in terms of background, ethnicity, and age. The MNIST handwritten digits dataset [22] is used for digit classification. We utilize the CIFAR-10 dataset [20] for image classification." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": "Data Preparation Protocol. Following previous SOTA approaches [5, 36, 39], we split each dataset into two disjoint parts: one part is used as private dataset " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " for training target model, and another part is used as a public dataset " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " to extract the prior information. Most importantly, throughout all experiments, public dataset " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " has no class intersection with private dataset " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " used for training target model. Note that this is essential to make sure that adversary uses " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " only to gain prior knowledge about features that are general to that task (i.e., face recognition), and does not have access to information about class-specific and private information used for training target model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 228, + 547, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 445 + ], + "type": "text", + "content": "Models. Following previous works, we implement several different models with varied complexities. As GMI [39] and KEDMI [5] use exactly similar model architecture in experiments, for comparison with these two algorithms, we use the same models. More specifically, for face recognition on CelebA and FFHQ, we use VGG16 [30], IR152 [14], and face.evoLve [7]–as SOTA face recognition model. For digit classification on MNIST, we use a CNN with 3 convolutional layers and 2 pooling layers. Finally, for image classification, following [5] we use VGG16 [30]. For a fair comparison with VMI, we follow its design in [36] and use ResNet-34 for face recognition CelebA, and ResNet-10 for digit classification on MNIST. The details of the target models, augmented models and datasets used in experiments are summarized in Table 2. We remark that when comparing our proposed method with each of the SOTA MI approaches, we use exactly the same target model and GAN for both SOTA and our approach." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 521 + ], + "type": "text", + "content": "Evaluation Metrics. To evaluate the performance of a MI attack, we need to assess whether the reconstructed image exposes private information about a target label/identity. In this work, following the literature, we conduct both qualitative evaluations by visual inspection, and quantitative evaluations using different metrics, including:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 526, + 547, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 547, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 547, + 659 + ], + "type": "text", + "content": "- Attack Accuracy (Attack Acc). Following [5, 36, 39], we use an evaluation model that predicts the label/identity of the reconstructed image. Similar to previous works, the evaluation model is different from the target model (different structure/initialization seed), but it is trained on the same private dataset (see Table 2). Intuitively, considering a highly accurate evaluation model, it can be viewed as a proxy for human inspection [39]. Therefore, if the evaluation model infers high accuracy on reconstructed images, it means these images are exposing private information about the private dataset, i.e. high attack accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 547, + 715 + ], + "type": "text", + "content": "- K-Nearest Neighbors Distance (KNN Dist). KNN Dist indicates the distance between the reconstructed image for a specific label/id and corresponding images in the private training dataset. More specifically, it measures the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16389" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 287, + 120 + ], + "type": "text", + "content": "shortest feature distance from the reconstructed image to the real images in the private dataset, given a class/id. It is measured as " + }, + { + "bbox": [ + 55, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 55, + 72, + 287, + 120 + ], + "type": "text", + "content": " distance between two images in the feature space, i.e., the penultimate layer of the evaluation model." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 122, + 280, + 262 + ], + "blocks": [ + { + "bbox": [ + 53, + 122, + 280, + 262 + ], + "lines": [ + { + "bbox": [ + 53, + 122, + 280, + 262 + ], + "spans": [ + { + "bbox": [ + 53, + 122, + 280, + 262 + ], + "type": "image", + "image_path": "fb179728287c4ce1926f04c27541decf13be3f6a3f1eb932e22a2850d54ed29f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "text", + "content": "Figure 4. Qualitative / Quantitative (Top1 Attack Acc., KNN Dist) results to demonstrate the efficacy of our proposed method. We use KEDMI [5] (SOTA), " + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv} = \\text{CelebA}" + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "text", + "content": " [24], " + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} = \\text{CelebA}" + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "text", + "content": " [24] and " + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "inline_equation", + "content": "M = \\text{IR152}" + }, + { + "bbox": [ + 46, + 266, + 288, + 344 + ], + "type": "text", + "content": " [14]. As one can observe, our proposed method achieves better reconstruction of private data both visually and quantitatively (validated by KNN results) resulting in a significant boost in attack performance." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 354, + 171, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 171, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 171, + 367 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "text", + "content": "Comparison with previous state-of-the-art. We use GMI [39], KEDMI [5], and VMI [36] as SOTA MI baselines. We reproduce all baseline results using official public implementations. We report results for GMI and KEDMI for CelebA/ CelebA experiments in Table 3. We report VMI results for CelebA/ CelebA experiments in Table 4. For each baseline setup, we report results for 3 variants: " + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "text", + "content": " LOM (Logit Maximization, Sec. 3.1), " + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "text", + "content": " MA (Model Augmentation, Sec. 3.2), " + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 372, + 287, + 491 + ], + "type": "text", + "content": " LOMMA (Logit Maximization + Model Augmentation). The details are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 498, + 287, + 588 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "text", + "content": "1. +LOM (Ours): We replace existing identity loss, " + }, + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "text", + "content": " with our improved identity loss " + }, + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 55, + 498, + 287, + 525 + ], + "type": "text", + "content": " (Sec. 3.1)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "text", + "content": "2. + MA (Ours): We replace existing identity loss, " + }, + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "inline_equation", + "content": "L_{id}" + }, + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "text", + "content": " with our proposed " + }, + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "inline_equation", + "content": "L_{id}^{aug}" + }, + { + "bbox": [ + 54, + 529, + 287, + 555 + ], + "type": "text", + "content": " (Sec. 3.2)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "text", + "content": "3. +LOMMA (Ours): We combine both " + }, + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "inline_equation", + "content": "L_{id}^{logit}" + }, + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "text", + "content": " (Sec. 3.1) and " + }, + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "inline_equation", + "content": "L_{id}^{aug}" + }, + { + "bbox": [ + 54, + 562, + 287, + 588 + ], + "type": "text", + "content": " (Sec. 3.2) for model inversion." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "As one can clearly observe from Table 3 and Table 4, our proposed methods yield significant improvement in MI attack accuracy in all experiment setups showing the efficacy of our proposed methods. Further, by combining both our proposed methods, we significantly boost attack accuracy. The KNN results also clearly show that our proposed methods are able to reconstruct data close to the private training data compared to existing SOTA MI algorithms. Particularly, we improve the KEDMI baseline [5] attack accuracy by " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "12.4\\%" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " under IR152 target classifier. We show private" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "content": "Table 3. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Following exact experiment setups in [5], here " + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv} =" + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "content": " CelebA, " + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} =" + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "content": " CelebA, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we achieve new SOTA MI performance (face.evoLve: " + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "inline_equation", + "content": "81.40\\% \\rightarrow 93.20\\%" + }, + { + "bbox": [ + 304, + 70, + 545, + 170 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 316, + 178, + 529, + 294 + ], + "blocks": [ + { + "bbox": [ + 316, + 178, + 529, + 294 + ], + "lines": [ + { + "bbox": [ + 316, + 178, + 529, + 294 + ], + "spans": [ + { + "bbox": [ + 316, + 178, + 529, + 294 + ], + "type": "table", + "html": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/IR152
KEDMI80.53 ± 3.86-1247.28
+ LOM (Ours)92.47 ± 1.4111.941168.55
+ MA (Ours)84.73 ± 3.764.201220.23
+ LOMMA (Ours)92.93 ± 1.1512.401138.62
GMI30.60 ± 6.54-1609.29
+ LOM (Ours)78.53 ± 3.4147.931289.62
+ MA (Ours)61.20 ± 4.3430.601389.99
+ LOMMA (Ours)82.40± 4.3751.801254.32
", + "image_path": "c92c7543d8564fd19112271b44b9de5d8f94bd31055f148a6031022bbe2a03c2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 317, + 308, + 529, + 394 + ], + "blocks": [ + { + "bbox": [ + 372, + 296, + 473, + 305 + ], + "lines": [ + { + "bbox": [ + 372, + 296, + 473, + 305 + ], + "spans": [ + { + "bbox": [ + 372, + 296, + 473, + 305 + ], + "type": "text", + "content": "CelebA/CelebA/face.evoLve" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 308, + 529, + 394 + ], + "lines": [ + { + "bbox": [ + 317, + 308, + 529, + 394 + ], + "spans": [ + { + "bbox": [ + 317, + 308, + 529, + 394 + ], + "type": "table", + "html": "
KEDMI81.40 ± 3.25-1248.32
+ LOM (Ours)92.53 ± 1.5111.131183.76
+ MA (Ours)85.07 ± 2.713.671222.02
+ LOMMA (Ours)93.20 ± 0.8511.801154.32
GMI27.07 ± 6.72-1635.87
+ LOM (Ours)61.67 ± 4.9234.601405.35
+ MA (Ours)74.13 ± 4.3247.061352.25
+ LOMMA (Ours)82.33 ± 3.5155.261257.50
", + "image_path": "aaaa07fcf9b7cca920537c7b6285deaf48f4d9a08be24022f9c26df89c0b9dae.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 317, + 406, + 529, + 494 + ], + "blocks": [ + { + "bbox": [ + 378, + 395, + 467, + 404 + ], + "lines": [ + { + "bbox": [ + 378, + 395, + 467, + 404 + ], + "spans": [ + { + "bbox": [ + 378, + 395, + 467, + 404 + ], + "type": "text", + "content": "CelebA/CelebA/VGG16" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 406, + 529, + 494 + ], + "lines": [ + { + "bbox": [ + 317, + 406, + 529, + 494 + ], + "spans": [ + { + "bbox": [ + 317, + 406, + 529, + 494 + ], + "type": "table", + "html": "
KEDMI74.00 ± 3.10-1289.88
+ LOM (Ours)89.07 ± 1.4615.071218.46
+ MA (Ours)82.00 ± 3.858.001248.33
+ LOMMA (Ours)90.27 ± 1.3616.271147.41
GMI19.07 ± 4.47-1715.60
+ LOM (Ours)69.67 ± 4.8050.601363.81
+ MA (Ours)51.73 ± 6.0332.661467.68
+ LOMMA (Ours)77.60 ± 4.6458.531296.26
", + "image_path": "5bc330dabadf1af0242c936e09f1725f274fd4c299d376f12646252f49a122a1.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 504, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 589 + ], + "type": "text", + "content": "training data and reconstructed samples for KEDMI [5] under IR152 target model including all 3 variants in Fig. 4. We remark that in the standard CelebA benchmark, our method boosts attack accuracy significantly thereby achieving more than " + }, + { + "bbox": [ + 304, + 504, + 545, + 589 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 504, + 545, + 589 + ], + "type": "text", + "content": " attack accuracy (Table 3) for the first time in contemporary MI literature. We also include CIFAR-10, MNIST and additional results in Supplementary." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Cross-dataset. Following [5], we conduct a series of experiments to study the effect of distribution shift between public and private data on attack performance and KNN distance. We use FFHQ [18] as the public dataset. In particular, we use FFHQ as public data for CelebA experiments. We train GAN models and three model augmentations using the public data. We remark that such setups closely replicate real-world MI attack scenario. We report top 1 accuracy and KNN distance for IR152, face.evoLve, and VGG16 target classifiers in Table 6. It is well known that baseline" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16390" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 200, + 269, + 274 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": "Table 4. We follow exact the experiment setup of [36] for VMI experiments. Specifically, we use StyleGAN [17] and Flow model [19] to learn the distribution of " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ". The best results are in **bold**. Following exact experiment setups in [36], here " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv} = \\text{CelebA}" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} = \\text{CelebA}" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ", target model " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "= \\text{ResNet-34}" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ", evaluation model " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "= \\text{IRSE50}" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ". We report top 1 attack accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance (KNN Dist). The top 5 attack accuracies are included in the Supplementary. The best results are in **bold**. By alleviating both these major problems in MI algorithms, we improve the attack accuracy by " + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "14.94\\%" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "inline_equation", + "content": "59.96\\% \\rightarrow 74.90\\%" + }, + { + "bbox": [ + 47, + 70, + 289, + 192 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 200, + 269, + 274 + ], + "lines": [ + { + "bbox": [ + 59, + 200, + 269, + 274 + ], + "spans": [ + { + "bbox": [ + 59, + 200, + 269, + 274 + ], + "type": "table", + "html": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/CelebA/ResNet-34
VMI59.96 ± 0.27-1.144
+ LOM (Ours)68.34 ± 0.368.381.131
+ MA (Ours)64.16 ± 0.274.201.140
+ LOMMA (Ours)74.90 ± 0.3414.941.109
", + "image_path": "a872274eee939835881cbcb744812fc3a581020c136abc343b8b45df75aa23a8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 335, + 287, + 398 + ], + "blocks": [ + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "lines": [ + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "type": "text", + "content": "Table 5. Results for SOTA defense model BiDO-HSIC [27]: Following exact experiment setups in BiDO-HSIC, " + }, + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv} = \\mathrm{CelebA}" + }, + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} = \\mathrm{CelebA}" + }, + { + "bbox": [ + 47, + 277, + 288, + 332 + ], + "type": "text", + "content": ", evaluation model = face.evoLve, target model = BiDO-HSIC. We report top 1 attack accuracies (Attack Acc.), and KNN distance (KNN Dist)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 335, + 287, + 398 + ], + "lines": [ + { + "bbox": [ + 48, + 335, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 48, + 335, + 287, + 398 + ], + "type": "table", + "html": "
MethodGMIKEDMI
Attack Acc ↑KNN Dist ↓Attack Acc ↑KNN Dist ↓
No Def.19.07 ± 4.471715.6074.00 ± 3.101289.88
Def. Model5.20 ± 2.751962.5842.80 ± 5.021469.75
+ LOM (Ours)55.80 ± 3.641397.0564.33 ± 1.821360.57
+ MA (Ours)23.93 ± 5.501634.8449.27 ± 4.021413.81
+ LOMMA (Ours)62.13 ± 4.041358.5470.47 ± 2.361293.25
", + "image_path": "44c86b3a3d4a1b0293472706b8ddad3c3cee9355aec6c3a945fa39d507583852.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 403, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 464 + ], + "type": "text", + "content": "attack performances will degrade due to distribution shift between public and private data [5]. But we remark that our proposed methods consistently improves the baseline SOTA attack performances. i.e. Our method boosts the attack accuracy of IR152 target model from " + }, + { + "bbox": [ + 46, + 403, + 287, + 464 + ], + "type": "inline_equation", + "content": "52.87\\% \\rightarrow 77.27\\%" + }, + { + "bbox": [ + 46, + 403, + 287, + 464 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": "MI under SOTA defense models. We further evaluate our method on SOTA MI defense models provided by BiDO-HSIC [27]. Specifically, we use the exact GAN and defense models provided by BiDO-HSIC which are trained on CelebA dataset. We then transfer knowledge from the defense model to " + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "inline_equation", + "content": "M_{\\text{aug}} = \\{\\text{Efficientnet-B0}, \\text{Efficientnet-B1}, \\text{Efficientnet-B2}\\}" + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "inline_equation", + "content": "D_{pub}" + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": ". Results using GMI and KEDMI are shown in Table 5. We observe that SOTA defense BiDO-HSIC is rather ineffective for our proposed MI." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 586, + 117, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 117, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 117, + 597 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Conclusion. We revisit SOTA MI and study two issues pertaining to all SOTA MI approaches. First, we analyze existing identity loss in SOTA and argue that it is sub-optimal for MI. We propose a new logit based identity loss that aligns better with the goal of MI. Second, we formalize the concept of MI overfitting and show that it has a considerable impact even in SOTA. Inspired by conventional data augmentation, we propose model augmentation to alleviate MI overfitting. Extensive experiments demonstrate that" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 167, + 529, + 463 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "text", + "content": "Table 6. We report the results for KEDMI and GMI for IR152, face.evoLve and VGG16 target model. Here " + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{priv} =" + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "text", + "content": " CelebA, " + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{pub} =" + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "text", + "content": " FFHQ, evaluation model = face.evoLve. We report top 1 accuracies, the improvement compared to the SOTA MI (Imp.), and KNN distance. Top 5 attack accuracies are included in the Supplementary. The best results are in bold. By alleviating both these major problems in MI algorithms, we improve the attack accuracy " + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "inline_equation", + "content": "24.40\\%" + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "text", + "content": " (IR152: " + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "inline_equation", + "content": "52.87\\% \\rightarrow 77.27\\%" + }, + { + "bbox": [ + 304, + 70, + 547, + 160 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 167, + 529, + 463 + ], + "lines": [ + { + "bbox": [ + 317, + 167, + 529, + 463 + ], + "spans": [ + { + "bbox": [ + 317, + 167, + 529, + 463 + ], + "type": "table", + "html": "
MethodAttack Acc ↑Imp. ↑KNN Dist ↓
CelebA/FFHQ/IR152
KEDMI52.87 ± 4.96-1418.83
+ LOM (Ours)67.73 ± 2.2914.861325.28
+ MA (Ours)64.13 ± 4.4911.261373.42
+ LOMMA (Ours)77.27 ± 2.0124.401292.80
GMI17.20 ± 5.31-1701.76
+ LOM (Ours)56.00 ± 5.2038.801427.59
+ MA (Ours)50.80 ± 6.8933.601462.92
+ LOMMA (Ours)72.00 ± 6.6254.801338.35
CelebA/FFHQ/face.evoLve
KEDMI51.87 ± 3.88-1440.19
+ LOM (Ours)69.73 ± 2.4717.861379.73
+ MA (Ours)65.73 ± 3.5113.861379.09
+ LOMMA (Ours)73.20 ± 2.2421.331321.00
GMI14.27 ± 4.42-1744.47
+ LOM (Ours)47.93 ± 4.8733.661498.19
+ MA (Ours)46.07 ± 4.8831.801500.10
+ LOMMA (Ours)64.33 ± 4.6950.061386.33
CelebA/FFHQ/VGG16
KEDMI41.27 ± 3.50-1490.09
+ LOM (Ours)55.07 ± 1.8813.801438.72
+ MA (Ours)52.07 ± 2.9210.801428.77
+ LOMMA (Ours)62.67 ± 2.2921.401366.94
GMI10.93 ± 3.47-1766.27
+ LOM (Ours)44.40 ± 5.9633.471508.84
+ MA (Ours)34.93 ± 4.5224.001547.93
+ LOMMA (Ours)58.73 ± 6.1847.801415.06
", + "image_path": "6140175d137d492267dc23474b549f7129c844fbe484f11293b2845175acf659.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 469, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 529 + ], + "type": "text", + "content": "our solutions can improve SOTA significantly, achieving for the first time over " + }, + { + "bbox": [ + 304, + 469, + 545, + 529 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 469, + 545, + 529 + ], + "type": "text", + "content": " attack accuracy under the standard benchmark. Our findings highlight rising threats based on MI and prompt serious consideration on privacy of machine learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "type": "text", + "content": "Limitations and Ethical Concerns. We follow previous work in experimental setups. The scale of our experiments is comparable to previous works. Furthermore, extension of our methods for blackbox/ label-only attacks can be considered in future. While our improved MI methods could have negative societal impacts if it is used by malicious users, our work contributes to increased awareness about privacy attacks on DNNs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programmes (AISG Award No.: AISG2-RP-2021-021; AISG Award No.: AISG2-TC-2022-007). This project is also supported by SUTD project PIE-SGP-AI-2018-01. We thank reviewers for their valuable comments. We also thank Loo Yi and Kelly Kuo for helpful discussion." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16391" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Milad Abdollahzadeh, Touba Malekzadeh, and Ngai-Man Cheung. 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Given limited GPU memory, training TAL end to end (i.e., from videos to predictions) on long videos is a significant challenge. Most methods can only train on pre-extracted features without optimizing them for the localization problem, consequently limiting localization performance. In this work, to extend the potential in TAL networks, we propose a novel end-to-end method $Re^{2}TAL$ , which rewrites pretrained video backbones for reversible TAL. $Re^{2}TAL$ builds a backbone with reversible modules, where the input can be recovered from the output such that the bulky intermediate activations can be cleared from memory during training. Instead of designing one single type of reversible module, we propose a network rewiring mechanism, to transform any module with a residual connection to a reversible module without changing any parameters. This provides two benefits: (1) a large variety of reversible networks are easily obtained from existing and even future model designs, and (2) the reversible models require much less training effort as they reuse the pre-trained parameters of their original non-reversible versions. $Re^{2}TAL$ , only using the RGB modality, reaches 37.01% average mAP on ActivityNet-v1.3, a new state-of-the-art record, and mAP 64.9% at tIoU=0.5 on THUMOS-14, outperforming all other RGB-only methods. Code is available at https://github.com/coolbay/Re2TAL.", + "bbox": [ + 75, + 325, + 473, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 767, + 209, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Temporal Action Localization (TAL) [36,53,73] is a fundamental problem of practical importance in video understanding. It aims to bound semantic actions within start and end timestamps. Localizing such video segments is very useful for a variety of tasks such as video-language grounding [23, 56], moment retrieval [9, 21], video captioning [30, 50]. Since video actions have a large variety of", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/34a4f3714da94bd724e9a05b4173b243067eb034d7f967811f9b5f1e4bc9ef7f.jpg", + "image_caption": [ + "Figure 1. Illustration of TAL network activations in training. Top: non-reversible network stores activations of all layers in memory. Bottom: reversible network only needs to store the activations of inter-stage downsampling layers. Backbone activations dominate memory occupation, compared to Localizer." + ], + "image_footnote": [], + "bbox": [ + 517, + 292, + 880, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "temporal durations and content, to produce high-fidelity localization, TAL approaches need to learn from a long temporal scope of the video, which contains a large number of frames. To accommodate all these frames along with their network activations in GPU memory is extremely challenging, given the current GPU memory size (e.g. the commodity GPU GTX1080Ti only has 11GB). Often, it is impossible to train one video sequence on a GPU without substantially downgrading the video spatial/temporal resolutions.", + "bbox": [ + 496, + 532, + 893, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To circumvent the GPU-memory bottleneck, most TAL methods deal with videos in two isolated steps (e.g. [4, 67, 69, 71-73]). First is a snippet-level feature extraction step, which simply extracts snippet representations using a pretrained video network (backbone) in inference mode. The backbone is usually a large neural network trained for an auxiliary task on a large dataset of trimmed video clips (e.g., action recognition on Kinetics-400 [28]). The second step trains a localizer on the pre-extracted features. In this way, only the activations of the TAL head need to be stored in memory, which is tiny compared to those of the backbone (see the illustration of the activation contrast between backbone and localizer in Fig. 1). However, this two-step strategy comes at a steep price. The pre-extracted features can suffer from domain shift from the auxiliary pre-training", + "bbox": [ + 496, + 674, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10637", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "task/data to TAL, and do not necessarily align with the representation needs of TAL. This is because they cannot be finetuned and must be used as-is in their misaligned state for TAL. A better alternative is to jointly train the backbone and localizer end to end. But as mentioned earlier, the enormous memory footprint of video activations in the backbone makes it extremely challenging. Is there a way for end-to-end training without compromising data dimensionality?", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Reversible networks [20, 25, 31, 48] provide an elegant solution to drastically reduce the feature activation memory during training. Their input can be recovered from the output via a reverse computation. Therefore, the intermediate activation maps, which are used for back propagation, do not need to be cached during the forward pass (as illustrated in Fig. 1). This offers a promising approach to enable memory-efficient end-to-end TAL training, and various reversible architectures have been proposed, such as RevNet [20], and RevViT [48]. However, these works design a specific reversible architecture and train for a particular dataset. Due to their new architecture, they also need to train the networks from scratch, requiring a significant amount of compute resources.", + "bbox": [ + 75, + 213, + 470, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conversely, it would be beneficial to be able to convert existing non-reversible video backbones to reversible ones, which would (1) avail a large variety of architectures and (2) allow us to reuse the large compute resources that had already been invested in training the non-reversible video backbones. Since pre-trained video backbones are a crucial part of TAL, the ability to convert off-the-shelf backbones to reversible ones is a key to unleash their power in this task.", + "bbox": [ + 75, + 428, + 468, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, for end-to-end TAL, we propose a principled approach to Rewire the architectural connections of a pre-trained non-reversible backbone to make it Reversible, dubbed $\\mathrm{Re}^2\\mathrm{TAL}$ . Network modules with a residual connection (res-module for short), such as a Resnet block [22] or a Transformer MLP/attention layer [14], are the most popular design recently. Given any network composed of residual modules, we can apply our rewiring technique to convert it to a corresponding reversible network without introducing or removing any trainable parameters. Instead of training from scratch, our reversible network can reuse the non-reversible network's parameters and only needs a small number of epochs for finetuning to reach similar performance. We summarize our contributions as follows.", + "bbox": [ + 75, + 550, + 468, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) We propose a novel approach to construct and train reversible video backbones parsimoniously by architectural rewiring from an off-the-shelf pre-trained video backbone. This not only provides a large collection of reversible candidates, but also allows reusing the large compute resources invested in pre-training these models. We apply our rewiring technique to various kinds of representative video backbones, including transformer-based Video Swin and ConvNet-based Slowfast, and demonstrate that our re", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "versible networks can reach the same performance of their non-reversible counterparts with only minimum finetuning effort (as low as 10 epochs compared to 300 epochs for training from scratch).", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(2) We propose a novel approach for end-to-end TAL training using reversible video networks. Without sacrificing spatial/temporal resolutions or network capability, our proposed approach dramatically reduces GPU memory usage, thus enabling end-to-end training on one 11GB GPU. We demonstrate on different localizers and different backbone architectures that we significantly boost TAL performance with our end-to-end training compared to traditional feature-based approaches.", + "(3) With our proposed $\\mathrm{Re}^2\\mathrm{TAL}$ , we use recent localizers in the literature to achieve a new state-of-the-art performance, $37.01\\%$ average mAP on ActivityNet-v1.3. We also reach the highest mAP among all methods that only use the RGB modality on THUMOS-14, $64.9\\%$ at tIoU $= 0.5$ , outperforming concurrent work TALLFormer [10]." + ], + "bbox": [ + 496, + 152, + 890, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 398, + 640, + 414 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Reversible Networks are a family of neural models based on the reversible real-valued non-volume preserving (real NVP) transformation introduced in [12, 13]. The transformation has been originally applied widely for image generation using generative flows [24, 29], and later used for various applications, such as compression [38], denoising [43], and steganography recovery [49]. Furthermore, it has also been repurposed for memory-efficient neural network training for a variety of architectures such as ConvNets [20, 25], Masked ConvNet [57], RNNs [47], Graph Networks [31] and more recently, Vision Transformers [48]. However, each of these methods only focuses on one or several specific architectures, and trains their newly proposed reversible architectures from scratch, thereby requiring large compute resources. In this work, we propose a rewiring scheme to adapt off-the-shelf models to reversible architectures which only utilize a small amount of compute for finetuning. This allows democratizing the reach of reversible architecture to arbitrary models and dataset settings by leveraging the architecture design effort and computational cost already spent in vanilla off-the-shelf models.", + "bbox": [ + 496, + 425, + 890, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Recognition Backbones. ConvNets have had a long and illustrious history of improving video understanding performance [7, 16-19, 26, 33, 52, 55, 61, 64, 65, 74]. Among those, Slowfast [17], which uses a slow pathway and a fast pathway to capture spatial semantics and temporal motion respectively, has been widely adopted for various tasks such as action detection [17], untrimmed video classification [44] and moment/natural language retrieval [21] for its high efficiency and efficacy. Recently, video transformers have ushered in a new life in the field of video repre", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10638", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sensation learning. Leveraging long-term temporal connection via the attention mechanism, transformers have quickly gain popularity as the backbone of choice for several video recognition workloads [3, 5, 15, 32, 45, 70]. Among those, Video Swin Transformer [45] introduces an inductive bias of locality to video transformers, leading to an outstanding speed-accuracy trade-off. However, most of the models are vanilla non-reversible architectures. In this work, we unleash the potential of reversible architectures for these models such that the good properties of reversible models, e.g. memory efficiency, can be infused into them. In particular, we show that the pretrained Video Swin Transformer [45] and SlowFast [17] models can be rewired to be reversible, and finetuned cheaply to improve temporal action localization performance with end-to-end training.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Temporal Action Localization (TAL). Due to the conflict between large video data and the GPU memory limit, most TAL methods using deep networks are two-step methods [4, 8, 34, 36, 37, 41, 46, 51, 54, 69, 71-73]. For example, using pre-extracted features, G-TAD [69] and VSGN [73] utilize graph convolutions to model temporal relations between snippets, and ActionFormer [71] leverages transformers to capture long-range context. To mitigate the performance gap between the two-step mechanism and real end-to-end training, some methods explore post-pretraining to enhance the video feature representations for TAL [2, 66, 68]. In the meanwhile, researchers also attempt to perform real end-to-end training by reducing network/data complexity [10, 35, 39, 40, 42, 63, 66]. R-C3D [66] is the end-to-end pioneer, but it uses a shallow network C3D [60], thus restricting the performance. PBRNet [39] and ASDF [35] downscale the frame resolution to $96 \\times 96$ . DaoTAD [63] makes RGB-only enough by using end-to-end training with various data augmentations. TALLFormer [10] proposes to use a feature bank strategy and only updates a portion of features during end-to-end training. Compared to these approaches, our method doesn't sacrifice any data dimensionality or data samples in training, and it supports very deep networks. We significantly reduce memory consumption while preserving the full data fidelity. Moreover, our work is complementary to these methods, and can also be used jointly to further reduce memory cost.", + "bbox": [ + 75, + 321, + 472, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method: $\\mathbf{Re}^2$ Temporal Action Localization", + "text_level": 1, + "bbox": [ + 76, + 744, + 465, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. TAL Formulation and Architecture", + "text_level": 1, + "bbox": [ + 76, + 768, + 383, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Temporal action localization (TAL) predicts the timestamps of actions from a video sequence, which is formulated as follows. Given a video sequence $V$ of $T$ frames $\\{I_t\\in \\mathbb{R}^{3\\times H\\times W}\\}_{t = 1}^T$ , TAL predicts a set $m$ of actions $\\Phi = \\{\\phi_m = (t_{m,s},t_{m,e},c_m,s_m)\\}_{m = 1}^M$ , where $t_{m,s}$ and $t_{m,e}$ are action start and end time respectively, $c_{m}$ is action label, and $s_m$ is prediction confidence. To achieve this, the following", + "bbox": [ + 76, + 792, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "two steps are required.", + "bbox": [ + 498, + 92, + 653, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the first step, the videos $V$ are encoded as $N$ features vectors $\\{\\mathbf{x}_n\\in \\mathbb{R}^C\\}_{n = 1}^N$ via a backbone. This backbone aggregates spatial information within video frames, as well as temporal information across frames. It is usually designed for an auxiliary task such as action recognition. Popular backbones can be categorized into Resnet-based architectures, such as I3D [7], R2+1D [62], SlowFast [17], and Transformer based architectures, such as ViViT [3], Video Swin Transformers [45].", + "bbox": [ + 496, + 107, + 890, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the second step, a localizer, uses a 'neck' to further aggregate the video features $\\{\\mathbf{x}_n\\}_{n=1}^N$ in the temporal domain, and a 'head', to make predictions of action boundaries, i.e., start and end timestamps $(t_{m,s}, t_{m,e})$ and categories. The neck contains layers of networks, e.g., 1D convolutional networks in BMN [36], Graph networks in G-TAD [69] and VSGN [73], and Transformers in RTD-Net [59] and Action-Former [71].", + "bbox": [ + 496, + 243, + 890, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As mentioned in Sec. 1, an optimal way to train the entire TAL network is to jointly train the backbone and the localizer end to end. However, it is substantially challenging to fit all activation maps of the long video sequence into limited GPU memory. In the following sections, we provide end-to-end TAL solution $\\mathrm{Re}^2\\mathrm{TAL}$ .", + "bbox": [ + 496, + 364, + 890, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Rewire for Reversibility, and Reuse", + "text_level": 1, + "bbox": [ + 498, + 468, + 807, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let's first analyze what in the GPU memory precludes end-to-end training of TAL. As mentioned in Sec. 1, the activation maps in the backbone are the major occupant in the memory. Concretely, given a batch of a video sequence of $T$ frames, each with resolution $S \\times S$ , to train them on a backbone of $L$ layers each with $C$ channels, the training memory complexity is $\\mathcal{O}(LCTS^2)$ . Downgrading any data dimensionality or the backbone capacity can reduce the memory complexity, but at the same time, may harm the prediction accuracy. We aim to reduce memory consumption without sacrificing the data dimensionality or the model capacity.", + "bbox": [ + 496, + 492, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Actually, the intermediate activations are stored in memory during training for the purpose of gradient computation in back propagation. If we can reconstruct them during back propagation, then there is no need for their memory occupation. Reversible networks [20, 25, 48, 49] is a superb solution for reconstructing the input from output, and various reversible architectures have been proposed recently (e.g., Revnet [20], RevViT [48]). However, the performance of TAL heavily depends on the backbone that is pre-trained on one or even multiple large-scale datasets. For example, the popular I3D [7] backbone is trained on Kinetics-400 [28] with its parameters initialized from Resnet [22] trained on ImageNet [11]. If we make up a new reversible network for TAL as is the case with previous reversible networks (e.g., [20, 25]), we need to go through all the expensive and time-consuming training stages to reach an equivalently", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10639", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/08886fa3a5b55aa5208253784c4d6b40e70b54821ba46b08a1daed351d3ae340.jpg", + "image_caption": [ + "Figure 2. Illustration of the proposed rewiring process. In this example, 3 consecutive residual modules in the same stage are rewired into 3 reversible modules. After rewiring, each residual connection skips one more $\\mathcal{F}$ block ahead. Note that beyond this example, our rewiring can process any number of such modules. good initialization for TAL." + ], + "image_footnote": [], + "bbox": [ + 94, + 85, + 452, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of proposing a new reversible architecture, we propose a principled approach to rewire a pre-trained nonreversible backbone to make it reversible. Given any module with a residual connection, we can convert it into a reversible module while preserving the same set of parameters. This technique has two advantages. First, we obtain a large and growing collection of various reversible architectures out of the box, by rewiring the existing networks and even future networks of higher performance. Second, we can reuse their pre-trained weights to initialize our reversible networks, eliminating the tremendous effort to train from scratch. In the following, we will describe our rewiring for reversibility $(\\mathbf{Re}^2)$ technique in detail.", + "bbox": [ + 75, + 354, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rewiring. Residual modules, i.e., modules with a residual connection, are the most commonly adopted design in concurrent neural network architectures, such as Resnet [22] and Transformers [14]. Given any residual modules, we can rewire them into reversible modules. Fig. 2 illustrates this process with an example of 3 consecutive residual modules that are in the same stage, i.e., there are no downsampling operations in between. Each of the original residual modules contains a block $\\mathcal{F}_i$ (blue boxes) where $i = 1,2,3,\\ldots$ and a residual connection (orange arrow). The blocks $\\mathcal{F}_i$ have the same input and output dimensions, and can contain any computations. For example, in Resnet, the building block consisting of convolution, batch normalization, and ReLU can be one $\\mathcal{F}_i$ block (e.g. Fig. 3 (a)). In Transformers, if $\\mathcal{F}_i$ represents an attention layer, then $\\mathcal{F}_{i + 1}$ is an MLP layer (e.g. Fig. 3 (b) and (c)). The residual connection in each module only skips one $\\mathcal{F}_i$ block in the same module.", + "bbox": [ + 75, + 551, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To rewire, we simply let the residual connection skip the next block $\\mathcal{F}_{i+1}$ as well as the current one $\\mathcal{F}_i$ . To be more specific, we keep the starting point of each residual connection, but make it end after two blocks, as shown in the second row of Fig. 2. As a result, two consecutive residual", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/19bd660c771f4ab8b073992c230f1110bcf4a6d0dbb598635ef055ac50e3d8e0.jpg", + "image_caption": [ + "Figure 3. Examples of $\\mathcal{F}$ blocks. (a) A reset basic block. (b) A transformer MLP layer. (c) A transformer attention layer." + ], + "image_footnote": [], + "bbox": [ + 511, + 90, + 629, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0c84f3bfca40427aae281fa4395eeb2a404aed586c33e411a933a8e5abcb0c90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 90, + 754, + 204 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/da1927aeb3639bb83813d9ed80bd8bc09cbf6bf244b2d1af5012e39f5e02ae87.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 90, + 880, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "connections become overlapped, and there are always two pathways of activations (gray and green in Fig. 2) throughout the modules, as shown in the third row of Fig. 2.", + "bbox": [ + 496, + 246, + 890, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To prepare a second pathway of input to the first module, we duplicate the input $x_0$ to obtain $y_0$ . To combine the results $x_3$ and $y_3$ of the two pathways, we simply average them at the end of the modules. This design guarantees that the dimensions of the input and output of every block $\\mathcal{F}_i$ are identical before and after the rewiring. Therefore, the structure of $\\mathcal{F}_i$ stays exactly the same.", + "bbox": [ + 496, + 291, + 892, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reversibility. In the following, we mathematically formulate the rewired modules to show their reversibility. To be concise, we use the first two modules as an example. Given the input activations $x_0$ and $y_0$ , and the blocks $\\mathcal{F}_1$ and $\\mathcal{F}_2$ , the output of the two blocks are $x_1, y_1$ and $x_2, y_2$ respectively, computed as follows", + "bbox": [ + 496, + 397, + 890, + 488 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} y _ {1} = x _ {0} \\\\ x _ {1} = \\mathcal {F} _ {1} \\left(x _ {0}\\right) + y _ {0}, \\end{array} \\right. \\Rightarrow \\left\\{ \\begin{array}{l} y _ {2} = x _ {1} \\\\ x _ {2} = \\mathcal {F} _ {2} \\left(x _ {1}\\right) + y _ {1}. \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 494, + 890, + 530 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above equations are reversible, which means that we can recover the input $x_{1}, y_{1}$ from $x_{2}, y_{2}$ , and then $x_{0}, y_{0}$ from $x_{1}, y_{1}$ . The reverse computation is formulated in the following equation", + "bbox": [ + 496, + 536, + 890, + 597 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} x _ {0} = y _ {1} \\\\ y _ {0} = x _ {1} - \\mathcal {F} _ {1} (x _ {0}), \\end{array} \\right. \\Leftarrow \\left\\{ \\begin{array}{l} x _ {1} = y _ {2} \\\\ y _ {1} = x _ {2} - \\mathcal {F} _ {2} (x _ {1}). \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 603, + 890, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A network with more modules follows the same strategy as in Eq. 1 and Eq. 2. When we stack multiple consecutive reversible modules as one network (as the example in Fig. 2), the entire network is reversible. In this case, we can start from the last module and sequentially reconstruct the input of each module with Eq. 2.", + "bbox": [ + 496, + 643, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reuse. As the structure and parameter dimensions of the $\\mathcal{F}_i$ block in our reversible modules after rewiring stay exactly the same as the $\\mathcal{F}_i$ block in the corresponding residual module, we can directly reuse the pre-trained parameters in the residual modules to initialize our reversible modules.", + "bbox": [ + 496, + 734, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our rewiring mechanism provides a large collection of reversible candidates. We can easily convert a network into a reversible one without designing a new architecture from scratch. Not only can we use the existing architectures, but we can also benefit from future even better models to obtain better reversible models. The reuse strategy", + "bbox": [ + 496, + 810, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10640", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d07afeb6b10c6b01876c890734973346a998a81e4f7bf9df2416ff21d3da7537.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 158, + 90, + 460, + 255 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/da45bad198941ef2bdaabb6d404572956ae6abcc7a39182e355c866f258a4350.jpg", + "image_caption": [ + "(b)", + "Figure 4. Comparison of different input arrangements for a TAL network. (a) Snippets input: the backbone processes many video snippets (a short clip of frames), often overlapped. (b) Frames input: the backbone takes all the frames in the video as one single input." + ], + "image_footnote": [], + "bbox": [ + 508, + 90, + 815, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "allows taking advantage of the large computing resources invested in those pre-trained models. We don't need to retrain the reversible network from scratch. Instead, we can train the reversible backbone with minimum effort (as low as 10 epochs compared to 300 epochs from scratch) while reaching the same performance as its residual counterpart.", + "bbox": [ + 75, + 301, + 470, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Reversible Temporal Action Localization", + "text_level": 1, + "bbox": [ + 76, + 402, + 426, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that the backbone is the heaviest part in the TAL network in terms of memory usage, as illustrated in Fig. 1, we target the backbone and apply our $\\mathrm{Re}^2$ technique described above to rewire it to obtain a reversible network.", + "bbox": [ + 75, + 426, + 468, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A backbone network, e.g., Video Swin Transformer [45], Slowfast [17], is usually comprised of several stages. Within each stage, the activation sizes stay the same. We convert all the modules into reversible ones following the rewiring method proposed in Sec. 3.2. During training, we can clear all the input and intermediate activations from GPU memory, and only store the final output of the stage during the forward pass (as shown in Fig. 1). In the back propagation, we re-compute all the activations based on the reverse process as in Eq. 2. As [48] pointed out, this re-computation doesn't incur too much more computational time since we can parallelize the process to make use of the spare computation of GPUs.", + "bbox": [ + 75, + 488, + 470, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Across stages, there are downsampling layers, which reduce the activation sizes. We leave the downsampling layers as they are and cache the activations inside to enable back propagation. Considering that there are only several downsampling layers, the memory occupation of these activations is acceptable.", + "bbox": [ + 75, + 685, + 468, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. End-to-End TAL Training", + "text_level": 1, + "bbox": [ + 76, + 786, + 316, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For end-to-end training with our $\\mathrm{Re}^2\\mathrm{TAL}$ , we just need to do the following: find a well-performing video backbone, rewire it into a reversible one, load the parameters from the original backbone to the reversible one and finetune for several epochs on the pretraining task, and train with a localizer end to end. This reversible TAL network is significantly", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "more efficient in memory usage, enabling end-to-end training a GPU of limited memory (e.g., as small as a 11GB commodity GPU). But is it a wise choice to directly adopt the training strategies from the feature-based methods?", + "bbox": [ + 496, + 301, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input frame arrangement. Since most TAL methods are designed and experimented with the pre-extracted, they have predisposed to particular design choices, such as extracting features with overlapped snippets to arrange the input frames. But we find it not ideal for end-to-end training.", + "bbox": [ + 496, + 363, + 890, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 4 (a) illustrates the framework commonly used in two-step (or feature-based) methods. To extract $N$ feature vectors as the localizer input, $N$ snippets need to be processed by the backbone independently. Each snippet contains a sequence of $D$ frames. The snippets are usually overlapped with one another to maintain temporal consistency, which causes duplicate computation and extra memory occupation. Consequently, at least $ND$ frames need to go through the backbone.", + "bbox": [ + 496, + 438, + 890, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This framework works fine with the two-step method, since feature extraction is one-off effort and all the snippets can be processed sequentially to circumvent the memory issue. However, end-to-end training cannot bear the extra memory cost. Therefore, we treat the entire video sequence as one single input instead, and the backbone aggregates all frames at one time, as shown in Fig. 4 (b). This mechanism not only reduces the cost incurred by the duplicate computation, but also has the advantage of aggregating long-term temporal information, in contrast to being restricted within the snippet as with the snippet mechanism. In this way, to obtain $N$ feature vectors, we just need to process $Ns$ frames, where $s$ is the overall strides in the backbone (e.g. $s = 2$ in Video Swin Transformers). Considering that $s$ is usually much smaller than $D$ , the frame-input mechanism is more efficient in memory and computation cost.", + "bbox": [ + 496, + 574, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 830, + 633, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and evaluation metrics. We present our experimental results on two representative datasets ActivityNet-v1.3 (ActivityNet for short) [6] and THUMOS-", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10641", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1354a507be8e9b48d10a8e32b9cc94a62ea287a3aa8c985f66f0ab2652455477.jpg", + "table_caption": [ + "Table 1. Advantage of end-to-end training. End-to-end training leads to significant mAP (\\%) boost for TAL with either backbone." + ], + "table_footnote": [], + "table_body": "
Re2Vswin-tinyRe2Slowfast-101
Method0.50.750.95Avg.0.50.750.95Avg.
Features51.1835.099.7234.4751.9836.009.4735.24
End2End53.2437.2310.4936.3853.6337.5310.6736.82
", + "bbox": [ + 78, + 122, + 468, + 188 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "14 (THUMOS for short) [27]. ActivityNet is a challenging large-scale dataset, with 19994 temporally annotated untrimmed videos in 200 action categories, which are split into training, validation and testing sets by the ratio of 2:1:1. THUMOS contains 413 temporally annotated untrimmed videos with 20 action categories, in which 200 videos are for training and 213 videos for validation1. For both datasets, we use mean Average Precision (mAP) at different tIoU thresholds as the evaluation metric. On ActivityNet, we choose 10 values in the range $[0.5, 0.95]$ with a step size 0.05 as tIoU thresholds; on THUMOS, we use tIoU thresholds $\\{0.3, 0.4, 0.5, 0.6, 0.7\\}$ ; following the official evaluation practice.", + "bbox": [ + 75, + 200, + 468, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Backbones and localizers of $\\mathbf{Re}^2\\mathbf{TAL}$ . For backbones, we choose two representative models from the Resnet and Transformer families respectively for experimental demonstration: Video Swin Transformers (Vswin for short) [45] and Slowfast [17], both well known for their powerful video representation and memory efficiency. For Vswin, we use three variants: tiny, small, and base; for Slowfast, we use 50, 101, and 152. For localizers, we experiment with the recent temporal action localization (TAL) methods VSGN [73] and ActionFormer [71].", + "bbox": [ + 75, + 400, + 468, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details of $\\mathbf{Re}^2\\mathbf{TAL}$ . We initialize all our reversible backbones with their non-reversible counterparts, and finetune for up to 30 epochs on Kinetics-400 with Cosine Annealing learning rate policy and Adamw (for Vswin) and SGD (for Slowfast) optimizers. Actually, in our experiments, we find 10 epochs of finetuning already reaches similarly good performance. With the pre-trained reversible backbone, we train TAL on a single GPU, A100 with batchsize $= 1$ for Vswin and V100 with batchsize $= 2$ for Slowfast. This is only possible due to the massive GPU memory savings from the reversible backbones. For the hyper-parameters, we follow the original training recipe of VSGN [73] and ActionFormer [71] for the learning rates and epochs in the localizers. We set the learning rates of the Vswin backbones 1 magnitude lower than the localizer, and those of the Slowfast backbones 2 magnitude lower. The spatial resolution is $224 \\times 224$ . For ActivityNet, the number of frame input is $T = 512$ , the number of feature vectors is $N = 256$ ; and for THUMOS, the number of frame input is $T = 1024$ , the number of features is $N = 512$ .", + "bbox": [ + 75, + 554, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a80a661632d5f88e945a4db0583816943763b6538856c662cb01f02f4f843ad2.jpg", + "image_caption": [ + "Figure 5. Performance improvement of end-to-end TAL upon feature-based in terms of action temporal duration." + ], + "image_footnote": [], + "bbox": [ + 511, + 87, + 880, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation and Analysis", + "text_level": 1, + "bbox": [ + 500, + 263, + 705, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we provide ablation study on ActivityNet and performance analysis to answer the following questions. (1) Why do we need end-to-end training? (2) How effective and efficient is our $\\mathrm{Re}^2\\mathrm{TAL}$ ? (3) What is the benefit of the proposed rewiring technique? (4) Which reversible backbone and localizer provides the best performance?", + "bbox": [ + 496, + 289, + 890, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.1 Why end-to-end training?", + "text_level": 1, + "bbox": [ + 500, + 415, + 733, + 430 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "With end-to-end training, we are able to optimize the features to adapt to the TAL task and dataset such that we can achieve higher performance than the feature-based method. To verify this, we compare end-to-end training to the feature-based training on our reversible TAL. In Tab. 1, we demonstrate the comparison on two types of backbones: $\\mathrm{Re}^2$ Vswin-tiny and $\\mathrm{Re}^2$ Slowfast-101 with VSGN [73] on ActivityNet. It shows that for both backbones, using end-to-end training leads to significant performance boost, gaining almost $2\\%$ mAP.", + "bbox": [ + 496, + 444, + 890, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further diagnose what kinds of actions end-to-end training improves the most, in Fig. 5 (a), we plot the accuracy gains brought by end-to-end training for five different groups of actions based on their temporal durations (in seconds): XS: (0s, 30s], S: (30s, 60s], M: (60s, 120s], L: (120s, 180s], and XL: $>180$ s (as suggested in [1]). We can see that the accuracy gains for different action durations are closely related to the numbers of samples in each duration category (the pie chart): short actions (XS and X) with many samples are obviously improved, though long actions (XL) with fewer samples is slightly sacrificed. Actually, short actions are a fundamental challenge in TAL [73]. End-to-end training provides an effective solution by enabling the backbone to learn feature representations to the benefit of short actions — the categories with more samples, thus preventing them fusing into the background. Short actions occupy the majority in the dataset, and their improvement leads to an overall performance boost. In Fig. 5 (b), we show that the false negative predictions are reduced by end-to-end training for all groups, more significantly for shorter ones.", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1The training and validation sets of THUMOS are temporally annotated videos from the validation and testing sets of UCF101 [58], respectively.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10642", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/647eafd7719f66f3c5cac431b6a7cefb7fb78ac42c836e1675da5e6b65081286.jpg", + "image_caption": [ + "Figure 6. $\\mathbf{Re}^{2}\\mathbf{TAL}$ models compared with original models at different spatial and temporal downscaling ratios. Spatial and temporal resolutions from left to right are as follows. $\\mathbf{Re}^{2}\\mathbf{TAL}$ : (112, 512), (224, 512); Original: (56, 512), (112, 192), (224, 192), (224, 512). The localizer VSGN [73] is used." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 279, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1bf6be083f4303f7633df6f7929aca619f6f2118a5fda752d847325c79f91a66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 468, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3bcfca41f9d99a92f6517aa771cb789968ee9ff11bf7d6f14f12b3e70436d189.jpg", + "image_caption": [ + "Figure 7. GPU memory consumption v.s. network sizes. The dot sizes represent the model sizes, and the y-axis is the GPU memory used for processing one video (batchsize=1). Our $\\mathrm{Re}^2\\mathrm{TAL}$ almost keeps the memory constant when only the network depths increase (e.g. from Vswin-tiny to small, from Slowfast-50 to 101), whereas the original models easily go out of memory when the network becomes larger." + ], + "image_footnote": [], + "bbox": [ + 78, + 272, + 277, + 380 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d8b89e8efed4997d084b4377ea81b63f4d8362e2c70e8496ddcdf445bde122b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 272, + 468, + 380 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.2 How effective and efficient is $\\mathbf{Re}^2\\mathbf{TAL}$ ?", + "text_level": 1, + "bbox": [ + 76, + 500, + 398, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "An alternative way to enable end-to-end training is to reduce data resolutions [39, 63]. In Fig. 6, we downscale the input videos in the spatial or temporal dimensions to adjust the memory requirements, and compare our $\\mathrm{Re}^2\\mathrm{TAL}$ models to their corresponding original models. We can see that under even smaller memory requirements, our $\\mathrm{Re}^2\\mathrm{TAL}$ models achieve higher performance than the original models that relies on sacrificing video resolutions to reduce memory.", + "bbox": [ + 75, + 525, + 468, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further visualize the memory efficiency of our $\\mathrm{Re}^2\\mathrm{TAL}$ compared to their non-reversible counterparts when trained end to end, we demonstrate the GPU memory consumption of the three Vswin backbones of different depths and widths and the three Slowfast backbones of different depths in Fig. 7. For Vswin backbones, we assume a GPU memory budget of 90GB, which is the size of A100. For Slowfast backbones, we assume our GPU budget is 11GB, which is the size of the commodity GPU such as GTX1080Ti. We can see that for either case, the nonreversible network will go out of memory when the model size reaches a certain level. In contrast, our $\\mathrm{Re}^2\\mathrm{TAL}$ almost keeps constant memory usage when only the network depth increases (from Vswin-tiny to small, from Slowfast-50 to $101)^2$ . With the low memory cost, our $\\mathrm{Re}^2\\mathrm{TAL}$ enables", + "bbox": [ + 75, + 647, + 470, + 875 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3bb5839034c1e57230b73182b601f4ccd6b12ae58bbd223f3b48426a52c9eb97.jpg", + "table_caption": [ + "Table 2. Comparison of feature representations between the $\\mathbf{Re}^2\\mathbf{TAL}$ and original models, in terms of average mAP (\\%) on the dataset ActivityNet. Vw: Vswin; Slowf: Slowfast." + ], + "table_footnote": [], + "table_body": "
ModelTinySmallBaseModel50101152
Vswin34.3633.8634.47Slowfast34.6035.0434.61
Re2Vw34.4734.0434.09Re2Slowf34.9335.2434.54
", + "bbox": [ + 501, + 133, + 888, + 186 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/99c21579003b42292d3126b92c0147c6186dc95920e0e8fc7012670b1220958f.jpg", + "table_caption": [ + "Table 3. Effectiveness of rewiring and reusing pre-trained video models. Reusing pre-trained models leads to significantly better performance than training from scratch (compare Row 1 to the rest). Reusing a better pre-trained model gives even higher performance (compare Row 2 to Row 3). Pret.: pretraining." + ], + "table_footnote": [], + "table_body": "
Pret. ModelPret. Dataset0.50.750.95Avg.
Vswin-baseNone44.5828.417.4028.68
Kinetics-40052.7236.738.8835.73
Kinetics-60052.4637.3710.3936.28
", + "bbox": [ + 504, + 266, + 883, + 333 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f4fb51c584677689195717ffb2502a710aa96785c06b4342149066ef1021d34e.jpg", + "table_caption": [ + "Table 4. Comparison of localization performance with different backbones and localizers, in terms of average mAP (\\%) on the dataset ActivityNet." + ], + "table_footnote": [], + "table_body": "
BackboneLocalizer0.50.750.95Avg.
Re2Vswin-tinyVSGN53.2437.2310.4936.38
ActionFormer54.7537.819.0336.80
Re2Slowfast-101VSGN53.6337.5310.6736.82
ActionFormer55.2537.869.0537.01
", + "bbox": [ + 504, + 383, + 883, + 465 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "end-to-end training with a deep Slowfast backbone on one single 11GB GPU. Moreover, $\\mathrm{Re}^2\\mathrm{TAL}$ doesn't incur much extra training time compared to its non-reversible counterpart. The time to train one epoch is the following, Vswintiny (114 mins) vs. $\\mathrm{Re}^2\\mathrm{V}$ swintiny (135 mins); Slowfast-50 (147 mins) vs. $\\mathrm{Re}^2\\mathrm{Slowfast - }50$ (158 mins).", + "bbox": [ + 498, + 477, + 890, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.3 Why rewiring and reuse?", + "text_level": 1, + "bbox": [ + 500, + 587, + 728, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We rewire existing network architectures to make them reversible, and reuse their parameters for initialization. This way we dramatically reduce the effort of training the reversible networks, and still reach the representation capability of the original non-reversible ones. To compare the video representation capabilities of both types of networks, we use them to extract video features and train a localizer (VSGN [73] in this case) with the features. We demonstrate their performance in Tab. 2, showing that our reversible models are comparable to the original models.", + "bbox": [ + 496, + 611, + 890, + 761 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "If there are two versions of the same non-reversible model trained in different ways and with different performance, will our $\\mathrm{Re}^2\\mathrm{TAL}$ models benefit more from the higher-performing version? Vswin-base happens to have such two versions: one trained on Kinetics-400 and the other trained on Kinetics-600, the latter with better performance. We initialize our $\\mathrm{Re}^2\\mathrm{V}$ swin-base with either ver", + "bbox": [ + 496, + 762, + 890, + 867 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2Memory increases from Vswin-small to base is due to the channel in", + "bbox": [ + 94, + 886, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "crease; memory reduction from Slowfast-101 to 152 is because the former one uses input configuration (8, 8) while the latter uses (4, 16).", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10643", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3fc14bd58532a0bee2c678e006556f994557f71df0d2552c40f30629216e2a13.jpg", + "table_caption": [ + "Table 5. Compared to the state-of-the-art for temporal action localization performance on ActivityNet-v1.3 and THUMOS-14, measured by mAPs (\\%) at different IoU thresholds according to their respective official metrics. E2E: end-to-end; Mem: memory (GB)." + ], + "table_footnote": [], + "table_body": "
MethodBackboneE2EFlowMemActivityNet-v1.3THUMOS-14
0.50.750.95Avg.0.30.40.50.60.7
TAL-Net [8]I3DX✓-38.2318.301.3020.2253.248.542.833.820.8
BMN [36]TSNX✓-50.0734.788.2933.8556.047.438.829.720.5
G-TAD [69]TSNX✓-50.3634.609.0234.0954.547.640.230.823.4
TSI [41]TSNX✓-51.1835.026.5934.1561.052.142.633.222.4
BC-GNN [4]TSNX✓-50.5634.759.3734.2657.149.140.431.223.1
VSGN [73]TSNX✓-52.3836.018.3735.0766.760.452.441.030.4
ActionFormer [71]I3DX✓-53.5036.208.2035.6082.177.871.059.443.9
PBRNet [39]I3D✓✓-53.9634.978.9835.0158.554.651.341.829.5
AFSD [35]I3D✓✓1252.4035.306.5034.4067.362.455.543.731.1
R-C3D [66]C3D✓X-26.80---44.835.628.9--
DaoTAD [63]I3D✓X11----62.8-53.8-30.1
TALLFormer [10]VSwin-Base✓X2954.1036.207.9035.6076.0-63.2-34.5
ActionFormer [71]VSwin-TinyXX-53.8335.827.2735.1770.864.755.742.227.0
ActionFormer + Re2TALRe2VSwin-Tiny✓X2454.7537.819.0336.8077.071.562.449.736.3
ActionFormer [71]Slowfast-101XX-53.9837.008.8736.0972.766.958.646.433.1
ActionFormer + Re2TALRe2Slowfast-101✓X6.855.2537.869.0537.0177.472.664.953.739.0
", + "bbox": [ + 93, + 123, + 874, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sion, and compare their performance on TAL in Tab. 3. By using the better version, the TAL performance obviously increases. In addition, using either version as initialization is better than training from scratch. This indicates that our rewiring-reuse strategy is very important for TAL performance, and reusing a better pre-trained model will benefit TAL even further. That means if a better training strategy for an existing model comes out, we can correspondingly obtain a more accurate reversible model.", + "bbox": [ + 75, + 402, + 470, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.1.4 Choice of Backbones and Localizers", + "text_level": 1, + "bbox": [ + 76, + 556, + 382, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 4, we demonstrate the results using the two different backbones $\\mathrm{Re}^2\\mathrm{V}$ swin-tiny and $\\mathrm{Re}^2\\mathrm{Slow}$ fast-101, and two different localizers VSGN [73] and ActionFormer [71] on ActivityNet. Since the ActionFormer localizer yields better performance for both $\\mathrm{Re}^2\\mathrm{V}$ swin-tiny and $\\mathrm{Re}^2\\mathrm{Slow}$ fast-101, we compare the ActionFormer results to other methods in the literature, and also apply them to the THUMOS dataset, as shown in Sec. 4.2.", + "bbox": [ + 75, + 580, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. State-of-the-Art Comparisons", + "text_level": 1, + "bbox": [ + 76, + 710, + 344, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare the performance of our $\\mathrm{Re}^2\\mathrm{TAL}$ to recent state-of-the-art (SOTA) methods in the literature in Tab. 5 on ActivityNet and THUMOS. On ActivityNet, our $\\mathrm{Re}^2\\mathrm{TAL}$ reaches a new SOTA performance: average mAP $37.01\\%$ , outperforming all other methods by significant margins. On THUMOS, ours surpasses the concurrent work TaLLFormer [10] with mAP $64.9\\%$ at tIoU=0.5, and the highest among all methods that only use the RGB modality.", + "bbox": [ + 75, + 734, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Furthermore, for an apple-to/apple comparison with the feature-based method ActionFormer, we re-ran ActionFormer using their official code with the RGB features ex", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tracted with the Vswin-tiny and Slowfast-101 backbones, corresponding to our $\\mathrm{Re}^2\\mathrm{V}$ swin-tiny and $\\mathrm{Re}^2\\mathrm{Slowfast - 101}$ , respectively. We see that our $\\mathrm{Re}^2\\mathrm{TAL}$ always outperforms vanilla ActionFormer under the same backbone categories (e.g. $\\mathrm{Re}^2\\mathrm{V}$ swin-tiny and Vswin-tiny are in the same backbone category; $\\mathrm{Re}^2\\mathrm{Slowfast - 101}$ and Slowfast-101 are in the same backbone category).", + "bbox": [ + 496, + 402, + 893, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 551, + 627, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a novel rewiring-to-reversibility $(\\mathrm{Re}^2)$ scheme to convert off-the-shelf models into reversible models while preserving the number of trainable parameters. The procedure allows reusing the compute invested in training large models and adds only a tiny sliver of finetuning compute. We apply the procedure to video backbones such as Video Swin (Vswin) and SlowFast to obtain $\\mathrm{Re}^2\\mathrm{V}$ win and $\\mathrm{Re}^2\\mathrm{Slow}$ fast backbones respectively. Further, we utilize the $\\mathrm{Re}^2$ backbones for memory-efficient end-to-end temporal action localization, reaching mAP $64.9\\%$ at tIoU $= 0.5$ on THUMOS-14, and average mAP $37.01\\%$ on ActivityNet-v1.3, establishing a new state-of-the-art. We hope that future work in this direction can explore extending the $\\mathrm{Re}^2$ method to other memory-bottlenecked tasks such as dense video captioning, movie summarization etc.", + "bbox": [ + 496, + 588, + 893, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence.", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10644", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 6", + "[2] Humam Alwassel, Silvio Giancola, and Bernard Ghanem. TSP: Temporally-sensitive pretraining of video encoders for localization tasks. 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In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 2" + ], + "bbox": [ + 501, + 90, + 893, + 655 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10647", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_model.json b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c3dc9b19d9b3f57439a454068c26c33a74cd3e49 --- /dev/null +++ b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_model.json @@ -0,0 +1,2345 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.225, + 0.13, + 0.748, + 0.177 + ], + "angle": 0, + "content": "\\(\\mathbf{Re}^{2}\\mathbf{TAL}\\): Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.203, + 0.885, + 0.258 + ], + "angle": 0, + "content": "Chen Zhao\\(^{1}\\) Shuming Liu\\(^{1}\\) Karttikeya Mangalam\\(^{2}\\) Bernard Ghanem\\(^{1}\\) \n\\(^{1}\\)King Abdullah University of Science and Technology (KAUST), Saudi Arabia \\(^{2}\\)UC Berkeley, US {chen.zhao, shuming.liu, bernard.ghanem}@kaust.edu.sa mangalam@berkeley.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.735 + ], + "angle": 0, + "content": "Temporal action localization (TAL) requires long-form reasoning to predict actions of various durations and complex content. Given limited GPU memory, training TAL end to end (i.e., from videos to predictions) on long videos is a significant challenge. Most methods can only train on pre-extracted features without optimizing them for the localization problem, consequently limiting localization performance. In this work, to extend the potential in TAL networks, we propose a novel end-to-end method \\(Re^{2}TAL\\), which rewrites pretrained video backbones for reversible TAL. \\(Re^{2}TAL\\) builds a backbone with reversible modules, where the input can be recovered from the output such that the bulky intermediate activations can be cleared from memory during training. Instead of designing one single type of reversible module, we propose a network rewiring mechanism, to transform any module with a residual connection to a reversible module without changing any parameters. This provides two benefits: (1) a large variety of reversible networks are easily obtained from existing and even future model designs, and (2) the reversible models require much less training effort as they reuse the pre-trained parameters of their original non-reversible versions. \\(Re^{2}TAL\\), only using the RGB modality, reaches 37.01% average mAP on ActivityNet-v1.3, a new state-of-the-art record, and mAP 64.9% at tIoU=0.5 on THUMOS-14, outperforming all other RGB-only methods. Code is available at https://github.com/coolbay/Re2TAL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.768, + 0.21, + 0.784 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Temporal Action Localization (TAL) [36,53,73] is a fundamental problem of practical importance in video understanding. It aims to bound semantic actions within start and end timestamps. Localizing such video segments is very useful for a variety of tasks such as video-language grounding [23, 56], moment retrieval [9, 21], video captioning [30, 50]. Since video actions have a large variety of" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.293, + 0.882, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.451, + 0.895, + 0.522 + ], + "angle": 0, + "content": "Figure 1. Illustration of TAL network activations in training. Top: non-reversible network stores activations of all layers in memory. Bottom: reversible network only needs to store the activations of inter-stage downsampling layers. Backbone activations dominate memory occupation, compared to Localizer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.895, + 0.672 + ], + "angle": 0, + "content": "temporal durations and content, to produce high-fidelity localization, TAL approaches need to learn from a long temporal scope of the video, which contains a large number of frames. To accommodate all these frames along with their network activations in GPU memory is extremely challenging, given the current GPU memory size (e.g. the commodity GPU GTX1080Ti only has 11GB). Often, it is impossible to train one video sequence on a GPU without substantially downgrading the video spatial/temporal resolutions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.903 + ], + "angle": 0, + "content": "To circumvent the GPU-memory bottleneck, most TAL methods deal with videos in two isolated steps (e.g. [4, 67, 69, 71-73]). First is a snippet-level feature extraction step, which simply extracts snippet representations using a pretrained video network (backbone) in inference mode. The backbone is usually a large neural network trained for an auxiliary task on a large dataset of trimmed video clips (e.g., action recognition on Kinetics-400 [28]). The second step trains a localizer on the pre-extracted features. In this way, only the activations of the TAL head need to be stored in memory, which is tiny compared to those of the backbone (see the illustration of the activation contrast between backbone and localizer in Fig. 1). However, this two-step strategy comes at a steep price. The pre-extracted features can suffer from domain shift from the auxiliary pre-training" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10637" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "task/data to TAL, and do not necessarily align with the representation needs of TAL. This is because they cannot be finetuned and must be used as-is in their misaligned state for TAL. A better alternative is to jointly train the backbone and localizer end to end. But as mentioned earlier, the enormous memory footprint of video activations in the backbone makes it extremely challenging. Is there a way for end-to-end training without compromising data dimensionality?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.471, + 0.426 + ], + "angle": 0, + "content": "Reversible networks [20, 25, 31, 48] provide an elegant solution to drastically reduce the feature activation memory during training. Their input can be recovered from the output via a reverse computation. Therefore, the intermediate activation maps, which are used for back propagation, do not need to be cached during the forward pass (as illustrated in Fig. 1). This offers a promising approach to enable memory-efficient end-to-end TAL training, and various reversible architectures have been proposed, such as RevNet [20], and RevViT [48]. However, these works design a specific reversible architecture and train for a particular dataset. Due to their new architecture, they also need to train the networks from scratch, requiring a significant amount of compute resources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.549 + ], + "angle": 0, + "content": "Conversely, it would be beneficial to be able to convert existing non-reversible video backbones to reversible ones, which would (1) avail a large variety of architectures and (2) allow us to reuse the large compute resources that had already been invested in training the non-reversible video backbones. Since pre-trained video backbones are a crucial part of TAL, the ability to convert off-the-shelf backbones to reversible ones is a key to unleash their power in this task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.763 + ], + "angle": 0, + "content": "In this work, for end-to-end TAL, we propose a principled approach to Rewire the architectural connections of a pre-trained non-reversible backbone to make it Reversible, dubbed \\(\\mathrm{Re}^2\\mathrm{TAL}\\). Network modules with a residual connection (res-module for short), such as a Resnet block [22] or a Transformer MLP/attention layer [14], are the most popular design recently. Given any network composed of residual modules, we can apply our rewiring technique to convert it to a corresponding reversible network without introducing or removing any trainable parameters. Instead of training from scratch, our reversible network can reuse the non-reversible network's parameters and only needs a small number of epochs for finetuning to reach similar performance. We summarize our contributions as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "(1) We propose a novel approach to construct and train reversible video backbones parsimoniously by architectural rewiring from an off-the-shelf pre-trained video backbone. This not only provides a large collection of reversible candidates, but also allows reusing the large compute resources invested in pre-training these models. We apply our rewiring technique to various kinds of representative video backbones, including transformer-based Video Swin and ConvNet-based Slowfast, and demonstrate that our re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "versible networks can reach the same performance of their non-reversible counterparts with only minimum finetuning effort (as low as 10 epochs compared to 300 epochs for training from scratch)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.289 + ], + "angle": 0, + "content": "(2) We propose a novel approach for end-to-end TAL training using reversible video networks. Without sacrificing spatial/temporal resolutions or network capability, our proposed approach dramatically reduces GPU memory usage, thus enabling end-to-end training on one 11GB GPU. We demonstrate on different localizers and different backbone architectures that we significantly boost TAL performance with our end-to-end training compared to traditional feature-based approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.382 + ], + "angle": 0, + "content": "(3) With our proposed \\(\\mathrm{Re}^2\\mathrm{TAL}\\), we use recent localizers in the literature to achieve a new state-of-the-art performance, \\(37.01\\%\\) average mAP on ActivityNet-v1.3. We also reach the highest mAP among all methods that only use the RGB modality on THUMOS-14, \\(64.9\\%\\) at tIoU \\(= 0.5\\), outperforming concurrent work TALLFormer [10]." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.642, + 0.415 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Reversible Networks are a family of neural models based on the reversible real-valued non-volume preserving (real NVP) transformation introduced in [12, 13]. The transformation has been originally applied widely for image generation using generative flows [24, 29], and later used for various applications, such as compression [38], denoising [43], and steganography recovery [49]. Furthermore, it has also been repurposed for memory-efficient neural network training for a variety of architectures such as ConvNets [20, 25], Masked ConvNet [57], RNNs [47], Graph Networks [31] and more recently, Vision Transformers [48]. However, each of these methods only focuses on one or several specific architectures, and trains their newly proposed reversible architectures from scratch, thereby requiring large compute resources. In this work, we propose a rewiring scheme to adapt off-the-shelf models to reversible architectures which only utilize a small amount of compute for finetuning. This allows democratizing the reach of reversible architecture to arbitrary models and dataset settings by leveraging the architecture design effort and computational cost already spent in vanilla off-the-shelf models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Video Recognition Backbones. ConvNets have had a long and illustrious history of improving video understanding performance [7, 16-19, 26, 33, 52, 55, 61, 64, 65, 74]. Among those, Slowfast [17], which uses a slow pathway and a fast pathway to capture spatial semantics and temporal motion respectively, has been widely adopted for various tasks such as action detection [17], untrimmed video classification [44] and moment/natural language retrieval [21] for its high efficiency and efficacy. Recently, video transformers have ushered in a new life in the field of video repre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10638" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "sensation learning. Leveraging long-term temporal connection via the attention mechanism, transformers have quickly gain popularity as the backbone of choice for several video recognition workloads [3, 5, 15, 32, 45, 70]. Among those, Video Swin Transformer [45] introduces an inductive bias of locality to video transformers, leading to an outstanding speed-accuracy trade-off. However, most of the models are vanilla non-reversible architectures. In this work, we unleash the potential of reversible architectures for these models such that the good properties of reversible models, e.g. memory efficiency, can be infused into them. In particular, we show that the pretrained Video Swin Transformer [45] and SlowFast [17] models can be rewired to be reversible, and finetuned cheaply to improve temporal action localization performance with end-to-end training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.473, + 0.732 + ], + "angle": 0, + "content": "Temporal Action Localization (TAL). Due to the conflict between large video data and the GPU memory limit, most TAL methods using deep networks are two-step methods [4, 8, 34, 36, 37, 41, 46, 51, 54, 69, 71-73]. For example, using pre-extracted features, G-TAD [69] and VSGN [73] utilize graph convolutions to model temporal relations between snippets, and ActionFormer [71] leverages transformers to capture long-range context. To mitigate the performance gap between the two-step mechanism and real end-to-end training, some methods explore post-pretraining to enhance the video feature representations for TAL [2, 66, 68]. In the meanwhile, researchers also attempt to perform real end-to-end training by reducing network/data complexity [10, 35, 39, 40, 42, 63, 66]. R-C3D [66] is the end-to-end pioneer, but it uses a shallow network C3D [60], thus restricting the performance. PBRNet [39] and ASDF [35] downscale the frame resolution to \\(96 \\times 96\\). DaoTAD [63] makes RGB-only enough by using end-to-end training with various data augmentations. TALLFormer [10] proposes to use a feature bank strategy and only updates a portion of features during end-to-end training. Compared to these approaches, our method doesn't sacrifice any data dimensionality or data samples in training, and it supports very deep networks. We significantly reduce memory consumption while preserving the full data fidelity. Moreover, our work is complementary to these methods, and can also be used jointly to further reduce memory cost." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.745, + 0.466, + 0.763 + ], + "angle": 0, + "content": "3. Method: \\(\\mathbf{Re}^2\\) Temporal Action Localization" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.385, + 0.785 + ], + "angle": 0, + "content": "3.1. TAL Formulation and Architecture" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.794, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Temporal action localization (TAL) predicts the timestamps of actions from a video sequence, which is formulated as follows. Given a video sequence \\(V\\) of \\(T\\) frames \\(\\{I_t\\in \\mathbb{R}^{3\\times H\\times W}\\}_{t = 1}^T\\), TAL predicts a set \\(m\\) of actions \\(\\Phi = \\{\\phi_m = (t_{m,s},t_{m,e},c_m,s_m)\\}_{m = 1}^M\\), where \\(t_{m,s}\\) and \\(t_{m,e}\\) are action start and end time respectively, \\(c_{m}\\) is action label, and \\(s_m\\) is prediction confidence. To achieve this, the following" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.093, + 0.654, + 0.107 + ], + "angle": 0, + "content": "two steps are required." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.243 + ], + "angle": 0, + "content": "In the first step, the videos \\(V\\) are encoded as \\(N\\) features vectors \\(\\{\\mathbf{x}_n\\in \\mathbb{R}^C\\}_{n = 1}^N\\) via a backbone. This backbone aggregates spatial information within video frames, as well as temporal information across frames. It is usually designed for an auxiliary task such as action recognition. Popular backbones can be categorized into Resnet-based architectures, such as I3D [7], R2+1D [62], SlowFast [17], and Transformer based architectures, such as ViViT [3], Video Swin Transformers [45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.365 + ], + "angle": 0, + "content": "In the second step, a localizer, uses a 'neck' to further aggregate the video features \\(\\{\\mathbf{x}_n\\}_{n=1}^N\\) in the temporal domain, and a 'head', to make predictions of action boundaries, i.e., start and end timestamps \\((t_{m,s}, t_{m,e})\\) and categories. The neck contains layers of networks, e.g., 1D convolutional networks in BMN [36], Graph networks in G-TAD [69] and VSGN [73], and Transformers in RTD-Net [59] and Action-Former [71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.456 + ], + "angle": 0, + "content": "As mentioned in Sec. 1, an optimal way to train the entire TAL network is to jointly train the backbone and the localizer end to end. However, it is substantially challenging to fit all activation maps of the long video sequence into limited GPU memory. In the following sections, we provide end-to-end TAL solution \\(\\mathrm{Re}^2\\mathrm{TAL}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.469, + 0.808, + 0.485 + ], + "angle": 0, + "content": "3.2. Rewire for Reversibility, and Reuse" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Let's first analyze what in the GPU memory precludes end-to-end training of TAL. As mentioned in Sec. 1, the activation maps in the backbone are the major occupant in the memory. Concretely, given a batch of a video sequence of \\(T\\) frames, each with resolution \\(S \\times S\\), to train them on a backbone of \\(L\\) layers each with \\(C\\) channels, the training memory complexity is \\(\\mathcal{O}(LCTS^2)\\). Downgrading any data dimensionality or the backbone capacity can reduce the memory complexity, but at the same time, may harm the prediction accuracy. We aim to reduce memory consumption without sacrificing the data dimensionality or the model capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Actually, the intermediate activations are stored in memory during training for the purpose of gradient computation in back propagation. If we can reconstruct them during back propagation, then there is no need for their memory occupation. Reversible networks [20, 25, 48, 49] is a superb solution for reconstructing the input from output, and various reversible architectures have been proposed recently (e.g., Revnet [20], RevViT [48]). However, the performance of TAL heavily depends on the backbone that is pre-trained on one or even multiple large-scale datasets. For example, the popular I3D [7] backbone is trained on Kinetics-400 [28] with its parameters initialized from Resnet [22] trained on ImageNet [11]. If we make up a new reversible network for TAL as is the case with previous reversible networks (e.g., [20, 25]), we need to go through all the expensive and time-consuming training stages to reach an equivalently" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10639" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.087, + 0.454, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed rewiring process. In this example, 3 consecutive residual modules in the same stage are rewired into 3 reversible modules. After rewiring, each residual connection skips one more \\(\\mathcal{F}\\) block ahead. Note that beyond this example, our rewiring can process any number of such modules. good initialization for TAL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.47, + 0.552 + ], + "angle": 0, + "content": "Instead of proposing a new reversible architecture, we propose a principled approach to rewire a pre-trained nonreversible backbone to make it reversible. Given any module with a residual connection, we can convert it into a reversible module while preserving the same set of parameters. This technique has two advantages. First, we obtain a large and growing collection of various reversible architectures out of the box, by rewiring the existing networks and even future networks of higher performance. Second, we can reuse their pre-trained weights to initialize our reversible networks, eliminating the tremendous effort to train from scratch. In the following, we will describe our rewiring for reversibility \\((\\mathbf{Re}^2)\\) technique in detail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Rewiring. Residual modules, i.e., modules with a residual connection, are the most commonly adopted design in concurrent neural network architectures, such as Resnet [22] and Transformers [14]. Given any residual modules, we can rewire them into reversible modules. Fig. 2 illustrates this process with an example of 3 consecutive residual modules that are in the same stage, i.e., there are no downsampling operations in between. Each of the original residual modules contains a block \\(\\mathcal{F}_i\\) (blue boxes) where \\(i = 1,2,3,\\ldots\\) and a residual connection (orange arrow). The blocks \\(\\mathcal{F}_i\\) have the same input and output dimensions, and can contain any computations. For example, in Resnet, the building block consisting of convolution, batch normalization, and ReLU can be one \\(\\mathcal{F}_i\\) block (e.g. Fig. 3 (a)). In Transformers, if \\(\\mathcal{F}_i\\) represents an attention layer, then \\(\\mathcal{F}_{i + 1}\\) is an MLP layer (e.g. Fig. 3 (b) and (c)). The residual connection in each module only skips one \\(\\mathcal{F}_i\\) block in the same module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To rewire, we simply let the residual connection skip the next block \\(\\mathcal{F}_{i+1}\\) as well as the current one \\(\\mathcal{F}_i\\). To be more specific, we keep the starting point of each residual connection, but make it end after two blocks, as shown in the second row of Fig. 2. As a result, two consecutive residual" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.092, + 0.63, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.092, + 0.755, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.092, + 0.882, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Figure 3. Examples of \\(\\mathcal{F}\\) blocks. (a) A reset basic block. (b) A transformer MLP layer. (c) A transformer attention layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.292 + ], + "angle": 0, + "content": "connections become overlapped, and there are always two pathways of activations (gray and green in Fig. 2) throughout the modules, as shown in the third row of Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.893, + 0.398 + ], + "angle": 0, + "content": "To prepare a second pathway of input to the first module, we duplicate the input \\( x_0 \\) to obtain \\( y_0 \\). To combine the results \\( x_3 \\) and \\( y_3 \\) of the two pathways, we simply average them at the end of the modules. This design guarantees that the dimensions of the input and output of every block \\( \\mathcal{F}_i \\) are identical before and after the rewiring. Therefore, the structure of \\( \\mathcal{F}_i \\) stays exactly the same." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Reversibility. In the following, we mathematically formulate the rewired modules to show their reversibility. To be concise, we use the first two modules as an example. Given the input activations \\( x_0 \\) and \\( y_0 \\), and the blocks \\( \\mathcal{F}_1 \\) and \\( \\mathcal{F}_2 \\), the output of the two blocks are \\( x_1, y_1 \\) and \\( x_2, y_2 \\) respectively, computed as follows" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.496, + 0.891, + 0.531 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} y _ {1} = x _ {0} \\\\ x _ {1} = \\mathcal {F} _ {1} \\left(x _ {0}\\right) + y _ {0}, \\end{array} \\right. \\Rightarrow \\left\\{ \\begin{array}{l} y _ {2} = x _ {1} \\\\ x _ {2} = \\mathcal {F} _ {2} \\left(x _ {1}\\right) + y _ {1}. \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.598 + ], + "angle": 0, + "content": "The above equations are reversible, which means that we can recover the input \\( x_{1}, y_{1} \\) from \\( x_{2}, y_{2} \\), and then \\( x_{0}, y_{0} \\) from \\( x_{1}, y_{1} \\). The reverse computation is formulated in the following equation" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.604, + 0.891, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} x _ {0} = y _ {1} \\\\ y _ {0} = x _ {1} - \\mathcal {F} _ {1} (x _ {0}), \\end{array} \\right. \\Leftarrow \\left\\{ \\begin{array}{l} x _ {1} = y _ {2} \\\\ y _ {1} = x _ {2} - \\mathcal {F} _ {2} (x _ {1}). \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.735 + ], + "angle": 0, + "content": "A network with more modules follows the same strategy as in Eq. 1 and Eq. 2. When we stack multiple consecutive reversible modules as one network (as the example in Fig. 2), the entire network is reversible. In this case, we can start from the last module and sequentially reconstruct the input of each module with Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Reuse. As the structure and parameter dimensions of the \\(\\mathcal{F}_i\\) block in our reversible modules after rewiring stay exactly the same as the \\(\\mathcal{F}_i\\) block in the corresponding residual module, we can directly reuse the pre-trained parameters in the residual modules to initialize our reversible modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Our rewiring mechanism provides a large collection of reversible candidates. We can easily convert a network into a reversible one without designing a new architecture from scratch. Not only can we use the existing architectures, but we can also benefit from future even better models to obtain better reversible models. The reuse strategy" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10640" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.091, + 0.462, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.302, + 0.256, + 0.318, + 0.265 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.091, + 0.816, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.256, + 0.661, + 0.266 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Figure 4. Comparison of different input arrangements for a TAL network. (a) Snippets input: the backbone processes many video snippets (a short clip of frames), often overlapped. (b) Frames input: the backbone takes all the frames in the video as one single input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.471, + 0.395 + ], + "angle": 0, + "content": "allows taking advantage of the large computing resources invested in those pre-trained models. We don't need to retrain the reversible network from scratch. Instead, we can train the reversible backbone with minimum effort (as low as 10 epochs compared to 300 epochs from scratch) while reaching the same performance as its residual counterpart." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.404, + 0.428, + 0.421 + ], + "angle": 0, + "content": "3.3. Reversible Temporal Action Localization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.47, + 0.488 + ], + "angle": 0, + "content": "Considering that the backbone is the heaviest part in the TAL network in terms of memory usage, as illustrated in Fig. 1, we target the backbone and apply our \\(\\mathrm{Re}^2\\) technique described above to rewire it to obtain a reversible network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.471, + 0.684 + ], + "angle": 0, + "content": "A backbone network, e.g., Video Swin Transformer [45], Slowfast [17], is usually comprised of several stages. Within each stage, the activation sizes stay the same. We convert all the modules into reversible ones following the rewiring method proposed in Sec. 3.2. During training, we can clear all the input and intermediate activations from GPU memory, and only store the final output of the stage during the forward pass (as shown in Fig. 1). In the back propagation, we re-compute all the activations based on the reverse process as in Eq. 2. As [48] pointed out, this re-computation doesn't incur too much more computational time since we can parallelize the process to make use of the spare computation of GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.47, + 0.777 + ], + "angle": 0, + "content": "Across stages, there are downsampling layers, which reduce the activation sizes. We leave the downsampling layers as they are and cache the activations inside to enable back propagation. Considering that there are only several downsampling layers, the memory occupation of these activations is acceptable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.317, + 0.803 + ], + "angle": 0, + "content": "3.4. End-to-End TAL Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For end-to-end training with our \\(\\mathrm{Re}^2\\mathrm{TAL}\\), we just need to do the following: find a well-performing video backbone, rewire it into a reversible one, load the parameters from the original backbone to the reversible one and finetune for several epochs on the pretraining task, and train with a localizer end to end. This reversible TAL network is significantly" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.363 + ], + "angle": 0, + "content": "more efficient in memory usage, enabling end-to-end training a GPU of limited memory (e.g., as small as a 11GB commodity GPU). But is it a wise choice to directly adopt the training strategies from the feature-based methods?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Input frame arrangement. Since most TAL methods are designed and experimented with the pre-extracted, they have predisposed to particular design choices, such as extracting features with overlapped snippets to arrange the input frames. But we find it not ideal for end-to-end training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.575 + ], + "angle": 0, + "content": "Fig. 4 (a) illustrates the framework commonly used in two-step (or feature-based) methods. To extract \\( N \\) feature vectors as the localizer input, \\( N \\) snippets need to be processed by the backbone independently. Each snippet contains a sequence of \\( D \\) frames. The snippets are usually overlapped with one another to maintain temporal consistency, which causes duplicate computation and extra memory occupation. Consequently, at least \\( ND \\) frames need to go through the backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.817 + ], + "angle": 0, + "content": "This framework works fine with the two-step method, since feature extraction is one-off effort and all the snippets can be processed sequentially to circumvent the memory issue. However, end-to-end training cannot bear the extra memory cost. Therefore, we treat the entire video sequence as one single input instead, and the backbone aggregates all frames at one time, as shown in Fig. 4 (b). This mechanism not only reduces the cost incurred by the duplicate computation, but also has the advantage of aggregating long-term temporal information, in contrast to being restricted within the snippet as with the snippet mechanism. In this way, to obtain \\( N \\) feature vectors, we just need to process \\( Ns \\) frames, where \\( s \\) is the overall strides in the backbone (e.g. \\( s = 2 \\) in Video Swin Transformers). Considering that \\( s \\) is usually much smaller than \\( D \\), the frame-input mechanism is more efficient in memory and computation cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.634, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets and evaluation metrics. We present our experimental results on two representative datasets ActivityNet-v1.3 (ActivityNet for short) [6] and THUMOS-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10641" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 1. Advantage of end-to-end training. End-to-end training leads to significant mAP (\\%) boost for TAL with either backbone." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.123, + 0.469, + 0.189 + ], + "angle": 0, + "content": "
Re2Vswin-tinyRe2Slowfast-101
Method0.50.750.95Avg.0.50.750.95Avg.
Features51.1835.099.7234.4751.9836.009.4735.24
End2End53.2437.2310.4936.3853.6337.5310.6736.82
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.202, + 0.47, + 0.399 + ], + "angle": 0, + "content": "14 (THUMOS for short) [27]. ActivityNet is a challenging large-scale dataset, with 19994 temporally annotated untrimmed videos in 200 action categories, which are split into training, validation and testing sets by the ratio of 2:1:1. THUMOS contains 413 temporally annotated untrimmed videos with 20 action categories, in which 200 videos are for training and 213 videos for validation1. For both datasets, we use mean Average Precision (mAP) at different tIoU thresholds as the evaluation metric. On ActivityNet, we choose 10 values in the range \\([0.5, 0.95]\\) with a step size 0.05 as tIoU thresholds; on THUMOS, we use tIoU thresholds \\(\\{0.3, 0.4, 0.5, 0.6, 0.7\\}\\); following the official evaluation practice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.469, + 0.552 + ], + "angle": 0, + "content": "Backbones and localizers of \\(\\mathbf{Re}^2\\mathbf{TAL}\\). For backbones, we choose two representative models from the Resnet and Transformer families respectively for experimental demonstration: Video Swin Transformers (Vswin for short) [45] and Slowfast [17], both well known for their powerful video representation and memory efficiency. For Vswin, we use three variants: tiny, small, and base; for Slowfast, we use 50, 101, and 152. For localizers, we experiment with the recent temporal action localization (TAL) methods VSGN [73] and ActionFormer [71]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Implementation Details of \\(\\mathbf{Re}^2\\mathbf{TAL}\\). We initialize all our reversible backbones with their non-reversible counterparts, and finetune for up to 30 epochs on Kinetics-400 with Cosine Annealing learning rate policy and Adamw (for Vswin) and SGD (for Slowfast) optimizers. Actually, in our experiments, we find 10 epochs of finetuning already reaches similarly good performance. With the pre-trained reversible backbone, we train TAL on a single GPU, A100 with batchsize \\(= 1\\) for Vswin and V100 with batchsize \\(= 2\\) for Slowfast. This is only possible due to the massive GPU memory savings from the reversible backbones. For the hyper-parameters, we follow the original training recipe of VSGN [73] and ActionFormer [71] for the learning rates and epochs in the localizers. We set the learning rates of the Vswin backbones 1 magnitude lower than the localizer, and those of the Slowfast backbones 2 magnitude lower. The spatial resolution is \\(224 \\times 224\\). For ActivityNet, the number of frame input is \\(T = 512\\), the number of feature vectors is \\(N = 256\\); and for THUMOS, the number of frame input is \\(T = 1024\\), the number of features is \\(N = 512\\)." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.088, + 0.882, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.218, + 0.892, + 0.247 + ], + "angle": 0, + "content": "Figure 5. Performance improvement of end-to-end TAL upon feature-based in terms of action temporal duration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.264, + 0.706, + 0.279 + ], + "angle": 0, + "content": "4.1. Ablation and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.381 + ], + "angle": 0, + "content": "In this section, we provide ablation study on ActivityNet and performance analysis to answer the following questions. (1) Why do we need end-to-end training? (2) How effective and efficient is our \\(\\mathrm{Re}^2\\mathrm{TAL}\\)? (3) What is the benefit of the proposed rewiring technique? (4) Which reversible backbone and localizer provides the best performance?" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.734, + 0.431 + ], + "angle": 0, + "content": "4.1.1 Why end-to-end training?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.595 + ], + "angle": 0, + "content": "With end-to-end training, we are able to optimize the features to adapt to the TAL task and dataset such that we can achieve higher performance than the feature-based method. To verify this, we compare end-to-end training to the feature-based training on our reversible TAL. In Tab. 1, we demonstrate the comparison on two types of backbones: \\(\\mathrm{Re}^2\\) Vswin-tiny and \\(\\mathrm{Re}^2\\) Slowfast-101 with VSGN [73] on ActivityNet. It shows that for both backbones, using end-to-end training leads to significant performance boost, gaining almost \\(2\\%\\) mAP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further diagnose what kinds of actions end-to-end training improves the most, in Fig. 5 (a), we plot the accuracy gains brought by end-to-end training for five different groups of actions based on their temporal durations (in seconds): XS: (0s, 30s], S: (30s, 60s], M: (60s, 120s], L: (120s, 180s], and XL: \\(>180\\)s (as suggested in [1]). We can see that the accuracy gains for different action durations are closely related to the numbers of samples in each duration category (the pie chart): short actions (XS and X) with many samples are obviously improved, though long actions (XL) with fewer samples is slightly sacrificed. Actually, short actions are a fundamental challenge in TAL [73]. End-to-end training provides an effective solution by enabling the backbone to learn feature representations to the benefit of short actions — the categories with more samples, thus preventing them fusing into the background. Short actions occupy the majority in the dataset, and their improvement leads to an overall performance boost. In Fig. 5 (b), we show that the false negative predictions are reduced by end-to-end training for all groups, more significantly for shorter ones." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "1The training and validation sets of THUMOS are temporally annotated videos from the validation and testing sets of UCF101 [58], respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10642" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.28, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.092, + 0.47, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.198, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 6. \\(\\mathbf{Re}^{2}\\mathbf{TAL}\\) models compared with original models at different spatial and temporal downscaling ratios. Spatial and temporal resolutions from left to right are as follows. \\(\\mathbf{Re}^{2}\\mathbf{TAL}\\): (112, 512), (224, 512); Original: (56, 512), (112, 192), (224, 192), (224, 512). The localizer VSGN [73] is used." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.273, + 0.278, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.273, + 0.47, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.484 + ], + "angle": 0, + "content": "Figure 7. GPU memory consumption v.s. network sizes. The dot sizes represent the model sizes, and the y-axis is the GPU memory used for processing one video (batchsize=1). Our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) almost keeps the memory constant when only the network depths increase (e.g. from Vswin-tiny to small, from Slowfast-50 to 101), whereas the original models easily go out of memory when the network becomes larger." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.4, + 0.515 + ], + "angle": 0, + "content": "4.1.2 How effective and efficient is \\(\\mathbf{Re}^2\\mathbf{TAL}\\)?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.648 + ], + "angle": 0, + "content": "An alternative way to enable end-to-end training is to reduce data resolutions [39, 63]. In Fig. 6, we downscale the input videos in the spatial or temporal dimensions to adjust the memory requirements, and compare our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) models to their corresponding original models. We can see that under even smaller memory requirements, our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) models achieve higher performance than the original models that relies on sacrificing video resolutions to reduce memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.471, + 0.875 + ], + "angle": 0, + "content": "To further visualize the memory efficiency of our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) compared to their non-reversible counterparts when trained end to end, we demonstrate the GPU memory consumption of the three Vswin backbones of different depths and widths and the three Slowfast backbones of different depths in Fig. 7. For Vswin backbones, we assume a GPU memory budget of 90GB, which is the size of A100. For Slowfast backbones, we assume our GPU budget is 11GB, which is the size of the commodity GPU such as GTX1080Ti. We can see that for either case, the nonreversible network will go out of memory when the model size reaches a certain level. In contrast, our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) almost keeps constant memory usage when only the network depth increases (from Vswin-tiny to small, from Slowfast-50 to \\(101)^2\\). With the low memory cost, our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) enables" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.131 + ], + "angle": 0, + "content": "Table 2. Comparison of feature representations between the \\(\\mathbf{Re}^2\\mathbf{TAL}\\) and original models, in terms of average mAP (\\%) on the dataset ActivityNet. Vw: Vswin; Slowf: Slowfast." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.135, + 0.889, + 0.187 + ], + "angle": 0, + "content": "
ModelTinySmallBaseModel50101152
Vswin34.3633.8634.47Slowfast34.6035.0434.61
Re2Vw34.4734.0434.09Re2Slowf34.9335.2434.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.19, + 0.892, + 0.26 + ], + "angle": 0, + "content": "Table 3. Effectiveness of rewiring and reusing pre-trained video models. Reusing pre-trained models leads to significantly better performance than training from scratch (compare Row 1 to the rest). Reusing a better pre-trained model gives even higher performance (compare Row 2 to Row 3). Pret.: pretraining." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.267, + 0.885, + 0.334 + ], + "angle": 0, + "content": "
Pret. ModelPret. Dataset0.50.750.95Avg.
Vswin-baseNone44.5828.417.4028.68
Kinetics-40052.7236.738.8835.73
Kinetics-60052.4637.3710.3936.28
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.337, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Table 4. Comparison of localization performance with different backbones and localizers, in terms of average mAP (\\%) on the dataset ActivityNet." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.384, + 0.885, + 0.466 + ], + "angle": 0, + "content": "
BackboneLocalizer0.50.750.95Avg.
Re2Vswin-tinyVSGN53.2437.2310.4936.38
ActionFormer54.7537.819.0336.80
Re2Slowfast-101VSGN53.6337.5310.6736.82
ActionFormer55.2537.869.0537.01
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.478, + 0.892, + 0.568 + ], + "angle": 0, + "content": "end-to-end training with a deep Slowfast backbone on one single 11GB GPU. Moreover, \\(\\mathrm{Re}^2\\mathrm{TAL}\\) doesn't incur much extra training time compared to its non-reversible counterpart. The time to train one epoch is the following, Vswintiny (114 mins) vs. \\(\\mathrm{Re}^2\\mathrm{V}\\) swintiny (135 mins); Slowfast-50 (147 mins) vs. \\(\\mathrm{Re}^2\\mathrm{Slowfast - }50\\) (158 mins)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.73, + 0.603 + ], + "angle": 0, + "content": "4.1.3 Why rewiring and reuse?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.762 + ], + "angle": 0, + "content": "We rewire existing network architectures to make them reversible, and reuse their parameters for initialization. This way we dramatically reduce the effort of training the reversible networks, and still reach the representation capability of the original non-reversible ones. To compare the video representation capabilities of both types of networks, we use them to extract video features and train a localizer (VSGN [73] in this case) with the features. We demonstrate their performance in Tab. 2, showing that our reversible models are comparable to the original models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.868 + ], + "angle": 0, + "content": "If there are two versions of the same non-reversible model trained in different ways and with different performance, will our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) models benefit more from the higher-performing version? Vswin-base happens to have such two versions: one trained on Kinetics-400 and the other trained on Kinetics-600, the latter with better performance. We initialize our \\(\\mathrm{Re}^2\\mathrm{V}\\) swin-base with either ver" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "2Memory increases from Vswin-small to base is due to the channel in" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "crease; memory reduction from Slowfast-101 to 152 is because the former one uses input configuration (8, 8) while the latter uses (4, 16)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10643" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 5. Compared to the state-of-the-art for temporal action localization performance on ActivityNet-v1.3 and THUMOS-14, measured by mAPs (\\%) at different IoU thresholds according to their respective official metrics. E2E: end-to-end; Mem: memory (GB)." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.124, + 0.875, + 0.389 + ], + "angle": 0, + "content": "
MethodBackboneE2EFlowMemActivityNet-v1.3THUMOS-14
0.50.750.95Avg.0.30.40.50.60.7
TAL-Net [8]I3DX✓-38.2318.301.3020.2253.248.542.833.820.8
BMN [36]TSNX✓-50.0734.788.2933.8556.047.438.829.720.5
G-TAD [69]TSNX✓-50.3634.609.0234.0954.547.640.230.823.4
TSI [41]TSNX✓-51.1835.026.5934.1561.052.142.633.222.4
BC-GNN [4]TSNX✓-50.5634.759.3734.2657.149.140.431.223.1
VSGN [73]TSNX✓-52.3836.018.3735.0766.760.452.441.030.4
ActionFormer [71]I3DX✓-53.5036.208.2035.6082.177.871.059.443.9
PBRNet [39]I3D✓✓-53.9634.978.9835.0158.554.651.341.829.5
AFSD [35]I3D✓✓1252.4035.306.5034.4067.362.455.543.731.1
R-C3D [66]C3D✓X-26.80---44.835.628.9--
DaoTAD [63]I3D✓X11----62.8-53.8-30.1
TALLFormer [10]VSwin-Base✓X2954.1036.207.9035.6076.0-63.2-34.5
ActionFormer [71]VSwin-TinyXX-53.8335.827.2735.1770.864.755.742.227.0
ActionFormer + Re2TALRe2VSwin-Tiny✓X2454.7537.819.0336.8077.071.562.449.736.3
ActionFormer [71]Slowfast-101XX-53.9837.008.8736.0972.766.958.646.433.1
ActionFormer + Re2TALRe2Slowfast-101✓X6.855.2537.869.0537.0177.472.664.953.739.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.471, + 0.538 + ], + "angle": 0, + "content": "sion, and compare their performance on TAL in Tab. 3. By using the better version, the TAL performance obviously increases. In addition, using either version as initialization is better than training from scratch. This indicates that our rewiring-reuse strategy is very important for TAL performance, and reusing a better pre-trained model will benefit TAL even further. That means if a better training strategy for an existing model comes out, we can correspondingly obtain a more accurate reversible model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.383, + 0.572 + ], + "angle": 0, + "content": "4.1.4 Choice of Backbones and Localizers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.702 + ], + "angle": 0, + "content": "In Tab. 4, we demonstrate the results using the two different backbones \\(\\mathrm{Re}^2\\mathrm{V}\\) swin-tiny and \\(\\mathrm{Re}^2\\mathrm{Slow}\\) fast-101, and two different localizers VSGN [73] and ActionFormer [71] on ActivityNet. Since the ActionFormer localizer yields better performance for both \\(\\mathrm{Re}^2\\mathrm{V}\\) swin-tiny and \\(\\mathrm{Re}^2\\mathrm{Slow}\\) fast-101, we compare the ActionFormer results to other methods in the literature, and also apply them to the THUMOS dataset, as shown in Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.345, + 0.729 + ], + "angle": 0, + "content": "4.2. State-of-the-Art Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.856 + ], + "angle": 0, + "content": "We compare the performance of our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) to recent state-of-the-art (SOTA) methods in the literature in Tab. 5 on ActivityNet and THUMOS. On ActivityNet, our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) reaches a new SOTA performance: average mAP \\(37.01\\%\\), outperforming all other methods by significant margins. On THUMOS, ours surpasses the concurrent work TaLLFormer [10] with mAP \\(64.9\\%\\) at tIoU=0.5, and the highest among all methods that only use the RGB modality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Furthermore, for an apple-to/apple comparison with the feature-based method ActionFormer, we re-ran ActionFormer using their official code with the RGB features ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.895, + 0.51 + ], + "angle": 0, + "content": "tracted with the Vswin-tiny and Slowfast-101 backbones, corresponding to our \\(\\mathrm{Re}^2\\mathrm{V}\\) swin-tiny and \\(\\mathrm{Re}^2\\mathrm{Slowfast - 101}\\), respectively. We see that our \\(\\mathrm{Re}^2\\mathrm{TAL}\\) always outperforms vanilla ActionFormer under the same backbone categories (e.g. \\(\\mathrm{Re}^2\\mathrm{V}\\) swin-tiny and Vswin-tiny are in the same backbone category; \\(\\mathrm{Re}^2\\mathrm{Slowfast - 101}\\) and Slowfast-101 are in the same backbone category)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.553, + 0.628, + 0.569 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.895, + 0.816 + ], + "angle": 0, + "content": "In this work, we propose a novel rewiring-to-reversibility \\((\\mathrm{Re}^2)\\) scheme to convert off-the-shelf models into reversible models while preserving the number of trainable parameters. The procedure allows reusing the compute invested in training large models and adds only a tiny sliver of finetuning compute. We apply the procedure to video backbones such as Video Swin (Vswin) and SlowFast to obtain \\(\\mathrm{Re}^2\\mathrm{V}\\) win and \\(\\mathrm{Re}^2\\mathrm{Slow}\\) fast backbones respectively. Further, we utilize the \\(\\mathrm{Re}^2\\) backbones for memory-efficient end-to-end temporal action localization, reaching mAP \\(64.9\\%\\) at tIoU \\(= 0.5\\) on THUMOS-14, and average mAP \\(37.01\\%\\) on ActivityNet-v1.3, establishing a new state-of-the-art. We hope that future work in this direction can explore extending the \\(\\mathrm{Re}^2\\) method to other memory-bottlenecked tasks such as dense video captioning, movie summarization etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10644" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Humam Alwassel, Silvio Giancola, and Bernard Ghanem. 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In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.894, + 0.656 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10647" + } + ] +] \ No newline at end of file diff --git a/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_origin.pdf b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b0dbdfbd17c2109dd4f37e534adb987bcf7c7ed2 --- /dev/null +++ b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/a7a6ab97-064a-45bd-98df-b72107741eea_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b4633341656b9ee7b2a88557be36a074b1e982380d055ea19aa9c8166e986820 +size 2126127 diff --git a/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/full.md b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d9d26204c196db81a015a090cd4cc3267436d817 --- /dev/null +++ b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/full.md @@ -0,0 +1,300 @@ +# $\mathbf{Re}^{2}\mathbf{TAL}$ : Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization + +Chen Zhao $^{1}$ Shuming Liu $^{1}$ Karttikeya Mangalam $^{2}$ Bernard Ghanem $^{1}$ $^{1}$ King Abdullah University of Science and Technology (KAUST), Saudi Arabia $^{2}$ UC Berkeley, US {chen.zhao, shuming.liu, bernard.ghanem}@kaust.edu.sa mangalam@berkeley.edu + +# Abstract + +Temporal action localization (TAL) requires long-form reasoning to predict actions of various durations and complex content. Given limited GPU memory, training TAL end to end (i.e., from videos to predictions) on long videos is a significant challenge. Most methods can only train on pre-extracted features without optimizing them for the localization problem, consequently limiting localization performance. In this work, to extend the potential in TAL networks, we propose a novel end-to-end method $Re^{2}TAL$ , which rewrites pretrained video backbones for reversible TAL. $Re^{2}TAL$ builds a backbone with reversible modules, where the input can be recovered from the output such that the bulky intermediate activations can be cleared from memory during training. Instead of designing one single type of reversible module, we propose a network rewiring mechanism, to transform any module with a residual connection to a reversible module without changing any parameters. This provides two benefits: (1) a large variety of reversible networks are easily obtained from existing and even future model designs, and (2) the reversible models require much less training effort as they reuse the pre-trained parameters of their original non-reversible versions. $Re^{2}TAL$ , only using the RGB modality, reaches 37.01% average mAP on ActivityNet-v1.3, a new state-of-the-art record, and mAP 64.9% at tIoU=0.5 on THUMOS-14, outperforming all other RGB-only methods. Code is available at https://github.com/coolbay/Re2TAL. + +# 1. Introduction + +Temporal Action Localization (TAL) [36,53,73] is a fundamental problem of practical importance in video understanding. It aims to bound semantic actions within start and end timestamps. Localizing such video segments is very useful for a variety of tasks such as video-language grounding [23, 56], moment retrieval [9, 21], video captioning [30, 50]. Since video actions have a large variety of + +![](images/34a4f3714da94bd724e9a05b4173b243067eb034d7f967811f9b5f1e4bc9ef7f.jpg) +Figure 1. Illustration of TAL network activations in training. Top: non-reversible network stores activations of all layers in memory. Bottom: reversible network only needs to store the activations of inter-stage downsampling layers. Backbone activations dominate memory occupation, compared to Localizer. + +temporal durations and content, to produce high-fidelity localization, TAL approaches need to learn from a long temporal scope of the video, which contains a large number of frames. To accommodate all these frames along with their network activations in GPU memory is extremely challenging, given the current GPU memory size (e.g. the commodity GPU GTX1080Ti only has 11GB). Often, it is impossible to train one video sequence on a GPU without substantially downgrading the video spatial/temporal resolutions. + +To circumvent the GPU-memory bottleneck, most TAL methods deal with videos in two isolated steps (e.g. [4, 67, 69, 71-73]). First is a snippet-level feature extraction step, which simply extracts snippet representations using a pretrained video network (backbone) in inference mode. The backbone is usually a large neural network trained for an auxiliary task on a large dataset of trimmed video clips (e.g., action recognition on Kinetics-400 [28]). The second step trains a localizer on the pre-extracted features. In this way, only the activations of the TAL head need to be stored in memory, which is tiny compared to those of the backbone (see the illustration of the activation contrast between backbone and localizer in Fig. 1). However, this two-step strategy comes at a steep price. The pre-extracted features can suffer from domain shift from the auxiliary pre-training + +task/data to TAL, and do not necessarily align with the representation needs of TAL. This is because they cannot be finetuned and must be used as-is in their misaligned state for TAL. A better alternative is to jointly train the backbone and localizer end to end. But as mentioned earlier, the enormous memory footprint of video activations in the backbone makes it extremely challenging. Is there a way for end-to-end training without compromising data dimensionality? + +Reversible networks [20, 25, 31, 48] provide an elegant solution to drastically reduce the feature activation memory during training. Their input can be recovered from the output via a reverse computation. Therefore, the intermediate activation maps, which are used for back propagation, do not need to be cached during the forward pass (as illustrated in Fig. 1). This offers a promising approach to enable memory-efficient end-to-end TAL training, and various reversible architectures have been proposed, such as RevNet [20], and RevViT [48]. However, these works design a specific reversible architecture and train for a particular dataset. Due to their new architecture, they also need to train the networks from scratch, requiring a significant amount of compute resources. + +Conversely, it would be beneficial to be able to convert existing non-reversible video backbones to reversible ones, which would (1) avail a large variety of architectures and (2) allow us to reuse the large compute resources that had already been invested in training the non-reversible video backbones. Since pre-trained video backbones are a crucial part of TAL, the ability to convert off-the-shelf backbones to reversible ones is a key to unleash their power in this task. + +In this work, for end-to-end TAL, we propose a principled approach to Rewire the architectural connections of a pre-trained non-reversible backbone to make it Reversible, dubbed $\mathrm{Re}^2\mathrm{TAL}$ . Network modules with a residual connection (res-module for short), such as a Resnet block [22] or a Transformer MLP/attention layer [14], are the most popular design recently. Given any network composed of residual modules, we can apply our rewiring technique to convert it to a corresponding reversible network without introducing or removing any trainable parameters. Instead of training from scratch, our reversible network can reuse the non-reversible network's parameters and only needs a small number of epochs for finetuning to reach similar performance. We summarize our contributions as follows. + +(1) We propose a novel approach to construct and train reversible video backbones parsimoniously by architectural rewiring from an off-the-shelf pre-trained video backbone. This not only provides a large collection of reversible candidates, but also allows reusing the large compute resources invested in pre-training these models. We apply our rewiring technique to various kinds of representative video backbones, including transformer-based Video Swin and ConvNet-based Slowfast, and demonstrate that our re + +versible networks can reach the same performance of their non-reversible counterparts with only minimum finetuning effort (as low as 10 epochs compared to 300 epochs for training from scratch). + +(2) We propose a novel approach for end-to-end TAL training using reversible video networks. Without sacrificing spatial/temporal resolutions or network capability, our proposed approach dramatically reduces GPU memory usage, thus enabling end-to-end training on one 11GB GPU. We demonstrate on different localizers and different backbone architectures that we significantly boost TAL performance with our end-to-end training compared to traditional feature-based approaches. +(3) With our proposed $\mathrm{Re}^2\mathrm{TAL}$ , we use recent localizers in the literature to achieve a new state-of-the-art performance, $37.01\%$ average mAP on ActivityNet-v1.3. We also reach the highest mAP among all methods that only use the RGB modality on THUMOS-14, $64.9\%$ at tIoU $= 0.5$ , outperforming concurrent work TALLFormer [10]. + +# 2. Related Work + +Reversible Networks are a family of neural models based on the reversible real-valued non-volume preserving (real NVP) transformation introduced in [12, 13]. The transformation has been originally applied widely for image generation using generative flows [24, 29], and later used for various applications, such as compression [38], denoising [43], and steganography recovery [49]. Furthermore, it has also been repurposed for memory-efficient neural network training for a variety of architectures such as ConvNets [20, 25], Masked ConvNet [57], RNNs [47], Graph Networks [31] and more recently, Vision Transformers [48]. However, each of these methods only focuses on one or several specific architectures, and trains their newly proposed reversible architectures from scratch, thereby requiring large compute resources. In this work, we propose a rewiring scheme to adapt off-the-shelf models to reversible architectures which only utilize a small amount of compute for finetuning. This allows democratizing the reach of reversible architecture to arbitrary models and dataset settings by leveraging the architecture design effort and computational cost already spent in vanilla off-the-shelf models. + +Video Recognition Backbones. ConvNets have had a long and illustrious history of improving video understanding performance [7, 16-19, 26, 33, 52, 55, 61, 64, 65, 74]. Among those, Slowfast [17], which uses a slow pathway and a fast pathway to capture spatial semantics and temporal motion respectively, has been widely adopted for various tasks such as action detection [17], untrimmed video classification [44] and moment/natural language retrieval [21] for its high efficiency and efficacy. Recently, video transformers have ushered in a new life in the field of video repre + +sensation learning. Leveraging long-term temporal connection via the attention mechanism, transformers have quickly gain popularity as the backbone of choice for several video recognition workloads [3, 5, 15, 32, 45, 70]. Among those, Video Swin Transformer [45] introduces an inductive bias of locality to video transformers, leading to an outstanding speed-accuracy trade-off. However, most of the models are vanilla non-reversible architectures. In this work, we unleash the potential of reversible architectures for these models such that the good properties of reversible models, e.g. memory efficiency, can be infused into them. In particular, we show that the pretrained Video Swin Transformer [45] and SlowFast [17] models can be rewired to be reversible, and finetuned cheaply to improve temporal action localization performance with end-to-end training. + +Temporal Action Localization (TAL). Due to the conflict between large video data and the GPU memory limit, most TAL methods using deep networks are two-step methods [4, 8, 34, 36, 37, 41, 46, 51, 54, 69, 71-73]. For example, using pre-extracted features, G-TAD [69] and VSGN [73] utilize graph convolutions to model temporal relations between snippets, and ActionFormer [71] leverages transformers to capture long-range context. To mitigate the performance gap between the two-step mechanism and real end-to-end training, some methods explore post-pretraining to enhance the video feature representations for TAL [2, 66, 68]. In the meanwhile, researchers also attempt to perform real end-to-end training by reducing network/data complexity [10, 35, 39, 40, 42, 63, 66]. R-C3D [66] is the end-to-end pioneer, but it uses a shallow network C3D [60], thus restricting the performance. PBRNet [39] and ASDF [35] downscale the frame resolution to $96 \times 96$ . DaoTAD [63] makes RGB-only enough by using end-to-end training with various data augmentations. TALLFormer [10] proposes to use a feature bank strategy and only updates a portion of features during end-to-end training. Compared to these approaches, our method doesn't sacrifice any data dimensionality or data samples in training, and it supports very deep networks. We significantly reduce memory consumption while preserving the full data fidelity. Moreover, our work is complementary to these methods, and can also be used jointly to further reduce memory cost. + +# 3. Method: $\mathbf{Re}^2$ Temporal Action Localization + +# 3.1. TAL Formulation and Architecture + +Temporal action localization (TAL) predicts the timestamps of actions from a video sequence, which is formulated as follows. Given a video sequence $V$ of $T$ frames $\{I_t\in \mathbb{R}^{3\times H\times W}\}_{t = 1}^T$ , TAL predicts a set $m$ of actions $\Phi = \{\phi_m = (t_{m,s},t_{m,e},c_m,s_m)\}_{m = 1}^M$ , where $t_{m,s}$ and $t_{m,e}$ are action start and end time respectively, $c_{m}$ is action label, and $s_m$ is prediction confidence. To achieve this, the following + +two steps are required. + +In the first step, the videos $V$ are encoded as $N$ features vectors $\{\mathbf{x}_n\in \mathbb{R}^C\}_{n = 1}^N$ via a backbone. This backbone aggregates spatial information within video frames, as well as temporal information across frames. It is usually designed for an auxiliary task such as action recognition. Popular backbones can be categorized into Resnet-based architectures, such as I3D [7], R2+1D [62], SlowFast [17], and Transformer based architectures, such as ViViT [3], Video Swin Transformers [45]. + +In the second step, a localizer, uses a 'neck' to further aggregate the video features $\{\mathbf{x}_n\}_{n=1}^N$ in the temporal domain, and a 'head', to make predictions of action boundaries, i.e., start and end timestamps $(t_{m,s}, t_{m,e})$ and categories. The neck contains layers of networks, e.g., 1D convolutional networks in BMN [36], Graph networks in G-TAD [69] and VSGN [73], and Transformers in RTD-Net [59] and Action-Former [71]. + +As mentioned in Sec. 1, an optimal way to train the entire TAL network is to jointly train the backbone and the localizer end to end. However, it is substantially challenging to fit all activation maps of the long video sequence into limited GPU memory. In the following sections, we provide end-to-end TAL solution $\mathrm{Re}^2\mathrm{TAL}$ . + +# 3.2. Rewire for Reversibility, and Reuse + +Let's first analyze what in the GPU memory precludes end-to-end training of TAL. As mentioned in Sec. 1, the activation maps in the backbone are the major occupant in the memory. Concretely, given a batch of a video sequence of $T$ frames, each with resolution $S \times S$ , to train them on a backbone of $L$ layers each with $C$ channels, the training memory complexity is $\mathcal{O}(LCTS^2)$ . Downgrading any data dimensionality or the backbone capacity can reduce the memory complexity, but at the same time, may harm the prediction accuracy. We aim to reduce memory consumption without sacrificing the data dimensionality or the model capacity. + +Actually, the intermediate activations are stored in memory during training for the purpose of gradient computation in back propagation. If we can reconstruct them during back propagation, then there is no need for their memory occupation. Reversible networks [20, 25, 48, 49] is a superb solution for reconstructing the input from output, and various reversible architectures have been proposed recently (e.g., Revnet [20], RevViT [48]). However, the performance of TAL heavily depends on the backbone that is pre-trained on one or even multiple large-scale datasets. For example, the popular I3D [7] backbone is trained on Kinetics-400 [28] with its parameters initialized from Resnet [22] trained on ImageNet [11]. If we make up a new reversible network for TAL as is the case with previous reversible networks (e.g., [20, 25]), we need to go through all the expensive and time-consuming training stages to reach an equivalently + +![](images/08886fa3a5b55aa5208253784c4d6b40e70b54821ba46b08a1daed351d3ae340.jpg) +Figure 2. Illustration of the proposed rewiring process. In this example, 3 consecutive residual modules in the same stage are rewired into 3 reversible modules. After rewiring, each residual connection skips one more $\mathcal{F}$ block ahead. Note that beyond this example, our rewiring can process any number of such modules. good initialization for TAL. + +Instead of proposing a new reversible architecture, we propose a principled approach to rewire a pre-trained nonreversible backbone to make it reversible. Given any module with a residual connection, we can convert it into a reversible module while preserving the same set of parameters. This technique has two advantages. First, we obtain a large and growing collection of various reversible architectures out of the box, by rewiring the existing networks and even future networks of higher performance. Second, we can reuse their pre-trained weights to initialize our reversible networks, eliminating the tremendous effort to train from scratch. In the following, we will describe our rewiring for reversibility $(\mathbf{Re}^2)$ technique in detail. + +Rewiring. Residual modules, i.e., modules with a residual connection, are the most commonly adopted design in concurrent neural network architectures, such as Resnet [22] and Transformers [14]. Given any residual modules, we can rewire them into reversible modules. Fig. 2 illustrates this process with an example of 3 consecutive residual modules that are in the same stage, i.e., there are no downsampling operations in between. Each of the original residual modules contains a block $\mathcal{F}_i$ (blue boxes) where $i = 1,2,3,\ldots$ and a residual connection (orange arrow). The blocks $\mathcal{F}_i$ have the same input and output dimensions, and can contain any computations. For example, in Resnet, the building block consisting of convolution, batch normalization, and ReLU can be one $\mathcal{F}_i$ block (e.g. Fig. 3 (a)). In Transformers, if $\mathcal{F}_i$ represents an attention layer, then $\mathcal{F}_{i + 1}$ is an MLP layer (e.g. Fig. 3 (b) and (c)). The residual connection in each module only skips one $\mathcal{F}_i$ block in the same module. + +To rewire, we simply let the residual connection skip the next block $\mathcal{F}_{i+1}$ as well as the current one $\mathcal{F}_i$ . To be more specific, we keep the starting point of each residual connection, but make it end after two blocks, as shown in the second row of Fig. 2. As a result, two consecutive residual + +![](images/19bd660c771f4ab8b073992c230f1110bcf4a6d0dbb598635ef055ac50e3d8e0.jpg) +Figure 3. Examples of $\mathcal{F}$ blocks. (a) A reset basic block. (b) A transformer MLP layer. (c) A transformer attention layer. + +![](images/0c84f3bfca40427aae281fa4395eeb2a404aed586c33e411a933a8e5abcb0c90.jpg) + +![](images/da1927aeb3639bb83813d9ed80bd8bc09cbf6bf244b2d1af5012e39f5e02ae87.jpg) + +connections become overlapped, and there are always two pathways of activations (gray and green in Fig. 2) throughout the modules, as shown in the third row of Fig. 2. + +To prepare a second pathway of input to the first module, we duplicate the input $x_0$ to obtain $y_0$ . To combine the results $x_3$ and $y_3$ of the two pathways, we simply average them at the end of the modules. This design guarantees that the dimensions of the input and output of every block $\mathcal{F}_i$ are identical before and after the rewiring. Therefore, the structure of $\mathcal{F}_i$ stays exactly the same. + +Reversibility. In the following, we mathematically formulate the rewired modules to show their reversibility. To be concise, we use the first two modules as an example. Given the input activations $x_0$ and $y_0$ , and the blocks $\mathcal{F}_1$ and $\mathcal{F}_2$ , the output of the two blocks are $x_1, y_1$ and $x_2, y_2$ respectively, computed as follows + +$$ +\left\{ \begin{array}{l} y _ {1} = x _ {0} \\ x _ {1} = \mathcal {F} _ {1} \left(x _ {0}\right) + y _ {0}, \end{array} \right. \Rightarrow \left\{ \begin{array}{l} y _ {2} = x _ {1} \\ x _ {2} = \mathcal {F} _ {2} \left(x _ {1}\right) + y _ {1}. \end{array} \right. \tag {1} +$$ + +The above equations are reversible, which means that we can recover the input $x_{1}, y_{1}$ from $x_{2}, y_{2}$ , and then $x_{0}, y_{0}$ from $x_{1}, y_{1}$ . The reverse computation is formulated in the following equation + +$$ +\left\{ \begin{array}{l} x _ {0} = y _ {1} \\ y _ {0} = x _ {1} - \mathcal {F} _ {1} (x _ {0}), \end{array} \right. \Leftarrow \left\{ \begin{array}{l} x _ {1} = y _ {2} \\ y _ {1} = x _ {2} - \mathcal {F} _ {2} (x _ {1}). \end{array} \right. \tag {2} +$$ + +A network with more modules follows the same strategy as in Eq. 1 and Eq. 2. When we stack multiple consecutive reversible modules as one network (as the example in Fig. 2), the entire network is reversible. In this case, we can start from the last module and sequentially reconstruct the input of each module with Eq. 2. + +Reuse. As the structure and parameter dimensions of the $\mathcal{F}_i$ block in our reversible modules after rewiring stay exactly the same as the $\mathcal{F}_i$ block in the corresponding residual module, we can directly reuse the pre-trained parameters in the residual modules to initialize our reversible modules. + +Our rewiring mechanism provides a large collection of reversible candidates. We can easily convert a network into a reversible one without designing a new architecture from scratch. Not only can we use the existing architectures, but we can also benefit from future even better models to obtain better reversible models. The reuse strategy + +![](images/d07afeb6b10c6b01876c890734973346a998a81e4f7bf9df2416ff21d3da7537.jpg) +(a) + +![](images/da45bad198941ef2bdaabb6d404572956ae6abcc7a39182e355c866f258a4350.jpg) +(b) +Figure 4. Comparison of different input arrangements for a TAL network. (a) Snippets input: the backbone processes many video snippets (a short clip of frames), often overlapped. (b) Frames input: the backbone takes all the frames in the video as one single input. + +allows taking advantage of the large computing resources invested in those pre-trained models. We don't need to retrain the reversible network from scratch. Instead, we can train the reversible backbone with minimum effort (as low as 10 epochs compared to 300 epochs from scratch) while reaching the same performance as its residual counterpart. + +# 3.3. Reversible Temporal Action Localization + +Considering that the backbone is the heaviest part in the TAL network in terms of memory usage, as illustrated in Fig. 1, we target the backbone and apply our $\mathrm{Re}^2$ technique described above to rewire it to obtain a reversible network. + +A backbone network, e.g., Video Swin Transformer [45], Slowfast [17], is usually comprised of several stages. Within each stage, the activation sizes stay the same. We convert all the modules into reversible ones following the rewiring method proposed in Sec. 3.2. During training, we can clear all the input and intermediate activations from GPU memory, and only store the final output of the stage during the forward pass (as shown in Fig. 1). In the back propagation, we re-compute all the activations based on the reverse process as in Eq. 2. As [48] pointed out, this re-computation doesn't incur too much more computational time since we can parallelize the process to make use of the spare computation of GPUs. + +Across stages, there are downsampling layers, which reduce the activation sizes. We leave the downsampling layers as they are and cache the activations inside to enable back propagation. Considering that there are only several downsampling layers, the memory occupation of these activations is acceptable. + +# 3.4. End-to-End TAL Training + +For end-to-end training with our $\mathrm{Re}^2\mathrm{TAL}$ , we just need to do the following: find a well-performing video backbone, rewire it into a reversible one, load the parameters from the original backbone to the reversible one and finetune for several epochs on the pretraining task, and train with a localizer end to end. This reversible TAL network is significantly + +more efficient in memory usage, enabling end-to-end training a GPU of limited memory (e.g., as small as a 11GB commodity GPU). But is it a wise choice to directly adopt the training strategies from the feature-based methods? + +Input frame arrangement. Since most TAL methods are designed and experimented with the pre-extracted, they have predisposed to particular design choices, such as extracting features with overlapped snippets to arrange the input frames. But we find it not ideal for end-to-end training. + +Fig. 4 (a) illustrates the framework commonly used in two-step (or feature-based) methods. To extract $N$ feature vectors as the localizer input, $N$ snippets need to be processed by the backbone independently. Each snippet contains a sequence of $D$ frames. The snippets are usually overlapped with one another to maintain temporal consistency, which causes duplicate computation and extra memory occupation. Consequently, at least $ND$ frames need to go through the backbone. + +This framework works fine with the two-step method, since feature extraction is one-off effort and all the snippets can be processed sequentially to circumvent the memory issue. However, end-to-end training cannot bear the extra memory cost. Therefore, we treat the entire video sequence as one single input instead, and the backbone aggregates all frames at one time, as shown in Fig. 4 (b). This mechanism not only reduces the cost incurred by the duplicate computation, but also has the advantage of aggregating long-term temporal information, in contrast to being restricted within the snippet as with the snippet mechanism. In this way, to obtain $N$ feature vectors, we just need to process $Ns$ frames, where $s$ is the overall strides in the backbone (e.g. $s = 2$ in Video Swin Transformers). Considering that $s$ is usually much smaller than $D$ , the frame-input mechanism is more efficient in memory and computation cost. + +# 4. Experiments + +Datasets and evaluation metrics. We present our experimental results on two representative datasets ActivityNet-v1.3 (ActivityNet for short) [6] and THUMOS- + +Table 1. Advantage of end-to-end training. End-to-end training leads to significant mAP (\%) boost for TAL with either backbone. + +
Re2Vswin-tinyRe2Slowfast-101
Method0.50.750.95Avg.0.50.750.95Avg.
Features51.1835.099.7234.4751.9836.009.4735.24
End2End53.2437.2310.4936.3853.6337.5310.6736.82
+ +14 (THUMOS for short) [27]. ActivityNet is a challenging large-scale dataset, with 19994 temporally annotated untrimmed videos in 200 action categories, which are split into training, validation and testing sets by the ratio of 2:1:1. THUMOS contains 413 temporally annotated untrimmed videos with 20 action categories, in which 200 videos are for training and 213 videos for validation1. For both datasets, we use mean Average Precision (mAP) at different tIoU thresholds as the evaluation metric. On ActivityNet, we choose 10 values in the range $[0.5, 0.95]$ with a step size 0.05 as tIoU thresholds; on THUMOS, we use tIoU thresholds $\{0.3, 0.4, 0.5, 0.6, 0.7\}$ ; following the official evaluation practice. + +Backbones and localizers of $\mathbf{Re}^2\mathbf{TAL}$ . For backbones, we choose two representative models from the Resnet and Transformer families respectively for experimental demonstration: Video Swin Transformers (Vswin for short) [45] and Slowfast [17], both well known for their powerful video representation and memory efficiency. For Vswin, we use three variants: tiny, small, and base; for Slowfast, we use 50, 101, and 152. For localizers, we experiment with the recent temporal action localization (TAL) methods VSGN [73] and ActionFormer [71]. + +Implementation Details of $\mathbf{Re}^2\mathbf{TAL}$ . We initialize all our reversible backbones with their non-reversible counterparts, and finetune for up to 30 epochs on Kinetics-400 with Cosine Annealing learning rate policy and Adamw (for Vswin) and SGD (for Slowfast) optimizers. Actually, in our experiments, we find 10 epochs of finetuning already reaches similarly good performance. With the pre-trained reversible backbone, we train TAL on a single GPU, A100 with batchsize $= 1$ for Vswin and V100 with batchsize $= 2$ for Slowfast. This is only possible due to the massive GPU memory savings from the reversible backbones. For the hyper-parameters, we follow the original training recipe of VSGN [73] and ActionFormer [71] for the learning rates and epochs in the localizers. We set the learning rates of the Vswin backbones 1 magnitude lower than the localizer, and those of the Slowfast backbones 2 magnitude lower. The spatial resolution is $224 \times 224$ . For ActivityNet, the number of frame input is $T = 512$ , the number of feature vectors is $N = 256$ ; and for THUMOS, the number of frame input is $T = 1024$ , the number of features is $N = 512$ . + +![](images/a80a661632d5f88e945a4db0583816943763b6538856c662cb01f02f4f843ad2.jpg) +Figure 5. Performance improvement of end-to-end TAL upon feature-based in terms of action temporal duration. + +# 4.1. Ablation and Analysis + +In this section, we provide ablation study on ActivityNet and performance analysis to answer the following questions. (1) Why do we need end-to-end training? (2) How effective and efficient is our $\mathrm{Re}^2\mathrm{TAL}$ ? (3) What is the benefit of the proposed rewiring technique? (4) Which reversible backbone and localizer provides the best performance? + +# 4.1.1 Why end-to-end training? + +With end-to-end training, we are able to optimize the features to adapt to the TAL task and dataset such that we can achieve higher performance than the feature-based method. To verify this, we compare end-to-end training to the feature-based training on our reversible TAL. In Tab. 1, we demonstrate the comparison on two types of backbones: $\mathrm{Re}^2$ Vswin-tiny and $\mathrm{Re}^2$ Slowfast-101 with VSGN [73] on ActivityNet. It shows that for both backbones, using end-to-end training leads to significant performance boost, gaining almost $2\%$ mAP. + +To further diagnose what kinds of actions end-to-end training improves the most, in Fig. 5 (a), we plot the accuracy gains brought by end-to-end training for five different groups of actions based on their temporal durations (in seconds): XS: (0s, 30s], S: (30s, 60s], M: (60s, 120s], L: (120s, 180s], and XL: $>180$ s (as suggested in [1]). We can see that the accuracy gains for different action durations are closely related to the numbers of samples in each duration category (the pie chart): short actions (XS and X) with many samples are obviously improved, though long actions (XL) with fewer samples is slightly sacrificed. Actually, short actions are a fundamental challenge in TAL [73]. End-to-end training provides an effective solution by enabling the backbone to learn feature representations to the benefit of short actions — the categories with more samples, thus preventing them fusing into the background. Short actions occupy the majority in the dataset, and their improvement leads to an overall performance boost. In Fig. 5 (b), we show that the false negative predictions are reduced by end-to-end training for all groups, more significantly for shorter ones. + +![](images/647eafd7719f66f3c5cac431b6a7cefb7fb78ac42c836e1675da5e6b65081286.jpg) +Figure 6. $\mathbf{Re}^{2}\mathbf{TAL}$ models compared with original models at different spatial and temporal downscaling ratios. Spatial and temporal resolutions from left to right are as follows. $\mathbf{Re}^{2}\mathbf{TAL}$ : (112, 512), (224, 512); Original: (56, 512), (112, 192), (224, 192), (224, 512). The localizer VSGN [73] is used. + +![](images/1bf6be083f4303f7633df6f7929aca619f6f2118a5fda752d847325c79f91a66.jpg) + +![](images/3bcfca41f9d99a92f6517aa771cb789968ee9ff11bf7d6f14f12b3e70436d189.jpg) +Figure 7. GPU memory consumption v.s. network sizes. The dot sizes represent the model sizes, and the y-axis is the GPU memory used for processing one video (batchsize=1). Our $\mathrm{Re}^2\mathrm{TAL}$ almost keeps the memory constant when only the network depths increase (e.g. from Vswin-tiny to small, from Slowfast-50 to 101), whereas the original models easily go out of memory when the network becomes larger. + +![](images/5d8b89e8efed4997d084b4377ea81b63f4d8362e2c70e8496ddcdf445bde122b.jpg) + +# 4.1.2 How effective and efficient is $\mathbf{Re}^2\mathbf{TAL}$ ? + +An alternative way to enable end-to-end training is to reduce data resolutions [39, 63]. In Fig. 6, we downscale the input videos in the spatial or temporal dimensions to adjust the memory requirements, and compare our $\mathrm{Re}^2\mathrm{TAL}$ models to their corresponding original models. We can see that under even smaller memory requirements, our $\mathrm{Re}^2\mathrm{TAL}$ models achieve higher performance than the original models that relies on sacrificing video resolutions to reduce memory. + +To further visualize the memory efficiency of our $\mathrm{Re}^2\mathrm{TAL}$ compared to their non-reversible counterparts when trained end to end, we demonstrate the GPU memory consumption of the three Vswin backbones of different depths and widths and the three Slowfast backbones of different depths in Fig. 7. For Vswin backbones, we assume a GPU memory budget of 90GB, which is the size of A100. For Slowfast backbones, we assume our GPU budget is 11GB, which is the size of the commodity GPU such as GTX1080Ti. We can see that for either case, the nonreversible network will go out of memory when the model size reaches a certain level. In contrast, our $\mathrm{Re}^2\mathrm{TAL}$ almost keeps constant memory usage when only the network depth increases (from Vswin-tiny to small, from Slowfast-50 to $101)^2$ . With the low memory cost, our $\mathrm{Re}^2\mathrm{TAL}$ enables + +Table 2. Comparison of feature representations between the $\mathbf{Re}^2\mathbf{TAL}$ and original models, in terms of average mAP (\%) on the dataset ActivityNet. Vw: Vswin; Slowf: Slowfast. + +
ModelTinySmallBaseModel50101152
Vswin34.3633.8634.47Slowfast34.6035.0434.61
Re2Vw34.4734.0434.09Re2Slowf34.9335.2434.54
+ +Table 3. Effectiveness of rewiring and reusing pre-trained video models. Reusing pre-trained models leads to significantly better performance than training from scratch (compare Row 1 to the rest). Reusing a better pre-trained model gives even higher performance (compare Row 2 to Row 3). Pret.: pretraining. + +
Pret. ModelPret. Dataset0.50.750.95Avg.
Vswin-baseNone44.5828.417.4028.68
Kinetics-40052.7236.738.8835.73
Kinetics-60052.4637.3710.3936.28
+ +Table 4. Comparison of localization performance with different backbones and localizers, in terms of average mAP (\%) on the dataset ActivityNet. + +
BackboneLocalizer0.50.750.95Avg.
Re2Vswin-tinyVSGN53.2437.2310.4936.38
ActionFormer54.7537.819.0336.80
Re2Slowfast-101VSGN53.6337.5310.6736.82
ActionFormer55.2537.869.0537.01
+ +end-to-end training with a deep Slowfast backbone on one single 11GB GPU. Moreover, $\mathrm{Re}^2\mathrm{TAL}$ doesn't incur much extra training time compared to its non-reversible counterpart. The time to train one epoch is the following, Vswintiny (114 mins) vs. $\mathrm{Re}^2\mathrm{V}$ swintiny (135 mins); Slowfast-50 (147 mins) vs. $\mathrm{Re}^2\mathrm{Slowfast - }50$ (158 mins). + +# 4.1.3 Why rewiring and reuse? + +We rewire existing network architectures to make them reversible, and reuse their parameters for initialization. This way we dramatically reduce the effort of training the reversible networks, and still reach the representation capability of the original non-reversible ones. To compare the video representation capabilities of both types of networks, we use them to extract video features and train a localizer (VSGN [73] in this case) with the features. We demonstrate their performance in Tab. 2, showing that our reversible models are comparable to the original models. + +If there are two versions of the same non-reversible model trained in different ways and with different performance, will our $\mathrm{Re}^2\mathrm{TAL}$ models benefit more from the higher-performing version? Vswin-base happens to have such two versions: one trained on Kinetics-400 and the other trained on Kinetics-600, the latter with better performance. We initialize our $\mathrm{Re}^2\mathrm{V}$ swin-base with either ver + +Table 5. Compared to the state-of-the-art for temporal action localization performance on ActivityNet-v1.3 and THUMOS-14, measured by mAPs (\%) at different IoU thresholds according to their respective official metrics. E2E: end-to-end; Mem: memory (GB). + +
MethodBackboneE2EFlowMemActivityNet-v1.3THUMOS-14
0.50.750.95Avg.0.30.40.50.60.7
TAL-Net [8]I3DX✓-38.2318.301.3020.2253.248.542.833.820.8
BMN [36]TSNX✓-50.0734.788.2933.8556.047.438.829.720.5
G-TAD [69]TSNX✓-50.3634.609.0234.0954.547.640.230.823.4
TSI [41]TSNX✓-51.1835.026.5934.1561.052.142.633.222.4
BC-GNN [4]TSNX✓-50.5634.759.3734.2657.149.140.431.223.1
VSGN [73]TSNX✓-52.3836.018.3735.0766.760.452.441.030.4
ActionFormer [71]I3DX✓-53.5036.208.2035.6082.177.871.059.443.9
PBRNet [39]I3D✓✓-53.9634.978.9835.0158.554.651.341.829.5
AFSD [35]I3D✓✓1252.4035.306.5034.4067.362.455.543.731.1
R-C3D [66]C3D✓X-26.80---44.835.628.9--
DaoTAD [63]I3D✓X11----62.8-53.8-30.1
TALLFormer [10]VSwin-Base✓X2954.1036.207.9035.6076.0-63.2-34.5
ActionFormer [71]VSwin-TinyXX-53.8335.827.2735.1770.864.755.742.227.0
ActionFormer + Re2TALRe2VSwin-Tiny✓X2454.7537.819.0336.8077.071.562.449.736.3
ActionFormer [71]Slowfast-101XX-53.9837.008.8736.0972.766.958.646.433.1
ActionFormer + Re2TALRe2Slowfast-101✓X6.855.2537.869.0537.0177.472.664.953.739.0
+ +sion, and compare their performance on TAL in Tab. 3. By using the better version, the TAL performance obviously increases. In addition, using either version as initialization is better than training from scratch. This indicates that our rewiring-reuse strategy is very important for TAL performance, and reusing a better pre-trained model will benefit TAL even further. That means if a better training strategy for an existing model comes out, we can correspondingly obtain a more accurate reversible model. + +# 4.1.4 Choice of Backbones and Localizers + +In Tab. 4, we demonstrate the results using the two different backbones $\mathrm{Re}^2\mathrm{V}$ swin-tiny and $\mathrm{Re}^2\mathrm{Slow}$ fast-101, and two different localizers VSGN [73] and ActionFormer [71] on ActivityNet. Since the ActionFormer localizer yields better performance for both $\mathrm{Re}^2\mathrm{V}$ swin-tiny and $\mathrm{Re}^2\mathrm{Slow}$ fast-101, we compare the ActionFormer results to other methods in the literature, and also apply them to the THUMOS dataset, as shown in Sec. 4.2. + +# 4.2. State-of-the-Art Comparisons + +We compare the performance of our $\mathrm{Re}^2\mathrm{TAL}$ to recent state-of-the-art (SOTA) methods in the literature in Tab. 5 on ActivityNet and THUMOS. On ActivityNet, our $\mathrm{Re}^2\mathrm{TAL}$ reaches a new SOTA performance: average mAP $37.01\%$ , outperforming all other methods by significant margins. On THUMOS, ours surpasses the concurrent work TaLLFormer [10] with mAP $64.9\%$ at tIoU=0.5, and the highest among all methods that only use the RGB modality. + +Furthermore, for an apple-to/apple comparison with the feature-based method ActionFormer, we re-ran ActionFormer using their official code with the RGB features ex + +tracted with the Vswin-tiny and Slowfast-101 backbones, corresponding to our $\mathrm{Re}^2\mathrm{V}$ swin-tiny and $\mathrm{Re}^2\mathrm{Slowfast - 101}$ , respectively. We see that our $\mathrm{Re}^2\mathrm{TAL}$ always outperforms vanilla ActionFormer under the same backbone categories (e.g. $\mathrm{Re}^2\mathrm{V}$ swin-tiny and Vswin-tiny are in the same backbone category; $\mathrm{Re}^2\mathrm{Slowfast - 101}$ and Slowfast-101 are in the same backbone category). + +# 5. Conclusions + +In this work, we propose a novel rewiring-to-reversibility $(\mathrm{Re}^2)$ scheme to convert off-the-shelf models into reversible models while preserving the number of trainable parameters. The procedure allows reusing the compute invested in training large models and adds only a tiny sliver of finetuning compute. We apply the procedure to video backbones such as Video Swin (Vswin) and SlowFast to obtain $\mathrm{Re}^2\mathrm{V}$ win and $\mathrm{Re}^2\mathrm{Slow}$ fast backbones respectively. Further, we utilize the $\mathrm{Re}^2$ backbones for memory-efficient end-to-end temporal action localization, reaching mAP $64.9\%$ at tIoU $= 0.5$ on THUMOS-14, and average mAP $37.01\%$ on ActivityNet-v1.3, establishing a new state-of-the-art. We hope that future work in this direction can explore extending the $\mathrm{Re}^2$ method to other memory-bottlenecked tasks such as dense video captioning, movie summarization etc. + +Acknowledgments. 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Video classification with channel-separated convolutional networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 2 +[62] Du Tran, Heng Wang, Lorenzo Torresani, Jamie Ray, Yann LeCun, and Manohar Paluri. A closer look at spatiotemporal convolutions for action recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2018. 3 +[63] Chenhao Wang, Hongxiang Cai, Yuxin Zou, and Yichao Xiong. RGB stream is enough for temporal action detection. arXiv preprint arXiv:2107.04362, 2021. 3, 7, 8 +[64] Chao-Yuan Wu, Christoph Feichtenhofer, Haoqi Fan, Kaiming He, Philipp Krahenbuhl, and Ross Girshick. Long-term feature banks for detailed video understanding. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 2 +[65] Saining Xie, Chen Sun, Jonathan Huang, Zhuowen Tu, and Kevin Murphy. Rethinking spatiotemporal feature learning for video understanding. In Proceedings of the European Conference on Computer Vision (ECCV), 2017. 2 +[66] Huijuan Xu, Abir Das, and Kate Saenko. R-C3D: Region convolutional 3D network for temporal activity detection. In + +Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017. 3, 8 +[67] Mengmeng Xu, Juan-Manuel Pérez-Rúa, Victor Escorcia, Brais Martinez, Xiatian Zhu, Li Zhang, Bernard Ghanem, and Tao Xiang. Boundary-sensitive pre-training for temporal localization in videos. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 1 +[68] Mengmeng Xu, Juan Manuel Perez Rua, Xiatian Zhu, Bernard Ghanem, and Brais Martinez. Low-fidelity video encoder optimization for temporal action localization. Advances in Neural Information Processing Systems (NeurIPS), 34, 2021. 3 +[69] Mengmeng Xu, Chen Zhao, David S Rojas, Ali Thabet, and Bernard Ghanem. G-tad: Sub-graph localization for temporal action detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 1, 3, 8 +[70] Shen Yan, Xuehan Xiong, Anurag Arnab, Zhichao Lu, Mi Zhang, Chen Sun, and Cordelia Schmid. Multiview transformers for video recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 3 +[71] Chenlin Zhang, Jianxin Wu, and Yin Li. ActionFormer: Localizing moments of actions with transformers. In Proceedings of the European Conference on Computer Vision (ECCV), 2022. 1, 3, 6, 8 +[72] Chen Zhao, Merey Ramazanova, Mengmeng Xu, and Bernard Ghanem. SegTAD: Precise temporal action detection via semantic segmentation. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, 2023. 1, 3 +[73] Chen Zhao, Ali K Thabet, and Bernard Ghanem. Video self-stitching graph network for temporal action localization. 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In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 2 \ No newline at end of file diff --git a/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/images.zip b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6d6398a25c5e1f68fb4b24d42e701aa065cf6057 --- /dev/null +++ b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:945326eeb17f2cd3e1234876d115f00aaaaa27baae095d7ba03ee15054b8c9e1 +size 423439 diff --git a/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/layout.json b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..af8162754b19e47282d01bd8483a73e9e90f6110 --- /dev/null +++ b/2023/Re2TAL_ Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization/layout.json @@ -0,0 +1,9788 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 137, + 102, + 457, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 102, + 457, + 140 + ], + "spans": [ + { + "bbox": [ + 137, + 102, + 457, + 140 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^{2}\\mathbf{TAL}" + }, + { + "bbox": [ + 137, + 102, + 457, + 140 + ], + "type": "text", + "content": ": Rewiring Pretrained Video Backbones for Reversible Temporal Action Localization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "spans": [ + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": "Chen Zhao" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": " Shuming Liu" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": " Karttikeya Mangalam" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": " Bernard Ghanem" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": "King Abdullah University of Science and Technology (KAUST), Saudi Arabia " + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 53, + 160, + 541, + 204 + ], + "type": "text", + "content": "UC Berkeley, US {chen.zhao, shuming.liu, bernard.ghanem}@kaust.edu.sa mangalam@berkeley.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "text", + "content": "Temporal action localization (TAL) requires long-form reasoning to predict actions of various durations and complex content. Given limited GPU memory, training TAL end to end (i.e., from videos to predictions) on long videos is a significant challenge. Most methods can only train on pre-extracted features without optimizing them for the localization problem, consequently limiting localization performance. In this work, to extend the potential in TAL networks, we propose a novel end-to-end method " + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "inline_equation", + "content": "Re^{2}TAL" + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "text", + "content": ", which rewrites pretrained video backbones for reversible TAL. " + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "inline_equation", + "content": "Re^{2}TAL" + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "text", + "content": " builds a backbone with reversible modules, where the input can be recovered from the output such that the bulky intermediate activations can be cleared from memory during training. Instead of designing one single type of reversible module, we propose a network rewiring mechanism, to transform any module with a residual connection to a reversible module without changing any parameters. This provides two benefits: (1) a large variety of reversible networks are easily obtained from existing and even future model designs, and (2) the reversible models require much less training effort as they reuse the pre-trained parameters of their original non-reversible versions. " + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "inline_equation", + "content": "Re^{2}TAL" + }, + { + "bbox": [ + 46, + 258, + 290, + 582 + ], + "type": "text", + "content": ", only using the RGB modality, reaches 37.01% average mAP on ActivityNet-v1.3, a new state-of-the-art record, and mAP 64.9% at tIoU=0.5 on THUMOS-14, outperforming all other RGB-only methods. Code is available at https://github.com/coolbay/Re2TAL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 608, + 128, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 608, + 128, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 608, + 128, + 620 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Temporal Action Localization (TAL) [36,53,73] is a fundamental problem of practical importance in video understanding. It aims to bound semantic actions within start and end timestamps. Localizing such video segments is very useful for a variety of tasks such as video-language grounding [23, 56], moment retrieval [9, 21], video captioning [30, 50]. Since video actions have a large variety of" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 232, + 539, + 353 + ], + "blocks": [ + { + "bbox": [ + 317, + 232, + 539, + 353 + ], + "lines": [ + { + "bbox": [ + 317, + 232, + 539, + 353 + ], + "spans": [ + { + "bbox": [ + 317, + 232, + 539, + 353 + ], + "type": "image", + "image_path": "34a4f3714da94bd724e9a05b4173b243067eb034d7f967811f9b5f1e4bc9ef7f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 357, + 547, + 413 + ], + "lines": [ + { + "bbox": [ + 304, + 357, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 547, + 413 + ], + "type": "text", + "content": "Figure 1. Illustration of TAL network activations in training. Top: non-reversible network stores activations of all layers in memory. Bottom: reversible network only needs to store the activations of inter-stage downsampling layers. Backbone activations dominate memory occupation, compared to Localizer." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 422, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 532 + ], + "type": "text", + "content": "temporal durations and content, to produce high-fidelity localization, TAL approaches need to learn from a long temporal scope of the video, which contains a large number of frames. To accommodate all these frames along with their network activations in GPU memory is extremely challenging, given the current GPU memory size (e.g. the commodity GPU GTX1080Ti only has 11GB). Often, it is impossible to train one video sequence on a GPU without substantially downgrading the video spatial/temporal resolutions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "content": "To circumvent the GPU-memory bottleneck, most TAL methods deal with videos in two isolated steps (e.g. [4, 67, 69, 71-73]). First is a snippet-level feature extraction step, which simply extracts snippet representations using a pretrained video network (backbone) in inference mode. The backbone is usually a large neural network trained for an auxiliary task on a large dataset of trimmed video clips (e.g., action recognition on Kinetics-400 [28]). The second step trains a localizer on the pre-extracted features. In this way, only the activations of the TAL head need to be stored in memory, which is tiny compared to those of the backbone (see the illustration of the activation contrast between backbone and localizer in Fig. 1). However, this two-step strategy comes at a steep price. The pre-extracted features can suffer from domain shift from the auxiliary pre-training" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10637" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "task/data to TAL, and do not necessarily align with the representation needs of TAL. This is because they cannot be finetuned and must be used as-is in their misaligned state for TAL. A better alternative is to jointly train the backbone and localizer end to end. But as mentioned earlier, the enormous memory footprint of video activations in the backbone makes it extremely challenging. Is there a way for end-to-end training without compromising data dimensionality?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 288, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 288, + 337 + ], + "type": "text", + "content": "Reversible networks [20, 25, 31, 48] provide an elegant solution to drastically reduce the feature activation memory during training. Their input can be recovered from the output via a reverse computation. Therefore, the intermediate activation maps, which are used for back propagation, do not need to be cached during the forward pass (as illustrated in Fig. 1). This offers a promising approach to enable memory-efficient end-to-end TAL training, and various reversible architectures have been proposed, such as RevNet [20], and RevViT [48]. However, these works design a specific reversible architecture and train for a particular dataset. Due to their new architecture, they also need to train the networks from scratch, requiring a significant amount of compute resources." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 339, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 434 + ], + "type": "text", + "content": "Conversely, it would be beneficial to be able to convert existing non-reversible video backbones to reversible ones, which would (1) avail a large variety of architectures and (2) allow us to reuse the large compute resources that had already been invested in training the non-reversible video backbones. Since pre-trained video backbones are a crucial part of TAL, the ability to convert off-the-shelf backbones to reversible ones is a key to unleash their power in this task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 604 + ], + "type": "text", + "content": "In this work, for end-to-end TAL, we propose a principled approach to Rewire the architectural connections of a pre-trained non-reversible backbone to make it Reversible, dubbed " + }, + { + "bbox": [ + 46, + 436, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 436, + 287, + 604 + ], + "type": "text", + "content": ". Network modules with a residual connection (res-module for short), such as a Resnet block [22] or a Transformer MLP/attention layer [14], are the most popular design recently. Given any network composed of residual modules, we can apply our rewiring technique to convert it to a corresponding reversible network without introducing or removing any trainable parameters. Instead of training from scratch, our reversible network can reuse the non-reversible network's parameters and only needs a small number of epochs for finetuning to reach similar performance. We summarize our contributions as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "(1) We propose a novel approach to construct and train reversible video backbones parsimoniously by architectural rewiring from an off-the-shelf pre-trained video backbone. This not only provides a large collection of reversible candidates, but also allows reusing the large compute resources invested in pre-training these models. We apply our rewiring technique to various kinds of representative video backbones, including transformer-based Video Swin and ConvNet-based Slowfast, and demonstrate that our re" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "versible networks can reach the same performance of their non-reversible counterparts with only minimum finetuning effort (as low as 10 epochs compared to 300 epochs for training from scratch)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 121, + 545, + 302 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": "(2) We propose a novel approach for end-to-end TAL training using reversible video networks. Without sacrificing spatial/temporal resolutions or network capability, our proposed approach dramatically reduces GPU memory usage, thus enabling end-to-end training on one 11GB GPU. We demonstrate on different localizers and different backbone architectures that we significantly boost TAL performance with our end-to-end training compared to traditional feature-based approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "content": "(3) With our proposed " + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "content": ", we use recent localizers in the literature to achieve a new state-of-the-art performance, " + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "inline_equation", + "content": "37.01\\%" + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "content": " average mAP on ActivityNet-v1.3. We also reach the highest mAP among all methods that only use the RGB modality on THUMOS-14, " + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "inline_equation", + "content": "64.9\\%" + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "content": " at tIoU " + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "inline_equation", + "content": "= 0.5" + }, + { + "bbox": [ + 304, + 230, + 545, + 302 + ], + "type": "text", + "content": ", outperforming concurrent work TALLFormer [10]." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 337, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 545, + 589 + ], + "type": "text", + "content": "Reversible Networks are a family of neural models based on the reversible real-valued non-volume preserving (real NVP) transformation introduced in [12, 13]. The transformation has been originally applied widely for image generation using generative flows [24, 29], and later used for various applications, such as compression [38], denoising [43], and steganography recovery [49]. Furthermore, it has also been repurposed for memory-efficient neural network training for a variety of architectures such as ConvNets [20, 25], Masked ConvNet [57], RNNs [47], Graph Networks [31] and more recently, Vision Transformers [48]. However, each of these methods only focuses on one or several specific architectures, and trains their newly proposed reversible architectures from scratch, thereby requiring large compute resources. In this work, we propose a rewiring scheme to adapt off-the-shelf models to reversible architectures which only utilize a small amount of compute for finetuning. This allows democratizing the reach of reversible architecture to arbitrary models and dataset settings by leveraging the architecture design effort and computational cost already spent in vanilla off-the-shelf models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Video Recognition Backbones. ConvNets have had a long and illustrious history of improving video understanding performance [7, 16-19, 26, 33, 52, 55, 61, 64, 65, 74]. Among those, Slowfast [17], which uses a slow pathway and a fast pathway to capture spatial semantics and temporal motion respectively, has been widely adopted for various tasks such as action detection [17], untrimmed video classification [44] and moment/natural language retrieval [21] for its high efficiency and efficacy. Recently, video transformers have ushered in a new life in the field of video repre" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10638" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "sensation learning. Leveraging long-term temporal connection via the attention mechanism, transformers have quickly gain popularity as the backbone of choice for several video recognition workloads [3, 5, 15, 32, 45, 70]. Among those, Video Swin Transformer [45] introduces an inductive bias of locality to video transformers, leading to an outstanding speed-accuracy trade-off. However, most of the models are vanilla non-reversible architectures. In this work, we unleash the potential of reversible architectures for these models such that the good properties of reversible models, e.g. memory efficiency, can be infused into them. In particular, we show that the pretrained Video Swin Transformer [45] and SlowFast [17] models can be rewired to be reversible, and finetuned cheaply to improve temporal action localization performance with end-to-end training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "text", + "content": "Temporal Action Localization (TAL). Due to the conflict between large video data and the GPU memory limit, most TAL methods using deep networks are two-step methods [4, 8, 34, 36, 37, 41, 46, 51, 54, 69, 71-73]. For example, using pre-extracted features, G-TAD [69] and VSGN [73] utilize graph convolutions to model temporal relations between snippets, and ActionFormer [71] leverages transformers to capture long-range context. To mitigate the performance gap between the two-step mechanism and real end-to-end training, some methods explore post-pretraining to enhance the video feature representations for TAL [2, 66, 68]. In the meanwhile, researchers also attempt to perform real end-to-end training by reducing network/data complexity [10, 35, 39, 40, 42, 63, 66]. R-C3D [66] is the end-to-end pioneer, but it uses a shallow network C3D [60], thus restricting the performance. PBRNet [39] and ASDF [35] downscale the frame resolution to " + }, + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "inline_equation", + "content": "96 \\times 96" + }, + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "text", + "content": ". DaoTAD [63] makes RGB-only enough by using end-to-end training with various data augmentations. TALLFormer [10] proposes to use a feature bank strategy and only updates a portion of features during end-to-end training. Compared to these approaches, our method doesn't sacrifice any data dimensionality or data samples in training, and it supports very deep networks. We significantly reduce memory consumption while preserving the full data fidelity. Moreover, our work is complementary to these methods, and can also be used jointly to further reduce memory cost." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 590, + 285, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 285, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 285, + 604 + ], + "type": "text", + "content": "3. Method: " + }, + { + "bbox": [ + 47, + 590, + 285, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^2" + }, + { + "bbox": [ + 47, + 590, + 285, + 604 + ], + "type": "text", + "content": " Temporal Action Localization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 235, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 235, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 235, + 621 + ], + "type": "text", + "content": "3.1. TAL Formulation and Architecture" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": "Temporal action localization (TAL) predicts the timestamps of actions from a video sequence, which is formulated as follows. Given a video sequence " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " frames " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{I_t\\in \\mathbb{R}^{3\\times H\\times W}\\}_{t = 1}^T" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": ", TAL predicts a set " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " of actions " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Phi = \\{\\phi_m = (t_{m,s},t_{m,e},c_m,s_m)\\}_{m = 1}^M" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_{m,s}" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_{m,e}" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " are action start and end time respectively, " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "c_{m}" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " is action label, and " + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 47, + 628, + 287, + 714 + ], + "type": "text", + "content": " is prediction confidence. To achieve this, the following" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 73, + 400, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 73, + 400, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 73, + 400, + 84 + ], + "type": "text", + "content": "two steps are required." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "text", + "content": "In the first step, the videos " + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "text", + "content": " are encoded as " + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "text", + "content": " features vectors " + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_n\\in \\mathbb{R}^C\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 85, + 545, + 192 + ], + "type": "text", + "content": " via a backbone. This backbone aggregates spatial information within video frames, as well as temporal information across frames. It is usually designed for an auxiliary task such as action recognition. Popular backbones can be categorized into Resnet-based architectures, such as I3D [7], R2+1D [62], SlowFast [17], and Transformer based architectures, such as ViViT [3], Video Swin Transformers [45]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "content": "In the second step, a localizer, uses a 'neck' to further aggregate the video features " + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "content": " in the temporal domain, and a 'head', to make predictions of action boundaries, i.e., start and end timestamps " + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "inline_equation", + "content": "(t_{m,s}, t_{m,e})" + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "content": " and categories. The neck contains layers of networks, e.g., 1D convolutional networks in BMN [36], Graph networks in G-TAD [69] and VSGN [73], and Transformers in RTD-Net [59] and Action-Former [71]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 289, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 361 + ], + "type": "text", + "content": "As mentioned in Sec. 1, an optimal way to train the entire TAL network is to jointly train the backbone and the localizer end to end. However, it is substantially challenging to fit all activation maps of the long video sequence into limited GPU memory. In the following sections, we provide end-to-end TAL solution " + }, + { + "bbox": [ + 304, + 289, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 304, + 289, + 545, + 361 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 371, + 494, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 494, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 494, + 384 + ], + "type": "text", + "content": "3.2. Rewire for Reversibility, and Reuse" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": "Let's first analyze what in the GPU memory precludes end-to-end training of TAL. As mentioned in Sec. 1, the activation maps in the backbone are the major occupant in the memory. Concretely, given a batch of a video sequence of " + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": " frames, each with resolution " + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "inline_equation", + "content": "S \\times S" + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": ", to train them on a backbone of " + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": " layers each with " + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": " channels, the training memory complexity is " + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(LCTS^2)" + }, + { + "bbox": [ + 304, + 390, + 545, + 521 + ], + "type": "text", + "content": ". Downgrading any data dimensionality or the backbone capacity can reduce the memory complexity, but at the same time, may harm the prediction accuracy. We aim to reduce memory consumption without sacrificing the data dimensionality or the model capacity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Actually, the intermediate activations are stored in memory during training for the purpose of gradient computation in back propagation. If we can reconstruct them during back propagation, then there is no need for their memory occupation. Reversible networks [20, 25, 48, 49] is a superb solution for reconstructing the input from output, and various reversible architectures have been proposed recently (e.g., Revnet [20], RevViT [48]). However, the performance of TAL heavily depends on the backbone that is pre-trained on one or even multiple large-scale datasets. For example, the popular I3D [7] backbone is trained on Kinetics-400 [28] with its parameters initialized from Resnet [22] trained on ImageNet [11]. If we make up a new reversible network for TAL as is the case with previous reversible networks (e.g., [20, 25]), we need to go through all the expensive and time-consuming training stages to reach an equivalently" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10639" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 68, + 277, + 205 + ], + "blocks": [ + { + "bbox": [ + 58, + 68, + 277, + 205 + ], + "lines": [ + { + "bbox": [ + 58, + 68, + 277, + 205 + ], + "spans": [ + { + "bbox": [ + 58, + 68, + 277, + 205 + ], + "type": "image", + "image_path": "08886fa3a5b55aa5208253784c4d6b40e70b54821ba46b08a1daed351d3ae340.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 287, + 280 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed rewiring process. In this example, 3 consecutive residual modules in the same stage are rewired into 3 reversible modules. After rewiring, each residual connection skips one more " + }, + { + "bbox": [ + 46, + 209, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 209, + 287, + 280 + ], + "type": "text", + "content": " block ahead. Note that beyond this example, our rewiring can process any number of such modules. good initialization for TAL." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 281, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 437 + ], + "type": "text", + "content": "Instead of proposing a new reversible architecture, we propose a principled approach to rewire a pre-trained nonreversible backbone to make it reversible. Given any module with a residual connection, we can convert it into a reversible module while preserving the same set of parameters. This technique has two advantages. First, we obtain a large and growing collection of various reversible architectures out of the box, by rewiring the existing networks and even future networks of higher performance. Second, we can reuse their pre-trained weights to initialize our reversible networks, eliminating the tremendous effort to train from scratch. In the following, we will describe our rewiring for reversibility " + }, + { + "bbox": [ + 46, + 281, + 287, + 437 + ], + "type": "inline_equation", + "content": "(\\mathbf{Re}^2)" + }, + { + "bbox": [ + 46, + 281, + 287, + 437 + ], + "type": "text", + "content": " technique in detail." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": "Rewiring. Residual modules, i.e., modules with a residual connection, are the most commonly adopted design in concurrent neural network architectures, such as Resnet [22] and Transformers [14]. Given any residual modules, we can rewire them into reversible modules. Fig. 2 illustrates this process with an example of 3 consecutive residual modules that are in the same stage, i.e., there are no downsampling operations in between. Each of the original residual modules contains a block " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " (blue boxes) where " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "i = 1,2,3,\\ldots" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " and a residual connection (orange arrow). The blocks " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " have the same input and output dimensions, and can contain any computations. For example, in Resnet, the building block consisting of convolution, batch normalization, and ReLU can be one " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " block (e.g. Fig. 3 (a)). In Transformers, if " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " represents an attention layer, then " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{i + 1}" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " is an MLP layer (e.g. Fig. 3 (b) and (c)). The residual connection in each module only skips one " + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 652 + ], + "type": "text", + "content": " block in the same module." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "To rewire, we simply let the residual connection skip the next block " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{i+1}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " as well as the current one " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ". To be more specific, we keep the starting point of each residual connection, but make it end after two blocks, as shown in the second row of Fig. 2. As a result, two consecutive residual" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 313, + 72, + 385, + 162 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 385, + 162 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 385, + 162 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 385, + 162 + ], + "type": "image", + "image_path": "19bd660c771f4ab8b073992c230f1110bcf4a6d0dbb598635ef055ac50e3d8e0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 168, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 191 + ], + "type": "text", + "content": "Figure 3. Examples of " + }, + { + "bbox": [ + 304, + 168, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 168, + 545, + 191 + ], + "type": "text", + "content": " blocks. (a) A reset basic block. (b) A transformer MLP layer. (c) A transformer attention layer." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 389, + 72, + 462, + 162 + ], + "blocks": [ + { + "bbox": [ + 389, + 72, + 462, + 162 + ], + "lines": [ + { + "bbox": [ + 389, + 72, + 462, + 162 + ], + "spans": [ + { + "bbox": [ + 389, + 72, + 462, + 162 + ], + "type": "image", + "image_path": "0c84f3bfca40427aae281fa4395eeb2a404aed586c33e411a933a8e5abcb0c90.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 468, + 72, + 539, + 163 + ], + "blocks": [ + { + "bbox": [ + 468, + 72, + 539, + 163 + ], + "lines": [ + { + "bbox": [ + 468, + 72, + 539, + 163 + ], + "spans": [ + { + "bbox": [ + 468, + 72, + 539, + 163 + ], + "type": "image", + "image_path": "da1927aeb3639bb83813d9ed80bd8bc09cbf6bf244b2d1af5012e39f5e02ae87.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 195, + 545, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 231 + ], + "type": "text", + "content": "connections become overlapped, and there are always two pathways of activations (gray and green in Fig. 2) throughout the modules, as shown in the third row of Fig. 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": "To prepare a second pathway of input to the first module, we duplicate the input " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "y_0" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": ". To combine the results " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "x_3" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "y_3" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": " of the two pathways, we simply average them at the end of the modules. This design guarantees that the dimensions of the input and output of every block " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": " are identical before and after the rewiring. Therefore, the structure of " + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 304, + 231, + 546, + 315 + ], + "type": "text", + "content": " stays exactly the same." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": "Reversibility. In the following, we mathematically formulate the rewired modules to show their reversibility. To be concise, we use the first two modules as an example. Given the input activations " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "y_0" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": ", and the blocks " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_1" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_2" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": ", the output of the two blocks are " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "x_1, y_1" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "inline_equation", + "content": "x_2, y_2" + }, + { + "bbox": [ + 304, + 315, + 545, + 387 + ], + "type": "text", + "content": " respectively, computed as follows" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 392, + 545, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 392, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 315, + 392, + 545, + 420 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} y _ {1} = x _ {0} \\\\ x _ {1} = \\mathcal {F} _ {1} \\left(x _ {0}\\right) + y _ {0}, \\end{array} \\right. \\Rightarrow \\left\\{ \\begin{array}{l} y _ {2} = x _ {1} \\\\ x _ {2} = \\mathcal {F} _ {2} \\left(x _ {1}\\right) + y _ {1}. \\end{array} \\right. \\tag {1}", + "image_path": "16be78bd7b2de5b264076b0776e9090897f75f524e6d7fde87e0a19f4cca2806.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "content": "The above equations are reversible, which means that we can recover the input " + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "inline_equation", + "content": "x_{1}, y_{1}" + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "inline_equation", + "content": "x_{2}, y_{2}" + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "content": ", and then " + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "inline_equation", + "content": "x_{0}, y_{0}" + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "inline_equation", + "content": "x_{1}, y_{1}" + }, + { + "bbox": [ + 304, + 425, + 545, + 473 + ], + "type": "text", + "content": ". The reverse computation is formulated in the following equation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 478, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 478, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 315, + 478, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} x _ {0} = y _ {1} \\\\ y _ {0} = x _ {1} - \\mathcal {F} _ {1} (x _ {0}), \\end{array} \\right. \\Leftarrow \\left\\{ \\begin{array}{l} x _ {1} = y _ {2} \\\\ y _ {1} = x _ {2} - \\mathcal {F} _ {2} (x _ {1}). \\end{array} \\right. \\tag {2}", + "image_path": "b0878437863cacba79c34b60a33697a55478b713f5f2a019d47e5675b5fa5e9a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": "A network with more modules follows the same strategy as in Eq. 1 and Eq. 2. When we stack multiple consecutive reversible modules as one network (as the example in Fig. 2), the entire network is reversible. In this case, we can start from the last module and sequentially reconstruct the input of each module with Eq. 2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "content": "Reuse. As the structure and parameter dimensions of the " + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "content": " block in our reversible modules after rewiring stay exactly the same as the " + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "content": " block in the corresponding residual module, we can directly reuse the pre-trained parameters in the residual modules to initialize our reversible modules." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "content": "Our rewiring mechanism provides a large collection of reversible candidates. We can easily convert a network into a reversible one without designing a new architecture from scratch. Not only can we use the existing architectures, but we can also benefit from future even better models to obtain better reversible models. The reuse strategy" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10640" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 72, + 282, + 202 + ], + "blocks": [ + { + "bbox": [ + 97, + 72, + 282, + 202 + ], + "lines": [ + { + "bbox": [ + 97, + 72, + 282, + 202 + ], + "spans": [ + { + "bbox": [ + 97, + 72, + 282, + 202 + ], + "type": "image", + "image_path": "d07afeb6b10c6b01876c890734973346a998a81e4f7bf9df2416ff21d3da7537.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 202, + 194, + 209 + ], + "lines": [ + { + "bbox": [ + 184, + 202, + 194, + 209 + ], + "spans": [ + { + "bbox": [ + 184, + 202, + 194, + 209 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 311, + 72, + 499, + 203 + ], + "blocks": [ + { + "bbox": [ + 311, + 72, + 499, + 203 + ], + "lines": [ + { + "bbox": [ + 311, + 72, + 499, + 203 + ], + "spans": [ + { + "bbox": [ + 311, + 72, + 499, + 203 + ], + "type": "image", + "image_path": "da45bad198941ef2bdaabb6d404572956ae6abcc7a39182e355c866f258a4350.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 394, + 202, + 404, + 210 + ], + "lines": [ + { + "bbox": [ + 394, + 202, + 404, + 210 + ], + "spans": [ + { + "bbox": [ + 394, + 202, + 404, + 210 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 213, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 545, + 236 + ], + "type": "text", + "content": "Figure 4. Comparison of different input arrangements for a TAL network. (a) Snippets input: the backbone processes many video snippets (a short clip of frames), often overlapped. (b) Frames input: the backbone takes all the frames in the video as one single input." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 288, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 312 + ], + "type": "text", + "content": "allows taking advantage of the large computing resources invested in those pre-trained models. We don't need to retrain the reversible network from scratch. Instead, we can train the reversible backbone with minimum effort (as low as 10 epochs compared to 300 epochs from scratch) while reaching the same performance as its residual counterpart." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 319, + 261, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 261, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 261, + 333 + ], + "type": "text", + "content": "3.3. Reversible Temporal Action Localization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 338, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 386 + ], + "type": "text", + "content": "Considering that the backbone is the heaviest part in the TAL network in terms of memory usage, as illustrated in Fig. 1, we target the backbone and apply our " + }, + { + "bbox": [ + 46, + 338, + 287, + 386 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2" + }, + { + "bbox": [ + 46, + 338, + 287, + 386 + ], + "type": "text", + "content": " technique described above to rewire it to obtain a reversible network." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 387, + 288, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 288, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 288, + 541 + ], + "type": "text", + "content": "A backbone network, e.g., Video Swin Transformer [45], Slowfast [17], is usually comprised of several stages. Within each stage, the activation sizes stay the same. We convert all the modules into reversible ones following the rewiring method proposed in Sec. 3.2. During training, we can clear all the input and intermediate activations from GPU memory, and only store the final output of the stage during the forward pass (as shown in Fig. 1). In the back propagation, we re-compute all the activations based on the reverse process as in Eq. 2. As [48] pointed out, this re-computation doesn't incur too much more computational time since we can parallelize the process to make use of the spare computation of GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 543, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 615 + ], + "type": "text", + "content": "Across stages, there are downsampling layers, which reduce the activation sizes. We leave the downsampling layers as they are and cache the activations inside to enable back propagation. Considering that there are only several downsampling layers, the memory occupation of these activations is acceptable." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 623, + 194, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 194, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 194, + 635 + ], + "type": "text", + "content": "3.4. End-to-End TAL Training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "For end-to-end training with our " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": ", we just need to do the following: find a well-performing video backbone, rewire it into a reversible one, load the parameters from the original backbone to the reversible one and finetune for several epochs on the pretraining task, and train with a localizer end to end. This reversible TAL network is significantly" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "type": "text", + "content": "more efficient in memory usage, enabling end-to-end training a GPU of limited memory (e.g., as small as a 11GB commodity GPU). But is it a wise choice to directly adopt the training strategies from the feature-based methods?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 288, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 347 + ], + "type": "text", + "content": "Input frame arrangement. Since most TAL methods are designed and experimented with the pre-extracted, they have predisposed to particular design choices, such as extracting features with overlapped snippets to arrange the input frames. But we find it not ideal for end-to-end training." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "content": "Fig. 4 (a) illustrates the framework commonly used in two-step (or feature-based) methods. To extract " + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "content": " feature vectors as the localizer input, " + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "content": " snippets need to be processed by the backbone independently. Each snippet contains a sequence of " + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "content": " frames. The snippets are usually overlapped with one another to maintain temporal consistency, which causes duplicate computation and extra memory occupation. Consequently, at least " + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "inline_equation", + "content": "ND" + }, + { + "bbox": [ + 304, + 347, + 545, + 455 + ], + "type": "text", + "content": " frames need to go through the backbone." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": "This framework works fine with the two-step method, since feature extraction is one-off effort and all the snippets can be processed sequentially to circumvent the memory issue. However, end-to-end training cannot bear the extra memory cost. Therefore, we treat the entire video sequence as one single input instead, and the backbone aggregates all frames at one time, as shown in Fig. 4 (b). This mechanism not only reduces the cost incurred by the duplicate computation, but also has the advantage of aggregating long-term temporal information, in contrast to being restricted within the snippet as with the snippet mechanism. In this way, to obtain " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": " feature vectors, we just need to process " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "Ns" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": " frames, where " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": " is the overall strides in the backbone (e.g. " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "s = 2" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": " in Video Swin Transformers). Considering that " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": " is usually much smaller than " + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 455, + 545, + 647 + ], + "type": "text", + "content": ", the frame-input mechanism is more efficient in memory and computation cost." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Datasets and evaluation metrics. We present our experimental results on two representative datasets ActivityNet-v1.3 (ActivityNet for short) [6] and THUMOS-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10641" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 97, + 287, + 149 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 1. Advantage of end-to-end training. End-to-end training leads to significant mAP (\\%) boost for TAL with either backbone." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 97, + 287, + 149 + ], + "lines": [ + { + "bbox": [ + 48, + 97, + 287, + 149 + ], + "spans": [ + { + "bbox": [ + 48, + 97, + 287, + 149 + ], + "type": "table", + "html": "
Re2Vswin-tinyRe2Slowfast-101
Method0.50.750.95Avg.0.50.750.95Avg.
Features51.1835.099.7234.4751.9836.009.4735.24
End2End53.2437.2310.4936.3853.6337.5310.6736.82
", + "image_path": "1354a507be8e9b48d10a8e32b9cc94a62ea287a3aa8c985f66f0ab2652455477.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "text", + "content": "14 (THUMOS for short) [27]. ActivityNet is a challenging large-scale dataset, with 19994 temporally annotated untrimmed videos in 200 action categories, which are split into training, validation and testing sets by the ratio of 2:1:1. THUMOS contains 413 temporally annotated untrimmed videos with 20 action categories, in which 200 videos are for training and 213 videos for validation1. For both datasets, we use mean Average Precision (mAP) at different tIoU thresholds as the evaluation metric. On ActivityNet, we choose 10 values in the range " + }, + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "inline_equation", + "content": "[0.5, 0.95]" + }, + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "text", + "content": " with a step size 0.05 as tIoU thresholds; on THUMOS, we use tIoU thresholds " + }, + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\{0.3, 0.4, 0.5, 0.6, 0.7\\}" + }, + { + "bbox": [ + 46, + 159, + 287, + 316 + ], + "type": "text", + "content": "; following the official evaluation practice." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 317, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 437 + ], + "type": "text", + "content": "Backbones and localizers of " + }, + { + "bbox": [ + 46, + 317, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^2\\mathbf{TAL}" + }, + { + "bbox": [ + 46, + 317, + 287, + 437 + ], + "type": "text", + "content": ". For backbones, we choose two representative models from the Resnet and Transformer families respectively for experimental demonstration: Video Swin Transformers (Vswin for short) [45] and Slowfast [17], both well known for their powerful video representation and memory efficiency. For Vswin, we use three variants: tiny, small, and base; for Slowfast, we use 50, 101, and 152. For localizers, we experiment with the recent temporal action localization (TAL) methods VSGN [73] and ActionFormer [71]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": "Implementation Details of " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^2\\mathbf{TAL}" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": ". We initialize all our reversible backbones with their non-reversible counterparts, and finetune for up to 30 epochs on Kinetics-400 with Cosine Annealing learning rate policy and Adamw (for Vswin) and SGD (for Slowfast) optimizers. Actually, in our experiments, we find 10 epochs of finetuning already reaches similarly good performance. With the pre-trained reversible backbone, we train TAL on a single GPU, A100 with batchsize " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "= 1" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": " for Vswin and V100 with batchsize " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "= 2" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": " for Slowfast. This is only possible due to the massive GPU memory savings from the reversible backbones. For the hyper-parameters, we follow the original training recipe of VSGN [73] and ActionFormer [71] for the learning rates and epochs in the localizers. We set the learning rates of the Vswin backbones 1 magnitude lower than the localizer, and those of the Slowfast backbones 2 magnitude lower. The spatial resolution is " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": ". For ActivityNet, the number of frame input is " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "T = 512" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": ", the number of feature vectors is " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "N = 256" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": "; and for THUMOS, the number of frame input is " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "T = 1024" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": ", the number of features is " + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "inline_equation", + "content": "N = 512" + }, + { + "bbox": [ + 46, + 439, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 313, + 69, + 539, + 169 + ], + "blocks": [ + { + "bbox": [ + 313, + 69, + 539, + 169 + ], + "lines": [ + { + "bbox": [ + 313, + 69, + 539, + 169 + ], + "spans": [ + { + "bbox": [ + 313, + 69, + 539, + 169 + ], + "type": "image", + "image_path": "a80a661632d5f88e945a4db0583816943763b6538856c662cb01f02f4f843ad2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 172, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 305, + 172, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 305, + 172, + 545, + 195 + ], + "type": "text", + "content": "Figure 5. Performance improvement of end-to-end TAL upon feature-based in terms of action temporal duration." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 209, + 432, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 432, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 432, + 220 + ], + "type": "text", + "content": "4.1. Ablation and Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 229, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 301 + ], + "type": "text", + "content": "In this section, we provide ablation study on ActivityNet and performance analysis to answer the following questions. (1) Why do we need end-to-end training? (2) How effective and efficient is our " + }, + { + "bbox": [ + 304, + 229, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 304, + 229, + 545, + 301 + ], + "type": "text", + "content": "? (3) What is the benefit of the proposed rewiring technique? (4) Which reversible backbone and localizer provides the best performance?" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 329, + 449, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 449, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 449, + 341 + ], + "type": "text", + "content": "4.1.1 Why end-to-end training?" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "text", + "content": "With end-to-end training, we are able to optimize the features to adapt to the TAL task and dataset such that we can achieve higher performance than the feature-based method. To verify this, we compare end-to-end training to the feature-based training on our reversible TAL. In Tab. 1, we demonstrate the comparison on two types of backbones: " + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2" + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "text", + "content": " Vswin-tiny and " + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2" + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "text", + "content": " Slowfast-101 with VSGN [73] on ActivityNet. It shows that for both backbones, using end-to-end training leads to significant performance boost, gaining almost " + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 352, + 545, + 471 + ], + "type": "text", + "content": " mAP." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "To further diagnose what kinds of actions end-to-end training improves the most, in Fig. 5 (a), we plot the accuracy gains brought by end-to-end training for five different groups of actions based on their temporal durations (in seconds): XS: (0s, 30s], S: (30s, 60s], M: (60s, 120s], L: (120s, 180s], and XL: " + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "inline_equation", + "content": ">180" + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "s (as suggested in [1]). We can see that the accuracy gains for different action durations are closely related to the numbers of samples in each duration category (the pie chart): short actions (XS and X) with many samples are obviously improved, though long actions (XL) with fewer samples is slightly sacrificed. Actually, short actions are a fundamental challenge in TAL [73]. End-to-end training provides an effective solution by enabling the backbone to learn feature representations to the benefit of short actions — the categories with more samples, thus preventing them fusing into the background. Short actions occupy the majority in the dataset, and their improvement leads to an overall performance boost. In Fig. 5 (b), we show that the false negative predictions are reduced by end-to-end training for all groups, more significantly for shorter ones." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "1The training and validation sets of THUMOS are temporally annotated videos from the validation and testing sets of UCF101 [58], respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10642" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 171, + 152 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 171, + 152 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 171, + 152 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 171, + 152 + ], + "type": "image", + "image_path": "647eafd7719f66f3c5cac431b6a7cefb7fb78ac42c836e1675da5e6b65081286.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": "Figure 6. " + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^{2}\\mathbf{TAL}" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": " models compared with original models at different spatial and temporal downscaling ratios. Spatial and temporal resolutions from left to right are as follows. " + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^{2}\\mathbf{TAL}" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": ": (112, 512), (224, 512); Original: (56, 512), (112, 192), (224, 192), (224, 512). The localizer VSGN [73] is used." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 72, + 287, + 152 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 287, + 152 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 287, + 152 + ], + "type": "image", + "image_path": "1bf6be083f4303f7633df6f7929aca619f6f2118a5fda752d847325c79f91a66.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 216, + 170, + 301 + ], + "blocks": [ + { + "bbox": [ + 48, + 216, + 170, + 301 + ], + "lines": [ + { + "bbox": [ + 48, + 216, + 170, + 301 + ], + "spans": [ + { + "bbox": [ + 48, + 216, + 170, + 301 + ], + "type": "image", + "image_path": "3bcfca41f9d99a92f6517aa771cb789968ee9ff11bf7d6f14f12b3e70436d189.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 306, + 287, + 383 + ], + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 383 + ], + "type": "text", + "content": "Figure 7. GPU memory consumption v.s. network sizes. The dot sizes represent the model sizes, and the y-axis is the GPU memory used for processing one video (batchsize=1). Our " + }, + { + "bbox": [ + 46, + 306, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 306, + 287, + 383 + ], + "type": "text", + "content": " almost keeps the memory constant when only the network depths increase (e.g. from Vswin-tiny to small, from Slowfast-50 to 101), whereas the original models easily go out of memory when the network becomes larger." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 173, + 216, + 287, + 301 + ], + "blocks": [ + { + "bbox": [ + 173, + 216, + 287, + 301 + ], + "lines": [ + { + "bbox": [ + 173, + 216, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 173, + 216, + 287, + 301 + ], + "type": "image", + "image_path": "5d8b89e8efed4997d084b4377ea81b63f4d8362e2c70e8496ddcdf445bde122b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 396, + 244, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 244, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 244, + 407 + ], + "type": "text", + "content": "4.1.2 How effective and efficient is " + }, + { + "bbox": [ + 47, + 396, + 244, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^2\\mathbf{TAL}" + }, + { + "bbox": [ + 47, + 396, + 244, + 407 + ], + "type": "text", + "content": "?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "text", + "content": "An alternative way to enable end-to-end training is to reduce data resolutions [39, 63]. In Fig. 6, we downscale the input videos in the spatial or temporal dimensions to adjust the memory requirements, and compare our " + }, + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "text", + "content": " models to their corresponding original models. We can see that under even smaller memory requirements, our " + }, + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 416, + 287, + 513 + ], + "type": "text", + "content": " models achieve higher performance than the original models that relies on sacrificing video resolutions to reduce memory." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "content": "To further visualize the memory efficiency of our " + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "content": " compared to their non-reversible counterparts when trained end to end, we demonstrate the GPU memory consumption of the three Vswin backbones of different depths and widths and the three Slowfast backbones of different depths in Fig. 7. For Vswin backbones, we assume a GPU memory budget of 90GB, which is the size of A100. For Slowfast backbones, we assume our GPU budget is 11GB, which is the size of the commodity GPU such as GTX1080Ti. We can see that for either case, the nonreversible network will go out of memory when the model size reaches a certain level. In contrast, our " + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "content": " almost keeps constant memory usage when only the network depth increases (from Vswin-tiny to small, from Slowfast-50 to " + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "inline_equation", + "content": "101)^2" + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "content": ". With the low memory cost, our " + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 513, + 288, + 693 + ], + "type": "text", + "content": " enables" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 106, + 544, + 148 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 103 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 103 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 103 + ], + "type": "text", + "content": "Table 2. Comparison of feature representations between the " + }, + { + "bbox": [ + 306, + 71, + 545, + 103 + ], + "type": "inline_equation", + "content": "\\mathbf{Re}^2\\mathbf{TAL}" + }, + { + "bbox": [ + 306, + 71, + 545, + 103 + ], + "type": "text", + "content": " and original models, in terms of average mAP (\\%) on the dataset ActivityNet. Vw: Vswin; Slowf: Slowfast." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 106, + 544, + 148 + ], + "lines": [ + { + "bbox": [ + 307, + 106, + 544, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 106, + 544, + 148 + ], + "type": "table", + "html": "
ModelTinySmallBaseModel50101152
Vswin34.3633.8634.47Slowfast34.6035.0434.61
Re2Vw34.4734.0434.09Re2Slowf34.9335.2434.54
", + "image_path": "3bb5839034c1e57230b73182b601f4ccd6b12ae58bbd223f3b48426a52c9eb97.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 211, + 541, + 264 + ], + "blocks": [ + { + "bbox": [ + 306, + 150, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 306, + 150, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 150, + 545, + 205 + ], + "type": "text", + "content": "Table 3. Effectiveness of rewiring and reusing pre-trained video models. Reusing pre-trained models leads to significantly better performance than training from scratch (compare Row 1 to the rest). Reusing a better pre-trained model gives even higher performance (compare Row 2 to Row 3). Pret.: pretraining." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 211, + 541, + 264 + ], + "lines": [ + { + "bbox": [ + 309, + 211, + 541, + 264 + ], + "spans": [ + { + "bbox": [ + 309, + 211, + 541, + 264 + ], + "type": "table", + "html": "
Pret. ModelPret. Dataset0.50.750.95Avg.
Vswin-baseNone44.5828.417.4028.68
Kinetics-40052.7236.738.8835.73
Kinetics-60052.4637.3710.3936.28
", + "image_path": "99c21579003b42292d3126b92c0147c6186dc95920e0e8fc7012670b1220958f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 309, + 304, + 541, + 369 + ], + "blocks": [ + { + "bbox": [ + 306, + 266, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 306, + 266, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 545, + 300 + ], + "type": "text", + "content": "Table 4. Comparison of localization performance with different backbones and localizers, in terms of average mAP (\\%) on the dataset ActivityNet." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 304, + 541, + 369 + ], + "lines": [ + { + "bbox": [ + 309, + 304, + 541, + 369 + ], + "spans": [ + { + "bbox": [ + 309, + 304, + 541, + 369 + ], + "type": "table", + "html": "
BackboneLocalizer0.50.750.95Avg.
Re2Vswin-tinyVSGN53.2437.2310.4936.38
ActionFormer54.7537.819.0336.80
Re2Slowfast-101VSGN53.6337.5310.6736.82
ActionFormer55.2537.869.0537.01
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The time to train one epoch is the following, Vswintiny (114 mins) vs. " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " swintiny (135 mins); Slowfast-50 (147 mins) vs. " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slowfast - }50" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " (158 mins)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 465, + 446, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 446, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 446, + 477 + ], + "type": "text", + "content": "4.1.3 Why rewiring and reuse?" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 484, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 603 + ], + "type": "text", + "content": "We rewire existing network architectures to make them reversible, and reuse their parameters for initialization. This way we dramatically reduce the effort of training the reversible networks, and still reach the representation capability of the original non-reversible ones. To compare the video representation capabilities of both types of networks, we use them to extract video features and train a localizer (VSGN [73] in this case) with the features. We demonstrate their performance in Tab. 2, showing that our reversible models are comparable to the original models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "content": "If there are two versions of the same non-reversible model trained in different ways and with different performance, will our " + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "content": " models benefit more from the higher-performing version? Vswin-base happens to have such two versions: one trained on Kinetics-400 and the other trained on Kinetics-600, the latter with better performance. We initialize our " + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "content": " swin-base with either ver" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "content": "2Memory increases from Vswin-small to base is due to the channel in" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "crease; memory reduction from Slowfast-101 to 152 is because the former one uses input configuration (8, 8) while the latter uses (4, 16)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10643" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 98, + 535, + 308 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 5. Compared to the state-of-the-art for temporal action localization performance on ActivityNet-v1.3 and THUMOS-14, measured by mAPs (\\%) at different IoU thresholds according to their respective official metrics. E2E: end-to-end; Mem: memory (GB)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 98, + 535, + 308 + ], + "lines": [ + { + "bbox": [ + 57, + 98, + 535, + 308 + ], + "spans": [ + { + "bbox": [ + 57, + 98, + 535, + 308 + ], + "type": "table", + "html": "
MethodBackboneE2EFlowMemActivityNet-v1.3THUMOS-14
0.50.750.95Avg.0.30.40.50.60.7
TAL-Net [8]I3DX✓-38.2318.301.3020.2253.248.542.833.820.8
BMN [36]TSNX✓-50.0734.788.2933.8556.047.438.829.720.5
G-TAD [69]TSNX✓-50.3634.609.0234.0954.547.640.230.823.4
TSI [41]TSNX✓-51.1835.026.5934.1561.052.142.633.222.4
BC-GNN [4]TSNX✓-50.5634.759.3734.2657.149.140.431.223.1
VSGN [73]TSNX✓-52.3836.018.3735.0766.760.452.441.030.4
ActionFormer [71]I3DX✓-53.5036.208.2035.6082.177.871.059.443.9
PBRNet [39]I3D✓✓-53.9634.978.9835.0158.554.651.341.829.5
AFSD [35]I3D✓✓1252.4035.306.5034.4067.362.455.543.731.1
R-C3D [66]C3D✓X-26.80---44.835.628.9--
DaoTAD [63]I3D✓X11----62.8-53.8-30.1
TALLFormer [10]VSwin-Base✓X2954.1036.207.9035.6076.0-63.2-34.5
ActionFormer [71]VSwin-TinyXX-53.8335.827.2735.1770.864.755.742.227.0
ActionFormer + Re2TALRe2VSwin-Tiny✓X2454.7537.819.0336.8077.071.562.449.736.3
ActionFormer [71]Slowfast-101XX-53.9837.008.8736.0972.766.958.646.433.1
ActionFormer + Re2TALRe2Slowfast-101✓X6.855.2537.869.0537.0177.472.664.953.739.0
", + "image_path": "3fc14bd58532a0bee2c678e006556f994557f71df0d2552c40f30629216e2a13.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 319, + 288, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 426 + ], + "type": "text", + "content": "sion, and compare their performance on TAL in Tab. 3. By using the better version, the TAL performance obviously increases. In addition, using either version as initialization is better than training from scratch. This indicates that our rewiring-reuse strategy is very important for TAL performance, and reusing a better pre-trained model will benefit TAL even further. That means if a better training strategy for an existing model comes out, we can correspondingly obtain a more accurate reversible model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 234, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 234, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 234, + 453 + ], + "type": "text", + "content": "4.1.4 Choice of Backbones and Localizers" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "content": "In Tab. 4, we demonstrate the results using the two different backbones " + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "content": " swin-tiny and " + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slow}" + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "content": " fast-101, and two different localizers VSGN [73] and ActionFormer [71] on ActivityNet. Since the ActionFormer localizer yields better performance for both " + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "content": " swin-tiny and " + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slow}" + }, + { + "bbox": [ + 46, + 460, + 287, + 555 + ], + "type": "text", + "content": " fast-101, we compare the ActionFormer results to other methods in the literature, and also apply them to the THUMOS dataset, as shown in Sec. 4.2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 563, + 211, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 211, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 211, + 577 + ], + "type": "text", + "content": "4.2. State-of-the-Art Comparisons" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": "We compare the performance of our " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " to recent state-of-the-art (SOTA) methods in the literature in Tab. 5 on ActivityNet and THUMOS. On ActivityNet, our " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " reaches a new SOTA performance: average mAP " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "37.01\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": ", outperforming all other methods by significant margins. On THUMOS, ours surpasses the concurrent work TaLLFormer [10] with mAP " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "64.9\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " at tIoU=0.5, and the highest among all methods that only use the RGB modality." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Furthermore, for an apple-to/apple comparison with the feature-based method ActionFormer, we re-ran ActionFormer using their official code with the RGB features ex" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": "tracted with the Vswin-tiny and Slowfast-101 backbones, corresponding to our " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " swin-tiny and " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slowfast - 101}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": ", respectively. We see that our " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{TAL}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " always outperforms vanilla ActionFormer under the same backbone categories (e.g. " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " swin-tiny and Vswin-tiny are in the same backbone category; " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slowfast - 101}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " and Slowfast-101 are in the same backbone category)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 437, + 384, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 384, + 450 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 384, + 450 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": "In this work, we propose a novel rewiring-to-reversibility " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "(\\mathrm{Re}^2)" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " scheme to convert off-the-shelf models into reversible models while preserving the number of trainable parameters. The procedure allows reusing the compute invested in training large models and adds only a tiny sliver of finetuning compute. We apply the procedure to video backbones such as Video Swin (Vswin) and SlowFast to obtain " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{V}" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " win and " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2\\mathrm{Slow}" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " fast backbones respectively. Further, we utilize the " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " backbones for memory-efficient end-to-end temporal action localization, reaching mAP " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "64.9\\%" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " at tIoU " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "= 0.5" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " on THUMOS-14, and average mAP " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "37.01\\%" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " on ActivityNet-v1.3, establishing a new state-of-the-art. We hope that future work in this direction can explore extending the " + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{Re}^2" + }, + { + "bbox": [ + 304, + 466, + 547, + 646 + ], + "type": "text", + "content": " method to other memory-bottlenecked tasks such as dense video captioning, movie summarization etc." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10644" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. 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(a) ReCo extends pre-trained text-to-image models (Stable Diffusion [34]) with an extra set of input position tokens (in dark blue color) that represent quantized spatial coordinates. Combining position and text tokens yields the region-controlled text input, which can specify an open-ended regional description precisely for any image region. (b) With the region-controlled text input, ReCo can better control the object count/relationship/size properties and improve the T2I semantic correctness. We empirically observe that position tokens are less likely to get overlooked than positional text words, especially when the input query is complicated or describes an unusual scene." + ], + "image_footnote": [], + "bbox": [ + 210, + 404, + 320, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0cc693adb99f8d377cf1602f4705aef56995fe3d0af7f2873a5184e2e0ba882b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 404, + 375, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77cfb08c87cc2b5dcd1c7ca33505cce7a8025dec9ea87c53d0bcf3a3902f15f4.jpg", + "image_caption": [ + "(b) Improve T2I Semantic Correctness" + ], + "image_footnote": [], + "bbox": [ + 395, + 281, + 504, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69e632407895a499851a904f077a7d1eef221bd4889aea718c661dec07e796a0.jpg", + "image_caption": [ + "Stable Diffusion", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 509, + 281, + 616, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/561401cbf8e9522c9a62112a588e83f71a46739b9d874ceedb2f2a88cb4c50bc.jpg", + "image_caption": [ + "A box contains ten donuts with varying types of glazes and toppings. {large square in the top, $<245>$ <1> $<535>$ <248>} red donut. {... ...} ... {large square in the top right, $<744>$ <18> <939> <257>} brown glazed chocolate donut", + "A chair that looks much larger than the white airplane in the background. {large square in the bottom, $<179>$ <454> <617> <957>} a chair. {medium long in the right, $<602>$ <330> <863> <416>} a white airplane." + ], + "image_footnote": [], + "bbox": [ + 395, + 404, + 504, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bf039c8697b2d0ce85944bc1bb806f3a4895fbed15d6308340d30a9c3deb9afe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 404, + 617, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d509457927530c0c24cc286e1fe6dc6274e911b6f1208183e62872469fd4d2f3.jpg", + "image_caption": [ + "Stable Diffusion", + "A boat below a traffic light with a park in the background. {large tall in the top, $<572>$ <0> <686> <314>} a traffic light with the green light on. {large square in the bottom, <298> <60> <730> <904>} a white boat on the lake." + ], + "image_footnote": [], + "bbox": [ + 638, + 281, + 746, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/350815402a06475956d08d963457185a4a04555c2e159658b241e9d3accf0301.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 750, + 281, + 857, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/10ccc87730ed298fc5ed20224487d3ac7560d6becbfbc8ec44c2102741eadcf3.jpg", + "image_caption": [ + "A zoomed out view of a man riding a horse through rural country side. {medium square in the bottom right, $< 610>$ $< 699>$ $< 799>$ $< 854>$ brown horse. {medium tall in the bottom right, $< 672>$ $< 630>$ $< 721>$ $< 753>$ a man in blue shirt." + ], + "image_footnote": [], + "bbox": [ + 638, + 404, + 746, + 488 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/240902b9eab99897fd1cc19e5cdbeeb87dc00c491a9f44d4052b325aa27714a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 404, + 857, + 488 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 621, + 313, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, large-scale text-to-image (T2I) models have shown impressive performance in generating high-fidelity images, but with limited controllability, e.g., precisely specifying the content in a specific region with a free-form text description. In this paper, we propose an effective technique for such regional control in T2I generation. We augment T2I models' inputs with an extra set of position tokens, which represent the quantized spatial coordinates. Each region is specified by four position tokens to represent the top-left and bottom-right corners, followed by an open-ended natural language regional description. Then, we fine-tune a pre-trained T2I model with such new input interface. Our model, dubbed as ReCo (Region-Controlled T2I), enables the region control for arbitrary objects described by open-ended regional texts rather than by object labels from a constrained category set. Empirically, ReCo achieves better image quality than the T2I model strengthened by posi", + "bbox": [ + 73, + 643, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tional words (FID: $8.82 \\rightarrow 7.36$ , SceneFID: $15.54 \\rightarrow 6.51$ on COCO), together with objects being more accurately placed, amounting to a $20.40\\%$ region classification accuracy improvement on COCO. Furthermore, we demonstrate that ReCo can better control the object count, spatial relationship, and region attributes such as color/size, with the free-form regional description. Human evaluation on PaintSkill shows that ReCo is $+19.28\\%$ and $+17.21\\%$ more accurate in generating images with correct object count and spatial relationship than the T2I model. Code is available at https://github.com/microsoft/ReCo.", + "bbox": [ + 496, + 622, + 893, + 789 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 811, + 632, + 827 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-image (T2I) generation aims to generate faithful images based on an input text query that describes the image content. By scaling up the training data and model size, large T2I models [31, 34, 36, 45] have recently shown", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14246", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "remarkable capabilities in generating high-fidelity images. However, the text-only query allows limited controllability, e.g., precisely specifying the content in a specific region. The naive way of using position-related text words, such as \"top left\" and \"bottom right,\" often results in ambiguous and verbose input queries, as shown in Figure 2 (a). Even worse, when the text query becomes long and complicated, or describes an unusual scene, T2I models [31,45] might overlook certain details and rather follow the visual or linguistic training prior. These two factors together make region control difficult. To get the desired image, users usually need to try a large number of paraphrased queries and pick an image that best fits the desired scene. The process known as \"prompt engineering\" is time-consuming and often fails to produce the desired image.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The desired region-controlled T2I generation is closely related to the layout-to-image generation [7,9,22,23,34,38, 44, 49]. As shown in Figure 2 (b), layout-to-image models take all object bounding boxes with labels from a close set of object vocabulary [24] as inputs. Despite showing promise in region control, they can hardly understand freeform text inputs, nor the region-level combination of open-ended text descriptions and spatial positions. The two input conditions of text and box provide complementary referring capabilities. Instead of separately modeling them as in text-to-image and layout-to-image generations, we study \"region-controlled T2I generation\" that seamlessly combines these two input conditions. As shown in Figure 2 (c), the new input interface allows users to provide open-ended descriptions for arbitrary image regions, such as precisely placing a \"brown glazed chocolate donut\" in a specific area.", + "bbox": [ + 75, + 320, + 472, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose ReCo (Region-Controlled T2I) that extends pre-trained T2I models to understand spatial coordinate inputs. The core idea is to introduce an extra set of input position tokens to indicate the spatial positions. The image width/height is quantized uniformly into $N_{\\mathrm{bins}}$ bins. Then, any float-valued coordinate can be approximated and tokenized by the nearest bin. With an extra embedding matrix $(E_P)$ , the position token can be mapped onto the same space as the text token. Instead of designing a text-only query with positional words \"in the top red donut\" as in Figure 2 (a), ReCo takes region-controlled text inputs $\\langle x_1\\rangle ,\\langle y_1\\rangle ,\\langle x_2\\rangle ,\\langle y_2\\rangle$ red donut,\" where $\\langle x\\rangle ,\\langle y\\rangle$ are the position tokens followed by the corresponding freeform text description. We then fine-tune a pre-trained T2I model with $E_P$ to generate the image from the extended input query. To best preserve the pre-trained T2I capability, ReCo training is designed to be similar to the T2I pretraining, i.e., introducing minimal extra model parameters $(E_P)$ , jointly encoding position and text tokens with the text encoder, and prefixing the image description before the extended regional descriptions in the input query.", + "bbox": [ + 75, + 565, + 472, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 1 visualizes ReCo's use cases and capabilities. As", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/db69a076f6754db5ca313be3e2496accc8f8d828c4679e6bb4ef863f301fdf31.jpg", + "image_caption": [ + "Figure 2. (a) With positional words (e.g., bottom/top/left/right and large/small/tall/long), the T2I model (Stable Diffusion [34]) does not manage to create objects with desired properties. (b) Layout-to-image generation [22, 34, 38, 49] takes all object boxes and labels as the input condition, but only works well with constrained object labels. (c) Our ReCo model synergically combines the text and box referring, allowing users to specify an open-ended regional text description precisely at any image region." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 890, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "shown in Figure 1 (a), ReCo could reliably follow the input spatial constraints and generate the most plausible images by automatically adjusting object statues, such as the view (front/side) and type (single-/double-deck) of the \"bus.\" Position tokens also allow the user to provide free-form regional descriptions, such as \"an orange cat wearing a red hat\" at a specific location. Furthermore, we empirically observe that position tokens are less likely to get overlooked or misunderstood than text words. As shown in Figure 1 (b), ReCo has better control over object count, spatial relationship, and size properties, especially when the query is long and complicated, or describes a scene that is less common in real life. In contrast, T2I models [34] may struggle with generating scenes with correct object counts (\"ten\"), relationships (\"boat below traffic light\"), relative sizes (\"chair larger than airplane\"), and camera views (\"zoomed out\").", + "bbox": [ + 496, + 385, + 890, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To evaluate the region control, we design a comprehensive experiment benchmark based on a pre-trained regional object classifier and an object detector. The object classifier is applied on the generated image regions, while the detector is applied on the whole image. A higher accuracy means a better alignment between the generated object layout and the region positions in user queries. On the COCO dataset [24], ReCo shows a better object classification accuracy $(42.02\\% \\rightarrow 62.42\\%)$ and detector averaged precision $(2.3 \\rightarrow 32.0)$ , compared with the T2I model with carefully designed positional words. For image generation quality, ReCo improves the FID from 8.82 to 7.36, and SceneFID from 15.54 to 6.51. Furthermore, human evaluations on PaintSkill [5] show $+19.28\\%$ and $+17.21\\%$ accuracy gain in more correctly generating the query-described object count and spatial relationship, indicating ReCo's capability in helping T2I models to generate challenging scenes.", + "bbox": [ + 496, + 628, + 892, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows.", + "bbox": [ + 517, + 885, + 821, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14247", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose ReCo that extends pre-trained T2I models to understand coordinate inputs. Thanks to the introduced position tokens in the region-controlled input query, users can easily specify free-form regional descriptions in arbitrary image regions.", + "- We instantiate ReCo based on Stable Diffusion. Extensive experiments show that ReCo strictly follows the regional instructions from the input query, and also generates higher-fidelity images.", + "- We design a comprehensive evaluation benchmark to validate ReCo's region-controlled T2I generation capability. ReCo significantly improves both the region control accuracy and the image generation quality over a wide range of datasets and designed prompts." + ], + "bbox": [ + 96, + 90, + 467, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 323, + 217, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-image generation. Text-to-image (T2I) generation aims to generate a high-fidelity image based on an open-ended image description. Early studies adopt conditional GANs [33, 42, 46-48] for T2I generation. Recent studies have made tremendous advances by scaling up both the data and model size, based on either auto-regressive [10, 45] or diffusion-based models [31, 34, 36]. We build our study on top of the successful large-scale pre-trained T2I models, and explore how to better control the T2I generation by extending a pre-trained T2I model to understand position tokens.", + "bbox": [ + 76, + 349, + 467, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Layout-to-image generation. Layout-to-image studies aim to generate an image from a complete layout, i.e., all bounding boxes and the paired object labels. Early studies [9,22,23,38,49] adopt GAN-based approaches by properly injecting the encoded layout as the input condition. Recent studies successfully apply the layout query as the input condition to the auto-regressive framework [10,44] and diffusion models [7, 34]. Our study is related to the layout-to-image generation as both directions require the model to understand coordinate inputs. The major difference is that our design synergically combines text and box to help T2I generation. Therefore, ReCo can take open-ended regional descriptions and benefit from large-scale T2I pre-training.", + "bbox": [ + 76, + 503, + 467, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unifying open-ended text and localization conditions. Previous studies have explored unifying open-ended text descriptions with localization referring (box, mask, mouse trace) as the input generation condition. One modeling approach [8, 10, 14, 17, 20, 28, 33] is to separately encode the image description in T2I and the layout condition in layout-to-image, and trains a model to jointly condition on both input types. TRECS [19] takes mouse traces in the localized narratives dataset [29] to better ground open-ended text descriptions with a localized position. Other than taking layout as user-generated inputs, previous studies [16, 21] have also explored predicting layout from text to ease the T2I generation of complex scenes. Unlike the motivation", + "bbox": [ + 76, + 704, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of training another conditional generation model parallel to T2I and layout-to-image, we explore how to effectively extend pre-trained T2I models to understand region queries, leading to significantly better controllability and generation quality than training from scratch. In short, we position ReCo as an improvement for T2I by providing a more flexible input interface and alleviating controllability issues, e.g., being difficult to override data prior when generating unusual scenes, and overlooking words in complex queries.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. ReCo Model", + "text_level": 1, + "bbox": [ + 500, + 238, + 629, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Region-Controlled T2I Generation (ReCo) extends T2I models with the ability to understand coordinate inputs. The core idea is to design a unified input token vocabulary containing both text words and position tokens to allow accurate and open-ended regional control. By seamlessly mixing text and position tokens in the input query, ReCo obtains the best from the two worlds of text-to-image and layout-to-image, i.e., the abilities of free-form description and precise position control. In this section, we present our ReCo implementation based on the open-sourced Stable Diffusion (SD) [34]. We start with the SD preliminaries in Section 3.1 and introduce the core ReCo design in Section 3.2.", + "bbox": [ + 496, + 263, + 890, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 453, + 638, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We take Stable Diffusion as an example to introduce the T2I model that ReCo is built upon. Stable Diffusion is developed upon the Latent Diffusion Model [34], and consists of an auto-encoder, a U-Net [35] for noise estimation, and a CLIP ViT-L/14 text encoder. For the auto-encoder, the encoder $\\mathcal{E}$ with a down-sampling factor of 8 encodes the image $x$ into a latent representation $z = \\mathcal{E}(x)$ that the diffusion process operates on, and the decoder $\\mathcal{D}$ reconstructs the image $\\hat{x} = \\mathcal{D}(z)$ from the latent $z$ . U-Net [35] is conditioned on denoising timestep $t$ and text condition $\\tau_{\\theta}(y(T))$ , where $y(T)$ is the input text query with text tokens $T$ and $\\tau_{\\theta}$ is the CLIP ViT-L/14 text encoder [30] that projects a sequence of tokenized texts into the sequence embedding.", + "bbox": [ + 496, + 476, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The core motivation of ReCo is to explore more effective and interaction-friendly conditioning signals $y$ , while best preserving the pre-trained T2I capability. Specifically, ReCo extends text tokens with an extra vocabulary specialized for spatial coordinate referring, i.e., position tokens $P$ which can be seamlessly used together with text tokens $T$ in a single input query $y$ . ReCo aims to show the benefit of synergetically combining text and position conditions for region-controlled T2I generation.", + "bbox": [ + 496, + 672, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Region-Controlled T2I Generation", + "text_level": 1, + "bbox": [ + 500, + 816, + 802, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ReCo input sequence. The text input in T2I generation provides a natural way of specifying the generation condition. However, text words may be ambiguous and verbose in providing regional specifications. For a better input", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14248", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d728d458dcd11621f39a1d00586a828569e11c33e84dcb2a2b9632a3f6ee1c84.jpg", + "image_caption": [ + "Figure 3. ReCo extends Stable Diffusion [34] with position tokens $P$ to support open-ended text description at both image- and region-level. We minimize the amount of introduced new model parameters (i.e., position token embedding $E_P$ ) to best preserve the pre-trained T2I capability. The diffusion model and text encoder are fine-tuned together to support the extended position token inputs." + ], + "image_footnote": [], + "bbox": [ + 102, + 80, + 344, + 292 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/53ec5439ab47e3a2e10d4ac64fd35b2a5c1d716eb34452bf807933c3ef48d674.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 80, + 869, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "query, ReCo introduces position tokens that can directly refer to a spatial position. Specifically, the position and size of each region can be represented by four floating numbers, i.e., top-left and bottom-right coordinates. By quantizing coordinates [3, 41, 43], we can represent the region by four discrete position tokens $P$ , $$ , $$ , $$ , $$ , arranged as a sequence similar to a short natural language sentence. The left side of Figure 3 illustrates the ReCo input sequence design. Same as T2I, we start the input query with the image description to make the best use of largescale T2I pre-training. The image description is followed by multiple region-controlled texts, i.e., the four position tokens and the corresponding open-ended regional description. The number of regional specifications is unlimited, allowing users to easily create complex scenes with more regions, or save time on composing input queries with fewer or even no regions. ReCo introduces position token embedding $E_{P} \\in \\mathbb{R}^{N_{\\mathrm{bins}} \\times D}$ alongside the pre-trained text word embedding, where $N_{\\mathrm{bins}}$ is the number of the position tokens, and $D$ is the token embedding dimension. The entire sequence is then processed jointly, and each token, either text or spatial, is projected into a $D$ -dim token embedding $e$ . The pre-trained CLIP text encoder from Stable Diffusion takes the token embeddings in, and projects them as the sequence embedding that the diffusion model conditions on.", + "bbox": [ + 75, + 351, + 472, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ReCo fine-tuning. ReCo extends the text-only query $y(T)$ with text tokens $T$ into ReCo input query $y(P, T)$ that combines the text word $T$ and position token $P$ . We fine-tune the Stable Diffusion with the same latent diffusion modeling objective [34], following the notations in Section 3.1:", + "bbox": [ + 75, + 731, + 470, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = \\mathbb {E} _ {\\mathcal {E} (x), y (P, T), \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, \\tau_ {\\theta} (y (P, T))) \\| _ {2} ^ {2} \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 814, + 475, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}$ and $\\tau_{\\theta}$ are the fine-tuned network modules. All model parameters except position token embedding $E_{P}$ are initiated from the pre-trained Stable Diffusion model. Both the image description and several regional descriptions are", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "required for ReCo model fine-tuning. For the training data, we run a state-of-the-part captioning model [40] on the cropped image regions (following the annotated bounding boxes) to get the regional descriptions. During fine-tuning, we resize the image with the short edge to 512 and randomly crop a square region as the input image $x$ . We will release the generated data and fine-tuned model for reproduction.", + "bbox": [ + 496, + 351, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We empirically observe that ReCo can well understand the introduced position tokens and precisely place objects at arbitrary specified regions. Furthermore, we find that position tokens can also help ReCo better model long input sequences that contain multiple detailed attribute descriptions, leading to fewer detailed descriptions being neglected or incorrectly generated than the text-only query. By introducing position tokens with a minimal change to the pre-trained T2I model, ReCo obtains the desired region controllability while best preserving the appealing T2I capability.", + "bbox": [ + 496, + 457, + 892, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 625, + 633, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 500, + 650, + 692, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ReCo takes region-controlled inputs specified by the users. However, gathering sufficient real user queries paired with images for quantitative evaluations may be challenging. Therefore, in addition to the arbitrarily-shaped boxes from PaintSkill [5] and manually designed challenging queries in Figure 7, we also include in-domain boxes from COCO [4] and LVIS [11] to construct evaluation queries.", + "bbox": [ + 496, + 672, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets. We quantitatively evaluate ReCo on COCO [4, 24], PaintSkill [5], and LVIS [11]. For input queries, we take image descriptions and boxes from the datasets [5,11, 24] and generate regional descriptions with GIT [40]. For COCO [4, 24], we follow the established T2I setting [32, 41, 45] that reports the results on a subset of 30,000 captions sampled from the COCO 2014 val set. We fine-tune stable diffusion with image-text pairs from the COCO 2014", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14249", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/0279fec91276070da1513dbad61d892d3a93a631c93ccffbc134b9c173c505fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodImage Descr.Region Descr.Region PositionRegion Control Metrics (↑)Image Quality Metrics
AP\\( AP_{50} \\)Object Acc.SceneFID (↓)FID (↓)
Real Images---36.856.171.41--
SD V1.4 Zero-shot✓--0.72.026.7535.8013.40
✓✓-0.72.027.6434.7213.88
✓✓Text0.61.828.1532.8614.57
SD COCO Fine-tune:
ReCoImage Descr.✓--0.92.629.1227.7810.44
ReCoRegion Descr.✓✓-1.02.932.3224.889.11
ReCoPosition Word✓✓Text2.37.542.0215.548.82
ReCo✓✓✓32.052.462.426.517.36
", + "bbox": [ + 125, + 80, + 841, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Region control accuracy and image generation quality evaluations on the COCO (2014) 30k validation subset [24, 32, 41, 45].", + "bbox": [ + 89, + 238, + 879, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GT reference", + "bbox": [ + 116, + 252, + 169, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SD T21 Finetune", + "bbox": [ + 191, + 252, + 259, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ours", + "bbox": [ + 297, + 252, + 320, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/712f14a1c3b51edbe1c702cb79c05c3db93ed111996bbec0a52de07f4ba226fc.jpg", + "image_caption": [ + "five birds nestled together on a tree branch sleeping. \n<769><242><999><639> a black and white bird with a blue beak and a white neck. <0><293> ..." + ], + "image_footnote": [], + "bbox": [ + 101, + 262, + 183, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e24fdf422a13e3964b5baa310e6dbbe2e5ba49ac725932024b1bf9b327987f2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 184, + 263, + 264, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/31f4bf8a194b2631a6a5f211a035e3b82bd50942c35a18fd2bd990aed0ef746d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 263, + 349, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c2aacb6a3d02f170dd81cd881de077f6409c126484fa66c053c87f0df2aa4b10.jpg", + "image_caption": [ + "two bicyclists sitting on a bench with a forest background. \n<607><715><738><817>a helmet on a person's head. \n<260><802><820><944>a wooden bench ...." + ], + "image_footnote": [], + "bbox": [ + 101, + 354, + 183, + 415 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/48f1659111d169ecf6a9ce6ff1f3501bf1f34fd642618c78f3bd58f8c5033e9b.jpg", + "image_caption": [ + "(a) Counting, Relationship" + ], + "image_footnote": [], + "bbox": [ + 184, + 354, + 266, + 416 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0359a0b2fa6c956788ba5f8be6eda3d4b6398de5a1187c4d04b43a34c26f473b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 354, + 349, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GT reference", + "bbox": [ + 375, + 252, + 429, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SD T21 Finetune", + "bbox": [ + 452, + 252, + 517, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ours", + "bbox": [ + 558, + 252, + 578, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3350a18fb73d0b9897a74885dd11b722750025591396c281fa01a71f2566288f.jpg", + "image_caption": [ + "a cat rubbing up against the camera persons legs. <186> <58> <646> <798> a gray cat is resting on the leg of a person. <719> <320> <727> <339> person wearing ..." + ], + "image_footnote": [], + "bbox": [ + 361, + 262, + 444, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cada04b8b49c89c1add2809a98b81a2b1d173eb34252db54cf996d76d22b6291.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 444, + 262, + 526, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c3ad0b55897f95c59e9ec6fb85f2e8d69cf929bc42eba75948bf5897d574aaf8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 262, + 609, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/143903b1c55709de44c94ccf20447ab14c26e969df2a8b84521e8ff80bc65e9a.jpg", + "image_caption": [ + "(b) Camera View", + "Figure 4. Qualitative results on COCO [24]. ReCo's extra regional control (shown in the dark blue color) can improve T2I generation on (a) object counting and relationships, (b) images with unique camera views, and (c) images with detailed regional attribute descriptions." + ], + "image_footnote": [], + "bbox": [ + 361, + 354, + 442, + 417 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/42810bd950b050ee0306a1e3ed99b0c49872d7f1b14b03fd302788747d4b704e.jpg", + "image_caption": [ + "a snowboard with his snowboard attached to his feet sitting on a slope. $< 0>$ $< 680>$ $< 999>$ $< 889>$ a snowboard on the slope. $< 148>$ $< 170>$ $< 788>$ $< 756>$ a man is ..." + ], + "image_footnote": [], + "bbox": [ + 444, + 354, + 526, + 417 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4717281bb0f37d1044da09ecab5abc8ea52c95607fad5eda0b6568b26a16b299.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 354, + 609, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GT reference", + "bbox": [ + 635, + 252, + 689, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ours", + "bbox": [ + 818, + 252, + 838, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d3a9a79742900030ada4187eeb9ad15220a185c5d294903840911fb6bc33aabf.jpg", + "image_caption": [ + "the clock on the side of the metal building is gold and black. $< 200>$ $< 130>$ $< 903>$ $< 914>$ a clock with roman numerals on it." + ], + "image_footnote": [], + "bbox": [ + 622, + 262, + 702, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b89004dd29ff1d96575bf654d8d40f87d1a9b4ab03ebc7f1e77bac3f8a38834f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 704, + 262, + 785, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4785a623edae4f1eb6cfb8d5f7cd36ef29c1c16b1c5db26be91f31d246816302.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 262, + 867, + 325 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0d13cf6231635e534d6f42e2520e88b35bd50a59d6b782778af6f928150b2fcf.jpg", + "image_caption": [ + "a man in a blue shirt riding a blue motorcycle and some people. $< 126>$ $< 43>$ $< 411>$ $< 878>$ a man wearing a blue shirt. $< 0>$ $< 254>$ $< 866>$ $< 864>$ blue motorcycle with ....", + "(c) Regional Attribute" + ], + "image_footnote": [], + "bbox": [ + 622, + 354, + 702, + 417 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f1f568b5a7e2adab53ba2d24f2764dabd2d269586f6515167338377b352cd25f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 354, + 785, + 417 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/db35eadb7d7d90c3fec066cfd720cbde47644ccaac1d4a80a6bf0cb8e5104c32.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 354, + 867, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "train set. PaintSkill [5] evaluates models' capabilities on following arbitrarily-shaped boxes and generating images with the correct object type/count/relationship. We conduct the T2I inference with val set prompts, which contain 1,050/2,520/3,528 queries for object recognition, counting, and spatial relationship skills, respectively. LVIS [11] tests if the model understands open-vocabulary regional descriptions, with the object categories unseen in COCO finetuning. We report the results on the 4,809 LVIS val images [11] from the COCO 2017 val set [18, 49]. We do not fine-tune ReCo when experimenting on PaintSkill and LVIS to test its generalization capability with out-of-domain data. Evaluation metrics. We evaluate ReCo with metrics on region control accuracy and image generation quality. For region control accuracy, we use Object Classification Accuracy [49] and DETR detector Average Precision (AP) [2]. Object accuracy trains a classifier with queried image crops to classify cropped regions on generated images. The generation model should generate objects in specified regions to obtain a high classification accuracy. DETR detector AP detects objects on generated images and compares the results with input object queries. Thus, higher accuracy and AP can indicate a better layout alignment. For image generation quality, we use the Fréchet Inception Distance (FID) [13] to evaluate the image quality. We take SceneFID [39] as an indicator for region-level visual quality, which computes FID on the regions cropped based on input object boxes. We", + "bbox": [ + 75, + 492, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "compute FID and SceneFID with the Clean-FID repo [27] against center-cropped COCO images. We further conduct human evaluations on PaintSkill, due to the lack of GT images and effective automatic evaluation metrics.", + "bbox": [ + 496, + 492, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We fine-tune ReCo from the Stable Diffusion v1.4 checkpoint. We introduce $N = 1000$ position tokens and increase the max length of the text encoder to 616. The batch size is 2048. We use AdamW optimizer [26] with a constant learning rate of $1e^{-4}$ to train the model for 20,000 steps, equivalent to around 100 epochs on COCO 2014 train set. The inference is conducted with 50 PLMS steps [25]. We select a classifier-free guidance scale [15] that gives the best region control performance, i.e., 4.0 for ReCo and 7.5 for original Stable Diffusion, detailed in Section 4.3. We do not use CLIP image re-ranking.", + "bbox": [ + 496, + 553, + 890, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Region-Controlled T2I Generation Results", + "text_level": 1, + "bbox": [ + 500, + 726, + 862, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "COCO. Table 1 reports the region-controlled T2I generation results on COCO. The first row \"real images\" provides an oracle reference number on applicable metrics. The top part of the table shows the results obtained with the pretrained Stable Diffusion (SD) model without fine-tuning on COCO, i.e., the zero-shot setting. As shown in the left three columns, we experiment with adding \"region description\" and \"region position\" information to the input query in addition to \"image description.\" Since T2I models can not understand coordinates, we carefully design positional text de", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14250", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3a6621d7a94237f26b8a6374cbadc7c510acd31120dce5ba92206bfb119a52ba.jpg", + "image_caption": [ + "Figure 5. Qualitative results on PaintSkill [5]. ReCo's extra regional control (shown in the dark blue color) can help T2I models more reliably generate scenes with exact object counts and unusual object relationships/relative sizes." + ], + "image_footnote": [], + "bbox": [ + 99, + 80, + 352, + 289 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7c49e04424c23c187b529cb9062619c4f00d8024642188dfa54ff044297c2502.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 80, + 609, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "scriptions, indicated by \"text\" in the \"region position\" column. Specifically, we describe a region with one of the three size words (small, medium, large), three possible region aspect ratios (long, square, tall), and nine possible locations (top left, top, ..., bottom right). We note that the resulting $\\mathrm{ReCo}_{\\mathrm{Position~Word}}$ serves as a strengthened T2I baseline for reference purposes, and it is unfair to directly compare it with ReCo that understands coordinates. The bottom part compares the main ReCo model with other variants finetuned with the corresponding input queries. The middle three rows report the results on region control accuracy. For AP and $\\mathrm{AP}_{50}$ , we use a DETR ResNet-50 object detector trained on COCO [1, 2] to get the detection results on images generated based on the input texts and boxes from the COCO 2017 val5k set [24]. The \"object accuracy\" column reports the region classification accuracy [49]. The trained ResNet-101 region classifier [12] yields a $71.41\\%$ oracle 80-class accuracy on real images. The right two columns report the image generation quality metrics SceneFID a nd FID, which evaluate the region and image visual qualities.", + "bbox": [ + 75, + 323, + 472, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "One advantage of ReCo is its strong region control capability. As shown in the bottom row, ReCo achieves an AP of 32.0, which is close to the real image oracle of 36.8. Despite the careful engineering of positional text words, $\\mathrm{ReCo}_{\\mathrm{Position~Word}}$ only achieves an AP of 2.3. Similarly, for object region classification, $62.42\\%$ of the cropped regions on ReCo-generated images can be correctly classified, compared with $42.02\\%$ of $\\mathrm{ReCo}_{\\mathrm{Position~Word}}$ . ReCo also improves the generated image quality, both at the region and image level. At the region level, ReCo achieves a SceneFID of 6.51, indicating strong capabilities in both generating high-fidelity objects and precisely placing them in the queried position. At the image level, ReCo improves the FID from 10.44 to 7.36 with the region-controlled text input that provides a localized and more detailed image description. We present additional FID comparisons to state-of-the-art conditional image generation methods in Table 5 (c).", + "bbox": [ + 75, + 627, + 472, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show representative qualitative results in Figure 4.", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2c0cdff6d8ccb53fd855e07aaa88871af0e9c54756ac7c2a244ec25987eade86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 80, + 870, + 286 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/16364da41f9f00fa7ecc1065625afc510c05129e10490ad9eca5b26f2f2962e4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSkillObject Accuracy (↑)
ObjectCountSpatialObjectCountSpatial
SD V1.4 Zero-shot97.1159.2848.2035.9722.3213.06
ReCoImage Descr.98.2360.4049.1138.9225.7915.17
ReCOPosition Word93.3368.1064.8750.7225.3522.82
ReCo98.5187.3882.0882.3063.4067.30
", + "bbox": [ + 500, + 321, + 890, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Evaluations on the images generated with PaintSkill [5] prompts. We evaluate skill correctness with human judges, and object classification accuracy with the COCO-trained classifier.", + "bbox": [ + 498, + 404, + 890, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(a) ReCo can more reliably generate images that involve counting or complex object relationships, e.g., “five birds” and “sitting on a bench.” (b) ReCo can more easily generate images with unique camera views by controlling the relative position and size of object boxes, e.g., “a top-down view of a cat” that T2I models struggle with. (c) Separating detailed regional descriptions with position tokens also helps ReCo better understand long queries and reduce attribute leakage, e.g., the color of the clock and person’s shirt.", + "bbox": [ + 496, + 457, + 890, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PaintSkill. Table 2 shows the skill correctness and region control accuracy evaluations on PaintSkill [5]. Skill correctness [5] evaluates if the generated images contain the query-described object type/count/relationship, i.e., the \"object,\" \"count,\" and \"spatial\" subsets. We use human judges to obtain the skill correctness accuracy. For region control, we use object classification accuracy to evaluate if the model follows those arbitrarily shaped and located object queries. We reuse the COCO region classifier introduced in Table 1.", + "bbox": [ + 496, + 595, + 890, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on the human evaluation for \"skill correctness,\" $87.38\\%$ and $82.08\\%$ of ReCo-generated images have the correct object count and spatial relationship (\"count\" and \"spatial\"), which is $+19.28\\%$ and $+17.21\\%$ more accurate than $\\mathrm{ReCo}_{\\mathrm{Position~Word}}$ , and $+26.98\\%$ and $+32.97\\%$ higher than the T2I model with image description only. The skill correctness improvements suggest that region-control text inputs could be an effective interface to help T2I models more reliably generate user-specified scenes. The object accuracy evaluation makes the criteria more strict by requiring the model to follow the exact input region positions, in ad", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14251", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/941a6f32fb41224b5e25a0f19ae7fd298e019cab86602a0407156c87558e518d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 89, + 176, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d288a72c84d0760eb9de50de19cda858cda1632d256f2f4529aae2168cf947f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 178, + 89, + 271, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/49222f6e37dfac2cff99e64a490cdb327c6e35ba0859bad3bec32b64e64cb950.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 90, + 364, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0cfe1b390e2b1da7a2ae28eff86986513ebe04202ab3c49732a483576d193b17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 90, + 460, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8cdfedcd8f7858502c2c746c607b94fabdc60d462a2dcffe35b2a84bcf78ad16.jpg", + "image_caption": [ + "lovesea \n(a) a living room that has a bunch of different couches. <816> <140> <999> <607> white curtain is shown in a room. <622> <642> ...", + "Figure 6. Qualitative results on LVIS [11]. ReCo can understand open-vocabulary regional descriptions, including keywords such as \"curtain,\" \"ferris wheel,\" \"sausage,\" and \"salt shaker.\"" + ], + "image_footnote": [], + "bbox": [ + 81, + 165, + 176, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cd240413cd1a90086205780acc43049acced89a442abde2311db0182e7490149.jpg", + "image_caption": [ + "(b) there are two large boats that are in the water. $\\langle 80\\rangle < 0 > < 196>$ $< 354>$ a ferris wheel is the sky with a black background. $< 676>\\dots$" + ], + "image_footnote": [], + "bbox": [ + 178, + 164, + 271, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/537e083a6041a685ae799eff203debff4ac8662efe5c96d7271f15a249021679.jpg", + "image_caption": [ + "(c) a lunch bowl with bread, sausage, tomato, and egg. $< 450>$ $< 267>$ $< 692>$ $< 567>$ a close up of a sausage and tomato. $< 550>$ $< 459>$ ..." + ], + "image_footnote": [], + "bbox": [ + 272, + 166, + 366, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ee684216779e7ba4faa75bcd44188d2f22c06da90108b037ac5e32360e2f42fb.jpg", + "image_caption": [ + "(d) a tray topped with two plates of food and a drink. <383> <653> <496> <836> a clear glass salt shaker <158> <331> <375> <555> ..." + ], + "image_footnote": [], + "bbox": [ + 367, + 166, + 460, + 239 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dition to skills. \"ReCo\" achieves a strong region control accuracy of $63.40\\%$ and $67.30\\%$ on count and skill subsets, surpassing \"ReCoPosition Word\" by $+38.05\\%$ and $+44.48\\%$ .", + "bbox": [ + 75, + 354, + 467, + 400 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PaintSkill contains input queries with randomly assigned object types, locations, and shapes. Because of the minimal constraints, many queries describe challenging scenes that appear less frequently in real life. We observe that ReCo not only precisely follows position queries, but also fits objects and their surroundings naturally, indicating an understanding of object properties. In Figure 5 (a), the three buses with different aspect ratios each have their unique viewing angle and direction, such that the object \"bus\" fits tightly with the given region. More interestingly, the directions of each bus go nicely with the road, making the image look real to humans. Figure 5 (b) shows challenging cases that require drawing two less commonly co-occurred objects into the same image. ReCo correctly fits \"bed\" and \"fire hydrant,\" \"boat\" and \"bus\" into the given region. More impressively, ReCo can create a scene that makes the generated image look plausible, e.g., \"looking through a window with a bed indoors,\" with the commonsense knowledge that \"bed\" is usually indoor while \"fire hydrant\" is usually outdoor. The randomly assigned region categories can also lead to objects with unusual relative sizes, e.g., the bag that is larger than the airplane in Figure 5 (c). ReCo shows an understanding of image perspectives by placing smaller objects such as \"backpack\" and \"dog\" near the camera position.", + "bbox": [ + 75, + 401, + 467, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LVIS. Table 3 reports the T2I generation results with out-of-vocabulary regional entities. We observe that ReCo can understand open-vocabulary regional descriptions, by transferring the open-vocab capability learned from large-scale T2I pre-training to regional descriptions. ReCo achieves the best SceneFID and object classification accuracy over the 1,203 LVIS classes of 10.08 and $23.42\\%$ . The results show that the ReCo position tokens can be used with open-vocabulary regional descriptions, despite being trained on", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/231d2fbbb636486a4c599b4a3e775ad37cb8384968a1395e2e759c0e5684b797.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodObject Acc. (↑)SceneFID (↓)FID (↓)
Real Images42.00--
SD V1.4 Zero-shot7.8840.6223.74
ReCoImage Descr.9.8228.9520.87
ReCoRegion Descr.11.0828.1517.96
ReCoPosition Word16.6020.2717.80
ReCo23.4210.0817.73
", + "bbox": [ + 501, + 88, + 890, + 184 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4c41583af8cf870d51913d59e82cb80ea3f20098378bf23ab49257b383e81714.jpg", + "table_caption": [ + "Table 3. Evaluations on the images generated with the 4,809 LVIS validation samples [11] from COCO val2017. The object classification is conducted over the 1,203 LVIS classes." + ], + "table_footnote": [], + "table_body": "
MethodCOCOLVIS
Acc.SceneFIDFIDAcc.SceneFIDFID
Real Images74.41--42.00--
ReCoOD Label69.708.079.0822.7913.9823.06
ReCo62.426.517.3623.4210.0817.73
", + "bbox": [ + 504, + 231, + 887, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Analyses on using open-ended texts (ReCo) vs. constrained object labels (ReCoOD Label) as the regional description.", + "bbox": [ + 500, + 301, + 890, + 329 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "COCO with 80 object types. Figure 6 shows examples of generating objects that are not annotated in COCO, e.g., \"curtain\" and \"loveseat\" in (a), \"ferris wheel\" and \"clock tower\" in (b), \"sausage\" and \"tomato\" in (c), \"salts\" in (d). Qualitative results. We next qualitatively show ReCo's other capabilities with manually designed input queries. Figure 1 (a) shows examples of arbitrary object manipulation and regional description control. As shown in the \"bus\" example, ReCo will automatically adjust the object viewing (from side to front) and type (from single- to double-deck) to reasonably fit the region constraint, indicating the knowledge about object \"bus.\" ReCo can also understand the free-form regional text and generate \"cats\" in the specified region with different attributes, e.g., \"wearing a red hat,\" \"pink,\" \"sleeping,\" etc. Figure 7 (a) shows an example of generating images with different object counts. ReCo's region control provides a strong tool for generating the exact object count, optionally with extra regional texts describing each object. Figure 7 (b) shows how we can use the box size to control the camera view, e.g., the precise control of the exact zoom-in ratio. Figure 7 (c) presents additional examples of images with unusual object relationships.", + "bbox": [ + 496, + 339, + 890, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Analysis", + "text_level": 1, + "bbox": [ + 500, + 681, + 601, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regional descriptions. Alternative to the open-ended freeform texts, regional descriptions can be object indexes from a constrained category set, as the setup in layout-to-image generation [9, 22, 23, 38, 49]. Table 4 compares ReCo with $\\mathrm{ReCo_{OD\\_Label}}$ on COCO [24] and LVIS [11]. The leftmost \"accuracy\" column on COCO shows the major advantage of $\\mathrm{ReCo_{OD\\_Label}}$ , i.e., when fine-tuned and tested with the same regional object vocabulary, $\\mathrm{ReCo_{OD\\_Label}}$ is $+7.28\\%$ higher in region control accuracy, compared with ReCo. However, the closed-vocabulary OD labels bring two disadvantages. First, the position tokens in $\\mathrm{ReCo_{OD\\_Label}}$ tend to only work with the seen vocabulary, i.e., the 80 COCO categories. When evaluated on other datasets such as LVIS or", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14252", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/751087d87f52c1d0ac96ab46e6f32cbf5d51602e72be526be369b0110f8ee196.jpg", + "image_caption": [ + "(a) Regional Description, A box contains {two, five, six, seven, ten, eleven, twelve} donuts with varying types Counting of glazes and toppings. $< 515>$ $< 576>$ $< 742>$ $< 766>$ chocolate donut $< 237>$ $< 518>$ ..." + ], + "image_footnote": [], + "bbox": [ + 109, + 104, + 184, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d89bdd4a8fc1e685a551b25096f0ed61137989f9174c185b8a26bf48f1668a84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 104, + 259, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbf2223502fbd4dc2820141bb8c488e5eae88dee40c41f99928bd83c9a4e5bcb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 104, + 336, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ff4e1fb92369809056f4349e7417ff20ef530b997b6db7b9c1320a2a3ecc6dfc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 336, + 104, + 413, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea691e79d8c7474a25499d46437d5ee0836513d4afa43da4dd1960804dec71bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 104, + 490, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e1f9585de3580b16c13c7116963fe6c2d9f653e2ebb894c4beb1520a4c3b7a29.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 104, + 566, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc9f15f86beee72afb0f5aefad25d0e58dd628e872b876bab9bfbed68501d59c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 104, + 643, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e40535e48ce20f7ed3b525c7dca54aedd8630cee04e9451f8cabef2dad416dc1.jpg", + "image_caption": [ + "(b) Camera View" + ], + "image_footnote": [], + "bbox": [ + 109, + 185, + 184, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7c906369727902013c0715a56a0b79d4c981fa7880463bb861021e9a4ce35da1.jpg", + "image_caption": [ + "[foamed in view, view, zoomed out view] of a man riding a horse through rural entry side. $< 546>$ $< 621>$ $< 885>$ $< 861>$ brown horse $< 654>$ $< 563>$ ..." + ], + "image_footnote": [], + "bbox": [ + 186, + 185, + 261, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/900441790bedfc38069103aed19f7e42611cd08e0e139282fa9a27df89213d21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 186, + 336, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f5d772412c612a82979196142022676c791d88aaa3b860855a19644caefbf3c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 186, + 413, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/346cebd04caa6407cc72a3cc5c18a975a33597d855362d543037859be96097fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 186, + 490, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e2ab5d6a73b5d3efd3b3b9ccecbeb8b0b4c191983fcb333b7a24ebfa620092e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 186, + 566, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01ebb19c98daf84a6bf314f7ff20fff364aac45c91e372e7f5d3e513da4a890f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 186, + 643, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/86bb28a94c9a14c469390f6bcce8fa8d66190b6ab58620960c581f0f1ce82f3f.jpg", + "image_caption": [ + "(c) Relationship", + "Figure 7. Qualitative results of ReCo-generated images with manually designed challenging input queries." + ], + "image_footnote": [], + "bbox": [ + 109, + 268, + 184, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ffd14bd12acbf00e290e5a9402572b58a6b4a08e1a4514f6bffd261f5df56f38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 268, + 261, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aee97006d4adb7691bdd3ed4216c0dcf894f810e2e2e28096d7acb6974ec4e09.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 268, + 336, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ee9a4fb628f31020b6132dc4bb9a48b86f8750915bb2a82acff701da467c4c58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 268, + 413, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1748c925dc3409d025b3531ff1afb2fbab3240f5ae540fc64a72a0d4156d7cb1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 268, + 490, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/24d5e105230c556d3faf2d32966dac0851d51d6e159208541f3df5f785d83b1d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 268, + 566, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7f6c6190fa77cbfdedb8b998a507aa5dcb6e03022a7999c2a283f85cda17d85a.jpg", + "image_caption": [ + "Input Regional Descriptions", + "1. chocolate donut with sprinkles" + ], + "image_footnote": [], + "bbox": [ + 653, + 104, + 728, + 162 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "2. red donut", + "bbox": [ + 732, + 104, + 779, + 113 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3. pink donut with sprinkles", + "bbox": [ + 732, + 113, + 838, + 121 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.brown glazed chocolate donut", + "bbox": [ + 732, + 121, + 856, + 128 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.coconut donut", + "bbox": [ + 732, + 130, + 797, + 138 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. donut with powdered sugar", + "bbox": [ + 732, + 138, + 846, + 147 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. pink donut", + "bbox": [ + 732, + 148, + 782, + 155 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8.brown donut", + "bbox": [ + 732, + 155, + 790, + 164 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "9. white frosted donut", + "bbox": [ + 732, + 165, + 816, + 172 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "10. dark vanilla donut", + "bbox": [ + 732, + 172, + 813, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "11. chocolate donut", + "bbox": [ + 732, + 181, + 808, + 190 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "12. donut with sprinkles", + "bbox": [ + 732, + 190, + 823, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13dd681157ad63afdedb998b554d512bb81e4559021792ffd2795c05182432a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 186, + 730, + 246 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1. a man in blue shirt", + "bbox": [ + 732, + 217, + 812, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "2.brown horse", + "bbox": [ + 732, + 224, + 790, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 653, + 252, + 730, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/564385db34bf46570da09ab7f26d2cbd49e50427e6e5faa0f819ce81e89a7b7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 252, + 857, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/730a260afaf904143ba91e27bba79f85b75a724558b805befbd50ea287fc28c4.jpg", + "image_caption": [ + "(a) Image Quality Metrics", + "Table 5. (a,b) Analyses of different guidance scales' influences [15] on image quality and region control accuracy. (c) Comparison with previous T2I works on the COCO (2014) validation 30k subset [24, 32, 41, 45]) in the fine-tuned setting." + ], + "image_footnote": [], + "bbox": [ + 109, + 366, + 284, + 486 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/89ec7bb082be14ebcbbf8fc55c55eb4c7f89b5cddb14b1081a215222bb3205f2.jpg", + "image_caption": [ + "(b) Region Control Metrics" + ], + "image_footnote": [], + "bbox": [ + 341, + 366, + 545, + 486 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5c5f3b7d9cd637ab1c3849ce2a0cf88aa5df5aaf5be18f49502fc9ed46392a26.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
(c) MethodFID (↓)
Random Train Images [10]2.47
Retrieval Baseline [45]6.82
XMC-GAN [46]9.33
CogView2 [6]17.7
LAFITE [50]8.12
Make-A-Scene [10]7.55
Parti [45]3.22
ReCoImage Descr.6.98
ReCoPosition Word5.98
ReCo5.18
", + "bbox": [ + 589, + 353, + 810, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "open-world use cases, the region control performance drops significantly, as shown in the \"accuracy\" column on LVIS. Second, $\\mathrm{ReCo_{OD}}$ Label only works well with constrained object labels, which fail to provide detailed regional descriptions, such as attributes and object relationships. Therefore, $\\mathrm{ReCo_{OD}}$ Label helps less in generating high-fidelity images, with FID 1.72 and 5.33 worse than ReCo on COCO and LVIS. Given the aforementioned limitations, we use the open-ended free-form regional descriptions in ReCo.", + "bbox": [ + 75, + 527, + 468, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Guidance scale and T2I SOTA comparison. Table 5 (a,b) examines how different classifier-free guidance scales [15] influence region control accuracy and image generation quality on the COCO 2014 val subset [24,32,41,45]. We empirically observe that scale of 1.5 yields the best image quality, and a slightly larger scale of 4.0 provides the best region control performance. Table 5 (c) compares ReCo with the state-of-the-art T2I methods in the finetuned setting. We reduce the guidance scale from the 4.0 in Table 1 to 1.5 for a fair comparison. We do not use any image-text contrastive models for results re-ranking. ReCo achieves an FID of 5.18, compared with 6.98 when we fine-tune Stable Diffusion with COCO T2I data without regional description. ReCo also outperforms the real image retrieval baseline [45] and most prior studies [6,10,46,50].", + "bbox": [ + 75, + 672, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our method has several limitations. First, ReCo might generate lower-quality images when the input query becomes too challenging, e.g., the unusual giant \"dog\" in Figure 7 (c). Second, for evaluation purposes, we train ReCo on the COCO train set. Despite preserving the open-vocabulary capability shown on LVIS, the generated image style does bias towards COCO. This limitation can potentially be alleviated by conducting the same ReCo finetuning on a small subset of pre-training data [37] used by the same T2I model [34]. We show this ReCo variant in the supplementary material. Finally, ReCo builds upon large-scale pre-trained T2I models such as Stable Diffusion [34] and shares similar possible generation biases.", + "bbox": [ + 496, + 527, + 890, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 727, + 617, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented ReCo that extends a pre-trained T2I model for region-controlled T2I generation. Our introduced position token allows the precise specification of open-ended regional descriptions on arbitrary image regions, leading to an effective new interface of region-controlled text input. We show that ReCo can help T2I generation in challenging cases, e.g., when the input query is complicated with detailed regional attributes or describes an unusual scene. Experiments validate ReCo's effectiveness on both region control accuracy and image generation quality.", + "bbox": [ + 496, + 748, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14253", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17907-17917, 2022. 8" + ], + "bbox": [ + 501, + 92, + 890, + 835 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14255", + "bbox": [ + 480, + 926, + 519, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ReCo_ Region-Controlled Text-to-Image Generation/7a126cec-3dba-421c-a0e8-e03b6864db48_model.json b/2023/ReCo_ Region-Controlled Text-to-Image Generation/7a126cec-3dba-421c-a0e8-e03b6864db48_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9f2ba115c7ce560f4f4e65e646f49c934c4f7766 --- /dev/null +++ b/2023/ReCo_ Region-Controlled Text-to-Image Generation/7a126cec-3dba-421c-a0e8-e03b6864db48_model.json @@ -0,0 +1,3036 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.221, + 0.131, + 0.75, + 0.154 + ], + "angle": 0, + "content": "ReCo: Region-Controlled Text-to-Image Generation" + }, + { + "type": "title", + "bbox": [ + 0.191, + 0.181, + 0.78, + 0.233 + ], + "angle": 0, + "content": "Zhengyuan Yang, Jianfeng Wang, Zhe Gan, Linjie Li, Kevin Lin, Chenfei Wu, Nan Duan, Zicheng Liu, Ce Liu, Michael Zeng, Lijuan Wang Microsoft" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.238, + 0.86, + 0.251 + ], + "angle": 0, + "content": "{zhengyang, jianfw, zhe.gan, lindsey.li, keli, chewu, nanduan, zliu, ce.liu, nzeng, lijuanw}@microsoft.com" + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.253, + 0.282, + 0.281 + ], + "angle": 0, + "content": "(a) New T2I Input Interface: Region-Controlled Text In" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.282, + 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+ }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.496, + 0.353, + 0.518 + ], + "angle": 0, + "content": "A cat on top of cabinets. \\(< 385>< 40>< 999>< 552>\\) an orange cat wearing a red hat." + }, + { + "type": "image_caption", + "bbox": [ + 0.396, + 0.253, + 0.635, + 0.266 + ], + "angle": 0, + "content": "(b) Improve T2I Semantic Correctness" + }, + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.269, + 0.497, + 0.279 + ], + "angle": 0, + "content": "Stable Diffusion" + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.282, + 0.506, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.269, + 0.578, + 0.279 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.282, + 0.617, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.367, + 0.619, + 0.404 + ], + "angle": 0, + "content": "A box contains ten donuts with varying types of glazes and toppings. {large square in the top, \\(<245>\\) <1> \\(<535>\\) <248>} red donut. {... ...} ... {large square in the top right, \\(<744>\\) <18> <939> <257>} brown glazed chocolate donut" + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.405, + 0.506, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.405, + 0.618, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.489, + 0.624, + 0.528 + ], + "angle": 0, + "content": "A chair that looks much larger than the white airplane in the background. {large square in the bottom, \\(<179>\\) <454> <617> <957>} a chair. {medium long in the right, \\(<602>\\) <330> <863> <416>} a white airplane." + }, + { + "type": "image_caption", + "bbox": [ + 0.651, + 0.269, + 0.739, + 0.279 + ], + "angle": 0, + "content": "Stable Diffusion" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.282, + 0.748, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.269, + 0.821, + 0.279 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.751, + 0.282, + 0.859, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.366, + 0.869, + 0.404 + ], + "angle": 0, + "content": "A boat below a traffic light with a park in the background. {large tall in the top, \\(<572>\\) <0> <686> <314>} a traffic light with the green light on. {large square in the bottom, <298> <60> <730> <904>} a white boat on the lake." + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.405, + 0.748, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.751, + 0.405, + 0.859, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.489, + 0.87, + 0.528 + ], + "angle": 0, + "content": "A zoomed out view of a man riding a horse through rural country side. {medium square in the bottom right, \\(< 610>\\) \\(< 699>\\) \\(< 799>\\) \\(< 854>\\) brown horse. {medium tall in the bottom right, \\(< 672>\\) \\(< 630>\\) \\(< 721>\\) \\(< 753>\\) a man in blue shirt." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.535, + 0.894, + 0.605 + ], + "angle": 0, + "content": "Figure 1. (a) ReCo extends pre-trained text-to-image models (Stable Diffusion [34]) with an extra set of input position tokens (in dark blue color) that represent quantized spatial coordinates. Combining position and text tokens yields the region-controlled text input, which can specify an open-ended regional description precisely for any image region. (b) With the region-controlled text input, ReCo can better control the object count/relationship/size properties and improve the T2I semantic correctness. We empirically observe that position tokens are less likely to get overlooked than positional text words, especially when the input query is complicated or describes an unusual scene." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.622, + 0.314, + 0.637 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.645, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recently, large-scale text-to-image (T2I) models have shown impressive performance in generating high-fidelity images, but with limited controllability, e.g., precisely specifying the content in a specific region with a free-form text description. In this paper, we propose an effective technique for such regional control in T2I generation. We augment T2I models' inputs with an extra set of position tokens, which represent the quantized spatial coordinates. Each region is specified by four position tokens to represent the top-left and bottom-right corners, followed by an open-ended natural language regional description. Then, we fine-tune a pre-trained T2I model with such new input interface. Our model, dubbed as ReCo (Region-Controlled T2I), enables the region control for arbitrary objects described by open-ended regional texts rather than by object labels from a constrained category set. Empirically, ReCo achieves better image quality than the T2I model strengthened by posi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.895, + 0.79 + ], + "angle": 0, + "content": "tional words (FID: \\(8.82 \\rightarrow 7.36\\), SceneFID: \\(15.54 \\rightarrow 6.51\\) on COCO), together with objects being more accurately placed, amounting to a \\(20.40\\%\\) region classification accuracy improvement on COCO. Furthermore, we demonstrate that ReCo can better control the object count, spatial relationship, and region attributes such as color/size, with the free-form regional description. Human evaluation on PaintSkill shows that ReCo is \\(+19.28\\%\\) and \\(+17.21\\%\\) more accurate in generating images with correct object count and spatial relationship than the T2I model. Code is available at https://github.com/microsoft/ReCo." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.812, + 0.633, + 0.828 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Text-to-image (T2I) generation aims to generate faithful images based on an input text query that describes the image content. By scaling up the training data and model size, large T2I models [31, 34, 36, 45] have recently shown" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "14246" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "remarkable capabilities in generating high-fidelity images. However, the text-only query allows limited controllability, e.g., precisely specifying the content in a specific region. The naive way of using position-related text words, such as \"top left\" and \"bottom right,\" often results in ambiguous and verbose input queries, as shown in Figure 2 (a). Even worse, when the text query becomes long and complicated, or describes an unusual scene, T2I models [31,45] might overlook certain details and rather follow the visual or linguistic training prior. These two factors together make region control difficult. To get the desired image, users usually need to try a large number of paraphrased queries and pick an image that best fits the desired scene. The process known as \"prompt engineering\" is time-consuming and often fails to produce the desired image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.473, + 0.563 + ], + "angle": 0, + "content": "The desired region-controlled T2I generation is closely related to the layout-to-image generation [7,9,22,23,34,38, 44, 49]. As shown in Figure 2 (b), layout-to-image models take all object bounding boxes with labels from a close set of object vocabulary [24] as inputs. Despite showing promise in region control, they can hardly understand freeform text inputs, nor the region-level combination of open-ended text descriptions and spatial positions. The two input conditions of text and box provide complementary referring capabilities. Instead of separately modeling them as in text-to-image and layout-to-image generations, we study \"region-controlled T2I generation\" that seamlessly combines these two input conditions. As shown in Figure 2 (c), the new input interface allows users to provide open-ended descriptions for arbitrary image regions, such as precisely placing a \"brown glazed chocolate donut\" in a specific area." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.473, + 0.884 + ], + "angle": 0, + "content": "To this end, we propose ReCo (Region-Controlled T2I) that extends pre-trained T2I models to understand spatial coordinate inputs. The core idea is to introduce an extra set of input position tokens to indicate the spatial positions. The image width/height is quantized uniformly into \\( N_{\\mathrm{bins}} \\) bins. Then, any float-valued coordinate can be approximated and tokenized by the nearest bin. With an extra embedding matrix \\( (E_P) \\), the position token can be mapped onto the same space as the text token. Instead of designing a text-only query with positional words \"in the top red donut\" as in Figure 2 (a), ReCo takes region-controlled text inputs \\( \\langle x_1\\rangle ,\\langle y_1\\rangle ,\\langle x_2\\rangle ,\\langle y_2\\rangle \\) red donut,\" where \\( \\langle x\\rangle ,\\langle y\\rangle \\) are the position tokens followed by the corresponding freeform text description. We then fine-tune a pre-trained T2I model with \\( E_P \\) to generate the image from the extended input query. To best preserve the pre-trained T2I capability, ReCo training is designed to be similar to the T2I pretraining, i.e., introducing minimal extra model parameters \\( (E_P) \\), jointly encoding position and text tokens with the text encoder, and prefixing the image description before the extended regional descriptions in the input query." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Figure 1 visualizes ReCo's use cases and capabilities. As" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.089, + 0.891, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.266, + 0.895, + 0.378 + ], + "angle": 0, + "content": "Figure 2. (a) With positional words (e.g., bottom/top/left/right and large/small/tall/long), the T2I model (Stable Diffusion [34]) does not manage to create objects with desired properties. (b) Layout-to-image generation [22, 34, 38, 49] takes all object boxes and labels as the input condition, but only works well with constrained object labels. (c) Our ReCo model synergically combines the text and box referring, allowing users to specify an open-ended regional text description precisely at any image region." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.628 + ], + "angle": 0, + "content": "shown in Figure 1 (a), ReCo could reliably follow the input spatial constraints and generate the most plausible images by automatically adjusting object statues, such as the view (front/side) and type (single-/double-deck) of the \"bus.\" Position tokens also allow the user to provide free-form regional descriptions, such as \"an orange cat wearing a red hat\" at a specific location. Furthermore, we empirically observe that position tokens are less likely to get overlooked or misunderstood than text words. As shown in Figure 1 (b), ReCo has better control over object count, spatial relationship, and size properties, especially when the query is long and complicated, or describes a scene that is less common in real life. In contrast, T2I models [34] may struggle with generating scenes with correct object counts (\"ten\"), relationships (\"boat below traffic light\"), relative sizes (\"chair larger than airplane\"), and camera views (\"zoomed out\")." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.884 + ], + "angle": 0, + "content": "To evaluate the region control, we design a comprehensive experiment benchmark based on a pre-trained regional object classifier and an object detector. The object classifier is applied on the generated image regions, while the detector is applied on the whole image. A higher accuracy means a better alignment between the generated object layout and the region positions in user queries. On the COCO dataset [24], ReCo shows a better object classification accuracy \\((42.02\\% \\rightarrow 62.42\\%)\\) and detector averaged precision \\((2.3 \\rightarrow 32.0)\\), compared with the T2I model with carefully designed positional words. For image generation quality, ReCo improves the FID from 8.82 to 7.36, and SceneFID from 15.54 to 6.51. Furthermore, human evaluations on PaintSkill [5] show \\(+19.28\\%\\) and \\(+17.21\\%\\) accuracy gain in more correctly generating the query-described object count and spatial relationship, indicating ReCo's capability in helping T2I models to generate challenging scenes." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.822, + 0.9 + ], + "angle": 0, + "content": "Our contributions are summarized as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "14247" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.097, + 0.092, + 0.468, + 0.168 + ], + "angle": 0, + "content": "- We propose ReCo that extends pre-trained T2I models to understand coordinate inputs. Thanks to the introduced position tokens in the region-controlled input query, users can easily specify free-form regional descriptions in arbitrary image regions." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.171, + 0.468, + 0.232 + ], + "angle": 0, + "content": "- We instantiate ReCo based on Stable Diffusion. Extensive experiments show that ReCo strictly follows the regional instructions from the input query, and also generates higher-fidelity images." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.235, + 0.468, + 0.31 + ], + "angle": 0, + "content": "- We design a comprehensive evaluation benchmark to validate ReCo's region-controlled T2I generation capability. ReCo significantly improves both the region control accuracy and the image generation quality over a wide range of datasets and designed prompts." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.092, + 0.468, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.324, + 0.218, + 0.34 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.468, + 0.501 + ], + "angle": 0, + "content": "Text-to-image generation. Text-to-image (T2I) generation aims to generate a high-fidelity image based on an open-ended image description. Early studies adopt conditional GANs [33, 42, 46-48] for T2I generation. Recent studies have made tremendous advances by scaling up both the data and model size, based on either auto-regressive [10, 45] or diffusion-based models [31, 34, 36]. We build our study on top of the successful large-scale pre-trained T2I models, and explore how to better control the T2I generation by extending a pre-trained T2I model to understand position tokens." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.505, + 0.468, + 0.702 + ], + "angle": 0, + "content": "Layout-to-image generation. Layout-to-image studies aim to generate an image from a complete layout, i.e., all bounding boxes and the paired object labels. Early studies [9,22,23,38,49] adopt GAN-based approaches by properly injecting the encoded layout as the input condition. Recent studies successfully apply the layout query as the input condition to the auto-regressive framework [10,44] and diffusion models [7, 34]. Our study is related to the layout-to-image generation as both directions require the model to understand coordinate inputs. The major difference is that our design synergically combines text and box to help T2I generation. Therefore, ReCo can take open-ended regional descriptions and benefit from large-scale T2I pre-training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Unifying open-ended text and localization conditions. Previous studies have explored unifying open-ended text descriptions with localization referring (box, mask, mouse trace) as the input generation condition. One modeling approach [8, 10, 14, 17, 20, 28, 33] is to separately encode the image description in T2I and the layout condition in layout-to-image, and trains a model to jointly condition on both input types. TRECS [19] takes mouse traces in the localized narratives dataset [29] to better ground open-ended text descriptions with a localized position. Other than taking layout as user-generated inputs, previous studies [16, 21] have also explored predicting layout from text to ease the T2I generation of complex scenes. Unlike the motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "of training another conditional generation model parallel to T2I and layout-to-image, we explore how to effectively extend pre-trained T2I models to understand region queries, leading to significantly better controllability and generation quality than training from scratch. In short, we position ReCo as an improvement for T2I by providing a more flexible input interface and alleviating controllability issues, e.g., being difficult to override data prior when generating unusual scenes, and overlooking words in complex queries." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.239, + 0.63, + 0.255 + ], + "angle": 0, + "content": "3. ReCo Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Region-Controlled T2I Generation (ReCo) extends T2I models with the ability to understand coordinate inputs. The core idea is to design a unified input token vocabulary containing both text words and position tokens to allow accurate and open-ended regional control. By seamlessly mixing text and position tokens in the input query, ReCo obtains the best from the two worlds of text-to-image and layout-to-image, i.e., the abilities of free-form description and precise position control. In this section, we present our ReCo implementation based on the open-sourced Stable Diffusion (SD) [34]. We start with the SD preliminaries in Section 3.1 and introduce the core ReCo design in Section 3.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.454, + 0.64, + 0.469 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.674 + ], + "angle": 0, + "content": "We take Stable Diffusion as an example to introduce the T2I model that ReCo is built upon. Stable Diffusion is developed upon the Latent Diffusion Model [34], and consists of an auto-encoder, a U-Net [35] for noise estimation, and a CLIP ViT-L/14 text encoder. For the auto-encoder, the encoder \\(\\mathcal{E}\\) with a down-sampling factor of 8 encodes the image \\(x\\) into a latent representation \\(z = \\mathcal{E}(x)\\) that the diffusion process operates on, and the decoder \\(\\mathcal{D}\\) reconstructs the image \\(\\hat{x} = \\mathcal{D}(z)\\) from the latent \\(z\\). U-Net [35] is conditioned on denoising timestep \\(t\\) and text condition \\(\\tau_{\\theta}(y(T))\\), where \\(y(T)\\) is the input text query with text tokens \\(T\\) and \\(\\tau_{\\theta}\\) is the CLIP ViT-L/14 text encoder [30] that projects a sequence of tokenized texts into the sequence embedding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.81 + ], + "angle": 0, + "content": "The core motivation of ReCo is to explore more effective and interaction-friendly conditioning signals \\( y \\), while best preserving the pre-trained T2I capability. Specifically, ReCo extends text tokens with an extra vocabulary specialized for spatial coordinate referring, i.e., position tokens \\( P \\) which can be seamlessly used together with text tokens \\( T \\) in a single input query \\( y \\). ReCo aims to show the benefit of synergetically combining text and position conditions for region-controlled T2I generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.803, + 0.833 + ], + "angle": 0, + "content": "3.2. Region-Controlled T2I Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ReCo input sequence. The text input in T2I generation provides a natural way of specifying the generation condition. However, text words may be ambiguous and verbose in providing regional specifications. For a better input" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "14248" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.082, + 0.345, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.081, + 0.87, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.895, + 0.342 + ], + "angle": 0, + "content": "Figure 3. ReCo extends Stable Diffusion [34] with position tokens \\( P \\) to support open-ended text description at both image- and region-level. We minimize the amount of introduced new model parameters (i.e., position token embedding \\( E_P \\)) to best preserve the pre-trained T2I capability. The diffusion model and text encoder are fine-tuned together to support the extended position token inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.729 + ], + "angle": 0, + "content": "query, ReCo introduces position tokens that can directly refer to a spatial position. Specifically, the position and size of each region can be represented by four floating numbers, i.e., top-left and bottom-right coordinates. By quantizing coordinates [3, 41, 43], we can represent the region by four discrete position tokens \\( P \\), \\( \\), \\( \\), \\( \\), \\( \\), arranged as a sequence similar to a short natural language sentence. The left side of Figure 3 illustrates the ReCo input sequence design. Same as T2I, we start the input query with the image description to make the best use of largescale T2I pre-training. The image description is followed by multiple region-controlled texts, i.e., the four position tokens and the corresponding open-ended regional description. The number of regional specifications is unlimited, allowing users to easily create complex scenes with more regions, or save time on composing input queries with fewer or even no regions. ReCo introduces position token embedding \\( E_{P} \\in \\mathbb{R}^{N_{\\mathrm{bins}} \\times D} \\) alongside the pre-trained text word embedding, where \\( N_{\\mathrm{bins}} \\) is the number of the position tokens, and \\( D \\) is the token embedding dimension. The entire sequence is then processed jointly, and each token, either text or spatial, is projected into a \\( D \\)-dim token embedding \\( e \\). The pre-trained CLIP text encoder from Stable Diffusion takes the token embeddings in, and projects them as the sequence embedding that the diffusion model conditions on." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.472, + 0.809 + ], + "angle": 0, + "content": "ReCo fine-tuning. ReCo extends the text-only query \\( y(T) \\) with text tokens \\( T \\) into ReCo input query \\( y(P, T) \\) that combines the text word \\( T \\) and position token \\( P \\). We fine-tune the Stable Diffusion with the same latent diffusion modeling objective [34], following the notations in Section 3.1:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.815, + 0.476, + 0.836 + ], + "angle": 0, + "content": "\\[\nL = \\mathbb {E} _ {\\mathcal {E} (x), y (P, T), \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, \\tau_ {\\theta} (y (P, T))) \\| _ {2} ^ {2} \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}\\) and \\(\\tau_{\\theta}\\) are the fine-tuned network modules. All model parameters except position token embedding \\(E_{P}\\) are initiated from the pre-trained Stable Diffusion model. Both the image description and several regional descriptions are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.457 + ], + "angle": 0, + "content": "required for ReCo model fine-tuning. For the training data, we run a state-of-the-part captioning model [40] on the cropped image regions (following the annotated bounding boxes) to get the regional descriptions. During fine-tuning, we resize the image with the short edge to 512 and randomly crop a square region as the input image \\( x \\). We will release the generated data and fine-tuned model for reproduction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.893, + 0.61 + ], + "angle": 0, + "content": "We empirically observe that ReCo can well understand the introduced position tokens and precisely place objects at arbitrary specified regions. Furthermore, we find that position tokens can also help ReCo better model long input sequences that contain multiple detailed attribute descriptions, leading to fewer detailed descriptions being neglected or incorrectly generated than the text-only query. By introducing position tokens with a minimal change to the pre-trained T2I model, ReCo obtains the desired region controllability while best preserving the appealing T2I capability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.626, + 0.634, + 0.643 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.694, + 0.667 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.779 + ], + "angle": 0, + "content": "ReCo takes region-controlled inputs specified by the users. However, gathering sufficient real user queries paired with images for quantitative evaluations may be challenging. Therefore, in addition to the arbitrarily-shaped boxes from PaintSkill [5] and manually designed challenging queries in Figure 7, we also include in-domain boxes from COCO [4] and LVIS [11] to construct evaluation queries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Datasets. We quantitatively evaluate ReCo on COCO [4, 24], PaintSkill [5], and LVIS [11]. For input queries, we take image descriptions and boxes from the datasets [5,11, 24] and generate regional descriptions with GIT [40]. For COCO [4, 24], we follow the established T2I setting [32, 41, 45] that reports the results on a subset of 30,000 captions sampled from the COCO 2014 val set. We fine-tune stable diffusion with image-text pairs from the COCO 2014" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "14249" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.127, + 0.081, + 0.842, + 0.238 + ], + "angle": 0, + "content": "
MethodImage Descr.Region Descr.Region PositionRegion Control Metrics (↑)Image Quality Metrics
AP\\( AP_{50} \\)Object Acc.SceneFID (↓)FID (↓)
Real Images---36.856.171.41--
SD V1.4 Zero-shot✓--0.72.026.7535.8013.40
✓✓-0.72.027.6434.7213.88
✓✓Text0.61.828.1532.8614.57
SD COCO Fine-tune:
ReCoImage Descr.✓--0.92.629.1227.7810.44
ReCoRegion Descr.✓✓-1.02.932.3224.889.11
ReCoPosition Word✓✓Text2.37.542.0215.548.82
ReCo✓✓✓32.052.462.426.517.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.239, + 0.88, + 0.251 + ], + "angle": 0, + "content": "Table 1. Region control accuracy and image generation quality evaluations on the COCO (2014) 30k validation subset [24, 32, 41, 45]." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.253, + 0.171, + 0.261 + ], + "angle": 0, + "content": "GT reference" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.253, + 0.26, + 0.261 + ], + "angle": 0, + "content": "SD T21 Finetune" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.253, + 0.321, + 0.261 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.263, + 0.184, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.185, + 0.264, + 0.266, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.264, + 0.35, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.328, + 0.338, + 0.354 + ], + "angle": 0, + "content": "five birds nestled together on a tree branch sleeping. \n<769><242><999><639> a black and white bird with a blue beak and a white neck. <0><293> ..." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.356, + 0.184, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.185, + 0.356, + 0.267, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.356, + 0.351, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.419, + 0.345, + 0.445 + ], + "angle": 0, + "content": "two bicyclists sitting on a bench with a forest background. \n<607><715><738><817>a helmet on a person's head. \n<260><802><820><944>a wooden bench ...." + }, + { + "type": "image_caption", + "bbox": [ + 0.158, + 0.447, + 0.3, + 0.458 + ], + "angle": 0, + "content": "(a) Counting, Relationship" + }, + { + "type": "text", + "bbox": [ + 0.376, + 0.253, + 0.431, + 0.261 + ], + "angle": 0, + "content": "GT reference" + }, + { + "type": "text", + "bbox": [ + 0.453, + 0.253, + 0.519, + 0.261 + ], + "angle": 0, + "content": "SD T21 Finetune" + }, + { + "type": "text", + "bbox": [ + 0.559, + 0.253, + 0.579, + 0.261 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.263, + 0.445, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.446, + 0.263, + 0.527, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.263, + 0.611, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.328, + 0.597, + 0.354 + ], + "angle": 0, + "content": "a cat rubbing up against the camera persons legs. <186> <58> <646> <798> a gray cat is resting on the leg of a person. <719> <320> <727> <339> person wearing ..." + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.356, + 0.444, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.445, + 0.356, + 0.527, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.356, + 0.611, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.42, + 0.597, + 0.446 + ], + "angle": 0, + "content": "a snowboard with his snowboard attached to his feet sitting on a slope. \\(< 0>\\) \\(< 680>\\) \\(< 999>\\) \\(< 889>\\) a snowboard on the slope. \\(< 148>\\) \\(< 170>\\) \\(< 788>\\) \\(< 756>\\) a man is ..." + }, + { + "type": "image_caption", + "bbox": [ + 0.443, + 0.447, + 0.534, + 0.457 + ], + "angle": 0, + "content": "(b) Camera View" + }, + { + "type": "text", + "bbox": [ + 0.636, + 0.253, + 0.69, + 0.261 + ], + "angle": 0, + "content": "GT reference" + }, + { + "type": "text", + "bbox": [ + 0.819, + 0.253, + 0.839, + 0.261 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.263, + 0.703, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.263, + 0.787, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.263, + 0.869, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.328, + 0.847, + 0.354 + ], + "angle": 0, + "content": "the clock on the side of the metal building is gold and black. \\(< 200>\\) \\(< 130>\\) \\(< 903>\\) \\(< 914>\\) a clock with roman numerals on it." + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.355, + 0.704, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.355, + 0.787, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.355, + 0.869, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.419, + 0.859, + 0.446 + ], + "angle": 0, + "content": "a man in a blue shirt riding a blue motorcycle and some people. \\(< 126>\\) \\(< 43>\\) \\(< 411>\\) \\(< 878>\\) a man wearing a blue shirt. \\(< 0>\\) \\(< 254>\\) \\(< 866>\\) \\(< 864>\\) blue motorcycle with ...." + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.447, + 0.806, + 0.458 + ], + "angle": 0, + "content": "(c) Regional Attribute" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.459, + 0.892, + 0.486 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on COCO [24]. ReCo's extra regional control (shown in the dark blue color) can improve T2I generation on (a) object counting and relationships, (b) images with unique camera views, and (c) images with detailed regional attribute descriptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.473, + 0.902 + ], + "angle": 0, + "content": "train set. PaintSkill [5] evaluates models' capabilities on following arbitrarily-shaped boxes and generating images with the correct object type/count/relationship. We conduct the T2I inference with val set prompts, which contain 1,050/2,520/3,528 queries for object recognition, counting, and spatial relationship skills, respectively. LVIS [11] tests if the model understands open-vocabulary regional descriptions, with the object categories unseen in COCO finetuning. We report the results on the 4,809 LVIS val images [11] from the COCO 2017 val set [18, 49]. We do not fine-tune ReCo when experimenting on PaintSkill and LVIS to test its generalization capability with out-of-domain data. Evaluation metrics. We evaluate ReCo with metrics on region control accuracy and image generation quality. For region control accuracy, we use Object Classification Accuracy [49] and DETR detector Average Precision (AP) [2]. Object accuracy trains a classifier with queried image crops to classify cropped regions on generated images. The generation model should generate objects in specified regions to obtain a high classification accuracy. DETR detector AP detects objects on generated images and compares the results with input object queries. Thus, higher accuracy and AP can indicate a better layout alignment. For image generation quality, we use the Fréchet Inception Distance (FID) [13] to evaluate the image quality. We take SceneFID [39] as an indicator for region-level visual quality, which computes FID on the regions cropped based on input object boxes. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.553 + ], + "angle": 0, + "content": "compute FID and SceneFID with the Clean-FID repo [27] against center-cropped COCO images. We further conduct human evaluations on PaintSkill, due to the lack of GT images and effective automatic evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Implementation details. We fine-tune ReCo from the Stable Diffusion v1.4 checkpoint. We introduce \\( N = 1000 \\) position tokens and increase the max length of the text encoder to 616. The batch size is 2048. We use AdamW optimizer [26] with a constant learning rate of \\( 1e^{-4} \\) to train the model for 20,000 steps, equivalent to around 100 epochs on COCO 2014 train set. The inference is conducted with 50 PLMS steps [25]. We select a classifier-free guidance scale [15] that gives the best region control performance, i.e., 4.0 for ReCo and 7.5 for original Stable Diffusion, detailed in Section 4.3. We do not use CLIP image re-ranking." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.863, + 0.742 + ], + "angle": 0, + "content": "4.2. Region-Controlled T2I Generation Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "COCO. Table 1 reports the region-controlled T2I generation results on COCO. The first row \"real images\" provides an oracle reference number on applicable metrics. The top part of the table shows the results obtained with the pretrained Stable Diffusion (SD) model without fine-tuning on COCO, i.e., the zero-shot setting. As shown in the left three columns, we experiment with adding \"region description\" and \"region position\" information to the input query in addition to \"image description.\" Since T2I models can not understand coordinates, we carefully design positional text de" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "14250" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.082, + 0.353, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.082, + 0.611, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on PaintSkill [5]. ReCo's extra regional control (shown in the dark blue color) can help T2I models more reliably generate scenes with exact object counts and unusual object relationships/relative sizes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.627 + ], + "angle": 0, + "content": "scriptions, indicated by \"text\" in the \"region position\" column. Specifically, we describe a region with one of the three size words (small, medium, large), three possible region aspect ratios (long, square, tall), and nine possible locations (top left, top, ..., bottom right). We note that the resulting \\(\\mathrm{ReCo}_{\\mathrm{Position~Word}}\\) serves as a strengthened T2I baseline for reference purposes, and it is unfair to directly compare it with ReCo that understands coordinates. The bottom part compares the main ReCo model with other variants finetuned with the corresponding input queries. The middle three rows report the results on region control accuracy. For AP and \\(\\mathrm{AP}_{50}\\), we use a DETR ResNet-50 object detector trained on COCO [1, 2] to get the detection results on images generated based on the input texts and boxes from the COCO 2017 val5k set [24]. The \"object accuracy\" column reports the region classification accuracy [49]. The trained ResNet-101 region classifier [12] yields a \\(71.41\\%\\) oracle 80-class accuracy on real images. The right two columns report the image generation quality metrics SceneFID a nd FID, which evaluate the region and image visual qualities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.473, + 0.884 + ], + "angle": 0, + "content": "One advantage of ReCo is its strong region control capability. As shown in the bottom row, ReCo achieves an AP of 32.0, which is close to the real image oracle of 36.8. Despite the careful engineering of positional text words, \\(\\mathrm{ReCo}_{\\mathrm{Position~Word}}\\) only achieves an AP of 2.3. Similarly, for object region classification, \\(62.42\\%\\) of the cropped regions on ReCo-generated images can be correctly classified, compared with \\(42.02\\%\\) of \\(\\mathrm{ReCo}_{\\mathrm{Position~Word}}\\). ReCo also improves the generated image quality, both at the region and image level. At the region level, ReCo achieves a SceneFID of 6.51, indicating strong capabilities in both generating high-fidelity objects and precisely placing them in the queried position. At the image level, ReCo improves the FID from 10.44 to 7.36 with the region-controlled text input that provides a localized and more detailed image description. We present additional FID comparisons to state-of-the-art conditional image generation methods in Table 5 (c)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We show representative qualitative results in Figure 4." + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.082, + 0.871, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.5, + 0.322, + 0.892, + 0.404 + ], + "angle": 0, + "content": "
MethodSkillObject Accuracy (↑)
ObjectCountSpatialObjectCountSpatial
SD V1.4 Zero-shot97.1159.2848.2035.9722.3213.06
ReCoImage Descr.98.2360.4049.1138.9225.7915.17
ReCOPosition Word93.3368.1064.8750.7225.3522.82
ReCo98.5187.3882.0882.3063.4067.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.405, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Table 2. Evaluations on the images generated with PaintSkill [5] prompts. We evaluate skill correctness with human judges, and object classification accuracy with the COCO-trained classifier." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.892, + 0.594 + ], + "angle": 0, + "content": "(a) ReCo can more reliably generate images that involve counting or complex object relationships, e.g., “five birds” and “sitting on a bench.” (b) ReCo can more easily generate images with unique camera views by controlling the relative position and size of object boxes, e.g., “a top-down view of a cat” that T2I models struggle with. (c) Separating detailed regional descriptions with position tokens also helps ReCo better understand long queries and reduce attribute leakage, e.g., the color of the clock and person’s shirt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.732 + ], + "angle": 0, + "content": "PaintSkill. Table 2 shows the skill correctness and region control accuracy evaluations on PaintSkill [5]. Skill correctness [5] evaluates if the generated images contain the query-described object type/count/relationship, i.e., the \"object,\" \"count,\" and \"spatial\" subsets. We use human judges to obtain the skill correctness accuracy. For region control, we use object classification accuracy to evaluate if the model follows those arbitrarily shaped and located object queries. We reuse the COCO region classifier introduced in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Based on the human evaluation for \"skill correctness,\" \\(87.38\\%\\) and \\(82.08\\%\\) of ReCo-generated images have the correct object count and spatial relationship (\"count\" and \"spatial\"), which is \\(+19.28\\%\\) and \\(+17.21\\%\\) more accurate than \\(\\mathrm{ReCo}_{\\mathrm{Position~Word}}\\), and \\(+26.98\\%\\) and \\(+32.97\\%\\) higher than the T2I model with image description only. The skill correctness improvements suggest that region-control text inputs could be an effective interface to help T2I models more reliably generate user-specified scenes. The object accuracy evaluation makes the criteria more strict by requiring the model to follow the exact input region positions, in ad" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "14251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.177, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.09, + 0.272, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.091, + 0.366, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.091, + 0.462, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.166, + 0.177, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.165, + 0.272, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.167, + 0.367, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.167, + 0.462, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.241, + 0.173, + 0.295 + ], + "angle": 0, + "content": "lovesea \n(a) a living room that has a bunch of different couches. <816> <140> <999> <607> white curtain is shown in a room. <622> <642> ..." + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.245, + 0.266, + 0.296 + ], + "angle": 0, + "content": "(b) there are two large boats that are in the water. \\(\\langle 80\\rangle < 0 > < 196>\\) \\(< 354>\\) a ferris wheel is the sky with a black background. \\(< 676>\\dots\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.245, + 0.365, + 0.296 + ], + "angle": 0, + "content": "(c) a lunch bowl with bread, sausage, tomato, and egg. \\(< 450>\\) \\(< 267>\\) \\(< 692>\\) \\(< 567>\\) a close up of a sausage and tomato. \\(< 550>\\) \\(< 459>\\) ..." + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.245, + 0.46, + 0.296 + ], + "angle": 0, + "content": "(d) a tray topped with two plates of food and a drink. <383> <653> <496> <836> a clear glass salt shaker <158> <331> <375> <555> ..." + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.301, + 0.468, + 0.342 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on LVIS [11]. ReCo can understand open-vocabulary regional descriptions, including keywords such as \"curtain,\" \"ferris wheel,\" \"sausage,\" and \"salt shaker.\"" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.468, + 0.401 + ], + "angle": 0, + "content": "dition to skills. \"ReCo\" achieves a strong region control accuracy of \\(63.40\\%\\) and \\(67.30\\%\\) on count and skill subsets, surpassing \"ReCoPosition Word\" by \\(+38.05\\%\\) and \\(+44.48\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.468, + 0.763 + ], + "angle": 0, + "content": "PaintSkill contains input queries with randomly assigned object types, locations, and shapes. Because of the minimal constraints, many queries describe challenging scenes that appear less frequently in real life. We observe that ReCo not only precisely follows position queries, but also fits objects and their surroundings naturally, indicating an understanding of object properties. In Figure 5 (a), the three buses with different aspect ratios each have their unique viewing angle and direction, such that the object \"bus\" fits tightly with the given region. More interestingly, the directions of each bus go nicely with the road, making the image look real to humans. Figure 5 (b) shows challenging cases that require drawing two less commonly co-occurred objects into the same image. ReCo correctly fits \"bed\" and \"fire hydrant,\" \"boat\" and \"bus\" into the given region. More impressively, ReCo can create a scene that makes the generated image look plausible, e.g., \"looking through a window with a bed indoors,\" with the commonsense knowledge that \"bed\" is usually indoor while \"fire hydrant\" is usually outdoor. The randomly assigned region categories can also lead to objects with unusual relative sizes, e.g., the bag that is larger than the airplane in Figure 5 (c). ReCo shows an understanding of image perspectives by placing smaller objects such as \"backpack\" and \"dog\" near the camera position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "LVIS. Table 3 reports the T2I generation results with out-of-vocabulary regional entities. We observe that ReCo can understand open-vocabulary regional descriptions, by transferring the open-vocab capability learned from large-scale T2I pre-training to regional descriptions. ReCo achieves the best SceneFID and object classification accuracy over the 1,203 LVIS classes of 10.08 and \\(23.42\\%\\). The results show that the ReCo position tokens can be used with open-vocabulary regional descriptions, despite being trained on" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.185 + ], + "angle": 0, + "content": "
MethodObject Acc. (↑)SceneFID (↓)FID (↓)
Real Images42.00--
SD V1.4 Zero-shot7.8840.6223.74
ReCoImage Descr.9.8228.9520.87
ReCoRegion Descr.11.0828.1517.96
ReCoPosition Word16.6020.2717.80
ReCo23.4210.0817.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.186, + 0.892, + 0.226 + ], + "angle": 0, + "content": "Table 3. Evaluations on the images generated with the 4,809 LVIS validation samples [11] from COCO val2017. The object classification is conducted over the 1,203 LVIS classes." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.232, + 0.888, + 0.302 + ], + "angle": 0, + "content": "
MethodCOCOLVIS
Acc.SceneFIDFIDAcc.SceneFIDFID
Real Images74.41--42.00--
ReCoOD Label69.708.079.0822.7913.9823.06
ReCo62.426.517.3623.4210.0817.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.303, + 0.891, + 0.33 + ], + "angle": 0, + "content": "Table 4. Analyses on using open-ended texts (ReCo) vs. constrained object labels (ReCoOD Label) as the regional description." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.892, + 0.673 + ], + "angle": 0, + "content": "COCO with 80 object types. Figure 6 shows examples of generating objects that are not annotated in COCO, e.g., \"curtain\" and \"loveseat\" in (a), \"ferris wheel\" and \"clock tower\" in (b), \"sausage\" and \"tomato\" in (c), \"salts\" in (d). Qualitative results. We next qualitatively show ReCo's other capabilities with manually designed input queries. Figure 1 (a) shows examples of arbitrary object manipulation and regional description control. As shown in the \"bus\" example, ReCo will automatically adjust the object viewing (from side to front) and type (from single- to double-deck) to reasonably fit the region constraint, indicating the knowledge about object \"bus.\" ReCo can also understand the free-form regional text and generate \"cats\" in the specified region with different attributes, e.g., \"wearing a red hat,\" \"pink,\" \"sleeping,\" etc. Figure 7 (a) shows an example of generating images with different object counts. ReCo's region control provides a strong tool for generating the exact object count, optionally with extra regional texts describing each object. Figure 7 (b) shows how we can use the box size to control the camera view, e.g., the precise control of the exact zoom-in ratio. Figure 7 (c) presents additional examples of images with unusual object relationships." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.602, + 0.697 + ], + "angle": 0, + "content": "4.3. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Regional descriptions. Alternative to the open-ended freeform texts, regional descriptions can be object indexes from a constrained category set, as the setup in layout-to-image generation [9, 22, 23, 38, 49]. Table 4 compares ReCo with \\(\\mathrm{ReCo_{OD\\_Label}}\\) on COCO [24] and LVIS [11]. The leftmost \"accuracy\" column on COCO shows the major advantage of \\(\\mathrm{ReCo_{OD\\_Label}}\\), i.e., when fine-tuned and tested with the same regional object vocabulary, \\(\\mathrm{ReCo_{OD\\_Label}}\\) is \\(+7.28\\%\\) higher in region control accuracy, compared with ReCo. However, the closed-vocabulary OD labels bring two disadvantages. First, the position tokens in \\(\\mathrm{ReCo_{OD\\_Label}}\\) tend to only work with the seen vocabulary, i.e., the 80 COCO categories. When evaluated on other datasets such as LVIS or" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "14252" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.083, + 0.643, + 0.105 + ], + "angle": 0, + "content": "(a) Regional Description, A box contains {two, five, six, seven, ten, eleven, twelve} donuts with varying types Counting of glazes and toppings. \\(< 515>\\) \\(< 576>\\) \\(< 742>\\) \\(< 766>\\) chocolate donut \\(< 237>\\) \\(< 518>\\) ..." + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.106, + 0.186, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.106, + 0.261, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.262, + 0.106, + 0.338, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.106, + 0.414, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.106, + 0.491, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.106, + 0.568, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.106, + 0.644, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.171, + 0.197, + 0.182 + ], + "angle": 0, + "content": "(b) Camera View" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.186, + 0.186, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.186, + 0.262, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.166, + 0.631, + 0.188 + ], + "angle": 0, + "content": "[foamed in view, view, zoomed out view] of a man riding a horse through rural entry side. \\(< 546>\\) \\(< 621>\\) \\(< 885>\\) \\(< 861>\\) brown horse \\(< 654>\\) \\(< 563>\\) ..." + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.188, + 0.338, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.188, + 0.415, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.188, + 0.491, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.188, + 0.567, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.188, + 0.644, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.254, + 0.192, + 0.265 + ], + "angle": 0, + "content": "(c) Relationship" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.269, + 0.186, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.269, + 0.262, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.269, + 0.338, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.269, + 0.414, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.269, + 0.491, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.269, + 0.567, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.658, + 0.085, + 0.797, + 0.096 + ], + "angle": 0, + "content": "Input Regional Descriptions" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.106, + 0.73, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.098, + 0.858, + 0.106 + ], + "angle": 0, + "content": "1. chocolate donut with sprinkles" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.106, + 0.781, + 0.114 + ], + "angle": 0, + "content": "2. red donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.114, + 0.839, + 0.122 + ], + "angle": 0, + "content": "3. pink donut with sprinkles" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.122, + 0.857, + 0.13 + ], + "angle": 0, + "content": "4.brown glazed chocolate donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.131, + 0.798, + 0.139 + ], + "angle": 0, + "content": "5.coconut donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.14, + 0.847, + 0.148 + ], + "angle": 0, + "content": "6. donut with powdered sugar" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.149, + 0.784, + 0.156 + ], + "angle": 0, + "content": "7. pink donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.156, + 0.792, + 0.165 + ], + "angle": 0, + "content": "8.brown donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.166, + 0.817, + 0.174 + ], + "angle": 0, + "content": "9. white frosted donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.174, + 0.815, + 0.182 + ], + "angle": 0, + "content": "10. dark vanilla donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.183, + 0.809, + 0.191 + ], + "angle": 0, + "content": "11. chocolate donut" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.191, + 0.825, + 0.2 + ], + "angle": 0, + "content": "12. donut with sprinkles" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.188, + 0.731, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.218, + 0.813, + 0.226 + ], + "angle": 0, + "content": "1. a man in blue shirt" + }, + { + "type": "text", + "bbox": [ + 0.733, + 0.226, + 0.791, + 0.234 + ], + "angle": 0, + "content": "2.brown horse" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.253, + 0.731, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.253, + 0.859, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.331, + 0.8, + 0.345 + ], + "angle": 0, + "content": "Figure 7. Qualitative results of ReCo-generated images with manually designed challenging input queries." + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.354, + 0.267, + 0.366 + ], + "angle": 0, + "content": "(a) Image Quality Metrics" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.367, + 0.285, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.354, + 0.513, + 0.366 + ], + "angle": 0, + "content": "(b) Region Control Metrics" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.367, + 0.547, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.59, + 0.354, + 0.812, + 0.482 + ], + "angle": 0, + "content": "
(c) MethodFID (↓)
Random Train Images [10]2.47
Retrieval Baseline [45]6.82
XMC-GAN [46]9.33
CogView2 [6]17.7
LAFITE [50]8.12
Make-A-Scene [10]7.55
Parti [45]3.22
ReCoImage Descr.6.98
ReCoPosition Word5.98
ReCo5.18
" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.49, + 0.891, + 0.517 + ], + "angle": 0, + "content": "Table 5. (a,b) Analyses of different guidance scales' influences [15] on image quality and region control accuracy. (c) Comparison with previous T2I works on the COCO (2014) validation 30k subset [24, 32, 41, 45]) in the fine-tuned setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.469, + 0.664 + ], + "angle": 0, + "content": "open-world use cases, the region control performance drops significantly, as shown in the \"accuracy\" column on LVIS. Second, \\(\\mathrm{ReCo_{OD}}\\) Label only works well with constrained object labels, which fail to provide detailed regional descriptions, such as attributes and object relationships. Therefore, \\(\\mathrm{ReCo_{OD}}\\) Label helps less in generating high-fidelity images, with FID 1.72 and 5.33 worse than ReCo on COCO and LVIS. Given the aforementioned limitations, we use the open-ended free-form regional descriptions in ReCo." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Guidance scale and T2I SOTA comparison. Table 5 (a,b) examines how different classifier-free guidance scales [15] influence region control accuracy and image generation quality on the COCO 2014 val subset [24,32,41,45]. We empirically observe that scale of 1.5 yields the best image quality, and a slightly larger scale of 4.0 provides the best region control performance. Table 5 (c) compares ReCo with the state-of-the-art T2I methods in the finetuned setting. We reduce the guidance scale from the 4.0 in Table 1 to 1.5 for a fair comparison. We do not use any image-text contrastive models for results re-ranking. ReCo achieves an FID of 5.18, compared with 6.98 when we fine-tune Stable Diffusion with COCO T2I data without regional description. ReCo also outperforms the real image retrieval baseline [45] and most prior studies [6,10,46,50]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.724 + ], + "angle": 0, + "content": "Limitations. Our method has several limitations. First, ReCo might generate lower-quality images when the input query becomes too challenging, e.g., the unusual giant \"dog\" in Figure 7 (c). Second, for evaluation purposes, we train ReCo on the COCO train set. Despite preserving the open-vocabulary capability shown on LVIS, the generated image style does bias towards COCO. This limitation can potentially be alleviated by conducting the same ReCo finetuning on a small subset of pre-training data [37] used by the same T2I model [34]. We show this ReCo variant in the supplementary material. Finally, ReCo builds upon large-scale pre-trained T2I models such as Stable Diffusion [34] and shares similar possible generation biases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.728, + 0.618, + 0.742 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We have presented ReCo that extends a pre-trained T2I model for region-controlled T2I generation. Our introduced position token allows the precise specification of open-ended regional descriptions on arbitrary image regions, leading to an effective new interface of region-controlled text input. We show that ReCo can help T2I generation in challenging cases, e.g., when the input query is complicated with detailed regional attributes or describes an unusual scene. Experiments validate ReCo's effectiveness on both region control accuracy and image generation quality." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "14253" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. Detr res50 checkpoint from the official detr repo. In https://dl.fbaipublicfiles.com/detr/detr-r50-e632da11.pth, 2020.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.242 + ], + "angle": 0, + "content": "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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(a) ReCo extends pre-trained text-to-image models (Stable Diffusion [34]) with an extra set of input position tokens (in dark blue color) that represent quantized spatial coordinates. Combining position and text tokens yields the region-controlled text input, which can specify an open-ended regional description precisely for any image region. (b) With the region-controlled text input, ReCo can better control the object count/relationship/size properties and improve the T2I semantic correctness. We empirically observe that position tokens are less likely to get overlooked than positional text words, especially when the input query is complicated or describes an unusual scene. + +![](images/0cc693adb99f8d377cf1602f4705aef56995fe3d0af7f2873a5184e2e0ba882b.jpg) + +![](images/77cfb08c87cc2b5dcd1c7ca33505cce7a8025dec9ea87c53d0bcf3a3902f15f4.jpg) +(b) Improve T2I Semantic Correctness + +![](images/69e632407895a499851a904f077a7d1eef221bd4889aea718c661dec07e796a0.jpg) +Stable Diffusion +Ours + +![](images/561401cbf8e9522c9a62112a588e83f71a46739b9d874ceedb2f2a88cb4c50bc.jpg) +A box contains ten donuts with varying types of glazes and toppings. {large square in the top, $<245>$ <1> $<535>$ <248>} red donut. {... ...} ... {large square in the top right, $<744>$ <18> <939> <257>} brown glazed chocolate donut +A chair that looks much larger than the white airplane in the background. {large square in the bottom, $<179>$ <454> <617> <957>} a chair. {medium long in the right, $<602>$ <330> <863> <416>} a white airplane. + +![](images/bf039c8697b2d0ce85944bc1bb806f3a4895fbed15d6308340d30a9c3deb9afe.jpg) + +![](images/d509457927530c0c24cc286e1fe6dc6274e911b6f1208183e62872469fd4d2f3.jpg) +Stable Diffusion +A boat below a traffic light with a park in the background. {large tall in the top, $<572>$ <0> <686> <314>} a traffic light with the green light on. {large square in the bottom, <298> <60> <730> <904>} a white boat on the lake. + +![](images/350815402a06475956d08d963457185a4a04555c2e159658b241e9d3accf0301.jpg) +Ours + +![](images/10ccc87730ed298fc5ed20224487d3ac7560d6becbfbc8ec44c2102741eadcf3.jpg) +A zoomed out view of a man riding a horse through rural country side. {medium square in the bottom right, $< 610>$ $< 699>$ $< 799>$ $< 854>$ brown horse. {medium tall in the bottom right, $< 672>$ $< 630>$ $< 721>$ $< 753>$ a man in blue shirt. + +![](images/240902b9eab99897fd1cc19e5cdbeeb87dc00c491a9f44d4052b325aa27714a5.jpg) + +# Abstract + +Recently, large-scale text-to-image (T2I) models have shown impressive performance in generating high-fidelity images, but with limited controllability, e.g., precisely specifying the content in a specific region with a free-form text description. In this paper, we propose an effective technique for such regional control in T2I generation. We augment T2I models' inputs with an extra set of position tokens, which represent the quantized spatial coordinates. Each region is specified by four position tokens to represent the top-left and bottom-right corners, followed by an open-ended natural language regional description. Then, we fine-tune a pre-trained T2I model with such new input interface. Our model, dubbed as ReCo (Region-Controlled T2I), enables the region control for arbitrary objects described by open-ended regional texts rather than by object labels from a constrained category set. Empirically, ReCo achieves better image quality than the T2I model strengthened by posi + +tional words (FID: $8.82 \rightarrow 7.36$ , SceneFID: $15.54 \rightarrow 6.51$ on COCO), together with objects being more accurately placed, amounting to a $20.40\%$ region classification accuracy improvement on COCO. Furthermore, we demonstrate that ReCo can better control the object count, spatial relationship, and region attributes such as color/size, with the free-form regional description. Human evaluation on PaintSkill shows that ReCo is $+19.28\%$ and $+17.21\%$ more accurate in generating images with correct object count and spatial relationship than the T2I model. Code is available at https://github.com/microsoft/ReCo. + +# 1. Introduction + +Text-to-image (T2I) generation aims to generate faithful images based on an input text query that describes the image content. By scaling up the training data and model size, large T2I models [31, 34, 36, 45] have recently shown + +remarkable capabilities in generating high-fidelity images. However, the text-only query allows limited controllability, e.g., precisely specifying the content in a specific region. The naive way of using position-related text words, such as "top left" and "bottom right," often results in ambiguous and verbose input queries, as shown in Figure 2 (a). Even worse, when the text query becomes long and complicated, or describes an unusual scene, T2I models [31,45] might overlook certain details and rather follow the visual or linguistic training prior. These two factors together make region control difficult. To get the desired image, users usually need to try a large number of paraphrased queries and pick an image that best fits the desired scene. The process known as "prompt engineering" is time-consuming and often fails to produce the desired image. + +The desired region-controlled T2I generation is closely related to the layout-to-image generation [7,9,22,23,34,38, 44, 49]. As shown in Figure 2 (b), layout-to-image models take all object bounding boxes with labels from a close set of object vocabulary [24] as inputs. Despite showing promise in region control, they can hardly understand freeform text inputs, nor the region-level combination of open-ended text descriptions and spatial positions. The two input conditions of text and box provide complementary referring capabilities. Instead of separately modeling them as in text-to-image and layout-to-image generations, we study "region-controlled T2I generation" that seamlessly combines these two input conditions. As shown in Figure 2 (c), the new input interface allows users to provide open-ended descriptions for arbitrary image regions, such as precisely placing a "brown glazed chocolate donut" in a specific area. + +To this end, we propose ReCo (Region-Controlled T2I) that extends pre-trained T2I models to understand spatial coordinate inputs. The core idea is to introduce an extra set of input position tokens to indicate the spatial positions. The image width/height is quantized uniformly into $N_{\mathrm{bins}}$ bins. Then, any float-valued coordinate can be approximated and tokenized by the nearest bin. With an extra embedding matrix $(E_P)$ , the position token can be mapped onto the same space as the text token. Instead of designing a text-only query with positional words "in the top red donut" as in Figure 2 (a), ReCo takes region-controlled text inputs $\langle x_1\rangle ,\langle y_1\rangle ,\langle x_2\rangle ,\langle y_2\rangle$ red donut," where $\langle x\rangle ,\langle y\rangle$ are the position tokens followed by the corresponding freeform text description. We then fine-tune a pre-trained T2I model with $E_P$ to generate the image from the extended input query. To best preserve the pre-trained T2I capability, ReCo training is designed to be similar to the T2I pretraining, i.e., introducing minimal extra model parameters $(E_P)$ , jointly encoding position and text tokens with the text encoder, and prefixing the image description before the extended regional descriptions in the input query. + +Figure 1 visualizes ReCo's use cases and capabilities. As + +![](images/db69a076f6754db5ca313be3e2496accc8f8d828c4679e6bb4ef863f301fdf31.jpg) +Figure 2. (a) With positional words (e.g., bottom/top/left/right and large/small/tall/long), the T2I model (Stable Diffusion [34]) does not manage to create objects with desired properties. (b) Layout-to-image generation [22, 34, 38, 49] takes all object boxes and labels as the input condition, but only works well with constrained object labels. (c) Our ReCo model synergically combines the text and box referring, allowing users to specify an open-ended regional text description precisely at any image region. + +shown in Figure 1 (a), ReCo could reliably follow the input spatial constraints and generate the most plausible images by automatically adjusting object statues, such as the view (front/side) and type (single-/double-deck) of the "bus." Position tokens also allow the user to provide free-form regional descriptions, such as "an orange cat wearing a red hat" at a specific location. Furthermore, we empirically observe that position tokens are less likely to get overlooked or misunderstood than text words. As shown in Figure 1 (b), ReCo has better control over object count, spatial relationship, and size properties, especially when the query is long and complicated, or describes a scene that is less common in real life. In contrast, T2I models [34] may struggle with generating scenes with correct object counts ("ten"), relationships ("boat below traffic light"), relative sizes ("chair larger than airplane"), and camera views ("zoomed out"). + +To evaluate the region control, we design a comprehensive experiment benchmark based on a pre-trained regional object classifier and an object detector. The object classifier is applied on the generated image regions, while the detector is applied on the whole image. A higher accuracy means a better alignment between the generated object layout and the region positions in user queries. On the COCO dataset [24], ReCo shows a better object classification accuracy $(42.02\% \rightarrow 62.42\%)$ and detector averaged precision $(2.3 \rightarrow 32.0)$ , compared with the T2I model with carefully designed positional words. For image generation quality, ReCo improves the FID from 8.82 to 7.36, and SceneFID from 15.54 to 6.51. Furthermore, human evaluations on PaintSkill [5] show $+19.28\%$ and $+17.21\%$ accuracy gain in more correctly generating the query-described object count and spatial relationship, indicating ReCo's capability in helping T2I models to generate challenging scenes. + +Our contributions are summarized as follows. + +- We propose ReCo that extends pre-trained T2I models to understand coordinate inputs. Thanks to the introduced position tokens in the region-controlled input query, users can easily specify free-form regional descriptions in arbitrary image regions. +- We instantiate ReCo based on Stable Diffusion. Extensive experiments show that ReCo strictly follows the regional instructions from the input query, and also generates higher-fidelity images. +- We design a comprehensive evaluation benchmark to validate ReCo's region-controlled T2I generation capability. ReCo significantly improves both the region control accuracy and the image generation quality over a wide range of datasets and designed prompts. + +# 2. Related Work + +Text-to-image generation. Text-to-image (T2I) generation aims to generate a high-fidelity image based on an open-ended image description. Early studies adopt conditional GANs [33, 42, 46-48] for T2I generation. Recent studies have made tremendous advances by scaling up both the data and model size, based on either auto-regressive [10, 45] or diffusion-based models [31, 34, 36]. We build our study on top of the successful large-scale pre-trained T2I models, and explore how to better control the T2I generation by extending a pre-trained T2I model to understand position tokens. + +Layout-to-image generation. Layout-to-image studies aim to generate an image from a complete layout, i.e., all bounding boxes and the paired object labels. Early studies [9,22,23,38,49] adopt GAN-based approaches by properly injecting the encoded layout as the input condition. Recent studies successfully apply the layout query as the input condition to the auto-regressive framework [10,44] and diffusion models [7, 34]. Our study is related to the layout-to-image generation as both directions require the model to understand coordinate inputs. The major difference is that our design synergically combines text and box to help T2I generation. Therefore, ReCo can take open-ended regional descriptions and benefit from large-scale T2I pre-training. + +Unifying open-ended text and localization conditions. Previous studies have explored unifying open-ended text descriptions with localization referring (box, mask, mouse trace) as the input generation condition. One modeling approach [8, 10, 14, 17, 20, 28, 33] is to separately encode the image description in T2I and the layout condition in layout-to-image, and trains a model to jointly condition on both input types. TRECS [19] takes mouse traces in the localized narratives dataset [29] to better ground open-ended text descriptions with a localized position. Other than taking layout as user-generated inputs, previous studies [16, 21] have also explored predicting layout from text to ease the T2I generation of complex scenes. Unlike the motivation + +of training another conditional generation model parallel to T2I and layout-to-image, we explore how to effectively extend pre-trained T2I models to understand region queries, leading to significantly better controllability and generation quality than training from scratch. In short, we position ReCo as an improvement for T2I by providing a more flexible input interface and alleviating controllability issues, e.g., being difficult to override data prior when generating unusual scenes, and overlooking words in complex queries. + +# 3. ReCo Model + +Region-Controlled T2I Generation (ReCo) extends T2I models with the ability to understand coordinate inputs. The core idea is to design a unified input token vocabulary containing both text words and position tokens to allow accurate and open-ended regional control. By seamlessly mixing text and position tokens in the input query, ReCo obtains the best from the two worlds of text-to-image and layout-to-image, i.e., the abilities of free-form description and precise position control. In this section, we present our ReCo implementation based on the open-sourced Stable Diffusion (SD) [34]. We start with the SD preliminaries in Section 3.1 and introduce the core ReCo design in Section 3.2. + +# 3.1. Preliminaries + +We take Stable Diffusion as an example to introduce the T2I model that ReCo is built upon. Stable Diffusion is developed upon the Latent Diffusion Model [34], and consists of an auto-encoder, a U-Net [35] for noise estimation, and a CLIP ViT-L/14 text encoder. For the auto-encoder, the encoder $\mathcal{E}$ with a down-sampling factor of 8 encodes the image $x$ into a latent representation $z = \mathcal{E}(x)$ that the diffusion process operates on, and the decoder $\mathcal{D}$ reconstructs the image $\hat{x} = \mathcal{D}(z)$ from the latent $z$ . U-Net [35] is conditioned on denoising timestep $t$ and text condition $\tau_{\theta}(y(T))$ , where $y(T)$ is the input text query with text tokens $T$ and $\tau_{\theta}$ is the CLIP ViT-L/14 text encoder [30] that projects a sequence of tokenized texts into the sequence embedding. + +The core motivation of ReCo is to explore more effective and interaction-friendly conditioning signals $y$ , while best preserving the pre-trained T2I capability. Specifically, ReCo extends text tokens with an extra vocabulary specialized for spatial coordinate referring, i.e., position tokens $P$ which can be seamlessly used together with text tokens $T$ in a single input query $y$ . ReCo aims to show the benefit of synergetically combining text and position conditions for region-controlled T2I generation. + +# 3.2. Region-Controlled T2I Generation + +ReCo input sequence. The text input in T2I generation provides a natural way of specifying the generation condition. However, text words may be ambiguous and verbose in providing regional specifications. For a better input + +![](images/d728d458dcd11621f39a1d00586a828569e11c33e84dcb2a2b9632a3f6ee1c84.jpg) +Figure 3. ReCo extends Stable Diffusion [34] with position tokens $P$ to support open-ended text description at both image- and region-level. We minimize the amount of introduced new model parameters (i.e., position token embedding $E_P$ ) to best preserve the pre-trained T2I capability. The diffusion model and text encoder are fine-tuned together to support the extended position token inputs. + +![](images/53ec5439ab47e3a2e10d4ac64fd35b2a5c1d716eb34452bf807933c3ef48d674.jpg) + +query, ReCo introduces position tokens that can directly refer to a spatial position. Specifically, the position and size of each region can be represented by four floating numbers, i.e., top-left and bottom-right coordinates. By quantizing coordinates [3, 41, 43], we can represent the region by four discrete position tokens $P$ , $$ , $$ , $$ , $$ , arranged as a sequence similar to a short natural language sentence. The left side of Figure 3 illustrates the ReCo input sequence design. Same as T2I, we start the input query with the image description to make the best use of largescale T2I pre-training. The image description is followed by multiple region-controlled texts, i.e., the four position tokens and the corresponding open-ended regional description. The number of regional specifications is unlimited, allowing users to easily create complex scenes with more regions, or save time on composing input queries with fewer or even no regions. ReCo introduces position token embedding $E_{P} \in \mathbb{R}^{N_{\mathrm{bins}} \times D}$ alongside the pre-trained text word embedding, where $N_{\mathrm{bins}}$ is the number of the position tokens, and $D$ is the token embedding dimension. The entire sequence is then processed jointly, and each token, either text or spatial, is projected into a $D$ -dim token embedding $e$ . The pre-trained CLIP text encoder from Stable Diffusion takes the token embeddings in, and projects them as the sequence embedding that the diffusion model conditions on. + +ReCo fine-tuning. ReCo extends the text-only query $y(T)$ with text tokens $T$ into ReCo input query $y(P, T)$ that combines the text word $T$ and position token $P$ . We fine-tune the Stable Diffusion with the same latent diffusion modeling objective [34], following the notations in Section 3.1: + +$$ +L = \mathbb {E} _ {\mathcal {E} (x), y (P, T), \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (z _ {t}, t, \tau_ {\theta} (y (P, T))) \| _ {2} ^ {2} \right], +$$ + +where $\epsilon_{\theta}$ and $\tau_{\theta}$ are the fine-tuned network modules. All model parameters except position token embedding $E_{P}$ are initiated from the pre-trained Stable Diffusion model. Both the image description and several regional descriptions are + +required for ReCo model fine-tuning. For the training data, we run a state-of-the-part captioning model [40] on the cropped image regions (following the annotated bounding boxes) to get the regional descriptions. During fine-tuning, we resize the image with the short edge to 512 and randomly crop a square region as the input image $x$ . We will release the generated data and fine-tuned model for reproduction. + +We empirically observe that ReCo can well understand the introduced position tokens and precisely place objects at arbitrary specified regions. Furthermore, we find that position tokens can also help ReCo better model long input sequences that contain multiple detailed attribute descriptions, leading to fewer detailed descriptions being neglected or incorrectly generated than the text-only query. By introducing position tokens with a minimal change to the pre-trained T2I model, ReCo obtains the desired region controllability while best preserving the appealing T2I capability. + +# 4. Experiments + +# 4.1. Experiment Settings + +ReCo takes region-controlled inputs specified by the users. However, gathering sufficient real user queries paired with images for quantitative evaluations may be challenging. Therefore, in addition to the arbitrarily-shaped boxes from PaintSkill [5] and manually designed challenging queries in Figure 7, we also include in-domain boxes from COCO [4] and LVIS [11] to construct evaluation queries. + +Datasets. We quantitatively evaluate ReCo on COCO [4, 24], PaintSkill [5], and LVIS [11]. For input queries, we take image descriptions and boxes from the datasets [5,11, 24] and generate regional descriptions with GIT [40]. For COCO [4, 24], we follow the established T2I setting [32, 41, 45] that reports the results on a subset of 30,000 captions sampled from the COCO 2014 val set. We fine-tune stable diffusion with image-text pairs from the COCO 2014 + +
MethodImage Descr.Region Descr.Region PositionRegion Control Metrics (↑)Image Quality Metrics
AP\( AP_{50} \)Object Acc.SceneFID (↓)FID (↓)
Real Images---36.856.171.41--
SD V1.4 Zero-shot✓--0.72.026.7535.8013.40
✓✓-0.72.027.6434.7213.88
✓✓Text0.61.828.1532.8614.57
SD COCO Fine-tune:
ReCoImage Descr.✓--0.92.629.1227.7810.44
ReCoRegion Descr.✓✓-1.02.932.3224.889.11
ReCoPosition Word✓✓Text2.37.542.0215.548.82
ReCo✓✓✓32.052.462.426.517.36
+ +Table 1. Region control accuracy and image generation quality evaluations on the COCO (2014) 30k validation subset [24, 32, 41, 45]. + +GT reference + +SD T21 Finetune + +Ours + +![](images/712f14a1c3b51edbe1c702cb79c05c3db93ed111996bbec0a52de07f4ba226fc.jpg) +five birds nestled together on a tree branch sleeping. +<769><242><999><639> a black and white bird with a blue beak and a white neck. <0><293> ... + +![](images/e24fdf422a13e3964b5baa310e6dbbe2e5ba49ac725932024b1bf9b327987f2e.jpg) + +![](images/31f4bf8a194b2631a6a5f211a035e3b82bd50942c35a18fd2bd990aed0ef746d.jpg) + +![](images/c2aacb6a3d02f170dd81cd881de077f6409c126484fa66c053c87f0df2aa4b10.jpg) +two bicyclists sitting on a bench with a forest background. +<607><715><738><817>a helmet on a person's head. +<260><802><820><944>a wooden bench .... + +![](images/48f1659111d169ecf6a9ce6ff1f3501bf1f34fd642618c78f3bd58f8c5033e9b.jpg) +(a) Counting, Relationship + +![](images/0359a0b2fa6c956788ba5f8be6eda3d4b6398de5a1187c4d04b43a34c26f473b.jpg) + +GT reference + +SD T21 Finetune + +Ours + +![](images/3350a18fb73d0b9897a74885dd11b722750025591396c281fa01a71f2566288f.jpg) +a cat rubbing up against the camera persons legs. <186> <58> <646> <798> a gray cat is resting on the leg of a person. <719> <320> <727> <339> person wearing ... + +![](images/cada04b8b49c89c1add2809a98b81a2b1d173eb34252db54cf996d76d22b6291.jpg) + +![](images/c3ad0b55897f95c59e9ec6fb85f2e8d69cf929bc42eba75948bf5897d574aaf8.jpg) + +![](images/143903b1c55709de44c94ccf20447ab14c26e969df2a8b84521e8ff80bc65e9a.jpg) +(b) Camera View +Figure 4. Qualitative results on COCO [24]. ReCo's extra regional control (shown in the dark blue color) can improve T2I generation on (a) object counting and relationships, (b) images with unique camera views, and (c) images with detailed regional attribute descriptions. + +![](images/42810bd950b050ee0306a1e3ed99b0c49872d7f1b14b03fd302788747d4b704e.jpg) +a snowboard with his snowboard attached to his feet sitting on a slope. $< 0>$ $< 680>$ $< 999>$ $< 889>$ a snowboard on the slope. $< 148>$ $< 170>$ $< 788>$ $< 756>$ a man is ... + +![](images/4717281bb0f37d1044da09ecab5abc8ea52c95607fad5eda0b6568b26a16b299.jpg) + +GT reference + +Ours + +![](images/d3a9a79742900030ada4187eeb9ad15220a185c5d294903840911fb6bc33aabf.jpg) +the clock on the side of the metal building is gold and black. $< 200>$ $< 130>$ $< 903>$ $< 914>$ a clock with roman numerals on it. + +![](images/b89004dd29ff1d96575bf654d8d40f87d1a9b4ab03ebc7f1e77bac3f8a38834f.jpg) + +![](images/4785a623edae4f1eb6cfb8d5f7cd36ef29c1c16b1c5db26be91f31d246816302.jpg) + +![](images/0d13cf6231635e534d6f42e2520e88b35bd50a59d6b782778af6f928150b2fcf.jpg) +a man in a blue shirt riding a blue motorcycle and some people. $< 126>$ $< 43>$ $< 411>$ $< 878>$ a man wearing a blue shirt. $< 0>$ $< 254>$ $< 866>$ $< 864>$ blue motorcycle with .... +(c) Regional Attribute + +![](images/f1f568b5a7e2adab53ba2d24f2764dabd2d269586f6515167338377b352cd25f.jpg) + +![](images/db35eadb7d7d90c3fec066cfd720cbde47644ccaac1d4a80a6bf0cb8e5104c32.jpg) + +train set. PaintSkill [5] evaluates models' capabilities on following arbitrarily-shaped boxes and generating images with the correct object type/count/relationship. We conduct the T2I inference with val set prompts, which contain 1,050/2,520/3,528 queries for object recognition, counting, and spatial relationship skills, respectively. LVIS [11] tests if the model understands open-vocabulary regional descriptions, with the object categories unseen in COCO finetuning. We report the results on the 4,809 LVIS val images [11] from the COCO 2017 val set [18, 49]. We do not fine-tune ReCo when experimenting on PaintSkill and LVIS to test its generalization capability with out-of-domain data. Evaluation metrics. We evaluate ReCo with metrics on region control accuracy and image generation quality. For region control accuracy, we use Object Classification Accuracy [49] and DETR detector Average Precision (AP) [2]. Object accuracy trains a classifier with queried image crops to classify cropped regions on generated images. The generation model should generate objects in specified regions to obtain a high classification accuracy. DETR detector AP detects objects on generated images and compares the results with input object queries. Thus, higher accuracy and AP can indicate a better layout alignment. For image generation quality, we use the Fréchet Inception Distance (FID) [13] to evaluate the image quality. We take SceneFID [39] as an indicator for region-level visual quality, which computes FID on the regions cropped based on input object boxes. We + +compute FID and SceneFID with the Clean-FID repo [27] against center-cropped COCO images. We further conduct human evaluations on PaintSkill, due to the lack of GT images and effective automatic evaluation metrics. + +Implementation details. We fine-tune ReCo from the Stable Diffusion v1.4 checkpoint. We introduce $N = 1000$ position tokens and increase the max length of the text encoder to 616. The batch size is 2048. We use AdamW optimizer [26] with a constant learning rate of $1e^{-4}$ to train the model for 20,000 steps, equivalent to around 100 epochs on COCO 2014 train set. The inference is conducted with 50 PLMS steps [25]. We select a classifier-free guidance scale [15] that gives the best region control performance, i.e., 4.0 for ReCo and 7.5 for original Stable Diffusion, detailed in Section 4.3. We do not use CLIP image re-ranking. + +# 4.2. Region-Controlled T2I Generation Results + +COCO. Table 1 reports the region-controlled T2I generation results on COCO. The first row "real images" provides an oracle reference number on applicable metrics. The top part of the table shows the results obtained with the pretrained Stable Diffusion (SD) model without fine-tuning on COCO, i.e., the zero-shot setting. As shown in the left three columns, we experiment with adding "region description" and "region position" information to the input query in addition to "image description." Since T2I models can not understand coordinates, we carefully design positional text de + +![](images/3a6621d7a94237f26b8a6374cbadc7c510acd31120dce5ba92206bfb119a52ba.jpg) +Figure 5. Qualitative results on PaintSkill [5]. ReCo's extra regional control (shown in the dark blue color) can help T2I models more reliably generate scenes with exact object counts and unusual object relationships/relative sizes. + +![](images/7c49e04424c23c187b529cb9062619c4f00d8024642188dfa54ff044297c2502.jpg) + +scriptions, indicated by "text" in the "region position" column. Specifically, we describe a region with one of the three size words (small, medium, large), three possible region aspect ratios (long, square, tall), and nine possible locations (top left, top, ..., bottom right). We note that the resulting $\mathrm{ReCo}_{\mathrm{Position~Word}}$ serves as a strengthened T2I baseline for reference purposes, and it is unfair to directly compare it with ReCo that understands coordinates. The bottom part compares the main ReCo model with other variants finetuned with the corresponding input queries. The middle three rows report the results on region control accuracy. For AP and $\mathrm{AP}_{50}$ , we use a DETR ResNet-50 object detector trained on COCO [1, 2] to get the detection results on images generated based on the input texts and boxes from the COCO 2017 val5k set [24]. The "object accuracy" column reports the region classification accuracy [49]. The trained ResNet-101 region classifier [12] yields a $71.41\%$ oracle 80-class accuracy on real images. The right two columns report the image generation quality metrics SceneFID a nd FID, which evaluate the region and image visual qualities. + +One advantage of ReCo is its strong region control capability. As shown in the bottom row, ReCo achieves an AP of 32.0, which is close to the real image oracle of 36.8. Despite the careful engineering of positional text words, $\mathrm{ReCo}_{\mathrm{Position~Word}}$ only achieves an AP of 2.3. Similarly, for object region classification, $62.42\%$ of the cropped regions on ReCo-generated images can be correctly classified, compared with $42.02\%$ of $\mathrm{ReCo}_{\mathrm{Position~Word}}$ . ReCo also improves the generated image quality, both at the region and image level. At the region level, ReCo achieves a SceneFID of 6.51, indicating strong capabilities in both generating high-fidelity objects and precisely placing them in the queried position. At the image level, ReCo improves the FID from 10.44 to 7.36 with the region-controlled text input that provides a localized and more detailed image description. We present additional FID comparisons to state-of-the-art conditional image generation methods in Table 5 (c). + +We show representative qualitative results in Figure 4. + +![](images/2c0cdff6d8ccb53fd855e07aaa88871af0e9c54756ac7c2a244ec25987eade86.jpg) + +
MethodSkillObject Accuracy (↑)
ObjectCountSpatialObjectCountSpatial
SD V1.4 Zero-shot97.1159.2848.2035.9722.3213.06
ReCoImage Descr.98.2360.4049.1138.9225.7915.17
ReCOPosition Word93.3368.1064.8750.7225.3522.82
ReCo98.5187.3882.0882.3063.4067.30
+ +Table 2. Evaluations on the images generated with PaintSkill [5] prompts. We evaluate skill correctness with human judges, and object classification accuracy with the COCO-trained classifier. + +(a) ReCo can more reliably generate images that involve counting or complex object relationships, e.g., “five birds” and “sitting on a bench.” (b) ReCo can more easily generate images with unique camera views by controlling the relative position and size of object boxes, e.g., “a top-down view of a cat” that T2I models struggle with. (c) Separating detailed regional descriptions with position tokens also helps ReCo better understand long queries and reduce attribute leakage, e.g., the color of the clock and person’s shirt. + +PaintSkill. Table 2 shows the skill correctness and region control accuracy evaluations on PaintSkill [5]. Skill correctness [5] evaluates if the generated images contain the query-described object type/count/relationship, i.e., the "object," "count," and "spatial" subsets. We use human judges to obtain the skill correctness accuracy. For region control, we use object classification accuracy to evaluate if the model follows those arbitrarily shaped and located object queries. We reuse the COCO region classifier introduced in Table 1. + +Based on the human evaluation for "skill correctness," $87.38\%$ and $82.08\%$ of ReCo-generated images have the correct object count and spatial relationship ("count" and "spatial"), which is $+19.28\%$ and $+17.21\%$ more accurate than $\mathrm{ReCo}_{\mathrm{Position~Word}}$ , and $+26.98\%$ and $+32.97\%$ higher than the T2I model with image description only. The skill correctness improvements suggest that region-control text inputs could be an effective interface to help T2I models more reliably generate user-specified scenes. The object accuracy evaluation makes the criteria more strict by requiring the model to follow the exact input region positions, in ad + +![](images/941a6f32fb41224b5e25a0f19ae7fd298e019cab86602a0407156c87558e518d.jpg) + +![](images/d288a72c84d0760eb9de50de19cda858cda1632d256f2f4529aae2168cf947f7.jpg) + +![](images/49222f6e37dfac2cff99e64a490cdb327c6e35ba0859bad3bec32b64e64cb950.jpg) + +![](images/0cfe1b390e2b1da7a2ae28eff86986513ebe04202ab3c49732a483576d193b17.jpg) + +![](images/8cdfedcd8f7858502c2c746c607b94fabdc60d462a2dcffe35b2a84bcf78ad16.jpg) +lovesea +(a) a living room that has a bunch of different couches. <816> <140> <999> <607> white curtain is shown in a room. <622> <642> ... +Figure 6. Qualitative results on LVIS [11]. ReCo can understand open-vocabulary regional descriptions, including keywords such as "curtain," "ferris wheel," "sausage," and "salt shaker." + +![](images/cd240413cd1a90086205780acc43049acced89a442abde2311db0182e7490149.jpg) +(b) there are two large boats that are in the water. $\langle 80\rangle < 0 > < 196>$ $< 354>$ a ferris wheel is the sky with a black background. $< 676>\dots$ + +![](images/537e083a6041a685ae799eff203debff4ac8662efe5c96d7271f15a249021679.jpg) +(c) a lunch bowl with bread, sausage, tomato, and egg. $< 450>$ $< 267>$ $< 692>$ $< 567>$ a close up of a sausage and tomato. $< 550>$ $< 459>$ ... + +![](images/ee684216779e7ba4faa75bcd44188d2f22c06da90108b037ac5e32360e2f42fb.jpg) +(d) a tray topped with two plates of food and a drink. <383> <653> <496> <836> a clear glass salt shaker <158> <331> <375> <555> ... + +dition to skills. "ReCo" achieves a strong region control accuracy of $63.40\%$ and $67.30\%$ on count and skill subsets, surpassing "ReCoPosition Word" by $+38.05\%$ and $+44.48\%$ . + +PaintSkill contains input queries with randomly assigned object types, locations, and shapes. Because of the minimal constraints, many queries describe challenging scenes that appear less frequently in real life. We observe that ReCo not only precisely follows position queries, but also fits objects and their surroundings naturally, indicating an understanding of object properties. In Figure 5 (a), the three buses with different aspect ratios each have their unique viewing angle and direction, such that the object "bus" fits tightly with the given region. More interestingly, the directions of each bus go nicely with the road, making the image look real to humans. Figure 5 (b) shows challenging cases that require drawing two less commonly co-occurred objects into the same image. ReCo correctly fits "bed" and "fire hydrant," "boat" and "bus" into the given region. More impressively, ReCo can create a scene that makes the generated image look plausible, e.g., "looking through a window with a bed indoors," with the commonsense knowledge that "bed" is usually indoor while "fire hydrant" is usually outdoor. The randomly assigned region categories can also lead to objects with unusual relative sizes, e.g., the bag that is larger than the airplane in Figure 5 (c). ReCo shows an understanding of image perspectives by placing smaller objects such as "backpack" and "dog" near the camera position. + +LVIS. Table 3 reports the T2I generation results with out-of-vocabulary regional entities. We observe that ReCo can understand open-vocabulary regional descriptions, by transferring the open-vocab capability learned from large-scale T2I pre-training to regional descriptions. ReCo achieves the best SceneFID and object classification accuracy over the 1,203 LVIS classes of 10.08 and $23.42\%$ . The results show that the ReCo position tokens can be used with open-vocabulary regional descriptions, despite being trained on + +
MethodObject Acc. (↑)SceneFID (↓)FID (↓)
Real Images42.00--
SD V1.4 Zero-shot7.8840.6223.74
ReCoImage Descr.9.8228.9520.87
ReCoRegion Descr.11.0828.1517.96
ReCoPosition Word16.6020.2717.80
ReCo23.4210.0817.73
+ +Table 3. Evaluations on the images generated with the 4,809 LVIS validation samples [11] from COCO val2017. The object classification is conducted over the 1,203 LVIS classes. + +
MethodCOCOLVIS
Acc.SceneFIDFIDAcc.SceneFIDFID
Real Images74.41--42.00--
ReCoOD Label69.708.079.0822.7913.9823.06
ReCo62.426.517.3623.4210.0817.73
+ +Table 4. Analyses on using open-ended texts (ReCo) vs. constrained object labels (ReCoOD Label) as the regional description. + +COCO with 80 object types. Figure 6 shows examples of generating objects that are not annotated in COCO, e.g., "curtain" and "loveseat" in (a), "ferris wheel" and "clock tower" in (b), "sausage" and "tomato" in (c), "salts" in (d). Qualitative results. We next qualitatively show ReCo's other capabilities with manually designed input queries. Figure 1 (a) shows examples of arbitrary object manipulation and regional description control. As shown in the "bus" example, ReCo will automatically adjust the object viewing (from side to front) and type (from single- to double-deck) to reasonably fit the region constraint, indicating the knowledge about object "bus." ReCo can also understand the free-form regional text and generate "cats" in the specified region with different attributes, e.g., "wearing a red hat," "pink," "sleeping," etc. Figure 7 (a) shows an example of generating images with different object counts. ReCo's region control provides a strong tool for generating the exact object count, optionally with extra regional texts describing each object. Figure 7 (b) shows how we can use the box size to control the camera view, e.g., the precise control of the exact zoom-in ratio. Figure 7 (c) presents additional examples of images with unusual object relationships. + +# 4.3. Analysis + +Regional descriptions. Alternative to the open-ended freeform texts, regional descriptions can be object indexes from a constrained category set, as the setup in layout-to-image generation [9, 22, 23, 38, 49]. Table 4 compares ReCo with $\mathrm{ReCo_{OD\_Label}}$ on COCO [24] and LVIS [11]. The leftmost "accuracy" column on COCO shows the major advantage of $\mathrm{ReCo_{OD\_Label}}$ , i.e., when fine-tuned and tested with the same regional object vocabulary, $\mathrm{ReCo_{OD\_Label}}$ is $+7.28\%$ higher in region control accuracy, compared with ReCo. However, the closed-vocabulary OD labels bring two disadvantages. First, the position tokens in $\mathrm{ReCo_{OD\_Label}}$ tend to only work with the seen vocabulary, i.e., the 80 COCO categories. When evaluated on other datasets such as LVIS or + +![](images/751087d87f52c1d0ac96ab46e6f32cbf5d51602e72be526be369b0110f8ee196.jpg) +(a) Regional Description, A box contains {two, five, six, seven, ten, eleven, twelve} donuts with varying types Counting of glazes and toppings. $< 515>$ $< 576>$ $< 742>$ $< 766>$ chocolate donut $< 237>$ $< 518>$ ... + +![](images/d89bdd4a8fc1e685a551b25096f0ed61137989f9174c185b8a26bf48f1668a84.jpg) + +![](images/bbf2223502fbd4dc2820141bb8c488e5eae88dee40c41f99928bd83c9a4e5bcb.jpg) + +![](images/ff4e1fb92369809056f4349e7417ff20ef530b997b6db7b9c1320a2a3ecc6dfc.jpg) + +![](images/ea691e79d8c7474a25499d46437d5ee0836513d4afa43da4dd1960804dec71bb.jpg) + +![](images/e1f9585de3580b16c13c7116963fe6c2d9f653e2ebb894c4beb1520a4c3b7a29.jpg) + +![](images/fc9f15f86beee72afb0f5aefad25d0e58dd628e872b876bab9bfbed68501d59c.jpg) + +![](images/e40535e48ce20f7ed3b525c7dca54aedd8630cee04e9451f8cabef2dad416dc1.jpg) +(b) Camera View + +![](images/7c906369727902013c0715a56a0b79d4c981fa7880463bb861021e9a4ce35da1.jpg) +[foamed in view, view, zoomed out view] of a man riding a horse through rural entry side. $< 546>$ $< 621>$ $< 885>$ $< 861>$ brown horse $< 654>$ $< 563>$ ... + +![](images/900441790bedfc38069103aed19f7e42611cd08e0e139282fa9a27df89213d21.jpg) + +![](images/f5d772412c612a82979196142022676c791d88aaa3b860855a19644caefbf3c2.jpg) + +![](images/346cebd04caa6407cc72a3cc5c18a975a33597d855362d543037859be96097fb.jpg) + +![](images/e2ab5d6a73b5d3efd3b3b9ccecbeb8b0b4c191983fcb333b7a24ebfa620092e5.jpg) + +![](images/01ebb19c98daf84a6bf314f7ff20fff364aac45c91e372e7f5d3e513da4a890f.jpg) + +![](images/86bb28a94c9a14c469390f6bcce8fa8d66190b6ab58620960c581f0f1ce82f3f.jpg) +(c) Relationship +Figure 7. Qualitative results of ReCo-generated images with manually designed challenging input queries. + +![](images/ffd14bd12acbf00e290e5a9402572b58a6b4a08e1a4514f6bffd261f5df56f38.jpg) + +![](images/aee97006d4adb7691bdd3ed4216c0dcf894f810e2e2e28096d7acb6974ec4e09.jpg) + +![](images/ee9a4fb628f31020b6132dc4bb9a48b86f8750915bb2a82acff701da467c4c58.jpg) + +![](images/1748c925dc3409d025b3531ff1afb2fbab3240f5ae540fc64a72a0d4156d7cb1.jpg) + +![](images/24d5e105230c556d3faf2d32966dac0851d51d6e159208541f3df5f785d83b1d.jpg) + +![](images/7f6c6190fa77cbfdedb8b998a507aa5dcb6e03022a7999c2a283f85cda17d85a.jpg) +Input Regional Descriptions +1. chocolate donut with sprinkles + +2. red donut + +3. pink donut with sprinkles + +4.brown glazed chocolate donut + +5.coconut donut + +6. donut with powdered sugar + +7. pink donut + +8.brown donut + +9. white frosted donut + +10. dark vanilla donut + +11. chocolate donut + +12. donut with sprinkles + +![](images/13dd681157ad63afdedb998b554d512bb81e4559021792ffd2795c05182432a0.jpg) + +1. a man in blue shirt + +2.brown horse + +![](images/564385db34bf46570da09ab7f26d2cbd49e50427e6e5faa0f819ce81e89a7b7b.jpg) + +![](images/730a260afaf904143ba91e27bba79f85b75a724558b805befbd50ea287fc28c4.jpg) +(a) Image Quality Metrics +Table 5. (a,b) Analyses of different guidance scales' influences [15] on image quality and region control accuracy. (c) Comparison with previous T2I works on the COCO (2014) validation 30k subset [24, 32, 41, 45]) in the fine-tuned setting. + +![](images/89ec7bb082be14ebcbbf8fc55c55eb4c7f89b5cddb14b1081a215222bb3205f2.jpg) +(b) Region Control Metrics + +
(c) MethodFID (↓)
Random Train Images [10]2.47
Retrieval Baseline [45]6.82
XMC-GAN [46]9.33
CogView2 [6]17.7
LAFITE [50]8.12
Make-A-Scene [10]7.55
Parti [45]3.22
ReCoImage Descr.6.98
ReCoPosition Word5.98
ReCo5.18
+ +open-world use cases, the region control performance drops significantly, as shown in the "accuracy" column on LVIS. Second, $\mathrm{ReCo_{OD}}$ Label only works well with constrained object labels, which fail to provide detailed regional descriptions, such as attributes and object relationships. Therefore, $\mathrm{ReCo_{OD}}$ Label helps less in generating high-fidelity images, with FID 1.72 and 5.33 worse than ReCo on COCO and LVIS. Given the aforementioned limitations, we use the open-ended free-form regional descriptions in ReCo. + +Guidance scale and T2I SOTA comparison. Table 5 (a,b) examines how different classifier-free guidance scales [15] influence region control accuracy and image generation quality on the COCO 2014 val subset [24,32,41,45]. We empirically observe that scale of 1.5 yields the best image quality, and a slightly larger scale of 4.0 provides the best region control performance. Table 5 (c) compares ReCo with the state-of-the-art T2I methods in the finetuned setting. We reduce the guidance scale from the 4.0 in Table 1 to 1.5 for a fair comparison. We do not use any image-text contrastive models for results re-ranking. ReCo achieves an FID of 5.18, compared with 6.98 when we fine-tune Stable Diffusion with COCO T2I data without regional description. ReCo also outperforms the real image retrieval baseline [45] and most prior studies [6,10,46,50]. + +Limitations. Our method has several limitations. First, ReCo might generate lower-quality images when the input query becomes too challenging, e.g., the unusual giant "dog" in Figure 7 (c). Second, for evaluation purposes, we train ReCo on the COCO train set. Despite preserving the open-vocabulary capability shown on LVIS, the generated image style does bias towards COCO. This limitation can potentially be alleviated by conducting the same ReCo finetuning on a small subset of pre-training data [37] used by the same T2I model [34]. We show this ReCo variant in the supplementary material. Finally, ReCo builds upon large-scale pre-trained T2I models such as Stable Diffusion [34] and shares similar possible generation biases. + +# 5. Conclusion + +We have presented ReCo that extends a pre-trained T2I model for region-controlled T2I generation. Our introduced position token allows the precise specification of open-ended regional descriptions on arbitrary image regions, leading to an effective new interface of region-controlled text input. We show that ReCo can help T2I generation in challenging cases, e.g., when the input query is complicated with detailed regional attributes or describes an unusual scene. 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(a) ReCo extends pre-trained text-to-image models (Stable Diffusion [34]) with an extra set of input position tokens (in dark blue color) that represent quantized spatial coordinates. Combining position and text tokens yields the region-controlled text input, which can specify an open-ended regional description precisely for any image region. (b) With the region-controlled text input, ReCo can better control the object count/relationship/size properties and improve the T2I semantic correctness. 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192, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 492, + 192, + 504 + ], + "spans": [ + { + "bbox": [ + 143, + 492, + 192, + 504 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "type": "text", + "content": "Recently, large-scale text-to-image (T2I) models have shown impressive performance in generating high-fidelity images, but with limited controllability, e.g., precisely specifying the content in a specific region with a free-form text description. In this paper, we propose an effective technique for such regional control in T2I generation. We augment T2I models' inputs with an extra set of position tokens, which represent the quantized spatial coordinates. Each region is specified by four position tokens to represent the top-left and bottom-right corners, followed by an open-ended natural language regional description. Then, we fine-tune a pre-trained T2I model with such new input interface. Our model, dubbed as ReCo (Region-Controlled T2I), enables the region control for arbitrary objects described by open-ended regional texts rather than by object labels from a constrained category set. Empirically, ReCo achieves better image quality than the T2I model strengthened by posi" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": "tional words (FID: " + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "inline_equation", + "content": "8.82 \\rightarrow 7.36" + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": ", SceneFID: " + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "inline_equation", + "content": "15.54 \\rightarrow 6.51" + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": " on COCO), together with objects being more accurately placed, amounting to a " + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "inline_equation", + "content": "20.40\\%" + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": " region classification accuracy improvement on COCO. Furthermore, we demonstrate that ReCo can better control the object count, spatial relationship, and region attributes such as color/size, with the free-form regional description. Human evaluation on PaintSkill shows that ReCo is " + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "inline_equation", + "content": "+19.28\\%" + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "inline_equation", + "content": "+17.21\\%" + }, + { + "bbox": [ + 304, + 493, + 547, + 625 + ], + "type": "text", + "content": " more accurate in generating images with correct object count and spatial relationship than the T2I model. Code is available at https://github.com/microsoft/ReCo." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 643, + 387, + 655 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 387, + 655 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 387, + 655 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Text-to-image (T2I) generation aims to generate faithful images based on an input text query that describes the image content. By scaling up the training data and model size, large T2I models [31, 34, 36, 45] have recently shown" + } + ] + } + ], + "index": 37 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "14246" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "remarkable capabilities in generating high-fidelity images. However, the text-only query allows limited controllability, e.g., precisely specifying the content in a specific region. The naive way of using position-related text words, such as \"top left\" and \"bottom right,\" often results in ambiguous and verbose input queries, as shown in Figure 2 (a). Even worse, when the text query becomes long and complicated, or describes an unusual scene, T2I models [31,45] might overlook certain details and rather follow the visual or linguistic training prior. These two factors together make region control difficult. To get the desired image, users usually need to try a large number of paraphrased queries and pick an image that best fits the desired scene. The process known as \"prompt engineering\" is time-consuming and often fails to produce the desired image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 254, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 289, + 445 + ], + "type": "text", + "content": "The desired region-controlled T2I generation is closely related to the layout-to-image generation [7,9,22,23,34,38, 44, 49]. As shown in Figure 2 (b), layout-to-image models take all object bounding boxes with labels from a close set of object vocabulary [24] as inputs. Despite showing promise in region control, they can hardly understand freeform text inputs, nor the region-level combination of open-ended text descriptions and spatial positions. The two input conditions of text and box provide complementary referring capabilities. Instead of separately modeling them as in text-to-image and layout-to-image generations, we study \"region-controlled T2I generation\" that seamlessly combines these two input conditions. As shown in Figure 2 (c), the new input interface allows users to provide open-ended descriptions for arbitrary image regions, such as precisely placing a \"brown glazed chocolate donut\" in a specific area." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": "To this end, we propose ReCo (Region-Controlled T2I) that extends pre-trained T2I models to understand spatial coordinate inputs. The core idea is to introduce an extra set of input position tokens to indicate the spatial positions. The image width/height is quantized uniformly into " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{bins}}" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": " bins. Then, any float-valued coordinate can be approximated and tokenized by the nearest bin. With an extra embedding matrix " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "(E_P)" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": ", the position token can be mapped onto the same space as the text token. Instead of designing a text-only query with positional words \"in the top red donut\" as in Figure 2 (a), ReCo takes region-controlled text inputs " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\langle x_1\\rangle ,\\langle y_1\\rangle ,\\langle x_2\\rangle ,\\langle y_2\\rangle" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": " red donut,\" where " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\langle x\\rangle ,\\langle y\\rangle" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": " are the position tokens followed by the corresponding freeform text description. We then fine-tune a pre-trained T2I model with " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "E_P" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": " to generate the image from the extended input query. To best preserve the pre-trained T2I capability, ReCo training is designed to be similar to the T2I pretraining, i.e., introducing minimal extra model parameters " + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "inline_equation", + "content": "(E_P)" + }, + { + "bbox": [ + 46, + 448, + 289, + 700 + ], + "type": "text", + "content": ", jointly encoding position and text tokens with the text encoder, and prefixing the image description before the extended regional descriptions in the input query." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Figure 1 visualizes ReCo's use cases and capabilities. As" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 545, + 209 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 545, + 209 + ], + "type": "image", + "image_path": "db69a076f6754db5ca313be3e2496accc8f8d828c4679e6bb4ef863f301fdf31.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 210, + 547, + 299 + ], + "lines": [ + { + "bbox": [ + 304, + 210, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 547, + 299 + ], + "type": "text", + "content": "Figure 2. (a) With positional words (e.g., bottom/top/left/right and large/small/tall/long), the T2I model (Stable Diffusion [34]) does not manage to create objects with desired properties. (b) Layout-to-image generation [22, 34, 38, 49] takes all object boxes and labels as the input condition, but only works well with constrained object labels. (c) Our ReCo model synergically combines the text and box referring, allowing users to specify an open-ended regional text description precisely at any image region." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 305, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 545, + 497 + ], + "type": "text", + "content": "shown in Figure 1 (a), ReCo could reliably follow the input spatial constraints and generate the most plausible images by automatically adjusting object statues, such as the view (front/side) and type (single-/double-deck) of the \"bus.\" Position tokens also allow the user to provide free-form regional descriptions, such as \"an orange cat wearing a red hat\" at a specific location. Furthermore, we empirically observe that position tokens are less likely to get overlooked or misunderstood than text words. As shown in Figure 1 (b), ReCo has better control over object count, spatial relationship, and size properties, especially when the query is long and complicated, or describes a scene that is less common in real life. In contrast, T2I models [34] may struggle with generating scenes with correct object counts (\"ten\"), relationships (\"boat below traffic light\"), relative sizes (\"chair larger than airplane\"), and camera views (\"zoomed out\")." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "content": "To evaluate the region control, we design a comprehensive experiment benchmark based on a pre-trained regional object classifier and an object detector. The object classifier is applied on the generated image regions, while the detector is applied on the whole image. A higher accuracy means a better alignment between the generated object layout and the region positions in user queries. On the COCO dataset [24], ReCo shows a better object classification accuracy " + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "inline_equation", + "content": "(42.02\\% \\rightarrow 62.42\\%)" + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "content": " and detector averaged precision " + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "inline_equation", + "content": "(2.3 \\rightarrow 32.0)" + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "content": ", compared with the T2I model with carefully designed positional words. For image generation quality, ReCo improves the FID from 8.82 to 7.36, and SceneFID from 15.54 to 6.51. Furthermore, human evaluations on PaintSkill [5] show " + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "inline_equation", + "content": "+19.28\\%" + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "inline_equation", + "content": "+17.21\\%" + }, + { + "bbox": [ + 304, + 498, + 546, + 700 + ], + "type": "text", + "content": " accuracy gain in more correctly generating the query-described object count and spatial relationship, indicating ReCo's capability in helping T2I models to generate challenging scenes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 701, + 503, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 503, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 503, + 712 + ], + "type": "text", + "content": "Our contributions are summarized as follows." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "14247" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 245 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 72, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 286, + 133 + ], + "type": "text", + "content": "- We propose ReCo that extends pre-trained T2I models to understand coordinate inputs. Thanks to the introduced position tokens in the region-controlled input query, users can easily specify free-form regional descriptions in arbitrary image regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 135, + 286, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 135, + 286, + 183 + ], + "spans": [ + { + "bbox": [ + 59, + 135, + 286, + 183 + ], + "type": "text", + "content": "- We instantiate ReCo based on Stable Diffusion. Extensive experiments show that ReCo strictly follows the regional instructions from the input query, and also generates higher-fidelity images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 186, + 286, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 186, + 286, + 245 + ], + "spans": [ + { + "bbox": [ + 59, + 186, + 286, + 245 + ], + "type": "text", + "content": "- We design a comprehensive evaluation benchmark to validate ReCo's region-controlled T2I generation capability. ReCo significantly improves both the region control accuracy and the image generation quality over a wide range of datasets and designed prompts." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 256, + 133, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 133, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 133, + 269 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 277, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 286, + 396 + ], + "type": "text", + "content": "Text-to-image generation. Text-to-image (T2I) generation aims to generate a high-fidelity image based on an open-ended image description. Early studies adopt conditional GANs [33, 42, 46-48] for T2I generation. Recent studies have made tremendous advances by scaling up both the data and model size, based on either auto-regressive [10, 45] or diffusion-based models [31, 34, 36]. We build our study on top of the successful large-scale pre-trained T2I models, and explore how to better control the T2I generation by extending a pre-trained T2I model to understand position tokens." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 286, + 555 + ], + "type": "text", + "content": "Layout-to-image generation. Layout-to-image studies aim to generate an image from a complete layout, i.e., all bounding boxes and the paired object labels. Early studies [9,22,23,38,49] adopt GAN-based approaches by properly injecting the encoded layout as the input condition. Recent studies successfully apply the layout query as the input condition to the auto-regressive framework [10,44] and diffusion models [7, 34]. Our study is related to the layout-to-image generation as both directions require the model to understand coordinate inputs. The major difference is that our design synergically combines text and box to help T2I generation. Therefore, ReCo can take open-ended regional descriptions and benefit from large-scale T2I pre-training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": "Unifying open-ended text and localization conditions. Previous studies have explored unifying open-ended text descriptions with localization referring (box, mask, mouse trace) as the input generation condition. One modeling approach [8, 10, 14, 17, 20, 28, 33] is to separately encode the image description in T2I and the layout condition in layout-to-image, and trains a model to jointly condition on both input types. TRECS [19] takes mouse traces in the localized narratives dataset [29] to better ground open-ended text descriptions with a localized position. Other than taking layout as user-generated inputs, previous studies [16, 21] have also explored predicting layout from text to ease the T2I generation of complex scenes. Unlike the motivation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "of training another conditional generation model parallel to T2I and layout-to-image, we explore how to effectively extend pre-trained T2I models to understand region queries, leading to significantly better controllability and generation quality than training from scratch. In short, we position ReCo as an improvement for T2I by providing a more flexible input interface and alleviating controllability issues, e.g., being difficult to override data prior when generating unusual scenes, and overlooking words in complex queries." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 189, + 385, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 189, + 385, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 189, + 385, + 201 + ], + "type": "text", + "content": "3. ReCo Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 209, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 353 + ], + "type": "text", + "content": "Region-Controlled T2I Generation (ReCo) extends T2I models with the ability to understand coordinate inputs. The core idea is to design a unified input token vocabulary containing both text words and position tokens to allow accurate and open-ended regional control. By seamlessly mixing text and position tokens in the input query, ReCo obtains the best from the two worlds of text-to-image and layout-to-image, i.e., the abilities of free-form description and precise position control. In this section, we present our ReCo implementation based on the open-sourced Stable Diffusion (SD) [34]. We start with the SD preliminaries in Section 3.1 and introduce the core ReCo design in Section 3.2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 359, + 391, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 359, + 391, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 359, + 391, + 371 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": "We take Stable Diffusion as an example to introduce the T2I model that ReCo is built upon. Stable Diffusion is developed upon the Latent Diffusion Model [34], and consists of an auto-encoder, a U-Net [35] for noise estimation, and a CLIP ViT-L/14 text encoder. For the auto-encoder, the encoder " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " with a down-sampling factor of 8 encodes the image " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " into a latent representation " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "z = \\mathcal{E}(x)" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " that the diffusion process operates on, and the decoder " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " reconstructs the image " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\hat{x} = \\mathcal{D}(z)" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " from the latent " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": ". U-Net [35] is conditioned on denoising timestep " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " and text condition " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}(y(T))" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "y(T)" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " is the input text query with text tokens " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 304, + 377, + 545, + 533 + ], + "type": "text", + "content": " is the CLIP ViT-L/14 text encoder [30] that projects a sequence of tokenized texts into the sequence embedding." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": "The core motivation of ReCo is to explore more effective and interaction-friendly conditioning signals " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": ", while best preserving the pre-trained T2I capability. Specifically, ReCo extends text tokens with an extra vocabulary specialized for spatial coordinate referring, i.e., position tokens " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": " which can be seamlessly used together with text tokens " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": " in a single input query " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": ". ReCo aims to show the benefit of synergetically combining text and position conditions for region-controlled T2I generation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 647, + 491, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 491, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 491, + 659 + ], + "type": "text", + "content": "3.2. Region-Controlled T2I Generation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "ReCo input sequence. The text input in T2I generation provides a natural way of specifying the generation condition. However, text words may be ambiguous and verbose in providing regional specifications. For a better input" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "14248" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 64, + 211, + 232 + ], + "blocks": [ + { + "bbox": [ + 63, + 64, + 211, + 232 + ], + "lines": [ + { + "bbox": [ + 63, + 64, + 211, + 232 + ], + "spans": [ + { + "bbox": [ + 63, + 64, + 211, + 232 + ], + "type": "image", + "image_path": "d728d458dcd11621f39a1d00586a828569e11c33e84dcb2a2b9632a3f6ee1c84.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "type": "text", + "content": "Figure 3. ReCo extends Stable Diffusion [34] with position tokens " + }, + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "type": "text", + "content": " to support open-ended text description at both image- and region-level. We minimize the amount of introduced new model parameters (i.e., position token embedding " + }, + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "type": "inline_equation", + "content": "E_P" + }, + { + "bbox": [ + 46, + 236, + 547, + 270 + ], + "type": "text", + "content": ") to best preserve the pre-trained T2I capability. The diffusion model and text encoder are fine-tuned together to support the extended position token inputs." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 233, + 64, + 532, + 234 + ], + "blocks": [ + { + "bbox": [ + 233, + 64, + 532, + 234 + ], + "lines": [ + { + "bbox": [ + 233, + 64, + 532, + 234 + ], + "spans": [ + { + "bbox": [ + 233, + 64, + 532, + 234 + ], + "type": "image", + "image_path": "53ec5439ab47e3a2e10d4ac64fd35b2a5c1d716eb34452bf807933c3ef48d674.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": "query, ReCo introduces position tokens that can directly refer to a spatial position. Specifically, the position and size of each region can be represented by four floating numbers, i.e., top-left and bottom-right coordinates. By quantizing coordinates [3, 41, 43], we can represent the region by four discrete position tokens " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ", arranged as a sequence similar to a short natural language sentence. The left side of Figure 3 illustrates the ReCo input sequence design. Same as T2I, we start the input query with the image description to make the best use of largescale T2I pre-training. The image description is followed by multiple region-controlled texts, i.e., the four position tokens and the corresponding open-ended regional description. The number of regional specifications is unlimited, allowing users to easily create complex scenes with more regions, or save time on composing input queries with fewer or even no regions. ReCo introduces position token embedding " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "E_{P} \\in \\mathbb{R}^{N_{\\mathrm{bins}} \\times D}" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": " alongside the pre-trained text word embedding, where " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{bins}}" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": " is the number of the position tokens, and " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": " is the token embedding dimension. The entire sequence is then processed jointly, and each token, either text or spatial, is projected into a " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": "-dim token embedding " + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 278, + 289, + 577 + ], + "type": "text", + "content": ". The pre-trained CLIP text encoder from Stable Diffusion takes the token embeddings in, and projects them as the sequence embedding that the diffusion model conditions on." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": "ReCo fine-tuning. ReCo extends the text-only query " + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "inline_equation", + "content": "y(T)" + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": " with text tokens " + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": " into ReCo input query " + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "inline_equation", + "content": "y(P, T)" + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": " that combines the text word " + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": " and position token " + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 579, + 288, + 640 + ], + "type": "text", + "content": ". We fine-tune the Stable Diffusion with the same latent diffusion modeling objective [34], following the notations in Section 3.1:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 645, + 291, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 291, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 291, + 662 + ], + "type": "interline_equation", + "content": "L = \\mathbb {E} _ {\\mathcal {E} (x), y (P, T), \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, \\tau_ {\\theta} (y (P, T))) \\| _ {2} ^ {2} \\right],", + "image_path": "a0d4fd5e9e22675fb119a025b93ff5b4983c2c58577afe7d72d15f9b8b88a3db.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " are the fine-tuned network modules. All model parameters except position token embedding " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "E_{P}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " are initiated from the pre-trained Stable Diffusion model. Both the image description and several regional descriptions are" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "text", + "content": "required for ReCo model fine-tuning. For the training data, we run a state-of-the-part captioning model [40] on the cropped image regions (following the annotated bounding boxes) to get the regional descriptions. During fine-tuning, we resize the image with the short edge to 512 and randomly crop a square region as the input image " + }, + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "text", + "content": ". We will release the generated data and fine-tuned model for reproduction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 362, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 546, + 483 + ], + "type": "text", + "content": "We empirically observe that ReCo can well understand the introduced position tokens and precisely place objects at arbitrary specified regions. Furthermore, we find that position tokens can also help ReCo better model long input sequences that contain multiple detailed attribute descriptions, leading to fewer detailed descriptions being neglected or incorrectly generated than the text-only query. By introducing position tokens with a minimal change to the pre-trained T2I model, ReCo obtains the desired region controllability while best preserving the appealing T2I capability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 515, + 424, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 424, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 424, + 528 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 616 + ], + "type": "text", + "content": "ReCo takes region-controlled inputs specified by the users. However, gathering sufficient real user queries paired with images for quantitative evaluations may be challenging. Therefore, in addition to the arbitrarily-shaped boxes from PaintSkill [5] and manually designed challenging queries in Figure 7, we also include in-domain boxes from COCO [4] and LVIS [11] to construct evaluation queries." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "Datasets. We quantitatively evaluate ReCo on COCO [4, 24], PaintSkill [5], and LVIS [11]. For input queries, we take image descriptions and boxes from the datasets [5,11, 24] and generate regional descriptions with GIT [40]. For COCO [4, 24], we follow the established T2I setting [32, 41, 45] that reports the results on a subset of 30,000 captions sampled from the COCO 2014 val set. We fine-tune stable diffusion with image-text pairs from the COCO 2014" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "14249" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 64, + 515, + 188 + ], + "blocks": [ + { + "bbox": [ + 77, + 64, + 515, + 188 + ], + "lines": [ + { + "bbox": [ + 77, + 64, + 515, + 188 + ], + "spans": [ + { + "bbox": [ + 77, + 64, + 515, + 188 + ], + "type": "table", + "html": "
MethodImage Descr.Region Descr.Region PositionRegion Control Metrics (↑)Image Quality Metrics
AP\\( AP_{50} \\)Object Acc.SceneFID (↓)FID (↓)
Real Images---36.856.171.41--
SD V1.4 Zero-shot✓--0.72.026.7535.8013.40
✓✓-0.72.027.6434.7213.88
✓✓Text0.61.828.1532.8614.57
SD COCO Fine-tune:
ReCoImage Descr.✓--0.92.629.1227.7810.44
ReCoRegion Descr.✓✓-1.02.932.3224.889.11
ReCoPosition Word✓✓Text2.37.542.0215.548.82
ReCo✓✓✓32.052.462.426.517.36
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PaintSkill [5] evaluates models' capabilities on following arbitrarily-shaped boxes and generating images with the correct object type/count/relationship. We conduct the T2I inference with val set prompts, which contain 1,050/2,520/3,528 queries for object recognition, counting, and spatial relationship skills, respectively. LVIS [11] tests if the model understands open-vocabulary regional descriptions, with the object categories unseen in COCO finetuning. We report the results on the 4,809 LVIS val images [11] from the COCO 2017 val set [18, 49]. We do not fine-tune ReCo when experimenting on PaintSkill and LVIS to test its generalization capability with out-of-domain data. Evaluation metrics. We evaluate ReCo with metrics on region control accuracy and image generation quality. For region control accuracy, we use Object Classification Accuracy [49] and DETR detector Average Precision (AP) [2]. Object accuracy trains a classifier with queried image crops to classify cropped regions on generated images. The generation model should generate objects in specified regions to obtain a high classification accuracy. DETR detector AP detects objects on generated images and compares the results with input object queries. Thus, higher accuracy and AP can indicate a better layout alignment. For image generation quality, we use the Fréchet Inception Distance (FID) [13] to evaluate the image quality. We take SceneFID [39] as an indicator for region-level visual quality, which computes FID on the regions cropped based on input object boxes. We" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 390, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 437 + ], + "type": "text", + "content": "compute FID and SceneFID with the Clean-FID repo [27] against center-cropped COCO images. We further conduct human evaluations on PaintSkill, due to the lack of GT images and effective automatic evaluation metrics." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "text", + "content": "Implementation details. We fine-tune ReCo from the Stable Diffusion v1.4 checkpoint. We introduce " + }, + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "inline_equation", + "content": "N = 1000" + }, + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "text", + "content": " position tokens and increase the max length of the text encoder to 616. The batch size is 2048. We use AdamW optimizer [26] with a constant learning rate of " + }, + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 304, + 438, + 545, + 570 + ], + "type": "text", + "content": " to train the model for 20,000 steps, equivalent to around 100 epochs on COCO 2014 train set. The inference is conducted with 50 PLMS steps [25]. We select a classifier-free guidance scale [15] that gives the best region control performance, i.e., 4.0 for ReCo and 7.5 for original Stable Diffusion, detailed in Section 4.3. We do not use CLIP image re-ranking." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 306, + 575, + 528, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 528, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 528, + 587 + ], + "type": "text", + "content": "4.2. Region-Controlled T2I Generation Results" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "COCO. Table 1 reports the region-controlled T2I generation results on COCO. The first row \"real images\" provides an oracle reference number on applicable metrics. The top part of the table shows the results obtained with the pretrained Stable Diffusion (SD) model without fine-tuning on COCO, i.e., the zero-shot setting. As shown in the left three columns, we experiment with adding \"region description\" and \"region position\" information to the input query in addition to \"image description.\" Since T2I models can not understand coordinates, we carefully design positional text de" + } + ] + } + ], + "index": 42 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "14250" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 64, + 216, + 229 + ], + "blocks": [ + { + "bbox": [ + 61, + 64, + 216, + 229 + ], + "lines": [ + { + "bbox": [ + 61, + 64, + 216, + 229 + ], + "spans": [ + { + "bbox": [ + 61, + 64, + 216, + 229 + ], + "type": "image", + "image_path": "3a6621d7a94237f26b8a6374cbadc7c510acd31120dce5ba92206bfb119a52ba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 229, + 545, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 545, + 251 + ], + "type": "text", + "content": "Figure 5. Qualitative results on PaintSkill [5]. ReCo's extra regional control (shown in the dark blue color) can help T2I models more reliably generate scenes with exact object counts and unusual object relationships/relative sizes." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 220, + 64, + 373, + 228 + ], + "blocks": [ + { + "bbox": [ + 220, + 64, + 373, + 228 + ], + "lines": [ + { + "bbox": [ + 220, + 64, + 373, + 228 + ], + "spans": [ + { + "bbox": [ + 220, + 64, + 373, + 228 + ], + "type": "image", + "image_path": "7c49e04424c23c187b529cb9062619c4f00d8024642188dfa54ff044297c2502.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "text", + "content": "scriptions, indicated by \"text\" in the \"region position\" column. Specifically, we describe a region with one of the three size words (small, medium, large), three possible region aspect ratios (long, square, tall), and nine possible locations (top left, top, ..., bottom right). We note that the resulting " + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo}_{\\mathrm{Position~Word}}" + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "text", + "content": " serves as a strengthened T2I baseline for reference purposes, and it is unfair to directly compare it with ReCo that understands coordinates. The bottom part compares the main ReCo model with other variants finetuned with the corresponding input queries. The middle three rows report the results on region control accuracy. For AP and " + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "text", + "content": ", we use a DETR ResNet-50 object detector trained on COCO [1, 2] to get the detection results on images generated based on the input texts and boxes from the COCO 2017 val5k set [24]. The \"object accuracy\" column reports the region classification accuracy [49]. The trained ResNet-101 region classifier [12] yields a " + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "inline_equation", + "content": "71.41\\%" + }, + { + "bbox": [ + 46, + 256, + 289, + 496 + ], + "type": "text", + "content": " oracle 80-class accuracy on real images. The right two columns report the image generation quality metrics SceneFID a nd FID, which evaluate the region and image visual qualities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "content": "One advantage of ReCo is its strong region control capability. As shown in the bottom row, ReCo achieves an AP of 32.0, which is close to the real image oracle of 36.8. Despite the careful engineering of positional text words, " + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo}_{\\mathrm{Position~Word}}" + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "content": " only achieves an AP of 2.3. Similarly, for object region classification, " + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "inline_equation", + "content": "62.42\\%" + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "content": " of the cropped regions on ReCo-generated images can be correctly classified, compared with " + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "inline_equation", + "content": "42.02\\%" + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo}_{\\mathrm{Position~Word}}" + }, + { + "bbox": [ + 46, + 497, + 289, + 700 + ], + "type": "text", + "content": ". ReCo also improves the generated image quality, both at the region and image level. At the region level, ReCo achieves a SceneFID of 6.51, indicating strong capabilities in both generating high-fidelity objects and precisely placing them in the queried position. At the image level, ReCo improves the FID from 10.44 to 7.36 with the region-controlled text input that provides a localized and more detailed image description. We present additional FID comparisons to state-of-the-art conditional image generation methods in Table 5 (c)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "We show representative qualitative results in Figure 4." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 380, + 64, + 533, + 227 + ], + "blocks": [ + { + "bbox": [ + 380, + 64, + 533, + 227 + ], + "lines": [ + { + "bbox": [ + 380, + 64, + 533, + 227 + ], + "spans": [ + { + "bbox": [ + 380, + 64, + 533, + 227 + ], + "type": "image", + "image_path": "2c0cdff6d8ccb53fd855e07aaa88871af0e9c54756ac7c2a244ec25987eade86.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 255, + 545, + 319 + ], + "blocks": [ + { + "bbox": [ + 306, + 255, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 306, + 255, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 545, + 319 + ], + "type": "table", + "html": "
MethodSkillObject Accuracy (↑)
ObjectCountSpatialObjectCountSpatial
SD V1.4 Zero-shot97.1159.2848.2035.9722.3213.06
ReCoImage Descr.98.2360.4049.1138.9225.7915.17
ReCOPosition Word93.3368.1064.8750.7225.3522.82
ReCo98.5187.3882.0882.3063.4067.30
", + "image_path": "16364da41f9f00fa7ecc1065625afc510c05129e10490ad9eca5b26f2f2962e4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 320, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 305, + 320, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 545, + 353 + ], + "type": "text", + "content": "Table 2. Evaluations on the images generated with PaintSkill [5] prompts. We evaluate skill correctness with human judges, and object classification accuracy with the COCO-trained classifier." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 362, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 545, + 470 + ], + "type": "text", + "content": "(a) ReCo can more reliably generate images that involve counting or complex object relationships, e.g., “five birds” and “sitting on a bench.” (b) ReCo can more easily generate images with unique camera views by controlling the relative position and size of object boxes, e.g., “a top-down view of a cat” that T2I models struggle with. (c) Separating detailed regional descriptions with position tokens also helps ReCo better understand long queries and reduce attribute leakage, e.g., the color of the clock and person’s shirt." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 472, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 579 + ], + "type": "text", + "content": "PaintSkill. Table 2 shows the skill correctness and region control accuracy evaluations on PaintSkill [5]. Skill correctness [5] evaluates if the generated images contain the query-described object type/count/relationship, i.e., the \"object,\" \"count,\" and \"spatial\" subsets. We use human judges to obtain the skill correctness accuracy. For region control, we use object classification accuracy to evaluate if the model follows those arbitrarily shaped and located object queries. We reuse the COCO region classifier introduced in Table 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Based on the human evaluation for \"skill correctness,\" " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "87.38\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "82.08\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " of ReCo-generated images have the correct object count and spatial relationship (\"count\" and \"spatial\"), which is " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "+19.28\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "+17.21\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " more accurate than " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo}_{\\mathrm{Position~Word}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "+26.98\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "+32.97\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " higher than the T2I model with image description only. The skill correctness improvements suggest that region-control text inputs could be an effective interface to help T2I models more reliably generate user-specified scenes. The object accuracy evaluation makes the criteria more strict by requiring the model to follow the exact input region positions, in ad" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "14251" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 108, + 129 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 108, + 129 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 108, + 129 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 108, + 129 + ], + "type": "image", + "image_path": "941a6f32fb41224b5e25a0f19ae7fd298e019cab86602a0407156c87558e518d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 109, + 71, + 166, + 129 + ], + "blocks": [ + { + "bbox": [ + 109, + 71, + 166, + 129 + ], + "lines": [ + { + "bbox": [ + 109, + 71, + 166, + 129 + ], + "spans": [ + { + "bbox": [ + 109, + 71, + 166, + 129 + ], + "type": "image", + "image_path": "d288a72c84d0760eb9de50de19cda858cda1632d256f2f4529aae2168cf947f7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 167, + 72, + 223, + 129 + ], + "blocks": [ + { + "bbox": [ + 167, + 72, + 223, + 129 + ], + "lines": [ + { + "bbox": [ + 167, + 72, + 223, + 129 + ], + "spans": [ + { + "bbox": [ + 167, + 72, + 223, + 129 + ], + "type": "image", + "image_path": "49222f6e37dfac2cff99e64a490cdb327c6e35ba0859bad3bec32b64e64cb950.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 225, + 72, + 282, + 129 + ], + "blocks": [ + { + "bbox": [ + 225, + 72, + 282, + 129 + ], + "lines": [ + { + "bbox": [ + 225, + 72, + 282, + 129 + ], + "spans": [ + { + "bbox": [ + 225, + 72, + 282, + 129 + ], + "type": "image", + "image_path": "0cfe1b390e2b1da7a2ae28eff86986513ebe04202ab3c49732a483576d193b17.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 131, + 108, + 190 + ], + "blocks": [ + { + "bbox": [ + 50, + 131, + 108, + 190 + ], + "lines": [ + { + "bbox": [ + 50, + 131, + 108, + 190 + ], + "spans": [ + { + "bbox": [ + 50, + 131, + 108, + 190 + ], + "type": "image", + "image_path": "8cdfedcd8f7858502c2c746c607b94fabdc60d462a2dcffe35b2a84bcf78ad16.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 190, + 105, + 233 + ], + "lines": [ + { + "bbox": [ + 50, + 190, + 105, + 233 + ], + "spans": [ + { + "bbox": [ + 50, + 190, + 105, + 233 + ], + "type": "text", + "content": "lovesea \n(a) a living room that has a bunch of different couches. <816> <140> <999> <607> white curtain is shown in a room. <622> <642> ..." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 238, + 286, + 270 + ], + "lines": [ + { + "bbox": [ + 47, + 238, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 286, + 270 + ], + "type": "text", + "content": "Figure 6. Qualitative results on LVIS [11]. ReCo can understand open-vocabulary regional descriptions, including keywords such as \"curtain,\" \"ferris wheel,\" \"sausage,\" and \"salt shaker.\"" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 109, + 130, + 166, + 190 + ], + "blocks": [ + { + "bbox": [ + 109, + 130, + 166, + 190 + ], + "lines": [ + { + "bbox": [ + 109, + 130, + 166, + 190 + ], + "spans": [ + { + "bbox": [ + 109, + 130, + 166, + 190 + ], + "type": "image", + "image_path": "cd240413cd1a90086205780acc43049acced89a442abde2311db0182e7490149.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "lines": [ + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "spans": [ + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "type": "text", + "content": "(b) there are two large boats that are in the water. " + }, + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "type": "inline_equation", + "content": "\\langle 80\\rangle < 0 > < 196>" + }, + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "type": "inline_equation", + "content": "< 354>" + }, + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "type": "text", + "content": " a ferris wheel is the sky with a black background. " + }, + { + "bbox": [ + 109, + 194, + 162, + 234 + ], + "type": "inline_equation", + "content": "< 676>\\dots" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 167, + 132, + 224, + 190 + ], + "blocks": [ + { + "bbox": [ + 167, + 132, + 224, + 190 + ], + "lines": [ + { + "bbox": [ + 167, + 132, + 224, + 190 + ], + "spans": [ + { + "bbox": [ + 167, + 132, + 224, + 190 + ], + "type": "image", + "image_path": "537e083a6041a685ae799eff203debff4ac8662efe5c96d7271f15a249021679.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "lines": [ + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "spans": [ + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "text", + "content": "(c) a lunch bowl with bread, sausage, tomato, and egg. " + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "inline_equation", + "content": "< 450>" + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "inline_equation", + "content": "< 267>" + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "inline_equation", + "content": "< 692>" + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "inline_equation", + "content": "< 567>" + }, + { + "bbox": [ + 167, + 194, + 223, + 234 + ], + "type": "text", + "content": " a close up of a sausage and tomato. 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Because of the minimal constraints, many queries describe challenging scenes that appear less frequently in real life. We observe that ReCo not only precisely follows position queries, but also fits objects and their surroundings naturally, indicating an understanding of object properties. In Figure 5 (a), the three buses with different aspect ratios each have their unique viewing angle and direction, such that the object \"bus\" fits tightly with the given region. More interestingly, the directions of each bus go nicely with the road, making the image look real to humans. Figure 5 (b) shows challenging cases that require drawing two less commonly co-occurred objects into the same image. ReCo correctly fits \"bed\" and \"fire hydrant,\" \"boat\" and \"bus\" into the given region. More impressively, ReCo can create a scene that makes the generated image look plausible, e.g., \"looking through a window with a bed indoors,\" with the commonsense knowledge that \"bed\" is usually indoor while \"fire hydrant\" is usually outdoor. The randomly assigned region categories can also lead to objects with unusual relative sizes, e.g., the bag that is larger than the airplane in Figure 5 (c). ReCo shows an understanding of image perspectives by placing smaller objects such as \"backpack\" and \"dog\" near the camera position." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "LVIS. Table 3 reports the T2I generation results with out-of-vocabulary regional entities. We observe that ReCo can understand open-vocabulary regional descriptions, by transferring the open-vocab capability learned from large-scale T2I pre-training to regional descriptions. ReCo achieves the best SceneFID and object classification accuracy over the 1,203 LVIS classes of 10.08 and " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "23.42\\%" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ". The results show that the ReCo position tokens can be used with open-vocabulary regional descriptions, despite being trained on" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 146 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 146 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 146 + ], + "type": "table", + "html": "
MethodObject Acc. (↑)SceneFID (↓)FID (↓)
Real Images42.00--
SD V1.4 Zero-shot7.8840.6223.74
ReCoImage Descr.9.8228.9520.87
ReCoRegion Descr.11.0828.1517.96
ReCoPosition Word16.6020.2717.80
ReCo23.4210.0817.73
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MethodCOCOLVIS
Acc.SceneFIDFIDAcc.SceneFIDFID
Real Images74.41--42.00--
ReCoOD Label69.708.079.0822.7913.9823.06
ReCo62.426.517.3623.4210.0817.73
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Figure 6 shows examples of generating objects that are not annotated in COCO, e.g., \"curtain\" and \"loveseat\" in (a), \"ferris wheel\" and \"clock tower\" in (b), \"sausage\" and \"tomato\" in (c), \"salts\" in (d). Qualitative results. We next qualitatively show ReCo's other capabilities with manually designed input queries. Figure 1 (a) shows examples of arbitrary object manipulation and regional description control. As shown in the \"bus\" example, ReCo will automatically adjust the object viewing (from side to front) and type (from single- to double-deck) to reasonably fit the region constraint, indicating the knowledge about object \"bus.\" ReCo can also understand the free-form regional text and generate \"cats\" in the specified region with different attributes, e.g., \"wearing a red hat,\" \"pink,\" \"sleeping,\" etc. Figure 7 (a) shows an example of generating images with different object counts. ReCo's region control provides a strong tool for generating the exact object count, optionally with extra regional texts describing each object. Figure 7 (b) shows how we can use the box size to control the camera view, e.g., the precise control of the exact zoom-in ratio. Figure 7 (c) presents additional examples of images with unusual object relationships." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 540, + 368, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 368, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 368, + 552 + ], + "type": "text", + "content": "4.3. Analysis" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Regional descriptions. Alternative to the open-ended freeform texts, regional descriptions can be object indexes from a constrained category set, as the setup in layout-to-image generation [9, 22, 23, 38, 49]. Table 4 compares ReCo with " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo_{OD\\_Label}}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " on COCO [24] and LVIS [11]. 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(a,b) Analyses of different guidance scales' influences [15] on image quality and region control accuracy. (c) Comparison with previous T2I works on the COCO (2014) validation 30k subset [24, 32, 41, 45]) in the fine-tuned setting." + } + ] + } + ], + "index": 49, + "angle": 0, + "type": "image_caption" + } + ], + "index": 45 + }, + { + "type": "image", + "bbox": [ + 209, + 290, + 334, + 385 + ], + "blocks": [ + { + "bbox": [ + 231, + 280, + 313, + 289 + ], + "lines": [ + { + "bbox": [ + 231, + 280, + 313, + 289 + ], + "spans": [ + { + "bbox": [ + 231, + 280, + 313, + 289 + ], + "type": "text", + "content": "(b) Region Control Metrics" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 209, + 290, + 334, + 385 + ], + "lines": [ + { + "bbox": [ + 209, + 290, + 334, + 385 + ], + "spans": [ + { + "bbox": [ + 209, + 290, + 334, + 385 + ], + "type": "image", + "image_path": "89ec7bb082be14ebcbbf8fc55c55eb4c7f89b5cddb14b1081a215222bb3205f2.jpg" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_body" + } + ], + "index": 47 + }, + { + "type": "table", + "bbox": [ + 361, + 280, + 496, + 381 + ], + "blocks": [ + { + "bbox": [ + 361, + 280, + 496, + 381 + ], + "lines": [ + { + "bbox": [ + 361, + 280, + 496, + 381 + ], + "spans": [ + { + "bbox": [ + 361, + 280, + 496, + 381 + ], + "type": "table", + "html": "
(c) MethodFID (↓)
Random Train Images [10]2.47
Retrieval Baseline [45]6.82
XMC-GAN [46]9.33
CogView2 [6]17.7
LAFITE [50]8.12
Make-A-Scene [10]7.55
Parti [45]3.22
ReCoImage Descr.6.98
ReCoPosition Word5.98
ReCo5.18
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Therefore, " + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{ReCo_{OD}}" + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "text", + "content": " Label helps less in generating high-fidelity images, with FID 1.72 and 5.33 worse than ReCo on COCO and LVIS. Given the aforementioned limitations, we use the open-ended free-form regional descriptions in ReCo." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": "Guidance scale and T2I SOTA comparison. Table 5 (a,b) examines how different classifier-free guidance scales [15] influence region control accuracy and image generation quality on the COCO 2014 val subset [24,32,41,45]. We empirically observe that scale of 1.5 yields the best image quality, and a slightly larger scale of 4.0 provides the best region control performance. Table 5 (c) compares ReCo with the state-of-the-art T2I methods in the finetuned setting. We reduce the guidance scale from the 4.0 in Table 1 to 1.5 for a fair comparison. We do not use any image-text contrastive models for results re-ranking. ReCo achieves an FID of 5.18, compared with 6.98 when we fine-tune Stable Diffusion with COCO T2I data without regional description. ReCo also outperforms the real image retrieval baseline [45] and most prior studies [6,10,46,50]." + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 418, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 573 + ], + "type": "text", + "content": "Limitations. Our method has several limitations. First, ReCo might generate lower-quality images when the input query becomes too challenging, e.g., the unusual giant \"dog\" in Figure 7 (c). Second, for evaluation purposes, we train ReCo on the COCO train set. Despite preserving the open-vocabulary capability shown on LVIS, the generated image style does bias towards COCO. This limitation can potentially be alleviated by conducting the same ReCo finetuning on a small subset of pre-training data [37] used by the same T2I model [34]. We show this ReCo variant in the supplementary material. Finally, ReCo builds upon large-scale pre-trained T2I models such as Stable Diffusion [34] and shares similar possible generation biases." + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 306, + 576, + 378, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 576, + 378, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 576, + 378, + 587 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 593, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 712 + ], + "type": "text", + "content": "We have presented ReCo that extends a pre-trained T2I model for region-controlled T2I generation. Our introduced position token allows the precise specification of open-ended regional descriptions on arbitrary image regions, leading to an effective new interface of region-controlled text input. We show that ReCo can help T2I generation in challenging cases, e.g., when the input query is complicated with detailed regional attributes or describes an unusual scene. Experiments validate ReCo's effectiveness on both region control accuracy and image generation quality." + } + ] + } + ], + "index": 54 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "14253" + } + ] + } + ], + "index": 55 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17907-17917, 2022. 8" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "text", + "content": "14255" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_content_list.json b/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe2414fb776c3fba436b2aa6b5befed29a06cdd --- /dev/null +++ b/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_content_list.json @@ -0,0 +1,1431 @@ +[ + { + "type": "text", + "text": "ReDirTrans: Latent-to-Latent Translation for Gaze and Head Redirection", + "text_level": 1, + "bbox": [ + 111, + 130, + 857, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shiwei Jin $^{1}$ , Zhen Wang $^{2}$ , Lei Wang $^{2}$ , Ning Bi $^{2}$ , Truong Nguyen $^{1}$", + "bbox": [ + 212, + 179, + 753, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ ECE Dept. UC San Diego, $^{2}$ Qualcomm Technologies, Inc.", + "bbox": [ + 243, + 198, + 723, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sjin，tqn001}@eng.ucsd.edu，{zhewang，wlei，nbi}@qti=qualcomm.com", + "bbox": [ + 191, + 218, + 772, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning-based gaze estimation methods require large amounts of training data with accurate gaze annotations. Facing such demanding requirements of gaze data collection and annotation, several image synthesis methods were proposed, which successfully redirected gaze directions precisely given the assigned conditions. However, these methods focused on changing gaze directions of the images that only include eyes or restricted ranges of faces with low resolution (less than $128 \\times 128$ ) to largely reduce interference from other attributes such as hairs, which limits application scenarios. To cope with this limitation, we proposed a portable network, called ReDirTrans, achieving latent-to-latent translation for redirecting gaze directions and head orientations in an interpretable manner. ReDirTrans projects input latent vectors into aimed-attribute embeddings only and redirects these embeddings with assigned pitch and yaw values. Then both the initial and edited embeddings are projected back (deprojected) to the initial latent space as residuals to modify the input latent vectors by subtraction and addition, representing old status removal and new status addition. The projection of aimed attributes only and subtraction-addition operations for status replacement essentially mitigate impacts on other attributes and the distribution of latent vectors. Thus, by combining ReDirTrans with a pretrained fixed e4e-StyleGAN pair, we created ReDirTrans-GAN, which enables accurately redirecting gaze in full-face images with $1024 \\times 1024$ resolution while preserving other attributes such as identity, expression, and hairstyle. Furthermore, we presented improvements for the downstream learning-based gaze estimation task, using redirected samples as dataset augmentation.", + "bbox": [ + 75, + 300, + 472, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 799, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gaze is a crucial non-verbal cue that conveys attention and awareness in interactions. Its potential applications include mental health assessment [5,18], social attitudes analysis [19], human-computer interaction [12], automotive assistance [30], AR/VR [6,34]. However, developing a robust", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": " unified learning-based gaze estimation model requires large amounts of data from multiple subjects with precise gaze annotations [42, 44]. Collecting and annotating such an appropriate dataset is complex and expensive. To overcome this challenge, several methods have been proposed to redirect gaze directions [17, 39, 41, 42, 44] in real images with assigned directional values to obtain and augment training data. Some works focused on generating eye images with new gaze directions by either 1) estimating warping maps [41, 42] to interpolate pixel values or 2) using encoder-generator pairs to generate redirected eye images [17, 39].", + "bbox": [ + 496, + 268, + 893, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ST-ED [44] was the first work to extend high-accuracy gaze redirection from eye images to face images. By disentangling several attributes, including person-specific appearance, it can explicitly control gaze directions and head orientations. However, due to the design of the encoder-decoder structure and limited ability to maintain appearance features by a $1 \\times 1024$ projected appearance embedding, ST-ED generates low-resolution ( $128 \\times 128$ ) images with restricted face range (no hair area), which narrows the application ranges and scenarios of gaze redirection.", + "bbox": [ + 496, + 439, + 893, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As for latent space manipulation for face editing tasks, large amounts of works [2-4, 14, 31, 35] were proposed to modify latent vectors in predefined latent spaces (W [21], $W^{+}$ [1] and $S$ [40]). Latent vectors in these latent spaces can work with StyleGAN [21, 22] to generate high-quality and high-fidelity face images with desired attribute editing. Among these methods, Wu et.al [40] proposed the latent space $S$ working with StyleGAN, which achieved only one degree-of-freedom gaze redirection by modifying a certain channel of latent vectors in $S$ by an uninterpreted value instead of pitch and yaw values of gaze directions.", + "bbox": [ + 496, + 595, + 895, + 761 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Considering these, we proposed a new method, called ReDirTrans, to achieve latent-to-latent translation for redirecting gaze directions and head orientations in high-resolution full-face images based on assigned directional values. Specifically, we designed a framework to project input latent vectors from a latent space into the aimed-attribute-only embedding space for an interpretable redirection process. This embedding space consists of estimated pseudo conditions and embeddings of aimed attributes,", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5547", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where conditions describe deviations from the canonical status and embeddings are the 'carriers' of the conditions. In this embedding space, all transformations are implemented by rotation matrices multiplication built from pitch and yaw values, which can make the redirection process more interpretable and consistent. After the redirection process, the original embeddings and redirected ones are both decoded back to the initial latent space as the residuals to modify the input latent vectors by subtraction and addition operations. These operations represent removing the old state and adding a new one, respectively. ReDirTrans only focuses on transforming embeddings of aimed attributes and achieves status replacement by the residuals outputted from weight-sharing deprojectors. ReDirTrans does not project or deproject other attributes with information loss; and it does not affect the distribution of input latent vectors. Thus ReDirTrans can also work in a predefined feature space with a fixed pretrained encoder-generator pair for the redirection task in desired-resolution images.", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 96, + 378, + 397, + 393 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A latent-to-latent framework, ReDirTrans, which projects latent vectors to an embedding space for an interpretable redirection process on aimed attributes and maintains other attributes, including appearance, in initial latent space with no information loss caused by projection-deprojection processes.", + "- A portable framework that can seamlessly integrate into a pretrained GAN inversion pipeline for high-accuracy redirection of gaze directions and head orientations, without the need for any parameter tuning of the encoder-generator pairs.", + "- A layer-wise architecture with learnable parameters that works with the fixed pretrained StyleGAN and achieves redirection tasks in high-resolution full-face images through ReDirTrans-GAN." + ], + "bbox": [ + 94, + 397, + 468, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 648, + 227, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gaze and Head Redirection. Methods for redirecting gaze directions can be broadly classified into two categories: warping-based methods and generator-based methods. Deepwarp [13, 23] presented a deep network to learn warping maps between pairs of eye images with different gaze directions, which required large amounts of data with annotations. Yu et al. [41] utilized a pretrained gaze estimator and synthetic eye images to reduce the reliance on annotated real data. Yu et al. [42] further extended the warping-based methods in an unsupervised manner by adding a gaze representation learning network. As for the generator-based methods, He et al. [17] developed a GAN-based network for generating eye images with new gaze directions. FAZE [26] proposed an encoder-decoder architecture to transform eye images into latent vectors for redirection with rotation ma", + "bbox": [ + 76, + 674, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "trix multiplication, and then decode the edited ones back to the synthetic images with new gaze directions. ST-ED [44] further extended the encoder-decoder pipeline from gaze redirection only to both head and gaze redirection over full face images by disentangling latent vectors, and achieving precise redirection performance. However, ST-ED generates images with a restricted face range (no hair area) with a size of $128 \\times 128$ . We further improve the redirection task by covering the full face range with $1024 \\times 1024$ resolution.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Latent Space Manipulation. Numerous methods investigated the latent space working with StyleGAN [21,22] to achieve semantic editing in image space due to its meaningful and highly disentangled properties. As for the supervised methods, InterFaceGAN [31] determined hyperplanes for the corresponding facial attribute editing based on provided labels. StyleFlow [2] proposed mapping a sample from a prior distribution to a latent distribution conditioned on the target attributes estimated by pretrained attribute classifiers. Given the unsupervised methods, GANSpace [15], SeFa [32] and TensorGAN [14] leveraged principal components analysis, eigenvector decomposition and higher-order singular value decomposition to discover semantic directions in latent space, respectively. Other self-supervised methods proposed mixing of latent codes from other samples for local editing [8, 9], or incorporating the language model CLIP [29] for text-driven editing [27].", + "bbox": [ + 496, + 228, + 892, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain Adaptation for Gaze Estimation. Domain gaps among different datasets restrict the application range of pretrained gaze estimation models. To narrow the gaps, a few domain adaptation approaches [37, 38] were proposed for the generic regression task. SimGAN [33] proposed an unsupervised domain adaptation method for narrowing the gaps between real and synthetic eye images. HGM [36] designed a unified 3D eyeball model for eye image synthesis and cross-dataset gaze estimation. PnP-GA [25] presented a gaze adaptation framework for generalizing gaze estimation in new domains based on collaborative learning. Qin et al. [28] utilized 3D face reconstruction to rotate head orientations together with changed eye gaze accordingly to enlarge overlapping gaze distributions among datasets. These adaptation methods typically rely on restricted face or eye images to alleviate interference from untargeted attributes. Our work incorporates the redirection task in a predefined meaningful feature space with controllable attributes to achieve high-resolution and full-face redirection.", + "bbox": [ + 496, + 486, + 893, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 805, + 591, + 820 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Problem Statements", + "text_level": 1, + "bbox": [ + 500, + 830, + 691, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our goal is to train a conditional latent-to-latent translation module for face editing with physical meaning, and it can work either with a trainable or fixed encoder-generator", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5548", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f5c6e3a7e2e0df519551640089b5b5c5d493548fa47b5346f49e1a3fa5da5a33.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 173, + 88, + 498, + 183 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ec5480c06c4c5c167c52ec0d1e80a2156a5c5558a68b28ab41120504d8d10485.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 89, + 795, + 183 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5f4b7b8c9616552a5f869255d18740c00ce4b85060deaf282cbf5b7aa5450ba3.jpg", + "image_caption": [ + "Figure 1. Conditional redirection pipeline and comparison among differentirectors. (a) We first encode the input image into the latent vector. Given the provided conditions, we modify the latent vector and send it to a generator for image synthesis with only aimed attribute redirection. (b) We compared our proposed redirector with two state-of-the-art methods by omitting common modules (basic encoders and decoders/generators) and focusing on the unique components: (b-1) VecGAN achieves editing in feature space $\\mathcal{F}$ given projected conditions from latent vectors with a global direction $f_{N}^{i}$ . (b-2) ST-ED projects the latent vector into conditions and embeddings of aimed attributes, and one appearance-related high dimensional embedding $z_0$ in embedding space $\\mathcal{Z}$ . After interpretable redirection process in space $\\mathcal{Z}$ , all embeddings are concatenated and projected back to space $\\mathcal{F}$ . (b-3) Our proposed ReDirTrans projects the latent vector into conditions and embeddings of aimed attributes only. After an interpretable redirection process, both original and redirected embeddings are deprojected back to initial space $\\mathcal{F}$ as residuals. These residuals modify the input latent vector by subtraction and addition operations, which represent the initial status removal and the new status addition, respectively. This approach efficiently reduces effects on other attributes (especially the appearance related information) with fewer parameters than ST-ED." + ], + "image_footnote": [ + "source branch", + "Z embedding space", + "$\\pmb{E}$ Encoder", + "P Projection", + "target branch", + "F latent space", + "G Generator" + ], + "bbox": [ + 173, + 186, + 498, + 335 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0cd82f76051154d049a7ab57ab5f4ff588c134953eb8ce395762bf76f91b62aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 186, + 790, + 335 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4973c70bc16e8b76a422e34b75caf80b261f535ec941f1ef79e58cace1ad58a5.jpg", + "image_caption": [], + "image_footnote": [ + "dition", + "$DP$ Deprojection", + "$\\ominus$ subtraction" + ], + "bbox": [ + 537, + 338, + 568, + 349 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/12797991c75f3c5169432b024e3c1d475eda5d10bc66be5d3179a59f1a10db7c.jpg", + "image_caption": [], + "image_footnote": [ + "matrix multiplication", + "element-wise multiplication" + ], + "bbox": [ + 619, + 338, + 643, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pair. This editing module first transforms input latent vectors from encoded feature space $\\mathcal{F}$ to an embedding space $\\mathcal{Z}$ for redirection in an interpretable manner. Then it departs the original and redirected embeddings back to the initial feature space $\\mathcal{F}$ for editing input latent vectors. The edited latent vectors are fed into a generator for image synthesis with the desired status of aimed facial attributes. The previous GAN-based work [10,14,31] achieved a certain facial attribute editing with a global latent residual multiplied by a scalar without physical meaning to describe the relative deviation from the original status. To make the whole process interpretable and achieve redirection directly based on the new gaze directions or head poses, we follow the assumption proposed by [44], where the dimension of an embedding is decided by the corresponding attribute's degree of the freedom (DoF) and redirection process is achieved by the rotation matrices multiplication. Thus the transformation equivariant mappings can be achieved between the embedding space $\\mathcal{Z}$ and image space. To be specific, normalized gazes or head poses can be represented by a two-dimensional embedding with the pitch and yaw as the controllable conditions. The embeddings can be edited (multi", + "bbox": [ + 75, + 566, + 472, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "plied) by the rotation matrices built from the pitch and yaw for achieving redirection (rotation) of aimed attributes in image space accordingly through our proposed director.", + "bbox": [ + 496, + 566, + 890, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Redirector Architecture", + "text_level": 1, + "bbox": [ + 498, + 619, + 720, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ST-ED is one of the state-of-the-art architectures for gaze and head poses redirection over face images [44] shown in Fig. 1 (b-2). ST-ED projects the input latent vector $f$ to non-varying embeddings $z^0$ and $M$ varying ones with corresponding estimated conditions $\\{(z^i, \\hat{c}^i) | i \\in [1, M]\\}$ , where $\\hat{c}^i$ describes the estimated amount of deviation from the canonical status of the attribute $i$ , and it can be compared with the ground truth $c^i$ for the learning of conditions from latent vectors. The non-varying embedding $z^0$ defines subject's appearance, whose dimension is much larger (over twenty times larger in ST-ED) than other varying embeddings. It is inefficient to project input latent vectors into a high-dimensional embedding to maintain non-varying information such as identity, hairstyle, etc. Thus, we propose a new redirector architecture, called ReDirTrans, shown in Fig. 1 (b-3), which transforms the source latent vector $f_s$ to the embeddings of aimed attributes through the projec", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5549", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7f8bedac0913d6095076889871048a6117eb3979ef7a8ba9e52ddc2e0d00cbcc.jpg", + "image_caption": [ + "Figure 2. ReDirTrans-GAN: Layer-wise ReDirTrans with fixed e4e and StyleGAN. Given the multi-layer representation of latent vectors in $W^{+} \\subseteq \\mathbb{R}^{18 \\times 512}$ , we feed each layer into an independent ReDirTrans for redirection task given the provided target condition $c_{t}^{i}$ , where $i$ represents a certain attribute. $\\tilde{c}^i$ denotes the pseudo condition estimated directly from the inverted image by a pretrained HeadGazeNet $\\xi_{hg}$ [44]. We calculate errors between estimated conditions $\\hat{c}_k^i, k \\in [1,18]$ from multiple ReDirTrans and $\\tilde{c}^i$ for supervising the trainable weights learning (green arrow) based on the Layer-wise Weights Loss described in Eq. 10 to decide which layers should contribute more to a certain attribute redirection. Given the estimated weights and initial latent vectors $f_{s}$ , we can acquire the final disentangled latent vector $\\hat{f}_{t,d}$ based on Eq. 2 for redirected samples synthesis." + ], + "image_footnote": [], + "bbox": [ + 174, + 90, + 802, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tor $P$ and redirects them given the newly provided target conditions $c_{t}$ . Then we deproject both original embeddings $\\mathbf{z}_{\\mathrm{s}}$ and redirected embeddings $\\hat{\\mathbf{z}}_{\\mathrm{t}}$ back to the feature space $\\mathcal{F}$ through the weights-sharing deprojectors $DP$ to acquire latent residuals. These residuals contain source and target status of aimed attributes, denoted as $\\Delta f_{s}^{i}$ and $\\Delta \\hat{f}_t^i$ , respectively. Inspired by addition and subtraction [10, 31] for face editing in feature space $\\mathcal{F}$ , the edited latent vector is", + "bbox": [ + 75, + 412, + 472, + 534 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {t} = f _ {s} + \\sum_ {i = 1} ^ {M} \\left(- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}\\right), i \\in [ 1, M ], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 544, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the subtraction means removing source status and the addition indicates bringing in new status. The projector $P$ ensures that the dimension of embeddings can be customized based on the degrees of freedom of desired attributes, and the transformations can be interpretable with physical meanings. The deprojector $DP$ enables the original and edited features in the same feature space, allowing ReDirTrans to be compatible with pretrained encoder-generator pairs that are typically trained together without intermediate (editing) modules. ReDirTrans reduces parameters by skipping projection (compression) and deprojection (decompression) of the features that are not relevant to the desired attributes, but vital for final image synthesis.", + "bbox": [ + 75, + 595, + 472, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Predefined Feature Space", + "text_level": 1, + "bbox": [ + 76, + 801, + 310, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Except for the trainable encoder-decoder (or -generator) pair to learn a specific feature space for redirection task as ST-ED did, ReDirTrans can also work in the predefined feature space to coordinate with fixed, pretrained encoder-generator pairs. For our implementation, we chose the", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$W^{+} \\in \\mathbb{R}^{18 \\times 512}$ feature space [1], which allows us to utilize StyleGAN [22] for generating high-quality, high-fidelity face images. We refer to this implementation as ReDirTrans-GAN. Considering multi-layer representation of the latent vector [1] and its semantic disentangled property between different layers [2, 15] in $W^{+}$ space, we proposed layer-wiseirectors, shown in Fig. 2, rather than using a single ReDirTrans to process all (18) layers of the latent vector. To largely reduce the interference between different layers during redirection, we assume that if one attribute's condition can be estimated from certain layers with less errors than the others, then we can 'modify' these certain layers with higher weights $p_k^i$ , $k \\in [1,18]$ than others to achieve redirection of the corresponding attribute $i$ only. $P^i = [p_1^i,\\dots ,p_{18}^i]^T \\in \\mathbb{R}^{18 \\times 1}$ , as part of network parameters, is trained given the loss function described in Eq. 10. The final disentangled latent vectors after redirection is", + "bbox": [ + 496, + 412, + 893, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {t, d} = f _ {s} + \\sum_ {i = 1} ^ {M} \\boldsymbol {P} ^ {i} \\odot (- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}), i \\in [ 1, M ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 688, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ means element-wise multiplication and $(- \\Delta f_{s}^{i} + \\Delta \\hat{f}_{t}^{i}) \\in \\mathbb{R}^{18 \\times 512}$ . One challenge regarding the predefined feature space comes from the inversion quality. There exist attribute differences between input images and inverted results, shown in Fig. 4 and 6, which means that the conditions in source images cannot be estimated from source latent vectors. To solve this, instead of using conditions from source images, we utilized estimated conditions from the inverted images, which ensures the correctness and consistence of conditions learning from latent vectors.", + "bbox": [ + 496, + 747, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5550", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training Pipeline", + "text_level": 1, + "bbox": [ + 76, + 90, + 246, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a pair of source and target face images, $I_{s}$ and $I_{t}$ from the same person, we utilize an encoder to first transform $I_{s}$ into the feature space $\\mathcal{F}$ , denoted as $f_{s}$ . We further disentangle $f_{s}$ into the gaze-direction-related embedding $z_{s}^{1}$ and the head-orientation-related embedding $z_{s}^{2}$ with corresponding estimated conditions: $\\hat{c}_s^1$ and $\\hat{c}_s^2$ by the projector $\\pmb{P}$ . Then we build rotation matrices using the pitch and yaw from estimated conditions $(\\hat{c}_s^1,\\hat{c}_s^2)$ and target conditions $(c_t^1,c_t^2)$ to normalize embeddings and redirect them to the new status, respectively:", + "bbox": [ + 75, + 113, + 472, + 265 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {N o r m a l i z a t i o n :} z _ {N} ^ {i} = \\mathbf {R} ^ {- 1} \\left(\\hat {c} _ {s} ^ {i}\\right) \\cdot z _ {s} ^ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 272, + 468, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Redirection: $\\hat{z}_t^i = \\mathbf{R}(c_t^i)\\cdot z_N^i$", + "bbox": [ + 153, + 294, + 380, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i \\in \\{1, 2\\}$ , representing gaze directions and head orientations, respectively, and $z_N^i$ denotes the normalized embedding of the corresponding attribute. We feed the original embedding $z_s^i$ and the modified embedding $\\hat{z}_t^i$ into the weights-sharing deprojectors $DP$ to transform these embeddings back to the feature space $\\mathcal{F}$ as the residuals. Given these residuals, we implement subtraction and addition operations over $f_s$ as described in Eq. 1 (or Eq. 2) to acquire the edited latent vector $\\hat{f_t}$ (or $\\hat{f_{t,d}}$ ), which is sent to a generator for synthesizing redirected face image $\\hat{I}_t$ . $\\hat{I}_t$ should have the same gaze direction and head orientation as $I_t$ .", + "bbox": [ + 75, + 316, + 472, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Learning Objectives", + "text_level": 1, + "bbox": [ + 76, + 493, + 269, + 510 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We supervise the relationship between the generated image $\\hat{I}_t$ and the target image $I_t$ with several loss functions: pixel-wise reconstruction loss, LPIPS metric [43] and attributes loss by a task-related pretrained model.", + "bbox": [ + 75, + 517, + 468, + 578 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\hat {I} _ {t} - I _ {t} \\right| \\right| _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 584, + 468, + 604 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L P I P S} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\psi (\\hat {I} _ {t}) - \\psi (I _ {t}) \\right| \\right| _ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 611, + 468, + 631 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a t t} (\\hat {I} _ {t}, I _ {t}) = \\langle \\xi_ {h g} (\\hat {I} _ {t}), \\xi_ {h g} (I _ {t}) \\rangle , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 635, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\psi (\\cdot)$ denotes the perceptual feature extractor [43], $\\xi_{hg}(\\cdot)$ represents the pretrained HeadGazeNet [44] to estimate the gaze and head pose from images and $\\langle u,v\\rangle =$ $\\arccos \\frac{u\\cdot v}{||u||\\cdot||v||}$", + "bbox": [ + 76, + 657, + 468, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Identity Loss. Identity preservation after redirection is critical for the face editing task. Considering this, we calculate the cosine similarity of the identity-related features between the source image and the redirected image:", + "bbox": [ + 75, + 724, + 468, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I D} (\\hat {I} _ {t}, I _ {s}) = 1 - \\langle \\phi (\\hat {I} _ {t}), \\phi (I _ {s}) \\rangle , \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 791, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi (\\cdot)$ denotes the pretrained ArcFace [11] model.", + "bbox": [ + 76, + 816, + 441, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Label Loss. We have ground truth of gaze directions and head orientations, which can guide the conditions learning from the input latent vectors for the normalization step:", + "bbox": [ + 75, + 838, + 468, + 883 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l a b} \\left(\\hat {c} _ {s} ^ {i}, c _ {s} ^ {i}\\right) = \\left\\langle \\hat {c} _ {s} ^ {i}, c _ {s} ^ {i} \\right\\rangle , i \\in \\{1, 2 \\}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 891, + 468, + 909 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Embedding Loss. The normalized embeddings only contain the canonical status of the corresponding attribute after the inverse rotation applied to the original estimated embeddings, shown in Fig. 1. Thus the normalized embeddings given a certain attribute across different samples within batch $B$ should be consistent. To reduce the number of possible pairs within a batch, we utilize the first normalized embedding $z_{N,1}^{i}$ as the basis:", + "bbox": [ + 496, + 90, + 892, + 213 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e m b} = \\frac {1}{B - 1} \\sum_ {j = 2} ^ {B} \\langle z _ {N, 1} ^ {i}, z _ {N, j} ^ {i} \\rangle , i \\in \\{1, 2 \\}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 223, + 892, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Layer-wise Weights Loss. This loss is specifically designed for the $W^{+}$ space to decide the weights $p_{i}$ of which layer should contribute more to the aimed attributes editing. Firstly, we calculate the layer-wise estimated conditions $\\hat{c}_k^i$ and calculate estimated pseudo labels $\\tilde{c}^i$ . Secondly, we have layer-wise estimated label errors by $\\langle \\hat{c}_k^i, \\tilde{c}^i \\rangle$ . Lastly, we calculate the cosine similarity between the reciprocal of label errors and weights of layers as the loss:", + "bbox": [ + 496, + 273, + 890, + 396 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p r o b} = \\langle \\left\\{p _ {k} \\right\\}, \\left\\{\\frac {1}{\\left\\langle \\hat {c} _ {k} ^ {i} , \\tilde {c} ^ {i} \\right\\rangle} \\right\\}, k \\in [ 1, K ], i \\in \\{1, 2 \\}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 404, + 890, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K$ is the number of layers for editing.", + "bbox": [ + 500, + 445, + 794, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Full Loss. The combined loss function for supervising the redirection process is:", + "bbox": [ + 496, + 465, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\lambda_ {r} \\mathcal {L} _ {r e c} + \\lambda_ {L} \\mathcal {L} _ {L P I P S} + \\lambda_ {I D} \\mathcal {L} _ {I D} + \\lambda_ {a} \\mathcal {L} _ {a t t} \\tag {11} \\\\ + \\lambda_ {l} \\mathcal {L} _ {l a b} + \\lambda_ {e} \\mathcal {L} _ {e m b} + \\lambda_ {p} \\mathcal {L} _ {p r o b}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 506, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{LPIPS}$ and $\\mathcal{L}_{prob}$ are utilized only when the pretrained StyleGAN is used as the generator.", + "bbox": [ + 496, + 550, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 594, + 633, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. datasets", + "text_level": 1, + "bbox": [ + 500, + 619, + 599, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilize GazeCapture [24] training subset to train the redirector and assess the performance with its test subset, MPIIFaceGaze and CelebA-HQ [20]. Supplementary material provides more information about these datasets.", + "bbox": [ + 496, + 642, + 890, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation Criteria", + "text_level": 1, + "bbox": [ + 500, + 710, + 687, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We follow metrics utilized by ST-ED [44] to evaluate different redirectors' performance.", + "bbox": [ + 496, + 734, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Redirection Error. We measure the redirection accuracy in image space by a pre-trained ResNet-50 based [16] head pose and gaze estimator $\\xi_{hg}^{\\prime}$ , which is unseen during the training. Given the target image $I_{t}$ and the generated one $\\hat{I}_t$ redirected by conditions of $I_{t}$ , we report the angular error between $\\xi_{hg}^{\\prime}(\\hat{I}_{t})$ and $\\xi_{hg}^{\\prime}(I_t)$ as the redirection errors.", + "bbox": [ + 496, + 765, + 890, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Disentanglement Error. We quantify the disentanglement error by the condition's fluctuation range of one attribute when we redirect the other one. The redirection", + "bbox": [ + 496, + 856, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5551", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/78d4d3d5b6d70b1821a163e2bed348f09c5e789b615da01ea0ca28714a33f7cf.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Within-dataset quantitative comparison (GazeCapture test subset) between different methods for redirecting head orientations and gaze directions. (Lower is better). Head (Gaze) Redir denotes the redirection accuracy in degree between the redirected image and the target image given head orientations (gaze directions). Head (Gaze) Induce denotes the errors in degree on gaze (head) when we redirect the head (gaze). $\\dagger$ denotes copied results from [44]. Other methods are retrained given previous papers." + ], + "table_body": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.6023.9890.7553.0670.257
He et al.†[17]4.6171.3920.5603.9250.223
VecGAN [10]2.2820.8240.4012.2050.197
ST-ED [44]2.3850.8000.3842.1870.208
ReDirTrans2.1630.7530.4292.1550.197
", + "bbox": [ + 78, + 88, + 486, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "angle $\\epsilon$ follows $\\mathcal{U}(-0.1\\pi, 0.1\\pi)$ . For example, when we redirect the head pose of the generated image $\\hat{I}_t$ by $\\epsilon$ and generate a new one $\\hat{I}_t'$ , we calculate the angular error of the estimated gaze directions between $\\xi_{hq}'(\\hat{I}_t)$ and $\\xi_{hq}'(I_t')$ .", + "bbox": [ + 75, + 366, + 468, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LPIPS. LPIPS is able to measure the distortion [43] and image similarity in gaze directions [17] between images, which is applied to evaluate the redirection performance.", + "bbox": [ + 75, + 428, + 468, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Redirectors in Learnable Latent Space", + "text_level": 1, + "bbox": [ + 76, + 484, + 410, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared quantitative performance of different redirectors, which were trained along with the trainable encoder-decoder pair designed by ST-ED on $128 \\times 128$ images with restricted face ranges, given the criteria proposed in Sec. 4.2. Table 1 and Table 2 present within-dataset and cross-dataset performance, respectively. From these tables, we observe that our proposed ReDirTrans achieved more accurate redirection and better LPIPS compared with other state-of-the-art methods by considering the extra embedding space $\\mathcal{Z}$ for redirecting embeddings of aimed attributes only and maintaining other attributes including the appearance-related information in the original latent space $\\mathcal{F}$ . ST-ED [44] projected input latent vectors into nine embeddings including the non-varying embedding $z^0$ . This appearance-related high dimensional embedding $z^0$ requires more parameters than ReDirTrans during projection. After redirecting the embeddings of aimed attributes, ST-ED deprojected a stack of $z^0$ , redirected embeddings, and rest unvaried embeddings of other attributes back to the feature space for decoding. This projection-deprojection process of non-varying embedding $z^0$ results in loss of appearance and worse LPIPS, as depicted in Fig. 3. VecGAN [10] was proposed to edit the attributes only within the feature space by addition and subtraction operations. Since there is no projection-deprojection process, given the original latent code, LPIPS performance is bet", + "bbox": [ + 75, + 508, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3823433c29fe5ce05dedd77fca01e4fd643f9584c050cf9acaf81c239125c34e.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Cross-dataset quantitative comparison (MPIIFaceGaze) between different methods for redirecting head orientations and gaze directions. (Lower is better). Notations are the same as them in the Table 1. $\\dagger$ denotes copied results from [44]. Other methods are retrained given previous papers." + ], + "table_body": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.4883.0310.7862.7830.260
He et al.†[17]5.0921.3720.6843.4110.241
VecGAN [10]2.6701.2420.3911.9410.207
ST-ED [44]2.3801.0850.3711.7820.212
ReDirTrans2.3800.9850.3911.7820.202
", + "bbox": [ + 500, + 88, + 908, + 218 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/900883f71044cfef1e7403209fb24c4db950020bb1a8cede28601898c264bb96.jpg", + "image_caption": [ + "Figure 3. Qualitative Comparison of ReDirTrans and ST-ED in GazeCapture. ReDirTrans preserves more facial attributes, such as lip thickness and sharpness of the beard." + ], + "image_footnote": [], + "bbox": [ + 501, + 313, + 893, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ter than ST-ED. However, as no extra embedding space was built for the aimed attributes editing, both redirection accuracy and the disentanglement process were affected.", + "bbox": [ + 496, + 560, + 893, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Redirectors in Predefined Latent Space", + "text_level": 1, + "bbox": [ + 498, + 619, + 836, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Except for using the trainable encoder-decoder pair of ST-ED, we also implemented our proposed ReDirTrans within a predefined feature space $W^{+}$ to achieve redirection task in full face images with desired resolution. We utilized e4e [35] as the pre-trained encoder, which can transform input images into latent vectors in $W^{+}$ , and we chose StyleGAN2 [22] as the pre-trained generator to build ReDirTrans-GAN. Fig. 4 shows qualitative comparison between ST-ED and ReDirTrans-GAN in the GazeCapture test subset with providing target images from the same subject. ReDirTrans-GAN successfully redirected gaze directions and head orientations to the status provided by target images while maintaining the same appearance patterns with $1024 \\times 1024$ full face images. Due to the design of ReDirTrans, which maintains unrelated attributes and appearance information in the initial latent space instead of going through the projection-deprojection pro", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5552", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/26c94784e46de8e0846e412019b9273e1a93394ed0febf5b5904e43b1144ea4a.jpg", + "image_caption": [ + "Figure 4. Qualitatively comparisons between ST-ED and ReDirTrans-GAN. Red boxes represent different face covering ranges." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 885, + 377 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ef3b99ff1055537cd41a4cbb5cf17c3a570fa255796182046874133d96840f74.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Q%GazeCaptureMPIIFaceGaze
Raw ↓Aug ↓Raw ↓Aug ↓
255.8755.2388.6077.096
504.7414.5066.7876.113
754.3084.2006.1655.767
", + "bbox": [ + 112, + 425, + 434, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Learning-based gaze estimation errors (in degrees) in GazeCapture and MPIIFaceGaze with or without redirected data augmentation. $Q\\%$ represents percent of labeled data in 10,000 images for training ReDirTrans-GAN. 'Raw' or 'Aug' mean training the gaze estimator with real data or with real & redirected data.", + "bbox": [ + 75, + 534, + 468, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cess, ReDirTrans-GAN keeps more facial attributes such as expressions, mustaches, bangs compared with ST-ED. Fig. 5 presents qualitative results with assigned conditions (pitch and yaw of gaze directions and head orientations) in CelebA-HQ [20]. ReDirTrans-GAN can achieve out-of-domain redirection tasks in predefined feature space while maintaining other facial attributes.", + "bbox": [ + 75, + 633, + 468, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Data Augmentation", + "text_level": 1, + "bbox": [ + 76, + 753, + 264, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To solve data scarcity of the downstream task: learning-based gaze estimation, we utilized redirected samples with assigned gaze directions and head orientations to augment training data. We randomly chose 10,000 images from the GazeCapture training subset to retrain ReDirTrans-GAN with using only $Q\\%$ ground-truth labels of them. The HeadGazeNet $\\xi_{hg}(\\cdot)$ was also retrained given the same $Q\\%$ labeled data and $Q \\in \\{25,50,75\\}$ . Then we utilized", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ReDirTrans-GAN to generate redirected samples given provided conditions over $Q\\%$ labeled real data and combined the real and redirected data as an augmented dataset with size $2 \\times 10,000 \\times Q\\%$ for training a gaze estimator. Table 3 presented within-dataset and cross-dataset performance and demonstrated consistent improvements for the downstream task given redirected samples as data augmentation.", + "bbox": [ + 496, + 428, + 890, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Challenge in Predefined Feature Space", + "text_level": 1, + "bbox": [ + 498, + 542, + 831, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One challenge for redirection tasks in predefined feature space comes from inconsistency between input and inverted images, mentioned in Sec. 3.3. We can observe that the existing gaze differences between input and inverted images in Fig. 4. In some cases, the gaze directions are changed after GAN inversion, which means that the encoded latent codes do not necessarily keep the original gaze directions. Thus, instead of using provided gaze directions of input images during the training, we utilized estimated gaze directions from inverted results to correctly normalize the gaze and head pose to the canonical status. This process ensures correctness when further new directions are added, making the training process more consistent.", + "bbox": [ + 496, + 566, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.7. Gaze Correction", + "text_level": 1, + "bbox": [ + 500, + 771, + 663, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ReDirTrans can correct gaze directions of inverted results by viewing input images as the target ones. e4e guarantees high editability, which is at the cost of inversion performance [35]. Fig. 6 shows several samples which failed to maintain input images' gaze directions even by the ReStyle encoder [3], which iteratively updates the latent codes given the differences between the input and inverted results. With", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5553", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e76d545135a9e754566768092cc957125a47d7ee27050711ad9b02010bfef34.jpg", + "image_caption": [ + "Figure 5. Redirection results given assigned (pitch, yaw) conditions of gaze directions (g) and head orientations (h). The first two columns are input and inversion results with e4e [35] and StyleGAN [22]. The following columns are redirected samples with assigned redirection values based on the latent code estimated from e4e." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 890, + 433 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcc8defdfcefe94c8f9471f111e865417cb1e448de5f2b149fc8a479d90e2af8.jpg", + "image_caption": [ + "Figure 6. Gaze correction in CelebA-HQ by viewing the same image as both the input and target." + ], + "image_footnote": [], + "bbox": [ + 78, + 508, + 468, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ReDirTrans-GAN, we can successfully correct the wrong gaze based on inverted results from e4e.", + "bbox": [ + 498, + 511, + 890, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 556, + 627, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce ReDirTrans, a novel architecture working in either learnable or predefined latent space for high-accuracy redirection of gaze directions and head orientations. ReDirTrans projects input latent vectors into aimed-attribute pseudo labels and embeddings for redirection in an interpretable manner. Both the original and redirected embeddings of aimed attributes are deprojected to the initial latent space for modifying the input latent vectors by subtraction and addition. This pipeline ensures no compression loss to other facial attributes, including appearance information, which essentially reduces effects on the distribution of input latent vectors in initial latent space. Thus we successfully implemented ReDirTrans-GAN in the predefined feature space working with fixed StyleGAN to achieve redirection in high-resolution full-face images, either by assigned values or estimated conditions from target images while maintaining other facial attributes. The redirected samples with assigned conditions can be utilized as data augmentation for further improving learning-based gaze estimation performance. In future work, instead of a pure 2D solution, 3D data can be included for further improvements.", + "bbox": [ + 496, + 583, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5554", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Advances in Neural Information Processing Systems, 33:13127-13138, 2020. 1, 2, 3, 4, 5, 6" + ], + "bbox": [ + 501, + 92, + 890, + 527 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5556", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_model.json b/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_model.json new file mode 100644 index 0000000000000000000000000000000000000000..30a6d22c8c580e6c5b00dd50cc8190e35cc626da --- /dev/null +++ b/2023/ReDirTrans_ Latent-to-Latent Translation for Gaze and Head Redirection/743e5765-daf6-4f6d-bed7-fe1d28d26c28_model.json @@ -0,0 +1,2068 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.131, + 0.859, + 0.152 + ], + "angle": 0, + "content": "ReDirTrans: Latent-to-Latent Translation for Gaze and Head Redirection" + }, + { + "type": "text", + "bbox": [ + 0.213, + 0.18, + 0.754, + 0.199 + ], + "angle": 0, + "content": "Shiwei Jin \\(^{1}\\), Zhen Wang \\(^{2}\\), Lei Wang \\(^{2}\\), Ning Bi \\(^{2}\\), Truong Nguyen \\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.199, + 0.725, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\) ECE Dept. UC San Diego, \\(^{2}\\) Qualcomm Technologies, Inc." + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.219, + 0.773, + 0.235 + ], + "angle": 0, + "content": "{sjin，tqn001}@eng.ucsd.edu，{zhewang，wlei，nbi}@qti=qualcomm.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.473, + 0.771 + ], + "angle": 0, + "content": "Learning-based gaze estimation methods require large amounts of training data with accurate gaze annotations. Facing such demanding requirements of gaze data collection and annotation, several image synthesis methods were proposed, which successfully redirected gaze directions precisely given the assigned conditions. However, these methods focused on changing gaze directions of the images that only include eyes or restricted ranges of faces with low resolution (less than \\(128 \\times 128\\)) to largely reduce interference from other attributes such as hairs, which limits application scenarios. To cope with this limitation, we proposed a portable network, called ReDirTrans, achieving latent-to-latent translation for redirecting gaze directions and head orientations in an interpretable manner. ReDirTrans projects input latent vectors into aimed-attribute embeddings only and redirects these embeddings with assigned pitch and yaw values. Then both the initial and edited embeddings are projected back (deprojected) to the initial latent space as residuals to modify the input latent vectors by subtraction and addition, representing old status removal and new status addition. The projection of aimed attributes only and subtraction-addition operations for status replacement essentially mitigate impacts on other attributes and the distribution of latent vectors. Thus, by combining ReDirTrans with a pretrained fixed e4e-StyleGAN pair, we created ReDirTrans-GAN, which enables accurately redirecting gaze in full-face images with \\(1024 \\times 1024\\) resolution while preserving other attributes such as identity, expression, and hairstyle. Furthermore, we presented improvements for the downstream learning-based gaze estimation task, using redirected samples as dataset augmentation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.8, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Gaze is a crucial non-verbal cue that conveys attention and awareness in interactions. Its potential applications include mental health assessment [5,18], social attitudes analysis [19], human-computer interaction [12], automotive assistance [30], AR/VR [6,34]. However, developing a robust" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.895, + 0.438 + ], + "angle": 0, + "content": " unified learning-based gaze estimation model requires large amounts of data from multiple subjects with precise gaze annotations [42, 44]. Collecting and annotating such an appropriate dataset is complex and expensive. To overcome this challenge, several methods have been proposed to redirect gaze directions [17, 39, 41, 42, 44] in real images with assigned directional values to obtain and augment training data. Some works focused on generating eye images with new gaze directions by either 1) estimating warping maps [41, 42] to interpolate pixel values or 2) using encoder-generator pairs to generate redirected eye images [17, 39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.895, + 0.592 + ], + "angle": 0, + "content": "ST-ED [44] was the first work to extend high-accuracy gaze redirection from eye images to face images. By disentangling several attributes, including person-specific appearance, it can explicitly control gaze directions and head orientations. However, due to the design of the encoder-decoder structure and limited ability to maintain appearance features by a \\(1 \\times 1024\\) projected appearance embedding, ST-ED generates low-resolution (\\(128 \\times 128\\)) images with restricted face range (no hair area), which narrows the application ranges and scenarios of gaze redirection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.896, + 0.762 + ], + "angle": 0, + "content": "As for latent space manipulation for face editing tasks, large amounts of works [2-4, 14, 31, 35] were proposed to modify latent vectors in predefined latent spaces (W [21], \\( W^{+} \\) [1] and \\( S \\) [40]). Latent vectors in these latent spaces can work with StyleGAN [21, 22] to generate high-quality and high-fidelity face images with desired attribute editing. Among these methods, Wu et.al [40] proposed the latent space \\( S \\) working with StyleGAN, which achieved only one degree-of-freedom gaze redirection by modifying a certain channel of latent vectors in \\( S \\) by an uninterpreted value instead of pitch and yaw values of gaze directions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Considering these, we proposed a new method, called ReDirTrans, to achieve latent-to-latent translation for redirecting gaze directions and head orientations in high-resolution full-face images based on assigned directional values. Specifically, we designed a framework to project input latent vectors from a latent space into the aimed-attribute-only embedding space for an interpretable redirection process. This embedding space consists of estimated pseudo conditions and embeddings of aimed attributes," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5547" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.379 + ], + "angle": 0, + "content": "where conditions describe deviations from the canonical status and embeddings are the 'carriers' of the conditions. In this embedding space, all transformations are implemented by rotation matrices multiplication built from pitch and yaw values, which can make the redirection process more interpretable and consistent. After the redirection process, the original embeddings and redirected ones are both decoded back to the initial latent space as the residuals to modify the input latent vectors by subtraction and addition operations. These operations represent removing the old state and adding a new one, respectively. ReDirTrans only focuses on transforming embeddings of aimed attributes and achieves status replacement by the residuals outputted from weight-sharing deprojectors. ReDirTrans does not project or deproject other attributes with information loss; and it does not affect the distribution of input latent vectors. Thus ReDirTrans can also work in a predefined feature space with a fixed pretrained encoder-generator pair for the redirection task in desired-resolution images." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.38, + 0.398, + 0.394 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.398, + 0.47, + 0.488 + ], + "angle": 0, + "content": "- A latent-to-latent framework, ReDirTrans, which projects latent vectors to an embedding space for an interpretable redirection process on aimed attributes and maintains other attributes, including appearance, in initial latent space with no information loss caused by projection-deprojection processes." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.493, + 0.47, + 0.569 + ], + "angle": 0, + "content": "- A portable framework that can seamlessly integrate into a pretrained GAN inversion pipeline for high-accuracy redirection of gaze directions and head orientations, without the need for any parameter tuning of the encoder-generator pairs." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.575, + 0.47, + 0.635 + ], + "angle": 0, + "content": "- A layer-wise architecture with learnable parameters that works with the fixed pretrained StyleGAN and achieves redirection tasks in high-resolution full-face images through ReDirTrans-GAN." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.398, + 0.47, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.649, + 0.228, + 0.665 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.675, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Gaze and Head Redirection. Methods for redirecting gaze directions can be broadly classified into two categories: warping-based methods and generator-based methods. Deepwarp [13, 23] presented a deep network to learn warping maps between pairs of eye images with different gaze directions, which required large amounts of data with annotations. Yu et al. [41] utilized a pretrained gaze estimator and synthetic eye images to reduce the reliance on annotated real data. Yu et al. [42] further extended the warping-based methods in an unsupervised manner by adding a gaze representation learning network. As for the generator-based methods, He et al. [17] developed a GAN-based network for generating eye images with new gaze directions. FAZE [26] proposed an encoder-decoder architecture to transform eye images into latent vectors for redirection with rotation ma" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "trix multiplication, and then decode the edited ones back to the synthetic images with new gaze directions. ST-ED [44] further extended the encoder-decoder pipeline from gaze redirection only to both head and gaze redirection over full face images by disentangling latent vectors, and achieving precise redirection performance. However, ST-ED generates images with a restricted face range (no hair area) with a size of \\(128 \\times 128\\). We further improve the redirection task by covering the full face range with \\(1024 \\times 1024\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.893, + 0.485 + ], + "angle": 0, + "content": "Latent Space Manipulation. Numerous methods investigated the latent space working with StyleGAN [21,22] to achieve semantic editing in image space due to its meaningful and highly disentangled properties. As for the supervised methods, InterFaceGAN [31] determined hyperplanes for the corresponding facial attribute editing based on provided labels. StyleFlow [2] proposed mapping a sample from a prior distribution to a latent distribution conditioned on the target attributes estimated by pretrained attribute classifiers. Given the unsupervised methods, GANSpace [15], SeFa [32] and TensorGAN [14] leveraged principal components analysis, eigenvector decomposition and higher-order singular value decomposition to discover semantic directions in latent space, respectively. Other self-supervised methods proposed mixing of latent codes from other samples for local editing [8, 9], or incorporating the language model CLIP [29] for text-driven editing [27]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.895, + 0.775 + ], + "angle": 0, + "content": "Domain Adaptation for Gaze Estimation. Domain gaps among different datasets restrict the application range of pretrained gaze estimation models. To narrow the gaps, a few domain adaptation approaches [37, 38] were proposed for the generic regression task. SimGAN [33] proposed an unsupervised domain adaptation method for narrowing the gaps between real and synthetic eye images. HGM [36] designed a unified 3D eyeball model for eye image synthesis and cross-dataset gaze estimation. PnP-GA [25] presented a gaze adaptation framework for generalizing gaze estimation in new domains based on collaborative learning. Qin et al. [28] utilized 3D face reconstruction to rotate head orientations together with changed eye gaze accordingly to enlarge overlapping gaze distributions among datasets. These adaptation methods typically rely on restricted face or eye images to alleviate interference from untargeted attributes. Our work incorporates the redirection task in a predefined meaningful feature space with controllable attributes to achieve high-resolution and full-face redirection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.806, + 0.593, + 0.821 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.692, + 0.846 + ], + "angle": 0, + "content": "3.1. Problem Statements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Our goal is to train a conditional latent-to-latent translation module for face editing with physical meaning, and it can work either with a trainable or fixed encoder-generator" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5548" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.174, + 0.089, + 0.499, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.09, + 0.797, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.187, + 0.499, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.187, + 0.792, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.174, + 0.339, + 0.253, + 0.351 + ], + "angle": 0, + "content": "source branch" + }, + { + "type": "image_footnote", + "bbox": [ + 0.253, + 0.339, + 0.365, + 0.351 + ], + "angle": 0, + "content": "Z embedding space" + }, + { + "type": "image_footnote", + "bbox": [ + 0.377, + 0.339, + 0.432, + 0.351 + ], + "angle": 0, + "content": "\\(\\pmb{E}\\) Encoder" + }, + { + "type": "image_footnote", + "bbox": [ + 0.45, + 0.339, + 0.519, + 0.351 + ], + "angle": 0, + "content": "P Projection" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.339, + 0.57, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.571, + 0.339, + 0.616, + 0.351 + ], + "angle": 0, + "content": "dition" + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.339, + 0.644, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.644, + 0.339, + 0.732, + 0.351 + ], + "angle": 0, + "content": "matrix multiplication" + }, + { + "type": "image_footnote", + "bbox": [ + 0.174, + 0.352, + 0.249, + 0.362 + ], + "angle": 0, + "content": "target branch" + }, + { + "type": "image_footnote", + "bbox": [ + 0.25, + 0.352, + 0.342, + 0.362 + ], + "angle": 0, + "content": "F latent space" + }, + { + "type": "image_footnote", + "bbox": [ + 0.352, + 0.352, + 0.44, + 0.362 + ], + "angle": 0, + "content": "G Generator" + }, + { + "type": "image_footnote", + "bbox": [ + 0.449, + 0.352, + 0.531, + 0.362 + ], + "angle": 0, + "content": "\\(DP\\) Deprojection" + }, + { + "type": "image_footnote", + "bbox": [ + 0.54, + 0.352, + 0.612, + 0.363 + ], + "angle": 0, + "content": "\\(\\ominus\\) subtraction" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.352, + 0.764, + 0.363 + ], + "angle": 0, + "content": "element-wise multiplication" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.895, + 0.528 + ], + "angle": 0, + "content": "Figure 1. Conditional redirection pipeline and comparison among differentirectors. (a) We first encode the input image into the latent vector. Given the provided conditions, we modify the latent vector and send it to a generator for image synthesis with only aimed attribute redirection. (b) We compared our proposed redirector with two state-of-the-art methods by omitting common modules (basic encoders and decoders/generators) and focusing on the unique components: (b-1) VecGAN achieves editing in feature space \\(\\mathcal{F}\\) given projected conditions from latent vectors with a global direction \\(f_{N}^{i}\\). (b-2) ST-ED projects the latent vector into conditions and embeddings of aimed attributes, and one appearance-related high dimensional embedding \\(z_0\\) in embedding space \\(\\mathcal{Z}\\). After interpretable redirection process in space \\(\\mathcal{Z}\\), all embeddings are concatenated and projected back to space \\(\\mathcal{F}\\). (b-3) Our proposed ReDirTrans projects the latent vector into conditions and embeddings of aimed attributes only. After an interpretable redirection process, both original and redirected embeddings are deprojected back to initial space \\(\\mathcal{F}\\) as residuals. These residuals modify the input latent vector by subtraction and addition operations, which represent the initial status removal and the new status addition, respectively. This approach efficiently reduces effects on other attributes (especially the appearance related information) with fewer parameters than ST-ED." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.473, + 0.9 + ], + "angle": 0, + "content": "pair. This editing module first transforms input latent vectors from encoded feature space \\(\\mathcal{F}\\) to an embedding space \\(\\mathcal{Z}\\) for redirection in an interpretable manner. Then it departs the original and redirected embeddings back to the initial feature space \\(\\mathcal{F}\\) for editing input latent vectors. The edited latent vectors are fed into a generator for image synthesis with the desired status of aimed facial attributes. The previous GAN-based work [10,14,31] achieved a certain facial attribute editing with a global latent residual multiplied by a scalar without physical meaning to describe the relative deviation from the original status. To make the whole process interpretable and achieve redirection directly based on the new gaze directions or head poses, we follow the assumption proposed by [44], where the dimension of an embedding is decided by the corresponding attribute's degree of the freedom (DoF) and redirection process is achieved by the rotation matrices multiplication. Thus the transformation equivariant mappings can be achieved between the embedding space \\(\\mathcal{Z}\\) and image space. To be specific, normalized gazes or head poses can be represented by a two-dimensional embedding with the pitch and yaw as the controllable conditions. The embeddings can be edited (multi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.614 + ], + "angle": 0, + "content": "plied) by the rotation matrices built from the pitch and yaw for achieving redirection (rotation) of aimed attributes in image space accordingly through our proposed director." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.621, + 0.722, + 0.636 + ], + "angle": 0, + "content": "3.2. Redirector Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ST-ED is one of the state-of-the-art architectures for gaze and head poses redirection over face images [44] shown in Fig. 1 (b-2). ST-ED projects the input latent vector \\( f \\) to non-varying embeddings \\( z^0 \\) and \\( M \\) varying ones with corresponding estimated conditions \\( \\{(z^i, \\hat{c}^i) | i \\in [1, M]\\} \\), where \\( \\hat{c}^i \\) describes the estimated amount of deviation from the canonical status of the attribute \\( i \\), and it can be compared with the ground truth \\( c^i \\) for the learning of conditions from latent vectors. The non-varying embedding \\( z^0 \\) defines subject's appearance, whose dimension is much larger (over twenty times larger in ST-ED) than other varying embeddings. It is inefficient to project input latent vectors into a high-dimensional embedding to maintain non-varying information such as identity, hairstyle, etc. Thus, we propose a new redirector architecture, called ReDirTrans, shown in Fig. 1 (b-3), which transforms the source latent vector \\( f_s \\) to the embeddings of aimed attributes through the projec" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5549" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.175, + 0.091, + 0.803, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 2. ReDirTrans-GAN: Layer-wise ReDirTrans with fixed e4e and StyleGAN. Given the multi-layer representation of latent vectors in \\( W^{+} \\subseteq \\mathbb{R}^{18 \\times 512} \\), we feed each layer into an independent ReDirTrans for redirection task given the provided target condition \\( c_{t}^{i} \\), where \\( i \\) represents a certain attribute. \\( \\tilde{c}^i \\) denotes the pseudo condition estimated directly from the inverted image by a pretrained HeadGazeNet \\( \\xi_{hg} \\) [44]. We calculate errors between estimated conditions \\( \\hat{c}_k^i, k \\in [1,18] \\) from multiple ReDirTrans and \\( \\tilde{c}^i \\) for supervising the trainable weights learning (green arrow) based on the Layer-wise Weights Loss described in Eq. 10 to decide which layers should contribute more to a certain attribute redirection. Given the estimated weights and initial latent vectors \\( f_{s} \\), we can acquire the final disentangled latent vector \\( \\hat{f}_{t,d} \\) based on Eq. 2 for redirected samples synthesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.473, + 0.535 + ], + "angle": 0, + "content": "tor \\( P \\) and redirects them given the newly provided target conditions \\( c_{t} \\). Then we deproject both original embeddings \\( \\mathbf{z}_{\\mathrm{s}} \\) and redirected embeddings \\( \\hat{\\mathbf{z}}_{\\mathrm{t}} \\) back to the feature space \\( \\mathcal{F} \\) through the weights-sharing deprojectors \\( DP \\) to acquire latent residuals. These residuals contain source and target status of aimed attributes, denoted as \\( \\Delta f_{s}^{i} \\) and \\( \\Delta \\hat{f}_t^i \\), respectively. Inspired by addition and subtraction [10, 31] for face editing in feature space \\( \\mathcal{F} \\), the edited latent vector is" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.545, + 0.47, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {t} = f _ {s} + \\sum_ {i = 1} ^ {M} \\left(- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}\\right), i \\in [ 1, M ], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.473, + 0.794 + ], + "angle": 0, + "content": "where the subtraction means removing source status and the addition indicates bringing in new status. The projector \\( P \\) ensures that the dimension of embeddings can be customized based on the degrees of freedom of desired attributes, and the transformations can be interpretable with physical meanings. The deprojector \\( DP \\) enables the original and edited features in the same feature space, allowing ReDirTrans to be compatible with pretrained encoder-generator pairs that are typically trained together without intermediate (editing) modules. ReDirTrans reduces parameters by skipping projection (compression) and deprojection (decompression) of the features that are not relevant to the desired attributes, but vital for final image synthesis." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.312, + 0.819 + ], + "angle": 0, + "content": "3.3. Predefined Feature Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Except for the trainable encoder-decoder (or -generator) pair to learn a specific feature space for redirection task as ST-ED did, ReDirTrans can also work in the predefined feature space to coordinate with fixed, pretrained encoder-generator pairs. For our implementation, we chose the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.895, + 0.671 + ], + "angle": 0, + "content": "\\(W^{+} \\in \\mathbb{R}^{18 \\times 512}\\) feature space [1], which allows us to utilize StyleGAN [22] for generating high-quality, high-fidelity face images. We refer to this implementation as ReDirTrans-GAN. Considering multi-layer representation of the latent vector [1] and its semantic disentangled property between different layers [2, 15] in \\(W^{+}\\) space, we proposed layer-wiseirectors, shown in Fig. 2, rather than using a single ReDirTrans to process all (18) layers of the latent vector. To largely reduce the interference between different layers during redirection, we assume that if one attribute's condition can be estimated from certain layers with less errors than the others, then we can 'modify' these certain layers with higher weights \\(p_k^i\\), \\(k \\in [1,18]\\) than others to achieve redirection of the corresponding attribute \\(i\\) only. \\(P^i = [p_1^i,\\dots ,p_{18}^i]^T \\in \\mathbb{R}^{18 \\times 1}\\), as part of network parameters, is trained given the loss function described in Eq. 10. The final disentangled latent vectors after redirection is" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.689, + 0.892, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {t, d} = f _ {s} + \\sum_ {i = 1} ^ {M} \\boldsymbol {P} ^ {i} \\odot (- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}), i \\in [ 1, M ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\odot\\) means element-wise multiplication and \\((- \\Delta f_{s}^{i} + \\Delta \\hat{f}_{t}^{i}) \\in \\mathbb{R}^{18 \\times 512}\\). One challenge regarding the predefined feature space comes from the inversion quality. There exist attribute differences between input images and inverted results, shown in Fig. 4 and 6, which means that the conditions in source images cannot be estimated from source latent vectors. To solve this, instead of using conditions from source images, we utilized estimated conditions from the inverted images, which ensures the correctness and consistence of conditions learning from latent vectors." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5550" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.248, + 0.108 + ], + "angle": 0, + "content": "3.4. Training Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.266 + ], + "angle": 0, + "content": "Given a pair of source and target face images, \\(I_{s}\\) and \\(I_{t}\\) from the same person, we utilize an encoder to first transform \\(I_{s}\\) into the feature space \\(\\mathcal{F}\\), denoted as \\(f_{s}\\). We further disentangle \\(f_{s}\\) into the gaze-direction-related embedding \\(z_{s}^{1}\\) and the head-orientation-related embedding \\(z_{s}^{2}\\) with corresponding estimated conditions: \\(\\hat{c}_s^1\\) and \\(\\hat{c}_s^2\\) by the projector \\(\\pmb{P}\\). Then we build rotation matrices using the pitch and yaw from estimated conditions \\((\\hat{c}_s^1,\\hat{c}_s^2)\\) and target conditions \\((c_t^1,c_t^2)\\) to normalize embeddings and redirect them to the new status, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.273, + 0.47, + 0.298 + ], + "angle": 0, + "content": "\\[\n\\text {N o r m a l i z a t i o n :} z _ {N} ^ {i} = \\mathbf {R} ^ {- 1} \\left(\\hat {c} _ {s} ^ {i}\\right) \\cdot z _ {s} ^ {i}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.295, + 0.381, + 0.312 + ], + "angle": 0, + "content": "Redirection: \\(\\hat{z}_t^i = \\mathbf{R}(c_t^i)\\cdot z_N^i\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.488 + ], + "angle": 0, + "content": "where \\( i \\in \\{1, 2\\} \\), representing gaze directions and head orientations, respectively, and \\( z_N^i \\) denotes the normalized embedding of the corresponding attribute. We feed the original embedding \\( z_s^i \\) and the modified embedding \\( \\hat{z}_t^i \\) into the weights-sharing deprojectors \\( DP \\) to transform these embeddings back to the feature space \\( \\mathcal{F} \\) as the residuals. Given these residuals, we implement subtraction and addition operations over \\( f_s \\) as described in Eq. 1 (or Eq. 2) to acquire the edited latent vector \\( \\hat{f_t} \\) (or \\( \\hat{f_{t,d}} \\)), which is sent to a generator for synthesizing redirected face image \\( \\hat{I}_t \\). \\( \\hat{I}_t \\) should have the same gaze direction and head orientation as \\( I_t \\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.494, + 0.271, + 0.511 + ], + "angle": 0, + "content": "3.5. Learning Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.579 + ], + "angle": 0, + "content": "We supervise the relationship between the generated image \\(\\hat{I}_t\\) and the target image \\(I_t\\) with several loss functions: pixel-wise reconstruction loss, LPIPS metric [43] and attributes loss by a task-related pretrained model." + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.585, + 0.47, + 0.606 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\hat {I} _ {t} - I _ {t} \\right| \\right| _ {2}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.612, + 0.47, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L P I P S} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\psi (\\hat {I} _ {t}) - \\psi (I _ {t}) \\right| \\right| _ {2}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.636, + 0.469, + 0.655 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a t t} (\\hat {I} _ {t}, I _ {t}) = \\langle \\xi_ {h g} (\\hat {I} _ {t}), \\xi_ {h g} (I _ {t}) \\rangle , \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.469, + 0.723 + ], + "angle": 0, + "content": "where \\(\\psi (\\cdot)\\) denotes the perceptual feature extractor [43], \\(\\xi_{hg}(\\cdot)\\) represents the pretrained HeadGazeNet [44] to estimate the gaze and head pose from images and \\(\\langle u,v\\rangle =\\) \\(\\arccos \\frac{u\\cdot v}{||u||\\cdot||v||}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Identity Loss. Identity preservation after redirection is critical for the face editing task. Considering this, we calculate the cosine similarity of the identity-related features between the source image and the redirected image:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.792, + 0.47, + 0.812 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I D} (\\hat {I} _ {t}, I _ {s}) = 1 - \\langle \\phi (\\hat {I} _ {t}), \\phi (I _ {s}) \\rangle , \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.818, + 0.442, + 0.835 + ], + "angle": 0, + "content": "where \\(\\phi (\\cdot)\\) denotes the pretrained ArcFace [11] model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.839, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Label Loss. We have ground truth of gaze directions and head orientations, which can guide the conditions learning from the input latent vectors for the normalization step:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.892, + 0.469, + 0.91 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l a b} \\left(\\hat {c} _ {s} ^ {i}, c _ {s} ^ {i}\\right) = \\left\\langle \\hat {c} _ {s} ^ {i}, c _ {s} ^ {i} \\right\\rangle , i \\in \\{1, 2 \\}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.214 + ], + "angle": 0, + "content": "Embedding Loss. The normalized embeddings only contain the canonical status of the corresponding attribute after the inverse rotation applied to the original estimated embeddings, shown in Fig. 1. Thus the normalized embeddings given a certain attribute across different samples within batch \\( B \\) should be consistent. To reduce the number of possible pairs within a batch, we utilize the first normalized embedding \\( z_{N,1}^{i} \\) as the basis:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.224, + 0.893, + 0.268 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e m b} = \\frac {1}{B - 1} \\sum_ {j = 2} ^ {B} \\langle z _ {N, 1} ^ {i}, z _ {N, j} ^ {i} \\rangle , i \\in \\{1, 2 \\}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Layer-wise Weights Loss. This loss is specifically designed for the \\( W^{+} \\) space to decide the weights \\( p_{i} \\) of which layer should contribute more to the aimed attributes editing. Firstly, we calculate the layer-wise estimated conditions \\( \\hat{c}_k^i \\) and calculate estimated pseudo labels \\( \\tilde{c}^i \\). Secondly, we have layer-wise estimated label errors by \\( \\langle \\hat{c}_k^i, \\tilde{c}^i \\rangle \\). Lastly, we calculate the cosine similarity between the reciprocal of label errors and weights of layers as the loss:" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.405, + 0.892, + 0.439 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p r o b} = \\langle \\left\\{p _ {k} \\right\\}, \\left\\{\\frac {1}{\\left\\langle \\hat {c} _ {k} ^ {i} , \\tilde {c} ^ {i} \\right\\rangle} \\right\\}, k \\in [ 1, K ], i \\in \\{1, 2 \\}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.446, + 0.795, + 0.462 + ], + "angle": 0, + "content": "where \\(K\\) is the number of layers for editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Full Loss. The combined loss function for supervising the redirection process is:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.507, + 0.892, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\lambda_ {r} \\mathcal {L} _ {r e c} + \\lambda_ {L} \\mathcal {L} _ {L P I P S} + \\lambda_ {I D} \\mathcal {L} _ {I D} + \\lambda_ {a} \\mathcal {L} _ {a t t} \\tag {11} \\\\ + \\lambda_ {l} \\mathcal {L} _ {l a b} + \\lambda_ {e} \\mathcal {L} _ {e m b} + \\lambda_ {p} \\mathcal {L} _ {p r o b}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.582 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{LPIPS}\\) and \\(\\mathcal{L}_{prob}\\) are utilized only when the pretrained StyleGAN is used as the generator." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.634, + 0.612 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.6, + 0.635 + ], + "angle": 0, + "content": "4.1. datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.703 + ], + "angle": 0, + "content": "We utilize GazeCapture [24] training subset to train the redirector and assess the performance with its test subset, MPIIFaceGaze and CelebA-HQ [20]. Supplementary material provides more information about these datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.688, + 0.727 + ], + "angle": 0, + "content": "4.2. Evaluation Criteria" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.765 + ], + "angle": 0, + "content": "We follow metrics utilized by ST-ED [44] to evaluate different redirectors' performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.892, + 0.857 + ], + "angle": 0, + "content": "Redirection Error. We measure the redirection accuracy in image space by a pre-trained ResNet-50 based [16] head pose and gaze estimator \\(\\xi_{hg}^{\\prime}\\), which is unseen during the training. Given the target image \\(I_{t}\\) and the generated one \\(\\hat{I}_t\\) redirected by conditions of \\(I_{t}\\), we report the angular error between \\(\\xi_{hg}^{\\prime}(\\hat{I}_{t})\\) and \\(\\xi_{hg}^{\\prime}(I_t)\\) as the redirection errors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Disentanglement Error. We quantify the disentanglement error by the condition's fluctuation range of one attribute when we redirect the other one. The redirection" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5551" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.487, + 0.219 + ], + "angle": 0, + "content": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.6023.9890.7553.0670.257
He et al.†[17]4.6171.3920.5603.9250.223
VecGAN [10]2.2820.8240.4012.2050.197
ST-ED [44]2.3850.8000.3842.1870.208
ReDirTrans2.1630.7530.4292.1550.197
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.342 + ], + "angle": 0, + "content": "Table 1. Within-dataset quantitative comparison (GazeCapture test subset) between different methods for redirecting head orientations and gaze directions. (Lower is better). Head (Gaze) Redir denotes the redirection accuracy in degree between the redirected image and the target image given head orientations (gaze directions). Head (Gaze) Induce denotes the errors in degree on gaze (head) when we redirect the head (gaze). \\(\\dagger\\) denotes copied results from [44]. Other methods are retrained given previous papers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.429 + ], + "angle": 0, + "content": "angle \\(\\epsilon\\) follows \\(\\mathcal{U}(-0.1\\pi, 0.1\\pi)\\). For example, when we redirect the head pose of the generated image \\(\\hat{I}_t\\) by \\(\\epsilon\\) and generate a new one \\(\\hat{I}_t'\\), we calculate the angular error of the estimated gaze directions between \\(\\xi_{hq}'(\\hat{I}_t)\\) and \\(\\xi_{hq}'(I_t')\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.475 + ], + "angle": 0, + "content": "LPIPS. LPIPS is able to measure the distortion [43] and image similarity in gaze directions [17] between images, which is applied to evaluate the redirection performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.411, + 0.501 + ], + "angle": 0, + "content": "4.3. Redirectors in Learnable Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We compared quantitative performance of different redirectors, which were trained along with the trainable encoder-decoder pair designed by ST-ED on \\(128 \\times 128\\) images with restricted face ranges, given the criteria proposed in Sec. 4.2. Table 1 and Table 2 present within-dataset and cross-dataset performance, respectively. From these tables, we observe that our proposed ReDirTrans achieved more accurate redirection and better LPIPS compared with other state-of-the-art methods by considering the extra embedding space \\(\\mathcal{Z}\\) for redirecting embeddings of aimed attributes only and maintaining other attributes including the appearance-related information in the original latent space \\(\\mathcal{F}\\). ST-ED [44] projected input latent vectors into nine embeddings including the non-varying embedding \\(z^0\\). This appearance-related high dimensional embedding \\(z^0\\) requires more parameters than ReDirTrans during projection. After redirecting the embeddings of aimed attributes, ST-ED deprojected a stack of \\(z^0\\), redirected embeddings, and rest unvaried embeddings of other attributes back to the feature space for decoding. This projection-deprojection process of non-varying embedding \\(z^0\\) results in loss of appearance and worse LPIPS, as depicted in Fig. 3. VecGAN [10] was proposed to edit the attributes only within the feature space by addition and subtraction operations. Since there is no projection-deprojection process, given the original latent code, LPIPS performance is bet" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.909, + 0.219 + ], + "angle": 0, + "content": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.4883.0310.7862.7830.260
He et al.†[17]5.0921.3720.6843.4110.241
VecGAN [10]2.6701.2420.3911.9410.207
ST-ED [44]2.3801.0850.3711.7820.212
ReDirTrans2.3800.9850.3911.7820.202
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.3 + ], + "angle": 0, + "content": "Table 2. Cross-dataset quantitative comparison (MPIIFaceGaze) between different methods for redirecting head orientations and gaze directions. (Lower is better). Notations are the same as them in the Table 1. \\(\\dagger\\) denotes copied results from [44]. Other methods are retrained given previous papers." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.314, + 0.895, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.533 + ], + "angle": 0, + "content": "Figure 3. Qualitative Comparison of ReDirTrans and ST-ED in GazeCapture. ReDirTrans preserves more facial attributes, such as lip thickness and sharpness of the beard." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.608 + ], + "angle": 0, + "content": "ter than ST-ED. However, as no extra embedding space was built for the aimed attributes editing, both redirection accuracy and the disentanglement process were affected." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.62, + 0.838, + 0.636 + ], + "angle": 0, + "content": "4.4. Redirectors in Predefined Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Except for using the trainable encoder-decoder pair of ST-ED, we also implemented our proposed ReDirTrans within a predefined feature space \\( W^{+} \\) to achieve redirection task in full face images with desired resolution. We utilized e4e [35] as the pre-trained encoder, which can transform input images into latent vectors in \\( W^{+} \\), and we chose StyleGAN2 [22] as the pre-trained generator to build ReDirTrans-GAN. Fig. 4 shows qualitative comparison between ST-ED and ReDirTrans-GAN in the GazeCapture test subset with providing target images from the same subject. ReDirTrans-GAN successfully redirected gaze directions and head orientations to the status provided by target images while maintaining the same appearance patterns with \\( 1024 \\times 1024 \\) full face images. Due to the design of ReDirTrans, which maintains unrelated attributes and appearance information in the initial latent space instead of going through the projection-deprojection pro" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "5552" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.089, + 0.887, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.388, + 0.861, + 0.404 + ], + "angle": 0, + "content": "Figure 4. Qualitatively comparisons between ST-ED and ReDirTrans-GAN. Red boxes represent different face covering ranges." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.426, + 0.436, + 0.526 + ], + "angle": 0, + "content": "
Q%GazeCaptureMPIIFaceGaze
Raw ↓Aug ↓Raw ↓Aug ↓
255.8755.2388.6077.096
504.7414.5066.7876.113
754.3084.2006.1655.767
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Table 3. Learning-based gaze estimation errors (in degrees) in GazeCapture and MPIIFaceGaze with or without redirected data augmentation. \\(Q\\%\\) represents percent of labeled data in 10,000 images for training ReDirTrans-GAN. 'Raw' or 'Aug' mean training the gaze estimator with real data or with real & redirected data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.742 + ], + "angle": 0, + "content": "cess, ReDirTrans-GAN keeps more facial attributes such as expressions, mustaches, bangs compared with ST-ED. Fig. 5 presents qualitative results with assigned conditions (pitch and yaw of gaze directions and head orientations) in CelebA-HQ [20]. ReDirTrans-GAN can achieve out-of-domain redirection tasks in predefined feature space while maintaining other facial attributes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.265, + 0.772 + ], + "angle": 0, + "content": "4.5. Data Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To solve data scarcity of the downstream task: learning-based gaze estimation, we utilized redirected samples with assigned gaze directions and head orientations to augment training data. We randomly chose 10,000 images from the GazeCapture training subset to retrain ReDirTrans-GAN with using only \\(Q\\%\\) ground-truth labels of them. The HeadGazeNet \\(\\xi_{hg}(\\cdot)\\) was also retrained given the same \\(Q\\%\\) labeled data and \\(Q \\in \\{25,50,75\\}\\). Then we utilized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.537 + ], + "angle": 0, + "content": "ReDirTrans-GAN to generate redirected samples given provided conditions over \\(Q\\%\\) labeled real data and combined the real and redirected data as an augmented dataset with size \\(2 \\times 10,000 \\times Q\\%\\) for training a gaze estimator. Table 3 presented within-dataset and cross-dataset performance and demonstrated consistent improvements for the downstream task given redirected samples as data augmentation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.544, + 0.833, + 0.56 + ], + "angle": 0, + "content": "4.6. Challenge in Predefined Feature Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.765 + ], + "angle": 0, + "content": "One challenge for redirection tasks in predefined feature space comes from inconsistency between input and inverted images, mentioned in Sec. 3.3. We can observe that the existing gaze differences between input and inverted images in Fig. 4. In some cases, the gaze directions are changed after GAN inversion, which means that the encoded latent codes do not necessarily keep the original gaze directions. Thus, instead of using provided gaze directions of input images during the training, we utilized estimated gaze directions from inverted results to correctly normalize the gaze and head pose to the canonical status. This process ensures correctness when further new directions are added, making the training process more consistent." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.664, + 0.787 + ], + "angle": 0, + "content": "4.7. Gaze Correction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ReDirTrans can correct gaze directions of inverted results by viewing input images as the target ones. e4e guarantees high editability, which is at the cost of inversion performance [35]. Fig. 6 shows several samples which failed to maintain input images' gaze directions even by the ReStyle encoder [3], which iteratively updates the latent codes given the differences between the input and inverted results. With" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5553" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.444, + 0.895, + 0.486 + ], + "angle": 0, + "content": "Figure 5. Redirection results given assigned (pitch, yaw) conditions of gaze directions (g) and head orientations (h). The first two columns are input and inversion results with e4e [35] and StyleGAN [22]. The following columns are redirected samples with assigned redirection values based on the latent code estimated from e4e." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.51, + 0.47, + 0.829 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.839, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Figure 6. Gaze correction in CelebA-HQ by viewing the same image as both the input and target." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.892, + 0.543 + ], + "angle": 0, + "content": "ReDirTrans-GAN, we can successfully correct the wrong gaze based on inverted results from e4e." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.628, + 0.573 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We introduce ReDirTrans, a novel architecture working in either learnable or predefined latent space for high-accuracy redirection of gaze directions and head orientations. ReDirTrans projects input latent vectors into aimed-attribute pseudo labels and embeddings for redirection in an interpretable manner. Both the original and redirected embeddings of aimed attributes are deprojected to the initial latent space for modifying the input latent vectors by subtraction and addition. This pipeline ensures no compression loss to other facial attributes, including appearance information, which essentially reduces effects on the distribution of input latent vectors in initial latent space. Thus we successfully implemented ReDirTrans-GAN in the predefined feature space working with fixed StyleGAN to achieve redirection in high-resolution full-face images, either by assigned values or estimated conditions from target images while maintaining other facial attributes. The redirected samples with assigned conditions can be utilized as data augmentation for further improving learning-based gaze estimation performance. In future work, instead of a pure 2D solution, 3D data can be included for further improvements." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5554" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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UC San Diego, $^{2}$ Qualcomm Technologies, Inc. + +{sjin，tqn001}@eng.ucsd.edu，{zhewang，wlei，nbi}@qti=qualcomm.com + +# Abstract + +Learning-based gaze estimation methods require large amounts of training data with accurate gaze annotations. Facing such demanding requirements of gaze data collection and annotation, several image synthesis methods were proposed, which successfully redirected gaze directions precisely given the assigned conditions. However, these methods focused on changing gaze directions of the images that only include eyes or restricted ranges of faces with low resolution (less than $128 \times 128$ ) to largely reduce interference from other attributes such as hairs, which limits application scenarios. To cope with this limitation, we proposed a portable network, called ReDirTrans, achieving latent-to-latent translation for redirecting gaze directions and head orientations in an interpretable manner. ReDirTrans projects input latent vectors into aimed-attribute embeddings only and redirects these embeddings with assigned pitch and yaw values. Then both the initial and edited embeddings are projected back (deprojected) to the initial latent space as residuals to modify the input latent vectors by subtraction and addition, representing old status removal and new status addition. The projection of aimed attributes only and subtraction-addition operations for status replacement essentially mitigate impacts on other attributes and the distribution of latent vectors. Thus, by combining ReDirTrans with a pretrained fixed e4e-StyleGAN pair, we created ReDirTrans-GAN, which enables accurately redirecting gaze in full-face images with $1024 \times 1024$ resolution while preserving other attributes such as identity, expression, and hairstyle. Furthermore, we presented improvements for the downstream learning-based gaze estimation task, using redirected samples as dataset augmentation. + +# 1. Introduction + +Gaze is a crucial non-verbal cue that conveys attention and awareness in interactions. Its potential applications include mental health assessment [5,18], social attitudes analysis [19], human-computer interaction [12], automotive assistance [30], AR/VR [6,34]. However, developing a robust + +unified learning-based gaze estimation model requires large amounts of data from multiple subjects with precise gaze annotations [42, 44]. Collecting and annotating such an appropriate dataset is complex and expensive. To overcome this challenge, several methods have been proposed to redirect gaze directions [17, 39, 41, 42, 44] in real images with assigned directional values to obtain and augment training data. Some works focused on generating eye images with new gaze directions by either 1) estimating warping maps [41, 42] to interpolate pixel values or 2) using encoder-generator pairs to generate redirected eye images [17, 39]. + +ST-ED [44] was the first work to extend high-accuracy gaze redirection from eye images to face images. By disentangling several attributes, including person-specific appearance, it can explicitly control gaze directions and head orientations. However, due to the design of the encoder-decoder structure and limited ability to maintain appearance features by a $1 \times 1024$ projected appearance embedding, ST-ED generates low-resolution ( $128 \times 128$ ) images with restricted face range (no hair area), which narrows the application ranges and scenarios of gaze redirection. + +As for latent space manipulation for face editing tasks, large amounts of works [2-4, 14, 31, 35] were proposed to modify latent vectors in predefined latent spaces (W [21], $W^{+}$ [1] and $S$ [40]). Latent vectors in these latent spaces can work with StyleGAN [21, 22] to generate high-quality and high-fidelity face images with desired attribute editing. Among these methods, Wu et.al [40] proposed the latent space $S$ working with StyleGAN, which achieved only one degree-of-freedom gaze redirection by modifying a certain channel of latent vectors in $S$ by an uninterpreted value instead of pitch and yaw values of gaze directions. + +Considering these, we proposed a new method, called ReDirTrans, to achieve latent-to-latent translation for redirecting gaze directions and head orientations in high-resolution full-face images based on assigned directional values. Specifically, we designed a framework to project input latent vectors from a latent space into the aimed-attribute-only embedding space for an interpretable redirection process. This embedding space consists of estimated pseudo conditions and embeddings of aimed attributes, + +where conditions describe deviations from the canonical status and embeddings are the 'carriers' of the conditions. In this embedding space, all transformations are implemented by rotation matrices multiplication built from pitch and yaw values, which can make the redirection process more interpretable and consistent. After the redirection process, the original embeddings and redirected ones are both decoded back to the initial latent space as the residuals to modify the input latent vectors by subtraction and addition operations. These operations represent removing the old state and adding a new one, respectively. ReDirTrans only focuses on transforming embeddings of aimed attributes and achieves status replacement by the residuals outputted from weight-sharing deprojectors. ReDirTrans does not project or deproject other attributes with information loss; and it does not affect the distribution of input latent vectors. Thus ReDirTrans can also work in a predefined feature space with a fixed pretrained encoder-generator pair for the redirection task in desired-resolution images. + +In summary, our contributions are as follows: + +- A latent-to-latent framework, ReDirTrans, which projects latent vectors to an embedding space for an interpretable redirection process on aimed attributes and maintains other attributes, including appearance, in initial latent space with no information loss caused by projection-deprojection processes. +- A portable framework that can seamlessly integrate into a pretrained GAN inversion pipeline for high-accuracy redirection of gaze directions and head orientations, without the need for any parameter tuning of the encoder-generator pairs. +- A layer-wise architecture with learnable parameters that works with the fixed pretrained StyleGAN and achieves redirection tasks in high-resolution full-face images through ReDirTrans-GAN. + +# 2. Related Works + +Gaze and Head Redirection. Methods for redirecting gaze directions can be broadly classified into two categories: warping-based methods and generator-based methods. Deepwarp [13, 23] presented a deep network to learn warping maps between pairs of eye images with different gaze directions, which required large amounts of data with annotations. Yu et al. [41] utilized a pretrained gaze estimator and synthetic eye images to reduce the reliance on annotated real data. Yu et al. [42] further extended the warping-based methods in an unsupervised manner by adding a gaze representation learning network. As for the generator-based methods, He et al. [17] developed a GAN-based network for generating eye images with new gaze directions. FAZE [26] proposed an encoder-decoder architecture to transform eye images into latent vectors for redirection with rotation ma + +trix multiplication, and then decode the edited ones back to the synthetic images with new gaze directions. ST-ED [44] further extended the encoder-decoder pipeline from gaze redirection only to both head and gaze redirection over full face images by disentangling latent vectors, and achieving precise redirection performance. However, ST-ED generates images with a restricted face range (no hair area) with a size of $128 \times 128$ . We further improve the redirection task by covering the full face range with $1024 \times 1024$ resolution. + +Latent Space Manipulation. Numerous methods investigated the latent space working with StyleGAN [21,22] to achieve semantic editing in image space due to its meaningful and highly disentangled properties. As for the supervised methods, InterFaceGAN [31] determined hyperplanes for the corresponding facial attribute editing based on provided labels. StyleFlow [2] proposed mapping a sample from a prior distribution to a latent distribution conditioned on the target attributes estimated by pretrained attribute classifiers. Given the unsupervised methods, GANSpace [15], SeFa [32] and TensorGAN [14] leveraged principal components analysis, eigenvector decomposition and higher-order singular value decomposition to discover semantic directions in latent space, respectively. Other self-supervised methods proposed mixing of latent codes from other samples for local editing [8, 9], or incorporating the language model CLIP [29] for text-driven editing [27]. + +Domain Adaptation for Gaze Estimation. Domain gaps among different datasets restrict the application range of pretrained gaze estimation models. To narrow the gaps, a few domain adaptation approaches [37, 38] were proposed for the generic regression task. SimGAN [33] proposed an unsupervised domain adaptation method for narrowing the gaps between real and synthetic eye images. HGM [36] designed a unified 3D eyeball model for eye image synthesis and cross-dataset gaze estimation. PnP-GA [25] presented a gaze adaptation framework for generalizing gaze estimation in new domains based on collaborative learning. Qin et al. [28] utilized 3D face reconstruction to rotate head orientations together with changed eye gaze accordingly to enlarge overlapping gaze distributions among datasets. These adaptation methods typically rely on restricted face or eye images to alleviate interference from untargeted attributes. Our work incorporates the redirection task in a predefined meaningful feature space with controllable attributes to achieve high-resolution and full-face redirection. + +# 3. Method + +# 3.1. Problem Statements + +Our goal is to train a conditional latent-to-latent translation module for face editing with physical meaning, and it can work either with a trainable or fixed encoder-generator + +![](images/f5c6e3a7e2e0df519551640089b5b5c5d493548fa47b5346f49e1a3fa5da5a33.jpg) + +![](images/ec5480c06c4c5c167c52ec0d1e80a2156a5c5558a68b28ab41120504d8d10485.jpg) + +Figure 1. Conditional redirection pipeline and comparison among differentirectors. (a) We first encode the input image into the latent vector. Given the provided conditions, we modify the latent vector and send it to a generator for image synthesis with only aimed attribute redirection. (b) We compared our proposed redirector with two state-of-the-art methods by omitting common modules (basic encoders and decoders/generators) and focusing on the unique components: (b-1) VecGAN achieves editing in feature space $\mathcal{F}$ given projected conditions from latent vectors with a global direction $f_{N}^{i}$ . (b-2) ST-ED projects the latent vector into conditions and embeddings of aimed attributes, and one appearance-related high dimensional embedding $z_0$ in embedding space $\mathcal{Z}$ . After interpretable redirection process in space $\mathcal{Z}$ , all embeddings are concatenated and projected back to space $\mathcal{F}$ . (b-3) Our proposed ReDirTrans projects the latent vector into conditions and embeddings of aimed attributes only. After an interpretable redirection process, both original and redirected embeddings are deprojected back to initial space $\mathcal{F}$ as residuals. These residuals modify the input latent vector by subtraction and addition operations, which represent the initial status removal and the new status addition, respectively. This approach efficiently reduces effects on other attributes (especially the appearance related information) with fewer parameters than ST-ED. +![](images/5f4b7b8c9616552a5f869255d18740c00ce4b85060deaf282cbf5b7aa5450ba3.jpg) +source branch +Z embedding space +$\pmb{E}$ Encoder +P Projection +target branch +F latent space +G Generator + +![](images/0cd82f76051154d049a7ab57ab5f4ff588c134953eb8ce395762bf76f91b62aa.jpg) + +![](images/4973c70bc16e8b76a422e34b75caf80b261f535ec941f1ef79e58cace1ad58a5.jpg) +dition +$DP$ Deprojection +$\ominus$ subtraction + +![](images/12797991c75f3c5169432b024e3c1d475eda5d10bc66be5d3179a59f1a10db7c.jpg) +matrix multiplication +element-wise multiplication + +pair. This editing module first transforms input latent vectors from encoded feature space $\mathcal{F}$ to an embedding space $\mathcal{Z}$ for redirection in an interpretable manner. Then it departs the original and redirected embeddings back to the initial feature space $\mathcal{F}$ for editing input latent vectors. The edited latent vectors are fed into a generator for image synthesis with the desired status of aimed facial attributes. The previous GAN-based work [10,14,31] achieved a certain facial attribute editing with a global latent residual multiplied by a scalar without physical meaning to describe the relative deviation from the original status. To make the whole process interpretable and achieve redirection directly based on the new gaze directions or head poses, we follow the assumption proposed by [44], where the dimension of an embedding is decided by the corresponding attribute's degree of the freedom (DoF) and redirection process is achieved by the rotation matrices multiplication. Thus the transformation equivariant mappings can be achieved between the embedding space $\mathcal{Z}$ and image space. To be specific, normalized gazes or head poses can be represented by a two-dimensional embedding with the pitch and yaw as the controllable conditions. The embeddings can be edited (multi + +plied) by the rotation matrices built from the pitch and yaw for achieving redirection (rotation) of aimed attributes in image space accordingly through our proposed director. + +# 3.2. Redirector Architecture + +ST-ED is one of the state-of-the-art architectures for gaze and head poses redirection over face images [44] shown in Fig. 1 (b-2). ST-ED projects the input latent vector $f$ to non-varying embeddings $z^0$ and $M$ varying ones with corresponding estimated conditions $\{(z^i, \hat{c}^i) | i \in [1, M]\}$ , where $\hat{c}^i$ describes the estimated amount of deviation from the canonical status of the attribute $i$ , and it can be compared with the ground truth $c^i$ for the learning of conditions from latent vectors. The non-varying embedding $z^0$ defines subject's appearance, whose dimension is much larger (over twenty times larger in ST-ED) than other varying embeddings. It is inefficient to project input latent vectors into a high-dimensional embedding to maintain non-varying information such as identity, hairstyle, etc. Thus, we propose a new redirector architecture, called ReDirTrans, shown in Fig. 1 (b-3), which transforms the source latent vector $f_s$ to the embeddings of aimed attributes through the projec + +![](images/7f8bedac0913d6095076889871048a6117eb3979ef7a8ba9e52ddc2e0d00cbcc.jpg) +Figure 2. ReDirTrans-GAN: Layer-wise ReDirTrans with fixed e4e and StyleGAN. Given the multi-layer representation of latent vectors in $W^{+} \subseteq \mathbb{R}^{18 \times 512}$ , we feed each layer into an independent ReDirTrans for redirection task given the provided target condition $c_{t}^{i}$ , where $i$ represents a certain attribute. $\tilde{c}^i$ denotes the pseudo condition estimated directly from the inverted image by a pretrained HeadGazeNet $\xi_{hg}$ [44]. We calculate errors between estimated conditions $\hat{c}_k^i, k \in [1,18]$ from multiple ReDirTrans and $\tilde{c}^i$ for supervising the trainable weights learning (green arrow) based on the Layer-wise Weights Loss described in Eq. 10 to decide which layers should contribute more to a certain attribute redirection. Given the estimated weights and initial latent vectors $f_{s}$ , we can acquire the final disentangled latent vector $\hat{f}_{t,d}$ based on Eq. 2 for redirected samples synthesis. + +tor $P$ and redirects them given the newly provided target conditions $c_{t}$ . Then we deproject both original embeddings $\mathbf{z}_{\mathrm{s}}$ and redirected embeddings $\hat{\mathbf{z}}_{\mathrm{t}}$ back to the feature space $\mathcal{F}$ through the weights-sharing deprojectors $DP$ to acquire latent residuals. These residuals contain source and target status of aimed attributes, denoted as $\Delta f_{s}^{i}$ and $\Delta \hat{f}_t^i$ , respectively. Inspired by addition and subtraction [10, 31] for face editing in feature space $\mathcal{F}$ , the edited latent vector is + +$$ +\hat {f} _ {t} = f _ {s} + \sum_ {i = 1} ^ {M} \left(- \Delta f _ {s} ^ {i} + \Delta \hat {f} _ {t} ^ {i}\right), i \in [ 1, M ], \tag {1} +$$ + +where the subtraction means removing source status and the addition indicates bringing in new status. The projector $P$ ensures that the dimension of embeddings can be customized based on the degrees of freedom of desired attributes, and the transformations can be interpretable with physical meanings. The deprojector $DP$ enables the original and edited features in the same feature space, allowing ReDirTrans to be compatible with pretrained encoder-generator pairs that are typically trained together without intermediate (editing) modules. ReDirTrans reduces parameters by skipping projection (compression) and deprojection (decompression) of the features that are not relevant to the desired attributes, but vital for final image synthesis. + +# 3.3. Predefined Feature Space + +Except for the trainable encoder-decoder (or -generator) pair to learn a specific feature space for redirection task as ST-ED did, ReDirTrans can also work in the predefined feature space to coordinate with fixed, pretrained encoder-generator pairs. For our implementation, we chose the + +$W^{+} \in \mathbb{R}^{18 \times 512}$ feature space [1], which allows us to utilize StyleGAN [22] for generating high-quality, high-fidelity face images. We refer to this implementation as ReDirTrans-GAN. Considering multi-layer representation of the latent vector [1] and its semantic disentangled property between different layers [2, 15] in $W^{+}$ space, we proposed layer-wiseirectors, shown in Fig. 2, rather than using a single ReDirTrans to process all (18) layers of the latent vector. To largely reduce the interference between different layers during redirection, we assume that if one attribute's condition can be estimated from certain layers with less errors than the others, then we can 'modify' these certain layers with higher weights $p_k^i$ , $k \in [1,18]$ than others to achieve redirection of the corresponding attribute $i$ only. $P^i = [p_1^i,\dots ,p_{18}^i]^T \in \mathbb{R}^{18 \times 1}$ , as part of network parameters, is trained given the loss function described in Eq. 10. The final disentangled latent vectors after redirection is + +$$ +\hat {f} _ {t, d} = f _ {s} + \sum_ {i = 1} ^ {M} \boldsymbol {P} ^ {i} \odot (- \Delta f _ {s} ^ {i} + \Delta \hat {f} _ {t} ^ {i}), i \in [ 1, M ], \tag {2} +$$ + +where $\odot$ means element-wise multiplication and $(- \Delta f_{s}^{i} + \Delta \hat{f}_{t}^{i}) \in \mathbb{R}^{18 \times 512}$ . One challenge regarding the predefined feature space comes from the inversion quality. There exist attribute differences between input images and inverted results, shown in Fig. 4 and 6, which means that the conditions in source images cannot be estimated from source latent vectors. To solve this, instead of using conditions from source images, we utilized estimated conditions from the inverted images, which ensures the correctness and consistence of conditions learning from latent vectors. + +# 3.4. Training Pipeline + +Given a pair of source and target face images, $I_{s}$ and $I_{t}$ from the same person, we utilize an encoder to first transform $I_{s}$ into the feature space $\mathcal{F}$ , denoted as $f_{s}$ . We further disentangle $f_{s}$ into the gaze-direction-related embedding $z_{s}^{1}$ and the head-orientation-related embedding $z_{s}^{2}$ with corresponding estimated conditions: $\hat{c}_s^1$ and $\hat{c}_s^2$ by the projector $\pmb{P}$ . Then we build rotation matrices using the pitch and yaw from estimated conditions $(\hat{c}_s^1,\hat{c}_s^2)$ and target conditions $(c_t^1,c_t^2)$ to normalize embeddings and redirect them to the new status, respectively: + +$$ +\text {N o r m a l i z a t i o n :} z _ {N} ^ {i} = \mathbf {R} ^ {- 1} \left(\hat {c} _ {s} ^ {i}\right) \cdot z _ {s} ^ {i}, \tag {3} +$$ + +Redirection: $\hat{z}_t^i = \mathbf{R}(c_t^i)\cdot z_N^i$ + +where $i \in \{1, 2\}$ , representing gaze directions and head orientations, respectively, and $z_N^i$ denotes the normalized embedding of the corresponding attribute. We feed the original embedding $z_s^i$ and the modified embedding $\hat{z}_t^i$ into the weights-sharing deprojectors $DP$ to transform these embeddings back to the feature space $\mathcal{F}$ as the residuals. Given these residuals, we implement subtraction and addition operations over $f_s$ as described in Eq. 1 (or Eq. 2) to acquire the edited latent vector $\hat{f_t}$ (or $\hat{f_{t,d}}$ ), which is sent to a generator for synthesizing redirected face image $\hat{I}_t$ . $\hat{I}_t$ should have the same gaze direction and head orientation as $I_t$ . + +# 3.5. Learning Objectives + +We supervise the relationship between the generated image $\hat{I}_t$ and the target image $I_t$ with several loss functions: pixel-wise reconstruction loss, LPIPS metric [43] and attributes loss by a task-related pretrained model. + +$$ +\mathcal {L} _ {r e c} (\hat {I} _ {t}, I _ {t}) = \left| \left| \hat {I} _ {t} - I _ {t} \right| \right| _ {2}, \tag {4} +$$ + +$$ +\mathcal {L} _ {L P I P S} (\hat {I} _ {t}, I _ {t}) = \left| \left| \psi (\hat {I} _ {t}) - \psi (I _ {t}) \right| \right| _ {2}, \tag {5} +$$ + +$$ +\mathcal {L} _ {a t t} (\hat {I} _ {t}, I _ {t}) = \langle \xi_ {h g} (\hat {I} _ {t}), \xi_ {h g} (I _ {t}) \rangle , \tag {6} +$$ + +where $\psi (\cdot)$ denotes the perceptual feature extractor [43], $\xi_{hg}(\cdot)$ represents the pretrained HeadGazeNet [44] to estimate the gaze and head pose from images and $\langle u,v\rangle =$ $\arccos \frac{u\cdot v}{||u||\cdot||v||}$ + +Identity Loss. Identity preservation after redirection is critical for the face editing task. Considering this, we calculate the cosine similarity of the identity-related features between the source image and the redirected image: + +$$ +\mathcal {L} _ {I D} (\hat {I} _ {t}, I _ {s}) = 1 - \langle \phi (\hat {I} _ {t}), \phi (I _ {s}) \rangle , \tag {7} +$$ + +where $\phi (\cdot)$ denotes the pretrained ArcFace [11] model. + +Label Loss. We have ground truth of gaze directions and head orientations, which can guide the conditions learning from the input latent vectors for the normalization step: + +$$ +\mathcal {L} _ {l a b} \left(\hat {c} _ {s} ^ {i}, c _ {s} ^ {i}\right) = \left\langle \hat {c} _ {s} ^ {i}, c _ {s} ^ {i} \right\rangle , i \in \{1, 2 \}. \tag {8} +$$ + +Embedding Loss. The normalized embeddings only contain the canonical status of the corresponding attribute after the inverse rotation applied to the original estimated embeddings, shown in Fig. 1. Thus the normalized embeddings given a certain attribute across different samples within batch $B$ should be consistent. To reduce the number of possible pairs within a batch, we utilize the first normalized embedding $z_{N,1}^{i}$ as the basis: + +$$ +\mathcal {L} _ {e m b} = \frac {1}{B - 1} \sum_ {j = 2} ^ {B} \langle z _ {N, 1} ^ {i}, z _ {N, j} ^ {i} \rangle , i \in \{1, 2 \}. \tag {9} +$$ + +Layer-wise Weights Loss. This loss is specifically designed for the $W^{+}$ space to decide the weights $p_{i}$ of which layer should contribute more to the aimed attributes editing. Firstly, we calculate the layer-wise estimated conditions $\hat{c}_k^i$ and calculate estimated pseudo labels $\tilde{c}^i$ . Secondly, we have layer-wise estimated label errors by $\langle \hat{c}_k^i, \tilde{c}^i \rangle$ . Lastly, we calculate the cosine similarity between the reciprocal of label errors and weights of layers as the loss: + +$$ +\mathcal {L} _ {p r o b} = \langle \left\{p _ {k} \right\}, \left\{\frac {1}{\left\langle \hat {c} _ {k} ^ {i} , \tilde {c} ^ {i} \right\rangle} \right\}, k \in [ 1, K ], i \in \{1, 2 \}, \tag {10} +$$ + +where $K$ is the number of layers for editing. + +Full Loss. The combined loss function for supervising the redirection process is: + +$$ +\begin{array}{l} \mathcal {L} = \lambda_ {r} \mathcal {L} _ {r e c} + \lambda_ {L} \mathcal {L} _ {L P I P S} + \lambda_ {I D} \mathcal {L} _ {I D} + \lambda_ {a} \mathcal {L} _ {a t t} \tag {11} \\ + \lambda_ {l} \mathcal {L} _ {l a b} + \lambda_ {e} \mathcal {L} _ {e m b} + \lambda_ {p} \mathcal {L} _ {p r o b}, \\ \end{array} +$$ + +where $\mathcal{L}_{LPIPS}$ and $\mathcal{L}_{prob}$ are utilized only when the pretrained StyleGAN is used as the generator. + +# 4. Experiments + +# 4.1. datasets + +We utilize GazeCapture [24] training subset to train the redirector and assess the performance with its test subset, MPIIFaceGaze and CelebA-HQ [20]. Supplementary material provides more information about these datasets. + +# 4.2. Evaluation Criteria + +We follow metrics utilized by ST-ED [44] to evaluate different redirectors' performance. + +Redirection Error. We measure the redirection accuracy in image space by a pre-trained ResNet-50 based [16] head pose and gaze estimator $\xi_{hg}^{\prime}$ , which is unseen during the training. Given the target image $I_{t}$ and the generated one $\hat{I}_t$ redirected by conditions of $I_{t}$ , we report the angular error between $\xi_{hg}^{\prime}(\hat{I}_{t})$ and $\xi_{hg}^{\prime}(I_t)$ as the redirection errors. + +Disentanglement Error. We quantify the disentanglement error by the condition's fluctuation range of one attribute when we redirect the other one. The redirection + +
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.6023.9890.7553.0670.257
He et al.†[17]4.6171.3920.5603.9250.223
VecGAN [10]2.2820.8240.4012.2050.197
ST-ED [44]2.3850.8000.3842.1870.208
ReDirTrans2.1630.7530.4292.1550.197
+ +Table 1. Within-dataset quantitative comparison (GazeCapture test subset) between different methods for redirecting head orientations and gaze directions. (Lower is better). Head (Gaze) Redir denotes the redirection accuracy in degree between the redirected image and the target image given head orientations (gaze directions). Head (Gaze) Induce denotes the errors in degree on gaze (head) when we redirect the head (gaze). $\dagger$ denotes copied results from [44]. Other methods are retrained given previous papers. + +angle $\epsilon$ follows $\mathcal{U}(-0.1\pi, 0.1\pi)$ . For example, when we redirect the head pose of the generated image $\hat{I}_t$ by $\epsilon$ and generate a new one $\hat{I}_t'$ , we calculate the angular error of the estimated gaze directions between $\xi_{hq}'(\hat{I}_t)$ and $\xi_{hq}'(I_t')$ . + +LPIPS. LPIPS is able to measure the distortion [43] and image similarity in gaze directions [17] between images, which is applied to evaluate the redirection performance. + +# 4.3. Redirectors in Learnable Latent Space + +We compared quantitative performance of different redirectors, which were trained along with the trainable encoder-decoder pair designed by ST-ED on $128 \times 128$ images with restricted face ranges, given the criteria proposed in Sec. 4.2. Table 1 and Table 2 present within-dataset and cross-dataset performance, respectively. From these tables, we observe that our proposed ReDirTrans achieved more accurate redirection and better LPIPS compared with other state-of-the-art methods by considering the extra embedding space $\mathcal{Z}$ for redirecting embeddings of aimed attributes only and maintaining other attributes including the appearance-related information in the original latent space $\mathcal{F}$ . ST-ED [44] projected input latent vectors into nine embeddings including the non-varying embedding $z^0$ . This appearance-related high dimensional embedding $z^0$ requires more parameters than ReDirTrans during projection. After redirecting the embeddings of aimed attributes, ST-ED deprojected a stack of $z^0$ , redirected embeddings, and rest unvaried embeddings of other attributes back to the feature space for decoding. This projection-deprojection process of non-varying embedding $z^0$ results in loss of appearance and worse LPIPS, as depicted in Fig. 3. VecGAN [10] was proposed to edit the attributes only within the feature space by addition and subtraction operations. Since there is no projection-deprojection process, given the original latent code, LPIPS performance is bet + +
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.4883.0310.7862.7830.260
He et al.†[17]5.0921.3720.6843.4110.241
VecGAN [10]2.6701.2420.3911.9410.207
ST-ED [44]2.3801.0850.3711.7820.212
ReDirTrans2.3800.9850.3911.7820.202
+ +Table 2. Cross-dataset quantitative comparison (MPIIFaceGaze) between different methods for redirecting head orientations and gaze directions. (Lower is better). Notations are the same as them in the Table 1. $\dagger$ denotes copied results from [44]. Other methods are retrained given previous papers. + +![](images/900883f71044cfef1e7403209fb24c4db950020bb1a8cede28601898c264bb96.jpg) +Figure 3. Qualitative Comparison of ReDirTrans and ST-ED in GazeCapture. ReDirTrans preserves more facial attributes, such as lip thickness and sharpness of the beard. + +ter than ST-ED. However, as no extra embedding space was built for the aimed attributes editing, both redirection accuracy and the disentanglement process were affected. + +# 4.4. Redirectors in Predefined Latent Space + +Except for using the trainable encoder-decoder pair of ST-ED, we also implemented our proposed ReDirTrans within a predefined feature space $W^{+}$ to achieve redirection task in full face images with desired resolution. We utilized e4e [35] as the pre-trained encoder, which can transform input images into latent vectors in $W^{+}$ , and we chose StyleGAN2 [22] as the pre-trained generator to build ReDirTrans-GAN. Fig. 4 shows qualitative comparison between ST-ED and ReDirTrans-GAN in the GazeCapture test subset with providing target images from the same subject. ReDirTrans-GAN successfully redirected gaze directions and head orientations to the status provided by target images while maintaining the same appearance patterns with $1024 \times 1024$ full face images. Due to the design of ReDirTrans, which maintains unrelated attributes and appearance information in the initial latent space instead of going through the projection-deprojection pro + +![](images/26c94784e46de8e0846e412019b9273e1a93394ed0febf5b5904e43b1144ea4a.jpg) +Figure 4. Qualitatively comparisons between ST-ED and ReDirTrans-GAN. Red boxes represent different face covering ranges. + +
Q%GazeCaptureMPIIFaceGaze
Raw ↓Aug ↓Raw ↓Aug ↓
255.8755.2388.6077.096
504.7414.5066.7876.113
754.3084.2006.1655.767
+ +Table 3. Learning-based gaze estimation errors (in degrees) in GazeCapture and MPIIFaceGaze with or without redirected data augmentation. $Q\%$ represents percent of labeled data in 10,000 images for training ReDirTrans-GAN. 'Raw' or 'Aug' mean training the gaze estimator with real data or with real & redirected data. + +cess, ReDirTrans-GAN keeps more facial attributes such as expressions, mustaches, bangs compared with ST-ED. Fig. 5 presents qualitative results with assigned conditions (pitch and yaw of gaze directions and head orientations) in CelebA-HQ [20]. ReDirTrans-GAN can achieve out-of-domain redirection tasks in predefined feature space while maintaining other facial attributes. + +# 4.5. Data Augmentation + +To solve data scarcity of the downstream task: learning-based gaze estimation, we utilized redirected samples with assigned gaze directions and head orientations to augment training data. We randomly chose 10,000 images from the GazeCapture training subset to retrain ReDirTrans-GAN with using only $Q\%$ ground-truth labels of them. The HeadGazeNet $\xi_{hg}(\cdot)$ was also retrained given the same $Q\%$ labeled data and $Q \in \{25,50,75\}$ . Then we utilized + +ReDirTrans-GAN to generate redirected samples given provided conditions over $Q\%$ labeled real data and combined the real and redirected data as an augmented dataset with size $2 \times 10,000 \times Q\%$ for training a gaze estimator. Table 3 presented within-dataset and cross-dataset performance and demonstrated consistent improvements for the downstream task given redirected samples as data augmentation. + +# 4.6. Challenge in Predefined Feature Space + +One challenge for redirection tasks in predefined feature space comes from inconsistency between input and inverted images, mentioned in Sec. 3.3. We can observe that the existing gaze differences between input and inverted images in Fig. 4. In some cases, the gaze directions are changed after GAN inversion, which means that the encoded latent codes do not necessarily keep the original gaze directions. Thus, instead of using provided gaze directions of input images during the training, we utilized estimated gaze directions from inverted results to correctly normalize the gaze and head pose to the canonical status. This process ensures correctness when further new directions are added, making the training process more consistent. + +# 4.7. Gaze Correction + +ReDirTrans can correct gaze directions of inverted results by viewing input images as the target ones. e4e guarantees high editability, which is at the cost of inversion performance [35]. Fig. 6 shows several samples which failed to maintain input images' gaze directions even by the ReStyle encoder [3], which iteratively updates the latent codes given the differences between the input and inverted results. With + +![](images/0e76d545135a9e754566768092cc957125a47d7ee27050711ad9b02010bfef34.jpg) +Figure 5. Redirection results given assigned (pitch, yaw) conditions of gaze directions (g) and head orientations (h). The first two columns are input and inversion results with e4e [35] and StyleGAN [22]. The following columns are redirected samples with assigned redirection values based on the latent code estimated from e4e. + +![](images/bcc8defdfcefe94c8f9471f111e865417cb1e448de5f2b149fc8a479d90e2af8.jpg) +Figure 6. Gaze correction in CelebA-HQ by viewing the same image as both the input and target. + +ReDirTrans-GAN, we can successfully correct the wrong gaze based on inverted results from e4e. + +# 5. Conclusions + +We introduce ReDirTrans, a novel architecture working in either learnable or predefined latent space for high-accuracy redirection of gaze directions and head orientations. ReDirTrans projects input latent vectors into aimed-attribute pseudo labels and embeddings for redirection in an interpretable manner. Both the original and redirected embeddings of aimed attributes are deprojected to the initial latent space for modifying the input latent vectors by subtraction and addition. This pipeline ensures no compression loss to other facial attributes, including appearance information, which essentially reduces effects on the distribution of input latent vectors in initial latent space. Thus we successfully implemented ReDirTrans-GAN in the predefined feature space working with fixed StyleGAN to achieve redirection in high-resolution full-face images, either by assigned values or estimated conditions from target images while maintaining other facial attributes. The redirected samples with assigned conditions can be utilized as data augmentation for further improving learning-based gaze estimation performance. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1532-1540, 2021. 2 +[33] Ashish Shrivastava, Tomas Pfister, Oncel Tuzel, Joshua Susskind, Wenda Wang, and Russell Webb. Learning from simulated and unsupervised images through adversarial training. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2107-2116, 2017. 2 +[34] Vincent Sitzmann, Ana Serrano, Amy Pavel, Maneesh Agrawala, Diego Gutierrez, Belen Masia, and Gordon Wetzstein. Saliency in vr: How do people explore virtual environments? IEEE transactions on visualization and computer graphics, 24(4):1633-1642, 2018. 1 +[35] Omer Tov, Yuval Alaluf, Yotam Nitzan, Or Patashnik, and Daniel Cohen-Or. Designing an encoder for stylegan image manipulation. ACM Transactions on Graphics (TOG), 40(4):1-14, 2021. 1, 6, 7, 8 +[36] Kang Wang, Rui Zhao, and Qiang Ji. A hierarchical generative model for eye image synthesis and eye gaze estimation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 440-448, 2018. 2 +[37] Erroll Wood, Tadas Baltrusaitis, Louis-Philippe Morency, Peter Robinson, and Andreas Bulling. A 3d morphable eye region model for gaze estimation. In European Conference on Computer Vision, pages 297–313. Springer, 2016. 2 +[38] Erroll Wood, Tadas Baltrusaitis, Louis-Philippe Morency, Peter Robinson, and Andreas Bulling. Learning an appearance-based gaze estimator from one million synthesised images. In Proceedings of the Ninth Biennial ACM + +Symposium on Eye Tracking Research & Applications, pages 131-138, 2016. 2 +[39] Erroll Wood, Tadas Baltrusaitis, Louis-Philippe Morency, Peter Robinson, and Andreas Bulling. Gazedirector: Fully articulated eye gaze redirection in video. In Computer Graphics Forum, volume 37, pages 217–225. Wiley Online Library, 2018. 1 +[40] Zongze Wu, Dani Lischinski, and Eli Shechtman. 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Self-learning transformations for improving gaze and head redirection. 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Facing such demanding requirements of gaze data collection and annotation, several image synthesis methods were proposed, which successfully redirected gaze directions precisely given the assigned conditions. However, these methods focused on changing gaze directions of the images that only include eyes or restricted ranges of faces with low resolution (less than " + }, + { + "bbox": [ + 46, + 238, + 289, + 610 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 46, + 238, + 289, + 610 + ], + "type": "text", + "content": ") to largely reduce interference from other attributes such as hairs, which limits application scenarios. To cope with this limitation, we proposed a portable network, called ReDirTrans, achieving latent-to-latent translation for redirecting gaze directions and head orientations in an interpretable manner. ReDirTrans projects input latent vectors into aimed-attribute embeddings only and redirects these embeddings with assigned pitch and yaw values. Then both the initial and edited embeddings are projected back (deprojected) to the initial latent space as residuals to modify the input latent vectors by subtraction and addition, representing old status removal and new status addition. The projection of aimed attributes only and subtraction-addition operations for status replacement essentially mitigate impacts on other attributes and the distribution of latent vectors. Thus, by combining ReDirTrans with a pretrained fixed e4e-StyleGAN pair, we created ReDirTrans-GAN, which enables accurately redirecting gaze in full-face images with " + }, + { + "bbox": [ + 46, + 238, + 289, + 610 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 238, + 289, + 610 + ], + "type": "text", + "content": " resolution while preserving other attributes such as identity, expression, and hairstyle. Furthermore, we presented improvements for the downstream learning-based gaze estimation task, using redirected samples as dataset augmentation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Gaze is a crucial non-verbal cue that conveys attention and awareness in interactions. Its potential applications include mental health assessment [5,18], social attitudes analysis [19], human-computer interaction [12], automotive assistance [30], AR/VR [6,34]. However, developing a robust" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 213, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 346 + ], + "type": "text", + "content": " unified learning-based gaze estimation model requires large amounts of data from multiple subjects with precise gaze annotations [42, 44]. Collecting and annotating such an appropriate dataset is complex and expensive. To overcome this challenge, several methods have been proposed to redirect gaze directions [17, 39, 41, 42, 44] in real images with assigned directional values to obtain and augment training data. Some works focused on generating eye images with new gaze directions by either 1) estimating warping maps [41, 42] to interpolate pixel values or 2) using encoder-generator pairs to generate redirected eye images [17, 39]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "text", + "content": "ST-ED [44] was the first work to extend high-accuracy gaze redirection from eye images to face images. By disentangling several attributes, including person-specific appearance, it can explicitly control gaze directions and head orientations. However, due to the design of the encoder-decoder structure and limited ability to maintain appearance features by a " + }, + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "inline_equation", + "content": "1 \\times 1024" + }, + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "text", + "content": " projected appearance embedding, ST-ED generates low-resolution (" + }, + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 348, + 547, + 468 + ], + "type": "text", + "content": ") images with restricted face range (no hair area), which narrows the application ranges and scenarios of gaze redirection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "content": "As for latent space manipulation for face editing tasks, large amounts of works [2-4, 14, 31, 35] were proposed to modify latent vectors in predefined latent spaces (W [21], " + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "inline_equation", + "content": "W^{+}" + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "content": " [1] and " + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "content": " [40]). Latent vectors in these latent spaces can work with StyleGAN [21, 22] to generate high-quality and high-fidelity face images with desired attribute editing. Among these methods, Wu et.al [40] proposed the latent space " + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "content": " working with StyleGAN, which achieved only one degree-of-freedom gaze redirection by modifying a certain channel of latent vectors in " + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 472, + 548, + 603 + ], + "type": "text", + "content": " by an uninterpreted value instead of pitch and yaw values of gaze directions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "Considering these, we proposed a new method, called ReDirTrans, to achieve latent-to-latent translation for redirecting gaze directions and head orientations in high-resolution full-face images based on assigned directional values. Specifically, we designed a framework to project input latent vectors from a latent space into the aimed-attribute-only embedding space for an interpretable redirection process. This embedding space consists of estimated pseudo conditions and embeddings of aimed attributes," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5547" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "where conditions describe deviations from the canonical status and embeddings are the 'carriers' of the conditions. In this embedding space, all transformations are implemented by rotation matrices multiplication built from pitch and yaw values, which can make the redirection process more interpretable and consistent. After the redirection process, the original embeddings and redirected ones are both decoded back to the initial latent space as the residuals to modify the input latent vectors by subtraction and addition operations. These operations represent removing the old state and adding a new one, respectively. ReDirTrans only focuses on transforming embeddings of aimed attributes and achieves status replacement by the residuals outputted from weight-sharing deprojectors. ReDirTrans does not project or deproject other attributes with information loss; and it does not affect the distribution of input latent vectors. Thus ReDirTrans can also work in a predefined feature space with a fixed pretrained encoder-generator pair for the redirection task in desired-resolution images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 300, + 243, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 300, + 243, + 312 + ], + "spans": [ + { + "bbox": [ + 59, + 300, + 243, + 312 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 315, + 287, + 502 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 315, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 315, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 58, + 315, + 287, + 386 + ], + "type": "text", + "content": "- A latent-to-latent framework, ReDirTrans, which projects latent vectors to an embedding space for an interpretable redirection process on aimed attributes and maintains other attributes, including appearance, in initial latent space with no information loss caused by projection-deprojection processes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 390, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 390, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 58, + 390, + 287, + 450 + ], + "type": "text", + "content": "- A portable framework that can seamlessly integrate into a pretrained GAN inversion pipeline for high-accuracy redirection of gaze directions and head orientations, without the need for any parameter tuning of the encoder-generator pairs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 455, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 455, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 58, + 455, + 287, + 502 + ], + "type": "text", + "content": "- A layer-wise architecture with learnable parameters that works with the fixed pretrained StyleGAN and achieves redirection tasks in high-resolution full-face images through ReDirTrans-GAN." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 514, + 139, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 139, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 139, + 526 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 534, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 289, + 714 + ], + "type": "text", + "content": "Gaze and Head Redirection. Methods for redirecting gaze directions can be broadly classified into two categories: warping-based methods and generator-based methods. Deepwarp [13, 23] presented a deep network to learn warping maps between pairs of eye images with different gaze directions, which required large amounts of data with annotations. Yu et al. [41] utilized a pretrained gaze estimator and synthetic eye images to reduce the reliance on annotated real data. Yu et al. [42] further extended the warping-based methods in an unsupervised manner by adding a gaze representation learning network. As for the generator-based methods, He et al. [17] developed a GAN-based network for generating eye images with new gaze directions. FAZE [26] proposed an encoder-decoder architecture to transform eye images into latent vectors for redirection with rotation ma" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "trix multiplication, and then decode the edited ones back to the synthetic images with new gaze directions. ST-ED [44] further extended the encoder-decoder pipeline from gaze redirection only to both head and gaze redirection over full face images by disentangling latent vectors, and achieving precise redirection performance. However, ST-ED generates images with a restricted face range (no hair area) with a size of " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ". We further improve the redirection task by covering the full face range with " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 181, + 546, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 546, + 384 + ], + "type": "text", + "content": "Latent Space Manipulation. Numerous methods investigated the latent space working with StyleGAN [21,22] to achieve semantic editing in image space due to its meaningful and highly disentangled properties. As for the supervised methods, InterFaceGAN [31] determined hyperplanes for the corresponding facial attribute editing based on provided labels. StyleFlow [2] proposed mapping a sample from a prior distribution to a latent distribution conditioned on the target attributes estimated by pretrained attribute classifiers. Given the unsupervised methods, GANSpace [15], SeFa [32] and TensorGAN [14] leveraged principal components analysis, eigenvector decomposition and higher-order singular value decomposition to discover semantic directions in latent space, respectively. Other self-supervised methods proposed mixing of latent codes from other samples for local editing [8, 9], or incorporating the language model CLIP [29] for text-driven editing [27]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 385, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 547, + 613 + ], + "type": "text", + "content": "Domain Adaptation for Gaze Estimation. Domain gaps among different datasets restrict the application range of pretrained gaze estimation models. To narrow the gaps, a few domain adaptation approaches [37, 38] were proposed for the generic regression task. SimGAN [33] proposed an unsupervised domain adaptation method for narrowing the gaps between real and synthetic eye images. HGM [36] designed a unified 3D eyeball model for eye image synthesis and cross-dataset gaze estimation. PnP-GA [25] presented a gaze adaptation framework for generalizing gaze estimation in new domains based on collaborative learning. Qin et al. [28] utilized 3D face reconstruction to rotate head orientations together with changed eye gaze accordingly to enlarge overlapping gaze distributions among datasets. These adaptation methods typically rely on restricted face or eye images to alleviate interference from untargeted attributes. Our work incorporates the redirection task in a predefined meaningful feature space with controllable attributes to achieve high-resolution and full-face redirection." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 638, + 362, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 638, + 362, + 650 + ], + "spans": [ + { + "bbox": [ + 306, + 638, + 362, + 650 + ], + "type": "text", + "content": "3. 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Conditional redirection pipeline and comparison among differentirectors. (a) We first encode the input image into the latent vector. Given the provided conditions, we modify the latent vector and send it to a generator for image synthesis with only aimed attribute redirection. (b) We compared our proposed redirector with two state-of-the-art methods by omitting common modules (basic encoders and decoders/generators) and focusing on the unique components: (b-1) VecGAN achieves editing in feature space " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": " given projected conditions from latent vectors with a global direction " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "f_{N}^{i}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": ". (b-2) ST-ED projects the latent vector into conditions and embeddings of aimed attributes, and one appearance-related high dimensional embedding " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": " in embedding space " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": ". After interpretable redirection process in space " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": ", all embeddings are concatenated and projected back to space " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": ". (b-3) Our proposed ReDirTrans projects the latent vector into conditions and embeddings of aimed attributes only. After an interpretable redirection process, both original and redirected embeddings are deprojected back to initial space " + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 297, + 547, + 418 + ], + "type": "text", + "content": " as residuals. These residuals modify the input latent vector by subtraction and addition operations, which represent the initial status removal and the new status addition, respectively. This approach efficiently reduces effects on other attributes (especially the appearance related information) with fewer parameters than ST-ED." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 306, + 148, + 484, + 266 + ], + "blocks": [ + { + "bbox": [ + 306, + 148, + 484, + 266 + ], + "lines": [ + { + "bbox": [ + 306, + 148, + 484, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 148, + 484, + 266 + ], + "type": "image", + "image_path": "0cd82f76051154d049a7ab57ab5f4ff588c134953eb8ce395762bf76f91b62aa.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 329, + 268, + 348, + 277 + ], + "blocks": [ + { + "bbox": [ + 329, + 268, + 348, + 277 + ], + "lines": [ + { + "bbox": [ + 329, + 268, + 348, + 277 + ], + "spans": [ + { + "bbox": [ + 329, + 268, + 348, + 277 + ], + "type": "image", + "image_path": "4973c70bc16e8b76a422e34b75caf80b261f535ec941f1ef79e58cace1ad58a5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 349, + 268, + 376, + 277 + ], + "lines": [ + { + "bbox": [ + 349, + 268, + 376, + 277 + ], + "spans": [ + { + "bbox": [ + 349, + 268, + 376, + 277 + ], + "type": "text", + "content": "dition" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 274, + 278, + 324, + 286 + ], + "lines": [ + { + "bbox": [ + 274, + 278, + 324, + 286 + ], + "spans": [ + { + "bbox": [ + 274, + 278, + 324, + 286 + ], + "type": "inline_equation", + "content": "DP" + }, + { + "bbox": [ + 274, + 278, + 324, + 286 + ], + "type": "text", + "content": " Deprojection" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 330, + 278, + 374, + 287 + ], + "lines": [ + { + "bbox": [ + 330, + 278, + 374, + 287 + ], + "spans": [ + { + "bbox": [ + 330, + 278, + 374, + 287 + ], + "type": "inline_equation", + "content": "\\ominus" + }, + { + "bbox": [ + 330, + 278, + 374, + 287 + ], + "type": "text", + "content": " subtraction" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 379, + 268, + 394, + 277 + ], + "blocks": [ + { + "bbox": [ + 379, + 268, + 394, + 277 + ], + "lines": [ + { + "bbox": [ + 379, + 268, + 394, + 277 + ], + "spans": [ + { + "bbox": [ + 379, + 268, + 394, + 277 + ], + "type": "image", + "image_path": "12797991c75f3c5169432b024e3c1d475eda5d10bc66be5d3179a59f1a10db7c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 394, + 268, + 447, + 277 + ], + "lines": [ + { + "bbox": [ + 394, + 268, + 447, + 277 + ], + "spans": [ + { + "bbox": [ + 394, + 268, + 447, + 277 + ], + "type": "text", + "content": "matrix multiplication" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 374, + 278, + 467, + 287 + ], + "lines": [ + { + "bbox": [ + 374, + 278, + 467, + 287 + ], + "spans": [ + { + "bbox": [ + 374, + 278, + 467, + 287 + ], + "type": "text", + "content": "element-wise multiplication" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "content": "pair. This editing module first transforms input latent vectors from encoded feature space " + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "content": " to an embedding space " + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "content": " for redirection in an interpretable manner. Then it departs the original and redirected embeddings back to the initial feature space " + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "content": " for editing input latent vectors. The edited latent vectors are fed into a generator for image synthesis with the desired status of aimed facial attributes. The previous GAN-based work [10,14,31] achieved a certain facial attribute editing with a global latent residual multiplied by a scalar without physical meaning to describe the relative deviation from the original status. To make the whole process interpretable and achieve redirection directly based on the new gaze directions or head poses, we follow the assumption proposed by [44], where the dimension of an embedding is decided by the corresponding attribute's degree of the freedom (DoF) and redirection process is achieved by the rotation matrices multiplication. Thus the transformation equivariant mappings can be achieved between the embedding space " + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 449, + 289, + 712 + ], + "type": "text", + "content": " and image space. To be specific, normalized gazes or head poses can be represented by a two-dimensional embedding with the pitch and yaw as the controllable conditions. The embeddings can be edited (multi" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 449, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 486 + ], + "type": "text", + "content": "plied) by the rotation matrices built from the pitch and yaw for achieving redirection (rotation) of aimed attributes in image space accordingly through our proposed director." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 491, + 441, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 441, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 441, + 503 + ], + "type": "text", + "content": "3.2. Redirector Architecture" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "ST-ED is one of the state-of-the-art architectures for gaze and head poses redirection over face images [44] shown in Fig. 1 (b-2). ST-ED projects the input latent vector " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " to non-varying embeddings " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " varying ones with corresponding estimated conditions " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{(z^i, \\hat{c}^i) | i \\in [1, M]\\}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{c}^i" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " describes the estimated amount of deviation from the canonical status of the attribute " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ", and it can be compared with the ground truth " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "c^i" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " for the learning of conditions from latent vectors. The non-varying embedding " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " defines subject's appearance, whose dimension is much larger (over twenty times larger in ST-ED) than other varying embeddings. It is inefficient to project input latent vectors into a high-dimensional embedding to maintain non-varying information such as identity, hairstyle, etc. Thus, we propose a new redirector architecture, called ReDirTrans, shown in Fig. 1 (b-3), which transforms the source latent vector " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_s" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " to the embeddings of aimed attributes through the projec" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5549" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 72, + 491, + 210 + ], + "blocks": [ + { + "bbox": [ + 107, + 72, + 491, + 210 + ], + "lines": [ + { + "bbox": [ + 107, + 72, + 491, + 210 + ], + "spans": [ + { + "bbox": [ + 107, + 72, + 491, + 210 + ], + "type": "image", + "image_path": "7f8bedac0913d6095076889871048a6117eb3979ef7a8ba9e52ddc2e0d00cbcc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": "Figure 2. ReDirTrans-GAN: Layer-wise ReDirTrans with fixed e4e and StyleGAN. Given the multi-layer representation of latent vectors in " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "W^{+} \\subseteq \\mathbb{R}^{18 \\times 512}" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": ", we feed each layer into an independent ReDirTrans for redirection task given the provided target condition " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "c_{t}^{i}" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " represents a certain attribute. " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "\\tilde{c}^i" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " denotes the pseudo condition estimated directly from the inverted image by a pretrained HeadGazeNet " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "\\xi_{hg}" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " [44]. We calculate errors between estimated conditions " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "\\hat{c}_k^i, k \\in [1,18]" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " from multiple ReDirTrans and " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "\\tilde{c}^i" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " for supervising the trainable weights learning (green arrow) based on the Layer-wise Weights Loss described in Eq. 10 to decide which layers should contribute more to a certain attribute redirection. Given the estimated weights and initial latent vectors " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": ", we can acquire the final disentangled latent vector " + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "inline_equation", + "content": "\\hat{f}_{t,d}" + }, + { + "bbox": [ + 46, + 219, + 547, + 298 + ], + "type": "text", + "content": " based on Eq. 2 for redirected samples synthesis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": "tor " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " and redirects them given the newly provided target conditions " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "c_{t}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": ". Then we deproject both original embeddings " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " and redirected embeddings " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{\\mathrm{t}}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " back to the feature space " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " through the weights-sharing deprojectors " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "DP" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " to acquire latent residuals. These residuals contain source and target status of aimed attributes, denoted as " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\Delta f_{s}^{i}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\Delta \\hat{f}_t^i" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": ", respectively. Inspired by addition and subtraction [10, 31] for face editing in feature space " + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 327, + 289, + 423 + ], + "type": "text", + "content": ", the edited latent vector is" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 431, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 431, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 80, + 431, + 287, + 464 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {t} = f _ {s} + \\sum_ {i = 1} ^ {M} \\left(- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}\\right), i \\in [ 1, M ], \\tag {1}", + "image_path": "860342997e77eb48f42efd69c19c0df9e48357b15f695feb04f34b5501d252ae.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "text", + "content": "where the subtraction means removing source status and the addition indicates bringing in new status. The projector " + }, + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "text", + "content": " ensures that the dimension of embeddings can be customized based on the degrees of freedom of desired attributes, and the transformations can be interpretable with physical meanings. The deprojector " + }, + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "inline_equation", + "content": "DP" + }, + { + "bbox": [ + 46, + 472, + 289, + 628 + ], + "type": "text", + "content": " enables the original and edited features in the same feature space, allowing ReDirTrans to be compatible with pretrained encoder-generator pairs that are typically trained together without intermediate (editing) modules. ReDirTrans reduces parameters by skipping projection (compression) and deprojection (decompression) of the features that are not relevant to the desired attributes, but vital for final image synthesis." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 190, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 190, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 190, + 648 + ], + "type": "text", + "content": "3.3. Predefined Feature Space" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Except for the trainable encoder-decoder (or -generator) pair to learn a specific feature space for redirection task as ST-ED did, ReDirTrans can also work in the predefined feature space to coordinate with fixed, pretrained encoder-generator pairs. For our implementation, we chose the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "W^{+} \\in \\mathbb{R}^{18 \\times 512}" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": " feature space [1], which allows us to utilize StyleGAN [22] for generating high-quality, high-fidelity face images. We refer to this implementation as ReDirTrans-GAN. Considering multi-layer representation of the latent vector [1] and its semantic disentangled property between different layers [2, 15] in " + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "W^{+}" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": " space, we proposed layer-wiseirectors, shown in Fig. 2, rather than using a single ReDirTrans to process all (18) layers of the latent vector. To largely reduce the interference between different layers during redirection, we assume that if one attribute's condition can be estimated from certain layers with less errors than the others, then we can 'modify' these certain layers with higher weights " + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "p_k^i" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "k \\in [1,18]" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": " than others to achieve redirection of the corresponding attribute " + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": " only. " + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "inline_equation", + "content": "P^i = [p_1^i,\\dots ,p_{18}^i]^T \\in \\mathbb{R}^{18 \\times 1}" + }, + { + "bbox": [ + 304, + 327, + 547, + 531 + ], + "type": "text", + "content": ", as part of network parameters, is trained given the loss function described in Eq. 10. The final disentangled latent vectors after redirection is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 545, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 545, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 317, + 545, + 545, + 578 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {t, d} = f _ {s} + \\sum_ {i = 1} ^ {M} \\boldsymbol {P} ^ {i} \\odot (- \\Delta f _ {s} ^ {i} + \\Delta \\hat {f} _ {t} ^ {i}), i \\in [ 1, M ], \\tag {2}", + "image_path": "b6307983e849492504981c801c5ebe14a051cbe3dc67d8a5042b7d28f5612994.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "text", + "content": " means element-wise multiplication and " + }, + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "inline_equation", + "content": "(- \\Delta f_{s}^{i} + \\Delta \\hat{f}_{t}^{i}) \\in \\mathbb{R}^{18 \\times 512}" + }, + { + "bbox": [ + 304, + 592, + 547, + 715 + ], + "type": "text", + "content": ". One challenge regarding the predefined feature space comes from the inversion quality. There exist attribute differences between input images and inverted results, shown in Fig. 4 and 6, which means that the conditions in source images cannot be estimated from source latent vectors. To solve this, instead of using conditions from source images, we utilized estimated conditions from the inverted images, which ensures the correctness and consistence of conditions learning from latent vectors." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5550" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "type": "text", + "content": "3.4. Training Pipeline" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": "Given a pair of source and target face images, " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " from the same person, we utilize an encoder to first transform " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " into the feature space " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": ". We further disentangle " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " into the gaze-direction-related embedding " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "z_{s}^{1}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " and the head-orientation-related embedding " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "z_{s}^{2}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " with corresponding estimated conditions: " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "\\hat{c}_s^1" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "\\hat{c}_s^2" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " by the projector " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "\\pmb{P}" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": ". Then we build rotation matrices using the pitch and yaw from estimated conditions " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "(\\hat{c}_s^1,\\hat{c}_s^2)" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " and target conditions " + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "inline_equation", + "content": "(c_t^1,c_t^2)" + }, + { + "bbox": [ + 46, + 90, + 289, + 210 + ], + "type": "text", + "content": " to normalize embeddings and redirect them to the new status, respectively:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 93, + 216, + 287, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 216, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 93, + 216, + 287, + 236 + ], + "type": "interline_equation", + "content": "\\text {N o r m a l i z a t i o n :} z _ {N} ^ {i} = \\mathbf {R} ^ {- 1} \\left(\\hat {c} _ {s} ^ {i}\\right) \\cdot z _ {s} ^ {i}, \\tag {3}", + "image_path": "13df3fd2901cb71cfb5863807ac0fbdd57f43c3b740daeef3f2ea4e49bf7a549.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 233, + 233, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 233, + 233, + 247 + ], + "spans": [ + { + "bbox": [ + 94, + 233, + 233, + 247 + ], + "type": "text", + "content": "Redirection: " + }, + { + "bbox": [ + 94, + 233, + 233, + 247 + ], + "type": "inline_equation", + "content": "\\hat{z}_t^i = \\mathbf{R}(c_t^i)\\cdot z_N^i" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "i \\in \\{1, 2\\}" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": ", representing gaze directions and head orientations, respectively, and " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "z_N^i" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " denotes the normalized embedding of the corresponding attribute. We feed the original embedding " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "z_s^i" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " and the modified embedding " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\hat{z}_t^i" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " into the weights-sharing deprojectors " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "DP" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " to transform these embeddings back to the feature space " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " as the residuals. Given these residuals, we implement subtraction and addition operations over " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "f_s" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " as described in Eq. 1 (or Eq. 2) to acquire the edited latent vector " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\hat{f_t}" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\hat{f_{t,d}}" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": "), which is sent to a generator for synthesizing redirected face image " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": " should have the same gaze direction and head orientation as " + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 251, + 289, + 386 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 391, + 165, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 391, + 165, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 391, + 165, + 404 + ], + "type": "text", + "content": "3.5. Learning Objectives" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "text", + "content": "We supervise the relationship between the generated image " + }, + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "text", + "content": " and the target image " + }, + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 410, + 287, + 458 + ], + "type": "text", + "content": " with several loss functions: pixel-wise reconstruction loss, LPIPS metric [43] and attributes loss by a task-related pretrained model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 111, + 463, + 287, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 463, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 111, + 463, + 287, + 479 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\hat {I} _ {t} - I _ {t} \\right| \\right| _ {2}, \\tag {4}", + "image_path": "df94bdca3660cd890d94c5743fd2ce289d12af35d6c9800ea9007c0a7b1552b1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 484, + 287, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 484, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 89, + 484, + 287, + 500 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L P I P S} (\\hat {I} _ {t}, I _ {t}) = \\left| \\left| \\psi (\\hat {I} _ {t}) - \\psi (I _ {t}) \\right| \\right| _ {2}, \\tag {5}", + "image_path": "a8b6fbf8033d2db72402a7d4436ab81823c456319696445670ae0ac84ad57dc6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 100, + 503, + 287, + 518 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 503, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 100, + 503, + 287, + 518 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a t t} (\\hat {I} _ {t}, I _ {t}) = \\langle \\xi_ {h g} (\\hat {I} _ {t}), \\xi_ {h g} (I _ {t}) \\rangle , \\tag {6}", + "image_path": "60ef82d0f7d274ef0d1f8826e675d94f8fb1a3bfc319cdcb211130ff5702b778.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "text", + "content": " denotes the perceptual feature extractor [43], " + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\xi_{hg}(\\cdot)" + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "text", + "content": " represents the pretrained HeadGazeNet [44] to estimate the gaze and head pose from images and " + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\langle u,v\\rangle =" + }, + { + "bbox": [ + 47, + 521, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\arccos \\frac{u\\cdot v}{||u||\\cdot||v||}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "type": "text", + "content": "Identity Loss. Identity preservation after redirection is critical for the face editing task. Considering this, we calculate the cosine similarity of the identity-related features between the source image and the redirected image:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 97, + 627, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 627, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 97, + 627, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I D} (\\hat {I} _ {t}, I _ {s}) = 1 - \\langle \\phi (\\hat {I} _ {t}), \\phi (I _ {s}) \\rangle , \\tag {7}", + "image_path": "c50d659a8014b90cc8c3acbb68d979f3a5a77483f59d1c56018487448f875c98.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 647, + 270, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 270, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 270, + 661 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 647, + 270, + 661 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 47, + 647, + 270, + 661 + ], + "type": "text", + "content": " denotes the pretrained ArcFace [11] model." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 664, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 700 + ], + "type": "text", + "content": "Label Loss. We have ground truth of gaze directions and head orientations, which can guide the conditions learning from the input latent vectors for the normalization step:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 94, + 706, + 287, + 720 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 706, + 287, + 720 + ], + "spans": [ + { + "bbox": [ + 94, + 706, + 287, + 720 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l a b} \\left(\\hat {c} _ {s} ^ {i}, c _ {s} ^ {i}\\right) = \\left\\langle \\hat {c} _ {s} ^ {i}, c _ {s} ^ {i} \\right\\rangle , i \\in \\{1, 2 \\}. \\tag {8}", + "image_path": "017872ae3a35debba5f93f0bc75b668c30bf474b2020446af383859a3b684358.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "text", + "content": "Embedding Loss. The normalized embeddings only contain the canonical status of the corresponding attribute after the inverse rotation applied to the original estimated embeddings, shown in Fig. 1. Thus the normalized embeddings given a certain attribute across different samples within batch " + }, + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "text", + "content": " should be consistent. To reduce the number of possible pairs within a batch, we utilize the first normalized embedding " + }, + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "inline_equation", + "content": "z_{N,1}^{i}" + }, + { + "bbox": [ + 304, + 72, + 546, + 169 + ], + "type": "text", + "content": " as the basis:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 334, + 177, + 546, + 212 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 177, + 546, + 212 + ], + "spans": [ + { + "bbox": [ + 334, + 177, + 546, + 212 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e m b} = \\frac {1}{B - 1} \\sum_ {j = 2} ^ {B} \\langle z _ {N, 1} ^ {i}, z _ {N, j} ^ {i} \\rangle , i \\in \\{1, 2 \\}. \\tag {9}", + "image_path": "139a226daa58edb755db76ede270cbdb73a8dd5e8932b0cc01cd0ab45850cb52.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": "Layer-wise Weights Loss. This loss is specifically designed for the " + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "inline_equation", + "content": "W^{+}" + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": " space to decide the weights " + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": " of which layer should contribute more to the aimed attributes editing. Firstly, we calculate the layer-wise estimated conditions " + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "inline_equation", + "content": "\\hat{c}_k^i" + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": " and calculate estimated pseudo labels " + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "inline_equation", + "content": "\\tilde{c}^i" + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": ". Secondly, we have layer-wise estimated label errors by " + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "inline_equation", + "content": "\\langle \\hat{c}_k^i, \\tilde{c}^i \\rangle" + }, + { + "bbox": [ + 304, + 217, + 545, + 314 + ], + "type": "text", + "content": ". Lastly, we calculate the cosine similarity between the reciprocal of label errors and weights of layers as the loss:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 320, + 545, + 347 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 545, + 347 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p r o b} = \\langle \\left\\{p _ {k} \\right\\}, \\left\\{\\frac {1}{\\left\\langle \\hat {c} _ {k} ^ {i} , \\tilde {c} ^ {i} \\right\\rangle} \\right\\}, k \\in [ 1, K ], i \\in \\{1, 2 \\}, \\tag {10}", + "image_path": "122b0f76eca802407f18a303d4613580ef419de4f94ef7a440f8ddd266af8051.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 353, + 486, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 353, + 486, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 353, + 486, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 353, + 486, + 365 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 353, + 486, + 365 + ], + "type": "text", + "content": " is the number of layers for editing." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 369, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 393 + ], + "type": "text", + "content": "Full Loss. The combined loss function for supervising the redirection process is:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 401, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 401, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 318, + 401, + 545, + 430 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\lambda_ {r} \\mathcal {L} _ {r e c} + \\lambda_ {L} \\mathcal {L} _ {L P I P S} + \\lambda_ {I D} \\mathcal {L} _ {I D} + \\lambda_ {a} \\mathcal {L} _ {a t t} \\tag {11} \\\\ + \\lambda_ {l} \\mathcal {L} _ {l a b} + \\lambda_ {e} \\mathcal {L} _ {e m b} + \\lambda_ {p} \\mathcal {L} _ {p r o b}, \\\\ \\end{array}", + "image_path": "b714b0ac691aac07c41b1898af0c7784ba7ff33de069684d41e762a8e2e159c7.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LPIPS}" + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{prob}" + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "content": " are utilized only when the pretrained StyleGAN is used as the generator." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 471, + 388, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 388, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 388, + 484 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 491, + 367, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 367, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 367, + 502 + ], + "type": "text", + "content": "4.1. datasets" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "content": "We utilize GazeCapture [24] training subset to train the redirector and assess the performance with its test subset, MPIIFaceGaze and CelebA-HQ [20]. Supplementary material provides more information about these datasets." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 563, + 421, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 421, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 421, + 575 + ], + "type": "text", + "content": "4.2. Evaluation Criteria" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 582, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 605 + ], + "type": "text", + "content": "We follow metrics utilized by ST-ED [44] to evaluate different redirectors' performance." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": "Redirection Error. We measure the redirection accuracy in image space by a pre-trained ResNet-50 based [16] head pose and gaze estimator " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "\\xi_{hg}^{\\prime}" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": ", which is unseen during the training. Given the target image " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": " and the generated one " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": " redirected by conditions of " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": ", we report the angular error between " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "\\xi_{hg}^{\\prime}(\\hat{I}_{t})" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "inline_equation", + "content": "\\xi_{hg}^{\\prime}(I_t)" + }, + { + "bbox": [ + 304, + 606, + 545, + 678 + ], + "type": "text", + "content": " as the redirection errors." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 678, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 545, + 712 + ], + "type": "text", + "content": "Disentanglement Error. We quantify the disentanglement error by the condition's fluctuation range of one attribute when we redirect the other one. The redirection" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5551" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 298, + 173 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 298, + 173 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 298, + 173 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 298, + 173 + ], + "type": "table", + "html": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.6023.9890.7553.0670.257
He et al.†[17]4.6171.3920.5603.9250.223
VecGAN [10]2.2820.8240.4012.2050.197
ST-ED [44]2.3850.8000.3842.1870.208
ReDirTrans2.1630.7530.4292.1550.197
", + "image_path": "78d4d3d5b6d70b1821a163e2bed348f09c5e789b615da01ea0ca28714a33f7cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 180, + 289, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 270 + ], + "type": "text", + "content": "Table 1. Within-dataset quantitative comparison (GazeCapture test subset) between different methods for redirecting head orientations and gaze directions. (Lower is better). Head (Gaze) Redir denotes the redirection accuracy in degree between the redirected image and the target image given head orientations (gaze directions). Head (Gaze) Induce denotes the errors in degree on gaze (head) when we redirect the head (gaze). " + }, + { + "bbox": [ + 46, + 180, + 289, + 270 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 180, + 289, + 270 + ], + "type": "text", + "content": " denotes copied results from [44]. Other methods are retrained given previous papers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": "angle " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": " follows " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\mathcal{U}(-0.1\\pi, 0.1\\pi)" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": ". For example, when we redirect the head pose of the generated image " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": " and generate a new one " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\hat{I}_t'" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": ", we calculate the angular error of the estimated gaze directions between " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\xi_{hq}'(\\hat{I}_t)" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\xi_{hq}'(I_t')" + }, + { + "bbox": [ + 46, + 290, + 287, + 339 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 339, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 376 + ], + "type": "text", + "content": "LPIPS. LPIPS is able to measure the distortion [43] and image similarity in gaze directions [17] between images, which is applied to evaluate the redirection performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 384, + 251, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 251, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 251, + 396 + ], + "type": "text", + "content": "4.3. Redirectors in Learnable Latent Space" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": "We compared quantitative performance of different redirectors, which were trained along with the trainable encoder-decoder pair designed by ST-ED on " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " images with restricted face ranges, given the criteria proposed in Sec. 4.2. Table 1 and Table 2 present within-dataset and cross-dataset performance, respectively. From these tables, we observe that our proposed ReDirTrans achieved more accurate redirection and better LPIPS compared with other state-of-the-art methods by considering the extra embedding space " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " for redirecting embeddings of aimed attributes only and maintaining other attributes including the appearance-related information in the original latent space " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". ST-ED [44] projected input latent vectors into nine embeddings including the non-varying embedding " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". This appearance-related high dimensional embedding " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " requires more parameters than ReDirTrans during projection. After redirecting the embeddings of aimed attributes, ST-ED deprojected a stack of " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ", redirected embeddings, and rest unvaried embeddings of other attributes back to the feature space for decoding. This projection-deprojection process of non-varying embedding " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " results in loss of appearance and worse LPIPS, as depicted in Fig. 3. VecGAN [10] was proposed to edit the attributes only within the feature space by addition and subtraction operations. Since there is no projection-deprojection process, given the original latent code, LPIPS performance is bet" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 556, + 173 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 556, + 173 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 556, + 173 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 556, + 173 + ], + "type": "table", + "html": "
Gaze RedirHead RedirGaze InduceHead InduceLPIPS
StarGAN†[7]4.4883.0310.7862.7830.260
He et al.†[17]5.0921.3720.6843.4110.241
VecGAN [10]2.6701.2420.3911.9410.207
ST-ED [44]2.3801.0850.3711.7820.212
ReDirTrans2.3800.9850.3911.7820.202
", + "image_path": "3823433c29fe5ce05dedd77fca01e4fd643f9584c050cf9acaf81c239125c34e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 304, + 180, + 547, + 237 + ], + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 237 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 237 + ], + "type": "text", + "content": "Table 2. Cross-dataset quantitative comparison (MPIIFaceGaze) between different methods for redirecting head orientations and gaze directions. (Lower is better). Notations are the same as them in the Table 1. " + }, + { + "bbox": [ + 304, + 180, + 547, + 237 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 304, + 180, + 547, + 237 + ], + "type": "text", + "content": " denotes copied results from [44]. Other methods are retrained given previous papers." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 248, + 547, + 383 + ], + "blocks": [ + { + "bbox": [ + 307, + 248, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 307, + 248, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 307, + 248, + 547, + 383 + ], + "type": "image", + "image_path": "900883f71044cfef1e7403209fb24c4db950020bb1a8cede28601898c264bb96.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 387, + 547, + 422 + ], + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 422 + ], + "type": "text", + "content": "Figure 3. Qualitative Comparison of ReDirTrans and ST-ED in GazeCapture. ReDirTrans preserves more facial attributes, such as lip thickness and sharpness of the beard." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 444, + 547, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 481 + ], + "type": "text", + "content": "ter than ST-ED. However, as no extra embedding space was built for the aimed attributes editing, both redirection accuracy and the disentanglement process were affected." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 491, + 512, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 512, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 512, + 503 + ], + "type": "text", + "content": "4.4. Redirectors in Predefined Latent Space" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "Except for using the trainable encoder-decoder pair of ST-ED, we also implemented our proposed ReDirTrans within a predefined feature space " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "W^{+}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " to achieve redirection task in full face images with desired resolution. We utilized e4e [35] as the pre-trained encoder, which can transform input images into latent vectors in " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "W^{+}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": ", and we chose StyleGAN2 [22] as the pre-trained generator to build ReDirTrans-GAN. Fig. 4 shows qualitative comparison between ST-ED and ReDirTrans-GAN in the GazeCapture test subset with providing target images from the same subject. ReDirTrans-GAN successfully redirected gaze directions and head orientations to the status provided by target images while maintaining the same appearance patterns with " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " full face images. Due to the design of ReDirTrans, which maintains unrelated attributes and appearance information in the initial latent space instead of going through the projection-deprojection pro" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "5552" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 542, + 299 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 542, + 299 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 542, + 299 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 542, + 299 + ], + "type": "image", + "image_path": "26c94784e46de8e0846e412019b9273e1a93394ed0febf5b5904e43b1144ea4a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 307, + 526, + 319 + ], + "lines": [ + { + "bbox": [ + 65, + 307, + 526, + 319 + ], + "spans": [ + { + "bbox": [ + 65, + 307, + 526, + 319 + ], + "type": "text", + "content": "Figure 4. Qualitatively comparisons between ST-ED and ReDirTrans-GAN. Red boxes represent different face covering ranges." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 337, + 266, + 416 + ], + "blocks": [ + { + "bbox": [ + 69, + 337, + 266, + 416 + ], + "lines": [ + { + "bbox": [ + 69, + 337, + 266, + 416 + ], + "spans": [ + { + "bbox": [ + 69, + 337, + 266, + 416 + ], + "type": "table", + "html": "
Q%GazeCaptureMPIIFaceGaze
Raw ↓Aug ↓Raw ↓Aug ↓
255.8755.2388.6077.096
504.7414.5066.7876.113
754.3084.2006.1655.767
", + "image_path": "ef3b99ff1055537cd41a4cbb5cf17c3a570fa255796182046874133d96840f74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 423, + 287, + 479 + ], + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 479 + ], + "type": "text", + "content": "Table 3. Learning-based gaze estimation errors (in degrees) in GazeCapture and MPIIFaceGaze with or without redirected data augmentation. " + }, + { + "bbox": [ + 46, + 423, + 287, + 479 + ], + "type": "inline_equation", + "content": "Q\\%" + }, + { + "bbox": [ + 46, + 423, + 287, + 479 + ], + "type": "text", + "content": " represents percent of labeled data in 10,000 images for training ReDirTrans-GAN. 'Raw' or 'Aug' mean training the gaze estimator with real data or with real & redirected data." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "text", + "content": "cess, ReDirTrans-GAN keeps more facial attributes such as expressions, mustaches, bangs compared with ST-ED. Fig. 5 presents qualitative results with assigned conditions (pitch and yaw of gaze directions and head orientations) in CelebA-HQ [20]. ReDirTrans-GAN can achieve out-of-domain redirection tasks in predefined feature space while maintaining other facial attributes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 162, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 162, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 162, + 611 + ], + "type": "text", + "content": "4.5. Data Augmentation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "To solve data scarcity of the downstream task: learning-based gaze estimation, we utilized redirected samples with assigned gaze directions and head orientations to augment training data. We randomly chose 10,000 images from the GazeCapture training subset to retrain ReDirTrans-GAN with using only " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "Q\\%" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " ground-truth labels of them. The HeadGazeNet " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\xi_{hg}(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " was also retrained given the same " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "Q\\%" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " labeled data and " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "Q \\in \\{25,50,75\\}" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": ". Then we utilized" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "text", + "content": "ReDirTrans-GAN to generate redirected samples given provided conditions over " + }, + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "inline_equation", + "content": "Q\\%" + }, + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "text", + "content": " labeled real data and combined the real and redirected data as an augmented dataset with size " + }, + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "inline_equation", + "content": "2 \\times 10,000 \\times Q\\%" + }, + { + "bbox": [ + 304, + 339, + 545, + 425 + ], + "type": "text", + "content": " for training a gaze estimator. Table 3 presented within-dataset and cross-dataset performance and demonstrated consistent improvements for the downstream task given redirected samples as data augmentation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 430, + 509, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 509, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 509, + 443 + ], + "type": "text", + "content": "4.6. Challenge in Predefined Feature Space" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "type": "text", + "content": "One challenge for redirection tasks in predefined feature space comes from inconsistency between input and inverted images, mentioned in Sec. 3.3. We can observe that the existing gaze differences between input and inverted images in Fig. 4. In some cases, the gaze directions are changed after GAN inversion, which means that the encoded latent codes do not necessarily keep the original gaze directions. Thus, instead of using provided gaze directions of input images during the training, we utilized estimated gaze directions from inverted results to correctly normalize the gaze and head pose to the canonical status. This process ensures correctness when further new directions are added, making the training process more consistent." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "type": "text", + "content": "4.7. Gaze Correction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "ReDirTrans can correct gaze directions of inverted results by viewing input images as the target ones. e4e guarantees high editability, which is at the cost of inversion performance [35]. Fig. 6 shows several samples which failed to maintain input images' gaze directions even by the ReStyle encoder [3], which iteratively updates the latent codes given the differences between the input and inverted results. With" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5553" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 545, + 343 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 343 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 343 + ], + "type": "image", + "image_path": "0e76d545135a9e754566768092cc957125a47d7ee27050711ad9b02010bfef34.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 351, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 351, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 547, + 384 + ], + "type": "text", + "content": "Figure 5. Redirection results given assigned (pitch, yaw) conditions of gaze directions (g) and head orientations (h). The first two columns are input and inversion results with e4e [35] and StyleGAN [22]. The following columns are redirected samples with assigned redirection values based on the latent code estimated from e4e." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 403, + 287, + 656 + ], + "blocks": [ + { + "bbox": [ + 48, + 403, + 287, + 656 + ], + "lines": [ + { + "bbox": [ + 48, + 403, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 48, + 403, + 287, + 656 + ], + "type": "image", + "image_path": "bcc8defdfcefe94c8f9471f111e865417cb1e448de5f2b149fc8a479d90e2af8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 664, + 287, + 688 + ], + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 688 + ], + "type": "text", + "content": "Figure 6. Gaze correction in CelebA-HQ by viewing the same image as both the input and target." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 405, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 405, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 545, + 430 + ], + "type": "text", + "content": "ReDirTrans-GAN, we can successfully correct the wrong gaze based on inverted results from e4e." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 441, + 384, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 384, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 384, + 453 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "content": "We introduce ReDirTrans, a novel architecture working in either learnable or predefined latent space for high-accuracy redirection of gaze directions and head orientations. ReDirTrans projects input latent vectors into aimed-attribute pseudo labels and embeddings for redirection in an interpretable manner. Both the original and redirected embeddings of aimed attributes are deprojected to the initial latent space for modifying the input latent vectors by subtraction and addition. This pipeline ensures no compression loss to other facial attributes, including appearance information, which essentially reduces effects on the distribution of input latent vectors in initial latent space. Thus we successfully implemented ReDirTrans-GAN in the predefined feature space working with fixed StyleGAN to achieve redirection in high-resolution full-face images, either by assigned values or estimated conditions from target images while maintaining other facial attributes. The redirected samples with assigned conditions can be utilized as data augmentation for further improving learning-based gaze estimation performance. 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Advances in Neural Information Processing Systems, 33:13127-13138, 2020. 1, 2, 3, 4, 5, 6" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5556" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_content_list.json b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d415e50e6cb9e960ce40008d2267430b2c370f7d --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_content_list.json @@ -0,0 +1,1238 @@ +[ + { + "type": "text", + "text": "ReLight My NeRF: A Dataset for Novel View Synthesis and Relighting of Real World Objects", + "text_level": 1, + "bbox": [ + 184, + 130, + 785, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Marco Toschi\\*, Riccardo De Matteo\\*,, Riccardo Spezialetti\\*, Daniele De Gregorio Eyecan.ai {marco.toschi, riccardo.spezialetti, daniele.degregorio}@eyecan.ai Luigi Di Stefano, Samuele Salti University of Bologna", + "bbox": [ + 158, + 203, + 810, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/39910bbb8513b8eb17635efbc10fa6fd960cc48237c61dede0e2932fedaa8630.jpg", + "image_caption": [ + "Figure 1. A random subset of scenes from our dataset. Our dataset enables the study of joint novel view synthesis and relighting from real images, as it provides scenes framed from the same viewpoint under varying light positions (shown along rows) as well as captured from different viewpoints under the same light position (shown along columns)." + ], + "image_footnote": [], + "bbox": [ + 81, + 297, + 890, + 500 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 564, + 313, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we focus on the problem of rendering novel views from a Neural Radiance Field (NeRF) under unobserved light conditions. To this end, we introduce a novel dataset, dubbed ReNe (Relighting NeRF), framing real world objects under one-light-at-time (OLAT) conditions, annotated with accurate ground-truth camera and light poses. Our acquisition pipeline leverages two robotic arms holding, respectively, a camera and an omni-directional point-wise light source. We release a total of 20 scenes depicting a variety of objects with complex geometry and challenging materials. Each scene includes 2000 images, acquired from 50 different points of views under 40 different OLAT conditions. By leveraging the dataset, we perform an ablation study on the relighting capability of variants of the vanilla NeRF architecture and identify a lightweight architecture that can render novel views of an object under novel light conditions, which we use to establish a non-trivial baseline for the dataset. Dataset and benchmark are available at https://eyecan-ai.github.io/rene.", + "bbox": [ + 75, + 597, + 473, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 564, + 632, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inverse rendering [29, 47, 52, 73] addresses the problem of estimating the physical attributes of an object, such as its geometry, material properties and lighting conditions, from a set of images or even just a single one. This task is a longstanding problem for the vision and graphics communities, since it unlocks the creation of novel renderings of an object from arbitrary viewpoints and under unobserved lighting conditions. An effective and robust solution to this problem would have significant value for a wide range of applications in gaming, robotics and augmented reality.", + "bbox": [ + 496, + 589, + 893, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, Neural Radiance Fields (NeRF) [36] has contributed tremendously to the novel view synthesis sub-task of inverse rendering pipelines. By mapping an input 5D vector (3D position and 2D viewing direction) to a 4D continuous field of volume density and color by means of a neural network, NeRF learns the geometry and appearance of a single scene from a set of posed images. The appealing results in novel view synthesis have attracted a lot of attention from the research community and triggered many follow-up", + "bbox": [ + 496, + 741, + 895, + 878 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Joint first authorship. $^\\circ$ Work done while at Eyecan.ai", + "bbox": [ + 522, + 886, + 821, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20762", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/3a6dbdce1352f4790069d7460ca992ecc7e27112dc1da073d1b3108d7cf986b5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetMultiple categoriesReal-WorldBackground ShadowsPublicLight Supervision
Gross et al. [14]X✓X✓✓
Sun et al. [57]X✓X✓✓
Wang et al. [68]X✓X✓✓
Zhang et al. [74]X✓X✓✓
Srinivasan et al. [55]✓XX✓✓
Zhang et al. [75]✓✓✓✓X
Zhang et al. [75]✓XX✓✓
Bi et al. [2]✓✓XX✓
ReNe✓✓✓✓✓
", + "bbox": [ + 84, + 88, + 460, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Overview of relighting datasets. Our dataset is the first one featuring a variety of objects and materials captured with real-world sensors that provides ground-truth light positions and also presents challenging cast shadows.", + "bbox": [ + 76, + 236, + 468, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "works aimed at overcoming the main limitations of NeRF, e.g. reduce inference runtime [23, 24, 27, 48, 49, 71], enable modeling of deformable objects [9, 25, 42, 45, 46, 62], and generalization to novel scenes [5, 15, 19, 39, 50, 53, 61, 63, 72]. However, less attention has been paid to the relighting ability of NeRFs. Although NeRF and its variants represent nowadays the most compelling strategy for view synthesis, the learned scene representation entangles material and lighting and, thus, cannot be directly used to generate views under novel, unseen lighting conditions. A few existing works [3, 4, 55, 75] try to overcome this structural NeRF limitation by learning to model the scene appearance as a function of reflectance, which accounts for both scene geometry and lighting modeling. However, these methods incur a great computation cost, mainly due to the need to explicitly model light visibility and/or the components of a microfacet Bidirectional Reflectance Distribution Function (BRDF) [65] like diffuse albedo, specular roughness, and point normals: for instance NeRV [55] uses 128 TPU cores for 1 day while [3] is trained on 4 GPUs for 2 days.", + "bbox": [ + 75, + 323, + 468, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As highlighted in Tab. 1, one of the main challenges to foster research in this direction is the absence of real-world datasets featuring generic and varied objects with ground-truth light direction, both at training and test time. The latter is key to create a realistic quantitative benchmark for relighting methods, whose availability is one of the main driving forces behind fast-paced development of a machine learning topic. Indeed, the above mentioned NeRF-like methods for relighting mainly consider a handful of synthetic images to provide quantitative results (3 and 4 scenes in NeRV [55] and NeRFactor [75], respectively) while no quantitative results are provided in [3]. The only dataset with scenes acquired by a real sensor is proposed in [2], which, however, assumes images captured under collocated view and lighting setup, i.e. a smartphone with flash light on, which limits the amount of cast shadows and simplifies the task. Moreover, the dataset is not publicly available. Some available real-world datasets with ground-truth light", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "positions feature human faces or portraits [14, 57, 68, 74]. In these datasets, the subject is usually seated in the center of a light-stage with cameras arranged over a dome array positioned in front of the subject. Although these dataset provide real scenes with ground-truth annotations for light positions, the background is masked-out and shadows cast on the background, which are hard to model because they require a precise knowledge about the geometry of the overall scene, are ignored.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, in this paper we try to answer the research questions: can we design a data acquisition methodology suitable to collect a set of images of an object under one light-at-time (OLAT) [74] illumination with high-quality camera and light pose annotations which requires minimal human supervision? We then leverage it to investigate a second question: can we design a novel Neural Radiance Field architecture to learn to perform relighting with reasonable computational requirements? To answer the first question, we design a capture system relying on two robotic arms. While one arm holds the camera and shots pictures from viewpoints uniformly distributed on a spherical wedge, the other moves the light source across points uniformly distributed on a dome. As a result, we collect the ReNe dataset, made of 20 scenes framing daily objects with challenging geometry, varied materials and visible cast shadows, composed of 50 camera view-points under 40 OLAT light conditions, i.e. 2000 frames per scene. Examples of images from the dataset are shown in Fig. 1. With a subset of images from each scene, we create a novel hold-out dataset for joint relighting and novel view synthesis evaluation that will be used as an online benchmark to foster research on this important topic. As regards the second question, thanks to the new dataset we conduct a study on the relighting capability of NeRF. In particular, we investigate on how the standard NeRF architecture can be modified to take into account the position of the light when generating the appearance of a scene. Our study shows that by estimating color with two separate sub-networks, one in charge of softshadow prediction and one responsible for neurally approximating the BRDF, we can perform an effective relighting, e.g. cast complex shadows. We provide results of our novel architecture as a reference baseline for the new benchmark.", + "bbox": [ + 496, + 227, + 890, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions include:", + "bbox": [ + 517, + 727, + 777, + 741 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- a novel dataset made out of sets of OLAT images of real-world objects, with accurate camera and light pose annotations;", + "- a study comparing different approaches to enable NeRF to perform relighting alongside novel view synthesis;", + "- a new architecture, where the stage responsible for radiance estimation is split into two separate networks," + ], + "bbox": [ + 517, + 753, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20763", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that can render novel views under novel unobserved lighting conditions;", + "bbox": [ + 109, + 90, + 468, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- a public benchmark for novel view synthesis and relighting of real world objects, that will be maintained on an online evaluation server.", + "bbox": [ + 96, + 133, + 468, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 193, + 218, + 209 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we focus on relighting static objects by Neural Radiance Fields. We briefly discuss the related works and their datasets below.", + "bbox": [ + 76, + 219, + 467, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image Relighting without NeRF. There exist several works in the field of image based relighting [8, 32, 44, 51]. The proposed methods differ for the adopted technique to model the light transport function in form of discrete light transport matrix. With recent advances in deep learning, new techniques have been introduced to address relighting [57], with many of them designed to relight human portraits [38, 58, 59, 70, 76]. Another bunch of works pursues joint relighting and novel view synthesis [11, 34, 74].", + "bbox": [ + 75, + 265, + 467, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Relighting Datasets. Most of relighting datasets contain captures of human bodies or face portraits, they leverage complex capture setups such as calibrated multi-view lightstages with cameras and LED lights, where the cameras are synchronized with the lights in order to flash one LED per capture [38,58,59,76]. Alternative works on generic objects do exist [51, 70], but they consider a mix of real and synthetic data, with the latter dominating the former in terms of number of images. The dataset most similar to ours is the one adopted by [2], which involves a robotic arm setup holding a Samsung Galaxy Note 8. However, this acquisition framework assumes a collocated view and lighting setup, e.g. built-in flash of a smart-phone camera lens, that inherently limits the shadows cast. Furthermore, the dataset has not been released.", + "bbox": [ + 75, + 401, + 467, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Radiance Fields. Novel view synthesis has been a longstanding problem within the computer vision and computer graphics fields [7, 13, 20]. The advent of deep learning gave rise to explicit methods that train CNNs for this very purpose [22, 26, 35, 54, 56, 64, 77]. In the past few years, NeRF has advanced greatly in becoming the main scene representation for view synthesis [36]. NeRF learns a continuous volumetric function parameterized by means of a fully connected neural network optimized over a set of observed images with known camera poses using gradient descent. Due to its effectiveness, NeRF has inspired many subsequent works that extend its continuous neural volumetric representation for generative modeling [5, 19, 53], dynamic scenes [10, 21, 21, 30, 41, 46, 69], non-rigidly deforming objects [9, 9, 40, 42, 43, 62], multi-resolution images [1, 60], phototourism images with changing illumination settings [30, 61] and relighting [2, 4, 30, 55].", + "bbox": [ + 75, + 628, + 467, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Radiance Fields for Relighting. One of main limi", + "bbox": [ + 76, + 885, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tations of NeRF is that is not suitable for relighting. Indeed, NeRF treats the particles within scene representation as elements that emit light instead of being modelled as particles that reflect the incoming light sent out from external light sources. To straddle this divide, Neural Reflectance Field [2] models both scene geometry and reflectance regressing volume density, normal and material properties, e.g. Bidirectional Reflectance Distribution Function (BRDF) [65], for any 3D location within the volume of a scene. The shading at each point is then estimated using the light, view direction, the normal at that point and the BRDF. For instance, [28] leverages a differentiable path tracer to optimize a spatially-varying BSDF tied to an environment map, that can be used to render novel views under a novel OLAT condition. Unfortunately, this approach requires marching rays from all points sampled along the camera ray to any source of lighting in the scene, which restricts it use only in a collocated camera-light setup. NeRV ameliorates the computational cost of [2] by replacing the visibility estimation between scene points and light sources with a neural approximation of the true visibility field, which acts as a lookup table during rendering. Thanks to this insight, NeRV simulates direct illumination from environment lighting as well as one-bounce indirect illumination. NeRD [4] does not model visibility or shadows, but uses an analytic BRDF model [6] to learn a volumetric representation which stores SVBRDF [16] parameters at each 3D point instead of a radiance field. A relightable textured mesh is then extracted from that volume to allow fast rendering and relighting. Finally, NeRFactor [75] starts from two pre-trained networks: a NeRF of the scene and a BRDF network trained on the MERL dataset [31]. This knowledge is then distilled into four MLP-based networks to predict for each surface location its normal vector, light visibility, albedo and a BRDF latent code. The MLP outputs are injected into classical volumetric rendering and the networks parameters are optimized minimizing the re-rendering loss.", + "bbox": [ + 496, + 90, + 890, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We take inspiration from this line of works to design the study reported in Sec. 5, where we split the MLP-stack of NeRF in two separate networks: one responsible for the visibility and one that resembles the BRDF.", + "bbox": [ + 496, + 648, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dataset Acquisition Framework", + "text_level": 1, + "bbox": [ + 500, + 724, + 790, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While providing both lights and cameras poses in a controlled manner with ground-truths annotations is straightforward in synthetic environments [55, 75], it is cumbersome and complex in the real world, especially if humans are involved, as done in [14, 57, 68, 74]. Our solution is to deploy extremely repeatable and safe machines such as industrial cobots (collaborative robots). In particular, we use a pair of robots, dubbed LightBot and CameraBot, to position the light and camera independently. Thanks to their high repeatability $(+/-0.03\\mathrm{mm})$ , we can calibrate their tra", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20764", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/46df05a747c37b785ab67f94291c6e0e1a50514b81c84a5ed06d971daecb09dc.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 91, + 106, + 529, + 299 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/106a6eeae19e044940a3512f51dd8454c3eaf4d4e794c94666c53f4e66b33ab5.jpg", + "image_caption": [ + "(b)", + "Figure 2. Overview of our dataset acquisition framework. (a) The LightBot and CameraBot moving light and camera respectively; the trajectories of the two robots are two non-intersecting sections of a hemisphere around the object of interest. (b) Grid of images in which each row depicts the same viewpoint as the light conditions change; each column, on the other hand, represents the same light condition as the viewpoint changes." + ], + "image_footnote": [], + "bbox": [ + 550, + 122, + 888, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "jectories with respect to a common world reference frame only once before acquisition starts, and then obtain accurate 6-DoF pose knowledge of both light and camera for all scenes by repeating the same trajectories. The proposed framework is sketched in Fig. 2a, while some acquisitions for the Robotoy scene are shown in Fig. 2b.", + "bbox": [ + 75, + 417, + 470, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Camera/Light Calibration. In order to calibrate both robots with respect to a common reference frame we use a ChArUco board [12]. We let the CameraBot see the board at each waypoint of its trajectory in order to calibrate extrinsic parameters for each view. Thanks to the high repeatability of the robot, it is possible to perform this procedure only once before we start to record scenes: the robot will be able to place the camera at the previously calibrated positions with negligible error. This allows us to register in a common reference frame all the camera poses for each scene without instrumenting the scene with a pattern, which alters the realism of the scene and makes the setup fragile, as the pattern may be inadvertently moved across scans. As for the LightBot, we assume that the center of the point light corresponds to the geometric center of the LED. We are then able to register it with the calibration pattern by letting the end effector physically touch the central reference point of the pattern with the center of the LED at calibration time. We note we cannot use the same procedure for the CameraBot as the camera optical center is behind the lens. That closes the calibration loop since both robots, now, will have the pattern itself as their world reference frame, thus a common coordinate system. Even with the LightBot, high repeatability assures that the light pose registered at calibration time will be identical across all scenes of the dataset.", + "bbox": [ + 75, + 523, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Trajectories. As depicted in Fig. 2a, we generate two trajectories, roughly belonging to the same hemisphere, whose upper part is used for the lights while the side part for the camera. This made it possible to capture several front-facing scenes with the light moving over the object of interest. With this setup, then, for each scene we collected 50 viewpoints each under 40 different light locations. To have waypoints uniformly distributed on the selected spherical region for each end effector, we create trajectories as sequences of centers of equal-area subregions, following the methodology proposed by [17]. For the sake of illustration, Fig. 2b shows a grid of images in which each row depicts frames with the same camera pose but different lighting conditions and vice-versa for columns.", + "bbox": [ + 496, + 417, + 892, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Background texture. In preliminary experiments with a uniform background as scenario, we found out that NeRF struggles to correctly estimate density in such a case and training does not converge. Hence, in our dataset textured walls are shown in the background.", + "bbox": [ + 496, + 636, + 893, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hardware. We equipped the LightBot and the CameraBot, respectively an Universal Robots UR5e and an Elite Robotics EC66, with a consumer headlight and an industrial camera. The headlight is the Velamp Metros IH523, equipped with 5 COB LEDs that provide a diffuse $100^{\\circ}$ beam up to $150\\mathrm{Lm}$ with 6000K light temperature. We used it at half power $(70\\mathrm{Lm})$ to maximize its runtime. The camera is a Basler acA1440-73gc with its optical axis mounted at $45^{\\circ}$ from the robot flange normal vector, this to simplify the computation of inverse kinematics of the CameraBot. Images are captured in camera's full 1.6MP resolution $(1440\\mathrm{px} \\times 1080\\mathrm{px})$ using a Basler lens with $8\\mathrm{mm}$ focal", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20765", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "length.", + "bbox": [ + 76, + 90, + 127, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. The ReNe Dataset", + "text_level": 1, + "bbox": [ + 76, + 119, + 253, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we summarize the data we collected using our framework to establish the ReNe dataset. Our dataset $\\mathcal{S} = \\{\\mathcal{I}_s\\}_{s=1}^S$ contains $S$ scenes, where each scene is a collection of RGB images $\\mathcal{I}_s = \\{I_{s,n,m} \\mid n = 1,\\dots,N,m = 1,\\dots,M\\}$ , $I_{n,m} \\in [0,1]^{H \\times W \\times 3}$ acquired using camera poses $\\mathcal{C}_s = \\{C_{s,n}\\}_{n=1}^N$ and lit with a point light source placed in $\\mathcal{G}_s = \\{G_{s,m}\\}_{m=1}^M$ . Each $C_n$ and $G_m$ represent the 6D pose $\\{\\mathbf{R},\\mathbf{t}\\} \\in SE(3)$ for camera and light source, respectively. $\\mathbf{R}$ denotes rotation, $\\mathbf{R} \\in SO(3)$ , and $\\mathbf{t}$ denotes translation, $\\mathbf{t} \\in \\mathbb{R}^3$ . The dataset features 40000 images divided in $S = 20$ scenes taken by $N = 50$ frontal points of views in $M = 40$ different lighting conditions, i.e. 2000 frames per scene.", + "bbox": [ + 76, + 147, + 472, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Train, Validation and Test splits. We split the datasets into train, val and test subsets to make it easy to compare in a fair and consistent way different approaches to NeRF relighting. In order to avoid data leakage from validation and test, we randomly create the set of held out viewpoints for validation, $\\mathcal{C}^{val}$ , and for testing, $\\mathcal{C}^{test}$ , as well as the set of held out light positions for testing, $\\mathcal{G}^{test}$ . Each of them consists of 3 indexes. To build the validation set, for each viewpoint $n_{val} \\in \\mathcal{C}^{val}$ , we randomly pick 3 light poses among the 37 available to form $\\mathcal{G}_{n_{val}}$ . In this way, in the validation set we have an unseen pair (viewpoint, light) composed of a viewpoint not present in the training set and a light used for other training viewpoints, $\\mathcal{I}^{val} = \\{I_{s,n_{val},m_{val}} | n_{val} \\in \\mathcal{C}_{val} \\wedge m_{val} \\in \\mathcal{G}_{n_{val}} \\wedge s = 1, \\ldots, S\\}$ . For test set, we build two sub-splits namely easy and hard. The former considers all the images $\\mathcal{I}^{easy} = \\{I_{s,n,m} | n \\in \\mathcal{C}^{test}, m = 1, \\ldots, M, m \\notin \\mathcal{G}^{test}\\}$ , while the latter is composed of images $\\mathcal{I}^{hard} = \\{I_{s,n,m} | (n,m) \\in \\mathcal{C}^{test} \\times \\mathcal{G}^{test}\\}$ . With this partition, the test set is comprised of novel viewpoints lit by light seen at training time in the easy split, and of novel viewpoints under a never seen light in the hard split. We sketch the splits in Fig. 3.", + "bbox": [ + 76, + 345, + 472, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Benchmarking the Relighting Capability of NeRF", + "text_level": 1, + "bbox": [ + 76, + 690, + 470, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the section, we explore our second research question: equipped with the ReNe dataset, can we add relighting capabilities to NeRF in a simple and lightweight way? We start with a brief overview of NeRF (Sec. 5.1), we then discuss alternative ways to make NeRF able to perform novel view synthesis and relighting simultaneously (Sec. 5.2). We compare our choices through an ablation study using the validation set described in Sec. 4, whose results are discussed in Sec. 5.3. Finally, in Sec. 5.4, we present the results for the best method on both test sets of the ReNe dataset.", + "bbox": [ + 75, + 734, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9bd5b16635ed9ed6177b4d95d5eec28efada5b0f61ed6112e11bfabac619bee0.jpg", + "image_caption": [ + "Figure 3. Dataset splits. Each scene $\\mathcal{I}_s$ is divided in 4 different splits: Samples used for training Samples used for validation Samples used for Easy Test Samples used for Hard Test Samples never used." + ], + "image_footnote": [], + "bbox": [ + 519, + 90, + 875, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. NeRF Overview", + "text_level": 1, + "bbox": [ + 500, + 511, + 658, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A Neural Radiance Field (NeRF) [36] maps a 5D input representing camera pose, i.e. 3D coordinates $\\mathbf{x} = (x,y,z)$ along with the 2D viewing directions $\\mathbf{d} = (\\theta ,\\phi)$ , into a 4D color-density output $(\\mathbf{c},\\sigma)$ by means of a function $F_{\\Theta}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma)$ approximated by the weights of an MLP. Specifically, here we consider a vanilla NeRF architecture [37] which estimates color and density using two MLPs as $(\\sigma ,\\mathbf{e}) = \\Psi_{geo}(\\mathbf{x})$ and $\\mathbf{c} = \\Psi_{rgb}(\\mathbf{e},\\mathbf{d})$ , with $\\sigma$ being interpreted as the probability of a ray terminating at $(x,y,z)$ and $\\mathbf{e}$ being a feature embedding. Following [33], the color $C(\\mathbf{r})$ rendered from a camera ray $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$ can be obtained solving the integral:", + "bbox": [ + 498, + 535, + 893, + 717 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) c (\\mathbf {r} (t), \\mathbf {d}) d t \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 729, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (\\mathbf{r}(s))ds\\right)$ represents the accumulated transmittance from $t_n$ to $t$ along the ray $r$ , and $t$ goes from near plane $t_n$ to far plane $t_f$ . The image formation procedure is performed by simply aggregating the result of the integral for all pixels, i.e. samples along the rays, of the target image. Although NeRF works well for synthesizing novel views, as shown by the previous equations, it has no way of modeling the incoming light since", + "bbox": [ + 496, + 773, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20766", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e872ec229f7b8765bbacd3bd4b084c5852bcff5cc34e89b9889f6055c05919df.jpg", + "image_caption": [ + "Figure 4. Overview of architectures. We start from the architecture of [37] and propose variants to inject information about the light position in the scene. Highlighted arrows in each variant underline an architectural change from the one that precedes." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "it only takes into account position and orientation for the camera. In the next section, we will introduce variations of the classical approach that also take into account the light position.", + "bbox": [ + 75, + 281, + 468, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Positional Encoding. As showed in NeRF [35] enconding $\\mathbf{x}$ and $\\mathbf{d}$ into a higher dimensional space allows the neural network to overcome its spectral bias and makes it able to reproduce the high-frequency content of the input signal. We follow [37] and encode $\\mathbf{x}$ using a multiresolution hash encoding, $h(\\mathbf{x})$ , whilst $\\mathbf{d}$ is projected onto the first 16 coefficients of the spherical harmonics, $\\zeta(\\mathbf{d})$ .", + "bbox": [ + 75, + 340, + 470, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. On The Relighting Capability of NeRF", + "text_level": 1, + "bbox": [ + 76, + 454, + 410, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, we take as a starting point the architecture presented in [37] and delineate 5 proposals to enable NeRF to perform relighting while adding minimum complexity to the architecture. Recalling Sec. 5.1, the naive architecture, namely V0, has two sub-networks, $\\Psi_{geo}$ , which outputs $\\sigma$ a measure of the particle density at $\\mathbf{x}$ , and $\\Psi_{rgb}$ which is responsible for the color, $\\mathbf{c}$ . Previous works [66, 66] demonstrated that $\\Psi_{geo}$ learns the scene geometry, while $\\Psi_{rgb}$ models the view-dependent color appearance. Hence, our key idea is to modify the input to the $\\Psi_{rgb}$ injecting light position and let the model learn the interaction between the geometry and light. We train one network on each scene minimizing the error between the ground-truth images and the rendered ones. As input data we consider a set of multi-view images of an object, $\\mathcal{I}_s$ , illuminated under known lighting conditions, $\\mathcal{G}_s$ , and the camera poses of these images, $\\mathcal{C}_s$ . We will consider the subscript $s$ implicit in what follows.", + "bbox": [ + 75, + 477, + 468, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "V1. A straightforward way to enable relighting with NeRF is to condition $\\Psi_{rgb}$ with a latent representation that stores the world position and orientation of the light, $G_{m}$ for a given observation $I_{n,m}$ . To do so, we flatten the $\\mathbf{R}$ and $\\mathbf{t}$ parts of $G_{m}$ and encode this 12-dimensional vector into a 156-dimensional latent code using the positional encoding with Fourier Features proposed in [36], $\\gamma (\\mathbf{R},\\mathbf{t})$ . Our procedure resembles the approach adopted by NeRF in the Wild [30], but the condition embedding is used to adapt NeRF to variable lighting conditions instead of transient", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "parts of the images.", + "bbox": [ + 498, + 282, + 632, + 297 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "V2. As the next iteration, we change the parameterization for $G_{m}$ . Instead of directly encoding $\\mathbf{R}$ and $\\mathbf{t}$ in the same way for each sample $\\mathbf{x}$ used to query $\\Psi_{rgb}$ , we construct a 3D unit vector $\\mathbf{l} = \\frac{\\mathbf{t} - \\mathbf{x}}{||\\mathbf{t} - \\mathbf{x}||}$ which let the network be aware of the relative position between the light source and the query location. Since, differently from the previous approach, $\\mathbf{l}$ changes for each query point, we conjecture this may help NeRF in modulating the output color $\\mathbf{c}$ based on the incoming light information. As done for $\\mathbf{d}$ , $\\mathbf{l}$ is encoded using the spherical harmonics, $\\zeta(\\mathbf{l})$ .", + "V3. The previous version resembles somehow the BRDF where $\\mathbf{l}$ acts as the incoming light direction at $\\mathbf{x}$ , and $\\mathbf{d}$ is the unit vector pointing from $\\mathbf{x}$ toward the camera. Following this analogy, we may consider $\\mathbf{e}$ to represent an $N$ -dimensional embedding of the normal vector at $\\mathbf{x}$ . Since all these information are relative to $\\mathbf{x}$ , we explore whether having $h(\\mathbf{x})$ as input can be beneficial for $\\Psi_{rgb}$ . Without such skip connection the knowledge about the location of the query point may vanish as the depth of the network increases.", + "V4. The previous version may be negatively influenced by the diverse scales of its inputs, which are on one side spherical and hash-grid encoded vectors like $\\zeta(\\mathbf{d})$ , $\\zeta(\\mathbf{l})$ , and $h(\\mathbf{x})$ while on the other there is the ReLU output $\\mathbf{e}$ . To test this hypothesis, we propose a variant where we concatenate $\\mathbf{e}$ with the output of the first layer of $\\Psi_{rgb}$ and use this vector as input for its second layer, rather than feeding $\\Psi_{rgb}$ directly with $\\mathbf{e}$ .", + "V5. The original NeRF learns a continuous 3D field of particles that absorb and emit light. As a result only the amount of outgoing light from a location is modeled, without taking into account the fact that the outgoing light is the result of interactions between incoming light and the material properties of an underlying surface. This issue can be alleviated by replacing Eq. (1) with a physically-based volume rendering for non-emissive and non-absorptive volumes, which replaces the emitted color of each 3D point along the ray, $c(\\mathbf{r}(t), \\mathbf{d})$ , with $L_{r}(\\mathbf{x}, \\omega_{o})$ that represents the scattered light at $\\mathbf{x}$ along $\\omega_{o}$ . As done in [2], assuming a single point light" + ], + "bbox": [ + 496, + 299, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20767", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "source of fixed intensity, $L_{r}$ can be approximated as:", + "bbox": [ + 76, + 90, + 426, + 106 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r} (\\mathbf {x}, \\omega_ {o}) = \\int_ {S} f _ {p} (\\mathbf {x}, \\omega_ {o}, \\omega_ {i}) L _ {i} (\\mathbf {x}, \\omega_ {i}) d \\omega_ {i} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 118, + 468, + 150 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $S$ is a unit sphere, $f_{p}$ represents a differentiable reflectance model (like the BRDF), and $L_{i}$ represents the incident radiance at $x$ from direction $\\omega_{i}$ . Please note that in this equation $\\omega_{o}$ corresponds to $\\mathbf{d}$ and $\\omega_{i}$ is analogous to $\\mathbf{l}$ . While we can assume that $f_{p}$ is approximated by $\\Psi_{rgb}$ , computing $L_{i}$ requires marching a large number of light rays for all shading points on all camera rays to determine the transmittance between the light and each 3D point. We avoid this cumbersome procedure by introducing a neural approximation of $L_{i}$ in the form of an MLP aimed at predicting a scalar value $o = \\Psi_{vis}(h(\\mathbf{x}),\\zeta (\\mathbf{l}))$ , which allows us to efficiently query the point-to-light visibility. The final pixel color is then obtained with $\\mathbf{c}^{\\star} = o\\cdot \\mathbf{c}$ .", + "bbox": [ + 76, + 161, + 472, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 367, + 227, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset. To assess the relative merits of the incremental modifications to NeRF proposed in the previous section and identify the best architecture, we consider a subset of scenes presenting a variety of challenges: Cube, that has thin wireframe structures and shadows; Savannah, that pictures a jagged leaves tree with a complex shadow; Reflective, that is full of specular reflections, and FlipFlop, where light passes through semi-transparent plastic strings.", + "bbox": [ + 75, + 391, + 468, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details. We used the torch-ngp pytorch implementation1 of Nvidia Instant-NGP [37] for fast training of Neural Radiance Fields models. During training, we randomly sample 4096 pixel rays as a batch to train our networks. We use Adam optimizer [18] with an initial learning rate of 0.01 (other Adam hyperparameters are left at default values of $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ ). For volumetric integration, we use 128 samples in coarse volume and 128 additional adaptive samples in fine volume to compute the final radiance. The optimization for a single scene typically takes around 100–200k iterations to converge on a single NVIDIA RTX 2080Ti GPU (about 5 hours). We use early-stopping if the model doesn’t improve for 10 consecutive epochs. We supervise the regressed RGB values with the ground truth values from the captured images using the L2 loss. For $\\Psi_{geo}$ we use 2 fully-connected ReLU layers with 64 channels, while $\\Psi_{rgb}$ and $\\Psi_{vis}$ uses 4 fully-connected ReLU layers with 64 channels.", + "bbox": [ + 75, + 513, + 470, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. For a quantitative evaluation of our methods we consider two widely adopted metrics of image quality assessment: Structural Similarity (SSIM) [67] and Peak Signal-to-Noise Ratio (PSNR) [35]. We report the results of the ablation study in Tab. 2. Results show how all the proposed modifications to NeRF improve performance and", + "bbox": [ + 75, + 785, + 470, + 876 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c581994137f4be865356fc9cb3d3c1b3bf62cbc2df5d673ce891e365d420985c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodγ(R, t)1skipinputsΨviasCubeSavannahReflectiveFlipFlop
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
V1✓XXXX24.370.5222.530.4423.570.5124.120.51
V2X✓XXX24.730.5423.700.5223.680.5224.420.56
V3X✓✓XX25.380.5624.390.5524.650.5825.060.57
V4X✓✓✓X25.410.5724.790.5824.240.5625.270.58
V5X✓✓✓✓26.110.6125.230.6125.000.5925.460.60
", + "bbox": [ + 504, + 88, + 888, + 157 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative relighting and view synthesis result of the proposed modifications to NeRF. For each scene, we report on the left the PSNR and on the right the SSIM. Legend: $\\gamma (\\mathbf{R},\\mathbf{t})$ indicates the use of absolute light position, $\\mathbf{l}$ of relative position wrt $\\mathbf{x}$ , skip indicates that $\\mathbf{x}$ is provided as input to $\\Psi_{rgb}$ , inputs that the embedding is inserted in $\\Psi_{rgb}$ at the second layer, while $\\Psi_{vis}$ that the MLP approximating $L_{i}(x,\\omega_{i})$ is used.", + "bbox": [ + 498, + 167, + 893, + 266 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3b2152d95fdc5369ac866aedcbe2243700ce335bfc0539df8c702593b8eaf08c.jpg", + "image_caption": [ + "Figure 5. Qualitative results for ablation. The same image as rendered by V1 and V5 networks. The side-by-side comparison clearly shows how V5 reproduces much sharper details in shadows (best seen in Reflective) and is able to better handle complex reflections (best seen in FlipFlop)." + ], + "image_footnote": [], + "bbox": [ + 501, + 280, + 893, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "contribute to the overall good results of the most effective version, which is V5. These results provide experimental support to the intuitions presented above about the higher effectiveness of feeding to the network the relative light position with respect to the sample $\\mathbf{x}$ instead of the absolute light pose (row 1 versus row 2), as well as the importance of providing $\\mathbf{x}$ as input to $\\Psi_{rgb}$ (row 2 versus row 3). Separating inputs to $\\Psi_{rgb}$ is also beneficial and, together with $\\Psi_{vis}$ contributes to the good performance of V5.", + "bbox": [ + 496, + 588, + 890, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Some qualitative examples comparing and contrasting V1 against V5 are reported in Fig. 5. Zooming in on cast shadows we can appreciate how careful handling of the light pose as well as the proposed modifications to the vanilla NeRF architecture enable rendering of sharper and more coherent shadows than the straightforward extension that conditions NeRF also on light pose.", + "bbox": [ + 496, + 726, + 890, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Results on benchmark", + "text_level": 1, + "bbox": [ + 500, + 845, + 707, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we report the performance for the best architecture on the overall set of held out test scenes in Tab. 3.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1https://github.com/ashawkey/torch-ngp", + "bbox": [ + 94, + 886, + 395, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20768", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6f2b86197a25be23443c671934311f8dc6e7b98bf62616d4c1e5fa468f9bf150.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
OursInstant-NGP
NameEasyHardEasyHard
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Apple26.440.6226.250.6220.890.4520.950.45
Cheetah25.660.6124.640.6019.370.4419.600.44
Cube24.900.5423.980.5320.140.4220.310.42
Dinosaurs25.750.6524.980.6419.580.4219.660.41
FlipFlop25.850.6125.420.6120.380.4520.360.45
Fruits25.930.6225.720.6220.160.4520.210.44
Garden25.740.6625.080.6619.760.4519.700.45
Helicopters25.120.6124.730.6119.340.3719.370.37
Kittens25.900.6424.960.6318.520.3718.650.37
Lego26.070.6125.770.6120.750.4620.760.46
Lunch25.840.6024.710.5919.320.4619.380.45
Plant26.550.6725.930.6720.620.4420.660.44
Reflective25.790.6125.280.6120.090.4320.110.42
Robotoy26.240.6525.550.6520.770.5020.780.50
Savannah25.150.6224.310.6119.080.4019.180.40
Shark25.590.5725.320.5620.540.4220.530.41
Stegosaurus25.870.6325.650.6320.840.4320.910.42
Tapes25.840.5825.410.5719.340.4119.550.41
Trucks25.800.6725.160.6619.810.4419.870.44
Wooden toys25.690.6125.240.6020.190.4820.220.48
Average25.790.6225.200.6119.970.4320.040.43
", + "bbox": [ + 83, + 88, + 460, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative results across all 20 scenes. We report both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) by comparing the novel view synthesized image with its corresponding groundtruth.", + "bbox": [ + 75, + 375, + 468, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our method against the pytorch implementation of Nvidia Instant-NGP [37]. Overall, the proposed architecture achieves satisfying results on this challenging task and sets a non trivial baseline for the online benchmark, clearly outperforming the naive baseline represented by the standard NeRF. We show some qualitative results for the easy test split in Fig. 6, and in Fig. 7 for the hard one. These qualitative results confirm that the model is capable of convincingly rendering and lighting the scene from unseen viewpoints and light positions while using a simple and lightweight architecture. Interestingly, the output of $\\Psi_{vis}$ , reported in the rightmost columns of the figures, well approximate point-to-light visibility, especially in the easy split, even if it has not received direct supervision to emulate it, and it even reproduces some indirect illumination effects, confirming the feasibility of a neural approximation of the incident radiance $L_{i}(\\mathbf{x},\\omega_{i})$ . Comparing with the ground-truth frame, while rendering of light on the object is indeed quite realistic, cast shadows are sharp and coherent with the scene geometry on the easy set, while more artifacts are present in the hard split.", + "bbox": [ + 75, + 459, + 472, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 791, + 333, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced the ReNe dataset, the first dual robot dataset framing real world objects under challenging one-light-at-time (OLAT) conditions and annotated with accurate camera and light poses. The main limitations of our dataset concern the absence of 360 degrees scans and the use of a challenging but unrealistic OLAT setup. By lever", + "bbox": [ + 75, + 816, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aging the training and validation splits of the dataset, we were able to perform an ablation study on lightweight modifications to a NeRF architecture that extend it to successfully perform novel view synthesis under unseen lighting. The best model emerged from the study has been tested on the held out test set to establish a non-trivial baseline for the benchmark. We hope the availability of a new dataset and baseline for the problem of NeRF relighting will attract new research around this challenging inverse rendering problem.", + "bbox": [ + 496, + 90, + 893, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8168d74da20a31e3860b0d18207a6b9bda9bf67ed4247d9a51970f7e2b4f3d2f.jpg", + "image_caption": [ + "Figure 6. We show one image from the easy test split $\\mathcal{I}^{easy}$ on the left. In the middle we can see the same image as rendered by our V5 model, while on the right the intermediate visibility output of $\\Psi_{vis}$ is shown, which is then multiplied by the predicted BRDF to determine the outgoing radiance at each point." + ], + "image_footnote": [], + "bbox": [ + 501, + 253, + 908, + 494 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4c52017d54a42edbe41d8c83da1a9812a62378bbcdcb67111a7cdcece59c0b65.jpg", + "image_caption": [ + "Figure 7. On the left the ground-truth image drawn from the hard test split $\\mathcal{I}^{hard}$ . In the middle the corresponding render produced by our V5 model. On the right the intermediate visibility output of our model." + ], + "image_footnote": [], + "bbox": [ + 500, + 587, + 910, + 830 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20769", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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ACM Transactions on Graphics (TOG), 40(1):1-17, 2021. 2, 3", + "[75] Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul Debevec, William T Freeman, and Jonathan T Barron. Nefactor: Neural factorization of shape and reflectance under an unknown illumination. ACM Transactions on Graphics (TOG), 40(6):1-18, 2021. 2, 3", + "[76] Hao Zhou, Sunil Hadap, Kalyan Sunkavalli, and David W Jacobs. Deep single-image portrait relighting. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7194-7202, 2019. 3", + "[77] Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 895 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20772", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_model.json b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_model.json new file mode 100644 index 0000000000000000000000000000000000000000..65002003819cc890f7c77eee1ed6f4ec0d911f47 --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_model.json @@ -0,0 +1,2136 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.787, + 0.177 + ], + "angle": 0, + "content": "ReLight My NeRF: A Dataset for Novel View Synthesis and Relighting of Real World Objects" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.204, + 0.812, + 0.293 + ], + "angle": 0, + "content": "Marco Toschi\\*, Riccardo De Matteo\\*,, Riccardo Spezialetti\\*, Daniele De Gregorio Eyecan.ai {marco.toschi, riccardo.spezialetti, daniele.degregorio}@eyecan.ai Luigi Di Stefano, Samuele Salti University of Bologna" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.298, + 0.891, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.51, + 0.895, + 0.555 + ], + "angle": 0, + "content": "Figure 1. A random subset of scenes from our dataset. Our dataset enables the study of joint novel view synthesis and relighting from real images, as it provides scenes framed from the same viewpoint under varying light positions (shown along rows) as well as captured from different viewpoints under the same light position (shown along columns)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.565, + 0.314, + 0.581 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.474, + 0.884 + ], + "angle": 0, + "content": "In this paper, we focus on the problem of rendering novel views from a Neural Radiance Field (NeRF) under unobserved light conditions. To this end, we introduce a novel dataset, dubbed ReNe (Relighting NeRF), framing real world objects under one-light-at-time (OLAT) conditions, annotated with accurate ground-truth camera and light poses. Our acquisition pipeline leverages two robotic arms holding, respectively, a camera and an omni-directional point-wise light source. We release a total of 20 scenes depicting a variety of objects with complex geometry and challenging materials. Each scene includes 2000 images, acquired from 50 different points of views under 40 different OLAT conditions. By leveraging the dataset, we perform an ablation study on the relighting capability of variants of the vanilla NeRF architecture and identify a lightweight architecture that can render novel views of an object under novel light conditions, which we use to establish a non-trivial baseline for the dataset. Dataset and benchmark are available at https://eyecan-ai.github.io/rene." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.565, + 0.633, + 0.581 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.895, + 0.741 + ], + "angle": 0, + "content": "Inverse rendering [29, 47, 52, 73] addresses the problem of estimating the physical attributes of an object, such as its geometry, material properties and lighting conditions, from a set of images or even just a single one. This task is a longstanding problem for the vision and graphics communities, since it unlocks the creation of novel renderings of an object from arbitrary viewpoints and under unobserved lighting conditions. An effective and robust solution to this problem would have significant value for a wide range of applications in gaming, robotics and augmented reality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.896, + 0.879 + ], + "angle": 0, + "content": "Recently, Neural Radiance Fields (NeRF) [36] has contributed tremendously to the novel view synthesis sub-task of inverse rendering pipelines. By mapping an input 5D vector (3D position and 2D viewing direction) to a 4D continuous field of volume density and color by means of a neural network, NeRF learns the geometry and appearance of a single scene from a set of posed images. The appealing results in novel view synthesis have attracted a lot of attention from the research community and triggered many follow-up" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.887, + 0.822, + 0.902 + ], + "angle": 0, + "content": "* Joint first authorship. \\(^\\circ\\) Work done while at Eyecan.ai" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20762" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.223 + ], + "angle": 0, + "content": "
DatasetMultiple categoriesReal-WorldBackground ShadowsPublicLight Supervision
Gross et al. [14]X✓X✓✓
Sun et al. [57]X✓X✓✓
Wang et al. [68]X✓X✓✓
Zhang et al. [74]X✓X✓✓
Srinivasan et al. [55]✓XX✓✓
Zhang et al. [75]✓✓✓✓X
Zhang et al. [75]✓XX✓✓
Bi et al. [2]✓✓XX✓
ReNe✓✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.237, + 0.47, + 0.293 + ], + "angle": 0, + "content": "Table 1. Overview of relighting datasets. Our dataset is the first one featuring a variety of objects and materials captured with real-world sensors that provides ground-truth light positions and also presents challenging cast shadows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.627 + ], + "angle": 0, + "content": "works aimed at overcoming the main limitations of NeRF, e.g. reduce inference runtime [23, 24, 27, 48, 49, 71], enable modeling of deformable objects [9, 25, 42, 45, 46, 62], and generalization to novel scenes [5, 15, 19, 39, 50, 53, 61, 63, 72]. However, less attention has been paid to the relighting ability of NeRFs. Although NeRF and its variants represent nowadays the most compelling strategy for view synthesis, the learned scene representation entangles material and lighting and, thus, cannot be directly used to generate views under novel, unseen lighting conditions. A few existing works [3, 4, 55, 75] try to overcome this structural NeRF limitation by learning to model the scene appearance as a function of reflectance, which accounts for both scene geometry and lighting modeling. However, these methods incur a great computation cost, mainly due to the need to explicitly model light visibility and/or the components of a microfacet Bidirectional Reflectance Distribution Function (BRDF) [65] like diffuse albedo, specular roughness, and point normals: for instance NeRV [55] uses 128 TPU cores for 1 day while [3] is trained on 4 GPUs for 2 days." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.902 + ], + "angle": 0, + "content": "As highlighted in Tab. 1, one of the main challenges to foster research in this direction is the absence of real-world datasets featuring generic and varied objects with ground-truth light direction, both at training and test time. The latter is key to create a realistic quantitative benchmark for relighting methods, whose availability is one of the main driving forces behind fast-paced development of a machine learning topic. Indeed, the above mentioned NeRF-like methods for relighting mainly consider a handful of synthetic images to provide quantitative results (3 and 4 scenes in NeRV [55] and NeRFactor [75], respectively) while no quantitative results are provided in [3]. The only dataset with scenes acquired by a real sensor is proposed in [2], which, however, assumes images captured under collocated view and lighting setup, i.e. a smartphone with flash light on, which limits the amount of cast shadows and simplifies the task. Moreover, the dataset is not publicly available. Some available real-world datasets with ground-truth light" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "positions feature human faces or portraits [14, 57, 68, 74]. In these datasets, the subject is usually seated in the center of a light-stage with cameras arranged over a dome array positioned in front of the subject. Although these dataset provide real scenes with ground-truth annotations for light positions, the background is masked-out and shadows cast on the background, which are hard to model because they require a precise knowledge about the geometry of the overall scene, are ignored." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.725 + ], + "angle": 0, + "content": "Therefore, in this paper we try to answer the research questions: can we design a data acquisition methodology suitable to collect a set of images of an object under one light-at-time (OLAT) [74] illumination with high-quality camera and light pose annotations which requires minimal human supervision? We then leverage it to investigate a second question: can we design a novel Neural Radiance Field architecture to learn to perform relighting with reasonable computational requirements? To answer the first question, we design a capture system relying on two robotic arms. While one arm holds the camera and shots pictures from viewpoints uniformly distributed on a spherical wedge, the other moves the light source across points uniformly distributed on a dome. As a result, we collect the ReNe dataset, made of 20 scenes framing daily objects with challenging geometry, varied materials and visible cast shadows, composed of 50 camera view-points under 40 OLAT light conditions, i.e. 2000 frames per scene. Examples of images from the dataset are shown in Fig. 1. With a subset of images from each scene, we create a novel hold-out dataset for joint relighting and novel view synthesis evaluation that will be used as an online benchmark to foster research on this important topic. As regards the second question, thanks to the new dataset we conduct a study on the relighting capability of NeRF. In particular, we investigate on how the standard NeRF architecture can be modified to take into account the position of the light when generating the appearance of a scene. Our study shows that by estimating color with two separate sub-networks, one in charge of softshadow prediction and one responsible for neurally approximating the BRDF, we can perform an effective relighting, e.g. cast complex shadows. We provide results of our novel architecture as a reference baseline for the new benchmark." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.728, + 0.778, + 0.742 + ], + "angle": 0, + "content": "In summary, our contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.755, + 0.892, + 0.799 + ], + "angle": 0, + "content": "- a novel dataset made out of sets of OLAT images of real-world objects, with accurate camera and light pose annotations;" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.813, + 0.891, + 0.856 + ], + "angle": 0, + "content": "- a study comparing different approaches to enable NeRF to perform relighting alongside novel view synthesis;" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "- a new architecture, where the stage responsible for radiance estimation is split into two separate networks," + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.755, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20763" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.11, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "that can render novel views under novel unobserved lighting conditions;" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.134, + 0.47, + 0.179 + ], + "angle": 0, + "content": "- a public benchmark for novel view synthesis and relighting of real world objects, that will be maintained on an online evaluation server." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.194, + 0.22, + 0.21 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.22, + 0.468, + 0.264 + ], + "angle": 0, + "content": "In this paper, we focus on relighting static objects by Neural Radiance Fields. We briefly discuss the related works and their datasets below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.468, + 0.401 + ], + "angle": 0, + "content": "Image Relighting without NeRF. There exist several works in the field of image based relighting [8, 32, 44, 51]. The proposed methods differ for the adopted technique to model the light transport function in form of discrete light transport matrix. With recent advances in deep learning, new techniques have been introduced to address relighting [57], with many of them designed to relight human portraits [38, 58, 59, 70, 76]. Another bunch of works pursues joint relighting and novel view synthesis [11, 34, 74]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.468, + 0.627 + ], + "angle": 0, + "content": "Relighting Datasets. Most of relighting datasets contain captures of human bodies or face portraits, they leverage complex capture setups such as calibrated multi-view lightstages with cameras and LED lights, where the cameras are synchronized with the lights in order to flash one LED per capture [38,58,59,76]. Alternative works on generic objects do exist [51, 70], but they consider a mix of real and synthetic data, with the latter dominating the former in terms of number of images. The dataset most similar to ours is the one adopted by [2], which involves a robotic arm setup holding a Samsung Galaxy Note 8. However, this acquisition framework assumes a collocated view and lighting setup, e.g. built-in flash of a smart-phone camera lens, that inherently limits the shadows cast. Furthermore, the dataset has not been released." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.468, + 0.885 + ], + "angle": 0, + "content": "Neural Radiance Fields. Novel view synthesis has been a longstanding problem within the computer vision and computer graphics fields [7, 13, 20]. The advent of deep learning gave rise to explicit methods that train CNNs for this very purpose [22, 26, 35, 54, 56, 64, 77]. In the past few years, NeRF has advanced greatly in becoming the main scene representation for view synthesis [36]. NeRF learns a continuous volumetric function parameterized by means of a fully connected neural network optimized over a set of observed images with known camera poses using gradient descent. Due to its effectiveness, NeRF has inspired many subsequent works that extend its continuous neural volumetric representation for generative modeling [5, 19, 53], dynamic scenes [10, 21, 21, 30, 41, 46, 69], non-rigidly deforming objects [9, 9, 40, 42, 43, 62], multi-resolution images [1, 60], phototourism images with changing illumination settings [30, 61] and relighting [2, 4, 30, 55]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Neural Radiance Fields for Relighting. One of main limi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.65 + ], + "angle": 0, + "content": "tations of NeRF is that is not suitable for relighting. Indeed, NeRF treats the particles within scene representation as elements that emit light instead of being modelled as particles that reflect the incoming light sent out from external light sources. To straddle this divide, Neural Reflectance Field [2] models both scene geometry and reflectance regressing volume density, normal and material properties, e.g. Bidirectional Reflectance Distribution Function (BRDF) [65], for any 3D location within the volume of a scene. The shading at each point is then estimated using the light, view direction, the normal at that point and the BRDF. For instance, [28] leverages a differentiable path tracer to optimize a spatially-varying BSDF tied to an environment map, that can be used to render novel views under a novel OLAT condition. Unfortunately, this approach requires marching rays from all points sampled along the camera ray to any source of lighting in the scene, which restricts it use only in a collocated camera-light setup. NeRV ameliorates the computational cost of [2] by replacing the visibility estimation between scene points and light sources with a neural approximation of the true visibility field, which acts as a lookup table during rendering. Thanks to this insight, NeRV simulates direct illumination from environment lighting as well as one-bounce indirect illumination. NeRD [4] does not model visibility or shadows, but uses an analytic BRDF model [6] to learn a volumetric representation which stores SVBRDF [16] parameters at each 3D point instead of a radiance field. A relightable textured mesh is then extracted from that volume to allow fast rendering and relighting. Finally, NeRFactor [75] starts from two pre-trained networks: a NeRF of the scene and a BRDF network trained on the MERL dataset [31]. This knowledge is then distilled into four MLP-based networks to predict for each surface location its normal vector, light visibility, albedo and a BRDF latent code. The MLP outputs are injected into classical volumetric rendering and the networks parameters are optimized minimizing the re-rendering loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.892, + 0.71 + ], + "angle": 0, + "content": "We take inspiration from this line of works to design the study reported in Sec. 5, where we split the MLP-stack of NeRF in two separate networks: one responsible for the visibility and one that resembles the BRDF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.792, + 0.741 + ], + "angle": 0, + "content": "3. Dataset Acquisition Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "While providing both lights and cameras poses in a controlled manner with ground-truths annotations is straightforward in synthetic environments [55, 75], it is cumbersome and complex in the real world, especially if humans are involved, as done in [14, 57, 68, 74]. Our solution is to deploy extremely repeatable and safe machines such as industrial cobots (collaborative robots). In particular, we use a pair of robots, dubbed LightBot and CameraBot, to position the light and camera independently. Thanks to their high repeatability \\((+/-0.03\\mathrm{mm})\\), we can calibrate their tra" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20764" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.107, + 0.53, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.313, + 0.317, + 0.324 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.123, + 0.89, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.312, + 0.729, + 0.324 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.337, + 0.893, + 0.392 + ], + "angle": 0, + "content": "Figure 2. Overview of our dataset acquisition framework. (a) The LightBot and CameraBot moving light and camera respectively; the trajectories of the two robots are two non-intersecting sections of a hemisphere around the object of interest. (b) Grid of images in which each row depicts the same viewpoint as the light conditions change; each column, on the other hand, represents the same light condition as the viewpoint changes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.471, + 0.51 + ], + "angle": 0, + "content": "jectories with respect to a common world reference frame only once before acquisition starts, and then obtain accurate 6-DoF pose knowledge of both light and camera for all scenes by repeating the same trajectories. The proposed framework is sketched in Fig. 2a, while some acquisitions for the Robotoy scene are shown in Fig. 2b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Camera/Light Calibration. In order to calibrate both robots with respect to a common reference frame we use a ChArUco board [12]. We let the CameraBot see the board at each waypoint of its trajectory in order to calibrate extrinsic parameters for each view. Thanks to the high repeatability of the robot, it is possible to perform this procedure only once before we start to record scenes: the robot will be able to place the camera at the previously calibrated positions with negligible error. This allows us to register in a common reference frame all the camera poses for each scene without instrumenting the scene with a pattern, which alters the realism of the scene and makes the setup fragile, as the pattern may be inadvertently moved across scans. As for the LightBot, we assume that the center of the point light corresponds to the geometric center of the LED. We are then able to register it with the calibration pattern by letting the end effector physically touch the central reference point of the pattern with the center of the LED at calibration time. We note we cannot use the same procedure for the CameraBot as the camera optical center is behind the lens. That closes the calibration loop since both robots, now, will have the pattern itself as their world reference frame, thus a common coordinate system. Even with the LightBot, high repeatability assures that the light pose registered at calibration time will be identical across all scenes of the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.631 + ], + "angle": 0, + "content": "Trajectories. As depicted in Fig. 2a, we generate two trajectories, roughly belonging to the same hemisphere, whose upper part is used for the lights while the side part for the camera. This made it possible to capture several front-facing scenes with the light moving over the object of interest. With this setup, then, for each scene we collected 50 viewpoints each under 40 different light locations. To have waypoints uniformly distributed on the selected spherical region for each end effector, we create trajectories as sequences of centers of equal-area subregions, following the methodology proposed by [17]. For the sake of illustration, Fig. 2b shows a grid of images in which each row depicts frames with the same camera pose but different lighting conditions and vice-versa for columns." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.894, + 0.713 + ], + "angle": 0, + "content": "Background texture. In preliminary experiments with a uniform background as scenario, we found out that NeRF struggles to correctly estimate density in such a case and training does not converge. Hence, in our dataset textured walls are shown in the background." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Hardware. We equipped the LightBot and the CameraBot, respectively an Universal Robots UR5e and an Elite Robotics EC66, with a consumer headlight and an industrial camera. The headlight is the Velamp Metros IH523, equipped with 5 COB LEDs that provide a diffuse \\(100^{\\circ}\\) beam up to \\(150\\mathrm{Lm}\\) with 6000K light temperature. We used it at half power \\((70\\mathrm{Lm})\\) to maximize its runtime. The camera is a Basler acA1440-73gc with its optical axis mounted at \\(45^{\\circ}\\) from the robot flange normal vector, this to simplify the computation of inverse kinematics of the CameraBot. Images are captured in camera's full 1.6MP resolution \\((1440\\mathrm{px} \\times 1080\\mathrm{px})\\) using a Basler lens with \\(8\\mathrm{mm}\\) focal" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20765" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.129, + 0.108 + ], + "angle": 0, + "content": "length." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.121, + 0.254, + 0.138 + ], + "angle": 0, + "content": "4. The ReNe Dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.148, + 0.473, + 0.344 + ], + "angle": 0, + "content": "In this section, we summarize the data we collected using our framework to establish the ReNe dataset. Our dataset \\( \\mathcal{S} = \\{\\mathcal{I}_s\\}_{s=1}^S \\) contains \\( S \\) scenes, where each scene is a collection of RGB images \\( \\mathcal{I}_s = \\{I_{s,n,m} \\mid n = 1,\\dots,N,m = 1,\\dots,M\\} \\), \\( I_{n,m} \\in [0,1]^{H \\times W \\times 3} \\) acquired using camera poses \\( \\mathcal{C}_s = \\{C_{s,n}\\}_{n=1}^N \\) and lit with a point light source placed in \\( \\mathcal{G}_s = \\{G_{s,m}\\}_{m=1}^M \\). Each \\( C_n \\) and \\( G_m \\) represent the 6D pose \\( \\{\\mathbf{R},\\mathbf{t}\\} \\in SE(3) \\) for camera and light source, respectively. \\( \\mathbf{R} \\) denotes rotation, \\( \\mathbf{R} \\in SO(3) \\), and \\( \\mathbf{t} \\) denotes translation, \\( \\mathbf{t} \\in \\mathbb{R}^3 \\). The dataset features 40000 images divided in \\( S = 20 \\) scenes taken by \\( N = 50 \\) frontal points of views in \\( M = 40 \\) different lighting conditions, i.e. 2000 frames per scene." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.473, + 0.678 + ], + "angle": 0, + "content": "Train, Validation and Test splits. We split the datasets into train, val and test subsets to make it easy to compare in a fair and consistent way different approaches to NeRF relighting. In order to avoid data leakage from validation and test, we randomly create the set of held out viewpoints for validation, \\( \\mathcal{C}^{val} \\), and for testing, \\( \\mathcal{C}^{test} \\), as well as the set of held out light positions for testing, \\( \\mathcal{G}^{test} \\). Each of them consists of 3 indexes. To build the validation set, for each viewpoint \\( n_{val} \\in \\mathcal{C}^{val} \\), we randomly pick 3 light poses among the 37 available to form \\( \\mathcal{G}_{n_{val}} \\). In this way, in the validation set we have an unseen pair (viewpoint, light) composed of a viewpoint not present in the training set and a light used for other training viewpoints, \\( \\mathcal{I}^{val} = \\{I_{s,n_{val},m_{val}} | n_{val} \\in \\mathcal{C}_{val} \\wedge m_{val} \\in \\mathcal{G}_{n_{val}} \\wedge s = 1, \\ldots, S\\} \\). For test set, we build two sub-splits namely easy and hard. The former considers all the images \\( \\mathcal{I}^{easy} = \\{I_{s,n,m} | n \\in \\mathcal{C}^{test}, m = 1, \\ldots, M, m \\notin \\mathcal{G}^{test}\\} \\), while the latter is composed of images \\( \\mathcal{I}^{hard} = \\{I_{s,n,m} | (n,m) \\in \\mathcal{C}^{test} \\times \\mathcal{G}^{test}\\} \\). With this partition, the test set is comprised of novel viewpoints lit by light seen at training time in the easy split, and of novel viewpoints under a never seen light in the hard split. We sketch the splits in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.691, + 0.472, + 0.725 + ], + "angle": 0, + "content": "5. Benchmarking the Relighting Capability of NeRF" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.9 + ], + "angle": 0, + "content": "In the section, we explore our second research question: equipped with the ReNe dataset, can we add relighting capabilities to NeRF in a simple and lightweight way? We start with a brief overview of NeRF (Sec. 5.1), we then discuss alternative ways to make NeRF able to perform novel view synthesis and relighting simultaneously (Sec. 5.2). We compare our choices through an ablation study using the validation set described in Sec. 4, whose results are discussed in Sec. 5.3. Finally, in Sec. 5.4, we present the results for the best method on both test sets of the ReNe dataset." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.091, + 0.877, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.429, + 0.895, + 0.486 + ], + "angle": 0, + "content": "Figure 3. Dataset splits. Each scene \\(\\mathcal{I}_s\\) is divided in 4 different splits: Samples used for training Samples used for validation Samples used for Easy Test Samples used for Hard Test Samples never used." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.66, + 0.527 + ], + "angle": 0, + "content": "5.1. NeRF Overview" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.536, + 0.894, + 0.718 + ], + "angle": 0, + "content": "A Neural Radiance Field (NeRF) [36] maps a 5D input representing camera pose, i.e. 3D coordinates \\(\\mathbf{x} = (x,y,z)\\) along with the 2D viewing directions \\(\\mathbf{d} = (\\theta ,\\phi)\\), into a 4D color-density output \\((\\mathbf{c},\\sigma)\\) by means of a function \\(F_{\\Theta}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma)\\) approximated by the weights of an MLP. Specifically, here we consider a vanilla NeRF architecture [37] which estimates color and density using two MLPs as \\((\\sigma ,\\mathbf{e}) = \\Psi_{geo}(\\mathbf{x})\\) and \\(\\mathbf{c} = \\Psi_{rgb}(\\mathbf{e},\\mathbf{d})\\), with \\(\\sigma\\) being interpreted as the probability of a ray terminating at \\((x,y,z)\\) and \\(\\mathbf{e}\\) being a feature embedding. Following [33], the color \\(C(\\mathbf{r})\\) rendered from a camera ray \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\) can be obtained solving the integral:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.73, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) c (\\mathbf {r} (t), \\mathbf {d}) d t \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.774, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\( T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (\\mathbf{r}(s))ds\\right) \\) represents the accumulated transmittance from \\( t_n \\) to \\( t \\) along the ray \\( r \\), and \\( t \\) goes from near plane \\( t_n \\) to far plane \\( t_f \\). The image formation procedure is performed by simply aggregating the result of the integral for all pixels, i.e. samples along the rays, of the target image. Although NeRF works well for synthesizing novel views, as shown by the previous equations, it has no way of modeling the incoming light since" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20766" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.893, + 0.259 + ], + "angle": 0, + "content": "Figure 4. Overview of architectures. We start from the architecture of [37] and propose variants to inject information about the light position in the scene. Highlighted arrows in each variant underline an architectural change from the one that precedes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.47, + 0.342 + ], + "angle": 0, + "content": "it only takes into account position and orientation for the camera. In the next section, we will introduce variations of the classical approach that also take into account the light position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.471, + 0.449 + ], + "angle": 0, + "content": "Positional Encoding. As showed in NeRF [35] enconding \\(\\mathbf{x}\\) and \\(\\mathbf{d}\\) into a higher dimensional space allows the neural network to overcome its spectral bias and makes it able to reproduce the high-frequency content of the input signal. We follow [37] and encode \\(\\mathbf{x}\\) using a multiresolution hash encoding, \\(h(\\mathbf{x})\\), whilst \\(\\mathbf{d}\\) is projected onto the first 16 coefficients of the spherical harmonics, \\(\\zeta(\\mathbf{d})\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.411, + 0.472 + ], + "angle": 0, + "content": "5.2. On The Relighting Capability of NeRF" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.75 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, we take as a starting point the architecture presented in [37] and delineate 5 proposals to enable NeRF to perform relighting while adding minimum complexity to the architecture. Recalling Sec. 5.1, the naive architecture, namely V0, has two sub-networks, \\(\\Psi_{geo}\\), which outputs \\(\\sigma\\) a measure of the particle density at \\(\\mathbf{x}\\), and \\(\\Psi_{rgb}\\) which is responsible for the color, \\(\\mathbf{c}\\). Previous works [66, 66] demonstrated that \\(\\Psi_{geo}\\) learns the scene geometry, while \\(\\Psi_{rgb}\\) models the view-dependent color appearance. Hence, our key idea is to modify the input to the \\(\\Psi_{rgb}\\) injecting light position and let the model learn the interaction between the geometry and light. We train one network on each scene minimizing the error between the ground-truth images and the rendered ones. As input data we consider a set of multi-view images of an object, \\(\\mathcal{I}_s\\), illuminated under known lighting conditions, \\(\\mathcal{G}_s\\), and the camera poses of these images, \\(\\mathcal{C}_s\\). We will consider the subscript \\(s\\) implicit in what follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "V1. A straightforward way to enable relighting with NeRF is to condition \\(\\Psi_{rgb}\\) with a latent representation that stores the world position and orientation of the light, \\(G_{m}\\) for a given observation \\(I_{n,m}\\). To do so, we flatten the \\(\\mathbf{R}\\) and \\(\\mathbf{t}\\) parts of \\(G_{m}\\) and encode this 12-dimensional vector into a 156-dimensional latent code using the positional encoding with Fourier Features proposed in [36], \\(\\gamma (\\mathbf{R},\\mathbf{t})\\). Our procedure resembles the approach adopted by NeRF in the Wild [30], but the condition embedding is used to adapt NeRF to variable lighting conditions instead of transient" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.633, + 0.298 + ], + "angle": 0, + "content": "parts of the images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.3, + 0.893, + 0.453 + ], + "angle": 0, + "content": "V2. As the next iteration, we change the parameterization for \\( G_{m} \\). Instead of directly encoding \\( \\mathbf{R} \\) and \\( \\mathbf{t} \\) in the same way for each sample \\( \\mathbf{x} \\) used to query \\( \\Psi_{rgb} \\), we construct a 3D unit vector \\( \\mathbf{l} = \\frac{\\mathbf{t} - \\mathbf{x}}{||\\mathbf{t} - \\mathbf{x}||} \\) which let the network be aware of the relative position between the light source and the query location. Since, differently from the previous approach, \\( \\mathbf{l} \\) changes for each query point, we conjecture this may help NeRF in modulating the output color \\( \\mathbf{c} \\) based on the incoming light information. As done for \\( \\mathbf{d} \\), \\( \\mathbf{l} \\) is encoded using the spherical harmonics, \\( \\zeta(\\mathbf{l}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.893, + 0.607 + ], + "angle": 0, + "content": "V3. The previous version resembles somehow the BRDF where \\(\\mathbf{l}\\) acts as the incoming light direction at \\(\\mathbf{x}\\), and \\(\\mathbf{d}\\) is the unit vector pointing from \\(\\mathbf{x}\\) toward the camera. Following this analogy, we may consider \\(\\mathbf{e}\\) to represent an \\(N\\)-dimensional embedding of the normal vector at \\(\\mathbf{x}\\). Since all these information are relative to \\(\\mathbf{x}\\), we explore whether having \\(h(\\mathbf{x})\\) as input can be beneficial for \\(\\Psi_{rgb}\\). Without such skip connection the knowledge about the location of the query point may vanish as the depth of the network increases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.732 + ], + "angle": 0, + "content": "V4. The previous version may be negatively influenced by the diverse scales of its inputs, which are on one side spherical and hash-grid encoded vectors like \\(\\zeta(\\mathbf{d})\\), \\(\\zeta(\\mathbf{l})\\), and \\(h(\\mathbf{x})\\) while on the other there is the ReLU output \\(\\mathbf{e}\\). To test this hypothesis, we propose a variant where we concatenate \\(\\mathbf{e}\\) with the output of the first layer of \\(\\Psi_{rgb}\\) and use this vector as input for its second layer, rather than feeding \\(\\Psi_{rgb}\\) directly with \\(\\mathbf{e}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "V5. The original NeRF learns a continuous 3D field of particles that absorb and emit light. As a result only the amount of outgoing light from a location is modeled, without taking into account the fact that the outgoing light is the result of interactions between incoming light and the material properties of an underlying surface. This issue can be alleviated by replacing Eq. (1) with a physically-based volume rendering for non-emissive and non-absorptive volumes, which replaces the emitted color of each 3D point along the ray, \\( c(\\mathbf{r}(t), \\mathbf{d}) \\), with \\( L_{r}(\\mathbf{x}, \\omega_{o}) \\) that represents the scattered light at \\( \\mathbf{x} \\) along \\( \\omega_{o} \\). As done in [2], assuming a single point light" + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.3, + 0.895, + 0.903 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20767" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.427, + 0.107 + ], + "angle": 0, + "content": "source of fixed intensity, \\( L_{r} \\) can be approximated as:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.119, + 0.47, + 0.151 + ], + "angle": 0, + "content": "\\[\nL _ {r} (\\mathbf {x}, \\omega_ {o}) = \\int_ {S} f _ {p} (\\mathbf {x}, \\omega_ {o}, \\omega_ {i}) L _ {i} (\\mathbf {x}, \\omega_ {i}) d \\omega_ {i} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.162, + 0.473, + 0.358 + ], + "angle": 0, + "content": "where \\(S\\) is a unit sphere, \\(f_{p}\\) represents a differentiable reflectance model (like the BRDF), and \\(L_{i}\\) represents the incident radiance at \\(x\\) from direction \\(\\omega_{i}\\). Please note that in this equation \\(\\omega_{o}\\) corresponds to \\(\\mathbf{d}\\) and \\(\\omega_{i}\\) is analogous to \\(\\mathbf{l}\\). While we can assume that \\(f_{p}\\) is approximated by \\(\\Psi_{rgb}\\), computing \\(L_{i}\\) requires marching a large number of light rays for all shading points on all camera rays to determine the transmittance between the light and each 3D point. We avoid this cumbersome procedure by introducing a neural approximation of \\(L_{i}\\) in the form of an MLP aimed at predicting a scalar value \\(o = \\Psi_{vis}(h(\\mathbf{x}),\\zeta (\\mathbf{l}))\\), which allows us to efficiently query the point-to-light visibility. The final pixel color is then obtained with \\(\\mathbf{c}^{\\star} = o\\cdot \\mathbf{c}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.368, + 0.228, + 0.385 + ], + "angle": 0, + "content": "5.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.47, + 0.514 + ], + "angle": 0, + "content": "Dataset. To assess the relative merits of the incremental modifications to NeRF proposed in the previous section and identify the best architecture, we consider a subset of scenes presenting a variety of challenges: Cube, that has thin wireframe structures and shadows; Savannah, that pictures a jagged leaves tree with a complex shadow; Reflective, that is full of specular reflections, and FlipFlop, where light passes through semi-transparent plastic strings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.471, + 0.785 + ], + "angle": 0, + "content": "Implementation Details. We used the torch-ngp pytorch implementation1 of Nvidia Instant-NGP [37] for fast training of Neural Radiance Fields models. During training, we randomly sample 4096 pixel rays as a batch to train our networks. We use Adam optimizer [18] with an initial learning rate of 0.01 (other Adam hyperparameters are left at default values of \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\)). For volumetric integration, we use 128 samples in coarse volume and 128 additional adaptive samples in fine volume to compute the final radiance. The optimization for a single scene typically takes around 100–200k iterations to converge on a single NVIDIA RTX 2080Ti GPU (about 5 hours). We use early-stopping if the model doesn’t improve for 10 consecutive epochs. We supervise the regressed RGB values with the ground truth values from the captured images using the L2 loss. For \\(\\Psi_{geo}\\) we use 2 fully-connected ReLU layers with 64 channels, while \\(\\Psi_{rgb}\\) and \\(\\Psi_{vis}\\) uses 4 fully-connected ReLU layers with 64 channels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.471, + 0.877 + ], + "angle": 0, + "content": "Results. For a quantitative evaluation of our methods we consider two widely adopted metrics of image quality assessment: Structural Similarity (SSIM) [67] and Peak Signal-to-Noise Ratio (PSNR) [35]. We report the results of the ablation study in Tab. 2. Results show how all the proposed modifications to NeRF improve performance and" + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.089, + 0.89, + 0.158 + ], + "angle": 0, + "content": "
Methodγ(R, t)1skipinputsΨviasCubeSavannahReflectiveFlipFlop
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
V1✓XXXX24.370.5222.530.4423.570.5124.120.51
V2X✓XXX24.730.5423.700.5223.680.5224.420.56
V3X✓✓XX25.380.5624.390.5524.650.5825.060.57
V4X✓✓✓X25.410.5724.790.5824.240.5625.270.58
V5X✓✓✓✓26.110.6125.230.6125.000.5925.460.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.168, + 0.894, + 0.267 + ], + "angle": 0, + "content": "Table 2. Quantitative relighting and view synthesis result of the proposed modifications to NeRF. For each scene, we report on the left the PSNR and on the right the SSIM. Legend: \\(\\gamma (\\mathbf{R},\\mathbf{t})\\) indicates the use of absolute light position, \\(\\mathbf{l}\\) of relative position wrt \\(\\mathbf{x}\\), skip indicates that \\(\\mathbf{x}\\) is provided as input to \\(\\Psi_{rgb}\\), inputs that the embedding is inserted in \\(\\Psi_{rgb}\\) at the second layer, while \\(\\Psi_{vis}\\) that the MLP approximating \\(L_{i}(x,\\omega_{i})\\) is used." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.281, + 0.895, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.49, + 0.893, + 0.561 + ], + "angle": 0, + "content": "Figure 5. Qualitative results for ablation. The same image as rendered by V1 and V5 networks. The side-by-side comparison clearly shows how V5 reproduces much sharper details in shadows (best seen in Reflective) and is able to better handle complex reflections (best seen in FlipFlop)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.892, + 0.726 + ], + "angle": 0, + "content": "contribute to the overall good results of the most effective version, which is V5. These results provide experimental support to the intuitions presented above about the higher effectiveness of feeding to the network the relative light position with respect to the sample \\(\\mathbf{x}\\) instead of the absolute light pose (row 1 versus row 2), as well as the importance of providing \\(\\mathbf{x}\\) as input to \\(\\Psi_{rgb}\\) (row 2 versus row 3). Separating inputs to \\(\\Psi_{rgb}\\) is also beneficial and, together with \\(\\Psi_{vis}\\) contributes to the good performance of V5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Some qualitative examples comparing and contrasting V1 against V5 are reported in Fig. 5. Zooming in on cast shadows we can appreciate how careful handling of the light pose as well as the proposed modifications to the vanilla NeRF architecture enable rendering of sharper and more coherent shadows than the straightforward extension that conditions NeRF also on light pose." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.708, + 0.861 + ], + "angle": 0, + "content": "5.4. Results on benchmark" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Finally, we report the performance for the best architecture on the overall set of held out test scenes in Tab. 3." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.396, + 0.901 + ], + "angle": 0, + "content": "1https://github.com/ashawkey/torch-ngp" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20768" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.462, + 0.365 + ], + "angle": 0, + "content": "
OursInstant-NGP
NameEasyHardEasyHard
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Apple26.440.6226.250.6220.890.4520.950.45
Cheetah25.660.6124.640.6019.370.4419.600.44
Cube24.900.5423.980.5320.140.4220.310.42
Dinosaurs25.750.6524.980.6419.580.4219.660.41
FlipFlop25.850.6125.420.6120.380.4520.360.45
Fruits25.930.6225.720.6220.160.4520.210.44
Garden25.740.6625.080.6619.760.4519.700.45
Helicopters25.120.6124.730.6119.340.3719.370.37
Kittens25.900.6424.960.6318.520.3718.650.37
Lego26.070.6125.770.6120.750.4620.760.46
Lunch25.840.6024.710.5919.320.4619.380.45
Plant26.550.6725.930.6720.620.4420.660.44
Reflective25.790.6125.280.6120.090.4320.110.42
Robotoy26.240.6525.550.6520.770.5020.780.50
Savannah25.150.6224.310.6119.080.4019.180.40
Shark25.590.5725.320.5620.540.4220.530.41
Stegosaurus25.870.6325.650.6320.840.4320.910.42
Tapes25.840.5825.410.5719.340.4119.550.41
Trucks25.800.6725.160.6619.810.4419.870.44
Wooden toys25.690.6125.240.6020.190.4820.220.48
Average25.790.6225.200.6119.970.4320.040.43
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.432 + ], + "angle": 0, + "content": "Table 3. Quantitative results across all 20 scenes. We report both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) by comparing the novel view synthesized image with its corresponding groundtruth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.779 + ], + "angle": 0, + "content": "We compare our method against the pytorch implementation of Nvidia Instant-NGP [37]. Overall, the proposed architecture achieves satisfying results on this challenging task and sets a non trivial baseline for the online benchmark, clearly outperforming the naive baseline represented by the standard NeRF. We show some qualitative results for the easy test split in Fig. 6, and in Fig. 7 for the hard one. These qualitative results confirm that the model is capable of convincingly rendering and lighting the scene from unseen viewpoints and light positions while using a simple and lightweight architecture. Interestingly, the output of \\(\\Psi_{vis}\\), reported in the rightmost columns of the figures, well approximate point-to-light visibility, especially in the easy split, even if it has not received direct supervision to emulate it, and it even reproduces some indirect illumination effects, confirming the feasibility of a neural approximation of the incident radiance \\(L_{i}(\\mathbf{x},\\omega_{i})\\). Comparing with the ground-truth frame, while rendering of light on the object is indeed quite realistic, cast shadows are sharp and coherent with the scene geometry on the easy set, while more artifacts are present in the hard split." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.792, + 0.334, + 0.808 + ], + "angle": 0, + "content": "6. Conclusion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.817, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We have introduced the ReNe dataset, the first dual robot dataset framing real world objects under challenging one-light-at-time (OLAT) conditions and annotated with accurate camera and light poses. The main limitations of our dataset concern the absence of 360 degrees scans and the use of a challenging but unrealistic OLAT setup. By lever" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.233 + ], + "angle": 0, + "content": "aging the training and validation splits of the dataset, we were able to perform an ablation study on lightweight modifications to a NeRF architecture that extend it to successfully perform novel view synthesis under unseen lighting. The best model emerged from the study has been tested on the held out test set to establish a non-trivial baseline for the benchmark. We hope the availability of a new dataset and baseline for the problem of NeRF relighting will attract new research around this challenging inverse rendering problem." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.255, + 0.91, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.504, + 0.895, + 0.575 + ], + "angle": 0, + "content": "Figure 6. We show one image from the easy test split \\( \\mathcal{I}^{easy} \\) on the left. In the middle we can see the same image as rendered by our V5 model, while on the right the intermediate visibility output of \\( \\Psi_{vis} \\) is shown, which is then multiplied by the predicted BRDF to determine the outgoing radiance at each point." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.588, + 0.911, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.842, + 0.895, + 0.896 + ], + "angle": 0, + "content": "Figure 7. On the left the ground-truth image drawn from the hard test split \\(\\mathcal{I}^{hard}\\). In the middle the corresponding render produced by our V5 model. On the right the intermediate visibility output of our model." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20769" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.896 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20772" + } + ] +] \ No newline at end of file diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_origin.pdf b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bf53b564ef2e7e28f5105164bb67add80a7206d5 --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/17ade2bb-9ad4-48d5-b13f-aa219a03e831_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1cadfd1f49b62cdc54e6ab54fbd1132f5255238b952b3ef97ab018ef27abefa4 +size 5980580 diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/full.md b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5522c3a011d0badd72b9b85fda8bd0eb17fcb8dc --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/full.md @@ -0,0 +1,255 @@ +# ReLight My NeRF: A Dataset for Novel View Synthesis and Relighting of Real World Objects + +Marco Toschi\*, Riccardo De Matteo\*,, Riccardo Spezialetti\*, Daniele De Gregorio Eyecan.ai {marco.toschi, riccardo.spezialetti, daniele.degregorio}@eyecan.ai Luigi Di Stefano, Samuele Salti University of Bologna + +![](images/39910bbb8513b8eb17635efbc10fa6fd960cc48237c61dede0e2932fedaa8630.jpg) +Figure 1. A random subset of scenes from our dataset. Our dataset enables the study of joint novel view synthesis and relighting from real images, as it provides scenes framed from the same viewpoint under varying light positions (shown along rows) as well as captured from different viewpoints under the same light position (shown along columns). + +# Abstract + +In this paper, we focus on the problem of rendering novel views from a Neural Radiance Field (NeRF) under unobserved light conditions. To this end, we introduce a novel dataset, dubbed ReNe (Relighting NeRF), framing real world objects under one-light-at-time (OLAT) conditions, annotated with accurate ground-truth camera and light poses. Our acquisition pipeline leverages two robotic arms holding, respectively, a camera and an omni-directional point-wise light source. We release a total of 20 scenes depicting a variety of objects with complex geometry and challenging materials. Each scene includes 2000 images, acquired from 50 different points of views under 40 different OLAT conditions. By leveraging the dataset, we perform an ablation study on the relighting capability of variants of the vanilla NeRF architecture and identify a lightweight architecture that can render novel views of an object under novel light conditions, which we use to establish a non-trivial baseline for the dataset. Dataset and benchmark are available at https://eyecan-ai.github.io/rene. + +# 1. Introduction + +Inverse rendering [29, 47, 52, 73] addresses the problem of estimating the physical attributes of an object, such as its geometry, material properties and lighting conditions, from a set of images or even just a single one. This task is a longstanding problem for the vision and graphics communities, since it unlocks the creation of novel renderings of an object from arbitrary viewpoints and under unobserved lighting conditions. An effective and robust solution to this problem would have significant value for a wide range of applications in gaming, robotics and augmented reality. + +Recently, Neural Radiance Fields (NeRF) [36] has contributed tremendously to the novel view synthesis sub-task of inverse rendering pipelines. By mapping an input 5D vector (3D position and 2D viewing direction) to a 4D continuous field of volume density and color by means of a neural network, NeRF learns the geometry and appearance of a single scene from a set of posed images. The appealing results in novel view synthesis have attracted a lot of attention from the research community and triggered many follow-up + +
DatasetMultiple categoriesReal-WorldBackground ShadowsPublicLight Supervision
Gross et al. [14]X✓X✓✓
Sun et al. [57]X✓X✓✓
Wang et al. [68]X✓X✓✓
Zhang et al. [74]X✓X✓✓
Srinivasan et al. [55]✓XX✓✓
Zhang et al. [75]✓✓✓✓X
Zhang et al. [75]✓XX✓✓
Bi et al. [2]✓✓XX✓
ReNe✓✓✓✓✓
+ +Table 1. Overview of relighting datasets. Our dataset is the first one featuring a variety of objects and materials captured with real-world sensors that provides ground-truth light positions and also presents challenging cast shadows. + +works aimed at overcoming the main limitations of NeRF, e.g. reduce inference runtime [23, 24, 27, 48, 49, 71], enable modeling of deformable objects [9, 25, 42, 45, 46, 62], and generalization to novel scenes [5, 15, 19, 39, 50, 53, 61, 63, 72]. However, less attention has been paid to the relighting ability of NeRFs. Although NeRF and its variants represent nowadays the most compelling strategy for view synthesis, the learned scene representation entangles material and lighting and, thus, cannot be directly used to generate views under novel, unseen lighting conditions. A few existing works [3, 4, 55, 75] try to overcome this structural NeRF limitation by learning to model the scene appearance as a function of reflectance, which accounts for both scene geometry and lighting modeling. However, these methods incur a great computation cost, mainly due to the need to explicitly model light visibility and/or the components of a microfacet Bidirectional Reflectance Distribution Function (BRDF) [65] like diffuse albedo, specular roughness, and point normals: for instance NeRV [55] uses 128 TPU cores for 1 day while [3] is trained on 4 GPUs for 2 days. + +As highlighted in Tab. 1, one of the main challenges to foster research in this direction is the absence of real-world datasets featuring generic and varied objects with ground-truth light direction, both at training and test time. The latter is key to create a realistic quantitative benchmark for relighting methods, whose availability is one of the main driving forces behind fast-paced development of a machine learning topic. Indeed, the above mentioned NeRF-like methods for relighting mainly consider a handful of synthetic images to provide quantitative results (3 and 4 scenes in NeRV [55] and NeRFactor [75], respectively) while no quantitative results are provided in [3]. The only dataset with scenes acquired by a real sensor is proposed in [2], which, however, assumes images captured under collocated view and lighting setup, i.e. a smartphone with flash light on, which limits the amount of cast shadows and simplifies the task. Moreover, the dataset is not publicly available. Some available real-world datasets with ground-truth light + +positions feature human faces or portraits [14, 57, 68, 74]. In these datasets, the subject is usually seated in the center of a light-stage with cameras arranged over a dome array positioned in front of the subject. Although these dataset provide real scenes with ground-truth annotations for light positions, the background is masked-out and shadows cast on the background, which are hard to model because they require a precise knowledge about the geometry of the overall scene, are ignored. + +Therefore, in this paper we try to answer the research questions: can we design a data acquisition methodology suitable to collect a set of images of an object under one light-at-time (OLAT) [74] illumination with high-quality camera and light pose annotations which requires minimal human supervision? We then leverage it to investigate a second question: can we design a novel Neural Radiance Field architecture to learn to perform relighting with reasonable computational requirements? To answer the first question, we design a capture system relying on two robotic arms. While one arm holds the camera and shots pictures from viewpoints uniformly distributed on a spherical wedge, the other moves the light source across points uniformly distributed on a dome. As a result, we collect the ReNe dataset, made of 20 scenes framing daily objects with challenging geometry, varied materials and visible cast shadows, composed of 50 camera view-points under 40 OLAT light conditions, i.e. 2000 frames per scene. Examples of images from the dataset are shown in Fig. 1. With a subset of images from each scene, we create a novel hold-out dataset for joint relighting and novel view synthesis evaluation that will be used as an online benchmark to foster research on this important topic. As regards the second question, thanks to the new dataset we conduct a study on the relighting capability of NeRF. In particular, we investigate on how the standard NeRF architecture can be modified to take into account the position of the light when generating the appearance of a scene. Our study shows that by estimating color with two separate sub-networks, one in charge of softshadow prediction and one responsible for neurally approximating the BRDF, we can perform an effective relighting, e.g. cast complex shadows. We provide results of our novel architecture as a reference baseline for the new benchmark. + +In summary, our contributions include: + +- a novel dataset made out of sets of OLAT images of real-world objects, with accurate camera and light pose annotations; +- a study comparing different approaches to enable NeRF to perform relighting alongside novel view synthesis; +- a new architecture, where the stage responsible for radiance estimation is split into two separate networks, + +that can render novel views under novel unobserved lighting conditions; + +- a public benchmark for novel view synthesis and relighting of real world objects, that will be maintained on an online evaluation server. + +# 2. Related Work + +In this paper, we focus on relighting static objects by Neural Radiance Fields. We briefly discuss the related works and their datasets below. + +Image Relighting without NeRF. There exist several works in the field of image based relighting [8, 32, 44, 51]. The proposed methods differ for the adopted technique to model the light transport function in form of discrete light transport matrix. With recent advances in deep learning, new techniques have been introduced to address relighting [57], with many of them designed to relight human portraits [38, 58, 59, 70, 76]. Another bunch of works pursues joint relighting and novel view synthesis [11, 34, 74]. + +Relighting Datasets. Most of relighting datasets contain captures of human bodies or face portraits, they leverage complex capture setups such as calibrated multi-view lightstages with cameras and LED lights, where the cameras are synchronized with the lights in order to flash one LED per capture [38,58,59,76]. Alternative works on generic objects do exist [51, 70], but they consider a mix of real and synthetic data, with the latter dominating the former in terms of number of images. The dataset most similar to ours is the one adopted by [2], which involves a robotic arm setup holding a Samsung Galaxy Note 8. However, this acquisition framework assumes a collocated view and lighting setup, e.g. built-in flash of a smart-phone camera lens, that inherently limits the shadows cast. Furthermore, the dataset has not been released. + +Neural Radiance Fields. Novel view synthesis has been a longstanding problem within the computer vision and computer graphics fields [7, 13, 20]. The advent of deep learning gave rise to explicit methods that train CNNs for this very purpose [22, 26, 35, 54, 56, 64, 77]. In the past few years, NeRF has advanced greatly in becoming the main scene representation for view synthesis [36]. NeRF learns a continuous volumetric function parameterized by means of a fully connected neural network optimized over a set of observed images with known camera poses using gradient descent. Due to its effectiveness, NeRF has inspired many subsequent works that extend its continuous neural volumetric representation for generative modeling [5, 19, 53], dynamic scenes [10, 21, 21, 30, 41, 46, 69], non-rigidly deforming objects [9, 9, 40, 42, 43, 62], multi-resolution images [1, 60], phototourism images with changing illumination settings [30, 61] and relighting [2, 4, 30, 55]. + +Neural Radiance Fields for Relighting. One of main limi + +tations of NeRF is that is not suitable for relighting. Indeed, NeRF treats the particles within scene representation as elements that emit light instead of being modelled as particles that reflect the incoming light sent out from external light sources. To straddle this divide, Neural Reflectance Field [2] models both scene geometry and reflectance regressing volume density, normal and material properties, e.g. Bidirectional Reflectance Distribution Function (BRDF) [65], for any 3D location within the volume of a scene. The shading at each point is then estimated using the light, view direction, the normal at that point and the BRDF. For instance, [28] leverages a differentiable path tracer to optimize a spatially-varying BSDF tied to an environment map, that can be used to render novel views under a novel OLAT condition. Unfortunately, this approach requires marching rays from all points sampled along the camera ray to any source of lighting in the scene, which restricts it use only in a collocated camera-light setup. NeRV ameliorates the computational cost of [2] by replacing the visibility estimation between scene points and light sources with a neural approximation of the true visibility field, which acts as a lookup table during rendering. Thanks to this insight, NeRV simulates direct illumination from environment lighting as well as one-bounce indirect illumination. NeRD [4] does not model visibility or shadows, but uses an analytic BRDF model [6] to learn a volumetric representation which stores SVBRDF [16] parameters at each 3D point instead of a radiance field. A relightable textured mesh is then extracted from that volume to allow fast rendering and relighting. Finally, NeRFactor [75] starts from two pre-trained networks: a NeRF of the scene and a BRDF network trained on the MERL dataset [31]. This knowledge is then distilled into four MLP-based networks to predict for each surface location its normal vector, light visibility, albedo and a BRDF latent code. The MLP outputs are injected into classical volumetric rendering and the networks parameters are optimized minimizing the re-rendering loss. + +We take inspiration from this line of works to design the study reported in Sec. 5, where we split the MLP-stack of NeRF in two separate networks: one responsible for the visibility and one that resembles the BRDF. + +# 3. Dataset Acquisition Framework + +While providing both lights and cameras poses in a controlled manner with ground-truths annotations is straightforward in synthetic environments [55, 75], it is cumbersome and complex in the real world, especially if humans are involved, as done in [14, 57, 68, 74]. Our solution is to deploy extremely repeatable and safe machines such as industrial cobots (collaborative robots). In particular, we use a pair of robots, dubbed LightBot and CameraBot, to position the light and camera independently. Thanks to their high repeatability $(+/-0.03\mathrm{mm})$ , we can calibrate their tra + +![](images/46df05a747c37b785ab67f94291c6e0e1a50514b81c84a5ed06d971daecb09dc.jpg) +(a) + +![](images/106a6eeae19e044940a3512f51dd8454c3eaf4d4e794c94666c53f4e66b33ab5.jpg) +(b) +Figure 2. Overview of our dataset acquisition framework. (a) The LightBot and CameraBot moving light and camera respectively; the trajectories of the two robots are two non-intersecting sections of a hemisphere around the object of interest. (b) Grid of images in which each row depicts the same viewpoint as the light conditions change; each column, on the other hand, represents the same light condition as the viewpoint changes. + +jectories with respect to a common world reference frame only once before acquisition starts, and then obtain accurate 6-DoF pose knowledge of both light and camera for all scenes by repeating the same trajectories. The proposed framework is sketched in Fig. 2a, while some acquisitions for the Robotoy scene are shown in Fig. 2b. + +Camera/Light Calibration. In order to calibrate both robots with respect to a common reference frame we use a ChArUco board [12]. We let the CameraBot see the board at each waypoint of its trajectory in order to calibrate extrinsic parameters for each view. Thanks to the high repeatability of the robot, it is possible to perform this procedure only once before we start to record scenes: the robot will be able to place the camera at the previously calibrated positions with negligible error. This allows us to register in a common reference frame all the camera poses for each scene without instrumenting the scene with a pattern, which alters the realism of the scene and makes the setup fragile, as the pattern may be inadvertently moved across scans. As for the LightBot, we assume that the center of the point light corresponds to the geometric center of the LED. We are then able to register it with the calibration pattern by letting the end effector physically touch the central reference point of the pattern with the center of the LED at calibration time. We note we cannot use the same procedure for the CameraBot as the camera optical center is behind the lens. That closes the calibration loop since both robots, now, will have the pattern itself as their world reference frame, thus a common coordinate system. Even with the LightBot, high repeatability assures that the light pose registered at calibration time will be identical across all scenes of the dataset. + +Trajectories. As depicted in Fig. 2a, we generate two trajectories, roughly belonging to the same hemisphere, whose upper part is used for the lights while the side part for the camera. This made it possible to capture several front-facing scenes with the light moving over the object of interest. With this setup, then, for each scene we collected 50 viewpoints each under 40 different light locations. To have waypoints uniformly distributed on the selected spherical region for each end effector, we create trajectories as sequences of centers of equal-area subregions, following the methodology proposed by [17]. For the sake of illustration, Fig. 2b shows a grid of images in which each row depicts frames with the same camera pose but different lighting conditions and vice-versa for columns. + +Background texture. In preliminary experiments with a uniform background as scenario, we found out that NeRF struggles to correctly estimate density in such a case and training does not converge. Hence, in our dataset textured walls are shown in the background. + +Hardware. We equipped the LightBot and the CameraBot, respectively an Universal Robots UR5e and an Elite Robotics EC66, with a consumer headlight and an industrial camera. The headlight is the Velamp Metros IH523, equipped with 5 COB LEDs that provide a diffuse $100^{\circ}$ beam up to $150\mathrm{Lm}$ with 6000K light temperature. We used it at half power $(70\mathrm{Lm})$ to maximize its runtime. The camera is a Basler acA1440-73gc with its optical axis mounted at $45^{\circ}$ from the robot flange normal vector, this to simplify the computation of inverse kinematics of the CameraBot. Images are captured in camera's full 1.6MP resolution $(1440\mathrm{px} \times 1080\mathrm{px})$ using a Basler lens with $8\mathrm{mm}$ focal + +length. + +# 4. The ReNe Dataset + +In this section, we summarize the data we collected using our framework to establish the ReNe dataset. Our dataset $\mathcal{S} = \{\mathcal{I}_s\}_{s=1}^S$ contains $S$ scenes, where each scene is a collection of RGB images $\mathcal{I}_s = \{I_{s,n,m} \mid n = 1,\dots,N,m = 1,\dots,M\}$ , $I_{n,m} \in [0,1]^{H \times W \times 3}$ acquired using camera poses $\mathcal{C}_s = \{C_{s,n}\}_{n=1}^N$ and lit with a point light source placed in $\mathcal{G}_s = \{G_{s,m}\}_{m=1}^M$ . Each $C_n$ and $G_m$ represent the 6D pose $\{\mathbf{R},\mathbf{t}\} \in SE(3)$ for camera and light source, respectively. $\mathbf{R}$ denotes rotation, $\mathbf{R} \in SO(3)$ , and $\mathbf{t}$ denotes translation, $\mathbf{t} \in \mathbb{R}^3$ . The dataset features 40000 images divided in $S = 20$ scenes taken by $N = 50$ frontal points of views in $M = 40$ different lighting conditions, i.e. 2000 frames per scene. + +Train, Validation and Test splits. We split the datasets into train, val and test subsets to make it easy to compare in a fair and consistent way different approaches to NeRF relighting. In order to avoid data leakage from validation and test, we randomly create the set of held out viewpoints for validation, $\mathcal{C}^{val}$ , and for testing, $\mathcal{C}^{test}$ , as well as the set of held out light positions for testing, $\mathcal{G}^{test}$ . Each of them consists of 3 indexes. To build the validation set, for each viewpoint $n_{val} \in \mathcal{C}^{val}$ , we randomly pick 3 light poses among the 37 available to form $\mathcal{G}_{n_{val}}$ . In this way, in the validation set we have an unseen pair (viewpoint, light) composed of a viewpoint not present in the training set and a light used for other training viewpoints, $\mathcal{I}^{val} = \{I_{s,n_{val},m_{val}} | n_{val} \in \mathcal{C}_{val} \wedge m_{val} \in \mathcal{G}_{n_{val}} \wedge s = 1, \ldots, S\}$ . For test set, we build two sub-splits namely easy and hard. The former considers all the images $\mathcal{I}^{easy} = \{I_{s,n,m} | n \in \mathcal{C}^{test}, m = 1, \ldots, M, m \notin \mathcal{G}^{test}\}$ , while the latter is composed of images $\mathcal{I}^{hard} = \{I_{s,n,m} | (n,m) \in \mathcal{C}^{test} \times \mathcal{G}^{test}\}$ . With this partition, the test set is comprised of novel viewpoints lit by light seen at training time in the easy split, and of novel viewpoints under a never seen light in the hard split. We sketch the splits in Fig. 3. + +# 5. Benchmarking the Relighting Capability of NeRF + +In the section, we explore our second research question: equipped with the ReNe dataset, can we add relighting capabilities to NeRF in a simple and lightweight way? We start with a brief overview of NeRF (Sec. 5.1), we then discuss alternative ways to make NeRF able to perform novel view synthesis and relighting simultaneously (Sec. 5.2). We compare our choices through an ablation study using the validation set described in Sec. 4, whose results are discussed in Sec. 5.3. Finally, in Sec. 5.4, we present the results for the best method on both test sets of the ReNe dataset. + +![](images/9bd5b16635ed9ed6177b4d95d5eec28efada5b0f61ed6112e11bfabac619bee0.jpg) +Figure 3. Dataset splits. Each scene $\mathcal{I}_s$ is divided in 4 different splits: Samples used for training Samples used for validation Samples used for Easy Test Samples used for Hard Test Samples never used. + +# 5.1. NeRF Overview + +A Neural Radiance Field (NeRF) [36] maps a 5D input representing camera pose, i.e. 3D coordinates $\mathbf{x} = (x,y,z)$ along with the 2D viewing directions $\mathbf{d} = (\theta ,\phi)$ , into a 4D color-density output $(\mathbf{c},\sigma)$ by means of a function $F_{\Theta}(\mathbf{x},\mathbf{d})\rightarrow (\mathbf{c},\sigma)$ approximated by the weights of an MLP. Specifically, here we consider a vanilla NeRF architecture [37] which estimates color and density using two MLPs as $(\sigma ,\mathbf{e}) = \Psi_{geo}(\mathbf{x})$ and $\mathbf{c} = \Psi_{rgb}(\mathbf{e},\mathbf{d})$ , with $\sigma$ being interpreted as the probability of a ray terminating at $(x,y,z)$ and $\mathbf{e}$ being a feature embedding. Following [33], the color $C(\mathbf{r})$ rendered from a camera ray $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$ can be obtained solving the integral: + +$$ +C (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (\mathbf {r} (t)) c (\mathbf {r} (t), \mathbf {d}) d t \tag {1} +$$ + +where $T(t) = \exp \left(-\int_{t_n}^t\sigma (\mathbf{r}(s))ds\right)$ represents the accumulated transmittance from $t_n$ to $t$ along the ray $r$ , and $t$ goes from near plane $t_n$ to far plane $t_f$ . The image formation procedure is performed by simply aggregating the result of the integral for all pixels, i.e. samples along the rays, of the target image. Although NeRF works well for synthesizing novel views, as shown by the previous equations, it has no way of modeling the incoming light since + +![](images/e872ec229f7b8765bbacd3bd4b084c5852bcff5cc34e89b9889f6055c05919df.jpg) +Figure 4. Overview of architectures. We start from the architecture of [37] and propose variants to inject information about the light position in the scene. Highlighted arrows in each variant underline an architectural change from the one that precedes. + +it only takes into account position and orientation for the camera. In the next section, we will introduce variations of the classical approach that also take into account the light position. + +Positional Encoding. As showed in NeRF [35] enconding $\mathbf{x}$ and $\mathbf{d}$ into a higher dimensional space allows the neural network to overcome its spectral bias and makes it able to reproduce the high-frequency content of the input signal. We follow [37] and encode $\mathbf{x}$ using a multiresolution hash encoding, $h(\mathbf{x})$ , whilst $\mathbf{d}$ is projected onto the first 16 coefficients of the spherical harmonics, $\zeta(\mathbf{d})$ . + +# 5.2. On The Relighting Capability of NeRF + +As illustrated in Fig. 4, we take as a starting point the architecture presented in [37] and delineate 5 proposals to enable NeRF to perform relighting while adding minimum complexity to the architecture. Recalling Sec. 5.1, the naive architecture, namely V0, has two sub-networks, $\Psi_{geo}$ , which outputs $\sigma$ a measure of the particle density at $\mathbf{x}$ , and $\Psi_{rgb}$ which is responsible for the color, $\mathbf{c}$ . Previous works [66, 66] demonstrated that $\Psi_{geo}$ learns the scene geometry, while $\Psi_{rgb}$ models the view-dependent color appearance. Hence, our key idea is to modify the input to the $\Psi_{rgb}$ injecting light position and let the model learn the interaction between the geometry and light. We train one network on each scene minimizing the error between the ground-truth images and the rendered ones. As input data we consider a set of multi-view images of an object, $\mathcal{I}_s$ , illuminated under known lighting conditions, $\mathcal{G}_s$ , and the camera poses of these images, $\mathcal{C}_s$ . We will consider the subscript $s$ implicit in what follows. + +V1. A straightforward way to enable relighting with NeRF is to condition $\Psi_{rgb}$ with a latent representation that stores the world position and orientation of the light, $G_{m}$ for a given observation $I_{n,m}$ . To do so, we flatten the $\mathbf{R}$ and $\mathbf{t}$ parts of $G_{m}$ and encode this 12-dimensional vector into a 156-dimensional latent code using the positional encoding with Fourier Features proposed in [36], $\gamma (\mathbf{R},\mathbf{t})$ . Our procedure resembles the approach adopted by NeRF in the Wild [30], but the condition embedding is used to adapt NeRF to variable lighting conditions instead of transient + +parts of the images. + +V2. As the next iteration, we change the parameterization for $G_{m}$ . Instead of directly encoding $\mathbf{R}$ and $\mathbf{t}$ in the same way for each sample $\mathbf{x}$ used to query $\Psi_{rgb}$ , we construct a 3D unit vector $\mathbf{l} = \frac{\mathbf{t} - \mathbf{x}}{||\mathbf{t} - \mathbf{x}||}$ which let the network be aware of the relative position between the light source and the query location. Since, differently from the previous approach, $\mathbf{l}$ changes for each query point, we conjecture this may help NeRF in modulating the output color $\mathbf{c}$ based on the incoming light information. As done for $\mathbf{d}$ , $\mathbf{l}$ is encoded using the spherical harmonics, $\zeta(\mathbf{l})$ . +V3. The previous version resembles somehow the BRDF where $\mathbf{l}$ acts as the incoming light direction at $\mathbf{x}$ , and $\mathbf{d}$ is the unit vector pointing from $\mathbf{x}$ toward the camera. Following this analogy, we may consider $\mathbf{e}$ to represent an $N$ -dimensional embedding of the normal vector at $\mathbf{x}$ . Since all these information are relative to $\mathbf{x}$ , we explore whether having $h(\mathbf{x})$ as input can be beneficial for $\Psi_{rgb}$ . Without such skip connection the knowledge about the location of the query point may vanish as the depth of the network increases. +V4. The previous version may be negatively influenced by the diverse scales of its inputs, which are on one side spherical and hash-grid encoded vectors like $\zeta(\mathbf{d})$ , $\zeta(\mathbf{l})$ , and $h(\mathbf{x})$ while on the other there is the ReLU output $\mathbf{e}$ . To test this hypothesis, we propose a variant where we concatenate $\mathbf{e}$ with the output of the first layer of $\Psi_{rgb}$ and use this vector as input for its second layer, rather than feeding $\Psi_{rgb}$ directly with $\mathbf{e}$ . +V5. The original NeRF learns a continuous 3D field of particles that absorb and emit light. As a result only the amount of outgoing light from a location is modeled, without taking into account the fact that the outgoing light is the result of interactions between incoming light and the material properties of an underlying surface. This issue can be alleviated by replacing Eq. (1) with a physically-based volume rendering for non-emissive and non-absorptive volumes, which replaces the emitted color of each 3D point along the ray, $c(\mathbf{r}(t), \mathbf{d})$ , with $L_{r}(\mathbf{x}, \omega_{o})$ that represents the scattered light at $\mathbf{x}$ along $\omega_{o}$ . As done in [2], assuming a single point light + +source of fixed intensity, $L_{r}$ can be approximated as: + +$$ +L _ {r} (\mathbf {x}, \omega_ {o}) = \int_ {S} f _ {p} (\mathbf {x}, \omega_ {o}, \omega_ {i}) L _ {i} (\mathbf {x}, \omega_ {i}) d \omega_ {i} \tag {2} +$$ + +where $S$ is a unit sphere, $f_{p}$ represents a differentiable reflectance model (like the BRDF), and $L_{i}$ represents the incident radiance at $x$ from direction $\omega_{i}$ . Please note that in this equation $\omega_{o}$ corresponds to $\mathbf{d}$ and $\omega_{i}$ is analogous to $\mathbf{l}$ . While we can assume that $f_{p}$ is approximated by $\Psi_{rgb}$ , computing $L_{i}$ requires marching a large number of light rays for all shading points on all camera rays to determine the transmittance between the light and each 3D point. We avoid this cumbersome procedure by introducing a neural approximation of $L_{i}$ in the form of an MLP aimed at predicting a scalar value $o = \Psi_{vis}(h(\mathbf{x}),\zeta (\mathbf{l}))$ , which allows us to efficiently query the point-to-light visibility. The final pixel color is then obtained with $\mathbf{c}^{\star} = o\cdot \mathbf{c}$ . + +# 5.3. Ablation study + +Dataset. To assess the relative merits of the incremental modifications to NeRF proposed in the previous section and identify the best architecture, we consider a subset of scenes presenting a variety of challenges: Cube, that has thin wireframe structures and shadows; Savannah, that pictures a jagged leaves tree with a complex shadow; Reflective, that is full of specular reflections, and FlipFlop, where light passes through semi-transparent plastic strings. + +Implementation Details. We used the torch-ngp pytorch implementation1 of Nvidia Instant-NGP [37] for fast training of Neural Radiance Fields models. During training, we randomly sample 4096 pixel rays as a batch to train our networks. We use Adam optimizer [18] with an initial learning rate of 0.01 (other Adam hyperparameters are left at default values of $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ ). For volumetric integration, we use 128 samples in coarse volume and 128 additional adaptive samples in fine volume to compute the final radiance. The optimization for a single scene typically takes around 100–200k iterations to converge on a single NVIDIA RTX 2080Ti GPU (about 5 hours). We use early-stopping if the model doesn’t improve for 10 consecutive epochs. We supervise the regressed RGB values with the ground truth values from the captured images using the L2 loss. For $\Psi_{geo}$ we use 2 fully-connected ReLU layers with 64 channels, while $\Psi_{rgb}$ and $\Psi_{vis}$ uses 4 fully-connected ReLU layers with 64 channels. + +Results. For a quantitative evaluation of our methods we consider two widely adopted metrics of image quality assessment: Structural Similarity (SSIM) [67] and Peak Signal-to-Noise Ratio (PSNR) [35]. We report the results of the ablation study in Tab. 2. Results show how all the proposed modifications to NeRF improve performance and + +
Methodγ(R, t)1skipinputsΨviasCubeSavannahReflectiveFlipFlop
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
V1✓XXXX24.370.5222.530.4423.570.5124.120.51
V2X✓XXX24.730.5423.700.5223.680.5224.420.56
V3X✓✓XX25.380.5624.390.5524.650.5825.060.57
V4X✓✓✓X25.410.5724.790.5824.240.5625.270.58
V5X✓✓✓✓26.110.6125.230.6125.000.5925.460.60
+ +Table 2. Quantitative relighting and view synthesis result of the proposed modifications to NeRF. For each scene, we report on the left the PSNR and on the right the SSIM. Legend: $\gamma (\mathbf{R},\mathbf{t})$ indicates the use of absolute light position, $\mathbf{l}$ of relative position wrt $\mathbf{x}$ , skip indicates that $\mathbf{x}$ is provided as input to $\Psi_{rgb}$ , inputs that the embedding is inserted in $\Psi_{rgb}$ at the second layer, while $\Psi_{vis}$ that the MLP approximating $L_{i}(x,\omega_{i})$ is used. + +![](images/3b2152d95fdc5369ac866aedcbe2243700ce335bfc0539df8c702593b8eaf08c.jpg) +Figure 5. Qualitative results for ablation. The same image as rendered by V1 and V5 networks. The side-by-side comparison clearly shows how V5 reproduces much sharper details in shadows (best seen in Reflective) and is able to better handle complex reflections (best seen in FlipFlop). + +contribute to the overall good results of the most effective version, which is V5. These results provide experimental support to the intuitions presented above about the higher effectiveness of feeding to the network the relative light position with respect to the sample $\mathbf{x}$ instead of the absolute light pose (row 1 versus row 2), as well as the importance of providing $\mathbf{x}$ as input to $\Psi_{rgb}$ (row 2 versus row 3). Separating inputs to $\Psi_{rgb}$ is also beneficial and, together with $\Psi_{vis}$ contributes to the good performance of V5. + +Some qualitative examples comparing and contrasting V1 against V5 are reported in Fig. 5. Zooming in on cast shadows we can appreciate how careful handling of the light pose as well as the proposed modifications to the vanilla NeRF architecture enable rendering of sharper and more coherent shadows than the straightforward extension that conditions NeRF also on light pose. + +# 5.4. Results on benchmark + +Finally, we report the performance for the best architecture on the overall set of held out test scenes in Tab. 3. + +
OursInstant-NGP
NameEasyHardEasyHard
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Apple26.440.6226.250.6220.890.4520.950.45
Cheetah25.660.6124.640.6019.370.4419.600.44
Cube24.900.5423.980.5320.140.4220.310.42
Dinosaurs25.750.6524.980.6419.580.4219.660.41
FlipFlop25.850.6125.420.6120.380.4520.360.45
Fruits25.930.6225.720.6220.160.4520.210.44
Garden25.740.6625.080.6619.760.4519.700.45
Helicopters25.120.6124.730.6119.340.3719.370.37
Kittens25.900.6424.960.6318.520.3718.650.37
Lego26.070.6125.770.6120.750.4620.760.46
Lunch25.840.6024.710.5919.320.4619.380.45
Plant26.550.6725.930.6720.620.4420.660.44
Reflective25.790.6125.280.6120.090.4320.110.42
Robotoy26.240.6525.550.6520.770.5020.780.50
Savannah25.150.6224.310.6119.080.4019.180.40
Shark25.590.5725.320.5620.540.4220.530.41
Stegosaurus25.870.6325.650.6320.840.4320.910.42
Tapes25.840.5825.410.5719.340.4119.550.41
Trucks25.800.6725.160.6619.810.4419.870.44
Wooden toys25.690.6125.240.6020.190.4820.220.48
Average25.790.6225.200.6119.970.4320.040.43
+ +Table 3. Quantitative results across all 20 scenes. We report both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) by comparing the novel view synthesized image with its corresponding groundtruth. + +We compare our method against the pytorch implementation of Nvidia Instant-NGP [37]. Overall, the proposed architecture achieves satisfying results on this challenging task and sets a non trivial baseline for the online benchmark, clearly outperforming the naive baseline represented by the standard NeRF. We show some qualitative results for the easy test split in Fig. 6, and in Fig. 7 for the hard one. These qualitative results confirm that the model is capable of convincingly rendering and lighting the scene from unseen viewpoints and light positions while using a simple and lightweight architecture. Interestingly, the output of $\Psi_{vis}$ , reported in the rightmost columns of the figures, well approximate point-to-light visibility, especially in the easy split, even if it has not received direct supervision to emulate it, and it even reproduces some indirect illumination effects, confirming the feasibility of a neural approximation of the incident radiance $L_{i}(\mathbf{x},\omega_{i})$ . Comparing with the ground-truth frame, while rendering of light on the object is indeed quite realistic, cast shadows are sharp and coherent with the scene geometry on the easy set, while more artifacts are present in the hard split. + +# 6. Conclusion and Limitations + +We have introduced the ReNe dataset, the first dual robot dataset framing real world objects under challenging one-light-at-time (OLAT) conditions and annotated with accurate camera and light poses. The main limitations of our dataset concern the absence of 360 degrees scans and the use of a challenging but unrealistic OLAT setup. By lever + +aging the training and validation splits of the dataset, we were able to perform an ablation study on lightweight modifications to a NeRF architecture that extend it to successfully perform novel view synthesis under unseen lighting. The best model emerged from the study has been tested on the held out test set to establish a non-trivial baseline for the benchmark. We hope the availability of a new dataset and baseline for the problem of NeRF relighting will attract new research around this challenging inverse rendering problem. + +![](images/8168d74da20a31e3860b0d18207a6b9bda9bf67ed4247d9a51970f7e2b4f3d2f.jpg) +Figure 6. We show one image from the easy test split $\mathcal{I}^{easy}$ on the left. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4578-4587, 2021. 2 +[73] Yizhou Yu, Paul Debevec, Jitendra Malik, and Tim Hawkins. Inverse global illumination: Recovering reflectance models of real scenes from photographs. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques, pages 215-224, 1999. 1 +[74] Xiuming Zhang, Sean Fanello, Yun-Ta Tsai, Tiancheng Sun, Tianfan Xue, Rohit Pandey, Sergio Orts-Escalano, Philip Davidson, Christoph Rhemann, Paul Debevec, et al. Neural light transport for relighting and view synthesis. ACM Transactions on Graphics (TOG), 40(1):1-17, 2021. 2, 3 +[75] Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul Debevec, William T Freeman, and Jonathan T Barron. Nefactor: Neural factorization of shape and reflectance under an unknown illumination. ACM Transactions on Graphics (TOG), 40(6):1-18, 2021. 2, 3 +[76] Hao Zhou, Sunil Hadap, Kalyan Sunkavalli, and David W Jacobs. 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Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018. 3 \ No newline at end of file diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/images.zip b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..9d2edcb9dec63c66b0ff8f2615a9e58ff1a0b54b --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fb963229f287da87ac9de208eaeb7d31a9654b91895655dca0536ac76f737946 +size 621852 diff --git a/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/layout.json b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..af036192ea2d5e17ac2e53f7d508d47f1b446648 --- /dev/null +++ b/2023/ReLight My NeRF_ A Dataset for Novel View Synthesis and Relighting of Real World Objects/layout.json @@ -0,0 +1,9408 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 113, + 103, + 481, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 103, + 481, + 140 + ], + "spans": [ + { + "bbox": [ + 113, + 103, + 481, + 140 + ], + "type": "text", + "content": "ReLight My NeRF: A Dataset for Novel View Synthesis and Relighting of Real World Objects" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 161, + 496, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 161, + 496, + 232 + ], + "spans": [ + { + "bbox": [ + 97, + 161, + 496, + 232 + ], + "type": "text", + "content": "Marco Toschi\\*, Riccardo De Matteo\\*,, Riccardo Spezialetti\\*, Daniele De Gregorio Eyecan.ai {marco.toschi, riccardo.spezialetti, daniele.degregorio}@eyecan.ai Luigi Di Stefano, Samuele Salti University of Bologna" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 236, + 545, + 396 + ], + "blocks": [ + { + "bbox": [ + 50, + 236, + 545, + 396 + ], + "lines": [ + { + "bbox": [ + 50, + 236, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 50, + 236, + 545, + 396 + ], + "type": "image", + "image_path": "39910bbb8513b8eb17635efbc10fa6fd960cc48237c61dede0e2932fedaa8630.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 403, + 547, + 439 + ], + "lines": [ + { + "bbox": [ + 46, + 403, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 547, + 439 + ], + "type": "text", + "content": "Figure 1. A random subset of scenes from our dataset. Our dataset enables the study of joint novel view synthesis and relighting from real images, as it provides scenes framed from the same viewpoint under varying light positions (shown along rows) as well as captured from different viewpoints under the same light position (shown along columns)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 447, + 192, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 447, + 192, + 460 + ], + "spans": [ + { + "bbox": [ + 143, + 447, + 192, + 460 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 473, + 290, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 290, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 290, + 700 + ], + "type": "text", + "content": "In this paper, we focus on the problem of rendering novel views from a Neural Radiance Field (NeRF) under unobserved light conditions. To this end, we introduce a novel dataset, dubbed ReNe (Relighting NeRF), framing real world objects under one-light-at-time (OLAT) conditions, annotated with accurate ground-truth camera and light poses. Our acquisition pipeline leverages two robotic arms holding, respectively, a camera and an omni-directional point-wise light source. We release a total of 20 scenes depicting a variety of objects with complex geometry and challenging materials. Each scene includes 2000 images, acquired from 50 different points of views under 40 different OLAT conditions. By leveraging the dataset, we perform an ablation study on the relighting capability of variants of the vanilla NeRF architecture and identify a lightweight architecture that can render novel views of an object under novel light conditions, which we use to establish a non-trivial baseline for the dataset. Dataset and benchmark are available at https://eyecan-ai.github.io/rene." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 447, + 387, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 447, + 387, + 460 + ], + "spans": [ + { + "bbox": [ + 307, + 447, + 387, + 460 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 467, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 547, + 586 + ], + "type": "text", + "content": "Inverse rendering [29, 47, 52, 73] addresses the problem of estimating the physical attributes of an object, such as its geometry, material properties and lighting conditions, from a set of images or even just a single one. This task is a longstanding problem for the vision and graphics communities, since it unlocks the creation of novel renderings of an object from arbitrary viewpoints and under unobserved lighting conditions. An effective and robust solution to this problem would have significant value for a wide range of applications in gaming, robotics and augmented reality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 587, + 548, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 548, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 548, + 696 + ], + "type": "text", + "content": "Recently, Neural Radiance Fields (NeRF) [36] has contributed tremendously to the novel view synthesis sub-task of inverse rendering pipelines. By mapping an input 5D vector (3D position and 2D viewing direction) to a 4D continuous field of volume density and color by means of a neural network, NeRF learns the geometry and appearance of a single scene from a set of posed images. The appealing results in novel view synthesis have attracted a lot of attention from the research community and triggered many follow-up" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 320, + 702, + 503, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 702, + 503, + 714 + ], + "spans": [ + { + "bbox": [ + 320, + 702, + 503, + 714 + ], + "type": "text", + "content": "* Joint first authorship. " + }, + { + "bbox": [ + 320, + 702, + 503, + 714 + ], + "type": "inline_equation", + "content": "^\\circ" + }, + { + "bbox": [ + 320, + 702, + 503, + 714 + ], + "type": "text", + "content": " Work done while at Eyecan.ai" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20762" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 282, + 176 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 176 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 176 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 176 + ], + "type": "table", + "html": "
DatasetMultiple categoriesReal-WorldBackground ShadowsPublicLight Supervision
Gross et al. [14]X✓X✓✓
Sun et al. [57]X✓X✓✓
Wang et al. [68]X✓X✓✓
Zhang et al. [74]X✓X✓✓
Srinivasan et al. [55]✓XX✓✓
Zhang et al. [75]✓✓✓✓X
Zhang et al. [75]✓XX✓✓
Bi et al. [2]✓✓XX✓
ReNe✓✓✓✓✓
", + "image_path": "3a6dbdce1352f4790069d7460ca992ecc7e27112dc1da073d1b3108d7cf986b5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 187, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 187, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 287, + 232 + ], + "type": "text", + "content": "Table 1. Overview of relighting datasets. Our dataset is the first one featuring a variety of objects and materials captured with real-world sensors that provides ground-truth light positions and also presents challenging cast shadows." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 256, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 496 + ], + "type": "text", + "content": "works aimed at overcoming the main limitations of NeRF, e.g. reduce inference runtime [23, 24, 27, 48, 49, 71], enable modeling of deformable objects [9, 25, 42, 45, 46, 62], and generalization to novel scenes [5, 15, 19, 39, 50, 53, 61, 63, 72]. However, less attention has been paid to the relighting ability of NeRFs. Although NeRF and its variants represent nowadays the most compelling strategy for view synthesis, the learned scene representation entangles material and lighting and, thus, cannot be directly used to generate views under novel, unseen lighting conditions. A few existing works [3, 4, 55, 75] try to overcome this structural NeRF limitation by learning to model the scene appearance as a function of reflectance, which accounts for both scene geometry and lighting modeling. However, these methods incur a great computation cost, mainly due to the need to explicitly model light visibility and/or the components of a microfacet Bidirectional Reflectance Distribution Function (BRDF) [65] like diffuse albedo, specular roughness, and point normals: for instance NeRV [55] uses 128 TPU cores for 1 day while [3] is trained on 4 GPUs for 2 days." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "As highlighted in Tab. 1, one of the main challenges to foster research in this direction is the absence of real-world datasets featuring generic and varied objects with ground-truth light direction, both at training and test time. The latter is key to create a realistic quantitative benchmark for relighting methods, whose availability is one of the main driving forces behind fast-paced development of a machine learning topic. Indeed, the above mentioned NeRF-like methods for relighting mainly consider a handful of synthetic images to provide quantitative results (3 and 4 scenes in NeRV [55] and NeRFactor [75], respectively) while no quantitative results are provided in [3]. The only dataset with scenes acquired by a real sensor is proposed in [2], which, however, assumes images captured under collocated view and lighting setup, i.e. a smartphone with flash light on, which limits the amount of cast shadows and simplifies the task. Moreover, the dataset is not publicly available. Some available real-world datasets with ground-truth light" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "positions feature human faces or portraits [14, 57, 68, 74]. In these datasets, the subject is usually seated in the center of a light-stage with cameras arranged over a dome array positioned in front of the subject. Although these dataset provide real scenes with ground-truth annotations for light positions, the background is masked-out and shadows cast on the background, which are hard to model because they require a precise knowledge about the geometry of the overall scene, are ignored." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 180, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 574 + ], + "type": "text", + "content": "Therefore, in this paper we try to answer the research questions: can we design a data acquisition methodology suitable to collect a set of images of an object under one light-at-time (OLAT) [74] illumination with high-quality camera and light pose annotations which requires minimal human supervision? We then leverage it to investigate a second question: can we design a novel Neural Radiance Field architecture to learn to perform relighting with reasonable computational requirements? To answer the first question, we design a capture system relying on two robotic arms. While one arm holds the camera and shots pictures from viewpoints uniformly distributed on a spherical wedge, the other moves the light source across points uniformly distributed on a dome. As a result, we collect the ReNe dataset, made of 20 scenes framing daily objects with challenging geometry, varied materials and visible cast shadows, composed of 50 camera view-points under 40 OLAT light conditions, i.e. 2000 frames per scene. Examples of images from the dataset are shown in Fig. 1. With a subset of images from each scene, we create a novel hold-out dataset for joint relighting and novel view synthesis evaluation that will be used as an online benchmark to foster research on this important topic. As regards the second question, thanks to the new dataset we conduct a study on the relighting capability of NeRF. In particular, we investigate on how the standard NeRF architecture can be modified to take into account the position of the light when generating the appearance of a scene. Our study shows that by estimating color with two separate sub-networks, one in charge of softshadow prediction and one responsible for neurally approximating the BRDF, we can perform an effective relighting, e.g. cast complex shadows. We provide results of our novel architecture as a reference baseline for the new benchmark." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 576, + 476, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 576, + 476, + 587 + ], + "spans": [ + { + "bbox": [ + 317, + 576, + 476, + 587 + ], + "type": "text", + "content": "In summary, our contributions include:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 597, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 597, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 597, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 545, + 632 + ], + "type": "text", + "content": "- a novel dataset made out of sets of OLAT images of real-world objects, with accurate camera and light pose annotations;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 643, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 643, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 317, + 643, + 545, + 677 + ], + "type": "text", + "content": "- a study comparing different approaches to enable NeRF to perform relighting alongside novel view synthesis;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "content": "- a new architecture, where the stage responsible for radiance estimation is split into two separate networks," + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20763" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 287, + 97 + ], + "type": "text", + "content": "that can render novel views under novel unobserved lighting conditions;" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 106, + 287, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 106, + 287, + 141 + ], + "spans": [ + { + "bbox": [ + 59, + 106, + 287, + 141 + ], + "type": "text", + "content": "- a public benchmark for novel view synthesis and relighting of real world objects, that will be maintained on an online evaluation server." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 153, + 134, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 153, + 134, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 153, + 134, + 166 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "type": "text", + "content": "In this paper, we focus on relighting static objects by Neural Radiance Fields. We briefly discuss the related works and their datasets below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 210, + 286, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 286, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 286, + 317 + ], + "type": "text", + "content": "Image Relighting without NeRF. There exist several works in the field of image based relighting [8, 32, 44, 51]. The proposed methods differ for the adopted technique to model the light transport function in form of discrete light transport matrix. With recent advances in deep learning, new techniques have been introduced to address relighting [57], with many of them designed to relight human portraits [38, 58, 59, 70, 76]. Another bunch of works pursues joint relighting and novel view synthesis [11, 34, 74]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 318, + 286, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 286, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 286, + 496 + ], + "type": "text", + "content": "Relighting Datasets. Most of relighting datasets contain captures of human bodies or face portraits, they leverage complex capture setups such as calibrated multi-view lightstages with cameras and LED lights, where the cameras are synchronized with the lights in order to flash one LED per capture [38,58,59,76]. Alternative works on generic objects do exist [51, 70], but they consider a mix of real and synthetic data, with the latter dominating the former in terms of number of images. The dataset most similar to ours is the one adopted by [2], which involves a robotic arm setup holding a Samsung Galaxy Note 8. However, this acquisition framework assumes a collocated view and lighting setup, e.g. built-in flash of a smart-phone camera lens, that inherently limits the shadows cast. Furthermore, the dataset has not been released." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 700 + ], + "type": "text", + "content": "Neural Radiance Fields. Novel view synthesis has been a longstanding problem within the computer vision and computer graphics fields [7, 13, 20]. The advent of deep learning gave rise to explicit methods that train CNNs for this very purpose [22, 26, 35, 54, 56, 64, 77]. In the past few years, NeRF has advanced greatly in becoming the main scene representation for view synthesis [36]. NeRF learns a continuous volumetric function parameterized by means of a fully connected neural network optimized over a set of observed images with known camera poses using gradient descent. Due to its effectiveness, NeRF has inspired many subsequent works that extend its continuous neural volumetric representation for generative modeling [5, 19, 53], dynamic scenes [10, 21, 21, 30, 41, 46, 69], non-rigidly deforming objects [9, 9, 40, 42, 43, 62], multi-resolution images [1, 60], phototourism images with changing illumination settings [30, 61] and relighting [2, 4, 30, 55]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": "Neural Radiance Fields for Relighting. One of main limi" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 514 + ], + "type": "text", + "content": "tations of NeRF is that is not suitable for relighting. Indeed, NeRF treats the particles within scene representation as elements that emit light instead of being modelled as particles that reflect the incoming light sent out from external light sources. To straddle this divide, Neural Reflectance Field [2] models both scene geometry and reflectance regressing volume density, normal and material properties, e.g. Bidirectional Reflectance Distribution Function (BRDF) [65], for any 3D location within the volume of a scene. The shading at each point is then estimated using the light, view direction, the normal at that point and the BRDF. For instance, [28] leverages a differentiable path tracer to optimize a spatially-varying BSDF tied to an environment map, that can be used to render novel views under a novel OLAT condition. Unfortunately, this approach requires marching rays from all points sampled along the camera ray to any source of lighting in the scene, which restricts it use only in a collocated camera-light setup. NeRV ameliorates the computational cost of [2] by replacing the visibility estimation between scene points and light sources with a neural approximation of the true visibility field, which acts as a lookup table during rendering. Thanks to this insight, NeRV simulates direct illumination from environment lighting as well as one-bounce indirect illumination. NeRD [4] does not model visibility or shadows, but uses an analytic BRDF model [6] to learn a volumetric representation which stores SVBRDF [16] parameters at each 3D point instead of a radiance field. A relightable textured mesh is then extracted from that volume to allow fast rendering and relighting. Finally, NeRFactor [75] starts from two pre-trained networks: a NeRF of the scene and a BRDF network trained on the MERL dataset [31]. This knowledge is then distilled into four MLP-based networks to predict for each surface location its normal vector, light visibility, albedo and a BRDF latent code. The MLP outputs are injected into classical volumetric rendering and the networks parameters are optimized minimizing the re-rendering loss." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": "We take inspiration from this line of works to design the study reported in Sec. 5, where we split the MLP-stack of NeRF in two separate networks: one responsible for the visibility and one that resembles the BRDF." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 574, + 484, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 484, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 484, + 586 + ], + "type": "text", + "content": "3. Dataset Acquisition Framework" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "While providing both lights and cameras poses in a controlled manner with ground-truths annotations is straightforward in synthetic environments [55, 75], it is cumbersome and complex in the real world, especially if humans are involved, as done in [14, 57, 68, 74]. Our solution is to deploy extremely repeatable and safe machines such as industrial cobots (collaborative robots). In particular, we use a pair of robots, dubbed LightBot and CameraBot, to position the light and camera independently. Thanks to their high repeatability " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "(+/-0.03\\mathrm{mm})" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", we can calibrate their tra" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20764" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 84, + 324, + 237 + ], + "blocks": [ + { + "bbox": [ + 56, + 84, + 324, + 237 + ], + "lines": [ + { + "bbox": [ + 56, + 84, + 324, + 237 + ], + "spans": [ + { + "bbox": [ + 56, + 84, + 324, + 237 + ], + "type": "image", + "image_path": "46df05a747c37b785ab67f94291c6e0e1a50514b81c84a5ed06d971daecb09dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 247, + 194, + 256 + ], + "lines": [ + { + "bbox": [ + 182, + 247, + 194, + 256 + ], + "spans": [ + { + "bbox": [ + 182, + 247, + 194, + 256 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 337, + 97, + 544, + 238 + ], + "blocks": [ + { + "bbox": [ + 337, + 97, + 544, + 238 + ], + "lines": [ + { + "bbox": [ + 337, + 97, + 544, + 238 + ], + "spans": [ + { + "bbox": [ + 337, + 97, + 544, + 238 + ], + "type": "image", + "image_path": "106a6eeae19e044940a3512f51dd8454c3eaf4d4e794c94666c53f4e66b33ab5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 247, + 446, + 256 + ], + "lines": [ + { + "bbox": [ + 435, + 247, + 446, + 256 + ], + "spans": [ + { + "bbox": [ + 435, + 247, + 446, + 256 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 546, + 310 + ], + "type": "text", + "content": "Figure 2. Overview of our dataset acquisition framework. (a) The LightBot and CameraBot moving light and camera respectively; the trajectories of the two robots are two non-intersecting sections of a hemisphere around the object of interest. (b) Grid of images in which each row depicts the same viewpoint as the light conditions change; each column, on the other hand, represents the same light condition as the viewpoint changes." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "type": "text", + "content": "jectories with respect to a common world reference frame only once before acquisition starts, and then obtain accurate 6-DoF pose knowledge of both light and camera for all scenes by repeating the same trajectories. The proposed framework is sketched in Fig. 2a, while some acquisitions for the Robotoy scene are shown in Fig. 2b." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 415, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 288, + 713 + ], + "type": "text", + "content": "Camera/Light Calibration. In order to calibrate both robots with respect to a common reference frame we use a ChArUco board [12]. We let the CameraBot see the board at each waypoint of its trajectory in order to calibrate extrinsic parameters for each view. Thanks to the high repeatability of the robot, it is possible to perform this procedure only once before we start to record scenes: the robot will be able to place the camera at the previously calibrated positions with negligible error. This allows us to register in a common reference frame all the camera poses for each scene without instrumenting the scene with a pattern, which alters the realism of the scene and makes the setup fragile, as the pattern may be inadvertently moved across scans. As for the LightBot, we assume that the center of the point light corresponds to the geometric center of the LED. We are then able to register it with the calibration pattern by letting the end effector physically touch the central reference point of the pattern with the center of the LED at calibration time. We note we cannot use the same procedure for the CameraBot as the camera optical center is behind the lens. That closes the calibration loop since both robots, now, will have the pattern itself as their world reference frame, thus a common coordinate system. Even with the LightBot, high repeatability assures that the light pose registered at calibration time will be identical across all scenes of the dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 331, + 546, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 499 + ], + "type": "text", + "content": "Trajectories. As depicted in Fig. 2a, we generate two trajectories, roughly belonging to the same hemisphere, whose upper part is used for the lights while the side part for the camera. This made it possible to capture several front-facing scenes with the light moving over the object of interest. With this setup, then, for each scene we collected 50 viewpoints each under 40 different light locations. To have waypoints uniformly distributed on the selected spherical region for each end effector, we create trajectories as sequences of centers of equal-area subregions, following the methodology proposed by [17]. For the sake of illustration, Fig. 2b shows a grid of images in which each row depicts frames with the same camera pose but different lighting conditions and vice-versa for columns." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 504, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 547, + 564 + ], + "type": "text", + "content": "Background texture. In preliminary experiments with a uniform background as scenario, we found out that NeRF struggles to correctly estimate density in such a case and training does not converge. Hence, in our dataset textured walls are shown in the background." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Hardware. We equipped the LightBot and the CameraBot, respectively an Universal Robots UR5e and an Elite Robotics EC66, with a consumer headlight and an industrial camera. The headlight is the Velamp Metros IH523, equipped with 5 COB LEDs that provide a diffuse " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "100^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " beam up to " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "150\\mathrm{Lm}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " with 6000K light temperature. We used it at half power " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "(70\\mathrm{Lm})" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " to maximize its runtime. The camera is a Basler acA1440-73gc with its optical axis mounted at " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " from the robot flange normal vector, this to simplify the computation of inverse kinematics of the CameraBot. Images are captured in camera's full 1.6MP resolution " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "(1440\\mathrm{px} \\times 1080\\mathrm{px})" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " using a Basler lens with " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "8\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " focal" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20765" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 78, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 78, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 78, + 85 + ], + "type": "text", + "content": "length." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 155, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 155, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 155, + 109 + ], + "type": "text", + "content": "4. The ReNe Dataset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": "In this section, we summarize the data we collected using our framework to establish the ReNe dataset. Our dataset " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\{\\mathcal{I}_s\\}_{s=1}^S" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " scenes, where each scene is a collection of RGB images " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_s = \\{I_{s,n,m} \\mid n = 1,\\dots,N,m = 1,\\dots,M\\}" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "I_{n,m} \\in [0,1]^{H \\times W \\times 3}" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " acquired using camera poses " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s = \\{C_{s,n}\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " and lit with a point light source placed in " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_s = \\{G_{s,m}\\}_{m=1}^M" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": ". Each " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "C_n" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "G_m" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " represent the 6D pose " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R},\\mathbf{t}\\} \\in SE(3)" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " for camera and light source, respectively. " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " denotes rotation, " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in SO(3)" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " denotes translation, " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": ". The dataset features 40000 images divided in " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "S = 20" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " scenes taken by " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "N = 50" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " frontal points of views in " + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "inline_equation", + "content": "M = 40" + }, + { + "bbox": [ + 47, + 117, + 289, + 272 + ], + "type": "text", + "content": " different lighting conditions, i.e. 2000 frames per scene." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": "Train, Validation and Test splits. We split the datasets into train, val and test subsets to make it easy to compare in a fair and consistent way different approaches to NeRF relighting. In order to avoid data leakage from validation and test, we randomly create the set of held out viewpoints for validation, " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{val}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ", and for testing, " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{test}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ", as well as the set of held out light positions for testing, " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{test}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ". Each of them consists of 3 indexes. To build the validation set, for each viewpoint " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "n_{val} \\in \\mathcal{C}^{val}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ", we randomly pick 3 light poses among the 37 available to form " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{n_{val}}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ". In this way, in the validation set we have an unseen pair (viewpoint, light) composed of a viewpoint not present in the training set and a light used for other training viewpoints, " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{val} = \\{I_{s,n_{val},m_{val}} | n_{val} \\in \\mathcal{C}_{val} \\wedge m_{val} \\in \\mathcal{G}_{n_{val}} \\wedge s = 1, \\ldots, S\\}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ". For test set, we build two sub-splits namely easy and hard. The former considers all the images " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{easy} = \\{I_{s,n,m} | n \\in \\mathcal{C}^{test}, m = 1, \\ldots, M, m \\notin \\mathcal{G}^{test}\\}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ", while the latter is composed of images " + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{hard} = \\{I_{s,n,m} | (n,m) \\in \\mathcal{C}^{test} \\times \\mathcal{G}^{test}\\}" + }, + { + "bbox": [ + 47, + 274, + 289, + 536 + ], + "type": "text", + "content": ". With this partition, the test set is comprised of novel viewpoints lit by light seen at training time in the easy split, and of novel viewpoints under a never seen light in the hard split. We sketch the splits in Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 547, + 288, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 288, + 574 + ], + "type": "text", + "content": "5. Benchmarking the Relighting Capability of NeRF" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 712 + ], + "type": "text", + "content": "In the section, we explore our second research question: equipped with the ReNe dataset, can we add relighting capabilities to NeRF in a simple and lightweight way? We start with a brief overview of NeRF (Sec. 5.1), we then discuss alternative ways to make NeRF able to perform novel view synthesis and relighting simultaneously (Sec. 5.2). We compare our choices through an ablation study using the validation set described in Sec. 4, whose results are discussed in Sec. 5.3. Finally, in Sec. 5.4, we present the results for the best method on both test sets of the ReNe dataset." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 318, + 72, + 536, + 331 + ], + "blocks": [ + { + "bbox": [ + 318, + 72, + 536, + 331 + ], + "lines": [ + { + "bbox": [ + 318, + 72, + 536, + 331 + ], + "spans": [ + { + "bbox": [ + 318, + 72, + 536, + 331 + ], + "type": "image", + "image_path": "9bd5b16635ed9ed6177b4d95d5eec28efada5b0f61ed6112e11bfabac619bee0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 339, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 305, + 339, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 547, + 384 + ], + "type": "text", + "content": "Figure 3. Dataset splits. Each scene " + }, + { + "bbox": [ + 305, + 339, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_s" + }, + { + "bbox": [ + 305, + 339, + 547, + 384 + ], + "type": "text", + "content": " is divided in 4 different splits: Samples used for training Samples used for validation Samples used for Easy Test Samples used for Hard Test Samples never used." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 405, + 403, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 403, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 403, + 417 + ], + "type": "text", + "content": "5.1. NeRF Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": "A Neural Radiance Field (NeRF) [36] maps a 5D input representing camera pose, i.e. 3D coordinates " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = (x,y,z)" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " along with the 2D viewing directions " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{d} = (\\theta ,\\phi)" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": ", into a 4D color-density output " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "(\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " by means of a function " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "F_{\\Theta}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " approximated by the weights of an MLP. Specifically, here we consider a vanilla NeRF architecture [37] which estimates color and density using two MLPs as " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "(\\sigma ,\\mathbf{e}) = \\Psi_{geo}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = \\Psi_{rgb}(\\mathbf{e},\\mathbf{d})" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " being interpreted as the probability of a ray terminating at " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " being a feature embedding. Following [33], the color " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " rendered from a camera ray " + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 305, + 424, + 547, + 568 + ], + "type": "text", + "content": " can be obtained solving the integral:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 349, + 578, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 578, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 349, + 578, + 545, + 605 + ], + "type": "interline_equation", + "content": "C (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) c (\\mathbf {r} (t), \\mathbf {d}) d t \\tag {1}", + "image_path": "a338bbd5cd8c2643317ddc7a06c928bb754319e1fc167f1384a5c1fa574b06b6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (\\mathbf{r}(s))ds\\right)" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": " represents the accumulated transmittance from " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": " along the ray " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": " goes from near plane " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": " to far plane " + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 613, + 547, + 715 + ], + "type": "text", + "content": ". The image formation procedure is performed by simply aggregating the result of the integral for all pixels, i.e. samples along the rays, of the target image. Although NeRF works well for synthesizing novel views, as shown by the previous equations, it has no way of modeling the incoming light since" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20766" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 173 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 173 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 173 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 173 + ], + "type": "image", + "image_path": "e872ec229f7b8765bbacd3bd4b084c5852bcff5cc34e89b9889f6055c05919df.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 546, + 205 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 546, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 546, + 205 + ], + "type": "text", + "content": "Figure 4. Overview of architectures. We start from the architecture of [37] and propose variants to inject information about the light position in the scene. Highlighted arrows in each variant underline an architectural change from the one that precedes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 223, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 223, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 287, + 270 + ], + "type": "text", + "content": "it only takes into account position and orientation for the camera. In the next section, we will introduce variations of the classical approach that also take into account the light position." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": "Positional Encoding. As showed in NeRF [35] enconding " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": " into a higher dimensional space allows the neural network to overcome its spectral bias and makes it able to reproduce the high-frequency content of the input signal. We follow [37] and encode " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": " using a multiresolution hash encoding, " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": ", whilst " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": " is projected onto the first 16 coefficients of the spherical harmonics, " + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "inline_equation", + "content": "\\zeta(\\mathbf{d})" + }, + { + "bbox": [ + 46, + 270, + 288, + 355 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 251, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 251, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 251, + 373 + ], + "type": "text", + "content": "5.2. On The Relighting Capability of NeRF" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": "As illustrated in Fig. 4, we take as a starting point the architecture presented in [37] and delineate 5 proposals to enable NeRF to perform relighting while adding minimum complexity to the architecture. Recalling Sec. 5.1, the naive architecture, namely V0, has two sub-networks, " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\Psi_{geo}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ", which outputs " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " a measure of the particle density at " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " which is responsible for the color, " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ". Previous works [66, 66] demonstrated that " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\Psi_{geo}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " learns the scene geometry, while " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " models the view-dependent color appearance. Hence, our key idea is to modify the input to the " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " injecting light position and let the model learn the interaction between the geometry and light. We train one network on each scene minimizing the error between the ground-truth images and the rendered ones. As input data we consider a set of multi-view images of an object, " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_s" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ", illuminated under known lighting conditions, " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_s" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ", and the camera poses of these images, " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": ". We will consider the subscript " + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 378, + 287, + 594 + ], + "type": "text", + "content": " implicit in what follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "V1. A straightforward way to enable relighting with NeRF is to condition " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " with a latent representation that stores the world position and orientation of the light, " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "G_{m}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " for a given observation " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{n,m}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". To do so, we flatten the " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " parts of " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "G_{m}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and encode this 12-dimensional vector into a 156-dimensional latent code using the positional encoding with Fourier Features proposed in [36], " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\gamma (\\mathbf{R},\\mathbf{t})" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". Our procedure resembles the approach adopted by NeRF in the Wild [30], but the condition embedding is used to adapt NeRF to variable lighting conditions instead of transient" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 224, + 387, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 387, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 387, + 236 + ], + "type": "text", + "content": "parts of the images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 237, + 547, + 715 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": "V2. As the next iteration, we change the parameterization for " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "G_{m}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": ". Instead of directly encoding " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " in the same way for each sample " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " used to query " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": ", we construct a 3D unit vector " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{l} = \\frac{\\mathbf{t} - \\mathbf{x}}{||\\mathbf{t} - \\mathbf{x}||}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " which let the network be aware of the relative position between the light source and the query location. Since, differently from the previous approach, " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " changes for each query point, we conjecture this may help NeRF in modulating the output color " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " based on the incoming light information. As done for " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": " is encoded using the spherical harmonics, " + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "inline_equation", + "content": "\\zeta(\\mathbf{l})" + }, + { + "bbox": [ + 304, + 237, + 546, + 358 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": "V3. The previous version resembles somehow the BRDF where " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": " acts as the incoming light direction at " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": " is the unit vector pointing from " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": " toward the camera. Following this analogy, we may consider " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": " to represent an " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": "-dimensional embedding of the normal vector at " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": ". Since all these information are relative to " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": ", we explore whether having " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": " as input can be beneficial for " + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 361, + 546, + 480 + ], + "type": "text", + "content": ". Without such skip connection the knowledge about the location of the query point may vanish as the depth of the network increases." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": "V4. The previous version may be negatively influenced by the diverse scales of its inputs, which are on one side spherical and hash-grid encoded vectors like " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\zeta(\\mathbf{d})" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\zeta(\\mathbf{l})" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": " while on the other there is the ReLU output " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": ". To test this hypothesis, we propose a variant where we concatenate " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": " with the output of the first layer of " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": " and use this vector as input for its second layer, rather than feeding " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": " directly with " + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "V5. The original NeRF learns a continuous 3D field of particles that absorb and emit light. As a result only the amount of outgoing light from a location is modeled, without taking into account the fact that the outgoing light is the result of interactions between incoming light and the material properties of an underlying surface. This issue can be alleviated by replacing Eq. (1) with a physically-based volume rendering for non-emissive and non-absorptive volumes, which replaces the emitted color of each 3D point along the ray, " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "c(\\mathbf{r}(t), \\mathbf{d})" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "L_{r}(\\mathbf{x}, \\omega_{o})" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " that represents the scattered light at " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " along " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\omega_{o}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ". As done in [2], assuming a single point light" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20767" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "text", + "content": "source of fixed intensity, " + }, + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "text", + "content": " can be approximated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 94, + 287, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 94, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 80, + 94, + 287, + 119 + ], + "type": "interline_equation", + "content": "L _ {r} (\\mathbf {x}, \\omega_ {o}) = \\int_ {S} f _ {p} (\\mathbf {x}, \\omega_ {o}, \\omega_ {i}) L _ {i} (\\mathbf {x}, \\omega_ {i}) d \\omega_ {i} \\tag {2}", + "image_path": "437cc7f72e3ec13ce0366601c4c14a7578320211ea75a99005845a2c6356486b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " is a unit sphere, " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "f_{p}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " represents a differentiable reflectance model (like the BRDF), and " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " represents the incident radiance at " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " from direction " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": ". Please note that in this equation " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\omega_{o}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " corresponds to " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " is analogous to " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": ". While we can assume that " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "f_{p}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " is approximated by " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": ", computing " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " requires marching a large number of light rays for all shading points on all camera rays to determine the transmittance between the light and each 3D point. We avoid this cumbersome procedure by introducing a neural approximation of " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": " in the form of an MLP aimed at predicting a scalar value " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "o = \\Psi_{vis}(h(\\mathbf{x}),\\zeta (\\mathbf{l}))" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": ", which allows us to efficiently query the point-to-light visibility. The final pixel color is then obtained with " + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\star} = o\\cdot \\mathbf{c}" + }, + { + "bbox": [ + 47, + 128, + 289, + 283 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 291, + 139, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 291, + 139, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 291, + 139, + 304 + ], + "type": "text", + "content": "5.3. Ablation study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 310, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 407 + ], + "type": "text", + "content": "Dataset. To assess the relative merits of the incremental modifications to NeRF proposed in the previous section and identify the best architecture, we consider a subset of scenes presenting a variety of challenges: Cube, that has thin wireframe structures and shadows; Savannah, that pictures a jagged leaves tree with a complex shadow; Reflective, that is full of specular reflections, and FlipFlop, where light passes through semi-transparent plastic strings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": "Implementation Details. We used the torch-ngp pytorch implementation1 of Nvidia Instant-NGP [37] for fast training of Neural Radiance Fields models. During training, we randomly sample 4096 pixel rays as a batch to train our networks. We use Adam optimizer [18] with an initial learning rate of 0.01 (other Adam hyperparameters are left at default values of " + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": "). For volumetric integration, we use 128 samples in coarse volume and 128 additional adaptive samples in fine volume to compute the final radiance. The optimization for a single scene typically takes around 100–200k iterations to converge on a single NVIDIA RTX 2080Ti GPU (about 5 hours). We use early-stopping if the model doesn’t improve for 10 consecutive epochs. We supervise the regressed RGB values with the ground truth values from the captured images using the L2 loss. For " + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "inline_equation", + "content": "\\Psi_{geo}" + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": " we use 2 fully-connected ReLU layers with 64 channels, while " + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "inline_equation", + "content": "\\Psi_{vis}" + }, + { + "bbox": [ + 46, + 407, + 288, + 621 + ], + "type": "text", + "content": " uses 4 fully-connected ReLU layers with 64 channels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 622, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 288, + 694 + ], + "type": "text", + "content": "Results. For a quantitative evaluation of our methods we consider two widely adopted metrics of image quality assessment: Structural Similarity (SSIM) [67] and Peak Signal-to-Noise Ratio (PSNR) [35]. We report the results of the ablation study in Tab. 2. Results show how all the proposed modifications to NeRF improve performance and" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 544, + 125 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 544, + 125 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 544, + 125 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 544, + 125 + ], + "type": "table", + "html": "
Methodγ(R, t)1skipinputsΨviasCubeSavannahReflectiveFlipFlop
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
V1✓XXXX24.370.5222.530.4423.570.5124.120.51
V2X✓XXX24.730.5423.700.5223.680.5224.420.56
V3X✓✓XX25.380.5624.390.5524.650.5825.060.57
V4X✓✓✓X25.410.5724.790.5824.240.5625.270.58
V5X✓✓✓✓26.110.6125.230.6125.000.5925.460.60
", + "image_path": "c581994137f4be865356fc9cb3d3c1b3bf62cbc2df5d673ce891e365d420985c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "lines": [ + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": "Table 2. Quantitative relighting and view synthesis result of the proposed modifications to NeRF. For each scene, we report on the left the PSNR and on the right the SSIM. Legend: " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\gamma (\\mathbf{R},\\mathbf{t})" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " indicates the use of absolute light position, " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " of relative position wrt " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": ", skip indicates that " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " is provided as input to " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": ", inputs that the embedding is inserted in " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " at the second layer, while " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\Psi_{vis}" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " that the MLP approximating " + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "inline_equation", + "content": "L_{i}(x,\\omega_{i})" + }, + { + "bbox": [ + 305, + 133, + 547, + 211 + ], + "type": "text", + "content": " is used." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 222, + 547, + 381 + ], + "blocks": [ + { + "bbox": [ + 307, + 222, + 547, + 381 + ], + "lines": [ + { + "bbox": [ + 307, + 222, + 547, + 381 + ], + "spans": [ + { + "bbox": [ + 307, + 222, + 547, + 381 + ], + "type": "image", + "image_path": "3b2152d95fdc5369ac866aedcbe2243700ce335bfc0539df8c702593b8eaf08c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 388, + 546, + 444 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 546, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 546, + 444 + ], + "type": "text", + "content": "Figure 5. Qualitative results for ablation. The same image as rendered by V1 and V5 networks. The side-by-side comparison clearly shows how V5 reproduces much sharper details in shadows (best seen in Reflective) and is able to better handle complex reflections (best seen in FlipFlop)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": "contribute to the overall good results of the most effective version, which is V5. These results provide experimental support to the intuitions presented above about the higher effectiveness of feeding to the network the relative light position with respect to the sample " + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": " instead of the absolute light pose (row 1 versus row 2), as well as the importance of providing " + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": " as input to " + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": " (row 2 versus row 3). Separating inputs to " + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\Psi_{rgb}" + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": " is also beneficial and, together with " + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\Psi_{vis}" + }, + { + "bbox": [ + 304, + 466, + 545, + 574 + ], + "type": "text", + "content": " contributes to the good performance of V5." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 575, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 659 + ], + "type": "text", + "content": "Some qualitative examples comparing and contrasting V1 against V5 are reported in Fig. 5. Zooming in on cast shadows we can appreciate how careful handling of the light pose as well as the proposed modifications to the vanilla NeRF architecture enable rendering of sharper and more coherent shadows than the straightforward extension that conditions NeRF also on light pose." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 670, + 433, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 433, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 433, + 681 + ], + "type": "text", + "content": "5.4. Results on benchmark" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "Finally, we report the performance for the best architecture on the overall set of held out test scenes in Tab. 3." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 242, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 242, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 242, + 713 + ], + "type": "text", + "content": "1https://github.com/ashawkey/torch-ngp" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20768" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 282, + 289 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 282, + 289 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 282, + 289 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 282, + 289 + ], + "type": "table", + "html": "
OursInstant-NGP
NameEasyHardEasyHard
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Apple26.440.6226.250.6220.890.4520.950.45
Cheetah25.660.6124.640.6019.370.4419.600.44
Cube24.900.5423.980.5320.140.4220.310.42
Dinosaurs25.750.6524.980.6419.580.4219.660.41
FlipFlop25.850.6125.420.6120.380.4520.360.45
Fruits25.930.6225.720.6220.160.4520.210.44
Garden25.740.6625.080.6619.760.4519.700.45
Helicopters25.120.6124.730.6119.340.3719.370.37
Kittens25.900.6424.960.6318.520.3718.650.37
Lego26.070.6125.770.6120.750.4620.760.46
Lunch25.840.6024.710.5919.320.4619.380.45
Plant26.550.6725.930.6720.620.4420.660.44
Reflective25.790.6125.280.6120.090.4320.110.42
Robotoy26.240.6525.550.6520.770.5020.780.50
Savannah25.150.6224.310.6119.080.4019.180.40
Shark25.590.5725.320.5620.540.4220.530.41
Stegosaurus25.870.6325.650.6320.840.4320.910.42
Tapes25.840.5825.410.5719.340.4119.550.41
Trucks25.800.6725.160.6619.810.4419.870.44
Wooden toys25.690.6125.240.6020.190.4820.220.48
Average25.790.6225.200.6119.970.4320.040.43
", + "image_path": "6f2b86197a25be23443c671934311f8dc6e7b98bf62616d4c1e5fa468f9bf150.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 287, + 342 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 342 + ], + "type": "text", + "content": "Table 3. Quantitative results across all 20 scenes. We report both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) by comparing the novel view synthesized image with its corresponding groundtruth." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "text", + "content": "We compare our method against the pytorch implementation of Nvidia Instant-NGP [37]. Overall, the proposed architecture achieves satisfying results on this challenging task and sets a non trivial baseline for the online benchmark, clearly outperforming the naive baseline represented by the standard NeRF. We show some qualitative results for the easy test split in Fig. 6, and in Fig. 7 for the hard one. These qualitative results confirm that the model is capable of convincingly rendering and lighting the scene from unseen viewpoints and light positions while using a simple and lightweight architecture. Interestingly, the output of " + }, + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "inline_equation", + "content": "\\Psi_{vis}" + }, + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "text", + "content": ", reported in the rightmost columns of the figures, well approximate point-to-light visibility, especially in the easy split, even if it has not received direct supervision to emulate it, and it even reproduces some indirect illumination effects, confirming the feasibility of a neural approximation of the incident radiance " + }, + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "inline_equation", + "content": "L_{i}(\\mathbf{x},\\omega_{i})" + }, + { + "bbox": [ + 46, + 364, + 289, + 616 + ], + "type": "text", + "content": ". Comparing with the ground-truth frame, while rendering of light on the object is indeed quite realistic, cast shadows are sharp and coherent with the scene geometry on the easy set, while more artifacts are present in the hard split." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 627, + 204, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 204, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 204, + 639 + ], + "type": "text", + "content": "6. Conclusion and Limitations" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 647, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 715 + ], + "type": "text", + "content": "We have introduced the ReNe dataset, the first dual robot dataset framing real world objects under challenging one-light-at-time (OLAT) conditions and annotated with accurate camera and light poses. The main limitations of our dataset concern the absence of 360 degrees scans and the use of a challenging but unrealistic OLAT setup. By lever" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 184 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 184 + ], + "type": "text", + "content": "aging the training and validation splits of the dataset, we were able to perform an ablation study on lightweight modifications to a NeRF architecture that extend it to successfully perform novel view synthesis under unseen lighting. The best model emerged from the study has been tested on the held out test set to establish a non-trivial baseline for the benchmark. We hope the availability of a new dataset and baseline for the problem of NeRF relighting will attract new research around this challenging inverse rendering problem." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 201, + 556, + 392 + ], + "blocks": [ + { + "bbox": [ + 307, + 201, + 556, + 392 + ], + "lines": [ + { + "bbox": [ + 307, + 201, + 556, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 201, + 556, + 392 + ], + "type": "image", + "image_path": "8168d74da20a31e3860b0d18207a6b9bda9bf67ed4247d9a51970f7e2b4f3d2f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "lines": [ + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "type": "text", + "content": "Figure 6. We show one image from the easy test split " + }, + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{easy}" + }, + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "type": "text", + "content": " on the left. In the middle we can see the same image as rendered by our V5 model, while on the right the intermediate visibility output of " + }, + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "type": "inline_equation", + "content": "\\Psi_{vis}" + }, + { + "bbox": [ + 305, + 399, + 547, + 455 + ], + "type": "text", + "content": " is shown, which is then multiplied by the predicted BRDF to determine the outgoing radiance at each point." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 465, + 557, + 658 + ], + "blocks": [ + { + "bbox": [ + 306, + 465, + 557, + 658 + ], + "lines": [ + { + "bbox": [ + 306, + 465, + 557, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 557, + 658 + ], + "type": "image", + "image_path": "4c52017d54a42edbe41d8c83da1a9812a62378bbcdcb67111a7cdcece59c0b65.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 666, + 547, + 709 + ], + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 709 + ], + "type": "text", + "content": "Figure 7. On the left the ground-truth image drawn from the hard test split " + }, + { + "bbox": [ + 304, + 666, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{hard}" + }, + { + "bbox": [ + 304, + 666, + 547, + 709 + ], + "type": "text", + "content": ". In the middle the corresponding render produced by our V5 model. On the right the intermediate visibility output of our model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20769" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018. 3" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20772" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_content_list.json b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..35a0f1566808d7448bfe7c898c9e6bf291176a5a --- /dev/null +++ b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_content_list.json @@ -0,0 +1,1553 @@ +[ + { + "type": "text", + "text": "ReVISE: Self-Supervised Speech Resynthesis with Visual Input for Universal and Generalized Speech Regeneration", + "text_level": 1, + "bbox": [ + 166, + 128, + 803, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei-Ning Hsu $^{1}$ , Tal Remez $^{1}$ , Bowen Shi $^{1,3}$ , Jacob Donley $^{2}$ , Yossi Adi $^{1,4}$", + "bbox": [ + 197, + 202, + 769, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ FAIR, Meta AI Research $^{2}$ Meta Reality Labs Research", + "bbox": [ + 256, + 223, + 712, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Toyota Technological Institute at Chicago $^{4}$ The Hebrew University of Jerusalem", + "bbox": [ + 163, + 241, + 818, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wnhsu,talr,bshi,jdonley,adiyoss}@meta.com", + "bbox": [ + 297, + 262, + 668, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 311, + 313, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior works on improving speech quality with visual input typically study each type of auditory distortion separately (e.g., separation, inpainting, video-to-speech) and present tailored algorithms. This paper proposes to unify these subjects and study Generalized Speech Regeneration, where the goal is not to reconstruct the exact reference clean signal, but to focus on improving certain aspects of speech while not necessarily preserving the rest such as voice. In particular, this paper concerns intelligibility, quality, and video synchronization. We cast the problem as audio-visual speech resynthesis, which is composed of two steps: pseudo audio-visual speech recognition (P-AVSR) and pseudo text-to-speech synthesis (P-TTS). P-AVSR and P-TTS are connected by discrete units derived from a self-supervised speech model. Moreover, we utilize self-supervised audio-visual speech model to initialize P-AVSR. The proposed model is coined ReVISE. ReVISE is the first high-quality model for in-the-wild video-to-speech synthesis and achieves superior performance on all LRS3 audio-visual regeneration tasks with a single model. To demonstrate its applicability in the real world, ReVISE is also evaluated on EasyCom, an audio-visual benchmark collected under challenging acoustic conditions with only 1.6 hours of training data. Similarly, ReVISE greatly suppresses noise and improves quality. Project page: https://wnhsu.github.io/ReVISE/.", + "bbox": [ + 75, + 344, + 472, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 768, + 207, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike anechoic studio recordings, speech in-the-wild is rarely clean: outdoor recordings are corrupted with all sorts of natural and non-natural sounds like wind and traffic noise [6]. Speech recorded indoor often contains reverberation, mechanical noise, and overlapping speech from non-target speakers [54]. On top of those, recording devices and network may also introduce other types of dis", + "bbox": [ + 75, + 794, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d7344cb8f72e4c6716d9987492ba4b1071d9f06f3e4668e2270e759352fc1181.jpg", + "image_caption": [ + "Figure 1. Illustration of AVSE with various distortion." + ], + "image_footnote": [], + "bbox": [ + 506, + 311, + 888, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tortion, such as amplitude clipping, band-pass filtering, and package loss [1]. Distortion makes it hard for both human and machines to comprehend speech [10, 31]. Improving the quality and the intelligibility of corrupted speech is essential for assistive listening and robust speech processing. Generating clean speech signal based on its corrupted version is herein referred to as speech enhancement.", + "bbox": [ + 496, + 487, + 890, + 593 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In speech enhancement, one line of research uses visual speech to provide auxiliary information [14, 17, 19, 57], which is known as audio-visual speech enhancement. Audio-visual speech (e.g., talking-head videos) can be seen as a multimodal view of the speech. Since visual modality is immune to acoustic noise, combining both views enables more robust estimation of shared generating factors such as textual content. Meanwhile, despite sharing the same goal of recovering corrupted speech, prior work often treats enhancement from each type of distortion as a separate problem: speech denoising and dereverberation addresses additive and convolutive non-speech noises [17], speech separation focuses on speech noises that exhibit similar characteristics to the target speech [19], speech inpainting aims to recover dropped audio frames [38], and video-to-speech synthesis is the extreme case of inpainting where all the frames are dropped [15, 36]. As a result, algorithms designed for one type of distortion may not be effective for another.", + "bbox": [ + 496, + 595, + 892, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we advocate a more holistic approach to audio-visual speech enhancement, where an algorithm", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18795", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "should be evaluated on all types of distortion, and a single model should also be effective on all types of corrupted data, shifting from building distortion-specific models to a universal model. Following [48], we coin the concept universal speech enhancement. In turn, we also argue that exact reconstruction of the reference clean speech is not an appropriate objective especially when the level of distortion is high. To address the issue, we propose to relax the objective and solve the generalized speech regeneration (GSR) problem: instead of focusing on exact reconstruction and measuring metrics like signal-to-noise ratios (SNRs), the goal of GSR is to enhance a predefined set of attributes, such as content intelligibility that can be measured by word error rates (WERs). In contrast, the model does not need to preserve other attributes.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper focuses on recovering intelligibility, synchronicity and quality. The task of improving those could be broken down into two steps: predicting the frame-level content and synthesizing high quality audio from it. Inspired by the resemblance to audio-visual speech recognition and speech synthesis, we propose ReVISE, short for Resynthesis with Visual Input for Speech REgeneration. ReVISE is composed of a pseudo audio-visual speech recognition model (P-AVSR) and a pseudo text-to-speech synthesis model (P-TTS); instead of using text as the output/input of the two models, self-supervised speech units that encode speech content [23, 44] are adopted to bridge them, making the system free of text supervision. Furthermore, observing the gain on speech recognition brought by self-supervised learning, we also initialize the P-AVSR with a self-supervised audio-visual speech model, AV-HuBERT [49], which significantly improves the performance, especially on low-resource setups.", + "bbox": [ + 75, + 321, + 472, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To demonstrate the universality and compare with the literature, we construct four types of corrupted speech using Lip-reading Sentences 3 (LRS3) [2] and AudioSet [20], including audio-visual denoising, separation, inpainting, and video-to-speech. Results suggest that ReVISE is the first model capable of high-quality in-the-wild video-to-speech synthesis, while prior models fail to produce intelligible content [21] or generate low-quality audio for in-the-wild videos [36]. Compared to a strong masking-based method [19] on denoising and separation, ReVISE achieves comparable performance on mid-/high-SNR conditions (0-20dB), and are significantly stronger on lower SNR conditions, reducing WERs by up to $37.5\\%$ absolute and improving MOS by up to 1.09. Finally, we also show that a single ReVISE model can tackle all four types of distortion with similar performance to distortion-specific models. To further show the data efficiency and effectiveness of ReVISE on real data, we evaluate it on EasyCom [13], an audio-visual speech dataset addressing the cocktail party problem which contains clean close-talking recordings and", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "noisy distant recordings with background noise, loud interfering speech, and room reverberation. Results show that ReVISE still shines in this challenging setup, reducing WER by up to $32\\%$ while other methods fail.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 500, + 169, + 629, + 186 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Audio-visual speech enhancement tasks", + "text_level": 1, + "bbox": [ + 500, + 195, + 836, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In general, audio-visual speech enhancement is the task of improving the quality of corrupted speech $\\tilde{x}_a$ given its corresponding talking head video $x_v$ . During training, tuples of $(\\tilde{x}_a,x_v,x_a)$ are provided where $x_{a}$ is the reference clean speech. The tasks are further divided depending on the type of distortion applied to $\\tilde{x}_a$ : speech denoising and dereverberation considers $\\tilde{x}_a[t] = x_a[t]*h[t] + n[t]$ with impulse response $h$ and additive noise $n$ ( $t$ indexes discrete time steps). Source separation considers $\\tilde{x}_a[t] = x_a[t] + x_a'[t]$ where $x_{a}^{\\prime}$ is an interfering speech sampled from the same marginal distribution as $x_{a}$ . For these two subtasks, masking-based methods (in magnitude spectrogram domain [16, 41], complex spectrogram domain [14, 19, 55], or on learned basis [33, 34]) are widely adopted where the enhancement model $f$ predicts a mask $\\hat{M} = f(\\tilde{x}_a,x_v)$ . It is feasible because the target speech can be written as $X = M\\cdot \\tilde{X}$ where $X$ and $\\tilde{X}$ are the clean and noisy speech in the target domain and $M$ is the ideal ratio mask. On the other hand, speech inpainting and video-to-speech synthesis considers $\\tilde{x}_a[t] = m[t]\\cdot x_a[t]$ where $m[t]\\in \\{0,1\\}$ for inpainting and $m[t] = 0$ for the latter. Masking-based methods are not feasible for these tasks. Hence, previous studies directly predict spectrogram [36, 38] or waveform [7, 37, 39] as $\\hat{x}_a = f(\\tilde{x}_a,x_v)$ and optimize the model with regression and adversarial losses. Nevertheless, previous models have not been able to generate realistic samples with in-the-wild datasets like LRS3, because these models are deterministic while the underlying mapping is highly stochastic, especially when there is a large portion of frames dropped.", + "bbox": [ + 496, + 219, + 893, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To accommodate general distortions, universal enhancement models have to adopt generation-based method [32, 43,45,48,50], otherwise they cannot handle distortions like package loss (i.e., inpainting). For the same reason, our proposed model is also generation-based. However, it differs from previous works in two main aspects. First, prior universal enhancement models are audio-based, which do not leverage auxiliary input like visual speech. Hence, source separation and enhancement from silence (i.e., cross-modal generation) are not attainable and hence have not been included. Second, regardless of the training objective (regression [40], adversarial [43,45,50], or score-matching [48]), previous universal models predict reference clean speech directly. We consider a different paradigm based on self-supervised speech resynthesis [44]: our model predicts a self-supervised representation $z = k(x_{a})$ of the reference", + "bbox": [ + 496, + 659, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18796", + "bbox": [ + 480, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "clean speech. A separate model is used to convert $z$ back to audio, which is described in the next section.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Self-supervised speech resynthesis", + "text_level": 1, + "bbox": [ + 76, + 132, + 375, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous studies show that discretized Self Supervised Learned (SSL) speech features from the Hidden Unit BERT (HuBERT) model [23] encode mostly phonetic information and less about speaker and noise characteristics. HuBERT is pre-trained with a masked cluster prediction objective, where spans of input waveform are randomly masked and the model is asked to predict cluster assignment for those frames. Unlike VQ-VAE [52], HuBERT does not learn to encode all the factors; instead, it encodes information pertinent to inferring the unseen content, such as phonetic information. These properties make HuBERT units great candidates for replacing speech for text-free speech generative models, because they encode less nuisance variation and a model can predicts these units more easily compared to predicting speech directly [29, 30]. Such needs motivates the development of speech resynthesis models that convert units back to audio, because these generative models still have to produce speech as their final output.", + "bbox": [ + 75, + 155, + 470, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[44] proposed the first end-to-end model directly generating waveform from SSL units by adapting HiFi-GAN [27] which was originally designed as a vocoder converting spectrogram to waveform. The adpated HiFi-GAN takes SSL units, pitch, and speaker embedding as input, the latter two of which are added to capture variation of training data not encoded in the SSL units. Empirically, [30] demonstrates that speaker embedding and F0 can be removed if the model is trained on a high-quality single-speaker dataset.", + "bbox": [ + 75, + 429, + 468, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 579, + 169, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Generalized Speech Regeneration", + "text_level": 1, + "bbox": [ + 76, + 604, + 372, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Without loss of generality, we assume that original speech $x_{a}$ and its auxiliary view $x_{v}$ are generated with a bijective mapping $g_{m,Y}$ as $x_{m} = g_{m,Y}(\\{y_{i}\\}_{i}), m \\in \\{a,v\\}$ given a set of factors $Y = \\{y_{i}\\}_{i}$ (e.g., pitch, speed, textual content) sampled from $p_{Y}$ . Corrupted speech $\\tilde{x}_{a}$ is generated with a corruption function $g_{d}$ as $\\tilde{x}_{a} = g_{d}(x_{a},d)$ given $x_{a}$ and distortion parameter $d$ sampled from $p_{d}$ . Audiovisual speech enhancement can be seen as estimating $p(Y \\mid g_{d}(x_{a},d), x_{v})$ . When the level of distortion is low, there are fewer $Y$ that can result in the same observed $\\tilde{x}_{a}$ after corruption. Formulating it as a regression problem and measuring the performance of reconstructing all factors with metrics like SNR is reasonable. However, when the level of distortion is high, there exist multiple sets of $Y$ rendering the same noisy speech $\\tilde{x}_{a}$ . Take video-to-speech as an example: while the content and the timing of each word can be more accurately inferred, the exact pitch is hard to infer from the video. In other words, $p(y_{i}|\\tilde{x}_{a},x_{v})$ is more", + "bbox": [ + 75, + 628, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "deterministic for some $y_{i}$ but not for the others.", + "bbox": [ + 498, + 90, + 813, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We argue that for these scenarios reconstructing the exact clean reference signal $x_{a}$ is an ill-posed problem. Instead, one should consider the generalized speech regeneration problem, where the goal is to generate an enhanced signal $\\hat{x}_a = f(\\tilde{x}_a,x_v)$ that is on the manifold of clean speech $g_{a,Y}(\\cdot)$ (high quality) and preserves the factors of interest (partial faithfulness). Let $g_{a,Y,i}^{-1}$ be the inverse mapping from speech to factor $y_{i}$ , and $\\{y_i\\}_{i\\in I^+}$ be the list of factors of interest (which should be a subset of factors that can be inferred from corrupted speech). Faithfulness is measured by the discrepancy between $g_{a,Y,i}^{-1}(\\hat{x}_a)$ and $g_{a,Y,i}^{-1}(x_a)$ for $i\\in I^{+}$ . In case of $y_{i}$ being the textual content, such discrepancy can be measured by the word error rate produced by an off-the-shelf speech recognizer for example. Quality can be measured by metrics commonly used for text-to-speech synthesis such as mean opinion scores, where human raters rate how realistic and clean the audio sounds regardless of the textual content. In this paper, we consider $\\{y_i\\}_{i\\in I^+}$ to be textual content and timing (synchronization with the video) and do not address other factors such as voice, which is not of primary importance for communication.", + "bbox": [ + 496, + 107, + 893, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. ReVISE", + "text_level": 1, + "bbox": [ + 500, + 436, + 601, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose to solve the problem in two stages: (i) predicting $\\{y_i\\}_{i\\in I^+}$ of the clean reference $x_{a}$ given $(\\tilde{x}_a,x_v)$ , and (ii) resynthesizing speech conditioned on $\\{y_i\\}_{i\\in I^+}$ . The two steps are handled by a pseudo audio-visual speech recognition module (P-AVSR) and a pseudo text-to-speech synthesis module (P-TTS), respectively, as shown in Fig. 2. The discrete SSL units derived from HuBERT [23] as described in Sec. 2.2 are used to represent $\\{y_i\\}_{i\\in I^+}$ . Using SSL units have two main benefits: not restricted by text availability and better encoding of non-verbal information.", + "bbox": [ + 496, + 460, + 893, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The P-AVSR module performs a task very similar to speech recognition. Inspired by the recent success of self-supervised pre-training for audio [4, 23] and audio-visual speech recognition [49], we initialize P-AVSR with AV-HuBERT [49], an SSL model achieving state-of-the-art performance on audio, visual, and audio-visual speech recognition. It is composed of a video encoder and an audio encoder as the modality-specific front-end, followed by a stack of transformer layers as the shared back-end taking concatenated audio and video features as input (Fig. 2 right). The model encodes waveform into features at a frame rate of $25\\mathrm{Hz}$ , while the SSL unit from HuBERT are encoded at $50\\mathrm{Hz}$ . To match the rate, a lightweight transposed convolution layer followed by a softmax layer is added as the prediction head, which is randomly initialized. The P-AVSR module is trained with a cross-entropy loss $L = \\sum_{t}\\sum_{j = 1}^{C}z_{t}^{j}\\log f_{t}^{j}(\\tilde{x}_{a},x_{v})$ , where $\\mathbf{z}_t$ denotes the one-hot discrete unit label of the $t$ -th frame, $f_{t}(\\tilde{x}_{a},x_{v})$ is the predicted distribution over discrete units from the en", + "bbox": [ + 496, + 613, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18797", + "bbox": [ + 480, + 925, + 519, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/83160bc853f3890e42cf950316a80228ed90c7ac5945cbe8c2703f967b5a7ce8.jpg", + "image_caption": [ + "Figure 2. Model diagram." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 467, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "hancer for the $t$ -th frame and C unit vocabulary size.", + "bbox": [ + 75, + 369, + 423, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the unit HiFi-GAN described in Sec. 2.2 for converting predicted $z$ into speech, which aims to faithfully produce the content and timing encoded in units. In fact, P-TTS can be trained with a different dataset from P-AVSR and this dataset determines the audio quality and the voice of ReVISE. With privacy consideration in mind, we use a high quality single speaker dataset with the speaker's consent to train this model. Consequently, ReVISE does not preserve voice and other fine-grained details and could generate speech of even higher quality than the original speech. Note that the P-TTS can be easily extended following [44].", + "bbox": [ + 75, + 383, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 565, + 269, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 590, + 179, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We consider two datasets for our experiments. The first one is Lip Reading Sentences 3 (LRS3) [2], which is a clean dataset based on TED talk videos. It contains 433 hours of audio-visual speech data and their corresponding text transcripts. Following prior work on speech enhancement, speech data are artificially corrupted to simulate enhancement tasks. Four tasks are created: (i) Speech denoising: in which we artificially mix a clean speech signal with a noise sample using randomly sampled Signal-to-Noise Ratio (SNR) in the range of [-20,20]. Noisy samples were selected from AudioSet [20]; (ii) Speech source separation: in which we follow a similar procedure to the speech denoising setup but instead of mixing the speech signal with a noisy sample, we mix it with another speech signal produced by a different speaker; (iii) Speech inpaiting: under this setup we randomly dropped (i.e., zero out) spans of $s \\in \\{20,30,40\\}$ frames, with probability $p \\in \\{0.3,0.4,0.5\\}$ . Each frame corresponds to 20ms, hence in case $s = 20$ we masked 400ms of audio. This process", + "bbox": [ + 75, + 613, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "can be seen as a packet loss simulation; and (iv) Video-to-speech synthesis: in this setup we use the LRS3 dataset without any augmentations, where our goal is to synthesize the audio given a silent video only.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second data is Easy Communications (Easy-Com) dataset [13], which includes real-life noisy speech and is designed to study the cocktail party problem in conversational augmented reality. We preprocess the data using official time-aligned transcripts and crop image ROIs based on lip bounding boxes, resulting in 1.64/0.59/0.35 hours for train-valid/test splits. The dataset is challenging due to motion blur, barrel distortion, interfering speech, noise, and reverberation1. Close-talking microphones are used for clean reference speech, and beamformed audio is used as model input, following [5,13,18]. ReVISE is trained using merged audio from all six channels, including close-talking microphone audio. More details can be found in the Appendix.", + "bbox": [ + 496, + 152, + 892, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Model", + "text_level": 1, + "bbox": [ + 500, + 358, + 586, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SSL speech tokenizer We use a BASE HuBERT model which is composed of a convolutional encoder and 12 Transformer layers. Each layer has embedding dimension of 768, feed-forward layer dimension of 3072, and 12 self-attention heads. The model is pre-trained for three iterations on 32 GPUs with 400K updates per iteration, using clusters of MFCC/6-th layer feature from iteration 1/9-th layer feature from iteration 2 as the target, with a codebook size of 100/500/1000, respectively, following the recipe of [30]. A total of 221K hours of unlabeled speech data combining multilingual Librispeech [46], Common Voice [3], and VoxPopuli [53] in eight languages (En, Es, Fr, De, Nl, It, Pl, Pt) are used for pre-training. The final SSL units $z$ used in ReVISE are generated by clustering the third iteration feature at the last layer with a codebook size of 2000 with K-means.", + "bbox": [ + 496, + 381, + 890, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "P-TTS We use the unit HiFi-GAN described in Sec. 2.2. The model is trained for 400K updates on 8 GPUs on the LJSpeech [25] dataset resampled to $16\\mathrm{kHz}$ to match the sample rate of other datasets. Similar to [30], F0 and speaker embedding are not used.", + "bbox": [ + 496, + 628, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "P-AVSR We use the LARGE AV-HuBERT model by default from [49]. It takes video and/or audio as input, where video is head-crop image frames at 25fps, and audio is 23-dimensional Mel filterbank sequence (FBank) computed with a 10ms frame shift and stacked every four frames to match the video. The video encoder is a ResNet-18 [35] model, while the audio-encoder is simply a linear projection. The features are concatenated frame-by-frame and passed to a stack of 24 Transformer layers, which has embedding and feed-forward layer dimension of 1024 and", + "bbox": [ + 496, + 724, + 890, + 876 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1We refer readers to the supplementary material to listen to the samples.", + "bbox": [ + 514, + 886, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18798", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4096 with 16 attention heads. For all but EasyCom experiments we use the publicly available checkpoints from [49] that were pre-trained on LRS3 and filtered VoxCeleb2 for initialization. For Easycom, a u-HuBERT model [24] pretrained additionally with Librilight [26] is used for initialization, which improves upon using [49]. The up-sampling module is one transposed convolution layer with stride of 2, kernel size of 4, and 768 channels, followed by GeLU activation [22]. The P-AVSR models are fine-tuned on 8 GPUs for less than 45K updates. Detailed fine-tuning configurations for each task are presented in the appendix.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 265, + 197, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the proposed model and baselines on the following axes: content, synchronization, quality, and low-level detail reconstruction. As discussed in Sec. 3.1, we focus on the first three axes, and the results for the last metric are included in the appendix for completeness.", + "bbox": [ + 75, + 287, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For content, we use the WER computed with a speech recognition model to measure the intelligibility quantitatively similar to [36, 37]. The public model from [56] is used, which reports a WER of $5.6\\%$ on LRS3 test split and $35.7\\%$ on the EasyCom close-talking validation set. For synchronization, following [21] we use SyncNet [9] metrics, the predicted temporal distance between audio and video (LSE-D) and the prediction's confidence (LSE-C) are averaged over the entire test set. For quality, we follow the tradition of text-to-speech synthesis evaluation and conduct subjective mean opinion score (MOS) studies with a scale from 1 to 5 and a 0.5 increment. We evaluate 50 randomly sampled files from the test set, where each sample was evaluated by at least 15 raters using the CrowdMOS package [47]. Finally, for reconstruction of low-level details as typically done in speech denoising studies, we include ESTOI [51] and Mel cepstral distortion (MCD) [28]. While MCD provides an estimate of the similarity of two signals by measuring the mel cepstra difference, ESTOI put more emphasis on speech properties.", + "bbox": [ + 75, + 364, + 472, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 678, + 163, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative results are presented in the section. We strongly recommend readers to watch the samples provided in the supplementary material for better understanding of the sample quality compared to the baselines.", + "bbox": [ + 75, + 703, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Ground truth and resynthesis performance", + "text_level": 1, + "bbox": [ + 76, + 771, + 444, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For reference, we first evaluate reference clean speech (Tgt. audio) and resynthesized clean speech (Tgt. audio resynthesis) with the proposed metrics and report the results in Tab. 1. The gap between the two is an approximation of how much information is lost when tokenizing speech into SSL units. It shows that intelligibility, synchronization, and quality are all slightly degraded. As ReVISE", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d9aa7c72a6f0557f1a7868e4ebbdea50686bca77afa3df6524589b2879ed1005.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio5.6%5.206.334.38±0.02--
Tgt. audio resynthesis10.6%5.026.404.16±0.0241.5910.01
Silent video to speech
SVTS-L, LRS381.5%5.076.462.12±0.0426.878.13
SVTS-L, LRS3+VoxEn67.4%5.536.002.23±0.0330.987.59
ReVISE (Ours)33.9%5.036.444.13±0.0228.5110.73
", + "bbox": [ + 503, + 89, + 893, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Full video-to-speech synthesis results on LRS3 test set.", + "bbox": [ + 504, + 194, + 885, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is trained to predict the tokens inferred from clean speech, if the ReVISE model have $100\\%$ prediction accuracy then the performance will be identical to the \"Tgt. audio resynthesis\" row here. Hence, the performance on the resynthesized speech roughly upper-bounds that of the ReVISE model.", + "bbox": [ + 496, + 234, + 893, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Video-to-speech synthesis", + "text_level": 1, + "bbox": [ + 498, + 321, + 732, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Tab. 1, we compare ReVISE with SVTS [36],2 which is the state-of-the-art model on the video-to-speech synthesis task. SVTS is composed of a video-to-spectrogram predictor and a separately trained neural vocoder. Its video-to-spectrogram predictor is trained with a regression loss, which takes as input a lip video and a speaker embedding extracted from a pre-trained fixed speaker encoder. Speaker embedding is needed because voice cannot be accurately inferred from the video. The model demonstrate strong results on two constrained datasets (LRW [8] and GRID [11]) which contain isolated words and fixed-length sentences with limited word choices, respectively.", + "bbox": [ + 496, + 345, + 890, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Tab. 1, because the audio quality generated by SVTS is mediocre (2.12 and 2.23 MOS), these samples are not very intelligible by machines, reflected by the highWER $81.5\\%$ and $67.4\\%$ when trained on LRS3 and $\\mathrm{LRS3 + VoxCeleb2}$ . In contrast, our proposed model generates much higher quality audio (4.13 MOS) and yields significantly lower WER $(33.9\\%)$ . Through manual inspection, we found a confidence score above 5 and distance below 6 implies good synchronization on LRS3. All methods generate audio fairly synchronized to the video.", + "bbox": [ + 496, + 527, + 892, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Audio-visual speech inpainting", + "text_level": 1, + "bbox": [ + 500, + 689, + 772, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We next evaluate ReVISE on the audio-visual speech inpainting task with three test splits, where $30\\%$ , $40\\%$ , and $50\\%$ of the frames are dropped with dropped spans longer than 400ms. While there have been several works studying audio-based speech inpainting or audio-visual inpainting for music [58], [38] is the only work we are aware of studying the audio-visual setup. However, their model was only evaluated on the constrained GRID dataset, showing a phone error rate of $13.7\\%$ . SVTS achieves a WER of $17.9\\%$ , hinting that [38] is likely worse than SVTS even", + "bbox": [ + 496, + 712, + 893, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2We obtained test set samples of SVTS from the authors for evaluation.", + "bbox": [ + 514, + 875, + 890, + 886 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3https://sites.google.com/view/scalable-vts", + "bbox": [ + 517, + 887, + 857, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18799", + "bbox": [ + 480, + 925, + 519, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/42ff9d533a03c4efa14944ea40b514ce4f25264d379abf9d1eeff5b432a05b4d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInp ModTestContWER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech inpainting
Inp. audioA30%44.1%4.377.0560.7536.54
40%53.5%4.017.3651.6944.71
50%60.3%3.787.6043.1652.82
DemucsA30%43.9%4.377.0459.4035.95
40%53.5%4.047.3450.5543.96
50%60.0%3.827.5742.2052.09
ResynthesisA30%51.2%4.207.1425.2711.57
40%60.1%3.947.3821.5511.91
50%66.3%3.687.6317.9712.09
ReVISE (Ours)AV30%14.9%5.016.4238.1510.23
40%18.1%4.996.4437.0510.31
50%19.2%5.046.4135.9910.33
", + "bbox": [ + 76, + 88, + 467, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "when having partial audio as input. Accordingly, we decide not to compare with [38] but compare with a publicly available strong generation-based audio enhancement model, Demucs [12], which was trained on DNS-Challenge, VCTK, WHAM, and WHAMR, containing 700hr of clean speech and 6,000hr of noise in total. In addition, we consider resynthesis as another baseline, which encodes and decodes the corrupted speech with the same SSL tokenizer and P-TTS model.", + "bbox": [ + 75, + 316, + 467, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"Inp. audio\" row presents the results evaluated on the corrupted audio in Tab. 2. We see that intelligibility degrades (WER increases from $5.6\\%$ to $60.3\\%$ ) as the percentage of dropped frames increases, and so does synchronization (5.20 to 3.78 for confidence and 6.33 to 7.60 for distance). The two audio-based baselines are not effective, showing similar or even worse results compared to the corrupted samples before enhancement. The little gain from Demucs over the inputting-audio baseline shows that existing enhancement approaches fail to generalize to inpainting. In contrast, our proposed model is effective on improving both intelligibility and synchronization. The WER drops from $60.3\\%$ to $19.2\\%$ after regeneration when half of the audio is missing in the corrupted audio. Comparing enhancing from no audio at all (video-to-speech synthesis) with enhancing from observing half of the audio (inpainting, $50\\%$ ), we observe a $14.7\\%$ WER reduction ( $33.9\\% \\rightarrow 19.2\\%$ ), showing that the model use the additional audio information effectively to improve content reconstruction. As for synchronization, ReVISE restore a similar level regardless of the percentage dropped.", + "bbox": [ + 75, + 454, + 468, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Audio-visual speech denoising", + "text_level": 1, + "bbox": [ + 76, + 785, + 344, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 3 presents results of audio-visual speech denoising on four test splits: lvl 1-4, which contain noisy samples of SNR in [10, 20], [0, 10], [-10, 0], and [-20, -10]. In addition to the two audio-based baselines from the previous section, the proposed model is also compared with VisualVoice [19] in this and the next section, which is a state", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a20df357d88e83be3d64a29941f5f531a046fef23fafd341d8e98254bab1e82b.jpg", + "table_caption": [ + "Table 2. Full speech inpainting results on LRS3 test set with ${30}\\% /{40}\\% /{50}\\%$ of frames dropped." + ], + "table_footnote": [], + "table_body": "
MethodModTestContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio--5.6%5.206.334.36±0.018--
Audio-visual speech denoising
Inp. audioAlvl 17.8%4.666.772.95±0.0387.215.07
lvl 220.0%3.807.522.82±0.0369.938.27
lvl 363.9%2.418.682.79±0.0245.9111.27
lvl 487.7%1.549.392.71±0.0425.5513.47
ResynthesisAlvl 113.3%4.986.464.33±0.0241.1810.02
lvl 225.9%4.786.644.37±0.0239.1610.19
lvl 369.4%3.647.613.63±0.0225.7111.27
lvl 490.8%2.118.853.34±0.039.2012.56
Demucs [12]Alvl 16.9%5.156.383.58±0.0492.593.73
lvl 215.1%4.956.573.63±0.0385.614.81
lvl 348.0%4.147.283.36±0.0365.946.81
lvl 481.3%2.438.752.89±0.0431.5210.25
VisualVoice [19]AVlvl 16.6%5.166.354.11±0.0392.203.89
lvl 28.8%5.196.353.94±0.0286.925.07
lvl 323.4%5.076.453.80±0.0274.166.45
lvl 458.0%4.536.863.25±0.0350.488.01
ReVISE (Ours)AVlvl 19.4%5.036.424.31±0.0241.2210.04
lvl 29.7%5.046.414.36±0.0240.9310.06
lvl 311.7%5.046.414.41±0.0239.7910.14
lvl 420.5%5.076.404.34±0.0235.8010.36
", + "bbox": [ + 498, + 88, + 890, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Full speech denoising results on LRS3 test set. SNR ranges for lvl $1/2/3/4$ are $[10,20]/[0,10]/[-10,0]/[-20,-10]$ dB.", + "bbox": [ + 498, + 327, + 890, + 356 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of-the-art model for audio-visual source separation and denoising. VisualVoice predicts a complex IRM given noisy audio, lip video, and speaker face image as input and the model is optimized with a combination of mask prediction loss, cross-modal matching loss (image and enhanced audio embeddings from the same speaker should be close) and consistency loss (embeddings of enhanced audio for the same speaker should be close). To have a fair comparison, we re-train VisualVoice models with the same dataset as ReVISE using a similar setup provided by the authors. We use the same public checkpoint for Demucs.", + "bbox": [ + 496, + 382, + 890, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In terms of intelligibility, we observe that the performance of resynthesizing corrupted audio is still bad. Demucs performs well for high SNR setup (lvl 1) but lags behind audio-visual models for the rest setups. VisualVoice achieves the best results on the [0, 20] dB SNR range, but ReVISE is much more robust to even a higher level of noise, reporting a WER of $20.5\\%$ at lvl 4. Synchronization scores follow a similar trend to WERs in terms of ranking across models and test splits. Quality of the proposed model is significantly higher (4.31-4.41 MOS) than all baselines, and is on par with the reference clean speech (4.36 MOS).", + "bbox": [ + 496, + 549, + 890, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.5. Audio-visual source separation", + "text_level": 1, + "bbox": [ + 500, + 726, + 772, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following Sec. 5.4, four noisy test sets are created with different levels of SNR. Comparing the speech source separation results in Tab. 4 and denoising results in Tab. 3, we observe that audio model (the public Demucs) performs worse with speech noise than with non-speech noise at the same SNR level. In contrast, audio-visual models report similar performance on the two tasks at high SNR, and better performance on separation at low SNR. These results suggest that it is easier to remove speech noise if the model have auxiliary information that it can use to identify the tar", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18800", + "bbox": [ + 480, + 926, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b190f77a93c54100e45cd6978479055ad1ed74b04f0ec19544abcc29aa657c0a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodModTestCont WER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech separation
Inp. audioAlvl 115.7%4.736.7485.563.29
lvl 265.7%3.857.4865.525.95
lvl 3102.3%2.938.2740.978.67
lvl 4105.5%2.468.6622.3310.51
Demucs [12]Alvl 111.75.066.4689.683.76
lvl 255.74.107.2566.806.27
lvl 3101.22.778.4226.3210.22
lvl 4106.22.158.9510.1512.14
VisualVoice [19]AVlvl 16.2%5.136.3794.692.43
lvl 27.8%5.126.3990.293.36
lvl 315.3%4.916.5778.824.80
lvl 451.8%4.207.1753.847.02
ReVISE (Ours)AVlvl 19.9%5.056.4141.3410.05
lvl 210.2%5.056.4140.9010.07
lvl 311.4%5.056.4140.0710.11
lvl 415.7%5.046.4137.9710.21
", + "bbox": [ + 96, + 88, + 450, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Full source separation results on LRS3 test set. SNR ranges for lv1 $1/2/3/4$ are $[10,20]/[0,10]/[-10,0]/[-20,-10]$ dB.", + "bbox": [ + 76, + 282, + 468, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "get speech. Comparing VisualVoice and ReVISE which are trained on the same data, it reveals a similar trend where ReVISE is still substantially better at low SNR.", + "bbox": [ + 76, + 337, + 468, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.6. Universal audio-visual speech regeneration", + "text_level": 1, + "bbox": [ + 76, + 391, + 442, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we build a single ReVISE model trained on all four types of distortion and compare it with corruption-specific models presented in earlier sections (Tab. 5) in terms of WER. Surprisingly, the universal model beats or matches the distortion-specific model on almost all tasks. The only exception is video-to-speech synthesis, on which the universal model is $0.5\\%$ WER worse.", + "bbox": [ + 75, + 415, + 468, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.7. AV regeneration on real data — EasyCom", + "text_level": 1, + "bbox": [ + 76, + 530, + 434, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We next study how effective ReVISE on EasyCom, a real noisy dataset that is much more challenging than LRS3 and has much fewer hours of training data. Tab. 6 compares ReVISE with several baseline methods enhancing single channel speech (ch2) or beamformed speech (bf) from multi-channel sources. Note that we attempted to re-train VisualVoice on EasyCom but were not successful on getting any meaningful results, likely due to the lack of data as well as the difficulty. In addition, we use a P-AVSR model that takes lip crops instead of head crops as input for this dataset, which provides slightly better performance. Ablation studies are included in the Appendix.", + "bbox": [ + 75, + 553, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ReVISE substantially enhances the intelligibility of noisy speech in both setups (WER: $87.5\\% \\rightarrow 55.0\\%$ on ch2 and $71.5\\% \\rightarrow 52.1\\%$ on bf), while Demucs only managed to reduce the WER by $0.7\\%$ and $1.7\\%$ , respectively. Moreover, the WER of the enhanced beamformed speech from ReVISE is only $4.4\\%$ away from resynthesized clean speech: the target ReVISE is trained to predict. One can expect the gap to clean speech ( $14.5\\%$ WER) will be reduced if the quality of the SSL units improves.", + "bbox": [ + 75, + 734, + 468, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 7 presents the subjective quality evaluation results for EasyCom. We first note that the quality of resynthesized", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "target audio (4.13 MOS) is in fact higher than the target audio itself (3.76 MOS). This is because the P-TTS module is trained on the high-quality LJSpeech, which has better quality than the EasyCom audio recorded by the close-talking microphones, as the latter still contain mild background noise and overlapping speech. Similarly, the predicted audio from the proposed ReVISE model also delivers similar levels of audio quality (4.19 and 4.11 with ch2 and beamformed input, respectively), which are significantly better than the original distant recordings (2.95 and 2.67) and the baseline methods (2.95 and 2.39 from Demucs).", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results suggest a crucial advantage of the proposed ReVISE model compared to previous studies: for ReVISE, the audio quality is not bounded by the enhancement training data (LRS3 and EasyCom), but determined by the quality of P-TTS training data. In contrast, prior works such as SVTS or VisualVoice could only produce audio that is as good as the enhancement target.", + "bbox": [ + 496, + 257, + 890, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.8. Limitations", + "text_level": 1, + "bbox": [ + 500, + 373, + 625, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We see from Tabs. 1 to 4 that while ReVISE outperforms or is on par with baseline methods on intelligibility, quality, and synchronization, it performs much worse than SVTS, Demucs, and VisualVoice on recovering low-level details. This is because ReVISE does not focus on reconstructing the exact reference signal; moreover, ReVISE does not aim to infer the speaker's voice either since the SSL units are shown to encode very little speaker information.", + "bbox": [ + 496, + 397, + 890, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In fact, it is not a deficiency that the proposed ReVISE model does not reconstruct the reference signal exactly. As shown in Tab. 7, the quality of the reference signal may be mediocre for real world datasets such as EasyCom. In that scenario, reconstructing the exact reference signal would lead to inferior performance compared to the proposed approach, where the training data for P-AVSR and P-TTS are decoupled, such that higher quality data can be used for the unit-to-speech module.", + "bbox": [ + 496, + 518, + 890, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.9. Ablation studies", + "text_level": 1, + "bbox": [ + 500, + 666, + 661, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies to evaluate the importance of pre-training P-AVSR, P-AVSR model size, selection of audio SSL units, and visual input. WER are reported here because intelligibility exhibits the highest variation across models reported earlier. Tab. 8 compares different SSL speech units on two tasks: clean speech resynthesis and video-to-speech generation. The two alternative types of units are derived from the BASE AV-HuBERT model trained on LRS3+VoxCeleb2 [49] and the BASE HuBERT model trained on Librispeech [23]. The corresponding P-TTS model are also trained on the same LJSpeech dataset. We see that performance on the two tasks are correlated, where units that loss less content information (lower Resyn WER) are better prediction targets for the P-AVSR model (lower", + "bbox": [ + 496, + 689, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18801", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3b99efb6bff975e4a66b5cbd41bcb195b4389abb1fc32ba5fa6461cf07250258.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
video-to-speech\nWER↓speech inpainting\n20%WER↓\n30%40%speech denoising\n1v1 1lvl 2lvl 3lvl 4source separation\nWER↓Avg.↓
lvl 1lvl 2lvl 3lvl 4
Separate ReVISE33.9%14.9%18.1%19.2%9.4%9.7%11.7%20.5%9.9%10.2%11.4%15.7%19.0%
Universal ReVISE34.5%14.9%17.9%19.2%8.7%9.4%11.5%20.3%9.1%9.7%10.9%15.5%18.9%
", + "bbox": [ + 81, + 89, + 890, + 154 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5c7531308f2fa30a2abbf182c61dffb01cf0c9d4369aba51de5b7b50ae1de72a.jpg", + "table_caption": [ + "Table 5. Comparing corruption-specific ReVISE with universal ReVISE on intelligibility measured by WER (\\%)." + ], + "table_footnote": [], + "table_body": "
MethodModWER↓ (ch2) (dev/test)WER↓ (bf) (dev/test)
Tgt. audioA35.7% / 37.6%
Tgt. audio resynthesisA43.2% / 47.7%
", + "bbox": [ + 81, + 202, + 465, + 271 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a9aef24b6065ef0e8b18e20f7790a944d2d9ca221084f3119ee59b5613826b9c.jpg", + "table_caption": [ + "Audio-visual speech enhancement" + ], + "table_footnote": [], + "table_body": "
Inp. audioA74.2% / 87.5%60.7% / 71.5%
Demucs [12]A76.9% / 86.8%63.4% / 69.8%
ResynthesisA79.6% / 91.0%68.7% / 77.6%
ReVISE (Ours)AV50.3% / 55.0%47.6% / 52.1%
", + "bbox": [ + 78, + 284, + 467, + 344 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8bce85c446b726b4e27ccf24d3b5c12753e9d104f926615c09a61d2ac4db0f41.jpg", + "table_caption": [ + "Table 6. Audio-visual speech enhancement results on EasyCom (ch2: channel 2, bf: beamforming). Synchronization results are not reported because SyncNet fails even on clean reference $x_{a}$ ." + ], + "table_footnote": [], + "table_body": "
MethodModMOS↑ (ch2)MOS↑ (bf)
Tgt. audioA3.76±0.04
Tgt. audio resynthesisA4.13±0.03
", + "bbox": [ + 78, + 412, + 467, + 474 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/88cc1a32ff5c67470e1b62717b8939187ea65a1c6831164fff50143ed71032e0.jpg", + "table_caption": [ + "Audio-visual speech enhancement" + ], + "table_footnote": [], + "table_body": "
Inp. audioA2.95±0.042.67±0.03
Demucs [12]A2.95±0.042.39±0.03
ResynthesisA3.97±0.043.98±0.03
ReVISE (Ours)AV4.19±0.024.11±0.04
", + "bbox": [ + 78, + 489, + 470, + 555 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9da79f00bb7ceb4e6cf631a0505084d8fc1f12d31dfa7790a997e36027d3d946.jpg", + "table_caption": [ + "Table 7. Subjective quality evaluation of audio-visual speech enhancement results on EasyCom test set (ch2: channel 2, bf: beamforming)." + ], + "table_footnote": [], + "table_body": "
UnitResyn WER↓V2S WER↓
AV-HuBERT (LRS3+VC2) [49]20.741.2
HuBERT (LS960) [23]17.435.2
HuBERT (VP+MLS+CV)10.633.9
", + "bbox": [ + 81, + 625, + 465, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "V2S WER). Tab. 9 (Left) shows pre-training brings significant gains (38.9% for BASE and 43.1% for LARGE) and LARGE model performs better with a 7.4% WER reduction.", + "bbox": [ + 76, + 763, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we study the importance of visual input by comparing an audio-visual ReVISE with an audio-only version of it. We consider the universal speech regeneration model setup but remove video-to-speech data as it is incompatible to the audio-only model. Tab. 9 (Right) presents aggregated results averaged over testing splits for each task.", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/18a15e54af8aae23bcfc80655b5c6b51cf78f22f87167a16b1a5c29d74962daa.jpg", + "table_caption": [ + "Table 8. Ablation studies on SSL unit choices. Clean audio resynthesis (Resyn) and video-to-speech (V2S) WERs are reported." + ], + "table_footnote": [], + "table_body": "
P-AVSRV2SWER↓
SizescratchPT
BASE81.042.9
LARGE78.635.5
", + "bbox": [ + 501, + 202, + 648, + 270 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4ade0b31ba362889d4e1cc67cfc3b52016513b8449fe03a95a75c0b50f3d7397.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModWER↓
DenSepInpaintV2S
AV12.611.417.434.8
A29.239.844.6n/a
", + "bbox": [ + 669, + 202, + 883, + 270 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. (Left) Ablation studies on model sizes and pre-training. Performance on video-to-speech is reported. (Right) Comparison of ReVISE and its audio-only counterpart.", + "bbox": [ + 498, + 280, + 890, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe that the model using both audio and video as input outperform the counterpart consistently with a large margin. Specifically, the level of degradation varies substantially across task: denoising is least effected (16.6%), followed by inpainting (27.2%) and separation (28.4%) — this shows that models rely heavily on visual information to determine the target speaker as well as infill the missing information from dropped frames. Last but not least, we note that the audio-visual ReVISE perform decently on video-to-speech synthesis despite not being trained on the task at all, suggesting zero-shot generalization to unseen distortion.", + "bbox": [ + 496, + 356, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 545, + 619, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents ReVISE, a novel paradigm for audiovisual speech regeneration that is universal and benefits greatly from the recent advances in self-supervised speech pre-training. Empirical studies demonstrate effectiveness of ReVISE on a popular benchmark with synthetic noise (LRS3) as well as on a conversational benchmark with real noisy data collected from extremely challenging acoustic conditions (EasyCom). In particular, audio enhanced by ReVISE is significantly more intelligible and of higher quality compared to those from the previous work.", + "bbox": [ + 496, + 573, + 890, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While this paper studies universal regeneration, it only concerns audio but not video distortion. For future work, we hope to study more general multimodal speech regeneration where the model can recover distortion in both modalities.", + "bbox": [ + 496, + 727, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 811, + 660, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The authors thank Rodrigo Schonburg for sharing SVTS samples for evaluations, thank Ruohan Gao for the assistance on VisualVoice code, and thank Stavros Petridis and Anurag Kumar for helpful discussions.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18802", + "bbox": [ + 480, + 925, + 519, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Amir Adler, Valentin Emiya, Maria G Jafari, Michael Elad, Rémi Gribonval, and Mark D Plumbley. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 283-292, 2019. 5" + ], + "bbox": [ + 78, + 90, + 468, + 667 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18805", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_model.json b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5531b9e4d6687a9b40cddde4e5be5a7c7c32f133 --- /dev/null +++ b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_model.json @@ -0,0 +1,2191 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.168, + 0.13, + 0.804, + 0.176 + ], + "angle": 0, + "content": "ReVISE: Self-Supervised Speech Resynthesis with Visual Input for Universal and Generalized Speech Regeneration" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.203, + 0.77, + 0.223 + ], + "angle": 0, + "content": "Wei-Ning Hsu\\(^{1}\\), Tal Remez\\(^{1}\\), Bowen Shi\\(^{1,3}\\), Jacob Donley\\(^{2}\\), Yossi Adi\\(^{1,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.224, + 0.714, + 0.242 + ], + "angle": 0, + "content": "\\(^{1}\\)FAIR, Meta AI Research \\(^{2}\\)Meta Reality Labs Research" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.242, + 0.82, + 0.261 + ], + "angle": 0, + "content": "\\(^{3}\\)Toyota Technological Institute at Chicago \\(^{4}\\)The Hebrew University of Jerusalem" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.263, + 0.669, + 0.278 + ], + "angle": 0, + "content": "{wnhsu,talr,bshi,jdonley,adiyoss}@meta.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.313, + 0.314, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.473, + 0.737 + ], + "angle": 0, + "content": "Prior works on improving speech quality with visual input typically study each type of auditory distortion separately (e.g., separation, inpainting, video-to-speech) and present tailored algorithms. This paper proposes to unify these subjects and study Generalized Speech Regeneration, where the goal is not to reconstruct the exact reference clean signal, but to focus on improving certain aspects of speech while not necessarily preserving the rest such as voice. In particular, this paper concerns intelligibility, quality, and video synchronization. We cast the problem as audio-visual speech resynthesis, which is composed of two steps: pseudo audio-visual speech recognition (P-AVSR) and pseudo text-to-speech synthesis (P-TTS). P-AVSR and P-TTS are connected by discrete units derived from a self-supervised speech model. Moreover, we utilize self-supervised audio-visual speech model to initialize P-AVSR. The proposed model is coined ReVISE. ReVISE is the first high-quality model for in-the-wild video-to-speech synthesis and achieves superior performance on all LRS3 audio-visual regeneration tasks with a single model. To demonstrate its applicability in the real world, ReVISE is also evaluated on EasyCom, an audio-visual benchmark collected under challenging acoustic conditions with only 1.6 hours of training data. Similarly, ReVISE greatly suppresses noise and improves quality. Project page: https://wnhsu.github.io/ReVISE/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.769, + 0.209, + 0.785 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Unlike anechoic studio recordings, speech in-the-wild is rarely clean: outdoor recordings are corrupted with all sorts of natural and non-natural sounds like wind and traffic noise [6]. Speech recorded indoor often contains reverberation, mechanical noise, and overlapping speech from non-target speakers [54]. On top of those, recording devices and network may also introduce other types of dis" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.313, + 0.889, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.442, + 0.857, + 0.457 + ], + "angle": 0, + "content": "Figure 1. Illustration of AVSE with various distortion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.594 + ], + "angle": 0, + "content": "tortion, such as amplitude clipping, band-pass filtering, and package loss [1]. Distortion makes it hard for both human and machines to comprehend speech [10, 31]. Improving the quality and the intelligibility of corrupted speech is essential for assistive listening and robust speech processing. Generating clean speech signal based on its corrupted version is herein referred to as speech enhancement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.869 + ], + "angle": 0, + "content": "In speech enhancement, one line of research uses visual speech to provide auxiliary information [14, 17, 19, 57], which is known as audio-visual speech enhancement. Audio-visual speech (e.g., talking-head videos) can be seen as a multimodal view of the speech. Since visual modality is immune to acoustic noise, combining both views enables more robust estimation of shared generating factors such as textual content. Meanwhile, despite sharing the same goal of recovering corrupted speech, prior work often treats enhancement from each type of distortion as a separate problem: speech denoising and dereverberation addresses additive and convolutive non-speech noises [17], speech separation focuses on speech noises that exhibit similar characteristics to the target speech [19], speech inpainting aims to recover dropped audio frames [38], and video-to-speech synthesis is the extreme case of inpainting where all the frames are dropped [15, 36]. As a result, algorithms designed for one type of distortion may not be effective for another." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we advocate a more holistic approach to audio-visual speech enhancement, where an algorithm" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "18795" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "should be evaluated on all types of distortion, and a single model should also be effective on all types of corrupted data, shifting from building distortion-specific models to a universal model. Following [48], we coin the concept universal speech enhancement. In turn, we also argue that exact reconstruction of the reference clean speech is not an appropriate objective especially when the level of distortion is high. To address the issue, we propose to relax the objective and solve the generalized speech regeneration (GSR) problem: instead of focusing on exact reconstruction and measuring metrics like signal-to-noise ratios (SNRs), the goal of GSR is to enhance a predefined set of attributes, such as content intelligibility that can be measured by word error rates (WERs). In contrast, the model does not need to preserve other attributes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.473, + 0.596 + ], + "angle": 0, + "content": "This paper focuses on recovering intelligibility, synchronicity and quality. The task of improving those could be broken down into two steps: predicting the frame-level content and synthesizing high quality audio from it. Inspired by the resemblance to audio-visual speech recognition and speech synthesis, we propose ReVISE, short for Resynthesis with Visual Input for Speech REgeneration. ReVISE is composed of a pseudo audio-visual speech recognition model (P-AVSR) and a pseudo text-to-speech synthesis model (P-TTS); instead of using text as the output/input of the two models, self-supervised speech units that encode speech content [23, 44] are adopted to bridge them, making the system free of text supervision. Furthermore, observing the gain on speech recognition brought by self-supervised learning, we also initialize the P-AVSR with a self-supervised audio-visual speech model, AV-HuBERT [49], which significantly improves the performance, especially on low-resource setups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To demonstrate the universality and compare with the literature, we construct four types of corrupted speech using Lip-reading Sentences 3 (LRS3) [2] and AudioSet [20], including audio-visual denoising, separation, inpainting, and video-to-speech. Results suggest that ReVISE is the first model capable of high-quality in-the-wild video-to-speech synthesis, while prior models fail to produce intelligible content [21] or generate low-quality audio for in-the-wild videos [36]. Compared to a strong masking-based method [19] on denoising and separation, ReVISE achieves comparable performance on mid-/high-SNR conditions (0-20dB), and are significantly stronger on lower SNR conditions, reducing WERs by up to \\(37.5\\%\\) absolute and improving MOS by up to 1.09. Finally, we also show that a single ReVISE model can tackle all four types of distortion with similar performance to distortion-specific models. To further show the data efficiency and effectiveness of ReVISE on real data, we evaluate it on EasyCom [13], an audio-visual speech dataset addressing the cocktail party problem which contains clean close-talking recordings and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "noisy distant recordings with background noise, loud interfering speech, and room reverberation. Results show that ReVISE still shines in this challenging setup, reducing WER by up to \\(32\\%\\) while other methods fail." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.17, + 0.63, + 0.187 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.196, + 0.838, + 0.212 + ], + "angle": 0, + "content": "2.1. Audio-visual speech enhancement tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.895, + 0.659 + ], + "angle": 0, + "content": "In general, audio-visual speech enhancement is the task of improving the quality of corrupted speech \\(\\tilde{x}_a\\) given its corresponding talking head video \\(x_v\\). During training, tuples of \\((\\tilde{x}_a,x_v,x_a)\\) are provided where \\(x_{a}\\) is the reference clean speech. The tasks are further divided depending on the type of distortion applied to \\(\\tilde{x}_a\\): speech denoising and dereverberation considers \\(\\tilde{x}_a[t] = x_a[t]*h[t] + n[t]\\) with impulse response \\(h\\) and additive noise \\(n\\) (\\(t\\) indexes discrete time steps). Source separation considers \\(\\tilde{x}_a[t] = x_a[t] + x_a'[t]\\) where \\(x_{a}^{\\prime}\\) is an interfering speech sampled from the same marginal distribution as \\(x_{a}\\). For these two subtasks, masking-based methods (in magnitude spectrogram domain [16, 41], complex spectrogram domain [14, 19, 55], or on learned basis [33, 34]) are widely adopted where the enhancement model \\(f\\) predicts a mask \\(\\hat{M} = f(\\tilde{x}_a,x_v)\\). It is feasible because the target speech can be written as \\(X = M\\cdot \\tilde{X}\\) where \\(X\\) and \\(\\tilde{X}\\) are the clean and noisy speech in the target domain and \\(M\\) is the ideal ratio mask. On the other hand, speech inpainting and video-to-speech synthesis considers \\(\\tilde{x}_a[t] = m[t]\\cdot x_a[t]\\) where \\(m[t]\\in \\{0,1\\}\\) for inpainting and \\(m[t] = 0\\) for the latter. Masking-based methods are not feasible for these tasks. Hence, previous studies directly predict spectrogram [36, 38] or waveform [7, 37, 39] as \\(\\hat{x}_a = f(\\tilde{x}_a,x_v)\\) and optimize the model with regression and adversarial losses. Nevertheless, previous models have not been able to generate realistic samples with in-the-wild datasets like LRS3, because these models are deterministic while the underlying mapping is highly stochastic, especially when there is a large portion of frames dropped." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.896, + 0.902 + ], + "angle": 0, + "content": "To accommodate general distortions, universal enhancement models have to adopt generation-based method [32, 43,45,48,50], otherwise they cannot handle distortions like package loss (i.e., inpainting). For the same reason, our proposed model is also generation-based. However, it differs from previous works in two main aspects. First, prior universal enhancement models are audio-based, which do not leverage auxiliary input like visual speech. Hence, source separation and enhancement from silence (i.e., cross-modal generation) are not attainable and hence have not been included. Second, regardless of the training objective (regression [40], adversarial [43,45,50], or score-matching [48]), previous universal models predict reference clean speech directly. We consider a different paradigm based on self-supervised speech resynthesis [44]: our model predicts a self-supervised representation \\(z = k(x_{a})\\) of the reference" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "18796" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "clean speech. A separate model is used to convert \\( z \\) back to audio, which is described in the next section." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.133, + 0.376, + 0.149 + ], + "angle": 0, + "content": "2.2. Self-supervised speech resynthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.156, + 0.471, + 0.429 + ], + "angle": 0, + "content": "Previous studies show that discretized Self Supervised Learned (SSL) speech features from the Hidden Unit BERT (HuBERT) model [23] encode mostly phonetic information and less about speaker and noise characteristics. HuBERT is pre-trained with a masked cluster prediction objective, where spans of input waveform are randomly masked and the model is asked to predict cluster assignment for those frames. Unlike VQ-VAE [52], HuBERT does not learn to encode all the factors; instead, it encodes information pertinent to inferring the unseen content, such as phonetic information. These properties make HuBERT units great candidates for replacing speech for text-free speech generative models, because they encode less nuisance variation and a model can predicts these units more easily compared to predicting speech directly [29, 30]. Such needs motivates the development of speech resynthesis models that convert units back to audio, because these generative models still have to produce speech as their final output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.567 + ], + "angle": 0, + "content": "[44] proposed the first end-to-end model directly generating waveform from SSL units by adapting HiFi-GAN [27] which was originally designed as a vocoder converting spectrogram to waveform. The adpated HiFi-GAN takes SSL units, pitch, and speaker embedding as input, the latter two of which are added to capture variation of training data not encoded in the SSL units. Empirically, [30] demonstrates that speaker embedding and F0 can be removed if the model is trained on a high-quality single-speaker dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.58, + 0.17, + 0.595 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.373, + 0.621 + ], + "angle": 0, + "content": "3.1. Generalized Speech Regeneration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Without loss of generality, we assume that original speech \\( x_{a} \\) and its auxiliary view \\( x_{v} \\) are generated with a bijective mapping \\( g_{m,Y} \\) as \\( x_{m} = g_{m,Y}(\\{y_{i}\\}_{i}), m \\in \\{a,v\\} \\) given a set of factors \\( Y = \\{y_{i}\\}_{i} \\) (e.g., pitch, speed, textual content) sampled from \\( p_{Y} \\). Corrupted speech \\( \\tilde{x}_{a} \\) is generated with a corruption function \\( g_{d} \\) as \\( \\tilde{x}_{a} = g_{d}(x_{a},d) \\) given \\( x_{a} \\) and distortion parameter \\( d \\) sampled from \\( p_{d} \\). Audiovisual speech enhancement can be seen as estimating \\( p(Y \\mid g_{d}(x_{a},d), x_{v}) \\). When the level of distortion is low, there are fewer \\( Y \\) that can result in the same observed \\( \\tilde{x}_{a} \\) after corruption. Formulating it as a regression problem and measuring the performance of reconstructing all factors with metrics like SNR is reasonable. However, when the level of distortion is high, there exist multiple sets of \\( Y \\) rendering the same noisy speech \\( \\tilde{x}_{a} \\). Take video-to-speech as an example: while the content and the timing of each word can be more accurately inferred, the exact pitch is hard to infer from the video. In other words, \\( p(y_{i}|\\tilde{x}_{a},x_{v}) \\) is more" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.814, + 0.107 + ], + "angle": 0, + "content": "deterministic for some \\(y_{i}\\) but not for the others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.895, + 0.427 + ], + "angle": 0, + "content": "We argue that for these scenarios reconstructing the exact clean reference signal \\( x_{a} \\) is an ill-posed problem. Instead, one should consider the generalized speech regeneration problem, where the goal is to generate an enhanced signal \\( \\hat{x}_a = f(\\tilde{x}_a,x_v) \\) that is on the manifold of clean speech \\( g_{a,Y}(\\cdot) \\) (high quality) and preserves the factors of interest (partial faithfulness). Let \\( g_{a,Y,i}^{-1} \\) be the inverse mapping from speech to factor \\( y_{i} \\), and \\( \\{y_i\\}_{i\\in I^+} \\) be the list of factors of interest (which should be a subset of factors that can be inferred from corrupted speech). Faithfulness is measured by the discrepancy between \\( g_{a,Y,i}^{-1}(\\hat{x}_a) \\) and \\( g_{a,Y,i}^{-1}(x_a) \\) for \\( i\\in I^{+} \\). In case of \\( y_{i} \\) being the textual content, such discrepancy can be measured by the word error rate produced by an off-the-shelf speech recognizer for example. Quality can be measured by metrics commonly used for text-to-speech synthesis such as mean opinion scores, where human raters rate how realistic and clean the audio sounds regardless of the textual content. In this paper, we consider \\( \\{y_i\\}_{i\\in I^+} \\) to be textual content and timing (synchronization with the video) and do not address other factors such as voice, which is not of primary importance for communication." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.602, + 0.453 + ], + "angle": 0, + "content": "3.2. ReVISE" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.895, + 0.613 + ], + "angle": 0, + "content": "We propose to solve the problem in two stages: (i) predicting \\(\\{y_i\\}_{i\\in I^+}\\) of the clean reference \\(x_{a}\\) given \\((\\tilde{x}_a,x_v)\\), and (ii) resynthesizing speech conditioned on \\(\\{y_i\\}_{i\\in I^+}\\). The two steps are handled by a pseudo audio-visual speech recognition module (P-AVSR) and a pseudo text-to-speech synthesis module (P-TTS), respectively, as shown in Fig. 2. The discrete SSL units derived from HuBERT [23] as described in Sec. 2.2 are used to represent \\(\\{y_i\\}_{i\\in I^+}\\). Using SSL units have two main benefits: not restricted by text availability and better encoding of non-verbal information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The P-AVSR module performs a task very similar to speech recognition. Inspired by the recent success of self-supervised pre-training for audio [4, 23] and audio-visual speech recognition [49], we initialize P-AVSR with AV-HuBERT [49], an SSL model achieving state-of-the-art performance on audio, visual, and audio-visual speech recognition. It is composed of a video encoder and an audio encoder as the modality-specific front-end, followed by a stack of transformer layers as the shared back-end taking concatenated audio and video features as input (Fig. 2 right). The model encodes waveform into features at a frame rate of \\(25\\mathrm{Hz}\\), while the SSL unit from HuBERT are encoded at \\(50\\mathrm{Hz}\\). To match the rate, a lightweight transposed convolution layer followed by a softmax layer is added as the prediction head, which is randomly initialized. The P-AVSR module is trained with a cross-entropy loss \\(L = \\sum_{t}\\sum_{j = 1}^{C}z_{t}^{j}\\log f_{t}^{j}(\\tilde{x}_{a},x_{v})\\), where \\(\\mathbf{z}_t\\) denotes the one-hot discrete unit label of the \\(t\\)-th frame, \\(f_{t}(\\tilde{x}_{a},x_{v})\\) is the predicted distribution over discrete units from the en" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.52, + 0.938 + ], + "angle": 0, + "content": "18797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.328, + 0.352, + 0.342 + ], + "angle": 0, + "content": "Figure 2. Model diagram." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.424, + 0.384 + ], + "angle": 0, + "content": "hancer for the \\(t\\)-th frame and C unit vocabulary size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.552 + ], + "angle": 0, + "content": "We use the unit HiFi-GAN described in Sec. 2.2 for converting predicted \\( z \\) into speech, which aims to faithfully produce the content and timing encoded in units. In fact, P-TTS can be trained with a different dataset from P-AVSR and this dataset determines the audio quality and the voice of ReVISE. With privacy consideration in mind, we use a high quality single speaker dataset with the speaker's consent to train this model. Consequently, ReVISE does not preserve voice and other fine-grained details and could generate speech of even higher quality than the original speech. Note that the P-TTS can be easily extended following [44]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.566, + 0.27, + 0.584 + ], + "angle": 0, + "content": "4. Experimental Setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.181, + 0.605 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We consider two datasets for our experiments. The first one is Lip Reading Sentences 3 (LRS3) [2], which is a clean dataset based on TED talk videos. It contains 433 hours of audio-visual speech data and their corresponding text transcripts. Following prior work on speech enhancement, speech data are artificially corrupted to simulate enhancement tasks. Four tasks are created: (i) Speech denoising: in which we artificially mix a clean speech signal with a noise sample using randomly sampled Signal-to-Noise Ratio (SNR) in the range of [-20,20]. Noisy samples were selected from AudioSet [20]; (ii) Speech source separation: in which we follow a similar procedure to the speech denoising setup but instead of mixing the speech signal with a noisy sample, we mix it with another speech signal produced by a different speaker; (iii) Speech inpaiting: under this setup we randomly dropped (i.e., zero out) spans of \\( s \\in \\{20,30,40\\} \\) frames, with probability \\( p \\in \\{0.3,0.4,0.5\\} \\). Each frame corresponds to 20ms, hence in case \\( s = 20 \\) we masked 400ms of audio. This process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "can be seen as a packet loss simulation; and (iv) Video-to-speech synthesis: in this setup we use the LRS3 dataset without any augmentations, where our goal is to synthesize the audio given a silent video only." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.893, + 0.349 + ], + "angle": 0, + "content": "The second data is Easy Communications (Easy-Com) dataset [13], which includes real-life noisy speech and is designed to study the cocktail party problem in conversational augmented reality. We preprocess the data using official time-aligned transcripts and crop image ROIs based on lip bounding boxes, resulting in 1.64/0.59/0.35 hours for train-valid/test splits. The dataset is challenging due to motion blur, barrel distortion, interfering speech, noise, and reverberation1. Close-talking microphones are used for clean reference speech, and beamformed audio is used as model input, following [5,13,18]. ReVISE is trained using merged audio from all six channels, including close-talking microphone audio. More details can be found in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.359, + 0.587, + 0.373 + ], + "angle": 0, + "content": "4.2. Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.609 + ], + "angle": 0, + "content": "SSL speech tokenizer We use a BASE HuBERT model which is composed of a convolutional encoder and 12 Transformer layers. Each layer has embedding dimension of 768, feed-forward layer dimension of 3072, and 12 self-attention heads. The model is pre-trained for three iterations on 32 GPUs with 400K updates per iteration, using clusters of MFCC/6-th layer feature from iteration 1/9-th layer feature from iteration 2 as the target, with a codebook size of 100/500/1000, respectively, following the recipe of [30]. A total of 221K hours of unlabeled speech data combining multilingual Librispeech [46], Common Voice [3], and VoxPopuli [53] in eight languages (En, Es, Fr, De, Nl, It, Pl, Pt) are used for pre-training. The final SSL units \\(z\\) used in ReVISE are generated by clustering the third iteration feature at the last layer with a codebook size of 2000 with K-means." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.706 + ], + "angle": 0, + "content": "P-TTS We use the unit HiFi-GAN described in Sec. 2.2. The model is trained for 400K updates on 8 GPUs on the LJSpeech [25] dataset resampled to \\(16\\mathrm{kHz}\\) to match the sample rate of other datasets. Similar to [30], F0 and speaker embedding are not used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.877 + ], + "angle": 0, + "content": "P-AVSR We use the LARGE AV-HuBERT model by default from [49]. It takes video and/or audio as input, where video is head-crop image frames at 25fps, and audio is 23-dimensional Mel filterbank sequence (FBank) computed with a 10ms frame shift and stacked every four frames to match the video. The video encoder is a ResNet-18 [35] model, while the audio-encoder is simply a linear projection. The features are concatenated frame-by-frame and passed to a stack of 24 Transformer layers, which has embedding and feed-forward layer dimension of 1024 and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1We refer readers to the supplementary material to listen to the samples." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "18798" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "4096 with 16 attention heads. For all but EasyCom experiments we use the publicly available checkpoints from [49] that were pre-trained on LRS3 and filtered VoxCeleb2 for initialization. For Easycom, a u-HuBERT model [24] pretrained additionally with Librilight [26] is used for initialization, which improves upon using [49]. The up-sampling module is one transposed convolution layer with stride of 2, kernel size of 4, and 768 channels, followed by GeLU activation [22]. The P-AVSR models are fine-tuned on 8 GPUs for less than 45K updates. Detailed fine-tuning configurations for each task are presented in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.266, + 0.199, + 0.28 + ], + "angle": 0, + "content": "4.3. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.47, + 0.365 + ], + "angle": 0, + "content": "We evaluate the proposed model and baselines on the following axes: content, synchronization, quality, and low-level detail reconstruction. As discussed in Sec. 3.1, we focus on the first three axes, and the results for the last metric are included in the appendix for completeness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.668 + ], + "angle": 0, + "content": "For content, we use the WER computed with a speech recognition model to measure the intelligibility quantitatively similar to [36, 37]. The public model from [56] is used, which reports a WER of \\(5.6\\%\\) on LRS3 test split and \\(35.7\\%\\) on the EasyCom close-talking validation set. For synchronization, following [21] we use SyncNet [9] metrics, the predicted temporal distance between audio and video (LSE-D) and the prediction's confidence (LSE-C) are averaged over the entire test set. For quality, we follow the tradition of text-to-speech synthesis evaluation and conduct subjective mean opinion score (MOS) studies with a scale from 1 to 5 and a 0.5 increment. We evaluate 50 randomly sampled files from the test set, where each sample was evaluated by at least 15 raters using the CrowdMOS package [47]. Finally, for reconstruction of low-level details as typically done in speech denoising studies, we include ESTOI [51] and Mel cepstral distortion (MCD) [28]. While MCD provides an estimate of the similarity of two signals by measuring the mel cepstra difference, ESTOI put more emphasis on speech properties." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.165, + 0.695 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Quantitative results are presented in the section. We strongly recommend readers to watch the samples provided in the supplementary material for better understanding of the sample quality compared to the baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.445, + 0.789 + ], + "angle": 0, + "content": "5.1. Ground truth and resynthesis performance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For reference, we first evaluate reference clean speech (Tgt. audio) and resynthesized clean speech (Tgt. audio resynthesis) with the proposed metrics and report the results in Tab. 1. The gap between the two is an approximation of how much information is lost when tokenizing speech into SSL units. It shows that intelligibility, synchronization, and quality are all slightly degraded. As ReVISE" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.09, + 0.895, + 0.186 + ], + "angle": 0, + "content": "
MethodContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio5.6%5.206.334.38±0.02--
Tgt. audio resynthesis10.6%5.026.404.16±0.0241.5910.01
Silent video to speech
SVTS-L, LRS381.5%5.076.462.12±0.0426.878.13
SVTS-L, LRS3+VoxEn67.4%5.536.002.23±0.0330.987.59
ReVISE (Ours)33.9%5.036.444.13±0.0228.5110.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.505, + 0.195, + 0.886, + 0.21 + ], + "angle": 0, + "content": "Table 1. Full video-to-speech synthesis results on LRS3 test set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.236, + 0.894, + 0.314 + ], + "angle": 0, + "content": "is trained to predict the tokens inferred from clean speech, if the ReVISE model have \\(100\\%\\) prediction accuracy then the performance will be identical to the \"Tgt. audio resynthesis\" row here. Hence, the performance on the resynthesized speech roughly upper-bounds that of the ReVISE model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.323, + 0.733, + 0.34 + ], + "angle": 0, + "content": "5.2. Video-to-speech synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.527 + ], + "angle": 0, + "content": "In Tab. 1, we compare ReVISE with SVTS [36],2 which is the state-of-the-art model on the video-to-speech synthesis task. SVTS is composed of a video-to-spectrogram predictor and a separately trained neural vocoder. Its video-to-spectrogram predictor is trained with a regression loss, which takes as input a lip video and a speaker embedding extracted from a pre-trained fixed speaker encoder. Speaker embedding is needed because voice cannot be accurately inferred from the video. The model demonstrate strong results on two constrained datasets (LRW [8] and GRID [11]) which contain isolated words and fixed-length sentences with limited word choices, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.893, + 0.68 + ], + "angle": 0, + "content": "As shown in Tab. 1, because the audio quality generated by SVTS is mediocre (2.12 and 2.23 MOS), these samples are not very intelligible by machines, reflected by the highWER \\(81.5\\%\\) and \\(67.4\\%\\) when trained on LRS3 and \\(\\mathrm{LRS3 + VoxCeleb2}\\) . In contrast, our proposed model generates much higher quality audio (4.13 MOS) and yields significantly lower WER \\((33.9\\%)\\) . Through manual inspection, we found a confidence score above 5 and distance below 6 implies good synchronization on LRS3. All methods generate audio fairly synchronized to the video." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.69, + 0.774, + 0.707 + ], + "angle": 0, + "content": "5.3. Audio-visual speech inpainting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.894, + 0.865 + ], + "angle": 0, + "content": "We next evaluate ReVISE on the audio-visual speech inpainting task with three test splits, where \\(30\\%\\), \\(40\\%\\), and \\(50\\%\\) of the frames are dropped with dropped spans longer than 400ms. While there have been several works studying audio-based speech inpainting or audio-visual inpainting for music [58], [38] is the only work we are aware of studying the audio-visual setup. However, their model was only evaluated on the constrained GRID dataset, showing a phone error rate of \\(13.7\\%\\). SVTS achieves a WER of \\(17.9\\%\\), hinting that [38] is likely worse than SVTS even" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.875, + 0.892, + 0.887 + ], + "angle": 0, + "content": "2We obtained test set samples of SVTS from the authors for evaluation." + }, + { + "type": "page_footnote", + "bbox": [ + 0.519, + 0.888, + 0.858, + 0.9 + ], + "angle": 0, + "content": "3https://sites.google.com/view/scalable-vts" + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.52, + 0.938 + ], + "angle": 0, + "content": "18799" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.468, + 0.251 + ], + "angle": 0, + "content": "
MethodInp ModTestContWER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech inpainting
Inp. audioA30%44.1%4.377.0560.7536.54
40%53.5%4.017.3651.6944.71
50%60.3%3.787.6043.1652.82
DemucsA30%43.9%4.377.0459.4035.95
40%53.5%4.047.3450.5543.96
50%60.0%3.827.5742.2052.09
ResynthesisA30%51.2%4.207.1425.2711.57
40%60.1%3.947.3821.5511.91
50%66.3%3.687.6317.9712.09
ReVISE (Ours)AV30%14.9%5.016.4238.1510.23
40%18.1%4.996.4437.0510.31
50%19.2%5.046.4135.9910.33
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.261, + 0.468, + 0.289 + ], + "angle": 0, + "content": "Table 2. Full speech inpainting results on LRS3 test set with \\( {30}\\% /{40}\\% /{50}\\% \\) of frames dropped." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.468, + 0.452 + ], + "angle": 0, + "content": "when having partial audio as input. Accordingly, we decide not to compare with [38] but compare with a publicly available strong generation-based audio enhancement model, Demucs [12], which was trained on DNS-Challenge, VCTK, WHAM, and WHAMR, containing 700hr of clean speech and 6,000hr of noise in total. In addition, we consider resynthesis as another baseline, which encodes and decodes the corrupted speech with the same SSL tokenizer and P-TTS model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.773 + ], + "angle": 0, + "content": "\"Inp. audio\" row presents the results evaluated on the corrupted audio in Tab. 2. We see that intelligibility degrades (WER increases from \\(5.6\\%\\) to \\(60.3\\%\\)) as the percentage of dropped frames increases, and so does synchronization (5.20 to 3.78 for confidence and 6.33 to 7.60 for distance). The two audio-based baselines are not effective, showing similar or even worse results compared to the corrupted samples before enhancement. The little gain from Demucs over the inputting-audio baseline shows that existing enhancement approaches fail to generalize to inpainting. In contrast, our proposed model is effective on improving both intelligibility and synchronization. The WER drops from \\(60.3\\%\\) to \\(19.2\\%\\) after regeneration when half of the audio is missing in the corrupted audio. Comparing enhancing from no audio at all (video-to-speech synthesis) with enhancing from observing half of the audio (inpainting, \\(50\\%\\)), we observe a \\(14.7\\%\\) WER reduction (\\(33.9\\% \\rightarrow 19.2\\%\\)), showing that the model use the additional audio information effectively to improve content reconstruction. As for synchronization, ReVISE restore a similar level regardless of the percentage dropped." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.345, + 0.803 + ], + "angle": 0, + "content": "5.4. Audio-visual speech denoising" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Tab. 3 presents results of audio-visual speech denoising on four test splits: lvl 1-4, which contain noisy samples of SNR in [10, 20], [0, 10], [-10, 0], and [-20, -10]. In addition to the two audio-based baselines from the previous section, the proposed model is also compared with VisualVoice [19] in this and the next section, which is a state" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.316 + ], + "angle": 0, + "content": "
MethodModTestContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio--5.6%5.206.334.36±0.018--
Audio-visual speech denoising
Inp. audioAlvl 17.8%4.666.772.95±0.0387.215.07
lvl 220.0%3.807.522.82±0.0369.938.27
lvl 363.9%2.418.682.79±0.0245.9111.27
lvl 487.7%1.549.392.71±0.0425.5513.47
ResynthesisAlvl 113.3%4.986.464.33±0.0241.1810.02
lvl 225.9%4.786.644.37±0.0239.1610.19
lvl 369.4%3.647.613.63±0.0225.7111.27
lvl 490.8%2.118.853.34±0.039.2012.56
Demucs [12]Alvl 16.9%5.156.383.58±0.0492.593.73
lvl 215.1%4.956.573.63±0.0385.614.81
lvl 348.0%4.147.283.36±0.0365.946.81
lvl 481.3%2.438.752.89±0.0431.5210.25
VisualVoice [19]AVlvl 16.6%5.166.354.11±0.0392.203.89
lvl 28.8%5.196.353.94±0.0286.925.07
lvl 323.4%5.076.453.80±0.0274.166.45
lvl 458.0%4.536.863.25±0.0350.488.01
ReVISE (Ours)AVlvl 19.4%5.036.424.31±0.0241.2210.04
lvl 29.7%5.046.414.36±0.0240.9310.06
lvl 311.7%5.046.414.41±0.0239.7910.14
lvl 420.5%5.076.404.34±0.0235.8010.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.328, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Table 3. Full speech denoising results on LRS3 test set. SNR ranges for lvl \\(1/2/3/4\\) are \\([10,20]/[0,10]/[-10,0]/[-20,-10]\\) dB." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.549 + ], + "angle": 0, + "content": "of-the-art model for audio-visual source separation and denoising. VisualVoice predicts a complex IRM given noisy audio, lip video, and speaker face image as input and the model is optimized with a combination of mask prediction loss, cross-modal matching loss (image and enhanced audio embeddings from the same speaker should be close) and consistency loss (embeddings of enhanced audio for the same speaker should be close). To have a fair comparison, we re-train VisualVoice models with the same dataset as ReVISE using a similar setup provided by the authors. We use the same public checkpoint for Demucs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.716 + ], + "angle": 0, + "content": "In terms of intelligibility, we observe that the performance of resynthesizing corrupted audio is still bad. Demucs performs well for high SNR setup (lvl 1) but lags behind audio-visual models for the rest setups. VisualVoice achieves the best results on the [0, 20] dB SNR range, but ReVISE is much more robust to even a higher level of noise, reporting a WER of \\(20.5\\%\\) at lvl 4. Synchronization scores follow a similar trend to WERs in terms of ranking across models and test splits. Quality of the proposed model is significantly higher (4.31-4.41 MOS) than all baselines, and is on par with the reference clean speech (4.36 MOS)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.774, + 0.743 + ], + "angle": 0, + "content": "5.5. Audio-visual source separation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Following Sec. 5.4, four noisy test sets are created with different levels of SNR. Comparing the speech source separation results in Tab. 4 and denoising results in Tab. 3, we observe that audio model (the public Demucs) performs worse with speech noise than with non-speech noise at the same SNR level. In contrast, audio-visual models report similar performance on the two tasks at high SNR, and better performance on separation at low SNR. These results suggest that it is easier to remove speech noise if the model have auxiliary information that it can use to identify the tar" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.52, + 0.938 + ], + "angle": 0, + "content": "18800" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.098, + 0.089, + 0.451, + 0.273 + ], + "angle": 0, + "content": "
MethodModTestCont WER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech separation
Inp. audioAlvl 115.7%4.736.7485.563.29
lvl 265.7%3.857.4865.525.95
lvl 3102.3%2.938.2740.978.67
lvl 4105.5%2.468.6622.3310.51
Demucs [12]Alvl 111.75.066.4689.683.76
lvl 255.74.107.2566.806.27
lvl 3101.22.778.4226.3210.22
lvl 4106.22.158.9510.1512.14
VisualVoice [19]AVlvl 16.2%5.136.3794.692.43
lvl 27.8%5.126.3990.293.36
lvl 315.3%4.916.5778.824.80
lvl 451.8%4.207.1753.847.02
ReVISE (Ours)AVlvl 19.9%5.056.4141.3410.05
lvl 210.2%5.056.4140.9010.07
lvl 311.4%5.056.4140.0710.11
lvl 415.7%5.046.4137.9710.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.283, + 0.47, + 0.313 + ], + "angle": 0, + "content": "Table 4. Full source separation results on LRS3 test set. SNR ranges for lv1 \\(1/2/3/4\\) are \\([10,20]/[0,10]/[-10,0]/[-20,-10]\\) dB." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.338, + 0.47, + 0.385 + ], + "angle": 0, + "content": "get speech. Comparing VisualVoice and ReVISE which are trained on the same data, it reveals a similar trend where ReVISE is still substantially better at low SNR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.392, + 0.443, + 0.41 + ], + "angle": 0, + "content": "5.6. Universal audio-visual speech regeneration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.47, + 0.522 + ], + "angle": 0, + "content": "In this section, we build a single ReVISE model trained on all four types of distortion and compare it with corruption-specific models presented in earlier sections (Tab. 5) in terms of WER. Surprisingly, the universal model beats or matches the distortion-specific model on almost all tasks. The only exception is video-to-speech synthesis, on which the universal model is \\(0.5\\%\\) WER worse." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.436, + 0.548 + ], + "angle": 0, + "content": "5.7. AV regeneration on real data — EasyCom" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.734 + ], + "angle": 0, + "content": "We next study how effective ReVISE on EasyCom, a real noisy dataset that is much more challenging than LRS3 and has much fewer hours of training data. Tab. 6 compares ReVISE with several baseline methods enhancing single channel speech (ch2) or beamformed speech (bf) from multi-channel sources. Note that we attempted to re-train VisualVoice on EasyCom but were not successful on getting any meaningful results, likely due to the lack of data as well as the difficulty. In addition, we use a P-AVSR model that takes lip crops instead of head crops as input for this dataset, which provides slightly better performance. Ablation studies are included in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.87 + ], + "angle": 0, + "content": "ReVISE substantially enhances the intelligibility of noisy speech in both setups (WER: \\(87.5\\% \\rightarrow 55.0\\%\\) on ch2 and \\(71.5\\% \\rightarrow 52.1\\%\\) on bf), while Demucs only managed to reduce the WER by \\(0.7\\%\\) and \\(1.7\\%\\), respectively. Moreover, the WER of the enhanced beamformed speech from ReVISE is only \\(4.4\\%\\) away from resynthesized clean speech: the target ReVISE is trained to predict. One can expect the gap to clean speech (\\(14.5\\%\\) WER) will be reduced if the quality of the SSL units improves." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Tab. 7 presents the subjective quality evaluation results for EasyCom. We first note that the quality of resynthesized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "target audio (4.13 MOS) is in fact higher than the target audio itself (3.76 MOS). This is because the P-TTS module is trained on the high-quality LJSpeech, which has better quality than the EasyCom audio recorded by the close-talking microphones, as the latter still contain mild background noise and overlapping speech. Similarly, the predicted audio from the proposed ReVISE model also delivers similar levels of audio quality (4.19 and 4.11 with ch2 and beamformed input, respectively), which are significantly better than the original distant recordings (2.95 and 2.67) and the baseline methods (2.95 and 2.39 from Demucs)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.365 + ], + "angle": 0, + "content": "The results suggest a crucial advantage of the proposed ReVISE model compared to previous studies: for ReVISE, the audio quality is not bounded by the enhancement training data (LRS3 and EasyCom), but determined by the quality of P-TTS training data. In contrast, prior works such as SVTS or VisualVoice could only produce audio that is as good as the enhancement target." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.374, + 0.627, + 0.389 + ], + "angle": 0, + "content": "5.8. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.519 + ], + "angle": 0, + "content": "We see from Tabs. 1 to 4 that while ReVISE outperforms or is on par with baseline methods on intelligibility, quality, and synchronization, it performs much worse than SVTS, Demucs, and VisualVoice on recovering low-level details. This is because ReVISE does not focus on reconstructing the exact reference signal; moreover, ReVISE does not aim to infer the speaker's voice either since the SSL units are shown to encode very little speaker information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.655 + ], + "angle": 0, + "content": "In fact, it is not a deficiency that the proposed ReVISE model does not reconstruct the reference signal exactly. As shown in Tab. 7, the quality of the reference signal may be mediocre for real world datasets such as EasyCom. In that scenario, reconstructing the exact reference signal would lead to inferior performance compared to the proposed approach, where the training data for P-AVSR and P-TTS are decoupled, such that higher quality data can be used for the unit-to-speech module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.662, + 0.682 + ], + "angle": 0, + "content": "5.9. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conduct ablation studies to evaluate the importance of pre-training P-AVSR, P-AVSR model size, selection of audio SSL units, and visual input. WER are reported here because intelligibility exhibits the highest variation across models reported earlier. Tab. 8 compares different SSL speech units on two tasks: clean speech resynthesis and video-to-speech generation. The two alternative types of units are derived from the BASE AV-HuBERT model trained on LRS3+VoxCeleb2 [49] and the BASE HuBERT model trained on Librispeech [23]. The corresponding P-TTS model are also trained on the same LJSpeech dataset. We see that performance on the two tasks are correlated, where units that loss less content information (lower Resyn WER) are better prediction targets for the P-AVSR model (lower" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.518, + 0.938 + ], + "angle": 0, + "content": "18801" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.155 + ], + "angle": 0, + "content": "
video-to-speech\nWER↓speech inpainting\n20%WER↓\n30%40%speech denoising\n1v1 1lvl 2lvl 3lvl 4source separation\nWER↓Avg.↓
lvl 1lvl 2lvl 3lvl 4
Separate ReVISE33.9%14.9%18.1%19.2%9.4%9.7%11.7%20.5%9.9%10.2%11.4%15.7%19.0%
Universal ReVISE34.5%14.9%17.9%19.2%8.7%9.4%11.5%20.3%9.1%9.7%10.9%15.5%18.9%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.149, + 0.164, + 0.82, + 0.179 + ], + "angle": 0, + "content": "Table 5. Comparing corruption-specific ReVISE with universal ReVISE on intelligibility measured by WER (\\%)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.203, + 0.466, + 0.272 + ], + "angle": 0, + "content": "
MethodModWER↓ (ch2) (dev/test)WER↓ (bf) (dev/test)
Tgt. audioA35.7% / 37.6%
Tgt. audio resynthesisA43.2% / 47.7%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.274, + 0.283, + 0.285 + ], + "angle": 0, + "content": "Audio-visual speech enhancement" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.285, + 0.468, + 0.345 + ], + "angle": 0, + "content": "
Inp. audioA74.2% / 87.5%60.7% / 71.5%
Demucs [12]A76.9% / 86.8%63.4% / 69.8%
ResynthesisA79.6% / 91.0%68.7% / 77.6%
ReVISE (Ours)AV50.3% / 55.0%47.6% / 52.1%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.355, + 0.47, + 0.397 + ], + "angle": 0, + "content": "Table 6. Audio-visual speech enhancement results on EasyCom (ch2: channel 2, bf: beamforming). Synchronization results are not reported because SyncNet fails even on clean reference \\( x_{a} \\)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.413, + 0.468, + 0.475 + ], + "angle": 0, + "content": "
MethodModMOS↑ (ch2)MOS↑ (bf)
Tgt. audioA3.76±0.04
Tgt. audio resynthesisA4.13±0.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.083, + 0.478, + 0.303, + 0.491 + ], + "angle": 0, + "content": "Audio-visual speech enhancement" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.491, + 0.472, + 0.556 + ], + "angle": 0, + "content": "
Inp. audioA2.95±0.042.67±0.03
Demucs [12]A2.95±0.042.39±0.03
ResynthesisA3.97±0.043.98±0.03
ReVISE (Ours)AV4.19±0.024.11±0.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.566, + 0.47, + 0.609 + ], + "angle": 0, + "content": "Table 7. Subjective quality evaluation of audio-visual speech enhancement results on EasyCom test set (ch2: channel 2, bf: beamforming)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.625, + 0.466, + 0.698 + ], + "angle": 0, + "content": "
UnitResyn WER↓V2S WER↓
AV-HuBERT (LRS3+VC2) [49]20.741.2
HuBERT (LS960) [23]17.435.2
HuBERT (VP+MLS+CV)10.633.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.707, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Table 8. Ablation studies on SSL unit choices. Clean audio resynthesis (Resyn) and video-to-speech (V2S) WERs are reported." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.764, + 0.469, + 0.809 + ], + "angle": 0, + "content": "V2S WER). Tab. 9 (Left) shows pre-training brings significant gains (38.9% for BASE and 43.1% for LARGE) and LARGE model performs better with a 7.4% WER reduction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Finally, we study the importance of visual input by comparing an audio-visual ReVISE with an audio-only version of it. We consider the universal speech regeneration model setup but remove video-to-speech data as it is incompatible to the audio-only model. Tab. 9 (Right) presents aggregated results averaged over testing splits for each task." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.203, + 0.65, + 0.271 + ], + "angle": 0, + "content": "
P-AVSRV2SWER↓
SizescratchPT
BASE81.042.9
LARGE78.635.5
" + }, + { + "type": "table", + "bbox": [ + 0.671, + 0.203, + 0.884, + 0.271 + ], + "angle": 0, + "content": "
ModWER↓
DenSepInpaintV2S
AV12.611.417.434.8
A29.239.844.6n/a
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.281, + 0.892, + 0.325 + ], + "angle": 0, + "content": "Table 9. (Left) Ablation studies on model sizes and pre-training. Performance on video-to-speech is reported. (Right) Comparison of ReVISE and its audio-only counterpart." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.525 + ], + "angle": 0, + "content": "We observe that the model using both audio and video as input outperform the counterpart consistently with a large margin. Specifically, the level of degradation varies substantially across task: denoising is least effected (16.6%), followed by inpainting (27.2%) and separation (28.4%) — this shows that models rely heavily on visual information to determine the target speaker as well as infill the missing information from dropped frames. Last but not least, we note that the audio-visual ReVISE perform decently on video-to-speech synthesis despite not being trained on the task at all, suggesting zero-shot generalization to unseen distortion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.546, + 0.62, + 0.563 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.727 + ], + "angle": 0, + "content": "This paper presents ReVISE, a novel paradigm for audiovisual speech regeneration that is universal and benefits greatly from the recent advances in self-supervised speech pre-training. Empirical studies demonstrate effectiveness of ReVISE on a popular benchmark with synthetic noise (LRS3) as well as on a conversational benchmark with real noisy data collected from extremely challenging acoustic conditions (EasyCom). In particular, audio enhanced by ReVISE is significantly more intelligible and of higher quality compared to those from the previous work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.789 + ], + "angle": 0, + "content": "While this paper studies universal regeneration, it only concerns audio but not video distortion. For future work, we hope to study more general multimodal speech regeneration where the model can recover distortion in both modalities." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.812, + 0.661, + 0.83 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The authors thank Rodrigo Schonburg for sharing SVTS samples for evaluations, thank Ruohan Gao for the assistance on VisualVoice code, and thank Stavros Petridis and Anurag Kumar for helpful discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.52, + 0.938 + ], + "angle": 0, + "content": "18802" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Amir Adler, Valentin Emiya, Maria G Jafari, Michael Elad, Rémi Gribonval, and Mark D Plumbley. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 283-292, 2019. 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "18805" + } + ] +] \ No newline at end of file diff --git a/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_origin.pdf b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1399e42ee0d0ec39760f79df96a513173d3c9cd4 --- /dev/null +++ b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/4c656091-f78e-4996-8f21-a624cfc397a6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ff0eaaf52d41628c5beff4aa6e6d5d087a3372a975519b4ad79c0f54a7b34c8e +size 530288 diff --git a/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/full.md b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ffce59ed9fbf91e7b981eb3d79e3f365813dd698 --- /dev/null +++ b/2023/ReVISE_ Self-Supervised Speech Resynthesis With Visual Input for Universal and Generalized Speech Regeneration/full.md @@ -0,0 +1,297 @@ +# ReVISE: Self-Supervised Speech Resynthesis with Visual Input for Universal and Generalized Speech Regeneration + +Wei-Ning Hsu $^{1}$ , Tal Remez $^{1}$ , Bowen Shi $^{1,3}$ , Jacob Donley $^{2}$ , Yossi Adi $^{1,4}$ + +$^{1}$ FAIR, Meta AI Research $^{2}$ Meta Reality Labs Research + +$^{3}$ Toyota Technological Institute at Chicago $^{4}$ The Hebrew University of Jerusalem + +{wnhsu,talr,bshi,jdonley,adiyoss}@meta.com + +# Abstract + +Prior works on improving speech quality with visual input typically study each type of auditory distortion separately (e.g., separation, inpainting, video-to-speech) and present tailored algorithms. This paper proposes to unify these subjects and study Generalized Speech Regeneration, where the goal is not to reconstruct the exact reference clean signal, but to focus on improving certain aspects of speech while not necessarily preserving the rest such as voice. In particular, this paper concerns intelligibility, quality, and video synchronization. We cast the problem as audio-visual speech resynthesis, which is composed of two steps: pseudo audio-visual speech recognition (P-AVSR) and pseudo text-to-speech synthesis (P-TTS). P-AVSR and P-TTS are connected by discrete units derived from a self-supervised speech model. Moreover, we utilize self-supervised audio-visual speech model to initialize P-AVSR. The proposed model is coined ReVISE. ReVISE is the first high-quality model for in-the-wild video-to-speech synthesis and achieves superior performance on all LRS3 audio-visual regeneration tasks with a single model. To demonstrate its applicability in the real world, ReVISE is also evaluated on EasyCom, an audio-visual benchmark collected under challenging acoustic conditions with only 1.6 hours of training data. Similarly, ReVISE greatly suppresses noise and improves quality. Project page: https://wnhsu.github.io/ReVISE/. + +# 1. Introduction + +Unlike anechoic studio recordings, speech in-the-wild is rarely clean: outdoor recordings are corrupted with all sorts of natural and non-natural sounds like wind and traffic noise [6]. Speech recorded indoor often contains reverberation, mechanical noise, and overlapping speech from non-target speakers [54]. On top of those, recording devices and network may also introduce other types of dis + +![](images/d7344cb8f72e4c6716d9987492ba4b1071d9f06f3e4668e2270e759352fc1181.jpg) +Figure 1. Illustration of AVSE with various distortion. + +tortion, such as amplitude clipping, band-pass filtering, and package loss [1]. Distortion makes it hard for both human and machines to comprehend speech [10, 31]. Improving the quality and the intelligibility of corrupted speech is essential for assistive listening and robust speech processing. Generating clean speech signal based on its corrupted version is herein referred to as speech enhancement. + +In speech enhancement, one line of research uses visual speech to provide auxiliary information [14, 17, 19, 57], which is known as audio-visual speech enhancement. Audio-visual speech (e.g., talking-head videos) can be seen as a multimodal view of the speech. Since visual modality is immune to acoustic noise, combining both views enables more robust estimation of shared generating factors such as textual content. Meanwhile, despite sharing the same goal of recovering corrupted speech, prior work often treats enhancement from each type of distortion as a separate problem: speech denoising and dereverberation addresses additive and convolutive non-speech noises [17], speech separation focuses on speech noises that exhibit similar characteristics to the target speech [19], speech inpainting aims to recover dropped audio frames [38], and video-to-speech synthesis is the extreme case of inpainting where all the frames are dropped [15, 36]. As a result, algorithms designed for one type of distortion may not be effective for another. + +In this paper, we advocate a more holistic approach to audio-visual speech enhancement, where an algorithm + +should be evaluated on all types of distortion, and a single model should also be effective on all types of corrupted data, shifting from building distortion-specific models to a universal model. Following [48], we coin the concept universal speech enhancement. In turn, we also argue that exact reconstruction of the reference clean speech is not an appropriate objective especially when the level of distortion is high. To address the issue, we propose to relax the objective and solve the generalized speech regeneration (GSR) problem: instead of focusing on exact reconstruction and measuring metrics like signal-to-noise ratios (SNRs), the goal of GSR is to enhance a predefined set of attributes, such as content intelligibility that can be measured by word error rates (WERs). In contrast, the model does not need to preserve other attributes. + +This paper focuses on recovering intelligibility, synchronicity and quality. The task of improving those could be broken down into two steps: predicting the frame-level content and synthesizing high quality audio from it. Inspired by the resemblance to audio-visual speech recognition and speech synthesis, we propose ReVISE, short for Resynthesis with Visual Input for Speech REgeneration. ReVISE is composed of a pseudo audio-visual speech recognition model (P-AVSR) and a pseudo text-to-speech synthesis model (P-TTS); instead of using text as the output/input of the two models, self-supervised speech units that encode speech content [23, 44] are adopted to bridge them, making the system free of text supervision. Furthermore, observing the gain on speech recognition brought by self-supervised learning, we also initialize the P-AVSR with a self-supervised audio-visual speech model, AV-HuBERT [49], which significantly improves the performance, especially on low-resource setups. + +To demonstrate the universality and compare with the literature, we construct four types of corrupted speech using Lip-reading Sentences 3 (LRS3) [2] and AudioSet [20], including audio-visual denoising, separation, inpainting, and video-to-speech. Results suggest that ReVISE is the first model capable of high-quality in-the-wild video-to-speech synthesis, while prior models fail to produce intelligible content [21] or generate low-quality audio for in-the-wild videos [36]. Compared to a strong masking-based method [19] on denoising and separation, ReVISE achieves comparable performance on mid-/high-SNR conditions (0-20dB), and are significantly stronger on lower SNR conditions, reducing WERs by up to $37.5\%$ absolute and improving MOS by up to 1.09. Finally, we also show that a single ReVISE model can tackle all four types of distortion with similar performance to distortion-specific models. To further show the data efficiency and effectiveness of ReVISE on real data, we evaluate it on EasyCom [13], an audio-visual speech dataset addressing the cocktail party problem which contains clean close-talking recordings and + +noisy distant recordings with background noise, loud interfering speech, and room reverberation. Results show that ReVISE still shines in this challenging setup, reducing WER by up to $32\%$ while other methods fail. + +# 2. Background + +# 2.1. Audio-visual speech enhancement tasks + +In general, audio-visual speech enhancement is the task of improving the quality of corrupted speech $\tilde{x}_a$ given its corresponding talking head video $x_v$ . During training, tuples of $(\tilde{x}_a,x_v,x_a)$ are provided where $x_{a}$ is the reference clean speech. The tasks are further divided depending on the type of distortion applied to $\tilde{x}_a$ : speech denoising and dereverberation considers $\tilde{x}_a[t] = x_a[t]*h[t] + n[t]$ with impulse response $h$ and additive noise $n$ ( $t$ indexes discrete time steps). Source separation considers $\tilde{x}_a[t] = x_a[t] + x_a'[t]$ where $x_{a}^{\prime}$ is an interfering speech sampled from the same marginal distribution as $x_{a}$ . For these two subtasks, masking-based methods (in magnitude spectrogram domain [16, 41], complex spectrogram domain [14, 19, 55], or on learned basis [33, 34]) are widely adopted where the enhancement model $f$ predicts a mask $\hat{M} = f(\tilde{x}_a,x_v)$ . It is feasible because the target speech can be written as $X = M\cdot \tilde{X}$ where $X$ and $\tilde{X}$ are the clean and noisy speech in the target domain and $M$ is the ideal ratio mask. On the other hand, speech inpainting and video-to-speech synthesis considers $\tilde{x}_a[t] = m[t]\cdot x_a[t]$ where $m[t]\in \{0,1\}$ for inpainting and $m[t] = 0$ for the latter. Masking-based methods are not feasible for these tasks. Hence, previous studies directly predict spectrogram [36, 38] or waveform [7, 37, 39] as $\hat{x}_a = f(\tilde{x}_a,x_v)$ and optimize the model with regression and adversarial losses. Nevertheless, previous models have not been able to generate realistic samples with in-the-wild datasets like LRS3, because these models are deterministic while the underlying mapping is highly stochastic, especially when there is a large portion of frames dropped. + +To accommodate general distortions, universal enhancement models have to adopt generation-based method [32, 43,45,48,50], otherwise they cannot handle distortions like package loss (i.e., inpainting). For the same reason, our proposed model is also generation-based. However, it differs from previous works in two main aspects. First, prior universal enhancement models are audio-based, which do not leverage auxiliary input like visual speech. Hence, source separation and enhancement from silence (i.e., cross-modal generation) are not attainable and hence have not been included. Second, regardless of the training objective (regression [40], adversarial [43,45,50], or score-matching [48]), previous universal models predict reference clean speech directly. We consider a different paradigm based on self-supervised speech resynthesis [44]: our model predicts a self-supervised representation $z = k(x_{a})$ of the reference + +clean speech. A separate model is used to convert $z$ back to audio, which is described in the next section. + +# 2.2. Self-supervised speech resynthesis + +Previous studies show that discretized Self Supervised Learned (SSL) speech features from the Hidden Unit BERT (HuBERT) model [23] encode mostly phonetic information and less about speaker and noise characteristics. HuBERT is pre-trained with a masked cluster prediction objective, where spans of input waveform are randomly masked and the model is asked to predict cluster assignment for those frames. Unlike VQ-VAE [52], HuBERT does not learn to encode all the factors; instead, it encodes information pertinent to inferring the unseen content, such as phonetic information. These properties make HuBERT units great candidates for replacing speech for text-free speech generative models, because they encode less nuisance variation and a model can predicts these units more easily compared to predicting speech directly [29, 30]. Such needs motivates the development of speech resynthesis models that convert units back to audio, because these generative models still have to produce speech as their final output. + +[44] proposed the first end-to-end model directly generating waveform from SSL units by adapting HiFi-GAN [27] which was originally designed as a vocoder converting spectrogram to waveform. The adpated HiFi-GAN takes SSL units, pitch, and speaker embedding as input, the latter two of which are added to capture variation of training data not encoded in the SSL units. Empirically, [30] demonstrates that speaker embedding and F0 can be removed if the model is trained on a high-quality single-speaker dataset. + +# 3. Method + +# 3.1. Generalized Speech Regeneration + +Without loss of generality, we assume that original speech $x_{a}$ and its auxiliary view $x_{v}$ are generated with a bijective mapping $g_{m,Y}$ as $x_{m} = g_{m,Y}(\{y_{i}\}_{i}), m \in \{a,v\}$ given a set of factors $Y = \{y_{i}\}_{i}$ (e.g., pitch, speed, textual content) sampled from $p_{Y}$ . Corrupted speech $\tilde{x}_{a}$ is generated with a corruption function $g_{d}$ as $\tilde{x}_{a} = g_{d}(x_{a},d)$ given $x_{a}$ and distortion parameter $d$ sampled from $p_{d}$ . Audiovisual speech enhancement can be seen as estimating $p(Y \mid g_{d}(x_{a},d), x_{v})$ . When the level of distortion is low, there are fewer $Y$ that can result in the same observed $\tilde{x}_{a}$ after corruption. Formulating it as a regression problem and measuring the performance of reconstructing all factors with metrics like SNR is reasonable. However, when the level of distortion is high, there exist multiple sets of $Y$ rendering the same noisy speech $\tilde{x}_{a}$ . Take video-to-speech as an example: while the content and the timing of each word can be more accurately inferred, the exact pitch is hard to infer from the video. In other words, $p(y_{i}|\tilde{x}_{a},x_{v})$ is more + +deterministic for some $y_{i}$ but not for the others. + +We argue that for these scenarios reconstructing the exact clean reference signal $x_{a}$ is an ill-posed problem. Instead, one should consider the generalized speech regeneration problem, where the goal is to generate an enhanced signal $\hat{x}_a = f(\tilde{x}_a,x_v)$ that is on the manifold of clean speech $g_{a,Y}(\cdot)$ (high quality) and preserves the factors of interest (partial faithfulness). Let $g_{a,Y,i}^{-1}$ be the inverse mapping from speech to factor $y_{i}$ , and $\{y_i\}_{i\in I^+}$ be the list of factors of interest (which should be a subset of factors that can be inferred from corrupted speech). Faithfulness is measured by the discrepancy between $g_{a,Y,i}^{-1}(\hat{x}_a)$ and $g_{a,Y,i}^{-1}(x_a)$ for $i\in I^{+}$ . In case of $y_{i}$ being the textual content, such discrepancy can be measured by the word error rate produced by an off-the-shelf speech recognizer for example. Quality can be measured by metrics commonly used for text-to-speech synthesis such as mean opinion scores, where human raters rate how realistic and clean the audio sounds regardless of the textual content. In this paper, we consider $\{y_i\}_{i\in I^+}$ to be textual content and timing (synchronization with the video) and do not address other factors such as voice, which is not of primary importance for communication. + +# 3.2. ReVISE + +We propose to solve the problem in two stages: (i) predicting $\{y_i\}_{i\in I^+}$ of the clean reference $x_{a}$ given $(\tilde{x}_a,x_v)$ , and (ii) resynthesizing speech conditioned on $\{y_i\}_{i\in I^+}$ . The two steps are handled by a pseudo audio-visual speech recognition module (P-AVSR) and a pseudo text-to-speech synthesis module (P-TTS), respectively, as shown in Fig. 2. The discrete SSL units derived from HuBERT [23] as described in Sec. 2.2 are used to represent $\{y_i\}_{i\in I^+}$ . Using SSL units have two main benefits: not restricted by text availability and better encoding of non-verbal information. + +The P-AVSR module performs a task very similar to speech recognition. Inspired by the recent success of self-supervised pre-training for audio [4, 23] and audio-visual speech recognition [49], we initialize P-AVSR with AV-HuBERT [49], an SSL model achieving state-of-the-art performance on audio, visual, and audio-visual speech recognition. It is composed of a video encoder and an audio encoder as the modality-specific front-end, followed by a stack of transformer layers as the shared back-end taking concatenated audio and video features as input (Fig. 2 right). The model encodes waveform into features at a frame rate of $25\mathrm{Hz}$ , while the SSL unit from HuBERT are encoded at $50\mathrm{Hz}$ . To match the rate, a lightweight transposed convolution layer followed by a softmax layer is added as the prediction head, which is randomly initialized. The P-AVSR module is trained with a cross-entropy loss $L = \sum_{t}\sum_{j = 1}^{C}z_{t}^{j}\log f_{t}^{j}(\tilde{x}_{a},x_{v})$ , where $\mathbf{z}_t$ denotes the one-hot discrete unit label of the $t$ -th frame, $f_{t}(\tilde{x}_{a},x_{v})$ is the predicted distribution over discrete units from the en + +![](images/83160bc853f3890e42cf950316a80228ed90c7ac5945cbe8c2703f967b5a7ce8.jpg) +Figure 2. Model diagram. + +hancer for the $t$ -th frame and C unit vocabulary size. + +We use the unit HiFi-GAN described in Sec. 2.2 for converting predicted $z$ into speech, which aims to faithfully produce the content and timing encoded in units. In fact, P-TTS can be trained with a different dataset from P-AVSR and this dataset determines the audio quality and the voice of ReVISE. With privacy consideration in mind, we use a high quality single speaker dataset with the speaker's consent to train this model. Consequently, ReVISE does not preserve voice and other fine-grained details and could generate speech of even higher quality than the original speech. Note that the P-TTS can be easily extended following [44]. + +# 4. Experimental Setup + +# 4.1. Datasets + +We consider two datasets for our experiments. The first one is Lip Reading Sentences 3 (LRS3) [2], which is a clean dataset based on TED talk videos. It contains 433 hours of audio-visual speech data and their corresponding text transcripts. Following prior work on speech enhancement, speech data are artificially corrupted to simulate enhancement tasks. Four tasks are created: (i) Speech denoising: in which we artificially mix a clean speech signal with a noise sample using randomly sampled Signal-to-Noise Ratio (SNR) in the range of [-20,20]. Noisy samples were selected from AudioSet [20]; (ii) Speech source separation: in which we follow a similar procedure to the speech denoising setup but instead of mixing the speech signal with a noisy sample, we mix it with another speech signal produced by a different speaker; (iii) Speech inpaiting: under this setup we randomly dropped (i.e., zero out) spans of $s \in \{20,30,40\}$ frames, with probability $p \in \{0.3,0.4,0.5\}$ . Each frame corresponds to 20ms, hence in case $s = 20$ we masked 400ms of audio. This process + +can be seen as a packet loss simulation; and (iv) Video-to-speech synthesis: in this setup we use the LRS3 dataset without any augmentations, where our goal is to synthesize the audio given a silent video only. + +The second data is Easy Communications (Easy-Com) dataset [13], which includes real-life noisy speech and is designed to study the cocktail party problem in conversational augmented reality. We preprocess the data using official time-aligned transcripts and crop image ROIs based on lip bounding boxes, resulting in 1.64/0.59/0.35 hours for train-valid/test splits. The dataset is challenging due to motion blur, barrel distortion, interfering speech, noise, and reverberation1. Close-talking microphones are used for clean reference speech, and beamformed audio is used as model input, following [5,13,18]. ReVISE is trained using merged audio from all six channels, including close-talking microphone audio. More details can be found in the Appendix. + +# 4.2. Model + +SSL speech tokenizer We use a BASE HuBERT model which is composed of a convolutional encoder and 12 Transformer layers. Each layer has embedding dimension of 768, feed-forward layer dimension of 3072, and 12 self-attention heads. The model is pre-trained for three iterations on 32 GPUs with 400K updates per iteration, using clusters of MFCC/6-th layer feature from iteration 1/9-th layer feature from iteration 2 as the target, with a codebook size of 100/500/1000, respectively, following the recipe of [30]. A total of 221K hours of unlabeled speech data combining multilingual Librispeech [46], Common Voice [3], and VoxPopuli [53] in eight languages (En, Es, Fr, De, Nl, It, Pl, Pt) are used for pre-training. The final SSL units $z$ used in ReVISE are generated by clustering the third iteration feature at the last layer with a codebook size of 2000 with K-means. + +P-TTS We use the unit HiFi-GAN described in Sec. 2.2. The model is trained for 400K updates on 8 GPUs on the LJSpeech [25] dataset resampled to $16\mathrm{kHz}$ to match the sample rate of other datasets. Similar to [30], F0 and speaker embedding are not used. + +P-AVSR We use the LARGE AV-HuBERT model by default from [49]. It takes video and/or audio as input, where video is head-crop image frames at 25fps, and audio is 23-dimensional Mel filterbank sequence (FBank) computed with a 10ms frame shift and stacked every four frames to match the video. The video encoder is a ResNet-18 [35] model, while the audio-encoder is simply a linear projection. The features are concatenated frame-by-frame and passed to a stack of 24 Transformer layers, which has embedding and feed-forward layer dimension of 1024 and + +4096 with 16 attention heads. For all but EasyCom experiments we use the publicly available checkpoints from [49] that were pre-trained on LRS3 and filtered VoxCeleb2 for initialization. For Easycom, a u-HuBERT model [24] pretrained additionally with Librilight [26] is used for initialization, which improves upon using [49]. The up-sampling module is one transposed convolution layer with stride of 2, kernel size of 4, and 768 channels, followed by GeLU activation [22]. The P-AVSR models are fine-tuned on 8 GPUs for less than 45K updates. Detailed fine-tuning configurations for each task are presented in the appendix. + +# 4.3. Evaluation + +We evaluate the proposed model and baselines on the following axes: content, synchronization, quality, and low-level detail reconstruction. As discussed in Sec. 3.1, we focus on the first three axes, and the results for the last metric are included in the appendix for completeness. + +For content, we use the WER computed with a speech recognition model to measure the intelligibility quantitatively similar to [36, 37]. The public model from [56] is used, which reports a WER of $5.6\%$ on LRS3 test split and $35.7\%$ on the EasyCom close-talking validation set. For synchronization, following [21] we use SyncNet [9] metrics, the predicted temporal distance between audio and video (LSE-D) and the prediction's confidence (LSE-C) are averaged over the entire test set. For quality, we follow the tradition of text-to-speech synthesis evaluation and conduct subjective mean opinion score (MOS) studies with a scale from 1 to 5 and a 0.5 increment. We evaluate 50 randomly sampled files from the test set, where each sample was evaluated by at least 15 raters using the CrowdMOS package [47]. Finally, for reconstruction of low-level details as typically done in speech denoising studies, we include ESTOI [51] and Mel cepstral distortion (MCD) [28]. While MCD provides an estimate of the similarity of two signals by measuring the mel cepstra difference, ESTOI put more emphasis on speech properties. + +# 5. Results + +Quantitative results are presented in the section. We strongly recommend readers to watch the samples provided in the supplementary material for better understanding of the sample quality compared to the baselines. + +# 5.1. Ground truth and resynthesis performance + +For reference, we first evaluate reference clean speech (Tgt. audio) and resynthesized clean speech (Tgt. audio resynthesis) with the proposed metrics and report the results in Tab. 1. The gap between the two is an approximation of how much information is lost when tokenizing speech into SSL units. It shows that intelligibility, synchronization, and quality are all slightly degraded. As ReVISE + +
MethodContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio5.6%5.206.334.38±0.02--
Tgt. audio resynthesis10.6%5.026.404.16±0.0241.5910.01
Silent video to speech
SVTS-L, LRS381.5%5.076.462.12±0.0426.878.13
SVTS-L, LRS3+VoxEn67.4%5.536.002.23±0.0330.987.59
ReVISE (Ours)33.9%5.036.444.13±0.0228.5110.73
+ +Table 1. Full video-to-speech synthesis results on LRS3 test set. + +is trained to predict the tokens inferred from clean speech, if the ReVISE model have $100\%$ prediction accuracy then the performance will be identical to the "Tgt. audio resynthesis" row here. Hence, the performance on the resynthesized speech roughly upper-bounds that of the ReVISE model. + +# 5.2. Video-to-speech synthesis + +In Tab. 1, we compare ReVISE with SVTS [36],2 which is the state-of-the-art model on the video-to-speech synthesis task. SVTS is composed of a video-to-spectrogram predictor and a separately trained neural vocoder. Its video-to-spectrogram predictor is trained with a regression loss, which takes as input a lip video and a speaker embedding extracted from a pre-trained fixed speaker encoder. Speaker embedding is needed because voice cannot be accurately inferred from the video. The model demonstrate strong results on two constrained datasets (LRW [8] and GRID [11]) which contain isolated words and fixed-length sentences with limited word choices, respectively. + +As shown in Tab. 1, because the audio quality generated by SVTS is mediocre (2.12 and 2.23 MOS), these samples are not very intelligible by machines, reflected by the highWER $81.5\%$ and $67.4\%$ when trained on LRS3 and $\mathrm{LRS3 + VoxCeleb2}$ . In contrast, our proposed model generates much higher quality audio (4.13 MOS) and yields significantly lower WER $(33.9\%)$ . Through manual inspection, we found a confidence score above 5 and distance below 6 implies good synchronization on LRS3. All methods generate audio fairly synchronized to the video. + +# 5.3. Audio-visual speech inpainting + +We next evaluate ReVISE on the audio-visual speech inpainting task with three test splits, where $30\%$ , $40\%$ , and $50\%$ of the frames are dropped with dropped spans longer than 400ms. While there have been several works studying audio-based speech inpainting or audio-visual inpainting for music [58], [38] is the only work we are aware of studying the audio-visual setup. However, their model was only evaluated on the constrained GRID dataset, showing a phone error rate of $13.7\%$ . SVTS achieves a WER of $17.9\%$ , hinting that [38] is likely worse than SVTS even + +
MethodInp ModTestContWER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech inpainting
Inp. audioA30%44.1%4.377.0560.7536.54
40%53.5%4.017.3651.6944.71
50%60.3%3.787.6043.1652.82
DemucsA30%43.9%4.377.0459.4035.95
40%53.5%4.047.3450.5543.96
50%60.0%3.827.5742.2052.09
ResynthesisA30%51.2%4.207.1425.2711.57
40%60.1%3.947.3821.5511.91
50%66.3%3.687.6317.9712.09
ReVISE (Ours)AV30%14.9%5.016.4238.1510.23
40%18.1%4.996.4437.0510.31
50%19.2%5.046.4135.9910.33
+ +when having partial audio as input. Accordingly, we decide not to compare with [38] but compare with a publicly available strong generation-based audio enhancement model, Demucs [12], which was trained on DNS-Challenge, VCTK, WHAM, and WHAMR, containing 700hr of clean speech and 6,000hr of noise in total. In addition, we consider resynthesis as another baseline, which encodes and decodes the corrupted speech with the same SSL tokenizer and P-TTS model. + +"Inp. audio" row presents the results evaluated on the corrupted audio in Tab. 2. We see that intelligibility degrades (WER increases from $5.6\%$ to $60.3\%$ ) as the percentage of dropped frames increases, and so does synchronization (5.20 to 3.78 for confidence and 6.33 to 7.60 for distance). The two audio-based baselines are not effective, showing similar or even worse results compared to the corrupted samples before enhancement. The little gain from Demucs over the inputting-audio baseline shows that existing enhancement approaches fail to generalize to inpainting. In contrast, our proposed model is effective on improving both intelligibility and synchronization. The WER drops from $60.3\%$ to $19.2\%$ after regeneration when half of the audio is missing in the corrupted audio. Comparing enhancing from no audio at all (video-to-speech synthesis) with enhancing from observing half of the audio (inpainting, $50\%$ ), we observe a $14.7\%$ WER reduction ( $33.9\% \rightarrow 19.2\%$ ), showing that the model use the additional audio information effectively to improve content reconstruction. As for synchronization, ReVISE restore a similar level regardless of the percentage dropped. + +# 5.4. Audio-visual speech denoising + +Tab. 3 presents results of audio-visual speech denoising on four test splits: lvl 1-4, which contain noisy samples of SNR in [10, 20], [0, 10], [-10, 0], and [-20, -10]. In addition to the two audio-based baselines from the previous section, the proposed model is also compared with VisualVoice [19] in this and the next section, which is a state + +Table 2. Full speech inpainting results on LRS3 test set with ${30}\% /{40}\% /{50}\%$ of frames dropped. + +
MethodModTestContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio--5.6%5.206.334.36±0.018--
Audio-visual speech denoising
Inp. audioAlvl 17.8%4.666.772.95±0.0387.215.07
lvl 220.0%3.807.522.82±0.0369.938.27
lvl 363.9%2.418.682.79±0.0245.9111.27
lvl 487.7%1.549.392.71±0.0425.5513.47
ResynthesisAlvl 113.3%4.986.464.33±0.0241.1810.02
lvl 225.9%4.786.644.37±0.0239.1610.19
lvl 369.4%3.647.613.63±0.0225.7111.27
lvl 490.8%2.118.853.34±0.039.2012.56
Demucs [12]Alvl 16.9%5.156.383.58±0.0492.593.73
lvl 215.1%4.956.573.63±0.0385.614.81
lvl 348.0%4.147.283.36±0.0365.946.81
lvl 481.3%2.438.752.89±0.0431.5210.25
VisualVoice [19]AVlvl 16.6%5.166.354.11±0.0392.203.89
lvl 28.8%5.196.353.94±0.0286.925.07
lvl 323.4%5.076.453.80±0.0274.166.45
lvl 458.0%4.536.863.25±0.0350.488.01
ReVISE (Ours)AVlvl 19.4%5.036.424.31±0.0241.2210.04
lvl 29.7%5.046.414.36±0.0240.9310.06
lvl 311.7%5.046.414.41±0.0239.7910.14
lvl 420.5%5.076.404.34±0.0235.8010.36
+ +Table 3. Full speech denoising results on LRS3 test set. SNR ranges for lvl $1/2/3/4$ are $[10,20]/[0,10]/[-10,0]/[-20,-10]$ dB. + +of-the-art model for audio-visual source separation and denoising. VisualVoice predicts a complex IRM given noisy audio, lip video, and speaker face image as input and the model is optimized with a combination of mask prediction loss, cross-modal matching loss (image and enhanced audio embeddings from the same speaker should be close) and consistency loss (embeddings of enhanced audio for the same speaker should be close). To have a fair comparison, we re-train VisualVoice models with the same dataset as ReVISE using a similar setup provided by the authors. We use the same public checkpoint for Demucs. + +In terms of intelligibility, we observe that the performance of resynthesizing corrupted audio is still bad. Demucs performs well for high SNR setup (lvl 1) but lags behind audio-visual models for the rest setups. VisualVoice achieves the best results on the [0, 20] dB SNR range, but ReVISE is much more robust to even a higher level of noise, reporting a WER of $20.5\%$ at lvl 4. Synchronization scores follow a similar trend to WERs in terms of ranking across models and test splits. Quality of the proposed model is significantly higher (4.31-4.41 MOS) than all baselines, and is on par with the reference clean speech (4.36 MOS). + +# 5.5. Audio-visual source separation + +Following Sec. 5.4, four noisy test sets are created with different levels of SNR. Comparing the speech source separation results in Tab. 4 and denoising results in Tab. 3, we observe that audio model (the public Demucs) performs worse with speech noise than with non-speech noise at the same SNR level. In contrast, audio-visual models report similar performance on the two tasks at high SNR, and better performance on separation at low SNR. These results suggest that it is easier to remove speech noise if the model have auxiliary information that it can use to identify the tar + +
MethodModTestCont WER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech separation
Inp. audioAlvl 115.7%4.736.7485.563.29
lvl 265.7%3.857.4865.525.95
lvl 3102.3%2.938.2740.978.67
lvl 4105.5%2.468.6622.3310.51
Demucs [12]Alvl 111.75.066.4689.683.76
lvl 255.74.107.2566.806.27
lvl 3101.22.778.4226.3210.22
lvl 4106.22.158.9510.1512.14
VisualVoice [19]AVlvl 16.2%5.136.3794.692.43
lvl 27.8%5.126.3990.293.36
lvl 315.3%4.916.5778.824.80
lvl 451.8%4.207.1753.847.02
ReVISE (Ours)AVlvl 19.9%5.056.4141.3410.05
lvl 210.2%5.056.4140.9010.07
lvl 311.4%5.056.4140.0710.11
lvl 415.7%5.046.4137.9710.21
+ +Table 4. Full source separation results on LRS3 test set. SNR ranges for lv1 $1/2/3/4$ are $[10,20]/[0,10]/[-10,0]/[-20,-10]$ dB. + +get speech. Comparing VisualVoice and ReVISE which are trained on the same data, it reveals a similar trend where ReVISE is still substantially better at low SNR. + +# 5.6. Universal audio-visual speech regeneration + +In this section, we build a single ReVISE model trained on all four types of distortion and compare it with corruption-specific models presented in earlier sections (Tab. 5) in terms of WER. Surprisingly, the universal model beats or matches the distortion-specific model on almost all tasks. The only exception is video-to-speech synthesis, on which the universal model is $0.5\%$ WER worse. + +# 5.7. AV regeneration on real data — EasyCom + +We next study how effective ReVISE on EasyCom, a real noisy dataset that is much more challenging than LRS3 and has much fewer hours of training data. Tab. 6 compares ReVISE with several baseline methods enhancing single channel speech (ch2) or beamformed speech (bf) from multi-channel sources. Note that we attempted to re-train VisualVoice on EasyCom but were not successful on getting any meaningful results, likely due to the lack of data as well as the difficulty. In addition, we use a P-AVSR model that takes lip crops instead of head crops as input for this dataset, which provides slightly better performance. Ablation studies are included in the Appendix. + +ReVISE substantially enhances the intelligibility of noisy speech in both setups (WER: $87.5\% \rightarrow 55.0\%$ on ch2 and $71.5\% \rightarrow 52.1\%$ on bf), while Demucs only managed to reduce the WER by $0.7\%$ and $1.7\%$ , respectively. Moreover, the WER of the enhanced beamformed speech from ReVISE is only $4.4\%$ away from resynthesized clean speech: the target ReVISE is trained to predict. One can expect the gap to clean speech ( $14.5\%$ WER) will be reduced if the quality of the SSL units improves. + +Tab. 7 presents the subjective quality evaluation results for EasyCom. We first note that the quality of resynthesized + +target audio (4.13 MOS) is in fact higher than the target audio itself (3.76 MOS). This is because the P-TTS module is trained on the high-quality LJSpeech, which has better quality than the EasyCom audio recorded by the close-talking microphones, as the latter still contain mild background noise and overlapping speech. Similarly, the predicted audio from the proposed ReVISE model also delivers similar levels of audio quality (4.19 and 4.11 with ch2 and beamformed input, respectively), which are significantly better than the original distant recordings (2.95 and 2.67) and the baseline methods (2.95 and 2.39 from Demucs). + +The results suggest a crucial advantage of the proposed ReVISE model compared to previous studies: for ReVISE, the audio quality is not bounded by the enhancement training data (LRS3 and EasyCom), but determined by the quality of P-TTS training data. In contrast, prior works such as SVTS or VisualVoice could only produce audio that is as good as the enhancement target. + +# 5.8. Limitations + +We see from Tabs. 1 to 4 that while ReVISE outperforms or is on par with baseline methods on intelligibility, quality, and synchronization, it performs much worse than SVTS, Demucs, and VisualVoice on recovering low-level details. This is because ReVISE does not focus on reconstructing the exact reference signal; moreover, ReVISE does not aim to infer the speaker's voice either since the SSL units are shown to encode very little speaker information. + +In fact, it is not a deficiency that the proposed ReVISE model does not reconstruct the reference signal exactly. As shown in Tab. 7, the quality of the reference signal may be mediocre for real world datasets such as EasyCom. In that scenario, reconstructing the exact reference signal would lead to inferior performance compared to the proposed approach, where the training data for P-AVSR and P-TTS are decoupled, such that higher quality data can be used for the unit-to-speech module. + +# 5.9. Ablation studies + +We conduct ablation studies to evaluate the importance of pre-training P-AVSR, P-AVSR model size, selection of audio SSL units, and visual input. WER are reported here because intelligibility exhibits the highest variation across models reported earlier. Tab. 8 compares different SSL speech units on two tasks: clean speech resynthesis and video-to-speech generation. The two alternative types of units are derived from the BASE AV-HuBERT model trained on LRS3+VoxCeleb2 [49] and the BASE HuBERT model trained on Librispeech [23]. The corresponding P-TTS model are also trained on the same LJSpeech dataset. We see that performance on the two tasks are correlated, where units that loss less content information (lower Resyn WER) are better prediction targets for the P-AVSR model (lower + +
video-to-speech +WER↓speech inpainting +20%WER↓ +30%40%speech denoising +1v1 1lvl 2lvl 3lvl 4source separation +WER↓Avg.↓
lvl 1lvl 2lvl 3lvl 4
Separate ReVISE33.9%14.9%18.1%19.2%9.4%9.7%11.7%20.5%9.9%10.2%11.4%15.7%19.0%
Universal ReVISE34.5%14.9%17.9%19.2%8.7%9.4%11.5%20.3%9.1%9.7%10.9%15.5%18.9%
+ +Table 5. Comparing corruption-specific ReVISE with universal ReVISE on intelligibility measured by WER (\%). + +
MethodModWER↓ (ch2) (dev/test)WER↓ (bf) (dev/test)
Tgt. audioA35.7% / 37.6%
Tgt. audio resynthesisA43.2% / 47.7%
+ +Audio-visual speech enhancement + +
Inp. audioA74.2% / 87.5%60.7% / 71.5%
Demucs [12]A76.9% / 86.8%63.4% / 69.8%
ResynthesisA79.6% / 91.0%68.7% / 77.6%
ReVISE (Ours)AV50.3% / 55.0%47.6% / 52.1%
+ +Table 6. Audio-visual speech enhancement results on EasyCom (ch2: channel 2, bf: beamforming). Synchronization results are not reported because SyncNet fails even on clean reference $x_{a}$ . + +
MethodModMOS↑ (ch2)MOS↑ (bf)
Tgt. audioA3.76±0.04
Tgt. audio resynthesisA4.13±0.03
+ +Audio-visual speech enhancement + +
Inp. audioA2.95±0.042.67±0.03
Demucs [12]A2.95±0.042.39±0.03
ResynthesisA3.97±0.043.98±0.03
ReVISE (Ours)AV4.19±0.024.11±0.04
+ +Table 7. Subjective quality evaluation of audio-visual speech enhancement results on EasyCom test set (ch2: channel 2, bf: beamforming). + +
UnitResyn WER↓V2S WER↓
AV-HuBERT (LRS3+VC2) [49]20.741.2
HuBERT (LS960) [23]17.435.2
HuBERT (VP+MLS+CV)10.633.9
+ +V2S WER). Tab. 9 (Left) shows pre-training brings significant gains (38.9% for BASE and 43.1% for LARGE) and LARGE model performs better with a 7.4% WER reduction. + +Finally, we study the importance of visual input by comparing an audio-visual ReVISE with an audio-only version of it. We consider the universal speech regeneration model setup but remove video-to-speech data as it is incompatible to the audio-only model. Tab. 9 (Right) presents aggregated results averaged over testing splits for each task. + +Table 8. Ablation studies on SSL unit choices. Clean audio resynthesis (Resyn) and video-to-speech (V2S) WERs are reported. + +
P-AVSRV2SWER↓
SizescratchPT
BASE81.042.9
LARGE78.635.5
+ +
ModWER↓
DenSepInpaintV2S
AV12.611.417.434.8
A29.239.844.6n/a
+ +Table 9. (Left) Ablation studies on model sizes and pre-training. Performance on video-to-speech is reported. (Right) Comparison of ReVISE and its audio-only counterpart. + +We observe that the model using both audio and video as input outperform the counterpart consistently with a large margin. Specifically, the level of degradation varies substantially across task: denoising is least effected (16.6%), followed by inpainting (27.2%) and separation (28.4%) — this shows that models rely heavily on visual information to determine the target speaker as well as infill the missing information from dropped frames. Last but not least, we note that the audio-visual ReVISE perform decently on video-to-speech synthesis despite not being trained on the task at all, suggesting zero-shot generalization to unseen distortion. + +# 6. Conclusion + +This paper presents ReVISE, a novel paradigm for audiovisual speech regeneration that is universal and benefits greatly from the recent advances in self-supervised speech pre-training. Empirical studies demonstrate effectiveness of ReVISE on a popular benchmark with synthetic noise (LRS3) as well as on a conversational benchmark with real noisy data collected from extremely challenging acoustic conditions (EasyCom). In particular, audio enhanced by ReVISE is significantly more intelligible and of higher quality compared to those from the previous work. + +While this paper studies universal regeneration, it only concerns audio but not video distortion. For future work, we hope to study more general multimodal speech regeneration where the model can recover distortion in both modalities. + +# Acknowledgement + +The authors thank Rodrigo Schonburg for sharing SVTS samples for evaluations, thank Ruohan Gao for the assistance on VisualVoice code, and thank Stavros Petridis and Anurag Kumar for helpful discussions. + +# References + +[1] Amir Adler, Valentin Emiya, Maria G Jafari, Michael Elad, Rémi Gribonval, and Mark D Plumbley. Audio inpainting. IEEE Transactions on Audio, Speech, and Language Processing, 20(3):922-932, 2011. 1 +[2] Triantafyllos Afouras, Joon Son Chung, and Andrew Zisserman. Lrs3-ted: a large-scale dataset for visual speech recognition. arXiv preprint arXiv:1809.00496, 2018. 2, 4 +[3] Rosana Ardila, Megan Branson, Kelly Davis, Michael Hen-cretty, Michael Kohler, Josh Meyer, Reuben Morais, Lindsay Saunders, Francis M Tyers, and Gregor Weber. 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Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": "Unlike anechoic studio recordings, speech in-the-wild is rarely clean: outdoor recordings are corrupted with all sorts of natural and non-natural sounds like wind and traffic noise [6]. Speech recorded indoor often contains reverberation, mechanical noise, and overlapping speech from non-target speakers [54]. On top of those, recording devices and network may also introduce other types of dis" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 247, + 544, + 340 + ], + "blocks": [ + { + "bbox": [ + 310, + 247, + 544, + 340 + ], + "lines": [ + { + "bbox": [ + 310, + 247, + 544, + 340 + ], + "spans": [ + { + "bbox": [ + 310, + 247, + 544, + 340 + ], + "type": "image", + "image_path": "d7344cb8f72e4c6716d9987492ba4b1071d9f06f3e4668e2270e759352fc1181.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 350, + 524, + 361 + ], + "lines": [ + { + "bbox": [ + 326, + 350, + 524, + 361 + ], + "spans": [ + { + "bbox": [ + 326, + 350, + 524, + 361 + ], + "type": "text", + "content": "Figure 1. Illustration of AVSE with various distortion." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 386, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 470 + ], + "type": "text", + "content": "tortion, such as amplitude clipping, band-pass filtering, and package loss [1]. Distortion makes it hard for both human and machines to comprehend speech [10, 31]. Improving the quality and the intelligibility of corrupted speech is essential for assistive listening and robust speech processing. Generating clean speech signal based on its corrupted version is herein referred to as speech enhancement." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 472, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 688 + ], + "type": "text", + "content": "In speech enhancement, one line of research uses visual speech to provide auxiliary information [14, 17, 19, 57], which is known as audio-visual speech enhancement. Audio-visual speech (e.g., talking-head videos) can be seen as a multimodal view of the speech. Since visual modality is immune to acoustic noise, combining both views enables more robust estimation of shared generating factors such as textual content. Meanwhile, despite sharing the same goal of recovering corrupted speech, prior work often treats enhancement from each type of distortion as a separate problem: speech denoising and dereverberation addresses additive and convolutive non-speech noises [17], speech separation focuses on speech noises that exhibit similar characteristics to the target speech [19], speech inpainting aims to recover dropped audio frames [38], and video-to-speech synthesis is the extreme case of inpainting where all the frames are dropped [15, 36]. As a result, algorithms designed for one type of distortion may not be effective for another." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we advocate a more holistic approach to audio-visual speech enhancement, where an algorithm" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "18795" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "should be evaluated on all types of distortion, and a single model should also be effective on all types of corrupted data, shifting from building distortion-specific models to a universal model. Following [48], we coin the concept universal speech enhancement. In turn, we also argue that exact reconstruction of the reference clean speech is not an appropriate objective especially when the level of distortion is high. To address the issue, we propose to relax the objective and solve the generalized speech regeneration (GSR) problem: instead of focusing on exact reconstruction and measuring metrics like signal-to-noise ratios (SNRs), the goal of GSR is to enhance a predefined set of attributes, such as content intelligibility that can be measured by word error rates (WERs). In contrast, the model does not need to preserve other attributes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 289, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 289, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 289, + 472 + ], + "type": "text", + "content": "This paper focuses on recovering intelligibility, synchronicity and quality. The task of improving those could be broken down into two steps: predicting the frame-level content and synthesizing high quality audio from it. Inspired by the resemblance to audio-visual speech recognition and speech synthesis, we propose ReVISE, short for Resynthesis with Visual Input for Speech REgeneration. ReVISE is composed of a pseudo audio-visual speech recognition model (P-AVSR) and a pseudo text-to-speech synthesis model (P-TTS); instead of using text as the output/input of the two models, self-supervised speech units that encode speech content [23, 44] are adopted to bridge them, making the system free of text supervision. Furthermore, observing the gain on speech recognition brought by self-supervised learning, we also initialize the P-AVSR with a self-supervised audio-visual speech model, AV-HuBERT [49], which significantly improves the performance, especially on low-resource setups." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "To demonstrate the universality and compare with the literature, we construct four types of corrupted speech using Lip-reading Sentences 3 (LRS3) [2] and AudioSet [20], including audio-visual denoising, separation, inpainting, and video-to-speech. Results suggest that ReVISE is the first model capable of high-quality in-the-wild video-to-speech synthesis, while prior models fail to produce intelligible content [21] or generate low-quality audio for in-the-wild videos [36]. Compared to a strong masking-based method [19] on denoising and separation, ReVISE achieves comparable performance on mid-/high-SNR conditions (0-20dB), and are significantly stronger on lower SNR conditions, reducing WERs by up to " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "37.5\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " absolute and improving MOS by up to 1.09. Finally, we also show that a single ReVISE model can tackle all four types of distortion with similar performance to distortion-specific models. To further show the data efficiency and effectiveness of ReVISE on real data, we evaluate it on EasyCom [13], an audio-visual speech dataset addressing the cocktail party problem which contains clean close-talking recordings and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "noisy distant recordings with background noise, loud interfering speech, and room reverberation. Results show that ReVISE still shines in this challenging setup, reducing WER by up to " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "32\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " while other methods fail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 134, + 385, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 134, + 385, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 134, + 385, + 148 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 155, + 512, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 155, + 512, + 167 + ], + "spans": [ + { + "bbox": [ + 306, + 155, + 512, + 167 + ], + "type": "text", + "content": "2.1. Audio-visual speech enhancement tasks" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": "In general, audio-visual speech enhancement is the task of improving the quality of corrupted speech " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{x}_a" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " given its corresponding talking head video " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "x_v" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": ". During training, tuples of " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "(\\tilde{x}_a,x_v,x_a)" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " are provided where " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " is the reference clean speech. The tasks are further divided depending on the type of distortion applied to " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{x}_a" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": ": speech denoising and dereverberation considers " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{x}_a[t] = x_a[t]*h[t] + n[t]" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " with impulse response " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " and additive noise " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " indexes discrete time steps). Source separation considers " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{x}_a[t] = x_a[t] + x_a'[t]" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "x_{a}^{\\prime}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " is an interfering speech sampled from the same marginal distribution as " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": ". For these two subtasks, masking-based methods (in magnitude spectrogram domain [16, 41], complex spectrogram domain [14, 19, 55], or on learned basis [33, 34]) are widely adopted where the enhancement model " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " predicts a mask " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\hat{M} = f(\\tilde{x}_a,x_v)" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": ". It is feasible because the target speech can be written as " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "X = M\\cdot \\tilde{X}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{X}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " are the clean and noisy speech in the target domain and " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " is the ideal ratio mask. On the other hand, speech inpainting and video-to-speech synthesis considers " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{x}_a[t] = m[t]\\cdot x_a[t]" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "m[t]\\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " for inpainting and " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "m[t] = 0" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " for the latter. Masking-based methods are not feasible for these tasks. Hence, previous studies directly predict spectrogram [36, 38] or waveform [7, 37, 39] as " + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\hat{x}_a = f(\\tilde{x}_a,x_v)" + }, + { + "bbox": [ + 304, + 174, + 547, + 521 + ], + "type": "text", + "content": " and optimize the model with regression and adversarial losses. Nevertheless, previous models have not been able to generate realistic samples with in-the-wild datasets like LRS3, because these models are deterministic while the underlying mapping is highly stochastic, especially when there is a large portion of frames dropped." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "text", + "content": "To accommodate general distortions, universal enhancement models have to adopt generation-based method [32, 43,45,48,50], otherwise they cannot handle distortions like package loss (i.e., inpainting). For the same reason, our proposed model is also generation-based. However, it differs from previous works in two main aspects. First, prior universal enhancement models are audio-based, which do not leverage auxiliary input like visual speech. Hence, source separation and enhancement from silence (i.e., cross-modal generation) are not attainable and hence have not been included. Second, regardless of the training objective (regression [40], adversarial [43,45,50], or score-matching [48]), previous universal models predict reference clean speech directly. We consider a different paradigm based on self-supervised speech resynthesis [44]: our model predicts a self-supervised representation " + }, + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "inline_equation", + "content": "z = k(x_{a})" + }, + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "text", + "content": " of the reference" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "text", + "content": "18796" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "clean speech. A separate model is used to convert " + }, + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": " back to audio, which is described in the next section." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 105, + 230, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 230, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 230, + 118 + ], + "type": "text", + "content": "2.2. Self-supervised speech resynthesis" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 123, + 288, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 123, + 288, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 123, + 288, + 339 + ], + "type": "text", + "content": "Previous studies show that discretized Self Supervised Learned (SSL) speech features from the Hidden Unit BERT (HuBERT) model [23] encode mostly phonetic information and less about speaker and noise characteristics. HuBERT is pre-trained with a masked cluster prediction objective, where spans of input waveform are randomly masked and the model is asked to predict cluster assignment for those frames. Unlike VQ-VAE [52], HuBERT does not learn to encode all the factors; instead, it encodes information pertinent to inferring the unseen content, such as phonetic information. These properties make HuBERT units great candidates for replacing speech for text-free speech generative models, because they encode less nuisance variation and a model can predicts these units more easily compared to predicting speech directly [29, 30]. Such needs motivates the development of speech resynthesis models that convert units back to audio, because these generative models still have to produce speech as their final output." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 340, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 449 + ], + "type": "text", + "content": "[44] proposed the first end-to-end model directly generating waveform from SSL units by adapting HiFi-GAN [27] which was originally designed as a vocoder converting spectrogram to waveform. The adpated HiFi-GAN takes SSL units, pitch, and speaker embedding as input, the latter two of which are added to capture variation of training data not encoded in the SSL units. Empirically, [30] demonstrates that speaker embedding and F0 can be removed if the model is trained on a high-quality single-speaker dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 459, + 104, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 104, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 104, + 471 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 228, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 228, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 228, + 491 + ], + "type": "text", + "content": "3.1. Generalized Speech Regeneration" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": "Without loss of generality, we assume that original speech " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " and its auxiliary view " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_{v}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " are generated with a bijective mapping " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "g_{m,Y}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_{m} = g_{m,Y}(\\{y_{i}\\}_{i}), m \\in \\{a,v\\}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " given a set of factors " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "Y = \\{y_{i}\\}_{i}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " (e.g., pitch, speed, textual content) sampled from " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_{Y}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": ". Corrupted speech " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{a}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " is generated with a corruption function " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "g_{d}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{a} = g_{d}(x_{a},d)" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " and distortion parameter " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " sampled from " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_{d}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": ". Audiovisual speech enhancement can be seen as estimating " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "p(Y \\mid g_{d}(x_{a},d), x_{v})" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": ". When the level of distortion is low, there are fewer " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " that can result in the same observed " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{a}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " after corruption. Formulating it as a regression problem and measuring the performance of reconstructing all factors with metrics like SNR is reasonable. However, when the level of distortion is high, there exist multiple sets of " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " rendering the same noisy speech " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{a}" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": ". Take video-to-speech as an example: while the content and the timing of each word can be more accurately inferred, the exact pitch is hard to infer from the video. In other words, " + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "inline_equation", + "content": "p(y_{i}|\\tilde{x}_{a},x_{v})" + }, + { + "bbox": [ + 46, + 498, + 288, + 715 + ], + "type": "text", + "content": " is more" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 498, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 498, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 498, + 84 + ], + "type": "text", + "content": "deterministic for some " + }, + { + "bbox": [ + 305, + 72, + 498, + 84 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 305, + 72, + 498, + 84 + ], + "type": "text", + "content": " but not for the others." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": "We argue that for these scenarios reconstructing the exact clean reference signal " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " is an ill-posed problem. Instead, one should consider the generalized speech regeneration problem, where the goal is to generate an enhanced signal " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\hat{x}_a = f(\\tilde{x}_a,x_v)" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " that is on the manifold of clean speech " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "g_{a,Y}(\\cdot)" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " (high quality) and preserves the factors of interest (partial faithfulness). Let " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "g_{a,Y,i}^{-1}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " be the inverse mapping from speech to factor " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i\\in I^+}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " be the list of factors of interest (which should be a subset of factors that can be inferred from corrupted speech). Faithfulness is measured by the discrepancy between " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "g_{a,Y,i}^{-1}(\\hat{x}_a)" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "g_{a,Y,i}^{-1}(x_a)" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "i\\in I^{+}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": ". In case of " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " being the textual content, such discrepancy can be measured by the word error rate produced by an off-the-shelf speech recognizer for example. Quality can be measured by metrics commonly used for text-to-speech synthesis such as mean opinion scores, where human raters rate how realistic and clean the audio sounds regardless of the textual content. In this paper, we consider " + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i\\in I^+}" + }, + { + "bbox": [ + 304, + 85, + 547, + 338 + ], + "type": "text", + "content": " to be textual content and timing (synchronization with the video) and do not address other factors such as voice, which is not of primary importance for communication." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 346, + 368, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 368, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 368, + 358 + ], + "type": "text", + "content": "3.2. ReVISE" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": "We propose to solve the problem in two stages: (i) predicting " + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i\\in I^+}" + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": " of the clean reference " + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "inline_equation", + "content": "(\\tilde{x}_a,x_v)" + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": ", and (ii) resynthesizing speech conditioned on " + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i\\in I^+}" + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": ". The two steps are handled by a pseudo audio-visual speech recognition module (P-AVSR) and a pseudo text-to-speech synthesis module (P-TTS), respectively, as shown in Fig. 2. The discrete SSL units derived from HuBERT [23] as described in Sec. 2.2 are used to represent " + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i\\in I^+}" + }, + { + "bbox": [ + 304, + 365, + 547, + 485 + ], + "type": "text", + "content": ". Using SSL units have two main benefits: not restricted by text availability and better encoding of non-verbal information." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": "The P-AVSR module performs a task very similar to speech recognition. Inspired by the recent success of self-supervised pre-training for audio [4, 23] and audio-visual speech recognition [49], we initialize P-AVSR with AV-HuBERT [49], an SSL model achieving state-of-the-art performance on audio, visual, and audio-visual speech recognition. It is composed of a video encoder and an audio encoder as the modality-specific front-end, followed by a stack of transformer layers as the shared back-end taking concatenated audio and video features as input (Fig. 2 right). The model encodes waveform into features at a frame rate of " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "25\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": ", while the SSL unit from HuBERT are encoded at " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "50\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": ". To match the rate, a lightweight transposed convolution layer followed by a softmax layer is added as the prediction head, which is randomly initialized. The P-AVSR module is trained with a cross-entropy loss " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "L = \\sum_{t}\\sum_{j = 1}^{C}z_{t}^{j}\\log f_{t}^{j}(\\tilde{x}_{a},x_{v})" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": " denotes the one-hot discrete unit label of the " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": "-th frame, " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "f_{t}(\\tilde{x}_{a},x_{v})" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": " is the predicted distribution over discrete units from the en" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "text", + "content": "18797" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 286, + 248 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 248 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 248 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 248 + ], + "type": "image", + "image_path": "83160bc853f3890e42cf950316a80228ed90c7ac5945cbe8c2703f967b5a7ce8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 119, + 259, + 215, + 270 + ], + "lines": [ + { + "bbox": [ + 119, + 259, + 215, + 270 + ], + "spans": [ + { + "bbox": [ + 119, + 259, + 215, + 270 + ], + "type": "text", + "content": "Figure 2. Model diagram." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 259, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 259, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 259, + 304 + ], + "type": "text", + "content": "hancer for the " + }, + { + "bbox": [ + 46, + 293, + 259, + 304 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 293, + 259, + 304 + ], + "type": "text", + "content": "-th frame and C unit vocabulary size." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 437 + ], + "type": "text", + "content": "We use the unit HiFi-GAN described in Sec. 2.2 for converting predicted " + }, + { + "bbox": [ + 46, + 304, + 287, + 437 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 304, + 287, + 437 + ], + "type": "text", + "content": " into speech, which aims to faithfully produce the content and timing encoded in units. In fact, P-TTS can be trained with a different dataset from P-AVSR and this dataset determines the audio quality and the voice of ReVISE. With privacy consideration in mind, we use a high quality single speaker dataset with the speaker's consent to train this model. Consequently, ReVISE does not preserve voice and other fine-grained details and could generate speech of even higher quality than the original speech. Note that the P-TTS can be easily extended following [44]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 448, + 165, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 165, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 165, + 462 + ], + "type": "text", + "content": "4. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 468, + 110, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 110, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 110, + 479 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": "We consider two datasets for our experiments. The first one is Lip Reading Sentences 3 (LRS3) [2], which is a clean dataset based on TED talk videos. It contains 433 hours of audio-visual speech data and their corresponding text transcripts. Following prior work on speech enhancement, speech data are artificially corrupted to simulate enhancement tasks. Four tasks are created: (i) Speech denoising: in which we artificially mix a clean speech signal with a noise sample using randomly sampled Signal-to-Noise Ratio (SNR) in the range of [-20,20]. Noisy samples were selected from AudioSet [20]; (ii) Speech source separation: in which we follow a similar procedure to the speech denoising setup but instead of mixing the speech signal with a noisy sample, we mix it with another speech signal produced by a different speaker; (iii) Speech inpaiting: under this setup we randomly dropped (i.e., zero out) spans of " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "s \\in \\{20,30,40\\}" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": " frames, with probability " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "p \\in \\{0.3,0.4,0.5\\}" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": ". Each frame corresponds to 20ms, hence in case " + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "inline_equation", + "content": "s = 20" + }, + { + "bbox": [ + 46, + 486, + 288, + 713 + ], + "type": "text", + "content": " we masked 400ms of audio. This process" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "can be seen as a packet loss simulation; and (iv) Video-to-speech synthesis: in this setup we use the LRS3 dataset without any augmentations, where our goal is to synthesize the audio given a silent video only." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 121, + 546, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 546, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 546, + 276 + ], + "type": "text", + "content": "The second data is Easy Communications (Easy-Com) dataset [13], which includes real-life noisy speech and is designed to study the cocktail party problem in conversational augmented reality. We preprocess the data using official time-aligned transcripts and crop image ROIs based on lip bounding boxes, resulting in 1.64/0.59/0.35 hours for train-valid/test splits. The dataset is challenging due to motion blur, barrel distortion, interfering speech, noise, and reverberation1. Close-talking microphones are used for clean reference speech, and beamformed audio is used as model input, following [5,13,18]. ReVISE is trained using merged audio from all six channels, including close-talking microphone audio. More details can be found in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 284, + 359, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 284, + 359, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 284, + 359, + 295 + ], + "type": "text", + "content": "4.2. Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 302, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 482 + ], + "type": "text", + "content": "SSL speech tokenizer We use a BASE HuBERT model which is composed of a convolutional encoder and 12 Transformer layers. Each layer has embedding dimension of 768, feed-forward layer dimension of 3072, and 12 self-attention heads. The model is pre-trained for three iterations on 32 GPUs with 400K updates per iteration, using clusters of MFCC/6-th layer feature from iteration 1/9-th layer feature from iteration 2 as the target, with a codebook size of 100/500/1000, respectively, following the recipe of [30]. A total of 221K hours of unlabeled speech data combining multilingual Librispeech [46], Common Voice [3], and VoxPopuli [53] in eight languages (En, Es, Fr, De, Nl, It, Pl, Pt) are used for pre-training. The final SSL units " + }, + { + "bbox": [ + 304, + 302, + 545, + 482 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 302, + 545, + 482 + ], + "type": "text", + "content": " used in ReVISE are generated by clustering the third iteration feature at the last layer with a codebook size of 2000 with K-means." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 559 + ], + "type": "text", + "content": "P-TTS We use the unit HiFi-GAN described in Sec. 2.2. The model is trained for 400K updates on 8 GPUs on the LJSpeech [25] dataset resampled to " + }, + { + "bbox": [ + 304, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "16\\mathrm{kHz}" + }, + { + "bbox": [ + 304, + 498, + 545, + 559 + ], + "type": "text", + "content": " to match the sample rate of other datasets. Similar to [30], F0 and speaker embedding are not used." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 574, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 694 + ], + "type": "text", + "content": "P-AVSR We use the LARGE AV-HuBERT model by default from [49]. It takes video and/or audio as input, where video is head-crop image frames at 25fps, and audio is 23-dimensional Mel filterbank sequence (FBank) computed with a 10ms frame shift and stacked every four frames to match the video. The video encoder is a ResNet-18 [35] model, while the audio-encoder is simply a linear projection. The features are concatenated frame-by-frame and passed to a stack of 24 Transformer layers, which has embedding and feed-forward layer dimension of 1024 and" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 545, + 713 + ], + "type": "text", + "content": "1We refer readers to the supplementary material to listen to the samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "18798" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "4096 with 16 attention heads. For all but EasyCom experiments we use the publicly available checkpoints from [49] that were pre-trained on LRS3 and filtered VoxCeleb2 for initialization. For Easycom, a u-HuBERT model [24] pretrained additionally with Librilight [26] is used for initialization, which improves upon using [49]. The up-sampling module is one transposed convolution layer with stride of 2, kernel size of 4, and 768 channels, followed by GeLU activation [22]. The P-AVSR models are fine-tuned on 8 GPUs for less than 45K updates. Detailed fine-tuning configurations for each task are presented in the appendix." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 210, + 121, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 121, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 121, + 221 + ], + "type": "text", + "content": "4.3. Evaluation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 289 + ], + "type": "text", + "content": "We evaluate the proposed model and baselines on the following axes: content, synchronization, quality, and low-level detail reconstruction. As discussed in Sec. 3.1, we focus on the first three axes, and the results for the last metric are included in the appendix for completeness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "text", + "content": "For content, we use the WER computed with a speech recognition model to measure the intelligibility quantitatively similar to [36, 37]. The public model from [56] is used, which reports a WER of " + }, + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "text", + "content": " on LRS3 test split and " + }, + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "inline_equation", + "content": "35.7\\%" + }, + { + "bbox": [ + 46, + 289, + 289, + 529 + ], + "type": "text", + "content": " on the EasyCom close-talking validation set. For synchronization, following [21] we use SyncNet [9] metrics, the predicted temporal distance between audio and video (LSE-D) and the prediction's confidence (LSE-C) are averaged over the entire test set. For quality, we follow the tradition of text-to-speech synthesis evaluation and conduct subjective mean opinion score (MOS) studies with a scale from 1 to 5 and a 0.5 increment. We evaluate 50 randomly sampled files from the test set, where each sample was evaluated by at least 15 raters using the CrowdMOS package [47]. Finally, for reconstruction of low-level details as typically done in speech denoising studies, we include ESTOI [51] and Mel cepstral distortion (MCD) [28]. While MCD provides an estimate of the similarity of two signals by measuring the mel cepstra difference, ESTOI put more emphasis on speech properties." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 537, + 100, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 100, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 100, + 550 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 605 + ], + "type": "text", + "content": "Quantitative results are presented in the section. We strongly recommend readers to watch the samples provided in the supplementary material for better understanding of the sample quality compared to the baselines." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 272, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 272, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 272, + 624 + ], + "type": "text", + "content": "5.1. Ground truth and resynthesis performance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "For reference, we first evaluate reference clean speech (Tgt. audio) and resynthesized clean speech (Tgt. audio resynthesis) with the proposed metrics and report the results in Tab. 1. The gap between the two is an approximation of how much information is lost when tokenizing speech into SSL units. It shows that intelligibility, synchronization, and quality are all slightly degraded. As ReVISE" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 71, + 547, + 147 + ], + "blocks": [ + { + "bbox": [ + 308, + 71, + 547, + 147 + ], + "lines": [ + { + "bbox": [ + 308, + 71, + 547, + 147 + ], + "spans": [ + { + "bbox": [ + 308, + 71, + 547, + 147 + ], + "type": "table", + "html": "
MethodContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio5.6%5.206.334.38±0.02--
Tgt. audio resynthesis10.6%5.026.404.16±0.0241.5910.01
Silent video to speech
SVTS-L, LRS381.5%5.076.462.12±0.0426.878.13
SVTS-L, LRS3+VoxEn67.4%5.536.002.23±0.0330.987.59
ReVISE (Ours)33.9%5.036.444.13±0.0228.5110.73
", + "image_path": "d9aa7c72a6f0557f1a7868e4ebbdea50686bca77afa3df6524589b2879ed1005.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 154, + 542, + 166 + ], + "lines": [ + { + "bbox": [ + 309, + 154, + 542, + 166 + ], + "spans": [ + { + "bbox": [ + 309, + 154, + 542, + 166 + ], + "type": "text", + "content": "Table 1. Full video-to-speech synthesis results on LRS3 test set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 186, + 547, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 547, + 248 + ], + "type": "text", + "content": "is trained to predict the tokens inferred from clean speech, if the ReVISE model have " + }, + { + "bbox": [ + 304, + 186, + 547, + 248 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 186, + 547, + 248 + ], + "type": "text", + "content": " prediction accuracy then the performance will be identical to the \"Tgt. audio resynthesis\" row here. Hence, the performance on the resynthesized speech roughly upper-bounds that of the ReVISE model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 255, + 448, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 448, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 448, + 269 + ], + "type": "text", + "content": "5.2. Video-to-speech synthesis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": "In Tab. 1, we compare ReVISE with SVTS [36],2 which is the state-of-the-art model on the video-to-speech synthesis task. SVTS is composed of a video-to-spectrogram predictor and a separately trained neural vocoder. Its video-to-spectrogram predictor is trained with a regression loss, which takes as input a lip video and a speaker embedding extracted from a pre-trained fixed speaker encoder. Speaker embedding is needed because voice cannot be accurately inferred from the video. The model demonstrate strong results on two constrained datasets (LRW [8] and GRID [11]) which contain isolated words and fixed-length sentences with limited word choices, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "content": "As shown in Tab. 1, because the audio quality generated by SVTS is mediocre (2.12 and 2.23 MOS), these samples are not very intelligible by machines, reflected by the highWER " + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "inline_equation", + "content": "81.5\\%" + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "inline_equation", + "content": "67.4\\%" + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "content": " when trained on LRS3 and " + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "inline_equation", + "content": "\\mathrm{LRS3 + VoxCeleb2}" + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "content": " . In contrast, our proposed model generates much higher quality audio (4.13 MOS) and yields significantly lower WER " + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "inline_equation", + "content": "(33.9\\%)" + }, + { + "bbox": [ + 304, + 418, + 546, + 538 + ], + "type": "text", + "content": " . Through manual inspection, we found a confidence score above 5 and distance below 6 implies good synchronization on LRS3. All methods generate audio fairly synchronized to the video." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 546, + 473, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 546, + 473, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 546, + 473, + 559 + ], + "type": "text", + "content": "5.3. Audio-visual speech inpainting" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": "We next evaluate ReVISE on the audio-visual speech inpainting task with three test splits, where " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": " of the frames are dropped with dropped spans longer than 400ms. While there have been several works studying audio-based speech inpainting or audio-visual inpainting for music [58], [38] is the only work we are aware of studying the audio-visual setup. However, their model was only evaluated on the constrained GRID dataset, showing a phone error rate of " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "13.7\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": ". SVTS achieves a WER of " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "17.9\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": ", hinting that [38] is likely worse than SVTS even" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 693, + 545, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 693, + 545, + 702 + ], + "spans": [ + { + "bbox": [ + 315, + 693, + 545, + 702 + ], + "type": "text", + "content": "2We obtained test set samples of SVTS from the authors for evaluation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "type": "text", + "content": "3https://sites.google.com/view/scalable-vts" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "text", + "content": "18799" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 286, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 286, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 286, + 198 + ], + "type": "table", + "html": "
MethodInp ModTestContWER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech inpainting
Inp. audioA30%44.1%4.377.0560.7536.54
40%53.5%4.017.3651.6944.71
50%60.3%3.787.6043.1652.82
DemucsA30%43.9%4.377.0459.4035.95
40%53.5%4.047.3450.5543.96
50%60.0%3.827.5742.2052.09
ResynthesisA30%51.2%4.207.1425.2711.57
40%60.1%3.947.3821.5511.91
50%66.3%3.687.6317.9712.09
ReVISE (Ours)AV30%14.9%5.016.4238.1510.23
40%18.1%4.996.4437.0510.31
50%19.2%5.046.4135.9910.33
", + "image_path": "42ff9d533a03c4efa14944ea40b514ce4f25264d379abf9d1eeff5b432a05b4d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 286, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 286, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 286, + 357 + ], + "type": "text", + "content": "when having partial audio as input. Accordingly, we decide not to compare with [38] but compare with a publicly available strong generation-based audio enhancement model, Demucs [12], which was trained on DNS-Challenge, VCTK, WHAM, and WHAMR, containing 700hr of clean speech and 6,000hr of noise in total. In addition, we consider resynthesis as another baseline, which encodes and decodes the corrupted speech with the same SSL tokenizer and P-TTS model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": "\"Inp. audio\" row presents the results evaluated on the corrupted audio in Tab. 2. We see that intelligibility degrades (WER increases from " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "60.3\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": ") as the percentage of dropped frames increases, and so does synchronization (5.20 to 3.78 for confidence and 6.33 to 7.60 for distance). The two audio-based baselines are not effective, showing similar or even worse results compared to the corrupted samples before enhancement. The little gain from Demucs over the inputting-audio baseline shows that existing enhancement approaches fail to generalize to inpainting. In contrast, our proposed model is effective on improving both intelligibility and synchronization. The WER drops from " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "60.3\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "19.2\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": " after regeneration when half of the audio is missing in the corrupted audio. Comparing enhancing from no audio at all (video-to-speech synthesis) with enhancing from observing half of the audio (inpainting, " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": "), we observe a " + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "14.7\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": " WER reduction (" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "inline_equation", + "content": "33.9\\% \\rightarrow 19.2\\%" + }, + { + "bbox": [ + 46, + 360, + 287, + 612 + ], + "type": "text", + "content": "), showing that the model use the additional audio information effectively to improve content reconstruction. As for synchronization, ReVISE restore a similar level regardless of the percentage dropped." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 622, + 211, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 211, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 211, + 635 + ], + "type": "text", + "content": "5.4. Audio-visual speech denoising" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Tab. 3 presents results of audio-visual speech denoising on four test splits: lvl 1-4, which contain noisy samples of SNR in [10, 20], [0, 10], [-10, 0], and [-20, -10]. In addition to the two audio-based baselines from the previous section, the proposed model is also compared with VisualVoice [19] in this and the next section, which is a state" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 47, + 206, + 286, + 228 + ], + "lines": [ + { + "bbox": [ + 47, + 206, + 286, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 286, + 228 + ], + "type": "text", + "content": "Table 2. Full speech inpainting results on LRS3 test set with " + }, + { + "bbox": [ + 47, + 206, + 286, + 228 + ], + "type": "inline_equation", + "content": "{30}\\% /{40}\\% /{50}\\%" + }, + { + "bbox": [ + 47, + 206, + 286, + 228 + ], + "type": "text", + "content": " of frames dropped." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 305, + 70, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 250 + ], + "type": "table", + "html": "
MethodModTestContWER↓SyncLSE-C↑LSE-D↓QualMOS↑Low-LevelESTOI ↑MCD ↓
Tgt. audio--5.6%5.206.334.36±0.018--
Audio-visual speech denoising
Inp. audioAlvl 17.8%4.666.772.95±0.0387.215.07
lvl 220.0%3.807.522.82±0.0369.938.27
lvl 363.9%2.418.682.79±0.0245.9111.27
lvl 487.7%1.549.392.71±0.0425.5513.47
ResynthesisAlvl 113.3%4.986.464.33±0.0241.1810.02
lvl 225.9%4.786.644.37±0.0239.1610.19
lvl 369.4%3.647.613.63±0.0225.7111.27
lvl 490.8%2.118.853.34±0.039.2012.56
Demucs [12]Alvl 16.9%5.156.383.58±0.0492.593.73
lvl 215.1%4.956.573.63±0.0385.614.81
lvl 348.0%4.147.283.36±0.0365.946.81
lvl 481.3%2.438.752.89±0.0431.5210.25
VisualVoice [19]AVlvl 16.6%5.166.354.11±0.0392.203.89
lvl 28.8%5.196.353.94±0.0286.925.07
lvl 323.4%5.076.453.80±0.0274.166.45
lvl 458.0%4.536.863.25±0.0350.488.01
ReVISE (Ours)AVlvl 19.4%5.036.424.31±0.0241.2210.04
lvl 29.7%5.046.414.36±0.0240.9310.06
lvl 311.7%5.046.414.41±0.0239.7910.14
lvl 420.5%5.076.404.34±0.0235.8010.36
", + "image_path": "a20df357d88e83be3d64a29941f5f531a046fef23fafd341d8e98254bab1e82b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "type": "text", + "content": "Table 3. Full speech denoising results on LRS3 test set. SNR ranges for lvl " + }, + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "type": "inline_equation", + "content": "1/2/3/4" + }, + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "type": "inline_equation", + "content": "[10,20]/[0,10]/[-10,0]/[-20,-10]" + }, + { + "bbox": [ + 305, + 259, + 545, + 282 + ], + "type": "text", + "content": " dB." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 303, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 434 + ], + "type": "text", + "content": "of-the-art model for audio-visual source separation and denoising. VisualVoice predicts a complex IRM given noisy audio, lip video, and speaker face image as input and the model is optimized with a combination of mask prediction loss, cross-modal matching loss (image and enhanced audio embeddings from the same speaker should be close) and consistency loss (embeddings of enhanced audio for the same speaker should be close). To have a fair comparison, we re-train VisualVoice models with the same dataset as ReVISE using a similar setup provided by the authors. We use the same public checkpoint for Demucs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 435, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 567 + ], + "type": "text", + "content": "In terms of intelligibility, we observe that the performance of resynthesizing corrupted audio is still bad. Demucs performs well for high SNR setup (lvl 1) but lags behind audio-visual models for the rest setups. VisualVoice achieves the best results on the [0, 20] dB SNR range, but ReVISE is much more robust to even a higher level of noise, reporting a WER of " + }, + { + "bbox": [ + 304, + 435, + 545, + 567 + ], + "type": "inline_equation", + "content": "20.5\\%" + }, + { + "bbox": [ + 304, + 435, + 545, + 567 + ], + "type": "text", + "content": " at lvl 4. Synchronization scores follow a similar trend to WERs in terms of ranking across models and test splits. Quality of the proposed model is significantly higher (4.31-4.41 MOS) than all baselines, and is on par with the reference clean speech (4.36 MOS)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "text", + "content": "5.5. Audio-visual source separation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Following Sec. 5.4, four noisy test sets are created with different levels of SNR. Comparing the speech source separation results in Tab. 4 and denoising results in Tab. 3, we observe that audio model (the public Demucs) performs worse with speech noise than with non-speech noise at the same SNR level. In contrast, audio-visual models report similar performance on the two tasks at high SNR, and better performance on separation at low SNR. These results suggest that it is easier to remove speech noise if the model have auxiliary information that it can use to identify the tar" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "text", + "content": "18800" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 276, + 216 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 276, + 216 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 276, + 216 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 276, + 216 + ], + "type": "table", + "html": "
MethodModTestCont WER↓SyncLow-Level
LSE-C↑LSE-D↓ESTOI ↑MCD ↓
Audio-visual speech separation
Inp. audioAlvl 115.7%4.736.7485.563.29
lvl 265.7%3.857.4865.525.95
lvl 3102.3%2.938.2740.978.67
lvl 4105.5%2.468.6622.3310.51
Demucs [12]Alvl 111.75.066.4689.683.76
lvl 255.74.107.2566.806.27
lvl 3101.22.778.4226.3210.22
lvl 4106.22.158.9510.1512.14
VisualVoice [19]AVlvl 16.2%5.136.3794.692.43
lvl 27.8%5.126.3990.293.36
lvl 315.3%4.916.5778.824.80
lvl 451.8%4.207.1753.847.02
ReVISE (Ours)AVlvl 19.9%5.056.4141.3410.05
lvl 210.2%5.056.4140.9010.07
lvl 311.4%5.056.4140.0710.11
lvl 415.7%5.046.4137.9710.21
", + "image_path": "b190f77a93c54100e45cd6978479055ad1ed74b04f0ec19544abcc29aa657c0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "type": "text", + "content": "Table 4. Full source separation results on LRS3 test set. SNR ranges for lv1 " + }, + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "type": "inline_equation", + "content": "1/2/3/4" + }, + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "type": "inline_equation", + "content": "[10,20]/[0,10]/[-10,0]/[-20,-10]" + }, + { + "bbox": [ + 47, + 224, + 287, + 247 + ], + "type": "text", + "content": " dB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 267, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 267, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 267, + 287, + 304 + ], + "type": "text", + "content": "get speech. Comparing VisualVoice and ReVISE which are trained on the same data, it reveals a similar trend where ReVISE is still substantially better at low SNR." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 310, + 271, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 310, + 271, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 310, + 271, + 324 + ], + "type": "text", + "content": "5.6. Universal audio-visual speech regeneration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 329, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 287, + 413 + ], + "type": "text", + "content": "In this section, we build a single ReVISE model trained on all four types of distortion and compare it with corruption-specific models presented in earlier sections (Tab. 5) in terms of WER. Surprisingly, the universal model beats or matches the distortion-specific model on almost all tasks. The only exception is video-to-speech synthesis, on which the universal model is " + }, + { + "bbox": [ + 46, + 329, + 287, + 413 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 329, + 287, + 413 + ], + "type": "text", + "content": " WER worse." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 420, + 266, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 266, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 266, + 434 + ], + "type": "text", + "content": "5.7. AV regeneration on real data — EasyCom" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": "We next study how effective ReVISE on EasyCom, a real noisy dataset that is much more challenging than LRS3 and has much fewer hours of training data. Tab. 6 compares ReVISE with several baseline methods enhancing single channel speech (ch2) or beamformed speech (bf) from multi-channel sources. Note that we attempted to re-train VisualVoice on EasyCom but were not successful on getting any meaningful results, likely due to the lack of data as well as the difficulty. In addition, we use a P-AVSR model that takes lip crops instead of head crops as input for this dataset, which provides slightly better performance. Ablation studies are included in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": "ReVISE substantially enhances the intelligibility of noisy speech in both setups (WER: " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "87.5\\% \\rightarrow 55.0\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " on ch2 and " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "71.5\\% \\rightarrow 52.1\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " on bf), while Demucs only managed to reduce the WER by " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": ", respectively. Moreover, the WER of the enhanced beamformed speech from ReVISE is only " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " away from resynthesized clean speech: the target ReVISE is trained to predict. One can expect the gap to clean speech (" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "14.5\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " WER) will be reduced if the quality of the SSL units improves." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Tab. 7 presents the subjective quality evaluation results for EasyCom. We first note that the quality of resynthesized" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "target audio (4.13 MOS) is in fact higher than the target audio itself (3.76 MOS). This is because the P-TTS module is trained on the high-quality LJSpeech, which has better quality than the EasyCom audio recorded by the close-talking microphones, as the latter still contain mild background noise and overlapping speech. Similarly, the predicted audio from the proposed ReVISE model also delivers similar levels of audio quality (4.19 and 4.11 with ch2 and beamformed input, respectively), which are significantly better than the original distant recordings (2.95 and 2.67) and the baseline methods (2.95 and 2.39 from Demucs)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 204, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 289 + ], + "type": "text", + "content": "The results suggest a crucial advantage of the proposed ReVISE model compared to previous studies: for ReVISE, the audio quality is not bounded by the enhancement training data (LRS3 and EasyCom), but determined by the quality of P-TTS training data. In contrast, prior works such as SVTS or VisualVoice could only produce audio that is as good as the enhancement target." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 296, + 383, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 383, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 383, + 308 + ], + "type": "text", + "content": "5.8. Limitations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "type": "text", + "content": "We see from Tabs. 1 to 4 that while ReVISE outperforms or is on par with baseline methods on intelligibility, quality, and synchronization, it performs much worse than SVTS, Demucs, and VisualVoice on recovering low-level details. This is because ReVISE does not focus on reconstructing the exact reference signal; moreover, ReVISE does not aim to infer the speaker's voice either since the SSL units are shown to encode very little speaker information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 411, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 518 + ], + "type": "text", + "content": "In fact, it is not a deficiency that the proposed ReVISE model does not reconstruct the reference signal exactly. As shown in Tab. 7, the quality of the reference signal may be mediocre for real world datasets such as EasyCom. In that scenario, reconstructing the exact reference signal would lead to inferior performance compared to the proposed approach, where the training data for P-AVSR and P-TTS are decoupled, such that higher quality data can be used for the unit-to-speech module." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 528, + 405, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 405, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 405, + 540 + ], + "type": "text", + "content": "5.9. Ablation studies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": "We conduct ablation studies to evaluate the importance of pre-training P-AVSR, P-AVSR model size, selection of audio SSL units, and visual input. WER are reported here because intelligibility exhibits the highest variation across models reported earlier. Tab. 8 compares different SSL speech units on two tasks: clean speech resynthesis and video-to-speech generation. The two alternative types of units are derived from the BASE AV-HuBERT model trained on LRS3+VoxCeleb2 [49] and the BASE HuBERT model trained on Librispeech [23]. The corresponding P-TTS model are also trained on the same LJSpeech dataset. We see that performance on the two tasks are correlated, where units that loss less content information (lower Resyn WER) are better prediction targets for the P-AVSR model (lower" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "18801" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 545, + 122 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 122 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 122 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 122 + ], + "type": "table", + "html": "
video-to-speech\nWER↓speech inpainting\n20%WER↓\n30%40%speech denoising\n1v1 1lvl 2lvl 3lvl 4source separation\nWER↓Avg.↓
lvl 1lvl 2lvl 3lvl 4
Separate ReVISE33.9%14.9%18.1%19.2%9.4%9.7%11.7%20.5%9.9%10.2%11.4%15.7%19.0%
Universal ReVISE34.5%14.9%17.9%19.2%8.7%9.4%11.5%20.3%9.1%9.7%10.9%15.5%18.9%
", + "image_path": "3b99efb6bff975e4a66b5cbd41bcb195b4389abb1fc32ba5fa6461cf07250258.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 160, + 285, + 215 + ], + "blocks": [ + { + "bbox": [ + 91, + 129, + 501, + 141 + ], + "lines": [ + { + "bbox": [ + 91, + 129, + 501, + 141 + ], + "spans": [ + { + "bbox": [ + 91, + 129, + 501, + 141 + ], + "type": "text", + "content": "Table 5. Comparing corruption-specific ReVISE with universal ReVISE on intelligibility measured by WER (\\%)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 160, + 285, + 215 + ], + "lines": [ + { + "bbox": [ + 50, + 160, + 285, + 215 + ], + "spans": [ + { + "bbox": [ + 50, + 160, + 285, + 215 + ], + "type": "table", + "html": "
MethodModWER↓ (ch2) (dev/test)WER↓ (bf) (dev/test)
Tgt. audioA35.7% / 37.6%
Tgt. audio resynthesisA43.2% / 47.7%
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Inp. audioA74.2% / 87.5%60.7% / 71.5%
Demucs [12]A76.9% / 86.8%63.4% / 69.8%
ResynthesisA79.6% / 91.0%68.7% / 77.6%
ReVISE (Ours)AV50.3% / 55.0%47.6% / 52.1%
", + "image_path": "a9aef24b6065ef0e8b18e20f7790a944d2d9ca221084f3119ee59b5613826b9c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 327, + 286, + 376 + ], + "blocks": [ + { + "bbox": [ + 47, + 281, + 287, + 314 + ], + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 314 + ], + "type": "text", + "content": "Table 6. Audio-visual speech enhancement results on EasyCom (ch2: channel 2, bf: beamforming). Synchronization results are not reported because SyncNet fails even on clean reference " + }, + { + "bbox": [ + 47, + 281, + 287, + 314 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 47, + 281, + 287, + 314 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 327, + 286, + 376 + ], + "lines": [ + { + "bbox": [ + 48, + 327, + 286, + 376 + ], + "spans": [ + { + "bbox": [ + 48, + 327, + 286, + 376 + ], + "type": "table", + "html": "
MethodModMOS↑ (ch2)MOS↑ (bf)
Tgt. audioA3.76±0.04
Tgt. audio resynthesisA4.13±0.03
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Inp. audioA2.95±0.042.67±0.03
Demucs [12]A2.95±0.042.39±0.03
ResynthesisA3.97±0.043.98±0.03
ReVISE (Ours)AV4.19±0.024.11±0.04
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UnitResyn WER↓V2S WER↓
AV-HuBERT (LRS3+VC2) [49]20.741.2
HuBERT (LS960) [23]17.435.2
HuBERT (VP+MLS+CV)10.633.9
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P-AVSRV2SWER↓
SizescratchPT
BASE81.042.9
LARGE78.635.5
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ModWER↓
DenSepInpaintV2S
AV12.611.417.434.8
A29.239.844.6n/a
", + "image_path": "4ade0b31ba362889d4e1cc67cfc3b52016513b8449fe03a95a75c0b50f3d7397.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 222, + 545, + 257 + ], + "lines": [ + { + "bbox": [ + 305, + 222, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 545, + 257 + ], + "type": "text", + "content": "Table 9. (Left) Ablation studies on model sizes and pre-training. Performance on video-to-speech is reported. (Right) Comparison of ReVISE and its audio-only counterpart." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 282, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 415 + ], + "type": "text", + "content": "We observe that the model using both audio and video as input outperform the counterpart consistently with a large margin. Specifically, the level of degradation varies substantially across task: denoising is least effected (16.6%), followed by inpainting (27.2%) and separation (28.4%) — this shows that models rely heavily on visual information to determine the target speaker as well as infill the missing information from dropped frames. Last but not least, we note that the audio-visual ReVISE perform decently on video-to-speech synthesis despite not being trained on the task at all, suggesting zero-shot generalization to unseen distortion." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 432, + 379, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 379, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 379, + 445 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 454, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 575 + ], + "type": "text", + "content": "This paper presents ReVISE, a novel paradigm for audiovisual speech regeneration that is universal and benefits greatly from the recent advances in self-supervised speech pre-training. Empirical studies demonstrate effectiveness of ReVISE on a popular benchmark with synthetic noise (LRS3) as well as on a conversational benchmark with real noisy data collected from extremely challenging acoustic conditions (EasyCom). In particular, audio enhanced by ReVISE is significantly more intelligible and of higher quality compared to those from the previous work." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 576, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 545, + 624 + ], + "type": "text", + "content": "While this paper studies universal regeneration, it only concerns audio but not video distortion. For future work, we hope to study more general multimodal speech regeneration where the model can recover distortion in both modalities." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 643, + 404, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 404, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 404, + 657 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "The authors thank Rodrigo Schonburg for sharing SVTS samples for evaluations, thank Ruohan Gao for the assistance on VisualVoice code, and thank Stavros Petridis and Anurag Kumar for helpful discussions." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "text", + "content": "18802" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Amir Adler, Valentin Emiya, Maria G Jafari, Michael Elad, Rémi Gribonval, and Mark D Plumbley. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 283-292, 2019. 5" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "18805" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_content_list.json b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0186fbad542b8c12936edb9598b7d153fcc80505 --- /dev/null +++ b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_content_list.json @@ -0,0 +1,1757 @@ +[ + { + "type": "text", + "text": "Real-time 6K Image Rescaling with Rate-distortion Optimization", + "text_level": 1, + "bbox": [ + 156, + 130, + 816, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chenyang Qi* Xin Yang* Ka Leong Cheng Ying-Cong Chen Qifeng Chen Hong Kong University of Science and Technology", + "bbox": [ + 135, + 180, + 870, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contemporary image rescaling aims at embedding a high-resolution (HR) image into a low-resolution (LR) thumbnail image that contains embedded information for HR image reconstruction. Unlike traditional image superresolution, this enables high-fidelity HR image restoration faithful to the original one, given the embedded information in the LR thumbnail. However, state-of-the-art image rescaling methods do not optimize the LR image file size for efficient sharing and fall short of real-time performance for ultra-high-resolution (e.g., 6K) image reconstruction. To address these two challenges, we propose a novel framework (HyperThunnail) for real-time 6K rate-distortion-aware image rescaling. Our framework first embeds an HR image into a JPEG LR thumbnail by an encoder with our proposed quantization prediction module, which minimizes the file size of the embedding LR JPEG thumbnail while maximizing HR reconstruction quality. Then, an efficient frequency-aware decoder reconstructs a high-fidelity HR image from the LR one in real time. Extensive experiments demonstrate that our framework outperforms previous image rescaling baselines in rate-distortion performance and can perform 6K image reconstruction in real time.", + "bbox": [ + 75, + 282, + 473, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 642, + 209, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With an increasing number of high-resolution (HR) images being produced and shared by users on the internet, a new challenge has arisen: how can we store and transfer HR images efficiently? Storing HR images on the cloud, such as iCloud, is becoming a widely adopted solution that saves storage on a user's mobile device (e.g., smartphones) as only their low-resolution (LR) counterparts are stored on the mobile device for an instant preview. However, when a user wants to obtain the full-resolution image, the entire HR image must be downloaded on the fly from the cloud, which can result in a poor user experience when the internet connection is unstable or not available.", + "bbox": [ + 75, + 667, + 468, + 847 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Real-time image rescaling can serve as a competitive solution to improving the user experience of cloud photo stor", + "bbox": [ + 76, + 849, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d6cb2ef8ea88dc088fd211959e86176b5304f5ec6d76505c5db28bbc11391393.jpg", + "image_caption": [ + "Figure 1. The application of 6K image rescaling in the context of cloud photo storage on smartphones (e.g., iCloud). As more high-resolution (HR) images are uploaded to cloud storage nowadays, challenges are brought to cloud service providers (CSPs) in fulfilling latency-sensitive image reading requests (e.g., zoom-in) through the internet. To facilitate faster transmission and high-quality visual content, our HyperThumbnail framework helps CSPs to encode an HR image into an LR JPEG thumbnail, which users could cache locally. When the internet is unstable or unavailable, our method can still reconstruct a high-fidelity HR image from the JPEG thumbnail in real time." + ], + "image_footnote": [], + "bbox": [ + 504, + 253, + 893, + 422 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "age, as shown in Fig. 1. Such a solution can first embed an HR image (on the cloud) into an LR JPEG thumbnail (on the mobile device) by an encoder, and the thumbnail provides an instant preview with little storage. When the user wants to zoom in on the thumbnail, the HR image with fine details can be reconstructed locally in real time. In addition, image rescaling has other applications in image sharing, as it can \"bypass\" the resolution limitation of some platforms (e.g., WhatsApp) to reconstruct a high-quality HR image from an LR one [57]. While modern smartphones and cameras can capture ultra-high-resolution images in 4K (iPhone 13) or even 6K (Blackmagic camera), we are interested in designing a real-time image rescaling framework for ultra-high-resolution images (e.g., 4K or 6K), which minimizes LR file size while maximizing HR and LR image quality.", + "bbox": [ + 496, + 597, + 893, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, existing image rescaling methods have their own flaws in practice, as shown in Table 1 where we compare different image rescaling methods in terms of their properties. One potential solution is to upsample the downsampled thumbnail with super-resolution (SR) meth", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 887, + 205, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14092", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/ad532d5136dc1553a67d2af078f9b1247c5b29faa3ae34f8e577c4b1790f44ef.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method(a) Downsampled JPEG + super-resolution [37](b) Flow-based rescaling [36, 55](c) Ours
ArchitectureHRLR.jpgHRHRLRHRHRLR.jpgHR
Reconstruction fidelityX✓✓
Rate-distortion optimizationXX✓
Real-time 6K reconstruction-X✓
", + "bbox": [ + 78, + 88, + 893, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. The comparison of different methods related to image rescaling. (a) Super-resolution from downsampled JPEG does not optimize rate-distortion performance and can hardly maintain high fidelity due to information lost in downsampling. (b) SOTA flow-based image rescaling methods also ignore the file size constraints and are not real-time for 6K reconstruction due to the limited speed of invertible networks. (c) Our framework optimizes rate-distortion performance while maintaining high-fidelity and real-time 6K image rescaling.", + "bbox": [ + 75, + 236, + 892, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ods [14, 17, 35, 37, 61, 62] (Table 1(a)). However, such a framework applies a simple downsampling strategy (e.g., Bilinear, Bicubic) to the HR image so that high-frequency details are basically lost in the LR thumbnail. Also, SR methods only focus on HR reconstruction, which leads to a sub-optimal image rescaling performance. Instead, dedicated image rescaling approaches aim to embed information into a visually pleasing LR image and then reconstruct the HR image with an upsampling module. Recently, state-of-the-art image rescaling works utilize normalizing flow [25, 36, 55, 57] show impressive image embedding and reconstruction capability that outperforms SR approaches, in terms of the reconstructed HR image quality. However, there are still some great challenges to apply these flow-based rescaling frameworks in real-world applications, as shown in Table 1(b). First, the file size of the LR thumbnail is not optimized. Second, the reconstruction stage of these image rescaling methods is computationally expensive due to their invertible network architecture with extensive use of dense blocks [23]: IRN [55] costs about a second to reconstruct a 4K image with 4x rescaling on a modern GPU, which is far from real time (Table 2).", + "bbox": [ + 75, + 308, + 472, + 641 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose the HyperThumbnail, a rate-distortion-aware framework for 6K real-time image rescaling, as shown in Table 1(c). In this framework, we embed an HR image into a low-bitrate JPEG thumbnail by an encoder and a quantization table predictor, as JPEG is a dominant image compression format today [3]. Then the JPEG thumbnail can be upscaled to its high-fidelity HR counterpart with our efficient decoder in real time. We leverage an asymmetric encoder-decoder architecture, where most computation is put in the encoder to keep the decoder lightweight. This makes it possible for our decoder to upscale a thumbnail to 6K in real time, significantly faster than previous flow-based image rescaling methods [36,55].", + "bbox": [ + 75, + 642, + 468, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meanwhile, the Rate-Distortion (RD) performance is an important and practical metric rarely studied in prior rescaling works. In this paper, we define the rate as the ratio between the thumbnail file size and the number of pixels", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in the HR image, also known as the bits-per-pixel (bpp). The distortion consists of two parts: the perceptual quality of the thumbnail (LR distortion) and the fidelity of the restored HR image (HR distortion). The rate-distortion performance evaluates an image rescaling framework in both storage cost and visual quality. Without explicit RD constraints, recent works in image rescaling [36, 55] do not consider RD performance in their models. While some works [26,47,53,54,58] leverage the rate constraint by embedding extra information in JPEG, they simply utilize a fixed differentiable JPEG module, which we argue is suboptimal for image rescaling. Because such a process deteriorates the information in the embedding images without considering their local distribution. Moreover, the quantization process of JPEG introduces noise in the frequency domain and introduces well-known JPEG artifacts, which brings great challenges to information restoration.", + "bbox": [ + 496, + 308, + 893, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To remedy these issues, our image rescaling framework is designed to jointly optimize image quality and bpp with entropy models. Instead of using fixed quantization tables in conventional JPEG (Sec. 3.1), we propose a novel quantization prediction module (QPM) that predicts image-adaptive quantization tables, which can optimize RD performance. We further adopt a frequency-aware decoder which alleviates JPEG artifacts in the thumbnails and improves HR reconstruction. Moreover, our asymmetric encoder-decoder framework can be extended to optimization-based compression.", + "bbox": [ + 496, + 565, + 893, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 517, + 732, + 821, + 744 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a 6K real-time rescaling framework with an asymmetric encoder-decoder architecture, named HyperThumbnail, which embeds a high-resolution image into a JPEG thumbnail that can be viewed in popular browsers. The decoder utilizes both spatial and frequency information to reconstruct high-fidelity images in real time for 6K image upsampling.", + "- We introduce a new quantization prediction module (QPM) that improves the RD performance in the en" + ], + "bbox": [ + 517, + 755, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14093", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "coding stage of our framework. Furthermore, we adopt rate-distortion-aware loss functions along with QPM to optimize the RD performance.", + "bbox": [ + 107, + 90, + 468, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- Experiments show that our framework outperforms state-of-the-art image rescaling methods with higher LR and HR image quality and faster reconstruction speed at similar file size.", + "bbox": [ + 96, + 159, + 468, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 242, + 218, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Image Super-resolution", + "text_level": 1, + "bbox": [ + 76, + 270, + 294, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image super-resolution (SR) targets at restoring HR images from LR images. Pioneering works on SR such as SRCNN [17], EDSR [37], and other successors [14, 33, 34, 61, 62] exploit deep neural networks to solve the challenges in image SR. Recently, Liang et al. [35] propose a Swin Transformer-based framework with state-of-the-art image SR performance. In addition, Wang et al. [50, 51] extend SRGAN [31] and demonstrate the potential of producing perceptually pleasing HR images with a GAN-based generator. Despite great recent progress, most of these methods assume a simple deterministic downsampling process (e.g., Bicubic downsampling [40]), which limits the reconstruction quality of high-frequency details in image SR.", + "bbox": [ + 75, + 297, + 470, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Image Rescaling", + "text_level": 1, + "bbox": [ + 76, + 511, + 240, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from SR, image rescaling aims to downsample the given HR image into a visually satisfying LR image with embedded information, and then reconstruct the HR image with high fidelity. A straightforward solution is downscaling using detail-preserving methods [29] and upscaling with heavy SR networks [14, 35, 37]. Recently, efforts have been made to apply invertible neural network (INN) to image rescaling. INN [9, 12, 15, 16, 19, 28, 30, 43] provides direct access to the inverse mapping of the forward function, making it a popular framework for image rescaling [13, 36, 55]. Xiao et al. [55] make the first attempt to model image downscaling and upscaling using invertible transformation. Liang et al. [36] further formulate the high-frequency components in INNs as a conditional distribution on LR image. However, the equivalence in the computational cost of the encoding and decoding process of INN makes it almost impossible to optimize the backward inference time independently, which limits its practicality in latency-aware scenarios. Besides, the file size of the embedding LR image in existing rescaling frameworks is yet to be studied. In this paper, we leverage the RD metric to evaluate the rescaling methods from a real-world perspective and compare our framework with existing image rescaling models in terms of their bpp and restored HR fidelity.", + "bbox": [ + 75, + 537, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Image Compression", + "text_level": 1, + "bbox": [ + 500, + 90, + 689, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of only shrinking the image size spatially, image compression approaches optimize the RD performance by first producing a compact bitstream, then decoding HR from the bitstream. Recently, learning-based methods [5-7,21,27,32,39,44,48,56] have improved RD performance by a large margin with neural encoders and decoders. However, these methods have not been widely adopted on the internet due to issues related to software compatibility or runtime efficiency. If users of neural compression need a thumbnail for easier manipulation and preview, they need to save another redundant file besides the bitstream, which is inconvenient and takes extra storage. Thus, traditional compression algorithms (e.g., JPEG [49]) are still popular on most social media platforms [3].", + "bbox": [ + 496, + 114, + 890, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we embed HR images into LR JPEG thumbnails and restore HR images with a 6K real-time decoder. Training neural networks with the non-differentiable JPEG algorithm is challenging. Previous works approximate JPEG either with the iterative optimization [26] or the differentiable degradation simulator [47, 63] during training, and revert to the conventional JPEG algorithm at test time. However, these methods do not optimize the RD performance in their models. In a concurrent work, Xiao et al. [54] extend IRN with a fixed JPEG compression module and an extra JPEG artifact removal module. However, they have not considered the bpp and the reconstruction quality as a joint optimization problem. In this work, we propose a novel differentiable JPEG process with the QPM guided by a bitrate loss for RD performance optimization. Moreover, our real-time decoder reconstructs the HR image from both the spatial and frequency domains of a thumbnail and further improves the reconstruction quality.", + "bbox": [ + 496, + 329, + 892, + 601 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 619, + 591, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. JPEG Preliminary", + "text_level": 1, + "bbox": [ + 500, + 646, + 679, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As our solution involves optimizing the rate-distortion (RD) performance of the JPEG thumbnail, we briefly summarize the JPEG algorithm [49] in this section. The JPEG algorithm compresses an image in three steps. First, given an RGB image $y \\in \\mathbb{R}^{3 \\times h \\times w}$ , the algorithm converts $y$ into the luma-chroma color space (YCbCr). Second, the converted image is divided into $8 \\times 8$ pixel blocks as $y \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8}$ , where $N = \\frac{h \\times w}{8 \\times 8}$ . Then, $y$ is transformed to its corresponding Discrete-Cosine-Transform (DCT) coefficients $C \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8}$ :", + "bbox": [ + 496, + 672, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC = \\left(C _ {Y}, C _ {C b}, C _ {C r}\\right) = \\mathrm {D C T} \\left(y _ {Y}, y _ {C b}, y _ {C r}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 838, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Third, the luma coefficient $C_Y$ and chroma coefficient $C_C = (C_{Cb}, C_{Cr})$ are quantized separately by two quan-", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14094", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3fb72b70a6cc82c75acfa2f156429f066a2c12a8ab9918dccac04ac029b2ad6f.jpg", + "image_caption": [ + "Figure 2. The overview of our approach. Given an HR input image $x$ , we first encode $x$ to its LR representation $y$ with the encoder $E$ , where the scaling factor is $s$ . Second, we transform $y$ to DCT coefficients $C$ and predict the quantization tables $Q_{L}, Q_{C}$ with our quantization prediction module (QPM). Third, we adopt an entropy model [6] to estimate the bitrate of the quantized coefficients $\\widetilde{C}$ at training stage. After the rounding and truncation, which we denoted as $[\\cdot]$ , the $[Q_{L}]$ , $[Q_{C}]$ and $[\\widetilde{C}]$ can be written and read with off-the-shelf JPEG API at the testing stage. To restore the HR, we extract features from $\\widehat{C}$ with a frequency feature extractor $f$ and produce the high-fidelity image $\\hat{x}$ with the decoder $D$ ." + ], + "image_footnote": [], + "bbox": [ + 101, + 89, + 880, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tization tables $Q_{L}$ and $Q_{C}$ :", + "bbox": [ + 76, + 511, + 261, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{[ Q _ {L} ]}, \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{[ Q _ {C} ]}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 536, + 468, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot]$ represents the rounding and truncation function. Unlike the original JPEG algorithm which applies a set of image-invariant quantization tables, our work predicts the $Q_{L}$ and $Q_{C}$ with the QPM (Sec. 3.3) for different images. As shown in the bottom-right of Fig. 2, the quantization tables $[Q] = ([Q_{L}],[Q_{C}])$ and quantized DCT coefficients $[\\widetilde{C}] = ([\\widetilde{C_{Y}}],[\\widetilde{C_{C}}])$ are encoded into a JPEG file. At the decoding phase, the JPEG decoder can extract $[Q],[\\widetilde{C}]$ from the JPEG file for image reconstruction with inverted operations of above steps:", + "bbox": [ + 75, + 579, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {C} _ {Y} = \\left[ \\widetilde {C} _ {Y} \\right] \\left[ Q _ {L} \\right], \\quad \\widehat {C} _ {C} = \\left[ \\widetilde {C} _ {C} \\right] \\left[ Q _ {C} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 744, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and $\\hat{y} = \\mathrm{IDCT}(\\hat{C})$ , where IDCT is the inverse operation of DCT, and $\\hat{C}$ is the abbreviation of $[\\widehat{C_Y},\\widehat{C_C}]$ .", + "bbox": [ + 75, + 773, + 472, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview of HyperThumbnail", + "text_level": 1, + "bbox": [ + 76, + 816, + 346, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by recent progress in high-fidelity efficient restoration through an efficient MLP [41] or a small transformer [22], we adopt an asymmetric encoder-decoder framework, which enables real-time reconstruction. Fig. 2", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "illustrates the overview of our framework. Given an HR input image $x \\in \\mathbb{R}^{3 \\times H \\times W}$ , we first generate its LR representation $y \\in \\mathbb{R}^{3 \\times \\frac{H}{s} \\times \\frac{W}{s}}$ through our encoder $E$ , where the $s$ is the rescaling factor and our encoder $E$ is an U-Net [45] with dense blocks [23]. To further decrease the file size, we transform $y$ to DCT coefficients $C \\in \\mathbb{R}^{3 \\times \\frac{H \\times W}{64 \\times s^2} \\times 8 \\times 8}$ . Then, we quantize $C$ with image-specific quantization tables $Q \\in \\mathbb{R}^{2 \\times 8 \\times 8}$ (Sec. 3.3). During the test time, we encode and decode $(Q, \\widehat{C})$ with off-the-shelf JPEG API, and then retrieve $(\\widehat{C}, \\hat{y})$ with Eqn. (3). In the upsampling stage, we reconstruct the high-fidelity HR $\\hat{x}$ with our efficient frequency-aware decoder in real time (Sec. 3.4).", + "bbox": [ + 496, + 511, + 890, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Quantization Prediction Module", + "text_level": 1, + "bbox": [ + 498, + 710, + 784, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As JPEG [49] is a widely adopted compression algorithm, some previous methods [26, 47, 58, 63] in image embedding also introduce JPEG (Sec. 3.1) to compress their encoded image. However, JPEG degrades the embedded information in the encoded image and leads to a performance drop in the decoding stage (Sec. 5). JPEG uses fixed quantization tables with constant values [49], which we believe is suboptimal since different images have different frequency distribution. Hence, besides encoding HR images to LR thumbnails, we also predict the quantization tables $Q$ for each thumbnail with the quantization prediction module", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14095", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(QPM), which boosts the RD performance of our framework significantly. The QPM is implemented as two separate 8-layer multilayer perceptron (MLPs): the luma predictor $\\mathrm{MLP}_L$ and the chroma predictor $\\mathrm{MLP}_C$ . For block $C_k = (C_{Y,k}, C_{C,k})$ , we vectorize $C_k$ into a 1D vector and produce its quantization table with QPM. Thus we have", + "bbox": [ + 76, + 90, + 468, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {L} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {L} (C _ {Y , k})}{| C _ {Y , k} |}, Q _ {C} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {C} (C _ {C , k})}{| C _ {C , k} |}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 188, + 472, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $|\\cdot|$ denotes the block counts. To facilitate the conventional JPEG codec, we take the average $Q$ as the quantization table for the whole image. Following the training stage of learned compression [7], we adopt the additive uniform noise $\\epsilon$ where each element follows $\\mathcal{U}(-\\frac{1}{2},\\frac{1}{2})$ to approximate the non-differentiable quantization noise introduced in Eqn. (2):", + "bbox": [ + 76, + 229, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{Q _ {L} + \\epsilon} + \\epsilon , \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{Q _ {C} + \\epsilon} + \\epsilon . \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 343, + 468, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the testing stage, we switch back to the standard quantization function in Eqn. (2) to fit the JPEG API. Experiments show that our QPM predicts better quantization tables $Q$ so that it improves the RD performance of our framework (Sec. 5). Our experiments in the supplement also show that our QPM improves the standard JPEG algorithm.", + "bbox": [ + 76, + 382, + 468, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Frequency-aware Decoder", + "text_level": 1, + "bbox": [ + 76, + 479, + 316, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned in Sec. 3.1, the JPEG quantization is applied on the DCT domain coefficients $\\widetilde{C}$ and leads to the well-known quantization noise. Previous works [47,53,58] usually decode the embedded information from the RGB domain of the JPEG image. However, we note that quantization noise can be approximated by simple independent uniform noise [6] in the DCT domain, but it is nonlinear and more complex to model in the RGB domain after IDCT.", + "bbox": [ + 76, + 503, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by recent works in JPEG artifact removal [18, 20, 52, 60] and image generation [42], we further propose a novel plug-in named frequency feature extractor $f$ for additional frequency domain perception. We first reshape the dequantized DCT coefficients into a sparse representation $\\widehat{C} \\in \\mathbb{R}^{192 \\times \\frac{H}{8s} \\times \\frac{W}{8s}}$ [42]. Then, we extract features $f(\\widehat{C}) \\in \\mathbb{R}^{24 \\times \\frac{H}{s} \\times \\frac{W}{s}}$ and concatenate $f(\\widehat{C})$ with the RGB image $\\hat{y}$ . The concatenated features are fed into the decoder to reconstruct the HR image $\\hat{x}$ :", + "bbox": [ + 76, + 625, + 468, + 761 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = D (\\hat {y} \\oplus f (\\hat {C})), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 768, + 468, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\oplus$ is the concatenation operator along the channel dimension. Since $\\widehat{C}$ is $\\frac{1}{8}$ of $\\hat{y}$ in the spatial resolution, $f$ takes negligible computational overhead. In this way, our decoder is lightweight enough to reconstruct 6K HR images in real time (Fig. 5). $f$ improves our RD performance and is more efficient than increasing the decoder capacity. Please refer to our supplement for more details of our architecture.", + "bbox": [ + 76, + 795, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training Objectives", + "text_level": 1, + "bbox": [ + 500, + 90, + 687, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Bitrate loss To optimize the RD performance of our framework, it is critical to estimate the code length (bitrate) of the quantized coefficients $\\widetilde{C}$ at the training stage. Inspired by Balle et al. [6], the rate $R$ of $\\widetilde{C}$ is estimated with differentiable fully-factorized entropy models:", + "bbox": [ + 496, + 113, + 890, + 188 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathrm{R} = \\mathrm{E}_{x\\sim p_x}[-\\log_2p_L(\\widetilde{C}_Y) - \\log_2p_C(\\widetilde{C}_{Cb}) - \\log_2p_C(\\widetilde{C}_{Cr})],$ (7) where $p_L$ and $p_C$ are two fully-factorized entropy models for luma and chroma coefficient maps, respectively. In our work, we reshape $\\widetilde{C}$ to $(3,64,\\frac{H}{8s},\\frac{W}{8s})$ , and assume the value of each pixel in $\\widetilde{C}$ to be independent following Balle et al. [6]. For accurate rate estimation, we train $p_L$ and $p_C$ to model the 64-channel probability density functions of $\\widetilde{C}_Y$ and $(\\widetilde{C}_{Cb},\\widetilde{C}_{Cr})$ by minimizing an auxiliary loss $L_{aux}$ [7]. The bpp of the restored image $\\hat{x}$ is calculated by", + "bbox": [ + 496, + 189, + 890, + 328 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {b p p} = \\frac {R}{H \\times W}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 335, + 890, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More details of auxiliary loss is provided in the supplement.", + "bbox": [ + 496, + 375, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction and guidance loss Thanks to the fully differentiable pipeline (Fig. 2), it is possible for us to train our encoder, QPM and decoder with similar loss terms used in previous works [36, 55]. Following IRN [55], we employ $L_{1}$ on the reconstructed $\\hat{x}$ and a $L_{2}$ guidance loss on the JPEG thumbnail $\\hat{y}$ :", + "bbox": [ + 496, + 388, + 890, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r e c o n} = \\frac {\\left| \\left| \\hat {x} - x \\right| \\right| _ {1}}{H \\times W}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 487, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {g u i d e}} = \\frac {\\left\\| \\hat {y} - y _ {\\text {r e f}} \\right\\| _ {2} ^ {2}}{(H / s) \\times (W / s)}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 520, + 890, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{ref}$ is a guidance image downsampled from $x$ with bicubic interpolation [40]. Altogether, we train our framework by minimizing the total loss $L_{rescale}$ :", + "bbox": [ + 496, + 561, + 890, + 608 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r e s c a l e} = L _ {r e c o n} + \\lambda_ {1} L _ {g u i d e} + \\lambda_ {2} L _ {b p p}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 618, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Empirically, we set $\\lambda_1 = 0.6$ . The target bpp of our framework could be adjusted by a loss scaling factor $\\lambda_{2}$ , which we set to 0.01 for most experiments. The total loss $L_{rescale}$ is adopted to optimize the parameters of the encoder, the decoder, and QPM.", + "bbox": [ + 496, + 643, + 890, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 731, + 632, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 756, + 689, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics We evaluate our upscaling efficiency using running time and multiply-accumulation operations (MACs). We evaluate the quality of our reconstructed and embedding images using the PSNR on RGB channels.", + "bbox": [ + 496, + 779, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rescaling methods are developed to embed an HR image into an LR one to reduce file size. However, there is no existing comprehensive evaluation of bitrate for these methods. Following previous compression approaches [6, 7, 56],", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14096", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5ecb5bbdbaef4204a99e304afc854006e23fcb35bf2a3c6333c01aa1f5bcf4c4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBitrate↓-Distortion↑ [1]Upscaling Efficiency↓Reconstructed HR PSNR↑
Down & Degradation & UpbppPSNRTime (ms)GMacsSet5Set14BSD100Urban100DIV2KFiveK-6k
Bicubic & JPEG & Bicubic0.2925.18--25.1423.4924.0221.0525.7026.90
Bicubic & JPEG & EDSR [37]0.2926.7791.01007.528.3425.7325.6023.5827.8327.23
Bicubic & JPEG & SwinIR [35]0.2926.934012.66208.728.5625.9925.7224.0928.0727.44
ComCNN & RecCNN [26]0.3227.02469.76014.728.2925.8425.7823.7027.9927.40
IRN [55] & JPEG0.3128.48977.84751.730.0027.2326.9125.7229.5427.96
HCFlow [36] & JPEG0.3028.761025.94626.029.9827.4127.0526.1929.7128.01
Ours-full0.3029.67247.91277.530.4828.2127.9327.3530.4928.51
Ours0.3029.4237.8156.230.2227.8727.6626.6230.1528.15
", + "bbox": [ + 80, + 88, + 890, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative evaluation of upscaling efficiency and reconstruction fidelity. We keep bpp around 0.3 on Kodak [1] for different methods, and the distortion is measured by the PSNR on the reconstructed HR images. Our approach outperforms other methods with better HR reconstruction and a significantly lower runtime. We measure the running time and GMacs of all models by upscaling a 960 × 540 LR image to a 3840 × 2160 HR image. The measurements are made on an Nvidia RTX 3090 GPU with PyTorch-1.11.0 in half-precision mode for a fair comparison.", + "bbox": [ + 75, + 250, + 893, + 318 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8de16a67099eb9792484bab29a6f1f6f62236aecbae86eb399c8a158da7b4f59.jpg", + "image_caption": [ + "Figure 3. Reconstructed HR images and LR thumbnails by different methods on the DIV2K [4] validation dataset. We crop the restored HR images to ease the comparison and visualize the LR counterparts at the bottom-right. The bpp is calculated on the whole image and the PSNR is evaluated on the cropped area of the reconstructed HR images." + ], + "image_footnote": [], + "bbox": [ + 76, + 321, + 906, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we evaluate the RD performance with the HR reconstruction PSNR against bits-per-pixel. Instead of estimating the bitrate from the entropy encoder (Eqn. (7)) during training, we use the real file size of JPEG thumbnails for evaluating the bitrate:", + "bbox": [ + 75, + 628, + 468, + 704 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {b p p} = \\mathbb {E} _ {x \\sim p _ {x}} [ \\frac {\\text {f i l e s i z e}}{H \\times W} ]. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 710, + 468, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since there exists a trade-off between image bitrate and fidelity, we visualize the rate-distortion curve of different models during our ablation study.", + "bbox": [ + 75, + 750, + 468, + 795 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We train our model with the widely-used DIV2K [4] image dataset, which contains 800 2K-resolution images in the training set and 100 more in the validation set. From the perspective of rescaling, we test our model on 4 conventional datasets: the Set5 [10], Set14 [59], BSD100 [38], and Urban100 [24]. To reveal our real-world performance, we collect first 20 images above 6K resolu", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion (ranked by their bpp) from MIT-Adobe FiveK [11] as another test set FiveK-6k. In addition, we evaluate the RD performance on Kodak dataset [1], which is widely adopted in image compression researches [8]. The details of the training strategy are provided in the supplement.", + "bbox": [ + 496, + 628, + 893, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Compare with Baselines", + "text_level": 1, + "bbox": [ + 500, + 723, + 723, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We consider three categories of reconstruction methods as our baselines: (1) downscaling with Bicubic interpolation, compressing with standard JPEG codec, and upscaling with state-of-the-art SR models [35, 37]; (2) autoencoder using standard JPEG transmission format [26]; (3) rescaling using symmetric invertible neural network [36, 55] and compressing the LR image using standard JPEG codec. For fair evaluation, we improve the RD performance of baselines using standard JPEG compression. We retrain SR models [35, 37] on LR JPEG compressed images to restore", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14097", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/da95cc986741791025b49eaad50217de728cf20c71725e1df7d5aacc90095269.jpg", + "image_caption": [ + "Bicubic $4\\times$" + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 155, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1d5324b6b6ca086bef8f8aea758a59ab2b9f84fb486af012699efb37a6cb3f02.jpg", + "image_caption": [ + "IRN 55/964× & JPEG qg = 96" + ], + "image_footnote": [], + "bbox": [ + 156, + 104, + 233, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5fe87f9f1c46175109eff22f66c2c106b275e3a17bbdbfe3a869e27075776c83.jpg", + "image_caption": [ + "HJGFlow [36]4× & JPEG q=90" + ], + "image_footnote": [], + "bbox": [ + 235, + 104, + 313, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7aa0be6458a94c8d32ea2e09cea00cd208d9963898b54b4d2593a02ca4f549bf.jpg", + "image_caption": [ + "Ours $4\\times$" + ], + "image_footnote": [], + "bbox": [ + 316, + 104, + 393, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26546278b6f4b90e23ad9de58cdd39e5e13915d1289c2cc759a25e421d9d35f6.jpg", + "image_caption": [ + "Ours-full $4\\times$" + ], + "image_footnote": [], + "bbox": [ + 395, + 104, + 473, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e872eb1d37d447c60212cdcd18d04fa05e02be71e42822644379021497cc1f30.jpg", + "image_caption": [ + "bpp↓/PSNR↑" + ], + "image_footnote": [], + "bbox": [ + 80, + 194, + 155, + 246 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6135e8ca76d7d567547bfa3c77379856925394aa9e66ffa316db202d89379b13.jpg", + "image_caption": [ + "0.510/26.67" + ], + "image_footnote": [], + "bbox": [ + 156, + 194, + 233, + 246 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8f02376ab54a28d6bd5ca0f828f08537d6e4aa4f07e897cdbd16c4e29ee349c7.jpg", + "image_caption": [ + "0.468/17.47" + ], + "image_footnote": [], + "bbox": [ + 235, + 194, + 313, + 246 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed04f7a352e9a6b8f48c0fd4148bf42a96f089221ddb646ab77463af6dcd755f.jpg", + "image_caption": [ + "0.430 / 27.99", + "Figure 4. Downscaled LR thumbnails by different methods on Set14 image comic. With a similar target bpp, our model introduces least artifacts in the thumbnail in comparison to baselines." + ], + "image_footnote": [], + "bbox": [ + 316, + 194, + 393, + 246 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6ec579650ce430376dc133716c0d64a29ce0aea67964cb9c1a3f3dac03ed5e4b.jpg", + "image_caption": [ + "0.446 / 27.90" + ], + "image_footnote": [], + "bbox": [ + 395, + 194, + 473, + 246 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "HR images. Besides, we retrain INN baselines [36, 55] and encoder-decoder baselines [26] with a differentiable JPEG module [46]. To compare our RD performance against baselines, we constrain their bpp on Kodak dataset to be around 0.3 by adjusting the quality factor of JPEG compression in all baselines. In our supplement, we provide an additional comparison with image compression (e.g., the original JPEG) and rescaling baselines using their original transmission format (e.g., lossless PNG), where our advantage is even larger.", + "bbox": [ + 75, + 340, + 467, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Upscaling efficiency and HR fidelity Table 2 presents the upscaling efficiency of all methods and reconstruction fidelity at around 0.3 bpp. We measure the running time and GMacs of upscaling a $960 \\times 540$ resolution LR image to a $3840 \\times 2160$ HR image on an Nvidia RTX 3090 GPU. We use PyTorch implementation with 16 bits floating-point precision for a fair comparison. As shown in Table 2, \"Ours\" model only costs $3.1\\%$ of the GMacs and $3.7\\%$ of upscaling time compared to HCFlow [36]. We still improve the reconstructed RGB PSNR by 0.61 dB on BSD100 test set with a significantly lower computation.", + "bbox": [ + 75, + 492, + 467, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, we train the \"Ours-full\" model with a larger decoder. \"Ours-full\" model achieves higher PSNR that outperforms HCFlow [36] and IRN [55] for more than 1.16 dB on Urban100 test set with only $24.2\\%$ of upscaling time. Fig. 3 provides the visual comparison of restored images. From left to right, we show perceptual differences from ground truth, $4\\times$ rescaling results of the baselines [36, 55] with JPEG, and our framework. For the first row, our models restore more textures of the glass and the pot lid. Similarly, among all reconstructions in the second row, only our model can recover the details on hair and earmuffs. Besides, the JPEG compression breaks the invertibility of the INN-based rescaling methods [36, 55], they failed to restore sharp and accurate high-frequency textures in the HR images.", + "bbox": [ + 75, + 657, + 467, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LR qualitative evaluation The visual quality of the LR thumbnails is also important because users preview them", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e30402c9f0fd60d7a3d0a2f30ac559179ef7ead8daa50b03fa0fe824f597514.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLR睫毛 PSNR↑
Down & DegradationKodakSet5Set14BSD100Urb100DIV2KFiveK-6k
Bicubic & JPEG37.7234.4135.7937.4336.6437.1435.14
IRN [55] & JPEG30.9530.0027.2326.9125.7229.5431.25
ComCNN & RecCNN [26]28.0026.7626.4727.4725.5728.1528.99
HCFlow [36] & JPEG19.8820.0819.4219.6518.9620.5220.31
Ours-full33.2131.8631.7632.4431.0133.3233.99
Ours33.5531.9631.9332.9031.1633.6234.24
", + "bbox": [ + 501, + 88, + 890, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative evaluation of the $4 \\times$ downsampled LR thumbnails by different methods. The target bitrate is around 0.3 bpp on Kodak [1] for all methods, and we take Bicubic LR as the ground truth. Our thumbnail preserves visual contents better.", + "bbox": [ + 496, + 200, + 890, + 257 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/432f4fa96166339edbc7d9586fa5271dd1751415914f2f60dbdaa16097122fd9.jpg", + "image_caption": [ + "Figure 5. Model runtime. We profile the $4 \\times$ encoder and decoder at different target resolution in half-precision mode. Especially, we convert our decoder from PyTorch to TensorRT for further inference time reduction." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 687, + 351 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed193456623e0935b07095c505c8bcbdbedc116a60a9fb2047df27a3f60a47a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 268, + 895, + 351 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "directly. Table 3 presents the average LR PSNR of corresponding models, we have the best LR PSNR against INN-based methods. In Fig. 4, we qualitatively compare the visual quality of the thumbnails encoded by rescaling methods. Our method generates LR thumbnails with significantly fewer artifacts without compromising much HR reconstruction quality, please see more analysis in Sec. 5.", + "bbox": [ + 496, + 431, + 890, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Real-time Inference on 6K Images", + "text_level": 1, + "bbox": [ + 500, + 556, + 797, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 shows our evaluation of the downscaling and upscaling runtime of our framework at multiple resolutions. Noted that we conduct the profiling in half-precision (FP16) mode. Besides, we also converted the trained decoder model from PyTorch to FP16 TensorRT model with torch2trt [2] API to further reduce the upscaling time without performance drop in HR reconstruction. As shown in Fig. 5(b), our efficient decoder can upscale an LR thumb-nail by $4 \\times$ in real time at 4K ( $3840 \\times 2160$ ) 70.8 FPS, 5K ( $5120 \\times 2880$ ) 38.8 FPS, or 6K ( $5760 \\times 3240$ ) 31.2 FPS on an RTX 3090 GPU.", + "bbox": [ + 496, + 582, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Extension for Optimization-based Rescaling", + "text_level": 1, + "bbox": [ + 500, + 768, + 872, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since the ground truth HR images are available for downscaling during the test stage, we may further optimize our encoder $E$ , QPM, and Entropy model, while fixing the pretrained decoder $D$ and feature extractor $f$ on the user's device. As shown in the Table 4, optimization-based rescaling improves the restoration PSNR 0.22dB with a lower bitrate on Set14 dataset.", + "bbox": [ + 496, + 794, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14098", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6a0e846fa3fdbbcc17327822175a987626724fb654ada9819f6980f1980cb44d.jpg", + "image_caption": [ + "kodim04 / kodim09" + ], + "image_footnote": [ + "bpp↓/LR↑/HR↑:kodim09" + ], + "bbox": [ + 86, + 95, + 205, + 164 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/339d5dc4f62a7e0800754a08f13eb3afd16c7f8e5cb5d31a17fe8e455a3576f2.jpg", + "image_caption": [ + "(a) Ours with Fixed JPEG tables, $q = 85$" + ], + "image_footnote": [ + "bpp↓/LR↑/HR↑:kodim04", + "0.263/26.91/30.54", + "0.251/26.96/31.35" + ], + "bbox": [ + 218, + 95, + 390, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dbb89a513afb441f9725b9ea9aeb785b693725a87118d9a9922b7015a9d20b97.jpg", + "image_caption": [ + "(b) Ours with Optimized tables" + ], + "image_footnote": [ + "0.289/29.10/30.93", + "0.276/29.17/31.71" + ], + "bbox": [ + 398, + 95, + 566, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7654218e5be60993354ae4425a8f1a746dedc55a1c648f68ce4884637fe87499.jpg", + "image_caption": [ + "(c) Ours with QPM kodim04" + ], + "image_footnote": [ + "-", + "0.240/34.38/32.03" + ], + "bbox": [ + 568, + 95, + 738, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f19b24cb2e072ad1594db23fbd1d8577b6df9b6569b8ae54394e22e15fc59186.jpg", + "image_caption": [ + "(d) Ours with QPM kodim09" + ], + "image_footnote": [], + "bbox": [ + 740, + 95, + 826, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c6b44ac9274c52091c536b0dd214354891be3412119d1163881797b471b06a8b.jpg", + "image_caption": [ + "Figure 6. Quantization tables on Kodak [1] images. We visualize the quantization table $Q_{L}$ (the green table) and $Q_{C}$ (the orange table) for $\\text{kodim04}$ and $\\text{kodim09}$ of different quantization approaches. The model trained with QPM achieves the best RD performance from every aspect. For more analysis, please refer to Sec. 5 in our paper." + ], + "image_footnote": [ + "0.246/31.03/34.34" + ], + "bbox": [ + 826, + 181, + 828, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/db151afcbe9eb404c28cd5f0bee842aa58d53ab37dae0d75522a4cd316416489.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodOptimizationbpp↓ / HR PSNR↑
ArchitectureiterationKodakSet5Set14
Ours00.301 / 29.420.379 / 30.230.359 / 27.74
1000.307 / 29.550.377 / 30.360.347 / 27.96
", + "bbox": [ + 78, + 263, + 467, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Quantitative evaluation for optimization-based rescaling.", + "bbox": [ + 76, + 337, + 465, + 351 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 367, + 228, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we study the effectiveness of our proposed Quantization Prediction Module, designed training loss and architectures on \"Ours\" model.", + "bbox": [ + 76, + 393, + 468, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantization prediction module To examine the effectiveness of our QPM, in Fig. 7, we quantitatively evaluate the RD performance on both the restored HR and the LR JPEG thumbnails of different quantization approaches. For \"fixed tables\" and \"optimized tables\", we initialize the quantization tables following the default JPEG. Particularly, for \"optimized tables,\" we also optimize the quantization tables at the training stage. We illustrate the curve for each model by adjusting the global quality factor $q$ on the quantization tables $Q$ following JPEG as $Q' = Q \\times q$ . The target bitrate goes lower when $q$ increases. In Fig. 6, we also visualize the quantization tables of different settings. We notice that compared to the corresponding value in the fixed or optimized table, the high-frequency quantization steps in the QPM predicted tables are much smaller and are image-specific, which may introduce less compression on the embedding pattern that is important for HR reconstruction. Consequently, compared to settings with image-invariant quantization, \"Ours\" model achieves the best quality on the reconstructed $\\hat{x}$ and introduces significantly fewer artifacts on the LR thumbnail $\\hat{y}$ , which also lowers the file-size of the thumbnails. To further investigate the effectiveness of QPM, we also leverage QPM to improve the RD performance of standard JPEG (without the downscaling and upscaling). Please refer to our supplement for more details.", + "bbox": [ + 76, + 450, + 468, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Guidance loss In Fig. 7, we also present the RD curve of the \"Ours w/o guidance loss\" model trained with $\\lambda_{1} = 0$ . At around 0.4 bpp, removing guidance loss raises the HR", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11188a3ef29aaabc908843e9d609148acc6a2b91104b8a61b27d8bf5c58c920d.jpg", + "image_caption": [ + "(a) RD curve of restored HR image", + "Figure 7. QPM versus image-invariant quantization. We first train our models with QPM, with a fixed JPEG table or with an optimized table, respectively. Then, we evaluate the at different target bitrate on Kodak [1] dataset. (a) the RD curve on reconstructed HR image $\\hat{x}$ and input $x$ ; (b) the RD curve on LR thumbnail $\\hat{y}$ and the Bicubic downsampled LR $y_{ref}$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 282, + 691, + 404 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e3027635cc3d040a7f674e22a92307379cc66cc7fcad8d5ef708fad1e52ac21.jpg", + "image_caption": [ + "(b) RD curve of LR thumbnail" + ], + "image_footnote": [], + "bbox": [ + 696, + 280, + 885, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PSNR by $0.09\\mathrm{dB}$ . However, the PSNR of LR thumbnail drops significantly from 34.1 dB to 13.06 dB. It is unacceptable for user-viewable thumbnails.", + "bbox": [ + 498, + 508, + 890, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Encoder decoder architecture As we study some variants of \"Ours\" model, we find that $f$ improves the quality of both encoded LR thumbnail (0.29 dB) and restored HR image (0.10 dB). Also, adopting $f$ is more effective than simply increasing the decoder capacity. Moreover, our study of the encoder capacity reveals that our framework does benefit from a larger encoder. More details are in our supplement.", + "bbox": [ + 498, + 569, + 892, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 705, + 617, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a new HyperThumbnail framework that can perform real-time 6K image reconstruction from an LR JPEG thumbnail. We utilize an asymmetric encoder-decoder architecture where the encoder takes most of the computation while the decoder is relatively lightweight for real-time performance. A new quantization prediction module is proposed to optimize the RD performance for image rescaling, which is not studied in prior work. 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Image Represent., 63, 2019. 3, 4" + ], + "bbox": [ + 501, + 92, + 890, + 729 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14101", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_model.json b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..15ab427fb2fc3d8e8c4e57dafd2bb90a7af82ee0 --- /dev/null +++ b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/cfbc14d6-4e76-42f6-ba1a-9d45e253283f_model.json @@ -0,0 +1,2684 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.157, + 0.131, + 0.817, + 0.154 + ], + "angle": 0, + "content": "Real-time 6K Image Rescaling with Rate-distortion Optimization" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.181, + 0.871, + 0.22 + ], + "angle": 0, + "content": "Chenyang Qi* Xin Yang* Ka Leong Cheng Ying-Cong Chen Qifeng Chen Hong Kong University of Science and Technology" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.474, + 0.617 + ], + "angle": 0, + "content": "Contemporary image rescaling aims at embedding a high-resolution (HR) image into a low-resolution (LR) thumbnail image that contains embedded information for HR image reconstruction. Unlike traditional image superresolution, this enables high-fidelity HR image restoration faithful to the original one, given the embedded information in the LR thumbnail. However, state-of-the-art image rescaling methods do not optimize the LR image file size for efficient sharing and fall short of real-time performance for ultra-high-resolution (e.g., 6K) image reconstruction. To address these two challenges, we propose a novel framework (HyperThunnail) for real-time 6K rate-distortion-aware image rescaling. Our framework first embeds an HR image into a JPEG LR thumbnail by an encoder with our proposed quantization prediction module, which minimizes the file size of the embedding LR JPEG thumbnail while maximizing HR reconstruction quality. Then, an efficient frequency-aware decoder reconstructs a high-fidelity HR image from the LR one in real time. Extensive experiments demonstrate that our framework outperforms previous image rescaling baselines in rate-distortion performance and can perform 6K image reconstruction in real time." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.643, + 0.21, + 0.658 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.848 + ], + "angle": 0, + "content": "With an increasing number of high-resolution (HR) images being produced and shared by users on the internet, a new challenge has arisen: how can we store and transfer HR images efficiently? Storing HR images on the cloud, such as iCloud, is becoming a widely adopted solution that saves storage on a user's mobile device (e.g., smartphones) as only their low-resolution (LR) counterparts are stored on the mobile device for an instant preview. However, when a user wants to obtain the full-resolution image, the entire HR image must be downloaded on the fly from the cloud, which can result in a poor user experience when the internet connection is unstable or not available." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Real-time image rescaling can serve as a competitive solution to improving the user experience of cloud photo stor" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.254, + 0.895, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.431, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Figure 1. The application of 6K image rescaling in the context of cloud photo storage on smartphones (e.g., iCloud). As more high-resolution (HR) images are uploaded to cloud storage nowadays, challenges are brought to cloud service providers (CSPs) in fulfilling latency-sensitive image reading requests (e.g., zoom-in) through the internet. To facilitate faster transmission and high-quality visual content, our HyperThumbnail framework helps CSPs to encode an HR image into an LR JPEG thumbnail, which users could cache locally. When the internet is unstable or unavailable, our method can still reconstruct a high-fidelity HR image from the JPEG thumbnail in real time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.825 + ], + "angle": 0, + "content": "age, as shown in Fig. 1. Such a solution can first embed an HR image (on the cloud) into an LR JPEG thumbnail (on the mobile device) by an encoder, and the thumbnail provides an instant preview with little storage. When the user wants to zoom in on the thumbnail, the HR image with fine details can be reconstructed locally in real time. In addition, image rescaling has other applications in image sharing, as it can \"bypass\" the resolution limitation of some platforms (e.g., WhatsApp) to reconstruct a high-quality HR image from an LR one [57]. While modern smartphones and cameras can capture ultra-high-resolution images in 4K (iPhone 13) or even 6K (Blackmagic camera), we are interested in designing a real-time image rescaling framework for ultra-high-resolution images (e.g., 4K or 6K), which minimizes LR file size while maximizing HR and LR image quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "However, existing image rescaling methods have their own flaws in practice, as shown in Table 1 where we compare different image rescaling methods in terms of their properties. One potential solution is to upsample the downsampled thumbnail with super-resolution (SR) meth" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.206, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14092" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.894, + 0.226 + ], + "angle": 0, + "content": "
Method(a) Downsampled JPEG + super-resolution [37](b) Flow-based rescaling [36, 55](c) Ours
ArchitectureHRLR.jpgHRHRLRHRHRLR.jpgHR
Reconstruction fidelityX✓✓
Rate-distortion optimizationXX✓
Real-time 6K reconstruction-X✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.237, + 0.893, + 0.294 + ], + "angle": 0, + "content": "Table 1. The comparison of different methods related to image rescaling. (a) Super-resolution from downsampled JPEG does not optimize rate-distortion performance and can hardly maintain high fidelity due to information lost in downsampling. (b) SOTA flow-based image rescaling methods also ignore the file size constraints and are not real-time for 6K reconstruction due to the limited speed of invertible networks. (c) Our framework optimizes rate-distortion performance while maintaining high-fidelity and real-time 6K image rescaling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.473, + 0.642 + ], + "angle": 0, + "content": "ods [14, 17, 35, 37, 61, 62] (Table 1(a)). However, such a framework applies a simple downsampling strategy (e.g., Bilinear, Bicubic) to the HR image so that high-frequency details are basically lost in the LR thumbnail. Also, SR methods only focus on HR reconstruction, which leads to a sub-optimal image rescaling performance. Instead, dedicated image rescaling approaches aim to embed information into a visually pleasing LR image and then reconstruct the HR image with an upsampling module. Recently, state-of-the-art image rescaling works utilize normalizing flow [25, 36, 55, 57] show impressive image embedding and reconstruction capability that outperforms SR approaches, in terms of the reconstructed HR image quality. However, there are still some great challenges to apply these flow-based rescaling frameworks in real-world applications, as shown in Table 1(b). First, the file size of the LR thumbnail is not optimized. Second, the reconstruction stage of these image rescaling methods is computationally expensive due to their invertible network architecture with extensive use of dense blocks [23]: IRN [55] costs about a second to reconstruct a 4K image with 4x rescaling on a modern GPU, which is far from real time (Table 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In this work, we propose the HyperThumbnail, a rate-distortion-aware framework for 6K real-time image rescaling, as shown in Table 1(c). In this framework, we embed an HR image into a low-bitrate JPEG thumbnail by an encoder and a quantization table predictor, as JPEG is a dominant image compression format today [3]. Then the JPEG thumbnail can be upscaled to its high-fidelity HR counterpart with our efficient decoder in real time. We leverage an asymmetric encoder-decoder architecture, where most computation is put in the encoder to keep the decoder lightweight. This makes it possible for our decoder to upscale a thumbnail to 6K in real time, significantly faster than previous flow-based image rescaling methods [36,55]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Meanwhile, the Rate-Distortion (RD) performance is an important and practical metric rarely studied in prior rescaling works. In this paper, we define the rate as the ratio between the thumbnail file size and the number of pixels" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.895, + 0.566 + ], + "angle": 0, + "content": "in the HR image, also known as the bits-per-pixel (bpp). The distortion consists of two parts: the perceptual quality of the thumbnail (LR distortion) and the fidelity of the restored HR image (HR distortion). The rate-distortion performance evaluates an image rescaling framework in both storage cost and visual quality. Without explicit RD constraints, recent works in image rescaling [36, 55] do not consider RD performance in their models. While some works [26,47,53,54,58] leverage the rate constraint by embedding extra information in JPEG, they simply utilize a fixed differentiable JPEG module, which we argue is suboptimal for image rescaling. Because such a process deteriorates the information in the embedding images without considering their local distribution. Moreover, the quantization process of JPEG introduces noise in the frequency domain and introduces well-known JPEG artifacts, which brings great challenges to information restoration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.732 + ], + "angle": 0, + "content": "To remedy these issues, our image rescaling framework is designed to jointly optimize image quality and bpp with entropy models. Instead of using fixed quantization tables in conventional JPEG (Sec. 3.1), we propose a novel quantization prediction module (QPM) that predicts image-adaptive quantization tables, which can optimize RD performance. We further adopt a frequency-aware decoder which alleviates JPEG artifacts in the thumbnails and improves HR reconstruction. Moreover, our asymmetric encoder-decoder framework can be extended to optimization-based compression." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.733, + 0.822, + 0.746 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.756, + 0.892, + 0.863 + ], + "angle": 0, + "content": "- We propose a 6K real-time rescaling framework with an asymmetric encoder-decoder architecture, named HyperThumbnail, which embeds a high-resolution image into a JPEG thumbnail that can be viewed in popular browsers. The decoder utilizes both spatial and frequency information to reconstruct high-fidelity images in real time for 6K image upsampling." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- We introduce a new quantization prediction module (QPM) that improves the RD performance in the en" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.756, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14093" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.109, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "coding stage of our framework. Furthermore, we adopt rate-distortion-aware loss functions along with QPM to optimize the RD performance." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.16, + 0.47, + 0.22 + ], + "angle": 0, + "content": "- Experiments show that our framework outperforms state-of-the-art image rescaling methods with higher LR and HR image quality and faster reconstruction speed at similar file size." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.243, + 0.22, + 0.259 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.271, + 0.295, + 0.287 + ], + "angle": 0, + "content": "2.1. Image Super-resolution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.471, + 0.493 + ], + "angle": 0, + "content": "Image super-resolution (SR) targets at restoring HR images from LR images. Pioneering works on SR such as SRCNN [17], EDSR [37], and other successors [14, 33, 34, 61, 62] exploit deep neural networks to solve the challenges in image SR. Recently, Liang et al. [35] propose a Swin Transformer-based framework with state-of-the-art image SR performance. In addition, Wang et al. [50, 51] extend SRGAN [31] and demonstrate the potential of producing perceptually pleasing HR images with a GAN-based generator. Despite great recent progress, most of these methods assume a simple deterministic downsampling process (e.g., Bicubic downsampling [40]), which limits the reconstruction quality of high-frequency details in image SR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.512, + 0.241, + 0.529 + ], + "angle": 0, + "content": "2.2. Image Rescaling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Different from SR, image rescaling aims to downsample the given HR image into a visually satisfying LR image with embedded information, and then reconstruct the HR image with high fidelity. A straightforward solution is downscaling using detail-preserving methods [29] and upscaling with heavy SR networks [14, 35, 37]. Recently, efforts have been made to apply invertible neural network (INN) to image rescaling. INN [9, 12, 15, 16, 19, 28, 30, 43] provides direct access to the inverse mapping of the forward function, making it a popular framework for image rescaling [13, 36, 55]. Xiao et al. [55] make the first attempt to model image downscaling and upscaling using invertible transformation. Liang et al. [36] further formulate the high-frequency components in INNs as a conditional distribution on LR image. However, the equivalence in the computational cost of the encoding and decoding process of INN makes it almost impossible to optimize the backward inference time independently, which limits its practicality in latency-aware scenarios. Besides, the file size of the embedding LR image in existing rescaling frameworks is yet to be studied. In this paper, we leverage the RD metric to evaluate the rescaling methods from a real-world perspective and compare our framework with existing image rescaling models in terms of their bpp and restored HR fidelity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.691, + 0.108 + ], + "angle": 0, + "content": "2.3. Image Compression" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Instead of only shrinking the image size spatially, image compression approaches optimize the RD performance by first producing a compact bitstream, then decoding HR from the bitstream. Recently, learning-based methods [5-7,21,27,32,39,44,48,56] have improved RD performance by a large margin with neural encoders and decoders. However, these methods have not been widely adopted on the internet due to issues related to software compatibility or runtime efficiency. If users of neural compression need a thumbnail for easier manipulation and preview, they need to save another redundant file besides the bitstream, which is inconvenient and takes extra storage. Thus, traditional compression algorithms (e.g., JPEG [49]) are still popular on most social media platforms [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.893, + 0.602 + ], + "angle": 0, + "content": "In this work, we embed HR images into LR JPEG thumbnails and restore HR images with a 6K real-time decoder. Training neural networks with the non-differentiable JPEG algorithm is challenging. Previous works approximate JPEG either with the iterative optimization [26] or the differentiable degradation simulator [47, 63] during training, and revert to the conventional JPEG algorithm at test time. However, these methods do not optimize the RD performance in their models. In a concurrent work, Xiao et al. [54] extend IRN with a fixed JPEG compression module and an extra JPEG artifact removal module. However, they have not considered the bpp and the reconstruction quality as a joint optimization problem. In this work, we propose a novel differentiable JPEG process with the QPM guided by a bitrate loss for RD performance optimization. Moreover, our real-time decoder reconstructs the HR image from both the spatial and frequency domains of a thumbnail and further improves the reconstruction quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.593, + 0.636 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.681, + 0.664 + ], + "angle": 0, + "content": "3.1. JPEG Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.822 + ], + "angle": 0, + "content": "As our solution involves optimizing the rate-distortion (RD) performance of the JPEG thumbnail, we briefly summarize the JPEG algorithm [49] in this section. The JPEG algorithm compresses an image in three steps. First, given an RGB image \\( y \\in \\mathbb{R}^{3 \\times h \\times w} \\), the algorithm converts \\( y \\) into the luma-chroma color space (YCbCr). Second, the converted image is divided into \\( 8 \\times 8 \\) pixel blocks as \\( y \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8} \\), where \\( N = \\frac{h \\times w}{8 \\times 8} \\). Then, \\( y \\) is transformed to its corresponding Discrete-Cosine-Transform (DCT) coefficients \\( C \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.839, + 0.892, + 0.856 + ], + "angle": 0, + "content": "\\[\nC = \\left(C _ {Y}, C _ {C b}, C _ {C r}\\right) = \\mathrm {D C T} \\left(y _ {Y}, y _ {C b}, y _ {C r}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Third, the luma coefficient \\( C_Y \\) and chroma coefficient \\( C_C = (C_{Cb}, C_{Cr}) \\) are quantized separately by two quan-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14094" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.881, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.407, + 0.896, + 0.493 + ], + "angle": 0, + "content": "Figure 2. The overview of our approach. Given an HR input image \\( x \\), we first encode \\( x \\) to its LR representation \\( y \\) with the encoder \\( E \\), where the scaling factor is \\( s \\). Second, we transform \\( y \\) to DCT coefficients \\( C \\) and predict the quantization tables \\( Q_{L}, Q_{C} \\) with our quantization prediction module (QPM). Third, we adopt an entropy model [6] to estimate the bitrate of the quantized coefficients \\( \\widetilde{C} \\) at training stage. After the rounding and truncation, which we denoted as \\( [\\cdot] \\), the \\( [Q_{L}] \\), \\( [Q_{C}] \\) and \\( [\\widetilde{C}] \\) can be written and read with off-the-shelf JPEG API at the testing stage. To restore the HR, we extract features from \\( \\widehat{C} \\) with a frequency feature extractor \\( f \\) and produce the high-fidelity image \\( \\hat{x} \\) with the decoder \\( D \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.512, + 0.262, + 0.528 + ], + "angle": 0, + "content": "tization tables \\(Q_{L}\\) and \\(Q_{C}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.537, + 0.47, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{[ Q _ {L} ]}, \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{[ Q _ {C} ]}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.734 + ], + "angle": 0, + "content": "where \\([\\cdot]\\) represents the rounding and truncation function. Unlike the original JPEG algorithm which applies a set of image-invariant quantization tables, our work predicts the \\(Q_{L}\\) and \\(Q_{C}\\) with the QPM (Sec. 3.3) for different images. As shown in the bottom-right of Fig. 2, the quantization tables \\([Q] = ([Q_{L}],[Q_{C}])\\) and quantized DCT coefficients \\([\\widetilde{C}] = ([\\widetilde{C_{Y}}],[\\widetilde{C_{C}}])\\) are encoded into a JPEG file. At the decoding phase, the JPEG decoder can extract \\([Q],[\\widetilde{C}]\\) from the JPEG file for image reconstruction with inverted operations of above steps:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.745, + 0.47, + 0.766 + ], + "angle": 0, + "content": "\\[\n\\widehat {C} _ {Y} = \\left[ \\widetilde {C} _ {Y} \\right] \\left[ Q _ {L} \\right], \\quad \\widehat {C} _ {C} = \\left[ \\widetilde {C} _ {C} \\right] \\left[ Q _ {C} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.775, + 0.473, + 0.809 + ], + "angle": 0, + "content": "and \\(\\hat{y} = \\mathrm{IDCT}(\\hat{C})\\), where IDCT is the inverse operation of DCT, and \\(\\hat{C}\\) is the abbreviation of \\([\\widehat{C_Y},\\widehat{C_C}]\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.348, + 0.833 + ], + "angle": 0, + "content": "3.2. Overview of HyperThumbnail" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inspired by recent progress in high-fidelity efficient restoration through an efficient MLP [41] or a small transformer [22], we adopt an asymmetric encoder-decoder framework, which enables real-time reconstruction. Fig. 2" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.699 + ], + "angle": 0, + "content": "illustrates the overview of our framework. Given an HR input image \\( x \\in \\mathbb{R}^{3 \\times H \\times W} \\), we first generate its LR representation \\( y \\in \\mathbb{R}^{3 \\times \\frac{H}{s} \\times \\frac{W}{s}} \\) through our encoder \\( E \\), where the \\( s \\) is the rescaling factor and our encoder \\( E \\) is an U-Net [45] with dense blocks [23]. To further decrease the file size, we transform \\( y \\) to DCT coefficients \\( C \\in \\mathbb{R}^{3 \\times \\frac{H \\times W}{64 \\times s^2} \\times 8 \\times 8} \\). Then, we quantize \\( C \\) with image-specific quantization tables \\( Q \\in \\mathbb{R}^{2 \\times 8 \\times 8} \\) (Sec. 3.3). During the test time, we encode and decode \\( (Q, \\widehat{C}) \\) with off-the-shelf JPEG API, and then retrieve \\( (\\widehat{C}, \\hat{y}) \\) with Eqn. (3). In the upsampling stage, we reconstruct the high-fidelity HR \\( \\hat{x} \\) with our efficient frequency-aware decoder in real time (Sec. 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.711, + 0.785, + 0.727 + ], + "angle": 0, + "content": "3.3. Quantization Prediction Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As JPEG [49] is a widely adopted compression algorithm, some previous methods [26, 47, 58, 63] in image embedding also introduce JPEG (Sec. 3.1) to compress their encoded image. However, JPEG degrades the embedded information in the encoded image and leads to a performance drop in the decoding stage (Sec. 5). JPEG uses fixed quantization tables with constant values [49], which we believe is suboptimal since different images have different frequency distribution. Hence, besides encoding HR images to LR thumbnails, we also predict the quantization tables \\( Q \\) for each thumbnail with the quantization prediction module" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14095" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.184 + ], + "angle": 0, + "content": "(QPM), which boosts the RD performance of our framework significantly. The QPM is implemented as two separate 8-layer multilayer perceptron (MLPs): the luma predictor \\(\\mathrm{MLP}_L\\) and the chroma predictor \\(\\mathrm{MLP}_C\\). For block \\(C_k = (C_{Y,k}, C_{C,k})\\), we vectorize \\(C_k\\) into a 1D vector and produce its quantization table with QPM. Thus we have" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.189, + 0.473, + 0.226 + ], + "angle": 0, + "content": "\\[\nQ _ {L} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {L} (C _ {Y , k})}{| C _ {Y , k} |}, Q _ {C} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {C} (C _ {C , k})}{| C _ {C , k} |}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.231, + 0.47, + 0.337 + ], + "angle": 0, + "content": "where \\(|\\cdot|\\) denotes the block counts. To facilitate the conventional JPEG codec, we take the average \\(Q\\) as the quantization table for the whole image. Following the training stage of learned compression [7], we adopt the additive uniform noise \\(\\epsilon\\) where each element follows \\(\\mathcal{U}(-\\frac{1}{2},\\frac{1}{2})\\) to approximate the non-differentiable quantization noise introduced in Eqn. (2):" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.344, + 0.47, + 0.378 + ], + "angle": 0, + "content": "\\[\n\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{Q _ {L} + \\epsilon} + \\epsilon , \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{Q _ {C} + \\epsilon} + \\epsilon . \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.383, + 0.47, + 0.474 + ], + "angle": 0, + "content": "In the testing stage, we switch back to the standard quantization function in Eqn. (2) to fit the JPEG API. Experiments show that our QPM predicts better quantization tables \\(Q\\) so that it improves the RD performance of our framework (Sec. 5). Our experiments in the supplement also show that our QPM improves the standard JPEG algorithm." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.481, + 0.317, + 0.497 + ], + "angle": 0, + "content": "3.4. Frequency-aware Decoder" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.505, + 0.47, + 0.625 + ], + "angle": 0, + "content": "As mentioned in Sec. 3.1, the JPEG quantization is applied on the DCT domain coefficients \\(\\widetilde{C}\\) and leads to the well-known quantization noise. Previous works [47,53,58] usually decode the embedded information from the RGB domain of the JPEG image. However, we note that quantization noise can be approximated by simple independent uniform noise [6] in the DCT domain, but it is nonlinear and more complex to model in the RGB domain after IDCT." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.626, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Inspired by recent works in JPEG artifact removal [18, 20, 52, 60] and image generation [42], we further propose a novel plug-in named frequency feature extractor \\( f \\) for additional frequency domain perception. We first reshape the dequantized DCT coefficients into a sparse representation \\( \\widehat{C} \\in \\mathbb{R}^{192 \\times \\frac{H}{8s} \\times \\frac{W}{8s}} \\) [42]. Then, we extract features \\( f(\\widehat{C}) \\in \\mathbb{R}^{24 \\times \\frac{H}{s} \\times \\frac{W}{s}} \\) and concatenate \\( f(\\widehat{C}) \\) with the RGB image \\( \\hat{y} \\). The concatenated features are fed into the decoder to reconstruct the HR image \\( \\hat{x} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.769, + 0.469, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = D (\\hat {y} \\oplus f (\\hat {C})), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\oplus\\) is the concatenation operator along the channel dimension. Since \\(\\widehat{C}\\) is \\(\\frac{1}{8}\\) of \\(\\hat{y}\\) in the spatial resolution, \\(f\\) takes negligible computational overhead. In this way, our decoder is lightweight enough to reconstruct 6K HR images in real time (Fig. 5). \\(f\\) improves our RD performance and is more efficient than increasing the decoder capacity. Please refer to our supplement for more details of our architecture." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.689, + 0.108 + ], + "angle": 0, + "content": "3.5. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.189 + ], + "angle": 0, + "content": "Bitrate loss To optimize the RD performance of our framework, it is critical to estimate the code length (bitrate) of the quantized coefficients \\(\\widetilde{C}\\) at the training stage. Inspired by Balle et al. [6], the rate \\(R\\) of \\(\\widetilde{C}\\) is estimated with differentiable fully-factorized entropy models:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.19, + 0.892, + 0.329 + ], + "angle": 0, + "content": "\\(\\mathrm{R} = \\mathrm{E}_{x\\sim p_x}[-\\log_2p_L(\\widetilde{C}_Y) - \\log_2p_C(\\widetilde{C}_{Cb}) - \\log_2p_C(\\widetilde{C}_{Cr})],\\) (7) where \\(p_L\\) and \\(p_C\\) are two fully-factorized entropy models for luma and chroma coefficient maps, respectively. In our work, we reshape \\(\\widetilde{C}\\) to \\((3,64,\\frac{H}{8s},\\frac{W}{8s})\\) , and assume the value of each pixel in \\(\\widetilde{C}\\) to be independent following Balle et al. [6]. For accurate rate estimation, we train \\(p_L\\) and \\(p_C\\) to model the 64-channel probability density functions of \\(\\widetilde{C}_Y\\) and \\((\\widetilde{C}_{Cb},\\widetilde{C}_{Cr})\\) by minimizing an auxiliary loss \\(L_{aux}\\) [7]. The bpp of the restored image \\(\\hat{x}\\) is calculated by" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.337, + 0.892, + 0.368 + ], + "angle": 0, + "content": "\\[\nL _ {b p p} = \\frac {R}{H \\times W}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.892, + 0.389 + ], + "angle": 0, + "content": "More details of auxiliary loss is provided in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.892, + 0.481 + ], + "angle": 0, + "content": "Reconstruction and guidance loss Thanks to the fully differentiable pipeline (Fig. 2), it is possible for us to train our encoder, QPM and decoder with similar loss terms used in previous works [36, 55]. Following IRN [55], we employ \\( L_{1} \\) on the reconstructed \\( \\hat{x} \\) and a \\( L_{2} \\) guidance loss on the JPEG thumbnail \\( \\hat{y} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.488, + 0.891, + 0.519 + ], + "angle": 0, + "content": "\\[\nL _ {r e c o n} = \\frac {\\left| \\left| \\hat {x} - x \\right| \\right| _ {1}}{H \\times W}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.521, + 0.891, + 0.556 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {g u i d e}} = \\frac {\\left\\| \\hat {y} - y _ {\\text {r e f}} \\right\\| _ {2} ^ {2}}{(H / s) \\times (W / s)}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.609 + ], + "angle": 0, + "content": "where \\( y_{ref} \\) is a guidance image downsampled from \\( x \\) with bicubic interpolation [40]. Altogether, we train our framework by minimizing the total loss \\( L_{rescale} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.619, + 0.891, + 0.636 + ], + "angle": 0, + "content": "\\[\nL _ {r e s c a l e} = L _ {r e c o n} + \\lambda_ {1} L _ {g u i d e} + \\lambda_ {2} L _ {b p p}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Empirically, we set \\(\\lambda_1 = 0.6\\). The target bpp of our framework could be adjusted by a loss scaling factor \\(\\lambda_{2}\\), which we set to 0.01 for most experiments. The total loss \\(L_{rescale}\\) is adopted to optimize the parameters of the encoder, the decoder, and QPM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.732, + 0.633, + 0.75 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.691, + 0.774 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Evaluation metrics We evaluate our upscaling efficiency using running time and multiply-accumulation operations (MACs). We evaluate the quality of our reconstructed and embedding images using the PSNR on RGB channels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Rescaling methods are developed to embed an HR image into an LR one to reduce file size. However, there is no existing comprehensive evaluation of bitrate for these methods. Following previous compression approaches [6, 7, 56]," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14096" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.891, + 0.242 + ], + "angle": 0, + "content": "
MethodBitrate↓-Distortion↑ [1]Upscaling Efficiency↓Reconstructed HR PSNR↑
Down & Degradation & UpbppPSNRTime (ms)GMacsSet5Set14BSD100Urban100DIV2KFiveK-6k
Bicubic & JPEG & Bicubic0.2925.18--25.1423.4924.0221.0525.7026.90
Bicubic & JPEG & EDSR [37]0.2926.7791.01007.528.3425.7325.6023.5827.8327.23
Bicubic & JPEG & SwinIR [35]0.2926.934012.66208.728.5625.9925.7224.0928.0727.44
ComCNN & RecCNN [26]0.3227.02469.76014.728.2925.8425.7823.7027.9927.40
IRN [55] & JPEG0.3128.48977.84751.730.0027.2326.9125.7229.5427.96
HCFlow [36] & JPEG0.3028.761025.94626.029.9827.4127.0526.1929.7128.01
Ours-full0.3029.67247.91277.530.4828.2127.9327.3530.4928.51
Ours0.3029.4237.8156.230.2227.8727.6626.6230.1528.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.25, + 0.895, + 0.319 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation of upscaling efficiency and reconstruction fidelity. We keep bpp around 0.3 on Kodak [1] for different methods, and the distortion is measured by the PSNR on the reconstructed HR images. Our approach outperforms other methods with better HR reconstruction and a significantly lower runtime. We measure the running time and GMacs of all models by upscaling a 960 × 540 LR image to a 3840 × 2160 HR image. The measurements are made on an Nvidia RTX 3090 GPU with PyTorch-1.11.0 in half-precision mode for a fair comparison." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.323, + 0.908, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.574, + 0.895, + 0.618 + ], + "angle": 0, + "content": "Figure 3. Reconstructed HR images and LR thumbnails by different methods on the DIV2K [4] validation dataset. We crop the restored HR images to ease the comparison and visualize the LR counterparts at the bottom-right. The bpp is calculated on the whole image and the PSNR is evaluated on the cropped area of the reconstructed HR images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.705 + ], + "angle": 0, + "content": "we evaluate the RD performance with the HR reconstruction PSNR against bits-per-pixel. Instead of estimating the bitrate from the entropy encoder (Eqn. (7)) during training, we use the real file size of JPEG thumbnails for evaluating the bitrate:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.711, + 0.47, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\operatorname {b p p} = \\mathbb {E} _ {x \\sim p _ {x}} [ \\frac {\\text {f i l e s i z e}}{H \\times W} ]. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.796 + ], + "angle": 0, + "content": "Since there exists a trade-off between image bitrate and fidelity, we visualize the rate-distortion curve of different models during our ablation study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Datasets We train our model with the widely-used DIV2K [4] image dataset, which contains 800 2K-resolution images in the training set and 100 more in the validation set. From the perspective of rescaling, we test our model on 4 conventional datasets: the Set5 [10], Set14 [59], BSD100 [38], and Urban100 [24]. To reveal our real-world performance, we collect first 20 images above 6K resolu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.707 + ], + "angle": 0, + "content": "tion (ranked by their bpp) from MIT-Adobe FiveK [11] as another test set FiveK-6k. In addition, we evaluate the RD performance on Kodak dataset [1], which is widely adopted in image compression researches [8]. The details of the training strategy are provided in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.724, + 0.74 + ], + "angle": 0, + "content": "4.2. Compare with Baselines" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We consider three categories of reconstruction methods as our baselines: (1) downscaling with Bicubic interpolation, compressing with standard JPEG codec, and upscaling with state-of-the-art SR models [35, 37]; (2) autoencoder using standard JPEG transmission format [26]; (3) rescaling using symmetric invertible neural network [36, 55] and compressing the LR image using standard JPEG codec. For fair evaluation, we improve the RD performance of baselines using standard JPEG compression. We retrain SR models [35, 37] on LR JPEG compressed images to restore" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14097" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.085, + 0.138, + 0.103 + ], + "angle": 0, + "content": "Bicubic \\(4\\times\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.163, + 0.086, + 0.228, + 0.104 + ], + "angle": 0, + "content": "IRN 55/964× & JPEG qg = 96" + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.086, + 0.315, + 0.104 + ], + "angle": 0, + "content": "HJGFlow [36]4× & JPEG q=90" + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.086, + 0.369, + 0.103 + ], + "angle": 0, + "content": "Ours \\(4\\times\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.41, + 0.086, + 0.455, + 0.103 + ], + "angle": 0, + "content": "Ours-full \\(4\\times\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.105, + 0.156, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.105, + 0.234, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.105, + 0.315, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.105, + 0.395, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.105, + 0.474, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.195, + 0.156, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.195, + 0.234, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.195, + 0.315, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.195, + 0.395, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.195, + 0.474, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.252, + 0.152, + 0.264 + ], + "angle": 0, + "content": "bpp↓/PSNR↑" + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.252, + 0.228, + 0.264 + ], + "angle": 0, + "content": "0.510/26.67" + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.252, + 0.307, + 0.263 + ], + "angle": 0, + "content": "0.468/17.47" + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.252, + 0.388, + 0.263 + ], + "angle": 0, + "content": "0.430 / 27.99" + }, + { + "type": "image_caption", + "bbox": [ + 0.401, + 0.252, + 0.466, + 0.263 + ], + "angle": 0, + "content": "0.446 / 27.90" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.47, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Downscaled LR thumbnails by different methods on Set14 image comic. With a similar target bpp, our model introduces least artifacts in the thumbnail in comparison to baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.468, + 0.492 + ], + "angle": 0, + "content": "HR images. Besides, we retrain INN baselines [36, 55] and encoder-decoder baselines [26] with a differentiable JPEG module [46]. To compare our RD performance against baselines, we constrain their bpp on Kodak dataset to be around 0.3 by adjusting the quality factor of JPEG compression in all baselines. In our supplement, we provide an additional comparison with image compression (e.g., the original JPEG) and rescaling baselines using their original transmission format (e.g., lossless PNG), where our advantage is even larger." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.468, + 0.658 + ], + "angle": 0, + "content": "Upscaling efficiency and HR fidelity Table 2 presents the upscaling efficiency of all methods and reconstruction fidelity at around 0.3 bpp. We measure the running time and GMacs of upscaling a \\(960 \\times 540\\) resolution LR image to a \\(3840 \\times 2160\\) HR image on an Nvidia RTX 3090 GPU. We use PyTorch implementation with 16 bits floating-point precision for a fair comparison. As shown in Table 2, \"Ours\" model only costs \\(3.1\\%\\) of the GMacs and \\(3.7\\%\\) of upscaling time compared to HCFlow [36]. We still improve the reconstructed RGB PSNR by 0.61 dB on BSD100 test set with a significantly lower computation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.87 + ], + "angle": 0, + "content": "In addition, we train the \"Ours-full\" model with a larger decoder. \"Ours-full\" model achieves higher PSNR that outperforms HCFlow [36] and IRN [55] for more than 1.16 dB on Urban100 test set with only \\(24.2\\%\\) of upscaling time. Fig. 3 provides the visual comparison of restored images. From left to right, we show perceptual differences from ground truth, \\(4\\times\\) rescaling results of the baselines [36, 55] with JPEG, and our framework. For the first row, our models restore more textures of the glass and the pot lid. Similarly, among all reconstructions in the second row, only our model can recover the details on hair and earmuffs. Besides, the JPEG compression breaks the invertibility of the INN-based rescaling methods [36, 55], they failed to restore sharp and accurate high-frequency textures in the HR images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "LR qualitative evaluation The visual quality of the LR thumbnails is also important because users preview them" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.194 + ], + "angle": 0, + "content": "
MethodLR睫毛 PSNR↑
Down & DegradationKodakSet5Set14BSD100Urb100DIV2KFiveK-6k
Bicubic & JPEG37.7234.4135.7937.4336.6437.1435.14
IRN [55] & JPEG30.9530.0027.2326.9125.7229.5431.25
ComCNN & RecCNN [26]28.0026.7626.4727.4725.5728.1528.99
HCFlow [36] & JPEG19.8820.0819.4219.6518.9620.5220.31
Ours-full33.2131.8631.7632.4431.0133.3233.99
Ours33.5531.9631.9332.9031.1633.6234.24
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of the \\(4 \\times\\) downsampled LR thumbnails by different methods. The target bitrate is around 0.3 bpp on Kodak [1] for all methods, and we take Bicubic LR as the ground truth. Our thumbnail preserves visual contents better." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.269, + 0.688, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.269, + 0.897, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Figure 5. Model runtime. We profile the \\(4 \\times\\) encoder and decoder at different target resolution in half-precision mode. Especially, we convert our decoder from PyTorch to TensorRT for further inference time reduction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.892, + 0.538 + ], + "angle": 0, + "content": "directly. Table 3 presents the average LR PSNR of corresponding models, we have the best LR PSNR against INN-based methods. In Fig. 4, we qualitatively compare the visual quality of the thumbnails encoded by rescaling methods. Our method generates LR thumbnails with significantly fewer artifacts without compromising much HR reconstruction quality, please see more analysis in Sec. 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.799, + 0.573 + ], + "angle": 0, + "content": "4.3. Real-time Inference on 6K Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Fig. 5 shows our evaluation of the downscaling and upscaling runtime of our framework at multiple resolutions. Noted that we conduct the profiling in half-precision (FP16) mode. Besides, we also converted the trained decoder model from PyTorch to FP16 TensorRT model with torch2trt [2] API to further reduce the upscaling time without performance drop in HR reconstruction. As shown in Fig. 5(b), our efficient decoder can upscale an LR thumb-nail by \\(4 \\times\\) in real time at 4K (\\(3840 \\times 2160\\)) 70.8 FPS, 5K (\\(5120 \\times 2880\\)) 38.8 FPS, or 6K (\\(5760 \\times 3240\\)) 31.2 FPS on an RTX 3090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.874, + 0.785 + ], + "angle": 0, + "content": "4.4. Extension for Optimization-based Rescaling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Since the ground truth HR images are available for downscaling during the test stage, we may further optimize our encoder \\( E \\), QPM, and Entropy model, while fixing the pretrained decoder \\( D \\) and feature extractor \\( f \\) on the user's device. As shown in the Table 4, optimization-based rescaling improves the restoration PSNR 0.22dB with a lower bitrate on Set14 dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14098" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.086, + 0.193, + 0.096 + ], + "angle": 0, + "content": "kodim04 / kodim09" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.097, + 0.207, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.078, + 0.168, + 0.214, + 0.18 + ], + "angle": 0, + "content": "bpp↓/LR↑/HR↑:kodim09" + }, + { + "type": "image_footnote", + "bbox": [ + 0.078, + 0.183, + 0.214, + 0.195 + ], + "angle": 0, + "content": "bpp↓/LR↑/HR↑:kodim04" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.086, + 0.214, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.086, + 0.396, + 0.097 + ], + "angle": 0, + "content": "(a) Ours with Fixed JPEG tables, \\(q = 85\\)" + }, + { + "type": "image", + "bbox": [ + 0.22, + 0.097, + 0.391, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.257, + 0.168, + 0.355, + 0.179 + ], + "angle": 0, + "content": "0.263/26.91/30.54" + }, + { + "type": "image_footnote", + "bbox": [ + 0.256, + 0.183, + 0.355, + 0.194 + ], + "angle": 0, + "content": "0.251/26.96/31.35" + }, + { + "type": "list", + "bbox": [ + 0.256, + 0.168, + 0.355, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.41, + 0.086, + 0.555, + 0.097 + ], + "angle": 0, + "content": "(b) Ours with Optimized tables" + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.097, + 0.568, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.434, + 0.168, + 0.532, + 0.179 + ], + "angle": 0, + "content": "0.289/29.10/30.93" + }, + { + "type": "image_footnote", + "bbox": [ + 0.434, + 0.183, + 0.532, + 0.194 + ], + "angle": 0, + "content": "0.276/29.17/31.71" + }, + { + "type": "list", + "bbox": [ + 0.434, + 0.168, + 0.532, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.086, + 0.722, + 0.097 + ], + "angle": 0, + "content": "(c) Ours with QPM kodim04" + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.097, + 0.74, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.604, + 0.168, + 0.679, + 0.177 + ], + "angle": 0, + "content": "-" + }, + { + "type": "image_footnote", + "bbox": [ + 0.605, + 0.183, + 0.704, + 0.194 + ], + "angle": 0, + "content": "0.240/34.38/32.03" + }, + { + "type": "list", + "bbox": [ + 0.569, + 0.086, + 0.74, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.758, + 0.086, + 0.894, + 0.097 + ], + "angle": 0, + "content": "(d) Ours with QPM kodim09" + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.097, + 0.827, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.777, + 0.168, + 0.875, + 0.179 + ], + "angle": 0, + "content": "0.246/31.03/34.34" + }, + { + "type": "image", + "bbox": [ + 0.828, + 0.183, + 0.829, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.198, + 0.894, + 0.241 + ], + "angle": 0, + "content": "Figure 6. Quantization tables on Kodak [1] images. We visualize the quantization table \\( Q_{L} \\) (the green table) and \\( Q_{C} \\) (the orange table) for \\( \\text{kodim04} \\) and \\( \\text{kodim09} \\) of different quantization approaches. The model trained with QPM achieves the best RD performance from every aspect. For more analysis, please refer to Sec. 5 in our paper." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.264, + 0.468, + 0.332 + ], + "angle": 0, + "content": "
MethodOptimizationbpp↓ / HR PSNR↑
ArchitectureiterationKodakSet5Set14
Ours00.301 / 29.420.379 / 30.230.359 / 27.74
1000.307 / 29.550.377 / 30.360.347 / 27.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.338, + 0.467, + 0.352 + ], + "angle": 0, + "content": "Table 4. Quantitative evaluation for optimization-based rescaling." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.368, + 0.229, + 0.385 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.469, + 0.439 + ], + "angle": 0, + "content": "In this section, we study the effectiveness of our proposed Quantization Prediction Module, designed training loss and architectures on \"Ours\" model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.451, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Quantization prediction module To examine the effectiveness of our QPM, in Fig. 7, we quantitatively evaluate the RD performance on both the restored HR and the LR JPEG thumbnails of different quantization approaches. For \"fixed tables\" and \"optimized tables\", we initialize the quantization tables following the default JPEG. Particularly, for \"optimized tables,\" we also optimize the quantization tables at the training stage. We illustrate the curve for each model by adjusting the global quality factor \\( q \\) on the quantization tables \\( Q \\) following JPEG as \\( Q' = Q \\times q \\). The target bitrate goes lower when \\( q \\) increases. In Fig. 6, we also visualize the quantization tables of different settings. We notice that compared to the corresponding value in the fixed or optimized table, the high-frequency quantization steps in the QPM predicted tables are much smaller and are image-specific, which may introduce less compression on the embedding pattern that is important for HR reconstruction. Consequently, compared to settings with image-invariant quantization, \"Ours\" model achieves the best quality on the reconstructed \\( \\hat{x} \\) and introduces significantly fewer artifacts on the LR thumbnail \\( \\hat{y} \\), which also lowers the file-size of the thumbnails. To further investigate the effectiveness of QPM, we also leverage QPM to improve the RD performance of standard JPEG (without the downscaling and upscaling). Please refer to our supplement for more details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Guidance loss In Fig. 7, we also present the RD curve of the \"Ours w/o guidance loss\" model trained with \\(\\lambda_{1} = 0\\). At around 0.4 bpp, removing guidance loss raises the HR" + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.268, + 0.683, + 0.28 + ], + "angle": 0, + "content": "(a) RD curve of restored HR image" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.284, + 0.692, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.723, + 0.268, + 0.865, + 0.279 + ], + "angle": 0, + "content": "(b) RD curve of LR thumbnail" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.281, + 0.886, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.408, + 0.893, + 0.492 + ], + "angle": 0, + "content": "Figure 7. QPM versus image-invariant quantization. We first train our models with QPM, with a fixed JPEG table or with an optimized table, respectively. Then, we evaluate the at different target bitrate on Kodak [1] dataset. (a) the RD curve on reconstructed HR image \\(\\hat{x}\\) and input \\(x\\); (b) the RD curve on LR thumbnail \\(\\hat{y}\\) and the Bicubic downsampled LR \\(y_{ref}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.51, + 0.892, + 0.556 + ], + "angle": 0, + "content": "PSNR by \\(0.09\\mathrm{dB}\\). However, the PSNR of LR thumbnail drops significantly from 34.1 dB to 13.06 dB. It is unacceptable for user-viewable thumbnails." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.57, + 0.893, + 0.677 + ], + "angle": 0, + "content": "Encoder decoder architecture As we study some variants of \"Ours\" model, we find that \\( f \\) improves the quality of both encoded LR thumbnail (0.29 dB) and restored HR image (0.10 dB). Also, adopting \\( f \\) is more effective than simply increasing the decoder capacity. Moreover, our study of the encoder capacity reveals that our framework does benefit from a larger encoder. More details are in our supplement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.706, + 0.619, + 0.721 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a new HyperThumbnail framework that can perform real-time 6K image reconstruction from an LR JPEG thumbnail. We utilize an asymmetric encoder-decoder architecture where the encoder takes most of the computation while the decoder is relatively lightweight for real-time performance. A new quantization prediction module is proposed to optimize the RD performance for image rescaling, which is not studied in prior work. 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Unlike traditional image superresolution, this enables high-fidelity HR image restoration faithful to the original one, given the embedded information in the LR thumbnail. However, state-of-the-art image rescaling methods do not optimize the LR image file size for efficient sharing and fall short of real-time performance for ultra-high-resolution (e.g., 6K) image reconstruction. To address these two challenges, we propose a novel framework (HyperThunnail) for real-time 6K rate-distortion-aware image rescaling. Our framework first embeds an HR image into a JPEG LR thumbnail by an encoder with our proposed quantization prediction module, which minimizes the file size of the embedding LR JPEG thumbnail while maximizing HR reconstruction quality. Then, an efficient frequency-aware decoder reconstructs a high-fidelity HR image from the LR one in real time. Extensive experiments demonstrate that our framework outperforms previous image rescaling baselines in rate-distortion performance and can perform 6K image reconstruction in real time. + +# 1. Introduction + +With an increasing number of high-resolution (HR) images being produced and shared by users on the internet, a new challenge has arisen: how can we store and transfer HR images efficiently? Storing HR images on the cloud, such as iCloud, is becoming a widely adopted solution that saves storage on a user's mobile device (e.g., smartphones) as only their low-resolution (LR) counterparts are stored on the mobile device for an instant preview. However, when a user wants to obtain the full-resolution image, the entire HR image must be downloaded on the fly from the cloud, which can result in a poor user experience when the internet connection is unstable or not available. + +Real-time image rescaling can serve as a competitive solution to improving the user experience of cloud photo stor + +![](images/d6cb2ef8ea88dc088fd211959e86176b5304f5ec6d76505c5db28bbc11391393.jpg) +Figure 1. The application of 6K image rescaling in the context of cloud photo storage on smartphones (e.g., iCloud). As more high-resolution (HR) images are uploaded to cloud storage nowadays, challenges are brought to cloud service providers (CSPs) in fulfilling latency-sensitive image reading requests (e.g., zoom-in) through the internet. To facilitate faster transmission and high-quality visual content, our HyperThumbnail framework helps CSPs to encode an HR image into an LR JPEG thumbnail, which users could cache locally. When the internet is unstable or unavailable, our method can still reconstruct a high-fidelity HR image from the JPEG thumbnail in real time. + +age, as shown in Fig. 1. Such a solution can first embed an HR image (on the cloud) into an LR JPEG thumbnail (on the mobile device) by an encoder, and the thumbnail provides an instant preview with little storage. When the user wants to zoom in on the thumbnail, the HR image with fine details can be reconstructed locally in real time. In addition, image rescaling has other applications in image sharing, as it can "bypass" the resolution limitation of some platforms (e.g., WhatsApp) to reconstruct a high-quality HR image from an LR one [57]. While modern smartphones and cameras can capture ultra-high-resolution images in 4K (iPhone 13) or even 6K (Blackmagic camera), we are interested in designing a real-time image rescaling framework for ultra-high-resolution images (e.g., 4K or 6K), which minimizes LR file size while maximizing HR and LR image quality. + +However, existing image rescaling methods have their own flaws in practice, as shown in Table 1 where we compare different image rescaling methods in terms of their properties. One potential solution is to upsample the downsampled thumbnail with super-resolution (SR) meth + +
Method(a) Downsampled JPEG + super-resolution [37](b) Flow-based rescaling [36, 55](c) Ours
ArchitectureHRLR.jpgHRHRLRHRHRLR.jpgHR
Reconstruction fidelityX✓✓
Rate-distortion optimizationXX✓
Real-time 6K reconstruction-X✓
+ +Table 1. The comparison of different methods related to image rescaling. (a) Super-resolution from downsampled JPEG does not optimize rate-distortion performance and can hardly maintain high fidelity due to information lost in downsampling. (b) SOTA flow-based image rescaling methods also ignore the file size constraints and are not real-time for 6K reconstruction due to the limited speed of invertible networks. (c) Our framework optimizes rate-distortion performance while maintaining high-fidelity and real-time 6K image rescaling. + +ods [14, 17, 35, 37, 61, 62] (Table 1(a)). However, such a framework applies a simple downsampling strategy (e.g., Bilinear, Bicubic) to the HR image so that high-frequency details are basically lost in the LR thumbnail. Also, SR methods only focus on HR reconstruction, which leads to a sub-optimal image rescaling performance. Instead, dedicated image rescaling approaches aim to embed information into a visually pleasing LR image and then reconstruct the HR image with an upsampling module. Recently, state-of-the-art image rescaling works utilize normalizing flow [25, 36, 55, 57] show impressive image embedding and reconstruction capability that outperforms SR approaches, in terms of the reconstructed HR image quality. However, there are still some great challenges to apply these flow-based rescaling frameworks in real-world applications, as shown in Table 1(b). First, the file size of the LR thumbnail is not optimized. Second, the reconstruction stage of these image rescaling methods is computationally expensive due to their invertible network architecture with extensive use of dense blocks [23]: IRN [55] costs about a second to reconstruct a 4K image with 4x rescaling on a modern GPU, which is far from real time (Table 2). + +In this work, we propose the HyperThumbnail, a rate-distortion-aware framework for 6K real-time image rescaling, as shown in Table 1(c). In this framework, we embed an HR image into a low-bitrate JPEG thumbnail by an encoder and a quantization table predictor, as JPEG is a dominant image compression format today [3]. Then the JPEG thumbnail can be upscaled to its high-fidelity HR counterpart with our efficient decoder in real time. We leverage an asymmetric encoder-decoder architecture, where most computation is put in the encoder to keep the decoder lightweight. This makes it possible for our decoder to upscale a thumbnail to 6K in real time, significantly faster than previous flow-based image rescaling methods [36,55]. + +Meanwhile, the Rate-Distortion (RD) performance is an important and practical metric rarely studied in prior rescaling works. In this paper, we define the rate as the ratio between the thumbnail file size and the number of pixels + +in the HR image, also known as the bits-per-pixel (bpp). The distortion consists of two parts: the perceptual quality of the thumbnail (LR distortion) and the fidelity of the restored HR image (HR distortion). The rate-distortion performance evaluates an image rescaling framework in both storage cost and visual quality. Without explicit RD constraints, recent works in image rescaling [36, 55] do not consider RD performance in their models. While some works [26,47,53,54,58] leverage the rate constraint by embedding extra information in JPEG, they simply utilize a fixed differentiable JPEG module, which we argue is suboptimal for image rescaling. Because such a process deteriorates the information in the embedding images without considering their local distribution. Moreover, the quantization process of JPEG introduces noise in the frequency domain and introduces well-known JPEG artifacts, which brings great challenges to information restoration. + +To remedy these issues, our image rescaling framework is designed to jointly optimize image quality and bpp with entropy models. Instead of using fixed quantization tables in conventional JPEG (Sec. 3.1), we propose a novel quantization prediction module (QPM) that predicts image-adaptive quantization tables, which can optimize RD performance. We further adopt a frequency-aware decoder which alleviates JPEG artifacts in the thumbnails and improves HR reconstruction. Moreover, our asymmetric encoder-decoder framework can be extended to optimization-based compression. + +Our contributions are summarized as follows: + +- We propose a 6K real-time rescaling framework with an asymmetric encoder-decoder architecture, named HyperThumbnail, which embeds a high-resolution image into a JPEG thumbnail that can be viewed in popular browsers. The decoder utilizes both spatial and frequency information to reconstruct high-fidelity images in real time for 6K image upsampling. +- We introduce a new quantization prediction module (QPM) that improves the RD performance in the en + +coding stage of our framework. Furthermore, we adopt rate-distortion-aware loss functions along with QPM to optimize the RD performance. + +- Experiments show that our framework outperforms state-of-the-art image rescaling methods with higher LR and HR image quality and faster reconstruction speed at similar file size. + +# 2. Related Work + +# 2.1. Image Super-resolution + +Image super-resolution (SR) targets at restoring HR images from LR images. Pioneering works on SR such as SRCNN [17], EDSR [37], and other successors [14, 33, 34, 61, 62] exploit deep neural networks to solve the challenges in image SR. Recently, Liang et al. [35] propose a Swin Transformer-based framework with state-of-the-art image SR performance. In addition, Wang et al. [50, 51] extend SRGAN [31] and demonstrate the potential of producing perceptually pleasing HR images with a GAN-based generator. Despite great recent progress, most of these methods assume a simple deterministic downsampling process (e.g., Bicubic downsampling [40]), which limits the reconstruction quality of high-frequency details in image SR. + +# 2.2. Image Rescaling + +Different from SR, image rescaling aims to downsample the given HR image into a visually satisfying LR image with embedded information, and then reconstruct the HR image with high fidelity. A straightforward solution is downscaling using detail-preserving methods [29] and upscaling with heavy SR networks [14, 35, 37]. Recently, efforts have been made to apply invertible neural network (INN) to image rescaling. INN [9, 12, 15, 16, 19, 28, 30, 43] provides direct access to the inverse mapping of the forward function, making it a popular framework for image rescaling [13, 36, 55]. Xiao et al. [55] make the first attempt to model image downscaling and upscaling using invertible transformation. Liang et al. [36] further formulate the high-frequency components in INNs as a conditional distribution on LR image. However, the equivalence in the computational cost of the encoding and decoding process of INN makes it almost impossible to optimize the backward inference time independently, which limits its practicality in latency-aware scenarios. Besides, the file size of the embedding LR image in existing rescaling frameworks is yet to be studied. In this paper, we leverage the RD metric to evaluate the rescaling methods from a real-world perspective and compare our framework with existing image rescaling models in terms of their bpp and restored HR fidelity. + +# 2.3. Image Compression + +Instead of only shrinking the image size spatially, image compression approaches optimize the RD performance by first producing a compact bitstream, then decoding HR from the bitstream. Recently, learning-based methods [5-7,21,27,32,39,44,48,56] have improved RD performance by a large margin with neural encoders and decoders. However, these methods have not been widely adopted on the internet due to issues related to software compatibility or runtime efficiency. If users of neural compression need a thumbnail for easier manipulation and preview, they need to save another redundant file besides the bitstream, which is inconvenient and takes extra storage. Thus, traditional compression algorithms (e.g., JPEG [49]) are still popular on most social media platforms [3]. + +In this work, we embed HR images into LR JPEG thumbnails and restore HR images with a 6K real-time decoder. Training neural networks with the non-differentiable JPEG algorithm is challenging. Previous works approximate JPEG either with the iterative optimization [26] or the differentiable degradation simulator [47, 63] during training, and revert to the conventional JPEG algorithm at test time. However, these methods do not optimize the RD performance in their models. In a concurrent work, Xiao et al. [54] extend IRN with a fixed JPEG compression module and an extra JPEG artifact removal module. However, they have not considered the bpp and the reconstruction quality as a joint optimization problem. In this work, we propose a novel differentiable JPEG process with the QPM guided by a bitrate loss for RD performance optimization. Moreover, our real-time decoder reconstructs the HR image from both the spatial and frequency domains of a thumbnail and further improves the reconstruction quality. + +# 3. Method + +# 3.1. JPEG Preliminary + +As our solution involves optimizing the rate-distortion (RD) performance of the JPEG thumbnail, we briefly summarize the JPEG algorithm [49] in this section. The JPEG algorithm compresses an image in three steps. First, given an RGB image $y \in \mathbb{R}^{3 \times h \times w}$ , the algorithm converts $y$ into the luma-chroma color space (YCbCr). Second, the converted image is divided into $8 \times 8$ pixel blocks as $y \in \mathbb{R}^{3 \times N \times 8 \times 8}$ , where $N = \frac{h \times w}{8 \times 8}$ . Then, $y$ is transformed to its corresponding Discrete-Cosine-Transform (DCT) coefficients $C \in \mathbb{R}^{3 \times N \times 8 \times 8}$ : + +$$ +C = \left(C _ {Y}, C _ {C b}, C _ {C r}\right) = \mathrm {D C T} \left(y _ {Y}, y _ {C b}, y _ {C r}\right). \tag {1} +$$ + +Third, the luma coefficient $C_Y$ and chroma coefficient $C_C = (C_{Cb}, C_{Cr})$ are quantized separately by two quan- + +![](images/3fb72b70a6cc82c75acfa2f156429f066a2c12a8ab9918dccac04ac029b2ad6f.jpg) +Figure 2. The overview of our approach. Given an HR input image $x$ , we first encode $x$ to its LR representation $y$ with the encoder $E$ , where the scaling factor is $s$ . Second, we transform $y$ to DCT coefficients $C$ and predict the quantization tables $Q_{L}, Q_{C}$ with our quantization prediction module (QPM). Third, we adopt an entropy model [6] to estimate the bitrate of the quantized coefficients $\widetilde{C}$ at training stage. After the rounding and truncation, which we denoted as $[\cdot]$ , the $[Q_{L}]$ , $[Q_{C}]$ and $[\widetilde{C}]$ can be written and read with off-the-shelf JPEG API at the testing stage. To restore the HR, we extract features from $\widehat{C}$ with a frequency feature extractor $f$ and produce the high-fidelity image $\hat{x}$ with the decoder $D$ . + +tization tables $Q_{L}$ and $Q_{C}$ : + +$$ +\widetilde {C _ {Y}} = \frac {C _ {Y}}{[ Q _ {L} ]}, \quad \widetilde {C _ {C}} = \frac {C _ {C}}{[ Q _ {C} ]}, \tag {2} +$$ + +where $[\cdot]$ represents the rounding and truncation function. Unlike the original JPEG algorithm which applies a set of image-invariant quantization tables, our work predicts the $Q_{L}$ and $Q_{C}$ with the QPM (Sec. 3.3) for different images. As shown in the bottom-right of Fig. 2, the quantization tables $[Q] = ([Q_{L}],[Q_{C}])$ and quantized DCT coefficients $[\widetilde{C}] = ([\widetilde{C_{Y}}],[\widetilde{C_{C}}])$ are encoded into a JPEG file. At the decoding phase, the JPEG decoder can extract $[Q],[\widetilde{C}]$ from the JPEG file for image reconstruction with inverted operations of above steps: + +$$ +\widehat {C} _ {Y} = \left[ \widetilde {C} _ {Y} \right] \left[ Q _ {L} \right], \quad \widehat {C} _ {C} = \left[ \widetilde {C} _ {C} \right] \left[ Q _ {C} \right], \tag {3} +$$ + +and $\hat{y} = \mathrm{IDCT}(\hat{C})$ , where IDCT is the inverse operation of DCT, and $\hat{C}$ is the abbreviation of $[\widehat{C_Y},\widehat{C_C}]$ . + +# 3.2. Overview of HyperThumbnail + +Inspired by recent progress in high-fidelity efficient restoration through an efficient MLP [41] or a small transformer [22], we adopt an asymmetric encoder-decoder framework, which enables real-time reconstruction. Fig. 2 + +illustrates the overview of our framework. Given an HR input image $x \in \mathbb{R}^{3 \times H \times W}$ , we first generate its LR representation $y \in \mathbb{R}^{3 \times \frac{H}{s} \times \frac{W}{s}}$ through our encoder $E$ , where the $s$ is the rescaling factor and our encoder $E$ is an U-Net [45] with dense blocks [23]. To further decrease the file size, we transform $y$ to DCT coefficients $C \in \mathbb{R}^{3 \times \frac{H \times W}{64 \times s^2} \times 8 \times 8}$ . Then, we quantize $C$ with image-specific quantization tables $Q \in \mathbb{R}^{2 \times 8 \times 8}$ (Sec. 3.3). During the test time, we encode and decode $(Q, \widehat{C})$ with off-the-shelf JPEG API, and then retrieve $(\widehat{C}, \hat{y})$ with Eqn. (3). In the upsampling stage, we reconstruct the high-fidelity HR $\hat{x}$ with our efficient frequency-aware decoder in real time (Sec. 3.4). + +# 3.3. Quantization Prediction Module + +As JPEG [49] is a widely adopted compression algorithm, some previous methods [26, 47, 58, 63] in image embedding also introduce JPEG (Sec. 3.1) to compress their encoded image. However, JPEG degrades the embedded information in the encoded image and leads to a performance drop in the decoding stage (Sec. 5). JPEG uses fixed quantization tables with constant values [49], which we believe is suboptimal since different images have different frequency distribution. Hence, besides encoding HR images to LR thumbnails, we also predict the quantization tables $Q$ for each thumbnail with the quantization prediction module + +(QPM), which boosts the RD performance of our framework significantly. The QPM is implemented as two separate 8-layer multilayer perceptron (MLPs): the luma predictor $\mathrm{MLP}_L$ and the chroma predictor $\mathrm{MLP}_C$ . For block $C_k = (C_{Y,k}, C_{C,k})$ , we vectorize $C_k$ into a 1D vector and produce its quantization table with QPM. Thus we have + +$$ +Q _ {L} = \frac {\sum_ {k} \mathrm {M L P} _ {L} (C _ {Y , k})}{| C _ {Y , k} |}, Q _ {C} = \frac {\sum_ {k} \mathrm {M L P} _ {C} (C _ {C , k})}{| C _ {C , k} |}, \tag {4} +$$ + +where $|\cdot|$ denotes the block counts. To facilitate the conventional JPEG codec, we take the average $Q$ as the quantization table for the whole image. Following the training stage of learned compression [7], we adopt the additive uniform noise $\epsilon$ where each element follows $\mathcal{U}(-\frac{1}{2},\frac{1}{2})$ to approximate the non-differentiable quantization noise introduced in Eqn. (2): + +$$ +\widetilde {C _ {Y}} = \frac {C _ {Y}}{Q _ {L} + \epsilon} + \epsilon , \quad \widetilde {C _ {C}} = \frac {C _ {C}}{Q _ {C} + \epsilon} + \epsilon . \tag {5} +$$ + +In the testing stage, we switch back to the standard quantization function in Eqn. (2) to fit the JPEG API. Experiments show that our QPM predicts better quantization tables $Q$ so that it improves the RD performance of our framework (Sec. 5). Our experiments in the supplement also show that our QPM improves the standard JPEG algorithm. + +# 3.4. Frequency-aware Decoder + +As mentioned in Sec. 3.1, the JPEG quantization is applied on the DCT domain coefficients $\widetilde{C}$ and leads to the well-known quantization noise. Previous works [47,53,58] usually decode the embedded information from the RGB domain of the JPEG image. However, we note that quantization noise can be approximated by simple independent uniform noise [6] in the DCT domain, but it is nonlinear and more complex to model in the RGB domain after IDCT. + +Inspired by recent works in JPEG artifact removal [18, 20, 52, 60] and image generation [42], we further propose a novel plug-in named frequency feature extractor $f$ for additional frequency domain perception. We first reshape the dequantized DCT coefficients into a sparse representation $\widehat{C} \in \mathbb{R}^{192 \times \frac{H}{8s} \times \frac{W}{8s}}$ [42]. Then, we extract features $f(\widehat{C}) \in \mathbb{R}^{24 \times \frac{H}{s} \times \frac{W}{s}}$ and concatenate $f(\widehat{C})$ with the RGB image $\hat{y}$ . The concatenated features are fed into the decoder to reconstruct the HR image $\hat{x}$ : + +$$ +\hat {x} = D (\hat {y} \oplus f (\hat {C})), \tag {6} +$$ + +where $\oplus$ is the concatenation operator along the channel dimension. Since $\widehat{C}$ is $\frac{1}{8}$ of $\hat{y}$ in the spatial resolution, $f$ takes negligible computational overhead. In this way, our decoder is lightweight enough to reconstruct 6K HR images in real time (Fig. 5). $f$ improves our RD performance and is more efficient than increasing the decoder capacity. Please refer to our supplement for more details of our architecture. + +# 3.5. Training Objectives + +Bitrate loss To optimize the RD performance of our framework, it is critical to estimate the code length (bitrate) of the quantized coefficients $\widetilde{C}$ at the training stage. Inspired by Balle et al. [6], the rate $R$ of $\widetilde{C}$ is estimated with differentiable fully-factorized entropy models: + +$\mathrm{R} = \mathrm{E}_{x\sim p_x}[-\log_2p_L(\widetilde{C}_Y) - \log_2p_C(\widetilde{C}_{Cb}) - \log_2p_C(\widetilde{C}_{Cr})],$ (7) where $p_L$ and $p_C$ are two fully-factorized entropy models for luma and chroma coefficient maps, respectively. In our work, we reshape $\widetilde{C}$ to $(3,64,\frac{H}{8s},\frac{W}{8s})$ , and assume the value of each pixel in $\widetilde{C}$ to be independent following Balle et al. [6]. For accurate rate estimation, we train $p_L$ and $p_C$ to model the 64-channel probability density functions of $\widetilde{C}_Y$ and $(\widetilde{C}_{Cb},\widetilde{C}_{Cr})$ by minimizing an auxiliary loss $L_{aux}$ [7]. The bpp of the restored image $\hat{x}$ is calculated by + +$$ +L _ {b p p} = \frac {R}{H \times W}. \tag {8} +$$ + +More details of auxiliary loss is provided in the supplement. + +Reconstruction and guidance loss Thanks to the fully differentiable pipeline (Fig. 2), it is possible for us to train our encoder, QPM and decoder with similar loss terms used in previous works [36, 55]. Following IRN [55], we employ $L_{1}$ on the reconstructed $\hat{x}$ and a $L_{2}$ guidance loss on the JPEG thumbnail $\hat{y}$ : + +$$ +L _ {r e c o n} = \frac {\left| \left| \hat {x} - x \right| \right| _ {1}}{H \times W}, \tag {9} +$$ + +$$ +L _ {\text {g u i d e}} = \frac {\left\| \hat {y} - y _ {\text {r e f}} \right\| _ {2} ^ {2}}{(H / s) \times (W / s)}, \tag {10} +$$ + +where $y_{ref}$ is a guidance image downsampled from $x$ with bicubic interpolation [40]. Altogether, we train our framework by minimizing the total loss $L_{rescale}$ : + +$$ +L _ {r e s c a l e} = L _ {r e c o n} + \lambda_ {1} L _ {g u i d e} + \lambda_ {2} L _ {b p p}. \tag {11} +$$ + +Empirically, we set $\lambda_1 = 0.6$ . The target bpp of our framework could be adjusted by a loss scaling factor $\lambda_{2}$ , which we set to 0.01 for most experiments. The total loss $L_{rescale}$ is adopted to optimize the parameters of the encoder, the decoder, and QPM. + +# 4. Experiments + +# 4.1. Experimental Setup + +Evaluation metrics We evaluate our upscaling efficiency using running time and multiply-accumulation operations (MACs). We evaluate the quality of our reconstructed and embedding images using the PSNR on RGB channels. + +Rescaling methods are developed to embed an HR image into an LR one to reduce file size. However, there is no existing comprehensive evaluation of bitrate for these methods. Following previous compression approaches [6, 7, 56], + +
MethodBitrate↓-Distortion↑ [1]Upscaling Efficiency↓Reconstructed HR PSNR↑
Down & Degradation & UpbppPSNRTime (ms)GMacsSet5Set14BSD100Urban100DIV2KFiveK-6k
Bicubic & JPEG & Bicubic0.2925.18--25.1423.4924.0221.0525.7026.90
Bicubic & JPEG & EDSR [37]0.2926.7791.01007.528.3425.7325.6023.5827.8327.23
Bicubic & JPEG & SwinIR [35]0.2926.934012.66208.728.5625.9925.7224.0928.0727.44
ComCNN & RecCNN [26]0.3227.02469.76014.728.2925.8425.7823.7027.9927.40
IRN [55] & JPEG0.3128.48977.84751.730.0027.2326.9125.7229.5427.96
HCFlow [36] & JPEG0.3028.761025.94626.029.9827.4127.0526.1929.7128.01
Ours-full0.3029.67247.91277.530.4828.2127.9327.3530.4928.51
Ours0.3029.4237.8156.230.2227.8727.6626.6230.1528.15
+ +Table 2. Quantitative evaluation of upscaling efficiency and reconstruction fidelity. We keep bpp around 0.3 on Kodak [1] for different methods, and the distortion is measured by the PSNR on the reconstructed HR images. Our approach outperforms other methods with better HR reconstruction and a significantly lower runtime. We measure the running time and GMacs of all models by upscaling a 960 × 540 LR image to a 3840 × 2160 HR image. The measurements are made on an Nvidia RTX 3090 GPU with PyTorch-1.11.0 in half-precision mode for a fair comparison. + +![](images/8de16a67099eb9792484bab29a6f1f6f62236aecbae86eb399c8a158da7b4f59.jpg) +Figure 3. Reconstructed HR images and LR thumbnails by different methods on the DIV2K [4] validation dataset. We crop the restored HR images to ease the comparison and visualize the LR counterparts at the bottom-right. The bpp is calculated on the whole image and the PSNR is evaluated on the cropped area of the reconstructed HR images. + +we evaluate the RD performance with the HR reconstruction PSNR against bits-per-pixel. Instead of estimating the bitrate from the entropy encoder (Eqn. (7)) during training, we use the real file size of JPEG thumbnails for evaluating the bitrate: + +$$ +\operatorname {b p p} = \mathbb {E} _ {x \sim p _ {x}} [ \frac {\text {f i l e s i z e}}{H \times W} ]. \tag {12} +$$ + +Since there exists a trade-off between image bitrate and fidelity, we visualize the rate-distortion curve of different models during our ablation study. + +Datasets We train our model with the widely-used DIV2K [4] image dataset, which contains 800 2K-resolution images in the training set and 100 more in the validation set. From the perspective of rescaling, we test our model on 4 conventional datasets: the Set5 [10], Set14 [59], BSD100 [38], and Urban100 [24]. To reveal our real-world performance, we collect first 20 images above 6K resolu + +tion (ranked by their bpp) from MIT-Adobe FiveK [11] as another test set FiveK-6k. In addition, we evaluate the RD performance on Kodak dataset [1], which is widely adopted in image compression researches [8]. The details of the training strategy are provided in the supplement. + +# 4.2. Compare with Baselines + +We consider three categories of reconstruction methods as our baselines: (1) downscaling with Bicubic interpolation, compressing with standard JPEG codec, and upscaling with state-of-the-art SR models [35, 37]; (2) autoencoder using standard JPEG transmission format [26]; (3) rescaling using symmetric invertible neural network [36, 55] and compressing the LR image using standard JPEG codec. For fair evaluation, we improve the RD performance of baselines using standard JPEG compression. We retrain SR models [35, 37] on LR JPEG compressed images to restore + +![](images/da95cc986741791025b49eaad50217de728cf20c71725e1df7d5aacc90095269.jpg) +Bicubic $4\times$ + +![](images/1d5324b6b6ca086bef8f8aea758a59ab2b9f84fb486af012699efb37a6cb3f02.jpg) +IRN 55/964× & JPEG qg = 96 + +![](images/5fe87f9f1c46175109eff22f66c2c106b275e3a17bbdbfe3a869e27075776c83.jpg) +HJGFlow [36]4× & JPEG q=90 + +![](images/7aa0be6458a94c8d32ea2e09cea00cd208d9963898b54b4d2593a02ca4f549bf.jpg) +Ours $4\times$ + +![](images/26546278b6f4b90e23ad9de58cdd39e5e13915d1289c2cc759a25e421d9d35f6.jpg) +Ours-full $4\times$ + +![](images/e872eb1d37d447c60212cdcd18d04fa05e02be71e42822644379021497cc1f30.jpg) +bpp↓/PSNR↑ + +![](images/6135e8ca76d7d567547bfa3c77379856925394aa9e66ffa316db202d89379b13.jpg) +0.510/26.67 + +![](images/8f02376ab54a28d6bd5ca0f828f08537d6e4aa4f07e897cdbd16c4e29ee349c7.jpg) +0.468/17.47 + +![](images/ed04f7a352e9a6b8f48c0fd4148bf42a96f089221ddb646ab77463af6dcd755f.jpg) +0.430 / 27.99 +Figure 4. Downscaled LR thumbnails by different methods on Set14 image comic. With a similar target bpp, our model introduces least artifacts in the thumbnail in comparison to baselines. + +![](images/6ec579650ce430376dc133716c0d64a29ce0aea67964cb9c1a3f3dac03ed5e4b.jpg) +0.446 / 27.90 + +HR images. Besides, we retrain INN baselines [36, 55] and encoder-decoder baselines [26] with a differentiable JPEG module [46]. To compare our RD performance against baselines, we constrain their bpp on Kodak dataset to be around 0.3 by adjusting the quality factor of JPEG compression in all baselines. In our supplement, we provide an additional comparison with image compression (e.g., the original JPEG) and rescaling baselines using their original transmission format (e.g., lossless PNG), where our advantage is even larger. + +Upscaling efficiency and HR fidelity Table 2 presents the upscaling efficiency of all methods and reconstruction fidelity at around 0.3 bpp. We measure the running time and GMacs of upscaling a $960 \times 540$ resolution LR image to a $3840 \times 2160$ HR image on an Nvidia RTX 3090 GPU. We use PyTorch implementation with 16 bits floating-point precision for a fair comparison. As shown in Table 2, "Ours" model only costs $3.1\%$ of the GMacs and $3.7\%$ of upscaling time compared to HCFlow [36]. We still improve the reconstructed RGB PSNR by 0.61 dB on BSD100 test set with a significantly lower computation. + +In addition, we train the "Ours-full" model with a larger decoder. "Ours-full" model achieves higher PSNR that outperforms HCFlow [36] and IRN [55] for more than 1.16 dB on Urban100 test set with only $24.2\%$ of upscaling time. Fig. 3 provides the visual comparison of restored images. From left to right, we show perceptual differences from ground truth, $4\times$ rescaling results of the baselines [36, 55] with JPEG, and our framework. For the first row, our models restore more textures of the glass and the pot lid. Similarly, among all reconstructions in the second row, only our model can recover the details on hair and earmuffs. Besides, the JPEG compression breaks the invertibility of the INN-based rescaling methods [36, 55], they failed to restore sharp and accurate high-frequency textures in the HR images. + +LR qualitative evaluation The visual quality of the LR thumbnails is also important because users preview them + +
MethodLR睫毛 PSNR↑
Down & DegradationKodakSet5Set14BSD100Urb100DIV2KFiveK-6k
Bicubic & JPEG37.7234.4135.7937.4336.6437.1435.14
IRN [55] & JPEG30.9530.0027.2326.9125.7229.5431.25
ComCNN & RecCNN [26]28.0026.7626.4727.4725.5728.1528.99
HCFlow [36] & JPEG19.8820.0819.4219.6518.9620.5220.31
Ours-full33.2131.8631.7632.4431.0133.3233.99
Ours33.5531.9631.9332.9031.1633.6234.24
+ +Table 3. Quantitative evaluation of the $4 \times$ downsampled LR thumbnails by different methods. The target bitrate is around 0.3 bpp on Kodak [1] for all methods, and we take Bicubic LR as the ground truth. Our thumbnail preserves visual contents better. + +![](images/432f4fa96166339edbc7d9586fa5271dd1751415914f2f60dbdaa16097122fd9.jpg) +Figure 5. Model runtime. We profile the $4 \times$ encoder and decoder at different target resolution in half-precision mode. Especially, we convert our decoder from PyTorch to TensorRT for further inference time reduction. + +![](images/ed193456623e0935b07095c505c8bcbdbedc116a60a9fb2047df27a3f60a47a2.jpg) + +directly. Table 3 presents the average LR PSNR of corresponding models, we have the best LR PSNR against INN-based methods. In Fig. 4, we qualitatively compare the visual quality of the thumbnails encoded by rescaling methods. Our method generates LR thumbnails with significantly fewer artifacts without compromising much HR reconstruction quality, please see more analysis in Sec. 5. + +# 4.3. Real-time Inference on 6K Images + +Fig. 5 shows our evaluation of the downscaling and upscaling runtime of our framework at multiple resolutions. Noted that we conduct the profiling in half-precision (FP16) mode. Besides, we also converted the trained decoder model from PyTorch to FP16 TensorRT model with torch2trt [2] API to further reduce the upscaling time without performance drop in HR reconstruction. As shown in Fig. 5(b), our efficient decoder can upscale an LR thumb-nail by $4 \times$ in real time at 4K ( $3840 \times 2160$ ) 70.8 FPS, 5K ( $5120 \times 2880$ ) 38.8 FPS, or 6K ( $5760 \times 3240$ ) 31.2 FPS on an RTX 3090 GPU. + +# 4.4. Extension for Optimization-based Rescaling + +Since the ground truth HR images are available for downscaling during the test stage, we may further optimize our encoder $E$ , QPM, and Entropy model, while fixing the pretrained decoder $D$ and feature extractor $f$ on the user's device. As shown in the Table 4, optimization-based rescaling improves the restoration PSNR 0.22dB with a lower bitrate on Set14 dataset. + +kodim04 / kodim09 +![](images/6a0e846fa3fdbbcc17327822175a987626724fb654ada9819f6980f1980cb44d.jpg) +bpp↓/LR↑/HR↑:kodim09 + +(a) Ours with Fixed JPEG tables, $q = 85$ +![](images/339d5dc4f62a7e0800754a08f13eb3afd16c7f8e5cb5d31a17fe8e455a3576f2.jpg) +bpp↓/LR↑/HR↑:kodim04 +0.263/26.91/30.54 +0.251/26.96/31.35 + +(b) Ours with Optimized tables +![](images/dbb89a513afb441f9725b9ea9aeb785b693725a87118d9a9922b7015a9d20b97.jpg) +0.289/29.10/30.93 +0.276/29.17/31.71 + +(c) Ours with QPM kodim04 +![](images/7654218e5be60993354ae4425a8f1a746dedc55a1c648f68ce4884637fe87499.jpg) +- +0.240/34.38/32.03 + +![](images/f19b24cb2e072ad1594db23fbd1d8577b6df9b6569b8ae54394e22e15fc59186.jpg) +(d) Ours with QPM kodim09 + +Figure 6. Quantization tables on Kodak [1] images. We visualize the quantization table $Q_{L}$ (the green table) and $Q_{C}$ (the orange table) for $\text{kodim04}$ and $\text{kodim09}$ of different quantization approaches. The model trained with QPM achieves the best RD performance from every aspect. For more analysis, please refer to Sec. 5 in our paper. +![](images/c6b44ac9274c52091c536b0dd214354891be3412119d1163881797b471b06a8b.jpg) +0.246/31.03/34.34 + +
MethodOptimizationbpp↓ / HR PSNR↑
ArchitectureiterationKodakSet5Set14
Ours00.301 / 29.420.379 / 30.230.359 / 27.74
1000.307 / 29.550.377 / 30.360.347 / 27.96
+ +Table 4. Quantitative evaluation for optimization-based rescaling. + +# 5. Ablation Study + +In this section, we study the effectiveness of our proposed Quantization Prediction Module, designed training loss and architectures on "Ours" model. + +Quantization prediction module To examine the effectiveness of our QPM, in Fig. 7, we quantitatively evaluate the RD performance on both the restored HR and the LR JPEG thumbnails of different quantization approaches. For "fixed tables" and "optimized tables", we initialize the quantization tables following the default JPEG. Particularly, for "optimized tables," we also optimize the quantization tables at the training stage. We illustrate the curve for each model by adjusting the global quality factor $q$ on the quantization tables $Q$ following JPEG as $Q' = Q \times q$ . The target bitrate goes lower when $q$ increases. In Fig. 6, we also visualize the quantization tables of different settings. We notice that compared to the corresponding value in the fixed or optimized table, the high-frequency quantization steps in the QPM predicted tables are much smaller and are image-specific, which may introduce less compression on the embedding pattern that is important for HR reconstruction. Consequently, compared to settings with image-invariant quantization, "Ours" model achieves the best quality on the reconstructed $\hat{x}$ and introduces significantly fewer artifacts on the LR thumbnail $\hat{y}$ , which also lowers the file-size of the thumbnails. To further investigate the effectiveness of QPM, we also leverage QPM to improve the RD performance of standard JPEG (without the downscaling and upscaling). Please refer to our supplement for more details. + +Guidance loss In Fig. 7, we also present the RD curve of the "Ours w/o guidance loss" model trained with $\lambda_{1} = 0$ . At around 0.4 bpp, removing guidance loss raises the HR + +![](images/11188a3ef29aaabc908843e9d609148acc6a2b91104b8a61b27d8bf5c58c920d.jpg) +(a) RD curve of restored HR image +Figure 7. QPM versus image-invariant quantization. We first train our models with QPM, with a fixed JPEG table or with an optimized table, respectively. Then, we evaluate the at different target bitrate on Kodak [1] dataset. (a) the RD curve on reconstructed HR image $\hat{x}$ and input $x$ ; (b) the RD curve on LR thumbnail $\hat{y}$ and the Bicubic downsampled LR $y_{ref}$ . + +![](images/6e3027635cc3d040a7f674e22a92307379cc66cc7fcad8d5ef708fad1e52ac21.jpg) +(b) RD curve of LR thumbnail + +PSNR by $0.09\mathrm{dB}$ . However, the PSNR of LR thumbnail drops significantly from 34.1 dB to 13.06 dB. It is unacceptable for user-viewable thumbnails. + +Encoder decoder architecture As we study some variants of "Ours" model, we find that $f$ improves the quality of both encoded LR thumbnail (0.29 dB) and restored HR image (0.10 dB). Also, adopting $f$ is more effective than simply increasing the decoder capacity. Moreover, our study of the encoder capacity reveals that our framework does benefit from a larger encoder. More details are in our supplement. + +# 6. Conclusion + +In this paper, we propose a new HyperThumbnail framework that can perform real-time 6K image reconstruction from an LR JPEG thumbnail. We utilize an asymmetric encoder-decoder architecture where the encoder takes most of the computation while the decoder is relatively lightweight for real-time performance. A new quantization prediction module is proposed to optimize the RD performance for image rescaling, which is not studied in prior work. 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Image Represent., 63, 2019. 3, 4 \ No newline at end of file diff --git a/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/images.zip b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fc6d40fa324b602f08b9eb75a57a1067a8e91c21 --- /dev/null +++ b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9da44b8785378ab98f244bd72e9e9974abcc8b3a154a1c9af7e3b6ca9e1e6a89 +size 639914 diff --git a/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/layout.json b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e25d8861aa6d20529553358ef6b45ff5f5f54428 --- /dev/null +++ b/2023/Real-Time 6K Image Rescaling With Rate-Distortion Optimization/layout.json @@ -0,0 +1,10844 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 96, + 103, + 500, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 103, + 500, + 121 + ], + "spans": [ + { + "bbox": [ + 96, + 103, + 500, + 121 + ], + "type": "text", + "content": "Real-time 6K Image Rescaling with Rate-distortion Optimization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 143, + 533, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 143, + 533, + 174 + ], + "spans": [ + { + "bbox": [ + 83, + 143, + 533, + 174 + ], + "type": "text", + "content": "Chenyang Qi* Xin Yang* Ka Leong Cheng Ying-Cong Chen Qifeng Chen Hong Kong University of Science and Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 224, + 290, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 290, + 488 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 290, + 488 + ], + "type": "text", + "content": "Contemporary image rescaling aims at embedding a high-resolution (HR) image into a low-resolution (LR) thumbnail image that contains embedded information for HR image reconstruction. Unlike traditional image superresolution, this enables high-fidelity HR image restoration faithful to the original one, given the embedded information in the LR thumbnail. However, state-of-the-art image rescaling methods do not optimize the LR image file size for efficient sharing and fall short of real-time performance for ultra-high-resolution (e.g., 6K) image reconstruction. To address these two challenges, we propose a novel framework (HyperThunnail) for real-time 6K rate-distortion-aware image rescaling. Our framework first embeds an HR image into a JPEG LR thumbnail by an encoder with our proposed quantization prediction module, which minimizes the file size of the embedding LR JPEG thumbnail while maximizing HR reconstruction quality. Then, an efficient frequency-aware decoder reconstructs a high-fidelity HR image from the LR one in real time. Extensive experiments demonstrate that our framework outperforms previous image rescaling baselines in rate-distortion performance and can perform 6K image reconstruction in real time." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 529, + 287, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 671 + ], + "type": "text", + "content": "With an increasing number of high-resolution (HR) images being produced and shared by users on the internet, a new challenge has arisen: how can we store and transfer HR images efficiently? Storing HR images on the cloud, such as iCloud, is becoming a widely adopted solution that saves storage on a user's mobile device (e.g., smartphones) as only their low-resolution (LR) counterparts are stored on the mobile device for an instant preview. However, when a user wants to obtain the full-resolution image, the entire HR image must be downloaded on the fly from the cloud, which can result in a poor user experience when the internet connection is unstable or not available." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "content": "Real-time image rescaling can serve as a competitive solution to improving the user experience of cloud photo stor" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 201, + 547, + 335 + ], + "blocks": [ + { + "bbox": [ + 309, + 201, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 309, + 201, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 309, + 201, + 547, + 335 + ], + "type": "image", + "image_path": "d6cb2ef8ea88dc088fd211959e86176b5304f5ec6d76505c5db28bbc11391393.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 341, + 547, + 462 + ], + "lines": [ + { + "bbox": [ + 305, + 341, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 547, + 462 + ], + "type": "text", + "content": "Figure 1. The application of 6K image rescaling in the context of cloud photo storage on smartphones (e.g., iCloud). As more high-resolution (HR) images are uploaded to cloud storage nowadays, challenges are brought to cloud service providers (CSPs) in fulfilling latency-sensitive image reading requests (e.g., zoom-in) through the internet. To facilitate faster transmission and high-quality visual content, our HyperThumbnail framework helps CSPs to encode an HR image into an LR JPEG thumbnail, which users could cache locally. When the internet is unstable or unavailable, our method can still reconstruct a high-fidelity HR image from the JPEG thumbnail in real time." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 473, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 653 + ], + "type": "text", + "content": "age, as shown in Fig. 1. Such a solution can first embed an HR image (on the cloud) into an LR JPEG thumbnail (on the mobile device) by an encoder, and the thumbnail provides an instant preview with little storage. When the user wants to zoom in on the thumbnail, the HR image with fine details can be reconstructed locally in real time. In addition, image rescaling has other applications in image sharing, as it can \"bypass\" the resolution limitation of some platforms (e.g., WhatsApp) to reconstruct a high-quality HR image from an LR one [57]. While modern smartphones and cameras can capture ultra-high-resolution images in 4K (iPhone 13) or even 6K (Blackmagic camera), we are interested in designing a real-time image rescaling framework for ultra-high-resolution images (e.g., 4K or 6K), which minimizes LR file size while maximizing HR and LR image quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "However, existing image rescaling methods have their own flaws in practice, as shown in Table 1 where we compare different image rescaling methods in terms of their properties. One potential solution is to upsample the downsampled thumbnail with super-resolution (SR) meth" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14092" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 178 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 178 + ], + "type": "table", + "html": "
Method(a) Downsampled JPEG + super-resolution [37](b) Flow-based rescaling [36, 55](c) Ours
ArchitectureHRLR.jpgHRHRLRHRHRLR.jpgHR
Reconstruction fidelityX✓✓
Rate-distortion optimizationXX✓
Real-time 6K reconstruction-X✓
", + "image_path": "ad532d5136dc1553a67d2af078f9b1247c5b29faa3ae34f8e577c4b1790f44ef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 187, + 546, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 546, + 232 + ], + "type": "text", + "content": "Table 1. The comparison of different methods related to image rescaling. (a) Super-resolution from downsampled JPEG does not optimize rate-distortion performance and can hardly maintain high fidelity due to information lost in downsampling. (b) SOTA flow-based image rescaling methods also ignore the file size constraints and are not real-time for 6K reconstruction due to the limited speed of invertible networks. (c) Our framework optimizes rate-distortion performance while maintaining high-fidelity and real-time 6K image rescaling." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 244, + 289, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 289, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 289, + 508 + ], + "type": "text", + "content": "ods [14, 17, 35, 37, 61, 62] (Table 1(a)). However, such a framework applies a simple downsampling strategy (e.g., Bilinear, Bicubic) to the HR image so that high-frequency details are basically lost in the LR thumbnail. Also, SR methods only focus on HR reconstruction, which leads to a sub-optimal image rescaling performance. Instead, dedicated image rescaling approaches aim to embed information into a visually pleasing LR image and then reconstruct the HR image with an upsampling module. Recently, state-of-the-art image rescaling works utilize normalizing flow [25, 36, 55, 57] show impressive image embedding and reconstruction capability that outperforms SR approaches, in terms of the reconstructed HR image quality. However, there are still some great challenges to apply these flow-based rescaling frameworks in real-world applications, as shown in Table 1(b). First, the file size of the LR thumbnail is not optimized. Second, the reconstruction stage of these image rescaling methods is computationally expensive due to their invertible network architecture with extensive use of dense blocks [23]: IRN [55] costs about a second to reconstruct a 4K image with 4x rescaling on a modern GPU, which is far from real time (Table 2)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 509, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 664 + ], + "type": "text", + "content": "In this work, we propose the HyperThumbnail, a rate-distortion-aware framework for 6K real-time image rescaling, as shown in Table 1(c). In this framework, we embed an HR image into a low-bitrate JPEG thumbnail by an encoder and a quantization table predictor, as JPEG is a dominant image compression format today [3]. Then the JPEG thumbnail can be upscaled to its high-fidelity HR counterpart with our efficient decoder in real time. We leverage an asymmetric encoder-decoder architecture, where most computation is put in the encoder to keep the decoder lightweight. This makes it possible for our decoder to upscale a thumbnail to 6K in real time, significantly faster than previous flow-based image rescaling methods [36,55]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Meanwhile, the Rate-Distortion (RD) performance is an important and practical metric rarely studied in prior rescaling works. In this paper, we define the rate as the ratio between the thumbnail file size and the number of pixels" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 244, + 547, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 547, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 547, + 448 + ], + "type": "text", + "content": "in the HR image, also known as the bits-per-pixel (bpp). The distortion consists of two parts: the perceptual quality of the thumbnail (LR distortion) and the fidelity of the restored HR image (HR distortion). The rate-distortion performance evaluates an image rescaling framework in both storage cost and visual quality. Without explicit RD constraints, recent works in image rescaling [36, 55] do not consider RD performance in their models. While some works [26,47,53,54,58] leverage the rate constraint by embedding extra information in JPEG, they simply utilize a fixed differentiable JPEG module, which we argue is suboptimal for image rescaling. Because such a process deteriorates the information in the embedding images without considering their local distribution. Moreover, the quantization process of JPEG introduces noise in the frequency domain and introduces well-known JPEG artifacts, which brings great challenges to information restoration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 448, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 579 + ], + "type": "text", + "content": "To remedy these issues, our image rescaling framework is designed to jointly optimize image quality and bpp with entropy models. Instead of using fixed quantization tables in conventional JPEG (Sec. 3.1), we propose a novel quantization prediction module (QPM) that predicts image-adaptive quantization tables, which can optimize RD performance. We further adopt a frequency-aware decoder which alleviates JPEG artifacts in the thumbnails and improves HR reconstruction. Moreover, our asymmetric encoder-decoder framework can be extended to optimization-based compression." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 580, + 503, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 580, + 503, + 590 + ], + "spans": [ + { + "bbox": [ + 317, + 580, + 503, + 590 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 598, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 598, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 598, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 317, + 598, + 545, + 683 + ], + "type": "text", + "content": "- We propose a 6K real-time rescaling framework with an asymmetric encoder-decoder architecture, named HyperThumbnail, which embeds a high-resolution image into a JPEG thumbnail that can be viewed in popular browsers. The decoder utilizes both spatial and frequency information to reconstruct high-fidelity images in real time for 6K image upsampling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "content": "- We introduce a new quantization prediction module (QPM) that improves the RD performance in the en" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14093" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "content": "coding stage of our framework. Furthermore, we adopt rate-distortion-aware loss functions along with QPM to optimize the RD performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 126, + 287, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 126, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 59, + 126, + 287, + 174 + ], + "type": "text", + "content": "- Experiments show that our framework outperforms state-of-the-art image rescaling methods with higher LR and HR image quality and faster reconstruction speed at similar file size." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 192, + 134, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 134, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 134, + 205 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 214, + 180, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 214, + 180, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 214, + 180, + 227 + ], + "type": "text", + "content": "2.1. Image Super-resolution" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 236, + 288, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 288, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 288, + 390 + ], + "type": "text", + "content": "Image super-resolution (SR) targets at restoring HR images from LR images. Pioneering works on SR such as SRCNN [17], EDSR [37], and other successors [14, 33, 34, 61, 62] exploit deep neural networks to solve the challenges in image SR. Recently, Liang et al. [35] propose a Swin Transformer-based framework with state-of-the-art image SR performance. In addition, Wang et al. [50, 51] extend SRGAN [31] and demonstrate the potential of producing perceptually pleasing HR images with a GAN-based generator. Despite great recent progress, most of these methods assume a simple deterministic downsampling process (e.g., Bicubic downsampling [40]), which limits the reconstruction quality of high-frequency details in image SR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 405, + 147, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 147, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 147, + 418 + ], + "type": "text", + "content": "2.2. Image Rescaling" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 715 + ], + "type": "text", + "content": "Different from SR, image rescaling aims to downsample the given HR image into a visually satisfying LR image with embedded information, and then reconstruct the HR image with high fidelity. A straightforward solution is downscaling using detail-preserving methods [29] and upscaling with heavy SR networks [14, 35, 37]. Recently, efforts have been made to apply invertible neural network (INN) to image rescaling. INN [9, 12, 15, 16, 19, 28, 30, 43] provides direct access to the inverse mapping of the forward function, making it a popular framework for image rescaling [13, 36, 55]. Xiao et al. [55] make the first attempt to model image downscaling and upscaling using invertible transformation. Liang et al. [36] further formulate the high-frequency components in INNs as a conditional distribution on LR image. However, the equivalence in the computational cost of the encoding and decoding process of INN makes it almost impossible to optimize the backward inference time independently, which limits its practicality in latency-aware scenarios. Besides, the file size of the embedding LR image in existing rescaling frameworks is yet to be studied. In this paper, we leverage the RD metric to evaluate the rescaling methods from a real-world perspective and compare our framework with existing image rescaling models in terms of their bpp and restored HR fidelity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 422, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 422, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 422, + 85 + ], + "type": "text", + "content": "2.3. Image Compression" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "content": "Instead of only shrinking the image size spatially, image compression approaches optimize the RD performance by first producing a compact bitstream, then decoding HR from the bitstream. Recently, learning-based methods [5-7,21,27,32,39,44,48,56] have improved RD performance by a large margin with neural encoders and decoders. However, these methods have not been widely adopted on the internet due to issues related to software compatibility or runtime efficiency. If users of neural compression need a thumbnail for easier manipulation and preview, they need to save another redundant file besides the bitstream, which is inconvenient and takes extra storage. Thus, traditional compression algorithms (e.g., JPEG [49]) are still popular on most social media platforms [3]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 261, + 546, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 546, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 546, + 476 + ], + "type": "text", + "content": "In this work, we embed HR images into LR JPEG thumbnails and restore HR images with a 6K real-time decoder. Training neural networks with the non-differentiable JPEG algorithm is challenging. Previous works approximate JPEG either with the iterative optimization [26] or the differentiable degradation simulator [47, 63] during training, and revert to the conventional JPEG algorithm at test time. However, these methods do not optimize the RD performance in their models. In a concurrent work, Xiao et al. [54] extend IRN with a fixed JPEG compression module and an extra JPEG artifact removal module. However, they have not considered the bpp and the reconstruction quality as a joint optimization problem. In this work, we propose a novel differentiable JPEG process with the QPM guided by a bitrate loss for RD performance optimization. Moreover, our real-time decoder reconstructs the HR image from both the spatial and frequency domains of a thumbnail and further improves the reconstruction quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 491, + 362, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 362, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 362, + 503 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 512, + 416, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 416, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 416, + 525 + ], + "type": "text", + "content": "3.1. JPEG Preliminary" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": "As our solution involves optimizing the rate-distortion (RD) performance of the JPEG thumbnail, we briefly summarize the JPEG algorithm [49] in this section. The JPEG algorithm compresses an image in three steps. First, given an RGB image " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{3 \\times h \\times w}" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": ", the algorithm converts " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": " into the luma-chroma color space (YCbCr). Second, the converted image is divided into " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": " pixel blocks as " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8}" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "N = \\frac{h \\times w}{8 \\times 8}" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": " is transformed to its corresponding Discrete-Cosine-Transform (DCT) coefficients " + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "inline_equation", + "content": "C \\in \\mathbb{R}^{3 \\times N \\times 8 \\times 8}" + }, + { + "bbox": [ + 304, + 533, + 545, + 651 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 332, + 664, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 664, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 332, + 664, + 545, + 677 + ], + "type": "interline_equation", + "content": "C = \\left(C _ {Y}, C _ {C b}, C _ {C r}\\right) = \\mathrm {D C T} \\left(y _ {Y}, y _ {C b}, y _ {C r}\\right). \\tag {1}", + "image_path": "fd2fe504386d57daca25b648fb47d57320f762d8da06969b00fdd1e0c4a7181a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Third, the luma coefficient " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "C_Y" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " and chroma coefficient " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "C_C = (C_{Cb}, C_{Cr})" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " are quantized separately by two quan-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14094" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 71, + 539, + 314 + ], + "blocks": [ + { + "bbox": [ + 62, + 71, + 539, + 314 + ], + "lines": [ + { + "bbox": [ + 62, + 71, + 539, + 314 + ], + "spans": [ + { + "bbox": [ + 62, + 71, + 539, + 314 + ], + "type": "image", + "image_path": "3fb72b70a6cc82c75acfa2f156429f066a2c12a8ab9918dccac04ac029b2ad6f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "lines": [ + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": "Figure 2. The overview of our approach. Given an HR input image " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": ", we first encode " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " to its LR representation " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " with the encoder " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": ", where the scaling factor is " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": ". Second, we transform " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " to DCT coefficients " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " and predict the quantization tables " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "Q_{L}, Q_{C}" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " with our quantization prediction module (QPM). Third, we adopt an entropy model [6] to estimate the bitrate of the quantized coefficients " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " at training stage. After the rounding and truncation, which we denoted as " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "[\\cdot]" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "[Q_{L}]" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "[Q_{C}]" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "[\\widetilde{C}]" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " can be written and read with off-the-shelf JPEG API at the testing stage. To restore the HR, we extract features from " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "\\widehat{C}" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " with a frequency feature extractor " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " and produce the high-fidelity image " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": " with the decoder " + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 322, + 548, + 390 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "text", + "content": "tization tables " + }, + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "inline_equation", + "content": "Q_{L}" + }, + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "inline_equation", + "content": "Q_{C}" + }, + { + "bbox": [ + 47, + 405, + 160, + 418 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 425, + 287, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 425, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 287, + 452 + ], + "type": "interline_equation", + "content": "\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{[ Q _ {L} ]}, \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{[ Q _ {C} ]}, \\tag {2}", + "image_path": "e391aeef609209c169b7b42bd431815a8588437e5e25d90395ebd6f9d92d3cd9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "[\\cdot]" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " represents the rounding and truncation function. Unlike the original JPEG algorithm which applies a set of image-invariant quantization tables, our work predicts the " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "Q_{L}" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "Q_{C}" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " with the QPM (Sec. 3.3) for different images. As shown in the bottom-right of Fig. 2, the quantization tables " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "[Q] = ([Q_{L}],[Q_{C}])" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " and quantized DCT coefficients " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "[\\widetilde{C}] = ([\\widetilde{C_{Y}}],[\\widetilde{C_{C}}])" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " are encoded into a JPEG file. At the decoding phase, the JPEG decoder can extract " + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "inline_equation", + "content": "[Q],[\\widetilde{C}]" + }, + { + "bbox": [ + 46, + 459, + 287, + 581 + ], + "type": "text", + "content": " from the JPEG file for image reconstruction with inverted operations of above steps:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 590, + 287, + 606 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 590, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 88, + 590, + 287, + 606 + ], + "type": "interline_equation", + "content": "\\widehat {C} _ {Y} = \\left[ \\widetilde {C} _ {Y} \\right] \\left[ Q _ {L} \\right], \\quad \\widehat {C} _ {C} = \\left[ \\widetilde {C} _ {C} \\right] \\left[ Q _ {C} \\right], \\tag {3}", + "image_path": "27690fc780f13fb85a61c9f671e0aaadbc6282fbb50b04907b72f01412e6cb7d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\mathrm{IDCT}(\\hat{C})" + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "text", + "content": ", where IDCT is the inverse operation of DCT, and " + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "text", + "content": " is the abbreviation of " + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "inline_equation", + "content": "[\\widehat{C_Y},\\widehat{C_C}]" + }, + { + "bbox": [ + 46, + 613, + 289, + 640 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 212, + 659 + ], + "type": "text", + "content": "3.2. Overview of HyperThumbnail" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Inspired by recent progress in high-fidelity efficient restoration through an efficient MLP [41] or a small transformer [22], we adopt an asymmetric encoder-decoder framework, which enables real-time reconstruction. Fig. 2" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": "illustrates the overview of our framework. Given an HR input image " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": ", we first generate its LR representation " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{3 \\times \\frac{H}{s} \\times \\frac{W}{s}}" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " through our encoder " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " is the rescaling factor and our encoder " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " is an U-Net [45] with dense blocks [23]. To further decrease the file size, we transform " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " to DCT coefficients " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "C \\in \\mathbb{R}^{3 \\times \\frac{H \\times W}{64 \\times s^2} \\times 8 \\times 8}" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": ". Then, we quantize " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " with image-specific quantization tables " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{2 \\times 8 \\times 8}" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " (Sec. 3.3). During the test time, we encode and decode " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "(Q, \\widehat{C})" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " with off-the-shelf JPEG API, and then retrieve " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "(\\widehat{C}, \\hat{y})" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " with Eqn. (3). In the upsampling stage, we reconstruct the high-fidelity HR " + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 304, + 405, + 545, + 553 + ], + "type": "text", + "content": " with our efficient frequency-aware decoder in real time (Sec. 3.4)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 563, + 480, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 480, + 575 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 480, + 575 + ], + "type": "text", + "content": "3.3. Quantization Prediction Module" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "As JPEG [49] is a widely adopted compression algorithm, some previous methods [26, 47, 58, 63] in image embedding also introduce JPEG (Sec. 3.1) to compress their encoded image. However, JPEG degrades the embedded information in the encoded image and leads to a performance drop in the decoding stage (Sec. 5). JPEG uses fixed quantization tables with constant values [49], which we believe is suboptimal since different images have different frequency distribution. Hence, besides encoding HR images to LR thumbnails, we also predict the quantization tables " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " for each thumbnail with the quantization prediction module" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14095" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": "(QPM), which boosts the RD performance of our framework significantly. The QPM is implemented as two separate 8-layer multilayer perceptron (MLPs): the luma predictor " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_L" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": " and the chroma predictor " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_C" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ". For block " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "C_k = (C_{Y,k}, C_{C,k})" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": ", we vectorize " + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "inline_equation", + "content": "C_k" + }, + { + "bbox": [ + 47, + 72, + 287, + 145 + ], + "type": "text", + "content": " into a 1D vector and produce its quantization table with QPM. Thus we have" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 149, + 289, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 149, + 289, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 149, + 289, + 178 + ], + "type": "interline_equation", + "content": "Q _ {L} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {L} (C _ {Y , k})}{| C _ {Y , k} |}, Q _ {C} = \\frac {\\sum_ {k} \\mathrm {M L P} _ {C} (C _ {C , k})}{| C _ {C , k} |}, \\tag {4}", + "image_path": "5f813d4c13fd21b9c1e0cd2e59f02ce617d3984324557f11515cb816b77dd3fa.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "content": " denotes the block counts. To facilitate the conventional JPEG codec, we take the average " + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "content": " as the quantization table for the whole image. Following the training stage of learned compression [7], we adopt the additive uniform noise " + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "content": " where each element follows " + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathcal{U}(-\\frac{1}{2},\\frac{1}{2})" + }, + { + "bbox": [ + 47, + 182, + 287, + 266 + ], + "type": "text", + "content": " to approximate the non-differentiable quantization noise introduced in Eqn. (2):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 272, + 287, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 272, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 80, + 272, + 287, + 299 + ], + "type": "interline_equation", + "content": "\\widetilde {C _ {Y}} = \\frac {C _ {Y}}{Q _ {L} + \\epsilon} + \\epsilon , \\quad \\widetilde {C _ {C}} = \\frac {C _ {C}}{Q _ {C} + \\epsilon} + \\epsilon . \\tag {5}", + "image_path": "cc50c53decab794c97d5f0638b286b28e3c74a29b9bbed5973ebba159779db8f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 303, + 287, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 303, + 287, + 375 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 287, + 375 + ], + "type": "text", + "content": "In the testing stage, we switch back to the standard quantization function in Eqn. (2) to fit the JPEG API. Experiments show that our QPM predicts better quantization tables " + }, + { + "bbox": [ + 47, + 303, + 287, + 375 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 303, + 287, + 375 + ], + "type": "text", + "content": " so that it improves the RD performance of our framework (Sec. 5). Our experiments in the supplement also show that our QPM improves the standard JPEG algorithm." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 380, + 194, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 194, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 194, + 393 + ], + "type": "text", + "content": "3.4. Frequency-aware Decoder" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 287, + 495 + ], + "type": "text", + "content": "As mentioned in Sec. 3.1, the JPEG quantization is applied on the DCT domain coefficients " + }, + { + "bbox": [ + 47, + 399, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 47, + 399, + 287, + 495 + ], + "type": "text", + "content": " and leads to the well-known quantization noise. Previous works [47,53,58] usually decode the embedded information from the RGB domain of the JPEG image. However, we note that quantization noise can be approximated by simple independent uniform noise [6] in the DCT domain, but it is nonlinear and more complex to model in the RGB domain after IDCT." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": "Inspired by recent works in JPEG artifact removal [18, 20, 52, 60] and image generation [42], we further propose a novel plug-in named frequency feature extractor " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": " for additional frequency domain perception. We first reshape the dequantized DCT coefficients into a sparse representation " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\widehat{C} \\in \\mathbb{R}^{192 \\times \\frac{H}{8s} \\times \\frac{W}{8s}}" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": " [42]. Then, we extract features " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "f(\\widehat{C}) \\in \\mathbb{R}^{24 \\times \\frac{H}{s} \\times \\frac{W}{s}}" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": " and concatenate " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "f(\\widehat{C})" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": " with the RGB image " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": ". The concatenated features are fed into the decoder to reconstruct the HR image " + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 47, + 495, + 287, + 603 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 609, + 287, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 609, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 119, + 609, + 287, + 623 + ], + "type": "interline_equation", + "content": "\\hat {x} = D (\\hat {y} \\oplus f (\\hat {C})), \\tag {6}", + "image_path": "0ca0fdce6ac37f6321e16bcf0dffd1c3b91d80df9768a54e29193e764af8de9f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " is the concatenation operator along the channel dimension. Since " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\widehat{C}" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\frac{1}{8}" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " in the spatial resolution, " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " takes negligible computational overhead. In this way, our decoder is lightweight enough to reconstruct 6K HR images in real time (Fig. 5). " + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 630, + 287, + 713 + ], + "type": "text", + "content": " improves our RD performance and is more efficient than increasing the decoder capacity. Please refer to our supplement for more details of our architecture." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 421, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 421, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 421, + 85 + ], + "type": "text", + "content": "3.5. Training Objectives" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "content": "Bitrate loss To optimize the RD performance of our framework, it is critical to estimate the code length (bitrate) of the quantized coefficients " + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "content": " at the training stage. Inspired by Balle et al. [6], the rate " + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "content": " is estimated with differentiable fully-factorized entropy models:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\mathrm{R} = \\mathrm{E}_{x\\sim p_x}[-\\log_2p_L(\\widetilde{C}_Y) - \\log_2p_C(\\widetilde{C}_{Cb}) - \\log_2p_C(\\widetilde{C}_{Cr})]," + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " (7) where " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "p_L" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "p_C" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " are two fully-factorized entropy models for luma and chroma coefficient maps, respectively. In our work, we reshape " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "(3,64,\\frac{H}{8s},\\frac{W}{8s})" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " , and assume the value of each pixel in " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\widetilde{C}" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " to be independent following Balle et al. [6]. For accurate rate estimation, we train " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "p_L" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "p_C" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " to model the 64-channel probability density functions of " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\widetilde{C}_Y" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "(\\widetilde{C}_{Cb},\\widetilde{C}_{Cr})" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " by minimizing an auxiliary loss " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "L_{aux}" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " [7]. The bpp of the restored image " + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 304, + 150, + 545, + 260 + ], + "type": "text", + "content": " is calculated by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 389, + 266, + 545, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 266, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 389, + 266, + 545, + 291 + ], + "type": "interline_equation", + "content": "L _ {b p p} = \\frac {R}{H \\times W}. \\tag {8}", + "image_path": "7f4b6ba99dda33e15cf5b0d559ca444423d1979a1f8bcb4281e72d4931720c13.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 297, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 308 + ], + "type": "text", + "content": "More details of auxiliary loss is provided in the supplement." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "content": "Reconstruction and guidance loss Thanks to the fully differentiable pipeline (Fig. 2), it is possible for us to train our encoder, QPM and decoder with similar loss terms used in previous works [36, 55]. Following IRN [55], we employ " + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "content": " on the reconstructed " + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "content": " and a " + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "content": " guidance loss on the JPEG thumbnail " + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 308, + 545, + 380 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 361, + 386, + 545, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 386, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 361, + 386, + 545, + 411 + ], + "type": "interline_equation", + "content": "L _ {r e c o n} = \\frac {\\left| \\left| \\hat {x} - x \\right| \\right| _ {1}}{H \\times W}, \\tag {9}", + "image_path": "15d54018749dea0327bb8cbc8eabc008805246595f5549ecd4b3708d431e5226.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 361, + 412, + 545, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 412, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 361, + 412, + 545, + 440 + ], + "type": "interline_equation", + "content": "L _ {\\text {g u i d e}} = \\frac {\\left\\| \\hat {y} - y _ {\\text {r e f}} \\right\\| _ {2} ^ {2}}{(H / s) \\times (W / s)}, \\tag {10}", + "image_path": "af541f05f20d8b61fce1a3b11bb51c950aa14177c2b1782711bfbfe391d96265.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "inline_equation", + "content": "y_{ref}" + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "text", + "content": " is a guidance image downsampled from " + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "text", + "content": " with bicubic interpolation [40]. Altogether, we train our framework by minimizing the total loss " + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "inline_equation", + "content": "L_{rescale}" + }, + { + "bbox": [ + 304, + 445, + 545, + 482 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 333, + 490, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 490, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 333, + 490, + 545, + 503 + ], + "type": "interline_equation", + "content": "L _ {r e s c a l e} = L _ {r e c o n} + \\lambda_ {1} L _ {g u i d e} + \\lambda_ {2} L _ {b p p}. \\tag {11}", + "image_path": "c26e2fbef7f262c21e45407d40a897a90a42407ba15705b6fbba707d07d472e2.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "text", + "content": "Empirically, we set " + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 0.6" + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "text", + "content": ". The target bpp of our framework could be adjusted by a loss scaling factor " + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "text", + "content": ", which we set to 0.01 for most experiments. The total loss " + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "inline_equation", + "content": "L_{rescale}" + }, + { + "bbox": [ + 304, + 510, + 545, + 570 + ], + "type": "text", + "content": " is adopted to optimize the parameters of the encoder, the decoder, and QPM." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 579, + 387, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 579, + 387, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 579, + 387, + 594 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 599, + 422, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 422, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 422, + 613 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "type": "text", + "content": "Evaluation metrics We evaluate our upscaling efficiency using running time and multiply-accumulation operations (MACs). We evaluate the quality of our reconstructed and embedding images using the PSNR on RGB channels." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Rescaling methods are developed to embed an HR image into an LR one to reduce file size. However, there is no existing comprehensive evaluation of bitrate for these methods. Following previous compression approaches [6, 7, 56]," + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14096" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 545, + 191 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 191 + ], + "type": "table", + "html": "
MethodBitrate↓-Distortion↑ [1]Upscaling Efficiency↓Reconstructed HR PSNR↑
Down & Degradation & UpbppPSNRTime (ms)GMacsSet5Set14BSD100Urban100DIV2KFiveK-6k
Bicubic & JPEG & Bicubic0.2925.18--25.1423.4924.0221.0525.7026.90
Bicubic & JPEG & EDSR [37]0.2926.7791.01007.528.3425.7325.6023.5827.8327.23
Bicubic & JPEG & SwinIR [35]0.2926.934012.66208.728.5625.9925.7224.0928.0727.44
ComCNN & RecCNN [26]0.3227.02469.76014.728.2925.8425.7823.7027.9927.40
IRN [55] & JPEG0.3128.48977.84751.730.0027.2326.9125.7229.5427.96
HCFlow [36] & JPEG0.3028.761025.94626.029.9827.4127.0526.1929.7128.01
Ours-full0.3029.67247.91277.530.4828.2127.9327.3530.4928.51
Ours0.3029.4237.8156.230.2227.8727.6626.6230.1528.15
", + "image_path": "5ecb5bbdbaef4204a99e304afc854006e23fcb35bf2a3c6333c01aa1f5bcf4c4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 198, + 547, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 252 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation of upscaling efficiency and reconstruction fidelity. We keep bpp around 0.3 on Kodak [1] for different methods, and the distortion is measured by the PSNR on the reconstructed HR images. Our approach outperforms other methods with better HR reconstruction and a significantly lower runtime. We measure the running time and GMacs of all models by upscaling a 960 × 540 LR image to a 3840 × 2160 HR image. The measurements are made on an Nvidia RTX 3090 GPU with PyTorch-1.11.0 in half-precision mode for a fair comparison." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 47, + 255, + 555, + 449 + ], + "blocks": [ + { + "bbox": [ + 47, + 255, + 555, + 449 + ], + "lines": [ + { + "bbox": [ + 47, + 255, + 555, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 555, + 449 + ], + "type": "image", + "image_path": "8de16a67099eb9792484bab29a6f1f6f62236aecbae86eb399c8a158da7b4f59.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 454, + 547, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 454, + 547, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 547, + 489 + ], + "type": "text", + "content": "Figure 3. Reconstructed HR images and LR thumbnails by different methods on the DIV2K [4] validation dataset. We crop the restored HR images to ease the comparison and visualize the LR counterparts at the bottom-right. The bpp is calculated on the whole image and the PSNR is evaluated on the cropped area of the reconstructed HR images." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": "we evaluate the RD performance with the HR reconstruction PSNR against bits-per-pixel. Instead of estimating the bitrate from the entropy encoder (Eqn. (7)) during training, we use the real file size of JPEG thumbnails for evaluating the bitrate:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 563, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 563, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\operatorname {b p p} = \\mathbb {E} _ {x \\sim p _ {x}} [ \\frac {\\text {f i l e s i z e}}{H \\times W} ]. \\tag {12}", + "image_path": "a215381336afeaadf3d30044b1c5b3baf1530e1e4e17bf6398d56a2633e7e2ab.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": "Since there exists a trade-off between image bitrate and fidelity, we visualize the rate-distortion curve of different models during our ablation study." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Datasets We train our model with the widely-used DIV2K [4] image dataset, which contains 800 2K-resolution images in the training set and 100 more in the validation set. From the perspective of rescaling, we test our model on 4 conventional datasets: the Set5 [10], Set14 [59], BSD100 [38], and Urban100 [24]. To reveal our real-world performance, we collect first 20 images above 6K resolu" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "type": "text", + "content": "tion (ranked by their bpp) from MIT-Adobe FiveK [11] as another test set FiveK-6k. In addition, we evaluate the RD performance on Kodak dataset [1], which is widely adopted in image compression researches [8]. The details of the training strategy are provided in the supplement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 573, + 443, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 443, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 443, + 586 + ], + "type": "text", + "content": "4.2. Compare with Baselines" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "We consider three categories of reconstruction methods as our baselines: (1) downscaling with Bicubic interpolation, compressing with standard JPEG codec, and upscaling with state-of-the-art SR models [35, 37]; (2) autoencoder using standard JPEG transmission format [26]; (3) rescaling using symmetric invertible neural network [36, 55] and compressing the LR image using standard JPEG codec. For fair evaluation, we improve the RD performance of baselines using standard JPEG compression. 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Downscaled LR thumbnails by different methods on Set14 image comic. With a similar target bpp, our model introduces least artifacts in the thumbnail in comparison to baselines." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 242, + 154, + 290, + 195 + ], + "blocks": [ + { + "bbox": [ + 242, + 154, + 290, + 195 + ], + "lines": [ + { + "bbox": [ + 242, + 154, + 290, + 195 + ], + "spans": [ + { + "bbox": [ + 242, + 154, + 290, + 195 + ], + "type": "image", + "image_path": "6ec579650ce430376dc133716c0d64a29ce0aea67964cb9c1a3f3dac03ed5e4b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 245, + 199, + 285, + 208 + ], + "lines": [ + { + "bbox": [ + 245, + 199, + 285, + 208 + ], + "spans": [ + { + "bbox": [ + 245, + 199, + 285, + 208 + ], + "type": "text", + "content": "0.446 / 27.90" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 270, + 286, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 286, + 389 + ], + "type": "text", + "content": "HR images. Besides, we retrain INN baselines [36, 55] and encoder-decoder baselines [26] with a differentiable JPEG module [46]. To compare our RD performance against baselines, we constrain their bpp on Kodak dataset to be around 0.3 by adjusting the quality factor of JPEG compression in all baselines. In our supplement, we provide an additional comparison with image compression (e.g., the original JPEG) and rescaling baselines using their original transmission format (e.g., lossless PNG), where our advantage is even larger." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "content": "Upscaling efficiency and HR fidelity Table 2 presents the upscaling efficiency of all methods and reconstruction fidelity at around 0.3 bpp. We measure the running time and GMacs of upscaling a " + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "inline_equation", + "content": "960 \\times 540" + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "content": " resolution LR image to a " + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "inline_equation", + "content": "3840 \\times 2160" + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "content": " HR image on an Nvidia RTX 3090 GPU. We use PyTorch implementation with 16 bits floating-point precision for a fair comparison. As shown in Table 2, \"Ours\" model only costs " + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "content": " of the GMacs and " + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 46, + 390, + 286, + 521 + ], + "type": "text", + "content": " of upscaling time compared to HCFlow [36]. We still improve the reconstructed RGB PSNR by 0.61 dB on BSD100 test set with a significantly lower computation." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "text", + "content": "In addition, we train the \"Ours-full\" model with a larger decoder. \"Ours-full\" model achieves higher PSNR that outperforms HCFlow [36] and IRN [55] for more than 1.16 dB on Urban100 test set with only " + }, + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "inline_equation", + "content": "24.2\\%" + }, + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "text", + "content": " of upscaling time. Fig. 3 provides the visual comparison of restored images. From left to right, we show perceptual differences from ground truth, " + }, + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 46, + 521, + 286, + 689 + ], + "type": "text", + "content": " rescaling results of the baselines [36, 55] with JPEG, and our framework. For the first row, our models restore more textures of the glass and the pot lid. Similarly, among all reconstructions in the second row, only our model can recover the details on hair and earmuffs. Besides, the JPEG compression breaks the invertibility of the INN-based rescaling methods [36, 55], they failed to restore sharp and accurate high-frequency textures in the HR images." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "LR qualitative evaluation The visual quality of the LR thumbnails is also important because users preview them" + } + ] + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 153 + ], + "type": "table", + "html": "
MethodLR睫毛 PSNR↑
Down & DegradationKodakSet5Set14BSD100Urb100DIV2KFiveK-6k
Bicubic & JPEG37.7234.4135.7937.4336.6437.1435.14
IRN [55] & JPEG30.9530.0027.2326.9125.7229.5431.25
ComCNN & RecCNN [26]28.0026.7626.4727.4725.5728.1528.99
HCFlow [36] & JPEG19.8820.0819.4219.6518.9620.5220.31
Ours-full33.2131.8631.7632.4431.0133.3233.99
Ours33.5531.9631.9332.9031.1633.6234.24
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Our thumbnail preserves visual contents better." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 421, + 278 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 421, + 278 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 421, + 278 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 421, + 278 + ], + "type": "image", + "image_path": "432f4fa96166339edbc7d9586fa5271dd1751415914f2f60dbdaa16097122fd9.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 281, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 324 + ], + "type": "text", + "content": "Figure 5. Model runtime. We profile the " + }, + { + "bbox": [ + 304, + 281, + 545, + 324 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 281, + 545, + 324 + ], + "type": "text", + "content": " encoder and decoder at different target resolution in half-precision mode. Especially, we convert our decoder from PyTorch to TensorRT for further inference time reduction." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 426, + 213, + 548, + 278 + ], + "blocks": [ + { + "bbox": [ + 426, + 213, + 548, + 278 + ], + "lines": [ + { + "bbox": [ + 426, + 213, + 548, + 278 + ], + "spans": [ + { + "bbox": [ + 426, + 213, + 548, + 278 + ], + "type": "image", + "image_path": "ed193456623e0935b07095c505c8bcbdbedc116a60a9fb2047df27a3f60a47a2.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": "directly. Table 3 presents the average LR PSNR of corresponding models, we have the best LR PSNR against INN-based methods. In Fig. 4, we qualitatively compare the visual quality of the thumbnails encoded by rescaling methods. Our method generates LR thumbnails with significantly fewer artifacts without compromising much HR reconstruction quality, please see more analysis in Sec. 5." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 441, + 488, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 488, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 488, + 453 + ], + "type": "text", + "content": "4.3. Real-time Inference on 6K Images" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": "Fig. 5 shows our evaluation of the downscaling and upscaling runtime of our framework at multiple resolutions. Noted that we conduct the profiling in half-precision (FP16) mode. Besides, we also converted the trained decoder model from PyTorch to FP16 TensorRT model with torch2trt [2] API to further reduce the upscaling time without performance drop in HR reconstruction. As shown in Fig. 5(b), our efficient decoder can upscale an LR thumb-nail by " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " in real time at 4K (" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "3840 \\times 2160" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ") 70.8 FPS, 5K (" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "5120 \\times 2880" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ") 38.8 FPS, or 6K (" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "5760 \\times 3240" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ") 31.2 FPS on an RTX 3090 GPU." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 609, + 534, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 534, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 534, + 621 + ], + "type": "text", + "content": "4.4. 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Quantization tables on Kodak [1] images. We visualize the quantization table " + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "inline_equation", + "content": "Q_{L}" + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "text", + "content": " (the green table) and " + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "inline_equation", + "content": "Q_{C}" + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "text", + "content": " (the orange table) for " + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\text{kodim04}" + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\text{kodim09}" + }, + { + "bbox": [ + 46, + 156, + 547, + 190 + ], + "type": "text", + "content": " of different quantization approaches. The model trained with QPM achieves the best RD performance from every aspect. For more analysis, please refer to Sec. 5 in our paper." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "table", + "bbox": [ + 48, + 209, + 286, + 262 + ], + "blocks": [ + { + "bbox": [ + 48, + 209, + 286, + 262 + ], + "lines": [ + { + "bbox": [ + 48, + 209, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 48, + 209, + 286, + 262 + ], + "type": "table", + "html": "
MethodOptimizationbpp↓ / HR PSNR↑
ArchitectureiterationKodakSet5Set14
Ours00.301 / 29.420.379 / 30.230.359 / 27.74
1000.307 / 29.550.377 / 30.360.347 / 27.96
", + "image_path": "db151afcbe9eb404c28cd5f0bee842aa58d53ab37dae0d75522a4cd316416489.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 47, + 267, + 285, + 278 + ], + "lines": [ + { + "bbox": [ + 47, + 267, + 285, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 267, + 285, + 278 + ], + "type": "text", + "content": "Table 4. Quantitative evaluation for optimization-based rescaling." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 291, + 140, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 291, + 140, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 291, + 140, + 304 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 312, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 287, + 347 + ], + "type": "text", + "content": "In this section, we study the effectiveness of our proposed Quantization Prediction Module, designed training loss and architectures on \"Ours\" model." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": "Quantization prediction module To examine the effectiveness of our QPM, in Fig. 7, we quantitatively evaluate the RD performance on both the restored HR and the LR JPEG thumbnails of different quantization approaches. For \"fixed tables\" and \"optimized tables\", we initialize the quantization tables following the default JPEG. Particularly, for \"optimized tables,\" we also optimize the quantization tables at the training stage. We illustrate the curve for each model by adjusting the global quality factor " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": " on the quantization tables " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": " following JPEG as " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "Q' = Q \\times q" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": ". The target bitrate goes lower when " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": " increases. In Fig. 6, we also visualize the quantization tables of different settings. We notice that compared to the corresponding value in the fixed or optimized table, the high-frequency quantization steps in the QPM predicted tables are much smaller and are image-specific, which may introduce less compression on the embedding pattern that is important for HR reconstruction. Consequently, compared to settings with image-invariant quantization, \"Ours\" model achieves the best quality on the reconstructed " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": " and introduces significantly fewer artifacts on the LR thumbnail " + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 357, + 287, + 657 + ], + "type": "text", + "content": ", which also lowers the file-size of the thumbnails. To further investigate the effectiveness of QPM, we also leverage QPM to improve the RD performance of standard JPEG (without the downscaling and upscaling). Please refer to our supplement for more details." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Guidance loss In Fig. 7, we also present the RD curve of the \"Ours w/o guidance loss\" model trained with " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 0" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ". At around 0.4 bpp, removing guidance loss raises the HR" + } + ] + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 307, + 224, + 423, + 320 + ], + "blocks": [ + { + "bbox": [ + 317, + 212, + 417, + 221 + ], + "lines": [ + { + "bbox": [ + 317, + 212, + 417, + 221 + ], + "spans": [ + { + "bbox": [ + 317, + 212, + 417, + 221 + ], + "type": "text", + "content": "(a) RD curve of restored HR image" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 224, + 423, + 320 + ], + "lines": [ + { + "bbox": [ + 307, + 224, + 423, + 320 + ], + "spans": [ + { + "bbox": [ + 307, + 224, + 423, + 320 + ], + "type": "image", + "image_path": "11188a3ef29aaabc908843e9d609148acc6a2b91104b8a61b27d8bf5c58c920d.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "text", + "content": "Figure 7. QPM versus image-invariant quantization. We first train our models with QPM, with a fixed JPEG table or with an optimized table, respectively. Then, we evaluate the at different target bitrate on Kodak [1] dataset. (a) the RD curve on reconstructed HR image " + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "text", + "content": " and input " + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "text", + "content": "; (b) the RD curve on LR thumbnail " + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "text", + "content": " and the Bicubic downsampled LR " + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "inline_equation", + "content": "y_{ref}" + }, + { + "bbox": [ + 305, + 323, + 546, + 389 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 426, + 222, + 542, + 319 + ], + "blocks": [ + { + "bbox": [ + 442, + 212, + 529, + 220 + ], + "lines": [ + { + "bbox": [ + 442, + 212, + 529, + 220 + ], + "spans": [ + { + "bbox": [ + 442, + 212, + 529, + 220 + ], + "type": "text", + "content": "(b) RD curve of LR thumbnail" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 426, + 222, + 542, + 319 + ], + "lines": [ + { + "bbox": [ + 426, + 222, + 542, + 319 + ], + "spans": [ + { + "bbox": [ + 426, + 222, + 542, + 319 + ], + "type": "image", + "image_path": "6e3027635cc3d040a7f674e22a92307379cc66cc7fcad8d5ef708fad1e52ac21.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + } + ], + "index": 34 + }, + { + "bbox": [ + 305, + 403, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 403, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 545, + 440 + ], + "type": "text", + "content": "PSNR by " + }, + { + "bbox": [ + 305, + 403, + 545, + 440 + ], + "type": "inline_equation", + "content": "0.09\\mathrm{dB}" + }, + { + "bbox": [ + 305, + 403, + 545, + 440 + ], + "type": "text", + "content": ". However, the PSNR of LR thumbnail drops significantly from 34.1 dB to 13.06 dB. It is unacceptable for user-viewable thumbnails." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "text", + "content": "Encoder decoder architecture As we study some variants of \"Ours\" model, we find that " + }, + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "text", + "content": " improves the quality of both encoded LR thumbnail (0.29 dB) and restored HR image (0.10 dB). Also, adopting " + }, + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 451, + 546, + 536 + ], + "type": "text", + "content": " is more effective than simply increasing the decoder capacity. Moreover, our study of the encoder capacity reveals that our framework does benefit from a larger encoder. More details are in our supplement." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 559, + 378, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 559, + 378, + 571 + ], + "spans": [ + { + "bbox": [ + 306, + 559, + 378, + 571 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we propose a new HyperThumbnail framework that can perform real-time 6K image reconstruction from an LR JPEG thumbnail. We utilize an asymmetric encoder-decoder architecture where the encoder takes most of the computation while the decoder is relatively lightweight for real-time performance. A new quantization prediction module is proposed to optimize the RD performance for image rescaling, which is not studied in prior work. 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In traditional filter-based denoising methods, this can be easily achieved by adjusting the filtering strength. However, for NN (Neural Network)-based models, adjusting the final denoising strength requires performing network inference each time, making it almost impossible for real-time user interaction. In this paper, we introduce Real-time Controllable Denoising (RCD), the first deep image and video denoising pipeline that provides a fully controllable user interface to edit arbitrary denoising levels in real-time with only one-time network inference. Unlike existing controllable denoising methods that require multiple denoisers and training stages, RCD replaces the last output layer (which usually outputs a single noise map) of an existing CNN-based model with a lightweight module that outputs multiple noise maps. We propose a novel Noise Decorrelation process to enforce the orthogonality of the noise feature maps, allowing arbitrary noise level control through noise map interpolation. This process is network-free and does not require network inference. Our experiments show that RCD can enable real-time editable image and video denoising for various existing heavy-weight models without sacrificing their original performance.", + "bbox": [ + 75, + 313, + 473, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 689, + 209, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image and video denoising are fundamental problems in computational photography and computer vision. With the development of deep neural networks [12, 26, 49, 59], model-based denoising methods have achieved tremendous success in generating clean images and videos with superior denoising scores [4,55,57]. However, it should be noted that the improvement in reconstruction accuracy (e.g., PSNR, SSIM) is not always accompanied by an improvement in visual quality, which is known as the Perception-Distortion trade-off [6]. In traditional denoising approaches, we can easily adjust the denoising level by tuning related control", + "bbox": [ + 75, + 715, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdd77edab6538da3437cabca7f82d78c93d883d789e685523ff8fc81834b3ad2.jpg", + "image_caption": [ + "Figure 1. Real-time controllable denoising allows users further tuning the restored results to achieve Perception-Distortion trade-off. A-B: tuning with changing denoising intensity. C-E: tuning without changing denoising intensity." + ], + "image_footnote": [], + "bbox": [ + 506, + 282, + 893, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "parameters and deriving our preferred visual results. However, for typical deep network methods, we can only restore the degraded image or video to a fixed output with a predetermined restoration level.", + "bbox": [ + 496, + 511, + 892, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, several modulation methods have been proposed to generate continuous restoration effects between two pre-defined denoising levels. These methods can be categorized into two kinds: interpolation-based methods [17,24,50,51], which use deep feature interpolation layers, and condition-network-based methods, which import an extra condition network for denoising control [9, 25, 39]. Essentially, both types of methods are designed based on the observation that the outputs of the network change continuously with the modulation of features/filters. This observation enables deep denoising control, but it also introduces several limitations. First, there is a lack of explainability, as the relationship between the control parameters (how to modulate features) and the control operation (how the network outputs are changed) is unclear [24]. This indicates that black-box operators (network layers) must be used to encode them. Second, the use of control parameters as network inputs requires entire network propagation each time control parameters change, resulting in a lack of efficiency. Lastly, current modulation methods often require an explicit degradation level during training, which is hard to obtain for real-world samples. As a result, current controllable denoising methods only focus on synthetic", + "bbox": [ + 496, + 570, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 886, + 205, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14028", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1d113a893b944b9e1cdb31efdda3e8da8e2523db04ba837d505e31a18be00de3.jpg", + "image_caption": [ + "Figure 2. Comparison of pipelines between conventional controllable denoising and our RCD. RCD achieves real-time noise control by manipulating editable noises directly." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 467, + 237 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "noise benchmarks. Furthermore, both interpolation-based and condition-network-based methods have their own drawbacks. Interpolation-based methods often require multiple training stages, including pretraining two basic models (start level and end level). On the other hand, condition-network-based methods are strenuous to jointly optimize the base network and the condition network.", + "bbox": [ + 75, + 306, + 468, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we research on the problem: Can we achieve real-time controllable denoising that abandons the auxiliary network and requires no network forward propagation for changing restoration effects at test time?", + "bbox": [ + 75, + 409, + 468, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Towards this goal, we propose Real-time Controllable Denoising method (RCD), a lightweight pipeline for enabling rapid denoising control to achieve Perception-Distortion Balance (See Fig. 1). Our RCD can be plugged into any noise-generate-based restoration methods [11, 46, 54, 55] with just a few additional calculations. Specifically, we replace the last layer of an existing denoising network (which usually outputs a single noise map) with a lightweight module that generates multiple noise maps with different noise levels. We utilize a novel Noise Decorrelation process to enforce the orthogonality of the noise distribution of these noise maps during training. As a result, we can attain arbitrary denoising effects by simple linear interpolation of these noise maps. Since this process does not require network inference, it makes real-time user interaction possible even for heavy denoising networks.", + "bbox": [ + 75, + 467, + 468, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 2 illustrates the fundamental differences between our RCD approach and conventional controllable denoising methods. In contrast to traditional methods that rely on control networks, the RCD pipeline generates editable noises of varying intensities/levels, providing explicit control by external parameters and enabling network-free, real-time denoising editing. Real-time editing capabilities offered by RCD create new opportunities for numerous applications that were previously impossible using conventional techniques, such as online video denoising editing, even during playback (e.g., mobile phone camera video quality tuning for ISP tuning engineers), as well as deploying controllable denoising on edge devices and embedded systems. Since the editing stage of RCD only involves image interpolation,", + "bbox": [ + 75, + 699, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "users can edit their desired results on low-performance devices without the need for GPUs/DSPs.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, unlike previous methods that only support changing noise levels, RCD allows users to adjust denoising results at a specific noise level by providing a new interface to modify the noise generation strategy. RCD is also the first validated method for controllable denoising on real-world benchmarks. It is noteworthy that existing controllable methods typically require training data with fixed-level noise to establish their maximum and minimum noise levels, which makes them unsuitable for most real-world benchmarks comprising data with varying and unbalanced noise levels.", + "bbox": [ + 496, + 119, + 893, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 517, + 279, + 879, + 294 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose RCD, a controllable denoising pipeline that firstly supports real-time denoising control ( $>$ $2000 \\times$ speedup compared to conventional controllable methods) and larger control capacity (more than just intensity) without multiple training stages [24] and auxiliary networks [50].", + "- RCD is the first method supporting controllable denoising on real-world benchmarks.", + "- We propose a general Noise Decorrelation technique to estimate editable noises.", + "- We achieve comparable or better results on widely-used real/synthetic image-denoising and videodenoising datasets with minimal additional computational cost." + ], + "bbox": [ + 517, + 306, + 890, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 536, + 648, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Denoising", + "text_level": 1, + "bbox": [ + 500, + 560, + 612, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional image and video denoising methods are often based on prior assumptions such as sparse image prior [3, 15, 16, 20], non-local similarity [7, 13, 14, 18], and other similar techniques [22, 41, 52]. However, with the recent development of deep learning networks, many learning-based methods have been proposed and achieved state-of-the-art performance. Early works [8] utilized multi-layer perceptron (MLP) to achieve comparable results with BM3D. In recent years, there has been rapid progress on CNN-based denoising methods [4, 10, 21, 47, 55, 57] and Transformer-based methods [32, 42, 54, 59], which have started to dominate the image/video denoising task. However, the abovementioned works mainly focus on designing novel network architectures to improve the denoising performance and usually generate a single output. Their lack of ability to adjust the output denoising level based on user's feedback has greatly restricted their practical use in many real-world applications. Moreover, although techniques like pruning [33, 38, 60] and quantization [45, 61] can accelerate such neural network-based methods, they are typically heavy, which restricts their application to real-time denoising control.", + "bbox": [ + 496, + 583, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14029", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e041ba5d99f57b30628567c97b1aee7488b72648530b2b52ed937aff0f213a23.jpg", + "image_caption": [ + "Figure 3. Pipeline overview of proposed RCD framework. A: Backbone network for generating multi-level noise maps. B: Noise Decorrelation module for editable noises. C: AutoTune module for providing reference control parameters for users." + ], + "image_footnote": [], + "bbox": [ + 81, + 73, + 890, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Controllable denoising", + "text_level": 1, + "bbox": [ + 76, + 449, + 290, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most conventional deep-learning methods for image/video denoising can only generate a fixed result with a specific restoration level. Recently, some controllable image/video denoising methods allow users to adjust the restoration effect without retraining the network. DNI [51] and AdaFM [24] used the observation that the learned filters of the models trained with different restoration levels are similar in visual patterns. DNI interpolated all the corresponding parameters between two related networks to derive smooth and continuous restoration effects, while AdaFM adopted feature modulation filters after each convolution layer. CFSNet [50] proposed an adaptive learning strategy of using interpolation coefficients to couple the intermediate features between the main branch and the tuning branch. Different from these interpolation-base methods, some other methods [9, 25, 39] regarded modulation as a conditional image restoration problem and adopted a joint training strategy. CUGAN [9] proposed a GAN-based image restoration framework to avoid the over-smooth problem, a common issue in PSNR-oriented methods. However, all of the above controllable methods can only be trained with synthetic degradations because they require explicit degradation levels during training. When applied on real-world data, as shown in [23], methods that trained for blind Additive White Gaussian Noise (AWGN) [35,55] may be overfitted and often suffer from dramatic performance drop. Besides the real-world image issue, all these controllable methods utilize an auxiliary conditional network and require one network inference for each different target", + "bbox": [ + 75, + 484, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "restoration level at test time, which makes them almost impossible for real-time application.", + "bbox": [ + 498, + 450, + 890, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 496, + 598, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Conventional Deep Denoising", + "text_level": 1, + "bbox": [ + 500, + 522, + 763, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Deep denoising methods trump traditional filter-based techniques by leveraging the neural networks' robust representation learning capability. Most current denoising methods [11,32,46] reason about the relationship between clean and noisy images by regressing noise maps with a neural generator. Specifically, given a noisy image $\\mathbf{I}_{\\mathbf{n}}$ and model $\\mathcal{M}:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times C}$ , we can derive the predicted clean image $\\mathbf{I}_{\\mathbf{c}}$ by: $\\mathbf{I}_{\\mathbf{c}} = \\mathbf{I}_{\\mathbf{n}} + \\mathcal{M}(\\mathbf{I}_{\\mathbf{n}})$ , where model $\\mathcal{M}$ is updated by minimizing the distance between the denoising result $\\mathbf{I}_{\\mathbf{c}}$ and the ground truth $\\mathbf{I}_{\\mathrm{gt}}$ . As we can see, this kind of approach generates a single fixed output result in a black-box manner, making it almost impossible to adjust the denoise operation explicitly.", + "bbox": [ + 496, + 546, + 890, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pipeline Overview", + "text_level": 1, + "bbox": [ + 500, + 746, + 676, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present Real-time Controllable Denoising (RCD), a novel deep learning-based pipeline for real-time controllable denoising. As illustrated in Fig. 3, RCD essentially consists of three parts: (1) A backbone network, i.e., $\\mathcal{M}_b:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times LC}$ , generates multiple fixed-level noise maps, where $L$ is the number of pre-defined noise levels (see (A) in Fig. 3). (2) A Noise Decorrelation (ND) block that enforces the editability of the generated noise maps (see (B) in Fig. 3). (3) An AutoTune", + "bbox": [ + 496, + 770, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14030", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "module that gives a default set of control parameters to generate the best denoising result.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the backbone network will generate multiple fixed-level noise maps, i.e., $\\{\\mathcal{N}_i\\}_{i=1}^L$ , for each noisy image input. The noise maps are then fed into the proposed Noise Decorrelation (ND) block, which makes noise maps orthogonal to each other. In this way, the decorrelated noise maps $\\{\\tilde{\\mathcal{N}}_i\\}_{i=1}^L$ will be zero-correlated and thus become linearly interpolable. At last, the AutoTune module will give a set of suggested control parameters $\\{\\bar{c}_i\\}_{i=1}^L$ to generate the final denoising result as follows:", + "bbox": [ + 75, + 119, + 470, + 250 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {\\mathbf {c}} = \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 260, + 468, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sum_{i=1}^{L} \\bar{c}_i = 1$ . Moreover, given the zero-correlated noise maps, users can also generate arbitrary strength denoising results by replacing $\\{\\bar{c}_i\\}_{i=1}^L$ with their own customized control parameters $\\{c_i\\}_{i=1}^L$ .", + "bbox": [ + 75, + 313, + 468, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Multi-level Noise Generation", + "text_level": 1, + "bbox": [ + 76, + 381, + 341, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a noisy input image $\\mathbf{I}_{\\mathbf{n}}$ , the backbone network aims to generate multiple noise maps $\\{\\mathcal{N}_i\\}_{i=1}^L$ , corresponding to a set of pre-defined noise levels $\\{l_i\\}_{i=1}^L$ , e.g. noise levels $\\{5, 10, 15, \\dots, 60\\}$ . Hence, we have", + "bbox": [ + 75, + 402, + 468, + 462 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma \\left(\\mathcal {N} _ {i}\\right) = l _ {i}, \\forall i = 1, \\dots , L, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 472, + 468, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ is the noise level operation that calculates the standard deviation of pixels in each noise map. To obtain multilevel noise maps, we replace the conventional last output layer of the denoising network with a convolutional layer with an output channel size of $L\\cdot C$ . Moreover, the level of the noise map is explicitly generated with the normalization operation, as given by", + "bbox": [ + 75, + 500, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} _ {i} = l _ {i} \\frac {\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)}}{\\sigma (\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)})}, \\forall i = 1, \\dots , L. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 609, + 468, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\mathcal{M}_b(\\mathbf{I_n})\\in \\mathbb{R}^{H\\times W\\times LC}$ is network output, and $\\mathcal{M}_b(\\mathbf{I_n})^{(i)}\\in \\mathbb{R}^{H\\times W\\times C}$ is the i-th component separated from the channel dimension. The derived $\\mathcal{N}_i$ can be considered as the noise map estimated at the given noise level $l_{i}$ .", + "bbox": [ + 75, + 654, + 468, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from prior controllable denoising methods with implicit interpolation in the network, we propose to explicitly interpolate the noise maps in Eqn. 3. Thanks to the separation of noise interpolation and network inference, our RCD can achieve real-time user interaction.", + "bbox": [ + 75, + 727, + 468, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the multi-level noise maps $\\mathcal{N}_i$ directly obtained by convolutional layers are usually highly correlated, which leads to the problem of noise level collapse. In other words, the noise map representations in different levels are redundant, implying that the number of noise maps at different noise strengths that participate in the linear interpolation in Eqn. 1 is implicitly reduced. Without any constraint,", + "bbox": [ + 75, + 799, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1b4247ed5206507bda03ecd23a3b5bec7bde408717d346b648ed047996d6b5f5.jpg", + "image_caption": [ + "Figure 4. Demonstration of Noise Decorrelation's influence on noise editing. $|\\Sigma|_F$ denotes norms of the covariance matrix for corresponding learned noises and $\\sigma$ is noise intensity." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "our experiments show that the single noise map at a certain noise level would dominate in the linear interpolation for a variety of input noisy images. To address this issue, we further introduce the Noise Decorrelation block to make representations of these noise maps much more informative in the following section.", + "bbox": [ + 496, + 277, + 890, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Noise Decorrelation", + "text_level": 1, + "bbox": [ + 500, + 372, + 689, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Noise Decorrelation (ND) block is designed to regularize the backbone network to generate editable noise maps at varying levels. In particular, this block is a parameter-free computational unit that enforces $\\mathcal{N}_i$ to be approximately zero-correlated with each other: $\\mathbf{cov}(\\mathcal{N}_i,\\mathcal{N}_j)\\approx 0,\\forall i,j\\in$ $\\{1,2,\\dots,L\\}$ , where $\\mathbf{cov}(\\cdot ,\\cdot)$ is covariance operator. Inspired by the success of using the decorrelation technique in network optimization and normalization, we adopt the whitening-based methods [29, 30] for noise decorrelation here. The noise maps are decorrelated using the inverse square root of their covariance matrix.", + "bbox": [ + 496, + 393, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for each predicted fixed-level noise map $\\mathcal{N}_i$ , it will firstly be reshaped to $\\mathcal{N}_i \\in \\mathbb{R}^{1 \\times M}$ , where $M = HWC$ . By stacking the reshaped $\\mathcal{N}_i$ over the first dimension, we have $\\mathbf{N} \\in \\mathbb{R}^{L \\times M}$ . We then calculate the noise covariance matrix $\\sigma$ by: $\\Sigma = \\frac{1}{M - 1} (\\mathbf{N} - \\bar{\\mathbf{N}})(\\mathbf{N} - \\bar{\\mathbf{N}})^T$ where $\\bar{\\mathbf{N}}$ is mean of $\\mathbf{N}$ over channel $M$ .", + "bbox": [ + 496, + 551, + 890, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Noise Decorrelation block needs to compute inverse square root $\\Sigma^{-\\frac{1}{2}} \\in \\mathbb{R}^{L \\times L}$ , which can be done by eigen decomposition or SVD. Since this kind of operation involves heavy computation [29], we instead adopt the more efficient Newton's Iteration to estimate $\\Sigma^{-\\frac{1}{2}}$ as in [5, 27]. Giving a covariance matrix $\\Sigma$ , Newton's Iteration calculates $\\Sigma^{-\\frac{1}{2}}$ by following the iterations below:", + "bbox": [ + 496, + 641, + 890, + 747 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Sigma_ {0} = I, \\\\ \\Sigma_ {k} = \\frac {1}{2} (3 \\Sigma_ {k - 1} - (\\Sigma_ {k - 1}) ^ {3} \\Sigma), k = 1, 2,.., T, \\end{array} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 753, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $k$ is the iteration index and $T$ is the iteration number (in our experiments $T = 3$ or 4). $\\Sigma_{k}$ is guaranteed to converge to $\\Sigma^{-\\frac{1}{2}}$ , if $\\| I - \\Sigma \\|_2 < 1$ [5]. This condition can be achieved by normalizing $\\Sigma$ to $\\frac{\\Sigma}{tr(\\Sigma)}$ , where $tr(.)$ is trace operator.", + "bbox": [ + 496, + 794, + 890, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The derived $\\Sigma^{-\\frac{1}{2}}$ can be regarded as a whitening matrix [43], which decorrelates the noise maps $\\mathbf{N}$ in", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14031", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a differentiable manner. The decorrelated noise maps $\\mathbf{N} \\in \\mathbb{R}^{\\tilde{H} \\times W \\times LC}$ can be obtained by calculating: $\\tilde{\\mathbf{N}} = \\Sigma^{-\\frac{1}{2}} \\mathbf{N}$ . We can then have our editable fixed-level noises $\\tilde{\\mathcal{N}}_i \\in \\mathbb{R}^{H \\times W \\times C}$ by reshaping $\\tilde{\\mathbf{N}}$ and splitting it into $L$ noise maps. After Noise Decorrelation, we apply the same normalization as Eqn. 3 to guarantee the noise strength of the decorrelated noises.", + "bbox": [ + 75, + 90, + 468, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The zero-correlated noise maps $\\tilde{\\mathcal{N}}_i$ present several excellent properties for controllable denoising. Firstly, the linearity of the noise level's square towards $\\tilde{\\mathcal{N}}_i$ is guaranteed. In other words, given an arbitrary set of control parameters $\\{c_i\\}_{i = 1}^L$ , we have", + "bbox": [ + 75, + 196, + 470, + 270 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V a r} \\left(\\sum_ {i = 1} ^ {L} c _ {i} \\tilde {\\mathcal {N}} _ {i}\\right) = \\sum_ {i = 1} ^ {L} c _ {i} ^ {2} \\mathbf {V a r} \\left(\\tilde {\\mathcal {N}} _ {i}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 277, + 468, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{Var}(\\cdot)$ denotes variance operator. Apparently, Eqn. 5 holds when elements of $\\{\\tilde{\\mathcal{N}}_i\\}_{i = 1,2,\\dots,m}$ are mutually zero-correlated. Eqn. 5 reveals the explicit relationship between the control parameters and the target noise level, which allows us to directly edit noises by interpolating $\\mathcal{N}_i$ using $c_{i}$ . Secondly, the Noise Decorrelation block can be regarded as a regularization tool that forces models to learn different noise formats for each level, which will increase the representation capacity of the denoising network [30].", + "bbox": [ + 75, + 328, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 4 demonstrates how the Noise Decorrelation block works. With ND block, the covariance of learned noises is reduced to almost zero (without it, $|\\Sigma|_F$ can be 751 and unignorable), allowing us to derive determined interpolated results with target noise intensity. In contrast, without the Noise Decorrelation blocks, the output noise level can not be guaranteed.", + "bbox": [ + 75, + 460, + 468, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. AutoTune Module", + "text_level": 1, + "bbox": [ + 76, + 568, + 251, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the decorrelated noise maps from the Noise Decorrelation block, the AutoTune module will predict a set of model-suggested control parameters, i.e., $\\{\\bar{c}_i\\}_{i=1}^L$ , to generate the default denoising result. Users can then use this set of parameters as a starting point to fine-tune their final desired denoising strength. Our AutoTune module is extremely lightweight, and is formulated as a single-layer module with temperature softmax activation. Specifically, $\\{\\bar{c}_i\\}_{i=1}^L$ can be obtained by: $\\bar{c}_i = \\frac{e^{\\frac{\\mathcal{A}(f)_i}{\\tau}}}{\\sum_{j=1}^n e^{\\frac{\\mathcal{A}(f)_j}{\\tau}}}$ , where $\\mathcal{A}$ is the NN layer, $f$ is the input feature maps, and $\\tau$ is temperature. In our experiments, $\\tau$ is set to be 0.05 for best performance. Following the design ethos of efficiency and least coupling to the backbone architecture, we directly choose the unnormalized model outputs $\\mathcal{M}(\\mathbf{I_n})$ as $f$ (see (C) in Fig. 3).", + "bbox": [ + 75, + 590, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. New Cardinality for Denoising Control.", + "text_level": 1, + "bbox": [ + 76, + 834, + 415, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike existing methods that only modulate noise intensity, our RCD control scheme allows users to further optimize the denoising result to a given noise intensity", + "bbox": [ + 75, + 856, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/db4f0e23544b9a9e4d9ee1d2d5e29b7736aca6ef68e7b0ad60743bde3b3da52b.jpg", + "image_caption": [ + "Figure 5. Example of RCD denoising results by AutoTune and HumanTune on Set8. AutoTune module provides reference control parameters, i.e., $\\{\\bar{c}_i\\}_{i=1}^L$ , to generate the denoising result, and it can be further improved by fine-grained artificial tuning (HumanTune), i.e., $\\{c_i\\}$ , without changing the noise intensity (both $\\sigma = 40$ )." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 883, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "by tuning $\\{c_i\\}$ , as long as the weighted mean of $l_{i}$ towards $c_{i}$ remains the same. Eqn. 5 shows that when $\\sum_{i = 1}^{L}c_{i}^{2}\\mathbf{Var}(\\tilde{\\mathcal{N}}_{i}) = \\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}$ is fixed, the variance of the output noise $\\mathbf{Var}(\\sum_{i = 1}^{L}c_{i}\\tilde{\\mathcal{N}}_{i})$ would be also fixed. By exploring $c_{i}$ under the condition of fixed $\\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}$ , we can further optimize the denoising results at a specific noise level by involving different components $(\\mathcal{N}_i)$ in the noise interpolation. As shown in Fig. 5, our AutoTune module can generate high-quality results using just the reference control parameters $\\{\\bar{c}_i\\}$ . Users can further improve the result by artificially tuning $\\{c_i\\}$ around $\\{\\bar{c}_i\\}$ , even at the same noise level.", + "bbox": [ + 496, + 349, + 890, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.7. Optimization Targets", + "text_level": 1, + "bbox": [ + 500, + 542, + 699, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To guarantee the visual quality of arbitrarily edited noise $\\sum_{i=1}^{L} c_i \\tilde{\\mathcal{N}}_i$ for any given set of control parameters $\\{c_i\\}_{i=1}^L$ , we adopt a multi-level concurrent training strategy by minimizing the difference between each level's noise output and the ground truth noise, i.e., $\\mathcal{L}_{level}$ , which is derived by:", + "bbox": [ + 496, + 565, + 890, + 640 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {l e v e l}} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\tilde {\\mathcal {N}} _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 652, + 890, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_{gt}$ , $\\mathbf{I}_{\\mathbf{n}}$ are ground truth clean image and the input noisy image. $\\mathcal{L}(.)$ can be any loss functions (e.g., L2 loss or PSNR loss).", + "bbox": [ + 496, + 705, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spectaculously, $\\mathbf{I}_{\\mathbf{n}} + \\tilde{\\mathcal{N}}_i$ can be regarded as corner cases of RCD when we use one-hot control parameters as input. Joint optimization of all the noise levels ensures that each element of $\\mathcal{N}_i$ can be trained as optimal noise estimation under the condition of fixed noise level $l_{i}$ .", + "bbox": [ + 496, + 750, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Together with the AutoTune module optimization, our final cost function can be written as:", + "bbox": [ + 496, + 821, + 890, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\mathcal {L} _ {\\text {l e v e l}} + \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 862, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14032", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9643ceb54f214acab7920c47c450b56878de1dcfed95e3d7d82f610500358357.jpg", + "table_caption": [ + "Table 1. Gaussian single image denoising results (PSNR). RCD is evaluated with AutoTune results. “-”: not reported" + ], + "table_footnote": [], + "table_body": "
MethodControllableCBSD68Kodak24McMasterUrban100
σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50
IRCNN [56]X33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [57]X33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [55]X33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [40]X33.9131.2828.0534.6332.1629.0534.6732.4029.28-
CResMD [25]✓33.97-28.06---
AdaFM-Net [24]✓34.1031.4328.13---
NAFNet [11]X34.1131.4928.2735.1432.7029.6835.0732.8229.7934.4132.0929.00
NAFNet-RCD (ours)✓34.1331.4928.2635.1532.7229.6935.1132.8429.8134.4532.1229.02
", + "bbox": [ + 78, + 95, + 915, + 233 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/48c4561fc16edf972c0c71dbda944c5d1c7347463c8419941dfd77d0d80e9e7e.jpg", + "table_caption": [ + "Table 2. Running time comparison for RCD and other controllable methods during test time. Full Pipeline compares full pipeline latency for the model to infer 1000 images, and Edit-only compares latency for editing one image with 1000 different control parameters." + ], + "table_footnote": [], + "table_body": "
MethodMulti-stage trainingFull PipelineEdit-only
AdaFM-Netrequired81.03s81.03s
CResMDNetnot required128.08128.08s
NAFNet-RCDnot required64.84s0.04s
", + "bbox": [ + 81, + 325, + 475, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is the loss weight ( $\\lambda = 0.1$ in our experiments), and $\\mathcal{L}(\\mathbf{I}_{gt},\\mathbf{I_n} + \\sum_{i = 1}^{n}\\bar{c}_i\\tilde{\\mathcal{N}}_i)$ optimizes the denoising result derived by the model-suggested control parameters.", + "bbox": [ + 75, + 391, + 468, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 450, + 209, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section is organized as follows: First, we demonstrate the effectiveness of our plug-in RCD with SOTA image denoising methods [11] in different scales on synthetic noise datasets. Next, to evaluate the ability of blind denoising on real-world data, we conduct experiments on popular real-world denoising dataset SIDD [1]. Then, we apply our real-time controllable RCD pipeline on video denoising applications. At last, we empirically discuss some design details described in the previous sections.", + "bbox": [ + 75, + 476, + 468, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Gaussian Single Image Denoising", + "text_level": 1, + "bbox": [ + 76, + 617, + 369, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Setup. To fully demonstrate the effectiveness of the proposed RCD, we choose the most recent SOTA method NAFNet [11] as our backbone. Following [54], we first conduct denoising experiments on several widely-used synthetic color image benchmarks (DIV2K [2], BSD400 [36], Flickr2K [53] and WaterlooED [34]) with additive white Gaussian noise ( $\\sigma \\in [0, 60]$ ). The training patch size is $128 \\times 128$ and the batch size is 64. We train our model with Adam [31] optimizer and learning rate $1e - 3$ for total 60K iterations. Consistent to [11], PSNR loss is adapted as the loss function. Both the baseline model (NAFNet) and its RCD variants (NAFNet-RCD) are trained from scratch. For settings of RCD, we initialize $L = 12$ and $\\{l_i\\} = [5, 10, \\dots, 60]$ for synthetic denoising training.", + "bbox": [ + 75, + 641, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Complexity analysis. Extensive adjustments of controllable parameters are often required to obtain one satisfying result for users. Therefore, editing time is vital", + "bbox": [ + 75, + 856, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for controllable methods. This section compares the inference and editing latency of our RCD and conventional controllable pipelines on GTX 1080Ti. As shown in Tab. 2, the proposed RCD not only outperforms other conventional controllable pipelines on inference time, but more importantly, can overwhelm those traditional controllable designs on editing time, which can be more than 2000 times faster (as editing process of RCD is network-free, without reliance on sub-networks). This comparison confirms that our RCD is more than enough for real-time image editing.", + "bbox": [ + 496, + 251, + 890, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results Analysis. We evaluate our proposed method on widely used synthetic noise datasets CBSD68 [37], Kodak24 [19], McMaster [58] and Urban100 [28] with noise levels $\\sigma(15)$ , $\\sigma(15)$ and $\\sigma(50)$ . RCD is evaluated with denoising results using AutoTune outputs $\\{\\bar{c}_i\\}$ . As shown in Tab. 1, NFANet-RCD achieves comparable performance to the baseline NFANet consistently on multiple datasets, indicating that our plug-in RCD module enables real-time controllable denoising for NAFNet without sacrificing its original denoising performance. Please note that NAFNet-RCD can yield comparable results to the backbone just by using the AutoTune outputs, and the performance can be further improved by manually tuning the control parameters (See Sec. 3.6.) We further show the qualitative performance of NAFNet-RCD in Fig. 6. NAFNet-RCD can recover more details of some degraded images, which may be benefited from RCD's richer representation capacity by integrating multiple noise maps.", + "bbox": [ + 496, + 395, + 892, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Slimmer Model Variants. Towards the goal of evaluating the compatibility and robustness of RCD, we conduct ablations by applying RCD to different-sized backbones. Specifically, we shrink the width and block numbers of NAFNet, denoting derived models as NAFNet-small $(\\frac{1}{4} \\times)$ and NAFNet-tiny $(\\frac{1}{16} \\times)$ . Tab. 3 reports the results of RCD with those scaled backbones. It can be observed that the RCD-variants can achieve comparable and even slightly better denoising results compared to their baselines, which further demonstrates RCD's robustness and effectiveness for different-sized backbones.", + "bbox": [ + 496, + 652, + 890, + 810 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Real Single Image Denoising", + "text_level": 1, + "bbox": [ + 500, + 819, + 756, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Setup (Real Image) Unlike existing controllable denoising methods [24,50] which focus on synthetic benchmarks, we are the first solution that attempts to extend controllable denoising to real-world SIDD datasets.", + "bbox": [ + 496, + 842, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14033", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fc24aa3dd446f86db11086e608e3b5005225d97c4d1c1b9e5794dd0cb9cde020.jpg", + "image_caption": [ + "Figure 6. Visual comparison of RCD and their baseline results on $\\sigma = 50$ denoising. GT: Ground truth. Base: Baseline model without RCD. AutoTune: RCD results by applying control parameters from AutoTune module." + ], + "image_footnote": [], + "bbox": [ + 83, + 68, + 480, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6f05db71269261da1b66f565f0b736153580927bc2b204ac244eec173cac2bfe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 68, + 883, + 247 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3dcb693b7302e94375aa0e963848558a9dd9ca8d5947bd91ea3a40a50f1fc5c0.jpg", + "table_caption": [ + "Table 3. Ablation of RCD on various backbone sizes." + ], + "table_footnote": [], + "table_body": "
MethodCBSD68\nσ = 15 σ = 25 σ = 50Kodak24\nσ = 15 σ = 25 σ = 50McMaster\nσ = 15 σ = 25 σ = 50Urban100\nσ = 15 σ = 25 σ = 50
NAFNet-tiny33.5834.3333.8532.96
NAFNet-RCD-tiny33.7131.0631.8833.22
NAFNet-small33.8431.1832.1833.61
NAFNet-RCD-small33.9631.3132.3233.92
NAFNet34.1131.4932.7034.41
NAFNet-RCD34.1331.4932.7234.45
", + "bbox": [ + 83, + 327, + 883, + 448 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/abaa8e808fece1a8ab58cc94e7a08f2f1871e313d3afc8671a40dc1385a342b1.jpg", + "table_caption": [ + "Table 4. Image denoising results on SIDD. Real noise: results on real-world SIDD test sets. Synthetic noise: results on SIDD test set with additive Gaussian noise ( $\\sigma = 25$ )." + ], + "table_footnote": [], + "table_body": "
MethodReal noiseSynthetic noise
PSNRSSIMPSNRSSIM
NAFNet-tiny42.190.979638.460.9551
NAFNet-RCD-tiny41.860.978138.600.9558
NAFNet43.220.981838.850.9481
NAFNet-RCD42.910.980639.140.9580
", + "bbox": [ + 78, + 517, + 491, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SIDD consists of real noisy images captured by smartphones with $\\sigma \\in [0,50]$ . Instead of using full SIDD data, we choose subsets of SIDD with $\\sigma \\in [0,12]$ (around $70\\%$ of the entire dataset) to train our RCD model, which is initialized with $L = 4$ and $\\{l_i\\} = [3,6,9,12]$ . The main reason is the lacking of high $\\sigma$ data at given levels in SIDD because of SIDD's highly long-tailed noise level distribution. Specifically, most noisy images in SIDD gather in $\\sigma < 12$ and the samples distribute sparsely when $\\sigma$ is large. Consistent to Sec. 4.1, we adopt NAFNet (SOTA methods for SIDD challenge [11]) as our backbone at two scales ( $1\\times$ , $\\frac{1}{16}\\times$ ). Both NAFNet-RCD and the corresponding baselines are trained on this subset with the same training settings as in [11].", + "bbox": [ + 75, + 637, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results and Analysis We conduct blind denoising experiments on SIDD with different RCD model scales to evaluate its adjustability to the real-world dataset. As shown in Tab. 4 (left), our RCD (AutoTune results) can", + "bbox": [ + 75, + 842, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "achieve high-quality controllable real-world denoising in both model scales. However, we note that enabling controllable denoising with RCD may still result in a slight decrease in quantitative results (about 0.3dB), which may be a result of unbalanced data for each level and short noise level interval ( $|l_{i+1} - l_i|$ , see more discussion in Sec. 4.4).", + "bbox": [ + 496, + 467, + 890, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SIDD with synthetic noise. We extensively conduct synthetic denoising experiments on SIDD to further show the compatibility of RCD on SIDD datasets. Following Sec. 4.1, we add random Gaussian noise $\\sigma \\in [0,60]$ to SIDD training data, and both methods are evaluated on $\\sigma = 50$ SIDD test samples. As shown in Tab. 4 (right), RCD models slightly outperform their baselines, demonstrating RCD's compatibility for SIDD. Moreover, this result can also indicate that RCD's performance drop on SIDD real image may arise from the noise distribution and RCD configurations, rather than RCD's adaptive capacity to SIDD data. See Appendix for more results and visualizations.", + "bbox": [ + 496, + 553, + 892, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Video Denoising", + "text_level": 1, + "bbox": [ + 500, + 733, + 661, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiment Setup Following common practice [32, 44, 46], we train our models on DAVIS training set and use DAVIS-test and Set-8 for benchmarking. Like in [46], we add Gaussian noise with random standard deviation between 5-50 on the DAVIS clean videos for training. The DAVIS set contains 30 color sequences of resolution $854 \\times 480$ , which will be randomly cropped into $128 \\times 128$ patches during training. Other training settings and hyperparameters are kept the same as [46] for a fair comparison.", + "bbox": [ + 496, + 756, + 890, + 885 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Choice of Basic model. We choose FastDVD [46] as", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14034", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05c5197532a41243cad10d54d7b703c53aa41d4e7c6e7895ba48bb2a2d8c0480.jpg", + "image_caption": [ + "Figure 7. Illustration of RCD control logics. Users can retouch the denoising level by tuning the Intensity bar ( $\\sigma = \\sqrt{\\sum_{i=1}^{L} c_i^2 l_i^2}$ ) and setup their perceptual preference at fixed level by tuning Component bar (changing $\\{c_i\\}$ while keeping $\\sigma$ )." + ], + "image_footnote": [], + "bbox": [ + 80, + 73, + 885, + 222 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our backbone model. Although recent methods [32,48] outperform FastDVD by 1-2 PSNR at most, they actually introduce huge models and extra heavy operations like patch clustering [48] and layer-wise frame-to-frame wrapping using optical flow [32] ( $>100 \\times$ slower than FastDVD).", + "bbox": [ + 75, + 286, + 467, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results and Analysis. Like [44], we evaluate our video denoising models with the input length of one frame and five frames. We denote RCD models for video denoising as \"FastDVD-RC\" and compare their quantitative AutoTune denoising results to baseline FastDVD in Tab. 5. Consistent with preceding sections, AutoTune results of FastDVD-RCD can demonstrate comparable performance to the default FastDVD, which means our RCD can also achieve lossless real-time noise editing in video scenarios. Unlike previous heavy controllable denoising methods, our real-time RCD can even allow users to do online video denoising editing without any latency.", + "bbox": [ + 75, + 358, + 467, + 530 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b8329bd57db2068417978b36cbd8ccd83f4ef3a86ae47d3e4f3acc9c676767c5.jpg", + "table_caption": [ + "Table 5. Video denoising results." + ], + "table_footnote": [], + "table_body": "
Test setσ1 frame5 frames
FastDVDFastDVD-RCDFastDVDFastDVD-RCD
DAVIS2034.1734.2135.6935.65
3032.4532.6934.0634.04
4031.3931.6032.8032.78
5030.2630.5731.8331.85
Set 82031.9932.0133.4333.46
3030.6130.6531.6231.71
4029.6229.8330.3630.42
5028.6128.8529.4129.60
", + "bbox": [ + 81, + 559, + 460, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Discussions", + "text_level": 1, + "bbox": [ + 76, + 676, + 202, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Selection of Denoising Levels. Differing from conventional denoising methods, RCD requires a group of predefined noise levels $\\{l_i\\}_{i=1}^L$ . To evaluate how the selection of $\\{l_i\\}_{i=1}^L$ affects RCD's performance, we conduct ablation studies on FastDVD-RCD by changing the number of noise maps $(L)$ (See Tab. 6.) All of the models are trained on noisy images with $\\sigma \\in (0,60]$ and uniformly sampled noise levels that $\\{l_i = \\frac{60}{L} * i\\}_{i=1}^L$ . We observe that larger $L$ means more fine-grained control on denoising, but it may incur a performance drop. In fact, when $n$ is large we find that $\\mathcal{L}_{level}$ will also keep large and be hard to optimize. Trading-off performance and control precision, we empirically choose $L = 12$ and noise level interval $|l_{i+1} - l_i| = 5$ as defaults.", + "bbox": [ + 75, + 699, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9b4cc1601a300bb37dc95cd32d2af51563685bae62f7974f73cb86bfde14bc3a.jpg", + "table_caption": [ + "Table 6. Ablations of FastDVD-RCD on different number of noise levels. Reported scores are PSNR of AutoTune outputs and GT." + ], + "table_footnote": [], + "table_body": "
Test SetσL = 1L = 2L = 12L = 30L = 60
Set82031.8731.4232.0131.3931.07
3030.5130.0930.6530.1229.75
4029.6029.3129.8329.3329.01
5028.6228.2928.8528.2228.05
", + "bbox": [ + 506, + 315, + 880, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Control Capacity. This section discusses the representation capacity of $c_{i}$ as control parameters. Generally, $c_{i}$ controls the denoising process on two aspects: intensity and components. Firstly, the noise levels of RCD outputs are identical and can be derived by $\\sigma = \\sqrt{\\sum_{i=1}^{L} c_{i}^{2} l_{i}^{2}}$ (See Sec. 3.4), which allows us to control the denoising intensity by changing $\\{c_{i}\\}$ . Fig. 7 depicts visualizations of RCD-controlled denoising under different intensity settings. Besides, as discussed in Sec. 3.6, RCD supports further optimization of the denoising results at specific noise intensity by tuning $c_{i}$ by involving different components of $\\tilde{\\mathcal{N}}_{i}$ . (Please be reminded that $\\tilde{\\mathcal{N}}_{i}$ is trained by $\\mathcal{L}_{\\text{level}}$ , denoting learned optimal denoising results at every fixed level $l_{i}$ .)", + "bbox": [ + 496, + 398, + 890, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Summary", + "text_level": 1, + "bbox": [ + 500, + 606, + 607, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present RCD framework that enables real-time noise editing for controllable denoising. Unlike existing continual-level denoising methods, RCD doesn't require multiple training stages and auxiliary networks. With the proposed Noise Decorrelation module, RCD transforms the control of denoising into white-box operations, with no requirement to feed control parameters to networks at test time, which enables real-time editing even for heavy network models. Extensive experiments on widely-used real/synthetic image and video denoising datasets demonstrate the robustness and effectiveness of our RCD.", + "bbox": [ + 496, + 631, + 890, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 801, + 679, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, and Shanghai Committee of Science and Technology (Grant No. 21DZ1100100).", + "bbox": [ + 496, + 827, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14035", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1692-1700, 2018. 6", + "[2] Eirikur Agustsson and Radu Timofte. 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PMLR, 2021. 2" + ], + "bbox": [ + 78, + 90, + 468, + 386 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14038", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Real-Time Controllable Denoising for Image and Video/64f70f4f-f112-41dc-9862-a65c1c758802_model.json b/2023/Real-Time Controllable Denoising for Image and Video/64f70f4f-f112-41dc-9862-a65c1c758802_model.json new file mode 100644 index 0000000000000000000000000000000000000000..df6a4659bb050e3901d3f91b861c8aa11d5df23d --- /dev/null +++ b/2023/Real-Time Controllable Denoising for Image and Video/64f70f4f-f112-41dc-9862-a65c1c758802_model.json @@ -0,0 +1,2279 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.21, + 0.13, + 0.761, + 0.151 + ], + "angle": 0, + "content": "Real-time Controllable Denoising for Image and Video" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.179, + 0.856, + 0.247 + ], + "angle": 0, + "content": "Zhaoyang Zhang\\(^{1*}\\) Yitong Jiang\\(^{1*}\\) Wenqi Shao\\(^{1,3}\\) Xiaogang Wang\\(^{1}\\) Ping Luo\\(^{2,3}\\) Kaimo Lin\\(^{4}\\) Jinwei Gu\\(^{1,3}\\) \n\\(^{1}\\)The Chinese University of Hong Kong \\(^{2}\\)The University of Hong Kong \\(^{3}\\)Shanghai AI Laboratory \\(^{4}\\)SenseBrain \n{zhaoyangzhang@link, ytjiang@link, weqish@link, xgwang@ee, jwgu@}.cuhk.edu.hk \nlinkaimol990@gmail.com, pluo@cs.hku.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.282, + 0.314, + 0.298 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.474, + 0.66 + ], + "angle": 0, + "content": "Controllable image denoising aims to generate clean samples with human perceptual priors and balance sharpness and smoothness. In traditional filter-based denoising methods, this can be easily achieved by adjusting the filtering strength. However, for NN (Neural Network)-based models, adjusting the final denoising strength requires performing network inference each time, making it almost impossible for real-time user interaction. In this paper, we introduce Real-time Controllable Denoising (RCD), the first deep image and video denoising pipeline that provides a fully controllable user interface to edit arbitrary denoising levels in real-time with only one-time network inference. Unlike existing controllable denoising methods that require multiple denoisers and training stages, RCD replaces the last output layer (which usually outputs a single noise map) of an existing CNN-based model with a lightweight module that outputs multiple noise maps. We propose a novel Noise Decorrelation process to enforce the orthogonality of the noise feature maps, allowing arbitrary noise level control through noise map interpolation. This process is network-free and does not require network inference. Our experiments show that RCD can enable real-time editable image and video denoising for various existing heavy-weight models without sacrificing their original performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.69, + 0.21, + 0.705 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Image and video denoising are fundamental problems in computational photography and computer vision. With the development of deep neural networks [12, 26, 49, 59], model-based denoising methods have achieved tremendous success in generating clean images and videos with superior denoising scores [4,55,57]. However, it should be noted that the improvement in reconstruction accuracy (e.g., PSNR, SSIM) is not always accompanied by an improvement in visual quality, which is known as the Perception-Distortion trade-off [6]. In traditional denoising approaches, we can easily adjust the denoising level by tuning related control" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.283, + 0.895, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.448, + 0.894, + 0.504 + ], + "angle": 0, + "content": "Figure 1. Real-time controllable denoising allows users further tuning the restored results to achieve Perception-Distortion trade-off. A-B: tuning with changing denoising intensity. C-E: tuning without changing denoising intensity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.893, + 0.569 + ], + "angle": 0, + "content": "parameters and deriving our preferred visual results. However, for typical deep network methods, we can only restore the degraded image or video to a fixed output with a predetermined restoration level." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In recent years, several modulation methods have been proposed to generate continuous restoration effects between two pre-defined denoising levels. These methods can be categorized into two kinds: interpolation-based methods [17,24,50,51], which use deep feature interpolation layers, and condition-network-based methods, which import an extra condition network for denoising control [9, 25, 39]. Essentially, both types of methods are designed based on the observation that the outputs of the network change continuously with the modulation of features/filters. This observation enables deep denoising control, but it also introduces several limitations. First, there is a lack of explainability, as the relationship between the control parameters (how to modulate features) and the control operation (how the network outputs are changed) is unclear [24]. This indicates that black-box operators (network layers) must be used to encode them. Second, the use of control parameters as network inputs requires entire network propagation each time control parameters change, resulting in a lack of efficiency. Lastly, current modulation methods often require an explicit degradation level during training, which is hard to obtain for real-world samples. As a result, current controllable denoising methods only focus on synthetic" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.206, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14028" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.468, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.249, + 0.472, + 0.292 + ], + "angle": 0, + "content": "Figure 2. Comparison of pipelines between conventional controllable denoising and our RCD. RCD achieves real-time noise control by manipulating editable noises directly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.47, + 0.408 + ], + "angle": 0, + "content": "noise benchmarks. Furthermore, both interpolation-based and condition-network-based methods have their own drawbacks. Interpolation-based methods often require multiple training stages, including pretraining two basic models (start level and end level). On the other hand, condition-network-based methods are strenuous to jointly optimize the base network and the condition network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.468 + ], + "angle": 0, + "content": "In this paper, we research on the problem: Can we achieve real-time controllable denoising that abandons the auxiliary network and requires no network forward propagation for changing restoration effects at test time?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Towards this goal, we propose Real-time Controllable Denoising method (RCD), a lightweight pipeline for enabling rapid denoising control to achieve Perception-Distortion Balance (See Fig. 1). Our RCD can be plugged into any noise-generate-based restoration methods [11, 46, 54, 55] with just a few additional calculations. Specifically, we replace the last layer of an existing denoising network (which usually outputs a single noise map) with a lightweight module that generates multiple noise maps with different noise levels. We utilize a novel Noise Decorrelation process to enforce the orthogonality of the noise distribution of these noise maps during training. As a result, we can attain arbitrary denoising effects by simple linear interpolation of these noise maps. Since this process does not require network inference, it makes real-time user interaction possible even for heavy denoising networks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Fig. 2 illustrates the fundamental differences between our RCD approach and conventional controllable denoising methods. In contrast to traditional methods that rely on control networks, the RCD pipeline generates editable noises of varying intensities/levels, providing explicit control by external parameters and enabling network-free, real-time denoising editing. Real-time editing capabilities offered by RCD create new opportunities for numerous applications that were previously impossible using conventional techniques, such as online video denoising editing, even during playback (e.g., mobile phone camera video quality tuning for ISP tuning engineers), as well as deploying controllable denoising on edge devices and embedded systems. Since the editing stage of RCD only involves image interpolation," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "users can edit their desired results on low-performance devices without the need for GPUs/DSPs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.121, + 0.894, + 0.278 + ], + "angle": 0, + "content": "Moreover, unlike previous methods that only support changing noise levels, RCD allows users to adjust denoising results at a specific noise level by providing a new interface to modify the noise generation strategy. RCD is also the first validated method for controllable denoising on real-world benchmarks. It is noteworthy that existing controllable methods typically require training data with fixed-level noise to establish their maximum and minimum noise levels, which makes them unsuitable for most real-world benchmarks comprising data with varying and unbalanced noise levels." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.28, + 0.88, + 0.295 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.307, + 0.892, + 0.395 + ], + "angle": 0, + "content": "- We propose RCD, a controllable denoising pipeline that firstly supports real-time denoising control (\\(>\\) \\(2000 \\times\\) speedup compared to conventional controllable methods) and larger control capacity (more than just intensity) without multiple training stages [24] and auxiliary networks [50]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.397, + 0.892, + 0.427 + ], + "angle": 0, + "content": "- RCD is the first method supporting controllable denoising on real-world benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.43, + 0.892, + 0.459 + ], + "angle": 0, + "content": "- We propose a general Noise Decorrelation technique to estimate editable noises." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.463, + 0.892, + 0.52 + ], + "angle": 0, + "content": "- We achieve comparable or better results on widely-used real/synthetic image-denoising and videodenoising datasets with minimal additional computational cost." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.307, + 0.892, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.537, + 0.65, + 0.553 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.614, + 0.577 + ], + "angle": 0, + "content": "2.1. Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Traditional image and video denoising methods are often based on prior assumptions such as sparse image prior [3, 15, 16, 20], non-local similarity [7, 13, 14, 18], and other similar techniques [22, 41, 52]. However, with the recent development of deep learning networks, many learning-based methods have been proposed and achieved state-of-the-art performance. Early works [8] utilized multi-layer perceptron (MLP) to achieve comparable results with BM3D. In recent years, there has been rapid progress on CNN-based denoising methods [4, 10, 21, 47, 55, 57] and Transformer-based methods [32, 42, 54, 59], which have started to dominate the image/video denoising task. However, the abovementioned works mainly focus on designing novel network architectures to improve the denoising performance and usually generate a single output. Their lack of ability to adjust the output denoising level based on user's feedback has greatly restricted their practical use in many real-world applications. Moreover, although techniques like pruning [33, 38, 60] and quantization [45, 61] can accelerate such neural network-based methods, they are typically heavy, which restricts their application to real-time denoising control." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14029" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.074, + 0.891, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 3. Pipeline overview of proposed RCD framework. A: Backbone network for generating multi-level noise maps. B: Noise Decorrelation module for editable noises. C: AutoTune module for providing reference control parameters for users." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.45, + 0.291, + 0.466 + ], + "angle": 0, + "content": "2.2. Controllable denoising" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Most conventional deep-learning methods for image/video denoising can only generate a fixed result with a specific restoration level. Recently, some controllable image/video denoising methods allow users to adjust the restoration effect without retraining the network. DNI [51] and AdaFM [24] used the observation that the learned filters of the models trained with different restoration levels are similar in visual patterns. DNI interpolated all the corresponding parameters between two related networks to derive smooth and continuous restoration effects, while AdaFM adopted feature modulation filters after each convolution layer. CFSNet [50] proposed an adaptive learning strategy of using interpolation coefficients to couple the intermediate features between the main branch and the tuning branch. Different from these interpolation-base methods, some other methods [9, 25, 39] regarded modulation as a conditional image restoration problem and adopted a joint training strategy. CUGAN [9] proposed a GAN-based image restoration framework to avoid the over-smooth problem, a common issue in PSNR-oriented methods. However, all of the above controllable methods can only be trained with synthetic degradations because they require explicit degradation levels during training. When applied on real-world data, as shown in [23], methods that trained for blind Additive White Gaussian Noise (AWGN) [35,55] may be overfitted and often suffer from dramatic performance drop. Besides the real-world image issue, all these controllable methods utilize an auxiliary conditional network and require one network inference for each different target" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.481 + ], + "angle": 0, + "content": "restoration level at test time, which makes them almost impossible for real-time application." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.599, + 0.512 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.523, + 0.764, + 0.54 + ], + "angle": 0, + "content": "3.1. Conventional Deep Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Deep denoising methods trump traditional filter-based techniques by leveraging the neural networks' robust representation learning capability. Most current denoising methods [11,32,46] reason about the relationship between clean and noisy images by regressing noise maps with a neural generator. Specifically, given a noisy image \\(\\mathbf{I}_{\\mathbf{n}}\\) and model \\(\\mathcal{M}:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times C}\\), we can derive the predicted clean image \\(\\mathbf{I}_{\\mathbf{c}}\\) by: \\(\\mathbf{I}_{\\mathbf{c}} = \\mathbf{I}_{\\mathbf{n}} + \\mathcal{M}(\\mathbf{I}_{\\mathbf{n}})\\), where model \\(\\mathcal{M}\\) is updated by minimizing the distance between the denoising result \\(\\mathbf{I}_{\\mathbf{c}}\\) and the ground truth \\(\\mathbf{I}_{\\mathrm{gt}}\\). As we can see, this kind of approach generates a single fixed output result in a black-box manner, making it almost impossible to adjust the denoise operation explicitly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.747, + 0.677, + 0.763 + ], + "angle": 0, + "content": "3.2. Pipeline Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we present Real-time Controllable Denoising (RCD), a novel deep learning-based pipeline for real-time controllable denoising. As illustrated in Fig. 3, RCD essentially consists of three parts: (1) A backbone network, i.e., \\(\\mathcal{M}_b:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times LC}\\), generates multiple fixed-level noise maps, where \\(L\\) is the number of pre-defined noise levels (see (A) in Fig. 3). (2) A Noise Decorrelation (ND) block that enforces the editability of the generated noise maps (see (B) in Fig. 3). (3) An AutoTune" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14030" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.12 + ], + "angle": 0, + "content": "module that gives a default set of control parameters to generate the best denoising result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.12, + 0.471, + 0.25 + ], + "angle": 0, + "content": "Specifically, the backbone network will generate multiple fixed-level noise maps, i.e., \\(\\{\\mathcal{N}_i\\}_{i=1}^L\\), for each noisy image input. The noise maps are then fed into the proposed Noise Decorrelation (ND) block, which makes noise maps orthogonal to each other. In this way, the decorrelated noise maps \\(\\{\\tilde{\\mathcal{N}}_i\\}_{i=1}^L\\) will be zero-correlated and thus become linearly interpolable. At last, the AutoTune module will give a set of suggested control parameters \\(\\{\\bar{c}_i\\}_{i=1}^L\\) to generate the final denoising result as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.261, + 0.47, + 0.302 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {\\mathbf {c}} = \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.377 + ], + "angle": 0, + "content": "where \\(\\sum_{i=1}^{L} \\bar{c}_i = 1\\). Moreover, given the zero-correlated noise maps, users can also generate arbitrary strength denoising results by replacing \\(\\{\\bar{c}_i\\}_{i=1}^L\\) with their own customized control parameters \\(\\{c_i\\}_{i=1}^L\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.382, + 0.342, + 0.397 + ], + "angle": 0, + "content": "3.3. Multi-level Noise Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.47, + 0.463 + ], + "angle": 0, + "content": "Given a noisy input image \\(\\mathbf{I}_{\\mathbf{n}}\\), the backbone network aims to generate multiple noise maps \\(\\{\\mathcal{N}_i\\}_{i=1}^L\\), corresponding to a set of pre-defined noise levels \\(\\{l_i\\}_{i=1}^L\\), e.g. noise levels \\(\\{5, 10, 15, \\dots, 60\\}\\). Hence, we have" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.473, + 0.469, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\sigma \\left(\\mathcal {N} _ {i}\\right) = l _ {i}, \\forall i = 1, \\dots , L, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.601 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the noise level operation that calculates the standard deviation of pixels in each noise map. To obtain multilevel noise maps, we replace the conventional last output layer of the denoising network with a convolutional layer with an output channel size of \\(L\\cdot C\\). Moreover, the level of the noise map is explicitly generated with the normalization operation, as given by" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.61, + 0.47, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} _ {i} = l _ {i} \\frac {\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)}}{\\sigma (\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)})}, \\forall i = 1, \\dots , L. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Here \\(\\mathcal{M}_b(\\mathbf{I_n})\\in \\mathbb{R}^{H\\times W\\times LC}\\) is network output, and \\(\\mathcal{M}_b(\\mathbf{I_n})^{(i)}\\in \\mathbb{R}^{H\\times W\\times C}\\) is the i-th component separated from the channel dimension. The derived \\(\\mathcal{N}_i\\) can be considered as the noise map estimated at the given noise level \\(l_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.8 + ], + "angle": 0, + "content": "Different from prior controllable denoising methods with implicit interpolation in the network, we propose to explicitly interpolate the noise maps in Eqn. 3. Thanks to the separation of noise interpolation and network inference, our RCD can achieve real-time user interaction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.471, + 0.902 + ], + "angle": 0, + "content": "However, the multi-level noise maps \\(\\mathcal{N}_i\\) directly obtained by convolutional layers are usually highly correlated, which leads to the problem of noise level collapse. In other words, the noise map representations in different levels are redundant, implying that the number of noise maps at different noise strengths that participate in the linear interpolation in Eqn. 1 is implicitly reduced. Without any constraint," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.895, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.226, + 0.894, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Demonstration of Noise Decorrelation's influence on noise editing. \\( |\\Sigma|_F \\) denotes norms of the covariance matrix for corresponding learned noises and \\( \\sigma \\) is noise intensity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.366 + ], + "angle": 0, + "content": "our experiments show that the single noise map at a certain noise level would dominate in the linear interpolation for a variety of input noisy images. To address this issue, we further introduce the Noise Decorrelation block to make representations of these noise maps much more informative in the following section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.373, + 0.691, + 0.387 + ], + "angle": 0, + "content": "3.4. Noise Decorrelation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.553 + ], + "angle": 0, + "content": "The Noise Decorrelation (ND) block is designed to regularize the backbone network to generate editable noise maps at varying levels. In particular, this block is a parameter-free computational unit that enforces \\(\\mathcal{N}_i\\) to be approximately zero-correlated with each other: \\(\\mathbf{cov}(\\mathcal{N}_i,\\mathcal{N}_j)\\approx 0,\\forall i,j\\in\\) \\(\\{1,2,\\dots,L\\}\\), where \\(\\mathbf{cov}(\\cdot ,\\cdot)\\) is covariance operator. Inspired by the success of using the decorrelation technique in network optimization and normalization, we adopt the whitening-based methods [29, 30] for noise decorrelation here. The noise maps are decorrelated using the inverse square root of their covariance matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.642 + ], + "angle": 0, + "content": "Specifically, for each predicted fixed-level noise map \\(\\mathcal{N}_i\\), it will firstly be reshaped to \\(\\mathcal{N}_i \\in \\mathbb{R}^{1 \\times M}\\), where \\(M = HWC\\). By stacking the reshaped \\(\\mathcal{N}_i\\) over the first dimension, we have \\(\\mathbf{N} \\in \\mathbb{R}^{L \\times M}\\). We then calculate the noise covariance matrix \\(\\sigma\\) by: \\(\\Sigma = \\frac{1}{M - 1} (\\mathbf{N} - \\bar{\\mathbf{N}})(\\mathbf{N} - \\bar{\\mathbf{N}})^T\\) where \\(\\bar{\\mathbf{N}}\\) is mean of \\(\\mathbf{N}\\) over channel \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.748 + ], + "angle": 0, + "content": "The Noise Decorrelation block needs to compute inverse square root \\(\\Sigma^{-\\frac{1}{2}} \\in \\mathbb{R}^{L \\times L}\\), which can be done by eigen decomposition or SVD. Since this kind of operation involves heavy computation [29], we instead adopt the more efficient Newton's Iteration to estimate \\(\\Sigma^{-\\frac{1}{2}}\\) as in [5, 27]. Giving a covariance matrix \\(\\Sigma\\), Newton's Iteration calculates \\(\\Sigma^{-\\frac{1}{2}}\\) by following the iterations below:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.755, + 0.892, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Sigma_ {0} = I, \\\\ \\Sigma_ {k} = \\frac {1}{2} (3 \\Sigma_ {k - 1} - (\\Sigma_ {k - 1}) ^ {3} \\Sigma), k = 1, 2,.., T, \\end{array} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.869 + ], + "angle": 0, + "content": "where \\( k \\) is the iteration index and \\( T \\) is the iteration number (in our experiments \\( T = 3 \\) or 4). \\( \\Sigma_{k} \\) is guaranteed to converge to \\( \\Sigma^{-\\frac{1}{2}} \\), if \\( \\| I - \\Sigma \\|_2 < 1 \\) [5]. This condition can be achieved by normalizing \\( \\Sigma \\) to \\( \\frac{\\Sigma}{tr(\\Sigma)} \\), where \\( tr(.) \\) is trace operator." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The derived \\(\\Sigma^{-\\frac{1}{2}}\\) can be regarded as a whitening matrix [43], which decorrelates the noise maps \\(\\mathbf{N}\\) in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14031" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.196 + ], + "angle": 0, + "content": "a differentiable manner. The decorrelated noise maps \\(\\mathbf{N} \\in \\mathbb{R}^{\\tilde{H} \\times W \\times LC}\\) can be obtained by calculating: \\(\\tilde{\\mathbf{N}} = \\Sigma^{-\\frac{1}{2}} \\mathbf{N}\\). We can then have our editable fixed-level noises \\(\\tilde{\\mathcal{N}}_i \\in \\mathbb{R}^{H \\times W \\times C}\\) by reshaping \\(\\tilde{\\mathbf{N}}\\) and splitting it into \\(L\\) noise maps. After Noise Decorrelation, we apply the same normalization as Eqn. 3 to guarantee the noise strength of the decorrelated noises." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.471, + 0.271 + ], + "angle": 0, + "content": "The zero-correlated noise maps \\(\\tilde{\\mathcal{N}}_i\\) present several excellent properties for controllable denoising. Firstly, the linearity of the noise level's square towards \\(\\tilde{\\mathcal{N}}_i\\) is guaranteed. In other words, given an arbitrary set of control parameters \\(\\{c_i\\}_{i = 1}^L\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.279, + 0.47, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V a r} \\left(\\sum_ {i = 1} ^ {L} c _ {i} \\tilde {\\mathcal {N}} _ {i}\\right) = \\sum_ {i = 1} ^ {L} c _ {i} ^ {2} \\mathbf {V a r} \\left(\\tilde {\\mathcal {N}} _ {i}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.469, + 0.461 + ], + "angle": 0, + "content": "where \\(\\mathbf{Var}(\\cdot)\\) denotes variance operator. Apparently, Eqn. 5 holds when elements of \\(\\{\\tilde{\\mathcal{N}}_i\\}_{i = 1,2,\\dots,m}\\) are mutually zero-correlated. Eqn. 5 reveals the explicit relationship between the control parameters and the target noise level, which allows us to directly edit noises by interpolating \\(\\mathcal{N}_i\\) using \\(c_{i}\\). Secondly, the Noise Decorrelation block can be regarded as a regularization tool that forces models to learn different noise formats for each level, which will increase the representation capacity of the denoising network [30]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.561 + ], + "angle": 0, + "content": "Fig. 4 demonstrates how the Noise Decorrelation block works. With ND block, the covariance of learned noises is reduced to almost zero (without it, \\(|\\Sigma|_F\\) can be 751 and unignorable), allowing us to derive determined interpolated results with target noise intensity. In contrast, without the Noise Decorrelation blocks, the output noise level can not be guaranteed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.569, + 0.253, + 0.584 + ], + "angle": 0, + "content": "3.5. AutoTune Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.827 + ], + "angle": 0, + "content": "Given the decorrelated noise maps from the Noise Decorrelation block, the AutoTune module will predict a set of model-suggested control parameters, i.e., \\(\\{\\bar{c}_i\\}_{i=1}^L\\), to generate the default denoising result. Users can then use this set of parameters as a starting point to fine-tune their final desired denoising strength. Our AutoTune module is extremely lightweight, and is formulated as a single-layer module with temperature softmax activation. Specifically, \\(\\{\\bar{c}_i\\}_{i=1}^L\\) can be obtained by: \\(\\bar{c}_i = \\frac{e^{\\frac{\\mathcal{A}(f)_i}{\\tau}}}{\\sum_{j=1}^n e^{\\frac{\\mathcal{A}(f)_j}{\\tau}}}\\), where \\(\\mathcal{A}\\) is the NN layer, \\(f\\) is the input feature maps, and \\(\\tau\\) is temperature. In our experiments, \\(\\tau\\) is set to be 0.05 for best performance. Following the design ethos of efficiency and least coupling to the backbone architecture, we directly choose the unnormalized model outputs \\(\\mathcal{M}(\\mathbf{I_n})\\) as \\(f\\) (see (C) in Fig. 3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.835, + 0.416, + 0.851 + ], + "angle": 0, + "content": "3.6. New Cardinality for Denoising Control." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.857, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Unlike existing methods that only modulate noise intensity, our RCD control scheme allows users to further optimize the denoising result to a given noise intensity" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.885, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.255, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 5. Example of RCD denoising results by AutoTune and HumanTune on Set8. AutoTune module provides reference control parameters, i.e., \\(\\{\\bar{c}_i\\}_{i=1}^L\\), to generate the denoising result, and it can be further improved by fine-grained artificial tuning (HumanTune), i.e., \\(\\{c_i\\}\\), without changing the noise intensity (both \\(\\sigma = 40\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.53 + ], + "angle": 0, + "content": "by tuning \\(\\{c_i\\}\\), as long as the weighted mean of \\(l_{i}\\) towards \\(c_{i}\\) remains the same. Eqn. 5 shows that when \\(\\sum_{i = 1}^{L}c_{i}^{2}\\mathbf{Var}(\\tilde{\\mathcal{N}}_{i}) = \\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}\\) is fixed, the variance of the output noise \\(\\mathbf{Var}(\\sum_{i = 1}^{L}c_{i}\\tilde{\\mathcal{N}}_{i})\\) would be also fixed. By exploring \\(c_{i}\\) under the condition of fixed \\(\\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}\\), we can further optimize the denoising results at a specific noise level by involving different components \\((\\mathcal{N}_i)\\) in the noise interpolation. As shown in Fig. 5, our AutoTune module can generate high-quality results using just the reference control parameters \\(\\{\\bar{c}_i\\}\\). Users can further improve the result by artificially tuning \\(\\{c_i\\}\\) around \\(\\{\\bar{c}_i\\}\\), even at the same noise level." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.7, + 0.559 + ], + "angle": 0, + "content": "3.7. Optimization Targets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.641 + ], + "angle": 0, + "content": "To guarantee the visual quality of arbitrarily edited noise \\(\\sum_{i=1}^{L} c_i \\tilde{\\mathcal{N}}_i\\) for any given set of control parameters \\(\\{c_i\\}_{i=1}^L\\), we adopt a multi-level concurrent training strategy by minimizing the difference between each level's noise output and the ground truth noise, i.e., \\(\\mathcal{L}_{level}\\), which is derived by:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.654, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {l e v e l}} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\tilde {\\mathcal {N}} _ {i}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.891, + 0.75 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_{gt}\\), \\(\\mathbf{I}_{\\mathbf{n}}\\) are ground truth clean image and the input noisy image. \\(\\mathcal{L}(.)\\) can be any loss functions (e.g., L2 loss or PSNR loss)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Spectaculously, \\(\\mathbf{I}_{\\mathbf{n}} + \\tilde{\\mathcal{N}}_i\\) can be regarded as corner cases of RCD when we use one-hot control parameters as input. Joint optimization of all the noise levels ensures that each element of \\(\\mathcal{N}_i\\) can be trained as optimal noise estimation under the condition of fixed noise level \\(l_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Together with the AutoTune module optimization, our final cost function can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.863, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\mathcal {L} _ {\\text {l e v e l}} + \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}\\right), \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14032" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.07, + 0.832, + 0.085 + ], + "angle": 0, + "content": "Table 1. Gaussian single image denoising results (PSNR). RCD is evaluated with AutoTune results. “-”: not reported" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.097, + 0.916, + 0.234 + ], + "angle": 0, + "content": "
MethodControllableCBSD68Kodak24McMasterUrban100
σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50
IRCNN [56]X33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [57]X33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [55]X33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [40]X33.9131.2828.0534.6332.1629.0534.6732.4029.28-
CResMD [25]✓33.97-28.06---
AdaFM-Net [24]✓34.1031.4328.13---
NAFNet [11]X34.1131.4928.2735.1432.7029.6835.0732.8229.7934.4132.0929.00
NAFNet-RCD (ours)✓34.1331.4928.2635.1532.7229.6935.1132.8429.8134.4532.1229.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.25, + 0.472, + 0.316 + ], + "angle": 0, + "content": "Table 2. Running time comparison for RCD and other controllable methods during test time. Full Pipeline compares full pipeline latency for the model to infer 1000 images, and Edit-only compares latency for editing one image with 1000 different control parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.327, + 0.476, + 0.38 + ], + "angle": 0, + "content": "
MethodMulti-stage trainingFull PipelineEdit-only
AdaFM-Netrequired81.03s81.03s
CResMDNetnot required128.08128.08s
NAFNet-RCDnot required64.84s0.04s
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.47, + 0.437 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the loss weight (\\(\\lambda = 0.1\\) in our experiments), and \\(\\mathcal{L}(\\mathbf{I}_{gt},\\mathbf{I_n} + \\sum_{i = 1}^{n}\\bar{c}_i\\tilde{\\mathcal{N}}_i)\\) optimizes the denoising result derived by the model-suggested control parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.21, + 0.469 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.606 + ], + "angle": 0, + "content": "This section is organized as follows: First, we demonstrate the effectiveness of our plug-in RCD with SOTA image denoising methods [11] in different scales on synthetic noise datasets. Next, to evaluate the ability of blind denoising on real-world data, we conduct experiments on popular real-world denoising dataset SIDD [1]. Then, we apply our real-time controllable RCD pipeline on video denoising applications. At last, we empirically discuss some design details described in the previous sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.618, + 0.37, + 0.635 + ], + "angle": 0, + "content": "4.1. Gaussian Single Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Experimental Setup. To fully demonstrate the effectiveness of the proposed RCD, we choose the most recent SOTA method NAFNet [11] as our backbone. Following [54], we first conduct denoising experiments on several widely-used synthetic color image benchmarks (DIV2K [2], BSD400 [36], Flickr2K [53] and WaterlooED [34]) with additive white Gaussian noise (\\(\\sigma \\in [0, 60]\\)). The training patch size is \\(128 \\times 128\\) and the batch size is 64. We train our model with Adam [31] optimizer and learning rate \\(1e - 3\\) for total 60K iterations. Consistent to [11], PSNR loss is adapted as the loss function. Both the baseline model (NAFNet) and its RCD variants (NAFNet-RCD) are trained from scratch. For settings of RCD, we initialize \\(L = 12\\) and \\(\\{l_i\\} = [5, 10, \\dots, 60]\\) for synthetic denoising training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.857, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Complexity analysis. Extensive adjustments of controllable parameters are often required to obtain one satisfying result for users. Therefore, editing time is vital" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.892, + 0.396 + ], + "angle": 0, + "content": "for controllable methods. This section compares the inference and editing latency of our RCD and conventional controllable pipelines on GTX 1080Ti. As shown in Tab. 2, the proposed RCD not only outperforms other conventional controllable pipelines on inference time, but more importantly, can overwhelm those traditional controllable designs on editing time, which can be more than 2000 times faster (as editing process of RCD is network-free, without reliance on sub-networks). This comparison confirms that our RCD is more than enough for real-time image editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.893, + 0.653 + ], + "angle": 0, + "content": "Results Analysis. We evaluate our proposed method on widely used synthetic noise datasets CBSD68 [37], Kodak24 [19], McMaster [58] and Urban100 [28] with noise levels \\(\\sigma(15)\\), \\(\\sigma(15)\\) and \\(\\sigma(50)\\). RCD is evaluated with denoising results using AutoTune outputs \\(\\{\\bar{c}_i\\}\\). As shown in Tab. 1, NFANet-RCD achieves comparable performance to the baseline NFANet consistently on multiple datasets, indicating that our plug-in RCD module enables real-time controllable denoising for NAFNet without sacrificing its original denoising performance. Please note that NAFNet-RCD can yield comparable results to the backbone just by using the AutoTune outputs, and the performance can be further improved by manually tuning the control parameters (See Sec. 3.6.) We further show the qualitative performance of NAFNet-RCD in Fig. 6. NAFNet-RCD can recover more details of some degraded images, which may be benefited from RCD's richer representation capacity by integrating multiple noise maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.811 + ], + "angle": 0, + "content": "Slimmer Model Variants. Towards the goal of evaluating the compatibility and robustness of RCD, we conduct ablations by applying RCD to different-sized backbones. Specifically, we shrink the width and block numbers of NAFNet, denoting derived models as NAFNet-small \\((\\frac{1}{4} \\times)\\) and NAFNet-tiny \\((\\frac{1}{16} \\times)\\). Tab. 3 reports the results of RCD with those scaled backbones. It can be observed that the RCD-variants can achieve comparable and even slightly better denoising results compared to their baselines, which further demonstrates RCD's robustness and effectiveness for different-sized backbones." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.82, + 0.757, + 0.837 + ], + "angle": 0, + "content": "4.2. Real Single Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.843, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Experimental Setup (Real Image) Unlike existing controllable denoising methods [24,50] which focus on synthetic benchmarks, we are the first solution that attempts to extend controllable denoising to real-world SIDD datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14033" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.069, + 0.482, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.069, + 0.885, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.262, + 0.893, + 0.29 + ], + "angle": 0, + "content": "Figure 6. Visual comparison of RCD and their baseline results on \\(\\sigma = 50\\) denoising. GT: Ground truth. Base: Baseline model without RCD. AutoTune: RCD results by applying control parameters from AutoTune module." + }, + { + "type": "table_caption", + "bbox": [ + 0.325, + 0.304, + 0.645, + 0.317 + ], + "angle": 0, + "content": "Table 3. Ablation of RCD on various backbone sizes." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.328, + 0.885, + 0.449 + ], + "angle": 0, + "content": "
MethodCBSD68\nσ = 15 σ = 25 σ = 50Kodak24\nσ = 15 σ = 25 σ = 50McMaster\nσ = 15 σ = 25 σ = 50Urban100\nσ = 15 σ = 25 σ = 50
NAFNet-tiny33.5834.3333.8532.96
NAFNet-RCD-tiny33.7131.0631.8833.22
NAFNet-small33.8431.1832.1833.61
NAFNet-RCD-small33.9631.3132.3233.92
NAFNet34.1131.4932.7034.41
NAFNet-RCD34.1331.4932.7234.45
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Table 4. Image denoising results on SIDD. Real noise: results on real-world SIDD test sets. Synthetic noise: results on SIDD test set with additive Gaussian noise (\\(\\sigma = 25\\))." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.518, + 0.493, + 0.61 + ], + "angle": 0, + "content": "
MethodReal noiseSynthetic noise
PSNRSSIMPSNRSSIM
NAFNet-tiny42.190.979638.460.9551
NAFNet-RCD-tiny41.860.978138.600.9558
NAFNet43.220.981838.850.9481
NAFNet-RCD42.910.980639.140.9580
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.839 + ], + "angle": 0, + "content": "SIDD consists of real noisy images captured by smartphones with \\(\\sigma \\in [0,50]\\). Instead of using full SIDD data, we choose subsets of SIDD with \\(\\sigma \\in [0,12]\\) (around \\(70\\%\\) of the entire dataset) to train our RCD model, which is initialized with \\(L = 4\\) and \\(\\{l_i\\} = [3,6,9,12]\\). The main reason is the lacking of high \\(\\sigma\\) data at given levels in SIDD because of SIDD's highly long-tailed noise level distribution. Specifically, most noisy images in SIDD gather in \\(\\sigma < 12\\) and the samples distribute sparsely when \\(\\sigma\\) is large. Consistent to Sec. 4.1, we adopt NAFNet (SOTA methods for SIDD challenge [11]) as our backbone at two scales (\\(1\\times\\), \\(\\frac{1}{16}\\times\\)). Both NAFNet-RCD and the corresponding baselines are trained on this subset with the same training settings as in [11]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.843, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Results and Analysis We conduct blind denoising experiments on SIDD with different RCD model scales to evaluate its adjustability to the real-world dataset. As shown in Tab. 4 (left), our RCD (AutoTune results) can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.554 + ], + "angle": 0, + "content": "achieve high-quality controllable real-world denoising in both model scales. However, we note that enabling controllable denoising with RCD may still result in a slight decrease in quantitative results (about 0.3dB), which may be a result of unbalanced data for each level and short noise level interval (\\(|l_{i+1} - l_i|\\), see more discussion in Sec. 4.4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.893, + 0.727 + ], + "angle": 0, + "content": "SIDD with synthetic noise. We extensively conduct synthetic denoising experiments on SIDD to further show the compatibility of RCD on SIDD datasets. Following Sec. 4.1, we add random Gaussian noise \\(\\sigma \\in [0,60]\\) to SIDD training data, and both methods are evaluated on \\(\\sigma = 50\\) SIDD test samples. As shown in Tab. 4 (right), RCD models slightly outperform their baselines, demonstrating RCD's compatibility for SIDD. Moreover, this result can also indicate that RCD's performance drop on SIDD real image may arise from the noise distribution and RCD configurations, rather than RCD's adaptive capacity to SIDD data. See Appendix for more results and visualizations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.734, + 0.663, + 0.751 + ], + "angle": 0, + "content": "4.3. Video Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.892, + 0.886 + ], + "angle": 0, + "content": "Experiment Setup Following common practice [32, 44, 46], we train our models on DAVIS training set and use DAVIS-test and Set-8 for benchmarking. Like in [46], we add Gaussian noise with random standard deviation between 5-50 on the DAVIS clean videos for training. The DAVIS set contains 30 color sequences of resolution \\(854 \\times 480\\), which will be randomly cropped into \\(128 \\times 128\\) patches during training. Other training settings and hyperparameters are kept the same as [46] for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Choice of Basic model. We choose FastDVD [46] as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14034" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.074, + 0.887, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.24, + 0.893, + 0.274 + ], + "angle": 0, + "content": "Figure 7. Illustration of RCD control logics. Users can retouch the denoising level by tuning the Intensity bar (\\(\\sigma = \\sqrt{\\sum_{i=1}^{L} c_i^2 l_i^2}\\)) and setup their perceptual preference at fixed level by tuning Component bar (changing \\(\\{c_i\\}\\) while keeping \\(\\sigma\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.468, + 0.359 + ], + "angle": 0, + "content": "our backbone model. Although recent methods [32,48] outperform FastDVD by 1-2 PSNR at most, they actually introduce huge models and extra heavy operations like patch clustering [48] and layer-wise frame-to-frame wrapping using optical flow [32] (\\(>100 \\times\\) slower than FastDVD)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.468, + 0.531 + ], + "angle": 0, + "content": "Results and Analysis. Like [44], we evaluate our video denoising models with the input length of one frame and five frames. We denote RCD models for video denoising as \"FastDVD-RC\" and compare their quantitative AutoTune denoising results to baseline FastDVD in Tab. 5. Consistent with preceding sections, AutoTune results of FastDVD-RCD can demonstrate comparable performance to the default FastDVD, which means our RCD can also achieve lossless real-time noise editing in video scenarios. Unlike previous heavy controllable denoising methods, our real-time RCD can even allow users to do online video denoising editing without any latency." + }, + { + "type": "table_caption", + "bbox": [ + 0.174, + 0.536, + 0.373, + 0.55 + ], + "angle": 0, + "content": "Table 5. Video denoising results." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.56, + 0.462, + 0.671 + ], + "angle": 0, + "content": "
Test setσ1 frame5 frames
FastDVDFastDVD-RCDFastDVDFastDVD-RCD
DAVIS2034.1734.2135.6935.65
3032.4532.6934.0634.04
4031.3931.6032.8032.78
5030.2630.5731.8331.85
Set 82031.9932.0133.4333.46
3030.6130.6531.6231.71
4029.6229.8330.3630.42
5028.6128.8529.4129.60
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.204, + 0.692 + ], + "angle": 0, + "content": "4.4. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Selection of Denoising Levels. Differing from conventional denoising methods, RCD requires a group of predefined noise levels \\(\\{l_i\\}_{i=1}^L\\). To evaluate how the selection of \\(\\{l_i\\}_{i=1}^L\\) affects RCD's performance, we conduct ablation studies on FastDVD-RCD by changing the number of noise maps \\((L)\\) (See Tab. 6.) All of the models are trained on noisy images with \\(\\sigma \\in (0,60]\\) and uniformly sampled noise levels that \\(\\{l_i = \\frac{60}{L} * i\\}_{i=1}^L\\). We observe that larger \\(L\\) means more fine-grained control on denoising, but it may incur a performance drop. In fact, when \\(n\\) is large we find that \\(\\mathcal{L}_{level}\\) will also keep large and be hard to optimize. Trading-off performance and control precision, we empirically choose \\(L = 12\\) and noise level interval \\(|l_{i+1} - l_i| = 5\\) as defaults." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.278, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Table 6. Ablations of FastDVD-RCD on different number of noise levels. Reported scores are PSNR of AutoTune outputs and GT." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.316, + 0.882, + 0.38 + ], + "angle": 0, + "content": "
Test SetσL = 1L = 2L = 12L = 30L = 60
Set82031.8731.4232.0131.3931.07
3030.5130.0930.6530.1229.75
4029.6029.3129.8329.3329.01
5028.6228.2928.8528.2228.05
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.596 + ], + "angle": 0, + "content": "Control Capacity. This section discusses the representation capacity of \\( c_{i} \\) as control parameters. Generally, \\( c_{i} \\) controls the denoising process on two aspects: intensity and components. Firstly, the noise levels of RCD outputs are identical and can be derived by \\( \\sigma = \\sqrt{\\sum_{i=1}^{L} c_{i}^{2} l_{i}^{2}} \\) (See Sec. 3.4), which allows us to control the denoising intensity by changing \\( \\{c_{i}\\} \\). Fig. 7 depicts visualizations of RCD-controlled denoising under different intensity settings. Besides, as discussed in Sec. 3.6, RCD supports further optimization of the denoising results at specific noise intensity by tuning \\( c_{i} \\) by involving different components of \\( \\tilde{\\mathcal{N}}_{i} \\). (Please be reminded that \\( \\tilde{\\mathcal{N}}_{i} \\) is trained by \\( \\mathcal{L}_{\\text{level}} \\), denoting learned optimal denoising results at every fixed level \\( l_{i} \\).)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.607, + 0.608, + 0.625 + ], + "angle": 0, + "content": "5. Summary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.79 + ], + "angle": 0, + "content": "We present RCD framework that enables real-time noise editing for controllable denoising. Unlike existing continual-level denoising methods, RCD doesn't require multiple training stages and auxiliary networks. With the proposed Noise Decorrelation module, RCD transforms the control of denoising into white-box operations, with no requirement to feed control parameters to networks at test time, which enables real-time editing even for heavy network models. Extensive experiments on widely-used real/synthetic image and video denoising datasets demonstrate the robustness and effectiveness of our RCD." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.803, + 0.681, + 0.82 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.828, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, and Shanghai Committee of Science and Technology (Grant No. 21DZ1100100)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14035" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.18 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. 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In traditional filter-based denoising methods, this can be easily achieved by adjusting the filtering strength. However, for NN (Neural Network)-based models, adjusting the final denoising strength requires performing network inference each time, making it almost impossible for real-time user interaction. In this paper, we introduce Real-time Controllable Denoising (RCD), the first deep image and video denoising pipeline that provides a fully controllable user interface to edit arbitrary denoising levels in real-time with only one-time network inference. Unlike existing controllable denoising methods that require multiple denoisers and training stages, RCD replaces the last output layer (which usually outputs a single noise map) of an existing CNN-based model with a lightweight module that outputs multiple noise maps. We propose a novel Noise Decorrelation process to enforce the orthogonality of the noise feature maps, allowing arbitrary noise level control through noise map interpolation. This process is network-free and does not require network inference. Our experiments show that RCD can enable real-time editable image and video denoising for various existing heavy-weight models without sacrificing their original performance. + +# 1. Introduction + +Image and video denoising are fundamental problems in computational photography and computer vision. With the development of deep neural networks [12, 26, 49, 59], model-based denoising methods have achieved tremendous success in generating clean images and videos with superior denoising scores [4,55,57]. However, it should be noted that the improvement in reconstruction accuracy (e.g., PSNR, SSIM) is not always accompanied by an improvement in visual quality, which is known as the Perception-Distortion trade-off [6]. In traditional denoising approaches, we can easily adjust the denoising level by tuning related control + +![](images/fdd77edab6538da3437cabca7f82d78c93d883d789e685523ff8fc81834b3ad2.jpg) +Figure 1. Real-time controllable denoising allows users further tuning the restored results to achieve Perception-Distortion trade-off. A-B: tuning with changing denoising intensity. C-E: tuning without changing denoising intensity. + +parameters and deriving our preferred visual results. However, for typical deep network methods, we can only restore the degraded image or video to a fixed output with a predetermined restoration level. + +In recent years, several modulation methods have been proposed to generate continuous restoration effects between two pre-defined denoising levels. These methods can be categorized into two kinds: interpolation-based methods [17,24,50,51], which use deep feature interpolation layers, and condition-network-based methods, which import an extra condition network for denoising control [9, 25, 39]. Essentially, both types of methods are designed based on the observation that the outputs of the network change continuously with the modulation of features/filters. This observation enables deep denoising control, but it also introduces several limitations. First, there is a lack of explainability, as the relationship between the control parameters (how to modulate features) and the control operation (how the network outputs are changed) is unclear [24]. This indicates that black-box operators (network layers) must be used to encode them. Second, the use of control parameters as network inputs requires entire network propagation each time control parameters change, resulting in a lack of efficiency. Lastly, current modulation methods often require an explicit degradation level during training, which is hard to obtain for real-world samples. As a result, current controllable denoising methods only focus on synthetic + +![](images/1d113a893b944b9e1cdb31efdda3e8da8e2523db04ba837d505e31a18be00de3.jpg) +Figure 2. Comparison of pipelines between conventional controllable denoising and our RCD. RCD achieves real-time noise control by manipulating editable noises directly. + +noise benchmarks. Furthermore, both interpolation-based and condition-network-based methods have their own drawbacks. Interpolation-based methods often require multiple training stages, including pretraining two basic models (start level and end level). On the other hand, condition-network-based methods are strenuous to jointly optimize the base network and the condition network. + +In this paper, we research on the problem: Can we achieve real-time controllable denoising that abandons the auxiliary network and requires no network forward propagation for changing restoration effects at test time? + +Towards this goal, we propose Real-time Controllable Denoising method (RCD), a lightweight pipeline for enabling rapid denoising control to achieve Perception-Distortion Balance (See Fig. 1). Our RCD can be plugged into any noise-generate-based restoration methods [11, 46, 54, 55] with just a few additional calculations. Specifically, we replace the last layer of an existing denoising network (which usually outputs a single noise map) with a lightweight module that generates multiple noise maps with different noise levels. We utilize a novel Noise Decorrelation process to enforce the orthogonality of the noise distribution of these noise maps during training. As a result, we can attain arbitrary denoising effects by simple linear interpolation of these noise maps. Since this process does not require network inference, it makes real-time user interaction possible even for heavy denoising networks. + +Fig. 2 illustrates the fundamental differences between our RCD approach and conventional controllable denoising methods. In contrast to traditional methods that rely on control networks, the RCD pipeline generates editable noises of varying intensities/levels, providing explicit control by external parameters and enabling network-free, real-time denoising editing. Real-time editing capabilities offered by RCD create new opportunities for numerous applications that were previously impossible using conventional techniques, such as online video denoising editing, even during playback (e.g., mobile phone camera video quality tuning for ISP tuning engineers), as well as deploying controllable denoising on edge devices and embedded systems. Since the editing stage of RCD only involves image interpolation, + +users can edit their desired results on low-performance devices without the need for GPUs/DSPs. + +Moreover, unlike previous methods that only support changing noise levels, RCD allows users to adjust denoising results at a specific noise level by providing a new interface to modify the noise generation strategy. RCD is also the first validated method for controllable denoising on real-world benchmarks. It is noteworthy that existing controllable methods typically require training data with fixed-level noise to establish their maximum and minimum noise levels, which makes them unsuitable for most real-world benchmarks comprising data with varying and unbalanced noise levels. + +Our main contributions can be summarized as follows: + +- We propose RCD, a controllable denoising pipeline that firstly supports real-time denoising control ( $>$ $2000 \times$ speedup compared to conventional controllable methods) and larger control capacity (more than just intensity) without multiple training stages [24] and auxiliary networks [50]. +- RCD is the first method supporting controllable denoising on real-world benchmarks. +- We propose a general Noise Decorrelation technique to estimate editable noises. +- We achieve comparable or better results on widely-used real/synthetic image-denoising and videodenoising datasets with minimal additional computational cost. + +# 2. Related Works + +# 2.1. Denoising + +Traditional image and video denoising methods are often based on prior assumptions such as sparse image prior [3, 15, 16, 20], non-local similarity [7, 13, 14, 18], and other similar techniques [22, 41, 52]. However, with the recent development of deep learning networks, many learning-based methods have been proposed and achieved state-of-the-art performance. Early works [8] utilized multi-layer perceptron (MLP) to achieve comparable results with BM3D. In recent years, there has been rapid progress on CNN-based denoising methods [4, 10, 21, 47, 55, 57] and Transformer-based methods [32, 42, 54, 59], which have started to dominate the image/video denoising task. However, the abovementioned works mainly focus on designing novel network architectures to improve the denoising performance and usually generate a single output. Their lack of ability to adjust the output denoising level based on user's feedback has greatly restricted their practical use in many real-world applications. Moreover, although techniques like pruning [33, 38, 60] and quantization [45, 61] can accelerate such neural network-based methods, they are typically heavy, which restricts their application to real-time denoising control. + +![](images/e041ba5d99f57b30628567c97b1aee7488b72648530b2b52ed937aff0f213a23.jpg) +Figure 3. Pipeline overview of proposed RCD framework. A: Backbone network for generating multi-level noise maps. B: Noise Decorrelation module for editable noises. C: AutoTune module for providing reference control parameters for users. + +# 2.2. Controllable denoising + +Most conventional deep-learning methods for image/video denoising can only generate a fixed result with a specific restoration level. Recently, some controllable image/video denoising methods allow users to adjust the restoration effect without retraining the network. DNI [51] and AdaFM [24] used the observation that the learned filters of the models trained with different restoration levels are similar in visual patterns. DNI interpolated all the corresponding parameters between two related networks to derive smooth and continuous restoration effects, while AdaFM adopted feature modulation filters after each convolution layer. CFSNet [50] proposed an adaptive learning strategy of using interpolation coefficients to couple the intermediate features between the main branch and the tuning branch. Different from these interpolation-base methods, some other methods [9, 25, 39] regarded modulation as a conditional image restoration problem and adopted a joint training strategy. CUGAN [9] proposed a GAN-based image restoration framework to avoid the over-smooth problem, a common issue in PSNR-oriented methods. However, all of the above controllable methods can only be trained with synthetic degradations because they require explicit degradation levels during training. When applied on real-world data, as shown in [23], methods that trained for blind Additive White Gaussian Noise (AWGN) [35,55] may be overfitted and often suffer from dramatic performance drop. Besides the real-world image issue, all these controllable methods utilize an auxiliary conditional network and require one network inference for each different target + +restoration level at test time, which makes them almost impossible for real-time application. + +# 3. Methods + +# 3.1. Conventional Deep Denoising + +Deep denoising methods trump traditional filter-based techniques by leveraging the neural networks' robust representation learning capability. Most current denoising methods [11,32,46] reason about the relationship between clean and noisy images by regressing noise maps with a neural generator. Specifically, given a noisy image $\mathbf{I}_{\mathbf{n}}$ and model $\mathcal{M}:\mathbb{R}^{H\times W\times C}\to \mathbb{R}^{H\times W\times C}$ , we can derive the predicted clean image $\mathbf{I}_{\mathbf{c}}$ by: $\mathbf{I}_{\mathbf{c}} = \mathbf{I}_{\mathbf{n}} + \mathcal{M}(\mathbf{I}_{\mathbf{n}})$ , where model $\mathcal{M}$ is updated by minimizing the distance between the denoising result $\mathbf{I}_{\mathbf{c}}$ and the ground truth $\mathbf{I}_{\mathrm{gt}}$ . As we can see, this kind of approach generates a single fixed output result in a black-box manner, making it almost impossible to adjust the denoise operation explicitly. + +# 3.2. Pipeline Overview + +In this section, we present Real-time Controllable Denoising (RCD), a novel deep learning-based pipeline for real-time controllable denoising. As illustrated in Fig. 3, RCD essentially consists of three parts: (1) A backbone network, i.e., $\mathcal{M}_b:\mathbb{R}^{H\times W\times C}\to \mathbb{R}^{H\times W\times LC}$ , generates multiple fixed-level noise maps, where $L$ is the number of pre-defined noise levels (see (A) in Fig. 3). (2) A Noise Decorrelation (ND) block that enforces the editability of the generated noise maps (see (B) in Fig. 3). (3) An AutoTune + +module that gives a default set of control parameters to generate the best denoising result. + +Specifically, the backbone network will generate multiple fixed-level noise maps, i.e., $\{\mathcal{N}_i\}_{i=1}^L$ , for each noisy image input. The noise maps are then fed into the proposed Noise Decorrelation (ND) block, which makes noise maps orthogonal to each other. In this way, the decorrelated noise maps $\{\tilde{\mathcal{N}}_i\}_{i=1}^L$ will be zero-correlated and thus become linearly interpolable. At last, the AutoTune module will give a set of suggested control parameters $\{\bar{c}_i\}_{i=1}^L$ to generate the final denoising result as follows: + +$$ +\mathbf {I} _ {\mathbf {c}} = \mathbf {I} _ {\mathbf {n}} + \sum_ {i = 1} ^ {L} \bar {c} _ {i} \tilde {\mathcal {N}} _ {i}, \tag {1} +$$ + +where $\sum_{i=1}^{L} \bar{c}_i = 1$ . Moreover, given the zero-correlated noise maps, users can also generate arbitrary strength denoising results by replacing $\{\bar{c}_i\}_{i=1}^L$ with their own customized control parameters $\{c_i\}_{i=1}^L$ . + +# 3.3. Multi-level Noise Generation + +Given a noisy input image $\mathbf{I}_{\mathbf{n}}$ , the backbone network aims to generate multiple noise maps $\{\mathcal{N}_i\}_{i=1}^L$ , corresponding to a set of pre-defined noise levels $\{l_i\}_{i=1}^L$ , e.g. noise levels $\{5, 10, 15, \dots, 60\}$ . Hence, we have + +$$ +\sigma \left(\mathcal {N} _ {i}\right) = l _ {i}, \forall i = 1, \dots , L, \tag {2} +$$ + +where $\sigma$ is the noise level operation that calculates the standard deviation of pixels in each noise map. To obtain multilevel noise maps, we replace the conventional last output layer of the denoising network with a convolutional layer with an output channel size of $L\cdot C$ . Moreover, the level of the noise map is explicitly generated with the normalization operation, as given by + +$$ +\mathcal {N} _ {i} = l _ {i} \frac {\mathcal {M} _ {b} (\mathbf {I} _ {\mathbf {n}}) ^ {(i)}}{\sigma (\mathcal {M} _ {b} (\mathbf {I} _ {\mathbf {n}}) ^ {(i)})}, \forall i = 1, \dots , L. \tag {3} +$$ + +Here $\mathcal{M}_b(\mathbf{I_n})\in \mathbb{R}^{H\times W\times LC}$ is network output, and $\mathcal{M}_b(\mathbf{I_n})^{(i)}\in \mathbb{R}^{H\times W\times C}$ is the i-th component separated from the channel dimension. The derived $\mathcal{N}_i$ can be considered as the noise map estimated at the given noise level $l_{i}$ . + +Different from prior controllable denoising methods with implicit interpolation in the network, we propose to explicitly interpolate the noise maps in Eqn. 3. Thanks to the separation of noise interpolation and network inference, our RCD can achieve real-time user interaction. + +However, the multi-level noise maps $\mathcal{N}_i$ directly obtained by convolutional layers are usually highly correlated, which leads to the problem of noise level collapse. In other words, the noise map representations in different levels are redundant, implying that the number of noise maps at different noise strengths that participate in the linear interpolation in Eqn. 1 is implicitly reduced. Without any constraint, + +![](images/1b4247ed5206507bda03ecd23a3b5bec7bde408717d346b648ed047996d6b5f5.jpg) +Figure 4. Demonstration of Noise Decorrelation's influence on noise editing. $|\Sigma|_F$ denotes norms of the covariance matrix for corresponding learned noises and $\sigma$ is noise intensity. + +our experiments show that the single noise map at a certain noise level would dominate in the linear interpolation for a variety of input noisy images. To address this issue, we further introduce the Noise Decorrelation block to make representations of these noise maps much more informative in the following section. + +# 3.4. Noise Decorrelation + +The Noise Decorrelation (ND) block is designed to regularize the backbone network to generate editable noise maps at varying levels. In particular, this block is a parameter-free computational unit that enforces $\mathcal{N}_i$ to be approximately zero-correlated with each other: $\mathbf{cov}(\mathcal{N}_i,\mathcal{N}_j)\approx 0,\forall i,j\in$ $\{1,2,\dots,L\}$ , where $\mathbf{cov}(\cdot ,\cdot)$ is covariance operator. Inspired by the success of using the decorrelation technique in network optimization and normalization, we adopt the whitening-based methods [29, 30] for noise decorrelation here. The noise maps are decorrelated using the inverse square root of their covariance matrix. + +Specifically, for each predicted fixed-level noise map $\mathcal{N}_i$ , it will firstly be reshaped to $\mathcal{N}_i \in \mathbb{R}^{1 \times M}$ , where $M = HWC$ . By stacking the reshaped $\mathcal{N}_i$ over the first dimension, we have $\mathbf{N} \in \mathbb{R}^{L \times M}$ . We then calculate the noise covariance matrix $\sigma$ by: $\Sigma = \frac{1}{M - 1} (\mathbf{N} - \bar{\mathbf{N}})(\mathbf{N} - \bar{\mathbf{N}})^T$ where $\bar{\mathbf{N}}$ is mean of $\mathbf{N}$ over channel $M$ . + +The Noise Decorrelation block needs to compute inverse square root $\Sigma^{-\frac{1}{2}} \in \mathbb{R}^{L \times L}$ , which can be done by eigen decomposition or SVD. Since this kind of operation involves heavy computation [29], we instead adopt the more efficient Newton's Iteration to estimate $\Sigma^{-\frac{1}{2}}$ as in [5, 27]. Giving a covariance matrix $\Sigma$ , Newton's Iteration calculates $\Sigma^{-\frac{1}{2}}$ by following the iterations below: + +$$ +\begin{array}{l} \Sigma_ {0} = I, \\ \Sigma_ {k} = \frac {1}{2} (3 \Sigma_ {k - 1} - (\Sigma_ {k - 1}) ^ {3} \Sigma), k = 1, 2,.., T, \end{array} \tag {4} +$$ + +where $k$ is the iteration index and $T$ is the iteration number (in our experiments $T = 3$ or 4). $\Sigma_{k}$ is guaranteed to converge to $\Sigma^{-\frac{1}{2}}$ , if $\| I - \Sigma \|_2 < 1$ [5]. This condition can be achieved by normalizing $\Sigma$ to $\frac{\Sigma}{tr(\Sigma)}$ , where $tr(.)$ is trace operator. + +The derived $\Sigma^{-\frac{1}{2}}$ can be regarded as a whitening matrix [43], which decorrelates the noise maps $\mathbf{N}$ in + +a differentiable manner. The decorrelated noise maps $\mathbf{N} \in \mathbb{R}^{\tilde{H} \times W \times LC}$ can be obtained by calculating: $\tilde{\mathbf{N}} = \Sigma^{-\frac{1}{2}} \mathbf{N}$ . We can then have our editable fixed-level noises $\tilde{\mathcal{N}}_i \in \mathbb{R}^{H \times W \times C}$ by reshaping $\tilde{\mathbf{N}}$ and splitting it into $L$ noise maps. After Noise Decorrelation, we apply the same normalization as Eqn. 3 to guarantee the noise strength of the decorrelated noises. + +The zero-correlated noise maps $\tilde{\mathcal{N}}_i$ present several excellent properties for controllable denoising. Firstly, the linearity of the noise level's square towards $\tilde{\mathcal{N}}_i$ is guaranteed. In other words, given an arbitrary set of control parameters $\{c_i\}_{i = 1}^L$ , we have + +$$ +\mathbf {V a r} \left(\sum_ {i = 1} ^ {L} c _ {i} \tilde {\mathcal {N}} _ {i}\right) = \sum_ {i = 1} ^ {L} c _ {i} ^ {2} \mathbf {V a r} \left(\tilde {\mathcal {N}} _ {i}\right), \tag {5} +$$ + +where $\mathbf{Var}(\cdot)$ denotes variance operator. Apparently, Eqn. 5 holds when elements of $\{\tilde{\mathcal{N}}_i\}_{i = 1,2,\dots,m}$ are mutually zero-correlated. Eqn. 5 reveals the explicit relationship between the control parameters and the target noise level, which allows us to directly edit noises by interpolating $\mathcal{N}_i$ using $c_{i}$ . Secondly, the Noise Decorrelation block can be regarded as a regularization tool that forces models to learn different noise formats for each level, which will increase the representation capacity of the denoising network [30]. + +Fig. 4 demonstrates how the Noise Decorrelation block works. With ND block, the covariance of learned noises is reduced to almost zero (without it, $|\Sigma|_F$ can be 751 and unignorable), allowing us to derive determined interpolated results with target noise intensity. In contrast, without the Noise Decorrelation blocks, the output noise level can not be guaranteed. + +# 3.5. AutoTune Module + +Given the decorrelated noise maps from the Noise Decorrelation block, the AutoTune module will predict a set of model-suggested control parameters, i.e., $\{\bar{c}_i\}_{i=1}^L$ , to generate the default denoising result. Users can then use this set of parameters as a starting point to fine-tune their final desired denoising strength. Our AutoTune module is extremely lightweight, and is formulated as a single-layer module with temperature softmax activation. Specifically, $\{\bar{c}_i\}_{i=1}^L$ can be obtained by: $\bar{c}_i = \frac{e^{\frac{\mathcal{A}(f)_i}{\tau}}}{\sum_{j=1}^n e^{\frac{\mathcal{A}(f)_j}{\tau}}}$ , where $\mathcal{A}$ is the NN layer, $f$ is the input feature maps, and $\tau$ is temperature. In our experiments, $\tau$ is set to be 0.05 for best performance. Following the design ethos of efficiency and least coupling to the backbone architecture, we directly choose the unnormalized model outputs $\mathcal{M}(\mathbf{I_n})$ as $f$ (see (C) in Fig. 3). + +# 3.6. New Cardinality for Denoising Control. + +Unlike existing methods that only modulate noise intensity, our RCD control scheme allows users to further optimize the denoising result to a given noise intensity + +![](images/db4f0e23544b9a9e4d9ee1d2d5e29b7736aca6ef68e7b0ad60743bde3b3da52b.jpg) +Figure 5. Example of RCD denoising results by AutoTune and HumanTune on Set8. AutoTune module provides reference control parameters, i.e., $\{\bar{c}_i\}_{i=1}^L$ , to generate the denoising result, and it can be further improved by fine-grained artificial tuning (HumanTune), i.e., $\{c_i\}$ , without changing the noise intensity (both $\sigma = 40$ ). + +by tuning $\{c_i\}$ , as long as the weighted mean of $l_{i}$ towards $c_{i}$ remains the same. Eqn. 5 shows that when $\sum_{i = 1}^{L}c_{i}^{2}\mathbf{Var}(\tilde{\mathcal{N}}_{i}) = \sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}$ is fixed, the variance of the output noise $\mathbf{Var}(\sum_{i = 1}^{L}c_{i}\tilde{\mathcal{N}}_{i})$ would be also fixed. By exploring $c_{i}$ under the condition of fixed $\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}$ , we can further optimize the denoising results at a specific noise level by involving different components $(\mathcal{N}_i)$ in the noise interpolation. As shown in Fig. 5, our AutoTune module can generate high-quality results using just the reference control parameters $\{\bar{c}_i\}$ . Users can further improve the result by artificially tuning $\{c_i\}$ around $\{\bar{c}_i\}$ , even at the same noise level. + +# 3.7. Optimization Targets + +To guarantee the visual quality of arbitrarily edited noise $\sum_{i=1}^{L} c_i \tilde{\mathcal{N}}_i$ for any given set of control parameters $\{c_i\}_{i=1}^L$ , we adopt a multi-level concurrent training strategy by minimizing the difference between each level's noise output and the ground truth noise, i.e., $\mathcal{L}_{level}$ , which is derived by: + +$$ +\mathcal {L} _ {\text {l e v e l}} = \frac {1}{L} \sum_ {i = 1} ^ {L} \mathcal {L} \left(\mathbf {I} _ {g t}, \mathbf {I} _ {\mathbf {n}} + \tilde {\mathcal {N}} _ {i}\right) \tag {6} +$$ + +where $\mathbf{I}_{gt}$ , $\mathbf{I}_{\mathbf{n}}$ are ground truth clean image and the input noisy image. $\mathcal{L}(.)$ can be any loss functions (e.g., L2 loss or PSNR loss). + +Spectaculously, $\mathbf{I}_{\mathbf{n}} + \tilde{\mathcal{N}}_i$ can be regarded as corner cases of RCD when we use one-hot control parameters as input. Joint optimization of all the noise levels ensures that each element of $\mathcal{N}_i$ can be trained as optimal noise estimation under the condition of fixed noise level $l_{i}$ . + +Together with the AutoTune module optimization, our final cost function can be written as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda \mathcal {L} _ {\text {l e v e l}} + \mathcal {L} \left(\mathbf {I} _ {g t}, \mathbf {I} _ {\mathbf {n}} + \sum_ {i = 1} ^ {L} \bar {c} _ {i} \tilde {\mathcal {N}} _ {i}\right), \tag {7} +$$ + +Table 1. Gaussian single image denoising results (PSNR). RCD is evaluated with AutoTune results. “-”: not reported + +
MethodControllableCBSD68Kodak24McMasterUrban100
σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50
IRCNN [56]X33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [57]X33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [55]X33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [40]X33.9131.2828.0534.6332.1629.0534.6732.4029.28-
CResMD [25]✓33.97-28.06---
AdaFM-Net [24]✓34.1031.4328.13---
NAFNet [11]X34.1131.4928.2735.1432.7029.6835.0732.8229.7934.4132.0929.00
NAFNet-RCD (ours)✓34.1331.4928.2635.1532.7229.6935.1132.8429.8134.4532.1229.02
+ +Table 2. Running time comparison for RCD and other controllable methods during test time. Full Pipeline compares full pipeline latency for the model to infer 1000 images, and Edit-only compares latency for editing one image with 1000 different control parameters. + +
MethodMulti-stage trainingFull PipelineEdit-only
AdaFM-Netrequired81.03s81.03s
CResMDNetnot required128.08128.08s
NAFNet-RCDnot required64.84s0.04s
+ +where $\lambda$ is the loss weight ( $\lambda = 0.1$ in our experiments), and $\mathcal{L}(\mathbf{I}_{gt},\mathbf{I_n} + \sum_{i = 1}^{n}\bar{c}_i\tilde{\mathcal{N}}_i)$ optimizes the denoising result derived by the model-suggested control parameters. + +# 4. Experiments + +This section is organized as follows: First, we demonstrate the effectiveness of our plug-in RCD with SOTA image denoising methods [11] in different scales on synthetic noise datasets. Next, to evaluate the ability of blind denoising on real-world data, we conduct experiments on popular real-world denoising dataset SIDD [1]. Then, we apply our real-time controllable RCD pipeline on video denoising applications. At last, we empirically discuss some design details described in the previous sections. + +# 4.1. Gaussian Single Image Denoising + +Experimental Setup. To fully demonstrate the effectiveness of the proposed RCD, we choose the most recent SOTA method NAFNet [11] as our backbone. Following [54], we first conduct denoising experiments on several widely-used synthetic color image benchmarks (DIV2K [2], BSD400 [36], Flickr2K [53] and WaterlooED [34]) with additive white Gaussian noise ( $\sigma \in [0, 60]$ ). The training patch size is $128 \times 128$ and the batch size is 64. We train our model with Adam [31] optimizer and learning rate $1e - 3$ for total 60K iterations. Consistent to [11], PSNR loss is adapted as the loss function. Both the baseline model (NAFNet) and its RCD variants (NAFNet-RCD) are trained from scratch. For settings of RCD, we initialize $L = 12$ and $\{l_i\} = [5, 10, \dots, 60]$ for synthetic denoising training. + +Complexity analysis. Extensive adjustments of controllable parameters are often required to obtain one satisfying result for users. Therefore, editing time is vital + +for controllable methods. This section compares the inference and editing latency of our RCD and conventional controllable pipelines on GTX 1080Ti. As shown in Tab. 2, the proposed RCD not only outperforms other conventional controllable pipelines on inference time, but more importantly, can overwhelm those traditional controllable designs on editing time, which can be more than 2000 times faster (as editing process of RCD is network-free, without reliance on sub-networks). This comparison confirms that our RCD is more than enough for real-time image editing. + +Results Analysis. We evaluate our proposed method on widely used synthetic noise datasets CBSD68 [37], Kodak24 [19], McMaster [58] and Urban100 [28] with noise levels $\sigma(15)$ , $\sigma(15)$ and $\sigma(50)$ . RCD is evaluated with denoising results using AutoTune outputs $\{\bar{c}_i\}$ . As shown in Tab. 1, NFANet-RCD achieves comparable performance to the baseline NFANet consistently on multiple datasets, indicating that our plug-in RCD module enables real-time controllable denoising for NAFNet without sacrificing its original denoising performance. Please note that NAFNet-RCD can yield comparable results to the backbone just by using the AutoTune outputs, and the performance can be further improved by manually tuning the control parameters (See Sec. 3.6.) We further show the qualitative performance of NAFNet-RCD in Fig. 6. NAFNet-RCD can recover more details of some degraded images, which may be benefited from RCD's richer representation capacity by integrating multiple noise maps. + +Slimmer Model Variants. Towards the goal of evaluating the compatibility and robustness of RCD, we conduct ablations by applying RCD to different-sized backbones. Specifically, we shrink the width and block numbers of NAFNet, denoting derived models as NAFNet-small $(\frac{1}{4} \times)$ and NAFNet-tiny $(\frac{1}{16} \times)$ . Tab. 3 reports the results of RCD with those scaled backbones. It can be observed that the RCD-variants can achieve comparable and even slightly better denoising results compared to their baselines, which further demonstrates RCD's robustness and effectiveness for different-sized backbones. + +# 4.2. Real Single Image Denoising + +Experimental Setup (Real Image) Unlike existing controllable denoising methods [24,50] which focus on synthetic benchmarks, we are the first solution that attempts to extend controllable denoising to real-world SIDD datasets. + +![](images/fc24aa3dd446f86db11086e608e3b5005225d97c4d1c1b9e5794dd0cb9cde020.jpg) +Figure 6. Visual comparison of RCD and their baseline results on $\sigma = 50$ denoising. GT: Ground truth. Base: Baseline model without RCD. AutoTune: RCD results by applying control parameters from AutoTune module. + +![](images/6f05db71269261da1b66f565f0b736153580927bc2b204ac244eec173cac2bfe.jpg) + +Table 3. Ablation of RCD on various backbone sizes. + +
MethodCBSD68 +σ = 15 σ = 25 σ = 50Kodak24 +σ = 15 σ = 25 σ = 50McMaster +σ = 15 σ = 25 σ = 50Urban100 +σ = 15 σ = 25 σ = 50
NAFNet-tiny33.5834.3333.8532.96
NAFNet-RCD-tiny33.7131.0631.8833.22
NAFNet-small33.8431.1832.1833.61
NAFNet-RCD-small33.9631.3132.3233.92
NAFNet34.1131.4932.7034.41
NAFNet-RCD34.1331.4932.7234.45
+ +Table 4. Image denoising results on SIDD. Real noise: results on real-world SIDD test sets. Synthetic noise: results on SIDD test set with additive Gaussian noise ( $\sigma = 25$ ). + +
MethodReal noiseSynthetic noise
PSNRSSIMPSNRSSIM
NAFNet-tiny42.190.979638.460.9551
NAFNet-RCD-tiny41.860.978138.600.9558
NAFNet43.220.981838.850.9481
NAFNet-RCD42.910.980639.140.9580
+ +SIDD consists of real noisy images captured by smartphones with $\sigma \in [0,50]$ . Instead of using full SIDD data, we choose subsets of SIDD with $\sigma \in [0,12]$ (around $70\%$ of the entire dataset) to train our RCD model, which is initialized with $L = 4$ and $\{l_i\} = [3,6,9,12]$ . The main reason is the lacking of high $\sigma$ data at given levels in SIDD because of SIDD's highly long-tailed noise level distribution. Specifically, most noisy images in SIDD gather in $\sigma < 12$ and the samples distribute sparsely when $\sigma$ is large. Consistent to Sec. 4.1, we adopt NAFNet (SOTA methods for SIDD challenge [11]) as our backbone at two scales ( $1\times$ , $\frac{1}{16}\times$ ). Both NAFNet-RCD and the corresponding baselines are trained on this subset with the same training settings as in [11]. + +Results and Analysis We conduct blind denoising experiments on SIDD with different RCD model scales to evaluate its adjustability to the real-world dataset. As shown in Tab. 4 (left), our RCD (AutoTune results) can + +achieve high-quality controllable real-world denoising in both model scales. However, we note that enabling controllable denoising with RCD may still result in a slight decrease in quantitative results (about 0.3dB), which may be a result of unbalanced data for each level and short noise level interval ( $|l_{i+1} - l_i|$ , see more discussion in Sec. 4.4). + +SIDD with synthetic noise. We extensively conduct synthetic denoising experiments on SIDD to further show the compatibility of RCD on SIDD datasets. Following Sec. 4.1, we add random Gaussian noise $\sigma \in [0,60]$ to SIDD training data, and both methods are evaluated on $\sigma = 50$ SIDD test samples. As shown in Tab. 4 (right), RCD models slightly outperform their baselines, demonstrating RCD's compatibility for SIDD. Moreover, this result can also indicate that RCD's performance drop on SIDD real image may arise from the noise distribution and RCD configurations, rather than RCD's adaptive capacity to SIDD data. See Appendix for more results and visualizations. + +# 4.3. Video Denoising + +Experiment Setup Following common practice [32, 44, 46], we train our models on DAVIS training set and use DAVIS-test and Set-8 for benchmarking. Like in [46], we add Gaussian noise with random standard deviation between 5-50 on the DAVIS clean videos for training. The DAVIS set contains 30 color sequences of resolution $854 \times 480$ , which will be randomly cropped into $128 \times 128$ patches during training. Other training settings and hyperparameters are kept the same as [46] for a fair comparison. + +Choice of Basic model. We choose FastDVD [46] as + +![](images/05c5197532a41243cad10d54d7b703c53aa41d4e7c6e7895ba48bb2a2d8c0480.jpg) +Figure 7. Illustration of RCD control logics. Users can retouch the denoising level by tuning the Intensity bar ( $\sigma = \sqrt{\sum_{i=1}^{L} c_i^2 l_i^2}$ ) and setup their perceptual preference at fixed level by tuning Component bar (changing $\{c_i\}$ while keeping $\sigma$ ). + +our backbone model. Although recent methods [32,48] outperform FastDVD by 1-2 PSNR at most, they actually introduce huge models and extra heavy operations like patch clustering [48] and layer-wise frame-to-frame wrapping using optical flow [32] ( $>100 \times$ slower than FastDVD). + +Results and Analysis. Like [44], we evaluate our video denoising models with the input length of one frame and five frames. We denote RCD models for video denoising as "FastDVD-RC" and compare their quantitative AutoTune denoising results to baseline FastDVD in Tab. 5. Consistent with preceding sections, AutoTune results of FastDVD-RCD can demonstrate comparable performance to the default FastDVD, which means our RCD can also achieve lossless real-time noise editing in video scenarios. Unlike previous heavy controllable denoising methods, our real-time RCD can even allow users to do online video denoising editing without any latency. + +Table 5. Video denoising results. + +
Test setσ1 frame5 frames
FastDVDFastDVD-RCDFastDVDFastDVD-RCD
DAVIS2034.1734.2135.6935.65
3032.4532.6934.0634.04
4031.3931.6032.8032.78
5030.2630.5731.8331.85
Set 82031.9932.0133.4333.46
3030.6130.6531.6231.71
4029.6229.8330.3630.42
5028.6128.8529.4129.60
+ +# 4.4. Discussions + +Selection of Denoising Levels. Differing from conventional denoising methods, RCD requires a group of predefined noise levels $\{l_i\}_{i=1}^L$ . To evaluate how the selection of $\{l_i\}_{i=1}^L$ affects RCD's performance, we conduct ablation studies on FastDVD-RCD by changing the number of noise maps $(L)$ (See Tab. 6.) All of the models are trained on noisy images with $\sigma \in (0,60]$ and uniformly sampled noise levels that $\{l_i = \frac{60}{L} * i\}_{i=1}^L$ . We observe that larger $L$ means more fine-grained control on denoising, but it may incur a performance drop. In fact, when $n$ is large we find that $\mathcal{L}_{level}$ will also keep large and be hard to optimize. Trading-off performance and control precision, we empirically choose $L = 12$ and noise level interval $|l_{i+1} - l_i| = 5$ as defaults. + +Table 6. Ablations of FastDVD-RCD on different number of noise levels. Reported scores are PSNR of AutoTune outputs and GT. + +
Test SetσL = 1L = 2L = 12L = 30L = 60
Set82031.8731.4232.0131.3931.07
3030.5130.0930.6530.1229.75
4029.6029.3129.8329.3329.01
5028.6228.2928.8528.2228.05
+ +Control Capacity. This section discusses the representation capacity of $c_{i}$ as control parameters. Generally, $c_{i}$ controls the denoising process on two aspects: intensity and components. Firstly, the noise levels of RCD outputs are identical and can be derived by $\sigma = \sqrt{\sum_{i=1}^{L} c_{i}^{2} l_{i}^{2}}$ (See Sec. 3.4), which allows us to control the denoising intensity by changing $\{c_{i}\}$ . Fig. 7 depicts visualizations of RCD-controlled denoising under different intensity settings. Besides, as discussed in Sec. 3.6, RCD supports further optimization of the denoising results at specific noise intensity by tuning $c_{i}$ by involving different components of $\tilde{\mathcal{N}}_{i}$ . (Please be reminded that $\tilde{\mathcal{N}}_{i}$ is trained by $\mathcal{L}_{\text{level}}$ , denoting learned optimal denoising results at every fixed level $l_{i}$ .) + +# 5. Summary + +We present RCD framework that enables real-time noise editing for controllable denoising. Unlike existing continual-level denoising methods, RCD doesn't require multiple training stages and auxiliary networks. With the proposed Noise Decorrelation module, RCD transforms the control of denoising into white-box operations, with no requirement to feed control parameters to networks at test time, which enables real-time editing even for heavy network models. Extensive experiments on widely-used real/synthetic image and video denoising datasets demonstrate the robustness and effectiveness of our RCD. + +# 6. Acknowledgement + +This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, and Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. 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In traditional filter-based denoising methods, this can be easily achieved by adjusting the filtering strength. However, for NN (Neural Network)-based models, adjusting the final denoising strength requires performing network inference each time, making it almost impossible for real-time user interaction. In this paper, we introduce Real-time Controllable Denoising (RCD), the first deep image and video denoising pipeline that provides a fully controllable user interface to edit arbitrary denoising levels in real-time with only one-time network inference. Unlike existing controllable denoising methods that require multiple denoisers and training stages, RCD replaces the last output layer (which usually outputs a single noise map) of an existing CNN-based model with a lightweight module that outputs multiple noise maps. We propose a novel Noise Decorrelation process to enforce the orthogonality of the noise feature maps, allowing arbitrary noise level control through noise map interpolation. This process is network-free and does not require network inference. Our experiments show that RCD can enable real-time editable image and video denoising for various existing heavy-weight models without sacrificing their original performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 546, + 128, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 128, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 128, + 558 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 567, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 693 + ], + "type": "text", + "content": "Image and video denoising are fundamental problems in computational photography and computer vision. With the development of deep neural networks [12, 26, 49, 59], model-based denoising methods have achieved tremendous success in generating clean images and videos with superior denoising scores [4,55,57]. However, it should be noted that the improvement in reconstruction accuracy (e.g., PSNR, SSIM) is not always accompanied by an improvement in visual quality, which is known as the Perception-Distortion trade-off [6]. In traditional denoising approaches, we can easily adjust the denoising level by tuning related control" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 224, + 547, + 342 + ], + "blocks": [ + { + "bbox": [ + 310, + 224, + 547, + 342 + ], + "lines": [ + { + "bbox": [ + 310, + 224, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 310, + 224, + 547, + 342 + ], + "type": "image", + "image_path": "fdd77edab6538da3437cabca7f82d78c93d883d789e685523ff8fc81834b3ad2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 354, + 547, + 399 + ], + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 399 + ], + "type": "text", + "content": "Figure 1. Real-time controllable denoising allows users further tuning the restored results to achieve Perception-Distortion trade-off. A-B: tuning with changing denoising intensity. C-E: tuning without changing denoising intensity." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 405, + 546, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 546, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 546, + 450 + ], + "type": "text", + "content": "parameters and deriving our preferred visual results. However, for typical deep network methods, we can only restore the degraded image or video to a fixed output with a predetermined restoration level." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 452, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 547, + 714 + ], + "type": "text", + "content": "In recent years, several modulation methods have been proposed to generate continuous restoration effects between two pre-defined denoising levels. These methods can be categorized into two kinds: interpolation-based methods [17,24,50,51], which use deep feature interpolation layers, and condition-network-based methods, which import an extra condition network for denoising control [9, 25, 39]. Essentially, both types of methods are designed based on the observation that the outputs of the network change continuously with the modulation of features/filters. This observation enables deep denoising control, but it also introduces several limitations. First, there is a lack of explainability, as the relationship between the control parameters (how to modulate features) and the control operation (how the network outputs are changed) is unclear [24]. This indicates that black-box operators (network layers) must be used to encode them. Second, the use of control parameters as network inputs requires entire network propagation each time control parameters change, resulting in a lack of efficiency. Lastly, current modulation methods often require an explicit degradation level during training, which is hard to obtain for real-world samples. As a result, current controllable denoising methods only focus on synthetic" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 126, + 712 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14028" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 286, + 188 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 286, + 188 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 286, + 188 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 286, + 188 + ], + "type": "image", + "image_path": "1d113a893b944b9e1cdb31efdda3e8da8e2523db04ba837d505e31a18be00de3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 197, + 288, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 197, + 288, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 288, + 231 + ], + "type": "text", + "content": "Figure 2. Comparison of pipelines between conventional controllable denoising and our RCD. RCD achieves real-time noise control by manipulating editable noises directly." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 323 + ], + "type": "text", + "content": "noise benchmarks. Furthermore, both interpolation-based and condition-network-based methods have their own drawbacks. Interpolation-based methods often require multiple training stages, including pretraining two basic models (start level and end level). On the other hand, condition-network-based methods are strenuous to jointly optimize the base network and the condition network." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 324, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 370 + ], + "type": "text", + "content": "In this paper, we research on the problem: Can we achieve real-time controllable denoising that abandons the auxiliary network and requires no network forward propagation for changing restoration effects at test time?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 370, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 553 + ], + "type": "text", + "content": "Towards this goal, we propose Real-time Controllable Denoising method (RCD), a lightweight pipeline for enabling rapid denoising control to achieve Perception-Distortion Balance (See Fig. 1). Our RCD can be plugged into any noise-generate-based restoration methods [11, 46, 54, 55] with just a few additional calculations. Specifically, we replace the last layer of an existing denoising network (which usually outputs a single noise map) with a lightweight module that generates multiple noise maps with different noise levels. We utilize a novel Noise Decorrelation process to enforce the orthogonality of the noise distribution of these noise maps during training. As a result, we can attain arbitrary denoising effects by simple linear interpolation of these noise maps. Since this process does not require network inference, it makes real-time user interaction possible even for heavy denoising networks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 554, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 288, + 714 + ], + "type": "text", + "content": "Fig. 2 illustrates the fundamental differences between our RCD approach and conventional controllable denoising methods. In contrast to traditional methods that rely on control networks, the RCD pipeline generates editable noises of varying intensities/levels, providing explicit control by external parameters and enabling network-free, real-time denoising editing. Real-time editing capabilities offered by RCD create new opportunities for numerous applications that were previously impossible using conventional techniques, such as online video denoising editing, even during playback (e.g., mobile phone camera video quality tuning for ISP tuning engineers), as well as deploying controllable denoising on edge devices and embedded systems. Since the editing stage of RCD only involves image interpolation," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "users can edit their desired results on low-performance devices without the need for GPUs/DSPs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 95, + 547, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 95, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 95, + 547, + 220 + ], + "type": "text", + "content": "Moreover, unlike previous methods that only support changing noise levels, RCD allows users to adjust denoising results at a specific noise level by providing a new interface to modify the noise generation strategy. RCD is also the first validated method for controllable denoising on real-world benchmarks. It is noteworthy that existing controllable methods typically require training data with fixed-level noise to establish their maximum and minimum noise levels, which makes them unsuitable for most real-world benchmarks comprising data with varying and unbalanced noise levels." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 221, + 538, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 221, + 538, + 233 + ], + "spans": [ + { + "bbox": [ + 317, + 221, + 538, + 233 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 243, + 545, + 411 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "type": "text", + "content": "- We propose RCD, a controllable denoising pipeline that firstly supports real-time denoising control (" + }, + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "type": "inline_equation", + "content": ">" + }, + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "type": "inline_equation", + "content": "2000 \\times" + }, + { + "bbox": [ + 317, + 243, + 545, + 312 + ], + "type": "text", + "content": " speedup compared to conventional controllable methods) and larger control capacity (more than just intensity) without multiple training stages [24] and auxiliary networks [50]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 314, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 314, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 317, + 314, + 545, + 338 + ], + "type": "text", + "content": "- RCD is the first method supporting controllable denoising on real-world benchmarks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 340, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 340, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 317, + 340, + 545, + 363 + ], + "type": "text", + "content": "- We propose a general Noise Decorrelation technique to estimate editable noises." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 366, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 366, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 317, + 366, + 545, + 411 + ], + "type": "text", + "content": "- We achieve comparable or better results on widely-used real/synthetic image-denoising and videodenoising datasets with minimal additional computational cost." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 425, + 397, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 425, + 397, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 425, + 397, + 437 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 444, + 375, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 375, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 375, + 456 + ], + "type": "text", + "content": "2.1. Denoising" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "content": "Traditional image and video denoising methods are often based on prior assumptions such as sparse image prior [3, 15, 16, 20], non-local similarity [7, 13, 14, 18], and other similar techniques [22, 41, 52]. However, with the recent development of deep learning networks, many learning-based methods have been proposed and achieved state-of-the-art performance. Early works [8] utilized multi-layer perceptron (MLP) to achieve comparable results with BM3D. In recent years, there has been rapid progress on CNN-based denoising methods [4, 10, 21, 47, 55, 57] and Transformer-based methods [32, 42, 54, 59], which have started to dominate the image/video denoising task. However, the abovementioned works mainly focus on designing novel network architectures to improve the denoising performance and usually generate a single output. Their lack of ability to adjust the output denoising level based on user's feedback has greatly restricted their practical use in many real-world applications. Moreover, although techniques like pruning [33, 38, 60] and quantization [45, 61] can accelerate such neural network-based methods, they are typically heavy, which restricts their application to real-time denoising control." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14029" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 58, + 545, + 320 + ], + "blocks": [ + { + "bbox": [ + 50, + 58, + 545, + 320 + ], + "lines": [ + { + "bbox": [ + 50, + 58, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 50, + 58, + 545, + 320 + ], + "type": "image", + "image_path": "e041ba5d99f57b30628567c97b1aee7488b72648530b2b52ed937aff0f213a23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "text", + "content": "Figure 3. Pipeline overview of proposed RCD framework. A: Backbone network for generating multi-level noise maps. B: Noise Decorrelation module for editable noises. C: AutoTune module for providing reference control parameters for users." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 356, + 178, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 178, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 178, + 369 + ], + "type": "text", + "content": "2.2. Controllable denoising" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 289, + 714 + ], + "type": "text", + "content": "Most conventional deep-learning methods for image/video denoising can only generate a fixed result with a specific restoration level. Recently, some controllable image/video denoising methods allow users to adjust the restoration effect without retraining the network. DNI [51] and AdaFM [24] used the observation that the learned filters of the models trained with different restoration levels are similar in visual patterns. DNI interpolated all the corresponding parameters between two related networks to derive smooth and continuous restoration effects, while AdaFM adopted feature modulation filters after each convolution layer. CFSNet [50] proposed an adaptive learning strategy of using interpolation coefficients to couple the intermediate features between the main branch and the tuning branch. Different from these interpolation-base methods, some other methods [9, 25, 39] regarded modulation as a conditional image restoration problem and adopted a joint training strategy. CUGAN [9] proposed a GAN-based image restoration framework to avoid the over-smooth problem, a common issue in PSNR-oriented methods. However, all of the above controllable methods can only be trained with synthetic degradations because they require explicit degradation levels during training. When applied on real-world data, as shown in [23], methods that trained for blind Additive White Gaussian Noise (AWGN) [35,55] may be overfitted and often suffer from dramatic performance drop. Besides the real-world image issue, all these controllable methods utilize an auxiliary conditional network and require one network inference for each different target" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 357, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 380 + ], + "type": "text", + "content": "restoration level at test time, which makes them almost impossible for real-time application." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 393, + 366, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 366, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 366, + 405 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 414, + 467, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 414, + 467, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 414, + 467, + 427 + ], + "type": "text", + "content": "3.1. Conventional Deep Denoising" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": "Deep denoising methods trump traditional filter-based techniques by leveraging the neural networks' robust representation learning capability. Most current denoising methods [11,32,46] reason about the relationship between clean and noisy images by regressing noise maps with a neural generator. Specifically, given a noisy image " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{n}}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": " and model " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{M}:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": ", we can derive the predicted clean image " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{c}}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": " by: " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{c}} = \\mathbf{I}_{\\mathbf{n}} + \\mathcal{M}(\\mathbf{I}_{\\mathbf{n}})" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": ", where model " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": " is updated by minimizing the distance between the denoising result " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{c}}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": " and the ground truth " + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathrm{gt}}" + }, + { + "bbox": [ + 304, + 433, + 545, + 582 + ], + "type": "text", + "content": ". As we can see, this kind of approach generates a single fixed output result in a black-box manner, making it almost impossible to adjust the denoise operation explicitly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 591, + 414, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 591, + 414, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 591, + 414, + 604 + ], + "type": "text", + "content": "3.2. Pipeline Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "text", + "content": "In this section, we present Real-time Controllable Denoising (RCD), a novel deep learning-based pipeline for real-time controllable denoising. As illustrated in Fig. 3, RCD essentially consists of three parts: (1) A backbone network, i.e., " + }, + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b:\\mathbb{R}^{H\\times W\\times C}\\to \\mathbb{R}^{H\\times W\\times LC}" + }, + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "text", + "content": ", generates multiple fixed-level noise maps, where " + }, + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 610, + 545, + 713 + ], + "type": "text", + "content": " is the number of pre-defined noise levels (see (A) in Fig. 3). (2) A Noise Decorrelation (ND) block that enforces the editability of the generated noise maps (see (B) in Fig. 3). (3) An AutoTune" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14030" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "module that gives a default set of control parameters to generate the best denoising result." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "text", + "content": "Specifically, the backbone network will generate multiple fixed-level noise maps, i.e., " + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "text", + "content": ", for each noisy image input. The noise maps are then fed into the proposed Noise Decorrelation (ND) block, which makes noise maps orthogonal to each other. In this way, the decorrelated noise maps " + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "inline_equation", + "content": "\\{\\tilde{\\mathcal{N}}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "text", + "content": " will be zero-correlated and thus become linearly interpolable. At last, the AutoTune module will give a set of suggested control parameters " + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 95, + 288, + 198 + ], + "type": "text", + "content": " to generate the final denoising result as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 123, + 206, + 287, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 206, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 123, + 206, + 287, + 239 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {\\mathbf {c}} = \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}, \\tag {1}", + "image_path": "4b3e2e1c3133ce45fc636edb0029f806b134a083b151e0a3befe83efef30df58.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{L} \\bar{c}_i = 1" + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "text", + "content": ". Moreover, given the zero-correlated noise maps, users can also generate arbitrary strength denoising results by replacing " + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "text", + "content": " with their own customized control parameters " + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 248, + 287, + 298 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 302, + 209, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 302, + 209, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 302, + 209, + 314 + ], + "type": "text", + "content": "3.3. Multi-level Noise Generation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "content": "Given a noisy input image " + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{n}}" + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "content": ", the backbone network aims to generate multiple noise maps " + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{N}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "content": ", corresponding to a set of pre-defined noise levels " + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\{l_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "content": ", e.g. noise levels " + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\{5, 10, 15, \\dots, 60\\}" + }, + { + "bbox": [ + 46, + 319, + 287, + 366 + ], + "type": "text", + "content": ". Hence, we have" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 374, + 287, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 374, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 113, + 374, + 287, + 387 + ], + "type": "interline_equation", + "content": "\\sigma \\left(\\mathcal {N} _ {i}\\right) = l _ {i}, \\forall i = 1, \\dots , L, \\tag {2}", + "image_path": "6c2ea7fc56fe59423b32cb4030fa897f4fe936b455535b1716731429e2aef561.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "text", + "content": " is the noise level operation that calculates the standard deviation of pixels in each noise map. To obtain multilevel noise maps, we replace the conventional last output layer of the denoising network with a convolutional layer with an output channel size of " + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "inline_equation", + "content": "L\\cdot C" + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "text", + "content": ". Moreover, the level of the noise map is explicitly generated with the normalization operation, as given by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 90, + 483, + 287, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 483, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 90, + 483, + 287, + 512 + ], + "type": "interline_equation", + "content": "\\mathcal {N} _ {i} = l _ {i} \\frac {\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)}}{\\sigma (\\mathcal {M} _ {b} (\\mathbf {I} _ {\\mathbf {n}}) ^ {(i)})}, \\forall i = 1, \\dots , L. \\tag {3}", + "image_path": "3e783d5bfb2f7114f1c9fd3d2a915cf0bbc565c161f33501990cbed1aa069d1e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b(\\mathbf{I_n})\\in \\mathbb{R}^{H\\times W\\times LC}" + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "content": " is network output, and " + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b(\\mathbf{I_n})^{(i)}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "content": " is the i-th component separated from the channel dimension. The derived " + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "content": " can be considered as the noise map estimated at the given noise level " + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 46, + 518, + 287, + 576 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 576, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 633 + ], + "type": "text", + "content": "Different from prior controllable denoising methods with implicit interpolation in the network, we propose to explicitly interpolate the noise maps in Eqn. 3. Thanks to the separation of noise interpolation and network inference, our RCD can achieve real-time user interaction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 633, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 633, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 288, + 714 + ], + "type": "text", + "content": "However, the multi-level noise maps " + }, + { + "bbox": [ + 46, + 633, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 633, + 288, + 714 + ], + "type": "text", + "content": " directly obtained by convolutional layers are usually highly correlated, which leads to the problem of noise level collapse. In other words, the noise map representations in different levels are redundant, implying that the number of noise maps at different noise strengths that participate in the linear interpolation in Eqn. 1 is implicitly reduced. Without any constraint," + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 173 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 173 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 173 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 173 + ], + "type": "image", + "image_path": "1b4247ed5206507bda03ecd23a3b5bec7bde408717d346b648ed047996d6b5f5.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "lines": [ + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "type": "text", + "content": "Figure 4. Demonstration of Noise Decorrelation's influence on noise editing. " + }, + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "type": "inline_equation", + "content": "|\\Sigma|_F" + }, + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "type": "text", + "content": " denotes norms of the covariance matrix for corresponding learned noises and " + }, + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 178, + 547, + 212 + ], + "type": "text", + "content": " is noise intensity." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 220, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 289 + ], + "type": "text", + "content": "our experiments show that the single noise map at a certain noise level would dominate in the linear interpolation for a variety of input noisy images. To address this issue, we further introduce the Noise Decorrelation block to make representations of these noise maps much more informative in the following section." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 295, + 422, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 295, + 422, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 295, + 422, + 306 + ], + "type": "text", + "content": "3.4. Noise Decorrelation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "text", + "content": "The Noise Decorrelation (ND) block is designed to regularize the backbone network to generate editable noise maps at varying levels. In particular, this block is a parameter-free computational unit that enforces " + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "text", + "content": " to be approximately zero-correlated with each other: " + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{cov}(\\mathcal{N}_i,\\mathcal{N}_j)\\approx 0,\\forall i,j\\in" + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\{1,2,\\dots,L\\}" + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{cov}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 312, + 545, + 437 + ], + "type": "text", + "content": " is covariance operator. Inspired by the success of using the decorrelation technique in network optimization and normalization, we adopt the whitening-based methods [29, 30] for noise decorrelation here. The noise maps are decorrelated using the inverse square root of their covariance matrix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": "Specifically, for each predicted fixed-level noise map " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": ", it will firstly be reshaped to " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i \\in \\mathbb{R}^{1 \\times M}" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "M = HWC" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": ". By stacking the reshaped " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": " over the first dimension, we have " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{N} \\in \\mathbb{R}^{L \\times M}" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": ". We then calculate the noise covariance matrix " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": " by: " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\Sigma = \\frac{1}{M - 1} (\\mathbf{N} - \\bar{\\mathbf{N}})(\\mathbf{N} - \\bar{\\mathbf{N}})^T" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{N}}" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": " is mean of " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": " over channel " + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 437, + 545, + 508 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "content": "The Noise Decorrelation block needs to compute inverse square root " + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}} \\in \\mathbb{R}^{L \\times L}" + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "content": ", which can be done by eigen decomposition or SVD. Since this kind of operation involves heavy computation [29], we instead adopt the more efficient Newton's Iteration to estimate " + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "content": " as in [5, 27]. Giving a covariance matrix " + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "content": ", Newton's Iteration calculates " + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 304, + 508, + 545, + 592 + ], + "type": "text", + "content": " by following the iterations below:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 326, + 597, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 597, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 326, + 597, + 545, + 624 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Sigma_ {0} = I, \\\\ \\Sigma_ {k} = \\frac {1}{2} (3 \\Sigma_ {k - 1} - (\\Sigma_ {k - 1}) ^ {3} \\Sigma), k = 1, 2,.., T, \\end{array} \\tag {4}", + "image_path": "b0bdbc9766a155a084e485dc4de021ebd55c57b3c2843e4568bcdfaf621d5d0a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " is the iteration index and " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " is the iteration number (in our experiments " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "T = 3" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " or 4). " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\Sigma_{k}" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " is guaranteed to converge to " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\| I - \\Sigma \\|_2 < 1" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " [5]. This condition can be achieved by normalizing " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\frac{\\Sigma}{tr(\\Sigma)}" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "inline_equation", + "content": "tr(.)" + }, + { + "bbox": [ + 304, + 629, + 545, + 688 + ], + "type": "text", + "content": " is trace operator." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "The derived " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Sigma^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " can be regarded as a whitening matrix [43], which decorrelates the noise maps " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " in" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14031" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": "a differentiable manner. The decorrelated noise maps " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{N} \\in \\mathbb{R}^{\\tilde{H} \\times W \\times LC}" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " can be obtained by calculating: " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{N}} = \\Sigma^{-\\frac{1}{2}} \\mathbf{N}" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": ". We can then have our editable fixed-level noises " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{N}}_i \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " by reshaping " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{N}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " and splitting it into " + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 72, + 287, + 155 + ], + "type": "text", + "content": " noise maps. After Noise Decorrelation, we apply the same normalization as Eqn. 3 to guarantee the noise strength of the decorrelated noises." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "text", + "content": "The zero-correlated noise maps " + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{N}}_i" + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "text", + "content": " present several excellent properties for controllable denoising. Firstly, the linearity of the noise level's square towards " + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{N}}_i" + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "text", + "content": " is guaranteed. In other words, given an arbitrary set of control parameters " + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i = 1}^L" + }, + { + "bbox": [ + 46, + 156, + 288, + 214 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 95, + 220, + 287, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 220, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 95, + 220, + 287, + 253 + ], + "type": "interline_equation", + "content": "\\mathbf {V a r} \\left(\\sum_ {i = 1} ^ {L} c _ {i} \\tilde {\\mathcal {N}} _ {i}\\right) = \\sum_ {i = 1} ^ {L} c _ {i} ^ {2} \\mathbf {V a r} \\left(\\tilde {\\mathcal {N}} _ {i}\\right), \\tag {5}", + "image_path": "6d7c766ea3c40a8f1feef8a48030351937badb99fa5f6b42dce83247ee7d11cd.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{Var}(\\cdot)" + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "content": " denotes variance operator. Apparently, Eqn. 5 holds when elements of " + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\{\\tilde{\\mathcal{N}}_i\\}_{i = 1,2,\\dots,m}" + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "content": " are mutually zero-correlated. Eqn. 5 reveals the explicit relationship between the control parameters and the target noise level, which allows us to directly edit noises by interpolating " + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 260, + 287, + 365 + ], + "type": "text", + "content": ". Secondly, the Noise Decorrelation block can be regarded as a regularization tool that forces models to learn different noise formats for each level, which will increase the representation capacity of the denoising network [30]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 287, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 444 + ], + "type": "text", + "content": "Fig. 4 demonstrates how the Noise Decorrelation block works. With ND block, the covariance of learned noises is reduced to almost zero (without it, " + }, + { + "bbox": [ + 46, + 365, + 287, + 444 + ], + "type": "inline_equation", + "content": "|\\Sigma|_F" + }, + { + "bbox": [ + 46, + 365, + 287, + 444 + ], + "type": "text", + "content": " can be 751 and unignorable), allowing us to derive determined interpolated results with target noise intensity. In contrast, without the Noise Decorrelation blocks, the output noise level can not be guaranteed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 450, + 154, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 450, + 154, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 450, + 154, + 462 + ], + "type": "text", + "content": "3.5. AutoTune Module" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": "Given the decorrelated noise maps from the Noise Decorrelation block, the AutoTune module will predict a set of model-suggested control parameters, i.e., " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": ", to generate the default denoising result. Users can then use this set of parameters as a starting point to fine-tune their final desired denoising strength. Our AutoTune module is extremely lightweight, and is formulated as a single-layer module with temperature softmax activation. Specifically, " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " can be obtained by: " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\bar{c}_i = \\frac{e^{\\frac{\\mathcal{A}(f)_i}{\\tau}}}{\\sum_{j=1}^n e^{\\frac{\\mathcal{A}(f)_j}{\\tau}}}" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " is the NN layer, " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " is the input feature maps, and " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " is temperature. In our experiments, " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " is set to be 0.05 for best performance. Following the design ethos of efficiency and least coupling to the backbone architecture, we directly choose the unnormalized model outputs " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\mathbf{I_n})" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 468, + 287, + 654 + ], + "type": "text", + "content": " (see (C) in Fig. 3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 661, + 254, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 254, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 254, + 673 + ], + "type": "text", + "content": "3.6. New Cardinality for Denoising Control." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "content": "Unlike existing methods that only modulate noise intensity, our RCD control scheme allows users to further optimize the denoising result to a given noise intensity" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 541, + 196 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 541, + 196 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 541, + 196 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 541, + 196 + ], + "type": "image", + "image_path": "db4f0e23544b9a9e4d9ee1d2d5e29b7736aca6ef68e7b0ad60743bde3b3da52b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "text", + "content": "Figure 5. Example of RCD denoising results by AutoTune and HumanTune on Set8. AutoTune module provides reference control parameters, i.e., " + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "text", + "content": ", to generate the denoising result, and it can be further improved by fine-grained artificial tuning (HumanTune), i.e., " + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\{c_i\\}" + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "text", + "content": ", without changing the noise intensity (both " + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\sigma = 40" + }, + { + "bbox": [ + 304, + 201, + 545, + 264 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": "by tuning " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\{c_i\\}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": ", as long as the weighted mean of " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " remains the same. Eqn. 5 shows that when " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\sum_{i = 1}^{L}c_{i}^{2}\\mathbf{Var}(\\tilde{\\mathcal{N}}_{i}) = \\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " is fixed, the variance of the output noise " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\mathbf{Var}(\\sum_{i = 1}^{L}c_{i}\\tilde{\\mathcal{N}}_{i})" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " would be also fixed. By exploring " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " under the condition of fixed " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\sum_{i = 1}^{L}c_{i}^{2}l_{i}^{2}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": ", we can further optimize the denoising results at a specific noise level by involving different components " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "(\\mathcal{N}_i)" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " in the noise interpolation. As shown in Fig. 5, our AutoTune module can generate high-quality results using just the reference control parameters " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": ". Users can further improve the result by artificially tuning " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\{c_i\\}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": " around " + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}" + }, + { + "bbox": [ + 304, + 277, + 545, + 419 + ], + "type": "text", + "content": ", even at the same noise level." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 430, + 428, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 428, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 428, + 442 + ], + "type": "text", + "content": "3.7. Optimization Targets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "text", + "content": "To guarantee the visual quality of arbitrarily edited noise " + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{L} c_i \\tilde{\\mathcal{N}}_i" + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "text", + "content": " for any given set of control parameters " + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "text", + "content": ", we adopt a multi-level concurrent training strategy by minimizing the difference between each level's noise output and the ground truth noise, i.e., " + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{level}" + }, + { + "bbox": [ + 304, + 448, + 545, + 507 + ], + "type": "text", + "content": ", which is derived by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 517, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 517, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 359, + 517, + 545, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {l e v e l}} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\tilde {\\mathcal {N}} _ {i}\\right) \\tag {6}", + "image_path": "d9cd0a71113ac6e0fb27875073c2f36d9a7b6732f7514ba4b2b98b816c8381da.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{gt}" + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{n}}" + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "content": " are ground truth clean image and the input noisy image. " + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(.)" + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "content": " can be any loss functions (e.g., L2 loss or PSNR loss)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "text", + "content": "Spectaculously, " + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{\\mathbf{n}} + \\tilde{\\mathcal{N}}_i" + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "text", + "content": " can be regarded as corner cases of RCD when we use one-hot control parameters as input. Joint optimization of all the noise levels ensures that each element of " + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "text", + "content": " can be trained as optimal noise estimation under the condition of fixed noise level " + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 594, + 545, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 651, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 545, + 673 + ], + "type": "text", + "content": "Together with the AutoTune module optimization, our final cost function can be written as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 338, + 683, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 683, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 338, + 683, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\mathcal {L} _ {\\text {l e v e l}} + \\mathcal {L} \\left(\\mathbf {I} _ {g t}, \\mathbf {I} _ {\\mathbf {n}} + \\sum_ {i = 1} ^ {L} \\bar {c} _ {i} \\tilde {\\mathcal {N}} _ {i}\\right), \\tag {7}", + "image_path": "2aded1affac678bd644bb88a19586acc325047ace7ba0d9bddc252571b589e71.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14032" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 76, + 560, + 185 + ], + "blocks": [ + { + "bbox": [ + 85, + 55, + 509, + 67 + ], + "lines": [ + { + "bbox": [ + 85, + 55, + 509, + 67 + ], + "spans": [ + { + "bbox": [ + 85, + 55, + 509, + 67 + ], + "type": "text", + "content": "Table 1. Gaussian single image denoising results (PSNR). RCD is evaluated with AutoTune results. “-”: not reported" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 76, + 560, + 185 + ], + "lines": [ + { + "bbox": [ + 48, + 76, + 560, + 185 + ], + "spans": [ + { + "bbox": [ + 48, + 76, + 560, + 185 + ], + "type": "table", + "html": "
MethodControllableCBSD68Kodak24McMasterUrban100
σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50σ = 15 σ = 25 σ = 50
IRCNN [56]X33.8631.1627.8634.6932.1828.9334.5832.1828.9133.7831.2027.70
FFDNet [57]X33.8731.2127.9634.6332.1328.9834.6632.3529.1833.8331.4028.05
DnCNN [55]X33.9031.2427.9534.6032.1428.9533.4531.5228.6232.9830.8127.59
DSNet [40]X33.9131.2828.0534.6332.1629.0534.6732.4029.28-
CResMD [25]✓33.97-28.06---
AdaFM-Net [24]✓34.1031.4328.13---
NAFNet [11]X34.1131.4928.2735.1432.7029.6835.0732.8229.7934.4132.0929.00
NAFNet-RCD (ours)✓34.1331.4928.2635.1532.7229.6935.1132.8429.8134.4532.1229.02
", + "image_path": "9643ceb54f214acab7920c47c450b56878de1dcfed95e3d7d82f610500358357.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 258, + 291, + 300 + ], + "blocks": [ + { + "bbox": [ + 46, + 198, + 288, + 250 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 288, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 288, + 250 + ], + "type": "text", + "content": "Table 2. Running time comparison for RCD and other controllable methods during test time. Full Pipeline compares full pipeline latency for the model to infer 1000 images, and Edit-only compares latency for editing one image with 1000 different control parameters." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 258, + 291, + 300 + ], + "lines": [ + { + "bbox": [ + 50, + 258, + 291, + 300 + ], + "spans": [ + { + "bbox": [ + 50, + 258, + 291, + 300 + ], + "type": "table", + "html": "
MethodMulti-stage trainingFull PipelineEdit-only
AdaFM-Netrequired81.03s81.03s
CResMDNetnot required128.08128.08s
NAFNet-RCDnot required64.84s0.04s
", + "image_path": "48c4561fc16edf972c0c71dbda944c5d1c7347463c8419941dfd77d0d80e9e7e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "text", + "content": " is the loss weight (" + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "text", + "content": " in our experiments), and " + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbf{I}_{gt},\\mathbf{I_n} + \\sum_{i = 1}^{n}\\bar{c}_i\\tilde{\\mathcal{N}}_i)" + }, + { + "bbox": [ + 46, + 310, + 287, + 346 + ], + "type": "text", + "content": " optimizes the denoising result derived by the model-suggested control parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 357, + 128, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 128, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 128, + 371 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 377, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 479 + ], + "type": "text", + "content": "This section is organized as follows: First, we demonstrate the effectiveness of our plug-in RCD with SOTA image denoising methods [11] in different scales on synthetic noise datasets. Next, to evaluate the ability of blind denoising on real-world data, we conduct experiments on popular real-world denoising dataset SIDD [1]. Then, we apply our real-time controllable RCD pipeline on video denoising applications. At last, we empirically discuss some design details described in the previous sections." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 489, + 226, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 226, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 226, + 502 + ], + "type": "text", + "content": "4.1. Gaussian Single Image Denoising" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": "Experimental Setup. To fully demonstrate the effectiveness of the proposed RCD, we choose the most recent SOTA method NAFNet [11] as our backbone. Following [54], we first conduct denoising experiments on several widely-used synthetic color image benchmarks (DIV2K [2], BSD400 [36], Flickr2K [53] and WaterlooED [34]) with additive white Gaussian noise (" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\sigma \\in [0, 60]" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": "). The training patch size is " + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": " and the batch size is 64. We train our model with Adam [31] optimizer and learning rate " + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "inline_equation", + "content": "1e - 3" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": " for total 60K iterations. Consistent to [11], PSNR loss is adapted as the loss function. Both the baseline model (NAFNet) and its RCD variants (NAFNet-RCD) are trained from scratch. For settings of RCD, we initialize " + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "inline_equation", + "content": "L = 12" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\{l_i\\} = [5, 10, \\dots, 60]" + }, + { + "bbox": [ + 46, + 508, + 287, + 677 + ], + "type": "text", + "content": " for synthetic denoising training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 678, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 713 + ], + "type": "text", + "content": "Complexity analysis. Extensive adjustments of controllable parameters are often required to obtain one satisfying result for users. Therefore, editing time is vital" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 199, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 545, + 313 + ], + "type": "text", + "content": "for controllable methods. This section compares the inference and editing latency of our RCD and conventional controllable pipelines on GTX 1080Ti. As shown in Tab. 2, the proposed RCD not only outperforms other conventional controllable pipelines on inference time, but more importantly, can overwhelm those traditional controllable designs on editing time, which can be more than 2000 times faster (as editing process of RCD is network-free, without reliance on sub-networks). This comparison confirms that our RCD is more than enough for real-time image editing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "content": "Results Analysis. We evaluate our proposed method on widely used synthetic noise datasets CBSD68 [37], Kodak24 [19], McMaster [58] and Urban100 [28] with noise levels " + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "inline_equation", + "content": "\\sigma(15)" + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "inline_equation", + "content": "\\sigma(15)" + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "inline_equation", + "content": "\\sigma(50)" + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "content": ". RCD is evaluated with denoising results using AutoTune outputs " + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "inline_equation", + "content": "\\{\\bar{c}_i\\}" + }, + { + "bbox": [ + 304, + 313, + 546, + 517 + ], + "type": "text", + "content": ". As shown in Tab. 1, NFANet-RCD achieves comparable performance to the baseline NFANet consistently on multiple datasets, indicating that our plug-in RCD module enables real-time controllable denoising for NAFNet without sacrificing its original denoising performance. Please note that NAFNet-RCD can yield comparable results to the backbone just by using the AutoTune outputs, and the performance can be further improved by manually tuning the control parameters (See Sec. 3.6.) We further show the qualitative performance of NAFNet-RCD in Fig. 6. NAFNet-RCD can recover more details of some degraded images, which may be benefited from RCD's richer representation capacity by integrating multiple noise maps." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "text", + "content": "Slimmer Model Variants. Towards the goal of evaluating the compatibility and robustness of RCD, we conduct ablations by applying RCD to different-sized backbones. Specifically, we shrink the width and block numbers of NAFNet, denoting derived models as NAFNet-small " + }, + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "inline_equation", + "content": "(\\frac{1}{4} \\times)" + }, + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "text", + "content": " and NAFNet-tiny " + }, + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "inline_equation", + "content": "(\\frac{1}{16} \\times)" + }, + { + "bbox": [ + 304, + 517, + 545, + 642 + ], + "type": "text", + "content": ". Tab. 3 reports the results of RCD with those scaled backbones. It can be observed that the RCD-variants can achieve comparable and even slightly better denoising results compared to their baselines, which further demonstrates RCD's robustness and effectiveness for different-sized backbones." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 649, + 463, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 649, + 463, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 649, + 463, + 662 + ], + "type": "text", + "content": "4.2. Real Single Image Denoising" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 667, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 667, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 667, + 545, + 713 + ], + "type": "text", + "content": "Experimental Setup (Real Image) Unlike existing controllable denoising methods [24,50] which focus on synthetic benchmarks, we are the first solution that attempts to extend controllable denoising to real-world SIDD datasets." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14033" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 54, + 294, + 196 + ], + "blocks": [ + { + "bbox": [ + 51, + 54, + 294, + 196 + ], + "lines": [ + { + "bbox": [ + 51, + 54, + 294, + 196 + ], + "spans": [ + { + "bbox": [ + 51, + 54, + 294, + 196 + ], + "type": "image", + "image_path": "fc24aa3dd446f86db11086e608e3b5005225d97c4d1c1b9e5794dd0cb9cde020.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 207, + 546, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 207, + 546, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 546, + 229 + ], + "type": "text", + "content": "Figure 6. Visual comparison of RCD and their baseline results on " + }, + { + "bbox": [ + 46, + 207, + 546, + 229 + ], + "type": "inline_equation", + "content": "\\sigma = 50" + }, + { + "bbox": [ + 46, + 207, + 546, + 229 + ], + "type": "text", + "content": " denoising. GT: Ground truth. Base: Baseline model without RCD. AutoTune: RCD results by applying control parameters from AutoTune module." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 297, + 54, + 541, + 196 + ], + "blocks": [ + { + "bbox": [ + 297, + 54, + 541, + 196 + ], + "lines": [ + { + "bbox": [ + 297, + 54, + 541, + 196 + ], + "spans": [ + { + "bbox": [ + 297, + 54, + 541, + 196 + ], + "type": "image", + "image_path": "6f05db71269261da1b66f565f0b736153580927bc2b204ac244eec173cac2bfe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 51, + 259, + 541, + 355 + ], + "blocks": [ + { + "bbox": [ + 198, + 240, + 394, + 251 + ], + "lines": [ + { + "bbox": [ + 198, + 240, + 394, + 251 + ], + "spans": [ + { + "bbox": [ + 198, + 240, + 394, + 251 + ], + "type": "text", + "content": "Table 3. Ablation of RCD on various backbone sizes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 259, + 541, + 355 + ], + "lines": [ + { + "bbox": [ + 51, + 259, + 541, + 355 + ], + "spans": [ + { + "bbox": [ + 51, + 259, + 541, + 355 + ], + "type": "table", + "html": "
MethodCBSD68\nσ = 15 σ = 25 σ = 50Kodak24\nσ = 15 σ = 25 σ = 50McMaster\nσ = 15 σ = 25 σ = 50Urban100\nσ = 15 σ = 25 σ = 50
NAFNet-tiny33.5834.3333.8532.96
NAFNet-RCD-tiny33.7131.0631.8833.22
NAFNet-small33.8431.1832.1833.61
NAFNet-RCD-small33.9631.3132.3233.92
NAFNet34.1131.4932.7034.41
NAFNet-RCD34.1331.4932.7234.45
", + "image_path": "3dcb693b7302e94375aa0e963848558a9dd9ca8d5947bd91ea3a40a50f1fc5c0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 410, + 301, + 483 + ], + "blocks": [ + { + "bbox": [ + 46, + 368, + 287, + 400 + ], + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 400 + ], + "type": "text", + "content": "Table 4. Image denoising results on SIDD. Real noise: results on real-world SIDD test sets. Synthetic noise: results on SIDD test set with additive Gaussian noise (" + }, + { + "bbox": [ + 46, + 368, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\sigma = 25" + }, + { + "bbox": [ + 46, + 368, + 287, + 400 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 410, + 301, + 483 + ], + "lines": [ + { + "bbox": [ + 48, + 410, + 301, + 483 + ], + "spans": [ + { + "bbox": [ + 48, + 410, + 301, + 483 + ], + "type": "table", + "html": "
MethodReal noiseSynthetic noise
PSNRSSIMPSNRSSIM
NAFNet-tiny42.190.979638.460.9551
NAFNet-RCD-tiny41.860.978138.600.9558
NAFNet43.220.981838.850.9481
NAFNet-RCD42.910.980639.140.9580
", + "image_path": "abaa8e808fece1a8ab58cc94e7a08f2f1871e313d3afc8671a40dc1385a342b1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": "SIDD consists of real noisy images captured by smartphones with " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\sigma \\in [0,50]" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": ". Instead of using full SIDD data, we choose subsets of SIDD with " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\sigma \\in [0,12]" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " (around " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " of the entire dataset) to train our RCD model, which is initialized with " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\{l_i\\} = [3,6,9,12]" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": ". The main reason is the lacking of high " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " data at given levels in SIDD because of SIDD's highly long-tailed noise level distribution. Specifically, most noisy images in SIDD gather in " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\sigma < 12" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " and the samples distribute sparsely when " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": " is large. Consistent to Sec. 4.1, we adopt NAFNet (SOTA methods for SIDD challenge [11]) as our backbone at two scales (" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "1\\times" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\frac{1}{16}\\times" + }, + { + "bbox": [ + 46, + 505, + 287, + 664 + ], + "type": "text", + "content": "). Both NAFNet-RCD and the corresponding baselines are trained on this subset with the same training settings as in [11]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 667, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 667, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 667, + 287, + 713 + ], + "type": "text", + "content": "Results and Analysis We conduct blind denoising experiments on SIDD with different RCD model scales to evaluate its adjustability to the real-world dataset. As shown in Tab. 4 (left), our RCD (AutoTune results) can" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 370, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 438 + ], + "type": "text", + "content": "achieve high-quality controllable real-world denoising in both model scales. However, we note that enabling controllable denoising with RCD may still result in a slight decrease in quantitative results (about 0.3dB), which may be a result of unbalanced data for each level and short noise level interval (" + }, + { + "bbox": [ + 304, + 370, + 545, + 438 + ], + "type": "inline_equation", + "content": "|l_{i+1} - l_i|" + }, + { + "bbox": [ + 304, + 370, + 545, + 438 + ], + "type": "text", + "content": ", see more discussion in Sec. 4.4)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "text", + "content": "SIDD with synthetic noise. We extensively conduct synthetic denoising experiments on SIDD to further show the compatibility of RCD on SIDD datasets. Following Sec. 4.1, we add random Gaussian noise " + }, + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "inline_equation", + "content": "\\sigma \\in [0,60]" + }, + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "text", + "content": " to SIDD training data, and both methods are evaluated on " + }, + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "inline_equation", + "content": "\\sigma = 50" + }, + { + "bbox": [ + 304, + 438, + 546, + 575 + ], + "type": "text", + "content": " SIDD test samples. As shown in Tab. 4 (right), RCD models slightly outperform their baselines, demonstrating RCD's compatibility for SIDD. Moreover, this result can also indicate that RCD's performance drop on SIDD real image may arise from the noise distribution and RCD configurations, rather than RCD's adaptive capacity to SIDD data. See Appendix for more results and visualizations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 581, + 405, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 581, + 405, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 581, + 405, + 594 + ], + "type": "text", + "content": "4.3. Video Denoising" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "text", + "content": "Experiment Setup Following common practice [32, 44, 46], we train our models on DAVIS training set and use DAVIS-test and Set-8 for benchmarking. Like in [46], we add Gaussian noise with random standard deviation between 5-50 on the DAVIS clean videos for training. The DAVIS set contains 30 color sequences of resolution " + }, + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "inline_equation", + "content": "854 \\times 480" + }, + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "text", + "content": ", which will be randomly cropped into " + }, + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 599, + 545, + 701 + ], + "type": "text", + "content": " patches during training. Other training settings and hyperparameters are kept the same as [46] for a fair comparison." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Choice of Basic model. We choose FastDVD [46] as" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14034" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 58, + 542, + 176 + ], + "blocks": [ + { + "bbox": [ + 49, + 58, + 542, + 176 + ], + "lines": [ + { + "bbox": [ + 49, + 58, + 542, + 176 + ], + "spans": [ + { + "bbox": [ + 49, + 58, + 542, + 176 + ], + "type": "image", + "image_path": "05c5197532a41243cad10d54d7b703c53aa41d4e7c6e7895ba48bb2a2d8c0480.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "text", + "content": "Figure 7. Illustration of RCD control logics. Users can retouch the denoising level by tuning the Intensity bar (" + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "inline_equation", + "content": "\\sigma = \\sqrt{\\sum_{i=1}^{L} c_i^2 l_i^2}" + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "text", + "content": ") and setup their perceptual preference at fixed level by tuning Component bar (changing " + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "inline_equation", + "content": "\\{c_i\\}" + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "text", + "content": " while keeping " + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 190, + 546, + 217 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 227, + 286, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 286, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 286, + 284 + ], + "type": "text", + "content": "our backbone model. Although recent methods [32,48] outperform FastDVD by 1-2 PSNR at most, they actually introduce huge models and extra heavy operations like patch clustering [48] and layer-wise frame-to-frame wrapping using optical flow [32] (" + }, + { + "bbox": [ + 46, + 227, + 286, + 284 + ], + "type": "inline_equation", + "content": ">100 \\times" + }, + { + "bbox": [ + 46, + 227, + 286, + 284 + ], + "type": "text", + "content": " slower than FastDVD)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 284, + 286, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 286, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 286, + 420 + ], + "type": "text", + "content": "Results and Analysis. Like [44], we evaluate our video denoising models with the input length of one frame and five frames. We denote RCD models for video denoising as \"FastDVD-RC\" and compare their quantitative AutoTune denoising results to baseline FastDVD in Tab. 5. Consistent with preceding sections, AutoTune results of FastDVD-RCD can demonstrate comparable performance to the default FastDVD, which means our RCD can also achieve lossless real-time noise editing in video scenarios. Unlike previous heavy controllable denoising methods, our real-time RCD can even allow users to do online video denoising editing without any latency." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 443, + 282, + 531 + ], + "blocks": [ + { + "bbox": [ + 106, + 424, + 228, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 228, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 228, + 435 + ], + "type": "text", + "content": "Table 5. Video denoising results." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 443, + 282, + 531 + ], + "lines": [ + { + "bbox": [ + 50, + 443, + 282, + 531 + ], + "spans": [ + { + "bbox": [ + 50, + 443, + 282, + 531 + ], + "type": "table", + "html": "
Test setσ1 frame5 frames
FastDVDFastDVD-RCDFastDVDFastDVD-RCD
DAVIS2034.1734.2135.6935.65
3032.4532.6934.0634.04
4031.3931.6032.8032.78
5030.2630.5731.8331.85
Set 82031.9932.0133.4333.46
3030.6130.6531.6231.71
4029.6229.8330.3630.42
5028.6128.8529.4129.60
", + "image_path": "b8329bd57db2068417978b36cbd8ccd83f4ef3a86ae47d3e4f3acc9c676767c5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 536, + 124, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 124, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 124, + 548 + ], + "type": "text", + "content": "4.4. Discussions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": "Selection of Denoising Levels. Differing from conventional denoising methods, RCD requires a group of predefined noise levels " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\{l_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": ". To evaluate how the selection of " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\{l_i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " affects RCD's performance, we conduct ablation studies on FastDVD-RCD by changing the number of noise maps " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "(L)" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " (See Tab. 6.) All of the models are trained on noisy images with " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\sigma \\in (0,60]" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " and uniformly sampled noise levels that " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\{l_i = \\frac{60}{L} * i\\}_{i=1}^L" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": ". We observe that larger " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " means more fine-grained control on denoising, but it may incur a performance drop. In fact, when " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " is large we find that " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{level}" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " will also keep large and be hard to optimize. Trading-off performance and control precision, we empirically choose " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "L = 12" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " and noise level interval " + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "inline_equation", + "content": "|l_{i+1} - l_i| = 5" + }, + { + "bbox": [ + 46, + 554, + 287, + 712 + ], + "type": "text", + "content": " as defaults." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 250, + 539, + 300 + ], + "blocks": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "type": "text", + "content": "Table 6. Ablations of FastDVD-RCD on different number of noise levels. Reported scores are PSNR of AutoTune outputs and GT." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 250, + 539, + 300 + ], + "lines": [ + { + "bbox": [ + 310, + 250, + 539, + 300 + ], + "spans": [ + { + "bbox": [ + 310, + 250, + 539, + 300 + ], + "type": "table", + "html": "
Test SetσL = 1L = 2L = 12L = 30L = 60
Set82031.8731.4232.0131.3931.07
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", + "image_path": "9b4cc1601a300bb37dc95cd32d2af51563685bae62f7974f73cb86bfde14bc3a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": "Control Capacity. This section discusses the representation capacity of " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " as control parameters. Generally, " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " controls the denoising process on two aspects: intensity and components. Firstly, the noise levels of RCD outputs are identical and can be derived by " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\sigma = \\sqrt{\\sum_{i=1}^{L} c_{i}^{2} l_{i}^{2}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " (See Sec. 3.4), which allows us to control the denoising intensity by changing " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\{c_{i}\\}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ". Fig. 7 depicts visualizations of RCD-controlled denoising under different intensity settings. Besides, as discussed in Sec. 3.6, RCD supports further optimization of the denoising results at specific noise intensity by tuning " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " by involving different components of " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{N}}_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ". (Please be reminded that " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{N}}_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " is trained by " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{level}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ", denoting learned optimal denoising results at every fixed level " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ".)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 480, + 372, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 480, + 372, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 480, + 372, + 495 + ], + "type": "text", + "content": "5. Summary" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 500, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 545, + 625 + ], + "type": "text", + "content": "We present RCD framework that enables real-time noise editing for controllable denoising. Unlike existing continual-level denoising methods, RCD doesn't require multiple training stages and auxiliary networks. With the proposed Noise Decorrelation module, RCD transforms the control of denoising into white-box operations, with no requirement to feed control parameters to networks at test time, which enables real-time editing even for heavy network models. Extensive experiments on widely-used real/synthetic image and video denoising datasets demonstrate the robustness and effectiveness of our RCD." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 635, + 416, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 416, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 416, + 649 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 655, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 655, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 655, + 545, + 712 + ], + "type": "text", + "content": "This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000, the General Research Fund of HK No.17200622, and Shanghai Committee of Science and Technology (Grant No. 21DZ1100100)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14035" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 142 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 142 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 142 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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PMLR, 2021. 2" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14038" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_content_list.json b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ced4f48a1ed29bd568461ca111e444398e8a3d3c --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_content_list.json @@ -0,0 +1,1331 @@ +[ + { + "type": "text", + "text": "Real-Time Evaluation in Online Continual Learning: A New Hope", + "text_level": 1, + "bbox": [ + 217, + 130, + 751, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yasir Ghunaim $^{1*}$", + "bbox": [ + 148, + 203, + 285, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adel Bibi $^{2*}$", + "bbox": [ + 331, + 203, + 424, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kumail Alhamoud1", + "bbox": [ + 470, + 203, + 627, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motasem Alfarra1", + "bbox": [ + 674, + 203, + 818, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hasan Abed Al Kader Hammoud1", + "bbox": [ + 89, + 220, + 362, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ameya Prabhu2", + "bbox": [ + 398, + 220, + 527, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Philip H.S. Torr", + "bbox": [ + 560, + 220, + 697, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bernard Ghanem1", + "bbox": [ + 733, + 220, + 875, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ King Abdullah University of Science and Technology (KAUST) $^{2}$ University of Oxford", + "bbox": [ + 130, + 250, + 833, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 301, + 313, + 318 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current evaluations of Continual Learning (CL) methods typically assume that there is no constraint on training time and computation. This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical real-time evaluation of continual learning, in which the stream does not wait for the model to complete training before revealing the next data for predictions. To do this, we evaluate current CL methods with respect to their computational costs. We conduct extensive experiments on CLOC, a large-scale dataset containing 39 million time-stamped images with geolocation labels. We show that a simple baseline outperforms state-of-the-art CL methods under this evaluation, questioning the applicability of existing methods in realistic settings. In addition, we explore various CL components commonly used in the literature, including memory sampling strategies and regularization approaches. We find that all considered methods fail to be competitive against our simple baseline. This surprisingly suggests that the majority of existing CL literature is tailored to a specific class of streams that is not practical. We hope that the evaluation we provide will be the first step towards a paradigm shift to consider the computational cost in the development of online continual learning methods.", + "bbox": [ + 76, + 334, + 472, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Neural Networks (DNNs) have demonstrated impressive success in solving complex tasks [20, 29, 42] when trained offline, for several passes, over large well-curated labeled datasets. However, in many real-world scenarios, data is only available in the form of a stream with a changing distribution. Due to this challenge, there has been a growing interest in the problem of learning from a time-varying stream, also known as Continual Learning (CL), which is", + "bbox": [ + 75, + 734, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a key challenge for DNNs due to a phenomenon known as catastrophic forgetting [17, 36]. In particular, when a DNN is trained with data from a new distribution, the DNN performance significantly drops on previously learned data.", + "bbox": [ + 500, + 304, + 890, + 364 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While mitigation efforts have been proposed, e.g. through regularizing the training [2, 25, 53], replaying previously seen examples [11, 23, 39], and many other approaches [16, 40, 51], current evaluation approaches are still far from real-world scenarios. For example, the majority of literature is on Offline Continual Learning, under which methods are allowed unlimited budget, both time and computation. Furthermore, the majority of CL evaluations are conducted on small-scale datasets with well-defined temporal distribution boundaries in the form of learning a sequence of tasks.", + "bbox": [ + 496, + 366, + 892, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To that end, there has recently been a growing interest in the more realistic setting - Online Continual Learning (OCL). In such a setup [1, 4, 21, 32], CL methods are restricted to a single training pass over a shuffled split of existing offline CL benchmarks. This is certainly a step forward towards resolving some of the unrealistic assumptions of offline CL. However, current evaluations do not sufficiently address the challenges of real-time learning for high-throughput streams with rapid distribution changes.", + "bbox": [ + 496, + 535, + 893, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To illustrate this, consider the problem of continuously learning a Twitter stream where 350K tweets are uploaded per minute on various trending topics [41]. Every uploaded tweet needs to be predicted with a DNN for misinformation and hate speech, among other things, while simultaneously learning and adapting to them. Given the scale at which data is being updated, there is an inherent key limitation on the time and computational budget affordable to learning incoming tweets, an aspect that is often overlooked in the prior art from the OCL literature. Consider an OCL method that is 10 times slower than the Twitter high throughput stream, i.e., it takes 10 minutes to train on one minute worth of tweets (350K tweets). This inefficiency results in an accumulation of $\\sim 3.1$ million new samples that need to be predicted and trained on. Since it is not acceptable to pause", + "bbox": [ + 496, + 674, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution.", + "bbox": [ + 99, + 862, + 218, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Correspondence to: yasir.ghunaim@kaust.edu.sa", + "bbox": [ + 102, + 876, + 413, + 888 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Code: github.com/Yasir-Ghunaim/RealtimeOCL", + "bbox": [ + 102, + 888, + 359, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11888", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d8bb06393f6c6e38cf71821998d6b2e26782c6921ea8c38fa1b5a4cd47f09c1e.jpg", + "image_caption": [ + "Figure 1. OCL Real-Time Evaluation Example. We show an example of real-time evaluation, using the CLOC dataset [7], of two different OCL methods $\\mathcal{A}$ and $\\mathcal{B}$ . Method $\\mathcal{B}$ is twice as slow as method $\\mathcal{A}$ . Both methods are evaluated on every incoming sample. Since $\\mathcal{A}$ has a stream-model relative complexity of one, i.e. $\\mathcal{C}_S(\\mathcal{A}) = 1$ , it is able to train on all the stream samples. In contrast, $\\mathcal{B}$ , which has a relative complexity of two, requires two time steps to train on a single stream batch. Thus, $\\mathcal{B}$ only trains on half of the stream samples." + ], + "image_footnote": [], + "bbox": [ + 83, + 92, + 885, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "all tweets from appearing online until the method training is complete, predictions for all new samples will be performed with an older version of the model. This poses a key challenge where efficient learning from streams becomes necessary. This is because slow-training OCL methods can result in subpar performance, as they resort to predicting new stream data using an older model. This behavior worsens for streams that experience a faster change in distribution.", + "bbox": [ + 75, + 417, + 468, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a real-time evaluation protocol for OCL that factors in training computational complexity. Given a stream, consider an OCL method $\\mathcal{A}$ that is as fast as the stream, i.e., $\\mathcal{A}$ can train on every step of revealed data before the stream presents new samples. Then, if an OCL $\\mathcal{B}$ is twice as expensive as $\\mathcal{A}$ , then $\\mathcal{B}$ will update the model for evaluation every other stream step, i.e., the model will be updated half the number of times compared to $\\mathcal{A}$ . Figure 1 illustrates our proposed real-time evaluation. This is in contrast to all prior art [3,4,6] that (1) unreasonably allows an unlimited computational budget to train on any given stream data, and (2) unfairly compares OCL methods despite having different training complexity levels. Using our real-time evaluation protocol, we benchmark many existing OCL methods against a simple and inexpensive baseline, which mitigates forgetting by simply storing and replaying recently seen samples.", + "bbox": [ + 75, + 537, + 468, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. We summarize our conclusions as follows: (1) We show that under our practical real-time evaluation, our simple baseline outperforms all the considered methods from the OCL literature, including recent SOTA approaches like ACE [6]. (2) We consider a complementary setup where the stream is as slow as the most training-expensive OCL method and compare that method against", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the compute-equivalent baseline. Under this computationally normalized setting, we find that the compute-equivalent baseline outperforms all existing methods. (3) Our experiments are consistent, holding for all the considered continual learning strategies, and extensive, amounting to more than 2 GPU-months. Our results highlight that the current progress in OCL needs to be rethought and a paradigm shift is needed. We hope our work will lead to a new direction for continual learning that takes into account the computational cost of each method.", + "bbox": [ + 496, + 417, + 892, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 584, + 640, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We briefly describe the current literature on offline and online continual learning. For a more comprehensive overview of the literature, we refer the reader to the detailed surveys by De Lange et al. [13] and Mai et al. [33].", + "bbox": [ + 496, + 609, + 890, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Offline Continual Learning. Traditional continual learning strategies, which aim to mitigate forgetting, can be organized into three families of methods. (i) Replay-based methods store input samples, or alternatively learn to generate representative samples, while the model learns from the data stream. Later, the method retransmits the model on the replay samples while the model learns from new data [32, 35, 45, 49, 50]. (ii) Regularization methods avoid the cost of storing samples and simply modify the model loss objective to regularize the training. While some of these methods penalize changes to important model parameters [2, 8, 25], other methods regularize the training by distilling knowledge from a model trained on past stream samples [18, 28, 46]. (iii) Parameter isolation methods train specific parameters for each task while freezing the param-", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11889", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eters that are related to other tasks [22, 34, 40]. Despite the progress made by these methods, they assume an offline stream that allows many passes over each continual learning task. Concurrent work Prabhu et al. [37] alleviates this problem by imposing computational budget constraints and finds that simple methods based on experience replay outperform most prior continual learning works. In contrast, we study the more pragmatic setup, where the stream reveals data in real time.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Online Learning for Reduced Forgetting. OCL was defined with a protocol where training data is only seen once in a sequence of labeled tasks [32]. To reduce catastrophic forgetting, the field initially progressed towards better gradient-based constraints like GEM [32] and AGEM [10]. RWalk [8] quantified forgetting and provided a more efficient approach to limit changes in important model parameters. TinyER [11] rediscovered the effectiveness of experience replay, and HAL [9] enhanced it with learned anchors. However, this setup assumes the availability of an oracle during test time to determine which classifier head to use for inference [33, 48]. Additionally, the benchmarks in this setup often have large constraints on the replay buffer size [10, 11]. Due to these limitations, the class-incremental scenario started to gain attention, which is a more realistic setting for OCL.", + "bbox": [ + 75, + 233, + 472, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In class-incremental online continual learning, benchmarks [3, 27] relaxed the need for task descriptors at test time, and introduced significantly larger buffer sizes in comparison to [10]. Multiple directions have emerged to tackle catastrophic forgetting in this setup. They can be classified into few groups. (i) Regularization-based approaches modify the classification objective to preserve previously learned representations or encourage more meaningful representations e.g. DER [5], ACE [6], and CoPE [14]. (ii) Sampling-based techniques focus on the optimal selection and storing of the most representative replay memory during online training, e.g. GSS [4], OCS [52], CBRS [12], CLIB [26], and InfoRS [47]. Alternatively, some sampling methods focus on better memory retrieval strategies that reduce forgetting, e.g. MIR [3], ASER [44], and GMED [24]. (iii) In other approaches, GDumb [38] proposed a degenerate solution to the problem of online learning ignoring the stream data and learning only on the memory samples. While these efforts have significantly advanced the field of OCL, they are mostly evaluated on benchmarks that do not reflect real-deployment conditions. First, these benchmarks heavily rely on artificially constructed small datasets with sudden shifts in classes. Second, these benchmarks are incapable of measuring whether models can rapidly adapt to new data under a fast-changing distribution shift, which is one of the main problems in classical online learning literature [43]. There have been efforts to address the second limitation by using new metrics that measure test accuracy", + "bbox": [ + 75, + 477, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "more frequently during training [6, 26]. However, these metrics capture the adaptation to held-out test data rather than to the incoming future data. To remedy these limitations, there has been a new surge of benchmarks proposing datasets and evaluation protocols, which we discuss next.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Online Learning for Rapid Adaptation. Recent OCL benchmarks, e.g. CLOC [7] and CLEAR [30], introduce data ordered by timestamps, forming a temporal stream of evolving visual concepts over a long span of time. They demonstrate that their data has a natural distribution shift over time, requiring rapid adaptation to newer data. Additionally, they mimic the traditional online learning setup by measuring the capacity for rapid adaptation with the evaluation being done on future data from the stream. Our work extends the efforts in this direction. We adopt the CLOC benchmark and propose a more realistic real-time evaluation that encourages efficient learning. It is worth mentioning that [19] has explored certain aspects of real-time evaluation in continual learning. However, they focus on efficiency for embedded device deployment, rather than rapid adaptation. Moreover, while their work investigates the computational cost associated with each training method, they only report the cost as an evaluation metric. In contrast, we constrain the training procedure by each method's computational cost.", + "bbox": [ + 496, + 169, + 892, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 484, + 635, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start with the classical problem statement for online continual learning. Then, we formally introduce our proposed real-time evaluation that factors in training complexity through delayed evaluations.", + "bbox": [ + 496, + 508, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Online Continual Learning", + "text_level": 1, + "bbox": [ + 500, + 579, + 746, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Online continual learning [7, 43] is the problem of learning a $\\theta$ parameterized function $f_{\\theta}:\\mathcal{X}\\to \\mathcal{V}$ that predicts a label $y\\in \\mathcal{V}$ for an input image $x\\in \\mathcal{X}$ . Unlike, classical supervised learning, the learning is performed on a distribution-varying stream $\\mathcal{S}$ revealing data sequentially over steps $t\\in \\{1,2,\\dots ,\\infty \\}$ . In particular, at every step $t$", + "bbox": [ + 496, + 601, + 890, + 694 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. $S$ reveals a set of images $\\{x_i^t\\}_{i = 1}^{n_t}\\sim \\mathcal{D}_{j\\leq t}$", + "2. $f_{\\theta_t}$ generates predictions $\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}$ for $\\{x_i^t\\}_{i = 1}^{n_t}$", + "3. $S$ reveals true labels $\\{y_i^t\\}_{i = 1}^t$", + "4. $f_{\\theta_t}$ is evaluated by comparing $\\{\\tilde{y}_i^t\\}_{i=1}^{n_t}$ to $\\{y_i^t\\}_{i=1}^{n_t}$ ;", + "5. A learning method trains $f_{\\theta_t}$ , a criterion computes the training loss, then the parameters are updated to $\\theta_{t + 1}$ ." + ], + "bbox": [ + 511, + 700, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that $\\mathcal{D}_{j\\leq t}$ denotes a varying distribution that might not necessarily need to change at every stream step $t$ .For example, if at step $t = 5$ we have $j = 1$ , this means the revealed data over all five previous steps is sampled from the", + "bbox": [ + 496, + 839, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11890", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bc26693a0f114c009287203d6f9c959f68238d015ce01eba65663c8abf472812.jpg", + "image_caption": [ + "Figure 2. OCL Real-Time Evaluation Setup. In OCL, models perform real-time prediction on each revealed sample from the stream. At the same time, model training is performed on the revealed samples dictated by the method's delay. In this example, we demonstrate the evaluation procedure when the stream-model complexity $k$ is larger than 1. Due to the mismatch between the stream speed and the model computational cost, an \"older version\" of the model predicts samples while the model is being trained. Therefore, k-1 potential training batches are skipped for each training step." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 867, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "same distribution $\\mathcal{D}_1$ . Moreover, observe that, unlike offline continual learning, online continual learning captures the capacity to adapt to new data since the prediction is performed before the training.", + "bbox": [ + 75, + 406, + 470, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Key Issues. As described earlier, the OCL evaluation in the literature [7, 43] overlooks the training complexity in step (5). Under such a setup, all OCL methods have their parameters updated to $\\theta_{t + 1}$ before the stream $S$ reveals images of the next step. Therefore, different OCL methods are evaluated irrespective of the training time and computational complexity at step (5). This is equivalent to evaluating different OCL methods on streams that present data at different rates. In real-time settings, the stream reveals data at a rate that is independent of the training complexity of the OCL method. To that end, we propose a real-time evaluation paradigm for OCL that factors in training complexity through delayed evaluations.", + "bbox": [ + 75, + 470, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Real-Time Evaluation for OCL", + "text_level": 1, + "bbox": [ + 76, + 679, + 352, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As mentioned earlier, we need to define a notion of a fixed stream rate. That is to say, the stream reveals data at a fixed rate irrespective of how long OCL methods take to update the model in step (5). For streams that are twice as fast as it takes to train $f_{\\theta}$ , OCL methods will have their model updated on only half the number of revealed sets of images from the stream. Note that the latest updated version of $f_{\\theta}$ will continue to provide predictions for newly revealed images during training even for those images the model did not train on. This setting reflects the realistic scenario of a server receiving many queries uploaded by users, where each query needs a prediction irrespective of whether an in-house model is being trained. Given a stream $S$ and", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "an OCL method $\\mathcal{A}$ , we first define the notion of stream-model relative complexity $\\mathcal{C}_S(\\mathcal{A})\\in \\mathbb{R}^+$ . In particular, for a stream-model relative complexity $\\mathcal{C}_S(\\mathcal{A}) = 1$ , the continual learning method $\\mathcal{A}$ can update the model $\\theta$ in step (5) before the stream $S$ reveals the data of the next step. For any stream-model relative complexity $\\mathcal{C}_A(\\mathcal{A}) = k > 1$ , the stream is $k$ -faster than the continual learning method $\\mathcal{A}$ . With this notation, we now propose our modified version of the OCL setting along with the corresponding real-time evaluation. Given a model $f_{\\theta_m}$ , a stream $S$ , and an OCL method $\\mathcal{A}$ with $\\mathcal{C}_S(\\mathcal{A}) = k$ , at every step $t$ ,", + "bbox": [ + 496, + 406, + 893, + 573 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. $S$ reveals a set of images $\\{x_{i}^{t}\\}_{i = 1}^{n_{t}}\\sim \\mathcal{D}_{j\\leq t}$", + "2. $f_{\\theta_m}$ generates predictions $\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}$ for $\\{x_i^t\\}_{i = 1}^{n_t}$ ;", + "3. $S$ reveals true labels $\\{y_i^t\\}_{i = 1}^t$", + "4. $f_{\\theta_m}$ is evaluated by comparing $\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}$ to $\\{y_i^t\\}_{i = 1}^{n_t}$ ;", + "5. If $\\mathrm{mod}(t - 1, k) = 0$ , then the continual learner $\\mathcal{A}$ completes updating $f_{\\theta_m} \\gets f_{\\theta_{m+1}}$ and a new instance of training on $f_{\\theta_m}$ commences (see Figure 2)." + ], + "bbox": [ + 511, + 580, + 890, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this setting, OCL methods that are computationally more expensive to train will be updated fewer times. Therefore, for streams $S$ where the distribution $\\mathcal{D}_j$ changes rapidly (perhaps as often as every stream step), OCL methods with a large stream-model relative complexity may produce erroneous predictions, since the models are not updated enough and cannot adapt to the distribution change.", + "bbox": [ + 496, + 731, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "On the Computation of $\\mathcal{C}_S$ . Since $\\mathcal{C}_S$ only measures the relative complexity between the stream and an underlying continual learning method, we first introduce a minimal inexpensive OCL method as a baseline (denoted $\\mathcal{A}$ ). For ease", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11891", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of comparison of the considered methods, we then assume that, due to the inexpensive nature of $\\mathcal{A}$ , online continual learning will be as fast as the stream where the stream-model relative complexity $\\mathcal{C}_{\\mathcal{S}} = 1$ . In particular, we consider a baseline that mitigates forgetting by simply storing and replaying recently seen samples. Then, given any other OCL method $\\mathcal{B}$ , we use the relative training FLOPs between $\\mathcal{B}$ and $\\mathcal{A}$ to determine $\\mathcal{C}_{\\mathcal{S}}(\\mathcal{B})$ . For example, ACE [6] only modifies the loss objective of the baseline, and thus it is equivalent to the baseline in computational complexity. On the other hand, PoLRS [7] maintains and performs operations on three copies of the model. These copies are trained on every incoming batch, making PoLRS require $3 \\times$ the FLOPs needed by the baseline. As noted earlier, a method of a stream-model relative complexity value of 3 performs the update in step (5) once every three stream steps. This corresponds to a delay in model updates by two steps. In Table 1, we summarize the corresponding delay of several popular OCL methods in our real-time evaluation setup.", + "bbox": [ + 75, + 90, + 472, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fair Comparison of OCL Methods with Different $\\mathcal{C}_{\\mathcal{S}}$ . We proposed a realistic setup of evaluating continual learners based on their training complexity with respect to the stream speed. However, one might argue that more expensive training routines could be accelerated by deploying more computational hardware allowing them to train on each revealed sample from the stream. For example, while PoLRS [7] requires $3 \\times$ more FLOPs than the simple baseline, one could deploy $3 \\times$ more hardware to make $\\mathcal{C}(\\mathcal{A}) = 1$ for PoLRS. This setup mimics the scenario of having a slow stream that matches the speed of the more expensive training method.", + "bbox": [ + 75, + 380, + 470, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While the aforementioned setup normalizes the computational requirement of a given learning method $\\mathcal{A}$ to match the stream speed, one should allow simpler training methods the same computational complexity. To that end, we propose boosting simpler and faster training methods to match the computational requirements of more complex methods. For example, we boost the simple experience replay method by sampling a larger number of instances from the replay buffer at each step $t$ to match the FLOPs of other training schemes. We note here that although this modification is both simple and naive, we found empirically that it is sufficient to outperform all considered OCL methods. We leave the rest of the implementation details to Section 4.2.", + "bbox": [ + 75, + 561, + 472, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 768, + 209, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare OCL methods under our proposed real-time evaluation setup given two stream speeds: fast and slow, which capture different application scenarios. We benchmark the majority of OCL methods, which we group into three categories. (1) Regularization-based OCL methods regularize training by modifying the classification loss. For example, RWalk [8] uses a regularizer to penalize abrupt", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1b180e120ea19f1a003a7077ea8feec1b21e88aeb138e05df49bf05e35f58246.jpg", + "table_caption": [ + "Table 1. Training complexity and delay of considered OCL methods. *Note that GSS has a complexity of 6.5 but we rounded it down to 6 to facilitate the setup. This rounding may give GSS a slight advantage, but nonetheless, it is outperformed by the baseline, ER, in all experiments." + ], + "table_footnote": [], + "table_body": "
CL StrategyMethod(A)C_S(A)Delay
Experience ReplayER [11]10
RegularizationsACE [6]10
LwF [28]4/31/3
RWalk [8]21
LR SchedulerPoLRS [7]32
Sampling StrategiesMIR [3]5/23/2
GSS [4]6*5
", + "bbox": [ + 504, + 169, + 883, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "changes in the parameters of the model. ACE [6] introduces an asymmetric loss to treat memory buffer samples differently from incoming stream samples, while LwF [28] distills knowledge from previous steps. (2) Learning rate scheduler methods, in this case PoLRS [7], dynamically adapt the learning rate to changes in the stream distribution. (3) Sampling-based methods alter the strategy used to update the memory buffer, e.g. GSS [4], or change the memory retrieval strategy, e.g. MIR [3].", + "bbox": [ + 496, + 348, + 893, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We use the large-scale online continual learning dataset CLOC [7], which contains 39 million time-stamped images exhibiting natural distribution shifts. The task is to identify the geolocation of a given image where the total number of geolocation labels is 712. To ensure consistency with CLOC [7], we adopt the same dataset split approach. Specifically, we use the first $5\\%$ of the stream for hyperparameter selection, uniformly sample $1\\%$ from the remaining stream to build a held-out set for measuring backward/forward transfer (reported in the appendix), and utilize the rest of the stream for training and online evaluation. Similar to CLOC [7], we compare OCL methods using the Average Online Accuracy metric, which measures the ability of models to adapt to incoming stream samples1.", + "bbox": [ + 496, + 487, + 893, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. At each step $t$ during the experiments, $S$ reveals a set of 128 images, and OCL methods augment the training batch with another 128 images sampled from a memory buffer. This routine is performed until a single pass over the stream is completed. We use ImageNet [15] pre-trained ResNet50 [7, 20] as a backbone. We use SGD with a learning rate of $5 \\times 10^{-3}$ for all OCL methods except for PoLRS [7], which works best with a learning rate of $1 \\times 10^{-3}$ . Unless otherwise stated, we set the size of the replay buffer to $4 \\times 10^{4}$ for all considered methods. We", + "bbox": [ + 496, + 700, + 893, + 852 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "This metric should not be mistaken for a training accuracy, as it evaluates the model on the next unseen training batch before the batch is used for model training.", + "bbox": [ + 498, + 862, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11892", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c78b09c573a981d844a311e78eb17cb19122ffa9695146a216b9646aca847598.jpg", + "image_caption": [ + "Figure 3. Fast Stream Evaluation. We compare the Average Online Accuracy of six methods from the OCL literature evaluated under the fast-stream setting. We observe that our inexpensive baseline, ER, outperforms all the considered methods. Surprisingly, the most computationally complex methods, MIR, PoLRS, and GSS, underperform the more efficient methods." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 441, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "use the same hyperparameters reported in all corresponding papers with the exception of the regularization parameter for RWalk [8]. We find that their reported regularization $\\lambda = 0.1$ is too small for the CLOC dataset; we cross validate it and find that $\\lambda = 2$ works best. Our implementation extends the codebase of Avalanche [31], which is a popular continual learning framework. We leave all the remaining implementation details and ablations to the appendix.", + "bbox": [ + 75, + 422, + 468, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Fast Stream: Real-Time Evaluation", + "text_level": 1, + "bbox": [ + 76, + 556, + 387, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first consider the fast-stream scenario, where the stream reveals data at a high rate. We consider the simple baseline $ER$ [11], which performs one gradient step on a batch of 256 (128 revealed by the stream and 128 from memory) images at every stream step. The 128 images from memory are sampled uniformly. For simplicity and ease of comparison, we assume that $ER$ has a stream-model relative complexity of $\\mathcal{C}_S(ER) = 1$ . Consequently, any OCL method that is computationally more expensive than $ER$ will not keep up with the stream speed, and thus will be forced to skip training on a fraction of the incoming stream samples.", + "bbox": [ + 75, + 580, + 468, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benchmarking Relative Complexity of OCL Methods. As discussed earlier, we use the total number of FLOPs required for each method to train on a stream as a proxy for the stream-model relative complexity $\\mathcal{C}_S$ . We first compute the total FLOPs required to train $ER$ on a small subset of CLOC composed of $10^3$ images with a batch size of 10. We then compute the corresponding FLOPs for various OCL methods and normalize them by the FLOPs of $ER$ . Since the backbone is shared across all methods, we further verify this normalized complexity by counting the effective number of", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "forward and backward passes of each method. Because we assume that $ER$ is effectively as fast as the stream, methods that are twice more expensive in FLOPs have a complexity $\\mathcal{C}_S$ of 2. We report in Table 1 the stream-model relative complexity for OCL methods compared against $ER$ . Note that PoLRS is 3 times as expensive as $ER$ since it requires training 3 different models to update the learning rate. In addition to the 128 images revealed by the stream and the 128 images sampled from memory at step $t$ , GSS performs additional forward and backward passes on $10 \\times 128$ memory samples to ensure diversity when updating the memory buffer [4]. Therefore, GSS is roughly 6 times more expensive than $ER$ . For each method in Table 1, we report the corresponding delay in stream steps, which is a consequence of some methods being slower than the stream. A delay of 2 means that the stream will reveal 2 steps worth of images before the model is updated.", + "bbox": [ + 496, + 90, + 893, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Training Efficiency. We start our analysis by investigating the effect of training efficiency on the performance of different OCL methods under the real-time evaluation setup. We plot the Average Online Accuracy curves per step in Figure 3, where the simple $ER$ baseline is in blue. Each method is evaluated according to its corresponding training delay reported in Table 1. Surprisingly, $ER$ outperforms all considered methods, and in some cases, by large margins. Interestingly, the most computationally intensive methods, MIR, PoLRS, and GSS, exhibit the lowest performance when real-time evaluation is considered. Specifically, the performance gap at the end of the stream reaches $11\\%$ . In fact, we note that the Average Online Accuracy values of all considered methods, irrespective of how recently they were introduced to the literature, are approximately ordered based on their stream-model relative complexity $\\mathcal{C}_S$ ; the larger $\\mathcal{C}_S$ is, the worse the performance is under real-time evaluation. We attribute this trend to the fact that these inefficient methods may not be capable of keeping up with the fast-changing distribution $\\mathcal{D}_j$ in the stream when they are subjected to a higher delay. For example, although PoLRS was proposed and tailored for the recent CLOC benchmark, it is significantly outperformed by the older method LwF when evaluated under the real-time paradigm. This hints that computational complexity can be a crutch for OCL methods learning on fast streams. Our results show that while the current literature aims to improve learning by leveraging more expensive and advanced learning routines, the penalty incurred by delay overshadows any potential improvements gained by the algorithmic contributions. Notably, the state-of-the-art ACE method, which is as efficient as $ER$ and thus evaluated under no training delay, performs almost as well as the baseline. Additionally, ACE outperforms more expensive methods when evaluated on small-scale datasets (refer to Small-Scale Experiments in the appendix). Overall, our findings suggest that practical", + "bbox": [ + 496, + 356, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11893", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f74505de5b70156da21c02dd8556dd29595539593a046e27e7ab430c53d6775e.jpg", + "image_caption": [ + "Figure 4. Fast Stream - Training Data Normalization. We compare each method against $ER$ and its delayed version $ER$ --. $ER$ -- performs extra gradient steps per time step to match the delay of the compared-against method, so it trains on fewer samples than $ER$ . We highlight that even when $ER$ -- is unfairly delayed to match each OCL method's delay, it outperforms all considered methods." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 264, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/94696f6633f3e79b6521a91eab3b65c59ac7623ae91f6e21ff77dbb61a904e6a.jpg", + "image_caption": [], + "image_footnote": [ + "ER (Delay = 0)" + ], + "bbox": [ + 264, + 85, + 419, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/434031a633944b9cea70c55f89ae82566fa3c9c5656d7dcb170561b4870d87d3.jpg", + "image_caption": [], + "image_footnote": [ + "ER--" + ], + "bbox": [ + 421, + 85, + 576, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/404a156c262df767b865239b0bb311c6c930065bff99c1cebb502b26a1b685a4.jpg", + "image_caption": [], + "image_footnote": [ + "OCL Method" + ], + "bbox": [ + 576, + 85, + 730, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf84bfb97c21b6ee7efc5bcd81f393c064aab76338c5cbb9663d258bbe317882.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 85, + 888, + 231 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "OCL methods, deployed in real-time applications, should prioritize efficient learning over expensive optimization.", + "bbox": [ + 75, + 311, + 470, + 343 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Data Normalization. Previously, we have shown that delayed evaluation leads to larger performance degradation as the delay gets longer. However, this could be attributed to the fact that OCL methods with larger delays end up effectively training on a fewer number of samples. This raises the questions: Do computationally more expensive methods with delays perform worse than ER because they cannot cope with the changing distribution in the stream? or is the performance degradation due to expensive OCL methods being trained on effectively a fewer number of training examples? To address these questions, we conduct pairwise comparisons between $ER$ and each previously reported OCL method. Assuming that the stream speed is fixed, we modify $ER$ to match the computational expense of the respective method by training on the same amount of data for a longer duration. To achieve this computational matching, we subject $ER$ to a delay by performing additional gradient descent steps at each stream step. We refer to this modified baseline as $ER$ --. The number of additional updates in $ER$ -- is determined such that its delay matches the delay of the corresponding OCL method. This guarantees that $ER$ -- trains on the same number of training examples compared to other OCL methods.", + "bbox": [ + 75, + 349, + 472, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 4 shows comparisons of $ER$ and $ER$ - to each of the considered OCL methods. Since the non-delayed $ER$ is more efficient than $ER$ -, $ER$ consistently outperforms $ER$ -, confirming that efficiency is key for the real-time evaluation of OCL. More interestingly, even though $ER$ - matches the complexity of each compared-against method and is subject to the same delay, it still outperforms all considered OCL methods. Moreover, while the gap between $ER$ - and expensive approaches, e.g. GSS, is smaller than the gap to $ER$ , expensive methods still lag behind $ER$ - by up to $3.5\\%$ . This demonstrates that the degraded performance of considered OCL methods is not due to the fewer number of observed training examples. On the contrary, expensive OCL meth", + "bbox": [ + 75, + 703, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ods seem to be unable to cope with distribution-changing streams. Under real-time evaluations of fast streams, simple methods such as $ER$ and $ER$ --- may be more suitable for real-world deployment.", + "bbox": [ + 496, + 311, + 893, + 373 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Slow Stream: Complexity Normalization", + "text_level": 1, + "bbox": [ + 498, + 388, + 849, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the fast stream setting, we considered the scenario where the stream is as fast as the $ER$ baseline, i.e., $\\mathcal{C}_S(ER) = 1$ . In this section, we consider streams that are as slow as the more expensive OCL methods. This setup motivates the following question: How do existing OCL methods perform if they were deployed on streams that match their training complexity? Slower streams may enable expensive methods to train on the entire stream, without having to skip any stream steps. Would previously considered methods, which struggled in the fast-stream setting, be suitable for OCL deployment in this slow-stream scenario? We compare various OCL methods under no delay against their corresponding modified baseline $ER++$ , which computes additional number of gradient steps per batch to match the complexity of the compared-against method, as determined from Table 1. This mimics the comparison on slow stream speeds, where no stream steps are skipped and comparisons are performed under normalized complexity. Note that ACE only modifies the loss objective of $ER$ , so it matches the complexity of the baseline $\\mathcal{C}_S(ACE) = 1$ . As a result, evaluating ACE in the slow-stream setting is identical to evaluating it in the fast-stream setting, which was already done in Figure 3. Therefore, we do not compare to ACE again in the following experiments.", + "bbox": [ + 496, + 414, + 893, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report the comparisons in Figure 5, where $ER++$ is shown in green and OCL methods in red. Moreover, we show $ER$ , which is unfavorably compared against both, in blue. While RWalk outperforms $ER$ in the slow stream setting, this is an unfair comparison, since $ER$ is not utilizing the fact that the stream is slow and that it can benefit from further training. Once we simply add a few iterations to $ER$ , i.e., $ER++$ , so as to match the training complexity of", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11894", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d3f25cf2d9015f09e296ed1a238df00064334ea23d3b21e2fb3c0008147157ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 85, + 264, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6630fb7cff583696e401548c7c32edfe9dd8f40315d96079a762c47684eea8f.jpg", + "image_caption": [ + "Figure 5. Slow Stream. We compare each method against $ER$ and $ER++$ , which performs extra gradient steps per time step to match the complexity $\\mathcal{C}_S$ of the compared-against method. $ER++$ outperforms all the considered methods, sometimes by large margins." + ], + "image_footnote": [], + "bbox": [ + 266, + 85, + 419, + 246 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a6da4bdbc97996e541ab3556a2dfd0bb1d8cc1aa7ae09ea761170fe71e31b299.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 85, + 575, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b43a29557df01c9d0116ac6b445f9abcacf6870e8af616547e2b1ed9548438e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 85, + 730, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48233bb0d19a7ca97bfac45805a187e8c0b4744fb019e9ab605cbd543970246c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 85, + 888, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RWalk, $ER++$ performs far better than RWalk. We find this to be consistent across all methods.", + "bbox": [ + 75, + 301, + 468, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interestingly, computationally intensive methods, e.g., GSS and MIR, perform worse even when compared to $ER$ , which does not exploit the fact that the stream is slow. $ER++$ is significantly better than GSS and MIR, by $17\\%$ and $11\\%$ respectively, expanding the performance gap to the baseline by around $15\\%$ and $7\\%$ . These results question the suitability of the previously proposed methods to realistic OCL setups with large-scale datasets. Moreover, our results suggest that a computationally unfair evaluation setup (i.e. not normalizing training complexity) in slow stream OCL can lead to misleading performance conclusions, as is the case with RWalk. We highlight that PoLRS was originally tested on a slightly different setup to the slow stream, which included extra information represented by a user album [7]. We find that when the album information is removed and their reported baseline, i.e., $ER$ , is tuned properly, PoLRS has a similar performance to $ER$ as shown in Figure 5. This is still surprising since PoLRS is three times more expensive than $ER$ . More surprisingly, when matching the training complexity of $ER$ to PoLRS on the slow stream, $ER++$ outperforms PoLRS by $9.5\\%$ . These results on the slow-stream setting support our earlier observation that current OCL methods are not yet suited for practical deployment.", + "bbox": [ + 75, + 333, + 468, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Effect of Memory Size", + "text_level": 1, + "bbox": [ + 76, + 694, + 284, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct experiments to test whether existing methods can outperform $ER$ under different memory buffer sizes. We repeat the fast-stream experiment from Section 4.1 with memory budgets of $1 \\times 10^{4}$ , $2 \\times 10^{4}$ , and $4 \\times 10^{4}$ samples. The results are summarized in Table 2. A larger memory size leads to a higher Average Online Accuracy across all methods. However, we emphasize that the trend across methods aligns with our previous finding that expensive-training OCL methods perform worse than their less expensive counterparts. This is evident from the ordering of the methods in Figure 3, which holds regardless of the memory budget. Notably, $ER$ outperforms all considered methods.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e7c78f32cad99650d1e80cc9ccdff74ea562659487700a5748830e687a08fc48.jpg", + "table_caption": [ + "Table 2. Memory Budget Analysis. We test the effect of varying the memory budget in the fast-stream setting. We observe that 1) increasing the memory size results in better performance regardless of the method, and 2) ER outperforms all the considered methods regardless of the memory budget." + ], + "table_footnote": [], + "table_body": "
MethodMemory Size
1 × 1042 × 1044 × 104
ER [11]18.0919.3720.27
ACE [6]17.5318.5519.42
LwF [28]16.8717.8718.69
RWalk [8]14.6015.2916.07
PoLRS [7]12.4012.9813.59
MIR [3]11.3711.6411.89
GSS [4]8.018.599.10
", + "bbox": [ + 549, + 375, + 839, + 539 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 554, + 617, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a real-time evaluation benchmark for online continual learning, including a fast stream that continues to reveal new data even when the model has not completed training. This realistic setup forces computationally intensive methods to skip more training samples, highlighting the differences in training complexity between the considered methods. Our results show that, under this setting, all considered methods underperform the simple $ER$ baseline. We also explored scenarios where we normalized the number of seen training data or the computational complexity per time step, leading to the same conclusion that current methods are not yet optimized for real-world deployment.", + "bbox": [ + 496, + 580, + 890, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence (SDAIA-KAUST AI), Saudi Aramco, and UKRI grant Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ameya Prabhu is funded by Meta AI Grant No DFR05540.", + "bbox": [ + 496, + 763, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11895", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Motasem Alfarra, Zhipeng Cai, Adel Bibi, Bernard Ghanem, and Matthias Müller. Simcs: Simulation for online domain-incremental continual segmentation. arXiv preprint arXiv:2211.16234, 2022. 1", + "[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In European Conference on Computer Vision (ECCV), 2018. 1, 2", + "[3] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. 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In International Conference on Machine Learning (ICML), 2017. 1" + ], + "bbox": [ + 501, + 92, + 890, + 771 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11897", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_model.json b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..940ac9f8612261e9e63901a632eb697627d70594 --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_model.json @@ -0,0 +1,2024 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.131, + 0.753, + 0.176 + ], + "angle": 0, + "content": "Real-Time Evaluation in Online Continual Learning: A New Hope" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.204, + 0.286, + 0.22 + ], + "angle": 0, + "content": "Yasir Ghunaim\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.332, + 0.204, + 0.426, + 0.22 + ], + "angle": 0, + "content": "Adel Bibi\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.472, + 0.204, + 0.629, + 0.22 + ], + "angle": 0, + "content": "Kumail Alhamoud1" + }, + { + "type": "text", + "bbox": [ + 0.675, + 0.204, + 0.82, + 0.22 + ], + "angle": 0, + "content": "Motasem Alfarra1" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.221, + 0.363, + 0.239 + ], + "angle": 0, + "content": "Hasan Abed Al Kader Hammoud1" + }, + { + "type": "text", + "bbox": [ + 0.399, + 0.221, + 0.528, + 0.24 + ], + "angle": 0, + "content": "Ameya Prabhu2" + }, + { + "type": "text", + "bbox": [ + 0.562, + 0.221, + 0.698, + 0.24 + ], + "angle": 0, + "content": "Philip H.S. Torr" + }, + { + "type": "text", + "bbox": [ + 0.735, + 0.221, + 0.877, + 0.239 + ], + "angle": 0, + "content": "Bernard Ghanem1" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.25, + 0.834, + 0.269 + ], + "angle": 0, + "content": "\\(^{1}\\) King Abdullah University of Science and Technology (KAUST) \\(^{2}\\) University of Oxford" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.303, + 0.314, + 0.319 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.473, + 0.683 + ], + "angle": 0, + "content": "Current evaluations of Continual Learning (CL) methods typically assume that there is no constraint on training time and computation. This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical real-time evaluation of continual learning, in which the stream does not wait for the model to complete training before revealing the next data for predictions. To do this, we evaluate current CL methods with respect to their computational costs. We conduct extensive experiments on CLOC, a large-scale dataset containing 39 million time-stamped images with geolocation labels. We show that a simple baseline outperforms state-of-the-art CL methods under this evaluation, questioning the applicability of existing methods in realistic settings. In addition, we explore various CL components commonly used in the literature, including memory sampling strategies and regularization approaches. We find that all considered methods fail to be competitive against our simple baseline. This surprisingly suggests that the majority of existing CL literature is tailored to a specific class of streams that is not practical. We hope that the evaluation we provide will be the first step towards a paradigm shift to consider the computational cost in the development of online continual learning methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Deep Neural Networks (DNNs) have demonstrated impressive success in solving complex tasks [20, 29, 42] when trained offline, for several passes, over large well-curated labeled datasets. However, in many real-world scenarios, data is only available in the form of a stream with a changing distribution. Due to this challenge, there has been a growing interest in the problem of learning from a time-varying stream, also known as Continual Learning (CL), which is" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.305, + 0.892, + 0.365 + ], + "angle": 0, + "content": "a key challenge for DNNs due to a phenomenon known as catastrophic forgetting [17, 36]. In particular, when a DNN is trained with data from a new distribution, the DNN performance significantly drops on previously learned data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.893, + 0.533 + ], + "angle": 0, + "content": "While mitigation efforts have been proposed, e.g. through regularizing the training [2, 25, 53], replaying previously seen examples [11, 23, 39], and many other approaches [16, 40, 51], current evaluation approaches are still far from real-world scenarios. For example, the majority of literature is on Offline Continual Learning, under which methods are allowed unlimited budget, both time and computation. Furthermore, the majority of CL evaluations are conducted on small-scale datasets with well-defined temporal distribution boundaries in the form of learning a sequence of tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.895, + 0.673 + ], + "angle": 0, + "content": "To that end, there has recently been a growing interest in the more realistic setting - Online Continual Learning (OCL). In such a setup [1, 4, 21, 32], CL methods are restricted to a single training pass over a shuffled split of existing offline CL benchmarks. This is certainly a step forward towards resolving some of the unrealistic assumptions of offline CL. However, current evaluations do not sufficiently address the challenges of real-time learning for high-throughput streams with rapid distribution changes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To illustrate this, consider the problem of continuously learning a Twitter stream where 350K tweets are uploaded per minute on various trending topics [41]. Every uploaded tweet needs to be predicted with a DNN for misinformation and hate speech, among other things, while simultaneously learning and adapting to them. Given the scale at which data is being updated, there is an inherent key limitation on the time and computational budget affordable to learning incoming tweets, an aspect that is often overlooked in the prior art from the OCL literature. Consider an OCL method that is 10 times slower than the Twitter high throughput stream, i.e., it takes 10 minutes to train on one minute worth of tweets (350K tweets). This inefficiency results in an accumulation of \\(\\sim 3.1\\) million new samples that need to be predicted and trained on. Since it is not acceptable to pause" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.863, + 0.22, + 0.876 + ], + "angle": 0, + "content": "* Equal Contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.877, + 0.415, + 0.889 + ], + "angle": 0, + "content": "Correspondence to: yasir.ghunaim@kaust.edu.sa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.889, + 0.36, + 0.9 + ], + "angle": 0, + "content": "Code: github.com/Yasir-Ghunaim/RealtimeOCL" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11888" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.093, + 0.887, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Figure 1. OCL Real-Time Evaluation Example. We show an example of real-time evaluation, using the CLOC dataset [7], of two different OCL methods \\(\\mathcal{A}\\) and \\(\\mathcal{B}\\). Method \\(\\mathcal{B}\\) is twice as slow as method \\(\\mathcal{A}\\). Both methods are evaluated on every incoming sample. Since \\(\\mathcal{A}\\) has a stream-model relative complexity of one, i.e. \\(\\mathcal{C}_S(\\mathcal{A}) = 1\\), it is able to train on all the stream samples. In contrast, \\(\\mathcal{B}\\), which has a relative complexity of two, requires two time steps to train on a single stream batch. Thus, \\(\\mathcal{B}\\) only trains on half of the stream samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.538 + ], + "angle": 0, + "content": "all tweets from appearing online until the method training is complete, predictions for all new samples will be performed with an older version of the model. This poses a key challenge where efficient learning from streams becomes necessary. This is because slow-training OCL methods can result in subpar performance, as they resort to predicting new stream data using an older model. This behavior worsens for streams that experience a faster change in distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.469, + 0.795 + ], + "angle": 0, + "content": "In this paper, we propose a real-time evaluation protocol for OCL that factors in training computational complexity. Given a stream, consider an OCL method \\(\\mathcal{A}\\) that is as fast as the stream, i.e., \\(\\mathcal{A}\\) can train on every step of revealed data before the stream presents new samples. Then, if an OCL \\(\\mathcal{B}\\) is twice as expensive as \\(\\mathcal{A}\\), then \\(\\mathcal{B}\\) will update the model for evaluation every other stream step, i.e., the model will be updated half the number of times compared to \\(\\mathcal{A}\\). Figure 1 illustrates our proposed real-time evaluation. This is in contrast to all prior art [3,4,6] that (1) unreasonably allows an unlimited computational budget to train on any given stream data, and (2) unfairly compares OCL methods despite having different training complexity levels. Using our real-time evaluation protocol, we benchmark many existing OCL methods against a simple and inexpensive baseline, which mitigates forgetting by simply storing and replaying recently seen samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Contributions. We summarize our conclusions as follows: (1) We show that under our practical real-time evaluation, our simple baseline outperforms all the considered methods from the OCL literature, including recent SOTA approaches like ACE [6]. (2) We consider a complementary setup where the stream is as slow as the most training-expensive OCL method and compare that method against" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.893, + 0.568 + ], + "angle": 0, + "content": "the compute-equivalent baseline. Under this computationally normalized setting, we find that the compute-equivalent baseline outperforms all existing methods. (3) Our experiments are consistent, holding for all the considered continual learning strategies, and extensive, amounting to more than 2 GPU-months. Our results highlight that the current progress in OCL needs to be rethought and a paradigm shift is needed. We hope our work will lead to a new direction for continual learning that takes into account the computational cost of each method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.585, + 0.642, + 0.601 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.672 + ], + "angle": 0, + "content": "We briefly describe the current literature on offline and online continual learning. For a more comprehensive overview of the literature, we refer the reader to the detailed surveys by De Lange et al. [13] and Mai et al. [33]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Offline Continual Learning. Traditional continual learning strategies, which aim to mitigate forgetting, can be organized into three families of methods. (i) Replay-based methods store input samples, or alternatively learn to generate representative samples, while the model learns from the data stream. Later, the method retransmits the model on the replay samples while the model learns from new data [32, 35, 45, 49, 50]. (ii) Regularization methods avoid the cost of storing samples and simply modify the model loss objective to regularize the training. While some of these methods penalize changes to important model parameters [2, 8, 25], other methods regularize the training by distilling knowledge from a model trained on past stream samples [18, 28, 46]. (iii) Parameter isolation methods train specific parameters for each task while freezing the param-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11889" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "eters that are related to other tasks [22, 34, 40]. Despite the progress made by these methods, they assume an offline stream that allows many passes over each continual learning task. Concurrent work Prabhu et al. [37] alleviates this problem by imposing computational budget constraints and finds that simple methods based on experience replay outperform most prior continual learning works. In contrast, we study the more pragmatic setup, where the stream reveals data in real time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.473, + 0.476 + ], + "angle": 0, + "content": "Online Learning for Reduced Forgetting. OCL was defined with a protocol where training data is only seen once in a sequence of labeled tasks [32]. To reduce catastrophic forgetting, the field initially progressed towards better gradient-based constraints like GEM [32] and AGEM [10]. RWalk [8] quantified forgetting and provided a more efficient approach to limit changes in important model parameters. TinyER [11] rediscovered the effectiveness of experience replay, and HAL [9] enhanced it with learned anchors. However, this setup assumes the availability of an oracle during test time to determine which classifier head to use for inference [33, 48]. Additionally, the benchmarks in this setup often have large constraints on the replay buffer size [10, 11]. Due to these limitations, the class-incremental scenario started to gain attention, which is a more realistic setting for OCL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In class-incremental online continual learning, benchmarks [3, 27] relaxed the need for task descriptors at test time, and introduced significantly larger buffer sizes in comparison to [10]. Multiple directions have emerged to tackle catastrophic forgetting in this setup. They can be classified into few groups. (i) Regularization-based approaches modify the classification objective to preserve previously learned representations or encourage more meaningful representations e.g. DER [5], ACE [6], and CoPE [14]. (ii) Sampling-based techniques focus on the optimal selection and storing of the most representative replay memory during online training, e.g. GSS [4], OCS [52], CBRS [12], CLIB [26], and InfoRS [47]. Alternatively, some sampling methods focus on better memory retrieval strategies that reduce forgetting, e.g. MIR [3], ASER [44], and GMED [24]. (iii) In other approaches, GDumb [38] proposed a degenerate solution to the problem of online learning ignoring the stream data and learning only on the memory samples. While these efforts have significantly advanced the field of OCL, they are mostly evaluated on benchmarks that do not reflect real-deployment conditions. First, these benchmarks heavily rely on artificially constructed small datasets with sudden shifts in classes. Second, these benchmarks are incapable of measuring whether models can rapidly adapt to new data under a fast-changing distribution shift, which is one of the main problems in classical online learning literature [43]. There have been efforts to address the second limitation by using new metrics that measure test accuracy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "more frequently during training [6, 26]. However, these metrics capture the adaptation to held-out test data rather than to the incoming future data. To remedy these limitations, there has been a new surge of benchmarks proposing datasets and evaluation protocols, which we discuss next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.893, + 0.472 + ], + "angle": 0, + "content": "Online Learning for Rapid Adaptation. Recent OCL benchmarks, e.g. CLOC [7] and CLEAR [30], introduce data ordered by timestamps, forming a temporal stream of evolving visual concepts over a long span of time. They demonstrate that their data has a natural distribution shift over time, requiring rapid adaptation to newer data. Additionally, they mimic the traditional online learning setup by measuring the capacity for rapid adaptation with the evaluation being done on future data from the stream. Our work extends the efforts in this direction. We adopt the CLOC benchmark and propose a more realistic real-time evaluation that encourages efficient learning. It is worth mentioning that [19] has explored certain aspects of real-time evaluation in continual learning. However, they focus on efficiency for embedded device deployment, rather than rapid adaptation. Moreover, while their work investigates the computational cost associated with each training method, they only report the cost as an evaluation metric. In contrast, we constrain the training procedure by each method's computational cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.636, + 0.503 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.572 + ], + "angle": 0, + "content": "We start with the classical problem statement for online continual learning. Then, we formally introduce our proposed real-time evaluation that factors in training complexity through delayed evaluations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.747, + 0.596 + ], + "angle": 0, + "content": "3.1. Online Continual Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Online continual learning [7, 43] is the problem of learning a \\(\\theta\\) parameterized function \\(f_{\\theta}:\\mathcal{X}\\to \\mathcal{V}\\) that predicts a label \\(y\\in \\mathcal{V}\\) for an input image \\(x\\in \\mathcal{X}\\). Unlike, classical supervised learning, the learning is performed on a distribution-varying stream \\(\\mathcal{S}\\) revealing data sequentially over steps \\(t\\in \\{1,2,\\dots ,\\infty \\}\\). In particular, at every step \\(t\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.701, + 0.818, + 0.72 + ], + "angle": 0, + "content": "1. \\(S\\) reveals a set of images \\(\\{x_i^t\\}_{i = 1}^{n_t}\\sim \\mathcal{D}_{j\\leq t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.726, + 0.842, + 0.745 + ], + "angle": 0, + "content": "2. \\(f_{\\theta_t}\\) generates predictions \\(\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}\\) for \\(\\{x_i^t\\}_{i = 1}^{n_t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.751, + 0.733, + 0.769 + ], + "angle": 0, + "content": "3. \\(S\\) reveals true labels \\(\\{y_i^t\\}_{i = 1}^t\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.775, + 0.868, + 0.794 + ], + "angle": 0, + "content": "4. \\(f_{\\theta_t}\\) is evaluated by comparing \\(\\{\\tilde{y}_i^t\\}_{i=1}^{n_t}\\) to \\(\\{y_i^t\\}_{i=1}^{n_t}\\);" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.801, + 0.892, + 0.832 + ], + "angle": 0, + "content": "5. A learning method trains \\( f_{\\theta_t} \\), a criterion computes the training loss, then the parameters are updated to \\( \\theta_{t + 1} \\)." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.701, + 0.892, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Note that \\(\\mathcal{D}_{j\\leq t}\\) denotes a varying distribution that might not necessarily need to change at every stream step \\(t\\) .For example, if at step \\(t = 5\\) we have \\(j = 1\\) , this means the revealed data over all five previous steps is sampled from the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11890" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.868, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.321, + 0.896, + 0.392 + ], + "angle": 0, + "content": "Figure 2. OCL Real-Time Evaluation Setup. In OCL, models perform real-time prediction on each revealed sample from the stream. At the same time, model training is performed on the revealed samples dictated by the method's delay. In this example, we demonstrate the evaluation procedure when the stream-model complexity \\( k \\) is larger than 1. Due to the mismatch between the stream speed and the model computational cost, an \"older version\" of the model predicts samples while the model is being trained. Therefore, k-1 potential training batches are skipped for each training step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.471, + 0.468 + ], + "angle": 0, + "content": "same distribution \\(\\mathcal{D}_1\\). Moreover, observe that, unlike offline continual learning, online continual learning captures the capacity to adapt to new data since the prediction is performed before the training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.668 + ], + "angle": 0, + "content": "Key Issues. As described earlier, the OCL evaluation in the literature [7, 43] overlooks the training complexity in step (5). Under such a setup, all OCL methods have their parameters updated to \\(\\theta_{t + 1}\\) before the stream \\(S\\) reveals images of the next step. Therefore, different OCL methods are evaluated irrespective of the training time and computational complexity at step (5). This is equivalent to evaluating different OCL methods on streams that present data at different rates. In real-time settings, the stream reveals data at a rate that is independent of the training complexity of the OCL method. To that end, we propose a real-time evaluation paradigm for OCL that factors in training complexity through delayed evaluations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.353, + 0.696 + ], + "angle": 0, + "content": "3.2. Real-Time Evaluation for OCL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "As mentioned earlier, we need to define a notion of a fixed stream rate. That is to say, the stream reveals data at a fixed rate irrespective of how long OCL methods take to update the model in step (5). For streams that are twice as fast as it takes to train \\( f_{\\theta} \\), OCL methods will have their model updated on only half the number of revealed sets of images from the stream. Note that the latest updated version of \\( f_{\\theta} \\) will continue to provide predictions for newly revealed images during training even for those images the model did not train on. This setting reflects the realistic scenario of a server receiving many queries uploaded by users, where each query needs a prediction irrespective of whether an in-house model is being trained. Given a stream \\( S \\) and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.895, + 0.574 + ], + "angle": 0, + "content": "an OCL method \\(\\mathcal{A}\\), we first define the notion of stream-model relative complexity \\(\\mathcal{C}_S(\\mathcal{A})\\in \\mathbb{R}^+\\). In particular, for a stream-model relative complexity \\(\\mathcal{C}_S(\\mathcal{A}) = 1\\), the continual learning method \\(\\mathcal{A}\\) can update the model \\(\\theta\\) in step (5) before the stream \\(S\\) reveals the data of the next step. For any stream-model relative complexity \\(\\mathcal{C}_A(\\mathcal{A}) = k > 1\\), the stream is \\(k\\)-faster than the continual learning method \\(\\mathcal{A}\\). With this notation, we now propose our modified version of the OCL setting along with the corresponding real-time evaluation. Given a model \\(f_{\\theta_m}\\), a stream \\(S\\), and an OCL method \\(\\mathcal{A}\\) with \\(\\mathcal{C}_S(\\mathcal{A}) = k\\), at every step \\(t\\)," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.582, + 0.818, + 0.6 + ], + "angle": 0, + "content": "1. \\(S\\) reveals a set of images \\(\\{x_{i}^{t}\\}_{i = 1}^{n_{t}}\\sim \\mathcal{D}_{j\\leq t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.605, + 0.848, + 0.623 + ], + "angle": 0, + "content": "2. \\(f_{\\theta_m}\\) generates predictions \\(\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}\\) for \\(\\{x_i^t\\}_{i = 1}^{n_t}\\);" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.733, + 0.647 + ], + "angle": 0, + "content": "3. \\(S\\) reveals true labels \\(\\{y_i^t\\}_{i = 1}^t\\)" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.653, + 0.874, + 0.671 + ], + "angle": 0, + "content": "4. \\(f_{\\theta_m}\\) is evaluated by comparing \\(\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}\\) to \\(\\{y_i^t\\}_{i = 1}^{n_t}\\);" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.677, + 0.892, + 0.723 + ], + "angle": 0, + "content": "5. If \\( \\mathrm{mod}(t - 1, k) = 0 \\), then the continual learner \\( \\mathcal{A} \\) completes updating \\( f_{\\theta_m} \\gets f_{\\theta_{m+1}} \\) and a new instance of training on \\( f_{\\theta_m} \\) commences (see Figure 2)." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.582, + 0.892, + 0.723 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.839 + ], + "angle": 0, + "content": "In this setting, OCL methods that are computationally more expensive to train will be updated fewer times. Therefore, for streams \\( S \\) where the distribution \\( \\mathcal{D}_j \\) changes rapidly (perhaps as often as every stream step), OCL methods with a large stream-model relative complexity may produce erroneous predictions, since the models are not updated enough and cannot adapt to the distribution change." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "On the Computation of \\(\\mathcal{C}_S\\). Since \\(\\mathcal{C}_S\\) only measures the relative complexity between the stream and an underlying continual learning method, we first introduce a minimal inexpensive OCL method as a baseline (denoted \\(\\mathcal{A}\\)). For ease" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11891" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.379 + ], + "angle": 0, + "content": "of comparison of the considered methods, we then assume that, due to the inexpensive nature of \\(\\mathcal{A}\\), online continual learning will be as fast as the stream where the stream-model relative complexity \\(\\mathcal{C}_{\\mathcal{S}} = 1\\). In particular, we consider a baseline that mitigates forgetting by simply storing and replaying recently seen samples. Then, given any other OCL method \\(\\mathcal{B}\\), we use the relative training FLOPs between \\(\\mathcal{B}\\) and \\(\\mathcal{A}\\) to determine \\(\\mathcal{C}_{\\mathcal{S}}(\\mathcal{B})\\). For example, ACE [6] only modifies the loss objective of the baseline, and thus it is equivalent to the baseline in computational complexity. On the other hand, PoLRS [7] maintains and performs operations on three copies of the model. These copies are trained on every incoming batch, making PoLRS require \\(3 \\times\\) the FLOPs needed by the baseline. As noted earlier, a method of a stream-model relative complexity value of 3 performs the update in step (5) once every three stream steps. This corresponds to a delay in model updates by two steps. In Table 1, we summarize the corresponding delay of several popular OCL methods in our real-time evaluation setup." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.472, + 0.562 + ], + "angle": 0, + "content": "Fair Comparison of OCL Methods with Different \\( \\mathcal{C}_{\\mathcal{S}} \\). We proposed a realistic setup of evaluating continual learners based on their training complexity with respect to the stream speed. However, one might argue that more expensive training routines could be accelerated by deploying more computational hardware allowing them to train on each revealed sample from the stream. For example, while PoLRS [7] requires \\( 3 \\times \\) more FLOPs than the simple baseline, one could deploy \\( 3 \\times \\) more hardware to make \\( \\mathcal{C}(\\mathcal{A}) = 1 \\) for PoLRS. This setup mimics the scenario of having a slow stream that matches the speed of the more expensive training method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.473, + 0.759 + ], + "angle": 0, + "content": "While the aforementioned setup normalizes the computational requirement of a given learning method \\(\\mathcal{A}\\) to match the stream speed, one should allow simpler training methods the same computational complexity. To that end, we propose boosting simpler and faster training methods to match the computational requirements of more complex methods. For example, we boost the simple experience replay method by sampling a larger number of instances from the replay buffer at each step \\(t\\) to match the FLOPs of other training schemes. We note here that although this modification is both simple and naive, we found empirically that it is sufficient to outperform all considered OCL methods. We leave the rest of the implementation details to Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.21, + 0.788 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We compare OCL methods under our proposed real-time evaluation setup given two stream speeds: fast and slow, which capture different application scenarios. We benchmark the majority of OCL methods, which we group into three categories. (1) Regularization-based OCL methods regularize training by modifying the classification loss. For example, RWalk [8] uses a regularizer to penalize abrupt" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.895, + 0.16 + ], + "angle": 0, + "content": "Table 1. Training complexity and delay of considered OCL methods. *Note that GSS has a complexity of 6.5 but we rounded it down to 6 to facilitate the setup. This rounding may give GSS a slight advantage, but nonetheless, it is outperformed by the baseline, ER, in all experiments." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.17, + 0.885, + 0.33 + ], + "angle": 0, + "content": "
CL StrategyMethod(A)C_S(A)Delay
Experience ReplayER [11]10
RegularizationsACE [6]10
LwF [28]4/31/3
RWalk [8]21
LR SchedulerPoLRS [7]32
Sampling StrategiesMIR [3]5/23/2
GSS [4]6*5
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.895, + 0.486 + ], + "angle": 0, + "content": "changes in the parameters of the model. ACE [6] introduces an asymmetric loss to treat memory buffer samples differently from incoming stream samples, while LwF [28] distills knowledge from previous steps. (2) Learning rate scheduler methods, in this case PoLRS [7], dynamically adapt the learning rate to changes in the stream distribution. (3) Sampling-based methods alter the strategy used to update the memory buffer, e.g. GSS [4], or change the memory retrieval strategy, e.g. MIR [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.895, + 0.7 + ], + "angle": 0, + "content": "Datasets. We use the large-scale online continual learning dataset CLOC [7], which contains 39 million time-stamped images exhibiting natural distribution shifts. The task is to identify the geolocation of a given image where the total number of geolocation labels is 712. To ensure consistency with CLOC [7], we adopt the same dataset split approach. Specifically, we use the first \\(5\\%\\) of the stream for hyperparameter selection, uniformly sample \\(1\\%\\) from the remaining stream to build a held-out set for measuring backward/forward transfer (reported in the appendix), and utilize the rest of the stream for training and online evaluation. Similar to CLOC [7], we compare OCL methods using the Average Online Accuracy metric, which measures the ability of models to adapt to incoming stream samples1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.853 + ], + "angle": 0, + "content": "Implementation Details. At each step \\( t \\) during the experiments, \\( S \\) reveals a set of 128 images, and OCL methods augment the training batch with another 128 images sampled from a memory buffer. This routine is performed until a single pass over the stream is completed. We use ImageNet [15] pre-trained ResNet50 [7, 20] as a backbone. We use SGD with a learning rate of \\( 5 \\times 10^{-3} \\) for all OCL methods except for PoLRS [7], which works best with a learning rate of \\( 1 \\times 10^{-3} \\). Unless otherwise stated, we set the size of the replay buffer to \\( 4 \\times 10^{4} \\) for all considered methods. We" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This metric should not be mistaken for a training accuracy, as it evaluates the model on the next unseen training batch before the batch is used for model training." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11892" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.442, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.321, + 0.472, + 0.406 + ], + "angle": 0, + "content": "Figure 3. Fast Stream Evaluation. We compare the Average Online Accuracy of six methods from the OCL literature evaluated under the fast-stream setting. We observe that our inexpensive baseline, ER, outperforms all the considered methods. Surprisingly, the most computationally complex methods, MIR, PoLRS, and GSS, underperform the more efficient methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.545 + ], + "angle": 0, + "content": "use the same hyperparameters reported in all corresponding papers with the exception of the regularization parameter for RWalk [8]. We find that their reported regularization \\(\\lambda = 0.1\\) is too small for the CLOC dataset; we cross validate it and find that \\(\\lambda = 2\\) works best. Our implementation extends the codebase of Avalanche [31], which is a popular continual learning framework. We leave all the remaining implementation details and ablations to the appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.388, + 0.572 + ], + "angle": 0, + "content": "4.1. Fast Stream: Real-Time Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.748 + ], + "angle": 0, + "content": "We first consider the fast-stream scenario, where the stream reveals data at a high rate. We consider the simple baseline \\(ER\\) [11], which performs one gradient step on a batch of 256 (128 revealed by the stream and 128 from memory) images at every stream step. The 128 images from memory are sampled uniformly. For simplicity and ease of comparison, we assume that \\(ER\\) has a stream-model relative complexity of \\(\\mathcal{C}_S(ER) = 1\\). Consequently, any OCL method that is computationally more expensive than \\(ER\\) will not keep up with the stream speed, and thus will be forced to skip training on a fraction of the incoming stream samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Benchmarking Relative Complexity of OCL Methods. As discussed earlier, we use the total number of FLOPs required for each method to train on a stream as a proxy for the stream-model relative complexity \\( \\mathcal{C}_S \\). We first compute the total FLOPs required to train \\( ER \\) on a small subset of CLOC composed of \\( 10^3 \\) images with a batch size of 10. We then compute the corresponding FLOPs for various OCL methods and normalize them by the FLOPs of \\( ER \\). Since the backbone is shared across all methods, we further verify this normalized complexity by counting the effective number of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.351 + ], + "angle": 0, + "content": "forward and backward passes of each method. Because we assume that \\( ER \\) is effectively as fast as the stream, methods that are twice more expensive in FLOPs have a complexity \\( \\mathcal{C}_S \\) of 2. We report in Table 1 the stream-model relative complexity for OCL methods compared against \\( ER \\). Note that PoLRS is 3 times as expensive as \\( ER \\) since it requires training 3 different models to update the learning rate. In addition to the 128 images revealed by the stream and the 128 images sampled from memory at step \\( t \\), GSS performs additional forward and backward passes on \\( 10 \\times 128 \\) memory samples to ensure diversity when updating the memory buffer [4]. Therefore, GSS is roughly 6 times more expensive than \\( ER \\). For each method in Table 1, we report the corresponding delay in stream steps, which is a consequence of some methods being slower than the stream. A delay of 2 means that the stream will reveal 2 steps worth of images before the model is updated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.904 + ], + "angle": 0, + "content": "Effect of Training Efficiency. We start our analysis by investigating the effect of training efficiency on the performance of different OCL methods under the real-time evaluation setup. We plot the Average Online Accuracy curves per step in Figure 3, where the simple \\(ER\\) baseline is in blue. Each method is evaluated according to its corresponding training delay reported in Table 1. Surprisingly, \\(ER\\) outperforms all considered methods, and in some cases, by large margins. Interestingly, the most computationally intensive methods, MIR, PoLRS, and GSS, exhibit the lowest performance when real-time evaluation is considered. Specifically, the performance gap at the end of the stream reaches \\(11\\%\\). In fact, we note that the Average Online Accuracy values of all considered methods, irrespective of how recently they were introduced to the literature, are approximately ordered based on their stream-model relative complexity \\(\\mathcal{C}_S\\); the larger \\(\\mathcal{C}_S\\) is, the worse the performance is under real-time evaluation. We attribute this trend to the fact that these inefficient methods may not be capable of keeping up with the fast-changing distribution \\(\\mathcal{D}_j\\) in the stream when they are subjected to a higher delay. For example, although PoLRS was proposed and tailored for the recent CLOC benchmark, it is significantly outperformed by the older method LwF when evaluated under the real-time paradigm. This hints that computational complexity can be a crutch for OCL methods learning on fast streams. Our results show that while the current literature aims to improve learning by leveraging more expensive and advanced learning routines, the penalty incurred by delay overshadows any potential improvements gained by the algorithmic contributions. Notably, the state-of-the-art ACE method, which is as efficient as \\(ER\\) and thus evaluated under no training delay, performs almost as well as the baseline. Additionally, ACE outperforms more expensive methods when evaluated on small-scale datasets (refer to Small-Scale Experiments in the appendix). Overall, our findings suggest that practical" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11893" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.265, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.087, + 0.42, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.087, + 0.577, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.578, + 0.087, + 0.732, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.087, + 0.89, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.328, + 0.235, + 0.446, + 0.248 + ], + "angle": 0, + "content": "ER (Delay = 0)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.468, + 0.235, + 0.584, + 0.248 + ], + "angle": 0, + "content": "ER--" + }, + { + "type": "image_footnote", + "bbox": [ + 0.585, + 0.235, + 0.662, + 0.248 + ], + "angle": 0, + "content": "OCL Method" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.895, + 0.298 + ], + "angle": 0, + "content": "Figure 4. Fast Stream - Training Data Normalization. We compare each method against \\(ER\\) and its delayed version \\(ER\\)--. \\(ER\\)-- performs extra gradient steps per time step to match the delay of the compared-against method, so it trains on fewer samples than \\(ER\\). We highlight that even when \\(ER\\)-- is unfairly delayed to match each OCL method's delay, it outperforms all considered methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.471, + 0.344 + ], + "angle": 0, + "content": "OCL methods, deployed in real-time applications, should prioritize efficient learning over expensive optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.473, + 0.699 + ], + "angle": 0, + "content": "Training Data Normalization. Previously, we have shown that delayed evaluation leads to larger performance degradation as the delay gets longer. However, this could be attributed to the fact that OCL methods with larger delays end up effectively training on a fewer number of samples. This raises the questions: Do computationally more expensive methods with delays perform worse than ER because they cannot cope with the changing distribution in the stream? or is the performance degradation due to expensive OCL methods being trained on effectively a fewer number of training examples? To address these questions, we conduct pairwise comparisons between \\(ER\\) and each previously reported OCL method. Assuming that the stream speed is fixed, we modify \\(ER\\) to match the computational expense of the respective method by training on the same amount of data for a longer duration. To achieve this computational matching, we subject \\(ER\\) to a delay by performing additional gradient descent steps at each stream step. We refer to this modified baseline as \\(ER\\)--. The number of additional updates in \\(ER\\)-- is determined such that its delay matches the delay of the corresponding OCL method. This guarantees that \\(ER\\)-- trains on the same number of training examples compared to other OCL methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Figure 4 shows comparisons of \\(ER\\) and \\(ER\\)- to each of the considered OCL methods. Since the non-delayed \\(ER\\) is more efficient than \\(ER\\)-, \\(ER\\) consistently outperforms \\(ER\\)-, confirming that efficiency is key for the real-time evaluation of OCL. More interestingly, even though \\(ER\\)- matches the complexity of each compared-against method and is subject to the same delay, it still outperforms all considered OCL methods. Moreover, while the gap between \\(ER\\)- and expensive approaches, e.g. GSS, is smaller than the gap to \\(ER\\), expensive methods still lag behind \\(ER\\)- by up to \\(3.5\\%\\). This demonstrates that the degraded performance of considered OCL methods is not due to the fewer number of observed training examples. On the contrary, expensive OCL meth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.895, + 0.374 + ], + "angle": 0, + "content": "ods seem to be unable to cope with distribution-changing streams. Under real-time evaluations of fast streams, simple methods such as \\(ER\\) and \\(ER\\)--- may be more suitable for real-world deployment." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.389, + 0.851, + 0.407 + ], + "angle": 0, + "content": "4.2. Slow Stream: Complexity Normalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.779 + ], + "angle": 0, + "content": "In the fast stream setting, we considered the scenario where the stream is as fast as the \\(ER\\) baseline, i.e., \\(\\mathcal{C}_S(ER) = 1\\). In this section, we consider streams that are as slow as the more expensive OCL methods. This setup motivates the following question: How do existing OCL methods perform if they were deployed on streams that match their training complexity? Slower streams may enable expensive methods to train on the entire stream, without having to skip any stream steps. Would previously considered methods, which struggled in the fast-stream setting, be suitable for OCL deployment in this slow-stream scenario? We compare various OCL methods under no delay against their corresponding modified baseline \\(ER++\\), which computes additional number of gradient steps per batch to match the complexity of the compared-against method, as determined from Table 1. This mimics the comparison on slow stream speeds, where no stream steps are skipped and comparisons are performed under normalized complexity. Note that ACE only modifies the loss objective of \\(ER\\), so it matches the complexity of the baseline \\(\\mathcal{C}_S(ACE) = 1\\). As a result, evaluating ACE in the slow-stream setting is identical to evaluating it in the fast-stream setting, which was already done in Figure 3. Therefore, we do not compare to ACE again in the following experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.896, + 0.902 + ], + "angle": 0, + "content": "We report the comparisons in Figure 5, where \\( ER++ \\) is shown in green and OCL methods in red. Moreover, we show \\( ER \\), which is unfavorably compared against both, in blue. While RWalk outperforms \\( ER \\) in the slow stream setting, this is an unfair comparison, since \\( ER \\) is not utilizing the fact that the stream is slow and that it can benefit from further training. Once we simply add a few iterations to \\( ER \\), i.e., \\( ER++ \\), so as to match the training complexity of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11894" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.265, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.087, + 0.42, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.087, + 0.576, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.578, + 0.087, + 0.732, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.087, + 0.89, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.893, + 0.283 + ], + "angle": 0, + "content": "Figure 5. Slow Stream. We compare each method against \\(ER\\) and \\(ER++\\), which performs extra gradient steps per time step to match the complexity \\(\\mathcal{C}_S\\) of the compared-against method. \\(ER++\\) outperforms all the considered methods, sometimes by large margins." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.469, + 0.331 + ], + "angle": 0, + "content": "RWalk, \\(ER++\\) performs far better than RWalk. We find this to be consistent across all methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.681 + ], + "angle": 0, + "content": "Interestingly, computationally intensive methods, e.g., GSS and MIR, perform worse even when compared to \\(ER\\), which does not exploit the fact that the stream is slow. \\(ER++\\) is significantly better than GSS and MIR, by \\(17\\%\\) and \\(11\\%\\) respectively, expanding the performance gap to the baseline by around \\(15\\%\\) and \\(7\\%\\). These results question the suitability of the previously proposed methods to realistic OCL setups with large-scale datasets. Moreover, our results suggest that a computationally unfair evaluation setup (i.e. not normalizing training complexity) in slow stream OCL can lead to misleading performance conclusions, as is the case with RWalk. We highlight that PoLRS was originally tested on a slightly different setup to the slow stream, which included extra information represented by a user album [7]. We find that when the album information is removed and their reported baseline, i.e., \\(ER\\), is tuned properly, PoLRS has a similar performance to \\(ER\\) as shown in Figure 5. This is still surprising since PoLRS is three times more expensive than \\(ER\\). More surprisingly, when matching the training complexity of \\(ER\\) to PoLRS on the slow stream, \\(ER++\\) outperforms PoLRS by \\(9.5\\%\\). These results on the slow-stream setting support our earlier observation that current OCL methods are not yet suited for practical deployment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.285, + 0.71 + ], + "angle": 0, + "content": "4.3. Effect of Memory Size" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We conduct experiments to test whether existing methods can outperform \\( ER \\) under different memory buffer sizes. We repeat the fast-stream experiment from Section 4.1 with memory budgets of \\( 1 \\times 10^{4} \\), \\( 2 \\times 10^{4} \\), and \\( 4 \\times 10^{4} \\) samples. The results are summarized in Table 2. A larger memory size leads to a higher Average Online Accuracy across all methods. However, we emphasize that the trend across methods aligns with our previous finding that expensive-training OCL methods perform worse than their less expensive counterparts. This is evident from the ordering of the methods in Figure 3, which holds regardless of the memory budget. Notably, \\( ER \\) outperforms all considered methods." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.37 + ], + "angle": 0, + "content": "Table 2. Memory Budget Analysis. We test the effect of varying the memory budget in the fast-stream setting. We observe that 1) increasing the memory size results in better performance regardless of the method, and 2) ER outperforms all the considered methods regardless of the memory budget." + }, + { + "type": "table", + "bbox": [ + 0.55, + 0.376, + 0.84, + 0.54 + ], + "angle": 0, + "content": "
MethodMemory Size
1 × 1042 × 1044 × 104
ER [11]18.0919.3720.27
ACE [6]17.5318.5519.42
LwF [28]16.8717.8718.69
RWalk [8]14.6015.2916.07
PoLRS [7]12.4012.9813.59
MIR [3]11.3711.6411.89
GSS [4]8.018.599.10
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.555, + 0.619, + 0.57 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.763 + ], + "angle": 0, + "content": "We proposed a real-time evaluation benchmark for online continual learning, including a fast stream that continues to reveal new data even when the model has not completed training. This realistic setup forces computationally intensive methods to skip more training samples, highlighting the differences in training complexity between the considered methods. Our results show that, under this setting, all considered methods underperform the simple \\(ER\\) baseline. We also explored scenarios where we normalized the number of seen training data or the computational complexity per time step, leading to the same conclusion that current methods are not yet optimized for real-world deployment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence (SDAIA-KAUST AI), Saudi Aramco, and UKRI grant Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. 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In International Conference on Machine Learning (ICML), 2017. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.772 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11897" + } + ] +] \ No newline at end of file diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_origin.pdf b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5ded27a55f5c6451595fe3591f50ca8df00ab912 --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/90670a33-6068-465e-a4fd-294478f9cef7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a3ad5039f3d9b1bc37286230ae9bebcad209f03a8ee4bb50f2296d230c1bc37a +size 2681334 diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/full.md b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/full.md new file mode 100644 index 0000000000000000000000000000000000000000..96daeb8bbaa4b9758572a4fb941290499e8f224c --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/full.md @@ -0,0 +1,253 @@ +# Real-Time Evaluation in Online Continual Learning: A New Hope + +Yasir Ghunaim $^{1*}$ + +Adel Bibi $^{2*}$ + +Kumail Alhamoud1 + +Motasem Alfarra1 + +Hasan Abed Al Kader Hammoud1 + +Ameya Prabhu2 + +Philip H.S. Torr + +Bernard Ghanem1 + +$^{1}$ King Abdullah University of Science and Technology (KAUST) $^{2}$ University of Oxford + +# Abstract + +Current evaluations of Continual Learning (CL) methods typically assume that there is no constraint on training time and computation. This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical real-time evaluation of continual learning, in which the stream does not wait for the model to complete training before revealing the next data for predictions. To do this, we evaluate current CL methods with respect to their computational costs. We conduct extensive experiments on CLOC, a large-scale dataset containing 39 million time-stamped images with geolocation labels. We show that a simple baseline outperforms state-of-the-art CL methods under this evaluation, questioning the applicability of existing methods in realistic settings. In addition, we explore various CL components commonly used in the literature, including memory sampling strategies and regularization approaches. We find that all considered methods fail to be competitive against our simple baseline. This surprisingly suggests that the majority of existing CL literature is tailored to a specific class of streams that is not practical. We hope that the evaluation we provide will be the first step towards a paradigm shift to consider the computational cost in the development of online continual learning methods. + +# 1. Introduction + +Deep Neural Networks (DNNs) have demonstrated impressive success in solving complex tasks [20, 29, 42] when trained offline, for several passes, over large well-curated labeled datasets. However, in many real-world scenarios, data is only available in the form of a stream with a changing distribution. Due to this challenge, there has been a growing interest in the problem of learning from a time-varying stream, also known as Continual Learning (CL), which is + +a key challenge for DNNs due to a phenomenon known as catastrophic forgetting [17, 36]. In particular, when a DNN is trained with data from a new distribution, the DNN performance significantly drops on previously learned data. + +While mitigation efforts have been proposed, e.g. through regularizing the training [2, 25, 53], replaying previously seen examples [11, 23, 39], and many other approaches [16, 40, 51], current evaluation approaches are still far from real-world scenarios. For example, the majority of literature is on Offline Continual Learning, under which methods are allowed unlimited budget, both time and computation. Furthermore, the majority of CL evaluations are conducted on small-scale datasets with well-defined temporal distribution boundaries in the form of learning a sequence of tasks. + +To that end, there has recently been a growing interest in the more realistic setting - Online Continual Learning (OCL). In such a setup [1, 4, 21, 32], CL methods are restricted to a single training pass over a shuffled split of existing offline CL benchmarks. This is certainly a step forward towards resolving some of the unrealistic assumptions of offline CL. However, current evaluations do not sufficiently address the challenges of real-time learning for high-throughput streams with rapid distribution changes. + +To illustrate this, consider the problem of continuously learning a Twitter stream where 350K tweets are uploaded per minute on various trending topics [41]. Every uploaded tweet needs to be predicted with a DNN for misinformation and hate speech, among other things, while simultaneously learning and adapting to them. Given the scale at which data is being updated, there is an inherent key limitation on the time and computational budget affordable to learning incoming tweets, an aspect that is often overlooked in the prior art from the OCL literature. Consider an OCL method that is 10 times slower than the Twitter high throughput stream, i.e., it takes 10 minutes to train on one minute worth of tweets (350K tweets). This inefficiency results in an accumulation of $\sim 3.1$ million new samples that need to be predicted and trained on. Since it is not acceptable to pause + +![](images/d8bb06393f6c6e38cf71821998d6b2e26782c6921ea8c38fa1b5a4cd47f09c1e.jpg) +Figure 1. OCL Real-Time Evaluation Example. We show an example of real-time evaluation, using the CLOC dataset [7], of two different OCL methods $\mathcal{A}$ and $\mathcal{B}$ . Method $\mathcal{B}$ is twice as slow as method $\mathcal{A}$ . Both methods are evaluated on every incoming sample. Since $\mathcal{A}$ has a stream-model relative complexity of one, i.e. $\mathcal{C}_S(\mathcal{A}) = 1$ , it is able to train on all the stream samples. In contrast, $\mathcal{B}$ , which has a relative complexity of two, requires two time steps to train on a single stream batch. Thus, $\mathcal{B}$ only trains on half of the stream samples. + +all tweets from appearing online until the method training is complete, predictions for all new samples will be performed with an older version of the model. This poses a key challenge where efficient learning from streams becomes necessary. This is because slow-training OCL methods can result in subpar performance, as they resort to predicting new stream data using an older model. This behavior worsens for streams that experience a faster change in distribution. + +In this paper, we propose a real-time evaluation protocol for OCL that factors in training computational complexity. Given a stream, consider an OCL method $\mathcal{A}$ that is as fast as the stream, i.e., $\mathcal{A}$ can train on every step of revealed data before the stream presents new samples. Then, if an OCL $\mathcal{B}$ is twice as expensive as $\mathcal{A}$ , then $\mathcal{B}$ will update the model for evaluation every other stream step, i.e., the model will be updated half the number of times compared to $\mathcal{A}$ . Figure 1 illustrates our proposed real-time evaluation. This is in contrast to all prior art [3,4,6] that (1) unreasonably allows an unlimited computational budget to train on any given stream data, and (2) unfairly compares OCL methods despite having different training complexity levels. Using our real-time evaluation protocol, we benchmark many existing OCL methods against a simple and inexpensive baseline, which mitigates forgetting by simply storing and replaying recently seen samples. + +Contributions. We summarize our conclusions as follows: (1) We show that under our practical real-time evaluation, our simple baseline outperforms all the considered methods from the OCL literature, including recent SOTA approaches like ACE [6]. (2) We consider a complementary setup where the stream is as slow as the most training-expensive OCL method and compare that method against + +the compute-equivalent baseline. Under this computationally normalized setting, we find that the compute-equivalent baseline outperforms all existing methods. (3) Our experiments are consistent, holding for all the considered continual learning strategies, and extensive, amounting to more than 2 GPU-months. Our results highlight that the current progress in OCL needs to be rethought and a paradigm shift is needed. We hope our work will lead to a new direction for continual learning that takes into account the computational cost of each method. + +# 2. Related Work + +We briefly describe the current literature on offline and online continual learning. For a more comprehensive overview of the literature, we refer the reader to the detailed surveys by De Lange et al. [13] and Mai et al. [33]. + +Offline Continual Learning. Traditional continual learning strategies, which aim to mitigate forgetting, can be organized into three families of methods. (i) Replay-based methods store input samples, or alternatively learn to generate representative samples, while the model learns from the data stream. Later, the method retransmits the model on the replay samples while the model learns from new data [32, 35, 45, 49, 50]. (ii) Regularization methods avoid the cost of storing samples and simply modify the model loss objective to regularize the training. While some of these methods penalize changes to important model parameters [2, 8, 25], other methods regularize the training by distilling knowledge from a model trained on past stream samples [18, 28, 46]. (iii) Parameter isolation methods train specific parameters for each task while freezing the param- + +eters that are related to other tasks [22, 34, 40]. Despite the progress made by these methods, they assume an offline stream that allows many passes over each continual learning task. Concurrent work Prabhu et al. [37] alleviates this problem by imposing computational budget constraints and finds that simple methods based on experience replay outperform most prior continual learning works. In contrast, we study the more pragmatic setup, where the stream reveals data in real time. + +Online Learning for Reduced Forgetting. OCL was defined with a protocol where training data is only seen once in a sequence of labeled tasks [32]. To reduce catastrophic forgetting, the field initially progressed towards better gradient-based constraints like GEM [32] and AGEM [10]. RWalk [8] quantified forgetting and provided a more efficient approach to limit changes in important model parameters. TinyER [11] rediscovered the effectiveness of experience replay, and HAL [9] enhanced it with learned anchors. However, this setup assumes the availability of an oracle during test time to determine which classifier head to use for inference [33, 48]. Additionally, the benchmarks in this setup often have large constraints on the replay buffer size [10, 11]. Due to these limitations, the class-incremental scenario started to gain attention, which is a more realistic setting for OCL. + +In class-incremental online continual learning, benchmarks [3, 27] relaxed the need for task descriptors at test time, and introduced significantly larger buffer sizes in comparison to [10]. Multiple directions have emerged to tackle catastrophic forgetting in this setup. They can be classified into few groups. (i) Regularization-based approaches modify the classification objective to preserve previously learned representations or encourage more meaningful representations e.g. DER [5], ACE [6], and CoPE [14]. (ii) Sampling-based techniques focus on the optimal selection and storing of the most representative replay memory during online training, e.g. GSS [4], OCS [52], CBRS [12], CLIB [26], and InfoRS [47]. Alternatively, some sampling methods focus on better memory retrieval strategies that reduce forgetting, e.g. MIR [3], ASER [44], and GMED [24]. (iii) In other approaches, GDumb [38] proposed a degenerate solution to the problem of online learning ignoring the stream data and learning only on the memory samples. While these efforts have significantly advanced the field of OCL, they are mostly evaluated on benchmarks that do not reflect real-deployment conditions. First, these benchmarks heavily rely on artificially constructed small datasets with sudden shifts in classes. Second, these benchmarks are incapable of measuring whether models can rapidly adapt to new data under a fast-changing distribution shift, which is one of the main problems in classical online learning literature [43]. There have been efforts to address the second limitation by using new metrics that measure test accuracy + +more frequently during training [6, 26]. However, these metrics capture the adaptation to held-out test data rather than to the incoming future data. To remedy these limitations, there has been a new surge of benchmarks proposing datasets and evaluation protocols, which we discuss next. + +Online Learning for Rapid Adaptation. Recent OCL benchmarks, e.g. CLOC [7] and CLEAR [30], introduce data ordered by timestamps, forming a temporal stream of evolving visual concepts over a long span of time. They demonstrate that their data has a natural distribution shift over time, requiring rapid adaptation to newer data. Additionally, they mimic the traditional online learning setup by measuring the capacity for rapid adaptation with the evaluation being done on future data from the stream. Our work extends the efforts in this direction. We adopt the CLOC benchmark and propose a more realistic real-time evaluation that encourages efficient learning. It is worth mentioning that [19] has explored certain aspects of real-time evaluation in continual learning. However, they focus on efficiency for embedded device deployment, rather than rapid adaptation. Moreover, while their work investigates the computational cost associated with each training method, they only report the cost as an evaluation metric. In contrast, we constrain the training procedure by each method's computational cost. + +# 3. Methodology + +We start with the classical problem statement for online continual learning. Then, we formally introduce our proposed real-time evaluation that factors in training complexity through delayed evaluations. + +# 3.1. Online Continual Learning + +Online continual learning [7, 43] is the problem of learning a $\theta$ parameterized function $f_{\theta}:\mathcal{X}\to \mathcal{V}$ that predicts a label $y\in \mathcal{V}$ for an input image $x\in \mathcal{X}$ . Unlike, classical supervised learning, the learning is performed on a distribution-varying stream $\mathcal{S}$ revealing data sequentially over steps $t\in \{1,2,\dots ,\infty \}$ . In particular, at every step $t$ + +1. $S$ reveals a set of images $\{x_i^t\}_{i = 1}^{n_t}\sim \mathcal{D}_{j\leq t}$ +2. $f_{\theta_t}$ generates predictions $\{\tilde{y}_i^t\}_{i = 1}^{n_t}$ for $\{x_i^t\}_{i = 1}^{n_t}$ +3. $S$ reveals true labels $\{y_i^t\}_{i = 1}^t$ +4. $f_{\theta_t}$ is evaluated by comparing $\{\tilde{y}_i^t\}_{i=1}^{n_t}$ to $\{y_i^t\}_{i=1}^{n_t}$ ; +5. A learning method trains $f_{\theta_t}$ , a criterion computes the training loss, then the parameters are updated to $\theta_{t + 1}$ . + +Note that $\mathcal{D}_{j\leq t}$ denotes a varying distribution that might not necessarily need to change at every stream step $t$ .For example, if at step $t = 5$ we have $j = 1$ , this means the revealed data over all five previous steps is sampled from the + +![](images/bc26693a0f114c009287203d6f9c959f68238d015ce01eba65663c8abf472812.jpg) +Figure 2. OCL Real-Time Evaluation Setup. In OCL, models perform real-time prediction on each revealed sample from the stream. At the same time, model training is performed on the revealed samples dictated by the method's delay. In this example, we demonstrate the evaluation procedure when the stream-model complexity $k$ is larger than 1. Due to the mismatch between the stream speed and the model computational cost, an "older version" of the model predicts samples while the model is being trained. Therefore, k-1 potential training batches are skipped for each training step. + +same distribution $\mathcal{D}_1$ . Moreover, observe that, unlike offline continual learning, online continual learning captures the capacity to adapt to new data since the prediction is performed before the training. + +Key Issues. As described earlier, the OCL evaluation in the literature [7, 43] overlooks the training complexity in step (5). Under such a setup, all OCL methods have their parameters updated to $\theta_{t + 1}$ before the stream $S$ reveals images of the next step. Therefore, different OCL methods are evaluated irrespective of the training time and computational complexity at step (5). This is equivalent to evaluating different OCL methods on streams that present data at different rates. In real-time settings, the stream reveals data at a rate that is independent of the training complexity of the OCL method. To that end, we propose a real-time evaluation paradigm for OCL that factors in training complexity through delayed evaluations. + +# 3.2. Real-Time Evaluation for OCL + +As mentioned earlier, we need to define a notion of a fixed stream rate. That is to say, the stream reveals data at a fixed rate irrespective of how long OCL methods take to update the model in step (5). For streams that are twice as fast as it takes to train $f_{\theta}$ , OCL methods will have their model updated on only half the number of revealed sets of images from the stream. Note that the latest updated version of $f_{\theta}$ will continue to provide predictions for newly revealed images during training even for those images the model did not train on. This setting reflects the realistic scenario of a server receiving many queries uploaded by users, where each query needs a prediction irrespective of whether an in-house model is being trained. Given a stream $S$ and + +an OCL method $\mathcal{A}$ , we first define the notion of stream-model relative complexity $\mathcal{C}_S(\mathcal{A})\in \mathbb{R}^+$ . In particular, for a stream-model relative complexity $\mathcal{C}_S(\mathcal{A}) = 1$ , the continual learning method $\mathcal{A}$ can update the model $\theta$ in step (5) before the stream $S$ reveals the data of the next step. For any stream-model relative complexity $\mathcal{C}_A(\mathcal{A}) = k > 1$ , the stream is $k$ -faster than the continual learning method $\mathcal{A}$ . With this notation, we now propose our modified version of the OCL setting along with the corresponding real-time evaluation. Given a model $f_{\theta_m}$ , a stream $S$ , and an OCL method $\mathcal{A}$ with $\mathcal{C}_S(\mathcal{A}) = k$ , at every step $t$ , + +1. $S$ reveals a set of images $\{x_{i}^{t}\}_{i = 1}^{n_{t}}\sim \mathcal{D}_{j\leq t}$ +2. $f_{\theta_m}$ generates predictions $\{\tilde{y}_i^t\}_{i = 1}^{n_t}$ for $\{x_i^t\}_{i = 1}^{n_t}$ ; +3. $S$ reveals true labels $\{y_i^t\}_{i = 1}^t$ +4. $f_{\theta_m}$ is evaluated by comparing $\{\tilde{y}_i^t\}_{i = 1}^{n_t}$ to $\{y_i^t\}_{i = 1}^{n_t}$ ; +5. If $\mathrm{mod}(t - 1, k) = 0$ , then the continual learner $\mathcal{A}$ completes updating $f_{\theta_m} \gets f_{\theta_{m+1}}$ and a new instance of training on $f_{\theta_m}$ commences (see Figure 2). + +In this setting, OCL methods that are computationally more expensive to train will be updated fewer times. Therefore, for streams $S$ where the distribution $\mathcal{D}_j$ changes rapidly (perhaps as often as every stream step), OCL methods with a large stream-model relative complexity may produce erroneous predictions, since the models are not updated enough and cannot adapt to the distribution change. + +On the Computation of $\mathcal{C}_S$ . Since $\mathcal{C}_S$ only measures the relative complexity between the stream and an underlying continual learning method, we first introduce a minimal inexpensive OCL method as a baseline (denoted $\mathcal{A}$ ). For ease + +of comparison of the considered methods, we then assume that, due to the inexpensive nature of $\mathcal{A}$ , online continual learning will be as fast as the stream where the stream-model relative complexity $\mathcal{C}_{\mathcal{S}} = 1$ . In particular, we consider a baseline that mitigates forgetting by simply storing and replaying recently seen samples. Then, given any other OCL method $\mathcal{B}$ , we use the relative training FLOPs between $\mathcal{B}$ and $\mathcal{A}$ to determine $\mathcal{C}_{\mathcal{S}}(\mathcal{B})$ . For example, ACE [6] only modifies the loss objective of the baseline, and thus it is equivalent to the baseline in computational complexity. On the other hand, PoLRS [7] maintains and performs operations on three copies of the model. These copies are trained on every incoming batch, making PoLRS require $3 \times$ the FLOPs needed by the baseline. As noted earlier, a method of a stream-model relative complexity value of 3 performs the update in step (5) once every three stream steps. This corresponds to a delay in model updates by two steps. In Table 1, we summarize the corresponding delay of several popular OCL methods in our real-time evaluation setup. + +Fair Comparison of OCL Methods with Different $\mathcal{C}_{\mathcal{S}}$ . We proposed a realistic setup of evaluating continual learners based on their training complexity with respect to the stream speed. However, one might argue that more expensive training routines could be accelerated by deploying more computational hardware allowing them to train on each revealed sample from the stream. For example, while PoLRS [7] requires $3 \times$ more FLOPs than the simple baseline, one could deploy $3 \times$ more hardware to make $\mathcal{C}(\mathcal{A}) = 1$ for PoLRS. This setup mimics the scenario of having a slow stream that matches the speed of the more expensive training method. + +While the aforementioned setup normalizes the computational requirement of a given learning method $\mathcal{A}$ to match the stream speed, one should allow simpler training methods the same computational complexity. To that end, we propose boosting simpler and faster training methods to match the computational requirements of more complex methods. For example, we boost the simple experience replay method by sampling a larger number of instances from the replay buffer at each step $t$ to match the FLOPs of other training schemes. We note here that although this modification is both simple and naive, we found empirically that it is sufficient to outperform all considered OCL methods. We leave the rest of the implementation details to Section 4.2. + +# 4. Experiments + +We compare OCL methods under our proposed real-time evaluation setup given two stream speeds: fast and slow, which capture different application scenarios. We benchmark the majority of OCL methods, which we group into three categories. (1) Regularization-based OCL methods regularize training by modifying the classification loss. For example, RWalk [8] uses a regularizer to penalize abrupt + +Table 1. Training complexity and delay of considered OCL methods. *Note that GSS has a complexity of 6.5 but we rounded it down to 6 to facilitate the setup. This rounding may give GSS a slight advantage, but nonetheless, it is outperformed by the baseline, ER, in all experiments. + +
CL StrategyMethod(A)C_S(A)Delay
Experience ReplayER [11]10
RegularizationsACE [6]10
LwF [28]4/31/3
RWalk [8]21
LR SchedulerPoLRS [7]32
Sampling StrategiesMIR [3]5/23/2
GSS [4]6*5
+ +changes in the parameters of the model. ACE [6] introduces an asymmetric loss to treat memory buffer samples differently from incoming stream samples, while LwF [28] distills knowledge from previous steps. (2) Learning rate scheduler methods, in this case PoLRS [7], dynamically adapt the learning rate to changes in the stream distribution. (3) Sampling-based methods alter the strategy used to update the memory buffer, e.g. GSS [4], or change the memory retrieval strategy, e.g. MIR [3]. + +Datasets. We use the large-scale online continual learning dataset CLOC [7], which contains 39 million time-stamped images exhibiting natural distribution shifts. The task is to identify the geolocation of a given image where the total number of geolocation labels is 712. To ensure consistency with CLOC [7], we adopt the same dataset split approach. Specifically, we use the first $5\%$ of the stream for hyperparameter selection, uniformly sample $1\%$ from the remaining stream to build a held-out set for measuring backward/forward transfer (reported in the appendix), and utilize the rest of the stream for training and online evaluation. Similar to CLOC [7], we compare OCL methods using the Average Online Accuracy metric, which measures the ability of models to adapt to incoming stream samples1. + +Implementation Details. At each step $t$ during the experiments, $S$ reveals a set of 128 images, and OCL methods augment the training batch with another 128 images sampled from a memory buffer. This routine is performed until a single pass over the stream is completed. We use ImageNet [15] pre-trained ResNet50 [7, 20] as a backbone. We use SGD with a learning rate of $5 \times 10^{-3}$ for all OCL methods except for PoLRS [7], which works best with a learning rate of $1 \times 10^{-3}$ . Unless otherwise stated, we set the size of the replay buffer to $4 \times 10^{4}$ for all considered methods. We + +![](images/c78b09c573a981d844a311e78eb17cb19122ffa9695146a216b9646aca847598.jpg) +Figure 3. Fast Stream Evaluation. We compare the Average Online Accuracy of six methods from the OCL literature evaluated under the fast-stream setting. We observe that our inexpensive baseline, ER, outperforms all the considered methods. Surprisingly, the most computationally complex methods, MIR, PoLRS, and GSS, underperform the more efficient methods. + +use the same hyperparameters reported in all corresponding papers with the exception of the regularization parameter for RWalk [8]. We find that their reported regularization $\lambda = 0.1$ is too small for the CLOC dataset; we cross validate it and find that $\lambda = 2$ works best. Our implementation extends the codebase of Avalanche [31], which is a popular continual learning framework. We leave all the remaining implementation details and ablations to the appendix. + +# 4.1. Fast Stream: Real-Time Evaluation + +We first consider the fast-stream scenario, where the stream reveals data at a high rate. We consider the simple baseline $ER$ [11], which performs one gradient step on a batch of 256 (128 revealed by the stream and 128 from memory) images at every stream step. The 128 images from memory are sampled uniformly. For simplicity and ease of comparison, we assume that $ER$ has a stream-model relative complexity of $\mathcal{C}_S(ER) = 1$ . Consequently, any OCL method that is computationally more expensive than $ER$ will not keep up with the stream speed, and thus will be forced to skip training on a fraction of the incoming stream samples. + +Benchmarking Relative Complexity of OCL Methods. As discussed earlier, we use the total number of FLOPs required for each method to train on a stream as a proxy for the stream-model relative complexity $\mathcal{C}_S$ . We first compute the total FLOPs required to train $ER$ on a small subset of CLOC composed of $10^3$ images with a batch size of 10. We then compute the corresponding FLOPs for various OCL methods and normalize them by the FLOPs of $ER$ . Since the backbone is shared across all methods, we further verify this normalized complexity by counting the effective number of + +forward and backward passes of each method. Because we assume that $ER$ is effectively as fast as the stream, methods that are twice more expensive in FLOPs have a complexity $\mathcal{C}_S$ of 2. We report in Table 1 the stream-model relative complexity for OCL methods compared against $ER$ . Note that PoLRS is 3 times as expensive as $ER$ since it requires training 3 different models to update the learning rate. In addition to the 128 images revealed by the stream and the 128 images sampled from memory at step $t$ , GSS performs additional forward and backward passes on $10 \times 128$ memory samples to ensure diversity when updating the memory buffer [4]. Therefore, GSS is roughly 6 times more expensive than $ER$ . For each method in Table 1, we report the corresponding delay in stream steps, which is a consequence of some methods being slower than the stream. A delay of 2 means that the stream will reveal 2 steps worth of images before the model is updated. + +Effect of Training Efficiency. We start our analysis by investigating the effect of training efficiency on the performance of different OCL methods under the real-time evaluation setup. We plot the Average Online Accuracy curves per step in Figure 3, where the simple $ER$ baseline is in blue. Each method is evaluated according to its corresponding training delay reported in Table 1. Surprisingly, $ER$ outperforms all considered methods, and in some cases, by large margins. Interestingly, the most computationally intensive methods, MIR, PoLRS, and GSS, exhibit the lowest performance when real-time evaluation is considered. Specifically, the performance gap at the end of the stream reaches $11\%$ . In fact, we note that the Average Online Accuracy values of all considered methods, irrespective of how recently they were introduced to the literature, are approximately ordered based on their stream-model relative complexity $\mathcal{C}_S$ ; the larger $\mathcal{C}_S$ is, the worse the performance is under real-time evaluation. We attribute this trend to the fact that these inefficient methods may not be capable of keeping up with the fast-changing distribution $\mathcal{D}_j$ in the stream when they are subjected to a higher delay. For example, although PoLRS was proposed and tailored for the recent CLOC benchmark, it is significantly outperformed by the older method LwF when evaluated under the real-time paradigm. This hints that computational complexity can be a crutch for OCL methods learning on fast streams. Our results show that while the current literature aims to improve learning by leveraging more expensive and advanced learning routines, the penalty incurred by delay overshadows any potential improvements gained by the algorithmic contributions. Notably, the state-of-the-art ACE method, which is as efficient as $ER$ and thus evaluated under no training delay, performs almost as well as the baseline. Additionally, ACE outperforms more expensive methods when evaluated on small-scale datasets (refer to Small-Scale Experiments in the appendix). Overall, our findings suggest that practical + +![](images/f74505de5b70156da21c02dd8556dd29595539593a046e27e7ab430c53d6775e.jpg) +Figure 4. Fast Stream - Training Data Normalization. We compare each method against $ER$ and its delayed version $ER$ --. $ER$ -- performs extra gradient steps per time step to match the delay of the compared-against method, so it trains on fewer samples than $ER$ . We highlight that even when $ER$ -- is unfairly delayed to match each OCL method's delay, it outperforms all considered methods. + +![](images/94696f6633f3e79b6521a91eab3b65c59ac7623ae91f6e21ff77dbb61a904e6a.jpg) +ER (Delay = 0) + +![](images/434031a633944b9cea70c55f89ae82566fa3c9c5656d7dcb170561b4870d87d3.jpg) +ER-- + +![](images/404a156c262df767b865239b0bb311c6c930065bff99c1cebb502b26a1b685a4.jpg) +OCL Method + +![](images/bf84bfb97c21b6ee7efc5bcd81f393c064aab76338c5cbb9663d258bbe317882.jpg) + +OCL methods, deployed in real-time applications, should prioritize efficient learning over expensive optimization. + +Training Data Normalization. Previously, we have shown that delayed evaluation leads to larger performance degradation as the delay gets longer. However, this could be attributed to the fact that OCL methods with larger delays end up effectively training on a fewer number of samples. This raises the questions: Do computationally more expensive methods with delays perform worse than ER because they cannot cope with the changing distribution in the stream? or is the performance degradation due to expensive OCL methods being trained on effectively a fewer number of training examples? To address these questions, we conduct pairwise comparisons between $ER$ and each previously reported OCL method. Assuming that the stream speed is fixed, we modify $ER$ to match the computational expense of the respective method by training on the same amount of data for a longer duration. To achieve this computational matching, we subject $ER$ to a delay by performing additional gradient descent steps at each stream step. We refer to this modified baseline as $ER$ --. The number of additional updates in $ER$ -- is determined such that its delay matches the delay of the corresponding OCL method. This guarantees that $ER$ -- trains on the same number of training examples compared to other OCL methods. + +Figure 4 shows comparisons of $ER$ and $ER$ - to each of the considered OCL methods. Since the non-delayed $ER$ is more efficient than $ER$ -, $ER$ consistently outperforms $ER$ -, confirming that efficiency is key for the real-time evaluation of OCL. More interestingly, even though $ER$ - matches the complexity of each compared-against method and is subject to the same delay, it still outperforms all considered OCL methods. Moreover, while the gap between $ER$ - and expensive approaches, e.g. GSS, is smaller than the gap to $ER$ , expensive methods still lag behind $ER$ - by up to $3.5\%$ . This demonstrates that the degraded performance of considered OCL methods is not due to the fewer number of observed training examples. On the contrary, expensive OCL meth + +ods seem to be unable to cope with distribution-changing streams. Under real-time evaluations of fast streams, simple methods such as $ER$ and $ER$ --- may be more suitable for real-world deployment. + +# 4.2. Slow Stream: Complexity Normalization + +In the fast stream setting, we considered the scenario where the stream is as fast as the $ER$ baseline, i.e., $\mathcal{C}_S(ER) = 1$ . In this section, we consider streams that are as slow as the more expensive OCL methods. This setup motivates the following question: How do existing OCL methods perform if they were deployed on streams that match their training complexity? Slower streams may enable expensive methods to train on the entire stream, without having to skip any stream steps. Would previously considered methods, which struggled in the fast-stream setting, be suitable for OCL deployment in this slow-stream scenario? We compare various OCL methods under no delay against their corresponding modified baseline $ER++$ , which computes additional number of gradient steps per batch to match the complexity of the compared-against method, as determined from Table 1. This mimics the comparison on slow stream speeds, where no stream steps are skipped and comparisons are performed under normalized complexity. Note that ACE only modifies the loss objective of $ER$ , so it matches the complexity of the baseline $\mathcal{C}_S(ACE) = 1$ . As a result, evaluating ACE in the slow-stream setting is identical to evaluating it in the fast-stream setting, which was already done in Figure 3. Therefore, we do not compare to ACE again in the following experiments. + +We report the comparisons in Figure 5, where $ER++$ is shown in green and OCL methods in red. Moreover, we show $ER$ , which is unfavorably compared against both, in blue. While RWalk outperforms $ER$ in the slow stream setting, this is an unfair comparison, since $ER$ is not utilizing the fact that the stream is slow and that it can benefit from further training. Once we simply add a few iterations to $ER$ , i.e., $ER++$ , so as to match the training complexity of + +![](images/d3f25cf2d9015f09e296ed1a238df00064334ea23d3b21e2fb3c0008147157ed.jpg) + +![](images/d6630fb7cff583696e401548c7c32edfe9dd8f40315d96079a762c47684eea8f.jpg) +Figure 5. Slow Stream. We compare each method against $ER$ and $ER++$ , which performs extra gradient steps per time step to match the complexity $\mathcal{C}_S$ of the compared-against method. $ER++$ outperforms all the considered methods, sometimes by large margins. + +![](images/a6da4bdbc97996e541ab3556a2dfd0bb1d8cc1aa7ae09ea761170fe71e31b299.jpg) + +![](images/b43a29557df01c9d0116ac6b445f9abcacf6870e8af616547e2b1ed9548438e6.jpg) + +![](images/48233bb0d19a7ca97bfac45805a187e8c0b4744fb019e9ab605cbd543970246c.jpg) + +RWalk, $ER++$ performs far better than RWalk. We find this to be consistent across all methods. + +Interestingly, computationally intensive methods, e.g., GSS and MIR, perform worse even when compared to $ER$ , which does not exploit the fact that the stream is slow. $ER++$ is significantly better than GSS and MIR, by $17\%$ and $11\%$ respectively, expanding the performance gap to the baseline by around $15\%$ and $7\%$ . These results question the suitability of the previously proposed methods to realistic OCL setups with large-scale datasets. Moreover, our results suggest that a computationally unfair evaluation setup (i.e. not normalizing training complexity) in slow stream OCL can lead to misleading performance conclusions, as is the case with RWalk. We highlight that PoLRS was originally tested on a slightly different setup to the slow stream, which included extra information represented by a user album [7]. We find that when the album information is removed and their reported baseline, i.e., $ER$ , is tuned properly, PoLRS has a similar performance to $ER$ as shown in Figure 5. This is still surprising since PoLRS is three times more expensive than $ER$ . More surprisingly, when matching the training complexity of $ER$ to PoLRS on the slow stream, $ER++$ outperforms PoLRS by $9.5\%$ . These results on the slow-stream setting support our earlier observation that current OCL methods are not yet suited for practical deployment. + +# 4.3. Effect of Memory Size + +We conduct experiments to test whether existing methods can outperform $ER$ under different memory buffer sizes. We repeat the fast-stream experiment from Section 4.1 with memory budgets of $1 \times 10^{4}$ , $2 \times 10^{4}$ , and $4 \times 10^{4}$ samples. The results are summarized in Table 2. A larger memory size leads to a higher Average Online Accuracy across all methods. However, we emphasize that the trend across methods aligns with our previous finding that expensive-training OCL methods perform worse than their less expensive counterparts. This is evident from the ordering of the methods in Figure 3, which holds regardless of the memory budget. Notably, $ER$ outperforms all considered methods. + +Table 2. Memory Budget Analysis. We test the effect of varying the memory budget in the fast-stream setting. We observe that 1) increasing the memory size results in better performance regardless of the method, and 2) ER outperforms all the considered methods regardless of the memory budget. + +
MethodMemory Size
1 × 1042 × 1044 × 104
ER [11]18.0919.3720.27
ACE [6]17.5318.5519.42
LwF [28]16.8717.8718.69
RWalk [8]14.6015.2916.07
PoLRS [7]12.4012.9813.59
MIR [3]11.3711.6411.89
GSS [4]8.018.599.10
+ +# 5. Conclusion + +We proposed a real-time evaluation benchmark for online continual learning, including a fast stream that continues to reveal new data even when the model has not completed training. This realistic setup forces computationally intensive methods to skip more training samples, highlighting the differences in training complexity between the considered methods. Our results show that, under this setting, all considered methods underperform the simple $ER$ baseline. We also explored scenarios where we normalized the number of seen training data or the computational complexity per time step, leading to the same conclusion that current methods are not yet optimized for real-world deployment. + +Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence (SDAIA-KAUST AI), Saudi Aramco, and UKRI grant Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ameya Prabhu is funded by Meta AI Grant No DFR05540. + +# References + +[1] Motasem Alfarra, Zhipeng Cai, Adel Bibi, Bernard Ghanem, and Matthias Müller. Simcs: Simulation for online domain-incremental continual segmentation. arXiv preprint arXiv:2211.16234, 2022. 1 +[2] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In European Conference on Computer Vision (ECCV), 2018. 1, 2 +[3] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. 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In International Conference on Machine Learning (ICML), 2017. 1 \ No newline at end of file diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/images.zip b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f87449628928c7217e7e3333c2882e31aaacf5ca --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c861a1e2b61bd3b603e33e68f8177fe6f5cdb8301e21daba5f13d220958a5f42 +size 343031 diff --git a/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/layout.json b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1915215436d22e8bac788a42b37a66adaebc065f --- /dev/null +++ b/2023/Real-Time Evaluation in Online Continual Learning_ A New Hope/layout.json @@ -0,0 +1,9780 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 133, + 103, + 460, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 103, + 460, + 139 + ], + "spans": [ + { + "bbox": [ + 133, + 103, + 460, + 139 + ], + "type": "text", + "content": "Real-Time Evaluation in Online Continual Learning: A New Hope" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 161, + 175, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 161, + 175, + 174 + ], + "spans": [ + { + "bbox": [ + 91, + 161, + 175, + 174 + ], + "type": "text", + "content": "Yasir Ghunaim" + }, + { + "bbox": [ + 91, + 161, + 175, + 174 + ], + "type": "inline_equation", + "content": "^{1*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 203, + 161, + 260, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 161, + 260, + 174 + ], + "spans": [ + { + "bbox": [ + 203, + 161, + 260, + 174 + ], + "type": "text", + "content": "Adel Bibi" + }, + { + "bbox": [ + 203, + 161, + 260, + 174 + ], + "type": "inline_equation", + "content": "^{2*}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 288, + 161, + 384, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 288, + 161, + 384, + 174 + ], + "spans": [ + { + "bbox": [ + 288, + 161, + 384, + 174 + ], + "type": "text", + "content": "Kumail Alhamoud1" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 413, + 161, + 501, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 413, + 161, + 501, + 174 + ], + "spans": [ + { + "bbox": [ + 413, + 161, + 501, + 174 + ], + "type": "text", + "content": "Motasem Alfarra1" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 175, + 222, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 175, + 222, + 189 + ], + "spans": [ + { + "bbox": [ + 55, + 175, + 222, + 189 + ], + "type": "text", + "content": "Hasan Abed Al Kader Hammoud1" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 244, + 175, + 323, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 244, + 175, + 323, + 190 + ], + "spans": [ + { + "bbox": [ + 244, + 175, + 323, + 190 + ], + "type": "text", + "content": "Ameya Prabhu2" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 343, + 175, + 427, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 175, + 427, + 190 + ], + "spans": [ + { + "bbox": [ + 343, + 175, + 427, + 190 + ], + "type": "text", + "content": "Philip H.S. 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This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical real-time evaluation of continual learning, in which the stream does not wait for the model to complete training before revealing the next data for predictions. To do this, we evaluate current CL methods with respect to their computational costs. We conduct extensive experiments on CLOC, a large-scale dataset containing 39 million time-stamped images with geolocation labels. We show that a simple baseline outperforms state-of-the-art CL methods under this evaluation, questioning the applicability of existing methods in realistic settings. In addition, we explore various CL components commonly used in the literature, including memory sampling strategies and regularization approaches. We find that all considered methods fail to be competitive against our simple baseline. This surprisingly suggests that the majority of existing CL literature is tailored to a specific class of streams that is not practical. We hope that the evaluation we provide will be the first step towards a paradigm shift to consider the computational cost in the development of online continual learning methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": "Deep Neural Networks (DNNs) have demonstrated impressive success in solving complex tasks [20, 29, 42] when trained offline, for several passes, over large well-curated labeled datasets. However, in many real-world scenarios, data is only available in the form of a stream with a changing distribution. Due to this challenge, there has been a growing interest in the problem of learning from a time-varying stream, also known as Continual Learning (CL), which is" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 241, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 545, + 289 + ], + "type": "text", + "content": "a key challenge for DNNs due to a phenomenon known as catastrophic forgetting [17, 36]. In particular, when a DNN is trained with data from a new distribution, the DNN performance significantly drops on previously learned data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 290, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 546, + 422 + ], + "type": "text", + "content": "While mitigation efforts have been proposed, e.g. through regularizing the training [2, 25, 53], replaying previously seen examples [11, 23, 39], and many other approaches [16, 40, 51], current evaluation approaches are still far from real-world scenarios. For example, the majority of literature is on Offline Continual Learning, under which methods are allowed unlimited budget, both time and computation. Furthermore, the majority of CL evaluations are conducted on small-scale datasets with well-defined temporal distribution boundaries in the form of learning a sequence of tasks." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 424, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 533 + ], + "type": "text", + "content": "To that end, there has recently been a growing interest in the more realistic setting - Online Continual Learning (OCL). In such a setup [1, 4, 21, 32], CL methods are restricted to a single training pass over a shuffled split of existing offline CL benchmarks. This is certainly a step forward towards resolving some of the unrealistic assumptions of offline CL. However, current evaluations do not sufficiently address the challenges of real-time learning for high-throughput streams with rapid distribution changes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": "To illustrate this, consider the problem of continuously learning a Twitter stream where 350K tweets are uploaded per minute on various trending topics [41]. Every uploaded tweet needs to be predicted with a DNN for misinformation and hate speech, among other things, while simultaneously learning and adapting to them. Given the scale at which data is being updated, there is an inherent key limitation on the time and computational budget affordable to learning incoming tweets, an aspect that is often overlooked in the prior art from the OCL literature. Consider an OCL method that is 10 times slower than the Twitter high throughput stream, i.e., it takes 10 minutes to train on one minute worth of tweets (350K tweets). This inefficiency results in an accumulation of " + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\sim 3.1" + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": " million new samples that need to be predicted and trained on. Since it is not acceptable to pause" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 683, + 134, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 683, + 134, + 693 + ], + "spans": [ + { + "bbox": [ + 61, + 683, + 134, + 693 + ], + "type": "text", + "content": "* Equal Contribution." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 63, + 694, + 253, + 704 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 694, + 253, + 704 + ], + "spans": [ + { + "bbox": [ + 63, + 694, + 253, + 704 + ], + "type": "text", + "content": "Correspondence to: yasir.ghunaim@kaust.edu.sa" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 63, + 704, + 220, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 704, + 220, + 712 + ], + "spans": [ + { + "bbox": [ + 63, + 704, + 220, + 712 + ], + "type": "text", + "content": "Code: github.com/Yasir-Ghunaim/RealtimeOCL" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11888" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 73, + 542, + 265 + ], + "blocks": [ + { + "bbox": [ + 51, + 73, + 542, + 265 + ], + "lines": [ + { + "bbox": [ + 51, + 73, + 542, + 265 + ], + "spans": [ + { + "bbox": [ + 51, + 73, + 542, + 265 + ], + "type": "image", + "image_path": "d8bb06393f6c6e38cf71821998d6b2e26782c6921ea8c38fa1b5a4cd47f09c1e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": "Figure 1. OCL Real-Time Evaluation Example. We show an example of real-time evaluation, using the CLOC dataset [7], of two different OCL methods " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": ". Method " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": " is twice as slow as method " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": ". Both methods are evaluated on every incoming sample. Since " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": " has a stream-model relative complexity of one, i.e. " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(\\mathcal{A}) = 1" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": ", it is able to train on all the stream samples. In contrast, " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": ", which has a relative complexity of two, requires two time steps to train on a single stream batch. Thus, " + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 274, + 546, + 319 + ], + "type": "text", + "content": " only trains on half of the stream samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 426 + ], + "type": "text", + "content": "all tweets from appearing online until the method training is complete, predictions for all new samples will be performed with an older version of the model. This poses a key challenge where efficient learning from streams becomes necessary. This is because slow-training OCL methods can result in subpar performance, as they resort to predicting new stream data using an older model. This behavior worsens for streams that experience a faster change in distribution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": "In this paper, we propose a real-time evaluation protocol for OCL that factors in training computational complexity. Given a stream, consider an OCL method " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": " that is as fast as the stream, i.e., " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": " can train on every step of revealed data before the stream presents new samples. Then, if an OCL " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": " is twice as expensive as " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": " will update the model for evaluation every other stream step, i.e., the model will be updated half the number of times compared to " + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": ". Figure 1 illustrates our proposed real-time evaluation. This is in contrast to all prior art [3,4,6] that (1) unreasonably allows an unlimited computational budget to train on any given stream data, and (2) unfairly compares OCL methods despite having different training complexity levels. Using our real-time evaluation protocol, we benchmark many existing OCL methods against a simple and inexpensive baseline, which mitigates forgetting by simply storing and replaying recently seen samples." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Contributions. We summarize our conclusions as follows: (1) We show that under our practical real-time evaluation, our simple baseline outperforms all the considered methods from the OCL literature, including recent SOTA approaches like ACE [6]. (2) We consider a complementary setup where the stream is as slow as the most training-expensive OCL method and compare that method against" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 331, + 546, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 449 + ], + "type": "text", + "content": "the compute-equivalent baseline. Under this computationally normalized setting, we find that the compute-equivalent baseline outperforms all existing methods. (3) Our experiments are consistent, holding for all the considered continual learning strategies, and extensive, amounting to more than 2 GPU-months. Our results highlight that the current progress in OCL needs to be rethought and a paradigm shift is needed. We hope our work will lead to a new direction for continual learning that takes into account the computational cost of each method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 483, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 532 + ], + "type": "text", + "content": "We briefly describe the current literature on offline and online continual learning. For a more comprehensive overview of the literature, we refer the reader to the detailed surveys by De Lange et al. [13] and Mai et al. [33]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Offline Continual Learning. Traditional continual learning strategies, which aim to mitigate forgetting, can be organized into three families of methods. (i) Replay-based methods store input samples, or alternatively learn to generate representative samples, while the model learns from the data stream. Later, the method retransmits the model on the replay samples while the model learns from new data [32, 35, 45, 49, 50]. (ii) Regularization methods avoid the cost of storing samples and simply modify the model loss objective to regularize the training. While some of these methods penalize changes to important model parameters [2, 8, 25], other methods regularize the training by distilling knowledge from a model trained on past stream samples [18, 28, 46]. (iii) Parameter isolation methods train specific parameters for each task while freezing the param-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11889" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "eters that are related to other tasks [22, 34, 40]. Despite the progress made by these methods, they assume an offline stream that allows many passes over each continual learning task. Concurrent work Prabhu et al. [37] alleviates this problem by imposing computational budget constraints and finds that simple methods based on experience replay outperform most prior continual learning works. In contrast, we study the more pragmatic setup, where the stream reveals data in real time." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 289, + 376 + ], + "type": "text", + "content": "Online Learning for Reduced Forgetting. OCL was defined with a protocol where training data is only seen once in a sequence of labeled tasks [32]. To reduce catastrophic forgetting, the field initially progressed towards better gradient-based constraints like GEM [32] and AGEM [10]. RWalk [8] quantified forgetting and provided a more efficient approach to limit changes in important model parameters. TinyER [11] rediscovered the effectiveness of experience replay, and HAL [9] enhanced it with learned anchors. However, this setup assumes the availability of an oracle during test time to determine which classifier head to use for inference [33, 48]. Additionally, the benchmarks in this setup often have large constraints on the replay buffer size [10, 11]. Due to these limitations, the class-incremental scenario started to gain attention, which is a more realistic setting for OCL." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 378, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 289, + 715 + ], + "type": "text", + "content": "In class-incremental online continual learning, benchmarks [3, 27] relaxed the need for task descriptors at test time, and introduced significantly larger buffer sizes in comparison to [10]. Multiple directions have emerged to tackle catastrophic forgetting in this setup. They can be classified into few groups. (i) Regularization-based approaches modify the classification objective to preserve previously learned representations or encourage more meaningful representations e.g. DER [5], ACE [6], and CoPE [14]. (ii) Sampling-based techniques focus on the optimal selection and storing of the most representative replay memory during online training, e.g. GSS [4], OCS [52], CBRS [12], CLIB [26], and InfoRS [47]. Alternatively, some sampling methods focus on better memory retrieval strategies that reduce forgetting, e.g. MIR [3], ASER [44], and GMED [24]. (iii) In other approaches, GDumb [38] proposed a degenerate solution to the problem of online learning ignoring the stream data and learning only on the memory samples. While these efforts have significantly advanced the field of OCL, they are mostly evaluated on benchmarks that do not reflect real-deployment conditions. First, these benchmarks heavily rely on artificially constructed small datasets with sudden shifts in classes. Second, these benchmarks are incapable of measuring whether models can rapidly adapt to new data under a fast-changing distribution shift, which is one of the main problems in classical online learning literature [43]. There have been efforts to address the second limitation by using new metrics that measure test accuracy" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "more frequently during training [6, 26]. However, these metrics capture the adaptation to held-out test data rather than to the incoming future data. To remedy these limitations, there has been a new surge of benchmarks proposing datasets and evaluation protocols, which we discuss next." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 134, + 546, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 546, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 546, + 373 + ], + "type": "text", + "content": "Online Learning for Rapid Adaptation. Recent OCL benchmarks, e.g. CLOC [7] and CLEAR [30], introduce data ordered by timestamps, forming a temporal stream of evolving visual concepts over a long span of time. They demonstrate that their data has a natural distribution shift over time, requiring rapid adaptation to newer data. Additionally, they mimic the traditional online learning setup by measuring the capacity for rapid adaptation with the evaluation being done on future data from the stream. Our work extends the efforts in this direction. We adopt the CLOC benchmark and propose a more realistic real-time evaluation that encourages efficient learning. It is worth mentioning that [19] has explored certain aspects of real-time evaluation in continual learning. However, they focus on efficiency for embedded device deployment, rather than rapid adaptation. Moreover, while their work investigates the computational cost associated with each training method, they only report the cost as an evaluation metric. In contrast, we constrain the training procedure by each method's computational cost." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 384, + 389, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 389, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 389, + 398 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 403, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 453 + ], + "type": "text", + "content": "We start with the classical problem statement for online continual learning. Then, we formally introduce our proposed real-time evaluation that factors in training complexity through delayed evaluations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 459, + 457, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 457, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 457, + 472 + ], + "type": "text", + "content": "3.1. Online Continual Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": "Online continual learning [7, 43] is the problem of learning a " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": " parameterized function " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "f_{\\theta}:\\mathcal{X}\\to \\mathcal{V}" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": " that predicts a label " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": " for an input image " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "x\\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": ". Unlike, classical supervised learning, the learning is performed on a distribution-varying stream " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": " revealing data sequentially over steps " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "t\\in \\{1,2,\\dots ,\\infty \\}" + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "text", + "content": ". In particular, at every step " + }, + { + "bbox": [ + 304, + 476, + 545, + 550 + ], + "type": "inline_equation", + "content": "t" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 555, + 545, + 658 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "spans": [ + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "type": "text", + "content": "1. " + }, + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "type": "text", + "content": " reveals a set of images " + }, + { + "bbox": [ + 313, + 555, + 500, + 570 + ], + "type": "inline_equation", + "content": "\\{x_i^t\\}_{i = 1}^{n_t}\\sim \\mathcal{D}_{j\\leq t}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "spans": [ + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "text", + "content": "2. " + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}" + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "text", + "content": " generates predictions " + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "inline_equation", + "content": "\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 574, + 515, + 590 + ], + "type": "inline_equation", + "content": "\\{x_i^t\\}_{i = 1}^{n_t}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "type": "text", + "content": "3. " + }, + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "type": "text", + "content": " reveals true labels " + }, + { + "bbox": [ + 313, + 594, + 448, + 609 + ], + "type": "inline_equation", + "content": "\\{y_i^t\\}_{i = 1}^t" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "spans": [ + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "text", + "content": "4. " + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}" + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "text", + "content": " is evaluated by comparing " + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "inline_equation", + "content": "\\{\\tilde{y}_i^t\\}_{i=1}^{n_t}" + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "inline_equation", + "content": "\\{y_i^t\\}_{i=1}^{n_t}" + }, + { + "bbox": [ + 313, + 613, + 531, + 628 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "text", + "content": "5. A learning method trains " + }, + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}" + }, + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "text", + "content": ", a criterion computes the training loss, then the parameters are updated to " + }, + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\theta_{t + 1}" + }, + { + "bbox": [ + 313, + 634, + 545, + 658 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{j\\leq t}" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " denotes a varying distribution that might not necessarily need to change at every stream step " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " .For example, if at step " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "t = 5" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " we have " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "j = 1" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " , this means the revealed data over all five previous steps is sampled from the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11890" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 531, + 247 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 531, + 247 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 531, + 247 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 531, + 247 + ], + "type": "image", + "image_path": "bc26693a0f114c009287203d6f9c959f68238d015ce01eba65663c8abf472812.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 254, + 548, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 548, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 548, + 310 + ], + "type": "text", + "content": "Figure 2. OCL Real-Time Evaluation Setup. In OCL, models perform real-time prediction on each revealed sample from the stream. At the same time, model training is performed on the revealed samples dictated by the method's delay. In this example, we demonstrate the evaluation procedure when the stream-model complexity " + }, + { + "bbox": [ + 46, + 254, + 548, + 310 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 254, + 548, + 310 + ], + "type": "text", + "content": " is larger than 1. Due to the mismatch between the stream speed and the model computational cost, an \"older version\" of the model predicts samples while the model is being trained. Therefore, k-1 potential training batches are skipped for each training step." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 322, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 288, + 370 + ], + "type": "text", + "content": "same distribution " + }, + { + "bbox": [ + 46, + 322, + 288, + 370 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 46, + 322, + 288, + 370 + ], + "type": "text", + "content": ". Moreover, observe that, unlike offline continual learning, online continual learning captures the capacity to adapt to new data since the prediction is performed before the training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "text", + "content": "Key Issues. As described earlier, the OCL evaluation in the literature [7, 43] overlooks the training complexity in step (5). Under such a setup, all OCL methods have their parameters updated to " + }, + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\theta_{t + 1}" + }, + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "text", + "content": " before the stream " + }, + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 373, + 287, + 529 + ], + "type": "text", + "content": " reveals images of the next step. Therefore, different OCL methods are evaluated irrespective of the training time and computational complexity at step (5). This is equivalent to evaluating different OCL methods on streams that present data at different rates. In real-time settings, the stream reveals data at a rate that is independent of the training complexity of the OCL method. To that end, we propose a real-time evaluation paradigm for OCL that factors in training complexity through delayed evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 538, + 216, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 216, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 216, + 551 + ], + "type": "text", + "content": "3.2. Real-Time Evaluation for OCL" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "As mentioned earlier, we need to define a notion of a fixed stream rate. That is to say, the stream reveals data at a fixed rate irrespective of how long OCL methods take to update the model in step (5). For streams that are twice as fast as it takes to train " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ", OCL methods will have their model updated on only half the number of revealed sets of images from the stream. Note that the latest updated version of " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " will continue to provide predictions for newly revealed images during training even for those images the model did not train on. This setting reflects the realistic scenario of a server receiving many queries uploaded by users, where each query needs a prediction irrespective of whether an in-house model is being trained. Given a stream " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": "an OCL method " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", we first define the notion of stream-model relative complexity " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(\\mathcal{A})\\in \\mathbb{R}^+" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ". In particular, for a stream-model relative complexity " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(\\mathcal{A}) = 1" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", the continual learning method " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": " can update the model " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": " in step (5) before the stream " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": " reveals the data of the next step. For any stream-model relative complexity " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_A(\\mathcal{A}) = k > 1" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", the stream is " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": "-faster than the continual learning method " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ". With this notation, we now propose our modified version of the OCL setting along with the corresponding real-time evaluation. Given a model " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "f_{\\theta_m}" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", a stream " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", and an OCL method " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(\\mathcal{A}) = k" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": ", at every step " + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 322, + 547, + 454 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 460, + 545, + 572 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "type": "text", + "content": "1. " + }, + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "type": "text", + "content": " reveals a set of images " + }, + { + "bbox": [ + 313, + 460, + 500, + 475 + ], + "type": "inline_equation", + "content": "\\{x_{i}^{t}\\}_{i = 1}^{n_{t}}\\sim \\mathcal{D}_{j\\leq t}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "text", + "content": "2. " + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "inline_equation", + "content": "f_{\\theta_m}" + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "text", + "content": " generates predictions " + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "inline_equation", + "content": "\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "inline_equation", + "content": "\\{x_i^t\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 313, + 479, + 518, + 493 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "type": "text", + "content": "3. " + }, + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "type": "text", + "content": " reveals true labels " + }, + { + "bbox": [ + 313, + 498, + 448, + 512 + ], + "type": "inline_equation", + "content": "\\{y_i^t\\}_{i = 1}^t" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "spans": [ + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "text", + "content": "4. " + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "inline_equation", + "content": "f_{\\theta_m}" + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "text", + "content": " is evaluated by comparing " + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "inline_equation", + "content": "\\{\\tilde{y}_i^t\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "inline_equation", + "content": "\\{y_i^t\\}_{i = 1}^{n_t}" + }, + { + "bbox": [ + 313, + 517, + 534, + 531 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "content": "5. If " + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "inline_equation", + "content": "\\mathrm{mod}(t - 1, k) = 0" + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "content": ", then the continual learner " + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "content": " completes updating " + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "inline_equation", + "content": "f_{\\theta_m} \\gets f_{\\theta_{m+1}}" + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "content": " and a new instance of training on " + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "inline_equation", + "content": "f_{\\theta_m}" + }, + { + "bbox": [ + 313, + 536, + 545, + 572 + ], + "type": "text", + "content": " commences (see Figure 2)." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "content": "In this setting, OCL methods that are computationally more expensive to train will be updated fewer times. Therefore, for streams " + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "content": " where the distribution " + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_j" + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "content": " changes rapidly (perhaps as often as every stream step), OCL methods with a large stream-model relative complexity may produce erroneous predictions, since the models are not updated enough and cannot adapt to the distribution change." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "On the Computation of " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " only measures the relative complexity between the stream and an underlying continual learning method, we first introduce a minimal inexpensive OCL method as a baseline (denoted " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "). For ease" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11891" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": "of comparison of the considered methods, we then assume that, due to the inexpensive nature of " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": ", online continual learning will be as fast as the stream where the stream-model relative complexity " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathcal{S}} = 1" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": ". In particular, we consider a baseline that mitigates forgetting by simply storing and replaying recently seen samples. Then, given any other OCL method " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": ", we use the relative training FLOPs between " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " to determine " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathcal{S}}(\\mathcal{B})" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": ". For example, ACE [6] only modifies the loss objective of the baseline, and thus it is equivalent to the baseline in computational complexity. On the other hand, PoLRS [7] maintains and performs operations on three copies of the model. These copies are trained on every incoming batch, making PoLRS require " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " the FLOPs needed by the baseline. As noted earlier, a method of a stream-model relative complexity value of 3 performs the update in step (5) once every three stream steps. This corresponds to a delay in model updates by two steps. In Table 1, we summarize the corresponding delay of several popular OCL methods in our real-time evaluation setup." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "content": "Fair Comparison of OCL Methods with Different " + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathcal{S}}" + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "content": ". We proposed a realistic setup of evaluating continual learners based on their training complexity with respect to the stream speed. However, one might argue that more expensive training routines could be accelerated by deploying more computational hardware allowing them to train on each revealed sample from the stream. For example, while PoLRS [7] requires " + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "content": " more FLOPs than the simple baseline, one could deploy " + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "content": " more hardware to make " + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\mathcal{A}) = 1" + }, + { + "bbox": [ + 46, + 301, + 288, + 445 + ], + "type": "text", + "content": " for PoLRS. This setup mimics the scenario of having a slow stream that matches the speed of the more expensive training method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "text", + "content": "While the aforementioned setup normalizes the computational requirement of a given learning method " + }, + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "text", + "content": " to match the stream speed, one should allow simpler training methods the same computational complexity. To that end, we propose boosting simpler and faster training methods to match the computational requirements of more complex methods. For example, we boost the simple experience replay method by sampling a larger number of instances from the replay buffer at each step " + }, + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 445, + 289, + 601 + ], + "type": "text", + "content": " to match the FLOPs of other training schemes. We note here that although this modification is both simple and naive, we found empirically that it is sufficient to outperform all considered OCL methods. We leave the rest of the implementation details to Section 4.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 128, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 128, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 128, + 624 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "We compare OCL methods under our proposed real-time evaluation setup given two stream speeds: fast and slow, which capture different application scenarios. We benchmark the majority of OCL methods, which we group into three categories. (1) Regularization-based OCL methods regularize training by modifying the classification loss. For example, RWalk [8] uses a regularizer to penalize abrupt" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 134, + 541, + 261 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": "Table 1. Training complexity and delay of considered OCL methods. *Note that GSS has a complexity of 6.5 but we rounded it down to 6 to facilitate the setup. This rounding may give GSS a slight advantage, but nonetheless, it is outperformed by the baseline, ER, in all experiments." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 134, + 541, + 261 + ], + "lines": [ + { + "bbox": [ + 309, + 134, + 541, + 261 + ], + "spans": [ + { + "bbox": [ + 309, + 134, + 541, + 261 + ], + "type": "table", + "html": "
CL StrategyMethod(A)C_S(A)Delay
Experience ReplayER [11]10
RegularizationsACE [6]10
LwF [28]4/31/3
RWalk [8]21
LR SchedulerPoLRS [7]32
Sampling StrategiesMIR [3]5/23/2
GSS [4]6*5
", + "image_path": "1b180e120ea19f1a003a7077ea8feec1b21e88aeb138e05df49bf05e35f58246.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 276, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 547, + 384 + ], + "type": "text", + "content": "changes in the parameters of the model. ACE [6] introduces an asymmetric loss to treat memory buffer samples differently from incoming stream samples, while LwF [28] distills knowledge from previous steps. (2) Learning rate scheduler methods, in this case PoLRS [7], dynamically adapt the learning rate to changes in the stream distribution. (3) Sampling-based methods alter the strategy used to update the memory buffer, e.g. GSS [4], or change the memory retrieval strategy, e.g. MIR [3]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "text", + "content": "Datasets. We use the large-scale online continual learning dataset CLOC [7], which contains 39 million time-stamped images exhibiting natural distribution shifts. The task is to identify the geolocation of a given image where the total number of geolocation labels is 712. To ensure consistency with CLOC [7], we adopt the same dataset split approach. Specifically, we use the first " + }, + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "text", + "content": " of the stream for hyperparameter selection, uniformly sample " + }, + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 386, + 547, + 554 + ], + "type": "text", + "content": " from the remaining stream to build a held-out set for measuring backward/forward transfer (reported in the appendix), and utilize the rest of the stream for training and online evaluation. Similar to CLOC [7], we compare OCL methods using the Average Online Accuracy metric, which measures the ability of models to adapt to incoming stream samples1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": "Implementation Details. At each step " + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": " during the experiments, " + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": " reveals a set of 128 images, and OCL methods augment the training batch with another 128 images sampled from a memory buffer. This routine is performed until a single pass over the stream is completed. We use ImageNet [15] pre-trained ResNet50 [7, 20] as a backbone. We use SGD with a learning rate of " + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": " for all OCL methods except for PoLRS [7], which works best with a learning rate of " + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": ". Unless otherwise stated, we set the size of the replay buffer to " + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "inline_equation", + "content": "4 \\times 10^{4}" + }, + { + "bbox": [ + 304, + 555, + 547, + 675 + ], + "type": "text", + "content": " for all considered methods. We" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "type": "text", + "content": "This metric should not be mistaken for a training accuracy, as it evaluates the model on the next unseen training batch before the batch is used for model training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11892" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 270, + 247 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 270, + 247 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 270, + 247 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 270, + 247 + ], + "type": "image", + "image_path": "c78b09c573a981d844a311e78eb17cb19122ffa9695146a216b9646aca847598.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 254, + 288, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 288, + 321 + ], + "type": "text", + "content": "Figure 3. Fast Stream Evaluation. We compare the Average Online Accuracy of six methods from the OCL literature evaluated under the fast-stream setting. We observe that our inexpensive baseline, ER, outperforms all the considered methods. Surprisingly, the most computationally complex methods, MIR, PoLRS, and GSS, underperform the more efficient methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "text", + "content": "use the same hyperparameters reported in all corresponding papers with the exception of the regularization parameter for RWalk [8]. We find that their reported regularization " + }, + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "text", + "content": " is too small for the CLOC dataset; we cross validate it and find that " + }, + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "inline_equation", + "content": "\\lambda = 2" + }, + { + "bbox": [ + 46, + 335, + 287, + 431 + ], + "type": "text", + "content": " works best. Our implementation extends the codebase of Avalanche [31], which is a popular continual learning framework. We leave all the remaining implementation details and ablations to the appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 237, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 237, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 237, + 453 + ], + "type": "text", + "content": "4.1. Fast Stream: Real-Time Evaluation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": "We first consider the fast-stream scenario, where the stream reveals data at a high rate. We consider the simple baseline " + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": " [11], which performs one gradient step on a batch of 256 (128 revealed by the stream and 128 from memory) images at every stream step. The 128 images from memory are sampled uniformly. For simplicity and ease of comparison, we assume that " + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": " has a stream-model relative complexity of " + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(ER) = 1" + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": ". Consequently, any OCL method that is computationally more expensive than " + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": " will not keep up with the stream speed, and thus will be forced to skip training on a fraction of the incoming stream samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Benchmarking Relative Complexity of OCL Methods. As discussed earlier, we use the total number of FLOPs required for each method to train on a stream as a proxy for the stream-model relative complexity " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": ". We first compute the total FLOPs required to train " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": " on a small subset of CLOC composed of " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "10^3" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": " images with a batch size of 10. We then compute the corresponding FLOPs for various OCL methods and normalize them by the FLOPs of " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": ". Since the backbone is shared across all methods, we further verify this normalized complexity by counting the effective number of" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "forward and backward passes of each method. Because we assume that " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " is effectively as fast as the stream, methods that are twice more expensive in FLOPs have a complexity " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " of 2. We report in Table 1 the stream-model relative complexity for OCL methods compared against " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ". Note that PoLRS is 3 times as expensive as " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " since it requires training 3 different models to update the learning rate. In addition to the 128 images revealed by the stream and the 128 images sampled from memory at step " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ", GSS performs additional forward and backward passes on " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "10 \\times 128" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " memory samples to ensure diversity when updating the memory buffer [4]. Therefore, GSS is roughly 6 times more expensive than " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ". For each method in Table 1, we report the corresponding delay in stream steps, which is a consequence of some methods being slower than the stream. A delay of 2 means that the stream will reveal 2 steps worth of images before the model is updated." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": "Effect of Training Efficiency. We start our analysis by investigating the effect of training efficiency on the performance of different OCL methods under the real-time evaluation setup. We plot the Average Online Accuracy curves per step in Figure 3, where the simple " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": " baseline is in blue. Each method is evaluated according to its corresponding training delay reported in Table 1. Surprisingly, " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": " outperforms all considered methods, and in some cases, by large margins. Interestingly, the most computationally intensive methods, MIR, PoLRS, and GSS, exhibit the lowest performance when real-time evaluation is considered. Specifically, the performance gap at the end of the stream reaches " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "11\\%" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": ". In fact, we note that the Average Online Accuracy values of all considered methods, irrespective of how recently they were introduced to the literature, are approximately ordered based on their stream-model relative complexity " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": "; the larger " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": " is, the worse the performance is under real-time evaluation. We attribute this trend to the fact that these inefficient methods may not be capable of keeping up with the fast-changing distribution " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_j" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": " in the stream when they are subjected to a higher delay. For example, although PoLRS was proposed and tailored for the recent CLOC benchmark, it is significantly outperformed by the older method LwF when evaluated under the real-time paradigm. This hints that computational complexity can be a crutch for OCL methods learning on fast streams. Our results show that while the current literature aims to improve learning by leveraging more expensive and advanced learning routines, the penalty incurred by delay overshadows any potential improvements gained by the algorithmic contributions. Notably, the state-of-the-art ACE method, which is as efficient as " + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": " and thus evaluated under no training delay, performs almost as well as the baseline. Additionally, ACE outperforms more expensive methods when evaluated on small-scale datasets (refer to Small-Scale Experiments in the appendix). Overall, our findings suggest that practical" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11893" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 162, + 183 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "type": "image", + "image_path": "f74505de5b70156da21c02dd8556dd29595539593a046e27e7ab430c53d6775e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": "Figure 4. Fast Stream - Training Data Normalization. We compare each method against " + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": " and its delayed version " + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": "--. " + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": "-- performs extra gradient steps per time step to match the delay of the compared-against method, so it trains on fewer samples than " + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": ". We highlight that even when " + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 547, + 236 + ], + "type": "text", + "content": "-- is unfairly delayed to match each OCL method's delay, it outperforms all considered methods." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 162, + 68, + 257, + 183 + ], + "blocks": [ + { + "bbox": [ + 162, + 68, + 257, + 183 + ], + "lines": [ + { + "bbox": [ + 162, + 68, + 257, + 183 + ], + "spans": [ + { + "bbox": [ + 162, + 68, + 257, + 183 + ], + "type": "image", + "image_path": "94696f6633f3e79b6521a91eab3b65c59ac7623ae91f6e21ff77dbb61a904e6a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 200, + 186, + 272, + 196 + ], + "lines": [ + { + "bbox": [ + 200, + 186, + 272, + 196 + ], + "spans": [ + { + "bbox": [ + 200, + 186, + 272, + 196 + ], + "type": "text", + "content": "ER (Delay = 0)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 258, + 68, + 353, + 183 + ], + "blocks": [ + { + "bbox": [ + 258, + 68, + 353, + 183 + ], + "lines": [ + { + "bbox": [ + 258, + 68, + 353, + 183 + ], + "spans": [ + { + "bbox": [ + 258, + 68, + 353, + 183 + ], + "type": "image", + "image_path": "434031a633944b9cea70c55f89ae82566fa3c9c5656d7dcb170561b4870d87d3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 286, + 186, + 357, + 196 + ], + "lines": [ + { + "bbox": [ + 286, + 186, + 357, + 196 + ], + "spans": [ + { + "bbox": [ + 286, + 186, + 357, + 196 + ], + "type": "text", + "content": "ER--" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 353, + 68, + 447, + 183 + ], + "blocks": [ + { + "bbox": [ + 353, + 68, + 447, + 183 + ], + "lines": [ + { + "bbox": [ + 353, + 68, + 447, + 183 + ], + "spans": [ + { + "bbox": [ + 353, + 68, + 447, + 183 + ], + "type": "image", + "image_path": "404a156c262df767b865239b0bb311c6c930065bff99c1cebb502b26a1b685a4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 186, + 405, + 196 + ], + "lines": [ + { + "bbox": [ + 358, + 186, + 405, + 196 + ], + "spans": [ + { + "bbox": [ + 358, + 186, + 405, + 196 + ], + "type": "text", + "content": "OCL Method" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 449, + 68, + 544, + 183 + ], + "blocks": [ + { + "bbox": [ + 449, + 68, + 544, + 183 + ], + "lines": [ + { + "bbox": [ + 449, + 68, + 544, + 183 + ], + "spans": [ + { + "bbox": [ + 449, + 68, + 544, + 183 + ], + "type": "image", + "image_path": "bf84bfb97c21b6ee7efc5bcd81f393c064aab76338c5cbb9663d258bbe317882.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 247, + 288, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 272 + ], + "type": "text", + "content": "OCL methods, deployed in real-time applications, should prioritize efficient learning over expensive optimization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": "Training Data Normalization. Previously, we have shown that delayed evaluation leads to larger performance degradation as the delay gets longer. However, this could be attributed to the fact that OCL methods with larger delays end up effectively training on a fewer number of samples. This raises the questions: Do computationally more expensive methods with delays perform worse than ER because they cannot cope with the changing distribution in the stream? or is the performance degradation due to expensive OCL methods being trained on effectively a fewer number of training examples? To address these questions, we conduct pairwise comparisons between " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": " and each previously reported OCL method. Assuming that the stream speed is fixed, we modify " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": " to match the computational expense of the respective method by training on the same amount of data for a longer duration. To achieve this computational matching, we subject " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": " to a delay by performing additional gradient descent steps at each stream step. We refer to this modified baseline as " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": "--. The number of additional updates in " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": "-- is determined such that its delay matches the delay of the corresponding OCL method. This guarantees that " + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 277, + 289, + 553 + ], + "type": "text", + "content": "-- trains on the same number of training examples compared to other OCL methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "Figure 4 shows comparisons of " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "- to each of the considered OCL methods. Since the non-delayed " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": " is more efficient than " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "-, " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": " consistently outperforms " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "-, confirming that efficiency is key for the real-time evaluation of OCL. More interestingly, even though " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "- matches the complexity of each compared-against method and is subject to the same delay, it still outperforms all considered OCL methods. Moreover, while the gap between " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "- and expensive approaches, e.g. GSS, is smaller than the gap to " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": ", expensive methods still lag behind " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": "- by up to " + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 46, + 557, + 288, + 714 + ], + "type": "text", + "content": ". This demonstrates that the degraded performance of considered OCL methods is not due to the fewer number of observed training examples. On the contrary, expensive OCL meth" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "text", + "content": "ods seem to be unable to cope with distribution-changing streams. Under real-time evaluations of fast streams, simple methods such as " + }, + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 247, + 547, + 296 + ], + "type": "text", + "content": "--- may be more suitable for real-world deployment." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 308, + 520, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 520, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 520, + 322 + ], + "type": "text", + "content": "4.2. Slow Stream: Complexity Normalization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": "In the fast stream setting, we considered the scenario where the stream is as fast as the " + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": " baseline, i.e., " + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(ER) = 1" + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": ". In this section, we consider streams that are as slow as the more expensive OCL methods. This setup motivates the following question: How do existing OCL methods perform if they were deployed on streams that match their training complexity? Slower streams may enable expensive methods to train on the entire stream, without having to skip any stream steps. Would previously considered methods, which struggled in the fast-stream setting, be suitable for OCL deployment in this slow-stream scenario? We compare various OCL methods under no delay against their corresponding modified baseline " + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": ", which computes additional number of gradient steps per batch to match the complexity of the compared-against method, as determined from Table 1. This mimics the comparison on slow stream speeds, where no stream steps are skipped and comparisons are performed under normalized complexity. Note that ACE only modifies the loss objective of " + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": ", so it matches the complexity of the baseline " + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S(ACE) = 1" + }, + { + "bbox": [ + 304, + 328, + 547, + 616 + ], + "type": "text", + "content": ". As a result, evaluating ACE in the slow-stream setting is identical to evaluating it in the fast-stream setting, which was already done in Figure 3. Therefore, we do not compare to ACE again in the following experiments." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "We report the comparisons in Figure 5, where " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " is shown in green and OCL methods in red. Moreover, we show " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": ", which is unfavorably compared against both, in blue. While RWalk outperforms " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " in the slow stream setting, this is an unfair comparison, since " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " is not utilizing the fact that the stream is slow and that it can benefit from further training. Once we simply add a few iterations to " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": ", so as to match the training complexity of" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11894" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 162, + 183 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 162, + 183 + ], + "type": "image", + "image_path": "d3f25cf2d9015f09e296ed1a238df00064334ea23d3b21e2fb3c0008147157ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 163, + 68, + 257, + 195 + ], + "blocks": [ + { + "bbox": [ + 163, + 68, + 257, + 195 + ], + "lines": [ + { + "bbox": [ + 163, + 68, + 257, + 195 + ], + "spans": [ + { + "bbox": [ + 163, + 68, + 257, + 195 + ], + "type": "image", + "image_path": "d6630fb7cff583696e401548c7c32edfe9dd8f40315d96079a762c47684eea8f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": "Figure 5. Slow Stream. We compare each method against " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": ", which performs extra gradient steps per time step to match the complexity " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_S" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": " of the compared-against method. " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": " outperforms all the considered methods, sometimes by large margins." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 258, + 68, + 352, + 196 + ], + "blocks": [ + { + "bbox": [ + 258, + 68, + 352, + 196 + ], + "lines": [ + { + "bbox": [ + 258, + 68, + 352, + 196 + ], + "spans": [ + { + "bbox": [ + 258, + 68, + 352, + 196 + ], + "type": "image", + "image_path": "a6da4bdbc97996e541ab3556a2dfd0bb1d8cc1aa7ae09ea761170fe71e31b299.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 353, + 68, + 447, + 196 + ], + "blocks": [ + { + "bbox": [ + 353, + 68, + 447, + 196 + ], + "lines": [ + { + "bbox": [ + 353, + 68, + 447, + 196 + ], + "spans": [ + { + "bbox": [ + 353, + 68, + 447, + 196 + ], + "type": "image", + "image_path": "b43a29557df01c9d0116ac6b445f9abcacf6870e8af616547e2b1ed9548438e6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 449, + 68, + 544, + 196 + ], + "blocks": [ + { + "bbox": [ + 449, + 68, + 544, + 196 + ], + "lines": [ + { + "bbox": [ + 449, + 68, + 544, + 196 + ], + "spans": [ + { + "bbox": [ + 449, + 68, + 544, + 196 + ], + "type": "image", + "image_path": "48233bb0d19a7ca97bfac45805a187e8c0b4744fb019e9ab605cbd543970246c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 239, + 287, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 262 + ], + "type": "text", + "content": "RWalk, " + }, + { + "bbox": [ + 46, + 239, + 287, + 262 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 46, + 239, + 287, + 262 + ], + "type": "text", + "content": " performs far better than RWalk. We find this to be consistent across all methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": "Interestingly, computationally intensive methods, e.g., GSS and MIR, perform worse even when compared to " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": ", which does not exploit the fact that the stream is slow. " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " is significantly better than GSS and MIR, by " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "11\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " respectively, expanding the performance gap to the baseline by around " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": ". These results question the suitability of the previously proposed methods to realistic OCL setups with large-scale datasets. Moreover, our results suggest that a computationally unfair evaluation setup (i.e. not normalizing training complexity) in slow stream OCL can lead to misleading performance conclusions, as is the case with RWalk. We highlight that PoLRS was originally tested on a slightly different setup to the slow stream, which included extra information represented by a user album [7]. We find that when the album information is removed and their reported baseline, i.e., " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": ", is tuned properly, PoLRS has a similar performance to " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " as shown in Figure 5. This is still surprising since PoLRS is three times more expensive than " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": ". More surprisingly, when matching the training complexity of " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " to PoLRS on the slow stream, " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "ER++" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": " outperforms PoLRS by " + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "inline_equation", + "content": "9.5\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 539 + ], + "type": "text", + "content": ". These results on the slow-stream setting support our earlier observation that current OCL methods are not yet suited for practical deployment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 550, + 174, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 174, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 174, + 562 + ], + "type": "text", + "content": "4.3. Effect of Memory Size" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "We conduct experiments to test whether existing methods can outperform " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " under different memory buffer sizes. We repeat the fast-stream experiment from Section 4.1 with memory budgets of " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{4}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 10^{4}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "4 \\times 10^{4}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " samples. The results are summarized in Table 2. A larger memory size leads to a higher Average Online Accuracy across all methods. However, we emphasize that the trend across methods aligns with our previous finding that expensive-training OCL methods perform worse than their less expensive counterparts. This is evident from the ordering of the methods in Figure 3, which holds regardless of the memory budget. Notably, " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " outperforms all considered methods." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 336, + 297, + 514, + 427 + ], + "blocks": [ + { + "bbox": [ + 305, + 237, + 545, + 293 + ], + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 293 + ], + "type": "text", + "content": "Table 2. Memory Budget Analysis. We test the effect of varying the memory budget in the fast-stream setting. We observe that 1) increasing the memory size results in better performance regardless of the method, and 2) ER outperforms all the considered methods regardless of the memory budget." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 336, + 297, + 514, + 427 + ], + "lines": [ + { + "bbox": [ + 336, + 297, + 514, + 427 + ], + "spans": [ + { + "bbox": [ + 336, + 297, + 514, + 427 + ], + "type": "table", + "html": "
MethodMemory Size
1 × 1042 × 1044 × 104
ER [11]18.0919.3720.27
ACE [6]17.5318.5519.42
LwF [28]16.8717.8718.69
RWalk [8]14.6015.2916.07
PoLRS [7]12.4012.9813.59
MIR [3]11.3711.6411.89
GSS [4]8.018.599.10
", + "image_path": "e7c78f32cad99650d1e80cc9ccdff74ea562659487700a5748830e687a08fc48.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 439, + 378, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 378, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 378, + 451 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 604 + ], + "type": "text", + "content": "We proposed a real-time evaluation benchmark for online continual learning, including a fast stream that continues to reveal new data even when the model has not completed training. This realistic setup forces computationally intensive methods to skip more training samples, highlighting the differences in training complexity between the considered methods. Our results show that, under this setting, all considered methods underperform the simple " + }, + { + "bbox": [ + 304, + 460, + 545, + 604 + ], + "type": "inline_equation", + "content": "ER" + }, + { + "bbox": [ + 304, + 460, + 545, + 604 + ], + "type": "text", + "content": " baseline. We also explored scenarios where we normalized the number of seen training data or the computational complexity per time step, leading to the same conclusion that current methods are not yet optimized for real-world deployment." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence (SDAIA-KAUST AI), Saudi Aramco, and UKRI grant Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ameya Prabhu is funded by Meta AI Grant No DFR05540." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11895" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Motasem Alfarra, Zhipeng Cai, Adel Bibi, Bernard Ghanem, and Matthias Müller. 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However, multiperson scenario within untrimmed videos is also important for practical applications, which has not been well concerned yet. To address this, we shed light on this research field for the first time with essential contributions on dataset, theory, and practices. In particular, a large-scale dataset termed MPEblink that involves 686 untrimmed videos with 8748 eyeblink events is proposed under multiperson conditions. The samples are captured from unconstrained films to reveal \"in the wild\" characteristics. Meanwhile, a real-time multi-person eyeblink detection method is also proposed. Being different from the existing counterparts, our proposition runs in a one-stage spatio-temporal way with end-to-end learning capacity. Specifically, it simultaneously addresses the sub-tasks of face detection, face tracking, and human instance-level eyeblink detection. This paradigm holds 2 main advantages: (1) eyeblink features can be facilitated via the face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, and (2) addressing these sub-tasks in parallel instead of sequential manner can save time remarkably to meet the real-time running requirement. Experiments on MPEblink verify the essential challenges of real-time multiperson eyeblink detection in the wild for untrimmed video. Our method also outperforms existing approaches by large margins and with a high inference speed.", + "bbox": [ + 75, + 438, + 473, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d4804999bcb9297efa3db13afb98246c8d1880b9649b2b9edd1290a3f1c50407.jpg", + "image_caption": [ + "Figure 1. The illustration on multi-person eyeblink detection. This task aims at being aware of the presence of people and detecting their eyeblink activities at instance level." + ], + "image_footnote": [], + "bbox": [ + 501, + 409, + 893, + 553 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 616, + 633, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Real-time eyeblink detection in the wild is a recently emerged challenging research task [19] that can widely serve for fatigue detection [2], face anti-spoofing [34], affective analysis [7], etc. Although remarkable progress has been made [9, 10, 19], the existing methods generally focus on single-person cases within trimmed videos. Multi-person scenario within untrimmed videos has not been well concerned yet. However, detecting long-term eyeblink behaviors at multi-instance level is more preferred for some practical application scenarios. For example, it can be used to estimate attendees' attention level and emotional state change during social interaction [9, 33]. Thus, effective and real-time multi-person eyeblink detection in the wild for untrimmed video is indeed required.", + "bbox": [ + 496, + 642, + 893, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we shed the light on this research problem with essential contributions on dataset, theory, and practices. First, a challenging labeled multi-person eyeblink de", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Yang Xiao is corresponding author (Yang_Xiao@hust.edu.cn).", + "bbox": [ + 99, + 886, + 437, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13854", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tection benchmark termed MPEblink is built under in-the-wild conditions. It consists of 686 untrimmed long videos captured from unconstrained movies to reveal the \"in the wild\" characteristics. The contained scenarios are realistic and diverse, such as social interactions and group activities. To our knowledge, MPEblink is the first multi-person eyeblink detection dataset that focuses on in-the-wild long videos. Fig. 1 illustrates a sample video with ground truth annotations within it. Different from the existing eyeblink detection benchmarks [10, 12, 19], the proposed benchmark aims at being aware of all the attendees along the whole video and detecting their eyeblinks at instance level. In summary, MPEblink is featured with multi-instance, unconstrained, and untrimmed, which makes it more challenging and realistic than previous formulations.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To perform eyeblink detection, previous methods [9, 10, 12, 19, 40] generally take a sequential approach containing face detection, face tracking, and classification on the pre-extracted local eye clues within a temporal window. Whereas such a pipeline seems reasonable, it has several critical drawbacks. First, the use of isolated components may lead to sub-optimal results as they are not jointly optimized and it is inefficient due to the inability to reuse the features of each stage. Second, the eyeblink features only contain the information from the pre-extracted local eye clues (i.e., a small part of face), lacking the useful information from global face context such as head pose and illumination condition that are crucial for detecting eyeblinks in the wild. Moreover, the pre-extracted local eye clues are also unreliable due to the localization challenge towards unconstrained scenarios. Third, the sequential approach leads to computational cost being sensitive to the subject amount, which is hard to meet the real-time running requirement.", + "bbox": [ + 75, + 319, + 472, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle these issues, we propose a one-stage multi-person eyeblink detection framework called InstBlink, which can simultaneously detect human faces, track them over time, and do eyeblink detection at instance level. InstBlink takes inspiration from the existing query-based methods [41, 45, 47, 48] and models the spatio-temporal face as well as eyeblink representations at instance level within each query. The insight is that the features can be effectively shared among these sub-tasks and the eyeblink features can be facilitated via face's global contexts (e.g., head pose and illumination condition) with joint optimization and interaction, especially in unconstrained in-the-wild cases. Experiments verify the superiority of InstBlink in both effectiveness and efficiency, while also highlighting the critical challenges of real-time multi-person eyeblink detection in the wild for untrimmed video.", + "bbox": [ + 75, + 594, + 472, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work lie in 3 folders:", + "bbox": [ + 96, + 838, + 439, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- To our knowledge, it is the first time that instance-level multi-person eyeblink detection in untrimmed videos is formally defined and explored;", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce an unconstrained multi-person eyeblink detection dataset MPEblink that contains 686 untrimmed videos with 8748 eyeblink events, featured with more realistic and challenging.", + "- We propose a one-stage multi-person eyeblink detection method that can jointly perform face detection, tracking, and instance-level eyeblink detection. Such a task-joint paradigm can benefit the sub-tasks uniformly." + ], + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 224, + 640, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Eyeblink detection dataset. Existing eyeblink detection datasets [1, 10, 12, 13, 34, 36] generally focus on constrained indoor cases with a consistent environmental setup. HUST-LEBW [19] extends the scenarios to the unconstrained outdoor cases. From then on, the community starts to pay more attention to eyeblink detection in the wild. Nevertheless, HUST-LEBW mainly focuses on single-person scenarios towards trimmed videos, which limits the application of methods in more realistic scenarios such as group activities and social interactions. To address such limitation, we introduce a new dataset termed MPEblink. The proposed dataset is featured with multi-person, unconstrained, and untrimmed, thus being more realistic and challenging.", + "bbox": [ + 496, + 251, + 893, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Eyeblink detection method. Existing methods generally judge eyeblinks from the pre-extracted local eye clues (e.g., local eye region [6, 9, 10, 19, 25] or landmarks around eyes [8, 14, 35, 40]). To obtain the local eye clues, the existing works generally run in a sequential way including face detection, face tracking, and landmark detection. Finally, the eyeblink result is classified from the pre-extracted local eye clues within a temporal window. Such a pipeline is inefficient due to the isolated optimization among different sub-tasks. Meanwhile, the eyeblink features only contain the information from the pre-extracted local eye clues, lacking useful global information such as head pose and illumination, and the pre-extracted eye clues are also unreliable due to the localization challenge toward unconstrained cases. Besides, due to the multi-stage characteristic, existing methods do not scale well with the number of people in the scene to meet the real-time running requirement. In this paper, we propose a one-stage eyeblink detection framework that can simultaneously detect human faces, track them along the time, and do eyeblink detection at instance level. Within it, eyeblink features can be facilitated via global face context, and the features can be effectively shared among the sub-task to achieve high inference speed.", + "bbox": [ + 496, + 448, + 893, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spatio-temporal action detection. Spatio-temporal action detection [15, 20, 22, 26, 27, 39, 48] aims at simultaneously obtaining the spatial and temporal location of an action, which is defined as an action tube [22]. The task only focuses on the isolated action tubes without instance awareness and thus can not make an instance-level analysis along the whole video. Different from that, our proposed multi-", + "bbox": [ + 496, + 796, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13855", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5791dc8380048a531f9c717700f130a2f84658177270a35ff2026eaf22030f37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 138, + 88, + 276, + 146 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0ca190674584b915f0c2834b48ea6900effd1fffa5fec3754bc2cf693026db8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 143, + 147, + 272, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e6b5d91740bbc4cf8af48b930233e89b776190c8e96fceb626c441608075a660.jpg", + "image_caption": [ + "Business party" + ], + "image_footnote": [], + "bbox": [ + 138, + 212, + 274, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/baa673c735adc997c0bd2c9e27ebe8ea7471064474dea79d118293e224e9ac70.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 88, + 416, + 146 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/93179e3283422f4ddf59edab857e547455dc5e1a69c0c62f121d651c3e338cdd.jpg", + "image_caption": [ + "Cooking in the kitchen" + ], + "image_footnote": [], + "bbox": [ + 279, + 155, + 415, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b867907f01e28c0fb917183f2389ef6097d636801fb46bef96a435d3392f0532.jpg", + "image_caption": [ + "Eating at restaurant", + "Public speech" + ], + "image_footnote": [], + "bbox": [ + 279, + 220, + 415, + 266 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3a3f04f9a67e0a847e49ef62bb9a28f99329a8b9ce9f51aeb3e667d690a1f71e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 418, + 88, + 553, + 147 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8dc1c45e8e3e8d4b28fd3d4e021405e34a8cfdbcbda3119bddbe94898efbf2ab.jpg", + "image_caption": [ + "Hiking", + "Daily life in prison" + ], + "image_footnote": [], + "bbox": [ + 418, + 155, + 552, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/87be4af61433df6e36b140abddfd45e3353b153f91e67eec94132fab0bacf72e.jpg", + "image_caption": [ + "Discussing in the classroom" + ], + "image_footnote": [], + "bbox": [ + 418, + 220, + 552, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6b321236ab5b771cbb6a3d5e3ad590ef8f05f3cd9fe0aca01d3271ac4d8f7d41.jpg", + "image_caption": [ + "Caring for baby" + ], + "image_footnote": [], + "bbox": [ + 557, + 88, + 692, + 147 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c42bbc5e05f9670374341dbbd816fd48dcc3a23272a155231aea984ac388a4c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 557, + 155, + 691, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/aa174d0f0fca4dcde01e15cf935dc1b195656778eecef4338a2c9cd855f4fda8.jpg", + "image_caption": [ + "Being threatened", + "Arguing in the car" + ], + "image_footnote": [], + "bbox": [ + 557, + 220, + 691, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/40fd90a6a9482c2bd821feff183174ef3f06ca2420c3ada035d8fe6e1934a647.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 88, + 828, + 147 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/49a64c37959133d9d89a9c49f0e40f5fa5514312e9ac52a9ad6540118ad3ec36.jpg", + "image_caption": [ + "Relaxing on the beach" + ], + "image_footnote": [], + "bbox": [ + 694, + 155, + 826, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/49225f73718ebf7b0f8e83064bba9d65fe8320559eb0c0f0d072534e51b94525.jpg", + "image_caption": [ + "Having a meeting", + "Being arrested" + ], + "image_footnote": [], + "bbox": [ + 694, + 220, + 826, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "person eyeblink detection task aims at simultaneously being aware of the presence of people and analyzing their eyeblink behaviors at instance level.", + "bbox": [ + 75, + 304, + 467, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Query-based methods. Query-based methods are impacting many computer vision tasks. After DETR [4], the pioneer that introduces the query-based framework to address object detection, numerous efforts have been subsequently paid to facilitate visual recognition under the query concept in the fields of object detection [24, 32, 41, 49], pose estimation [38], action detection [30, 48], and segmentation [5, 43, 45, 47]. Inspired by these, we build the first one-stage multi-person eyeblink detection framework for untrimmed video. We propose a unified solution to simultaneously model the instance-level face and eyeblink representations in the whole video.", + "bbox": [ + 75, + 349, + 468, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The MPEblink Benchmark", + "text_level": 1, + "bbox": [ + 76, + 542, + 328, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing eyeblink detection datasets generally focus on single-person scenarios, and are also limited in aspects of constrained conditions or trimmed short videos. To explore unconstrained eyeblink detection under multi-person and untrimmed scenarios, we construct a large-scale multiperson eyeblink detection dataset termed MPEblink to shed the light on this research topic that has not been well studied before. The distinguishing characteristics of MPEblink lie in 3 aspects: multi-person, unconstrained, and untrimmed long video, which makes it more realistic and challenging than previous datasets.", + "bbox": [ + 75, + 568, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Formulation", + "text_level": 1, + "bbox": [ + 76, + 741, + 250, + 756 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We think that a good multi-person eyeblink detection algorithm should be able to (1) detect and track human instances' faces reliably to ensure the instance-level analysis ability along the whole video, and (2) detect eyeblink boundaries accurately within each human instance to ensure the precise awareness of their eyeblink behaviors.", + "bbox": [ + 75, + 763, + 467, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, for an untrimmed video with $T$ frames and $N_{gt}$ people in it, towards the $j$ -th person, let $\\hat{l}^j \\in \\mathbb{R}^{T \\times 4}$ denote its face bounding boxes across the video. $\\hat{c}^j \\in \\mathbb{R}^T$", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3b44294e0c49981d5de1626105f2158d73af39838d92873bb0453207be72c041.jpg", + "image_caption": [ + "Figure 2. The snapshots within MPEblink. Our dataset is featured with more realistic and diverse scenarios." + ], + "image_footnote": [], + "bbox": [ + 513, + 301, + 694, + 404 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/95b895209233e881656d616468890da66354da2bb1331a70065756cc6f7efd83.jpg", + "image_caption": [ + "Figure 3. Occlusion and people in & out cases during interaction among instances." + ], + "image_footnote": [], + "bbox": [ + 697, + 301, + 875, + 405 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a56eb44ecca6d801bbf8f648ac694e96a09625b4c2f2ae1e483db9c251625993.jpg", + "image_caption": [ + "Figure 4. An example of rapid and consecutive eyeblinks in untrimmed video." + ], + "image_footnote": [], + "bbox": [ + 511, + 446, + 875, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "is given as the face labels to reflect the face existence of this instance in each frame (i.e., $\\hat{c}_t^j\\in \\{1,0\\}$ , where $\\hat{c}_t^j = 0$ indicates that the face is not visible due to serious occlusion or departure at time $t$ ). $\\hat{l}_t^j$ is also set to $\\varnothing$ when the person is not visible. We use $\\hat{l}^j$ and $\\hat{c}^j$ to represent the instance-level information of each person. Suppose person $j$ blinks $\\hat{K}^j$ times in the video. Let $\\hat{B}_{\\hat{k}}^{j} = \\left[\\hat{s}_{\\hat{k}}^{j},\\hat{e}_{\\hat{k}}^{j}\\right]$ denote the $\\hat{k}$ -th eyeblink event within this person, where $\\hat{s}_k^j$ and $\\hat{e}_k^j$ denote its starting and ending time. Suppose a multi-person eyeblink detection algorithm produces $H$ human instance hypotheses. Within each human instance hypothesis $i$ , it needs to produce a sequence of predicted face bounding boxes $l^i$ , face classification scores $c^i$ , and $K^i$ eyeblink proposals $B_{k}^{i} = [s_{k}^{i},e_{k}^{i}]$ . Better performance can be acquired when predictions get closer to ground truths.", + "bbox": [ + 498, + 539, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Data Collection", + "text_level": 1, + "bbox": [ + 500, + 786, + 656, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We collect 686 untrimmed video clips with various lengths (i.e., 7.1-85.9s) from 86 different unconstrained movies that involve the \"in the wild\" characteristics. Some snapshots of the acquired samples are shown in Fig. 2. It can be observed that the samples are with variational indoor and outdoor scenarios for different themes. Thus, the", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13856", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/eb032ac8d6bfb289539096c539b4cb938bb4a6c6b21e38f3fc4e86c1f62164ad.jpg", + "table_caption": [ + "Table 1. High-level statistics of MPEblink dataset and existing eyeblink detection datasets." + ], + "table_footnote": [], + "table_body": "
Talking Face [1]ZJU [34]Eyeblink8 [12]Silesian5 [36]Researcher's Night [13]mEBAL [10]HUST-LEBW [19]MPEblink (Ours)
Num. of videos180851076000673686
Video length3.3m4.1-4.7s2.7-8.9m1.4-2.7m0.3-3.4m0.6s0.5s7.1-85.9s
Unconstrained××××××√√
Instances/video11111111-8
Blink count61255353300186730003818748
", + "bbox": [ + 109, + 107, + 857, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "acquired samples from these movies are much more realistic and closer to practical applications. Meanwhile, due to the high divergence of the selected movie data source, the captured multi-person eyeblink samples are also of great challenges for effectively detecting eyeblinks. For instance, the pose, illumination condition, expression, and face size among instances differ a lot, even within the same video. Moreover, because of the various types of interaction among instances, there may exist severe occlusion or people in and out scenarios as shown in Fig. 3, making it harder for both instance localization and their eyeblink event detection. Besides, different from the existing unconstrained counterpart [19] that mainly focuses on trimmed short videos, the samples from MPEblink are untrimmed. As a result, we not only need to recognize eyeblink but also need to locate the starting and ending time of each eyeblink event, which is more challenging especially when rapid and consecutive eyeblinks occur. An example is shown in Fig. 4. It can be observed that the appearance difference among eye statuses is small when consecutive rapid eyeblinks happen, making it hard to distinguish the boundary of each eyeblink. Considering the above challenges together, it can be summarized that unconstrained multi-person eyeblink detection in untrimmed videos is indeed a challenging research task.", + "bbox": [ + 76, + 199, + 472, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Data Annotation", + "text_level": 1, + "bbox": [ + 76, + 571, + 243, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For human instances in each video, we labeled their face bounding boxes exhaustively across the whole video. To facilitate the research of landmark-based methods and include a broader range of applications, 68 facial landmark positions [44] are also annotated. Technically, this part of the annotation is under a semi-supervised manner: we use the state-of-the-art face analysis engine InsightFace [21] to achieve face bounding box [16] and landmark [44] detection. To track instances across frames, a matching strategy that considers bounding box IoU and similarity among deep face features [11] is designed. Besides, human annotators carefully check the annotation quality and correct the wrong bounding boxes and tracking results generated by the algorithm. For eyeblink events within each instance, human annotators carefully define their start and end frame. Finally, 8748 eyeblink events are labeled.", + "bbox": [ + 75, + 595, + 470, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Data Statistics", + "text_level": 1, + "bbox": [ + 76, + 845, + 225, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The dataset statistics comparison among MPEblink and the other eyeblink detection datasets are given in Table 1.", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Actually, MPEblink provides the largest number of eyeblink events (i.e., 8748) within 686 untrimmed videos. The biggest difference from the previous datasets is that the videos in our dataset contain various numbers of human instances (i.e., 1-8) with exhaustive annotation. The videos are captured under unconstrained in-the-wild conditions with high diversity as shown in Fig. 2. Compared with the existing in-the-wild counterpart [19] that generally focuses on trimmed short videos, the length of videos from our dataset is much longer and more diverse. In summary, MPEblink is featured with more realistic and challenging and thus has broader application values.", + "bbox": [ + 496, + 199, + 893, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 392, + 684, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing metrics for eyeblink detection only focus on single-person cases without multi-instance awareness. To address this limitation we introduce 2 new metrics termed Inst-AP and Blink-AP to give attention to both instance awareness quality and eyeblink detection quality.", + "bbox": [ + 496, + 415, + 893, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inst-AP. It aims to evaluate the instance detection and tracking ability of methods, which is the basis for analyzing the eyeblink behaviors of each instance. We modify the standard evaluation metric video-AP in spatio-temporal action detection [22] to fit our task. Different from the original implementation, the 3D IoU is calculated between each instance proposal (i.e., a sequence of face bounding boxes) and ground truth across the whole video, rather than the action tube only. As a result, the proposed metric can reveal the algorithm's ability for detection and tracking instances, while video-AP can just reveal the localization ability of the isolated action tube without instance-level awareness. We report the averaged Inst-AP under the IoU from $50\\% -95\\%$ with step $5\\%$ . During calculating Inst-AP, each obtained true positive (TP) prediction has matched with one ground-truth instance, and thus, we can calculate the eyeblink detection accuracy of these TP predictions using the proposed Blink-AP. The TP predictions under IoU of $50\\%$ are used to calculate the subsequent Blink-AP.", + "bbox": [ + 496, + 492, + 892, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Blink-AP. This metric is used to reflect the model's eyeblink detection ability within each instance. We tailor the standard AP metric in temporal action detection [3] into our task. Only the matched (i.e., true positive) predictions when calculating Inst-AP are taken into consideration in this metric as the blink accuracy of these predictions is rarely affected by the face detection and tracking accuracy. We report the Blink-AP under the temporal IoU of $50\\%$ and $75\\%$ .", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13857", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9bfae63d377a8f3063276720be0be8ea0451843f768b2bcaadb9a4e9939f1fa5.jpg", + "image_caption": [ + "Figure 5. Overview of the InstBlink framework." + ], + "image_footnote": [], + "bbox": [ + 155, + 85, + 816, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 265, + 169, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present our InstBlink that takes a video clip as input and directly outputs the face positions of each instance and their eyeblink intervals in the whole video clip. The InstBlink design takes inspiration from the existing query-based methods [4, 41, 45, 47, 48] but formulates the architecture to model both face and eyeblink representations at instance level along the video clip. The overall architecture is illustrated in Fig. 5.", + "bbox": [ + 75, + 290, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a video clip $I \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}$ where $T$ denotes the number of frames and $H \\times W$ is the spatial size of each frame, InstBlink first applies a backbone network to extract video feature $F_v \\in \\mathbb{R}^{T \\times C \\times H' \\times W'}$ where $C$ is the channel number and $H' \\times W'$ is the spatial size of the feature. Afterwards, a query-based architecture iterates $M$ times, which consists of 3 components: the Query Interaction Module (QIM), Video Interaction Module (VIM), and task-specific heads (i.e., face head and blink head). At the end of each interaction, the queries will be updated and the instance-level face and eyeblink predictions will be output by the task-specific heads. During inference, the output from the last iteration will be used as the final prediction results.", + "bbox": [ + 75, + 410, + 470, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Instance Query", + "text_level": 1, + "bbox": [ + 76, + 616, + 232, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Within InstBlink, the spatio-temporal instance queries $\\{q^i\\}_{i = 1}^N$ are responsible for characterizing every human instance's joint face and eyeblink features in a video. Each query contains $T$ embeddings (i.e., $q^{i}\\in \\mathbb{R}^{T\\times C}$ ), where $C$ is the feature dimension. Each embedding generally focuses on the instance's face and eyeblink representations in the corresponding frame. Each query is also paired with a proposal tube $p^i\\in \\mathbb{R}^{T\\times 4}$ (i.e., spatio-temporal bounding boxes across the time), which aims at indicating the face location of $i$ -th instance across the entire video clip. At the first iteration of each complete forward propagation, $q^{i}$ and $p^i$ are initialized by copying 2 learnable parameters $\\bar{q}^i\\in \\mathbb{R}^{1\\times C}$ and $\\bar{p}^i\\in \\mathbb{R}^{1\\times 4}T$ times along the temporal dimension.", + "bbox": [ + 76, + 638, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Query Interaction Module (QIM)", + "text_level": 1, + "bbox": [ + 76, + 847, + 370, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "QIM targets at (1) enhancing the association between the specific query and its corresponding human instance and (2)", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "modeling spatio-temporal face and eyeblink representations of the associated instance. Specifically, we first adopt a spatial self-attention layer to allow spatial interaction among queries within each frame:", + "bbox": [ + 496, + 266, + 890, + 327 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N}\\right), \\quad t \\in [ 1, T ], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 333, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where MHSA is the multi-head self-attention [42]. Spatial interaction can build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions. Then, temporal self-attention is used within each query along the temporal dimension to realize temporal interaction:", + "bbox": [ + 496, + 366, + 890, + 457 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T}\\right), \\quad i \\in [ 1, N ]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 464, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Applying temporal interaction within each query allows the embeddings from different frames to communicate with each other to facilitate instance tracking and model temporal eyeblink representations of the corresponding instance.", + "bbox": [ + 496, + 496, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Video Interaction Module (VIM)", + "text_level": 1, + "bbox": [ + 498, + 565, + 787, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VIM aims at collecting the face and eyeblink information of the target instance from the video feature. Particularly, the dynamic filters [41] $m^i$ are first generated from each query embeddings $q^i$ . Then, the filters will filter an RoI feature by dynamic convolution to extract highly related features for both face and eyeblink. The RoI feature is obtained by applying RoI align [17] on the video feature using the proposal tube $p^i$ . After obtaining the filtered feature, a linear projection is applied to form the updated query feature $\\tilde{q}^i$ . The updated query feature will be used to make both face and eyeblink predictions by the task-specific heads.", + "bbox": [ + 496, + 588, + 890, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Task-specific Heads", + "text_level": 1, + "bbox": [ + 500, + 762, + 687, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The instance-level face and eyeblink predictions can be obtained simultaneously by applying task-specific heads on the query features. The heads are shared among queries.", + "bbox": [ + 496, + 785, + 890, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Face head. Given the updated query feature $\\tilde{q}^i$ , a Multilayer Perceptron (MLP) layer with Sigmoid normalization is used to indicate the existence of human faces as", + "bbox": [ + 496, + 830, + 890, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {c} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 883, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13858", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/75e73e428a4fc55a87d3314dff7d34bd59f876eaf1a1b7ea6739550f6e14349e.jpg", + "image_caption": [ + "Figure 6. An example of the blink merging procedure, which takes the frame-level eyeblink scores $b^{i}$ and outputs the interval-level eyeblink results $B^{i}$ . The threshold is set to 0.3 for demonstration." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 470, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $c^i\\in \\mathbb{R}^T$ denotes the face classification scores across frames. Face localization is achieved in a similar way as", + "bbox": [ + 76, + 212, + 468, + 244 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nl ^ {i} = M L P _ {l} \\left(\\tilde {q} ^ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 253, + 468, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $l^i \\in \\mathbb{R}^{T \\times 4}$ denotes the face bounding boxes across frames. It will also be used to renew the proposal tube $p^i$ . Blink head. Eyeblink prediction towards $\\tilde{q}^i$ is achieved by an MLP layer with Sigmoid normalization as", + "bbox": [ + 76, + 280, + 468, + 343 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nb ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {b} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 352, + 468, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $b^{i} \\in \\mathbb{R}^{T}$ is the frame-level eyeblink scores. Each element $b_{t}^{i}$ in it indicates the possibility that the $t$ -th frame is inside an eyeblink event. During inference, we simply merge the adjacent frame-level eyeblink predictions based on a threshold (e.g., 0.3 in our implementation) to form the final interval-level eyeblink predictions $B_{k}^{i} = [s_{k}^{i}, e_{k}^{i}]$ where $k \\in K$ is the $k$ -th eyeblink interval within the total K eyeblink predictions. An intuitive example of the merging procedure is shown in Fig. 6.", + "bbox": [ + 75, + 378, + 468, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Different from the existing works that only extract features from the local eye region, our blink head also considers useful global information such as global face appearance, head pose, and illumination condition to aid the implicit eye localization and eyeblink characterization. The reason is that the blink head directly filters global features from the query embeddings where the global face context is already stored. During training, the eyeblink clues will not only flow back to the RoI feature, but also to the instance query to enhance the eyeblink-related feature representation ability of queries. Moreover, because of the shared feature among blink head and face head, a kind of interaction and synergy is built where the information flow from blink head can also benefit the face representations to boost the face detection and tracking ability as verified in Sec. 5.3.", + "bbox": [ + 75, + 517, + 468, + 743 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As we have $N$ queries, we finally obtain the predictions from them in parallel:", + "bbox": [ + 76, + 743, + 468, + 773 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{y ^ {i} \\right\\} _ {i = 1} ^ {N} = \\left\\{\\left(c ^ {i}, l ^ {i}, b ^ {i}\\right) \\right\\} _ {i = 1} ^ {N}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 782, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Training", + "text_level": 1, + "bbox": [ + 76, + 814, + 181, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To optimize InstBlink, one-to-one assignment between instance-level predictions $\\left\\{y^{i}\\right\\}_{i = 1}^{N}$ and ground truths is first conducted based on their instance-level face tracklet similarity. Then, the loss is calculated concerning face and", + "bbox": [ + 75, + 837, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "eyeblink items jointly for optimization. As in Sec. 3.1, the ground truth annotations can be summarized as", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\hat {y} ^ {j} \\right\\} _ {j = 1} ^ {N _ {g t}} = \\left\\{\\left(\\hat {c} ^ {j}, \\hat {l} ^ {j}, \\hat {b} ^ {j}\\right) \\right\\} _ {j = 1} ^ {N _ {g t}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 130, + 890, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{c}^j\\in \\mathbb{R}^T$ $\\hat{l}^j\\in \\mathbb{R}^{T\\times 4}$ , and $\\hat{b}^j\\in \\mathbb{R}^T$ indicate the frame-level face existence, face position (i.e., bounding box) and eyeblink existence (i.e., $\\hat{b}_t^j = 1$ indicates frame t is inside an eyeblink event and conversely for $\\hat{b}_t^j = 0$ , which can be derived from $\\hat{B}^j$ using an inverse process in Fig. 6 ) respectively. We use Hungarian algorithm [23] to perform instance-level bipartite matching between predictions and ground truths. The matching cost is given as", + "bbox": [ + 496, + 172, + 890, + 297 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {H u n g}} \\left(y ^ {i}, \\hat {y} ^ {j}\\right) = \\sum_ {t = 1} ^ {T} \\left[ \\mathcal {L} _ {c l s} \\left(c _ {t} ^ {i}, \\hat {c} _ {t} ^ {j}\\right) \\right. \\tag {8} \\\\ \\left. + 1 _ {\\left\\{\\hat {c} _ {t} ^ {j} \\neq 0 \\right\\}} \\left(\\mathcal {L} _ {\\text {b o x}} \\left(l _ {t} ^ {i}, \\hat {l} _ {t} ^ {j}\\right)\\right) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 301, + 890, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{cls}$ indicates the focal loss [29] for face existence classification. $\\mathcal{L}_{box}$ is the combination of L1 loss and GIoU loss [37] for face localization. The loss weights are the same as [41, 47]. After obtaining the optimal assignment $\\hat{\\sigma}$ between predictions and ground truths, the network is optimized by the loss as", + "bbox": [ + 496, + 378, + 890, + 470 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {j = 1} ^ {N _ {g t}} \\left(\\mathcal {L} _ {\\text {f a c e}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right) + \\lambda \\mathcal {L} _ {\\text {b l i n k}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 478, + 890, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $y^{\\hat{\\sigma}(j)}$ is the prediction that has been matched with the ground truth instance $\\hat{y}^j$ . $\\mathcal{L}_{face}$ is the face tracklet detection loss that shares the same form as $\\mathcal{L}_{Hung}$ (i.e., $\\mathcal{L}_{face}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\mathcal{L}_{Hung}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)})$ ), and $\\mathcal{L}_{blink}$ denotes instance-level eyeblink detection loss as $\\mathcal{L}_{blink}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\sum_{t=1}^{T} \\mathcal{L}_{cls}(\\hat{b}_t^j, \\hat{b}_t^{\\hat{\\sigma}(j)})$ with $\\lambda = 5$ . For unmatched predictions, only $\\sum_{t=1}^{T} \\mathcal{L}_{cls}(c_t^i, \\hat{c}_t^i = 0)$ is used to supervise their face existence classification output $c^i$ to be close to 0 (i.e., no face).", + "bbox": [ + 496, + 534, + 890, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 500, + 694, + 624, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and evaluation metrics. We first conduct experiments on the proposed MPEblink dataset. We split the dataset into 423 training videos, 128 validation videos, and 135 test videos. The videos from the same movie will only appear in one set. We train the network on the training set, validate it on the validation set and report the performance on the test set. We report Inst-AP to reveal the instance localization ability and Blink-AP to reveal the eyeblink detection ability within instances, as introduced in Sec. 3.5. Meanwhile, experiments are also conducted on HUST-LEBW for single-person and trimmed cases. Recall, Precision, and F1 score are reported following [19].", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13859", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/db422afdf29900ab4121cf50082a0293421fa39cde213466d8e87bbfd04db768.jpg", + "table_caption": [ + "Table 2. The main results on the MPEblink dataset." + ], + "table_footnote": [], + "table_body": "
TypeMethodBlink-AP50Blink-AP75Inst-AP
LandmarkSoukupová and Cech [40]0.500.0556.70
Blink detection+ [35]0.620.08
RegionHu et al. [19]2.680.04
Daza et al.5.850.88
InstBlink (Ours)27.197.1667.89
", + "bbox": [ + 86, + 103, + 454, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation details. We use ResNet-50-FPN [18, 28] backbone. The network is pre-trained on YouTube-VIS [46] under [47] for a general instance representation ability. The query number $N$ and iteration time $M$ are set to 50 and 4 respectively. AdamW [31] optimizer with a batch size of 8 is used to train the model. The initial learning rate is set to 2.5e-5 for the backbone and 2.5e-4 for the other parts. At the training stage, for the sake of memory efficiency, we use the frame rate of 12 FPS for image sampling and the input clip length is set to 11 that is longer than most eyeblink events (i.e., 0.2-0.4s). The frames are also resized to $640 \\times 360$ before sending into the network. The whole training procedure lasts for 10,000 iterations and the learning rate is multiplied by 0.1 at iteration 6000 and 9000. During test, the original frame rate is used and the input clip length is set to 36 with a stride of 18. The predictions within adjacent clips are linked via concerning face bounding box IoU.", + "bbox": [ + 76, + 200, + 472, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Benchmark Results on MPEblink Dataset", + "text_level": 1, + "bbox": [ + 76, + 468, + 433, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. Multi-person eyeblink detection in untrimmed videos is a new task that has not been well concerned before. Therefore, we tailor the existing eyeblink detection approaches with a unified instance detection and tracking method. Specifically, we use the state-of-the-art face analysis toolbox InsightFace [21] to achieve face [16] and landmark [44] detection. To track each instance, we link the face bounding boxes from the adjacent frames based on their similarity on box IoU. After obtaining the instance tracklets (i.e., a sequence of face bounding boxes and landmarks), we employ 4 representative eyeblink detection method [9, 19, 35, 40] within each instance tracklets. Such a sequential pipeline is commonly used in the existing approaches under the single-person assumption.", + "bbox": [ + 75, + 491, + 468, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main results. From Table 2, it can be summarized that:", + "bbox": [ + 76, + 704, + 447, + 717 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- All of the multi-person eyeblink detection algorithms cannot achieve a satisfactory performance (i.e., Blink-AP $_{50}$ lower than $30\\%$ and Blink-AP $_{75}$ lower than $10\\%$ ). This indicates that eyeblink detection under multi-person, untrimmed, and unconstrained scenarios is indeed challenging and has not been well solved yet.", + "- For Blink-AP, InstBlink significantly outperforms the others by large margins (i.e., $21\\%$ at least of Blink- $\\mathrm{AP}_{50}$ and $6\\%$ at least of Blink- $\\mathrm{AP}_{75}$ ), which verifies the superiority of the proposed framework. We argue that one essential reason is that our framework can model a better long-term temporal eyeblink representation than the frame-based method [9]" + ], + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and the sliding window based methods [19, 35, 40]. Moreover, under the proposed framework, eyeblink features can be facilitated via face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, while previous works that utilize a sequential manner cannot. From Table 2, it can also be summarized that the landmark-based methods [35, 40] perform poorer than the region-based counterparts. We think that one essential reason is that landmark detection is unreliable under unconstrained conditions. A similar conclusion has already been made in [19] but the property of multi-person and long video in MPEblink make it worse for landmark-based eyeblink detection methods. Our method is region-based, but localizes eye region in an implicit way where global face context is included and thus becomes more robust.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- InstBlink also outperforms others on Inst-AP. We think that is because our framework can better model the long-term spatio-temporal instance representations, while the counterparts achieve tracking under a tracking-by-detection framework, which contains limited spatio-temporal modeling and may suffer from heavy occlusion.", + "bbox": [ + 496, + 316, + 890, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inference speed analysis. The result is listed in Table 3, assuming the 4 compared methods use InsightFace for face & landmark detection and InstBlink inferences within a clip length of 36. It can be seen that InstBlink is also of high inference speed (i.e., 112 FPS for network forwarding) while the real-time capacity of other methods is not superior. As the number of instances increases, their running time also increases while our method is not sensitive to the number of people because of the one-stage inference property.", + "bbox": [ + 496, + 409, + 890, + 545 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Benchmark Results on HUST-LEBW Dataset", + "text_level": 1, + "bbox": [ + 498, + 556, + 883, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiments are also conducted on the HUST-LEBW dataset to explore the generality of InstBlink towards single-person and trimmed in-the-wild cases. The results are given in Table 4. For models trained on the HUST-LEBW dataset, our method still outperforms others by a large margin (i.e., $3.78\\%$ on F1 score), even with limited training data (less than 450 trimmed samples) to train our one-stage model for multiple tasks (face detection, tracking, and eyeblink detection). Meanwhile, the model trained on MPEblink can obtain $83.45\\%$ F1 score on HUST-LEBW. This indeed verifies the strong generalization ability of InstBlink and MPEblink towards eyeblink detection task.", + "bbox": [ + 496, + 579, + 890, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 771, + 653, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial and temporal modeling in QIM. From Table 5, we can see that (1) without applying temporal interaction, the performance of Blink-AP drops from $27.19\\%$ to $4.58\\%$ . This indicates that temporal modeling is critical for eyeblink detection in untrimmed videos (i.e., only using appearance features can not accurately localize eyeblinks). It can also be observed that temporal interaction facilitates", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13860", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9b4ffe4ae10932d970ea722b75777e047233ffe4fff69f3a3fc90de60c5f2970.jpg", + "table_caption": [ + "Table 3. The inference speed comparison on a single NVIDIA 3090 GPU, assuming the compared methods use InsightFace for face detection (time consumption $T = 9.3\\mathrm{ms}$ including pre-processing) and landmark detection. #faces denotes the face amount in the scene." + ], + "table_footnote": [], + "table_body": "
MethodInstBlink (Ours)Soukupová and Cech [40]Blink detection+ [35]Hu et al. [19]Daza et al. [9]
Time/image (ms)8.9 + 2.6 for data processingT(=9.3)+5.4×#facesT+5.4×#facesT+5.7×#facesT+9.1×#faces
", + "bbox": [ + 138, + 121, + 826, + 159 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b46ddf0aef5ffab3dd5e016572a08f7882af1ff38fcf7b21fcf4e165405763e7.jpg", + "table_caption": [ + "Table 4. Performance comparison on the HUST-LEBW dataset, where InstBlink CROSS indicates InstBlink trained on MPEblink and tested on HUST-LEBW." + ], + "table_footnote": [], + "table_body": "
Training setMethodEyeRecallPrecisionF1
HUST-LEBW [19]Soukupová and Cech [40]Left36.0764.7146.32
Right30.1657.5839.58
Hu et al. [19]Left54.1089.1967.35
Right44.4476.7156.28
Blink detection+ [35]Both58.9980.0567.90
InstBlink (Ours)Both97.6456.6271.68
mEBAL [10]Daza et al. [10]Left96.0360.8074.46
Right79.5073.4876.37
Daza et al. [9]Both93.3975.3383.39
MPEblinkInstBlink CROSS (Ours)Both91.3476.8283.45
", + "bbox": [ + 84, + 213, + 460, + 353 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9e0ee2a9611c080ba6b0a2d1f2da0b8a5bec3dcb93935160b508f33aa41dbbd1.jpg", + "table_caption": [ + "Table 5. Ablation studies on QIM and VIM." + ], + "table_footnote": [], + "table_body": "
MethodBlink-AP50Blink-AP75Inst-AP
w/o QIM3.200.3958.93
w/o temporal interaction in QIM4.580.5563.61
w/o spatial interaction in QIM26.656.1862.45
w/o filter operation in VIM22.274.5965.01
Full model27.197.1667.89
", + "bbox": [ + 83, + 375, + 460, + 454 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2d86711f2b3a4b61c3d6ac83ba947a36ad0946b81b685a13084971e74a51b008.jpg", + "table_caption": [ + "Table 6. The performance comparison with and without blink head on the MPEblink dataset." + ], + "table_footnote": [], + "table_body": "
Blink headInst-APInst-AP50Inst-AP75
×65.8681.7371.23
✓67.8984.5173.76
", + "bbox": [ + 138, + 489, + 401, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the performance of Inst-AP. We argue that this is because it can also build instance-level association among the features across frames to facilitate the instance tracking ability. (2) Spatial interaction can boost Inst-AP by a large margin (i.e., $5.44\\%$ ) and slightly boost Blink-AP, as it may build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions.", + "bbox": [ + 75, + 546, + 468, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Filter operation in VIM. As in Table 5, compared with directly using RoI features to update query, using filtered RoI features can boost $4.92\\%$ on Blink-AP50 and $2.88\\%$ on Inst-AP. We speculate that the filter operation can activate task-specific RoI features and resist background. Thus, finer face and eyeblink clues can be collected to update queries.", + "bbox": [ + 75, + 667, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Multi-task learning mechanism. Here we study the effect of the blink head from a multi-task learning perspective. As shown in Table 6, adding blink head can also boost $2.03\\%$ on Inst-AP, which demonstrates that features for face detection and tracking can also benefit from eyeblink clues.", + "bbox": [ + 75, + 758, + 468, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 76, + 845, + 269, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the prediction results of InstBlink in Fig. 7. The examples show that our model can aware the attendees", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb30a3bb0b2e8c241324f2fd3b505751dfad66fdb9ff3763b1d4770c71dca209.jpg", + "image_caption": [ + "Figure 7. Qualitative examples of the predictions of InstBlink." + ], + "image_footnote": [], + "bbox": [ + 509, + 167, + 879, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "robustly and detect their eyeblinks under different facial appearance and head pose. Nevertheless, it can not distinguish the rapid consecutive eyeblinks, which also reveals the challenge of eyeblink detection in untrimmed videos.", + "bbox": [ + 498, + 369, + 890, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions and Limitations", + "text_level": 1, + "bbox": [ + 500, + 440, + 764, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we shed the light on a new research task termed multi-person eyeblink detection in the wild for untrimmed video. We formally define the task and introduce a multi-person eyeblink detection dataset named MPEblink. To perform multi-person eyeblink detection in untrimmed videos, we introduce a one-stage multi-person eyeblink detection framework InstBlink. Experiment results demonstrate the superiority of InstBlink in both effectiveness and efficiency. However, our SOTA performance is still unsatisfactory (i.e., $\\mathrm{Blink - AP}_{50} < 30\\%$ ). This verifies the challenges of unconstrained multi-person eyeblink detection in long videos. Besides, although the proposed dataset focuses on multi-person, unconstrained, and untrimmed scenarios that are more realistic and have a broader application value, there are lack of crowd scenes (e.g., $>10$ instances) within it. In the future, we will pay more attention to the crowd scenes and enrich the dataset.", + "bbox": [ + 498, + 462, + 890, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 727, + 651, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is jointly supported by the National Natural Science Foundation of China (Grant No. 62271221 and U1913602), and Natural Science Foundation of Guangdong Province (Grant No. 2023A1515011260). Joey Tianyi Zhou is funded by the SERC (Science and Engineering Research Council) Central Research Fund (Use-Inspired Basic Research), and the Singapore Government's Research, and Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering Domain) under programmatic Grant A18A1b0045.", + "bbox": [ + 496, + 750, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13861", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Talking face video. Face&Gesture Recognition Working Group, IST-2000-26434. 2, 4", + "[2] Luis Miguel Bergasa, Jesús Nuevo, Miguel A Sotelo, Rafael Barea, and María Elena Lopez. Real-time system for monitoring driver vigilance. 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International Conference on Learning Representations (ICLR), 2021. 3" + ], + "bbox": [ + 501, + 92, + 890, + 642 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13863", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Real-Time Multi-Person Eyeblink Detection in the Wild for Untrimmed Video/ae1d0533-ce28-4e72-a6ef-27b8f2c1f68e_model.json b/2023/Real-Time Multi-Person Eyeblink Detection in the Wild for Untrimmed Video/ae1d0533-ce28-4e72-a6ef-27b8f2c1f68e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6e346bef89c2536632af8bb8b92c440a074dbd31 --- /dev/null +++ b/2023/Real-Time Multi-Person Eyeblink Detection in the Wild for Untrimmed Video/ae1d0533-ce28-4e72-a6ef-27b8f2c1f68e_model.json @@ -0,0 +1,2530 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.131, + 0.877, + 0.155 + ], + "angle": 0, + "content": "Real-time Multi-person Eyeblink Detection in the Wild for Untrimmed Video" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.18, + 0.846, + 0.217 + ], + "angle": 0, + "content": "Wenzheng Zeng\\(^{1}\\), Yang Xiao\\(^{1\\dagger}\\), Sicheng Wei\\(^{1}\\), Jinfang Gan\\(^{1}\\), Xintao Zhang\\(^{1}\\), Zhiguo Cao\\(^{1}\\), Zhiwen Fang\\(^{2,3}\\) and Joey Tianyi Zhou\\(^{4,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.218, + 0.83, + 0.252 + ], + "angle": 0, + "content": "1Key Laboratory of Image Processing and Intelligent Control, Ministry of Education, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.253, + 0.794, + 0.269 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.271, + 0.872, + 0.305 + ], + "angle": 0, + "content": "\\(^{3}\\)Department of Rehabilitation Medicine, Zhujiang Hospital, Southern Medical University, Guangzhou 510280, China \\(^{4}\\)Centre for Frontier AI Research, Agency for Science, Technology and Research (A*STAR), Singapore" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.306, + 0.858, + 0.36 + ], + "angle": 0, + "content": "\\(^{5}\\)Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore {wenzhengzeng, Yang-Xiao, sichengwei, jinfangan, u202115202, zgcao}@hust.edu.cn, fzw310@smu.edu.cn, zhouty@cfar.a-star.edu.sg" + }, + { + "type": "list", + "bbox": [ + 0.098, + 0.271, + 0.872, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.302, + 0.361, + 0.661, + 0.375 + ], + "angle": 0, + "content": "https://github.com/wenzhengzeng/MPEblink" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.41, + 0.314, + 0.426 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.474, + 0.878 + ], + "angle": 0, + "content": "Real-time eyeblink detection in the wild can widely serve for fatigue detection, face anti-spoofing, emotion analysis, etc. The existing research efforts generally focus on single-person cases towards trimmed video. However, multiperson scenario within untrimmed videos is also important for practical applications, which has not been well concerned yet. To address this, we shed light on this research field for the first time with essential contributions on dataset, theory, and practices. In particular, a large-scale dataset termed MPEblink that involves 686 untrimmed videos with 8748 eyeblink events is proposed under multiperson conditions. The samples are captured from unconstrained films to reveal \"in the wild\" characteristics. Meanwhile, a real-time multi-person eyeblink detection method is also proposed. Being different from the existing counterparts, our proposition runs in a one-stage spatio-temporal way with end-to-end learning capacity. Specifically, it simultaneously addresses the sub-tasks of face detection, face tracking, and human instance-level eyeblink detection. This paradigm holds 2 main advantages: (1) eyeblink features can be facilitated via the face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, and (2) addressing these sub-tasks in parallel instead of sequential manner can save time remarkably to meet the real-time running requirement. Experiments on MPEblink verify the essential challenges of real-time multiperson eyeblink detection in the wild for untrimmed video. Our method also outperforms existing approaches by large margins and with a high inference speed." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.41, + 0.895, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.558, + 0.895, + 0.601 + ], + "angle": 0, + "content": "Figure 1. The illustration on multi-person eyeblink detection. This task aims at being aware of the presence of people and detecting their eyeblink activities at instance level." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.617, + 0.634, + 0.633 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.895, + 0.854 + ], + "angle": 0, + "content": "Real-time eyeblink detection in the wild is a recently emerged challenging research task [19] that can widely serve for fatigue detection [2], face anti-spoofing [34], affective analysis [7], etc. Although remarkable progress has been made [9, 10, 19], the existing methods generally focus on single-person cases within trimmed videos. Multi-person scenario within untrimmed videos has not been well concerned yet. However, detecting long-term eyeblink behaviors at multi-instance level is more preferred for some practical application scenarios. For example, it can be used to estimate attendees' attention level and emotional state change during social interaction [9, 33]. Thus, effective and real-time multi-person eyeblink detection in the wild for untrimmed video is indeed required." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To this end, we shed the light on this research problem with essential contributions on dataset, theory, and practices. First, a challenging labeled multi-person eyeblink de" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.438, + 0.902 + ], + "angle": 0, + "content": "†Yang Xiao is corresponding author (Yang_Xiao@hust.edu.cn)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13854" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "tection benchmark termed MPEblink is built under in-the-wild conditions. It consists of 686 untrimmed long videos captured from unconstrained movies to reveal the \"in the wild\" characteristics. The contained scenarios are realistic and diverse, such as social interactions and group activities. To our knowledge, MPEblink is the first multi-person eyeblink detection dataset that focuses on in-the-wild long videos. Fig. 1 illustrates a sample video with ground truth annotations within it. Different from the existing eyeblink detection benchmarks [10, 12, 19], the proposed benchmark aims at being aware of all the attendees along the whole video and detecting their eyeblinks at instance level. In summary, MPEblink is featured with multi-instance, unconstrained, and untrimmed, which makes it more challenging and realistic than previous formulations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.593 + ], + "angle": 0, + "content": "To perform eyeblink detection, previous methods [9, 10, 12, 19, 40] generally take a sequential approach containing face detection, face tracking, and classification on the pre-extracted local eye clues within a temporal window. Whereas such a pipeline seems reasonable, it has several critical drawbacks. First, the use of isolated components may lead to sub-optimal results as they are not jointly optimized and it is inefficient due to the inability to reuse the features of each stage. Second, the eyeblink features only contain the information from the pre-extracted local eye clues (i.e., a small part of face), lacking the useful information from global face context such as head pose and illumination condition that are crucial for detecting eyeblinks in the wild. Moreover, the pre-extracted local eye clues are also unreliable due to the localization challenge towards unconstrained scenarios. Third, the sequential approach leads to computational cost being sensitive to the subject amount, which is hard to meet the real-time running requirement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.473, + 0.837 + ], + "angle": 0, + "content": "To tackle these issues, we propose a one-stage multi-person eyeblink detection framework called InstBlink, which can simultaneously detect human faces, track them over time, and do eyeblink detection at instance level. InstBlink takes inspiration from the existing query-based methods [41, 45, 47, 48] and models the spatio-temporal face as well as eyeblink representations at instance level within each query. The insight is that the features can be effectively shared among these sub-tasks and the eyeblink features can be facilitated via face's global contexts (e.g., head pose and illumination condition) with joint optimization and interaction, especially in unconstrained in-the-wild cases. Experiments verify the superiority of InstBlink in both effectiveness and efficiency, while also highlighting the critical challenges of real-time multi-person eyeblink detection in the wild for untrimmed video." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.839, + 0.441, + 0.853 + ], + "angle": 0, + "content": "The main contributions of this work lie in 3 folders:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "- To our knowledge, it is the first time that instance-level multi-person eyeblink detection in untrimmed videos is formally defined and explored;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "- We introduce an unconstrained multi-person eyeblink detection dataset MPEblink that contains 686 untrimmed videos with 8748 eyeblink events, featured with more realistic and challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.894, + 0.213 + ], + "angle": 0, + "content": "- We propose a one-stage multi-person eyeblink detection method that can jointly perform face detection, tracking, and instance-level eyeblink detection. Such a task-joint paradigm can benefit the sub-tasks uniformly." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.226, + 0.642, + 0.243 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Eyeblink detection dataset. Existing eyeblink detection datasets [1, 10, 12, 13, 34, 36] generally focus on constrained indoor cases with a consistent environmental setup. HUST-LEBW [19] extends the scenarios to the unconstrained outdoor cases. From then on, the community starts to pay more attention to eyeblink detection in the wild. Nevertheless, HUST-LEBW mainly focuses on single-person scenarios towards trimmed videos, which limits the application of methods in more realistic scenarios such as group activities and social interactions. To address such limitation, we introduce a new dataset termed MPEblink. The proposed dataset is featured with multi-person, unconstrained, and untrimmed, thus being more realistic and challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.895, + 0.795 + ], + "angle": 0, + "content": "Eyeblink detection method. Existing methods generally judge eyeblinks from the pre-extracted local eye clues (e.g., local eye region [6, 9, 10, 19, 25] or landmarks around eyes [8, 14, 35, 40]). To obtain the local eye clues, the existing works generally run in a sequential way including face detection, face tracking, and landmark detection. Finally, the eyeblink result is classified from the pre-extracted local eye clues within a temporal window. Such a pipeline is inefficient due to the isolated optimization among different sub-tasks. Meanwhile, the eyeblink features only contain the information from the pre-extracted local eye clues, lacking useful global information such as head pose and illumination, and the pre-extracted eye clues are also unreliable due to the localization challenge toward unconstrained cases. Besides, due to the multi-stage characteristic, existing methods do not scale well with the number of people in the scene to meet the real-time running requirement. In this paper, we propose a one-stage eyeblink detection framework that can simultaneously detect human faces, track them along the time, and do eyeblink detection at instance level. Within it, eyeblink features can be facilitated via global face context, and the features can be effectively shared among the sub-task to achieve high inference speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.797, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Spatio-temporal action detection. Spatio-temporal action detection [15, 20, 22, 26, 27, 39, 48] aims at simultaneously obtaining the spatial and temporal location of an action, which is defined as an action tube [22]. The task only focuses on the isolated action tubes without instance awareness and thus can not make an instance-level analysis along the whole video. Different from that, our proposed multi-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.089, + 0.277, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.148, + 0.273, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.213, + 0.276, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.267, + 0.241, + 0.276 + ], + "angle": 0, + "content": "Business party" + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.089, + 0.417, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.148, + 0.4, + 0.156 + ], + "angle": 0, + "content": "Cooking in the kitchen" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.156, + 0.416, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.213, + 0.396, + 0.221 + ], + "angle": 0, + "content": "Eating at restaurant" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.221, + 0.416, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.268, + 0.381, + 0.276 + ], + "angle": 0, + "content": "Public speech" + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.089, + 0.554, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.472, + 0.149, + 0.504, + 0.156 + ], + "angle": 0, + "content": "Hiking" + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.156, + 0.553, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.213, + 0.528, + 0.221 + ], + "angle": 0, + "content": "Daily life in prison" + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.221, + 0.553, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.267, + 0.548, + 0.276 + ], + "angle": 0, + "content": "Discussing in the classroom" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.089, + 0.693, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.148, + 0.661, + 0.156 + ], + "angle": 0, + "content": "Caring for baby" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.156, + 0.692, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.213, + 0.663, + 0.221 + ], + "angle": 0, + "content": "Being threatened" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.221, + 0.692, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.267, + 0.668, + 0.277 + ], + "angle": 0, + "content": "Arguing in the car" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.089, + 0.829, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.716, + 0.149, + 0.814, + 0.156 + ], + "angle": 0, + "content": "Relaxing on the beach" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.156, + 0.828, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.213, + 0.803, + 0.221 + ], + "angle": 0, + "content": "Having a meeting" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.221, + 0.828, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.267, + 0.799, + 0.276 + ], + "angle": 0, + "content": "Being arrested" + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.282, + 0.803, + 0.295 + ], + "angle": 0, + "content": "Figure 2. The snapshots within MPEblink. Our dataset is featured with more realistic and diverse scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.468, + 0.349 + ], + "angle": 0, + "content": "person eyeblink detection task aims at simultaneously being aware of the presence of people and analyzing their eyeblink behaviors at instance level." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.531 + ], + "angle": 0, + "content": "Query-based methods. Query-based methods are impacting many computer vision tasks. After DETR [4], the pioneer that introduces the query-based framework to address object detection, numerous efforts have been subsequently paid to facilitate visual recognition under the query concept in the fields of object detection [24, 32, 41, 49], pose estimation [38], action detection [30, 48], and segmentation [5, 43, 45, 47]. Inspired by these, we build the first one-stage multi-person eyeblink detection framework for untrimmed video. We propose a unified solution to simultaneously model the instance-level face and eyeblink representations in the whole video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.33, + 0.559 + ], + "angle": 0, + "content": "3. The MPEblink Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Existing eyeblink detection datasets generally focus on single-person scenarios, and are also limited in aspects of constrained conditions or trimmed short videos. To explore unconstrained eyeblink detection under multi-person and untrimmed scenarios, we construct a large-scale multiperson eyeblink detection dataset termed MPEblink to shed the light on this research topic that has not been well studied before. The distinguishing characteristics of MPEblink lie in 3 aspects: multi-person, unconstrained, and untrimmed long video, which makes it more realistic and challenging than previous datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.251, + 0.757 + ], + "angle": 0, + "content": "3.1. Task Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.855 + ], + "angle": 0, + "content": "We think that a good multi-person eyeblink detection algorithm should be able to (1) detect and track human instances' faces reliably to ensure the instance-level analysis ability along the whole video, and (2) detect eyeblink boundaries accurately within each human instance to ensure the precise awareness of their eyeblink behaviors." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Formally, for an untrimmed video with \\(T\\) frames and \\(N_{gt}\\) people in it, towards the \\(j\\)-th person, let \\(\\hat{l}^j \\in \\mathbb{R}^{T \\times 4}\\) denote its face bounding boxes across the video. \\(\\hat{c}^j \\in \\mathbb{R}^T\\)" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.303, + 0.695, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.303, + 0.877, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.412, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Figure 3. Occlusion and people in & out cases during interaction among instances." + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.448, + 0.877, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Figure 4. An example of rapid and consecutive eyeblinks in untrimmed video." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.54, + 0.892, + 0.778 + ], + "angle": 0, + "content": "is given as the face labels to reflect the face existence of this instance in each frame (i.e., \\(\\hat{c}_t^j\\in \\{1,0\\}\\), where \\(\\hat{c}_t^j = 0\\) indicates that the face is not visible due to serious occlusion or departure at time \\(t\\)). \\(\\hat{l}_t^j\\) is also set to \\(\\varnothing\\) when the person is not visible. We use \\(\\hat{l}^j\\) and \\(\\hat{c}^j\\) to represent the instance-level information of each person. Suppose person \\(j\\) blinks \\(\\hat{K}^j\\) times in the video. Let \\(\\hat{B}_{\\hat{k}}^{j} = \\left[\\hat{s}_{\\hat{k}}^{j},\\hat{e}_{\\hat{k}}^{j}\\right]\\) denote the \\(\\hat{k}\\)-th eyeblink event within this person, where \\(\\hat{s}_k^j\\) and \\(\\hat{e}_k^j\\) denote its starting and ending time. Suppose a multi-person eyeblink detection algorithm produces \\(H\\) human instance hypotheses. Within each human instance hypothesis \\(i\\), it needs to produce a sequence of predicted face bounding boxes \\(l^i\\), face classification scores \\(c^i\\), and \\(K^i\\) eyeblink proposals \\(B_{k}^{i} = [s_{k}^{i},e_{k}^{i}]\\). Better performance can be acquired when predictions get closer to ground truths." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.657, + 0.802 + ], + "angle": 0, + "content": "3.2. Data Collection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We collect 686 untrimmed video clips with various lengths (i.e., 7.1-85.9s) from 86 different unconstrained movies that involve the \"in the wild\" characteristics. Some snapshots of the acquired samples are shown in Fig. 2. It can be observed that the samples are with variational indoor and outdoor scenarios for different themes. Thus, the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13856" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.217, + 0.089, + 0.754, + 0.104 + ], + "angle": 0, + "content": "Table 1. High-level statistics of MPEblink dataset and existing eyeblink detection datasets." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.108, + 0.859, + 0.187 + ], + "angle": 0, + "content": "
Talking Face [1]ZJU [34]Eyeblink8 [12]Silesian5 [36]Researcher's Night [13]mEBAL [10]HUST-LEBW [19]MPEblink (Ours)
Num. of videos180851076000673686
Video length3.3m4.1-4.7s2.7-8.9m1.4-2.7m0.3-3.4m0.6s0.5s7.1-85.9s
Unconstrained××××××√√
Instances/video11111111-8
Blink count61255353300186730003818748
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.2, + 0.473, + 0.562 + ], + "angle": 0, + "content": "acquired samples from these movies are much more realistic and closer to practical applications. Meanwhile, due to the high divergence of the selected movie data source, the captured multi-person eyeblink samples are also of great challenges for effectively detecting eyeblinks. For instance, the pose, illumination condition, expression, and face size among instances differ a lot, even within the same video. Moreover, because of the various types of interaction among instances, there may exist severe occlusion or people in and out scenarios as shown in Fig. 3, making it harder for both instance localization and their eyeblink event detection. Besides, different from the existing unconstrained counterpart [19] that mainly focuses on trimmed short videos, the samples from MPEblink are untrimmed. As a result, we not only need to recognize eyeblink but also need to locate the starting and ending time of each eyeblink event, which is more challenging especially when rapid and consecutive eyeblinks occur. An example is shown in Fig. 4. It can be observed that the appearance difference among eye statuses is small when consecutive rapid eyeblinks happen, making it hard to distinguish the boundary of each eyeblink. Considering the above challenges together, it can be summarized that unconstrained multi-person eyeblink detection in untrimmed videos is indeed a challenging research task." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.572, + 0.245, + 0.587 + ], + "angle": 0, + "content": "3.3. Data Annotation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.471, + 0.837 + ], + "angle": 0, + "content": "For human instances in each video, we labeled their face bounding boxes exhaustively across the whole video. To facilitate the research of landmark-based methods and include a broader range of applications, 68 facial landmark positions [44] are also annotated. Technically, this part of the annotation is under a semi-supervised manner: we use the state-of-the-art face analysis engine InsightFace [21] to achieve face bounding box [16] and landmark [44] detection. To track instances across frames, a matching strategy that considers bounding box IoU and similarity among deep face features [11] is designed. Besides, human annotators carefully check the annotation quality and correct the wrong bounding boxes and tracking results generated by the algorithm. For eyeblink events within each instance, human annotators carefully define their start and end frame. Finally, 8748 eyeblink events are labeled." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.226, + 0.862 + ], + "angle": 0, + "content": "3.4. Data Statistics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The dataset statistics comparison among MPEblink and the other eyeblink detection datasets are given in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.895, + 0.382 + ], + "angle": 0, + "content": "Actually, MPEblink provides the largest number of eyeblink events (i.e., 8748) within 686 untrimmed videos. The biggest difference from the previous datasets is that the videos in our dataset contain various numbers of human instances (i.e., 1-8) with exhaustive annotation. The videos are captured under unconstrained in-the-wild conditions with high diversity as shown in Fig. 2. Compared with the existing in-the-wild counterpart [19] that generally focuses on trimmed short videos, the length of videos from our dataset is much longer and more diverse. In summary, MPEblink is featured with more realistic and challenging and thus has broader application values." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.393, + 0.685, + 0.407 + ], + "angle": 0, + "content": "3.5. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.894, + 0.492 + ], + "angle": 0, + "content": "Existing metrics for eyeblink detection only focus on single-person cases without multi-instance awareness. To address this limitation we introduce 2 new metrics termed Inst-AP and Blink-AP to give attention to both instance awareness quality and eyeblink detection quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.893, + 0.78 + ], + "angle": 0, + "content": "Inst-AP. It aims to evaluate the instance detection and tracking ability of methods, which is the basis for analyzing the eyeblink behaviors of each instance. We modify the standard evaluation metric video-AP in spatio-temporal action detection [22] to fit our task. Different from the original implementation, the 3D IoU is calculated between each instance proposal (i.e., a sequence of face bounding boxes) and ground truth across the whole video, rather than the action tube only. As a result, the proposed metric can reveal the algorithm's ability for detection and tracking instances, while video-AP can just reveal the localization ability of the isolated action tube without instance-level awareness. We report the averaged Inst-AP under the IoU from \\(50\\% -95\\%\\) with step \\(5\\%\\). During calculating Inst-AP, each obtained true positive (TP) prediction has matched with one ground-truth instance, and thus, we can calculate the eyeblink detection accuracy of these TP predictions using the proposed Blink-AP. The TP predictions under IoU of \\(50\\%\\) are used to calculate the subsequent Blink-AP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Blink-AP. This metric is used to reflect the model's eyeblink detection ability within each instance. We tailor the standard AP metric in temporal action detection [3] into our task. Only the matched (i.e., true positive) predictions when calculating Inst-AP are taken into consideration in this metric as the blink accuracy of these predictions is rarely affected by the face detection and tracking accuracy. We report the Blink-AP under the temporal IoU of \\(50\\%\\) and \\(75\\%\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13857" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.087, + 0.817, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.34, + 0.244, + 0.629, + 0.258 + ], + "angle": 0, + "content": "Figure 5. Overview of the InstBlink framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.266, + 0.17, + 0.281 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.47, + 0.412 + ], + "angle": 0, + "content": "In this section, we present our InstBlink that takes a video clip as input and directly outputs the face positions of each instance and their eyeblink intervals in the whole video clip. The InstBlink design takes inspiration from the existing query-based methods [4, 41, 45, 47, 48] but formulates the architecture to model both face and eyeblink representations at instance level along the video clip. The overall architecture is illustrated in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.471, + 0.609 + ], + "angle": 0, + "content": "Given a video clip \\( I \\in \\mathbb{R}^{T \\times 3 \\times H \\times W} \\) where \\( T \\) denotes the number of frames and \\( H \\times W \\) is the spatial size of each frame, InstBlink first applies a backbone network to extract video feature \\( F_v \\in \\mathbb{R}^{T \\times C \\times H' \\times W'} \\) where \\( C \\) is the channel number and \\( H' \\times W' \\) is the spatial size of the feature. Afterwards, a query-based architecture iterates \\( M \\) times, which consists of 3 components: the Query Interaction Module (QIM), Video Interaction Module (VIM), and task-specific heads (i.e., face head and blink head). At the end of each interaction, the queries will be updated and the instance-level face and eyeblink predictions will be output by the task-specific heads. During inference, the output from the last iteration will be used as the final prediction results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.617, + 0.233, + 0.634 + ], + "angle": 0, + "content": "4.1. Instance Query" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.64, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Within InstBlink, the spatio-temporal instance queries \\(\\{q^i\\}_{i = 1}^N\\) are responsible for characterizing every human instance's joint face and eyeblink features in a video. Each query contains \\(T\\) embeddings (i.e., \\(q^{i}\\in \\mathbb{R}^{T\\times C}\\)), where \\(C\\) is the feature dimension. Each embedding generally focuses on the instance's face and eyeblink representations in the corresponding frame. Each query is also paired with a proposal tube \\(p^i\\in \\mathbb{R}^{T\\times 4}\\) (i.e., spatio-temporal bounding boxes across the time), which aims at indicating the face location of \\(i\\)-th instance across the entire video clip. At the first iteration of each complete forward propagation, \\(q^{i}\\) and \\(p^i\\) are initialized by copying 2 learnable parameters \\(\\bar{q}^i\\in \\mathbb{R}^{1\\times C}\\) and \\(\\bar{p}^i\\in \\mathbb{R}^{1\\times 4}T\\) times along the temporal dimension." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.371, + 0.865 + ], + "angle": 0, + "content": "4.2. Query Interaction Module (QIM)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "QIM targets at (1) enhancing the association between the specific query and its corresponding human instance and (2)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.328 + ], + "angle": 0, + "content": "modeling spatio-temporal face and eyeblink representations of the associated instance. Specifically, we first adopt a spatial self-attention layer to allow spatial interaction among queries within each frame:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.334, + 0.892, + 0.361 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N}\\right), \\quad t \\in [ 1, T ], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.458 + ], + "angle": 0, + "content": "where MHSA is the multi-head self-attention [42]. Spatial interaction can build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions. Then, temporal self-attention is used within each query along the temporal dimension to realize temporal interaction:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.465, + 0.892, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T}\\right), \\quad i \\in [ 1, N ]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.558 + ], + "angle": 0, + "content": "Applying temporal interaction within each query allows the embeddings from different frames to communicate with each other to facilitate instance tracking and model temporal eyeblink representations of the corresponding instance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.566, + 0.788, + 0.581 + ], + "angle": 0, + "content": "4.3. Video Interaction Module (VIM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.892, + 0.756 + ], + "angle": 0, + "content": "VIM aims at collecting the face and eyeblink information of the target instance from the video feature. Particularly, the dynamic filters [41] \\( m^i \\) are first generated from each query embeddings \\( q^i \\). Then, the filters will filter an RoI feature by dynamic convolution to extract highly related features for both face and eyeblink. The RoI feature is obtained by applying RoI align [17] on the video feature using the proposal tube \\( p^i \\). After obtaining the filtered feature, a linear projection is applied to form the updated query feature \\( \\tilde{q}^i \\). The updated query feature will be used to make both face and eyeblink predictions by the task-specific heads." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.688, + 0.779 + ], + "angle": 0, + "content": "4.4. Task-specific Heads" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.786, + 0.892, + 0.831 + ], + "angle": 0, + "content": "The instance-level face and eyeblink predictions can be obtained simultaneously by applying task-specific heads on the query features. The heads are shared among queries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.832, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Face head. Given the updated query feature \\(\\tilde{q}^i\\), a Multilayer Perceptron (MLP) layer with Sigmoid normalization is used to indicate the existence of human faces as" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.884, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nc ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {c} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13858" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.472, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.164, + 0.47, + 0.207 + ], + "angle": 0, + "content": "Figure 6. An example of the blink merging procedure, which takes the frame-level eyeblink scores \\( b^{i} \\) and outputs the interval-level eyeblink results \\( B^{i} \\). The threshold is set to 0.3 for demonstration." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.213, + 0.47, + 0.245 + ], + "angle": 0, + "content": "where \\(c^i\\in \\mathbb{R}^T\\) denotes the face classification scores across frames. Face localization is achieved in a similar way as" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.254, + 0.469, + 0.273 + ], + "angle": 0, + "content": "\\[\nl ^ {i} = M L P _ {l} \\left(\\tilde {q} ^ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.281, + 0.469, + 0.344 + ], + "angle": 0, + "content": "where \\(l^i \\in \\mathbb{R}^{T \\times 4}\\) denotes the face bounding boxes across frames. It will also be used to renew the proposal tube \\(p^i\\). Blink head. Eyeblink prediction towards \\(\\tilde{q}^i\\) is achieved by an MLP layer with Sigmoid normalization as" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.353, + 0.469, + 0.372 + ], + "angle": 0, + "content": "\\[\nb ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {b} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.469, + 0.517 + ], + "angle": 0, + "content": "where \\( b^{i} \\in \\mathbb{R}^{T} \\) is the frame-level eyeblink scores. Each element \\( b_{t}^{i} \\) in it indicates the possibility that the \\( t \\)-th frame is inside an eyeblink event. During inference, we simply merge the adjacent frame-level eyeblink predictions based on a threshold (e.g., 0.3 in our implementation) to form the final interval-level eyeblink predictions \\( B_{k}^{i} = [s_{k}^{i}, e_{k}^{i}] \\) where \\( k \\in K \\) is the \\( k \\)-th eyeblink interval within the total K eyeblink predictions. An intuitive example of the merging procedure is shown in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.469, + 0.744 + ], + "angle": 0, + "content": "Different from the existing works that only extract features from the local eye region, our blink head also considers useful global information such as global face appearance, head pose, and illumination condition to aid the implicit eye localization and eyeblink characterization. The reason is that the blink head directly filters global features from the query embeddings where the global face context is already stored. During training, the eyeblink clues will not only flow back to the RoI feature, but also to the instance query to enhance the eyeblink-related feature representation ability of queries. Moreover, because of the shared feature among blink head and face head, a kind of interaction and synergy is built where the information flow from blink head can also benefit the face representations to boost the face detection and tracking ability as verified in Sec. 5.3." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.744, + 0.469, + 0.774 + ], + "angle": 0, + "content": "As we have \\(N\\) queries, we finally obtain the predictions from them in parallel:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.784, + 0.469, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\left\\{y ^ {i} \\right\\} _ {i = 1} ^ {N} = \\left\\{\\left(c ^ {i}, l ^ {i}, b ^ {i}\\right) \\right\\} _ {i = 1} ^ {N}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.182, + 0.831 + ], + "angle": 0, + "content": "4.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.838, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To optimize InstBlink, one-to-one assignment between instance-level predictions \\(\\left\\{y^{i}\\right\\}_{i = 1}^{N}\\) and ground truths is first conducted based on their instance-level face tracklet similarity. Then, the loss is calculated concerning face and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "eyeblink items jointly for optimization. As in Sec. 3.1, the ground truth annotations can be summarized as" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.131, + 0.892, + 0.164 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\hat {y} ^ {j} \\right\\} _ {j = 1} ^ {N _ {g t}} = \\left\\{\\left(\\hat {c} ^ {j}, \\hat {l} ^ {j}, \\hat {b} ^ {j}\\right) \\right\\} _ {j = 1} ^ {N _ {g t}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.173, + 0.892, + 0.298 + ], + "angle": 0, + "content": "where \\(\\hat{c}^j\\in \\mathbb{R}^T\\) \\(\\hat{l}^j\\in \\mathbb{R}^{T\\times 4}\\) , and \\(\\hat{b}^j\\in \\mathbb{R}^T\\) indicate the frame-level face existence, face position (i.e., bounding box) and eyeblink existence (i.e., \\(\\hat{b}_t^j = 1\\) indicates frame t is inside an eyeblink event and conversely for \\(\\hat{b}_t^j = 0\\) , which can be derived from \\(\\hat{B}^j\\) using an inverse process in Fig. 6 ) respectively. We use Hungarian algorithm [23] to perform instance-level bipartite matching between predictions and ground truths. The matching cost is given as" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.302, + 0.892, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {H u n g}} \\left(y ^ {i}, \\hat {y} ^ {j}\\right) = \\sum_ {t = 1} ^ {T} \\left[ \\mathcal {L} _ {c l s} \\left(c _ {t} ^ {i}, \\hat {c} _ {t} ^ {j}\\right) \\right. \\tag {8} \\\\ \\left. + 1 _ {\\left\\{\\hat {c} _ {t} ^ {j} \\neq 0 \\right\\}} \\left(\\mathcal {L} _ {\\text {b o x}} \\left(l _ {t} ^ {i}, \\hat {l} _ {t} ^ {j}\\right)\\right) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.471 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{cls}\\) indicates the focal loss [29] for face existence classification. \\(\\mathcal{L}_{box}\\) is the combination of L1 loss and GIoU loss [37] for face localization. The loss weights are the same as [41, 47]. After obtaining the optimal assignment \\(\\hat{\\sigma}\\) between predictions and ground truths, the network is optimized by the loss as" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.479, + 0.892, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {j = 1} ^ {N _ {g t}} \\left(\\mathcal {L} _ {\\text {f a c e}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right) + \\lambda \\mathcal {L} _ {\\text {b l i n k}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.682 + ], + "angle": 0, + "content": "where \\(y^{\\hat{\\sigma}(j)}\\) is the prediction that has been matched with the ground truth instance \\(\\hat{y}^j\\). \\(\\mathcal{L}_{face}\\) is the face tracklet detection loss that shares the same form as \\(\\mathcal{L}_{Hung}\\) (i.e., \\(\\mathcal{L}_{face}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\mathcal{L}_{Hung}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)})\\)), and \\(\\mathcal{L}_{blink}\\) denotes instance-level eyeblink detection loss as \\(\\mathcal{L}_{blink}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\sum_{t=1}^{T} \\mathcal{L}_{cls}(\\hat{b}_t^j, \\hat{b}_t^{\\hat{\\sigma}(j)})\\) with \\(\\lambda = 5\\). For unmatched predictions, only \\(\\sum_{t=1}^{T} \\mathcal{L}_{cls}(c_t^i, \\hat{c}_t^i = 0)\\) is used to supervise their face existence classification output \\(c^i\\) to be close to 0 (i.e., no face)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.625, + 0.712 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset and evaluation metrics. We first conduct experiments on the proposed MPEblink dataset. We split the dataset into 423 training videos, 128 validation videos, and 135 test videos. The videos from the same movie will only appear in one set. We train the network on the training set, validate it on the validation set and report the performance on the test set. We report Inst-AP to reveal the instance localization ability and Blink-AP to reveal the eyeblink detection ability within instances, as introduced in Sec. 3.5. Meanwhile, experiments are also conducted on HUST-LEBW for single-person and trimmed cases. Recall, Precision, and F1 score are reported following [19]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13859" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.09, + 0.427, + 0.103 + ], + "angle": 0, + "content": "Table 2. The main results on the MPEblink dataset." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.104, + 0.455, + 0.194 + ], + "angle": 0, + "content": "
TypeMethodBlink-AP50Blink-AP75Inst-AP
LandmarkSoukupová and Cech [40]0.500.0556.70
Blink detection+ [35]0.620.08
RegionHu et al. [19]2.680.04
Daza et al.5.850.88
InstBlink (Ours)27.197.1667.89
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.201, + 0.473, + 0.46 + ], + "angle": 0, + "content": "Implementation details. We use ResNet-50-FPN [18, 28] backbone. The network is pre-trained on YouTube-VIS [46] under [47] for a general instance representation ability. The query number \\(N\\) and iteration time \\(M\\) are set to 50 and 4 respectively. AdamW [31] optimizer with a batch size of 8 is used to train the model. The initial learning rate is set to 2.5e-5 for the backbone and 2.5e-4 for the other parts. At the training stage, for the sake of memory efficiency, we use the frame rate of 12 FPS for image sampling and the input clip length is set to 11 that is longer than most eyeblink events (i.e., 0.2-0.4s). The frames are also resized to \\(640 \\times 360\\) before sending into the network. The whole training procedure lasts for 10,000 iterations and the learning rate is multiplied by 0.1 at iteration 6000 and 9000. During test, the original frame rate is used and the input clip length is set to 36 with a stride of 18. The predictions within adjacent clips are linked via concerning face bounding box IoU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.469, + 0.434, + 0.484 + ], + "angle": 0, + "content": "5.1. Benchmark Results on MPEblink Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Baselines. Multi-person eyeblink detection in untrimmed videos is a new task that has not been well concerned before. Therefore, we tailor the existing eyeblink detection approaches with a unified instance detection and tracking method. Specifically, we use the state-of-the-art face analysis toolbox InsightFace [21] to achieve face [16] and landmark [44] detection. To track each instance, we link the face bounding boxes from the adjacent frames based on their similarity on box IoU. After obtaining the instance tracklets (i.e., a sequence of face bounding boxes and landmarks), we employ 4 representative eyeblink detection method [9, 19, 35, 40] within each instance tracklets. Such a sequential pipeline is commonly used in the existing approaches under the single-person assumption." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.448, + 0.718 + ], + "angle": 0, + "content": "Main results. From Table 2, it can be summarized that:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.47, + 0.81 + ], + "angle": 0, + "content": "- All of the multi-person eyeblink detection algorithms cannot achieve a satisfactory performance (i.e., Blink-AP\\(_{50}\\) lower than \\(30\\%\\) and Blink-AP\\(_{75}\\) lower than \\(10\\%\\)). This indicates that eyeblink detection under multi-person, untrimmed, and unconstrained scenarios is indeed challenging and has not been well solved yet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- For Blink-AP, InstBlink significantly outperforms the others by large margins (i.e., \\(21\\%\\) at least of Blink- \\(\\mathrm{AP}_{50}\\) and \\(6\\%\\) at least of Blink- \\(\\mathrm{AP}_{75}\\)), which verifies the superiority of the proposed framework. We argue that one essential reason is that our framework can model a better long-term temporal eyeblink representation than the frame-based method [9]" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.317 + ], + "angle": 0, + "content": "and the sliding window based methods [19, 35, 40]. Moreover, under the proposed framework, eyeblink features can be facilitated via face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, while previous works that utilize a sequential manner cannot. From Table 2, it can also be summarized that the landmark-based methods [35, 40] perform poorer than the region-based counterparts. We think that one essential reason is that landmark detection is unreliable under unconstrained conditions. A similar conclusion has already been made in [19] but the property of multi-person and long video in MPEblink make it worse for landmark-based eyeblink detection methods. Our method is region-based, but localizes eye region in an implicit way where global face context is included and thus becomes more robust." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- InstBlink also outperforms others on Inst-AP. We think that is because our framework can better model the long-term spatio-temporal instance representations, while the counterparts achieve tracking under a tracking-by-detection framework, which contains limited spatio-temporal modeling and may suffer from heavy occlusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Inference speed analysis. The result is listed in Table 3, assuming the 4 compared methods use InsightFace for face & landmark detection and InstBlink inferences within a clip length of 36. It can be seen that InstBlink is also of high inference speed (i.e., 112 FPS for network forwarding) while the real-time capacity of other methods is not superior. As the number of instances increases, their running time also increases while our method is not sensitive to the number of people because of the one-stage inference property." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.557, + 0.884, + 0.571 + ], + "angle": 0, + "content": "5.2. Benchmark Results on HUST-LEBW Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Experiments are also conducted on the HUST-LEBW dataset to explore the generality of InstBlink towards single-person and trimmed in-the-wild cases. The results are given in Table 4. For models trained on the HUST-LEBW dataset, our method still outperforms others by a large margin (i.e., \\(3.78\\%\\) on F1 score), even with limited training data (less than 450 trimmed samples) to train our one-stage model for multiple tasks (face detection, tracking, and eyeblink detection). Meanwhile, the model trained on MPEblink can obtain \\(83.45\\%\\) F1 score on HUST-LEBW. This indeed verifies the strong generalization ability of InstBlink and MPEblink towards eyeblink detection task." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.655, + 0.787 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Spatial and temporal modeling in QIM. From Table 5, we can see that (1) without applying temporal interaction, the performance of Blink-AP drops from \\(27.19\\%\\) to \\(4.58\\%\\). This indicates that temporal modeling is critical for eyeblink detection in untrimmed videos (i.e., only using appearance features can not accurately localize eyeblinks). It can also be observed that temporal interaction facilitates" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13860" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 3. The inference speed comparison on a single NVIDIA 3090 GPU, assuming the compared methods use InsightFace for face detection (time consumption \\( T = 9.3\\mathrm{ms} \\) including pre-processing) and landmark detection. #faces denotes the face amount in the scene." + }, + { + "type": "table", + "bbox": [ + 0.139, + 0.122, + 0.827, + 0.16 + ], + "angle": 0, + "content": "
MethodInstBlink (Ours)Soukupová and Cech [40]Blink detection+ [35]Hu et al. [19]Daza et al. [9]
Time/image (ms)8.9 + 2.6 for data processingT(=9.3)+5.4×#facesT+5.4×#facesT+5.7×#facesT+9.1×#faces
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.17, + 0.47, + 0.21 + ], + "angle": 0, + "content": "Table 4. Performance comparison on the HUST-LEBW dataset, where InstBlink CROSS indicates InstBlink trained on MPEblink and tested on HUST-LEBW." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.214, + 0.462, + 0.354 + ], + "angle": 0, + "content": "
Training setMethodEyeRecallPrecisionF1
HUST-LEBW [19]Soukupová and Cech [40]Left36.0764.7146.32
Right30.1657.5839.58
Hu et al. [19]Left54.1089.1967.35
Right44.4476.7156.28
Blink detection+ [35]Both58.9980.0567.90
InstBlink (Ours)Both97.6456.6271.68
mEBAL [10]Daza et al. [10]Left96.0360.8074.46
Right79.5073.4876.37
Daza et al. [9]Both93.3975.3383.39
MPEblinkInstBlink CROSS (Ours)Both91.3476.8283.45
" + }, + { + "type": "table_caption", + "bbox": [ + 0.142, + 0.362, + 0.404, + 0.374 + ], + "angle": 0, + "content": "Table 5. Ablation studies on QIM and VIM." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.376, + 0.462, + 0.455 + ], + "angle": 0, + "content": "
MethodBlink-AP50Blink-AP75Inst-AP
w/o QIM3.200.3958.93
w/o temporal interaction in QIM4.580.5563.61
w/o spatial interaction in QIM26.656.1862.45
w/o filter operation in VIM22.274.5965.01
Full model27.197.1667.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.461, + 0.47, + 0.488 + ], + "angle": 0, + "content": "Table 6. The performance comparison with and without blink head on the MPEblink dataset." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.491, + 0.403, + 0.538 + ], + "angle": 0, + "content": "
Blink headInst-APInst-AP50Inst-AP75
×65.8681.7371.23
✓67.8984.5173.76
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.667 + ], + "angle": 0, + "content": "the performance of Inst-AP. We argue that this is because it can also build instance-level association among the features across frames to facilitate the instance tracking ability. (2) Spatial interaction can boost Inst-AP by a large margin (i.e., \\(5.44\\%\\) ) and slightly boost Blink-AP, as it may build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Filter operation in VIM. As in Table 5, compared with directly using RoI features to update query, using filtered RoI features can boost \\(4.92\\%\\) on Blink-AP50 and \\(2.88\\%\\) on Inst-AP. We speculate that the filter operation can activate task-specific RoI features and resist background. Thus, finer face and eyeblink clues can be collected to update queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.47, + 0.835 + ], + "angle": 0, + "content": "Multi-task learning mechanism. Here we study the effect of the blink head from a multi-task learning perspective. As shown in Table 6, adding blink head can also boost \\(2.03\\%\\) on Inst-AP, which demonstrates that features for face detection and tracking can also benefit from eyeblink clues." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.27, + 0.863 + ], + "angle": 0, + "content": "5.4. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We visualize the prediction results of InstBlink in Fig. 7. The examples show that our model can aware the attendees" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.169, + 0.88, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.35, + 0.88, + 0.365 + ], + "angle": 0, + "content": "Figure 7. Qualitative examples of the predictions of InstBlink." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.432 + ], + "angle": 0, + "content": "robustly and detect their eyeblinks under different facial appearance and head pose. Nevertheless, it can not distinguish the rapid consecutive eyeblinks, which also reveals the challenge of eyeblink detection in untrimmed videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.441, + 0.766, + 0.457 + ], + "angle": 0, + "content": "6. Conclusions and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.719 + ], + "angle": 0, + "content": "In this work, we shed the light on a new research task termed multi-person eyeblink detection in the wild for untrimmed video. We formally define the task and introduce a multi-person eyeblink detection dataset named MPEblink. To perform multi-person eyeblink detection in untrimmed videos, we introduce a one-stage multi-person eyeblink detection framework InstBlink. Experiment results demonstrate the superiority of InstBlink in both effectiveness and efficiency. However, our SOTA performance is still unsatisfactory (i.e., \\(\\mathrm{Blink - AP}_{50} < 30\\%\\)). This verifies the challenges of unconstrained multi-person eyeblink detection in long videos. Besides, although the proposed dataset focuses on multi-person, unconstrained, and untrimmed scenarios that are more realistic and have a broader application value, there are lack of crowd scenes (e.g., \\(>10\\) instances) within it. In the future, we will pay more attention to the crowd scenes and enrich the dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.728, + 0.652, + 0.746 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work is jointly supported by the National Natural Science Foundation of China (Grant No. 62271221 and U1913602), and Natural Science Foundation of Guangdong Province (Grant No. 2023A1515011260). Joey Tianyi Zhou is funded by the SERC (Science and Engineering Research Council) Central Research Fund (Use-Inspired Basic Research), and the Singapore Government's Research, and Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering Domain) under programmatic Grant A18A1b0045." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13861" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Talking face video. Face&Gesture Recognition Working Group, IST-2000-26434. 2, 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.469, + 0.199 + ], + "angle": 0, + "content": "[2] Luis Miguel Bergasa, Jesús Nuevo, Miguel A Sotelo, Rafael Barea, and María Elena Lopez. Real-time system for monitoring driver vigilance. 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However, multiperson scenario within untrimmed videos is also important for practical applications, which has not been well concerned yet. To address this, we shed light on this research field for the first time with essential contributions on dataset, theory, and practices. In particular, a large-scale dataset termed MPEblink that involves 686 untrimmed videos with 8748 eyeblink events is proposed under multiperson conditions. The samples are captured from unconstrained films to reveal "in the wild" characteristics. Meanwhile, a real-time multi-person eyeblink detection method is also proposed. Being different from the existing counterparts, our proposition runs in a one-stage spatio-temporal way with end-to-end learning capacity. Specifically, it simultaneously addresses the sub-tasks of face detection, face tracking, and human instance-level eyeblink detection. This paradigm holds 2 main advantages: (1) eyeblink features can be facilitated via the face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, and (2) addressing these sub-tasks in parallel instead of sequential manner can save time remarkably to meet the real-time running requirement. Experiments on MPEblink verify the essential challenges of real-time multiperson eyeblink detection in the wild for untrimmed video. Our method also outperforms existing approaches by large margins and with a high inference speed. + +![](images/d4804999bcb9297efa3db13afb98246c8d1880b9649b2b9edd1290a3f1c50407.jpg) +Figure 1. The illustration on multi-person eyeblink detection. This task aims at being aware of the presence of people and detecting their eyeblink activities at instance level. + +# 1. Introduction + +Real-time eyeblink detection in the wild is a recently emerged challenging research task [19] that can widely serve for fatigue detection [2], face anti-spoofing [34], affective analysis [7], etc. Although remarkable progress has been made [9, 10, 19], the existing methods generally focus on single-person cases within trimmed videos. Multi-person scenario within untrimmed videos has not been well concerned yet. However, detecting long-term eyeblink behaviors at multi-instance level is more preferred for some practical application scenarios. For example, it can be used to estimate attendees' attention level and emotional state change during social interaction [9, 33]. Thus, effective and real-time multi-person eyeblink detection in the wild for untrimmed video is indeed required. + +To this end, we shed the light on this research problem with essential contributions on dataset, theory, and practices. First, a challenging labeled multi-person eyeblink de + +tection benchmark termed MPEblink is built under in-the-wild conditions. It consists of 686 untrimmed long videos captured from unconstrained movies to reveal the "in the wild" characteristics. The contained scenarios are realistic and diverse, such as social interactions and group activities. To our knowledge, MPEblink is the first multi-person eyeblink detection dataset that focuses on in-the-wild long videos. Fig. 1 illustrates a sample video with ground truth annotations within it. Different from the existing eyeblink detection benchmarks [10, 12, 19], the proposed benchmark aims at being aware of all the attendees along the whole video and detecting their eyeblinks at instance level. In summary, MPEblink is featured with multi-instance, unconstrained, and untrimmed, which makes it more challenging and realistic than previous formulations. + +To perform eyeblink detection, previous methods [9, 10, 12, 19, 40] generally take a sequential approach containing face detection, face tracking, and classification on the pre-extracted local eye clues within a temporal window. Whereas such a pipeline seems reasonable, it has several critical drawbacks. First, the use of isolated components may lead to sub-optimal results as they are not jointly optimized and it is inefficient due to the inability to reuse the features of each stage. Second, the eyeblink features only contain the information from the pre-extracted local eye clues (i.e., a small part of face), lacking the useful information from global face context such as head pose and illumination condition that are crucial for detecting eyeblinks in the wild. Moreover, the pre-extracted local eye clues are also unreliable due to the localization challenge towards unconstrained scenarios. Third, the sequential approach leads to computational cost being sensitive to the subject amount, which is hard to meet the real-time running requirement. + +To tackle these issues, we propose a one-stage multi-person eyeblink detection framework called InstBlink, which can simultaneously detect human faces, track them over time, and do eyeblink detection at instance level. InstBlink takes inspiration from the existing query-based methods [41, 45, 47, 48] and models the spatio-temporal face as well as eyeblink representations at instance level within each query. The insight is that the features can be effectively shared among these sub-tasks and the eyeblink features can be facilitated via face's global contexts (e.g., head pose and illumination condition) with joint optimization and interaction, especially in unconstrained in-the-wild cases. Experiments verify the superiority of InstBlink in both effectiveness and efficiency, while also highlighting the critical challenges of real-time multi-person eyeblink detection in the wild for untrimmed video. + +The main contributions of this work lie in 3 folders: + +- To our knowledge, it is the first time that instance-level multi-person eyeblink detection in untrimmed videos is formally defined and explored; + +- We introduce an unconstrained multi-person eyeblink detection dataset MPEblink that contains 686 untrimmed videos with 8748 eyeblink events, featured with more realistic and challenging. +- We propose a one-stage multi-person eyeblink detection method that can jointly perform face detection, tracking, and instance-level eyeblink detection. Such a task-joint paradigm can benefit the sub-tasks uniformly. + +# 2. Related Work + +Eyeblink detection dataset. Existing eyeblink detection datasets [1, 10, 12, 13, 34, 36] generally focus on constrained indoor cases with a consistent environmental setup. HUST-LEBW [19] extends the scenarios to the unconstrained outdoor cases. From then on, the community starts to pay more attention to eyeblink detection in the wild. Nevertheless, HUST-LEBW mainly focuses on single-person scenarios towards trimmed videos, which limits the application of methods in more realistic scenarios such as group activities and social interactions. To address such limitation, we introduce a new dataset termed MPEblink. The proposed dataset is featured with multi-person, unconstrained, and untrimmed, thus being more realistic and challenging. + +Eyeblink detection method. Existing methods generally judge eyeblinks from the pre-extracted local eye clues (e.g., local eye region [6, 9, 10, 19, 25] or landmarks around eyes [8, 14, 35, 40]). To obtain the local eye clues, the existing works generally run in a sequential way including face detection, face tracking, and landmark detection. Finally, the eyeblink result is classified from the pre-extracted local eye clues within a temporal window. Such a pipeline is inefficient due to the isolated optimization among different sub-tasks. Meanwhile, the eyeblink features only contain the information from the pre-extracted local eye clues, lacking useful global information such as head pose and illumination, and the pre-extracted eye clues are also unreliable due to the localization challenge toward unconstrained cases. Besides, due to the multi-stage characteristic, existing methods do not scale well with the number of people in the scene to meet the real-time running requirement. In this paper, we propose a one-stage eyeblink detection framework that can simultaneously detect human faces, track them along the time, and do eyeblink detection at instance level. Within it, eyeblink features can be facilitated via global face context, and the features can be effectively shared among the sub-task to achieve high inference speed. + +Spatio-temporal action detection. Spatio-temporal action detection [15, 20, 22, 26, 27, 39, 48] aims at simultaneously obtaining the spatial and temporal location of an action, which is defined as an action tube [22]. The task only focuses on the isolated action tubes without instance awareness and thus can not make an instance-level analysis along the whole video. Different from that, our proposed multi- + +![](images/5791dc8380048a531f9c717700f130a2f84658177270a35ff2026eaf22030f37.jpg) + +![](images/0ca190674584b915f0c2834b48ea6900effd1fffa5fec3754bc2cf693026db8b.jpg) + +![](images/e6b5d91740bbc4cf8af48b930233e89b776190c8e96fceb626c441608075a660.jpg) +Business party + +![](images/baa673c735adc997c0bd2c9e27ebe8ea7471064474dea79d118293e224e9ac70.jpg) + +![](images/93179e3283422f4ddf59edab857e547455dc5e1a69c0c62f121d651c3e338cdd.jpg) +Cooking in the kitchen + +![](images/b867907f01e28c0fb917183f2389ef6097d636801fb46bef96a435d3392f0532.jpg) +Eating at restaurant +Public speech + +![](images/3a3f04f9a67e0a847e49ef62bb9a28f99329a8b9ce9f51aeb3e667d690a1f71e.jpg) + +![](images/8dc1c45e8e3e8d4b28fd3d4e021405e34a8cfdbcbda3119bddbe94898efbf2ab.jpg) +Hiking +Daily life in prison + +![](images/87be4af61433df6e36b140abddfd45e3353b153f91e67eec94132fab0bacf72e.jpg) +Discussing in the classroom + +![](images/6b321236ab5b771cbb6a3d5e3ad590ef8f05f3cd9fe0aca01d3271ac4d8f7d41.jpg) +Caring for baby + +![](images/c42bbc5e05f9670374341dbbd816fd48dcc3a23272a155231aea984ac388a4c9.jpg) + +![](images/aa174d0f0fca4dcde01e15cf935dc1b195656778eecef4338a2c9cd855f4fda8.jpg) +Being threatened +Arguing in the car + +![](images/40fd90a6a9482c2bd821feff183174ef3f06ca2420c3ada035d8fe6e1934a647.jpg) + +![](images/49a64c37959133d9d89a9c49f0e40f5fa5514312e9ac52a9ad6540118ad3ec36.jpg) +Relaxing on the beach + +![](images/49225f73718ebf7b0f8e83064bba9d65fe8320559eb0c0f0d072534e51b94525.jpg) +Having a meeting +Being arrested + +person eyeblink detection task aims at simultaneously being aware of the presence of people and analyzing their eyeblink behaviors at instance level. + +Query-based methods. Query-based methods are impacting many computer vision tasks. After DETR [4], the pioneer that introduces the query-based framework to address object detection, numerous efforts have been subsequently paid to facilitate visual recognition under the query concept in the fields of object detection [24, 32, 41, 49], pose estimation [38], action detection [30, 48], and segmentation [5, 43, 45, 47]. Inspired by these, we build the first one-stage multi-person eyeblink detection framework for untrimmed video. We propose a unified solution to simultaneously model the instance-level face and eyeblink representations in the whole video. + +# 3. The MPEblink Benchmark + +Existing eyeblink detection datasets generally focus on single-person scenarios, and are also limited in aspects of constrained conditions or trimmed short videos. To explore unconstrained eyeblink detection under multi-person and untrimmed scenarios, we construct a large-scale multiperson eyeblink detection dataset termed MPEblink to shed the light on this research topic that has not been well studied before. The distinguishing characteristics of MPEblink lie in 3 aspects: multi-person, unconstrained, and untrimmed long video, which makes it more realistic and challenging than previous datasets. + +# 3.1. Task Formulation + +We think that a good multi-person eyeblink detection algorithm should be able to (1) detect and track human instances' faces reliably to ensure the instance-level analysis ability along the whole video, and (2) detect eyeblink boundaries accurately within each human instance to ensure the precise awareness of their eyeblink behaviors. + +Formally, for an untrimmed video with $T$ frames and $N_{gt}$ people in it, towards the $j$ -th person, let $\hat{l}^j \in \mathbb{R}^{T \times 4}$ denote its face bounding boxes across the video. $\hat{c}^j \in \mathbb{R}^T$ + +![](images/3b44294e0c49981d5de1626105f2158d73af39838d92873bb0453207be72c041.jpg) +Figure 2. The snapshots within MPEblink. Our dataset is featured with more realistic and diverse scenarios. + +![](images/95b895209233e881656d616468890da66354da2bb1331a70065756cc6f7efd83.jpg) +Figure 3. Occlusion and people in & out cases during interaction among instances. + +![](images/a56eb44ecca6d801bbf8f648ac694e96a09625b4c2f2ae1e483db9c251625993.jpg) +Figure 4. An example of rapid and consecutive eyeblinks in untrimmed video. + +is given as the face labels to reflect the face existence of this instance in each frame (i.e., $\hat{c}_t^j\in \{1,0\}$ , where $\hat{c}_t^j = 0$ indicates that the face is not visible due to serious occlusion or departure at time $t$ ). $\hat{l}_t^j$ is also set to $\varnothing$ when the person is not visible. We use $\hat{l}^j$ and $\hat{c}^j$ to represent the instance-level information of each person. Suppose person $j$ blinks $\hat{K}^j$ times in the video. Let $\hat{B}_{\hat{k}}^{j} = \left[\hat{s}_{\hat{k}}^{j},\hat{e}_{\hat{k}}^{j}\right]$ denote the $\hat{k}$ -th eyeblink event within this person, where $\hat{s}_k^j$ and $\hat{e}_k^j$ denote its starting and ending time. Suppose a multi-person eyeblink detection algorithm produces $H$ human instance hypotheses. Within each human instance hypothesis $i$ , it needs to produce a sequence of predicted face bounding boxes $l^i$ , face classification scores $c^i$ , and $K^i$ eyeblink proposals $B_{k}^{i} = [s_{k}^{i},e_{k}^{i}]$ . Better performance can be acquired when predictions get closer to ground truths. + +# 3.2. Data Collection + +We collect 686 untrimmed video clips with various lengths (i.e., 7.1-85.9s) from 86 different unconstrained movies that involve the "in the wild" characteristics. Some snapshots of the acquired samples are shown in Fig. 2. It can be observed that the samples are with variational indoor and outdoor scenarios for different themes. Thus, the + +Table 1. High-level statistics of MPEblink dataset and existing eyeblink detection datasets. + +
Talking Face [1]ZJU [34]Eyeblink8 [12]Silesian5 [36]Researcher's Night [13]mEBAL [10]HUST-LEBW [19]MPEblink (Ours)
Num. of videos180851076000673686
Video length3.3m4.1-4.7s2.7-8.9m1.4-2.7m0.3-3.4m0.6s0.5s7.1-85.9s
Unconstrained××××××√√
Instances/video11111111-8
Blink count61255353300186730003818748
+ +acquired samples from these movies are much more realistic and closer to practical applications. Meanwhile, due to the high divergence of the selected movie data source, the captured multi-person eyeblink samples are also of great challenges for effectively detecting eyeblinks. For instance, the pose, illumination condition, expression, and face size among instances differ a lot, even within the same video. Moreover, because of the various types of interaction among instances, there may exist severe occlusion or people in and out scenarios as shown in Fig. 3, making it harder for both instance localization and their eyeblink event detection. Besides, different from the existing unconstrained counterpart [19] that mainly focuses on trimmed short videos, the samples from MPEblink are untrimmed. As a result, we not only need to recognize eyeblink but also need to locate the starting and ending time of each eyeblink event, which is more challenging especially when rapid and consecutive eyeblinks occur. An example is shown in Fig. 4. It can be observed that the appearance difference among eye statuses is small when consecutive rapid eyeblinks happen, making it hard to distinguish the boundary of each eyeblink. Considering the above challenges together, it can be summarized that unconstrained multi-person eyeblink detection in untrimmed videos is indeed a challenging research task. + +# 3.3. Data Annotation + +For human instances in each video, we labeled their face bounding boxes exhaustively across the whole video. To facilitate the research of landmark-based methods and include a broader range of applications, 68 facial landmark positions [44] are also annotated. Technically, this part of the annotation is under a semi-supervised manner: we use the state-of-the-art face analysis engine InsightFace [21] to achieve face bounding box [16] and landmark [44] detection. To track instances across frames, a matching strategy that considers bounding box IoU and similarity among deep face features [11] is designed. Besides, human annotators carefully check the annotation quality and correct the wrong bounding boxes and tracking results generated by the algorithm. For eyeblink events within each instance, human annotators carefully define their start and end frame. Finally, 8748 eyeblink events are labeled. + +# 3.4. Data Statistics + +The dataset statistics comparison among MPEblink and the other eyeblink detection datasets are given in Table 1. + +Actually, MPEblink provides the largest number of eyeblink events (i.e., 8748) within 686 untrimmed videos. The biggest difference from the previous datasets is that the videos in our dataset contain various numbers of human instances (i.e., 1-8) with exhaustive annotation. The videos are captured under unconstrained in-the-wild conditions with high diversity as shown in Fig. 2. Compared with the existing in-the-wild counterpart [19] that generally focuses on trimmed short videos, the length of videos from our dataset is much longer and more diverse. In summary, MPEblink is featured with more realistic and challenging and thus has broader application values. + +# 3.5. Evaluation Metrics + +Existing metrics for eyeblink detection only focus on single-person cases without multi-instance awareness. To address this limitation we introduce 2 new metrics termed Inst-AP and Blink-AP to give attention to both instance awareness quality and eyeblink detection quality. + +Inst-AP. It aims to evaluate the instance detection and tracking ability of methods, which is the basis for analyzing the eyeblink behaviors of each instance. We modify the standard evaluation metric video-AP in spatio-temporal action detection [22] to fit our task. Different from the original implementation, the 3D IoU is calculated between each instance proposal (i.e., a sequence of face bounding boxes) and ground truth across the whole video, rather than the action tube only. As a result, the proposed metric can reveal the algorithm's ability for detection and tracking instances, while video-AP can just reveal the localization ability of the isolated action tube without instance-level awareness. We report the averaged Inst-AP under the IoU from $50\% -95\%$ with step $5\%$ . During calculating Inst-AP, each obtained true positive (TP) prediction has matched with one ground-truth instance, and thus, we can calculate the eyeblink detection accuracy of these TP predictions using the proposed Blink-AP. The TP predictions under IoU of $50\%$ are used to calculate the subsequent Blink-AP. + +Blink-AP. This metric is used to reflect the model's eyeblink detection ability within each instance. We tailor the standard AP metric in temporal action detection [3] into our task. Only the matched (i.e., true positive) predictions when calculating Inst-AP are taken into consideration in this metric as the blink accuracy of these predictions is rarely affected by the face detection and tracking accuracy. We report the Blink-AP under the temporal IoU of $50\%$ and $75\%$ . + +![](images/9bfae63d377a8f3063276720be0be8ea0451843f768b2bcaadb9a4e9939f1fa5.jpg) +Figure 5. Overview of the InstBlink framework. + +# 4. Method + +In this section, we present our InstBlink that takes a video clip as input and directly outputs the face positions of each instance and their eyeblink intervals in the whole video clip. The InstBlink design takes inspiration from the existing query-based methods [4, 41, 45, 47, 48] but formulates the architecture to model both face and eyeblink representations at instance level along the video clip. The overall architecture is illustrated in Fig. 5. + +Given a video clip $I \in \mathbb{R}^{T \times 3 \times H \times W}$ where $T$ denotes the number of frames and $H \times W$ is the spatial size of each frame, InstBlink first applies a backbone network to extract video feature $F_v \in \mathbb{R}^{T \times C \times H' \times W'}$ where $C$ is the channel number and $H' \times W'$ is the spatial size of the feature. Afterwards, a query-based architecture iterates $M$ times, which consists of 3 components: the Query Interaction Module (QIM), Video Interaction Module (VIM), and task-specific heads (i.e., face head and blink head). At the end of each interaction, the queries will be updated and the instance-level face and eyeblink predictions will be output by the task-specific heads. During inference, the output from the last iteration will be used as the final prediction results. + +# 4.1. Instance Query + +Within InstBlink, the spatio-temporal instance queries $\{q^i\}_{i = 1}^N$ are responsible for characterizing every human instance's joint face and eyeblink features in a video. Each query contains $T$ embeddings (i.e., $q^{i}\in \mathbb{R}^{T\times C}$ ), where $C$ is the feature dimension. Each embedding generally focuses on the instance's face and eyeblink representations in the corresponding frame. Each query is also paired with a proposal tube $p^i\in \mathbb{R}^{T\times 4}$ (i.e., spatio-temporal bounding boxes across the time), which aims at indicating the face location of $i$ -th instance across the entire video clip. At the first iteration of each complete forward propagation, $q^{i}$ and $p^i$ are initialized by copying 2 learnable parameters $\bar{q}^i\in \mathbb{R}^{1\times C}$ and $\bar{p}^i\in \mathbb{R}^{1\times 4}T$ times along the temporal dimension. + +# 4.2. Query Interaction Module (QIM) + +QIM targets at (1) enhancing the association between the specific query and its corresponding human instance and (2) + +modeling spatio-temporal face and eyeblink representations of the associated instance. Specifically, we first adopt a spatial self-attention layer to allow spatial interaction among queries within each frame: + +$$ +\left\{\boldsymbol {q} _ {t} ^ {i} \right\} _ {i = 1} ^ {N} = \operatorname {M H S A} \left(\left\{\boldsymbol {q} _ {t} ^ {i} \right\} _ {i = 1} ^ {N}\right), \quad t \in [ 1, T ], \tag {1} +$$ + +where MHSA is the multi-head self-attention [42]. Spatial interaction can build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions. Then, temporal self-attention is used within each query along the temporal dimension to realize temporal interaction: + +$$ +\left\{\boldsymbol {q} _ {t} ^ {i} \right\} _ {t = 1} ^ {T} = \operatorname {M H S A} \left(\left\{\boldsymbol {q} _ {t} ^ {i} \right\} _ {t = 1} ^ {T}\right), \quad i \in [ 1, N ]. \tag {2} +$$ + +Applying temporal interaction within each query allows the embeddings from different frames to communicate with each other to facilitate instance tracking and model temporal eyeblink representations of the corresponding instance. + +# 4.3. Video Interaction Module (VIM) + +VIM aims at collecting the face and eyeblink information of the target instance from the video feature. Particularly, the dynamic filters [41] $m^i$ are first generated from each query embeddings $q^i$ . Then, the filters will filter an RoI feature by dynamic convolution to extract highly related features for both face and eyeblink. The RoI feature is obtained by applying RoI align [17] on the video feature using the proposal tube $p^i$ . After obtaining the filtered feature, a linear projection is applied to form the updated query feature $\tilde{q}^i$ . The updated query feature will be used to make both face and eyeblink predictions by the task-specific heads. + +# 4.4. Task-specific Heads + +The instance-level face and eyeblink predictions can be obtained simultaneously by applying task-specific heads on the query features. The heads are shared among queries. + +Face head. Given the updated query feature $\tilde{q}^i$ , a Multilayer Perceptron (MLP) layer with Sigmoid normalization is used to indicate the existence of human faces as + +$$ +c ^ {i} = \operatorname {S i g m o i d} \left(M L P _ {c} \left(\tilde {q} ^ {i}\right)\right), \tag {3} +$$ + +![](images/75e73e428a4fc55a87d3314dff7d34bd59f876eaf1a1b7ea6739550f6e14349e.jpg) +Figure 6. An example of the blink merging procedure, which takes the frame-level eyeblink scores $b^{i}$ and outputs the interval-level eyeblink results $B^{i}$ . The threshold is set to 0.3 for demonstration. + +where $c^i\in \mathbb{R}^T$ denotes the face classification scores across frames. Face localization is achieved in a similar way as + +$$ +l ^ {i} = M L P _ {l} \left(\tilde {q} ^ {i}\right), \tag {4} +$$ + +where $l^i \in \mathbb{R}^{T \times 4}$ denotes the face bounding boxes across frames. It will also be used to renew the proposal tube $p^i$ . Blink head. Eyeblink prediction towards $\tilde{q}^i$ is achieved by an MLP layer with Sigmoid normalization as + +$$ +b ^ {i} = \operatorname {S i g m o i d} \left(M L P _ {b} \left(\tilde {q} ^ {i}\right)\right), \tag {5} +$$ + +where $b^{i} \in \mathbb{R}^{T}$ is the frame-level eyeblink scores. Each element $b_{t}^{i}$ in it indicates the possibility that the $t$ -th frame is inside an eyeblink event. During inference, we simply merge the adjacent frame-level eyeblink predictions based on a threshold (e.g., 0.3 in our implementation) to form the final interval-level eyeblink predictions $B_{k}^{i} = [s_{k}^{i}, e_{k}^{i}]$ where $k \in K$ is the $k$ -th eyeblink interval within the total K eyeblink predictions. An intuitive example of the merging procedure is shown in Fig. 6. + +Different from the existing works that only extract features from the local eye region, our blink head also considers useful global information such as global face appearance, head pose, and illumination condition to aid the implicit eye localization and eyeblink characterization. The reason is that the blink head directly filters global features from the query embeddings where the global face context is already stored. During training, the eyeblink clues will not only flow back to the RoI feature, but also to the instance query to enhance the eyeblink-related feature representation ability of queries. Moreover, because of the shared feature among blink head and face head, a kind of interaction and synergy is built where the information flow from blink head can also benefit the face representations to boost the face detection and tracking ability as verified in Sec. 5.3. + +As we have $N$ queries, we finally obtain the predictions from them in parallel: + +$$ +\left\{y ^ {i} \right\} _ {i = 1} ^ {N} = \left\{\left(c ^ {i}, l ^ {i}, b ^ {i}\right) \right\} _ {i = 1} ^ {N}. \tag {6} +$$ + +# 4.5. Training + +To optimize InstBlink, one-to-one assignment between instance-level predictions $\left\{y^{i}\right\}_{i = 1}^{N}$ and ground truths is first conducted based on their instance-level face tracklet similarity. Then, the loss is calculated concerning face and + +eyeblink items jointly for optimization. As in Sec. 3.1, the ground truth annotations can be summarized as + +$$ +\left\{\hat {y} ^ {j} \right\} _ {j = 1} ^ {N _ {g t}} = \left\{\left(\hat {c} ^ {j}, \hat {l} ^ {j}, \hat {b} ^ {j}\right) \right\} _ {j = 1} ^ {N _ {g t}}, \tag {7} +$$ + +where $\hat{c}^j\in \mathbb{R}^T$ $\hat{l}^j\in \mathbb{R}^{T\times 4}$ , and $\hat{b}^j\in \mathbb{R}^T$ indicate the frame-level face existence, face position (i.e., bounding box) and eyeblink existence (i.e., $\hat{b}_t^j = 1$ indicates frame t is inside an eyeblink event and conversely for $\hat{b}_t^j = 0$ , which can be derived from $\hat{B}^j$ using an inverse process in Fig. 6 ) respectively. We use Hungarian algorithm [23] to perform instance-level bipartite matching between predictions and ground truths. The matching cost is given as + +$$ +\begin{array}{l} \mathcal {L} _ {\text {H u n g}} \left(y ^ {i}, \hat {y} ^ {j}\right) = \sum_ {t = 1} ^ {T} \left[ \mathcal {L} _ {c l s} \left(c _ {t} ^ {i}, \hat {c} _ {t} ^ {j}\right) \right. \tag {8} \\ \left. + 1 _ {\left\{\hat {c} _ {t} ^ {j} \neq 0 \right\}} \left(\mathcal {L} _ {\text {b o x}} \left(l _ {t} ^ {i}, \hat {l} _ {t} ^ {j}\right)\right) \right], \\ \end{array} +$$ + +where $\mathcal{L}_{cls}$ indicates the focal loss [29] for face existence classification. $\mathcal{L}_{box}$ is the combination of L1 loss and GIoU loss [37] for face localization. The loss weights are the same as [41, 47]. After obtaining the optimal assignment $\hat{\sigma}$ between predictions and ground truths, the network is optimized by the loss as + +$$ +\mathcal {L} = \sum_ {j = 1} ^ {N _ {g t}} \left(\mathcal {L} _ {\text {f a c e}} \left(\hat {y} ^ {j}, \hat {y} ^ {\tilde {\sigma} (j)}\right) + \lambda \mathcal {L} _ {\text {b l i n k}} \left(\hat {y} ^ {j}, \hat {y} ^ {\tilde {\sigma} (j)}\right)\right), \tag {9} +$$ + +where $y^{\hat{\sigma}(j)}$ is the prediction that has been matched with the ground truth instance $\hat{y}^j$ . $\mathcal{L}_{face}$ is the face tracklet detection loss that shares the same form as $\mathcal{L}_{Hung}$ (i.e., $\mathcal{L}_{face}(\hat{y}^j, \hat{y}^{\hat{\sigma}(j)}) = \mathcal{L}_{Hung}(\hat{y}^j, \hat{y}^{\hat{\sigma}(j)})$ ), and $\mathcal{L}_{blink}$ denotes instance-level eyeblink detection loss as $\mathcal{L}_{blink}(\hat{y}^j, \hat{y}^{\hat{\sigma}(j)}) = \sum_{t=1}^{T} \mathcal{L}_{cls}(\hat{b}_t^j, \hat{b}_t^{\hat{\sigma}(j)})$ with $\lambda = 5$ . For unmatched predictions, only $\sum_{t=1}^{T} \mathcal{L}_{cls}(c_t^i, \hat{c}_t^i = 0)$ is used to supervise their face existence classification output $c^i$ to be close to 0 (i.e., no face). + +# 5. Experiment + +Dataset and evaluation metrics. We first conduct experiments on the proposed MPEblink dataset. We split the dataset into 423 training videos, 128 validation videos, and 135 test videos. The videos from the same movie will only appear in one set. We train the network on the training set, validate it on the validation set and report the performance on the test set. We report Inst-AP to reveal the instance localization ability and Blink-AP to reveal the eyeblink detection ability within instances, as introduced in Sec. 3.5. Meanwhile, experiments are also conducted on HUST-LEBW for single-person and trimmed cases. Recall, Precision, and F1 score are reported following [19]. + +Table 2. The main results on the MPEblink dataset. + +
TypeMethodBlink-AP50Blink-AP75Inst-AP
LandmarkSoukupová and Cech [40]0.500.0556.70
Blink detection+ [35]0.620.08
RegionHu et al. [19]2.680.04
Daza et al.5.850.88
InstBlink (Ours)27.197.1667.89
+ +Implementation details. We use ResNet-50-FPN [18, 28] backbone. The network is pre-trained on YouTube-VIS [46] under [47] for a general instance representation ability. The query number $N$ and iteration time $M$ are set to 50 and 4 respectively. AdamW [31] optimizer with a batch size of 8 is used to train the model. The initial learning rate is set to 2.5e-5 for the backbone and 2.5e-4 for the other parts. At the training stage, for the sake of memory efficiency, we use the frame rate of 12 FPS for image sampling and the input clip length is set to 11 that is longer than most eyeblink events (i.e., 0.2-0.4s). The frames are also resized to $640 \times 360$ before sending into the network. The whole training procedure lasts for 10,000 iterations and the learning rate is multiplied by 0.1 at iteration 6000 and 9000. During test, the original frame rate is used and the input clip length is set to 36 with a stride of 18. The predictions within adjacent clips are linked via concerning face bounding box IoU. + +# 5.1. Benchmark Results on MPEblink Dataset + +Baselines. Multi-person eyeblink detection in untrimmed videos is a new task that has not been well concerned before. Therefore, we tailor the existing eyeblink detection approaches with a unified instance detection and tracking method. Specifically, we use the state-of-the-art face analysis toolbox InsightFace [21] to achieve face [16] and landmark [44] detection. To track each instance, we link the face bounding boxes from the adjacent frames based on their similarity on box IoU. After obtaining the instance tracklets (i.e., a sequence of face bounding boxes and landmarks), we employ 4 representative eyeblink detection method [9, 19, 35, 40] within each instance tracklets. Such a sequential pipeline is commonly used in the existing approaches under the single-person assumption. + +Main results. From Table 2, it can be summarized that: + +- All of the multi-person eyeblink detection algorithms cannot achieve a satisfactory performance (i.e., Blink-AP $_{50}$ lower than $30\%$ and Blink-AP $_{75}$ lower than $10\%$ ). This indicates that eyeblink detection under multi-person, untrimmed, and unconstrained scenarios is indeed challenging and has not been well solved yet. +- For Blink-AP, InstBlink significantly outperforms the others by large margins (i.e., $21\%$ at least of Blink- $\mathrm{AP}_{50}$ and $6\%$ at least of Blink- $\mathrm{AP}_{75}$ ), which verifies the superiority of the proposed framework. We argue that one essential reason is that our framework can model a better long-term temporal eyeblink representation than the frame-based method [9] + +and the sliding window based methods [19, 35, 40]. Moreover, under the proposed framework, eyeblink features can be facilitated via face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, while previous works that utilize a sequential manner cannot. From Table 2, it can also be summarized that the landmark-based methods [35, 40] perform poorer than the region-based counterparts. We think that one essential reason is that landmark detection is unreliable under unconstrained conditions. A similar conclusion has already been made in [19] but the property of multi-person and long video in MPEblink make it worse for landmark-based eyeblink detection methods. Our method is region-based, but localizes eye region in an implicit way where global face context is included and thus becomes more robust. + +- InstBlink also outperforms others on Inst-AP. We think that is because our framework can better model the long-term spatio-temporal instance representations, while the counterparts achieve tracking under a tracking-by-detection framework, which contains limited spatio-temporal modeling and may suffer from heavy occlusion. + +Inference speed analysis. The result is listed in Table 3, assuming the 4 compared methods use InsightFace for face & landmark detection and InstBlink inferences within a clip length of 36. It can be seen that InstBlink is also of high inference speed (i.e., 112 FPS for network forwarding) while the real-time capacity of other methods is not superior. As the number of instances increases, their running time also increases while our method is not sensitive to the number of people because of the one-stage inference property. + +# 5.2. Benchmark Results on HUST-LEBW Dataset + +Experiments are also conducted on the HUST-LEBW dataset to explore the generality of InstBlink towards single-person and trimmed in-the-wild cases. The results are given in Table 4. For models trained on the HUST-LEBW dataset, our method still outperforms others by a large margin (i.e., $3.78\%$ on F1 score), even with limited training data (less than 450 trimmed samples) to train our one-stage model for multiple tasks (face detection, tracking, and eyeblink detection). Meanwhile, the model trained on MPEblink can obtain $83.45\%$ F1 score on HUST-LEBW. This indeed verifies the strong generalization ability of InstBlink and MPEblink towards eyeblink detection task. + +# 5.3. Ablation Study + +Spatial and temporal modeling in QIM. From Table 5, we can see that (1) without applying temporal interaction, the performance of Blink-AP drops from $27.19\%$ to $4.58\%$ . This indicates that temporal modeling is critical for eyeblink detection in untrimmed videos (i.e., only using appearance features can not accurately localize eyeblinks). It can also be observed that temporal interaction facilitates + +Table 3. The inference speed comparison on a single NVIDIA 3090 GPU, assuming the compared methods use InsightFace for face detection (time consumption $T = 9.3\mathrm{ms}$ including pre-processing) and landmark detection. #faces denotes the face amount in the scene. + +
MethodInstBlink (Ours)Soukupová and Cech [40]Blink detection+ [35]Hu et al. [19]Daza et al. [9]
Time/image (ms)8.9 + 2.6 for data processingT(=9.3)+5.4×#facesT+5.4×#facesT+5.7×#facesT+9.1×#faces
+ +Table 4. Performance comparison on the HUST-LEBW dataset, where InstBlink CROSS indicates InstBlink trained on MPEblink and tested on HUST-LEBW. + +
Training setMethodEyeRecallPrecisionF1
HUST-LEBW [19]Soukupová and Cech [40]Left36.0764.7146.32
Right30.1657.5839.58
Hu et al. [19]Left54.1089.1967.35
Right44.4476.7156.28
Blink detection+ [35]Both58.9980.0567.90
InstBlink (Ours)Both97.6456.6271.68
mEBAL [10]Daza et al. [10]Left96.0360.8074.46
Right79.5073.4876.37
Daza et al. [9]Both93.3975.3383.39
MPEblinkInstBlink CROSS (Ours)Both91.3476.8283.45
+ +Table 5. Ablation studies on QIM and VIM. + +
MethodBlink-AP50Blink-AP75Inst-AP
w/o QIM3.200.3958.93
w/o temporal interaction in QIM4.580.5563.61
w/o spatial interaction in QIM26.656.1862.45
w/o filter operation in VIM22.274.5965.01
Full model27.197.1667.89
+ +Table 6. The performance comparison with and without blink head on the MPEblink dataset. + +
Blink headInst-APInst-AP50Inst-AP75
×65.8681.7371.23
✓67.8984.5173.76
+ +the performance of Inst-AP. We argue that this is because it can also build instance-level association among the features across frames to facilitate the instance tracking ability. (2) Spatial interaction can boost Inst-AP by a large margin (i.e., $5.44\%$ ) and slightly boost Blink-AP, as it may build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions. + +Filter operation in VIM. As in Table 5, compared with directly using RoI features to update query, using filtered RoI features can boost $4.92\%$ on Blink-AP50 and $2.88\%$ on Inst-AP. We speculate that the filter operation can activate task-specific RoI features and resist background. Thus, finer face and eyeblink clues can be collected to update queries. + +Multi-task learning mechanism. Here we study the effect of the blink head from a multi-task learning perspective. As shown in Table 6, adding blink head can also boost $2.03\%$ on Inst-AP, which demonstrates that features for face detection and tracking can also benefit from eyeblink clues. + +# 5.4. Qualitative Analysis + +We visualize the prediction results of InstBlink in Fig. 7. The examples show that our model can aware the attendees + +![](images/cb30a3bb0b2e8c241324f2fd3b505751dfad66fdb9ff3763b1d4770c71dca209.jpg) +Figure 7. Qualitative examples of the predictions of InstBlink. + +robustly and detect their eyeblinks under different facial appearance and head pose. Nevertheless, it can not distinguish the rapid consecutive eyeblinks, which also reveals the challenge of eyeblink detection in untrimmed videos. + +# 6. Conclusions and Limitations + +In this work, we shed the light on a new research task termed multi-person eyeblink detection in the wild for untrimmed video. We formally define the task and introduce a multi-person eyeblink detection dataset named MPEblink. To perform multi-person eyeblink detection in untrimmed videos, we introduce a one-stage multi-person eyeblink detection framework InstBlink. Experiment results demonstrate the superiority of InstBlink in both effectiveness and efficiency. However, our SOTA performance is still unsatisfactory (i.e., $\mathrm{Blink - AP}_{50} < 30\%$ ). This verifies the challenges of unconstrained multi-person eyeblink detection in long videos. Besides, although the proposed dataset focuses on multi-person, unconstrained, and untrimmed scenarios that are more realistic and have a broader application value, there are lack of crowd scenes (e.g., $>10$ instances) within it. In the future, we will pay more attention to the crowd scenes and enrich the dataset. + +# Acknowledgment + +This work is jointly supported by the National Natural Science Foundation of China (Grant No. 62271221 and U1913602), and Natural Science Foundation of Guangdong Province (Grant No. 2023A1515011260). Joey Tianyi Zhou is funded by the SERC (Science and Engineering Research Council) Central Research Fund (Use-Inspired Basic Research), and the Singapore Government's Research, and Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering Domain) under programmatic Grant A18A1b0045. + +# References + +[1] Talking face video. Face&Gesture Recognition Working Group, IST-2000-26434. 2, 4 +[2] Luis Miguel Bergasa, Jesús Nuevo, Miguel A Sotelo, Rafael Barea, and María Elena Lopez. Real-time system for monitoring driver vigilance. IEEE Transactions on Intelligent Transportation Systems, 7(1):63-77, 2006. 1 +[3] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In Proc. 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"https://github.com/wenzhengzeng/MPEblink" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 324, + 192, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 324, + 192, + 337 + ], + "spans": [ + { + "bbox": [ + 143, + 324, + 192, + 337 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 347, + 290, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 290, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 290, + 695 + ], + "type": "text", + "content": "Real-time eyeblink detection in the wild can widely serve for fatigue detection, face anti-spoofing, emotion analysis, etc. The existing research efforts generally focus on single-person cases towards trimmed video. However, multiperson scenario within untrimmed videos is also important for practical applications, which has not been well concerned yet. To address this, we shed light on this research field for the first time with essential contributions on dataset, theory, and practices. In particular, a large-scale dataset termed MPEblink that involves 686 untrimmed videos with 8748 eyeblink events is proposed under multiperson conditions. The samples are captured from unconstrained films to reveal \"in the wild\" characteristics. Meanwhile, a real-time multi-person eyeblink detection method is also proposed. Being different from the existing counterparts, our proposition runs in a one-stage spatio-temporal way with end-to-end learning capacity. Specifically, it simultaneously addresses the sub-tasks of face detection, face tracking, and human instance-level eyeblink detection. This paradigm holds 2 main advantages: (1) eyeblink features can be facilitated via the face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, and (2) addressing these sub-tasks in parallel instead of sequential manner can save time remarkably to meet the real-time running requirement. Experiments on MPEblink verify the essential challenges of real-time multiperson eyeblink detection in the wild for untrimmed video. Our method also outperforms existing approaches by large margins and with a high inference speed." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 324, + 547, + 438 + ], + "blocks": [ + { + "bbox": [ + 307, + 324, + 547, + 438 + ], + "lines": [ + { + "bbox": [ + 307, + 324, + 547, + 438 + ], + "spans": [ + { + "bbox": [ + 307, + 324, + 547, + 438 + ], + "type": "image", + "image_path": "d4804999bcb9297efa3db13afb98246c8d1880b9649b2b9edd1290a3f1c50407.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "lines": [ + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "type": "text", + "content": "Figure 1. The illustration on multi-person eyeblink detection. This task aims at being aware of the presence of people and detecting their eyeblink activities at instance level." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 488, + 388, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 488, + 388, + 501 + ], + "spans": [ + { + "bbox": [ + 306, + 488, + 388, + 501 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 676 + ], + "type": "text", + "content": "Real-time eyeblink detection in the wild is a recently emerged challenging research task [19] that can widely serve for fatigue detection [2], face anti-spoofing [34], affective analysis [7], etc. Although remarkable progress has been made [9, 10, 19], the existing methods generally focus on single-person cases within trimmed videos. Multi-person scenario within untrimmed videos has not been well concerned yet. However, detecting long-term eyeblink behaviors at multi-instance level is more preferred for some practical application scenarios. For example, it can be used to estimate attendees' attention level and emotional state change during social interaction [9, 33]. Thus, effective and real-time multi-person eyeblink detection in the wild for untrimmed video is indeed required." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "To this end, we shed the light on this research problem with essential contributions on dataset, theory, and practices. First, a challenging labeled multi-person eyeblink de" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 268, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 268, + 714 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 268, + 714 + ], + "type": "text", + "content": "†Yang Xiao is corresponding author (Yang_Xiao@hust.edu.cn)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13854" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "tection benchmark termed MPEblink is built under in-the-wild conditions. It consists of 686 untrimmed long videos captured from unconstrained movies to reveal the \"in the wild\" characteristics. The contained scenarios are realistic and diverse, such as social interactions and group activities. To our knowledge, MPEblink is the first multi-person eyeblink detection dataset that focuses on in-the-wild long videos. Fig. 1 illustrates a sample video with ground truth annotations within it. Different from the existing eyeblink detection benchmarks [10, 12, 19], the proposed benchmark aims at being aware of all the attendees along the whole video and detecting their eyeblinks at instance level. In summary, MPEblink is featured with multi-instance, unconstrained, and untrimmed, which makes it more challenging and realistic than previous formulations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 253, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 289, + 469 + ], + "type": "text", + "content": "To perform eyeblink detection, previous methods [9, 10, 12, 19, 40] generally take a sequential approach containing face detection, face tracking, and classification on the pre-extracted local eye clues within a temporal window. Whereas such a pipeline seems reasonable, it has several critical drawbacks. First, the use of isolated components may lead to sub-optimal results as they are not jointly optimized and it is inefficient due to the inability to reuse the features of each stage. Second, the eyeblink features only contain the information from the pre-extracted local eye clues (i.e., a small part of face), lacking the useful information from global face context such as head pose and illumination condition that are crucial for detecting eyeblinks in the wild. Moreover, the pre-extracted local eye clues are also unreliable due to the localization challenge towards unconstrained scenarios. Third, the sequential approach leads to computational cost being sensitive to the subject amount, which is hard to meet the real-time running requirement." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 471, + 289, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 289, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 289, + 662 + ], + "type": "text", + "content": "To tackle these issues, we propose a one-stage multi-person eyeblink detection framework called InstBlink, which can simultaneously detect human faces, track them over time, and do eyeblink detection at instance level. InstBlink takes inspiration from the existing query-based methods [41, 45, 47, 48] and models the spatio-temporal face as well as eyeblink representations at instance level within each query. The insight is that the features can be effectively shared among these sub-tasks and the eyeblink features can be facilitated via face's global contexts (e.g., head pose and illumination condition) with joint optimization and interaction, especially in unconstrained in-the-wild cases. Experiments verify the superiority of InstBlink in both effectiveness and efficiency, while also highlighting the critical challenges of real-time multi-person eyeblink detection in the wild for untrimmed video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 664, + 269, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 664, + 269, + 675 + ], + "spans": [ + { + "bbox": [ + 59, + 664, + 269, + 675 + ], + "type": "text", + "content": "The main contributions of this work lie in 3 folders:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "- To our knowledge, it is the first time that instance-level multi-person eyeblink detection in untrimmed videos is formally defined and explored;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "- We introduce an unconstrained multi-person eyeblink detection dataset MPEblink that contains 686 untrimmed videos with 8748 eyeblink events, featured with more realistic and challenging." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 121, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 168 + ], + "type": "text", + "content": "- We propose a one-stage multi-person eyeblink detection method that can jointly perform face detection, tracking, and instance-level eyeblink detection. Such a task-joint paradigm can benefit the sub-tasks uniformly." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 199, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 547, + 354 + ], + "type": "text", + "content": "Eyeblink detection dataset. Existing eyeblink detection datasets [1, 10, 12, 13, 34, 36] generally focus on constrained indoor cases with a consistent environmental setup. HUST-LEBW [19] extends the scenarios to the unconstrained outdoor cases. From then on, the community starts to pay more attention to eyeblink detection in the wild. Nevertheless, HUST-LEBW mainly focuses on single-person scenarios towards trimmed videos, which limits the application of methods in more realistic scenarios such as group activities and social interactions. To address such limitation, we introduce a new dataset termed MPEblink. The proposed dataset is featured with multi-person, unconstrained, and untrimmed, thus being more realistic and challenging." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 355, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 547, + 629 + ], + "type": "text", + "content": "Eyeblink detection method. Existing methods generally judge eyeblinks from the pre-extracted local eye clues (e.g., local eye region [6, 9, 10, 19, 25] or landmarks around eyes [8, 14, 35, 40]). To obtain the local eye clues, the existing works generally run in a sequential way including face detection, face tracking, and landmark detection. Finally, the eyeblink result is classified from the pre-extracted local eye clues within a temporal window. Such a pipeline is inefficient due to the isolated optimization among different sub-tasks. Meanwhile, the eyeblink features only contain the information from the pre-extracted local eye clues, lacking useful global information such as head pose and illumination, and the pre-extracted eye clues are also unreliable due to the localization challenge toward unconstrained cases. Besides, due to the multi-stage characteristic, existing methods do not scale well with the number of people in the scene to meet the real-time running requirement. In this paper, we propose a one-stage eyeblink detection framework that can simultaneously detect human faces, track them along the time, and do eyeblink detection at instance level. Within it, eyeblink features can be facilitated via global face context, and the features can be effectively shared among the sub-task to achieve high inference speed." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 631, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 631, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 631, + 547, + 715 + ], + "type": "text", + "content": "Spatio-temporal action detection. Spatio-temporal action detection [15, 20, 22, 26, 27, 39, 48] aims at simultaneously obtaining the spatial and temporal location of an action, which is defined as an action tube [22]. The task only focuses on the isolated action tubes without instance awareness and thus can not make an instance-level analysis along the whole video. 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"Being arrested" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 241, + 286, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 286, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 286, + 276 + ], + "type": "text", + "content": "person eyeblink detection task aims at simultaneously being aware of the presence of people and analyzing their eyeblink behaviors at instance level." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 277, + 287, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 420 + ], + "type": "text", + "content": "Query-based methods. Query-based methods are impacting many computer vision tasks. After DETR [4], the pioneer that introduces the query-based framework to address object detection, numerous efforts have been subsequently paid to facilitate visual recognition under the query concept in the fields of object detection [24, 32, 41, 49], pose estimation [38], action detection [30, 48], and segmentation [5, 43, 45, 47]. Inspired by these, we build the first one-stage multi-person eyeblink detection framework for untrimmed video. We propose a unified solution to simultaneously model the instance-level face and eyeblink representations in the whole video." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 430, + 201, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 201, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 201, + 442 + ], + "type": "text", + "content": "3. The MPEblink Benchmark" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 581 + ], + "type": "text", + "content": "Existing eyeblink detection datasets generally focus on single-person scenarios, and are also limited in aspects of constrained conditions or trimmed short videos. To explore unconstrained eyeblink detection under multi-person and untrimmed scenarios, we construct a large-scale multiperson eyeblink detection dataset termed MPEblink to shed the light on this research topic that has not been well studied before. The distinguishing characteristics of MPEblink lie in 3 aspects: multi-person, unconstrained, and untrimmed long video, which makes it more realistic and challenging than previous datasets." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 153, + 599 + ], + "type": "text", + "content": "3.1. Task Formulation" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 605, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 677 + ], + "type": "text", + "content": "We think that a good multi-person eyeblink detection algorithm should be able to (1) detect and track human instances' faces reliably to ensure the instance-level analysis ability along the whole video, and (2) detect eyeblink boundaries accurately within each human instance to ensure the precise awareness of their eyeblink behaviors." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Formally, for an untrimmed video with " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " frames and " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "N_{gt}" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " people in it, towards the " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "-th person, let " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\hat{l}^j \\in \\mathbb{R}^{T \\times 4}" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " denote its face bounding boxes across the video. " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\hat{c}^j \\in \\mathbb{R}^T" + } + ] + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 314, + 239, + 425, + 320 + ], + "blocks": [ + { + "bbox": [ + 100, + 223, + 491, + 233 + ], + "lines": [ + { + "bbox": [ + 100, + 223, + 491, + 233 + ], + "spans": [ + { + "bbox": [ + 100, + 223, + 491, + 233 + ], + "type": "text", + "content": "Figure 2. The snapshots within MPEblink. Our dataset is featured with more realistic and diverse scenarios." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 314, + 239, + 425, + 320 + ], + "lines": [ + { + "bbox": [ + 314, + 239, + 425, + 320 + ], + "spans": [ + { + "bbox": [ + 314, + 239, + 425, + 320 + ], + "type": "image", + "image_path": "3b44294e0c49981d5de1626105f2158d73af39838d92873bb0453207be72c041.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "type": "image", + "bbox": [ + 427, + 239, + 536, + 321 + ], + "blocks": [ + { + "bbox": [ + 427, + 239, + 536, + 321 + ], + "lines": [ + { + "bbox": [ + 427, + 239, + 536, + 321 + ], + "spans": [ + { + "bbox": [ + 427, + 239, + 536, + 321 + ], + "type": "image", + "image_path": "95b895209233e881656d616468890da66354da2bb1331a70065756cc6f7efd83.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 326, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 305, + 326, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 326, + 545, + 348 + ], + "type": "text", + "content": "Figure 3. Occlusion and people in & out cases during interaction among instances." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 37 + }, + { + "type": "image", + "bbox": [ + 313, + 354, + 536, + 392 + ], + "blocks": [ + { + "bbox": [ + 313, + 354, + 536, + 392 + ], + "lines": [ + { + "bbox": [ + 313, + 354, + 536, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 354, + 536, + 392 + ], + "type": "image", + "image_path": "a56eb44ecca6d801bbf8f648ac694e96a09625b4c2f2ae1e483db9c251625993.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 397, + 545, + 419 + ], + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 419 + ], + "type": "text", + "content": "Figure 4. An example of rapid and consecutive eyeblinks in untrimmed video." + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_caption" + } + ], + "index": 39 + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": "is given as the face labels to reflect the face existence of this instance in each frame (i.e., " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{c}_t^j\\in \\{1,0\\}" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{c}_t^j = 0" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " indicates that the face is not visible due to serious occlusion or departure at time " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{l}_t^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " is also set to " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " when the person is not visible. We use " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{l}^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{c}^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " to represent the instance-level information of each person. Suppose person " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " blinks " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{K}^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " times in the video. Let " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{B}_{\\hat{k}}^{j} = \\left[\\hat{s}_{\\hat{k}}^{j},\\hat{e}_{\\hat{k}}^{j}\\right]" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{k}" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": "-th eyeblink event within this person, where " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{s}_k^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{e}_k^j" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " denote its starting and ending time. Suppose a multi-person eyeblink detection algorithm produces " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " human instance hypotheses. Within each human instance hypothesis " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": ", it needs to produce a sequence of predicted face bounding boxes " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "l^i" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": ", face classification scores " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "c^i" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "K^i" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": " eyeblink proposals " + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "inline_equation", + "content": "B_{k}^{i} = [s_{k}^{i},e_{k}^{i}]" + }, + { + "bbox": [ + 305, + 427, + 545, + 616 + ], + "type": "text", + "content": ". Better performance can be acquired when predictions get closer to ground truths." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 623, + 402, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 402, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 402, + 635 + ], + "type": "text", + "content": "3.2. Data Collection" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "We collect 686 untrimmed video clips with various lengths (i.e., 7.1-85.9s) from 86 different unconstrained movies that involve the \"in the wild\" characteristics. Some snapshots of the acquired samples are shown in Fig. 2. It can be observed that the samples are with variational indoor and outdoor scenarios for different themes. Thus, the" + } + ] + } + ], + "index": 43 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13856" + } + ] + } + ], + "index": 44 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 85, + 525, + 148 + ], + "blocks": [ + { + "bbox": [ + 132, + 70, + 461, + 82 + ], + "lines": [ + { + "bbox": [ + 132, + 70, + 461, + 82 + ], + "spans": [ + { + "bbox": [ + 132, + 70, + 461, + 82 + ], + "type": "text", + "content": "Table 1. High-level statistics of MPEblink dataset and existing eyeblink detection datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 85, + 525, + 148 + ], + "lines": [ + { + "bbox": [ + 67, + 85, + 525, + 148 + ], + "spans": [ + { + "bbox": [ + 67, + 85, + 525, + 148 + ], + "type": "table", + "html": "
Talking Face [1]ZJU [34]Eyeblink8 [12]Silesian5 [36]Researcher's Night [13]mEBAL [10]HUST-LEBW [19]MPEblink (Ours)
Num. of videos180851076000673686
Video length3.3m4.1-4.7s2.7-8.9m1.4-2.7m0.3-3.4m0.6s0.5s7.1-85.9s
Unconstrained××××××√√
Instances/video11111111-8
Blink count61255353300186730003818748
", + "image_path": "eb032ac8d6bfb289539096c539b4cb938bb4a6c6b21e38f3fc4e86c1f62164ad.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 158, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 158, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 289, + 445 + ], + "type": "text", + "content": "acquired samples from these movies are much more realistic and closer to practical applications. Meanwhile, due to the high divergence of the selected movie data source, the captured multi-person eyeblink samples are also of great challenges for effectively detecting eyeblinks. For instance, the pose, illumination condition, expression, and face size among instances differ a lot, even within the same video. Moreover, because of the various types of interaction among instances, there may exist severe occlusion or people in and out scenarios as shown in Fig. 3, making it harder for both instance localization and their eyeblink event detection. Besides, different from the existing unconstrained counterpart [19] that mainly focuses on trimmed short videos, the samples from MPEblink are untrimmed. As a result, we not only need to recognize eyeblink but also need to locate the starting and ending time of each eyeblink event, which is more challenging especially when rapid and consecutive eyeblinks occur. An example is shown in Fig. 4. It can be observed that the appearance difference among eye statuses is small when consecutive rapid eyeblinks happen, making it hard to distinguish the boundary of each eyeblink. Considering the above challenges together, it can be summarized that unconstrained multi-person eyeblink detection in untrimmed videos is indeed a challenging research task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 453, + 149, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 149, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 149, + 464 + ], + "type": "text", + "content": "3.3. Data Annotation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 662 + ], + "type": "text", + "content": "For human instances in each video, we labeled their face bounding boxes exhaustively across the whole video. To facilitate the research of landmark-based methods and include a broader range of applications, 68 facial landmark positions [44] are also annotated. Technically, this part of the annotation is under a semi-supervised manner: we use the state-of-the-art face analysis engine InsightFace [21] to achieve face bounding box [16] and landmark [44] detection. To track instances across frames, a matching strategy that considers bounding box IoU and similarity among deep face features [11] is designed. Besides, human annotators carefully check the annotation quality and correct the wrong bounding boxes and tracking results generated by the algorithm. For eyeblink events within each instance, human annotators carefully define their start and end frame. Finally, 8748 eyeblink events are labeled." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 138, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 138, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 138, + 682 + ], + "type": "text", + "content": "3.4. Data Statistics" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "The dataset statistics comparison among MPEblink and the other eyeblink detection datasets are given in Table 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "type": "text", + "content": "Actually, MPEblink provides the largest number of eyeblink events (i.e., 8748) within 686 untrimmed videos. The biggest difference from the previous datasets is that the videos in our dataset contain various numbers of human instances (i.e., 1-8) with exhaustive annotation. The videos are captured under unconstrained in-the-wild conditions with high diversity as shown in Fig. 2. Compared with the existing in-the-wild counterpart [19] that generally focuses on trimmed short videos, the length of videos from our dataset is much longer and more diverse. In summary, MPEblink is featured with more realistic and challenging and thus has broader application values." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 311, + 419, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 311, + 419, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 419, + 322 + ], + "type": "text", + "content": "3.5. Evaluation Metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 329, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 389 + ], + "type": "text", + "content": "Existing metrics for eyeblink detection only focus on single-person cases without multi-instance awareness. To address this limitation we introduce 2 new metrics termed Inst-AP and Blink-AP to give attention to both instance awareness quality and eyeblink detection quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "text", + "content": "Inst-AP. It aims to evaluate the instance detection and tracking ability of methods, which is the basis for analyzing the eyeblink behaviors of each instance. We modify the standard evaluation metric video-AP in spatio-temporal action detection [22] to fit our task. Different from the original implementation, the 3D IoU is calculated between each instance proposal (i.e., a sequence of face bounding boxes) and ground truth across the whole video, rather than the action tube only. As a result, the proposed metric can reveal the algorithm's ability for detection and tracking instances, while video-AP can just reveal the localization ability of the isolated action tube without instance-level awareness. We report the averaged Inst-AP under the IoU from " + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "inline_equation", + "content": "50\\% -95\\%" + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "text", + "content": " with step " + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "text", + "content": ". During calculating Inst-AP, each obtained true positive (TP) prediction has matched with one ground-truth instance, and thus, we can calculate the eyeblink detection accuracy of these TP predictions using the proposed Blink-AP. The TP predictions under IoU of " + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 390, + 546, + 617 + ], + "type": "text", + "content": " are used to calculate the subsequent Blink-AP." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Blink-AP. This metric is used to reflect the model's eyeblink detection ability within each instance. We tailor the standard AP metric in temporal action detection [3] into our task. Only the matched (i.e., true positive) predictions when calculating Inst-AP are taken into consideration in this metric as the blink accuracy of these predictions is rarely affected by the face detection and tracking accuracy. We report the Blink-AP under the temporal IoU of " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13857" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 68, + 500, + 190 + ], + "blocks": [ + { + "bbox": [ + 95, + 68, + 500, + 190 + ], + "lines": [ + { + "bbox": [ + 95, + 68, + 500, + 190 + ], + "spans": [ + { + "bbox": [ + 95, + 68, + 500, + 190 + ], + "type": "image", + "image_path": "9bfae63d377a8f3063276720be0be8ea0451843f768b2bcaadb9a4e9939f1fa5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 208, + 193, + 384, + 204 + ], + "lines": [ + { + "bbox": [ + 208, + 193, + 384, + 204 + ], + "spans": [ + { + "bbox": [ + 208, + 193, + 384, + 204 + ], + "type": "text", + "content": "Figure 5. Overview of the InstBlink framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 210, + 104, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 104, + 222 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 104, + 222 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 230, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 287, + 326 + ], + "type": "text", + "content": "In this section, we present our InstBlink that takes a video clip as input and directly outputs the face positions of each instance and their eyeblink intervals in the whole video clip. The InstBlink design takes inspiration from the existing query-based methods [4, 41, 45, 47, 48] but formulates the architecture to model both face and eyeblink representations at instance level along the video clip. The overall architecture is illustrated in Fig. 5." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": "Given a video clip " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{T \\times 3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " denotes the number of frames and " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " is the spatial size of each frame, InstBlink first applies a backbone network to extract video feature " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "F_v \\in \\mathbb{R}^{T \\times C \\times H' \\times W'}" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " is the channel number and " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "H' \\times W'" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " is the spatial size of the feature. Afterwards, a query-based architecture iterates " + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 325, + 288, + 482 + ], + "type": "text", + "content": " times, which consists of 3 components: the Query Interaction Module (QIM), Video Interaction Module (VIM), and task-specific heads (i.e., face head and blink head). At the end of each interaction, the queries will be updated and the instance-level face and eyeblink predictions will be output by the task-specific heads. During inference, the output from the last iteration will be used as the final prediction results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 488, + 142, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 142, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 142, + 502 + ], + "type": "text", + "content": "4.1. Instance Query" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": "Within InstBlink, the spatio-temporal instance queries " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\{q^i\\}_{i = 1}^N" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " are responsible for characterizing every human instance's joint face and eyeblink features in a video. Each query contains " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " embeddings (i.e., " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "q^{i}\\in \\mathbb{R}^{T\\times C}" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": "), where " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " is the feature dimension. Each embedding generally focuses on the instance's face and eyeblink representations in the corresponding frame. Each query is also paired with a proposal tube " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "p^i\\in \\mathbb{R}^{T\\times 4}" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " (i.e., spatio-temporal bounding boxes across the time), which aims at indicating the face location of " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": "-th instance across the entire video clip. At the first iteration of each complete forward propagation, " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "q^{i}" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "p^i" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " are initialized by copying 2 learnable parameters " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\bar{q}^i\\in \\mathbb{R}^{1\\times C}" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\bar{p}^i\\in \\mathbb{R}^{1\\times 4}T" + }, + { + "bbox": [ + 47, + 506, + 287, + 665 + ], + "type": "text", + "content": " times along the temporal dimension." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 227, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 227, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 227, + 685 + ], + "type": "text", + "content": "4.2. Query Interaction Module (QIM)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "QIM targets at (1) enhancing the association between the specific query and its corresponding human instance and (2)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 211, + 545, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 259 + ], + "type": "text", + "content": "modeling spatio-temporal face and eyeblink representations of the associated instance. Specifically, we first adopt a spatial self-attention layer to allow spatial interaction among queries within each frame:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 332, + 264, + 545, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 264, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 332, + 264, + 545, + 285 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {i = 1} ^ {N}\\right), \\quad t \\in [ 1, T ], \\tag {1}", + "image_path": "f4bbc8e18a42c37081d1eb04f9a2f507720bb2f89865f244c929156e037aaf29.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 290, + 545, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 362 + ], + "type": "text", + "content": "where MHSA is the multi-head self-attention [42]. Spatial interaction can build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions. Then, temporal self-attention is used within each query along the temporal dimension to realize temporal interaction:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 368, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 368, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 331, + 368, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T} = \\operatorname {M H S A} \\left(\\left\\{\\boldsymbol {q} _ {t} ^ {i} \\right\\} _ {t = 1} ^ {T}\\right), \\quad i \\in [ 1, N ]. \\tag {2}", + "image_path": "a6a76f5c05da5e820ea8304bfe5ba31aff8c38cf9cc17f4f7282ce11333030bc.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 393, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 441 + ], + "type": "text", + "content": "Applying temporal interaction within each query allows the embeddings from different frames to communicate with each other to facilitate instance tracking and model temporal eyeblink representations of the corresponding instance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 448, + 482, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 482, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 482, + 460 + ], + "type": "text", + "content": "4.3. Video Interaction Module (VIM)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "content": "VIM aims at collecting the face and eyeblink information of the target instance from the video feature. Particularly, the dynamic filters [41] " + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "inline_equation", + "content": "m^i" + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "content": " are first generated from each query embeddings " + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "inline_equation", + "content": "q^i" + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "content": ". Then, the filters will filter an RoI feature by dynamic convolution to extract highly related features for both face and eyeblink. The RoI feature is obtained by applying RoI align [17] on the video feature using the proposal tube " + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "inline_equation", + "content": "p^i" + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "content": ". After obtaining the filtered feature, a linear projection is applied to form the updated query feature " + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\tilde{q}^i" + }, + { + "bbox": [ + 304, + 466, + 545, + 598 + ], + "type": "text", + "content": ". The updated query feature will be used to make both face and eyeblink predictions by the task-specific heads." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 604, + 421, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 421, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 421, + 616 + ], + "type": "text", + "content": "4.4. Task-specific Heads" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 622, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 622, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 622, + 545, + 658 + ], + "type": "text", + "content": "The instance-level face and eyeblink predictions can be obtained simultaneously by applying task-specific heads on the query features. The heads are shared among queries." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "text", + "content": "Face head. Given the updated query feature " + }, + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\tilde{q}^i" + }, + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "text", + "content": ", a Multilayer Perceptron (MLP) layer with Sigmoid normalization is used to indicate the existence of human faces as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "c ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {c} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {3}", + "image_path": "4b811d387cb909fc4133b65ee1253a48d1eb4f936b320a23fb107e1cd0417c9e.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13858" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 288, + 129 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 288, + 129 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 288, + 129 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 288, + 129 + ], + "type": "image", + "image_path": "75e73e428a4fc55a87d3314dff7d34bd59f876eaf1a1b7ea6739550f6e14349e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "lines": [ + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "type": "text", + "content": "Figure 6. An example of the blink merging procedure, which takes the frame-level eyeblink scores " + }, + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "type": "inline_equation", + "content": "b^{i}" + }, + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "type": "text", + "content": " and outputs the interval-level eyeblink results " + }, + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "type": "inline_equation", + "content": "B^{i}" + }, + { + "bbox": [ + 46, + 129, + 287, + 163 + ], + "type": "text", + "content": ". The threshold is set to 0.3 for demonstration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 168, + 287, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 168, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 287, + 194 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 168, + 287, + 194 + ], + "type": "inline_equation", + "content": "c^i\\in \\mathbb{R}^T" + }, + { + "bbox": [ + 47, + 168, + 287, + 194 + ], + "type": "text", + "content": " denotes the face classification scores across frames. Face localization is achieved in a similar way as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 126, + 201, + 287, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 201, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 126, + 201, + 287, + 216 + ], + "type": "interline_equation", + "content": "l ^ {i} = M L P _ {l} \\left(\\tilde {q} ^ {i}\\right), \\tag {4}", + "image_path": "726f091e7569801408c7ffe1eaa4929c4ee2d2677bcd768252ed845e08e04279.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "inline_equation", + "content": "l^i \\in \\mathbb{R}^{T \\times 4}" + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "text", + "content": " denotes the face bounding boxes across frames. It will also be used to renew the proposal tube " + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "inline_equation", + "content": "p^i" + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "text", + "content": ". Blink head. Eyeblink prediction towards " + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "inline_equation", + "content": "\\tilde{q}^i" + }, + { + "bbox": [ + 47, + 222, + 287, + 272 + ], + "type": "text", + "content": " is achieved by an MLP layer with Sigmoid normalization as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 101, + 279, + 287, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 279, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 101, + 279, + 287, + 294 + ], + "type": "interline_equation", + "content": "b ^ {i} = \\operatorname {S i g m o i d} \\left(M L P _ {b} \\left(\\tilde {q} ^ {i}\\right)\\right), \\tag {5}", + "image_path": "70334339db2bd6909073e98d118bfe69afff4e54cc338976fad5977ebeda9b04.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "b^{i} \\in \\mathbb{R}^{T}" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": " is the frame-level eyeblink scores. Each element " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "b_{t}^{i}" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": " in it indicates the possibility that the " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": "-th frame is inside an eyeblink event. During inference, we simply merge the adjacent frame-level eyeblink predictions based on a threshold (e.g., 0.3 in our implementation) to form the final interval-level eyeblink predictions " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "B_{k}^{i} = [s_{k}^{i}, e_{k}^{i}]" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 300, + 287, + 409 + ], + "type": "text", + "content": "-th eyeblink interval within the total K eyeblink predictions. An intuitive example of the merging procedure is shown in Fig. 6." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": "Different from the existing works that only extract features from the local eye region, our blink head also considers useful global information such as global face appearance, head pose, and illumination condition to aid the implicit eye localization and eyeblink characterization. The reason is that the blink head directly filters global features from the query embeddings where the global face context is already stored. During training, the eyeblink clues will not only flow back to the RoI feature, but also to the instance query to enhance the eyeblink-related feature representation ability of queries. Moreover, because of the shared feature among blink head and face head, a kind of interaction and synergy is built where the information flow from blink head can also benefit the face representations to boost the face detection and tracking ability as verified in Sec. 5.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 589, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 589, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 589, + 287, + 613 + ], + "type": "text", + "content": "As we have " + }, + { + "bbox": [ + 47, + 589, + 287, + 613 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 589, + 287, + 613 + ], + "type": "text", + "content": " queries, we finally obtain the predictions from them in parallel:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 620, + 287, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 620, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 108, + 620, + 287, + 639 + ], + "type": "interline_equation", + "content": "\\left\\{y ^ {i} \\right\\} _ {i = 1} ^ {N} = \\left\\{\\left(c ^ {i}, l ^ {i}, b ^ {i}\\right) \\right\\} _ {i = 1} ^ {N}. \\tag {6}", + "image_path": "d617f9d4bcf2dbae2d5ca2331b8a3c575320daa8e4dc7441e93b1678f8a9df54.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 645, + 111, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 111, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 111, + 658 + ], + "type": "text", + "content": "4.5. Training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 663, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 663, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 663, + 287, + 714 + ], + "type": "text", + "content": "To optimize InstBlink, one-to-one assignment between instance-level predictions " + }, + { + "bbox": [ + 46, + 663, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\left\\{y^{i}\\right\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 46, + 663, + 287, + 714 + ], + "type": "text", + "content": " and ground truths is first conducted based on their instance-level face tracklet similarity. Then, the loss is calculated concerning face and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "eyeblink items jointly for optimization. As in Sec. 3.1, the ground truth annotations can be summarized as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 361, + 103, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 103, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 361, + 103, + 545, + 129 + ], + "type": "interline_equation", + "content": "\\left\\{\\hat {y} ^ {j} \\right\\} _ {j = 1} ^ {N _ {g t}} = \\left\\{\\left(\\hat {c} ^ {j}, \\hat {l} ^ {j}, \\hat {b} ^ {j}\\right) \\right\\} _ {j = 1} ^ {N _ {g t}}, \\tag {7}", + "image_path": "aec0fc46ae6523e01cdcf7fc469a0dc908b4d61face6e2f3e2b1df5ddf17cc38.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{c}^j\\in \\mathbb{R}^T" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{l}^j\\in \\mathbb{R}^{T\\times 4}" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{b}^j\\in \\mathbb{R}^T" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": " indicate the frame-level face existence, face position (i.e., bounding box) and eyeblink existence (i.e., " + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{b}_t^j = 1" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": " indicates frame t is inside an eyeblink event and conversely for " + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{b}_t^j = 0" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": " , which can be derived from " + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\hat{B}^j" + }, + { + "bbox": [ + 304, + 137, + 545, + 236 + ], + "type": "text", + "content": " using an inverse process in Fig. 6 ) respectively. We use Hungarian algorithm [23] to perform instance-level bipartite matching between predictions and ground truths. The matching cost is given as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 239, + 545, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 239, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 335, + 239, + 545, + 294 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {H u n g}} \\left(y ^ {i}, \\hat {y} ^ {j}\\right) = \\sum_ {t = 1} ^ {T} \\left[ \\mathcal {L} _ {c l s} \\left(c _ {t} ^ {i}, \\hat {c} _ {t} ^ {j}\\right) \\right. \\tag {8} \\\\ \\left. + 1 _ {\\left\\{\\hat {c} _ {t} ^ {j} \\neq 0 \\right\\}} \\left(\\mathcal {L} _ {\\text {b o x}} \\left(l _ {t} ^ {i}, \\hat {l} _ {t} ^ {j}\\right)\\right) \\right], \\\\ \\end{array}", + "image_path": "8ef9c7fbf4ea7ab9e7acfbd981d0fb1c3f6efe9d45b214e7ada502d8a122cb7d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "text", + "content": " indicates the focal loss [29] for face existence classification. " + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{box}" + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "text", + "content": " is the combination of L1 loss and GIoU loss [37] for face localization. The loss weights are the same as [41, 47]. After obtaining the optimal assignment " + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}" + }, + { + "bbox": [ + 304, + 300, + 545, + 373 + ], + "type": "text", + "content": " between predictions and ground truths, the network is optimized by the loss as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 311, + 379, + 545, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 379, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 311, + 379, + 545, + 414 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {j = 1} ^ {N _ {g t}} \\left(\\mathcal {L} _ {\\text {f a c e}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right) + \\lambda \\mathcal {L} _ {\\text {b l i n k}} \\left(\\hat {y} ^ {j}, \\hat {y} ^ {\\tilde {\\sigma} (j)}\\right)\\right), \\tag {9}", + "image_path": "ce50d5ca0d8184abe2f24e7fee2f8c49ff7e60aed0dceeb0faaaeba9d2e75c83.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "y^{\\hat{\\sigma}(j)}" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " is the prediction that has been matched with the ground truth instance " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{y}^j" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{face}" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " is the face tracklet detection loss that shares the same form as " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{Hung}" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{face}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\mathcal{L}_{Hung}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)})" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{blink}" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " denotes instance-level eyeblink detection loss as " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{blink}(\\hat{y}^j, \\hat{y}^{\\hat{\\sigma}(j)}) = \\sum_{t=1}^{T} \\mathcal{L}_{cls}(\\hat{b}_t^j, \\hat{b}_t^{\\hat{\\sigma}(j)})" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\lambda = 5" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": ". For unmatched predictions, only " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\sum_{t=1}^{T} \\mathcal{L}_{cls}(c_t^i, \\hat{c}_t^i = 0)" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " is used to supervise their face existence classification output " + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "inline_equation", + "content": "c^i" + }, + { + "bbox": [ + 304, + 423, + 545, + 540 + ], + "type": "text", + "content": " to be close to 0 (i.e., no face)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 550, + 382, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 382, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 382, + 563 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Dataset and evaluation metrics. We first conduct experiments on the proposed MPEblink dataset. We split the dataset into 423 training videos, 128 validation videos, and 135 test videos. The videos from the same movie will only appear in one set. We train the network on the training set, validate it on the validation set and report the performance on the test set. We report Inst-AP to reveal the instance localization ability and Blink-AP to reveal the eyeblink detection ability within instances, as introduced in Sec. 3.5. Meanwhile, experiments are also conducted on HUST-LEBW for single-person and trimmed cases. Recall, Precision, and F1 score are reported following [19]." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13859" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 82, + 278, + 153 + ], + "blocks": [ + { + "bbox": [ + 73, + 71, + 261, + 81 + ], + "lines": [ + { + "bbox": [ + 73, + 71, + 261, + 81 + ], + "spans": [ + { + "bbox": [ + 73, + 71, + 261, + 81 + ], + "type": "text", + "content": "Table 2. The main results on the MPEblink dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 82, + 278, + 153 + ], + "lines": [ + { + "bbox": [ + 53, + 82, + 278, + 153 + ], + "spans": [ + { + "bbox": [ + 53, + 82, + 278, + 153 + ], + "type": "table", + "html": "
TypeMethodBlink-AP50Blink-AP75Inst-AP
LandmarkSoukupová and Cech [40]0.500.0556.70
Blink detection+ [35]0.620.08
RegionHu et al. [19]2.680.04
Daza et al.5.850.88
InstBlink (Ours)27.197.1667.89
", + "image_path": "db422afdf29900ab4121cf50082a0293421fa39cde213466d8e87bbfd04db768.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "text", + "content": "Implementation details. We use ResNet-50-FPN [18, 28] backbone. The network is pre-trained on YouTube-VIS [46] under [47] for a general instance representation ability. The query number " + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "text", + "content": " and iteration time " + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "text", + "content": " are set to 50 and 4 respectively. AdamW [31] optimizer with a batch size of 8 is used to train the model. The initial learning rate is set to 2.5e-5 for the backbone and 2.5e-4 for the other parts. At the training stage, for the sake of memory efficiency, we use the frame rate of 12 FPS for image sampling and the input clip length is set to 11 that is longer than most eyeblink events (i.e., 0.2-0.4s). The frames are also resized to " + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "inline_equation", + "content": "640 \\times 360" + }, + { + "bbox": [ + 47, + 159, + 289, + 364 + ], + "type": "text", + "content": " before sending into the network. The whole training procedure lasts for 10,000 iterations and the learning rate is multiplied by 0.1 at iteration 6000 and 9000. During test, the original frame rate is used and the input clip length is set to 36 with a stride of 18. The predictions within adjacent clips are linked via concerning face bounding box IoU." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 371, + 265, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 265, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 265, + 383 + ], + "type": "text", + "content": "5.1. Benchmark Results on MPEblink Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 557 + ], + "type": "text", + "content": "Baselines. Multi-person eyeblink detection in untrimmed videos is a new task that has not been well concerned before. Therefore, we tailor the existing eyeblink detection approaches with a unified instance detection and tracking method. Specifically, we use the state-of-the-art face analysis toolbox InsightFace [21] to achieve face [16] and landmark [44] detection. To track each instance, we link the face bounding boxes from the adjacent frames based on their similarity on box IoU. After obtaining the instance tracklets (i.e., a sequence of face bounding boxes and landmarks), we employ 4 representative eyeblink detection method [9, 19, 35, 40] within each instance tracklets. Such a sequential pipeline is commonly used in the existing approaches under the single-person assumption." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 558, + 274, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 274, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 274, + 568 + ], + "type": "text", + "content": "Main results. From Table 2, it can be summarized that:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": "- All of the multi-person eyeblink detection algorithms cannot achieve a satisfactory performance (i.e., Blink-AP" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "_{50}" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " lower than " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " and Blink-AP" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "_{75}" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " lower than " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": "). This indicates that eyeblink detection under multi-person, untrimmed, and unconstrained scenarios is indeed challenging and has not been well solved yet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "- For Blink-AP, InstBlink significantly outperforms the others by large margins (i.e., " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "21\\%" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " at least of Blink- " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " at least of Blink- " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "), which verifies the superiority of the proposed framework. We argue that one essential reason is that our framework can model a better long-term temporal eyeblink representation than the frame-based method [9]" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "and the sliding window based methods [19, 35, 40]. Moreover, under the proposed framework, eyeblink features can be facilitated via face's global context (e.g., head pose and illumination condition) with joint optimization and interaction, while previous works that utilize a sequential manner cannot. From Table 2, it can also be summarized that the landmark-based methods [35, 40] perform poorer than the region-based counterparts. We think that one essential reason is that landmark detection is unreliable under unconstrained conditions. A similar conclusion has already been made in [19] but the property of multi-person and long video in MPEblink make it worse for landmark-based eyeblink detection methods. Our method is region-based, but localizes eye region in an implicit way where global face context is included and thus becomes more robust." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 251, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 323 + ], + "type": "text", + "content": "- InstBlink also outperforms others on Inst-AP. We think that is because our framework can better model the long-term spatio-temporal instance representations, while the counterparts achieve tracking under a tracking-by-detection framework, which contains limited spatio-temporal modeling and may suffer from heavy occlusion." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 324, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 432 + ], + "type": "text", + "content": "Inference speed analysis. The result is listed in Table 3, assuming the 4 compared methods use InsightFace for face & landmark detection and InstBlink inferences within a clip length of 36. It can be seen that InstBlink is also of high inference speed (i.e., 112 FPS for network forwarding) while the real-time capacity of other methods is not superior. As the number of instances increases, their running time also increases while our method is not sensitive to the number of people because of the one-stage inference property." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 441, + 541, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 541, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 541, + 452 + ], + "type": "text", + "content": "5.2. Benchmark Results on HUST-LEBW Dataset" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "content": "Experiments are also conducted on the HUST-LEBW dataset to explore the generality of InstBlink towards single-person and trimmed in-the-wild cases. The results are given in Table 4. For models trained on the HUST-LEBW dataset, our method still outperforms others by a large margin (i.e., " + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "inline_equation", + "content": "3.78\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "content": " on F1 score), even with limited training data (less than 450 trimmed samples) to train our one-stage model for multiple tasks (face detection, tracking, and eyeblink detection). Meanwhile, the model trained on MPEblink can obtain " + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "inline_equation", + "content": "83.45\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "content": " F1 score on HUST-LEBW. This indeed verifies the strong generalization ability of InstBlink and MPEblink towards eyeblink detection task." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 611, + 400, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 400, + 623 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 400, + 623 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Spatial and temporal modeling in QIM. From Table 5, we can see that (1) without applying temporal interaction, the performance of Blink-AP drops from " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "27.19\\%" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "4.58\\%" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ". This indicates that temporal modeling is critical for eyeblink detection in untrimmed videos (i.e., only using appearance features can not accurately localize eyeblinks). It can also be observed that temporal interaction facilitates" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13860" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 96, + 506, + 126 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 3. The inference speed comparison on a single NVIDIA 3090 GPU, assuming the compared methods use InsightFace for face detection (time consumption " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "T = 9.3\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " including pre-processing) and landmark detection. #faces denotes the face amount in the scene." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 96, + 506, + 126 + ], + "lines": [ + { + "bbox": [ + 85, + 96, + 506, + 126 + ], + "spans": [ + { + "bbox": [ + 85, + 96, + 506, + 126 + ], + "type": "table", + "html": "
MethodInstBlink (Ours)Soukupová and Cech [40]Blink detection+ [35]Hu et al. [19]Daza et al. [9]
Time/image (ms)8.9 + 2.6 for data processingT(=9.3)+5.4×#facesT+5.4×#facesT+5.7×#facesT+9.1×#faces
", + "image_path": "9b4ffe4ae10932d970ea722b75777e047233ffe4fff69f3a3fc90de60c5f2970.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 169, + 282, + 280 + ], + "blocks": [ + { + "bbox": [ + 47, + 134, + 287, + 166 + ], + "lines": [ + { + "bbox": [ + 47, + 134, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 287, + 166 + ], + "type": "text", + "content": "Table 4. Performance comparison on the HUST-LEBW dataset, where InstBlink CROSS indicates InstBlink trained on MPEblink and tested on HUST-LEBW." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 169, + 282, + 280 + ], + "lines": [ + { + "bbox": [ + 52, + 169, + 282, + 280 + ], + "spans": [ + { + "bbox": [ + 52, + 169, + 282, + 280 + ], + "type": "table", + "html": "
Training setMethodEyeRecallPrecisionF1
HUST-LEBW [19]Soukupová and Cech [40]Left36.0764.7146.32
Right30.1657.5839.58
Hu et al. [19]Left54.1089.1967.35
Right44.4476.7156.28
Blink detection+ [35]Both58.9980.0567.90
InstBlink (Ours)Both97.6456.6271.68
mEBAL [10]Daza et al. [10]Left96.0360.8074.46
Right79.5073.4876.37
Daza et al. [9]Both93.3975.3383.39
MPEblinkInstBlink CROSS (Ours)Both91.3476.8283.45
", + "image_path": "b46ddf0aef5ffab3dd5e016572a08f7882af1ff38fcf7b21fcf4e165405763e7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 51, + 297, + 282, + 360 + ], + "blocks": [ + { + "bbox": [ + 86, + 286, + 247, + 296 + ], + "lines": [ + { + "bbox": [ + 86, + 286, + 247, + 296 + ], + "spans": [ + { + "bbox": [ + 86, + 286, + 247, + 296 + ], + "type": "text", + "content": "Table 5. Ablation studies on QIM and VIM." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 297, + 282, + 360 + ], + "lines": [ + { + "bbox": [ + 51, + 297, + 282, + 360 + ], + "spans": [ + { + "bbox": [ + 51, + 297, + 282, + 360 + ], + "type": "table", + "html": "
MethodBlink-AP50Blink-AP75Inst-AP
w/o QIM3.200.3958.93
w/o temporal interaction in QIM4.580.5563.61
w/o spatial interaction in QIM26.656.1862.45
w/o filter operation in VIM22.274.5965.01
Full model27.197.1667.89
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Blink headInst-APInst-AP50Inst-AP75
×65.8681.7371.23
✓67.8984.5173.76
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(2) Spatial interaction can boost Inst-AP by a large margin (i.e., " + }, + { + "bbox": [ + 46, + 433, + 287, + 528 + ], + "type": "inline_equation", + "content": "5.44\\%" + }, + { + "bbox": [ + 46, + 433, + 287, + 528 + ], + "type": "text", + "content": " ) and slightly boost Blink-AP, as it may build strong communication among queries to better model the instance features under complex circumstances such as occlusion due to human interactions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "content": "Filter operation in VIM. As in Table 5, compared with directly using RoI features to update query, using filtered RoI features can boost " + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "inline_equation", + "content": "4.92\\%" + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "content": " on Blink-AP50 and " + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "inline_equation", + "content": "2.88\\%" + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "content": " on Inst-AP. We speculate that the filter operation can activate task-specific RoI features and resist background. Thus, finer face and eyeblink clues can be collected to update queries." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 601, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 661 + ], + "type": "text", + "content": "Multi-task learning mechanism. Here we study the effect of the blink head from a multi-task learning perspective. As shown in Table 6, adding blink head can also boost " + }, + { + "bbox": [ + 46, + 601, + 287, + 661 + ], + "type": "inline_equation", + "content": "2.03\\%" + }, + { + "bbox": [ + 46, + 601, + 287, + 661 + ], + "type": "text", + "content": " on Inst-AP, which demonstrates that features for face detection and tracking can also benefit from eyeblink clues." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "type": "text", + "content": "5.4. Qualitative Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We visualize the prediction results of InstBlink in Fig. 7. The examples show that our model can aware the attendees" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 312, + 133, + 538, + 274 + ], + "blocks": [ + { + "bbox": [ + 312, + 133, + 538, + 274 + ], + "lines": [ + { + "bbox": [ + 312, + 133, + 538, + 274 + ], + "spans": [ + { + "bbox": [ + 312, + 133, + 538, + 274 + ], + "type": "image", + "image_path": "cb30a3bb0b2e8c241324f2fd3b505751dfad66fdb9ff3763b1d4770c71dca209.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 277, + 538, + 289 + ], + "lines": [ + { + "bbox": [ + 312, + 277, + 538, + 289 + ], + "spans": [ + { + "bbox": [ + 312, + 277, + 538, + 289 + ], + "type": "text", + "content": "Figure 7. Qualitative examples of the predictions of InstBlink." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 293, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 342 + ], + "type": "text", + "content": "robustly and detect their eyeblinks under different facial appearance and head pose. Nevertheless, it can not distinguish the rapid consecutive eyeblinks, which also reveals the challenge of eyeblink detection in untrimmed videos." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 349, + 468, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 468, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 468, + 361 + ], + "type": "text", + "content": "6. Conclusions and Limitations" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "text", + "content": "In this work, we shed the light on a new research task termed multi-person eyeblink detection in the wild for untrimmed video. We formally define the task and introduce a multi-person eyeblink detection dataset named MPEblink. To perform multi-person eyeblink detection in untrimmed videos, we introduce a one-stage multi-person eyeblink detection framework InstBlink. Experiment results demonstrate the superiority of InstBlink in both effectiveness and efficiency. However, our SOTA performance is still unsatisfactory (i.e., " + }, + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\mathrm{Blink - AP}_{50} < 30\\%" + }, + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "text", + "content": "). This verifies the challenges of unconstrained multi-person eyeblink detection in long videos. Besides, although the proposed dataset focuses on multi-person, unconstrained, and untrimmed scenarios that are more realistic and have a broader application value, there are lack of crowd scenes (e.g., " + }, + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "inline_equation", + "content": ">10" + }, + { + "bbox": [ + 305, + 366, + 545, + 569 + ], + "type": "text", + "content": " instances) within it. In the future, we will pay more attention to the crowd scenes and enrich the dataset." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 576, + 399, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 576, + 399, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 576, + 399, + 590 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 712 + ], + "type": "text", + "content": "This work is jointly supported by the National Natural Science Foundation of China (Grant No. 62271221 and U1913602), and Natural Science Foundation of Guangdong Province (Grant No. 2023A1515011260). Joey Tianyi Zhou is funded by the SERC (Science and Engineering Research Council) Central Research Fund (Use-Inspired Basic Research), and the Singapore Government's Research, and Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering Domain) under programmatic Grant A18A1b0045." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13861" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Talking face video. 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International Conference on Learning Representations (ICLR), 2021. 3" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13863" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_content_list.json b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..eb430245f84275d6bb10661ae458f7500b77ce75 --- /dev/null +++ b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_content_list.json @@ -0,0 +1,1556 @@ +[ + { + "type": "text", + "text": "Real-Time Neural Light Field on Mobile Devices", + "text_level": 1, + "bbox": [ + 240, + 130, + 728, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junli Cao $^{1}$ \nYun Fu $^{2}$ $^{1}$ Snap Inc. \n $^{2}$ Northeastern University", + "bbox": [ + 127, + 178, + 839, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent efforts in Neural Rendering Fields (NeRF) have shown impressive results on novel view synthesis by utilizing implicit neural representation to represent 3D scenes. Due to the process of volumetric rendering, the inference speed for NeRF is extremely slow, limiting the application scenarios of utilizing NeRF on resource-constrained hardware, such as mobile devices. Many works have been conducted to reduce the latency of running NeRF models. However, most of them still require high-end GPU for acceleration or extra storage memory, which is all unavailable on mobile devices. Another emerging direction utilizes the neural light field (NeLF) for speedup, as only one forward pass is performed on a ray to predict the pixel color. Nevertheless, to reach a similar rendering quality as NeRF, the network in NeLF is designed with intensive computation, which is not mobile-friendly. In this work, we propose an efficient network that runs in real-time on mobile devices for neural rendering. We follow the setting of NeLF to train our network. Unlike existing works, we introduce a novel network architecture that runs efficiently on mobile devices with low latency and small size, i.e., saving $15 \\times \\sim 24 \\times$ storage compared with MobileNeRF. Our model achieves high-resolution generation while maintaining real-time inference for both synthetic and real-world scenes on mobile devices, e.g., 18.04ms (iPhone 13) for rendering one $1008 \\times 756$ image of real 3D scenes. Additionally, we achieve similar image quality as NeRF and better quality than MobileNeRF (PSNR 26.15 vs. 25.91 on the real-world forward-facing dataset)1.", + "bbox": [ + 75, + 301, + 473, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 771, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Remarkable progress seen in the domain of neural rendering [33] promises to democratize asset creation and rendering, where no mesh, texture, or material is required - only a neural network that learns a representation of an object or a scene from multi-view observations. The trained", + "bbox": [ + 75, + 797, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fef2965b302550dc264ad99a606696b6ff6980d7c2879f1826e725b8d93ca13f.jpg", + "image_caption": [ + "Figure 1. Examples of deploying our approach on mobile devices for real-time interaction with users. Due to the small model size (8.3MB) and fast inference speed $(18\\sim 26\\mathrm{ms}$ per image on iPhone 13), we can build neural rendering applications where users interact with 3D objects on their devices, enabling various applications such as virtual try-on. We use publicly available software to make the on-device application for visualization [1,3]." + ], + "image_footnote": [], + "bbox": [ + 504, + 268, + 679, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57156ce59d767573d681c41698c0310bfe8ebc3676a6d57a96f343ff02c0bf5b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 268, + 890, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "model can be queried at arbitrary viewpoints to generate novel views. To be made widely available, this exciting application requires such methods to run on resource-constrained devices, such as mobile phones, conforming to their limitations in computing, wireless connectivity, and hard drive capacity.", + "bbox": [ + 496, + 566, + 890, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, the impressive image quality and capabilities of NeRF [33] come with a price of slow rendering speed. To return the color of the queried pixel, hundreds of points need to be sampled along the ray that ends up in that pixel, which is then integrated to get the radiance. To enable real-time applications, many works have been proposed [12, 34, 37, 45], yet, they still require high-end GPUs for rendering and hence are not available for resource-constrained applications on mobile or edge devices. An attempt is made to trade rendering speed with storage in MobileNeRF [10]. While showing promising acceleration results, their method requires storage for texturing saving. For example, for a single real-world scene from the forward-facing dataset [33], MobileNeRF requires 201.5MB of storage. Clearly, downloading and storing tens, hundreds, or even thousands of such scenes in MobileNeRF", + "bbox": [ + 496, + 659, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1More demo examples in our Webpage.", + "bbox": [ + 94, + 886, + 307, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8328", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "format on a device is prohibitively expensive.", + "bbox": [ + 76, + 90, + 379, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A different approach is taken in Neural Light Fields (NeLF) that directly maps a ray to the RGB color of the pixel by performing only one forward pass per ray, resulting in faster rendering speed [5, 25, 28, 41]. Training NeLF is challenging and hence requires increased network capacity. For example, Wang et al. [41] propose an 88-layer fully-connected network with residual connections to distill a pretrained radiance model effectively. While their approach achieves better rendering results than vanilla NeRF at $30 \\times$ speedup, running it on mobile devices is still not possible, as it takes three seconds to render one $200 \\times 200$ image on iPhone 13 shown in our experiments.", + "bbox": [ + 75, + 107, + 468, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose MobileR2L, a real-time neural rendering model built with mobile devices in mind. Our training follows a similar distillation procedure introduced in R2L [41]. Differently, instead of using an MLP, a backbone network used by most neural representations, we show that a well-designed convolutional network can achieve real-time speed with the rendering quality similar to MLP. In particular, we revisit the network design choices made in R2L and propose to use the $1 \\times 1$ Conv layer in the backbone. A further challenge with running a NeRF or NeLF on mobile devices is an excessive requirement of RAM. For example, to render an $800 \\times 800$ image, one needs to sample 640,000 rays that need to be stored, causing out-of-memory issues. In 3D-aware generative models [9, 15, 20], this issue is alleviated by rendering a radiance feature volume and upsampling it with a convolutional network to obtain a higher resolution. Inspired by this, we render a light-field volume that is upsampled to the required resolution. Our MobileR2L features several major advantages over existing works:", + "bbox": [ + 75, + 287, + 472, + 592 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- MobileR2L achieves real-time inference speed on mobile devices (Tab. 3) with better rendering quality, e.g., PSNR, than MobileNeRF on the synthetic and real-world datasets (Tab. 1).", + "- MobileR2L requires an order of magnitude less storage, reducing the model size to 8.3MB, which is $15.2 \\times \\sim 24.3 \\times$ less than MobileNeRF." + ], + "bbox": [ + 78, + 603, + 467, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to these contributions, MobileR2L can unlock wide adoption of neural rendering in real-world applications on mobile devices, such as a virtual try-on, where the real-time interaction between devices and users is achieved (Fig. 1).", + "bbox": [ + 75, + 722, + 468, + 782 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 799, + 225, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Radiance Field (NeRF). NeRF [33] shows the possibility of representing a scene with a simple multi-layer perceptron (MLP) network. Going forward, many extensions follow up in improving rendering quality (e.g., MipNeRF [6], MipNeRF 360 [7], and Ref-NeRF [40]),", + "bbox": [ + 75, + 824, + 467, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rendering efficiency (e.g., NSVF [29], Nex [43], AutoInt [27], FastNeRF [13], Baking [16], Plenoctree [45], KiloNeRF [37], DeRF [36], DoNeRF [35], R2L [41], and MobileNeRF [10]) and training efficiency (e.g., Plenoxels [12], and Instant-NGP [34]).", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efficient NeRF Rendering. Since this paper falls into the category of improving rendering efficiency as we target real-time rendering on mobile devices, we single out the papers of this group and discuss them in length here. There are generally four groups. (1) The first group trades speed with space, i.e., they precompute and cache scene representations and the rendering reduces to table lookup. Efficient data structure like sparse octree, e.g., Plenoctree [45], is usually utilized to make the rendering even faster. (2) The second attempts reduce the number of sampled points along the camera ray during rendering as it is the root cause of prohibitively slow rendering speed. Fewer sampled points typically lead to performance degradation, so as compensation, they usually introduce extra information, such as depth, e.g., DoNeRF [35], or mesh, e.g., MobileNeRF [10], to maintain the visual quality. (3) The third group takes a \"divide and conquer\" strategy. DeRF [36] decomposes the scene spatially to Voronoi diagrams and learns each diagram with a small network. KiloNeRF [37] also employs a decomposition scheme. Differently, they decompose the scene into thousands of small regular grids. Each is addressed with a small network. Such decomposition poses challenges to parallelism. Thus they utilize customized parallelism implementation to obtain speedup. (4) The fourth group is a newly surging one, represented by the recent works RSEN [5] and R2L [41]. They achieve rendering efficiency by representing the scene with NeLF (neural light field) instead of NeRF. NeLF avoids the dense sampling on camera ray, resulting in a much faster rendering speed than NeRF. On the downside, NeLF is typically much harder to learn than NeRF. As a remedy, these works (such as [41]) typically integrate a pre-trained NeRF model as a teacher to synthesize additional pseudo data for distillation [8, 19]. Therefore, the resulting model is fast with a reasonably small representation size, i.e., the model size.", + "bbox": [ + 496, + 170, + 892, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Light Field (NeLF). Light field is a different way of representing scenes. The idea has a long history in the computer graphics community, e.g., Light fields [25] and Lumigraphs [14] cache plenty of images and enable real-time rendering at the cost of limited camera pose and excessive storage overhead. One of the most intriguing properties of NeLF is that rendering one image only requires one network forward, resulting in a significantly faster speed than NeRF-based methods. With the recent surge of the neural radiance field, some works attempt to revive the idea of the neural light field for efficient neural rendering. Sitzmann et al. [38] materialize the idea of using a neural network to model the scene, and the rendering process reduces to", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8329", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a single network forward. Despite the encouraging idea, their method has only been evaluated on scenes with simple shapes, not matching the quality of NeRF on complex real-world scenes. Later, RSEN [5] and R2L [41] are introduced. RSEN divides the space into many voxel grids. Only in each grid, it is a NeLF, which needs alpha-composition to render the final color, making their method a mixture of NeLF and NeRF. R2L [41] is a pure NeLF network that avoids the alpha-composition step in rendering, which is also one of the most relevant works to this paper. However, R2L is still not compact and fast enough for mobile devices. Based on our empirical study, an R2L model runs for around three seconds per frame on iPhone 13 even for low-resolution like $200 \\times 200$ . This paper is meant to push the NeRF-to-NeLF idea even further, making it able to perform real-time rendering on mobile devices.", + "bbox": [ + 75, + 90, + 472, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will mainly compare to MobileNeRF [10] in this paper as it is the only method, to our best knowledge, that can run on mobile devices with matching quality to NeRF [33].", + "bbox": [ + 75, + 333, + 468, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 395, + 174, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Prerequisites: NeRF and R2L", + "text_level": 1, + "bbox": [ + 76, + 421, + 341, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRF. NeRF [33] represents the scene implicitly with an MLP network $F_{\\Theta}$ , which maps the 5D coordinates (spatial location $(x, y, z)$ and view direction $(\\theta, \\phi)$ ) to a 1D volume density (opacity, denoted as $\\sigma$ here) and 3D radiance (denoted as $\\mathbf{c}$ ) such that $F_{\\Theta}: \\mathbb{R}^5 \\mapsto \\mathbb{R}^4$ . Each pixel of an image is associated with a camera ray. To predict the color $\\hat{C}$ of a pixel, the NeRF method samples many points (denoted as $N$ below) along the camera ray and accumulates the radiance $\\mathbf{c}$ of all these points via alpha compositing [23, 31, 33]:", + "bbox": [ + 75, + 445, + 472, + 583 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\cdot \\mathbf {c} _ {i},\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 594, + 400, + 630 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {c} _ {i}, \\sigma_ {i}\\right) = F _ {\\Theta} \\left(\\mathbf {r} \\left(t _ {i}\\right), \\mathbf {d}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 633, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 652, + 318, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{r}$ means the camera ray; $\\mathbf{r}(t_i) = \\mathbf{o} + t_i\\mathbf{d}$ represents the location of a point on the ray with origin $\\mathbf{o}$ and direction $\\mathbf{d}$ ; $t_i$ is the Euclidean distance, i.e., a scalar, of the point away from the origin; and $\\delta_{i} = t_{i + 1} - t_{i}$ refers to the distance between two adjacent sampled points. A stratified sampling approach is employed in NeRF [33] to sample the $t_i$ in Eqn. 1. To enrich the input information, the position and direction coordinates are encoded by positional encoding [39], which maps a scalar $(\\mathbb{R})$ to a higher dimensional space $(\\mathbb{R}^{2L + 1})$ through cosine and sine functions, where $L$ (a predefined constant) stands for the frequency order (in the original NeRF [33], $L = 10$ for positional coordinates and $L = 4$ for direction coordinates).", + "bbox": [ + 75, + 704, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b78159630dc54ca21e0dc603244559a5c6325bebbfff217d5ab29de9e90eceb6.jpg", + "image_caption": [ + "Figure 2. Training and Inference Pipeline. The training involves a teacher model to generate pseudo data, which is used to learn the MobileR2L. The teacher model, e.g., NeRF, is trained on real images. Once we have the teacher model, we use it to generate pseudo images, e.g., images with the resolution of $800 \\times 800$ , in addition to down-scaled rays, e.g., rays with spatial size as $100 \\times 100$ , that share the same origin with the pseudo images to train the MobileR2L. After that, we use the real data to fine-tune MobileR2L. For inference, we directly forward the rays into the pre-trained MobileR2L to render images." + ], + "image_footnote": [], + "bbox": [ + 503, + 88, + 893, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The whole formulation and training of NeRF are straightforward. One critical problem preventing fast inference in NeRF is that the $N$ , i.e., the number of sampled points, in Eqn. 1 is pretty large (256 in the original NeRF paper due to their two-stage coarse-to-fine design). Therefore, the rendering computation for even a single pixel is prohibitively heavy. The solution proposed by R2L [41] is distilling the NeRF representation to NeLF.", + "bbox": [ + 496, + 396, + 890, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "R2L. Essentially, a NeLF function maps the oriented ray to RGB. To enrich the input information, R2L proposes a new ray representation – they also sample points along the ray just like NeRF [33] does; but differently, they concatenate the points to one vector, which is used as the ray representation and fed into a neural network to learn the RGB. Similar to NeRF, positional encoding [39] is also adopted in R2L to map each scalar coordinate to a high dimensional space. During training, the points are randomly (by a uniform distribution) sampled; during testing, the points are fixed.", + "bbox": [ + 496, + 518, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The output of the R2L model is directly RGB, no density learned, and there is no extra alpha-compositing step, which makes R2L much faster than NeRF in rendering. One downside of the NeLF framework is, as shown in R2L [41], the NeLF representation is much harder to learn than NeRF; so as a remedy, R2L proposes an 88-layer deep ResMLP (residual MLP) architecture (much deeper than the network of NeRF) to serve as the mapping function.", + "bbox": [ + 496, + 671, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "R2L has two stages in training. In the first stage, they use a pre-trained NeRF model as a teacher to synthesize excessive (origin, direction, RGB) triplets as pseudo data; and then fed the pseudo data to train the deep ResMLP. This stage can make the R2L model achieve comparable performance to the teacher NeRF model. In the second stage, they finetune the R2L network from the first stage on", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8330", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d7c8040e2e44d3d779ad3cbb716ec182549120e74ec758444c4015fba315ff6f.jpg", + "image_caption": [ + "Figure 3. Overview of Network. The input tensor of MobileR2L has 4D shape: batch, channel, height, and width. The backbone includes residual blocks (RB) that is repeated 28 times ( $N = 28$ ). Following the backbone, there are two types of super-resolution (SR) modules. The first SR module $(\\mathrm{SR}^1)$ has kernel size $4 \\times 4$ in the Transpose CONV layer that doubles the input $H, W$ to $2H, 2W$ , whereas the second SR module $(\\mathrm{SR}^2)$ has kernel size $3 \\times 3$ , tripling the spatial size to $3H, 3W$ . The configuration of $3 \\times \\mathrm{SR}^1$ is used in the synthetic $360^\\circ$ dataset that upsamples the input $8 \\times$ . For the real-world forward-facing dataset, we use the combination of $2 \\times \\mathrm{SR}^1 + \\mathrm{SR}^2$ that upsamples the input $12 \\times$ . Moreover, we use various output channels across RB and SR: $C_1 = 256$ , $C_2 = 64$ , and $C_3 = 16$ ." + ], + "image_footnote": [], + "bbox": [ + 101, + 94, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the original data – this step can further boost the rendering quality as shown in the R2L work [41].", + "bbox": [ + 75, + 417, + 470, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. MobileR2L", + "text_level": 1, + "bbox": [ + 76, + 458, + 200, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Overview", + "text_level": 1, + "bbox": [ + 76, + 482, + 199, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We follow the learning process of R2L to train our proposed MobileR2L, namely, using a pre-trained teacher model, such as NeRF [33], to generate pseudo data for the training of a lightweight neural network. To reduce the inference speed, we aim only to forward the network once when rendering an image. However, under the design of R2L, although one pixel only requires one network forward, directly feeding rays with large spatial size, e.g., $800 \\times 800$ , into a network causes memory issues. Therefore, R2L forwards a partial of rays each time, increasing the speed overhead. To solve the problem, we introduce super-resolution modules, which upsample the low-resolution input, e.g., $100 \\times 100$ , to a high-resolution image. Thus, we can obtain a high-resolution image with only one forward pass of the neural network during inference time. The training and inference pipeline is illustrated in Fig. 2, and we introduce more details for our network architecture in the following.", + "bbox": [ + 75, + 507, + 472, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Network Architectures", + "text_level": 1, + "bbox": [ + 76, + 785, + 290, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The input rays can be represented as $\\mathbf{x} \\in \\mathbb{R}^{B,6,H,W}$ , where $B$ denotes the batch size and $H$ and $W$ denote the spatial size. The ray origin and view directions are concatenated as the second dimension of $\\mathbf{x}$ . We then apply positional encoding $\\gamma(\\cdot)$ on $\\mathbf{x}$ to map the ray origin and view directions into a higher dimension. Thus, we get the input of our neural", + "bbox": [ + 75, + 808, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "network as $\\gamma (\\mathbf{x})$", + "bbox": [ + 500, + 417, + 614, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The network includes two main parts: an efficient backbone and Super-Resolution (SR) modules for high-resolution rendering, with the architecture provided in Fig. 3. Instead of using Fully Connected (FC) or linear layers for the network that is adopted by existing works [33, 41], we only apply convolution (CONV) layers in the backbone and super-resolution modules.", + "bbox": [ + 496, + 431, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are two main reasons for replacing FC with CONV layers. First, the CONV layer is better optimized by compilers than the FC layer [30]. Under the same number of parameters, the model with CONV $1 \\times 1$ runs around $27\\%$ faster than the model with FC layers, as shown in Tab. 4. Second, suppose FC is used in the backbone, in that case, extra Reshape and Permute operations are required to modify the dimension of the output features from the FC to make the features compatible with the CONV layer in the super-resolution modules, as the FC and CONV calculate different tensor dimensions. However, such Reshape or Permute operation might not be hardware-friendly on some mobile devices [26]. With the CONV employed as the operator in the network, we then present more details for the backbone and SR modules.", + "bbox": [ + 496, + 537, + 892, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Efficient Backbone. The architecture of the backbone follows the design of residual blocks from R2L [41]. Different from R2L, we adopt the CONV layer instead of the FC layer in each residual block. The CONV layer has the kernel size and stride as 1. Additionally, we use the normalization and activation functions in each residual block, which can improve the network performance without introducing latency overhead (see experimental details in Tab. 4). The normalization and activation are chosen as batch normaliza", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8331", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion [21] and GeLU [17]. The backbone contains 60 CONV layers in total.", + "bbox": [ + 75, + 90, + 467, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Super-Resolution Modules. To reduce the latency when running the neural rendering on mobile devices, we aim to forward the neural network once to get the synthetic image. However, the existing network design of the neural light field requires large memory for rendering a high-resolution image, which surpasses the memory constraint on mobile devices. For example, rendering an image of $800 \\times 800$ requires the prediction of 640,000 rays. Forwarding these rays at once using the network from R2L [41] causes the out of memory issue even on the Nvidia Tesla A100 GPU (40G memory).", + "bbox": [ + 75, + 119, + 467, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To reduce the memory and latency cost for high-resolution generation, instead of forwarding the number of rays that equals to the number of pixels, we only forward a partial of rays and learn all the pixels via super-resolution. Specifically, we propose to use the super-resolution modules following the efficient backbone to upsample the output to a high-resolution image. For example, to generate a $800 \\times 800$ image, we forward a 4D tensor $\\mathbf{x}$ with spatial size as $100 \\times 100$ to the network and upsample the output from backbone three times (i.e., upsample by $2 \\times$ each time). The SR module includes two stacked residual blocks. The first block includes three CONV layers with one as a 2D Transpose CONV layer and two CONV $1 \\times 1$ layers; the second block includes two CONV $1 \\times 1$ layers. After the SR modules, we apply another CONV layer followed by the Sigmoid activation to predict the final RGB color. We denote our model as $D60-SR3$ where it contains 60 CONV layers in the efficient backbone and 3 SR modules.", + "bbox": [ + 75, + 287, + 467, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 573, + 207, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We conduct the comparisons mainly on two datasets: realistic synthetic $360^{\\circ}$ [33] and real-world forward-facing [32, 33]. The synthetic $360^{\\circ}$ dataset contains 8 path-traced scenes, with each scene including 100 images for training and 200 images for testing. Forward-facing contains 8 real-world scenes captured by cellphones, where the images in each scene vary from 20 to 60, and 1/8 images are used for testing. We conduct our experiments (training and testing) on the resolution of $800 \\times 800$ for synthetic $360^{\\circ}$ and $1008 \\times 756$ ( $4 \\times$ down-scaled from the original resolution) for forward-facing.", + "bbox": [ + 75, + 598, + 467, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We follow the training scheme of R2L [41], i.e., using a teacher model to render pseudo images for the training of MobileR2L network. Specifically, we synthesize 10K pseudo images from the pretrained teacher model [2] for each scene. We first train our MobileR2L on the generated pseudo data and then fine-tune it on the real data, as shown in Fig. 2. In all the experiments, we employ Adam [24] optimizer with an initial learning rate $5 \\times 10^{-4}$ that decays during the training. Our experiments", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/05ed2fe425cd59f6feadb60c2392b68446ae8affd2ee70a4e558a49ef00ae9f2.jpg", + "table_caption": [ + "Table 1. Quantitative Comparison on Synthetic $360^{\\circ}$ and Forward-facing. Our method obtains better results on the three metrics than NeRF for the two datasets. Compared with MoibleNeRF and SNeRG, we achieve better results on most of the metrics." + ], + "table_footnote": [], + "table_body": "
Synthetic 360°Forward-facing
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF [33]31.010.9470.08126.500.8110.250
NeRF-Pytorch [44]30.920.9910.04526.260.9650.153
SNeRG [16]30.380.9500.05025.630.8180.183
MoibleNeRF [10]30.900.9470.06225.910.8250.183
MobileR2L (Ours)31.340.9930.05126.150.9660.187
Our Teacher33.090.9610.05226.850.8270.226
", + "bbox": [ + 506, + 170, + 888, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are conducted on a cluster of Nvidia V100 and A100 GPUs with the batch size as 54 for the main results on the synthetic $360^{\\circ}$ and batch size as 36 on the forward-facing dataset.", + "bbox": [ + 498, + 309, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Different from R2L, the spatial size of the input rays and the output rendered images in our approach are different. For each high-resolution image generated by the teacher model, we save the input rays corresponding to a lower-resolution image where the camera origins and directions are the same as the high-resolution one while the focal length is down-scaled accordingly. Additionally, we do not sample the rays from different images as in R2L. Instead, the rays in each training sample share the same origin and reserve their spatial locations.", + "bbox": [ + 496, + 354, + 890, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering the training data of the synthetic $360^{\\circ}$ and forward-facing datasets have different resolutions, the spatial size of the inputs for the two datasets are slightly different. Our network takes input with the spatial size of $100 \\times 100$ for the synthetic $360^{\\circ}$ dataset and upsamples by $8 \\times$ to render $800 \\times 800$ RGB images. In contrast, the spatial size of $84 \\times 63$ is used in the forward-facing dataset, and $1008 \\times 756$ image ( $12 \\times$ upsampling) is rendered. The kernel size and padding are adjusted in the last transposed CONV layer to achieve $8 \\times$ and $12 \\times$ upsampling with the 3 SR blocks.", + "bbox": [ + 496, + 506, + 890, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Comparisons", + "text_level": 1, + "bbox": [ + 500, + 681, + 637, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rendering Performance. To understand the image quality of various methods, we report three common metrics: PSNR, SSIM [42], and LPIPS [46], on the realistic synthetic $360^{\\circ}$ and real forward-facing datasets, as demonstrated in Tab. 1. Compared with NeRF [33], our approach achieves better results on PSNR, SSIM, and LPIPS for the synthetic $360^{\\circ}$ dataset. On the forward-facing dataset, we obtain better SSIM and LPIPS than NeRF [33]. Similarly, our method achieves better results for all three metrics than MobileNeRF [10] on the synthetic $360^{\\circ}$ dataset and better PSNR and SSIM on the forward-facing dataset. Compared to SNeRG [16], our method obtains better PSNR and SSIM.", + "bbox": [ + 496, + 703, + 890, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also show the performance of the teacher model used", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8332", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5fd7a6642c63608340bf6b784255b928509af907e8352b58a0fce8678ab29304.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 109, + 99, + 171, + 147 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7a2131094147d260d25a1d439c21056e0e0c405a45598e4386da43c4a46dfd1.jpg", + "image_caption": [ + "Lego", + "Fern" + ], + "image_footnote": [], + "bbox": [ + 89, + 172, + 202, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b55c15ab20f22fb52be3bdf2518128f0bd22f82e6baf6fdb4559282fe4dd7ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 205, + 93, + 290, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0bd481d43cd0f8ad706f03693b6f28c0b20b6b7de5eb3d98fbf668f0a84df39a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 93, + 377, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/69babc26c8eabe28ba2db8f35764caf7fe7d449244a3fb30ab0d676fb331876e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 93, + 465, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5635a21ef9217b8f63dac0cdc13df8818ad4afa8dddc0edb4f08542687800653.jpg", + "image_caption": [ + "(a) GT", + "(a) GT" + ], + "image_footnote": [], + "bbox": [ + 205, + 172, + 290, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a99a03eb7189e3e57d94043f5e8c5cabbfe6dbcdf6deab9e0d7ad70a22dcecc2.jpg", + "image_caption": [ + "(b) NeRF", + "(b) NeRF" + ], + "image_footnote": [], + "bbox": [ + 292, + 172, + 375, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/db78f6ac0c3ed541b168b580a4f7bbad2d3904ae571c3a6c7720e158e1ead060.jpg", + "image_caption": [ + "(c) Ours", + "(c) Ours" + ], + "image_footnote": [], + "bbox": [ + 380, + 172, + 465, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cb0d4918fa053bd8a6acab3026711329187b3dd22c8eda4c2e101081ad7a896.jpg", + "image_caption": [ + "Figure 4. Visual comparison between our method and NeRF [33] (trained via NeRF-Pytorch [44]) on the synthetic $360^{\\circ}$ Lego (size: $800 \\times 800 \\times 3$ ) and real-world forward-facing scene Fern (size: $1008 \\times 756 \\times 3$ ). Best viewed in color. Please refer to our webpage for more visual comparison results." + ], + "image_footnote": [], + "bbox": [ + 81, + 359, + 467, + 452 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b32c4171038d900d2ed385cc33b9b48cfef85bccbb67322329c5b09f73270db0.jpg", + "image_caption": [ + "Figure 5. Zoom-in comparisons. Top row: MobileNeRF [10]. Results are obtained from the code and demo released by the authors. Bottom row: MobileR2L. Our approach renders high-quality images even for zoom-in views." + ], + "image_footnote": [], + "bbox": [ + 81, + 463, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in training MobileR2L in Tab. 1 (Our Teacher). Note that there is still a performance gap between the student model (MobileR2L) and the teacher model. However, as we show following (Tab. 5), a better teacher model can lead to a student model with higher performance. Compared with MoibleNeRF and SNeRG, our approach has the advantage that we can directly leverage the high-performing teacher models to help improve student training in different application scenarios. We further show the qualitative comparison results in Fig. 4. On the synthetic scene Lego, our MobileR2L outperforms NeRF clearly, delivering sharper and less distorted shapes and textures. On the real-world scene Fern, our result is less noisy, and the details, e.g., the leaf tips, are sharper. Additionally, we provide the zoom-in comparison with MoibleNeRF [10] in Fig. 5. Our method achieves high-quality rendering for zoom-in view, which is", + "bbox": [ + 75, + 657, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0bb0855902f337fea6f496e7fb01b3423c349a9378e06d31aa9242ad1bb48f08.jpg", + "table_caption": [ + "Table 2. Analysis of Storage (MB) required for different rendering methods. Our method has a clear advantage over existing works with much less storage required." + ], + "table_footnote": [], + "table_body": "
Synthetic 360°Forward-facing
MobileNeRF [10]SNeRG [16]OursMobileNeRF [10]SNeRG [16]Ours
Disk storage125.886.88.3201.5337.38.3
", + "bbox": [ + 503, + 142, + 888, + 171 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/930baa9cdae9e2f3dd913b62f293b384955ca694b2e881ef656373e047f14254.jpg", + "table_caption": [ + "Table 3. Analysis of Inference Speed. Latency (ms) is obtained on iPhone with iOS 16. Following MoibleNeRF [10], we use the notation $\\frac{M}{N}$ to indicate that $M$ out of $N$ scenes in the Forward-facing dataset that can not run on devices. Specifically, MobileNeRF can not render Leaves and Orchids in Forward-facing." + ], + "table_footnote": [], + "table_body": "
Synthetic 360°Forward-facing
MobileNeRF [10]OursMobileNeRF [10]Ours
iPhone 1317.5426.2127.15 2/818.04
iPhone 1416.6722.6520.98 2/816.48
", + "bbox": [ + 504, + 292, + 888, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "especially important for 3D assets that users might perform zoom-in to look for more image details.", + "bbox": [ + 498, + 397, + 890, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Disk Storage. One significant advantage of our method is that we do not require extra storage, even for complex scenes. As shown in Tab. 2, the storage of our approach is $8.3\\mathrm{MB}$ for both synthetic $360^{\\circ}$ and forward-facing datasets. The mesh-based methods like MobileNeRF demand more storage for real-world scenes due to saving more complex textures. As a result, our approach takes $24.3\\times$ less disk storage than MobileNeRF on the forward-facing, and $15.2\\times$ less storage on the synthetic $360^{\\circ}$ dataset.", + "bbox": [ + 496, + 433, + 890, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference Speed. We profile and report the rendering speed of our proposed approach on iPhones (13, and 14, iOS 16) in Tab. 3. The models are compiled with CoreMLTools [11]. Our proposed method runs faster on real forward-facing scenes than the realistic synthetic $360^{\\circ}$ scenes. The latency discrepancy between the two datasets comes from the different input spatial sizes. MobileNeRF shows a lower latency than our models on the realistic synthetic $360^{\\circ}$ but higher on the real-world scenes. Both methods can run in real-time on devices. Note that MobileNeRF cannot render two scenes, i.e., Leaves and Orchids, due to memory issues, as they require complex textures to model the geometry. In contrast, our approach is robust for different scenes.", + "bbox": [ + 496, + 575, + 890, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discussion. From the comparison of the rendering quality, disk storage, and inference speed, it can be seen that MobileR2L achieves overall better performance than MobileN-eRF. More importantly, considering the usage of neural rendering on real-world applications, MobileR2L is more suitable as it requires much less storage, reducing the constraint for hardware and can render real-world scenes in real-time on mobile devices.", + "bbox": [ + 496, + 779, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8333", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Analysis", + "text_level": 1, + "bbox": [ + 76, + 90, + 250, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here we perform the ablation analysis to understand the design choices of the network. We use the scene of Chair from the synthetic $360^{\\circ}$ to conduct the analysis. All models are trained for 200K iterations.", + "bbox": [ + 75, + 113, + 468, + 172 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Options for Backbone. We study the two available operators for designing the backbone. MLP and $1 \\times 1$ CONV layer are essentially equivalent operators and perform the same calculations, thus resulting in similar performance. However, we observe around $27\\%$ latency reduction on mobile devices (iPhone 13) when replacing the MLP layer with the $1 \\times 1$ CONV layer. Specifically, as shown in Tab. 4, we design two networks, i.e., MLP and CONV2D, with only residual blocks as in Fig. 3 but removing the activation, normalization, and super-resolution modules. We use the input size as $100 \\times 100$ for the two models. Since the super-resolution modules are omitted, we train the two networks for generating $100 \\times 100$ images. As can be seen, the CONV2D model has a faster inference speed than MLP with similar performance. This is due to the fact that CONV operation is better-optimized than MLP on mobile devices. Additionally, due to the intrinsic design of our proposed MobileR2L, employing MLP layers requires two additional operators, i.e., Permute and Reshape, before feeding the internal features to super-resolution modules, while Permute and Reshape involve data movement that adds unnecessary overheads on some edge devices [26].", + "bbox": [ + 75, + 174, + 470, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of Activation Function. R2L [41] and NeRF [33] use ReLU [4] activation as non-linearity function. In our proposed MobileR2L, we use GELU [18] instead. As shown in Tab. 4, by comparing the $CONV2D + ReLU$ and $CONV2D + GeLU$ , which are two networks trained with ReLU and GeLU activations, we notice that GeLU brings about 0.17 PSNR boost without any additional latency overhead. Similarly, we show that incorporating BatchNorm [22] layer into the ResBlock is also beneficial for better performance without introducing extra latency, as shown by $CONV2D + GeLU + BN$ in Tab. 4. The three networks in the experiments are also trained to render $100 \\times 100$ images.", + "bbox": [ + 75, + 507, + 470, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on Input Dimension. We further analyze the optimal spatial resolution for the input tensor. Specifically, we benchmark the performance of three approaches, namely, $50 \\times 50 - \\text{NeRF Teacher}$ , $100 \\times 100 - \\text{NeRF Teacher}$ , and $200 \\times 200 - \\text{NeRF Teacher}$ with the spatial size of input as the square of 50, 100, and 200 respectively. These models contain super-resolution modules to render $800 \\times 800$ images and are trained with the NeRF [33] as a teacher model. Results are presented in Tab. 5. The model using a small input spatial size, i.e., $50 \\times 50$ , achieves $2 \\times$ speedup than the model with a larger size, i.e., $100 \\times 100$ , as less computation is required. However, the performance is also degraded by 0.25 PSNR. Further increasing the input spatial size to $200 \\times 200$ makes the model unable to achieve real-time in-", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/15dbdc0d49437959f4681710eb8e7b033e00d93e1a7dce09cc7a7c2ebbea4082.jpg", + "table_caption": [ + "Table 4. Analysis of Network Design. For all the comparisons, we use the input tensor with the spatial size as $100 \\times 100$ and render the image with spatial size. The latency (ms) is measured on iPhone 13 (iOS16) with models compiled with CoreMLTools [11]" + ], + "table_footnote": [], + "table_body": "
PSNR↑SSIM↑LPIPS↓Latency↓
MLP19.130.97590.663019.57
CONV2D19.160.97590.630114.30
CONV2D + ReLU26.820.99490.028216.20
CONV2D + GeLU26.990.99490.073017.00
CONV2D + GeLU + BN27.180.99540.025917.00
", + "bbox": [ + 504, + 157, + 888, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/07e96748ddfc2aef40cd26fec2a1ef8482d45bf492246a05a5cc08aa574fae4a.jpg", + "table_caption": [ + "Table 5. Analysis of the spatial size of the input, usage of teacher model, and ray presentation. Besides image quality metrics, we show the number of parameters for each model and the latency when running on iPhone 13." + ], + "table_footnote": [], + "table_body": "
ParamsPSNR↑SSIM↑LPIPS↓Latency↓
50 × 50 - NeRF Teacher3.9M30.400.99650.068613.04
100 × 100 - NeRF Teacher3.9M30.650.99660.066826.21
200 × 200 - NeRF Teacher3.9M---73.76
800 × 800 - w/o SR3.9M---Error
100 × 100 - MipNeRF Teacher3.9M30.830.09970.056426.21
100 × 100 - MipNeRF Teacher, K16, L104.1M30.900.99680.058331.05
100 × 100 - MipNeRF Teacher, K16, L10, D1006.8M31.370.99720.047044.52
", + "bbox": [ + 504, + 330, + 890, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ference. Thus, we do not report the rendering performance of the models with $200 \\times 200$ input size.", + "bbox": [ + 498, + 457, + 890, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of SR modules. We further show the necessity of using SR modules. We use the spatial size of $800 \\times 800$ as the network input to render images with the same spatial size. We denote the setting as $800 \\times 800 - w / o$ SR in Tab. 5. Profiling the latency of such a network leads to compilation errors due to intensive memory usage. Thus, our proposed SR module is essential for high-resolution synthesis without introducing prohibitive computation overhead.", + "bbox": [ + 496, + 488, + 890, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Choice of Teacher Models. Since both R2L [41] and MobileR2L use a teacher model for generating pseudo data to train a lightweight network, we study whether a more powerful teacher model can improve performance. To conduct the experiments, we use MipNeRF [6] as the teacher model for the training MobileR2L, given MipNeRF shows better performance than NeRF on the synthetic $360^{\\circ}$ dataset. We denote the approach as $100 \\times 100 -$ MipNeRF Teacher. Through the comparison with $100 \\times 100 -$ NeRF Teacher, as in Tab. 5, we notice the quality of the rendered images is improved, e.g., the PSNR is increased by 0.18, without the extra cost of latency. The comparison demonstrates that our approach has the potential to render higher-quality images when better teacher models are provided.", + "bbox": [ + 496, + 611, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on Ray Representation. Here we analyze how the ray representation affects the latency-performance trade-off of MobileR2L. We follow the same ray representation paradigm as in R2L [41] and positional encoding as in NeRF [33]. Specifically, R2L sample $K$ 3D points along", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8334", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the ray, and each point is mapped to a higher dimension by positional encoding with $L$ positional coordinates. R2L sets $K = 16$ and $L = 10$ , resulting in a vector with a dimension of 1,008. We apply the same setting to MobileR2L and denote the model as $100 \\times 100$ , $K_{16}$ , $L_{10}$ -MipNeRF Teacher in Tab. 5. For our implementation in MobileR2L, we set $K = 8$ and $L = 6$ for the model, which has the dimension per ray as 312. The model is $100 \\times 100$ -MipNeRF Teacher. By comparing the performance of the two models, we notice that larger $K$ and $L$ lead to negligible PSNR improvement (0.07), yet higher inference latency and bigger model size (more parameters). Therefore, we chose $K = 8$ and $L = 6$ for the consideration of model size and latency - they are the more important metrics when deploying neural rendering models on mobile devices.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Depth of the Backbone. Lastly, we show the effects of the backbone depth on the model performance. We use the depth as 60 for our backbone. By increasing the number of residual blocks in the backbone, i.e., setting depth as 100, we obverse better model performance at the cost of higher latency, as shown by comparing the last two rows in Tab. 5. Using depth as 100 significantly increases the latency and the number of parameters, and the model fails to run in real time. Thus, we chose depth as 60, given the better trade-off between latency, model size, and performance.", + "bbox": [ + 75, + 316, + 472, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Real-World Application", + "text_level": 1, + "bbox": [ + 76, + 477, + 297, + 493 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here we demonstrate the usage of our technique for building a real-world application. Given the small size and faster inference speed of our model, we create a shoes try-on application that runs on mobile devices. Users can directly try on the shoes rendered by MobileR2L using their devices, enabling real-time interaction.", + "bbox": [ + 75, + 500, + 468, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The pipeline for building the application is illustrated in Fig. 6. We first use iPhone to capture 100 shoe images for training. The images are then segmented to remove the background. After that, we train a NeRF model [33] to generate pseudo data, which is later used for learning MobileR2L to render images in $1008 \\times 756$ resolution. We apply foot tracking and overlay the rendered shoe on top of the user's feet. As can be seen from Fig. 6, our model is able to render high-quality images from various views for different users. The try-on usage proves the potential of leveraging neural rendering for building various real-time interactive applications such as Augment Reality.", + "bbox": [ + 75, + 590, + 470, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 784, + 326, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work presents MobileR2L, the first neural light network that renders images with similar quality as NeRF [33] while running in real-time on model devices. We perform extensive experiments to design an optimized network architecture that can be trained via data distillation to render high-resolution images, e.g., $800 \\times 800$ . Additionally,", + "bbox": [ + 75, + 809, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d923b7f34ecce8d146025a3af31e3879d37f907ae8395299dfd4e329bb9bf8d.jpg", + "image_caption": [ + "(a) Example Images from Collected Data" + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 645, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/23b1efac456c0bb1b7dc3661d3854dbf68d87322815b3c04839c2800adf1a3c4.jpg", + "image_caption": [ + "(b) Segmented Images" + ], + "image_footnote": [], + "bbox": [ + 514, + 176, + 630, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/baac3193307d63efa3292e67bf92ad0b558e53923a696352f75b4721cf74900b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 88, + 769, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6de13707ba3094539ba866d9cd6c002590d31af35aa37738c7c6ae32d32f3fb3.jpg", + "image_caption": [ + "(c) Novel View Synthesis for Virtual Try-On" + ], + "image_footnote": [], + "bbox": [ + 710, + 170, + 767, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcc19e1d1520af58ef2c4db821a804d8a45ddd74dc7dd50e0c128d883a3239fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 88, + 830, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ddb2f28e8799e96f7e1dd23e6fc9a0624a02d5e10fcfcf2fb0fae26cfab91324.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 170, + 828, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ce7338fe83a6b70c382a8f4bc4a3c12087acce92dc85e0c0470ebd8925d117a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 833, + 88, + 890, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d352db590897b23a9b3765ad99cc8ac0c89dc015f7e5ddf8df06b4055a580cf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 834, + 170, + 890, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/02d545f524cfca394a554a4982ba1ed62a31e24f8c4ec897776b136adf39236c.jpg", + "image_caption": [ + "Figure 6. Virtual Try-On Application. From the collected images using a cellphone (a), we segment the foreground shoe (b) to train a MobileR2L model. We deploy the model on mobile devices, and users can directly try the shoe. The model renders images for novel views when users rotate the phone or change the foot positions (c).", + "Room", + "Figure 7. Visual comparison on the real-world scene Room. Both our model and NeRF fail to synthesize the whiteboard writings on the upper-left of the cutout patch." + ], + "image_footnote": [], + "bbox": [ + 511, + 376, + 625, + 443 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a93316771dfbc4e5a7b4effa07eda2a4bebe5ee75a24cf148a4b9a4adebd0d3c.jpg", + "image_caption": [ + "(a) GT" + ], + "image_footnote": [], + "bbox": [ + 629, + 376, + 712, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5c6500f3a60e6200bc88d82d65a4b011cbd5cf8f265b9634f64c481c27b63c0f.jpg", + "image_caption": [ + "(b) NeRF" + ], + "image_footnote": [], + "bbox": [ + 715, + 376, + 800, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ff6ffe67e1d17985fc3b9a06f7516032e27069d1a7b77f217644ffe751fd2160.jpg", + "image_caption": [ + "(c) Ours" + ], + "image_footnote": [], + "bbox": [ + 803, + 376, + 888, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "since we do not require other information besides the neural network, MobileR2L dramatically saves the representation storage in stark contrast to other mesh-based methods like MoibleNeRF [10]. Furthermore, we prove that with our design, neural rendering can be used to build real-world applications, achieving real-time user interaction.", + "bbox": [ + 498, + 537, + 890, + 627 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although MobileR2L achieves promising inference speed with small model sizes, there are still two limitations of the current work that can be improved. First, we follow the training recipe of R2L [41], and R2L uses 10K pseudo images generated by the teacher NeRF model to train the student model. The number of training images is much more than the images used to train the teacher NeRF (which only requires around 100 images), resulting in a longer training time than NeRF-based methods. Therefore, a future direction could be reducing the training costs for distillation-based works like R2L and this work. Second, MobileR2L fails to generate some high-frequency details in the images. We show examples in Fig. 7. Using a larger model may alleviate this problem given a larger model capacity. Nevertheless, the inference latency will also increase accordingly on mobile devices. Future efforts may focus on optimizing the network and training pipeline to boost the performance of the current model.", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8335", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lens studio. https://ar.sun.com/en-US/lens-studio.1", + "[2] Nerf-factory. https://github.com/kakaobrain/NeRF-Factory.5", + "[3] Snap ml. https://docs.snap.com/lens-studio/references/guides/lens-features/machine-learning/ml-overview.1", + "[4] Abien Fred Agarap. 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R2l: Distilling neural radiance field to neural light field for efficient novel view synthesis. In ECCV, 2022. 2, 3, 4, 5, 7, 8, 11", + "[42] Zhou Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4):600-612, 2004. 5", + "[43] Suttisak Wizadwongsa, Pakkapon Phongthawee, Jiraphon Yenphraphai, and Supasorn Suwajanakorn. Nex: Real-time view synthesis with neural basis expansion. In CVPR, 2021. 2", + "[44] Lin Yen-Chen. Nerf-pytorch. https://github.com/yenchenlin/nerf-pytorch/, 2020. 5, 6, 11, 12", + "[45] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5752-5761, 2021. 1, 2", + "[46] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric, 2018. 5" + ], + "bbox": [ + 78, + 90, + 468, + 757 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8337", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_model.json b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_model.json new file mode 100644 index 0000000000000000000000000000000000000000..efe7a95c6c0e2a1a6a5c7b800a63eed46cfc3dc3 --- /dev/null +++ b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.241, + 0.131, + 0.73, + 0.153 + ], + "angle": 0, + "content": "Real-Time Neural Light Field on Mobile Devices" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.179, + 0.841, + 0.236 + ], + "angle": 0, + "content": "Junli Cao\\(^{1}\\) \nYun Fu\\(^{2}\\) \n\\(^{1}\\)Snap Inc. \n\\(^{2}\\)Northeastern University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.741 + ], + "angle": 0, + "content": "Recent efforts in Neural Rendering Fields (NeRF) have shown impressive results on novel view synthesis by utilizing implicit neural representation to represent 3D scenes. Due to the process of volumetric rendering, the inference speed for NeRF is extremely slow, limiting the application scenarios of utilizing NeRF on resource-constrained hardware, such as mobile devices. Many works have been conducted to reduce the latency of running NeRF models. However, most of them still require high-end GPU for acceleration or extra storage memory, which is all unavailable on mobile devices. Another emerging direction utilizes the neural light field (NeLF) for speedup, as only one forward pass is performed on a ray to predict the pixel color. Nevertheless, to reach a similar rendering quality as NeRF, the network in NeLF is designed with intensive computation, which is not mobile-friendly. In this work, we propose an efficient network that runs in real-time on mobile devices for neural rendering. We follow the setting of NeLF to train our network. Unlike existing works, we introduce a novel network architecture that runs efficiently on mobile devices with low latency and small size, i.e., saving \\(15 \\times \\sim 24 \\times\\) storage compared with MobileNeRF. Our model achieves high-resolution generation while maintaining real-time inference for both synthetic and real-world scenes on mobile devices, e.g., 18.04ms (iPhone 13) for rendering one \\(1008 \\times 756\\) image of real 3D scenes. Additionally, we achieve similar image quality as NeRF and better quality than MobileNeRF (PSNR 26.15 vs. 25.91 on the real-world forward-facing dataset)1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.772, + 0.21, + 0.788 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Remarkable progress seen in the domain of neural rendering [33] promises to democratize asset creation and rendering, where no mesh, texture, or material is required - only a neural network that learns a representation of an object or a scene from multi-view observations. The trained" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.269, + 0.681, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.27, + 0.891, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.442, + 0.895, + 0.541 + ], + "angle": 0, + "content": "Figure 1. Examples of deploying our approach on mobile devices for real-time interaction with users. Due to the small model size (8.3MB) and fast inference speed \\((18\\sim 26\\mathrm{ms}\\) per image on iPhone 13), we can build neural rendering applications where users interact with 3D objects on their devices, enabling various applications such as virtual try-on. We use publicly available software to make the on-device application for visualization [1,3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.659 + ], + "angle": 0, + "content": "model can be queried at arbitrary viewpoints to generate novel views. To be made widely available, this exciting application requires such methods to run on resource-constrained devices, such as mobile phones, conforming to their limitations in computing, wireless connectivity, and hard drive capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Unfortunately, the impressive image quality and capabilities of NeRF [33] come with a price of slow rendering speed. To return the color of the queried pixel, hundreds of points need to be sampled along the ray that ends up in that pixel, which is then integrated to get the radiance. To enable real-time applications, many works have been proposed [12, 34, 37, 45], yet, they still require high-end GPUs for rendering and hence are not available for resource-constrained applications on mobile or edge devices. An attempt is made to trade rendering speed with storage in MobileNeRF [10]. While showing promising acceleration results, their method requires storage for texturing saving. For example, for a single real-world scene from the forward-facing dataset [33], MobileNeRF requires 201.5MB of storage. Clearly, downloading and storing tens, hundreds, or even thousands of such scenes in MobileNeRF" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.308, + 0.901 + ], + "angle": 0, + "content": "1More demo examples in our Webpage." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8328" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.38, + 0.106 + ], + "angle": 0, + "content": "format on a device is prohibitively expensive." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.47, + 0.289 + ], + "angle": 0, + "content": "A different approach is taken in Neural Light Fields (NeLF) that directly maps a ray to the RGB color of the pixel by performing only one forward pass per ray, resulting in faster rendering speed [5, 25, 28, 41]. Training NeLF is challenging and hence requires increased network capacity. For example, Wang et al. [41] propose an 88-layer fully-connected network with residual connections to distill a pretrained radiance model effectively. While their approach achieves better rendering results than vanilla NeRF at \\(30 \\times\\) speedup, running it on mobile devices is still not possible, as it takes three seconds to render one \\(200 \\times 200\\) image on iPhone 13 shown in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.593 + ], + "angle": 0, + "content": "In this work, we propose MobileR2L, a real-time neural rendering model built with mobile devices in mind. Our training follows a similar distillation procedure introduced in R2L [41]. Differently, instead of using an MLP, a backbone network used by most neural representations, we show that a well-designed convolutional network can achieve real-time speed with the rendering quality similar to MLP. In particular, we revisit the network design choices made in R2L and propose to use the \\( 1 \\times 1 \\) Conv layer in the backbone. A further challenge with running a NeRF or NeLF on mobile devices is an excessive requirement of RAM. For example, to render an \\( 800 \\times 800 \\) image, one needs to sample 640,000 rays that need to be stored, causing out-of-memory issues. In 3D-aware generative models [9, 15, 20], this issue is alleviated by rendering a radiance feature volume and upsampling it with a convolutional network to obtain a higher resolution. Inspired by this, we render a light-field volume that is upsampled to the required resolution. Our MobileR2L features several major advantages over existing works:" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.604, + 0.468, + 0.663 + ], + "angle": 0, + "content": "- MobileR2L achieves real-time inference speed on mobile devices (Tab. 3) with better rendering quality, e.g., PSNR, than MobileNeRF on the synthetic and real-world datasets (Tab. 1)." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.665, + 0.468, + 0.709 + ], + "angle": 0, + "content": "- MobileR2L requires an order of magnitude less storage, reducing the model size to 8.3MB, which is \\(15.2 \\times \\sim 24.3 \\times\\) less than MobileNeRF." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.604, + 0.468, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.47, + 0.784 + ], + "angle": 0, + "content": "Due to these contributions, MobileR2L can unlock wide adoption of neural rendering in real-world applications on mobile devices, such as a virtual try-on, where the real-time interaction between devices and users is achieved (Fig. 1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.227, + 0.815 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.903 + ], + "angle": 0, + "content": "Neural Radiance Field (NeRF). NeRF [33] shows the possibility of representing a scene with a simple multi-layer perceptron (MLP) network. Going forward, many extensions follow up in improving rendering quality (e.g., MipNeRF [6], MipNeRF 360 [7], and Ref-NeRF [40])," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "rendering efficiency (e.g., NSVF [29], Nex [43], AutoInt [27], FastNeRF [13], Baking [16], Plenoctree [45], KiloNeRF [37], DeRF [36], DoNeRF [35], R2L [41], and MobileNeRF [10]) and training efficiency (e.g., Plenoxels [12], and Instant-NGP [34])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.893, + 0.701 + ], + "angle": 0, + "content": "Efficient NeRF Rendering. Since this paper falls into the category of improving rendering efficiency as we target real-time rendering on mobile devices, we single out the papers of this group and discuss them in length here. There are generally four groups. (1) The first group trades speed with space, i.e., they precompute and cache scene representations and the rendering reduces to table lookup. Efficient data structure like sparse octree, e.g., Plenoctree [45], is usually utilized to make the rendering even faster. (2) The second attempts reduce the number of sampled points along the camera ray during rendering as it is the root cause of prohibitively slow rendering speed. Fewer sampled points typically lead to performance degradation, so as compensation, they usually introduce extra information, such as depth, e.g., DoNeRF [35], or mesh, e.g., MobileNeRF [10], to maintain the visual quality. (3) The third group takes a \"divide and conquer\" strategy. DeRF [36] decomposes the scene spatially to Voronoi diagrams and learns each diagram with a small network. KiloNeRF [37] also employs a decomposition scheme. Differently, they decompose the scene into thousands of small regular grids. Each is addressed with a small network. Such decomposition poses challenges to parallelism. Thus they utilize customized parallelism implementation to obtain speedup. (4) The fourth group is a newly surging one, represented by the recent works RSEN [5] and R2L [41]. They achieve rendering efficiency by representing the scene with NeLF (neural light field) instead of NeRF. NeLF avoids the dense sampling on camera ray, resulting in a much faster rendering speed than NeRF. On the downside, NeLF is typically much harder to learn than NeRF. As a remedy, these works (such as [41]) typically integrate a pre-trained NeRF model as a teacher to synthesize additional pseudo data for distillation [8, 19]. Therefore, the resulting model is fast with a reasonably small representation size, i.e., the model size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Neural Light Field (NeLF). Light field is a different way of representing scenes. The idea has a long history in the computer graphics community, e.g., Light fields [25] and Lumigraphs [14] cache plenty of images and enable real-time rendering at the cost of limited camera pose and excessive storage overhead. One of the most intriguing properties of NeLF is that rendering one image only requires one network forward, resulting in a significantly faster speed than NeRF-based methods. With the recent surge of the neural radiance field, some works attempt to revive the idea of the neural light field for efficient neural rendering. Sitzmann et al. [38] materialize the idea of using a neural network to model the scene, and the rendering process reduces to" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8329" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.332 + ], + "angle": 0, + "content": "a single network forward. Despite the encouraging idea, their method has only been evaluated on scenes with simple shapes, not matching the quality of NeRF on complex real-world scenes. Later, RSEN [5] and R2L [41] are introduced. RSEN divides the space into many voxel grids. Only in each grid, it is a NeLF, which needs alpha-composition to render the final color, making their method a mixture of NeLF and NeRF. R2L [41] is a pure NeLF network that avoids the alpha-composition step in rendering, which is also one of the most relevant works to this paper. However, R2L is still not compact and fast enough for mobile devices. Based on our empirical study, an R2L model runs for around three seconds per frame on iPhone 13 even for low-resolution like \\(200 \\times 200\\). This paper is meant to push the NeRF-to-NeLF idea even further, making it able to perform real-time rendering on mobile devices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.381 + ], + "angle": 0, + "content": "We will mainly compare to MobileNeRF [10] in this paper as it is the only method, to our best knowledge, that can run on mobile devices with matching quality to NeRF [33]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.396, + 0.176, + 0.412 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.343, + 0.437 + ], + "angle": 0, + "content": "3.1. Prerequisites: NeRF and R2L" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.473, + 0.584 + ], + "angle": 0, + "content": "NeRF. NeRF [33] represents the scene implicitly with an MLP network \\( F_{\\Theta} \\), which maps the 5D coordinates (spatial location \\( (x, y, z) \\) and view direction \\( (\\theta, \\phi) \\)) to a 1D volume density (opacity, denoted as \\( \\sigma \\) here) and 3D radiance (denoted as \\( \\mathbf{c} \\)) such that \\( F_{\\Theta}: \\mathbb{R}^5 \\mapsto \\mathbb{R}^4 \\). Each pixel of an image is associated with a camera ray. To predict the color \\( \\hat{C} \\) of a pixel, the NeRF method samples many points (denoted as \\( N \\) below) along the camera ray and accumulates the radiance \\( \\mathbf{c} \\) of all these points via alpha compositing [23, 31, 33]:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.595, + 0.401, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\cdot \\mathbf {c} _ {i},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.635, + 0.47, + 0.651 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {c} _ {i}, \\sigma_ {i}\\right) = F _ {\\Theta} \\left(\\mathbf {r} \\left(t _ {i}\\right), \\mathbf {d}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.654, + 0.32, + 0.692 + ], + "angle": 0, + "content": "\\[\nT _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{r}\\) means the camera ray; \\(\\mathbf{r}(t_i) = \\mathbf{o} + t_i\\mathbf{d}\\) represents the location of a point on the ray with origin \\(\\mathbf{o}\\) and direction \\(\\mathbf{d}\\); \\(t_i\\) is the Euclidean distance, i.e., a scalar, of the point away from the origin; and \\(\\delta_{i} = t_{i + 1} - t_{i}\\) refers to the distance between two adjacent sampled points. A stratified sampling approach is employed in NeRF [33] to sample the \\(t_i\\) in Eqn. 1. To enrich the input information, the position and direction coordinates are encoded by positional encoding [39], which maps a scalar \\((\\mathbb{R})\\) to a higher dimensional space \\((\\mathbb{R}^{2L + 1})\\) through cosine and sine functions, where \\(L\\) (a predefined constant) stands for the frequency order (in the original NeRF [33], \\(L = 10\\) for positional coordinates and \\(L = 4\\) for direction coordinates)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.089, + 0.895, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.227, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Figure 2. Training and Inference Pipeline. The training involves a teacher model to generate pseudo data, which is used to learn the MobileR2L. The teacher model, e.g., NeRF, is trained on real images. Once we have the teacher model, we use it to generate pseudo images, e.g., images with the resolution of \\(800 \\times 800\\), in addition to down-scaled rays, e.g., rays with spatial size as \\(100 \\times 100\\), that share the same origin with the pseudo images to train the MobileR2L. After that, we use the real data to fine-tune MobileR2L. For inference, we directly forward the rays into the pre-trained MobileR2L to render images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.518 + ], + "angle": 0, + "content": "The whole formulation and training of NeRF are straightforward. One critical problem preventing fast inference in NeRF is that the \\(N\\), i.e., the number of sampled points, in Eqn. 1 is pretty large (256 in the original NeRF paper due to their two-stage coarse-to-fine design). Therefore, the rendering computation for even a single pixel is prohibitively heavy. The solution proposed by R2L [41] is distilling the NeRF representation to NeLF." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.672 + ], + "angle": 0, + "content": "R2L. Essentially, a NeLF function maps the oriented ray to RGB. To enrich the input information, R2L proposes a new ray representation – they also sample points along the ray just like NeRF [33] does; but differently, they concatenate the points to one vector, which is used as the ray representation and fed into a neural network to learn the RGB. Similar to NeRF, positional encoding [39] is also adopted in R2L to map each scalar coordinate to a high dimensional space. During training, the points are randomly (by a uniform distribution) sampled; during testing, the points are fixed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.794 + ], + "angle": 0, + "content": "The output of the R2L model is directly RGB, no density learned, and there is no extra alpha-compositing step, which makes R2L much faster than NeRF in rendering. One downside of the NeLF framework is, as shown in R2L [41], the NeLF representation is much harder to learn than NeRF; so as a remedy, R2L proposes an 88-layer deep ResMLP (residual MLP) architecture (much deeper than the network of NeRF) to serve as the mapping function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "R2L has two stages in training. In the first stage, they use a pre-trained NeRF model as a teacher to synthesize excessive (origin, direction, RGB) triplets as pseudo data; and then fed the pseudo data to train the deep ResMLP. This stage can make the R2L model achieve comparable performance to the teacher NeRF model. In the second stage, they finetune the R2L network from the first stage on" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8330" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.095, + 0.891, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.896, + 0.392 + ], + "angle": 0, + "content": "Figure 3. Overview of Network. The input tensor of MobileR2L has 4D shape: batch, channel, height, and width. The backbone includes residual blocks (RB) that is repeated 28 times (\\(N = 28\\)). Following the backbone, there are two types of super-resolution (SR) modules. The first SR module \\((\\mathrm{SR}^1)\\) has kernel size \\(4 \\times 4\\) in the Transpose CONV layer that doubles the input \\(H, W\\) to \\(2H, 2W\\), whereas the second SR module \\((\\mathrm{SR}^2)\\) has kernel size \\(3 \\times 3\\), tripling the spatial size to \\(3H, 3W\\). The configuration of \\(3 \\times \\mathrm{SR}^1\\) is used in the synthetic \\(360^\\circ\\) dataset that upsamples the input \\(8 \\times\\). For the real-world forward-facing dataset, we use the combination of \\(2 \\times \\mathrm{SR}^1 + \\mathrm{SR}^2\\) that upsamples the input \\(12 \\times\\). Moreover, we use various output channels across RB and SR: \\(C_1 = 256\\), \\(C_2 = 64\\), and \\(C_3 = 16\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.471, + 0.449 + ], + "angle": 0, + "content": "the original data – this step can further boost the rendering quality as shown in the R2L work [41]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.459, + 0.202, + 0.473 + ], + "angle": 0, + "content": "3.2. MobileR2L" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.2, + 0.497 + ], + "angle": 0, + "content": "3.2.1 Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.766 + ], + "angle": 0, + "content": "We follow the learning process of R2L to train our proposed MobileR2L, namely, using a pre-trained teacher model, such as NeRF [33], to generate pseudo data for the training of a lightweight neural network. To reduce the inference speed, we aim only to forward the network once when rendering an image. However, under the design of R2L, although one pixel only requires one network forward, directly feeding rays with large spatial size, e.g., \\(800 \\times 800\\), into a network causes memory issues. Therefore, R2L forwards a partial of rays each time, increasing the speed overhead. To solve the problem, we introduce super-resolution modules, which upsample the low-resolution input, e.g., \\(100 \\times 100\\), to a high-resolution image. Thus, we can obtain a high-resolution image with only one forward pass of the neural network during inference time. The training and inference pipeline is illustrated in Fig. 2, and we introduce more details for our network architecture in the following." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.292, + 0.8 + ], + "angle": 0, + "content": "3.2.2 Network Architectures" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The input rays can be represented as \\(\\mathbf{x} \\in \\mathbb{R}^{B,6,H,W}\\), where \\(B\\) denotes the batch size and \\(H\\) and \\(W\\) denote the spatial size. The ray origin and view directions are concatenated as the second dimension of \\(\\mathbf{x}\\). We then apply positional encoding \\(\\gamma(\\cdot)\\) on \\(\\mathbf{x}\\) to map the ray origin and view directions into a higher dimension. Thus, we get the input of our neural" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.419, + 0.616, + 0.433 + ], + "angle": 0, + "content": "network as \\(\\gamma (\\mathbf{x})\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.538 + ], + "angle": 0, + "content": "The network includes two main parts: an efficient backbone and Super-Resolution (SR) modules for high-resolution rendering, with the architecture provided in Fig. 3. Instead of using Fully Connected (FC) or linear layers for the network that is adopted by existing works [33, 41], we only apply convolution (CONV) layers in the backbone and super-resolution modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.764 + ], + "angle": 0, + "content": "There are two main reasons for replacing FC with CONV layers. First, the CONV layer is better optimized by compilers than the FC layer [30]. Under the same number of parameters, the model with CONV \\(1 \\times 1\\) runs around \\(27\\%\\) faster than the model with FC layers, as shown in Tab. 4. Second, suppose FC is used in the backbone, in that case, extra Reshape and Permute operations are required to modify the dimension of the output features from the FC to make the features compatible with the CONV layer in the super-resolution modules, as the FC and CONV calculate different tensor dimensions. However, such Reshape or Permute operation might not be hardware-friendly on some mobile devices [26]. With the CONV employed as the operator in the network, we then present more details for the backbone and SR modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Efficient Backbone. The architecture of the backbone follows the design of residual blocks from R2L [41]. Different from R2L, we adopt the CONV layer instead of the FC layer in each residual block. The CONV layer has the kernel size and stride as 1. Additionally, we use the normalization and activation functions in each residual block, which can improve the network performance without introducing latency overhead (see experimental details in Tab. 4). The normalization and activation are chosen as batch normaliza" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8331" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.468, + 0.121 + ], + "angle": 0, + "content": "tion [21] and GeLU [17]. The backbone contains 60 CONV layers in total." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.121, + 0.468, + 0.287 + ], + "angle": 0, + "content": "Super-Resolution Modules. To reduce the latency when running the neural rendering on mobile devices, we aim to forward the neural network once to get the synthetic image. However, the existing network design of the neural light field requires large memory for rendering a high-resolution image, which surpasses the memory constraint on mobile devices. For example, rendering an image of \\(800 \\times 800\\) requires the prediction of 640,000 rays. Forwarding these rays at once using the network from R2L [41] causes the out of memory issue even on the Nvidia Tesla A100 GPU (40G memory)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.468, + 0.558 + ], + "angle": 0, + "content": "To reduce the memory and latency cost for high-resolution generation, instead of forwarding the number of rays that equals to the number of pixels, we only forward a partial of rays and learn all the pixels via super-resolution. Specifically, we propose to use the super-resolution modules following the efficient backbone to upsample the output to a high-resolution image. For example, to generate a \\(800 \\times 800\\) image, we forward a 4D tensor \\(\\mathbf{x}\\) with spatial size as \\(100 \\times 100\\) to the network and upsample the output from backbone three times (i.e., upsample by \\(2 \\times\\) each time). The SR module includes two stacked residual blocks. The first block includes three CONV layers with one as a 2D Transpose CONV layer and two CONV \\(1 \\times 1\\) layers; the second block includes two CONV \\(1 \\times 1\\) layers. After the SR modules, we apply another CONV layer followed by the Sigmoid activation to predict the final RGB color. We denote our model as \\(D60-SR3\\) where it contains 60 CONV layers in the efficient backbone and 3 SR modules." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.208, + 0.59 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.764 + ], + "angle": 0, + "content": "Datasets. We conduct the comparisons mainly on two datasets: realistic synthetic \\(360^{\\circ}\\) [33] and real-world forward-facing [32, 33]. The synthetic \\(360^{\\circ}\\) dataset contains 8 path-traced scenes, with each scene including 100 images for training and 200 images for testing. Forward-facing contains 8 real-world scenes captured by cellphones, where the images in each scene vary from 20 to 60, and 1/8 images are used for testing. We conduct our experiments (training and testing) on the resolution of \\(800 \\times 800\\) for synthetic \\(360^{\\circ}\\) and \\(1008 \\times 756\\) (\\(4 \\times\\) down-scaled from the original resolution) for forward-facing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. We follow the training scheme of R2L [41], i.e., using a teacher model to render pseudo images for the training of MobileR2L network. Specifically, we synthesize 10K pseudo images from the pretrained teacher model [2] for each scene. We first train our MobileR2L on the generated pseudo data and then fine-tune it on the real data, as shown in Fig. 2. In all the experiments, we employ Adam [24] optimizer with an initial learning rate \\(5 \\times 10^{-4}\\) that decays during the training. Our experiments" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.158 + ], + "angle": 0, + "content": "Table 1. Quantitative Comparison on Synthetic \\(360^{\\circ}\\) and Forward-facing. Our method obtains better results on the three metrics than NeRF for the two datasets. Compared with MoibleNeRF and SNeRG, we achieve better results on most of the metrics." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.171, + 0.889, + 0.274 + ], + "angle": 0, + "content": "
Synthetic 360°Forward-facing
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF [33]31.010.9470.08126.500.8110.250
NeRF-Pytorch [44]30.920.9910.04526.260.9650.153
SNeRG [16]30.380.9500.05025.630.8180.183
MoibleNeRF [10]30.900.9470.06225.910.8250.183
MobileR2L (Ours)31.340.9930.05126.150.9660.187
Our Teacher33.090.9610.05226.850.8270.226
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.356 + ], + "angle": 0, + "content": "are conducted on a cluster of Nvidia V100 and A100 GPUs with the batch size as 54 for the main results on the synthetic \\(360^{\\circ}\\) and batch size as 36 on the forward-facing dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Different from R2L, the spatial size of the input rays and the output rendered images in our approach are different. For each high-resolution image generated by the teacher model, we save the input rays corresponding to a lower-resolution image where the camera origins and directions are the same as the high-resolution one while the focal length is down-scaled accordingly. Additionally, we do not sample the rays from different images as in R2L. Instead, the rays in each training sample share the same origin and reserve their spatial locations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Considering the training data of the synthetic \\(360^{\\circ}\\) and forward-facing datasets have different resolutions, the spatial size of the inputs for the two datasets are slightly different. Our network takes input with the spatial size of \\(100 \\times 100\\) for the synthetic \\(360^{\\circ}\\) dataset and upsamples by \\(8 \\times\\) to render \\(800 \\times 800\\) RGB images. In contrast, the spatial size of \\(84 \\times 63\\) is used in the forward-facing dataset, and \\(1008 \\times 756\\) image (\\(12 \\times\\) upsampling) is rendered. The kernel size and padding are adjusted in the last transposed CONV layer to achieve \\(8 \\times\\) and \\(12 \\times\\) upsampling with the 3 SR blocks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.638, + 0.697 + ], + "angle": 0, + "content": "4.1. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Rendering Performance. To understand the image quality of various methods, we report three common metrics: PSNR, SSIM [42], and LPIPS [46], on the realistic synthetic \\(360^{\\circ}\\) and real forward-facing datasets, as demonstrated in Tab. 1. Compared with NeRF [33], our approach achieves better results on PSNR, SSIM, and LPIPS for the synthetic \\(360^{\\circ}\\) dataset. On the forward-facing dataset, we obtain better SSIM and LPIPS than NeRF [33]. Similarly, our method achieves better results for all three metrics than MobileNeRF [10] on the synthetic \\(360^{\\circ}\\) dataset and better PSNR and SSIM on the forward-facing dataset. Compared to SNeRG [16], our method obtains better PSNR and SSIM." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also show the performance of the teacher model used" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8332" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.1, + 0.172, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.16, + 0.168, + 0.173 + ], + "angle": 0, + "content": "Lego" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.174, + 0.204, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.245, + 0.168, + 0.257 + ], + "angle": 0, + "content": "Fern" + }, + { + "type": "image", + "bbox": [ + 0.206, + 0.094, + 0.292, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.16, + 0.272, + 0.173 + ], + "angle": 0, + "content": "(a) GT" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.094, + 0.379, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.303, + 0.16, + 0.37, + 0.173 + ], + "angle": 0, + "content": "(b) NeRF" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.094, + 0.467, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.16, + 0.453, + 0.173 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image", + "bbox": [ + 0.207, + 0.174, + 0.291, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.244, + 0.273, + 0.258 + ], + "angle": 0, + "content": "(a) GT" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.174, + 0.377, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.302, + 0.244, + 0.37, + 0.258 + ], + "angle": 0, + "content": "(b) NeRF" + }, + { + "type": "image", + "bbox": [ + 0.382, + 0.174, + 0.466, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.244, + 0.453, + 0.258 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.272, + 0.469, + 0.342 + ], + "angle": 0, + "content": "Figure 4. Visual comparison between our method and NeRF [33] (trained via NeRF-Pytorch [44]) on the synthetic \\(360^{\\circ}\\) Lego (size: \\(800 \\times 800 \\times 3\\)) and real-world forward-facing scene Fern (size: \\(1008 \\times 756 \\times 3\\)). Best viewed in color. Please refer to our webpage for more visual comparison results." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.361, + 0.468, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.464, + 0.47, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.57, + 0.469, + 0.627 + ], + "angle": 0, + "content": "Figure 5. Zoom-in comparisons. Top row: MobileNeRF [10]. Results are obtained from the code and demo released by the authors. Bottom row: MobileR2L. Our approach renders high-quality images even for zoom-in views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.901 + ], + "angle": 0, + "content": "in training MobileR2L in Tab. 1 (Our Teacher). Note that there is still a performance gap between the student model (MobileR2L) and the teacher model. However, as we show following (Tab. 5), a better teacher model can lead to a student model with higher performance. Compared with MoibleNeRF and SNeRG, our approach has the advantage that we can directly leverage the high-performing teacher models to help improve student training in different application scenarios. We further show the qualitative comparison results in Fig. 4. On the synthetic scene Lego, our MobileR2L outperforms NeRF clearly, delivering sharper and less distorted shapes and textures. On the real-world scene Fern, our result is less noisy, and the details, e.g., the leaf tips, are sharper. Additionally, we provide the zoom-in comparison with MoibleNeRF [10] in Fig. 5. Our method achieves high-quality rendering for zoom-in view, which is" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 2. Analysis of Storage (MB) required for different rendering methods. Our method has a clear advantage over existing works with much less storage required." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.143, + 0.89, + 0.172 + ], + "angle": 0, + "content": "
Synthetic 360°Forward-facing
MobileNeRF [10]SNeRG [16]OursMobileNeRF [10]SNeRG [16]Ours
Disk storage125.886.88.3201.5337.38.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.212, + 0.892, + 0.281 + ], + "angle": 0, + "content": "Table 3. Analysis of Inference Speed. Latency (ms) is obtained on iPhone with iOS 16. Following MoibleNeRF [10], we use the notation \\( \\frac{M}{N} \\) to indicate that \\( M \\) out of \\( N \\) scenes in the Forward-facing dataset that can not run on devices. Specifically, MobileNeRF can not render Leaves and Orchids in Forward-facing." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.293, + 0.889, + 0.347 + ], + "angle": 0, + "content": "
Synthetic 360°Forward-facing
MobileNeRF [10]OursMobileNeRF [10]Ours
iPhone 1317.5426.2127.15 2/818.04
iPhone 1416.6722.6520.98 2/816.48
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.398, + 0.891, + 0.428 + ], + "angle": 0, + "content": "especially important for 3D assets that users might perform zoom-in to look for more image details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.571 + ], + "angle": 0, + "content": "Disk Storage. One significant advantage of our method is that we do not require extra storage, even for complex scenes. As shown in Tab. 2, the storage of our approach is \\(8.3\\mathrm{MB}\\) for both synthetic \\(360^{\\circ}\\) and forward-facing datasets. The mesh-based methods like MobileNeRF demand more storage for real-world scenes due to saving more complex textures. As a result, our approach takes \\(24.3\\times\\) less disk storage than MobileNeRF on the forward-facing, and \\(15.2\\times\\) less storage on the synthetic \\(360^{\\circ}\\) dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.773 + ], + "angle": 0, + "content": "Inference Speed. We profile and report the rendering speed of our proposed approach on iPhones (13, and 14, iOS 16) in Tab. 3. The models are compiled with CoreMLTools [11]. Our proposed method runs faster on real forward-facing scenes than the realistic synthetic \\(360^{\\circ}\\) scenes. The latency discrepancy between the two datasets comes from the different input spatial sizes. MobileNeRF shows a lower latency than our models on the realistic synthetic \\(360^{\\circ}\\) but higher on the real-world scenes. Both methods can run in real-time on devices. Note that MobileNeRF cannot render two scenes, i.e., Leaves and Orchids, due to memory issues, as they require complex textures to model the geometry. In contrast, our approach is robust for different scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Discussion. From the comparison of the rendering quality, disk storage, and inference speed, it can be seen that MobileR2L achieves overall better performance than MobileN-eRF. More importantly, considering the usage of neural rendering on real-world applications, MobileR2L is more suitable as it requires much less storage, reducing the constraint for hardware and can render real-world scenes in real-time on mobile devices." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8333" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.251, + 0.108 + ], + "angle": 0, + "content": "4.2. Ablation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.174 + ], + "angle": 0, + "content": "Here we perform the ablation analysis to understand the design choices of the network. We use the scene of Chair from the synthetic \\(360^{\\circ}\\) to conduct the analysis. All models are trained for 200K iterations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.175, + 0.471, + 0.508 + ], + "angle": 0, + "content": "Options for Backbone. We study the two available operators for designing the backbone. MLP and \\(1 \\times 1\\) CONV layer are essentially equivalent operators and perform the same calculations, thus resulting in similar performance. However, we observe around \\(27\\%\\) latency reduction on mobile devices (iPhone 13) when replacing the MLP layer with the \\(1 \\times 1\\) CONV layer. Specifically, as shown in Tab. 4, we design two networks, i.e., MLP and CONV2D, with only residual blocks as in Fig. 3 but removing the activation, normalization, and super-resolution modules. We use the input size as \\(100 \\times 100\\) for the two models. Since the super-resolution modules are omitted, we train the two networks for generating \\(100 \\times 100\\) images. As can be seen, the CONV2D model has a faster inference speed than MLP with similar performance. This is due to the fact that CONV operation is better-optimized than MLP on mobile devices. Additionally, due to the intrinsic design of our proposed MobileR2L, employing MLP layers requires two additional operators, i.e., Permute and Reshape, before feeding the internal features to super-resolution modules, while Permute and Reshape involve data movement that adds unnecessary overheads on some edge devices [26]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.471, + 0.689 + ], + "angle": 0, + "content": "Analysis of Activation Function. R2L [41] and NeRF [33] use ReLU [4] activation as non-linearity function. In our proposed MobileR2L, we use GELU [18] instead. As shown in Tab. 4, by comparing the \\(CONV2D + ReLU\\) and \\(CONV2D + GeLU\\), which are two networks trained with ReLU and GeLU activations, we notice that GeLU brings about 0.17 PSNR boost without any additional latency overhead. Similarly, we show that incorporating BatchNorm [22] layer into the ResBlock is also beneficial for better performance without introducing extra latency, as shown by \\(CONV2D + GeLU + BN\\) in Tab. 4. The three networks in the experiments are also trained to render \\(100 \\times 100\\) images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Analysis on Input Dimension. We further analyze the optimal spatial resolution for the input tensor. Specifically, we benchmark the performance of three approaches, namely, \\(50 \\times 50 - \\text{NeRF Teacher}\\), \\(100 \\times 100 - \\text{NeRF Teacher}\\), and \\(200 \\times 200 - \\text{NeRF Teacher}\\) with the spatial size of input as the square of 50, 100, and 200 respectively. These models contain super-resolution modules to render \\(800 \\times 800\\) images and are trained with the NeRF [33] as a teacher model. Results are presented in Tab. 5. The model using a small input spatial size, i.e., \\(50 \\times 50\\), achieves \\(2 \\times\\) speedup than the model with a larger size, i.e., \\(100 \\times 100\\), as less computation is required. However, the performance is also degraded by 0.25 PSNR. Further increasing the input spatial size to \\(200 \\times 200\\) makes the model unable to achieve real-time in-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.147 + ], + "angle": 0, + "content": "Table 4. Analysis of Network Design. For all the comparisons, we use the input tensor with the spatial size as \\(100 \\times 100\\) and render the image with spatial size. The latency (ms) is measured on iPhone 13 (iOS16) with models compiled with CoreMLTools [11]" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.158, + 0.89, + 0.236 + ], + "angle": 0, + "content": "
PSNR↑SSIM↑LPIPS↓Latency↓
MLP19.130.97590.663019.57
CONV2D19.160.97590.630114.30
CONV2D + ReLU26.820.99490.028216.20
CONV2D + GeLU26.990.99490.073017.00
CONV2D + GeLU + BN27.180.99540.025917.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.265, + 0.894, + 0.321 + ], + "angle": 0, + "content": "Table 5. Analysis of the spatial size of the input, usage of teacher model, and ray presentation. Besides image quality metrics, we show the number of parameters for each model and the latency when running on iPhone 13." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.332, + 0.891, + 0.417 + ], + "angle": 0, + "content": "
ParamsPSNR↑SSIM↑LPIPS↓Latency↓
50 × 50 - NeRF Teacher3.9M30.400.99650.068613.04
100 × 100 - NeRF Teacher3.9M30.650.99660.066826.21
200 × 200 - NeRF Teacher3.9M---73.76
800 × 800 - w/o SR3.9M---Error
100 × 100 - MipNeRF Teacher3.9M30.830.09970.056426.21
100 × 100 - MipNeRF Teacher, K16, L104.1M30.900.99680.058331.05
100 × 100 - MipNeRF Teacher, K16, L10, D1006.8M31.370.99720.047044.52
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.458, + 0.892, + 0.488 + ], + "angle": 0, + "content": "ference. Thus, we do not report the rendering performance of the models with \\(200 \\times 200\\) input size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.611 + ], + "angle": 0, + "content": "Analysis of SR modules. We further show the necessity of using SR modules. We use the spatial size of \\(800 \\times 800\\) as the network input to render images with the same spatial size. We denote the setting as \\(800 \\times 800 - w / o\\) SR in Tab. 5. Profiling the latency of such a network leads to compilation errors due to intensive memory usage. Thus, our proposed SR module is essential for high-resolution synthesis without introducing prohibitive computation overhead." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Choice of Teacher Models. Since both R2L [41] and MobileR2L use a teacher model for generating pseudo data to train a lightweight network, we study whether a more powerful teacher model can improve performance. To conduct the experiments, we use MipNeRF [6] as the teacher model for the training MobileR2L, given MipNeRF shows better performance than NeRF on the synthetic \\(360^{\\circ}\\) dataset. We denote the approach as \\(100 \\times 100 -\\) MipNeRF Teacher. Through the comparison with \\(100 \\times 100 -\\) NeRF Teacher, as in Tab. 5, we notice the quality of the rendered images is improved, e.g., the PSNR is increased by 0.18, without the extra cost of latency. The comparison demonstrates that our approach has the potential to render higher-quality images when better teacher models are provided." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Analysis on Ray Representation. Here we analyze how the ray representation affects the latency-performance trade-off of MobileR2L. We follow the same ray representation paradigm as in R2L [41] and positional encoding as in NeRF [33]. Specifically, R2L sample \\(K\\) 3D points along" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8334" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.317 + ], + "angle": 0, + "content": "the ray, and each point is mapped to a higher dimension by positional encoding with \\( L \\) positional coordinates. R2L sets \\( K = 16 \\) and \\( L = 10 \\), resulting in a vector with a dimension of 1,008. We apply the same setting to MobileR2L and denote the model as \\( 100 \\times 100 \\), \\( K_{16} \\), \\( L_{10} \\)-MipNeRF Teacher in Tab. 5. For our implementation in MobileR2L, we set \\( K = 8 \\) and \\( L = 6 \\) for the model, which has the dimension per ray as 312. The model is \\( 100 \\times 100 \\)-MipNeRF Teacher. By comparing the performance of the two models, we notice that larger \\( K \\) and \\( L \\) lead to negligible PSNR improvement (0.07), yet higher inference latency and bigger model size (more parameters). Therefore, we chose \\( K = 8 \\) and \\( L = 6 \\) for the consideration of model size and latency - they are the more important metrics when deploying neural rendering models on mobile devices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.469 + ], + "angle": 0, + "content": "Depth of the Backbone. Lastly, we show the effects of the backbone depth on the model performance. We use the depth as 60 for our backbone. By increasing the number of residual blocks in the backbone, i.e., setting depth as 100, we obverse better model performance at the cost of higher latency, as shown by comparing the last two rows in Tab. 5. Using depth as 100 significantly increases the latency and the number of parameters, and the model fails to run in real time. Thus, we chose depth as 60, given the better trade-off between latency, model size, and performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.478, + 0.299, + 0.494 + ], + "angle": 0, + "content": "4.3. Real-World Application" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.59 + ], + "angle": 0, + "content": "Here we demonstrate the usage of our technique for building a real-world application. Given the small size and faster inference speed of our model, we create a shoes try-on application that runs on mobile devices. Users can directly try on the shoes rendered by MobileR2L using their devices, enabling real-time interaction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.471, + 0.773 + ], + "angle": 0, + "content": "The pipeline for building the application is illustrated in Fig. 6. We first use iPhone to capture 100 shoe images for training. The images are then segmented to remove the background. After that, we train a NeRF model [33] to generate pseudo data, which is later used for learning MobileR2L to render images in \\(1008 \\times 756\\) resolution. We apply foot tracking and overlay the rendered shoe on top of the user's feet. As can be seen from Fig. 6, our model is able to render high-quality images from various views for different users. The try-on usage proves the potential of leveraging neural rendering for building various real-time interactive applications such as Augment Reality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.327, + 0.801 + ], + "angle": 0, + "content": "5. Limitation and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This work presents MobileR2L, the first neural light network that renders images with similar quality as NeRF [33] while running in real-time on model devices. We perform extensive experiments to design an optimized network architecture that can be trained via data distillation to render high-resolution images, e.g., \\(800 \\times 800\\). Additionally," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.646, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.17, + 0.646, + 0.177 + ], + "angle": 0, + "content": "(a) Example Images from Collected Data" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.178, + 0.631, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.254, + 0.615, + 0.263 + ], + "angle": 0, + "content": "(b) Segmented Images" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.089, + 0.77, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.171, + 0.769, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.089, + 0.831, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.171, + 0.829, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.834, + 0.089, + 0.892, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.836, + 0.171, + 0.892, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.254, + 0.873, + 0.263 + ], + "angle": 0, + "content": "(c) Novel View Synthesis for Virtual Try-On" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.278, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Figure 6. Virtual Try-On Application. From the collected images using a cellphone (a), we segment the foreground shoe (b) to train a MobileR2L model. We deploy the model on mobile devices, and users can directly try the shoe. The model renders images for novel views when users rotate the phone or change the foot positions (c)." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.377, + 0.627, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.449, + 0.593, + 0.46 + ], + "angle": 0, + "content": "Room" + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.377, + 0.714, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.447, + 0.696, + 0.461 + ], + "angle": 0, + "content": "(a) GT" + }, + { + "type": "image", + "bbox": [ + 0.716, + 0.377, + 0.802, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.447, + 0.794, + 0.461 + ], + "angle": 0, + "content": "(b) NeRF" + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.377, + 0.89, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.817, + 0.447, + 0.876, + 0.461 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.475, + 0.892, + 0.517 + ], + "angle": 0, + "content": "Figure 7. Visual comparison on the real-world scene Room. Both our model and NeRF fail to synthesize the whiteboard writings on the upper-left of the cutout patch." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.628 + ], + "angle": 0, + "content": "since we do not require other information besides the neural network, MobileR2L dramatically saves the representation storage in stark contrast to other mesh-based methods like MoibleNeRF [10]. Furthermore, we prove that with our design, neural rendering can be used to build real-world applications, achieving real-time user interaction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Although MobileR2L achieves promising inference speed with small model sizes, there are still two limitations of the current work that can be improved. First, we follow the training recipe of R2L [41], and R2L uses 10K pseudo images generated by the teacher NeRF model to train the student model. The number of training images is much more than the images used to train the teacher NeRF (which only requires around 100 images), resulting in a longer training time than NeRF-based methods. Therefore, a future direction could be reducing the training costs for distillation-based works like R2L and this work. Second, MobileR2L fails to generate some high-frequency details in the images. We show examples in Fig. 7. Using a larger model may alleviate this problem given a larger model capacity. Nevertheless, the inference latency will also increase accordingly on mobile devices. Future efforts may focus on optimizing the network and training pipeline to boost the performance of the current model." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8335" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Lens studio. https://ar.sun.com/en-US/lens-studio.1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.468, + 0.171 + ], + "angle": 0, + "content": "[2] Nerf-factory. https://github.com/kakaobrain/NeRF-Factory.5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.468, + 0.213 + ], + "angle": 0, + "content": "[3] Snap ml. https://docs.snap.com/lens-studio/references/guides/lens-features/machine-learning/ml-overview.1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.215, + 0.468, + 0.242 + ], + "angle": 0, + "content": "[4] Abien Fred Agarap. 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The unreasonable effectiveness of deep features as a perceptual metric, 2018. 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.758 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8337" + } + ] +] \ No newline at end of file diff --git a/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_origin.pdf b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..693cd8d0398a8d69184d5b8cdab6171efea881f5 --- /dev/null +++ b/2023/Real-Time Neural Light Field on Mobile Devices/7cb4e48b-56d2-4da2-9743-cd9d9c1bc604_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9561ae2f8d28b0f4308d61916ca72c0ddc5ee0a81730f3d104e8751b402707f8 +size 8161334 diff --git a/2023/Real-Time Neural Light Field on Mobile Devices/full.md b/2023/Real-Time Neural Light Field on Mobile Devices/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1f30a9073b85b53eeff4ccacc7ccd9627a8b9b6a --- /dev/null +++ b/2023/Real-Time Neural Light Field on Mobile Devices/full.md @@ -0,0 +1,306 @@ +# Real-Time Neural Light Field on Mobile Devices + +Junli Cao $^{1}$ +Yun Fu $^{2}$ $^{1}$ Snap Inc. + $^{2}$ Northeastern University + +# Abstract + +Recent efforts in Neural Rendering Fields (NeRF) have shown impressive results on novel view synthesis by utilizing implicit neural representation to represent 3D scenes. Due to the process of volumetric rendering, the inference speed for NeRF is extremely slow, limiting the application scenarios of utilizing NeRF on resource-constrained hardware, such as mobile devices. Many works have been conducted to reduce the latency of running NeRF models. However, most of them still require high-end GPU for acceleration or extra storage memory, which is all unavailable on mobile devices. Another emerging direction utilizes the neural light field (NeLF) for speedup, as only one forward pass is performed on a ray to predict the pixel color. Nevertheless, to reach a similar rendering quality as NeRF, the network in NeLF is designed with intensive computation, which is not mobile-friendly. In this work, we propose an efficient network that runs in real-time on mobile devices for neural rendering. We follow the setting of NeLF to train our network. Unlike existing works, we introduce a novel network architecture that runs efficiently on mobile devices with low latency and small size, i.e., saving $15 \times \sim 24 \times$ storage compared with MobileNeRF. Our model achieves high-resolution generation while maintaining real-time inference for both synthetic and real-world scenes on mobile devices, e.g., 18.04ms (iPhone 13) for rendering one $1008 \times 756$ image of real 3D scenes. Additionally, we achieve similar image quality as NeRF and better quality than MobileNeRF (PSNR 26.15 vs. 25.91 on the real-world forward-facing dataset)1. + +# 1. Introduction + +Remarkable progress seen in the domain of neural rendering [33] promises to democratize asset creation and rendering, where no mesh, texture, or material is required - only a neural network that learns a representation of an object or a scene from multi-view observations. The trained + +![](images/fef2965b302550dc264ad99a606696b6ff6980d7c2879f1826e725b8d93ca13f.jpg) +Figure 1. Examples of deploying our approach on mobile devices for real-time interaction with users. Due to the small model size (8.3MB) and fast inference speed $(18\sim 26\mathrm{ms}$ per image on iPhone 13), we can build neural rendering applications where users interact with 3D objects on their devices, enabling various applications such as virtual try-on. We use publicly available software to make the on-device application for visualization [1,3]. + +![](images/57156ce59d767573d681c41698c0310bfe8ebc3676a6d57a96f343ff02c0bf5b.jpg) + +model can be queried at arbitrary viewpoints to generate novel views. To be made widely available, this exciting application requires such methods to run on resource-constrained devices, such as mobile phones, conforming to their limitations in computing, wireless connectivity, and hard drive capacity. + +Unfortunately, the impressive image quality and capabilities of NeRF [33] come with a price of slow rendering speed. To return the color of the queried pixel, hundreds of points need to be sampled along the ray that ends up in that pixel, which is then integrated to get the radiance. To enable real-time applications, many works have been proposed [12, 34, 37, 45], yet, they still require high-end GPUs for rendering and hence are not available for resource-constrained applications on mobile or edge devices. An attempt is made to trade rendering speed with storage in MobileNeRF [10]. While showing promising acceleration results, their method requires storage for texturing saving. For example, for a single real-world scene from the forward-facing dataset [33], MobileNeRF requires 201.5MB of storage. Clearly, downloading and storing tens, hundreds, or even thousands of such scenes in MobileNeRF + +format on a device is prohibitively expensive. + +A different approach is taken in Neural Light Fields (NeLF) that directly maps a ray to the RGB color of the pixel by performing only one forward pass per ray, resulting in faster rendering speed [5, 25, 28, 41]. Training NeLF is challenging and hence requires increased network capacity. For example, Wang et al. [41] propose an 88-layer fully-connected network with residual connections to distill a pretrained radiance model effectively. While their approach achieves better rendering results than vanilla NeRF at $30 \times$ speedup, running it on mobile devices is still not possible, as it takes three seconds to render one $200 \times 200$ image on iPhone 13 shown in our experiments. + +In this work, we propose MobileR2L, a real-time neural rendering model built with mobile devices in mind. Our training follows a similar distillation procedure introduced in R2L [41]. Differently, instead of using an MLP, a backbone network used by most neural representations, we show that a well-designed convolutional network can achieve real-time speed with the rendering quality similar to MLP. In particular, we revisit the network design choices made in R2L and propose to use the $1 \times 1$ Conv layer in the backbone. A further challenge with running a NeRF or NeLF on mobile devices is an excessive requirement of RAM. For example, to render an $800 \times 800$ image, one needs to sample 640,000 rays that need to be stored, causing out-of-memory issues. In 3D-aware generative models [9, 15, 20], this issue is alleviated by rendering a radiance feature volume and upsampling it with a convolutional network to obtain a higher resolution. Inspired by this, we render a light-field volume that is upsampled to the required resolution. Our MobileR2L features several major advantages over existing works: + +- MobileR2L achieves real-time inference speed on mobile devices (Tab. 3) with better rendering quality, e.g., PSNR, than MobileNeRF on the synthetic and real-world datasets (Tab. 1). +- MobileR2L requires an order of magnitude less storage, reducing the model size to 8.3MB, which is $15.2 \times \sim 24.3 \times$ less than MobileNeRF. + +Due to these contributions, MobileR2L can unlock wide adoption of neural rendering in real-world applications on mobile devices, such as a virtual try-on, where the real-time interaction between devices and users is achieved (Fig. 1). + +# 2. Related Works + +Neural Radiance Field (NeRF). NeRF [33] shows the possibility of representing a scene with a simple multi-layer perceptron (MLP) network. Going forward, many extensions follow up in improving rendering quality (e.g., MipNeRF [6], MipNeRF 360 [7], and Ref-NeRF [40]), + +rendering efficiency (e.g., NSVF [29], Nex [43], AutoInt [27], FastNeRF [13], Baking [16], Plenoctree [45], KiloNeRF [37], DeRF [36], DoNeRF [35], R2L [41], and MobileNeRF [10]) and training efficiency (e.g., Plenoxels [12], and Instant-NGP [34]). + +Efficient NeRF Rendering. Since this paper falls into the category of improving rendering efficiency as we target real-time rendering on mobile devices, we single out the papers of this group and discuss them in length here. There are generally four groups. (1) The first group trades speed with space, i.e., they precompute and cache scene representations and the rendering reduces to table lookup. Efficient data structure like sparse octree, e.g., Plenoctree [45], is usually utilized to make the rendering even faster. (2) The second attempts reduce the number of sampled points along the camera ray during rendering as it is the root cause of prohibitively slow rendering speed. Fewer sampled points typically lead to performance degradation, so as compensation, they usually introduce extra information, such as depth, e.g., DoNeRF [35], or mesh, e.g., MobileNeRF [10], to maintain the visual quality. (3) The third group takes a "divide and conquer" strategy. DeRF [36] decomposes the scene spatially to Voronoi diagrams and learns each diagram with a small network. KiloNeRF [37] also employs a decomposition scheme. Differently, they decompose the scene into thousands of small regular grids. Each is addressed with a small network. Such decomposition poses challenges to parallelism. Thus they utilize customized parallelism implementation to obtain speedup. (4) The fourth group is a newly surging one, represented by the recent works RSEN [5] and R2L [41]. They achieve rendering efficiency by representing the scene with NeLF (neural light field) instead of NeRF. NeLF avoids the dense sampling on camera ray, resulting in a much faster rendering speed than NeRF. On the downside, NeLF is typically much harder to learn than NeRF. As a remedy, these works (such as [41]) typically integrate a pre-trained NeRF model as a teacher to synthesize additional pseudo data for distillation [8, 19]. Therefore, the resulting model is fast with a reasonably small representation size, i.e., the model size. + +Neural Light Field (NeLF). Light field is a different way of representing scenes. The idea has a long history in the computer graphics community, e.g., Light fields [25] and Lumigraphs [14] cache plenty of images and enable real-time rendering at the cost of limited camera pose and excessive storage overhead. One of the most intriguing properties of NeLF is that rendering one image only requires one network forward, resulting in a significantly faster speed than NeRF-based methods. With the recent surge of the neural radiance field, some works attempt to revive the idea of the neural light field for efficient neural rendering. Sitzmann et al. [38] materialize the idea of using a neural network to model the scene, and the rendering process reduces to + +a single network forward. Despite the encouraging idea, their method has only been evaluated on scenes with simple shapes, not matching the quality of NeRF on complex real-world scenes. Later, RSEN [5] and R2L [41] are introduced. RSEN divides the space into many voxel grids. Only in each grid, it is a NeLF, which needs alpha-composition to render the final color, making their method a mixture of NeLF and NeRF. R2L [41] is a pure NeLF network that avoids the alpha-composition step in rendering, which is also one of the most relevant works to this paper. However, R2L is still not compact and fast enough for mobile devices. Based on our empirical study, an R2L model runs for around three seconds per frame on iPhone 13 even for low-resolution like $200 \times 200$ . This paper is meant to push the NeRF-to-NeLF idea even further, making it able to perform real-time rendering on mobile devices. + +We will mainly compare to MobileNeRF [10] in this paper as it is the only method, to our best knowledge, that can run on mobile devices with matching quality to NeRF [33]. + +# 3. Methods + +# 3.1. Prerequisites: NeRF and R2L + +NeRF. NeRF [33] represents the scene implicitly with an MLP network $F_{\Theta}$ , which maps the 5D coordinates (spatial location $(x, y, z)$ and view direction $(\theta, \phi)$ ) to a 1D volume density (opacity, denoted as $\sigma$ here) and 3D radiance (denoted as $\mathbf{c}$ ) such that $F_{\Theta}: \mathbb{R}^5 \mapsto \mathbb{R}^4$ . Each pixel of an image is associated with a camera ray. To predict the color $\hat{C}$ of a pixel, the NeRF method samples many points (denoted as $N$ below) along the camera ray and accumulates the radiance $\mathbf{c}$ of all these points via alpha compositing [23, 31, 33]: + +$$ +\hat {C} (\mathbf {r}) = \sum_ {i = 1} ^ {N} T _ {i} \cdot \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) \cdot \mathbf {c} _ {i}, +$$ + +$$ +\left(\mathbf {c} _ {i}, \sigma_ {i}\right) = F _ {\Theta} \left(\mathbf {r} \left(t _ {i}\right), \mathbf {d}\right), \tag {1} +$$ + +$$ +T _ {i} = \exp \left(- \sum_ {j = 1} ^ {i - 1} \sigma_ {j} \delta_ {j}\right), +$$ + +where $\mathbf{r}$ means the camera ray; $\mathbf{r}(t_i) = \mathbf{o} + t_i\mathbf{d}$ represents the location of a point on the ray with origin $\mathbf{o}$ and direction $\mathbf{d}$ ; $t_i$ is the Euclidean distance, i.e., a scalar, of the point away from the origin; and $\delta_{i} = t_{i + 1} - t_{i}$ refers to the distance between two adjacent sampled points. A stratified sampling approach is employed in NeRF [33] to sample the $t_i$ in Eqn. 1. To enrich the input information, the position and direction coordinates are encoded by positional encoding [39], which maps a scalar $(\mathbb{R})$ to a higher dimensional space $(\mathbb{R}^{2L + 1})$ through cosine and sine functions, where $L$ (a predefined constant) stands for the frequency order (in the original NeRF [33], $L = 10$ for positional coordinates and $L = 4$ for direction coordinates). + +![](images/b78159630dc54ca21e0dc603244559a5c6325bebbfff217d5ab29de9e90eceb6.jpg) +Figure 2. Training and Inference Pipeline. The training involves a teacher model to generate pseudo data, which is used to learn the MobileR2L. The teacher model, e.g., NeRF, is trained on real images. Once we have the teacher model, we use it to generate pseudo images, e.g., images with the resolution of $800 \times 800$ , in addition to down-scaled rays, e.g., rays with spatial size as $100 \times 100$ , that share the same origin with the pseudo images to train the MobileR2L. After that, we use the real data to fine-tune MobileR2L. For inference, we directly forward the rays into the pre-trained MobileR2L to render images. + +The whole formulation and training of NeRF are straightforward. One critical problem preventing fast inference in NeRF is that the $N$ , i.e., the number of sampled points, in Eqn. 1 is pretty large (256 in the original NeRF paper due to their two-stage coarse-to-fine design). Therefore, the rendering computation for even a single pixel is prohibitively heavy. The solution proposed by R2L [41] is distilling the NeRF representation to NeLF. + +R2L. Essentially, a NeLF function maps the oriented ray to RGB. To enrich the input information, R2L proposes a new ray representation – they also sample points along the ray just like NeRF [33] does; but differently, they concatenate the points to one vector, which is used as the ray representation and fed into a neural network to learn the RGB. Similar to NeRF, positional encoding [39] is also adopted in R2L to map each scalar coordinate to a high dimensional space. During training, the points are randomly (by a uniform distribution) sampled; during testing, the points are fixed. + +The output of the R2L model is directly RGB, no density learned, and there is no extra alpha-compositing step, which makes R2L much faster than NeRF in rendering. One downside of the NeLF framework is, as shown in R2L [41], the NeLF representation is much harder to learn than NeRF; so as a remedy, R2L proposes an 88-layer deep ResMLP (residual MLP) architecture (much deeper than the network of NeRF) to serve as the mapping function. + +R2L has two stages in training. In the first stage, they use a pre-trained NeRF model as a teacher to synthesize excessive (origin, direction, RGB) triplets as pseudo data; and then fed the pseudo data to train the deep ResMLP. This stage can make the R2L model achieve comparable performance to the teacher NeRF model. In the second stage, they finetune the R2L network from the first stage on + +![](images/d7c8040e2e44d3d779ad3cbb716ec182549120e74ec758444c4015fba315ff6f.jpg) +Figure 3. Overview of Network. The input tensor of MobileR2L has 4D shape: batch, channel, height, and width. The backbone includes residual blocks (RB) that is repeated 28 times ( $N = 28$ ). Following the backbone, there are two types of super-resolution (SR) modules. The first SR module $(\mathrm{SR}^1)$ has kernel size $4 \times 4$ in the Transpose CONV layer that doubles the input $H, W$ to $2H, 2W$ , whereas the second SR module $(\mathrm{SR}^2)$ has kernel size $3 \times 3$ , tripling the spatial size to $3H, 3W$ . The configuration of $3 \times \mathrm{SR}^1$ is used in the synthetic $360^\circ$ dataset that upsamples the input $8 \times$ . For the real-world forward-facing dataset, we use the combination of $2 \times \mathrm{SR}^1 + \mathrm{SR}^2$ that upsamples the input $12 \times$ . Moreover, we use various output channels across RB and SR: $C_1 = 256$ , $C_2 = 64$ , and $C_3 = 16$ . + +the original data – this step can further boost the rendering quality as shown in the R2L work [41]. + +# 3.2. MobileR2L + +# 3.2.1 Overview + +We follow the learning process of R2L to train our proposed MobileR2L, namely, using a pre-trained teacher model, such as NeRF [33], to generate pseudo data for the training of a lightweight neural network. To reduce the inference speed, we aim only to forward the network once when rendering an image. However, under the design of R2L, although one pixel only requires one network forward, directly feeding rays with large spatial size, e.g., $800 \times 800$ , into a network causes memory issues. Therefore, R2L forwards a partial of rays each time, increasing the speed overhead. To solve the problem, we introduce super-resolution modules, which upsample the low-resolution input, e.g., $100 \times 100$ , to a high-resolution image. Thus, we can obtain a high-resolution image with only one forward pass of the neural network during inference time. The training and inference pipeline is illustrated in Fig. 2, and we introduce more details for our network architecture in the following. + +# 3.2.2 Network Architectures + +The input rays can be represented as $\mathbf{x} \in \mathbb{R}^{B,6,H,W}$ , where $B$ denotes the batch size and $H$ and $W$ denote the spatial size. The ray origin and view directions are concatenated as the second dimension of $\mathbf{x}$ . We then apply positional encoding $\gamma(\cdot)$ on $\mathbf{x}$ to map the ray origin and view directions into a higher dimension. Thus, we get the input of our neural + +network as $\gamma (\mathbf{x})$ + +The network includes two main parts: an efficient backbone and Super-Resolution (SR) modules for high-resolution rendering, with the architecture provided in Fig. 3. Instead of using Fully Connected (FC) or linear layers for the network that is adopted by existing works [33, 41], we only apply convolution (CONV) layers in the backbone and super-resolution modules. + +There are two main reasons for replacing FC with CONV layers. First, the CONV layer is better optimized by compilers than the FC layer [30]. Under the same number of parameters, the model with CONV $1 \times 1$ runs around $27\%$ faster than the model with FC layers, as shown in Tab. 4. Second, suppose FC is used in the backbone, in that case, extra Reshape and Permute operations are required to modify the dimension of the output features from the FC to make the features compatible with the CONV layer in the super-resolution modules, as the FC and CONV calculate different tensor dimensions. However, such Reshape or Permute operation might not be hardware-friendly on some mobile devices [26]. With the CONV employed as the operator in the network, we then present more details for the backbone and SR modules. + +Efficient Backbone. The architecture of the backbone follows the design of residual blocks from R2L [41]. Different from R2L, we adopt the CONV layer instead of the FC layer in each residual block. The CONV layer has the kernel size and stride as 1. Additionally, we use the normalization and activation functions in each residual block, which can improve the network performance without introducing latency overhead (see experimental details in Tab. 4). The normalization and activation are chosen as batch normaliza + +tion [21] and GeLU [17]. The backbone contains 60 CONV layers in total. + +Super-Resolution Modules. To reduce the latency when running the neural rendering on mobile devices, we aim to forward the neural network once to get the synthetic image. However, the existing network design of the neural light field requires large memory for rendering a high-resolution image, which surpasses the memory constraint on mobile devices. For example, rendering an image of $800 \times 800$ requires the prediction of 640,000 rays. Forwarding these rays at once using the network from R2L [41] causes the out of memory issue even on the Nvidia Tesla A100 GPU (40G memory). + +To reduce the memory and latency cost for high-resolution generation, instead of forwarding the number of rays that equals to the number of pixels, we only forward a partial of rays and learn all the pixels via super-resolution. Specifically, we propose to use the super-resolution modules following the efficient backbone to upsample the output to a high-resolution image. For example, to generate a $800 \times 800$ image, we forward a 4D tensor $\mathbf{x}$ with spatial size as $100 \times 100$ to the network and upsample the output from backbone three times (i.e., upsample by $2 \times$ each time). The SR module includes two stacked residual blocks. The first block includes three CONV layers with one as a 2D Transpose CONV layer and two CONV $1 \times 1$ layers; the second block includes two CONV $1 \times 1$ layers. After the SR modules, we apply another CONV layer followed by the Sigmoid activation to predict the final RGB color. We denote our model as $D60-SR3$ where it contains 60 CONV layers in the efficient backbone and 3 SR modules. + +# 4. Experiments + +Datasets. We conduct the comparisons mainly on two datasets: realistic synthetic $360^{\circ}$ [33] and real-world forward-facing [32, 33]. The synthetic $360^{\circ}$ dataset contains 8 path-traced scenes, with each scene including 100 images for training and 200 images for testing. Forward-facing contains 8 real-world scenes captured by cellphones, where the images in each scene vary from 20 to 60, and 1/8 images are used for testing. We conduct our experiments (training and testing) on the resolution of $800 \times 800$ for synthetic $360^{\circ}$ and $1008 \times 756$ ( $4 \times$ down-scaled from the original resolution) for forward-facing. + +Implementation Details. We follow the training scheme of R2L [41], i.e., using a teacher model to render pseudo images for the training of MobileR2L network. Specifically, we synthesize 10K pseudo images from the pretrained teacher model [2] for each scene. We first train our MobileR2L on the generated pseudo data and then fine-tune it on the real data, as shown in Fig. 2. In all the experiments, we employ Adam [24] optimizer with an initial learning rate $5 \times 10^{-4}$ that decays during the training. Our experiments + +Table 1. Quantitative Comparison on Synthetic $360^{\circ}$ and Forward-facing. Our method obtains better results on the three metrics than NeRF for the two datasets. Compared with MoibleNeRF and SNeRG, we achieve better results on most of the metrics. + +
Synthetic 360°Forward-facing
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF [33]31.010.9470.08126.500.8110.250
NeRF-Pytorch [44]30.920.9910.04526.260.9650.153
SNeRG [16]30.380.9500.05025.630.8180.183
MoibleNeRF [10]30.900.9470.06225.910.8250.183
MobileR2L (Ours)31.340.9930.05126.150.9660.187
Our Teacher33.090.9610.05226.850.8270.226
+ +are conducted on a cluster of Nvidia V100 and A100 GPUs with the batch size as 54 for the main results on the synthetic $360^{\circ}$ and batch size as 36 on the forward-facing dataset. + +Different from R2L, the spatial size of the input rays and the output rendered images in our approach are different. For each high-resolution image generated by the teacher model, we save the input rays corresponding to a lower-resolution image where the camera origins and directions are the same as the high-resolution one while the focal length is down-scaled accordingly. Additionally, we do not sample the rays from different images as in R2L. Instead, the rays in each training sample share the same origin and reserve their spatial locations. + +Considering the training data of the synthetic $360^{\circ}$ and forward-facing datasets have different resolutions, the spatial size of the inputs for the two datasets are slightly different. Our network takes input with the spatial size of $100 \times 100$ for the synthetic $360^{\circ}$ dataset and upsamples by $8 \times$ to render $800 \times 800$ RGB images. In contrast, the spatial size of $84 \times 63$ is used in the forward-facing dataset, and $1008 \times 756$ image ( $12 \times$ upsampling) is rendered. The kernel size and padding are adjusted in the last transposed CONV layer to achieve $8 \times$ and $12 \times$ upsampling with the 3 SR blocks. + +# 4.1. Comparisons + +Rendering Performance. To understand the image quality of various methods, we report three common metrics: PSNR, SSIM [42], and LPIPS [46], on the realistic synthetic $360^{\circ}$ and real forward-facing datasets, as demonstrated in Tab. 1. Compared with NeRF [33], our approach achieves better results on PSNR, SSIM, and LPIPS for the synthetic $360^{\circ}$ dataset. On the forward-facing dataset, we obtain better SSIM and LPIPS than NeRF [33]. Similarly, our method achieves better results for all three metrics than MobileNeRF [10] on the synthetic $360^{\circ}$ dataset and better PSNR and SSIM on the forward-facing dataset. Compared to SNeRG [16], our method obtains better PSNR and SSIM. + +We also show the performance of the teacher model used + +![](images/5fd7a6642c63608340bf6b784255b928509af907e8352b58a0fce8678ab29304.jpg) + +![](images/b7a2131094147d260d25a1d439c21056e0e0c405a45598e4386da43c4a46dfd1.jpg) +Lego +Fern + +![](images/4b55c15ab20f22fb52be3bdf2518128f0bd22f82e6baf6fdb4559282fe4dd7ec.jpg) + +![](images/0bd481d43cd0f8ad706f03693b6f28c0b20b6b7de5eb3d98fbf668f0a84df39a.jpg) + +![](images/69babc26c8eabe28ba2db8f35764caf7fe7d449244a3fb30ab0d676fb331876e.jpg) + +![](images/5635a21ef9217b8f63dac0cdc13df8818ad4afa8dddc0edb4f08542687800653.jpg) +(a) GT +(a) GT + +![](images/a99a03eb7189e3e57d94043f5e8c5cabbfe6dbcdf6deab9e0d7ad70a22dcecc2.jpg) +(b) NeRF +(b) NeRF + +![](images/db78f6ac0c3ed541b168b580a4f7bbad2d3904ae571c3a6c7720e158e1ead060.jpg) +(c) Ours +(c) Ours + +![](images/2cb0d4918fa053bd8a6acab3026711329187b3dd22c8eda4c2e101081ad7a896.jpg) +Figure 4. Visual comparison between our method and NeRF [33] (trained via NeRF-Pytorch [44]) on the synthetic $360^{\circ}$ Lego (size: $800 \times 800 \times 3$ ) and real-world forward-facing scene Fern (size: $1008 \times 756 \times 3$ ). Best viewed in color. Please refer to our webpage for more visual comparison results. + +![](images/b32c4171038d900d2ed385cc33b9b48cfef85bccbb67322329c5b09f73270db0.jpg) +Figure 5. Zoom-in comparisons. Top row: MobileNeRF [10]. Results are obtained from the code and demo released by the authors. Bottom row: MobileR2L. Our approach renders high-quality images even for zoom-in views. + +in training MobileR2L in Tab. 1 (Our Teacher). Note that there is still a performance gap between the student model (MobileR2L) and the teacher model. However, as we show following (Tab. 5), a better teacher model can lead to a student model with higher performance. Compared with MoibleNeRF and SNeRG, our approach has the advantage that we can directly leverage the high-performing teacher models to help improve student training in different application scenarios. We further show the qualitative comparison results in Fig. 4. On the synthetic scene Lego, our MobileR2L outperforms NeRF clearly, delivering sharper and less distorted shapes and textures. On the real-world scene Fern, our result is less noisy, and the details, e.g., the leaf tips, are sharper. Additionally, we provide the zoom-in comparison with MoibleNeRF [10] in Fig. 5. Our method achieves high-quality rendering for zoom-in view, which is + +Table 2. Analysis of Storage (MB) required for different rendering methods. Our method has a clear advantage over existing works with much less storage required. + +
Synthetic 360°Forward-facing
MobileNeRF [10]SNeRG [16]OursMobileNeRF [10]SNeRG [16]Ours
Disk storage125.886.88.3201.5337.38.3
+ +Table 3. Analysis of Inference Speed. Latency (ms) is obtained on iPhone with iOS 16. Following MoibleNeRF [10], we use the notation $\frac{M}{N}$ to indicate that $M$ out of $N$ scenes in the Forward-facing dataset that can not run on devices. Specifically, MobileNeRF can not render Leaves and Orchids in Forward-facing. + +
Synthetic 360°Forward-facing
MobileNeRF [10]OursMobileNeRF [10]Ours
iPhone 1317.5426.2127.15 2/818.04
iPhone 1416.6722.6520.98 2/816.48
+ +especially important for 3D assets that users might perform zoom-in to look for more image details. + +Disk Storage. One significant advantage of our method is that we do not require extra storage, even for complex scenes. As shown in Tab. 2, the storage of our approach is $8.3\mathrm{MB}$ for both synthetic $360^{\circ}$ and forward-facing datasets. The mesh-based methods like MobileNeRF demand more storage for real-world scenes due to saving more complex textures. As a result, our approach takes $24.3\times$ less disk storage than MobileNeRF on the forward-facing, and $15.2\times$ less storage on the synthetic $360^{\circ}$ dataset. + +Inference Speed. We profile and report the rendering speed of our proposed approach on iPhones (13, and 14, iOS 16) in Tab. 3. The models are compiled with CoreMLTools [11]. Our proposed method runs faster on real forward-facing scenes than the realistic synthetic $360^{\circ}$ scenes. The latency discrepancy between the two datasets comes from the different input spatial sizes. MobileNeRF shows a lower latency than our models on the realistic synthetic $360^{\circ}$ but higher on the real-world scenes. Both methods can run in real-time on devices. Note that MobileNeRF cannot render two scenes, i.e., Leaves and Orchids, due to memory issues, as they require complex textures to model the geometry. In contrast, our approach is robust for different scenes. + +Discussion. From the comparison of the rendering quality, disk storage, and inference speed, it can be seen that MobileR2L achieves overall better performance than MobileN-eRF. More importantly, considering the usage of neural rendering on real-world applications, MobileR2L is more suitable as it requires much less storage, reducing the constraint for hardware and can render real-world scenes in real-time on mobile devices. + +# 4.2. Ablation Analysis + +Here we perform the ablation analysis to understand the design choices of the network. We use the scene of Chair from the synthetic $360^{\circ}$ to conduct the analysis. All models are trained for 200K iterations. + +Options for Backbone. We study the two available operators for designing the backbone. MLP and $1 \times 1$ CONV layer are essentially equivalent operators and perform the same calculations, thus resulting in similar performance. However, we observe around $27\%$ latency reduction on mobile devices (iPhone 13) when replacing the MLP layer with the $1 \times 1$ CONV layer. Specifically, as shown in Tab. 4, we design two networks, i.e., MLP and CONV2D, with only residual blocks as in Fig. 3 but removing the activation, normalization, and super-resolution modules. We use the input size as $100 \times 100$ for the two models. Since the super-resolution modules are omitted, we train the two networks for generating $100 \times 100$ images. As can be seen, the CONV2D model has a faster inference speed than MLP with similar performance. This is due to the fact that CONV operation is better-optimized than MLP on mobile devices. Additionally, due to the intrinsic design of our proposed MobileR2L, employing MLP layers requires two additional operators, i.e., Permute and Reshape, before feeding the internal features to super-resolution modules, while Permute and Reshape involve data movement that adds unnecessary overheads on some edge devices [26]. + +Analysis of Activation Function. R2L [41] and NeRF [33] use ReLU [4] activation as non-linearity function. In our proposed MobileR2L, we use GELU [18] instead. As shown in Tab. 4, by comparing the $CONV2D + ReLU$ and $CONV2D + GeLU$ , which are two networks trained with ReLU and GeLU activations, we notice that GeLU brings about 0.17 PSNR boost without any additional latency overhead. Similarly, we show that incorporating BatchNorm [22] layer into the ResBlock is also beneficial for better performance without introducing extra latency, as shown by $CONV2D + GeLU + BN$ in Tab. 4. The three networks in the experiments are also trained to render $100 \times 100$ images. + +Analysis on Input Dimension. We further analyze the optimal spatial resolution for the input tensor. Specifically, we benchmark the performance of three approaches, namely, $50 \times 50 - \text{NeRF Teacher}$ , $100 \times 100 - \text{NeRF Teacher}$ , and $200 \times 200 - \text{NeRF Teacher}$ with the spatial size of input as the square of 50, 100, and 200 respectively. These models contain super-resolution modules to render $800 \times 800$ images and are trained with the NeRF [33] as a teacher model. Results are presented in Tab. 5. The model using a small input spatial size, i.e., $50 \times 50$ , achieves $2 \times$ speedup than the model with a larger size, i.e., $100 \times 100$ , as less computation is required. However, the performance is also degraded by 0.25 PSNR. Further increasing the input spatial size to $200 \times 200$ makes the model unable to achieve real-time in- + +Table 4. Analysis of Network Design. For all the comparisons, we use the input tensor with the spatial size as $100 \times 100$ and render the image with spatial size. The latency (ms) is measured on iPhone 13 (iOS16) with models compiled with CoreMLTools [11] + +
PSNR↑SSIM↑LPIPS↓Latency↓
MLP19.130.97590.663019.57
CONV2D19.160.97590.630114.30
CONV2D + ReLU26.820.99490.028216.20
CONV2D + GeLU26.990.99490.073017.00
CONV2D + GeLU + BN27.180.99540.025917.00
+ +Table 5. Analysis of the spatial size of the input, usage of teacher model, and ray presentation. Besides image quality metrics, we show the number of parameters for each model and the latency when running on iPhone 13. + +
ParamsPSNR↑SSIM↑LPIPS↓Latency↓
50 × 50 - NeRF Teacher3.9M30.400.99650.068613.04
100 × 100 - NeRF Teacher3.9M30.650.99660.066826.21
200 × 200 - NeRF Teacher3.9M---73.76
800 × 800 - w/o SR3.9M---Error
100 × 100 - MipNeRF Teacher3.9M30.830.09970.056426.21
100 × 100 - MipNeRF Teacher, K16, L104.1M30.900.99680.058331.05
100 × 100 - MipNeRF Teacher, K16, L10, D1006.8M31.370.99720.047044.52
+ +ference. Thus, we do not report the rendering performance of the models with $200 \times 200$ input size. + +Analysis of SR modules. We further show the necessity of using SR modules. We use the spatial size of $800 \times 800$ as the network input to render images with the same spatial size. We denote the setting as $800 \times 800 - w / o$ SR in Tab. 5. Profiling the latency of such a network leads to compilation errors due to intensive memory usage. Thus, our proposed SR module is essential for high-resolution synthesis without introducing prohibitive computation overhead. + +Choice of Teacher Models. Since both R2L [41] and MobileR2L use a teacher model for generating pseudo data to train a lightweight network, we study whether a more powerful teacher model can improve performance. To conduct the experiments, we use MipNeRF [6] as the teacher model for the training MobileR2L, given MipNeRF shows better performance than NeRF on the synthetic $360^{\circ}$ dataset. We denote the approach as $100 \times 100 -$ MipNeRF Teacher. Through the comparison with $100 \times 100 -$ NeRF Teacher, as in Tab. 5, we notice the quality of the rendered images is improved, e.g., the PSNR is increased by 0.18, without the extra cost of latency. The comparison demonstrates that our approach has the potential to render higher-quality images when better teacher models are provided. + +Analysis on Ray Representation. Here we analyze how the ray representation affects the latency-performance trade-off of MobileR2L. We follow the same ray representation paradigm as in R2L [41] and positional encoding as in NeRF [33]. Specifically, R2L sample $K$ 3D points along + +the ray, and each point is mapped to a higher dimension by positional encoding with $L$ positional coordinates. R2L sets $K = 16$ and $L = 10$ , resulting in a vector with a dimension of 1,008. We apply the same setting to MobileR2L and denote the model as $100 \times 100$ , $K_{16}$ , $L_{10}$ -MipNeRF Teacher in Tab. 5. For our implementation in MobileR2L, we set $K = 8$ and $L = 6$ for the model, which has the dimension per ray as 312. The model is $100 \times 100$ -MipNeRF Teacher. By comparing the performance of the two models, we notice that larger $K$ and $L$ lead to negligible PSNR improvement (0.07), yet higher inference latency and bigger model size (more parameters). Therefore, we chose $K = 8$ and $L = 6$ for the consideration of model size and latency - they are the more important metrics when deploying neural rendering models on mobile devices. + +Depth of the Backbone. Lastly, we show the effects of the backbone depth on the model performance. We use the depth as 60 for our backbone. By increasing the number of residual blocks in the backbone, i.e., setting depth as 100, we obverse better model performance at the cost of higher latency, as shown by comparing the last two rows in Tab. 5. Using depth as 100 significantly increases the latency and the number of parameters, and the model fails to run in real time. Thus, we chose depth as 60, given the better trade-off between latency, model size, and performance. + +# 4.3. Real-World Application + +Here we demonstrate the usage of our technique for building a real-world application. Given the small size and faster inference speed of our model, we create a shoes try-on application that runs on mobile devices. Users can directly try on the shoes rendered by MobileR2L using their devices, enabling real-time interaction. + +The pipeline for building the application is illustrated in Fig. 6. We first use iPhone to capture 100 shoe images for training. The images are then segmented to remove the background. After that, we train a NeRF model [33] to generate pseudo data, which is later used for learning MobileR2L to render images in $1008 \times 756$ resolution. We apply foot tracking and overlay the rendered shoe on top of the user's feet. As can be seen from Fig. 6, our model is able to render high-quality images from various views for different users. The try-on usage proves the potential of leveraging neural rendering for building various real-time interactive applications such as Augment Reality. + +# 5. Limitation and Conclusion + +This work presents MobileR2L, the first neural light network that renders images with similar quality as NeRF [33] while running in real-time on model devices. We perform extensive experiments to design an optimized network architecture that can be trained via data distillation to render high-resolution images, e.g., $800 \times 800$ . Additionally, + +![](images/2d923b7f34ecce8d146025a3af31e3879d37f907ae8395299dfd4e329bb9bf8d.jpg) +(a) Example Images from Collected Data + +![](images/23b1efac456c0bb1b7dc3661d3854dbf68d87322815b3c04839c2800adf1a3c4.jpg) +(b) Segmented Images + +![](images/baac3193307d63efa3292e67bf92ad0b558e53923a696352f75b4721cf74900b.jpg) + +![](images/6de13707ba3094539ba866d9cd6c002590d31af35aa37738c7c6ae32d32f3fb3.jpg) +(c) Novel View Synthesis for Virtual Try-On + +![](images/bcc19e1d1520af58ef2c4db821a804d8a45ddd74dc7dd50e0c128d883a3239fc.jpg) + +![](images/ddb2f28e8799e96f7e1dd23e6fc9a0624a02d5e10fcfcf2fb0fae26cfab91324.jpg) + +![](images/ce7338fe83a6b70c382a8f4bc4a3c12087acce92dc85e0c0470ebd8925d117a4.jpg) + +![](images/4d352db590897b23a9b3765ad99cc8ac0c89dc015f7e5ddf8df06b4055a580cf.jpg) + +![](images/02d545f524cfca394a554a4982ba1ed62a31e24f8c4ec897776b136adf39236c.jpg) +Figure 6. Virtual Try-On Application. From the collected images using a cellphone (a), we segment the foreground shoe (b) to train a MobileR2L model. We deploy the model on mobile devices, and users can directly try the shoe. The model renders images for novel views when users rotate the phone or change the foot positions (c). +Room +Figure 7. Visual comparison on the real-world scene Room. Both our model and NeRF fail to synthesize the whiteboard writings on the upper-left of the cutout patch. + +![](images/a93316771dfbc4e5a7b4effa07eda2a4bebe5ee75a24cf148a4b9a4adebd0d3c.jpg) +(a) GT + +![](images/5c6500f3a60e6200bc88d82d65a4b011cbd5cf8f265b9634f64c481c27b63c0f.jpg) +(b) NeRF + +![](images/ff6ffe67e1d17985fc3b9a06f7516032e27069d1a7b77f217644ffe751fd2160.jpg) +(c) Ours + +since we do not require other information besides the neural network, MobileR2L dramatically saves the representation storage in stark contrast to other mesh-based methods like MoibleNeRF [10]. Furthermore, we prove that with our design, neural rendering can be used to build real-world applications, achieving real-time user interaction. + +Although MobileR2L achieves promising inference speed with small model sizes, there are still two limitations of the current work that can be improved. First, we follow the training recipe of R2L [41], and R2L uses 10K pseudo images generated by the teacher NeRF model to train the student model. The number of training images is much more than the images used to train the teacher NeRF (which only requires around 100 images), resulting in a longer training time than NeRF-based methods. Therefore, a future direction could be reducing the training costs for distillation-based works like R2L and this work. Second, MobileR2L fails to generate some high-frequency details in the images. We show examples in Fig. 7. Using a larger model may alleviate this problem given a larger model capacity. Nevertheless, the inference latency will also increase accordingly on mobile devices. Future efforts may focus on optimizing the network and training pipeline to boost the performance of the current model. + +# References + +[1] Lens studio. https://ar.sun.com/en-US/lens-studio.1 +[2] Nerf-factory. https://github.com/kakaobrain/NeRF-Factory.5 +[3] Snap ml. https://docs.snap.com/lens-studio/references/guides/lens-features/machine-learning/ml-overview.1 +[4] Abien Fred Agarap. Deep learning using rectified linear units (relu), 2018. 7 +[5] Benjamin Attal, Jia-Bin Huang, Michael Zollhöfer, Johannes Kopf, and Changil Kim. Learning neural light fields with ray-space embedding. In CVPR, 2022. 2, 3 +[6] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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Mobilenerf: Exploiting the polygon rasterization pipeline for efficient neural field rendering on mobile architectures. arXiv preprint arXiv:2208.00277, 2022. 1, 2, 3, 5, 6, 8, 12 +[11] CoreMLTools. Use coremltools to convert models from third-party libraries to core ml., 2021. 6, 7, 11 +[12] Fridovich-Keil and Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In CVPR, 2022. 1, 2 +[13] Stephan J Garbin, Marek Kowalski, Matthew Johnson, Jamie Shotton, and Julien Valentin. Fastnerf: High-fidelity neural rendering at 200fps. arXiv preprint arXiv:2103.10380, 2021. 2 +[14] Steven J Gortler, Radek Grzeszcuk, Richard Szeliski, and Michael F Cohen. The lumigraph. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques, 1996. 2 +[15] Jiatao Gu, Lingjie Liu, Peng Wang, and Christian Theobalt. Stylererf: A style-based 3d-aware generator for high-resolution image synthesis. arXiv preprint arXiv:2110.08985, 2021. 2 +[16] Peter Hedman, Pratul P Srinivasan, Ben Mildenhall, Jonathan T Barron, and Paul Debevec. Baking neural radiance fields for real-time view synthesis. In Proceedings + +of the IEEE/CVF International Conference on Computer Vision, pages 5875-5884, 2021. 2, 5, 6 +[17] Dan Hendrycks and Kevin Gimpel. Gaussian error linear units (gelus). arXiv preprint arXiv:1606.08415, 2016. 5 +[18] Dan Hendrycks and Kevin Gimpel. Gaussian error linear units (gelus), 2016. 7 +[19] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. In NIPS Workshop, 2014. 2 +[20] Yang Hong, Bo Peng, Haiyao Xiao, Ligang Liu, and Juyong Zhang. Headnerf: A realtime nerf-based parametric head model. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Jun 2022. 2 +[21] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International conference on machine learning, pages 448-456. PMLR, 2015. 5 +[22] Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift, 2015. 7 +[23] James T Kajiya and Brian P Von Herzen. Ray tracing volume densities. SIGGRAPH, 18(3):165-174, 1984. 3 +[24] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2014. 5 +[25] Marc Levoy and Pat Hanrahan. Light field rendering. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 31-42, 1996. 2 +[26] Yanyu Li, Geng Yuan, Yang Wen, Eric Hu, Georgios Evangelidis, Sergey Tulyakov, Yanzhi Wang, and Jian Ren. Efficientformer: Vision transformers at mobilenet speed. arXiv preprint arXiv:2206.01191, 2022. 4, 7 +[27] David B Lindell, Julien NP Martel, and Gordon Wetzstein. Autoint: Automatic integration for fast neural volume rendering. In CVPR, 2021. 2 +[28] Celong Liu, Zhong Li, Junsong Yuan, and Yi Xu. Neulf: Efficient novel view synthesis with neural 4d light field. In EGSR, 2022. 2 +[29] Lingjie Liu, Jiatao Gu, Kyaw Zaw Lin, Tat-Seng Chua, and Christian Theobalt. Neural sparse voxel fields. In NeurIPS, 2020. 2 +[30] Xingyu Liu, Jeff Pool, Song Han, and William J Dally. Efficient sparse-winograd convolutional neural networks. arXiv preprint arXiv:1802.06367, 2018. 4 +[31] Nelson Max. Optical models for direct volume rendering. TVCG, 1(2):99-108, 1995. 3 +[32] Ben Mildenhall, Pratul P Srinivasan, Rodrigo Ortiz-Cayon, Nima Khademi Kalantari, Ravi Ramamoorthi, Ren Ng, and Abhishek Kar. Local light field fusion: Practical view synthesis with prescriptive sampling guidelines. ACM Transactions on Graphics (TOG), 38(4):1-14, 2019. 5 +[33] Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In ECCV, 2020. 1, 2, 3, 4, 5, 6, 7, 8, 11, 12 +[34] Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM Trans. Graph., 41(4):102:1-102:15, July 2022. 1, 2 + +[35] Thomas Neff, Pascal Stadlbauer, Mathias Parger, Andreas Kurz, Joerg H. Mueller, Chakravarty R. Alla Chaitanya, Anton S. Kaplanyan, and Markus Steinberger. DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks. Comput. Graph. Forum, 2021. 2 +[36] Daniel Rebain, Wei Jiang, Soroosh Yazdani, Ke Li, Kwang Moo Yi, and Andrea Tagliasacchi. Derf: Decomposed radiance fields. In CVPR, 2021. 2 +[37] Christian Reiser, Songyou Peng, Yiyi Liao, and Andreas Geiger. Kilonerf: Speeding up neural radiance fields with thousands of tiny mlps. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14335-14345, 2021. 1, 2 +[38] Vincent Sitzmann, Semon Rezchikov, William T Freeman, Joshua B Tenenbaum, and Fredo Durand. Light field networks: Neural scene representations with single-evaluation rendering. In NeurIPS, 2021. 2 +[39] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In NeurIPS, 2017. 3 +[40] Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. Ref-nerf: Structured view-dependent appearance for neural radiance fields. In CVPR, 2022. 2 +[41] Huan Wang, Jian Ren, Zeng Huang, Kyle Olszewski, Mengei Chai, Yun Fu, and Sergey Tulyakov. R2l: Distilling neural radiance field to neural light field for efficient novel view synthesis. In ECCV, 2022. 2, 3, 4, 5, 7, 8, 11 +[42] Zhou Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4):600-612, 2004. 5 +[43] Suttisak Wizadwongsa, Pakkapon Phongthawee, Jiraphon Yenphraphai, and Supasorn Suwajanakorn. Nex: Real-time view synthesis with neural basis expansion. In CVPR, 2021. 2 +[44] Lin Yen-Chen. Nerf-pytorch. https://github.com/yenchenlin/nerf-pytorch/, 2020. 5, 6, 11, 12 +[45] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5752-5761, 2021. 1, 2 +[46] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. 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Additionally, we achieve similar image quality as NeRF and better quality than MobileNeRF (PSNR 26.15 vs. 25.91 on the real-world forward-facing dataset)1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "content": "Remarkable progress seen in the domain of neural rendering [33] promises to democratize asset creation and rendering, where no mesh, texture, or material is required - only a neural network that learns a representation of an object or a scene from multi-view observations. The trained" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 213, + 416, + 340 + ], + "blocks": [ + { + "bbox": [ + 309, + 213, + 416, + 340 + ], + "lines": [ + { + "bbox": [ + 309, + 213, + 416, + 340 + ], + "spans": [ + { + "bbox": [ + 309, + 213, + 416, + 340 + ], + "type": "image", + "image_path": "fef2965b302550dc264ad99a606696b6ff6980d7c2879f1826e725b8d93ca13f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 350, + 547, + 428 + ], + "lines": [ + { + "bbox": [ + 304, + 350, + 547, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 547, + 428 + ], + "type": "text", + "content": "Figure 1. Examples of deploying our approach on mobile devices for real-time interaction with users. Due to the small model size (8.3MB) and fast inference speed " + }, + { + "bbox": [ + 304, + 350, + 547, + 428 + ], + "type": "inline_equation", + "content": "(18\\sim 26\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 350, + 547, + 428 + ], + "type": "text", + "content": " per image on iPhone 13), we can build neural rendering applications where users interact with 3D objects on their devices, enabling various applications such as virtual try-on. We use publicly available software to make the on-device application for visualization [1,3]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 430, + 213, + 545, + 340 + ], + "blocks": [ + { + "bbox": [ + 430, + 213, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 430, + 213, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 430, + 213, + 545, + 340 + ], + "type": "image", + "image_path": "57156ce59d767573d681c41698c0310bfe8ebc3676a6d57a96f343ff02c0bf5b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "content": "model can be queried at arbitrary viewpoints to generate novel views. To be made widely available, this exciting application requires such methods to run on resource-constrained devices, such as mobile phones, conforming to their limitations in computing, wireless connectivity, and hard drive capacity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "Unfortunately, the impressive image quality and capabilities of NeRF [33] come with a price of slow rendering speed. To return the color of the queried pixel, hundreds of points need to be sampled along the ray that ends up in that pixel, which is then integrated to get the radiance. To enable real-time applications, many works have been proposed [12, 34, 37, 45], yet, they still require high-end GPUs for rendering and hence are not available for resource-constrained applications on mobile or edge devices. An attempt is made to trade rendering speed with storage in MobileNeRF [10]. While showing promising acceleration results, their method requires storage for texturing saving. For example, for a single real-world scene from the forward-facing dataset [33], MobileNeRF requires 201.5MB of storage. Clearly, downloading and storing tens, hundreds, or even thousands of such scenes in MobileNeRF" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 188, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 188, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 188, + 713 + ], + "type": "text", + "content": "1More demo examples in our Webpage." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8328" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "type": "text", + "content": "format on a device is prohibitively expensive." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "text", + "content": "A different approach is taken in Neural Light Fields (NeLF) that directly maps a ray to the RGB color of the pixel by performing only one forward pass per ray, resulting in faster rendering speed [5, 25, 28, 41]. Training NeLF is challenging and hence requires increased network capacity. For example, Wang et al. [41] propose an 88-layer fully-connected network with residual connections to distill a pretrained radiance model effectively. While their approach achieves better rendering results than vanilla NeRF at " + }, + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "inline_equation", + "content": "30 \\times" + }, + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "text", + "content": " speedup, running it on mobile devices is still not possible, as it takes three seconds to render one " + }, + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "inline_equation", + "content": "200 \\times 200" + }, + { + "bbox": [ + 46, + 85, + 287, + 228 + ], + "type": "text", + "content": " image on iPhone 13 shown in our experiments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "text", + "content": "In this work, we propose MobileR2L, a real-time neural rendering model built with mobile devices in mind. Our training follows a similar distillation procedure introduced in R2L [41]. Differently, instead of using an MLP, a backbone network used by most neural representations, we show that a well-designed convolutional network can achieve real-time speed with the rendering quality similar to MLP. In particular, we revisit the network design choices made in R2L and propose to use the " + }, + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "text", + "content": " Conv layer in the backbone. A further challenge with running a NeRF or NeLF on mobile devices is an excessive requirement of RAM. For example, to render an " + }, + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 228, + 289, + 469 + ], + "type": "text", + "content": " image, one needs to sample 640,000 rays that need to be stored, causing out-of-memory issues. In 3D-aware generative models [9, 15, 20], this issue is alleviated by rendering a radiance feature volume and upsampling it with a convolutional network to obtain a higher resolution. Inspired by this, we render a light-field volume that is upsampled to the required resolution. Our MobileR2L features several major advantages over existing works:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 478, + 286, + 561 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 48, + 478, + 286, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 478, + 286, + 525 + ], + "spans": [ + { + "bbox": [ + 48, + 478, + 286, + 525 + ], + "type": "text", + "content": "- MobileR2L achieves real-time inference speed on mobile devices (Tab. 3) with better rendering quality, e.g., PSNR, than MobileNeRF on the synthetic and real-world datasets (Tab. 1)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 526, + 286, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 526, + 286, + 561 + ], + "spans": [ + { + "bbox": [ + 48, + 526, + 286, + 561 + ], + "type": "text", + "content": "- MobileR2L requires an order of magnitude less storage, reducing the model size to 8.3MB, which is " + }, + { + "bbox": [ + 48, + 526, + 286, + 561 + ], + "type": "inline_equation", + "content": "15.2 \\times \\sim 24.3 \\times" + }, + { + "bbox": [ + 48, + 526, + 286, + 561 + ], + "type": "text", + "content": " less than MobileNeRF." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 572, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 620 + ], + "type": "text", + "content": "Due to these contributions, MobileR2L can unlock wide adoption of neural rendering in real-world applications on mobile devices, such as a virtual try-on, where the real-time interaction between devices and users is achieved (Fig. 1)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 633, + 138, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 138, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 138, + 645 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "type": "text", + "content": "Neural Radiance Field (NeRF). NeRF [33] shows the possibility of representing a scene with a simple multi-layer perceptron (MLP) network. Going forward, many extensions follow up in improving rendering quality (e.g., MipNeRF [6], MipNeRF 360 [7], and Ref-NeRF [40])," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "rendering efficiency (e.g., NSVF [29], Nex [43], AutoInt [27], FastNeRF [13], Baking [16], Plenoctree [45], KiloNeRF [37], DeRF [36], DoNeRF [35], R2L [41], and MobileNeRF [10]) and training efficiency (e.g., Plenoxels [12], and Instant-NGP [34])." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 135, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 546, + 555 + ], + "type": "text", + "content": "Efficient NeRF Rendering. Since this paper falls into the category of improving rendering efficiency as we target real-time rendering on mobile devices, we single out the papers of this group and discuss them in length here. There are generally four groups. (1) The first group trades speed with space, i.e., they precompute and cache scene representations and the rendering reduces to table lookup. Efficient data structure like sparse octree, e.g., Plenoctree [45], is usually utilized to make the rendering even faster. (2) The second attempts reduce the number of sampled points along the camera ray during rendering as it is the root cause of prohibitively slow rendering speed. Fewer sampled points typically lead to performance degradation, so as compensation, they usually introduce extra information, such as depth, e.g., DoNeRF [35], or mesh, e.g., MobileNeRF [10], to maintain the visual quality. (3) The third group takes a \"divide and conquer\" strategy. DeRF [36] decomposes the scene spatially to Voronoi diagrams and learns each diagram with a small network. KiloNeRF [37] also employs a decomposition scheme. Differently, they decompose the scene into thousands of small regular grids. Each is addressed with a small network. Such decomposition poses challenges to parallelism. Thus they utilize customized parallelism implementation to obtain speedup. (4) The fourth group is a newly surging one, represented by the recent works RSEN [5] and R2L [41]. They achieve rendering efficiency by representing the scene with NeLF (neural light field) instead of NeRF. NeLF avoids the dense sampling on camera ray, resulting in a much faster rendering speed than NeRF. On the downside, NeLF is typically much harder to learn than NeRF. As a remedy, these works (such as [41]) typically integrate a pre-trained NeRF model as a teacher to synthesize additional pseudo data for distillation [8, 19]. Therefore, the resulting model is fast with a reasonably small representation size, i.e., the model size." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "Neural Light Field (NeLF). Light field is a different way of representing scenes. The idea has a long history in the computer graphics community, e.g., Light fields [25] and Lumigraphs [14] cache plenty of images and enable real-time rendering at the cost of limited camera pose and excessive storage overhead. One of the most intriguing properties of NeLF is that rendering one image only requires one network forward, resulting in a significantly faster speed than NeRF-based methods. With the recent surge of the neural radiance field, some works attempt to revive the idea of the neural light field for efficient neural rendering. Sitzmann et al. [38] materialize the idea of using a neural network to model the scene, and the rendering process reduces to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8329" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "content": "a single network forward. Despite the encouraging idea, their method has only been evaluated on scenes with simple shapes, not matching the quality of NeRF on complex real-world scenes. Later, RSEN [5] and R2L [41] are introduced. RSEN divides the space into many voxel grids. Only in each grid, it is a NeLF, which needs alpha-composition to render the final color, making their method a mixture of NeLF and NeRF. R2L [41] is a pure NeLF network that avoids the alpha-composition step in rendering, which is also one of the most relevant works to this paper. However, R2L is still not compact and fast enough for mobile devices. Based on our empirical study, an R2L model runs for around three seconds per frame on iPhone 13 even for low-resolution like " + }, + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "inline_equation", + "content": "200 \\times 200" + }, + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "content": ". This paper is meant to push the NeRF-to-NeLF idea even further, making it able to perform real-time rendering on mobile devices." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 301 + ], + "type": "text", + "content": "We will mainly compare to MobileNeRF [10] in this paper as it is the only method, to our best knowledge, that can run on mobile devices with matching quality to NeRF [33]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 313, + 107, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 313, + 107, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 313, + 107, + 326 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 334, + 209, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 209, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 209, + 346 + ], + "type": "text", + "content": "3.1. Prerequisites: NeRF and R2L" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": "NeRF. NeRF [33] represents the scene implicitly with an MLP network " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "F_{\\Theta}" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": ", which maps the 5D coordinates (spatial location " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "(x, y, z)" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": " and view direction " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "(\\theta, \\phi)" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": ") to a 1D volume density (opacity, denoted as " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": " here) and 3D radiance (denoted as " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": ") such that " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "F_{\\Theta}: \\mathbb{R}^5 \\mapsto \\mathbb{R}^4" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": ". Each pixel of an image is associated with a camera ray. To predict the color " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": " of a pixel, the NeRF method samples many points (denoted as " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": " below) along the camera ray and accumulates the radiance " + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 353, + 289, + 462 + ], + "type": "text", + "content": " of all these points via alpha compositing [23, 31, 33]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 471, + 245, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 471, + 245, + 499 + ], + "spans": [ + { + "bbox": [ + 96, + 471, + 245, + 499 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\cdot \\mathbf {c} _ {i},", + "image_path": "aae9b7613428e6029ca190b440b3d4365b43cec0620682cdb8171036d4a4ae79.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 89, + 502, + 287, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 502, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 89, + 502, + 287, + 515 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {c} _ {i}, \\sigma_ {i}\\right) = F _ {\\Theta} \\left(\\mathbf {r} \\left(t _ {i}\\right), \\mathbf {d}\\right), \\tag {1}", + "image_path": "a4c44cbc787e55ad87e01215af0864f5438c29b0e04a7f24f0da5e6b22b5447e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 517, + 195, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 517, + 195, + 548 + ], + "spans": [ + { + "bbox": [ + 107, + 517, + 195, + 548 + ], + "type": "interline_equation", + "content": "T _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right),", + "image_path": "c1dceb248709fd4d3f33eddcc833c7c4d47e6433c8243479a9e2faf23288c8d1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " means the camera ray; " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t_i) = \\mathbf{o} + t_i\\mathbf{d}" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " represents the location of a point on the ray with origin " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " and direction " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " is the Euclidean distance, i.e., a scalar, of the point away from the origin; and " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{i} = t_{i + 1} - t_{i}" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " refers to the distance between two adjacent sampled points. A stratified sampling approach is employed in NeRF [33] to sample the " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " in Eqn. 1. To enrich the input information, the position and direction coordinates are encoded by positional encoding [39], which maps a scalar " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "(\\mathbb{R})" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " to a higher dimensional space " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "(\\mathbb{R}^{2L + 1})" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " through cosine and sine functions, where " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " (a predefined constant) stands for the frequency order (in the original NeRF [33], " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "L = 10" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " for positional coordinates and " + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": " for direction coordinates)." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 70, + 547, + 171 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 547, + 171 + ], + "type": "image", + "image_path": "b78159630dc54ca21e0dc603244559a5c6325bebbfff217d5ab29de9e90eceb6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "type": "text", + "content": "Figure 2. Training and Inference Pipeline. The training involves a teacher model to generate pseudo data, which is used to learn the MobileR2L. The teacher model, e.g., NeRF, is trained on real images. Once we have the teacher model, we use it to generate pseudo images, e.g., images with the resolution of " + }, + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "type": "text", + "content": ", in addition to down-scaled rays, e.g., rays with spatial size as " + }, + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 304, + 179, + 547, + 291 + ], + "type": "text", + "content": ", that share the same origin with the pseudo images to train the MobileR2L. After that, we use the real data to fine-tune MobileR2L. For inference, we directly forward the rays into the pre-trained MobileR2L to render images." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 314, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 410 + ], + "type": "text", + "content": "The whole formulation and training of NeRF are straightforward. One critical problem preventing fast inference in NeRF is that the " + }, + { + "bbox": [ + 304, + 314, + 545, + 410 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 314, + 545, + 410 + ], + "type": "text", + "content": ", i.e., the number of sampled points, in Eqn. 1 is pretty large (256 in the original NeRF paper due to their two-stage coarse-to-fine design). Therefore, the rendering computation for even a single pixel is prohibitively heavy. The solution proposed by R2L [41] is distilling the NeRF representation to NeLF." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": "R2L. Essentially, a NeLF function maps the oriented ray to RGB. To enrich the input information, R2L proposes a new ray representation – they also sample points along the ray just like NeRF [33] does; but differently, they concatenate the points to one vector, which is used as the ray representation and fed into a neural network to learn the RGB. Similar to NeRF, positional encoding [39] is also adopted in R2L to map each scalar coordinate to a high dimensional space. During training, the points are randomly (by a uniform distribution) sampled; during testing, the points are fixed." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": "The output of the R2L model is directly RGB, no density learned, and there is no extra alpha-compositing step, which makes R2L much faster than NeRF in rendering. One downside of the NeLF framework is, as shown in R2L [41], the NeLF representation is much harder to learn than NeRF; so as a remedy, R2L proposes an 88-layer deep ResMLP (residual MLP) architecture (much deeper than the network of NeRF) to serve as the mapping function." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "R2L has two stages in training. In the first stage, they use a pre-trained NeRF model as a teacher to synthesize excessive (origin, direction, RGB) triplets as pseudo data; and then fed the pseudo data to train the deep ResMLP. This stage can make the R2L model achieve comparable performance to the teacher NeRF model. In the second stage, they finetune the R2L network from the first stage on" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8330" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 75, + 545, + 233 + ], + "blocks": [ + { + "bbox": [ + 62, + 75, + 545, + 233 + ], + "lines": [ + { + "bbox": [ + 62, + 75, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 62, + 75, + 545, + 233 + ], + "type": "image", + "image_path": "d7c8040e2e44d3d779ad3cbb716ec182549120e74ec758444c4015fba315ff6f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": "Figure 3. Overview of Network. The input tensor of MobileR2L has 4D shape: batch, channel, height, and width. The backbone includes residual blocks (RB) that is repeated 28 times (" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "N = 28" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": "). Following the backbone, there are two types of super-resolution (SR) modules. The first SR module " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "(\\mathrm{SR}^1)" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " has kernel size " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " in the Transpose CONV layer that doubles the input " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "2H, 2W" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ", whereas the second SR module " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "(\\mathrm{SR}^2)" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " has kernel size " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ", tripling the spatial size to " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "3H, 3W" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ". The configuration of " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "3 \\times \\mathrm{SR}^1" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " is used in the synthetic " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "360^\\circ" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " dataset that upsamples the input " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ". For the real-world forward-facing dataset, we use the combination of " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "2 \\times \\mathrm{SR}^1 + \\mathrm{SR}^2" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": " that upsamples the input " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "12 \\times" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ". Moreover, we use various output channels across RB and SR: " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "C_1 = 256" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "C_2 = 64" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "inline_equation", + "content": "C_3 = 16" + }, + { + "bbox": [ + 46, + 243, + 548, + 310 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 288, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 355 + ], + "type": "text", + "content": "the original data – this step can further boost the rendering quality as shown in the R2L work [41]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 363, + 123, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 123, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 123, + 374 + ], + "type": "text", + "content": "3.2. MobileR2L" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 382, + 122, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 122, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 122, + 393 + ], + "type": "text", + "content": "3.2.1 Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "text", + "content": "We follow the learning process of R2L to train our proposed MobileR2L, namely, using a pre-trained teacher model, such as NeRF [33], to generate pseudo data for the training of a lightweight neural network. To reduce the inference speed, we aim only to forward the network once when rendering an image. However, under the design of R2L, although one pixel only requires one network forward, directly feeding rays with large spatial size, e.g., " + }, + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "text", + "content": ", into a network causes memory issues. Therefore, R2L forwards a partial of rays each time, increasing the speed overhead. To solve the problem, we introduce super-resolution modules, which upsample the low-resolution input, e.g., " + }, + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 402, + 289, + 606 + ], + "type": "text", + "content": ", to a high-resolution image. Thus, we can obtain a high-resolution image with only one forward pass of the neural network during inference time. The training and inference pipeline is illustrated in Fig. 2, and we introduce more details for our network architecture in the following." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 622, + 178, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 178, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 178, + 633 + ], + "type": "text", + "content": "3.2.2 Network Architectures" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": "The input rays can be represented as " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{B,6,H,W}" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": " denotes the batch size and " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": " denote the spatial size. The ray origin and view directions are concatenated as the second dimension of " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": ". We then apply positional encoding " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\gamma(\\cdot)" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 640, + 288, + 715 + ], + "type": "text", + "content": " to map the ray origin and view directions into a higher dimension. Thus, we get the input of our neural" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 331, + 376, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 376, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 376, + 342 + ], + "type": "text", + "content": "network as " + }, + { + "bbox": [ + 306, + 331, + 376, + 342 + ], + "type": "inline_equation", + "content": "\\gamma (\\mathbf{x})" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": "The network includes two main parts: an efficient backbone and Super-Resolution (SR) modules for high-resolution rendering, with the architecture provided in Fig. 3. Instead of using Fully Connected (FC) or linear layers for the network that is adopted by existing works [33, 41], we only apply convolution (CONV) layers in the backbone and super-resolution modules." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "text", + "content": "There are two main reasons for replacing FC with CONV layers. First, the CONV layer is better optimized by compilers than the FC layer [30]. Under the same number of parameters, the model with CONV " + }, + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "text", + "content": " runs around " + }, + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 304, + 426, + 546, + 605 + ], + "type": "text", + "content": " faster than the model with FC layers, as shown in Tab. 4. Second, suppose FC is used in the backbone, in that case, extra Reshape and Permute operations are required to modify the dimension of the output features from the FC to make the features compatible with the CONV layer in the super-resolution modules, as the FC and CONV calculate different tensor dimensions. However, such Reshape or Permute operation might not be hardware-friendly on some mobile devices [26]. With the CONV employed as the operator in the network, we then present more details for the backbone and SR modules." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Efficient Backbone. The architecture of the backbone follows the design of residual blocks from R2L [41]. Different from R2L, we adopt the CONV layer instead of the FC layer in each residual block. The CONV layer has the kernel size and stride as 1. Additionally, we use the normalization and activation functions in each residual block, which can improve the network performance without introducing latency overhead (see experimental details in Tab. 4). The normalization and activation are chosen as batch normaliza" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "8331" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "content": "tion [21] and GeLU [17]. The backbone contains 60 CONV layers in total." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 286, + 227 + ], + "type": "text", + "content": "Super-Resolution Modules. To reduce the latency when running the neural rendering on mobile devices, we aim to forward the neural network once to get the synthetic image. However, the existing network design of the neural light field requires large memory for rendering a high-resolution image, which surpasses the memory constraint on mobile devices. For example, rendering an image of " + }, + { + "bbox": [ + 46, + 95, + 286, + 227 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 95, + 286, + 227 + ], + "type": "text", + "content": " requires the prediction of 640,000 rays. Forwarding these rays at once using the network from R2L [41] causes the out of memory issue even on the Nvidia Tesla A100 GPU (40G memory)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": "To reduce the memory and latency cost for high-resolution generation, instead of forwarding the number of rays that equals to the number of pixels, we only forward a partial of rays and learn all the pixels via super-resolution. Specifically, we propose to use the super-resolution modules following the efficient backbone to upsample the output to a high-resolution image. For example, to generate a " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " image, we forward a 4D tensor " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " with spatial size as " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " to the network and upsample the output from backbone three times (i.e., upsample by " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " each time). The SR module includes two stacked residual blocks. The first block includes three CONV layers with one as a 2D Transpose CONV layer and two CONV " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " layers; the second block includes two CONV " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " layers. After the SR modules, we apply another CONV layer followed by the Sigmoid activation to predict the final RGB color. We denote our model as " + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "inline_equation", + "content": "D60-SR3" + }, + { + "bbox": [ + 46, + 228, + 286, + 441 + ], + "type": "text", + "content": " where it contains 60 CONV layers in the efficient backbone and 3 SR modules." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 454, + 127, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 127, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 127, + 467 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": "Datasets. We conduct the comparisons mainly on two datasets: realistic synthetic " + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " [33] and real-world forward-facing [32, 33]. The synthetic " + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " dataset contains 8 path-traced scenes, with each scene including 100 images for training and 200 images for testing. Forward-facing contains 8 real-world scenes captured by cellphones, where the images in each scene vary from 20 to 60, and 1/8 images are used for testing. We conduct our experiments (training and testing) on the resolution of " + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " for synthetic " + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "1008 \\times 756" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 474, + 286, + 605 + ], + "type": "text", + "content": " down-scaled from the original resolution) for forward-facing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Implementation Details. We follow the training scheme of R2L [41], i.e., using a teacher model to render pseudo images for the training of MobileR2L network. Specifically, we synthesize 10K pseudo images from the pretrained teacher model [2] for each scene. We first train our MobileR2L on the generated pseudo data and then fine-tune it on the real data, as shown in Fig. 2. In all the experiments, we employ Adam [24] optimizer with an initial learning rate " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " that decays during the training. Our experiments" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 310, + 135, + 544, + 217 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "content": "Table 1. Quantitative Comparison on Synthetic " + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "content": " and Forward-facing. Our method obtains better results on the three metrics than NeRF for the two datasets. Compared with MoibleNeRF and SNeRG, we achieve better results on most of the metrics." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 135, + 544, + 217 + ], + "lines": [ + { + "bbox": [ + 310, + 135, + 544, + 217 + ], + "spans": [ + { + "bbox": [ + 310, + 135, + 544, + 217 + ], + "type": "table", + "html": "
Synthetic 360°Forward-facing
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeRF [33]31.010.9470.08126.500.8110.250
NeRF-Pytorch [44]30.920.9910.04526.260.9650.153
SNeRG [16]30.380.9500.05025.630.8180.183
MoibleNeRF [10]30.900.9470.06225.910.8250.183
MobileR2L (Ours)31.340.9930.05126.150.9660.187
Our Teacher33.090.9610.05226.850.8270.226
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For each high-resolution image generated by the teacher model, we save the input rays corresponding to a lower-resolution image where the camera origins and directions are the same as the high-resolution one while the focal length is down-scaled accordingly. Additionally, we do not sample the rays from different images as in R2L. Instead, the rays in each training sample share the same origin and reserve their spatial locations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": "Considering the training data of the synthetic " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " and forward-facing datasets have different resolutions, the spatial size of the inputs for the two datasets are slightly different. Our network takes input with the spatial size of " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " for the synthetic " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " dataset and upsamples by " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " to render " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " RGB images. In contrast, the spatial size of " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "84 \\times 63" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " is used in the forward-facing dataset, and " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "1008 \\times 756" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " image (" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "12 \\times" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " upsampling) is rendered. The kernel size and padding are adjusted in the last transposed CONV layer to achieve " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "inline_equation", + "content": "12 \\times" + }, + { + "bbox": [ + 304, + 401, + 545, + 532 + ], + "type": "text", + "content": " upsampling with the 3 SR blocks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 540, + 390, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 390, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 390, + 552 + ], + "type": "text", + "content": "4.1. Comparisons" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": "Rendering Performance. To understand the image quality of various methods, we report three common metrics: PSNR, SSIM [42], and LPIPS [46], on the realistic synthetic " + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": " and real forward-facing datasets, as demonstrated in Tab. 1. Compared with NeRF [33], our approach achieves better results on PSNR, SSIM, and LPIPS for the synthetic " + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": " dataset. On the forward-facing dataset, we obtain better SSIM and LPIPS than NeRF [33]. Similarly, our method achieves better results for all three metrics than MobileNeRF [10] on the synthetic " + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": " dataset and better PSNR and SSIM on the forward-facing dataset. Compared to SNeRG [16], our method obtains better PSNR and SSIM." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "We also show the performance of the teacher model used" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8332" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 79, + 105, + 117 + ], + "blocks": [ + { + "bbox": [ + 67, + 79, + 105, + 117 + ], + "lines": [ + { + "bbox": [ + 67, + 79, + 105, + 117 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"Figure 4. Visual comparison between our method and NeRF [33] (trained via NeRF-Pytorch [44]) on the synthetic " + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "text", + "content": " Lego (size: " + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "inline_equation", + "content": "800 \\times 800 \\times 3" + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "text", + "content": ") and real-world forward-facing scene Fern (size: " + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "inline_equation", + "content": "1008 \\times 756 \\times 3" + }, + { + "bbox": [ + 47, + 215, + 287, + 270 + ], + "type": "text", + "content": "). Best viewed in color. Please refer to our webpage for more visual comparison results." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 285, + 286, + 358 + ], + "lines": [ + { + "bbox": [ + 50, + 285, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 50, + 285, + 286, + 358 + ], + "type": "image", + "image_path": "2cb0d4918fa053bd8a6acab3026711329187b3dd22c8eda4c2e101081ad7a896.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 50, + 367, + 287, + 441 + ], + "blocks": [ + { + "bbox": [ + 50, + 367, + 287, + 441 + ], + "lines": [ + { + "bbox": [ + 50, + 367, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 50, + 367, + 287, + 441 + ], + "type": "image", + "image_path": "b32c4171038d900d2ed385cc33b9b48cfef85bccbb67322329c5b09f73270db0.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 451, + 287, + 496 + ], + "lines": [ + { + "bbox": [ + 46, + 451, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 287, + 496 + ], + "type": "text", + "content": "Figure 5. Zoom-in comparisons. Top row: MobileNeRF [10]. Results are obtained from the code and demo released by the authors. Bottom row: MobileR2L. Our approach renders high-quality images even for zoom-in views." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "content": "in training MobileR2L in Tab. 1 (Our Teacher). Note that there is still a performance gap between the student model (MobileR2L) and the teacher model. However, as we show following (Tab. 5), a better teacher model can lead to a student model with higher performance. Compared with MoibleNeRF and SNeRG, our approach has the advantage that we can directly leverage the high-performing teacher models to help improve student training in different application scenarios. We further show the qualitative comparison results in Fig. 4. On the synthetic scene Lego, our MobileR2L outperforms NeRF clearly, delivering sharper and less distorted shapes and textures. On the real-world scene Fern, our result is less noisy, and the details, e.g., the leaf tips, are sharper. Additionally, we provide the zoom-in comparison with MoibleNeRF [10] in Fig. 5. Our method achieves high-quality rendering for zoom-in view, which is" + } + ] + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 308, + 113, + 544, + 136 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 104 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 104 + ], + "type": "text", + "content": "Table 2. Analysis of Storage (MB) required for different rendering methods. Our method has a clear advantage over existing works with much less storage required." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 113, + 544, + 136 + ], + "lines": [ + { + "bbox": [ + 308, + 113, + 544, + 136 + ], + "spans": [ + { + "bbox": [ + 308, + 113, + 544, + 136 + ], + "type": "table", + "html": "
Synthetic 360°Forward-facing
MobileNeRF [10]SNeRG [16]OursMobileNeRF [10]SNeRG [16]Ours
Disk storage125.886.88.3201.5337.38.3
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Synthetic 360°Forward-facing
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iPhone 1317.5426.2127.15 2/818.04
iPhone 1416.6722.6520.98 2/816.48
", + "image_path": "930baa9cdae9e2f3dd913b62f293b384955ca694b2e881ef656373e047f14254.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "table_body" + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "type": "text", + "content": "especially important for 3D assets that users might perform zoom-in to look for more image details." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": "Disk Storage. One significant advantage of our method is that we do not require extra storage, even for complex scenes. As shown in Tab. 2, the storage of our approach is " + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "inline_equation", + "content": "8.3\\mathrm{MB}" + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": " for both synthetic " + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": " and forward-facing datasets. The mesh-based methods like MobileNeRF demand more storage for real-world scenes due to saving more complex textures. As a result, our approach takes " + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "inline_equation", + "content": "24.3\\times" + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": " less disk storage than MobileNeRF on the forward-facing, and " + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "inline_equation", + "content": "15.2\\times" + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": " less storage on the synthetic " + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 343, + 545, + 452 + ], + "type": "text", + "content": " dataset." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "content": "Inference Speed. We profile and report the rendering speed of our proposed approach on iPhones (13, and 14, iOS 16) in Tab. 3. The models are compiled with CoreMLTools [11]. Our proposed method runs faster on real forward-facing scenes than the realistic synthetic " + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "content": " scenes. The latency discrepancy between the two datasets comes from the different input spatial sizes. MobileNeRF shows a lower latency than our models on the realistic synthetic " + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 612 + ], + "type": "text", + "content": " but higher on the real-world scenes. Both methods can run in real-time on devices. Note that MobileNeRF cannot render two scenes, i.e., Leaves and Orchids, due to memory issues, as they require complex textures to model the geometry. In contrast, our approach is robust for different scenes." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "content": "Discussion. From the comparison of the rendering quality, disk storage, and inference speed, it can be seen that MobileR2L achieves overall better performance than MobileN-eRF. More importantly, considering the usage of neural rendering on real-world applications, MobileR2L is more suitable as it requires much less storage, reducing the constraint for hardware and can render real-world scenes in real-time on mobile devices." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8333" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 153, + 85 + ], + "type": "text", + "content": "4.2. Ablation Analysis" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "text", + "content": "Here we perform the ablation analysis to understand the design choices of the network. We use the scene of Chair from the synthetic " + }, + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "text", + "content": " to conduct the analysis. All models are trained for 200K iterations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": "Options for Backbone. We study the two available operators for designing the backbone. MLP and " + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": " CONV layer are essentially equivalent operators and perform the same calculations, thus resulting in similar performance. However, we observe around " + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": " latency reduction on mobile devices (iPhone 13) when replacing the MLP layer with the " + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": " CONV layer. Specifically, as shown in Tab. 4, we design two networks, i.e., MLP and CONV2D, with only residual blocks as in Fig. 3 but removing the activation, normalization, and super-resolution modules. We use the input size as " + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": " for the two models. Since the super-resolution modules are omitted, we train the two networks for generating " + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 138, + 288, + 402 + ], + "type": "text", + "content": " images. As can be seen, the CONV2D model has a faster inference speed than MLP with similar performance. This is due to the fact that CONV operation is better-optimized than MLP on mobile devices. Additionally, due to the intrinsic design of our proposed MobileR2L, employing MLP layers requires two additional operators, i.e., Permute and Reshape, before feeding the internal features to super-resolution modules, while Permute and Reshape involve data movement that adds unnecessary overheads on some edge devices [26]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "content": "Analysis of Activation Function. R2L [41] and NeRF [33] use ReLU [4] activation as non-linearity function. In our proposed MobileR2L, we use GELU [18] instead. As shown in Tab. 4, by comparing the " + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "inline_equation", + "content": "CONV2D + ReLU" + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "inline_equation", + "content": "CONV2D + GeLU" + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "content": ", which are two networks trained with ReLU and GeLU activations, we notice that GeLU brings about 0.17 PSNR boost without any additional latency overhead. Similarly, we show that incorporating BatchNorm [22] layer into the ResBlock is also beneficial for better performance without introducing extra latency, as shown by " + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "inline_equation", + "content": "CONV2D + GeLU + BN" + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "content": " in Tab. 4. The three networks in the experiments are also trained to render " + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 402, + 288, + 545 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "Analysis on Input Dimension. We further analyze the optimal spatial resolution for the input tensor. Specifically, we benchmark the performance of three approaches, namely, " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "50 \\times 50 - \\text{NeRF Teacher}" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "100 \\times 100 - \\text{NeRF Teacher}" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "200 \\times 200 - \\text{NeRF Teacher}" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " with the spatial size of input as the square of 50, 100, and 200 respectively. These models contain super-resolution modules to render " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " images and are trained with the NeRF [33] as a teacher model. Results are presented in Tab. 5. The model using a small input spatial size, i.e., " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "50 \\times 50" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ", achieves " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " speedup than the model with a larger size, i.e., " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ", as less computation is required. However, the performance is also degraded by 0.25 PSNR. Further increasing the input spatial size to " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "200 \\times 200" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " makes the model unable to achieve real-time in-" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 125, + 544, + 186 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 116 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 116 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 116 + ], + "type": "text", + "content": "Table 4. Analysis of Network Design. For all the comparisons, we use the input tensor with the spatial size as " + }, + { + "bbox": [ + 305, + 70, + 545, + 116 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 305, + 70, + 545, + 116 + ], + "type": "text", + "content": " and render the image with spatial size. The latency (ms) is measured on iPhone 13 (iOS16) with models compiled with CoreMLTools [11]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 125, + 544, + 186 + ], + "lines": [ + { + "bbox": [ + 309, + 125, + 544, + 186 + ], + "spans": [ + { + "bbox": [ + 309, + 125, + 544, + 186 + ], + "type": "table", + "html": "
PSNR↑SSIM↑LPIPS↓Latency↓
MLP19.130.97590.663019.57
CONV2D19.160.97590.630114.30
CONV2D + ReLU26.820.99490.028216.20
CONV2D + GeLU26.990.99490.073017.00
CONV2D + GeLU + BN27.180.99540.025917.00
", + "image_path": "15dbdc0d49437959f4681710eb8e7b033e00d93e1a7dce09cc7a7c2ebbea4082.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 262, + 545, + 330 + ], + "blocks": [ + { + "bbox": [ + 305, + 209, + 547, + 254 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 254 + ], + "type": "text", + "content": "Table 5. Analysis of the spatial size of the input, usage of teacher model, and ray presentation. Besides image quality metrics, we show the number of parameters for each model and the latency when running on iPhone 13." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 262, + 545, + 330 + ], + "lines": [ + { + "bbox": [ + 309, + 262, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 309, + 262, + 545, + 330 + ], + "type": "table", + "html": "
ParamsPSNR↑SSIM↑LPIPS↓Latency↓
50 × 50 - NeRF Teacher3.9M30.400.99650.068613.04
100 × 100 - NeRF Teacher3.9M30.650.99660.066826.21
200 × 200 - NeRF Teacher3.9M---73.76
800 × 800 - w/o SR3.9M---Error
100 × 100 - MipNeRF Teacher3.9M30.830.09970.056426.21
100 × 100 - MipNeRF Teacher, K16, L104.1M30.900.99680.058331.05
100 × 100 - MipNeRF Teacher, K16, L10, D1006.8M31.370.99720.047044.52
", + "image_path": "07e96748ddfc2aef40cd26fec2a1ef8482d45bf492246a05a5cc08aa574fae4a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 362, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 362, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 305, + 362, + 545, + 386 + ], + "type": "text", + "content": "ference. Thus, we do not report the rendering performance of the models with " + }, + { + "bbox": [ + 305, + 362, + 545, + 386 + ], + "type": "inline_equation", + "content": "200 \\times 200" + }, + { + "bbox": [ + 305, + 362, + 545, + 386 + ], + "type": "text", + "content": " input size." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "text", + "content": "Analysis of SR modules. We further show the necessity of using SR modules. We use the spatial size of " + }, + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "text", + "content": " as the network input to render images with the same spatial size. We denote the setting as " + }, + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "inline_equation", + "content": "800 \\times 800 - w / o" + }, + { + "bbox": [ + 304, + 387, + 545, + 483 + ], + "type": "text", + "content": " SR in Tab. 5. Profiling the latency of such a network leads to compilation errors due to intensive memory usage. Thus, our proposed SR module is essential for high-resolution synthesis without introducing prohibitive computation overhead." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "text", + "content": "Choice of Teacher Models. Since both R2L [41] and MobileR2L use a teacher model for generating pseudo data to train a lightweight network, we study whether a more powerful teacher model can improve performance. To conduct the experiments, we use MipNeRF [6] as the teacher model for the training MobileR2L, given MipNeRF shows better performance than NeRF on the synthetic " + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "text", + "content": " dataset. We denote the approach as " + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "inline_equation", + "content": "100 \\times 100 -" + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "text", + "content": " MipNeRF Teacher. Through the comparison with " + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "inline_equation", + "content": "100 \\times 100 -" + }, + { + "bbox": [ + 304, + 484, + 545, + 652 + ], + "type": "text", + "content": " NeRF Teacher, as in Tab. 5, we notice the quality of the rendered images is improved, e.g., the PSNR is increased by 0.18, without the extra cost of latency. The comparison demonstrates that our approach has the potential to render higher-quality images when better teacher models are provided." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "Analysis on Ray Representation. Here we analyze how the ray representation affects the latency-performance trade-off of MobileR2L. We follow the same ray representation paradigm as in R2L [41] and positional encoding as in NeRF [33]. Specifically, R2L sample " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": " 3D points along" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8334" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "the ray, and each point is mapped to a higher dimension by positional encoding with " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " positional coordinates. R2L sets " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L = 10" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ", resulting in a vector with a dimension of 1,008. We apply the same setting to MobileR2L and denote the model as " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "K_{16}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L_{10}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "-MipNeRF Teacher in Tab. 5. For our implementation in MobileR2L, we set " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "K = 8" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L = 6" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " for the model, which has the dimension per ray as 312. The model is " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "-MipNeRF Teacher. By comparing the performance of the two models, we notice that larger " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " lead to negligible PSNR improvement (0.07), yet higher inference latency and bigger model size (more parameters). Therefore, we chose " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "K = 8" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "L = 6" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " for the consideration of model size and latency - they are the more important metrics when deploying neural rendering models on mobile devices." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 371 + ], + "type": "text", + "content": "Depth of the Backbone. Lastly, we show the effects of the backbone depth on the model performance. We use the depth as 60 for our backbone. By increasing the number of residual blocks in the backbone, i.e., setting depth as 100, we obverse better model performance at the cost of higher latency, as shown by comparing the last two rows in Tab. 5. Using depth as 100 significantly increases the latency and the number of parameters, and the model fails to run in real time. Thus, we chose depth as 60, given the better trade-off between latency, model size, and performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 378, + 182, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 182, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 182, + 391 + ], + "type": "text", + "content": "4.3. Real-World Application" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "type": "text", + "content": "Here we demonstrate the usage of our technique for building a real-world application. Given the small size and faster inference speed of our model, we create a shoes try-on application that runs on mobile devices. Users can directly try on the shoes rendered by MobileR2L using their devices, enabling real-time interaction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 288, + 612 + ], + "type": "text", + "content": "The pipeline for building the application is illustrated in Fig. 6. We first use iPhone to capture 100 shoe images for training. The images are then segmented to remove the background. After that, we train a NeRF model [33] to generate pseudo data, which is later used for learning MobileR2L to render images in " + }, + { + "bbox": [ + 46, + 468, + 288, + 612 + ], + "type": "inline_equation", + "content": "1008 \\times 756" + }, + { + "bbox": [ + 46, + 468, + 288, + 612 + ], + "type": "text", + "content": " resolution. We apply foot tracking and overlay the rendered shoe on top of the user's feet. As can be seen from Fig. 6, our model is able to render high-quality images from various views for different users. The try-on usage proves the potential of leveraging neural rendering for building various real-time interactive applications such as Augment Reality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 621, + 200, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 200, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 200, + 634 + ], + "type": "text", + "content": "5. Limitation and Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": "This work presents MobileR2L, the first neural light network that renders images with similar quality as NeRF [33] while running in real-time on model devices. We perform extensive experiments to design an optimized network architecture that can be trained via data distillation to render high-resolution images, e.g., " + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": ". Additionally," + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 395, + 134 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 395, + 134 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 395, + 134 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 395, + 134 + ], + "type": "image", + "image_path": "2d923b7f34ecce8d146025a3af31e3879d37f907ae8395299dfd4e329bb9bf8d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 134, + 395, + 140 + ], + "lines": [ + { + "bbox": [ + 310, + 134, + 395, + 140 + ], + "spans": [ + { + "bbox": [ + 310, + 134, + 395, + 140 + ], + "type": "text", + "content": "(a) Example Images from Collected Data" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 140, + 386, + 201 + ], + "blocks": [ + { + "bbox": [ + 315, + 140, + 386, + 201 + ], + "lines": [ + { + "bbox": [ + 315, + 140, + 386, + 201 + ], + "spans": [ + { + "bbox": [ + 315, + 140, + 386, + 201 + ], + "type": "image", + "image_path": "23b1efac456c0bb1b7dc3661d3854dbf68d87322815b3c04839c2800adf1a3c4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 201, + 376, + 208 + ], + "lines": [ + { + "bbox": [ + 329, + 201, + 376, + 208 + ], + "spans": [ + { + "bbox": [ + 329, + 201, + 376, + 208 + ], + "type": "text", + "content": "(b) Segmented Images" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 435, + 70, + 471, + 133 + ], + "blocks": [ + { + "bbox": [ + 435, + 70, + 471, + 133 + ], + "lines": [ + { + "bbox": [ + 435, + 70, + 471, + 133 + ], + "spans": [ + { + "bbox": [ + 435, + 70, + 471, + 133 + ], + "type": "image", + "image_path": "baac3193307d63efa3292e67bf92ad0b558e53923a696352f75b4721cf74900b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 435, + 135, + 470, + 198 + ], + "blocks": [ + { + "bbox": [ + 435, + 135, + 470, + 198 + ], + "lines": [ + { + "bbox": [ + 435, + 135, + 470, + 198 + ], + "spans": [ + { + "bbox": [ + 435, + 135, + 470, + 198 + ], + "type": "image", + "image_path": "6de13707ba3094539ba866d9cd6c002590d31af35aa37738c7c6ae32d32f3fb3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 201, + 534, + 208 + ], + "lines": [ + { + "bbox": [ + 443, + 201, + 534, + 208 + ], + "spans": [ + { + "bbox": [ + 443, + 201, + 534, + 208 + ], + "type": "text", + "content": "(c) Novel View Synthesis for Virtual Try-On" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 474, + 70, + 508, + 133 + ], + "blocks": [ + { + "bbox": [ + 474, + 70, + 508, + 133 + ], + "lines": [ + { + "bbox": [ + 474, + 70, + 508, + 133 + ], + "spans": [ + { + "bbox": [ + 474, + 70, + 508, + 133 + ], + "type": "image", + "image_path": "bcc19e1d1520af58ef2c4db821a804d8a45ddd74dc7dd50e0c128d883a3239fc.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 471, + 135, + 507, + 198 + ], + "blocks": [ + { + "bbox": [ + 471, + 135, + 507, + 198 + ], + "lines": [ + { + "bbox": [ + 471, + 135, + 507, + 198 + ], + "spans": [ + { + "bbox": [ + 471, + 135, + 507, + 198 + ], + "type": "image", + "image_path": "ddb2f28e8799e96f7e1dd23e6fc9a0624a02d5e10fcfcf2fb0fae26cfab91324.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 510, + 70, + 545, + 133 + ], + "blocks": [ + { + "bbox": [ + 510, + 70, + 545, + 133 + ], + "lines": [ + { + "bbox": [ + 510, + 70, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 510, + 70, + 545, + 133 + ], + "type": "image", + "image_path": "ce7338fe83a6b70c382a8f4bc4a3c12087acce92dc85e0c0470ebd8925d117a4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 511, + 135, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 511, + 135, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 511, + 135, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 511, + 135, + 545, + 198 + ], + "type": "image", + "image_path": "4d352db590897b23a9b3765ad99cc8ac0c89dc015f7e5ddf8df06b4055a580cf.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 313, + 298, + 383, + 351 + ], + "blocks": [ + { + "bbox": [ + 305, + 220, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 285 + ], + "type": "text", + "content": "Figure 6. Virtual Try-On Application. From the collected images using a cellphone (a), we segment the foreground shoe (b) to train a MobileR2L model. We deploy the model on mobile devices, and users can directly try the shoe. The model renders images for novel views when users rotate the phone or change the foot positions (c)." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 298, + 383, + 351 + ], + "lines": [ + { + "bbox": [ + 313, + 298, + 383, + 351 + ], + "spans": [ + { + "bbox": [ + 313, + 298, + 383, + 351 + ], + "type": "image", + "image_path": "02d545f524cfca394a554a4982ba1ed62a31e24f8c4ec897776b136adf39236c.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 335, + 355, + 362, + 364 + ], + "lines": [ + { + "bbox": [ + 335, + 355, + 362, + 364 + ], + "spans": [ + { + "bbox": [ + 335, + 355, + 362, + 364 + ], + "type": "text", + "content": "Room" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "type": "text", + "content": "Figure 7. Visual comparison on the real-world scene Room. Both our model and NeRF fail to synthesize the whiteboard writings on the upper-left of the cutout patch." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 385, + 298, + 436, + 350 + ], + "blocks": [ + { + "bbox": [ + 385, + 298, + 436, + 350 + ], + "lines": [ + { + "bbox": [ + 385, + 298, + 436, + 350 + ], + "spans": [ + { + "bbox": [ + 385, + 298, + 436, + 350 + ], + "type": "image", + "image_path": "a93316771dfbc4e5a7b4effa07eda2a4bebe5ee75a24cf148a4b9a4adebd0d3c.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 395, + 354, + 425, + 365 + ], + "lines": [ + { + "bbox": [ + 395, + 354, + 425, + 365 + ], + "spans": [ + { + "bbox": [ + 395, + 354, + 425, + 365 + ], + "type": "text", + "content": "(a) GT" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 438, + 298, + 490, + 350 + ], + "blocks": [ + { + "bbox": [ + 438, + 298, + 490, + 350 + ], + "lines": [ + { + "bbox": [ + 438, + 298, + 490, + 350 + ], + "spans": [ + { + "bbox": [ + 438, + 298, + 490, + 350 + ], + "type": "image", + "image_path": "5c6500f3a60e6200bc88d82d65a4b011cbd5cf8f265b9634f64c481c27b63c0f.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 354, + 485, + 365 + ], + "lines": [ + { + "bbox": [ + 443, + 354, + 485, + 365 + ], + "spans": [ + { + "bbox": [ + 443, + 354, + 485, + 365 + ], + "type": "text", + "content": "(b) NeRF" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 492, + 298, + 544, + 350 + ], + "blocks": [ + { + "bbox": [ + 492, + 298, + 544, + 350 + ], + "lines": [ + { + "bbox": [ + 492, + 298, + 544, + 350 + ], + "spans": [ + { + "bbox": [ + 492, + 298, + 544, + 350 + ], + "type": "image", + "image_path": "ff6ffe67e1d17985fc3b9a06f7516032e27069d1a7b77f217644ffe751fd2160.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 500, + 354, + 536, + 365 + ], + "lines": [ + { + "bbox": [ + 500, + 354, + 536, + 365 + ], + "spans": [ + { + "bbox": [ + 500, + 354, + 536, + 365 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 426, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 497 + ], + "type": "text", + "content": "since we do not require other information besides the neural network, MobileR2L dramatically saves the representation storage in stark contrast to other mesh-based methods like MoibleNeRF [10]. Furthermore, we prove that with our design, neural rendering can be used to build real-world applications, achieving real-time user interaction." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "Although MobileR2L achieves promising inference speed with small model sizes, there are still two limitations of the current work that can be improved. First, we follow the training recipe of R2L [41], and R2L uses 10K pseudo images generated by the teacher NeRF model to train the student model. The number of training images is much more than the images used to train the teacher NeRF (which only requires around 100 images), resulting in a longer training time than NeRF-based methods. Therefore, a future direction could be reducing the training costs for distillation-based works like R2L and this work. Second, MobileR2L fails to generate some high-frequency details in the images. We show examples in Fig. 7. Using a larger model may alleviate this problem given a larger model capacity. Nevertheless, the inference latency will also increase accordingly on mobile devices. Future efforts may focus on optimizing the network and training pipeline to boost the performance of the current model." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8335" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Lens studio. https://ar.sun.com/en-US/lens-studio.1" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 135 + ], + "type": "text", + "content": "[2] Nerf-factory. https://github.com/kakaobrain/NeRF-Factory.5" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 137, + 286, + 168 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 137, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 53, + 137, + 286, + 168 + ], + "type": "text", + "content": "[3] Snap ml. https://docs.snap.com/lens-studio/references/guides/lens-features/machine-learning/ml-overview.1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 170, + 286, + 191 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 170, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 53, + 170, + 286, + 191 + ], + "type": "text", + "content": "[4] Abien Fred Agarap. 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The unreasonable effectiveness of deep features as a perceptual metric, 2018. 5" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8337" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_content_list.json b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c291d8a12f5a4ed26ef4d349064713f1ac4448f8 --- /dev/null +++ b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_content_list.json @@ -0,0 +1,1454 @@ +[ + { + "type": "text", + "text": "RealFusion", + "text_level": 1, + "bbox": [ + 426, + 131, + 545, + 148 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$360^{\\circ}$ Reconstruction of Any Object from a Single Image", + "text_level": 1, + "bbox": [ + 204, + 154, + 764, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Luke Melas-Kyriazi Iro Laina Christian Rupprecht Andrea Vedaldi", + "bbox": [ + 189, + 203, + 777, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Geometry Group, Department of Engineering Science, University of Oxford", + "bbox": [ + 236, + 241, + 730, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lukemk,iro,chrisr,vedaldi}@robots.ox.ac.uk", + "bbox": [ + 295, + 258, + 673, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://lukemelas.github.io/realfusion", + "bbox": [ + 372, + 277, + 594, + 291 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99fa49f81138854e22de6a0adcadde15dbb1fc372321a2801f92ec55f9f7c6cb.jpg", + "image_caption": [ + "Figure 1. RealFusion generates a full $360^{\\circ}$ reconstruction of any object given a single image of it (left column). It does so by leveraging an existing diffusion-based 2D image generator. From the given image, it synthesizes a prompt that causes the diffusion model to \"dream up\" other views of the object. It then extracts a neural radiance field from the original image and the diffusion model-based prior, thereby reconstructing the object in full. Both appearance and geometry are reconstructed faithfully and extrapolated in a plausible manner." + ], + "image_footnote": [], + "bbox": [ + 78, + 320, + 155, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a76aafcee24c77f2f85cd778ae188e94334cedb1e283a15cb8b8f3230136d767.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 321, + 890, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 625, + 313, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We consider the problem of reconstructing a full $360^{\\circ}$ photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to \"dream up\" novel views of the object. Using the recent DreamFusion method, we fuse the given input view, the conditional prior, and other regularizers into a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible", + "bbox": [ + 75, + 675, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in the image.", + "bbox": [ + 500, + 627, + 588, + 641 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 676, + 630, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We consider the problem of obtaining a $360^{\\circ}$ photographic reconstruction of any object given a single image of it. The challenge is that a single image does not contain sufficient information for 3D reconstruction. Without access to multiple views, an image only provides weak evidence about the 3D shape of the object, and only for one side of it. Even so, there is proof that this task can be solved: any skilled 3D artist can take a picture of almost any object and, given sufficient time and effort, create a plausible 3D model of it. The artist can do so by tapping into their vast knowledge of the natural world and the objects it contains, making up for the information missing from the image.", + "bbox": [ + 496, + 703, + 890, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hence, monocular 3D reconstruction requires combining", + "bbox": [ + 519, + 887, + 890, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8446", + "bbox": [ + 482, + 925, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "visual geometry with a powerful statistical model of the 3D world. Diffusion-based 2D image generators like DALL-E 2 [30], Imagen [35], and Stable Diffusion [33] are able to generate high-quality images from ambiguous inputs such as text, showing that powerful priors for 2D images can be learned. However, extending them to 3D is not easy because, while one can access billions of 2D images for training [36], the same cannot be said for 3D data.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A simpler approach is to extract or distill 3D information from an existing 2D generator. A 2D image generator can in fact be used to sample or validate multiple views of a given object, which can then be used to perform 3D reconstruction. This idea was already demonstrated with GAN-based generators for simple data like faces and synthetic objects [2, 6, 8, 24, 25, 47]. Better 2D generators have since resulted in better results, culminating in methods such as DreamFusion [27], which can produce high-quality 3D models from an existing 2D generator and text.", + "bbox": [ + 75, + 213, + 468, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we port distillation approaches from text-based generation to monocular 3D reconstruction. This is not a trivial change because conditioning generation on an image provides a much more fine-grained specification of the object than text. This in turn requires the 2D diffusion model to hallucinate new views of a specific object instead of some object of a given type. The latter is difficult because the coverage of generator models is limited [1], meaning that not every version of an object is captured well by the model. We find empirically that this is a key problem.", + "bbox": [ + 75, + 366, + 468, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We address this issue by introducing RealFusion, a new method for 3D reconstruction from a single image. We express the object's 3D geometry and appearance by means of a neural radiance field. Then, we fit the radiance field to the given input image by minimizing the usual rendering loss. At the same time, we sample random other views of the object, and constrain them with the diffusion prior, using a technique similar to DreamFusion.", + "bbox": [ + 75, + 518, + 468, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We find that, due to the coverage issue, this idea does not work well out of the box, but can be improved via adequately conditioning the 2D diffusion model. The idea is to configure the prior to \"dream up\" or sample images that may plausibly constitute other views of the given object. We do so by automatically engineering the diffusion prompt from random augmentations of the given image. In this manner, the diffusion model provides sufficiently strong constraints to allow meaningful 3D reconstruction.", + "bbox": [ + 73, + 642, + 468, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to setting the prompt correctly, we also add some regularizers: shading the underlying geometry and randomly dropping out texture (also similar to DreamFusion), smoothing the normals of the surface, and fitting the model in a coarse-to-fine fashion, capturing first the overall structure of the object and only then the fine-grained details. We also focus on efficiency and base our model on Instant-NGP [23]. In this manner, we achieve reconstructions in the", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "span of hours instead of days if we were to adopt traditional MLP-based NeRF models.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We assess our approach by using random images captured in the wild as well as existing benchmark datasets. Note that we do not train a fully-fledged 2D-to-3D model and we are not limited to specific object categories; rather, we perform reconstruction on an image-by-image basis using a pretrained 2D generator as a prior. Nonetheless, we can surpass quantitatively and qualitatively previous single-image reconstructors, including Shelf-Supervised Mesh Prediction [50], which uses supervision tailored specifically for 3D reconstruction.", + "bbox": [ + 496, + 123, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Qualitatively, we obtain plausible 3D reconstructions that are a good match for the provided input image (Fig. 1). Our reconstructions are not perfect, as the diffusion prior clearly does its best to explain the available image evidence but cannot always match all the details. Even so, we believe that our results convincingly demonstrate the viability of this approach and trace a path for future improvements.", + "bbox": [ + 496, + 275, + 890, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we make the following contributions: (1) We propose RealFusion, a method that can extract from a single image of an object a $360^{\\circ}$ photographic 3D reconstruction without assumptions on the type of object imaged or 3D supervision of any kind; (2) We do so by leveraging an existing 2D diffusion image generator via a new single-image variant of textual inversion; (3) We also introduce new regularizers and provide an efficient implementation using InstantNGP; (4) We demonstrate state-of-the-art reconstruction results on a number of in-the-wild images and images from existing datasets when compared to alternative approaches.", + "bbox": [ + 496, + 382, + 890, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 582, + 635, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Radiance fields. The problem of reconstructing photometry and geometry together has been dramatically revitalized by the introduction of neural radiance fields (RFs). NeRF [20] in particular noticed that a coordinate MLP provides a compact and yet expressive representation of 3D fields, and can be used to model RFs with great effectiveness. Many variants of NeRF-like models have since appeared. For instance, some [18, 41, 43] use sign distance functions (SDFs) to recover cleaner geometry. These approaches assume that dozens if not hundreds of views of each scene are available for reconstruction. Here, we use radiance fields for single-image reconstruction by using a diffusion model to \"dream up\" the missing views.", + "bbox": [ + 496, + 608, + 890, + 805 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-view reconstruction. Many authors have attempted to improve the statistical efficiency of NeRF-like models by learning or incorporating various kinds of priors. Most of these approaches train deep networks specifically for the goal of inferring NeRFs from a small number of views; examples include IBRNet [44], NeRF-WCE [9], Pixel", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8447", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e2a25611d42a2f91350482683038bab9a9a46499b331043d8b431436995722b2.jpg", + "image_caption": [ + "Figure 2. Method diagram. Our method optimizes a neural radiance field using two objectives simultaneously: a reconstruction objective and a prior objective. The reconstruction objective ensures that the radiance field resembles the input image from a specific, fixed view. The prior objective uses a large pre-trained diffusion model to ensure that the radiance field looks like the given object from randomly sampled novel viewpoints. The key to making this process work well is to condition the diffusion model on a prompt with a custom token $\\langle \\mathbf{e} \\rangle$ , which is generated prior to reconstruction using single-image textual inversion." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 467, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRF [51], NeRFormer [31], and ViewFormer [16]. These models still generally require more than one input view at test time and multi-view data for training. Closer to our work, NeRF-on-a-Diet [13] reduces the number of images needed for NeRF optimization by generating random views and measuring their \"semantic compatibility\" via CLIP embeddings [28], but it also still requires several input views.", + "bbox": [ + 75, + 435, + 468, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Single-view reconstruction. Some authors have attempted to recover full 3D representations from single images, but this generally requires multi-view data for training, as well as learning models that are specific to a specific object category. 3D-R2N2 [4], Pix2Vox [48], and LegoFormer [49] learn to reconstruct volumetric representation of simple objects, mainly from synthetic data like ShapeNet [3]. More recently, CodeNeRF [14] predicts a full radiance field and AutoRF [22] learns a similar autoencoder specifically for cars. Shelf-Supervised Mesh Prediction [50] and SS3D [42] learn to reconstruct a broad set of object categories by refining a mesh extracted from a coarse predicted volume. The former learns independent models for each category, whereas the latter unites them into a unified model via distillation.", + "bbox": [ + 75, + 547, + 468, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Extracting 3D models from 2D generators. Several authors have proposed to extract 3D models from 2D image generators, originally using GANs [2, 6, 8, 24, 25, 47]. Also related to our work, CLIP-Mesh [15] and Dream Fields [12] use a pre-trained image-text model [28] to condition 3D generation on textual prompts and do not require 3D supervision. Recently, DreamFusion [27] builds on this idea using a diffusion model as a prior. These models, however,", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/92f5abf00ec70c1fc6815f5c90ad4a73d56ef3f575c36cec5d7c6897549515ba.jpg", + "image_caption": [ + "Figure 3. Examples demonstrating the level of detail of information captured by the optimized embedding $\\langle \\mathbf{e} \\rangle$ . Rows 1-2 show input images and masks. The images are used to optimize $\\langle \\mathbf{e} \\rangle$ via our single-image textual inversion process. Rows 3-5 show examples of 2D images generated using $\\langle \\mathbf{e} \\rangle$ in new prompts, which we hope demonstrate the type of information encoded in $\\langle \\mathbf{e} \\rangle$ . Rows 6-7 show RealFusion's output, optimized using the prompt \"An image of a $\\langle \\mathbf{e} \\rangle$ \"." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 888, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are used as either pure generators or generators conditioned on vague cues such as class identity or textual descriptions. Here, we build on the DreamFusion approach, extending the idea to single-view reconstruction.", + "bbox": [ + 498, + 507, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, the authors of [46] have proposed to directly generate multiple 2D views of an object, which can then be reconstructed in 3D using a NeRF-like model. This is also reminiscent of our approach, but their model requires multiview data for training, is only tested on synthetic data, and requires to explicitly sample multiple views for reconstruction (in our case they remain implicit).", + "bbox": [ + 498, + 568, + 890, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models. Diffusion denoising probabilistic models are a class of generative models based on iteratively reversing a Markovian noising process. Early works formulated the problem as learning a variational lower bound [10], or framed it as optimizing a score-based generative model [37, 38] or as the discretization of a continuous stochastic process [39]. Recent improvements include the use of faster and deterministic sampling [10, 19, 45], class-conditional models [5, 38], text-conditional models [26], and modeling in latent space [34].", + "bbox": [ + 498, + 676, + 890, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 844, + 589, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We review the background and notation in Sec. 3.1, and then discuss our RealFusion method in Sec. 3.2.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8448", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Radiance fields, diffusion and distillation", + "text_level": 1, + "bbox": [ + 76, + 90, + 426, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Radiance fields. A radiance field (RF) is a pair of functions $(\\sigma(\\boldsymbol{x}), c(\\boldsymbol{x}))$ mapping a 3D point $\\boldsymbol{x} \\in \\mathbb{R}^3$ to an opacity value $\\sigma(\\boldsymbol{x}) \\in \\mathbb{R}_+$ and a color value $c(\\boldsymbol{x}) \\in \\mathbb{R}^3$ . The RF is called neural when these two functions are implemented by a neural network.", + "bbox": [ + 75, + 114, + 468, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The RF represents the shape and appearance of an object. In order to generate an image of it, one renders the RF using the emission-absorption model [21]. This can be modeled as a function $I = \\mathcal{R}(\\sigma, c, \\pi) \\in \\mathbb{R}^{3 \\times H \\times W}$ that extracts a color image $I$ from the radiance field $(\\sigma, c)$ given a viewpoint $\\pi \\in \\mathrm{SE}(3)$ . The rendering function $R(\\sigma, c, \\pi)$ is differentiable, which allows training the model by means of a standard optimizer. Specifically, the RF is fitted to a dataset $\\mathcal{D} = \\{(I, \\pi)\\}$ of images $I$ with known camera parameters by minimizing the $L_{2}$ image reconstruction error", + "bbox": [ + 75, + 190, + 470, + 340 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c}} (\\sigma , c; \\mathcal {D}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, \\pi) \\in \\mathcal {D}} \\| I - R (\\sigma , c, \\pi) \\| ^ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 353, + 468, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to obtain good-quality results, one typically requires a dataset of dozens or hundreds of views.", + "bbox": [ + 75, + 400, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we consider the case in which we are given exactly one input image $I_0$ corresponding to some (unknown) camera $\\pi_0$ . In this case, we can also assume any standard viewpoint $\\pi_0$ for that single camera. Optimizing Eq. (1) with a single training image leads to severe over-fitting: it is straightforward to find a pair $(\\sigma, c)$ that has zero loss and yet does not capture any sensible 3D model of the object. Below we will leverage a pre-trained 2D image prior to (implicitly) dream up novel views of the object and provide the missing information for 3D reconstruction.", + "bbox": [ + 75, + 431, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion models. A diffusion model draws a sample from a probability distribution $p(I)$ by inverting a process that gradually adds noise to the image $I$ . The diffusion process is associated with a noising schedule $\\{\\alpha_t \\in (0,1)\\}_{t=1}^T$ , which defines how much noise is added at each time step. The noisy version of sample $I$ at time $t$ can then be written $I_t = \\alpha_t I + \\sigma_t \\epsilon$ , where $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ , is a sample from a Gaussian distribution and $\\sigma_t^2 = 1 - \\alpha_t^2$ . One then learns a denoising neural network $\\hat{\\epsilon} = \\Phi(I_t; t)$ that takes as input the noisy image $I_t$ and the noise level $t$ and predicts the noise component $\\epsilon$ . Iterated applications of the network generate $I = I_0$ from $I_T \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ .", + "bbox": [ + 75, + 585, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The diffusion model is trained on large collections $\\mathcal{D}' = \\{I\\}$ of images by minimizing the loss", + "bbox": [ + 76, + 767, + 468, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i f f}} \\left(\\Phi ; \\mathcal {D} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {D} ^ {\\prime} |} \\sum_ {I \\in \\mathcal {D} ^ {\\prime}} \\left| \\left| \\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t\\right) - \\epsilon \\right| \\right| ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 810, + 468, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This model can be easily extended to draw samples from a distribution $p(x|e)$ conditioned on a prompt $e$ . Conditioning on the prompt is obtained by adding $e$ as an additional", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "input of the network $\\Phi$ , and the strength of conditioning can be controlled via classifier-free guidance [5, 11].", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DreamFusion and Score Distillation Sampling (SDS). Given a 2D diffusion model $p(I|e)$ and a prompt $e$ , DreamFusion extracts from it a 3D rendition of the corresponding concept, represented by a RF $(\\sigma, c)$ . It does so by randomly sampling a camera parameter $\\pi$ , rendering a corresponding view $I$ , assessing the likelihood of the view based on the model $p(I|e)$ , and updating the RF to increase the likelihood of the generated view based on the model.", + "bbox": [ + 496, + 125, + 890, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, DreamFusion uses the denoising network as a frozen critic and takes a gradient step", + "bbox": [ + 496, + 244, + 890, + 275 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {(\\sigma , c)} \\mathcal {L} _ {\\mathrm {S D S}} (\\sigma , c; \\pi , e, t) = \\\\ E _ {t, \\epsilon} \\left[ w (t) \\left(\\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t, \\boldsymbol {e}\\right) - \\epsilon\\right) \\cdot \\frac {\\partial I}{\\partial (\\sigma , c)} \\right], \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 290, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I = R(\\sigma, c, \\pi)$ is the image rendered from a randomly-sampled viewpoint $\\pi$ and $w(t)$ is a timestep-dependent weighting function. This process is called Score Distillation Sampling (SDS).", + "bbox": [ + 496, + 351, + 890, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One final aspect of DreamFusion is essential for understanding our contribution in the following section: DreamFusion finds that it is necessary to use classifier-free guidance [5] with a very high guidance weight of 100, much larger than one would use for image sampling, in order to obtain good 3D shapes. As a result, the generations tend to have limited diversity; they produce only the most likely objects for a given prompt, which is incompatible with our goal of reconstructing any given object.", + "bbox": [ + 496, + 412, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. RealFusion", + "text_level": 1, + "bbox": [ + 500, + 556, + 624, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our goal is to reconstruct a 3D model of the object contained in a single image $I_0$ , utilizing the prior captured in the diffusion model $\\Phi$ to make up for the missing information. We do this by optimizing a radiance field using two simultaneous objectives: (1) a reconstruction objective (Eq. (1)) from a fixed viewpoint, and (2) a SDS-based prior objective (Eq. (3)) on novel views randomly sampled at each iteration. Figure 2 provides a diagram of the method.", + "bbox": [ + 496, + 580, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Single-image textual inversion as a substitute for alternative views. The most important component of our method is the use of single-image textual inversion as a substitute for alternative views. Ideally, we would like to condition our reconstruction process on multi-view images of the object in $I_0$ , i.e., on samples from $p(I|I_0)$ .", + "bbox": [ + 496, + 704, + 890, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since these images are not available, our idea is to engineer a text prompt $e^{(I_0)}$ specifically for image $I_0$ as a proxy for this multi-view information, i.e., as an approximation of $p(I|I_0)$ . We do so by generating random augmentations $h(I_0), h \\in H$ of the input image, which serve as pseudo-alternative-views. We use these augmentations as a mini-dataset $\\mathcal{D}' = \\{h(I_0)\\}_{h \\in H}$ and optimize the diffusion loss", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8449", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4fa14015df1ed4e2cd8170d4cb6cec249e1083904621c6607bac898d54e0a9c8.jpg", + "image_caption": [ + "Figure 4. Qualitative results. RealFusion reconstructions from a single input view. Each pair of columns shows the textured object and the underlying 3D shape, as a shaded surface. Different pairs of columns show different viewpoints." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 890, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{\\mathrm{diff}}(\\Phi (\\cdot ;e^{(I_0)}))$ of Eq. (2) with respect to the prompt $e^{(I_0)}$ while freezing all other text embeddings and model parameters.", + "bbox": [ + 75, + 564, + 468, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, our prompt is derived automatically from the template \"an image of a $\\langle \\mathbf{e} \\rangle$ \", where \" $\\langle \\mathbf{e} \\rangle$ ( $= e^{(I_0)}$ ) is a newizable token introduced to the vocabulary of the text encoder of our diffusion model (see the supplementary material for details). A caption or description of $I_0$ is not needed. Our optimization procedure mirrors and generalizes the recently-proposed textual-inversion method of [7]. Differently from [7], we work in the single-image setting and utilize image augmentations for training rather than multiple views.", + "bbox": [ + 75, + 612, + 470, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To help convey the intuition behind $\\langle \\mathbf{e} \\rangle$ , consider an attempt at reconstructing an image of a fish using the generic text prompt \"An image of a fish\" with losses (2) and (3). In our experience, this often produces a reconstruction which looks like the input fish from the input viewpoint, but looks like some different, more-generic fish from the backside. By contrast, using the prompt \"An image of a $\\langle \\mathbf{e} \\rangle$ \", the reconstruction resembles the input fish from all angles. An example of exactly this case is shown in Fig. 7, and Fig. 3", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "demonstrates the amount of detail captured in the embedding $\\langle \\mathbf{e}\\rangle$", + "bbox": [ + 498, + 565, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Coarse-to-fine training. We use the diffusion prior described above to optimize an RF in a coarse-to-fine manner. Before describing our coarse-to-fine training methodology, we first briefly introduce the underlying RF model, i.e., InstantNGP [23]. InstantNGP is a grid-based model which stores features at the vertices of a set of feature grids $\\{G_i\\}_{i=1}^L$ at multiple resolutions. The resolution is chosen to be a geometric progression between the coarsest and finest resolutions, and feature grids are trained simultaneously.", + "bbox": [ + 496, + 612, + 892, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We choose InstantNGP over a conventional MLP due to its computational efficiency. However, InstantNGP tends to produce small irregularities on the surface of the object. We find that training in a coarse-to-fine manner helps to alleviate these issues: for the first half of training we only optimize the lower-resolution feature grids $\\{G_i\\}_{i=1}^{L/2}$ , and then in the second half of training we optimize all feature grids $\\{G_i\\}_{i=1}^L$ . Using this strategy, we obtain the benefits of both efficient training and high-quality results.", + "bbox": [ + 496, + 762, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8450", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b562f2299d6329edc74616c43df25c6844bb06f0e348ff67e8eb9f18007fef57.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison with prior work. We show the results of our method and the category-level method of [50] on real-world images from the CO3D dataset [31]. Each pair of rows show two novel views produced by [50] and our method. For [50], we use category-specific models for each CO3D category (in this case, motorcycles, cups, and backpacks). Despite not requiring any category-specific information, our method is able to reconstruct objects at a higher level of detail than [50]." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 467, + 294 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5197fa2640e80a46031fa205a6f86bda7d6adafdee330d53848837506ab203ee.jpg", + "image_caption": [ + "Figure 6. Diversity of 3D reconstructions from a single image. Above, we see our method's ability to generate a diverse set of object reconstructions given the same input image. In particular, the method produces different textures on the backsides of the generated objects, despite all objects matching the input image from the reference view." + ], + "image_footnote": [], + "bbox": [ + 81, + 417, + 460, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Normal vector regularization. We introduce a regularization term to encourage our geometry to have smoothly varying normal vectors. Notably, we perform this regularization in $2D$ rather than in 3D because we found that it reduces the variance of the regularizer and improves results.", + "bbox": [ + 75, + 689, + 467, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "At each iteration, in addition to computing RGB and opacity values, we also compute normals for each point along the ray and aggregate these via the ray marching equation to obtain normals1 $N \\in \\mathcal{R}^{3 \\times H \\times W}$ . Our loss is:", + "bbox": [ + 75, + 765, + 467, + 824 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {n o r m a l s}} = \\| N - \\operatorname {s t o p g r a d} (\\operatorname {b l u r} (N, k)) \\| ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 837, + 467, + 854 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5a6fc2a253babff581d669d68995eb18f1b8ba4cfe168e663b2ea5f720756dc2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
F-scoreCLIP-similarity
[50]Ours[50]Ours
Backpack7.5812.220.720.74
Chair8.2610.230.650.76
Motorcycle8.668.720.690.70
Orange6.2710.160.710.74
Skateboard7.745.890.740.74
Teddybear12.8910.080.730.82
Vase6.309.720.690.71
Mean8.249.580.700.74
", + "bbox": [ + 511, + 88, + 880, + 255 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison. We compare our method with Shelf-Supervised [50] on seven object categories. The F-score and CLIP-similarity metrics are designed to measure the quality of reconstruction shape and appearance, respectively. For both metrics, higher is better. Metrics are averaged over three images per category. Our method outperforms [50] in aggregate, despite the fact that [50] uses a different category-specific model for each category.", + "bbox": [ + 496, + 266, + 890, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where stopgrad is a stop-gradient operation and $\\mathrm{blur}(\\cdot ,k)$ is a Gaussian blur with kernel size $k$ (we use $k = 9$ ).", + "bbox": [ + 498, + 390, + 890, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mask loss. In addition to the input image, our model also utilizes a mask of the object that one wishes to reconstruct. In practice, we use an off-the-shelf image matting model to obtain this mask for all images. The loss is simply the $L^2$ norm of the difference between the rendered opacities from the fixed reference viewpoint $\\hat{M} = \\mathcal{R}(\\sigma, \\pi_0) \\in \\mathcal{R}^{H \\times W}$ and the object mask $M$ : $\\mathcal{L}_{\\mathrm{mask}} = \\| \\hat{M} - M \\|^2$", + "bbox": [ + 496, + 424, + 890, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our final objective then consists of four terms:", + "bbox": [ + 517, + 530, + 826, + 544 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\sigma , c} \\mathcal {L} = \\nabla \\mathcal {L} _ {\\mathrm {S D S}} + \\lambda_ {\\text {n o r m a l s}} \\cdot \\nabla \\mathcal {L} _ {\\text {n o r m a l s}} \\\\ + \\lambda_ {\\text {i m a g e}} \\cdot \\nabla \\mathcal {L} _ {\\text {i m a g e}} + \\lambda_ {\\text {m a s k}} \\cdot \\nabla \\mathcal {L} _ {\\text {m a s k}} \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 561, + 890, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the first two terms are regularizers and the remaining ones are data terms.", + "bbox": [ + 498, + 608, + 890, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 652, + 632, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 678, + 712, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Regarding hyperparameters, we use nearly the same set of hyper-parameters for all experiments—there is no per-scene hyper-parameter adjustment. For our diffusion model prior, we employ the open-source Stable Diffusion model [34] trained on the LAION [36] dataset. At each optimization step, we first render from the reconstruction camera and compute our reconstruction losses $\\mathcal{L}_{\\mathrm{image}}$ and $\\mathcal{L}_{\\mathrm{mask}}$ . We then render from a randomly sampled camera to obtain a novel view and use this view for $\\mathcal{L}_{\\mathrm{SDS}}$ and $\\mathcal{L}_{\\mathrm{normals}}$ . We use $\\lambda_{\\mathrm{image}} = 5.0$ , $\\lambda_{\\mathrm{mask}} = 0.5$ , and $\\lambda_{\\mathrm{normals}} = 0.5$ .", + "bbox": [ + 496, + 700, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1 Normals may be computed either by taking the gradient of the density field or by using finite differences. We found that using finite differences works well in practice.", + "bbox": [ + 76, + 862, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2There is one small exception to this rule, which is that for a small number of images where the camera angle was clearly at an angle higher than $15^{\\circ}$ above the horizontal plane, we used a camera angle of 30 or $40^{\\circ}$ .", + "bbox": [ + 500, + 862, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8451", + "bbox": [ + 482, + 926, + 513, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8cfc2e1856e99898a74ad8d3e265f81a9f73698176df06d570f54dc8816b0abd.jpg", + "image_caption": [ + "Figure 7. A visualization of the effect of single-image textual inversion on reconstruction quality. In each pair of rows, the top row shows the result of utilizing a standard text prompt for our diffusion-model-based loss (e.g., \"An image of a statue of a cat\"). The bottom row shows the result of utilizing a text prompt optimized for the input image in a fully-automatic manner; this textual inversion process dramatically improves object reconstruction." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 869, + 345 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/596b75f035a042c0e7677ed95137e4d4eca68973f9f3be862497d0456a467994.jpg", + "image_caption": [ + "Figure 8. Effect of coarse-to-fine training. The top row of each pair is generated by optimizing all levels of a multi-resolution 3D feature grid from the first optimization step, whereas the bottom row is optimized in a coarse-to-fine manner." + ], + "image_footnote": [], + "bbox": [ + 78, + 415, + 467, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regarding camera sampling, lighting, and shading, we keep nearly all parameters the same as [27]. We describe our setup in detail in the supplementary material.", + "bbox": [ + 75, + 666, + 468, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Quantitative results", + "text_level": 1, + "bbox": [ + 76, + 724, + 266, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "There are only few methods that attempt to reconstruct arbitrary objects in 3D. The most recent and best-performing of these is Shelf-Supervised Mesh Prediction [50], which we compare to here. They provide 50 pretrained category-level models for 50 different categories in OpenImages [17]. Since we aim to compute metrics using 3D or multi-view ground truth, we evaluate on seven categories from the CO3D dataset [32] with corresponding OpenImages categories. For each of these seven categories, we select three images at random and run both RealFusion", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b1743ff122f0b51f8b25b1a0fbd31b64185866c4e9462cae1d2d524f3f7e5552.jpg", + "image_caption": [ + "Figure 9. Effect of normal smoothness on reconstruction quality. Each pair of rows show the reconstruction without and with the normal smoothness regularization term (4). The regularizer improves the visual appearance of surfaces and reduces the number of irregularities on the surface of reconstructed objects. In most cases, we also find that it helps to improve the overall realism of the reconstructed shape." + ], + "image_footnote": [], + "bbox": [ + 501, + 415, + 888, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and Shelf-Supervised to obtain reconstructions.", + "bbox": [ + 498, + 719, + 813, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first test the quality of the recovered 3D shape in Fig. 5. [50] directly predicts a mesh, while we extract a mesh from our predicted radiance field using marching cubes. CO3D comes with sparse point-cloud reconstructions of objects obtained using multi-view geometry. For evaluation, we sample points from the reconstructed meshes and align them optimally with the ground truth point cloud by first estimating a scaling factor and then using Iterated Closest Point (ICP). Finally, we compute the F-score [40] with a threshold of 0.05 to measure the distance between the predicted and ground truth point clouds. Results are", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8452", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/312ac77e375873e769e5cc74e5c3cd4b2b5ac42b569d4510097a28e1d102126b.jpg", + "image_caption": [ + "Figure 10. Comparing Stable Diffusion and CLIP priors. Results from two different priors: Stable Diffusion [34] and CLIP [29]. Stable Diffusion yields much higher-quality reconstructions, capturing more plausible object shapes." + ], + "image_footnote": [], + "bbox": [ + 80, + 85, + 467, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7cb77fa022b16327958075aeae5f1ccde1a916858c6e9cec273234da9738922d.jpg", + "image_caption": [ + "Figure 11. Failure cases. In the first two examples, the model simply fails to properly reconstruct the object geometry, and produces a semi-transparent scene which lacks a well-defined geometry. The third case is different in that the geometry is highly realistic, but the texture paints two Pikachu faces, one on each side of the object; this problem is sometimes called the Janus problem, after the two-faced Roman god." + ], + "image_footnote": [], + "bbox": [ + 81, + 316, + 460, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shown in Tab. 1.", + "text_level": 1, + "bbox": [ + 76, + 611, + 187, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to evaluate the quality of the reproduced appearance, we also compare novel-view renderings from our and their method. Ideally, these renderings should produce views that are visually close to the real views. In order to test this hypothesis, we check whether the generated views are close or not to the other views given in CO3D. We report (Tab. 1) the CLIP embedding similarity of the generated images with respect to the closest CO3D view available (i.e., the view with maximum similarity).", + "bbox": [ + 75, + 627, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative results", + "text_level": 1, + "bbox": [ + 76, + 771, + 253, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 4 shows additional qualitative results from multiple viewpoints. Fig. 6 explores the ability of RealFusion to sample the space of possible solutions by repeating the reconstruction several times, starting from the same input image. There is little variance in the reconstructions of the front side of the object, but significant variance for its backside.", + "bbox": [ + 75, + 794, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 11 shows two typical failure modes of RealFusion: in some cases, the model fails to converge, and in others, it copies the front view to the back of the object, even if this is not semantically correct.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Analysis and Ablations", + "text_level": 1, + "bbox": [ + 500, + 171, + 712, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "One of the key components of RealFusion is our use of single-image textual inversion, which allows the model to correctly imagine novel views of a specific object. Fig. 7 shows that this component plays indeed a critical role in the quality and consistency of the reconstructions. Without textual inversion, the model often reconstructs the backside of the object in the form of a generic instance from the object category. For example, the backside of the cat statue in the top row of Fig. 7 is essentially a different statue of a more generic-looking cat, whereas the model trained with textual inversion resembles the true object from all angles.", + "bbox": [ + 496, + 196, + 890, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other components of the model are also significant. Fig. 8 shows that coarse-to-fine optimization reduces the presence of low-level artifacts and results in smoother, visually pleasing surfaces. Fig. 9 shows that the normal smoothness regularizer of Eq. (4) further results in smoother, more realistic meshes. Fig. 10 shows that using Stable Diffusion works significantly better than relying on an alternative such as CLIP.", + "bbox": [ + 496, + 367, + 890, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 511, + 625, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced RealFusion, a new approach to obtain full $360^{\\circ}$ photographic reconstructions of any object given a single image of it. To achieve this, we leverage an off-the-shelf diffusion model trained using only pairs of 2D images and text (but no 3D supervision) and optimize a token embedding to represent the object depicted in the image. We use this conditional prior to learn an efficient, multi-scale radiance field representation of the reconstructed object, incorporating an additional regularizer to smooth out the reconstructed surface. The resulting method can generate plausible 3D reconstructions of objects captured in the wild which are faithful to the input image. Future improvements could be obtained by specializing the diffusion model for the task of new-view synthesis.", + "bbox": [ + 496, + 540, + 890, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethics. We use the CO3D dataset in a manner compatible with their terms; it does not contain personal information. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html.", + "bbox": [ + 496, + 758, + 890, + 833 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. L. M. K. is supported by the Rhodes Trust. A. V., I. L. and C. R. are supported by ERC-UNION-CoG-101001212. I. L. and C. R. are also supported by VisualAI EP/T028572/1.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8453", + "bbox": [ + 480, + 926, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Bau, Jun-Yan Zhu, Jonas Wulff, William S. Peebles, Bolei Zhou, Hendrik Strobelt, and Antonio Torralba. Seeing what a GAN cannot generate. In Proc. ICCV, 2019. 2", + "[2] Eric R. Chan, Connor Z. Lin, Matthew A. Chan, Koki Nagano, Boxiao Pan, Shalini De Mello, Orazio Gallo, Leonidas J. Guibas, Jonathan Tremblay, Sameh Khamis, Tero Karras, and Gordon Wetzstein. Efficient geometry-aware 3D generative adversarial networks. In Proc. CVPR, 2022. 2, 3", + "[3] Angel X. Chang, Thomas A. Funkhouser, Leonidas J. 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CVPR, pages 4578-4587, 2021. 3" + ], + "bbox": [ + 501, + 92, + 890, + 539 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8455", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_model.json b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..16fe43c579e0378f9e0e3e46aa15cd3d043aeef5 --- /dev/null +++ b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.427, + 0.132, + 0.546, + 0.15 + ], + "angle": 0, + "content": "RealFusion" + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.155, + 0.766, + 0.176 + ], + "angle": 0, + "content": "\\(360^{\\circ}\\) Reconstruction of Any Object from a Single Image" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.204, + 0.778, + 0.222 + ], + "angle": 0, + "content": "Luke Melas-Kyriazi Iro Laina Christian Rupprecht Andrea Vedaldi" + }, + { + "type": "text", + "bbox": [ + 0.238, + 0.242, + 0.732, + 0.257 + ], + "angle": 0, + "content": "Visual Geometry Group, Department of Engineering Science, University of Oxford" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.26, + 0.674, + 0.274 + ], + "angle": 0, + "content": "{lukemk,iro,chrisr,vedaldi}@robots.ox.ac.uk" + }, + { + "type": "text", + "bbox": [ + 0.373, + 0.278, + 0.595, + 0.292 + ], + "angle": 0, + "content": "https://lukemelas.github.io/realfusion" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.321, + 0.156, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.159, + 0.323, + 0.891, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.549, + 0.893, + 0.606 + ], + "angle": 0, + "content": "Figure 1. RealFusion generates a full \\(360^{\\circ}\\) reconstruction of any object given a single image of it (left column). It does so by leveraging an existing diffusion-based 2D image generator. From the given image, it synthesizes a prompt that causes the diffusion model to \"dream up\" other views of the object. It then extracts a neural radiance field from the original image and the diffusion model-based prior, thereby reconstructing the object in full. Both appearance and geometry are reconstructed faithfully and extrapolated in a plausible manner." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.626, + 0.314, + 0.641 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We consider the problem of reconstructing a full \\(360^{\\circ}\\) photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to \"dream up\" novel views of the object. Using the recent DreamFusion method, we fuse the given input view, the conditional prior, and other regularizers into a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.628, + 0.589, + 0.642 + ], + "angle": 0, + "content": "in the image." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.677, + 0.631, + 0.692 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.885 + ], + "angle": 0, + "content": "We consider the problem of obtaining a \\(360^{\\circ}\\) photographic reconstruction of any object given a single image of it. The challenge is that a single image does not contain sufficient information for 3D reconstruction. Without access to multiple views, an image only provides weak evidence about the 3D shape of the object, and only for one side of it. Even so, there is proof that this task can be solved: any skilled 3D artist can take a picture of almost any object and, given sufficient time and effort, create a plausible 3D model of it. The artist can do so by tapping into their vast knowledge of the natural world and the objects it contains, making up for the information missing from the image." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.888, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Hence, monocular 3D reconstruction requires combining" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.926, + 0.516, + 0.937 + ], + "angle": 0, + "content": "8446" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "visual geometry with a powerful statistical model of the 3D world. Diffusion-based 2D image generators like DALL-E 2 [30], Imagen [35], and Stable Diffusion [33] are able to generate high-quality images from ambiguous inputs such as text, showing that powerful priors for 2D images can be learned. However, extending them to 3D is not easy because, while one can access billions of 2D images for training [36], the same cannot be said for 3D data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.47, + 0.365 + ], + "angle": 0, + "content": "A simpler approach is to extract or distill 3D information from an existing 2D generator. A 2D image generator can in fact be used to sample or validate multiple views of a given object, which can then be used to perform 3D reconstruction. This idea was already demonstrated with GAN-based generators for simple data like faces and synthetic objects [2, 6, 8, 24, 25, 47]. Better 2D generators have since resulted in better results, culminating in methods such as DreamFusion [27], which can produce high-quality 3D models from an existing 2D generator and text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.519 + ], + "angle": 0, + "content": "In this paper, we port distillation approaches from text-based generation to monocular 3D reconstruction. This is not a trivial change because conditioning generation on an image provides a much more fine-grained specification of the object than text. This in turn requires the 2D diffusion model to hallucinate new views of a specific object instead of some object of a given type. The latter is difficult because the coverage of generator models is limited [1], meaning that not every version of an object is captured well by the model. We find empirically that this is a key problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.641 + ], + "angle": 0, + "content": "We address this issue by introducing RealFusion, a new method for 3D reconstruction from a single image. We express the object's 3D geometry and appearance by means of a neural radiance field. Then, we fit the radiance field to the given input image by minimizing the usual rendering loss. At the same time, we sample random other views of the object, and constrain them with the diffusion prior, using a technique similar to DreamFusion." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.643, + 0.47, + 0.779 + ], + "angle": 0, + "content": "We find that, due to the coverage issue, this idea does not work well out of the box, but can be improved via adequately conditioning the 2D diffusion model. The idea is to configure the prior to \"dream up\" or sample images that may plausibly constitute other views of the given object. We do so by automatically engineering the diffusion prompt from random augmentations of the given image. In this manner, the diffusion model provides sufficiently strong constraints to allow meaningful 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In addition to setting the prompt correctly, we also add some regularizers: shading the underlying geometry and randomly dropping out texture (also similar to DreamFusion), smoothing the normals of the surface, and fitting the model in a coarse-to-fine fashion, capturing first the overall structure of the object and only then the fine-grained details. We also focus on efficiency and base our model on Instant-NGP [23]. In this manner, we achieve reconstructions in the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "span of hours instead of days if we were to adopt traditional MLP-based NeRF models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.124, + 0.892, + 0.273 + ], + "angle": 0, + "content": "We assess our approach by using random images captured in the wild as well as existing benchmark datasets. Note that we do not train a fully-fledged 2D-to-3D model and we are not limited to specific object categories; rather, we perform reconstruction on an image-by-image basis using a pretrained 2D generator as a prior. Nonetheless, we can surpass quantitatively and qualitatively previous single-image reconstructors, including Shelf-Supervised Mesh Prediction [50], which uses supervision tailored specifically for 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.382 + ], + "angle": 0, + "content": "Qualitatively, we obtain plausible 3D reconstructions that are a good match for the provided input image (Fig. 1). Our reconstructions are not perfect, as the diffusion prior clearly does its best to explain the available image evidence but cannot always match all the details. Even so, we believe that our results convincingly demonstrate the viability of this approach and trace a path for future improvements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.565 + ], + "angle": 0, + "content": "To summarize, we make the following contributions: (1) We propose RealFusion, a method that can extract from a single image of an object a \\(360^{\\circ}\\) photographic 3D reconstruction without assumptions on the type of object imaged or 3D supervision of any kind; (2) We do so by leveraging an existing 2D diffusion image generator via a new single-image variant of textual inversion; (3) We also introduce new regularizers and provide an efficient implementation using InstantNGP; (4) We demonstrate state-of-the-art reconstruction results on a number of in-the-wild images and images from existing datasets when compared to alternative approaches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.583, + 0.637, + 0.599 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Radiance fields. The problem of reconstructing photometry and geometry together has been dramatically revitalized by the introduction of neural radiance fields (RFs). NeRF [20] in particular noticed that a coordinate MLP provides a compact and yet expressive representation of 3D fields, and can be used to model RFs with great effectiveness. Many variants of NeRF-like models have since appeared. For instance, some [18, 41, 43] use sign distance functions (SDFs) to recover cleaner geometry. These approaches assume that dozens if not hundreds of views of each scene are available for reconstruction. Here, we use radiance fields for single-image reconstruction by using a diffusion model to \"dream up\" the missing views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Few-view reconstruction. Many authors have attempted to improve the statistical efficiency of NeRF-like models by learning or incorporating various kinds of priors. Most of these approaches train deep networks specifically for the goal of inferring NeRFs from a small number of views; examples include IBRNet [44], NeRF-WCE [9], Pixel" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "8447" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.468, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.473, + 0.418 + ], + "angle": 0, + "content": "Figure 2. Method diagram. Our method optimizes a neural radiance field using two objectives simultaneously: a reconstruction objective and a prior objective. The reconstruction objective ensures that the radiance field resembles the input image from a specific, fixed view. The prior objective uses a large pre-trained diffusion model to ensure that the radiance field looks like the given object from randomly sampled novel viewpoints. The key to making this process work well is to condition the diffusion model on a prompt with a custom token \\(\\langle \\mathbf{e} \\rangle\\), which is generated prior to reconstruction using single-image textual inversion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.543 + ], + "angle": 0, + "content": "NeRF [51], NeRFormer [31], and ViewFormer [16]. These models still generally require more than one input view at test time and multi-view data for training. Closer to our work, NeRF-on-a-Diet [13] reduces the number of images needed for NeRF optimization by generating random views and measuring their \"semantic compatibility\" via CLIP embeddings [28], but it also still requires several input views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Single-view reconstruction. Some authors have attempted to recover full 3D representations from single images, but this generally requires multi-view data for training, as well as learning models that are specific to a specific object category. 3D-R2N2 [4], Pix2Vox [48], and LegoFormer [49] learn to reconstruct volumetric representation of simple objects, mainly from synthetic data like ShapeNet [3]. More recently, CodeNeRF [14] predicts a full radiance field and AutoRF [22] learns a similar autoencoder specifically for cars. Shelf-Supervised Mesh Prediction [50] and SS3D [42] learn to reconstruct a broad set of object categories by refining a mesh extracted from a coarse predicted volume. The former learns independent models for each category, whereas the latter unites them into a unified model via distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Extracting 3D models from 2D generators. Several authors have proposed to extract 3D models from 2D image generators, originally using GANs [2, 6, 8, 24, 25, 47]. Also related to our work, CLIP-Mesh [15] and Dream Fields [12] use a pre-trained image-text model [28] to condition 3D generation on textual prompts and do not require 3D supervision. Recently, DreamFusion [27] builds on this idea using a diffusion model as a prior. These models, however," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.889, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.381, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Figure 3. Examples demonstrating the level of detail of information captured by the optimized embedding \\(\\langle \\mathbf{e} \\rangle\\). Rows 1-2 show input images and masks. The images are used to optimize \\(\\langle \\mathbf{e} \\rangle\\) via our single-image textual inversion process. Rows 3-5 show examples of 2D images generated using \\(\\langle \\mathbf{e} \\rangle\\) in new prompts, which we hope demonstrate the type of information encoded in \\(\\langle \\mathbf{e} \\rangle\\). Rows 6-7 show RealFusion's output, optimized using the prompt \"An image of a \\(\\langle \\mathbf{e} \\rangle\\)\"." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.508, + 0.892, + 0.568 + ], + "angle": 0, + "content": "are used as either pure generators or generators conditioned on vague cues such as class identity or textual descriptions. Here, we build on the DreamFusion approach, extending the idea to single-view reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.569, + 0.892, + 0.675 + ], + "angle": 0, + "content": "Recently, the authors of [46] have proposed to directly generate multiple 2D views of an object, which can then be reconstructed in 3D using a NeRF-like model. This is also reminiscent of our approach, but their model requires multiview data for training, is only tested on synthetic data, and requires to explicitly sample multiple views for reconstruction (in our case they remain implicit)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.678, + 0.892, + 0.83 + ], + "angle": 0, + "content": "Diffusion models. Diffusion denoising probabilistic models are a class of generative models based on iteratively reversing a Markovian noising process. Early works formulated the problem as learning a variational lower bound [10], or framed it as optimizing a score-based generative model [37, 38] or as the discretization of a continuous stochastic process [39]. Recent improvements include the use of faster and deterministic sampling [10, 19, 45], class-conditional models [5, 38], text-conditional models [26], and modeling in latent space [34]." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.845, + 0.591, + 0.86 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We review the background and notation in Sec. 3.1, and then discuss our RealFusion method in Sec. 3.2." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "8448" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.427, + 0.108 + ], + "angle": 0, + "content": "3.1. Radiance fields, diffusion and distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.189 + ], + "angle": 0, + "content": "Radiance fields. A radiance field (RF) is a pair of functions \\((\\sigma(\\boldsymbol{x}), c(\\boldsymbol{x}))\\) mapping a 3D point \\(\\boldsymbol{x} \\in \\mathbb{R}^3\\) to an opacity value \\(\\sigma(\\boldsymbol{x}) \\in \\mathbb{R}_+\\) and a color value \\(c(\\boldsymbol{x}) \\in \\mathbb{R}^3\\). The RF is called neural when these two functions are implemented by a neural network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.191, + 0.471, + 0.342 + ], + "angle": 0, + "content": "The RF represents the shape and appearance of an object. In order to generate an image of it, one renders the RF using the emission-absorption model [21]. This can be modeled as a function \\( I = \\mathcal{R}(\\sigma, c, \\pi) \\in \\mathbb{R}^{3 \\times H \\times W} \\) that extracts a color image \\( I \\) from the radiance field \\( (\\sigma, c) \\) given a viewpoint \\( \\pi \\in \\mathrm{SE}(3) \\). The rendering function \\( R(\\sigma, c, \\pi) \\) is differentiable, which allows training the model by means of a standard optimizer. Specifically, the RF is fitted to a dataset \\( \\mathcal{D} = \\{(I, \\pi)\\} \\) of images \\( I \\) with known camera parameters by minimizing the \\( L_{2} \\) image reconstruction error" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.354, + 0.47, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c}} (\\sigma , c; \\mathcal {D}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, \\pi) \\in \\mathcal {D}} \\| I - R (\\sigma , c, \\pi) \\| ^ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.469, + 0.43 + ], + "angle": 0, + "content": "In order to obtain good-quality results, one typically requires a dataset of dozens or hundreds of views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.469, + 0.581 + ], + "angle": 0, + "content": "Here, we consider the case in which we are given exactly one input image \\( I_0 \\) corresponding to some (unknown) camera \\( \\pi_0 \\). In this case, we can also assume any standard viewpoint \\( \\pi_0 \\) for that single camera. Optimizing Eq. (1) with a single training image leads to severe over-fitting: it is straightforward to find a pair \\( (\\sigma, c) \\) that has zero loss and yet does not capture any sensible 3D model of the object. Below we will leverage a pre-trained 2D image prior to (implicitly) dream up novel views of the object and provide the missing information for 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.469, + 0.766 + ], + "angle": 0, + "content": "Diffusion models. A diffusion model draws a sample from a probability distribution \\( p(I) \\) by inverting a process that gradually adds noise to the image \\( I \\). The diffusion process is associated with a noising schedule \\( \\{\\alpha_t \\in (0,1)\\}_{t=1}^T \\), which defines how much noise is added at each time step. The noisy version of sample \\( I \\) at time \\( t \\) can then be written \\( I_t = \\alpha_t I + \\sigma_t \\epsilon \\), where \\( \\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}) \\), is a sample from a Gaussian distribution and \\( \\sigma_t^2 = 1 - \\alpha_t^2 \\). One then learns a denoising neural network \\( \\hat{\\epsilon} = \\Phi(I_t; t) \\) that takes as input the noisy image \\( I_t \\) and the noise level \\( t \\) and predicts the noise component \\( \\epsilon \\). Iterated applications of the network generate \\( I = I_0 \\) from \\( I_T \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.768, + 0.469, + 0.798 + ], + "angle": 0, + "content": "The diffusion model is trained on large collections \\(\\mathcal{D}' = \\{I\\}\\) of images by minimizing the loss" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.811, + 0.469, + 0.843 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i f f}} \\left(\\Phi ; \\mathcal {D} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {D} ^ {\\prime} |} \\sum_ {I \\in \\mathcal {D} ^ {\\prime}} \\left| \\left| \\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t\\right) - \\epsilon \\right| \\right| ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "This model can be easily extended to draw samples from a distribution \\( p(x|e) \\) conditioned on a prompt \\( e \\). Conditioning on the prompt is obtained by adding \\( e \\) as an additional" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "input of the network \\(\\Phi\\), and the strength of conditioning can be controlled via classifier-free guidance [5, 11]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.125, + 0.892, + 0.244 + ], + "angle": 0, + "content": "DreamFusion and Score Distillation Sampling (SDS). Given a 2D diffusion model \\( p(I|e) \\) and a prompt \\( e \\), DreamFusion extracts from it a 3D rendition of the corresponding concept, represented by a RF \\( (\\sigma, c) \\). It does so by randomly sampling a camera parameter \\( \\pi \\), rendering a corresponding view \\( I \\), assessing the likelihood of the view based on the model \\( p(I|e) \\), and updating the RF to increase the likelihood of the generated view based on the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.246, + 0.892, + 0.276 + ], + "angle": 0, + "content": "In practice, DreamFusion uses the denoising network as a frozen critic and takes a gradient step" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.291, + 0.892, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {(\\sigma , c)} \\mathcal {L} _ {\\mathrm {S D S}} (\\sigma , c; \\pi , e, t) = \\\\ E _ {t, \\epsilon} \\left[ w (t) \\left(\\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t, \\boldsymbol {e}\\right) - \\epsilon\\right) \\cdot \\frac {\\partial I}{\\partial (\\sigma , c)} \\right], \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.412 + ], + "angle": 0, + "content": "where \\( I = R(\\sigma, c, \\pi) \\) is the image rendered from a randomly-sampled viewpoint \\( \\pi \\) and \\( w(t) \\) is a timestep-dependent weighting function. This process is called Score Distillation Sampling (SDS)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.549 + ], + "angle": 0, + "content": "One final aspect of DreamFusion is essential for understanding our contribution in the following section: DreamFusion finds that it is necessary to use classifier-free guidance [5] with a very high guidance weight of 100, much larger than one would use for image sampling, in order to obtain good 3D shapes. As a result, the generations tend to have limited diversity; they produce only the most likely objects for a given prompt, which is incompatible with our goal of reconstructing any given object." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.625, + 0.572 + ], + "angle": 0, + "content": "3.2. RealFusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Our goal is to reconstruct a 3D model of the object contained in a single image \\( I_0 \\), utilizing the prior captured in the diffusion model \\( \\Phi \\) to make up for the missing information. We do this by optimizing a radiance field using two simultaneous objectives: (1) a reconstruction objective (Eq. (1)) from a fixed viewpoint, and (2) a SDS-based prior objective (Eq. (3)) on novel views randomly sampled at each iteration. Figure 2 provides a diagram of the method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.796 + ], + "angle": 0, + "content": "Single-image textual inversion as a substitute for alternative views. The most important component of our method is the use of single-image textual inversion as a substitute for alternative views. Ideally, we would like to condition our reconstruction process on multi-view images of the object in \\( I_0 \\), i.e., on samples from \\( p(I|I_0) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since these images are not available, our idea is to engineer a text prompt \\( e^{(I_0)} \\) specifically for image \\( I_0 \\) as a proxy for this multi-view information, i.e., as an approximation of \\( p(I|I_0) \\). We do so by generating random augmentations \\( h(I_0), h \\in H \\) of the input image, which serve as pseudo-alternative-views. We use these augmentations as a mini-dataset \\( \\mathcal{D}' = \\{h(I_0)\\}_{h \\in H} \\) and optimize the diffusion loss" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "8449" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.891, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.511, + 0.895, + 0.542 + ], + "angle": 0, + "content": "Figure 4. Qualitative results. RealFusion reconstructions from a single input view. Each pair of columns shows the textured object and the underlying 3D shape, as a shaded surface. Different pairs of columns show different viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.61 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{\\mathrm{diff}}(\\Phi (\\cdot ;e^{(I_0)}))\\) of Eq. (2) with respect to the prompt \\(e^{(I_0)}\\) while freezing all other text embeddings and model parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.763 + ], + "angle": 0, + "content": "In practice, our prompt is derived automatically from the template \"an image of a \\(\\langle \\mathbf{e} \\rangle\\)\", where \" \\(\\langle \\mathbf{e} \\rangle\\) (\\(= e^{(I_0)}\\)) is a newizable token introduced to the vocabulary of the text encoder of our diffusion model (see the supplementary material for details). A caption or description of \\(I_0\\) is not needed. Our optimization procedure mirrors and generalizes the recently-proposed textual-inversion method of [7]. Differently from [7], we work in the single-image setting and utilize image augmentations for training rather than multiple views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To help convey the intuition behind \\(\\langle \\mathbf{e} \\rangle\\), consider an attempt at reconstructing an image of a fish using the generic text prompt \"An image of a fish\" with losses (2) and (3). In our experience, this often produces a reconstruction which looks like the input fish from the input viewpoint, but looks like some different, more-generic fish from the backside. By contrast, using the prompt \"An image of a \\(\\langle \\mathbf{e} \\rangle\\)\", the reconstruction resembles the input fish from all angles. An example of exactly this case is shown in Fig. 7, and Fig. 3" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.566, + 0.892, + 0.597 + ], + "angle": 0, + "content": "demonstrates the amount of detail captured in the embedding \\(\\langle \\mathbf{e}\\rangle\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.893, + 0.751 + ], + "angle": 0, + "content": "Coarse-to-fine training. We use the diffusion prior described above to optimize an RF in a coarse-to-fine manner. Before describing our coarse-to-fine training methodology, we first briefly introduce the underlying RF model, i.e., InstantNGP [23]. InstantNGP is a grid-based model which stores features at the vertices of a set of feature grids \\(\\{G_i\\}_{i=1}^L\\) at multiple resolutions. The resolution is chosen to be a geometric progression between the coarsest and finest resolutions, and feature grids are trained simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We choose InstantNGP over a conventional MLP due to its computational efficiency. However, InstantNGP tends to produce small irregularities on the surface of the object. We find that training in a coarse-to-fine manner helps to alleviate these issues: for the first half of training we only optimize the lower-resolution feature grids \\(\\{G_i\\}_{i=1}^{L/2}\\), and then in the second half of training we optimize all feature grids \\(\\{G_i\\}_{i=1}^L\\). Using this strategy, we obtain the benefits of both efficient training and high-quality results." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "8450" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.468, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.47, + 0.407 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison with prior work. We show the results of our method and the category-level method of [50] on real-world images from the CO3D dataset [31]. Each pair of rows show two novel views produced by [50] and our method. For [50], we use category-specific models for each CO3D category (in this case, motorcycles, cups, and backpacks). Despite not requiring any category-specific information, our method is able to reconstruct objects at a higher level of detail than [50]." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.418, + 0.462, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.592, + 0.468, + 0.675 + ], + "angle": 0, + "content": "Figure 6. Diversity of 3D reconstructions from a single image. Above, we see our method's ability to generate a diverse set of object reconstructions given the same input image. In particular, the method produces different textures on the backsides of the generated objects, despite all objects matching the input image from the reference view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.468, + 0.765 + ], + "angle": 0, + "content": "Normal vector regularization. We introduce a regularization term to encourage our geometry to have smoothly varying normal vectors. Notably, we perform this regularization in \\(2D\\) rather than in 3D because we found that it reduces the variance of the regularizer and improves results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.468, + 0.825 + ], + "angle": 0, + "content": "At each iteration, in addition to computing RGB and opacity values, we also compute normals for each point along the ray and aggregate these via the ray marching equation to obtain normals1 \\(N \\in \\mathcal{R}^{3 \\times H \\times W}\\). Our loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.838, + 0.468, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {n o r m a l s}} = \\| N - \\operatorname {s t o p g r a d} (\\operatorname {b l u r} (N, k)) \\| ^ {2} \\tag {4}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.468, + 0.9 + ], + "angle": 0, + "content": "1 Normals may be computed either by taking the gradient of the density field or by using finite differences. We found that using finite differences works well in practice." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.089, + 0.882, + 0.256 + ], + "angle": 0, + "content": "
F-scoreCLIP-similarity
[50]Ours[50]Ours
Backpack7.5812.220.720.74
Chair8.2610.230.650.76
Motorcycle8.668.720.690.70
Orange6.2710.160.710.74
Skateboard7.745.890.740.74
Teddybear12.8910.080.730.82
Vase6.309.720.690.71
Mean8.249.580.700.74
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison. We compare our method with Shelf-Supervised [50] on seven object categories. The F-score and CLIP-similarity metrics are designed to measure the quality of reconstruction shape and appearance, respectively. For both metrics, higher is better. Metrics are averaged over three images per category. Our method outperforms [50] in aggregate, despite the fact that [50] uses a different category-specific model for each category." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.391, + 0.892, + 0.422 + ], + "angle": 0, + "content": "where stopgrad is a stop-gradient operation and \\(\\mathrm{blur}(\\cdot ,k)\\) is a Gaussian blur with kernel size \\(k\\) (we use \\(k = 9\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.892, + 0.531 + ], + "angle": 0, + "content": "Mask loss. In addition to the input image, our model also utilizes a mask of the object that one wishes to reconstruct. In practice, we use an off-the-shelf image matting model to obtain this mask for all images. The loss is simply the \\(L^2\\) norm of the difference between the rendered opacities from the fixed reference viewpoint \\(\\hat{M} = \\mathcal{R}(\\sigma, \\pi_0) \\in \\mathcal{R}^{H \\times W}\\) and the object mask \\(M\\): \\(\\mathcal{L}_{\\mathrm{mask}} = \\| \\hat{M} - M \\|^2\\)" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.531, + 0.827, + 0.545 + ], + "angle": 0, + "content": "Our final objective then consists of four terms:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.562, + 0.891, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\sigma , c} \\mathcal {L} = \\nabla \\mathcal {L} _ {\\mathrm {S D S}} + \\lambda_ {\\text {n o r m a l s}} \\cdot \\nabla \\mathcal {L} _ {\\text {n o r m a l s}} \\\\ + \\lambda_ {\\text {i m a g e}} \\cdot \\nabla \\mathcal {L} _ {\\text {i m a g e}} + \\lambda_ {\\text {m a s k}} \\cdot \\nabla \\mathcal {L} _ {\\text {m a s k}} \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.609, + 0.891, + 0.638 + ], + "angle": 0, + "content": "where the first two terms are regularizers and the remaining ones are data terms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.654, + 0.633, + 0.671 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.714, + 0.695 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Regarding hyperparameters, we use nearly the same set of hyper-parameters for all experiments—there is no per-scene hyper-parameter adjustment. For our diffusion model prior, we employ the open-source Stable Diffusion model [34] trained on the LAION [36] dataset. At each optimization step, we first render from the reconstruction camera and compute our reconstruction losses \\(\\mathcal{L}_{\\mathrm{image}}\\) and \\(\\mathcal{L}_{\\mathrm{mask}}\\). We then render from a randomly sampled camera to obtain a novel view and use this view for \\(\\mathcal{L}_{\\mathrm{SDS}}\\) and \\(\\mathcal{L}_{\\mathrm{normals}}\\). We use \\(\\lambda_{\\mathrm{image}} = 5.0\\), \\(\\lambda_{\\mathrm{mask}} = 0.5\\), and \\(\\lambda_{\\mathrm{normals}} = 0.5\\)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2There is one small exception to this rule, which is that for a small number of images where the camera angle was clearly at an angle higher than \\(15^{\\circ}\\) above the horizontal plane, we used a camera angle of 30 or \\(40^{\\circ}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.514, + 0.938 + ], + "angle": 0, + "content": "8451" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.089, + 0.87, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.348, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Figure 7. A visualization of the effect of single-image textual inversion on reconstruction quality. In each pair of rows, the top row shows the result of utilizing a standard text prompt for our diffusion-model-based loss (e.g., \"An image of a statue of a cat\"). The bottom row shows the result of utilizing a text prompt optimized for the input image in a fully-automatic manner; this textual inversion process dramatically improves object reconstruction." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.416, + 0.468, + 0.594 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.595, + 0.471, + 0.651 + ], + "angle": 0, + "content": "Figure 8. Effect of coarse-to-fine training. The top row of each pair is generated by optimizing all levels of a multi-resolution 3D feature grid from the first optimization step, whereas the bottom row is optimized in a coarse-to-fine manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Regarding camera sampling, lighting, and shading, we keep nearly all parameters the same as [27]. We describe our setup in detail in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.267, + 0.74 + ], + "angle": 0, + "content": "4.2. Quantitative results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "There are only few methods that attempt to reconstruct arbitrary objects in 3D. The most recent and best-performing of these is Shelf-Supervised Mesh Prediction [50], which we compare to here. They provide 50 pretrained category-level models for 50 different categories in OpenImages [17]. Since we aim to compute metrics using 3D or multi-view ground truth, we evaluate on seven categories from the CO3D dataset [32] with corresponding OpenImages categories. For each of these seven categories, we select three images at random and run both RealFusion" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.416, + 0.889, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.692 + ], + "angle": 0, + "content": "Figure 9. Effect of normal smoothness on reconstruction quality. Each pair of rows show the reconstruction without and with the normal smoothness regularization term (4). The regularizer improves the visual appearance of surfaces and reduces the number of irregularities on the surface of reconstructed objects. In most cases, we also find that it helps to improve the overall realism of the reconstructed shape." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.814, + 0.734 + ], + "angle": 0, + "content": "and Shelf-Supervised to obtain reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We first test the quality of the recovered 3D shape in Fig. 5. [50] directly predicts a mesh, while we extract a mesh from our predicted radiance field using marching cubes. CO3D comes with sparse point-cloud reconstructions of objects obtained using multi-view geometry. For evaluation, we sample points from the reconstructed meshes and align them optimally with the ground truth point cloud by first estimating a scaling factor and then using Iterated Closest Point (ICP). Finally, we compute the F-score [40] with a threshold of 0.05 to measure the distance between the predicted and ground truth point clouds. Results are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "8452" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.468, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.47, + 0.307 + ], + "angle": 0, + "content": "Figure 10. Comparing Stable Diffusion and CLIP priors. Results from two different priors: Stable Diffusion [34] and CLIP [29]. Stable Diffusion yields much higher-quality reconstructions, capturing more plausible object shapes." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.317, + 0.462, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.6 + ], + "angle": 0, + "content": "Figure 11. Failure cases. In the first two examples, the model simply fails to properly reconstruct the object geometry, and produces a semi-transparent scene which lacks a well-defined geometry. The third case is different in that the geometry is highly realistic, but the texture paints two Pikachu faces, one on each side of the object; this problem is sometimes called the Janus problem, after the two-faced Roman god." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.612, + 0.189, + 0.626 + ], + "angle": 0, + "content": "shown in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.763 + ], + "angle": 0, + "content": "In order to evaluate the quality of the reproduced appearance, we also compare novel-view renderings from our and their method. Ideally, these renderings should produce views that are visually close to the real views. In order to test this hypothesis, we check whether the generated views are close or not to the other views given in CO3D. We report (Tab. 1) the CLIP embedding similarity of the generated images with respect to the closest CO3D view available (i.e., the view with maximum similarity)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.254, + 0.788 + ], + "angle": 0, + "content": "4.3. Qualitative results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Fig. 4 shows additional qualitative results from multiple viewpoints. Fig. 6 explores the ability of RealFusion to sample the space of possible solutions by repeating the reconstruction several times, starting from the same input image. There is little variance in the reconstructions of the front side of the object, but significant variance for its backside." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Fig. 11 shows two typical failure modes of RealFusion: in some cases, the model fails to converge, and in others, it copies the front view to the back of the object, even if this is not semantically correct." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.172, + 0.714, + 0.187 + ], + "angle": 0, + "content": "4.4. Analysis and Ablations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.365 + ], + "angle": 0, + "content": "One of the key components of RealFusion is our use of single-image textual inversion, which allows the model to correctly imagine novel views of a specific object. Fig. 7 shows that this component plays indeed a critical role in the quality and consistency of the reconstructions. Without textual inversion, the model often reconstructs the backside of the object in the form of a generic instance from the object category. For example, the backside of the cat statue in the top row of Fig. 7 is essentially a different statue of a more generic-looking cat, whereas the model trained with textual inversion resembles the true object from all angles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.487 + ], + "angle": 0, + "content": "Other components of the model are also significant. Fig. 8 shows that coarse-to-fine optimization reduces the presence of low-level artifacts and results in smoother, visually pleasing surfaces. Fig. 9 shows that the normal smoothness regularizer of Eq. (4) further results in smoother, more realistic meshes. Fig. 10 shows that using Stable Diffusion works significantly better than relying on an alternative such as CLIP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.627, + 0.527 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.752 + ], + "angle": 0, + "content": "We have introduced RealFusion, a new approach to obtain full \\(360^{\\circ}\\) photographic reconstructions of any object given a single image of it. To achieve this, we leverage an off-the-shelf diffusion model trained using only pairs of 2D images and text (but no 3D supervision) and optimize a token embedding to represent the object depicted in the image. We use this conditional prior to learn an efficient, multi-scale radiance field representation of the reconstructed object, incorporating an additional regularizer to smooth out the reconstructed surface. The resulting method can generate plausible 3D reconstructions of objects captured in the wild which are faithful to the input image. Future improvements could be obtained by specializing the diffusion model for the task of new-view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.759, + 0.892, + 0.834 + ], + "angle": 0, + "content": "Ethics. We use the CO3D dataset in a manner compatible with their terms; it does not contain personal information. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. L. M. K. is supported by the Rhodes Trust. A. V., I. L. and C. R. are supported by ERC-UNION-CoG-101001212. I. L. and C. 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CVPR, pages 4578-4587, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "8455" + } + ] +] \ No newline at end of file diff --git a/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_origin.pdf b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..123167c3195e6b66f7d6bff619af711063b627ee --- /dev/null +++ b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/cb32ed0a-6d89-4ef5-bddb-3a82c64b06eb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:663d784c7ef956fcf8f2f8d1b1f5999081017d41d21334cc1cd0183c8d93a9a4 +size 9402003 diff --git a/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/full.md b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4124159fcdaa4be360ac219e780ae2d5d44bfa49 --- /dev/null +++ b/2023/RealFusion_ 360deg Reconstruction of Any Object From a Single Image/full.md @@ -0,0 +1,282 @@ +# RealFusion + +# $360^{\circ}$ Reconstruction of Any Object from a Single Image + +Luke Melas-Kyriazi Iro Laina Christian Rupprecht Andrea Vedaldi + +Visual Geometry Group, Department of Engineering Science, University of Oxford + +{lukemk,iro,chrisr,vedaldi}@robots.ox.ac.uk + +https://lukemelas.github.io/realfusion + +![](images/99fa49f81138854e22de6a0adcadde15dbb1fc372321a2801f92ec55f9f7c6cb.jpg) +Figure 1. RealFusion generates a full $360^{\circ}$ reconstruction of any object given a single image of it (left column). It does so by leveraging an existing diffusion-based 2D image generator. From the given image, it synthesizes a prompt that causes the diffusion model to "dream up" other views of the object. It then extracts a neural radiance field from the original image and the diffusion model-based prior, thereby reconstructing the object in full. Both appearance and geometry are reconstructed faithfully and extrapolated in a plausible manner. + +![](images/a76aafcee24c77f2f85cd778ae188e94334cedb1e283a15cb8b8f3230136d767.jpg) + +# Abstract + +We consider the problem of reconstructing a full $360^{\circ}$ photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to "dream up" novel views of the object. Using the recent DreamFusion method, we fuse the given input view, the conditional prior, and other regularizers into a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible + +in the image. + +# 1. Introduction + +We consider the problem of obtaining a $360^{\circ}$ photographic reconstruction of any object given a single image of it. The challenge is that a single image does not contain sufficient information for 3D reconstruction. Without access to multiple views, an image only provides weak evidence about the 3D shape of the object, and only for one side of it. Even so, there is proof that this task can be solved: any skilled 3D artist can take a picture of almost any object and, given sufficient time and effort, create a plausible 3D model of it. The artist can do so by tapping into their vast knowledge of the natural world and the objects it contains, making up for the information missing from the image. + +Hence, monocular 3D reconstruction requires combining + +visual geometry with a powerful statistical model of the 3D world. Diffusion-based 2D image generators like DALL-E 2 [30], Imagen [35], and Stable Diffusion [33] are able to generate high-quality images from ambiguous inputs such as text, showing that powerful priors for 2D images can be learned. However, extending them to 3D is not easy because, while one can access billions of 2D images for training [36], the same cannot be said for 3D data. + +A simpler approach is to extract or distill 3D information from an existing 2D generator. A 2D image generator can in fact be used to sample or validate multiple views of a given object, which can then be used to perform 3D reconstruction. This idea was already demonstrated with GAN-based generators for simple data like faces and synthetic objects [2, 6, 8, 24, 25, 47]. Better 2D generators have since resulted in better results, culminating in methods such as DreamFusion [27], which can produce high-quality 3D models from an existing 2D generator and text. + +In this paper, we port distillation approaches from text-based generation to monocular 3D reconstruction. This is not a trivial change because conditioning generation on an image provides a much more fine-grained specification of the object than text. This in turn requires the 2D diffusion model to hallucinate new views of a specific object instead of some object of a given type. The latter is difficult because the coverage of generator models is limited [1], meaning that not every version of an object is captured well by the model. We find empirically that this is a key problem. + +We address this issue by introducing RealFusion, a new method for 3D reconstruction from a single image. We express the object's 3D geometry and appearance by means of a neural radiance field. Then, we fit the radiance field to the given input image by minimizing the usual rendering loss. At the same time, we sample random other views of the object, and constrain them with the diffusion prior, using a technique similar to DreamFusion. + +We find that, due to the coverage issue, this idea does not work well out of the box, but can be improved via adequately conditioning the 2D diffusion model. The idea is to configure the prior to "dream up" or sample images that may plausibly constitute other views of the given object. We do so by automatically engineering the diffusion prompt from random augmentations of the given image. In this manner, the diffusion model provides sufficiently strong constraints to allow meaningful 3D reconstruction. + +In addition to setting the prompt correctly, we also add some regularizers: shading the underlying geometry and randomly dropping out texture (also similar to DreamFusion), smoothing the normals of the surface, and fitting the model in a coarse-to-fine fashion, capturing first the overall structure of the object and only then the fine-grained details. We also focus on efficiency and base our model on Instant-NGP [23]. In this manner, we achieve reconstructions in the + +span of hours instead of days if we were to adopt traditional MLP-based NeRF models. + +We assess our approach by using random images captured in the wild as well as existing benchmark datasets. Note that we do not train a fully-fledged 2D-to-3D model and we are not limited to specific object categories; rather, we perform reconstruction on an image-by-image basis using a pretrained 2D generator as a prior. Nonetheless, we can surpass quantitatively and qualitatively previous single-image reconstructors, including Shelf-Supervised Mesh Prediction [50], which uses supervision tailored specifically for 3D reconstruction. + +Qualitatively, we obtain plausible 3D reconstructions that are a good match for the provided input image (Fig. 1). Our reconstructions are not perfect, as the diffusion prior clearly does its best to explain the available image evidence but cannot always match all the details. Even so, we believe that our results convincingly demonstrate the viability of this approach and trace a path for future improvements. + +To summarize, we make the following contributions: (1) We propose RealFusion, a method that can extract from a single image of an object a $360^{\circ}$ photographic 3D reconstruction without assumptions on the type of object imaged or 3D supervision of any kind; (2) We do so by leveraging an existing 2D diffusion image generator via a new single-image variant of textual inversion; (3) We also introduce new regularizers and provide an efficient implementation using InstantNGP; (4) We demonstrate state-of-the-art reconstruction results on a number of in-the-wild images and images from existing datasets when compared to alternative approaches. + +# 2. Related work + +Radiance fields. The problem of reconstructing photometry and geometry together has been dramatically revitalized by the introduction of neural radiance fields (RFs). NeRF [20] in particular noticed that a coordinate MLP provides a compact and yet expressive representation of 3D fields, and can be used to model RFs with great effectiveness. Many variants of NeRF-like models have since appeared. For instance, some [18, 41, 43] use sign distance functions (SDFs) to recover cleaner geometry. These approaches assume that dozens if not hundreds of views of each scene are available for reconstruction. Here, we use radiance fields for single-image reconstruction by using a diffusion model to "dream up" the missing views. + +Few-view reconstruction. Many authors have attempted to improve the statistical efficiency of NeRF-like models by learning or incorporating various kinds of priors. Most of these approaches train deep networks specifically for the goal of inferring NeRFs from a small number of views; examples include IBRNet [44], NeRF-WCE [9], Pixel + +![](images/e2a25611d42a2f91350482683038bab9a9a46499b331043d8b431436995722b2.jpg) +Figure 2. Method diagram. Our method optimizes a neural radiance field using two objectives simultaneously: a reconstruction objective and a prior objective. The reconstruction objective ensures that the radiance field resembles the input image from a specific, fixed view. The prior objective uses a large pre-trained diffusion model to ensure that the radiance field looks like the given object from randomly sampled novel viewpoints. The key to making this process work well is to condition the diffusion model on a prompt with a custom token $\langle \mathbf{e} \rangle$ , which is generated prior to reconstruction using single-image textual inversion. + +NeRF [51], NeRFormer [31], and ViewFormer [16]. These models still generally require more than one input view at test time and multi-view data for training. Closer to our work, NeRF-on-a-Diet [13] reduces the number of images needed for NeRF optimization by generating random views and measuring their "semantic compatibility" via CLIP embeddings [28], but it also still requires several input views. + +Single-view reconstruction. Some authors have attempted to recover full 3D representations from single images, but this generally requires multi-view data for training, as well as learning models that are specific to a specific object category. 3D-R2N2 [4], Pix2Vox [48], and LegoFormer [49] learn to reconstruct volumetric representation of simple objects, mainly from synthetic data like ShapeNet [3]. More recently, CodeNeRF [14] predicts a full radiance field and AutoRF [22] learns a similar autoencoder specifically for cars. Shelf-Supervised Mesh Prediction [50] and SS3D [42] learn to reconstruct a broad set of object categories by refining a mesh extracted from a coarse predicted volume. The former learns independent models for each category, whereas the latter unites them into a unified model via distillation. + +Extracting 3D models from 2D generators. Several authors have proposed to extract 3D models from 2D image generators, originally using GANs [2, 6, 8, 24, 25, 47]. Also related to our work, CLIP-Mesh [15] and Dream Fields [12] use a pre-trained image-text model [28] to condition 3D generation on textual prompts and do not require 3D supervision. Recently, DreamFusion [27] builds on this idea using a diffusion model as a prior. These models, however, + +![](images/92f5abf00ec70c1fc6815f5c90ad4a73d56ef3f575c36cec5d7c6897549515ba.jpg) +Figure 3. Examples demonstrating the level of detail of information captured by the optimized embedding $\langle \mathbf{e} \rangle$ . Rows 1-2 show input images and masks. The images are used to optimize $\langle \mathbf{e} \rangle$ via our single-image textual inversion process. Rows 3-5 show examples of 2D images generated using $\langle \mathbf{e} \rangle$ in new prompts, which we hope demonstrate the type of information encoded in $\langle \mathbf{e} \rangle$ . Rows 6-7 show RealFusion's output, optimized using the prompt "An image of a $\langle \mathbf{e} \rangle$ ". + +are used as either pure generators or generators conditioned on vague cues such as class identity or textual descriptions. Here, we build on the DreamFusion approach, extending the idea to single-view reconstruction. + +Recently, the authors of [46] have proposed to directly generate multiple 2D views of an object, which can then be reconstructed in 3D using a NeRF-like model. This is also reminiscent of our approach, but their model requires multiview data for training, is only tested on synthetic data, and requires to explicitly sample multiple views for reconstruction (in our case they remain implicit). + +Diffusion models. Diffusion denoising probabilistic models are a class of generative models based on iteratively reversing a Markovian noising process. Early works formulated the problem as learning a variational lower bound [10], or framed it as optimizing a score-based generative model [37, 38] or as the discretization of a continuous stochastic process [39]. Recent improvements include the use of faster and deterministic sampling [10, 19, 45], class-conditional models [5, 38], text-conditional models [26], and modeling in latent space [34]. + +# 3. Method + +We review the background and notation in Sec. 3.1, and then discuss our RealFusion method in Sec. 3.2. + +# 3.1. Radiance fields, diffusion and distillation + +Radiance fields. A radiance field (RF) is a pair of functions $(\sigma(\boldsymbol{x}), c(\boldsymbol{x}))$ mapping a 3D point $\boldsymbol{x} \in \mathbb{R}^3$ to an opacity value $\sigma(\boldsymbol{x}) \in \mathbb{R}_+$ and a color value $c(\boldsymbol{x}) \in \mathbb{R}^3$ . The RF is called neural when these two functions are implemented by a neural network. + +The RF represents the shape and appearance of an object. In order to generate an image of it, one renders the RF using the emission-absorption model [21]. This can be modeled as a function $I = \mathcal{R}(\sigma, c, \pi) \in \mathbb{R}^{3 \times H \times W}$ that extracts a color image $I$ from the radiance field $(\sigma, c)$ given a viewpoint $\pi \in \mathrm{SE}(3)$ . The rendering function $R(\sigma, c, \pi)$ is differentiable, which allows training the model by means of a standard optimizer. Specifically, the RF is fitted to a dataset $\mathcal{D} = \{(I, \pi)\}$ of images $I$ with known camera parameters by minimizing the $L_{2}$ image reconstruction error + +$$ +\mathcal {L} _ {\text {r e c}} (\sigma , c; \mathcal {D}) = \frac {1}{| \mathcal {D} |} \sum_ {(I, \pi) \in \mathcal {D}} \| I - R (\sigma , c, \pi) \| ^ {2}. \tag {1} +$$ + +In order to obtain good-quality results, one typically requires a dataset of dozens or hundreds of views. + +Here, we consider the case in which we are given exactly one input image $I_0$ corresponding to some (unknown) camera $\pi_0$ . In this case, we can also assume any standard viewpoint $\pi_0$ for that single camera. Optimizing Eq. (1) with a single training image leads to severe over-fitting: it is straightforward to find a pair $(\sigma, c)$ that has zero loss and yet does not capture any sensible 3D model of the object. Below we will leverage a pre-trained 2D image prior to (implicitly) dream up novel views of the object and provide the missing information for 3D reconstruction. + +Diffusion models. A diffusion model draws a sample from a probability distribution $p(I)$ by inverting a process that gradually adds noise to the image $I$ . The diffusion process is associated with a noising schedule $\{\alpha_t \in (0,1)\}_{t=1}^T$ , which defines how much noise is added at each time step. The noisy version of sample $I$ at time $t$ can then be written $I_t = \alpha_t I + \sigma_t \epsilon$ , where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , is a sample from a Gaussian distribution and $\sigma_t^2 = 1 - \alpha_t^2$ . One then learns a denoising neural network $\hat{\epsilon} = \Phi(I_t; t)$ that takes as input the noisy image $I_t$ and the noise level $t$ and predicts the noise component $\epsilon$ . Iterated applications of the network generate $I = I_0$ from $I_T \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ . + +The diffusion model is trained on large collections $\mathcal{D}' = \{I\}$ of images by minimizing the loss + +$$ +\mathcal {L} _ {\text {d i f f}} \left(\Phi ; \mathcal {D} ^ {\prime}\right) = \frac {1}{| \mathcal {D} ^ {\prime} |} \sum_ {I \in \mathcal {D} ^ {\prime}} \left| \left| \Phi \left(\alpha_ {t} I + \sigma_ {t} \epsilon ; t\right) - \epsilon \right| \right| ^ {2}. \tag {2} +$$ + +This model can be easily extended to draw samples from a distribution $p(x|e)$ conditioned on a prompt $e$ . Conditioning on the prompt is obtained by adding $e$ as an additional + +input of the network $\Phi$ , and the strength of conditioning can be controlled via classifier-free guidance [5, 11]. + +DreamFusion and Score Distillation Sampling (SDS). Given a 2D diffusion model $p(I|e)$ and a prompt $e$ , DreamFusion extracts from it a 3D rendition of the corresponding concept, represented by a RF $(\sigma, c)$ . It does so by randomly sampling a camera parameter $\pi$ , rendering a corresponding view $I$ , assessing the likelihood of the view based on the model $p(I|e)$ , and updating the RF to increase the likelihood of the generated view based on the model. + +In practice, DreamFusion uses the denoising network as a frozen critic and takes a gradient step + +$$ +\begin{array}{l} \nabla_ {(\sigma , c)} \mathcal {L} _ {\mathrm {S D S}} (\sigma , c; \pi , e, t) = \\ E _ {t, \epsilon} \left[ w (t) \left(\Phi \left(\alpha_ {t} I + \sigma_ {t} \epsilon ; t, \boldsymbol {e}\right) - \epsilon\right) \cdot \frac {\partial I}{\partial (\sigma , c)} \right], \tag {3} \\ \end{array} +$$ + +where $I = R(\sigma, c, \pi)$ is the image rendered from a randomly-sampled viewpoint $\pi$ and $w(t)$ is a timestep-dependent weighting function. This process is called Score Distillation Sampling (SDS). + +One final aspect of DreamFusion is essential for understanding our contribution in the following section: DreamFusion finds that it is necessary to use classifier-free guidance [5] with a very high guidance weight of 100, much larger than one would use for image sampling, in order to obtain good 3D shapes. As a result, the generations tend to have limited diversity; they produce only the most likely objects for a given prompt, which is incompatible with our goal of reconstructing any given object. + +# 3.2. RealFusion + +Our goal is to reconstruct a 3D model of the object contained in a single image $I_0$ , utilizing the prior captured in the diffusion model $\Phi$ to make up for the missing information. We do this by optimizing a radiance field using two simultaneous objectives: (1) a reconstruction objective (Eq. (1)) from a fixed viewpoint, and (2) a SDS-based prior objective (Eq. (3)) on novel views randomly sampled at each iteration. Figure 2 provides a diagram of the method. + +Single-image textual inversion as a substitute for alternative views. The most important component of our method is the use of single-image textual inversion as a substitute for alternative views. Ideally, we would like to condition our reconstruction process on multi-view images of the object in $I_0$ , i.e., on samples from $p(I|I_0)$ . + +Since these images are not available, our idea is to engineer a text prompt $e^{(I_0)}$ specifically for image $I_0$ as a proxy for this multi-view information, i.e., as an approximation of $p(I|I_0)$ . We do so by generating random augmentations $h(I_0), h \in H$ of the input image, which serve as pseudo-alternative-views. We use these augmentations as a mini-dataset $\mathcal{D}' = \{h(I_0)\}_{h \in H}$ and optimize the diffusion loss + +![](images/4fa14015df1ed4e2cd8170d4cb6cec249e1083904621c6607bac898d54e0a9c8.jpg) +Figure 4. Qualitative results. RealFusion reconstructions from a single input view. Each pair of columns shows the textured object and the underlying 3D shape, as a shaded surface. Different pairs of columns show different viewpoints. + +$\mathcal{L}_{\mathrm{diff}}(\Phi (\cdot ;e^{(I_0)}))$ of Eq. (2) with respect to the prompt $e^{(I_0)}$ while freezing all other text embeddings and model parameters. + +In practice, our prompt is derived automatically from the template "an image of a $\langle \mathbf{e} \rangle$ ", where " $\langle \mathbf{e} \rangle$ ( $= e^{(I_0)}$ ) is a newizable token introduced to the vocabulary of the text encoder of our diffusion model (see the supplementary material for details). A caption or description of $I_0$ is not needed. Our optimization procedure mirrors and generalizes the recently-proposed textual-inversion method of [7]. Differently from [7], we work in the single-image setting and utilize image augmentations for training rather than multiple views. + +To help convey the intuition behind $\langle \mathbf{e} \rangle$ , consider an attempt at reconstructing an image of a fish using the generic text prompt "An image of a fish" with losses (2) and (3). In our experience, this often produces a reconstruction which looks like the input fish from the input viewpoint, but looks like some different, more-generic fish from the backside. By contrast, using the prompt "An image of a $\langle \mathbf{e} \rangle$ ", the reconstruction resembles the input fish from all angles. An example of exactly this case is shown in Fig. 7, and Fig. 3 + +demonstrates the amount of detail captured in the embedding $\langle \mathbf{e}\rangle$ + +Coarse-to-fine training. We use the diffusion prior described above to optimize an RF in a coarse-to-fine manner. Before describing our coarse-to-fine training methodology, we first briefly introduce the underlying RF model, i.e., InstantNGP [23]. InstantNGP is a grid-based model which stores features at the vertices of a set of feature grids $\{G_i\}_{i=1}^L$ at multiple resolutions. The resolution is chosen to be a geometric progression between the coarsest and finest resolutions, and feature grids are trained simultaneously. + +We choose InstantNGP over a conventional MLP due to its computational efficiency. However, InstantNGP tends to produce small irregularities on the surface of the object. We find that training in a coarse-to-fine manner helps to alleviate these issues: for the first half of training we only optimize the lower-resolution feature grids $\{G_i\}_{i=1}^{L/2}$ , and then in the second half of training we optimize all feature grids $\{G_i\}_{i=1}^L$ . Using this strategy, we obtain the benefits of both efficient training and high-quality results. + +![](images/b562f2299d6329edc74616c43df25c6844bb06f0e348ff67e8eb9f18007fef57.jpg) +Figure 5. Qualitative comparison with prior work. We show the results of our method and the category-level method of [50] on real-world images from the CO3D dataset [31]. Each pair of rows show two novel views produced by [50] and our method. For [50], we use category-specific models for each CO3D category (in this case, motorcycles, cups, and backpacks). Despite not requiring any category-specific information, our method is able to reconstruct objects at a higher level of detail than [50]. + +![](images/5197fa2640e80a46031fa205a6f86bda7d6adafdee330d53848837506ab203ee.jpg) +Figure 6. Diversity of 3D reconstructions from a single image. Above, we see our method's ability to generate a diverse set of object reconstructions given the same input image. In particular, the method produces different textures on the backsides of the generated objects, despite all objects matching the input image from the reference view. + +Normal vector regularization. We introduce a regularization term to encourage our geometry to have smoothly varying normal vectors. Notably, we perform this regularization in $2D$ rather than in 3D because we found that it reduces the variance of the regularizer and improves results. + +At each iteration, in addition to computing RGB and opacity values, we also compute normals for each point along the ray and aggregate these via the ray marching equation to obtain normals1 $N \in \mathcal{R}^{3 \times H \times W}$ . Our loss is: + +$$ +\mathcal {L} _ {\text {n o r m a l s}} = \| N - \operatorname {s t o p g r a d} (\operatorname {b l u r} (N, k)) \| ^ {2} \tag {4} +$$ + +
F-scoreCLIP-similarity
[50]Ours[50]Ours
Backpack7.5812.220.720.74
Chair8.2610.230.650.76
Motorcycle8.668.720.690.70
Orange6.2710.160.710.74
Skateboard7.745.890.740.74
Teddybear12.8910.080.730.82
Vase6.309.720.690.71
Mean8.249.580.700.74
+ +Table 1. Quantitative comparison. We compare our method with Shelf-Supervised [50] on seven object categories. The F-score and CLIP-similarity metrics are designed to measure the quality of reconstruction shape and appearance, respectively. For both metrics, higher is better. Metrics are averaged over three images per category. Our method outperforms [50] in aggregate, despite the fact that [50] uses a different category-specific model for each category. + +where stopgrad is a stop-gradient operation and $\mathrm{blur}(\cdot ,k)$ is a Gaussian blur with kernel size $k$ (we use $k = 9$ ). + +Mask loss. In addition to the input image, our model also utilizes a mask of the object that one wishes to reconstruct. In practice, we use an off-the-shelf image matting model to obtain this mask for all images. The loss is simply the $L^2$ norm of the difference between the rendered opacities from the fixed reference viewpoint $\hat{M} = \mathcal{R}(\sigma, \pi_0) \in \mathcal{R}^{H \times W}$ and the object mask $M$ : $\mathcal{L}_{\mathrm{mask}} = \| \hat{M} - M \|^2$ + +Our final objective then consists of four terms: + +$$ +\begin{array}{l} \nabla_ {\sigma , c} \mathcal {L} = \nabla \mathcal {L} _ {\mathrm {S D S}} + \lambda_ {\text {n o r m a l s}} \cdot \nabla \mathcal {L} _ {\text {n o r m a l s}} \\ + \lambda_ {\text {i m a g e}} \cdot \nabla \mathcal {L} _ {\text {i m a g e}} + \lambda_ {\text {m a s k}} \cdot \nabla \mathcal {L} _ {\text {m a s k}} \tag {5} \\ \end{array} +$$ + +where the first two terms are regularizers and the remaining ones are data terms. + +# 4. Experiments + +# 4.1. Implementation details + +Regarding hyperparameters, we use nearly the same set of hyper-parameters for all experiments—there is no per-scene hyper-parameter adjustment. For our diffusion model prior, we employ the open-source Stable Diffusion model [34] trained on the LAION [36] dataset. At each optimization step, we first render from the reconstruction camera and compute our reconstruction losses $\mathcal{L}_{\mathrm{image}}$ and $\mathcal{L}_{\mathrm{mask}}$ . We then render from a randomly sampled camera to obtain a novel view and use this view for $\mathcal{L}_{\mathrm{SDS}}$ and $\mathcal{L}_{\mathrm{normals}}$ . We use $\lambda_{\mathrm{image}} = 5.0$ , $\lambda_{\mathrm{mask}} = 0.5$ , and $\lambda_{\mathrm{normals}} = 0.5$ . + +![](images/8cfc2e1856e99898a74ad8d3e265f81a9f73698176df06d570f54dc8816b0abd.jpg) +Figure 7. A visualization of the effect of single-image textual inversion on reconstruction quality. In each pair of rows, the top row shows the result of utilizing a standard text prompt for our diffusion-model-based loss (e.g., "An image of a statue of a cat"). The bottom row shows the result of utilizing a text prompt optimized for the input image in a fully-automatic manner; this textual inversion process dramatically improves object reconstruction. + +![](images/596b75f035a042c0e7677ed95137e4d4eca68973f9f3be862497d0456a467994.jpg) +Figure 8. Effect of coarse-to-fine training. The top row of each pair is generated by optimizing all levels of a multi-resolution 3D feature grid from the first optimization step, whereas the bottom row is optimized in a coarse-to-fine manner. + +Regarding camera sampling, lighting, and shading, we keep nearly all parameters the same as [27]. We describe our setup in detail in the supplementary material. + +# 4.2. Quantitative results + +There are only few methods that attempt to reconstruct arbitrary objects in 3D. The most recent and best-performing of these is Shelf-Supervised Mesh Prediction [50], which we compare to here. They provide 50 pretrained category-level models for 50 different categories in OpenImages [17]. Since we aim to compute metrics using 3D or multi-view ground truth, we evaluate on seven categories from the CO3D dataset [32] with corresponding OpenImages categories. For each of these seven categories, we select three images at random and run both RealFusion + +![](images/b1743ff122f0b51f8b25b1a0fbd31b64185866c4e9462cae1d2d524f3f7e5552.jpg) +Figure 9. Effect of normal smoothness on reconstruction quality. Each pair of rows show the reconstruction without and with the normal smoothness regularization term (4). The regularizer improves the visual appearance of surfaces and reduces the number of irregularities on the surface of reconstructed objects. In most cases, we also find that it helps to improve the overall realism of the reconstructed shape. + +and Shelf-Supervised to obtain reconstructions. + +We first test the quality of the recovered 3D shape in Fig. 5. [50] directly predicts a mesh, while we extract a mesh from our predicted radiance field using marching cubes. CO3D comes with sparse point-cloud reconstructions of objects obtained using multi-view geometry. For evaluation, we sample points from the reconstructed meshes and align them optimally with the ground truth point cloud by first estimating a scaling factor and then using Iterated Closest Point (ICP). Finally, we compute the F-score [40] with a threshold of 0.05 to measure the distance between the predicted and ground truth point clouds. Results are + +![](images/312ac77e375873e769e5cc74e5c3cd4b2b5ac42b569d4510097a28e1d102126b.jpg) +Figure 10. Comparing Stable Diffusion and CLIP priors. Results from two different priors: Stable Diffusion [34] and CLIP [29]. Stable Diffusion yields much higher-quality reconstructions, capturing more plausible object shapes. + +![](images/7cb77fa022b16327958075aeae5f1ccde1a916858c6e9cec273234da9738922d.jpg) +Figure 11. Failure cases. In the first two examples, the model simply fails to properly reconstruct the object geometry, and produces a semi-transparent scene which lacks a well-defined geometry. The third case is different in that the geometry is highly realistic, but the texture paints two Pikachu faces, one on each side of the object; this problem is sometimes called the Janus problem, after the two-faced Roman god. + +# shown in Tab. 1. + +In order to evaluate the quality of the reproduced appearance, we also compare novel-view renderings from our and their method. Ideally, these renderings should produce views that are visually close to the real views. In order to test this hypothesis, we check whether the generated views are close or not to the other views given in CO3D. We report (Tab. 1) the CLIP embedding similarity of the generated images with respect to the closest CO3D view available (i.e., the view with maximum similarity). + +# 4.3. Qualitative results + +Fig. 4 shows additional qualitative results from multiple viewpoints. Fig. 6 explores the ability of RealFusion to sample the space of possible solutions by repeating the reconstruction several times, starting from the same input image. There is little variance in the reconstructions of the front side of the object, but significant variance for its backside. + +Fig. 11 shows two typical failure modes of RealFusion: in some cases, the model fails to converge, and in others, it copies the front view to the back of the object, even if this is not semantically correct. + +# 4.4. Analysis and Ablations + +One of the key components of RealFusion is our use of single-image textual inversion, which allows the model to correctly imagine novel views of a specific object. Fig. 7 shows that this component plays indeed a critical role in the quality and consistency of the reconstructions. Without textual inversion, the model often reconstructs the backside of the object in the form of a generic instance from the object category. For example, the backside of the cat statue in the top row of Fig. 7 is essentially a different statue of a more generic-looking cat, whereas the model trained with textual inversion resembles the true object from all angles. + +Other components of the model are also significant. Fig. 8 shows that coarse-to-fine optimization reduces the presence of low-level artifacts and results in smoother, visually pleasing surfaces. Fig. 9 shows that the normal smoothness regularizer of Eq. (4) further results in smoother, more realistic meshes. Fig. 10 shows that using Stable Diffusion works significantly better than relying on an alternative such as CLIP. + +# 5. Conclusions + +We have introduced RealFusion, a new approach to obtain full $360^{\circ}$ photographic reconstructions of any object given a single image of it. To achieve this, we leverage an off-the-shelf diffusion model trained using only pairs of 2D images and text (but no 3D supervision) and optimize a token embedding to represent the object depicted in the image. We use this conditional prior to learn an efficient, multi-scale radiance field representation of the reconstructed object, incorporating an additional regularizer to smooth out the reconstructed surface. The resulting method can generate plausible 3D reconstructions of objects captured in the wild which are faithful to the input image. Future improvements could be obtained by specializing the diffusion model for the task of new-view synthesis. + +Ethics. We use the CO3D dataset in a manner compatible with their terms; it does not contain personal information. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html. + +Acknowledgments. L. M. K. is supported by the Rhodes Trust. A. V., I. L. and C. 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RealFusion generates a full " + }, + { + "bbox": [ + 46, + 434, + 546, + 479 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 434, + 546, + 479 + ], + "type": "text", + "content": " reconstruction of any object given a single image of it (left column). It does so by leveraging an existing diffusion-based 2D image generator. From the given image, it synthesizes a prompt that causes the diffusion model to \"dream up\" other views of the object. It then extracts a neural radiance field from the original image and the diffusion model-based prior, thereby reconstructing the object in full. Both appearance and geometry are reconstructed faithfully and extrapolated in a plausible manner." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 97, + 255, + 545, + 422 + ], + "blocks": [ + { + "bbox": [ + 97, + 255, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 97, + 255, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 97, + 255, + 545, + 422 + ], + "type": "image", + "image_path": "a76aafcee24c77f2f85cd778ae188e94334cedb1e283a15cb8b8f3230136d767.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "spans": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 535, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 289, + 715 + ], + "type": "text", + "content": "We consider the problem of reconstructing a full " + }, + { + "bbox": [ + 46, + 535, + 289, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 535, + 289, + 715 + ], + "type": "text", + "content": " photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to \"dream up\" novel views of the object. Using the recent DreamFusion method, we fuse the given input view, the conditional prior, and other regularizers into a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 497, + 360, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 360, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 360, + 508 + ], + "type": "text", + "content": "in the image." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 536, + 386, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 386, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 386, + 548 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": "We consider the problem of obtaining a " + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 557, + 545, + 700 + ], + "type": "text", + "content": " photographic reconstruction of any object given a single image of it. The challenge is that a single image does not contain sufficient information for 3D reconstruction. Without access to multiple views, an image only provides weak evidence about the 3D shape of the object, and only for one side of it. Even so, there is proof that this task can be solved: any skilled 3D artist can take a picture of almost any object and, given sufficient time and effort, create a plausible 3D model of it. The artist can do so by tapping into their vast knowledge of the natural world and the objects it contains, making up for the information missing from the image." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 703, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 703, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 318, + 703, + 545, + 715 + ], + "type": "text", + "content": "Hence, monocular 3D reconstruction requires combining" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "type": "text", + "content": "8446" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "visual geometry with a powerful statistical model of the 3D world. Diffusion-based 2D image generators like DALL-E 2 [30], Imagen [35], and Stable Diffusion [33] are able to generate high-quality images from ambiguous inputs such as text, showing that powerful priors for 2D images can be learned. However, extending them to 3D is not easy because, while one can access billions of 2D images for training [36], the same cannot be said for 3D data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 287, + 289 + ], + "type": "text", + "content": "A simpler approach is to extract or distill 3D information from an existing 2D generator. A 2D image generator can in fact be used to sample or validate multiple views of a given object, which can then be used to perform 3D reconstruction. This idea was already demonstrated with GAN-based generators for simple data like faces and synthetic objects [2, 6, 8, 24, 25, 47]. Better 2D generators have since resulted in better results, culminating in methods such as DreamFusion [27], which can produce high-quality 3D models from an existing 2D generator and text." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 290, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 411 + ], + "type": "text", + "content": "In this paper, we port distillation approaches from text-based generation to monocular 3D reconstruction. This is not a trivial change because conditioning generation on an image provides a much more fine-grained specification of the object than text. This in turn requires the 2D diffusion model to hallucinate new views of a specific object instead of some object of a given type. The latter is difficult because the coverage of generator models is limited [1], meaning that not every version of an object is captured well by the model. We find empirically that this is a key problem." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 507 + ], + "type": "text", + "content": "We address this issue by introducing RealFusion, a new method for 3D reconstruction from a single image. We express the object's 3D geometry and appearance by means of a neural radiance field. Then, we fit the radiance field to the given input image by minimizing the usual rendering loss. At the same time, we sample random other views of the object, and constrain them with the diffusion prior, using a technique similar to DreamFusion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 509, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 509, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 45, + 509, + 287, + 616 + ], + "type": "text", + "content": "We find that, due to the coverage issue, this idea does not work well out of the box, but can be improved via adequately conditioning the 2D diffusion model. The idea is to configure the prior to \"dream up\" or sample images that may plausibly constitute other views of the given object. We do so by automatically engineering the diffusion prompt from random augmentations of the given image. In this manner, the diffusion model provides sufficiently strong constraints to allow meaningful 3D reconstruction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "In addition to setting the prompt correctly, we also add some regularizers: shading the underlying geometry and randomly dropping out texture (also similar to DreamFusion), smoothing the normals of the surface, and fitting the model in a coarse-to-fine fashion, capturing first the overall structure of the object and only then the fine-grained details. We also focus on efficiency and base our model on Instant-NGP [23]. In this manner, we achieve reconstructions in the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "span of hours instead of days if we were to adopt traditional MLP-based NeRF models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 98, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 98, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 98, + 545, + 216 + ], + "type": "text", + "content": "We assess our approach by using random images captured in the wild as well as existing benchmark datasets. Note that we do not train a fully-fledged 2D-to-3D model and we are not limited to specific object categories; rather, we perform reconstruction on an image-by-image basis using a pretrained 2D generator as a prior. Nonetheless, we can surpass quantitatively and qualitatively previous single-image reconstructors, including Shelf-Supervised Mesh Prediction [50], which uses supervision tailored specifically for 3D reconstruction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 218, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 302 + ], + "type": "text", + "content": "Qualitatively, we obtain plausible 3D reconstructions that are a good match for the provided input image (Fig. 1). Our reconstructions are not perfect, as the diffusion prior clearly does its best to explain the available image evidence but cannot always match all the details. Even so, we believe that our results convincingly demonstrate the viability of this approach and trace a path for future improvements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 303, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 447 + ], + "type": "text", + "content": "To summarize, we make the following contributions: (1) We propose RealFusion, a method that can extract from a single image of an object a " + }, + { + "bbox": [ + 304, + 303, + 545, + 447 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 303, + 545, + 447 + ], + "type": "text", + "content": " photographic 3D reconstruction without assumptions on the type of object imaged or 3D supervision of any kind; (2) We do so by leveraging an existing 2D diffusion image generator via a new single-image variant of textual inversion; (3) We also introduce new regularizers and provide an efficient implementation using InstantNGP; (4) We demonstrate state-of-the-art reconstruction results on a number of in-the-wild images and images from existing datasets when compared to alternative approaches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 461, + 389, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 389, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 389, + 474 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 482, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 638 + ], + "type": "text", + "content": "Radiance fields. The problem of reconstructing photometry and geometry together has been dramatically revitalized by the introduction of neural radiance fields (RFs). NeRF [20] in particular noticed that a coordinate MLP provides a compact and yet expressive representation of 3D fields, and can be used to model RFs with great effectiveness. Many variants of NeRF-like models have since appeared. For instance, some [18, 41, 43] use sign distance functions (SDFs) to recover cleaner geometry. These approaches assume that dozens if not hundreds of views of each scene are available for reconstruction. Here, we use radiance fields for single-image reconstruction by using a diffusion model to \"dream up\" the missing views." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Few-view reconstruction. Many authors have attempted to improve the statistical efficiency of NeRF-like models by learning or incorporating various kinds of priors. Most of these approaches train deep networks specifically for the goal of inferring NeRFs from a small number of views; examples include IBRNet [44], NeRF-WCE [9], Pixel" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "8447" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 286, + 205 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "type": "image", + "image_path": "e2a25611d42a2f91350482683038bab9a9a46499b331043d8b431436995722b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 289, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 289, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 289, + 331 + ], + "type": "text", + "content": "Figure 2. Method diagram. Our method optimizes a neural radiance field using two objectives simultaneously: a reconstruction objective and a prior objective. The reconstruction objective ensures that the radiance field resembles the input image from a specific, fixed view. The prior objective uses a large pre-trained diffusion model to ensure that the radiance field looks like the given object from randomly sampled novel viewpoints. The key to making this process work well is to condition the diffusion model on a prompt with a custom token " + }, + { + "bbox": [ + 46, + 220, + 289, + 331 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 46, + 220, + 289, + 331 + ], + "type": "text", + "content": ", which is generated prior to reconstruction using single-image textual inversion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 345, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 430 + ], + "type": "text", + "content": "NeRF [51], NeRFormer [31], and ViewFormer [16]. These models still generally require more than one input view at test time and multi-view data for training. Closer to our work, NeRF-on-a-Diet [13] reduces the number of images needed for NeRF optimization by generating random views and measuring their \"semantic compatibility\" via CLIP embeddings [28], but it also still requires several input views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 613 + ], + "type": "text", + "content": "Single-view reconstruction. Some authors have attempted to recover full 3D representations from single images, but this generally requires multi-view data for training, as well as learning models that are specific to a specific object category. 3D-R2N2 [4], Pix2Vox [48], and LegoFormer [49] learn to reconstruct volumetric representation of simple objects, mainly from synthetic data like ShapeNet [3]. More recently, CodeNeRF [14] predicts a full radiance field and AutoRF [22] learns a similar autoencoder specifically for cars. Shelf-Supervised Mesh Prediction [50] and SS3D [42] learn to reconstruct a broad set of object categories by refining a mesh extracted from a coarse predicted volume. The former learns independent models for each category, whereas the latter unites them into a unified model via distillation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Extracting 3D models from 2D generators. Several authors have proposed to extract 3D models from 2D image generators, originally using GANs [2, 6, 8, 24, 25, 47]. Also related to our work, CLIP-Mesh [15] and Dream Fields [12] use a pre-trained image-text model [28] to condition 3D generation on textual prompts and do not require 3D supervision. Recently, DreamFusion [27] builds on this idea using a diffusion model as a prior. These models, however," + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 544, + 293 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 544, + 293 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 544, + 293 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 544, + 293 + ], + "type": "image", + "image_path": "92f5abf00ec70c1fc6815f5c90ad4a73d56ef3f575c36cec5d7c6897549515ba.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "lines": [ + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": "Figure 3. Examples demonstrating the level of detail of information captured by the optimized embedding " + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": ". Rows 1-2 show input images and masks. The images are used to optimize " + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": " via our single-image textual inversion process. Rows 3-5 show examples of 2D images generated using " + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": " in new prompts, which we hope demonstrate the type of information encoded in " + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": ". Rows 6-7 show RealFusion's output, optimized using the prompt \"An image of a " + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 305, + 301, + 545, + 390 + ], + "type": "text", + "content": "\"." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 402, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 545, + 449 + ], + "type": "text", + "content": "are used as either pure generators or generators conditioned on vague cues such as class identity or textual descriptions. Here, we build on the DreamFusion approach, extending the idea to single-view reconstruction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 450, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 545, + 534 + ], + "type": "text", + "content": "Recently, the authors of [46] have proposed to directly generate multiple 2D views of an object, which can then be reconstructed in 3D using a NeRF-like model. This is also reminiscent of our approach, but their model requires multiview data for training, is only tested on synthetic data, and requires to explicitly sample multiple views for reconstruction (in our case they remain implicit)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 536, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 536, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 305, + 536, + 545, + 657 + ], + "type": "text", + "content": "Diffusion models. Diffusion denoising probabilistic models are a class of generative models based on iteratively reversing a Markovian noising process. Early works formulated the problem as learning a variational lower bound [10], or framed it as optimizing a score-based generative model [37, 38] or as the discretization of a continuous stochastic process [39]. Recent improvements include the use of faster and deterministic sampling [10, 19, 45], class-conditional models [5, 38], text-conditional models [26], and modeling in latent space [34]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 361, + 681 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "We review the background and notation in Sec. 3.1, and then discuss our RealFusion method in Sec. 3.2." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "8448" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "type": "text", + "content": "3.1. Radiance fields, diffusion and distillation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "content": "Radiance fields. A radiance field (RF) is a pair of functions " + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "inline_equation", + "content": "(\\sigma(\\boldsymbol{x}), c(\\boldsymbol{x}))" + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "content": " mapping a 3D point " + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "content": " to an opacity value " + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "inline_equation", + "content": "\\sigma(\\boldsymbol{x}) \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "content": " and a color value " + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "inline_equation", + "content": "c(\\boldsymbol{x}) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 91, + 287, + 149 + ], + "type": "text", + "content": ". The RF is called neural when these two functions are implemented by a neural network." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": "The RF represents the shape and appearance of an object. In order to generate an image of it, one renders the RF using the emission-absorption model [21]. This can be modeled as a function " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "I = \\mathcal{R}(\\sigma, c, \\pi) \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " that extracts a color image " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " from the radiance field " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "(\\sigma, c)" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " given a viewpoint " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "\\pi \\in \\mathrm{SE}(3)" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": ". The rendering function " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "R(\\sigma, c, \\pi)" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " is differentiable, which allows training the model by means of a standard optimizer. Specifically, the RF is fitted to a dataset " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(I, \\pi)\\}" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " of images " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " with known camera parameters by minimizing the " + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 151, + 288, + 270 + ], + "type": "text", + "content": " image reconstruction error" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 280, + 287, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 280, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 71, + 280, + 287, + 310 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c}} (\\sigma , c; \\mathcal {D}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, \\pi) \\in \\mathcal {D}} \\| I - R (\\sigma , c, \\pi) \\| ^ {2}. \\tag {1}", + "image_path": "a82f3f87ca042b4f5b42a4282933bb4bdf223a8d7866d8a4329d773f0172cae2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 317, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 340 + ], + "type": "text", + "content": "In order to obtain good-quality results, one typically requires a dataset of dozens or hundreds of views." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "content": "Here, we consider the case in which we are given exactly one input image " + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "content": " corresponding to some (unknown) camera " + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\pi_0" + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "content": ". In this case, we can also assume any standard viewpoint " + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\pi_0" + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "content": " for that single camera. Optimizing Eq. (1) with a single training image leads to severe over-fitting: it is straightforward to find a pair " + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "inline_equation", + "content": "(\\sigma, c)" + }, + { + "bbox": [ + 46, + 342, + 287, + 460 + ], + "type": "text", + "content": " that has zero loss and yet does not capture any sensible 3D model of the object. Below we will leverage a pre-trained 2D image prior to (implicitly) dream up novel views of the object and provide the missing information for 3D reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": "Diffusion models. A diffusion model draws a sample from a probability distribution " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "p(I)" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " by inverting a process that gradually adds noise to the image " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ". The diffusion process is associated with a noising schedule " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\{\\alpha_t \\in (0,1)\\}_{t=1}^T" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ", which defines how much noise is added at each time step. The noisy version of sample " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " can then be written " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I_t = \\alpha_t I + \\sigma_t \\epsilon" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ", is a sample from a Gaussian distribution and " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\sigma_t^2 = 1 - \\alpha_t^2" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ". One then learns a denoising neural network " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon} = \\Phi(I_t; t)" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " that takes as input the noisy image " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " and the noise level " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " and predicts the noise component " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": ". Iterated applications of the network generate " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I = I_0" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "inline_equation", + "content": "I_T \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 464, + 287, + 606 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 608, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 608, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 608, + 287, + 632 + ], + "type": "text", + "content": "The diffusion model is trained on large collections " + }, + { + "bbox": [ + 47, + 608, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{D}' = \\{I\\}" + }, + { + "bbox": [ + 47, + 608, + 287, + 632 + ], + "type": "text", + "content": " of images by minimizing the loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 642, + 287, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 642, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 61, + 642, + 287, + 667 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i f f}} \\left(\\Phi ; \\mathcal {D} ^ {\\prime}\\right) = \\frac {1}{| \\mathcal {D} ^ {\\prime} |} \\sum_ {I \\in \\mathcal {D} ^ {\\prime}} \\left| \\left| \\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t\\right) - \\epsilon \\right| \\right| ^ {2}. \\tag {2}", + "image_path": "828a93ab779a3b3bf4f2d4202b831b2072b315468f2ba9ab86504b4f327ac404.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "This model can be easily extended to draw samples from a distribution " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "p(x|e)" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " conditioned on a prompt " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": ". Conditioning on the prompt is obtained by adding " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " as an additional" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "input of the network " + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": ", and the strength of conditioning can be controlled via classifier-free guidance [5, 11]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": "DreamFusion and Score Distillation Sampling (SDS). Given a 2D diffusion model " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "p(I|e)" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": " and a prompt " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": ", DreamFusion extracts from it a 3D rendition of the corresponding concept, represented by a RF " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "(\\sigma, c)" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": ". It does so by randomly sampling a camera parameter " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": ", rendering a corresponding view " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": ", assessing the likelihood of the view based on the model " + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "inline_equation", + "content": "p(I|e)" + }, + { + "bbox": [ + 304, + 99, + 545, + 193 + ], + "type": "text", + "content": ", and updating the RF to increase the likelihood of the generated view based on the model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 194, + 545, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 218 + ], + "type": "text", + "content": "In practice, DreamFusion uses the denoising network as a frozen critic and takes a gradient step" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 230, + 545, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 230, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 315, + 230, + 545, + 271 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {(\\sigma , c)} \\mathcal {L} _ {\\mathrm {S D S}} (\\sigma , c; \\pi , e, t) = \\\\ E _ {t, \\epsilon} \\left[ w (t) \\left(\\Phi \\left(\\alpha_ {t} I + \\sigma_ {t} \\epsilon ; t, \\boldsymbol {e}\\right) - \\epsilon\\right) \\cdot \\frac {\\partial I}{\\partial (\\sigma , c)} \\right], \\tag {3} \\\\ \\end{array}", + "image_path": "40628c89564e3343217a1c65b28da82531cda6c4a31dc96ba8e2eee33be4634c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "inline_equation", + "content": "I = R(\\sigma, c, \\pi)" + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": " is the image rendered from a randomly-sampled viewpoint " + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "inline_equation", + "content": "w(t)" + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": " is a timestep-dependent weighting function. This process is called Score Distillation Sampling (SDS)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "type": "text", + "content": "One final aspect of DreamFusion is essential for understanding our contribution in the following section: DreamFusion finds that it is necessary to use classifier-free guidance [5] with a very high guidance weight of 100, much larger than one would use for image sampling, in order to obtain good 3D shapes. As a result, the generations tend to have limited diversity; they produce only the most likely objects for a given prompt, which is incompatible with our goal of reconstructing any given object." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 441, + 382, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 382, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 382, + 453 + ], + "type": "text", + "content": "3.2. RealFusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "text", + "content": "Our goal is to reconstruct a 3D model of the object contained in a single image " + }, + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "text", + "content": ", utilizing the prior captured in the diffusion model " + }, + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 460, + 545, + 555 + ], + "type": "text", + "content": " to make up for the missing information. We do this by optimizing a radiance field using two simultaneous objectives: (1) a reconstruction objective (Eq. (1)) from a fixed viewpoint, and (2) a SDS-based prior objective (Eq. (3)) on novel views randomly sampled at each iteration. Figure 2 provides a diagram of the method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "text", + "content": "Single-image textual inversion as a substitute for alternative views. The most important component of our method is the use of single-image textual inversion as a substitute for alternative views. Ideally, we would like to condition our reconstruction process on multi-view images of the object in " + }, + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "text", + "content": ", i.e., on samples from " + }, + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "inline_equation", + "content": "p(I|I_0)" + }, + { + "bbox": [ + 304, + 558, + 545, + 630 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Since these images are not available, our idea is to engineer a text prompt " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "e^{(I_0)}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " specifically for image " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " as a proxy for this multi-view information, i.e., as an approximation of " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "p(I|I_0)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ". We do so by generating random augmentations " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "h(I_0), h \\in H" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " of the input image, which serve as pseudo-alternative-views. We use these augmentations as a mini-dataset " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}' = \\{h(I_0)\\}_{h \\in H}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " and optimize the diffusion loss" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "8449" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 545, + 397 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 397 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 397 + ], + "type": "image", + "image_path": "4fa14015df1ed4e2cd8170d4cb6cec249e1083904621c6607bac898d54e0a9c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 404, + 547, + 429 + ], + "lines": [ + { + "bbox": [ + 46, + 404, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 547, + 429 + ], + "type": "text", + "content": "Figure 4. Qualitative results. RealFusion reconstructions from a single input view. Each pair of columns shows the textured object and the underlying 3D shape, as a shaded surface. Different pairs of columns show different viewpoints." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{diff}}(\\Phi (\\cdot ;e^{(I_0)}))" + }, + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "type": "text", + "content": " of Eq. (2) with respect to the prompt " + }, + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "type": "inline_equation", + "content": "e^{(I_0)}" + }, + { + "bbox": [ + 46, + 447, + 287, + 483 + ], + "type": "text", + "content": " while freezing all other text embeddings and model parameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "content": "In practice, our prompt is derived automatically from the template \"an image of a " + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "content": "\", where \" " + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "inline_equation", + "content": "= e^{(I_0)}" + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "content": ") is a newizable token introduced to the vocabulary of the text encoder of our diffusion model (see the supplementary material for details). A caption or description of " + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 485, + 288, + 604 + ], + "type": "text", + "content": " is not needed. Our optimization procedure mirrors and generalizes the recently-proposed textual-inversion method of [7]. Differently from [7], we work in the single-image setting and utilize image augmentations for training rather than multiple views." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "To help convey the intuition behind " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", consider an attempt at reconstructing an image of a fish using the generic text prompt \"An image of a fish\" with losses (2) and (3). In our experience, this often produces a reconstruction which looks like the input fish from the input viewpoint, but looks like some different, more-generic fish from the backside. By contrast, using the prompt \"An image of a " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e} \\rangle" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "\", the reconstruction resembles the input fish from all angles. An example of exactly this case is shown in Fig. 7, and Fig. 3" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "content": "demonstrates the amount of detail captured in the embedding " + }, + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{e}\\rangle" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 485, + 546, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 546, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 546, + 594 + ], + "type": "text", + "content": "Coarse-to-fine training. We use the diffusion prior described above to optimize an RF in a coarse-to-fine manner. Before describing our coarse-to-fine training methodology, we first briefly introduce the underlying RF model, i.e., InstantNGP [23]. InstantNGP is a grid-based model which stores features at the vertices of a set of feature grids " + }, + { + "bbox": [ + 304, + 485, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\{G_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 485, + 546, + 594 + ], + "type": "text", + "content": " at multiple resolutions. The resolution is chosen to be a geometric progression between the coarsest and finest resolutions, and feature grids are trained simultaneously." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "text", + "content": "We choose InstantNGP over a conventional MLP due to its computational efficiency. However, InstantNGP tends to produce small irregularities on the surface of the object. We find that training in a coarse-to-fine manner helps to alleviate these issues: for the first half of training we only optimize the lower-resolution feature grids " + }, + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{G_i\\}_{i=1}^{L/2}" + }, + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "text", + "content": ", and then in the second half of training we optimize all feature grids " + }, + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{G_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 604, + 547, + 715 + ], + "type": "text", + "content": ". Using this strategy, we obtain the benefits of both efficient training and high-quality results." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "8450" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 286, + 233 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 286, + 233 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 286, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 286, + 233 + ], + "type": "image", + "image_path": "b562f2299d6329edc74616c43df25c6844bb06f0e348ff67e8eb9f18007fef57.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 287, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 287, + 322 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison with prior work. We show the results of our method and the category-level method of [50] on real-world images from the CO3D dataset [31]. Each pair of rows show two novel views produced by [50] and our method. For [50], we use category-specific models for each CO3D category (in this case, motorcycles, cups, and backpacks). Despite not requiring any category-specific information, our method is able to reconstruct objects at a higher level of detail than [50]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 331, + 282, + 460 + ], + "blocks": [ + { + "bbox": [ + 50, + 331, + 282, + 460 + ], + "lines": [ + { + "bbox": [ + 50, + 331, + 282, + 460 + ], + "spans": [ + { + "bbox": [ + 50, + 331, + 282, + 460 + ], + "type": "image", + "image_path": "5197fa2640e80a46031fa205a6f86bda7d6adafdee330d53848837506ab203ee.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 468, + 286, + 534 + ], + "lines": [ + { + "bbox": [ + 46, + 468, + 286, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 286, + 534 + ], + "type": "text", + "content": "Figure 6. Diversity of 3D reconstructions from a single image. Above, we see our method's ability to generate a diverse set of object reconstructions given the same input image. In particular, the method produces different textures on the backsides of the generated objects, despite all objects matching the input image from the reference view." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 546, + 286, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 286, + 605 + ], + "type": "text", + "content": "Normal vector regularization. We introduce a regularization term to encourage our geometry to have smoothly varying normal vectors. Notably, we perform this regularization in " + }, + { + "bbox": [ + 46, + 546, + 286, + 605 + ], + "type": "inline_equation", + "content": "2D" + }, + { + "bbox": [ + 46, + 546, + 286, + 605 + ], + "type": "text", + "content": " rather than in 3D because we found that it reduces the variance of the regularizer and improves results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 606, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 286, + 653 + ], + "type": "text", + "content": "At each iteration, in addition to computing RGB and opacity values, we also compute normals for each point along the ray and aggregate these via the ray marching equation to obtain normals1 " + }, + { + "bbox": [ + 46, + 606, + 286, + 653 + ], + "type": "inline_equation", + "content": "N \\in \\mathcal{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 606, + 286, + 653 + ], + "type": "text", + "content": ". Our loss is:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 80, + 663, + 286, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 663, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 80, + 663, + 286, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {n o r m a l s}} = \\| N - \\operatorname {s t o p g r a d} (\\operatorname {b l u r} (N, k)) \\| ^ {2} \\tag {4}", + "image_path": "a742851d1d8cefadafcf7442c634e7c77a59fee70f5bfb4b30401a31a7d4ca17.jpg" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 313, + 70, + 539, + 202 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 539, + 202 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 539, + 202 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 539, + 202 + ], + "type": "table", + "html": "
F-scoreCLIP-similarity
[50]Ours[50]Ours
Backpack7.5812.220.720.74
Chair8.2610.230.650.76
Motorcycle8.668.720.690.70
Orange6.2710.160.710.74
Skateboard7.745.890.740.74
Teddybear12.8910.080.730.82
Vase6.309.720.690.71
Mean8.249.580.700.74
", + "image_path": "5a6fc2a253babff581d669d68995eb18f1b8ba4cfe168e663b2ea5f720756dc2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 211, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 289 + ], + "type": "text", + "content": "Table 1. Quantitative comparison. We compare our method with Shelf-Supervised [50] on seven object categories. The F-score and CLIP-similarity metrics are designed to measure the quality of reconstruction shape and appearance, respectively. For both metrics, higher is better. Metrics are averaged over three images per category. Our method outperforms [50] in aggregate, despite the fact that [50] uses a different category-specific model for each category." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "text", + "content": "where stopgrad is a stop-gradient operation and " + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathrm{blur}(\\cdot ,k)" + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "text", + "content": " is a Gaussian blur with kernel size " + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "text", + "content": " (we use " + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "inline_equation", + "content": "k = 9" + }, + { + "bbox": [ + 305, + 309, + 545, + 334 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "text", + "content": "Mask loss. In addition to the input image, our model also utilizes a mask of the object that one wishes to reconstruct. In practice, we use an off-the-shelf image matting model to obtain this mask for all images. The loss is simply the " + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "text", + "content": " norm of the difference between the rendered opacities from the fixed reference viewpoint " + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\hat{M} = \\mathcal{R}(\\sigma, \\pi_0) \\in \\mathcal{R}^{H \\times W}" + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "text", + "content": " and the object mask " + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 336, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}} = \\| \\hat{M} - M \\|^2" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 420, + 506, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 420, + 506, + 431 + ], + "spans": [ + { + "bbox": [ + 317, + 420, + 506, + 431 + ], + "type": "text", + "content": "Our final objective then consists of four terms:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 445, + 545, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 445, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 315, + 445, + 545, + 473 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\sigma , c} \\mathcal {L} = \\nabla \\mathcal {L} _ {\\mathrm {S D S}} + \\lambda_ {\\text {n o r m a l s}} \\cdot \\nabla \\mathcal {L} _ {\\text {n o r m a l s}} \\\\ + \\lambda_ {\\text {i m a g e}} \\cdot \\nabla \\mathcal {L} _ {\\text {i m a g e}} + \\lambda_ {\\text {m a s k}} \\cdot \\nabla \\mathcal {L} _ {\\text {m a s k}} \\tag {5} \\\\ \\end{array}", + "image_path": "6506ccec509aa5303c53a7101844c13d0a0b3ffbaddd0dc341851d2f09eaeae4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 482, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 482, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 305, + 482, + 545, + 505 + ], + "type": "text", + "content": "where the first two terms are regularizers and the remaining ones are data terms." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 517, + 387, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 387, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 387, + 531 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 537, + 436, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 436, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 436, + 550 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": "Regarding hyperparameters, we use nearly the same set of hyper-parameters for all experiments—there is no per-scene hyper-parameter adjustment. For our diffusion model prior, we employ the open-source Stable Diffusion model [34] trained on the LAION [36] dataset. At each optimization step, we first render from the reconstruction camera and compute our reconstruction losses " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{image}}" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}}" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": ". We then render from a randomly sampled camera to obtain a novel view and use this view for " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SDS}}" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{normals}}" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{image}} = 5.0" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mask}} = 0.5" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{normals}} = 0.5" + }, + { + "bbox": [ + 304, + 555, + 545, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "type": "text", + "content": "1 Normals may be computed either by taking the gradient of the density field or by using finite differences. We found that using finite differences works well in practice." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "2There is one small exception to this rule, which is that for a small number of images where the camera angle was clearly at an angle higher than " + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "inline_equation", + "content": "15^{\\circ}" + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": " above the horizontal plane, we used a camera angle of 30 or " + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "inline_equation", + "content": "40^{\\circ}" + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "type": "text", + "content": "8451" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 532, + 274 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 532, + 274 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 532, + 274 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 532, + 274 + ], + "type": "image", + "image_path": "8cfc2e1856e99898a74ad8d3e265f81a9f73698176df06d570f54dc8816b0abd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 275, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 547, + 319 + ], + "type": "text", + "content": "Figure 7. A visualization of the effect of single-image textual inversion on reconstruction quality. In each pair of rows, the top row shows the result of utilizing a standard text prompt for our diffusion-model-based loss (e.g., \"An image of a statue of a cat\"). The bottom row shows the result of utilizing a text prompt optimized for the input image in a fully-automatic manner; this textual inversion process dramatically improves object reconstruction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 329, + 286, + 470 + ], + "blocks": [ + { + "bbox": [ + 48, + 329, + 286, + 470 + ], + "lines": [ + { + "bbox": [ + 48, + 329, + 286, + 470 + ], + "spans": [ + { + "bbox": [ + 48, + 329, + 286, + 470 + ], + "type": "image", + "image_path": "596b75f035a042c0e7677ed95137e4d4eca68973f9f3be862497d0456a467994.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 471, + 288, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 471, + 288, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 288, + 515 + ], + "type": "text", + "content": "Figure 8. Effect of coarse-to-fine training. The top row of each pair is generated by optimizing all levels of a multi-resolution 3D feature grid from the first optimization step, whereas the bottom row is optimized in a coarse-to-fine manner." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 528, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 287, + 564 + ], + "type": "text", + "content": "Regarding camera sampling, lighting, and shading, we keep nearly all parameters the same as [27]. We describe our setup in detail in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 574, + 163, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 163, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 163, + 586 + ], + "type": "text", + "content": "4.2. Quantitative results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "There are only few methods that attempt to reconstruct arbitrary objects in 3D. The most recent and best-performing of these is Shelf-Supervised Mesh Prediction [50], which we compare to here. They provide 50 pretrained category-level models for 50 different categories in OpenImages [17]. Since we aim to compute metrics using 3D or multi-view ground truth, we evaluate on seven categories from the CO3D dataset [32] with corresponding OpenImages categories. For each of these seven categories, we select three images at random and run both RealFusion" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 329, + 544, + 471 + ], + "blocks": [ + { + "bbox": [ + 307, + 329, + 544, + 471 + ], + "lines": [ + { + "bbox": [ + 307, + 329, + 544, + 471 + ], + "spans": [ + { + "bbox": [ + 307, + 329, + 544, + 471 + ], + "type": "image", + "image_path": "b1743ff122f0b51f8b25b1a0fbd31b64185866c4e9462cae1d2d524f3f7e5552.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 471, + 545, + 548 + ], + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 548 + ], + "type": "text", + "content": "Figure 9. Effect of normal smoothness on reconstruction quality. Each pair of rows show the reconstruction without and with the normal smoothness regularization term (4). The regularizer improves the visual appearance of surfaces and reduces the number of irregularities on the surface of reconstructed objects. In most cases, we also find that it helps to improve the overall realism of the reconstructed shape." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 570, + 498, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 498, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 498, + 581 + ], + "type": "text", + "content": "and Shelf-Supervised to obtain reconstructions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "We first test the quality of the recovered 3D shape in Fig. 5. [50] directly predicts a mesh, while we extract a mesh from our predicted radiance field using marching cubes. CO3D comes with sparse point-cloud reconstructions of objects obtained using multi-view geometry. For evaluation, we sample points from the reconstructed meshes and align them optimally with the ground truth point cloud by first estimating a scaling factor and then using Iterated Closest Point (ICP). Finally, we compute the F-score [40] with a threshold of 0.05 to measure the distance between the predicted and ground truth point clouds. Results are" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "8452" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 286, + 198 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 286, + 198 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 286, + 198 + ], + "type": "image", + "image_path": "312ac77e375873e769e5cc74e5c3cd4b2b5ac42b569d4510097a28e1d102126b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "type": "text", + "content": "Figure 10. Comparing Stable Diffusion and CLIP priors. Results from two different priors: Stable Diffusion [34] and CLIP [29]. Stable Diffusion yields much higher-quality reconstructions, capturing more plausible object shapes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 251, + 282, + 389 + ], + "blocks": [ + { + "bbox": [ + 50, + 251, + 282, + 389 + ], + "lines": [ + { + "bbox": [ + 50, + 251, + 282, + 389 + ], + "spans": [ + { + "bbox": [ + 50, + 251, + 282, + 389 + ], + "type": "image", + "image_path": "7cb77fa022b16327958075aeae5f1ccde1a916858c6e9cec273234da9738922d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 475 + ], + "type": "text", + "content": "Figure 11. Failure cases. In the first two examples, the model simply fails to properly reconstruct the object geometry, and produces a semi-transparent scene which lacks a well-defined geometry. The third case is different in that the geometry is highly realistic, but the texture paints two Pikachu faces, one on each side of the object; this problem is sometimes called the Janus problem, after the two-faced Roman god." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 484, + 115, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 115, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 115, + 495 + ], + "type": "text", + "content": "shown in Tab. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "text", + "content": "In order to evaluate the quality of the reproduced appearance, we also compare novel-view renderings from our and their method. Ideally, these renderings should produce views that are visually close to the real views. In order to test this hypothesis, we check whether the generated views are close or not to the other views given in CO3D. We report (Tab. 1) the CLIP embedding similarity of the generated images with respect to the closest CO3D view available (i.e., the view with maximum similarity)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 155, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 155, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 155, + 624 + ], + "type": "text", + "content": "4.3. Qualitative results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "type": "text", + "content": "Fig. 4 shows additional qualitative results from multiple viewpoints. Fig. 6 explores the ability of RealFusion to sample the space of possible solutions by repeating the reconstruction several times, starting from the same input image. There is little variance in the reconstructions of the front side of the object, but significant variance for its backside." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "Fig. 11 shows two typical failure modes of RealFusion: in some cases, the model fails to converge, and in others, it copies the front view to the back of the object, even if this is not semantically correct." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 136, + 436, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 136, + 436, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 136, + 436, + 148 + ], + "type": "text", + "content": "4.4. Analysis and Ablations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 156, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 289 + ], + "type": "text", + "content": "One of the key components of RealFusion is our use of single-image textual inversion, which allows the model to correctly imagine novel views of a specific object. Fig. 7 shows that this component plays indeed a critical role in the quality and consistency of the reconstructions. Without textual inversion, the model often reconstructs the backside of the object in the form of a generic instance from the object category. For example, the backside of the cat statue in the top row of Fig. 7 is essentially a different statue of a more generic-looking cat, whereas the model trained with textual inversion resembles the true object from all angles." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 291, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 385 + ], + "type": "text", + "content": "Other components of the model are also significant. Fig. 8 shows that coarse-to-fine optimization reduces the presence of low-level artifacts and results in smoother, visually pleasing surfaces. Fig. 9 shows that the normal smoothness regularizer of Eq. (4) further results in smoother, more realistic meshes. Fig. 10 shows that using Stable Diffusion works significantly better than relying on an alternative such as CLIP." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 405, + 383, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 383, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 383, + 417 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 428, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 595 + ], + "type": "text", + "content": "We have introduced RealFusion, a new approach to obtain full " + }, + { + "bbox": [ + 304, + 428, + 545, + 595 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 428, + 545, + 595 + ], + "type": "text", + "content": " photographic reconstructions of any object given a single image of it. To achieve this, we leverage an off-the-shelf diffusion model trained using only pairs of 2D images and text (but no 3D supervision) and optimize a token embedding to represent the object depicted in the image. We use this conditional prior to learn an efficient, multi-scale radiance field representation of the reconstructed object, incorporating an additional regularizer to smooth out the reconstructed surface. The resulting method can generate plausible 3D reconstructions of objects captured in the wild which are faithful to the input image. Future improvements could be obtained by specializing the diffusion model for the task of new-view synthesis." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 601, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 660 + ], + "type": "text", + "content": "Ethics. We use the CO3D dataset in a manner compatible with their terms; it does not contain personal information. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. L. M. K. is supported by the Rhodes Trust. A. V., I. L. and C. R. are supported by ERC-UNION-CoG-101001212. I. L. and C. 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James1", + "bbox": [ + 517, + 180, + 642, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mark Rau1 \nJiajun Wu1", + "bbox": [ + 687, + 180, + 777, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 312, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Objects make unique sounds under different perturbations, environment conditions, and poses relative to the listener. While prior works have modeled impact sounds and sound propagation in simulation, we lack a standard dataset of impact sound fields of real objects for audio-visual learning and calibration of the sim-to-real gap. We present REALIMPACT, a large-scale dataset of real object impact sounds recorded under controlled conditions. REALIMPACT contains 150,000 recordings of impact sounds of 50 everyday objects with detailed annotations, including their impact locations, microphone locations, contact force profiles, material labels, and RGBD images.* We make preliminary attempts to use our dataset as a reference to current simulation methods for estimating object impact sounds that match the real world. Moreover, we demonstrate the usefulness of our dataset as a testbed for acoustic and audio-visual learning via the evaluation of two benchmark tasks, including listener location classification and visual acoustic matching.", + "bbox": [ + 75, + 300, + 473, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 614, + 209, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object sounds permeate our everyday natural environments as we both actively interact with them and passively perceive events in our environment. The sound of a drinking glass bouncing on the floor assuages our fear that the glass would shatter. The click made by a knife making contact with a cutting board assures us that we have diced cleanly through a vegetable. And listening to the sound a painted mug makes when we tap it informs us of whether it is made of ceramic or metal. What we perceive from sound complements what we perceive from vision by reinforcing, disambiguating, or augmenting it.", + "bbox": [ + 75, + 640, + 468, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding the cause-and-effect relationships in these sounds at a fine-grained level can inform us about an object's material properties and geometry, as well as its contact and other environmental conditions. Capturing", + "bbox": [ + 75, + 806, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "these relationships from real-world data can help us improve our models toward more realistic physical simulations, with applications in virtual reality, animation, and training learning-based frameworks in simulation.", + "bbox": [ + 500, + 270, + 890, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The sounds we perceive from objects are the result of many intricate physical processes: they encode important properties about the object itself (e.g., geometry, material, mechanical properties), as well as the surrounding environment (e.g., room size, other passive objects present, materials of furniture in the room). More specifically, when a hard object is struck, it vibrates according to its mass and stiffness, and the shape of the object determines the mode shapes of the dominant vibration patterns ( $\\S 3.1$ ). Acoustic waves are then emitted into the medium, typically air, bouncing around in the room and interacting with surrounding objects and the room itself before reaching our ear or a microphone to be perceived as pressure fluctuations ( $\\S 3.2$ ).", + "bbox": [ + 496, + 334, + 892, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior work has explored using physical simulation [26, 54] or learning-based methods [28, 29] to reconstruct the sound generation process virtually, as well as building 3D environments with simulated spatial audio for embodied audio-visual learning [7, 15, 18, 35, 42]. However, there has been little work on building physical apparatuses and feasible measurement process to quantify sounds made by the everyday objects, despite their importance and intimate relationship with our daily lives. As a result, the evaluations of the methods above are largely established on subjective metrics such as user studies.", + "bbox": [ + 496, + 534, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this gap, we introduce REALIMPACT, a dataset containing 150k recordings of 50 everyday objects, each being struck from 5 distinct impact positions. For each impact point, we capture sounds at 600 field points to provide comprehensive coverage of the frequency components of the sounds and how they are distributed spatially. REALIMPACT thus provides all the inputs most current simulation frameworks needed to simulate each sound, while also providing the ground truth recording for comparison. We show that REALIMPACT can be used for various downstream auditory and audio-visual learning tasks, such as listener location classification (§5.2) and visual acoustic matching (§5.3). These results demonstrate that sound", + "bbox": [ + 496, + 704, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The project page and dataset are available at https://samuelpclarke.com/realimpact/", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1516", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fields can help improve machine perception and understanding of the world, and motivate further studies of even more accurate simulation methodologies to reduce the sim-to-real gap for future applications.", + "bbox": [ + 78, + 90, + 467, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We make three contributions. First, we design an automated setup for collecting high-fidelity, annotated recordings of sounds by controlled striking of everyday objects. Second, using this setup, we acquire a large dataset of spatialized object sounds, REALIMPACT. Third, we motivate the utility of REALIMPACT by (a) using it to perform comparisons to results generated by current state-of-the-art sound simulation frameworks and (b) evaluating two benchmark tasks for acoustic and audio-visual learning.", + "bbox": [ + 78, + 152, + 467, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 78, + 301, + 217, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Datasets of Object Sounds. Many datasets of object sounds have been introduced, each varying in the details of their collection, based on the applications they target. The Greatest Hits Dataset [40] includes audio-video recordings of thousands of impacts between real objects from the wild. The recordings were not taken in a controlled environment, and each impact is induced by a human with a drumstick, polluting each object's impact sound with the sound of the rather resonant drumstick. The Sound-20K Dataset [59] is a fully synthetic dataset of 20,000 simulated recordings of objects being dropped in virtual environments. More recently, ObjectFolder [17,21] is introduced as a large dataset of trained implicit models for generating the sounds objects make when impacted at arbitrary locations. However, these are once again trained only on data from simulation, and they do not model the acoustic transfer properties of the objects, only their structural vibratory response.", + "bbox": [ + 78, + 321, + 467, + 578 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Physics-based Sound Rendering. Realistic sound rendering has been a long-held goal in computer music, interactive virtual environments, and computer animation [27, 34, 51, 55]. By modeling the underlying physical processes of vibrations, the computer graphics community demonstrated convincing synthesized sounds for vibrating solids [26, 31, 38, 39], shells [5], rods [47], and even fluids [32, 55]. [26, 55] further showed that it is important for high-quality sound rendering to capture the amplitude and spatial structure of radiating sound fields. However, computing these acoustic transfer fields is time-consuming as they are typically solved in the frequency domain, one frequency at a time. In KLEINPAT [54], the authors showed that by conflating multiple vibrating modes into one time-domain solve, getting all-frequency transfer maps can be done much faster, usually on the order of minutes. These models require careful simulation and material parameters tuning for the best results. To alleviate this issue, several works proposed to sample audio clips [45] and impulse responses [53] to reconstruct the material definitions. Recently, a few works [28, 29] have explored using learning to", + "bbox": [ + 78, + 583, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "approximate both the vibration and transfer computations using simulated training data. We provide timely real data that such simulations could use to validate their outputs and tune their performances.", + "bbox": [ + 503, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recording Sounds Made by Real Objects. Whereas many learning-based frameworks have traditionally used simulation results as their \"ground truth\" for learning acoustic models of object vibrations and their transfer, some works have proposed to fit acoustic object models directly from data using digital signal processing with more relaxed model assumptions about rigid body vibrations.", + "bbox": [ + 503, + 155, + 890, + 261 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pai et al. [41] describe a framework for scanning physical objects across multiple modalities, measuring visual, tactile, and audio properties of some everyday objects. They fit a data-driven acoustic model based on modal vibration for an object by striking it at different points and recording the ensuing sound from a single position per impact point, assuming constant acoustic transfer across the object. DiffImpact [12] similarly fits modal models to real recordings of objects, but assumes a constant modal response and transfer across the object since their data lacked annotations of the impact point and microphone location. Perhaps most similar to our work, Corbett et al. [13] collect recordings of striking an object at three different impact points, positioning a microphone at 19 different positions per impact point. We collect recordings from an order of magnitude more microphone positions to empirically demonstrate that acoustic transfer varies rather drastically over a much finer resolution than can be captured at 19 different locations.", + "bbox": [ + 503, + 261, + 890, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Also, while these prior works have collected datasets from real audio, none have publicly released their datasets. Furthermore, since many simulation frameworks are designed to simulate audio of objects vibrating freely in an anechoic space, the recordings collected by these works are unsuitable for a fair comparison, since they are recorded with objects in contact conditions like resting on tables or grasped in hands, which greatly hinder free vibrations. In contrast, we propose a novel capture system where objects rest on a thread mesh in an acoustically treated room, which more closely approximates free vibration in an anechoic environment.", + "bbox": [ + 503, + 534, + 890, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, from outside the domain of object impact sounds, Bellows et al. [4] have an extensive project measuring the sound directivity of musical instruments while being played by musicians. The measurements take place in a large anechoic chamber and are recorded with a rotating semi-circular microphone array resulting in 2,522 unique microphone positions. The raw measurements are not provided, but the directivity patterns are available as spherical harmonic decompositions [3].", + "bbox": [ + 503, + 714, + 890, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Learning of Sounds in Space. Both audio and visual data convey crucial spatial information. Recent inspiring works have explored many interesting tasks connecting", + "bbox": [ + 503, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1517", + "bbox": [ + 485, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c7a3f27ed18d67c51f5be931de184088fe12eb884858e3b6c9eb34358419821a.jpg", + "image_caption": [ + "Figure 1. Pipeline for the acquisition of spatialized impact sounds: (Left) The object is placed at the center of the measurement platform and aligned with mesh threads. The impact hammer is positioned to strike a target vertex on the object. (Center) The gantry moves the microphones to 40 different positions within a semi-cylinder of the object, with the automated hammer mechanism striking the object to record the sound at each position. (Right) By the end of the recording process, for each of the 5 vertices of each object, recordings from 600 different microphone positions have been collected within the semi-cylinder to one side of the object, as shown." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 405, + 369 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3d27dfe90ca06562f9dc57bb86a2f6c9ed0facee86a41545779ba2cd9e773538.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 90, + 651, + 371 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dd6ce316362c1941b4aed88dcdaf5444bb768ec392b6be3da1eba3c3acf36ab8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 90, + 890, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "visual learning and sound in 3D space, including visually-guided audio spatialization [20,22,37,57,61], sound source localization in video frames [1,6,48], learning audio-visual spatial correspondence [9, 58], and building audio-visual 3D environments [7, 15] for an array of embodied learning tasks [8, 14, 16, 18, 35, 42]. We show how our dataset can be used to evaluate real-world performance of auditory and audiovisual learning frameworks on two novel tasks.", + "bbox": [ + 75, + 465, + 472, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Physics-Based Sound Synthesis", + "text_level": 1, + "bbox": [ + 76, + 606, + 362, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We begin with some background about physics-based sound simulation for rigid objects to motivate design choices for our dataset and provide context for our baseline simulation frameworks and their parameters. Here we briefly summarize a commonly used sound synthesis pipeline for rigid objects. For a more detailed introduction, we recommend the article from James et al. [27].", + "bbox": [ + 75, + 633, + 468, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Modal Sound Synthesis", + "text_level": 1, + "bbox": [ + 76, + 753, + 294, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When a contact force is applied to an object (e.g., your dinner plate hits the dishwasher handle), depending on the location of contact, various vibration modes can get excited and eventually die down due to internal damping. Mathematically, the vibration's displacement vector $\\pmb{u}(t)$ can be low-rank approximated as", + "bbox": [ + 75, + 777, + 470, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {u} (t) = U \\boldsymbol {q} (t) = \\left[ \\hat {\\boldsymbol {u}} _ {1} \\dots \\hat {\\boldsymbol {u}} _ {K} \\right] \\boldsymbol {q} (t), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 883, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $U$ is the modal matrix with mode shapes $\\hat{\\pmb{u}}_i$ and $\\pmb {q}(t)\\in \\mathbb{R}^{K}$ the modal coordinates. The equations of motion are", + "bbox": [ + 498, + 465, + 892, + 511 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nM \\ddot {\\boldsymbol {u}} + C \\dot {\\boldsymbol {u}} + K \\boldsymbol {u} = \\boldsymbol {f}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 512, + 890, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $M$ , $C$ , and $K$ are the mass, damping, and stiffness matrix, respectively*, and $\\pmb{f}$ is the external force vector. It is typically assumed in the literature that the damping can be approximated by Rayleigh damping, $C = \\alpha M + \\beta K$ ; with this convenient assumption, Eq. (2) can be re-written in the subspace defined by $U$ as", + "bbox": [ + 496, + 531, + 893, + 623 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\ddot {\\boldsymbol {q}} + (\\alpha \\mathbf {I} + \\beta \\Lambda) \\dot {\\boldsymbol {q}} + \\Lambda \\boldsymbol {u} = U ^ {\\intercal} \\boldsymbol {f}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 628, + 890, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{I}$ is the identity matrix and $\\Lambda = \\mathrm{diag}(\\omega_1^2,\\dots,\\omega_K^2)$ is a diagonal matrix of involving angular frequencies $\\omega_{i}$ . Since the damping can significantly affect material perception [30], the Rayleigh damping can potentially model real-world objects poorly. In addition, there are two scalar properties $\\alpha$ and $\\beta$ to fit, and in previous work, these are typically hand-picked to produce sounds that are closest to a given material. Also note that this formulation is based on linear modal analysis [49,50], which assumes the vibrations are infinitesimal, or, in other words, the object is approximately rigid.", + "bbox": [ + 496, + 652, + 893, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Acoustic Transfer", + "text_level": 1, + "bbox": [ + 500, + 825, + 671, + 842 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sound radiates from an object's surface into the surrounding medium as pressure waves. Since the modes de", + "bbox": [ + 498, + 849, + 892, + 880 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "*Formulas of how to compute these matrices can be found in [39].", + "bbox": [ + 522, + 886, + 872, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1518", + "bbox": [ + 483, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "cay slowly over time, it is convenient to work in the frequency domain [26]. The distribution of the wave magnitudes in space, $\\hat{p} (x;\\omega)$ , is referred to in the literature [26] as the acoustic transfer function. With a given set of vibrational boundary conditions, such as those given by Eq. (3), one can solve the frequency-domain Helmholtz equation [5,26,31] using boundary element methods [2, 11, 23] or a time-domain wave equation before reconstructing the acoustic transfer fields [54]. To display the acoustic transfer fields at runtime, we may compress the representation using multi-point dipole sources [26] or single-point multipole sources [60]. Another increasingly popular way of storing and displaying the field is to leverage the radial structure (or lack thereof) in the far-field radiation to store Far-field Acoustic Transfer (FFAT) maps, which are rectangular, image-like textures that capture the angular radiation pattern of a given object. FFAT maps can be quickly reparametrized (e.g., equalized, time-delayed) at runtime to display object impact sounds with user interactions [54].", + "bbox": [ + 75, + 90, + 472, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. The REALIMPACT Dataset", + "text_level": 1, + "bbox": [ + 76, + 390, + 326, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce REALIMPACT, a dataset of 150,000 real object impact sounds. Along with these sounds, we record the force profiles from the impact hammer we used to strike the objects, as well as an RGBD image of the object from each azimuth angle and radial distance from which the audio recording is measured. Below, we introduce the hardware setup for collecting the data, the objects we use, and our data collection pipeline.", + "bbox": [ + 75, + 415, + 470, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Hardware Setup", + "text_level": 1, + "bbox": [ + 76, + 545, + 241, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We collect all recordings in an acoustically treated room (see Appendix B for additional details). We designed a cylindrical gantry system for moving the microphones to precise positions in space, shown in Figure 1. The gantry system moves a 1.82-meter-tall vertical column of 15 Dayton Audio EMM6 calibrated measurement microphones which are evenly and precisely spaced along the column. It moves this column precisely in two degrees of freedom: azimuth and distance, with a precision of $1^{\\circ}$ and $1\\mathrm{mm}$ , respectively. We suspended a mesh of polyester threads precisely at the axis of rotation of this gantry, centering it vertically along the column of 15 microphones. This mesh holds the objects in place while minimizing contact damping and maximizing the acoustic transparency of the surface holding the object. Furthermore, the layout of the mesh provides visual guidance for precisely positioning the objects in a repeatable manner.", + "bbox": [ + 75, + 568, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To measure the acoustic transfer from the object to the microphones, the impact force needs to be recorded, allowing an input-output relation to be found. We used a PCB 086E80 impact hammer to strike each object. The impact hammer is incorporated into a custom automated striking", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0226a2f28c77d17a852dc420f4b34ccd1571453f58df7354037cdc38b40fdd54.jpg", + "image_caption": [ + "Figure 2. The real objects used in our dataset. Objects are clustered by material: (from top left) wood, ceramic, glass, plastic, (from bottom center) iron, steel, and polycarbonate." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "mechanism, which strikes objects precisely and repeatedly while being as silent as possible. The mechanism uses a motor to wind the hammer back to contact an electromagnet; then, upon recording, the electromagnet releases the hammer. Actuating the electromagnet is completely silent, so the noise created by this mechanism is minimal during each strike. This mechanism is mounted on a microphone stand to be able to position it rigidly to strike objects at arbitrary locations. See Appendix C and D for additional details on the recording apparatus and hammer impacts, respectively.", + "bbox": [ + 496, + 368, + 890, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The impact hammer has a calibrated force transducer in its tip, measuring contact forces at the same temporal resolution as our audio. The impact hammer and microphones are all read in a time-synchronized fashion by using two Motu 8M audio interfaces connected by an optical cable. Each audio interface has digitally-controlled amplifier gains, which must be tuned up or down for object sounds that are relatively quiet or loud, respectively, to boost the signal as much as possible while also preventing clipping. Because these gains are digitally controlled, we can record and adjust them in a precise and repeatable manner throughout our experiments. The recordings were made at a sample rate of $48000\\mathrm{Hz}$ .", + "bbox": [ + 496, + 520, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also attach a RealSense D415 RGBD camera to the column, aligned with the first microphone above mesh-level, to take RGBD images with our audio measurements.", + "bbox": [ + 496, + 715, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Objects", + "text_level": 1, + "bbox": [ + 500, + 771, + 596, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We purchase 50 objects from the ObjectFolder dataset [19], which is comprised of commonly used household objects like a ceramic mug, drinking cup, plastic bin, and wood vase. Each object in REALIMPACT has a high-resolution 3D mesh model generated from a scan of the real object [21], which can be used in simulation frameworks. We select objects which are rigid and consist of a single ho", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1519", + "bbox": [ + 483, + 944, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6be6931513078ed9bfa715c27d8c412fde871647417790ecc1ee09148f5cb9c7.jpg", + "image_caption": [ + "Figure 3. An RGBD image and audio recordings from all 15 microphones are collected at each gantry position for each vertex we impact on an object." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 452, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "mogeneous material belonging to one of the following categories: ceramic, glass, wood, plastic, iron, polycarbonate, and steel—materials that have $\\alpha$ and $\\beta$ parameters available and widely used in the physics-based sound rendering literature [28, 29, 54]. Figure 2 shows all objects used for data collection. These objects all have a scale and mass suitable for data collection using our hardware setup.", + "bbox": [ + 75, + 383, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Data Collection Pipeline", + "text_level": 1, + "bbox": [ + 76, + 497, + 299, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each object, we first place the object on the supporting mesh, matching the features of the mesh to the distinctive geometric features of the object to position it in a repeatable manner. We then select 5 vertices from the virtual mesh at which to strike the object. For each vertex, we first position the hammer mechanism to strike the vertex. Since our gantry collects recordings on a semi-cylinder to one side of the object, we position the hammer mechanism to the opposite side of the semi-cylinder both to not impinge the motion of the gantry and to minimize blocking acoustic radiation from the surface of the object toward the microphones. For each vertex, we move the gantry to 40 positions: a grid of 10 angles in 20-degree increments from 0 through 180, at 4 distances of 0.23, 0.56, 0.90, and 1.23 meters from the center of the mesh. We take an RGBD image at each position in addition to the audio recordings. A diagram of the microphone positions relative to an example object is shown in Figure 1. An example of each of the modalities captured from one position is shown in Figure 3. See the Supplementary Materials for an example video of how an object is recorded.", + "bbox": [ + 75, + 521, + 470, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Processing", + "text_level": 1, + "bbox": [ + 76, + 847, + 194, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The impact hammer strikes are not necessarily constant across measurements, but the discrepancy can be corrected", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/990379c52b812374016f798925e4c28f4f9306cb91bd05551ee36c3ace8e6ee9.jpg", + "image_caption": [ + "Figure 4. Comparing different azimuth resolutions for mode shape transfer maps of a ceramic bowl, measured at $23~\\mathrm{cm}$ from the center. The top row shows maps measured at a resolution of 1 degree, while the bottom row shows those measured at a resolution of 20 degrees." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 883, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "since the force is measured. This is achieved by deconvolving the force signal from the microphone signal with frequency domain division as $m_{c} = \\mathcal{F}^{-1}\\left(\\mathcal{F}(m) / \\mathcal{F}(i)\\right)$ , where $i$ is the impact hammer signal, $m$ is the microphone signal, and $m_{c}$ is the corrected microphone signal. $\\mathcal{F}$ and $\\mathcal{F}^{-1}$ are the forward and inverse discrete Fourier transforms, respectively. The hammer signal is windowed such that only the samples within 1% of the force peak are kept, and all other samples are deemed noise and set as zero, reducing noise in the corrected microphone signal.", + "bbox": [ + 496, + 335, + 890, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To create transfer maps of the recordings, mode fitting is performed on each corrected microphone signal. The modes are fit using the method of [10]. First, the vibrational frequencies are fit with a simple peak-picking algorithm performed on $\\mathcal{F}(m_c)$ . Decay rates are fit by band-passing $m_{c}$ at the mode frequencies, applying a Root-Mean-Squared level detector, and using linear regression to estimate the slope of the energy envelope. The amplitudes are set as the magnitude of the mode frequency peak in $\\mathcal{F}(m_c)$ . Transfer maps are then formed for each vibrational frequency by displaying the magnitude at each measurement location with respect to rotation and height, as shown in Figures 4 and 5.", + "bbox": [ + 496, + 488, + 892, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Validation", + "text_level": 1, + "bbox": [ + 500, + 699, + 616, + 713 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial Sampling. We use a $20^{\\circ}$ resolution of azimuth angle for the spatial sampling as a compromise to reduce measurement time while still adding benefit for certain sound-related tasks. We take one set of measurements with $1^{\\circ}$ rotations on one of our objects (a ceramic bowl) as a comparison. Figure 4 shows measured acoustic transfer maps for sample vibrational frequencies with both $1^{\\circ}$ and $20^{\\circ}$ microphone rotations. The lowest-frequency mode shape varies gradually with the azimuth angle. But note that at the highest-frequency mode shape shown, the frequency of the repeating spatial pattern is beyond the Nyquist frequency of our azimuth sampling resolution. We show the implica", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1520", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5618d0b865f164cbe0fa9e5e1afe3ff024f85dacd5ac694827f969da9191cf4a.jpg", + "image_caption": [ + "Figure 5. Measuring repeatability of our measurements by visualizing transfer maps of vibrational frequencies of the ceramic bowl, measured at $23~\\mathrm{cm}$ from the center. The top row shows the mean of 10 trials of measurements, while the bottom shows the relative standard deviation of the 10 trials." + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 462, + 224 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tions of attempting to naively interpolate from these low-resolution transfer maps in Appendix E.", + "bbox": [ + 75, + 313, + 467, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Repeatability. We verify two aspects of the repeatability of our design: the repeatability of the gantry's position and the repeatability of our resulting audio measurements. While our gantry is capable of achieving high angular precision while it is controlled, we completely power it off during each recording, in order to eliminate motor and power supply noises from our recordings. During these periods, the wheels may settle into the carpet at a slightly different angle than we have commanded. We perform four trials of moving to the commanded angles and find that the maximum angular error across all trials did not exceed $1^{\\circ}$ , with the mean error being $0.26^{\\circ}$ . This translates to a maximum error of $2\\mathrm{cm}$ in Cartesian space, only reached when the gantry is at its farthest distance from the center.", + "bbox": [ + 75, + 358, + 467, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the repeatability of our measurements, we conduct 10 trials of our measurements on the same ceramic bowl, striking the same target vertex and using the sample positions we used throughout our dataset. We show the mean and standard deviations of the transfers we measured at some sample vibrational frequencies in Figure 5, with results of objects of additional materials in Appendix F. Our results suggest that variations may be highest at the boundaries of nodes in the transfer map. At these locations, minor errors in the azimuth angle could cause significant changes in transfer measurement. Furthermore, at these positions, the signal is lower at this frequency, so the effects of noise can be more pronounced.", + "bbox": [ + 75, + 570, + 467, + 765 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Applications", + "text_level": 1, + "bbox": [ + 76, + 781, + 207, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate some use cases of REALIMPACT with practical, multimodal applications.", + "bbox": [ + 76, + 806, + 467, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Comparing Simulated and Real Impact Sounds", + "text_level": 1, + "bbox": [ + 76, + 845, + 467, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our first task is to compare sounds synthesized by existing sound rendering methods to the recordings of RE-", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ALIMPACT in order to demonstrate typical measurement and modeling discrepancies. For this purpose, we ran each baseline method out-of-the-box without any attempt to fine-tune its model and/or hyperparameters, including material parameters, such as elastic stiffness (Young's modulus) and damping (e.g., $\\alpha$ and $\\beta$ in the case of KLEINPAT). We also did not unify the finite element analysis representations across different methods, including finite element type (KLEINPAT uses first-order tetrahedral elements, whereas ObjectFolder 2.0 uses second-order ones), and tetrahedral meshes. These out-of-the-box comparisons simplify the analysis and highlight the ability to benchmark any existing or new simulation methods given a dataset such as REALIMPACT, but exhibit various modeling oversights. We leave the work to narrow the gap between each baseline to the dataset as future work. We provide more conjectures on why these discrepancies exist in the limitations section.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We provide high-level descriptions of each baseline and refer the readers to Appendix G or directly to the linked work for more details:", + "bbox": [ + 496, + 361, + 890, + 405 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- WHITE NOISE: Random noise which has been adjusted to the same loudness as the average loudness of the recordings on a per-object basis.", + "- RANDOM IMPACT SOUND: A random impact sound recording from our dataset.", + "- KLEINPAT [54]: The modal analysis is run using first-order tetrahedral elements, and the Far-field Acoustic Transfer (FFAT) maps are done using a one-term $(1 / r)$ scalar expansion.", + "- NEURALSOUND [29]: The modal analysis is run using an optimization which is warm-started with the outputs of a 3D sparse U-net on voxelized meshes. The FFAT maps are predicted directly by a ResNet-like encoder-decoder structure. For both steps, we use the pretrained weights.", + "- OBJECTFOLDER 2.0 [21]: The modal analysis is predicted by an implicit neural representation trained on simulation data using second-order tetrahedral elements. No acoustic transfer values exist in this baseline so we used $\\hat{p}(\\boldsymbol{x};\\omega) = 1$ throughout." + ], + "bbox": [ + 517, + 412, + 890, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that the final three baselines all require material properties of the object as input; we uniformly apply the same parameters from Table 4 of [54] for all objects with the same material label in our dataset.", + "bbox": [ + 496, + 736, + 890, + 795 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We evaluate using the following metrics: 1) L1 spectral loss, a loss based on taking the average L1 distance between log-magnitude spectrograms of different window sizes (used for impact sounds in [12]); 2) envelope distance, which measures the distance between two audio samples' envelopes over time (used for spatial audio in [37]); and", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1521", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/477a22fe36b2deb052e14367dc930af346406c5f914ca0e02975b28cbb1dcc57.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
REALIMPACT DeconvolvedREALIMPACT Deconvolved + Denoised
L1 SpectralEnvelope (×10-3)CDPAML1 SpectralEnvelope (×10-3)CDPAM
WHITE NOISE4.689.541.385.229.871.39
RANDOM IMPACT SOUND0.7284.170.1210.1504.970.0880
KLEINPAT [54]0.6324.630.1170.09824.630.0975
NEURAL SOUND [29]0.67323.00.1020.13322.80.0750
OBJECT FOLDER 2.0 [21]0.74725.60.2970.23625.40.289
", + "bbox": [ + 81, + 88, + 885, + 218 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Comparing with simulated object impact sounds. Lower is better for all metrics.", + "bbox": [ + 220, + 220, + 746, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/77ec6ffd46ac5b86447088367bfdda4d62ed97c4f5234fdc82ee019dc8c0b61e.jpg", + "image_caption": [ + "Figure 6. Comparison of spectrograms from our collected recordings versus simulation frameworks. Each spectrogram represents the sound recorded or simulated from a sample point at (8, 22, 13) cm in Cartesian space from the center of the base of the object, and each row corresponds to striking the same vertex on the object." + ], + "image_footnote": [], + "bbox": [ + 81, + 247, + 890, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3) CDPAM [36], a learning-based perceptual distance metric trained from human judgments of detectable differences between clips.", + "bbox": [ + 75, + 506, + 468, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To mitigate the effects of measurement noise in our evaluation, we compare each baseline both to our deconvolved recordings and to denoised versions of our recordings, which have been denoised with the algorithm of [46]. Whereas many denoising algorithms are optimized for human speech, this algorithm has been optimized and validated against broader categories of audio signals from nature. Comparisons of example spectrograms and their denoised counterparts are shown in Appendix H.", + "bbox": [ + 75, + 551, + 468, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results are shown in Table 1, and qualitative examples are shown in Fig. 6, comparing our recordings of real impact sounds with the simulated sounds using methods from [21, 29, 54]. The KLEINPAT baseline performs best according to a spectral loss, whereas NEURAL-SOUND performs best according to the perceptual CDPAM loss. Both of these baselines significantly outperform ObjectFolder, suggesting that explicitly modeling the acoustic transfer of objects rather than merely their structural vibrations is essential for achieving realism. A random impact sound only outperforms baselines in Envelope Loss when the recording has not been denoised. Each baseline other than white noise performs better on all metrics when compared against denoised versions of our recordings, suggest-", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing that our raw recordings have non-negligible measurement noise, which must be accounted for in future comparisons.", + "bbox": [ + 498, + 506, + 890, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Listener Location Classification", + "text_level": 1, + "bbox": [ + 500, + 560, + 781, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Identifying the location of the listener with respect to the sound source is of great practical interest to many applications in virtual reality and robotics [8, 43, 44]. In this task, we want to identify the microphone position (angle, height, or distance) from the impact sound recording.", + "bbox": [ + 496, + 583, + 890, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For each impact in REALIMPACT, we have the recordings of the impact sound from 600 different listener locations collected from 10 different angles, 15 different heights, and 4 different distances, as illustrated in Fig. 1.", + "bbox": [ + 496, + 659, + 890, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Particularly, we set up three separate classification subtasks: 1) angle classification, where the goal is to classify the sound into the 10 angle categories $(0^{\\circ}, 20^{\\circ}, \\dots, 180^{\\circ})$ ; 2) height classification, where the goal is to classify the sound into the 15 height categories, each corresponding to the height of our 15 microphones; and 3) distance classification, where the goal is to classify the sound into the 4 distance categories $(0.23 \\mathrm{~m}, 0.56 \\mathrm{~m}, 0.90 \\mathrm{~m}$ , and $1.23 \\mathrm{~m})$ .", + "bbox": [ + 496, + 719, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For each subtask, we split 90/10 percent of impact sound recordings of an object into the train/test set, respectively. We train a ResNet-18 [24] network that takes the magnitude spectrogram of the impact sound as input to predict the an", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1522", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f5f6307845934e27f1419c67e3abeab234db28502119184fca3dd058795cd464.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AngleHeightDistance
CHANCE10.06.725.0
Ours57.960.767.4
", + "bbox": [ + 130, + 88, + 415, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "gle, height, or distance category. Table 2 shows the results averaged across all 50 objects. We observe that predicting height is comparatively easier. We suspect that differences in height strongly influence the spectral details for easier classification.", + "bbox": [ + 75, + 210, + 468, + 286 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Visual Acoustic Matching", + "text_level": 1, + "bbox": [ + 76, + 294, + 310, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The ability to match a source sound with the correct corresponding visual input plays an important role in tasks such as speech and speaker recognition [33, 52] or object and event localization [25, 56]. This task aims to match a sound recording with the correct corresponding image. We set up this matching task as binary classification.", + "bbox": [ + 75, + 316, + 467, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For 20 of our objects, we have a total of 200 RGBD images taken simultaneously with our audio recordings, which are collected at a fixed height from the 10 different angles and 4 different distances from which we took audio recordings for each of the 5 different vertices. We generate positive pairs by pairing each sound recording to an image taken at the corresponding angle and vertex. The height and distance of the image are fixed, so there are 50 possible images that the sound recordings correspond to. The distance of the paired RGBD image is selected such that the image captures the position of both the object and the impact hammer. Negative pairs are generated by pairing sound recordings with images that are not at the correct angle and vertex.", + "bbox": [ + 75, + 409, + 467, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We randomly select two heights to be held out for validation and test sets, while the remaining 13 heights are used for the train set. We train an audio-visual network with a ResNet-18 backbone for both the image and audio streams. The network takes in an RGB image as visual input and an impact sound recording as audio input. A fusion layer combines the audio and visual information, and a final fully-connected layer is used to extract audio-visual features for binary classification. Table 3 shows the quantitative results of the visual acoustic matching task averaged across 20 objects, and we show example inputs and outputs in Appendix I.", + "bbox": [ + 75, + 604, + 467, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 800, + 333, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented REALIMPACT, a first-of-its-kind, large dataset of 150k real impact sounds systematically collected in an acoustically treated room, and demonstrated its several use cases on benchmarking existing simulation algorithms and applications on several auditory and audiovisual tasks.", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/19db2ae184a8bed3ab60d9627232cf8b66ed7d134e5ec57d8a63e43bbc2b673c.jpg", + "table_caption": [ + "Table 2. Listener location classification results. We report the accuracy (in %) for angle, height, and distance classification, respectively." + ], + "table_footnote": [], + "table_body": "
Accuracy ↑RMSE ↓
CHANCE50.059.7
Ours75.147.7
", + "bbox": [ + 566, + 88, + 821, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative results of visual acoustic matching. We report the accuracy results (in %). RMSE angle error (in degrees) is the root-mean-square error in the difference between the angles of the image and sound recording. $\\uparrow$ or $\\downarrow$ signify higher or lower values are better, respectively.", + "bbox": [ + 498, + 154, + 890, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The microphone array stack used in our measurement process is somewhat coarse to capture high-frequency details (e.g., the $12\\mathrm{cm}$ microphone spacing in elevation roughly corresponds to the wavelength of $3\\mathrm{kHz}$ ). The angular resolution is chosen at only 20 degrees and can result in aliasing and distortion in the otherwise symmetric radiation fields, as shown in $\\S 4.5$ . The diversity of the recorded objects is restricted by the size and load capacity of our supporting thread mesh, and the microphone stack arm. The material descriptions of the objects are artificially lumped into the categories defined in previous work [54], but they may not describe the diversity of real-world materials (e.g., different kinds of steels will have different mechanical properties that might affect stiffness and thus the frequency distributions). Future work should look at more efficient ways of capture and sample a wider range of objects.", + "bbox": [ + 496, + 241, + 890, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The comparison of real impact sounds to those generated by current simulation methods exhibit various discrepancies. Many things can lead to the gap between simulations and real recordings: object scanning resolution and reconstruction accuracy, material stiffness and damping parameters, finite-element analysis differences (e.g., element type), and insufficient meshing resolution. Also we did not explicitly model hollow objects in the comparisons despite some of our objects being hollow and/or thin, and contact damping models are missing, which can affect the perceived damping rates and thus the envelope accuracy. As a result, many of the out-of-the-box simulation models' vibrational frequencies do not agree, let alone their estimates of spatialized sound amplitudes, etc. Many of these oversights will affect the comparison \"fairness\" but it also demonstrates a significant benefit of the REALIMPACT dataset: for the first time, we can measure these models using the same yard stick. We hope that this dataset provides future incentives to improve not just the simulation methods and their usage, but also the capture process and datasets that can move the field forward in a significant way.", + "bbox": [ + 496, + 483, + 890, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work is in part supported by Adobe, NSF CCRI #2120095, NSF RI #2211258, ONR MURI N00014-22-1-2740, AFOSR YIP FA9550-23-1-0127, the Stanford Institute for Human-Centered AI (HAI), Amazon, and Meta.", + "bbox": [ + 498, + 825, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1523", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.152, + 0.131, + 0.82, + 0.154 + ], + "angle": 0, + "content": "REALIMPACT: A Dataset of Impact Sound Fields for Real Objects" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.18, + 0.317, + 0.216 + ], + "angle": 0, + "content": "Samuel Clarke1 Julia Xu1" + }, + { + "type": "text", + "bbox": [ + 0.352, + 0.181, + 0.488, + 0.216 + ], + "angle": 0, + "content": "Ruohan Gao1 \nJui-Hsien Wang2" + }, + { + "type": "text", + "bbox": [ + 0.308, + 0.217, + 0.471, + 0.235 + ], + "angle": 0, + "content": "1Stanford University" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.181, + 0.643, + 0.216 + ], + "angle": 0, + "content": "Mason Wang1 \nDoug L. James1" + }, + { + "type": "text", + "bbox": [ + 0.689, + 0.181, + 0.778, + 0.216 + ], + "angle": 0, + "content": "Mark Rau1 \nJiajun Wu1" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.313, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.59 + ], + "angle": 0, + "content": "Objects make unique sounds under different perturbations, environment conditions, and poses relative to the listener. While prior works have modeled impact sounds and sound propagation in simulation, we lack a standard dataset of impact sound fields of real objects for audio-visual learning and calibration of the sim-to-real gap. We present REALIMPACT, a large-scale dataset of real object impact sounds recorded under controlled conditions. REALIMPACT contains 150,000 recordings of impact sounds of 50 everyday objects with detailed annotations, including their impact locations, microphone locations, contact force profiles, material labels, and RGBD images.* We make preliminary attempts to use our dataset as a reference to current simulation methods for estimating object impact sounds that match the real world. Moreover, we demonstrate the usefulness of our dataset as a testbed for acoustic and audio-visual learning via the evaluation of two benchmark tasks, including listener location classification and visual acoustic matching." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.616, + 0.21, + 0.631 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Object sounds permeate our everyday natural environments as we both actively interact with them and passively perceive events in our environment. The sound of a drinking glass bouncing on the floor assuages our fear that the glass would shatter. The click made by a knife making contact with a cutting board assures us that we have diced cleanly through a vegetable. And listening to the sound a painted mug makes when we tap it informs us of whether it is made of ceramic or metal. What we perceive from sound complements what we perceive from vision by reinforcing, disambiguating, or augmenting it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Understanding the cause-and-effect relationships in these sounds at a fine-grained level can inform us about an object's material properties and geometry, as well as its contact and other environmental conditions. Capturing" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.271, + 0.892, + 0.331 + ], + "angle": 0, + "content": "these relationships from real-world data can help us improve our models toward more realistic physical simulations, with applications in virtual reality, animation, and training learning-based frameworks in simulation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.893, + 0.532 + ], + "angle": 0, + "content": "The sounds we perceive from objects are the result of many intricate physical processes: they encode important properties about the object itself (e.g., geometry, material, mechanical properties), as well as the surrounding environment (e.g., room size, other passive objects present, materials of furniture in the room). More specifically, when a hard object is struck, it vibrates according to its mass and stiffness, and the shape of the object determines the mode shapes of the dominant vibration patterns (\\(\\S 3.1\\)). Acoustic waves are then emitted into the medium, typically air, bouncing around in the room and interacting with surrounding objects and the room itself before reaching our ear or a microphone to be perceived as pressure fluctuations (\\(\\S 3.2\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.895, + 0.701 + ], + "angle": 0, + "content": "Prior work has explored using physical simulation [26, 54] or learning-based methods [28, 29] to reconstruct the sound generation process virtually, as well as building 3D environments with simulated spatial audio for embodied audio-visual learning [7, 15, 18, 35, 42]. However, there has been little work on building physical apparatuses and feasible measurement process to quantify sounds made by the everyday objects, despite their importance and intimate relationship with our daily lives. As a result, the evaluations of the methods above are largely established on subjective metrics such as user studies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To address this gap, we introduce REALIMPACT, a dataset containing 150k recordings of 50 everyday objects, each being struck from 5 distinct impact positions. For each impact point, we capture sounds at 600 field points to provide comprehensive coverage of the frequency components of the sounds and how they are distributed spatially. REALIMPACT thus provides all the inputs most current simulation frameworks needed to simulate each sound, while also providing the ground truth recording for comparison. We show that REALIMPACT can be used for various downstream auditory and audio-visual learning tasks, such as listener location classification (§5.2) and visual acoustic matching (§5.3). These results demonstrate that sound" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*The project page and dataset are available at https://samuelpclarke.com/realimpact/" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1516" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.152 + ], + "angle": 0, + "content": "fields can help improve machine perception and understanding of the world, and motivate further studies of even more accurate simulation methodologies to reduce the sim-to-real gap for future applications." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.153, + 0.468, + 0.287 + ], + "angle": 0, + "content": "We make three contributions. First, we design an automated setup for collecting high-fidelity, annotated recordings of sounds by controlled striking of everyday objects. Second, using this setup, we acquire a large dataset of spatialized object sounds, REALIMPACT. Third, we motivate the utility of REALIMPACT by (a) using it to perform comparisons to results generated by current state-of-the-art sound simulation frameworks and (b) evaluating two benchmark tasks for acoustic and audio-visual learning." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.302, + 0.218, + 0.318 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.322, + 0.468, + 0.579 + ], + "angle": 0, + "content": "Datasets of Object Sounds. Many datasets of object sounds have been introduced, each varying in the details of their collection, based on the applications they target. The Greatest Hits Dataset [40] includes audio-video recordings of thousands of impacts between real objects from the wild. The recordings were not taken in a controlled environment, and each impact is induced by a human with a drumstick, polluting each object's impact sound with the sound of the rather resonant drumstick. The Sound-20K Dataset [59] is a fully synthetic dataset of 20,000 simulated recordings of objects being dropped in virtual environments. More recently, ObjectFolder [17,21] is introduced as a large dataset of trained implicit models for generating the sounds objects make when impacted at arbitrary locations. However, these are once again trained only on data from simulation, and they do not model the acoustic transfer properties of the objects, only their structural vibratory response." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.584, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Physics-based Sound Rendering. Realistic sound rendering has been a long-held goal in computer music, interactive virtual environments, and computer animation [27, 34, 51, 55]. By modeling the underlying physical processes of vibrations, the computer graphics community demonstrated convincing synthesized sounds for vibrating solids [26, 31, 38, 39], shells [5], rods [47], and even fluids [32, 55]. [26, 55] further showed that it is important for high-quality sound rendering to capture the amplitude and spatial structure of radiating sound fields. However, computing these acoustic transfer fields is time-consuming as they are typically solved in the frequency domain, one frequency at a time. In KLEINPAT [54], the authors showed that by conflating multiple vibrating modes into one time-domain solve, getting all-frequency transfer maps can be done much faster, usually on the order of minutes. These models require careful simulation and material parameters tuning for the best results. To alleviate this issue, several works proposed to sample audio clips [45] and impulse responses [53] to reconstruct the material definitions. Recently, a few works [28, 29] have explored using learning to" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.891, + 0.151 + ], + "angle": 0, + "content": "approximate both the vibration and transfer computations using simulated training data. We provide timely real data that such simulations could use to validate their outputs and tune their performances." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.156, + 0.891, + 0.262 + ], + "angle": 0, + "content": "Recording Sounds Made by Real Objects. Whereas many learning-based frameworks have traditionally used simulation results as their \"ground truth\" for learning acoustic models of object vibrations and their transfer, some works have proposed to fit acoustic object models directly from data using digital signal processing with more relaxed model assumptions about rigid body vibrations." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.262, + 0.891, + 0.533 + ], + "angle": 0, + "content": "Pai et al. [41] describe a framework for scanning physical objects across multiple modalities, measuring visual, tactile, and audio properties of some everyday objects. They fit a data-driven acoustic model based on modal vibration for an object by striking it at different points and recording the ensuing sound from a single position per impact point, assuming constant acoustic transfer across the object. DiffImpact [12] similarly fits modal models to real recordings of objects, but assumes a constant modal response and transfer across the object since their data lacked annotations of the impact point and microphone location. Perhaps most similar to our work, Corbett et al. [13] collect recordings of striking an object at three different impact points, positioning a microphone at 19 different positions per impact point. We collect recordings from an order of magnitude more microphone positions to empirically demonstrate that acoustic transfer varies rather drastically over a much finer resolution than can be captured at 19 different locations." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.535, + 0.891, + 0.713 + ], + "angle": 0, + "content": "Also, while these prior works have collected datasets from real audio, none have publicly released their datasets. Furthermore, since many simulation frameworks are designed to simulate audio of objects vibrating freely in an anechoic space, the recordings collected by these works are unsuitable for a fair comparison, since they are recorded with objects in contact conditions like resting on tables or grasped in hands, which greatly hinder free vibrations. In contrast, we propose a novel capture system where objects rest on a thread mesh in an acoustically treated room, which more closely approximates free vibration in an anechoic environment." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.715, + 0.891, + 0.851 + ], + "angle": 0, + "content": "Finally, from outside the domain of object impact sounds, Bellows et al. [4] have an extensive project measuring the sound directivity of musical instruments while being played by musicians. The measurements take place in a large anechoic chamber and are recorded with a rotating semi-circular microphone array resulting in 2,522 unique microphone positions. The raw measurements are not provided, but the directivity patterns are available as spherical harmonic decompositions [3]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Visual Learning of Sounds in Space. Both audio and visual data convey crucial spatial information. Recent inspiring works have explored many interesting tasks connecting" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1517" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.406, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.409, + 0.091, + 0.653, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.091, + 0.892, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.895, + 0.456 + ], + "angle": 0, + "content": "Figure 1. Pipeline for the acquisition of spatialized impact sounds: (Left) The object is placed at the center of the measurement platform and aligned with mesh threads. The impact hammer is positioned to strike a target vertex on the object. (Center) The gantry moves the microphones to 40 different positions within a semi-cylinder of the object, with the automated hammer mechanism striking the object to record the sound at each position. (Right) By the end of the recording process, for each of the 5 vertices of each object, recordings from 600 different microphone positions have been collected within the semi-cylinder to one side of the object, as shown." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.473, + 0.59 + ], + "angle": 0, + "content": "visual learning and sound in 3D space, including visually-guided audio spatialization [20,22,37,57,61], sound source localization in video frames [1,6,48], learning audio-visual spatial correspondence [9, 58], and building audio-visual 3D environments [7, 15] for an array of embodied learning tasks [8, 14, 16, 18, 35, 42]. We show how our dataset can be used to evaluate real-world performance of auditory and audiovisual learning frameworks on two novel tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.364, + 0.625 + ], + "angle": 0, + "content": "3. Physics-Based Sound Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.741 + ], + "angle": 0, + "content": "We begin with some background about physics-based sound simulation for rigid objects to motivate design choices for our dataset and provide context for our baseline simulation frameworks and their parameters. Here we briefly summarize a commonly used sound synthesis pipeline for rigid objects. For a more detailed introduction, we recommend the article from James et al. [27]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.295, + 0.77 + ], + "angle": 0, + "content": "3.1. Modal Sound Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.471, + 0.871 + ], + "angle": 0, + "content": "When a contact force is applied to an object (e.g., your dinner plate hits the dishwasher handle), depending on the location of contact, various vibration modes can get excited and eventually die down due to internal damping. Mathematically, the vibration's displacement vector \\(\\pmb{u}(t)\\) can be low-rank approximated as" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.885, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {u} (t) = U \\boldsymbol {q} (t) = \\left[ \\hat {\\boldsymbol {u}} _ {1} \\dots \\hat {\\boldsymbol {u}} _ {K} \\right] \\boldsymbol {q} (t), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.893, + 0.512 + ], + "angle": 0, + "content": "where \\(U\\) is the modal matrix with mode shapes \\(\\hat{\\pmb{u}}_i\\) and \\(\\pmb {q}(t)\\in \\mathbb{R}^{K}\\) the modal coordinates. The equations of motion are" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.513, + 0.892, + 0.528 + ], + "angle": 0, + "content": "\\[\nM \\ddot {\\boldsymbol {u}} + C \\dot {\\boldsymbol {u}} + K \\boldsymbol {u} = \\boldsymbol {f}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.894, + 0.624 + ], + "angle": 0, + "content": "where \\(M\\), \\(C\\), and \\(K\\) are the mass, damping, and stiffness matrix, respectively*, and \\(\\pmb{f}\\) is the external force vector. It is typically assumed in the literature that the damping can be approximated by Rayleigh damping, \\(C = \\alpha M + \\beta K\\); with this convenient assumption, Eq. (2) can be re-written in the subspace defined by \\(U\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.63, + 0.892, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\ddot {\\boldsymbol {q}} + (\\alpha \\mathbf {I} + \\beta \\Lambda) \\dot {\\boldsymbol {q}} + \\Lambda \\boldsymbol {u} = U ^ {\\intercal} \\boldsymbol {f}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.895, + 0.82 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}\\) is the identity matrix and \\(\\Lambda = \\mathrm{diag}(\\omega_1^2,\\dots,\\omega_K^2)\\) is a diagonal matrix of involving angular frequencies \\(\\omega_{i}\\). Since the damping can significantly affect material perception [30], the Rayleigh damping can potentially model real-world objects poorly. In addition, there are two scalar properties \\(\\alpha\\) and \\(\\beta\\) to fit, and in previous work, these are typically hand-picked to produce sounds that are closest to a given material. Also note that this formulation is based on linear modal analysis [49,50], which assumes the vibrations are infinitesimal, or, in other words, the object is approximately rigid." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.827, + 0.673, + 0.843 + ], + "angle": 0, + "content": "3.2. Acoustic Transfer" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.85, + 0.893, + 0.881 + ], + "angle": 0, + "content": "Sound radiates from an object's surface into the surrounding medium as pressure waves. Since the modes de" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.887, + 0.874, + 0.902 + ], + "angle": 0, + "content": "*Formulas of how to compute these matrices can be found in [39]." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1518" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.381 + ], + "angle": 0, + "content": "cay slowly over time, it is convenient to work in the frequency domain [26]. The distribution of the wave magnitudes in space, \\(\\hat{p} (x;\\omega)\\), is referred to in the literature [26] as the acoustic transfer function. With a given set of vibrational boundary conditions, such as those given by Eq. (3), one can solve the frequency-domain Helmholtz equation [5,26,31] using boundary element methods [2, 11, 23] or a time-domain wave equation before reconstructing the acoustic transfer fields [54]. To display the acoustic transfer fields at runtime, we may compress the representation using multi-point dipole sources [26] or single-point multipole sources [60]. Another increasingly popular way of storing and displaying the field is to leverage the radial structure (or lack thereof) in the far-field radiation to store Far-field Acoustic Transfer (FFAT) maps, which are rectangular, image-like textures that capture the angular radiation pattern of a given object. FFAT maps can be quickly reparametrized (e.g., equalized, time-delayed) at runtime to display object impact sounds with user interactions [54]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.391, + 0.328, + 0.408 + ], + "angle": 0, + "content": "4. The REALIMPACT Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.538 + ], + "angle": 0, + "content": "We introduce REALIMPACT, a dataset of 150,000 real object impact sounds. Along with these sounds, we record the force profiles from the impact hammer we used to strike the objects, as well as an RGBD image of the object from each azimuth angle and radial distance from which the audio recording is measured. Below, we introduce the hardware setup for collecting the data, the objects we use, and our data collection pipeline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.546, + 0.242, + 0.563 + ], + "angle": 0, + "content": "4.1. Hardware Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We collect all recordings in an acoustically treated room (see Appendix B for additional details). We designed a cylindrical gantry system for moving the microphones to precise positions in space, shown in Figure 1. The gantry system moves a 1.82-meter-tall vertical column of 15 Dayton Audio EMM6 calibrated measurement microphones which are evenly and precisely spaced along the column. It moves this column precisely in two degrees of freedom: azimuth and distance, with a precision of \\(1^{\\circ}\\) and \\(1\\mathrm{mm}\\), respectively. We suspended a mesh of polyester threads precisely at the axis of rotation of this gantry, centering it vertically along the column of 15 microphones. This mesh holds the objects in place while minimizing contact damping and maximizing the acoustic transparency of the surface holding the object. Furthermore, the layout of the mesh provides visual guidance for precisely positioning the objects in a repeatable manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To measure the acoustic transfer from the object to the microphones, the impact force needs to be recorded, allowing an input-output relation to be found. We used a PCB 086E80 impact hammer to strike each object. The impact hammer is incorporated into a custom automated striking" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.892, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.313, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Figure 2. The real objects used in our dataset. Objects are clustered by material: (from top left) wood, ceramic, glass, plastic, (from bottom center) iron, steel, and polycarbonate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.521 + ], + "angle": 0, + "content": "mechanism, which strikes objects precisely and repeatedly while being as silent as possible. The mechanism uses a motor to wind the hammer back to contact an electromagnet; then, upon recording, the electromagnet releases the hammer. Actuating the electromagnet is completely silent, so the noise created by this mechanism is minimal during each strike. This mechanism is mounted on a microphone stand to be able to position it rigidly to strike objects at arbitrary locations. See Appendix C and D for additional details on the recording apparatus and hammer impacts, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.717 + ], + "angle": 0, + "content": "The impact hammer has a calibrated force transducer in its tip, measuring contact forces at the same temporal resolution as our audio. The impact hammer and microphones are all read in a time-synchronized fashion by using two Motu 8M audio interfaces connected by an optical cable. Each audio interface has digitally-controlled amplifier gains, which must be tuned up or down for object sounds that are relatively quiet or loud, respectively, to boost the signal as much as possible while also preventing clipping. Because these gains are digitally controlled, we can record and adjust them in a precise and repeatable manner throughout our experiments. The recordings were made at a sample rate of \\(48000\\mathrm{Hz}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.763 + ], + "angle": 0, + "content": "We also attach a RealSense D415 RGBD camera to the column, aligned with the first microphone above mesh-level, to take RGBD images with our audio measurements." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.597, + 0.789 + ], + "angle": 0, + "content": "4.2. Objects" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We purchase 50 objects from the ObjectFolder dataset [19], which is comprised of commonly used household objects like a ceramic mug, drinking cup, plastic bin, and wood vase. Each object in REALIMPACT has a high-resolution 3D mesh model generated from a scan of the real object [21], which can be used in simulation frameworks. We select objects which are rigid and consist of a single ho" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1519" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.089, + 0.454, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.372 + ], + "angle": 0, + "content": "Figure 3. An RGBD image and audio recordings from all 15 microphones are collected at each gantry position for each vertex we impact on an object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.49 + ], + "angle": 0, + "content": "mogeneous material belonging to one of the following categories: ceramic, glass, wood, plastic, iron, polycarbonate, and steel—materials that have \\(\\alpha\\) and \\(\\beta\\) parameters available and widely used in the physics-based sound rendering literature [28, 29, 54]. Figure 2 shows all objects used for data collection. These objects all have a scale and mass suitable for data collection using our hardware setup." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.3, + 0.515 + ], + "angle": 0, + "content": "4.3. Data Collection Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.471, + 0.839 + ], + "angle": 0, + "content": "For each object, we first place the object on the supporting mesh, matching the features of the mesh to the distinctive geometric features of the object to position it in a repeatable manner. We then select 5 vertices from the virtual mesh at which to strike the object. For each vertex, we first position the hammer mechanism to strike the vertex. Since our gantry collects recordings on a semi-cylinder to one side of the object, we position the hammer mechanism to the opposite side of the semi-cylinder both to not impinge the motion of the gantry and to minimize blocking acoustic radiation from the surface of the object toward the microphones. For each vertex, we move the gantry to 40 positions: a grid of 10 angles in 20-degree increments from 0 through 180, at 4 distances of 0.23, 0.56, 0.90, and 1.23 meters from the center of the mesh. We take an RGBD image at each position in addition to the audio recordings. A diagram of the microphone positions relative to an example object is shown in Figure 1. An example of each of the modalities captured from one position is shown in Figure 3. See the Supplementary Materials for an example video of how an object is recorded." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.196, + 0.864 + ], + "angle": 0, + "content": "4.4. Processing" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The impact hammer strikes are not necessarily constant across measurements, but the discrepancy can be corrected" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.885, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.249, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Figure 4. Comparing different azimuth resolutions for mode shape transfer maps of a ceramic bowl, measured at \\(23~\\mathrm{cm}\\) from the center. The top row shows maps measured at a resolution of 1 degree, while the bottom row shows those measured at a resolution of 20 degrees." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.892, + 0.488 + ], + "angle": 0, + "content": "since the force is measured. This is achieved by deconvolving the force signal from the microphone signal with frequency domain division as \\( m_{c} = \\mathcal{F}^{-1}\\left(\\mathcal{F}(m) / \\mathcal{F}(i)\\right) \\), where \\( i \\) is the impact hammer signal, \\( m \\) is the microphone signal, and \\( m_{c} \\) is the corrected microphone signal. \\( \\mathcal{F} \\) and \\( \\mathcal{F}^{-1} \\) are the forward and inverse discrete Fourier transforms, respectively. The hammer signal is windowed such that only the samples within 1% of the force peak are kept, and all other samples are deemed noise and set as zero, reducing noise in the corrected microphone signal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.893, + 0.686 + ], + "angle": 0, + "content": "To create transfer maps of the recordings, mode fitting is performed on each corrected microphone signal. The modes are fit using the method of [10]. First, the vibrational frequencies are fit with a simple peak-picking algorithm performed on \\(\\mathcal{F}(m_c)\\). Decay rates are fit by band-passing \\(m_{c}\\) at the mode frequencies, applying a Root-Mean-Squared level detector, and using linear regression to estimate the slope of the energy envelope. The amplitudes are set as the magnitude of the mode frequency peak in \\(\\mathcal{F}(m_c)\\). Transfer maps are then formed for each vibrational frequency by displaying the magnitude at each measurement location with respect to rotation and height, as shown in Figures 4 and 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.7, + 0.617, + 0.714 + ], + "angle": 0, + "content": "4.5. Validation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Spatial Sampling. We use a \\(20^{\\circ}\\) resolution of azimuth angle for the spatial sampling as a compromise to reduce measurement time while still adding benefit for certain sound-related tasks. We take one set of measurements with \\(1^{\\circ}\\) rotations on one of our objects (a ceramic bowl) as a comparison. Figure 4 shows measured acoustic transfer maps for sample vibrational frequencies with both \\(1^{\\circ}\\) and \\(20^{\\circ}\\) microphone rotations. The lowest-frequency mode shape varies gradually with the azimuth angle. But note that at the highest-frequency mode shape shown, the frequency of the repeating spatial pattern is beyond the Nyquist frequency of our azimuth sampling resolution. We show the implica" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1520" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.464, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.299 + ], + "angle": 0, + "content": "Figure 5. Measuring repeatability of our measurements by visualizing transfer maps of vibrational frequencies of the ceramic bowl, measured at \\(23~\\mathrm{cm}\\) from the center. The top row shows the mean of 10 trials of measurements, while the bottom shows the relative standard deviation of the 10 trials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.468, + 0.344 + ], + "angle": 0, + "content": "tions of attempting to naively interpolate from these low-resolution transfer maps in Appendix E." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.468, + 0.569 + ], + "angle": 0, + "content": "Repeatability. We verify two aspects of the repeatability of our design: the repeatability of the gantry's position and the repeatability of our resulting audio measurements. While our gantry is capable of achieving high angular precision while it is controlled, we completely power it off during each recording, in order to eliminate motor and power supply noises from our recordings. During these periods, the wheels may settle into the carpet at a slightly different angle than we have commanded. We perform four trials of moving to the commanded angles and find that the maximum angular error across all trials did not exceed \\(1^{\\circ}\\), with the mean error being \\(0.26^{\\circ}\\). This translates to a maximum error of \\(2\\mathrm{cm}\\) in Cartesian space, only reached when the gantry is at its farthest distance from the center." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.468, + 0.766 + ], + "angle": 0, + "content": "For the repeatability of our measurements, we conduct 10 trials of our measurements on the same ceramic bowl, striking the same target vertex and using the sample positions we used throughout our dataset. We show the mean and standard deviations of the transfers we measured at some sample vibrational frequencies in Figure 5, with results of objects of additional materials in Appendix F. Our results suggest that variations may be highest at the boundaries of nodes in the transfer map. At these locations, minor errors in the azimuth angle could cause significant changes in transfer measurement. Furthermore, at these positions, the signal is lower at this frequency, so the effects of noise can be more pronounced." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.782, + 0.208, + 0.799 + ], + "angle": 0, + "content": "5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.807, + 0.468, + 0.838 + ], + "angle": 0, + "content": "In this section, we demonstrate some use cases of REALIMPACT with practical, multimodal applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.468, + 0.864 + ], + "angle": 0, + "content": "5.1. Comparing Simulated and Real Impact Sounds" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our first task is to compare sounds synthesized by existing sound rendering methods to the recordings of RE-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "ALIMPACT in order to demonstrate typical measurement and modeling discrepancies. For this purpose, we ran each baseline method out-of-the-box without any attempt to fine-tune its model and/or hyperparameters, including material parameters, such as elastic stiffness (Young's modulus) and damping (e.g., \\(\\alpha\\) and \\(\\beta\\) in the case of KLEINPAT). We also did not unify the finite element analysis representations across different methods, including finite element type (KLEINPAT uses first-order tetrahedral elements, whereas ObjectFolder 2.0 uses second-order ones), and tetrahedral meshes. These out-of-the-box comparisons simplify the analysis and highlight the ability to benchmark any existing or new simulation methods given a dataset such as REALIMPACT, but exhibit various modeling oversights. We leave the work to narrow the gap between each baseline to the dataset as future work. We provide more conjectures on why these discrepancies exist in the limitations section." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.892, + 0.406 + ], + "angle": 0, + "content": "Baselines. We provide high-level descriptions of each baseline and refer the readers to Appendix G or directly to the linked work for more details:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.413, + 0.891, + 0.458 + ], + "angle": 0, + "content": "- WHITE NOISE: Random noise which has been adjusted to the same loudness as the average loudness of the recordings on a per-object basis." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.462, + 0.891, + 0.491 + ], + "angle": 0, + "content": "- RANDOM IMPACT SOUND: A random impact sound recording from our dataset." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.496, + 0.891, + 0.556 + ], + "angle": 0, + "content": "- KLEINPAT [54]: The modal analysis is run using first-order tetrahedral elements, and the Far-field Acoustic Transfer (FFAT) maps are done using a one-term \\((1 / r)\\) scalar expansion." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.56, + 0.891, + 0.65 + ], + "angle": 0, + "content": "- NEURALSOUND [29]: The modal analysis is run using an optimization which is warm-started with the outputs of a 3D sparse U-net on voxelized meshes. The FFAT maps are predicted directly by a ResNet-like encoder-decoder structure. For both steps, we use the pretrained weights." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.655, + 0.891, + 0.729 + ], + "angle": 0, + "content": "- OBJECTFOLDER 2.0 [21]: The modal analysis is predicted by an implicit neural representation trained on simulation data using second-order tetrahedral elements. No acoustic transfer values exist in this baseline so we used \\(\\hat{p}(\\boldsymbol{x};\\omega) = 1\\) throughout." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.413, + 0.891, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.892, + 0.796 + ], + "angle": 0, + "content": "Note that the final three baselines all require material properties of the object as input; we uniformly apply the same parameters from Table 4 of [54] for all objects with the same material label in our dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Metrics. We evaluate using the following metrics: 1) L1 spectral loss, a loss based on taking the average L1 distance between log-magnitude spectrograms of different window sizes (used for impact sounds in [12]); 2) envelope distance, which measures the distance between two audio samples' envelopes over time (used for spatial audio in [37]); and" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1521" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.887, + 0.219 + ], + "angle": 0, + "content": "
REALIMPACT DeconvolvedREALIMPACT Deconvolved + Denoised
L1 SpectralEnvelope (×10-3)CDPAML1 SpectralEnvelope (×10-3)CDPAM
WHITE NOISE4.689.541.385.229.871.39
RANDOM IMPACT SOUND0.7284.170.1210.1504.970.0880
KLEINPAT [54]0.6324.630.1170.09824.630.0975
NEURAL SOUND [29]0.67323.00.1020.13322.80.0750
OBJECT FOLDER 2.0 [21]0.74725.60.2970.23625.40.289
" + }, + { + "type": "table_caption", + "bbox": [ + 0.221, + 0.222, + 0.747, + 0.235 + ], + "angle": 0, + "content": "Table 1. Comparing with simulated object impact sounds. Lower is better for all metrics." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.248, + 0.891, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.45, + 0.893, + 0.494 + ], + "angle": 0, + "content": "Figure 6. Comparison of spectrograms from our collected recordings versus simulation frameworks. Each spectrogram represents the sound recorded or simulated from a sample point at (8, 22, 13) cm in Cartesian space from the center of the base of the object, and each row corresponds to striking the same vertex on the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.553 + ], + "angle": 0, + "content": "3) CDPAM [36], a learning-based perceptual distance metric trained from human judgments of detectable differences between clips." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.689 + ], + "angle": 0, + "content": "To mitigate the effects of measurement noise in our evaluation, we compare each baseline both to our deconvolved recordings and to denoised versions of our recordings, which have been denoised with the algorithm of [46]. Whereas many denoising algorithms are optimized for human speech, this algorithm has been optimized and validated against broader categories of audio signals from nature. Comparisons of example spectrograms and their denoised counterparts are shown in Appendix H." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Quantitative results are shown in Table 1, and qualitative examples are shown in Fig. 6, comparing our recordings of real impact sounds with the simulated sounds using methods from [21, 29, 54]. The KLEINPAT baseline performs best according to a spectral loss, whereas NEURAL-SOUND performs best according to the perceptual CDPAM loss. Both of these baselines significantly outperform ObjectFolder, suggesting that explicitly modeling the acoustic transfer of objects rather than merely their structural vibrations is essential for achieving realism. A random impact sound only outperforms baselines in Envelope Loss when the recording has not been denoised. Each baseline other than white noise performs better on all metrics when compared against denoised versions of our recordings, suggest-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.551 + ], + "angle": 0, + "content": "ing that our raw recordings have non-negligible measurement noise, which must be accounted for in future comparisons." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.782, + 0.575 + ], + "angle": 0, + "content": "5.2. Listener Location Classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Identifying the location of the listener with respect to the sound source is of great practical interest to many applications in virtual reality and robotics [8, 43, 44]. In this task, we want to identify the microphone position (angle, height, or distance) from the impact sound recording." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.719 + ], + "angle": 0, + "content": "For each impact in REALIMPACT, we have the recordings of the impact sound from 600 different listener locations collected from 10 different angles, 15 different heights, and 4 different distances, as illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Particularly, we set up three separate classification subtasks: 1) angle classification, where the goal is to classify the sound into the 10 angle categories \\((0^{\\circ}, 20^{\\circ}, \\dots, 180^{\\circ})\\); 2) height classification, where the goal is to classify the sound into the 15 height categories, each corresponding to the height of our 15 microphones; and 3) distance classification, where the goal is to classify the sound into the 4 distance categories \\((0.23 \\mathrm{~m}, 0.56 \\mathrm{~m}, 0.90 \\mathrm{~m}\\), and \\(1.23 \\mathrm{~m})\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For each subtask, we split 90/10 percent of impact sound recordings of an object into the train/test set, respectively. We train a ResNet-18 [24] network that takes the magnitude spectrogram of the impact sound as input to predict the an" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1522" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.131, + 0.089, + 0.416, + 0.151 + ], + "angle": 0, + "content": "
AngleHeightDistance
CHANCE10.06.725.0
Ours57.960.767.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.155, + 0.47, + 0.198 + ], + "angle": 0, + "content": "Table 2. Listener location classification results. We report the accuracy (in %) for angle, height, and distance classification, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.211, + 0.47, + 0.287 + ], + "angle": 0, + "content": "gle, height, or distance category. Table 2 shows the results averaged across all 50 objects. We observe that predicting height is comparatively easier. We suspect that differences in height strongly influence the spectral details for easier classification." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.295, + 0.312, + 0.312 + ], + "angle": 0, + "content": "5.3. Visual Acoustic Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.468, + 0.409 + ], + "angle": 0, + "content": "The ability to match a source sound with the correct corresponding visual input plays an important role in tasks such as speech and speaker recognition [33, 52] or object and event localization [25, 56]. This task aims to match a sound recording with the correct corresponding image. We set up this matching task as binary classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.468, + 0.605 + ], + "angle": 0, + "content": "For 20 of our objects, we have a total of 200 RGBD images taken simultaneously with our audio recordings, which are collected at a fixed height from the 10 different angles and 4 different distances from which we took audio recordings for each of the 5 different vertices. We generate positive pairs by pairing each sound recording to an image taken at the corresponding angle and vertex. The height and distance of the image are fixed, so there are 50 possible images that the sound recordings correspond to. The distance of the paired RGBD image is selected such that the image captures the position of both the object and the impact hammer. Negative pairs are generated by pairing sound recordings with images that are not at the correct angle and vertex." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.468, + 0.788 + ], + "angle": 0, + "content": "We randomly select two heights to be held out for validation and test sets, while the remaining 13 heights are used for the train set. We train an audio-visual network with a ResNet-18 backbone for both the image and audio streams. The network takes in an RGB image as visual input and an impact sound recording as audio input. A fusion layer combines the audio and visual information, and a final fully-connected layer is used to extract audio-visual features for binary classification. Table 3 shows the quantitative results of the visual acoustic matching task averaged across 20 objects, and we show example inputs and outputs in Appendix I." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.334, + 0.816 + ], + "angle": 0, + "content": "6. Limitations and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We presented REALIMPACT, a first-of-its-kind, large dataset of 150k real impact sounds systematically collected in an acoustically treated room, and demonstrated its several use cases on benchmarking existing simulation algorithms and applications on several auditory and audiovisual tasks." + }, + { + "type": "table", + "bbox": [ + 0.568, + 0.089, + 0.822, + 0.151 + ], + "angle": 0, + "content": "
Accuracy ↑RMSE ↓
CHANCE50.059.7
Ours75.147.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.155, + 0.892, + 0.225 + ], + "angle": 0, + "content": "Table 3. Quantitative results of visual acoustic matching. We report the accuracy results (in %). RMSE angle error (in degrees) is the root-mean-square error in the difference between the angles of the image and sound recording. \\(\\uparrow\\) or \\(\\downarrow\\) signify higher or lower values are better, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.242, + 0.892, + 0.483 + ], + "angle": 0, + "content": "The microphone array stack used in our measurement process is somewhat coarse to capture high-frequency details (e.g., the \\(12\\mathrm{cm}\\) microphone spacing in elevation roughly corresponds to the wavelength of \\(3\\mathrm{kHz}\\)). The angular resolution is chosen at only 20 degrees and can result in aliasing and distortion in the otherwise symmetric radiation fields, as shown in \\(\\S 4.5\\). The diversity of the recorded objects is restricted by the size and load capacity of our supporting thread mesh, and the microphone stack arm. The material descriptions of the objects are artificially lumped into the categories defined in previous work [54], but they may not describe the diversity of real-world materials (e.g., different kinds of steels will have different mechanical properties that might affect stiffness and thus the frequency distributions). Future work should look at more efficient ways of capture and sample a wider range of objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.801 + ], + "angle": 0, + "content": "The comparison of real impact sounds to those generated by current simulation methods exhibit various discrepancies. Many things can lead to the gap between simulations and real recordings: object scanning resolution and reconstruction accuracy, material stiffness and damping parameters, finite-element analysis differences (e.g., element type), and insufficient meshing resolution. Also we did not explicitly model hollow objects in the comparisons despite some of our objects being hollow and/or thin, and contact damping models are missing, which can affect the perceived damping rates and thus the envelope accuracy. As a result, many of the out-of-the-box simulation models' vibrational frequencies do not agree, let alone their estimates of spatialized sound amplitudes, etc. Many of these oversights will affect the comparison \"fairness\" but it also demonstrates a significant benefit of the REALIMPACT dataset: for the first time, we can measure these models using the same yard stick. We hope that this dataset provides future incentives to improve not just the simulation methods and their usage, but also the capture process and datasets that can move the field forward in a significant way." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. This work is in part supported by Adobe, NSF CCRI #2120095, NSF RI #2211258, ONR MURI N00014-22-1-2740, AFOSR YIP FA9550-23-1-0127, the Stanford Institute for Human-Centered AI (HAI), Amazon, and Meta." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1523" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. 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James1 + +Mark Rau1 +Jiajun Wu1 + +# Abstract + +Objects make unique sounds under different perturbations, environment conditions, and poses relative to the listener. While prior works have modeled impact sounds and sound propagation in simulation, we lack a standard dataset of impact sound fields of real objects for audio-visual learning and calibration of the sim-to-real gap. We present REALIMPACT, a large-scale dataset of real object impact sounds recorded under controlled conditions. REALIMPACT contains 150,000 recordings of impact sounds of 50 everyday objects with detailed annotations, including their impact locations, microphone locations, contact force profiles, material labels, and RGBD images.* We make preliminary attempts to use our dataset as a reference to current simulation methods for estimating object impact sounds that match the real world. Moreover, we demonstrate the usefulness of our dataset as a testbed for acoustic and audio-visual learning via the evaluation of two benchmark tasks, including listener location classification and visual acoustic matching. + +# 1. Introduction + +Object sounds permeate our everyday natural environments as we both actively interact with them and passively perceive events in our environment. The sound of a drinking glass bouncing on the floor assuages our fear that the glass would shatter. The click made by a knife making contact with a cutting board assures us that we have diced cleanly through a vegetable. And listening to the sound a painted mug makes when we tap it informs us of whether it is made of ceramic or metal. What we perceive from sound complements what we perceive from vision by reinforcing, disambiguating, or augmenting it. + +Understanding the cause-and-effect relationships in these sounds at a fine-grained level can inform us about an object's material properties and geometry, as well as its contact and other environmental conditions. Capturing + +these relationships from real-world data can help us improve our models toward more realistic physical simulations, with applications in virtual reality, animation, and training learning-based frameworks in simulation. + +The sounds we perceive from objects are the result of many intricate physical processes: they encode important properties about the object itself (e.g., geometry, material, mechanical properties), as well as the surrounding environment (e.g., room size, other passive objects present, materials of furniture in the room). More specifically, when a hard object is struck, it vibrates according to its mass and stiffness, and the shape of the object determines the mode shapes of the dominant vibration patterns ( $\S 3.1$ ). Acoustic waves are then emitted into the medium, typically air, bouncing around in the room and interacting with surrounding objects and the room itself before reaching our ear or a microphone to be perceived as pressure fluctuations ( $\S 3.2$ ). + +Prior work has explored using physical simulation [26, 54] or learning-based methods [28, 29] to reconstruct the sound generation process virtually, as well as building 3D environments with simulated spatial audio for embodied audio-visual learning [7, 15, 18, 35, 42]. However, there has been little work on building physical apparatuses and feasible measurement process to quantify sounds made by the everyday objects, despite their importance and intimate relationship with our daily lives. As a result, the evaluations of the methods above are largely established on subjective metrics such as user studies. + +To address this gap, we introduce REALIMPACT, a dataset containing 150k recordings of 50 everyday objects, each being struck from 5 distinct impact positions. For each impact point, we capture sounds at 600 field points to provide comprehensive coverage of the frequency components of the sounds and how they are distributed spatially. REALIMPACT thus provides all the inputs most current simulation frameworks needed to simulate each sound, while also providing the ground truth recording for comparison. We show that REALIMPACT can be used for various downstream auditory and audio-visual learning tasks, such as listener location classification (§5.2) and visual acoustic matching (§5.3). These results demonstrate that sound + +fields can help improve machine perception and understanding of the world, and motivate further studies of even more accurate simulation methodologies to reduce the sim-to-real gap for future applications. + +We make three contributions. First, we design an automated setup for collecting high-fidelity, annotated recordings of sounds by controlled striking of everyday objects. Second, using this setup, we acquire a large dataset of spatialized object sounds, REALIMPACT. Third, we motivate the utility of REALIMPACT by (a) using it to perform comparisons to results generated by current state-of-the-art sound simulation frameworks and (b) evaluating two benchmark tasks for acoustic and audio-visual learning. + +# 2. Related Work + +Datasets of Object Sounds. Many datasets of object sounds have been introduced, each varying in the details of their collection, based on the applications they target. The Greatest Hits Dataset [40] includes audio-video recordings of thousands of impacts between real objects from the wild. The recordings were not taken in a controlled environment, and each impact is induced by a human with a drumstick, polluting each object's impact sound with the sound of the rather resonant drumstick. The Sound-20K Dataset [59] is a fully synthetic dataset of 20,000 simulated recordings of objects being dropped in virtual environments. More recently, ObjectFolder [17,21] is introduced as a large dataset of trained implicit models for generating the sounds objects make when impacted at arbitrary locations. However, these are once again trained only on data from simulation, and they do not model the acoustic transfer properties of the objects, only their structural vibratory response. + +Physics-based Sound Rendering. Realistic sound rendering has been a long-held goal in computer music, interactive virtual environments, and computer animation [27, 34, 51, 55]. By modeling the underlying physical processes of vibrations, the computer graphics community demonstrated convincing synthesized sounds for vibrating solids [26, 31, 38, 39], shells [5], rods [47], and even fluids [32, 55]. [26, 55] further showed that it is important for high-quality sound rendering to capture the amplitude and spatial structure of radiating sound fields. However, computing these acoustic transfer fields is time-consuming as they are typically solved in the frequency domain, one frequency at a time. In KLEINPAT [54], the authors showed that by conflating multiple vibrating modes into one time-domain solve, getting all-frequency transfer maps can be done much faster, usually on the order of minutes. These models require careful simulation and material parameters tuning for the best results. To alleviate this issue, several works proposed to sample audio clips [45] and impulse responses [53] to reconstruct the material definitions. Recently, a few works [28, 29] have explored using learning to + +approximate both the vibration and transfer computations using simulated training data. We provide timely real data that such simulations could use to validate their outputs and tune their performances. + +Recording Sounds Made by Real Objects. Whereas many learning-based frameworks have traditionally used simulation results as their "ground truth" for learning acoustic models of object vibrations and their transfer, some works have proposed to fit acoustic object models directly from data using digital signal processing with more relaxed model assumptions about rigid body vibrations. + +Pai et al. [41] describe a framework for scanning physical objects across multiple modalities, measuring visual, tactile, and audio properties of some everyday objects. They fit a data-driven acoustic model based on modal vibration for an object by striking it at different points and recording the ensuing sound from a single position per impact point, assuming constant acoustic transfer across the object. DiffImpact [12] similarly fits modal models to real recordings of objects, but assumes a constant modal response and transfer across the object since their data lacked annotations of the impact point and microphone location. Perhaps most similar to our work, Corbett et al. [13] collect recordings of striking an object at three different impact points, positioning a microphone at 19 different positions per impact point. We collect recordings from an order of magnitude more microphone positions to empirically demonstrate that acoustic transfer varies rather drastically over a much finer resolution than can be captured at 19 different locations. + +Also, while these prior works have collected datasets from real audio, none have publicly released their datasets. Furthermore, since many simulation frameworks are designed to simulate audio of objects vibrating freely in an anechoic space, the recordings collected by these works are unsuitable for a fair comparison, since they are recorded with objects in contact conditions like resting on tables or grasped in hands, which greatly hinder free vibrations. In contrast, we propose a novel capture system where objects rest on a thread mesh in an acoustically treated room, which more closely approximates free vibration in an anechoic environment. + +Finally, from outside the domain of object impact sounds, Bellows et al. [4] have an extensive project measuring the sound directivity of musical instruments while being played by musicians. The measurements take place in a large anechoic chamber and are recorded with a rotating semi-circular microphone array resulting in 2,522 unique microphone positions. The raw measurements are not provided, but the directivity patterns are available as spherical harmonic decompositions [3]. + +Visual Learning of Sounds in Space. Both audio and visual data convey crucial spatial information. Recent inspiring works have explored many interesting tasks connecting + +![](images/c7a3f27ed18d67c51f5be931de184088fe12eb884858e3b6c9eb34358419821a.jpg) +Figure 1. Pipeline for the acquisition of spatialized impact sounds: (Left) The object is placed at the center of the measurement platform and aligned with mesh threads. The impact hammer is positioned to strike a target vertex on the object. (Center) The gantry moves the microphones to 40 different positions within a semi-cylinder of the object, with the automated hammer mechanism striking the object to record the sound at each position. (Right) By the end of the recording process, for each of the 5 vertices of each object, recordings from 600 different microphone positions have been collected within the semi-cylinder to one side of the object, as shown. + +![](images/3d27dfe90ca06562f9dc57bb86a2f6c9ed0facee86a41545779ba2cd9e773538.jpg) + +![](images/dd6ce316362c1941b4aed88dcdaf5444bb768ec392b6be3da1eba3c3acf36ab8.jpg) + +visual learning and sound in 3D space, including visually-guided audio spatialization [20,22,37,57,61], sound source localization in video frames [1,6,48], learning audio-visual spatial correspondence [9, 58], and building audio-visual 3D environments [7, 15] for an array of embodied learning tasks [8, 14, 16, 18, 35, 42]. We show how our dataset can be used to evaluate real-world performance of auditory and audiovisual learning frameworks on two novel tasks. + +# 3. Physics-Based Sound Synthesis + +We begin with some background about physics-based sound simulation for rigid objects to motivate design choices for our dataset and provide context for our baseline simulation frameworks and their parameters. Here we briefly summarize a commonly used sound synthesis pipeline for rigid objects. For a more detailed introduction, we recommend the article from James et al. [27]. + +# 3.1. Modal Sound Synthesis + +When a contact force is applied to an object (e.g., your dinner plate hits the dishwasher handle), depending on the location of contact, various vibration modes can get excited and eventually die down due to internal damping. Mathematically, the vibration's displacement vector $\pmb{u}(t)$ can be low-rank approximated as + +$$ +\boldsymbol {u} (t) = U \boldsymbol {q} (t) = \left[ \hat {\boldsymbol {u}} _ {1} \dots \hat {\boldsymbol {u}} _ {K} \right] \boldsymbol {q} (t), \tag {1} +$$ + +where $U$ is the modal matrix with mode shapes $\hat{\pmb{u}}_i$ and $\pmb {q}(t)\in \mathbb{R}^{K}$ the modal coordinates. The equations of motion are + +$$ +M \ddot {\boldsymbol {u}} + C \dot {\boldsymbol {u}} + K \boldsymbol {u} = \boldsymbol {f}, \tag {2} +$$ + +where $M$ , $C$ , and $K$ are the mass, damping, and stiffness matrix, respectively*, and $\pmb{f}$ is the external force vector. It is typically assumed in the literature that the damping can be approximated by Rayleigh damping, $C = \alpha M + \beta K$ ; with this convenient assumption, Eq. (2) can be re-written in the subspace defined by $U$ as + +$$ +\ddot {\boldsymbol {q}} + (\alpha \mathbf {I} + \beta \Lambda) \dot {\boldsymbol {q}} + \Lambda \boldsymbol {u} = U ^ {\intercal} \boldsymbol {f}, \tag {3} +$$ + +where $\mathbf{I}$ is the identity matrix and $\Lambda = \mathrm{diag}(\omega_1^2,\dots,\omega_K^2)$ is a diagonal matrix of involving angular frequencies $\omega_{i}$ . Since the damping can significantly affect material perception [30], the Rayleigh damping can potentially model real-world objects poorly. In addition, there are two scalar properties $\alpha$ and $\beta$ to fit, and in previous work, these are typically hand-picked to produce sounds that are closest to a given material. Also note that this formulation is based on linear modal analysis [49,50], which assumes the vibrations are infinitesimal, or, in other words, the object is approximately rigid. + +# 3.2. Acoustic Transfer + +Sound radiates from an object's surface into the surrounding medium as pressure waves. Since the modes de + +cay slowly over time, it is convenient to work in the frequency domain [26]. The distribution of the wave magnitudes in space, $\hat{p} (x;\omega)$ , is referred to in the literature [26] as the acoustic transfer function. With a given set of vibrational boundary conditions, such as those given by Eq. (3), one can solve the frequency-domain Helmholtz equation [5,26,31] using boundary element methods [2, 11, 23] or a time-domain wave equation before reconstructing the acoustic transfer fields [54]. To display the acoustic transfer fields at runtime, we may compress the representation using multi-point dipole sources [26] or single-point multipole sources [60]. Another increasingly popular way of storing and displaying the field is to leverage the radial structure (or lack thereof) in the far-field radiation to store Far-field Acoustic Transfer (FFAT) maps, which are rectangular, image-like textures that capture the angular radiation pattern of a given object. FFAT maps can be quickly reparametrized (e.g., equalized, time-delayed) at runtime to display object impact sounds with user interactions [54]. + +# 4. The REALIMPACT Dataset + +We introduce REALIMPACT, a dataset of 150,000 real object impact sounds. Along with these sounds, we record the force profiles from the impact hammer we used to strike the objects, as well as an RGBD image of the object from each azimuth angle and radial distance from which the audio recording is measured. Below, we introduce the hardware setup for collecting the data, the objects we use, and our data collection pipeline. + +# 4.1. Hardware Setup + +We collect all recordings in an acoustically treated room (see Appendix B for additional details). We designed a cylindrical gantry system for moving the microphones to precise positions in space, shown in Figure 1. The gantry system moves a 1.82-meter-tall vertical column of 15 Dayton Audio EMM6 calibrated measurement microphones which are evenly and precisely spaced along the column. It moves this column precisely in two degrees of freedom: azimuth and distance, with a precision of $1^{\circ}$ and $1\mathrm{mm}$ , respectively. We suspended a mesh of polyester threads precisely at the axis of rotation of this gantry, centering it vertically along the column of 15 microphones. This mesh holds the objects in place while minimizing contact damping and maximizing the acoustic transparency of the surface holding the object. Furthermore, the layout of the mesh provides visual guidance for precisely positioning the objects in a repeatable manner. + +To measure the acoustic transfer from the object to the microphones, the impact force needs to be recorded, allowing an input-output relation to be found. We used a PCB 086E80 impact hammer to strike each object. The impact hammer is incorporated into a custom automated striking + +![](images/0226a2f28c77d17a852dc420f4b34ccd1571453f58df7354037cdc38b40fdd54.jpg) +Figure 2. The real objects used in our dataset. Objects are clustered by material: (from top left) wood, ceramic, glass, plastic, (from bottom center) iron, steel, and polycarbonate. + +mechanism, which strikes objects precisely and repeatedly while being as silent as possible. The mechanism uses a motor to wind the hammer back to contact an electromagnet; then, upon recording, the electromagnet releases the hammer. Actuating the electromagnet is completely silent, so the noise created by this mechanism is minimal during each strike. This mechanism is mounted on a microphone stand to be able to position it rigidly to strike objects at arbitrary locations. See Appendix C and D for additional details on the recording apparatus and hammer impacts, respectively. + +The impact hammer has a calibrated force transducer in its tip, measuring contact forces at the same temporal resolution as our audio. The impact hammer and microphones are all read in a time-synchronized fashion by using two Motu 8M audio interfaces connected by an optical cable. Each audio interface has digitally-controlled amplifier gains, which must be tuned up or down for object sounds that are relatively quiet or loud, respectively, to boost the signal as much as possible while also preventing clipping. Because these gains are digitally controlled, we can record and adjust them in a precise and repeatable manner throughout our experiments. The recordings were made at a sample rate of $48000\mathrm{Hz}$ . + +We also attach a RealSense D415 RGBD camera to the column, aligned with the first microphone above mesh-level, to take RGBD images with our audio measurements. + +# 4.2. Objects + +We purchase 50 objects from the ObjectFolder dataset [19], which is comprised of commonly used household objects like a ceramic mug, drinking cup, plastic bin, and wood vase. Each object in REALIMPACT has a high-resolution 3D mesh model generated from a scan of the real object [21], which can be used in simulation frameworks. We select objects which are rigid and consist of a single ho + +![](images/6be6931513078ed9bfa715c27d8c412fde871647417790ecc1ee09148f5cb9c7.jpg) +Figure 3. An RGBD image and audio recordings from all 15 microphones are collected at each gantry position for each vertex we impact on an object. + +mogeneous material belonging to one of the following categories: ceramic, glass, wood, plastic, iron, polycarbonate, and steel—materials that have $\alpha$ and $\beta$ parameters available and widely used in the physics-based sound rendering literature [28, 29, 54]. Figure 2 shows all objects used for data collection. These objects all have a scale and mass suitable for data collection using our hardware setup. + +# 4.3. Data Collection Pipeline + +For each object, we first place the object on the supporting mesh, matching the features of the mesh to the distinctive geometric features of the object to position it in a repeatable manner. We then select 5 vertices from the virtual mesh at which to strike the object. For each vertex, we first position the hammer mechanism to strike the vertex. Since our gantry collects recordings on a semi-cylinder to one side of the object, we position the hammer mechanism to the opposite side of the semi-cylinder both to not impinge the motion of the gantry and to minimize blocking acoustic radiation from the surface of the object toward the microphones. For each vertex, we move the gantry to 40 positions: a grid of 10 angles in 20-degree increments from 0 through 180, at 4 distances of 0.23, 0.56, 0.90, and 1.23 meters from the center of the mesh. We take an RGBD image at each position in addition to the audio recordings. A diagram of the microphone positions relative to an example object is shown in Figure 1. An example of each of the modalities captured from one position is shown in Figure 3. See the Supplementary Materials for an example video of how an object is recorded. + +# 4.4. Processing + +The impact hammer strikes are not necessarily constant across measurements, but the discrepancy can be corrected + +![](images/990379c52b812374016f798925e4c28f4f9306cb91bd05551ee36c3ace8e6ee9.jpg) +Figure 4. Comparing different azimuth resolutions for mode shape transfer maps of a ceramic bowl, measured at $23~\mathrm{cm}$ from the center. The top row shows maps measured at a resolution of 1 degree, while the bottom row shows those measured at a resolution of 20 degrees. + +since the force is measured. This is achieved by deconvolving the force signal from the microphone signal with frequency domain division as $m_{c} = \mathcal{F}^{-1}\left(\mathcal{F}(m) / \mathcal{F}(i)\right)$ , where $i$ is the impact hammer signal, $m$ is the microphone signal, and $m_{c}$ is the corrected microphone signal. $\mathcal{F}$ and $\mathcal{F}^{-1}$ are the forward and inverse discrete Fourier transforms, respectively. The hammer signal is windowed such that only the samples within 1% of the force peak are kept, and all other samples are deemed noise and set as zero, reducing noise in the corrected microphone signal. + +To create transfer maps of the recordings, mode fitting is performed on each corrected microphone signal. The modes are fit using the method of [10]. First, the vibrational frequencies are fit with a simple peak-picking algorithm performed on $\mathcal{F}(m_c)$ . Decay rates are fit by band-passing $m_{c}$ at the mode frequencies, applying a Root-Mean-Squared level detector, and using linear regression to estimate the slope of the energy envelope. The amplitudes are set as the magnitude of the mode frequency peak in $\mathcal{F}(m_c)$ . Transfer maps are then formed for each vibrational frequency by displaying the magnitude at each measurement location with respect to rotation and height, as shown in Figures 4 and 5. + +# 4.5. Validation + +Spatial Sampling. We use a $20^{\circ}$ resolution of azimuth angle for the spatial sampling as a compromise to reduce measurement time while still adding benefit for certain sound-related tasks. We take one set of measurements with $1^{\circ}$ rotations on one of our objects (a ceramic bowl) as a comparison. Figure 4 shows measured acoustic transfer maps for sample vibrational frequencies with both $1^{\circ}$ and $20^{\circ}$ microphone rotations. The lowest-frequency mode shape varies gradually with the azimuth angle. But note that at the highest-frequency mode shape shown, the frequency of the repeating spatial pattern is beyond the Nyquist frequency of our azimuth sampling resolution. We show the implica + +![](images/5618d0b865f164cbe0fa9e5e1afe3ff024f85dacd5ac694827f969da9191cf4a.jpg) +Figure 5. Measuring repeatability of our measurements by visualizing transfer maps of vibrational frequencies of the ceramic bowl, measured at $23~\mathrm{cm}$ from the center. The top row shows the mean of 10 trials of measurements, while the bottom shows the relative standard deviation of the 10 trials. + +tions of attempting to naively interpolate from these low-resolution transfer maps in Appendix E. + +Repeatability. We verify two aspects of the repeatability of our design: the repeatability of the gantry's position and the repeatability of our resulting audio measurements. While our gantry is capable of achieving high angular precision while it is controlled, we completely power it off during each recording, in order to eliminate motor and power supply noises from our recordings. During these periods, the wheels may settle into the carpet at a slightly different angle than we have commanded. We perform four trials of moving to the commanded angles and find that the maximum angular error across all trials did not exceed $1^{\circ}$ , with the mean error being $0.26^{\circ}$ . This translates to a maximum error of $2\mathrm{cm}$ in Cartesian space, only reached when the gantry is at its farthest distance from the center. + +For the repeatability of our measurements, we conduct 10 trials of our measurements on the same ceramic bowl, striking the same target vertex and using the sample positions we used throughout our dataset. We show the mean and standard deviations of the transfers we measured at some sample vibrational frequencies in Figure 5, with results of objects of additional materials in Appendix F. Our results suggest that variations may be highest at the boundaries of nodes in the transfer map. At these locations, minor errors in the azimuth angle could cause significant changes in transfer measurement. Furthermore, at these positions, the signal is lower at this frequency, so the effects of noise can be more pronounced. + +# 5. Applications + +In this section, we demonstrate some use cases of REALIMPACT with practical, multimodal applications. + +# 5.1. Comparing Simulated and Real Impact Sounds + +Our first task is to compare sounds synthesized by existing sound rendering methods to the recordings of RE- + +ALIMPACT in order to demonstrate typical measurement and modeling discrepancies. For this purpose, we ran each baseline method out-of-the-box without any attempt to fine-tune its model and/or hyperparameters, including material parameters, such as elastic stiffness (Young's modulus) and damping (e.g., $\alpha$ and $\beta$ in the case of KLEINPAT). We also did not unify the finite element analysis representations across different methods, including finite element type (KLEINPAT uses first-order tetrahedral elements, whereas ObjectFolder 2.0 uses second-order ones), and tetrahedral meshes. These out-of-the-box comparisons simplify the analysis and highlight the ability to benchmark any existing or new simulation methods given a dataset such as REALIMPACT, but exhibit various modeling oversights. We leave the work to narrow the gap between each baseline to the dataset as future work. We provide more conjectures on why these discrepancies exist in the limitations section. + +Baselines. We provide high-level descriptions of each baseline and refer the readers to Appendix G or directly to the linked work for more details: + +- WHITE NOISE: Random noise which has been adjusted to the same loudness as the average loudness of the recordings on a per-object basis. +- RANDOM IMPACT SOUND: A random impact sound recording from our dataset. +- KLEINPAT [54]: The modal analysis is run using first-order tetrahedral elements, and the Far-field Acoustic Transfer (FFAT) maps are done using a one-term $(1 / r)$ scalar expansion. +- NEURALSOUND [29]: The modal analysis is run using an optimization which is warm-started with the outputs of a 3D sparse U-net on voxelized meshes. The FFAT maps are predicted directly by a ResNet-like encoder-decoder structure. For both steps, we use the pretrained weights. +- OBJECTFOLDER 2.0 [21]: The modal analysis is predicted by an implicit neural representation trained on simulation data using second-order tetrahedral elements. No acoustic transfer values exist in this baseline so we used $\hat{p}(\boldsymbol{x};\omega) = 1$ throughout. + +Note that the final three baselines all require material properties of the object as input; we uniformly apply the same parameters from Table 4 of [54] for all objects with the same material label in our dataset. + +Metrics. We evaluate using the following metrics: 1) L1 spectral loss, a loss based on taking the average L1 distance between log-magnitude spectrograms of different window sizes (used for impact sounds in [12]); 2) envelope distance, which measures the distance between two audio samples' envelopes over time (used for spatial audio in [37]); and + +
REALIMPACT DeconvolvedREALIMPACT Deconvolved + Denoised
L1 SpectralEnvelope (×10-3)CDPAML1 SpectralEnvelope (×10-3)CDPAM
WHITE NOISE4.689.541.385.229.871.39
RANDOM IMPACT SOUND0.7284.170.1210.1504.970.0880
KLEINPAT [54]0.6324.630.1170.09824.630.0975
NEURAL SOUND [29]0.67323.00.1020.13322.80.0750
OBJECT FOLDER 2.0 [21]0.74725.60.2970.23625.40.289
+ +Table 1. Comparing with simulated object impact sounds. Lower is better for all metrics. + +![](images/77ec6ffd46ac5b86447088367bfdda4d62ed97c4f5234fdc82ee019dc8c0b61e.jpg) +Figure 6. Comparison of spectrograms from our collected recordings versus simulation frameworks. Each spectrogram represents the sound recorded or simulated from a sample point at (8, 22, 13) cm in Cartesian space from the center of the base of the object, and each row corresponds to striking the same vertex on the object. + +3) CDPAM [36], a learning-based perceptual distance metric trained from human judgments of detectable differences between clips. + +To mitigate the effects of measurement noise in our evaluation, we compare each baseline both to our deconvolved recordings and to denoised versions of our recordings, which have been denoised with the algorithm of [46]. Whereas many denoising algorithms are optimized for human speech, this algorithm has been optimized and validated against broader categories of audio signals from nature. Comparisons of example spectrograms and their denoised counterparts are shown in Appendix H. + +Quantitative results are shown in Table 1, and qualitative examples are shown in Fig. 6, comparing our recordings of real impact sounds with the simulated sounds using methods from [21, 29, 54]. The KLEINPAT baseline performs best according to a spectral loss, whereas NEURAL-SOUND performs best according to the perceptual CDPAM loss. Both of these baselines significantly outperform ObjectFolder, suggesting that explicitly modeling the acoustic transfer of objects rather than merely their structural vibrations is essential for achieving realism. A random impact sound only outperforms baselines in Envelope Loss when the recording has not been denoised. Each baseline other than white noise performs better on all metrics when compared against denoised versions of our recordings, suggest- + +ing that our raw recordings have non-negligible measurement noise, which must be accounted for in future comparisons. + +# 5.2. Listener Location Classification + +Identifying the location of the listener with respect to the sound source is of great practical interest to many applications in virtual reality and robotics [8, 43, 44]. In this task, we want to identify the microphone position (angle, height, or distance) from the impact sound recording. + +For each impact in REALIMPACT, we have the recordings of the impact sound from 600 different listener locations collected from 10 different angles, 15 different heights, and 4 different distances, as illustrated in Fig. 1. + +Particularly, we set up three separate classification subtasks: 1) angle classification, where the goal is to classify the sound into the 10 angle categories $(0^{\circ}, 20^{\circ}, \dots, 180^{\circ})$ ; 2) height classification, where the goal is to classify the sound into the 15 height categories, each corresponding to the height of our 15 microphones; and 3) distance classification, where the goal is to classify the sound into the 4 distance categories $(0.23 \mathrm{~m}, 0.56 \mathrm{~m}, 0.90 \mathrm{~m}$ , and $1.23 \mathrm{~m})$ . + +For each subtask, we split 90/10 percent of impact sound recordings of an object into the train/test set, respectively. We train a ResNet-18 [24] network that takes the magnitude spectrogram of the impact sound as input to predict the an + +
AngleHeightDistance
CHANCE10.06.725.0
Ours57.960.767.4
+ +gle, height, or distance category. Table 2 shows the results averaged across all 50 objects. We observe that predicting height is comparatively easier. We suspect that differences in height strongly influence the spectral details for easier classification. + +# 5.3. Visual Acoustic Matching + +The ability to match a source sound with the correct corresponding visual input plays an important role in tasks such as speech and speaker recognition [33, 52] or object and event localization [25, 56]. This task aims to match a sound recording with the correct corresponding image. We set up this matching task as binary classification. + +For 20 of our objects, we have a total of 200 RGBD images taken simultaneously with our audio recordings, which are collected at a fixed height from the 10 different angles and 4 different distances from which we took audio recordings for each of the 5 different vertices. We generate positive pairs by pairing each sound recording to an image taken at the corresponding angle and vertex. The height and distance of the image are fixed, so there are 50 possible images that the sound recordings correspond to. The distance of the paired RGBD image is selected such that the image captures the position of both the object and the impact hammer. Negative pairs are generated by pairing sound recordings with images that are not at the correct angle and vertex. + +We randomly select two heights to be held out for validation and test sets, while the remaining 13 heights are used for the train set. We train an audio-visual network with a ResNet-18 backbone for both the image and audio streams. The network takes in an RGB image as visual input and an impact sound recording as audio input. A fusion layer combines the audio and visual information, and a final fully-connected layer is used to extract audio-visual features for binary classification. Table 3 shows the quantitative results of the visual acoustic matching task averaged across 20 objects, and we show example inputs and outputs in Appendix I. + +# 6. Limitations and Conclusion + +We presented REALIMPACT, a first-of-its-kind, large dataset of 150k real impact sounds systematically collected in an acoustically treated room, and demonstrated its several use cases on benchmarking existing simulation algorithms and applications on several auditory and audiovisual tasks. + +Table 2. Listener location classification results. We report the accuracy (in %) for angle, height, and distance classification, respectively. + +
Accuracy ↑RMSE ↓
CHANCE50.059.7
Ours75.147.7
+ +Table 3. Quantitative results of visual acoustic matching. We report the accuracy results (in %). RMSE angle error (in degrees) is the root-mean-square error in the difference between the angles of the image and sound recording. $\uparrow$ or $\downarrow$ signify higher or lower values are better, respectively. + +The microphone array stack used in our measurement process is somewhat coarse to capture high-frequency details (e.g., the $12\mathrm{cm}$ microphone spacing in elevation roughly corresponds to the wavelength of $3\mathrm{kHz}$ ). The angular resolution is chosen at only 20 degrees and can result in aliasing and distortion in the otherwise symmetric radiation fields, as shown in $\S 4.5$ . The diversity of the recorded objects is restricted by the size and load capacity of our supporting thread mesh, and the microphone stack arm. The material descriptions of the objects are artificially lumped into the categories defined in previous work [54], but they may not describe the diversity of real-world materials (e.g., different kinds of steels will have different mechanical properties that might affect stiffness and thus the frequency distributions). Future work should look at more efficient ways of capture and sample a wider range of objects. + +The comparison of real impact sounds to those generated by current simulation methods exhibit various discrepancies. Many things can lead to the gap between simulations and real recordings: object scanning resolution and reconstruction accuracy, material stiffness and damping parameters, finite-element analysis differences (e.g., element type), and insufficient meshing resolution. Also we did not explicitly model hollow objects in the comparisons despite some of our objects being hollow and/or thin, and contact damping models are missing, which can affect the perceived damping rates and thus the envelope accuracy. As a result, many of the out-of-the-box simulation models' vibrational frequencies do not agree, let alone their estimates of spatialized sound amplitudes, etc. Many of these oversights will affect the comparison "fairness" but it also demonstrates a significant benefit of the REALIMPACT dataset: for the first time, we can measure these models using the same yard stick. We hope that this dataset provides future incentives to improve not just the simulation methods and their usage, but also the capture process and datasets that can move the field forward in a significant way. + +Acknowledgments. This work is in part supported by Adobe, NSF CCRI #2120095, NSF RI #2211258, ONR MURI N00014-22-1-2740, AFOSR YIP FA9550-23-1-0127, the Stanford Institute for Human-Centered AI (HAI), Amazon, and Meta. + +# References + +[1] Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In ICCV, 2017. 3 +[2] M. Bebendorf. Approximation of boundary element matrices. Numerical Mathematics, 86(4):565-589, Oct 2000. 4 +[3] Samuel D. Bellows. Directivity. https://scholarsarchive.byu.edu/directivity/. Accessed: 2022-06-06. 2 +[4] Samuel David Bellows and Timothy Ward Leishman. Spherical harmonic expansions of high-resolution musical instrument directivities. In Proceedings of Meetings on Acoustics, 2018. 2 +[5] Jeffrey N Chadwick, Steven S An, and Doug L James. Harmonic shells: a practical nonlinear sound model for near-rigid thin shells. ACM Transactions on Graphics (TOG), 28(5):1-119, 2009. 2, 4 +[6] Changan Chen, Ruohan Gao, Paul Calamia, and Kristen Grauman. Visual acoustic matching. 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ACM Transactions on Graphics (TOG), 35(4):1-13, 2016. 2 + +[33] Jiyoung Lee, Soo-Whan Chung, Sunok Kim, Hong-Goo Kang, and Kwanghoon Sohn. Looking into your speech: Learning cross-modal affinity for audio-visual speech separation. In CVPR, 2021. 8 +[34] Shiguang Liu and Dinesh Manocha. Sound synthesis, propagation, and rendering: a survey. arXiv preprint arXiv:2011.05538, 2020. 2 +[35] Sagnik Majumder and Kristen Grauman. Active audio-visual separation of dynamic sound sources. In ECCV, 2022. 1, 3 +[36] Pranay Manocha, Zeyu Jin, Richard Zhang, and Adam Finkelstein. CDPAM: Contrastive learning for perceptual audio similarity. In ICASSP, 2021. 7 +[37] Pedro Morgado, Nono Vasconcelos, Timothy Langlois, and Oliver Wang. Self-supervised generation of spatial audio for $360^{\circ}$ video. In NeurIPS, 2018. 3, 6 +[38] James F O'Brien, Perry R Cook, and Georg Essl. Synthesizing sounds from physically based motion. In SIGGRAPH, 2001. 2 +[39] James F O'Brien, Chen Shen, and Christine M Gatchalian. Synthesizing sounds from rigid-body simulations. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2002. 2, 3 +[40] Andrew Owens, Phillip Isola, Josh McDermott, Antonio Torralba, Edward H Adelson, and William T Freeman. Visually indicated sounds. In CVPR, 2016. 2 +[41] Dinesh K Pai, Kees van den Doel, Doug L James, Jochen Lang, John E Lloyd, Joshua L Richmond, and Som H Yau. Scanning physical interaction behavior of 3D objects. In SIGGRAPH, 2001. 2 +[42] S. Purushwalkam, S. V. A. Gari, V. K. Ithapu, C. Schissler, P. Robinson, A. Gupta, and K. Grauman. Audio-visual floor-plan reconstruction. In ICCV, 2021. 1, 3 +[43] Chinmay Rajguru, Giada Brianza, and Gianluca Memoli. Sound localization in web-based 3D environments. Scientific Reports, 12(1):1-13, 2022. 7 +[44] Caleb Rascon and Ivan Meza. Localization of sound sources in robotics: A review. Robotics and Autonomous Systems, 96:184-210, 2017. 7 +[45] Zhimin Ren, Hengchin Yeh, and Ming C Lin. Example-guided physically based modal sound synthesis. ACM Transactions on Graphics (TOG), 32(1):1-16, 2013. 2 +[46] Tim Sainburg, Marvin Thielk, and Timothy Q Gentner. Finding, visualizing, and quantifying latent structure across diverse animal vocal repertoires. PLoS Computational Biology, 16(10):e1008228, 2020. 7 +[47] Eston Schweickart, Doug L James, and Steve Marschner. Animating elastic rods with sound. ACM Transactions on Graphics (TOG), 36(4):1-10, 2017. 2 +[48] Arda Senocak, Tae-Hyun Oh, Junsik Kim, Ming-Hsuan Yang, and In So Kweon. Learning to localize sound source in visual scenes. In CVPR, 2018. 3 +[49] Ahmed A Shabana. Theory of Vibration: An Introduction. Springer Science & Business Media, 2012. 3 +[50] Ahmed A Shabana. Dynamics of Multibody Systems. Cambridge university press, 2013. 3 +[51] Julius O Smith. Physical Audio Signal Processing for virtual musical instruments and digital audio effects. Center + +for Computer Research in Music and Acoustics (CCRMA), Stanford University, 2010. 2 +[52] Amirsina Torfi, Seyed Mehdi Iranmanesh, Nasser Nasrabadi, and Jeremy Dawson. 3D convolutional neural networks for cross audio-visual matching recognition. IEEE Access, 5:22081-22091, 2017. 8 +[53] James Traer, Maddie Cusimano, and Josh H McDermott. A perceptually inspired generative model of rigid-body contact sounds. In International Conference on Digital Audio Effects (DAFx), 2019. 2 +[54] Jui-Hsien Wang and Doug L James. Kleinpat: Optimal mode conflation for time-domain precomputation of acoustic transfer. ACM Transactions on Graphics (TOG), 38(4):1-12, 2019. 1, 2, 4, 5, 6, 7, 8 +[55] Jui-Hsien Wang, Ante Qu, Timothy R. Langlois, and Doug L. James. Toward wave-based sound synthesis for computer animation. ACM Transactions on Graphics (TOG), 37(4):1-16, 2018. 2 +[56] Yu Wu, Linchao Zhu, Yan Yan, and Yi Yang. Dual attention matching for audio-visual event localization. In ICCV, 2019. 8 +[57] Xudong Xu, Hang Zhou, Ziwei Liu, Bo Dai, Xiaogang Wang, and Dahua Lin. Visually informed binaural audio generation without binaural audiios. In CVPR, 2021. 3 +[58] Karren Yang, Bryan Russell, and Justin Salamon. Telling left from right: Learning spatial correspondence of sight and sound. In CVPR, 2020. 3 +[59] Zhoutong Zhang, Jiajun Wu, Qiujia Li, Zhengjia Huang, James Traer, Josh H McDermott, Joshua B Tenenbaum, and William T Freeman. Generative modeling of audible shapes for object perception. In ICCV, 2017. 2 +[60] Changxi Zheng and Doug L. James. Rigid-body fracture sound with precomputed soundbanks. ACM Transactions on Graphics (TOG), 29(4):1-13, 2010. 4 +[61] Hang Zhou, Xudong Xu, Dahua Lin, Xiaogang Wang, and Ziwei Liu. Sep-stereo: Visually guided stereophonic audio generation by associating source separation. In ECCV, 2020. 3 \ No newline at end of file diff --git a/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/images.zip b/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..eab293ebfd76b8c8b81d24d7b9f2fb82f2ce70fe --- /dev/null +++ b/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:371edfc3fe6f752d7f5f9613c8c6928da10d7c41f20d682e6057ed51e436bf8e +size 426492 diff --git a/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/layout.json b/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..24ac9ed198d0a5488b399e5d29578b096f13b6ea --- /dev/null +++ b/2023/RealImpact_ A Dataset of Impact Sound Fields for Real Objects/layout.json @@ -0,0 +1,7707 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "spans": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "type": "text", + "content": "REALIMPACT: A Dataset of Impact Sound Fields for Real Objects" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 142, + 194, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 142, + 194, + 171 + ], + "spans": [ + { + "bbox": [ + 116, + 142, + 194, + 171 + ], + "type": "text", + "content": "Samuel Clarke1 Julia Xu1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 215, + 143, + 298, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 215, + 143, + 298, + 171 + ], + "spans": [ + { + "bbox": [ + 215, + 143, + 298, + 171 + ], + "type": "text", + "content": "Ruohan Gao1 \nJui-Hsien Wang2" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 188, + 171, + 288, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 188, + 171, + 288, + 186 + ], + "spans": [ + { + "bbox": [ + 188, + 171, + 288, + 186 + ], + "type": "text", + "content": "1Stanford University" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 143, + 393, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 143, + 393, + 171 + ], + "spans": [ + { + "bbox": [ + 317, + 143, + 393, + 171 + ], + "type": "text", + "content": "Mason Wang1 \nDoug L. 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While prior works have modeled impact sounds and sound propagation in simulation, we lack a standard dataset of impact sound fields of real objects for audio-visual learning and calibration of the sim-to-real gap. We present REALIMPACT, a large-scale dataset of real object impact sounds recorded under controlled conditions. REALIMPACT contains 150,000 recordings of impact sounds of 50 everyday objects with detailed annotations, including their impact locations, microphone locations, contact force profiles, material labels, and RGBD images.* We make preliminary attempts to use our dataset as a reference to current simulation methods for estimating object impact sounds that match the real world. Moreover, we demonstrate the usefulness of our dataset as a testbed for acoustic and audio-visual learning via the evaluation of two benchmark tasks, including listener location classification and visual acoustic matching." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 487, + 128, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 128, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 128, + 499 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 507, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 639 + ], + "type": "text", + "content": "Object sounds permeate our everyday natural environments as we both actively interact with them and passively perceive events in our environment. The sound of a drinking glass bouncing on the floor assuages our fear that the glass would shatter. The click made by a knife making contact with a cutting board assures us that we have diced cleanly through a vegetable. And listening to the sound a painted mug makes when we tap it informs us of whether it is made of ceramic or metal. What we perceive from sound complements what we perceive from vision by reinforcing, disambiguating, or augmenting it." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "content": "Understanding the cause-and-effect relationships in these sounds at a fine-grained level can inform us about an object's material properties and geometry, as well as its contact and other environmental conditions. Capturing" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 214, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 214, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 214, + 545, + 262 + ], + "type": "text", + "content": "these relationships from real-world data can help us improve our models toward more realistic physical simulations, with applications in virtual reality, animation, and training learning-based frameworks in simulation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "text", + "content": "The sounds we perceive from objects are the result of many intricate physical processes: they encode important properties about the object itself (e.g., geometry, material, mechanical properties), as well as the surrounding environment (e.g., room size, other passive objects present, materials of furniture in the room). More specifically, when a hard object is struck, it vibrates according to its mass and stiffness, and the shape of the object determines the mode shapes of the dominant vibration patterns (" + }, + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "inline_equation", + "content": "\\S 3.1" + }, + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "text", + "content": "). Acoustic waves are then emitted into the medium, typically air, bouncing around in the room and interacting with surrounding objects and the room itself before reaching our ear or a microphone to be perceived as pressure fluctuations (" + }, + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "inline_equation", + "content": "\\S 3.2" + }, + { + "bbox": [ + 304, + 265, + 546, + 421 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 423, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 547, + 555 + ], + "type": "text", + "content": "Prior work has explored using physical simulation [26, 54] or learning-based methods [28, 29] to reconstruct the sound generation process virtually, as well as building 3D environments with simulated spatial audio for embodied audio-visual learning [7, 15, 18, 35, 42]. However, there has been little work on building physical apparatuses and feasible measurement process to quantify sounds made by the everyday objects, despite their importance and intimate relationship with our daily lives. As a result, the evaluations of the methods above are largely established on subjective metrics such as user studies." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "To address this gap, we introduce REALIMPACT, a dataset containing 150k recordings of 50 everyday objects, each being struck from 5 distinct impact positions. For each impact point, we capture sounds at 600 field points to provide comprehensive coverage of the frequency components of the sounds and how they are distributed spatially. REALIMPACT thus provides all the inputs most current simulation frameworks needed to simulate each sound, while also providing the ground truth recording for comparison. We show that REALIMPACT can be used for various downstream auditory and audio-visual learning tasks, such as listener location classification (§5.2) and visual acoustic matching (§5.3). These results demonstrate that sound" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "*The project page and dataset are available at https://samuelpclarke.com/realimpact/" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1516" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 120 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 120 + ], + "type": "text", + "content": "fields can help improve machine perception and understanding of the world, and motivate further studies of even more accurate simulation methodologies to reduce the sim-to-real gap for future applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 121, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 121, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 121, + 286, + 227 + ], + "type": "text", + "content": "We make three contributions. First, we design an automated setup for collecting high-fidelity, annotated recordings of sounds by controlled striking of everyday objects. Second, using this setup, we acquire a large dataset of spatialized object sounds, REALIMPACT. Third, we motivate the utility of REALIMPACT by (a) using it to perform comparisons to results generated by current state-of-the-art sound simulation frameworks and (b) evaluating two benchmark tasks for acoustic and audio-visual learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 239, + 133, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 239, + 133, + 251 + ], + "spans": [ + { + "bbox": [ + 48, + 239, + 133, + 251 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 255, + 286, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 255, + 286, + 458 + ], + "spans": [ + { + "bbox": [ + 48, + 255, + 286, + 458 + ], + "type": "text", + "content": "Datasets of Object Sounds. Many datasets of object sounds have been introduced, each varying in the details of their collection, based on the applications they target. The Greatest Hits Dataset [40] includes audio-video recordings of thousands of impacts between real objects from the wild. The recordings were not taken in a controlled environment, and each impact is induced by a human with a drumstick, polluting each object's impact sound with the sound of the rather resonant drumstick. The Sound-20K Dataset [59] is a fully synthetic dataset of 20,000 simulated recordings of objects being dropped in virtual environments. More recently, ObjectFolder [17,21] is introduced as a large dataset of trained implicit models for generating the sounds objects make when impacted at arbitrary locations. However, these are once again trained only on data from simulation, and they do not model the acoustic transfer properties of the objects, only their structural vibratory response." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 462, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 462, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 462, + 286, + 712 + ], + "type": "text", + "content": "Physics-based Sound Rendering. Realistic sound rendering has been a long-held goal in computer music, interactive virtual environments, and computer animation [27, 34, 51, 55]. By modeling the underlying physical processes of vibrations, the computer graphics community demonstrated convincing synthesized sounds for vibrating solids [26, 31, 38, 39], shells [5], rods [47], and even fluids [32, 55]. [26, 55] further showed that it is important for high-quality sound rendering to capture the amplitude and spatial structure of radiating sound fields. However, computing these acoustic transfer fields is time-consuming as they are typically solved in the frequency domain, one frequency at a time. In KLEINPAT [54], the authors showed that by conflating multiple vibrating modes into one time-domain solve, getting all-frequency transfer maps can be done much faster, usually on the order of minutes. These models require careful simulation and material parameters tuning for the best results. To alleviate this issue, several works proposed to sample audio clips [45] and impulse responses [53] to reconstruct the material definitions. Recently, a few works [28, 29] have explored using learning to" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 545, + 119 + ], + "type": "text", + "content": "approximate both the vibration and transfer computations using simulated training data. We provide timely real data that such simulations could use to validate their outputs and tune their performances." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 123, + 545, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 123, + 545, + 207 + ], + "spans": [ + { + "bbox": [ + 308, + 123, + 545, + 207 + ], + "type": "text", + "content": "Recording Sounds Made by Real Objects. Whereas many learning-based frameworks have traditionally used simulation results as their \"ground truth\" for learning acoustic models of object vibrations and their transfer, some works have proposed to fit acoustic object models directly from data using digital signal processing with more relaxed model assumptions about rigid body vibrations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 207, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 207, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 308, + 207, + 545, + 422 + ], + "type": "text", + "content": "Pai et al. [41] describe a framework for scanning physical objects across multiple modalities, measuring visual, tactile, and audio properties of some everyday objects. They fit a data-driven acoustic model based on modal vibration for an object by striking it at different points and recording the ensuing sound from a single position per impact point, assuming constant acoustic transfer across the object. DiffImpact [12] similarly fits modal models to real recordings of objects, but assumes a constant modal response and transfer across the object since their data lacked annotations of the impact point and microphone location. Perhaps most similar to our work, Corbett et al. [13] collect recordings of striking an object at three different impact points, positioning a microphone at 19 different positions per impact point. We collect recordings from an order of magnitude more microphone positions to empirically demonstrate that acoustic transfer varies rather drastically over a much finer resolution than can be captured at 19 different locations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 423, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 423, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 308, + 423, + 545, + 564 + ], + "type": "text", + "content": "Also, while these prior works have collected datasets from real audio, none have publicly released their datasets. Furthermore, since many simulation frameworks are designed to simulate audio of objects vibrating freely in an anechoic space, the recordings collected by these works are unsuitable for a fair comparison, since they are recorded with objects in contact conditions like resting on tables or grasped in hands, which greatly hinder free vibrations. In contrast, we propose a novel capture system where objects rest on a thread mesh in an acoustically treated room, which more closely approximates free vibration in an anechoic environment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 566, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 566, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 308, + 566, + 545, + 673 + ], + "type": "text", + "content": "Finally, from outside the domain of object impact sounds, Bellows et al. [4] have an extensive project measuring the sound directivity of musical instruments while being played by musicians. The measurements take place in a large anechoic chamber and are recorded with a rotating semi-circular microphone array resulting in 2,522 unique microphone positions. The raw measurements are not provided, but the directivity patterns are available as spherical harmonic decompositions [3]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "type": "text", + "content": "Visual Learning of Sounds in Space. Both audio and visual data convey crucial spatial information. Recent inspiring works have explored many interesting tasks connecting" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "type": "text", + "content": "1517" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 248, + 293 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 248, + 293 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 248, + 293 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 248, + 293 + ], + "type": "image", + "image_path": "c7a3f27ed18d67c51f5be931de184088fe12eb884858e3b6c9eb34358419821a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 547, + 361 + ], + "type": "text", + "content": "Figure 1. Pipeline for the acquisition of spatialized impact sounds: (Left) The object is placed at the center of the measurement platform and aligned with mesh threads. The impact hammer is positioned to strike a target vertex on the object. (Center) The gantry moves the microphones to 40 different positions within a semi-cylinder of the object, with the automated hammer mechanism striking the object to record the sound at each position. (Right) By the end of the recording process, for each of the 5 vertices of each object, recordings from 600 different microphone positions have been collected within the semi-cylinder to one side of the object, as shown." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 250, + 72, + 399, + 294 + ], + "blocks": [ + { + "bbox": [ + 250, + 72, + 399, + 294 + ], + "lines": [ + { + "bbox": [ + 250, + 72, + 399, + 294 + ], + "spans": [ + { + "bbox": [ + 250, + 72, + 399, + 294 + ], + "type": "image", + "image_path": "3d27dfe90ca06562f9dc57bb86a2f6c9ed0facee86a41545779ba2cd9e773538.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 402, + 72, + 545, + 294 + ], + "blocks": [ + { + "bbox": [ + 402, + 72, + 545, + 294 + ], + "lines": [ + { + "bbox": [ + 402, + 72, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 402, + 72, + 545, + 294 + ], + "type": "image", + "image_path": "dd6ce316362c1941b4aed88dcdaf5444bb768ec392b6be3da1eba3c3acf36ab8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 289, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 289, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 289, + 467 + ], + "type": "text", + "content": "visual learning and sound in 3D space, including visually-guided audio spatialization [20,22,37,57,61], sound source localization in video frames [1,6,48], learning audio-visual spatial correspondence [9, 58], and building audio-visual 3D environments [7, 15] for an array of embodied learning tasks [8, 14, 16, 18, 35, 42]. We show how our dataset can be used to evaluate real-world performance of auditory and audiovisual learning frameworks on two novel tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 480, + 222, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 222, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 222, + 495 + ], + "type": "text", + "content": "3. Physics-Based Sound Synthesis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 502, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 586 + ], + "type": "text", + "content": "We begin with some background about physics-based sound simulation for rigid objects to motivate design choices for our dataset and provide context for our baseline simulation frameworks and their parameters. Here we briefly summarize a commonly used sound synthesis pipeline for rigid objects. For a more detailed introduction, we recommend the article from James et al. [27]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 180, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 180, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 180, + 609 + ], + "type": "text", + "content": "3.1. Modal Sound Synthesis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 288, + 689 + ], + "type": "text", + "content": "When a contact force is applied to an object (e.g., your dinner plate hits the dishwasher handle), depending on the location of contact, various vibration modes can get excited and eventually die down due to internal damping. Mathematically, the vibration's displacement vector " + }, + { + "bbox": [ + 46, + 616, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{u}(t)" + }, + { + "bbox": [ + 46, + 616, + 288, + 689 + ], + "type": "text", + "content": " can be low-rank approximated as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 97, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 97, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {u} (t) = U \\boldsymbol {q} (t) = \\left[ \\hat {\\boldsymbol {u}} _ {1} \\dots \\hat {\\boldsymbol {u}} _ {K} \\right] \\boldsymbol {q} (t), \\tag {1}", + "image_path": "c9e7ab398eb386836be655c6762ea32b08d60d0383be336e87c90cd93237a72e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "content": " is the modal matrix with mode shapes " + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{u}}_i" + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "inline_equation", + "content": "\\pmb {q}(t)\\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 305, + 369, + 546, + 405 + ], + "type": "text", + "content": " the modal coordinates. The equations of motion are" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 406, + 545, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 406, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 376, + 406, + 545, + 418 + ], + "type": "interline_equation", + "content": "M \\ddot {\\boldsymbol {u}} + C \\dot {\\boldsymbol {u}} + K \\boldsymbol {u} = \\boldsymbol {f}, \\tag {2}", + "image_path": "0770bb86c361d0004ade5b6c21e44bfe9ac7b00d24e00afc0339a5320d1f68bf.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": " are the mass, damping, and stiffness matrix, respectively*, and " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": " is the external force vector. It is typically assumed in the literature that the damping can be approximated by Rayleigh damping, " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "C = \\alpha M + \\beta K" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": "; with this convenient assumption, Eq. (2) can be re-written in the subspace defined by " + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 421, + 547, + 494 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 498, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 498, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 359, + 498, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\ddot {\\boldsymbol {q}} + (\\alpha \\mathbf {I} + \\beta \\Lambda) \\dot {\\boldsymbol {q}} + \\Lambda \\boldsymbol {u} = U ^ {\\intercal} \\boldsymbol {f}, \\tag {3}", + "image_path": "adb6e3831c178fc780803694a755f0ac700c35eb62c80ac4df5e0c7aedd39c5d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": " is the identity matrix and " + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "inline_equation", + "content": "\\Lambda = \\mathrm{diag}(\\omega_1^2,\\dots,\\omega_K^2)" + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": " is a diagonal matrix of involving angular frequencies " + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": ". Since the damping can significantly affect material perception [30], the Rayleigh damping can potentially model real-world objects poorly. In addition, there are two scalar properties " + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": " to fit, and in previous work, these are typically hand-picked to produce sounds that are closest to a given material. Also note that this formulation is based on linear modal analysis [49,50], which assumes the vibrations are infinitesimal, or, in other words, the object is approximately rigid." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 654, + 411, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 411, + 667 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 411, + 667 + ], + "type": "text", + "content": "3.2. Acoustic Transfer" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 673, + 546, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 673, + 546, + 697 + ], + "spans": [ + { + "bbox": [ + 305, + 673, + 546, + 697 + ], + "type": "text", + "content": "Sound radiates from an object's surface into the surrounding medium as pressure waves. Since the modes de" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 320, + 702, + 534, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 702, + 534, + 714 + ], + "spans": [ + { + "bbox": [ + 320, + 702, + 534, + 714 + ], + "type": "text", + "content": "*Formulas of how to compute these matrices can be found in [39]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "text", + "content": "1518" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "content": "cay slowly over time, it is convenient to work in the frequency domain [26]. The distribution of the wave magnitudes in space, " + }, + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "inline_equation", + "content": "\\hat{p} (x;\\omega)" + }, + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "content": ", is referred to in the literature [26] as the acoustic transfer function. With a given set of vibrational boundary conditions, such as those given by Eq. (3), one can solve the frequency-domain Helmholtz equation [5,26,31] using boundary element methods [2, 11, 23] or a time-domain wave equation before reconstructing the acoustic transfer fields [54]. To display the acoustic transfer fields at runtime, we may compress the representation using multi-point dipole sources [26] or single-point multipole sources [60]. Another increasingly popular way of storing and displaying the field is to leverage the radial structure (or lack thereof) in the far-field radiation to store Far-field Acoustic Transfer (FFAT) maps, which are rectangular, image-like textures that capture the angular radiation pattern of a given object. FFAT maps can be quickly reparametrized (e.g., equalized, time-delayed) at runtime to display object impact sounds with user interactions [54]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 309, + 200, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 309, + 200, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 309, + 200, + 323 + ], + "type": "text", + "content": "4. The REALIMPACT Dataset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 329, + 288, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 426 + ], + "type": "text", + "content": "We introduce REALIMPACT, a dataset of 150,000 real object impact sounds. Along with these sounds, we record the force profiles from the impact hammer we used to strike the objects, as well as an RGBD image of the object from each azimuth angle and radial distance from which the audio recording is measured. Below, we introduce the hardware setup for collecting the data, the objects we use, and our data collection pipeline." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 432, + 148, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 148, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 148, + 445 + ], + "type": "text", + "content": "4.1. Hardware Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "content": "We collect all recordings in an acoustically treated room (see Appendix B for additional details). We designed a cylindrical gantry system for moving the microphones to precise positions in space, shown in Figure 1. The gantry system moves a 1.82-meter-tall vertical column of 15 Dayton Audio EMM6 calibrated measurement microphones which are evenly and precisely spaced along the column. It moves this column precisely in two degrees of freedom: azimuth and distance, with a precision of " + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "inline_equation", + "content": "1\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "content": ", respectively. We suspended a mesh of polyester threads precisely at the axis of rotation of this gantry, centering it vertically along the column of 15 microphones. This mesh holds the objects in place while minimizing contact damping and maximizing the acoustic transparency of the surface holding the object. Furthermore, the layout of the mesh provides visual guidance for precisely positioning the objects in a repeatable manner." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "To measure the acoustic transfer from the object to the microphones, the impact force needs to be recorded, allowing an input-output relation to be found. We used a PCB 086E80 impact hammer to strike each object. The impact hammer is incorporated into a custom automated striking" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 239 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 239 + ], + "type": "image", + "image_path": "0226a2f28c77d17a852dc420f4b34ccd1571453f58df7354037cdc38b40fdd54.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "type": "text", + "content": "Figure 2. The real objects used in our dataset. Objects are clustered by material: (from top left) wood, ceramic, glass, plastic, (from bottom center) iron, steel, and polycarbonate." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 292, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 412 + ], + "type": "text", + "content": "mechanism, which strikes objects precisely and repeatedly while being as silent as possible. The mechanism uses a motor to wind the hammer back to contact an electromagnet; then, upon recording, the electromagnet releases the hammer. Actuating the electromagnet is completely silent, so the noise created by this mechanism is minimal during each strike. This mechanism is mounted on a microphone stand to be able to position it rigidly to strike objects at arbitrary locations. See Appendix C and D for additional details on the recording apparatus and hammer impacts, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 412, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 567 + ], + "type": "text", + "content": "The impact hammer has a calibrated force transducer in its tip, measuring contact forces at the same temporal resolution as our audio. The impact hammer and microphones are all read in a time-synchronized fashion by using two Motu 8M audio interfaces connected by an optical cable. Each audio interface has digitally-controlled amplifier gains, which must be tuned up or down for object sounds that are relatively quiet or loud, respectively, to boost the signal as much as possible while also preventing clipping. Because these gains are digitally controlled, we can record and adjust them in a precise and repeatable manner throughout our experiments. The recordings were made at a sample rate of " + }, + { + "bbox": [ + 304, + 412, + 545, + 567 + ], + "type": "inline_equation", + "content": "48000\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 412, + 545, + 567 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 567, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 604 + ], + "type": "text", + "content": "We also attach a RealSense D415 RGBD camera to the column, aligned with the first microphone above mesh-level, to take RGBD images with our audio measurements." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 611, + 365, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 365, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 365, + 624 + ], + "type": "text", + "content": "4.2. Objects" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "We purchase 50 objects from the ObjectFolder dataset [19], which is comprised of commonly used household objects like a ceramic mug, drinking cup, plastic bin, and wood vase. Each object in REALIMPACT has a high-resolution 3D mesh model generated from a scan of the real object [21], which can be used in simulation frameworks. We select objects which are rigid and consist of a single ho" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "text", + "content": "1519" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 277, + 259 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 277, + 259 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 277, + 259 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 277, + 259 + ], + "type": "image", + "image_path": "6be6931513078ed9bfa715c27d8c412fde871647417790ecc1ee09148f5cb9c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 261, + 287, + 294 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 294 + ], + "type": "text", + "content": "Figure 3. An RGBD image and audio recordings from all 15 microphones are collected at each gantry position for each vertex we impact on an object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "text", + "content": "mogeneous material belonging to one of the following categories: ceramic, glass, wood, plastic, iron, polycarbonate, and steel—materials that have " + }, + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 304, + 287, + 388 + ], + "type": "text", + "content": " parameters available and widely used in the physics-based sound rendering literature [28, 29, 54]. Figure 2 shows all objects used for data collection. These objects all have a scale and mass suitable for data collection using our hardware setup." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 394, + 183, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 183, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 183, + 407 + ], + "type": "text", + "content": "4.3. Data Collection Pipeline" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 413, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 288, + 664 + ], + "type": "text", + "content": "For each object, we first place the object on the supporting mesh, matching the features of the mesh to the distinctive geometric features of the object to position it in a repeatable manner. We then select 5 vertices from the virtual mesh at which to strike the object. For each vertex, we first position the hammer mechanism to strike the vertex. Since our gantry collects recordings on a semi-cylinder to one side of the object, we position the hammer mechanism to the opposite side of the semi-cylinder both to not impinge the motion of the gantry and to minimize blocking acoustic radiation from the surface of the object toward the microphones. For each vertex, we move the gantry to 40 positions: a grid of 10 angles in 20-degree increments from 0 through 180, at 4 distances of 0.23, 0.56, 0.90, and 1.23 meters from the center of the mesh. We take an RGBD image at each position in addition to the audio recordings. A diagram of the microphone positions relative to an example object is shown in Figure 1. An example of each of the modalities captured from one position is shown in Figure 3. See the Supplementary Materials for an example video of how an object is recorded." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 119, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 119, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 119, + 684 + ], + "type": "text", + "content": "4.4. Processing" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The impact hammer strikes are not necessarily constant across measurements, but the discrepancy can be corrected" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 541, + 194 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "type": "image", + "image_path": "990379c52b812374016f798925e4c28f4f9306cb91bd05551ee36c3ace8e6ee9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 197, + 545, + 252 + ], + "lines": [ + { + "bbox": [ + 305, + 197, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 305, + 197, + 545, + 252 + ], + "type": "text", + "content": "Figure 4. Comparing different azimuth resolutions for mode shape transfer maps of a ceramic bowl, measured at " + }, + { + "bbox": [ + 305, + 197, + 545, + 252 + ], + "type": "inline_equation", + "content": "23~\\mathrm{cm}" + }, + { + "bbox": [ + 305, + 197, + 545, + 252 + ], + "type": "text", + "content": " from the center. The top row shows maps measured at a resolution of 1 degree, while the bottom row shows those measured at a resolution of 20 degrees." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": "since the force is measured. This is achieved by deconvolving the force signal from the microphone signal with frequency domain division as " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "m_{c} = \\mathcal{F}^{-1}\\left(\\mathcal{F}(m) / \\mathcal{F}(i)\\right)" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": " is the impact hammer signal, " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": " is the microphone signal, and " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": " is the corrected microphone signal. " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{-1}" + }, + { + "bbox": [ + 304, + 266, + 545, + 386 + ], + "type": "text", + "content": " are the forward and inverse discrete Fourier transforms, respectively. The hammer signal is windowed such that only the samples within 1% of the force peak are kept, and all other samples are deemed noise and set as zero, reducing noise in the corrected microphone signal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "text", + "content": "To create transfer maps of the recordings, mode fitting is performed on each corrected microphone signal. The modes are fit using the method of [10]. First, the vibrational frequencies are fit with a simple peak-picking algorithm performed on " + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(m_c)" + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "text", + "content": ". Decay rates are fit by band-passing " + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "inline_equation", + "content": "m_{c}" + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "text", + "content": " at the mode frequencies, applying a Root-Mean-Squared level detector, and using linear regression to estimate the slope of the energy envelope. The amplitudes are set as the magnitude of the mode frequency peak in " + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(m_c)" + }, + { + "bbox": [ + 304, + 387, + 546, + 543 + ], + "type": "text", + "content": ". Transfer maps are then formed for each vibrational frequency by displaying the magnitude at each measurement location with respect to rotation and height, as shown in Figures 4 and 5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 554, + 377, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 554, + 377, + 565 + ], + "spans": [ + { + "bbox": [ + 306, + 554, + 377, + 565 + ], + "type": "text", + "content": "4.5. Validation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Spatial Sampling. We use a " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "20^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " resolution of azimuth angle for the spatial sampling as a compromise to reduce measurement time while still adding benefit for certain sound-related tasks. We take one set of measurements with " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " rotations on one of our objects (a ceramic bowl) as a comparison. Figure 4 shows measured acoustic transfer maps for sample vibrational frequencies with both " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "20^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " microphone rotations. The lowest-frequency mode shape varies gradually with the azimuth angle. But note that at the highest-frequency mode shape shown, the frequency of the repeating spatial pattern is beyond the Nyquist frequency of our azimuth sampling resolution. We show the implica" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1520" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 283, + 178 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 283, + 178 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 283, + 178 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 283, + 178 + ], + "type": "image", + "image_path": "5618d0b865f164cbe0fa9e5e1afe3ff024f85dacd5ac694827f969da9191cf4a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 181, + 287, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 236 + ], + "type": "text", + "content": "Figure 5. Measuring repeatability of our measurements by visualizing transfer maps of vibrational frequencies of the ceramic bowl, measured at " + }, + { + "bbox": [ + 46, + 181, + 287, + 236 + ], + "type": "inline_equation", + "content": "23~\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 181, + 287, + 236 + ], + "type": "text", + "content": " from the center. The top row shows the mean of 10 trials of measurements, while the bottom shows the relative standard deviation of the 10 trials." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 248, + 286, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 286, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 286, + 272 + ], + "type": "text", + "content": "tions of attempting to naively interpolate from these low-resolution transfer maps in Appendix E." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "text", + "content": "Repeatability. We verify two aspects of the repeatability of our design: the repeatability of the gantry's position and the repeatability of our resulting audio measurements. While our gantry is capable of achieving high angular precision while it is controlled, we completely power it off during each recording, in order to eliminate motor and power supply noises from our recordings. During these periods, the wheels may settle into the carpet at a slightly different angle than we have commanded. We perform four trials of moving to the commanded angles and find that the maximum angular error across all trials did not exceed " + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "text", + "content": ", with the mean error being " + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "inline_equation", + "content": "0.26^{\\circ}" + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "text", + "content": ". This translates to a maximum error of " + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 284, + 286, + 450 + ], + "type": "text", + "content": " in Cartesian space, only reached when the gantry is at its farthest distance from the center." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 452, + 286, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 286, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 286, + 606 + ], + "type": "text", + "content": "For the repeatability of our measurements, we conduct 10 trials of our measurements on the same ceramic bowl, striking the same target vertex and using the sample positions we used throughout our dataset. We show the mean and standard deviations of the transfers we measured at some sample vibrational frequencies in Figure 5, with results of objects of additional materials in Appendix F. Our results suggest that variations may be highest at the boundaries of nodes in the transfer map. At these locations, minor errors in the azimuth angle could cause significant changes in transfer measurement. Furthermore, at these positions, the signal is lower at this frequency, so the effects of noise can be more pronounced." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 619, + 127, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 619, + 127, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 619, + 127, + 632 + ], + "type": "text", + "content": "5. Applications" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "type": "text", + "content": "In this section, we demonstrate some use cases of REALIMPACT with practical, multimodal applications." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 670, + 286, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 286, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 286, + 684 + ], + "type": "text", + "content": "5.1. Comparing Simulated and Real Impact Sounds" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Our first task is to compare sounds synthesized by existing sound rendering methods to the recordings of RE-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "ALIMPACT in order to demonstrate typical measurement and modeling discrepancies. For this purpose, we ran each baseline method out-of-the-box without any attempt to fine-tune its model and/or hyperparameters, including material parameters, such as elastic stiffness (Young's modulus) and damping (e.g., " + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": " in the case of KLEINPAT). We also did not unify the finite element analysis representations across different methods, including finite element type (KLEINPAT uses first-order tetrahedral elements, whereas ObjectFolder 2.0 uses second-order ones), and tetrahedral meshes. These out-of-the-box comparisons simplify the analysis and highlight the ability to benchmark any existing or new simulation methods given a dataset such as REALIMPACT, but exhibit various modeling oversights. We leave the work to narrow the gap between each baseline to the dataset as future work. We provide more conjectures on why these discrepancies exist in the limitations section." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 286, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 545, + 321 + ], + "type": "text", + "content": "Baselines. We provide high-level descriptions of each baseline and refer the readers to Appendix G or directly to the linked work for more details:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 327, + 545, + 577 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 317, + 327, + 545, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 327, + 545, + 362 + ], + "spans": [ + { + "bbox": [ + 317, + 327, + 545, + 362 + ], + "type": "text", + "content": "- WHITE NOISE: Random noise which has been adjusted to the same loudness as the average loudness of the recordings on a per-object basis." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 365, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 365, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 317, + 365, + 545, + 388 + ], + "type": "text", + "content": "- RANDOM IMPACT SOUND: A random impact sound recording from our dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 392, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 392, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 317, + 392, + 545, + 440 + ], + "type": "text", + "content": "- KLEINPAT [54]: The modal analysis is run using first-order tetrahedral elements, and the Far-field Acoustic Transfer (FFAT) maps are done using a one-term " + }, + { + "bbox": [ + 317, + 392, + 545, + 440 + ], + "type": "inline_equation", + "content": "(1 / r)" + }, + { + "bbox": [ + 317, + 392, + 545, + 440 + ], + "type": "text", + "content": " scalar expansion." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 443, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 443, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 317, + 443, + 545, + 514 + ], + "type": "text", + "content": "- NEURALSOUND [29]: The modal analysis is run using an optimization which is warm-started with the outputs of a 3D sparse U-net on voxelized meshes. The FFAT maps are predicted directly by a ResNet-like encoder-decoder structure. For both steps, we use the pretrained weights." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 518, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 518, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 317, + 518, + 545, + 577 + ], + "type": "text", + "content": "- OBJECTFOLDER 2.0 [21]: The modal analysis is predicted by an implicit neural representation trained on simulation data using second-order tetrahedral elements. No acoustic transfer values exist in this baseline so we used " + }, + { + "bbox": [ + 317, + 518, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\hat{p}(\\boldsymbol{x};\\omega) = 1" + }, + { + "bbox": [ + 317, + 518, + 545, + 577 + ], + "type": "text", + "content": " throughout." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 583, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 545, + 630 + ], + "type": "text", + "content": "Note that the final three baselines all require material properties of the object as input; we uniformly apply the same parameters from Table 4 of [54] for all objects with the same material label in our dataset." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Metrics. We evaluate using the following metrics: 1) L1 spectral loss, a loss based on taking the average L1 distance between log-magnitude spectrograms of different window sizes (used for impact sounds in [12]); 2) envelope distance, which measures the distance between two audio samples' envelopes over time (used for spatial audio in [37]); and" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1521" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 542, + 173 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 542, + 173 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 542, + 173 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 542, + 173 + ], + "type": "table", + "html": "
REALIMPACT DeconvolvedREALIMPACT Deconvolved + Denoised
L1 SpectralEnvelope (×10-3)CDPAML1 SpectralEnvelope (×10-3)CDPAM
WHITE NOISE4.689.541.385.229.871.39
RANDOM IMPACT SOUND0.7284.170.1210.1504.970.0880
KLEINPAT [54]0.6324.630.1170.09824.630.0975
NEURAL SOUND [29]0.67323.00.1020.13322.80.0750
OBJECT FOLDER 2.0 [21]0.74725.60.2970.23625.40.289
", + "image_path": "477a22fe36b2deb052e14367dc930af346406c5f914ca0e02975b28cbb1dcc57.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 135, + 175, + 457, + 186 + ], + "lines": [ + { + "bbox": [ + 135, + 175, + 457, + 186 + ], + "spans": [ + { + "bbox": [ + 135, + 175, + 457, + 186 + ], + "type": "text", + "content": "Table 1. Comparing with simulated object impact sounds. Lower is better for all metrics." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 196, + 545, + 355 + ], + "blocks": [ + { + "bbox": [ + 50, + 196, + 545, + 355 + ], + "lines": [ + { + "bbox": [ + 50, + 196, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 50, + 196, + 545, + 355 + ], + "type": "image", + "image_path": "77ec6ffd46ac5b86447088367bfdda4d62ed97c4f5234fdc82ee019dc8c0b61e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 356, + 546, + 391 + ], + "lines": [ + { + "bbox": [ + 46, + 356, + 546, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 546, + 391 + ], + "type": "text", + "content": "Figure 6. Comparison of spectrograms from our collected recordings versus simulation frameworks. Each spectrogram represents the sound recorded or simulated from a sample point at (8, 22, 13) cm in Cartesian space from the center of the base of the object, and each row corresponds to striking the same vertex on the object." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": "3) CDPAM [36], a learning-based perceptual distance metric trained from human judgments of detectable differences between clips." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 545 + ], + "type": "text", + "content": "To mitigate the effects of measurement noise in our evaluation, we compare each baseline both to our deconvolved recordings and to denoised versions of our recordings, which have been denoised with the algorithm of [46]. Whereas many denoising algorithms are optimized for human speech, this algorithm has been optimized and validated against broader categories of audio signals from nature. Comparisons of example spectrograms and their denoised counterparts are shown in Appendix H." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "Quantitative results are shown in Table 1, and qualitative examples are shown in Fig. 6, comparing our recordings of real impact sounds with the simulated sounds using methods from [21, 29, 54]. The KLEINPAT baseline performs best according to a spectral loss, whereas NEURAL-SOUND performs best according to the perceptual CDPAM loss. Both of these baselines significantly outperform ObjectFolder, suggesting that explicitly modeling the acoustic transfer of objects rather than merely their structural vibrations is essential for achieving realism. A random impact sound only outperforms baselines in Envelope Loss when the recording has not been denoised. Each baseline other than white noise performs better on all metrics when compared against denoised versions of our recordings, suggest-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 401, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 436 + ], + "type": "text", + "content": "ing that our raw recordings have non-negligible measurement noise, which must be accounted for in future comparisons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 444, + 478, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 478, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 478, + 455 + ], + "type": "text", + "content": "5.2. Listener Location Classification" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": "Identifying the location of the listener with respect to the sound source is of great practical interest to many applications in virtual reality and robotics [8, 43, 44]. In this task, we want to identify the microphone position (angle, height, or distance) from the impact sound recording." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 522, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 569 + ], + "type": "text", + "content": "For each impact in REALIMPACT, we have the recordings of the impact sound from 600 different listener locations collected from 10 different angles, 15 different heights, and 4 different distances, as illustrated in Fig. 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "Particularly, we set up three separate classification subtasks: 1) angle classification, where the goal is to classify the sound into the 10 angle categories " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "(0^{\\circ}, 20^{\\circ}, \\dots, 180^{\\circ})" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "; 2) height classification, where the goal is to classify the sound into the 15 height categories, each corresponding to the height of our 15 microphones; and 3) distance classification, where the goal is to classify the sound into the 4 distance categories " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "(0.23 \\mathrm{~m}, 0.56 \\mathrm{~m}, 0.90 \\mathrm{~m}" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "1.23 \\mathrm{~m})" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "For each subtask, we split 90/10 percent of impact sound recordings of an object into the train/test set, respectively. We train a ResNet-18 [24] network that takes the magnitude spectrogram of the impact sound as input to predict the an" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1522" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 254, + 119 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 254, + 119 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 254, + 119 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 254, + 119 + ], + "type": "table", + "html": "
AngleHeightDistance
CHANCE10.06.725.0
Ours57.960.767.4
", + "image_path": "f5f6307845934e27f1419c67e3abeab234db28502119184fca3dd058795cd464.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 227 + ], + "type": "text", + "content": "gle, height, or distance category. Table 2 shows the results averaged across all 50 objects. We observe that predicting height is comparatively easier. We suspect that differences in height strongly influence the spectral details for easier classification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 233, + 190, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 233, + 190, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 190, + 247 + ], + "type": "text", + "content": "5.3. Visual Acoustic Matching" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": "The ability to match a source sound with the correct corresponding visual input plays an important role in tasks such as speech and speaker recognition [33, 52] or object and event localization [25, 56]. This task aims to match a sound recording with the correct corresponding image. We set up this matching task as binary classification." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 324, + 286, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 286, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 286, + 479 + ], + "type": "text", + "content": "For 20 of our objects, we have a total of 200 RGBD images taken simultaneously with our audio recordings, which are collected at a fixed height from the 10 different angles and 4 different distances from which we took audio recordings for each of the 5 different vertices. We generate positive pairs by pairing each sound recording to an image taken at the corresponding angle and vertex. The height and distance of the image are fixed, so there are 50 possible images that the sound recordings correspond to. The distance of the paired RGBD image is selected such that the image captures the position of both the object and the impact hammer. Negative pairs are generated by pairing sound recordings with images that are not at the correct angle and vertex." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 479, + 286, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 286, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 286, + 624 + ], + "type": "text", + "content": "We randomly select two heights to be held out for validation and test sets, while the remaining 13 heights are used for the train set. We train an audio-visual network with a ResNet-18 backbone for both the image and audio streams. The network takes in an RGB image as visual input and an impact sound recording as audio input. A fusion layer combines the audio and visual information, and a final fully-connected layer is used to extract audio-visual features for binary classification. Table 3 shows the quantitative results of the visual acoustic matching task averaged across 20 objects, and we show example inputs and outputs in Appendix I." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 634, + 204, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 204, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 204, + 646 + ], + "type": "text", + "content": "6. Limitations and Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "We presented REALIMPACT, a first-of-its-kind, large dataset of 150k real impact sounds systematically collected in an acoustically treated room, and demonstrated its several use cases on benchmarking existing simulation algorithms and applications on several auditory and audiovisual tasks." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 347, + 70, + 503, + 119 + ], + "blocks": [ + { + "bbox": [ + 46, + 122, + 287, + 156 + ], + "lines": [ + { + "bbox": [ + 46, + 122, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 287, + 156 + ], + "type": "text", + "content": "Table 2. Listener location classification results. We report the accuracy (in %) for angle, height, and distance classification, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 347, + 70, + 503, + 119 + ], + "lines": [ + { + "bbox": [ + 347, + 70, + 503, + 119 + ], + "spans": [ + { + "bbox": [ + 347, + 70, + 503, + 119 + ], + "type": "table", + "html": "
Accuracy ↑RMSE ↓
CHANCE50.059.7
Ours75.147.7
", + "image_path": "19db2ae184a8bed3ab60d9627232cf8b66ed7d134e5ec57d8a63e43bbc2b673c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "type": "text", + "content": "Table 3. Quantitative results of visual acoustic matching. We report the accuracy results (in %). RMSE angle error (in degrees) is the root-mean-square error in the difference between the angles of the image and sound recording. " + }, + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 305, + 122, + 545, + 178 + ], + "type": "text", + "content": " signify higher or lower values are better, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "text", + "content": "The microphone array stack used in our measurement process is somewhat coarse to capture high-frequency details (e.g., the " + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "inline_equation", + "content": "12\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "text", + "content": " microphone spacing in elevation roughly corresponds to the wavelength of " + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "inline_equation", + "content": "3\\mathrm{kHz}" + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "text", + "content": "). The angular resolution is chosen at only 20 degrees and can result in aliasing and distortion in the otherwise symmetric radiation fields, as shown in " + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\S 4.5" + }, + { + "bbox": [ + 304, + 191, + 545, + 382 + ], + "type": "text", + "content": ". The diversity of the recorded objects is restricted by the size and load capacity of our supporting thread mesh, and the microphone stack arm. The material descriptions of the objects are artificially lumped into the categories defined in previous work [54], but they may not describe the diversity of real-world materials (e.g., different kinds of steels will have different mechanical properties that might affect stiffness and thus the frequency distributions). Future work should look at more efficient ways of capture and sample a wider range of objects." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 383, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 634 + ], + "type": "text", + "content": "The comparison of real impact sounds to those generated by current simulation methods exhibit various discrepancies. Many things can lead to the gap between simulations and real recordings: object scanning resolution and reconstruction accuracy, material stiffness and damping parameters, finite-element analysis differences (e.g., element type), and insufficient meshing resolution. Also we did not explicitly model hollow objects in the comparisons despite some of our objects being hollow and/or thin, and contact damping models are missing, which can affect the perceived damping rates and thus the envelope accuracy. As a result, many of the out-of-the-box simulation models' vibrational frequencies do not agree, let alone their estimates of spatialized sound amplitudes, etc. Many of these oversights will affect the comparison \"fairness\" but it also demonstrates a significant benefit of the REALIMPACT dataset: for the first time, we can measure these models using the same yard stick. We hope that this dataset provides future incentives to improve not just the simulation methods and their usage, but also the capture process and datasets that can move the field forward in a significant way." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. This work is in part supported by Adobe, NSF CCRI #2120095, NSF RI #2211258, ONR MURI N00014-22-1-2740, AFOSR YIP FA9550-23-1-0127, the Stanford Institute for Human-Centered AI (HAI), Amazon, and Meta." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1523" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Relja Arandjelovic and Andrew Zisserman. 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Mahdi H. Miangoleh1 Zoya Bylinskii2 Eric Kee2 Eli Shechtman2 Yaqiz Aksoy1", + "bbox": [ + 127, + 172, + 833, + 193 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Simon Fraser University $^{2}$ Adobe Research", + "bbox": [ + 285, + 200, + 679, + 219 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e56abe4fd2431b703629682f6aa8815177a684493cd83c35c52d06caf1d45a93.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 76, + 252, + 377, + 411 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/86ce6a45e1f51f8b721443f9092342e7f5dfb8317e4d419d3bb34093ffe59ff3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 257, + 486, + 301 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/42f77cab3bcab39653bb584f7e4911c987e489371a1170fcd03718e5db74f3e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 379, + 303, + 486, + 359 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7333eca4b9da782dfe282a881c60a9c2a09a8b2f565437ea289dd72aff052138.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 379, + 362, + 486, + 406 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9d1e1a4f1eab1910090823f6a2a0b66f3fb777af59598c19cb23e51dcfca1902.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 257, + 581, + 406 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99824e2372e6826fb2cc085b0fe26f7eeb1d6ea0eb1e9dad010c94d2353847ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 591, + 253, + 890, + 410 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d4dbab14608167b15dbe312c9d2b6fcaff2b868883ac0c5476702d909a6fe066.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 422, + 215, + 564 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/00b4f77e8817a7279b7d46be76ac92863752a28794b2d2f4bfd17d217a7307af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 222, + 458, + 297, + 534 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/071b8c5532c553f77256e07da5bb23da443094198dc5040ad2ae8dd5e4400e95.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 303, + 424, + 439, + 563 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6d2387a4876ec1cb39138d6270b2642f614db8a59e71a111513c73e1277fbcfc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 446, + 424, + 581, + 563 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ff83774c45af2ad11c7e2b1d9697d4119ee6371952e43a364dd8835cb418525f.jpg", + "image_caption": [ + "Figure 1. (top) We develop a saliency-based image enhancement method that can be applied to multiple regions in the image to demephasize objects (steps 1, 2) or enhance subjects (steps 3, 4). (bottom) Our novel realism loss allows us to apply realistic edits to a wide variety of objects while state-of-the-art methods [1, 17] may generate less realistic editing results." + ], + "image_footnote": [], + "bbox": [ + 589, + 416, + 890, + 570 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 625, + 313, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Common editing operations performed by professional photographers include the cleanup operations: de-emphasizing distracting elements and enhancing subjects. These edits are challenging, requiring a delicate balance between manipulating the viewer's attention while maintaining photo realism. While recent approaches can boast successful examples of attention attenuation or amplification, most of them also suffer from frequent unrealistic edits. We propose a realism loss for saliency-guided image enhancement to maintain high realism across varying image types, while attenuating distractors and amplifying objects of interest. Evaluations with professional photographers confirm that we achieve the dual objective of realism and effectiveness, and outperform the recent approaches on their own datasets, while requiring a smaller memory footprint and runtime. We thus offer a viable solution for automating image enhancement and photo cleanup operations.", + "bbox": [ + 73, + 643, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 630, + 630, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In everyday photography, the composition of a photo typically encompasses subjects on which the photographer intends to focus our attention, rather than other distracting things. When distracting things cannot be avoided, photographers routinely edit their photos to de-emphasize them. Conversely, when the subjects are not sufficiently visible, photographers routinely emphasize them. Among the most common emphasis and de-emphasis operations performed by professionals are the elementary ones: changing the saturation, exposure, or the color of each element. Although conceptually simple, these operations are challenging to apply because they must delicately balance the effects on the viewer attention with photo realism.", + "bbox": [ + 496, + 657, + 890, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To automate this editing process, recent works use saliency models as a guide [1,2,4,8,16,17]. These saliency models [3,7,10,14,19] aim to predict the regions in the", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "186", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "image that catch the viewer's attention, and saliency-guided image editing methods are optimized to increase or decrease the predicted saliency of a selected region. Optimizing solely based on the predicted saliency, however, often results in unrealistic edits, as illustrated in Fig. 1. This issue results from the instability of saliency models under the image editing operations, as saliency models are trained on unedited images. Unrealistic edits can have low predicted saliency even when they are highly noticeable to human observers, or vice versa. This was also noted by Aberman et al. [1], and is illustrated in Fig. 2.", + "bbox": [ + 75, + 90, + 472, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous methods tried to enforce realism using adversarial setups [2, 4, 8, 17], GAN priors [1, 8], or cycle consistency [2] but with limited success (Fig. 1). Finding the exact point when an image edit stops looking realistic is challenging. Rather than focusing on the entire image, in this work, we propose a method for measuring the realism of a local edit. To train our network, we generate realistic image edits by subtle perturbations to exposure, saturation, color or white balance, as well as very unrealistic edits by applying extreme adjustments. Although our network is trained with only positive and negative examples at the extremes, we successfully learn a continuous measure of realism for a variety of editing operations as shown in Fig. 3.", + "bbox": [ + 75, + 257, + 472, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our realism metric to saliency-guided image editing by training the system to optimize the saliency of a selected region while being penalized for deviations from realism. We show that a combined loss allows us to enhance or suppress a selected region successfully while maintaining high realism. Our method can be also be applied to multiple regions in a photograph as shown in Fig. 1.", + "bbox": [ + 75, + 454, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Evaluations with professional photographers and photo editors confirm our claim that we maintain high realism and succeed at redirecting attention in the edited photo. Further, our results are robust to different types of images including human faces, and are stable across different permutations of edit parameters. Taken together with our model size of 26Mb and run-time of 8ms, these results demonstrate that we have a more viable solution for broader use than the approaches that are available for these tasks to date.", + "bbox": [ + 75, + 560, + 472, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 709, + 218, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Various image enhancement methods have been introduced in the literature to amplify a region of interest or de-emphasise distracting regions, improve image aesthetics, and redirect the viewer's attention. This task has been referred to as attention retargeting [15] or reattentionizing [18] as well. Earlier methods [5,15,20,22,23] incorporated prior knowledge of saliency cues (saturation, sharpness, color, gamut, etc.) to guide the editing process to achieve the desired change in saliency. But, relying solely on saliency cues both limits the diversity of generated edits, and creates unrealistic edits due to the lack of semantic", + "bbox": [ + 75, + 734, + 472, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/aaf1fb2d0518bd051437d1937d2fa424a5dd6ca71a84c1ff316a34fdbb0f2122.jpg", + "image_caption": [ + "Original image" + ], + "image_footnote": [], + "bbox": [ + 501, + 104, + 598, + 195 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/af30ae7160142775f660cee5aadb7b879b928f296a4d031ae58bbfe5ed57b283.jpg", + "image_caption": [ + "Figure 2. Predicted saliency maps [7] for the original images and edited versions, with extreme edits applied. Note that saliency models are typically trained with realistic images. This makes them susceptible to inaccurate predictions for unrealistic inputs, as the green woman in the top row estimated to have low saliency." + ], + "image_footnote": [], + "bbox": [ + 501, + 195, + 598, + 246 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c3a907f1b78db61d9d3587053c45c1989c00978f786d7dfbe5addc41c2c81099.jpg", + "image_caption": [ + "Saliency map" + ], + "image_footnote": [], + "bbox": [ + 599, + 104, + 694, + 178 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9ffbeb94f704c93408b24f2a059d6b6f1d19105d5c6a8d676feb84217a09055e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 599, + 178, + 694, + 246 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/af874ae7afe0f2208e3166875c3ce10af3fc631e0bf569b3133e8d89f9dd1cd9.jpg", + "image_caption": [ + "Edited image" + ], + "image_footnote": [], + "bbox": [ + 697, + 104, + 792, + 195 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6dcd9ac78f5bb7d8bc8337923d8625293e7924df7142309384f14bb415fa26b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 195, + 792, + 246 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6c72891dfb6bd2eddccc2ee3e204a261e45a99de4813b46af6359a43963ac6bd.jpg", + "image_caption": [ + "Saliency map" + ], + "image_footnote": [], + "bbox": [ + 794, + 104, + 890, + 178 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/008a2af1596f0a901d546163043e19c9fbdc0a0e8eb5c19032859864be2d6f21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 794, + 178, + 890, + 246 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "constraints. As our experiments show, OHR [15] tends to generate unrealistic color changes that are semantically incorrect, and WRS [23] is limited to contrast and saturation adjustments with limited effectiveness.", + "bbox": [ + 496, + 333, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent works leverage saliency estimation networks [3, 7, 10, 14, 19] to optimize for a desired saliency map instead of relying on prior saliency cues. Saliency models are trained to output a heatmap that represents where human gaze would be concentrated in an image. These models are not trained to respond to the realism of the input image. Hence they might predict an inconsistent decrease or increase in the saliency of a region when unrealistic or semantically implausible edits are applied, which would be otherwise jarring to human viewers (Fig. 2). Using saliency as the only supervision can result in unrealistic images.", + "bbox": [ + 496, + 397, + 892, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To prevent unrealistic edits, prior works enforce constraints on the allowable changes, use adversarial training [2, 4, 8, 17] or exploit learned priors from GAN-based models [1, 8]. For instance, Mechrez et al. [16] and Aberman et al. (Warping) [1] constrain the result to match the input content in order to maintain its appearance. Aberman et al. (CNN and Recolorization) [1] use a regularization term that limits the amount of change an image can undergo to maintain the realism. Mejjati et al. [17] designed a global parametric approach to limit the editing operations to a set of common photographic ones. Chen et al. [2] exploit cycle consistency to keep the output within the domain of the input image. Gatys et al. [4] use a texture loss alongside the VGG perceptual loss as a proxy for realism.", + "bbox": [ + 496, + 566, + 893, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lalonde et al. [11] argue that humans prefer color consistency within images, regardless of object semantics. They use color statistics to measure realism and use it to recolor the images to match the background in compositing task. Zhu et al. [26] train a network to discriminate between natural images and computer-generated composites and use it as a realism measure for compositing task. Realism is also a crucial factor in GANs, as highlighted by [9].", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "187", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/79464e95935a8890826a1e345c22950c4850ac2e5a855ee01a016dc51d99ff77.jpg", + "table_caption": [ + "Table 1. Parameter value ranges used to generate real and fake training images for the realism estimation network." + ], + "table_footnote": [], + "table_body": "
ExposureSaturationColor curveWhite balancingNumber of edits
Real[0.85, 1.15][0.85, 1.15][0.85, 1.15]Not allowed[1, 3]
Fake[0.5, 0.75] ∪ [1.5, 2][0, 0.5] ∪ [1.5 - 2][0.5, 2][0.9, 1][2, 4]
Fake(human specific)[0.5, 0.75] ∪ [1.25, 1.5][0.5, 0.75] ∪ [1.25, 1.5][0.5, 2]Not allowed[2, 3]
", + "bbox": [ + 84, + 104, + 885, + 167 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/523762469cbad24df67942d9031eecee69c44b939be73e688d98eac63eb2f68b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 181, + 183, + 282 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fcbb1b301b78ae7b093ad69836d865672d8dfa2fb81bfd3b57dfb8c109f8be40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 183, + 305, + 273 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1131b506930c809879f39a28ab32b5e81b81448bfe6a68ef0ad5813ba775f787.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 307, + 184, + 416, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/65623b33fefe2ec03b15151c0fac5d9f0eb0d690aad87c7d9d329890fa586596.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 184, + 531, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ad2bf69290a8b081e70afd9ebb19a8a9c7f44c37c820c759d40d4c7f51849558.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 184, + 645, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5fd10cc5e8c6b2f9a9d3849e4273f69f355aa220e04ce3e11092c57f4c850020.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 184, + 705, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/491e6841422c4038bf6781575d096ba0ee73fba94155328fa6643e5e323ae6be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 184, + 761, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5bd0ccf83a44fe815a2b3052cb79b1d3bfd01c9e68c2a13016059b4a519191c5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 184, + 820, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/535e5b6bf97b34ea44800d5f3ec703f4b236f881cc993bb6422f51c86e79047c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 823, + 184, + 879, + 280 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3fe69fa891ed3fcbdc4344c84d62d348385b9b9c85132676e89963a36694f675.jpg", + "image_caption": [ + "Figure 3. The efficacy of the realism estimation network is illustrated over a range of exposure and saturation adjustments. Left is $\\Delta \\mathcal{R}$ plotted (vertical axis) for example images (second column) when selected regions (third column) are edited. Right, the edited images are shown with the corresponding change in estimated realism (inset numbers), and the value of the editing parameter applied (underneath)." + ], + "image_footnote": [], + "bbox": [ + 84, + 284, + 184, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3f0c77046483687790402277c2099eaa014764739de66084db6c67093ddef599.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 284, + 305, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/070e6f033eed4c022373bf6b08268c6ce146d46f9330db5f06e9e6190af330d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 307, + 284, + 416, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cb4baaf50c240c2fcd8d46bc948303a01e3bdc74c3b94edd99a7c518beaece97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 284, + 531, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2231d02a5cf9d289345bce597c7779867fbb883c1b75f3d1dc58c5cc621293a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 284, + 645, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/da7e037a78e41865d447679e42ddc1fe48fbadcfacb094ac7cb7244a688dd620.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 284, + 705, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/08caa98646d22482a4d94015aa5cb0b2f1a01f75b886717fc5b539b7ac28f745.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 284, + 763, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dfbaf4ba37638113f5d23ae3680f948dfcd799703666011313a0e1f090d5c568.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 284, + 820, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c8544a41c71175fa09e1e3dfd68ff99963909154bda3d9fe7843c3709f6f9291.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 823, + 284, + 879, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present a new method for estimating the realism of a local edit. Combining our realism loss with saliency guidance, we show that we can successfully apply attention attenuation or amplification while keeping the final result realistic without requiring data annotated with realism or bulky GAN priors to estimate realism.", + "bbox": [ + 75, + 448, + 468, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Realism Network", + "text_level": 1, + "bbox": [ + 76, + 555, + 246, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When editing specific regions in an image, it is challenging to maintain the overall realism of the photograph. How quickly realism starts to degrade depends on the contents and size of the image regions, the overall composition of the scene, as well as the type of edits being applied. This makes the problem of defining precisely when an image edit stops looking realistic particularly challenging.", + "bbox": [ + 75, + 580, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we propose to train a realism network using only realistic and unrealistic examples at the extremes. We generate realistic edits by slightly perturbing image values, and unrealistic edits by applying aggressive edits. We show that, despite being trained on binary data, our network can estimate continuous realism scores that can adapt to different types of image regions and scenes. Our approach was inspired by the work of Zhu et al. [26], who similarly learn their realism from binary real and synthetic composites.", + "bbox": [ + 75, + 688, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate real and fake samples, we exploit different parameter ranges for commonly used editing operations - exposure, saturation, color curve, and white balancing (formal definitions in the Supplementary Material). For instance, increasing the exposure of a region too much can", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "result in an unrealistic image, while a subtle increase to saturation will not significantly affect the realism. Based on experimentation, we determined the set of parameter ranges in Tab. 1 to apply to image regions to create our training data.", + "bbox": [ + 496, + 448, + 890, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate a training example, we first select a random number of edits (between 1-4), then an order for the edit operations (e.g., exposure, saturation, color curve, white balancing), and values for each of the operations, sampled uniformly at random from the pre-specified ranges in Tab. 1. We apply these edits in the selected order to a region segment in an MS-COCO image [12]. Fake examples are generated by purposefully selecting extreme values. Real examples are generated by sampling subtle edits within narrower ranges. Because of the semantic importance of human faces and increased sensitivity to edits in facial regions, we enforce smaller parameter ranges when applying edits to faces. Fig. 4 shows several examples.", + "bbox": [ + 496, + 508, + 890, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use the Pix2Pix [6] network architecture followed by two MLP layers to estimate the realism score $\\mathcal{R}$ of the input. For our samples in the training data, $\\mathcal{R}$ is defined as 1 for real and 0 for fake samples. We also condition the output on the input region by feeding the region's mask $M$ as input to the network. We use squared error [13] as the critic to compute the loss on the estimated value:", + "bbox": [ + 496, + 705, + 890, + 810 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s c}} = \\frac {1}{2} \\mathcal {R} \\left(I _ {\\text {f a k e}}, M\\right) ^ {2} + \\frac {1}{2} \\left(\\mathcal {R} \\left(I _ {\\text {r e a l}}, M\\right) - 1\\right) ^ {2} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 818, + 890, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I_{\\text{fake}}$ and $I_{\\text{real}}$ are the generated fake and real samples. To measure the effect of the edit on the realism of the image, we compute the difference between the scores", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "188", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/22b4a60b2c730aea0f38bba89b437305e5555cf31fc478077c36421bde29edab.jpg", + "image_caption": [ + "input image" + ], + "image_footnote": [], + "bbox": [ + 80, + 99, + 174, + 159 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/03736c736377979b37bf43d9134b74200f42ab9c99eeed352040f93599cecf6d.jpg", + "image_caption": [ + "mask" + ], + "image_footnote": [], + "bbox": [ + 176, + 99, + 271, + 159 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4a0a79412b08ed55c0e1fe5271030261d1cd025c6428824b43bb414dcda08ab9.jpg", + "image_caption": [ + "real sample" + ], + "image_footnote": [], + "bbox": [ + 274, + 99, + 370, + 159 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4d02041288aad014cbe82bf3bc8cf1934c2e0e5a4c291ece93e26974cbc4491f.jpg", + "image_caption": [ + "fake sample" + ], + "image_footnote": [], + "bbox": [ + 372, + 99, + 467, + 159 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/67c6393477e39e978f6ba03a1ff34f162fcee54650285deae42693ef1fbeaffa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 161, + 174, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e47c5b9d615a125972549b67ba9ced94910c20511490d26477063ee6a727a81e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 176, + 161, + 271, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7e013ee51966eb2c6fddddbab19fa09bd8089229c33eda5edd756795c20bb3aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 161, + 370, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d356ef9a8def814d325434f68c9e3fb637a1dcfee5df195999e3980b18a21803.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 161, + 467, + 220 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8887b35525fd7edbbe645162c616341476e6756bfc5c0d36df2eba403d4386f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 220, + 174, + 279 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/09405ba0433a8a897dc574cd8c5332d33c0061bcac52f21306b1276e790c8306.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 176, + 220, + 271, + 279 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0e927f3a314c24b374607e076ab3fc6fc73077692ef50658e1adc24faa799bed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 220, + 370, + 279 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3c6c8be9fb92f317befd01547187b0dd0f908b40d5bc57e7806f8a940d6ec8e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 220, + 467, + 279 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/18eff5f06f7de915ce64ff22d1134c6bb61ec999d07f1d1ab9c5f7119fbd5726.jpg", + "image_caption": [ + "Figure 4. Examples of fake and real images that are used to train the realism estimation network. See Section 3 for more details." + ], + "image_footnote": [], + "bbox": [ + 80, + 282, + 174, + 340 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9f984f6eab4fc07b1ac0b1c1de6cbe5f9d5b8ba70f54acdca84a96a52e4b5f50.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 176, + 282, + 271, + 340 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/51be0d266cf6c68cfcc12b8c0202ec65f4463d9592ec61023f7a38966bd61a44.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 282, + 370, + 340 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1e5962353525750138cbaeece2ed47f36dbcf7b95fd871db48465294fe56cbb8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 282, + 467, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "estimated for the original image $I$ and the edited image $I^{\\prime}$", + "bbox": [ + 76, + 386, + 464, + 402 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\mathcal {R} (I ^ {\\prime}, I, M) = \\mathcal {R} (I ^ {\\prime}, M) - \\mathcal {R} (I, M), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 419, + 467, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the edited region is defined by the mask $M$ .", + "bbox": [ + 76, + 452, + 410, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As Fig. 3 demonstrates $\\Delta \\mathcal{R}$ gives us continuous realism values for a range of edit parameters, despite the network being trained only on extreme cases. It also shows that the range of edits that are considered realistic by our network is not the same for each image and depends on the subject and editing operation. We show more examples of edits that are classified realistic or unrealistic by our network in Fig. 9 and the Supplementary Material.", + "bbox": [ + 75, + 470, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Saliency Guided Image Enhancement", + "text_level": 1, + "bbox": [ + 76, + 612, + 415, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We develop a saliency-guided image editing pipeline that enforces our realism loss to generate realistic and effective object enhancement or distractor suppression results for a given mask. Our system can estimate a set of editing parameters for any permutation of 4 editing operators: exposure, saturation, color curve, and white balancing.", + "bbox": [ + 75, + 641, + 468, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In constructing our system, we borrow many ideas from the existing saliency-guided image editing literature, and focus our design improvements on improving the realism of the results, especially by including our proposed realism loss. Since these edit operations are non-linear, different orderings of edits changes the end results. As a result, we condition the regressed parameters on the permutation of the edit operations by feeding the permutation as an input to the network. More details on the architecture of the network and the embedding used to encode the permutation is included in the Supplementary Material.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Saliency Loss A pretrained saliency model [7] (SalNet) is used as a proxy for the viewer attention that would be captured by image regions before and after applying the edits, to supervise the image editing process.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We measure the change in the saliency of the region of interest as the expected value of its relative change within the masked region:", + "bbox": [ + 498, + 152, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS (I, I ^ {\\prime}, M) = \\mathbb {E} _ {M} \\left[ \\frac {S a l N e t (I) - S a l N e t \\left(I ^ {\\prime}\\right)}{S a l N e t (I)} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 207, + 890, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{E}$ denotes the expectation and $M$ is the region mask.", + "bbox": [ + 498, + 250, + 888, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As Fig. 2 shows, the predicted saliency heatmaps can change drastically when applied to unrealistic edits. As a result, relying on conventional metrics (e.g., absolute and relative differences by [1, 17], Binary cross entropy by [2] and KL-divergence by [4]) to measure the change in saliency can cause large rewards or penalties during optimization. Infinitely large rewards for an unreal edit reduces the effectiveness of the realism term in the final loss function. To tackle this issue we define our saliency loss function as:", + "bbox": [ + 496, + 266, + 890, + 401 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s a l}} = \\exp \\left(w _ {\\mathrm {s a l}} S \\left(I, I ^ {\\prime}, M\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 416, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When saliency moves in the desired direction, the exponential squashes the loss, converging to the minimum and reducing the penalty quickly, acting as a soft margin. This converging behaviour prevents large rewards that can be generated by unrealistic edits during training. The exponential term imposes larger penalties when saliency moves in the wrong direction, providing robustness against outliers and faster convergence. $w_{sal}$ controls the absolute value of the loss to balance the weight of saliency loss in our final loss, which we set to 5 and -1 for amplification and attenuation, respectively.", + "bbox": [ + 496, + 439, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Realism Loss The realism loss is defined as:", + "bbox": [ + 500, + 625, + 807, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e a l i s m}} = R e L U \\left(- \\Delta \\mathcal {R} \\left(I ^ {\\prime}, I, M\\right) - b _ {r}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 651, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This loss is designed to penalize unrealistic edits, while giving no rewards for edits that improve the estimated realism score of the input. This prevents the network from being penalized by images that receive a low realism score even before any edits are applied. ReLU and offset $b_{r}$ provide a margin that allows a slight decrease in realism without a penalty which we set to 0.1 in our experiments.", + "bbox": [ + 496, + 678, + 890, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train two separate networks for each. The final network objective is the product of the two loss functions:", + "bbox": [ + 498, + 785, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\left(1 + \\mathcal {L} _ {\\text {r e a l i s m}}\\right) \\times \\mathcal {L} _ {\\text {s a l}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 827, + 890, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this formulation, the realism score acts as a weight for the penalty imposed on the change in the saliency. This allows us to balance the realism and saliency objectives.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "189", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/674e73ff803d84b37c9b76fb66062c020f5001665c89f667de9e5579f2cee235.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 80, + 103, + 142, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a98a37bad8ddb806d3250900c7baeca2c25edaa98d490cb66ce214d9bcec3655.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 153, + 104, + 200, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a9446a398355e291d77d3b1d746185cb04cd3cac425ff114c46cd8a8faf952cc.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 210, + 103, + 274, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/43839945dba9c65df9c63ae7bb5c4c832c358115d9bbb06a50cae0af83aa3da9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 103, + 331, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7663b1b6360ee353b160ac5e01b7f562bba842ba2dcd1ac488be10b998505714.jpg", + "image_caption": [ + "Deepsal [1]" + ], + "image_footnote": [], + "bbox": [ + 343, + 103, + 406, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3cfdcd560cb527914a62d7c538f7fdb8babcdc71ae95fd97a214801997f3ab96.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 104, + 467, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1329578e38f38d77bdde716ed87bea42676a3b865e5853b7204d379f676c893b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 172, + 142, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3bbde154481c544144f84df7585edfbb81fbcd0553d30ba71650ccd9f3e1525d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 153, + 172, + 200, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/02306e78ae81478a24ddca63b2d7cf3f04a24b6ae5f25449426442266b021c41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 172, + 274, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2d544baf8e4f0b05afb8a7ae7b1fa9154996ed8c9a2e3420255f636fd81f0425.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 172, + 331, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0641d056ade22e5ead63e24a1e296c23b97a138356b657e9a3540db0a9bbcc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 172, + 406, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ab9bd7ced6182431e51fa7b5c573ddd573a6fe3608c62eb621d07bffa8d49a7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 172, + 462, + 198 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c8452fde715f54f12fdb11b603e14f692eb08b1e96c17c774dd11595e3ecac3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 210, + 142, + 275 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e8fe706dd4062330e84a332b198ff6246c4af6443a52cc7a695c8c97f0e60a5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 210, + 202, + 273 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/220db1fcffde423104bf0d1e5e28d18ca7099f7484576687b8b2a260d8832c18.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 210, + 274, + 273 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/89f7d611ba0f3e6f21eb93b5146843946cb81da49399b3f9f8f0e94b12925100.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 210, + 333, + 273 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/64bb11ebfa2776a537607c49c0000bd5e0d50b026cc64ece2f781d49bee2e154.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 210, + 406, + 273 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8d46a7e3b84e35889971a5821b7e6d8efb4b43791967597f3731c6d84220a8f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 210, + 467, + 273 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8a1dd1c0d7d5abc0b71a59210b97badc80bbbeb390dece1d8d9b943ac3aaecba.jpg", + "image_caption": [ + "Figure 5. Saliency attenuation compared to Deepsal [1] on the images provided by the authors on their project webpage. Our method is able to effectively attenuate the saliency of the target region without applying an unrealistic camouflage." + ], + "image_footnote": [], + "bbox": [ + 80, + 277, + 142, + 343 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1fad9ffaabedf36770c473c0827e0daec70aeccf37dd00040fd21400093ec951.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 277, + 202, + 342 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2a89150c1984cce5c5cd8f84ce409f343234274c67bd8960f1b8ce6c429c7958.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 277, + 274, + 342 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8f30414d86206e6616c529032bf440ad6a7c8041fac50879396531031a0c18ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 277, + 334, + 342 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/65d4de9f46979dd56e52c5a258a6c29067fb8626b350cdb441dafe5736b5cc2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 277, + 406, + 342 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/29fcc1686ff6f545c7e04039e2840cedff5656d039ba605260cfb3a68177ec64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 277, + 467, + 342 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use an EfficientNet-lite3 [21] backbone and cascaded MLP layers as decoders to estimate parameters for each of the edit operations. A detailed explanation of the architecture specifics, datasets and training is provided in Supplementary Material.", + "bbox": [ + 76, + 415, + 468, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 517, + 310, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our method against state of the art saliency based image editing approaches - Deepsal [1], Gazeshift [17] and MEC [16]. MEC provides results on their dataset alongside pre-computed results of WRS [23] and OHR [15] on the same dataset. We use this dataset to compare against WRS and OHR as well as MEC.", + "bbox": [ + 76, + 546, + 468, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The EfficientNet [21] backbone used in our architecture is known for its small size. Our results are thus generated significantly faster than the other state-of-the-art (SOTA) methods with bulkier architectures and slower per-image optimizations. Based on speed measures reported in [17] Table 1c, MEC takes more than a day, OHR needs 30 seconds and Gazeshift takes 8 seconds to process each image, while our model requires only 8ms per image.", + "bbox": [ + 76, + 641, + 468, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We present both qualitative and quantitative results. Since our method takes the permutation of the edits as input during inference time we select the permutation at random for the presented results unless mentioned otherwise.", + "bbox": [ + 76, + 765, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Qualitative Comparison", + "text_level": 1, + "bbox": [ + 500, + 90, + 720, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figs. 5, 6, and 7 illustrate our results compared to the SOTA. They show our method performs different edits based on the contents of the image. It can apply more significant color changes that camouflage the distractor $(2^{\\mathrm{nd}}$ and $4^{\\mathrm{th}}$ rows of Fig. 6, $3^{\\mathrm{rd}}$ row of Fig. 5) or very subtle edits for human faces $(1^{\\mathrm{st}}$ row of Fig. 6). The intensity and characteristics of the applied edits depends on semantics.", + "bbox": [ + 496, + 114, + 890, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The use of adversarial loss in Gazeshift [17] and the regularization used in Deepsal [1] constrain the edits their methods apply without taking realism explicitly into account. As results show, they often apply unrealistic edits (e.g., the camouflaged signs in Fig. 5 or the unnatural skin tone and the color artifacts in Fig. 6) or very subtle edits with lower effectiveness.", + "bbox": [ + 496, + 220, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MEC [16] reuses the color patterns and textures available in the image to update the target region. On the other hand different regions and textures can correspond to different semantics. Consequently, as illustrated in Fig. 7a this method can apply incompatible color and texture values to produce unrealistic edits (green crocodile eye, orange traffic sign) or ineffective enhancements (brown bird). Fig. 7b provides a comparison on their distractor suppression image set. Our method performs comparable in terms of effectiveness and generates realistic results consistently.", + "bbox": [ + 496, + 327, + 890, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "OHR [15] tries to maximize the color distinction between the masked region and the rest of the image for the image enhancement task. Without explicit realism modeling, it tends to generate unrealistic colors (e.g., blue crocodile, bird, and horse in Fig. 7a). While incorrect colors increase the saliency of these regions, they do so at the cost of realism. For similar reasons, this method is ineffective suppressing distractors (Fig. 7b).", + "bbox": [ + 496, + 479, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "WRS [23] does not generate unrealistic images, but also makes edits that are hardly noticeable, and less effective at enhancing or suppressing the target regions. We believe this is due to the purposely limited range of allowed edit parameters (luminance, saturation and sharpness).", + "bbox": [ + 496, + 599, + 890, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. What Do Photographers Think?", + "text_level": 1, + "bbox": [ + 500, + 686, + 782, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To include the perspective of professional photographers in comparing our results to others, we ran a user study. We report our results using three choices of parameter orderings: choosing the one that achieves the Best Saliency, the one that generates the Best Realism (according to our realism estimation network), and a permutation of parameters selected at Random as used for the qualitative figures.", + "bbox": [ + 496, + 710, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "User Study We recruited 8 professionals from UpWork, all of whom have multiple years of experience with photography, as well as using Photoshop to edit photos. We used the Appen platform for hosting our rating tasks.", + "bbox": [ + 500, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1Deepsal, WRS and MEC do not provide an open-source implementation. Hence, we relied on the results included on their project pages. Also, Deepsal authors kindly provided us with results on Adobe Stock dataset for their \"convolutional network\" variation.", + "bbox": [ + 76, + 849, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "190", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8a53c614ea083348e103a3fc4476d52431fe2c1420d76dda2ea2f90b9edf16d9.jpg", + "image_caption": [ + "Figure 6. Saliency modulation compared to GazeShift [17] and Deepsal [1] on Adobe Stock images from [17]." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 609, + 429 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2df726e8aa4fb412c92710525e2fb13fcb7715ebc20e4d42857483b02d78e2f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 88, + 893, + 429 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d818a347ef52d037a2d446c3d37c043a36170f538e4f573fc6f2f74b754ff01b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 458, + 480, + 691 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe536d135db8b2522230045c99701696dd7b61fa7bf91bf50d9fe3a20a306405.jpg", + "image_caption": [ + "Figure 7. Saliency modulation compared to MEC [16], WRS [23] and OHR [15] on the Mechrez dataset [16]." + ], + "image_footnote": [], + "bbox": [ + 483, + 458, + 888, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our study participants were presented with a panel of 3 images: the original image, mask, and an edited result from one of methods evaluated. They were asked to \"rate each image based on 2 criteria\" - effectiveness and realism, with the following definitions provided for the attenuate version of the task: \"The images were edited to make certain objects and regions less distracting. An image edit is effective if the masked objects/regions have indeed become less distracting. An image edit is realistic if the photo does not look edited.\" For the amplify version of the task, the wording for effectiveness was modified to: \"The im", + "bbox": [ + 75, + 729, + 473, + 896 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ages were edited to make certain objects and regions pop-out (more attention-capturing, or salient). An image edit is effective if the masked objects/regions have indeed become more attention-capturing.\" Images were randomly shuffled in each task, so the photographers rated the images and methods independently of each other.", + "bbox": [ + 496, + 729, + 893, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results In Tab. 2 we compare our approach to GazeShift and Deepsal on the 30 Adobe Stock images from [17]. We find that our approach achieves significantly higher scores for both effectiveness and realism compared to GazeShift in", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "191", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b47f9ad1f0d1e99fe3d27c9cd06072119c7bcac087f449553e5a0a777348aa30.jpg", + "table_caption": [ + "Table 2. Photographer ratings (on a 1 to 10 scale, higher is better) of effectiveness (i.e., achieve objective of attenuation or amplification of saliency) and realism (i.e., photo looks natural) on the dataset of 30 Adobe stock images. Numbers are the mean score across 8 photographers, with standard deviation in parentheses." + ], + "table_footnote": [], + "table_body": "
MethodSaliency AttenuationSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
GazeShift [17]4.78 (2.89)5.93 (3.13)7.36 (2.37)7.07 (2.76)
DeepSal [1]4.04 (2.90)8.49 (2.72)--
Ours - Best Realism6.56 (2.73)6.78 (2.70)7.39 (2.17)8.31 (1.89)
Ours - Random6.36 (2.79)6.34 (2.88)7.36 (2.21)8.27 (1.94)
Ours - Best Saliency6.64 (2.79)6.31 (2.70)7.50 (2.08)8.15 (2.10)
", + "bbox": [ + 81, + 161, + 467, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e05d202ff6bd6d556c5010f8fb49ed1fa175ba32d094ed54304610b8235f8b05.jpg", + "table_caption": [ + "Table 3. Photographer ratings as in Tab. 2 on (a) Mechrez [16] dataset and (b) the 14 images from DeepSal project webpage [1]" + ], + "table_footnote": [], + "table_body": "
MethodSaliency AttenuationMethodSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
Deepsal [1]7.08 (2.84)5.82 (3.43)MEC [16]7.06 (2.68)7.31 (2.93)
WRS [23]5.41 (3.22)7.97 (2.70)
Ours - Random6.83 (2.52)7.41 (2.70)OHR [15]7.04 (3.04)5.18 (3.76)
Ours - Random6.24 (2.9)8.88 (1.74)
(b)
", + "bbox": [ + 81, + 277, + 467, + 343 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the attenuation task. This matches our qualitative observations that GazeShift is not successful at the task of attenuating distractor. GazeShift specializes in amplifying saliency in image regions, and we achieve similar performance on this task, while also maintaining significantly higher realism levels. In addition, results show a poor effectiveness score for Deepsal as a result of subtle edits in Fig. 6. Subtle edits mean the realism score remains high since the results are almost identical to the original images.", + "bbox": [ + 75, + 351, + 467, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since Deepsal was ineffective on Adobe Stock images, to provide a fair comparison we also compare to Deepsal on 14 images they provided on their project page in Tab. 3a. We achieve significantly higher realism scores while being similarly effective at reducing the saliency of the distractors. This matches our qualitative observations that Deepsal edits can be quite extreme and not always photo realistic.", + "bbox": [ + 75, + 487, + 467, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 3b shows user study results on Mechrez dataset [16].2 We used 77 images from the dataset to perform the user study. Results confirm that our results are superior in the realism while we achieve a comparable effectiveness compared MEC. WRS's low effectiveness yields a high realism score as its results are almost identical to the input; while the unrealistic color changes by OHR result in low realism and effectiveness scores.", + "bbox": [ + 75, + 592, + 467, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 722, + 228, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We trained a variation of our method in which instead of a fixed realism score estimation model we used a discriminator as adversarial loss. We trained the discriminator as part of an adversarial training approach, similar to related work [2, 4, 17]. We used the input image as the real sample and the generated image as the fake sample during training. Fig. 8 illustrates sample results with this training strategy. Since the discriminator is trained to penalize \"any edits\"", + "bbox": [ + 75, + 744, + 467, + 866 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a879f63575a952e3215679c5605db540383c8aaa8885e9e9d839bab01363e272.jpg", + "image_caption": [ + "Input image", + "Figure 8. When the model trained via adversarial training produces results that are effective at reducing saliency, the resulting images are not realistic according to our user study." + ], + "image_footnote": [], + "bbox": [ + 501, + 99, + 586, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c8d51c7ae5a9f4cfafcdb0aa1619b1b87b70b0b197401c5c60d2b2fdf4da2dbe.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 606, + 99, + 710, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/25a13bee357db83fe9085346adb2bf1efa1fcfca4d5f90e0f0643e999a80f4a3.jpg", + "image_caption": [ + "Adversarial training" + ], + "image_footnote": [], + "bbox": [ + 736, + 99, + 843, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8b98bcd1baeea115b74cd5f72eb9697bc9f9773c4687e6400a46a91e69396c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 852, + 99, + 890, + 133 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2639ae48266256492b7c30f3914666626d588b7466179e80ef32f4536addeb6d.jpg", + "table_caption": [ + "Table 4. Photographer ratings as in Tab. 2 comparing our main method to a variation with adversarial training instead of our fixed realism network." + ], + "table_footnote": [], + "table_body": "
MethodSaliency Attenuation
Effectiveness ↑Realism ↑
Adversarial Training5.06 (2.84)7.36 (3.07)
Ours - Random6.36 (2.79)6.34 (2.88)
", + "bbox": [ + 560, + 311, + 828, + 358 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "applied in the previous steps of training it encourages the network to apply subtle edits and hence a drop in effectiveness of the method. On the other hand, due to the lack of explicit realism training, the edits are unrealistic while the effectiveness is reasonable. Ratings reported in Tab. 4 also confirm our findings.", + "bbox": [ + 498, + 383, + 890, + 473 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Diversity and Optimality of Estimated Edits", + "text_level": 1, + "bbox": [ + 500, + 482, + 872, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 9b illustrates the distribution of edit parameters estimated by our parameter estimation network for different images on ADE20K [24, 25] dataset. It shows that edit parameters are different for each image and is based on its content. Also, it shows that the range of estimated edits is not the same as the ranges used in Tab. 1 for real samples.", + "bbox": [ + 498, + 506, + 890, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate if the estimated edits are close to optimal with respect to realism, we provide Fig. 9a. In the figure we show a realism heatmap obtained by adding a small additive constant to the estimated edit parameter of saturation and exposure. Heatmaps show the estimated edit parameters (center of the heatmap) are in the optimal realism region. Changing the edit parameters in each direction reduces the realism of the end result.", + "bbox": [ + 498, + 597, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Generalization to Multiple Image Regions", + "text_level": 1, + "bbox": [ + 500, + 726, + 856, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since our model only modifies the region of interest, and performs a forward pass efficiently, we can run it on multiple regions and multiple masks by generating edit parameters for each region, in an iterative manner. Examples are provided in Figs. 1 and 10. We used the same approach with Gazeshift [17], which edits the whole image by estimating two sets of edit parameters, one for the region of interest (foreground) and one for the background. This formulation of Gazeshift makes iterative editing impractical, since there would be contradictory objectives between the", + "bbox": [ + 498, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "$^{2}$ Dataset has only 10 images for attenuation task, which is inadequate for a meaningful user study. Hence we only provide amplification results.", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "192", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/347300b4e5dfe3e80eed0f428547ab1b9a77ff8763de8bb21ef19e8adba761dc.jpg", + "image_caption": [ + "(a) A heatmap visualizes the realism score achieved when we change the estimated saturation (x-axis) and exposure (y-axis). Our estimated values (center of the heatmap) achieve the optimal realism while changing the parameters in any direction reduces the realism. Sample edited images and their corresponding location in the heatmap are also visualized." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 553, + 301 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/997ebff0f137825fe1948a82de0d4048e45ee601bd2cf3013c03982b2f5acfff.jpg", + "image_caption": [ + "(b) The diversity of estimated parameters on ADE20K [24, 25] dataset. The x-axis is the range of each parameter. The attenuation task is blue, and amplification is labeled red." + ], + "image_footnote": [], + "bbox": [ + 588, + 114, + 875, + 296 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e924c57b8cc9da8f01d4050f705763fb6eb08c70b7a006052214bb1d72ea9ac3.jpg", + "image_caption": [ + "Figure 9. Visualizing diversity and optimality of edit parameters estimated by our method", + "Figure 10. Given an input image and masks to attenuate and amplify(left), Gazeshift when used iteratively on each object suffers from color artifacts (center top, faces, bowl and watermelons). Ours produces a notably more realistic and effective result (right). Contradictory objective of edits applied to background and foreground, Gazeshift fails to generalize to multiple regions and omitting the background edits (center bottom) reduces the effectiveness of the edits. Image credit: @tysonbrand" + ], + "image_footnote": [], + "bbox": [ + 78, + 380, + 468, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "iterations (what is foreground in one iteration becomes a background in the next iteration). For a more practical comparison, we omit background edits when running Gazeshift. Figure 10 shows that Gazeshift performance suffers on an iterative saliency enhancement task, but our method is able to generalize to multiple regions robustly.", + "bbox": [ + 75, + 667, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Limitations", + "text_level": 1, + "bbox": [ + 76, + 770, + 204, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The global edits (applying the same edits to every pixel inside a mask), used in both our method and Gazeshift [17] require an accurate mask of the target region. As shown in Fig. 11 mask imperfections can cause unsmooth transitions around the boundaries. In these cases, pixel-wise optimization approaches like Deepsal [1] and MEC [16] do not suffer from heavy artifacts due to mask imperfections.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f17285b3ddb311a9d3cbf680f5270dc08aa270d7e3f6cc426adea45049c5df8.jpg", + "image_caption": [ + "Figure 11. The effect of non-smooth mask boundaries. Left, an input image has a mask with a sharp edge. Center, our method and Gazeshift [17] produce strong boundary artifacts around the mask region (see inset). Right, MEC [16] and Deepsal [1] do not exhibit this problem because they operate in a pixel-wise manner." + ], + "image_footnote": [], + "bbox": [ + 501, + 381, + 893, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Future work", + "text_level": 1, + "bbox": [ + 500, + 641, + 764, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We describe a method to edit images using conventional image editing operators to attenuate or amplify the attention captured by a target region while preserving image realism. Realism is achieved by introducing an explicit, and separate realism network that is pre-trained to distinguish edited images. This strategy to achieve realism is distinct from prevailing approaches, including adversarial training schemes, as it introduces an additional form of weak supervision—manually specified ranges of parameter values that correspond to realistic and unrealistic (\"fake\") edits. Training with this realism critic makes it possible to estimate saliency modulating image edits that are significantly more realistic and robust. Together with our millisecond-level inference time, our approach offers a practical and deployable application of saliency guided image editing.", + "bbox": [ + 496, + 674, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "193", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kfir Aberman, Junfeng He, Yossi Gandelsman, Inbar Mosseri, David E. Jacobs, Kai Kohlhoff, Yael Pritch, and Michael Rubinstein. Deep saliency prior for reducing visual distraction. In Proc. CVPR, 2021. 1, 2, 4, 5, 6, 7, 8", + "[2] Yen-Chung Chen, Keng-Jui Chang, Yi-Hsuan Tsai, Yu-Chiang Frank Wang, and Wei-Chen Chiu. Guide your eyes: Learning image manipulation under saliency guidance. In Proc. 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ICCV, 2015. 2, 3" + ], + "bbox": [ + 501, + 92, + 890, + 530 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "194", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_model.json b/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c705d49b030673b1de4157789e9d6b7fc8fd659b --- /dev/null +++ b/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_model.json @@ -0,0 +1,2748 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.131, + 0.723, + 0.154 + ], + "angle": 0, + "content": "Realistic Saliency Guided Image Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.173, + 0.834, + 0.194 + ], + "angle": 0, + "content": "S. Mahdi H. Miangoleh1 Zoya Bylinskii2 Eric Kee2 Eli Shechtman2 Yaqiz Aksoy1" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.201, + 0.681, + 0.22 + ], + "angle": 0, + "content": "\\(^{1}\\) Simon Fraser University \\(^{2}\\) Adobe Research" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.253, + 0.379, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.298, + 0.256, + 0.377, + 0.269 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.258, + 0.488, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.304, + 0.487, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.363, + 0.488, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.258, + 0.583, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.592, + 0.255, + 0.892, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.424, + 0.216, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.459, + 0.298, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.305, + 0.425, + 0.441, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.447, + 0.425, + 0.583, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.417, + 0.892, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.572, + 0.894, + 0.614 + ], + "angle": 0, + "content": "Figure 1. (top) We develop a saliency-based image enhancement method that can be applied to multiple regions in the image to demephasize objects (steps 1, 2) or enhance subjects (steps 3, 4). (bottom) Our novel realism loss allows us to apply realistic edits to a wide variety of objects while state-of-the-art methods [1, 17] may generate less realistic editing results." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.626, + 0.314, + 0.641 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.645, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Common editing operations performed by professional photographers include the cleanup operations: de-emphasizing distracting elements and enhancing subjects. These edits are challenging, requiring a delicate balance between manipulating the viewer's attention while maintaining photo realism. While recent approaches can boast successful examples of attention attenuation or amplification, most of them also suffer from frequent unrealistic edits. We propose a realism loss for saliency-guided image enhancement to maintain high realism across varying image types, while attenuating distractors and amplifying objects of interest. Evaluations with professional photographers confirm that we achieve the dual objective of realism and effectiveness, and outperform the recent approaches on their own datasets, while requiring a smaller memory footprint and runtime. We thus offer a viable solution for automating image enhancement and photo cleanup operations." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.631, + 0.631, + 0.646 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.853 + ], + "angle": 0, + "content": "In everyday photography, the composition of a photo typically encompasses subjects on which the photographer intends to focus our attention, rather than other distracting things. When distracting things cannot be avoided, photographers routinely edit their photos to de-emphasize them. Conversely, when the subjects are not sufficiently visible, photographers routinely emphasize them. Among the most common emphasis and de-emphasis operations performed by professionals are the elementary ones: changing the saturation, exposure, or the color of each element. Although conceptually simple, these operations are challenging to apply because they must delicately balance the effects on the viewer attention with photo realism." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To automate this editing process, recent works use saliency models as a guide [1,2,4,8,16,17]. These saliency models [3,7,10,14,19] aim to predict the regions in the" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "186" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.257 + ], + "angle": 0, + "content": "image that catch the viewer's attention, and saliency-guided image editing methods are optimized to increase or decrease the predicted saliency of a selected region. Optimizing solely based on the predicted saliency, however, often results in unrealistic edits, as illustrated in Fig. 1. This issue results from the instability of saliency models under the image editing operations, as saliency models are trained on unedited images. Unrealistic edits can have low predicted saliency even when they are highly noticeable to human observers, or vice versa. This was also noted by Aberman et al. [1], and is illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.454 + ], + "angle": 0, + "content": "Previous methods tried to enforce realism using adversarial setups [2, 4, 8, 17], GAN priors [1, 8], or cycle consistency [2] but with limited success (Fig. 1). Finding the exact point when an image edit stops looking realistic is challenging. Rather than focusing on the entire image, in this work, we propose a method for measuring the realism of a local edit. To train our network, we generate realistic image edits by subtle perturbations to exposure, saturation, color or white balance, as well as very unrealistic edits by applying extreme adjustments. Although our network is trained with only positive and negative examples at the extremes, we successfully learn a continuous measure of realism for a variety of editing operations as shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.56 + ], + "angle": 0, + "content": "We apply our realism metric to saliency-guided image editing by training the system to optimize the saliency of a selected region while being penalized for deviations from realism. We show that a combined loss allows us to enhance or suppress a selected region successfully while maintaining high realism. Our method can be also be applied to multiple regions in a photograph as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.473, + 0.696 + ], + "angle": 0, + "content": "Evaluations with professional photographers and photo editors confirm our claim that we maintain high realism and succeed at redirecting attention in the edited photo. Further, our results are robust to different types of images including human faces, and are stable across different permutations of edit parameters. Taken together with our model size of 26Mb and run-time of 8ms, these results demonstrate that we have a more viable solution for broader use than the approaches that are available for these tasks to date." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.22, + 0.725 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Various image enhancement methods have been introduced in the literature to amplify a region of interest or de-emphasise distracting regions, improve image aesthetics, and redirect the viewer's attention. This task has been referred to as attention retargeting [15] or reattentionizing [18] as well. Earlier methods [5,15,20,22,23] incorporated prior knowledge of saliency cues (saturation, sharpness, color, gamut, etc.) to guide the editing process to achieve the desired change in saliency. But, relying solely on saliency cues both limits the diversity of generated edits, and creates unrealistic edits due to the lack of semantic" + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.095, + 0.588, + 0.105 + ], + "angle": 0, + "content": "Original image" + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.095, + 0.68, + 0.105 + ], + "angle": 0, + "content": "Saliency map" + }, + { + "type": "image_caption", + "bbox": [ + 0.715, + 0.095, + 0.774, + 0.105 + ], + "angle": 0, + "content": "Edited image" + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.095, + 0.871, + 0.105 + ], + "angle": 0, + "content": "Saliency map" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.106, + 0.599, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.196, + 0.599, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.106, + 0.696, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.179, + 0.696, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.106, + 0.794, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.196, + 0.794, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.106, + 0.892, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.179, + 0.892, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.251, + 0.894, + 0.321 + ], + "angle": 0, + "content": "Figure 2. Predicted saliency maps [7] for the original images and edited versions, with extreme edits applied. Note that saliency models are typically trained with realistic images. This makes them susceptible to inaccurate predictions for unrealistic inputs, as the green woman in the top row estimated to have low saliency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.894, + 0.395 + ], + "angle": 0, + "content": "constraints. As our experiments show, OHR [15] tends to generate unrealistic color changes that are semantically incorrect, and WRS [23] is limited to contrast and saturation adjustments with limited effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.893, + 0.565 + ], + "angle": 0, + "content": "Recent works leverage saliency estimation networks [3, 7, 10, 14, 19] to optimize for a desired saliency map instead of relying on prior saliency cues. Saliency models are trained to output a heatmap that represents where human gaze would be concentrated in an image. These models are not trained to respond to the realism of the input image. Hence they might predict an inconsistent decrease or increase in the saliency of a region when unrealistic or semantically implausible edits are applied, which would be otherwise jarring to human viewers (Fig. 2). Using saliency as the only supervision can result in unrealistic images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.894, + 0.779 + ], + "angle": 0, + "content": "To prevent unrealistic edits, prior works enforce constraints on the allowable changes, use adversarial training [2, 4, 8, 17] or exploit learned priors from GAN-based models [1, 8]. For instance, Mechrez et al. [16] and Aberman et al. (Warping) [1] constrain the result to match the input content in order to maintain its appearance. Aberman et al. (CNN and Recolorization) [1] use a regularization term that limits the amount of change an image can undergo to maintain the realism. Mejjati et al. [17] designed a global parametric approach to limit the editing operations to a set of common photographic ones. Chen et al. [2] exploit cycle consistency to keep the output within the domain of the input image. Gatys et al. [4] use a texture loss alongside the VGG perceptual loss as a proxy for realism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Lalonde et al. [11] argue that humans prefer color consistency within images, regardless of object semantics. They use color statistics to measure realism and use it to recolor the images to match the background in compositing task. Zhu et al. [26] train a network to discriminate between natural images and computer-generated composites and use it as a realism measure for compositing task. Realism is also a crucial factor in GANs, as highlighted by [9]." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "187" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.147, + 0.09, + 0.82, + 0.103 + ], + "angle": 0, + "content": "Table 1. Parameter value ranges used to generate real and fake training images for the realism estimation network." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.106, + 0.887, + 0.169 + ], + "angle": 0, + "content": "
ExposureSaturationColor curveWhite balancingNumber of edits
Real[0.85, 1.15][0.85, 1.15][0.85, 1.15]Not allowed[1, 3]
Fake[0.5, 0.75] ∪ [1.5, 2][0, 0.5] ∪ [1.5 - 2][0.5, 2][0.9, 1][2, 4]
Fake(human specific)[0.5, 0.75] ∪ [1.25, 1.5][0.5, 0.75] ∪ [1.25, 1.5][0.5, 2]Not allowed[2, 3]
" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.183, + 0.184, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.184, + 0.306, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.185, + 0.418, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.185, + 0.532, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.185, + 0.647, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.649, + 0.185, + 0.706, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.185, + 0.763, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.185, + 0.821, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.185, + 0.88, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.285, + 0.185, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.285, + 0.306, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.285, + 0.418, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.285, + 0.532, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.285, + 0.647, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.649, + 0.285, + 0.706, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.285, + 0.764, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.285, + 0.821, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.285, + 0.88, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.391, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Figure 3. The efficacy of the realism estimation network is illustrated over a range of exposure and saturation adjustments. Left is \\(\\Delta \\mathcal{R}\\) plotted (vertical axis) for example images (second column) when selected regions (third column) are edited. Right, the edited images are shown with the corresponding change in estimated realism (inset numbers), and the value of the editing parameter applied (underneath)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.54 + ], + "angle": 0, + "content": "We present a new method for estimating the realism of a local edit. Combining our realism loss with saliency guidance, we show that we can successfully apply attention attenuation or amplification while keeping the final result realistic without requiring data annotated with realism or bulky GAN priors to estimate realism." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.556, + 0.247, + 0.571 + ], + "angle": 0, + "content": "3. Realism Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.469, + 0.688 + ], + "angle": 0, + "content": "When editing specific regions in an image, it is challenging to maintain the overall realism of the photograph. How quickly realism starts to degrade depends on the contents and size of the image regions, the overall composition of the scene, as well as the type of edits being applied. This makes the problem of defining precisely when an image edit stops looking realistic particularly challenging." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.825 + ], + "angle": 0, + "content": "In this work, we propose to train a realism network using only realistic and unrealistic examples at the extremes. We generate realistic edits by slightly perturbing image values, and unrealistic edits by applying aggressive edits. We show that, despite being trained on binary data, our network can estimate continuous realism scores that can adapt to different types of image regions and scenes. Our approach was inspired by the work of Zhu et al. [26], who similarly learn their realism from binary real and synthetic composites." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To generate real and fake samples, we exploit different parameter ranges for commonly used editing operations - exposure, saturation, color curve, and white balancing (formal definitions in the Supplementary Material). For instance, increasing the exposure of a region too much can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.509 + ], + "angle": 0, + "content": "result in an unrealistic image, while a subtle increase to saturation will not significantly affect the realism. Based on experimentation, we determined the set of parameter ranges in Tab. 1 to apply to image regions to create our training data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.705 + ], + "angle": 0, + "content": "To generate a training example, we first select a random number of edits (between 1-4), then an order for the edit operations (e.g., exposure, saturation, color curve, white balancing), and values for each of the operations, sampled uniformly at random from the pre-specified ranges in Tab. 1. We apply these edits in the selected order to a region segment in an MS-COCO image [12]. Fake examples are generated by purposefully selecting extreme values. Real examples are generated by sampling subtle edits within narrower ranges. Because of the semantic importance of human faces and increased sensitivity to edits in facial regions, we enforce smaller parameter ranges when applying edits to faces. Fig. 4 shows several examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.811 + ], + "angle": 0, + "content": "We use the Pix2Pix [6] network architecture followed by two MLP layers to estimate the realism score \\(\\mathcal{R}\\) of the input. For our samples in the training data, \\(\\mathcal{R}\\) is defined as 1 for real and 0 for fake samples. We also condition the output on the input region by feeding the region's mask \\(M\\) as input to the network. We use squared error [13] as the critic to compute the loss on the estimated value:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.819, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s c}} = \\frac {1}{2} \\mathcal {R} \\left(I _ {\\text {f a k e}}, M\\right) ^ {2} + \\frac {1}{2} \\left(\\mathcal {R} \\left(I _ {\\text {r e a l}}, M\\right) - 1\\right) ^ {2} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( I_{\\text{fake}} \\) and \\( I_{\\text{real}} \\) are the generated fake and real samples. To measure the effect of the edit on the realism of the image, we compute the difference between the scores" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "188" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.09, + 0.158, + 0.099 + ], + "angle": 0, + "content": "input image" + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.09, + 0.238, + 0.098 + ], + "angle": 0, + "content": "mask" + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.09, + 0.348, + 0.098 + ], + "angle": 0, + "content": "real sample" + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.09, + 0.445, + 0.098 + ], + "angle": 0, + "content": "fake sample" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.101, + 0.175, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.101, + 0.272, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.101, + 0.371, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.101, + 0.468, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.162, + 0.175, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.162, + 0.272, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.162, + 0.371, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.162, + 0.468, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.222, + 0.175, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.222, + 0.272, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.222, + 0.371, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.222, + 0.468, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.283, + 0.175, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.283, + 0.272, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.283, + 0.371, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.283, + 0.468, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.346, + 0.468, + 0.373 + ], + "angle": 0, + "content": "Figure 4. Examples of fake and real images that are used to train the realism estimation network. See Section 3 for more details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.387, + 0.465, + 0.403 + ], + "angle": 0, + "content": "estimated for the original image \\(I\\) and the edited image \\(I^{\\prime}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.42, + 0.468, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\Delta \\mathcal {R} (I ^ {\\prime}, I, M) = \\mathcal {R} (I ^ {\\prime}, M) - \\mathcal {R} (I, M), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.453, + 0.411, + 0.469 + ], + "angle": 0, + "content": "where the edited region is defined by the mask \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.469, + 0.592 + ], + "angle": 0, + "content": "As Fig. 3 demonstrates \\(\\Delta \\mathcal{R}\\) gives us continuous realism values for a range of edit parameters, despite the network being trained only on extreme cases. It also shows that the range of edits that are considered realistic by our network is not the same for each image and depends on the subject and editing operation. We show more examples of edits that are classified realistic or unrealistic by our network in Fig. 9 and the Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.613, + 0.416, + 0.631 + ], + "angle": 0, + "content": "4. Saliency Guided Image Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.469, + 0.732 + ], + "angle": 0, + "content": "We develop a saliency-guided image editing pipeline that enforces our realism loss to generate realistic and effective object enhancement or distractor suppression results for a given mask. Our system can estimate a set of editing parameters for any permutation of 4 editing operators: exposure, saturation, color curve, and white balancing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In constructing our system, we borrow many ideas from the existing saliency-guided image editing literature, and focus our design improvements on improving the realism of the results, especially by including our proposed realism loss. Since these edit operations are non-linear, different orderings of edits changes the end results. As a result, we condition the regressed parameters on the permutation of the edit operations by feeding the permutation as an input to the network. More details on the architecture of the network and the embedding used to encode the permutation is included in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Saliency Loss A pretrained saliency model [7] (SalNet) is used as a proxy for the viewer attention that would be captured by image regions before and after applying the edits, to supervise the image editing process." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.892, + 0.197 + ], + "angle": 0, + "content": "We measure the change in the saliency of the region of interest as the expected value of its relative change within the masked region:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.208, + 0.892, + 0.242 + ], + "angle": 0, + "content": "\\[\nS (I, I ^ {\\prime}, M) = \\mathbb {E} _ {M} \\left[ \\frac {S a l N e t (I) - S a l N e t \\left(I ^ {\\prime}\\right)}{S a l N e t (I)} \\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.251, + 0.89, + 0.266 + ], + "angle": 0, + "content": "where \\(\\mathbb{E}\\) denotes the expectation and \\(M\\) is the region mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.402 + ], + "angle": 0, + "content": "As Fig. 2 shows, the predicted saliency heatmaps can change drastically when applied to unrealistic edits. As a result, relying on conventional metrics (e.g., absolute and relative differences by [1, 17], Binary cross entropy by [2] and KL-divergence by [4]) to measure the change in saliency can cause large rewards or penalties during optimization. Infinitely large rewards for an unreal edit reduces the effectiveness of the realism term in the final loss function. To tackle this issue we define our saliency loss function as:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.417, + 0.891, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s a l}} = \\exp \\left(w _ {\\mathrm {s a l}} S \\left(I, I ^ {\\prime}, M\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.606 + ], + "angle": 0, + "content": "When saliency moves in the desired direction, the exponential squashes the loss, converging to the minimum and reducing the penalty quickly, acting as a soft margin. This converging behaviour prevents large rewards that can be generated by unrealistic edits during training. The exponential term imposes larger penalties when saliency moves in the wrong direction, providing robustness against outliers and faster convergence. \\( w_{sal} \\) controls the absolute value of the loss to balance the weight of saliency loss in our final loss, which we set to 5 and -1 for amplification and attenuation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.625, + 0.808, + 0.639 + ], + "angle": 0, + "content": "Realism Loss The realism loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.652, + 0.891, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e a l i s m}} = R e L U \\left(- \\Delta \\mathcal {R} \\left(I ^ {\\prime}, I, M\\right) - b _ {r}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.892, + 0.785 + ], + "angle": 0, + "content": "This loss is designed to penalize unrealistic edits, while giving no rewards for edits that improve the estimated realism score of the input. This prevents the network from being penalized by images that receive a low realism score even before any edits are applied. ReLU and offset \\( b_{r} \\) provide a margin that allows a slight decrease in realism without a penalty which we set to 0.1 in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.786, + 0.891, + 0.815 + ], + "angle": 0, + "content": "We train two separate networks for each. The final network objective is the product of the two loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.828, + 0.891, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\left(1 + \\mathcal {L} _ {\\text {r e a l i s m}}\\right) \\times \\mathcal {L} _ {\\text {s a l}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "In this formulation, the realism score acts as a weight for the penalty imposed on the change in the saliency. This allows us to balance the realism and saliency objectives." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "189" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.09, + 0.184, + 0.102 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.09, + 0.29, + 0.101 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.09, + 0.434, + 0.102 + ], + "angle": 0, + "content": "Deepsal [1]" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.104, + 0.143, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.154, + 0.105, + 0.201, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.104, + 0.275, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.104, + 0.333, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.104, + 0.408, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.105, + 0.468, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.173, + 0.143, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.155, + 0.173, + 0.201, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.173, + 0.275, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.173, + 0.333, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.173, + 0.408, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.173, + 0.464, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.211, + 0.143, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.212, + 0.204, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.211, + 0.275, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.211, + 0.334, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.211, + 0.408, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.212, + 0.468, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.278, + 0.143, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.278, + 0.204, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.278, + 0.275, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.278, + 0.335, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.278, + 0.408, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.278, + 0.468, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.348, + 0.47, + 0.404 + ], + "angle": 0, + "content": "Figure 5. Saliency attenuation compared to Deepsal [1] on the images provided by the authors on their project webpage. Our method is able to effectively attenuate the saliency of the target region without applying an unrealistic camouflage." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.416, + 0.47, + 0.492 + ], + "angle": 0, + "content": "We use an EfficientNet-lite3 [21] backbone and cascaded MLP layers as decoders to estimate parameters for each of the edit operations. A detailed explanation of the architecture specifics, datasets and training is provided in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.518, + 0.311, + 0.535 + ], + "angle": 0, + "content": "5. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.547, + 0.469, + 0.638 + ], + "angle": 0, + "content": "We compare our method against state of the art saliency based image editing approaches - Deepsal [1], Gazeshift [17] and MEC [16]. MEC provides results on their dataset alongside pre-computed results of WRS [23] and OHR [15] on the same dataset. We use this dataset to compare against WRS and OHR as well as MEC." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.642, + 0.469, + 0.763 + ], + "angle": 0, + "content": "The EfficientNet [21] backbone used in our architecture is known for its small size. Our results are thus generated significantly faster than the other state-of-the-art (SOTA) methods with bulkier architectures and slower per-image optimizations. Based on speed measures reported in [17] Table 1c, MEC takes more than a day, OHR needs 30 seconds and Gazeshift takes 8 seconds to process each image, while our model requires only 8ms per image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.766, + 0.469, + 0.826 + ], + "angle": 0, + "content": "We present both qualitative and quantitative results. Since our method takes the permutation of the edits as input during inference time we select the permutation at random for the presented results unless mentioned otherwise." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.722, + 0.107 + ], + "angle": 0, + "content": "5.1. Qualitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.22 + ], + "angle": 0, + "content": "Figs. 5, 6, and 7 illustrate our results compared to the SOTA. They show our method performs different edits based on the contents of the image. It can apply more significant color changes that camouflage the distractor \\((2^{\\mathrm{nd}}\\) and \\(4^{\\mathrm{th}}\\) rows of Fig. 6, \\(3^{\\mathrm{rd}}\\) row of Fig. 5) or very subtle edits for human faces \\((1^{\\mathrm{st}}\\) row of Fig. 6). The intensity and characteristics of the applied edits depends on semantics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.222, + 0.892, + 0.326 + ], + "angle": 0, + "content": "The use of adversarial loss in Gazeshift [17] and the regularization used in Deepsal [1] constrain the edits their methods apply without taking realism explicitly into account. As results show, they often apply unrealistic edits (e.g., the camouflaged signs in Fig. 5 or the unnatural skin tone and the color artifacts in Fig. 6) or very subtle edits with lower effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.478 + ], + "angle": 0, + "content": "MEC [16] reuses the color patterns and textures available in the image to update the target region. On the other hand different regions and textures can correspond to different semantics. Consequently, as illustrated in Fig. 7a this method can apply incompatible color and texture values to produce unrealistic edits (green crocodile eye, orange traffic sign) or ineffective enhancements (brown bird). Fig. 7b provides a comparison on their distractor suppression image set. Our method performs comparable in terms of effectiveness and generates realistic results consistently." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.892, + 0.6 + ], + "angle": 0, + "content": "OHR [15] tries to maximize the color distinction between the masked region and the rest of the image for the image enhancement task. Without explicit realism modeling, it tends to generate unrealistic colors (e.g., blue crocodile, bird, and horse in Fig. 7a). While incorrect colors increase the saliency of these regions, they do so at the cost of realism. For similar reasons, this method is ineffective suppressing distractors (Fig. 7b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.677 + ], + "angle": 0, + "content": "WRS [23] does not generate unrealistic images, but also makes edits that are hardly noticeable, and less effective at enhancing or suppressing the target regions. We believe this is due to the purposely limited range of allowed edit parameters (luminance, saturation and sharpness)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.688, + 0.783, + 0.705 + ], + "angle": 0, + "content": "5.2. What Do Photographers Think?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.818 + ], + "angle": 0, + "content": "To include the perspective of professional photographers in comparing our results to others, we ran a user study. We report our results using three choices of parameter orderings: choosing the one that achieves the Best Saliency, the one that generates the Best Realism (according to our realism estimation network), and a permutation of parameters selected at Random as used for the qualitative figures." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "User Study We recruited 8 professionals from UpWork, all of whom have multiple years of experience with photography, as well as using Photoshop to edit photos. We used the Appen platform for hosting our rating tasks." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.851, + 0.469, + 0.9 + ], + "angle": 0, + "content": "1Deepsal, WRS and MEC do not provide an open-source implementation. Hence, we relied on the results included on their project pages. Also, Deepsal authors kindly provided us with results on Adobe Stock dataset for their \"convolutional network\" variation." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "190" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.61, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.089, + 0.895, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.433, + 0.812, + 0.448 + ], + "angle": 0, + "content": "Figure 6. Saliency modulation compared to GazeShift [17] and Deepsal [1] on Adobe Stock images from [17]." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.459, + 0.481, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.459, + 0.89, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.707, + 0.808, + 0.722 + ], + "angle": 0, + "content": "Figure 7. Saliency modulation compared to MEC [16], WRS [23] and OHR [15] on the Mechrez dataset [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.474, + 0.897 + ], + "angle": 0, + "content": "Our study participants were presented with a panel of 3 images: the original image, mask, and an edited result from one of methods evaluated. They were asked to \"rate each image based on 2 criteria\" - effectiveness and realism, with the following definitions provided for the attenuate version of the task: \"The images were edited to make certain objects and regions less distracting. An image edit is effective if the masked objects/regions have indeed become less distracting. An image edit is realistic if the photo does not look edited.\" For the amplify version of the task, the wording for effectiveness was modified to: \"The im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.895, + 0.822 + ], + "angle": 0, + "content": "ages were edited to make certain objects and regions pop-out (more attention-capturing, or salient). An image edit is effective if the masked objects/regions have indeed become more attention-capturing.\" Images were randomly shuffled in each task, so the photographers rated the images and methods independently of each other." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results In Tab. 2 we compare our approach to GazeShift and Deepsal on the 30 Adobe Stock images from [17]. We find that our approach achieves significantly higher scores for both effectiveness and realism compared to GazeShift in" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.51, + 0.957 + ], + "angle": 0, + "content": "191" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.159 + ], + "angle": 0, + "content": "Table 2. Photographer ratings (on a 1 to 10 scale, higher is better) of effectiveness (i.e., achieve objective of attenuation or amplification of saliency) and realism (i.e., photo looks natural) on the dataset of 30 Adobe stock images. Numbers are the mean score across 8 photographers, with standard deviation in parentheses." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.162, + 0.468, + 0.236 + ], + "angle": 0, + "content": "
MethodSaliency AttenuationSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
GazeShift [17]4.78 (2.89)5.93 (3.13)7.36 (2.37)7.07 (2.76)
DeepSal [1]4.04 (2.90)8.49 (2.72)--
Ours - Best Realism6.56 (2.73)6.78 (2.70)7.39 (2.17)8.31 (1.89)
Ours - Random6.36 (2.79)6.34 (2.88)7.36 (2.21)8.27 (1.94)
Ours - Best Saliency6.64 (2.79)6.31 (2.70)7.50 (2.08)8.15 (2.10)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.248, + 0.468, + 0.276 + ], + "angle": 0, + "content": "Table 3. Photographer ratings as in Tab. 2 on (a) Mechrez [16] dataset and (b) the 14 images from DeepSal project webpage [1]" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.279, + 0.468, + 0.344 + ], + "angle": 0, + "content": "
MethodSaliency AttenuationMethodSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
Deepsal [1]7.08 (2.84)5.82 (3.43)MEC [16]7.06 (2.68)7.31 (2.93)
WRS [23]5.41 (3.22)7.97 (2.70)
Ours - Random6.83 (2.52)7.41 (2.70)OHR [15]7.04 (3.04)5.18 (3.76)
Ours - Random6.24 (2.9)8.88 (1.74)
(b)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.468, + 0.488 + ], + "angle": 0, + "content": "the attenuation task. This matches our qualitative observations that GazeShift is not successful at the task of attenuating distractor. GazeShift specializes in amplifying saliency in image regions, and we achieve similar performance on this task, while also maintaining significantly higher realism levels. In addition, results show a poor effectiveness score for Deepsal as a result of subtle edits in Fig. 6. Subtle edits mean the realism score remains high since the results are almost identical to the original images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.468, + 0.593 + ], + "angle": 0, + "content": "Since Deepsal was ineffective on Adobe Stock images, to provide a fair comparison we also compare to Deepsal on 14 images they provided on their project page in Tab. 3a. We achieve significantly higher realism scores while being similarly effective at reducing the saliency of the distractors. This matches our qualitative observations that Deepsal edits can be quite extreme and not always photo realistic." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.468, + 0.713 + ], + "angle": 0, + "content": "Tab. 3b shows user study results on Mechrez dataset [16].2 We used 77 images from the dataset to perform the user study. Results confirm that our results are superior in the realism while we achieve a comparable effectiveness compared MEC. WRS's low effectiveness yields a high realism score as its results are almost identical to the input; while the unrealistic color changes by OHR result in low realism and effectiveness scores." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.23, + 0.739 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.468, + 0.867 + ], + "angle": 0, + "content": "We trained a variation of our method in which instead of a fixed realism score estimation model we used a discriminator as adversarial loss. We trained the discriminator as part of an adversarial training approach, similar to related work [2, 4, 17]. We used the input image as the real sample and the generated image as the fake sample during training. Fig. 8 illustrates sample results with this training strategy. Since the discriminator is trained to penalize \"any edits\"" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)Dataset has only 10 images for attenuation task, which is inadequate for a meaningful user study. Hence we only provide amplification results." + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.09, + 0.598, + 0.1 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.101, + 0.587, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.09, + 0.71, + 0.1 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.101, + 0.712, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.09, + 0.87, + 0.1 + ], + "angle": 0, + "content": "Adversarial training" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.101, + 0.844, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.853, + 0.101, + 0.892, + 0.134 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.213, + 0.892, + 0.254 + ], + "angle": 0, + "content": "Figure 8. When the model trained via adversarial training produces results that are effective at reducing saliency, the resulting images are not realistic according to our user study." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.268, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Table 4. Photographer ratings as in Tab. 2 comparing our main method to a variation with adversarial training instead of our fixed realism network." + }, + { + "type": "table", + "bbox": [ + 0.561, + 0.313, + 0.829, + 0.359 + ], + "angle": 0, + "content": "
MethodSaliency Attenuation
Effectiveness ↑Realism ↑
Adversarial Training5.06 (2.84)7.36 (3.07)
Ours - Random6.36 (2.79)6.34 (2.88)
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.474 + ], + "angle": 0, + "content": "applied in the previous steps of training it encourages the network to apply subtle edits and hence a drop in effectiveness of the method. On the other hand, due to the lack of explicit realism training, the edits are unrealistic while the effectiveness is reasonable. Ratings reported in Tab. 4 also confirm our findings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.483, + 0.874, + 0.5 + ], + "angle": 0, + "content": "5.4. Diversity and Optimality of Estimated Edits" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Fig. 9b illustrates the distribution of edit parameters estimated by our parameter estimation network for different images on ADE20K [24, 25] dataset. It shows that edit parameters are different for each image and is based on its content. Also, it shows that the range of estimated edits is not the same as the ranges used in Tab. 1 for real samples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.892, + 0.716 + ], + "angle": 0, + "content": "To evaluate if the estimated edits are close to optimal with respect to realism, we provide Fig. 9a. In the figure we show a realism heatmap obtained by adding a small additive constant to the estimated edit parameter of saturation and exposure. Heatmaps show the estimated edit parameters (center of the heatmap) are in the optimal realism region. Changing the edit parameters in each direction reduces the realism of the end result." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.857, + 0.743 + ], + "angle": 0, + "content": "5.5. Generalization to Multiple Image Regions" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since our model only modifies the region of interest, and performs a forward pass efficiently, we can run it on multiple regions and multiple masks by generating edit parameters for each region, in an iterative manner. Examples are provided in Figs. 1 and 10. We used the same approach with Gazeshift [17], which edits the whole image by estimating two sets of edit parameters, one for the region of interest (foreground) and one for the background. This formulation of Gazeshift makes iterative editing impractical, since there would be contradictory objectives between the" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "192" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.554, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.303, + 0.554, + 0.352 + ], + "angle": 0, + "content": "(a) A heatmap visualizes the realism score achieved when we change the estimated saturation (x-axis) and exposure (y-axis). Our estimated values (center of the heatmap) achieve the optimal realism while changing the parameters in any direction reduces the realism. Sample edited images and their corresponding location in the heatmap are also visualized." + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.116, + 0.877, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.303, + 0.89, + 0.34 + ], + "angle": 0, + "content": "(b) The diversity of estimated parameters on ADE20K [24, 25] dataset. The x-axis is the range of each parameter. The attenuation task is blue, and amplification is labeled red." + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.358, + 0.754, + 0.373 + ], + "angle": 0, + "content": "Figure 9. Visualizing diversity and optimality of edit parameters estimated by our method" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.381, + 0.47, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.657 + ], + "angle": 0, + "content": "Figure 10. Given an input image and masks to attenuate and amplify(left), Gazeshift when used iteratively on each object suffers from color artifacts (center top, faces, bowl and watermelons). Ours produces a notably more realistic and effective result (right). Contradictory objective of edits applied to background and foreground, Gazeshift fails to generalize to multiple regions and omitting the background edits (center bottom) reduces the effectiveness of the edits. Image credit: @tysonbrand" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.759 + ], + "angle": 0, + "content": "iterations (what is foreground in one iteration becomes a background in the next iteration). For a more practical comparison, we omit background edits when running Gazeshift. Figure 10 shows that Gazeshift performance suffers on an iterative saliency enhancement task, but our method is able to generalize to multiple regions robustly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.205, + 0.787 + ], + "angle": 0, + "content": "5.6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The global edits (applying the same edits to every pixel inside a mask), used in both our method and Gazeshift [17] require an accurate mask of the target region. As shown in Fig. 11 mask imperfections can cause unsmooth transitions around the boundaries. In these cases, pixel-wise optimization approaches like Deepsal [1] and MEC [16] do not suffer from heavy artifacts due to mask imperfections." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.382, + 0.895, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.55, + 0.894, + 0.621 + ], + "angle": 0, + "content": "Figure 11. The effect of non-smooth mask boundaries. Left, an input image has a mask with a sharp edge. Center, our method and Gazeshift [17] produce strong boundary artifacts around the mask region (see inset). Right, MEC [16] and Deepsal [1] do not exhibit this problem because they operate in a pixel-wise manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.766, + 0.658 + ], + "angle": 0, + "content": "6. Conclusion and Future work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We describe a method to edit images using conventional image editing operators to attenuate or amplify the attention captured by a target region while preserving image realism. Realism is achieved by introducing an explicit, and separate realism network that is pre-trained to distinguish edited images. This strategy to achieve realism is distinct from prevailing approaches, including adversarial training schemes, as it introduces an additional form of weak supervision—manually specified ranges of parameter values that correspond to realistic and unrealistic (\"fake\") edits. Training with this realism critic makes it possible to estimate saliency modulating image edits that are significantly more realistic and robust. Together with our millisecond-level inference time, our approach offers a practical and deployable application of saliency guided image editing." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "193" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Kfir Aberman, Junfeng He, Yossi Gandelsman, Inbar Mosseri, David E. Jacobs, Kai Kohlhoff, Yael Pritch, and Michael Rubinstein. Deep saliency prior for reducing visual distraction. In Proc. CVPR, 2021. 1, 2, 4, 5, 6, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.47, + 0.225 + ], + "angle": 0, + "content": "[2] Yen-Chung Chen, Keng-Jui Chang, Yi-Hsuan Tsai, Yu-Chiang Frank Wang, and Wei-Chen Chiu. Guide your eyes: Learning image manipulation under saliency guidance. 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ICCV, 2015. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "194" + } + ] +] \ No newline at end of file diff --git a/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_origin.pdf b/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2daa4c9ffe6aaac4d54279cb402c9b739cd1a557 --- /dev/null +++ b/2023/Realistic Saliency Guided Image Enhancement/8e3ac21f-6601-42a5-a41c-6bcc6930276d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d9e3755fa1da9153e47b725c1a3d0f2ccb43c1d51646c6c422e7dabacb4583e9 +size 7847844 diff --git a/2023/Realistic Saliency Guided Image Enhancement/full.md b/2023/Realistic Saliency Guided Image Enhancement/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9bf09deaa97bbbbfaf715a705c7ce822b5a051ba --- /dev/null +++ b/2023/Realistic Saliency Guided Image Enhancement/full.md @@ -0,0 +1,425 @@ +# Realistic Saliency Guided Image Enhancement + +S. Mahdi H. Miangoleh1 Zoya Bylinskii2 Eric Kee2 Eli Shechtman2 Yaqiz Aksoy1 + +$^{1}$ Simon Fraser University $^{2}$ Adobe Research + +![](images/e56abe4fd2431b703629682f6aa8815177a684493cd83c35c52d06caf1d45a93.jpg) +Input image + +![](images/86ce6a45e1f51f8b721443f9092342e7f5dfb8317e4d419d3bb34093ffe59ff3.jpg) + +![](images/42f77cab3bcab39653bb584f7e4911c987e489371a1170fcd03718e5db74f3e0.jpg) + +![](images/7333eca4b9da782dfe282a881c60a9c2a09a8b2f565437ea289dd72aff052138.jpg) + +![](images/9d1e1a4f1eab1910090823f6a2a0b66f3fb777af59598c19cb23e51dcfca1902.jpg) + +![](images/99824e2372e6826fb2cc085b0fe26f7eeb1d6ea0eb1e9dad010c94d2353847ef.jpg) + +![](images/d4dbab14608167b15dbe312c9d2b6fcaff2b868883ac0c5476702d909a6fe066.jpg) + +![](images/00b4f77e8817a7279b7d46be76ac92863752a28794b2d2f4bfd17d217a7307af.jpg) + +![](images/071b8c5532c553f77256e07da5bb23da443094198dc5040ad2ae8dd5e4400e95.jpg) + +![](images/6d2387a4876ec1cb39138d6270b2642f614db8a59e71a111513c73e1277fbcfc.jpg) + +![](images/ff83774c45af2ad11c7e2b1d9697d4119ee6371952e43a364dd8835cb418525f.jpg) +Figure 1. (top) We develop a saliency-based image enhancement method that can be applied to multiple regions in the image to demephasize objects (steps 1, 2) or enhance subjects (steps 3, 4). (bottom) Our novel realism loss allows us to apply realistic edits to a wide variety of objects while state-of-the-art methods [1, 17] may generate less realistic editing results. + +# Abstract + +Common editing operations performed by professional photographers include the cleanup operations: de-emphasizing distracting elements and enhancing subjects. These edits are challenging, requiring a delicate balance between manipulating the viewer's attention while maintaining photo realism. While recent approaches can boast successful examples of attention attenuation or amplification, most of them also suffer from frequent unrealistic edits. We propose a realism loss for saliency-guided image enhancement to maintain high realism across varying image types, while attenuating distractors and amplifying objects of interest. Evaluations with professional photographers confirm that we achieve the dual objective of realism and effectiveness, and outperform the recent approaches on their own datasets, while requiring a smaller memory footprint and runtime. We thus offer a viable solution for automating image enhancement and photo cleanup operations. + +# 1. Introduction + +In everyday photography, the composition of a photo typically encompasses subjects on which the photographer intends to focus our attention, rather than other distracting things. When distracting things cannot be avoided, photographers routinely edit their photos to de-emphasize them. Conversely, when the subjects are not sufficiently visible, photographers routinely emphasize them. Among the most common emphasis and de-emphasis operations performed by professionals are the elementary ones: changing the saturation, exposure, or the color of each element. Although conceptually simple, these operations are challenging to apply because they must delicately balance the effects on the viewer attention with photo realism. + +To automate this editing process, recent works use saliency models as a guide [1,2,4,8,16,17]. These saliency models [3,7,10,14,19] aim to predict the regions in the + +image that catch the viewer's attention, and saliency-guided image editing methods are optimized to increase or decrease the predicted saliency of a selected region. Optimizing solely based on the predicted saliency, however, often results in unrealistic edits, as illustrated in Fig. 1. This issue results from the instability of saliency models under the image editing operations, as saliency models are trained on unedited images. Unrealistic edits can have low predicted saliency even when they are highly noticeable to human observers, or vice versa. This was also noted by Aberman et al. [1], and is illustrated in Fig. 2. + +Previous methods tried to enforce realism using adversarial setups [2, 4, 8, 17], GAN priors [1, 8], or cycle consistency [2] but with limited success (Fig. 1). Finding the exact point when an image edit stops looking realistic is challenging. Rather than focusing on the entire image, in this work, we propose a method for measuring the realism of a local edit. To train our network, we generate realistic image edits by subtle perturbations to exposure, saturation, color or white balance, as well as very unrealistic edits by applying extreme adjustments. Although our network is trained with only positive and negative examples at the extremes, we successfully learn a continuous measure of realism for a variety of editing operations as shown in Fig. 3. + +We apply our realism metric to saliency-guided image editing by training the system to optimize the saliency of a selected region while being penalized for deviations from realism. We show that a combined loss allows us to enhance or suppress a selected region successfully while maintaining high realism. Our method can be also be applied to multiple regions in a photograph as shown in Fig. 1. + +Evaluations with professional photographers and photo editors confirm our claim that we maintain high realism and succeed at redirecting attention in the edited photo. Further, our results are robust to different types of images including human faces, and are stable across different permutations of edit parameters. Taken together with our model size of 26Mb and run-time of 8ms, these results demonstrate that we have a more viable solution for broader use than the approaches that are available for these tasks to date. + +# 2. Related Work + +Various image enhancement methods have been introduced in the literature to amplify a region of interest or de-emphasise distracting regions, improve image aesthetics, and redirect the viewer's attention. This task has been referred to as attention retargeting [15] or reattentionizing [18] as well. Earlier methods [5,15,20,22,23] incorporated prior knowledge of saliency cues (saturation, sharpness, color, gamut, etc.) to guide the editing process to achieve the desired change in saliency. But, relying solely on saliency cues both limits the diversity of generated edits, and creates unrealistic edits due to the lack of semantic + +![](images/aaf1fb2d0518bd051437d1937d2fa424a5dd6ca71a84c1ff316a34fdbb0f2122.jpg) +Original image + +![](images/af30ae7160142775f660cee5aadb7b879b928f296a4d031ae58bbfe5ed57b283.jpg) +Figure 2. Predicted saliency maps [7] for the original images and edited versions, with extreme edits applied. Note that saliency models are typically trained with realistic images. This makes them susceptible to inaccurate predictions for unrealistic inputs, as the green woman in the top row estimated to have low saliency. + +![](images/c3a907f1b78db61d9d3587053c45c1989c00978f786d7dfbe5addc41c2c81099.jpg) +Saliency map + +![](images/9ffbeb94f704c93408b24f2a059d6b6f1d19105d5c6a8d676feb84217a09055e.jpg) + +![](images/af874ae7afe0f2208e3166875c3ce10af3fc631e0bf569b3133e8d89f9dd1cd9.jpg) +Edited image + +![](images/6dcd9ac78f5bb7d8bc8337923d8625293e7924df7142309384f14bb415fa26b0.jpg) + +![](images/6c72891dfb6bd2eddccc2ee3e204a261e45a99de4813b46af6359a43963ac6bd.jpg) +Saliency map + +![](images/008a2af1596f0a901d546163043e19c9fbdc0a0e8eb5c19032859864be2d6f21.jpg) + +constraints. As our experiments show, OHR [15] tends to generate unrealistic color changes that are semantically incorrect, and WRS [23] is limited to contrast and saturation adjustments with limited effectiveness. + +Recent works leverage saliency estimation networks [3, 7, 10, 14, 19] to optimize for a desired saliency map instead of relying on prior saliency cues. Saliency models are trained to output a heatmap that represents where human gaze would be concentrated in an image. These models are not trained to respond to the realism of the input image. Hence they might predict an inconsistent decrease or increase in the saliency of a region when unrealistic or semantically implausible edits are applied, which would be otherwise jarring to human viewers (Fig. 2). Using saliency as the only supervision can result in unrealistic images. + +To prevent unrealistic edits, prior works enforce constraints on the allowable changes, use adversarial training [2, 4, 8, 17] or exploit learned priors from GAN-based models [1, 8]. For instance, Mechrez et al. [16] and Aberman et al. (Warping) [1] constrain the result to match the input content in order to maintain its appearance. Aberman et al. (CNN and Recolorization) [1] use a regularization term that limits the amount of change an image can undergo to maintain the realism. Mejjati et al. [17] designed a global parametric approach to limit the editing operations to a set of common photographic ones. Chen et al. [2] exploit cycle consistency to keep the output within the domain of the input image. Gatys et al. [4] use a texture loss alongside the VGG perceptual loss as a proxy for realism. + +Lalonde et al. [11] argue that humans prefer color consistency within images, regardless of object semantics. They use color statistics to measure realism and use it to recolor the images to match the background in compositing task. Zhu et al. [26] train a network to discriminate between natural images and computer-generated composites and use it as a realism measure for compositing task. Realism is also a crucial factor in GANs, as highlighted by [9]. + +Table 1. Parameter value ranges used to generate real and fake training images for the realism estimation network. + +
ExposureSaturationColor curveWhite balancingNumber of edits
Real[0.85, 1.15][0.85, 1.15][0.85, 1.15]Not allowed[1, 3]
Fake[0.5, 0.75] ∪ [1.5, 2][0, 0.5] ∪ [1.5 - 2][0.5, 2][0.9, 1][2, 4]
Fake(human specific)[0.5, 0.75] ∪ [1.25, 1.5][0.5, 0.75] ∪ [1.25, 1.5][0.5, 2]Not allowed[2, 3]
+ +![](images/523762469cbad24df67942d9031eecee69c44b939be73e688d98eac63eb2f68b.jpg) + +![](images/fcbb1b301b78ae7b093ad69836d865672d8dfa2fb81bfd3b57dfb8c109f8be40.jpg) + +![](images/1131b506930c809879f39a28ab32b5e81b81448bfe6a68ef0ad5813ba775f787.jpg) + +![](images/65623b33fefe2ec03b15151c0fac5d9f0eb0d690aad87c7d9d329890fa586596.jpg) + +![](images/ad2bf69290a8b081e70afd9ebb19a8a9c7f44c37c820c759d40d4c7f51849558.jpg) + +![](images/5fd10cc5e8c6b2f9a9d3849e4273f69f355aa220e04ce3e11092c57f4c850020.jpg) + +![](images/491e6841422c4038bf6781575d096ba0ee73fba94155328fa6643e5e323ae6be.jpg) + +![](images/5bd0ccf83a44fe815a2b3052cb79b1d3bfd01c9e68c2a13016059b4a519191c5.jpg) + +![](images/535e5b6bf97b34ea44800d5f3ec703f4b236f881cc993bb6422f51c86e79047c.jpg) + +![](images/3fe69fa891ed3fcbdc4344c84d62d348385b9b9c85132676e89963a36694f675.jpg) +Figure 3. The efficacy of the realism estimation network is illustrated over a range of exposure and saturation adjustments. Left is $\Delta \mathcal{R}$ plotted (vertical axis) for example images (second column) when selected regions (third column) are edited. Right, the edited images are shown with the corresponding change in estimated realism (inset numbers), and the value of the editing parameter applied (underneath). + +![](images/3f0c77046483687790402277c2099eaa014764739de66084db6c67093ddef599.jpg) + +![](images/070e6f033eed4c022373bf6b08268c6ce146d46f9330db5f06e9e6190af330d8.jpg) + +![](images/cb4baaf50c240c2fcd8d46bc948303a01e3bdc74c3b94edd99a7c518beaece97.jpg) + +![](images/2231d02a5cf9d289345bce597c7779867fbb883c1b75f3d1dc58c5cc621293a7.jpg) + +![](images/da7e037a78e41865d447679e42ddc1fe48fbadcfacb094ac7cb7244a688dd620.jpg) + +![](images/08caa98646d22482a4d94015aa5cb0b2f1a01f75b886717fc5b539b7ac28f745.jpg) + +![](images/dfbaf4ba37638113f5d23ae3680f948dfcd799703666011313a0e1f090d5c568.jpg) + +![](images/c8544a41c71175fa09e1e3dfd68ff99963909154bda3d9fe7843c3709f6f9291.jpg) + +We present a new method for estimating the realism of a local edit. Combining our realism loss with saliency guidance, we show that we can successfully apply attention attenuation or amplification while keeping the final result realistic without requiring data annotated with realism or bulky GAN priors to estimate realism. + +# 3. Realism Network + +When editing specific regions in an image, it is challenging to maintain the overall realism of the photograph. How quickly realism starts to degrade depends on the contents and size of the image regions, the overall composition of the scene, as well as the type of edits being applied. This makes the problem of defining precisely when an image edit stops looking realistic particularly challenging. + +In this work, we propose to train a realism network using only realistic and unrealistic examples at the extremes. We generate realistic edits by slightly perturbing image values, and unrealistic edits by applying aggressive edits. We show that, despite being trained on binary data, our network can estimate continuous realism scores that can adapt to different types of image regions and scenes. Our approach was inspired by the work of Zhu et al. [26], who similarly learn their realism from binary real and synthetic composites. + +To generate real and fake samples, we exploit different parameter ranges for commonly used editing operations - exposure, saturation, color curve, and white balancing (formal definitions in the Supplementary Material). For instance, increasing the exposure of a region too much can + +result in an unrealistic image, while a subtle increase to saturation will not significantly affect the realism. Based on experimentation, we determined the set of parameter ranges in Tab. 1 to apply to image regions to create our training data. + +To generate a training example, we first select a random number of edits (between 1-4), then an order for the edit operations (e.g., exposure, saturation, color curve, white balancing), and values for each of the operations, sampled uniformly at random from the pre-specified ranges in Tab. 1. We apply these edits in the selected order to a region segment in an MS-COCO image [12]. Fake examples are generated by purposefully selecting extreme values. Real examples are generated by sampling subtle edits within narrower ranges. Because of the semantic importance of human faces and increased sensitivity to edits in facial regions, we enforce smaller parameter ranges when applying edits to faces. Fig. 4 shows several examples. + +We use the Pix2Pix [6] network architecture followed by two MLP layers to estimate the realism score $\mathcal{R}$ of the input. For our samples in the training data, $\mathcal{R}$ is defined as 1 for real and 0 for fake samples. We also condition the output on the input region by feeding the region's mask $M$ as input to the network. We use squared error [13] as the critic to compute the loss on the estimated value: + +$$ +\mathcal {L} _ {\text {d i s c}} = \frac {1}{2} \mathcal {R} \left(I _ {\text {f a k e}}, M\right) ^ {2} + \frac {1}{2} \left(\mathcal {R} \left(I _ {\text {r e a l}}, M\right) - 1\right) ^ {2} \tag {1} +$$ + +where $I_{\text{fake}}$ and $I_{\text{real}}$ are the generated fake and real samples. To measure the effect of the edit on the realism of the image, we compute the difference between the scores + +![](images/22b4a60b2c730aea0f38bba89b437305e5555cf31fc478077c36421bde29edab.jpg) +input image + +![](images/03736c736377979b37bf43d9134b74200f42ab9c99eeed352040f93599cecf6d.jpg) +mask + +![](images/4a0a79412b08ed55c0e1fe5271030261d1cd025c6428824b43bb414dcda08ab9.jpg) +real sample + +![](images/4d02041288aad014cbe82bf3bc8cf1934c2e0e5a4c291ece93e26974cbc4491f.jpg) +fake sample + +![](images/67c6393477e39e978f6ba03a1ff34f162fcee54650285deae42693ef1fbeaffa.jpg) + +![](images/e47c5b9d615a125972549b67ba9ced94910c20511490d26477063ee6a727a81e.jpg) + +![](images/7e013ee51966eb2c6fddddbab19fa09bd8089229c33eda5edd756795c20bb3aa.jpg) + +![](images/d356ef9a8def814d325434f68c9e3fb637a1dcfee5df195999e3980b18a21803.jpg) + +![](images/8887b35525fd7edbbe645162c616341476e6756bfc5c0d36df2eba403d4386f4.jpg) + +![](images/09405ba0433a8a897dc574cd8c5332d33c0061bcac52f21306b1276e790c8306.jpg) + +![](images/0e927f3a314c24b374607e076ab3fc6fc73077692ef50658e1adc24faa799bed.jpg) + +![](images/3c6c8be9fb92f317befd01547187b0dd0f908b40d5bc57e7806f8a940d6ec8e1.jpg) + +![](images/18eff5f06f7de915ce64ff22d1134c6bb61ec999d07f1d1ab9c5f7119fbd5726.jpg) +Figure 4. Examples of fake and real images that are used to train the realism estimation network. See Section 3 for more details. + +![](images/9f984f6eab4fc07b1ac0b1c1de6cbe5f9d5b8ba70f54acdca84a96a52e4b5f50.jpg) + +![](images/51be0d266cf6c68cfcc12b8c0202ec65f4463d9592ec61023f7a38966bd61a44.jpg) + +![](images/1e5962353525750138cbaeece2ed47f36dbcf7b95fd871db48465294fe56cbb8.jpg) + +estimated for the original image $I$ and the edited image $I^{\prime}$ + +$$ +\Delta \mathcal {R} (I ^ {\prime}, I, M) = \mathcal {R} (I ^ {\prime}, M) - \mathcal {R} (I, M), \tag {2} +$$ + +where the edited region is defined by the mask $M$ . + +As Fig. 3 demonstrates $\Delta \mathcal{R}$ gives us continuous realism values for a range of edit parameters, despite the network being trained only on extreme cases. It also shows that the range of edits that are considered realistic by our network is not the same for each image and depends on the subject and editing operation. We show more examples of edits that are classified realistic or unrealistic by our network in Fig. 9 and the Supplementary Material. + +# 4. Saliency Guided Image Enhancement + +We develop a saliency-guided image editing pipeline that enforces our realism loss to generate realistic and effective object enhancement or distractor suppression results for a given mask. Our system can estimate a set of editing parameters for any permutation of 4 editing operators: exposure, saturation, color curve, and white balancing. + +In constructing our system, we borrow many ideas from the existing saliency-guided image editing literature, and focus our design improvements on improving the realism of the results, especially by including our proposed realism loss. Since these edit operations are non-linear, different orderings of edits changes the end results. As a result, we condition the regressed parameters on the permutation of the edit operations by feeding the permutation as an input to the network. More details on the architecture of the network and the embedding used to encode the permutation is included in the Supplementary Material. + +Saliency Loss A pretrained saliency model [7] (SalNet) is used as a proxy for the viewer attention that would be captured by image regions before and after applying the edits, to supervise the image editing process. + +We measure the change in the saliency of the region of interest as the expected value of its relative change within the masked region: + +$$ +S (I, I ^ {\prime}, M) = \mathbb {E} _ {M} \left[ \frac {S a l N e t (I) - S a l N e t \left(I ^ {\prime}\right)}{S a l N e t (I)} \right] \tag {3} +$$ + +where $\mathbb{E}$ denotes the expectation and $M$ is the region mask. + +As Fig. 2 shows, the predicted saliency heatmaps can change drastically when applied to unrealistic edits. As a result, relying on conventional metrics (e.g., absolute and relative differences by [1, 17], Binary cross entropy by [2] and KL-divergence by [4]) to measure the change in saliency can cause large rewards or penalties during optimization. Infinitely large rewards for an unreal edit reduces the effectiveness of the realism term in the final loss function. To tackle this issue we define our saliency loss function as: + +$$ +\mathcal {L} _ {\mathrm {s a l}} = \exp \left(w _ {\mathrm {s a l}} S \left(I, I ^ {\prime}, M\right)\right) \tag {4} +$$ + +When saliency moves in the desired direction, the exponential squashes the loss, converging to the minimum and reducing the penalty quickly, acting as a soft margin. This converging behaviour prevents large rewards that can be generated by unrealistic edits during training. The exponential term imposes larger penalties when saliency moves in the wrong direction, providing robustness against outliers and faster convergence. $w_{sal}$ controls the absolute value of the loss to balance the weight of saliency loss in our final loss, which we set to 5 and -1 for amplification and attenuation, respectively. + +Realism Loss The realism loss is defined as: + +$$ +\mathcal {L} _ {\text {r e a l i s m}} = R e L U \left(- \Delta \mathcal {R} \left(I ^ {\prime}, I, M\right) - b _ {r}\right) \tag {5} +$$ + +This loss is designed to penalize unrealistic edits, while giving no rewards for edits that improve the estimated realism score of the input. This prevents the network from being penalized by images that receive a low realism score even before any edits are applied. ReLU and offset $b_{r}$ provide a margin that allows a slight decrease in realism without a penalty which we set to 0.1 in our experiments. + +We train two separate networks for each. The final network objective is the product of the two loss functions: + +$$ +\mathcal {L} = \left(1 + \mathcal {L} _ {\text {r e a l i s m}}\right) \times \mathcal {L} _ {\text {s a l}}. \tag {6} +$$ + +In this formulation, the realism score acts as a weight for the penalty imposed on the change in the saliency. This allows us to balance the realism and saliency objectives. + +![](images/674e73ff803d84b37c9b76fb66062c020f5001665c89f667de9e5579f2cee235.jpg) +Input image + +![](images/a98a37bad8ddb806d3250900c7baeca2c25edaa98d490cb66ce214d9bcec3655.jpg) + +![](images/a9446a398355e291d77d3b1d746185cb04cd3cac425ff114c46cd8a8faf952cc.jpg) +Ours + +![](images/43839945dba9c65df9c63ae7bb5c4c832c358115d9bbb06a50cae0af83aa3da9.jpg) + +![](images/7663b1b6360ee353b160ac5e01b7f562bba842ba2dcd1ac488be10b998505714.jpg) +Deepsal [1] + +![](images/3cfdcd560cb527914a62d7c538f7fdb8babcdc71ae95fd97a214801997f3ab96.jpg) + +![](images/1329578e38f38d77bdde716ed87bea42676a3b865e5853b7204d379f676c893b.jpg) + +![](images/3bbde154481c544144f84df7585edfbb81fbcd0553d30ba71650ccd9f3e1525d.jpg) + +![](images/02306e78ae81478a24ddca63b2d7cf3f04a24b6ae5f25449426442266b021c41.jpg) + +![](images/2d544baf8e4f0b05afb8a7ae7b1fa9154996ed8c9a2e3420255f636fd81f0425.jpg) + +![](images/f0641d056ade22e5ead63e24a1e296c23b97a138356b657e9a3540db0a9bbcc0.jpg) + +![](images/ab9bd7ced6182431e51fa7b5c573ddd573a6fe3608c62eb621d07bffa8d49a7c.jpg) + +![](images/5c8452fde715f54f12fdb11b603e14f692eb08b1e96c17c774dd11595e3ecac3.jpg) + +![](images/e8fe706dd4062330e84a332b198ff6246c4af6443a52cc7a695c8c97f0e60a5d.jpg) + +![](images/220db1fcffde423104bf0d1e5e28d18ca7099f7484576687b8b2a260d8832c18.jpg) + +![](images/89f7d611ba0f3e6f21eb93b5146843946cb81da49399b3f9f8f0e94b12925100.jpg) + +![](images/64bb11ebfa2776a537607c49c0000bd5e0d50b026cc64ece2f781d49bee2e154.jpg) + +![](images/8d46a7e3b84e35889971a5821b7e6d8efb4b43791967597f3731c6d84220a8f6.jpg) + +![](images/8a1dd1c0d7d5abc0b71a59210b97badc80bbbeb390dece1d8d9b943ac3aaecba.jpg) +Figure 5. Saliency attenuation compared to Deepsal [1] on the images provided by the authors on their project webpage. Our method is able to effectively attenuate the saliency of the target region without applying an unrealistic camouflage. + +![](images/1fad9ffaabedf36770c473c0827e0daec70aeccf37dd00040fd21400093ec951.jpg) + +![](images/2a89150c1984cce5c5cd8f84ce409f343234274c67bd8960f1b8ce6c429c7958.jpg) + +![](images/8f30414d86206e6616c529032bf440ad6a7c8041fac50879396531031a0c18ff.jpg) + +![](images/65d4de9f46979dd56e52c5a258a6c29067fb8626b350cdb441dafe5736b5cc2e.jpg) + +![](images/29fcc1686ff6f545c7e04039e2840cedff5656d039ba605260cfb3a68177ec64.jpg) + +We use an EfficientNet-lite3 [21] backbone and cascaded MLP layers as decoders to estimate parameters for each of the edit operations. A detailed explanation of the architecture specifics, datasets and training is provided in Supplementary Material. + +# 5. Experiments and Results + +We compare our method against state of the art saliency based image editing approaches - Deepsal [1], Gazeshift [17] and MEC [16]. MEC provides results on their dataset alongside pre-computed results of WRS [23] and OHR [15] on the same dataset. We use this dataset to compare against WRS and OHR as well as MEC. + +The EfficientNet [21] backbone used in our architecture is known for its small size. Our results are thus generated significantly faster than the other state-of-the-art (SOTA) methods with bulkier architectures and slower per-image optimizations. Based on speed measures reported in [17] Table 1c, MEC takes more than a day, OHR needs 30 seconds and Gazeshift takes 8 seconds to process each image, while our model requires only 8ms per image. + +We present both qualitative and quantitative results. Since our method takes the permutation of the edits as input during inference time we select the permutation at random for the presented results unless mentioned otherwise. + +# 5.1. Qualitative Comparison + +Figs. 5, 6, and 7 illustrate our results compared to the SOTA. They show our method performs different edits based on the contents of the image. It can apply more significant color changes that camouflage the distractor $(2^{\mathrm{nd}}$ and $4^{\mathrm{th}}$ rows of Fig. 6, $3^{\mathrm{rd}}$ row of Fig. 5) or very subtle edits for human faces $(1^{\mathrm{st}}$ row of Fig. 6). The intensity and characteristics of the applied edits depends on semantics. + +The use of adversarial loss in Gazeshift [17] and the regularization used in Deepsal [1] constrain the edits their methods apply without taking realism explicitly into account. As results show, they often apply unrealistic edits (e.g., the camouflaged signs in Fig. 5 or the unnatural skin tone and the color artifacts in Fig. 6) or very subtle edits with lower effectiveness. + +MEC [16] reuses the color patterns and textures available in the image to update the target region. On the other hand different regions and textures can correspond to different semantics. Consequently, as illustrated in Fig. 7a this method can apply incompatible color and texture values to produce unrealistic edits (green crocodile eye, orange traffic sign) or ineffective enhancements (brown bird). Fig. 7b provides a comparison on their distractor suppression image set. Our method performs comparable in terms of effectiveness and generates realistic results consistently. + +OHR [15] tries to maximize the color distinction between the masked region and the rest of the image for the image enhancement task. Without explicit realism modeling, it tends to generate unrealistic colors (e.g., blue crocodile, bird, and horse in Fig. 7a). While incorrect colors increase the saliency of these regions, they do so at the cost of realism. For similar reasons, this method is ineffective suppressing distractors (Fig. 7b). + +WRS [23] does not generate unrealistic images, but also makes edits that are hardly noticeable, and less effective at enhancing or suppressing the target regions. We believe this is due to the purposely limited range of allowed edit parameters (luminance, saturation and sharpness). + +# 5.2. What Do Photographers Think? + +To include the perspective of professional photographers in comparing our results to others, we ran a user study. We report our results using three choices of parameter orderings: choosing the one that achieves the Best Saliency, the one that generates the Best Realism (according to our realism estimation network), and a permutation of parameters selected at Random as used for the qualitative figures. + +User Study We recruited 8 professionals from UpWork, all of whom have multiple years of experience with photography, as well as using Photoshop to edit photos. We used the Appen platform for hosting our rating tasks. + +![](images/8a53c614ea083348e103a3fc4476d52431fe2c1420d76dda2ea2f90b9edf16d9.jpg) +Figure 6. Saliency modulation compared to GazeShift [17] and Deepsal [1] on Adobe Stock images from [17]. + +![](images/2df726e8aa4fb412c92710525e2fb13fcb7715ebc20e4d42857483b02d78e2f0.jpg) + +![](images/d818a347ef52d037a2d446c3d37c043a36170f538e4f573fc6f2f74b754ff01b.jpg) + +![](images/fe536d135db8b2522230045c99701696dd7b61fa7bf91bf50d9fe3a20a306405.jpg) +Figure 7. Saliency modulation compared to MEC [16], WRS [23] and OHR [15] on the Mechrez dataset [16]. + +Our study participants were presented with a panel of 3 images: the original image, mask, and an edited result from one of methods evaluated. They were asked to "rate each image based on 2 criteria" - effectiveness and realism, with the following definitions provided for the attenuate version of the task: "The images were edited to make certain objects and regions less distracting. An image edit is effective if the masked objects/regions have indeed become less distracting. An image edit is realistic if the photo does not look edited." For the amplify version of the task, the wording for effectiveness was modified to: "The im + +ages were edited to make certain objects and regions pop-out (more attention-capturing, or salient). An image edit is effective if the masked objects/regions have indeed become more attention-capturing." Images were randomly shuffled in each task, so the photographers rated the images and methods independently of each other. + +Results In Tab. 2 we compare our approach to GazeShift and Deepsal on the 30 Adobe Stock images from [17]. We find that our approach achieves significantly higher scores for both effectiveness and realism compared to GazeShift in + +Table 2. Photographer ratings (on a 1 to 10 scale, higher is better) of effectiveness (i.e., achieve objective of attenuation or amplification of saliency) and realism (i.e., photo looks natural) on the dataset of 30 Adobe stock images. Numbers are the mean score across 8 photographers, with standard deviation in parentheses. + +
MethodSaliency AttenuationSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
GazeShift [17]4.78 (2.89)5.93 (3.13)7.36 (2.37)7.07 (2.76)
DeepSal [1]4.04 (2.90)8.49 (2.72)--
Ours - Best Realism6.56 (2.73)6.78 (2.70)7.39 (2.17)8.31 (1.89)
Ours - Random6.36 (2.79)6.34 (2.88)7.36 (2.21)8.27 (1.94)
Ours - Best Saliency6.64 (2.79)6.31 (2.70)7.50 (2.08)8.15 (2.10)
+ +Table 3. Photographer ratings as in Tab. 2 on (a) Mechrez [16] dataset and (b) the 14 images from DeepSal project webpage [1] + +
MethodSaliency AttenuationMethodSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
Deepsal [1]7.08 (2.84)5.82 (3.43)MEC [16]7.06 (2.68)7.31 (2.93)
WRS [23]5.41 (3.22)7.97 (2.70)
Ours - Random6.83 (2.52)7.41 (2.70)OHR [15]7.04 (3.04)5.18 (3.76)
Ours - Random6.24 (2.9)8.88 (1.74)
(b)
+ +the attenuation task. This matches our qualitative observations that GazeShift is not successful at the task of attenuating distractor. GazeShift specializes in amplifying saliency in image regions, and we achieve similar performance on this task, while also maintaining significantly higher realism levels. In addition, results show a poor effectiveness score for Deepsal as a result of subtle edits in Fig. 6. Subtle edits mean the realism score remains high since the results are almost identical to the original images. + +Since Deepsal was ineffective on Adobe Stock images, to provide a fair comparison we also compare to Deepsal on 14 images they provided on their project page in Tab. 3a. We achieve significantly higher realism scores while being similarly effective at reducing the saliency of the distractors. This matches our qualitative observations that Deepsal edits can be quite extreme and not always photo realistic. + +Tab. 3b shows user study results on Mechrez dataset [16].2 We used 77 images from the dataset to perform the user study. Results confirm that our results are superior in the realism while we achieve a comparable effectiveness compared MEC. WRS's low effectiveness yields a high realism score as its results are almost identical to the input; while the unrealistic color changes by OHR result in low realism and effectiveness scores. + +# 5.3. Ablation Study + +We trained a variation of our method in which instead of a fixed realism score estimation model we used a discriminator as adversarial loss. We trained the discriminator as part of an adversarial training approach, similar to related work [2, 4, 17]. We used the input image as the real sample and the generated image as the fake sample during training. Fig. 8 illustrates sample results with this training strategy. Since the discriminator is trained to penalize "any edits" + +![](images/a879f63575a952e3215679c5605db540383c8aaa8885e9e9d839bab01363e272.jpg) +Input image +Figure 8. When the model trained via adversarial training produces results that are effective at reducing saliency, the resulting images are not realistic according to our user study. + +![](images/c8d51c7ae5a9f4cfafcdb0aa1619b1b87b70b0b197401c5c60d2b2fdf4da2dbe.jpg) +Ours + +![](images/25a13bee357db83fe9085346adb2bf1efa1fcfca4d5f90e0f0643e999a80f4a3.jpg) +Adversarial training + +![](images/f8b98bcd1baeea115b74cd5f72eb9697bc9f9773c4687e6400a46a91e69396c0.jpg) + +Table 4. Photographer ratings as in Tab. 2 comparing our main method to a variation with adversarial training instead of our fixed realism network. + +
MethodSaliency Attenuation
Effectiveness ↑Realism ↑
Adversarial Training5.06 (2.84)7.36 (3.07)
Ours - Random6.36 (2.79)6.34 (2.88)
+ +applied in the previous steps of training it encourages the network to apply subtle edits and hence a drop in effectiveness of the method. On the other hand, due to the lack of explicit realism training, the edits are unrealistic while the effectiveness is reasonable. Ratings reported in Tab. 4 also confirm our findings. + +# 5.4. Diversity and Optimality of Estimated Edits + +Fig. 9b illustrates the distribution of edit parameters estimated by our parameter estimation network for different images on ADE20K [24, 25] dataset. It shows that edit parameters are different for each image and is based on its content. Also, it shows that the range of estimated edits is not the same as the ranges used in Tab. 1 for real samples. + +To evaluate if the estimated edits are close to optimal with respect to realism, we provide Fig. 9a. In the figure we show a realism heatmap obtained by adding a small additive constant to the estimated edit parameter of saturation and exposure. Heatmaps show the estimated edit parameters (center of the heatmap) are in the optimal realism region. Changing the edit parameters in each direction reduces the realism of the end result. + +# 5.5. Generalization to Multiple Image Regions + +Since our model only modifies the region of interest, and performs a forward pass efficiently, we can run it on multiple regions and multiple masks by generating edit parameters for each region, in an iterative manner. Examples are provided in Figs. 1 and 10. We used the same approach with Gazeshift [17], which edits the whole image by estimating two sets of edit parameters, one for the region of interest (foreground) and one for the background. This formulation of Gazeshift makes iterative editing impractical, since there would be contradictory objectives between the + +![](images/347300b4e5dfe3e80eed0f428547ab1b9a77ff8763de8bb21ef19e8adba761dc.jpg) +(a) A heatmap visualizes the realism score achieved when we change the estimated saturation (x-axis) and exposure (y-axis). Our estimated values (center of the heatmap) achieve the optimal realism while changing the parameters in any direction reduces the realism. Sample edited images and their corresponding location in the heatmap are also visualized. + +![](images/997ebff0f137825fe1948a82de0d4048e45ee601bd2cf3013c03982b2f5acfff.jpg) +(b) The diversity of estimated parameters on ADE20K [24, 25] dataset. The x-axis is the range of each parameter. The attenuation task is blue, and amplification is labeled red. + +![](images/e924c57b8cc9da8f01d4050f705763fb6eb08c70b7a006052214bb1d72ea9ac3.jpg) +Figure 9. Visualizing diversity and optimality of edit parameters estimated by our method +Figure 10. Given an input image and masks to attenuate and amplify(left), Gazeshift when used iteratively on each object suffers from color artifacts (center top, faces, bowl and watermelons). Ours produces a notably more realistic and effective result (right). Contradictory objective of edits applied to background and foreground, Gazeshift fails to generalize to multiple regions and omitting the background edits (center bottom) reduces the effectiveness of the edits. Image credit: @tysonbrand + +iterations (what is foreground in one iteration becomes a background in the next iteration). For a more practical comparison, we omit background edits when running Gazeshift. Figure 10 shows that Gazeshift performance suffers on an iterative saliency enhancement task, but our method is able to generalize to multiple regions robustly. + +# 5.6. Limitations + +The global edits (applying the same edits to every pixel inside a mask), used in both our method and Gazeshift [17] require an accurate mask of the target region. As shown in Fig. 11 mask imperfections can cause unsmooth transitions around the boundaries. In these cases, pixel-wise optimization approaches like Deepsal [1] and MEC [16] do not suffer from heavy artifacts due to mask imperfections. + +![](images/5f17285b3ddb311a9d3cbf680f5270dc08aa270d7e3f6cc426adea45049c5df8.jpg) +Figure 11. The effect of non-smooth mask boundaries. Left, an input image has a mask with a sharp edge. Center, our method and Gazeshift [17] produce strong boundary artifacts around the mask region (see inset). Right, MEC [16] and Deepsal [1] do not exhibit this problem because they operate in a pixel-wise manner. + +# 6. Conclusion and Future work + +We describe a method to edit images using conventional image editing operators to attenuate or amplify the attention captured by a target region while preserving image realism. Realism is achieved by introducing an explicit, and separate realism network that is pre-trained to distinguish edited images. This strategy to achieve realism is distinct from prevailing approaches, including adversarial training schemes, as it introduces an additional form of weak supervision—manually specified ranges of parameter values that correspond to realistic and unrealistic ("fake") edits. Training with this realism critic makes it possible to estimate saliency modulating image edits that are significantly more realistic and robust. Together with our millisecond-level inference time, our approach offers a practical and deployable application of saliency guided image editing. + +# References + +[1] Kfir Aberman, Junfeng He, Yossi Gandelsman, Inbar Mosseri, David E. Jacobs, Kai Kohlhoff, Yael Pritch, and Michael Rubinstein. Deep saliency prior for reducing visual distraction. In Proc. CVPR, 2021. 1, 2, 4, 5, 6, 7, 8 +[2] Yen-Chung Chen, Keng-Jui Chang, Yi-Hsuan Tsai, Yu-Chiang Frank Wang, and Wei-Chen Chiu. Guide your eyes: Learning image manipulation under saliency guidance. In Proc. BMVC, 2019. 1, 2, 4, 7 +[3] Camilo Fosco, Anelise Newman, Pat Sukhum, Yun Bin Zhang, Nanxuan Zhao, Aude Oliva, and Zoya Bylinskii. How much time do you have? modeling multi-duration saliency. In Proc. CVPR, 2020. 1, 2 +[4] Leon A. Gatys, Matthias Kümmerer, Thomas S. A. Wallis, and Matthias Bethge. Guiding human gaze with convolutional neural networks. arXiv:2109.01980 [cs.CV], 2017. 1, 2, 4, 7 +[5] Aiko Hagiwara, Akihiro Sugimoto, and Kazuhiko Kawamoto. Saliency-based image editing for guiding visual attention. In Proc. PETMEI, 2011. 2 +[6] Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-image translation with conditional adversarial networks. In Proc. CVPR, 2017. 3 +[7] Sen Jia and Neil D.B. Bruce. EML-NET: An Expandable Multi-layer NETwork for saliency prediction. Image Vis. Comput., 95:103887, 2020. 1, 2, 4 +[8] Lai Jiang, Mai Xu, Xiaofei Wang, and Leonid Sigal. Saliency-guided image translation. In Proc. CVPR, 2021. 1, 2 +[9] Alexia Jolicoeur-Martineau. The relativistic discriminator: a key element missing from standard gan. In Proc. ICLR, 2019. 2 +[10] Matthias Kummerer, Thomas SA Wallis, Leon A Gatys, and Matthias Bethge. Understanding low-and high-level contributions to fixation prediction. In Proc. CVPR, 2017. 1, 2 +[11] Jean-Francois Lalonde and Alexei A Efros. Using color compatibility for assessing image realism. In Proc. ICCV, 2007. 2 +[12] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Proc. ECCV, 2014. 3 +[13] Xudong Mao, Qing Li, Haoran Xie, Raymond YK Lau, Zhen Wang, and Stephen Paul Smolley. Least squares generative adversarial networks. In Proc. ICCV, 2017. 3 +[14] R. Margolin, A. Tal, and L. Zelnik-Manor. What makes a patch distinct? In Proc. CVPR, 2013. 1, 2 +[15] Victor A. Mateescu and Ivan V. Bajic. Attention retargeting by color manipulation in images. In Proc. PIPV, 2014. 2, 5, 6, 7 +[16] Roey Mechrez, Eli Shechtman, and Lihi Zelnik-Manor. Saliency driven image manipulation. Mach. Vis. Appl., 30(2):189-202, 2019. 1, 2, 5, 6, 7, 8 +[17] Youssef Alami Mejjati, Celso F. Gomez, Kwang In Kim, Eli Shechtman, and Zoya Bylinskii. Look here! a parametric learning based approach to redirect visual attention. In Proc. ECCV, 2020. 1, 2, 4, 5, 6, 7, 8 + +[18] Tam Nguyen, Bingbing ni, Hairong Liu, Wei Xia, Jiebo Luo, Mohan Kankanhalli, and Shuicheng Yan. Image reattentionizing. IEEE Trans. Multimed., 15(8):1910-1919, 2013. 2 +[19] Junting Pan, Cristian Canton, Kevin McGuinness, Noel E. O'Connor, Jordi Torres, Elisa Sayrol, and Xavier and Giro-i Nieto. Salgan: Visual saliency prediction with generative adversarial networks. arXiv:1701.01081 [cs.CV], 2017.1.2 +[20] Sara L. Su, Frédo Durand, and Maneesh Agrawala. De-emphasis of distracting image regions using texture power maps. In Proc. APGV, 2005. 2 +[21] Mingxing Tan and Quoc Le. Efficientnet: Rethinking model scaling for convolutional neural networks. In Proc. ICML, 2019. 5 +[22] Javier Vazquez-Corral and Marcelo Bertalmio. Gamut mapping for visual attention retargeting. In Proc. CIC, 2017. 2 +[23] Lai-Kuan Wong and Kok-Lim Low. Saliency retargeting: An approach to enhance image aesthetics. In Proc. WACV, 2011, 2, 5, 6, 7 +[24] Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In Proc. CVPR, 2017. 7, 8 +[25] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. Int. J. Comput. Vision, 127(3):302-321, 2019. 7, 8 +[26] Jun-Yan Zhu, Philipp Krahenbuhl, Eli Shechtman, and Alexei A. Efros. Learning a discriminative model for the perception of realism in composite images. In Proc. 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(top) We develop a saliency-based image enhancement method that can be applied to multiple regions in the image to demephasize objects (steps 1, 2) or enhance subjects (steps 3, 4). (bottom) Our novel realism loss allows us to apply realistic edits to a wide variety of objects while state-of-the-art methods [1, 17] may generate less realistic editing results." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "spans": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 510, + 289, + 715 + ], + "type": "text", + "content": "Common editing operations performed by professional photographers include the cleanup operations: de-emphasizing distracting elements and enhancing subjects. These edits are challenging, requiring a delicate balance between manipulating the viewer's attention while maintaining photo realism. While recent approaches can boast successful examples of attention attenuation or amplification, most of them also suffer from frequent unrealistic edits. We propose a realism loss for saliency-guided image enhancement to maintain high realism across varying image types, while attenuating distractors and amplifying objects of interest. Evaluations with professional photographers confirm that we achieve the dual objective of realism and effectiveness, and outperform the recent approaches on their own datasets, while requiring a smaller memory footprint and runtime. We thus offer a viable solution for automating image enhancement and photo cleanup operations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 499, + 386, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 499, + 386, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 499, + 386, + 511 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 521, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 675 + ], + "type": "text", + "content": "In everyday photography, the composition of a photo typically encompasses subjects on which the photographer intends to focus our attention, rather than other distracting things. When distracting things cannot be avoided, photographers routinely edit their photos to de-emphasize them. Conversely, when the subjects are not sufficiently visible, photographers routinely emphasize them. Among the most common emphasis and de-emphasis operations performed by professionals are the elementary ones: changing the saturation, exposure, or the color of each element. Although conceptually simple, these operations are challenging to apply because they must delicately balance the effects on the viewer attention with photo realism." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "To automate this editing process, recent works use saliency models as a guide [1,2,4,8,16,17]. These saliency models [3,7,10,14,19] aim to predict the regions in the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "186" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": "image that catch the viewer's attention, and saliency-guided image editing methods are optimized to increase or decrease the predicted saliency of a selected region. Optimizing solely based on the predicted saliency, however, often results in unrealistic edits, as illustrated in Fig. 1. This issue results from the instability of saliency models under the image editing operations, as saliency models are trained on unedited images. Unrealistic edits can have low predicted saliency even when they are highly noticeable to human observers, or vice versa. This was also noted by Aberman et al. [1], and is illustrated in Fig. 2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 359 + ], + "type": "text", + "content": "Previous methods tried to enforce realism using adversarial setups [2, 4, 8, 17], GAN priors [1, 8], or cycle consistency [2] but with limited success (Fig. 1). Finding the exact point when an image edit stops looking realistic is challenging. Rather than focusing on the entire image, in this work, we propose a method for measuring the realism of a local edit. To train our network, we generate realistic image edits by subtle perturbations to exposure, saturation, color or white balance, as well as very unrealistic edits by applying extreme adjustments. Although our network is trained with only positive and negative examples at the extremes, we successfully learn a continuous measure of realism for a variety of editing operations as shown in Fig. 3." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 360, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 443 + ], + "type": "text", + "content": "We apply our realism metric to saliency-guided image editing by training the system to optimize the saliency of a selected region while being penalized for deviations from realism. We show that a combined loss allows us to enhance or suppress a selected region successfully while maintaining high realism. Our method can be also be applied to multiple regions in a photograph as shown in Fig. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 444, + 289, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 289, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 289, + 551 + ], + "type": "text", + "content": "Evaluations with professional photographers and photo editors confirm our claim that we maintain high realism and succeed at redirecting attention in the edited photo. Further, our results are robust to different types of images including human faces, and are stable across different permutations of edit parameters. Taken together with our model size of 26Mb and run-time of 8ms, these results demonstrate that we have a more viable solution for broader use than the approaches that are available for these tasks to date." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 713 + ], + "type": "text", + "content": "Various image enhancement methods have been introduced in the literature to amplify a region of interest or de-emphasise distracting regions, improve image aesthetics, and redirect the viewer's attention. This task has been referred to as attention retargeting [15] or reattentionizing [18] as well. Earlier methods [5,15,20,22,23] incorporated prior knowledge of saliency cues (saturation, sharpness, color, gamut, etc.) to guide the editing process to achieve the desired change in saliency. But, relying solely on saliency cues both limits the diversity of generated edits, and creates unrealistic edits due to the lack of semantic" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 83, + 366, + 155 + ], + "blocks": [ + { + "bbox": [ + 318, + 75, + 359, + 83 + ], + "lines": [ + { + "bbox": [ + 318, + 75, + 359, + 83 + ], + "spans": [ + { + "bbox": [ + 318, + 75, + 359, + 83 + ], + "type": "text", + "content": "Original image" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 83, + 366, + 155 + ], + "lines": [ + { + "bbox": [ + 307, + 83, + 366, + 155 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 366, + 155 + ], + "type": "image", + "image_path": "aaf1fb2d0518bd051437d1937d2fa424a5dd6ca71a84c1ff316a34fdbb0f2122.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 155, + 366, + 195 + ], + "blocks": [ + { + "bbox": [ + 307, + 155, + 366, + 195 + ], + "lines": [ + { + "bbox": [ + 307, + 155, + 366, + 195 + ], + "spans": [ + { + "bbox": [ + 307, + 155, + 366, + 195 + ], + "type": "image", + "image_path": "af30ae7160142775f660cee5aadb7b879b928f296a4d031ae58bbfe5ed57b283.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 198, + 547, + 254 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 254 + ], + "type": "text", + "content": "Figure 2. Predicted saliency maps [7] for the original images and edited versions, with extreme edits applied. Note that saliency models are typically trained with realistic images. This makes them susceptible to inaccurate predictions for unrealistic inputs, as the green woman in the top row estimated to have low saliency." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 367, + 83, + 425, + 141 + ], + "blocks": [ + { + "bbox": [ + 378, + 75, + 416, + 83 + ], + "lines": [ + { + "bbox": [ + 378, + 75, + 416, + 83 + ], + "spans": [ + { + "bbox": [ + 378, + 75, + 416, + 83 + ], + "type": "text", + "content": "Saliency map" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 367, + 83, + 425, + 141 + ], + "lines": [ + { + "bbox": [ + 367, + 83, + 425, + 141 + ], + "spans": [ + { + "bbox": [ + 367, + 83, + 425, + 141 + ], + "type": "image", + "image_path": "c3a907f1b78db61d9d3587053c45c1989c00978f786d7dfbe5addc41c2c81099.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 367, + 141, + 425, + 195 + ], + "blocks": [ + { + "bbox": [ + 367, + 141, + 425, + 195 + ], + "lines": [ + { + "bbox": [ + 367, + 141, + 425, + 195 + ], + "spans": [ + { + "bbox": [ + 367, + 141, + 425, + 195 + ], + "type": "image", + "image_path": "9ffbeb94f704c93408b24f2a059d6b6f1d19105d5c6a8d676feb84217a09055e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 83, + 485, + 155 + ], + "blocks": [ + { + "bbox": [ + 437, + 75, + 473, + 83 + ], + "lines": [ + { + "bbox": [ + 437, + 75, + 473, + 83 + ], + "spans": [ + { + "bbox": [ + 437, + 75, + 473, + 83 + ], + "type": "text", + "content": "Edited image" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 83, + 485, + 155 + ], + "lines": [ + { + "bbox": [ + 427, + 83, + 485, + 155 + ], + "spans": [ + { + "bbox": [ + 427, + 83, + 485, + 155 + ], + "type": "image", + "image_path": "af874ae7afe0f2208e3166875c3ce10af3fc631e0bf569b3133e8d89f9dd1cd9.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 155, + 485, + 195 + ], + "blocks": [ + { + "bbox": [ + 427, + 155, + 485, + 195 + ], + "lines": [ + { + "bbox": [ + 427, + 155, + 485, + 195 + ], + "spans": [ + { + "bbox": [ + 427, + 155, + 485, + 195 + ], + "type": "image", + "image_path": "6dcd9ac78f5bb7d8bc8337923d8625293e7924df7142309384f14bb415fa26b0.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 486, + 83, + 545, + 141 + ], + "blocks": [ + { + "bbox": [ + 495, + 75, + 533, + 83 + ], + "lines": [ + { + "bbox": [ + 495, + 75, + 533, + 83 + ], + "spans": [ + { + "bbox": [ + 495, + 75, + 533, + 83 + ], + "type": "text", + "content": "Saliency map" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 486, + 83, + 545, + 141 + ], + "lines": [ + { + "bbox": [ + 486, + 83, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 486, + 83, + 545, + 141 + ], + "type": "image", + "image_path": "6c72891dfb6bd2eddccc2ee3e204a261e45a99de4813b46af6359a43963ac6bd.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 486, + 141, + 545, + 195 + ], + "blocks": [ + { + "bbox": [ + 486, + 141, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 486, + 141, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 486, + 141, + 545, + 195 + ], + "type": "image", + "image_path": "008a2af1596f0a901d546163043e19c9fbdc0a0e8eb5c19032859864be2d6f21.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 264, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 547, + 312 + ], + "type": "text", + "content": "constraints. As our experiments show, OHR [15] tends to generate unrealistic color changes that are semantically incorrect, and WRS [23] is limited to contrast and saturation adjustments with limited effectiveness." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 315, + 546, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 546, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 546, + 447 + ], + "type": "text", + "content": "Recent works leverage saliency estimation networks [3, 7, 10, 14, 19] to optimize for a desired saliency map instead of relying on prior saliency cues. Saliency models are trained to output a heatmap that represents where human gaze would be concentrated in an image. These models are not trained to respond to the realism of the input image. Hence they might predict an inconsistent decrease or increase in the saliency of a region when unrealistic or semantically implausible edits are applied, which would be otherwise jarring to human viewers (Fig. 2). Using saliency as the only supervision can result in unrealistic images." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 449, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 616 + ], + "type": "text", + "content": "To prevent unrealistic edits, prior works enforce constraints on the allowable changes, use adversarial training [2, 4, 8, 17] or exploit learned priors from GAN-based models [1, 8]. For instance, Mechrez et al. [16] and Aberman et al. (Warping) [1] constrain the result to match the input content in order to maintain its appearance. Aberman et al. (CNN and Recolorization) [1] use a regularization term that limits the amount of change an image can undergo to maintain the realism. Mejjati et al. [17] designed a global parametric approach to limit the editing operations to a set of common photographic ones. Chen et al. [2] exploit cycle consistency to keep the output within the domain of the input image. Gatys et al. [4] use a texture loss alongside the VGG perceptual loss as a proxy for realism." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Lalonde et al. [11] argue that humans prefer color consistency within images, regardless of object semantics. They use color statistics to measure realism and use it to recolor the images to match the background in compositing task. Zhu et al. [26] train a network to discriminate between natural images and computer-generated composites and use it as a realism measure for compositing task. Realism is also a crucial factor in GANs, as highlighted by [9]." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "187" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 83, + 542, + 133 + ], + "blocks": [ + { + "bbox": [ + 89, + 71, + 501, + 81 + ], + "lines": [ + { + "bbox": [ + 89, + 71, + 501, + 81 + ], + "spans": [ + { + "bbox": [ + 89, + 71, + 501, + 81 + ], + "type": "text", + "content": "Table 1. Parameter value ranges used to generate real and fake training images for the realism estimation network." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 83, + 542, + 133 + ], + "lines": [ + { + "bbox": [ + 52, + 83, + 542, + 133 + ], + "spans": [ + { + "bbox": [ + 52, + 83, + 542, + 133 + ], + "type": "table", + "html": "
ExposureSaturationColor curveWhite balancingNumber of edits
Real[0.85, 1.15][0.85, 1.15][0.85, 1.15]Not allowed[1, 3]
Fake[0.5, 0.75] ∪ [1.5, 2][0, 0.5] ∪ [1.5 - 2][0.5, 2][0.9, 1][2, 4]
Fake(human specific)[0.5, 0.75] ∪ [1.25, 1.5][0.5, 0.75] ∪ [1.25, 1.5][0.5, 2]Not allowed[2, 3]
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The efficacy of the realism estimation network is illustrated over a range of exposure and saturation adjustments. Left is " + }, + { + "bbox": [ + 46, + 309, + 545, + 343 + ], + "type": "inline_equation", + "content": "\\Delta \\mathcal{R}" + }, + { + "bbox": [ + 46, + 309, + 545, + 343 + ], + "type": "text", + "content": " plotted (vertical axis) for example images (second column) when selected regions (third column) are edited. Right, the edited images are shown with the corresponding change in estimated realism (inset numbers), and the value of the editing parameter applied (underneath)." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 116, + 225, + 187, + 304 + ], + "blocks": [ + { + "bbox": [ + 116, + 225, + 187, + 304 + ], + "lines": [ + { + "bbox": [ + 116, + 225, + 187, + 304 + ], + "spans": [ + { + "bbox": [ + 116, + 225, + 187, + 304 + ], + "type": "image", + "image_path": "3f0c77046483687790402277c2099eaa014764739de66084db6c67093ddef599.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 188, + 225, + 255, + 304 + ], + "blocks": [ + { + "bbox": [ + 188, + 225, + 255, + 304 + ], + "lines": [ + { + "bbox": [ + 188, + 225, + 255, + 304 + ], + "spans": [ + { + "bbox": [ + 188, + 225, + 255, + 304 + ], + "type": "image", + "image_path": "070e6f033eed4c022373bf6b08268c6ce146d46f9330db5f06e9e6190af330d8.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 258, + 225, + 325, + 304 + ], + "blocks": [ + { + "bbox": [ + 258, + 225, + 325, + 304 + ], + "lines": [ + { + "bbox": [ + 258, + 225, + 325, + 304 + ], + "spans": [ + { + "bbox": [ + 258, + 225, + 325, + 304 + ], + "type": "image", + "image_path": "cb4baaf50c240c2fcd8d46bc948303a01e3bdc74c3b94edd99a7c518beaece97.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 328, + 225, + 395, + 304 + ], + "blocks": [ + { + "bbox": [ + 328, + 225, + 395, + 304 + ], + "lines": [ + { + "bbox": [ + 328, + 225, + 395, + 304 + ], + "spans": [ + { + "bbox": [ + 328, + 225, + 395, + 304 + ], + "type": "image", + "image_path": "2231d02a5cf9d289345bce597c7779867fbb883c1b75f3d1dc58c5cc621293a7.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 397, + 225, + 432, + 304 + ], + "blocks": [ + { + "bbox": [ + 397, + 225, + 432, + 304 + ], + "lines": [ + { + "bbox": [ + 397, + 225, + 432, + 304 + ], + "spans": [ + { + "bbox": [ + 397, + 225, + 432, + 304 + ], + "type": "image", + "image_path": "da7e037a78e41865d447679e42ddc1fe48fbadcfacb094ac7cb7244a688dd620.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 434, + 225, + 467, + 304 + ], + "blocks": [ + { + "bbox": [ + 434, + 225, + 467, + 304 + ], + "lines": [ + { + "bbox": [ + 434, + 225, + 467, + 304 + ], + "spans": [ + { + "bbox": [ + 434, + 225, + 467, + 304 + ], + "type": "image", + "image_path": "08caa98646d22482a4d94015aa5cb0b2f1a01f75b886717fc5b539b7ac28f745.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 470, + 225, + 502, + 304 + ], + "blocks": [ + { + "bbox": [ + 470, + 225, + 502, + 304 + ], + "lines": [ + { + "bbox": [ + 470, + 225, + 502, + 304 + ], + "spans": [ + { + "bbox": [ + 470, + 225, + 502, + 304 + ], + "type": "image", + "image_path": "dfbaf4ba37638113f5d23ae3680f948dfcd799703666011313a0e1f090d5c568.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 504, + 225, + 538, + 304 + ], + "blocks": [ + { + "bbox": [ + 504, + 225, + 538, + 304 + ], + "lines": [ + { + "bbox": [ + 504, + 225, + 538, + 304 + ], + "spans": [ + { + "bbox": [ + 504, + 225, + 538, + 304 + ], + "type": "image", + "image_path": "c8544a41c71175fa09e1e3dfd68ff99963909154bda3d9fe7843c3709f6f9291.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 427 + ], + "type": "text", + "content": "We present a new method for estimating the realism of a local edit. Combining our realism loss with saliency guidance, we show that we can successfully apply attention attenuation or amplification while keeping the final result realistic without requiring data annotated with realism or bulky GAN priors to estimate realism." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 440, + 151, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 151, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 151, + 452 + ], + "type": "text", + "content": "3. Realism Network" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "type": "text", + "content": "When editing specific regions in an image, it is challenging to maintain the overall realism of the photograph. How quickly realism starts to degrade depends on the contents and size of the image regions, the overall composition of the scene, as well as the type of edits being applied. This makes the problem of defining precisely when an image edit stops looking realistic particularly challenging." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": "In this work, we propose to train a realism network using only realistic and unrealistic examples at the extremes. We generate realistic edits by slightly perturbing image values, and unrealistic edits by applying aggressive edits. We show that, despite being trained on binary data, our network can estimate continuous realism scores that can adapt to different types of image regions and scenes. Our approach was inspired by the work of Zhu et al. [26], who similarly learn their realism from binary real and synthetic composites." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "To generate real and fake samples, we exploit different parameter ranges for commonly used editing operations - exposure, saturation, color curve, and white balancing (formal definitions in the Supplementary Material). For instance, increasing the exposure of a region too much can" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 355, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 403 + ], + "type": "text", + "content": "result in an unrealistic image, while a subtle increase to saturation will not significantly affect the realism. Based on experimentation, we determined the set of parameter ranges in Tab. 1 to apply to image regions to create our training data." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 403, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 558 + ], + "type": "text", + "content": "To generate a training example, we first select a random number of edits (between 1-4), then an order for the edit operations (e.g., exposure, saturation, color curve, white balancing), and values for each of the operations, sampled uniformly at random from the pre-specified ranges in Tab. 1. We apply these edits in the selected order to a region segment in an MS-COCO image [12]. Fake examples are generated by purposefully selecting extreme values. Real examples are generated by sampling subtle edits within narrower ranges. Because of the semantic importance of human faces and increased sensitivity to edits in facial regions, we enforce smaller parameter ranges when applying edits to faces. Fig. 4 shows several examples." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "text", + "content": "We use the Pix2Pix [6] network architecture followed by two MLP layers to estimate the realism score " + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "text", + "content": " of the input. For our samples in the training data, " + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "text", + "content": " is defined as 1 for real and 0 for fake samples. We also condition the output on the input region by feeding the region's mask " + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 559, + 545, + 642 + ], + "type": "text", + "content": " as input to the network. We use squared error [13] as the critic to compute the loss on the estimated value:" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 319, + 648, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 648, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 319, + 648, + 545, + 672 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s c}} = \\frac {1}{2} \\mathcal {R} \\left(I _ {\\text {f a k e}}, M\\right) ^ {2} + \\frac {1}{2} \\left(\\mathcal {R} \\left(I _ {\\text {r e a l}}, M\\right) - 1\\right) ^ {2} \\tag {1}", + "image_path": "3996ec1110449663b61e814baa2a3c7df40bea9c5d9eb2f15ab860e0baf383ff.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{\\text{fake}}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{\\text{real}}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " are the generated fake and real samples. 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Examples of fake and real images that are used to train the realism estimation network. See Section 3 for more details." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 108, + 224, + 166, + 270 + ], + "blocks": [ + { + "bbox": [ + 108, + 224, + 166, + 270 + ], + "lines": [ + { + "bbox": [ + 108, + 224, + 166, + 270 + ], + "spans": [ + { + "bbox": [ + 108, + 224, + 166, + 270 + ], + "type": "image", + "image_path": "9f984f6eab4fc07b1ac0b1c1de6cbe5f9d5b8ba70f54acdca84a96a52e4b5f50.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 168, + 224, + 227, + 270 + ], + "blocks": [ + { + "bbox": [ + 168, + 224, + 227, + 270 + ], + "lines": [ + { + "bbox": [ + 168, + 224, + 227, + 270 + ], + "spans": [ + { + "bbox": [ + 168, + 224, + 227, + 270 + ], + "type": "image", + "image_path": "51be0d266cf6c68cfcc12b8c0202ec65f4463d9592ec61023f7a38966bd61a44.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 228, + 224, + 286, + 270 + ], + "blocks": [ + { + "bbox": [ + 228, + 224, + 286, + 270 + ], + "lines": [ + { + "bbox": [ + 228, + 224, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 228, + 224, + 286, + 270 + ], + "type": "image", + "image_path": "1e5962353525750138cbaeece2ed47f36dbcf7b95fd871db48465294fe56cbb8.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "type": "text", + "content": "estimated for the original image " + }, + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "type": "text", + "content": " and the edited image " + }, + { + "bbox": [ + 47, + 306, + 284, + 319 + ], + "type": "inline_equation", + "content": "I^{\\prime}" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 85, + 332, + 286, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 332, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 85, + 332, + 286, + 345 + ], + "type": "interline_equation", + "content": "\\Delta \\mathcal {R} (I ^ {\\prime}, I, M) = \\mathcal {R} (I ^ {\\prime}, M) - \\mathcal {R} (I, M), \\tag {2}", + "image_path": "a26f69254f98c2d4bcbf7d6dbd96873ce689a5f06b8c6cb7122e3eb8040dd862.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 358, + 251, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 251, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 251, + 371 + ], + "type": "text", + "content": "where the edited region is defined by the mask " + }, + { + "bbox": [ + 47, + 358, + 251, + 371 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 358, + 251, + 371 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 373, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 468 + ], + "type": "text", + "content": "As Fig. 3 demonstrates " + }, + { + "bbox": [ + 46, + 373, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\Delta \\mathcal{R}" + }, + { + "bbox": [ + 46, + 373, + 287, + 468 + ], + "type": "text", + "content": " gives us continuous realism values for a range of edit parameters, despite the network being trained only on extreme cases. It also shows that the range of edits that are considered realistic by our network is not the same for each image and depends on the subject and editing operation. We show more examples of edits that are classified realistic or unrealistic by our network in Fig. 9 and the Supplementary Material." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 485, + 254, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 254, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 254, + 499 + ], + "type": "text", + "content": "4. Saliency Guided Image Enhancement" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": "We develop a saliency-guided image editing pipeline that enforces our realism loss to generate realistic and effective object enhancement or distractor suppression results for a given mask. Our system can estimate a set of editing parameters for any permutation of 4 editing operators: exposure, saturation, color curve, and white balancing." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "In constructing our system, we borrow many ideas from the existing saliency-guided image editing literature, and focus our design improvements on improving the realism of the results, especially by including our proposed realism loss. Since these edit operations are non-linear, different orderings of edits changes the end results. As a result, we condition the regressed parameters on the permutation of the edit operations by feeding the permutation as an input to the network. More details on the architecture of the network and the embedding used to encode the permutation is included in the Supplementary Material." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "Saliency Loss A pretrained saliency model [7] (SalNet) is used as a proxy for the viewer attention that would be captured by image regions before and after applying the edits, to supervise the image editing process." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "content": "We measure the change in the saliency of the region of interest as the expected value of its relative change within the masked region:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 319, + 164, + 545, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 164, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 319, + 164, + 545, + 191 + ], + "type": "interline_equation", + "content": "S (I, I ^ {\\prime}, M) = \\mathbb {E} _ {M} \\left[ \\frac {S a l N e t (I) - S a l N e t \\left(I ^ {\\prime}\\right)}{S a l N e t (I)} \\right] \\tag {3}", + "image_path": "6755fb866073b2135c79af3c89abe8be4fd289b6aabefbae3e2f03e969f38dbb.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "inline_equation", + "content": "\\mathbb{E}" + }, + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "text", + "content": " denotes the expectation and " + }, + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 198, + 544, + 210 + ], + "type": "text", + "content": " is the region mask." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 211, + 545, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 318 + ], + "type": "text", + "content": "As Fig. 2 shows, the predicted saliency heatmaps can change drastically when applied to unrealistic edits. As a result, relying on conventional metrics (e.g., absolute and relative differences by [1, 17], Binary cross entropy by [2] and KL-divergence by [4]) to measure the change in saliency can cause large rewards or penalties during optimization. Infinitely large rewards for an unreal edit reduces the effectiveness of the realism term in the final loss function. To tackle this issue we define our saliency loss function as:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 366, + 330, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 330, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 366, + 330, + 545, + 342 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s a l}} = \\exp \\left(w _ {\\mathrm {s a l}} S \\left(I, I ^ {\\prime}, M\\right)\\right) \\tag {4}", + "image_path": "391df6ed298f8e6ee00c9d9e4d83cab4fbd77439a31395019804704b857aca09.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 348, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 479 + ], + "type": "text", + "content": "When saliency moves in the desired direction, the exponential squashes the loss, converging to the minimum and reducing the penalty quickly, acting as a soft margin. This converging behaviour prevents large rewards that can be generated by unrealistic edits during training. The exponential term imposes larger penalties when saliency moves in the wrong direction, providing robustness against outliers and faster convergence. " + }, + { + "bbox": [ + 304, + 348, + 545, + 479 + ], + "type": "inline_equation", + "content": "w_{sal}" + }, + { + "bbox": [ + 304, + 348, + 545, + 479 + ], + "type": "text", + "content": " controls the absolute value of the loss to balance the weight of saliency loss in our final loss, which we set to 5 and -1 for amplification and attenuation, respectively." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 495, + 494, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 494, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 494, + 506 + ], + "type": "text", + "content": "Realism Loss The realism loss is defined as:" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 343, + 516, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 516, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 343, + 516, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e a l i s m}} = R e L U \\left(- \\Delta \\mathcal {R} \\left(I ^ {\\prime}, I, M\\right) - b _ {r}\\right) \\tag {5}", + "image_path": "f680f5ffd6361b8e5fb66d958d77f936e7e69b8567a42095e43b15a3fe6808e6.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 537, + 545, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 545, + 621 + ], + "type": "text", + "content": "This loss is designed to penalize unrealistic edits, while giving no rewards for edits that improve the estimated realism score of the input. This prevents the network from being penalized by images that receive a low realism score even before any edits are applied. ReLU and offset " + }, + { + "bbox": [ + 304, + 537, + 545, + 621 + ], + "type": "inline_equation", + "content": "b_{r}" + }, + { + "bbox": [ + 304, + 537, + 545, + 621 + ], + "type": "text", + "content": " provide a margin that allows a slight decrease in realism without a penalty which we set to 0.1 in our experiments." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 305, + 622, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 622, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 305, + 622, + 545, + 645 + ], + "type": "text", + "content": "We train two separate networks for each. 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A detailed explanation of the architecture specifics, datasets and training is provided in Supplementary Material." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 47, + 410, + 190, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 190, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 190, + 423 + ], + "type": "text", + "content": "5. Experiments and Results" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 433, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 287, + 505 + ], + "type": "text", + "content": "We compare our method against state of the art saliency based image editing approaches - Deepsal [1], Gazeshift [17] and MEC [16]. MEC provides results on their dataset alongside pre-computed results of WRS [23] and OHR [15] on the same dataset. We use this dataset to compare against WRS and OHR as well as MEC." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 508, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 287, + 604 + ], + "type": "text", + "content": "The EfficientNet [21] backbone used in our architecture is known for its small size. Our results are thus generated significantly faster than the other state-of-the-art (SOTA) methods with bulkier architectures and slower per-image optimizations. Based on speed measures reported in [17] Table 1c, MEC takes more than a day, OHR needs 30 seconds and Gazeshift takes 8 seconds to process each image, while our model requires only 8ms per image." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": "We present both qualitative and quantitative results. Since our method takes the permutation of the edits as input during inference time we select the permutation at random for the presented results unless mentioned otherwise." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "text", + "content": "5.1. Qualitative Comparison" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "content": "Figs. 5, 6, and 7 illustrate our results compared to the SOTA. They show our method performs different edits based on the contents of the image. It can apply more significant color changes that camouflage the distractor " + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "inline_equation", + "content": "(2^{\\mathrm{nd}}" + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "inline_equation", + "content": "4^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "content": " rows of Fig. 6, " + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "inline_equation", + "content": "3^{\\mathrm{rd}}" + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "content": " row of Fig. 5) or very subtle edits for human faces " + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "inline_equation", + "content": "(1^{\\mathrm{st}}" + }, + { + "bbox": [ + 304, + 91, + 545, + 174 + ], + "type": "text", + "content": " row of Fig. 6). The intensity and characteristics of the applied edits depends on semantics." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "type": "text", + "content": "The use of adversarial loss in Gazeshift [17] and the regularization used in Deepsal [1] constrain the edits their methods apply without taking realism explicitly into account. As results show, they often apply unrealistic edits (e.g., the camouflaged signs in Fig. 5 or the unnatural skin tone and the color artifacts in Fig. 6) or very subtle edits with lower effectiveness." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 259, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 378 + ], + "type": "text", + "content": "MEC [16] reuses the color patterns and textures available in the image to update the target region. On the other hand different regions and textures can correspond to different semantics. Consequently, as illustrated in Fig. 7a this method can apply incompatible color and texture values to produce unrealistic edits (green crocodile eye, orange traffic sign) or ineffective enhancements (brown bird). Fig. 7b provides a comparison on their distractor suppression image set. Our method performs comparable in terms of effectiveness and generates realistic results consistently." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 380, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 475 + ], + "type": "text", + "content": "OHR [15] tries to maximize the color distinction between the masked region and the rest of the image for the image enhancement task. Without explicit realism modeling, it tends to generate unrealistic colors (e.g., blue crocodile, bird, and horse in Fig. 7a). While incorrect colors increase the saliency of these regions, they do so at the cost of realism. For similar reasons, this method is ineffective suppressing distractors (Fig. 7b)." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "type": "text", + "content": "WRS [23] does not generate unrealistic images, but also makes edits that are hardly noticeable, and less effective at enhancing or suppressing the target regions. We believe this is due to the purposely limited range of allowed edit parameters (luminance, saturation and sharpness)." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 544, + 479, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 479, + 558 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 479, + 558 + ], + "type": "text", + "content": "5.2. What Do Photographers Think?" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 563, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 647 + ], + "type": "text", + "content": "To include the perspective of professional photographers in comparing our results to others, we ran a user study. We report our results using three choices of parameter orderings: choosing the one that achieves the Best Saliency, the one that generates the Best Realism (according to our realism estimation network), and a permutation of parameters selected at Random as used for the qualitative figures." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 306, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 545, + 713 + ], + "type": "text", + "content": "User Study We recruited 8 professionals from UpWork, all of whom have multiple years of experience with photography, as well as using Photoshop to edit photos. We used the Appen platform for hosting our rating tasks." + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "text", + "content": "1Deepsal, WRS and MEC do not provide an open-source implementation. Hence, we relied on the results included on their project pages. Also, Deepsal authors kindly provided us with results on Adobe Stock dataset for their \"convolutional network\" variation." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "190" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 373, + 340 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 373, + 340 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 373, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 373, + 340 + ], + "type": "image", + "image_path": "8a53c614ea083348e103a3fc4476d52431fe2c1420d76dda2ea2f90b9edf16d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 96, + 342, + 496, + 354 + ], + "lines": [ + { + "bbox": [ + 96, + 342, + 496, + 354 + ], + "spans": [ + { + "bbox": [ + 96, + 342, + 496, + 354 + ], + "type": "text", + "content": "Figure 6. Saliency modulation compared to GazeShift [17] and Deepsal [1] on Adobe Stock images from [17]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 381, + 70, + 547, + 340 + ], + "blocks": [ + { + "bbox": [ + 381, + 70, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 381, + 70, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 381, + 70, + 547, + 340 + ], + "type": "image", + "image_path": "2df726e8aa4fb412c92710525e2fb13fcb7715ebc20e4d42857483b02d78e2f0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 47, + 363, + 294, + 548 + ], + "blocks": [ + { + "bbox": [ + 47, + 363, + 294, + 548 + ], + "lines": [ + { + "bbox": [ + 47, + 363, + 294, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 294, + 548 + ], + "type": "image", + "image_path": "d818a347ef52d037a2d446c3d37c043a36170f538e4f573fc6f2f74b754ff01b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 296, + 363, + 544, + 557 + ], + "blocks": [ + { + "bbox": [ + 296, + 363, + 544, + 557 + ], + "lines": [ + { + "bbox": [ + 296, + 363, + 544, + 557 + ], + "spans": [ + { + "bbox": [ + 296, + 363, + 544, + 557 + ], + "type": "image", + "image_path": "fe536d135db8b2522230045c99701696dd7b61fa7bf91bf50d9fe3a20a306405.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 559, + 494, + 571 + ], + "lines": [ + { + "bbox": [ + 97, + 559, + 494, + 571 + ], + "spans": [ + { + "bbox": [ + 97, + 559, + 494, + 571 + ], + "type": "text", + "content": "Figure 7. Saliency modulation compared to MEC [16], WRS [23] and OHR [15] on the Mechrez dataset [16]." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 578, + 290, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 290, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 290, + 710 + ], + "type": "text", + "content": "Our study participants were presented with a panel of 3 images: the original image, mask, and an edited result from one of methods evaluated. They were asked to \"rate each image based on 2 criteria\" - effectiveness and realism, with the following definitions provided for the attenuate version of the task: \"The images were edited to make certain objects and regions less distracting. An image edit is effective if the masked objects/regions have indeed become less distracting. An image edit is realistic if the photo does not look edited.\" For the amplify version of the task, the wording for effectiveness was modified to: \"The im" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 578, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 651 + ], + "type": "text", + "content": "ages were edited to make certain objects and regions pop-out (more attention-capturing, or salient). An image edit is effective if the masked objects/regions have indeed become more attention-capturing.\" Images were randomly shuffled in each task, so the photographers rated the images and methods independently of each other." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Results In Tab. 2 we compare our approach to GazeShift and Deepsal on the 30 Adobe Stock images from [17]. We find that our approach achieves significantly higher scores for both effectiveness and realism compared to GazeShift in" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "191" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 128, + 286, + 186 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 125 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 125 + ], + "type": "text", + "content": "Table 2. Photographer ratings (on a 1 to 10 scale, higher is better) of effectiveness (i.e., achieve objective of attenuation or amplification of saliency) and realism (i.e., photo looks natural) on the dataset of 30 Adobe stock images. Numbers are the mean score across 8 photographers, with standard deviation in parentheses." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 128, + 286, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 128, + 286, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 128, + 286, + 186 + ], + "type": "table", + "html": "
MethodSaliency AttenuationSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
GazeShift [17]4.78 (2.89)5.93 (3.13)7.36 (2.37)7.07 (2.76)
DeepSal [1]4.04 (2.90)8.49 (2.72)--
Ours - Best Realism6.56 (2.73)6.78 (2.70)7.39 (2.17)8.31 (1.89)
Ours - Random6.36 (2.79)6.34 (2.88)7.36 (2.21)8.27 (1.94)
Ours - Best Saliency6.64 (2.79)6.31 (2.70)7.50 (2.08)8.15 (2.10)
", + "image_path": "b47f9ad1f0d1e99fe3d27c9cd06072119c7bcac087f449553e5a0a777348aa30.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 220, + 286, + 272 + ], + "blocks": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "lines": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "type": "text", + "content": "Table 3. Photographer ratings as in Tab. 2 on (a) Mechrez [16] dataset and (b) the 14 images from DeepSal project webpage [1]" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 220, + 286, + 272 + ], + "lines": [ + { + "bbox": [ + 50, + 220, + 286, + 272 + ], + "spans": [ + { + "bbox": [ + 50, + 220, + 286, + 272 + ], + "type": "table", + "html": "
MethodSaliency AttenuationMethodSaliency Amplification
Effectiveness ↑Realism ↑Effectiveness ↑Realism ↑
Deepsal [1]7.08 (2.84)5.82 (3.43)MEC [16]7.06 (2.68)7.31 (2.93)
WRS [23]5.41 (3.22)7.97 (2.70)
Ours - Random6.83 (2.52)7.41 (2.70)OHR [15]7.04 (3.04)5.18 (3.76)
Ours - Random6.24 (2.9)8.88 (1.74)
(b)
", + "image_path": "e05d202ff6bd6d556c5010f8fb49ed1fa175ba32d094ed54304610b8235f8b05.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 278, + 286, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 286, + 386 + ], + "type": "text", + "content": "the attenuation task. This matches our qualitative observations that GazeShift is not successful at the task of attenuating distractor. GazeShift specializes in amplifying saliency in image regions, and we achieve similar performance on this task, while also maintaining significantly higher realism levels. In addition, results show a poor effectiveness score for Deepsal as a result of subtle edits in Fig. 6. Subtle edits mean the realism score remains high since the results are almost identical to the original images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 386, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 286, + 469 + ], + "type": "text", + "content": "Since Deepsal was ineffective on Adobe Stock images, to provide a fair comparison we also compare to Deepsal on 14 images they provided on their project page in Tab. 3a. We achieve significantly higher realism scores while being similarly effective at reducing the saliency of the distractors. This matches our qualitative observations that Deepsal edits can be quite extreme and not always photo realistic." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 469, + 286, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 286, + 564 + ], + "type": "text", + "content": "Tab. 3b shows user study results on Mechrez dataset [16].2 We used 77 images from the dataset to perform the user study. Results confirm that our results are superior in the realism while we achieve a comparable effectiveness compared MEC. WRS's low effectiveness yields a high realism score as its results are almost identical to the input; while the unrealistic color changes by OHR result in low realism and effectiveness scores." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 572, + 140, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 140, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 140, + 585 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 286, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 286, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 286, + 686 + ], + "type": "text", + "content": "We trained a variation of our method in which instead of a fixed realism score estimation model we used a discriminator as adversarial loss. We trained the discriminator as part of an adversarial training approach, similar to related work [2, 4, 17]. We used the input image as the real sample and the generated image as the fake sample during training. Fig. 8 illustrates sample results with this training strategy. Since the discriminator is trained to penalize \"any edits\"" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 79, + 359, + 166 + ], + "blocks": [ + { + "bbox": [ + 331, + 71, + 365, + 79 + ], + "lines": [ + { + "bbox": [ + 331, + 71, + 365, + 79 + ], + "spans": [ + { + "bbox": [ + 331, + 71, + 365, + 79 + ], + "type": "text", + "content": "Input image" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 79, + 359, + 166 + ], + "lines": [ + { + "bbox": [ + 307, + 79, + 359, + 166 + ], + "spans": [ + { + "bbox": [ + 307, + 79, + 359, + 166 + ], + "type": "image", + "image_path": "a879f63575a952e3215679c5605db540383c8aaa8885e9e9d839bab01363e272.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 168, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 306, + 168, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 168, + 545, + 201 + ], + "type": "text", + "content": "Figure 8. When the model trained via adversarial training produces results that are effective at reducing saliency, the resulting images are not realistic according to our user study." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 371, + 79, + 435, + 166 + ], + "blocks": [ + { + "bbox": [ + 419, + 71, + 434, + 79 + ], + "lines": [ + { + "bbox": [ + 419, + 71, + 434, + 79 + ], + "spans": [ + { + "bbox": [ + 419, + 71, + 434, + 79 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 371, + 79, + 435, + 166 + ], + "lines": [ + { + "bbox": [ + 371, + 79, + 435, + 166 + ], + "spans": [ + { + "bbox": [ + 371, + 79, + 435, + 166 + ], + "type": "image", + "image_path": "c8d51c7ae5a9f4cfafcdb0aa1619b1b87b70b0b197401c5c60d2b2fdf4da2dbe.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 451, + 79, + 516, + 166 + ], + "blocks": [ + { + "bbox": [ + 476, + 71, + 532, + 79 + ], + "lines": [ + { + "bbox": [ + 476, + 71, + 532, + 79 + ], + "spans": [ + { + "bbox": [ + 476, + 71, + 532, + 79 + ], + "type": "text", + "content": "Adversarial training" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 451, + 79, + 516, + 166 + ], + "lines": [ + { + "bbox": [ + 451, + 79, + 516, + 166 + ], + "spans": [ + { + "bbox": [ + 451, + 79, + 516, + 166 + ], + "type": "image", + "image_path": "25a13bee357db83fe9085346adb2bf1efa1fcfca4d5f90e0f0643e999a80f4a3.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 522, + 79, + 545, + 106 + ], + "blocks": [ + { + "bbox": [ + 522, + 79, + 545, + 106 + ], + "lines": [ + { + "bbox": [ + 522, + 79, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 522, + 79, + 545, + 106 + ], + "type": "image", + "image_path": "f8b98bcd1baeea115b74cd5f72eb9697bc9f9773c4687e6400a46a91e69396c0.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 343, + 247, + 507, + 284 + ], + "blocks": [ + { + "bbox": [ + 306, + 212, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 306, + 212, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 212, + 545, + 243 + ], + "type": "text", + "content": "Table 4. Photographer ratings as in Tab. 2 comparing our main method to a variation with adversarial training instead of our fixed realism network." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 343, + 247, + 507, + 284 + ], + "lines": [ + { + "bbox": [ + 343, + 247, + 507, + 284 + ], + "spans": [ + { + "bbox": [ + 343, + 247, + 507, + 284 + ], + "type": "table", + "html": "
MethodSaliency Attenuation
Effectiveness ↑Realism ↑
Adversarial Training5.06 (2.84)7.36 (3.07)
Ours - Random6.36 (2.79)6.34 (2.88)
", + "image_path": "2639ae48266256492b7c30f3914666626d588b7466179e80ef32f4536addeb6d.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 304, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 375 + ], + "type": "text", + "content": "applied in the previous steps of training it encourages the network to apply subtle edits and hence a drop in effectiveness of the method. On the other hand, due to the lack of explicit realism training, the edits are unrealistic while the effectiveness is reasonable. Ratings reported in Tab. 4 also confirm our findings." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 382, + 534, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 382, + 534, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 534, + 396 + ], + "type": "text", + "content": "5.4. Diversity and Optimality of Estimated Edits" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 401, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 472 + ], + "type": "text", + "content": "Fig. 9b illustrates the distribution of edit parameters estimated by our parameter estimation network for different images on ADE20K [24, 25] dataset. It shows that edit parameters are different for each image and is based on its content. Also, it shows that the range of estimated edits is not the same as the ranges used in Tab. 1 for real samples." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 473, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 567 + ], + "type": "text", + "content": "To evaluate if the estimated edits are close to optimal with respect to realism, we provide Fig. 9a. In the figure we show a realism heatmap obtained by adding a small additive constant to the estimated edit parameter of saturation and exposure. Heatmaps show the estimated edit parameters (center of the heatmap) are in the optimal realism region. Changing the edit parameters in each direction reduces the realism of the end result." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 575, + 524, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 524, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 524, + 588 + ], + "type": "text", + "content": "5.5. Generalization to Multiple Image Regions" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": "Since our model only modifies the region of interest, and performs a forward pass efficiently, we can run it on multiple regions and multiple masks by generating edit parameters for each region, in an iterative manner. Examples are provided in Figs. 1 and 10. We used the same approach with Gazeshift [17], which edits the whole image by estimating two sets of edit parameters, one for the region of interest (foreground) and one for the background. This formulation of Gazeshift makes iterative editing impractical, since there would be contradictory objectives between the" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "Dataset has only 10 images for attenuation task, which is inadequate for a meaningful user study. Hence we only provide amplification results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "192" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 339, + 239 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 339, + 239 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 339, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 339, + 239 + ], + "type": "image", + "image_path": "347300b4e5dfe3e80eed0f428547ab1b9a77ff8763de8bb21ef19e8adba761dc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 239, + 339, + 278 + ], + "lines": [ + { + "bbox": [ + 47, + 239, + 339, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 339, + 278 + ], + "type": "text", + "content": "(a) A heatmap visualizes the realism score achieved when we change the estimated saturation (x-axis) and exposure (y-axis). Our estimated values (center of the heatmap) achieve the optimal realism while changing the parameters in any direction reduces the realism. Sample edited images and their corresponding location in the heatmap are also visualized." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 360, + 91, + 536, + 235 + ], + "blocks": [ + { + "bbox": [ + 360, + 91, + 536, + 235 + ], + "lines": [ + { + "bbox": [ + 360, + 91, + 536, + 235 + ], + "spans": [ + { + "bbox": [ + 360, + 91, + 536, + 235 + ], + "type": "image", + "image_path": "997ebff0f137825fe1948a82de0d4048e45ee601bd2cf3013c03982b2f5acfff.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 239, + 544, + 269 + ], + "lines": [ + { + "bbox": [ + 351, + 239, + 544, + 269 + ], + "spans": [ + { + "bbox": [ + 351, + 239, + 544, + 269 + ], + "type": "text", + "content": "(b) The diversity of estimated parameters on ADE20K [24, 25] dataset. The x-axis is the range of each parameter. The attenuation task is blue, and amplification is labeled red." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 301, + 287, + 426 + ], + "blocks": [ + { + "bbox": [ + 132, + 283, + 461, + 295 + ], + "lines": [ + { + "bbox": [ + 132, + 283, + 461, + 295 + ], + "spans": [ + { + "bbox": [ + 132, + 283, + 461, + 295 + ], + "type": "text", + "content": "Figure 9. Visualizing diversity and optimality of edit parameters estimated by our method" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 301, + 287, + 426 + ], + "lines": [ + { + "bbox": [ + 48, + 301, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 48, + 301, + 287, + 426 + ], + "type": "image", + "image_path": "e924c57b8cc9da8f01d4050f705763fb6eb08c70b7a006052214bb1d72ea9ac3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 432, + 287, + 520 + ], + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 520 + ], + "type": "text", + "content": "Figure 10. Given an input image and masks to attenuate and amplify(left), Gazeshift when used iteratively on each object suffers from color artifacts (center top, faces, bowl and watermelons). Ours produces a notably more realistic and effective result (right). Contradictory objective of edits applied to background and foreground, Gazeshift fails to generalize to multiple regions and omitting the background edits (center bottom) reduces the effectiveness of the edits. Image credit: @tysonbrand" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 601 + ], + "type": "text", + "content": "iterations (what is foreground in one iteration becomes a background in the next iteration). For a more practical comparison, we omit background edits when running Gazeshift. Figure 10 shows that Gazeshift performance suffers on an iterative saliency enhancement task, but our method is able to generalize to multiple regions robustly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 610, + 125, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 125, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 125, + 623 + ], + "type": "text", + "content": "5.6. Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "The global edits (applying the same edits to every pixel inside a mask), used in both our method and Gazeshift [17] require an accurate mask of the target region. As shown in Fig. 11 mask imperfections can cause unsmooth transitions around the boundaries. In these cases, pixel-wise optimization approaches like Deepsal [1] and MEC [16] do not suffer from heavy artifacts due to mask imperfections." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 302, + 547, + 430 + ], + "blocks": [ + { + "bbox": [ + 307, + 302, + 547, + 430 + ], + "lines": [ + { + "bbox": [ + 307, + 302, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 307, + 302, + 547, + 430 + ], + "type": "image", + "image_path": "5f17285b3ddb311a9d3cbf680f5270dc08aa270d7e3f6cc426adea45049c5df8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 435, + 547, + 491 + ], + "lines": [ + { + "bbox": [ + 305, + 435, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 547, + 491 + ], + "type": "text", + "content": "Figure 11. The effect of non-smooth mask boundaries. Left, an input image has a mask with a sharp edge. Center, our method and Gazeshift [17] produce strong boundary artifacts around the mask region (see inset). Right, MEC [16] and Deepsal [1] do not exhibit this problem because they operate in a pixel-wise manner." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 508, + 468, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 468, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 468, + 521 + ], + "type": "text", + "content": "6. Conclusion and Future work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "content": "We describe a method to edit images using conventional image editing operators to attenuate or amplify the attention captured by a target region while preserving image realism. Realism is achieved by introducing an explicit, and separate realism network that is pre-trained to distinguish edited images. This strategy to achieve realism is distinct from prevailing approaches, including adversarial training schemes, as it introduces an additional form of weak supervision—manually specified ranges of parameter values that correspond to realistic and unrealistic (\"fake\") edits. Training with this realism critic makes it possible to estimate saliency modulating image edits that are significantly more realistic and robust. Together with our millisecond-level inference time, our approach offers a practical and deployable application of saliency guided image editing." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "193" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Kfir Aberman, Junfeng He, Yossi Gandelsman, Inbar Mosseri, David E. 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ICCV, 2015. 2, 3" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "194" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_content_list.json b/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..165113ab0fcbd373f179e0d120432d29b0a6ae1e --- /dev/null +++ b/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_content_list.json @@ -0,0 +1,1354 @@ +[ + { + "type": "text", + "text": "ReasonNet: End-to-End Driving with Temporal and Global Reasoning", + "text_level": 1, + "bbox": [ + 130, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hao Shao $^{1}$ Letian Wang $^{2}$ Ruobing Chen $^{1}$ Steven L. Waslander $^{2}$ Hongsheng Li $^{3}$ Yu Liu $^{1,4*}$", + "bbox": [ + 289, + 179, + 686, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ SenseTime Research $^{2}$ University of Toronto $^{3}$ CUHK MMLab $^{4}$ Shanghai Artificial Intelligence Laboratory", + "bbox": [ + 217, + 222, + 751, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 292, + 313, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The large-scale deployment of autonomous vehicles is yet to come, and one of the major remaining challenges lies in urban dense traffic scenarios. In such cases, it remains challenging to predict the future evolution of the scene and future behaviors of objects, and to deal with rare adverse events such as the sudden appearance of occluded objects. In this paper, we present ReasonNet, a novel end-to-end driving framework that extensively exploits both temporal and global information of the driving scene. By reasoning on the temporal behavior of objects, our method can effectively process the interactions and relationships among features in different frames. Reasoning about the global information of the scene can also improve overall perception performance and benefit the detection of adverse events, especially the anticipation of potential danger from occluded objects. For comprehensive evaluation on occlusion events, we also release publicly a driving simulation benchmark DriveOcclusionSim consisting of diverse occlusion events. We conduct extensive experiments on multiple CARLA benchmarks, where our model outperforms all prior methods, ranking first on the sensor track of the public CARLA Leaderboard [53].", + "bbox": [ + 75, + 325, + 473, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite significant recent progress in the field of autonomous driving, truly large-scale deployment of autonomous vehicles (AVs) on public roads has yet to be established. The majority of the remaining issues lie in navigating dense urban traffic scenes, where a large number of different dynamic objects (e.g. vehicles, bicycles, pedestrians), complex road geometries and road user interactions are involved. In such circumstances, currently deployed or tested solutions could make incorrect or unexpected decisions, resulting in severe accidents or traffic infractions [4, 24, 53]. Two of the major challenges behind", + "bbox": [ + 75, + 710, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8598ce30dd9fdd1287de354205a66857ba9ca5f7b4636ab2e595e51c5c577d69.jpg", + "image_caption": [ + "Figure 1. Temporal reasoning on the historic behaviors of surrounding objects can benefit the prediction of the scene evolution and objects' future behaviors. Global reasoning on the interaction among objects and the environment allows for inference about unobservable space and occluded objects, anticipating potential danger and enhancing perception/driving performance." + ], + "image_footnote": [], + "bbox": [ + 511, + 294, + 877, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "such autonomous incompetence include 1) how to achieve a comprehensive understanding of the driving scene and, more importantly, how to make high-fidelity predictions on the future evolution of the driving scene; 2) how to deal with rare adverse events in long-tail distributions, such as undetected but relevant objects in occluded regions.", + "bbox": [ + 496, + 582, + 892, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Comprehensive scene understanding and high-fidelity prediction of how objects in the scene will move in the future are vital for autonomous vehicles to take safe and reliable actions. Toward this end, modularized methods were proposed to decompose the task into three sequential subtasks: detection [37-40, 42], tracking [5, 65], and forecasting [6, 26, 28, 32, 33, 59-61]. While more interpretability is provided by developing each module independently, these sub-tasks are still regarded as open research questions and errors in each sub-task can propagate and accumulate, leading to unstable overall performance. In contrast, end-to-end driving methods [9, 10, 51] have recently emerged as a promising method to solve these subtasks in a monolithic manner directly. However, a high-fidelity future prediction necessitates sufficient temporal reasoning over the historic", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13723", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "information of the scene [22, 50], which is usually only somewhat considered in previous end-to-end driving methods if not completely ignored. For example, [10, 15] only exploited scene information in the current frame, and [54] simply concatenated features in historic frames for temporal reasoning. In such cases, the interactions and relationships amongst features in different frames and objects cannot be sufficiently modeled. Thus in this paper, we propose a temporal reasoning module to effectively fuse information from different frames for better driving performance.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, rare adverse events in long-tail distributions remain a notoriously challenging issue on the way toward large scale deployment of autonomous vehicles. For example, one such challenge is the difficulty in detecting occluded but relevant objects in the scene. While a large amount of research has focused on improving perception performance [37, 57], the occluded objects essentially lie out of the scope of observable elements, and failure to consider such objects can result in either dangerous or overly cautious driving behavior. Our observation is that, while humans also suffer from similar limitations to autonomous vehicles regarding occluded objects, they are able to reason about these unobservable spaces by exploiting global information of the scene such as road geometry and driving interaction patterns, to anticipate potential danger even under occlusion. For example, when one human driver notices another vehicle braking abruptly, the driver may reason the presence of an occluded object (e.g., a pedestrian) ahead, reminding himself to drive cautiously. Thus, our insight is that, a safe and intelligent autonomous vehicle should also master the global reasoning capability to have a better perception of the scene. In this paper, we propose a transformer-based global reasoning module to sufficiently fuse information of the environment and objects, and analyze their interactions for better scene understanding. Such global reasoning capability not only benefits interaction modeling with occluded objects, but also improves overall perception performance. Examples of such performance gains include better traffic light status identification by reasoning over other vehicles' actions and more accurate future trajectory forecasting by reasoning over interactions among objects. Besides, considering the fact that the occlusion events lie in the long-tail distribution and have been rare in currently available datasets, we also construct a Driving in Occlusion Simulation benchmark (DOS) consisting of 4 occlusion scenarios, each with 25 cases, as a comprehensive occlusion event evaluation benchmark in the field of end-to-end autonomous driving.", + "bbox": [ + 75, + 244, + 472, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel end-to-end driving framework named temporal and global reasoning network (ReasonNet), which provides enhanced reasoning on the temporal evolution and the global information of the scene, for better perception performance and driving quality. Our", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contributions are three-fold:", + "bbox": [ + 498, + 90, + 687, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel temporal and global reasoning Network (ReasonNet) to enhance historic scene reasoning for high-fidelity prediction of the scene's future evolution and improve global contextual perception performance even under occlusion.", + "- We present a new benchmark called Driving in Occlusion Simulation benchmark (DOS), which consists of diverse occlusion scenarios in urban driving for systematic evaluation in occlusion events, and make the benchmark publicly available.", + "- We experimentally validate our method on multiple benchmarks with complex and adversarial urban scenarios. Our model ranks first on the sensor track of the CARLA autonomous driving leaderboard." + ], + "bbox": [ + 517, + 118, + 890, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 362, + 637, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-end Autonomous Driving End-to-end autonomous driving in urban scenarios has become more studied recently thanks to the CARLA simulator and leaderboard [21]. Recent works mainly consist of reinforcement learning (RL) and imitation learning (IL) methods. The reinforcement Learning methods train the agents by constantly interacting with simulated environments and learning from these experiences. Latent DRL [54] first trains an embedding space as a latent representation of the environment observation, and then conducts reinforcement learning with the latent observation. Roach [66] utilizes an RL agent with privileged information of the environment to distill a model only with regular information (e.g. sensor) as the final agent. WOR [9] builds a model-based RL agent along with the world model and reward model. The final agent is distilled from the expert knowledge acquired from these pretrained models. Imitation learning methods aim at learning from an expert agent to bypass interacting with the environment. Early IL methods include CIL [17] and CILRS [18], which apply a conditional architecture with different network branches for different navigation commands. LBC [11] first trains an imitation learning agent with privileged information, which is then distilled into a model using sensor data. Transfuser [15, 47] designs a multi-modal transformer to fuse information between the front camera image and LiDAR data. LAV [10] exploits data of not only the ego vehicle but also surrounding vehicles for data augmentation by learning a viewpoint-invariant spatial intermediate representation. TCP [63] proposes a network with two branches which generates the control signal and waypoints respectively. An adaptive ensemble is applied to fuse the two output signals. InterFuser [51] uses a transformer to fuse and process multimodal multi-view sensors for comprehensive scene understanding.", + "bbox": [ + 496, + 387, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13724", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attention for Autonomous Driving The attention mechanism has been demonstrated to be a powerful module in many areas of deep learning, including the context of driving. The classic attention-based Transformer architecture [55] was originally established in Natural Language Processing. Transformer (VIT) was then applied in Computer Vision (vision Transformer, VIT [20, 49]) and attains excellent performance onImagenet classification. Later generations move on to generalize the attention mechanism to the driving domain, including motion forecasting [23, 36, 58], driver attention prediction [25, 34] and object tracking [45, 52]. In the field of end-to-end autonomous driving, TransFuser [15, 47] exploits several transformer modules for the fusion of data from the front view camera and LiDAR. NEAT [14] uses intermediate attention maps to iteratively compress 2D image features into a compact bird-eye-view (BEV) representation for driving. InterFuser [51] utilizes a transformer encoder and decoder to fuse information and decode the feature into interpretable embeddings.", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-task Learning Our end-to-end driving framework adopts multi-task learning, with a joint objective of object detection, occupancy forecasting, traffic sign prediction and waypoint prediction. MotionNet [62] proposes a spatio-temporal pyramid network for joint perception and motion prediction based on BEV maps. PnPNet [41] proposes a new object trajectory representation and multi-object tracker to handle occlusion and false positives. IntentNet [7] predicts the high-level intentions of each agent from semantic HD maps building. ST-P3 [29] proposes an egocentric-aligned accumulation technique to preserve geometry information in 3D space and utilize a dual pathway modeling to consider past motion variations.", + "bbox": [ + 76, + 378, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 585, + 169, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim at learning a driving policy $\\pi$ that generates raw control commands by taking multi-view multi-modal sensor readings, vehicle measurements, and navigation commands as inputs. As shown in Figure 2, the proposed ReasonNet consists of three parts: 1) a perception module that extracts bird's-eye-view (BEV) features from LiDAR and RGB data; 2) a temporal reasoning module that processes temporal information and maintains a memory bank storing historic features; 3) a global reasoning module that captures the interaction/relationship amongst objects and the environment, to detect adverse events (e.g. occlusion) and improve overall perception performance. This section will introduce these modules in detail.", + "bbox": [ + 76, + 612, + 472, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Perception Module", + "text_level": 1, + "bbox": [ + 76, + 816, + 261, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The perception module is responsible for processing and fusing different sensor data at the early stage of our framework, based on which temporal and global reasoning can be conducted by later modules. Specifically, five sensors", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are utilized: four RGB cameras (left, front, right and rear) $I_{\\mathrm{rgb}} = I_{0,1,2,3}$ and one LiDAR sensor $I_{\\mathrm{lidar}} = I_4$ . Four image inputs are obtained from the four cameras, and an additional focus-view image input is center-cropped from the front image to capture distant traffic lights. Point cloud data is retrieved from the LiDAR sensor. Our perception module includes a 2D backbone to embed image input into keys and values, a 3D backbone to embed LiDAR input into queries, and a BEV decoder that utilizes these keys, values, and queries to obtain features of the bird's-eye view (BEV) map, waypoints, and traffic signs.", + "bbox": [ + 496, + 90, + 893, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image Input For each image input of $I_{rgb}$ , a 2D CNN backbone ResNet [27] is applied to generate a feature map $f_{i}$ . Then, we use a convolution layer to map the channels of $f_{i}$ to $C_v$ and flatten it to one-dimensional tokens. A sinusoidal positional encoding and learnable sensor embeddings are added to the tokens, so that the following network can distinguish them from different cameras and relative positions. Finally, tokens of different images are passed through a standard transformer encoder with $K_{e}$ layers. Each layer consists of Multi-Headed Self-Attention [55], MLP blocks and layer normalization [3]. This image fusion operation can contribute to a better perception of global context from multi-view inputs, generating keys and values for the image-LiDAR fusion in BEV decoder.", + "bbox": [ + 496, + 258, + 893, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LiDAR Input For the LiDAR input, we use PointPillars [35] as our 3D perception backbone to process points in the ego-vehicle-centered area $x \\in [-H_b, H - H_b]$ and $y \\in [-W/2, W/2]$ . Specifically, we use a simplified version of PointNet [48] to encode the information of raw LiDAR points. Each pillar includes the points in a $0.25\\mathrm{m} \\times 0.25\\mathrm{m}$ area. The extracted feature map is downsampled to $C_v \\times H \\times W$ for computation reduction and then serves as BEV queries used in the BEV decoder and memory bank.", + "bbox": [ + 496, + 473, + 893, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sensor-Fusion BEV Decoder The BEV decoder follows a standard transformer architecture design with $K_{\\text{bev}}$ layers to fuse tokens from different sensors. Tokens from the RGB images are fed as values and keys into the decoder, and tokens from the LiDAR points are fed as the $H \\times W$ queries to generate BEV features. In addition, two other kinds of queries for the prediction of traffic signs and waypoints w are also fed into the decoder. Following InterFuser [51], we use a 2-layer MLP as the traffic sign classifier to predict the traffic light state and whether there is a stop sign ahead; we then use a single-layer GRU [16] to auto-regressively generate consecutive waypoints $\\{\\mathbf{w}_t\\}_{t=1}^{T_f}$ conditioned on the goal location of the ego vehicle. $T_f$ denotes the number of the predicted time steps. To pretrain the perception module in the first training stage, the generated BEV feature is passed through a one-stage CenterPoint [64] to generate the $H \\times W \\times 7$ BEV map covering an $H_m \\times W_m$ spatial region, where the seven channels represent object existence", + "bbox": [ + 496, + 627, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13725", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ffa23ef9e4cc4f74a46012831c6e9b88d72af9bcf3260c2bc093b8df31fbfc96.jpg", + "image_caption": [ + "Figure 2. The proposed ReasonNet consists of three modules: 1) the perception module fuses different sensor data to generate the BEV feature, traffic sign feature, and waypoints in the early stage of our framework; 2) the temporal reasoning module processes current and historic features and maintains a memory bank to store historic features; 3) the global reasoning module models the interaction and relationship among objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance." + ], + "image_footnote": [], + "bbox": [ + 114, + 93, + 854, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "probability, offset from grid center, bounding box extent, heading angle and velocity for objects at each grid cell.", + "bbox": [ + 75, + 474, + 470, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Temporal Reasoning module", + "text_level": 1, + "bbox": [ + 76, + 512, + 334, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to existing end-to-end driving methods that only exploit scene information of the current frame [10, 15] or simply concatenate features of historic frames [54], we propose a temporal reasoning module that can sufficiently store and fuse temporal information to benefit the motion forecasting of traffic participants and the tracking of intermittently occluded objects. As shown in Figure 2, our temporal reasoning module includes temporal processing to fuse current and historic features through an attention mechanism, and maintains a memory bank which stores historic short-term and long-term feature keys and values.", + "bbox": [ + 75, + 535, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal Processing Considering that information in different historic frames could have different relevance to the current scene, we apply an attention-based memory reading from the historic features. Specifically, for each historic frame $t$ stored in the memory, we first measure its relevance by calculating the normalized similarity $\\mathbf{S}$ between the historic-frame feature key $\\mathbf{k} \\in \\mathbb{R}^{C_k \\times T_h \\times H \\times W^1}$ and the current-frame feature query $\\mathbf{q} \\in \\mathbb{R}^{C_k \\times H \\times W}$ :", + "bbox": [ + 75, + 700, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS (\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}) = \\frac {(\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}}{\\sum_ {i = 0 , j = 0} ^ {i = H - 1 , j = W - 1} (\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 829, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We map every query element to a distribution over $H\\times W$ memory elements and correspondingly aggregate their values $\\mathbf{v}$ to obtain the readout feature $\\mathbf{M}\\in \\mathbb{R}^{C_v\\times T_h\\times H\\times W}$ for each frame $t$ stored in the memory:", + "bbox": [ + 498, + 474, + 890, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {t, h, w} = \\sum_ {i = 0, j = 0} ^ {i = H - 1, j = W - 1} \\mathbf {v} _ {t, i, j} S \\left(\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 558, + 890, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aggregated features from all historic frames are then concatenated with the current-frame feature value to get $\\mathbf{M}' \\in \\mathbb{R}^{C_v \\times (T_h + 1) \\times H \\times W}$ , which is then passed through a GRU to progressively fuse temporal information and get $\\mathbf{M}_{fused} \\in \\mathbb{R}^{C_v \\times H \\times W}$ as the final output of the module. Technically, we take the L2 similarity proposed in STCN [13] as the similarity measure function, which is more stable than the dot product [46]. The current-frame feature query $\\mathbf{q}$ is obtained by passing the features from the 3D backbone $\\mathbf{F} \\in \\mathbb{R}^{C_v \\times H \\times W}$ through a query encoder (several convolution layers). The historic-frame feature key $\\mathbf{k}$ and value $\\mathbf{v}$ are taken from the temporal memory bank.", + "bbox": [ + 496, + 613, + 892, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Memory Bank Maintaining As above, we have introduced the temporal processing at one single frame. After every $\\tau$ frame, the obtained feature key and value at that frame will be used to update the memory bank. Specifically, the current-frame feature query $\\mathbf{q}$ is directly copied and fed into the memory bank as the memory key without extra computation. The final output $\\mathbf{M}_{\\text{used}}$ will first be encoded", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "${}^{1}C,H,W$ denotes the channel,height,and width of the feature respectively, ${T}_{h}$ denotes the number of the frames stored in the memory bank.", + "bbox": [ + 76, + 875, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13726", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to a BEV map $\\mathbf{M}_p$ . The BEV map $\\mathbf{M}_p$ will be concatenated with the final output $\\mathbf{M}_{fused}$ and passed through a value encoder to obtain the memory value $\\mathbf{v}$ , which is fed into the memory back. With the above key-value pairs, the memory bank maintains two kinds of buffer: the short-term and long-term buffer. On the one hand, the new key-value pair will be appended to the short-term buffer, as a high-resolution memory of the scene in the past few seconds for accurate feature matching. Considering the limited GPU memory resources, we limit the buffer size and older key-value pairs will be discarded when the limit number $T_s$ is reached. However, when these older features are discarded, the long-term behavior of the traffic participants is missing, which can be crucial for motion forecasting in complex traffic scenarios. Thus on the other hand, inspired by XMem [12], the memory bank also maintains a long-term buffer that selectively stores important/representative key-value feature pairs discarded by the short-term buffer. Considering the fact that the objects surrounding the ego vehicle are sparse most of the time², the long-term buffer selectively stores key-value features ( $\\mathbf{k}$ and $\\mathbf{v}$ ) which meet one of the two criteria: 1) their corresponding location in the BEV map $\\mathbf{M}_p$ has a high probability of object existence; 2) their usage frequency is in top-K of all candidate key-value features. The usage frequency is defined by its cumulative normalized similarity (Eq. 1). The features selected by the above criteria are appended to the last frame of memory. And if the last memory frame is full, we will initialize one new frame with the zero vector and set it as the last frame to store new features. When the number of frames reaches the limit $T_l$ , the obsolete memory will be removed. Such a compact storing strategy can efficiently track long-term representative features and intermittently occluded objects, while balancing the resources required.", + "bbox": [ + 76, + 90, + 472, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Global Reasoning module", + "text_level": 1, + "bbox": [ + 76, + 614, + 312, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rare adverse events such as occluded objects are a notorious issue for the practical deployment of AVs. Our insight is that humans perceive their surroundings not only through sensors, but also by exploiting global information on the scene to reason over the unobservable spaces. For instance, when a vehicle performs an emergency stop without a clear reason, humans can infer that there is potentially an occluded object ahead of the vehicle and will drive more cautiously. Thus we propose the global reasoning module to capture the interaction and relationship between objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance. The module consists of three parts: 1) an object-environment and object-object interaction modeling process; 2) an occupancy decoder to generate the occupancy map; 3) a consistency loss", + "bbox": [ + 75, + 638, + 472, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to encourage consistent prediction of waypoints and the occupancy map.", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Interaction Modeling The object-environment and object-object interaction modeling process aims at reasoning about the relationship among objects and the environment. On the one hand, $\\mathbf{M}_{\\text {fused }}$ features whose corresponding location in the BEV map $\\mathbf{M}_p$ has a high probability of object existence will be extracted to represent object features. On the other hand, $\\mathbf{M}_{\\text {fused }}$ features will also be downsampled to represent the environment features. All object and environment features are used to construct a graph, which is passed through a graph attention network (GAT) [56] for interaction modeling.", + "bbox": [ + 496, + 121, + 893, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Occupancy Decoder Taking the features outputted by the GAT as keys and values, and the learnable positional embeddings as queries, the occupancy decoder utilizes a transformer decoder with $K_{\\text{opy}}$ layers to generate: 1) the traffic sign feature, which is then concatenated with the traffic sign feature from the BEV decoder to generate the final traffic sign prediction; 2) the occupancy map feature, which is then applied with convolution operation to generate the occupancy map $\\mathbf{O}_t \\in \\mathbb{R}^{T_f \\times H \\times W}$ . At a future time $t$ , each cell in the occupancy map contains a value in the range [0,1] representing the probability that the cell is occupied.", + "bbox": [ + 496, + 287, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consistency Loss Currently, our framework predicts the waypoints and the occupancy map independently, which are not necessarily consistent. For example, the waypoints could overlap some obstacles in the occupancy map. Thus we propose a consistency loss to discourage waypoints' crossing the high-probability region of the occupancy map. Further, the consistency loss also encourages generating longer waypoint trajectories for efficient driving. Specifically, the consistency loss aims at minimizing the average object existence probability of the cells that cover the predicted waypoints, and maximizing the average $l_{2}$ length of the waypoint trajectory w:", + "bbox": [ + 496, + 454, + 892, + 635 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s i s t e n c y}} = \\frac {1}{T _ {f}} \\left(\\sum_ {t = 0} ^ {T _ {f}} \\frac {\\sum_ {i = 0} ^ {N _ {c} ^ {t}} \\mathbf {O} _ {t , i}}{N _ {c} ^ {t}} - \\lambda \\sum_ {t = 0} ^ {T _ {f}} \\| \\mathbf {w} _ {t} \\| _ {1}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 652, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ",where $N_{c}^{t}$ denotes the number of covered cell at step $t$ $\\mathbf{O}_{t,i}$ denotes the object existence probability at cell $i$ at time $t$", + "bbox": [ + 496, + 703, + 890, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Control", + "text_level": 1, + "bbox": [ + 500, + 741, + 596, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [11], we use two PID controllers for latitudinal and longitudinal control, to track the heading and velocity of predicted waypoints respectively. If a red traffic light or stop sign is detected, the ego-vehicle will brake. Additionally, an emergency stop will also be performed if the ego vehicle's current bounding box crosses the area in the occupancy map that has a high object existence probability or if the future waypoints overlap with objects in the BEV map.", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "Based on the data collected from the CARLA simulator, only $7\\%$ of the ego-vehicle-centered BEV map area is occupied by active objects.", + "bbox": [ + 76, + 875, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13727", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c1eae2d0d4652ea695059e001eda8185737677d78563f5f761428eb769353f88.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 90, + 261, + 231 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/57a4848366f41fdba3d5959448325e93c316736cbbc1149bbdaf0f9835790a43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 449, + 229 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e940d0958ef94cf4a0039e43622654f8b8ca1d884aff28f66b3de681d501bfaf.jpg", + "image_caption": [ + "Figure 3. An illustration for the four types of occlusion scenarios included in the proposed DOS benchmark. The orange color denotes the ego car. The blue/green dots denote the occluded/visible trajectory of the occluded dangerous object." + ], + "image_footnote": [], + "bbox": [ + 96, + 236, + 259, + 373 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/26a21544aaaf574accadaea58c6f4b1f364c849fede13cd3b37896c82a2571c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 234, + 447, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Training Setup", + "text_level": 1, + "bbox": [ + 76, + 449, + 230, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training of our framework consists of two stages. In the first stage, we train the perception module to predict BEV features, traffic sign features, and waypoints. Specifically, the loss of BEV features and traffic sign features is computed with additional prediction heads, which are discarded in the next stage. In the second stage, we freeze the perception module and train the other two modules. Five loss terms are considered: 1) the waypoints loss $\\mathcal{L}_w$ that minimizes the error between predicted waypoints and expert waypoints; 2) the BEV map loss $\\mathcal{L}_{BEV}$ that follows [10,64] to minimize the current-frame BEV map prediction error; 3) the traffic sign loss $\\mathcal{L}_{sign}$ for the traffic regulation prediction; 4) occupancy map loss $\\mathcal{L}_{opy}$ that minimizes the occupancy prediction error in a future horizon; 5) the consistency loss $\\mathcal{L}_{consistency}$ which encourages a consistent generation of the waypoints and occupancy map. These loss terms are balanced by corresponding loss weights.", + "bbox": [ + 75, + 473, + 472, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Drive in Occlusion Sim (DOS) Benchmark", + "text_level": 1, + "bbox": [ + 76, + 747, + 455, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to address the issue that occlusion events are rare in existing datasets and benchmarks, we present the Drive in Occlusion Simulation benchmark (DOS), a CARLA-based framework providing diverse driving scenarios with occluded objects. As shown in Figure 3, the proposed DOS benchmark includes four types of challenging occlusion driving scenarios:", + "bbox": [ + 75, + 773, + 468, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Parked Cars (#1)** The ego vehicle is driving in a straight", + "bbox": [ + 76, + 885, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b8c6fda6b20f72b70ff6a0676d32ab91d6308263826a27a452829e1e20a18763.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RankMethodDS ↑RC ↑IS ↑
1ReasonNet (Ours)79.9589.890.89
2InterFuser [51]76.1888.230.84
3TCP [63]75.1485.630.87
4LAV [10]61.8594.460.64
5TransFuser [15]61.1886.690.71
6Latent TransFuser [15]45.2066.310.72
7GRIAD [8]36.7961.850.60
8TransFuser+ [1]34.5869.840.56
", + "bbox": [ + 501, + 88, + 890, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance comparison on the public CARLA leaderboard [53] (accessed Nov 2022). For all three metrics, higher is better. Our method ranks first overall on the leaderboard, with the highest driving score (DS) and infraction score (IS), and the second highest route completion (RC).", + "bbox": [ + 496, + 239, + 893, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lane with parked cars on the side. Pedestrians can first appear on the sidewalk (visible) and then suddenly emerge through the occluded areas between parked cars (occluded).", + "bbox": [ + 496, + 325, + 890, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sudden Brake (#2) The ego vehicle is driving in a straight lane along with other vehicles ahead. Pedestrians can suddenly emerge from the sidewalks, causing the other vehicles to brake while remaining invisible to the ego vehicle.", + "bbox": [ + 496, + 372, + 890, + 433 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Left Turn (#3) The ego vehicle intends to perform an unprotected left turn at an intersection, but a truck in the opposite lane blocks the view of oncoming traffic, intermittently obscuring vehicles driving straight through the intersection.", + "bbox": [ + 496, + 434, + 890, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Red Light Infraction (#4) The ego vehicle is crossing an intersection after some trucks. A left-to-right vehicle running a red light suddenly appears, forcing the trucks to brake promptly. But the ego vehicle's view toward the running-light vehicle is blocked by the trucks, so it remains invisible to the ego vehicle.", + "bbox": [ + 496, + 494, + 890, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Each of the four scenarios in the DOS benchmark comprises 25 different cases varying in the road environment and background traffic. Compared to a previous occlusion benchmark AUTOCASTSIM [19], the DOS benchmark: 1) includes occlusions of both vehicles and pedestrians, instead of only vehicles; 2) includes 100 cases of 4 scenarios, instead of only 3 cases of 3 scenarios; 3) considers specific occlusions that can potentially be resolved by temporal reasoning (intermittent occlusion, #1, #3) and global reasoning (constant occlusion but with interaction clues, #2, #4) about the scene, instead of random occlusions as in AUTOCASTSIM. Thus our scenarios can also serve as a good tracking-with-intermittent-occlusion benchmark and a People-as-Sensor [2,31] benchmark.", + "bbox": [ + 496, + 592, + 890, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 820, + 633, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 500, + 845, + 676, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation We implement and evaluate our approach on the open-source CARLA simulator with version", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13728", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2da1d1f783a8df111ffc0715d761c9879dbdcd5908d93fa69f4f2dde2dc4cc23.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingTown 05 LongDOS
TsTlDS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
0066.7±3.897.6±2.70.68±0.030.18±0.030.05±0.020.03±0.0322±1.628±3.426±2.125±1.6
1067.9±3.496.8±2.30.70±0.020.16±0.040.04±0.030.05±0.0230±3.638±3.632±2.832±3.4
2068.1±3.196.9±3.40.70±0.030.16±0.030.04±0.020.05±0.0328±5.548±4.138±4.452±3.9
2170.9±2.095.7±3.10.74±0.020.13±0.020.04±0.020.06±0.0455±4.457±4.148±4.155±5.5
4070.5±2.196.4±2.50.73±0.040.14±0.030.03±0.020.06±0.0332±5.458±4.440±5.555±4.9
4273.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "bbox": [ + 119, + 88, + 846, + 208 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Ablation study on different short-term buffer size $T_{s}$ and long-term buffer size $T_{l}$ , on the Town 05 Long benchmark and the proposed DOS benchmark. Performance is evaluated over three runs. CR: Collision rate, Red: Red light violation, Blocked: Vehicle blocked, SR: Success rate. SR#1 denotes the first kind of scenario in the DOS benchmark. As the two buffer sizes increase, improvement is witnessed in all metrics but the road completion.", + "bbox": [ + 75, + 212, + 893, + 268 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "0.9.10.1 [21]. We use ResNet-50 pretrained on ImageNet as the 2D backbone and PointPillars trained from scratch as the 3D backbone. We predict $T_{f} = 4$ time steps for the waypoints and occupancy map, and the interval between each time step is 0.5 seconds. The memory bank maintains $T_{s} = 4$ frames in the short-term buffer and $T_{l} = 2$ frames in the long-term buffer. The memory bank is updated every $\\tau = 2$ frame. We refer readers to Appendix A for more details.", + "bbox": [ + 75, + 282, + 470, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset Collection We collect an expert dataset of 2M frames by running a rule-based expert agent on all 8 public towns and 21 types of weather, with the access to the privileged information in the CARLA simulator. We randomly set routes, spawn dynamic objects and adversarial scenarios provided in [47], to diversify the collected data. To ensure the temporal continuity of collected data, the data are collected at a high frequency of 10HZ.", + "bbox": [ + 75, + 425, + 468, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics We consider three major metrics introduced by the CARLA LeaderBoard: route completion ratio (RC), infraction score (IS), and driving score (DS). The route completion ratio is the percentage of the route completed. The infraction score measures infractions triggered. When collisions or traffic rule violations occur, the infraction score will decay by a discount factor. The driving score is the product of the route completion ratio and the infraction score, describing both driving progress and safety, and thus is the primary ranking metric in the CARLA Leaderboard.", + "bbox": [ + 75, + 551, + 468, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Comparison to the state of the art", + "text_level": 1, + "bbox": [ + 76, + 734, + 372, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 shows the top 8 entries on the public CARLA Leaderboard. Readers can refer to Sec 2 for descriptions of these methods. Our method outperforms all prior methods, with the highest driving score and infraction score, and the second highest route completion. The previous leading method InterFuser uses a transformer for sensor fusion but lacks temporal and global reasoning. Compared to InterFuser, our method improved the driving score, road completion, and infraction score by $5\\%$ , $2\\%$ , and $6\\%$ respectively.", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 282, + 650, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We investigate the effect of the temporal and global reasoning modules on the Town05 Long benchmark and the DOS benchmark. For each scenario in DOS, we take 5 cases for training and 20 cases for evaluation. In addition to the three metrics mentioned earlier, we also present four more metrics for detailed analysis: collision rate (CR), red light violation (Red), ego vehicle blocked frequency (Blocked), and success rate (SR). The first three metrics are normalized by the driven distance (km). Visualizations of how the temporal reasoning and global reasoning work can be found at Figure 4 and Figure 5 respectively.", + "bbox": [ + 496, + 306, + 893, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Memory Size Table 2 studies the effect of different short-term buffer size $T_{s}$ and long-term buffer size $T_{l}$ . The overall observation is that, as the two buffer sizes increase, improvement is witnessed in all metrics but road completion. Specifically, when the long-term memory is removed $(T_{l} = 0)$ , the average success rates drop sharply from 71.5 to 36 on DOS scenarios that require keeping track of intermittently occluded objects (#1 and #3). If we remove the temporal reasoning module $(T_{s} = T_{l} = 0)$ , the driving score on the Town05 benchmark drops by $9\\%$ , and the average success rate on the DOS benchmark drops by $46\\%$ . We hypothesize that the drop in performance is because 1) it can be really hard to accurately estimate the objects' future motion based only on single-frame data; 2) temporal information can help keep track of objects that are intermittently occluded; 3) the global reasoning module may also work poorly when historic information is missing.", + "bbox": [ + 496, + 476, + 893, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Long-Term Memory Selection Strategy Table 3 studies the performance of different long-term memory selection strategies. Specifically, the proposed strategy in Sec 3.2 includes two selection criteria. So here we ablate the effect of the two criteria by 1) only selecting the short-term feature with top- $K$ usages (usage-based); 2) only selecting the feature with a high probability of the existence of an object (object-based). Besides, we also compared a random selection strategy. As in Table 3, the random selection strategy has the poorest performance especially on the DOS benchmark, as random selection could miss important and repre", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13729", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/efeeb0dba7f6472cb4c92057fb19ac8cae6765e7d9c61294bc2540810769eb81.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingTown 05 LongDOS
DS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
Random71.2±5.496.6±2.40.74±0.040.13±0.040.03±0.010.06±0.0233±4.455±6.242±5.553±5.4
Usage-based72.0±3.995.9±2.20.75±0.040.12±0.030.03±0.010.06±0.0245±4.262±3.453±2.862±3.9
Object-based72.2±3.796.1±3.00.75±0.030.12±0.030.03±0.010.05±0.0257±4.165±3.673±4.460±3.7
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "bbox": [ + 119, + 88, + 848, + 180 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/58f1444b8a50ab208a3bb0af8a5387462ab0ca57b98a071b20be1b4157dcb116.jpg", + "table_caption": [ + "Table 3. Ablation study on different long-term memory selection strategies. Our proposed strategy considering both the usage and object criteria outperforms the random selection strategy and the two methods with only one criteria, especially on the DOS benchmark." + ], + "table_footnote": [], + "table_body": "
SettingTown 05 LongDOS
DS↑RC↑IS↑CR↓Red↓Blocked↓SR#1↑SR#2↑SR#3↑SR#4↑
No global reasoning68.9±4.697.4±2.90.71±0.040.15±0.040.05±0.020.05±0.0228±2.834±3.429±2.027±3.6
No consistency loss72.2±3.496.1±3.20.75±0.030.12±0.020.03±0.020.06±0.0360±4.172±3.977±4.968±4.2
No traffic sign prediction71.1±2.796.0±4.10.74±0.030.11±0.030.05±0.030.07±0.0362±4.472±4.082±2.870±4.1
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "bbox": [ + 119, + 219, + 849, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on the global reasoning module. The performance would drop when 1) the entire global reasoning module is removed; 2) the consistency loss is not applied; 3) the traffic sign feature from the reasoning module is not utilized.", + "bbox": [ + 75, + 309, + 892, + 338 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9613b839e8bd58fb83e07d216bd2ad745bcc41c36d9b9a72fac42a3739848dde.jpg", + "image_caption": [ + "Figure 4. Visualization of the attention map between one object's current-frame feature query and the historic-frame feature stored in the short-term buffer, in two cases. The object's current-frame feature consistently attends to its corresponding region in the historic feature map." + ], + "image_footnote": [], + "bbox": [ + 89, + 349, + 454, + 492 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/585ff0ea3058373efb47131d1ac58a3d64446dc93b3ceb2fe7729ec534c1fe8b.jpg", + "image_caption": [ + "Figure 5. We show two cases of how our framework reasons the presence of the occluded object. In the first case, a pedestrian first appeared on the sidewalk (visible) and then emerges between two parked cars (occluded). In the second case, a vehicle runs the red light, forcing trucks to brake abruptly. But the ego vehicle's view toward the running-light vehicle is blocked by the front trucks, so the running-light vehicle remains invisible to the ego vehicle. The rectangles mark the occluded objects." + ], + "image_footnote": [], + "bbox": [ + 93, + 570, + 454, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sentative features on the scene. Compared to our strategy utilizing both criteria, the two ablations omitting one of the criteria have a performance drop, especially on the DOS benchmark. The usage-based strategy performs worse than the object-based, showing that the features of objects could be more informative for capturing historic behaviors.", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Global Reasoning Design Table 4 studies the performance when different designs of the global reasoning module are applied. First, we remove the entire module and observe a significant drop in all metrics but the road completion. For instance, the average success rate on the DOS benchmark dropped from 71.5 to 29.5. This demonstrates the effectiveness of global reasoning, especially in occlusion events. Second, we ablated the consistency loss, which could alleviate the sub-optimal issues in collected expert data. A removal of consistency loss leads to a lower driving score and higher collision rate on the Town 05 benchmark and a lower success rate on the DOS benchmark. Third, excluding the traffic sign feature from the global reasoning model results in an increase on the red light violation. One explanation is that the traffic sign feature from the global reasoning module could help reason the distant traffic light state according to other road participants' behavior.", + "bbox": [ + 496, + 351, + 893, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 642, + 619, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present ReasonNet, a novel end-to-end autonomous driving framework including two major components: a temporal reasoning module and a global reasoning module. The temporal reasoning module processes the historic information on the driving scene for high-fidelity forecasting of other road participants and dynamically maintains a temporal memory bank. The global reasoning module models the interaction and relationship among the objects and environment to detect adverse events especially occlusion, and improve overall perception performance. Our method pushes the state-of-the-art performance of the CARLA leaderboard by a considerable margin. Moreover, we also publicly release a new benchmark DOS consisting of diverse occlusion scenarios, to facilitate the study of occlusion detection in the field of end-to-end autonomous driving.", + "bbox": [ + 496, + 674, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13730", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Expert drivers for autonomous driving. https://kait0.github.io/files/master_thesis_bernhard_jaeger.pdf, 2021.6, 13", + "[2] Oladapo Afolabi, Katherine Driggs-Campbell, Roy Dong, Mykel J Kochenderfer, and S Shankar Sastry. People as sensors: Imputing maps from human actions. In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 2342-2348. 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In Proceedings of the" + ], + "bbox": [ + 78, + 90, + 470, + 901 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "IEEE/CVF International Conference on Computer Vision, pages 15222-15232, 2021. 2, 13, 14", + "bbox": [ + 532, + 90, + 890, + 119 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13733", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_model.json b/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5399bed64e1d30c153cdd2366d66d0afade7d256 --- /dev/null +++ b/2023/ReasonNet_ End-to-End Driving With Temporal and Global Reasoning/1fe839d8-63ad-45a1-a78b-7253a9b6afed_model.json @@ -0,0 +1,2070 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.131, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "ReasonNet: End-to-End Driving with Temporal and Global Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.18, + 0.687, + 0.218 + ], + "angle": 0, + "content": "Hao Shao\\(^{1}\\) Letian Wang\\(^{2}\\) Ruobing Chen\\(^{1}\\) Steven L. Waslander\\(^{2}\\) Hongsheng Li\\(^{3}\\) Yu Liu\\(^{1,4*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.223, + 0.753, + 0.261 + ], + "angle": 0, + "content": "\\(^{1}\\)SenseTime Research \\(^{2}\\)University of Toronto \\(^{3}\\)CUHK MMLab \\(^{4}\\)Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.294, + 0.314, + 0.31 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.659 + ], + "angle": 0, + "content": "The large-scale deployment of autonomous vehicles is yet to come, and one of the major remaining challenges lies in urban dense traffic scenarios. In such cases, it remains challenging to predict the future evolution of the scene and future behaviors of objects, and to deal with rare adverse events such as the sudden appearance of occluded objects. In this paper, we present ReasonNet, a novel end-to-end driving framework that extensively exploits both temporal and global information of the driving scene. By reasoning on the temporal behavior of objects, our method can effectively process the interactions and relationships among features in different frames. Reasoning about the global information of the scene can also improve overall perception performance and benefit the detection of adverse events, especially the anticipation of potential danger from occluded objects. For comprehensive evaluation on occlusion events, we also release publicly a driving simulation benchmark DriveOcclusionSim consisting of diverse occlusion events. We conduct extensive experiments on multiple CARLA benchmarks, where our model outperforms all prior methods, ranking first on the sensor track of the public CARLA Leaderboard [53]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.687, + 0.21, + 0.703 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Despite significant recent progress in the field of autonomous driving, truly large-scale deployment of autonomous vehicles (AVs) on public roads has yet to be established. The majority of the remaining issues lie in navigating dense urban traffic scenes, where a large number of different dynamic objects (e.g. vehicles, bicycles, pedestrians), complex road geometries and road user interactions are involved. In such circumstances, currently deployed or tested solutions could make incorrect or unexpected decisions, resulting in severe accidents or traffic infractions [4, 24, 53]. Two of the major challenges behind" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.295, + 0.878, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.485, + 0.895, + 0.571 + ], + "angle": 0, + "content": "Figure 1. Temporal reasoning on the historic behaviors of surrounding objects can benefit the prediction of the scene evolution and objects' future behaviors. Global reasoning on the interaction among objects and the environment allows for inference about unobservable space and occluded objects, anticipating potential danger and enhancing perception/driving performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.893, + 0.674 + ], + "angle": 0, + "content": "such autonomous incompetence include 1) how to achieve a comprehensive understanding of the driving scene and, more importantly, how to make high-fidelity predictions on the future evolution of the driving scene; 2) how to deal with rare adverse events in long-tail distributions, such as undetected but relevant objects in occluded regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Comprehensive scene understanding and high-fidelity prediction of how objects in the scene will move in the future are vital for autonomous vehicles to take safe and reliable actions. Toward this end, modularized methods were proposed to decompose the task into three sequential subtasks: detection [37-40, 42], tracking [5, 65], and forecasting [6, 26, 28, 32, 33, 59-61]. While more interpretability is provided by developing each module independently, these sub-tasks are still regarded as open research questions and errors in each sub-task can propagate and accumulate, leading to unstable overall performance. In contrast, end-to-end driving methods [9, 10, 51] have recently emerged as a promising method to solve these subtasks in a monolithic manner directly. However, a high-fidelity future prediction necessitates sufficient temporal reasoning over the historic" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13723" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "information of the scene [22, 50], which is usually only somewhat considered in previous end-to-end driving methods if not completely ignored. For example, [10, 15] only exploited scene information in the current frame, and [54] simply concatenated features in historic frames for temporal reasoning. In such cases, the interactions and relationships amongst features in different frames and objects cannot be sufficiently modeled. Thus in this paper, we propose a temporal reasoning module to effectively fuse information from different frames for better driving performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.822 + ], + "angle": 0, + "content": "On the other hand, rare adverse events in long-tail distributions remain a notoriously challenging issue on the way toward large scale deployment of autonomous vehicles. For example, one such challenge is the difficulty in detecting occluded but relevant objects in the scene. While a large amount of research has focused on improving perception performance [37, 57], the occluded objects essentially lie out of the scope of observable elements, and failure to consider such objects can result in either dangerous or overly cautious driving behavior. Our observation is that, while humans also suffer from similar limitations to autonomous vehicles regarding occluded objects, they are able to reason about these unobservable spaces by exploiting global information of the scene such as road geometry and driving interaction patterns, to anticipate potential danger even under occlusion. For example, when one human driver notices another vehicle braking abruptly, the driver may reason the presence of an occluded object (e.g., a pedestrian) ahead, reminding himself to drive cautiously. Thus, our insight is that, a safe and intelligent autonomous vehicle should also master the global reasoning capability to have a better perception of the scene. In this paper, we propose a transformer-based global reasoning module to sufficiently fuse information of the environment and objects, and analyze their interactions for better scene understanding. Such global reasoning capability not only benefits interaction modeling with occluded objects, but also improves overall perception performance. Examples of such performance gains include better traffic light status identification by reasoning over other vehicles' actions and more accurate future trajectory forecasting by reasoning over interactions among objects. Besides, considering the fact that the occlusion events lie in the long-tail distribution and have been rare in currently available datasets, we also construct a Driving in Occlusion Simulation benchmark (DOS) consisting of 4 occlusion scenarios, each with 25 cases, as a comprehensive occlusion event evaluation benchmark in the field of end-to-end autonomous driving." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a novel end-to-end driving framework named temporal and global reasoning network (ReasonNet), which provides enhanced reasoning on the temporal evolution and the global information of the scene, for better perception performance and driving quality. Our" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.688, + 0.106 + ], + "angle": 0, + "content": "contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.119, + 0.892, + 0.195 + ], + "angle": 0, + "content": "- We propose a novel temporal and global reasoning Network (ReasonNet) to enhance historic scene reasoning for high-fidelity prediction of the scene's future evolution and improve global contextual perception performance even under occlusion." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.204, + 0.892, + 0.28 + ], + "angle": 0, + "content": "- We present a new benchmark called Driving in Occlusion Simulation benchmark (DOS), which consists of diverse occlusion scenarios in urban driving for systematic evaluation in occlusion events, and make the benchmark publicly available." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.289, + 0.892, + 0.351 + ], + "angle": 0, + "content": "- We experimentally validate our method on multiple benchmarks with complex and adversarial urban scenarios. Our model ranks first on the sensor track of the CARLA autonomous driving leaderboard." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.119, + 0.892, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.363, + 0.638, + 0.379 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.903 + ], + "angle": 0, + "content": "End-to-end Autonomous Driving End-to-end autonomous driving in urban scenarios has become more studied recently thanks to the CARLA simulator and leaderboard [21]. Recent works mainly consist of reinforcement learning (RL) and imitation learning (IL) methods. The reinforcement Learning methods train the agents by constantly interacting with simulated environments and learning from these experiences. Latent DRL [54] first trains an embedding space as a latent representation of the environment observation, and then conducts reinforcement learning with the latent observation. Roach [66] utilizes an RL agent with privileged information of the environment to distill a model only with regular information (e.g. sensor) as the final agent. WOR [9] builds a model-based RL agent along with the world model and reward model. The final agent is distilled from the expert knowledge acquired from these pretrained models. Imitation learning methods aim at learning from an expert agent to bypass interacting with the environment. Early IL methods include CIL [17] and CILRS [18], which apply a conditional architecture with different network branches for different navigation commands. LBC [11] first trains an imitation learning agent with privileged information, which is then distilled into a model using sensor data. Transfuser [15, 47] designs a multi-modal transformer to fuse information between the front camera image and LiDAR data. LAV [10] exploits data of not only the ego vehicle but also surrounding vehicles for data augmentation by learning a viewpoint-invariant spatial intermediate representation. TCP [63] proposes a network with two branches which generates the control signal and waypoints respectively. An adaptive ensemble is applied to fuse the two output signals. InterFuser [51] uses a transformer to fuse and process multimodal multi-view sensors for comprehensive scene understanding." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13724" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.379 + ], + "angle": 0, + "content": "Attention for Autonomous Driving The attention mechanism has been demonstrated to be a powerful module in many areas of deep learning, including the context of driving. The classic attention-based Transformer architecture [55] was originally established in Natural Language Processing. Transformer (VIT) was then applied in Computer Vision (vision Transformer, VIT [20, 49]) and attains excellent performance onImagenet classification. Later generations move on to generalize the attention mechanism to the driving domain, including motion forecasting [23, 36, 58], driver attention prediction [25, 34] and object tracking [45, 52]. In the field of end-to-end autonomous driving, TransFuser [15, 47] exploits several transformer modules for the fusion of data from the front view camera and LiDAR. NEAT [14] uses intermediate attention maps to iteratively compress 2D image features into a compact bird-eye-view (BEV) representation for driving. InterFuser [51] utilizes a transformer encoder and decoder to fuse information and decode the feature into interpretable embeddings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Multi-task Learning Our end-to-end driving framework adopts multi-task learning, with a joint objective of object detection, occupancy forecasting, traffic sign prediction and waypoint prediction. MotionNet [62] proposes a spatio-temporal pyramid network for joint perception and motion prediction based on BEV maps. PnPNet [41] proposes a new object trajectory representation and multi-object tracker to handle occlusion and false positives. IntentNet [7] predicts the high-level intentions of each agent from semantic HD maps building. ST-P3 [29] proposes an egocentric-aligned accumulation technique to preserve geometry information in 3D space and utilize a dual pathway modeling to consider past motion variations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.587, + 0.17, + 0.603 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.613, + 0.473, + 0.809 + ], + "angle": 0, + "content": "We aim at learning a driving policy \\(\\pi\\) that generates raw control commands by taking multi-view multi-modal sensor readings, vehicle measurements, and navigation commands as inputs. As shown in Figure 2, the proposed ReasonNet consists of three parts: 1) a perception module that extracts bird's-eye-view (BEV) features from LiDAR and RGB data; 2) a temporal reasoning module that processes temporal information and maintains a memory bank storing historic features; 3) a global reasoning module that captures the interaction/relationship amongst objects and the environment, to detect adverse events (e.g. occlusion) and improve overall perception performance. This section will introduce these modules in detail." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.262, + 0.834 + ], + "angle": 0, + "content": "3.1. Perception Module" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "The perception module is responsible for processing and fusing different sensor data at the early stage of our framework, based on which temporal and global reasoning can be conducted by later modules. Specifically, five sensors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.259 + ], + "angle": 0, + "content": "are utilized: four RGB cameras (left, front, right and rear) \\( I_{\\mathrm{rgb}} = I_{0,1,2,3} \\) and one LiDAR sensor \\( I_{\\mathrm{lidar}} = I_4 \\). Four image inputs are obtained from the four cameras, and an additional focus-view image input is center-cropped from the front image to capture distant traffic lights. Point cloud data is retrieved from the LiDAR sensor. Our perception module includes a 2D backbone to embed image input into keys and values, a 3D backbone to embed LiDAR input into queries, and a BEV decoder that utilizes these keys, values, and queries to obtain features of the bird's-eye view (BEV) map, waypoints, and traffic signs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.26, + 0.895, + 0.472 + ], + "angle": 0, + "content": "Image Input For each image input of \\( I_{rgb} \\), a 2D CNN backbone ResNet [27] is applied to generate a feature map \\( f_{i} \\). Then, we use a convolution layer to map the channels of \\( f_{i} \\) to \\( C_v \\) and flatten it to one-dimensional tokens. A sinusoidal positional encoding and learnable sensor embeddings are added to the tokens, so that the following network can distinguish them from different cameras and relative positions. Finally, tokens of different images are passed through a standard transformer encoder with \\( K_{e} \\) layers. Each layer consists of Multi-Headed Self-Attention [55], MLP blocks and layer normalization [3]. This image fusion operation can contribute to a better perception of global context from multi-view inputs, generating keys and values for the image-LiDAR fusion in BEV decoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.895, + 0.627 + ], + "angle": 0, + "content": "LiDAR Input For the LiDAR input, we use PointPillars [35] as our 3D perception backbone to process points in the ego-vehicle-centered area \\( x \\in [-H_b, H - H_b] \\) and \\( y \\in [-W/2, W/2] \\). Specifically, we use a simplified version of PointNet [48] to encode the information of raw LiDAR points. Each pillar includes the points in a \\( 0.25\\mathrm{m} \\times 0.25\\mathrm{m} \\) area. The extracted feature map is downsampled to \\( C_v \\times H \\times W \\) for computation reduction and then serves as BEV queries used in the BEV decoder and memory bank." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Sensor-Fusion BEV Decoder The BEV decoder follows a standard transformer architecture design with \\( K_{\\text{bev}} \\) layers to fuse tokens from different sensors. Tokens from the RGB images are fed as values and keys into the decoder, and tokens from the LiDAR points are fed as the \\( H \\times W \\) queries to generate BEV features. In addition, two other kinds of queries for the prediction of traffic signs and waypoints w are also fed into the decoder. Following InterFuser [51], we use a 2-layer MLP as the traffic sign classifier to predict the traffic light state and whether there is a stop sign ahead; we then use a single-layer GRU [16] to auto-regressively generate consecutive waypoints \\( \\{\\mathbf{w}_t\\}_{t=1}^{T_f} \\) conditioned on the goal location of the ego vehicle. \\( T_f \\) denotes the number of the predicted time steps. To pretrain the perception module in the first training stage, the generated BEV feature is passed through a one-stage CenterPoint [64] to generate the \\( H \\times W \\times 7 \\) BEV map covering an \\( H_m \\times W_m \\) spatial region, where the seven channels represent object existence" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13725" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.094, + 0.855, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.404, + 0.895, + 0.463 + ], + "angle": 0, + "content": "Figure 2. The proposed ReasonNet consists of three modules: 1) the perception module fuses different sensor data to generate the BEV feature, traffic sign feature, and waypoints in the early stage of our framework; 2) the temporal reasoning module processes current and historic features and maintains a memory bank to store historic features; 3) the global reasoning module models the interaction and relationship among objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.471, + 0.506 + ], + "angle": 0, + "content": "probability, offset from grid center, bounding box extent, heading angle and velocity for objects at each grid cell." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.336, + 0.529 + ], + "angle": 0, + "content": "3.2. Temporal Reasoning module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Compared to existing end-to-end driving methods that only exploit scene information of the current frame [10, 15] or simply concatenate features of historic frames [54], we propose a temporal reasoning module that can sufficiently store and fuse temporal information to benefit the motion forecasting of traffic participants and the tracking of intermittently occluded objects. As shown in Figure 2, our temporal reasoning module includes temporal processing to fuse current and historic features through an attention mechanism, and maintains a memory bank which stores historic short-term and long-term feature keys and values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Temporal Processing Considering that information in different historic frames could have different relevance to the current scene, we apply an attention-based memory reading from the historic features. Specifically, for each historic frame \\(t\\) stored in the memory, we first measure its relevance by calculating the normalized similarity \\(\\mathbf{S}\\) between the historic-frame feature key \\(\\mathbf{k} \\in \\mathbb{R}^{C_k \\times T_h \\times H \\times W^1}\\) and the current-frame feature query \\(\\mathbf{q} \\in \\mathbb{R}^{C_k \\times H \\times W}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.83, + 0.47, + 0.868 + ], + "angle": 0, + "content": "\\[\nS (\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}) = \\frac {(\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}}{\\sum_ {i = 0 , j = 0} ^ {i = H - 1 , j = W - 1} (\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}} \\tag {1}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\( {}^{1}C,H,W \\) denotes the channel,height,and width of the feature respectively, \\( {T}_{h} \\) denotes the number of the frames stored in the memory bank." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.475, + 0.892, + 0.536 + ], + "angle": 0, + "content": "We map every query element to a distribution over \\(H\\times W\\) memory elements and correspondingly aggregate their values \\(\\mathbf{v}\\) to obtain the readout feature \\(\\mathbf{M}\\in \\mathbb{R}^{C_v\\times T_h\\times H\\times W}\\) for each frame \\(t\\) stored in the memory:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.559, + 0.892, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {t, h, w} = \\sum_ {i = 0, j = 0} ^ {i = H - 1, j = W - 1} \\mathbf {v} _ {t, i, j} S \\left(\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.795 + ], + "angle": 0, + "content": "The aggregated features from all historic frames are then concatenated with the current-frame feature value to get \\(\\mathbf{M}' \\in \\mathbb{R}^{C_v \\times (T_h + 1) \\times H \\times W}\\), which is then passed through a GRU to progressively fuse temporal information and get \\(\\mathbf{M}_{fused} \\in \\mathbb{R}^{C_v \\times H \\times W}\\) as the final output of the module. Technically, we take the L2 similarity proposed in STCN [13] as the similarity measure function, which is more stable than the dot product [46]. The current-frame feature query \\(\\mathbf{q}\\) is obtained by passing the features from the 3D backbone \\(\\mathbf{F} \\in \\mathbb{R}^{C_v \\times H \\times W}\\) through a query encoder (several convolution layers). The historic-frame feature key \\(\\mathbf{k}\\) and value \\(\\mathbf{v}\\) are taken from the temporal memory bank." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Memory Bank Maintaining As above, we have introduced the temporal processing at one single frame. After every \\(\\tau\\) frame, the obtained feature key and value at that frame will be used to update the memory bank. Specifically, the current-frame feature query \\(\\mathbf{q}\\) is directly copied and fed into the memory bank as the memory key without extra computation. The final output \\(\\mathbf{M}_{\\text{used}}\\) will first be encoded" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13726" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.608 + ], + "angle": 0, + "content": "to a BEV map \\(\\mathbf{M}_p\\). The BEV map \\(\\mathbf{M}_p\\) will be concatenated with the final output \\(\\mathbf{M}_{fused}\\) and passed through a value encoder to obtain the memory value \\(\\mathbf{v}\\), which is fed into the memory back. With the above key-value pairs, the memory bank maintains two kinds of buffer: the short-term and long-term buffer. On the one hand, the new key-value pair will be appended to the short-term buffer, as a high-resolution memory of the scene in the past few seconds for accurate feature matching. Considering the limited GPU memory resources, we limit the buffer size and older key-value pairs will be discarded when the limit number \\(T_s\\) is reached. However, when these older features are discarded, the long-term behavior of the traffic participants is missing, which can be crucial for motion forecasting in complex traffic scenarios. Thus on the other hand, inspired by XMem [12], the memory bank also maintains a long-term buffer that selectively stores important/representative key-value feature pairs discarded by the short-term buffer. Considering the fact that the objects surrounding the ego vehicle are sparse most of the time², the long-term buffer selectively stores key-value features (\\(\\mathbf{k}\\) and \\(\\mathbf{v}\\)) which meet one of the two criteria: 1) their corresponding location in the BEV map \\(\\mathbf{M}_p\\) has a high probability of object existence; 2) their usage frequency is in top-K of all candidate key-value features. The usage frequency is defined by its cumulative normalized similarity (Eq. 1). The features selected by the above criteria are appended to the last frame of memory. And if the last memory frame is full, we will initialize one new frame with the zero vector and set it as the last frame to store new features. When the number of frames reaches the limit \\(T_l\\), the obsolete memory will be removed. Such a compact storing strategy can efficiently track long-term representative features and intermittently occluded objects, while balancing the resources required." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.615, + 0.313, + 0.631 + ], + "angle": 0, + "content": "3.3. Global Reasoning module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.473, + 0.866 + ], + "angle": 0, + "content": "Rare adverse events such as occluded objects are a notorious issue for the practical deployment of AVs. Our insight is that humans perceive their surroundings not only through sensors, but also by exploiting global information on the scene to reason over the unobservable spaces. For instance, when a vehicle performs an emergency stop without a clear reason, humans can infer that there is potentially an occluded object ahead of the vehicle and will drive more cautiously. Thus we propose the global reasoning module to capture the interaction and relationship between objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance. The module consists of three parts: 1) an object-environment and object-object interaction modeling process; 2) an occupancy decoder to generate the occupancy map; 3) a consistency loss" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Based on the data collected from the CARLA simulator, only \\(7\\%\\) of the ego-vehicle-centered BEV map area is occupied by active objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "to encourage consistent prediction of waypoints and the occupancy map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.287 + ], + "angle": 0, + "content": "Interaction Modeling The object-environment and object-object interaction modeling process aims at reasoning about the relationship among objects and the environment. On the one hand, \\(\\mathbf{M}_{\\text {fused }}\\) features whose corresponding location in the BEV map \\(\\mathbf{M}_p\\) has a high probability of object existence will be extracted to represent object features. On the other hand, \\(\\mathbf{M}_{\\text {fused }}\\) features will also be downsampled to represent the environment features. All object and environment features are used to construct a graph, which is passed through a graph attention network (GAT) [56] for interaction modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.455 + ], + "angle": 0, + "content": "Occupancy Decoder Taking the features outputted by the GAT as keys and values, and the learnable positional embeddings as queries, the occupancy decoder utilizes a transformer decoder with \\( K_{\\text{opy}} \\) layers to generate: 1) the traffic sign feature, which is then concatenated with the traffic sign feature from the BEV decoder to generate the final traffic sign prediction; 2) the occupancy map feature, which is then applied with convolution operation to generate the occupancy map \\( \\mathbf{O}_t \\in \\mathbb{R}^{T_f \\times H \\times W} \\). At a future time \\( t \\), each cell in the occupancy map contains a value in the range [0,1] representing the probability that the cell is occupied." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.893, + 0.636 + ], + "angle": 0, + "content": "Consistency Loss Currently, our framework predicts the waypoints and the occupancy map independently, which are not necessarily consistent. For example, the waypoints could overlap some obstacles in the occupancy map. Thus we propose a consistency loss to discourage waypoints' crossing the high-probability region of the occupancy map. Further, the consistency loss also encourages generating longer waypoint trajectories for efficient driving. Specifically, the consistency loss aims at minimizing the average object existence probability of the cells that cover the predicted waypoints, and maximizing the average \\( l_{2} \\) length of the waypoint trajectory w:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.654, + 0.892, + 0.699 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s i s t e n c y}} = \\frac {1}{T _ {f}} \\left(\\sum_ {t = 0} ^ {T _ {f}} \\frac {\\sum_ {i = 0} ^ {N _ {c} ^ {t}} \\mathbf {O} _ {t , i}}{N _ {c} ^ {t}} - \\lambda \\sum_ {t = 0} ^ {T _ {f}} \\| \\mathbf {w} _ {t} \\| _ {1}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.735 + ], + "angle": 0, + "content": ",where \\(N_{c}^{t}\\) denotes the number of covered cell at step \\(t\\) \\(\\mathbf{O}_{t,i}\\) denotes the object existence probability at cell \\(i\\) at time \\(t\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.597, + 0.756 + ], + "angle": 0, + "content": "3.4. Control" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Following [11], we use two PID controllers for latitudinal and longitudinal control, to track the heading and velocity of predicted waypoints respectively. If a red traffic light or stop sign is detected, the ego-vehicle will brake. Additionally, an emergency stop will also be performed if the ego vehicle's current bounding box crosses the area in the occupancy map that has a high object existence probability or if the future waypoints overlap with objects in the BEV map." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13727" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.092, + 0.262, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.45, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.237, + 0.261, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.236, + 0.448, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.378, + 0.47, + 0.435 + ], + "angle": 0, + "content": "Figure 3. An illustration for the four types of occlusion scenarios included in the proposed DOS benchmark. The orange color denotes the ego car. The blue/green dots denote the occluded/visible trajectory of the occluded dangerous object." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.45, + 0.231, + 0.466 + ], + "angle": 0, + "content": "3.5. Training Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.473, + 0.732 + ], + "angle": 0, + "content": "The training of our framework consists of two stages. In the first stage, we train the perception module to predict BEV features, traffic sign features, and waypoints. Specifically, the loss of BEV features and traffic sign features is computed with additional prediction heads, which are discarded in the next stage. In the second stage, we freeze the perception module and train the other two modules. Five loss terms are considered: 1) the waypoints loss \\(\\mathcal{L}_w\\) that minimizes the error between predicted waypoints and expert waypoints; 2) the BEV map loss \\(\\mathcal{L}_{BEV}\\) that follows [10,64] to minimize the current-frame BEV map prediction error; 3) the traffic sign loss \\(\\mathcal{L}_{sign}\\) for the traffic regulation prediction; 4) occupancy map loss \\(\\mathcal{L}_{opy}\\) that minimizes the occupancy prediction error in a future horizon; 5) the consistency loss \\(\\mathcal{L}_{consistency}\\) which encourages a consistent generation of the waypoints and occupancy map. These loss terms are balanced by corresponding loss weights." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.748, + 0.456, + 0.765 + ], + "angle": 0, + "content": "4. Drive in Occlusion Sim (DOS) Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.47, + 0.88 + ], + "angle": 0, + "content": "In order to address the issue that occlusion events are rare in existing datasets and benchmarks, we present the Drive in Occlusion Simulation benchmark (DOS), a CARLA-based framework providing diverse driving scenarios with occluded objects. As shown in Figure 3, the proposed DOS benchmark includes four types of challenging occlusion driving scenarios:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.471, + 0.902 + ], + "angle": 0, + "content": "**Parked Cars (#1)** The ego vehicle is driving in a straight" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.236 + ], + "angle": 0, + "content": "
RankMethodDS ↑RC ↑IS ↑
1ReasonNet (Ours)79.9589.890.89
2InterFuser [51]76.1888.230.84
3TCP [63]75.1485.630.87
4LAV [10]61.8594.460.64
5TransFuser [15]61.1886.690.71
6Latent TransFuser [15]45.2066.310.72
7GRIAD [8]36.7961.850.60
8TransFuser+ [1]34.5869.840.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.241, + 0.894, + 0.312 + ], + "angle": 0, + "content": "Table 1. Performance comparison on the public CARLA leaderboard [53] (accessed Nov 2022). For all three metrics, higher is better. Our method ranks first overall on the leaderboard, with the highest driving score (DS) and infraction score (IS), and the second highest route completion (RC)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.372 + ], + "angle": 0, + "content": "lane with parked cars on the side. Pedestrians can first appear on the sidewalk (visible) and then suddenly emerge through the occluded areas between parked cars (occluded)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Sudden Brake (#2) The ego vehicle is driving in a straight lane along with other vehicles ahead. Pedestrians can suddenly emerge from the sidewalks, causing the other vehicles to brake while remaining invisible to the ego vehicle." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.892, + 0.495 + ], + "angle": 0, + "content": "Left Turn (#3) The ego vehicle intends to perform an unprotected left turn at an intersection, but a truck in the opposite lane blocks the view of oncoming traffic, intermittently obscuring vehicles driving straight through the intersection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Red Light Infraction (#4) The ego vehicle is crossing an intersection after some trucks. A left-to-right vehicle running a red light suddenly appears, forcing the trucks to brake promptly. But the ego vehicle's view toward the running-light vehicle is blocked by the trucks, so it remains invisible to the ego vehicle." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Each of the four scenarios in the DOS benchmark comprises 25 different cases varying in the road environment and background traffic. Compared to a previous occlusion benchmark AUTOCASTSIM [19], the DOS benchmark: 1) includes occlusions of both vehicles and pedestrians, instead of only vehicles; 2) includes 100 cases of 4 scenarios, instead of only 3 cases of 3 scenarios; 3) considers specific occlusions that can potentially be resolved by temporal reasoning (intermittent occlusion, #1, #3) and global reasoning (constant occlusion but with interaction clues, #2, #4) about the scene, instead of random occlusions as in AUTOCASTSIM. Thus our scenarios can also serve as a good tracking-with-intermittent-occlusion benchmark and a People-as-Sensor [2,31] benchmark." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.821, + 0.634, + 0.838 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.677, + 0.864 + ], + "angle": 0, + "content": "5.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Implementation We implement and evaluate our approach on the open-source CARLA simulator with version" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13728" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.847, + 0.209 + ], + "angle": 0, + "content": "
SettingTown 05 LongDOS
TsTlDS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
0066.7±3.897.6±2.70.68±0.030.18±0.030.05±0.020.03±0.0322±1.628±3.426±2.125±1.6
1067.9±3.496.8±2.30.70±0.020.16±0.040.04±0.030.05±0.0230±3.638±3.632±2.832±3.4
2068.1±3.196.9±3.40.70±0.030.16±0.030.04±0.020.05±0.0328±5.548±4.138±4.452±3.9
2170.9±2.095.7±3.10.74±0.020.13±0.020.04±0.020.06±0.0455±4.457±4.148±4.155±5.5
4070.5±2.196.4±2.50.73±0.040.14±0.030.03±0.020.06±0.0332±5.458±4.440±5.555±4.9
4273.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.213, + 0.895, + 0.27 + ], + "angle": 0, + "content": "Table 2. Ablation study on different short-term buffer size \\( T_{s} \\) and long-term buffer size \\( T_{l} \\), on the Town 05 Long benchmark and the proposed DOS benchmark. Performance is evaluated over three runs. CR: Collision rate, Red: Red light violation, Blocked: Vehicle blocked, SR: Success rate. SR#1 denotes the first kind of scenario in the DOS benchmark. As the two buffer sizes increase, improvement is witnessed in all metrics but the road completion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.472, + 0.419 + ], + "angle": 0, + "content": "0.9.10.1 [21]. We use ResNet-50 pretrained on ImageNet as the 2D backbone and PointPillars trained from scratch as the 3D backbone. We predict \\( T_{f} = 4 \\) time steps for the waypoints and occupancy map, and the interval between each time step is 0.5 seconds. The memory bank maintains \\( T_{s} = 4 \\) frames in the short-term buffer and \\( T_{l} = 2 \\) frames in the long-term buffer. The memory bank is updated every \\( \\tau = 2 \\) frame. We refer readers to Appendix A for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.47, + 0.548 + ], + "angle": 0, + "content": "Dataset Collection We collect an expert dataset of 2M frames by running a rule-based expert agent on all 8 public towns and 21 types of weather, with the access to the privileged information in the CARLA simulator. We randomly set routes, spawn dynamic objects and adversarial scenarios provided in [47], to diversify the collected data. To ensure the temporal continuity of collected data, the data are collected at a high frequency of 10HZ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.706 + ], + "angle": 0, + "content": "Metrics We consider three major metrics introduced by the CARLA LeaderBoard: route completion ratio (RC), infraction score (IS), and driving score (DS). The route completion ratio is the percentage of the route completed. The infraction score measures infractions triggered. When collisions or traffic rule violations occur, the infraction score will decay by a discount factor. The driving score is the product of the route completion ratio and the infraction score, describing both driving progress and safety, and thus is the primary ranking metric in the CARLA Leaderboard." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.373, + 0.751 + ], + "angle": 0, + "content": "5.2. Comparison to the state of the art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Table 1 shows the top 8 entries on the public CARLA Leaderboard. Readers can refer to Sec 2 for descriptions of these methods. Our method outperforms all prior methods, with the highest driving score and infraction score, and the second highest route completion. The previous leading method InterFuser uses a transformer for sensor fusion but lacks temporal and global reasoning. Compared to InterFuser, our method improved the driving score, road completion, and infraction score by \\(5\\%\\), \\(2\\%\\), and \\(6\\%\\) respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.283, + 0.651, + 0.3 + ], + "angle": 0, + "content": "5.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.895, + 0.475 + ], + "angle": 0, + "content": "We investigate the effect of the temporal and global reasoning modules on the Town05 Long benchmark and the DOS benchmark. For each scenario in DOS, we take 5 cases for training and 20 cases for evaluation. In addition to the three metrics mentioned earlier, we also present four more metrics for detailed analysis: collision rate (CR), red light violation (Red), ego vehicle blocked frequency (Blocked), and success rate (SR). The first three metrics are normalized by the driven distance (km). Visualizations of how the temporal reasoning and global reasoning work can be found at Figure 4 and Figure 5 respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Memory Size Table 2 studies the effect of different short-term buffer size \\( T_{s} \\) and long-term buffer size \\( T_{l} \\). The overall observation is that, as the two buffer sizes increase, improvement is witnessed in all metrics but road completion. Specifically, when the long-term memory is removed \\( (T_{l} = 0) \\), the average success rates drop sharply from 71.5 to 36 on DOS scenarios that require keeping track of intermittently occluded objects (#1 and #3). If we remove the temporal reasoning module \\( (T_{s} = T_{l} = 0) \\), the driving score on the Town05 benchmark drops by \\( 9\\% \\), and the average success rate on the DOS benchmark drops by \\( 46\\% \\). We hypothesize that the drop in performance is because 1) it can be really hard to accurately estimate the objects' future motion based only on single-frame data; 2) temporal information can help keep track of objects that are intermittently occluded; 3) the global reasoning module may also work poorly when historic information is missing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Long-Term Memory Selection Strategy Table 3 studies the performance of different long-term memory selection strategies. Specifically, the proposed strategy in Sec 3.2 includes two selection criteria. So here we ablate the effect of the two criteria by 1) only selecting the short-term feature with top- \\( K \\) usages (usage-based); 2) only selecting the feature with a high probability of the existence of an object (object-based). Besides, we also compared a random selection strategy. As in Table 3, the random selection strategy has the poorest performance especially on the DOS benchmark, as random selection could miss important and repre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13729" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.849, + 0.181 + ], + "angle": 0, + "content": "
SettingTown 05 LongDOS
DS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
Random71.2±5.496.6±2.40.74±0.040.13±0.040.03±0.010.06±0.0233±4.455±6.242±5.553±5.4
Usage-based72.0±3.995.9±2.20.75±0.040.12±0.030.03±0.010.06±0.0245±4.262±3.453±2.862±3.9
Object-based72.2±3.796.1±3.00.75±0.030.12±0.030.03±0.010.05±0.0257±4.165±3.673±4.460±3.7
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.185, + 0.894, + 0.214 + ], + "angle": 0, + "content": "Table 3. Ablation study on different long-term memory selection strategies. Our proposed strategy considering both the usage and object criteria outperforms the random selection strategy and the two methods with only one criteria, especially on the DOS benchmark." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.22, + 0.85, + 0.307 + ], + "angle": 0, + "content": "
SettingTown 05 LongDOS
DS↑RC↑IS↑CR↓Red↓Blocked↓SR#1↑SR#2↑SR#3↑SR#4↑
No global reasoning68.9±4.697.4±2.90.71±0.040.15±0.040.05±0.020.05±0.0228±2.834±3.429±2.027±3.6
No consistency loss72.2±3.496.1±3.20.75±0.030.12±0.020.03±0.020.06±0.0360±4.172±3.977±4.968±4.2
No traffic sign prediction71.1±2.796.0±4.10.74±0.030.11±0.030.05±0.030.07±0.0362±4.472±4.082±2.870±4.1
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.31, + 0.893, + 0.339 + ], + "angle": 0, + "content": "Table 4. Ablation study on the global reasoning module. The performance would drop when 1) the entire global reasoning module is removed; 2) the consistency loss is not applied; 3) the traffic sign feature from the reasoning module is not utilized." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.351, + 0.455, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.499, + 0.471, + 0.569 + ], + "angle": 0, + "content": "Figure 4. Visualization of the attention map between one object's current-frame feature query and the historic-frame feature stored in the short-term buffer, in two cases. The object's current-frame feature consistently attends to its corresponding region in the historic feature map." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.571, + 0.455, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.691, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Figure 5. We show two cases of how our framework reasons the presence of the occluded object. In the first case, a pedestrian first appeared on the sidewalk (visible) and then emerges between two parked cars (occluded). In the second case, a vehicle runs the red light, forcing trucks to brake abruptly. But the ego vehicle's view toward the running-light vehicle is blocked by the front trucks, so the running-light vehicle remains invisible to the ego vehicle. The rectangles mark the occluded objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.903 + ], + "angle": 0, + "content": "sentative features on the scene. Compared to our strategy utilizing both criteria, the two ablations omitting one of the criteria have a performance drop, especially on the DOS benchmark. The usage-based strategy performs worse than the object-based, showing that the features of objects could be more informative for capturing historic behaviors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Global Reasoning Design Table 4 studies the performance when different designs of the global reasoning module are applied. First, we remove the entire module and observe a significant drop in all metrics but the road completion. For instance, the average success rate on the DOS benchmark dropped from 71.5 to 29.5. This demonstrates the effectiveness of global reasoning, especially in occlusion events. Second, we ablated the consistency loss, which could alleviate the sub-optimal issues in collected expert data. A removal of consistency loss leads to a lower driving score and higher collision rate on the Town 05 benchmark and a lower success rate on the DOS benchmark. Third, excluding the traffic sign feature from the global reasoning model results in an increase on the red light violation. One explanation is that the traffic sign feature from the global reasoning module could help reason the distant traffic light state according to other road participants' behavior." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.62, + 0.658 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We present ReasonNet, a novel end-to-end autonomous driving framework including two major components: a temporal reasoning module and a global reasoning module. The temporal reasoning module processes the historic information on the driving scene for high-fidelity forecasting of other road participants and dynamically maintains a temporal memory bank. The global reasoning module models the interaction and relationship among the objects and environment to detect adverse events especially occlusion, and improve overall perception performance. Our method pushes the state-of-the-art performance of the CARLA leaderboard by a considerable margin. Moreover, we also publicly release a new benchmark DOS consisting of diverse occlusion scenarios, to facilitate the study of occlusion detection in the field of end-to-end autonomous driving." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13730" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.476, + 0.156 + ], + "angle": 0, + "content": "[1] Expert drivers for autonomous driving. https://kait0.github.io/files/master_thesis_bernhard_jaeger.pdf, 2021.6, 13" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.471, + 0.228 + ], + "angle": 0, + "content": "[2] Oladapo Afolabi, Katherine Driggs-Campbell, Roy Dong, Mykel J Kochenderfer, and S Shankar Sastry. People as sensors: Imputing maps from human actions. 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Waslander $^{2}$ Hongsheng Li $^{3}$ Yu Liu $^{1,4*}$ + +$^{1}$ SenseTime Research $^{2}$ University of Toronto $^{3}$ CUHK MMLab $^{4}$ Shanghai Artificial Intelligence Laboratory + +# Abstract + +The large-scale deployment of autonomous vehicles is yet to come, and one of the major remaining challenges lies in urban dense traffic scenarios. In such cases, it remains challenging to predict the future evolution of the scene and future behaviors of objects, and to deal with rare adverse events such as the sudden appearance of occluded objects. In this paper, we present ReasonNet, a novel end-to-end driving framework that extensively exploits both temporal and global information of the driving scene. By reasoning on the temporal behavior of objects, our method can effectively process the interactions and relationships among features in different frames. Reasoning about the global information of the scene can also improve overall perception performance and benefit the detection of adverse events, especially the anticipation of potential danger from occluded objects. For comprehensive evaluation on occlusion events, we also release publicly a driving simulation benchmark DriveOcclusionSim consisting of diverse occlusion events. We conduct extensive experiments on multiple CARLA benchmarks, where our model outperforms all prior methods, ranking first on the sensor track of the public CARLA Leaderboard [53]. + +# 1. Introduction + +Despite significant recent progress in the field of autonomous driving, truly large-scale deployment of autonomous vehicles (AVs) on public roads has yet to be established. The majority of the remaining issues lie in navigating dense urban traffic scenes, where a large number of different dynamic objects (e.g. vehicles, bicycles, pedestrians), complex road geometries and road user interactions are involved. In such circumstances, currently deployed or tested solutions could make incorrect or unexpected decisions, resulting in severe accidents or traffic infractions [4, 24, 53]. Two of the major challenges behind + +![](images/8598ce30dd9fdd1287de354205a66857ba9ca5f7b4636ab2e595e51c5c577d69.jpg) +Figure 1. Temporal reasoning on the historic behaviors of surrounding objects can benefit the prediction of the scene evolution and objects' future behaviors. Global reasoning on the interaction among objects and the environment allows for inference about unobservable space and occluded objects, anticipating potential danger and enhancing perception/driving performance. + +such autonomous incompetence include 1) how to achieve a comprehensive understanding of the driving scene and, more importantly, how to make high-fidelity predictions on the future evolution of the driving scene; 2) how to deal with rare adverse events in long-tail distributions, such as undetected but relevant objects in occluded regions. + +Comprehensive scene understanding and high-fidelity prediction of how objects in the scene will move in the future are vital for autonomous vehicles to take safe and reliable actions. Toward this end, modularized methods were proposed to decompose the task into three sequential subtasks: detection [37-40, 42], tracking [5, 65], and forecasting [6, 26, 28, 32, 33, 59-61]. While more interpretability is provided by developing each module independently, these sub-tasks are still regarded as open research questions and errors in each sub-task can propagate and accumulate, leading to unstable overall performance. In contrast, end-to-end driving methods [9, 10, 51] have recently emerged as a promising method to solve these subtasks in a monolithic manner directly. However, a high-fidelity future prediction necessitates sufficient temporal reasoning over the historic + +information of the scene [22, 50], which is usually only somewhat considered in previous end-to-end driving methods if not completely ignored. For example, [10, 15] only exploited scene information in the current frame, and [54] simply concatenated features in historic frames for temporal reasoning. In such cases, the interactions and relationships amongst features in different frames and objects cannot be sufficiently modeled. Thus in this paper, we propose a temporal reasoning module to effectively fuse information from different frames for better driving performance. + +On the other hand, rare adverse events in long-tail distributions remain a notoriously challenging issue on the way toward large scale deployment of autonomous vehicles. For example, one such challenge is the difficulty in detecting occluded but relevant objects in the scene. While a large amount of research has focused on improving perception performance [37, 57], the occluded objects essentially lie out of the scope of observable elements, and failure to consider such objects can result in either dangerous or overly cautious driving behavior. Our observation is that, while humans also suffer from similar limitations to autonomous vehicles regarding occluded objects, they are able to reason about these unobservable spaces by exploiting global information of the scene such as road geometry and driving interaction patterns, to anticipate potential danger even under occlusion. For example, when one human driver notices another vehicle braking abruptly, the driver may reason the presence of an occluded object (e.g., a pedestrian) ahead, reminding himself to drive cautiously. Thus, our insight is that, a safe and intelligent autonomous vehicle should also master the global reasoning capability to have a better perception of the scene. In this paper, we propose a transformer-based global reasoning module to sufficiently fuse information of the environment and objects, and analyze their interactions for better scene understanding. Such global reasoning capability not only benefits interaction modeling with occluded objects, but also improves overall perception performance. Examples of such performance gains include better traffic light status identification by reasoning over other vehicles' actions and more accurate future trajectory forecasting by reasoning over interactions among objects. Besides, considering the fact that the occlusion events lie in the long-tail distribution and have been rare in currently available datasets, we also construct a Driving in Occlusion Simulation benchmark (DOS) consisting of 4 occlusion scenarios, each with 25 cases, as a comprehensive occlusion event evaluation benchmark in the field of end-to-end autonomous driving. + +In this paper, we propose a novel end-to-end driving framework named temporal and global reasoning network (ReasonNet), which provides enhanced reasoning on the temporal evolution and the global information of the scene, for better perception performance and driving quality. Our + +contributions are three-fold: + +- We propose a novel temporal and global reasoning Network (ReasonNet) to enhance historic scene reasoning for high-fidelity prediction of the scene's future evolution and improve global contextual perception performance even under occlusion. +- We present a new benchmark called Driving in Occlusion Simulation benchmark (DOS), which consists of diverse occlusion scenarios in urban driving for systematic evaluation in occlusion events, and make the benchmark publicly available. +- We experimentally validate our method on multiple benchmarks with complex and adversarial urban scenarios. Our model ranks first on the sensor track of the CARLA autonomous driving leaderboard. + +# 2. Related work + +End-to-end Autonomous Driving End-to-end autonomous driving in urban scenarios has become more studied recently thanks to the CARLA simulator and leaderboard [21]. Recent works mainly consist of reinforcement learning (RL) and imitation learning (IL) methods. The reinforcement Learning methods train the agents by constantly interacting with simulated environments and learning from these experiences. Latent DRL [54] first trains an embedding space as a latent representation of the environment observation, and then conducts reinforcement learning with the latent observation. Roach [66] utilizes an RL agent with privileged information of the environment to distill a model only with regular information (e.g. sensor) as the final agent. WOR [9] builds a model-based RL agent along with the world model and reward model. The final agent is distilled from the expert knowledge acquired from these pretrained models. Imitation learning methods aim at learning from an expert agent to bypass interacting with the environment. Early IL methods include CIL [17] and CILRS [18], which apply a conditional architecture with different network branches for different navigation commands. LBC [11] first trains an imitation learning agent with privileged information, which is then distilled into a model using sensor data. Transfuser [15, 47] designs a multi-modal transformer to fuse information between the front camera image and LiDAR data. LAV [10] exploits data of not only the ego vehicle but also surrounding vehicles for data augmentation by learning a viewpoint-invariant spatial intermediate representation. TCP [63] proposes a network with two branches which generates the control signal and waypoints respectively. An adaptive ensemble is applied to fuse the two output signals. InterFuser [51] uses a transformer to fuse and process multimodal multi-view sensors for comprehensive scene understanding. + +Attention for Autonomous Driving The attention mechanism has been demonstrated to be a powerful module in many areas of deep learning, including the context of driving. The classic attention-based Transformer architecture [55] was originally established in Natural Language Processing. Transformer (VIT) was then applied in Computer Vision (vision Transformer, VIT [20, 49]) and attains excellent performance onImagenet classification. Later generations move on to generalize the attention mechanism to the driving domain, including motion forecasting [23, 36, 58], driver attention prediction [25, 34] and object tracking [45, 52]. In the field of end-to-end autonomous driving, TransFuser [15, 47] exploits several transformer modules for the fusion of data from the front view camera and LiDAR. NEAT [14] uses intermediate attention maps to iteratively compress 2D image features into a compact bird-eye-view (BEV) representation for driving. InterFuser [51] utilizes a transformer encoder and decoder to fuse information and decode the feature into interpretable embeddings. + +Multi-task Learning Our end-to-end driving framework adopts multi-task learning, with a joint objective of object detection, occupancy forecasting, traffic sign prediction and waypoint prediction. MotionNet [62] proposes a spatio-temporal pyramid network for joint perception and motion prediction based on BEV maps. PnPNet [41] proposes a new object trajectory representation and multi-object tracker to handle occlusion and false positives. IntentNet [7] predicts the high-level intentions of each agent from semantic HD maps building. ST-P3 [29] proposes an egocentric-aligned accumulation technique to preserve geometry information in 3D space and utilize a dual pathway modeling to consider past motion variations. + +# 3. Method + +We aim at learning a driving policy $\pi$ that generates raw control commands by taking multi-view multi-modal sensor readings, vehicle measurements, and navigation commands as inputs. As shown in Figure 2, the proposed ReasonNet consists of three parts: 1) a perception module that extracts bird's-eye-view (BEV) features from LiDAR and RGB data; 2) a temporal reasoning module that processes temporal information and maintains a memory bank storing historic features; 3) a global reasoning module that captures the interaction/relationship amongst objects and the environment, to detect adverse events (e.g. occlusion) and improve overall perception performance. This section will introduce these modules in detail. + +# 3.1. Perception Module + +The perception module is responsible for processing and fusing different sensor data at the early stage of our framework, based on which temporal and global reasoning can be conducted by later modules. Specifically, five sensors + +are utilized: four RGB cameras (left, front, right and rear) $I_{\mathrm{rgb}} = I_{0,1,2,3}$ and one LiDAR sensor $I_{\mathrm{lidar}} = I_4$ . Four image inputs are obtained from the four cameras, and an additional focus-view image input is center-cropped from the front image to capture distant traffic lights. Point cloud data is retrieved from the LiDAR sensor. Our perception module includes a 2D backbone to embed image input into keys and values, a 3D backbone to embed LiDAR input into queries, and a BEV decoder that utilizes these keys, values, and queries to obtain features of the bird's-eye view (BEV) map, waypoints, and traffic signs. + +Image Input For each image input of $I_{rgb}$ , a 2D CNN backbone ResNet [27] is applied to generate a feature map $f_{i}$ . Then, we use a convolution layer to map the channels of $f_{i}$ to $C_v$ and flatten it to one-dimensional tokens. A sinusoidal positional encoding and learnable sensor embeddings are added to the tokens, so that the following network can distinguish them from different cameras and relative positions. Finally, tokens of different images are passed through a standard transformer encoder with $K_{e}$ layers. Each layer consists of Multi-Headed Self-Attention [55], MLP blocks and layer normalization [3]. This image fusion operation can contribute to a better perception of global context from multi-view inputs, generating keys and values for the image-LiDAR fusion in BEV decoder. + +LiDAR Input For the LiDAR input, we use PointPillars [35] as our 3D perception backbone to process points in the ego-vehicle-centered area $x \in [-H_b, H - H_b]$ and $y \in [-W/2, W/2]$ . Specifically, we use a simplified version of PointNet [48] to encode the information of raw LiDAR points. Each pillar includes the points in a $0.25\mathrm{m} \times 0.25\mathrm{m}$ area. The extracted feature map is downsampled to $C_v \times H \times W$ for computation reduction and then serves as BEV queries used in the BEV decoder and memory bank. + +Sensor-Fusion BEV Decoder The BEV decoder follows a standard transformer architecture design with $K_{\text{bev}}$ layers to fuse tokens from different sensors. Tokens from the RGB images are fed as values and keys into the decoder, and tokens from the LiDAR points are fed as the $H \times W$ queries to generate BEV features. In addition, two other kinds of queries for the prediction of traffic signs and waypoints w are also fed into the decoder. Following InterFuser [51], we use a 2-layer MLP as the traffic sign classifier to predict the traffic light state and whether there is a stop sign ahead; we then use a single-layer GRU [16] to auto-regressively generate consecutive waypoints $\{\mathbf{w}_t\}_{t=1}^{T_f}$ conditioned on the goal location of the ego vehicle. $T_f$ denotes the number of the predicted time steps. To pretrain the perception module in the first training stage, the generated BEV feature is passed through a one-stage CenterPoint [64] to generate the $H \times W \times 7$ BEV map covering an $H_m \times W_m$ spatial region, where the seven channels represent object existence + +![](images/ffa23ef9e4cc4f74a46012831c6e9b88d72af9bcf3260c2bc093b8df31fbfc96.jpg) +Figure 2. The proposed ReasonNet consists of three modules: 1) the perception module fuses different sensor data to generate the BEV feature, traffic sign feature, and waypoints in the early stage of our framework; 2) the temporal reasoning module processes current and historic features and maintains a memory bank to store historic features; 3) the global reasoning module models the interaction and relationship among objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance. + +probability, offset from grid center, bounding box extent, heading angle and velocity for objects at each grid cell. + +# 3.2. Temporal Reasoning module + +Compared to existing end-to-end driving methods that only exploit scene information of the current frame [10, 15] or simply concatenate features of historic frames [54], we propose a temporal reasoning module that can sufficiently store and fuse temporal information to benefit the motion forecasting of traffic participants and the tracking of intermittently occluded objects. As shown in Figure 2, our temporal reasoning module includes temporal processing to fuse current and historic features through an attention mechanism, and maintains a memory bank which stores historic short-term and long-term feature keys and values. + +Temporal Processing Considering that information in different historic frames could have different relevance to the current scene, we apply an attention-based memory reading from the historic features. Specifically, for each historic frame $t$ stored in the memory, we first measure its relevance by calculating the normalized similarity $\mathbf{S}$ between the historic-frame feature key $\mathbf{k} \in \mathbb{R}^{C_k \times T_h \times H \times W^1}$ and the current-frame feature query $\mathbf{q} \in \mathbb{R}^{C_k \times H \times W}$ : + +$$ +S (\mathbf {q} _ {h, w}, \mathbf {k} _ {t, i, j}) = \frac {(\mathbf {k} _ {t , i , j} - \mathbf {q} _ {h , w}) ^ {2}}{\sum_ {i = 0 , j = 0} ^ {i = H - 1 , j = W - 1} (\mathbf {k} _ {t , i , j} - \mathbf {q} _ {h , w}) ^ {2}} \tag {1} +$$ + +We map every query element to a distribution over $H\times W$ memory elements and correspondingly aggregate their values $\mathbf{v}$ to obtain the readout feature $\mathbf{M}\in \mathbb{R}^{C_v\times T_h\times H\times W}$ for each frame $t$ stored in the memory: + +$$ +\mathbf {M} _ {t, h, w} = \sum_ {i = 0, j = 0} ^ {i = H - 1, j = W - 1} \mathbf {v} _ {t, i, j} S \left(\mathbf {q} _ {h, w}, \mathbf {k} _ {t, i, j}\right) \tag {2} +$$ + +The aggregated features from all historic frames are then concatenated with the current-frame feature value to get $\mathbf{M}' \in \mathbb{R}^{C_v \times (T_h + 1) \times H \times W}$ , which is then passed through a GRU to progressively fuse temporal information and get $\mathbf{M}_{fused} \in \mathbb{R}^{C_v \times H \times W}$ as the final output of the module. Technically, we take the L2 similarity proposed in STCN [13] as the similarity measure function, which is more stable than the dot product [46]. The current-frame feature query $\mathbf{q}$ is obtained by passing the features from the 3D backbone $\mathbf{F} \in \mathbb{R}^{C_v \times H \times W}$ through a query encoder (several convolution layers). The historic-frame feature key $\mathbf{k}$ and value $\mathbf{v}$ are taken from the temporal memory bank. + +Memory Bank Maintaining As above, we have introduced the temporal processing at one single frame. After every $\tau$ frame, the obtained feature key and value at that frame will be used to update the memory bank. Specifically, the current-frame feature query $\mathbf{q}$ is directly copied and fed into the memory bank as the memory key without extra computation. The final output $\mathbf{M}_{\text{used}}$ will first be encoded + +to a BEV map $\mathbf{M}_p$ . The BEV map $\mathbf{M}_p$ will be concatenated with the final output $\mathbf{M}_{fused}$ and passed through a value encoder to obtain the memory value $\mathbf{v}$ , which is fed into the memory back. With the above key-value pairs, the memory bank maintains two kinds of buffer: the short-term and long-term buffer. On the one hand, the new key-value pair will be appended to the short-term buffer, as a high-resolution memory of the scene in the past few seconds for accurate feature matching. Considering the limited GPU memory resources, we limit the buffer size and older key-value pairs will be discarded when the limit number $T_s$ is reached. However, when these older features are discarded, the long-term behavior of the traffic participants is missing, which can be crucial for motion forecasting in complex traffic scenarios. Thus on the other hand, inspired by XMem [12], the memory bank also maintains a long-term buffer that selectively stores important/representative key-value feature pairs discarded by the short-term buffer. Considering the fact that the objects surrounding the ego vehicle are sparse most of the time², the long-term buffer selectively stores key-value features ( $\mathbf{k}$ and $\mathbf{v}$ ) which meet one of the two criteria: 1) their corresponding location in the BEV map $\mathbf{M}_p$ has a high probability of object existence; 2) their usage frequency is in top-K of all candidate key-value features. The usage frequency is defined by its cumulative normalized similarity (Eq. 1). The features selected by the above criteria are appended to the last frame of memory. And if the last memory frame is full, we will initialize one new frame with the zero vector and set it as the last frame to store new features. When the number of frames reaches the limit $T_l$ , the obsolete memory will be removed. Such a compact storing strategy can efficiently track long-term representative features and intermittently occluded objects, while balancing the resources required. + +# 3.3. Global Reasoning module + +Rare adverse events such as occluded objects are a notorious issue for the practical deployment of AVs. Our insight is that humans perceive their surroundings not only through sensors, but also by exploiting global information on the scene to reason over the unobservable spaces. For instance, when a vehicle performs an emergency stop without a clear reason, humans can infer that there is potentially an occluded object ahead of the vehicle and will drive more cautiously. Thus we propose the global reasoning module to capture the interaction and relationship between objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance. The module consists of three parts: 1) an object-environment and object-object interaction modeling process; 2) an occupancy decoder to generate the occupancy map; 3) a consistency loss + +to encourage consistent prediction of waypoints and the occupancy map. + +Interaction Modeling The object-environment and object-object interaction modeling process aims at reasoning about the relationship among objects and the environment. On the one hand, $\mathbf{M}_{\text {fused }}$ features whose corresponding location in the BEV map $\mathbf{M}_p$ has a high probability of object existence will be extracted to represent object features. On the other hand, $\mathbf{M}_{\text {fused }}$ features will also be downsampled to represent the environment features. All object and environment features are used to construct a graph, which is passed through a graph attention network (GAT) [56] for interaction modeling. + +Occupancy Decoder Taking the features outputted by the GAT as keys and values, and the learnable positional embeddings as queries, the occupancy decoder utilizes a transformer decoder with $K_{\text{opy}}$ layers to generate: 1) the traffic sign feature, which is then concatenated with the traffic sign feature from the BEV decoder to generate the final traffic sign prediction; 2) the occupancy map feature, which is then applied with convolution operation to generate the occupancy map $\mathbf{O}_t \in \mathbb{R}^{T_f \times H \times W}$ . At a future time $t$ , each cell in the occupancy map contains a value in the range [0,1] representing the probability that the cell is occupied. + +Consistency Loss Currently, our framework predicts the waypoints and the occupancy map independently, which are not necessarily consistent. For example, the waypoints could overlap some obstacles in the occupancy map. Thus we propose a consistency loss to discourage waypoints' crossing the high-probability region of the occupancy map. Further, the consistency loss also encourages generating longer waypoint trajectories for efficient driving. Specifically, the consistency loss aims at minimizing the average object existence probability of the cells that cover the predicted waypoints, and maximizing the average $l_{2}$ length of the waypoint trajectory w: + +$$ +\mathcal {L} _ {\text {c o n s i s t e n c y}} = \frac {1}{T _ {f}} \left(\sum_ {t = 0} ^ {T _ {f}} \frac {\sum_ {i = 0} ^ {N _ {c} ^ {t}} \mathbf {O} _ {t , i}}{N _ {c} ^ {t}} - \lambda \sum_ {t = 0} ^ {T _ {f}} \| \mathbf {w} _ {t} \| _ {1}\right) \tag {3} +$$ + +,where $N_{c}^{t}$ denotes the number of covered cell at step $t$ $\mathbf{O}_{t,i}$ denotes the object existence probability at cell $i$ at time $t$ + +# 3.4. Control + +Following [11], we use two PID controllers for latitudinal and longitudinal control, to track the heading and velocity of predicted waypoints respectively. If a red traffic light or stop sign is detected, the ego-vehicle will brake. Additionally, an emergency stop will also be performed if the ego vehicle's current bounding box crosses the area in the occupancy map that has a high object existence probability or if the future waypoints overlap with objects in the BEV map. + +![](images/c1eae2d0d4652ea695059e001eda8185737677d78563f5f761428eb769353f88.jpg) + +![](images/57a4848366f41fdba3d5959448325e93c316736cbbc1149bbdaf0f9835790a43.jpg) + +![](images/e940d0958ef94cf4a0039e43622654f8b8ca1d884aff28f66b3de681d501bfaf.jpg) +Figure 3. An illustration for the four types of occlusion scenarios included in the proposed DOS benchmark. The orange color denotes the ego car. The blue/green dots denote the occluded/visible trajectory of the occluded dangerous object. + +![](images/26a21544aaaf574accadaea58c6f4b1f364c849fede13cd3b37896c82a2571c6.jpg) + +# 3.5. Training Setup + +The training of our framework consists of two stages. In the first stage, we train the perception module to predict BEV features, traffic sign features, and waypoints. Specifically, the loss of BEV features and traffic sign features is computed with additional prediction heads, which are discarded in the next stage. In the second stage, we freeze the perception module and train the other two modules. Five loss terms are considered: 1) the waypoints loss $\mathcal{L}_w$ that minimizes the error between predicted waypoints and expert waypoints; 2) the BEV map loss $\mathcal{L}_{BEV}$ that follows [10,64] to minimize the current-frame BEV map prediction error; 3) the traffic sign loss $\mathcal{L}_{sign}$ for the traffic regulation prediction; 4) occupancy map loss $\mathcal{L}_{opy}$ that minimizes the occupancy prediction error in a future horizon; 5) the consistency loss $\mathcal{L}_{consistency}$ which encourages a consistent generation of the waypoints and occupancy map. These loss terms are balanced by corresponding loss weights. + +# 4. Drive in Occlusion Sim (DOS) Benchmark + +In order to address the issue that occlusion events are rare in existing datasets and benchmarks, we present the Drive in Occlusion Simulation benchmark (DOS), a CARLA-based framework providing diverse driving scenarios with occluded objects. As shown in Figure 3, the proposed DOS benchmark includes four types of challenging occlusion driving scenarios: + +**Parked Cars (#1)** The ego vehicle is driving in a straight + +
RankMethodDS ↑RC ↑IS ↑
1ReasonNet (Ours)79.9589.890.89
2InterFuser [51]76.1888.230.84
3TCP [63]75.1485.630.87
4LAV [10]61.8594.460.64
5TransFuser [15]61.1886.690.71
6Latent TransFuser [15]45.2066.310.72
7GRIAD [8]36.7961.850.60
8TransFuser+ [1]34.5869.840.56
+ +Table 1. Performance comparison on the public CARLA leaderboard [53] (accessed Nov 2022). For all three metrics, higher is better. Our method ranks first overall on the leaderboard, with the highest driving score (DS) and infraction score (IS), and the second highest route completion (RC). + +lane with parked cars on the side. Pedestrians can first appear on the sidewalk (visible) and then suddenly emerge through the occluded areas between parked cars (occluded). + +Sudden Brake (#2) The ego vehicle is driving in a straight lane along with other vehicles ahead. Pedestrians can suddenly emerge from the sidewalks, causing the other vehicles to brake while remaining invisible to the ego vehicle. + +Left Turn (#3) The ego vehicle intends to perform an unprotected left turn at an intersection, but a truck in the opposite lane blocks the view of oncoming traffic, intermittently obscuring vehicles driving straight through the intersection. + +Red Light Infraction (#4) The ego vehicle is crossing an intersection after some trucks. A left-to-right vehicle running a red light suddenly appears, forcing the trucks to brake promptly. But the ego vehicle's view toward the running-light vehicle is blocked by the trucks, so it remains invisible to the ego vehicle. + +Each of the four scenarios in the DOS benchmark comprises 25 different cases varying in the road environment and background traffic. Compared to a previous occlusion benchmark AUTOCASTSIM [19], the DOS benchmark: 1) includes occlusions of both vehicles and pedestrians, instead of only vehicles; 2) includes 100 cases of 4 scenarios, instead of only 3 cases of 3 scenarios; 3) considers specific occlusions that can potentially be resolved by temporal reasoning (intermittent occlusion, #1, #3) and global reasoning (constant occlusion but with interaction clues, #2, #4) about the scene, instead of random occlusions as in AUTOCASTSIM. Thus our scenarios can also serve as a good tracking-with-intermittent-occlusion benchmark and a People-as-Sensor [2,31] benchmark. + +# 5. Experiments + +# 5.1. Experiment Setup + +Implementation We implement and evaluate our approach on the open-source CARLA simulator with version + +
SettingTown 05 LongDOS
TsTlDS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
0066.7±3.897.6±2.70.68±0.030.18±0.030.05±0.020.03±0.0322±1.628±3.426±2.125±1.6
1067.9±3.496.8±2.30.70±0.020.16±0.040.04±0.030.05±0.0230±3.638±3.632±2.832±3.4
2068.1±3.196.9±3.40.70±0.030.16±0.030.04±0.020.05±0.0328±5.548±4.138±4.452±3.9
2170.9±2.095.7±3.10.74±0.020.13±0.020.04±0.020.06±0.0455±4.457±4.148±4.155±5.5
4070.5±2.196.4±2.50.73±0.040.14±0.030.03±0.020.06±0.0332±5.458±4.440±5.555±4.9
4273.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
+ +Table 2. Ablation study on different short-term buffer size $T_{s}$ and long-term buffer size $T_{l}$ , on the Town 05 Long benchmark and the proposed DOS benchmark. Performance is evaluated over three runs. CR: Collision rate, Red: Red light violation, Blocked: Vehicle blocked, SR: Success rate. SR#1 denotes the first kind of scenario in the DOS benchmark. As the two buffer sizes increase, improvement is witnessed in all metrics but the road completion. + +0.9.10.1 [21]. We use ResNet-50 pretrained on ImageNet as the 2D backbone and PointPillars trained from scratch as the 3D backbone. We predict $T_{f} = 4$ time steps for the waypoints and occupancy map, and the interval between each time step is 0.5 seconds. The memory bank maintains $T_{s} = 4$ frames in the short-term buffer and $T_{l} = 2$ frames in the long-term buffer. The memory bank is updated every $\tau = 2$ frame. We refer readers to Appendix A for more details. + +Dataset Collection We collect an expert dataset of 2M frames by running a rule-based expert agent on all 8 public towns and 21 types of weather, with the access to the privileged information in the CARLA simulator. We randomly set routes, spawn dynamic objects and adversarial scenarios provided in [47], to diversify the collected data. To ensure the temporal continuity of collected data, the data are collected at a high frequency of 10HZ. + +Metrics We consider three major metrics introduced by the CARLA LeaderBoard: route completion ratio (RC), infraction score (IS), and driving score (DS). The route completion ratio is the percentage of the route completed. The infraction score measures infractions triggered. When collisions or traffic rule violations occur, the infraction score will decay by a discount factor. The driving score is the product of the route completion ratio and the infraction score, describing both driving progress and safety, and thus is the primary ranking metric in the CARLA Leaderboard. + +# 5.2. Comparison to the state of the art + +Table 1 shows the top 8 entries on the public CARLA Leaderboard. Readers can refer to Sec 2 for descriptions of these methods. Our method outperforms all prior methods, with the highest driving score and infraction score, and the second highest route completion. The previous leading method InterFuser uses a transformer for sensor fusion but lacks temporal and global reasoning. Compared to InterFuser, our method improved the driving score, road completion, and infraction score by $5\%$ , $2\%$ , and $6\%$ respectively. + +# 5.3. Ablation study + +We investigate the effect of the temporal and global reasoning modules on the Town05 Long benchmark and the DOS benchmark. For each scenario in DOS, we take 5 cases for training and 20 cases for evaluation. In addition to the three metrics mentioned earlier, we also present four more metrics for detailed analysis: collision rate (CR), red light violation (Red), ego vehicle blocked frequency (Blocked), and success rate (SR). The first three metrics are normalized by the driven distance (km). Visualizations of how the temporal reasoning and global reasoning work can be found at Figure 4 and Figure 5 respectively. + +Memory Size Table 2 studies the effect of different short-term buffer size $T_{s}$ and long-term buffer size $T_{l}$ . The overall observation is that, as the two buffer sizes increase, improvement is witnessed in all metrics but road completion. Specifically, when the long-term memory is removed $(T_{l} = 0)$ , the average success rates drop sharply from 71.5 to 36 on DOS scenarios that require keeping track of intermittently occluded objects (#1 and #3). If we remove the temporal reasoning module $(T_{s} = T_{l} = 0)$ , the driving score on the Town05 benchmark drops by $9\%$ , and the average success rate on the DOS benchmark drops by $46\%$ . We hypothesize that the drop in performance is because 1) it can be really hard to accurately estimate the objects' future motion based only on single-frame data; 2) temporal information can help keep track of objects that are intermittently occluded; 3) the global reasoning module may also work poorly when historic information is missing. + +Long-Term Memory Selection Strategy Table 3 studies the performance of different long-term memory selection strategies. Specifically, the proposed strategy in Sec 3.2 includes two selection criteria. So here we ablate the effect of the two criteria by 1) only selecting the short-term feature with top- $K$ usages (usage-based); 2) only selecting the feature with a high probability of the existence of an object (object-based). Besides, we also compared a random selection strategy. As in Table 3, the random selection strategy has the poorest performance especially on the DOS benchmark, as random selection could miss important and repre + +
SettingTown 05 LongDOS
DS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
Random71.2±5.496.6±2.40.74±0.040.13±0.040.03±0.010.06±0.0233±4.455±6.242±5.553±5.4
Usage-based72.0±3.995.9±2.20.75±0.040.12±0.030.03±0.010.06±0.0245±4.262±3.453±2.862±3.9
Object-based72.2±3.796.1±3.00.75±0.030.12±0.030.03±0.010.05±0.0257±4.165±3.673±4.460±3.7
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
+ +Table 3. Ablation study on different long-term memory selection strategies. Our proposed strategy considering both the usage and object criteria outperforms the random selection strategy and the two methods with only one criteria, especially on the DOS benchmark. + +
SettingTown 05 LongDOS
DS↑RC↑IS↑CR↓Red↓Blocked↓SR#1↑SR#2↑SR#3↑SR#4↑
No global reasoning68.9±4.697.4±2.90.71±0.040.15±0.040.05±0.020.05±0.0228±2.834±3.429±2.027±3.6
No consistency loss72.2±3.496.1±3.20.75±0.030.12±0.020.03±0.020.06±0.0360±4.172±3.977±4.968±4.2
No traffic sign prediction71.1±2.796.0±4.10.74±0.030.11±0.030.05±0.030.07±0.0362±4.472±4.082±2.870±4.1
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
+ +Table 4. Ablation study on the global reasoning module. The performance would drop when 1) the entire global reasoning module is removed; 2) the consistency loss is not applied; 3) the traffic sign feature from the reasoning module is not utilized. + +![](images/9613b839e8bd58fb83e07d216bd2ad745bcc41c36d9b9a72fac42a3739848dde.jpg) +Figure 4. Visualization of the attention map between one object's current-frame feature query and the historic-frame feature stored in the short-term buffer, in two cases. The object's current-frame feature consistently attends to its corresponding region in the historic feature map. + +![](images/585ff0ea3058373efb47131d1ac58a3d64446dc93b3ceb2fe7729ec534c1fe8b.jpg) +Figure 5. We show two cases of how our framework reasons the presence of the occluded object. In the first case, a pedestrian first appeared on the sidewalk (visible) and then emerges between two parked cars (occluded). In the second case, a vehicle runs the red light, forcing trucks to brake abruptly. But the ego vehicle's view toward the running-light vehicle is blocked by the front trucks, so the running-light vehicle remains invisible to the ego vehicle. The rectangles mark the occluded objects. + +sentative features on the scene. Compared to our strategy utilizing both criteria, the two ablations omitting one of the criteria have a performance drop, especially on the DOS benchmark. The usage-based strategy performs worse than the object-based, showing that the features of objects could be more informative for capturing historic behaviors. + +Global Reasoning Design Table 4 studies the performance when different designs of the global reasoning module are applied. First, we remove the entire module and observe a significant drop in all metrics but the road completion. For instance, the average success rate on the DOS benchmark dropped from 71.5 to 29.5. This demonstrates the effectiveness of global reasoning, especially in occlusion events. Second, we ablated the consistency loss, which could alleviate the sub-optimal issues in collected expert data. A removal of consistency loss leads to a lower driving score and higher collision rate on the Town 05 benchmark and a lower success rate on the DOS benchmark. Third, excluding the traffic sign feature from the global reasoning model results in an increase on the red light violation. One explanation is that the traffic sign feature from the global reasoning module could help reason the distant traffic light state according to other road participants' behavior. + +# 6. Conclusion + +We present ReasonNet, a novel end-to-end autonomous driving framework including two major components: a temporal reasoning module and a global reasoning module. The temporal reasoning module processes the historic information on the driving scene for high-fidelity forecasting of other road participants and dynamically maintains a temporal memory bank. The global reasoning module models the interaction and relationship among the objects and environment to detect adverse events especially occlusion, and improve overall perception performance. Our method pushes the state-of-the-art performance of the CARLA leaderboard by a considerable margin. Moreover, we also publicly release a new benchmark DOS consisting of diverse occlusion scenarios, to facilitate the study of occlusion detection in the field of end-to-end autonomous driving. + +# References + +[1] Expert drivers for autonomous driving. https://kait0.github.io/files/master_thesis_bernhard_jaeger.pdf, 2021.6, 13 +[2] Oladapo Afolabi, Katherine Driggs-Campbell, Roy Dong, Mykel J Kochenderfer, and S Shankar Sastry. People as sensors: Imputing maps from human actions. 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In such cases, it remains challenging to predict the future evolution of the scene and future behaviors of objects, and to deal with rare adverse events such as the sudden appearance of occluded objects. In this paper, we present ReasonNet, a novel end-to-end driving framework that extensively exploits both temporal and global information of the driving scene. By reasoning on the temporal behavior of objects, our method can effectively process the interactions and relationships among features in different frames. Reasoning about the global information of the scene can also improve overall perception performance and benefit the detection of adverse events, especially the anticipation of potential danger from occluded objects. For comprehensive evaluation on occlusion events, we also release publicly a driving simulation benchmark DriveOcclusionSim consisting of diverse occlusion events. We conduct extensive experiments on multiple CARLA benchmarks, where our model outperforms all prior methods, ranking first on the sensor track of the public CARLA Leaderboard [53]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 696 + ], + "type": "text", + "content": "Despite significant recent progress in the field of autonomous driving, truly large-scale deployment of autonomous vehicles (AVs) on public roads has yet to be established. The majority of the remaining issues lie in navigating dense urban traffic scenes, where a large number of different dynamic objects (e.g. vehicles, bicycles, pedestrians), complex road geometries and road user interactions are involved. In such circumstances, currently deployed or tested solutions could make incorrect or unexpected decisions, resulting in severe accidents or traffic infractions [4, 24, 53]. Two of the major challenges behind" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 233, + 537, + 379 + ], + "blocks": [ + { + "bbox": [ + 313, + 233, + 537, + 379 + ], + "lines": [ + { + "bbox": [ + 313, + 233, + 537, + 379 + ], + "spans": [ + { + "bbox": [ + 313, + 233, + 537, + 379 + ], + "type": "image", + "image_path": "8598ce30dd9fdd1287de354205a66857ba9ca5f7b4636ab2e595e51c5c577d69.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 384, + 547, + 452 + ], + "lines": [ + { + "bbox": [ + 305, + 384, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 547, + 452 + ], + "type": "text", + "content": "Figure 1. Temporal reasoning on the historic behaviors of surrounding objects can benefit the prediction of the scene evolution and objects' future behaviors. Global reasoning on the interaction among objects and the environment allows for inference about unobservable space and occluded objects, anticipating potential danger and enhancing perception/driving performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 461, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 546, + 533 + ], + "type": "text", + "content": "such autonomous incompetence include 1) how to achieve a comprehensive understanding of the driving scene and, more importantly, how to make high-fidelity predictions on the future evolution of the driving scene; 2) how to deal with rare adverse events in long-tail distributions, such as undetected but relevant objects in occluded regions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "Comprehensive scene understanding and high-fidelity prediction of how objects in the scene will move in the future are vital for autonomous vehicles to take safe and reliable actions. Toward this end, modularized methods were proposed to decompose the task into three sequential subtasks: detection [37-40, 42], tracking [5, 65], and forecasting [6, 26, 28, 32, 33, 59-61]. While more interpretability is provided by developing each module independently, these sub-tasks are still regarded as open research questions and errors in each sub-task can propagate and accumulate, leading to unstable overall performance. In contrast, end-to-end driving methods [9, 10, 51] have recently emerged as a promising method to solve these subtasks in a monolithic manner directly. However, a high-fidelity future prediction necessitates sufficient temporal reasoning over the historic" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13723" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "information of the scene [22, 50], which is usually only somewhat considered in previous end-to-end driving methods if not completely ignored. For example, [10, 15] only exploited scene information in the current frame, and [54] simply concatenated features in historic frames for temporal reasoning. In such cases, the interactions and relationships amongst features in different frames and objects cannot be sufficiently modeled. Thus in this paper, we propose a temporal reasoning module to effectively fuse information from different frames for better driving performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 651 + ], + "type": "text", + "content": "On the other hand, rare adverse events in long-tail distributions remain a notoriously challenging issue on the way toward large scale deployment of autonomous vehicles. For example, one such challenge is the difficulty in detecting occluded but relevant objects in the scene. While a large amount of research has focused on improving perception performance [37, 57], the occluded objects essentially lie out of the scope of observable elements, and failure to consider such objects can result in either dangerous or overly cautious driving behavior. Our observation is that, while humans also suffer from similar limitations to autonomous vehicles regarding occluded objects, they are able to reason about these unobservable spaces by exploiting global information of the scene such as road geometry and driving interaction patterns, to anticipate potential danger even under occlusion. For example, when one human driver notices another vehicle braking abruptly, the driver may reason the presence of an occluded object (e.g., a pedestrian) ahead, reminding himself to drive cautiously. Thus, our insight is that, a safe and intelligent autonomous vehicle should also master the global reasoning capability to have a better perception of the scene. In this paper, we propose a transformer-based global reasoning module to sufficiently fuse information of the environment and objects, and analyze their interactions for better scene understanding. Such global reasoning capability not only benefits interaction modeling with occluded objects, but also improves overall perception performance. Examples of such performance gains include better traffic light status identification by reasoning over other vehicles' actions and more accurate future trajectory forecasting by reasoning over interactions among objects. Besides, considering the fact that the occlusion events lie in the long-tail distribution and have been rare in currently available datasets, we also construct a Driving in Occlusion Simulation benchmark (DOS) consisting of 4 occlusion scenarios, each with 25 cases, as a comprehensive occlusion event evaluation benchmark in the field of end-to-end autonomous driving." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we propose a novel end-to-end driving framework named temporal and global reasoning network (ReasonNet), which provides enhanced reasoning on the temporal evolution and the global information of the scene, for better perception performance and driving quality. Our" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 421, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 421, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 421, + 83 + ], + "type": "text", + "content": "contributions are three-fold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 94, + 545, + 277 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 317, + 94, + 545, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 94, + 545, + 154 + ], + "spans": [ + { + "bbox": [ + 317, + 94, + 545, + 154 + ], + "type": "text", + "content": "- We propose a novel temporal and global reasoning Network (ReasonNet) to enhance historic scene reasoning for high-fidelity prediction of the scene's future evolution and improve global contextual perception performance even under occlusion." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 161, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 161, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 317, + 161, + 545, + 221 + ], + "type": "text", + "content": "- We present a new benchmark called Driving in Occlusion Simulation benchmark (DOS), which consists of diverse occlusion scenarios in urban driving for systematic evaluation in occlusion events, and make the benchmark publicly available." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 545, + 277 + ], + "type": "text", + "content": "- We experimentally validate our method on multiple benchmarks with complex and adversarial urban scenarios. Our model ranks first on the sensor track of the CARLA autonomous driving leaderboard." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 287, + 390, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 390, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 390, + 300 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 307, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 715 + ], + "type": "text", + "content": "End-to-end Autonomous Driving End-to-end autonomous driving in urban scenarios has become more studied recently thanks to the CARLA simulator and leaderboard [21]. Recent works mainly consist of reinforcement learning (RL) and imitation learning (IL) methods. The reinforcement Learning methods train the agents by constantly interacting with simulated environments and learning from these experiences. Latent DRL [54] first trains an embedding space as a latent representation of the environment observation, and then conducts reinforcement learning with the latent observation. Roach [66] utilizes an RL agent with privileged information of the environment to distill a model only with regular information (e.g. sensor) as the final agent. WOR [9] builds a model-based RL agent along with the world model and reward model. The final agent is distilled from the expert knowledge acquired from these pretrained models. Imitation learning methods aim at learning from an expert agent to bypass interacting with the environment. Early IL methods include CIL [17] and CILRS [18], which apply a conditional architecture with different network branches for different navigation commands. LBC [11] first trains an imitation learning agent with privileged information, which is then distilled into a model using sensor data. Transfuser [15, 47] designs a multi-modal transformer to fuse information between the front camera image and LiDAR data. LAV [10] exploits data of not only the ego vehicle but also surrounding vehicles for data augmentation by learning a viewpoint-invariant spatial intermediate representation. TCP [63] proposes a network with two branches which generates the control signal and waypoints respectively. An adaptive ensemble is applied to fuse the two output signals. InterFuser [51] uses a transformer to fuse and process multimodal multi-view sensors for comprehensive scene understanding." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13724" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "Attention for Autonomous Driving The attention mechanism has been demonstrated to be a powerful module in many areas of deep learning, including the context of driving. The classic attention-based Transformer architecture [55] was originally established in Natural Language Processing. Transformer (VIT) was then applied in Computer Vision (vision Transformer, VIT [20, 49]) and attains excellent performance onImagenet classification. Later generations move on to generalize the attention mechanism to the driving domain, including motion forecasting [23, 36, 58], driver attention prediction [25, 34] and object tracking [45, 52]. In the field of end-to-end autonomous driving, TransFuser [15, 47] exploits several transformer modules for the fusion of data from the front view camera and LiDAR. NEAT [14] uses intermediate attention maps to iteratively compress 2D image features into a compact bird-eye-view (BEV) representation for driving. InterFuser [51] utilizes a transformer encoder and decoder to fuse information and decode the feature into interpretable embeddings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 289, + 456 + ], + "type": "text", + "content": "Multi-task Learning Our end-to-end driving framework adopts multi-task learning, with a joint objective of object detection, occupancy forecasting, traffic sign prediction and waypoint prediction. MotionNet [62] proposes a spatio-temporal pyramid network for joint perception and motion prediction based on BEV maps. PnPNet [41] proposes a new object trajectory representation and multi-object tracker to handle occlusion and false positives. IntentNet [7] predicts the high-level intentions of each agent from semantic HD maps building. ST-P3 [29] proposes an egocentric-aligned accumulation technique to preserve geometry information in 3D space and utilize a dual pathway modeling to consider past motion variations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 464, + 104, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 104, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 104, + 477 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 485, + 289, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 289, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 289, + 640 + ], + "type": "text", + "content": "We aim at learning a driving policy " + }, + { + "bbox": [ + 47, + 485, + 289, + 640 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 485, + 289, + 640 + ], + "type": "text", + "content": " that generates raw control commands by taking multi-view multi-modal sensor readings, vehicle measurements, and navigation commands as inputs. As shown in Figure 2, the proposed ReasonNet consists of three parts: 1) a perception module that extracts bird's-eye-view (BEV) features from LiDAR and RGB data; 2) a temporal reasoning module that processes temporal information and maintains a memory bank storing historic features; 3) a global reasoning module that captures the interaction/relationship amongst objects and the environment, to detect adverse events (e.g. occlusion) and improve overall perception performance. This section will introduce these modules in detail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 647, + 160, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 160, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 160, + 660 + ], + "type": "text", + "content": "3.1. Perception Module" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "The perception module is responsible for processing and fusing different sensor data at the early stage of our framework, based on which temporal and global reasoning can be conducted by later modules. Specifically, five sensors" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": "are utilized: four RGB cameras (left, front, right and rear) " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{rgb}} = I_{0,1,2,3}" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " and one LiDAR sensor " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{lidar}} = I_4" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ". Four image inputs are obtained from the four cameras, and an additional focus-view image input is center-cropped from the front image to capture distant traffic lights. Point cloud data is retrieved from the LiDAR sensor. Our perception module includes a 2D backbone to embed image input into keys and values, a 3D backbone to embed LiDAR input into queries, and a BEV decoder that utilizes these keys, values, and queries to obtain features of the bird's-eye view (BEV) map, waypoints, and traffic signs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": "Image Input For each image input of " + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "inline_equation", + "content": "I_{rgb}" + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": ", a 2D CNN backbone ResNet [27] is applied to generate a feature map " + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": ". Then, we use a convolution layer to map the channels of " + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "inline_equation", + "content": "C_v" + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": " and flatten it to one-dimensional tokens. A sinusoidal positional encoding and learnable sensor embeddings are added to the tokens, so that the following network can distinguish them from different cameras and relative positions. Finally, tokens of different images are passed through a standard transformer encoder with " + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "inline_equation", + "content": "K_{e}" + }, + { + "bbox": [ + 304, + 205, + 547, + 373 + ], + "type": "text", + "content": " layers. Each layer consists of Multi-Headed Self-Attention [55], MLP blocks and layer normalization [3]. This image fusion operation can contribute to a better perception of global context from multi-view inputs, generating keys and values for the image-LiDAR fusion in BEV decoder." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "content": "LiDAR Input For the LiDAR input, we use PointPillars [35] as our 3D perception backbone to process points in the ego-vehicle-centered area " + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "inline_equation", + "content": "x \\in [-H_b, H - H_b]" + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "inline_equation", + "content": "y \\in [-W/2, W/2]" + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "content": ". Specifically, we use a simplified version of PointNet [48] to encode the information of raw LiDAR points. Each pillar includes the points in a " + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "inline_equation", + "content": "0.25\\mathrm{m} \\times 0.25\\mathrm{m}" + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "content": " area. The extracted feature map is downsampled to " + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "inline_equation", + "content": "C_v \\times H \\times W" + }, + { + "bbox": [ + 304, + 375, + 547, + 496 + ], + "type": "text", + "content": " for computation reduction and then serves as BEV queries used in the BEV decoder and memory bank." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": "Sensor-Fusion BEV Decoder The BEV decoder follows a standard transformer architecture design with " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "K_{\\text{bev}}" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " layers to fuse tokens from different sensors. Tokens from the RGB images are fed as values and keys into the decoder, and tokens from the LiDAR points are fed as the " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " queries to generate BEV features. In addition, two other kinds of queries for the prediction of traffic signs and waypoints w are also fed into the decoder. Following InterFuser [51], we use a 2-layer MLP as the traffic sign classifier to predict the traffic light state and whether there is a stop sign ahead; we then use a single-layer GRU [16] to auto-regressively generate consecutive waypoints " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{w}_t\\}_{t=1}^{T_f}" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " conditioned on the goal location of the ego vehicle. " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "T_f" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " denotes the number of the predicted time steps. To pretrain the perception module in the first training stage, the generated BEV feature is passed through a one-stage CenterPoint [64] to generate the " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "H \\times W \\times 7" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " BEV map covering an " + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "inline_equation", + "content": "H_m \\times W_m" + }, + { + "bbox": [ + 304, + 497, + 548, + 715 + ], + "type": "text", + "content": " spatial region, where the seven channels represent object existence" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13725" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 74, + 523, + 313 + ], + "blocks": [ + { + "bbox": [ + 70, + 74, + 523, + 313 + ], + "lines": [ + { + "bbox": [ + 70, + 74, + 523, + 313 + ], + "spans": [ + { + "bbox": [ + 70, + 74, + 523, + 313 + ], + "type": "image", + "image_path": "ffa23ef9e4cc4f74a46012831c6e9b88d72af9bcf3260c2bc093b8df31fbfc96.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 319, + 547, + 366 + ], + "lines": [ + { + "bbox": [ + 45, + 319, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 45, + 319, + 547, + 366 + ], + "type": "text", + "content": "Figure 2. The proposed ReasonNet consists of three modules: 1) the perception module fuses different sensor data to generate the BEV feature, traffic sign feature, and waypoints in the early stage of our framework; 2) the temporal reasoning module processes current and historic features and maintains a memory bank to store historic features; 3) the global reasoning module models the interaction and relationship among objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 376, + 288, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 400 + ], + "type": "text", + "content": "probability, offset from grid center, bounding box extent, heading angle and velocity for objects at each grid cell." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 406, + 205, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 205, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 205, + 418 + ], + "type": "text", + "content": "3.2. Temporal Reasoning module" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 555 + ], + "type": "text", + "content": "Compared to existing end-to-end driving methods that only exploit scene information of the current frame [10, 15] or simply concatenate features of historic frames [54], we propose a temporal reasoning module that can sufficiently store and fuse temporal information to benefit the motion forecasting of traffic participants and the tracking of intermittently occluded objects. As shown in Figure 2, our temporal reasoning module includes temporal processing to fuse current and historic features through an attention mechanism, and maintains a memory bank which stores historic short-term and long-term feature keys and values." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": "Temporal Processing Considering that information in different historic frames could have different relevance to the current scene, we apply an attention-based memory reading from the historic features. Specifically, for each historic frame " + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": " stored in the memory, we first measure its relevance by calculating the normalized similarity " + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": " between the historic-frame feature key " + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{k} \\in \\mathbb{R}^{C_k \\times T_h \\times H \\times W^1}" + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": " and the current-frame feature query " + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in \\mathbb{R}^{C_k \\times H \\times W}" + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 657, + 287, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 657, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 55, + 657, + 287, + 687 + ], + "type": "interline_equation", + "content": "S (\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}) = \\frac {(\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}}{\\sum_ {i = 0 , j = 0} ^ {i = H - 1 , j = W - 1} (\\mathbf {k} _ {t , i , j} - \\mathbf {q} _ {h , w}) ^ {2}} \\tag {1}", + "image_path": "1183fa1b82825135b91d5c556d7fb252ec33666bddd16e216899e0bab8bb22c5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "content": "We map every query element to a distribution over " + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "content": " memory elements and correspondingly aggregate their values " + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "content": " to obtain the readout feature " + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\mathbf{M}\\in \\mathbb{R}^{C_v\\times T_h\\times H\\times W}" + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "content": " for each frame " + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 376, + 545, + 424 + ], + "type": "text", + "content": " stored in the memory:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 442, + 545, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 442, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 332, + 442, + 545, + 478 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {t, h, w} = \\sum_ {i = 0, j = 0} ^ {i = H - 1, j = W - 1} \\mathbf {v} _ {t, i, j} S \\left(\\mathbf {q} _ {h, w}, \\mathbf {k} _ {t, i, j}\\right) \\tag {2}", + "image_path": "9de5cdc8f0ad7a02609318243bd2391436582e88ea5b4d1df9b9e5dafa3ac53d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": "The aggregated features from all historic frames are then concatenated with the current-frame feature value to get " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{M}' \\in \\mathbb{R}^{C_v \\times (T_h + 1) \\times H \\times W}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": ", which is then passed through a GRU to progressively fuse temporal information and get " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{fused} \\in \\mathbb{R}^{C_v \\times H \\times W}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": " as the final output of the module. Technically, we take the L2 similarity proposed in STCN [13] as the similarity measure function, which is more stable than the dot product [46]. The current-frame feature query " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": " is obtained by passing the features from the 3D backbone " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{C_v \\times H \\times W}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": " through a query encoder (several convolution layers). The historic-frame feature key " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{k}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 486, + 546, + 629 + ], + "type": "text", + "content": " are taken from the temporal memory bank." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Memory Bank Maintaining As above, we have introduced the temporal processing at one single frame. After every " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": " frame, the obtained feature key and value at that frame will be used to update the memory bank. Specifically, the current-frame feature query " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": " is directly copied and fed into the memory bank as the memory key without extra computation. The final output " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\text{used}}" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": " will first be encoded" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "inline_equation", + "content": "{}^{1}C,H,W" + }, + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "text", + "content": " denotes the channel,height,and width of the feature respectively, " + }, + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "inline_equation", + "content": "{T}_{h}" + }, + { + "bbox": [ + 47, + 693, + 287, + 715 + ], + "type": "text", + "content": " denotes the number of the frames stored in the memory bank." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13726" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": "to a BEV map " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": ". The BEV map " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": " will be concatenated with the final output " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{fused}" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": " and passed through a value encoder to obtain the memory value " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": ", which is fed into the memory back. With the above key-value pairs, the memory bank maintains two kinds of buffer: the short-term and long-term buffer. On the one hand, the new key-value pair will be appended to the short-term buffer, as a high-resolution memory of the scene in the past few seconds for accurate feature matching. Considering the limited GPU memory resources, we limit the buffer size and older key-value pairs will be discarded when the limit number " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "T_s" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": " is reached. However, when these older features are discarded, the long-term behavior of the traffic participants is missing, which can be crucial for motion forecasting in complex traffic scenarios. Thus on the other hand, inspired by XMem [12], the memory bank also maintains a long-term buffer that selectively stores important/representative key-value feature pairs discarded by the short-term buffer. Considering the fact that the objects surrounding the ego vehicle are sparse most of the time², the long-term buffer selectively stores key-value features (" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{k}" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": ") which meet one of the two criteria: 1) their corresponding location in the BEV map " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": " has a high probability of object existence; 2) their usage frequency is in top-K of all candidate key-value features. The usage frequency is defined by its cumulative normalized similarity (Eq. 1). The features selected by the above criteria are appended to the last frame of memory. And if the last memory frame is full, we will initialize one new frame with the zero vector and set it as the last frame to store new features. When the number of frames reaches the limit " + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "inline_equation", + "content": "T_l" + }, + { + "bbox": [ + 47, + 72, + 289, + 481 + ], + "type": "text", + "content": ", the obsolete memory will be removed. Such a compact storing strategy can efficiently track long-term representative features and intermittently occluded objects, while balancing the resources required." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 487, + 191, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 191, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 191, + 499 + ], + "type": "text", + "content": "3.3. Global Reasoning module" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 506, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 289, + 685 + ], + "type": "text", + "content": "Rare adverse events such as occluded objects are a notorious issue for the practical deployment of AVs. Our insight is that humans perceive their surroundings not only through sensors, but also by exploiting global information on the scene to reason over the unobservable spaces. For instance, when a vehicle performs an emergency stop without a clear reason, humans can infer that there is potentially an occluded object ahead of the vehicle and will drive more cautiously. Thus we propose the global reasoning module to capture the interaction and relationship between objects and the environment to detect adverse events (e.g. occlusion) and improve overall perception performance. The module consists of three parts: 1) an object-environment and object-object interaction modeling process; 2) an occupancy decoder to generate the occupancy map; 3) a consistency loss" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "to encourage consistent prediction of waypoints and the occupancy map." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "text", + "content": "Interaction Modeling The object-environment and object-object interaction modeling process aims at reasoning about the relationship among objects and the environment. On the one hand, " + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\text {fused }}" + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "text", + "content": " features whose corresponding location in the BEV map " + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p" + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "text", + "content": " has a high probability of object existence will be extracted to represent object features. On the other hand, " + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\text {fused }}" + }, + { + "bbox": [ + 304, + 96, + 547, + 227 + ], + "type": "text", + "content": " features will also be downsampled to represent the environment features. All object and environment features are used to construct a graph, which is passed through a graph attention network (GAT) [56] for interaction modeling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": "Occupancy Decoder Taking the features outputted by the GAT as keys and values, and the learnable positional embeddings as queries, the occupancy decoder utilizes a transformer decoder with " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "K_{\\text{opy}}" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": " layers to generate: 1) the traffic sign feature, which is then concatenated with the traffic sign feature from the BEV decoder to generate the final traffic sign prediction; 2) the occupancy map feature, which is then applied with convolution operation to generate the occupancy map " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_t \\in \\mathbb{R}^{T_f \\times H \\times W}" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": ". At a future time " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": ", each cell in the occupancy map contains a value in the range [0,1] representing the probability that the cell is occupied." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 360, + 546, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 546, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 546, + 503 + ], + "type": "text", + "content": "Consistency Loss Currently, our framework predicts the waypoints and the occupancy map independently, which are not necessarily consistent. For example, the waypoints could overlap some obstacles in the occupancy map. Thus we propose a consistency loss to discourage waypoints' crossing the high-probability region of the occupancy map. Further, the consistency loss also encourages generating longer waypoint trajectories for efficient driving. Specifically, the consistency loss aims at minimizing the average object existence probability of the cells that cover the predicted waypoints, and maximizing the average " + }, + { + "bbox": [ + 304, + 360, + 546, + 503 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 360, + 546, + 503 + ], + "type": "text", + "content": " length of the waypoint trajectory w:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 517, + 545, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 517, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 314, + 517, + 545, + 553 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s i s t e n c y}} = \\frac {1}{T _ {f}} \\left(\\sum_ {t = 0} ^ {T _ {f}} \\frac {\\sum_ {i = 0} ^ {N _ {c} ^ {t}} \\mathbf {O} _ {t , i}}{N _ {c} ^ {t}} - \\lambda \\sum_ {t = 0} ^ {T _ {f}} \\| \\mathbf {w} _ {t} \\| _ {1}\\right) \\tag {3}", + "image_path": "7a8b8603cae14972c38b131e545ffae12a996c7b488de09c38324a34ee75f781.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "text", + "content": ",where " + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "inline_equation", + "content": "N_{c}^{t}" + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "text", + "content": " denotes the number of covered cell at step " + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_{t,i}" + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "text", + "content": " denotes the object existence probability at cell " + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 557, + 545, + 582 + ], + "type": "inline_equation", + "content": "t" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 587, + 365, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 365, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 365, + 598 + ], + "type": "text", + "content": "3.4. Control" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Following [11], we use two PID controllers for latitudinal and longitudinal control, to track the heading and velocity of predicted waypoints respectively. If a red traffic light or stop sign is detected, the ego-vehicle will brake. Additionally, an emergency stop will also be performed if the ego vehicle's current bounding box crosses the area in the occupancy map that has a high object existence probability or if the future waypoints overlap with objects in the BEV map." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "text", + "content": "Based on the data collected from the CARLA simulator, only " + }, + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "text", + "content": " of the ego-vehicle-centered BEV map area is occupied by active objects." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13727" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 160, + 183 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 160, + 183 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 160, + 183 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 160, + 183 + ], + "type": "image", + "image_path": "c1eae2d0d4652ea695059e001eda8185737677d78563f5f761428eb769353f88.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 72, + 275, + 182 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 275, + 182 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 275, + 182 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 275, + 182 + ], + "type": "image", + "image_path": "57a4848366f41fdba3d5959448325e93c316736cbbc1149bbdaf0f9835790a43.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 59, + 187, + 159, + 296 + ], + "blocks": [ + { + "bbox": [ + 59, + 187, + 159, + 296 + ], + "lines": [ + { + "bbox": [ + 59, + 187, + 159, + 296 + ], + "spans": [ + { + "bbox": [ + 59, + 187, + 159, + 296 + ], + "type": "image", + "image_path": "e940d0958ef94cf4a0039e43622654f8b8ca1d884aff28f66b3de681d501bfaf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 299, + 287, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 299, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 287, + 344 + ], + "type": "text", + "content": "Figure 3. An illustration for the four types of occlusion scenarios included in the proposed DOS benchmark. The orange color denotes the ego car. The blue/green dots denote the occluded/visible trajectory of the occluded dangerous object." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 173, + 186, + 274, + 296 + ], + "blocks": [ + { + "bbox": [ + 173, + 186, + 274, + 296 + ], + "lines": [ + { + "bbox": [ + 173, + 186, + 274, + 296 + ], + "spans": [ + { + "bbox": [ + 173, + 186, + 274, + 296 + ], + "type": "image", + "image_path": "26a21544aaaf574accadaea58c6f4b1f364c849fede13cd3b37896c82a2571c6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 356, + 141, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 141, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 141, + 369 + ], + "type": "text", + "content": "3.5. Training Setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": "The training of our framework consists of two stages. In the first stage, we train the perception module to predict BEV features, traffic sign features, and waypoints. Specifically, the loss of BEV features and traffic sign features is computed with additional prediction heads, which are discarded in the next stage. In the second stage, we freeze the perception module and train the other two modules. Five loss terms are considered: 1) the waypoints loss " + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_w" + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": " that minimizes the error between predicted waypoints and expert waypoints; 2) the BEV map loss " + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{BEV}" + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": " that follows [10,64] to minimize the current-frame BEV map prediction error; 3) the traffic sign loss " + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sign}" + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": " for the traffic regulation prediction; 4) occupancy map loss " + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{opy}" + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": " that minimizes the occupancy prediction error in a future horizon; 5) the consistency loss " + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{consistency}" + }, + { + "bbox": [ + 46, + 375, + 289, + 579 + ], + "type": "text", + "content": " which encourages a consistent generation of the waypoints and occupancy map. These loss terms are balanced by corresponding loss weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 592, + 279, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 279, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 279, + 605 + ], + "type": "text", + "content": "4. Drive in Occlusion Sim (DOS) Benchmark" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "content": "In order to address the issue that occlusion events are rare in existing datasets and benchmarks, we present the Drive in Occlusion Simulation benchmark (DOS), a CARLA-based framework providing diverse driving scenarios with occluded objects. As shown in Figure 3, the proposed DOS benchmark includes four types of challenging occlusion driving scenarios:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "content": "**Parked Cars (#1)** The ego vehicle is driving in a straight" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 186 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 186 + ], + "type": "table", + "html": "
RankMethodDS ↑RC ↑IS ↑
1ReasonNet (Ours)79.9589.890.89
2InterFuser [51]76.1888.230.84
3TCP [63]75.1485.630.87
4LAV [10]61.8594.460.64
5TransFuser [15]61.1886.690.71
6Latent TransFuser [15]45.2066.310.72
7GRIAD [8]36.7961.850.60
8TransFuser+ [1]34.5869.840.56
", + "image_path": "b8c6fda6b20f72b70ff6a0676d32ab91d6308263826a27a452829e1e20a18763.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 190, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 304, + 190, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 190, + 547, + 247 + ], + "type": "text", + "content": "Table 1. Performance comparison on the public CARLA leaderboard [53] (accessed Nov 2022). For all three metrics, higher is better. Our method ranks first overall on the leaderboard, with the highest driving score (DS) and infraction score (IS), and the second highest route completion (RC)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 294 + ], + "type": "text", + "content": "lane with parked cars on the side. Pedestrians can first appear on the sidewalk (visible) and then suddenly emerge through the occluded areas between parked cars (occluded)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 295, + 545, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 343 + ], + "type": "text", + "content": "Sudden Brake (#2) The ego vehicle is driving in a straight lane along with other vehicles ahead. Pedestrians can suddenly emerge from the sidewalks, causing the other vehicles to brake while remaining invisible to the ego vehicle." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 344, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 545, + 392 + ], + "type": "text", + "content": "Left Turn (#3) The ego vehicle intends to perform an unprotected left turn at an intersection, but a truck in the opposite lane blocks the view of oncoming traffic, intermittently obscuring vehicles driving straight through the intersection." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "Red Light Infraction (#4) The ego vehicle is crossing an intersection after some trucks. A left-to-right vehicle running a red light suddenly appears, forcing the trucks to brake promptly. But the ego vehicle's view toward the running-light vehicle is blocked by the trucks, so it remains invisible to the ego vehicle." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 469, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 636 + ], + "type": "text", + "content": "Each of the four scenarios in the DOS benchmark comprises 25 different cases varying in the road environment and background traffic. Compared to a previous occlusion benchmark AUTOCASTSIM [19], the DOS benchmark: 1) includes occlusions of both vehicles and pedestrians, instead of only vehicles; 2) includes 100 cases of 4 scenarios, instead of only 3 cases of 3 scenarios; 3) considers specific occlusions that can potentially be resolved by temporal reasoning (intermittent occlusion, #1, #3) and global reasoning (constant occlusion but with interaction clues, #2, #4) about the scene, instead of random occlusions as in AUTOCASTSIM. Thus our scenarios can also serve as a good tracking-with-intermittent-occlusion benchmark and a People-as-Sensor [2,31] benchmark." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 650, + 388, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 650, + 388, + 663 + ], + "spans": [ + { + "bbox": [ + 306, + 650, + 388, + 663 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 670, + 414, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 414, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 414, + 684 + ], + "type": "text", + "content": "5.1. Experiment Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Implementation We implement and evaluate our approach on the open-source CARLA simulator with version" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13728" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 518, + 165 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 518, + 165 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 518, + 165 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 518, + 165 + ], + "type": "table", + "html": "
SettingTown 05 LongDOS
TsTlDS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
0066.7±3.897.6±2.70.68±0.030.18±0.030.05±0.020.03±0.0322±1.628±3.426±2.125±1.6
1067.9±3.496.8±2.30.70±0.020.16±0.040.04±0.030.05±0.0230±3.638±3.632±2.832±3.4
2068.1±3.196.9±3.40.70±0.030.16±0.030.04±0.020.05±0.0328±5.548±4.138±4.452±3.9
2170.9±2.095.7±3.10.74±0.020.13±0.020.04±0.020.06±0.0455±4.457±4.148±4.155±5.5
4070.5±2.196.4±2.50.73±0.040.14±0.030.03±0.020.06±0.0332±5.458±4.440±5.555±4.9
4273.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "image_path": "2da1d1f783a8df111ffc0715d761c9879dbdcd5908d93fa69f4f2dde2dc4cc23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "text", + "content": "Table 2. Ablation study on different short-term buffer size " + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "text", + "content": " and long-term buffer size " + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "inline_equation", + "content": "T_{l}" + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "text", + "content": ", on the Town 05 Long benchmark and the proposed DOS benchmark. Performance is evaluated over three runs. CR: Collision rate, Red: Red light violation, Blocked: Vehicle blocked, SR: Success rate. SR#1 denotes the first kind of scenario in the DOS benchmark. As the two buffer sizes increase, improvement is witnessed in all metrics but the road completion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "content": "0.9.10.1 [21]. We use ResNet-50 pretrained on ImageNet as the 2D backbone and PointPillars trained from scratch as the 3D backbone. We predict " + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "inline_equation", + "content": "T_{f} = 4" + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "content": " time steps for the waypoints and occupancy map, and the interval between each time step is 0.5 seconds. The memory bank maintains " + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "inline_equation", + "content": "T_{s} = 4" + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "content": " frames in the short-term buffer and " + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "inline_equation", + "content": "T_{l} = 2" + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "content": " frames in the long-term buffer. The memory bank is updated every " + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\tau = 2" + }, + { + "bbox": [ + 46, + 224, + 288, + 331 + ], + "type": "text", + "content": " frame. We refer readers to Appendix A for more details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 434 + ], + "type": "text", + "content": "Dataset Collection We collect an expert dataset of 2M frames by running a rule-based expert agent on all 8 public towns and 21 types of weather, with the access to the privileged information in the CARLA simulator. We randomly set routes, spawn dynamic objects and adversarial scenarios provided in [47], to diversify the collected data. To ensure the temporal continuity of collected data, the data are collected at a high frequency of 10HZ." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 559 + ], + "type": "text", + "content": "Metrics We consider three major metrics introduced by the CARLA LeaderBoard: route completion ratio (RC), infraction score (IS), and driving score (DS). The route completion ratio is the percentage of the route completed. The infraction score measures infractions triggered. When collisions or traffic rule violations occur, the infraction score will decay by a discount factor. The driving score is the product of the route completion ratio and the infraction score, describing both driving progress and safety, and thus is the primary ranking metric in the CARLA Leaderboard." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 582, + 228, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 228, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 228, + 594 + ], + "type": "text", + "content": "5.2. Comparison to the state of the art" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Table 1 shows the top 8 entries on the public CARLA Leaderboard. Readers can refer to Sec 2 for descriptions of these methods. Our method outperforms all prior methods, with the highest driving score and infraction score, and the second highest route completion. The previous leading method InterFuser uses a transformer for sensor fusion but lacks temporal and global reasoning. Compared to InterFuser, our method improved the driving score, road completion, and infraction score by " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 224, + 398, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 398, + 237 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 398, + 237 + ], + "type": "text", + "content": "5.3. Ablation study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 243, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 376 + ], + "type": "text", + "content": "We investigate the effect of the temporal and global reasoning modules on the Town05 Long benchmark and the DOS benchmark. For each scenario in DOS, we take 5 cases for training and 20 cases for evaluation. In addition to the three metrics mentioned earlier, we also present four more metrics for detailed analysis: collision rate (CR), red light violation (Red), ego vehicle blocked frequency (Blocked), and success rate (SR). The first three metrics are normalized by the driven distance (km). Visualizations of how the temporal reasoning and global reasoning work can be found at Figure 4 and Figure 5 respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": "Memory Size Table 2 studies the effect of different short-term buffer size " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": " and long-term buffer size " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "T_{l}" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": ". The overall observation is that, as the two buffer sizes increase, improvement is witnessed in all metrics but road completion. Specifically, when the long-term memory is removed " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "(T_{l} = 0)" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": ", the average success rates drop sharply from 71.5 to 36 on DOS scenarios that require keeping track of intermittently occluded objects (#1 and #3). If we remove the temporal reasoning module " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "(T_{s} = T_{l} = 0)" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": ", the driving score on the Town05 benchmark drops by " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": ", and the average success rate on the DOS benchmark drops by " + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "inline_equation", + "content": "46\\%" + }, + { + "bbox": [ + 304, + 377, + 547, + 581 + ], + "type": "text", + "content": ". We hypothesize that the drop in performance is because 1) it can be really hard to accurately estimate the objects' future motion based only on single-frame data; 2) temporal information can help keep track of objects that are intermittently occluded; 3) the global reasoning module may also work poorly when historic information is missing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Long-Term Memory Selection Strategy Table 3 studies the performance of different long-term memory selection strategies. Specifically, the proposed strategy in Sec 3.2 includes two selection criteria. So here we ablate the effect of the two criteria by 1) only selecting the short-term feature with top- " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " usages (usage-based); 2) only selecting the feature with a high probability of the existence of an object (object-based). Besides, we also compared a random selection strategy. As in Table 3, the random selection strategy has the poorest performance especially on the DOS benchmark, as random selection could miss important and repre" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13729" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 519, + 143 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 519, + 143 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 519, + 143 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 519, + 143 + ], + "type": "table", + "html": "
SettingTown 05 LongDOS
DS ↑RC ↑IS ↑CR ↓Red ↓Blocked ↓SR#1 ↑SR#2 ↑SR#3 ↑SR#4 ↑
Random71.2±5.496.6±2.40.74±0.040.13±0.040.03±0.010.06±0.0233±4.455±6.242±5.553±5.4
Usage-based72.0±3.995.9±2.20.75±0.040.12±0.030.03±0.010.06±0.0245±4.262±3.453±2.862±3.9
Object-based72.2±3.796.1±3.00.75±0.030.12±0.030.03±0.010.05±0.0257±4.165±3.673±4.460±3.7
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "image_path": "efeeb0dba7f6472cb4c92057fb19ac8cae6765e7d9c61294bc2540810769eb81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 73, + 174, + 520, + 243 + ], + "blocks": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "lines": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 547, + 169 + ], + "type": "text", + "content": "Table 3. Ablation study on different long-term memory selection strategies. Our proposed strategy considering both the usage and object criteria outperforms the random selection strategy and the two methods with only one criteria, especially on the DOS benchmark." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 174, + 520, + 243 + ], + "lines": [ + { + "bbox": [ + 73, + 174, + 520, + 243 + ], + "spans": [ + { + "bbox": [ + 73, + 174, + 520, + 243 + ], + "type": "table", + "html": "
SettingTown 05 LongDOS
DS↑RC↑IS↑CR↓Red↓Blocked↓SR#1↑SR#2↑SR#3↑SR#4↑
No global reasoning68.9±4.697.4±2.90.71±0.040.15±0.040.05±0.020.05±0.0228±2.834±3.429±2.027±3.6
No consistency loss72.2±3.496.1±3.20.75±0.030.12±0.020.03±0.020.06±0.0360±4.172±3.977±4.968±4.2
No traffic sign prediction71.1±2.796.0±4.10.74±0.030.11±0.030.05±0.030.07±0.0362±4.472±4.082±2.870±4.1
Full (Ours)73.2±1.995.9±2.30.76±0.030.11±0.020.03±0.010.07±0.0363±4.273±3.680±4.270±5.5
", + "image_path": "58f1444b8a50ab208a3bb0af8a5387462ab0ca57b98a071b20be1b4157dcb116.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 245, + 546, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 546, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 546, + 268 + ], + "type": "text", + "content": "Table 4. Ablation study on the global reasoning module. The performance would drop when 1) the entire global reasoning module is removed; 2) the consistency loss is not applied; 3) the traffic sign feature from the reasoning module is not utilized." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 55, + 277, + 278, + 390 + ], + "blocks": [ + { + "bbox": [ + 55, + 277, + 278, + 390 + ], + "lines": [ + { + "bbox": [ + 55, + 277, + 278, + 390 + ], + "spans": [ + { + "bbox": [ + 55, + 277, + 278, + 390 + ], + "type": "image", + "image_path": "9613b839e8bd58fb83e07d216bd2ad745bcc41c36d9b9a72fac42a3739848dde.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 395, + 288, + 450 + ], + "lines": [ + { + "bbox": [ + 46, + 395, + 288, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 288, + 450 + ], + "type": "text", + "content": "Figure 4. Visualization of the attention map between one object's current-frame feature query and the historic-frame feature stored in the short-term buffer, in two cases. The object's current-frame feature consistently attends to its corresponding region in the historic feature map." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 57, + 452, + 278, + 538 + ], + "blocks": [ + { + "bbox": [ + 57, + 452, + 278, + 538 + ], + "lines": [ + { + "bbox": [ + 57, + 452, + 278, + 538 + ], + "spans": [ + { + "bbox": [ + 57, + 452, + 278, + 538 + ], + "type": "image", + "image_path": "585ff0ea3058373efb47131d1ac58a3d64446dc93b3ceb2fe7729ec534c1fe8b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 547, + 287, + 635 + ], + "lines": [ + { + "bbox": [ + 46, + 547, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 287, + 635 + ], + "type": "text", + "content": "Figure 5. We show two cases of how our framework reasons the presence of the occluded object. In the first case, a pedestrian first appeared on the sidewalk (visible) and then emerges between two parked cars (occluded). In the second case, a vehicle runs the red light, forcing trucks to brake abruptly. But the ego vehicle's view toward the running-light vehicle is blocked by the front trucks, so the running-light vehicle remains invisible to the ego vehicle. The rectangles mark the occluded objects." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "sentative features on the scene. Compared to our strategy utilizing both criteria, the two ablations omitting one of the criteria have a performance drop, especially on the DOS benchmark. The usage-based strategy performs worse than the object-based, showing that the features of objects could be more informative for capturing historic behaviors." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 278, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 547, + 483 + ], + "type": "text", + "content": "Global Reasoning Design Table 4 studies the performance when different designs of the global reasoning module are applied. First, we remove the entire module and observe a significant drop in all metrics but the road completion. For instance, the average success rate on the DOS benchmark dropped from 71.5 to 29.5. This demonstrates the effectiveness of global reasoning, especially in occlusion events. Second, we ablated the consistency loss, which could alleviate the sub-optimal issues in collected expert data. A removal of consistency loss leads to a lower driving score and higher collision rate on the Town 05 benchmark and a lower success rate on the DOS benchmark. Third, excluding the traffic sign feature from the global reasoning model results in an increase on the red light violation. One explanation is that the traffic sign feature from the global reasoning module could help reason the distant traffic light state according to other road participants' behavior." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": "We present ReasonNet, a novel end-to-end autonomous driving framework including two major components: a temporal reasoning module and a global reasoning module. The temporal reasoning module processes the historic information on the driving scene for high-fidelity forecasting of other road participants and dynamically maintains a temporal memory bank. The global reasoning module models the interaction and relationship among the objects and environment to detect adverse events especially occlusion, and improve overall perception performance. Our method pushes the state-of-the-art performance of the CARLA leaderboard by a considerable margin. Moreover, we also publicly release a new benchmark DOS consisting of diverse occlusion scenarios, to facilitate the study of occlusion detection in the field of end-to-end autonomous driving." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13730" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 291, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 291, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 291, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 291, + 123 + ], + "type": "text", + "content": "[1] Expert drivers for autonomous driving. https://kait0.github.io/files/master_thesis_bernhard_jaeger.pdf, 2021.6, 13" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 125, + 288, + 180 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 125, + 288, + 180 + ], + "spans": [ + { + "bbox": [ + 53, + 125, + 288, + 180 + ], + "type": "text", + "content": "[2] Oladapo Afolabi, Katherine Driggs-Campbell, Roy Dong, Mykel J Kochenderfer, and S Shankar Sastry. 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To that end, we develop a new update patch for BN, particularly tailored for the exemplar-based class-incremental learning (CIL). The main issue of BN in CIL is the imbalance of training data between current and past tasks in a mini-batch, which makes the empirical mean and variance as well as the learnable affine transformation parameters of BN heavily biased toward the current task — contributing to the forgetting of past tasks. While one of the recent BN variants has been developed for \"online\" CIL, in which the training is done with a single epoch, we show that their method does not necessarily bring gains for \"offline\" CIL, in which a model is trained with multiple epochs on the imbalanced training data. The main reason for the ineffectiveness of their method lies in not fully addressing the data imbalance issue, especially in computing the gradients for learning the affine transformation parameters of BN. Accordingly, our new hyperparameter-free variant, dubbed as Task-Balanced BN (TBBN), is proposed to more correctly resolve the imbalance issue by making a horizontally-concatenated task-balanced batch using both reshape and repeat operations during training. Based on our experiments on class incremental learning of CIFAR-100, ImageNet-100, and five dissimilar task datasets, we demonstrate that our TBBN, which works exactly the same as the vanilla BN in the inference time, is easily applicable to most existing exemplar-based offline CIL algorithms and consistently outperforms other BN variants.", + "bbox": [ + 76, + 362, + 473, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 824, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, continual learning (CL) has been actively studied to efficiently learn a neural network on sequentially", + "bbox": [ + 76, + 849, + 468, + 880 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "arriving datasets while eliminating the process of re-training from scratch at each arrival of a new dataset [9]. However, since the model is typically trained on a dataset that is heavily skewed toward the current task at each step, the resulting neural network often suffers from suboptimal trade-off between stability and plasticity [25] during CL. To overcome this issue, various studies have been focused on addressing the so-called catastrophic forgetting phenomenon [9, 28].", + "bbox": [ + 500, + 332, + 895, + 454 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among different CL settings, the class-incremental learning (CIL) setting where the classifier needs to learn previously unseen classes at each incremental step has recently drawn attention due to its practicality [1, 3, 6, 12, 15, 26, 39, 42, 44]. Most state-of-the-art CIL algorithms maintain a small exemplar memory to store a subset of previously used training data and combine it with the current task dataset to mitigate the forgetting of past knowledge. A key issue of exemplar-based CIL is that the model prediction becomes heavily biased towards more recently learned classes, due to the imbalance between the training data from the current task (that are abundantly available) and past tasks (with limited access through exemplar memory). In response, recently proposed solutions to biased predictions include bias correction [39], unified classifier [15], and separated softmax [1], which greatly improved the overall accuracy of CIL methods across all classes learned so far.", + "bbox": [ + 496, + 457, + 895, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite such progress, relatively less focus has been made on backbone architectures under CIL on computer vision tasks. Specifically, the popular CNN-based models (e.g., ResNet [13]) are mainly used as feature extractors, and those models are equipped with Batch Normalization (BN) [17] by default. However, since BN is designed for single-task training on CNNs, applying BN directly to exemplar-based CIL results in statistics biased toward the current task due to the imbalance between current and past tasks' data in a mini-batch. Recently, [29] pointed out this issue in CIL, dubbed as cross-task normalization effect, and proposed a new normalization scheme called Continual Normalization", + "bbox": [ + 496, + 719, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author (E-mail: tsmoon@snu.ac.kr)", + "bbox": [ + 94, + 887, + 400, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20127", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(CN), which applies Group Normalization (GN) [40] across the channel dimension before running BN across the batch dimension. Therefore, the difference in feature distributions among tasks is essentially removed by GN, and the following BN computes task-balanced mean and variance statistics which is shown to outperform vanilla BN on online CIL settings.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we argue that CN only partially resolves the bias issue in exemplar-based CIL. Specifically, we find that the gradients on the affine transformation parameters remain biased towards the current task when using CN. As a result, it leads to inconsistent performance gains in the offline CIL setting, which is considered more practical than online CIL. To this end, we propose a simple yet novel hyperparameter-free normalization layer, dubbed as Task-Balanced Batch Normalization (TBBN), which effectively resolves the bias issue. Our method employs adaptive reshape and repeat operations on the mini-batch feature map during training in order to compute task-balanced normalization statistics and gradients for learning the affine transformation parameters. Our method does not require any hyperparameter as the size-inputs for reshape and repeat operations are determined adaptively. Furthermore, the application of TBBN during testing is identical to vanilla BN, requiring no change on the backbone architecture. Through extensive offline CIL experiments on CIFAR-100, ImageNet-100, and five dissimilar task datasets, we show that a simple replacement of BN layers in the backbone CNN model with TBBN benefits most state-of-the-art exemplar-based CIL algorithms towards an additional boost in performance. Our analysis shows that the gain of TBBN is consistent across various backbone architectures and datasets, suggesting its potential to become a correct choice for exemplar-based offline CIL algorithms.", + "bbox": [ + 75, + 198, + 473, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 603, + 218, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Exemplar-based CIL. Among various work in offline CIL, iCaRL [30] is the first to propose an exemplar-based method via utilization of nearest-mean-of-exemplars classification and representation learning. EEIL [6] next devised a distillation-based CIL method with both balanced fin-tuning and representative memory updating. BiC [39] focused on the biased prediction aspect due to data imbalance in CIL and proposed a novel yet simple idea to attach an additional layer that corrects biased predictions. Inspired by LWF [21], LUCIR [15] developed a method that overcomes catastrophic forgetting via a more sophisticated cosine normalization-based loss function. PODNet [12] proposed another distillation-based method that focuses on spatial-based loss to reduce representation forgetting. Most recently, two state-of-the-art knowledge distillation-based CIL methods have been proposed. First, SS-IL [1] demonstrated that a pure softmax mainly causes biased predictions in CIL, leading to the Separated Softmax layer that achieved significant", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "performance gains. Second, AFC [18] devised a novel regularization for knowledge distillation to minimize the changes of important features when learning new tasks.", + "bbox": [ + 496, + 90, + 893, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, online CIL also has attracted attention [2,33], but their performance is significantly lower in the benchmark (e.g., CIFAR-100) than offline CIL counterparts, as reported in the survey paper [23].", + "bbox": [ + 496, + 137, + 893, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Normalization layer. One initial motivation for devising Batch Normalization (BN) [17] was to address internal covariate shift of a neural net. However, the belief in internal covariate shift was broken by follow-up studies, and the benefits from BN in terms of training perspective were analyzed in various directions [4, 32]. Thereafter, several normalization layers devised for various computer vision tasks have been proposed, each with their respective advantages [14, 16, 22, 37, 40], and for more diverse tasks, such as meta-learning [5], domain adaptation [38], task-incremental learning [20], and online CL [29].", + "bbox": [ + 496, + 199, + 895, + 367 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 383, + 638, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notation. We assume the setting of offline CIL as proposed in [1]; namely, a dataset $\\mathcal{D}_t$ for each task $t$ arrives incrementally, and we use $T$ to denote the total number of tasks. Each $\\mathcal{D}_t$ consists of pairs of an input image $\\boldsymbol{x}_t$ and its target label $y_t$ . We assume that each incrementally added task introduces $m$ new classes that the model has never observed previously, and hence the total number of classes observed until task $t$ equals $C_t = m \\cdot t$ . Therefore, the target label in each task is labeled as $y_t \\in \\{C_{t-1} + 1, \\dots, C_t\\} \\triangleq \\mathcal{C}_t$ . To save exemplars from previous tasks, we use exemplar memory denoted by $\\mathcal{M}$ . While $\\mathcal{M}$ is updated via a sampling algorithm after training on each task, the memory size is set to not exceed $|\\mathcal{M}|$ over the entire course of tasks. In particular, exemplar memory $\\mathcal{M}_{t-1}$ maintains $\\left\\lfloor \\frac{|\\mathcal{M}|}{C_{t-1}} \\right\\rfloor$ images per each past class and is used for training task $t$ . To merge instances from current as well as previous tasks, we consider a training mini-batch size of $B = B_c + B_p$ , where $B_c$ and $B_p$ denote the number of data samples from $\\mathcal{D}_t$ and $\\mathcal{M}_{t-1}$ , respectively. Without loss of generality, we assume that each mini-batch $(\\boldsymbol{x}^B, y^B) \\sim (\\mathcal{D}_t \\cup \\mathcal{M}_{t-1})$ is a concatenation of $B_c$ samples from $\\mathcal{D}_t$ with $B_p$ samples from $\\mathcal{M}_{t-1}$ : $\\boldsymbol{x}^B = [\\boldsymbol{x}_1; \\dots; \\boldsymbol{x}_{B_c}; \\boldsymbol{x}_{B_c+1}; \\dots; \\boldsymbol{x}_B]$ and $y^B = [y_1; \\dots; y_{B_c}; y_{B_c+1}; \\dots; y_B]$ with $\\{(x_i, y_i)\\}_{i=1}^{B_c} \\subset \\mathcal{D}_t$ and $\\{(x_i, y_i)\\}_{i=B_c+1}^{B} \\subset \\mathcal{M}_{t-1}$ . Note that $B_c$ is greater than $B_p$ in typical CIL settings, and it is this imbalance that is generally known to cause predictions biased towards the current task [1, 3, 39]. Therefore, we set the sampling ratio between $B_c$ and $B_p$ as $B_c: B_p = 3:1$ in our experiments. Lastly, we use $\\boldsymbol{h} \\in \\mathbb{R}^{B \\times C \\times D}$ to denote the input feature map for an intermediate BN layer given $\\boldsymbol{x}^B$ as input. Here, $C$ and $D$ denote the number of channels and feature dimension, respectively.", + "bbox": [ + 496, + 410, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20128", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Batch Normalization. Due to its powerful practicality and efficiency, Batch Normalization (BN) [17] has been the go-to normalization layer across various state-of-the-art neural network architectures [13, 34, 36]. During training, BN calculates the empirical mean $\\hat{\\mu} \\in \\mathbb{R}^C$ and variance $\\hat{\\sigma}^2 \\in \\mathbb{R}^C$ of the given mini-batch as", + "bbox": [ + 76, + 90, + 472, + 181 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mu} _ {c} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\boldsymbol {h} _ {b, c, d}, \\hat {\\sigma} _ {c} ^ {2} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\left(\\boldsymbol {h} _ {b, c, d} - \\hat {\\mu} _ {c}\\right) ^ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 186, + 468, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The feature map $\\pmb{h}$ is then normalized to have zero-mean unit-variance using $\\hat{\\mu}$ and $\\hat{\\sigma}^2$ to obtain $\\hat{\\pmb{h}} \\in \\mathbb{R}^{B \\times C \\times D}$ . The normalized feature $\\hat{\\pmb{h}}$ is lastly affine-transformed with a trainable scale and shift parameters $\\gamma, \\beta \\in \\mathbb{R}^C$ to $\\pmb{y}$ :", + "bbox": [ + 76, + 242, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {h}} _ {b} = \\frac {\\boldsymbol {h} _ {b} - \\hat {\\mu} \\cdot \\mathbb {1} ^ {\\intercal}}{\\sqrt {\\hat {\\sigma} ^ {2} \\cdot \\mathbb {1} ^ {\\intercal} + \\epsilon \\cdot \\mathbb {1} ^ {\\intercal}}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 311, + 468, + 344 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} _ {b} = \\gamma \\cdot \\mathbb {1} ^ {\\mathrm {T}} \\odot \\hat {\\boldsymbol {h}} _ {b} + \\beta \\cdot \\mathbb {1} ^ {\\mathrm {T}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 347, + 468, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\mathbb{1} \\in \\mathbb{R}^D$ is the all-1 vector, $\\odot$ denotes the element-wise multiplication, and $b$ is the data index within the minibatch. Note the division and $\\sqrt{\\cdot}$ in (2) are also done in an element-wise sense. The $\\epsilon$ term is a small value added for numerical stability, which we set as $\\epsilon = 10^{-5}$ in the experiments. It is worth noting that $\\gamma$ and $\\beta$ are trained by computing the gradients", + "bbox": [ + 76, + 376, + 472, + 482 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial \\gamma_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\odot \\hat {\\boldsymbol {h}} _ {b, c, d}, \\quad \\frac {\\partial \\mathcal {L}}{\\partial \\beta_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 492, + 468, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "under a loss function $\\mathcal{L}$ . For the normalization in the test phase, running $\\mu$ and $\\sigma^2$ are updated incrementally at each $i$ -th training iteration via exponential moving average:", + "bbox": [ + 76, + 546, + 468, + 592 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {(i)} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\mu} _ {(i)} + (1 - \\alpha) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\mu_ {(i - 1)}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 597, + 388, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {(i)} ^ {2} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\sigma} _ {(i)} ^ {2} + \\left((1 - \\alpha) \\frac {V - 1}{V}\\right) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\sigma_ {(i - 1)} ^ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 617, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $V = B \\cdot D$ represents the vessel's correction, and $\\alpha$ is the momentum hyperparameter generally set as 0.1.", + "bbox": [ + 76, + 662, + 468, + 693 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Main Method", + "text_level": 1, + "bbox": [ + 76, + 705, + 215, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Motivation", + "text_level": 1, + "bbox": [ + 76, + 729, + 199, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While exemplar memory is essential for achieving state-of-the-art performance in offline CIL [24], most methods use well-known backbone classification models (e.g., ResNet-18 [13]) with vanilla BN layers without much scrutiny over the issue of data-imbalance between current and previous tasks. One notable exception is Continual Normalization (CN) [29], but CN has only shown promise in online CIL settings where the data-imbalance causes relatively less of an impact than in offline CIL due to the single epoch learning. It is not clear whether CN is also effective in offline CIL, where", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the imbalanced mini-batches are used for multiple epochs. We conjecture that while CN performs task-balancing by normalizing each channel (or groups of channels) along the spatial dimension, this comes at a cost in discriminative power as it normalizes features from all tasks equally without any separation between tasks. In a later section, we find through experimentation that this limitation is especially detrimental in offline CIL, as CN leads to negligible gain over BN or even worse performance in some cases.", + "bbox": [ + 496, + 90, + 893, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a concrete motivation, we consider a toy example to reflect upon the necessity of devising a correct BN mechanism for the exemplar memory-based CIL. Consider a synthetic input feature distribution for an intermediate BN layer shown in Figure 1. Figure 1(a) visualizes 2-D data samples generated from a mixture of four different Gaussian distributions, each representing the feature distribution for each given task. $^{1}$ In a joint training setting, the mini-batch samples are uniformly sampled across four tasks, and thus the empirical mean and variance obtained from BN would approach the true population mean and variance. Such mean and variance will then successfully standardize the samples in a mini-batch during both training and testing phases via the procedure given in (2) and (3).", + "bbox": [ + 496, + 227, + 893, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In an exemplar memory-based CIL setting, however, there is a severe imbalance among samples in the training minibatch, since the majority of the samples comes from the current task (Task 4) as shown in Figure 1(b). In this case, the mean and variance calculated by the BN layer is clearly biased towards those of the current task, failing to match the true statistics at test time. In other words, using the biased mean and variance obtained during training to normalize test samples leads the samples to deviate from a standardized distribution. It is evident that such mismatch between the train and test sample distributions can cause performance deterioration since the trainable parameters in BN are obtained from normalized training samples. An obvious remedy would be to obtain the task-balanced empirical mean and variance during training, and use them in the BN layer to normalize the test samples. Figure 1(c) and 1(d) highlight the difference between the test normalization done by CN and our TBBN, respectively, which computes the empirical mean and variance from the mini-batch in Figure 1(b). Note that while both successfully normalize test samples in a task-balanced way, CN tends to lose the discriminative structure among the tasks due to the intermediate GN step. In constraint, our TBBN, as will be described in details below, normalizes the test data features while maintaining the discriminative structure.", + "bbox": [ + 496, + 438, + 895, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition to the mismatch during test time, a naive application of BN on the biased mini-batch samples can also", + "bbox": [ + 498, + 800, + 893, + 830 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1In fact, we generated 20 dimensional Gaussian vectors, which is generated by concatenating i.i.d. 2-D Gaussians 10 times, and only the first two dimensions are shown in the figures. The normalization by CN and TBBN shown in Figure 1(c)(d) are done by obtaining the statistics from the entire 20 dimensions (which exemplifies the channel dimension in a feature map).", + "bbox": [ + 498, + 838, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20129", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b90dec4ffa72fa2d4ac64564b1b21641248e40ea1ad0abc1edfa314339d1e365.jpg", + "image_caption": [ + "(a) True population distribution" + ], + "image_footnote": [], + "bbox": [ + 106, + 95, + 289, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bcfa77a1f70ec99aa979f3706012e9e00d2b1d867d807fd1024448744da8f263.jpg", + "image_caption": [ + "Figure 1. (a) 2-D visualizations on a mixture of four Gaussian distributions, each representing a feature map distribution of each task. (b) Imbalanced training data in exemplar-based CIL while learning Task 4, deviating from true test distribution. (c) Test set normalization result of CN that computes normalization statistics from data in (b). (d) Test set normalization result of our proposed TBBN that computes normalization statistics from data in (b)." + ], + "image_footnote": [], + "bbox": [ + 299, + 95, + 483, + 229 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ab1fc997e6e9e9a63c95d4f49bf6ac2583e93c73c6d10bea3bf207ccf64311b0.jpg", + "image_caption": [ + "(b) Biased train data during CIL" + ], + "image_footnote": [], + "bbox": [ + 493, + 95, + 671, + 229 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/739d66c3751315a71741237ab8668c4c42d3ed1a055de809a7ec50ab058a6e68.jpg", + "image_caption": [ + "(c) Test data normalized via CN", + "(d) Test data normalized via TBBN" + ], + "image_footnote": [], + "bbox": [ + 679, + 95, + 857, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cause an issue during training. That is, when training for a current task (e.g., Task 4 in Figure 1) is finished, the empirical mean and variance obtained by a BN layer would be heavily biased towards the most recent task. When a new task arrives (say, Task 5), since only a small number of samples from Task 4 is saved in the exemplar memory, the new empirical mean and variance will now become biased towards Task 5, drifting away from the previous statistics updated via the exponential moving average in (5). This mismatch during training can also significantly alter the learned representations of the past task samples in the exemplar memory after normalization. Therefore, this necessitates re-training of subsequent layers, unintentionally causing forgetting of previously learned representations.", + "bbox": [ + 75, + 316, + 472, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With regards to the two aforementioned issues, we argue that it is crucial to calculate the task-balanced mean and variance for BN layers in exemplar memory-based CIL. While a similar observation has also been made in the recent work [29], we go one step further and note that the affine transformation parameters of BN (i.e. $\\gamma$ and $\\beta$ in (3)) should also be learned in a task-balanced manner. For a demonstration purpose, we train a ResNet-18 model with vanilla BN and exemplar memory of size $|\\mathcal{M}| = 2000$ on ImageNet-100 split to 10 tasks with 10 classes per task. We test four different CIL procedures including two oracle-based approaches that can access the entire training set during test time to exhibit the necessity of task-balanced statistics and affine-transformations. In Figure 2, JOINT denotes the algorithm that jointly trains the model on all tasks at once, providing an upper bound in average accuracy. On the other hand, FT is the fine-tuning baseline that simply fine-tunes the model on samples from the current task and exemplar memory for each task. Note that FT performs poorly on previous tasks except for the final task, clearly reflecting the issue of biased predictions. UPDATE $(\\mu, \\sigma^2)$ is an oracle scheme that freezes all trainable parameters of the trained FT model, and only recomputes the mean and variance of all BN layers using the entire dataset such that they match the task-balanced", + "bbox": [ + 75, + 537, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "population statistics. Finally, UPDATE $(\\mu, \\sigma^2)$ AND $(\\gamma, \\beta)$ denotes another oracle scheme that also re-trains the $(\\gamma, \\beta)$ parameters for all BN layers on the entire dataset, in addition to recomputing the $(\\mu, \\sigma^2)$ statistics.", + "bbox": [ + 496, + 315, + 893, + 377 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4d11ed290620cd92269f90f2cc33f5bda57c4e296edf56c4d3c94c0c19e6b59e.jpg", + "image_caption": [ + "Figure 2. Individual task and average accuracies on ImageNet-100 split into 10 tasks for CIL. $y$ -axis shows the accuracy for each task and the average accuracy across all tasks after full training. Recomputing the affine-transformation parameters $(\\gamma, \\beta)$ as well as empirical statistics $(\\mu, \\sigma^2)$ based on the full dataset leads to significant boost in performance." + ], + "image_footnote": [], + "bbox": [ + 542, + 382, + 849, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 2 displays the classification accuracy of four methods on every 2nd task and the average accuracy across all tasks, all measured after training up to the final task. The slight drop in performance of UPDATE $(\\mu, \\sigma^2)$ compared to FT shows that only obtaining the task-balanced $(\\mu, \\sigma^2)$ is not sufficient due to mismatch between the updated $(\\mu, \\sigma^2)$ and the frozen $(\\gamma, \\beta)$ . In contrast, when affine-transformation parameters are also recomputed with task-balanced data, we observe a significant boost in average accuracy. This is particularly interesting as the affine-transformation parameters account for less than $1\\%$ of the entire model parameters, and simply making them task-balanced along with the empirical $(\\mu, \\sigma^2)$ statistics in BN layers can bring a significant performance boost under a simple FT baseline. Inspired by this example, we develop our Task-Balanced Batch Normalization (TBBN) layer in the next section.", + "bbox": [ + 496, + 659, + 895, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20130", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7a837f430596d765dc7eb88cc567e6faefcabf1bdb4b62d58292201ec2fe9571.jpg", + "image_caption": [ + "Figure 3. Illustration of the forward (blue arrows) and backward (red arrows) propagations of TBBN. By applying both reshape and repeat operations to a given input of BN layer, TBBN induces that task-balanced calculation and training of $(\\mu, \\sigma^2)$ and $(\\gamma, \\beta)$ , respectively." + ], + "image_footnote": [], + "bbox": [ + 122, + 90, + 851, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Task-Balanced Batch Normalization (TBBN)", + "text_level": 1, + "bbox": [ + 75, + 308, + 455, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To solve the problem of BN in the exemplar-based CIL, we propose Task-Balanced Batch Normalization (TBBN) consisting of two components: 1) Task-balanced $\\mu$ and $\\sigma^2$ calculation and 2) Task-balanced training of $\\gamma$ and $\\beta$ .", + "bbox": [ + 75, + 327, + 470, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Task-balanced $\\mu$ and $\\sigma^2$ calculation. As discussed in the previous section, the class imbalance between the current and previous data biases the mean and variance toward the current task. Instead, we propose a task-balanced algorithm that better computes the empirical mean and variance in the current batch. As shown in Figure 3, we design the two different tensor operations: reshape and repeat, applying them to the current and previous parts, respectively. We determine the number of repeat/reshape operations $r$ by the following (6). It determines the value of $r$ , which is used to balance the number of batches sampled from the exemplar memory $(\\frac{B_p}{t - 1})$ and the number of batches of the current task $(\\frac{B_c}{r})$ after reshaping with $r$ , so that the ratio between them becomes 1:1. Note that $r$ is a hyperparameter that need not be externally tuned, but that our method provides a task-adaptive guidance for automatically selecting $r$ :", + "bbox": [ + 75, + 388, + 473, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {B _ {c}}{r} = \\frac {B _ {p}}{t - 1}, \\text {h e n c e ,} r = \\frac {B _ {c}}{B _ {p}} \\cdot (t - 1), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 642, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $t = 2, \\dots, T$ , and $r$ is set to 1 when $t = 1$ .", + "bbox": [ + 75, + 684, + 419, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $h_{B_c}$ be the input feature map of a BN layer for the current task $t$ . After applying the reshape operation $\\mathbf{H}_{B_c} = F_S(h_{B_c}; r) : \\mathbb{R}^{B_c \\times C \\times D} \\to \\mathbb{R}^{B_c / r \\times C \\cdot r \\times D}$ with $r$ , we divide $h_{B_c}$ into $r$ splits, where each split has $\\frac{B_c}{r}$ numbers of data from the current task. Similarly, let $h_{B_p}$ denote the data from the previous tasks. As $h_{B_p}$ consists of the data uniformly sampled from task 1 to $t - 1$ , $\\frac{B_p}{t - 1}$ numbers of data belongs to $h_{B_p}$ for each previous task in expectation. The key insight is that we can make every split balanced by repeating $h_{B_p}$ by $r$ times if the task ratios $\\frac{B_c}{r}$ and $\\frac{B_p}{t - 1}$ become equivalent. So that, we repeat $h_{B_p}$ for $r$ times by applying a tensor repeat function $\\mathbf{H}_{B_p} = F_P(h_{B_p}; r) : \\mathbb{R}^{B_p \\times C \\times D} \\to \\mathbb{R}^{B_p \\times C \\cdot r \\times D}$ . Then, we concatenate both tensors along batch", + "bbox": [ + 75, + 700, + 473, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "axis, $\\mathbf{H} = (\\mathbf{H}_{B_c};\\mathbf{H}_{B_p})\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}$ , and calculate a task-balanced empirical mean $\\tilde{\\mu}\\in \\mathbb{R}^{C\\cdot r}$ and variance $\\tilde{\\sigma}^2\\in \\mathbb{R}^{C\\cdot r}$ from a horizontally-concatenated task-balanced batch $\\mathbf{H}$ . To update running mean $\\mu \\in \\mathbb{R}^{C}$ and variance $\\sigma^2\\in \\mathbb{R}^C$ for test phase, we average $\\tilde{\\mu}$ and $\\tilde{\\sigma}^2$ over $r$ splits, later applying these to the exponential moving average (5) to update $\\mu$ and $\\sigma^2$ .", + "bbox": [ + 496, + 308, + 893, + 414 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Task-balanced training of $\\gamma$ and $\\beta$ . Additionally, we propose a way to train learnable parameters of BN ( $\\gamma$ and $\\beta$ ) in a task-balanced way to the current task. After calculating the task-balanced $\\tilde{\\mu}$ and $\\tilde{\\sigma}^2$ from $\\mathbf{H}$ , we apply these to normalize the horizontally-concatenated task-balanced batch $\\mathbf{H}$ via (2). Then, the normalized feature map $\\tilde{\\mathbf{H}} \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}$ is affine-transformed by (3) with $\\tilde{\\gamma} = F_{RP}(\\gamma) \\in \\mathbb{R}^{C \\cdot r}$ and $\\tilde{\\beta} = F_{RP}(\\beta) \\in \\mathbb{R}^{C \\cdot r}$ , resulting in the affine-transformed feature $\\mathbf{Y} = (\\mathbf{Y}_{B_c}; \\mathbf{Y}_{B_p}) \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}$ . However, due to the different size of batch axis with the original batch size ( $B_c / r + B_p \\neq B$ ), $\\mathbf{Y}$ cannot be directly forward-propagated toward a next layer. To solve this problem, first, we apply a reverse operation of reshape to $\\mathbf{Y}_{B_c}$ to obtain $\\mathbf{y}_{B_c} \\in \\mathbb{R}^{B_c \\times C \\times D}$ , where $F_S^{-1}(\\mathbf{Y}_{B_c}; r): \\mathbb{R}^{B / r \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_c \\times C \\times D}$ . Next, for the case of $\\mathbf{Y}_{B_p}$ , we get $\\mathbf{y}_{B_p} \\in \\mathbb{R}^{B_p \\times C \\times D}$ by averaging $\\mathbf{Y}_{B_p}$ over $r$ repeats along the axis of channel, such as $\\mathbf{y}_{B_p} = F_A(\\mathbf{Y}_{B_p}; r): \\mathbb{R}^{B_p \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_p \\times C \\times D}$ . Finally, we forward-propagate the concatenated feature $\\mathbf{y} = (\\mathbf{y}_{B_c}; \\mathbf{y}_{B_p}) \\in \\mathbb{R}^{B \\times C \\times D}$ toward the next layer.", + "bbox": [ + 496, + 415, + 895, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Why does TBBN work?", + "text_level": 1, + "bbox": [ + 498, + 729, + 720, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Calculating task-balanced $\\mu$ and $\\sigma^2$ . When performing the standard BN while fixing the number of data instances from previous tasks as $B_{p}$ , the individual statistics $(\\mu^{BN},\\sigma^{BN})$ becomes dominated by the current task. As the exponential moving average iteratively averages over biased empirical statistics, BN fails to asymptotically recover population mean and variance. This is especially clear when expanding the BN mean $\\mu_t^{BN}$ during training on task $t$ in terms of means $\\mu_{i}$ of the $i$ -th task. Assuming that each task contributes uniformly in the global data distribution, $\\mu_t^{BN}$", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20131", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "deviates from the true global mean $\\mu_t^*$ by", + "bbox": [ + 76, + 90, + 351, + 107 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} ^ {*} - \\mu_ {t} ^ {B N} = \\frac {B - B _ {c} t}{t (t - 1) B} \\sum_ {i = 1} ^ {t} \\mu_ {i} + \\frac {B _ {c} t - B}{(t - 1) B} \\mu_ {t}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 112, + 468, + 152 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In a nutshell, BN fails to recover the true population mean unless the mini-batch is balanced such that $B_{c} = B / t$ . Our proposed TBBN creates $r$ task-balanced bags of bootstrapped samples such that this balancing is satisfied, and approximates the population statistics $(\\mu^{*},\\sigma^{2*})$ in an unbiased manner.", + "bbox": [ + 75, + 157, + 468, + 232 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training $\\gamma$ and $\\beta$ with task-balanced gradients. Note that the gradient for training $\\beta$ and $\\gamma$ of the original BN, shown in (4), is biased toward the current task due to the imbalance between $B_{c}$ and $B_{p}$ in the mini-batch. On the other hand, the above task-balanced process makes both $\\beta$ and $\\gamma$ to be trained in a task-balanced way during backpropagation. First, a gradient of $\\mathbf{y}$ is back-propagated toward the BN layer and it can be denoted as: $\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{y}} = (\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})\\in \\mathbb{R}^{B\\times C\\times D}$ . Then, the gradients of each current and task's batch pass the backward operation of $F_{S}^{-1}$ and $F_{A}$ , respectively. As a result, the gradient of $\\mathbf{Y}$ becomes:", + "bbox": [ + 75, + 233, + 470, + 401 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y}} = \\left(F _ {S, g} ^ {- 1} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right); F _ {A, g} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 405, + 468, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in which $\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}}\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}$ . $F_{S,g}^{p - 1}$ and $F_{A,g}$ stands for the backward operation of $F_{S,g}^{-1}$ and $F_{A}$ , respectively. The backward operation of $F_{S,g}^{-1}$ is the reverse-direction-reshape of a given gradient: $F_{S,g}^{-1}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = F_S(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r): \\mathbb{R}^{B_c\\times C\\times D}\\to \\mathbb{R}^{B_c / r\\times C\\cdot r\\times D}$ . In the case of $F_{A}$ , the backward operation becomes $F_{A,g}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = ((\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_1 / r;\\dots ;(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_r / r):\\mathbb{R}^{B_p\\times C\\times D}\\to \\mathbb{R}^{B_p\\times C\\cdot r\\times D}$ , where distributes and expands the input gradient divided by $r$ , for $r$ times. As a result, a gradient of $\\beta$ and $\\gamma$ becomes:", + "bbox": [ + 75, + 436, + 470, + 604 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\frac {\\partial \\mathcal {L}}{\\partial \\gamma} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}} \\odot \\tilde {\\mathbf {H}} _ {b, d}; r\\right) (9) \\\\ \\frac {\\partial \\mathcal {L}}{\\partial \\beta} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}}; r\\right), (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 609, + 468, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in which $F_{P,g}$ denotes the backward operation of $F_{P}$ , which is the sum of gradients over $r$ : $F_{P,g}(\\pmb{g}; r) = \\sum_{i=1}^{r}((\\pmb{g}_i); \\dots; (\\pmb{g}_r)) : \\mathbb{R}^{C \\cdot r} \\to \\mathbb{R}^C$ , and $\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{Y}_{b,d}} \\in \\mathbb{R}^C$ and $\\tilde{\\mathbf{H}}_{b,d} \\in \\mathbb{R}^C$ . Note that the core differences with the gradients of the original BN shown in (4): First, the summed up gradients are configured to be task-balanced. Second, in the case of the gradient of $\\gamma$ , the task-balanced batch $\\tilde{\\mathbf{H}}$ , normalized by the task-balanced mean and variance, is used to get the gradient. As a result, $\\gamma$ and $\\beta$ can be trained in a more task-balanced way, so that they can do their part of BN at test time where the entire task's test data is given jointly.", + "bbox": [ + 75, + 699, + 468, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that both the pseudo code and implementation details of TBBN are proposed in supplementary materials.", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 90, + 705, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and Evaluation. We mainly evaluate our method on the offline CIL settings leveraging CIFAR-100 [19] and ImageNet-100 [10] datasets: for each dataset, we divide 100 classes into 10 disjoint sets, and consider each set to constitute a single task (i.e. $T = 10$ and $m = 10$ ). Following previous work [7,9,24], we evaluate all normalization methods based on four different metrics, such as final accuracy $(A_{f})$ , average accuracy $(A_{a})$ , forgetting measure $(F)$ , and learning accuracy $(A_{l})$ . The detailed explanation for the metrics can be found in the supplementary materials.", + "bbox": [ + 496, + 111, + 893, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. For backbone architectures, we follow the offline CIL setup proposed in [24] using ResNet-32 [13] for CIFAR-100 [19] and ResNet-18 for ImageNet-100 [10]. In addition, we use exemplar memory with size $|\\mathcal{M}| = 2000$ and incrementally update $\\mathcal{M}$ via a class-balanced random sampling strategy after each task. To test our method under various offline CIL algorithms, we consider EEIL [6] and LUCIR [15], for which implementations are available in the benchmark environment provided by [24]. We also run SS-IL [1], POD-Net [12] and AFC [18], which are considered state-of-the-art in offline CIL, using their official code. Finetuning (FT) stands for a naive baseline which only utilizes the exemplar memory without using any explicit methods. For comparison across different normalization approaches, we simply replace all BN layers in the backbone model with one of the following: Instance Normalization (IN) [37], Group Normalization (GN) [40], Switch Normalization (SN) [22], Batch Renormalization (BRN) [16], Continual Normalization (CN) [29], and our proposed TBBN. We use official implementations for each baseline method published by the respective authors. Note that CN and GN require a hyperparameter $G$ that sets the group size during feature-level normalization. For our experiments, we use $G = 16$ when training ResNet-32 on CIFAR-100 and $G = 32$ when training ResNet-18 on ImageNet-100. Further details on experimental settings are in the supplementary material.", + "bbox": [ + 496, + 263, + 893, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Quantitative Results", + "text_level": 1, + "bbox": [ + 500, + 669, + 692, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of normalization layers in offline CIL. Table 1 shows experimental results for FT on 10-task offline CIL setups on CIFAR-100 and ImageNet-100. First, we find that normalization layers previously developed for single task supervised learning (e.g., IN [37], GN [40], SN [22] and BRN [16]) are not effective in offline CIL scenarios compared to BN. Both IN and GN especially show notable performance degradation with respect to all four metrics. Furthermore, CN [29] does not lead to significant improvement, which is in contrast to the performance gain previously demonstrated in online CIL by the original paper. This shows that the benefit of adding the channel-level GN to BN is obscured when naïve BN is exposed to imbalanced minibatches for multiple epochs. On the other hand, we confirm", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20132", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that simply replacing BN with TBBN increases both $A_{f}$ and $A_{a}$ in both datasets without any additional hyperparameters. We find that the performance gain mainly comes from the increased stability as well as plasticity as we see improvements in both $F$ and $A_{l}$ . TBBN especially shows significantly less forgetting, supporting our insight that preventing sample statistics from becoming biased to the current task via task-balanced normalization effectively retains information from past tasks leading to a better accuracy.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b0bfe51498fd21e45ec26c773534827d2bcf30b63aca9a7ebce12086e391d8a7.jpg", + "table_caption": [ + "Table 1. Experimental results for FT with varying normalization layers on CIFAR-100 and ImageNet-100. Bold indicates the best performance in each metric." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
BN35.4153.8843.4878.7939.4059.6048.0287.42
IN31.7246.8447.7279.4433.4553.5950.6984.66
GN31.2644.5344.0175.2728.8347.7949.7979.19
SN36.2953.6442.9179.2039.4559.5548.0487.79
BRN36.0852.5844.3480.4237.4957.7748.1386.57
CN35.0654.4343.8280.6441.9660.0245.3287.28
CN*36.0554.1844.8180.8540.4659.0346.7487.20
TBBN38.4656.1741.9080.3643.2061.6943.6287.82
", + "bbox": [ + 81, + 282, + 465, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Applying TBBN to other CIL baselines. We also confirm that the advantage of TBBN is extended to other CIL methods. We consider the same 10-task offline CIL setup from CIFAR-100 and ImageNet-100, and run a total of six different CIL methods while simply replacing the BN layers in the model with either CN or TBBN.", + "bbox": [ + 75, + 416, + 468, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows the corresponding results. First, the most recently proposed CIL methods, SSIL and AFC, achieve the best performance in terms of final accuracy $A_{f}$ . Especially in ImageNet-100, they surpass all other baselines in both $A_{f}$ and $A_{a}$ , as previously reported in the original papers. Second, replacing BN with CN does not show consistent improvement across datasets and CIL methods. For instance, while EEIL+CN produces a considerable performance gain in ImageNet-100, CN fails to outperform BN when combined with more recent CIL algorithms such as PODNet and AFC. On the other hand, our TBBN consistently improves performance in $A_{f}$ and $A_{a}$ except when applied on PODNet in CIFAR-100. Following the observation in the previous experiment, we again confirm that the performance gain of TBBN is mostly due to reduction in $F$ (i.e. enhanced stability) while maintaining or increasing $A_{l}$ (i.e. enhanced plasticity). In all, applying TBBN to the SOTA baselines achieves new SOTA performance in both datasets. We plotted a graph of these experiments in the supplementary materials, and we could confirm that TBBN enhances the average accuracy at every step of training compared to BN, while CN shows performance loss for some PODNet and AFC.", + "bbox": [ + 75, + 507, + 472, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Applying TBBN to other architectures. To check the applicability of TBBN to other architectures, we selected four CNN-based architectures (e.g., ResNet-34 [13], ShuffleNet-V2 [43], MobileNet-V2 [31], and MnasNet (x0.5) [35])", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b8ff7bfe00cf714a60b0b6c337b1f5a478889b4b6eba97ce0c06a4866f1d8ad0.jpg", + "table_caption": [ + "Table 2. Experimental results for various representative offline CIL methods. Bold indicates the best performance in each metric." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
FT+BN35.4153.8843.3878.7939.4059.6048.0287.42
+CN35.0654.4343.8280.6441.9660.0245.3287.28
+TBBN38.4656.1741.9080.3643.2061.6943.6287.82
EEIL+BN39.8255.2539.4079.2240.0661.1547.7887.84
+CN39.9855.0939.3179.2942.4861.4344.4486.92
+TBBN41.9357.5337.8079.9345.1863.4842.6687.84
LUCIR+BN38.0654.2032.3570.4142.2663.8241.6883.94
+CN38.0755.6033.7871.8540.4461.4442.0483.48
+TBBN41.4556.1329.2370.6843.7264.3640.1883.90
PODNet+BN38.1052.9514.7052.5849.0565.4122.4069.99
+CN34.8050.2615.6950.5246.2062.9123.6668.50
+TBBN37.9052.9813.9051.7849.3065.7021.8569.76
SSL+BN41.3453.0015.6456.0249.5665.7921.2069.94
+CN40.7452.3814.6054.4450.5864.8118.5665.04
+TBBN43.8054.2815.1259.3751.3066.5119.5870.64
AFC+BN39.9053.9333.1773.1052.5067.5319.7072.22
+CN37.5051.1633.4070.9448.0065.2120.1070.68
+TBBN41.3057.3132.8973.5754.0068.6819.0073.22
", + "bbox": [ + 503, + 123, + 888, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which contain the BN layer as a default, and conducted experiments by replacing BN with TBBN in the 10 tasks scenario using the ImageNet-100 dataset. Table 3 demonstrates that our TBBN can be successfully applied to various types of architecture, increasing both $\\mathrm{A}_f$ and $\\mathrm{A}_a$ concurrently.", + "bbox": [ + 496, + 354, + 893, + 431 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/636e5e5944293361d1bbc71a72e131495577408ca8db9c67d1e99f575fabbf9c.jpg", + "table_caption": [ + "Table 3. Experimental results with varying backbone architectures on ImageNet-100. Bold indicates the best performance." + ], + "table_footnote": [], + "table_body": "
MethodResNet-34ShuffleNet-V2MobileNet-v2MnasNet (x0.5)
Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)
FT+BN41.3862.0034.7455.3738.8657.4336.2454.96
+TBBN46.7264.7635.8258.1742.6660.4140.9457.09
SSIL+BN51.1865.2743.8659.6947.7262.2545.1059.81
+TBBN52.3066.3644.7260.0748.6263.3747.0660.24
", + "bbox": [ + 503, + 472, + 888, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on dissimilar tasks. Several benchmark datasets (e.g., CIFAR-10/-100 and ImageNet dataset) have been used to evaluate a CIL method. The CIL scenario made from random class orderings of these datasets has small domain shifts due to high similarity between tasks [24]. In this regard, we believe that the CIL scenario using CIFAR-100 and ImageNet-100 datasets is not the best setting to check whether the proposed normalization layer is suitable for the CIL. Therefore, we design the CIL scenario, which has large domain shifts, with five distinct datasets such as CIFAR-10 [19], SVHN [27], STL-10 [8], MNIST [11] and Fashion-MNIST [41]. We divide 10 classes of each dataset into 2 tasks and construct the CIL scenario consisting of 10 tasks (2 tasks $\\times$ 5 datasets). Note that task ordering is randomly shuffled by random seed and more details for experimental settings are proposed in the supplementary materials.", + "bbox": [ + 496, + 551, + 893, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 4, we observe that applying CN is sometimes harmful and only achieves minor improvement for FT and LUCIR. On the other hand, we again confirm that TBBN constantly makes enhancement of $A_{f}$ and $A_{a}$ by diminishing $F$ but well maintaining $A_{l}$ , for all methods. This result underscores the robustness of our TBBN even for the difficult CIL scenario consisting of dissimilar tasks.", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20133", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bf011d889dce11a49df29c1470ba7c7159eb629596f07dd7c192ea8000306525.jpg", + "table_caption": [ + "Table 4. Experimental results with dissimilar tasks using ResNet-18. Bold indicates the best performance in each metric." + ], + "table_footnote": [], + "table_body": "
MethodAf(↑)Aa(↑)F(↓)Al(↑)
FT+BN59.6065.8531.4891.08
+CN61.4171.0029.9091.40
+TBBN63.4271.3228.0591.47
EEIL+BN62.0472.2829.4691.50
+CN61.7372.4029.2791.00
+TBBN64.8872.8026.6791.55
LUCIR+BN62.4272.9128.0990.35
+CN62.9972.8126.7089.49
+TBBN63.6473.7226.7390.23
SSL+BN66.1570.6210.1372.59
+CN65.6470.569.1669.66
+TBBN67.0071.779.7472.86
", + "bbox": [ + 135, + 109, + 406, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 76, + 287, + 269, + 304 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Reduction in biased predictions. For a more detailed analysis for the effect of TBBN, we investigated a type of misclassification, by following the experiment proposed in [3], and the analysis results for finetuning with the ImageNet-100 dataset (10-tasks) are reported in Figure 4. This figure presents the number of four types of misclassification. For example, $\\mathrm{C} \\rightarrow \\mathrm{P}$ stands for the number of misclassification current task's data to another class in previous tasks ( $t = 1, \\dots, 9$ ). Among four types, $\\mathrm{P} \\rightarrow \\mathrm{C}$ , which is the number of misclassification of the previous task's data toward the current task's class, is called as biased prediction, knowing as the major cause of degrading performance in CIL [1,39]. As already reported in previous works [3,39], $\\mathrm{FT} + \\mathrm{BN}$ seriously suffers from the biased prediction, resulting in the largest number of total misclassification. In the case of both CN variants and TBBN, we confirm that the gain of reducing the total number of misclassifications comes from diminishing the number of biased predictions ( $\\mathrm{P} \\rightarrow \\mathrm{C}$ ), Especially, our TBBN significantly alleviates the biased prediction than CN variants. As a result, $\\mathrm{FT} + \\mathrm{TBBN}$ achieves the lowest number of total misclassifications despite the increase of $\\mathrm{P} \\rightarrow \\mathrm{P}$ caused by the reduced biased prediction.", + "bbox": [ + 75, + 306, + 470, + 638 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7eca4c5bf37d1876cea82c8de8be5c02af830a61783b6099233e9014bc9a5cf0.jpg", + "image_caption": [ + "Figure 4. Analysis for four types of misclassification errors ( $y$ -axis) after training the model until the final task ( $t = 10$ )." + ], + "image_footnote": [], + "bbox": [ + 132, + 647, + 411, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation studies. Table 5 presents ablation study for TBBN using the CIFAR-100 dataset (10 tasks). First, both Case 1 and Case 2 represent the ablation study for task-balanced mean and variance. We confirm that only calculating task", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "balanced running mean $\\mu$ and variance $\\sigma^2$ in (5) for test phase (Case 1) or using a task-balanced running mean $\\tilde{\\sigma}$ and variance $\\tilde{\\sigma}^2$ for training phase (Case 2) affect final performance negatively, due to mismatch of values $(\\mu, \\sigma^2)$ for normalization in training and test phases. Case 3 shows the experimental result where calculating task-balanced mean and variance is only applied. However, as we already confirmed in Figure 2 of the Section 4.1, only considering task-balanced mean and variance cannot make a difference in performance with the original BN. The opposite case (Case 4) where $\\gamma$ and $\\beta$ are trained in a task-balanced manner also shows a similar tendency, demonstrating the performance enhancement by TBBN can be obtained only when the proposed components are used together.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additionally, we compare GPU memory cost, training time and inference time of each case. Because of both reshape and repeat operations consisting of TBBN, TBBN requires maximum $\\times 1.6$ of GPU memory and takes more $\\times 1.3$ of training time than the original BN. However, note that there is no additional cost at test time because TBBN works to be identical to the original BN.", + "bbox": [ + 496, + 304, + 893, + 411 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9b2c4d5bc96a70f3e868c26471fc84e93758d0c06ea0de813fd8daf981741fb0.jpg", + "table_caption": [ + "Table 5. Ablation study using CIFAR-100 with ResNet-32." + ], + "table_footnote": [], + "table_body": "
MethodTask-balanced μ and σ2? TrainTask-balanced γ and β? TestAf(↑)Aa(↑)Peak MemoryTrain Time (total)Test Time (per batch)
TBBN✓✓38.4656.17
Case 1X✓29.7846.992525MiB (×1.6)6.0h (×1.3)0.6s (×1.0)
Case 2✓X0.939.69
Case 3✓✓35.4553.15
Case 4XX36.2153.25
BNXX35.7153.881545MiB4.6h0.6s
", + "bbox": [ + 503, + 438, + 890, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Concluding Remarks", + "text_level": 1, + "bbox": [ + 500, + 553, + 702, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a simple but effective method, called Task-Balance Batch Normalization, for exemplar-based CIL. Starting from an analysis of the problem of the original BN, namely, the biased mean and variance calculation toward the current task, we devise a novel method to calculate the task-balanced mean and variance for normalization. Furthermore, we propose a method for the task-balanced training of parameters for affine transformation. From extensive experiments with CIFAR-100, ImageNet-100 and dissimilar tasks, we demonstrate that our TBBN can be easily applied to various existing CIL methods, further improving their performance.", + "bbox": [ + 496, + 580, + 893, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 767, + 679, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partly done while Sungmin Cha did a research internship at Advanced ML Lab, LG AI Research. The work was also supported in part by NRF grant [NRF-2021R1A2C2007884], IITP grant [No.2021-0-01343, No.2021-0-02068, No.2022-0-00113, No.2022-0-00959] funded by the Korean government (MSIT), and SNU-LG AI Research Center.", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20134", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 13208-13217, 2020." + ], + "bbox": [ + 501, + 92, + 893, + 229 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20136", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Rebalancing Batch Normalization for Exemplar-Based Class-Incremental Learning/5041066b-589d-4c40-92f0-14b7543c2197_model.json b/2023/Rebalancing Batch Normalization for Exemplar-Based Class-Incremental Learning/5041066b-589d-4c40-92f0-14b7543c2197_model.json new file mode 100644 index 0000000000000000000000000000000000000000..82747a6d3e9d2ba143c651446b0cad29ffb28fb2 --- /dev/null +++ b/2023/Rebalancing Batch Normalization for Exemplar-Based Class-Incremental Learning/5041066b-589d-4c40-92f0-14b7543c2197_model.json @@ -0,0 +1,1903 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.258, + 0.131, + 0.717, + 0.177 + ], + "angle": 0, + "content": "Rebalancing Batch Normalization for Exemplar-based Class-Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.202, + 0.899, + 0.223 + ], + "angle": 0, + "content": "Sungmin Cha\\(^{1}\\), Sungjun Cho\\(^{2}\\), Dasol Hwang\\(^{2}\\), Sunwon Hong\\(^{1}\\), Moontae Lee\\(^{2,3}\\), and Taesup Moon\\(^{1,4,5*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.224, + 0.882, + 0.298 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of ECE, Seoul National University \\(^{2}\\)LG AI Research \\(^{3}\\)University of Illinois Chicago \\(^{4}\\)ASRI / INMC / IPAI / AIIS, Seoul National University \\(^{5}\\)SNU-LG AI Research Center sungmin.cha@snu.ac.kr, {sungjun.cho, dasol.hwang}@lgresearch.ai, zghdtnsz96@snu.ac.kr, moontae.lee@lgresearch.ai, tsmoon@snu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.332, + 0.314, + 0.348 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.363, + 0.474, + 0.817 + ], + "angle": 0, + "content": "Batch Normalization (BN) and its variants has been extensively studied for neural nets in various computer vision tasks, but relatively little work has been dedicated to studying the effect of BN in continual learning. To that end, we develop a new update patch for BN, particularly tailored for the exemplar-based class-incremental learning (CIL). The main issue of BN in CIL is the imbalance of training data between current and past tasks in a mini-batch, which makes the empirical mean and variance as well as the learnable affine transformation parameters of BN heavily biased toward the current task — contributing to the forgetting of past tasks. While one of the recent BN variants has been developed for \"online\" CIL, in which the training is done with a single epoch, we show that their method does not necessarily bring gains for \"offline\" CIL, in which a model is trained with multiple epochs on the imbalanced training data. The main reason for the ineffectiveness of their method lies in not fully addressing the data imbalance issue, especially in computing the gradients for learning the affine transformation parameters of BN. Accordingly, our new hyperparameter-free variant, dubbed as Task-Balanced BN (TBBN), is proposed to more correctly resolve the imbalance issue by making a horizontally-concatenated task-balanced batch using both reshape and repeat operations during training. Based on our experiments on class incremental learning of CIFAR-100, ImageNet-100, and five dissimilar task datasets, we demonstrate that our TBBN, which works exactly the same as the vanilla BN in the inference time, is easily applicable to most existing exemplar-based offline CIL algorithms and consistently outperforms other BN variants." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.825, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.47, + 0.881 + ], + "angle": 0, + "content": "In recent years, continual learning (CL) has been actively studied to efficiently learn a neural network on sequentially" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.333, + 0.896, + 0.455 + ], + "angle": 0, + "content": "arriving datasets while eliminating the process of re-training from scratch at each arrival of a new dataset [9]. However, since the model is typically trained on a dataset that is heavily skewed toward the current task at each step, the resulting neural network often suffers from suboptimal trade-off between stability and plasticity [25] during CL. To overcome this issue, various studies have been focused on addressing the so-called catastrophic forgetting phenomenon [9, 28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.897, + 0.716 + ], + "angle": 0, + "content": "Among different CL settings, the class-incremental learning (CIL) setting where the classifier needs to learn previously unseen classes at each incremental step has recently drawn attention due to its practicality [1, 3, 6, 12, 15, 26, 39, 42, 44]. Most state-of-the-art CIL algorithms maintain a small exemplar memory to store a subset of previously used training data and combine it with the current task dataset to mitigate the forgetting of past knowledge. A key issue of exemplar-based CIL is that the model prediction becomes heavily biased towards more recently learned classes, due to the imbalance between the training data from the current task (that are abundantly available) and past tasks (with limited access through exemplar memory). In response, recently proposed solutions to biased predictions include bias correction [39], unified classifier [15], and separated softmax [1], which greatly improved the overall accuracy of CIL methods across all classes learned so far." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Despite such progress, relatively less focus has been made on backbone architectures under CIL on computer vision tasks. Specifically, the popular CNN-based models (e.g., ResNet [13]) are mainly used as feature extractors, and those models are equipped with Batch Normalization (BN) [17] by default. However, since BN is designed for single-task training on CNNs, applying BN directly to exemplar-based CIL results in statistics biased toward the current task due to the imbalance between current and past tasks' data in a mini-batch. Recently, [29] pointed out this issue in CIL, dubbed as cross-task normalization effect, and proposed a new normalization scheme called Continual Normalization" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.401, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author (E-mail: tsmoon@snu.ac.kr)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20127" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "(CN), which applies Group Normalization (GN) [40] across the channel dimension before running BN across the batch dimension. Therefore, the difference in feature distributions among tasks is essentially removed by GN, and the following BN computes task-balanced mean and variance statistics which is shown to outperform vanilla BN on online CIL settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.474, + 0.591 + ], + "angle": 0, + "content": "In this paper, we argue that CN only partially resolves the bias issue in exemplar-based CIL. Specifically, we find that the gradients on the affine transformation parameters remain biased towards the current task when using CN. As a result, it leads to inconsistent performance gains in the offline CIL setting, which is considered more practical than online CIL. To this end, we propose a simple yet novel hyperparameter-free normalization layer, dubbed as Task-Balanced Batch Normalization (TBBN), which effectively resolves the bias issue. Our method employs adaptive reshape and repeat operations on the mini-batch feature map during training in order to compute task-balanced normalization statistics and gradients for learning the affine transformation parameters. Our method does not require any hyperparameter as the size-inputs for reshape and repeat operations are determined adaptively. Furthermore, the application of TBBN during testing is identical to vanilla BN, requiring no change on the backbone architecture. Through extensive offline CIL experiments on CIFAR-100, ImageNet-100, and five dissimilar task datasets, we show that a simple replacement of BN layers in the backbone CNN model with TBBN benefits most state-of-the-art exemplar-based CIL algorithms towards an additional boost in performance. Our analysis shows that the gain of TBBN is consistent across various backbone architectures and datasets, suggesting its potential to become a correct choice for exemplar-based offline CIL algorithms." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.604, + 0.22, + 0.62 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Exemplar-based CIL. Among various work in offline CIL, iCaRL [30] is the first to propose an exemplar-based method via utilization of nearest-mean-of-exemplars classification and representation learning. EEIL [6] next devised a distillation-based CIL method with both balanced fin-tuning and representative memory updating. BiC [39] focused on the biased prediction aspect due to data imbalance in CIL and proposed a novel yet simple idea to attach an additional layer that corrects biased predictions. Inspired by LWF [21], LUCIR [15] developed a method that overcomes catastrophic forgetting via a more sophisticated cosine normalization-based loss function. PODNet [12] proposed another distillation-based method that focuses on spatial-based loss to reduce representation forgetting. Most recently, two state-of-the-art knowledge distillation-based CIL methods have been proposed. First, SS-IL [1] demonstrated that a pure softmax mainly causes biased predictions in CIL, leading to the Separated Softmax layer that achieved significant" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.137 + ], + "angle": 0, + "content": "performance gains. Second, AFC [18] devised a novel regularization for knowledge distillation to minimize the changes of important features when learning new tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.895, + 0.199 + ], + "angle": 0, + "content": "On the other hand, online CIL also has attracted attention [2,33], but their performance is significantly lower in the benchmark (e.g., CIFAR-100) than offline CIL counterparts, as reported in the survey paper [23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.897, + 0.368 + ], + "angle": 0, + "content": "Normalization layer. One initial motivation for devising Batch Normalization (BN) [17] was to address internal covariate shift of a neural net. However, the belief in internal covariate shift was broken by follow-up studies, and the benefits from BN in terms of training perspective were analyzed in various directions [4, 32]. Thereafter, several normalization layers devised for various computer vision tasks have been proposed, each with their respective advantages [14, 16, 22, 37, 40], and for more diverse tasks, such as meta-learning [5], domain adaptation [38], task-incremental learning [20], and online CL [29]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.64, + 0.4 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Notation. We assume the setting of offline CIL as proposed in [1]; namely, a dataset \\(\\mathcal{D}_t\\) for each task \\(t\\) arrives incrementally, and we use \\(T\\) to denote the total number of tasks. Each \\(\\mathcal{D}_t\\) consists of pairs of an input image \\(\\boldsymbol{x}_t\\) and its target label \\(y_t\\). We assume that each incrementally added task introduces \\(m\\) new classes that the model has never observed previously, and hence the total number of classes observed until task \\(t\\) equals \\(C_t = m \\cdot t\\). Therefore, the target label in each task is labeled as \\(y_t \\in \\{C_{t-1} + 1, \\dots, C_t\\} \\triangleq \\mathcal{C}_t\\). To save exemplars from previous tasks, we use exemplar memory denoted by \\(\\mathcal{M}\\). While \\(\\mathcal{M}\\) is updated via a sampling algorithm after training on each task, the memory size is set to not exceed \\(|\\mathcal{M}|\\) over the entire course of tasks. In particular, exemplar memory \\(\\mathcal{M}_{t-1}\\) maintains \\(\\left\\lfloor \\frac{|\\mathcal{M}|}{C_{t-1}} \\right\\rfloor\\) images per each past class and is used for training task \\(t\\). To merge instances from current as well as previous tasks, we consider a training mini-batch size of \\(B = B_c + B_p\\), where \\(B_c\\) and \\(B_p\\) denote the number of data samples from \\(\\mathcal{D}_t\\) and \\(\\mathcal{M}_{t-1}\\), respectively. Without loss of generality, we assume that each mini-batch \\((\\boldsymbol{x}^B, y^B) \\sim (\\mathcal{D}_t \\cup \\mathcal{M}_{t-1})\\) is a concatenation of \\(B_c\\) samples from \\(\\mathcal{D}_t\\) with \\(B_p\\) samples from \\(\\mathcal{M}_{t-1}\\): \\(\\boldsymbol{x}^B = [\\boldsymbol{x}_1; \\dots; \\boldsymbol{x}_{B_c}; \\boldsymbol{x}_{B_c+1}; \\dots; \\boldsymbol{x}_B]\\) and \\(y^B = [y_1; \\dots; y_{B_c}; y_{B_c+1}; \\dots; y_B]\\) with \\(\\{(x_i, y_i)\\}_{i=1}^{B_c} \\subset \\mathcal{D}_t\\) and \\(\\{(x_i, y_i)\\}_{i=B_c+1}^{B} \\subset \\mathcal{M}_{t-1}\\). Note that \\(B_c\\) is greater than \\(B_p\\) in typical CIL settings, and it is this imbalance that is generally known to cause predictions biased towards the current task [1, 3, 39]. Therefore, we set the sampling ratio between \\(B_c\\) and \\(B_p\\) as \\(B_c: B_p = 3:1\\) in our experiments. Lastly, we use \\(\\boldsymbol{h} \\in \\mathbb{R}^{B \\times C \\times D}\\) to denote the input feature map for an intermediate BN layer given \\(\\boldsymbol{x}^B\\) as input. Here, \\(C\\) and \\(D\\) denote the number of channels and feature dimension, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20128" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.182 + ], + "angle": 0, + "content": "Batch Normalization. Due to its powerful practicality and efficiency, Batch Normalization (BN) [17] has been the go-to normalization layer across various state-of-the-art neural network architectures [13, 34, 36]. During training, BN calculates the empirical mean \\(\\hat{\\mu} \\in \\mathbb{R}^C\\) and variance \\(\\hat{\\sigma}^2 \\in \\mathbb{R}^C\\) of the given mini-batch as" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.188, + 0.47, + 0.242 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mu} _ {c} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\boldsymbol {h} _ {b, c, d}, \\hat {\\sigma} _ {c} ^ {2} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\left(\\boldsymbol {h} _ {b, c, d} - \\hat {\\mu} _ {c}\\right) ^ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.243, + 0.473, + 0.304 + ], + "angle": 0, + "content": "The feature map \\( \\pmb{h} \\) is then normalized to have zero-mean unit-variance using \\( \\hat{\\mu} \\) and \\( \\hat{\\sigma}^2 \\) to obtain \\( \\hat{\\pmb{h}} \\in \\mathbb{R}^{B \\times C \\times D} \\). The normalized feature \\( \\hat{\\pmb{h}} \\) is lastly affine-transformed with a trainable scale and shift parameters \\( \\gamma, \\beta \\in \\mathbb{R}^C \\) to \\( \\pmb{y} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.313, + 0.47, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {h}} _ {b} = \\frac {\\boldsymbol {h} _ {b} - \\hat {\\mu} \\cdot \\mathbb {1} ^ {\\intercal}}{\\sqrt {\\hat {\\sigma} ^ {2} \\cdot \\mathbb {1} ^ {\\intercal} + \\epsilon \\cdot \\mathbb {1} ^ {\\intercal}}} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.348, + 0.47, + 0.366 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} _ {b} = \\gamma \\cdot \\mathbb {1} ^ {\\mathrm {T}} \\odot \\hat {\\boldsymbol {h}} _ {b} + \\beta \\cdot \\mathbb {1} ^ {\\mathrm {T}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.473, + 0.483 + ], + "angle": 0, + "content": "in which \\(\\mathbb{1} \\in \\mathbb{R}^D\\) is the all-1 vector, \\(\\odot\\) denotes the element-wise multiplication, and \\(b\\) is the data index within the minibatch. Note the division and \\(\\sqrt{\\cdot}\\) in (2) are also done in an element-wise sense. The \\(\\epsilon\\) term is a small value added for numerical stability, which we set as \\(\\epsilon = 10^{-5}\\) in the experiments. It is worth noting that \\(\\gamma\\) and \\(\\beta\\) are trained by computing the gradients" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.493, + 0.47, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial \\gamma_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\odot \\hat {\\boldsymbol {h}} _ {b, c, d}, \\quad \\frac {\\partial \\mathcal {L}}{\\partial \\beta_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.547, + 0.47, + 0.593 + ], + "angle": 0, + "content": "under a loss function \\(\\mathcal{L}\\). For the normalization in the test phase, running \\(\\mu\\) and \\(\\sigma^2\\) are updated incrementally at each \\(i\\)-th training iteration via exponential moving average:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.598, + 0.389, + 0.616 + ], + "angle": 0, + "content": "\\[\n\\mu_ {(i)} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\mu} _ {(i)} + (1 - \\alpha) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\mu_ {(i - 1)}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.618, + 0.469, + 0.663 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {(i)} ^ {2} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\sigma} _ {(i)} ^ {2} + \\left((1 - \\alpha) \\frac {V - 1}{V}\\right) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\sigma_ {(i - 1)} ^ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.663, + 0.47, + 0.694 + ], + "angle": 0, + "content": "in which \\( V = B \\cdot D \\) represents the vessel's correction, and \\( \\alpha \\) is the momentum hyperparameter generally set as 0.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.707, + 0.217, + 0.723 + ], + "angle": 0, + "content": "4. Main Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.731, + 0.2, + 0.745 + ], + "angle": 0, + "content": "4.1. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "While exemplar memory is essential for achieving state-of-the-art performance in offline CIL [24], most methods use well-known backbone classification models (e.g., ResNet-18 [13]) with vanilla BN layers without much scrutiny over the issue of data-imbalance between current and previous tasks. One notable exception is Continual Normalization (CN) [29], but CN has only shown promise in online CIL settings where the data-imbalance causes relatively less of an impact than in offline CIL due to the single epoch learning. It is not clear whether CN is also effective in offline CIL, where" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.227 + ], + "angle": 0, + "content": "the imbalanced mini-batches are used for multiple epochs. We conjecture that while CN performs task-balancing by normalizing each channel (or groups of channels) along the spatial dimension, this comes at a cost in discriminative power as it normalizes features from all tasks equally without any separation between tasks. In a later section, we find through experimentation that this limitation is especially detrimental in offline CIL, as CN leads to negligible gain over BN or even worse performance in some cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.438 + ], + "angle": 0, + "content": "For a concrete motivation, we consider a toy example to reflect upon the necessity of devising a correct BN mechanism for the exemplar memory-based CIL. Consider a synthetic input feature distribution for an intermediate BN layer shown in Figure 1. Figure 1(a) visualizes 2-D data samples generated from a mixture of four different Gaussian distributions, each representing the feature distribution for each given task.\\(^{1}\\) In a joint training setting, the mini-batch samples are uniformly sampled across four tasks, and thus the empirical mean and variance obtained from BN would approach the true population mean and variance. Such mean and variance will then successfully standardize the samples in a mini-batch during both training and testing phases via the procedure given in (2) and (3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.897, + 0.8 + ], + "angle": 0, + "content": "In an exemplar memory-based CIL setting, however, there is a severe imbalance among samples in the training minibatch, since the majority of the samples comes from the current task (Task 4) as shown in Figure 1(b). In this case, the mean and variance calculated by the BN layer is clearly biased towards those of the current task, failing to match the true statistics at test time. In other words, using the biased mean and variance obtained during training to normalize test samples leads the samples to deviate from a standardized distribution. It is evident that such mismatch between the train and test sample distributions can cause performance deterioration since the trainable parameters in BN are obtained from normalized training samples. An obvious remedy would be to obtain the task-balanced empirical mean and variance during training, and use them in the BN layer to normalize the test samples. Figure 1(c) and 1(d) highlight the difference between the test normalization done by CN and our TBBN, respectively, which computes the empirical mean and variance from the mini-batch in Figure 1(b). Note that while both successfully normalize test samples in a task-balanced way, CN tends to lose the discriminative structure among the tasks due to the intermediate GN step. In constraint, our TBBN, as will be described in details below, normalizes the test data features while maintaining the discriminative structure." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.801, + 0.895, + 0.832 + ], + "angle": 0, + "content": "In addition to the mismatch during test time, a naive application of BN on the biased mini-batch samples can also" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.839, + 0.895, + 0.901 + ], + "angle": 0, + "content": "1In fact, we generated 20 dimensional Gaussian vectors, which is generated by concatenating i.i.d. 2-D Gaussians 10 times, and only the first two dimensions are shown in the figures. The normalization by CN and TBBN shown in Figure 1(c)(d) are done by obtaining the statistics from the entire 20 dimensions (which exemplifies the channel dimension in a feature map)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20129" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.096, + 0.29, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.236, + 0.285, + 0.248 + ], + "angle": 0, + "content": "(a) True population distribution" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.096, + 0.485, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.236, + 0.481, + 0.248 + ], + "angle": 0, + "content": "(b) Biased train data during CIL" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.097, + 0.672, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.236, + 0.671, + 0.248 + ], + "angle": 0, + "content": "(c) Test data normalized via CN" + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.097, + 0.859, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.236, + 0.863, + 0.248 + ], + "angle": 0, + "content": "(d) Test data normalized via TBBN" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.894, + 0.308 + ], + "angle": 0, + "content": "Figure 1. (a) 2-D visualizations on a mixture of four Gaussian distributions, each representing a feature map distribution of each task. (b) Imbalanced training data in exemplar-based CIL while learning Task 4, deviating from true test distribution. (c) Test set normalization result of CN that computes normalization statistics from data in (b). (d) Test set normalization result of our proposed TBBN that computes normalization statistics from data in (b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.473, + 0.528 + ], + "angle": 0, + "content": "cause an issue during training. That is, when training for a current task (e.g., Task 4 in Figure 1) is finished, the empirical mean and variance obtained by a BN layer would be heavily biased towards the most recent task. When a new task arrives (say, Task 5), since only a small number of samples from Task 4 is saved in the exemplar memory, the new empirical mean and variance will now become biased towards Task 5, drifting away from the previous statistics updated via the exponential moving average in (5). This mismatch during training can also significantly alter the learned representations of the past task samples in the exemplar memory after normalization. Therefore, this necessitates re-training of subsequent layers, unintentionally causing forgetting of previously learned representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.902 + ], + "angle": 0, + "content": "With regards to the two aforementioned issues, we argue that it is crucial to calculate the task-balanced mean and variance for BN layers in exemplar memory-based CIL. While a similar observation has also been made in the recent work [29], we go one step further and note that the affine transformation parameters of BN (i.e. \\(\\gamma\\) and \\(\\beta\\) in (3)) should also be learned in a task-balanced manner. For a demonstration purpose, we train a ResNet-18 model with vanilla BN and exemplar memory of size \\(|\\mathcal{M}| = 2000\\) on ImageNet-100 split to 10 tasks with 10 classes per task. We test four different CIL procedures including two oracle-based approaches that can access the entire training set during test time to exhibit the necessity of task-balanced statistics and affine-transformations. In Figure 2, JOINT denotes the algorithm that jointly trains the model on all tasks at once, providing an upper bound in average accuracy. On the other hand, FT is the fine-tuning baseline that simply fine-tunes the model on samples from the current task and exemplar memory for each task. Note that FT performs poorly on previous tasks except for the final task, clearly reflecting the issue of biased predictions. UPDATE \\((\\mu, \\sigma^2)\\) is an oracle scheme that freezes all trainable parameters of the trained FT model, and only recomputes the mean and variance of all BN layers using the entire dataset such that they match the task-balanced" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.895, + 0.378 + ], + "angle": 0, + "content": "population statistics. Finally, UPDATE \\((\\mu, \\sigma^2)\\) AND \\((\\gamma, \\beta)\\) denotes another oracle scheme that also re-trains the \\((\\gamma, \\beta)\\) parameters for all BN layers on the entire dataset, in addition to recomputing the \\((\\mu, \\sigma^2)\\) statistics." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.383, + 0.85, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.653 + ], + "angle": 0, + "content": "Figure 2. Individual task and average accuracies on ImageNet-100 split into 10 tasks for CIL. \\( y \\)-axis shows the accuracy for each task and the average accuracy across all tasks after full training. Recomputing the affine-transformation parameters \\( (\\gamma, \\beta) \\) as well as empirical statistics \\( (\\mu, \\sigma^2) \\) based on the full dataset leads to significant boost in performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Figure 2 displays the classification accuracy of four methods on every 2nd task and the average accuracy across all tasks, all measured after training up to the final task. The slight drop in performance of UPDATE \\((\\mu, \\sigma^2)\\) compared to FT shows that only obtaining the task-balanced \\((\\mu, \\sigma^2)\\) is not sufficient due to mismatch between the updated \\((\\mu, \\sigma^2)\\) and the frozen \\((\\gamma, \\beta)\\). In contrast, when affine-transformation parameters are also recomputed with task-balanced data, we observe a significant boost in average accuracy. This is particularly interesting as the affine-transformation parameters account for less than \\(1\\%\\) of the entire model parameters, and simply making them task-balanced along with the empirical \\((\\mu, \\sigma^2)\\) statistics in BN layers can bring a significant performance boost under a simple FT baseline. Inspired by this example, we develop our Task-Balanced Batch Normalization (TBBN) layer in the next section." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20130" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.092, + 0.852, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 3. Illustration of the forward (blue arrows) and backward (red arrows) propagations of TBBN. By applying both reshape and repeat operations to a given input of BN layer, TBBN induces that task-balanced calculation and training of \\((\\mu, \\sigma^2)\\) and \\((\\gamma, \\beta)\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.309, + 0.457, + 0.325 + ], + "angle": 0, + "content": "4.2. Task-Balanced Batch Normalization (TBBN)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.471, + 0.388 + ], + "angle": 0, + "content": "To solve the problem of BN in the exemplar-based CIL, we propose Task-Balanced Batch Normalization (TBBN) consisting of two components: 1) Task-balanced \\(\\mu\\) and \\(\\sigma^2\\) calculation and 2) Task-balanced training of \\(\\gamma\\) and \\(\\beta\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.474, + 0.635 + ], + "angle": 0, + "content": "Task-balanced \\(\\mu\\) and \\(\\sigma^2\\) calculation. As discussed in the previous section, the class imbalance between the current and previous data biases the mean and variance toward the current task. Instead, we propose a task-balanced algorithm that better computes the empirical mean and variance in the current batch. As shown in Figure 3, we design the two different tensor operations: reshape and repeat, applying them to the current and previous parts, respectively. We determine the number of repeat/reshape operations \\(r\\) by the following (6). It determines the value of \\(r\\), which is used to balance the number of batches sampled from the exemplar memory \\((\\frac{B_p}{t - 1})\\) and the number of batches of the current task \\((\\frac{B_c}{r})\\) after reshaping with \\(r\\), so that the ratio between them becomes 1:1. Note that \\(r\\) is a hyperparameter that need not be externally tuned, but that our method provides a task-adaptive guidance for automatically selecting \\(r\\):" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.643, + 0.47, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\frac {B _ {c}}{r} = \\frac {B _ {p}}{t - 1}, \\text {h e n c e ,} r = \\frac {B _ {c}}{B _ {p}} \\cdot (t - 1), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.421, + 0.699 + ], + "angle": 0, + "content": "in which \\( t = 2, \\dots, T \\), and \\( r \\) is set to 1 when \\( t = 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.474, + 0.902 + ], + "angle": 0, + "content": "Let \\( h_{B_c} \\) be the input feature map of a BN layer for the current task \\( t \\). After applying the reshape operation \\( \\mathbf{H}_{B_c} = F_S(h_{B_c}; r) : \\mathbb{R}^{B_c \\times C \\times D} \\to \\mathbb{R}^{B_c / r \\times C \\cdot r \\times D} \\) with \\( r \\), we divide \\( h_{B_c} \\) into \\( r \\) splits, where each split has \\( \\frac{B_c}{r} \\) numbers of data from the current task. Similarly, let \\( h_{B_p} \\) denote the data from the previous tasks. As \\( h_{B_p} \\) consists of the data uniformly sampled from task 1 to \\( t - 1 \\), \\( \\frac{B_p}{t - 1} \\) numbers of data belongs to \\( h_{B_p} \\) for each previous task in expectation. The key insight is that we can make every split balanced by repeating \\( h_{B_p} \\) by \\( r \\) times if the task ratios \\( \\frac{B_c}{r} \\) and \\( \\frac{B_p}{t - 1} \\) become equivalent. So that, we repeat \\( h_{B_p} \\) for \\( r \\) times by applying a tensor repeat function \\( \\mathbf{H}_{B_p} = F_P(h_{B_p}; r) : \\mathbb{R}^{B_p \\times C \\times D} \\to \\mathbb{R}^{B_p \\times C \\cdot r \\times D} \\). Then, we concatenate both tensors along batch" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.895, + 0.415 + ], + "angle": 0, + "content": "axis, \\(\\mathbf{H} = (\\mathbf{H}_{B_c};\\mathbf{H}_{B_p})\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}\\), and calculate a task-balanced empirical mean \\(\\tilde{\\mu}\\in \\mathbb{R}^{C\\cdot r}\\) and variance \\(\\tilde{\\sigma}^2\\in \\mathbb{R}^{C\\cdot r}\\) from a horizontally-concatenated task-balanced batch \\(\\mathbf{H}\\). To update running mean \\(\\mu \\in \\mathbb{R}^{C}\\) and variance \\(\\sigma^2\\in \\mathbb{R}^C\\) for test phase, we average \\(\\tilde{\\mu}\\) and \\(\\tilde{\\sigma}^2\\) over \\(r\\) splits, later applying these to the exponential moving average (5) to update \\(\\mu\\) and \\(\\sigma^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.897, + 0.723 + ], + "angle": 0, + "content": "Task-balanced training of \\(\\gamma\\) and \\(\\beta\\). Additionally, we propose a way to train learnable parameters of BN (\\(\\gamma\\) and \\(\\beta\\)) in a task-balanced way to the current task. After calculating the task-balanced \\(\\tilde{\\mu}\\) and \\(\\tilde{\\sigma}^2\\) from \\(\\mathbf{H}\\), we apply these to normalize the horizontally-concatenated task-balanced batch \\(\\mathbf{H}\\) via (2). Then, the normalized feature map \\(\\tilde{\\mathbf{H}} \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}\\) is affine-transformed by (3) with \\(\\tilde{\\gamma} = F_{RP}(\\gamma) \\in \\mathbb{R}^{C \\cdot r}\\) and \\(\\tilde{\\beta} = F_{RP}(\\beta) \\in \\mathbb{R}^{C \\cdot r}\\), resulting in the affine-transformed feature \\(\\mathbf{Y} = (\\mathbf{Y}_{B_c}; \\mathbf{Y}_{B_p}) \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}\\). However, due to the different size of batch axis with the original batch size (\\(B_c / r + B_p \\neq B\\)), \\(\\mathbf{Y}\\) cannot be directly forward-propagated toward a next layer. To solve this problem, first, we apply a reverse operation of reshape to \\(\\mathbf{Y}_{B_c}\\) to obtain \\(\\mathbf{y}_{B_c} \\in \\mathbb{R}^{B_c \\times C \\times D}\\), where \\(F_S^{-1}(\\mathbf{Y}_{B_c}; r): \\mathbb{R}^{B / r \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_c \\times C \\times D}\\). Next, for the case of \\(\\mathbf{Y}_{B_p}\\), we get \\(\\mathbf{y}_{B_p} \\in \\mathbb{R}^{B_p \\times C \\times D}\\) by averaging \\(\\mathbf{Y}_{B_p}\\) over \\(r\\) repeats along the axis of channel, such as \\(\\mathbf{y}_{B_p} = F_A(\\mathbf{Y}_{B_p}; r): \\mathbb{R}^{B_p \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_p \\times C \\times D}\\). Finally, we forward-propagate the concatenated feature \\(\\mathbf{y} = (\\mathbf{y}_{B_c}; \\mathbf{y}_{B_p}) \\in \\mathbb{R}^{B \\times C \\times D}\\) toward the next layer." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.731, + 0.722, + 0.745 + ], + "angle": 0, + "content": "4.2.1 Why does TBBN work?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Calculating task-balanced \\(\\mu\\) and \\(\\sigma^2\\). When performing the standard BN while fixing the number of data instances from previous tasks as \\(B_{p}\\), the individual statistics \\((\\mu^{BN},\\sigma^{BN})\\) becomes dominated by the current task. As the exponential moving average iteratively averages over biased empirical statistics, BN fails to asymptotically recover population mean and variance. This is especially clear when expanding the BN mean \\(\\mu_t^{BN}\\) during training on task \\(t\\) in terms of means \\(\\mu_{i}\\) of the \\(i\\)-th task. Assuming that each task contributes uniformly in the global data distribution, \\(\\mu_t^{BN}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20131" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.352, + 0.108 + ], + "angle": 0, + "content": "deviates from the true global mean \\(\\mu_t^*\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.113, + 0.47, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} ^ {*} - \\mu_ {t} ^ {B N} = \\frac {B - B _ {c} t}{t (t - 1) B} \\sum_ {i = 1} ^ {t} \\mu_ {i} + \\frac {B _ {c} t - B}{(t - 1) B} \\mu_ {t}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.158, + 0.47, + 0.233 + ], + "angle": 0, + "content": "In a nutshell, BN fails to recover the true population mean unless the mini-batch is balanced such that \\( B_{c} = B / t \\). Our proposed TBBN creates \\( r \\) task-balanced bags of bootstrapped samples such that this balancing is satisfied, and approximates the population statistics \\( (\\mu^{*},\\sigma^{2*}) \\) in an unbiased manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.471, + 0.402 + ], + "angle": 0, + "content": "Training \\(\\gamma\\) and \\(\\beta\\) with task-balanced gradients. Note that the gradient for training \\(\\beta\\) and \\(\\gamma\\) of the original BN, shown in (4), is biased toward the current task due to the imbalance between \\(B_{c}\\) and \\(B_{p}\\) in the mini-batch. On the other hand, the above task-balanced process makes both \\(\\beta\\) and \\(\\gamma\\) to be trained in a task-balanced way during backpropagation. First, a gradient of \\(\\mathbf{y}\\) is back-propagated toward the BN layer and it can be denoted as: \\(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{y}} = (\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})\\in \\mathbb{R}^{B\\times C\\times D}\\). Then, the gradients of each current and task's batch pass the backward operation of \\(F_{S}^{-1}\\) and \\(F_{A}\\), respectively. As a result, the gradient of \\(\\mathbf{Y}\\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.406, + 0.469, + 0.437 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y}} = \\left(F _ {S, g} ^ {- 1} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right); F _ {A, g} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.472, + 0.606 + ], + "angle": 0, + "content": "in which \\(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}}\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}\\). \\(F_{S,g}^{p - 1}\\) and \\(F_{A,g}\\) stands for the backward operation of \\(F_{S,g}^{-1}\\) and \\(F_{A}\\), respectively. The backward operation of \\(F_{S,g}^{-1}\\) is the reverse-direction-reshape of a given gradient: \\(F_{S,g}^{-1}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = F_S(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r): \\mathbb{R}^{B_c\\times C\\times D}\\to \\mathbb{R}^{B_c / r\\times C\\cdot r\\times D}\\). In the case of \\(F_{A}\\), the backward operation becomes \\(F_{A,g}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = ((\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_1 / r;\\dots ;(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_r / r):\\mathbb{R}^{B_p\\times C\\times D}\\to \\mathbb{R}^{B_p\\times C\\cdot r\\times D}\\), where distributes and expands the input gradient divided by \\(r\\), for \\(r\\) times. As a result, a gradient of \\(\\beta\\) and \\(\\gamma\\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.61, + 0.47, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\frac {\\partial \\mathcal {L}}{\\partial \\gamma} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}} \\odot \\tilde {\\mathbf {H}} _ {b, d}; r\\right) (9) \\\\ \\frac {\\partial \\mathcal {L}}{\\partial \\beta} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}}; r\\right), (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.871 + ], + "angle": 0, + "content": "in which \\(F_{P,g}\\) denotes the backward operation of \\(F_{P}\\), which is the sum of gradients over \\(r\\): \\(F_{P,g}(\\pmb{g}; r) = \\sum_{i=1}^{r}((\\pmb{g}_i); \\dots; (\\pmb{g}_r)) : \\mathbb{R}^{C \\cdot r} \\to \\mathbb{R}^C\\), and \\(\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{Y}_{b,d}} \\in \\mathbb{R}^C\\) and \\(\\tilde{\\mathbf{H}}_{b,d} \\in \\mathbb{R}^C\\). Note that the core differences with the gradients of the original BN shown in (4): First, the summed up gradients are configured to be task-balanced. Second, in the case of the gradient of \\(\\gamma\\), the task-balanced batch \\(\\tilde{\\mathbf{H}}\\), normalized by the task-balanced mean and variance, is used to get the gradient. As a result, \\(\\gamma\\) and \\(\\beta\\) can be trained in a more task-balanced way, so that they can do their part of BN at test time where the entire task's test data is given jointly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Note that both the pseudo code and implementation details of TBBN are proposed in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.706, + 0.108 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.112, + 0.895, + 0.263 + ], + "angle": 0, + "content": "Datasets and Evaluation. We mainly evaluate our method on the offline CIL settings leveraging CIFAR-100 [19] and ImageNet-100 [10] datasets: for each dataset, we divide 100 classes into 10 disjoint sets, and consider each set to constitute a single task (i.e. \\( T = 10 \\) and \\( m = 10 \\)). Following previous work [7,9,24], we evaluate all normalization methods based on four different metrics, such as final accuracy \\( (A_{f}) \\), average accuracy \\( (A_{a}) \\), forgetting measure \\( (F) \\), and learning accuracy \\( (A_{l}) \\). The detailed explanation for the metrics can be found in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.895, + 0.657 + ], + "angle": 0, + "content": "Baselines. For backbone architectures, we follow the offline CIL setup proposed in [24] using ResNet-32 [13] for CIFAR-100 [19] and ResNet-18 for ImageNet-100 [10]. In addition, we use exemplar memory with size \\( |\\mathcal{M}| = 2000 \\) and incrementally update \\( \\mathcal{M} \\) via a class-balanced random sampling strategy after each task. To test our method under various offline CIL algorithms, we consider EEIL [6] and LUCIR [15], for which implementations are available in the benchmark environment provided by [24]. We also run SS-IL [1], POD-Net [12] and AFC [18], which are considered state-of-the-art in offline CIL, using their official code. Finetuning (FT) stands for a naive baseline which only utilizes the exemplar memory without using any explicit methods. For comparison across different normalization approaches, we simply replace all BN layers in the backbone model with one of the following: Instance Normalization (IN) [37], Group Normalization (GN) [40], Switch Normalization (SN) [22], Batch Renormalization (BRN) [16], Continual Normalization (CN) [29], and our proposed TBBN. We use official implementations for each baseline method published by the respective authors. Note that CN and GN require a hyperparameter \\( G \\) that sets the group size during feature-level normalization. For our experiments, we use \\( G = 16 \\) when training ResNet-32 on CIFAR-100 and \\( G = 32 \\) when training ResNet-18 on ImageNet-100. Further details on experimental settings are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.67, + 0.694, + 0.685 + ], + "angle": 0, + "content": "5.1. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Effect of normalization layers in offline CIL. Table 1 shows experimental results for FT on 10-task offline CIL setups on CIFAR-100 and ImageNet-100. First, we find that normalization layers previously developed for single task supervised learning (e.g., IN [37], GN [40], SN [22] and BRN [16]) are not effective in offline CIL scenarios compared to BN. Both IN and GN especially show notable performance degradation with respect to all four metrics. Furthermore, CN [29] does not lead to significant improvement, which is in contrast to the performance gain previously demonstrated in online CIL by the original paper. This shows that the benefit of adding the channel-level GN to BN is obscured when naïve BN is exposed to imbalanced minibatches for multiple epochs. On the other hand, we confirm" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20132" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "that simply replacing BN with TBBN increases both \\( A_{f} \\) and \\( A_{a} \\) in both datasets without any additional hyperparameters. We find that the performance gain mainly comes from the increased stability as well as plasticity as we see improvements in both \\( F \\) and \\( A_{l} \\). TBBN especially shows significantly less forgetting, supporting our insight that preventing sample statistics from becoming biased to the current task via task-balanced normalization effectively retains information from past tasks leading to a better accuracy." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.242, + 0.472, + 0.283 + ], + "angle": 0, + "content": "Table 1. Experimental results for FT with varying normalization layers on CIFAR-100 and ImageNet-100. Bold indicates the best performance in each metric." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.283, + 0.467, + 0.41 + ], + "angle": 0, + "content": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
BN35.4153.8843.4878.7939.4059.6048.0287.42
IN31.7246.8447.7279.4433.4553.5950.6984.66
GN31.2644.5344.0175.2728.8347.7949.7979.19
SN36.2953.6442.9179.2039.4559.5548.0487.79
BRN36.0852.5844.3480.4237.4957.7748.1386.57
CN35.0654.4343.8280.6441.9660.0245.3287.28
CN*36.0554.1844.8180.8540.4659.0346.7487.20
TBBN38.4656.1741.9080.3643.2061.6943.6287.82
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Applying TBBN to other CIL baselines. We also confirm that the advantage of TBBN is extended to other CIL methods. We consider the same 10-task offline CIL setup from CIFAR-100 and ImageNet-100, and run a total of six different CIL methods while simply replacing the BN layers in the model with either CN or TBBN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.84 + ], + "angle": 0, + "content": "Table 2 shows the corresponding results. First, the most recently proposed CIL methods, SSIL and AFC, achieve the best performance in terms of final accuracy \\( A_{f} \\). Especially in ImageNet-100, they surpass all other baselines in both \\( A_{f} \\) and \\( A_{a} \\), as previously reported in the original papers. Second, replacing BN with CN does not show consistent improvement across datasets and CIL methods. For instance, while EEIL+CN produces a considerable performance gain in ImageNet-100, CN fails to outperform BN when combined with more recent CIL algorithms such as PODNet and AFC. On the other hand, our TBBN consistently improves performance in \\( A_{f} \\) and \\( A_{a} \\) except when applied on PODNet in CIFAR-100. Following the observation in the previous experiment, we again confirm that the performance gain of TBBN is mostly due to reduction in \\( F \\) (i.e. enhanced stability) while maintaining or increasing \\( A_{l} \\) (i.e. enhanced plasticity). In all, applying TBBN to the SOTA baselines achieves new SOTA performance in both datasets. We plotted a graph of these experiments in the supplementary materials, and we could confirm that TBBN enhances the average accuracy at every step of training compared to BN, while CN shows performance loss for some PODNet and AFC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Applying TBBN to other architectures. To check the applicability of TBBN to other architectures, we selected four CNN-based architectures (e.g., ResNet-34 [13], ShuffleNet-V2 [43], MobileNet-V2 [31], and MnasNet (x0.5) [35])" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. Experimental results for various representative offline CIL methods. Bold indicates the best performance in each metric." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.124, + 0.89, + 0.34 + ], + "angle": 0, + "content": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
FT+BN35.4153.8843.3878.7939.4059.6048.0287.42
+CN35.0654.4343.8280.6441.9660.0245.3287.28
+TBBN38.4656.1741.9080.3643.2061.6943.6287.82
EEIL+BN39.8255.2539.4079.2240.0661.1547.7887.84
+CN39.9855.0939.3179.2942.4861.4344.4486.92
+TBBN41.9357.5337.8079.9345.1863.4842.6687.84
LUCIR+BN38.0654.2032.3570.4142.2663.8241.6883.94
+CN38.0755.6033.7871.8540.4461.4442.0483.48
+TBBN41.4556.1329.2370.6843.7264.3640.1883.90
PODNet+BN38.1052.9514.7052.5849.0565.4122.4069.99
+CN34.8050.2615.6950.5246.2062.9123.6668.50
+TBBN37.9052.9813.9051.7849.3065.7021.8569.76
SSL+BN41.3453.0015.6456.0249.5665.7921.2069.94
+CN40.7452.3814.6054.4450.5864.8118.5665.04
+TBBN43.8054.2815.1259.3751.3066.5119.5870.64
AFC+BN39.9053.9333.1773.1052.5067.5319.7072.22
+CN37.5051.1633.4070.9448.0065.2120.1070.68
+TBBN41.3057.3132.8973.5754.0068.6819.0073.22
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.895, + 0.432 + ], + "angle": 0, + "content": "which contain the BN layer as a default, and conducted experiments by replacing BN with TBBN in the 10 tasks scenario using the ImageNet-100 dataset. Table 3 demonstrates that our TBBN can be successfully applied to various types of architecture, increasing both \\(\\mathrm{A}_f\\) and \\(\\mathrm{A}_a\\) concurrently." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.447, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Table 3. Experimental results with varying backbone architectures on ImageNet-100. Bold indicates the best performance." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.473, + 0.89, + 0.545 + ], + "angle": 0, + "content": "
MethodResNet-34ShuffleNet-V2MobileNet-v2MnasNet (x0.5)
Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)
FT+BN41.3862.0034.7455.3738.8657.4336.2454.96
+TBBN46.7264.7635.8258.1742.6660.4140.9457.09
SSIL+BN51.1865.2743.8659.6947.7262.2545.1059.81
+TBBN52.3066.3644.7260.0748.6263.3747.0660.24
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.895, + 0.794 + ], + "angle": 0, + "content": "Results on dissimilar tasks. Several benchmark datasets (e.g., CIFAR-10/-100 and ImageNet dataset) have been used to evaluate a CIL method. The CIL scenario made from random class orderings of these datasets has small domain shifts due to high similarity between tasks [24]. In this regard, we believe that the CIL scenario using CIFAR-100 and ImageNet-100 datasets is not the best setting to check whether the proposed normalization layer is suitable for the CIL. Therefore, we design the CIL scenario, which has large domain shifts, with five distinct datasets such as CIFAR-10 [19], SVHN [27], STL-10 [8], MNIST [11] and Fashion-MNIST [41]. We divide 10 classes of each dataset into 2 tasks and construct the CIL scenario consisting of 10 tasks (2 tasks \\(\\times\\) 5 datasets). Note that task ordering is randomly shuffled by random seed and more details for experimental settings are proposed in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In Table 4, we observe that applying CN is sometimes harmful and only achieves minor improvement for FT and LUCIR. On the other hand, we again confirm that TBBN constantly makes enhancement of \\( A_{f} \\) and \\( A_{a} \\) by diminishing \\( F \\) but well maintaining \\( A_{l} \\), for all methods. This result underscores the robustness of our TBBN even for the difficult CIL scenario consisting of dissimilar tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20133" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.08, + 0.472, + 0.108 + ], + "angle": 0, + "content": "Table 4. Experimental results with dissimilar tasks using ResNet-18. Bold indicates the best performance in each metric." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.11, + 0.407, + 0.276 + ], + "angle": 0, + "content": "
MethodAf(↑)Aa(↑)F(↓)Al(↑)
FT+BN59.6065.8531.4891.08
+CN61.4171.0029.9091.40
+TBBN63.4271.3228.0591.47
EEIL+BN62.0472.2829.4691.50
+CN61.7372.4029.2791.00
+TBBN64.8872.8026.6791.55
LUCIR+BN62.4272.9128.0990.35
+CN62.9972.8126.7089.49
+TBBN63.6473.7226.7390.23
SSL+BN66.1570.6210.1372.59
+CN65.6470.569.1669.66
+TBBN67.0071.779.7472.86
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.289, + 0.27, + 0.305 + ], + "angle": 0, + "content": "5.2. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.472, + 0.64 + ], + "angle": 0, + "content": "Reduction in biased predictions. For a more detailed analysis for the effect of TBBN, we investigated a type of misclassification, by following the experiment proposed in [3], and the analysis results for finetuning with the ImageNet-100 dataset (10-tasks) are reported in Figure 4. This figure presents the number of four types of misclassification. For example, \\(\\mathrm{C} \\rightarrow \\mathrm{P}\\) stands for the number of misclassification current task's data to another class in previous tasks (\\(t = 1, \\dots, 9\\)). Among four types, \\(\\mathrm{P} \\rightarrow \\mathrm{C}\\), which is the number of misclassification of the previous task's data toward the current task's class, is called as biased prediction, knowing as the major cause of degrading performance in CIL [1,39]. As already reported in previous works [3,39], \\(\\mathrm{FT} + \\mathrm{BN}\\) seriously suffers from the biased prediction, resulting in the largest number of total misclassification. In the case of both CN variants and TBBN, we confirm that the gain of reducing the total number of misclassifications comes from diminishing the number of biased predictions (\\(\\mathrm{P} \\rightarrow \\mathrm{C}\\)), Especially, our TBBN significantly alleviates the biased prediction than CN variants. As a result, \\(\\mathrm{FT} + \\mathrm{TBBN}\\) achieves the lowest number of total misclassifications despite the increase of \\(\\mathrm{P} \\rightarrow \\mathrm{P}\\) caused by the reduced biased prediction." + }, + { + "type": "image", + "bbox": [ + 0.133, + 0.648, + 0.413, + 0.806 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.807, + 0.471, + 0.835 + ], + "angle": 0, + "content": "Figure 4. Analysis for four types of misclassification errors (\\(y\\)-axis) after training the model until the final task (\\(t = 10\\))." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Ablation studies. Table 5 presents ablation study for TBBN using the CIFAR-100 dataset (10 tasks). First, both Case 1 and Case 2 represent the ablation study for task-balanced mean and variance. We confirm that only calculating task" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.304 + ], + "angle": 0, + "content": "balanced running mean \\(\\mu\\) and variance \\(\\sigma^2\\) in (5) for test phase (Case 1) or using a task-balanced running mean \\(\\tilde{\\sigma}\\) and variance \\(\\tilde{\\sigma}^2\\) for training phase (Case 2) affect final performance negatively, due to mismatch of values \\((\\mu, \\sigma^2)\\) for normalization in training and test phases. Case 3 shows the experimental result where calculating task-balanced mean and variance is only applied. However, as we already confirmed in Figure 2 of the Section 4.1, only considering task-balanced mean and variance cannot make a difference in performance with the original BN. The opposite case (Case 4) where \\(\\gamma\\) and \\(\\beta\\) are trained in a task-balanced manner also shows a similar tendency, demonstrating the performance enhancement by TBBN can be obtained only when the proposed components are used together." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.305, + 0.895, + 0.412 + ], + "angle": 0, + "content": "Additionally, we compare GPU memory cost, training time and inference time of each case. Because of both reshape and repeat operations consisting of TBBN, TBBN requires maximum \\(\\times 1.6\\) of GPU memory and takes more \\(\\times 1.3\\) of training time than the original BN. However, note that there is no additional cost at test time because TBBN works to be identical to the original BN." + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.419, + 0.871, + 0.433 + ], + "angle": 0, + "content": "Table 5. Ablation study using CIFAR-100 with ResNet-32." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.439, + 0.892, + 0.53 + ], + "angle": 0, + "content": "
MethodTask-balanced μ and σ2? TrainTask-balanced γ and β? TestAf(↑)Aa(↑)Peak MemoryTrain Time (total)Test Time (per batch)
TBBN✓✓38.4656.17
Case 1X✓29.7846.992525MiB (×1.6)6.0h (×1.3)0.6s (×1.0)
Case 2✓X0.939.69
Case 3✓✓35.4553.15
Case 4XX36.2153.25
BNXX35.7153.881545MiB4.6h0.6s
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.554, + 0.704, + 0.571 + ], + "angle": 0, + "content": "6. Concluding Remarks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.749 + ], + "angle": 0, + "content": "We propose a simple but effective method, called Task-Balance Batch Normalization, for exemplar-based CIL. Starting from an analysis of the problem of the original BN, namely, the biased mean and variance calculation toward the current task, we devise a novel method to calculate the task-balanced mean and variance for normalization. Furthermore, we propose a method for the task-balanced training of parameters for affine transformation. From extensive experiments with CIFAR-100, ImageNet-100 and dissimilar tasks, we demonstrate that our TBBN can be easily applied to various existing CIL methods, further improving their performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.681, + 0.786 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work was partly done while Sungmin Cha did a research internship at Advanced ML Lab, LG AI Research. The work was also supported in part by NRF grant [NRF-2021R1A2C2007884], IITP grant [No.2021-0-01343, No.2021-0-02068, No.2022-0-00113, No.2022-0-00959] funded by the Korean government (MSIT), and SNU-LG AI Research Center." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20134" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. 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To that end, we develop a new update patch for BN, particularly tailored for the exemplar-based class-incremental learning (CIL). The main issue of BN in CIL is the imbalance of training data between current and past tasks in a mini-batch, which makes the empirical mean and variance as well as the learnable affine transformation parameters of BN heavily biased toward the current task — contributing to the forgetting of past tasks. While one of the recent BN variants has been developed for "online" CIL, in which the training is done with a single epoch, we show that their method does not necessarily bring gains for "offline" CIL, in which a model is trained with multiple epochs on the imbalanced training data. The main reason for the ineffectiveness of their method lies in not fully addressing the data imbalance issue, especially in computing the gradients for learning the affine transformation parameters of BN. Accordingly, our new hyperparameter-free variant, dubbed as Task-Balanced BN (TBBN), is proposed to more correctly resolve the imbalance issue by making a horizontally-concatenated task-balanced batch using both reshape and repeat operations during training. Based on our experiments on class incremental learning of CIFAR-100, ImageNet-100, and five dissimilar task datasets, we demonstrate that our TBBN, which works exactly the same as the vanilla BN in the inference time, is easily applicable to most existing exemplar-based offline CIL algorithms and consistently outperforms other BN variants. + +# 1. Introduction + +In recent years, continual learning (CL) has been actively studied to efficiently learn a neural network on sequentially + +arriving datasets while eliminating the process of re-training from scratch at each arrival of a new dataset [9]. However, since the model is typically trained on a dataset that is heavily skewed toward the current task at each step, the resulting neural network often suffers from suboptimal trade-off between stability and plasticity [25] during CL. To overcome this issue, various studies have been focused on addressing the so-called catastrophic forgetting phenomenon [9, 28]. + +Among different CL settings, the class-incremental learning (CIL) setting where the classifier needs to learn previously unseen classes at each incremental step has recently drawn attention due to its practicality [1, 3, 6, 12, 15, 26, 39, 42, 44]. Most state-of-the-art CIL algorithms maintain a small exemplar memory to store a subset of previously used training data and combine it with the current task dataset to mitigate the forgetting of past knowledge. A key issue of exemplar-based CIL is that the model prediction becomes heavily biased towards more recently learned classes, due to the imbalance between the training data from the current task (that are abundantly available) and past tasks (with limited access through exemplar memory). In response, recently proposed solutions to biased predictions include bias correction [39], unified classifier [15], and separated softmax [1], which greatly improved the overall accuracy of CIL methods across all classes learned so far. + +Despite such progress, relatively less focus has been made on backbone architectures under CIL on computer vision tasks. Specifically, the popular CNN-based models (e.g., ResNet [13]) are mainly used as feature extractors, and those models are equipped with Batch Normalization (BN) [17] by default. However, since BN is designed for single-task training on CNNs, applying BN directly to exemplar-based CIL results in statistics biased toward the current task due to the imbalance between current and past tasks' data in a mini-batch. Recently, [29] pointed out this issue in CIL, dubbed as cross-task normalization effect, and proposed a new normalization scheme called Continual Normalization + +(CN), which applies Group Normalization (GN) [40] across the channel dimension before running BN across the batch dimension. Therefore, the difference in feature distributions among tasks is essentially removed by GN, and the following BN computes task-balanced mean and variance statistics which is shown to outperform vanilla BN on online CIL settings. + +In this paper, we argue that CN only partially resolves the bias issue in exemplar-based CIL. Specifically, we find that the gradients on the affine transformation parameters remain biased towards the current task when using CN. As a result, it leads to inconsistent performance gains in the offline CIL setting, which is considered more practical than online CIL. To this end, we propose a simple yet novel hyperparameter-free normalization layer, dubbed as Task-Balanced Batch Normalization (TBBN), which effectively resolves the bias issue. Our method employs adaptive reshape and repeat operations on the mini-batch feature map during training in order to compute task-balanced normalization statistics and gradients for learning the affine transformation parameters. Our method does not require any hyperparameter as the size-inputs for reshape and repeat operations are determined adaptively. Furthermore, the application of TBBN during testing is identical to vanilla BN, requiring no change on the backbone architecture. Through extensive offline CIL experiments on CIFAR-100, ImageNet-100, and five dissimilar task datasets, we show that a simple replacement of BN layers in the backbone CNN model with TBBN benefits most state-of-the-art exemplar-based CIL algorithms towards an additional boost in performance. Our analysis shows that the gain of TBBN is consistent across various backbone architectures and datasets, suggesting its potential to become a correct choice for exemplar-based offline CIL algorithms. + +# 2. Related Work + +Exemplar-based CIL. Among various work in offline CIL, iCaRL [30] is the first to propose an exemplar-based method via utilization of nearest-mean-of-exemplars classification and representation learning. EEIL [6] next devised a distillation-based CIL method with both balanced fin-tuning and representative memory updating. BiC [39] focused on the biased prediction aspect due to data imbalance in CIL and proposed a novel yet simple idea to attach an additional layer that corrects biased predictions. Inspired by LWF [21], LUCIR [15] developed a method that overcomes catastrophic forgetting via a more sophisticated cosine normalization-based loss function. PODNet [12] proposed another distillation-based method that focuses on spatial-based loss to reduce representation forgetting. Most recently, two state-of-the-art knowledge distillation-based CIL methods have been proposed. First, SS-IL [1] demonstrated that a pure softmax mainly causes biased predictions in CIL, leading to the Separated Softmax layer that achieved significant + +performance gains. Second, AFC [18] devised a novel regularization for knowledge distillation to minimize the changes of important features when learning new tasks. + +On the other hand, online CIL also has attracted attention [2,33], but their performance is significantly lower in the benchmark (e.g., CIFAR-100) than offline CIL counterparts, as reported in the survey paper [23]. + +Normalization layer. One initial motivation for devising Batch Normalization (BN) [17] was to address internal covariate shift of a neural net. However, the belief in internal covariate shift was broken by follow-up studies, and the benefits from BN in terms of training perspective were analyzed in various directions [4, 32]. Thereafter, several normalization layers devised for various computer vision tasks have been proposed, each with their respective advantages [14, 16, 22, 37, 40], and for more diverse tasks, such as meta-learning [5], domain adaptation [38], task-incremental learning [20], and online CL [29]. + +# 3. Preliminaries + +Notation. We assume the setting of offline CIL as proposed in [1]; namely, a dataset $\mathcal{D}_t$ for each task $t$ arrives incrementally, and we use $T$ to denote the total number of tasks. Each $\mathcal{D}_t$ consists of pairs of an input image $\boldsymbol{x}_t$ and its target label $y_t$ . We assume that each incrementally added task introduces $m$ new classes that the model has never observed previously, and hence the total number of classes observed until task $t$ equals $C_t = m \cdot t$ . Therefore, the target label in each task is labeled as $y_t \in \{C_{t-1} + 1, \dots, C_t\} \triangleq \mathcal{C}_t$ . To save exemplars from previous tasks, we use exemplar memory denoted by $\mathcal{M}$ . While $\mathcal{M}$ is updated via a sampling algorithm after training on each task, the memory size is set to not exceed $|\mathcal{M}|$ over the entire course of tasks. In particular, exemplar memory $\mathcal{M}_{t-1}$ maintains $\left\lfloor \frac{|\mathcal{M}|}{C_{t-1}} \right\rfloor$ images per each past class and is used for training task $t$ . To merge instances from current as well as previous tasks, we consider a training mini-batch size of $B = B_c + B_p$ , where $B_c$ and $B_p$ denote the number of data samples from $\mathcal{D}_t$ and $\mathcal{M}_{t-1}$ , respectively. Without loss of generality, we assume that each mini-batch $(\boldsymbol{x}^B, y^B) \sim (\mathcal{D}_t \cup \mathcal{M}_{t-1})$ is a concatenation of $B_c$ samples from $\mathcal{D}_t$ with $B_p$ samples from $\mathcal{M}_{t-1}$ : $\boldsymbol{x}^B = [\boldsymbol{x}_1; \dots; \boldsymbol{x}_{B_c}; \boldsymbol{x}_{B_c+1}; \dots; \boldsymbol{x}_B]$ and $y^B = [y_1; \dots; y_{B_c}; y_{B_c+1}; \dots; y_B]$ with $\{(x_i, y_i)\}_{i=1}^{B_c} \subset \mathcal{D}_t$ and $\{(x_i, y_i)\}_{i=B_c+1}^{B} \subset \mathcal{M}_{t-1}$ . Note that $B_c$ is greater than $B_p$ in typical CIL settings, and it is this imbalance that is generally known to cause predictions biased towards the current task [1, 3, 39]. Therefore, we set the sampling ratio between $B_c$ and $B_p$ as $B_c: B_p = 3:1$ in our experiments. Lastly, we use $\boldsymbol{h} \in \mathbb{R}^{B \times C \times D}$ to denote the input feature map for an intermediate BN layer given $\boldsymbol{x}^B$ as input. Here, $C$ and $D$ denote the number of channels and feature dimension, respectively. + +Batch Normalization. Due to its powerful practicality and efficiency, Batch Normalization (BN) [17] has been the go-to normalization layer across various state-of-the-art neural network architectures [13, 34, 36]. During training, BN calculates the empirical mean $\hat{\mu} \in \mathbb{R}^C$ and variance $\hat{\sigma}^2 \in \mathbb{R}^C$ of the given mini-batch as + +$$ +\hat {\mu} _ {c} = \frac {1}{B D} \sum_ {b = 1} ^ {B} \sum_ {d = 1} ^ {D} \boldsymbol {h} _ {b, c, d}, \hat {\sigma} _ {c} ^ {2} = \frac {1}{B D} \sum_ {b = 1} ^ {B} \sum_ {d = 1} ^ {D} \left(\boldsymbol {h} _ {b, c, d} - \hat {\mu} _ {c}\right) ^ {2}. \tag {1} +$$ + +The feature map $\pmb{h}$ is then normalized to have zero-mean unit-variance using $\hat{\mu}$ and $\hat{\sigma}^2$ to obtain $\hat{\pmb{h}} \in \mathbb{R}^{B \times C \times D}$ . The normalized feature $\hat{\pmb{h}}$ is lastly affine-transformed with a trainable scale and shift parameters $\gamma, \beta \in \mathbb{R}^C$ to $\pmb{y}$ : + +$$ +\hat {\boldsymbol {h}} _ {b} = \frac {\boldsymbol {h} _ {b} - \hat {\mu} \cdot \mathbb {1} ^ {\intercal}}{\sqrt {\hat {\sigma} ^ {2} \cdot \mathbb {1} ^ {\intercal} + \epsilon \cdot \mathbb {1} ^ {\intercal}}} \tag {2} +$$ + +$$ +\boldsymbol {y} _ {b} = \gamma \cdot \mathbb {1} ^ {\mathrm {T}} \odot \hat {\boldsymbol {h}} _ {b} + \beta \cdot \mathbb {1} ^ {\mathrm {T}}, \tag {3} +$$ + +in which $\mathbb{1} \in \mathbb{R}^D$ is the all-1 vector, $\odot$ denotes the element-wise multiplication, and $b$ is the data index within the minibatch. Note the division and $\sqrt{\cdot}$ in (2) are also done in an element-wise sense. The $\epsilon$ term is a small value added for numerical stability, which we set as $\epsilon = 10^{-5}$ in the experiments. It is worth noting that $\gamma$ and $\beta$ are trained by computing the gradients + +$$ +\frac {\partial \mathcal {L}}{\partial \gamma_ {c}} = \sum_ {b, d = 1} ^ {B, D} \frac {\partial \mathcal {L}}{\partial \boldsymbol {y} _ {b , c , d}} \odot \hat {\boldsymbol {h}} _ {b, c, d}, \quad \frac {\partial \mathcal {L}}{\partial \beta_ {c}} = \sum_ {b, d = 1} ^ {B, D} \frac {\partial \mathcal {L}}{\partial \boldsymbol {y} _ {b , c , d}} \tag {4} +$$ + +under a loss function $\mathcal{L}$ . For the normalization in the test phase, running $\mu$ and $\sigma^2$ are updated incrementally at each $i$ -th training iteration via exponential moving average: + +$$ +\mu_ {(i)} = \alpha \cdot \mathbb {1} ^ {\intercal} \odot \hat {\mu} _ {(i)} + (1 - \alpha) \cdot \mathbb {1} ^ {\intercal} \odot \mu_ {(i - 1)} +$$ + +$$ +\sigma_ {(i)} ^ {2} = \alpha \cdot \mathbb {1} ^ {\intercal} \odot \hat {\sigma} _ {(i)} ^ {2} + \left((1 - \alpha) \frac {V - 1}{V}\right) \cdot \mathbb {1} ^ {\intercal} \odot \sigma_ {(i - 1)} ^ {2} \tag {5} +$$ + +in which $V = B \cdot D$ represents the vessel's correction, and $\alpha$ is the momentum hyperparameter generally set as 0.1. + +# 4. Main Method + +# 4.1. Motivation + +While exemplar memory is essential for achieving state-of-the-art performance in offline CIL [24], most methods use well-known backbone classification models (e.g., ResNet-18 [13]) with vanilla BN layers without much scrutiny over the issue of data-imbalance between current and previous tasks. One notable exception is Continual Normalization (CN) [29], but CN has only shown promise in online CIL settings where the data-imbalance causes relatively less of an impact than in offline CIL due to the single epoch learning. It is not clear whether CN is also effective in offline CIL, where + +the imbalanced mini-batches are used for multiple epochs. We conjecture that while CN performs task-balancing by normalizing each channel (or groups of channels) along the spatial dimension, this comes at a cost in discriminative power as it normalizes features from all tasks equally without any separation between tasks. In a later section, we find through experimentation that this limitation is especially detrimental in offline CIL, as CN leads to negligible gain over BN or even worse performance in some cases. + +For a concrete motivation, we consider a toy example to reflect upon the necessity of devising a correct BN mechanism for the exemplar memory-based CIL. Consider a synthetic input feature distribution for an intermediate BN layer shown in Figure 1. Figure 1(a) visualizes 2-D data samples generated from a mixture of four different Gaussian distributions, each representing the feature distribution for each given task. $^{1}$ In a joint training setting, the mini-batch samples are uniformly sampled across four tasks, and thus the empirical mean and variance obtained from BN would approach the true population mean and variance. Such mean and variance will then successfully standardize the samples in a mini-batch during both training and testing phases via the procedure given in (2) and (3). + +In an exemplar memory-based CIL setting, however, there is a severe imbalance among samples in the training minibatch, since the majority of the samples comes from the current task (Task 4) as shown in Figure 1(b). In this case, the mean and variance calculated by the BN layer is clearly biased towards those of the current task, failing to match the true statistics at test time. In other words, using the biased mean and variance obtained during training to normalize test samples leads the samples to deviate from a standardized distribution. It is evident that such mismatch between the train and test sample distributions can cause performance deterioration since the trainable parameters in BN are obtained from normalized training samples. An obvious remedy would be to obtain the task-balanced empirical mean and variance during training, and use them in the BN layer to normalize the test samples. Figure 1(c) and 1(d) highlight the difference between the test normalization done by CN and our TBBN, respectively, which computes the empirical mean and variance from the mini-batch in Figure 1(b). Note that while both successfully normalize test samples in a task-balanced way, CN tends to lose the discriminative structure among the tasks due to the intermediate GN step. In constraint, our TBBN, as will be described in details below, normalizes the test data features while maintaining the discriminative structure. + +In addition to the mismatch during test time, a naive application of BN on the biased mini-batch samples can also + +![](images/b90dec4ffa72fa2d4ac64564b1b21641248e40ea1ad0abc1edfa314339d1e365.jpg) +(a) True population distribution + +![](images/bcfa77a1f70ec99aa979f3706012e9e00d2b1d867d807fd1024448744da8f263.jpg) +Figure 1. (a) 2-D visualizations on a mixture of four Gaussian distributions, each representing a feature map distribution of each task. (b) Imbalanced training data in exemplar-based CIL while learning Task 4, deviating from true test distribution. (c) Test set normalization result of CN that computes normalization statistics from data in (b). (d) Test set normalization result of our proposed TBBN that computes normalization statistics from data in (b). + +![](images/ab1fc997e6e9e9a63c95d4f49bf6ac2583e93c73c6d10bea3bf207ccf64311b0.jpg) +(b) Biased train data during CIL + +![](images/739d66c3751315a71741237ab8668c4c42d3ed1a055de809a7ec50ab058a6e68.jpg) +(c) Test data normalized via CN +(d) Test data normalized via TBBN + +cause an issue during training. That is, when training for a current task (e.g., Task 4 in Figure 1) is finished, the empirical mean and variance obtained by a BN layer would be heavily biased towards the most recent task. When a new task arrives (say, Task 5), since only a small number of samples from Task 4 is saved in the exemplar memory, the new empirical mean and variance will now become biased towards Task 5, drifting away from the previous statistics updated via the exponential moving average in (5). This mismatch during training can also significantly alter the learned representations of the past task samples in the exemplar memory after normalization. Therefore, this necessitates re-training of subsequent layers, unintentionally causing forgetting of previously learned representations. + +With regards to the two aforementioned issues, we argue that it is crucial to calculate the task-balanced mean and variance for BN layers in exemplar memory-based CIL. While a similar observation has also been made in the recent work [29], we go one step further and note that the affine transformation parameters of BN (i.e. $\gamma$ and $\beta$ in (3)) should also be learned in a task-balanced manner. For a demonstration purpose, we train a ResNet-18 model with vanilla BN and exemplar memory of size $|\mathcal{M}| = 2000$ on ImageNet-100 split to 10 tasks with 10 classes per task. We test four different CIL procedures including two oracle-based approaches that can access the entire training set during test time to exhibit the necessity of task-balanced statistics and affine-transformations. In Figure 2, JOINT denotes the algorithm that jointly trains the model on all tasks at once, providing an upper bound in average accuracy. On the other hand, FT is the fine-tuning baseline that simply fine-tunes the model on samples from the current task and exemplar memory for each task. Note that FT performs poorly on previous tasks except for the final task, clearly reflecting the issue of biased predictions. UPDATE $(\mu, \sigma^2)$ is an oracle scheme that freezes all trainable parameters of the trained FT model, and only recomputes the mean and variance of all BN layers using the entire dataset such that they match the task-balanced + +population statistics. Finally, UPDATE $(\mu, \sigma^2)$ AND $(\gamma, \beta)$ denotes another oracle scheme that also re-trains the $(\gamma, \beta)$ parameters for all BN layers on the entire dataset, in addition to recomputing the $(\mu, \sigma^2)$ statistics. + +![](images/4d11ed290620cd92269f90f2cc33f5bda57c4e296edf56c4d3c94c0c19e6b59e.jpg) +Figure 2. Individual task and average accuracies on ImageNet-100 split into 10 tasks for CIL. $y$ -axis shows the accuracy for each task and the average accuracy across all tasks after full training. Recomputing the affine-transformation parameters $(\gamma, \beta)$ as well as empirical statistics $(\mu, \sigma^2)$ based on the full dataset leads to significant boost in performance. + +Figure 2 displays the classification accuracy of four methods on every 2nd task and the average accuracy across all tasks, all measured after training up to the final task. The slight drop in performance of UPDATE $(\mu, \sigma^2)$ compared to FT shows that only obtaining the task-balanced $(\mu, \sigma^2)$ is not sufficient due to mismatch between the updated $(\mu, \sigma^2)$ and the frozen $(\gamma, \beta)$ . In contrast, when affine-transformation parameters are also recomputed with task-balanced data, we observe a significant boost in average accuracy. This is particularly interesting as the affine-transformation parameters account for less than $1\%$ of the entire model parameters, and simply making them task-balanced along with the empirical $(\mu, \sigma^2)$ statistics in BN layers can bring a significant performance boost under a simple FT baseline. Inspired by this example, we develop our Task-Balanced Batch Normalization (TBBN) layer in the next section. + +![](images/7a837f430596d765dc7eb88cc567e6faefcabf1bdb4b62d58292201ec2fe9571.jpg) +Figure 3. Illustration of the forward (blue arrows) and backward (red arrows) propagations of TBBN. By applying both reshape and repeat operations to a given input of BN layer, TBBN induces that task-balanced calculation and training of $(\mu, \sigma^2)$ and $(\gamma, \beta)$ , respectively. + +# 4.2. Task-Balanced Batch Normalization (TBBN) + +To solve the problem of BN in the exemplar-based CIL, we propose Task-Balanced Batch Normalization (TBBN) consisting of two components: 1) Task-balanced $\mu$ and $\sigma^2$ calculation and 2) Task-balanced training of $\gamma$ and $\beta$ . + +Task-balanced $\mu$ and $\sigma^2$ calculation. As discussed in the previous section, the class imbalance between the current and previous data biases the mean and variance toward the current task. Instead, we propose a task-balanced algorithm that better computes the empirical mean and variance in the current batch. As shown in Figure 3, we design the two different tensor operations: reshape and repeat, applying them to the current and previous parts, respectively. We determine the number of repeat/reshape operations $r$ by the following (6). It determines the value of $r$ , which is used to balance the number of batches sampled from the exemplar memory $(\frac{B_p}{t - 1})$ and the number of batches of the current task $(\frac{B_c}{r})$ after reshaping with $r$ , so that the ratio between them becomes 1:1. Note that $r$ is a hyperparameter that need not be externally tuned, but that our method provides a task-adaptive guidance for automatically selecting $r$ : + +$$ +\frac {B _ {c}}{r} = \frac {B _ {p}}{t - 1}, \text {h e n c e ,} r = \frac {B _ {c}}{B _ {p}} \cdot (t - 1), \tag {6} +$$ + +in which $t = 2, \dots, T$ , and $r$ is set to 1 when $t = 1$ . + +Let $h_{B_c}$ be the input feature map of a BN layer for the current task $t$ . After applying the reshape operation $\mathbf{H}_{B_c} = F_S(h_{B_c}; r) : \mathbb{R}^{B_c \times C \times D} \to \mathbb{R}^{B_c / r \times C \cdot r \times D}$ with $r$ , we divide $h_{B_c}$ into $r$ splits, where each split has $\frac{B_c}{r}$ numbers of data from the current task. Similarly, let $h_{B_p}$ denote the data from the previous tasks. As $h_{B_p}$ consists of the data uniformly sampled from task 1 to $t - 1$ , $\frac{B_p}{t - 1}$ numbers of data belongs to $h_{B_p}$ for each previous task in expectation. The key insight is that we can make every split balanced by repeating $h_{B_p}$ by $r$ times if the task ratios $\frac{B_c}{r}$ and $\frac{B_p}{t - 1}$ become equivalent. So that, we repeat $h_{B_p}$ for $r$ times by applying a tensor repeat function $\mathbf{H}_{B_p} = F_P(h_{B_p}; r) : \mathbb{R}^{B_p \times C \times D} \to \mathbb{R}^{B_p \times C \cdot r \times D}$ . Then, we concatenate both tensors along batch + +axis, $\mathbf{H} = (\mathbf{H}_{B_c};\mathbf{H}_{B_p})\in \mathbb{R}^{(B_c / r + B_p)\times C\cdot r\times D}$ , and calculate a task-balanced empirical mean $\tilde{\mu}\in \mathbb{R}^{C\cdot r}$ and variance $\tilde{\sigma}^2\in \mathbb{R}^{C\cdot r}$ from a horizontally-concatenated task-balanced batch $\mathbf{H}$ . To update running mean $\mu \in \mathbb{R}^{C}$ and variance $\sigma^2\in \mathbb{R}^C$ for test phase, we average $\tilde{\mu}$ and $\tilde{\sigma}^2$ over $r$ splits, later applying these to the exponential moving average (5) to update $\mu$ and $\sigma^2$ . + +Task-balanced training of $\gamma$ and $\beta$ . Additionally, we propose a way to train learnable parameters of BN ( $\gamma$ and $\beta$ ) in a task-balanced way to the current task. After calculating the task-balanced $\tilde{\mu}$ and $\tilde{\sigma}^2$ from $\mathbf{H}$ , we apply these to normalize the horizontally-concatenated task-balanced batch $\mathbf{H}$ via (2). Then, the normalized feature map $\tilde{\mathbf{H}} \in \mathbb{R}^{(B_c / r + B_p) \times C \cdot r \times D}$ is affine-transformed by (3) with $\tilde{\gamma} = F_{RP}(\gamma) \in \mathbb{R}^{C \cdot r}$ and $\tilde{\beta} = F_{RP}(\beta) \in \mathbb{R}^{C \cdot r}$ , resulting in the affine-transformed feature $\mathbf{Y} = (\mathbf{Y}_{B_c}; \mathbf{Y}_{B_p}) \in \mathbb{R}^{(B_c / r + B_p) \times C \cdot r \times D}$ . However, due to the different size of batch axis with the original batch size ( $B_c / r + B_p \neq B$ ), $\mathbf{Y}$ cannot be directly forward-propagated toward a next layer. To solve this problem, first, we apply a reverse operation of reshape to $\mathbf{Y}_{B_c}$ to obtain $\mathbf{y}_{B_c} \in \mathbb{R}^{B_c \times C \times D}$ , where $F_S^{-1}(\mathbf{Y}_{B_c}; r): \mathbb{R}^{B / r \times C \cdot r \times D} \to \mathbb{R}^{B_c \times C \times D}$ . Next, for the case of $\mathbf{Y}_{B_p}$ , we get $\mathbf{y}_{B_p} \in \mathbb{R}^{B_p \times C \times D}$ by averaging $\mathbf{Y}_{B_p}$ over $r$ repeats along the axis of channel, such as $\mathbf{y}_{B_p} = F_A(\mathbf{Y}_{B_p}; r): \mathbb{R}^{B_p \times C \cdot r \times D} \to \mathbb{R}^{B_p \times C \times D}$ . Finally, we forward-propagate the concatenated feature $\mathbf{y} = (\mathbf{y}_{B_c}; \mathbf{y}_{B_p}) \in \mathbb{R}^{B \times C \times D}$ toward the next layer. + +# 4.2.1 Why does TBBN work? + +Calculating task-balanced $\mu$ and $\sigma^2$ . When performing the standard BN while fixing the number of data instances from previous tasks as $B_{p}$ , the individual statistics $(\mu^{BN},\sigma^{BN})$ becomes dominated by the current task. As the exponential moving average iteratively averages over biased empirical statistics, BN fails to asymptotically recover population mean and variance. This is especially clear when expanding the BN mean $\mu_t^{BN}$ during training on task $t$ in terms of means $\mu_{i}$ of the $i$ -th task. Assuming that each task contributes uniformly in the global data distribution, $\mu_t^{BN}$ + +deviates from the true global mean $\mu_t^*$ by + +$$ +\mu_ {t} ^ {*} - \mu_ {t} ^ {B N} = \frac {B - B _ {c} t}{t (t - 1) B} \sum_ {i = 1} ^ {t} \mu_ {i} + \frac {B _ {c} t - B}{(t - 1) B} \mu_ {t}. \tag {7} +$$ + +In a nutshell, BN fails to recover the true population mean unless the mini-batch is balanced such that $B_{c} = B / t$ . Our proposed TBBN creates $r$ task-balanced bags of bootstrapped samples such that this balancing is satisfied, and approximates the population statistics $(\mu^{*},\sigma^{2*})$ in an unbiased manner. + +Training $\gamma$ and $\beta$ with task-balanced gradients. Note that the gradient for training $\beta$ and $\gamma$ of the original BN, shown in (4), is biased toward the current task due to the imbalance between $B_{c}$ and $B_{p}$ in the mini-batch. On the other hand, the above task-balanced process makes both $\beta$ and $\gamma$ to be trained in a task-balanced way during backpropagation. First, a gradient of $\mathbf{y}$ is back-propagated toward the BN layer and it can be denoted as: $\frac{\partial\mathcal{L}}{\partial\mathbf{y}} = (\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_c}};\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_p}})\in \mathbb{R}^{B\times C\times D}$ . Then, the gradients of each current and task's batch pass the backward operation of $F_{S}^{-1}$ and $F_{A}$ , respectively. As a result, the gradient of $\mathbf{Y}$ becomes: + +$$ +\frac {\partial \mathcal {L}}{\partial \mathbf {Y}} = \left(F _ {S, g} ^ {- 1} \left(\frac {\partial \mathcal {L}}{\partial \mathbf {Y} _ {B _ {r}}}; r\right); F _ {A, g} \left(\frac {\partial \mathcal {L}}{\partial \mathbf {Y} _ {B _ {r}}}; r\right)\right), \tag {8} +$$ + +in which $\frac{\partial\mathcal{L}}{\partial\mathbf{Y}}\in \mathbb{R}^{(B_c / r + B_p)\times C\cdot r\times D}$ . $F_{S,g}^{p - 1}$ and $F_{A,g}$ stands for the backward operation of $F_{S,g}^{-1}$ and $F_{A}$ , respectively. The backward operation of $F_{S,g}^{-1}$ is the reverse-direction-reshape of a given gradient: $F_{S,g}^{-1}(\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_c}};r) = F_S(\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_c}};r): \mathbb{R}^{B_c\times C\times D}\to \mathbb{R}^{B_c / r\times C\cdot r\times D}$ . In the case of $F_{A}$ , the backward operation becomes $F_{A,g}(\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_c}};r) = ((\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_p}})_1 / r;\dots ;(\frac{\partial\mathcal{L}}{\partial\mathbf{Y}_{B_p}})_r / r):\mathbb{R}^{B_p\times C\times D}\to \mathbb{R}^{B_p\times C\cdot r\times D}$ , where distributes and expands the input gradient divided by $r$ , for $r$ times. As a result, a gradient of $\beta$ and $\gamma$ becomes: + +$$ +\begin{array}{l} \frac {\partial \mathcal {L}}{\partial \gamma} = F _ {P, g} \left(\sum_ {b, d = 1} ^ {\left(B _ {c} / r + B _ {p}\right), D} \frac {\partial \mathcal {L}}{\partial \mathbf {Y} _ {b , d}} \odot \tilde {\mathbf {H}} _ {b, d}; r\right) (9) \\ \frac {\partial \mathcal {L}}{\partial \beta} = F _ {P, g} \left(\sum_ {b, d = 1} ^ {\left(B _ {c} / r + B _ {p}\right), D} \frac {\partial \mathcal {L}}{\partial \mathbf {Y} _ {b , d}}; r\right), (10) \\ \end{array} +$$ + +in which $F_{P,g}$ denotes the backward operation of $F_{P}$ , which is the sum of gradients over $r$ : $F_{P,g}(\pmb{g}; r) = \sum_{i=1}^{r}((\pmb{g}_i); \dots; (\pmb{g}_r)) : \mathbb{R}^{C \cdot r} \to \mathbb{R}^C$ , and $\frac{\partial \mathcal{L}}{\partial \mathbf{Y}_{b,d}} \in \mathbb{R}^C$ and $\tilde{\mathbf{H}}_{b,d} \in \mathbb{R}^C$ . Note that the core differences with the gradients of the original BN shown in (4): First, the summed up gradients are configured to be task-balanced. Second, in the case of the gradient of $\gamma$ , the task-balanced batch $\tilde{\mathbf{H}}$ , normalized by the task-balanced mean and variance, is used to get the gradient. As a result, $\gamma$ and $\beta$ can be trained in a more task-balanced way, so that they can do their part of BN at test time where the entire task's test data is given jointly. + +Note that both the pseudo code and implementation details of TBBN are proposed in supplementary materials. + +# 5. Experimental Results + +Datasets and Evaluation. We mainly evaluate our method on the offline CIL settings leveraging CIFAR-100 [19] and ImageNet-100 [10] datasets: for each dataset, we divide 100 classes into 10 disjoint sets, and consider each set to constitute a single task (i.e. $T = 10$ and $m = 10$ ). Following previous work [7,9,24], we evaluate all normalization methods based on four different metrics, such as final accuracy $(A_{f})$ , average accuracy $(A_{a})$ , forgetting measure $(F)$ , and learning accuracy $(A_{l})$ . The detailed explanation for the metrics can be found in the supplementary materials. + +Baselines. For backbone architectures, we follow the offline CIL setup proposed in [24] using ResNet-32 [13] for CIFAR-100 [19] and ResNet-18 for ImageNet-100 [10]. In addition, we use exemplar memory with size $|\mathcal{M}| = 2000$ and incrementally update $\mathcal{M}$ via a class-balanced random sampling strategy after each task. To test our method under various offline CIL algorithms, we consider EEIL [6] and LUCIR [15], for which implementations are available in the benchmark environment provided by [24]. We also run SS-IL [1], POD-Net [12] and AFC [18], which are considered state-of-the-art in offline CIL, using their official code. Finetuning (FT) stands for a naive baseline which only utilizes the exemplar memory without using any explicit methods. For comparison across different normalization approaches, we simply replace all BN layers in the backbone model with one of the following: Instance Normalization (IN) [37], Group Normalization (GN) [40], Switch Normalization (SN) [22], Batch Renormalization (BRN) [16], Continual Normalization (CN) [29], and our proposed TBBN. We use official implementations for each baseline method published by the respective authors. Note that CN and GN require a hyperparameter $G$ that sets the group size during feature-level normalization. For our experiments, we use $G = 16$ when training ResNet-32 on CIFAR-100 and $G = 32$ when training ResNet-18 on ImageNet-100. Further details on experimental settings are in the supplementary material. + +# 5.1. Quantitative Results + +Effect of normalization layers in offline CIL. Table 1 shows experimental results for FT on 10-task offline CIL setups on CIFAR-100 and ImageNet-100. First, we find that normalization layers previously developed for single task supervised learning (e.g., IN [37], GN [40], SN [22] and BRN [16]) are not effective in offline CIL scenarios compared to BN. Both IN and GN especially show notable performance degradation with respect to all four metrics. Furthermore, CN [29] does not lead to significant improvement, which is in contrast to the performance gain previously demonstrated in online CIL by the original paper. This shows that the benefit of adding the channel-level GN to BN is obscured when naïve BN is exposed to imbalanced minibatches for multiple epochs. On the other hand, we confirm + +that simply replacing BN with TBBN increases both $A_{f}$ and $A_{a}$ in both datasets without any additional hyperparameters. We find that the performance gain mainly comes from the increased stability as well as plasticity as we see improvements in both $F$ and $A_{l}$ . TBBN especially shows significantly less forgetting, supporting our insight that preventing sample statistics from becoming biased to the current task via task-balanced normalization effectively retains information from past tasks leading to a better accuracy. + +Table 1. Experimental results for FT with varying normalization layers on CIFAR-100 and ImageNet-100. Bold indicates the best performance in each metric. + +
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
BN35.4153.8843.4878.7939.4059.6048.0287.42
IN31.7246.8447.7279.4433.4553.5950.6984.66
GN31.2644.5344.0175.2728.8347.7949.7979.19
SN36.2953.6442.9179.2039.4559.5548.0487.79
BRN36.0852.5844.3480.4237.4957.7748.1386.57
CN35.0654.4343.8280.6441.9660.0245.3287.28
CN*36.0554.1844.8180.8540.4659.0346.7487.20
TBBN38.4656.1741.9080.3643.2061.6943.6287.82
+ +Applying TBBN to other CIL baselines. We also confirm that the advantage of TBBN is extended to other CIL methods. We consider the same 10-task offline CIL setup from CIFAR-100 and ImageNet-100, and run a total of six different CIL methods while simply replacing the BN layers in the model with either CN or TBBN. + +Table 2 shows the corresponding results. First, the most recently proposed CIL methods, SSIL and AFC, achieve the best performance in terms of final accuracy $A_{f}$ . Especially in ImageNet-100, they surpass all other baselines in both $A_{f}$ and $A_{a}$ , as previously reported in the original papers. Second, replacing BN with CN does not show consistent improvement across datasets and CIL methods. For instance, while EEIL+CN produces a considerable performance gain in ImageNet-100, CN fails to outperform BN when combined with more recent CIL algorithms such as PODNet and AFC. On the other hand, our TBBN consistently improves performance in $A_{f}$ and $A_{a}$ except when applied on PODNet in CIFAR-100. Following the observation in the previous experiment, we again confirm that the performance gain of TBBN is mostly due to reduction in $F$ (i.e. enhanced stability) while maintaining or increasing $A_{l}$ (i.e. enhanced plasticity). In all, applying TBBN to the SOTA baselines achieves new SOTA performance in both datasets. We plotted a graph of these experiments in the supplementary materials, and we could confirm that TBBN enhances the average accuracy at every step of training compared to BN, while CN shows performance loss for some PODNet and AFC. + +Applying TBBN to other architectures. To check the applicability of TBBN to other architectures, we selected four CNN-based architectures (e.g., ResNet-34 [13], ShuffleNet-V2 [43], MobileNet-V2 [31], and MnasNet (x0.5) [35]) + +Table 2. Experimental results for various representative offline CIL methods. Bold indicates the best performance in each metric. + +
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
FT+BN35.4153.8843.3878.7939.4059.6048.0287.42
+CN35.0654.4343.8280.6441.9660.0245.3287.28
+TBBN38.4656.1741.9080.3643.2061.6943.6287.82
EEIL+BN39.8255.2539.4079.2240.0661.1547.7887.84
+CN39.9855.0939.3179.2942.4861.4344.4486.92
+TBBN41.9357.5337.8079.9345.1863.4842.6687.84
LUCIR+BN38.0654.2032.3570.4142.2663.8241.6883.94
+CN38.0755.6033.7871.8540.4461.4442.0483.48
+TBBN41.4556.1329.2370.6843.7264.3640.1883.90
PODNet+BN38.1052.9514.7052.5849.0565.4122.4069.99
+CN34.8050.2615.6950.5246.2062.9123.6668.50
+TBBN37.9052.9813.9051.7849.3065.7021.8569.76
SSL+BN41.3453.0015.6456.0249.5665.7921.2069.94
+CN40.7452.3814.6054.4450.5864.8118.5665.04
+TBBN43.8054.2815.1259.3751.3066.5119.5870.64
AFC+BN39.9053.9333.1773.1052.5067.5319.7072.22
+CN37.5051.1633.4070.9448.0065.2120.1070.68
+TBBN41.3057.3132.8973.5754.0068.6819.0073.22
+ +which contain the BN layer as a default, and conducted experiments by replacing BN with TBBN in the 10 tasks scenario using the ImageNet-100 dataset. Table 3 demonstrates that our TBBN can be successfully applied to various types of architecture, increasing both $\mathrm{A}_f$ and $\mathrm{A}_a$ concurrently. + +Table 3. Experimental results with varying backbone architectures on ImageNet-100. Bold indicates the best performance. + +
MethodResNet-34ShuffleNet-V2MobileNet-v2MnasNet (x0.5)
Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)
FT+BN41.3862.0034.7455.3738.8657.4336.2454.96
+TBBN46.7264.7635.8258.1742.6660.4140.9457.09
SSIL+BN51.1865.2743.8659.6947.7262.2545.1059.81
+TBBN52.3066.3644.7260.0748.6263.3747.0660.24
+ +Results on dissimilar tasks. Several benchmark datasets (e.g., CIFAR-10/-100 and ImageNet dataset) have been used to evaluate a CIL method. The CIL scenario made from random class orderings of these datasets has small domain shifts due to high similarity between tasks [24]. In this regard, we believe that the CIL scenario using CIFAR-100 and ImageNet-100 datasets is not the best setting to check whether the proposed normalization layer is suitable for the CIL. Therefore, we design the CIL scenario, which has large domain shifts, with five distinct datasets such as CIFAR-10 [19], SVHN [27], STL-10 [8], MNIST [11] and Fashion-MNIST [41]. We divide 10 classes of each dataset into 2 tasks and construct the CIL scenario consisting of 10 tasks (2 tasks $\times$ 5 datasets). Note that task ordering is randomly shuffled by random seed and more details for experimental settings are proposed in the supplementary materials. + +In Table 4, we observe that applying CN is sometimes harmful and only achieves minor improvement for FT and LUCIR. On the other hand, we again confirm that TBBN constantly makes enhancement of $A_{f}$ and $A_{a}$ by diminishing $F$ but well maintaining $A_{l}$ , for all methods. This result underscores the robustness of our TBBN even for the difficult CIL scenario consisting of dissimilar tasks. + +Table 4. Experimental results with dissimilar tasks using ResNet-18. Bold indicates the best performance in each metric. + +
MethodAf(↑)Aa(↑)F(↓)Al(↑)
FT+BN59.6065.8531.4891.08
+CN61.4171.0029.9091.40
+TBBN63.4271.3228.0591.47
EEIL+BN62.0472.2829.4691.50
+CN61.7372.4029.2791.00
+TBBN64.8872.8026.6791.55
LUCIR+BN62.4272.9128.0990.35
+CN62.9972.8126.7089.49
+TBBN63.6473.7226.7390.23
SSL+BN66.1570.6210.1372.59
+CN65.6470.569.1669.66
+TBBN67.0071.779.7472.86
+ +# 5.2. Qualitative Analysis + +Reduction in biased predictions. For a more detailed analysis for the effect of TBBN, we investigated a type of misclassification, by following the experiment proposed in [3], and the analysis results for finetuning with the ImageNet-100 dataset (10-tasks) are reported in Figure 4. This figure presents the number of four types of misclassification. For example, $\mathrm{C} \rightarrow \mathrm{P}$ stands for the number of misclassification current task's data to another class in previous tasks ( $t = 1, \dots, 9$ ). Among four types, $\mathrm{P} \rightarrow \mathrm{C}$ , which is the number of misclassification of the previous task's data toward the current task's class, is called as biased prediction, knowing as the major cause of degrading performance in CIL [1,39]. As already reported in previous works [3,39], $\mathrm{FT} + \mathrm{BN}$ seriously suffers from the biased prediction, resulting in the largest number of total misclassification. In the case of both CN variants and TBBN, we confirm that the gain of reducing the total number of misclassifications comes from diminishing the number of biased predictions ( $\mathrm{P} \rightarrow \mathrm{C}$ ), Especially, our TBBN significantly alleviates the biased prediction than CN variants. As a result, $\mathrm{FT} + \mathrm{TBBN}$ achieves the lowest number of total misclassifications despite the increase of $\mathrm{P} \rightarrow \mathrm{P}$ caused by the reduced biased prediction. + +![](images/7eca4c5bf37d1876cea82c8de8be5c02af830a61783b6099233e9014bc9a5cf0.jpg) +Figure 4. Analysis for four types of misclassification errors ( $y$ -axis) after training the model until the final task ( $t = 10$ ). + +Ablation studies. Table 5 presents ablation study for TBBN using the CIFAR-100 dataset (10 tasks). First, both Case 1 and Case 2 represent the ablation study for task-balanced mean and variance. We confirm that only calculating task + +balanced running mean $\mu$ and variance $\sigma^2$ in (5) for test phase (Case 1) or using a task-balanced running mean $\tilde{\sigma}$ and variance $\tilde{\sigma}^2$ for training phase (Case 2) affect final performance negatively, due to mismatch of values $(\mu, \sigma^2)$ for normalization in training and test phases. Case 3 shows the experimental result where calculating task-balanced mean and variance is only applied. However, as we already confirmed in Figure 2 of the Section 4.1, only considering task-balanced mean and variance cannot make a difference in performance with the original BN. The opposite case (Case 4) where $\gamma$ and $\beta$ are trained in a task-balanced manner also shows a similar tendency, demonstrating the performance enhancement by TBBN can be obtained only when the proposed components are used together. + +Additionally, we compare GPU memory cost, training time and inference time of each case. Because of both reshape and repeat operations consisting of TBBN, TBBN requires maximum $\times 1.6$ of GPU memory and takes more $\times 1.3$ of training time than the original BN. However, note that there is no additional cost at test time because TBBN works to be identical to the original BN. + +Table 5. Ablation study using CIFAR-100 with ResNet-32. + +
MethodTask-balanced μ and σ2? TrainTask-balanced γ and β? TestAf(↑)Aa(↑)Peak MemoryTrain Time (total)Test Time (per batch)
TBBN✓✓38.4656.17
Case 1X✓29.7846.992525MiB (×1.6)6.0h (×1.3)0.6s (×1.0)
Case 2✓X0.939.69
Case 3✓✓35.4553.15
Case 4XX36.2153.25
BNXX35.7153.881545MiB4.6h0.6s
+ +# 6. Concluding Remarks + +We propose a simple but effective method, called Task-Balance Batch Normalization, for exemplar-based CIL. Starting from an analysis of the problem of the original BN, namely, the biased mean and variance calculation toward the current task, we devise a novel method to calculate the task-balanced mean and variance for normalization. Furthermore, we propose a method for the task-balanced training of parameters for affine transformation. From extensive experiments with CIFAR-100, ImageNet-100 and dissimilar tasks, we demonstrate that our TBBN can be easily applied to various existing CIL methods, further improving their performance. + +# 7. Acknowledgement + +This work was partly done while Sungmin Cha did a research internship at Advanced ML Lab, LG AI Research. The work was also supported in part by NRF grant [NRF-2021R1A2C2007884], IITP grant [No.2021-0-01343, No.2021-0-02068, No.2022-0-00113, No.2022-0-00959] funded by the Korean government (MSIT), and SNU-LG AI Research Center. + +# References + +[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision (CVPR), pages 844-853, 2021. +[2] Rahaf Aljundi, Eugene Belilovsky, Tinne Tuytelaars, Laurent Charlin, Massimo Caccia, Min Lin, and Lucas Page-Caccia. Online continual learning with maximal interfered retrieval. In Advances in Neural Information Processing Systems (NeurIPS), volume 32, 2019. +[3] Eden Belouadah and Adrian Popescu. II2m: Class incremental learning with dual memory. 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neural nets in various computer vision tasks, but relatively little work has been dedicated to studying the effect of BN in continual learning. To that end, we develop a new update patch for BN, particularly tailored for the exemplar-based class-incremental learning (CIL). The main issue of BN in CIL is the imbalance of training data between current and past tasks in a mini-batch, which makes the empirical mean and variance as well as the learnable affine transformation parameters of BN heavily biased toward the current task — contributing to the forgetting of past tasks. While one of the recent BN variants has been developed for \"online\" CIL, in which the training is done with a single epoch, we show that their method does not necessarily bring gains for \"offline\" CIL, in which a model is trained with multiple epochs on the imbalanced training data. The main reason for the ineffectiveness of their method lies in not fully addressing the data imbalance issue, especially in computing the gradients for learning the affine transformation parameters of BN. Accordingly, our new hyperparameter-free variant, dubbed as Task-Balanced BN (TBBN), is proposed to more correctly resolve the imbalance issue by making a horizontally-concatenated task-balanced batch using both reshape and repeat operations during training. Based on our experiments on class incremental learning of CIFAR-100, ImageNet-100, and five dissimilar task datasets, we demonstrate that our TBBN, which works exactly the same as the vanilla BN in the inference time, is easily applicable to most existing exemplar-based offline CIL algorithms and consistently outperforms other BN variants." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 653, + 128, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 653, + 128, + 665 + ], + "spans": [ + { + "bbox": [ + 48, + 653, + 128, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "type": "text", + "content": "In recent years, continual learning (CL) has been actively studied to efficiently learn a neural network on sequentially" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 263, + 548, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 263, + 548, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 263, + 548, + 360 + ], + "type": "text", + "content": "arriving datasets while eliminating the process of re-training from scratch at each arrival of a new dataset [9]. However, since the model is typically trained on a dataset that is heavily skewed toward the current task at each step, the resulting neural network often suffers from suboptimal trade-off between stability and plasticity [25] during CL. To overcome this issue, various studies have been focused on addressing the so-called catastrophic forgetting phenomenon [9, 28]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 362, + 548, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 548, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 548, + 567 + ], + "type": "text", + "content": "Among different CL settings, the class-incremental learning (CIL) setting where the classifier needs to learn previously unseen classes at each incremental step has recently drawn attention due to its practicality [1, 3, 6, 12, 15, 26, 39, 42, 44]. Most state-of-the-art CIL algorithms maintain a small exemplar memory to store a subset of previously used training data and combine it with the current task dataset to mitigate the forgetting of past knowledge. A key issue of exemplar-based CIL is that the model prediction becomes heavily biased towards more recently learned classes, due to the imbalance between the training data from the current task (that are abundantly available) and past tasks (with limited access through exemplar memory). In response, recently proposed solutions to biased predictions include bias correction [39], unified classifier [15], and separated softmax [1], which greatly improved the overall accuracy of CIL methods across all classes learned so far." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 713 + ], + "type": "text", + "content": "Despite such progress, relatively less focus has been made on backbone architectures under CIL on computer vision tasks. Specifically, the popular CNN-based models (e.g., ResNet [13]) are mainly used as feature extractors, and those models are equipped with Batch Normalization (BN) [17] by default. However, since BN is designed for single-task training on CNNs, applying BN directly to exemplar-based CIL results in statistics biased toward the current task due to the imbalance between current and past tasks' data in a mini-batch. Recently, [29] pointed out this issue in CIL, dubbed as cross-task normalization effect, and proposed a new normalization scheme called Continual Normalization" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 245, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 245, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 245, + 713 + ], + "type": "text", + "content": "*Corresponding author (E-mail: tsmoon@snu.ac.kr)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20127" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "(CN), which applies Group Normalization (GN) [40] across the channel dimension before running BN across the batch dimension. Therefore, the difference in feature distributions among tasks is essentially removed by GN, and the following BN computes task-balanced mean and variance statistics which is shown to outperform vanilla BN on online CIL settings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 290, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 290, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 290, + 468 + ], + "type": "text", + "content": "In this paper, we argue that CN only partially resolves the bias issue in exemplar-based CIL. Specifically, we find that the gradients on the affine transformation parameters remain biased towards the current task when using CN. As a result, it leads to inconsistent performance gains in the offline CIL setting, which is considered more practical than online CIL. To this end, we propose a simple yet novel hyperparameter-free normalization layer, dubbed as Task-Balanced Batch Normalization (TBBN), which effectively resolves the bias issue. Our method employs adaptive reshape and repeat operations on the mini-batch feature map during training in order to compute task-balanced normalization statistics and gradients for learning the affine transformation parameters. Our method does not require any hyperparameter as the size-inputs for reshape and repeat operations are determined adaptively. Furthermore, the application of TBBN during testing is identical to vanilla BN, requiring no change on the backbone architecture. Through extensive offline CIL experiments on CIFAR-100, ImageNet-100, and five dissimilar task datasets, we show that a simple replacement of BN layers in the backbone CNN model with TBBN benefits most state-of-the-art exemplar-based CIL algorithms towards an additional boost in performance. Our analysis shows that the gain of TBBN is consistent across various backbone architectures and datasets, suggesting its potential to become a correct choice for exemplar-based offline CIL algorithms." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 478, + 134, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 134, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 134, + 491 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "Exemplar-based CIL. Among various work in offline CIL, iCaRL [30] is the first to propose an exemplar-based method via utilization of nearest-mean-of-exemplars classification and representation learning. EEIL [6] next devised a distillation-based CIL method with both balanced fin-tuning and representative memory updating. BiC [39] focused on the biased prediction aspect due to data imbalance in CIL and proposed a novel yet simple idea to attach an additional layer that corrects biased predictions. Inspired by LWF [21], LUCIR [15] developed a method that overcomes catastrophic forgetting via a more sophisticated cosine normalization-based loss function. PODNet [12] proposed another distillation-based method that focuses on spatial-based loss to reduce representation forgetting. Most recently, two state-of-the-art knowledge distillation-based CIL methods have been proposed. First, SS-IL [1] demonstrated that a pure softmax mainly causes biased predictions in CIL, leading to the Separated Softmax layer that achieved significant" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "content": "performance gains. Second, AFC [18] devised a novel regularization for knowledge distillation to minimize the changes of important features when learning new tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 109, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 547, + 157 + ], + "type": "text", + "content": "On the other hand, online CIL also has attracted attention [2,33], but their performance is significantly lower in the benchmark (e.g., CIFAR-100) than offline CIL counterparts, as reported in the survey paper [23]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 158, + 548, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 548, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 548, + 291 + ], + "type": "text", + "content": "Normalization layer. One initial motivation for devising Batch Normalization (BN) [17] was to address internal covariate shift of a neural net. However, the belief in internal covariate shift was broken by follow-up studies, and the benefits from BN in terms of training perspective were analyzed in various directions [4, 32]. Thereafter, several normalization layers devised for various computer vision tasks have been proposed, each with their respective advantages [14, 16, 22, 37, 40], and for more diverse tasks, such as meta-learning [5], domain adaptation [38], task-incremental learning [20], and online CL [29]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 304, + 391, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 391, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 391, + 316 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": "Notation. We assume the setting of offline CIL as proposed in [1]; namely, a dataset " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " for each task " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " arrives incrementally, and we use " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " to denote the total number of tasks. Each " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " consists of pairs of an input image " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and its target label " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "y_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". We assume that each incrementally added task introduces " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " new classes that the model has never observed previously, and hence the total number of classes observed until task " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "C_t = m \\cdot t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". Therefore, the target label in each task is labeled as " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "y_t \\in \\{C_{t-1} + 1, \\dots, C_t\\} \\triangleq \\mathcal{C}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". To save exemplars from previous tasks, we use exemplar memory denoted by " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". While " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " is updated via a sampling algorithm after training on each task, the memory size is set to not exceed " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "|\\mathcal{M}|" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " over the entire course of tasks. In particular, exemplar memory " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t-1}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " maintains " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\left\\lfloor \\frac{|\\mathcal{M}|}{C_{t-1}} \\right\\rfloor" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " images per each past class and is used for training task " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". To merge instances from current as well as previous tasks, we consider a training mini-batch size of " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B = B_c + B_p" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_c" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_p" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " denote the number of data samples from " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t-1}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ", respectively. Without loss of generality, we assume that each mini-batch " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "(\\boldsymbol{x}^B, y^B) \\sim (\\mathcal{D}_t \\cup \\mathcal{M}_{t-1})" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " is a concatenation of " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_c" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " samples from " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_p" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " samples from " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{t-1}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^B = [\\boldsymbol{x}_1; \\dots; \\boldsymbol{x}_{B_c}; \\boldsymbol{x}_{B_c+1}; \\dots; \\boldsymbol{x}_B]" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "y^B = [y_1; \\dots; y_{B_c}; y_{B_c+1}; \\dots; y_B]" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\{(x_i, y_i)\\}_{i=1}^{B_c} \\subset \\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\{(x_i, y_i)\\}_{i=B_c+1}^{B} \\subset \\mathcal{M}_{t-1}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_c" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " is greater than " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_p" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " in typical CIL settings, and it is this imbalance that is generally known to cause predictions biased towards the current task [1, 3, 39]. Therefore, we set the sampling ratio between " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_c" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_p" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "B_c: B_p = 3:1" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " in our experiments. Lastly, we use " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{h} \\in \\mathbb{R}^{B \\times C \\times D}" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " to denote the input feature map for an intermediate BN layer given " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^B" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " as input. Here, " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 325, + 548, + 715 + ], + "type": "text", + "content": " denote the number of channels and feature dimension, respectively." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20128" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": "Batch Normalization. Due to its powerful practicality and efficiency, Batch Normalization (BN) [17] has been the go-to normalization layer across various state-of-the-art neural network architectures [13, 34, 36]. During training, BN calculates the empirical mean " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "\\hat{\\mu} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}^2 \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": " of the given mini-batch as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 148, + 287, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 191 + ], + "type": "interline_equation", + "content": "\\hat {\\mu} _ {c} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\boldsymbol {h} _ {b, c, d}, \\hat {\\sigma} _ {c} ^ {2} = \\frac {1}{B D} \\sum_ {b = 1} ^ {B} \\sum_ {d = 1} ^ {D} \\left(\\boldsymbol {h} _ {b, c, d} - \\hat {\\mu} _ {c}\\right) ^ {2}. \\tag {1}", + "image_path": "4f87a914d910ce7698a898ec2fe158bd4badd54e97b8d37b0fc9258e246c0150.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": "The feature map " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\pmb{h}" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": " is then normalized to have zero-mean unit-variance using " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\mu}" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}^2" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{h}} \\in \\mathbb{R}^{B \\times C \\times D}" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": ". The normalized feature " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{h}}" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": " is lastly affine-transformed with a trainable scale and shift parameters " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\gamma, \\beta \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 47, + 192, + 289, + 240 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 247, + 287, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 247, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 116, + 247, + 287, + 273 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {h}} _ {b} = \\frac {\\boldsymbol {h} _ {b} - \\hat {\\mu} \\cdot \\mathbb {1} ^ {\\intercal}}{\\sqrt {\\hat {\\sigma} ^ {2} \\cdot \\mathbb {1} ^ {\\intercal} + \\epsilon \\cdot \\mathbb {1} ^ {\\intercal}}} \\tag {2}", + "image_path": "73153874085887c2e13da5773cb50c19c135f46536d1c4c5a5aa706ca61029a3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 275, + 287, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 275, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 111, + 275, + 287, + 289 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} _ {b} = \\gamma \\cdot \\mathbb {1} ^ {\\mathrm {T}} \\odot \\hat {\\boldsymbol {h}} _ {b} + \\beta \\cdot \\mathbb {1} ^ {\\mathrm {T}}, \\tag {3}", + "image_path": "60ddbebd95c6bd5e53f70e10352a804839281f34656a2108c1ff966dc2ca0799.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\mathbb{1} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " is the all-1 vector, " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " denotes the element-wise multiplication, and " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " is the data index within the minibatch. Note the division and " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\sqrt{\\cdot}" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " in (2) are also done in an element-wise sense. The " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " term is a small value added for numerical stability, which we set as " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-5}" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " in the experiments. It is worth noting that " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 298, + 289, + 382 + ], + "type": "text", + "content": " are trained by computing the gradients" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 390, + 287, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 390, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 53, + 390, + 287, + 425 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial \\gamma_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\odot \\hat {\\boldsymbol {h}} _ {b, c, d}, \\quad \\frac {\\partial \\mathcal {L}}{\\partial \\beta_ {c}} = \\sum_ {b, d = 1} ^ {B, D} \\frac {\\partial \\mathcal {L}}{\\partial \\boldsymbol {y} _ {b , c , d}} \\tag {4}", + "image_path": "fb26163fc5ffbbbdeabf82a6d9c8a4bc5b204254b60207304246d4d2e7f77035.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "content": "under a loss function " + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "content": ". For the normalization in the test phase, running " + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "content": " are updated incrementally at each " + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 433, + 287, + 469 + ], + "type": "text", + "content": "-th training iteration via exponential moving average:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 473, + 238, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 473, + 238, + 487 + ], + "spans": [ + { + "bbox": [ + 53, + 473, + 238, + 487 + ], + "type": "interline_equation", + "content": "\\mu_ {(i)} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\mu} _ {(i)} + (1 - \\alpha) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\mu_ {(i - 1)}", + "image_path": "f2878aeb1f4291035ca1060ff81cf1859de03762dc785f314cf03d3a41d400a5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 489, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 489, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 53, + 489, + 287, + 525 + ], + "type": "interline_equation", + "content": "\\sigma_ {(i)} ^ {2} = \\alpha \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\hat {\\sigma} _ {(i)} ^ {2} + \\left((1 - \\alpha) \\frac {V - 1}{V}\\right) \\cdot \\mathbb {1} ^ {\\intercal} \\odot \\sigma_ {(i - 1)} ^ {2} \\tag {5}", + "image_path": "e9c81c635026aaa7d2a5fd1e6ced7b52c660f601920f433ffe787f92f9bc9d4e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "inline_equation", + "content": "V = B \\cdot D" + }, + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "text", + "content": " represents the vessel's correction, and " + }, + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 525, + 287, + 549 + ], + "type": "text", + "content": " is the momentum hyperparameter generally set as 0.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 559, + 132, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 132, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 132, + 572 + ], + "type": "text", + "content": "4. Main Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 578, + 122, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 122, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 122, + 590 + ], + "type": "text", + "content": "4.1. Motivation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "While exemplar memory is essential for achieving state-of-the-art performance in offline CIL [24], most methods use well-known backbone classification models (e.g., ResNet-18 [13]) with vanilla BN layers without much scrutiny over the issue of data-imbalance between current and previous tasks. One notable exception is Continual Normalization (CN) [29], but CN has only shown promise in online CIL settings where the data-imbalance causes relatively less of an impact than in offline CIL due to the single epoch learning. It is not clear whether CN is also effective in offline CIL, where" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": "the imbalanced mini-batches are used for multiple epochs. We conjecture that while CN performs task-balancing by normalizing each channel (or groups of channels) along the spatial dimension, this comes at a cost in discriminative power as it normalizes features from all tasks equally without any separation between tasks. In a later section, we find through experimentation that this limitation is especially detrimental in offline CIL, as CN leads to negligible gain over BN or even worse performance in some cases." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 180, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 346 + ], + "type": "text", + "content": "For a concrete motivation, we consider a toy example to reflect upon the necessity of devising a correct BN mechanism for the exemplar memory-based CIL. Consider a synthetic input feature distribution for an intermediate BN layer shown in Figure 1. Figure 1(a) visualizes 2-D data samples generated from a mixture of four different Gaussian distributions, each representing the feature distribution for each given task." + }, + { + "bbox": [ + 304, + 180, + 547, + 346 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 180, + 547, + 346 + ], + "type": "text", + "content": " In a joint training setting, the mini-batch samples are uniformly sampled across four tasks, and thus the empirical mean and variance obtained from BN would approach the true population mean and variance. Such mean and variance will then successfully standardize the samples in a mini-batch during both training and testing phases via the procedure given in (2) and (3)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 347, + 548, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 548, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 548, + 633 + ], + "type": "text", + "content": "In an exemplar memory-based CIL setting, however, there is a severe imbalance among samples in the training minibatch, since the majority of the samples comes from the current task (Task 4) as shown in Figure 1(b). In this case, the mean and variance calculated by the BN layer is clearly biased towards those of the current task, failing to match the true statistics at test time. In other words, using the biased mean and variance obtained during training to normalize test samples leads the samples to deviate from a standardized distribution. It is evident that such mismatch between the train and test sample distributions can cause performance deterioration since the trainable parameters in BN are obtained from normalized training samples. An obvious remedy would be to obtain the task-balanced empirical mean and variance during training, and use them in the BN layer to normalize the test samples. Figure 1(c) and 1(d) highlight the difference between the test normalization done by CN and our TBBN, respectively, which computes the empirical mean and variance from the mini-batch in Figure 1(b). Note that while both successfully normalize test samples in a task-balanced way, CN tends to lose the discriminative structure among the tasks due to the intermediate GN step. In constraint, our TBBN, as will be described in details below, normalizes the test data features while maintaining the discriminative structure." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 634, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 634, + 547, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 634, + 547, + 658 + ], + "type": "text", + "content": "In addition to the mismatch during test time, a naive application of BN on the biased mini-batch samples can also" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 664, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 664, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 664, + 547, + 713 + ], + "type": "text", + "content": "1In fact, we generated 20 dimensional Gaussian vectors, which is generated by concatenating i.i.d. 2-D Gaussians 10 times, and only the first two dimensions are shown in the figures. The normalization by CN and TBBN shown in Figure 1(c)(d) are done by obtaining the statistics from the entire 20 dimensions (which exemplifies the channel dimension in a feature map)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20129" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 76, + 177, + 183 + ], + "blocks": [ + { + "bbox": [ + 65, + 76, + 177, + 183 + ], + "lines": [ + { + "bbox": [ + 65, + 76, + 177, + 183 + ], + "spans": [ + { + "bbox": [ + 65, + 76, + 177, + 183 + ], + "type": "image", + "image_path": "b90dec4ffa72fa2d4ac64564b1b21641248e40ea1ad0abc1edfa314339d1e365.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 186, + 174, + 196 + ], + "lines": [ + { + "bbox": [ + 70, + 186, + 174, + 196 + ], + "spans": [ + { + "bbox": [ + 70, + 186, + 174, + 196 + ], + "type": "text", + "content": "(a) True population distribution" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 183, + 76, + 296, + 182 + ], + "blocks": [ + { + "bbox": [ + 183, + 76, + 296, + 182 + ], + "lines": [ + { + "bbox": [ + 183, + 76, + 296, + 182 + ], + "spans": [ + { + "bbox": [ + 183, + 76, + 296, + 182 + ], + "type": "image", + "image_path": "bcfa77a1f70ec99aa979f3706012e9e00d2b1d867d807fd1024448744da8f263.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 547, + 243 + ], + "type": "text", + "content": "Figure 1. (a) 2-D visualizations on a mixture of four Gaussian distributions, each representing a feature map distribution of each task. (b) Imbalanced training data in exemplar-based CIL while learning Task 4, deviating from true test distribution. (c) Test set normalization result of CN that computes normalization statistics from data in (b). (d) Test set normalization result of our proposed TBBN that computes normalization statistics from data in (b)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 302, + 76, + 411, + 182 + ], + "blocks": [ + { + "bbox": [ + 188, + 186, + 294, + 196 + ], + "lines": [ + { + "bbox": [ + 188, + 186, + 294, + 196 + ], + "spans": [ + { + "bbox": [ + 188, + 186, + 294, + 196 + ], + "type": "text", + "content": "(b) Biased train data during CIL" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 302, + 76, + 411, + 182 + ], + "lines": [ + { + "bbox": [ + 302, + 76, + 411, + 182 + ], + "spans": [ + { + "bbox": [ + 302, + 76, + 411, + 182 + ], + "type": "image", + "image_path": "ab1fc997e6e9e9a63c95d4f49bf6ac2583e93c73c6d10bea3bf207ccf64311b0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 416, + 76, + 525, + 182 + ], + "blocks": [ + { + "bbox": [ + 304, + 186, + 410, + 196 + ], + "lines": [ + { + "bbox": [ + 304, + 186, + 410, + 196 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 410, + 196 + ], + "type": "text", + "content": "(c) Test data normalized via CN" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 416, + 76, + 525, + 182 + ], + "lines": [ + { + "bbox": [ + 416, + 76, + 525, + 182 + ], + "spans": [ + { + "bbox": [ + 416, + 76, + 525, + 182 + ], + "type": "image", + "image_path": "739d66c3751315a71741237ab8668c4c42d3ed1a055de809a7ec50ab058a6e68.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 414, + 186, + 528, + 196 + ], + "lines": [ + { + "bbox": [ + 414, + 186, + 528, + 196 + ], + "spans": [ + { + "bbox": [ + 414, + 186, + 528, + 196 + ], + "type": "text", + "content": "(d) Test data normalized via TBBN" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 251, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 418 + ], + "type": "text", + "content": "cause an issue during training. That is, when training for a current task (e.g., Task 4 in Figure 1) is finished, the empirical mean and variance obtained by a BN layer would be heavily biased towards the most recent task. When a new task arrives (say, Task 5), since only a small number of samples from Task 4 is saved in the exemplar memory, the new empirical mean and variance will now become biased towards Task 5, drifting away from the previous statistics updated via the exponential moving average in (5). This mismatch during training can also significantly alter the learned representations of the past task samples in the exemplar memory after normalization. Therefore, this necessitates re-training of subsequent layers, unintentionally causing forgetting of previously learned representations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "content": "With regards to the two aforementioned issues, we argue that it is crucial to calculate the task-balanced mean and variance for BN layers in exemplar memory-based CIL. While a similar observation has also been made in the recent work [29], we go one step further and note that the affine transformation parameters of BN (i.e. " + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "content": " in (3)) should also be learned in a task-balanced manner. For a demonstration purpose, we train a ResNet-18 model with vanilla BN and exemplar memory of size " + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "inline_equation", + "content": "|\\mathcal{M}| = 2000" + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "content": " on ImageNet-100 split to 10 tasks with 10 classes per task. We test four different CIL procedures including two oracle-based approaches that can access the entire training set during test time to exhibit the necessity of task-balanced statistics and affine-transformations. In Figure 2, JOINT denotes the algorithm that jointly trains the model on all tasks at once, providing an upper bound in average accuracy. On the other hand, FT is the fine-tuning baseline that simply fine-tunes the model on samples from the current task and exemplar memory for each task. Note that FT performs poorly on previous tasks except for the final task, clearly reflecting the issue of biased predictions. UPDATE " + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 46, + 426, + 289, + 714 + ], + "type": "text", + "content": " is an oracle scheme that freezes all trainable parameters of the trained FT model, and only recomputes the mean and variance of all BN layers using the entire dataset such that they match the task-balanced" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "content": "population statistics. Finally, UPDATE " + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "content": " AND " + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "inline_equation", + "content": "(\\gamma, \\beta)" + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "content": " denotes another oracle scheme that also re-trains the " + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "inline_equation", + "content": "(\\gamma, \\beta)" + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "content": " parameters for all BN layers on the entire dataset, in addition to recomputing the " + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 250, + 547, + 299 + ], + "type": "text", + "content": " statistics." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 332, + 303, + 520, + 449 + ], + "blocks": [ + { + "bbox": [ + 332, + 303, + 520, + 449 + ], + "lines": [ + { + "bbox": [ + 332, + 303, + 520, + 449 + ], + "spans": [ + { + "bbox": [ + 332, + 303, + 520, + 449 + ], + "type": "image", + "image_path": "4d11ed290620cd92269f90f2cc33f5bda57c4e296edf56c4d3c94c0c19e6b59e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "lines": [ + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "text", + "content": "Figure 2. Individual task and average accuracies on ImageNet-100 split into 10 tasks for CIL. " + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "text", + "content": "-axis shows the accuracy for each task and the average accuracy across all tasks after full training. Recomputing the affine-transformation parameters " + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "inline_equation", + "content": "(\\gamma, \\beta)" + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "text", + "content": " as well as empirical statistics " + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 451, + 547, + 517 + ], + "type": "text", + "content": " based on the full dataset leads to significant boost in performance." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": "Figure 2 displays the classification accuracy of four methods on every 2nd task and the average accuracy across all tasks, all measured after training up to the final task. The slight drop in performance of UPDATE " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": " compared to FT shows that only obtaining the task-balanced " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": " is not sufficient due to mismatch between the updated " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": " and the frozen " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "(\\gamma, \\beta)" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": ". In contrast, when affine-transformation parameters are also recomputed with task-balanced data, we observe a significant boost in average accuracy. This is particularly interesting as the affine-transformation parameters account for less than " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": " of the entire model parameters, and simply making them task-balanced along with the empirical " + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 522, + 548, + 713 + ], + "type": "text", + "content": " statistics in BN layers can bring a significant performance boost under a simple FT baseline. Inspired by this example, we develop our Task-Balanced Batch Normalization (TBBN) layer in the next section." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20130" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 72, + 521, + 213 + ], + "blocks": [ + { + "bbox": [ + 75, + 72, + 521, + 213 + ], + "lines": [ + { + "bbox": [ + 75, + 72, + 521, + 213 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 521, + 213 + ], + "type": "image", + "image_path": "7a837f430596d765dc7eb88cc567e6faefcabf1bdb4b62d58292201ec2fe9571.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "type": "text", + "content": "Figure 3. Illustration of the forward (blue arrows) and backward (red arrows) propagations of TBBN. By applying both reshape and repeat operations to a given input of BN layer, TBBN induces that task-balanced calculation and training of " + }, + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "type": "inline_equation", + "content": "(\\gamma, \\beta)" + }, + { + "bbox": [ + 46, + 216, + 547, + 240 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 244, + 279, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 279, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 279, + 257 + ], + "type": "text", + "content": "4.2. Task-Balanced Batch Normalization (TBBN)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "content": "To solve the problem of BN in the exemplar-based CIL, we propose Task-Balanced Batch Normalization (TBBN) consisting of two components: 1) Task-balanced " + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "content": " calculation and 2) Task-balanced training of " + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 259, + 288, + 307 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": "Task-balanced " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " calculation. As discussed in the previous section, the class imbalance between the current and previous data biases the mean and variance toward the current task. Instead, we propose a task-balanced algorithm that better computes the empirical mean and variance in the current batch. As shown in Figure 3, we design the two different tensor operations: reshape and repeat, applying them to the current and previous parts, respectively. We determine the number of repeat/reshape operations " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " by the following (6). It determines the value of " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": ", which is used to balance the number of batches sampled from the exemplar memory " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "(\\frac{B_p}{t - 1})" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " and the number of batches of the current task " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "(\\frac{B_c}{r})" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " after reshaping with " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": ", so that the ratio between them becomes 1:1. Note that " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": " is a hyperparameter that need not be externally tuned, but that our method provides a task-adaptive guidance for automatically selecting " + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 308, + 290, + 502 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 509, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 509, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 86, + 509, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\frac {B _ {c}}{r} = \\frac {B _ {p}}{t - 1}, \\text {h e n c e ,} r = \\frac {B _ {c}}{B _ {p}} \\cdot (t - 1), \\tag {6}", + "image_path": "52570c3949d5215e59afcfa53971fa7f6ff9684b98db2411e07f93510bbc6947.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "inline_equation", + "content": "t = 2, \\dots, T" + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "text", + "content": " is set to 1 when " + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 46, + 542, + 257, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_c}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " be the input feature map of a BN layer for the current task " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": ". After applying the reshape operation " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{B_c} = F_S(h_{B_c}; r) : \\mathbb{R}^{B_c \\times C \\times D} \\to \\mathbb{R}^{B_c / r \\times C \\cdot r \\times D}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": ", we divide " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_c}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " splits, where each split has " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\frac{B_c}{r}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " numbers of data from the current task. Similarly, let " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_p}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " denote the data from the previous tasks. As " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_p}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " consists of the data uniformly sampled from task 1 to " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\frac{B_p}{t - 1}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " numbers of data belongs to " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_p}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " for each previous task in expectation. The key insight is that we can make every split balanced by repeating " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_p}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " times if the task ratios " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\frac{B_c}{r}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\frac{B_p}{t - 1}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " become equivalent. So that, we repeat " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "h_{B_p}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": " times by applying a tensor repeat function " + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{B_p} = F_P(h_{B_p}; r) : \\mathbb{R}^{B_p \\times C \\times D} \\to \\mathbb{R}^{B_p \\times C \\cdot r \\times D}" + }, + { + "bbox": [ + 46, + 555, + 290, + 714 + ], + "type": "text", + "content": ". Then, we concatenate both tensors along batch" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": "axis, " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\mathbf{H} = (\\mathbf{H}_{B_c};\\mathbf{H}_{B_p})\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": ", and calculate a task-balanced empirical mean " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}\\in \\mathbb{R}^{C\\cdot r}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2\\in \\mathbb{R}^{C\\cdot r}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " from a horizontally-concatenated task-balanced batch " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": ". To update running mean " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\mu \\in \\mathbb{R}^{C}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\sigma^2\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " for test phase, we average " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " splits, later applying these to the exponential moving average (5) to update " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 244, + 547, + 328 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": "Task-balanced training of " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ". Additionally, we propose a way to train learnable parameters of BN (" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ") in a task-balanced way to the current task. After calculating the task-balanced " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ", we apply these to normalize the horizontally-concatenated task-balanced batch " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " via (2). Then, the normalized feature map " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{H}} \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " is affine-transformed by (3) with " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\tilde{\\gamma} = F_{RP}(\\gamma) \\in \\mathbb{R}^{C \\cdot r}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\tilde{\\beta} = F_{RP}(\\beta) \\in \\mathbb{R}^{C \\cdot r}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ", resulting in the affine-transformed feature " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = (\\mathbf{Y}_{B_c}; \\mathbf{Y}_{B_p}) \\in \\mathbb{R}^{(B_c / r + B_p) \\times C \\cdot r \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ". However, due to the different size of batch axis with the original batch size (" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "B_c / r + B_p \\neq B" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " cannot be directly forward-propagated toward a next layer. To solve this problem, first, we apply a reverse operation of reshape to " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{B_c}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{B_c} \\in \\mathbb{R}^{B_c \\times C \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "F_S^{-1}(\\mathbf{Y}_{B_c}; r): \\mathbb{R}^{B / r \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_c \\times C \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ". Next, for the case of " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{B_p}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ", we get " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{B_p} \\in \\mathbb{R}^{B_p \\times C \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " by averaging " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{B_p}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " repeats along the axis of channel, such as " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{B_p} = F_A(\\mathbf{Y}_{B_p}; r): \\mathbb{R}^{B_p \\times C \\cdot r \\times D} \\to \\mathbb{R}^{B_p \\times C \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": ". Finally, we forward-propagate the concatenated feature " + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = (\\mathbf{y}_{B_c}; \\mathbf{y}_{B_p}) \\in \\mathbb{R}^{B \\times C \\times D}" + }, + { + "bbox": [ + 304, + 329, + 548, + 572 + ], + "type": "text", + "content": " toward the next layer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 578, + 441, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 578, + 441, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 441, + 590 + ], + "type": "text", + "content": "4.2.1 Why does TBBN work?" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Calculating task-balanced " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ". When performing the standard BN while fixing the number of data instances from previous tasks as " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "B_{p}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ", the individual statistics " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "(\\mu^{BN},\\sigma^{BN})" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " becomes dominated by the current task. As the exponential moving average iteratively averages over biased empirical statistics, BN fails to asymptotically recover population mean and variance. This is especially clear when expanding the BN mean " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mu_t^{BN}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " during training on task " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " in terms of means " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "-th task. Assuming that each task contributes uniformly in the global data distribution, " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mu_t^{BN}" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20131" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 215, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 215, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 215, + 85 + ], + "type": "text", + "content": "deviates from the true global mean " + }, + { + "bbox": [ + 47, + 72, + 215, + 85 + ], + "type": "inline_equation", + "content": "\\mu_t^*" + }, + { + "bbox": [ + 47, + 72, + 215, + 85 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 89, + 287, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 89, + 287, + 121 + ], + "spans": [ + { + "bbox": [ + 70, + 89, + 287, + 121 + ], + "type": "interline_equation", + "content": "\\mu_ {t} ^ {*} - \\mu_ {t} ^ {B N} = \\frac {B - B _ {c} t}{t (t - 1) B} \\sum_ {i = 1} ^ {t} \\mu_ {i} + \\frac {B _ {c} t - B}{(t - 1) B} \\mu_ {t}. \\tag {7}", + "image_path": "381a7625bb91607965116c187bd79a038f1eacfa38675387f768b8323b24a028.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "text", + "content": "In a nutshell, BN fails to recover the true population mean unless the mini-batch is balanced such that " + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "inline_equation", + "content": "B_{c} = B / t" + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "text", + "content": ". Our proposed TBBN creates " + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "text", + "content": " task-balanced bags of bootstrapped samples such that this balancing is satisfied, and approximates the population statistics " + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "inline_equation", + "content": "(\\mu^{*},\\sigma^{2*})" + }, + { + "bbox": [ + 46, + 125, + 287, + 184 + ], + "type": "text", + "content": " in an unbiased manner." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": "Training " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " with task-balanced gradients. Note that the gradient for training " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " of the original BN, shown in (4), is biased toward the current task due to the imbalance between " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "B_{c}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "B_{p}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " in the mini-batch. On the other hand, the above task-balanced process makes both " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " to be trained in a task-balanced way during backpropagation. First, a gradient of " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " is back-propagated toward the BN layer and it can be denoted as: " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{y}} = (\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})\\in \\mathbb{R}^{B\\times C\\times D}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": ". Then, the gradients of each current and task's batch pass the backward operation of " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "F_{S}^{-1}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "F_{A}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": ", respectively. As a result, the gradient of " + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 185, + 288, + 318 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 321, + 287, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 321, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 77, + 321, + 287, + 346 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y}} = \\left(F _ {S, g} ^ {- 1} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right); F _ {A, g} \\left(\\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {B _ {r}}}; r\\right)\\right), \\tag {8}", + "image_path": "6ed59fdf9ec274e10e7fec5150c684ef0a56a5b580c16ae5732ca216b377ec09.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}}\\in \\mathbb{R}^{(B_c / r + B_p)\\times C\\cdot r\\times D}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{S,g}^{p - 1}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{A,g}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " stands for the backward operation of " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{S,g}^{-1}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{A}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ", respectively. The backward operation of " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{S,g}^{-1}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " is the reverse-direction-reshape of a given gradient: " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{S,g}^{-1}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = F_S(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r): \\mathbb{R}^{B_c\\times C\\times D}\\to \\mathbb{R}^{B_c / r\\times C\\cdot r\\times D}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ". In the case of " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{A}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ", the backward operation becomes " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "F_{A,g}(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_c}};r) = ((\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_1 / r;\\dots ;(\\frac{\\partial\\mathcal{L}}{\\partial\\mathbf{Y}_{B_p}})_r / r):\\mathbb{R}^{B_p\\times C\\times D}\\to \\mathbb{R}^{B_p\\times C\\cdot r\\times D}" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ", where distributes and expands the input gradient divided by " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " times. As a result, a gradient of " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 346, + 288, + 479 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 483, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 483, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 64, + 483, + 287, + 552 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\frac {\\partial \\mathcal {L}}{\\partial \\gamma} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}} \\odot \\tilde {\\mathbf {H}} _ {b, d}; r\\right) (9) \\\\ \\frac {\\partial \\mathcal {L}}{\\partial \\beta} = F _ {P, g} \\left(\\sum_ {b, d = 1} ^ {\\left(B _ {c} / r + B _ {p}\\right), D} \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {Y} _ {b , d}}; r\\right), (10) \\\\ \\end{array}", + "image_path": "cae25271cc29556a8502c2ae58ea4aefd9b21fca8f5c729d97274b716f93697a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "F_{P,g}" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": " denotes the backward operation of " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "F_{P}" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ", which is the sum of gradients over " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "F_{P,g}(\\pmb{g}; r) = \\sum_{i=1}^{r}((\\pmb{g}_i); \\dots; (\\pmb{g}_r)) : \\mathbb{R}^{C \\cdot r} \\to \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{Y}_{b,d}} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{H}}_{b,d} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ". Note that the core differences with the gradients of the original BN shown in (4): First, the summed up gradients are configured to be task-balanced. Second, in the case of the gradient of " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ", the task-balanced batch " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{H}}" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": ", normalized by the task-balanced mean and variance, is used to get the gradient. As a result, " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 554, + 287, + 689 + ], + "type": "text", + "content": " can be trained in a more task-balanced way, so that they can do their part of BN at test time where the entire task's test data is given jointly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "Note that both the pseudo code and implementation details of TBBN are proposed in supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "spans": [ + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": "Datasets and Evaluation. We mainly evaluate our method on the offline CIL settings leveraging CIFAR-100 [19] and ImageNet-100 [10] datasets: for each dataset, we divide 100 classes into 10 disjoint sets, and consider each set to constitute a single task (i.e. " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "T = 10" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "m = 10" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": "). Following previous work [7,9,24], we evaluate all normalization methods based on four different metrics, such as final accuracy " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "(A_{f})" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": ", average accuracy " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "(A_{a})" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": ", forgetting measure " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "(F)" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": ", and learning accuracy " + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "inline_equation", + "content": "(A_{l})" + }, + { + "bbox": [ + 304, + 88, + 547, + 208 + ], + "type": "text", + "content": ". The detailed explanation for the metrics can be found in the supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": "Baselines. For backbone architectures, we follow the offline CIL setup proposed in [24] using ResNet-32 [13] for CIFAR-100 [19] and ResNet-18 for ImageNet-100 [10]. In addition, we use exemplar memory with size " + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "inline_equation", + "content": "|\\mathcal{M}| = 2000" + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": " and incrementally update " + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": " via a class-balanced random sampling strategy after each task. To test our method under various offline CIL algorithms, we consider EEIL [6] and LUCIR [15], for which implementations are available in the benchmark environment provided by [24]. We also run SS-IL [1], POD-Net [12] and AFC [18], which are considered state-of-the-art in offline CIL, using their official code. Finetuning (FT) stands for a naive baseline which only utilizes the exemplar memory without using any explicit methods. For comparison across different normalization approaches, we simply replace all BN layers in the backbone model with one of the following: Instance Normalization (IN) [37], Group Normalization (GN) [40], Switch Normalization (SN) [22], Batch Renormalization (BRN) [16], Continual Normalization (CN) [29], and our proposed TBBN. We use official implementations for each baseline method published by the respective authors. Note that CN and GN require a hyperparameter " + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": " that sets the group size during feature-level normalization. For our experiments, we use " + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "inline_equation", + "content": "G = 16" + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": " when training ResNet-32 on CIFAR-100 and " + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "inline_equation", + "content": "G = 32" + }, + { + "bbox": [ + 304, + 209, + 547, + 520 + ], + "type": "text", + "content": " when training ResNet-18 on ImageNet-100. Further details on experimental settings are in the supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 530, + 424, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 530, + 424, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 530, + 424, + 542 + ], + "type": "text", + "content": "5.1. Quantitative Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "Effect of normalization layers in offline CIL. Table 1 shows experimental results for FT on 10-task offline CIL setups on CIFAR-100 and ImageNet-100. First, we find that normalization layers previously developed for single task supervised learning (e.g., IN [37], GN [40], SN [22] and BRN [16]) are not effective in offline CIL scenarios compared to BN. Both IN and GN especially show notable performance degradation with respect to all four metrics. Furthermore, CN [29] does not lead to significant improvement, which is in contrast to the performance gain previously demonstrated in online CIL by the original paper. This shows that the benefit of adding the channel-level GN to BN is obscured when naïve BN is exposed to imbalanced minibatches for multiple epochs. On the other hand, we confirm" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20132" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "that simply replacing BN with TBBN increases both " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "A_{f}" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "A_{a}" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": " in both datasets without any additional hyperparameters. We find that the performance gain mainly comes from the increased stability as well as plasticity as we see improvements in both " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "A_{l}" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": ". TBBN especially shows significantly less forgetting, supporting our insight that preventing sample statistics from becoming biased to the current task via task-balanced normalization effectively retains information from past tasks leading to a better accuracy." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 224, + 285, + 324 + ], + "blocks": [ + { + "bbox": [ + 47, + 191, + 288, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 191, + 288, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 288, + 224 + ], + "type": "text", + "content": "Table 1. Experimental results for FT with varying normalization layers on CIFAR-100 and ImageNet-100. Bold indicates the best performance in each metric." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 224, + 285, + 324 + ], + "lines": [ + { + "bbox": [ + 50, + 224, + 285, + 324 + ], + "spans": [ + { + "bbox": [ + 50, + 224, + 285, + 324 + ], + "type": "table", + "html": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
BN35.4153.8843.4878.7939.4059.6048.0287.42
IN31.7246.8447.7279.4433.4553.5950.6984.66
GN31.2644.5344.0175.2728.8347.7949.7979.19
SN36.2953.6442.9179.2039.4559.5548.0487.79
BRN36.0852.5844.3480.4237.4957.7748.1386.57
CN35.0654.4343.8280.6441.9660.0245.3287.28
CN*36.0554.1844.8180.8540.4659.0346.7487.20
TBBN38.4656.1741.9080.3643.2061.6943.6287.82
", + "image_path": "b0bfe51498fd21e45ec26c773534827d2bcf30b63aca9a7ebce12086e391d8a7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 287, + 400 + ], + "type": "text", + "content": "Applying TBBN to other CIL baselines. We also confirm that the advantage of TBBN is extended to other CIL methods. We consider the same 10-task offline CIL setup from CIFAR-100 and ImageNet-100, and run a total of six different CIL methods while simply replacing the BN layers in the model with either CN or TBBN." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": "Table 2 shows the corresponding results. First, the most recently proposed CIL methods, SSIL and AFC, achieve the best performance in terms of final accuracy " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{f}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": ". Especially in ImageNet-100, they surpass all other baselines in both " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{f}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{a}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": ", as previously reported in the original papers. Second, replacing BN with CN does not show consistent improvement across datasets and CIL methods. For instance, while EEIL+CN produces a considerable performance gain in ImageNet-100, CN fails to outperform BN when combined with more recent CIL algorithms such as PODNet and AFC. On the other hand, our TBBN consistently improves performance in " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{f}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{a}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": " except when applied on PODNet in CIFAR-100. Following the observation in the previous experiment, we again confirm that the performance gain of TBBN is mostly due to reduction in " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": " (i.e. enhanced stability) while maintaining or increasing " + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "inline_equation", + "content": "A_{l}" + }, + { + "bbox": [ + 46, + 402, + 289, + 665 + ], + "type": "text", + "content": " (i.e. enhanced plasticity). In all, applying TBBN to the SOTA baselines achieves new SOTA performance in both datasets. We plotted a graph of these experiments in the supplementary materials, and we could confirm that TBBN enhances the average accuracy at every step of training compared to BN, while CN shows performance loss for some PODNet and AFC." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Applying TBBN to other architectures. To check the applicability of TBBN to other architectures, we selected four CNN-based architectures (e.g., ResNet-34 [13], ShuffleNet-V2 [43], MobileNet-V2 [31], and MnasNet (x0.5) [35])" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 98, + 544, + 269 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "type": "text", + "content": "Table 2. Experimental results for various representative offline CIL methods. Bold indicates the best performance in each metric." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 98, + 544, + 269 + ], + "lines": [ + { + "bbox": [ + 308, + 98, + 544, + 269 + ], + "spans": [ + { + "bbox": [ + 308, + 98, + 544, + 269 + ], + "type": "table", + "html": "
MethodCIFAR-100 w/ ResNet-32ImageNet-100 w/ ResNet-18
Af(↑)Aa(↑)F(↓)Al(↑)Af(↑)Aa(↑)F(↓)Al(↑)
FT+BN35.4153.8843.3878.7939.4059.6048.0287.42
+CN35.0654.4343.8280.6441.9660.0245.3287.28
+TBBN38.4656.1741.9080.3643.2061.6943.6287.82
EEIL+BN39.8255.2539.4079.2240.0661.1547.7887.84
+CN39.9855.0939.3179.2942.4861.4344.4486.92
+TBBN41.9357.5337.8079.9345.1863.4842.6687.84
LUCIR+BN38.0654.2032.3570.4142.2663.8241.6883.94
+CN38.0755.6033.7871.8540.4461.4442.0483.48
+TBBN41.4556.1329.2370.6843.7264.3640.1883.90
PODNet+BN38.1052.9514.7052.5849.0565.4122.4069.99
+CN34.8050.2615.6950.5246.2062.9123.6668.50
+TBBN37.9052.9813.9051.7849.3065.7021.8569.76
SSL+BN41.3453.0015.6456.0249.5665.7921.2069.94
+CN40.7452.3814.6054.4450.5864.8118.5665.04
+TBBN43.8054.2815.1259.3751.3066.5119.5870.64
AFC+BN39.9053.9333.1773.1052.5067.5319.7072.22
+CN37.5051.1633.4070.9448.0065.2120.1070.68
+TBBN41.3057.3132.8973.5754.0068.6819.0073.22
", + "image_path": "b8ff7bfe00cf714a60b0b6c337b1f5a478889b4b6eba97ce0c06a4866f1d8ad0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "text", + "content": "which contain the BN layer as a default, and conducted experiments by replacing BN with TBBN in the 10 tasks scenario using the ImageNet-100 dataset. Table 3 demonstrates that our TBBN can be successfully applied to various types of architecture, increasing both " + }, + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathrm{A}_f" + }, + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathrm{A}_a" + }, + { + "bbox": [ + 304, + 281, + 547, + 342 + ], + "type": "text", + "content": " concurrently." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 374, + 544, + 431 + ], + "blocks": [ + { + "bbox": [ + 305, + 354, + 545, + 374 + ], + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 374 + ], + "type": "text", + "content": "Table 3. Experimental results with varying backbone architectures on ImageNet-100. Bold indicates the best performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 374, + 544, + 431 + ], + "lines": [ + { + "bbox": [ + 308, + 374, + 544, + 431 + ], + "spans": [ + { + "bbox": [ + 308, + 374, + 544, + 431 + ], + "type": "table", + "html": "
MethodResNet-34ShuffleNet-V2MobileNet-v2MnasNet (x0.5)
Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)Af(↑)Aa(↑)
FT+BN41.3862.0034.7455.3738.8657.4336.2454.96
+TBBN46.7264.7635.8258.1742.6660.4140.9457.09
SSIL+BN51.1865.2743.8659.6947.7262.2545.1059.81
+TBBN52.3066.3644.7260.0748.6263.3747.0660.24
", + "image_path": "636e5e5944293361d1bbc71a72e131495577408ca8db9c67d1e99f575fabbf9c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "content": "Results on dissimilar tasks. Several benchmark datasets (e.g., CIFAR-10/-100 and ImageNet dataset) have been used to evaluate a CIL method. The CIL scenario made from random class orderings of these datasets has small domain shifts due to high similarity between tasks [24]. In this regard, we believe that the CIL scenario using CIFAR-100 and ImageNet-100 datasets is not the best setting to check whether the proposed normalization layer is suitable for the CIL. Therefore, we design the CIL scenario, which has large domain shifts, with five distinct datasets such as CIFAR-10 [19], SVHN [27], STL-10 [8], MNIST [11] and Fashion-MNIST [41]. We divide 10 classes of each dataset into 2 tasks and construct the CIL scenario consisting of 10 tasks (2 tasks " + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "content": " 5 datasets). Note that task ordering is randomly shuffled by random seed and more details for experimental settings are proposed in the supplementary materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "In Table 4, we observe that applying CN is sometimes harmful and only achieves minor improvement for FT and LUCIR. On the other hand, we again confirm that TBBN constantly makes enhancement of " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "A_{f}" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "A_{a}" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " by diminishing " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " but well maintaining " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "A_{l}" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": ", for all methods. This result underscores the robustness of our TBBN even for the difficult CIL scenario consisting of dissimilar tasks." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20133" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 87, + 249, + 218 + ], + "blocks": [ + { + "bbox": [ + 47, + 63, + 288, + 85 + ], + "lines": [ + { + "bbox": [ + 47, + 63, + 288, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 63, + 288, + 85 + ], + "type": "text", + "content": "Table 4. Experimental results with dissimilar tasks using ResNet-18. Bold indicates the best performance in each metric." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 87, + 249, + 218 + ], + "lines": [ + { + "bbox": [ + 83, + 87, + 249, + 218 + ], + "spans": [ + { + "bbox": [ + 83, + 87, + 249, + 218 + ], + "type": "table", + "html": "
MethodAf(↑)Aa(↑)F(↓)Al(↑)
FT+BN59.6065.8531.4891.08
+CN61.4171.0029.9091.40
+TBBN63.4271.3228.0591.47
EEIL+BN62.0472.2829.4691.50
+CN61.7372.4029.2791.00
+TBBN64.8872.8026.6791.55
LUCIR+BN62.4272.9128.0990.35
+CN62.9972.8126.7089.49
+TBBN63.6473.7226.7390.23
SSL+BN66.1570.6210.1372.59
+CN65.6470.569.1669.66
+TBBN67.0071.779.7472.86
", + "image_path": "bf011d889dce11a49df29c1470ba7c7159eb629596f07dd7c192ea8000306525.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 228, + 165, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 165, + 241 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 165, + 241 + ], + "type": "text", + "content": "5.2. Qualitative Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": "Reduction in biased predictions. For a more detailed analysis for the effect of TBBN, we investigated a type of misclassification, by following the experiment proposed in [3], and the analysis results for finetuning with the ImageNet-100 dataset (10-tasks) are reported in Figure 4. This figure presents the number of four types of misclassification. For example, " + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{C} \\rightarrow \\mathrm{P}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": " stands for the number of misclassification current task's data to another class in previous tasks (" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "t = 1, \\dots, 9" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": "). Among four types, " + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{P} \\rightarrow \\mathrm{C}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": ", which is the number of misclassification of the previous task's data toward the current task's class, is called as biased prediction, knowing as the major cause of degrading performance in CIL [1,39]. As already reported in previous works [3,39], " + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{FT} + \\mathrm{BN}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": " seriously suffers from the biased prediction, resulting in the largest number of total misclassification. In the case of both CN variants and TBBN, we confirm that the gain of reducing the total number of misclassifications comes from diminishing the number of biased predictions (" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{P} \\rightarrow \\mathrm{C}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": "), Especially, our TBBN significantly alleviates the biased prediction than CN variants. As a result, " + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{FT} + \\mathrm{TBBN}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": " achieves the lowest number of total misclassifications despite the increase of " + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{P} \\rightarrow \\mathrm{P}" + }, + { + "bbox": [ + 46, + 243, + 288, + 506 + ], + "type": "text", + "content": " caused by the reduced biased prediction." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 81, + 513, + 252, + 638 + ], + "blocks": [ + { + "bbox": [ + 81, + 513, + 252, + 638 + ], + "lines": [ + { + "bbox": [ + 81, + 513, + 252, + 638 + ], + "spans": [ + { + "bbox": [ + 81, + 513, + 252, + 638 + ], + "type": "image", + "image_path": "7eca4c5bf37d1876cea82c8de8be5c02af830a61783b6099233e9014bc9a5cf0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "lines": [ + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "type": "text", + "content": "Figure 4. Analysis for four types of misclassification errors (" + }, + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "type": "text", + "content": "-axis) after training the model until the final task (" + }, + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "type": "inline_equation", + "content": "t = 10" + }, + { + "bbox": [ + 47, + 639, + 288, + 661 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "Ablation studies. Table 5 presents ablation study for TBBN using the CIFAR-100 dataset (10 tasks). First, both Case 1 and Case 2 represent the ablation study for task-balanced mean and variance. We confirm that only calculating task" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "balanced running mean " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " in (5) for test phase (Case 1) or using a task-balanced running mean " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " for training phase (Case 2) affect final performance negatively, due to mismatch of values " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " for normalization in training and test phases. Case 3 shows the experimental result where calculating task-balanced mean and variance is only applied. However, as we already confirmed in Figure 2 of the Section 4.1, only considering task-balanced mean and variance cannot make a difference in performance with the original BN. The opposite case (Case 4) where " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " are trained in a task-balanced manner also shows a similar tendency, demonstrating the performance enhancement by TBBN can be obtained only when the proposed components are used together." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "text", + "content": "Additionally, we compare GPU memory cost, training time and inference time of each case. Because of both reshape and repeat operations consisting of TBBN, TBBN requires maximum " + }, + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\times 1.6" + }, + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "text", + "content": " of GPU memory and takes more " + }, + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\times 1.3" + }, + { + "bbox": [ + 304, + 241, + 547, + 326 + ], + "type": "text", + "content": " of training time than the original BN. However, note that there is no additional cost at test time because TBBN works to be identical to the original BN." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 347, + 545, + 419 + ], + "blocks": [ + { + "bbox": [ + 318, + 331, + 533, + 342 + ], + "lines": [ + { + "bbox": [ + 318, + 331, + 533, + 342 + ], + "spans": [ + { + "bbox": [ + 318, + 331, + 533, + 342 + ], + "type": "text", + "content": "Table 5. Ablation study using CIFAR-100 with ResNet-32." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 347, + 545, + 419 + ], + "lines": [ + { + "bbox": [ + 308, + 347, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 308, + 347, + 545, + 419 + ], + "type": "table", + "html": "
MethodTask-balanced μ and σ2? TrainTask-balanced γ and β? TestAf(↑)Aa(↑)Peak MemoryTrain Time (total)Test Time (per batch)
TBBN✓✓38.4656.17
Case 1X✓29.7846.992525MiB (×1.6)6.0h (×1.3)0.6s (×1.0)
Case 2✓X0.939.69
Case 3✓✓35.4553.15
Case 4XX36.2153.25
BNXX35.7153.881545MiB4.6h0.6s
", + "image_path": "9b2c4d5bc96a70f3e868c26471fc84e93758d0c06ea0de813fd8daf981741fb0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 438, + 430, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 430, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 430, + 452 + ], + "type": "text", + "content": "6. Concluding Remarks" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 460, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 593 + ], + "type": "text", + "content": "We propose a simple but effective method, called Task-Balance Batch Normalization, for exemplar-based CIL. Starting from an analysis of the problem of the original BN, namely, the biased mean and variance calculation toward the current task, we devise a novel method to calculate the task-balanced mean and variance for normalization. Furthermore, we propose a method for the task-balanced training of parameters for affine transformation. From extensive experiments with CIFAR-100, ImageNet-100 and dissimilar tasks, we demonstrate that our TBBN can be easily applied to various existing CIL methods, further improving their performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 608, + 416, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 416, + 622 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 416, + 622 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "This work was partly done while Sungmin Cha did a research internship at Advanced ML Lab, LG AI Research. The work was also supported in part by NRF grant [NRF-2021R1A2C2007884], IITP grant [No.2021-0-01343, No.2021-0-02068, No.2022-0-00113, No.2022-0-00959] funded by the Korean government (MSIT), and SNU-LG AI Research Center." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20134" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. 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A deep face model pretrained on high-resolution face images introduces a cluster of recognizable instances (grey spike), dubbed unrecognizable identities (UIs) in [9]. (a) shows the bimodal distribution for a very low-resolution face dataset [6] based on distance against the UIs. Interestingly, a portion of hard-to-recognize faces (red peak) lie close to the UIs, indicating their low recognizability. (b) We propose to improve the recognizability of hard-to-recognize instances by pushing them away from the UIs center. Consequently, faces with higher recognizability indexes are further apart from UIs center in the embedding space. Our method not only induces more discriminative representations but also translates face quality into a measurable indicator that closely matches human cognition." + ], + "image_footnote": [], + "bbox": [ + 81, + 290, + 888, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 547, + 313, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Very low-resolution face recognition (VLRFR) poses unique challenges, such as tiny regions of interest and poor resolution due to extreme standoff distance or wide viewing angle of the acquisition devices. In this paper, we study principled approaches to elevate the recognizability of a face in the embedding space instead of the visual quality. We first formulate a robust learning-based face recognizability measure, namely recognizability index (RI), based on two criteria: (i) proximity of each face embedding against the unrecognizable faces cluster center and (ii) closeness of each face embedding against its positive and negative class prototypes. We then devise an index diversion loss to push the hard-to-recognize face embedding with low RI away from unrecognizable faces cluster to boost the RI, which reflects better recognizability. Additionally, a perceptibility attention mechanism is introduced to attend to the most recognizable face regions, which offers better explanatory and discriminative traits for embedding learning. Our proposed model is trained end-to-end and simultaneously serves recognizability-aware embedding learning and face quality estimation. To address VLRFR, our extensive eval", + "bbox": [ + 73, + 583, + 472, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "uations on three challenging low-resolution datasets and face quality assessment demonstrate the superiority of the proposed model over the state-of-the-art methods.", + "bbox": [ + 496, + 549, + 892, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 617, + 630, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In real-world face recognition deployment scenarios, the pixel resolution of the detected face images is significantly deflated, due to extreme long-range distance and broad viewing angle of the acquisition devices, especially in surveillance applications. These tiny regions of interest are, in general, ranging from $16 \\times 16$ to $32 \\times 32$ pixels [60], thereby suffering from poor pixel resolution, in addition to unrestricted noises such as poor illumination conditions, non-frontal poses with awful angles, unconstrained facial expressions, blurriness, and occlusions [45]. It is noteworthy that these contaminated very low-resolution (VLR) face images undermine the overall performance of a face model trained with its high-resolution (HR) counterparts; therefore, there is a lack of generalizability to resolve the VLR face recognition (VLRFR) problem [6]. Apart from that, training of a VLRFR model often suffers from very limited representative face examples to extract meaningful", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9957", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "identity-specific patterns. These issues are further escalated due to ambiguous inter-class variations for the heavily distorted face instances with perceptually similar identities in particular [40]. Whilst matching a probe to a gallery set of the same resolution (i.e. VLR to VLR) is still an open challenge, the resolution gap between galleries and probes triggers another problem in cross-resolution matching (typically HR galleries to VLR probes). Hence, the generalization performance of the prevalent deep learning models for VLRFR is still far from satisfactory.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As a whole, most existing works designated for VLRFR improve the face quality of the VLR instances based on an auxiliary set of HR face images [28]. The generic operation modes are either in image domain (super-resolution, image synthesis) [52, 54, 58], embedding domain (resolution-invariant features, coupled mappings) [33, 44], or at classifier level (transfer learning, knowledge distillation) [13, 14, 20, 39]. However, most of these state-of-the-art models require mated HR-VLR pairs of the same subject. This is unrealistic in practice as the HR-VLR pairs are often unavailable.", + "bbox": [ + 75, + 244, + 472, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As far as face recognition is concerned, face recognizability (also known as face quality [17, 18]) can be deemed as a utility of how well a face image is for discrimination purposes. In other words, face quality is closely related to face recognition performance. Some works thus focus on predicting a face image's suitability for face recognition, commonly known as Face Image Quality Assessment (FIQA) [1, 18]. FIQA focuses either on (i) creating propositions to label the training data with face image quality scores and solve a regression problem [17, 18, 36], or (ii) linking the face embedding properties to FIQ scores [4,25,35,38,45]. The second approach shows better quality estimation, with the possible reason that the first approach is prone to mislabeling of ground truth quality [35, 45]. However, the second approach may not be optimal since the FIQ scores are estimated based on the embedding properties rather than through a learning process [2].", + "bbox": [ + 75, + 414, + 472, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, [9] reported an intriguing observation that a deep learning-based face model induces an unrecognizable cluster in the embedding space. The cluster, known as unrecognizable identities (UIs), is formed by unrecognizable face examples, owing to diverse inferior quality factors, including VLR, motion blurred, poor illumination, occlusion, etc. Hence, these face examples with varying ground truths incline to lie close to the UIs, rather than their respective identity clusters. This observation inspires us to analyze the embedding distribution of the VLR face images against the UIs center. Interestingly, the extreme bimodal distribution in Fig. 1 discloses that a significant number of the VLR faces in TinyFace [6], i.e., a realistic VLR face dataset, are hard-to-recognize from the human perspective and therefore rendered next to the UIs cluster. We reckon that mining", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "representative patterns from these hard-to-recognize faces is more meaningful for face recognition, in place of defining them as the elements of UIs. Apart from that, a more reliable objective quality metric is needed to better interpret each VLR face example in terms of its embedding recognizability for recognizability-aware embedding learning.", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead of perceptual quality, this work aims to elevate the recognizability of every VLR face embedding. In a nutshell, we formulate a learning-based recognizability index (RI) with respect to the Cosine proximity of each embedding instance with (i) the UIs cluster, and (ii) the associated positive and negative prototypes. In the meantime, the index diversion (ID) loss is presented to detach the hard-to-recognize embeddings from the UIs cluster, alongside a perceptibility attention mechanism. We underline that embedding learning in the direction opposing the UIs contributes to a higher explanatory power whilst promoting inter-class separation, particularly for hard-to-recognize instances. For clarity, we summarize our contributions as follows:", + "bbox": [ + 496, + 181, + 893, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel approach is proposed to address the VLRFR, including VLR-VLR and HR-VLR matching, by leveraging the face recognizability notion in the embedding space to improve the hard-to-recognize instances.", + "- A robust learning-based face recognizability, dubbed RI, is put forward. RI relies on the face embeddings' intrinsic proximity relationship against the UIs cluster, positive, and negative class prototypes.", + "- An index diversion (ID) loss is devised to enhance the RI for face embeddings. Further, we put forward a perceptibility attention mechanism to guide embedding learning from the most salient face regions.", + "- Our proposed model trained in an end-to-end manner not only renders a more discriminative embedding space for VLRFR but simultaneously serves recognizability-aware embedding learning and face recognizability estimation." + ], + "bbox": [ + 517, + 388, + 890, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 693, + 640, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Very Low-Resolution Face Recognition. Existing HR image dependence approaches for VLRFR can be categorized into image domain, embedding domain, and classifier. Under the image domain, the super-resolution (SR) model learns a mapping function to upscale VLR into HR images to improve faces' visual quality [41, 54]. Several successors' works [19, 52, 53, 58] relate recognition to visual quality. However, these works require mated HR-VLR pairs of the same subject to be available for embedding learning, which is unrealistic.", + "bbox": [ + 496, + 718, + 893, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "At both embedding domain and classifier levels, most knowledge distillation (KD) aimed to transfer the knowl-", + "bbox": [ + 496, + 869, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9958", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "edge of the HR domain to the VLR face model via a teacher-student network configuration [14]. To achieve cross-resolution distillation, [13] employed an additional network to bridge the teacher and student network, while [34] compared the face embeddings of teacher and student networks with a regression loss. On the other hand, distribution distillation loss [20], non-identity-specific mutual information [32] and implicit identity-extended augmentation [31] have also been explored to mitigate the performance gap between HR and VLR instances. [40] reconstructed an HR embedding to approximate the class variations of VLR instances while learning similar features for HR and VLR images. However, despite their high visual quality, some HR faces may not be recognized. In fact, [6, 29, 56] suggest that improving visual quality can undermine identity-specific traits important to the downstream recognition task. Our proposed method involves no auxiliary HR images. We aim to improve the hard-to-recognize instances based on the recognizability notion rather than visual quality.", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, Li et al. [30] proposed a rival margin on the hardest non-target logits to maximize the separation against the nearest negative classes. However, low-quality face images with perceptually similar identities are close to each other. Therefore, enforcing separation for a low-quality face image only from the nearest non-target class hardly learns meaningful characteristics to differentiate the two identities. On the contrary, we strive to enlarge the overall inter-class dissimilarity by enhancing image recognizability.", + "bbox": [ + 75, + 380, + 468, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Face Image Quality Assessment (FIQA) can be mainly divided into two categories. The first category is to solve a regression problem to assess the training images with FIQ scores [1, 2, 17, 18, 36, 51]. The FIQ scores include human quality annotation [1], the intra-class Euclidean distance between an instance and an ICAO [49] compliance instance [17, 18], the similarity between random positive mated pairs [51], the discriminability on each instance [2] and the Wasserstein distance between intra and inter-class distributions [36]. The second category directly utilizes the intrinsic properties of face embeddings to estimate face quality without explicit regression learning. For instance, [45] defined the robustness of stochastic embeddings as FIQ score. However, the computational cost is significant as the assessed instance is required to pass through the network multiple times at different dropout rates. [38] and [35] relied on uncertainty variation and embedding norm of the face embeddings as the FIQ scores, respectively.", + "bbox": [ + 75, + 518, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Aside from face quality, several works also explore classifiability according to face quality. Instead of using the fixed Gaussian mean as the face embedding [38], [4] proposed to learn a Gaussian mean alongside an uncertainty to reduce the adverse effects of noisy samples. In [21], the easy instances are first learned before the hard ones based on the adaptive margin angular loss. [48] defined hard sam", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/977718739eee28fe08889a0506a1c01ef1837f7f175f3007cffa795584492bf8.jpg", + "image_caption": [ + "Figure 2. Our proposed model comprises three main modules: (i) recognition module learns the face embeddings $v_{i}$ by optimizing the class prototypes for the recognition task; (ii) perceptibility regression module is designed to learn the recognizability index, $\\hat{\\xi}$ thereby enabling the recognizability prediction for any samples including the unseen ones; and (iii) perceptibility attention module performs channel and spatial-wise attention on the embeddings that approximate the projection away from the UIs cluster, $v^{\\prime}$ . The RI is learned based on two criteria, as shown on the bottom right, where $y$ is the target class, $j$ is the non-target class across all $C$ identities, and $\\bar{v}_{UI}$ is the mean of UI cluster embeddings." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ples and increased the weight of their negative cosine similarities with a preset constant. [35] assigned margins based on the embeddings' norm. As a successor, Kim et al. [25] refined the decision on adaptive margin, which only emphasizes hard instances when necessary.", + "bbox": [ + 496, + 473, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While most FIQA methods struggle to learn adaptive margins for competent quality-aware embedding [2], we strive to improve embedding learning based on the proposed RI. We demonstrate that RI characterizes the image quality better, and our model can extract meaningful semantics important to face recognition in Sec. 4.", + "bbox": [ + 496, + 549, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 654, + 635, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Recognizability Index (RI) Formulation", + "text_level": 1, + "bbox": [ + 500, + 680, + 841, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A face model trains a discriminative embedding space by enforcing intra-class compactness and inter-class discrepancy. Interestingly, [36] discloses the relationship between face quality and recognition performance by computing the Wasserstein distances between intra-class and inter-class similarity distributions. Hence, it is suggested that face recognizability can be quantified by intra-class and inter-class similarity measures.", + "bbox": [ + 496, + 703, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our disposition, the recognizable instances are pushed closer to their positive prototype and further apart from negative prototypes upon convergence. Meanwhile, the hard-to-recognize instances can hardly be pulled toward their positive prototypes, and are usually surrounded by negative", + "bbox": [ + 496, + 825, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9959", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ones. Among all negative prototypes, the nearest negative prototype is chosen for inter-class proximity estimation.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each instance $i$ , the intra-class and the inter-class proximity of its L2-normalized embedding $\\widehat{v}_i$ with respect to its positive prototype $\\boldsymbol{w}_{y_i}$ and the nearest negative prototype $\\boldsymbol{w}_j, j \\neq y_i$ across a set of $C$ identities are as follows:", + "bbox": [ + 75, + 121, + 468, + 183 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} ^ {P} = 1 - \\cos \\left(\\theta_ {y _ {i}}\\right), d _ {i} ^ {N} = 1 - \\max _ {j \\in \\{1, \\dots , C \\} \\backslash \\{y _ {i} \\}} \\cos \\left(\\theta_ {j}\\right) (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 207, + 468, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_{y_i}$ is the positive angle between $\\widehat{\\pmb{v}}_i$ and $\\pmb{w}_{y_i}$ and $\\theta_{j}$ is the negative angle between $\\widehat{\\pmb{v}}_i$ and $\\pmb{w}_j$ . On the other hand, feeding the unrecognizable faces to the model induces a UIs cluster in the embedding space [9]. Given the UIs cluster center, i.e., the average across all normalized UIs embeddings, $\\overline{\\pmb{v}}_{U1}$ , the proximity between $\\widehat{\\pmb{v}}_i$ and $\\overline{\\pmb{v}}_{U1}$ is defined as:", + "bbox": [ + 75, + 243, + 468, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} ^ {U I} = 1 - \\cos \\left(\\theta_ {U I _ {i}}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 342, + 468, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_{UI_i}$ is the angle between $\\widehat{\\pmb{v}}_i$ and $\\overline{\\pmb{v}}_{UI}$ . Since the proximity is in terms of Cosine distance, the instances closest to the UIs cluster center (computed with the smallest $d_i^{UI}$ ) are referred to as hard-to-recognize instances, and vice versa. Since the proximity of each instance differs with respect to its positive and negative prototypes alongside the UIs cluster center, the association of Eq. (1) and Eq. (2) can serve to estimate the face quality. Given an imposed $\\epsilon = 1e^{-7}$ to avoid division by zero, we define a recognizability measure, dubbed Recognizability Index (RI), $\\xi_i$ as follows:", + "bbox": [ + 75, + 364, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\xi_ {i} = d _ {i} ^ {U I} \\frac {d _ {i} ^ {N}}{d _ {i} ^ {P} + \\epsilon} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 527, + 468, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Perceptibility Regression Module", + "text_level": 1, + "bbox": [ + 76, + 571, + 369, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As our model serves recognizability-aware embedding learning and quality estimation simultaneously, we introduce a perceptibility regression module (yellow) as in Fig. 2. The input to the regression module is a flattened feature map learned from the backbone network, navigating through a dropout layer and a fully-connected regression layer to yield a learnable RI, denoted by $\\widehat{\\xi}_i$ . To match $\\widehat{\\xi}_i$ to $\\xi_i$ in Eq. (3), we apply the smooth L1 loss [15] as follows:", + "bbox": [ + 75, + 594, + 468, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {L 1} = \\left\\{ \\begin{array}{l l} 0. 5 \\left(\\xi_ {i} - \\widehat {\\xi} _ {i}\\right) ^ {2} / \\beta & \\text {i f} \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| < \\beta \\\\ \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| - 0. 5 \\times \\beta & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 728, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is a threshold that switches between L1 and L2-losses. In the early training stage, the L1 loss computes consistent gradients to approximate $\\widehat{\\xi}$ towards $\\xi$ . When the regression error falls below the confidence interval, the L2 loss exhibits a smoother transition in the loss surface to facilitate convergence. In our experiments, we fix $\\beta = 0.75$ . It is noteworthy that the RI from the regression module differs from ERS [9] in the following perspectives: (i) ERS", + "bbox": [ + 75, + 777, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "does not consider the intra-class and inter-class proximities, and (ii) ERS requires the UIs cluster center to be known for recognizability score estimation, but our model simply withdraws the UIs cluster during the deployment. In other words, upon training completion, the regression module incorporates the proximity relation in Eq. (3) and allows the face quality prediction on any unknown samples without involving the UIs cluster.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Index Diversion Loss", + "text_level": 1, + "bbox": [ + 500, + 219, + 697, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Having RI obtained from the perceptibility regression module, the next following goal is to enhance the hard-to-recognize instances' recognizability. We first model the RI distribution of the UIs cluster. According to the Central Limit Theorem [12], the Gaussian distribution is the most general distribution for fitting values derived from Gaussian or non-Gaussian random variables. Motivated by this, we can either estimate the mean and the variance of the Gaussian by forwarding the UIs through the perceptibility regression module or simply assume RI follows the standard Gaussian distribution with $\\mathcal{N}(0,1)$ . We opt for the latter as it has better interpretability and a more stable RI to resolve the hard-to-recognize instances.", + "bbox": [ + 496, + 242, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we define the diversion of the estimated $\\widehat{\\xi}_i$ as:", + "bbox": [ + 519, + 438, + 862, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd i v = \\frac {\\widehat {\\xi} _ {i} - \\mu_ {U I}}{\\sigma_ {U I}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 455, + 890, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the range of $\\hat{\\xi}_i$ is arbitrary, it is rescaled with respect to $\\mu_{UI}$ and $\\sigma_{UI}$ of the UI distribution as:", + "bbox": [ + 498, + 493, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {U I} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} s _ {k}, \\sigma_ {U I} = \\sqrt {\\frac {\\sum_ {k = 1} ^ {K} \\left(s _ {k} - \\mu_ {U I}\\right) ^ {2}}{K - 1}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 525, + 890, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_k$ denotes the RI of a random UI instance that is assumed to be i.i.d and follows $\\mathcal{N}(\\mu, \\sigma^2)$ . Here, we set $K = 5,000$ . In accordance with Eq. (5), the index diversion (ID) loss is formulated as:", + "bbox": [ + 498, + 569, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {I D} = \\max (0, \\tau - d i v) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 632, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is the confidence interval hyperparameter. The ID loss enforces a deviation of at least $\\tau$ between $\\widehat{\\xi}_i$ and $\\mu_{UI}$ . As a hard-to-recognize instance is associated with a small $\\widehat{\\xi}_i$ , it induces a relatively large ID loss. We attempt to push the hard-to-recognize instances outside the designated $\\tau$ by minimizing the ID loss. In other words, the ID loss is equivalent to enforcing a statistically significant deviation of $\\mu_{UI}$ from the estimated $\\widehat{\\xi}_i$ of VLR instances in the upper tail. Note that although the ID loss enforces a confidence interval, it does not divert $\\widehat{\\xi}_i$ infinitely as the $\\widehat{\\xi}_i$ is still bounded to RI under the constraint of Eq. (4).", + "bbox": [ + 496, + 652, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the ID loss is dedicated to differentiable learning of the recognizability measure, we argue that the statistical diversion of $\\widehat{\\xi}_i$ contributes to a more meaningful enhancement of recognizability in the embedding space, especially for the hard-to-recognize face images.", + "bbox": [ + 496, + 823, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9960", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Perceptibility Attention Module", + "text_level": 1, + "bbox": [ + 76, + 90, + 357, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In [9], Deng et al. showed that diverting the embedding's direction from the UIs cluster center results in face recognition improvement in the inference stage. Given the embedding vector of a VLR face instance $\\mathbf{v}_i$ and the L2-normalized UIs cluster center $\\overline{\\mathbf{v}}_{UI}$ , we define the embedding projected in the direction away from the UIs cluster $\\mathbf{v}_i'$ based on [9] as:", + "bbox": [ + 75, + 114, + 468, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {i} ^ {\\prime} = \\boldsymbol {v} _ {i} - \\langle \\boldsymbol {v} _ {i}, \\bar {\\boldsymbol {v}} _ {U I} \\rangle \\bar {\\boldsymbol {v}} _ {U I} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 233, + 468, + 251 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conjecture that the embedding projection away from the UIs cluster center is beneficial to alleviate the model's inadequacy to highlight the meaningful features when the face is obscure. Different from the conventional attention models for the classification tasks, we seek to explore the most salient feature representation with the greatest significance for recognizability by approximating $\\boldsymbol{v}_i'$ through an attention module. Inspired by [50], we design a perceptibility attention module that attends to the spatial and channel dimension of the instances' feature map sequentially. The attended feature maps are fed into a linearly connected layer to learn an attended embedding $\\boldsymbol{v}_i^{attn}$ at the same dimension as $\\boldsymbol{v}_i'$ . Lastly, we utilize the mean squared error loss and formalize the regression problem as:", + "bbox": [ + 75, + 263, + 470, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {M S E} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\left(\\boldsymbol {v} _ {i} ^ {\\prime} - \\boldsymbol {v} _ {i} ^ {\\text {a t t n}}\\right) ^ {2} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 478, + 468, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $B$ is the batch size. We argue that the projection of embeddings away from the UIs cluster can be deemed as RI-enhanced embeddings. This guides our model to attend to the parts of embedding that contain the richer interpretive contents important to recognition purposes. Therefore, introducing an attention module permits our model to attend to the most salient face regions, i.e., eyes, nose, etc., of a VLR face instance. In compliance with Eq. (4), (7) and (9), the overall loss function is expressed as follows:", + "bbox": [ + 75, + 526, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t o t a l} = L _ {c l s} + \\alpha L _ {L 1} + \\beta L _ {I D} + \\gamma L _ {M S E} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 676, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we opt for ArcFace [8] as the classification loss, $L_{cls}$ , $\\alpha$ , $\\beta$ , and $\\gamma$ are the weighting factors for each loss term.", + "bbox": [ + 76, + 705, + 467, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 753, + 310, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. To confront the real-world VLRFR problem, our experiments are conducted on three realistic LR face datasets, namely TinyFace [6], SurvFace [7], and SCFace [16] under an open-set evaluation protocol, given the identity labels are disjoint across training and testing sets. We assemble an unlabeled UI face dataset from two public person re-identification repositories by the MTCNN face detector [57], including LPW [42] and MARS [59]. Notably,", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "most of the detected faces are unrecognizable, thereby facilitating the generation of an UIs cluster. The details of each dataset are provided in Sec. A of in supplemental material.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experiment Settings. Our experiments utilize Mobile-FaceNet [5] and ResNet-50 [8] pretrained on the VGGFace2 [3] dataset as the representation encoder. For each dataset, we fine-tune these models using the respective training examples for performance evaluation. Our baseline model is the counterpart trained only with the ArcFace loss. We provide our experimental setup and other relevant settings in Sec. B of the supplemental material.", + "bbox": [ + 498, + 137, + 890, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We summarize the overall performance in rank-1 identification rate (IR) (\\%) for TinyFace and SCFace. On the contrary, we report the positive identification rate (TPIR) (\\%) @ false positive identification rate (FPIR), and true positive rate (TPR) (\\%) @ false acceptance rate (FAR) (\\%) for SurvFace, due to the inclusion of non-mated face images in its testing set [7].", + "bbox": [ + 498, + 258, + 890, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the characterization of face image quality, we provide the Error versus Reject Curve (ERC) [2, 18, 36], where portions of low-quality face images are screened out with respect to quality indexes. This evaluation is assessed in terms of False Non-Match Rate (FNMR) [26] at a specific threshold for a fixed False Match Rate (FMR) [26].", + "bbox": [ + 498, + 364, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Comparison with SoTA Methods", + "text_level": 1, + "bbox": [ + 500, + 465, + 785, + 481 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare the generalization performance on two open-set face identification tasks, VLR-VLR (TinyFace and SurvFace) and HR-VLR (SCFace), to the most recent SoTAs in Table 1, 2, and $3^{1}$ . The former task is relatively challenging as only the noisy VLR examples are provided for probe-to-gallery matching. However, the latter suffers from a severe resolution gap between the HR galleries and the VLR probes. We disclose that the proposed model is not only resistant to the resolution gap but also a viable solution to the downstream VLR-VLR task. On the other hand, we leave the column blank for KD and resolution-invariant methods without involving the VLR datasets for fine-tuning, seeing that these VLR datasets are relatively small-scale and therefore easily prone to over-fitting.", + "bbox": [ + 498, + 489, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "TinyFace. We substantiate that our model outperforms other recent SoTAs designated for VLRFR by a remarkable margin, both with and without distractors (a summation of 153,428 face images of unknown identities in the gallery set). Specifically, we demonstrate that improving recognizability at the feature level is more meaningful than super-resolving the visual quality of the VLR face images, e.g. [6, 24, 39, 58]. With a quality-adapted margin for embedding learning, we discern that AdaFace [25] only readjusts the decision boundary - remaining the feature recog", + "bbox": [ + 498, + 700, + 890, + 852 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "In the \"fine-tuned\" column of these tables, we indicate $\\sharp$ , $\\dagger$ , and $\\checkmark$ as fine-tuning on super-resolved, synthetic down-sampled VLR, and native VLR face images respectively.", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9961", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4557ab41c370dcdeb249bd128e9c1cf19c599f720135add48407114a34bdef28.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsFine-TunedRank-1 IR (%)
w/ disw/o dis
CSRI (ACCV19) [6]#44.80-
TURL (CVPR20) [39]63.89-
RIFR (T-BIOM20) [24]70.40-
VividGAN (TIP21) [58]#47.16-
MIND-Net (SPL21) [32]✓66.8273.52
AdaFace (CVPR22) [25]68.21-
IDEA-Net (TIFS22) [31]✓68.13-
AdaFace (Reproduce)✓71.3875.67
Ours✓73.0677.22
", + "bbox": [ + 78, + 88, + 480, + 287 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/183d3fcf1e765636cfa9d559af6c797ebaae3b736b6e83dc6e3cb28f43c3ac62.jpg", + "table_caption": [ + "Table 1. IR Comparison on TinyFace using ResNet-50" + ], + "table_footnote": [], + "table_body": "
MethodsFine-TunedRank-1 IR (%)
4.2m2.6m1.0mAvg.
TCN (ICASSP10) [55]✓74.6094.9098.6089.37
T-C (IVC20) [34]†70.2093.7098.1087.33
FAN (ACCV19) [52]✓77.5095.0098.3090.30
RAN (ECCV20) [11]✓81.3097.8098.8092.63
DDL (ECCV20) [20]✓86.8098.3098.3094.40
RIFR (T-BIOM20) [24]88.3098.3098.6095.00
MIND-Net (SPL21) [32]✓81.7598.0099.2593.00
DSN (APSIPA21) [27]✓93.0098.5098.5096.70
DRVNet (TPAMI21) [40]✓76.8092.8097.5089.03
RPCL (NN22) [30]✓90.4098.0098.0095.46
NPT (TPAMI22) [23]85.6999.0899.0896.61
IDEA-Net (TIFS22) [31]✓90.7698.5099.2596.17
AdaFace (Reproduce)✓95.3898.4699.8497.89
Ours✓97.0799.2399.8098.70
", + "bbox": [ + 495, + 88, + 888, + 287 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/569fa08b09fedfbb1f7a478b5a06cc611b9a7b0649af63564f9862ae509ab265.jpg", + "table_caption": [ + "Table 2. IR Comparison on SCFace using ResNet-50" + ], + "table_footnote": [], + "table_body": "
MethodsFine-TunedTPR(%)@FARTPIR20(%)@FPIR
0.30.10.010.0010.30.20.1
CSRI (ACCV19) [6, 22]#78.6053.1018.0912.04---
FAN (ACCV19) [52]71.3044.5912.942.75---
RAN (ECCV20) [11]----26.5021.6014.90
SST (ECCV20) [10]✓87.0068.2135.7222.1812.389.716.61
DSN (APSIPA21) [27]75.0952.7421.4111.02---
DDAT (PR21) [22]90.4075.5040.4016.40---
IDEA-Net (TIFS22) [11]----26.2421.8215.61
AdaFace (Reproduce)✓87.4177.4858.6340.0931.5027.7421.93
Ours✓90.2180.9964.6048.4833.2029.3422.81
", + "bbox": [ + 76, + 316, + 893, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. TPR(%)@FAR and TPIR20(%)@FPIR Comparison on SurvFace using ResNet-50", + "bbox": [ + 210, + 484, + 756, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "nizability unchanged.", + "bbox": [ + 76, + 518, + 222, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SCFace. For the HR-VLR evaluation, our model remains superior to other SoTAs over the three probe sets. This is attributed to: (i) the enhanced recognizability bridges the resolution gap between the HR and the VLR face features; and (ii) the attention module singles out the most salient regions from VLR and HR faces, resulting in better cross-resolution matching scores, especially for the face images captured from $4.2m$ (the largest standoff distances compared to $1.0m$ and $2.6m$ ).", + "bbox": [ + 75, + 535, + 470, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SurvFace. Being the most challenging VLR face dataset for the VLR-VLR deployment scenario, SurvFace evaluates both open-set identification and verification tasks in the presence of 141,736 unmated distractors as a part of the probe set. We disclose that our model significantly outperforms other SoTAs under the most rigorous settings, i.e., TPR@FAR=0.001 and TPIR20@FPIR=0.01. While [11,22,52] are trained based on synthetic LR images downsampled from HR-paired counterparts for visual quality improvement, we underline that none of these SoTAs resolves the VLRFR by means of refining feature recognizability.", + "bbox": [ + 75, + 671, + 468, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Analysis", + "text_level": 1, + "bbox": [ + 76, + 851, + 250, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Each Loss Component. We present in Table 4 an ablation analysis to explore the effect of each loss term", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "using MobileFaceNet on TinyFace without gallery distractors. Compare to our baseline model (trained using only ArcFace), the inclusion of ID loss in Baseline I discloses that learning to enhance the recognizability of the hard-to-recognize instances offers a performance improvement close to $1.0\\%$ . Baseline II, on the other hand, reveals that the perceptibility attention module allows the most salient characteristics to be attended, resulting in at least $1.2\\%$ of performance gain. Meanwhile, Baseline III demonstrates that our model benefits from learning an RI based on an estimated RI as shown in Eq. (4). It is believed that learning the softmax prototypes simultaneously with the RI prompts our model to encode the embedding recognizability at each training step. As a result, the learned RI can be viewed as an index of the model's confidence corresponding to the classifiability of any face image, including the unknown instances. Overall, our model trained with all loss terms outperforms the baselines and two most relevant SoTAs, i.e., MagFace [35], and AdaFace [25]. An important reason is that these SoTAs are reliant on the embedding's norm that does not always convey face recognizability, particularly for the VLR face images. This is substantiated by our empirical proofs in the following section.", + "bbox": [ + 496, + 518, + 893, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intuition of Hyperparameter Selection. In Fig. 3, we conduct the study of each weighting factor on each hyper", + "bbox": [ + 498, + 869, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9962", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/500c5216d867eafe0dd6e1e497ab685ea82a51164214236534cb6bd12b75391d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLclsLIDLMSELL1Rank-1 IR (%)
Cross Entropy [43]✓68.884
NormFace [46]✓68.026
CosFace [47]✓70.306
MV-Softmax [48]✓70.547
CurricularFace [21]✓70.655
MagFace [35]✓70.467
AdaFace [25]✓70.359
Baseline (ArcFace) [8]✓70.333
I✓✓71.298
II✓✓71.540
III✓✓71.674
Ours✓✓✓✓71.915
", + "bbox": [ + 81, + 88, + 472, + 238 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation Analysis for each Loss Term on TinyFace without Distractors using MobileFaceNet.", + "bbox": [ + 76, + 242, + 468, + 270 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86a631936821ca9cb8bd3ff5c1999ff99a132246fe77d2743ca7ea1e00e1efe8.jpg", + "image_caption": [ + "Figure 3. Ablation Studies for Hyperparameters $\\alpha, \\beta$ , and $\\gamma$ ." + ], + "image_footnote": [], + "bbox": [ + 78, + 282, + 464, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "parameter by fixing the remaining weighting factors to be their optimal values in accordance to Table 5. We refer to Eq. (10) where $\\alpha, \\beta, \\gamma$ correspond to the weighting of $L_{L1}, L_{ID}, L_{MSE}$ respectively. Suppose that we attempt to study the various weighting factors of $L_{L1}$ via manipulating the values of $\\alpha$ , we fix $\\gamma = 1$ and $\\beta = 2$ . The effects of $\\alpha$ are shown as the $\\alpha$ curve, and the same is applied to $\\beta$ and $\\gamma$ curves. Our ablations show that an overly large $\\alpha (>10)$ may experience difficulty in convergence [2], and 5 is the best choice. For $\\beta$ , the findings suggest a weighting factor slightly less than the $\\alpha$ ensures better recognizability of the instances while still being upper bound by the devised RI. Lastly, we discover that $L_{MSE}$ converges fast, and a higher $\\gamma$ hinders the overall model convergence, resulting in performance depreciation. A smaller $\\gamma$ is thus recommended and set to be 1 in our experiment.", + "bbox": [ + 75, + 446, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Face Recognizability-Aware Embeddings. We conduct a toy experiment with 5 easy-to-recognize (IDs 0,2,3,5,7) and 3 hard-to-recognize (IDs 1,4,6) face examples to examine the embedding space learned by SoTAs and our model in Fig. 4. The UIs center is visualized as a reference index of recognizability, where a poor recognizability (hard-to-recognize) instance is essentially projected close to the UIs center. It is discerned that the competing models are incapable of separating the hard-to-recognize clusters from the UIs center. On the contrary, our model is inclined to divert the hard-to-recognize instances from the UIs center, yielding a well-separable (therefore a more discriminative) embedding space to resolve the downstream VLRFR task.", + "bbox": [ + 75, + 688, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Perceptibility Attention Module. We portray", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a2d8305b9c8a52a7133fbecff4f21613c443362cae2f1db8746d8e59d28c65f7.jpg", + "image_caption": [ + "Figure 4. 2D embedding space for a toy problem with 8 identities (IDs). The IDs denoted with a \"√\" contain hard-to-recognize instances, even from the human perspective. We visualize the UIs center as a reference index of recognizability, i.e., embeddings further away from the UIs center can better be recognized." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 880, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa1b706775f53a24447f830e89b24382ef15b2109d27aa172cfa404bd4a0f6f6.jpg", + "image_caption": [ + "Figure 5. Class activation maps for several VLR face images generated based on ArcFace, AdaFace, and Ours." + ], + "image_footnote": [], + "bbox": [ + 508, + 270, + 879, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the Class Activation Maps [37] obtained from ArcFace [8], Adaface [25], and our method for comparison. Interestingly, we observe from Fig. 5 that attending to the embeddings away from the UIs center focuses more on the salient face features, i.e. eyes, nose, and mouth, even when the face images appear to be obscure. We provide the extended heatmap visualizations in Fig. 11 of supplemental material.", + "bbox": [ + 496, + 482, + 890, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Face Image Quality Assessment (FIQA)", + "text_level": 1, + "bbox": [ + 500, + 602, + 841, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Learned RI from Perceptibility Regression Module. In Fig. 6, the effect of ID loss reveals a greater negatively-skewed distribution of RI than other SoTAs (extended version in Fig. 9), indicating an improvement in recognizability, notably the hard-to-recognize instances. We discern that the proposed RI is a robust indicator in characterizing the recognizability notion - the highest and the lowest RI reflect the best-quality and the poor-quality face images, respectively. We also provide in Fig. 6 the face images with the lowest quality scores estimated by other competing scores. Through the comparison, RI is deemed proportional to the human cognitive level in terms of recognizability for the VLR face images under extreme poses, illuminations, occlusions, and others in the wild conditions.", + "bbox": [ + 496, + 627, + 890, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Error versus Rejection Curve (ERC). To further substantiate the RI's robustness, we perform a verification task on TinyFace [6] by randomly sampling 20,888 positive and 50,000 negative pairs from its gallery and probe sets to show", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9963", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a6bf592ef4bee07739cc7551e89264161ee9c04b4f67b2f8859b4b999b11b983.jpg", + "image_caption": [ + "Figure 6. To facilitate direct comparison, all quality measures are normalized to ranges between 0 and 1. (Left) Visualization of RI sorted from the lowest scores (the poorest quality) to the highest (the best quality) in TinyFace [6] dataset. It is disclosed that the proposed RI characterizes the face quality better, closely simulating the human cognitive level. (Right) The VLR face images estimated with the lowest quality scores based on MagFace [35], CR-FIQA [2] and ERS [9]. In place of hard-to-recognize instances, we observe that several high-quality face instances are mistakenly assigned with low-quality scores, particularly MagFace and CR-FIQA." + ], + "image_footnote": [], + "bbox": [ + 80, + 85, + 614, + 364 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1523a86b61ef08c0b036c916b6ad645e9e3fe8cafbe1764dee32808aef85f5b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 88, + 885, + 363 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/07ff506db35875925765bf08c7b2c7360d3261e2a25dd871d6897de91cbd25f5.jpg", + "image_caption": [ + "Figure 7. Whilst Fig. 6 shows that the learned RI can characterize face quality well, we further demonstrate in this figure that the learned RI is a reliable recognizability metric by means of analyzing false non-match rate (FNMR). In particular, FNMR decreases gradually when the ratio of unconsidered VLR face images increases (sampled based on the lowest RI). This indicates that the learn RI well characterizes the recognizability of the VLR face images, such that the most recognizable VLR face images are learned with the highest RIs (corresponding to the right of the left-skewed RI distribution) for FNMR evaluation." + ], + "image_footnote": [], + "bbox": [ + 84, + 449, + 359, + 616 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f354129eee6380fb02ba044c0dce4ddf8ae1d96e3bc60ffbf07508020afd4224.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 348, + 450, + 612, + 616 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94e5817c2ef5911ad9e92c36fea466a0bdfca24a23836fa8f473a09aad6609b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 450, + 877, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ERC in Fig. 7. The learned $\\widehat{\\xi}_i$ outperforms SoTA in achieving stable and true rejection of unrecognized pairs in the rank of recognizability, especially when the FMR is at $1e^{-4}$ .", + "bbox": [ + 75, + 715, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 772, + 194, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper addresses the problem arising from the hard-to-recognize faces in VLR images. Rather than treating these faces as UIs, we take a principled recognizability notion to characterize the recognizability of each image with a robust indicator, specifically the recognizability index (RI). The recognizability of an instance can thus be adjusted based on RI. Interestingly, attending to the embeddings pro", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "jected away from the UIs cluster provides more explanatory power to the model to highlight the facial features more precisely. We evaluate the proposed method trained in an end-to-end manner on three VLR datasets and achieve SoTA for both VLRFR and FIQA.", + "bbox": [ + 496, + 715, + 892, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 814, + 666, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NO. 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IEEE Transactions on image processing, 21(1):327-340, 2011. 1" + ], + "bbox": [ + 78, + 90, + 468, + 458 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "9967", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_model.json b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1e44a63c1ed1d0c4bf2c9bb1fbb462d09eb2ad8c --- /dev/null +++ b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_model.json @@ -0,0 +1,2202 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.121, + 0.13, + 0.852, + 0.177 + ], + "angle": 0, + "content": "Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.203, + 0.871, + 0.24 + ], + "angle": 0, + "content": "Jacky Chen Long Chai\\(^{1}\\) Tiong-Sik Ng\\(^{1}\\) Cheng-Yaw Low\\(^{2}\\) Jaewoo Park\\(^{1}\\) Andrew Beng Jin Teoh\\(^{1}\\) \n\\(^{1}\\)Yonsei University \\(^{2}\\)Institute for Basic Science" + }, + { + "type": "text", + "bbox": [ + 0.136, + 0.241, + 0.828, + 0.258 + ], + "angle": 0, + "content": "1{jackyccl,ngtiongsik,julypraise,bjteoh}@yonsei.ac.kr 2{chengyawlow}@ibs.re.kr" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.291, + 0.889, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.435, + 0.26, + 0.45 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.435, + 0.71, + 0.45 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.452, + 0.893, + 0.537 + ], + "angle": 0, + "content": "Figure 1. A deep face model pretrained on high-resolution face images introduces a cluster of recognizable instances (grey spike), dubbed unrecognizable identities (UIs) in [9]. (a) shows the bimodal distribution for a very low-resolution face dataset [6] based on distance against the UIs. Interestingly, a portion of hard-to-recognize faces (red peak) lie close to the UIs, indicating their low recognizability. (b) We propose to improve the recognizability of hard-to-recognize instances by pushing them away from the UIs center. Consequently, faces with higher recognizability indexes are further apart from UIs center in the embedding space. Our method not only induces more discriminative representations but also translates face quality into a measurable indicator that closely matches human cognition." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.548, + 0.314, + 0.563 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.584, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Very low-resolution face recognition (VLRFR) poses unique challenges, such as tiny regions of interest and poor resolution due to extreme standoff distance or wide viewing angle of the acquisition devices. In this paper, we study principled approaches to elevate the recognizability of a face in the embedding space instead of the visual quality. We first formulate a robust learning-based face recognizability measure, namely recognizability index (RI), based on two criteria: (i) proximity of each face embedding against the unrecognizable faces cluster center and (ii) closeness of each face embedding against its positive and negative class prototypes. We then devise an index diversion loss to push the hard-to-recognize face embedding with low RI away from unrecognizable faces cluster to boost the RI, which reflects better recognizability. Additionally, a perceptibility attention mechanism is introduced to attend to the most recognizable face regions, which offers better explanatory and discriminative traits for embedding learning. Our proposed model is trained end-to-end and simultaneously serves recognizability-aware embedding learning and face quality estimation. To address VLRFR, our extensive eval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.893, + 0.596 + ], + "angle": 0, + "content": "uations on three challenging low-resolution datasets and face quality assessment demonstrate the superiority of the proposed model over the state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.618, + 0.631, + 0.634 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In real-world face recognition deployment scenarios, the pixel resolution of the detected face images is significantly deflated, due to extreme long-range distance and broad viewing angle of the acquisition devices, especially in surveillance applications. These tiny regions of interest are, in general, ranging from \\(16 \\times 16\\) to \\(32 \\times 32\\) pixels [60], thereby suffering from poor pixel resolution, in addition to unrestricted noises such as poor illumination conditions, non-frontal poses with awful angles, unconstrained facial expressions, blurriness, and occlusions [45]. It is noteworthy that these contaminated very low-resolution (VLR) face images undermine the overall performance of a face model trained with its high-resolution (HR) counterparts; therefore, there is a lack of generalizability to resolve the VLR face recognition (VLRFR) problem [6]. Apart from that, training of a VLRFR model often suffers from very limited representative face examples to extract meaningful" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9957" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "identity-specific patterns. These issues are further escalated due to ambiguous inter-class variations for the heavily distorted face instances with perceptually similar identities in particular [40]. Whilst matching a probe to a gallery set of the same resolution (i.e. VLR to VLR) is still an open challenge, the resolution gap between galleries and probes triggers another problem in cross-resolution matching (typically HR galleries to VLR probes). Hence, the generalization performance of the prevalent deep learning models for VLRFR is still far from satisfactory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.412 + ], + "angle": 0, + "content": "As a whole, most existing works designated for VLRFR improve the face quality of the VLR instances based on an auxiliary set of HR face images [28]. The generic operation modes are either in image domain (super-resolution, image synthesis) [52, 54, 58], embedding domain (resolution-invariant features, coupled mappings) [33, 44], or at classifier level (transfer learning, knowledge distillation) [13, 14, 20, 39]. However, most of these state-of-the-art models require mated HR-VLR pairs of the same subject. This is unrealistic in practice as the HR-VLR pairs are often unavailable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.473, + 0.673 + ], + "angle": 0, + "content": "As far as face recognition is concerned, face recognizability (also known as face quality [17, 18]) can be deemed as a utility of how well a face image is for discrimination purposes. In other words, face quality is closely related to face recognition performance. Some works thus focus on predicting a face image's suitability for face recognition, commonly known as Face Image Quality Assessment (FIQA) [1, 18]. FIQA focuses either on (i) creating propositions to label the training data with face image quality scores and solve a regression problem [17, 18, 36], or (ii) linking the face embedding properties to FIQ scores [4,25,35,38,45]. The second approach shows better quality estimation, with the possible reason that the first approach is prone to mislabeling of ground truth quality [35, 45]. However, the second approach may not be optimal since the FIQ scores are estimated based on the embedding properties rather than through a learning process [2]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recently, [9] reported an intriguing observation that a deep learning-based face model induces an unrecognizable cluster in the embedding space. The cluster, known as unrecognizable identities (UIs), is formed by unrecognizable face examples, owing to diverse inferior quality factors, including VLR, motion blurred, poor illumination, occlusion, etc. Hence, these face examples with varying ground truths incline to lie close to the UIs, rather than their respective identity clusters. This observation inspires us to analyze the embedding distribution of the VLR face images against the UIs center. Interestingly, the extreme bimodal distribution in Fig. 1 discloses that a significant number of the VLR faces in TinyFace [6], i.e., a realistic VLR face dataset, are hard-to-recognize from the human perspective and therefore rendered next to the UIs cluster. We reckon that mining" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.895, + 0.182 + ], + "angle": 0, + "content": "representative patterns from these hard-to-recognize faces is more meaningful for face recognition, in place of defining them as the elements of UIs. Apart from that, a more reliable objective quality metric is needed to better interpret each VLR face example in terms of its embedding recognizability for recognizability-aware embedding learning." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.183, + 0.895, + 0.379 + ], + "angle": 0, + "content": "Instead of perceptual quality, this work aims to elevate the recognizability of every VLR face embedding. In a nutshell, we formulate a learning-based recognizability index (RI) with respect to the Cosine proximity of each embedding instance with (i) the UIs cluster, and (ii) the associated positive and negative prototypes. In the meantime, the index diversion (ID) loss is presented to detach the hard-to-recognize embeddings from the UIs cluster, alongside a perceptibility attention mechanism. We underline that embedding learning in the direction opposing the UIs contributes to a higher explanatory power whilst promoting inter-class separation, particularly for hard-to-recognize instances. For clarity, we summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.389, + 0.892, + 0.452 + ], + "angle": 0, + "content": "- A novel approach is proposed to address the VLRFR, including VLR-VLR and HR-VLR matching, by leveraging the face recognizability notion in the embedding space to improve the hard-to-recognize instances." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.461, + 0.892, + 0.523 + ], + "angle": 0, + "content": "- A robust learning-based face recognizability, dubbed RI, is put forward. RI relies on the face embeddings' intrinsic proximity relationship against the UIs cluster, positive, and negative class prototypes." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.533, + 0.892, + 0.593 + ], + "angle": 0, + "content": "- An index diversion (ID) loss is devised to enhance the RI for face embeddings. Further, we put forward a perceptibility attention mechanism to guide embedding learning from the most salient face regions." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.604, + 0.892, + 0.68 + ], + "angle": 0, + "content": "- Our proposed model trained in an end-to-end manner not only renders a more discriminative embedding space for VLRFR but simultaneously serves recognizability-aware embedding learning and face recognizability estimation." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.389, + 0.892, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.642, + 0.71 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.719, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Very Low-Resolution Face Recognition. Existing HR image dependence approaches for VLRFR can be categorized into image domain, embedding domain, and classifier. Under the image domain, the super-resolution (SR) model learns a mapping function to upscale VLR into HR images to improve faces' visual quality [41, 54]. Several successors' works [19, 52, 53, 58] relate recognition to visual quality. However, these works require mated HR-VLR pairs of the same subject to be available for embedding learning, which is unrealistic." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "At both embedding domain and classifier levels, most knowledge distillation (KD) aimed to transfer the knowl-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9958" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.379 + ], + "angle": 0, + "content": "edge of the HR domain to the VLR face model via a teacher-student network configuration [14]. To achieve cross-resolution distillation, [13] employed an additional network to bridge the teacher and student network, while [34] compared the face embeddings of teacher and student networks with a regression loss. On the other hand, distribution distillation loss [20], non-identity-specific mutual information [32] and implicit identity-extended augmentation [31] have also been explored to mitigate the performance gap between HR and VLR instances. [40] reconstructed an HR embedding to approximate the class variations of VLR instances while learning similar features for HR and VLR images. However, despite their high visual quality, some HR faces may not be recognized. In fact, [6, 29, 56] suggest that improving visual quality can undermine identity-specific traits important to the downstream recognition task. Our proposed method involves no auxiliary HR images. We aim to improve the hard-to-recognize instances based on the recognizability notion rather than visual quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.518 + ], + "angle": 0, + "content": "Recently, Li et al. [30] proposed a rival margin on the hardest non-target logits to maximize the separation against the nearest negative classes. However, low-quality face images with perceptually similar identities are close to each other. Therefore, enforcing separation for a low-quality face image only from the nearest non-target class hardly learns meaningful characteristics to differentiate the two identities. On the contrary, we strive to enlarge the overall inter-class dissimilarity by enhancing image recognizability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Face Image Quality Assessment (FIQA) can be mainly divided into two categories. The first category is to solve a regression problem to assess the training images with FIQ scores [1, 2, 17, 18, 36, 51]. The FIQ scores include human quality annotation [1], the intra-class Euclidean distance between an instance and an ICAO [49] compliance instance [17, 18], the similarity between random positive mated pairs [51], the discriminability on each instance [2] and the Wasserstein distance between intra and inter-class distributions [36]. The second category directly utilizes the intrinsic properties of face embeddings to estimate face quality without explicit regression learning. For instance, [45] defined the robustness of stochastic embeddings as FIQ score. However, the computational cost is significant as the assessed instance is required to pass through the network multiple times at different dropout rates. [38] and [35] relied on uncertainty variation and embedding norm of the face embeddings as the FIQ scores, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Aside from face quality, several works also explore classifiability according to face quality. Instead of using the fixed Gaussian mean as the face embedding [38], [4] proposed to learn a Gaussian mean alongside an uncertainty to reduce the adverse effects of noisy samples. In [21], the easy instances are first learned before the hard ones based on the adaptive margin angular loss. [48] defined hard sam" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.891, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.301, + 0.895, + 0.455 + ], + "angle": 0, + "content": "Figure 2. Our proposed model comprises three main modules: (i) recognition module learns the face embeddings \\( v_{i} \\) by optimizing the class prototypes for the recognition task; (ii) perceptibility regression module is designed to learn the recognizability index, \\( \\hat{\\xi} \\) thereby enabling the recognizability prediction for any samples including the unseen ones; and (iii) perceptibility attention module performs channel and spatial-wise attention on the embeddings that approximate the projection away from the UIs cluster, \\( v^{\\prime} \\). The RI is learned based on two criteria, as shown on the bottom right, where \\( y \\) is the target class, \\( j \\) is the non-target class across all \\( C \\) identities, and \\( \\bar{v}_{UI} \\) is the mean of UI cluster embeddings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.548 + ], + "angle": 0, + "content": "ples and increased the weight of their negative cosine similarities with a preset constant. [35] assigned margins based on the embeddings' norm. As a successor, Kim et al. [25] refined the decision on adaptive margin, which only emphasizes hard instances when necessary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.641 + ], + "angle": 0, + "content": "While most FIQA methods struggle to learn adaptive margins for competent quality-aware embedding [2], we strive to improve embedding learning based on the proposed RI. We demonstrate that RI characterizes the image quality better, and our model can extract meaningful semantics important to face recognition in Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.637, + 0.673 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.842, + 0.698 + ], + "angle": 0, + "content": "3.1. Recognizability Index (RI) Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.825 + ], + "angle": 0, + "content": "A face model trains a discriminative embedding space by enforcing intra-class compactness and inter-class discrepancy. Interestingly, [36] discloses the relationship between face quality and recognition performance by computing the Wasserstein distances between intra-class and inter-class similarity distributions. Hence, it is suggested that face recognizability can be quantified by intra-class and inter-class similarity measures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In our disposition, the recognizable instances are pushed closer to their positive prototype and further apart from negative prototypes upon convergence. Meanwhile, the hard-to-recognize instances can hardly be pulled toward their positive prototypes, and are usually surrounded by negative" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9959" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "ones. Among all negative prototypes, the nearest negative prototype is chosen for inter-class proximity estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.47, + 0.184 + ], + "angle": 0, + "content": "For each instance \\(i\\), the intra-class and the inter-class proximity of its L2-normalized embedding \\(\\widehat{v}_i\\) with respect to its positive prototype \\(\\boldsymbol{w}_{y_i}\\) and the nearest negative prototype \\(\\boldsymbol{w}_j, j \\neq y_i\\) across a set of \\(C\\) identities are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.208, + 0.47, + 0.235 + ], + "angle": 0, + "content": "\\[\nd _ {i} ^ {P} = 1 - \\cos \\left(\\theta_ {y _ {i}}\\right), d _ {i} ^ {N} = 1 - \\max _ {j \\in \\{1, \\dots , C \\} \\backslash \\{y _ {i} \\}} \\cos \\left(\\theta_ {j}\\right) (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.244, + 0.469, + 0.336 + ], + "angle": 0, + "content": "where \\(\\theta_{y_i}\\) is the positive angle between \\(\\widehat{\\pmb{v}}_i\\) and \\(\\pmb{w}_{y_i}\\) and \\(\\theta_{j}\\) is the negative angle between \\(\\widehat{\\pmb{v}}_i\\) and \\(\\pmb{w}_j\\). On the other hand, feeding the unrecognizable faces to the model induces a UIs cluster in the embedding space [9]. Given the UIs cluster center, i.e., the average across all normalized UIs embeddings, \\(\\overline{\\pmb{v}}_{U1}\\), the proximity between \\(\\widehat{\\pmb{v}}_i\\) and \\(\\overline{\\pmb{v}}_{U1}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.343, + 0.469, + 0.361 + ], + "angle": 0, + "content": "\\[\nd _ {i} ^ {U I} = 1 - \\cos \\left(\\theta_ {U I _ {i}}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.518 + ], + "angle": 0, + "content": "where \\(\\theta_{UI_i}\\) is the angle between \\(\\widehat{\\pmb{v}}_i\\) and \\(\\overline{\\pmb{v}}_{UI}\\). Since the proximity is in terms of Cosine distance, the instances closest to the UIs cluster center (computed with the smallest \\(d_i^{UI}\\)) are referred to as hard-to-recognize instances, and vice versa. Since the proximity of each instance differs with respect to its positive and negative prototypes alongside the UIs cluster center, the association of Eq. (1) and Eq. (2) can serve to estimate the face quality. Given an imposed \\(\\epsilon = 1e^{-7}\\) to avoid division by zero, we define a recognizability measure, dubbed Recognizability Index (RI), \\(\\xi_i\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.528, + 0.47, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\xi_ {i} = d _ {i} ^ {U I} \\frac {d _ {i} ^ {N}}{d _ {i} ^ {P} + \\epsilon} \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.37, + 0.589 + ], + "angle": 0, + "content": "3.2. Perceptibility Regression Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.469, + 0.718 + ], + "angle": 0, + "content": "As our model serves recognizability-aware embedding learning and quality estimation simultaneously, we introduce a perceptibility regression module (yellow) as in Fig. 2. The input to the regression module is a flattened feature map learned from the backbone network, navigating through a dropout layer and a fully-connected regression layer to yield a learnable RI, denoted by \\(\\widehat{\\xi}_i\\). To match \\(\\widehat{\\xi}_i\\) to \\(\\xi_i\\) in Eq. (3), we apply the smooth L1 loss [15] as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.729, + 0.469, + 0.77 + ], + "angle": 0, + "content": "\\[\nL _ {L 1} = \\left\\{ \\begin{array}{l l} 0. 5 \\left(\\xi_ {i} - \\widehat {\\xi} _ {i}\\right) ^ {2} / \\beta & \\text {i f} \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| < \\beta \\\\ \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| - 0. 5 \\times \\beta & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a threshold that switches between L1 and L2-losses. In the early training stage, the L1 loss computes consistent gradients to approximate \\(\\widehat{\\xi}\\) towards \\(\\xi\\). When the regression error falls below the confidence interval, the L2 loss exhibits a smoother transition in the loss surface to facilitate convergence. In our experiments, we fix \\(\\beta = 0.75\\). It is noteworthy that the RI from the regression module differs from ERS [9] in the following perspectives: (i) ERS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "does not consider the intra-class and inter-class proximities, and (ii) ERS requires the UIs cluster center to be known for recognizability score estimation, but our model simply withdraws the UIs cluster during the deployment. In other words, upon training completion, the regression module incorporates the proximity relation in Eq. (3) and allows the face quality prediction on any unknown samples without involving the UIs cluster." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.22, + 0.698, + 0.235 + ], + "angle": 0, + "content": "3.3. Index Diversion Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.438 + ], + "angle": 0, + "content": "Having RI obtained from the perceptibility regression module, the next following goal is to enhance the hard-to-recognize instances' recognizability. We first model the RI distribution of the UIs cluster. According to the Central Limit Theorem [12], the Gaussian distribution is the most general distribution for fitting values derived from Gaussian or non-Gaussian random variables. Motivated by this, we can either estimate the mean and the variance of the Gaussian by forwarding the UIs through the perceptibility regression module or simply assume RI follows the standard Gaussian distribution with \\(\\mathcal{N}(0,1)\\). We opt for the latter as it has better interpretability and a more stable RI to resolve the hard-to-recognize instances." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.439, + 0.864, + 0.456 + ], + "angle": 0, + "content": "Thus, we define the diversion of the estimated \\(\\widehat{\\xi}_i\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.642, + 0.457, + 0.892, + 0.489 + ], + "angle": 0, + "content": "\\[\nd i v = \\frac {\\widehat {\\xi} _ {i} - \\mu_ {U I}}{\\sigma_ {U I}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.494, + 0.892, + 0.525 + ], + "angle": 0, + "content": "Since the range of \\(\\hat{\\xi}_i\\) is arbitrary, it is rescaled with respect to \\(\\mu_{UI}\\) and \\(\\sigma_{UI}\\) of the UI distribution as:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.526, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mu_ {U I} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} s _ {k}, \\sigma_ {U I} = \\sqrt {\\frac {\\sum_ {k = 1} ^ {K} \\left(s _ {k} - \\mu_ {U I}\\right) ^ {2}}{K - 1}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.57, + 0.892, + 0.629 + ], + "angle": 0, + "content": "where \\( s_k \\) denotes the RI of a random UI instance that is assumed to be i.i.d and follows \\( \\mathcal{N}(\\mu, \\sigma^2) \\). Here, we set \\( K = 5,000 \\). In accordance with Eq. (5), the index diversion (ID) loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.633, + 0.892, + 0.65 + ], + "angle": 0, + "content": "\\[\nL _ {I D} = \\max (0, \\tau - d i v) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.824 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the confidence interval hyperparameter. The ID loss enforces a deviation of at least \\(\\tau\\) between \\(\\widehat{\\xi}_i\\) and \\(\\mu_{UI}\\). As a hard-to-recognize instance is associated with a small \\(\\widehat{\\xi}_i\\), it induces a relatively large ID loss. We attempt to push the hard-to-recognize instances outside the designated \\(\\tau\\) by minimizing the ID loss. In other words, the ID loss is equivalent to enforcing a statistically significant deviation of \\(\\mu_{UI}\\) from the estimated \\(\\widehat{\\xi}_i\\) of VLR instances in the upper tail. Note that although the ID loss enforces a confidence interval, it does not divert \\(\\widehat{\\xi}_i\\) infinitely as the \\(\\widehat{\\xi}_i\\) is still bounded to RI under the constraint of Eq. (4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since the ID loss is dedicated to differentiable learning of the recognizability measure, we argue that the statistical diversion of \\(\\widehat{\\xi}_i\\) contributes to a more meaningful enhancement of recognizability in the embedding space, especially for the hard-to-recognize face images." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9960" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.358, + 0.108 + ], + "angle": 0, + "content": "3.4. Perceptibility Attention Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.222 + ], + "angle": 0, + "content": "In [9], Deng et al. showed that diverting the embedding's direction from the UIs cluster center results in face recognition improvement in the inference stage. Given the embedding vector of a VLR face instance \\( \\mathbf{v}_i \\) and the L2-normalized UIs cluster center \\( \\overline{\\mathbf{v}}_{UI} \\), we define the embedding projected in the direction away from the UIs cluster \\( \\mathbf{v}_i' \\) based on [9] as:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.234, + 0.47, + 0.252 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {i} ^ {\\prime} = \\boldsymbol {v} _ {i} - \\langle \\boldsymbol {v} _ {i}, \\bar {\\boldsymbol {v}} _ {U I} \\rangle \\bar {\\boldsymbol {v}} _ {U I} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.265, + 0.471, + 0.476 + ], + "angle": 0, + "content": "We conjecture that the embedding projection away from the UIs cluster center is beneficial to alleviate the model's inadequacy to highlight the meaningful features when the face is obscure. Different from the conventional attention models for the classification tasks, we seek to explore the most salient feature representation with the greatest significance for recognizability by approximating \\( \\boldsymbol{v}_i' \\) through an attention module. Inspired by [50], we design a perceptibility attention module that attends to the spatial and channel dimension of the instances' feature map sequentially. The attended feature maps are fed into a linearly connected layer to learn an attended embedding \\( \\boldsymbol{v}_i^{attn} \\) at the same dimension as \\( \\boldsymbol{v}_i' \\). Lastly, we utilize the mean squared error loss and formalize the regression problem as:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.479, + 0.47, + 0.52 + ], + "angle": 0, + "content": "\\[\nL _ {M S E} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\left(\\boldsymbol {v} _ {i} ^ {\\prime} - \\boldsymbol {v} _ {i} ^ {\\text {a t t n}}\\right) ^ {2} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.664 + ], + "angle": 0, + "content": "where \\( B \\) is the batch size. We argue that the projection of embeddings away from the UIs cluster can be deemed as RI-enhanced embeddings. This guides our model to attend to the parts of embedding that contain the richer interpretive contents important to recognition purposes. Therefore, introducing an attention module permits our model to attend to the most salient face regions, i.e., eyes, nose, etc., of a VLR face instance. In compliance with Eq. (4), (7) and (9), the overall loss function is expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.678, + 0.469, + 0.695 + ], + "angle": 0, + "content": "\\[\nL _ {t o t a l} = L _ {c l s} + \\alpha L _ {L 1} + \\beta L _ {I D} + \\gamma L _ {M S E} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.707, + 0.468, + 0.738 + ], + "angle": 0, + "content": "where we opt for ArcFace [8] as the classification loss, \\(L_{cls}\\), \\(\\alpha\\), \\(\\beta\\), and \\(\\gamma\\) are the weighting factors for each loss term." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.312, + 0.77 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Datasets. To confront the real-world VLRFR problem, our experiments are conducted on three realistic LR face datasets, namely TinyFace [6], SurvFace [7], and SCFace [16] under an open-set evaluation protocol, given the identity labels are disjoint across training and testing sets. We assemble an unlabeled UI face dataset from two public person re-identification repositories by the MTCNN face detector [57], including LPW [42] and MARS [59]. Notably," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "most of the detected faces are unrecognizable, thereby facilitating the generation of an UIs cluster. The details of each dataset are provided in Sec. A of in supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Experiment Settings. Our experiments utilize Mobile-FaceNet [5] and ResNet-50 [8] pretrained on the VGGFace2 [3] dataset as the representation encoder. For each dataset, we fine-tune these models using the respective training examples for performance evaluation. Our baseline model is the counterpart trained only with the ArcFace loss. We provide our experimental setup and other relevant settings in Sec. B of the supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.259, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Evaluation Metrics. We summarize the overall performance in rank-1 identification rate (IR) (\\%) for TinyFace and SCFace. On the contrary, we report the positive identification rate (TPIR) (\\%) @ false positive identification rate (FPIR), and true positive rate (TPR) (\\%) @ false acceptance rate (FAR) (\\%) for SurvFace, due to the inclusion of non-mated face images in its testing set [7]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.365, + 0.892, + 0.456 + ], + "angle": 0, + "content": "To evaluate the characterization of face image quality, we provide the Error versus Reject Curve (ERC) [2, 18, 36], where portions of low-quality face images are screened out with respect to quality indexes. This evaluation is assessed in terms of False Non-Match Rate (FNMR) [26] at a specific threshold for a fixed False Match Rate (FMR) [26]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.466, + 0.787, + 0.482 + ], + "angle": 0, + "content": "4.1. Comparison with SoTA Methods" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.701 + ], + "angle": 0, + "content": "We compare the generalization performance on two open-set face identification tasks, VLR-VLR (TinyFace and SurvFace) and HR-VLR (SCFace), to the most recent SoTAs in Table 1, 2, and \\(3^{1}\\). The former task is relatively challenging as only the noisy VLR examples are provided for probe-to-gallery matching. However, the latter suffers from a severe resolution gap between the HR galleries and the VLR probes. We disclose that the proposed model is not only resistant to the resolution gap but also a viable solution to the downstream VLR-VLR task. On the other hand, we leave the column blank for KD and resolution-invariant methods without involving the VLR datasets for fine-tuning, seeing that these VLR datasets are relatively small-scale and therefore easily prone to over-fitting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.702, + 0.892, + 0.853 + ], + "angle": 0, + "content": "TinyFace. We substantiate that our model outperforms other recent SoTAs designated for VLRFR by a remarkable margin, both with and without distractors (a summation of 153,428 face images of unknown identities in the gallery set). Specifically, we demonstrate that improving recognizability at the feature level is more meaningful than super-resolving the visual quality of the VLR face images, e.g. [6, 24, 39, 58]. With a quality-adapted margin for embedding learning, we discern that AdaFace [25] only readjusts the decision boundary - remaining the feature recog" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the \"fine-tuned\" column of these tables, we indicate \\(\\sharp\\), \\(\\dagger\\), and \\(\\checkmark\\) as fine-tuning on super-resolved, synthetic down-sampled VLR, and native VLR face images respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9961" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.482, + 0.289 + ], + "angle": 0, + "content": "
MethodsFine-TunedRank-1 IR (%)
w/ disw/o dis
CSRI (ACCV19) [6]#44.80-
TURL (CVPR20) [39]63.89-
RIFR (T-BIOM20) [24]70.40-
VividGAN (TIP21) [58]#47.16-
MIND-Net (SPL21) [32]✓66.8273.52
AdaFace (CVPR22) [25]68.21-
IDEA-Net (TIFS22) [31]✓68.13-
AdaFace (Reproduce)✓71.3875.67
Ours✓73.0677.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.116, + 0.292, + 0.442, + 0.306 + ], + "angle": 0, + "content": "Table 1. IR Comparison on TinyFace using ResNet-50" + }, + { + "type": "table", + "bbox": [ + 0.496, + 0.089, + 0.89, + 0.289 + ], + "angle": 0, + "content": "
MethodsFine-TunedRank-1 IR (%)
4.2m2.6m1.0mAvg.
TCN (ICASSP10) [55]✓74.6094.9098.6089.37
T-C (IVC20) [34]†70.2093.7098.1087.33
FAN (ACCV19) [52]✓77.5095.0098.3090.30
RAN (ECCV20) [11]✓81.3097.8098.8092.63
DDL (ECCV20) [20]✓86.8098.3098.3094.40
RIFR (T-BIOM20) [24]88.3098.3098.6095.00
MIND-Net (SPL21) [32]✓81.7598.0099.2593.00
DSN (APSIPA21) [27]✓93.0098.5098.5096.70
DRVNet (TPAMI21) [40]✓76.8092.8097.5089.03
RPCL (NN22) [30]✓90.4098.0098.0095.46
NPT (TPAMI22) [23]85.6999.0899.0896.61
IDEA-Net (TIFS22) [31]✓90.7698.5099.2596.17
AdaFace (Reproduce)✓95.3898.4699.8497.89
Ours✓97.0799.2399.8098.70
" + }, + { + "type": "table_caption", + "bbox": [ + 0.532, + 0.293, + 0.851, + 0.307 + ], + "angle": 0, + "content": "Table 2. IR Comparison on SCFace using ResNet-50" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.318, + 0.895, + 0.481 + ], + "angle": 0, + "content": "
MethodsFine-TunedTPR(%)@FARTPIR20(%)@FPIR
0.30.10.010.0010.30.20.1
CSRI (ACCV19) [6, 22]#78.6053.1018.0912.04---
FAN (ACCV19) [52]71.3044.5912.942.75---
RAN (ECCV20) [11]----26.5021.6014.90
SST (ECCV20) [10]✓87.0068.2135.7222.1812.389.716.61
DSN (APSIPA21) [27]75.0952.7421.4111.02---
DDAT (PR21) [22]90.4075.5040.4016.40---
IDEA-Net (TIFS22) [11]----26.2421.8215.61
AdaFace (Reproduce)✓87.4177.4858.6340.0931.5027.7421.93
Ours✓90.2180.9964.6048.4833.2029.3422.81
" + }, + { + "type": "table_caption", + "bbox": [ + 0.212, + 0.485, + 0.757, + 0.5 + ], + "angle": 0, + "content": "Table 3. TPR(%)@FAR and TPIR20(%)@FPIR Comparison on SurvFace using ResNet-50" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.519, + 0.223, + 0.534 + ], + "angle": 0, + "content": "nizability unchanged." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.471, + 0.671 + ], + "angle": 0, + "content": "SCFace. For the HR-VLR evaluation, our model remains superior to other SoTAs over the three probe sets. This is attributed to: (i) the enhanced recognizability bridges the resolution gap between the HR and the VLR face features; and (ii) the attention module singles out the most salient regions from VLR and HR faces, resulting in better cross-resolution matching scores, especially for the face images captured from \\(4.2m\\) (the largest standoff distances compared to \\(1.0m\\) and \\(2.6m\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.84 + ], + "angle": 0, + "content": "SurvFace. Being the most challenging VLR face dataset for the VLR-VLR deployment scenario, SurvFace evaluates both open-set identification and verification tasks in the presence of 141,736 unmated distractors as a part of the probe set. We disclose that our model significantly outperforms other SoTAs under the most rigorous settings, i.e., TPR@FAR=0.001 and TPIR20@FPIR=0.01. While [11,22,52] are trained based on synthetic LR images downsampled from HR-paired counterparts for visual quality improvement, we underline that none of these SoTAs resolves the VLRFR by means of refining feature recognizability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.852, + 0.251, + 0.868 + ], + "angle": 0, + "content": "4.2. Ablation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Effect of Each Loss Component. We present in Table 4 an ablation analysis to explore the effect of each loss term" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.895, + 0.868 + ], + "angle": 0, + "content": "using MobileFaceNet on TinyFace without gallery distractors. Compare to our baseline model (trained using only ArcFace), the inclusion of ID loss in Baseline I discloses that learning to enhance the recognizability of the hard-to-recognize instances offers a performance improvement close to \\(1.0\\%\\). Baseline II, on the other hand, reveals that the perceptibility attention module allows the most salient characteristics to be attended, resulting in at least \\(1.2\\%\\) of performance gain. Meanwhile, Baseline III demonstrates that our model benefits from learning an RI based on an estimated RI as shown in Eq. (4). It is believed that learning the softmax prototypes simultaneously with the RI prompts our model to encode the embedding recognizability at each training step. As a result, the learned RI can be viewed as an index of the model's confidence corresponding to the classifiability of any face image, including the unknown instances. Overall, our model trained with all loss terms outperforms the baselines and two most relevant SoTAs, i.e., MagFace [35], and AdaFace [25]. An important reason is that these SoTAs are reliant on the embedding's norm that does not always convey face recognizability, particularly for the VLR face images. This is substantiated by our empirical proofs in the following section." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Intuition of Hyperparameter Selection. In Fig. 3, we conduct the study of each weighting factor on each hyper" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9962" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.239 + ], + "angle": 0, + "content": "
MethodLclsLIDLMSELL1Rank-1 IR (%)
Cross Entropy [43]✓68.884
NormFace [46]✓68.026
CosFace [47]✓70.306
MV-Softmax [48]✓70.547
CurricularFace [21]✓70.655
MagFace [35]✓70.467
AdaFace [25]✓70.359
Baseline (ArcFace) [8]✓70.333
I✓✓71.298
II✓✓71.540
III✓✓71.674
Ours✓✓✓✓71.915
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.243, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Table 4. Ablation Analysis for each Loss Term on TinyFace without Distractors using MobileFaceNet." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.284, + 0.465, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.412, + 0.454, + 0.427 + ], + "angle": 0, + "content": "Figure 3. Ablation Studies for Hyperparameters \\(\\alpha, \\beta\\), and \\(\\gamma\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.688 + ], + "angle": 0, + "content": "parameter by fixing the remaining weighting factors to be their optimal values in accordance to Table 5. We refer to Eq. (10) where \\(\\alpha, \\beta, \\gamma\\) correspond to the weighting of \\(L_{L1}, L_{ID}, L_{MSE}\\) respectively. Suppose that we attempt to study the various weighting factors of \\(L_{L1}\\) via manipulating the values of \\(\\alpha\\), we fix \\(\\gamma = 1\\) and \\(\\beta = 2\\). The effects of \\(\\alpha\\) are shown as the \\(\\alpha\\) curve, and the same is applied to \\(\\beta\\) and \\(\\gamma\\) curves. Our ablations show that an overly large \\(\\alpha (>10)\\) may experience difficulty in convergence [2], and 5 is the best choice. For \\(\\beta\\), the findings suggest a weighting factor slightly less than the \\(\\alpha\\) ensures better recognizability of the instances while still being upper bound by the devised RI. Lastly, we discover that \\(L_{MSE}\\) converges fast, and a higher \\(\\gamma\\) hinders the overall model convergence, resulting in performance depreciation. A smaller \\(\\gamma\\) is thus recommended and set to be 1 in our experiment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.884 + ], + "angle": 0, + "content": "Face Recognizability-Aware Embeddings. We conduct a toy experiment with 5 easy-to-recognize (IDs 0,2,3,5,7) and 3 hard-to-recognize (IDs 1,4,6) face examples to examine the embedding space learned by SoTAs and our model in Fig. 4. The UIs center is visualized as a reference index of recognizability, where a poor recognizability (hard-to-recognize) instance is essentially projected close to the UIs center. It is discerned that the competing models are incapable of separating the hard-to-recognize clusters from the UIs center. On the contrary, our model is inclined to divert the hard-to-recognize instances from the UIs center, yielding a well-separable (therefore a more discriminative) embedding space to resolve the downstream VLRFR task." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Effect of Perceptibility Attention Module. We portray" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.882, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.186, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Figure 4. 2D embedding space for a toy problem with 8 identities (IDs). The IDs denoted with a \"√\" contain hard-to-recognize instances, even from the human perspective. We visualize the UIs center as a reference index of recognizability, i.e., embeddings further away from the UIs center can better be recognized." + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.271, + 0.88, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Figure 5. Class activation maps for several VLR face images generated based on ArcFace, AdaFace, and Ours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.59 + ], + "angle": 0, + "content": "the Class Activation Maps [37] obtained from ArcFace [8], Adaface [25], and our method for comparison. Interestingly, we observe from Fig. 5 that attending to the embeddings away from the UIs center focuses more on the salient face features, i.e. eyes, nose, and mouth, even when the face images appear to be obscure. We provide the extended heatmap visualizations in Fig. 11 of supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.842, + 0.62 + ], + "angle": 0, + "content": "4.3. Face Image Quality Assessment (FIQA)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.838 + ], + "angle": 0, + "content": "Learned RI from Perceptibility Regression Module. In Fig. 6, the effect of ID loss reveals a greater negatively-skewed distribution of RI than other SoTAs (extended version in Fig. 9), indicating an improvement in recognizability, notably the hard-to-recognize instances. We discern that the proposed RI is a robust indicator in characterizing the recognizability notion - the highest and the lowest RI reflect the best-quality and the poor-quality face images, respectively. We also provide in Fig. 6 the face images with the lowest quality scores estimated by other competing scores. Through the comparison, RI is deemed proportional to the human cognitive level in terms of recognizability for the VLR face images under extreme poses, illuminations, occlusions, and others in the wild conditions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Error versus Rejection Curve (ERC). To further substantiate the RI's robustness, we perform a verification task on TinyFace [6] by randomly sampling 20,888 positive and 50,000 negative pairs from its gallery and probe sets to show" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9963" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.615, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.089, + 0.887, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Figure 6. To facilitate direct comparison, all quality measures are normalized to ranges between 0 and 1. (Left) Visualization of RI sorted from the lowest scores (the poorest quality) to the highest (the best quality) in TinyFace [6] dataset. It is disclosed that the proposed RI characterizes the face quality better, closely simulating the human cognitive level. (Right) The VLR face images estimated with the lowest quality scores based on MagFace [35], CR-FIQA [2] and ERS [9]. In place of hard-to-recognize instances, we observe that several high-quality face instances are mistakenly assigned with low-quality scores, particularly MagFace and CR-FIQA." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.45, + 0.36, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.451, + 0.613, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.452, + 0.878, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.628, + 0.893, + 0.699 + ], + "angle": 0, + "content": "Figure 7. Whilst Fig. 6 shows that the learned RI can characterize face quality well, we further demonstrate in this figure that the learned RI is a reliable recognizability metric by means of analyzing false non-match rate (FNMR). In particular, FNMR decreases gradually when the ratio of unconsidered VLR face images increases (sampled based on the lowest RI). This indicates that the learn RI well characterizes the recognizability of the VLR face images, such that the most recognizable VLR face images are learned with the highest RIs (corresponding to the right of the left-skewed RI distribution) for FNMR evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.763 + ], + "angle": 0, + "content": "ERC in Fig. 7. The learned \\(\\widehat{\\xi}_i\\) outperforms SoTA in achieving stable and true rejection of unrecognized pairs in the rank of recognizability, especially when the FMR is at \\(1e^{-4}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.773, + 0.196, + 0.789 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "This paper addresses the problem arising from the hard-to-recognize faces in VLR images. Rather than treating these faces as UIs, we take a principled recognizability notion to characterize the recognizability of each image with a robust indicator, specifically the recognizability index (RI). The recognizability of an instance can thus be adjusted based on RI. Interestingly, attending to the embeddings pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.893, + 0.793 + ], + "angle": 0, + "content": "jected away from the UIs cluster provides more explanatory power to the model to highlight the facial features more precisely. We evaluate the proposed method trained in an end-to-end manner on three VLR datasets and achieve SoTA for both VLRFR and FIQA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.667, + 0.832 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NO. 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IEEE Transactions on image processing, 21(1):327-340, 2011. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "9967" + } + ] +] \ No newline at end of file diff --git a/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_origin.pdf b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c97fed611f3a5837c76ae82172e15dbdeac135d9 --- /dev/null +++ b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/252ce840-97f6-49d3-b68f-e8e81b6429b4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:473c58881fba54e939503e536b2847725c0fae0dc032eff93d1aeff489c3047a +size 3094308 diff --git a/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/full.md b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a0fdbc608ae9af0aabed60a8e1bde19ba2481477 --- /dev/null +++ b/2023/Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation/full.md @@ -0,0 +1,308 @@ +# Recognizability Embedding Enhancement for Very Low-Resolution Face Recognition and Quality Estimation + +Jacky Chen Long Chai $^{1}$ Tiong-Sik Ng $^{1}$ Cheng-Yaw Low $^{2}$ Jaewoo Park $^{1}$ Andrew Beng Jin Teoh $^{1}$ $^{1}$ Yonsei University $^{2}$ Institute for Basic Science + +1{jackyccl,ngtiongsik,julypraise,bjteoh}@yonsei.ac.kr 2{chengyawlow}@ibs.re.kr + +![](images/4de8e5bb2d03ea9f24863e2bfb00ba1c028b1b0ca1309527c5641e080cb05e39.jpg) +(a) +(b) +Figure 1. A deep face model pretrained on high-resolution face images introduces a cluster of recognizable instances (grey spike), dubbed unrecognizable identities (UIs) in [9]. (a) shows the bimodal distribution for a very low-resolution face dataset [6] based on distance against the UIs. Interestingly, a portion of hard-to-recognize faces (red peak) lie close to the UIs, indicating their low recognizability. (b) We propose to improve the recognizability of hard-to-recognize instances by pushing them away from the UIs center. Consequently, faces with higher recognizability indexes are further apart from UIs center in the embedding space. Our method not only induces more discriminative representations but also translates face quality into a measurable indicator that closely matches human cognition. + +# Abstract + +Very low-resolution face recognition (VLRFR) poses unique challenges, such as tiny regions of interest and poor resolution due to extreme standoff distance or wide viewing angle of the acquisition devices. In this paper, we study principled approaches to elevate the recognizability of a face in the embedding space instead of the visual quality. We first formulate a robust learning-based face recognizability measure, namely recognizability index (RI), based on two criteria: (i) proximity of each face embedding against the unrecognizable faces cluster center and (ii) closeness of each face embedding against its positive and negative class prototypes. We then devise an index diversion loss to push the hard-to-recognize face embedding with low RI away from unrecognizable faces cluster to boost the RI, which reflects better recognizability. Additionally, a perceptibility attention mechanism is introduced to attend to the most recognizable face regions, which offers better explanatory and discriminative traits for embedding learning. Our proposed model is trained end-to-end and simultaneously serves recognizability-aware embedding learning and face quality estimation. To address VLRFR, our extensive eval + +uations on three challenging low-resolution datasets and face quality assessment demonstrate the superiority of the proposed model over the state-of-the-art methods. + +# 1. Introduction + +In real-world face recognition deployment scenarios, the pixel resolution of the detected face images is significantly deflated, due to extreme long-range distance and broad viewing angle of the acquisition devices, especially in surveillance applications. These tiny regions of interest are, in general, ranging from $16 \times 16$ to $32 \times 32$ pixels [60], thereby suffering from poor pixel resolution, in addition to unrestricted noises such as poor illumination conditions, non-frontal poses with awful angles, unconstrained facial expressions, blurriness, and occlusions [45]. It is noteworthy that these contaminated very low-resolution (VLR) face images undermine the overall performance of a face model trained with its high-resolution (HR) counterparts; therefore, there is a lack of generalizability to resolve the VLR face recognition (VLRFR) problem [6]. Apart from that, training of a VLRFR model often suffers from very limited representative face examples to extract meaningful + +identity-specific patterns. These issues are further escalated due to ambiguous inter-class variations for the heavily distorted face instances with perceptually similar identities in particular [40]. Whilst matching a probe to a gallery set of the same resolution (i.e. VLR to VLR) is still an open challenge, the resolution gap between galleries and probes triggers another problem in cross-resolution matching (typically HR galleries to VLR probes). Hence, the generalization performance of the prevalent deep learning models for VLRFR is still far from satisfactory. + +As a whole, most existing works designated for VLRFR improve the face quality of the VLR instances based on an auxiliary set of HR face images [28]. The generic operation modes are either in image domain (super-resolution, image synthesis) [52, 54, 58], embedding domain (resolution-invariant features, coupled mappings) [33, 44], or at classifier level (transfer learning, knowledge distillation) [13, 14, 20, 39]. However, most of these state-of-the-art models require mated HR-VLR pairs of the same subject. This is unrealistic in practice as the HR-VLR pairs are often unavailable. + +As far as face recognition is concerned, face recognizability (also known as face quality [17, 18]) can be deemed as a utility of how well a face image is for discrimination purposes. In other words, face quality is closely related to face recognition performance. Some works thus focus on predicting a face image's suitability for face recognition, commonly known as Face Image Quality Assessment (FIQA) [1, 18]. FIQA focuses either on (i) creating propositions to label the training data with face image quality scores and solve a regression problem [17, 18, 36], or (ii) linking the face embedding properties to FIQ scores [4,25,35,38,45]. The second approach shows better quality estimation, with the possible reason that the first approach is prone to mislabeling of ground truth quality [35, 45]. However, the second approach may not be optimal since the FIQ scores are estimated based on the embedding properties rather than through a learning process [2]. + +Recently, [9] reported an intriguing observation that a deep learning-based face model induces an unrecognizable cluster in the embedding space. The cluster, known as unrecognizable identities (UIs), is formed by unrecognizable face examples, owing to diverse inferior quality factors, including VLR, motion blurred, poor illumination, occlusion, etc. Hence, these face examples with varying ground truths incline to lie close to the UIs, rather than their respective identity clusters. This observation inspires us to analyze the embedding distribution of the VLR face images against the UIs center. Interestingly, the extreme bimodal distribution in Fig. 1 discloses that a significant number of the VLR faces in TinyFace [6], i.e., a realistic VLR face dataset, are hard-to-recognize from the human perspective and therefore rendered next to the UIs cluster. We reckon that mining + +representative patterns from these hard-to-recognize faces is more meaningful for face recognition, in place of defining them as the elements of UIs. Apart from that, a more reliable objective quality metric is needed to better interpret each VLR face example in terms of its embedding recognizability for recognizability-aware embedding learning. + +Instead of perceptual quality, this work aims to elevate the recognizability of every VLR face embedding. In a nutshell, we formulate a learning-based recognizability index (RI) with respect to the Cosine proximity of each embedding instance with (i) the UIs cluster, and (ii) the associated positive and negative prototypes. In the meantime, the index diversion (ID) loss is presented to detach the hard-to-recognize embeddings from the UIs cluster, alongside a perceptibility attention mechanism. We underline that embedding learning in the direction opposing the UIs contributes to a higher explanatory power whilst promoting inter-class separation, particularly for hard-to-recognize instances. For clarity, we summarize our contributions as follows: + +- A novel approach is proposed to address the VLRFR, including VLR-VLR and HR-VLR matching, by leveraging the face recognizability notion in the embedding space to improve the hard-to-recognize instances. +- A robust learning-based face recognizability, dubbed RI, is put forward. RI relies on the face embeddings' intrinsic proximity relationship against the UIs cluster, positive, and negative class prototypes. +- An index diversion (ID) loss is devised to enhance the RI for face embeddings. Further, we put forward a perceptibility attention mechanism to guide embedding learning from the most salient face regions. +- Our proposed model trained in an end-to-end manner not only renders a more discriminative embedding space for VLRFR but simultaneously serves recognizability-aware embedding learning and face recognizability estimation. + +# 2. Related Work + +Very Low-Resolution Face Recognition. Existing HR image dependence approaches for VLRFR can be categorized into image domain, embedding domain, and classifier. Under the image domain, the super-resolution (SR) model learns a mapping function to upscale VLR into HR images to improve faces' visual quality [41, 54]. Several successors' works [19, 52, 53, 58] relate recognition to visual quality. However, these works require mated HR-VLR pairs of the same subject to be available for embedding learning, which is unrealistic. + +At both embedding domain and classifier levels, most knowledge distillation (KD) aimed to transfer the knowl- + +edge of the HR domain to the VLR face model via a teacher-student network configuration [14]. To achieve cross-resolution distillation, [13] employed an additional network to bridge the teacher and student network, while [34] compared the face embeddings of teacher and student networks with a regression loss. On the other hand, distribution distillation loss [20], non-identity-specific mutual information [32] and implicit identity-extended augmentation [31] have also been explored to mitigate the performance gap between HR and VLR instances. [40] reconstructed an HR embedding to approximate the class variations of VLR instances while learning similar features for HR and VLR images. However, despite their high visual quality, some HR faces may not be recognized. In fact, [6, 29, 56] suggest that improving visual quality can undermine identity-specific traits important to the downstream recognition task. Our proposed method involves no auxiliary HR images. We aim to improve the hard-to-recognize instances based on the recognizability notion rather than visual quality. + +Recently, Li et al. [30] proposed a rival margin on the hardest non-target logits to maximize the separation against the nearest negative classes. However, low-quality face images with perceptually similar identities are close to each other. Therefore, enforcing separation for a low-quality face image only from the nearest non-target class hardly learns meaningful characteristics to differentiate the two identities. On the contrary, we strive to enlarge the overall inter-class dissimilarity by enhancing image recognizability. + +Face Image Quality Assessment (FIQA) can be mainly divided into two categories. The first category is to solve a regression problem to assess the training images with FIQ scores [1, 2, 17, 18, 36, 51]. The FIQ scores include human quality annotation [1], the intra-class Euclidean distance between an instance and an ICAO [49] compliance instance [17, 18], the similarity between random positive mated pairs [51], the discriminability on each instance [2] and the Wasserstein distance between intra and inter-class distributions [36]. The second category directly utilizes the intrinsic properties of face embeddings to estimate face quality without explicit regression learning. For instance, [45] defined the robustness of stochastic embeddings as FIQ score. However, the computational cost is significant as the assessed instance is required to pass through the network multiple times at different dropout rates. [38] and [35] relied on uncertainty variation and embedding norm of the face embeddings as the FIQ scores, respectively. + +Aside from face quality, several works also explore classifiability according to face quality. Instead of using the fixed Gaussian mean as the face embedding [38], [4] proposed to learn a Gaussian mean alongside an uncertainty to reduce the adverse effects of noisy samples. In [21], the easy instances are first learned before the hard ones based on the adaptive margin angular loss. [48] defined hard sam + +![](images/977718739eee28fe08889a0506a1c01ef1837f7f175f3007cffa795584492bf8.jpg) +Figure 2. Our proposed model comprises three main modules: (i) recognition module learns the face embeddings $v_{i}$ by optimizing the class prototypes for the recognition task; (ii) perceptibility regression module is designed to learn the recognizability index, $\hat{\xi}$ thereby enabling the recognizability prediction for any samples including the unseen ones; and (iii) perceptibility attention module performs channel and spatial-wise attention on the embeddings that approximate the projection away from the UIs cluster, $v^{\prime}$ . The RI is learned based on two criteria, as shown on the bottom right, where $y$ is the target class, $j$ is the non-target class across all $C$ identities, and $\bar{v}_{UI}$ is the mean of UI cluster embeddings. + +ples and increased the weight of their negative cosine similarities with a preset constant. [35] assigned margins based on the embeddings' norm. As a successor, Kim et al. [25] refined the decision on adaptive margin, which only emphasizes hard instances when necessary. + +While most FIQA methods struggle to learn adaptive margins for competent quality-aware embedding [2], we strive to improve embedding learning based on the proposed RI. We demonstrate that RI characterizes the image quality better, and our model can extract meaningful semantics important to face recognition in Sec. 4. + +# 3. Methodology + +# 3.1. Recognizability Index (RI) Formulation + +A face model trains a discriminative embedding space by enforcing intra-class compactness and inter-class discrepancy. Interestingly, [36] discloses the relationship between face quality and recognition performance by computing the Wasserstein distances between intra-class and inter-class similarity distributions. Hence, it is suggested that face recognizability can be quantified by intra-class and inter-class similarity measures. + +In our disposition, the recognizable instances are pushed closer to their positive prototype and further apart from negative prototypes upon convergence. Meanwhile, the hard-to-recognize instances can hardly be pulled toward their positive prototypes, and are usually surrounded by negative + +ones. Among all negative prototypes, the nearest negative prototype is chosen for inter-class proximity estimation. + +For each instance $i$ , the intra-class and the inter-class proximity of its L2-normalized embedding $\widehat{v}_i$ with respect to its positive prototype $\boldsymbol{w}_{y_i}$ and the nearest negative prototype $\boldsymbol{w}_j, j \neq y_i$ across a set of $C$ identities are as follows: + +$$ +d _ {i} ^ {P} = 1 - \cos \left(\theta_ {y _ {i}}\right), d _ {i} ^ {N} = 1 - \max _ {j \in \{1, \dots , C \} \backslash \{y _ {i} \}} \cos \left(\theta_ {j}\right) (1) +$$ + +where $\theta_{y_i}$ is the positive angle between $\widehat{\pmb{v}}_i$ and $\pmb{w}_{y_i}$ and $\theta_{j}$ is the negative angle between $\widehat{\pmb{v}}_i$ and $\pmb{w}_j$ . On the other hand, feeding the unrecognizable faces to the model induces a UIs cluster in the embedding space [9]. Given the UIs cluster center, i.e., the average across all normalized UIs embeddings, $\overline{\pmb{v}}_{U1}$ , the proximity between $\widehat{\pmb{v}}_i$ and $\overline{\pmb{v}}_{U1}$ is defined as: + +$$ +d _ {i} ^ {U I} = 1 - \cos \left(\theta_ {U I _ {i}}\right) \tag {2} +$$ + +where $\theta_{UI_i}$ is the angle between $\widehat{\pmb{v}}_i$ and $\overline{\pmb{v}}_{UI}$ . Since the proximity is in terms of Cosine distance, the instances closest to the UIs cluster center (computed with the smallest $d_i^{UI}$ ) are referred to as hard-to-recognize instances, and vice versa. Since the proximity of each instance differs with respect to its positive and negative prototypes alongside the UIs cluster center, the association of Eq. (1) and Eq. (2) can serve to estimate the face quality. Given an imposed $\epsilon = 1e^{-7}$ to avoid division by zero, we define a recognizability measure, dubbed Recognizability Index (RI), $\xi_i$ as follows: + +$$ +\xi_ {i} = d _ {i} ^ {U I} \frac {d _ {i} ^ {N}}{d _ {i} ^ {P} + \epsilon} \tag {3} +$$ + +# 3.2. Perceptibility Regression Module + +As our model serves recognizability-aware embedding learning and quality estimation simultaneously, we introduce a perceptibility regression module (yellow) as in Fig. 2. The input to the regression module is a flattened feature map learned from the backbone network, navigating through a dropout layer and a fully-connected regression layer to yield a learnable RI, denoted by $\widehat{\xi}_i$ . To match $\widehat{\xi}_i$ to $\xi_i$ in Eq. (3), we apply the smooth L1 loss [15] as follows: + +$$ +L _ {L 1} = \left\{ \begin{array}{l l} 0. 5 \left(\xi_ {i} - \widehat {\xi} _ {i}\right) ^ {2} / \beta & \text {i f} \left| \xi_ {i} - \widehat {\xi} _ {i} \right| < \beta \\ \left| \xi_ {i} - \widehat {\xi} _ {i} \right| - 0. 5 \times \beta & \text {o t h e r w i s e} \end{array} \right. \tag {4} +$$ + +where $\beta$ is a threshold that switches between L1 and L2-losses. In the early training stage, the L1 loss computes consistent gradients to approximate $\widehat{\xi}$ towards $\xi$ . When the regression error falls below the confidence interval, the L2 loss exhibits a smoother transition in the loss surface to facilitate convergence. In our experiments, we fix $\beta = 0.75$ . It is noteworthy that the RI from the regression module differs from ERS [9] in the following perspectives: (i) ERS + +does not consider the intra-class and inter-class proximities, and (ii) ERS requires the UIs cluster center to be known for recognizability score estimation, but our model simply withdraws the UIs cluster during the deployment. In other words, upon training completion, the regression module incorporates the proximity relation in Eq. (3) and allows the face quality prediction on any unknown samples without involving the UIs cluster. + +# 3.3. Index Diversion Loss + +Having RI obtained from the perceptibility regression module, the next following goal is to enhance the hard-to-recognize instances' recognizability. We first model the RI distribution of the UIs cluster. According to the Central Limit Theorem [12], the Gaussian distribution is the most general distribution for fitting values derived from Gaussian or non-Gaussian random variables. Motivated by this, we can either estimate the mean and the variance of the Gaussian by forwarding the UIs through the perceptibility regression module or simply assume RI follows the standard Gaussian distribution with $\mathcal{N}(0,1)$ . We opt for the latter as it has better interpretability and a more stable RI to resolve the hard-to-recognize instances. + +Thus, we define the diversion of the estimated $\widehat{\xi}_i$ as: + +$$ +d i v = \frac {\widehat {\xi} _ {i} - \mu_ {U I}}{\sigma_ {U I}} \tag {5} +$$ + +Since the range of $\hat{\xi}_i$ is arbitrary, it is rescaled with respect to $\mu_{UI}$ and $\sigma_{UI}$ of the UI distribution as: + +$$ +\mu_ {U I} = \frac {1}{K} \sum_ {k = 1} ^ {K} s _ {k}, \sigma_ {U I} = \sqrt {\frac {\sum_ {k = 1} ^ {K} \left(s _ {k} - \mu_ {U I}\right) ^ {2}}{K - 1}} \tag {6} +$$ + +where $s_k$ denotes the RI of a random UI instance that is assumed to be i.i.d and follows $\mathcal{N}(\mu, \sigma^2)$ . Here, we set $K = 5,000$ . In accordance with Eq. (5), the index diversion (ID) loss is formulated as: + +$$ +L _ {I D} = \max (0, \tau - d i v) \tag {7} +$$ + +where $\tau$ is the confidence interval hyperparameter. The ID loss enforces a deviation of at least $\tau$ between $\widehat{\xi}_i$ and $\mu_{UI}$ . As a hard-to-recognize instance is associated with a small $\widehat{\xi}_i$ , it induces a relatively large ID loss. We attempt to push the hard-to-recognize instances outside the designated $\tau$ by minimizing the ID loss. In other words, the ID loss is equivalent to enforcing a statistically significant deviation of $\mu_{UI}$ from the estimated $\widehat{\xi}_i$ of VLR instances in the upper tail. Note that although the ID loss enforces a confidence interval, it does not divert $\widehat{\xi}_i$ infinitely as the $\widehat{\xi}_i$ is still bounded to RI under the constraint of Eq. (4). + +Since the ID loss is dedicated to differentiable learning of the recognizability measure, we argue that the statistical diversion of $\widehat{\xi}_i$ contributes to a more meaningful enhancement of recognizability in the embedding space, especially for the hard-to-recognize face images. + +# 3.4. Perceptibility Attention Module + +In [9], Deng et al. showed that diverting the embedding's direction from the UIs cluster center results in face recognition improvement in the inference stage. Given the embedding vector of a VLR face instance $\mathbf{v}_i$ and the L2-normalized UIs cluster center $\overline{\mathbf{v}}_{UI}$ , we define the embedding projected in the direction away from the UIs cluster $\mathbf{v}_i'$ based on [9] as: + +$$ +\boldsymbol {v} _ {i} ^ {\prime} = \boldsymbol {v} _ {i} - \langle \boldsymbol {v} _ {i}, \bar {\boldsymbol {v}} _ {U I} \rangle \bar {\boldsymbol {v}} _ {U I} \tag {8} +$$ + +We conjecture that the embedding projection away from the UIs cluster center is beneficial to alleviate the model's inadequacy to highlight the meaningful features when the face is obscure. Different from the conventional attention models for the classification tasks, we seek to explore the most salient feature representation with the greatest significance for recognizability by approximating $\boldsymbol{v}_i'$ through an attention module. Inspired by [50], we design a perceptibility attention module that attends to the spatial and channel dimension of the instances' feature map sequentially. The attended feature maps are fed into a linearly connected layer to learn an attended embedding $\boldsymbol{v}_i^{attn}$ at the same dimension as $\boldsymbol{v}_i'$ . Lastly, we utilize the mean squared error loss and formalize the regression problem as: + +$$ +L _ {M S E} = \frac {1}{B} \sum_ {i = 1} ^ {B} \left(\boldsymbol {v} _ {i} ^ {\prime} - \boldsymbol {v} _ {i} ^ {\text {a t t n}}\right) ^ {2} \tag {9} +$$ + +where $B$ is the batch size. We argue that the projection of embeddings away from the UIs cluster can be deemed as RI-enhanced embeddings. This guides our model to attend to the parts of embedding that contain the richer interpretive contents important to recognition purposes. Therefore, introducing an attention module permits our model to attend to the most salient face regions, i.e., eyes, nose, etc., of a VLR face instance. In compliance with Eq. (4), (7) and (9), the overall loss function is expressed as follows: + +$$ +L _ {t o t a l} = L _ {c l s} + \alpha L _ {L 1} + \beta L _ {I D} + \gamma L _ {M S E} \tag {10} +$$ + +where we opt for ArcFace [8] as the classification loss, $L_{cls}$ , $\alpha$ , $\beta$ , and $\gamma$ are the weighting factors for each loss term. + +# 4. Experiments and Results + +Datasets. To confront the real-world VLRFR problem, our experiments are conducted on three realistic LR face datasets, namely TinyFace [6], SurvFace [7], and SCFace [16] under an open-set evaluation protocol, given the identity labels are disjoint across training and testing sets. We assemble an unlabeled UI face dataset from two public person re-identification repositories by the MTCNN face detector [57], including LPW [42] and MARS [59]. Notably, + +most of the detected faces are unrecognizable, thereby facilitating the generation of an UIs cluster. The details of each dataset are provided in Sec. A of in supplemental material. + +Experiment Settings. Our experiments utilize Mobile-FaceNet [5] and ResNet-50 [8] pretrained on the VGGFace2 [3] dataset as the representation encoder. For each dataset, we fine-tune these models using the respective training examples for performance evaluation. Our baseline model is the counterpart trained only with the ArcFace loss. We provide our experimental setup and other relevant settings in Sec. B of the supplemental material. + +Evaluation Metrics. We summarize the overall performance in rank-1 identification rate (IR) (\%) for TinyFace and SCFace. On the contrary, we report the positive identification rate (TPIR) (\%) @ false positive identification rate (FPIR), and true positive rate (TPR) (\%) @ false acceptance rate (FAR) (\%) for SurvFace, due to the inclusion of non-mated face images in its testing set [7]. + +To evaluate the characterization of face image quality, we provide the Error versus Reject Curve (ERC) [2, 18, 36], where portions of low-quality face images are screened out with respect to quality indexes. This evaluation is assessed in terms of False Non-Match Rate (FNMR) [26] at a specific threshold for a fixed False Match Rate (FMR) [26]. + +# 4.1. Comparison with SoTA Methods + +We compare the generalization performance on two open-set face identification tasks, VLR-VLR (TinyFace and SurvFace) and HR-VLR (SCFace), to the most recent SoTAs in Table 1, 2, and $3^{1}$ . The former task is relatively challenging as only the noisy VLR examples are provided for probe-to-gallery matching. However, the latter suffers from a severe resolution gap between the HR galleries and the VLR probes. We disclose that the proposed model is not only resistant to the resolution gap but also a viable solution to the downstream VLR-VLR task. On the other hand, we leave the column blank for KD and resolution-invariant methods without involving the VLR datasets for fine-tuning, seeing that these VLR datasets are relatively small-scale and therefore easily prone to over-fitting. + +TinyFace. We substantiate that our model outperforms other recent SoTAs designated for VLRFR by a remarkable margin, both with and without distractors (a summation of 153,428 face images of unknown identities in the gallery set). Specifically, we demonstrate that improving recognizability at the feature level is more meaningful than super-resolving the visual quality of the VLR face images, e.g. [6, 24, 39, 58]. With a quality-adapted margin for embedding learning, we discern that AdaFace [25] only readjusts the decision boundary - remaining the feature recog + +
MethodsFine-TunedRank-1 IR (%)
w/ disw/o dis
CSRI (ACCV19) [6]#44.80-
TURL (CVPR20) [39]63.89-
RIFR (T-BIOM20) [24]70.40-
VividGAN (TIP21) [58]#47.16-
MIND-Net (SPL21) [32]✓66.8273.52
AdaFace (CVPR22) [25]68.21-
IDEA-Net (TIFS22) [31]✓68.13-
AdaFace (Reproduce)✓71.3875.67
Ours✓73.0677.22
+ +Table 1. IR Comparison on TinyFace using ResNet-50 + +
MethodsFine-TunedRank-1 IR (%)
4.2m2.6m1.0mAvg.
TCN (ICASSP10) [55]✓74.6094.9098.6089.37
T-C (IVC20) [34]†70.2093.7098.1087.33
FAN (ACCV19) [52]✓77.5095.0098.3090.30
RAN (ECCV20) [11]✓81.3097.8098.8092.63
DDL (ECCV20) [20]✓86.8098.3098.3094.40
RIFR (T-BIOM20) [24]88.3098.3098.6095.00
MIND-Net (SPL21) [32]✓81.7598.0099.2593.00
DSN (APSIPA21) [27]✓93.0098.5098.5096.70
DRVNet (TPAMI21) [40]✓76.8092.8097.5089.03
RPCL (NN22) [30]✓90.4098.0098.0095.46
NPT (TPAMI22) [23]85.6999.0899.0896.61
IDEA-Net (TIFS22) [31]✓90.7698.5099.2596.17
AdaFace (Reproduce)✓95.3898.4699.8497.89
Ours✓97.0799.2399.8098.70
+ +Table 2. IR Comparison on SCFace using ResNet-50 + +
MethodsFine-TunedTPR(%)@FARTPIR20(%)@FPIR
0.30.10.010.0010.30.20.1
CSRI (ACCV19) [6, 22]#78.6053.1018.0912.04---
FAN (ACCV19) [52]71.3044.5912.942.75---
RAN (ECCV20) [11]----26.5021.6014.90
SST (ECCV20) [10]✓87.0068.2135.7222.1812.389.716.61
DSN (APSIPA21) [27]75.0952.7421.4111.02---
DDAT (PR21) [22]90.4075.5040.4016.40---
IDEA-Net (TIFS22) [11]----26.2421.8215.61
AdaFace (Reproduce)✓87.4177.4858.6340.0931.5027.7421.93
Ours✓90.2180.9964.6048.4833.2029.3422.81
+ +Table 3. TPR(%)@FAR and TPIR20(%)@FPIR Comparison on SurvFace using ResNet-50 + +nizability unchanged. + +SCFace. For the HR-VLR evaluation, our model remains superior to other SoTAs over the three probe sets. This is attributed to: (i) the enhanced recognizability bridges the resolution gap between the HR and the VLR face features; and (ii) the attention module singles out the most salient regions from VLR and HR faces, resulting in better cross-resolution matching scores, especially for the face images captured from $4.2m$ (the largest standoff distances compared to $1.0m$ and $2.6m$ ). + +SurvFace. Being the most challenging VLR face dataset for the VLR-VLR deployment scenario, SurvFace evaluates both open-set identification and verification tasks in the presence of 141,736 unmated distractors as a part of the probe set. We disclose that our model significantly outperforms other SoTAs under the most rigorous settings, i.e., TPR@FAR=0.001 and TPIR20@FPIR=0.01. While [11,22,52] are trained based on synthetic LR images downsampled from HR-paired counterparts for visual quality improvement, we underline that none of these SoTAs resolves the VLRFR by means of refining feature recognizability. + +# 4.2. Ablation Analysis + +Effect of Each Loss Component. We present in Table 4 an ablation analysis to explore the effect of each loss term + +using MobileFaceNet on TinyFace without gallery distractors. Compare to our baseline model (trained using only ArcFace), the inclusion of ID loss in Baseline I discloses that learning to enhance the recognizability of the hard-to-recognize instances offers a performance improvement close to $1.0\%$ . Baseline II, on the other hand, reveals that the perceptibility attention module allows the most salient characteristics to be attended, resulting in at least $1.2\%$ of performance gain. Meanwhile, Baseline III demonstrates that our model benefits from learning an RI based on an estimated RI as shown in Eq. (4). It is believed that learning the softmax prototypes simultaneously with the RI prompts our model to encode the embedding recognizability at each training step. As a result, the learned RI can be viewed as an index of the model's confidence corresponding to the classifiability of any face image, including the unknown instances. Overall, our model trained with all loss terms outperforms the baselines and two most relevant SoTAs, i.e., MagFace [35], and AdaFace [25]. An important reason is that these SoTAs are reliant on the embedding's norm that does not always convey face recognizability, particularly for the VLR face images. This is substantiated by our empirical proofs in the following section. + +Intuition of Hyperparameter Selection. In Fig. 3, we conduct the study of each weighting factor on each hyper + +
MethodLclsLIDLMSELL1Rank-1 IR (%)
Cross Entropy [43]✓68.884
NormFace [46]✓68.026
CosFace [47]✓70.306
MV-Softmax [48]✓70.547
CurricularFace [21]✓70.655
MagFace [35]✓70.467
AdaFace [25]✓70.359
Baseline (ArcFace) [8]✓70.333
I✓✓71.298
II✓✓71.540
III✓✓71.674
Ours✓✓✓✓71.915
+ +Table 4. Ablation Analysis for each Loss Term on TinyFace without Distractors using MobileFaceNet. + +![](images/86a631936821ca9cb8bd3ff5c1999ff99a132246fe77d2743ca7ea1e00e1efe8.jpg) +Figure 3. Ablation Studies for Hyperparameters $\alpha, \beta$ , and $\gamma$ . + +parameter by fixing the remaining weighting factors to be their optimal values in accordance to Table 5. We refer to Eq. (10) where $\alpha, \beta, \gamma$ correspond to the weighting of $L_{L1}, L_{ID}, L_{MSE}$ respectively. Suppose that we attempt to study the various weighting factors of $L_{L1}$ via manipulating the values of $\alpha$ , we fix $\gamma = 1$ and $\beta = 2$ . The effects of $\alpha$ are shown as the $\alpha$ curve, and the same is applied to $\beta$ and $\gamma$ curves. Our ablations show that an overly large $\alpha (>10)$ may experience difficulty in convergence [2], and 5 is the best choice. For $\beta$ , the findings suggest a weighting factor slightly less than the $\alpha$ ensures better recognizability of the instances while still being upper bound by the devised RI. Lastly, we discover that $L_{MSE}$ converges fast, and a higher $\gamma$ hinders the overall model convergence, resulting in performance depreciation. A smaller $\gamma$ is thus recommended and set to be 1 in our experiment. + +Face Recognizability-Aware Embeddings. We conduct a toy experiment with 5 easy-to-recognize (IDs 0,2,3,5,7) and 3 hard-to-recognize (IDs 1,4,6) face examples to examine the embedding space learned by SoTAs and our model in Fig. 4. The UIs center is visualized as a reference index of recognizability, where a poor recognizability (hard-to-recognize) instance is essentially projected close to the UIs center. It is discerned that the competing models are incapable of separating the hard-to-recognize clusters from the UIs center. On the contrary, our model is inclined to divert the hard-to-recognize instances from the UIs center, yielding a well-separable (therefore a more discriminative) embedding space to resolve the downstream VLRFR task. + +Effect of Perceptibility Attention Module. We portray + +![](images/a2d8305b9c8a52a7133fbecff4f21613c443362cae2f1db8746d8e59d28c65f7.jpg) +Figure 4. 2D embedding space for a toy problem with 8 identities (IDs). The IDs denoted with a "√" contain hard-to-recognize instances, even from the human perspective. We visualize the UIs center as a reference index of recognizability, i.e., embeddings further away from the UIs center can better be recognized. + +![](images/fa1b706775f53a24447f830e89b24382ef15b2109d27aa172cfa404bd4a0f6f6.jpg) +Figure 5. Class activation maps for several VLR face images generated based on ArcFace, AdaFace, and Ours. + +the Class Activation Maps [37] obtained from ArcFace [8], Adaface [25], and our method for comparison. Interestingly, we observe from Fig. 5 that attending to the embeddings away from the UIs center focuses more on the salient face features, i.e. eyes, nose, and mouth, even when the face images appear to be obscure. We provide the extended heatmap visualizations in Fig. 11 of supplemental material. + +# 4.3. Face Image Quality Assessment (FIQA) + +Learned RI from Perceptibility Regression Module. In Fig. 6, the effect of ID loss reveals a greater negatively-skewed distribution of RI than other SoTAs (extended version in Fig. 9), indicating an improvement in recognizability, notably the hard-to-recognize instances. We discern that the proposed RI is a robust indicator in characterizing the recognizability notion - the highest and the lowest RI reflect the best-quality and the poor-quality face images, respectively. We also provide in Fig. 6 the face images with the lowest quality scores estimated by other competing scores. Through the comparison, RI is deemed proportional to the human cognitive level in terms of recognizability for the VLR face images under extreme poses, illuminations, occlusions, and others in the wild conditions. + +Error versus Rejection Curve (ERC). To further substantiate the RI's robustness, we perform a verification task on TinyFace [6] by randomly sampling 20,888 positive and 50,000 negative pairs from its gallery and probe sets to show + +![](images/a6bf592ef4bee07739cc7551e89264161ee9c04b4f67b2f8859b4b999b11b983.jpg) +Figure 6. To facilitate direct comparison, all quality measures are normalized to ranges between 0 and 1. (Left) Visualization of RI sorted from the lowest scores (the poorest quality) to the highest (the best quality) in TinyFace [6] dataset. It is disclosed that the proposed RI characterizes the face quality better, closely simulating the human cognitive level. (Right) The VLR face images estimated with the lowest quality scores based on MagFace [35], CR-FIQA [2] and ERS [9]. In place of hard-to-recognize instances, we observe that several high-quality face instances are mistakenly assigned with low-quality scores, particularly MagFace and CR-FIQA. + +![](images/1523a86b61ef08c0b036c916b6ad645e9e3fe8cafbe1764dee32808aef85f5b8.jpg) + +![](images/07ff506db35875925765bf08c7b2c7360d3261e2a25dd871d6897de91cbd25f5.jpg) +Figure 7. Whilst Fig. 6 shows that the learned RI can characterize face quality well, we further demonstrate in this figure that the learned RI is a reliable recognizability metric by means of analyzing false non-match rate (FNMR). In particular, FNMR decreases gradually when the ratio of unconsidered VLR face images increases (sampled based on the lowest RI). This indicates that the learn RI well characterizes the recognizability of the VLR face images, such that the most recognizable VLR face images are learned with the highest RIs (corresponding to the right of the left-skewed RI distribution) for FNMR evaluation. + +![](images/f354129eee6380fb02ba044c0dce4ddf8ae1d96e3bc60ffbf07508020afd4224.jpg) + +![](images/94e5817c2ef5911ad9e92c36fea466a0bdfca24a23836fa8f473a09aad6609b0.jpg) + +ERC in Fig. 7. The learned $\widehat{\xi}_i$ outperforms SoTA in achieving stable and true rejection of unrecognized pairs in the rank of recognizability, especially when the FMR is at $1e^{-4}$ . + +# 5. Conclusion + +This paper addresses the problem arising from the hard-to-recognize faces in VLR images. Rather than treating these faces as UIs, we take a principled recognizability notion to characterize the recognizability of each image with a robust indicator, specifically the recognizability index (RI). The recognizability of an instance can thus be adjusted based on RI. Interestingly, attending to the embeddings pro + +jected away from the UIs cluster provides more explanatory power to the model to highlight the facial features more precisely. We evaluate the proposed method trained in an end-to-end manner on three VLR datasets and achieve SoTA for both VLRFR and FIQA. + +# Acknowledgements + +This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NO. NRF-2022R1A2C1010710) and Institute for Basic Science (IBS-R029-C2) Korea. + +# References + +[1] Lacey Best-Rowden and Anil K Jain. Learning face image quality from human assessments. IEEE Transactions on Information Forensics and Security, 13(12):3064-3077, 2018. 2, 3 +[2] Fadi Boutros, Meiling Fang, Marcel Klemt, Biying Fu, and Naser Damer. 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IEEE signal processing letters, 23(10):1499-1503, 2016. 5, 1 +[58] Yang Zhang, Ivor W Tsang, Jun Li, Ping Liu, Xiaobo Lu, and Xin Yu. Face hallucination with finishing touches. IEEE Transactions on Image Processing, 30:1728-1743, 2021. 2, 5, 6 +[59] Liang Zheng, Zhi Bie, Yifan Sun, Jingdong Wang, Chi Su, Shengjin Wang, and Qi Tian. Mars: A video benchmark for large-scale person re-identification. In Proceedings of the European Conference on Computer Vision, pages 868–884. Springer, 2016. 5, 1 +[60] Wilman WW Zou and Pong C Yuen. Very low resolution face recognition problem. 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A deep face model pretrained on high-resolution face images introduces a cluster of recognizable instances (grey spike), dubbed unrecognizable identities (UIs) in [9]. (a) shows the bimodal distribution for a very low-resolution face dataset [6] based on distance against the UIs. Interestingly, a portion of hard-to-recognize faces (red peak) lie close to the UIs, indicating their low recognizability. (b) We propose to improve the recognizability of hard-to-recognize instances by pushing them away from the UIs center. Consequently, faces with higher recognizability indexes are further apart from UIs center in the embedding space. Our method not only induces more discriminative representations but also translates face quality into a measurable indicator that closely matches human cognition." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 434, + 192, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 434, + 192, + 445 + ], + "spans": [ + { + "bbox": [ + 143, + 434, + 192, + 445 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 462, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 462, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 462, + 289, + 714 + ], + "type": "text", + "content": "Very low-resolution face recognition (VLRFR) poses unique challenges, such as tiny regions of interest and poor resolution due to extreme standoff distance or wide viewing angle of the acquisition devices. In this paper, we study principled approaches to elevate the recognizability of a face in the embedding space instead of the visual quality. We first formulate a robust learning-based face recognizability measure, namely recognizability index (RI), based on two criteria: (i) proximity of each face embedding against the unrecognizable faces cluster center and (ii) closeness of each face embedding against its positive and negative class prototypes. We then devise an index diversion loss to push the hard-to-recognize face embedding with low RI away from unrecognizable faces cluster to boost the RI, which reflects better recognizability. Additionally, a perceptibility attention mechanism is introduced to attend to the most recognizable face regions, which offers better explanatory and discriminative traits for embedding learning. Our proposed model is trained end-to-end and simultaneously serves recognizability-aware embedding learning and face quality estimation. To address VLRFR, our extensive eval" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 435, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 546, + 472 + ], + "type": "text", + "content": "uations on three challenging low-resolution datasets and face quality assessment demonstrate the superiority of the proposed model over the state-of-the-art methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 489, + 386, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 386, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 386, + 502 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "In real-world face recognition deployment scenarios, the pixel resolution of the detected face images is significantly deflated, due to extreme long-range distance and broad viewing angle of the acquisition devices, especially in surveillance applications. These tiny regions of interest are, in general, ranging from " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " pixels [60], thereby suffering from poor pixel resolution, in addition to unrestricted noises such as poor illumination conditions, non-frontal poses with awful angles, unconstrained facial expressions, blurriness, and occlusions [45]. It is noteworthy that these contaminated very low-resolution (VLR) face images undermine the overall performance of a face model trained with its high-resolution (HR) counterparts; therefore, there is a lack of generalizability to resolve the VLR face recognition (VLRFR) problem [6]. Apart from that, training of a VLRFR model often suffers from very limited representative face examples to extract meaningful" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9957" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "identity-specific patterns. These issues are further escalated due to ambiguous inter-class variations for the heavily distorted face instances with perceptually similar identities in particular [40]. Whilst matching a probe to a gallery set of the same resolution (i.e. VLR to VLR) is still an open challenge, the resolution gap between galleries and probes triggers another problem in cross-resolution matching (typically HR galleries to VLR probes). Hence, the generalization performance of the prevalent deep learning models for VLRFR is still far from satisfactory." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 326 + ], + "type": "text", + "content": "As a whole, most existing works designated for VLRFR improve the face quality of the VLR instances based on an auxiliary set of HR face images [28]. The generic operation modes are either in image domain (super-resolution, image synthesis) [52, 54, 58], embedding domain (resolution-invariant features, coupled mappings) [33, 44], or at classifier level (transfer learning, knowledge distillation) [13, 14, 20, 39]. However, most of these state-of-the-art models require mated HR-VLR pairs of the same subject. This is unrealistic in practice as the HR-VLR pairs are often unavailable." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 328, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 289, + 533 + ], + "type": "text", + "content": "As far as face recognition is concerned, face recognizability (also known as face quality [17, 18]) can be deemed as a utility of how well a face image is for discrimination purposes. In other words, face quality is closely related to face recognition performance. Some works thus focus on predicting a face image's suitability for face recognition, commonly known as Face Image Quality Assessment (FIQA) [1, 18]. FIQA focuses either on (i) creating propositions to label the training data with face image quality scores and solve a regression problem [17, 18, 36], or (ii) linking the face embedding properties to FIQ scores [4,25,35,38,45]. The second approach shows better quality estimation, with the possible reason that the first approach is prone to mislabeling of ground truth quality [35, 45]. However, the second approach may not be optimal since the FIQ scores are estimated based on the embedding properties rather than through a learning process [2]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "Recently, [9] reported an intriguing observation that a deep learning-based face model induces an unrecognizable cluster in the embedding space. The cluster, known as unrecognizable identities (UIs), is formed by unrecognizable face examples, owing to diverse inferior quality factors, including VLR, motion blurred, poor illumination, occlusion, etc. Hence, these face examples with varying ground truths incline to lie close to the UIs, rather than their respective identity clusters. This observation inspires us to analyze the embedding distribution of the VLR face images against the UIs center. Interestingly, the extreme bimodal distribution in Fig. 1 discloses that a significant number of the VLR faces in TinyFace [6], i.e., a realistic VLR face dataset, are hard-to-recognize from the human perspective and therefore rendered next to the UIs cluster. We reckon that mining" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "representative patterns from these hard-to-recognize faces is more meaningful for face recognition, in place of defining them as the elements of UIs. Apart from that, a more reliable objective quality metric is needed to better interpret each VLR face example in terms of its embedding recognizability for recognizability-aware embedding learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 144, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 300 + ], + "type": "text", + "content": "Instead of perceptual quality, this work aims to elevate the recognizability of every VLR face embedding. In a nutshell, we formulate a learning-based recognizability index (RI) with respect to the Cosine proximity of each embedding instance with (i) the UIs cluster, and (ii) the associated positive and negative prototypes. In the meantime, the index diversion (ID) loss is presented to detach the hard-to-recognize embeddings from the UIs cluster, alongside a perceptibility attention mechanism. We underline that embedding learning in the direction opposing the UIs contributes to a higher explanatory power whilst promoting inter-class separation, particularly for hard-to-recognize instances. For clarity, we summarize our contributions as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 308, + 545, + 538 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 308, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 308, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 317, + 308, + 545, + 357 + ], + "type": "text", + "content": "- A novel approach is proposed to address the VLRFR, including VLR-VLR and HR-VLR matching, by leveraging the face recognizability notion in the embedding space to improve the hard-to-recognize instances." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 365, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 365, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 317, + 365, + 545, + 414 + ], + "type": "text", + "content": "- A robust learning-based face recognizability, dubbed RI, is put forward. RI relies on the face embeddings' intrinsic proximity relationship against the UIs cluster, positive, and negative class prototypes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 422, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 422, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 545, + 469 + ], + "type": "text", + "content": "- An index diversion (ID) loss is devised to enhance the RI for face embeddings. Further, we put forward a perceptibility attention mechanism to guide embedding learning from the most salient face regions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 478, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 478, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 317, + 478, + 545, + 538 + ], + "type": "text", + "content": "- Our proposed model trained in an end-to-end manner not only renders a more discriminative embedding space for VLRFR but simultaneously serves recognizability-aware embedding learning and face recognizability estimation." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 549, + 392, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 392, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 392, + 562 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 569, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 689 + ], + "type": "text", + "content": "Very Low-Resolution Face Recognition. Existing HR image dependence approaches for VLRFR can be categorized into image domain, embedding domain, and classifier. Under the image domain, the super-resolution (SR) model learns a mapping function to upscale VLR into HR images to improve faces' visual quality [41, 54]. Several successors' works [19, 52, 53, 58] relate recognition to visual quality. However, these works require mated HR-VLR pairs of the same subject to be available for embedding learning, which is unrealistic." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 713 + ], + "type": "text", + "content": "At both embedding domain and classifier levels, most knowledge distillation (KD) aimed to transfer the knowl-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9958" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "edge of the HR domain to the VLR face model via a teacher-student network configuration [14]. To achieve cross-resolution distillation, [13] employed an additional network to bridge the teacher and student network, while [34] compared the face embeddings of teacher and student networks with a regression loss. On the other hand, distribution distillation loss [20], non-identity-specific mutual information [32] and implicit identity-extended augmentation [31] have also been explored to mitigate the performance gap between HR and VLR instances. [40] reconstructed an HR embedding to approximate the class variations of VLR instances while learning similar features for HR and VLR images. However, despite their high visual quality, some HR faces may not be recognized. In fact, [6, 29, 56] suggest that improving visual quality can undermine identity-specific traits important to the downstream recognition task. Our proposed method involves no auxiliary HR images. We aim to improve the hard-to-recognize instances based on the recognizability notion rather than visual quality." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 301, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 410 + ], + "type": "text", + "content": "Recently, Li et al. [30] proposed a rival margin on the hardest non-target logits to maximize the separation against the nearest negative classes. However, low-quality face images with perceptually similar identities are close to each other. Therefore, enforcing separation for a low-quality face image only from the nearest non-target class hardly learns meaningful characteristics to differentiate the two identities. On the contrary, we strive to enlarge the overall inter-class dissimilarity by enhancing image recognizability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 411, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 628 + ], + "type": "text", + "content": "Face Image Quality Assessment (FIQA) can be mainly divided into two categories. The first category is to solve a regression problem to assess the training images with FIQ scores [1, 2, 17, 18, 36, 51]. The FIQ scores include human quality annotation [1], the intra-class Euclidean distance between an instance and an ICAO [49] compliance instance [17, 18], the similarity between random positive mated pairs [51], the discriminability on each instance [2] and the Wasserstein distance between intra and inter-class distributions [36]. The second category directly utilizes the intrinsic properties of face embeddings to estimate face quality without explicit regression learning. For instance, [45] defined the robustness of stochastic embeddings as FIQ score. However, the computational cost is significant as the assessed instance is required to pass through the network multiple times at different dropout rates. [38] and [35] relied on uncertainty variation and embedding norm of the face embeddings as the FIQ scores, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Aside from face quality, several works also explore classifiability according to face quality. Instead of using the fixed Gaussian mean as the face embedding [38], [4] proposed to learn a Gaussian mean alongside an uncertainty to reduce the adverse effects of noisy samples. In [21], the easy instances are first learned before the hard ones based on the adaptive margin angular loss. [48] defined hard sam" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 236 + ], + "type": "image", + "image_path": "977718739eee28fe08889a0506a1c01ef1837f7f175f3007cffa795584492bf8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "lines": [ + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": "Figure 2. Our proposed model comprises three main modules: (i) recognition module learns the face embeddings " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " by optimizing the class prototypes for the recognition task; (ii) perceptibility regression module is designed to learn the recognizability index, " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "\\hat{\\xi}" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " thereby enabling the recognizability prediction for any samples including the unseen ones; and (iii) perceptibility attention module performs channel and spatial-wise attention on the embeddings that approximate the projection away from the UIs cluster, " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "v^{\\prime}" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": ". The RI is learned based on two criteria, as shown on the bottom right, where " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " is the target class, " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " is the non-target class across all " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " identities, and " + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "inline_equation", + "content": "\\bar{v}_{UI}" + }, + { + "bbox": [ + 305, + 238, + 547, + 360 + ], + "type": "text", + "content": " is the mean of UI cluster embeddings." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 375, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 434 + ], + "type": "text", + "content": "ples and increased the weight of their negative cosine similarities with a preset constant. [35] assigned margins based on the embeddings' norm. As a successor, Kim et al. [25] refined the decision on adaptive margin, which only emphasizes hard instances when necessary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 435, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 507 + ], + "type": "text", + "content": "While most FIQA methods struggle to learn adaptive margins for competent quality-aware embedding [2], we strive to improve embedding learning based on the proposed RI. We demonstrate that RI characterizes the image quality better, and our model can extract meaningful semantics important to face recognition in Sec. 4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 518, + 389, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 389, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 389, + 533 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 539, + 515, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 515, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 515, + 552 + ], + "type": "text", + "content": "3.1. Recognizability Index (RI) Formulation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 653 + ], + "type": "text", + "content": "A face model trains a discriminative embedding space by enforcing intra-class compactness and inter-class discrepancy. Interestingly, [36] discloses the relationship between face quality and recognition performance by computing the Wasserstein distances between intra-class and inter-class similarity distributions. Hence, it is suggested that face recognizability can be quantified by intra-class and inter-class similarity measures." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "content": "In our disposition, the recognizable instances are pushed closer to their positive prototype and further apart from negative prototypes upon convergence. Meanwhile, the hard-to-recognize instances can hardly be pulled toward their positive prototypes, and are usually surrounded by negative" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9959" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "ones. Among all negative prototypes, the nearest negative prototype is chosen for inter-class proximity estimation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": "For each instance " + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": ", the intra-class and the inter-class proximity of its L2-normalized embedding " + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\widehat{v}_i" + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": " with respect to its positive prototype " + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_{y_i}" + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": " and the nearest negative prototype " + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}_j, j \\neq y_i" + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": " across a set of " + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 96, + 287, + 145 + ], + "type": "text", + "content": " identities are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 164, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 164, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 52, + 164, + 287, + 186 + ], + "type": "interline_equation", + "content": "d _ {i} ^ {P} = 1 - \\cos \\left(\\theta_ {y _ {i}}\\right), d _ {i} ^ {N} = 1 - \\max _ {j \\in \\{1, \\dots , C \\} \\backslash \\{y _ {i} \\}} \\cos \\left(\\theta_ {j}\\right) (1)", + "image_path": "d015d1d076adb8c015dfa0368d34039c561dba5826e448bdefe54b330ff95a15.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\theta_{y_i}" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " is the positive angle between " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{v}}_i" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{w}_{y_i}" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " is the negative angle between " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{v}}_i" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{w}_j" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": ". On the other hand, feeding the unrecognizable faces to the model induces a UIs cluster in the embedding space [9]. Given the UIs cluster center, i.e., the average across all normalized UIs embeddings, " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\overline{\\pmb{v}}_{U1}" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": ", the proximity between " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{v}}_i" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\overline{\\pmb{v}}_{U1}" + }, + { + "bbox": [ + 46, + 193, + 287, + 266 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 125, + 271, + 287, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 271, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 125, + 271, + 287, + 285 + ], + "type": "interline_equation", + "content": "d _ {i} ^ {U I} = 1 - \\cos \\left(\\theta_ {U I _ {i}}\\right) \\tag {2}", + "image_path": "a6c4a3151fc21c9cf4ffc4e02442c7381ce5ae2b2f06207d9cb2b76a406ac917.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\theta_{UI_i}" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": " is the angle between " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{v}}_i" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\overline{\\pmb{v}}_{UI}" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": ". Since the proximity is in terms of Cosine distance, the instances closest to the UIs cluster center (computed with the smallest " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "d_i^{UI}" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": ") are referred to as hard-to-recognize instances, and vice versa. Since the proximity of each instance differs with respect to its positive and negative prototypes alongside the UIs cluster center, the association of Eq. (1) and Eq. (2) can serve to estimate the face quality. Given an imposed " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\epsilon = 1e^{-7}" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": " to avoid division by zero, we define a recognizability measure, dubbed Recognizability Index (RI), " + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\xi_i" + }, + { + "bbox": [ + 46, + 289, + 287, + 410 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 132, + 418, + 287, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 418, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 132, + 418, + 287, + 447 + ], + "type": "interline_equation", + "content": "\\xi_ {i} = d _ {i} ^ {U I} \\frac {d _ {i} ^ {N}}{d _ {i} ^ {P} + \\epsilon} \\tag {3}", + "image_path": "d149457bba070c9537a70349bdf5d6338b3c9e391b7a425cb24555a65d3a5061.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "type": "text", + "content": "3.2. Perceptibility Regression Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "text", + "content": "As our model serves recognizability-aware embedding learning and quality estimation simultaneously, we introduce a perceptibility regression module (yellow) as in Fig. 2. The input to the regression module is a flattened feature map learned from the backbone network, navigating through a dropout layer and a fully-connected regression layer to yield a learnable RI, denoted by " + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "text", + "content": ". To match " + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\xi_i" + }, + { + "bbox": [ + 46, + 471, + 287, + 568 + ], + "type": "text", + "content": " in Eq. (3), we apply the smooth L1 loss [15] as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 72, + 577, + 287, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 577, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 72, + 577, + 287, + 609 + ], + "type": "interline_equation", + "content": "L _ {L 1} = \\left\\{ \\begin{array}{l l} 0. 5 \\left(\\xi_ {i} - \\widehat {\\xi} _ {i}\\right) ^ {2} / \\beta & \\text {i f} \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| < \\beta \\\\ \\left| \\xi_ {i} - \\widehat {\\xi} _ {i} \\right| - 0. 5 \\times \\beta & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}", + "image_path": "11b85a5d7c1f194b8764acc19c2b1b580d9dba53e224acd450e45ecef738e806.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "content": " is a threshold that switches between L1 and L2-losses. In the early training stage, the L1 loss computes consistent gradients to approximate " + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}" + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "content": ". When the regression error falls below the confidence interval, the L2 loss exhibits a smoother transition in the loss surface to facilitate convergence. In our experiments, we fix " + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\beta = 0.75" + }, + { + "bbox": [ + 46, + 616, + 287, + 715 + ], + "type": "text", + "content": ". It is noteworthy that the RI from the regression module differs from ERS [9] in the following perspectives: (i) ERS" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "does not consider the intra-class and inter-class proximities, and (ii) ERS requires the UIs cluster center to be known for recognizability score estimation, but our model simply withdraws the UIs cluster during the deployment. In other words, upon training completion, the regression module incorporates the proximity relation in Eq. (3) and allows the face quality prediction on any unknown samples without involving the UIs cluster." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 174, + 427, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 174, + 427, + 186 + ], + "spans": [ + { + "bbox": [ + 306, + 174, + 427, + 186 + ], + "type": "text", + "content": "3.3. Index Diversion Loss" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 192, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 346 + ], + "type": "text", + "content": "Having RI obtained from the perceptibility regression module, the next following goal is to enhance the hard-to-recognize instances' recognizability. We first model the RI distribution of the UIs cluster. According to the Central Limit Theorem [12], the Gaussian distribution is the most general distribution for fitting values derived from Gaussian or non-Gaussian random variables. Motivated by this, we can either estimate the mean and the variance of the Gaussian by forwarding the UIs through the perceptibility regression module or simply assume RI follows the standard Gaussian distribution with " + }, + { + "bbox": [ + 304, + 192, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,1)" + }, + { + "bbox": [ + 304, + 192, + 545, + 346 + ], + "type": "text", + "content": ". We opt for the latter as it has better interpretability and a more stable RI to resolve the hard-to-recognize instances." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 347, + 528, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 347, + 528, + 361 + ], + "spans": [ + { + "bbox": [ + 318, + 347, + 528, + 361 + ], + "type": "text", + "content": "Thus, we define the diversion of the estimated " + }, + { + "bbox": [ + 318, + 347, + 528, + 361 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 318, + 347, + 528, + 361 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 392, + 361, + 545, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 361, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 392, + 361, + 545, + 387 + ], + "type": "interline_equation", + "content": "d i v = \\frac {\\widehat {\\xi} _ {i} - \\mu_ {U I}}{\\sigma_ {U I}} \\tag {5}", + "image_path": "bd2a4b700a37b5ec80ef8d0ac0b048465131f6c15f08ee09fa85a14e30486fa4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "text", + "content": "Since the range of " + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\hat{\\xi}_i" + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "text", + "content": " is arbitrary, it is rescaled with respect to " + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mu_{UI}" + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\sigma_{UI}" + }, + { + "bbox": [ + 305, + 391, + 545, + 415 + ], + "type": "text", + "content": " of the UI distribution as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 331, + 416, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 416, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 331, + 416, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\mu_ {U I} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} s _ {k}, \\sigma_ {U I} = \\sqrt {\\frac {\\sum_ {k = 1} ^ {K} \\left(s _ {k} - \\mu_ {U I}\\right) ^ {2}}{K - 1}} \\tag {6}", + "image_path": "ac30e4957385d891d2cc5a4b82190a1e66b50b49f3f7878846ec4fae0da51baa.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": " denotes the RI of a random UI instance that is assumed to be i.i.d and follows " + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mu, \\sigma^2)" + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": ". Here, we set " + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "inline_equation", + "content": "K = 5,000" + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": ". In accordance with Eq. (5), the index diversion (ID) loss is formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 375, + 501, + 545, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 501, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 375, + 501, + 545, + 514 + ], + "type": "interline_equation", + "content": "L _ {I D} = \\max (0, \\tau - d i v) \\tag {7}", + "image_path": "53a69a4996991190f2e3b447607e2d5bd0e83c9375dc220d780e2fbb270161bb.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " is the confidence interval hyperparameter. The ID loss enforces a deviation of at least " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mu_{UI}" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": ". As a hard-to-recognize instance is associated with a small " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": ", it induces a relatively large ID loss. We attempt to push the hard-to-recognize instances outside the designated " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " by minimizing the ID loss. In other words, the ID loss is equivalent to enforcing a statistically significant deviation of " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mu_{UI}" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " from the estimated " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " of VLR instances in the upper tail. Note that although the ID loss enforces a confidence interval, it does not divert " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " infinitely as the " + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 517, + 545, + 652 + ], + "type": "text", + "content": " is still bounded to RI under the constraint of Eq. (4)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": "Since the ID loss is dedicated to differentiable learning of the recognizability measure, we argue that the statistical diversion of " + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": " contributes to a more meaningful enhancement of recognizability in the embedding space, especially for the hard-to-recognize face images." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9960" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 219, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 219, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 219, + 85 + ], + "type": "text", + "content": "3.4. Perceptibility Attention Module" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": "In [9], Deng et al. showed that diverting the embedding's direction from the UIs cluster center results in face recognition improvement in the inference stage. Given the embedding vector of a VLR face instance " + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": " and the L2-normalized UIs cluster center " + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{v}}_{UI}" + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": ", we define the embedding projected in the direction away from the UIs cluster " + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i'" + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": " based on [9] as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 119, + 185, + 287, + 199 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 185, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 119, + 185, + 287, + 199 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {i} ^ {\\prime} = \\boldsymbol {v} _ {i} - \\langle \\boldsymbol {v} _ {i}, \\bar {\\boldsymbol {v}} _ {U I} \\rangle \\bar {\\boldsymbol {v}} _ {U I} \\tag {8}", + "image_path": "7c56442e4f292d53b729985668935175ab19a2f86eeb4f3c51219453764338fc.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "text", + "content": "We conjecture that the embedding projection away from the UIs cluster center is beneficial to alleviate the model's inadequacy to highlight the meaningful features when the face is obscure. Different from the conventional attention models for the classification tasks, we seek to explore the most salient feature representation with the greatest significance for recognizability by approximating " + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\boldsymbol{v}_i'" + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "text", + "content": " through an attention module. Inspired by [50], we design a perceptibility attention module that attends to the spatial and channel dimension of the instances' feature map sequentially. The attended feature maps are fed into a linearly connected layer to learn an attended embedding " + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\boldsymbol{v}_i^{attn}" + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "text", + "content": " at the same dimension as " + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\boldsymbol{v}_i'" + }, + { + "bbox": [ + 46, + 209, + 288, + 376 + ], + "type": "text", + "content": ". Lastly, we utilize the mean squared error loss and formalize the regression problem as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 379, + 287, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 379, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 379, + 287, + 411 + ], + "type": "interline_equation", + "content": "L _ {M S E} = \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\left(\\boldsymbol {v} _ {i} ^ {\\prime} - \\boldsymbol {v} _ {i} ^ {\\text {a t t n}}\\right) ^ {2} \\tag {9}", + "image_path": "c5754972d23c79ad94086150ce4afcf935f913d276b727cf1abe9229a5b15a49.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 417, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 417, + 287, + 525 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 417, + 287, + 525 + ], + "type": "text", + "content": " is the batch size. We argue that the projection of embeddings away from the UIs cluster can be deemed as RI-enhanced embeddings. This guides our model to attend to the parts of embedding that contain the richer interpretive contents important to recognition purposes. Therefore, introducing an attention module permits our model to attend to the most salient face regions, i.e., eyes, nose, etc., of a VLR face instance. In compliance with Eq. (4), (7) and (9), the overall loss function is expressed as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 71, + 536, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 536, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 71, + 536, + 287, + 550 + ], + "type": "interline_equation", + "content": "L _ {t o t a l} = L _ {c l s} + \\alpha L _ {L 1} + \\beta L _ {I D} + \\gamma L _ {M S E} \\tag {10}", + "image_path": "50d376f4d927660624d8e75e5cc4462bf9bca4d7160ae5a8e4a14308048a067a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "content": "where we opt for ArcFace [8] as the classification loss, " + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "inline_equation", + "content": "L_{cls}" + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 559, + 286, + 584 + ], + "type": "text", + "content": " are the weighting factors for each loss term." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 597, + 190, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 190, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 190, + 609 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Datasets. To confront the real-world VLRFR problem, our experiments are conducted on three realistic LR face datasets, namely TinyFace [6], SurvFace [7], and SCFace [16] under an open-set evaluation protocol, given the identity labels are disjoint across training and testing sets. We assemble an unlabeled UI face dataset from two public person re-identification repositories by the MTCNN face detector [57], including LPW [42] and MARS [59]. Notably," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "most of the detected faces are unrecognizable, thereby facilitating the generation of an UIs cluster. The details of each dataset are provided in Sec. A of in supplemental material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 109, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 545, + 204 + ], + "type": "text", + "content": "Experiment Settings. Our experiments utilize Mobile-FaceNet [5] and ResNet-50 [8] pretrained on the VGGFace2 [3] dataset as the representation encoder. For each dataset, we fine-tune these models using the respective training examples for performance evaluation. Our baseline model is the counterpart trained only with the ArcFace loss. We provide our experimental setup and other relevant settings in Sec. B of the supplemental material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 205, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 288 + ], + "type": "text", + "content": "Evaluation Metrics. We summarize the overall performance in rank-1 identification rate (IR) (\\%) for TinyFace and SCFace. On the contrary, we report the positive identification rate (TPIR) (\\%) @ false positive identification rate (FPIR), and true positive rate (TPR) (\\%) @ false acceptance rate (FAR) (\\%) for SurvFace, due to the inclusion of non-mated face images in its testing set [7]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 289, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 361 + ], + "type": "text", + "content": "To evaluate the characterization of face image quality, we provide the Error versus Reject Curve (ERC) [2, 18, 36], where portions of low-quality face images are screened out with respect to quality indexes. This evaluation is assessed in terms of False Non-Match Rate (FNMR) [26] at a specific threshold for a fixed False Match Rate (FMR) [26]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 369, + 481, + 381 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 481, + 381 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 481, + 381 + ], + "type": "text", + "content": "4.1. Comparison with SoTA Methods" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 388, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 555 + ], + "type": "text", + "content": "We compare the generalization performance on two open-set face identification tasks, VLR-VLR (TinyFace and SurvFace) and HR-VLR (SCFace), to the most recent SoTAs in Table 1, 2, and " + }, + { + "bbox": [ + 305, + 388, + 545, + 555 + ], + "type": "inline_equation", + "content": "3^{1}" + }, + { + "bbox": [ + 305, + 388, + 545, + 555 + ], + "type": "text", + "content": ". The former task is relatively challenging as only the noisy VLR examples are provided for probe-to-gallery matching. However, the latter suffers from a severe resolution gap between the HR galleries and the VLR probes. We disclose that the proposed model is not only resistant to the resolution gap but also a viable solution to the downstream VLR-VLR task. On the other hand, we leave the column blank for KD and resolution-invariant methods without involving the VLR datasets for fine-tuning, seeing that these VLR datasets are relatively small-scale and therefore easily prone to over-fitting." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 555, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 555, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 305, + 555, + 545, + 675 + ], + "type": "text", + "content": "TinyFace. We substantiate that our model outperforms other recent SoTAs designated for VLRFR by a remarkable margin, both with and without distractors (a summation of 153,428 face images of unknown identities in the gallery set). Specifically, we demonstrate that improving recognizability at the feature level is more meaningful than super-resolving the visual quality of the VLR face images, e.g. [6, 24, 39, 58]. With a quality-adapted margin for embedding learning, we discern that AdaFace [25] only readjusts the decision boundary - remaining the feature recog" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "In the \"fine-tuned\" column of these tables, we indicate " + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sharp" + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": " as fine-tuning on super-resolved, synthetic down-sampled VLR, and native VLR face images respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "9961" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 294, + 228 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 294, + 228 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 294, + 228 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 294, + 228 + ], + "type": "table", + "html": "
MethodsFine-TunedRank-1 IR (%)
w/ disw/o dis
CSRI (ACCV19) [6]#44.80-
TURL (CVPR20) [39]63.89-
RIFR (T-BIOM20) [24]70.40-
VividGAN (TIP21) [58]#47.16-
MIND-Net (SPL21) [32]✓66.8273.52
AdaFace (CVPR22) [25]68.21-
IDEA-Net (TIFS22) [31]✓68.13-
AdaFace (Reproduce)✓71.3875.67
Ours✓73.0677.22
", + "image_path": "4557ab41c370dcdeb249bd128e9c1cf19c599f720135add48407114a34bdef28.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 303, + 70, + 544, + 228 + ], + "blocks": [ + { + "bbox": [ + 70, + 231, + 270, + 242 + ], + "lines": [ + { + "bbox": [ + 70, + 231, + 270, + 242 + ], + "spans": [ + { + "bbox": [ + 70, + 231, + 270, + 242 + ], + "type": "text", + "content": "Table 1. IR Comparison on TinyFace using ResNet-50" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 303, + 70, + 544, + 228 + ], + "lines": [ + { + "bbox": [ + 303, + 70, + 544, + 228 + ], + "spans": [ + { + "bbox": [ + 303, + 70, + 544, + 228 + ], + "type": "table", + "html": "
MethodsFine-TunedRank-1 IR (%)
4.2m2.6m1.0mAvg.
TCN (ICASSP10) [55]✓74.6094.9098.6089.37
T-C (IVC20) [34]†70.2093.7098.1087.33
FAN (ACCV19) [52]✓77.5095.0098.3090.30
RAN (ECCV20) [11]✓81.3097.8098.8092.63
DDL (ECCV20) [20]✓86.8098.3098.3094.40
RIFR (T-BIOM20) [24]88.3098.3098.6095.00
MIND-Net (SPL21) [32]✓81.7598.0099.2593.00
DSN (APSIPA21) [27]✓93.0098.5098.5096.70
DRVNet (TPAMI21) [40]✓76.8092.8097.5089.03
RPCL (NN22) [30]✓90.4098.0098.0095.46
NPT (TPAMI22) [23]85.6999.0899.0896.61
IDEA-Net (TIFS22) [31]✓90.7698.5099.2596.17
AdaFace (Reproduce)✓95.3898.4699.8497.89
Ours✓97.0799.2399.8098.70
", + "image_path": "183d3fcf1e765636cfa9d559af6c797ebaae3b736b6e83dc6e3cb28f43c3ac62.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 47, + 251, + 547, + 380 + ], + "blocks": [ + { + "bbox": [ + 325, + 232, + 520, + 243 + ], + "lines": [ + { + "bbox": [ + 325, + 232, + 520, + 243 + ], + "spans": [ + { + "bbox": [ + 325, + 232, + 520, + 243 + ], + "type": "text", + "content": "Table 2. IR Comparison on SCFace using ResNet-50" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 251, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 47, + 251, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 547, + 380 + ], + "type": "table", + "html": "
MethodsFine-TunedTPR(%)@FARTPIR20(%)@FPIR
0.30.10.010.0010.30.20.1
CSRI (ACCV19) [6, 22]#78.6053.1018.0912.04---
FAN (ACCV19) [52]71.3044.5912.942.75---
RAN (ECCV20) [11]----26.5021.6014.90
SST (ECCV20) [10]✓87.0068.2135.7222.1812.389.716.61
DSN (APSIPA21) [27]75.0952.7421.4111.02---
DDAT (PR21) [22]90.4075.5040.4016.40---
IDEA-Net (TIFS22) [11]----26.2421.8215.61
AdaFace (Reproduce)✓87.4177.4858.6340.0931.5027.7421.93
Ours✓90.2180.9964.6048.4833.2029.3422.81
", + "image_path": "569fa08b09fedfbb1f7a478b5a06cc611b9a7b0649af63564f9862ae509ab265.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 384, + 463, + 396 + ], + "lines": [ + { + "bbox": [ + 129, + 384, + 463, + 396 + ], + "spans": [ + { + "bbox": [ + 129, + 384, + 463, + 396 + ], + "type": "text", + "content": "Table 3. TPR(%)@FAR and TPIR20(%)@FPIR Comparison on SurvFace using ResNet-50" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 411, + 136, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 136, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 136, + 422 + ], + "type": "text", + "content": "nizability unchanged." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "text", + "content": "SCFace. For the HR-VLR evaluation, our model remains superior to other SoTAs over the three probe sets. This is attributed to: (i) the enhanced recognizability bridges the resolution gap between the HR and the VLR face features; and (ii) the attention module singles out the most salient regions from VLR and HR faces, resulting in better cross-resolution matching scores, especially for the face images captured from " + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "inline_equation", + "content": "4.2m" + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "text", + "content": " (the largest standoff distances compared to " + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "inline_equation", + "content": "1.0m" + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "inline_equation", + "content": "2.6m" + }, + { + "bbox": [ + 46, + 424, + 288, + 531 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 532, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 665 + ], + "type": "text", + "content": "SurvFace. Being the most challenging VLR face dataset for the VLR-VLR deployment scenario, SurvFace evaluates both open-set identification and verification tasks in the presence of 141,736 unmated distractors as a part of the probe set. We disclose that our model significantly outperforms other SoTAs under the most rigorous settings, i.e., TPR@FAR=0.001 and TPIR20@FPIR=0.01. While [11,22,52] are trained based on synthetic LR images downsampled from HR-paired counterparts for visual quality improvement, we underline that none of these SoTAs resolves the VLRFR by means of refining feature recognizability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 674, + 153, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 674, + 153, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 674, + 153, + 687 + ], + "type": "text", + "content": "4.2. Ablation Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Effect of Each Loss Component. We present in Table 4 an ablation analysis to explore the effect of each loss term" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "text", + "content": "using MobileFaceNet on TinyFace without gallery distractors. Compare to our baseline model (trained using only ArcFace), the inclusion of ID loss in Baseline I discloses that learning to enhance the recognizability of the hard-to-recognize instances offers a performance improvement close to " + }, + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "text", + "content": ". Baseline II, on the other hand, reveals that the perceptibility attention module allows the most salient characteristics to be attended, resulting in at least " + }, + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 411, + 547, + 687 + ], + "type": "text", + "content": " of performance gain. Meanwhile, Baseline III demonstrates that our model benefits from learning an RI based on an estimated RI as shown in Eq. (4). It is believed that learning the softmax prototypes simultaneously with the RI prompts our model to encode the embedding recognizability at each training step. As a result, the learned RI can be viewed as an index of the model's confidence corresponding to the classifiability of any face image, including the unknown instances. Overall, our model trained with all loss terms outperforms the baselines and two most relevant SoTAs, i.e., MagFace [35], and AdaFace [25]. An important reason is that these SoTAs are reliant on the embedding's norm that does not always convey face recognizability, particularly for the VLR face images. This is substantiated by our empirical proofs in the following section." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "content": "Intuition of Hyperparameter Selection. In Fig. 3, we conduct the study of each weighting factor on each hyper" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9962" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 289, + 189 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 189 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 189 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 189 + ], + "type": "table", + "html": "
MethodLclsLIDLMSELL1Rank-1 IR (%)
Cross Entropy [43]✓68.884
NormFace [46]✓68.026
CosFace [47]✓70.306
MV-Softmax [48]✓70.547
CurricularFace [21]✓70.655
MagFace [35]✓70.467
AdaFace [25]✓70.359
Baseline (ArcFace) [8]✓70.333
I✓✓71.298
II✓✓71.540
III✓✓71.674
Ours✓✓✓✓71.915
", + "image_path": "500c5216d867eafe0dd6e1e497ab685ea82a51164214236534cb6bd12b75391d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 192, + 287, + 214 + ], + "lines": [ + { + "bbox": [ + 47, + 192, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 287, + 214 + ], + "type": "text", + "content": "Table 4. Ablation Analysis for each Loss Term on TinyFace without Distractors using MobileFaceNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 224, + 284, + 323 + ], + "blocks": [ + { + "bbox": [ + 48, + 224, + 284, + 323 + ], + "lines": [ + { + "bbox": [ + 48, + 224, + 284, + 323 + ], + "spans": [ + { + "bbox": [ + 48, + 224, + 284, + 323 + ], + "type": "image", + "image_path": "86a631936821ca9cb8bd3ff5c1999ff99a132246fe77d2743ca7ea1e00e1efe8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "lines": [ + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "spans": [ + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "type": "text", + "content": "Figure 3. Ablation Studies for Hyperparameters " + }, + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta" + }, + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 56, + 326, + 277, + 338 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": "parameter by fixing the remaining weighting factors to be their optimal values in accordance to Table 5. We refer to Eq. (10) where " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " correspond to the weighting of " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{L1}, L_{ID}, L_{MSE}" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " respectively. Suppose that we attempt to study the various weighting factors of " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{L1}" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " via manipulating the values of " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": ", we fix " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\gamma = 1" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\beta = 2" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": ". The effects of " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " are shown as the " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " curve, and the same is applied to " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " curves. Our ablations show that an overly large " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha (>10)" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " may experience difficulty in convergence [2], and 5 is the best choice. For " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": ", the findings suggest a weighting factor slightly less than the " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " ensures better recognizability of the instances while still being upper bound by the devised RI. Lastly, we discover that " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{MSE}" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " converges fast, and a higher " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " hinders the overall model convergence, resulting in performance depreciation. A smaller " + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": " is thus recommended and set to be 1 in our experiment." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": "Face Recognizability-Aware Embeddings. We conduct a toy experiment with 5 easy-to-recognize (IDs 0,2,3,5,7) and 3 hard-to-recognize (IDs 1,4,6) face examples to examine the embedding space learned by SoTAs and our model in Fig. 4. The UIs center is visualized as a reference index of recognizability, where a poor recognizability (hard-to-recognize) instance is essentially projected close to the UIs center. It is discerned that the competing models are incapable of separating the hard-to-recognize clusters from the UIs center. On the contrary, our model is inclined to divert the hard-to-recognize instances from the UIs center, yielding a well-separable (therefore a more discriminative) embedding space to resolve the downstream VLRFR task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Effect of Perceptibility Attention Module. We portray" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 539, + 144 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 539, + 144 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 539, + 144 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 539, + 144 + ], + "type": "image", + "image_path": "a2d8305b9c8a52a7133fbecff4f21613c443362cae2f1db8746d8e59d28c65f7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 147, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 305, + 147, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 545, + 202 + ], + "type": "text", + "content": "Figure 4. 2D embedding space for a toy problem with 8 identities (IDs). The IDs denoted with a \"√\" contain hard-to-recognize instances, even from the human perspective. We visualize the UIs center as a reference index of recognizability, i.e., embeddings further away from the UIs center can better be recognized." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 311, + 214, + 538, + 334 + ], + "blocks": [ + { + "bbox": [ + 311, + 214, + 538, + 334 + ], + "lines": [ + { + "bbox": [ + 311, + 214, + 538, + 334 + ], + "spans": [ + { + "bbox": [ + 311, + 214, + 538, + 334 + ], + "type": "image", + "image_path": "fa1b706775f53a24447f830e89b24382ef15b2109d27aa172cfa404bd4a0f6f6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 342, + 545, + 364 + ], + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 364 + ], + "type": "text", + "content": "Figure 5. Class activation maps for several VLR face images generated based on ArcFace, AdaFace, and Ours." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 382, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 467 + ], + "type": "text", + "content": "the Class Activation Maps [37] obtained from ArcFace [8], Adaface [25], and our method for comparison. Interestingly, we observe from Fig. 5 that attending to the embeddings away from the UIs center focuses more on the salient face features, i.e. eyes, nose, and mouth, even when the face images appear to be obscure. We provide the extended heatmap visualizations in Fig. 11 of supplemental material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 477, + 515, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 515, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 515, + 491 + ], + "type": "text", + "content": "4.3. Face Image Quality Assessment (FIQA)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 497, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 663 + ], + "type": "text", + "content": "Learned RI from Perceptibility Regression Module. In Fig. 6, the effect of ID loss reveals a greater negatively-skewed distribution of RI than other SoTAs (extended version in Fig. 9), indicating an improvement in recognizability, notably the hard-to-recognize instances. We discern that the proposed RI is a robust indicator in characterizing the recognizability notion - the highest and the lowest RI reflect the best-quality and the poor-quality face images, respectively. We also provide in Fig. 6 the face images with the lowest quality scores estimated by other competing scores. Through the comparison, RI is deemed proportional to the human cognitive level in terms of recognizability for the VLR face images under extreme poses, illuminations, occlusions, and others in the wild conditions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Error versus Rejection Curve (ERC). To further substantiate the RI's robustness, we perform a verification task on TinyFace [6] by randomly sampling 20,888 positive and 50,000 negative pairs from its gallery and probe sets to show" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9963" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 376, + 289 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 376, + 289 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 376, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 376, + 289 + ], + "type": "image", + "image_path": "a6bf592ef4bee07739cc7551e89264161ee9c04b4f67b2f8859b4b999b11b983.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 546, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 546, + 350 + ], + "type": "text", + "content": "Figure 6. To facilitate direct comparison, all quality measures are normalized to ranges between 0 and 1. (Left) Visualization of RI sorted from the lowest scores (the poorest quality) to the highest (the best quality) in TinyFace [6] dataset. It is disclosed that the proposed RI characterizes the face quality better, closely simulating the human cognitive level. (Right) The VLR face images estimated with the lowest quality scores based on MagFace [35], CR-FIQA [2] and ERS [9]. In place of hard-to-recognize instances, we observe that several high-quality face instances are mistakenly assigned with low-quality scores, particularly MagFace and CR-FIQA." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 379, + 70, + 542, + 288 + ], + "blocks": [ + { + "bbox": [ + 379, + 70, + 542, + 288 + ], + "lines": [ + { + "bbox": [ + 379, + 70, + 542, + 288 + ], + "spans": [ + { + "bbox": [ + 379, + 70, + 542, + 288 + ], + "type": "image", + "image_path": "1523a86b61ef08c0b036c916b6ad645e9e3fe8cafbe1764dee32808aef85f5b8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 52, + 356, + 220, + 488 + ], + "blocks": [ + { + "bbox": [ + 52, + 356, + 220, + 488 + ], + "lines": [ + { + "bbox": [ + 52, + 356, + 220, + 488 + ], + "spans": [ + { + "bbox": [ + 52, + 356, + 220, + 488 + ], + "type": "image", + "image_path": "07ff506db35875925765bf08c7b2c7360d3261e2a25dd871d6897de91cbd25f5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 497, + 546, + 553 + ], + "lines": [ + { + "bbox": [ + 46, + 497, + 546, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 546, + 553 + ], + "type": "text", + "content": "Figure 7. Whilst Fig. 6 shows that the learned RI can characterize face quality well, we further demonstrate in this figure that the learned RI is a reliable recognizability metric by means of analyzing false non-match rate (FNMR). In particular, FNMR decreases gradually when the ratio of unconsidered VLR face images increases (sampled based on the lowest RI). This indicates that the learn RI well characterizes the recognizability of the VLR face images, such that the most recognizable VLR face images are learned with the highest RIs (corresponding to the right of the left-skewed RI distribution) for FNMR evaluation." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 213, + 357, + 375, + 488 + ], + "blocks": [ + { + "bbox": [ + 213, + 357, + 375, + 488 + ], + "lines": [ + { + "bbox": [ + 213, + 357, + 375, + 488 + ], + "spans": [ + { + "bbox": [ + 213, + 357, + 375, + 488 + ], + "type": "image", + "image_path": "f354129eee6380fb02ba044c0dce4ddf8ae1d96e3bc60ffbf07508020afd4224.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 376, + 357, + 537, + 487 + ], + "blocks": [ + { + "bbox": [ + 376, + 357, + 537, + 487 + ], + "lines": [ + { + "bbox": [ + 376, + 357, + 537, + 487 + ], + "spans": [ + { + "bbox": [ + 376, + 357, + 537, + 487 + ], + "type": "image", + "image_path": "94e5817c2ef5911ad9e92c36fea466a0bdfca24a23836fa8f473a09aad6609b0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": "ERC in Fig. 7. The learned " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\widehat{\\xi}_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": " outperforms SoTA in achieving stable and true rejection of unrecognized pairs in the rank of recognizability, especially when the FMR is at " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 612, + 119, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 119, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 119, + 624 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "This paper addresses the problem arising from the hard-to-recognize faces in VLR images. Rather than treating these faces as UIs, we take a principled recognizability notion to characterize the recognizability of each image with a robust indicator, specifically the recognizability index (RI). The recognizability of an instance can thus be adjusted based on RI. Interestingly, attending to the embeddings pro" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 567, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 546, + 628 + ], + "type": "text", + "content": "jected away from the UIs cluster provides more explanatory power to the model to highlight the facial features more precisely. We evaluate the proposed method trained in an end-to-end manner on three VLR datasets and achieve SoTA for both VLRFR and FIQA." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 645, + 408, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 408, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 408, + 658 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NO. NRF-2022R1A2C1010710) and Institute for Basic Science (IBS-R029-C2) Korea." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9964" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Lacey Best-Rowden and Anil K Jain. 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IEEE Transactions on image processing, 21(1):327-340, 2011. 1" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "9967" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_content_list.json b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e8f2ee70e394407620abbe9f0c57cb908f60f509 --- /dev/null +++ b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_content_list.json @@ -0,0 +1,1960 @@ +[ + { + "type": "text", + "text": "Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives", + "text_level": 1, + "bbox": [ + 89, + 130, + 880, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Daniel Widdowson \nComputer Science department \nUniversity of Liverpool, UK \nd.e.widdowson@liverpool.ac.uk", + "bbox": [ + 207, + 204, + 464, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vitaliy Kurlin \nComputer Science department \nUniversity of Liverpool, UK \nvitaliy.kurlin@gmail.com", + "bbox": [ + 519, + 203, + 761, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 309, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances.", + "bbox": [ + 76, + 340, + 470, + 402 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description).", + "bbox": [ + 76, + 407, + 468, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points.", + "bbox": [ + 75, + 489, + 468, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Strong motivations for complete invariants", + "text_level": 1, + "bbox": [ + 76, + 613, + 459, + 631 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In Computer Vision, real objects such as cars and solid obstacles are considered rigid and often represented by a finite set $C \\subset \\mathbb{R}^n$ (called a cloud) of $m$ unlabeled (or unordered) points, usually in low dimensions $n = 2, 3, 4$ .", + "bbox": [ + 76, + 638, + 468, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The rigidity of many real objects motivates the most fundamental equivalence of rigid motion [67], a composition of translations and rotations in $\\mathbb{R}^n$ . In a general metric space $M$ , the most relevant equivalence is isometry: any map $M \\to M$ maintaining all inter-point distances in $M$ .", + "bbox": [ + 76, + 705, + 468, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Any isometry in $\\mathbb{R}^n$ is a composition of a mirror reflection with some rigid motion. Any orientation-preserving isometry can be realized as a continuous rigid motion.", + "bbox": [ + 76, + 787, + 468, + 834 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is no sense in distinguishing rigid objects that are related by isometry or having the same shape. Formally, the shape of a cloud $C$ is its isometry class [48] defined as a collection of all infinitely many clouds isometric to $C$ .", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The only reliable tool for distinguishing clouds up to isometry is an invariant defined as a function or property preserved by any isometry. Since any isometry is bijective, the number of points is an isometry invariant, but the coordinates of points are not invariants even under translation. This simple invariant is incomplete (non-injective) because non-isometric clouds can have different numbers of points.", + "bbox": [ + 496, + 309, + 890, + 416 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Any invariant $I$ maps all isometric clouds to the same value. There are no isometric clouds $C \\cong C'$ with $I(C) \\neq I(C')$ , meaning that $I$ has no false negatives. Isometry invariants are also called equivariant descriptors [55].", + "bbox": [ + 496, + 420, + 890, + 481 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A complete invariant $I$ should distinguish all nonisometric clouds, so if $C \\neq C'$ then $I(C) \\neq I(C')$ . Equivalently, if $I(C) = I(C')$ then $C \\cong C'$ , so $I$ has no false positives. Then $I$ can be considered as a DNA-style code or genome that identifies any cloud uniquely up to isometry.", + "bbox": [ + 496, + 484, + 890, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since real data is always noisy and motions of rigid objects are important to track, a useful complete invariant must be also continuous under the movement of points.", + "bbox": [ + 496, + 564, + 890, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A complete and continuous invariant for $m = 3$ points consists of three pairwise distances (sides of a triangle) and is known in school as the SSS theorem [68]. But all pairwise distances are incomplete for $m \\geq 4$ [9], see Fig. 1.", + "bbox": [ + 496, + 613, + 890, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Problem 1.1 (complete isometry invariants with computable continuous metrics). For any cloud of $m$ unlabeled points in $\\mathbb{R}^n$ , find an invariant $I$ satisfying the properties", + "bbox": [ + 496, + 684, + 890, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$(\\pmb{a})$ completeness: $C, C'$ are isometric $\\Leftrightarrow I(C) = I(C')$ ;", + "bbox": [ + 496, + 736, + 880, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) Lipschitz continuity: if any point of $C$ is perturbed within its $\\varepsilon$ -neighborhood then $I(C)$ changes by at most $\\lambda \\varepsilon$ for a constant $\\lambda$ and a metric $d$ satisfying these axioms:", + "bbox": [ + 496, + 758, + 890, + 805 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1) $d(I(C),I(C')) = 0$ if and only if $C\\cong C^{\\prime}$ are isometric,", + "bbox": [ + 500, + 808, + 887, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2) symmetry: $d(I(C), I(C')) = d(I(C'), I(C))$ ,", + "bbox": [ + 500, + 827, + 828, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3) $d(I(C),I(C')) + d(I(C'),I(C''))\\geq d(I(C),I(C''))$", + "bbox": [ + 500, + 845, + 883, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(c) computability: $I$ and $d$ are computed in a polynomial time in the number $m$ of points for a fixed dimension $n$ .", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1275", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3d8a2270bc0f87dbbfc1632d76df8dd156fd60d26a619e8c6ff33a75ad59e1f.jpg", + "image_caption": [ + "Figure 1. Left: the cloud $T = \\{(1,1), (-1,1), (-2,0), (2,0)\\}$ . Right: the kite $K = \\{(0,1), (-1,0), (0, -1), (3,0)\\}$ . $T$ and $K$ have the same 6 pairwise distances $\\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4$ ." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 470, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Condition (1.1b) asking for a continuous metric is stronger than the completeness in (1.1a). Detecting an isometry $C \\cong C'$ gives a discontinuous metric, say $d = 1$ for all non-isometric clouds $C \\not\\cong C'$ even if $C, C'$ are nearly identical. Any metric $d$ satisfying the first axiom in (1.1b) detects an isometry $C \\cong C'$ by checking if $d = 0$ .", + "bbox": [ + 75, + 246, + 468, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Theorem 4.7 will solve Problem 1.1 for any $m$ in $\\mathbb{R}^n$ . Continuous invariants in Theorem 3.10 are conjectured to be complete (no known counter-examples) in any metric space. The first author implemented all algorithms, the second author wrote all theory, proofs, examples in [38, 39].", + "bbox": [ + 75, + 340, + 468, + 416 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Past work on cloud recognition/classification", + "text_level": 1, + "bbox": [ + 76, + 430, + 468, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Labeled clouds $C \\subset \\mathbb{R}^n$ are easy for isometry classification because the matrix of distances $d_{ij}$ between indexed points $p_i, p_j$ allows us to reconstruct $C$ by using the known distances to the previously constructed points [28, Theorem 9]. For any clouds of the same number $m$ of labeled points, the difference between $m \\times m$ matrices of distances (or Gram matrices of $p_i \\cdot p_j$ ) can be converted into a continuous metric by taking a matrix norm. If the given points are unlabeled, comparing $m \\times m$ matrices requires $m!$ permutations, which makes this approach impractical.", + "bbox": [ + 75, + 454, + 468, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multidimensional scaling (MDS). For a given $m \\times m$ distance matrix of any $m$ -point cloud $A$ , MDS [57] finds an embedding $A \\subset \\mathbb{R}^k$ (if it exists) preserving all distances of $M$ for a dimension $k \\leq m$ . A final embedding $A \\subset \\mathbb{R}^k$ uses eigenvectors whose ambiguity up to signs gives an exponential comparison time that can be close to $O(2^m)$ .", + "bbox": [ + 75, + 609, + 468, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Isometry detection refers to a simpler version of Problem 1.1 to algorithmically detect a potential isometry between given clouds of $m$ points in $\\mathbb{R}^n$ . The best algorithm by Brass and Knauer [10] takes $O(m^{\\lceil n/3 \\rceil} \\log m)$ time, so $O(m \\log m)$ in $\\mathbb{R}^3$ . These algorithms output a binary answer (yes/no) without quantifying similarity between non-isometric clouds by a continuous metric.", + "bbox": [ + 75, + 704, + 468, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Hausdorff distance [30] can be defined for any subsets $A, B$ in an ambient metric space as $d_H(A, B) = \\max \\{\\vec{d}_H(A, B), \\vec{d}_H(B, A)\\}$ , where the directed Hausdorff distance is $\\vec{d}_H(A, B) = \\sup_{p \\in A} \\inf_{q \\in B} |p - q|$ . To take into account isometries, one can minimize the Hausdorff distance", + "bbox": [ + 75, + 813, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "over all isometries [15, 17, 32]. For $n = 2$ , the Hausdorff distance minimized over isometries in $\\mathbb{R}^2$ for sets of at most $m$ point needs $O(m^{5}\\log m)$ time [16]. For a given $\\varepsilon > 0$ and $n > 2$ , the related problem to decide if $d_H \\leq \\varepsilon$ up to translations has the time complexity $O(m^{\\lceil (n + 1) / 2\\rceil})$ [69, Chapter 4, Corollary 6]. For general isometry, only approximate algorithms tackled minimizations for infinitely many rotations initially in $\\mathbb{R}^3$ [26] and in $\\mathbb{R}^n$ [4, Lemma 5.5].", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Gromov-Wasserstein distances can be defined for metric-measure spaces, not necessarily sitting in a common ambient space. The simplest Gromov-Hausdorff (GH) distance cannot be approximated with any factor less than 3 in polynomial time unless $\\mathrm{P} = \\mathrm{NP}$ [56, Corollary 3.8]. Polynomial-time algorithms for GH were designed for ultrametric spaces [45]. However, GH spaces are challenging even for point clouds sets in $\\mathbb{R}$ , see [41] and [74].", + "bbox": [ + 496, + 215, + 890, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Heat Kernel Signature (HKS) is a complete isometry invariant of a manifold $M$ whose the Laplace-Beltrami operator has distinct eigenvalues by [64, Theorem 1]. If $M$ is sampled by points, HKS can be discretized and remains continuous [64, section 4] but the completeness is unclear.", + "bbox": [ + 496, + 340, + 890, + 416 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Equivariant descriptors can be experimentally optimized [47, 59] on big datasets of clouds that are split into predefined clusters. Using more hidden parameters can improve accuracy on any finite dataset at a higher cost but will require more work for any new data. Point cloud registration filters outliers [58], samples rotations for Scale Invariant Feature Transform or uses a basis [52, 63, 65, 76], which can be unstable under perturbations of a cloud. The PCA-based complete invariant of unlabelled clouds [35] can discontinuously change when a basis degenerates to a lower dimensional subspace but inspired Complete Neural Networks [31] though without the Lipschitz continuity.", + "bbox": [ + 496, + 420, + 890, + 601 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geometric Deep Learning produces descriptors that are equivariant by design [13] and go beyond Euclidean space $\\mathbb{R}^n$ [14], hence aiming to experimentally solve Problem 1.1. Motivated by obstacles in [1, 18, 19, 29, 40], Problem 1.1 needs a justified solution without relying on finite data.", + "bbox": [ + 496, + 604, + 890, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geometric Data Science solves analogs of Problem 1.1 for any real data objects considered up to practical equivalences instead of rigid motion on clouds [23, 24, 61]: 1-periodic discrete series [5, 6, 35], 2D lattices [12, 37], 3D lattices [11, 34, 36, 46], periodic point sets in $\\mathbb{R}^3$ [20, 62] and in higher dimensions [2-4]. The applications of to crystalline materials [7, 53, 66, 75] led to the Crystal Isometry Principle [70, 71, 73] extending Mendeleev's table of elements to the Crystal Isometry Space of all periodic crystals parametrised by complete invariants like a geographic map of a planet.", + "bbox": [ + 496, + 685, + 890, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Local distributions of distances in Mémoli's seminal work [43, 44] for metric-measure spaces, or shape distributions [8,27,42,49], are first-order versions of the new SDD below.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1276", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Simplewise Distance Distribution (SDD)", + "text_level": 1, + "bbox": [ + 76, + 89, + 444, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will refine Sorted Distance Vector in any metric space to get a complete invariant in $\\mathbb{R}^n$ as shown in Fig. 2. All proofs from sections 3 and 4 are in [38,39], respectively.", + "bbox": [ + 76, + 114, + 467, + 162 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f244f8e4ca360e29f3b73f2a4047b410aa17cca8d0f67065a75b8d86d2209106.jpg", + "image_caption": [ + "Figure 2. Hierarchy of new invariants on top of the classical SDV." + ], + "image_footnote": [], + "bbox": [ + 78, + 174, + 467, + 289 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The lexicographic order $u < v$ on vectors $u = (u_{1},\\ldots ,u_{h})$ and $v = (v_{1},\\dots ,v_{h})$ in $\\mathbb{R}^h$ means that if the first $i$ (possibly, $i = 0$ ) coordinates of $u,v$ coincide then $u_{i + 1} < v_{i + 1}$ . Let $S_{h}$ denote the permutation group on indices $1,\\ldots ,h$ .", + "bbox": [ + 75, + 332, + 467, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3.1 (RDD(C;A)). Let $C$ be a cloud of $m$ unlabeled points in a space with a metric $d$ . Let $A = (p_1, \\ldots, p_h) \\subset C$ be an ordered subset of $1 \\leq h < m$ points. Let $D(A)$ be the triangular distance matrix whose entry $D(A)_{i,j-1}$ is $d(p_i, p_j)$ for $1 \\leq i < j \\leq h$ , all other entries are filled by zeros. Any permutation $\\xi \\in S_h$ acts on $D(A)$ by mapping $D(A)_{ij}$ to $D(A)_{kl}$ , where $k \\leq l$ is the pair of indices $\\xi(i), \\xi(j) - 1$ written in increasing order.", + "bbox": [ + 75, + 404, + 467, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For any other point $q \\in C - A$ , write distances from $q$ to $p_1, \\ldots, p_h$ as a column. The $h \\times (m - h)$ -matrix $R(C; A)$ is formed by these $m - h$ lexicographically ordered columns. The action of $\\xi$ on $R(C; A)$ maps any $i$ -th row to the $\\xi(i)$ -th row, after which all columns can be written again in the lexicographic order. The Relative Distance Distribution $\\mathrm{RDD}(C; A)$ is the equivalence class of the pair $[D(A), R(C; A)]$ of matrices up to permutations $\\xi \\in S_h$ .", + "bbox": [ + 75, + 531, + 467, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a 1-point subset $A = \\{p_1\\}$ with $h = 1$ , the matrix $D(A)$ is empty and $R(C;A)$ is a single row of distances (in the increasing order) from $p_1$ to all other points $q \\in C$ . For a 2-point subset $A = (p_1,p_2)$ with $h = 2$ , the matrix $D(A)$ is the single number $d(p_1,p_2)$ and $R(C;A)$ consists of two rows of distances from $p_1, p_2$ to all other points $q \\in C$ .", + "bbox": [ + 75, + 662, + 467, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Example 3.2 (RDD for a 3-point cloud $C$ ). Let $C \\subset \\mathbb{R}^2$ consist of $p_1, p_2, p_3$ with inter-point distances $a \\leq b \\leq c$ ordered counter-clockwise as in Fig. 3 (left). Then", + "bbox": [ + 75, + 765, + 467, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R D D} (C; p _ {1}) = [ \\emptyset ; (b, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {2} \\\\ p _ {3} \\end{array} \\right)) = [ a; \\left( \\begin{array}{c} c \\\\ b \\end{array} \\right) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 823, + 477, + 858 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R D D} (C; p _ {2}) = [ \\emptyset ; (a, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {3} \\\\ p _ {1} \\end{array} \\right)) = [ b; \\left( \\begin{array}{c} a \\\\ c \\end{array} \\right) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 869, + 478, + 904 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/805b7e74f33947f847a616f36781dc3fc1e11fe3dc86fada565addb507f49067.jpg", + "image_caption": [ + "Figure 3. Left: a cloud $C = \\{p_1, p_2, p_3\\}$ with distances $a \\leq b \\leq c$ . Middle: the triangular cloud $R = \\{(0,0), (4,0), (0,3)\\}$ . Right: the square cloud $S = \\{(1,0), (-1,0), (0,1), (-1,0)\\}$ ." + ], + "image_footnote": [], + "bbox": [ + 498, + 87, + 890, + 179 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R D D} (C; p _ {3}) = [ \\emptyset ; (a, b) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {1} \\\\ p _ {2} \\end{array} \\right)) = [ c; \\left( \\begin{array}{c} b \\\\ a \\end{array} \\right) ].\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 253, + 900, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will always represent RDD for a specified order $A = (p_i, p_j)$ of points that are written as a column. Swapping the points $p_1 \\leftrightarrow p_2$ makes the last RDD above equivalent to another form: $\\mathrm{RDD}(C; \\left( \\begin{array}{c} p_2 \\\\ p_1 \\end{array} \\right)) = [c; \\left( \\begin{array}{c} a \\\\ b \\end{array} \\right)]$ .", + "bbox": [ + 498, + 292, + 890, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Though $\\mathrm{RDD}(C;A)$ is defined up to a permutation $\\xi$ of $h$ points in $A\\subset C$ , we later use only $h = n$ , which makes comparisons of RDDs practical in dimensions $n = 2,3$ . Metrics on isometry classes of $C$ will be independent of $\\xi$ .", + "bbox": [ + 498, + 377, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3.3 (Simplewise Distance Distribution $\\mathrm{SDD}(C;h)$ ). Let $C$ be a cloud of $m$ unlabeled points in a metric space. For an integer $1\\leq h < m$ , the Simplewise Distance Distribution $\\mathrm{SDD}(C;h)$ is the unordered set of $\\mathrm{RDD}(C;A)$ for all unordered $h$ -point subsets $A\\subset C$ .", + "bbox": [ + 498, + 448, + 892, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For $h = 1$ and any $m$ -point cloud $C$ , the distribution $\\mathrm{SDD}(C;1)$ can be considered as a matrix of $m$ rows of ordered distances from every point $p \\in C$ to all other $m - 1$ points. If we lexicographically order these $m$ rows and collapse any $l > 1$ identical rows into a single one with the weight $l / m$ , then we get the Pointwise Distance Distribution $\\mathrm{PDD}(C; m - 1)$ introduced in [71, Definition 3.1].", + "bbox": [ + 496, + 534, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The PDD was simplified to the easier-to-compare vector of Average Minimum Distances [73]: $\\mathrm{AMD}_k(C) = \\frac{1}{m}\\sum_{i=1}^{m}d_{ik}$ , where $d_{ik}$ is the distance from a point $p_i\\in C$ to its $k$ -th nearest neighbor in $C$ . These neighbor-based invariants can be computed in a near-linear time in $m$ [22] and were pairwise compared for all all 660K+ periodic crystals in the world's largest database of real materials [71]. Definition 3.4 similarly maps SDD to a smaller invariant.", + "bbox": [ + 496, + 643, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall that the 1st moment of a set of numbers $a_1, \\ldots, a_k$ is the average $\\mu = \\frac{1}{k} \\sum_{i=1}^{k} a_i$ . The 2nd moment is the standard deviation $\\sigma = \\sqrt{\\frac{1}{k} \\sum_{i=1}^{k} (a_i - \\mu)^2}$ . For $l \\geq 3$ , the $l$ -th standardized moment [33, section 2.7] is $\\frac{1}{k} \\sum_{i=1}^{k} \\left( \\frac{a_i - \\mu}{\\sigma} \\right)^l$ .", + "bbox": [ + 496, + 782, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1277", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3.4 (Simplexwise Distance Moments SDM). For any $m$ -point cloud $C$ in a metric space, let $A \\subset C$ be a subset of $h$ unordered points. The Sorted Distance Vector SDV( $A$ ) is the list of all $\\frac{h(h - 1)}{2}$ pairwise distances between points of $A$ written in increasing order. The vector $\\vec{R}(C; A) \\in \\mathbb{R}^{m - h}$ is obtained from the $h \\times (m - h)$ matrix $R(C; A)$ in Definition 3.1 by writing the vector of $m - h$ column averages in increasing order.", + "bbox": [ + 76, + 90, + 472, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The pair $[\\mathrm{SDV}(A); \\vec{R}(C; A)]$ is the Average Distance Distribution $\\mathrm{ADD}(C; A)$ considered as a vector of length $\\frac{h(h - 3)}{2} + m$ . The unordered collection of $\\mathrm{ADD}(C; A)$ for all $\\binom{m}{h}$ unordered subsets $A \\subset C$ is the Average Simplewise Distribution $\\mathrm{ASD}(C; h)$ . The Simplewise Distance Moment $\\mathrm{SDM}(C; h, l)$ is the $l$ -th (standardized for $l \\geq 3$ ) moment of $\\mathrm{ASD}(C; h)$ considered as a probability distribution of $\\binom{m}{h}$ vectors, separately for each coordinate.", + "bbox": [ + 76, + 215, + 472, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Example 3.5 (SDD and SDM for $T, K$ ). Fig. 1 shows the non-isometric 4-point clouds $T, K$ with the same Sorted Distance Vector $\\mathrm{SDV} = \\{\\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4\\}$ , see infinitely many examples in [9]. The arrows on the edges of $T, K$ show orders of points in each pair of vertices for RDDs. Then $T, K$ are distinguished up to isometry by $\\mathrm{SDD}(T; 2) \\neq \\mathrm{SDD}(K; 2)$ in Table 1. The 1st coordinate of $\\mathrm{SDM}(C; 2, 1) \\in \\mathbb{R}^3$ is the average of 6 distances from $\\mathrm{SDV}(T) = \\mathrm{SDV}(K)$ but the other two coordinates (column averages from $R(C; A)$ matrices) differ.", + "bbox": [ + 75, + 351, + 472, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Some of the $\\binom{m}{h}$ RDDs in $\\mathrm{SDD}(C; h)$ can be identical as in Example 3.5. If we collapse any $l > 1$ identical RDDs into a single RDD with the weight $l / \\binom{m}{h}$ , SDD can be considered as a weighted probability distribution of RDDs.", + "bbox": [ + 76, + 512, + 470, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $m - h$ permutable columns of the matrix $R(C;A)$ in RDD from Definition 3.1 can be interpreted as $m - h$ unlabeled points in $\\mathbb{R}^h$ . Since any isometry is bijective, the simplest metric respecting bijections is the bottleneck distance, which is also called the Wasserstein distance $W_{\\infty}$ .", + "bbox": [ + 76, + 578, + 470, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 3.6 (bottleneck distance $W_{\\infty}$ ). For any vector $v = (v_{1},\\ldots ,v_{n})\\in \\mathbb{R}^{n}$ , the Minkowski norm is $||v||_{\\infty} = \\max_{i = 1,\\dots ,n}|v_i|$ . For any vectors or matrices $N,N^{\\prime}$ of the same size, the Minkowski distance is $L_{\\infty}(N,N^{\\prime}) = \\max_{i,j}|N_{ij} - N_{ij}^{\\prime}|$ . For clouds $C,C^{\\prime}\\subset \\mathbb{R}^{n}$ of $m$ unlabeled points, the bottleneck distance $W_{\\infty}(C,C^{\\prime}) = \\inf_{g:C\\to C^{\\prime}}\\sup_{p\\in C}||p - g(p)||_{\\infty}$ is minimized over all bijections $g:C\\to C'$ .", + "bbox": [ + 76, + 665, + 472, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 3.7 (the max metric $M_{\\infty}$ on RDDs). For any $m$ point clouds and ordered $h$ -point subsets $A\\subset C$ and $A^{\\prime}\\subset C^{\\prime}$ set $d(\\xi) = \\max \\{L_{\\infty}(\\xi (D(A)),D(A^{\\prime})),W_{\\infty}(\\xi (R(C;A)),R(C^{\\prime};A^{\\prime}))\\}$ for a permutation $\\xi \\in S_h$ on $h$ points. Then the max metric $M_{\\infty}(\\mathrm{RDD}(C;A),\\mathrm{RDD}(C^{\\prime};A^{\\prime})) = \\min_{\\xi \\in S_h}d(\\xi)$ satisfies all", + "bbox": [ + 75, + 804, + 475, + 904 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/f20644f5350cecdfcced54bd7e254e1275e5087ef8c050eb218c2d5fa6bd6f75.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RDD(T; A) in SDD(T; 2)RDD(K; A) in SDD(K; 2)
[√2, (2/√10 4)] × 2[√2, (2/√2 4)] × 2
[2, (√2/√10 2)][2, (√2/√2 2)]
[√10, (√2/2 4)] × 2[√10, (√2/4 2)] × 2
[4, (√2/√10 2)][4, (√2/√10 2)]
ADD(T; A) in ASD(T; 2)ADD(K; A) in ASD(K; 2)
[√2, (2+/√10/2, 4+/√10/2)] × 2[√2, (2+/√2/2, 4+/√10/2)] × 2
[2, (√2/√10/2, 4+/√10/2)][2, (√2,√10)]
[√10, (2+/√2/2, 4+/√2/2)] × 2[√10, (2+/√10/2, 4+/√2/2)] × 2
[4, (√2+/√10/2, 4+/√10/2)][4, (√2+/√10/2, 4+/√10/2)]
SDM1 = 3 + √2 + √10/3SDM1 = 3 + √2 + √10/3
SDM2 = 6 + 2√2 + 4√10/12SDM2 = 8 + 5√2 + 3√10/12
SDM3 = 16+ 4√2 + 4√10/12SDM3 = 16+ 3√2 + 5√10/12
", + "bbox": [ + 498, + 90, + 929, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. The Simplewise Distance Distributions from Definition 3.3 for the 4-point clouds $T, K \\subset \\mathbb{R}^2$ in Fig. 1. The symbol $\\times 2$ indicates a doubled RDD. The three bottom rows show coordinates of $\\mathrm{SDM}(C;2,1) \\in \\mathbb{R}^3$ from Definition 3.4 for $h = 2$ , $l = 1$ and both $C = T, K$ . Different elements are highlighted.", + "bbox": [ + 498, + 521, + 893, + 593 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "metric axioms on RDDs from Definition 3.1 and can be computed in time $O(h!(h^2 + m^{1.5}\\log^h m))$ .", + "bbox": [ + 498, + 619, + 890, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We will use only $h = n$ for Euclidean space $\\mathbb{R}^n$ , so the factor $h!$ in Lemma 3.7 is practically small for $n = 2, 3$ .", + "bbox": [ + 498, + 660, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $h = 1$ and a 1-point subset $A \\subset C$ , the matrix $D(A)$ is empty, so $d(\\xi) = W_{\\infty}(\\xi(R(C; A)), R(C'; A'))$ . The metric $M_{\\infty}$ on RDDs will be used for intermediate costs to get metrics between two unordered collections of RDDs by using standard Definitions 3.8 and 3.9 below.", + "bbox": [ + 496, + 695, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 3.8 (Linear Assignment Cost LAC [25]). For any $k \\times k$ matrix of costs $c(i,j) \\geq 0, i,j \\in \\{1,\\dots,k\\}$ , the Linear Assignment Cost LAC $= \\frac{1}{k}\\min_{g}\\sum_{i = 1}^{k}c(i,g(i))$ is minimized for all bijections $g$ on the indices $1,\\ldots ,k$ .", + "bbox": [ + 496, + 782, + 893, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The normalization factor $\\frac{1}{k}$ in LAC makes this metric better comparable with EMD whose weights sum up to 1.", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1278", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 3.9 (Earth Mover's Distance on distributions). Let $B = \\{B_{1},\\ldots ,B_{k}\\}$ be a finite unordered set of objects with weights $w(B_{i})$ $i = 1,\\dots ,k$ . Consider another set $D = \\{D_1,\\dots ,D_l\\}$ with weights $w(D_j)$ $j = 1,\\dots ,l$ Assume that a distance between $B_{i}$ $D_{j}$ is measured by a metric $d(B_i,D_j)$ . A flow from $B$ to $D$ is a $k\\times l$ matrix whose entry $f_{ij}\\in [0,1]$ represents a partial flow from an object $B_{i}$ to $D_{j}$ . The Earth Mover's Distance [54] is the minimum of $\\mathrm{EMD}(B,D) = \\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij}d(B_i,D_j)$ over $f_{ij}\\in [0,1]$ subject to $\\sum_{j = 1}^{l}f_{ij}\\leq w(B_i)$ for $i = 1,\\ldots ,k$ $\\sum_{i = 1}^{k}f_{ij}\\leq w(D_j)$ for $j = 1,\\ldots ,l$ and $\\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij} = 1$", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The first condition $\\sum_{j=1}^{l} f_{ij} \\leq w(B_i)$ means that not more than the weight $w(B_i)$ of the object $B_i$ 'flows' into all $D_j$ via the flows $f_{ij}$ , $j = 1, \\ldots, l$ . The second condition $\\sum_{i=1}^{k} f_{ij} \\leq w(D_j)$ means that all flows $f_{ij}$ from $B_i$ for $i = 1, \\ldots, k$ 'flow' to $D_j$ up to its weight $w(D_j)$ . The last condition $\\sum_{i=1}^{k} \\sum_{j=1}^{l} f_{ij} = 1$ forces all $B_i$ to collectively 'flow' into all $D_j$ . LAC [25] and EMD [54] can be computed in a near cubic time in the sizes of given sets of objects.", + "bbox": [ + 76, + 324, + 472, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorems 3.10(c) and 4.7 will extend $O(m^{1.5}\\log^n m)$ algorithms for fixed clouds of $m$ unlabeled points in [21, Theorem 6.5] to the harder case of isometry classes but keep the polynomial time in $m$ for a fixed dimension $n$ . All complexities are for a random-access machine (RAM) model.", + "bbox": [ + 75, + 500, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 3.10 (invariance and continuity of SDDs). $(a)$ For $h\\geq 1$ and any cloud $C$ of $m$ unlabeled points in a metric space, $\\mathrm{SDD}(C;h)$ is an isometry invariant, which can be computed in time $O(m^{h + 1} / (h - 1)!$ .For any $l\\geq 1$ , the invariant $\\mathrm{SDM}(C;h,l)\\in \\mathbb{R}^{m + \\frac{h(h - 3)}{2}}$ has the same time.", + "bbox": [ + 76, + 582, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For any $m$ -point clouds $C, C'$ in their own metric spaces and $h \\geq 1$ , let the Simplexwise Distance Distributions $\\mathrm{SDD}(C; h)$ and $\\mathrm{SDD}(C'; h)$ consist of $k = \\binom{m}{h}$ RDDs with equal weights $\\frac{1}{k}$ without collapsing identical RDDs.", + "bbox": [ + 76, + 665, + 468, + 727 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(b) Using the $k \\times k$ matrix of costs computed by the metric $M_{\\infty}$ between RDDs from SDD( $C; h$ ) and SDD( $C'$ ; $h$ ), the Linear Assignment Cost LAC from Definition 3.8 satisfies all metric axioms on SDDs and can be computed in time $O(h!(h^2 + m^{1.5}\\log^h m)k^2 + k^3\\log k)$ .", + "(c) Let $\\mathrm{SDD}(C; h)$ and $\\mathrm{SDD}(C'; h)$ have a maximum size $l \\leq k$ after collapsing identical RDDs. Then EMD from Definition 3.9 satisfies all metric axioms on SDDs and is computed in time $O(h!(h^2 + m^{1.5} \\log^h m) l^2 + l^3 \\log l)$ .", + "(d) Let $C'$ be obtained from $C$ by perturbing each point within its $\\varepsilon$ -neighborhood. For any $h \\geq 1$ , $\\operatorname{SDD}(C; h)$" + ], + "bbox": [ + 76, + 727, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "changes by at most $2\\varepsilon$ in the LAC and EMD metrics. The lower bound holds: $\\mathrm{EMD}\\big(\\mathrm{SDD}(C;h),\\mathrm{SDD}(C';h)\\big)\\geq |\\mathrm{SDM}(C;h,1) - \\mathrm{SDM}(C';h,1)|_{\\infty}.$", + "bbox": [ + 498, + 90, + 893, + 138 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 3.10(d) substantially generalizes the fact that perturbing two points in their $\\varepsilon$ -neighborhoods changes the Euclidean distance between these points by at most $2\\varepsilon$ .", + "bbox": [ + 498, + 147, + 893, + 193 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conjecture that $\\mathrm{SDD}(C;h)$ is a complete isometry invariant of a cloud $C\\subset \\mathbb{R}^n$ for some $h\\geq n - 1$ . [38, section 4] shows that $\\mathrm{SDD}(C;2)$ distinguished all infinitely many known pairs [50, Fig. S4] of non-isometric $m$ -point clouds $C,C^{\\prime}\\subset \\mathbb{R}^{3}$ with identical $\\mathrm{PDD}(C) = \\mathrm{SDD}(C;1)$ .", + "bbox": [ + 498, + 196, + 893, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Simplewise Centered Distribution (SCD)", + "text_level": 1, + "bbox": [ + 498, + 286, + 872, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While all constructions of section 3 hold in any metric space, this section develops faster continuous metrics for complete isometry invariants of unlabeled clouds in $\\mathbb{R}^n$ .", + "bbox": [ + 498, + 311, + 892, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Euclidean structure of $\\mathbb{R}^n$ allows us to translate the center of mass $\\frac{1}{m}\\sum_{p\\in C}p$ of a given $m$ -point cloud $C\\subset \\mathbb{R}^n$ to the origin $0\\in \\mathbb{R}^n$ . Then Problem 1.1 reduces to only rotations around 0 from the orthogonal group $\\mathrm{O}(\\mathbb{R}^n)$ .", + "bbox": [ + 498, + 362, + 892, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Though the center of mass is uniquely determined by any cloud $C \\subset \\mathbb{R}^n$ of unlabeled points, real applications may offer one or several labeled points of $C$ that substantially speed up metrics on invariants. For example, an atomic neighborhood in a solid material is a cloud $C \\subset \\mathbb{R}^3$ of atoms around a central atom, which may not be the center of mass of $C$ , but is suitable for all methods below.", + "bbox": [ + 498, + 439, + 893, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section studies metrics on complete invariants of $C \\subset \\mathbb{R}^n$ up to rotations around the origin $0 \\in \\mathbb{R}^n$ , which may or may not belong to $C$ or be its center of mass.", + "bbox": [ + 498, + 549, + 893, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For any subset $A = \\{p_1, \\ldots, p_{n-1}\\} \\subset C$ , the distance matrix $D(A \\cup \\{0\\})$ from Definition 3.1 has size $(n-1) \\times (n-1)$ and its last column can be chosen to include the distances from $n-1$ points of $A$ to the origin at $0 \\in \\mathbb{R}^n$ .", + "bbox": [ + 498, + 598, + 892, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Any $n$ vectors $v_{1},\\ldots ,v_{n}\\in \\mathbb{R}^{n}$ can be written as columns in the $n\\times n$ matrix whose determinant has a sign $\\pm 1$ or 0 if $v_{1},\\ldots ,v_{n}$ are linearly dependent. Any permutation $\\xi \\in S_n$ on indices $1,\\dots ,n$ is a composition of some $t$ transpositions $i\\leftrightarrow j$ and has $\\mathrm{sign}(\\xi) = (-1)^t$", + "bbox": [ + 498, + 662, + 893, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Definition 4.1 (Simplewise Centered Distribution SCD). Let $C \\subset \\mathbb{R}^n$ be any cloud of $m$ unlabeled points. For any ordered subset $A$ of points $p_1, \\ldots, p_{n-1} \\in C$ , the matrix $R(C; A)$ from Definition 3.1 has a column of Euclidean distances $|q - p_1|, \\ldots, |q - p_{n-1}|$ . At the bottom of this column, add the distance $|q - 0|$ to the origin and the sign of the determinant of the $n \\times n$ matrix consisting of the vectors $q - p_1, \\ldots, q - p_{n-1}, q$ . The resulting $(n+1) \\times (m-n+1)$ -matrix with signs in the bottom $(n+1)$ -st row is the oriented relative distance matrix $M(C; A \\cup \\{0\\})$ .", + "bbox": [ + 498, + 750, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1279", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Any permutation $\\xi \\in S_{n - 1}$ of $n - 1$ points of $A$ acts on $D(A)$ , permutes the first $n - 1$ rows of $M(C; A \\cup \\{0\\})$ and multiplies every sign in the $(n + 1)$ -st row by $\\mathrm{sign}(\\xi)$ .", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Oriented Centered Distribution $\\mathrm{OCD}(C;A)$ is the equivalence class of pairs $[D(A\\cup \\{0\\}),M(C;A\\cup \\{0\\})]$ considered up to permutations $\\xi \\in S_{n - 1}$ of points of $A$", + "bbox": [ + 76, + 138, + 468, + 185 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Simplewise Centered Distribution $\\operatorname{SCD}(C)$ is the unordered set of the distributions $\\operatorname{OCD}(C; A)$ for all $\\binom{m}{n-1}$ unordered $(n-1)$ -point subsets $A \\subset C$ . The mirror image $\\overline{\\operatorname{SCD}}(C)$ is obtained from $\\operatorname{SCD}(C)$ by reversing signs.", + "bbox": [ + 76, + 186, + 468, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Definition 4.1 needs no permutations for any $C \\subset \\mathbb{R}^2$ as $n - 1 = 1$ . Columns of $M(C; A \\cup \\{0\\})$ can be lexicographically ordered without affecting the metric in Lemma 4.6. Some of the $\\binom{m}{n-1}$ OCDs in $\\operatorname{SCD}(C)$ can be identical as in Example 4.2(b). If we collapse any $l > 1$ identical OCDs into a single OCD with the weight $l / \\binom{m}{h}$ , SCD can be considered as a weighted probability distribution of OCDs.", + "bbox": [ + 76, + 256, + 468, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Example 4.2 (SCD for clouds in Fig. 3). (a) Let $R \\subset \\mathbb{R}^2$ consist of the vertices $p_1 = (0,0)$ , $p_2 = (4,0)$ , $p_3 = (0,3)$ of the right-angled triangle in Fig. 3 (middle). Though $p_1 = (0,0)$ is included in $R$ and is not its center of mass, $\\operatorname{SCD}(R)$", + "bbox": [ + 76, + 371, + 468, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "still makes sense. In $\\mathrm{OCD}(R;p_1) = [0,\\left( \\begin{array}{ll}4 & 3\\\\ 4 & 3\\\\ 0 & 0 \\end{array} \\right)]$ , the matrix $D(\\{p_1,0\\})$ is $|p_{1} - 0| = 0$ , the top row has $|p_2-$", + "bbox": [ + 76, + 431, + 468, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$p_1| = 4, |p_3 - p_1| = 3.$ In OCD $(R;p_{2}) = [4,\\left( \\begin{array}{cc}4 & 5\\\\ 0 & 3\\\\ 0 & - \\end{array} \\right)]$", + "bbox": [ + 76, + 492, + 467, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the first row has $|p_1 - p_2| = 4$ , $|p_3 - p_2| = 5$ , the second row has $|p_1 - 0| = 0$ , $|p_3 - 0| = 3$ , $\\det \\left( \\begin{array}{cc} -4 & 0 \\\\ 3 & 3 \\end{array} \\right) <$", + "bbox": [ + 76, + 537, + 468, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "0. In $\\mathrm{OCD}(R; p_3) = [3, \\begin{pmatrix} 3 & 5 \\\\ 0 & 4 \\\\ 0 & + \\end{pmatrix}]$ , the first row has", + "bbox": [ + 76, + 583, + 468, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$|p_1 - p_3| = 3, |p_2 - p_3| = 5,$ the second row has $|p_1 - 0| = 0$ $|p_2 - 0| = 4,$ det $\\left( \\begin{array}{cc}4 & 4\\\\ -3 & 0 \\end{array} \\right) > 0.$ So $\\operatorname {SCD}(R)$ consists of the three Oriented Centered Distributions OCDs above.", + "bbox": [ + 76, + 630, + 467, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "If we reflect $R$ with respect to the $x$ -axis, the new cloud $\\bar{R}$ of the points $p_1, p_2, \\bar{p}_3 = (0, -3)$ has $\\operatorname{SCD}(\\bar{R}) = \\overline{\\operatorname{SCD}}(R)$ with $\\operatorname{OCD}(\\bar{R}; p_1) = \\operatorname{OCD}(R)$ , $\\operatorname{OCD}(\\bar{R}; p_2) =$", + "bbox": [ + 76, + 693, + 468, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[4, $\\left( \\begin{array}{ll}4 & 5\\\\ 0 & 3\\\\ 0 & + \\end{array} \\right),\\mathrm{OCD}(R;\\bar{p}_3) = [3,\\left( \\begin{array}{ll}3 & 5\\\\ 0 & 4\\\\ 0 & - \\end{array} \\right)]$ whose", + "bbox": [ + 76, + 738, + 468, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "signs changed under reflection, so $\\operatorname{SCD}(R) \\neq \\operatorname{SCD}(\\bar{R})$ .", + "bbox": [ + 76, + 784, + 449, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(b) Let $S \\subset \\mathbb{R}^2$ consist of $m = 4$ points $(\\pm 1,0), (0,\\pm 1)$ that are vertices of the square in Fig. 3 (right). The center of mass is $0 \\in \\mathbb{R}^2$ and has a distance 1 to each point of $S$ .", + "bbox": [ + 76, + 805, + 468, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each 1-point subset $A = \\{p\\} \\subset S$ , the distance matrix $D(A \\cup \\{0\\})$ on two points is the single number 1. The matrix $M(S; A \\cup \\{0\\})$ has $m - n + 1 = 3$ columns. For $p_1 =$", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(1,0), we have $M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right)) = \\left( \\begin{array}{ccc} \\sqrt{2} & \\sqrt{2} & 2 \\\\ 1 & 1 & 1 \\\\ - & + & 0 \\end{array} \\right)$ ,", + "bbox": [ + 500, + 87, + 888, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the columns are ordered according to $p_2 = (0, -1)$ , $p_3 = (0, 1)$ , $p_4 = (-1, 0)$ in Fig. 3 (right). The sign in the bottom right corner is 0 because the points $p_1, 0, p_4$ are in a straight line. Due to the rotational symmetry, $M(S; \\{p_i, 0\\})$ is independent of $i = 1, 2, 3, 4$ . So $\\operatorname{SCD}(S)$ can be considered as one $\\mathrm{OCD} = [1, M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right))]$ of weight 1.", + "bbox": [ + 498, + 136, + 890, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Example 4.2(b) illustrates the key discontinuity challenge: if $p_4 = (-1,0)$ is perturbed, the corresponding sign can discontinuously change to $+1$ or $-1$ . To get a continuous metric on OCDs, we will multiply each sign by a continuous strength function that vanishes for any zero sign.", + "bbox": [ + 498, + 246, + 890, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Definition 4.3 (strength $\\sigma(A)$ of a simplex). For a set $A$ of $n + 1$ points $q = p_0, p_1, \\ldots, p_n$ in $\\mathbb{R}^n$ , let $p(A) = \\frac{1}{2} \\sum_{i \\neq j}^{n + 1} |p_i - p_j|$ be half of the sum of all pairwise distances.", + "bbox": [ + 498, + 329, + 890, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Let $V(A)$ denote the volume the $n$ -dimensional simplex on the set $A$ . Define the strength $\\sigma(A) = V^2(A) / p^{2n-1}(A)$ .", + "bbox": [ + 498, + 393, + 890, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For $n = 2$ and a triangle $A$ with sides $a, b, c$ in $\\mathbb{R}^2$ , Heron's formula gives $\\sigma(A) = \\frac{(p - a)(p - b)(p - c)}{p^2}$ ,", + "bbox": [ + 498, + 425, + 890, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$p = \\frac{a + b + c}{2} = p(A)$ is the half-perimeter of $A$ .", + "bbox": [ + 498, + 470, + 828, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For $n = 1$ and a set $A = p_0, p_1 \\subset \\mathbb{R}$ , the volume is $V(A) = |p_0 - p_1| = 2p(A)$ , so $\\sigma(A) = 2|p_0 - p_1|$ .", + "bbox": [ + 500, + 503, + 890, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The strength $\\sigma(A)$ depends only on the distance matrix $D(A)$ from Definition 3.1, so the notation $\\sigma(A)$ is used only for brevity. In any $\\mathbb{R}^n$ , the squared volume $V^2(A)$ is expressed by the Cayley-Menger determinant [60] in pairwise distances between points of $A$ . Importantly, the strength $\\sigma(A)$ vanishes when the simplex on a set $A$ degenerates.", + "bbox": [ + 498, + 536, + 890, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 4.7 will need the continuity of $s\\sigma(A)$ , when a sign $s \\in \\{\\pm 1\\}$ from a bottom row of ORD discontinuously changes while passing through a degenerate set $A$ . The proof of the continuity of $\\sigma(A)$ in Theorem 4.4 gives an explicit upper bound for a Lipschitz constant $c_n$ below.", + "bbox": [ + 498, + 628, + 890, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 4.4 (Lipschitz continuity of the strength $\\sigma$ ). Let a cloud $A'$ be obtained from another $(n + 1)$ -point cloud $A \\subset \\mathbb{R}^n$ by perturbing every point within its $\\varepsilon$ -neighborhood. The strength $\\sigma(A)$ from Definition 4.3 is Lipschitz continuous so that $|\\sigma(A') - \\sigma(A)| \\leq 2\\varepsilon c_n$ for a constant $c_n$ .", + "bbox": [ + 498, + 710, + 890, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Example 4.5 (strength $\\sigma(A)$ and its upper bounds). [39, Theorem 4.2] proves upper bounds for the Lipschitz constant of the strength: $c_2 = 2\\sqrt{3}$ , $c_3 \\approx 0.43$ , $c_4 \\approx 0.01$ , which quickly tend to 0 due to the 'curse of dimensionality'. The plots in Fig. 4 illustrate that the strength $\\sigma(\\cdot)$ behaves smoothly in the $x$ -coordinate of a vertex and its derivative $|\\frac{\\partial \\sigma}{\\partial x}|$ is much smaller than the proved bounds $c_n$ above.", + "bbox": [ + 498, + 794, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1280", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6c99299b34d3c32721cc2166ca76bf6ae4ccdfaf9df90f677eef5d5bd951d39f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 472, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1c47d83f32470969c515674c5ca6a2ba65a8e1eb5a3af9109417aa7599fe7ca8.jpg", + "image_caption": [ + "Figure 4. The strength $\\sigma$ (solid curve) and its derivative $\\frac{\\partial\\sigma}{\\partial x}$ (dashed curve) in the $x$ -coordinate of a point from $A$ were averaged over 3000 random triangles (top) and tetrahedra (bottom)." + ], + "image_footnote": [], + "bbox": [ + 80, + 241, + 472, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The strength $\\sigma(A)$ from Definition 4.3 will take care of extra signs in ORDs and allows us to prove the analogue of Lemma 3.7 for a similar time complexity with $h = n$ .", + "bbox": [ + 75, + 470, + 472, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Lemma 4.6 (metric on OCDs). Using the strength $\\sigma$ from Definition 4.3, we consider the bottleneck distance $W_{\\infty}$ on the set of permutable $m - n + 1$ columns of $M(C; A \\cup \\{0\\})$ as on the set of $m - n + 1$ unlabeled points $\\left(v, \\frac{s}{c_n} \\sigma(A \\cup \\{0, q\\})\\right) \\in \\mathbb{R}^{n + 1}$ . For another $\\mathrm{OCD}' = [D(A' \\cup \\{0\\}); M(C'; A' \\cup \\{0\\})]$ and any permutation $\\xi \\in S_{n - 1}$ of indices $1, \\ldots, n - 1$ acting on $D(A \\cup \\{0\\})$ and the first $n - 1$ rows of $M(C; A \\cup \\{0\\})$ , set $d_o(\\xi) = \\max \\{L, W\\}$ ,", + "bbox": [ + 73, + 523, + 472, + 662 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nw h e r e L = L _ {\\infty} \\left(\\xi (D (A \\cup \\{0 \\})), D (A ^ {\\prime} \\cup \\{0 \\})\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 669, + 437, + 695 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nW = W _ {\\infty} \\left(\\xi (M (C; A \\cup \\{0 \\})), M (C ^ {\\prime}; A ^ {\\prime} \\cup \\{0 \\})\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 703, + 444, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Then $M_{\\infty}(\\mathrm{OCD}, \\mathrm{OCD}') = \\min_{\\xi \\in S_{n-1}} d_o(\\xi)$ satisfies all metric axioms on Oriented Centered Distributions (OCDs) and is computed in time $O((n - 1)! (n^2 + m^{1.5} \\log^n m))$ .", + "bbox": [ + 75, + 734, + 468, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The coefficient $\\frac{1}{c_n}$ normalizes the Lipschitz constant $c_{n}$ of $\\sigma$ to 1 in line with changes of distances by at most $2\\varepsilon$ when points are perturbed within their $\\varepsilon$ -neighborhoods. An equality $\\operatorname{SCD}(C) = \\operatorname{SCD}(C')$ is interpreted as a bijection between unordered sets $\\operatorname{SCD}(C) \\to \\operatorname{SCD}(C')$ matching all OCDs, which is best detected by checking if metrics in Theorem 4.7 between these SCDs is 0.", + "bbox": [ + 75, + 794, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Theorem 4.7 (completeness and continuity of SCD). $(\\pmb{a})$ The Simplexwise Centered Distribution $\\operatorname{SCD}(C)$ in Definition 4.1 is a complete isometry invariant of clouds $C \\subset \\mathbb{R}^n$ of $m$ unlabeled points with a center of mass at the origin $0 \\in \\mathbb{R}^n$ , and can be computed in time $O(m^n / (n - 4)!)$ .", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "So any clouds $C, C' \\subset \\mathbb{R}^n$ are related by rigid motion (isometry, respectively) if and only if $\\operatorname{SCD}(C) = \\operatorname{SCD}(C')$ ( $\\operatorname{SCD}(C)$ equals $\\operatorname{SCD}(C')$ or its mirror image $\\overline{\\operatorname{SCD}}(C')$ , respectively). For any $m$ -point clouds $C, C' \\subset \\mathbb{R}^n$ , let $\\operatorname{SCD}(C)$ and $\\operatorname{SCD}(C')$ consist of $k = \\binom{m}{n-1}$ OCDs.", + "bbox": [ + 496, + 169, + 893, + 247 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(b) For the $k \\times k$ matrix of costs computed by the metric $M_{\\infty}$ between OCDs in $\\operatorname{SCD}(C)$ and $\\operatorname{SCD}(C')$ , LAC from Definition 3.8 satisfies all metric axioms on SCDs and needs time $O((n - 1)! (n^2 + m^{1.5} \\log^n m) k^2 + k^3 \\log k)$ .", + "(c) Let SCDs have a maximum size $l \\leq k$ after collapsing identical OCDs. Then EMD from Definition 3.9 satisfies all metric axioms on SCDs and can be computed in time $O((n - 1)! (n^2 + m^{1.5} \\log^n m) l^2 + l^3 \\log l)$ .", + "(d) Let $C'$ be obtained from a cloud $C \\subset \\mathbb{R}^n$ by perturbing each point within its $\\varepsilon$ -neighborhood. Then $\\operatorname{SCD}(C)$ changes by at most $2\\varepsilon$ in the LAC and EMD metrics." + ], + "bbox": [ + 496, + 250, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "If we estimate $l \\leq k = \\binom{m}{n-1} = m(m-1) \\ldots (m-n+2)/n!$ as $O(m^{n-1}/n!)$ , Theorem 4.7(b,c) gives time $O(n(m^{n-1}/n!)^3 \\log m)$ for metrics on SCDs, which is $O(m^3 \\log m)$ for $n=2$ , and $O(m^6 \\log m)$ for $n=3$ .", + "bbox": [ + 498, + 431, + 890, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Though the above time estimates are very rough upper bounds, the time $O(m^3 \\log m)$ in $\\mathbb{R}^2$ is faster than the only past time $O(m^5 \\log m)$ for comparing $m$ -point clouds by the Hausdorff distance minimized over isometries [16].", + "bbox": [ + 496, + 498, + 890, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Definition 4.8 (Centered Distance Moments CDM). For any $m$ -point cloud $C \\subset \\mathbb{R}^n$ , let $A \\subset C$ be a subset of $n - 1$ unordered points. The Centered Interpoint Distance list $\\mathrm{CID}(A)$ is the increasing list of all $\\frac{(n - 1)(n - 2)}{2}$ pairwise distances between points of $A$ , followed by $n - 1$ increasing distances from $A$ to the origin $0$ . For each column of the $(n + 1) \\times (m - n + 1)$ matrix $M(C; A \\cup \\{0\\})$ in Definition 4.1, compute the average of the first $n - 1$ distances. Write these averages in increasing order, append the list of increasing distances $|q - 0|$ from the $n$ -th row of $M(C; A \\cup \\{0\\})$ , and also append the vector of increasing values of $\\frac{s}{c_n} \\sigma(A \\cup \\{0\\})$ taking signs $s$ from the $(n + 1)$ -st row of $M(C; A \\cup \\{0\\})$ . Let $\\vec{M}(C; A) \\in \\mathbb{R}^{3(m - n + 1)}$ be the final vector.", + "bbox": [ + 496, + 564, + 893, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The pair $[\\mathrm{CID}(A); \\vec{M}(C; A)]$ is the Average Centered Vector $\\mathrm{ACV}(C; A)$ considered as a vector of length $\\frac{n(n-1)}{2} + 3(m-n+1)$ . The unordered set of $\\mathrm{ACV}(C; A)$ for all $\\binom{m}{n-1}$ unordered subsets $A \\subset C$ is the Average Centered Distribution $\\mathrm{ACD}(C)$ . The Centered Distance Moment $\\mathrm{CDM}(C;l)$ is the $l$ -th (standardized for $l \\geq 3$ ) moment of $\\mathrm{ACD}(C)$ considered as a probability distribution of $\\binom{m}{n-1}$ vectors, separately for each coordinate.", + "bbox": [ + 496, + 776, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1281", + "bbox": [ + 483, + 945, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Example 4.9 (CDM for clouds in Fig. 3). (a) For $n = 2$ and the cloud $R \\subset \\mathbb{R}^2$ of $m = 3$ vertices $p_1 = (0,0)$ , $p_2 = (4,0)$ , $p_3 = (0,3)$ of the right-angled triangle in Fig. 3 (middle), we continue Example 4.2(a) and", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\text{flatten} \\, \\mathrm{OCD}(R; p_1) = [0, \\begin{pmatrix} 4 & 3 \\\\ 4 & 3 \\\\ 0 & 0 \\end{pmatrix}]$ into the vector", + "bbox": [ + 73, + 151, + 468, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\operatorname{ACV}(R; p_1) = [0; 3, 4; 3, 4; 0, 0]$ of length $\\frac{n(n-1)}{2} + 3(m-n+1) = 7$ , whose four parts $(1+2+2+2=7)$ are in increasing order, similarly for $p_2, p_3$ . The Average Centered Distribution can be written as a $3 \\times 7$ matrix with unordered", + "bbox": [ + 73, + 196, + 468, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rows: $\\operatorname{ACD}(R) = \\left( \\begin{array}{c|cc|cc|cc}0 & 3 & 4 & 3 & 4 & 0 & 0\\\\ 4 & 4 & 5 & 0 & 3 & 0 & -6 / c_2\\\\ 3 & 3 & 5 & 0 & 4 & 0 & 6 / c_2 \\end{array} \\right).$", + "bbox": [ + 73, + 256, + 467, + 304 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The area of the triangle on $R$ equals 6 and can be normalized by $c_2 = 2\\sqrt{3}$ to get $6 / c_2 = \\sqrt{3}$ , see [39, section 4]. The 1st moment is $\\mathrm{CDM}(R;1) = \\frac{1}{3}(7;10,14;3,11;0)$ .", + "bbox": [ + 75, + 303, + 467, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(b) For $n = 2$ and the cloud $S \\subset \\mathbb{R}^2$ of $m = 4$ vertices of the square in Fig. 3 (right), Example 4.2(a) com", + "bbox": [ + 75, + 358, + 467, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "puted $\\operatorname {SCD}(R)$ as one OCD $= [1,\\left( \\begin{array}{rrr}\\sqrt{2} & \\sqrt{2} & 2\\\\ 1 & 1 & 1\\\\ - & + & 0 \\end{array} \\right)]$", + "bbox": [ + 75, + 388, + 467, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "which flattens to $\\mathrm{ACV} = (1; \\sqrt{2}, \\sqrt{2}, 2; 1, 1, 1; -\\frac{1}{2}, \\frac{1}{2}, 0) = \\mathrm{ACD}(S) = \\mathrm{CDM}(S; 1) \\in \\mathbb{R}^{10}$ , where $\\frac{1}{2}$ is the area of the triangle on the vertices $(0, 0)$ , $(1, 0)$ , $(0, 1)$ .", + "bbox": [ + 75, + 436, + 467, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Corollary 4.10 (time for continuous metrics on CDMs). For any cloud $C \\subset \\mathbb{R}^n$ of $m$ unlabeled points, the Centered Distance Moment $\\mathrm{CDM}(C;l)$ in Definition 4.8 is computed in time $O(m^n /(n - 4)!$ . The metric $L_{\\infty}$ on CDMs needs $O(n^{2} + m)$ time and $\\mathrm{EMD}\\bigl (\\mathrm{SCD}(C),\\mathrm{SCD}(C^{\\prime})\\bigr)\\geq |\\mathrm{CDM}(C;1) - \\mathrm{CDM}(C^{\\prime};1)|_{\\infty}$ holds.", + "bbox": [ + 75, + 496, + 467, + 587 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Experiments and discussion of future work", + "text_level": 1, + "bbox": [ + 76, + 604, + 460, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper advocates a scientific approach to any data exemplified by Problem 1.1, where rigid motion on clouds can be replaced by another equivalence of other data. The scientific principles such as axioms should be always respected. Only the first coincidence axiom in (1.1b) guarantees no duplicate data. If the triangle inequality fails with any additive error, results of clustering can be pre-determined [51].", + "bbox": [ + 75, + 631, + 467, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The notorious $m!$ challenge of $m$ unlabeled points in Problem 1.1 was solved in $\\mathbb{R}^n$ by Theorem 4.7, also up to rigid motion by using the novel strength of a simplex to smooth signs of determinants due to hard Theorem 4.4.", + "bbox": [ + 75, + 743, + 467, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results above sufficiently justify re-focusing future efforts from experimental attempts at Problem 1.1 to higher level tasks such as predicting properties of rigid objects, e.g. crystalline materials, using the complete invariants with no false negatives and no false positives for all possible data since no experiments can beat the proved $100\\%$ guarantee.", + "bbox": [ + 73, + 809, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To tackle the limitation of comparing only clouds having a fixed number $m$ of points, the Earth Mover's Distance (EMD) continuously can compare any distributions (SDD or SCD) of different sizes. Using EMD instead of the bottleneck distance $W_{\\infty}$ on $m - h$ (or $m - n + 1$ ) columns of matrices in Definitions 3.3 and 4.1 increases a time from $O(m^{1.5}\\log m)$ to $O(m^3\\log m)$ but the total time remains the same due to a near cubic time in the last step.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The running time in real applications is smaller for several reasons. First, the shape (isometry class) of any rigid body in $\\mathbb{R}^3$ is determined by only $m = 4$ labeled points in general position. Even when points are unlabeled, dozens of corners or feature points suffice to represent a rigid shape well enough. Second, the key size $l$ (number of distinct Oriented Centered Distributions) in Theorem 4.7 is often smaller than $m$ , especially for symmetric objects, see $l = 1 < m = 4$ in Example 4.2. The SCD invariants are on top of others due to their completeness and continuity.", + "bbox": [ + 496, + 215, + 890, + 367 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The past work [71, 73] used the simpler Pointwise Distance Distribution (PDD) to complete $200\\mathrm{B}+$ pairwise comparisons of all $660\\mathrm{K}+$ periodic crystals in the world's largest database of real materials. This experiment took only a couple of days on a modest desktop and established the Crystal Isometry Principle saying that any real periodic crystal is uniquely determined by the geometry of its atomic centers without chemical elements. So the type of any atom is provably reconstructable from distances to atomic neighbors.", + "bbox": [ + 496, + 371, + 890, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The new invariants allow us to go deeper and compare atomic clouds from higher level periodic crystals. Fig. 5 visualizes all $300\\mathrm{K}+$ atomic clouds extracted from all $10\\mathrm{K}+$ crystalline drugs in the Cambridge Structural Database (CSD) by using SDV invariants for $5 + 1$ atoms including the central one. Future maps will use stronger invariants.", + "bbox": [ + 496, + 511, + 890, + 601 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2315396e036fee7189c52ed0d76368eb2534de7f0d5d3114caf18042071517b1.jpg", + "image_caption": [ + "Figure 5. Two principal directions of SDVs for all $300\\mathrm{K}+$ atomic clouds from all $10\\mathrm{K}+$ drugs in the CSD, colored by 25 elements." + ], + "image_footnote": [], + "bbox": [ + 519, + 614, + 890, + 766 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was supported by the Royal Academy Engineering fellowship IF2122/186, and EPSRC grants EP/R018472/1, EP/X018474/1. We thank the Data Science Theory and Applications group (Liverpool) and reviewers of this conference version [72] for helpful suggestions.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1282", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Naveed Akhtar and Ajmal Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. IEEE Access, 6:14410-14430, 2018. 2", + "[2] Olga Anosova and Vitaliy Kurlin. Introduction to periodic geometry and topology. arXiv:2103.02749. 2", + "[3] Olga Anosova and Vitaliy Kurlin. An isometry classification of periodic point sets. In LNCS (Proceedings of DGMM), volume 12708, pages 229-241, 2021. 2", + "[4] Olga Anosova and Vitaliy Kurlin. 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Scientific Reports, 12(1):1-13, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 888 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1284", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_model.json b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2e8b9289c2ce6c02acfd861f0600b24f655faa7b --- /dev/null +++ b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_model.json @@ -0,0 +1,2805 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.131, + 0.882, + 0.177 + ], + "angle": 0, + "content": "Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.205, + 0.465, + 0.274 + ], + "angle": 0, + "content": "Daniel Widdowson \nComputer Science department \nUniversity of Liverpool, UK \nd.e.widdowson@liverpool.ac.uk" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.204, + 0.763, + 0.274 + ], + "angle": 0, + "content": "Vitaliy Kurlin \nComputer Science department \nUniversity of Liverpool, UK \nvitaliy.kurlin@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.31, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.471, + 0.404 + ], + "angle": 0, + "content": "Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.614, + 0.46, + 0.632 + ], + "angle": 0, + "content": "1. Strong motivations for complete invariants" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.64, + 0.47, + 0.702 + ], + "angle": 0, + "content": "In Computer Vision, real objects such as cars and solid obstacles are considered rigid and often represented by a finite set \\(C \\subset \\mathbb{R}^n\\) (called a cloud) of \\(m\\) unlabeled (or unordered) points, usually in low dimensions \\(n = 2, 3, 4\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.707, + 0.47, + 0.784 + ], + "angle": 0, + "content": "The rigidity of many real objects motivates the most fundamental equivalence of rigid motion [67], a composition of translations and rotations in \\(\\mathbb{R}^n\\). In a general metric space \\(M\\), the most relevant equivalence is isometry: any map \\(M \\to M\\) maintaining all inter-point distances in \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.789, + 0.47, + 0.835 + ], + "angle": 0, + "content": "Any isometry in \\(\\mathbb{R}^n\\) is a composition of a mirror reflection with some rigid motion. Any orientation-preserving isometry can be realized as a continuous rigid motion." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "There is no sense in distinguishing rigid objects that are related by isometry or having the same shape. Formally, the shape of a cloud \\( C \\) is its isometry class [48] defined as a collection of all infinitely many clouds isometric to \\( C \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.417 + ], + "angle": 0, + "content": "The only reliable tool for distinguishing clouds up to isometry is an invariant defined as a function or property preserved by any isometry. Since any isometry is bijective, the number of points is an isometry invariant, but the coordinates of points are not invariants even under translation. This simple invariant is incomplete (non-injective) because non-isometric clouds can have different numbers of points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.892, + 0.482 + ], + "angle": 0, + "content": "Any invariant \\(I\\) maps all isometric clouds to the same value. There are no isometric clouds \\(C \\cong C'\\) with \\(I(C) \\neq I(C')\\), meaning that \\(I\\) has no false negatives. Isometry invariants are also called equivariant descriptors [55]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.562 + ], + "angle": 0, + "content": "A complete invariant \\( I \\) should distinguish all nonisometric clouds, so if \\( C \\neq C' \\) then \\( I(C) \\neq I(C') \\). Equivalently, if \\( I(C) = I(C') \\) then \\( C \\cong C' \\), so \\( I \\) has no false positives. Then \\( I \\) can be considered as a DNA-style code or genome that identifies any cloud uniquely up to isometry." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Since real data is always noisy and motions of rigid objects are important to track, a useful complete invariant must be also continuous under the movement of points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.675 + ], + "angle": 0, + "content": "A complete and continuous invariant for \\( m = 3 \\) points consists of three pairwise distances (sides of a triangle) and is known in school as the SSS theorem [68]. But all pairwise distances are incomplete for \\( m \\geq 4 \\) [9], see Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Problem 1.1 (complete isometry invariants with computable continuous metrics). For any cloud of \\( m \\) unlabeled points in \\( \\mathbb{R}^n \\), find an invariant \\( I \\) satisfying the properties" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.882, + 0.754 + ], + "angle": 0, + "content": "\\((\\pmb{a})\\) completeness: \\(C, C'\\) are isometric \\(\\Leftrightarrow I(C) = I(C')\\);" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.806 + ], + "angle": 0, + "content": "(b) Lipschitz continuity: if any point of \\( C \\) is perturbed within its \\( \\varepsilon \\)-neighborhood then \\( I(C) \\) changes by at most \\( \\lambda \\varepsilon \\) for a constant \\( \\lambda \\) and a metric \\( d \\) satisfying these axioms:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.809, + 0.888, + 0.826 + ], + "angle": 0, + "content": "1) \\(d(I(C),I(C')) = 0\\) if and only if \\(C\\cong C^{\\prime}\\) are isometric," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.828, + 0.83, + 0.845 + ], + "angle": 0, + "content": "2) symmetry: \\( d(I(C), I(C')) = d(I(C'), I(C)) \\)," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.847, + 0.884, + 0.865 + ], + "angle": 0, + "content": "3) \\(d(I(C),I(C')) + d(I(C'),I(C''))\\geq d(I(C),I(C''))\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "(c) computability: \\( I \\) and \\( d \\) are computed in a polynomial time in the number \\( m \\) of points for a fixed dimension \\( n \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1275" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.089, + 0.472, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.178, + 0.47, + 0.221 + ], + "angle": 0, + "content": "Figure 1. Left: the cloud \\( T = \\{(1,1), (-1,1), (-2,0), (2,0)\\} \\). Right: the kite \\( K = \\{(0,1), (-1,0), (0, -1), (3,0)\\} \\). \\( T \\) and \\( K \\) have the same 6 pairwise distances \\( \\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.469, + 0.337 + ], + "angle": 0, + "content": "Condition (1.1b) asking for a continuous metric is stronger than the completeness in (1.1a). Detecting an isometry \\( C \\cong C' \\) gives a discontinuous metric, say \\( d = 1 \\) for all non-isometric clouds \\( C \\not\\cong C' \\) even if \\( C, C' \\) are nearly identical. Any metric \\( d \\) satisfying the first axiom in (1.1b) detects an isometry \\( C \\cong C' \\) by checking if \\( d = 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.469, + 0.417 + ], + "angle": 0, + "content": "Theorem 4.7 will solve Problem 1.1 for any \\(m\\) in \\(\\mathbb{R}^n\\). Continuous invariants in Theorem 3.10 are conjectured to be complete (no known counter-examples) in any metric space. The first author implemented all algorithms, the second author wrote all theory, proofs, examples in [38, 39]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.431, + 0.469, + 0.447 + ], + "angle": 0, + "content": "2. Past work on cloud recognition/classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.469, + 0.607 + ], + "angle": 0, + "content": "Labeled clouds \\(C \\subset \\mathbb{R}^n\\) are easy for isometry classification because the matrix of distances \\(d_{ij}\\) between indexed points \\(p_i, p_j\\) allows us to reconstruct \\(C\\) by using the known distances to the previously constructed points [28, Theorem 9]. For any clouds of the same number \\(m\\) of labeled points, the difference between \\(m \\times m\\) matrices of distances (or Gram matrices of \\(p_i \\cdot p_j\\)) can be converted into a continuous metric by taking a matrix norm. If the given points are unlabeled, comparing \\(m \\times m\\) matrices requires \\(m!\\) permutations, which makes this approach impractical." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.469, + 0.701 + ], + "angle": 0, + "content": "Multidimensional scaling (MDS). For a given \\( m \\times m \\) distance matrix of any \\( m \\)-point cloud \\( A \\), MDS [57] finds an embedding \\( A \\subset \\mathbb{R}^k \\) (if it exists) preserving all distances of \\( M \\) for a dimension \\( k \\leq m \\). A final embedding \\( A \\subset \\mathbb{R}^k \\) uses eigenvectors whose ambiguity up to signs gives an exponential comparison time that can be close to \\( O(2^m) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.81 + ], + "angle": 0, + "content": "Isometry detection refers to a simpler version of Problem 1.1 to algorithmically detect a potential isometry between given clouds of \\( m \\) points in \\( \\mathbb{R}^n \\). The best algorithm by Brass and Knauer [10] takes \\( O(m^{\\lceil n/3 \\rceil} \\log m) \\) time, so \\( O(m \\log m) \\) in \\( \\mathbb{R}^3 \\). These algorithms output a binary answer (yes/no) without quantifying similarity between non-isometric clouds by a continuous metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.469, + 0.9 + ], + "angle": 0, + "content": "The Hausdorff distance [30] can be defined for any subsets \\(A, B\\) in an ambient metric space as \\(d_H(A, B) = \\max \\{\\vec{d}_H(A, B), \\vec{d}_H(B, A)\\}\\), where the directed Hausdorff distance is \\(\\vec{d}_H(A, B) = \\sup_{p \\in A} \\inf_{q \\in B} |p - q|\\). To take into account isometries, one can minimize the Hausdorff distance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "over all isometries [15, 17, 32]. For \\( n = 2 \\), the Hausdorff distance minimized over isometries in \\( \\mathbb{R}^2 \\) for sets of at most \\( m \\) point needs \\( O(m^{5}\\log m) \\) time [16]. For a given \\( \\varepsilon > 0 \\) and \\( n > 2 \\), the related problem to decide if \\( d_H \\leq \\varepsilon \\) up to translations has the time complexity \\( O(m^{\\lceil (n + 1) / 2\\rceil}) \\) [69, Chapter 4, Corollary 6]. For general isometry, only approximate algorithms tackled minimizations for infinitely many rotations initially in \\( \\mathbb{R}^3 \\) [26] and in \\( \\mathbb{R}^n \\) [4, Lemma 5.5]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.216, + 0.892, + 0.337 + ], + "angle": 0, + "content": "The Gromov-Wasserstein distances can be defined for metric-measure spaces, not necessarily sitting in a common ambient space. The simplest Gromov-Hausdorff (GH) distance cannot be approximated with any factor less than 3 in polynomial time unless \\( \\mathrm{P} = \\mathrm{NP} \\) [56, Corollary 3.8]. Polynomial-time algorithms for GH were designed for ultrametric spaces [45]. However, GH spaces are challenging even for point clouds sets in \\( \\mathbb{R} \\), see [41] and [74]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.417 + ], + "angle": 0, + "content": "The Heat Kernel Signature (HKS) is a complete isometry invariant of a manifold \\(M\\) whose the Laplace-Beltrami operator has distinct eigenvalues by [64, Theorem 1]. If \\(M\\) is sampled by points, HKS can be discretized and remains continuous [64, section 4] but the completeness is unclear." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Equivariant descriptors can be experimentally optimized [47, 59] on big datasets of clouds that are split into predefined clusters. Using more hidden parameters can improve accuracy on any finite dataset at a higher cost but will require more work for any new data. Point cloud registration filters outliers [58], samples rotations for Scale Invariant Feature Transform or uses a basis [52, 63, 65, 76], which can be unstable under perturbations of a cloud. The PCA-based complete invariant of unlabelled clouds [35] can discontinuously change when a basis degenerates to a lower dimensional subspace but inspired Complete Neural Networks [31] though without the Lipschitz continuity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Geometric Deep Learning produces descriptors that are equivariant by design [13] and go beyond Euclidean space \\(\\mathbb{R}^n\\) [14], hence aiming to experimentally solve Problem 1.1. Motivated by obstacles in [1, 18, 19, 29, 40], Problem 1.1 needs a justified solution without relying on finite data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Geometric Data Science solves analogs of Problem 1.1 for any real data objects considered up to practical equivalences instead of rigid motion on clouds [23, 24, 61]: 1-periodic discrete series [5, 6, 35], 2D lattices [12, 37], 3D lattices [11, 34, 36, 46], periodic point sets in \\(\\mathbb{R}^3\\) [20, 62] and in higher dimensions [2-4]. The applications of to crystalline materials [7, 53, 66, 75] led to the Crystal Isometry Principle [70, 71, 73] extending Mendeleev's table of elements to the Crystal Isometry Space of all periodic crystals parametrised by complete invariants like a geographic map of a planet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Local distributions of distances in Mémoli's seminal work [43, 44] for metric-measure spaces, or shape distributions [8,27,42,49], are first-order versions of the new SDD below." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1276" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.445, + 0.108 + ], + "angle": 0, + "content": "3. Simplewise Distance Distribution (SDD)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.468, + 0.163 + ], + "angle": 0, + "content": "We will refine Sorted Distance Vector in any metric space to get a complete invariant in \\(\\mathbb{R}^n\\) as shown in Fig. 2. All proofs from sections 3 and 4 are in [38,39], respectively." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.175, + 0.468, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.301, + 0.468, + 0.316 + ], + "angle": 0, + "content": "Figure 2. Hierarchy of new invariants on top of the classical SDV." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.468, + 0.395 + ], + "angle": 0, + "content": "The lexicographic order \\(u < v\\) on vectors \\(u = (u_{1},\\ldots ,u_{h})\\) and \\(v = (v_{1},\\dots ,v_{h})\\) in \\(\\mathbb{R}^h\\) means that if the first \\(i\\) (possibly, \\(i = 0\\)) coordinates of \\(u,v\\) coincide then \\(u_{i + 1} < v_{i + 1}\\). Let \\(S_{h}\\) denote the permutation group on indices \\(1,\\ldots ,h\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.468, + 0.527 + ], + "angle": 0, + "content": "Definition 3.1 (RDD(C;A)). Let \\(C\\) be a cloud of \\(m\\) unlabeled points in a space with a metric \\(d\\). Let \\(A = (p_1, \\ldots, p_h) \\subset C\\) be an ordered subset of \\(1 \\leq h < m\\) points. Let \\(D(A)\\) be the triangular distance matrix whose entry \\(D(A)_{i,j-1}\\) is \\(d(p_i, p_j)\\) for \\(1 \\leq i < j \\leq h\\), all other entries are filled by zeros. Any permutation \\(\\xi \\in S_h\\) acts on \\(D(A)\\) by mapping \\(D(A)_{ij}\\) to \\(D(A)_{kl}\\), where \\(k \\leq l\\) is the pair of indices \\(\\xi(i), \\xi(j) - 1\\) written in increasing order." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.468, + 0.653 + ], + "angle": 0, + "content": "For any other point \\(q \\in C - A\\), write distances from \\(q\\) to \\(p_1, \\ldots, p_h\\) as a column. The \\(h \\times (m - h)\\)-matrix \\(R(C; A)\\) is formed by these \\(m - h\\) lexicographically ordered columns. The action of \\(\\xi\\) on \\(R(C; A)\\) maps any \\(i\\)-th row to the \\(\\xi(i)\\)-th row, after which all columns can be written again in the lexicographic order. The Relative Distance Distribution \\(\\mathrm{RDD}(C; A)\\) is the equivalence class of the pair \\([D(A), R(C; A)]\\) of matrices up to permutations \\(\\xi \\in S_h\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.468, + 0.755 + ], + "angle": 0, + "content": "For a 1-point subset \\( A = \\{p_1\\} \\) with \\( h = 1 \\), the matrix \\( D(A) \\) is empty and \\( R(C;A) \\) is a single row of distances (in the increasing order) from \\( p_1 \\) to all other points \\( q \\in C \\). For a 2-point subset \\( A = (p_1,p_2) \\) with \\( h = 2 \\), the matrix \\( D(A) \\) is the single number \\( d(p_1,p_2) \\) and \\( R(C;A) \\) consists of two rows of distances from \\( p_1, p_2 \\) to all other points \\( q \\in C \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.468, + 0.813 + ], + "angle": 0, + "content": "Example 3.2 (RDD for a 3-point cloud \\(C\\)). Let \\(C \\subset \\mathbb{R}^2\\) consist of \\(p_1, p_2, p_3\\) with inter-point distances \\(a \\leq b \\leq c\\) ordered counter-clockwise as in Fig. 3 (left). Then" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.824, + 0.478, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R D D} (C; p _ {1}) = [ \\emptyset ; (b, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {2} \\\\ p _ {3} \\end{array} \\right)) = [ a; \\left( \\begin{array}{c} c \\\\ b \\end{array} \\right) ],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.871, + 0.48, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R D D} (C; p _ {2}) = [ \\emptyset ; (a, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {3} \\\\ p _ {1} \\end{array} \\right)) = [ b; \\left( \\begin{array}{c} a \\\\ c \\end{array} \\right) ],\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.088, + 0.892, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.188, + 0.892, + 0.232 + ], + "angle": 0, + "content": "Figure 3. Left: a cloud \\( C = \\{p_1, p_2, p_3\\} \\) with distances \\( a \\leq b \\leq c \\). Middle: the triangular cloud \\( R = \\{(0,0), (4,0), (0,3)\\} \\). Right: the square cloud \\( S = \\{(1,0), (-1,0), (0,1), (-1,0)\\} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.254, + 0.901, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R D D} (C; p _ {3}) = [ \\emptyset ; (a, b) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {1} \\\\ p _ {2} \\end{array} \\right)) = [ c; \\left( \\begin{array}{c} b \\\\ a \\end{array} \\right) ].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.293, + 0.892, + 0.37 + ], + "angle": 0, + "content": "We will always represent RDD for a specified order \\( A = (p_i, p_j) \\) of points that are written as a column. Swapping the points \\( p_1 \\leftrightarrow p_2 \\) makes the last RDD above equivalent to another form: \\( \\mathrm{RDD}(C; \\left( \\begin{array}{c} p_2 \\\\ p_1 \\end{array} \\right)) = [c; \\left( \\begin{array}{c} a \\\\ b \\end{array} \\right)] \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.378, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Though \\(\\mathrm{RDD}(C;A)\\) is defined up to a permutation \\(\\xi\\) of \\(h\\) points in \\(A\\subset C\\), we later use only \\(h = n\\), which makes comparisons of RDDs practical in dimensions \\(n = 2,3\\). Metrics on isometry classes of \\(C\\) will be independent of \\(\\xi\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.893, + 0.525 + ], + "angle": 0, + "content": "Definition 3.3 (Simplewise Distance Distribution \\(\\mathrm{SDD}(C;h)\\)). Let \\(C\\) be a cloud of \\(m\\) unlabeled points in a metric space. For an integer \\(1\\leq h < m\\), the Simplewise Distance Distribution \\(\\mathrm{SDD}(C;h)\\) is the unordered set of \\(\\mathrm{RDD}(C;A)\\) for all unordered \\(h\\)-point subsets \\(A\\subset C\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.641 + ], + "angle": 0, + "content": "For \\( h = 1 \\) and any \\( m \\)-point cloud \\( C \\), the distribution \\( \\mathrm{SDD}(C;1) \\) can be considered as a matrix of \\( m \\) rows of ordered distances from every point \\( p \\in C \\) to all other \\( m - 1 \\) points. If we lexicographically order these \\( m \\) rows and collapse any \\( l > 1 \\) identical rows into a single one with the weight \\( l / m \\), then we get the Pointwise Distance Distribution \\( \\mathrm{PDD}(C; m - 1) \\) introduced in [71, Definition 3.1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.779 + ], + "angle": 0, + "content": "The PDD was simplified to the easier-to-compare vector of Average Minimum Distances [73]: \\(\\mathrm{AMD}_k(C) = \\frac{1}{m}\\sum_{i=1}^{m}d_{ik}\\), where \\(d_{ik}\\) is the distance from a point \\(p_i\\in C\\) to its \\(k\\)-th nearest neighbor in \\(C\\). These neighbor-based invariants can be computed in a near-linear time in \\(m\\) [22] and were pairwise compared for all all 660K+ periodic crystals in the world's largest database of real materials [71]. Definition 3.4 similarly maps SDD to a smaller invariant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.783, + 0.892, + 0.905 + ], + "angle": 0, + "content": "Recall that the 1st moment of a set of numbers \\(a_1, \\ldots, a_k\\) is the average \\(\\mu = \\frac{1}{k} \\sum_{i=1}^{k} a_i\\). The 2nd moment is the standard deviation \\(\\sigma = \\sqrt{\\frac{1}{k} \\sum_{i=1}^{k} (a_i - \\mu)^2}\\). For \\(l \\geq 3\\), the \\(l\\)-th standardized moment [33, section 2.7] is \\(\\frac{1}{k} \\sum_{i=1}^{k} \\left( \\frac{a_i - \\mu}{\\sigma} \\right)^l\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "1277" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.214 + ], + "angle": 0, + "content": "Definition 3.4 (Simplexwise Distance Moments SDM). For any \\( m \\)-point cloud \\( C \\) in a metric space, let \\( A \\subset C \\) be a subset of \\( h \\) unordered points. The Sorted Distance Vector SDV(\\( A \\)) is the list of all \\( \\frac{h(h - 1)}{2} \\) pairwise distances between points of \\( A \\) written in increasing order. The vector \\( \\vec{R}(C; A) \\in \\mathbb{R}^{m - h} \\) is obtained from the \\( h \\times (m - h) \\) matrix \\( R(C; A) \\) in Definition 3.1 by writing the vector of \\( m - h \\) column averages in increasing order." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.217, + 0.473, + 0.345 + ], + "angle": 0, + "content": "The pair \\([\\mathrm{SDV}(A); \\vec{R}(C; A)]\\) is the Average Distance Distribution \\(\\mathrm{ADD}(C; A)\\) considered as a vector of length \\(\\frac{h(h - 3)}{2} + m\\). The unordered collection of \\(\\mathrm{ADD}(C; A)\\) for all \\(\\binom{m}{h}\\) unordered subsets \\(A \\subset C\\) is the Average Simplewise Distribution \\(\\mathrm{ASD}(C; h)\\). The Simplewise Distance Moment \\(\\mathrm{SDM}(C; h, l)\\) is the \\(l\\)-th (standardized for \\(l \\geq 3\\)) moment of \\(\\mathrm{ASD}(C; h)\\) considered as a probability distribution of \\(\\binom{m}{h}\\) vectors, separately for each coordinate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.505 + ], + "angle": 0, + "content": "Example 3.5 (SDD and SDM for \\( T, K \\)). Fig. 1 shows the non-isometric 4-point clouds \\( T, K \\) with the same Sorted Distance Vector \\( \\mathrm{SDV} = \\{\\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4\\} \\), see infinitely many examples in [9]. The arrows on the edges of \\( T, K \\) show orders of points in each pair of vertices for RDDs. Then \\( T, K \\) are distinguished up to isometry by \\( \\mathrm{SDD}(T; 2) \\neq \\mathrm{SDD}(K; 2) \\) in Table 1. The 1st coordinate of \\( \\mathrm{SDM}(C; 2, 1) \\in \\mathbb{R}^3 \\) is the average of 6 distances from \\( \\mathrm{SDV}(T) = \\mathrm{SDV}(K) \\) but the other two coordinates (column averages from \\( R(C; A) \\) matrices) differ." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.513, + 0.471, + 0.576 + ], + "angle": 0, + "content": "Some of the \\(\\binom{m}{h}\\) RDDs in \\(\\mathrm{SDD}(C; h)\\) can be identical as in Example 3.5. If we collapse any \\(l > 1\\) identical RDDs into a single RDD with the weight \\(l / \\binom{m}{h}\\), SDD can be considered as a weighted probability distribution of RDDs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.579, + 0.471, + 0.656 + ], + "angle": 0, + "content": "The \\(m - h\\) permutable columns of the matrix \\(R(C;A)\\) in RDD from Definition 3.1 can be interpreted as \\(m - h\\) unlabeled points in \\(\\mathbb{R}^h\\). Since any isometry is bijective, the simplest metric respecting bijections is the bottleneck distance, which is also called the Wasserstein distance \\(W_{\\infty}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.666, + 0.473, + 0.797 + ], + "angle": 0, + "content": "Definition 3.6 (bottleneck distance \\( W_{\\infty} \\)). For any vector \\( v = (v_{1},\\ldots ,v_{n})\\in \\mathbb{R}^{n} \\), the Minkowski norm is \\( ||v||_{\\infty} = \\max_{i = 1,\\dots ,n}|v_i| \\). For any vectors or matrices \\( N,N^{\\prime} \\) of the same size, the Minkowski distance is \\( L_{\\infty}(N,N^{\\prime}) = \\max_{i,j}|N_{ij} - N_{ij}^{\\prime}| \\). For clouds \\( C,C^{\\prime}\\subset \\mathbb{R}^{n} \\) of \\( m \\) unlabeled points, the bottleneck distance \\( W_{\\infty}(C,C^{\\prime}) = \\inf_{g:C\\to C^{\\prime}}\\sup_{p\\in C}||p - g(p)||_{\\infty} \\) is minimized over all bijections \\( g:C\\to C' \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.805, + 0.477, + 0.905 + ], + "angle": 0, + "content": "Lemma 3.7 (the max metric \\(M_{\\infty}\\) on RDDs). For any \\(m\\) point clouds and ordered \\(h\\) -point subsets \\(A\\subset C\\) and \\(A^{\\prime}\\subset C^{\\prime}\\) set \\(d(\\xi) = \\max \\{L_{\\infty}(\\xi (D(A)),D(A^{\\prime})),W_{\\infty}(\\xi (R(C;A)),R(C^{\\prime};A^{\\prime}))\\}\\) for a permutation \\(\\xi \\in S_h\\) on \\(h\\) points. Then the max metric \\(M_{\\infty}(\\mathrm{RDD}(C;A),\\mathrm{RDD}(C^{\\prime};A^{\\prime})) = \\min_{\\xi \\in S_h}d(\\xi)\\) satisfies all" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.091, + 0.93, + 0.511 + ], + "angle": 0, + "content": "
RDD(T; A) in SDD(T; 2)RDD(K; A) in SDD(K; 2)
[√2, (2/√10 4)] × 2[√2, (2/√2 4)] × 2
[2, (√2/√10 2)][2, (√2/√2 2)]
[√10, (√2/2 4)] × 2[√10, (√2/4 2)] × 2
[4, (√2/√10 2)][4, (√2/√10 2)]
ADD(T; A) in ASD(T; 2)ADD(K; A) in ASD(K; 2)
[√2, (2+/√10/2, 4+/√10/2)] × 2[√2, (2+/√2/2, 4+/√10/2)] × 2
[2, (√2/√10/2, 4+/√10/2)][2, (√2,√10)]
[√10, (2+/√2/2, 4+/√2/2)] × 2[√10, (2+/√10/2, 4+/√2/2)] × 2
[4, (√2+/√10/2, 4+/√10/2)][4, (√2+/√10/2, 4+/√10/2)]
SDM1 = 3 + √2 + √10/3SDM1 = 3 + √2 + √10/3
SDM2 = 6 + 2√2 + 4√10/12SDM2 = 8 + 5√2 + 3√10/12
SDM3 = 16+ 4√2 + 4√10/12SDM3 = 16+ 3√2 + 5√10/12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.522, + 0.895, + 0.594 + ], + "angle": 0, + "content": "Table 1. The Simplewise Distance Distributions from Definition 3.3 for the 4-point clouds \\( T, K \\subset \\mathbb{R}^2 \\) in Fig. 1. The symbol \\( \\times 2 \\) indicates a doubled RDD. The three bottom rows show coordinates of \\( \\mathrm{SDM}(C;2,1) \\in \\mathbb{R}^3 \\) from Definition 3.4 for \\( h = 2 \\), \\( l = 1 \\) and both \\( C = T, K \\). Different elements are highlighted." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.62, + 0.892, + 0.651 + ], + "angle": 0, + "content": "metric axioms on RDDs from Definition 3.1 and can be computed in time \\( O(h!(h^2 + m^{1.5}\\log^h m)) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.661, + 0.892, + 0.692 + ], + "angle": 0, + "content": "We will use only \\( h = n \\) for Euclidean space \\( \\mathbb{R}^n \\), so the factor \\( h! \\) in Lemma 3.7 is practically small for \\( n = 2, 3 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.892, + 0.772 + ], + "angle": 0, + "content": "For \\( h = 1 \\) and a 1-point subset \\( A \\subset C \\), the matrix \\( D(A) \\) is empty, so \\( d(\\xi) = W_{\\infty}(\\xi(R(C; A)), R(C'; A')) \\). The metric \\( M_{\\infty} \\) on RDDs will be used for intermediate costs to get metrics between two unordered collections of RDDs by using standard Definitions 3.8 and 3.9 below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.783, + 0.895, + 0.861 + ], + "angle": 0, + "content": "Definition 3.8 (Linear Assignment Cost LAC [25]). For any \\( k \\times k \\) matrix of costs \\( c(i,j) \\geq 0, i,j \\in \\{1,\\dots,k\\} \\), the Linear Assignment Cost LAC \\( = \\frac{1}{k}\\min_{g}\\sum_{i = 1}^{k}c(i,g(i)) \\) is minimized for all bijections \\( g \\) on the indices \\( 1,\\ldots ,k \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The normalization factor \\(\\frac{1}{k}\\) in LAC makes this metric better comparable with EMD whose weights sum up to 1." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1278" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.317 + ], + "angle": 0, + "content": "Definition 3.9 (Earth Mover's Distance on distributions). Let \\(B = \\{B_{1},\\ldots ,B_{k}\\}\\) be a finite unordered set of objects with weights \\(w(B_{i})\\) \\(i = 1,\\dots ,k\\) . Consider another set \\(D = \\{D_1,\\dots ,D_l\\}\\) with weights \\(w(D_j)\\) \\(j = 1,\\dots ,l\\) Assume that a distance between \\(B_{i}\\) \\(D_{j}\\) is measured by a metric \\(d(B_i,D_j)\\) . A flow from \\(B\\) to \\(D\\) is a \\(k\\times l\\) matrix whose entry \\(f_{ij}\\in [0,1]\\) represents a partial flow from an object \\(B_{i}\\) to \\(D_{j}\\) . The Earth Mover's Distance [54] is the minimum of \\(\\mathrm{EMD}(B,D) = \\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij}d(B_i,D_j)\\) over \\(f_{ij}\\in [0,1]\\) subject to \\(\\sum_{j = 1}^{l}f_{ij}\\leq w(B_i)\\) for \\(i = 1,\\ldots ,k\\) \\(\\sum_{i = 1}^{k}f_{ij}\\leq w(D_j)\\) for \\(j = 1,\\ldots ,l\\) and \\(\\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij} = 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.325, + 0.473, + 0.499 + ], + "angle": 0, + "content": "The first condition \\(\\sum_{j=1}^{l} f_{ij} \\leq w(B_i)\\) means that not more than the weight \\(w(B_i)\\) of the object \\(B_i\\) 'flows' into all \\(D_j\\) via the flows \\(f_{ij}\\), \\(j = 1, \\ldots, l\\). The second condition \\(\\sum_{i=1}^{k} f_{ij} \\leq w(D_j)\\) means that all flows \\(f_{ij}\\) from \\(B_i\\) for \\(i = 1, \\ldots, k\\) 'flow' to \\(D_j\\) up to its weight \\(w(D_j)\\). The last condition \\(\\sum_{i=1}^{k} \\sum_{j=1}^{l} f_{ij} = 1\\) forces all \\(B_i\\) to collectively 'flow' into all \\(D_j\\). LAC [25] and EMD [54] can be computed in a near cubic time in the sizes of given sets of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Theorems 3.10(c) and 4.7 will extend \\( O(m^{1.5}\\log^n m) \\) algorithms for fixed clouds of \\( m \\) unlabeled points in [21, Theorem 6.5] to the harder case of isometry classes but keep the polynomial time in \\( m \\) for a fixed dimension \\( n \\). All complexities are for a random-access machine (RAM) model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.47, + 0.663 + ], + "angle": 0, + "content": "Theorem 3.10 (invariance and continuity of SDDs). \\((a)\\) For \\(h\\geq 1\\) and any cloud \\(C\\) of \\(m\\) unlabeled points in a metric space, \\(\\mathrm{SDD}(C;h)\\) is an isometry invariant, which can be computed in time \\(O(m^{h + 1} / (h - 1)!\\) .For any \\(l\\geq 1\\) , the invariant \\(\\mathrm{SDM}(C;h,l)\\in \\mathbb{R}^{m + \\frac{h(h - 3)}{2}}\\) has the same time." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.666, + 0.47, + 0.728 + ], + "angle": 0, + "content": "For any \\( m \\)-point clouds \\( C, C' \\) in their own metric spaces and \\( h \\geq 1 \\), let the Simplexwise Distance Distributions \\( \\mathrm{SDD}(C; h) \\) and \\( \\mathrm{SDD}(C'; h) \\) consist of \\( k = \\binom{m}{h} \\) RDDs with equal weights \\( \\frac{1}{k} \\) without collapsing identical RDDs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.728, + 0.47, + 0.805 + ], + "angle": 0, + "content": "(b) Using the \\( k \\times k \\) matrix of costs computed by the metric \\( M_{\\infty} \\) between RDDs from SDD(\\( C; h \\)) and SDD(\\( C' \\); \\( h \\)), the Linear Assignment Cost LAC from Definition 3.8 satisfies all metric axioms on SDDs and can be computed in time \\( O(h!(h^2 + m^{1.5}\\log^h m)k^2 + k^3\\log k) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.807, + 0.47, + 0.869 + ], + "angle": 0, + "content": "(c) Let \\(\\mathrm{SDD}(C; h)\\) and \\(\\mathrm{SDD}(C'; h)\\) have a maximum size \\(l \\leq k\\) after collapsing identical RDDs. Then EMD from Definition 3.9 satisfies all metric axioms on SDDs and is computed in time \\(O(h!(h^2 + m^{1.5} \\log^h m) l^2 + l^3 \\log l)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "(d) Let \\(C'\\) be obtained from \\(C\\) by perturbing each point within its \\(\\varepsilon\\)-neighborhood. For any \\(h \\geq 1\\), \\(\\operatorname{SDD}(C; h)\\)" + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.728, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.894, + 0.139 + ], + "angle": 0, + "content": "changes by at most \\(2\\varepsilon\\) in the LAC and EMD metrics. The lower bound holds: \\(\\mathrm{EMD}\\big(\\mathrm{SDD}(C;h),\\mathrm{SDD}(C';h)\\big)\\geq |\\mathrm{SDM}(C;h,1) - \\mathrm{SDM}(C';h,1)|_{\\infty}.\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.148, + 0.894, + 0.194 + ], + "angle": 0, + "content": "Theorem 3.10(d) substantially generalizes the fact that perturbing two points in their \\(\\varepsilon\\)-neighborhoods changes the Euclidean distance between these points by at most \\(2\\varepsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.197, + 0.894, + 0.275 + ], + "angle": 0, + "content": "We conjecture that \\(\\mathrm{SDD}(C;h)\\) is a complete isometry invariant of a cloud \\(C\\subset \\mathbb{R}^n\\) for some \\(h\\geq n - 1\\). [38, section 4] shows that \\(\\mathrm{SDD}(C;2)\\) distinguished all infinitely many known pairs [50, Fig. S4] of non-isometric \\(m\\)-point clouds \\(C,C^{\\prime}\\subset \\mathbb{R}^{3}\\) with identical \\(\\mathrm{PDD}(C) = \\mathrm{SDD}(C;1)\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.287, + 0.874, + 0.305 + ], + "angle": 0, + "content": "4. Simplewise Centered Distribution (SCD)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.313, + 0.893, + 0.358 + ], + "angle": 0, + "content": "While all constructions of section 3 hold in any metric space, this section develops faster continuous metrics for complete isometry invariants of unlabeled clouds in \\(\\mathbb{R}^n\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.363, + 0.893, + 0.436 + ], + "angle": 0, + "content": "The Euclidean structure of \\(\\mathbb{R}^n\\) allows us to translate the center of mass \\(\\frac{1}{m}\\sum_{p\\in C}p\\) of a given \\(m\\)-point cloud \\(C\\subset \\mathbb{R}^n\\) to the origin \\(0\\in \\mathbb{R}^n\\). Then Problem 1.1 reduces to only rotations around 0 from the orthogonal group \\(\\mathrm{O}(\\mathbb{R}^n)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.894, + 0.545 + ], + "angle": 0, + "content": "Though the center of mass is uniquely determined by any cloud \\(C \\subset \\mathbb{R}^n\\) of unlabeled points, real applications may offer one or several labeled points of \\(C\\) that substantially speed up metrics on invariants. For example, an atomic neighborhood in a solid material is a cloud \\(C \\subset \\mathbb{R}^3\\) of atoms around a central atom, which may not be the center of mass of \\(C\\), but is suitable for all methods below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.55, + 0.894, + 0.595 + ], + "angle": 0, + "content": "This section studies metrics on complete invariants of \\(C \\subset \\mathbb{R}^n\\) up to rotations around the origin \\(0 \\in \\mathbb{R}^n\\), which may or may not belong to \\(C\\) or be its center of mass." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.893, + 0.66 + ], + "angle": 0, + "content": "For any subset \\( A = \\{p_1, \\ldots, p_{n-1}\\} \\subset C \\), the distance matrix \\( D(A \\cup \\{0\\}) \\) from Definition 3.1 has size \\( (n-1) \\times (n-1) \\) and its last column can be chosen to include the distances from \\( n-1 \\) points of \\( A \\) to the origin at \\( 0 \\in \\mathbb{R}^n \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.664, + 0.894, + 0.74 + ], + "angle": 0, + "content": "Any \\(n\\) vectors \\(v_{1},\\ldots ,v_{n}\\in \\mathbb{R}^{n}\\) can be written as columns in the \\(n\\times n\\) matrix whose determinant has a sign \\(\\pm 1\\) or 0 if \\(v_{1},\\ldots ,v_{n}\\) are linearly dependent. Any permutation \\(\\xi \\in S_n\\) on indices \\(1,\\dots ,n\\) is a composition of some \\(t\\) transpositions \\(i\\leftrightarrow j\\) and has \\(\\mathrm{sign}(\\xi) = (-1)^t\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Definition 4.1 (Simplewise Centered Distribution SCD). Let \\(C \\subset \\mathbb{R}^n\\) be any cloud of \\(m\\) unlabeled points. For any ordered subset \\(A\\) of points \\(p_1, \\ldots, p_{n-1} \\in C\\), the matrix \\(R(C; A)\\) from Definition 3.1 has a column of Euclidean distances \\(|q - p_1|, \\ldots, |q - p_{n-1}|\\). At the bottom of this column, add the distance \\(|q - 0|\\) to the origin and the sign of the determinant of the \\(n \\times n\\) matrix consisting of the vectors \\(q - p_1, \\ldots, q - p_{n-1}, q\\). The resulting \\((n+1) \\times (m-n+1)\\)-matrix with signs in the bottom \\((n+1)\\)-st row is the oriented relative distance matrix \\(M(C; A \\cup \\{0\\})\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1279" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "Any permutation \\(\\xi \\in S_{n - 1}\\) of \\(n - 1\\) points of \\(A\\) acts on \\(D(A)\\), permutes the first \\(n - 1\\) rows of \\(M(C; A \\cup \\{0\\})\\) and multiplies every sign in the \\((n + 1)\\)-st row by \\(\\mathrm{sign}(\\xi)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.14, + 0.469, + 0.186 + ], + "angle": 0, + "content": "The Oriented Centered Distribution \\(\\mathrm{OCD}(C;A)\\) is the equivalence class of pairs \\([D(A\\cup \\{0\\}),M(C;A\\cup \\{0\\})]\\) considered up to permutations \\(\\xi \\in S_{n - 1}\\) of points of \\(A\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.188, + 0.469, + 0.251 + ], + "angle": 0, + "content": "The Simplewise Centered Distribution \\(\\operatorname{SCD}(C)\\) is the unordered set of the distributions \\(\\operatorname{OCD}(C; A)\\) for all \\(\\binom{m}{n-1}\\) unordered \\((n-1)\\)-point subsets \\(A \\subset C\\). The mirror image \\(\\overline{\\operatorname{SCD}}(C)\\) is obtained from \\(\\operatorname{SCD}(C)\\) by reversing signs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.257, + 0.469, + 0.364 + ], + "angle": 0, + "content": "Definition 4.1 needs no permutations for any \\(C \\subset \\mathbb{R}^2\\) as \\(n - 1 = 1\\). Columns of \\(M(C; A \\cup \\{0\\})\\) can be lexicographically ordered without affecting the metric in Lemma 4.6. Some of the \\(\\binom{m}{n-1}\\) OCDs in \\(\\operatorname{SCD}(C)\\) can be identical as in Example 4.2(b). If we collapse any \\(l > 1\\) identical OCDs into a single OCD with the weight \\(l / \\binom{m}{h}\\), SCD can be considered as a weighted probability distribution of OCDs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.469, + 0.433 + ], + "angle": 0, + "content": "Example 4.2 (SCD for clouds in Fig. 3). (a) Let \\( R \\subset \\mathbb{R}^2 \\) consist of the vertices \\( p_1 = (0,0) \\), \\( p_2 = (4,0) \\), \\( p_3 = (0,3) \\) of the right-angled triangle in Fig. 3 (middle). Though \\( p_1 = (0,0) \\) is included in \\( R \\) and is not its center of mass, \\( \\operatorname{SCD}(R) \\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.433, + 0.469, + 0.493 + ], + "angle": 0, + "content": "still makes sense. In \\(\\mathrm{OCD}(R;p_1) = [0,\\left( \\begin{array}{ll}4 & 3\\\\ 4 & 3\\\\ 0 & 0 \\end{array} \\right)]\\), the matrix \\(D(\\{p_1,0\\})\\) is \\(|p_{1} - 0| = 0\\), the top row has \\(|p_2-\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.493, + 0.468, + 0.539 + ], + "angle": 0, + "content": "\\(p_1| = 4, |p_3 - p_1| = 3.\\) In OCD \\((R;p_{2}) = [4,\\left( \\begin{array}{cc}4 & 5\\\\ 0 & 3\\\\ 0 & - \\end{array} \\right)]\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.539, + 0.469, + 0.584 + ], + "angle": 0, + "content": "the first row has \\( |p_1 - p_2| = 4 \\), \\( |p_3 - p_2| = 5 \\), the second row has \\( |p_1 - 0| = 0 \\), \\( |p_3 - 0| = 3 \\), \\( \\det \\left( \\begin{array}{cc} -4 & 0 \\\\ 3 & 3 \\end{array} \\right) < \\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.584, + 0.469, + 0.631 + ], + "angle": 0, + "content": "0. In \\(\\mathrm{OCD}(R; p_3) = [3, \\begin{pmatrix} 3 & 5 \\\\ 0 & 4 \\\\ 0 & + \\end{pmatrix}]\\), the first row has" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.631, + 0.468, + 0.689 + ], + "angle": 0, + "content": "\\(|p_1 - p_3| = 3, |p_2 - p_3| = 5,\\) the second row has \\(|p_1 - 0| = 0\\) \\(|p_2 - 0| = 4,\\) det \\(\\left( \\begin{array}{cc}4 & 4\\\\ -3 & 0 \\end{array} \\right) > 0.\\) So \\(\\operatorname {SCD}(R)\\) consists of the three Oriented Centered Distributions OCDs above." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.694, + 0.47, + 0.739 + ], + "angle": 0, + "content": "If we reflect \\( R \\) with respect to the \\( x \\)-axis, the new cloud \\( \\bar{R} \\) of the points \\( p_1, p_2, \\bar{p}_3 = (0, -3) \\) has \\( \\operatorname{SCD}(\\bar{R}) = \\overline{\\operatorname{SCD}}(R) \\) with \\( \\operatorname{OCD}(\\bar{R}; p_1) = \\operatorname{OCD}(R) \\), \\( \\operatorname{OCD}(\\bar{R}; p_2) = \\)" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.739, + 0.469, + 0.785 + ], + "angle": 0, + "content": "[4, \\(\\left( \\begin{array}{ll}4 & 5\\\\ 0 & 3\\\\ 0 & + \\end{array} \\right),\\mathrm{OCD}(R;\\bar{p}_3) = [3,\\left( \\begin{array}{ll}3 & 5\\\\ 0 & 4\\\\ 0 & - \\end{array} \\right)]\\) whose" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.45, + 0.801 + ], + "angle": 0, + "content": "signs changed under reflection, so \\(\\operatorname{SCD}(R) \\neq \\operatorname{SCD}(\\bar{R})\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.806, + 0.469, + 0.853 + ], + "angle": 0, + "content": "(b) Let \\( S \\subset \\mathbb{R}^2 \\) consist of \\( m = 4 \\) points \\( (\\pm 1,0), (0,\\pm 1) \\) that are vertices of the square in Fig. 3 (right). The center of mass is \\( 0 \\in \\mathbb{R}^2 \\) and has a distance 1 to each point of \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For each 1-point subset \\( A = \\{p\\} \\subset S \\), the distance matrix \\( D(A \\cup \\{0\\}) \\) on two points is the single number 1. The matrix \\( M(S; A \\cup \\{0\\}) \\) has \\( m - n + 1 = 3 \\) columns. For \\( p_1 = \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.088, + 0.89, + 0.137 + ], + "angle": 0, + "content": "(1,0), we have \\( M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right)) = \\left( \\begin{array}{ccc} \\sqrt{2} & \\sqrt{2} & 2 \\\\ 1 & 1 & 1 \\\\ - & + & 0 \\end{array} \\right) \\)," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.137, + 0.892, + 0.243 + ], + "angle": 0, + "content": "where the columns are ordered according to \\( p_2 = (0, -1) \\), \\( p_3 = (0, 1) \\), \\( p_4 = (-1, 0) \\) in Fig. 3 (right). The sign in the bottom right corner is 0 because the points \\( p_1, 0, p_4 \\) are in a straight line. Due to the rotational symmetry, \\( M(S; \\{p_i, 0\\}) \\) is independent of \\( i = 1, 2, 3, 4 \\). So \\( \\operatorname{SCD}(S) \\) can be considered as one \\( \\mathrm{OCD} = [1, M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right))] \\) of weight 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.247, + 0.892, + 0.324 + ], + "angle": 0, + "content": "Example 4.2(b) illustrates the key discontinuity challenge: if \\( p_4 = (-1,0) \\) is perturbed, the corresponding sign can discontinuously change to \\( +1 \\) or \\( -1 \\). To get a continuous metric on OCDs, we will multiply each sign by a continuous strength function that vanishes for any zero sign." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.33, + 0.892, + 0.394 + ], + "angle": 0, + "content": "Definition 4.3 (strength \\(\\sigma(A)\\) of a simplex). For a set \\(A\\) of \\(n + 1\\) points \\(q = p_0, p_1, \\ldots, p_n\\) in \\(\\mathbb{R}^n\\), let \\(p(A) = \\frac{1}{2} \\sum_{i \\neq j}^{n + 1} |p_i - p_j|\\) be half of the sum of all pairwise distances." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Let \\( V(A) \\) denote the volume the \\( n \\)-dimensional simplex on the set \\( A \\). Define the strength \\( \\sigma(A) = V^2(A) / p^{2n-1}(A) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.472 + ], + "angle": 0, + "content": "For \\(n = 2\\) and a triangle \\(A\\) with sides \\(a, b, c\\) in \\(\\mathbb{R}^2\\), Heron's formula gives \\(\\sigma(A) = \\frac{(p - a)(p - b)(p - c)}{p^2}\\)," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.472, + 0.83, + 0.5 + ], + "angle": 0, + "content": "\\(p = \\frac{a + b + c}{2} = p(A)\\) is the half-perimeter of \\(A\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.504, + 0.892, + 0.535 + ], + "angle": 0, + "content": "For \\( n = 1 \\) and a set \\( A = p_0, p_1 \\subset \\mathbb{R} \\), the volume is \\( V(A) = |p_0 - p_1| = 2p(A) \\), so \\( \\sigma(A) = 2|p_0 - p_1| \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.537, + 0.892, + 0.627 + ], + "angle": 0, + "content": "The strength \\(\\sigma(A)\\) depends only on the distance matrix \\(D(A)\\) from Definition 3.1, so the notation \\(\\sigma(A)\\) is used only for brevity. In any \\(\\mathbb{R}^n\\), the squared volume \\(V^2(A)\\) is expressed by the Cayley-Menger determinant [60] in pairwise distances between points of \\(A\\). Importantly, the strength \\(\\sigma(A)\\) vanishes when the simplex on a set \\(A\\) degenerates." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.63, + 0.892, + 0.706 + ], + "angle": 0, + "content": "Theorem 4.7 will need the continuity of \\( s\\sigma(A) \\), when a sign \\( s \\in \\{\\pm 1\\} \\) from a bottom row of ORD discontinuously changes while passing through a degenerate set \\( A \\). The proof of the continuity of \\( \\sigma(A) \\) in Theorem 4.4 gives an explicit upper bound for a Lipschitz constant \\( c_n \\) below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.712, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Theorem 4.4 (Lipschitz continuity of the strength \\(\\sigma\\)). Let a cloud \\(A'\\) be obtained from another \\((n + 1)\\)-point cloud \\(A \\subset \\mathbb{R}^n\\) by perturbing every point within its \\(\\varepsilon\\)-neighborhood. The strength \\(\\sigma(A)\\) from Definition 4.3 is Lipschitz continuous so that \\(|\\sigma(A') - \\sigma(A)| \\leq 2\\varepsilon c_n\\) for a constant \\(c_n\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Example 4.5 (strength \\(\\sigma(A)\\) and its upper bounds). [39, Theorem 4.2] proves upper bounds for the Lipschitz constant of the strength: \\(c_2 = 2\\sqrt{3}\\), \\(c_3 \\approx 0.43\\), \\(c_4 \\approx 0.01\\), which quickly tend to 0 due to the 'curse of dimensionality'. The plots in Fig. 4 illustrate that the strength \\(\\sigma(\\cdot)\\) behaves smoothly in the \\(x\\)-coordinate of a vertex and its derivative \\(|\\frac{\\partial \\sigma}{\\partial x}|\\) is much smaller than the proved bounds \\(c_n\\) above." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1280" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.473, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.242, + 0.473, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.404, + 0.47, + 0.448 + ], + "angle": 0, + "content": "Figure 4. The strength \\(\\sigma\\) (solid curve) and its derivative \\(\\frac{\\partial\\sigma}{\\partial x}\\) (dashed curve) in the \\(x\\)-coordinate of a point from \\(A\\) were averaged over 3000 random triangles (top) and tetrahedra (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.473, + 0.518 + ], + "angle": 0, + "content": "The strength \\(\\sigma(A)\\) from Definition 4.3 will take care of extra signs in ORDs and allows us to prove the analogue of Lemma 3.7 for a similar time complexity with \\(h = n\\)." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.525, + 0.473, + 0.663 + ], + "angle": 0, + "content": "Lemma 4.6 (metric on OCDs). Using the strength \\(\\sigma\\) from Definition 4.3, we consider the bottleneck distance \\(W_{\\infty}\\) on the set of permutable \\(m - n + 1\\) columns of \\(M(C; A \\cup \\{0\\})\\) as on the set of \\(m - n + 1\\) unlabeled points \\(\\left(v, \\frac{s}{c_n} \\sigma(A \\cup \\{0, q\\})\\right) \\in \\mathbb{R}^{n + 1}\\). For another \\(\\mathrm{OCD}' = [D(A' \\cup \\{0\\}); M(C'; A' \\cup \\{0\\})]\\) and any permutation \\(\\xi \\in S_{n - 1}\\) of indices \\(1, \\ldots, n - 1\\) acting on \\(D(A \\cup \\{0\\})\\) and the first \\(n - 1\\) rows of \\(M(C; A \\cup \\{0\\})\\), set \\(d_o(\\xi) = \\max \\{L, W\\}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.67, + 0.438, + 0.696 + ], + "angle": 0, + "content": "\\[\nw h e r e L = L _ {\\infty} \\left(\\xi (D (A \\cup \\{0 \\})), D (A ^ {\\prime} \\cup \\{0 \\})\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.704, + 0.445, + 0.73 + ], + "angle": 0, + "content": "\\[\nW = W _ {\\infty} \\left(\\xi (M (C; A \\cup \\{0 \\})), M (C ^ {\\prime}; A ^ {\\prime} \\cup \\{0 \\})\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.789 + ], + "angle": 0, + "content": "Then \\( M_{\\infty}(\\mathrm{OCD}, \\mathrm{OCD}') = \\min_{\\xi \\in S_{n-1}} d_o(\\xi) \\) satisfies all metric axioms on Oriented Centered Distributions (OCDs) and is computed in time \\( O((n - 1)! (n^2 + m^{1.5} \\log^n m)) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.9 + ], + "angle": 0, + "content": "The coefficient \\(\\frac{1}{c_n}\\) normalizes the Lipschitz constant \\(c_{n}\\) of \\(\\sigma\\) to 1 in line with changes of distances by at most \\(2\\varepsilon\\) when points are perturbed within their \\(\\varepsilon\\)-neighborhoods. An equality \\(\\operatorname{SCD}(C) = \\operatorname{SCD}(C')\\) is interpreted as a bijection between unordered sets \\(\\operatorname{SCD}(C) \\to \\operatorname{SCD}(C')\\) matching all OCDs, which is best detected by checking if metrics in Theorem 4.7 between these SCDs is 0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "Theorem 4.7 (completeness and continuity of SCD). \\((\\pmb{a})\\) The Simplexwise Centered Distribution \\(\\operatorname{SCD}(C)\\) in Definition 4.1 is a complete isometry invariant of clouds \\(C \\subset \\mathbb{R}^n\\) of \\(m\\) unlabeled points with a center of mass at the origin \\(0 \\in \\mathbb{R}^n\\), and can be computed in time \\(O(m^n / (n - 4)!)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.894, + 0.248 + ], + "angle": 0, + "content": "So any clouds \\(C, C' \\subset \\mathbb{R}^n\\) are related by rigid motion (isometry, respectively) if and only if \\(\\operatorname{SCD}(C) = \\operatorname{SCD}(C')\\) (\\(\\operatorname{SCD}(C)\\) equals \\(\\operatorname{SCD}(C')\\) or its mirror image \\(\\overline{\\operatorname{SCD}}(C')\\), respectively). For any \\(m\\)-point clouds \\(C, C' \\subset \\mathbb{R}^n\\), let \\(\\operatorname{SCD}(C)\\) and \\(\\operatorname{SCD}(C')\\) consist of \\(k = \\binom{m}{n-1}\\) OCDs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.313 + ], + "angle": 0, + "content": "(b) For the \\(k \\times k\\) matrix of costs computed by the metric \\(M_{\\infty}\\) between OCDs in \\(\\operatorname{SCD}(C)\\) and \\(\\operatorname{SCD}(C')\\), LAC from Definition 3.8 satisfies all metric axioms on SCDs and needs time \\(O((n - 1)! (n^2 + m^{1.5} \\log^n m) k^2 + k^3 \\log k)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.892, + 0.378 + ], + "angle": 0, + "content": "(c) Let SCDs have a maximum size \\( l \\leq k \\) after collapsing identical OCDs. Then EMD from Definition 3.9 satisfies all metric axioms on SCDs and can be computed in time \\( O((n - 1)! (n^2 + m^{1.5} \\log^n m) l^2 + l^3 \\log l) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.428 + ], + "angle": 0, + "content": "(d) Let \\( C' \\) be obtained from a cloud \\( C \\subset \\mathbb{R}^n \\) by perturbing each point within its \\( \\varepsilon \\)-neighborhood. Then \\( \\operatorname{SCD}(C) \\) changes by at most \\( 2\\varepsilon \\) in the LAC and EMD metrics." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.497 + ], + "angle": 0, + "content": "If we estimate \\( l \\leq k = \\binom{m}{n-1} = m(m-1) \\ldots (m-n+2)/n! \\) as \\( O(m^{n-1}/n!) \\), Theorem 4.7(b,c) gives time \\( O(n(m^{n-1}/n!)^3 \\log m) \\) for metrics on SCDs, which is \\( O(m^3 \\log m) \\) for \\( n=2 \\), and \\( O(m^6 \\log m) \\) for \\( n=3 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Though the above time estimates are very rough upper bounds, the time \\( O(m^3 \\log m) \\) in \\( \\mathbb{R}^2 \\) is faster than the only past time \\( O(m^5 \\log m) \\) for comparing \\( m \\)-point clouds by the Hausdorff distance minimized over isometries [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.894, + 0.775 + ], + "angle": 0, + "content": "Definition 4.8 (Centered Distance Moments CDM). For any \\( m \\)-point cloud \\( C \\subset \\mathbb{R}^n \\), let \\( A \\subset C \\) be a subset of \\( n - 1 \\) unordered points. The Centered Interpoint Distance list \\( \\mathrm{CID}(A) \\) is the increasing list of all \\( \\frac{(n - 1)(n - 2)}{2} \\) pairwise distances between points of \\( A \\), followed by \\( n - 1 \\) increasing distances from \\( A \\) to the origin \\( 0 \\). For each column of the \\( (n + 1) \\times (m - n + 1) \\) matrix \\( M(C; A \\cup \\{0\\}) \\) in Definition 4.1, compute the average of the first \\( n - 1 \\) distances. Write these averages in increasing order, append the list of increasing distances \\( |q - 0| \\) from the \\( n \\)-th row of \\( M(C; A \\cup \\{0\\}) \\), and also append the vector of increasing values of \\( \\frac{s}{c_n} \\sigma(A \\cup \\{0\\}) \\) taking signs \\( s \\) from the \\( (n + 1) \\)-st row of \\( M(C; A \\cup \\{0\\}) \\). Let \\( \\vec{M}(C; A) \\in \\mathbb{R}^{3(m - n + 1)} \\) be the final vector." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.777, + 0.894, + 0.904 + ], + "angle": 0, + "content": "The pair \\([\\mathrm{CID}(A); \\vec{M}(C; A)]\\) is the Average Centered Vector \\(\\mathrm{ACV}(C; A)\\) considered as a vector of length \\(\\frac{n(n-1)}{2} + 3(m-n+1)\\). The unordered set of \\(\\mathrm{ACV}(C; A)\\) for all \\(\\binom{m}{n-1}\\) unordered subsets \\(A \\subset C\\) is the Average Centered Distribution \\(\\mathrm{ACD}(C)\\). The Centered Distance Moment \\(\\mathrm{CDM}(C;l)\\) is the \\(l\\)-th (standardized for \\(l \\geq 3\\)) moment of \\(\\mathrm{ACD}(C)\\) considered as a probability distribution of \\(\\binom{m}{n-1}\\) vectors, separately for each coordinate." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1281" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Example 4.9 (CDM for clouds in Fig. 3). (a) For \\( n = 2 \\) and the cloud \\( R \\subset \\mathbb{R}^2 \\) of \\( m = 3 \\) vertices \\( p_1 = (0,0) \\), \\( p_2 = (4,0) \\), \\( p_3 = (0,3) \\) of the right-angled triangle in Fig. 3 (middle), we continue Example 4.2(a) and" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.152, + 0.47, + 0.198 + ], + "angle": 0, + "content": "\\( \\text{flatten} \\, \\mathrm{OCD}(R; p_1) = [0, \\begin{pmatrix} 4 & 3 \\\\ 4 & 3 \\\\ 0 & 0 \\end{pmatrix}] \\) into the vector" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.198, + 0.47, + 0.259 + ], + "angle": 0, + "content": "\\(\\operatorname{ACV}(R; p_1) = [0; 3, 4; 3, 4; 0, 0]\\) of length \\(\\frac{n(n-1)}{2} + 3(m-n+1) = 7\\), whose four parts \\((1+2+2+2=7)\\) are in increasing order, similarly for \\(p_2, p_3\\). The Average Centered Distribution can be written as a \\(3 \\times 7\\) matrix with unordered" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.257, + 0.468, + 0.305 + ], + "angle": 0, + "content": "rows: \\(\\operatorname{ACD}(R) = \\left( \\begin{array}{c|cc|cc|cc}0 & 3 & 4 & 3 & 4 & 0 & 0\\\\ 4 & 4 & 5 & 0 & 3 & 0 & -6 / c_2\\\\ 3 & 3 & 5 & 0 & 4 & 0 & 6 / c_2 \\end{array} \\right).\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.468, + 0.35 + ], + "angle": 0, + "content": "The area of the triangle on \\( R \\) equals 6 and can be normalized by \\( c_2 = 2\\sqrt{3} \\) to get \\( 6 / c_2 = \\sqrt{3} \\), see [39, section 4]. The 1st moment is \\( \\mathrm{CDM}(R;1) = \\frac{1}{3}(7;10,14;3,11;0) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.468, + 0.389 + ], + "angle": 0, + "content": "(b) For \\( n = 2 \\) and the cloud \\( S \\subset \\mathbb{R}^2 \\) of \\( m = 4 \\) vertices of the square in Fig. 3 (right), Example 4.2(a) com" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.468, + 0.437 + ], + "angle": 0, + "content": "puted \\(\\operatorname {SCD}(R)\\) as one OCD \\(= [1,\\left( \\begin{array}{rrr}\\sqrt{2} & \\sqrt{2} & 2\\\\ 1 & 1 & 1\\\\ - & + & 0 \\end{array} \\right)]\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.468, + 0.483 + ], + "angle": 0, + "content": "which flattens to \\(\\mathrm{ACV} = (1; \\sqrt{2}, \\sqrt{2}, 2; 1, 1, 1; -\\frac{1}{2}, \\frac{1}{2}, 0) = \\mathrm{ACD}(S) = \\mathrm{CDM}(S; 1) \\in \\mathbb{R}^{10}\\), where \\(\\frac{1}{2}\\) is the area of the triangle on the vertices \\((0, 0)\\), \\((1, 0)\\), \\((0, 1)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.468, + 0.588 + ], + "angle": 0, + "content": "Corollary 4.10 (time for continuous metrics on CDMs). For any cloud \\(C \\subset \\mathbb{R}^n\\) of \\(m\\) unlabeled points, the Centered Distance Moment \\(\\mathrm{CDM}(C;l)\\) in Definition 4.8 is computed in time \\(O(m^n /(n - 4)!\\). The metric \\(L_{\\infty}\\) on CDMs needs \\(O(n^{2} + m)\\) time and \\(\\mathrm{EMD}\\bigl (\\mathrm{SCD}(C),\\mathrm{SCD}(C^{\\prime})\\bigr)\\geq |\\mathrm{CDM}(C;1) - \\mathrm{CDM}(C^{\\prime};1)|_{\\infty}\\) holds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.462, + 0.623 + ], + "angle": 0, + "content": "5. Experiments and discussion of future work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.468, + 0.737 + ], + "angle": 0, + "content": "This paper advocates a scientific approach to any data exemplified by Problem 1.1, where rigid motion on clouds can be replaced by another equivalence of other data. The scientific principles such as axioms should be always respected. Only the first coincidence axiom in (1.1b) guarantees no duplicate data. If the triangle inequality fails with any additive error, results of clustering can be pre-determined [51]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.468, + 0.804 + ], + "angle": 0, + "content": "The notorious \\( m! \\) challenge of \\( m \\) unlabeled points in Problem 1.1 was solved in \\( \\mathbb{R}^n \\) by Theorem 4.7, also up to rigid motion by using the novel strength of a simplex to smooth signs of determinants due to hard Theorem 4.4." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.81, + 0.468, + 0.9 + ], + "angle": 0, + "content": "The results above sufficiently justify re-focusing future efforts from experimental attempts at Problem 1.1 to higher level tasks such as predicting properties of rigid objects, e.g. crystalline materials, using the complete invariants with no false negatives and no false positives for all possible data since no experiments can beat the proved \\(100\\%\\) guarantee." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "To tackle the limitation of comparing only clouds having a fixed number \\( m \\) of points, the Earth Mover's Distance (EMD) continuously can compare any distributions (SDD or SCD) of different sizes. Using EMD instead of the bottleneck distance \\( W_{\\infty} \\) on \\( m - h \\) (or \\( m - n + 1 \\)) columns of matrices in Definitions 3.3 and 4.1 increases a time from \\( O(m^{1.5}\\log m) \\) to \\( O(m^3\\log m) \\) but the total time remains the same due to a near cubic time in the last step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.217, + 0.892, + 0.368 + ], + "angle": 0, + "content": "The running time in real applications is smaller for several reasons. First, the shape (isometry class) of any rigid body in \\(\\mathbb{R}^3\\) is determined by only \\(m = 4\\) labeled points in general position. Even when points are unlabeled, dozens of corners or feature points suffice to represent a rigid shape well enough. Second, the key size \\(l\\) (number of distinct Oriented Centered Distributions) in Theorem 4.7 is often smaller than \\(m\\), especially for symmetric objects, see \\(l = 1 < m = 4\\) in Example 4.2. The SCD invariants are on top of others due to their completeness and continuity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.508 + ], + "angle": 0, + "content": "The past work [71, 73] used the simpler Pointwise Distance Distribution (PDD) to complete \\(200\\mathrm{B}+\\) pairwise comparisons of all \\(660\\mathrm{K}+\\) periodic crystals in the world's largest database of real materials. This experiment took only a couple of days on a modest desktop and established the Crystal Isometry Principle saying that any real periodic crystal is uniquely determined by the geometry of its atomic centers without chemical elements. So the type of any atom is provably reconstructable from distances to atomic neighbors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.602 + ], + "angle": 0, + "content": "The new invariants allow us to go deeper and compare atomic clouds from higher level periodic crystals. Fig. 5 visualizes all \\(300\\mathrm{K}+\\) atomic clouds extracted from all \\(10\\mathrm{K}+\\) crystalline drugs in the Cambridge Structural Database (CSD) by using SDV invariants for \\(5 + 1\\) atoms including the central one. Future maps will use stronger invariants." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.615, + 0.892, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.776, + 0.89, + 0.804 + ], + "angle": 0, + "content": "Figure 5. Two principal directions of SDVs for all \\(300\\mathrm{K}+\\) atomic clouds from all \\(10\\mathrm{K}+\\) drugs in the CSD, colored by 25 elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This research was supported by the Royal Academy Engineering fellowship IF2122/186, and EPSRC grants EP/R018472/1, EP/X018474/1. We thank the Data Science Theory and Applications group (Liverpool) and reviewers of this conference version [72] for helpful suggestions." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1282" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Naveed Akhtar and Ajmal Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. IEEE Access, 6:14410-14430, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[2] Olga Anosova and Vitaliy Kurlin. 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Scientific Reports, 12(1):1-13, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.889 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1284" + } + ] +] \ No newline at end of file diff --git a/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_origin.pdf b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4672be4e4512a8c53f9313ec14cde44977225eca --- /dev/null +++ b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/e95e50bd-aaeb-4127-84a7-6d0f727b579f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b87ffeb98771ec241509d8e4dd33f7865c652db075a747d69cd4ab60c88030c4 +size 1384902 diff --git a/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/full.md b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7ccb0da7fbae2db6a1a7b293ffabce8d632e703c --- /dev/null +++ b/2023/Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives/full.md @@ -0,0 +1,404 @@ +# Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives + +Daniel Widdowson +Computer Science department +University of Liverpool, UK +d.e.widdowson@liverpool.ac.uk + +Vitaliy Kurlin +Computer Science department +University of Liverpool, UK +vitaliy.kurlin@gmail.com + +# Abstract + +Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. + +Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description). + +Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points. + +# 1. Strong motivations for complete invariants + +In Computer Vision, real objects such as cars and solid obstacles are considered rigid and often represented by a finite set $C \subset \mathbb{R}^n$ (called a cloud) of $m$ unlabeled (or unordered) points, usually in low dimensions $n = 2, 3, 4$ . + +The rigidity of many real objects motivates the most fundamental equivalence of rigid motion [67], a composition of translations and rotations in $\mathbb{R}^n$ . In a general metric space $M$ , the most relevant equivalence is isometry: any map $M \to M$ maintaining all inter-point distances in $M$ . + +Any isometry in $\mathbb{R}^n$ is a composition of a mirror reflection with some rigid motion. Any orientation-preserving isometry can be realized as a continuous rigid motion. + +There is no sense in distinguishing rigid objects that are related by isometry or having the same shape. Formally, the shape of a cloud $C$ is its isometry class [48] defined as a collection of all infinitely many clouds isometric to $C$ . + +The only reliable tool for distinguishing clouds up to isometry is an invariant defined as a function or property preserved by any isometry. Since any isometry is bijective, the number of points is an isometry invariant, but the coordinates of points are not invariants even under translation. This simple invariant is incomplete (non-injective) because non-isometric clouds can have different numbers of points. + +Any invariant $I$ maps all isometric clouds to the same value. There are no isometric clouds $C \cong C'$ with $I(C) \neq I(C')$ , meaning that $I$ has no false negatives. Isometry invariants are also called equivariant descriptors [55]. + +A complete invariant $I$ should distinguish all nonisometric clouds, so if $C \neq C'$ then $I(C) \neq I(C')$ . Equivalently, if $I(C) = I(C')$ then $C \cong C'$ , so $I$ has no false positives. Then $I$ can be considered as a DNA-style code or genome that identifies any cloud uniquely up to isometry. + +Since real data is always noisy and motions of rigid objects are important to track, a useful complete invariant must be also continuous under the movement of points. + +A complete and continuous invariant for $m = 3$ points consists of three pairwise distances (sides of a triangle) and is known in school as the SSS theorem [68]. But all pairwise distances are incomplete for $m \geq 4$ [9], see Fig. 1. + +Problem 1.1 (complete isometry invariants with computable continuous metrics). For any cloud of $m$ unlabeled points in $\mathbb{R}^n$ , find an invariant $I$ satisfying the properties + +$(\pmb{a})$ completeness: $C, C'$ are isometric $\Leftrightarrow I(C) = I(C')$ ; + +(b) Lipschitz continuity: if any point of $C$ is perturbed within its $\varepsilon$ -neighborhood then $I(C)$ changes by at most $\lambda \varepsilon$ for a constant $\lambda$ and a metric $d$ satisfying these axioms: + +1) $d(I(C),I(C')) = 0$ if and only if $C\cong C^{\prime}$ are isometric, + +2) symmetry: $d(I(C), I(C')) = d(I(C'), I(C))$ , + +3) $d(I(C),I(C')) + d(I(C'),I(C''))\geq d(I(C),I(C''))$ + +(c) computability: $I$ and $d$ are computed in a polynomial time in the number $m$ of points for a fixed dimension $n$ . + +![](images/d3d8a2270bc0f87dbbfc1632d76df8dd156fd60d26a619e8c6ff33a75ad59e1f.jpg) +Figure 1. Left: the cloud $T = \{(1,1), (-1,1), (-2,0), (2,0)\}$ . Right: the kite $K = \{(0,1), (-1,0), (0, -1), (3,0)\}$ . $T$ and $K$ have the same 6 pairwise distances $\sqrt{2}, \sqrt{2}, 2, \sqrt{10}, \sqrt{10}, 4$ . + +Condition (1.1b) asking for a continuous metric is stronger than the completeness in (1.1a). Detecting an isometry $C \cong C'$ gives a discontinuous metric, say $d = 1$ for all non-isometric clouds $C \not\cong C'$ even if $C, C'$ are nearly identical. Any metric $d$ satisfying the first axiom in (1.1b) detects an isometry $C \cong C'$ by checking if $d = 0$ . + +Theorem 4.7 will solve Problem 1.1 for any $m$ in $\mathbb{R}^n$ . Continuous invariants in Theorem 3.10 are conjectured to be complete (no known counter-examples) in any metric space. The first author implemented all algorithms, the second author wrote all theory, proofs, examples in [38, 39]. + +# 2. Past work on cloud recognition/classification + +Labeled clouds $C \subset \mathbb{R}^n$ are easy for isometry classification because the matrix of distances $d_{ij}$ between indexed points $p_i, p_j$ allows us to reconstruct $C$ by using the known distances to the previously constructed points [28, Theorem 9]. For any clouds of the same number $m$ of labeled points, the difference between $m \times m$ matrices of distances (or Gram matrices of $p_i \cdot p_j$ ) can be converted into a continuous metric by taking a matrix norm. If the given points are unlabeled, comparing $m \times m$ matrices requires $m!$ permutations, which makes this approach impractical. + +Multidimensional scaling (MDS). For a given $m \times m$ distance matrix of any $m$ -point cloud $A$ , MDS [57] finds an embedding $A \subset \mathbb{R}^k$ (if it exists) preserving all distances of $M$ for a dimension $k \leq m$ . A final embedding $A \subset \mathbb{R}^k$ uses eigenvectors whose ambiguity up to signs gives an exponential comparison time that can be close to $O(2^m)$ . + +Isometry detection refers to a simpler version of Problem 1.1 to algorithmically detect a potential isometry between given clouds of $m$ points in $\mathbb{R}^n$ . The best algorithm by Brass and Knauer [10] takes $O(m^{\lceil n/3 \rceil} \log m)$ time, so $O(m \log m)$ in $\mathbb{R}^3$ . These algorithms output a binary answer (yes/no) without quantifying similarity between non-isometric clouds by a continuous metric. + +The Hausdorff distance [30] can be defined for any subsets $A, B$ in an ambient metric space as $d_H(A, B) = \max \{\vec{d}_H(A, B), \vec{d}_H(B, A)\}$ , where the directed Hausdorff distance is $\vec{d}_H(A, B) = \sup_{p \in A} \inf_{q \in B} |p - q|$ . To take into account isometries, one can minimize the Hausdorff distance + +over all isometries [15, 17, 32]. For $n = 2$ , the Hausdorff distance minimized over isometries in $\mathbb{R}^2$ for sets of at most $m$ point needs $O(m^{5}\log m)$ time [16]. For a given $\varepsilon > 0$ and $n > 2$ , the related problem to decide if $d_H \leq \varepsilon$ up to translations has the time complexity $O(m^{\lceil (n + 1) / 2\rceil})$ [69, Chapter 4, Corollary 6]. For general isometry, only approximate algorithms tackled minimizations for infinitely many rotations initially in $\mathbb{R}^3$ [26] and in $\mathbb{R}^n$ [4, Lemma 5.5]. + +The Gromov-Wasserstein distances can be defined for metric-measure spaces, not necessarily sitting in a common ambient space. The simplest Gromov-Hausdorff (GH) distance cannot be approximated with any factor less than 3 in polynomial time unless $\mathrm{P} = \mathrm{NP}$ [56, Corollary 3.8]. Polynomial-time algorithms for GH were designed for ultrametric spaces [45]. However, GH spaces are challenging even for point clouds sets in $\mathbb{R}$ , see [41] and [74]. + +The Heat Kernel Signature (HKS) is a complete isometry invariant of a manifold $M$ whose the Laplace-Beltrami operator has distinct eigenvalues by [64, Theorem 1]. If $M$ is sampled by points, HKS can be discretized and remains continuous [64, section 4] but the completeness is unclear. + +Equivariant descriptors can be experimentally optimized [47, 59] on big datasets of clouds that are split into predefined clusters. Using more hidden parameters can improve accuracy on any finite dataset at a higher cost but will require more work for any new data. Point cloud registration filters outliers [58], samples rotations for Scale Invariant Feature Transform or uses a basis [52, 63, 65, 76], which can be unstable under perturbations of a cloud. The PCA-based complete invariant of unlabelled clouds [35] can discontinuously change when a basis degenerates to a lower dimensional subspace but inspired Complete Neural Networks [31] though without the Lipschitz continuity. + +Geometric Deep Learning produces descriptors that are equivariant by design [13] and go beyond Euclidean space $\mathbb{R}^n$ [14], hence aiming to experimentally solve Problem 1.1. Motivated by obstacles in [1, 18, 19, 29, 40], Problem 1.1 needs a justified solution without relying on finite data. + +Geometric Data Science solves analogs of Problem 1.1 for any real data objects considered up to practical equivalences instead of rigid motion on clouds [23, 24, 61]: 1-periodic discrete series [5, 6, 35], 2D lattices [12, 37], 3D lattices [11, 34, 36, 46], periodic point sets in $\mathbb{R}^3$ [20, 62] and in higher dimensions [2-4]. The applications of to crystalline materials [7, 53, 66, 75] led to the Crystal Isometry Principle [70, 71, 73] extending Mendeleev's table of elements to the Crystal Isometry Space of all periodic crystals parametrised by complete invariants like a geographic map of a planet. + +Local distributions of distances in Mémoli's seminal work [43, 44] for metric-measure spaces, or shape distributions [8,27,42,49], are first-order versions of the new SDD below. + +# 3. Simplewise Distance Distribution (SDD) + +We will refine Sorted Distance Vector in any metric space to get a complete invariant in $\mathbb{R}^n$ as shown in Fig. 2. All proofs from sections 3 and 4 are in [38,39], respectively. + +![](images/f244f8e4ca360e29f3b73f2a4047b410aa17cca8d0f67065a75b8d86d2209106.jpg) +Figure 2. Hierarchy of new invariants on top of the classical SDV. + +The lexicographic order $u < v$ on vectors $u = (u_{1},\ldots ,u_{h})$ and $v = (v_{1},\dots ,v_{h})$ in $\mathbb{R}^h$ means that if the first $i$ (possibly, $i = 0$ ) coordinates of $u,v$ coincide then $u_{i + 1} < v_{i + 1}$ . Let $S_{h}$ denote the permutation group on indices $1,\ldots ,h$ . + +Definition 3.1 (RDD(C;A)). Let $C$ be a cloud of $m$ unlabeled points in a space with a metric $d$ . Let $A = (p_1, \ldots, p_h) \subset C$ be an ordered subset of $1 \leq h < m$ points. Let $D(A)$ be the triangular distance matrix whose entry $D(A)_{i,j-1}$ is $d(p_i, p_j)$ for $1 \leq i < j \leq h$ , all other entries are filled by zeros. Any permutation $\xi \in S_h$ acts on $D(A)$ by mapping $D(A)_{ij}$ to $D(A)_{kl}$ , where $k \leq l$ is the pair of indices $\xi(i), \xi(j) - 1$ written in increasing order. + +For any other point $q \in C - A$ , write distances from $q$ to $p_1, \ldots, p_h$ as a column. The $h \times (m - h)$ -matrix $R(C; A)$ is formed by these $m - h$ lexicographically ordered columns. The action of $\xi$ on $R(C; A)$ maps any $i$ -th row to the $\xi(i)$ -th row, after which all columns can be written again in the lexicographic order. The Relative Distance Distribution $\mathrm{RDD}(C; A)$ is the equivalence class of the pair $[D(A), R(C; A)]$ of matrices up to permutations $\xi \in S_h$ . + +For a 1-point subset $A = \{p_1\}$ with $h = 1$ , the matrix $D(A)$ is empty and $R(C;A)$ is a single row of distances (in the increasing order) from $p_1$ to all other points $q \in C$ . For a 2-point subset $A = (p_1,p_2)$ with $h = 2$ , the matrix $D(A)$ is the single number $d(p_1,p_2)$ and $R(C;A)$ consists of two rows of distances from $p_1, p_2$ to all other points $q \in C$ . + +Example 3.2 (RDD for a 3-point cloud $C$ ). Let $C \subset \mathbb{R}^2$ consist of $p_1, p_2, p_3$ with inter-point distances $a \leq b \leq c$ ordered counter-clockwise as in Fig. 3 (left). Then + +$$ +\operatorname {R D D} (C; p _ {1}) = [ \emptyset ; (b, c) ], \operatorname {R D D} (C; \left( \begin{array}{c} p _ {2} \\ p _ {3} \end{array} \right)) = [ a; \left( \begin{array}{c} c \\ b \end{array} \right) ], +$$ + +$$ +\operatorname {R D D} (C; p _ {2}) = [ \emptyset ; (a, c) ], \operatorname {R D D} (C; \left( \begin{array}{c} p _ {3} \\ p _ {1} \end{array} \right)) = [ b; \left( \begin{array}{c} a \\ c \end{array} \right) ], +$$ + +![](images/805b7e74f33947f847a616f36781dc3fc1e11fe3dc86fada565addb507f49067.jpg) +Figure 3. Left: a cloud $C = \{p_1, p_2, p_3\}$ with distances $a \leq b \leq c$ . Middle: the triangular cloud $R = \{(0,0), (4,0), (0,3)\}$ . Right: the square cloud $S = \{(1,0), (-1,0), (0,1), (-1,0)\}$ . + +$$ +\operatorname {R D D} (C; p _ {3}) = [ \emptyset ; (a, b) ], \operatorname {R D D} (C; \left( \begin{array}{c} p _ {1} \\ p _ {2} \end{array} \right)) = [ c; \left( \begin{array}{c} b \\ a \end{array} \right) ]. +$$ + +We will always represent RDD for a specified order $A = (p_i, p_j)$ of points that are written as a column. Swapping the points $p_1 \leftrightarrow p_2$ makes the last RDD above equivalent to another form: $\mathrm{RDD}(C; \left( \begin{array}{c} p_2 \\ p_1 \end{array} \right)) = [c; \left( \begin{array}{c} a \\ b \end{array} \right)]$ . + +Though $\mathrm{RDD}(C;A)$ is defined up to a permutation $\xi$ of $h$ points in $A\subset C$ , we later use only $h = n$ , which makes comparisons of RDDs practical in dimensions $n = 2,3$ . Metrics on isometry classes of $C$ will be independent of $\xi$ . + +Definition 3.3 (Simplewise Distance Distribution $\mathrm{SDD}(C;h)$ ). Let $C$ be a cloud of $m$ unlabeled points in a metric space. For an integer $1\leq h < m$ , the Simplewise Distance Distribution $\mathrm{SDD}(C;h)$ is the unordered set of $\mathrm{RDD}(C;A)$ for all unordered $h$ -point subsets $A\subset C$ . + +For $h = 1$ and any $m$ -point cloud $C$ , the distribution $\mathrm{SDD}(C;1)$ can be considered as a matrix of $m$ rows of ordered distances from every point $p \in C$ to all other $m - 1$ points. If we lexicographically order these $m$ rows and collapse any $l > 1$ identical rows into a single one with the weight $l / m$ , then we get the Pointwise Distance Distribution $\mathrm{PDD}(C; m - 1)$ introduced in [71, Definition 3.1]. + +The PDD was simplified to the easier-to-compare vector of Average Minimum Distances [73]: $\mathrm{AMD}_k(C) = \frac{1}{m}\sum_{i=1}^{m}d_{ik}$ , where $d_{ik}$ is the distance from a point $p_i\in C$ to its $k$ -th nearest neighbor in $C$ . These neighbor-based invariants can be computed in a near-linear time in $m$ [22] and were pairwise compared for all all 660K+ periodic crystals in the world's largest database of real materials [71]. Definition 3.4 similarly maps SDD to a smaller invariant. + +Recall that the 1st moment of a set of numbers $a_1, \ldots, a_k$ is the average $\mu = \frac{1}{k} \sum_{i=1}^{k} a_i$ . The 2nd moment is the standard deviation $\sigma = \sqrt{\frac{1}{k} \sum_{i=1}^{k} (a_i - \mu)^2}$ . For $l \geq 3$ , the $l$ -th standardized moment [33, section 2.7] is $\frac{1}{k} \sum_{i=1}^{k} \left( \frac{a_i - \mu}{\sigma} \right)^l$ . + +Definition 3.4 (Simplexwise Distance Moments SDM). For any $m$ -point cloud $C$ in a metric space, let $A \subset C$ be a subset of $h$ unordered points. The Sorted Distance Vector SDV( $A$ ) is the list of all $\frac{h(h - 1)}{2}$ pairwise distances between points of $A$ written in increasing order. The vector $\vec{R}(C; A) \in \mathbb{R}^{m - h}$ is obtained from the $h \times (m - h)$ matrix $R(C; A)$ in Definition 3.1 by writing the vector of $m - h$ column averages in increasing order. + +The pair $[\mathrm{SDV}(A); \vec{R}(C; A)]$ is the Average Distance Distribution $\mathrm{ADD}(C; A)$ considered as a vector of length $\frac{h(h - 3)}{2} + m$ . The unordered collection of $\mathrm{ADD}(C; A)$ for all $\binom{m}{h}$ unordered subsets $A \subset C$ is the Average Simplewise Distribution $\mathrm{ASD}(C; h)$ . The Simplewise Distance Moment $\mathrm{SDM}(C; h, l)$ is the $l$ -th (standardized for $l \geq 3$ ) moment of $\mathrm{ASD}(C; h)$ considered as a probability distribution of $\binom{m}{h}$ vectors, separately for each coordinate. + +Example 3.5 (SDD and SDM for $T, K$ ). Fig. 1 shows the non-isometric 4-point clouds $T, K$ with the same Sorted Distance Vector $\mathrm{SDV} = \{\sqrt{2}, \sqrt{2}, 2, \sqrt{10}, \sqrt{10}, 4\}$ , see infinitely many examples in [9]. The arrows on the edges of $T, K$ show orders of points in each pair of vertices for RDDs. Then $T, K$ are distinguished up to isometry by $\mathrm{SDD}(T; 2) \neq \mathrm{SDD}(K; 2)$ in Table 1. The 1st coordinate of $\mathrm{SDM}(C; 2, 1) \in \mathbb{R}^3$ is the average of 6 distances from $\mathrm{SDV}(T) = \mathrm{SDV}(K)$ but the other two coordinates (column averages from $R(C; A)$ matrices) differ. + +Some of the $\binom{m}{h}$ RDDs in $\mathrm{SDD}(C; h)$ can be identical as in Example 3.5. If we collapse any $l > 1$ identical RDDs into a single RDD with the weight $l / \binom{m}{h}$ , SDD can be considered as a weighted probability distribution of RDDs. + +The $m - h$ permutable columns of the matrix $R(C;A)$ in RDD from Definition 3.1 can be interpreted as $m - h$ unlabeled points in $\mathbb{R}^h$ . Since any isometry is bijective, the simplest metric respecting bijections is the bottleneck distance, which is also called the Wasserstein distance $W_{\infty}$ . + +Definition 3.6 (bottleneck distance $W_{\infty}$ ). For any vector $v = (v_{1},\ldots ,v_{n})\in \mathbb{R}^{n}$ , the Minkowski norm is $||v||_{\infty} = \max_{i = 1,\dots ,n}|v_i|$ . For any vectors or matrices $N,N^{\prime}$ of the same size, the Minkowski distance is $L_{\infty}(N,N^{\prime}) = \max_{i,j}|N_{ij} - N_{ij}^{\prime}|$ . For clouds $C,C^{\prime}\subset \mathbb{R}^{n}$ of $m$ unlabeled points, the bottleneck distance $W_{\infty}(C,C^{\prime}) = \inf_{g:C\to C^{\prime}}\sup_{p\in C}||p - g(p)||_{\infty}$ is minimized over all bijections $g:C\to C'$ . + +Lemma 3.7 (the max metric $M_{\infty}$ on RDDs). For any $m$ point clouds and ordered $h$ -point subsets $A\subset C$ and $A^{\prime}\subset C^{\prime}$ set $d(\xi) = \max \{L_{\infty}(\xi (D(A)),D(A^{\prime})),W_{\infty}(\xi (R(C;A)),R(C^{\prime};A^{\prime}))\}$ for a permutation $\xi \in S_h$ on $h$ points. Then the max metric $M_{\infty}(\mathrm{RDD}(C;A),\mathrm{RDD}(C^{\prime};A^{\prime})) = \min_{\xi \in S_h}d(\xi)$ satisfies all + +
RDD(T; A) in SDD(T; 2)RDD(K; A) in SDD(K; 2)
[√2, (2/√10 4)] × 2[√2, (2/√2 4)] × 2
[2, (√2/√10 2)][2, (√2/√2 2)]
[√10, (√2/2 4)] × 2[√10, (√2/4 2)] × 2
[4, (√2/√10 2)][4, (√2/√10 2)]
ADD(T; A) in ASD(T; 2)ADD(K; A) in ASD(K; 2)
[√2, (2+/√10/2, 4+/√10/2)] × 2[√2, (2+/√2/2, 4+/√10/2)] × 2
[2, (√2/√10/2, 4+/√10/2)][2, (√2,√10)]
[√10, (2+/√2/2, 4+/√2/2)] × 2[√10, (2+/√10/2, 4+/√2/2)] × 2
[4, (√2+/√10/2, 4+/√10/2)][4, (√2+/√10/2, 4+/√10/2)]
SDM1 = 3 + √2 + √10/3SDM1 = 3 + √2 + √10/3
SDM2 = 6 + 2√2 + 4√10/12SDM2 = 8 + 5√2 + 3√10/12
SDM3 = 16+ 4√2 + 4√10/12SDM3 = 16+ 3√2 + 5√10/12
+ +Table 1. The Simplewise Distance Distributions from Definition 3.3 for the 4-point clouds $T, K \subset \mathbb{R}^2$ in Fig. 1. The symbol $\times 2$ indicates a doubled RDD. The three bottom rows show coordinates of $\mathrm{SDM}(C;2,1) \in \mathbb{R}^3$ from Definition 3.4 for $h = 2$ , $l = 1$ and both $C = T, K$ . Different elements are highlighted. + +metric axioms on RDDs from Definition 3.1 and can be computed in time $O(h!(h^2 + m^{1.5}\log^h m))$ . + +We will use only $h = n$ for Euclidean space $\mathbb{R}^n$ , so the factor $h!$ in Lemma 3.7 is practically small for $n = 2, 3$ . + +For $h = 1$ and a 1-point subset $A \subset C$ , the matrix $D(A)$ is empty, so $d(\xi) = W_{\infty}(\xi(R(C; A)), R(C'; A'))$ . The metric $M_{\infty}$ on RDDs will be used for intermediate costs to get metrics between two unordered collections of RDDs by using standard Definitions 3.8 and 3.9 below. + +Definition 3.8 (Linear Assignment Cost LAC [25]). For any $k \times k$ matrix of costs $c(i,j) \geq 0, i,j \in \{1,\dots,k\}$ , the Linear Assignment Cost LAC $= \frac{1}{k}\min_{g}\sum_{i = 1}^{k}c(i,g(i))$ is minimized for all bijections $g$ on the indices $1,\ldots ,k$ . + +The normalization factor $\frac{1}{k}$ in LAC makes this metric better comparable with EMD whose weights sum up to 1. + +Definition 3.9 (Earth Mover's Distance on distributions). Let $B = \{B_{1},\ldots ,B_{k}\}$ be a finite unordered set of objects with weights $w(B_{i})$ $i = 1,\dots ,k$ . Consider another set $D = \{D_1,\dots ,D_l\}$ with weights $w(D_j)$ $j = 1,\dots ,l$ Assume that a distance between $B_{i}$ $D_{j}$ is measured by a metric $d(B_i,D_j)$ . A flow from $B$ to $D$ is a $k\times l$ matrix whose entry $f_{ij}\in [0,1]$ represents a partial flow from an object $B_{i}$ to $D_{j}$ . The Earth Mover's Distance [54] is the minimum of $\mathrm{EMD}(B,D) = \sum_{i = 1}^{k}\sum_{j = 1}^{l}f_{ij}d(B_i,D_j)$ over $f_{ij}\in [0,1]$ subject to $\sum_{j = 1}^{l}f_{ij}\leq w(B_i)$ for $i = 1,\ldots ,k$ $\sum_{i = 1}^{k}f_{ij}\leq w(D_j)$ for $j = 1,\ldots ,l$ and $\sum_{i = 1}^{k}\sum_{j = 1}^{l}f_{ij} = 1$ + +The first condition $\sum_{j=1}^{l} f_{ij} \leq w(B_i)$ means that not more than the weight $w(B_i)$ of the object $B_i$ 'flows' into all $D_j$ via the flows $f_{ij}$ , $j = 1, \ldots, l$ . The second condition $\sum_{i=1}^{k} f_{ij} \leq w(D_j)$ means that all flows $f_{ij}$ from $B_i$ for $i = 1, \ldots, k$ 'flow' to $D_j$ up to its weight $w(D_j)$ . The last condition $\sum_{i=1}^{k} \sum_{j=1}^{l} f_{ij} = 1$ forces all $B_i$ to collectively 'flow' into all $D_j$ . LAC [25] and EMD [54] can be computed in a near cubic time in the sizes of given sets of objects. + +Theorems 3.10(c) and 4.7 will extend $O(m^{1.5}\log^n m)$ algorithms for fixed clouds of $m$ unlabeled points in [21, Theorem 6.5] to the harder case of isometry classes but keep the polynomial time in $m$ for a fixed dimension $n$ . All complexities are for a random-access machine (RAM) model. + +Theorem 3.10 (invariance and continuity of SDDs). $(a)$ For $h\geq 1$ and any cloud $C$ of $m$ unlabeled points in a metric space, $\mathrm{SDD}(C;h)$ is an isometry invariant, which can be computed in time $O(m^{h + 1} / (h - 1)!$ .For any $l\geq 1$ , the invariant $\mathrm{SDM}(C;h,l)\in \mathbb{R}^{m + \frac{h(h - 3)}{2}}$ has the same time. + +For any $m$ -point clouds $C, C'$ in their own metric spaces and $h \geq 1$ , let the Simplexwise Distance Distributions $\mathrm{SDD}(C; h)$ and $\mathrm{SDD}(C'; h)$ consist of $k = \binom{m}{h}$ RDDs with equal weights $\frac{1}{k}$ without collapsing identical RDDs. + +(b) Using the $k \times k$ matrix of costs computed by the metric $M_{\infty}$ between RDDs from SDD( $C; h$ ) and SDD( $C'$ ; $h$ ), the Linear Assignment Cost LAC from Definition 3.8 satisfies all metric axioms on SDDs and can be computed in time $O(h!(h^2 + m^{1.5}\log^h m)k^2 + k^3\log k)$ . +(c) Let $\mathrm{SDD}(C; h)$ and $\mathrm{SDD}(C'; h)$ have a maximum size $l \leq k$ after collapsing identical RDDs. Then EMD from Definition 3.9 satisfies all metric axioms on SDDs and is computed in time $O(h!(h^2 + m^{1.5} \log^h m) l^2 + l^3 \log l)$ . +(d) Let $C'$ be obtained from $C$ by perturbing each point within its $\varepsilon$ -neighborhood. For any $h \geq 1$ , $\operatorname{SDD}(C; h)$ + +changes by at most $2\varepsilon$ in the LAC and EMD metrics. The lower bound holds: $\mathrm{EMD}\big(\mathrm{SDD}(C;h),\mathrm{SDD}(C';h)\big)\geq |\mathrm{SDM}(C;h,1) - \mathrm{SDM}(C';h,1)|_{\infty}.$ + +Theorem 3.10(d) substantially generalizes the fact that perturbing two points in their $\varepsilon$ -neighborhoods changes the Euclidean distance between these points by at most $2\varepsilon$ . + +We conjecture that $\mathrm{SDD}(C;h)$ is a complete isometry invariant of a cloud $C\subset \mathbb{R}^n$ for some $h\geq n - 1$ . [38, section 4] shows that $\mathrm{SDD}(C;2)$ distinguished all infinitely many known pairs [50, Fig. S4] of non-isometric $m$ -point clouds $C,C^{\prime}\subset \mathbb{R}^{3}$ with identical $\mathrm{PDD}(C) = \mathrm{SDD}(C;1)$ . + +# 4. Simplewise Centered Distribution (SCD) + +While all constructions of section 3 hold in any metric space, this section develops faster continuous metrics for complete isometry invariants of unlabeled clouds in $\mathbb{R}^n$ . + +The Euclidean structure of $\mathbb{R}^n$ allows us to translate the center of mass $\frac{1}{m}\sum_{p\in C}p$ of a given $m$ -point cloud $C\subset \mathbb{R}^n$ to the origin $0\in \mathbb{R}^n$ . Then Problem 1.1 reduces to only rotations around 0 from the orthogonal group $\mathrm{O}(\mathbb{R}^n)$ . + +Though the center of mass is uniquely determined by any cloud $C \subset \mathbb{R}^n$ of unlabeled points, real applications may offer one or several labeled points of $C$ that substantially speed up metrics on invariants. For example, an atomic neighborhood in a solid material is a cloud $C \subset \mathbb{R}^3$ of atoms around a central atom, which may not be the center of mass of $C$ , but is suitable for all methods below. + +This section studies metrics on complete invariants of $C \subset \mathbb{R}^n$ up to rotations around the origin $0 \in \mathbb{R}^n$ , which may or may not belong to $C$ or be its center of mass. + +For any subset $A = \{p_1, \ldots, p_{n-1}\} \subset C$ , the distance matrix $D(A \cup \{0\})$ from Definition 3.1 has size $(n-1) \times (n-1)$ and its last column can be chosen to include the distances from $n-1$ points of $A$ to the origin at $0 \in \mathbb{R}^n$ . + +Any $n$ vectors $v_{1},\ldots ,v_{n}\in \mathbb{R}^{n}$ can be written as columns in the $n\times n$ matrix whose determinant has a sign $\pm 1$ or 0 if $v_{1},\ldots ,v_{n}$ are linearly dependent. Any permutation $\xi \in S_n$ on indices $1,\dots ,n$ is a composition of some $t$ transpositions $i\leftrightarrow j$ and has $\mathrm{sign}(\xi) = (-1)^t$ + +Definition 4.1 (Simplewise Centered Distribution SCD). Let $C \subset \mathbb{R}^n$ be any cloud of $m$ unlabeled points. For any ordered subset $A$ of points $p_1, \ldots, p_{n-1} \in C$ , the matrix $R(C; A)$ from Definition 3.1 has a column of Euclidean distances $|q - p_1|, \ldots, |q - p_{n-1}|$ . At the bottom of this column, add the distance $|q - 0|$ to the origin and the sign of the determinant of the $n \times n$ matrix consisting of the vectors $q - p_1, \ldots, q - p_{n-1}, q$ . The resulting $(n+1) \times (m-n+1)$ -matrix with signs in the bottom $(n+1)$ -st row is the oriented relative distance matrix $M(C; A \cup \{0\})$ . + +Any permutation $\xi \in S_{n - 1}$ of $n - 1$ points of $A$ acts on $D(A)$ , permutes the first $n - 1$ rows of $M(C; A \cup \{0\})$ and multiplies every sign in the $(n + 1)$ -st row by $\mathrm{sign}(\xi)$ . + +The Oriented Centered Distribution $\mathrm{OCD}(C;A)$ is the equivalence class of pairs $[D(A\cup \{0\}),M(C;A\cup \{0\})]$ considered up to permutations $\xi \in S_{n - 1}$ of points of $A$ + +The Simplewise Centered Distribution $\operatorname{SCD}(C)$ is the unordered set of the distributions $\operatorname{OCD}(C; A)$ for all $\binom{m}{n-1}$ unordered $(n-1)$ -point subsets $A \subset C$ . The mirror image $\overline{\operatorname{SCD}}(C)$ is obtained from $\operatorname{SCD}(C)$ by reversing signs. + +Definition 4.1 needs no permutations for any $C \subset \mathbb{R}^2$ as $n - 1 = 1$ . Columns of $M(C; A \cup \{0\})$ can be lexicographically ordered without affecting the metric in Lemma 4.6. Some of the $\binom{m}{n-1}$ OCDs in $\operatorname{SCD}(C)$ can be identical as in Example 4.2(b). If we collapse any $l > 1$ identical OCDs into a single OCD with the weight $l / \binom{m}{h}$ , SCD can be considered as a weighted probability distribution of OCDs. + +Example 4.2 (SCD for clouds in Fig. 3). (a) Let $R \subset \mathbb{R}^2$ consist of the vertices $p_1 = (0,0)$ , $p_2 = (4,0)$ , $p_3 = (0,3)$ of the right-angled triangle in Fig. 3 (middle). Though $p_1 = (0,0)$ is included in $R$ and is not its center of mass, $\operatorname{SCD}(R)$ + +still makes sense. In $\mathrm{OCD}(R;p_1) = [0,\left( \begin{array}{ll}4 & 3\\ 4 & 3\\ 0 & 0 \end{array} \right)]$ , the matrix $D(\{p_1,0\})$ is $|p_{1} - 0| = 0$ , the top row has $|p_2-$ + +$p_1| = 4, |p_3 - p_1| = 3.$ In OCD $(R;p_{2}) = [4,\left( \begin{array}{cc}4 & 5\\ 0 & 3\\ 0 & - \end{array} \right)]$ + +the first row has $|p_1 - p_2| = 4$ , $|p_3 - p_2| = 5$ , the second row has $|p_1 - 0| = 0$ , $|p_3 - 0| = 3$ , $\det \left( \begin{array}{cc} -4 & 0 \\ 3 & 3 \end{array} \right) <$ + +0. In $\mathrm{OCD}(R; p_3) = [3, \begin{pmatrix} 3 & 5 \\ 0 & 4 \\ 0 & + \end{pmatrix}]$ , the first row has + +$|p_1 - p_3| = 3, |p_2 - p_3| = 5,$ the second row has $|p_1 - 0| = 0$ $|p_2 - 0| = 4,$ det $\left( \begin{array}{cc}4 & 4\\ -3 & 0 \end{array} \right) > 0.$ So $\operatorname {SCD}(R)$ consists of the three Oriented Centered Distributions OCDs above. + +If we reflect $R$ with respect to the $x$ -axis, the new cloud $\bar{R}$ of the points $p_1, p_2, \bar{p}_3 = (0, -3)$ has $\operatorname{SCD}(\bar{R}) = \overline{\operatorname{SCD}}(R)$ with $\operatorname{OCD}(\bar{R}; p_1) = \operatorname{OCD}(R)$ , $\operatorname{OCD}(\bar{R}; p_2) =$ + +[4, $\left( \begin{array}{ll}4 & 5\\ 0 & 3\\ 0 & + \end{array} \right),\mathrm{OCD}(R;\bar{p}_3) = [3,\left( \begin{array}{ll}3 & 5\\ 0 & 4\\ 0 & - \end{array} \right)]$ whose + +signs changed under reflection, so $\operatorname{SCD}(R) \neq \operatorname{SCD}(\bar{R})$ . + +(b) Let $S \subset \mathbb{R}^2$ consist of $m = 4$ points $(\pm 1,0), (0,\pm 1)$ that are vertices of the square in Fig. 3 (right). The center of mass is $0 \in \mathbb{R}^2$ and has a distance 1 to each point of $S$ . + +For each 1-point subset $A = \{p\} \subset S$ , the distance matrix $D(A \cup \{0\})$ on two points is the single number 1. The matrix $M(S; A \cup \{0\})$ has $m - n + 1 = 3$ columns. For $p_1 =$ + +(1,0), we have $M(S; \left( \begin{array}{c} p_1 \\ 0 \end{array} \right)) = \left( \begin{array}{ccc} \sqrt{2} & \sqrt{2} & 2 \\ 1 & 1 & 1 \\ - & + & 0 \end{array} \right)$ , + +where the columns are ordered according to $p_2 = (0, -1)$ , $p_3 = (0, 1)$ , $p_4 = (-1, 0)$ in Fig. 3 (right). The sign in the bottom right corner is 0 because the points $p_1, 0, p_4$ are in a straight line. Due to the rotational symmetry, $M(S; \{p_i, 0\})$ is independent of $i = 1, 2, 3, 4$ . So $\operatorname{SCD}(S)$ can be considered as one $\mathrm{OCD} = [1, M(S; \left( \begin{array}{c} p_1 \\ 0 \end{array} \right))]$ of weight 1. + +Example 4.2(b) illustrates the key discontinuity challenge: if $p_4 = (-1,0)$ is perturbed, the corresponding sign can discontinuously change to $+1$ or $-1$ . To get a continuous metric on OCDs, we will multiply each sign by a continuous strength function that vanishes for any zero sign. + +Definition 4.3 (strength $\sigma(A)$ of a simplex). For a set $A$ of $n + 1$ points $q = p_0, p_1, \ldots, p_n$ in $\mathbb{R}^n$ , let $p(A) = \frac{1}{2} \sum_{i \neq j}^{n + 1} |p_i - p_j|$ be half of the sum of all pairwise distances. + +Let $V(A)$ denote the volume the $n$ -dimensional simplex on the set $A$ . Define the strength $\sigma(A) = V^2(A) / p^{2n-1}(A)$ . + +For $n = 2$ and a triangle $A$ with sides $a, b, c$ in $\mathbb{R}^2$ , Heron's formula gives $\sigma(A) = \frac{(p - a)(p - b)(p - c)}{p^2}$ , + +$p = \frac{a + b + c}{2} = p(A)$ is the half-perimeter of $A$ . + +For $n = 1$ and a set $A = p_0, p_1 \subset \mathbb{R}$ , the volume is $V(A) = |p_0 - p_1| = 2p(A)$ , so $\sigma(A) = 2|p_0 - p_1|$ . + +The strength $\sigma(A)$ depends only on the distance matrix $D(A)$ from Definition 3.1, so the notation $\sigma(A)$ is used only for brevity. In any $\mathbb{R}^n$ , the squared volume $V^2(A)$ is expressed by the Cayley-Menger determinant [60] in pairwise distances between points of $A$ . Importantly, the strength $\sigma(A)$ vanishes when the simplex on a set $A$ degenerates. + +Theorem 4.7 will need the continuity of $s\sigma(A)$ , when a sign $s \in \{\pm 1\}$ from a bottom row of ORD discontinuously changes while passing through a degenerate set $A$ . The proof of the continuity of $\sigma(A)$ in Theorem 4.4 gives an explicit upper bound for a Lipschitz constant $c_n$ below. + +Theorem 4.4 (Lipschitz continuity of the strength $\sigma$ ). Let a cloud $A'$ be obtained from another $(n + 1)$ -point cloud $A \subset \mathbb{R}^n$ by perturbing every point within its $\varepsilon$ -neighborhood. The strength $\sigma(A)$ from Definition 4.3 is Lipschitz continuous so that $|\sigma(A') - \sigma(A)| \leq 2\varepsilon c_n$ for a constant $c_n$ . + +Example 4.5 (strength $\sigma(A)$ and its upper bounds). [39, Theorem 4.2] proves upper bounds for the Lipschitz constant of the strength: $c_2 = 2\sqrt{3}$ , $c_3 \approx 0.43$ , $c_4 \approx 0.01$ , which quickly tend to 0 due to the 'curse of dimensionality'. The plots in Fig. 4 illustrate that the strength $\sigma(\cdot)$ behaves smoothly in the $x$ -coordinate of a vertex and its derivative $|\frac{\partial \sigma}{\partial x}|$ is much smaller than the proved bounds $c_n$ above. + +![](images/6c99299b34d3c32721cc2166ca76bf6ae4ccdfaf9df90f677eef5d5bd951d39f.jpg) + +![](images/1c47d83f32470969c515674c5ca6a2ba65a8e1eb5a3af9109417aa7599fe7ca8.jpg) +Figure 4. The strength $\sigma$ (solid curve) and its derivative $\frac{\partial\sigma}{\partial x}$ (dashed curve) in the $x$ -coordinate of a point from $A$ were averaged over 3000 random triangles (top) and tetrahedra (bottom). + +The strength $\sigma(A)$ from Definition 4.3 will take care of extra signs in ORDs and allows us to prove the analogue of Lemma 3.7 for a similar time complexity with $h = n$ . + +Lemma 4.6 (metric on OCDs). Using the strength $\sigma$ from Definition 4.3, we consider the bottleneck distance $W_{\infty}$ on the set of permutable $m - n + 1$ columns of $M(C; A \cup \{0\})$ as on the set of $m - n + 1$ unlabeled points $\left(v, \frac{s}{c_n} \sigma(A \cup \{0, q\})\right) \in \mathbb{R}^{n + 1}$ . For another $\mathrm{OCD}' = [D(A' \cup \{0\}); M(C'; A' \cup \{0\})]$ and any permutation $\xi \in S_{n - 1}$ of indices $1, \ldots, n - 1$ acting on $D(A \cup \{0\})$ and the first $n - 1$ rows of $M(C; A \cup \{0\})$ , set $d_o(\xi) = \max \{L, W\}$ , + +$$ +w h e r e L = L _ {\infty} \left(\xi (D (A \cup \{0 \})), D (A ^ {\prime} \cup \{0 \})\right), +$$ + +$$ +W = W _ {\infty} \left(\xi (M (C; A \cup \{0 \})), M (C ^ {\prime}; A ^ {\prime} \cup \{0 \})\right). +$$ + +Then $M_{\infty}(\mathrm{OCD}, \mathrm{OCD}') = \min_{\xi \in S_{n-1}} d_o(\xi)$ satisfies all metric axioms on Oriented Centered Distributions (OCDs) and is computed in time $O((n - 1)! (n^2 + m^{1.5} \log^n m))$ . + +The coefficient $\frac{1}{c_n}$ normalizes the Lipschitz constant $c_{n}$ of $\sigma$ to 1 in line with changes of distances by at most $2\varepsilon$ when points are perturbed within their $\varepsilon$ -neighborhoods. An equality $\operatorname{SCD}(C) = \operatorname{SCD}(C')$ is interpreted as a bijection between unordered sets $\operatorname{SCD}(C) \to \operatorname{SCD}(C')$ matching all OCDs, which is best detected by checking if metrics in Theorem 4.7 between these SCDs is 0. + +Theorem 4.7 (completeness and continuity of SCD). $(\pmb{a})$ The Simplexwise Centered Distribution $\operatorname{SCD}(C)$ in Definition 4.1 is a complete isometry invariant of clouds $C \subset \mathbb{R}^n$ of $m$ unlabeled points with a center of mass at the origin $0 \in \mathbb{R}^n$ , and can be computed in time $O(m^n / (n - 4)!)$ . + +So any clouds $C, C' \subset \mathbb{R}^n$ are related by rigid motion (isometry, respectively) if and only if $\operatorname{SCD}(C) = \operatorname{SCD}(C')$ ( $\operatorname{SCD}(C)$ equals $\operatorname{SCD}(C')$ or its mirror image $\overline{\operatorname{SCD}}(C')$ , respectively). For any $m$ -point clouds $C, C' \subset \mathbb{R}^n$ , let $\operatorname{SCD}(C)$ and $\operatorname{SCD}(C')$ consist of $k = \binom{m}{n-1}$ OCDs. + +(b) For the $k \times k$ matrix of costs computed by the metric $M_{\infty}$ between OCDs in $\operatorname{SCD}(C)$ and $\operatorname{SCD}(C')$ , LAC from Definition 3.8 satisfies all metric axioms on SCDs and needs time $O((n - 1)! (n^2 + m^{1.5} \log^n m) k^2 + k^3 \log k)$ . +(c) Let SCDs have a maximum size $l \leq k$ after collapsing identical OCDs. Then EMD from Definition 3.9 satisfies all metric axioms on SCDs and can be computed in time $O((n - 1)! (n^2 + m^{1.5} \log^n m) l^2 + l^3 \log l)$ . +(d) Let $C'$ be obtained from a cloud $C \subset \mathbb{R}^n$ by perturbing each point within its $\varepsilon$ -neighborhood. Then $\operatorname{SCD}(C)$ changes by at most $2\varepsilon$ in the LAC and EMD metrics. + +If we estimate $l \leq k = \binom{m}{n-1} = m(m-1) \ldots (m-n+2)/n!$ as $O(m^{n-1}/n!)$ , Theorem 4.7(b,c) gives time $O(n(m^{n-1}/n!)^3 \log m)$ for metrics on SCDs, which is $O(m^3 \log m)$ for $n=2$ , and $O(m^6 \log m)$ for $n=3$ . + +Though the above time estimates are very rough upper bounds, the time $O(m^3 \log m)$ in $\mathbb{R}^2$ is faster than the only past time $O(m^5 \log m)$ for comparing $m$ -point clouds by the Hausdorff distance minimized over isometries [16]. + +Definition 4.8 (Centered Distance Moments CDM). For any $m$ -point cloud $C \subset \mathbb{R}^n$ , let $A \subset C$ be a subset of $n - 1$ unordered points. The Centered Interpoint Distance list $\mathrm{CID}(A)$ is the increasing list of all $\frac{(n - 1)(n - 2)}{2}$ pairwise distances between points of $A$ , followed by $n - 1$ increasing distances from $A$ to the origin $0$ . For each column of the $(n + 1) \times (m - n + 1)$ matrix $M(C; A \cup \{0\})$ in Definition 4.1, compute the average of the first $n - 1$ distances. Write these averages in increasing order, append the list of increasing distances $|q - 0|$ from the $n$ -th row of $M(C; A \cup \{0\})$ , and also append the vector of increasing values of $\frac{s}{c_n} \sigma(A \cup \{0\})$ taking signs $s$ from the $(n + 1)$ -st row of $M(C; A \cup \{0\})$ . Let $\vec{M}(C; A) \in \mathbb{R}^{3(m - n + 1)}$ be the final vector. + +The pair $[\mathrm{CID}(A); \vec{M}(C; A)]$ is the Average Centered Vector $\mathrm{ACV}(C; A)$ considered as a vector of length $\frac{n(n-1)}{2} + 3(m-n+1)$ . The unordered set of $\mathrm{ACV}(C; A)$ for all $\binom{m}{n-1}$ unordered subsets $A \subset C$ is the Average Centered Distribution $\mathrm{ACD}(C)$ . The Centered Distance Moment $\mathrm{CDM}(C;l)$ is the $l$ -th (standardized for $l \geq 3$ ) moment of $\mathrm{ACD}(C)$ considered as a probability distribution of $\binom{m}{n-1}$ vectors, separately for each coordinate. + +Example 4.9 (CDM for clouds in Fig. 3). (a) For $n = 2$ and the cloud $R \subset \mathbb{R}^2$ of $m = 3$ vertices $p_1 = (0,0)$ , $p_2 = (4,0)$ , $p_3 = (0,3)$ of the right-angled triangle in Fig. 3 (middle), we continue Example 4.2(a) and + +$\text{flatten} \, \mathrm{OCD}(R; p_1) = [0, \begin{pmatrix} 4 & 3 \\ 4 & 3 \\ 0 & 0 \end{pmatrix}]$ into the vector + +$\operatorname{ACV}(R; p_1) = [0; 3, 4; 3, 4; 0, 0]$ of length $\frac{n(n-1)}{2} + 3(m-n+1) = 7$ , whose four parts $(1+2+2+2=7)$ are in increasing order, similarly for $p_2, p_3$ . The Average Centered Distribution can be written as a $3 \times 7$ matrix with unordered + +rows: $\operatorname{ACD}(R) = \left( \begin{array}{c|cc|cc|cc}0 & 3 & 4 & 3 & 4 & 0 & 0\\ 4 & 4 & 5 & 0 & 3 & 0 & -6 / c_2\\ 3 & 3 & 5 & 0 & 4 & 0 & 6 / c_2 \end{array} \right).$ + +The area of the triangle on $R$ equals 6 and can be normalized by $c_2 = 2\sqrt{3}$ to get $6 / c_2 = \sqrt{3}$ , see [39, section 4]. The 1st moment is $\mathrm{CDM}(R;1) = \frac{1}{3}(7;10,14;3,11;0)$ . + +(b) For $n = 2$ and the cloud $S \subset \mathbb{R}^2$ of $m = 4$ vertices of the square in Fig. 3 (right), Example 4.2(a) com + +puted $\operatorname {SCD}(R)$ as one OCD $= [1,\left( \begin{array}{rrr}\sqrt{2} & \sqrt{2} & 2\\ 1 & 1 & 1\\ - & + & 0 \end{array} \right)]$ + +which flattens to $\mathrm{ACV} = (1; \sqrt{2}, \sqrt{2}, 2; 1, 1, 1; -\frac{1}{2}, \frac{1}{2}, 0) = \mathrm{ACD}(S) = \mathrm{CDM}(S; 1) \in \mathbb{R}^{10}$ , where $\frac{1}{2}$ is the area of the triangle on the vertices $(0, 0)$ , $(1, 0)$ , $(0, 1)$ . + +Corollary 4.10 (time for continuous metrics on CDMs). For any cloud $C \subset \mathbb{R}^n$ of $m$ unlabeled points, the Centered Distance Moment $\mathrm{CDM}(C;l)$ in Definition 4.8 is computed in time $O(m^n /(n - 4)!$ . The metric $L_{\infty}$ on CDMs needs $O(n^{2} + m)$ time and $\mathrm{EMD}\bigl (\mathrm{SCD}(C),\mathrm{SCD}(C^{\prime})\bigr)\geq |\mathrm{CDM}(C;1) - \mathrm{CDM}(C^{\prime};1)|_{\infty}$ holds. + +# 5. Experiments and discussion of future work + +This paper advocates a scientific approach to any data exemplified by Problem 1.1, where rigid motion on clouds can be replaced by another equivalence of other data. The scientific principles such as axioms should be always respected. Only the first coincidence axiom in (1.1b) guarantees no duplicate data. If the triangle inequality fails with any additive error, results of clustering can be pre-determined [51]. + +The notorious $m!$ challenge of $m$ unlabeled points in Problem 1.1 was solved in $\mathbb{R}^n$ by Theorem 4.7, also up to rigid motion by using the novel strength of a simplex to smooth signs of determinants due to hard Theorem 4.4. + +The results above sufficiently justify re-focusing future efforts from experimental attempts at Problem 1.1 to higher level tasks such as predicting properties of rigid objects, e.g. crystalline materials, using the complete invariants with no false negatives and no false positives for all possible data since no experiments can beat the proved $100\%$ guarantee. + +To tackle the limitation of comparing only clouds having a fixed number $m$ of points, the Earth Mover's Distance (EMD) continuously can compare any distributions (SDD or SCD) of different sizes. Using EMD instead of the bottleneck distance $W_{\infty}$ on $m - h$ (or $m - n + 1$ ) columns of matrices in Definitions 3.3 and 4.1 increases a time from $O(m^{1.5}\log m)$ to $O(m^3\log m)$ but the total time remains the same due to a near cubic time in the last step. + +The running time in real applications is smaller for several reasons. First, the shape (isometry class) of any rigid body in $\mathbb{R}^3$ is determined by only $m = 4$ labeled points in general position. Even when points are unlabeled, dozens of corners or feature points suffice to represent a rigid shape well enough. Second, the key size $l$ (number of distinct Oriented Centered Distributions) in Theorem 4.7 is often smaller than $m$ , especially for symmetric objects, see $l = 1 < m = 4$ in Example 4.2. The SCD invariants are on top of others due to their completeness and continuity. + +The past work [71, 73] used the simpler Pointwise Distance Distribution (PDD) to complete $200\mathrm{B}+$ pairwise comparisons of all $660\mathrm{K}+$ periodic crystals in the world's largest database of real materials. This experiment took only a couple of days on a modest desktop and established the Crystal Isometry Principle saying that any real periodic crystal is uniquely determined by the geometry of its atomic centers without chemical elements. So the type of any atom is provably reconstructable from distances to atomic neighbors. + +The new invariants allow us to go deeper and compare atomic clouds from higher level periodic crystals. Fig. 5 visualizes all $300\mathrm{K}+$ atomic clouds extracted from all $10\mathrm{K}+$ crystalline drugs in the Cambridge Structural Database (CSD) by using SDV invariants for $5 + 1$ atoms including the central one. Future maps will use stronger invariants. + +![](images/2315396e036fee7189c52ed0d76368eb2534de7f0d5d3114caf18042071517b1.jpg) +Figure 5. Two principal directions of SDVs for all $300\mathrm{K}+$ atomic clouds from all $10\mathrm{K}+$ drugs in the CSD, colored by 25 elements. + +This research was supported by the Royal Academy Engineering fellowship IF2122/186, and EPSRC grants EP/R018472/1, EP/X018474/1. We thank the Data Science Theory and Applications group (Liverpool) and reviewers of this conference version [72] for helpful suggestions. + +# References + +[1] Naveed Akhtar and Ajmal Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. IEEE Access, 6:14410-14430, 2018. 2 +[2] Olga Anosova and Vitaliy Kurlin. Introduction to periodic geometry and topology. arXiv:2103.02749. 2 +[3] Olga Anosova and Vitaliy Kurlin. An isometry classification of periodic point sets. 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The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 323, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 384 + ], + "type": "text", + "content": "Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 486, + 281, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 281, + 500 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 281, + 500 + ], + "type": "text", + "content": "1. Strong motivations for complete invariants" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "text", + "content": "In Computer Vision, real objects such as cars and solid obstacles are considered rigid and often represented by a finite set " + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "text", + "content": " (called a cloud) of " + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "text", + "content": " unlabeled (or unordered) points, usually in low dimensions " + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "inline_equation", + "content": "n = 2, 3, 4" + }, + { + "bbox": [ + 47, + 506, + 287, + 555 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "content": "The rigidity of many real objects motivates the most fundamental equivalence of rigid motion [67], a composition of translations and rotations in " + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "content": ". In a general metric space " + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "content": ", the most relevant equivalence is isometry: any map " + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "inline_equation", + "content": "M \\to M" + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "content": " maintaining all inter-point distances in " + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 559, + 287, + 620 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 624, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 287, + 661 + ], + "type": "text", + "content": "Any isometry in " + }, + { + "bbox": [ + 47, + 624, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 47, + 624, + 287, + 661 + ], + "type": "text", + "content": " is a composition of a mirror reflection with some rigid motion. Any orientation-preserving isometry can be realized as a continuous rigid motion." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "There is no sense in distinguishing rigid objects that are related by isometry or having the same shape. Formally, the shape of a cloud " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is its isometry class [48] defined as a collection of all infinitely many clouds isometric to " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 245, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 330 + ], + "type": "text", + "content": "The only reliable tool for distinguishing clouds up to isometry is an invariant defined as a function or property preserved by any isometry. Since any isometry is bijective, the number of points is an isometry invariant, but the coordinates of points are not invariants even under translation. This simple invariant is incomplete (non-injective) because non-isometric clouds can have different numbers of points." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "content": "Any invariant " + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "content": " maps all isometric clouds to the same value. There are no isometric clouds " + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "inline_equation", + "content": "C \\cong C'" + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "inline_equation", + "content": "I(C) \\neq I(C')" + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "content": ", meaning that " + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 333, + 545, + 381 + ], + "type": "text", + "content": " has no false negatives. Isometry invariants are also called equivariant descriptors [55]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": "A complete invariant " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": " should distinguish all nonisometric clouds, so if " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "C \\neq C'" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": " then " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "I(C) \\neq I(C')" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": ". Equivalently, if " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "I(C) = I(C')" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": " then " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "C \\cong C'" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": ", so " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": " has no false positives. Then " + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 384, + 545, + 445 + ], + "type": "text", + "content": " can be considered as a DNA-style code or genome that identifies any cloud uniquely up to isometry." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 483 + ], + "type": "text", + "content": "Since real data is always noisy and motions of rigid objects are important to track, a useful complete invariant must be also continuous under the movement of points." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "text", + "content": "A complete and continuous invariant for " + }, + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "inline_equation", + "content": "m = 3" + }, + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "text", + "content": " points consists of three pairwise distances (sides of a triangle) and is known in school as the SSS theorem [68]. But all pairwise distances are incomplete for " + }, + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "inline_equation", + "content": "m \\geq 4" + }, + { + "bbox": [ + 304, + 486, + 545, + 534 + ], + "type": "text", + "content": " [9], see Fig. 1." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": "Problem 1.1 (complete isometry invariants with computable continuous metrics). For any cloud of " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": " unlabeled points in " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": ", find an invariant " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": " satisfying the properties" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "inline_equation", + "content": "(\\pmb{a})" + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "text", + "content": " completeness: " + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "inline_equation", + "content": "C, C'" + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "text", + "content": " are isometric " + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "inline_equation", + "content": "\\Leftrightarrow I(C) = I(C')" + }, + { + "bbox": [ + 304, + 583, + 539, + 597 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": "(b) Lipschitz continuity: if any point of " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": " is perturbed within its " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": "-neighborhood then " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "I(C)" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": " changes by at most " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\lambda \\varepsilon" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": " for a constant " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": " and a metric " + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 601, + 545, + 638 + ], + "type": "text", + "content": " satisfying these axioms:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "spans": [ + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "text", + "content": "1) " + }, + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "inline_equation", + "content": "d(I(C),I(C')) = 0" + }, + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "text", + "content": " if and only if " + }, + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "inline_equation", + "content": "C\\cong C^{\\prime}" + }, + { + "bbox": [ + 306, + 640, + 543, + 654 + ], + "type": "text", + "content": " are isometric," + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 655, + 507, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 655, + 507, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 655, + 507, + 669 + ], + "type": "text", + "content": "2) symmetry: " + }, + { + "bbox": [ + 306, + 655, + 507, + 669 + ], + "type": "inline_equation", + "content": "d(I(C), I(C')) = d(I(C'), I(C))" + }, + { + "bbox": [ + 306, + 655, + 507, + 669 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 670, + 541, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 541, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 541, + 685 + ], + "type": "text", + "content": "3) " + }, + { + "bbox": [ + 306, + 670, + 541, + 685 + ], + "type": "inline_equation", + "content": "d(I(C),I(C')) + d(I(C'),I(C''))\\geq d(I(C),I(C''))" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "(c) computability: " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " are computed in a polynomial time in the number " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " of points for a fixed dimension " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1275" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 288, + 133 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 288, + 133 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 288, + 133 + ], + "type": "image", + "image_path": "d3d8a2270bc0f87dbbfc1632d76df8dd156fd60d26a619e8c6ff33a75ad59e1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": "Figure 1. Left: the cloud " + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "T = \\{(1,1), (-1,1), (-2,0), (2,0)\\}" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": ". Right: the kite " + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "K = \\{(0,1), (-1,0), (0, -1), (3,0)\\}" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": " have the same 6 pairwise distances " + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4" + }, + { + "bbox": [ + 46, + 140, + 287, + 175 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": "Condition (1.1b) asking for a continuous metric is stronger than the completeness in (1.1a). Detecting an isometry " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "C \\cong C'" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " gives a discontinuous metric, say " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "d = 1" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " for all non-isometric clouds " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "C \\not\\cong C'" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " even if " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "C, C'" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " are nearly identical. Any metric " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " satisfying the first axiom in (1.1b) detects an isometry " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "C \\cong C'" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": " by checking if " + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "inline_equation", + "content": "d = 0" + }, + { + "bbox": [ + 46, + 195, + 287, + 266 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "text", + "content": "Theorem 4.7 will solve Problem 1.1 for any " + }, + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 270, + 287, + 330 + ], + "type": "text", + "content": ". Continuous invariants in Theorem 3.10 are conjectured to be complete (no known counter-examples) in any metric space. The first author implemented all algorithms, the second author wrote all theory, proofs, examples in [38, 39]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 341, + 287, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 287, + 354 + ], + "type": "text", + "content": "2. Past work on cloud recognition/classification" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": "Labeled clouds " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " are easy for isometry classification because the matrix of distances " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "d_{ij}" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " between indexed points " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "p_i, p_j" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " allows us to reconstruct " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " by using the known distances to the previously constructed points [28, Theorem 9]. For any clouds of the same number " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " of labeled points, the difference between " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "m \\times m" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " matrices of distances (or Gram matrices of " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "p_i \\cdot p_j" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": ") can be converted into a continuous metric by taking a matrix norm. If the given points are unlabeled, comparing " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "m \\times m" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " matrices requires " + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "inline_equation", + "content": "m!" + }, + { + "bbox": [ + 46, + 360, + 287, + 480 + ], + "type": "text", + "content": " permutations, which makes this approach impractical." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": "Multidimensional scaling (MDS). For a given " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "m \\times m" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": " distance matrix of any " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": ", MDS [57] finds an embedding " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "A \\subset \\mathbb{R}^k" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": " (if it exists) preserving all distances of " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": " for a dimension " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "k \\leq m" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": ". A final embedding " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "A \\subset \\mathbb{R}^k" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": " uses eigenvectors whose ambiguity up to signs gives an exponential comparison time that can be close to " + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "inline_equation", + "content": "O(2^m)" + }, + { + "bbox": [ + 46, + 483, + 287, + 555 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": "Isometry detection refers to a simpler version of Problem 1.1 to algorithmically detect a potential isometry between given clouds of " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " points in " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": ". The best algorithm by Brass and Knauer [10] takes " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "O(m^{\\lceil n/3 \\rceil} \\log m)" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " time, so " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "O(m \\log m)" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": ". These algorithms output a binary answer (yes/no) without quantifying similarity between non-isometric clouds by a continuous metric." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "text", + "content": "The Hausdorff distance [30] can be defined for any subsets " + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "inline_equation", + "content": "A, B" + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "text", + "content": " in an ambient metric space as " + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "inline_equation", + "content": "d_H(A, B) = \\max \\{\\vec{d}_H(A, B), \\vec{d}_H(B, A)\\}" + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "text", + "content": ", where the directed Hausdorff distance is " + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\vec{d}_H(A, B) = \\sup_{p \\in A} \\inf_{q \\in B} |p - q|" + }, + { + "bbox": [ + 46, + 644, + 287, + 712 + ], + "type": "text", + "content": ". To take into account isometries, one can minimize the Hausdorff distance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "over all isometries [15, 17, 32]. For " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "n = 2" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ", the Hausdorff distance minimized over isometries in " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " for sets of at most " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " point needs " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "O(m^{5}\\log m)" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " time [16]. For a given " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\varepsilon > 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "n > 2" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ", the related problem to decide if " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "d_H \\leq \\varepsilon" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " up to translations has the time complexity " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "O(m^{\\lceil (n + 1) / 2\\rceil})" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " [69, Chapter 4, Corollary 6]. For general isometry, only approximate algorithms tackled minimizations for infinitely many rotations initially in " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " [26] and in " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " [4, Lemma 5.5]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "text", + "content": "The Gromov-Wasserstein distances can be defined for metric-measure spaces, not necessarily sitting in a common ambient space. The simplest Gromov-Hausdorff (GH) distance cannot be approximated with any factor less than 3 in polynomial time unless " + }, + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\mathrm{P} = \\mathrm{NP}" + }, + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "text", + "content": " [56, Corollary 3.8]. Polynomial-time algorithms for GH were designed for ultrametric spaces [45]. However, GH spaces are challenging even for point clouds sets in " + }, + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\mathbb{R}" + }, + { + "bbox": [ + 304, + 171, + 545, + 266 + ], + "type": "text", + "content": ", see [41] and [74]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "text", + "content": "The Heat Kernel Signature (HKS) is a complete isometry invariant of a manifold " + }, + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "text", + "content": " whose the Laplace-Beltrami operator has distinct eigenvalues by [64, Theorem 1]. If " + }, + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 270, + 545, + 330 + ], + "type": "text", + "content": " is sampled by points, HKS can be discretized and remains continuous [64, section 4] but the completeness is unclear." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 333, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 545, + 476 + ], + "type": "text", + "content": "Equivariant descriptors can be experimentally optimized [47, 59] on big datasets of clouds that are split into predefined clusters. Using more hidden parameters can improve accuracy on any finite dataset at a higher cost but will require more work for any new data. Point cloud registration filters outliers [58], samples rotations for Scale Invariant Feature Transform or uses a basis [52, 63, 65, 76], which can be unstable under perturbations of a cloud. The PCA-based complete invariant of unlabelled clouds [35] can discontinuously change when a basis degenerates to a lower dimensional subspace but inspired Complete Neural Networks [31] though without the Lipschitz continuity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 479, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 539 + ], + "type": "text", + "content": "Geometric Deep Learning produces descriptors that are equivariant by design [13] and go beyond Euclidean space " + }, + { + "bbox": [ + 304, + 479, + 545, + 539 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 479, + 545, + 539 + ], + "type": "text", + "content": " [14], hence aiming to experimentally solve Problem 1.1. Motivated by obstacles in [1, 18, 19, 29, 40], Problem 1.1 needs a justified solution without relying on finite data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 543, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 673 + ], + "type": "text", + "content": "Geometric Data Science solves analogs of Problem 1.1 for any real data objects considered up to practical equivalences instead of rigid motion on clouds [23, 24, 61]: 1-periodic discrete series [5, 6, 35], 2D lattices [12, 37], 3D lattices [11, 34, 36, 46], periodic point sets in " + }, + { + "bbox": [ + 304, + 543, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 543, + 545, + 673 + ], + "type": "text", + "content": " [20, 62] and in higher dimensions [2-4]. The applications of to crystalline materials [7, 53, 66, 75] led to the Crystal Isometry Principle [70, 71, 73] extending Mendeleev's table of elements to the Crystal Isometry Space of all periodic crystals parametrised by complete invariants like a geographic map of a planet." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Local distributions of distances in Mémoli's seminal work [43, 44] for metric-measure spaces, or shape distributions [8,27,42,49], are first-order versions of the new SDD below." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1276" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 272, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 272, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 272, + 85 + ], + "type": "text", + "content": "3. Simplewise Distance Distribution (SDD)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 129 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 129 + ], + "type": "text", + "content": "We will refine Sorted Distance Vector in any metric space to get a complete invariant in " + }, + { + "bbox": [ + 47, + 91, + 286, + 129 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 47, + 91, + 286, + 129 + ], + "type": "text", + "content": " as shown in Fig. 2. All proofs from sections 3 and 4 are in [38,39], respectively." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 138, + 286, + 229 + ], + "blocks": [ + { + "bbox": [ + 48, + 138, + 286, + 229 + ], + "lines": [ + { + "bbox": [ + 48, + 138, + 286, + 229 + ], + "spans": [ + { + "bbox": [ + 48, + 138, + 286, + 229 + ], + "type": "image", + "image_path": "f244f8e4ca360e29f3b73f2a4047b410aa17cca8d0f67065a75b8d86d2209106.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 238, + 286, + 250 + ], + "lines": [ + { + "bbox": [ + 47, + 238, + 286, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 286, + 250 + ], + "type": "text", + "content": "Figure 2. Hierarchy of new invariants on top of the classical SDV." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": "The lexicographic order " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "u < v" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " on vectors " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "u = (u_{1},\\ldots ,u_{h})" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "v = (v_{1},\\dots ,v_{h})" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^h" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " means that if the first " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " (possibly, " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "i = 0" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": ") coordinates of " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "u,v" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " coincide then " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "u_{i + 1} < v_{i + 1}" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "S_{h}" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": " denote the permutation group on indices " + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "inline_equation", + "content": "1,\\ldots ,h" + }, + { + "bbox": [ + 46, + 263, + 286, + 312 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": "Definition 3.1 (RDD(C;A)). Let " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " be a cloud of " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " unlabeled points in a space with a metric " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "A = (p_1, \\ldots, p_h) \\subset C" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " be an ordered subset of " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "1 \\leq h < m" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " points. Let " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " be the triangular distance matrix whose entry " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "D(A)_{i,j-1}" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "d(p_i, p_j)" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "1 \\leq i < j \\leq h" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": ", all other entries are filled by zeros. Any permutation " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "\\xi \\in S_h" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " acts on " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " by mapping " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "D(A)_{ij}" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "D(A)_{kl}" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "k \\leq l" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " is the pair of indices " + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "inline_equation", + "content": "\\xi(i), \\xi(j) - 1" + }, + { + "bbox": [ + 46, + 320, + 286, + 417 + ], + "type": "text", + "content": " written in increasing order." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": "For any other point " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "q \\in C - A" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": ", write distances from " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "p_1, \\ldots, p_h" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " as a column. The " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "h \\times (m - h)" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": "-matrix " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "R(C; A)" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " is formed by these " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "m - h" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " lexicographically ordered columns. The action of " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "R(C; A)" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " maps any " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": "-th row to the " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\xi(i)" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": "-th row, after which all columns can be written again in the lexicographic order. The Relative Distance Distribution " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\mathrm{RDD}(C; A)" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " is the equivalence class of the pair " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "[D(A), R(C; A)]" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": " of matrices up to permutations " + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\xi \\in S_h" + }, + { + "bbox": [ + 46, + 421, + 286, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": "For a 1-point subset " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "A = \\{p_1\\}" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "h = 1" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": ", the matrix " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " is empty and " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "R(C;A)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " is a single row of distances (in the increasing order) from " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " to all other points " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "q \\in C" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": ". For a 2-point subset " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "A = (p_1,p_2)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "h = 2" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": ", the matrix " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " is the single number " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "d(p_1,p_2)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "R(C;A)" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " consists of two rows of distances from " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "p_1, p_2" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": " to all other points " + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "inline_equation", + "content": "q \\in C" + }, + { + "bbox": [ + 46, + 525, + 286, + 597 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "content": "Example 3.2 (RDD for a 3-point cloud " + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "content": "). Let " + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "content": " consist of " + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "inline_equation", + "content": "p_1, p_2, p_3" + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "content": " with inter-point distances " + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "inline_equation", + "content": "a \\leq b \\leq c" + }, + { + "bbox": [ + 46, + 606, + 286, + 643 + ], + "type": "text", + "content": " ordered counter-clockwise as in Fig. 3 (left). Then" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 652, + 292, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 292, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 292, + 680 + ], + "type": "interline_equation", + "content": "\\operatorname {R D D} (C; p _ {1}) = [ \\emptyset ; (b, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {2} \\\\ p _ {3} \\end{array} \\right)) = [ a; \\left( \\begin{array}{c} c \\\\ b \\end{array} \\right) ],", + "image_path": "a0a9792460d1095f8c980f57a2907b8b119fb63271a084df0f37ac260b98db91.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 293, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 293, + 716 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 293, + 716 + ], + "type": "interline_equation", + "content": "\\operatorname {R D D} (C; p _ {2}) = [ \\emptyset ; (a, c) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {3} \\\\ p _ {1} \\end{array} \\right)) = [ b; \\left( \\begin{array}{c} a \\\\ c \\end{array} \\right) ],", + "image_path": "6ea7d86fcea142631bd763c19157e68509589aa6fdc7c5982560a1179483af0b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 305, + 69, + 545, + 142 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 545, + 142 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 545, + 142 + ], + "type": "image", + "image_path": "805b7e74f33947f847a616f36781dc3fc1e11fe3dc86fada565addb507f49067.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "text", + "content": "Figure 3. Left: a cloud " + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "inline_equation", + "content": "C = \\{p_1, p_2, p_3\\}" + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "text", + "content": " with distances " + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "inline_equation", + "content": "a \\leq b \\leq c" + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "text", + "content": ". Middle: the triangular cloud " + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "inline_equation", + "content": "R = \\{(0,0), (4,0), (0,3)\\}" + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "text", + "content": ". Right: the square cloud " + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "inline_equation", + "content": "S = \\{(1,0), (-1,0), (0,1), (-1,0)\\}" + }, + { + "bbox": [ + 305, + 148, + 545, + 183 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 201, + 551, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 201, + 551, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 201, + 551, + 228 + ], + "type": "interline_equation", + "content": "\\operatorname {R D D} (C; p _ {3}) = [ \\emptyset ; (a, b) ], \\operatorname {R D D} (C; \\left( \\begin{array}{c} p _ {1} \\\\ p _ {2} \\end{array} \\right)) = [ c; \\left( \\begin{array}{c} b \\\\ a \\end{array} \\right) ].", + "image_path": "fb9593594d2abf46facfec75691010ed0aff341665e2946af87bfd19bfbe8fee.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "text", + "content": "We will always represent RDD for a specified order " + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "inline_equation", + "content": "A = (p_i, p_j)" + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "text", + "content": " of points that are written as a column. Swapping the points " + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "inline_equation", + "content": "p_1 \\leftrightarrow p_2" + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "text", + "content": " makes the last RDD above equivalent to another form: " + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{RDD}(C; \\left( \\begin{array}{c} p_2 \\\\ p_1 \\end{array} \\right)) = [c; \\left( \\begin{array}{c} a \\\\ b \\end{array} \\right)]" + }, + { + "bbox": [ + 305, + 232, + 545, + 293 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": "Though " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathrm{RDD}(C;A)" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": " is defined up to a permutation " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": " points in " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "A\\subset C" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": ", we later use only " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "h = n" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": ", which makes comparisons of RDDs practical in dimensions " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "n = 2,3" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": ". Metrics on isometry classes of " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": " will be independent of " + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 305, + 299, + 545, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": "Definition 3.3 (Simplewise Distance Distribution " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;h)" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": "). Let " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": " be a cloud of " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": " unlabeled points in a metric space. For an integer " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "1\\leq h < m" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": ", the Simplewise Distance Distribution " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;h)" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": " is the unordered set of " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{RDD}(C;A)" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": " for all unordered " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": "-point subsets " + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "inline_equation", + "content": "A\\subset C" + }, + { + "bbox": [ + 305, + 355, + 546, + 415 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "h = 1" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " and any " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": ", the distribution " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;1)" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " can be considered as a matrix of " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " rows of ordered distances from every point " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "p \\in C" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " to all other " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "m - 1" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " points. If we lexicographically order these " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " rows and collapse any " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "l > 1" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " identical rows into a single one with the weight " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "l / m" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": ", then we get the Pointwise Distance Distribution " + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathrm{PDD}(C; m - 1)" + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": " introduced in [71, Definition 3.1]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": "The PDD was simplified to the easier-to-compare vector of Average Minimum Distances [73]: " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{AMD}_k(C) = \\frac{1}{m}\\sum_{i=1}^{m}d_{ik}" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "d_{ik}" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": " is the distance from a point " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "p_i\\in C" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": " to its " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": "-th nearest neighbor in " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": ". These neighbor-based invariants can be computed in a near-linear time in " + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 510, + 545, + 616 + ], + "type": "text", + "content": " [22] and were pairwise compared for all all 660K+ periodic crystals in the world's largest database of real materials [71]. Definition 3.4 similarly maps SDD to a smaller invariant." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": "Recall that the 1st moment of a set of numbers " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "a_1, \\ldots, a_k" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": " is the average " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mu = \\frac{1}{k} \\sum_{i=1}^{k} a_i" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": ". The 2nd moment is the standard deviation " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\sigma = \\sqrt{\\frac{1}{k} \\sum_{i=1}^{k} (a_i - \\mu)^2}" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "l \\geq 3" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": "-th standardized moment [33, section 2.7] is " + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\frac{1}{k} \\sum_{i=1}^{k} \\left( \\frac{a_i - \\mu}{\\sigma} \\right)^l" + }, + { + "bbox": [ + 304, + 620, + 545, + 716 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1277" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": "Definition 3.4 (Simplexwise Distance Moments SDM). For any " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " in a metric space, let " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " be a subset of " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " unordered points. The Sorted Distance Vector SDV(" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": ") is the list of all " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "\\frac{h(h - 1)}{2}" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " pairwise distances between points of " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " written in increasing order. The vector " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "\\vec{R}(C; A) \\in \\mathbb{R}^{m - h}" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " is obtained from the " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "h \\times (m - h)" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "R(C; A)" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " in Definition 3.1 by writing the vector of " + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "inline_equation", + "content": "m - h" + }, + { + "bbox": [ + 47, + 72, + 289, + 169 + ], + "type": "text", + "content": " column averages in increasing order." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": "The pair " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "[\\mathrm{SDV}(A); \\vec{R}(C; A)]" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " is the Average Distance Distribution " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{ADD}(C; A)" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " considered as a vector of length " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\frac{h(h - 3)}{2} + m" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": ". The unordered collection of " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{ADD}(C; A)" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\binom{m}{h}" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " unordered subsets " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " is the Average Simplewise Distribution " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{ASD}(C; h)" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": ". The Simplewise Distance Moment " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{SDM}(C; h, l)" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": "-th (standardized for " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "l \\geq 3" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": ") moment of " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{ASD}(C; h)" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " considered as a probability distribution of " + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\binom{m}{h}" + }, + { + "bbox": [ + 47, + 171, + 289, + 273 + ], + "type": "text", + "content": " vectors, separately for each coordinate." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": "Example 3.5 (SDD and SDM for " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "T, K" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": "). Fig. 1 shows the non-isometric 4-point clouds " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "T, K" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " with the same Sorted Distance Vector " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\mathrm{SDV} = \\{\\sqrt{2}, \\sqrt{2}, 2, \\sqrt{10}, \\sqrt{10}, 4\\}" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": ", see infinitely many examples in [9]. The arrows on the edges of " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "T, K" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " show orders of points in each pair of vertices for RDDs. Then " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "T, K" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " are distinguished up to isometry by " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(T; 2) \\neq \\mathrm{SDD}(K; 2)" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " in Table 1. The 1st coordinate of " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\mathrm{SDM}(C; 2, 1) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " is the average of 6 distances from " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\mathrm{SDV}(T) = \\mathrm{SDV}(K)" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " but the other two coordinates (column averages from " + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "inline_equation", + "content": "R(C; A)" + }, + { + "bbox": [ + 46, + 278, + 289, + 399 + ], + "type": "text", + "content": " matrices) differ." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "content": "Some of the " + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "inline_equation", + "content": "\\binom{m}{h}" + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "content": " RDDs in " + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C; h)" + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "content": " can be identical as in Example 3.5. If we collapse any " + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "inline_equation", + "content": "l > 1" + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "content": " identical RDDs into a single RDD with the weight " + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "inline_equation", + "content": "l / \\binom{m}{h}" + }, + { + "bbox": [ + 47, + 406, + 288, + 456 + ], + "type": "text", + "content": ", SDD can be considered as a weighted probability distribution of RDDs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "inline_equation", + "content": "m - h" + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": " permutable columns of the matrix " + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "inline_equation", + "content": "R(C;A)" + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": " in RDD from Definition 3.1 can be interpreted as " + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "inline_equation", + "content": "m - h" + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": " unlabeled points in " + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^h" + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": ". Since any isometry is bijective, the simplest metric respecting bijections is the bottleneck distance, which is also called the Wasserstein distance " + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "inline_equation", + "content": "W_{\\infty}" + }, + { + "bbox": [ + 47, + 458, + 288, + 519 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": "Definition 3.6 (bottleneck distance " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "W_{\\infty}" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": "). For any vector " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "v = (v_{1},\\ldots ,v_{n})\\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": ", the Minkowski norm is " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "||v||_{\\infty} = \\max_{i = 1,\\dots ,n}|v_i|" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": ". For any vectors or matrices " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "N,N^{\\prime}" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": " of the same size, the Minkowski distance is " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "L_{\\infty}(N,N^{\\prime}) = \\max_{i,j}|N_{ij} - N_{ij}^{\\prime}|" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": ". For clouds " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "C,C^{\\prime}\\subset \\mathbb{R}^{n}" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": " unlabeled points, the bottleneck distance " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "W_{\\infty}(C,C^{\\prime}) = \\inf_{g:C\\to C^{\\prime}}\\sup_{p\\in C}||p - g(p)||_{\\infty}" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": " is minimized over all bijections " + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "inline_equation", + "content": "g:C\\to C'" + }, + { + "bbox": [ + 47, + 527, + 289, + 631 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "spans": [ + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": "Lemma 3.7 (the max metric " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "M_{\\infty}" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " on RDDs). For any " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " point clouds and ordered " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " -point subsets " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "A\\subset C" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "A^{\\prime}\\subset C^{\\prime}" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " set " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "d(\\xi) = \\max \\{L_{\\infty}(\\xi (D(A)),D(A^{\\prime})),W_{\\infty}(\\xi (R(C;A)),R(C^{\\prime};A^{\\prime}))\\}" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " for a permutation " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "\\xi \\in S_h" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " points. Then the max metric " + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "inline_equation", + "content": "M_{\\infty}(\\mathrm{RDD}(C;A),\\mathrm{RDD}(C^{\\prime};A^{\\prime})) = \\min_{\\xi \\in S_h}d(\\xi)" + }, + { + "bbox": [ + 46, + 637, + 291, + 716 + ], + "type": "text", + "content": " satisfies all" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 305, + 72, + 569, + 404 + ], + "blocks": [ + { + "bbox": [ + 305, + 72, + 569, + 404 + ], + "lines": [ + { + "bbox": [ + 305, + 72, + 569, + 404 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 569, + 404 + ], + "type": "table", + "html": "
RDD(T; A) in SDD(T; 2)RDD(K; A) in SDD(K; 2)
[√2, (2/√10 4)] × 2[√2, (2/√2 4)] × 2
[2, (√2/√10 2)][2, (√2/√2 2)]
[√10, (√2/2 4)] × 2[√10, (√2/4 2)] × 2
[4, (√2/√10 2)][4, (√2/√10 2)]
ADD(T; A) in ASD(T; 2)ADD(K; A) in ASD(K; 2)
[√2, (2+/√10/2, 4+/√10/2)] × 2[√2, (2+/√2/2, 4+/√10/2)] × 2
[2, (√2/√10/2, 4+/√10/2)][2, (√2,√10)]
[√10, (2+/√2/2, 4+/√2/2)] × 2[√10, (2+/√10/2, 4+/√2/2)] × 2
[4, (√2+/√10/2, 4+/√10/2)][4, (√2+/√10/2, 4+/√10/2)]
SDM1 = 3 + √2 + √10/3SDM1 = 3 + √2 + √10/3
SDM2 = 6 + 2√2 + 4√10/12SDM2 = 8 + 5√2 + 3√10/12
SDM3 = 16+ 4√2 + 4√10/12SDM3 = 16+ 3√2 + 5√10/12
", + "image_path": "f20644f5350cecdfcced54bd7e254e1275e5087ef8c050eb218c2d5fa6bd6f75.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "lines": [ + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": "Table 1. The Simplewise Distance Distributions from Definition 3.3 for the 4-point clouds " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "T, K \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": " in Fig. 1. The symbol " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": " indicates a doubled RDD. The three bottom rows show coordinates of " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "\\mathrm{SDM}(C;2,1) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": " from Definition 3.4 for " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "h = 2" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": " and both " + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "inline_equation", + "content": "C = T, K" + }, + { + "bbox": [ + 305, + 413, + 547, + 470 + ], + "type": "text", + "content": ". Different elements are highlighted." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 491, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 515 + ], + "type": "text", + "content": "metric axioms on RDDs from Definition 3.1 and can be computed in time " + }, + { + "bbox": [ + 305, + 491, + 545, + 515 + ], + "type": "inline_equation", + "content": "O(h!(h^2 + m^{1.5}\\log^h m))" + }, + { + "bbox": [ + 305, + 491, + 545, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "content": "We will use only " + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "h = n" + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "content": " for Euclidean space " + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "content": ", so the factor " + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "h!" + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "content": " in Lemma 3.7 is practically small for " + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "inline_equation", + "content": "n = 2, 3" + }, + { + "bbox": [ + 305, + 523, + 545, + 548 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "inline_equation", + "content": "h = 1" + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": " and a 1-point subset " + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": ", the matrix " + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": " is empty, so " + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "inline_equation", + "content": "d(\\xi) = W_{\\infty}(\\xi(R(C; A)), R(C'; A'))" + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": ". The metric " + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "inline_equation", + "content": "M_{\\infty}" + }, + { + "bbox": [ + 304, + 551, + 545, + 611 + ], + "type": "text", + "content": " on RDDs will be used for intermediate costs to get metrics between two unordered collections of RDDs by using standard Definitions 3.8 and 3.9 below." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": "Definition 3.8 (Linear Assignment Cost LAC [25]). For any " + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": " matrix of costs " + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "inline_equation", + "content": "c(i,j) \\geq 0, i,j \\in \\{1,\\dots,k\\}" + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": ", the Linear Assignment Cost LAC " + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "inline_equation", + "content": "= \\frac{1}{k}\\min_{g}\\sum_{i = 1}^{k}c(i,g(i))" + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": " is minimized for all bijections " + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": " on the indices " + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "inline_equation", + "content": "1,\\ldots ,k" + }, + { + "bbox": [ + 304, + 620, + 547, + 681 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "The normalization factor " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\frac{1}{k}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " in LAC makes this metric better comparable with EMD whose weights sum up to 1." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1278" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "Definition 3.9 (Earth Mover's Distance on distributions). Let " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "B = \\{B_{1},\\ldots ,B_{k}\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " be a finite unordered set of objects with weights " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "w(B_{i})" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "i = 1,\\dots ,k" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " . Consider another set " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "D = \\{D_1,\\dots ,D_l\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " with weights " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "w(D_j)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "j = 1,\\dots ,l" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " Assume that a distance between " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "B_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "D_{j}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " is measured by a metric " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "d(B_i,D_j)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " . A flow from " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "k\\times l" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " matrix whose entry " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "f_{ij}\\in [0,1]" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " represents a partial flow from an object " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "B_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "D_{j}" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " . The Earth Mover's Distance [54] is the minimum of " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathrm{EMD}(B,D) = \\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij}d(B_i,D_j)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "f_{ij}\\in [0,1]" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " subject to " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\sum_{j = 1}^{l}f_{ij}\\leq w(B_i)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "i = 1,\\ldots ,k" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\sum_{i = 1}^{k}f_{ij}\\leq w(D_j)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "j = 1,\\ldots ,l" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\sum_{i = 1}^{k}\\sum_{j = 1}^{l}f_{ij} = 1" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": "The first condition " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\sum_{j=1}^{l} f_{ij} \\leq w(B_i)" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " means that not more than the weight " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "w(B_i)" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " of the object " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "B_i" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " 'flows' into all " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "D_j" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " via the flows " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "f_{ij}" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "j = 1, \\ldots, l" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": ". The second condition " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{k} f_{ij} \\leq w(D_j)" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " means that all flows " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "f_{ij}" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "B_i" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "i = 1, \\ldots, k" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " 'flow' to " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "D_j" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " up to its weight " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "w(D_j)" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": ". The last condition " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{k} \\sum_{j=1}^{l} f_{ij} = 1" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " forces all " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "B_i" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": " to collectively 'flow' into all " + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "inline_equation", + "content": "D_j" + }, + { + "bbox": [ + 47, + 257, + 289, + 395 + ], + "type": "text", + "content": ". LAC [25] and EMD [54] can be computed in a near cubic time in the sizes of given sets of objects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": "Theorems 3.10(c) and 4.7 will extend " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "O(m^{1.5}\\log^n m)" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": " algorithms for fixed clouds of " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": " unlabeled points in [21, Theorem 6.5] to the harder case of isometry classes but keep the polynomial time in " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": " for a fixed dimension " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": ". All complexities are for a random-access machine (RAM) model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": "Theorem 3.10 (invariance and continuity of SDDs). " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "(a)" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " For " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "h\\geq 1" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " and any cloud " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " unlabeled points in a metric space, " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;h)" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " is an isometry invariant, which can be computed in time " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "O(m^{h + 1} / (h - 1)!" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " .For any " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "l\\geq 1" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " , the invariant " + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{SDM}(C;h,l)\\in \\mathbb{R}^{m + \\frac{h(h - 3)}{2}}" + }, + { + "bbox": [ + 47, + 461, + 287, + 525 + ], + "type": "text", + "content": " has the same time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": "For any " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": "-point clouds " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "C, C'" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": " in their own metric spaces and " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "h \\geq 1" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": ", let the Simplexwise Distance Distributions " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C; h)" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C'; h)" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": " consist of " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "k = \\binom{m}{h}" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": " RDDs with equal weights " + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\frac{1}{k}" + }, + { + "bbox": [ + 47, + 527, + 287, + 576 + ], + "type": "text", + "content": " without collapsing identical RDDs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 576, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": "(b) Using the " + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": " matrix of costs computed by the metric " + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "M_{\\infty}" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": " between RDDs from SDD(" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "C; h" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": ") and SDD(" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "C'" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": "), the Linear Assignment Cost LAC from Definition 3.8 satisfies all metric axioms on SDDs and can be computed in time " + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "inline_equation", + "content": "O(h!(h^2 + m^{1.5}\\log^h m)k^2 + k^3\\log k)" + }, + { + "bbox": [ + 47, + 576, + 287, + 637 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "content": "(c) Let " + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C; h)" + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C'; h)" + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "content": " have a maximum size " + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "inline_equation", + "content": "l \\leq k" + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "content": " after collapsing identical RDDs. Then EMD from Definition 3.9 satisfies all metric axioms on SDDs and is computed in time " + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "inline_equation", + "content": "O(h!(h^2 + m^{1.5} \\log^h m) l^2 + l^3 \\log l)" + }, + { + "bbox": [ + 47, + 639, + 287, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "(d) Let " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "C'" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " be obtained from " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " by perturbing each point within its " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "-neighborhood. For any " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "h \\geq 1" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\operatorname{SDD}(C; h)" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "type": "text", + "content": "changes by at most " + }, + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "2\\varepsilon" + }, + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "type": "text", + "content": " in the LAC and EMD metrics. The lower bound holds: " + }, + { + "bbox": [ + 305, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "\\mathrm{EMD}\\big(\\mathrm{SDD}(C;h),\\mathrm{SDD}(C';h)\\big)\\geq |\\mathrm{SDM}(C;h,1) - \\mathrm{SDM}(C';h,1)|_{\\infty}." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "spans": [ + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "text", + "content": "Theorem 3.10(d) substantially generalizes the fact that perturbing two points in their " + }, + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "text", + "content": "-neighborhoods changes the Euclidean distance between these points by at most " + }, + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "inline_equation", + "content": "2\\varepsilon" + }, + { + "bbox": [ + 305, + 117, + 547, + 153 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": "We conjecture that " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;h)" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": " is a complete isometry invariant of a cloud " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "C\\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": " for some " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "h\\geq n - 1" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": ". [38, section 4] shows that " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{SDD}(C;2)" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": " distinguished all infinitely many known pairs [50, Fig. S4] of non-isometric " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": "-point clouds " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "C,C^{\\prime}\\subset \\mathbb{R}^{3}" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": " with identical " + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{PDD}(C) = \\mathrm{SDD}(C;1)" + }, + { + "bbox": [ + 305, + 156, + 547, + 217 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 227, + 534, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 227, + 534, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 227, + 534, + 241 + ], + "type": "text", + "content": "4. Simplewise Centered Distribution (SCD)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 247, + 546, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 546, + 283 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 546, + 283 + ], + "type": "text", + "content": "While all constructions of section 3 hold in any metric space, this section develops faster continuous metrics for complete isometry invariants of unlabeled clouds in " + }, + { + "bbox": [ + 305, + 247, + 546, + 283 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 247, + 546, + 283 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": "The Euclidean structure of " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": " allows us to translate the center of mass " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "\\frac{1}{m}\\sum_{p\\in C}p" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": " of a given " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "C\\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": " to the origin " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "0\\in \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": ". Then Problem 1.1 reduces to only rotations around 0 from the orthogonal group " + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "inline_equation", + "content": "\\mathrm{O}(\\mathbb{R}^n)" + }, + { + "bbox": [ + 305, + 287, + 546, + 345 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "content": "Though the center of mass is uniquely determined by any cloud " + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "content": " of unlabeled points, real applications may offer one or several labeled points of " + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "content": " that substantially speed up metrics on invariants. For example, an atomic neighborhood in a solid material is a cloud " + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "content": " of atoms around a central atom, which may not be the center of mass of " + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 348, + 547, + 431 + ], + "type": "text", + "content": ", but is suitable for all methods below." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "text", + "content": "This section studies metrics on complete invariants of " + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "text", + "content": " up to rotations around the origin " + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "inline_equation", + "content": "0 \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "text", + "content": ", which may or may not belong to " + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 435, + 547, + 471 + ], + "type": "text", + "content": " or be its center of mass." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": "For any subset " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "A = \\{p_1, \\ldots, p_{n-1}\\} \\subset C" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": ", the distance matrix " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "D(A \\cup \\{0\\})" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": " from Definition 3.1 has size " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "(n-1) \\times (n-1)" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": " and its last column can be chosen to include the distances from " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "n-1" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": " points of " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": " to the origin at " + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "inline_equation", + "content": "0 \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 474, + 546, + 522 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": "Any " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " vectors " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "v_{1},\\ldots ,v_{n}\\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " can be written as columns in the " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "n\\times n" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " matrix whose determinant has a sign " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\pm 1" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " or 0 if " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "v_{1},\\ldots ,v_{n}" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " are linearly dependent. Any permutation " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\xi \\in S_n" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " on indices " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "1,\\dots ,n" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " is a composition of some " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " transpositions " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "i\\leftrightarrow j" + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "text", + "content": " and has " + }, + { + "bbox": [ + 305, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}(\\xi) = (-1)^t" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": "Definition 4.1 (Simplewise Centered Distribution SCD). Let " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " be any cloud of " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " unlabeled points. For any ordered subset " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " of points " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "p_1, \\ldots, p_{n-1} \\in C" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": ", the matrix " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "R(C; A)" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " from Definition 3.1 has a column of Euclidean distances " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "|q - p_1|, \\ldots, |q - p_{n-1}|" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": ". At the bottom of this column, add the distance " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "|q - 0|" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " to the origin and the sign of the determinant of the " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "n \\times n" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": " matrix consisting of the vectors " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "q - p_1, \\ldots, q - p_{n-1}, q" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": ". The resulting " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "(n+1) \\times (m-n+1)" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": "-matrix with signs in the bottom " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "(n+1)" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": "-st row is the oriented relative distance matrix " + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 305, + 594, + 547, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1279" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "Any permutation " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\xi \\in S_{n - 1}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " points of " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " acts on " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": ", permutes the first " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " rows of " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " and multiplies every sign in the " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "(n + 1)" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "-st row by " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}(\\xi)" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "text", + "content": "The Oriented Centered Distribution " + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "inline_equation", + "content": "\\mathrm{OCD}(C;A)" + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "text", + "content": " is the equivalence class of pairs " + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "inline_equation", + "content": "[D(A\\cup \\{0\\}),M(C;A\\cup \\{0\\})]" + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "text", + "content": " considered up to permutations " + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "inline_equation", + "content": "\\xi \\in S_{n - 1}" + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "text", + "content": " of points of " + }, + { + "bbox": [ + 47, + 110, + 287, + 147 + ], + "type": "inline_equation", + "content": "A" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": "The Simplewise Centered Distribution " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": " is the unordered set of the distributions " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\operatorname{OCD}(C; A)" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\binom{m}{n-1}" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": " unordered " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "(n-1)" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": "-point subsets " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": ". The mirror image " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\overline{\\operatorname{SCD}}(C)" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": " is obtained from " + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 47, + 148, + 287, + 198 + ], + "type": "text", + "content": " by reversing signs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": "Definition 4.1 needs no permutations for any " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "n - 1 = 1" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": ". Columns of " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": " can be lexicographically ordered without affecting the metric in Lemma 4.6. Some of the " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "\\binom{m}{n-1}" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": " OCDs in " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": " can be identical as in Example 4.2(b). If we collapse any " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "l > 1" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": " identical OCDs into a single OCD with the weight " + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "inline_equation", + "content": "l / \\binom{m}{h}" + }, + { + "bbox": [ + 47, + 203, + 287, + 288 + ], + "type": "text", + "content": ", SCD can be considered as a weighted probability distribution of OCDs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": "Example 4.2 (SCD for clouds in Fig. 3). (a) Let " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "R \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": " consist of the vertices " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "p_1 = (0,0)" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "p_2 = (4,0)" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "p_3 = (0,3)" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": " of the right-angled triangle in Fig. 3 (middle). Though " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "p_1 = (0,0)" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": " is included in " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "text", + "content": " and is not its center of mass, " + }, + { + "bbox": [ + 47, + 294, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(R)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": "still makes sense. In " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathrm{OCD}(R;p_1) = [0,\\left( \\begin{array}{ll}4 & 3\\\\ 4 & 3\\\\ 0 & 0 \\end{array} \\right)]" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": ", the matrix " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "D(\\{p_1,0\\})" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "|p_{1} - 0| = 0" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": ", the top row has " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "|p_2-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 390, + 286, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 286, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 286, + 426 + ], + "type": "inline_equation", + "content": "p_1| = 4, |p_3 - p_1| = 3." + }, + { + "bbox": [ + 47, + 390, + 286, + 426 + ], + "type": "text", + "content": " In OCD " + }, + { + "bbox": [ + 47, + 390, + 286, + 426 + ], + "type": "inline_equation", + "content": "(R;p_{2}) = [4,\\left( \\begin{array}{cc}4 & 5\\\\ 0 & 3\\\\ 0 & - \\end{array} \\right)]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "content": "the first row has " + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "inline_equation", + "content": "|p_1 - p_2| = 4" + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "inline_equation", + "content": "|p_3 - p_2| = 5" + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "content": ", the second row has " + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "inline_equation", + "content": "|p_1 - 0| = 0" + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "inline_equation", + "content": "|p_3 - 0| = 3" + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 426, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\det \\left( \\begin{array}{cc} -4 & 0 \\\\ 3 & 3 \\end{array} \\right) <" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 462, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 287, + 499 + ], + "type": "text", + "content": "0. In " + }, + { + "bbox": [ + 47, + 462, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathrm{OCD}(R; p_3) = [3, \\begin{pmatrix} 3 & 5 \\\\ 0 & 4 \\\\ 0 & + \\end{pmatrix}]" + }, + { + "bbox": [ + 47, + 462, + 287, + 499 + ], + "type": "text", + "content": ", the first row has" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "inline_equation", + "content": "|p_1 - p_3| = 3, |p_2 - p_3| = 5," + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "text", + "content": " the second row has " + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "inline_equation", + "content": "|p_1 - 0| = 0" + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "inline_equation", + "content": "|p_2 - 0| = 4," + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "text", + "content": " det " + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "inline_equation", + "content": "\\left( \\begin{array}{cc}4 & 4\\\\ -3 & 0 \\end{array} \\right) > 0." + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "text", + "content": " So " + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "inline_equation", + "content": "\\operatorname {SCD}(R)" + }, + { + "bbox": [ + 47, + 499, + 286, + 545 + ], + "type": "text", + "content": " consists of the three Oriented Centered Distributions OCDs above." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": "If we reflect " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": " with respect to the " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": "-axis, the new cloud " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\bar{R}" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": " of the points " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "p_1, p_2, \\bar{p}_3 = (0, -3)" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": " has " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(\\bar{R}) = \\overline{\\operatorname{SCD}}(R)" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\operatorname{OCD}(\\bar{R}; p_1) = \\operatorname{OCD}(R)" + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 549, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\operatorname{OCD}(\\bar{R}; p_2) =" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 585, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 287, + 621 + ], + "type": "text", + "content": "[4, " + }, + { + "bbox": [ + 47, + 585, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\left( \\begin{array}{ll}4 & 5\\\\ 0 & 3\\\\ 0 & + \\end{array} \\right),\\mathrm{OCD}(R;\\bar{p}_3) = [3,\\left( \\begin{array}{ll}3 & 5\\\\ 0 & 4\\\\ 0 & - \\end{array} \\right)]" + }, + { + "bbox": [ + 47, + 585, + 287, + 621 + ], + "type": "text", + "content": " whose" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 621, + 275, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 275, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 275, + 634 + ], + "type": "text", + "content": "signs changed under reflection, so " + }, + { + "bbox": [ + 47, + 621, + 275, + 634 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(R) \\neq \\operatorname{SCD}(\\bar{R})" + }, + { + "bbox": [ + 47, + 621, + 275, + 634 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": "(b) Let " + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "inline_equation", + "content": "S \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": " consist of " + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "inline_equation", + "content": "m = 4" + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "inline_equation", + "content": "(\\pm 1,0), (0,\\pm 1)" + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": " that are vertices of the square in Fig. 3 (right). The center of mass is " + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "inline_equation", + "content": "0 \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": " and has a distance 1 to each point of " + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 638, + 287, + 675 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "For each 1-point subset " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "A = \\{p\\} \\subset S" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ", the distance matrix " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "D(A \\cup \\{0\\})" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " on two points is the single number 1. The matrix " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "M(S; A \\cup \\{0\\})" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " has " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "m - n + 1 = 3" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " columns. For " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_1 =" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 69, + 544, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 69, + 544, + 108 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 544, + 108 + ], + "type": "text", + "content": "(1,0), we have " + }, + { + "bbox": [ + 306, + 69, + 544, + 108 + ], + "type": "inline_equation", + "content": "M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right)) = \\left( \\begin{array}{ccc} \\sqrt{2} & \\sqrt{2} & 2 \\\\ 1 & 1 & 1 \\\\ - & + & 0 \\end{array} \\right)" + }, + { + "bbox": [ + 306, + 69, + 544, + 108 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": "where the columns are ordered according to " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "p_2 = (0, -1)" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "p_3 = (0, 1)" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "p_4 = (-1, 0)" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": " in Fig. 3 (right). The sign in the bottom right corner is 0 because the points " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "p_1, 0, p_4" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": " are in a straight line. Due to the rotational symmetry, " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "M(S; \\{p_i, 0\\})" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": " is independent of " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "i = 1, 2, 3, 4" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": ". So " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(S)" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": " can be considered as one " + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathrm{OCD} = [1, M(S; \\left( \\begin{array}{c} p_1 \\\\ 0 \\end{array} \\right))]" + }, + { + "bbox": [ + 305, + 108, + 545, + 192 + ], + "type": "text", + "content": " of weight 1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "text", + "content": "Example 4.2(b) illustrates the key discontinuity challenge: if " + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "inline_equation", + "content": "p_4 = (-1,0)" + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "text", + "content": " is perturbed, the corresponding sign can discontinuously change to " + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "inline_equation", + "content": "+1" + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 305, + 195, + 545, + 256 + ], + "type": "text", + "content": ". To get a continuous metric on OCDs, we will multiply each sign by a continuous strength function that vanishes for any zero sign." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": "Definition 4.3 (strength " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": " of a simplex). For a set " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "n + 1" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "q = p_0, p_1, \\ldots, p_n" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "p(A) = \\frac{1}{2} \\sum_{i \\neq j}^{n + 1} |p_i - p_j|" + }, + { + "bbox": [ + 305, + 261, + 545, + 312 + ], + "type": "text", + "content": " be half of the sum of all pairwise distances." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "inline_equation", + "content": "V(A)" + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": " denote the volume the " + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": "-dimensional simplex on the set " + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": ". Define the strength " + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "inline_equation", + "content": "\\sigma(A) = V^2(A) / p^{2n-1}(A)" + }, + { + "bbox": [ + 305, + 312, + 545, + 335 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "inline_equation", + "content": "n = 2" + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": " and a triangle " + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": " with sides " + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "inline_equation", + "content": "a, b, c" + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2" + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": ", Heron's formula gives " + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\sigma(A) = \\frac{(p - a)(p - b)(p - c)}{p^2}" + }, + { + "bbox": [ + 305, + 337, + 545, + 373 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "type": "inline_equation", + "content": "p = \\frac{a + b + c}{2} = p(A)" + }, + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "type": "text", + "content": " is the half-perimeter of " + }, + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 373, + 507, + 396 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "content": " and a set " + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "inline_equation", + "content": "A = p_0, p_1 \\subset \\mathbb{R}" + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "content": ", the volume is " + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "inline_equation", + "content": "V(A) = |p_0 - p_1| = 2p(A)" + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "content": ", so " + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "inline_equation", + "content": "\\sigma(A) = 2|p_0 - p_1|" + }, + { + "bbox": [ + 306, + 399, + 545, + 423 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": "The strength " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " depends only on the distance matrix " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "D(A)" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " from Definition 3.1, so the notation " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " is used only for brevity. In any " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": ", the squared volume " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "V^2(A)" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " is expressed by the Cayley-Menger determinant [60] in pairwise distances between points of " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": ". Importantly, the strength " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " vanishes when the simplex on a set " + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 425, + 545, + 496 + ], + "type": "text", + "content": " degenerates." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": "Theorem 4.7 will need the continuity of " + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "s\\sigma(A)" + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": ", when a sign " + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "s \\in \\{\\pm 1\\}" + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": " from a bottom row of ORD discontinuously changes while passing through a degenerate set " + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": ". The proof of the continuity of " + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": " in Theorem 4.4 gives an explicit upper bound for a Lipschitz constant " + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "inline_equation", + "content": "c_n" + }, + { + "bbox": [ + 305, + 498, + 545, + 559 + ], + "type": "text", + "content": " below." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": "Theorem 4.4 (Lipschitz continuity of the strength " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": "). Let a cloud " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": " be obtained from another " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "(n + 1)" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "A \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": " by perturbing every point within its " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": "-neighborhood. The strength " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": " from Definition 4.3 is Lipschitz continuous so that " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "|\\sigma(A') - \\sigma(A)| \\leq 2\\varepsilon c_n" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": " for a constant " + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "c_n" + }, + { + "bbox": [ + 305, + 563, + 545, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": "Example 4.5 (strength " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": " and its upper bounds). [39, Theorem 4.2] proves upper bounds for the Lipschitz constant of the strength: " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "c_2 = 2\\sqrt{3}" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "c_3 \\approx 0.43" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "c_4 \\approx 0.01" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": ", which quickly tend to 0 due to the 'curse of dimensionality'. The plots in Fig. 4 illustrate that the strength " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": " behaves smoothly in the " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": "-coordinate of a vertex and its derivative " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "|\\frac{\\partial \\sigma}{\\partial x}|" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": " is much smaller than the proved bounds " + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "c_n" + }, + { + "bbox": [ + 305, + 629, + 545, + 715 + ], + "type": "text", + "content": " above." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1280" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 289, + 191 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 289, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 289, + 191 + ], + "type": "image", + "image_path": "6c99299b34d3c32721cc2166ca76bf6ae4ccdfaf9df90f677eef5d5bd951d39f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 191, + 289, + 312 + ], + "blocks": [ + { + "bbox": [ + 49, + 191, + 289, + 312 + ], + "lines": [ + { + "bbox": [ + 49, + 191, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 49, + 191, + 289, + 312 + ], + "type": "image", + "image_path": "1c47d83f32470969c515674c5ca6a2ba65a8e1eb5a3af9109417aa7599fe7ca8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "text", + "content": "Figure 4. The strength " + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "text", + "content": " (solid curve) and its derivative " + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\sigma}{\\partial x}" + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "text", + "content": " (dashed curve) in the " + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "text", + "content": "-coordinate of a point from " + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 319, + 287, + 354 + ], + "type": "text", + "content": " were averaged over 3000 random triangles (top) and tetrahedra (bottom)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "text", + "content": "The strength " + }, + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "inline_equation", + "content": "\\sigma(A)" + }, + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "text", + "content": " from Definition 4.3 will take care of extra signs in ORDs and allows us to prove the analogue of Lemma 3.7 for a similar time complexity with " + }, + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "inline_equation", + "content": "h = n" + }, + { + "bbox": [ + 46, + 373, + 289, + 410 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": "Lemma 4.6 (metric on OCDs). Using the strength " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " from Definition 4.3, we consider the bottleneck distance " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "W_{\\infty}" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " on the set of permutable " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "m - n + 1" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " columns of " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " as on the set of " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "m - n + 1" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " unlabeled points " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "\\left(v, \\frac{s}{c_n} \\sigma(A \\cup \\{0, q\\})\\right) \\in \\mathbb{R}^{n + 1}" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": ". For another " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "\\mathrm{OCD}' = [D(A' \\cup \\{0\\}); M(C'; A' \\cup \\{0\\})]" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " and any permutation " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "\\xi \\in S_{n - 1}" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " of indices " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "1, \\ldots, n - 1" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " acting on " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "D(A \\cup \\{0\\})" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " and the first " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": " rows of " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": ", set " + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "inline_equation", + "content": "d_o(\\xi) = \\max \\{L, W\\}" + }, + { + "bbox": [ + 45, + 415, + 289, + 525 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 530, + 268, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 530, + 268, + 551 + ], + "spans": [ + { + "bbox": [ + 67, + 530, + 268, + 551 + ], + "type": "interline_equation", + "content": "w h e r e L = L _ {\\infty} \\left(\\xi (D (A \\cup \\{0 \\})), D (A ^ {\\prime} \\cup \\{0 \\})\\right),", + "image_path": "835dc489e788fd6c9bd8bb53fc04599cec916fd3d783ddc4f2eccce852235670.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 557, + 272, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 557, + 272, + 578 + ], + "spans": [ + { + "bbox": [ + 61, + 557, + 272, + 578 + ], + "type": "interline_equation", + "content": "W = W _ {\\infty} \\left(\\xi (M (C; A \\cup \\{0 \\})), M (C ^ {\\prime}; A ^ {\\prime} \\cup \\{0 \\})\\right).", + "image_path": "22a25de504b0092f2e8f1932b5e432cda14ae4a6483015e3b9f83bcff1e9f898.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "text", + "content": "Then " + }, + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "inline_equation", + "content": "M_{\\infty}(\\mathrm{OCD}, \\mathrm{OCD}') = \\min_{\\xi \\in S_{n-1}} d_o(\\xi)" + }, + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "text", + "content": " satisfies all metric axioms on Oriented Centered Distributions (OCDs) and is computed in time " + }, + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "inline_equation", + "content": "O((n - 1)! (n^2 + m^{1.5} \\log^n m))" + }, + { + "bbox": [ + 46, + 582, + 287, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": "The coefficient " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\frac{1}{c_n}" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " normalizes the Lipschitz constant " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "c_{n}" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " to 1 in line with changes of distances by at most " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "2\\varepsilon" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " when points are perturbed within their " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": "-neighborhoods. An equality " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C) = \\operatorname{SCD}(C')" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " is interpreted as a bijection between unordered sets " + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C) \\to \\operatorname{SCD}(C')" + }, + { + "bbox": [ + 46, + 629, + 288, + 712 + ], + "type": "text", + "content": " matching all OCDs, which is best detected by checking if metrics in Theorem 4.7 between these SCDs is 0." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "Theorem 4.7 (completeness and continuity of SCD). " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "(\\pmb{a})" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " The Simplexwise Centered Distribution " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " in Definition 4.1 is a complete isometry invariant of clouds " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " unlabeled points with a center of mass at the origin " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "0 \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", and can be computed in time " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "O(m^n / (n - 4)!)" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": "So any clouds " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "C, C' \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " are related by rigid motion (isometry, respectively) if and only if " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C) = \\operatorname{SCD}(C')" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C')" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " or its mirror image " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\overline{\\operatorname{SCD}}(C')" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": ", respectively). For any " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": "-point clouds " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "C, C' \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C')" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " consist of " + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "inline_equation", + "content": "k = \\binom{m}{n-1}" + }, + { + "bbox": [ + 304, + 134, + 547, + 196 + ], + "type": "text", + "content": " OCDs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 198, + 545, + 338 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": "(b) For the " + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": " matrix of costs computed by the metric " + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "inline_equation", + "content": "M_{\\infty}" + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": " between OCDs in " + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C')" + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": ", LAC from Definition 3.8 satisfies all metric axioms on SCDs and needs time " + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "inline_equation", + "content": "O((n - 1)! (n^2 + m^{1.5} \\log^n m) k^2 + k^3 \\log k)" + }, + { + "bbox": [ + 304, + 198, + 545, + 247 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "text", + "content": "(c) Let SCDs have a maximum size " + }, + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "inline_equation", + "content": "l \\leq k" + }, + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "text", + "content": " after collapsing identical OCDs. Then EMD from Definition 3.9 satisfies all metric axioms on SCDs and can be computed in time " + }, + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "inline_equation", + "content": "O((n - 1)! (n^2 + m^{1.5} \\log^n m) l^2 + l^3 \\log l)" + }, + { + "bbox": [ + 304, + 251, + 545, + 299 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": "(d) Let " + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "C'" + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": " be obtained from a cloud " + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": " by perturbing each point within its " + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": "-neighborhood. Then " + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\operatorname{SCD}(C)" + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": " changes by at most " + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "inline_equation", + "content": "2\\varepsilon" + }, + { + "bbox": [ + 304, + 302, + 545, + 338 + ], + "type": "text", + "content": " in the LAC and EMD metrics." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": "If we estimate " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "l \\leq k = \\binom{m}{n-1} = m(m-1) \\ldots (m-n+2)/n!" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "O(m^{n-1}/n!)" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": ", Theorem 4.7(b,c) gives time " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "O(n(m^{n-1}/n!)^3 \\log m)" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": " for metrics on SCDs, which is " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "O(m^3 \\log m)" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "n=2" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "O(m^6 \\log m)" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "inline_equation", + "content": "n=3" + }, + { + "bbox": [ + 305, + 342, + 545, + 393 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": "Though the above time estimates are very rough upper bounds, the time " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "O(m^3 \\log m)" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " is faster than the only past time " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "O(m^5 \\log m)" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": " for comparing " + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 395, + 545, + 443 + ], + "type": "text", + "content": "-point clouds by the Hausdorff distance minimized over isometries [16]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": "Definition 4.8 (Centered Distance Moments CDM). For any " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": "-point cloud " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " be a subset of " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " unordered points. The Centered Interpoint Distance list " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\mathrm{CID}(A)" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " is the increasing list of all " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\frac{(n - 1)(n - 2)}{2}" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " pairwise distances between points of " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": ", followed by " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " increasing distances from " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " to the origin " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "0" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": ". For each column of the " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "(n + 1) \\times (m - n + 1)" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " in Definition 4.1, compute the average of the first " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " distances. Write these averages in increasing order, append the list of increasing distances " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "|q - 0|" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": "-th row of " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": ", and also append the vector of increasing values of " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\frac{s}{c_n} \\sigma(A \\cup \\{0\\})" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " taking signs " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "(n + 1)" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": "-st row of " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "M(C; A \\cup \\{0\\})" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "inline_equation", + "content": "\\vec{M}(C; A) \\in \\mathbb{R}^{3(m - n + 1)}" + }, + { + "bbox": [ + 304, + 447, + 547, + 613 + ], + "type": "text", + "content": " be the final vector." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": "The pair " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "[\\mathrm{CID}(A); \\vec{M}(C; A)]" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " is the Average Centered Vector " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{ACV}(C; A)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " considered as a vector of length " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\frac{n(n-1)}{2} + 3(m-n+1)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": ". The unordered set of " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{ACV}(C; A)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\binom{m}{n-1}" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " unordered subsets " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "A \\subset C" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " is the Average Centered Distribution " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{ACD}(C)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": ". The Centered Distance Moment " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{CDM}(C;l)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": "-th (standardized for " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "l \\geq 3" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": ") moment of " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{ACD}(C)" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " considered as a probability distribution of " + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\binom{m}{n-1}" + }, + { + "bbox": [ + 304, + 615, + 547, + 715 + ], + "type": "text", + "content": " vectors, separately for each coordinate." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "text", + "content": "1281" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "Example 4.9 (CDM for clouds in Fig. 3). (a) For " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "n = 2" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " and the cloud " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "R \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "m = 3" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " vertices " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p_1 = (0,0)" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p_2 = (4,0)" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p_3 = (0,3)" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " of the right-angled triangle in Fig. 3 (middle), we continue Example 4.2(a) and" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 120, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 120, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 45, + 120, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\text{flatten} \\, \\mathrm{OCD}(R; p_1) = [0, \\begin{pmatrix} 4 & 3 \\\\ 4 & 3 \\\\ 0 & 0 \\end{pmatrix}]" + }, + { + "bbox": [ + 45, + 120, + 287, + 156 + ], + "type": "text", + "content": " into the vector" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\operatorname{ACV}(R; p_1) = [0; 3, 4; 3, 4; 0, 0]" + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "content": " of length " + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\frac{n(n-1)}{2} + 3(m-n+1) = 7" + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "content": ", whose four parts " + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "(1+2+2+2=7)" + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "content": " are in increasing order, similarly for " + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "p_2, p_3" + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "content": ". The Average Centered Distribution can be written as a " + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "inline_equation", + "content": "3 \\times 7" + }, + { + "bbox": [ + 45, + 156, + 287, + 205 + ], + "type": "text", + "content": " matrix with unordered" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 203, + 286, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 203, + 286, + 241 + ], + "spans": [ + { + "bbox": [ + 45, + 203, + 286, + 241 + ], + "type": "text", + "content": "rows: " + }, + { + "bbox": [ + 45, + 203, + 286, + 241 + ], + "type": "inline_equation", + "content": "\\operatorname{ACD}(R) = \\left( \\begin{array}{c|cc|cc|cc}0 & 3 & 4 & 3 & 4 & 0 & 0\\\\ 4 & 4 & 5 & 0 & 3 & 0 & -6 / c_2\\\\ 3 & 3 & 5 & 0 & 4 & 0 & 6 / c_2 \\end{array} \\right)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "content": "The area of the triangle on " + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "content": " equals 6 and can be normalized by " + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "inline_equation", + "content": "c_2 = 2\\sqrt{3}" + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "inline_equation", + "content": "6 / c_2 = \\sqrt{3}" + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "content": ", see [39, section 4]. The 1st moment is " + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "inline_equation", + "content": "\\mathrm{CDM}(R;1) = \\frac{1}{3}(7;10,14;3,11;0)" + }, + { + "bbox": [ + 46, + 240, + 286, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "text", + "content": "(b) For " + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "inline_equation", + "content": "n = 2" + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "text", + "content": " and the cloud " + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "inline_equation", + "content": "S \\subset \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "inline_equation", + "content": "m = 4" + }, + { + "bbox": [ + 46, + 284, + 286, + 308 + ], + "type": "text", + "content": " vertices of the square in Fig. 3 (right), Example 4.2(a) com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "type": "text", + "content": "puted " + }, + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "type": "inline_equation", + "content": "\\operatorname {SCD}(R)" + }, + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "type": "text", + "content": " as one OCD " + }, + { + "bbox": [ + 46, + 308, + 286, + 346 + ], + "type": "inline_equation", + "content": "= [1,\\left( \\begin{array}{rrr}\\sqrt{2} & \\sqrt{2} & 2\\\\ 1 & 1 & 1\\\\ - & + & 0 \\end{array} \\right)]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": "which flattens to " + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "inline_equation", + "content": "\\mathrm{ACV} = (1; \\sqrt{2}, \\sqrt{2}, 2; 1, 1, 1; -\\frac{1}{2}, \\frac{1}{2}, 0) = \\mathrm{ACD}(S) = \\mathrm{CDM}(S; 1) \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "inline_equation", + "content": "\\frac{1}{2}" + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": " is the area of the triangle on the vertices " + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "inline_equation", + "content": "(0, 0)" + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "inline_equation", + "content": "(1, 0)" + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "inline_equation", + "content": "(0, 1)" + }, + { + "bbox": [ + 46, + 346, + 286, + 382 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": "Corollary 4.10 (time for continuous metrics on CDMs). For any cloud " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "C \\subset \\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " unlabeled points, the Centered Distance Moment " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "\\mathrm{CDM}(C;l)" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " in Definition 4.8 is computed in time " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "O(m^n /(n - 4)!" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": ". The metric " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " on CDMs needs " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "O(n^{2} + m)" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " time and " + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "inline_equation", + "content": "\\mathrm{EMD}\\bigl (\\mathrm{SCD}(C),\\mathrm{SCD}(C^{\\prime})\\bigr)\\geq |\\mathrm{CDM}(C;1) - \\mathrm{CDM}(C^{\\prime};1)|_{\\infty}" + }, + { + "bbox": [ + 46, + 393, + 286, + 465 + ], + "type": "text", + "content": " holds." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 479, + 282, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 282, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 282, + 493 + ], + "type": "text", + "content": "5. Experiments and discussion of future work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 500, + 286, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 286, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 286, + 583 + ], + "type": "text", + "content": "This paper advocates a scientific approach to any data exemplified by Problem 1.1, where rigid motion on clouds can be replaced by another equivalence of other data. The scientific principles such as axioms should be always respected. Only the first coincidence axiom in (1.1b) guarantees no duplicate data. If the triangle inequality fails with any additive error, results of clustering can be pre-determined [51]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "text", + "content": "The notorious " + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "inline_equation", + "content": "m!" + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "text", + "content": " challenge of " + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "text", + "content": " unlabeled points in Problem 1.1 was solved in " + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 589, + 286, + 636 + ], + "type": "text", + "content": " by Theorem 4.7, also up to rigid motion by using the novel strength of a simplex to smooth signs of determinants due to hard Theorem 4.4." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 641, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 641, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 641, + 286, + 712 + ], + "type": "text", + "content": "The results above sufficiently justify re-focusing future efforts from experimental attempts at Problem 1.1 to higher level tasks such as predicting properties of rigid objects, e.g. crystalline materials, using the complete invariants with no false negatives and no false positives for all possible data since no experiments can beat the proved " + }, + { + "bbox": [ + 45, + 641, + 286, + 712 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 45, + 641, + 286, + 712 + ], + "type": "text", + "content": " guarantee." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "To tackle the limitation of comparing only clouds having a fixed number " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " of points, the Earth Mover's Distance (EMD) continuously can compare any distributions (SDD or SCD) of different sizes. Using EMD instead of the bottleneck distance " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "W_{\\infty}" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "m - h" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "m - n + 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": ") columns of matrices in Definitions 3.3 and 4.1 increases a time from " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "O(m^{1.5}\\log m)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "O(m^3\\log m)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " but the total time remains the same due to a near cubic time in the last step." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": "The running time in real applications is smaller for several reasons. First, the shape (isometry class) of any rigid body in " + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": " is determined by only " + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "inline_equation", + "content": "m = 4" + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": " labeled points in general position. Even when points are unlabeled, dozens of corners or feature points suffice to represent a rigid shape well enough. Second, the key size " + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": " (number of distinct Oriented Centered Distributions) in Theorem 4.7 is often smaller than " + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": ", especially for symmetric objects, see " + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "inline_equation", + "content": "l = 1 < m = 4" + }, + { + "bbox": [ + 304, + 171, + 545, + 291 + ], + "type": "text", + "content": " in Example 4.2. The SCD invariants are on top of others due to their completeness and continuity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "text", + "content": "The past work [71, 73] used the simpler Pointwise Distance Distribution (PDD) to complete " + }, + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "inline_equation", + "content": "200\\mathrm{B}+" + }, + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "text", + "content": " pairwise comparisons of all " + }, + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "inline_equation", + "content": "660\\mathrm{K}+" + }, + { + "bbox": [ + 304, + 294, + 545, + 402 + ], + "type": "text", + "content": " periodic crystals in the world's largest database of real materials. This experiment took only a couple of days on a modest desktop and established the Crystal Isometry Principle saying that any real periodic crystal is uniquely determined by the geometry of its atomic centers without chemical elements. So the type of any atom is provably reconstructable from distances to atomic neighbors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "text", + "content": "The new invariants allow us to go deeper and compare atomic clouds from higher level periodic crystals. Fig. 5 visualizes all " + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "inline_equation", + "content": "300\\mathrm{K}+" + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "text", + "content": " atomic clouds extracted from all " + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "inline_equation", + "content": "10\\mathrm{K}+" + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "text", + "content": " crystalline drugs in the Cambridge Structural Database (CSD) by using SDV invariants for " + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "inline_equation", + "content": "5 + 1" + }, + { + "bbox": [ + 304, + 405, + 545, + 476 + ], + "type": "text", + "content": " atoms including the central one. Future maps will use stronger invariants." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 318, + 487, + 545, + 607 + ], + "blocks": [ + { + "bbox": [ + 318, + 487, + 545, + 607 + ], + "lines": [ + { + "bbox": [ + 318, + 487, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 318, + 487, + 545, + 607 + ], + "type": "image", + "image_path": "2315396e036fee7189c52ed0d76368eb2534de7f0d5d3114caf18042071517b1.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "lines": [ + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "spans": [ + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "type": "text", + "content": "Figure 5. Two principal directions of SDVs for all " + }, + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "type": "inline_equation", + "content": "300\\mathrm{K}+" + }, + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "type": "text", + "content": " atomic clouds from all " + }, + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "type": "inline_equation", + "content": "10\\mathrm{K}+" + }, + { + "bbox": [ + 305, + 614, + 544, + 636 + ], + "type": "text", + "content": " drugs in the CSD, colored by 25 elements." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "This research was supported by the Royal Academy Engineering fellowship IF2122/186, and EPSRC grants EP/R018472/1, EP/X018474/1. 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Given videos of a deformable category and a skeleton, we reconstruct an animatable 3D model that factorizes variations across instances (e.g., cheetah's and sphynx's are both cats but with different shape morphology, skeleton dimensions, and texture) from time-specific variations within an instance (e.g., skeleton articulations and elastic shape deformation). Left: Input videos; Middle-left: 3D shape, skeleton, and skinning weights (visualized as surface colors) in the canonical space; Middle-right: Disentangled between-instance and within-instance variations over time. Right: Morphology and motion transferred across the two instances." + ], + "image_footnote": [], + "bbox": [ + 88, + 247, + 890, + 373 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 482, + 313, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building animatable 3D models is challenging due to the need for 3D scans, laborious registration, and rigging. Recently, differentiable rendering provides a pathway to obtain high-quality 3D models from monocular videos, but these are limited to rigid categories or single instances. We present RAC, a method to build category-level 3D models from monocular videos, disentangling variations over instances and motion over time. Three key ideas are introduced to solve this problem: (1) specializing a category-level skeleton to instances, (2) a method for latent space regularization that encourages shared structure across a category while maintaining instance details, and (3) using 3D background models to disentangle objects from the background. We build 3D models for humans, cats and dogs given monocular videos. Project page: https://gengshany.github.io/rac-www/.", + "bbox": [ + 73, + 513, + 470, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 785, + 209, + 800 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We aim to build animatable 3D models for deformable object categories. Prior work has done so for targeted categories such as people (e.g., SMPL [1, 30]) and quadruped animals (e.g., SMAL [4]), but such methods appear challenging to scale due to the need of 3D supervision and registration. Recently, test-time optimization through differ", + "bbox": [ + 75, + 811, + 468, + 905 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "entiable rendering [40, 41, 44, 56, 69] provides a pathway to generate high-quality 3D models of deformable objects and scenes from monocular videos. However, such models are typically built independently for each object instance or scene. In contrast, we would like to build category models that can generate different instances along with deformations, given causally-captured video collections.", + "bbox": [ + 496, + 483, + 892, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Though scalable, such data is challenging to leverage in practice. One challenge is how to learn the morphological variation of instances within a category. For example, huskys and corgis are both dogs, but have different body shapes, skeleton dimensions, and texture appearance. Such variations are difficult to disentangle from the variations within a single instance, e.g., as a dog articulates, stretches its muscles, and even moves into different illumination conditions. Approaches for disentangling such factors require enormous efforts in capture and registration [1, 5], and doing so without explicit supervision remains an open challenge.", + "bbox": [ + 496, + 594, + 893, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another challenge arises from the impoverished nature of in-the-wild videos: objects are often partially observable at a limited number of viewpoints, and input signals such as segmentation masks can be inaccurate for such \"in-the-wild\" data. When dealing with partial or impoverished video inputs, one would want the model to listen to the common structures learned across a category - e.g., dogs have two ears. On the other hand, one would want the model to", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16995", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/521d8f830e1715dd9cd836701a97296d0d2a7360609c12335a0dd98cf4696236.jpg", + "image_caption": [ + "Figure 2. Disentangling morphologies $\\beta$ and articulation $\\theta$ . We show different morphologies (body shape and clothing) given the same rest pose (top) and bouncing pose (bottom)." + ], + "image_footnote": [], + "bbox": [ + 88, + 98, + 885, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "stay faithful to the input views.", + "bbox": [ + 76, + 309, + 282, + 323 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach addresses these challenges by exploiting three insights: (1) We learn skeletons with constant bone lengths within a video, allowing for better disentanglement of between-instance morphology and within-instance articulation. (2) We regularize the unobserved body parts to be coherent across instances while remaining faithful to the input views with a novel code-swapping technique. (3) We make use of a category-level background model that, while not 3D accurate, produces far better segmentation masks. We learn animatable 3D models of cats, dogs, and humans which outperform prior art. Because our models register different instances with a canonical skeleton, we also demonstrate motion transfer across instances.", + "bbox": [ + 75, + 325, + 470, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 539, + 225, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-based 3D Reconstruction. A large body of work in 3D human and animal reconstruction uses parametric shape models [30, 42, 55, 61, 73, 74], which are built from registered 3D scans of human or animals, and serve to recover 3D shapes given a single image or video at test time [2, 3, 3, 21, 21, 46, 72]. A recent research focus is to combine statistical human body mode with implicit functions [17, 25, 47-49, 63, 71] to improve the robustness and fidelity of the reconstruction. Although parametric body models achieve great success in reconstructing humans with large amounts of ground-truth 3D data, it is unclear how to apply the same methodology to categories with limited 3D data, such as animals, and how to scale to real-life imagery with diverse clothing and body poses. RAC builds category-level shape models from in-the-wild videos and demonstrates the potential to reconstruct 3D categories without sophisticated manual processing.", + "bbox": [ + 75, + 566, + 468, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Category Reconstruction from Image Collections. A number of recent methods build deformable 3D models of object categories from images with weak 2D annotations, such as keypoints and object silhouettes, obtained from human annotators or predicted by off-the-shelf mod", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "els [13, 18, 22, 28, 53, 59, 70]. However, those methods do not distinguish between morphological variations and motion over time. Moreover, they often apply heavy regularization on shape and deformation to avoid degenerate solutions, which also smooths out fine-grained details. Recent research combines neural implicit functions [33, 34] with category modeling in the context of 3D data generation [6, 7, 37], where shape and appearance variations over a category are modeled with conditional NeRFs. However, reconstructions are typically focused on near-rigid objects such as faces and vehicles.", + "bbox": [ + 496, + 308, + 892, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Articulated Object Reconstruction from Videos. Compared to image collections, videos provide signals to reconstruct object motions and disentangle them from morphological variations. Some works [26, 39, 51] reconstruct articulated bodies from videos, but they either assume synchronized multi-view recordings or articulated 3D skeleton inputs that make their approaches less general. Some other works [67-69] learn animatable 3D models from monocular videos capturing the same object instance, without disentangling morphology and motion. There are recent methods [27, 58, 68] using in-the-wild videos to reconstruct 3D models animals, but their quality are relatively low.", + "bbox": [ + 496, + 474, + 893, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 672, + 589, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given video recordings of different instances from a category and a pre-defined skeleton, we build animatable 3D models including instance-specific morphology (Sec. 3.1), time-varying articulation and deformation (Sec. 3.2), as well as a video-specific 3D background model (Sec. 3.3). The models are optimized using differentiable rendering (Sec. 3.4). An overview is shown in Fig. 3.", + "bbox": [ + 496, + 698, + 890, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Between-Instance Variation", + "text_level": 1, + "bbox": [ + 500, + 816, + 748, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fusing videos of different instances into a category model requires handling the morphological variations, which includes the changes in both internal skeleton and outward appearance (shape and color). We define a video-", + "bbox": [ + 496, + 840, + 892, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16996", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/901ce8519be8cfbf8e05ce8c7bc871bc8e342b183120adad36c86863e33e31c1.jpg", + "image_caption": [ + "Figure 3. Morphological variations vs time-varying articulation and deformation. (a) Canonical shape $\\mathbf{T}$ , skinning weights $\\mathbf{W}$ , and joint locations $\\mathbf{J}$ . (b) To represent morphological differences between instances, we use a morphology code $\\beta$ that specifies instance shape and appearance $\\mathbf{T}_{\\beta}$ , skinning weights $\\mathbf{W}_{\\beta}$ for a canonical skeleton $\\mathbf{J}$ . (c) $\\beta$ also predicts a change in bone lengths $\\Delta \\mathbf{J}_{\\beta}$ which further stretches instance shape into $\\mathbf{T}_{\\beta}^{s}$ by elongating body parts. (d) Time-varying articulations are modeled with an articulation vector $\\theta$ by linearly blending rigid bone transformations in the dual quaternion space. Time-varying deformations (such as muscle deformation) are modeled with a deformation vector $\\omega_{d}$ through invertible 3D warping fields." + ], + "image_footnote": [], + "bbox": [ + 86, + 94, + 872, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "specific morphology code $\\beta$ to control the variations of both the shape and the skeleton.", + "bbox": [ + 75, + 313, + 468, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To model between-instance shape variations, one could use dense warping fields to deform a canonical template into instance-specific shapes [62]. However, warping fields cannot explain topological changes (e.g., different clothing). Instead, we define a hierarchical representation: a conditional canonical field [8, 41, 57] to handle fine-grained variations over a category (e.g., the ears of dogs) and a stretchable bone model [14, 60] to represent coarse shape variations (e.g., height and size of body parts).", + "bbox": [ + 75, + 344, + 468, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conditional Field T. In the canonical space, a 3D point $\\mathbf{X} \\in \\mathbb{R}^3$ is associated with three properties: signed distance $d \\in \\mathbb{R}$ , color $\\mathbf{c} \\in \\mathbb{R}^3$ , and canonical features $\\psi \\in \\mathbb{R}^{16}$ , which is used to register pixel observations to the canonical space [35,68]. These properties are predicted by multi-layer perceptron (MLP) networks:", + "bbox": [ + 76, + 479, + 470, + 570 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left(d, \\mathbf {c} ^ {t}\\right) = \\mathbf {M L P} _ {\\mathrm {S D F}} \\left(\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\omega} _ {a}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 579, + 468, + 595 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\psi = \\mathbf {M L P} _ {\\psi} (\\mathbf {X}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 599, + 468, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the shape and color are conditioned on a videospecific morphology code $\\beta \\in \\mathbb{R}^{32}$ [16, 37]. We further ask the color to be dependent on an appearance code $\\omega_{a}\\in \\mathbb{R}^{64}$ that captures frame-specific appearance such as shadows and illumination changes [32].", + "bbox": [ + 75, + 625, + 468, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Skeleton J. Unlike shape and color, the bone structures are not directly observable from imagery, making it ambiguous to infer. Methods for automatic skeletal rigging [23, 38, 65] either heavily rely on shape priors, or appear sensitive to input data. Instead, we provide a category-level skeleton topology, which has a fixed tree topology with $(\\mathrm{B} + 1)$ bones and B joints (B=25 for quadruped and B=18 for human). To model cross-instance morphological changes, we define per-instance joint locations as:", + "bbox": [ + 75, + 699, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {J} = \\mathbf {M L P} _ {\\mathbf {J}} (\\beta) \\in \\mathbb {R} ^ {3 \\times B}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 843, + 468, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As we will discuss next, the change in joint locations not only stretches the skeleton, but also results in the elongation", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of canonical shapes as shown in Fig. 3 (c). The skeleton topology is fixed through optimization but $\\mathbf{J}$ is specialized to each video.", + "bbox": [ + 496, + 313, + 890, + 357 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "**Skinning Field W.** For a given 3D location $\\mathbf{X}$ , we define skinning weight vector $\\mathbf{W} \\in \\mathbb{R}^{B + 1}$ following BANMo:", + "bbox": [ + 496, + 358, + 890, + 390 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} = \\sigma_ {\\text {s o f t m a x}} \\left(d _ {\\sigma} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta}) + \\mathbf {M L P} _ {\\mathbf {W}} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta})\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 410, + 890, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\theta$ is a articulation code and $d_{\\sigma}(\\mathbf{X},\\boldsymbol {\\beta},\\boldsymbol {\\theta})$ is the Mahalanobis distance between $\\mathbf{X}$ and Gaussian bones under articulation $\\pmb{\\theta}$ and morphology $\\beta$ , refined by a delta skinning MLP. Each Gaussian bone has three parameters for center, orientation, and scale respectively, where the centers are computed as the midpoint of two adjacent joints, the orientations are determined by the parent joints, and the scales are optimized.", + "bbox": [ + 496, + 433, + 890, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stretchable Bone Deformation. To represent variations of body dimension and part size, prior work [30, 74] learns a PCA basis from registered 3D scans. Since 3D registrations are not available for in-the-wild videos, we optimize a parametric model through differentiable rendering. Given the stretched joint locations, the model deforms the canonical shape $\\mathbf{T}_{\\beta}$ with blend skinning equations,", + "bbox": [ + 496, + 554, + 890, + 660 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {T} _ {\\beta} ^ {s} = \\left(\\mathbf {W} _ {\\beta} \\mathbf {G} _ {\\beta}\\right) \\mathbf {T} _ {\\beta}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 666, + 890, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{G}_{\\beta}$ transforms the bone coordinates, and $\\mathbf{W}_{\\beta}$ is the instance-specific skinning weights in Eq. (4).", + "bbox": [ + 496, + 688, + 890, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Within-Instance Variation", + "text_level": 1, + "bbox": [ + 500, + 726, + 736, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We represent within-instance variations as time-varying warp fields between the canonical space and posed space at time $t$ . Similar to HumanNeRF [57], we decompose motion as articulations that explains the near-rigid component (e.g., skeletal motion) and deformation that explains the remaining nonrigid movements (e.g., cloth deformation). Note given the complexity of body movements, it is almost certain the pre-defined skeleton would ignore certain movable body parts. Adding deformation is crucial to achieving high-fidelity reconstruction.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16997", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/66bdc7596c30f6829c9ace97837a1c01556eb74e477244a33baaa4b77a7690aa.jpg", + "image_caption": [ + "Figure 4. Different $\\beta$ morphologies of dogs (top) and cats (bottom). Our reconstructions show variance in ear shape and limb size over dog breeds, as well as variance in limb and body size over cat breeds." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 890, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Time-varying Articulation. To model the time-varying skeletal movements, we define per-frame joint angles:", + "bbox": [ + 76, + 253, + 468, + 285 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {M L P} _ {\\mathbf {A}} (\\boldsymbol {\\theta}) \\in \\mathbb {R} ^ {3 \\times B} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 289, + 468, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta \\in \\mathbb{R}^{16}$ is a low-dimensional articulation parameter, and each joint has three degrees of freedom. Given joint angles and the per-video joint locations, we compute bone transformations $\\mathbf{G} \\in \\mathbb{R}^{3 \\times 4 \\times B}$ via forward kinematics. We apply dual quaternion blend skinning (DQB) [19] to get the warping field for each spatial point,", + "bbox": [ + 75, + 313, + 468, + 404 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} (\\boldsymbol {\\beta}, \\theta) = \\left(\\mathbf {W} _ {\\boldsymbol {\\beta}} \\mathbf {G}\\right) \\mathbf {T} _ {\\boldsymbol {\\beta}} ^ {s}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 410, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dual quaternion skinning blends SE(3) transformations in dual quaternion space and ensures valid SE(3) after blending, which reduces artifacts around twisted body parts. Note stretching in Eq. (5) can be fused with articulation as a single blend skinning operation.", + "bbox": [ + 75, + 433, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Time-varying Soft Deformation. To further explain the dynamics induced by non-skeleton movements (such as the cat belly and human clothes), we add a neural deformation field [24, 40] $\\mathcal{D}(\\cdot)$ that is flexible enough to model highly nonrigid deformation. Applying the fine-grained warping after blend skinning, we have", + "bbox": [ + 75, + 508, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) = \\mathcal {D} (\\mathbf {D} (\\boldsymbol {\\beta}, \\theta), \\omega_ {d}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 606, + 468, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\omega_{d}$ is a frame-specific deformation code. Inspired by CaDeX [24], we use real-NVP [9] to ensure the 3D deformation fields are invertible by construction.", + "bbox": [ + 75, + 628, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Invertibility of 3D Warping Fields. For a given time instance $t$ , we have defined a forward warping field $\\mathcal{W}^{t,\\rightarrow}$ that transforms 3D points from the canonical space to the specified time instance, and a backward warping field $\\mathcal{W}^{t,\\leftarrow}$ to transform points in the inverse direction. Both warping fields include stretching (Eq. (5)), articulation. (Eq. (7)), and deformation (Eq. (8)) operations. Notably, we only need to define each operation in the forward warping fields. The deformation operation is, by construction, invertible. To invert stretching and articulation, we invert SE (3) transformations $\\mathbf{G}$ in the blend skinning equations and compute the skinning weights with Eq. (4) using the corresponding morphology and articulation codes. A 3D cycle loss is used to ensure that the warping fields are self-consistent after a forward-backward cycle [29, 69].", + "bbox": [ + 75, + 674, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Scene Model", + "text_level": 1, + "bbox": [ + 500, + 253, + 633, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reconstructing objects from in-the-wild video footage is challenging due to failures in segmentation, which is often caused by out-of-frame body parts, occlusions, and challenging lighting. Inspired by background subtraction [15, 50], we build a model of the background to robustify our method against inaccurate object segmentation.", + "bbox": [ + 496, + 277, + 890, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In background subtraction, moving objects can be segmented by comparing input images to a background model (e.g., a median image). We generalize this idea to model the background scene in 3D as a per-video NeRF, which can be rendered as color pixels at a moving camera frame and compared to the input frame. We design a conditional background model that generates density and color of a scene conditioned on a per-video background code $\\gamma$ :", + "bbox": [ + 496, + 369, + 892, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(\\sigma , \\mathbf {c} ^ {t}) = \\mathbf {M L P} _ {\\mathbf {b g}} (\\mathbf {X}, \\mathbf {v}, \\gamma), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 502, + 890, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{v}$ is the viewing direction. To render images, we compose the density and color of the object field and the background NeRF in the view space [37], and compute the expected color and optical flow. Background modeling and composite rendering allows us to remove the object silhouette loss, and improves the quality of results. Interestingly, we find that even coarse geometric reconstructions of the background still can improve the rendered 2D object silhouette, which in turn is useful for improving the quality of object reconstructions (Fig. 5). We ablate the design choice in Tab. 1.", + "bbox": [ + 496, + 532, + 892, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Losses and Regularization", + "text_level": 1, + "bbox": [ + 500, + 709, + 736, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the videos and a predefined skeleton, we optimize the parameters discussed above: (1) canonical parameters $\\{\\beta ,\\mathbf{J},\\mathbf{T},\\mathbf{W}\\}$ including per-video morphology codes and canonical templates; (2) motion parameters $\\{\\theta ,\\omega_{\\mathrm{d}},\\mathbf{A},\\mathbf{D}\\}$ including per-frame codes as well as articulation and soft deformation MLPs. (3) background parameters $\\{\\gamma ,\\mathbf{B}\\}$ including video background codes and a background NeRF. The overall objective function contains a image reconstruction loss term and regularization terms.", + "bbox": [ + 496, + 733, + 890, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reconstruction Losses. The reconstruction loss is defined as the difference between rendered and observed images,", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16998", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5967c2a979763aec1857e1d2fe04cc0add0d83358f3a59bd1f0081cc32c359e7.jpg", + "image_caption": [ + "Figure 5. Joint foreground and background reconstruction. We jointly reconstruct objects and their background, while refining the segmentation. Note the input silhouette is noisy (e.g., tail was not segmented), and background modeling helps produce an accurate refined silhouette. As a result, RAC is robust to inaccurate segmentation (e.g., tail movements marked by the red box)." + ], + "image_footnote": [], + "bbox": [ + 80, + 103, + 467, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "including object silhouette, color, flow, and features:", + "bbox": [ + 76, + 481, + 423, + 498 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {s i l}} + \\mathcal {L} _ {\\mathrm {r g b}} + \\mathcal {L} _ {\\mathrm {O F}} + \\mathcal {L} _ {\\text {f e a t}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 508, + 468, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We update the model parameter by minimizing $\\mathcal{L}$ through differentiable volume rendering in the same way as BANMo [69]. Off-the-shelf estimates of object silhouettes are used as supervision to kick-start the optimization. Then the weight of silhouette term is set to 0 after several iterations of optimization, while composite rendering of foreground and background itself is capable of separating the object and the non-object components.", + "bbox": [ + 75, + 537, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Morphology Code $(\\beta)$ Regularization. Existing differentiable rendering methods are able to faithfully reconstruct the input view but not able to hallucinate a reasonable solution for occluded body parts [40, 69]. See Fig. 9 for an example. One solution is to regularize the instance-specific morphology code $\\beta$ to be consistent with the body shapes observed in other videos. Traditional approaches might do this by adding variational noise (as in a VAE) or adversarial losses (as in a GAN). We found good results with the following easy-to-implement approach: we randomly swap the morphology code $\\beta$ of two videos during optimization; this regularizes the model to effectively learn a single morphology code that works well across all videos. But naively applying this approach would produce a single morphology that would not specialize to each object instance. To enable specialization, we gradually decrease the probability", + "bbox": [ + 75, + 659, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative results on AMA sequences. 3D Chamfer distance $(\\mathrm{cm},\\downarrow)$ and F-score $(\\% ,\\uparrow)$ averaged over all frames. Our model is trained on 47 human videos spanning existing human datasets (as described in Sec.4.2); we also train BANMo on the same set. Other baselines are trained on 3D human data and relies on SMPL model. Results with $^S$ indicates variants trained on single instances. Our model outperforms prior works.", + "bbox": [ + 498, + 88, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/821a5d980aeb00f43c2e92ab76df054bdf160cd7f542a08f1f5a50166dcf09fa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodsambabouncing
CDF@2%F@5%CDF@2%F@5
HuMoR9.847.583.711.545.282.3
ICON10.139.985.29.753.586.4
\\( BANMo^S \\)8.062.289.17.664.791.1
BANMo9.354.485.510.254.486.5
\\( RACS \\)6.470.993.26.966.792.8
RAC6.072.594.48.063.891.4
w/o skeleton8.659.687.79.359.587.8
w/o \\( \\beta \\)8.558.987.58.462.590.6
\\( \\beta swap\\rightarrow ||\\beta||_2^2 \\)6.569.093.88.064.891.3
+ bkgd NeRF6.370.993.77.465.591.8
", + "bbox": [ + 501, + 196, + 888, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of swaps during the optimization, from $\\mathcal{P} = 1.0\\to 0.05$", + "bbox": [ + 498, + 396, + 877, + 410 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Joint J Regularization. Due to the non-observable nature of the joint locations, there might exist multiple joint configurations leading to similar reconstruction error. To register the skeleton with the canonical shape, we minimize Sinkhorn divergence [11] between the canonical surface $\\mathbf{T}_{\\beta}$ and the joint locations $\\mathbf{J}_{\\beta}$ , which forces them to occupy the same space. We extract the canonical mesh with marching cubes [31] as a proxy of the canonical surface. Sinkhorn distance interpolates between Wasserstein and kernel distances and defines a soft way to measure the distance between shapes with different density distributions.", + "bbox": [ + 496, + 411, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Soft Deformation Regularization The soft deformation field has the capacity of explaining not only the soft deformations, but also the skeleton articulations. Therefore, we penalize the L2 norm of the soft deformation vectors at randomly sampled morphology and articulations,", + "bbox": [ + 496, + 577, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s o f t}} = \\left\\| \\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) - \\mathbf {D} (\\boldsymbol {\\beta}, \\theta) \\right\\|. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 665, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 708, + 633, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We build RAC on BANMo and compute bone transformations from a kinematic tree. The soft deformation field follows CaDeX, where we find that two invertible blocks are capable of handling moderate deformations. To evaluate surface reconstruction accuracy, we extract the canonical mesh $\\mathbf{T}$ by finding the zero-level set of SDF with marching cubes on a $256^3$ grid. To get the shape at a specific time, the canonical mesh is forward-warmed with $\\mathcal{W}^{t,\\rightarrow}$ .", + "bbox": [ + 496, + 733, + 890, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization Details We use AdamW to optimize the model for 36k iterations with 16384 rays per batch (taking", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16999", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cdc65e3af494bf348565670417375061d2280e813346a4904f7d1baa6f844bfb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 91, + 99, + 202, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a2f12a939bc2dc3176250c1cf114e080065aa9891cdf15d1f381ed502a81bd2f.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 91, + 191, + 202, + 286 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c0aa60e64edd177a6d15578e873f206b5da6ea348b5a320dbd231dec7651011e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 114, + 377, + 189 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fcdb658186a022c24e98e736f229749e420daaee973f9281a33394134adbb80f.jpg", + "image_caption": [ + "Humor" + ], + "image_footnote": [], + "bbox": [ + 225, + 196, + 377, + 280 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/24d9bc05de90080fc41d34e0f5e416541cfd26b5b32dbf3cd1c27771a2a90573.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 388, + 104, + 537, + 188 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/957528914f77a0e93ebf91d5876117296deebb9703fe77f594d11ac3a79d0854.jpg", + "image_caption": [ + "ICON" + ], + "image_footnote": [], + "bbox": [ + 385, + 193, + 519, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e0d443b62a43d6f1431b1ed587fc5d4fcc72716bf6fc5c768e7d62bd5c60a725.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 553, + 102, + 709, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9a981709050b626273d5f57acff29d27031840d8197c440f383d99e92aba4d37.jpg", + "image_caption": [ + "BANMo" + ], + "image_footnote": [], + "bbox": [ + 570, + 193, + 691, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/31a17709cb3dc9c79dce6796b1805d0c614f83b6e982aa179ff8369e148b85aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 102, + 885, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e81229935615306865d679284d6bee2dc6083d779ad9091cf254c104ad4ea7bf.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 728, + 193, + 859, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/10b2cd81e1b3901a192a58d156ab6625b71b8ed3d3199bcec3ce58484f2be133.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 319, + 153, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1e26fddb52eefe34c0b6f52a2a2aca1a83a3daf5b5834302f1a730a5e6a71e64.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 84, + 361, + 153, + 402 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8b1e70b98264f69628f5156ba985fd3e1bfffd8c6c45ae150cd6c7b1a90ea885.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 156, + 318, + 218, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/daa0c32ce95a72c7735fee04272219b53d217c966f778684f7540b5fad104f87.jpg", + "image_caption": [ + "BARC" + ], + "image_footnote": [], + "bbox": [ + 169, + 369, + 207, + 401 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c547e3eeb2834f6a53d914a1d405ef9b909190f619ec78bea4290aa07974eea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 228, + 319, + 264, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5a110603b6180f4280f9581d101a989b1c79e49b4d691d345ee03b31cb47b872.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison. We compare with BANMo and model-based methods (HuMoR, ICON, BARC). Top: human reconstruction on (AMA). Bottom: dogs and cats reconstruction on internet videos." + ], + "image_footnote": [], + "bbox": [ + 220, + 369, + 272, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BARC", + "bbox": [ + 199, + 411, + 238, + 422 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/df3ae3f3a34afb426c90f8f78fb0d1b5f47a1f5a60e2fbb12ba36c0d74e3d3b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 319, + 352, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a9fc89922d0f58bacdac474ebf030fe018827329c73ca1de0b1b260da981074.jpg", + "image_caption": [ + "BANMo" + ], + "image_footnote": [], + "bbox": [ + 307, + 364, + 338, + 402 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/37d41583f80b545900de0ac932666ec6888b18593cf077518cbd9b363c51fc9b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 319, + 403, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/698493caf8c288090f03f2fc87a987fb7954e21d753f2b90512b430da5020173.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 364, + 408, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ours", + "bbox": [ + 465, + 411, + 495, + 422 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7868af2d919e8ddc269c2afddee9172a92c8cc6d8ae77b7866cbb81180975975.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 318, + 480, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/115b075bd39dcfdd7b7ab5a8af218099d1b860c6600119c775572d986bbfaf42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 436, + 364, + 462, + 404 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5be084b54e749e47b3e3a82193fe47a36c8fbd92fbab24749ce76063f4ac6645.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 319, + 529, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fdc3c0f9ab01e113cb053370ea28ce427de17bc4f6787ca6425979db49ad76cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 364, + 537, + 405 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ours", + "bbox": [ + 465, + 411, + 495, + 422 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06027588513cb0d16c863c9c62897c48a1954f938cbd1c40d9586ce8059e1713.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 547, + 318, + 622, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/882909f6fb0f49438db7e1d79c13cec9a0099088d74544ef6000020a1acb84f1.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 560, + 364, + 609, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/14fb9cedeebde41cdd01a0b268a8d253ae38c5ac2603bcb5e64a186b30ace90b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 319, + 700, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/63790c13868d0f3ed103941f144dea5f06ce432b027a2ffc6383cd362b0e5cce.jpg", + "image_caption": [ + "BANMo" + ], + "image_footnote": [], + "bbox": [ + 650, + 364, + 753, + 404 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1bf3d636af67d31cfe7c72f1bd8e8e461030b1a882a666247adc043fb805e048.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 318, + 862, + 357 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/29c27978c9c9e221a5a87bb0b9e50d01fd107094c3b4f53ab6dc3d564489ff8d.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 769, + 363, + 874, + 404 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "around 24 hours on 8 RTX-3090 GPUs). We fist pre-train the background model with RGB, optical flow, and surface normal losses while ignoring foreground pixels. Then we combine background models with the object model for composite rendering optimization. The weights for the loss terms are tuned to have similar initial magnitude. The object root poses are initialized with single-image viewpoint networks trained for humans and quadruped animals following BANMo [69]. For all categories, we start with the same shape (a unit sphere) and a known skeleton topology. Both the shape and the joint locations are specialized to the input dataset, as shown in Fig. 7.", + "bbox": [ + 75, + 477, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Reconstructing Humans", + "text_level": 1, + "bbox": [ + 76, + 665, + 302, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We combine existing human datasets, including AMA, MonoPerfCap, DAVIS, and BANMo to get 47 human videos with 6,382 images [43, 54, 64]. AMA contains multi-view videos, but we treat them as monocular videos and do not use the time-synchronization or camera extrinsics. During preprocessing, we use PointRend [20] to extract object segmentation, CSE [36] for pixel features, VCN-robust [66] for optical flow, and omnidata [10] for surface normal estimation.", + "bbox": [ + 75, + 689, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We use AMA for evaluation since it contains ground-truth meshes and follow BANMo to compute both Chamfer distances and F-scores. Chamfer distance computes the average distance between the ground-truth and the estimated surface points by finding the nearest-neighbor", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/59afb268b8bb6fcca7f65471eb6d5b9bdc01256790957d79e7133c011b946ddc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 477, + 566, + 518 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7675815efc7501591ba6194488a6812a33f7ee65c282d864eb8dfc95c81d7a27.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 598, + 486, + 671, + 521 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f28bccb06acef71e26f2b3a7eb21d014d86d768058e8a676c312dca25eebaadb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 481, + 800, + 537 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a9129d53ae6c463b535c392f29f0b25e22085343c75547ab7c7a829def829c2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 813, + 492, + 890, + 534 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c434c3f53ee18dea123ae3900576595ba2aea9f1afdfd26f220611738231173.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 542, + 562, + 582 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/51057911ddf72d044b0a54edb5d382307267703d7b9ea50b52554cf92e781d24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 551, + 666, + 583 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b24a3a4e61988364280aee5fe31a818561fb1145ee5fdfdcc9410cc9e02ce4cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 547, + 810, + 599 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2fb586c70f55ed14e6a705fe5fad26309fa7a0f8a301177ea969541a84ca1187.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 816, + 555, + 890, + 597 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89a2a1027eae31651f7783a1800ea751907de00fa9fb377c27b0e38e963bc58a.jpg", + "image_caption": [ + "Initial Shape and Skeleton" + ], + "image_footnote": [], + "bbox": [ + 511, + 609, + 578, + 662 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/791f680bd2681693c12e1ef2438c9887eb0b53e2e16c1152980ca9521a2fac2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 599, + 621, + 656, + 662 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6595551257b1e1c04a71425d5a51256285c42c2759ac60efbeabe73dd81d84a7.jpg", + "image_caption": [ + "Final Shape and Skeleton (mean morphology)" + ], + "image_footnote": [], + "bbox": [ + 707, + 608, + 785, + 681 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/419600c37175505e55fb96a9e5cdf055c476c60bad98615fb6cbef6cb0c3084d.jpg", + "image_caption": [ + "Figure 7. Shape and skeleton optimization. From top to bottom, we visualize the canonical shape and skeleton of our dog, cat, and human models. Left: Canonical shape and skeleton before optimization. Right: Canonical shape and skeleton after optimization." + ], + "image_footnote": [], + "bbox": [ + 816, + 623, + 874, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "matches, but it is sensitive to outliers. F-score at distance thresholds $d \\in \\{1\\%, 2\\%, 5\\% \\}$ of the human bounding box size [52] provides a more informative quantification of surface reconstruction error at different granularity. To account for the unknown scale, we align the predicted mesh with the ground-truth mesh using their depth in the view space.", + "bbox": [ + 496, + 779, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. On AMA, we compare with template-free BANMo [69] and model-based methods, including Hu", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17000", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MoR [45] and ICON [63]. BANMo reconstructs an animatable 3D model from multiple monocular videos of the same instance, powered by differentiable rendering optimization. We optimize BANMo on the same dataset with the same amount of computation and iterations as ours. HuMoR is a temporal pose and shape predictor for humans. It performs test-time optimization on video sequences leveraging OpenPose keypoint detection and motion priors trained on large-scale human motion capture dataset. We run it on each video sequence, and processing 170 video frames takes around two hours on a machine with Titan-X GPU. ICON is the recent SOTA method on single view human reconstruction. It combines statistical human body models (SMPL) with implicit functions and is trained on 3D human scans with clothing. Notably, it performs test-time optimization to fit surface normal predictions to improve the pose accuracy and reconstruction fidelity. We run it per frame, and processing a 170 frame video takes around three hours on an RTX-3090 GPU.", + "bbox": [ + 76, + 90, + 472, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We show qualitative comparison with baselines in Fig. 6 top row, and quantitative results in Tab. 1. On the handstand sequence, HuMoR works well for common poses but fails where the performer is not in an upright pose. ICON works generally well, but the hand distances appear not physically plausible (too short) from a novel viewpoint. BANMo reconstruction also failed to reconstruct the unnatural upside-down pose. In contrast, RAC successfully reconstructs the handstand pose with plausible hand distances. On the samba sequence, HuMoR correctly predicts body poses, but fails to reconstruct the cloth and its deformation. ICON predicts a broken dress and distorted human looks from a novel viewpoint, possibly due to lack of diverse training data from dressed humans. When applied to 47 videos of different humans, BANMo fails to model the cloth correctly, possibly because a limited number of control points are not expressive enough to model the morphological variations over humans wearing different clothes. RAC models between-shape variations using a conditional canonical model and successfully reconstructs cloth deformation using the soft deformation field.", + "bbox": [ + 76, + 378, + 472, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our quantitative results align with qualitative observations, where RAC outperforms all baselines except being slightly worse than BANMo trained on single instances (S). However, RAC trained on single instances (S) or multiple instances (M) outperforms BANMo trained in either fashion. In particular, BANMo results are notably worse when trained on multiple instances, indicating the difficulty in building category models. In contrast, RAC become better when trained on multiple instances.", + "bbox": [ + 75, + 696, + 470, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Reconstructing Cats and Dogs", + "text_level": 1, + "bbox": [ + 76, + 845, + 346, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset. We collect 76 cat videos and 85 dog videos from Internet videos, as well as public data from BANMo. All", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the videos are casually-captured monocular videos. We extract video frames at 10 FPS, including 9,734 frames for cats and 11,657 frames for dogs. We perform the same preprocessing as human reconstruction.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We compare with BANMo and model-based BARC [46]. BARC is the current SOTA for dog shape and pose estimation. It trains a feed-forward network using CG dog models and images with keypoint labels. The shape model is based on SMAL, which uses manual rigging and registration to fit 3D animal toys. We run BARC on individual images.", + "bbox": [ + 496, + 151, + 893, + 256 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We show qualitative results in Fig. 6 bottom row. For dog videos, we find that BARC worked well to predict coarse shapes and poses. However, the results are biased towards certain dog breeds. For instance, BARC predicts a long jaw when the dog has a short jaw (top row), and predicts round ears when the dog has sharp ears (bottom). BANMo was able to reconstruct a reasonable coarse shape, but failed to capture the fine details (e.g., the shape of the ear and the size of the head) with only 25 control points. In contrast, RAC was able to faithfully capture the coarse shape and fine details of the dogs. Unlike dogs, cats have fewer variations in body shape and size, where we find that BANMo works well in most cases. However, for the body parts not visible from the reference viewpoint, BANMo often estimates a squashed shape, which may be caused by the entangled morphology and articulations. In contrast, RAC accurately infers reasonable body parts and articulations even when they are not visible.", + "bbox": [ + 496, + 256, + 892, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Diagnostics", + "text_level": 1, + "bbox": [ + 500, + 537, + 625, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Large Morphological Changes. We reconstruct eight videos of different quadruped animals together to \"stress test\" our method. The dataset contains two dog videos, two cat videos, and one video for goat, bear, camel, and cow, respectively. The result is shown in Fig. 8.", + "bbox": [ + 496, + 560, + 890, + 636 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/70aa9bfa0afb61e8d0cfab36061fcbc6da3e338ee7cb67e5b4b37f0167c29acb.jpg", + "image_caption": [ + "Figure 8. Quadruped Category Reconstruction. Using a smaller code swapping probability $P = 0.01$ results in more faithful instance shape, but less smooth results. A larger $P$ produces smoother results, but some instance-specific features disappear." + ], + "image_footnote": [], + "bbox": [ + 500, + 648, + 879, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Morphology Code $\\beta$ Removing morphology code $\\beta$ from the canonical field degrades it to a standard NeRF. We rerun the experiments and the results are shown in Tab. 1 as well as Fig. 9. Without the morphology code, our reconstructions are forced to share the same canonical shape, which", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17001", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "as discussed in Sec 3.1, failed to handle fine deformations and topological changes (e.g., clothing), leading to worse results in all metrics.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Morphology Code Regularization To test the effectiveness of the morphology code regularization, we set $\\mathcal{P} = 0$ throughout the optimization. The results are shown in Tab. 1 and Fig. 9. Without regularization of the morphology code, the reconstructed shape may appear reasonable from the reference viewpoint, but severely distorted from a novel viewpoint. We posit the body parts that are not well-covered in the video are inherently difficult to infer. As a result, the shapes become degenerate without relying on priors from other videos in the dataset. Tab. 1 also shows that code swapping outperforms norm regularization [12] $(||\\beta ||_2^2)$ . We posit norm regularization forces codes to be similar, but does not constrain their output space, while code swapping encourages any code to explain any image in the data. In practice, we find that code swapping generates valid outputs when we interpolate between codes.", + "bbox": [ + 75, + 137, + 472, + 380 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d024532bcd0d182de131a33e83cc6761f690282271c02e7adb41fa5cb982a5d8.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 78, + 393, + 137, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b3e9fe0046ff3d680e035e99dbd93fdb5221f3e17004840ab6c703dba7fe043e.jpg", + "image_caption": [ + "Full Model" + ], + "image_footnote": [], + "bbox": [ + 145, + 393, + 184, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3729881d6a63aa04bd5b0fb77885464a12976a46e358b9ecf9aa130c7b7fdf04.jpg", + "image_caption": [ + "Figure 9. Ablation study on morphology modeling." + ], + "image_footnote": [], + "bbox": [ + 194, + 393, + 238, + 453 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bd3d626caf2617c56f351ea98f7e22b57cc6d46e1aa9310470e2f49391fd1a1c.jpg", + "image_caption": [ + "w/o $\\beta$ code" + ], + "image_footnote": [], + "bbox": [ + 251, + 393, + 290, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4c9fe9c916d93e84e1ce6ef53d01a2a82d55cd879cf5d7a113e2cbdd6539d55.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 393, + 333, + 454 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6999c24307d8dbc36ef2f6fc5e78fa945de247c1fd2c34382dd5c154fbc7b4a0.jpg", + "image_caption": [ + "w/o $\\beta$ regularization" + ], + "image_footnote": [], + "bbox": [ + 349, + 393, + 395, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Soft Deformation. After removing the soft deformation field, RAC fails to recover body parts that are not controlled by the skeleton (Fig. 10), such as the ears of the dog.", + "bbox": [ + 75, + 512, + 468, + 559 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be390aa15ce6fcf12228a8d2b625d38a1c7c1c87206653deaf67e4c857d051da.jpg", + "image_caption": [ + "Reference" + ], + "image_footnote": [], + "bbox": [ + 81, + 575, + 187, + 630 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/614dce14e97ec08c3b67978a54c5e0681493d702687a1b3e7c2409f92ab80b21.jpg", + "image_caption": [ + "Full Model" + ], + "image_footnote": [], + "bbox": [ + 196, + 580, + 271, + 626 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6bc51ed74e9c67477363bf87394dda4fedc7c4060414a200f4c6072ce54aaacd.jpg", + "image_caption": [ + "Skeleton Visualization" + ], + "image_footnote": [], + "bbox": [ + 295, + 579, + 372, + 625 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e07c7be17d6854c048f9b72b54660b94ef8444fb2e24b32521b55881e778e199.jpg", + "image_caption": [ + "w/o $\\omega_{d}$", + "Figure 10. Ablation study on soft deformation $\\omega_{d}$ ." + ], + "image_footnote": [], + "bbox": [ + 395, + 580, + 467, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Motion Transfer. Given the category model with disentangled morphology and articulations, we can easily transfer an articulation in frame $t$ to other video by setting the articulation parameter to $\\theta_{t}$ , while keeping the morphology parameter $\\beta$ the same. We show motion transfer across human in Fig. 2. Please visit our website for video results of dogs, cats, and humans.", + "bbox": [ + 75, + 686, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Skeleton vs Control Points. Control point deformations are flexible but do not preserve body dimensions (e.g., a line segment can be stretched longer by its end points). As a result, body and limb dimensions can change, creating two problems: (1) articulated shapes look squashy from novel views, and (2) variations in body dimensions are entangled with control-point deformations. In contrast, skeleton de", + "bbox": [ + 75, + 795, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formation preserves body dimensions. It produces better results (Tab. 1) and better motion re-targeting (Fig. 11).", + "bbox": [ + 498, + 90, + 890, + 122 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4bc559a512745433d7eeb6e2dc21162e622b9da82799b72667adc63b8820e07f.jpg", + "image_caption": [ + "Figure 11. Skeleton vs control-points for motion transfer. RAC with control points fails to maintain the body dimensions during motion, and produces squashy results when transferred to a new morphology. RAC with skeleton disentangles motion from morphology, allowing for better motion transfer." + ], + "image_footnote": [], + "bbox": [ + 503, + 128, + 870, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Stretchable Bones allow for control of bone dimensions after optimization. We show an example of a Dachshund (Source1) warped to a Heeler (Source2) by modifying bone dimensions while keeping the shape unchanged.", + "bbox": [ + 496, + 376, + 890, + 438 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2a260052764f627e441b22a3d99fe3e9788177e7e29bd0766041902757960e5.jpg", + "image_caption": [ + "Figure 12. Disentanglement of bone dimensions and shape." + ], + "image_footnote": [], + "bbox": [ + 509, + 445, + 877, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 500, + 594, + 612, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a scalable way of building animatable category models by learning from monocular videos. It disentangles morphology variations between instances and motion within an instance, allowing motion transfer over a category. RAC reaches state-of-the-art reconstruction quality for cats, dogs, and humans in terms of mid-level reconstruction, but details are still missing (such as human hand and toes). Similar to BANMo, RAC requires rough viewpoint initialization. Although we have shown either a pretrained viewpoint estimator or roughly annotated camera viewpoints (in the supplement) are sufficient, it would be interesting to study a more generic way to initialize viewpoints. We also show that category-level skeleton improves motion reconstruction, and leave jointly inferring skeleton structure together with object shape for future work.", + "bbox": [ + 496, + 619, + 890, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by the Qualcomm Innovation Fellowship and the CMU Argo AI Center for Autonomous Vehicle Research.", + "bbox": [ + 496, + 845, + 890, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17002", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. 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In CVPR, 2017. 2, 3" + ], + "bbox": [ + 78, + 90, + 468, + 672 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17005", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_model.json b/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..86b289b73d84ecc5677a3329831e0f4da64eb9a6 --- /dev/null +++ b/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_model.json @@ -0,0 +1,3181 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.225, + 0.131, + 0.748, + 0.154 + ], + "angle": 0, + "content": "Reconstructing Animatable Categories from Videos" + }, + { + "type": "title", + "bbox": [ + 0.209, + 0.181, + 0.761, + 0.221 + ], + "angle": 0, + "content": "Gengshan Yang Chaoyang Wang N Dinesh Reddy Deva Ramanan Carnegie Mellon University" + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.248, + 0.891, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.393, + 0.893, + 0.464 + ], + "angle": 0, + "content": "Figure 1. Given videos of a deformable category and a skeleton, we reconstruct an animatable 3D model that factorizes variations across instances (e.g., cheetah's and sphynx's are both cats but with different shape morphology, skeleton dimensions, and texture) from time-specific variations within an instance (e.g., skeleton articulations and elastic shape deformation). Left: Input videos; Middle-left: 3D shape, skeleton, and skinning weights (visualized as surface colors) in the canonical space; Middle-right: Disentangled between-instance and within-instance variations over time. Right: Morphology and motion transferred across the two instances." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.483, + 0.314, + 0.499 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.515, + 0.471, + 0.756 + ], + "angle": 0, + "content": "Building animatable 3D models is challenging due to the need for 3D scans, laborious registration, and rigging. Recently, differentiable rendering provides a pathway to obtain high-quality 3D models from monocular videos, but these are limited to rigid categories or single instances. We present RAC, a method to build category-level 3D models from monocular videos, disentangling variations over instances and motion over time. Three key ideas are introduced to solve this problem: (1) specializing a category-level skeleton to instances, (2) a method for latent space regularization that encourages shared structure across a category while maintaining instance details, and (3) using 3D background models to disentangle objects from the background. We build 3D models for humans, cats and dogs given monocular videos. Project page: https://gengshany.github.io/rac-www/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.786, + 0.21, + 0.801 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.812, + 0.47, + 0.906 + ], + "angle": 0, + "content": "We aim to build animatable 3D models for deformable object categories. Prior work has done so for targeted categories such as people (e.g., SMPL [1, 30]) and quadruped animals (e.g., SMAL [4]), but such methods appear challenging to scale due to the need of 3D supervision and registration. Recently, test-time optimization through differ" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.893, + 0.59 + ], + "angle": 0, + "content": "entiable rendering [40, 41, 44, 56, 69] provides a pathway to generate high-quality 3D models of deformable objects and scenes from monocular videos. However, such models are typically built independently for each object instance or scene. In contrast, we would like to build category models that can generate different instances along with deformations, given causally-captured video collections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.895, + 0.777 + ], + "angle": 0, + "content": "Though scalable, such data is challenging to leverage in practice. One challenge is how to learn the morphological variation of instances within a category. For example, huskys and corgis are both dogs, but have different body shapes, skeleton dimensions, and texture appearance. Such variations are difficult to disentangle from the variations within a single instance, e.g., as a dog articulates, stretches its muscles, and even moves into different illumination conditions. Approaches for disentangling such factors require enormous efforts in capture and registration [1, 5], and doing so without explicit supervision remains an open challenge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Another challenge arises from the impoverished nature of in-the-wild videos: objects are often partially observable at a limited number of viewpoints, and input signals such as segmentation masks can be inaccurate for such \"in-the-wild\" data. When dealing with partial or impoverished video inputs, one would want the model to listen to the common structures learned across a category - e.g., dogs have two ears. On the other hand, one would want the model to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16995" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.099, + 0.887, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.893, + 0.283 + ], + "angle": 0, + "content": "Figure 2. Disentangling morphologies \\(\\beta\\) and articulation \\(\\theta\\). We show different morphologies (body shape and clothing) given the same rest pose (top) and bouncing pose (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.31, + 0.284, + 0.324 + ], + "angle": 0, + "content": "stay faithful to the input views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.471, + 0.522 + ], + "angle": 0, + "content": "Our approach addresses these challenges by exploiting three insights: (1) We learn skeletons with constant bone lengths within a video, allowing for better disentanglement of between-instance morphology and within-instance articulation. (2) We regularize the unobserved body parts to be coherent across instances while remaining faithful to the input views with a novel code-swapping technique. (3) We make use of a category-level background model that, while not 3D accurate, produces far better segmentation masks. We learn animatable 3D models of cats, dogs, and humans which outperform prior art. Because our models register different instances with a canonical skeleton, we also demonstrate motion transfer across instances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.54, + 0.226, + 0.557 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Model-based 3D Reconstruction. A large body of work in 3D human and animal reconstruction uses parametric shape models [30, 42, 55, 61, 73, 74], which are built from registered 3D scans of human or animals, and serve to recover 3D shapes given a single image or video at test time [2, 3, 3, 21, 21, 46, 72]. A recent research focus is to combine statistical human body mode with implicit functions [17, 25, 47-49, 63, 71] to improve the robustness and fidelity of the reconstruction. Although parametric body models achieve great success in reconstructing humans with large amounts of ground-truth 3D data, it is unclear how to apply the same methodology to categories with limited 3D data, such as animals, and how to scale to real-life imagery with diverse clothing and body poses. RAC builds category-level shape models from in-the-wild videos and demonstrates the potential to reconstruct 3D categories without sophisticated manual processing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Category Reconstruction from Image Collections. A number of recent methods build deformable 3D models of object categories from images with weak 2D annotations, such as keypoints and object silhouettes, obtained from human annotators or predicted by off-the-shelf mod" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.893, + 0.475 + ], + "angle": 0, + "content": "els [13, 18, 22, 28, 53, 59, 70]. However, those methods do not distinguish between morphological variations and motion over time. Moreover, they often apply heavy regularization on shape and deformation to avoid degenerate solutions, which also smooths out fine-grained details. Recent research combines neural implicit functions [33, 34] with category modeling in the context of 3D data generation [6, 7, 37], where shape and appearance variations over a category are modeled with conditional NeRFs. However, reconstructions are typically focused on near-rigid objects such as faces and vehicles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.895, + 0.658 + ], + "angle": 0, + "content": "Articulated Object Reconstruction from Videos. Compared to image collections, videos provide signals to reconstruct object motions and disentangle them from morphological variations. Some works [26, 39, 51] reconstruct articulated bodies from videos, but they either assume synchronized multi-view recordings or articulated 3D skeleton inputs that make their approaches less general. Some other works [67-69] learn animatable 3D models from monocular videos capturing the same object instance, without disentangling morphology and motion. There are recent methods [27, 58, 68] using in-the-wild videos to reconstruct 3D models animals, but their quality are relatively low." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.673, + 0.591, + 0.689 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Given video recordings of different instances from a category and a pre-defined skeleton, we build animatable 3D models including instance-specific morphology (Sec. 3.1), time-varying articulation and deformation (Sec. 3.2), as well as a video-specific 3D background model (Sec. 3.3). The models are optimized using differentiable rendering (Sec. 3.4). An overview is shown in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.749, + 0.832 + ], + "angle": 0, + "content": "3.1. Between-Instance Variation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Fusing videos of different instances into a category model requires handling the morphological variations, which includes the changes in both internal skeleton and outward appearance (shape and color). We define a video-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16996" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.095, + 0.874, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.204, + 0.895, + 0.288 + ], + "angle": 0, + "content": "Figure 3. Morphological variations vs time-varying articulation and deformation. (a) Canonical shape \\(\\mathbf{T}\\), skinning weights \\(\\mathbf{W}\\), and joint locations \\(\\mathbf{J}\\). (b) To represent morphological differences between instances, we use a morphology code \\(\\beta\\) that specifies instance shape and appearance \\(\\mathbf{T}_{\\beta}\\), skinning weights \\(\\mathbf{W}_{\\beta}\\) for a canonical skeleton \\(\\mathbf{J}\\). (c) \\(\\beta\\) also predicts a change in bone lengths \\(\\Delta \\mathbf{J}_{\\beta}\\) which further stretches instance shape into \\(\\mathbf{T}_{\\beta}^{s}\\) by elongating body parts. (d) Time-varying articulations are modeled with an articulation vector \\(\\theta\\) by linearly blending rigid bone transformations in the dual quaternion space. Time-varying deformations (such as muscle deformation) are modeled with a deformation vector \\(\\omega_{d}\\) through invertible 3D warping fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.344 + ], + "angle": 0, + "content": "specific morphology code \\(\\beta\\) to control the variations of both the shape and the skeleton." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.48 + ], + "angle": 0, + "content": "To model between-instance shape variations, one could use dense warping fields to deform a canonical template into instance-specific shapes [62]. However, warping fields cannot explain topological changes (e.g., different clothing). Instead, we define a hierarchical representation: a conditional canonical field [8, 41, 57] to handle fine-grained variations over a category (e.g., the ears of dogs) and a stretchable bone model [14, 60] to represent coarse shape variations (e.g., height and size of body parts)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.481, + 0.471, + 0.571 + ], + "angle": 0, + "content": "Conditional Field T. In the canonical space, a 3D point \\(\\mathbf{X} \\in \\mathbb{R}^3\\) is associated with three properties: signed distance \\(d \\in \\mathbb{R}\\), color \\(\\mathbf{c} \\in \\mathbb{R}^3\\), and canonical features \\(\\psi \\in \\mathbb{R}^{16}\\), which is used to register pixel observations to the canonical space [35,68]. These properties are predicted by multi-layer perceptron (MLP) networks:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.58, + 0.469, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\left(d, \\mathbf {c} ^ {t}\\right) = \\mathbf {M L P} _ {\\mathrm {S D F}} \\left(\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\omega} _ {a}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.6, + 0.469, + 0.616 + ], + "angle": 0, + "content": "\\[\n\\psi = \\mathbf {M L P} _ {\\psi} (\\mathbf {X}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.469, + 0.7 + ], + "angle": 0, + "content": "where the shape and color are conditioned on a videospecific morphology code \\(\\beta \\in \\mathbb{R}^{32}\\) [16, 37]. We further ask the color to be dependent on an appearance code \\(\\omega_{a}\\in \\mathbb{R}^{64}\\) that captures frame-specific appearance such as shadows and illumination changes [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Skeleton J. Unlike shape and color, the bone structures are not directly observable from imagery, making it ambiguous to infer. Methods for automatic skeletal rigging [23, 38, 65] either heavily rely on shape priors, or appear sensitive to input data. Instead, we provide a category-level skeleton topology, which has a fixed tree topology with \\((\\mathrm{B} + 1)\\) bones and B joints (B=25 for quadruped and B=18 for human). To model cross-instance morphological changes, we define per-instance joint locations as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.844, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathbf {J} = \\mathbf {M L P} _ {\\mathbf {J}} (\\beta) \\in \\mathbb {R} ^ {3 \\times B}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As we will discuss next, the change in joint locations not only stretches the skeleton, but also results in the elongation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.892, + 0.358 + ], + "angle": 0, + "content": "of canonical shapes as shown in Fig. 3 (c). The skeleton topology is fixed through optimization but \\(\\mathbf{J}\\) is specialized to each video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.391 + ], + "angle": 0, + "content": "**Skinning Field W.** For a given 3D location \\(\\mathbf{X}\\), we define skinning weight vector \\(\\mathbf{W} \\in \\mathbb{R}^{B + 1}\\) following BANMo:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.411, + 0.892, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} = \\sigma_ {\\text {s o f t m a x}} \\left(d _ {\\sigma} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta}) + \\mathbf {M L P} _ {\\mathbf {W}} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta})\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.554 + ], + "angle": 0, + "content": "where \\(\\theta\\) is a articulation code and \\(d_{\\sigma}(\\mathbf{X},\\boldsymbol {\\beta},\\boldsymbol {\\theta})\\) is the Mahalanobis distance between \\(\\mathbf{X}\\) and Gaussian bones under articulation \\(\\pmb{\\theta}\\) and morphology \\(\\beta\\), refined by a delta skinning MLP. Each Gaussian bone has three parameters for center, orientation, and scale respectively, where the centers are computed as the midpoint of two adjacent joints, the orientations are determined by the parent joints, and the scales are optimized." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.555, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Stretchable Bone Deformation. To represent variations of body dimension and part size, prior work [30, 74] learns a PCA basis from registered 3D scans. Since 3D registrations are not available for in-the-wild videos, we optimize a parametric model through differentiable rendering. Given the stretched joint locations, the model deforms the canonical shape \\(\\mathbf{T}_{\\beta}\\) with blend skinning equations," + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.667, + 0.891, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\mathbf {T} _ {\\beta} ^ {s} = \\left(\\mathbf {W} _ {\\beta} \\mathbf {G} _ {\\beta}\\right) \\mathbf {T} _ {\\beta}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.72 + ], + "angle": 0, + "content": "where \\(\\mathbf{G}_{\\beta}\\) transforms the bone coordinates, and \\(\\mathbf{W}_{\\beta}\\) is the instance-specific skinning weights in Eq. (4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.738, + 0.741 + ], + "angle": 0, + "content": "3.2. Within-Instance Variation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We represent within-instance variations as time-varying warp fields between the canonical space and posed space at time \\( t \\). Similar to HumanNeRF [57], we decompose motion as articulations that explains the near-rigid component (e.g., skeletal motion) and deformation that explains the remaining nonrigid movements (e.g., cloth deformation). Note given the complexity of body movements, it is almost certain the pre-defined skeleton would ignore certain movable body parts. Adding deformation is crucial to achieving high-fidelity reconstruction." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16997" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.892, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.2, + 0.894, + 0.228 + ], + "angle": 0, + "content": "Figure 4. Different \\(\\beta\\) morphologies of dogs (top) and cats (bottom). Our reconstructions show variance in ear shape and limb size over dog breeds, as well as variance in limb and body size over cat breeds." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.255, + 0.47, + 0.286 + ], + "angle": 0, + "content": "Time-varying Articulation. To model the time-varying skeletal movements, we define per-frame joint angles:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.29, + 0.469, + 0.309 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {M L P} _ {\\mathbf {A}} (\\boldsymbol {\\theta}) \\in \\mathbb {R} ^ {3 \\times B} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.469, + 0.405 + ], + "angle": 0, + "content": "where \\(\\theta \\in \\mathbb{R}^{16}\\) is a low-dimensional articulation parameter, and each joint has three degrees of freedom. Given joint angles and the per-video joint locations, we compute bone transformations \\(\\mathbf{G} \\in \\mathbb{R}^{3 \\times 4 \\times B}\\) via forward kinematics. We apply dual quaternion blend skinning (DQB) [19] to get the warping field for each spatial point," + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.411, + 0.469, + 0.43 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} (\\boldsymbol {\\beta}, \\theta) = \\left(\\mathbf {W} _ {\\boldsymbol {\\beta}} \\mathbf {G}\\right) \\mathbf {T} _ {\\boldsymbol {\\beta}} ^ {s}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.469, + 0.509 + ], + "angle": 0, + "content": "Dual quaternion skinning blends SE(3) transformations in dual quaternion space and ensures valid SE(3) after blending, which reduces artifacts around twisted body parts. Note stretching in Eq. (5) can be fused with articulation as a single blend skinning operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.469, + 0.6 + ], + "angle": 0, + "content": "Time-varying Soft Deformation. To further explain the dynamics induced by non-skeleton movements (such as the cat belly and human clothes), we add a neural deformation field [24, 40] \\(\\mathcal{D}(\\cdot)\\) that is flexible enough to model highly nonrigid deformation. Applying the fine-grained warping after blend skinning, we have" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.607, + 0.469, + 0.624 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) = \\mathcal {D} (\\mathbf {D} (\\boldsymbol {\\beta}, \\theta), \\omega_ {d}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.674 + ], + "angle": 0, + "content": "where \\(\\omega_{d}\\) is a frame-specific deformation code. Inspired by CaDeX [24], we use real-NVP [9] to ensure the 3D deformation fields are invertible by construction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Invertibility of 3D Warping Fields. For a given time instance \\( t \\), we have defined a forward warping field \\( \\mathcal{W}^{t,\\rightarrow} \\) that transforms 3D points from the canonical space to the specified time instance, and a backward warping field \\( \\mathcal{W}^{t,\\leftarrow} \\) to transform points in the inverse direction. Both warping fields include stretching (Eq. (5)), articulation. (Eq. (7)), and deformation (Eq. (8)) operations. Notably, we only need to define each operation in the forward warping fields. The deformation operation is, by construction, invertible. To invert stretching and articulation, we invert SE (3) transformations \\( \\mathbf{G} \\) in the blend skinning equations and compute the skinning weights with Eq. (4) using the corresponding morphology and articulation codes. A 3D cycle loss is used to ensure that the warping fields are self-consistent after a forward-backward cycle [29, 69]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.255, + 0.635, + 0.269 + ], + "angle": 0, + "content": "3.3. Scene Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.369 + ], + "angle": 0, + "content": "Reconstructing objects from in-the-wild video footage is challenging due to failures in segmentation, which is often caused by out-of-frame body parts, occlusions, and challenging lighting. Inspired by background subtraction [15, 50], we build a model of the background to robustify our method against inaccurate object segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.893, + 0.49 + ], + "angle": 0, + "content": "In background subtraction, moving objects can be segmented by comparing input images to a background model (e.g., a median image). We generalize this idea to model the background scene in 3D as a per-video NeRF, which can be rendered as color pixels at a moving camera frame and compared to the input frame. We design a conditional background model that generates density and color of a scene conditioned on a per-video background code \\(\\gamma\\):" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.503, + 0.891, + 0.521 + ], + "angle": 0, + "content": "\\[\n(\\sigma , \\mathbf {c} ^ {t}) = \\mathbf {M L P} _ {\\mathbf {b g}} (\\mathbf {X}, \\mathbf {v}, \\gamma), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.893, + 0.699 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}\\) is the viewing direction. To render images, we compose the density and color of the object field and the background NeRF in the view space [37], and compute the expected color and optical flow. Background modeling and composite rendering allows us to remove the object silhouette loss, and improves the quality of results. Interestingly, we find that even coarse geometric reconstructions of the background still can improve the rendered 2D object silhouette, which in turn is useful for improving the quality of object reconstructions (Fig. 5). We ablate the design choice in Tab. 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.738, + 0.726 + ], + "angle": 0, + "content": "3.4. Losses and Regularization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Given the videos and a predefined skeleton, we optimize the parameters discussed above: (1) canonical parameters \\(\\{\\beta ,\\mathbf{J},\\mathbf{T},\\mathbf{W}\\}\\) including per-video morphology codes and canonical templates; (2) motion parameters \\(\\{\\theta ,\\omega_{\\mathrm{d}},\\mathbf{A},\\mathbf{D}\\}\\) including per-frame codes as well as articulation and soft deformation MLPs. (3) background parameters \\(\\{\\gamma ,\\mathbf{B}\\}\\) including video background codes and a background NeRF. The overall objective function contains a image reconstruction loss term and regularization terms." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Reconstruction Losses. The reconstruction loss is defined as the difference between rendered and observed images," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16998" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.104, + 0.468, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.371, + 0.472, + 0.455 + ], + "angle": 0, + "content": "Figure 5. Joint foreground and background reconstruction. We jointly reconstruct objects and their background, while refining the segmentation. Note the input silhouette is noisy (e.g., tail was not segmented), and background modeling helps produce an accurate refined silhouette. As a result, RAC is robust to inaccurate segmentation (e.g., tail movements marked by the red box)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.482, + 0.424, + 0.499 + ], + "angle": 0, + "content": "including object silhouette, color, flow, and features:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.51, + 0.469, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {s i l}} + \\mathcal {L} _ {\\mathrm {r g b}} + \\mathcal {L} _ {\\mathrm {O F}} + \\mathcal {L} _ {\\text {f e a t}}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.659 + ], + "angle": 0, + "content": "We update the model parameter by minimizing \\(\\mathcal{L}\\) through differentiable volume rendering in the same way as BANMo [69]. Off-the-shelf estimates of object silhouettes are used as supervision to kick-start the optimization. Then the weight of silhouette term is set to 0 after several iterations of optimization, while composite rendering of foreground and background itself is capable of separating the object and the non-object components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Morphology Code \\((\\beta)\\) Regularization. Existing differentiable rendering methods are able to faithfully reconstruct the input view but not able to hallucinate a reasonable solution for occluded body parts [40, 69]. See Fig. 9 for an example. One solution is to regularize the instance-specific morphology code \\(\\beta\\) to be consistent with the body shapes observed in other videos. Traditional approaches might do this by adding variational noise (as in a VAE) or adversarial losses (as in a GAN). We found good results with the following easy-to-implement approach: we randomly swap the morphology code \\(\\beta\\) of two videos during optimization; this regularizes the model to effectively learn a single morphology code that works well across all videos. But naively applying this approach would produce a single morphology that would not specialize to each object instance. To enable specialization, we gradually decrease the probability" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.188 + ], + "angle": 0, + "content": "Table 1. Quantitative results on AMA sequences. 3D Chamfer distance \\((\\mathrm{cm},\\downarrow)\\) and F-score \\((\\% ,\\uparrow)\\) averaged over all frames. Our model is trained on 47 human videos spanning existing human datasets (as described in Sec.4.2); we also train BANMo on the same set. Other baselines are trained on 3D human data and relies on SMPL model. Results with \\(^S\\) indicates variants trained on single instances. Our model outperforms prior works." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.198, + 0.89, + 0.371 + ], + "angle": 0, + "content": "
Methodsambabouncing
CDF@2%F@5%CDF@2%F@5
HuMoR9.847.583.711.545.282.3
ICON10.139.985.29.753.586.4
\\( BANMo^S \\)8.062.289.17.664.791.1
BANMo9.354.485.510.254.486.5
\\( RACS \\)6.470.993.26.966.792.8
RAC6.072.594.48.063.891.4
w/o skeleton8.659.687.79.359.587.8
w/o \\( \\beta \\)8.558.987.58.462.590.6
\\( \\beta swap\\rightarrow ||\\beta||_2^2 \\)6.569.093.88.064.891.3
+ bkgd NeRF6.370.993.77.465.591.8
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.878, + 0.411 + ], + "angle": 0, + "content": "of swaps during the optimization, from \\(\\mathcal{P} = 1.0\\to 0.05\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Joint J Regularization. Due to the non-observable nature of the joint locations, there might exist multiple joint configurations leading to similar reconstruction error. To register the skeleton with the canonical shape, we minimize Sinkhorn divergence [11] between the canonical surface \\(\\mathbf{T}_{\\beta}\\) and the joint locations \\(\\mathbf{J}_{\\beta}\\), which forces them to occupy the same space. We extract the canonical mesh with marching cubes [31] as a proxy of the canonical surface. Sinkhorn distance interpolates between Wasserstein and kernel distances and defines a soft way to measure the distance between shapes with different density distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.654 + ], + "angle": 0, + "content": "Soft Deformation Regularization The soft deformation field has the capacity of explaining not only the soft deformations, but also the skeleton articulations. Therefore, we penalize the L2 norm of the soft deformation vectors at randomly sampled morphology and articulations," + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.666, + 0.891, + 0.683 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s o f t}} = \\left\\| \\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) - \\mathbf {D} (\\boldsymbol {\\beta}, \\theta) \\right\\|. \\tag {11}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.709, + 0.634, + 0.727 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Implementation Details. We build RAC on BANMo and compute bone transformations from a kinematic tree. The soft deformation field follows CaDeX, where we find that two invertible blocks are capable of handling moderate deformations. To evaluate surface reconstruction accuracy, we extract the canonical mesh \\(\\mathbf{T}\\) by finding the zero-level set of SDF with marching cubes on a \\(256^3\\) grid. To get the shape at a specific time, the canonical mesh is forward-warmed with \\(\\mathcal{W}^{t,\\rightarrow}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Optimization Details We use AdamW to optimize the model for 36k iterations with 16384 rays per batch (taking" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16999" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.101, + 0.203, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.192, + 0.203, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.29, + 0.166, + 0.303 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.225, + 0.116, + 0.379, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.197, + 0.379, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.272, + 0.29, + 0.315, + 0.302 + ], + "angle": 0, + "content": "Humor" + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.105, + 0.538, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.194, + 0.52, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.29, + 0.471, + 0.302 + ], + "angle": 0, + "content": "ICON" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.103, + 0.71, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.194, + 0.692, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.29, + 0.665, + 0.302 + ], + "angle": 0, + "content": "BANMo" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.103, + 0.887, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.194, + 0.86, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.29, + 0.819, + 0.302 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.32, + 0.155, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.362, + 0.155, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.412, + 0.136, + 0.424 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.157, + 0.319, + 0.219, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.17, + 0.37, + 0.209, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.412, + 0.24, + 0.423 + ], + "angle": 0, + "content": "BARC" + }, + { + "type": "image", + "bbox": [ + 0.229, + 0.32, + 0.266, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.37, + 0.274, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.412, + 0.239, + 0.423 + ], + "angle": 0, + "content": "BARC" + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.32, + 0.353, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.365, + 0.339, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.326, + 0.412, + 0.375, + 0.423 + ], + "angle": 0, + "content": "BANMo" + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.32, + 0.405, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.365, + 0.41, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.467, + 0.412, + 0.496, + 0.423 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.319, + 0.482, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.365, + 0.464, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.32, + 0.53, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.366, + 0.539, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.467, + 0.412, + 0.496, + 0.423 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.549, + 0.319, + 0.623, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.561, + 0.365, + 0.61, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.412, + 0.608, + 0.423 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.32, + 0.702, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.365, + 0.754, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.412, + 0.721, + 0.423 + ], + "angle": 0, + "content": "BANMo" + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.319, + 0.864, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.364, + 0.875, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.412, + 0.824, + 0.423 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.435, + 0.892, + 0.464 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison. We compare with BANMo and model-based methods (HuMoR, ICON, BARC). Top: human reconstruction on (AMA). Bottom: dogs and cats reconstruction on internet videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.659 + ], + "angle": 0, + "content": "around 24 hours on 8 RTX-3090 GPUs). We fist pre-train the background model with RGB, optical flow, and surface normal losses while ignoring foreground pixels. Then we combine background models with the object model for composite rendering optimization. The weights for the loss terms are tuned to have similar initial magnitude. The object root poses are initialized with single-image viewpoint networks trained for humans and quadruped animals following BANMo [69]. For all categories, we start with the same shape (a unit sphere) and a known skeleton topology. Both the shape and the joint locations are specialized to the input dataset, as shown in Fig. 7." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.303, + 0.683 + ], + "angle": 0, + "content": "4.1. Reconstructing Humans" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Dataset. We combine existing human datasets, including AMA, MonoPerfCap, DAVIS, and BANMo to get 47 human videos with 6,382 images [43, 54, 64]. AMA contains multi-view videos, but we treat them as monocular videos and do not use the time-synchronization or camera extrinsics. During preprocessing, we use PointRend [20] to extract object segmentation, CSE [36] for pixel features, VCN-robust [66] for optical flow, and omnidata [10] for surface normal estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Metrics. We use AMA for evaluation since it contains ground-truth meshes and follow BANMo to compute both Chamfer distances and F-scores. Chamfer distance computes the average distance between the ground-truth and the estimated surface points by finding the nearest-neighbor" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.478, + 0.567, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.487, + 0.672, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.482, + 0.801, + 0.538 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.815, + 0.493, + 0.892, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.543, + 0.563, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.552, + 0.668, + 0.584 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.549, + 0.812, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.817, + 0.556, + 0.892, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.611, + 0.58, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.622, + 0.657, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.609, + 0.787, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.818, + 0.624, + 0.875, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.681, + 0.645, + 0.692 + ], + "angle": 0, + "content": "Initial Shape and Skeleton" + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.681, + 0.889, + 0.693 + ], + "angle": 0, + "content": "Final Shape and Skeleton (mean morphology)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.708, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Figure 7. Shape and skeleton optimization. From top to bottom, we visualize the canonical shape and skeleton of our dog, cat, and human models. Left: Canonical shape and skeleton before optimization. Right: Canonical shape and skeleton after optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.87 + ], + "angle": 0, + "content": "matches, but it is sensitive to outliers. F-score at distance thresholds \\( d \\in \\{1\\%, 2\\%, 5\\% \\} \\) of the human bounding box size [52] provides a more informative quantification of surface reconstruction error at different granularity. To account for the unknown scale, we align the predicted mesh with the ground-truth mesh using their depth in the view space." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Baselines. On AMA, we compare with template-free BANMo [69] and model-based methods, including Hu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17000" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.378 + ], + "angle": 0, + "content": "MoR [45] and ICON [63]. BANMo reconstructs an animatable 3D model from multiple monocular videos of the same instance, powered by differentiable rendering optimization. We optimize BANMo on the same dataset with the same amount of computation and iterations as ours. HuMoR is a temporal pose and shape predictor for humans. It performs test-time optimization on video sequences leveraging OpenPose keypoint detection and motion priors trained on large-scale human motion capture dataset. We run it on each video sequence, and processing 170 video frames takes around two hours on a machine with Titan-X GPU. ICON is the recent SOTA method on single view human reconstruction. It combines statistical human body models (SMPL) with implicit functions and is trained on 3D human scans with clothing. Notably, it performs test-time optimization to fit surface normal predictions to improve the pose accuracy and reconstruction fidelity. We run it per frame, and processing a 170 frame video takes around three hours on an RTX-3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.473, + 0.697 + ], + "angle": 0, + "content": "Results. We show qualitative comparison with baselines in Fig. 6 top row, and quantitative results in Tab. 1. On the handstand sequence, HuMoR works well for common poses but fails where the performer is not in an upright pose. ICON works generally well, but the hand distances appear not physically plausible (too short) from a novel viewpoint. BANMo reconstruction also failed to reconstruct the unnatural upside-down pose. In contrast, RAC successfully reconstructs the handstand pose with plausible hand distances. On the samba sequence, HuMoR correctly predicts body poses, but fails to reconstruct the cloth and its deformation. ICON predicts a broken dress and distorted human looks from a novel viewpoint, possibly due to lack of diverse training data from dressed humans. When applied to 47 videos of different humans, BANMo fails to model the cloth correctly, possibly because a limited number of control points are not expressive enough to model the morphological variations over humans wearing different clothes. RAC models between-shape variations using a conditional canonical model and successfully reconstructs cloth deformation using the soft deformation field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.472, + 0.835 + ], + "angle": 0, + "content": "Our quantitative results align with qualitative observations, where RAC outperforms all baselines except being slightly worse than BANMo trained on single instances (S). However, RAC trained on single instances (S) or multiple instances (M) outperforms BANMo trained in either fashion. In particular, BANMo results are notably worse when trained on multiple instances, indicating the difficulty in building category models. In contrast, RAC become better when trained on multiple instances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.348, + 0.864 + ], + "angle": 0, + "content": "4.2. Reconstructing Cats and Dogs" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Dataset. We collect 76 cat videos and 85 dog videos from Internet videos, as well as public data from BANMo. All" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "the videos are casually-captured monocular videos. We extract video frames at 10 FPS, including 9,734 frames for cats and 11,657 frames for dogs. We perform the same preprocessing as human reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.894, + 0.257 + ], + "angle": 0, + "content": "Baselines. We compare with BANMo and model-based BARC [46]. BARC is the current SOTA for dog shape and pose estimation. It trains a feed-forward network using CG dog models and images with keypoint labels. The shape model is based on SMAL, which uses manual rigging and registration to fit 3D animal toys. We run BARC on individual images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Results. We show qualitative results in Fig. 6 bottom row. For dog videos, we find that BARC worked well to predict coarse shapes and poses. However, the results are biased towards certain dog breeds. For instance, BARC predicts a long jaw when the dog has a short jaw (top row), and predicts round ears when the dog has sharp ears (bottom). BANMo was able to reconstruct a reasonable coarse shape, but failed to capture the fine details (e.g., the shape of the ear and the size of the head) with only 25 control points. In contrast, RAC was able to faithfully capture the coarse shape and fine details of the dogs. Unlike dogs, cats have fewer variations in body shape and size, where we find that BANMo works well in most cases. However, for the body parts not visible from the reference viewpoint, BANMo often estimates a squashed shape, which may be caused by the entangled morphology and articulations. In contrast, RAC accurately infers reasonable body parts and articulations even when they are not visible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.538, + 0.627, + 0.554 + ], + "angle": 0, + "content": "4.3. Diagnostics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Large Morphological Changes. We reconstruct eight videos of different quadruped animals together to \"stress test\" our method. The dataset contains two dog videos, two cat videos, and one video for goat, bear, camel, and cow, respectively. The result is shown in Fig. 8." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.649, + 0.88, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.755, + 0.892, + 0.813 + ], + "angle": 0, + "content": "Figure 8. Quadruped Category Reconstruction. Using a smaller code swapping probability \\( P = 0.01 \\) results in more faithful instance shape, but less smooth results. A larger \\( P \\) produces smoother results, but some instance-specific features disappear." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Morphology Code \\(\\beta\\) Removing morphology code \\(\\beta\\) from the canonical field degrades it to a standard NeRF. We rerun the experiments and the results are shown in Tab. 1 as well as Fig. 9. Without the morphology code, our reconstructions are forced to share the same canonical shape, which" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17001" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "as discussed in Sec 3.1, failed to handle fine deformations and topological changes (e.g., clothing), leading to worse results in all metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.473, + 0.381 + ], + "angle": 0, + "content": "Morphology Code Regularization To test the effectiveness of the morphology code regularization, we set \\(\\mathcal{P} = 0\\) throughout the optimization. The results are shown in Tab. 1 and Fig. 9. Without regularization of the morphology code, the reconstructed shape may appear reasonable from the reference viewpoint, but severely distorted from a novel viewpoint. We posit the body parts that are not well-covered in the video are inherently difficult to infer. As a result, the shapes become degenerate without relying on priors from other videos in the dataset. Tab. 1 also shows that code swapping outperforms norm regularization [12] \\((||\\beta ||_2^2)\\). We posit norm regularization forces codes to be similar, but does not constrain their output space, while code swapping encourages any code to explain any image in the data. In practice, we find that code swapping generates valid outputs when we interpolate between codes." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.394, + 0.138, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.46, + 0.133, + 0.47 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.146, + 0.394, + 0.186, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.459, + 0.213, + 0.47 + ], + "angle": 0, + "content": "Full Model" + }, + { + "type": "image", + "bbox": [ + 0.195, + 0.394, + 0.239, + 0.454 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.394, + 0.291, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.394, + 0.334, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.272, + 0.459, + 0.326, + 0.47 + ], + "angle": 0, + "content": "w/o \\(\\beta\\) code" + }, + { + "type": "image", + "bbox": [ + 0.351, + 0.394, + 0.397, + 0.454 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.459, + 0.459, + 0.471 + ], + "angle": 0, + "content": "w/o \\(\\beta\\) regularization" + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.474, + 0.432, + 0.495 + ], + "angle": 0, + "content": "Figure 9. Ablation study on morphology modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Soft Deformation. After removing the soft deformation field, RAC fails to recover body parts that are not controlled by the skeleton (Fig. 10), such as the ears of the dog." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.577, + 0.189, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.633, + 0.162, + 0.643 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.581, + 0.272, + 0.627 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.633, + 0.266, + 0.643 + ], + "angle": 0, + "content": "Full Model" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.58, + 0.373, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.633, + 0.393, + 0.643 + ], + "angle": 0, + "content": "Skeleton Visualization" + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.581, + 0.468, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.421, + 0.633, + 0.46, + 0.644 + ], + "angle": 0, + "content": "w/o \\(\\omega_{d}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.656, + 0.43, + 0.671 + ], + "angle": 0, + "content": "Figure 10. Ablation study on soft deformation \\(\\omega_{d}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Motion Transfer. Given the category model with disentangled morphology and articulations, we can easily transfer an articulation in frame \\( t \\) to other video by setting the articulation parameter to \\( \\theta_{t} \\), while keeping the morphology parameter \\( \\beta \\) the same. We show motion transfer across human in Fig. 2. Please visit our website for video results of dogs, cats, and humans." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Skeleton vs Control Points. Control point deformations are flexible but do not preserve body dimensions (e.g., a line segment can be stretched longer by its end points). As a result, body and limb dimensions can change, creating two problems: (1) articulated shapes look squashy from novel views, and (2) variations in body dimensions are entangled with control-point deformations. In contrast, skeleton de" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "formation preserves body dimensions. It produces better results (Tab. 1) and better motion re-targeting (Fig. 11)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.13, + 0.872, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Figure 11. Skeleton vs control-points for motion transfer. RAC with control points fails to maintain the body dimensions during motion, and produces squashy results when transferred to a new morphology. RAC with skeleton disentangles motion from morphology, allowing for better motion transfer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Stretchable Bones allow for control of bone dimensions after optimization. We show an example of a Dachshund (Source1) warped to a Heeler (Source2) by modifying bone dimensions while keeping the shape unchanged." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.446, + 0.878, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.563, + 0.872, + 0.578 + ], + "angle": 0, + "content": "Figure 12. Disentanglement of bone dimensions and shape." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.614, + 0.61 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.846 + ], + "angle": 0, + "content": "We have presented a scalable way of building animatable category models by learning from monocular videos. It disentangles morphology variations between instances and motion within an instance, allowing motion transfer over a category. RAC reaches state-of-the-art reconstruction quality for cats, dogs, and humans in terms of mid-level reconstruction, but details are still missing (such as human hand and toes). Similar to BANMo, RAC requires rough viewpoint initialization. Although we have shown either a pretrained viewpoint estimator or roughly annotated camera viewpoints (in the supplement) are sufficient, it would be interesting to study a more generic way to initialize viewpoints. We also show that category-level skeleton improves motion reconstruction, and leave jointly inferring skeleton structure together with object shape for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.847, + 0.892, + 0.891 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the Qualcomm Innovation Fellowship and the CMU Argo AI Center for Autonomous Vehicle Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17002" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.173 + ], + "angle": 0, + "content": "[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. 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In CVPR, 2017. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17005" + } + ] +] \ No newline at end of file diff --git a/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_origin.pdf b/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f2a4d4788ddbdc9964ef9787e99fa0c713c09661 --- /dev/null +++ b/2023/Reconstructing Animatable Categories From Videos/152172cb-1c63-4d7d-b307-3d80c30f42e9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c6ad0b7d694efb9db2e89a3d88a7b0646a34bdc56e50cde8857f4e218cdae20 +size 2441367 diff --git a/2023/Reconstructing Animatable Categories From Videos/full.md b/2023/Reconstructing Animatable Categories From Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f2015925ad4385be2f0c6b4dc8c7b6cbb2cd70fb --- /dev/null +++ b/2023/Reconstructing Animatable Categories From Videos/full.md @@ -0,0 +1,454 @@ +# Reconstructing Animatable Categories from Videos + +# Gengshan Yang Chaoyang Wang N Dinesh Reddy Deva Ramanan Carnegie Mellon University + +![](images/517d045bea384deb33b1c73e678a7ac3f973b8ba37aedf16d6ad011bd468b2d0.jpg) +Figure 1. Given videos of a deformable category and a skeleton, we reconstruct an animatable 3D model that factorizes variations across instances (e.g., cheetah's and sphynx's are both cats but with different shape morphology, skeleton dimensions, and texture) from time-specific variations within an instance (e.g., skeleton articulations and elastic shape deformation). Left: Input videos; Middle-left: 3D shape, skeleton, and skinning weights (visualized as surface colors) in the canonical space; Middle-right: Disentangled between-instance and within-instance variations over time. Right: Morphology and motion transferred across the two instances. + +# Abstract + +Building animatable 3D models is challenging due to the need for 3D scans, laborious registration, and rigging. Recently, differentiable rendering provides a pathway to obtain high-quality 3D models from monocular videos, but these are limited to rigid categories or single instances. We present RAC, a method to build category-level 3D models from monocular videos, disentangling variations over instances and motion over time. Three key ideas are introduced to solve this problem: (1) specializing a category-level skeleton to instances, (2) a method for latent space regularization that encourages shared structure across a category while maintaining instance details, and (3) using 3D background models to disentangle objects from the background. We build 3D models for humans, cats and dogs given monocular videos. Project page: https://gengshany.github.io/rac-www/. + +# 1. Introduction + +We aim to build animatable 3D models for deformable object categories. Prior work has done so for targeted categories such as people (e.g., SMPL [1, 30]) and quadruped animals (e.g., SMAL [4]), but such methods appear challenging to scale due to the need of 3D supervision and registration. Recently, test-time optimization through differ + +entiable rendering [40, 41, 44, 56, 69] provides a pathway to generate high-quality 3D models of deformable objects and scenes from monocular videos. However, such models are typically built independently for each object instance or scene. In contrast, we would like to build category models that can generate different instances along with deformations, given causally-captured video collections. + +Though scalable, such data is challenging to leverage in practice. One challenge is how to learn the morphological variation of instances within a category. For example, huskys and corgis are both dogs, but have different body shapes, skeleton dimensions, and texture appearance. Such variations are difficult to disentangle from the variations within a single instance, e.g., as a dog articulates, stretches its muscles, and even moves into different illumination conditions. Approaches for disentangling such factors require enormous efforts in capture and registration [1, 5], and doing so without explicit supervision remains an open challenge. + +Another challenge arises from the impoverished nature of in-the-wild videos: objects are often partially observable at a limited number of viewpoints, and input signals such as segmentation masks can be inaccurate for such "in-the-wild" data. When dealing with partial or impoverished video inputs, one would want the model to listen to the common structures learned across a category - e.g., dogs have two ears. On the other hand, one would want the model to + +![](images/521d8f830e1715dd9cd836701a97296d0d2a7360609c12335a0dd98cf4696236.jpg) +Figure 2. Disentangling morphologies $\beta$ and articulation $\theta$ . We show different morphologies (body shape and clothing) given the same rest pose (top) and bouncing pose (bottom). + +stay faithful to the input views. + +Our approach addresses these challenges by exploiting three insights: (1) We learn skeletons with constant bone lengths within a video, allowing for better disentanglement of between-instance morphology and within-instance articulation. (2) We regularize the unobserved body parts to be coherent across instances while remaining faithful to the input views with a novel code-swapping technique. (3) We make use of a category-level background model that, while not 3D accurate, produces far better segmentation masks. We learn animatable 3D models of cats, dogs, and humans which outperform prior art. Because our models register different instances with a canonical skeleton, we also demonstrate motion transfer across instances. + +# 2. Related Works + +Model-based 3D Reconstruction. A large body of work in 3D human and animal reconstruction uses parametric shape models [30, 42, 55, 61, 73, 74], which are built from registered 3D scans of human or animals, and serve to recover 3D shapes given a single image or video at test time [2, 3, 3, 21, 21, 46, 72]. A recent research focus is to combine statistical human body mode with implicit functions [17, 25, 47-49, 63, 71] to improve the robustness and fidelity of the reconstruction. Although parametric body models achieve great success in reconstructing humans with large amounts of ground-truth 3D data, it is unclear how to apply the same methodology to categories with limited 3D data, such as animals, and how to scale to real-life imagery with diverse clothing and body poses. RAC builds category-level shape models from in-the-wild videos and demonstrates the potential to reconstruct 3D categories without sophisticated manual processing. + +Category Reconstruction from Image Collections. A number of recent methods build deformable 3D models of object categories from images with weak 2D annotations, such as keypoints and object silhouettes, obtained from human annotators or predicted by off-the-shelf mod + +els [13, 18, 22, 28, 53, 59, 70]. However, those methods do not distinguish between morphological variations and motion over time. Moreover, they often apply heavy regularization on shape and deformation to avoid degenerate solutions, which also smooths out fine-grained details. Recent research combines neural implicit functions [33, 34] with category modeling in the context of 3D data generation [6, 7, 37], where shape and appearance variations over a category are modeled with conditional NeRFs. However, reconstructions are typically focused on near-rigid objects such as faces and vehicles. + +Articulated Object Reconstruction from Videos. Compared to image collections, videos provide signals to reconstruct object motions and disentangle them from morphological variations. Some works [26, 39, 51] reconstruct articulated bodies from videos, but they either assume synchronized multi-view recordings or articulated 3D skeleton inputs that make their approaches less general. Some other works [67-69] learn animatable 3D models from monocular videos capturing the same object instance, without disentangling morphology and motion. There are recent methods [27, 58, 68] using in-the-wild videos to reconstruct 3D models animals, but their quality are relatively low. + +# 3. Method + +Given video recordings of different instances from a category and a pre-defined skeleton, we build animatable 3D models including instance-specific morphology (Sec. 3.1), time-varying articulation and deformation (Sec. 3.2), as well as a video-specific 3D background model (Sec. 3.3). The models are optimized using differentiable rendering (Sec. 3.4). An overview is shown in Fig. 3. + +# 3.1. Between-Instance Variation + +Fusing videos of different instances into a category model requires handling the morphological variations, which includes the changes in both internal skeleton and outward appearance (shape and color). We define a video- + +![](images/901ce8519be8cfbf8e05ce8c7bc871bc8e342b183120adad36c86863e33e31c1.jpg) +Figure 3. Morphological variations vs time-varying articulation and deformation. (a) Canonical shape $\mathbf{T}$ , skinning weights $\mathbf{W}$ , and joint locations $\mathbf{J}$ . (b) To represent morphological differences between instances, we use a morphology code $\beta$ that specifies instance shape and appearance $\mathbf{T}_{\beta}$ , skinning weights $\mathbf{W}_{\beta}$ for a canonical skeleton $\mathbf{J}$ . (c) $\beta$ also predicts a change in bone lengths $\Delta \mathbf{J}_{\beta}$ which further stretches instance shape into $\mathbf{T}_{\beta}^{s}$ by elongating body parts. (d) Time-varying articulations are modeled with an articulation vector $\theta$ by linearly blending rigid bone transformations in the dual quaternion space. Time-varying deformations (such as muscle deformation) are modeled with a deformation vector $\omega_{d}$ through invertible 3D warping fields. + +specific morphology code $\beta$ to control the variations of both the shape and the skeleton. + +To model between-instance shape variations, one could use dense warping fields to deform a canonical template into instance-specific shapes [62]. However, warping fields cannot explain topological changes (e.g., different clothing). Instead, we define a hierarchical representation: a conditional canonical field [8, 41, 57] to handle fine-grained variations over a category (e.g., the ears of dogs) and a stretchable bone model [14, 60] to represent coarse shape variations (e.g., height and size of body parts). + +Conditional Field T. In the canonical space, a 3D point $\mathbf{X} \in \mathbb{R}^3$ is associated with three properties: signed distance $d \in \mathbb{R}$ , color $\mathbf{c} \in \mathbb{R}^3$ , and canonical features $\psi \in \mathbb{R}^{16}$ , which is used to register pixel observations to the canonical space [35,68]. These properties are predicted by multi-layer perceptron (MLP) networks: + +$$ +\left(d, \mathbf {c} ^ {t}\right) = \mathbf {M L P} _ {\mathrm {S D F}} \left(\mathbf {X}, \boldsymbol {\beta}, \boldsymbol {\omega} _ {a}\right), \tag {1} +$$ + +$$ +\psi = \mathbf {M L P} _ {\psi} (\mathbf {X}), \tag {2} +$$ + +where the shape and color are conditioned on a videospecific morphology code $\beta \in \mathbb{R}^{32}$ [16, 37]. We further ask the color to be dependent on an appearance code $\omega_{a}\in \mathbb{R}^{64}$ that captures frame-specific appearance such as shadows and illumination changes [32]. + +Skeleton J. Unlike shape and color, the bone structures are not directly observable from imagery, making it ambiguous to infer. Methods for automatic skeletal rigging [23, 38, 65] either heavily rely on shape priors, or appear sensitive to input data. Instead, we provide a category-level skeleton topology, which has a fixed tree topology with $(\mathrm{B} + 1)$ bones and B joints (B=25 for quadruped and B=18 for human). To model cross-instance morphological changes, we define per-instance joint locations as: + +$$ +\mathbf {J} = \mathbf {M L P} _ {\mathbf {J}} (\beta) \in \mathbb {R} ^ {3 \times B}. \tag {3} +$$ + +As we will discuss next, the change in joint locations not only stretches the skeleton, but also results in the elongation + +of canonical shapes as shown in Fig. 3 (c). The skeleton topology is fixed through optimization but $\mathbf{J}$ is specialized to each video. + +**Skinning Field W.** For a given 3D location $\mathbf{X}$ , we define skinning weight vector $\mathbf{W} \in \mathbb{R}^{B + 1}$ following BANMo: + +$$ +\mathbf {W} = \sigma_ {\text {s o f t m a x}} \left(d _ {\sigma} (\mathbf {X}, \boldsymbol {\beta}, \boldsymbol {\theta}) + \mathbf {M L P} _ {\mathbf {W}} (\mathbf {X}, \boldsymbol {\beta}, \boldsymbol {\theta})\right), \tag {4} +$$ + +where $\theta$ is a articulation code and $d_{\sigma}(\mathbf{X},\boldsymbol {\beta},\boldsymbol {\theta})$ is the Mahalanobis distance between $\mathbf{X}$ and Gaussian bones under articulation $\pmb{\theta}$ and morphology $\beta$ , refined by a delta skinning MLP. Each Gaussian bone has three parameters for center, orientation, and scale respectively, where the centers are computed as the midpoint of two adjacent joints, the orientations are determined by the parent joints, and the scales are optimized. + +Stretchable Bone Deformation. To represent variations of body dimension and part size, prior work [30, 74] learns a PCA basis from registered 3D scans. Since 3D registrations are not available for in-the-wild videos, we optimize a parametric model through differentiable rendering. Given the stretched joint locations, the model deforms the canonical shape $\mathbf{T}_{\beta}$ with blend skinning equations, + +$$ +\mathbf {T} _ {\beta} ^ {s} = \left(\mathbf {W} _ {\beta} \mathbf {G} _ {\beta}\right) \mathbf {T} _ {\beta}, \tag {5} +$$ + +where $\mathbf{G}_{\beta}$ transforms the bone coordinates, and $\mathbf{W}_{\beta}$ is the instance-specific skinning weights in Eq. (4). + +# 3.2. Within-Instance Variation + +We represent within-instance variations as time-varying warp fields between the canonical space and posed space at time $t$ . Similar to HumanNeRF [57], we decompose motion as articulations that explains the near-rigid component (e.g., skeletal motion) and deformation that explains the remaining nonrigid movements (e.g., cloth deformation). Note given the complexity of body movements, it is almost certain the pre-defined skeleton would ignore certain movable body parts. Adding deformation is crucial to achieving high-fidelity reconstruction. + +![](images/66bdc7596c30f6829c9ace97837a1c01556eb74e477244a33baaa4b77a7690aa.jpg) +Figure 4. Different $\beta$ morphologies of dogs (top) and cats (bottom). Our reconstructions show variance in ear shape and limb size over dog breeds, as well as variance in limb and body size over cat breeds. + +Time-varying Articulation. To model the time-varying skeletal movements, we define per-frame joint angles: + +$$ +\mathbf {Q} = \mathbf {M L P} _ {\mathbf {A}} (\boldsymbol {\theta}) \in \mathbb {R} ^ {3 \times B} \tag {6} +$$ + +where $\theta \in \mathbb{R}^{16}$ is a low-dimensional articulation parameter, and each joint has three degrees of freedom. Given joint angles and the per-video joint locations, we compute bone transformations $\mathbf{G} \in \mathbb{R}^{3 \times 4 \times B}$ via forward kinematics. We apply dual quaternion blend skinning (DQB) [19] to get the warping field for each spatial point, + +$$ +\mathbf {D} (\boldsymbol {\beta}, \theta) = \left(\mathbf {W} _ {\boldsymbol {\beta}} \mathbf {G}\right) \mathbf {T} _ {\boldsymbol {\beta}} ^ {s}. \tag {7} +$$ + +Dual quaternion skinning blends SE(3) transformations in dual quaternion space and ensures valid SE(3) after blending, which reduces artifacts around twisted body parts. Note stretching in Eq. (5) can be fused with articulation as a single blend skinning operation. + +Time-varying Soft Deformation. To further explain the dynamics induced by non-skeleton movements (such as the cat belly and human clothes), we add a neural deformation field [24, 40] $\mathcal{D}(\cdot)$ that is flexible enough to model highly nonrigid deformation. Applying the fine-grained warping after blend skinning, we have + +$$ +\mathbf {D} (\boldsymbol {\beta}, \theta , \omega_ {d}) = \mathcal {D} (\mathbf {D} (\boldsymbol {\beta}, \theta), \omega_ {d}), \tag {8} +$$ + +where $\omega_{d}$ is a frame-specific deformation code. Inspired by CaDeX [24], we use real-NVP [9] to ensure the 3D deformation fields are invertible by construction. + +Invertibility of 3D Warping Fields. For a given time instance $t$ , we have defined a forward warping field $\mathcal{W}^{t,\rightarrow}$ that transforms 3D points from the canonical space to the specified time instance, and a backward warping field $\mathcal{W}^{t,\leftarrow}$ to transform points in the inverse direction. Both warping fields include stretching (Eq. (5)), articulation. (Eq. (7)), and deformation (Eq. (8)) operations. Notably, we only need to define each operation in the forward warping fields. The deformation operation is, by construction, invertible. To invert stretching and articulation, we invert SE (3) transformations $\mathbf{G}$ in the blend skinning equations and compute the skinning weights with Eq. (4) using the corresponding morphology and articulation codes. A 3D cycle loss is used to ensure that the warping fields are self-consistent after a forward-backward cycle [29, 69]. + +# 3.3. Scene Model + +Reconstructing objects from in-the-wild video footage is challenging due to failures in segmentation, which is often caused by out-of-frame body parts, occlusions, and challenging lighting. Inspired by background subtraction [15, 50], we build a model of the background to robustify our method against inaccurate object segmentation. + +In background subtraction, moving objects can be segmented by comparing input images to a background model (e.g., a median image). We generalize this idea to model the background scene in 3D as a per-video NeRF, which can be rendered as color pixels at a moving camera frame and compared to the input frame. We design a conditional background model that generates density and color of a scene conditioned on a per-video background code $\gamma$ : + +$$ +(\sigma , \mathbf {c} ^ {t}) = \mathbf {M L P} _ {\mathbf {b g}} (\mathbf {X}, \mathbf {v}, \gamma), \tag {9} +$$ + +where $\mathbf{v}$ is the viewing direction. To render images, we compose the density and color of the object field and the background NeRF in the view space [37], and compute the expected color and optical flow. Background modeling and composite rendering allows us to remove the object silhouette loss, and improves the quality of results. Interestingly, we find that even coarse geometric reconstructions of the background still can improve the rendered 2D object silhouette, which in turn is useful for improving the quality of object reconstructions (Fig. 5). We ablate the design choice in Tab. 1. + +# 3.4. Losses and Regularization + +Given the videos and a predefined skeleton, we optimize the parameters discussed above: (1) canonical parameters $\{\beta ,\mathbf{J},\mathbf{T},\mathbf{W}\}$ including per-video morphology codes and canonical templates; (2) motion parameters $\{\theta ,\omega_{\mathrm{d}},\mathbf{A},\mathbf{D}\}$ including per-frame codes as well as articulation and soft deformation MLPs. (3) background parameters $\{\gamma ,\mathbf{B}\}$ including video background codes and a background NeRF. The overall objective function contains a image reconstruction loss term and regularization terms. + +Reconstruction Losses. The reconstruction loss is defined as the difference between rendered and observed images, + +![](images/5967c2a979763aec1857e1d2fe04cc0add0d83358f3a59bd1f0081cc32c359e7.jpg) +Figure 5. Joint foreground and background reconstruction. We jointly reconstruct objects and their background, while refining the segmentation. Note the input silhouette is noisy (e.g., tail was not segmented), and background modeling helps produce an accurate refined silhouette. As a result, RAC is robust to inaccurate segmentation (e.g., tail movements marked by the red box). + +including object silhouette, color, flow, and features: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {s i l}} + \mathcal {L} _ {\mathrm {r g b}} + \mathcal {L} _ {\mathrm {O F}} + \mathcal {L} _ {\text {f e a t}}. \tag {10} +$$ + +We update the model parameter by minimizing $\mathcal{L}$ through differentiable volume rendering in the same way as BANMo [69]. Off-the-shelf estimates of object silhouettes are used as supervision to kick-start the optimization. Then the weight of silhouette term is set to 0 after several iterations of optimization, while composite rendering of foreground and background itself is capable of separating the object and the non-object components. + +Morphology Code $(\beta)$ Regularization. Existing differentiable rendering methods are able to faithfully reconstruct the input view but not able to hallucinate a reasonable solution for occluded body parts [40, 69]. See Fig. 9 for an example. One solution is to regularize the instance-specific morphology code $\beta$ to be consistent with the body shapes observed in other videos. Traditional approaches might do this by adding variational noise (as in a VAE) or adversarial losses (as in a GAN). We found good results with the following easy-to-implement approach: we randomly swap the morphology code $\beta$ of two videos during optimization; this regularizes the model to effectively learn a single morphology code that works well across all videos. But naively applying this approach would produce a single morphology that would not specialize to each object instance. To enable specialization, we gradually decrease the probability + +Table 1. Quantitative results on AMA sequences. 3D Chamfer distance $(\mathrm{cm},\downarrow)$ and F-score $(\% ,\uparrow)$ averaged over all frames. Our model is trained on 47 human videos spanning existing human datasets (as described in Sec.4.2); we also train BANMo on the same set. Other baselines are trained on 3D human data and relies on SMPL model. Results with $^S$ indicates variants trained on single instances. Our model outperforms prior works. + +
Methodsambabouncing
CDF@2%F@5%CDF@2%F@5
HuMoR9.847.583.711.545.282.3
ICON10.139.985.29.753.586.4
\( BANMo^S \)8.062.289.17.664.791.1
BANMo9.354.485.510.254.486.5
\( RACS \)6.470.993.26.966.792.8
RAC6.072.594.48.063.891.4
w/o skeleton8.659.687.79.359.587.8
w/o \( \beta \)8.558.987.58.462.590.6
\( \beta swap\rightarrow ||\beta||_2^2 \)6.569.093.88.064.891.3
+ bkgd NeRF6.370.993.77.465.591.8
+ +of swaps during the optimization, from $\mathcal{P} = 1.0\to 0.05$ + +Joint J Regularization. Due to the non-observable nature of the joint locations, there might exist multiple joint configurations leading to similar reconstruction error. To register the skeleton with the canonical shape, we minimize Sinkhorn divergence [11] between the canonical surface $\mathbf{T}_{\beta}$ and the joint locations $\mathbf{J}_{\beta}$ , which forces them to occupy the same space. We extract the canonical mesh with marching cubes [31] as a proxy of the canonical surface. Sinkhorn distance interpolates between Wasserstein and kernel distances and defines a soft way to measure the distance between shapes with different density distributions. + +Soft Deformation Regularization The soft deformation field has the capacity of explaining not only the soft deformations, but also the skeleton articulations. Therefore, we penalize the L2 norm of the soft deformation vectors at randomly sampled morphology and articulations, + +$$ +\mathcal {L} _ {\text {s o f t}} = \left\| \mathbf {D} (\boldsymbol {\beta}, \theta , \omega_ {d}) - \mathbf {D} (\boldsymbol {\beta}, \theta) \right\|. \tag {11} +$$ + +# 4. Experiments + +Implementation Details. We build RAC on BANMo and compute bone transformations from a kinematic tree. The soft deformation field follows CaDeX, where we find that two invertible blocks are capable of handling moderate deformations. To evaluate surface reconstruction accuracy, we extract the canonical mesh $\mathbf{T}$ by finding the zero-level set of SDF with marching cubes on a $256^3$ grid. To get the shape at a specific time, the canonical mesh is forward-warmed with $\mathcal{W}^{t,\rightarrow}$ . + +Optimization Details We use AdamW to optimize the model for 36k iterations with 16384 rays per batch (taking + +![](images/cdc65e3af494bf348565670417375061d2280e813346a4904f7d1baa6f844bfb.jpg) + +![](images/a2f12a939bc2dc3176250c1cf114e080065aa9891cdf15d1f381ed502a81bd2f.jpg) +Input + +![](images/c0aa60e64edd177a6d15578e873f206b5da6ea348b5a320dbd231dec7651011e.jpg) + +![](images/fcdb658186a022c24e98e736f229749e420daaee973f9281a33394134adbb80f.jpg) +Humor + +![](images/24d9bc05de90080fc41d34e0f5e416541cfd26b5b32dbf3cd1c27771a2a90573.jpg) + +![](images/957528914f77a0e93ebf91d5876117296deebb9703fe77f594d11ac3a79d0854.jpg) +ICON + +![](images/e0d443b62a43d6f1431b1ed587fc5d4fcc72716bf6fc5c768e7d62bd5c60a725.jpg) + +![](images/9a981709050b626273d5f57acff29d27031840d8197c440f383d99e92aba4d37.jpg) +BANMo + +![](images/31a17709cb3dc9c79dce6796b1805d0c614f83b6e982aa179ff8369e148b85aa.jpg) + +![](images/e81229935615306865d679284d6bee2dc6083d779ad9091cf254c104ad4ea7bf.jpg) +Ours + +![](images/10b2cd81e1b3901a192a58d156ab6625b71b8ed3d3199bcec3ce58484f2be133.jpg) + +![](images/1e26fddb52eefe34c0b6f52a2a2aca1a83a3daf5b5834302f1a730a5e6a71e64.jpg) +Input + +![](images/8b1e70b98264f69628f5156ba985fd3e1bfffd8c6c45ae150cd6c7b1a90ea885.jpg) + +![](images/daa0c32ce95a72c7735fee04272219b53d217c966f778684f7540b5fad104f87.jpg) +BARC + +![](images/0c547e3eeb2834f6a53d914a1d405ef9b909190f619ec78bea4290aa07974eea.jpg) + +![](images/5a110603b6180f4280f9581d101a989b1c79e49b4d691d345ee03b31cb47b872.jpg) +Figure 6. Qualitative comparison. We compare with BANMo and model-based methods (HuMoR, ICON, BARC). Top: human reconstruction on (AMA). Bottom: dogs and cats reconstruction on internet videos. + +BARC + +![](images/df3ae3f3a34afb426c90f8f78fb0d1b5f47a1f5a60e2fbb12ba36c0d74e3d3b2.jpg) + +![](images/1a9fc89922d0f58bacdac474ebf030fe018827329c73ca1de0b1b260da981074.jpg) +BANMo + +![](images/37d41583f80b545900de0ac932666ec6888b18593cf077518cbd9b363c51fc9b.jpg) + +![](images/698493caf8c288090f03f2fc87a987fb7954e21d753f2b90512b430da5020173.jpg) + +Ours + +![](images/7868af2d919e8ddc269c2afddee9172a92c8cc6d8ae77b7866cbb81180975975.jpg) + +![](images/115b075bd39dcfdd7b7ab5a8af218099d1b860c6600119c775572d986bbfaf42.jpg) + +![](images/5be084b54e749e47b3e3a82193fe47a36c8fbd92fbab24749ce76063f4ac6645.jpg) + +![](images/fdc3c0f9ab01e113cb053370ea28ce427de17bc4f6787ca6425979db49ad76cd.jpg) + +Ours + +![](images/06027588513cb0d16c863c9c62897c48a1954f938cbd1c40d9586ce8059e1713.jpg) + +![](images/882909f6fb0f49438db7e1d79c13cec9a0099088d74544ef6000020a1acb84f1.jpg) +Input + +![](images/14fb9cedeebde41cdd01a0b268a8d253ae38c5ac2603bcb5e64a186b30ace90b.jpg) + +![](images/63790c13868d0f3ed103941f144dea5f06ce432b027a2ffc6383cd362b0e5cce.jpg) +BANMo + +![](images/1bf3d636af67d31cfe7c72f1bd8e8e461030b1a882a666247adc043fb805e048.jpg) + +![](images/29c27978c9c9e221a5a87bb0b9e50d01fd107094c3b4f53ab6dc3d564489ff8d.jpg) +Ours + +around 24 hours on 8 RTX-3090 GPUs). We fist pre-train the background model with RGB, optical flow, and surface normal losses while ignoring foreground pixels. Then we combine background models with the object model for composite rendering optimization. The weights for the loss terms are tuned to have similar initial magnitude. The object root poses are initialized with single-image viewpoint networks trained for humans and quadruped animals following BANMo [69]. For all categories, we start with the same shape (a unit sphere) and a known skeleton topology. Both the shape and the joint locations are specialized to the input dataset, as shown in Fig. 7. + +# 4.1. Reconstructing Humans + +Dataset. We combine existing human datasets, including AMA, MonoPerfCap, DAVIS, and BANMo to get 47 human videos with 6,382 images [43, 54, 64]. AMA contains multi-view videos, but we treat them as monocular videos and do not use the time-synchronization or camera extrinsics. During preprocessing, we use PointRend [20] to extract object segmentation, CSE [36] for pixel features, VCN-robust [66] for optical flow, and omnidata [10] for surface normal estimation. + +Metrics. We use AMA for evaluation since it contains ground-truth meshes and follow BANMo to compute both Chamfer distances and F-scores. Chamfer distance computes the average distance between the ground-truth and the estimated surface points by finding the nearest-neighbor + +![](images/59afb268b8bb6fcca7f65471eb6d5b9bdc01256790957d79e7133c011b946ddc.jpg) + +![](images/7675815efc7501591ba6194488a6812a33f7ee65c282d864eb8dfc95c81d7a27.jpg) + +![](images/f28bccb06acef71e26f2b3a7eb21d014d86d768058e8a676c312dca25eebaadb.jpg) + +![](images/a9129d53ae6c463b535c392f29f0b25e22085343c75547ab7c7a829def829c2f.jpg) + +![](images/0c434c3f53ee18dea123ae3900576595ba2aea9f1afdfd26f220611738231173.jpg) + +![](images/51057911ddf72d044b0a54edb5d382307267703d7b9ea50b52554cf92e781d24.jpg) + +![](images/b24a3a4e61988364280aee5fe31a818561fb1145ee5fdfdcc9410cc9e02ce4cc.jpg) + +![](images/2fb586c70f55ed14e6a705fe5fad26309fa7a0f8a301177ea969541a84ca1187.jpg) + +![](images/89a2a1027eae31651f7783a1800ea751907de00fa9fb377c27b0e38e963bc58a.jpg) +Initial Shape and Skeleton + +![](images/791f680bd2681693c12e1ef2438c9887eb0b53e2e16c1152980ca9521a2fac2a.jpg) + +![](images/6595551257b1e1c04a71425d5a51256285c42c2759ac60efbeabe73dd81d84a7.jpg) +Final Shape and Skeleton (mean morphology) + +![](images/419600c37175505e55fb96a9e5cdf055c476c60bad98615fb6cbef6cb0c3084d.jpg) +Figure 7. Shape and skeleton optimization. From top to bottom, we visualize the canonical shape and skeleton of our dog, cat, and human models. Left: Canonical shape and skeleton before optimization. Right: Canonical shape and skeleton after optimization. + +matches, but it is sensitive to outliers. F-score at distance thresholds $d \in \{1\%, 2\%, 5\% \}$ of the human bounding box size [52] provides a more informative quantification of surface reconstruction error at different granularity. To account for the unknown scale, we align the predicted mesh with the ground-truth mesh using their depth in the view space. + +Baselines. On AMA, we compare with template-free BANMo [69] and model-based methods, including Hu + +MoR [45] and ICON [63]. BANMo reconstructs an animatable 3D model from multiple monocular videos of the same instance, powered by differentiable rendering optimization. We optimize BANMo on the same dataset with the same amount of computation and iterations as ours. HuMoR is a temporal pose and shape predictor for humans. It performs test-time optimization on video sequences leveraging OpenPose keypoint detection and motion priors trained on large-scale human motion capture dataset. We run it on each video sequence, and processing 170 video frames takes around two hours on a machine with Titan-X GPU. ICON is the recent SOTA method on single view human reconstruction. It combines statistical human body models (SMPL) with implicit functions and is trained on 3D human scans with clothing. Notably, it performs test-time optimization to fit surface normal predictions to improve the pose accuracy and reconstruction fidelity. We run it per frame, and processing a 170 frame video takes around three hours on an RTX-3090 GPU. + +Results. We show qualitative comparison with baselines in Fig. 6 top row, and quantitative results in Tab. 1. On the handstand sequence, HuMoR works well for common poses but fails where the performer is not in an upright pose. ICON works generally well, but the hand distances appear not physically plausible (too short) from a novel viewpoint. BANMo reconstruction also failed to reconstruct the unnatural upside-down pose. In contrast, RAC successfully reconstructs the handstand pose with plausible hand distances. On the samba sequence, HuMoR correctly predicts body poses, but fails to reconstruct the cloth and its deformation. ICON predicts a broken dress and distorted human looks from a novel viewpoint, possibly due to lack of diverse training data from dressed humans. When applied to 47 videos of different humans, BANMo fails to model the cloth correctly, possibly because a limited number of control points are not expressive enough to model the morphological variations over humans wearing different clothes. RAC models between-shape variations using a conditional canonical model and successfully reconstructs cloth deformation using the soft deformation field. + +Our quantitative results align with qualitative observations, where RAC outperforms all baselines except being slightly worse than BANMo trained on single instances (S). However, RAC trained on single instances (S) or multiple instances (M) outperforms BANMo trained in either fashion. In particular, BANMo results are notably worse when trained on multiple instances, indicating the difficulty in building category models. In contrast, RAC become better when trained on multiple instances. + +# 4.2. Reconstructing Cats and Dogs + +Dataset. We collect 76 cat videos and 85 dog videos from Internet videos, as well as public data from BANMo. All + +the videos are casually-captured monocular videos. We extract video frames at 10 FPS, including 9,734 frames for cats and 11,657 frames for dogs. We perform the same preprocessing as human reconstruction. + +Baselines. We compare with BANMo and model-based BARC [46]. BARC is the current SOTA for dog shape and pose estimation. It trains a feed-forward network using CG dog models and images with keypoint labels. The shape model is based on SMAL, which uses manual rigging and registration to fit 3D animal toys. We run BARC on individual images. + +Results. We show qualitative results in Fig. 6 bottom row. For dog videos, we find that BARC worked well to predict coarse shapes and poses. However, the results are biased towards certain dog breeds. For instance, BARC predicts a long jaw when the dog has a short jaw (top row), and predicts round ears when the dog has sharp ears (bottom). BANMo was able to reconstruct a reasonable coarse shape, but failed to capture the fine details (e.g., the shape of the ear and the size of the head) with only 25 control points. In contrast, RAC was able to faithfully capture the coarse shape and fine details of the dogs. Unlike dogs, cats have fewer variations in body shape and size, where we find that BANMo works well in most cases. However, for the body parts not visible from the reference viewpoint, BANMo often estimates a squashed shape, which may be caused by the entangled morphology and articulations. In contrast, RAC accurately infers reasonable body parts and articulations even when they are not visible. + +# 4.3. Diagnostics + +Large Morphological Changes. We reconstruct eight videos of different quadruped animals together to "stress test" our method. The dataset contains two dog videos, two cat videos, and one video for goat, bear, camel, and cow, respectively. The result is shown in Fig. 8. + +![](images/70aa9bfa0afb61e8d0cfab36061fcbc6da3e338ee7cb67e5b4b37f0167c29acb.jpg) +Figure 8. Quadruped Category Reconstruction. Using a smaller code swapping probability $P = 0.01$ results in more faithful instance shape, but less smooth results. A larger $P$ produces smoother results, but some instance-specific features disappear. + +Morphology Code $\beta$ Removing morphology code $\beta$ from the canonical field degrades it to a standard NeRF. We rerun the experiments and the results are shown in Tab. 1 as well as Fig. 9. Without the morphology code, our reconstructions are forced to share the same canonical shape, which + +as discussed in Sec 3.1, failed to handle fine deformations and topological changes (e.g., clothing), leading to worse results in all metrics. + +Morphology Code Regularization To test the effectiveness of the morphology code regularization, we set $\mathcal{P} = 0$ throughout the optimization. The results are shown in Tab. 1 and Fig. 9. Without regularization of the morphology code, the reconstructed shape may appear reasonable from the reference viewpoint, but severely distorted from a novel viewpoint. We posit the body parts that are not well-covered in the video are inherently difficult to infer. As a result, the shapes become degenerate without relying on priors from other videos in the dataset. Tab. 1 also shows that code swapping outperforms norm regularization [12] $(||\beta ||_2^2)$ . We posit norm regularization forces codes to be similar, but does not constrain their output space, while code swapping encourages any code to explain any image in the data. In practice, we find that code swapping generates valid outputs when we interpolate between codes. + +![](images/d024532bcd0d182de131a33e83cc6761f690282271c02e7adb41fa5cb982a5d8.jpg) +Reference + +![](images/b3e9fe0046ff3d680e035e99dbd93fdb5221f3e17004840ab6c703dba7fe043e.jpg) +Full Model + +![](images/3729881d6a63aa04bd5b0fb77885464a12976a46e358b9ecf9aa130c7b7fdf04.jpg) +Figure 9. Ablation study on morphology modeling. + +![](images/bd3d626caf2617c56f351ea98f7e22b57cc6d46e1aa9310470e2f49391fd1a1c.jpg) +w/o $\beta$ code + +![](images/b4c9fe9c916d93e84e1ce6ef53d01a2a82d55cd879cf5d7a113e2cbdd6539d55.jpg) + +![](images/6999c24307d8dbc36ef2f6fc5e78fa945de247c1fd2c34382dd5c154fbc7b4a0.jpg) +w/o $\beta$ regularization + +Soft Deformation. After removing the soft deformation field, RAC fails to recover body parts that are not controlled by the skeleton (Fig. 10), such as the ears of the dog. + +![](images/be390aa15ce6fcf12228a8d2b625d38a1c7c1c87206653deaf67e4c857d051da.jpg) +Reference + +![](images/614dce14e97ec08c3b67978a54c5e0681493d702687a1b3e7c2409f92ab80b21.jpg) +Full Model + +![](images/6bc51ed74e9c67477363bf87394dda4fedc7c4060414a200f4c6072ce54aaacd.jpg) +Skeleton Visualization + +![](images/e07c7be17d6854c048f9b72b54660b94ef8444fb2e24b32521b55881e778e199.jpg) +w/o $\omega_{d}$ +Figure 10. Ablation study on soft deformation $\omega_{d}$ . + +Motion Transfer. Given the category model with disentangled morphology and articulations, we can easily transfer an articulation in frame $t$ to other video by setting the articulation parameter to $\theta_{t}$ , while keeping the morphology parameter $\beta$ the same. We show motion transfer across human in Fig. 2. Please visit our website for video results of dogs, cats, and humans. + +Skeleton vs Control Points. Control point deformations are flexible but do not preserve body dimensions (e.g., a line segment can be stretched longer by its end points). As a result, body and limb dimensions can change, creating two problems: (1) articulated shapes look squashy from novel views, and (2) variations in body dimensions are entangled with control-point deformations. In contrast, skeleton de + +formation preserves body dimensions. It produces better results (Tab. 1) and better motion re-targeting (Fig. 11). + +![](images/4bc559a512745433d7eeb6e2dc21162e622b9da82799b72667adc63b8820e07f.jpg) +Figure 11. Skeleton vs control-points for motion transfer. RAC with control points fails to maintain the body dimensions during motion, and produces squashy results when transferred to a new morphology. RAC with skeleton disentangles motion from morphology, allowing for better motion transfer. + +Stretchable Bones allow for control of bone dimensions after optimization. We show an example of a Dachshund (Source1) warped to a Heeler (Source2) by modifying bone dimensions while keeping the shape unchanged. + +![](images/f2a260052764f627e441b22a3d99fe3e9788177e7e29bd0766041902757960e5.jpg) +Figure 12. Disentanglement of bone dimensions and shape. + +# 5. Discussion + +We have presented a scalable way of building animatable category models by learning from monocular videos. It disentangles morphology variations between instances and motion within an instance, allowing motion transfer over a category. RAC reaches state-of-the-art reconstruction quality for cats, dogs, and humans in terms of mid-level reconstruction, but details are still missing (such as human hand and toes). Similar to BANMo, RAC requires rough viewpoint initialization. Although we have shown either a pretrained viewpoint estimator or roughly annotated camera viewpoints (in the supplement) are sufficient, it would be interesting to study a more generic way to initialize viewpoints. We also show that category-level skeleton improves motion reconstruction, and leave jointly inferring skeleton structure together with object shape for future work. + +Acknowledgement This work was supported by the Qualcomm Innovation Fellowship and the CMU Argo AI Center for Autonomous Vehicle Research. + +# References + +[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. In ACM SIGGRAPH 2005 Papers, pages 408-416. 2005. 1 +[2] Marc Badger, Yufu Wang, Adarsh Modh, Ammon Perkes, Nikos Kolotouros, Bernd Pfrommer, Marc Schmidt, and Kostas Daniilidis. 3D bird reconstruction: a dataset, model, and shape recovery from a single view. 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In CVPR, 2017. 2, 3 \ No newline at end of file diff --git a/2023/Reconstructing Animatable Categories From Videos/images.zip b/2023/Reconstructing Animatable Categories From Videos/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..355be3d314d7f62874c8284f949094f08696c934 --- /dev/null +++ b/2023/Reconstructing Animatable Categories From Videos/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5cc12115e1d53e570d48664a94158aa3313d8283c4a95ea95c43997a03efba84 +size 486435 diff --git a/2023/Reconstructing Animatable Categories From Videos/layout.json b/2023/Reconstructing Animatable Categories From Videos/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1091dd3651fc0e991e4c1f430c2071d12c5ce821 --- /dev/null +++ b/2023/Reconstructing Animatable Categories From Videos/layout.json @@ -0,0 +1,11727 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 137, + 103, + 457, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 103, + 457, + 121 + ], + "spans": [ + { + "bbox": [ + 137, + 103, + 457, + 121 + ], + "type": "text", + "content": "Reconstructing Animatable Categories from Videos" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 143, + 465, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 143, + 465, + 175 + ], + "spans": [ + { + "bbox": [ + 127, + 143, + 465, + 175 + ], + "type": "text", + "content": "Gengshan Yang Chaoyang Wang N Dinesh Reddy Deva Ramanan Carnegie Mellon University" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 54, + 196, + 545, + 296 + ], + "blocks": [ + { + "bbox": [ + 54, + 196, + 545, + 296 + ], + "lines": [ + { + "bbox": [ + 54, + 196, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 54, + 196, + 545, + 296 + ], + "type": "image", + "image_path": "517d045bea384deb33b1c73e678a7ac3f973b8ba37aedf16d6ad011bd468b2d0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 311, + 546, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 311, + 546, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 546, + 367 + ], + "type": "text", + "content": "Figure 1. Given videos of a deformable category and a skeleton, we reconstruct an animatable 3D model that factorizes variations across instances (e.g., cheetah's and sphynx's are both cats but with different shape morphology, skeleton dimensions, and texture) from time-specific variations within an instance (e.g., skeleton articulations and elastic shape deformation). Left: Input videos; Middle-left: 3D shape, skeleton, and skinning weights (visualized as surface colors) in the canonical space; Middle-right: Disentangled between-instance and within-instance variations over time. Right: Morphology and motion transferred across the two instances." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "spans": [ + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 407, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 407, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 45, + 407, + 288, + 598 + ], + "type": "text", + "content": "Building animatable 3D models is challenging due to the need for 3D scans, laborious registration, and rigging. Recently, differentiable rendering provides a pathway to obtain high-quality 3D models from monocular videos, but these are limited to rigid categories or single instances. We present RAC, a method to build category-level 3D models from monocular videos, disentangling variations over instances and motion over time. Three key ideas are introduced to solve this problem: (1) specializing a category-level skeleton to instances, (2) a method for latent space regularization that encourages shared structure across a category while maintaining instance details, and (3) using 3D background models to disentangle objects from the background. We build 3D models for humans, cats and dogs given monocular videos. Project page: https://gengshany.github.io/rac-www/." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 622, + 128, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 128, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 128, + 634 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 643, + 287, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 643, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 643, + 287, + 717 + ], + "type": "text", + "content": "We aim to build animatable 3D models for deformable object categories. Prior work has done so for targeted categories such as people (e.g., SMPL [1, 30]) and quadruped animals (e.g., SMAL [4]), but such methods appear challenging to scale due to the need of 3D supervision and registration. Recently, test-time optimization through differ" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 383, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 546, + 467 + ], + "type": "text", + "content": "entiable rendering [40, 41, 44, 56, 69] provides a pathway to generate high-quality 3D models of deformable objects and scenes from monocular videos. However, such models are typically built independently for each object instance or scene. In contrast, we would like to build category models that can generate different instances along with deformations, given causally-captured video collections." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 471, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 547, + 615 + ], + "type": "text", + "content": "Though scalable, such data is challenging to leverage in practice. One challenge is how to learn the morphological variation of instances within a category. For example, huskys and corgis are both dogs, but have different body shapes, skeleton dimensions, and texture appearance. Such variations are difficult to disentangle from the variations within a single instance, e.g., as a dog articulates, stretches its muscles, and even moves into different illumination conditions. Approaches for disentangling such factors require enormous efforts in capture and registration [1, 5], and doing so without explicit supervision remains an open challenge." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Another challenge arises from the impoverished nature of in-the-wild videos: objects are often partially observable at a limited number of viewpoints, and input signals such as segmentation masks can be inaccurate for such \"in-the-wild\" data. When dealing with partial or impoverished video inputs, one would want the model to listen to the common structures learned across a category - e.g., dogs have two ears. On the other hand, one would want the model to" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16995" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 78, + 542, + 190 + ], + "blocks": [ + { + "bbox": [ + 54, + 78, + 542, + 190 + ], + "lines": [ + { + "bbox": [ + 54, + 78, + 542, + 190 + ], + "spans": [ + { + "bbox": [ + 54, + 78, + 542, + 190 + ], + "type": "image", + "image_path": "521d8f830e1715dd9cd836701a97296d0d2a7360609c12335a0dd98cf4696236.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": "Figure 2. Disentangling morphologies " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": " and articulation " + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 201, + 546, + 224 + ], + "type": "text", + "content": ". We show different morphologies (body shape and clothing) given the same rest pose (top) and bouncing pose (bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 245, + 173, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 173, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 173, + 256 + ], + "type": "text", + "content": "stay faithful to the input views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 258, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 413 + ], + "type": "text", + "content": "Our approach addresses these challenges by exploiting three insights: (1) We learn skeletons with constant bone lengths within a video, allowing for better disentanglement of between-instance morphology and within-instance articulation. (2) We regularize the unobserved body parts to be coherent across instances while remaining faithful to the input views with a novel code-swapping technique. (3) We make use of a category-level background model that, while not 3D accurate, produces far better segmentation masks. We learn animatable 3D models of cats, dogs, and humans which outperform prior art. Because our models register different instances with a canonical skeleton, we also demonstrate motion transfer across instances." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 427, + 138, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 138, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 138, + 441 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 652 + ], + "type": "text", + "content": "Model-based 3D Reconstruction. A large body of work in 3D human and animal reconstruction uses parametric shape models [30, 42, 55, 61, 73, 74], which are built from registered 3D scans of human or animals, and serve to recover 3D shapes given a single image or video at test time [2, 3, 3, 21, 21, 46, 72]. A recent research focus is to combine statistical human body mode with implicit functions [17, 25, 47-49, 63, 71] to improve the robustness and fidelity of the reconstruction. Although parametric body models achieve great success in reconstructing humans with large amounts of ground-truth 3D data, it is unclear how to apply the same methodology to categories with limited 3D data, such as animals, and how to scale to real-life imagery with diverse clothing and body poses. RAC builds category-level shape models from in-the-wild videos and demonstrates the potential to reconstruct 3D categories without sophisticated manual processing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Category Reconstruction from Image Collections. A number of recent methods build deformable 3D models of object categories from images with weak 2D annotations, such as keypoints and object silhouettes, obtained from human annotators or predicted by off-the-shelf mod" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 244, + 546, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 546, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 546, + 376 + ], + "type": "text", + "content": "els [13, 18, 22, 28, 53, 59, 70]. However, those methods do not distinguish between morphological variations and motion over time. Moreover, they often apply heavy regularization on shape and deformation to avoid degenerate solutions, which also smooths out fine-grained details. Recent research combines neural implicit functions [33, 34] with category modeling in the context of 3D data generation [6, 7, 37], where shape and appearance variations over a category are modeled with conditional NeRFs. However, reconstructions are typically focused on near-rigid objects such as faces and vehicles." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 376, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 521 + ], + "type": "text", + "content": "Articulated Object Reconstruction from Videos. Compared to image collections, videos provide signals to reconstruct object motions and disentangle them from morphological variations. Some works [26, 39, 51] reconstruct articulated bodies from videos, but they either assume synchronized multi-view recordings or articulated 3D skeleton inputs that make their approaches less general. Some other works [67-69] learn animatable 3D models from monocular videos capturing the same object instance, without disentangling morphology and motion. There are recent methods [27, 58, 68] using in-the-wild videos to reconstruct 3D models animals, but their quality are relatively low." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 553, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 545, + 639 + ], + "type": "text", + "content": "Given video recordings of different instances from a category and a pre-defined skeleton, we build animatable 3D models including instance-specific morphology (Sec. 3.1), time-varying articulation and deformation (Sec. 3.2), as well as a video-specific 3D background model (Sec. 3.3). The models are optimized using differentiable rendering (Sec. 3.4). An overview is shown in Fig. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 647, + 458, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 458, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 458, + 658 + ], + "type": "text", + "content": "3.1. Between-Instance Variation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "type": "text", + "content": "Fusing videos of different instances into a category model requires handling the morphological variations, which includes the changes in both internal skeleton and outward appearance (shape and color). We define a video-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16996" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 534, + 155 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 534, + 155 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 534, + 155 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 534, + 155 + ], + "type": "image", + "image_path": "901ce8519be8cfbf8e05ce8c7bc871bc8e342b183120adad36c86863e33e31c1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": "Figure 3. Morphological variations vs time-varying articulation and deformation. (a) Canonical shape " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": ", skinning weights " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": ", and joint locations " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": ". (b) To represent morphological differences between instances, we use a morphology code " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " that specifies instance shape and appearance " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\beta}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": ", skinning weights " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\beta}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " for a canonical skeleton " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": ". (c) " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " also predicts a change in bone lengths " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{J}_{\\beta}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " which further stretches instance shape into " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\beta}^{s}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " by elongating body parts. (d) Time-varying articulations are modeled with an articulation vector " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " by linearly blending rigid bone transformations in the dual quaternion space. Time-varying deformations (such as muscle deformation) are modeled with a deformation vector " + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\omega_{d}" + }, + { + "bbox": [ + 46, + 161, + 547, + 228 + ], + "type": "text", + "content": " through invertible 3D warping fields." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 248, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 272 + ], + "type": "text", + "content": "specific morphology code " + }, + { + "bbox": [ + 46, + 248, + 287, + 272 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 248, + 287, + 272 + ], + "type": "text", + "content": " to control the variations of both the shape and the skeleton." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 273, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 380 + ], + "type": "text", + "content": "To model between-instance shape variations, one could use dense warping fields to deform a canonical template into instance-specific shapes [62]. However, warping fields cannot explain topological changes (e.g., different clothing). Instead, we define a hierarchical representation: a conditional canonical field [8, 41, 57] to handle fine-grained variations over a category (e.g., the ears of dogs) and a stretchable bone model [14, 60] to represent coarse shape variations (e.g., height and size of body parts)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "content": "Conditional Field T. In the canonical space, a 3D point " + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "content": " is associated with three properties: signed distance " + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "inline_equation", + "content": "d \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "content": ", color " + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "content": ", and canonical features " + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "inline_equation", + "content": "\\psi \\in \\mathbb{R}^{16}" + }, + { + "bbox": [ + 47, + 380, + 288, + 452 + ], + "type": "text", + "content": ", which is used to register pixel observations to the canonical space [35,68]. These properties are predicted by multi-layer perceptron (MLP) networks:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 101, + 459, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 459, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 101, + 459, + 287, + 472 + ], + "type": "interline_equation", + "content": "\\left(d, \\mathbf {c} ^ {t}\\right) = \\mathbf {M L P} _ {\\mathrm {S D F}} \\left(\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\omega} _ {a}\\right), \\tag {1}", + "image_path": "0c99b68d5425327873c76f94a7ccabf0e1e888719e5005b66459a72df2a5fc12.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 120, + 475, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 475, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 120, + 475, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\psi = \\mathbf {M L P} _ {\\psi} (\\mathbf {X}), \\tag {2}", + "image_path": "38527b369c3cbc71964fa00880421a959aec3e6648e7f86bf1bfabb81183dbfd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "text", + "content": "where the shape and color are conditioned on a videospecific morphology code " + }, + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "text", + "content": " [16, 37]. We further ask the color to be dependent on an appearance code " + }, + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\omega_{a}\\in \\mathbb{R}^{64}" + }, + { + "bbox": [ + 46, + 495, + 287, + 554 + ], + "type": "text", + "content": " that captures frame-specific appearance such as shadows and illumination changes [32]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "text", + "content": "Skeleton J. Unlike shape and color, the bone structures are not directly observable from imagery, making it ambiguous to infer. Methods for automatic skeletal rigging [23, 38, 65] either heavily rely on shape priors, or appear sensitive to input data. Instead, we provide a category-level skeleton topology, which has a fixed tree topology with " + }, + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "inline_equation", + "content": "(\\mathrm{B} + 1)" + }, + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "text", + "content": " bones and B joints (B=25 for quadruped and B=18 for human). To model cross-instance morphological changes, we define per-instance joint locations as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 113, + 668, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 668, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 113, + 668, + 287, + 682 + ], + "type": "interline_equation", + "content": "\\mathbf {J} = \\mathbf {M L P} _ {\\mathbf {J}} (\\beta) \\in \\mathbb {R} ^ {3 \\times B}. \\tag {3}", + "image_path": "0233e3738862e1c4712634b853edb665a32667214bc921b3c9363d4fb2564260.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "As we will discuss next, the change in joint locations not only stretches the skeleton, but also results in the elongation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 248, + 545, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 545, + 283 + ], + "type": "text", + "content": "of canonical shapes as shown in Fig. 3 (c). The skeleton topology is fixed through optimization but " + }, + { + "bbox": [ + 304, + 248, + 545, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 304, + 248, + 545, + 283 + ], + "type": "text", + "content": " is specialized to each video." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "text", + "content": "**Skinning Field W.** For a given 3D location " + }, + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "text", + "content": ", we define skinning weight vector " + }, + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{B + 1}" + }, + { + "bbox": [ + 304, + 284, + 545, + 309 + ], + "type": "text", + "content": " following BANMo:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 325, + 545, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 325, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 315, + 325, + 545, + 339 + ], + "type": "interline_equation", + "content": "\\mathbf {W} = \\sigma_ {\\text {s o f t m a x}} \\left(d _ {\\sigma} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta}) + \\mathbf {M L P} _ {\\mathbf {W}} (\\mathbf {X}, \\boldsymbol {\\beta}, \\boldsymbol {\\theta})\\right), \\tag {4}", + "image_path": "c68a6c180efd8d79d458d7196c367d40b7abfdadeb9bcf698739424472685c69.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": " is a articulation code and " + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "inline_equation", + "content": "d_{\\sigma}(\\mathbf{X},\\boldsymbol {\\beta},\\boldsymbol {\\theta})" + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": " is the Mahalanobis distance between " + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": " and Gaussian bones under articulation " + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": " and morphology " + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 343, + 545, + 438 + ], + "type": "text", + "content": ", refined by a delta skinning MLP. Each Gaussian bone has three parameters for center, orientation, and scale respectively, where the centers are computed as the midpoint of two adjacent joints, the orientations are determined by the parent joints, and the scales are optimized." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 439, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 439, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 439, + 545, + 523 + ], + "type": "text", + "content": "Stretchable Bone Deformation. To represent variations of body dimension and part size, prior work [30, 74] learns a PCA basis from registered 3D scans. Since 3D registrations are not available for in-the-wild videos, we optimize a parametric model through differentiable rendering. Given the stretched joint locations, the model deforms the canonical shape " + }, + { + "bbox": [ + 304, + 439, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\beta}" + }, + { + "bbox": [ + 304, + 439, + 545, + 523 + ], + "type": "text", + "content": " with blend skinning equations," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 381, + 528, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 528, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 381, + 528, + 545, + 542 + ], + "type": "interline_equation", + "content": "\\mathbf {T} _ {\\beta} ^ {s} = \\left(\\mathbf {W} _ {\\beta} \\mathbf {G} _ {\\beta}\\right) \\mathbf {T} _ {\\beta}, \\tag {5}", + "image_path": "9e81e0d9d7b5807cbd7a949c60906bd0a71de02a0d3a603cd81bf3b5cce3fe73.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{\\beta}" + }, + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "text", + "content": " transforms the bone coordinates, and " + }, + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\beta}" + }, + { + "bbox": [ + 304, + 545, + 545, + 570 + ], + "type": "text", + "content": " is the instance-specific skinning weights in Eq. (4)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 575, + 451, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 451, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 451, + 586 + ], + "type": "text", + "content": "3.2. Within-Instance Variation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We represent within-instance variations as time-varying warp fields between the canonical space and posed space at time " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". Similar to HumanNeRF [57], we decompose motion as articulations that explains the near-rigid component (e.g., skeletal motion) and deformation that explains the remaining nonrigid movements (e.g., cloth deformation). Note given the complexity of body movements, it is almost certain the pre-defined skeleton would ignore certain movable body parts. Adding deformation is crucial to achieving high-fidelity reconstruction." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16997" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 545, + 149 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 545, + 149 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 545, + 149 + ], + "type": "image", + "image_path": "66bdc7596c30f6829c9ace97837a1c01556eb74e477244a33baaa4b77a7690aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 158, + 547, + 180 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 547, + 180 + ], + "type": "text", + "content": "Figure 4. Different " + }, + { + "bbox": [ + 46, + 158, + 547, + 180 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 158, + 547, + 180 + ], + "type": "text", + "content": " morphologies of dogs (top) and cats (bottom). Our reconstructions show variance in ear shape and limb size over dog breeds, as well as variance in limb and body size over cat breeds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "content": "Time-varying Articulation. To model the time-varying skeletal movements, we define per-frame joint angles:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 229, + 287, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 229, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 113, + 229, + 287, + 244 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {M L P} _ {\\mathbf {A}} (\\boldsymbol {\\theta}) \\in \\mathbb {R} ^ {3 \\times B} \\tag {6}", + "image_path": "d8ba068e3ba0d50e93e6a87d1c9d71406140d372f0f2fddd8f23e321003343f0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{16}" + }, + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "text", + "content": " is a low-dimensional articulation parameter, and each joint has three degrees of freedom. Given joint angles and the per-video joint locations, we compute bone transformations " + }, + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{G} \\in \\mathbb{R}^{3 \\times 4 \\times B}" + }, + { + "bbox": [ + 46, + 248, + 287, + 320 + ], + "type": "text", + "content": " via forward kinematics. We apply dual quaternion blend skinning (DQB) [19] to get the warping field for each spatial point," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 325, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 325, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 116, + 325, + 287, + 340 + ], + "type": "interline_equation", + "content": "\\mathbf {D} (\\boldsymbol {\\beta}, \\theta) = \\left(\\mathbf {W} _ {\\boldsymbol {\\beta}} \\mathbf {G}\\right) \\mathbf {T} _ {\\boldsymbol {\\beta}} ^ {s}. \\tag {7}", + "image_path": "76f55c965ed98684427c2eaf36729fcb2361731813e96a76181ec74568e0f586.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 343, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 287, + 403 + ], + "type": "text", + "content": "Dual quaternion skinning blends SE(3) transformations in dual quaternion space and ensures valid SE(3) after blending, which reduces artifacts around twisted body parts. Note stretching in Eq. (5) can be fused with articulation as a single blend skinning operation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 403, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 475 + ], + "type": "text", + "content": "Time-varying Soft Deformation. To further explain the dynamics induced by non-skeleton movements (such as the cat belly and human clothes), we add a neural deformation field [24, 40] " + }, + { + "bbox": [ + 46, + 403, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 403, + 287, + 475 + ], + "type": "text", + "content": " that is flexible enough to model highly nonrigid deformation. Applying the fine-grained warping after blend skinning, we have" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 101, + 480, + 287, + 494 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 480, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 101, + 480, + 287, + 494 + ], + "type": "interline_equation", + "content": "\\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) = \\mathcal {D} (\\mathbf {D} (\\boldsymbol {\\beta}, \\theta), \\omega_ {d}), \\tag {8}", + "image_path": "3dd3485dfd0de577f4eef3b7fd47e51db54da36f79358021c23ed564309936d3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\omega_{d}" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": " is a frame-specific deformation code. Inspired by CaDeX [24], we use real-NVP [9] to ensure the 3D deformation fields are invertible by construction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": "Invertibility of 3D Warping Fields. For a given time instance " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": ", we have defined a forward warping field " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^{t,\\rightarrow}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " that transforms 3D points from the canonical space to the specified time instance, and a backward warping field " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^{t,\\leftarrow}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " to transform points in the inverse direction. Both warping fields include stretching (Eq. (5)), articulation. (Eq. (7)), and deformation (Eq. (8)) operations. Notably, we only need to define each operation in the forward warping fields. The deformation operation is, by construction, invertible. To invert stretching and articulation, we invert SE (3) transformations " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " in the blend skinning equations and compute the skinning weights with Eq. (4) using the corresponding morphology and articulation codes. A 3D cycle loss is used to ensure that the warping fields are self-consistent after a forward-backward cycle [29, 69]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 201, + 388, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 201, + 388, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 201, + 388, + 213 + ], + "type": "text", + "content": "3.3. Scene Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 220, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 292 + ], + "type": "text", + "content": "Reconstructing objects from in-the-wild video footage is challenging due to failures in segmentation, which is often caused by out-of-frame body parts, occlusions, and challenging lighting. Inspired by background subtraction [15, 50], we build a model of the background to robustify our method against inaccurate object segmentation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 293, + 546, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 388 + ], + "type": "text", + "content": "In background subtraction, moving objects can be segmented by comparing input images to a background model (e.g., a median image). We generalize this idea to model the background scene in 3D as a per-video NeRF, which can be rendered as color pixels at a moving camera frame and compared to the input frame. We design a conditional background model that generates density and color of a scene conditioned on a per-video background code " + }, + { + "bbox": [ + 304, + 293, + 546, + 388 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 293, + 546, + 388 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 366, + 398, + 545, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 398, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 366, + 398, + 545, + 412 + ], + "type": "interline_equation", + "content": "(\\sigma , \\mathbf {c} ^ {t}) = \\mathbf {M L P} _ {\\mathbf {b g}} (\\mathbf {X}, \\mathbf {v}, \\gamma), \\tag {9}", + "image_path": "b0bf9061fb8945c98b3f19074822a08d897030c610b778b139eff674bd9e50ee.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 422, + 546, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 546, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 546, + 553 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 422, + 546, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 422, + 546, + 553 + ], + "type": "text", + "content": " is the viewing direction. To render images, we compose the density and color of the object field and the background NeRF in the view space [37], and compute the expected color and optical flow. Background modeling and composite rendering allows us to remove the object silhouette loss, and improves the quality of results. Interestingly, we find that even coarse geometric reconstructions of the background still can improve the rendered 2D object silhouette, which in turn is useful for improving the quality of object reconstructions (Fig. 5). We ablate the design choice in Tab. 1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 562, + 451, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 451, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 451, + 574 + ], + "type": "text", + "content": "3.4. Losses and Regularization" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": "Given the videos and a predefined skeleton, we optimize the parameters discussed above: (1) canonical parameters " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\{\\beta ,\\mathbf{J},\\mathbf{T},\\mathbf{W}\\}" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": " including per-video morphology codes and canonical templates; (2) motion parameters " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\{\\theta ,\\omega_{\\mathrm{d}},\\mathbf{A},\\mathbf{D}\\}" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": " including per-frame codes as well as articulation and soft deformation MLPs. (3) background parameters " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\{\\gamma ,\\mathbf{B}\\}" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": " including video background codes and a background NeRF. The overall objective function contains a image reconstruction loss term and regularization terms." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Reconstruction Losses. The reconstruction loss is defined as the difference between rendered and observed images," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16998" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 82, + 286, + 284 + ], + "blocks": [ + { + "bbox": [ + 49, + 82, + 286, + 284 + ], + "lines": [ + { + "bbox": [ + 49, + 82, + 286, + 284 + ], + "spans": [ + { + "bbox": [ + 49, + 82, + 286, + 284 + ], + "type": "image", + "image_path": "5967c2a979763aec1857e1d2fe04cc0add0d83358f3a59bd1f0081cc32c359e7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 293, + 288, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 360 + ], + "type": "text", + "content": "Figure 5. Joint foreground and background reconstruction. We jointly reconstruct objects and their background, while refining the segmentation. Note the input silhouette is noisy (e.g., tail was not segmented), and background modeling helps produce an accurate refined silhouette. As a result, RAC is robust to inaccurate segmentation (e.g., tail movements marked by the red box)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 381, + 259, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 259, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 259, + 395 + ], + "type": "text", + "content": "including object silhouette, color, flow, and features:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 103, + 403, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 403, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 103, + 403, + 287, + 417 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {s i l}} + \\mathcal {L} _ {\\mathrm {r g b}} + \\mathcal {L} _ {\\mathrm {O F}} + \\mathcal {L} _ {\\text {f e a t}}. \\tag {10}", + "image_path": "56b5215af7a3a755daab8c24dba7f032f141d3bc4024772939a2f8e7d164f7eb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 521 + ], + "type": "text", + "content": "We update the model parameter by minimizing " + }, + { + "bbox": [ + 46, + 426, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 426, + 287, + 521 + ], + "type": "text", + "content": " through differentiable volume rendering in the same way as BANMo [69]. Off-the-shelf estimates of object silhouettes are used as supervision to kick-start the optimization. Then the weight of silhouette term is set to 0 after several iterations of optimization, while composite rendering of foreground and background itself is capable of separating the object and the non-object components." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": "Morphology Code " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\beta)" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " Regularization. Existing differentiable rendering methods are able to faithfully reconstruct the input view but not able to hallucinate a reasonable solution for occluded body parts [40, 69]. See Fig. 9 for an example. One solution is to regularize the instance-specific morphology code " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " to be consistent with the body shapes observed in other videos. Traditional approaches might do this by adding variational noise (as in a VAE) or adversarial losses (as in a GAN). We found good results with the following easy-to-implement approach: we randomly swap the morphology code " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " of two videos during optimization; this regularizes the model to effectively learn a single morphology code that works well across all videos. But naively applying this approach would produce a single morphology that would not specialize to each object instance. To enable specialization, we gradually decrease the probability" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "text", + "content": "Table 1. Quantitative results on AMA sequences. 3D Chamfer distance " + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "inline_equation", + "content": "(\\mathrm{cm},\\downarrow)" + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "text", + "content": " and F-score " + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "inline_equation", + "content": "(\\% ,\\uparrow)" + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "text", + "content": " averaged over all frames. Our model is trained on 47 human videos spanning existing human datasets (as described in Sec.4.2); we also train BANMo on the same set. Other baselines are trained on 3D human data and relies on SMPL model. Results with " + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "inline_equation", + "content": "^S" + }, + { + "bbox": [ + 305, + 70, + 545, + 148 + ], + "type": "text", + "content": " indicates variants trained on single instances. Our model outperforms prior works." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 156, + 544, + 293 + ], + "blocks": [ + { + "bbox": [ + 307, + 156, + 544, + 293 + ], + "lines": [ + { + "bbox": [ + 307, + 156, + 544, + 293 + ], + "spans": [ + { + "bbox": [ + 307, + 156, + 544, + 293 + ], + "type": "table", + "html": "
Methodsambabouncing
CDF@2%F@5%CDF@2%F@5
HuMoR9.847.583.711.545.282.3
ICON10.139.985.29.753.586.4
\\( BANMo^S \\)8.062.289.17.664.791.1
BANMo9.354.485.510.254.486.5
\\( RACS \\)6.470.993.26.966.792.8
RAC6.072.594.48.063.891.4
w/o skeleton8.659.687.79.359.587.8
w/o \\( \\beta \\)8.558.987.58.462.590.6
\\( \\beta swap\\rightarrow ||\\beta||_2^2 \\)6.569.093.88.064.891.3
+ bkgd NeRF6.370.993.77.465.591.8
", + "image_path": "821a5d980aeb00f43c2e92ab76df054bdf160cd7f542a08f1f5a50166dcf09fa.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 314, + 537, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 314, + 537, + 325 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 537, + 325 + ], + "type": "text", + "content": "of swaps during the optimization, from " + }, + { + "bbox": [ + 305, + 314, + 537, + 325 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = 1.0\\to 0.05" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "text", + "content": "Joint J Regularization. Due to the non-observable nature of the joint locations, there might exist multiple joint configurations leading to similar reconstruction error. To register the skeleton with the canonical shape, we minimize Sinkhorn divergence [11] between the canonical surface " + }, + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\beta}" + }, + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "text", + "content": " and the joint locations " + }, + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\beta}" + }, + { + "bbox": [ + 304, + 326, + 545, + 456 + ], + "type": "text", + "content": ", which forces them to occupy the same space. We extract the canonical mesh with marching cubes [31] as a proxy of the canonical surface. Sinkhorn distance interpolates between Wasserstein and kernel distances and defines a soft way to measure the distance between shapes with different density distributions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 517 + ], + "type": "text", + "content": "Soft Deformation Regularization The soft deformation field has the capacity of explaining not only the soft deformations, but also the skeleton articulations. Therefore, we penalize the L2 norm of the soft deformation vectors at randomly sampled morphology and articulations," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 354, + 527, + 545, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 527, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 354, + 527, + 545, + 540 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s o f t}} = \\left\\| \\mathbf {D} (\\boldsymbol {\\beta}, \\theta , \\omega_ {d}) - \\mathbf {D} (\\boldsymbol {\\beta}, \\theta) \\right\\|. \\tag {11}", + "image_path": "2f194dd179716fd9fb3e3dc57108aeb5e0c0d19d043ffe67b576be5e65a15a73.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 561, + 388, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 388, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 388, + 575 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": "Implementation Details. We build RAC on BANMo and compute bone transformations from a kinematic tree. The soft deformation field follows CaDeX, where we find that two invertible blocks are capable of handling moderate deformations. To evaluate surface reconstruction accuracy, we extract the canonical mesh " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": " by finding the zero-level set of SDF with marching cubes on a " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "256^3" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": " grid. To get the shape at a specific time, the canonical mesh is forward-warmed with " + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^{t,\\rightarrow}" + }, + { + "bbox": [ + 304, + 581, + 545, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Optimization Details We use AdamW to optimize the model for 36k iterations with 16384 rays per batch (taking" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16999" + } + ] + } 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We fist pre-train the background model with RGB, optical flow, and surface normal losses while ignoring foreground pixels. Then we combine background models with the object model for composite rendering optimization. The weights for the loss terms are tuned to have similar initial magnitude. The object root poses are initialized with single-image viewpoint networks trained for humans and quadruped animals following BANMo [69]. For all categories, we start with the same shape (a unit sphere) and a known skeleton topology. Both the shape and the joint locations are specialized to the input dataset, as shown in Fig. 7." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 47, + 527, + 185, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 185, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 185, + 540 + ], + "type": "text", + "content": "4.1. 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[ + { + "bbox": [ + 500, + 494, + 535, + 534 + ], + "type": "image", + "image_path": "419600c37175505e55fb96a9e5cdf055c476c60bad98615fb6cbef6cb0c3084d.jpg" + } + ] + } + ], + "index": 60, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 560, + 545, + 605 + ], + "lines": [ + { + "bbox": [ + 304, + 560, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 560, + 545, + 605 + ], + "type": "text", + "content": "Figure 7. Shape and skeleton optimization. From top to bottom, we visualize the canonical shape and skeleton of our dog, cat, and human models. Left: Canonical shape and skeleton before optimization. Right: Canonical shape and skeleton after optimization." + } + ] + } + ], + "index": 63, + "angle": 0, + "type": "image_caption" + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "content": "matches, but it is sensitive to outliers. F-score at distance thresholds " + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "inline_equation", + "content": "d \\in \\{1\\%, 2\\%, 5\\% \\}" + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "content": " of the human bounding box size [52] provides a more informative quantification of surface reconstruction error at different granularity. To account for the unknown scale, we align the predicted mesh with the ground-truth mesh using their depth in the view space." + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Baselines. On AMA, we compare with template-free BANMo [69] and model-based methods, including Hu" + } + ] + } + ], + "index": 65 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17000" + } + ] + } + ], + "index": 66 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "text", + "content": "MoR [45] and ICON [63]. BANMo reconstructs an animatable 3D model from multiple monocular videos of the same instance, powered by differentiable rendering optimization. We optimize BANMo on the same dataset with the same amount of computation and iterations as ours. HuMoR is a temporal pose and shape predictor for humans. It performs test-time optimization on video sequences leveraging OpenPose keypoint detection and motion priors trained on large-scale human motion capture dataset. We run it on each video sequence, and processing 170 video frames takes around two hours on a machine with Titan-X GPU. ICON is the recent SOTA method on single view human reconstruction. It combines statistical human body models (SMPL) with implicit functions and is trained on 3D human scans with clothing. Notably, it performs test-time optimization to fit surface normal predictions to improve the pose accuracy and reconstruction fidelity. We run it per frame, and processing a 170 frame video takes around three hours on an RTX-3090 GPU." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 289, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 289, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 289, + 552 + ], + "type": "text", + "content": "Results. We show qualitative comparison with baselines in Fig. 6 top row, and quantitative results in Tab. 1. On the handstand sequence, HuMoR works well for common poses but fails where the performer is not in an upright pose. ICON works generally well, but the hand distances appear not physically plausible (too short) from a novel viewpoint. BANMo reconstruction also failed to reconstruct the unnatural upside-down pose. In contrast, RAC successfully reconstructs the handstand pose with plausible hand distances. On the samba sequence, HuMoR correctly predicts body poses, but fails to reconstruct the cloth and its deformation. ICON predicts a broken dress and distorted human looks from a novel viewpoint, possibly due to lack of diverse training data from dressed humans. When applied to 47 videos of different humans, BANMo fails to model the cloth correctly, possibly because a limited number of control points are not expressive enough to model the morphological variations over humans wearing different clothes. RAC models between-shape variations using a conditional canonical model and successfully reconstructs cloth deformation using the soft deformation field." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 552, + 288, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 661 + ], + "type": "text", + "content": "Our quantitative results align with qualitative observations, where RAC outperforms all baselines except being slightly worse than BANMo trained on single instances (S). However, RAC trained on single instances (S) or multiple instances (M) outperforms BANMo trained in either fashion. In particular, BANMo results are notably worse when trained on multiple instances, indicating the difficulty in building category models. In contrast, RAC become better when trained on multiple instances." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 670, + 212, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 212, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 212, + 684 + ], + "type": "text", + "content": "4.2. Reconstructing Cats and Dogs" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Dataset. We collect 76 cat videos and 85 dog videos from Internet videos, as well as public data from BANMo. All" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "the videos are casually-captured monocular videos. We extract video frames at 10 FPS, including 9,734 frames for cats and 11,657 frames for dogs. We perform the same preprocessing as human reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 120, + 547, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 547, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 547, + 203 + ], + "type": "text", + "content": "Baselines. We compare with BANMo and model-based BARC [46]. BARC is the current SOTA for dog shape and pose estimation. It trains a feed-forward network using CG dog models and images with keypoint labels. The shape model is based on SMAL, which uses manual rigging and registration to fit 3D animal toys. We run BARC on individual images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 203, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 546, + 419 + ], + "type": "text", + "content": "Results. We show qualitative results in Fig. 6 bottom row. For dog videos, we find that BARC worked well to predict coarse shapes and poses. However, the results are biased towards certain dog breeds. For instance, BARC predicts a long jaw when the dog has a short jaw (top row), and predicts round ears when the dog has sharp ears (bottom). BANMo was able to reconstruct a reasonable coarse shape, but failed to capture the fine details (e.g., the shape of the ear and the size of the head) with only 25 control points. In contrast, RAC was able to faithfully capture the coarse shape and fine details of the dogs. Unlike dogs, cats have fewer variations in body shape and size, where we find that BANMo works well in most cases. However, for the body parts not visible from the reference viewpoint, BANMo often estimates a squashed shape, which may be caused by the entangled morphology and articulations. In contrast, RAC accurately infers reasonable body parts and articulations even when they are not visible." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 426, + 383, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 383, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 383, + 438 + ], + "type": "text", + "content": "4.3. Diagnostics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "type": "text", + "content": "Large Morphological Changes. We reconstruct eight videos of different quadruped animals together to \"stress test\" our method. The dataset contains two dog videos, two cat videos, and one video for goat, bear, camel, and cow, respectively. The result is shown in Fig. 8." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 306, + 514, + 538, + 588 + ], + "blocks": [ + { + "bbox": [ + 306, + 514, + 538, + 588 + ], + "lines": [ + { + "bbox": [ + 306, + 514, + 538, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 538, + 588 + ], + "type": "image", + "image_path": "70aa9bfa0afb61e8d0cfab36061fcbc6da3e338ee7cb67e5b4b37f0167c29acb.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "lines": [ + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "type": "text", + "content": "Figure 8. Quadruped Category Reconstruction. Using a smaller code swapping probability " + }, + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "type": "inline_equation", + "content": "P = 0.01" + }, + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "type": "text", + "content": " results in more faithful instance shape, but less smooth results. A larger " + }, + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 597, + 545, + 643 + ], + "type": "text", + "content": " produces smoother results, but some instance-specific features disappear." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Morphology Code " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " Removing morphology code " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " from the canonical field degrades it to a standard NeRF. We rerun the experiments and the results are shown in Tab. 1 as well as Fig. 9. Without the morphology code, our reconstructions are forced to share the same canonical shape, which" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17001" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "as discussed in Sec 3.1, failed to handle fine deformations and topological changes (e.g., clothing), leading to worse results in all metrics." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "text", + "content": "Morphology Code Regularization To test the effectiveness of the morphology code regularization, we set " + }, + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = 0" + }, + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "text", + "content": " throughout the optimization. The results are shown in Tab. 1 and Fig. 9. Without regularization of the morphology code, the reconstructed shape may appear reasonable from the reference viewpoint, but severely distorted from a novel viewpoint. We posit the body parts that are not well-covered in the video are inherently difficult to infer. As a result, the shapes become degenerate without relying on priors from other videos in the dataset. Tab. 1 also shows that code swapping outperforms norm regularization [12] " + }, + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "inline_equation", + "content": "(||\\beta ||_2^2)" + }, + { + "bbox": [ + 46, + 109, + 289, + 301 + ], + "type": "text", + "content": ". We posit norm regularization forces codes to be similar, but does not constrain their output space, while code swapping encourages any code to explain any image in the data. In practice, we find that code swapping generates valid outputs when we interpolate between codes." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 312, + 84, + 361 + ], + "blocks": [ + { + "bbox": [ + 48, + 312, + 84, + 361 + ], + "lines": [ + { + "bbox": [ + 48, + 312, + 84, + 361 + ], + "spans": [ + { + "bbox": [ + 48, + 312, + 84, + 361 + ], + "type": "image", + "image_path": "d024532bcd0d182de131a33e83cc6761f690282271c02e7adb41fa5cb982a5d8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 364, + 81, + 372 + ], + "lines": [ + { + "bbox": [ + 50, + 364, + 81, + 372 + ], + "spans": [ + { + "bbox": [ + 50, + 364, + 81, + 372 + ], + "type": "text", + "content": "Reference" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 89, + 312, + 113, + 360 + ], + "blocks": [ + { + "bbox": [ + 89, + 312, + 113, + 360 + ], + "lines": [ + { + "bbox": [ + 89, + 312, + 113, + 360 + ], + "spans": [ + { + "bbox": [ + 89, + 312, + 113, + 360 + ], + "type": "image", + "image_path": "b3e9fe0046ff3d680e035e99dbd93fdb5221f3e17004840ab6c703dba7fe043e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 363, + 130, + 372 + ], + "lines": [ + { + "bbox": [ + 97, + 363, + 130, + 372 + ], + "spans": [ + { + "bbox": [ + 97, + 363, + 130, + 372 + ], + "type": "text", + "content": "Full Model" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 119, + 312, + 146, + 359 + ], + "blocks": [ + { + "bbox": [ + 119, + 312, + 146, + 359 + ], + "lines": [ + { + "bbox": [ + 119, + 312, + 146, + 359 + ], + "spans": [ + { + "bbox": [ + 119, + 312, + 146, + 359 + ], + "type": "image", + "image_path": "3729881d6a63aa04bd5b0fb77885464a12976a46e358b9ecf9aa130c7b7fdf04.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 375, + 264, + 392 + ], + "lines": [ + { + "bbox": [ + 69, + 375, + 264, + 392 + ], + "spans": [ + { + "bbox": [ + 69, + 375, + 264, + 392 + ], + "type": "text", + "content": "Figure 9. 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Ablation study on soft deformation " + }, + { + "bbox": [ + 70, + 519, + 263, + 531 + ], + "type": "inline_equation", + "content": "\\omega_{d}" + }, + { + "bbox": [ + 70, + 519, + 263, + 531 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": "Motion Transfer. Given the category model with disentangled morphology and articulations, we can easily transfer an articulation in frame " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " to other video by setting the articulation parameter to " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": ", while keeping the morphology parameter " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " the same. We show motion transfer across human in Fig. 2. Please visit our website for video results of dogs, cats, and humans." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": "Skeleton vs Control Points. Control point deformations are flexible but do not preserve body dimensions (e.g., a line segment can be stretched longer by its end points). As a result, body and limb dimensions can change, creating two problems: (1) articulated shapes look squashy from novel views, and (2) variations in body dimensions are entangled with control-point deformations. In contrast, skeleton de" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": "formation preserves body dimensions. It produces better results (Tab. 1) and better motion re-targeting (Fig. 11)." + } + ] + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 308, + 102, + 533, + 223 + ], + "blocks": [ + { + "bbox": [ + 308, + 102, + 533, + 223 + ], + "lines": [ + { + "bbox": [ + 308, + 102, + 533, + 223 + ], + "spans": [ + { + "bbox": [ + 308, + 102, + 533, + 223 + ], + "type": "image", + "image_path": "4bc559a512745433d7eeb6e2dc21162e622b9da82799b72667adc63b8820e07f.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 230, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 285 + ], + "type": "text", + "content": "Figure 11. Skeleton vs control-points for motion transfer. RAC with control points fails to maintain the body dimensions during motion, and produces squashy results when transferred to a new morphology. RAC with skeleton disentangles motion from morphology, allowing for better motion transfer." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 298, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 347 + ], + "type": "text", + "content": "Stretchable Bones allow for control of bone dimensions after optimization. We show an example of a Dachshund (Source1) warped to a Heeler (Source2) by modifying bone dimensions while keeping the shape unchanged." + } + ] + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 312, + 353, + 537, + 439 + ], + "blocks": [ + { + "bbox": [ + 312, + 353, + 537, + 439 + ], + "lines": [ + { + "bbox": [ + 312, + 353, + 537, + 439 + ], + "spans": [ + { + "bbox": [ + 312, + 353, + 537, + 439 + ], + "type": "image", + "image_path": "f2a260052764f627e441b22a3d99fe3e9788177e7e29bd0766041902757960e5.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 445, + 533, + 457 + ], + "lines": [ + { + "bbox": [ + 317, + 445, + 533, + 457 + ], + "spans": [ + { + "bbox": [ + 317, + 445, + 533, + 457 + ], + "type": "text", + "content": "Figure 12. Disentanglement of bone dimensions and shape." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 491, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 670 + ], + "type": "text", + "content": "We have presented a scalable way of building animatable category models by learning from monocular videos. It disentangles morphology variations between instances and motion within an instance, allowing motion transfer over a category. RAC reaches state-of-the-art reconstruction quality for cats, dogs, and humans in terms of mid-level reconstruction, but details are still missing (such as human hand and toes). Similar to BANMo, RAC requires rough viewpoint initialization. Although we have shown either a pretrained viewpoint estimator or roughly annotated camera viewpoints (in the supplement) are sufficient, it would be interesting to study a more generic way to initialize viewpoints. We also show that category-level skeleton improves motion reconstruction, and leave jointly inferring skeleton structure together with object shape for future work." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "type": "text", + "content": "Acknowledgement This work was supported by the Qualcomm Innovation Fellowship and the CMU Argo AI Center for Autonomous Vehicle Research." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17002" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 137 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 137 + ], + "type": "text", + "content": "[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 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Kuchenbecker Michael J. Black", + "bbox": [ + 299, + 199, + 669, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Max Planck Institute for Intelligent Systems, Stuttgart and Tübingen, Germany", + "bbox": [ + 250, + 218, + 718, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{forte,kjk}@is.mpg.de {kulits,chuang2,vchoutas,dtzionas,black}@tue.mpg.de", + "bbox": [ + 151, + 237, + 808, + 250 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dec574879ff276e02bd3d1f927ee8f2f09b5c6534eb19ab083d45f383d3cf6ab.jpg", + "image_caption": [ + "Figure 1. Given a monocular, in-the-wild video of a sign-language sign, SGNify automatically reconstructs a 3D body with accurate hand pose, facial motion, and body pose. Note that motion blur obscures the finger articulations in several video frames; this is a common problem. Our novel linguistic priors enable accurate 3D reconstruction despite such image degradation." + ], + "image_footnote": [], + "bbox": [ + 138, + 267, + 888, + 441 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 517, + 313, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sign language (SL) is the primary method of communication for the 70 million Deaf people around the world. Video dictionaries of isolated signs are a core SL learning tool. Replacing these with 3D avatars can aid learning and enable AR/VR applications, improving access to technology and online media. However, little work has attempted to estimate expressive 3D avatars from SL video; occlusion, noise, and motion blur make this task difficult. We address this by introducing novel linguistic priors that are universally applicable to SL and provide constraints on 3D hand pose that help resolve ambiguities within isolated signs. Our method, SGNify, captures fine-grained hand pose, facial expression, and body movement fully automatically from in-the-wild monocular SL videos. We evaluate SGNify quantitatively by using a commercial motion-capture system to compute 3D avatars synchronized with monocular video. SGNify outperforms state-of-the-art 3D body-pose-and shape-estimation methods on SL videos. A perceptual study shows that SGNify's 3D reconstructions are significantly more comprehensible and natural than those of previous methods and are on par with the source videos. Code and data are available at sgnify.is.tue.mpg.de.", + "bbox": [ + 73, + 550, + 472, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 517, + 630, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is estimated that over 466 million people have disabling hearing loss [13] and more than 70 million people use sign language (SL) as their primary means of communication [52]. Increasing use of digital communication motivates research on capturing, understanding, modeling, and synthesizing expressive 3D SL avatars. Existing datasets and dictionaries used in SL recognition (SLR), translation (SLT), and production (SLP) are primarily limited to 2D video because the technology required to capture 3D movement is prohibitively expensive, requires expertise to operate, and may limit the movements of the signer. Dictionaries of isolated signs are a core SL learning tool, and many SLs have online 2D video dictionaries. The Deaf community is actively seeking 3D dictionaries of isolated signs to aid learning [40]. The current approach to creating such 3D signing dictionaries is fully manual, requiring an artist or a HamNoSys [21] expert, and the resulting avatars often move unnaturally [3]. We aim to automatically reconstruct expressive 3D signing avatars from monocular SL video, which we term Sign Language Capture (SLC). We focus on SLC of isolated signs.", + "bbox": [ + 496, + 547, + 890, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D reconstruction of human pose and shape has received significant attention, but accurate 3D hand-pose estimation", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12791", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "remains challenging from in-the-wild video. Challenges include the high number of degrees of freedom present in hands [5], frequent occurrence of self-contact and self-occlusions [37, 46], low resolution, and motion blur caused by fast motions [50] that cause hand pose to be unrecognizable in many frames (see Fig. 1). To address these issues, we exploit the linguistic nature of SL itself to develop novel priors that help disambiguate hand poses in SL videos, leading to accurate 3D reconstructions. This is a novel use of linguistic \"side information\" to improve 3D reconstruction.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on hand movements and poses, Battison [4] defines five linguistic classes that contain all SL signs. We build on that work to define eight classes and formalize these as mathematical priors on 3D hand shape. We combine Battison's first two classes and place all one-handed signs in class 0, while two-handed signs are arranged in classes 1, 2, or 3, depending on how the non-dominant hand participates in the articulation of the sign. We then divide each of these four classes into two subclasses depending on whether the pose of the active hand(s) changes during the articulation of the sign. We introduce two class-dependent SL linguistic constraints that capture 1) symmetry and 2) hand-pose invariance. Under Battison's SL symmetry condition [4], when both hands actively move, the articulation of the fingers must be identical; the same is true for one class of two-handed signs in which only the dominant hand moves. We formalize this concept as a regularization term that encourages the pose of the two hands to be similar for such signs. Coupling the hand poses in this way effectively increases the image evidence for a pose, which improves estimates for challenging videos. Our invariance constraint uses the observation that hand pose is either static or transitions smoothly from one pose to another during the articulation of the sign; other significant changes to hand pose are not common in SL. Specifically, we extract a characteristic \"reference pose sequence\" (RPS) to describe each local hand pose during the sign articulation, and we penalize differences between the RPS and the estimated hand pose in each frame. These two priors of symmetry and hand-pose invariance are universally applicable to all sign languages.", + "bbox": [ + 75, + 244, + 472, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The hands alone, however, are not sufficient to accurately reproduce SL. Information is conveyed holistically in SL through hand gestures, facial expressions, and upper-body movements in 3D space. To combine these, we use a 3D whole-body model, SMPL-X [41], that jointly models this information (see Fig. 1).", + "bbox": [ + 75, + 700, + 468, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our novel hand-pose constraints are formulated to be incorporated into the loss function for training a neural network regressor or into the objective function of optimization-based methods. In general, optimization-based methods are more computationally intensive but produce more accurate results when limited training data is available, so we take this approach here and build on the", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SMPLify-X method [41]. To appropriately incorporate our terms into the objective function, we need to know the class of the sign. We train a simple model that extracts features from the raw video and determines the class to which the depicted sign belongs. While SMPLify-X is a good foundation for the hands and body, we find that it does not capture expressive facial motions well. Consequently, we use a more expressive face regressor, SPECTRE [19], to capture the face parameters. We call our method SGNify.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To quantitatively evaluate SGNify, we capture a native German (DGS) signer with a frontal RGB camera synchronized with a 54-camera Vicon motion capture system and recover ground-truth meshes from the Vicon markers [34]. We run SGNify on the RGB video and compute 3D vertex-to-vertex (V2V) error between our resulting avatars and the ground-truth meshes. We find that SGNify reconstructs SMPL-X meshes more accurately than the competition.", + "bbox": [ + 496, + 227, + 890, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct a perceptual evaluation in which we present proficient signers with a video of either an estimated SMPL-X avatar or the real-person source video and task them with identifying the sign being performed. Participants also rate their ease in recognizing the sign and the naturalness of the articulation. Our results show that SGNify reconstructs 3D signs that are as recognizable as the original videos and consistently more recognizable, easier to understand, and more natural than the existing state of the art. We also evaluate SGNify in a multi-view setting and on continuous signing videos. Despite not being designed for the latter, SGNify captures the meaning in continuous SL.", + "bbox": [ + 496, + 348, + 890, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SGNify represents a step towards the automatic reconstruction of natural 3D avatars from sign-language videos. Our key contribution is the introduction of novel linguistic priors that are universal and helpful to constrain the problem of hand-pose estimation from SL video. SGNify is designed to work on video from different SL dictionaries across languages, backgrounds, people, trimming, image resolution, and framing, as visible in Sup. Mat. and in the video on our project page. This capability is critical to capture 3D signing at scale, which will enable progress on learning SL avatars. Our code and motion-capture dataset are available for research purposes at sgnify.is.tue.mpg.de.", + "bbox": [ + 496, + 529, + 890, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 723, + 640, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Expressive 3D Humans From RGB Images: Until recently, human-posed estimation has focused on the estimation of 2D [12] or 3D [51] joints of the hands and body, as well as those of facial features [6] from single images. In addition to methods that estimate a sparse set of landmarks, there are multiple methods that estimate the parameters of morphable models for the hand [22, 32, 36, 58], face [11, 16, 18, 20], and body [8, 25, 27–29, 33, 39, 57]. The advent of expressive 3D body models like SMPL-X [41], Adam [26], and GHUM [54] has enabled research on esti", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12792", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mating the full 3D body surface [9, 17, 41, 44, 49, 53, 55]. Such body models are ideal for representing the expressiveness of SL but have rarely been applied to this domain [30]. Human Pose for Sign Language: To enable detailed 3D pose estimation from images, How2Sign [14] provides 3D skeleton reconstructions for three hours of data captured in a Panoptic Studio [24]. However, the skeletal representation lacks the richness of a full 3D body model and omits surface details that are important for communication [38]. Kratimenos et al. [30] use SMPLify-X to estimate 3D pose and shape on the GSLL sign-language dataset [48]. They compare SL recognition accuracy using features from raw RGB images, OpenPose [7] 2D skeletons, and SMPL-X bodies and observe the best automated recognition results with SMPL-X, illustrating the benefit of using a 3D model. They also highlight the importance of capturing the face and body; in an ablation study, they show that neglecting the face and body harms recognition accuracy [30]. However, their SMPL-X reconstructions use existing off-the-shelf methods and lack visual realism. SMPLify-X [41] and other recent 3D pose-reconstruction methods [17, 44], as well as keypoint detectors, struggle when applied to SL video due to challenging self-occlusion, hand-hand and hand-body interactions [38], motion blur [50], and cropping inherent to SL. SignPose [31] is a 3D-pose-lifting method for SL; it uses manually created synthetic SL animations to infer a textured avatar from single RGB images. SignPose requires all OpenPose keypoints above the pelvis to be detected, which is unrealistic in noisy SL videos. We address these challenges by incorporating sign-language knowledge in the form of linguistic constraints. Since the early 2000s, the integration of linguistic information has been known to be beneficial to both SLR [10] and SLP [35], but this strategy has not previously been applied to SLC.", + "bbox": [ + 76, + 90, + 472, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 617, + 169, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce SGNify, an offline method for reconstructing 3D body shape and pose of SL from monocular RGB video. SGNify centers around a key insight: SL signs follow universal linguistic rules that can be formulated as class-specific priors and used to improve hand-pose estimation. Our full pipeline is shown in Fig. 2.", + "bbox": [ + 76, + 642, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. SMPLify-SL: Baseline for Sign-Language Video", + "text_level": 1, + "bbox": [ + 76, + 742, + 449, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our baseline method builds on SMPLify-X [41], which estimates SMPL-X [41] parameters from RGB images. SMPL-X is a 3D body model, representing whole-body pose and shape, including finger articulations and facial expressions. SMPL-X is a function, $M(\\theta, \\beta, \\psi)$ , parameterized by body pose $\\theta$ (including hand pose $\\theta_h$ ), body shape $\\beta$ , and facial expressions $\\psi$ , that outputs a 3D body mesh.", + "bbox": [ + 76, + 763, + 467, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To create a strong baseline, we extend SMPLify-X to video by adapting it in the following ways: (1) We cope", + "bbox": [ + 76, + 869, + 467, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with the upper-body framing typical of SL videos by changing the heuristic used for camera initialization and the estimation of the out-of-view lower-body joints. (2) Since human motion is locally smooth in time, we initialize $\\theta_t \\in \\mathbb{R}^{|\\theta|}$ with $\\theta_{t-1}$ and include a zero-velocity loss on the hands and body to encourage smooth reconstructions. (3) We estimate shape parameters $(\\beta)$ over multiple frames by taking the median of the parameter estimates and not-optimizing them during the per-frame reconstruction. (4) To better capture the frequent hand-hand and hand-body interactions (mainly with the face and the chest), we employ the more robust self-contact loss of Müller et al. [39] instead of the original SMPLify-X interpenetration term. (5) For each frame, we pre-compute the facial expressions $(\\psi)$ and jaw poses with SPECTRE [19]. These parameters are substituted into SMPL-X at the end of the optimization. SPECTRE can be swapped for any method whose expression parameters are consistent with those of SMPL-X, e.g., EMOCA [11]. We denote the baseline SMPLify-SL.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Linguistic Constraints", + "text_level": 1, + "bbox": [ + 500, + 388, + 707, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "State-of-the-art optimization- and regression-based human pose estimation methods struggle on SL video, particularly with the estimation of hand pose. We address this challenge by formulating linguistic constraints as additional losses on hand pose and integrating them into the SMPLify-SL objective function. First, we adapt the five sign-classification and morpheme-structure conditions introduced for American Sign Language (ASL) by Battison [4] to divide signs into four primary classes:", + "bbox": [ + 496, + 412, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class 0: one-handed signs in which only the dominant hand articulates the sign.", + "bbox": [ + 498, + 550, + 890, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class 1: two-handed signs in which both hands are active. They share the same poses and perform the same movement in a synchronous or alternating pattern. This class includes all signs that follow Battison's symmetry condition [4].", + "bbox": [ + 498, + 580, + 890, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class 2: two-handed signs in which the dominant hand is active, the non-dominant hand is passive (its position and pose do not change during the articulation of the sign), and the two hands have the same initial pose.", + "bbox": [ + 498, + 641, + 890, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class 3: two-handed signs in which the dominant hand is active, the non-dominant hand is passive, and the two hands have different hand poses. All signs in this class follow Battison's dominance condition [4].", + "bbox": [ + 498, + 702, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We further divide each class into two subclasses: subclass $a$ contains signs in which the hand pose of the active hand(s) does not change throughout the articulation of the sign (static), and subclass $b$ contains all signs in which the hand pose changes (transitioning).", + "bbox": [ + 496, + 763, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that the division into these classes is not limited to ASL; Eccarius et al. [15] show that the phonological and prosodic properties of ASL can be successfully transferred to other sign-language lexicons.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12793", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2b9b269b73bd003ac69d8400855935080979a542e74423eff972365f0d280248.jpg", + "image_caption": [ + "Figure 2. Given a video of a sign-language (SL) sign as input, our method preprocesses the data to first extract 2D keypoints. The hand keypoints are used to select candidate frames for estimating the reference hand poses $(\\theta_{ref,i}^{h},\\theta_{ref,f}^{h})$ and, for static hand poses, also $\\theta_{ref}^{h}$ . The initial and final reference hand poses $(\\theta_{ref,i}^{h}$ and $\\theta_{ref,f}^{h})$ , together with wrist-keypoint features detected across the sequence, are then fed into our sign-group classifier, which automatically classifies signs in monocular SL video into six groups based on linguistic rules universally applicable to SL [4]. Using the predicted group labels and the relevant reference hand poses, SGNify applies the appropriate linguistic constraints to improve SL 3D hand-pose estimation, especially when the video frame is ambiguous." + ], + "image_footnote": [], + "bbox": [ + 114, + 85, + 857, + 294 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/edea10561f01ad102b4b5fde5ab40e753a2ed7f233978f5ff11d7222990c85c9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ClassHand-Pose SymmetryHand-Pose Invariance
DominantNon-dominant
0aXstaticX
0bXtransitioningX
1a✓staticstatic
1b✓transitioningtransitioning
2a✓staticstatic
2bXtransitioningstatic
3aXstaticstatic
3bXtransitioningstatic
", + "bbox": [ + 89, + 405, + 459, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Linguistic constraints defining the eight sign classes.", + "bbox": [ + 89, + 599, + 454, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then convert these linguistic classes into two 3D pose constraints: hand-pose symmetry and hand-pose invariance. Signs in the same class share the same constraints (see Tab. 1 and Tab. S.1 in Sup. Mat.).", + "bbox": [ + 75, + 630, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Below we describe only the new terms added to the SMPLify-X objective. Please see Sup. Mat. for the full SGNify objective.", + "bbox": [ + 75, + 691, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Hand-Pose Symmetry", + "text_level": 1, + "bbox": [ + 76, + 753, + 284, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We encourage the left and right hand poses to match for the relevant classes (classes 1a, 1b, and 2a in Tab. 1):", + "bbox": [ + 75, + 777, + 468, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s} = \\lambda_ {s} \\| \\theta_ {t} ^ {r} - r \\left(\\theta_ {t} ^ {l}\\right) \\| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 814, + 468, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_t^r$ is the finger articulation of the right hand, and $r(\\theta_t^l)$ is a reflection function to represent the articulation of the fingers of the left hand as if it were a right hand. This loss penalizes differences in finger poses between the hands.", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Hand-Pose Invariance", + "text_level": 1, + "bbox": [ + 500, + 414, + 709, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each sign has a characteristic reference hand pose sequence (RPS). The RPS defines the hand pose that we expect at each time $t$ during the articulation of the sign. The hand-posed-invariance constraint penalizes differences between the reference hand pose $\\theta_{\\text{ref},t}^{h} \\in \\mathbf{RPS}^{h}$ and the estimated hand pose $\\theta_{t}^{h}$ :", + "bbox": [ + 496, + 438, + 893, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i} ^ {h} = \\lambda_ {i} \\| \\theta_ {\\text {r e f}, t} ^ {h} - \\theta_ {t} ^ {h} \\| _ {2} ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 542, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h$ represents either the left or the right hand.", + "bbox": [ + 498, + 573, + 834, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Throughout each sign, the hand pose either stays static or transitions between two poses. When static, only one hand pose, $\\theta_{ref}^{h}$ , is representative of the RPS. Signs where the hand pose is transitioning are characterized by two reference hand poses, $\\theta_{ref,i}^{h}$ and $\\theta_{ref,f}^{h}$ , corresponding respectively to the initial and final poses. We interpolate $\\theta_{ref,i}^{h}$ and $\\theta_{ref,f}^{h}$ with spherical linear interpolation [45] to obtain intermediate poses. We presently do not consider signs with repeated hand-posed transitions, e.g., STORY in ASL, which occur in a small percentage of signs ( $\\sim 3\\%$ ).", + "bbox": [ + 496, + 588, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Automatization", + "text_level": 1, + "bbox": [ + 500, + 753, + 656, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To work fully automatically, SGNify must 1) estimate the poses needed to enforce the hand-pose-invariance constraint and 2) classify which sign group is present in a video sequence (see Fig. 2).", + "bbox": [ + 496, + 777, + 890, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To estimate the reference hand poses $(\\theta_{ref}^{h},\\theta_{ref,i}^{h}$ and $\\theta_{ref,f}^{h})$ , our method selects candidate frames in the core part of the sign using hand-keypoint detection confidences, and it uses SMPLify-X (adapted to SL cropping) to reconstruct", + "bbox": [ + 496, + 837, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12794", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a preliminary 3D hand pose for each candidate frame. With static hand poses, $\\theta_{ref}^{h}$ is obtained by taking the average hand poses of these candidates. With transitioning hand poses, the core part of a sign is divided into two intervals, and $\\theta_{ref,i}^{h}$ and $\\theta_{ref,f}^{h}$ correspond to the average hand poses of the candidate frames in the first and second intervals, respectively (see Sup. Mat. for more details).", + "bbox": [ + 75, + 90, + 468, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The constraints applied to each sign depend on its sign group; we have six sign groups because classes 1a & 2a share the same constraints, as do 2b & 3b (Tab. 1). There is insufficient paired data to train a CNN classifier, so we use an intuitive and interpretable decision tree trained on extracted 2D and 3D pose features. Our features are invariant to the handedness of the signer and include: 1) the minimum of the maximum height differences of each wrist across the sequence: $\\min (\\{w_r\\}_{\\max} - \\{w_r\\}_{\\min},\\{w_l\\}_{\\max} - \\{w_l\\}_{\\min})$ where $w_{l}$ and $w_{r}$ are the heights of the left and right wrists, respectively. 2) the cosine distance between the initial poses of each hand: $\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,i}^{l})$ , 3) the maximum of the two cosine distances between each initial and final hand pose: $\\max (\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,f}^{r}),\\mathrm{CosDist}(\\theta_{ref,i}^{l},\\theta_{ref,f}^{l}))$", + "bbox": [ + 75, + 199, + 470, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our sign-group classifier on the over 3,000 videos from the Corpus-based Dictionary of Polish Sign Language (CDPSL) [1]; these are annotated with HamNoSys [21]. We construct a grammar to convert HamNoSys annotations into our group labels (see Sup. Mat.) Row 1 of Figure 3 shows a sample frame from CDPSL. This dataset is not used in our quantitative analysis or perceptual study.", + "bbox": [ + 75, + 412, + 468, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. SGNify Extensions", + "text_level": 1, + "bbox": [ + 76, + 530, + 256, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we follow Huang et al. [23] to extend SGNify to work on multi-view videos. Second, we propose a baseline method for continuous SLC (CSLC). CSLC introduces additional challenges, such as the segmentation of sentences into signs; this is an active field of research. When a sentence is given as input, we use Renz et al. [43] to segment the input video and then process each segment with SGNify. The first frame of each segment is initialized from the last frame of the previous one. These extensions are not our main contribution and are described in Sup. Mat.", + "bbox": [ + 75, + 554, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset", + "text_level": 1, + "bbox": [ + 76, + 722, + 163, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To quantitatively evaluate SGNify as a viable method for SLC, we collected motion-capture data with ground-truth SMPL-X bodies articulating signs. Our dataset represents the first publicly available expressive full-4D capture of isolated SL signs. The experimental procedure was reviewed by the ethics council of the University of Tübingen without objections or remarks (709/2021B02).", + "bbox": [ + 75, + 748, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In consultation with a Deaf DGS teacher and a DGS interpreter, we defined a German SL corpus consisting of 57 isolated signs. The selected signs cover a wide range of", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8180a60f27e89700190d7f51d0def58152704b4c25915dd688001f597d5199ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 90, + 694, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1018b7a0ce74a933d22405df86e6e28cf93ea5809723e32c5ab005dca291dd17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 172, + 694, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/17f36ffde17a14fdd80203e2a15f187411df4217850c2d03755f229f209e3703.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 260, + 694, + 353 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8982790361a65b1677898f628b735a5408ee237c513f279012fbfda33bd867fc.jpg", + "image_caption": [ + "Figure 3. Samples frames reconstructed by SGNify. The input videos are from diverse multilingual datasets. Row 1: Polish SL sign GDANSK (GDANSK, class 1a) from the dataset [1] used for training our sign-group classifier. Row 2: DGS sign BLUME (FLOWER, class 3b) from our captured dataset used in the quantitative evaluation. Row 3: ASL sign DOLL (class 0a) from the dataset [47] used in the perceptual study. Row 4: South African SL sign ARCHERY (class 2a) from the in-the-wild dataset [42]." + ], + "image_footnote": [], + "bbox": [ + 503, + 353, + 694, + 436 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1c0aff61dd4232689cd82d30a03298552a32374085a58e805ffda04294139c04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 90, + 890, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4d83b534e869607ada7e907922bac7bd5a7a7e82f3473a6a7b61e4a2e8fe221b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 172, + 890, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2c582c2e1b48a0820e364b43ef70be0d1c7e1ad94db02ad98de7d68876bb6c05.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 260, + 890, + 353 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8df943c8d11584a8ced6b3c7ef0d4d46d4302bdd441bfe0bf63d536efa777117.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 353, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9e532b24dd4baf01d05a2252ff005b1b7bc1c08b87c8a24efe2f8cd475011d34.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Class0a0b1a1b2a2b3a3b
# Signs123143112102
", + "bbox": [ + 547, + 578, + 846, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Number of signs captured for each class.", + "bbox": [ + 547, + 632, + 841, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "challenges for SLC, such as self-contact and self-occlusion. Table 2 summarizes the number of signs collected for each of the eight classes. Signs of subclass $b$ are less common, and this is reflected in our corpus.", + "bbox": [ + 496, + 671, + 890, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We captured a native right-handed DGS signer with a Vicon mocap system at 120 fps, synchronized with a frontal $4112 \\times 3008$ RGB camera at 60 fps, framing an upper-body view as typically found in SL video. The hands start and end at rest at the signer's sides, and each sign lasts between 1.7 and 3.5 seconds after trimming. In total, our dataset comprises 16,608 mocap frames and 8,304 RGB frames. To obtain ground-truth SMPL-X meshes, we scanned the participant in a 4D body scanner in several poses. The SMPL-X mesh was registered to these scans and averaged to obtain a personalized body-shape mesh. MoSh++ was then used", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12795", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9baf3842e09d21239602ede9be77bbee50712c52efb2a0d59bbfd7c37adaec94.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodUpper BodyLeft HandRight Hand
FrankMocap [44]78.0720.4719.62
PIXIE [17]60.1125.0222.42
PyMAF-X [56]68.6121.4619.19
SMPLify-SL56.0722.2318.83
SGNify55.6319.2217.50
", + "bbox": [ + 81, + 88, + 455, + 195 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/341c0a156eca8d5410b64081d9fab6e7dfe8b6e20b18bcf6b33f582ac8357ac8.jpg", + "table_caption": [ + "Table 3. Evaluation on our ground-truth mocap dataset: mean TR-V2V error (mm) for five methods and three body regions." + ], + "table_footnote": [], + "table_body": "
MethodSymInvLeft HandRight HandBoth Hands
SMPLify-SLXX20.3018.7819.54
SGNify✓X18.4418.3918.41
SGNifyX✓19.7617.1618.46
SGNify✓✓17.7217.2917.50
", + "bbox": [ + 81, + 243, + 455, + 325 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bfc945a805b4f5cb859ac505affd349701499e63cac8d0e98d458e45e44e2fae.jpg", + "table_caption": [ + "Table 4. Evaluating how the linguistic constraints of symmetry and invariance affect mean TR-V2V error (mm) in symmetric signs." + ], + "table_footnote": [], + "table_body": "
MethodInvLeft HandRight HandBoth Hands
SMPLify-SL✗26.0918.8920.50
SGNify✓22.2217.7018.60
", + "bbox": [ + 81, + 373, + 460, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Evaluating how the linguistic constraint of hand-pose invariance affects mean TR-V2V error (mm) in asymmetric signs.", + "bbox": [ + 76, + 440, + 467, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to fit this mesh to the mocap markers [34]. Marker-based mocap is useful for evaluating ground truth but is not practical for SLC at scale: it is expensive and requires expertise, the reflective markers attached to the signer can influence contact-heavy motions, and processing the resulting data is time consuming. If our monocular method can approach the performance of mocap, it will be widely applicable.", + "bbox": [ + 75, + 489, + 467, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 609, + 207, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 635, + 295, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We quantitatively evaluate SGNify, compare it with state-of-the-art methods, and quantify the improvement derived from each linguistic constraint. To emulate in-the-wild data, which might have very low resolution, lowramerate, and an occluded lower body, we pre-processed our high-quality video data to a resolution of $514 \\times 300$ at 30 fps, and we cropped the input images above the pelvis (see Row 2 of Fig. 3). We used the synchronized meshes captured from the observed Vicon markers [34] as ground truth for evaluation. Since all tested methods estimate SMPL-X meshes with the same topology, we compute the mean pervertex error (TR-V2V) by considering the vertices above the pelvis. The prefix \"TR\" means that we translationally align the mesh reconstructed for each frame with the ground truth; i.e., we center the meshes before computing these errors. Since the starting and ending transitions are not part of", + "bbox": [ + 75, + 657, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the sign itself, we manually annotate the expressive central portion of each sign from the raw videos and compute the quantitative results on only these central frames (in total, 2,872 RGB frames).", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3 shows the mean TR-V2V error across the 57 signs for four methods and three body regions. The columns labeled \"Upper Body\" report the error computed when considering the hands and the upper body (vertices above the pelvis). We include the head but not the face because our mocap system struggles to reconstruct face details using only 27 markers. We separately report the TR-V2V errors for the left and right hands because of the central role they play in SL. We provide a visualization of the vertices selected for each of these evaluations in Sup. Mat. This experiment compares SGNify with FrankMocap [44], PIXIE [17], PyMAF-X [56], and our baseline SMPLify-SL. SGNify achieves the lowest error for the upper body and both hands, beating the state-of-the-art methods.", + "bbox": [ + 496, + 152, + 890, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tables 4 and 5 show the improvements derived from each linguistic constraint. Table 4 reports the mean TR-V2V in symmetric signs (classes 1a, 1b, and 2a) when using no constraints, i.e., SMPLify-SL (Row 1), only one constraint (Rows 2 and 3), or both linguistic constraints (Row 4). When one linguistic constraint is used, the TR-V2V of both hands decreases. We observe that the symmetry constraint has the overall greater effect of the two. When the non-dominant hand is passive, it is often rotated at an angle difficult to capture from a frontal camera; this behavior might explain the greater effect of the symmetry constraint on the left hand. When both constraints are applied, we observe a more substantial decrease in the TR-V2V error of the left hand and a slight increase in the error of the right hand compared to when only the hand-pose invariance is applied to the right hand. We believe this happens because the symmetry constraint enforces symmetry between the two hands without knowing which hand reconstruction is more correct, and, for the same reason as above, detecting an accurate RPS for the non-dominant hand is often more challenging; overall, however, using both constraints greatly benefits the reconstruction. In Tab. 5, we separately evaluate performance on signs that do not present symmetry between the two hands (classes 0a, 0b, 2b, 3a, and 3b). As expected, the invariance prior included in SGNify improves the performance on all metrics. These quantitative results indicate that our linguistic constraints improve the reconstructions.", + "bbox": [ + 496, + 364, + 890, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Perceptual Study", + "text_level": 1, + "bbox": [ + 500, + 785, + 666, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct an online perceptual study to 1) compare SGNify with the best-performing state-of-the-art method for SL and 2) evaluate the improvement derived from the linguistic constraints (SGNify vs. SMPLify-SL). Even though FrankMocap has a lower hand error than PyMAF-X and PixIE, it has significant errors in the lower body when", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12796", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the full body is not seen, and higher errors in the upper body; these errors greatly affect the perceptual experience, making it unsuitable for the SL task, as already noticed in [31]. We thus use PyMAF-X since its hand-pose estimates are more accurate than pixIE (see Tab. 3).", + "bbox": [ + 75, + 90, + 467, + 165 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Approval of all experimental procedures for this study was granted by the Ethics Council of the Max Planck Society under the Haptic Intelligence Department's framework agreement under protocol number F027A. No participants are employed by our institution, and all are compensated 20 USD for their time.", + "bbox": [ + 75, + 167, + 467, + 257 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our study involves 20 adult participants who all stated that they have an advanced level of proficiency (expert level) in ASL. We discarded responses from other potential participants who did not correctly recognize at least $70\\%$ of the signs presented via real-person video. 15 of the final 20 participants $(75\\%)$ are Deaf, and one participant is left-handed. Participant ages are $46.75 \\pm 11.78$ .", + "bbox": [ + 75, + 260, + 467, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We used SGNify, SMPLify-SL, and PyMAF-X to reconstruct avatars from 50 videos taken from The American Sign Language Handshape Dictionary [47]; see Row 3 of Fig. 3 for an example. After responding to demographic questions, each participant evaluates the same six training videos to calibrate their responses to the quality of the presented reconstructions. We divide the remaining 44 signs into four batches (real-person RGB video, SGNify, SMPLify-SL, and PyMAF-X) that are balanced by sign class and sign frequency. We include real-person video to obtain an upper-bound on recognition performance and, as mentioned, to filter participants. We assign each participant to one of four surveys. Each survey contains all 44 test signs, and the four methods are rotated through the four sign batches across surveys. We further shuffle the questions in each survey for each user.", + "bbox": [ + 75, + 368, + 467, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The participant enters the sign they believe the avatar or the real person is articulating in each video. They rate their ease in recognizing the presented sign using a visual analog scale (VAS) ranging from 0 to 100 with five standard labels ranging from \"very difficult\" to \"very easy.\" They also evaluate the naturalness of the articulation on a VAS-labeled scale from \"very unnatural\" to \"very natural.\" Participants are able to replay each video. We provide additional space for comments for each sign and at the end of the study. The self-reported participant carefulness is $84.45 \\pm 11.44$ on a scale from 0 to 100.", + "bbox": [ + 75, + 611, + 467, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The sign annotations submitted by participants are graded as either \"incorrect\" (no credit), \"partially correct\" (half credit), or \"completely correct\" (full credit). We calculate the rates at which each participant recognized the signs for each method. We visualize the resulting $20 \\times 4$ matrix of recognition rates with box plots in the left plot of Fig. 4. Participants recognize signs in real-person videos with an average accuracy of $90.9\\%$ and signs reconstructed", + "bbox": [ + 75, + 780, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by SGNify with $86.2\\%$ accuracy. Signs reconstructed with SMPLify-SL and PyMAF-X are recognized less accurately, at $74.8\\%$ and $62.0\\%$ , respectively. We evaluate the statistical significance of these recognition rates. Some distributions failed a Shapiro-Wilk normality test, so we used the non-parametric Friedman test which shows that the method used (real video, SGNify, SMPLify-SL, or PyMAF-X) has a statistically significant effect $(p < 0.001)$ on recognition rate. Pairwise comparison with Wilcoxon signed-rank tests and a Bonferroni post-hoc correction reveal that the average sign recognition rate with real video and SGNify are both significantly higher than SMPLify-SL and PyMAF-X. Importantly, sign recognition rates with real video and SGNify are not significantly different from one another.", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The central plot of Fig. 4 shows the participants' perceived easiness in recognizing the sign. These four distributions passed the normality test and were analyzed with a one-way repeated-measures ANOVA with a Bonferroni post-hoc correction for pairwise comparisons. As expected, real videos are perceived to be significantly easier to recognize than the three reconstruction methods. However, signs reconstructed with SGNify and SMPLify-SL are significantly easier to recognize than those by PyMAF-X.", + "bbox": [ + 496, + 304, + 890, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The right plot of Fig. 4 shows the participants' perceived naturalness of the articulation of the signs. All four distributions passed the normality test, so they were analyzed in the same way as perceived easiness. All methods are statistically different one from another, with real video receiving the highest naturalness ratings, followed by SGNify, SMPLify-SL, and PyMAF-X. Nearly all participants reported in the comments that they want avatars with more expressive face motions and smoother hand and body motions.", + "bbox": [ + 496, + 443, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "These results show that SGNify outperforms the state-of-the-art, PyMAF-X, in all qualitative metrics. Incorporating SL linguistic priors into our baseline SMPLify-SL yields statistically significant perceptual improvements, as judged by 20 expert signers. Most importantly, SGNify achieves a high sign-recognition rate that is not different from that of real-person video on the selected set of ASL signs.", + "bbox": [ + 496, + 580, + 890, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A few participants suggested having clothed (rather than \"nude\") avatars and introducing more human-like features. We thus conduct a second perceptual study to see whether these recommendations have a positive impact on the intelligibility of SGNify's reconstructions. Thirteen participants from the first study participated in this follow-up; the study design is the same. The tested methods are the real video and three different SGNify avatars: the solid purple avatar from the first study, the same avatar wearing a black long-sleeved t-shirt, and a fully textured human character adapted from Meshcapade [2] (see Sup. Mat.). This study comprises 24 signs (including the four for participant training) from the same ASL dataset [47] but different from those of the first study. Our results reveal that adding the", + "bbox": [ + 496, + 688, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12797", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6cd9a27685d9c0683b62630d990b89441ead75532f6cb62fcef41942b4b2f685.jpg", + "image_caption": [ + "Figure 4. Box plots of the data from the perceptual study. The circle shows the mean, and the central line shows the median. The top and bottom box edges show the interquartile range (IQR), and the whiskers encompass the range up to 1.5 times the IQR. Outliers are marked with $^+$ . Statistically significant pairwise differences are indicated with a line and a $\\star$ . Left: Distribution of the rate at which participants recognized signs presented with each of the four methods. Real Video and SGNify achieve significantly higher recognition rates than both SMPLify-SL and PyMAF-X. Center: Distribution of the average easiness ratings participants assigned to recognizing signs presented by the four methods. All pairwise combinations except SGNify-SMPLify-SL are significantly different. Right: Distribution of the average articulation naturalness ratings participants assigned to the four methods. All pairwise combinations are significantly different." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 346, + 349 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b4c1dcb236fd10a733c6d33b854cc85b4f66dbd05644451c062db369301481e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 88, + 612, + 345 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93566bfab244c6c47e6d718b7768b882168e09be02a1637a80a351f2e9c3ea85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 88, + 875, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "t-shirt and using a fully textured avatar do not benefit actual or perceived sign recognition or the perceived naturalness of the reconstruction. As in the previous study, recognition of SGNify's reconstructions were not statistically different from real video.", + "bbox": [ + 75, + 484, + 470, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 573, + 191, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our results show that SGNify performs quantitatively better than the state of the art, in particular due to the inclusion of our novel linguistic constraints. However, we believe that a per-frame metric is not ideal for SL. To recognize a sign, the temporal evolution is crucial, and this is not captured by V2V. For example, the few slightly inaccurate frames of the SMPLify-SL reconstruction of DOLL (see video on our project page) confused many signers during the perceptual study. Small changes over time can disrupt perception, while overall V2V error remains small. In the end, what matters is whether the meaning is clear to a human. We think a perceptual study provides key insights that complement metric evaluation. The perceptual study indicated that SGNify significantly outperforms the state of the art and, most importantly, produces the first 3D avatars to achieve a sign-recognition accuracy that is not statistically different from the source videos. Our perceptual study also highlights the next challenge for SLC: the need for improvements in the face including facial expressions, tongue and eye movements, mouth morphemes, and eyebrows.", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 483, + 627, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present SGNify, which estimates 3D avatars of isolated SL signs from monocular RGB video. Quantitative and qualitative experiments show that SGNify outperforms the state of the art in estimating challenging SL hand poses by leveraging constraints derived from linguistics. SGNify represents a step towards the capture of realistic 3D avatars from SL videos in the wild. Future work should explore the use of our constraints in training regression methods, real-time processing, and continuous signing.", + "bbox": [ + 496, + 508, + 890, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments We thank Galina Henz and Tsvetelina Alexiadis for trial coordination; Matvey Safroshkin, Markus Höschle, Senya Polikovsky, Tobias Bauch, Taylor McConnell (TM), and Bernard Javot for the capture setup; TM for data-cleaning coordination; Leyre Sánchez Vinuela, Andres Camilo Mendoza Patino, and Yasemin Fincan for data cleaning; Nima Ghorbani and Giorgio Becherini for MoSh++; Joachim Tesch for help with Blender; Benjamin Pellkofer and Joey Burns for IT support; Yao Feng, Anastasios Yiannakidis, and Radek Danček for discussions on facial methods; Haliza Mat Husin and Mayumi Mohan for help with statistics; and the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Maria-Paola Forte and Peter Kulits.", + "bbox": [ + 496, + 652, + 893, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Disclosure: https://files.is.tue.mpg.de/black/CoI_CVPR_2023.txt", + "bbox": [ + 500, + 869, + 890, + 886 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12798", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] CDPSL: Corpus-based Dictionary of Polish Sign Language. https://www.slownikpjm.uw.edu.pl/.5", + "[2] Meshcapade GmbH, Tübingen, Germany. https://meshcapade.com, 2022.7", + "[3] Ahmed H. 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In International Conference on Computer Vision (ICCV), pages 813-822, 2019. 2" + ], + "bbox": [ + 503, + 90, + 890, + 657 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12801", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Reconstructing Signing Avatars From Video Using Linguistic Priors/f36e0963-996f-4cc3-af93-ef4d550fb47d_model.json b/2023/Reconstructing Signing Avatars From Video Using Linguistic Priors/f36e0963-996f-4cc3-af93-ef4d550fb47d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..00d90e96bd74037b3893c6afa4d85b86b8af6159 --- /dev/null +++ b/2023/Reconstructing Signing Avatars From Video Using Linguistic Priors/f36e0963-996f-4cc3-af93-ef4d550fb47d_model.json @@ -0,0 +1,2191 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.131, + 0.829, + 0.154 + ], + "angle": 0, + "content": "Reconstructing Signing Avatars From Video Using Linguistic Priors" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.181, + 0.256, + 0.198 + ], + "angle": 0, + "content": "Maria-Paola Forte" + }, + { + "type": "text", + "bbox": [ + 0.276, + 0.182, + 0.372, + 0.198 + ], + "angle": 0, + "content": "Peter Kulits" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.182, + 0.535, + 0.198 + ], + "angle": 0, + "content": "Chun-Hao Huang" + }, + { + "type": "text", + "bbox": [ + 0.552, + 0.182, + 0.694, + 0.198 + ], + "angle": 0, + "content": "Vasileios Choutas" + }, + { + "type": "text", + "bbox": [ + 0.716, + 0.182, + 0.86, + 0.197 + ], + "angle": 0, + "content": "Dimitrios Tzionas" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.2, + 0.671, + 0.216 + ], + "angle": 0, + "content": "Katherine J. Kuchenbecker Michael J. Black" + }, + { + "type": "text", + "bbox": [ + 0.251, + 0.219, + 0.719, + 0.234 + ], + "angle": 0, + "content": "Max Planck Institute for Intelligent Systems, Stuttgart and Tübingen, Germany" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.238, + 0.81, + 0.251 + ], + "angle": 0, + "content": "{forte,kjk}@is.mpg.de {kulits,chuang2,vchoutas,dtzionas,black}@tue.mpg.de" + }, + { + "type": "image", + "bbox": [ + 0.14, + 0.268, + 0.89, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.444, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Figure 1. Given a monocular, in-the-wild video of a sign-language sign, SGNify automatically reconstructs a 3D body with accurate hand pose, facial motion, and body pose. Note that motion blur obscures the finger articulations in several video frames; this is a common problem. Our novel linguistic priors enable accurate 3D reconstruction despite such image degradation." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.518, + 0.314, + 0.533 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.551, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Sign language (SL) is the primary method of communication for the 70 million Deaf people around the world. Video dictionaries of isolated signs are a core SL learning tool. Replacing these with 3D avatars can aid learning and enable AR/VR applications, improving access to technology and online media. However, little work has attempted to estimate expressive 3D avatars from SL video; occlusion, noise, and motion blur make this task difficult. We address this by introducing novel linguistic priors that are universally applicable to SL and provide constraints on 3D hand pose that help resolve ambiguities within isolated signs. Our method, SGNify, captures fine-grained hand pose, facial expression, and body movement fully automatically from in-the-wild monocular SL videos. We evaluate SGNify quantitatively by using a commercial motion-capture system to compute 3D avatars synchronized with monocular video. SGNify outperforms state-of-the-art 3D body-pose-and shape-estimation methods on SL videos. A perceptual study shows that SGNify's 3D reconstructions are significantly more comprehensible and natural than those of previous methods and are on par with the source videos. Code and data are available at sgnify.is.tue.mpg.de." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.518, + 0.631, + 0.533 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.866 + ], + "angle": 0, + "content": "It is estimated that over 466 million people have disabling hearing loss [13] and more than 70 million people use sign language (SL) as their primary means of communication [52]. Increasing use of digital communication motivates research on capturing, understanding, modeling, and synthesizing expressive 3D SL avatars. Existing datasets and dictionaries used in SL recognition (SLR), translation (SLT), and production (SLP) are primarily limited to 2D video because the technology required to capture 3D movement is prohibitively expensive, requires expertise to operate, and may limit the movements of the signer. Dictionaries of isolated signs are a core SL learning tool, and many SLs have online 2D video dictionaries. The Deaf community is actively seeking 3D dictionaries of isolated signs to aid learning [40]. The current approach to creating such 3D signing dictionaries is fully manual, requiring an artist or a HamNoSys [21] expert, and the resulting avatars often move unnaturally [3]. We aim to automatically reconstruct expressive 3D signing avatars from monocular SL video, which we term Sign Language Capture (SLC). We focus on SLC of isolated signs." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "3D reconstruction of human pose and shape has received significant attention, but accurate 3D hand-pose estimation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12791" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "remains challenging from in-the-wild video. Challenges include the high number of degrees of freedom present in hands [5], frequent occurrence of self-contact and self-occlusions [37, 46], low resolution, and motion blur caused by fast motions [50] that cause hand pose to be unrecognizable in many frames (see Fig. 1). To address these issues, we exploit the linguistic nature of SL itself to develop novel priors that help disambiguate hand poses in SL videos, leading to accurate 3D reconstructions. This is a novel use of linguistic \"side information\" to improve 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.699 + ], + "angle": 0, + "content": "Based on hand movements and poses, Battison [4] defines five linguistic classes that contain all SL signs. We build on that work to define eight classes and formalize these as mathematical priors on 3D hand shape. We combine Battison's first two classes and place all one-handed signs in class 0, while two-handed signs are arranged in classes 1, 2, or 3, depending on how the non-dominant hand participates in the articulation of the sign. We then divide each of these four classes into two subclasses depending on whether the pose of the active hand(s) changes during the articulation of the sign. We introduce two class-dependent SL linguistic constraints that capture 1) symmetry and 2) hand-pose invariance. Under Battison's SL symmetry condition [4], when both hands actively move, the articulation of the fingers must be identical; the same is true for one class of two-handed signs in which only the dominant hand moves. We formalize this concept as a regularization term that encourages the pose of the two hands to be similar for such signs. Coupling the hand poses in this way effectively increases the image evidence for a pose, which improves estimates for challenging videos. Our invariance constraint uses the observation that hand pose is either static or transitions smoothly from one pose to another during the articulation of the sign; other significant changes to hand pose are not common in SL. Specifically, we extract a characteristic \"reference pose sequence\" (RPS) to describe each local hand pose during the sign articulation, and we penalize differences between the RPS and the estimated hand pose in each frame. These two priors of symmetry and hand-pose invariance are universally applicable to all sign languages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.793 + ], + "angle": 0, + "content": "The hands alone, however, are not sufficient to accurately reproduce SL. Information is conveyed holistically in SL through hand gestures, facial expressions, and upper-body movements in 3D space. To combine these, we use a 3D whole-body model, SMPL-X [41], that jointly models this information (see Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our novel hand-pose constraints are formulated to be incorporated into the loss function for training a neural network regressor or into the objective function of optimization-based methods. In general, optimization-based methods are more computationally intensive but produce more accurate results when limited training data is available, so we take this approach here and build on the" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "SMPLify-X method [41]. To appropriately incorporate our terms into the objective function, we need to know the class of the sign. We train a simple model that extracts features from the raw video and determines the class to which the depicted sign belongs. While SMPLify-X is a good foundation for the hands and body, we find that it does not capture expressive facial motions well. Consequently, we use a more expressive face regressor, SPECTRE [19], to capture the face parameters. We call our method SGNify." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.228, + 0.892, + 0.348 + ], + "angle": 0, + "content": "To quantitatively evaluate SGNify, we capture a native German (DGS) signer with a frontal RGB camera synchronized with a 54-camera Vicon motion capture system and recover ground-truth meshes from the Vicon markers [34]. We run SGNify on the RGB video and compute 3D vertex-to-vertex (V2V) error between our resulting avatars and the ground-truth meshes. We find that SGNify reconstructs SMPL-X meshes more accurately than the competition." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.349, + 0.892, + 0.529 + ], + "angle": 0, + "content": "We conduct a perceptual evaluation in which we present proficient signers with a video of either an estimated SMPL-X avatar or the real-person source video and task them with identifying the sign being performed. Participants also rate their ease in recognizing the sign and the naturalness of the articulation. Our results show that SGNify reconstructs 3D signs that are as recognizable as the original videos and consistently more recognizable, easier to understand, and more natural than the existing state of the art. We also evaluate SGNify in a multi-view setting and on continuous signing videos. Despite not being designed for the latter, SGNify captures the meaning in continuous SL." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.53, + 0.892, + 0.711 + ], + "angle": 0, + "content": "SGNify represents a step towards the automatic reconstruction of natural 3D avatars from sign-language videos. Our key contribution is the introduction of novel linguistic priors that are universal and helpful to constrain the problem of hand-pose estimation from SL video. SGNify is designed to work on video from different SL dictionaries across languages, backgrounds, people, trimming, image resolution, and framing, as visible in Sup. Mat. and in the video on our project page. This capability is critical to capture 3D signing at scale, which will enable progress on learning SL avatars. Our code and motion-capture dataset are available for research purposes at sgnify.is.tue.mpg.de." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.642, + 0.74 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Expressive 3D Humans From RGB Images: Until recently, human-posed estimation has focused on the estimation of 2D [12] or 3D [51] joints of the hands and body, as well as those of facial features [6] from single images. In addition to methods that estimate a sparse set of landmarks, there are multiple methods that estimate the parameters of morphable models for the hand [22, 32, 36, 58], face [11, 16, 18, 20], and body [8, 25, 27–29, 33, 39, 57]. The advent of expressive 3D body models like SMPL-X [41], Adam [26], and GHUM [54] has enabled research on esti" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12792" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.607 + ], + "angle": 0, + "content": "mating the full 3D body surface [9, 17, 41, 44, 49, 53, 55]. Such body models are ideal for representing the expressiveness of SL but have rarely been applied to this domain [30]. Human Pose for Sign Language: To enable detailed 3D pose estimation from images, How2Sign [14] provides 3D skeleton reconstructions for three hours of data captured in a Panoptic Studio [24]. However, the skeletal representation lacks the richness of a full 3D body model and omits surface details that are important for communication [38]. Kratimenos et al. [30] use SMPLify-X to estimate 3D pose and shape on the GSLL sign-language dataset [48]. They compare SL recognition accuracy using features from raw RGB images, OpenPose [7] 2D skeletons, and SMPL-X bodies and observe the best automated recognition results with SMPL-X, illustrating the benefit of using a 3D model. They also highlight the importance of capturing the face and body; in an ablation study, they show that neglecting the face and body harms recognition accuracy [30]. However, their SMPL-X reconstructions use existing off-the-shelf methods and lack visual realism. SMPLify-X [41] and other recent 3D pose-reconstruction methods [17, 44], as well as keypoint detectors, struggle when applied to SL video due to challenging self-occlusion, hand-hand and hand-body interactions [38], motion blur [50], and cropping inherent to SL. SignPose [31] is a 3D-pose-lifting method for SL; it uses manually created synthetic SL animations to infer a textured avatar from single RGB images. SignPose requires all OpenPose keypoints above the pelvis to be detected, which is unrealistic in noisy SL videos. We address these challenges by incorporating sign-language knowledge in the form of linguistic constraints. Since the early 2000s, the integration of linguistic information has been known to be beneficial to both SLR [10] and SLP [35], but this strategy has not previously been applied to SLC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.618, + 0.17, + 0.634 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.643, + 0.47, + 0.735 + ], + "angle": 0, + "content": "We introduce SGNify, an offline method for reconstructing 3D body shape and pose of SL from monocular RGB video. SGNify centers around a key insight: SL signs follow universal linguistic rules that can be formulated as class-specific priors and used to improve hand-pose estimation. Our full pipeline is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.45, + 0.759 + ], + "angle": 0, + "content": "3.1. SMPLify-SL: Baseline for Sign-Language Video" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.468, + 0.87 + ], + "angle": 0, + "content": "Our baseline method builds on SMPLify-X [41], which estimates SMPL-X [41] parameters from RGB images. SMPL-X is a 3D body model, representing whole-body pose and shape, including finger articulations and facial expressions. SMPL-X is a function, \\( M(\\theta, \\beta, \\psi) \\), parameterized by body pose \\( \\theta \\) (including hand pose \\( \\theta_h \\)), body shape \\( \\beta \\), and facial expressions \\( \\psi \\), that outputs a 3D body mesh." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "To create a strong baseline, we extend SMPLify-X to video by adapting it in the following ways: (1) We cope" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.38 + ], + "angle": 0, + "content": "with the upper-body framing typical of SL videos by changing the heuristic used for camera initialization and the estimation of the out-of-view lower-body joints. (2) Since human motion is locally smooth in time, we initialize \\(\\theta_t \\in \\mathbb{R}^{|\\theta|}\\) with \\(\\theta_{t-1}\\) and include a zero-velocity loss on the hands and body to encourage smooth reconstructions. (3) We estimate shape parameters \\((\\beta)\\) over multiple frames by taking the median of the parameter estimates and not-optimizing them during the per-frame reconstruction. (4) To better capture the frequent hand-hand and hand-body interactions (mainly with the face and the chest), we employ the more robust self-contact loss of Müller et al. [39] instead of the original SMPLify-X interpenetration term. (5) For each frame, we pre-compute the facial expressions \\((\\psi)\\) and jaw poses with SPECTRE [19]. These parameters are substituted into SMPL-X at the end of the optimization. SPECTRE can be swapped for any method whose expression parameters are consistent with those of SMPL-X, e.g., EMOCA [11]. We denote the baseline SMPLify-SL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.39, + 0.708, + 0.405 + ], + "angle": 0, + "content": "3.2. Linguistic Constraints" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.549 + ], + "angle": 0, + "content": "State-of-the-art optimization- and regression-based human pose estimation methods struggle on SL video, particularly with the estimation of hand pose. We address this challenge by formulating linguistic constraints as additional losses on hand pose and integrating them into the SMPLify-SL objective function. First, we adapt the five sign-classification and morpheme-structure conditions introduced for American Sign Language (ASL) by Battison [4] to divide signs into four primary classes:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.551, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Class 0: one-handed signs in which only the dominant hand articulates the sign." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.892, + 0.642 + ], + "angle": 0, + "content": "Class 1: two-handed signs in which both hands are active. They share the same poses and perform the same movement in a synchronous or alternating pattern. This class includes all signs that follow Battison's symmetry condition [4]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.642, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Class 2: two-handed signs in which the dominant hand is active, the non-dominant hand is passive (its position and pose do not change during the articulation of the sign), and the two hands have the same initial pose." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.703, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Class 3: two-handed signs in which the dominant hand is active, the non-dominant hand is passive, and the two hands have different hand poses. All signs in this class follow Battison's dominance condition [4]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We further divide each class into two subclasses: subclass \\( a \\) contains signs in which the hand pose of the active hand(s) does not change throughout the articulation of the sign (static), and subclass \\( b \\) contains all signs in which the hand pose changes (transitioning)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Note that the division into these classes is not limited to ASL; Eccarius et al. [15] show that the phonological and prosodic properties of ASL can be successfully transferred to other sign-language lexicons." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12793" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.087, + 0.859, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.895, + 0.39 + ], + "angle": 0, + "content": "Figure 2. Given a video of a sign-language (SL) sign as input, our method preprocesses the data to first extract 2D keypoints. The hand keypoints are used to select candidate frames for estimating the reference hand poses \\((\\theta_{ref,i}^{h},\\theta_{ref,f}^{h})\\) and, for static hand poses, also \\(\\theta_{ref}^{h}\\). The initial and final reference hand poses \\((\\theta_{ref,i}^{h}\\) and \\(\\theta_{ref,f}^{h})\\), together with wrist-keypoint features detected across the sequence, are then fed into our sign-group classifier, which automatically classifies signs in monocular SL video into six groups based on linguistic rules universally applicable to SL [4]. Using the predicted group labels and the relevant reference hand poses, SGNify applies the appropriate linguistic constraints to improve SL 3D hand-pose estimation, especially when the video frame is ambiguous." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.406, + 0.46, + 0.59 + ], + "angle": 0, + "content": "
ClassHand-Pose SymmetryHand-Pose Invariance
DominantNon-dominant
0aXstaticX
0bXtransitioningX
1a✓staticstatic
1b✓transitioningtransitioning
2a✓staticstatic
2bXtransitioningstatic
3aXstaticstatic
3bXtransitioningstatic
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.6, + 0.455, + 0.614 + ], + "angle": 0, + "content": "Table 1. Linguistic constraints defining the eight sign classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.691 + ], + "angle": 0, + "content": "We then convert these linguistic classes into two 3D pose constraints: hand-pose symmetry and hand-pose invariance. Signs in the same class share the same constraints (see Tab. 1 and Tab. S.1 in Sup. Mat.)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Below we describe only the new terms added to the SMPLify-X objective. Please see Sup. Mat. for the full SGNify objective." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.285, + 0.77 + ], + "angle": 0, + "content": "3.2.1 Hand-Pose Symmetry" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.47, + 0.809 + ], + "angle": 0, + "content": "We encourage the left and right hand poses to match for the relevant classes (classes 1a, 1b, and 2a in Tab. 1):" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.815, + 0.469, + 0.834 + ], + "angle": 0, + "content": "\\[\nL _ {s} = \\lambda_ {s} \\| \\theta_ {t} ^ {r} - r \\left(\\theta_ {t} ^ {l}\\right) \\| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\theta_t^r\\) is the finger articulation of the right hand, and \\(r(\\theta_t^l)\\) is a reflection function to represent the articulation of the fingers of the left hand as if it were a right hand. This loss penalizes differences in finger poses between the hands." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.415, + 0.71, + 0.43 + ], + "angle": 0, + "content": "3.2.2 Hand-Pose Invariance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.894, + 0.533 + ], + "angle": 0, + "content": "Each sign has a characteristic reference hand pose sequence (RPS). The RPS defines the hand pose that we expect at each time \\( t \\) during the articulation of the sign. The hand-posed-invariance constraint penalizes differences between the reference hand pose \\( \\theta_{\\text{ref},t}^{h} \\in \\mathbf{RPS}^{h} \\) and the estimated hand pose \\( \\theta_{t}^{h} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.543, + 0.892, + 0.563 + ], + "angle": 0, + "content": "\\[\nL _ {i} ^ {h} = \\lambda_ {i} \\| \\theta_ {\\text {r e f}, t} ^ {h} - \\theta_ {t} ^ {h} \\| _ {2} ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.574, + 0.836, + 0.589 + ], + "angle": 0, + "content": "where \\(h\\) represents either the left or the right hand." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Throughout each sign, the hand pose either stays static or transitions between two poses. When static, only one hand pose, \\(\\theta_{ref}^{h}\\), is representative of the RPS. Signs where the hand pose is transitioning are characterized by two reference hand poses, \\(\\theta_{ref,i}^{h}\\) and \\(\\theta_{ref,f}^{h}\\), corresponding respectively to the initial and final poses. We interpolate \\(\\theta_{ref,i}^{h}\\) and \\(\\theta_{ref,f}^{h}\\) with spherical linear interpolation [45] to obtain intermediate poses. We presently do not consider signs with repeated hand-posed transitions, e.g., STORY in ASL, which occur in a small percentage of signs (\\(\\sim 3\\%\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.657, + 0.769 + ], + "angle": 0, + "content": "3.3. Automatization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.838 + ], + "angle": 0, + "content": "To work fully automatically, SGNify must 1) estimate the poses needed to enforce the hand-pose-invariance constraint and 2) classify which sign group is present in a video sequence (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.838, + 0.894, + 0.902 + ], + "angle": 0, + "content": "To estimate the reference hand poses \\((\\theta_{ref}^{h},\\theta_{ref,i}^{h}\\) and \\(\\theta_{ref,f}^{h})\\) , our method selects candidate frames in the core part of the sign using hand-keypoint detection confidences, and it uses SMPLify-X (adapted to SL cropping) to reconstruct" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12794" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.199 + ], + "angle": 0, + "content": "a preliminary 3D hand pose for each candidate frame. With static hand poses, \\(\\theta_{ref}^{h}\\) is obtained by taking the average hand poses of these candidates. With transitioning hand poses, the core part of a sign is divided into two intervals, and \\(\\theta_{ref,i}^{h}\\) and \\(\\theta_{ref,f}^{h}\\) correspond to the average hand poses of the candidate frames in the first and second intervals, respectively (see Sup. Mat. for more details)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.471, + 0.413 + ], + "angle": 0, + "content": "The constraints applied to each sign depend on its sign group; we have six sign groups because classes 1a & 2a share the same constraints, as do 2b & 3b (Tab. 1). There is insufficient paired data to train a CNN classifier, so we use an intuitive and interpretable decision tree trained on extracted 2D and 3D pose features. Our features are invariant to the handedness of the signer and include: 1) the minimum of the maximum height differences of each wrist across the sequence: \\(\\min (\\{w_r\\}_{\\max} - \\{w_r\\}_{\\min},\\{w_l\\}_{\\max} - \\{w_l\\}_{\\min})\\) where \\(w_{l}\\) and \\(w_{r}\\) are the heights of the left and right wrists, respectively. 2) the cosine distance between the initial poses of each hand: \\(\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,i}^{l})\\) , 3) the maximum of the two cosine distances between each initial and final hand pose: \\(\\max (\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,f}^{r}),\\mathrm{CosDist}(\\theta_{ref,i}^{l},\\theta_{ref,f}^{l}))\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.518 + ], + "angle": 0, + "content": "We train our sign-group classifier on the over 3,000 videos from the Corpus-based Dictionary of Polish Sign Language (CDPSL) [1]; these are annotated with HamNoSys [21]. We construct a grammar to convert HamNoSys annotations into our group labels (see Sup. Mat.) Row 1 of Figure 3 shows a sample frame from CDPSL. This dataset is not used in our quantitative analysis or perceptual study." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.258, + 0.546 + ], + "angle": 0, + "content": "3.4. SGNify Extensions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.706 + ], + "angle": 0, + "content": "First, we follow Huang et al. [23] to extend SGNify to work on multi-view videos. Second, we propose a baseline method for continuous SLC (CSLC). CSLC introduces additional challenges, such as the segmentation of sentences into signs; this is an active field of research. When a sentence is given as input, we use Renz et al. [43] to segment the input video and then process each segment with SGNify. The first frame of each segment is initialized from the last frame of the previous one. These extensions are not our main contribution and are described in Sup. Mat." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.165, + 0.737 + ], + "angle": 0, + "content": "4. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.469, + 0.854 + ], + "angle": 0, + "content": "To quantitatively evaluate SGNify as a viable method for SLC, we collected motion-capture data with ground-truth SMPL-X bodies articulating signs. Our dataset represents the first publicly available expressive full-4D capture of isolated SL signs. The experimental procedure was reviewed by the ethics council of the University of Tübingen without objections or remarks (709/2021B02)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In consultation with a Deaf DGS teacher and a DGS interpreter, we defined a German SL corpus consisting of 57 isolated signs. The selected signs cover a wide range of" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.091, + 0.696, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.174, + 0.696, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.261, + 0.696, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.354, + 0.696, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.091, + 0.891, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.174, + 0.891, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.261, + 0.891, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.354, + 0.891, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Figure 3. Samples frames reconstructed by SGNify. The input videos are from diverse multilingual datasets. Row 1: Polish SL sign GDANSK (GDANSK, class 1a) from the dataset [1] used for training our sign-group classifier. Row 2: DGS sign BLUME (FLOWER, class 3b) from our captured dataset used in the quantitative evaluation. Row 3: ASL sign DOLL (class 0a) from the dataset [47] used in the perceptual study. Row 4: South African SL sign ARCHERY (class 2a) from the in-the-wild dataset [42]." + }, + { + "type": "table", + "bbox": [ + 0.548, + 0.579, + 0.847, + 0.622 + ], + "angle": 0, + "content": "
Class0a0b1a1b2a2b3a3b
# Signs123143112102
" + }, + { + "type": "table_caption", + "bbox": [ + 0.548, + 0.633, + 0.842, + 0.647 + ], + "angle": 0, + "content": "Table 2. Number of signs captured for each class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.891, + 0.733 + ], + "angle": 0, + "content": "challenges for SLC, such as self-contact and self-occlusion. Table 2 summarizes the number of signs collected for each of the eight classes. Signs of subclass \\( b \\) are less common, and this is reflected in our corpus." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We captured a native right-handed DGS signer with a Vicon mocap system at 120 fps, synchronized with a frontal \\(4112 \\times 3008\\) RGB camera at 60 fps, framing an upper-body view as typically found in SL video. The hands start and end at rest at the signer's sides, and each sign lasts between 1.7 and 3.5 seconds after trimming. In total, our dataset comprises 16,608 mocap frames and 8,304 RGB frames. To obtain ground-truth SMPL-X meshes, we scanned the participant in a 4D body scanner in several poses. The SMPL-X mesh was registered to these scans and averaged to obtain a personalized body-shape mesh. MoSh++ was then used" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12795" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.457, + 0.196 + ], + "angle": 0, + "content": "
MethodUpper BodyLeft HandRight Hand
FrankMocap [44]78.0720.4719.62
PIXIE [17]60.1125.0222.42
PyMAF-X [56]68.6121.4619.19
SMPLify-SL56.0722.2318.83
SGNify55.6319.2217.50
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.2, + 0.468, + 0.228 + ], + "angle": 0, + "content": "Table 3. Evaluation on our ground-truth mocap dataset: mean TR-V2V error (mm) for five methods and three body regions." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.244, + 0.457, + 0.326 + ], + "angle": 0, + "content": "
MethodSymInvLeft HandRight HandBoth Hands
SMPLify-SLXX20.3018.7819.54
SGNify✓X18.4418.3918.41
SGNifyX✓19.7617.1618.46
SGNify✓✓17.7217.2917.50
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.331, + 0.468, + 0.358 + ], + "angle": 0, + "content": "Table 4. Evaluating how the linguistic constraints of symmetry and invariance affect mean TR-V2V error (mm) in symmetric signs." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.374, + 0.462, + 0.435 + ], + "angle": 0, + "content": "
MethodInvLeft HandRight HandBoth Hands
SMPLify-SL✗26.0918.8920.50
SGNify✓22.2217.7018.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.441, + 0.468, + 0.469 + ], + "angle": 0, + "content": "Table 5. Evaluating how the linguistic constraint of hand-pose invariance affects mean TR-V2V error (mm) in asymmetric signs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.468, + 0.596 + ], + "angle": 0, + "content": "to fit this mesh to the mocap markers [34]. Marker-based mocap is useful for evaluating ground truth but is not practical for SLC at scale: it is expensive and requires expertise, the reflective markers attached to the signer can influence contact-heavy motions, and processing the resulting data is time consuming. If our monocular method can approach the performance of mocap, it will be widely applicable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.611, + 0.208, + 0.627 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.297, + 0.65 + ], + "angle": 0, + "content": "5.1.Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We quantitatively evaluate SGNify, compare it with state-of-the-art methods, and quantify the improvement derived from each linguistic constraint. To emulate in-the-wild data, which might have very low resolution, lowramerate, and an occluded lower body, we pre-processed our high-quality video data to a resolution of \\(514 \\times 300\\) at 30 fps, and we cropped the input images above the pelvis (see Row 2 of Fig. 3). We used the synchronized meshes captured from the observed Vicon markers [34] as ground truth for evaluation. Since all tested methods estimate SMPL-X meshes with the same topology, we compute the mean pervertex error (TR-V2V) by considering the vertices above the pelvis. The prefix \"TR\" means that we translationally align the mesh reconstructed for each frame with the ground truth; i.e., we center the meshes before computing these errors. Since the starting and ending transitions are not part of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.891, + 0.151 + ], + "angle": 0, + "content": "the sign itself, we manually annotate the expressive central portion of each sign from the raw videos and compute the quantitative results on only these central frames (in total, 2,872 RGB frames)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Table 3 shows the mean TR-V2V error across the 57 signs for four methods and three body regions. The columns labeled \"Upper Body\" report the error computed when considering the hands and the upper body (vertices above the pelvis). We include the head but not the face because our mocap system struggles to reconstruct face details using only 27 markers. We separately report the TR-V2V errors for the left and right hands because of the central role they play in SL. We provide a visualization of the vertices selected for each of these evaluations in Sup. Mat. This experiment compares SGNify with FrankMocap [44], PIXIE [17], PyMAF-X [56], and our baseline SMPLify-SL. SGNify achieves the lowest error for the upper body and both hands, beating the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.773 + ], + "angle": 0, + "content": "Tables 4 and 5 show the improvements derived from each linguistic constraint. Table 4 reports the mean TR-V2V in symmetric signs (classes 1a, 1b, and 2a) when using no constraints, i.e., SMPLify-SL (Row 1), only one constraint (Rows 2 and 3), or both linguistic constraints (Row 4). When one linguistic constraint is used, the TR-V2V of both hands decreases. We observe that the symmetry constraint has the overall greater effect of the two. When the non-dominant hand is passive, it is often rotated at an angle difficult to capture from a frontal camera; this behavior might explain the greater effect of the symmetry constraint on the left hand. When both constraints are applied, we observe a more substantial decrease in the TR-V2V error of the left hand and a slight increase in the error of the right hand compared to when only the hand-pose invariance is applied to the right hand. We believe this happens because the symmetry constraint enforces symmetry between the two hands without knowing which hand reconstruction is more correct, and, for the same reason as above, detecting an accurate RPS for the non-dominant hand is often more challenging; overall, however, using both constraints greatly benefits the reconstruction. In Tab. 5, we separately evaluate performance on signs that do not present symmetry between the two hands (classes 0a, 0b, 2b, 3a, and 3b). As expected, the invariance prior included in SGNify improves the performance on all metrics. These quantitative results indicate that our linguistic constraints improve the reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.667, + 0.803 + ], + "angle": 0, + "content": "5.2. Perceptual Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We conduct an online perceptual study to 1) compare SGNify with the best-performing state-of-the-art method for SL and 2) evaluate the improvement derived from the linguistic constraints (SGNify vs. SMPLify-SL). Even though FrankMocap has a lower hand error than PyMAF-X and PixIE, it has significant errors in the lower body when" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12796" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.166 + ], + "angle": 0, + "content": "the full body is not seen, and higher errors in the upper body; these errors greatly affect the perceptual experience, making it unsuitable for the SL task, as already noticed in [31]. We thus use PyMAF-X since its hand-pose estimates are more accurate than pixIE (see Tab. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.468, + 0.258 + ], + "angle": 0, + "content": "Approval of all experimental procedures for this study was granted by the Ethics Council of the Max Planck Society under the Haptic Intelligence Department's framework agreement under protocol number F027A. No participants are employed by our institution, and all are compensated 20 USD for their time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.468, + 0.366 + ], + "angle": 0, + "content": "Our study involves 20 adult participants who all stated that they have an advanced level of proficiency (expert level) in ASL. We discarded responses from other potential participants who did not correctly recognize at least \\(70\\%\\) of the signs presented via real-person video. 15 of the final 20 participants \\((75\\%)\\) are Deaf, and one participant is left-handed. Participant ages are \\(46.75 \\pm 11.78\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.468, + 0.609 + ], + "angle": 0, + "content": "We used SGNify, SMPLify-SL, and PyMAF-X to reconstruct avatars from 50 videos taken from The American Sign Language Handshape Dictionary [47]; see Row 3 of Fig. 3 for an example. After responding to demographic questions, each participant evaluates the same six training videos to calibrate their responses to the quality of the presented reconstructions. We divide the remaining 44 signs into four batches (real-person RGB video, SGNify, SMPLify-SL, and PyMAF-X) that are balanced by sign class and sign frequency. We include real-person video to obtain an upper-bound on recognition performance and, as mentioned, to filter participants. We assign each participant to one of four surveys. Each survey contains all 44 test signs, and the four methods are rotated through the four sign batches across surveys. We further shuffle the questions in each survey for each user." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.776 + ], + "angle": 0, + "content": "The participant enters the sign they believe the avatar or the real person is articulating in each video. They rate their ease in recognizing the presented sign using a visual analog scale (VAS) ranging from 0 to 100 with five standard labels ranging from \"very difficult\" to \"very easy.\" They also evaluate the naturalness of the articulation on a VAS-labeled scale from \"very unnatural\" to \"very natural.\" Participants are able to replay each video. We provide additional space for comments for each sign and at the end of the study. The self-reported participant carefulness is \\(84.45 \\pm 11.44\\) on a scale from 0 to 100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.468, + 0.9 + ], + "angle": 0, + "content": "The sign annotations submitted by participants are graded as either \"incorrect\" (no credit), \"partially correct\" (half credit), or \"completely correct\" (full credit). We calculate the rates at which each participant recognized the signs for each method. We visualize the resulting \\(20 \\times 4\\) matrix of recognition rates with box plots in the left plot of Fig. 4. Participants recognize signs in real-person videos with an average accuracy of \\(90.9\\%\\) and signs reconstructed" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.302 + ], + "angle": 0, + "content": "by SGNify with \\(86.2\\%\\) accuracy. Signs reconstructed with SMPLify-SL and PyMAF-X are recognized less accurately, at \\(74.8\\%\\) and \\(62.0\\%\\), respectively. We evaluate the statistical significance of these recognition rates. Some distributions failed a Shapiro-Wilk normality test, so we used the non-parametric Friedman test which shows that the method used (real video, SGNify, SMPLify-SL, or PyMAF-X) has a statistically significant effect \\((p < 0.001)\\) on recognition rate. Pairwise comparison with Wilcoxon signed-rank tests and a Bonferroni post-hoc correction reveal that the average sign recognition rate with real video and SGNify are both significantly higher than SMPLify-SL and PyMAF-X. Importantly, sign recognition rates with real video and SGNify are not significantly different from one another." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.305, + 0.892, + 0.44 + ], + "angle": 0, + "content": "The central plot of Fig. 4 shows the participants' perceived easiness in recognizing the sign. These four distributions passed the normality test and were analyzed with a one-way repeated-measures ANOVA with a Bonferroni post-hoc correction for pairwise comparisons. As expected, real videos are perceived to be significantly easier to recognize than the three reconstruction methods. However, signs reconstructed with SGNify and SMPLify-SL are significantly easier to recognize than those by PyMAF-X." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.579 + ], + "angle": 0, + "content": "The right plot of Fig. 4 shows the participants' perceived naturalness of the articulation of the signs. All four distributions passed the normality test, so they were analyzed in the same way as perceived easiness. All methods are statistically different one from another, with real video receiving the highest naturalness ratings, followed by SGNify, SMPLify-SL, and PyMAF-X. Nearly all participants reported in the comments that they want avatars with more expressive face motions and smoother hand and body motions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.687 + ], + "angle": 0, + "content": "These results show that SGNify outperforms the state-of-the-art, PyMAF-X, in all qualitative metrics. Incorporating SL linguistic priors into our baseline SMPLify-SL yields statistically significant perceptual improvements, as judged by 20 expert signers. Most importantly, SGNify achieves a high sign-recognition rate that is not different from that of real-person video on the selected set of ASL signs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.9 + ], + "angle": 0, + "content": "A few participants suggested having clothed (rather than \"nude\") avatars and introducing more human-like features. We thus conduct a second perceptual study to see whether these recommendations have a positive impact on the intelligibility of SGNify's reconstructions. Thirteen participants from the first study participated in this follow-up; the study design is the same. The tested methods are the real video and three different SGNify avatars: the solid purple avatar from the first study, the same avatar wearing a black long-sleeved t-shirt, and a fully textured human character adapted from Meshcapade [2] (see Sup. Mat.). This study comprises 24 signs (including the four for participant training) from the same ASL dataset [47] but different from those of the first study. Our results reveal that adding the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "12797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.348, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.089, + 0.613, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.089, + 0.877, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.361, + 0.895, + 0.461 + ], + "angle": 0, + "content": "Figure 4. Box plots of the data from the perceptual study. The circle shows the mean, and the central line shows the median. The top and bottom box edges show the interquartile range (IQR), and the whiskers encompass the range up to 1.5 times the IQR. Outliers are marked with \\(^+\\). Statistically significant pairwise differences are indicated with a line and a \\(\\star\\). Left: Distribution of the rate at which participants recognized signs presented with each of the four methods. Real Video and SGNify achieve significantly higher recognition rates than both SMPLify-SL and PyMAF-X. Center: Distribution of the average easiness ratings participants assigned to recognizing signs presented by the four methods. All pairwise combinations except SGNify-SMPLify-SL are significantly different. Right: Distribution of the average articulation naturalness ratings participants assigned to the four methods. All pairwise combinations are significantly different." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.472, + 0.56 + ], + "angle": 0, + "content": "t-shirt and using a fully textured avatar do not benefit actual or perceived sign recognition or the perceived naturalness of the reconstruction. As in the previous study, recognition of SGNify's reconstructions were not statistically different from real video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.192, + 0.589 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our results show that SGNify performs quantitatively better than the state of the art, in particular due to the inclusion of our novel linguistic constraints. However, we believe that a per-frame metric is not ideal for SL. To recognize a sign, the temporal evolution is crucial, and this is not captured by V2V. For example, the few slightly inaccurate frames of the SMPLify-SL reconstruction of DOLL (see video on our project page) confused many signers during the perceptual study. Small changes over time can disrupt perception, while overall V2V error remains small. In the end, what matters is whether the meaning is clear to a human. We think a perceptual study provides key insights that complement metric evaluation. The perceptual study indicated that SGNify significantly outperforms the state of the art and, most importantly, produces the first 3D avatars to achieve a sign-recognition accuracy that is not statistically different from the source videos. Our perceptual study also highlights the next challenge for SLC: the need for improvements in the face including facial expressions, tongue and eye movements, mouth morphemes, and eyebrows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.628, + 0.499 + ], + "angle": 0, + "content": "7. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.646 + ], + "angle": 0, + "content": "We present SGNify, which estimates 3D avatars of isolated SL signs from monocular RGB video. Quantitative and qualitative experiments show that SGNify outperforms the state of the art in estimating challenging SL hand poses by leveraging constraints derived from linguistics. SGNify represents a step towards the capture of realistic 3D avatars from SL videos in the wild. Future work should explore the use of our constraints in training regression methods, real-time processing, and continuous signing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.895, + 0.867 + ], + "angle": 0, + "content": "Acknowledgments We thank Galina Henz and Tsvetelina Alexiadis for trial coordination; Matvey Safroshkin, Markus Höschle, Senya Polikovsky, Tobias Bauch, Taylor McConnell (TM), and Bernard Javot for the capture setup; TM for data-cleaning coordination; Leyre Sánchez Vinuela, Andres Camilo Mendoza Patino, and Yasemin Fincan for data cleaning; Nima Ghorbani and Giorgio Becherini for MoSh++; Joachim Tesch for help with Blender; Benjamin Pellkofer and Joey Burns for IT support; Yao Feng, Anastasios Yiannakidis, and Radek Danček for discussions on facial methods; Haliza Mat Husin and Mayumi Mohan for help with statistics; and the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Maria-Paola Forte and Peter Kulits." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.887 + ], + "angle": 0, + "content": "Disclosure: https://files.is.tue.mpg.de/black/CoI_CVPR_2023.txt" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12798" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.115, + 0.468, + 0.16 + ], + "angle": 0, + "content": "[1] CDPSL: Corpus-based Dictionary of Polish Sign Language. https://www.slownikpjm.uw.edu.pl/.5" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.165, + 0.466, + 0.194 + ], + "angle": 0, + "content": "[2] Meshcapade GmbH, Tübingen, Germany. https://meshcapade.com, 2022.7" + }, + { + "type": "ref_text", + "bbox": [ + 0.089, + 0.199, + 0.469, + 0.273 + ], + "angle": 0, + "content": "[3] Ahmed H. 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Kuchenbecker Michael J. Black + +Max Planck Institute for Intelligent Systems, Stuttgart and Tübingen, Germany + +{forte,kjk}@is.mpg.de {kulits,chuang2,vchoutas,dtzionas,black}@tue.mpg.de + +![](images/dec574879ff276e02bd3d1f927ee8f2f09b5c6534eb19ab083d45f383d3cf6ab.jpg) +Figure 1. Given a monocular, in-the-wild video of a sign-language sign, SGNify automatically reconstructs a 3D body with accurate hand pose, facial motion, and body pose. Note that motion blur obscures the finger articulations in several video frames; this is a common problem. Our novel linguistic priors enable accurate 3D reconstruction despite such image degradation. + +# Abstract + +Sign language (SL) is the primary method of communication for the 70 million Deaf people around the world. Video dictionaries of isolated signs are a core SL learning tool. Replacing these with 3D avatars can aid learning and enable AR/VR applications, improving access to technology and online media. However, little work has attempted to estimate expressive 3D avatars from SL video; occlusion, noise, and motion blur make this task difficult. We address this by introducing novel linguistic priors that are universally applicable to SL and provide constraints on 3D hand pose that help resolve ambiguities within isolated signs. Our method, SGNify, captures fine-grained hand pose, facial expression, and body movement fully automatically from in-the-wild monocular SL videos. We evaluate SGNify quantitatively by using a commercial motion-capture system to compute 3D avatars synchronized with monocular video. SGNify outperforms state-of-the-art 3D body-pose-and shape-estimation methods on SL videos. A perceptual study shows that SGNify's 3D reconstructions are significantly more comprehensible and natural than those of previous methods and are on par with the source videos. Code and data are available at sgnify.is.tue.mpg.de. + +# 1. Introduction + +It is estimated that over 466 million people have disabling hearing loss [13] and more than 70 million people use sign language (SL) as their primary means of communication [52]. Increasing use of digital communication motivates research on capturing, understanding, modeling, and synthesizing expressive 3D SL avatars. Existing datasets and dictionaries used in SL recognition (SLR), translation (SLT), and production (SLP) are primarily limited to 2D video because the technology required to capture 3D movement is prohibitively expensive, requires expertise to operate, and may limit the movements of the signer. Dictionaries of isolated signs are a core SL learning tool, and many SLs have online 2D video dictionaries. The Deaf community is actively seeking 3D dictionaries of isolated signs to aid learning [40]. The current approach to creating such 3D signing dictionaries is fully manual, requiring an artist or a HamNoSys [21] expert, and the resulting avatars often move unnaturally [3]. We aim to automatically reconstruct expressive 3D signing avatars from monocular SL video, which we term Sign Language Capture (SLC). We focus on SLC of isolated signs. + +3D reconstruction of human pose and shape has received significant attention, but accurate 3D hand-pose estimation + +remains challenging from in-the-wild video. Challenges include the high number of degrees of freedom present in hands [5], frequent occurrence of self-contact and self-occlusions [37, 46], low resolution, and motion blur caused by fast motions [50] that cause hand pose to be unrecognizable in many frames (see Fig. 1). To address these issues, we exploit the linguistic nature of SL itself to develop novel priors that help disambiguate hand poses in SL videos, leading to accurate 3D reconstructions. This is a novel use of linguistic "side information" to improve 3D reconstruction. + +Based on hand movements and poses, Battison [4] defines five linguistic classes that contain all SL signs. We build on that work to define eight classes and formalize these as mathematical priors on 3D hand shape. We combine Battison's first two classes and place all one-handed signs in class 0, while two-handed signs are arranged in classes 1, 2, or 3, depending on how the non-dominant hand participates in the articulation of the sign. We then divide each of these four classes into two subclasses depending on whether the pose of the active hand(s) changes during the articulation of the sign. We introduce two class-dependent SL linguistic constraints that capture 1) symmetry and 2) hand-pose invariance. Under Battison's SL symmetry condition [4], when both hands actively move, the articulation of the fingers must be identical; the same is true for one class of two-handed signs in which only the dominant hand moves. We formalize this concept as a regularization term that encourages the pose of the two hands to be similar for such signs. Coupling the hand poses in this way effectively increases the image evidence for a pose, which improves estimates for challenging videos. Our invariance constraint uses the observation that hand pose is either static or transitions smoothly from one pose to another during the articulation of the sign; other significant changes to hand pose are not common in SL. Specifically, we extract a characteristic "reference pose sequence" (RPS) to describe each local hand pose during the sign articulation, and we penalize differences between the RPS and the estimated hand pose in each frame. These two priors of symmetry and hand-pose invariance are universally applicable to all sign languages. + +The hands alone, however, are not sufficient to accurately reproduce SL. Information is conveyed holistically in SL through hand gestures, facial expressions, and upper-body movements in 3D space. To combine these, we use a 3D whole-body model, SMPL-X [41], that jointly models this information (see Fig. 1). + +Our novel hand-pose constraints are formulated to be incorporated into the loss function for training a neural network regressor or into the objective function of optimization-based methods. In general, optimization-based methods are more computationally intensive but produce more accurate results when limited training data is available, so we take this approach here and build on the + +SMPLify-X method [41]. To appropriately incorporate our terms into the objective function, we need to know the class of the sign. We train a simple model that extracts features from the raw video and determines the class to which the depicted sign belongs. While SMPLify-X is a good foundation for the hands and body, we find that it does not capture expressive facial motions well. Consequently, we use a more expressive face regressor, SPECTRE [19], to capture the face parameters. We call our method SGNify. + +To quantitatively evaluate SGNify, we capture a native German (DGS) signer with a frontal RGB camera synchronized with a 54-camera Vicon motion capture system and recover ground-truth meshes from the Vicon markers [34]. We run SGNify on the RGB video and compute 3D vertex-to-vertex (V2V) error between our resulting avatars and the ground-truth meshes. We find that SGNify reconstructs SMPL-X meshes more accurately than the competition. + +We conduct a perceptual evaluation in which we present proficient signers with a video of either an estimated SMPL-X avatar or the real-person source video and task them with identifying the sign being performed. Participants also rate their ease in recognizing the sign and the naturalness of the articulation. Our results show that SGNify reconstructs 3D signs that are as recognizable as the original videos and consistently more recognizable, easier to understand, and more natural than the existing state of the art. We also evaluate SGNify in a multi-view setting and on continuous signing videos. Despite not being designed for the latter, SGNify captures the meaning in continuous SL. + +SGNify represents a step towards the automatic reconstruction of natural 3D avatars from sign-language videos. Our key contribution is the introduction of novel linguistic priors that are universal and helpful to constrain the problem of hand-pose estimation from SL video. SGNify is designed to work on video from different SL dictionaries across languages, backgrounds, people, trimming, image resolution, and framing, as visible in Sup. Mat. and in the video on our project page. This capability is critical to capture 3D signing at scale, which will enable progress on learning SL avatars. Our code and motion-capture dataset are available for research purposes at sgnify.is.tue.mpg.de. + +# 2. Related Work + +Expressive 3D Humans From RGB Images: Until recently, human-posed estimation has focused on the estimation of 2D [12] or 3D [51] joints of the hands and body, as well as those of facial features [6] from single images. In addition to methods that estimate a sparse set of landmarks, there are multiple methods that estimate the parameters of morphable models for the hand [22, 32, 36, 58], face [11, 16, 18, 20], and body [8, 25, 27–29, 33, 39, 57]. The advent of expressive 3D body models like SMPL-X [41], Adam [26], and GHUM [54] has enabled research on esti + +mating the full 3D body surface [9, 17, 41, 44, 49, 53, 55]. Such body models are ideal for representing the expressiveness of SL but have rarely been applied to this domain [30]. Human Pose for Sign Language: To enable detailed 3D pose estimation from images, How2Sign [14] provides 3D skeleton reconstructions for three hours of data captured in a Panoptic Studio [24]. However, the skeletal representation lacks the richness of a full 3D body model and omits surface details that are important for communication [38]. Kratimenos et al. [30] use SMPLify-X to estimate 3D pose and shape on the GSLL sign-language dataset [48]. They compare SL recognition accuracy using features from raw RGB images, OpenPose [7] 2D skeletons, and SMPL-X bodies and observe the best automated recognition results with SMPL-X, illustrating the benefit of using a 3D model. They also highlight the importance of capturing the face and body; in an ablation study, they show that neglecting the face and body harms recognition accuracy [30]. However, their SMPL-X reconstructions use existing off-the-shelf methods and lack visual realism. SMPLify-X [41] and other recent 3D pose-reconstruction methods [17, 44], as well as keypoint detectors, struggle when applied to SL video due to challenging self-occlusion, hand-hand and hand-body interactions [38], motion blur [50], and cropping inherent to SL. SignPose [31] is a 3D-pose-lifting method for SL; it uses manually created synthetic SL animations to infer a textured avatar from single RGB images. SignPose requires all OpenPose keypoints above the pelvis to be detected, which is unrealistic in noisy SL videos. We address these challenges by incorporating sign-language knowledge in the form of linguistic constraints. Since the early 2000s, the integration of linguistic information has been known to be beneficial to both SLR [10] and SLP [35], but this strategy has not previously been applied to SLC. + +# 3. Method + +We introduce SGNify, an offline method for reconstructing 3D body shape and pose of SL from monocular RGB video. SGNify centers around a key insight: SL signs follow universal linguistic rules that can be formulated as class-specific priors and used to improve hand-pose estimation. Our full pipeline is shown in Fig. 2. + +# 3.1. SMPLify-SL: Baseline for Sign-Language Video + +Our baseline method builds on SMPLify-X [41], which estimates SMPL-X [41] parameters from RGB images. SMPL-X is a 3D body model, representing whole-body pose and shape, including finger articulations and facial expressions. SMPL-X is a function, $M(\theta, \beta, \psi)$ , parameterized by body pose $\theta$ (including hand pose $\theta_h$ ), body shape $\beta$ , and facial expressions $\psi$ , that outputs a 3D body mesh. + +To create a strong baseline, we extend SMPLify-X to video by adapting it in the following ways: (1) We cope + +with the upper-body framing typical of SL videos by changing the heuristic used for camera initialization and the estimation of the out-of-view lower-body joints. (2) Since human motion is locally smooth in time, we initialize $\theta_t \in \mathbb{R}^{|\theta|}$ with $\theta_{t-1}$ and include a zero-velocity loss on the hands and body to encourage smooth reconstructions. (3) We estimate shape parameters $(\beta)$ over multiple frames by taking the median of the parameter estimates and not-optimizing them during the per-frame reconstruction. (4) To better capture the frequent hand-hand and hand-body interactions (mainly with the face and the chest), we employ the more robust self-contact loss of Müller et al. [39] instead of the original SMPLify-X interpenetration term. (5) For each frame, we pre-compute the facial expressions $(\psi)$ and jaw poses with SPECTRE [19]. These parameters are substituted into SMPL-X at the end of the optimization. SPECTRE can be swapped for any method whose expression parameters are consistent with those of SMPL-X, e.g., EMOCA [11]. We denote the baseline SMPLify-SL. + +# 3.2. Linguistic Constraints + +State-of-the-art optimization- and regression-based human pose estimation methods struggle on SL video, particularly with the estimation of hand pose. We address this challenge by formulating linguistic constraints as additional losses on hand pose and integrating them into the SMPLify-SL objective function. First, we adapt the five sign-classification and morpheme-structure conditions introduced for American Sign Language (ASL) by Battison [4] to divide signs into four primary classes: + +Class 0: one-handed signs in which only the dominant hand articulates the sign. + +Class 1: two-handed signs in which both hands are active. They share the same poses and perform the same movement in a synchronous or alternating pattern. This class includes all signs that follow Battison's symmetry condition [4]. + +Class 2: two-handed signs in which the dominant hand is active, the non-dominant hand is passive (its position and pose do not change during the articulation of the sign), and the two hands have the same initial pose. + +Class 3: two-handed signs in which the dominant hand is active, the non-dominant hand is passive, and the two hands have different hand poses. All signs in this class follow Battison's dominance condition [4]. + +We further divide each class into two subclasses: subclass $a$ contains signs in which the hand pose of the active hand(s) does not change throughout the articulation of the sign (static), and subclass $b$ contains all signs in which the hand pose changes (transitioning). + +Note that the division into these classes is not limited to ASL; Eccarius et al. [15] show that the phonological and prosodic properties of ASL can be successfully transferred to other sign-language lexicons. + +![](images/2b9b269b73bd003ac69d8400855935080979a542e74423eff972365f0d280248.jpg) +Figure 2. Given a video of a sign-language (SL) sign as input, our method preprocesses the data to first extract 2D keypoints. The hand keypoints are used to select candidate frames for estimating the reference hand poses $(\theta_{ref,i}^{h},\theta_{ref,f}^{h})$ and, for static hand poses, also $\theta_{ref}^{h}$ . The initial and final reference hand poses $(\theta_{ref,i}^{h}$ and $\theta_{ref,f}^{h})$ , together with wrist-keypoint features detected across the sequence, are then fed into our sign-group classifier, which automatically classifies signs in monocular SL video into six groups based on linguistic rules universally applicable to SL [4]. Using the predicted group labels and the relevant reference hand poses, SGNify applies the appropriate linguistic constraints to improve SL 3D hand-pose estimation, especially when the video frame is ambiguous. + +
ClassHand-Pose SymmetryHand-Pose Invariance
DominantNon-dominant
0aXstaticX
0bXtransitioningX
1a✓staticstatic
1b✓transitioningtransitioning
2a✓staticstatic
2bXtransitioningstatic
3aXstaticstatic
3bXtransitioningstatic
+ +Table 1. Linguistic constraints defining the eight sign classes. + +We then convert these linguistic classes into two 3D pose constraints: hand-pose symmetry and hand-pose invariance. Signs in the same class share the same constraints (see Tab. 1 and Tab. S.1 in Sup. Mat.). + +Below we describe only the new terms added to the SMPLify-X objective. Please see Sup. Mat. for the full SGNify objective. + +# 3.2.1 Hand-Pose Symmetry + +We encourage the left and right hand poses to match for the relevant classes (classes 1a, 1b, and 2a in Tab. 1): + +$$ +L _ {s} = \lambda_ {s} \| \theta_ {t} ^ {r} - r \left(\theta_ {t} ^ {l}\right) \| _ {2} ^ {2}, \tag {1} +$$ + +where $\theta_t^r$ is the finger articulation of the right hand, and $r(\theta_t^l)$ is a reflection function to represent the articulation of the fingers of the left hand as if it were a right hand. This loss penalizes differences in finger poses between the hands. + +# 3.2.2 Hand-Pose Invariance + +Each sign has a characteristic reference hand pose sequence (RPS). The RPS defines the hand pose that we expect at each time $t$ during the articulation of the sign. The hand-posed-invariance constraint penalizes differences between the reference hand pose $\theta_{\text{ref},t}^{h} \in \mathbf{RPS}^{h}$ and the estimated hand pose $\theta_{t}^{h}$ : + +$$ +L _ {i} ^ {h} = \lambda_ {i} \| \theta_ {\text {r e f}, t} ^ {h} - \theta_ {t} ^ {h} \| _ {2} ^ {2}, \tag {2} +$$ + +where $h$ represents either the left or the right hand. + +Throughout each sign, the hand pose either stays static or transitions between two poses. When static, only one hand pose, $\theta_{ref}^{h}$ , is representative of the RPS. Signs where the hand pose is transitioning are characterized by two reference hand poses, $\theta_{ref,i}^{h}$ and $\theta_{ref,f}^{h}$ , corresponding respectively to the initial and final poses. We interpolate $\theta_{ref,i}^{h}$ and $\theta_{ref,f}^{h}$ with spherical linear interpolation [45] to obtain intermediate poses. We presently do not consider signs with repeated hand-posed transitions, e.g., STORY in ASL, which occur in a small percentage of signs ( $\sim 3\%$ ). + +# 3.3. Automatization + +To work fully automatically, SGNify must 1) estimate the poses needed to enforce the hand-pose-invariance constraint and 2) classify which sign group is present in a video sequence (see Fig. 2). + +To estimate the reference hand poses $(\theta_{ref}^{h},\theta_{ref,i}^{h}$ and $\theta_{ref,f}^{h})$ , our method selects candidate frames in the core part of the sign using hand-keypoint detection confidences, and it uses SMPLify-X (adapted to SL cropping) to reconstruct + +a preliminary 3D hand pose for each candidate frame. With static hand poses, $\theta_{ref}^{h}$ is obtained by taking the average hand poses of these candidates. With transitioning hand poses, the core part of a sign is divided into two intervals, and $\theta_{ref,i}^{h}$ and $\theta_{ref,f}^{h}$ correspond to the average hand poses of the candidate frames in the first and second intervals, respectively (see Sup. Mat. for more details). + +The constraints applied to each sign depend on its sign group; we have six sign groups because classes 1a & 2a share the same constraints, as do 2b & 3b (Tab. 1). There is insufficient paired data to train a CNN classifier, so we use an intuitive and interpretable decision tree trained on extracted 2D and 3D pose features. Our features are invariant to the handedness of the signer and include: 1) the minimum of the maximum height differences of each wrist across the sequence: $\min (\{w_r\}_{\max} - \{w_r\}_{\min},\{w_l\}_{\max} - \{w_l\}_{\min})$ where $w_{l}$ and $w_{r}$ are the heights of the left and right wrists, respectively. 2) the cosine distance between the initial poses of each hand: $\mathrm{CosDist}(\theta_{ref,i}^{r},\theta_{ref,i}^{l})$ , 3) the maximum of the two cosine distances between each initial and final hand pose: $\max (\mathrm{CosDist}(\theta_{ref,i}^{r},\theta_{ref,f}^{r}),\mathrm{CosDist}(\theta_{ref,i}^{l},\theta_{ref,f}^{l}))$ + +We train our sign-group classifier on the over 3,000 videos from the Corpus-based Dictionary of Polish Sign Language (CDPSL) [1]; these are annotated with HamNoSys [21]. We construct a grammar to convert HamNoSys annotations into our group labels (see Sup. Mat.) Row 1 of Figure 3 shows a sample frame from CDPSL. This dataset is not used in our quantitative analysis or perceptual study. + +# 3.4. SGNify Extensions + +First, we follow Huang et al. [23] to extend SGNify to work on multi-view videos. Second, we propose a baseline method for continuous SLC (CSLC). CSLC introduces additional challenges, such as the segmentation of sentences into signs; this is an active field of research. When a sentence is given as input, we use Renz et al. [43] to segment the input video and then process each segment with SGNify. The first frame of each segment is initialized from the last frame of the previous one. These extensions are not our main contribution and are described in Sup. Mat. + +# 4. Dataset + +To quantitatively evaluate SGNify as a viable method for SLC, we collected motion-capture data with ground-truth SMPL-X bodies articulating signs. Our dataset represents the first publicly available expressive full-4D capture of isolated SL signs. The experimental procedure was reviewed by the ethics council of the University of Tübingen without objections or remarks (709/2021B02). + +In consultation with a Deaf DGS teacher and a DGS interpreter, we defined a German SL corpus consisting of 57 isolated signs. The selected signs cover a wide range of + +![](images/8180a60f27e89700190d7f51d0def58152704b4c25915dd688001f597d5199ab.jpg) + +![](images/1018b7a0ce74a933d22405df86e6e28cf93ea5809723e32c5ab005dca291dd17.jpg) + +![](images/17f36ffde17a14fdd80203e2a15f187411df4217850c2d03755f229f209e3703.jpg) + +![](images/8982790361a65b1677898f628b735a5408ee237c513f279012fbfda33bd867fc.jpg) +Figure 3. Samples frames reconstructed by SGNify. The input videos are from diverse multilingual datasets. Row 1: Polish SL sign GDANSK (GDANSK, class 1a) from the dataset [1] used for training our sign-group classifier. Row 2: DGS sign BLUME (FLOWER, class 3b) from our captured dataset used in the quantitative evaluation. Row 3: ASL sign DOLL (class 0a) from the dataset [47] used in the perceptual study. Row 4: South African SL sign ARCHERY (class 2a) from the in-the-wild dataset [42]. + +![](images/1c0aff61dd4232689cd82d30a03298552a32374085a58e805ffda04294139c04.jpg) + +![](images/4d83b534e869607ada7e907922bac7bd5a7a7e82f3473a6a7b61e4a2e8fe221b.jpg) + +![](images/2c582c2e1b48a0820e364b43ef70be0d1c7e1ad94db02ad98de7d68876bb6c05.jpg) + +![](images/8df943c8d11584a8ced6b3c7ef0d4d46d4302bdd441bfe0bf63d536efa777117.jpg) + +
Class0a0b1a1b2a2b3a3b
# Signs123143112102
+ +Table 2. Number of signs captured for each class. + +challenges for SLC, such as self-contact and self-occlusion. Table 2 summarizes the number of signs collected for each of the eight classes. Signs of subclass $b$ are less common, and this is reflected in our corpus. + +We captured a native right-handed DGS signer with a Vicon mocap system at 120 fps, synchronized with a frontal $4112 \times 3008$ RGB camera at 60 fps, framing an upper-body view as typically found in SL video. The hands start and end at rest at the signer's sides, and each sign lasts between 1.7 and 3.5 seconds after trimming. In total, our dataset comprises 16,608 mocap frames and 8,304 RGB frames. To obtain ground-truth SMPL-X meshes, we scanned the participant in a 4D body scanner in several poses. The SMPL-X mesh was registered to these scans and averaged to obtain a personalized body-shape mesh. MoSh++ was then used + +
MethodUpper BodyLeft HandRight Hand
FrankMocap [44]78.0720.4719.62
PIXIE [17]60.1125.0222.42
PyMAF-X [56]68.6121.4619.19
SMPLify-SL56.0722.2318.83
SGNify55.6319.2217.50
+ +Table 3. Evaluation on our ground-truth mocap dataset: mean TR-V2V error (mm) for five methods and three body regions. + +
MethodSymInvLeft HandRight HandBoth Hands
SMPLify-SLXX20.3018.7819.54
SGNify✓X18.4418.3918.41
SGNifyX✓19.7617.1618.46
SGNify✓✓17.7217.2917.50
+ +Table 4. Evaluating how the linguistic constraints of symmetry and invariance affect mean TR-V2V error (mm) in symmetric signs. + +
MethodInvLeft HandRight HandBoth Hands
SMPLify-SL✗26.0918.8920.50
SGNify✓22.2217.7018.60
+ +Table 5. Evaluating how the linguistic constraint of hand-pose invariance affects mean TR-V2V error (mm) in asymmetric signs. + +to fit this mesh to the mocap markers [34]. Marker-based mocap is useful for evaluating ground truth but is not practical for SLC at scale: it is expensive and requires expertise, the reflective markers attached to the signer can influence contact-heavy motions, and processing the resulting data is time consuming. If our monocular method can approach the performance of mocap, it will be widely applicable. + +# 5. Experiments + +# 5.1.Quantitative Evaluation + +We quantitatively evaluate SGNify, compare it with state-of-the-art methods, and quantify the improvement derived from each linguistic constraint. To emulate in-the-wild data, which might have very low resolution, lowramerate, and an occluded lower body, we pre-processed our high-quality video data to a resolution of $514 \times 300$ at 30 fps, and we cropped the input images above the pelvis (see Row 2 of Fig. 3). We used the synchronized meshes captured from the observed Vicon markers [34] as ground truth for evaluation. Since all tested methods estimate SMPL-X meshes with the same topology, we compute the mean pervertex error (TR-V2V) by considering the vertices above the pelvis. The prefix "TR" means that we translationally align the mesh reconstructed for each frame with the ground truth; i.e., we center the meshes before computing these errors. Since the starting and ending transitions are not part of + +the sign itself, we manually annotate the expressive central portion of each sign from the raw videos and compute the quantitative results on only these central frames (in total, 2,872 RGB frames). + +Table 3 shows the mean TR-V2V error across the 57 signs for four methods and three body regions. The columns labeled "Upper Body" report the error computed when considering the hands and the upper body (vertices above the pelvis). We include the head but not the face because our mocap system struggles to reconstruct face details using only 27 markers. We separately report the TR-V2V errors for the left and right hands because of the central role they play in SL. We provide a visualization of the vertices selected for each of these evaluations in Sup. Mat. This experiment compares SGNify with FrankMocap [44], PIXIE [17], PyMAF-X [56], and our baseline SMPLify-SL. SGNify achieves the lowest error for the upper body and both hands, beating the state-of-the-art methods. + +Tables 4 and 5 show the improvements derived from each linguistic constraint. Table 4 reports the mean TR-V2V in symmetric signs (classes 1a, 1b, and 2a) when using no constraints, i.e., SMPLify-SL (Row 1), only one constraint (Rows 2 and 3), or both linguistic constraints (Row 4). When one linguistic constraint is used, the TR-V2V of both hands decreases. We observe that the symmetry constraint has the overall greater effect of the two. When the non-dominant hand is passive, it is often rotated at an angle difficult to capture from a frontal camera; this behavior might explain the greater effect of the symmetry constraint on the left hand. When both constraints are applied, we observe a more substantial decrease in the TR-V2V error of the left hand and a slight increase in the error of the right hand compared to when only the hand-pose invariance is applied to the right hand. We believe this happens because the symmetry constraint enforces symmetry between the two hands without knowing which hand reconstruction is more correct, and, for the same reason as above, detecting an accurate RPS for the non-dominant hand is often more challenging; overall, however, using both constraints greatly benefits the reconstruction. In Tab. 5, we separately evaluate performance on signs that do not present symmetry between the two hands (classes 0a, 0b, 2b, 3a, and 3b). As expected, the invariance prior included in SGNify improves the performance on all metrics. These quantitative results indicate that our linguistic constraints improve the reconstructions. + +# 5.2. Perceptual Study + +We conduct an online perceptual study to 1) compare SGNify with the best-performing state-of-the-art method for SL and 2) evaluate the improvement derived from the linguistic constraints (SGNify vs. SMPLify-SL). Even though FrankMocap has a lower hand error than PyMAF-X and PixIE, it has significant errors in the lower body when + +the full body is not seen, and higher errors in the upper body; these errors greatly affect the perceptual experience, making it unsuitable for the SL task, as already noticed in [31]. We thus use PyMAF-X since its hand-pose estimates are more accurate than pixIE (see Tab. 3). + +Approval of all experimental procedures for this study was granted by the Ethics Council of the Max Planck Society under the Haptic Intelligence Department's framework agreement under protocol number F027A. No participants are employed by our institution, and all are compensated 20 USD for their time. + +Our study involves 20 adult participants who all stated that they have an advanced level of proficiency (expert level) in ASL. We discarded responses from other potential participants who did not correctly recognize at least $70\%$ of the signs presented via real-person video. 15 of the final 20 participants $(75\%)$ are Deaf, and one participant is left-handed. Participant ages are $46.75 \pm 11.78$ . + +We used SGNify, SMPLify-SL, and PyMAF-X to reconstruct avatars from 50 videos taken from The American Sign Language Handshape Dictionary [47]; see Row 3 of Fig. 3 for an example. After responding to demographic questions, each participant evaluates the same six training videos to calibrate their responses to the quality of the presented reconstructions. We divide the remaining 44 signs into four batches (real-person RGB video, SGNify, SMPLify-SL, and PyMAF-X) that are balanced by sign class and sign frequency. We include real-person video to obtain an upper-bound on recognition performance and, as mentioned, to filter participants. We assign each participant to one of four surveys. Each survey contains all 44 test signs, and the four methods are rotated through the four sign batches across surveys. We further shuffle the questions in each survey for each user. + +The participant enters the sign they believe the avatar or the real person is articulating in each video. They rate their ease in recognizing the presented sign using a visual analog scale (VAS) ranging from 0 to 100 with five standard labels ranging from "very difficult" to "very easy." They also evaluate the naturalness of the articulation on a VAS-labeled scale from "very unnatural" to "very natural." Participants are able to replay each video. We provide additional space for comments for each sign and at the end of the study. The self-reported participant carefulness is $84.45 \pm 11.44$ on a scale from 0 to 100. + +The sign annotations submitted by participants are graded as either "incorrect" (no credit), "partially correct" (half credit), or "completely correct" (full credit). We calculate the rates at which each participant recognized the signs for each method. We visualize the resulting $20 \times 4$ matrix of recognition rates with box plots in the left plot of Fig. 4. Participants recognize signs in real-person videos with an average accuracy of $90.9\%$ and signs reconstructed + +by SGNify with $86.2\%$ accuracy. Signs reconstructed with SMPLify-SL and PyMAF-X are recognized less accurately, at $74.8\%$ and $62.0\%$ , respectively. We evaluate the statistical significance of these recognition rates. Some distributions failed a Shapiro-Wilk normality test, so we used the non-parametric Friedman test which shows that the method used (real video, SGNify, SMPLify-SL, or PyMAF-X) has a statistically significant effect $(p < 0.001)$ on recognition rate. Pairwise comparison with Wilcoxon signed-rank tests and a Bonferroni post-hoc correction reveal that the average sign recognition rate with real video and SGNify are both significantly higher than SMPLify-SL and PyMAF-X. Importantly, sign recognition rates with real video and SGNify are not significantly different from one another. + +The central plot of Fig. 4 shows the participants' perceived easiness in recognizing the sign. These four distributions passed the normality test and were analyzed with a one-way repeated-measures ANOVA with a Bonferroni post-hoc correction for pairwise comparisons. As expected, real videos are perceived to be significantly easier to recognize than the three reconstruction methods. However, signs reconstructed with SGNify and SMPLify-SL are significantly easier to recognize than those by PyMAF-X. + +The right plot of Fig. 4 shows the participants' perceived naturalness of the articulation of the signs. All four distributions passed the normality test, so they were analyzed in the same way as perceived easiness. All methods are statistically different one from another, with real video receiving the highest naturalness ratings, followed by SGNify, SMPLify-SL, and PyMAF-X. Nearly all participants reported in the comments that they want avatars with more expressive face motions and smoother hand and body motions. + +These results show that SGNify outperforms the state-of-the-art, PyMAF-X, in all qualitative metrics. Incorporating SL linguistic priors into our baseline SMPLify-SL yields statistically significant perceptual improvements, as judged by 20 expert signers. Most importantly, SGNify achieves a high sign-recognition rate that is not different from that of real-person video on the selected set of ASL signs. + +A few participants suggested having clothed (rather than "nude") avatars and introducing more human-like features. We thus conduct a second perceptual study to see whether these recommendations have a positive impact on the intelligibility of SGNify's reconstructions. Thirteen participants from the first study participated in this follow-up; the study design is the same. The tested methods are the real video and three different SGNify avatars: the solid purple avatar from the first study, the same avatar wearing a black long-sleeved t-shirt, and a fully textured human character adapted from Meshcapade [2] (see Sup. Mat.). This study comprises 24 signs (including the four for participant training) from the same ASL dataset [47] but different from those of the first study. Our results reveal that adding the + +![](images/6cd9a27685d9c0683b62630d990b89441ead75532f6cb62fcef41942b4b2f685.jpg) +Figure 4. Box plots of the data from the perceptual study. The circle shows the mean, and the central line shows the median. The top and bottom box edges show the interquartile range (IQR), and the whiskers encompass the range up to 1.5 times the IQR. Outliers are marked with $^+$ . Statistically significant pairwise differences are indicated with a line and a $\star$ . Left: Distribution of the rate at which participants recognized signs presented with each of the four methods. Real Video and SGNify achieve significantly higher recognition rates than both SMPLify-SL and PyMAF-X. Center: Distribution of the average easiness ratings participants assigned to recognizing signs presented by the four methods. All pairwise combinations except SGNify-SMPLify-SL are significantly different. Right: Distribution of the average articulation naturalness ratings participants assigned to the four methods. All pairwise combinations are significantly different. + +![](images/6b4c1dcb236fd10a733c6d33b854cc85b4f66dbd05644451c062db369301481e.jpg) + +![](images/93566bfab244c6c47e6d718b7768b882168e09be02a1637a80a351f2e9c3ea85.jpg) + +t-shirt and using a fully textured avatar do not benefit actual or perceived sign recognition or the perceived naturalness of the reconstruction. As in the previous study, recognition of SGNify's reconstructions were not statistically different from real video. + +# 6. Discussion + +Our results show that SGNify performs quantitatively better than the state of the art, in particular due to the inclusion of our novel linguistic constraints. However, we believe that a per-frame metric is not ideal for SL. To recognize a sign, the temporal evolution is crucial, and this is not captured by V2V. For example, the few slightly inaccurate frames of the SMPLify-SL reconstruction of DOLL (see video on our project page) confused many signers during the perceptual study. Small changes over time can disrupt perception, while overall V2V error remains small. In the end, what matters is whether the meaning is clear to a human. We think a perceptual study provides key insights that complement metric evaluation. The perceptual study indicated that SGNify significantly outperforms the state of the art and, most importantly, produces the first 3D avatars to achieve a sign-recognition accuracy that is not statistically different from the source videos. Our perceptual study also highlights the next challenge for SLC: the need for improvements in the face including facial expressions, tongue and eye movements, mouth morphemes, and eyebrows. + +# 7. Conclusions + +We present SGNify, which estimates 3D avatars of isolated SL signs from monocular RGB video. Quantitative and qualitative experiments show that SGNify outperforms the state of the art in estimating challenging SL hand poses by leveraging constraints derived from linguistics. SGNify represents a step towards the capture of realistic 3D avatars from SL videos in the wild. Future work should explore the use of our constraints in training regression methods, real-time processing, and continuous signing. + +Acknowledgments We thank Galina Henz and Tsvetelina Alexiadis for trial coordination; Matvey Safroshkin, Markus Höschle, Senya Polikovsky, Tobias Bauch, Taylor McConnell (TM), and Bernard Javot for the capture setup; TM for data-cleaning coordination; Leyre Sánchez Vinuela, Andres Camilo Mendoza Patino, and Yasemin Fincan for data cleaning; Nima Ghorbani and Giorgio Becherini for MoSh++; Joachim Tesch for help with Blender; Benjamin Pellkofer and Joey Burns for IT support; Yao Feng, Anastasios Yiannakidis, and Radek Danček for discussions on facial methods; Haliza Mat Husin and Mayumi Mohan for help with statistics; and the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Maria-Paola Forte and Peter Kulits. + +Disclosure: https://files.is.tue.mpg.de/black/CoI_CVPR_2023.txt + +# References + +[1] CDPSL: Corpus-based Dictionary of Polish Sign Language. https://www.slownikpjm.uw.edu.pl/.5 +[2] Meshcapade GmbH, Tübingen, Germany. https://meshcapade.com, 2022.7 +[3] Ahmed H. 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Image and Vision Computing (IVS), 32(8):533-549, 2014. 3 +[49] Shashank Tripathi, Lea Müller, Chun-Hao P. Huang, Taheri Omid, Michael J. Black, and Dimitrios Tzionas. 3D human pose estimation via intuitive physics. In Computer Vision and Pattern Recognition (CVPR), 2023. 3 +[50] Manuel Vázquez-Enriquez, Jose L. Alba-Castro, Laura Docio-Fernández, and Eduardo Rodríguez-Banga. Isolated sign language recognition with multiscale spatial-temporal graph convolutional networks. In Computer Vision and Pattern Recognition (CVPR), pages 3462–3471, 2021. 2, 3 +[51] Jinbao Wang, Shujie Tan, Xiantong Zhen, Shuo Xu, Feng Zheng, Zhenyu He, and Ling Shao. Deep 3D + +human pose estimation: A review. Computer Vision and Image Understanding, 210:103225, 2021. 2 +[52] World Federation of the Deaf. Who we are. http://wfdeaf.org/who-we-are/.1 +[53] Donglai Xiang, Hanbyul Joo, and Yaser Sheikh. Monocular total capture: Posing face, body, and hands in the wild. In Computer Vision and Pattern Recognition (CVPR), pages 10957-10966, 2019. 3 +[54] Hongyi Xu, Eduard Gabriel Bazavan, Andrei Zanfir, William T. Freeman, Rahul Sukthankar, and Cristian Sminchisescu. GHUM & GHUML: Generative 3D human shape and articulated pose models. In Computer Vision and Pattern Recognition (CVPR), pages 6183-6192, 2020. 2 +[55] Andrei Zanfir, Eduard Gabriel Bazavan, Mihai Zanfir, William T. Freeman, Rahul Sukthankar, and Cristian Sminchisescu. Neural descent for visual 3D human pose and shape. In Computer Vision and Pattern Recognition (CVPR), pages 14484-14493, 2021. 3 +[56] Hongwen Zhang, Yating Tian, Yuxiang Zhang, Mengcheng Li, Liang An, Zhenan Sun, and Yebin Liu. PyMAF-X: Towards well-aligned full-body model regression from monocular images. arXiv preprint arXiv:2207.06400, 2022. 6 +[57] Hongwen Zhang, Yating Tian, Xinchi Zhou, Wanli Ouyang, Yebin Liu, Limin Wang, and Zhenan Sun. PyMAF: 3D human pose and shape regression with pyramidal mesh alignment feedback loop. In International Conference on Computer Vision (ICCV), pages 11426-11436, 2021. 2 +[58] Christian Zimmermann, Duygu Ceylan, Jimei Yang, Bryan Russell, Max Argus, and Thomas Brox. FreiHAND: A dataset for markerless capture of hand pose and shape from single RGB images. 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Given a monocular, in-the-wild video of a sign-language sign, SGNify automatically reconstructs a 3D body with accurate hand pose, facial motion, and body pose. Note that motion blur obscures the finger articulations in several video frames; this is a common problem. Our novel linguistic priors enable accurate 3D reconstruction despite such image degradation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 143, + 410, + 192, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 410, + 192, + 422 + ], + "spans": [ + { + "bbox": [ + 143, + 410, + 192, + 422 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "type": "text", + "content": "Sign language (SL) is the primary method of communication for the 70 million Deaf people around the world. Video dictionaries of isolated signs are a core SL learning tool. Replacing these with 3D avatars can aid learning and enable AR/VR applications, improving access to technology and online media. However, little work has attempted to estimate expressive 3D avatars from SL video; occlusion, noise, and motion blur make this task difficult. We address this by introducing novel linguistic priors that are universally applicable to SL and provide constraints on 3D hand pose that help resolve ambiguities within isolated signs. Our method, SGNify, captures fine-grained hand pose, facial expression, and body movement fully automatically from in-the-wild monocular SL videos. We evaluate SGNify quantitatively by using a commercial motion-capture system to compute 3D avatars synchronized with monocular video. SGNify outperforms state-of-the-art 3D body-pose-and shape-estimation methods on SL videos. A perceptual study shows that SGNify's 3D reconstructions are significantly more comprehensible and natural than those of previous methods and are on par with the source videos. Code and data are available at sgnify.is.tue.mpg.de." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 307, + 410, + 386, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 410, + 386, + 422 + ], + "spans": [ + { + "bbox": [ + 307, + 410, + 386, + 422 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 434, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 685 + ], + "type": "text", + "content": "It is estimated that over 466 million people have disabling hearing loss [13] and more than 70 million people use sign language (SL) as their primary means of communication [52]. Increasing use of digital communication motivates research on capturing, understanding, modeling, and synthesizing expressive 3D SL avatars. Existing datasets and dictionaries used in SL recognition (SLR), translation (SLT), and production (SLP) are primarily limited to 2D video because the technology required to capture 3D movement is prohibitively expensive, requires expertise to operate, and may limit the movements of the signer. Dictionaries of isolated signs are a core SL learning tool, and many SLs have online 2D video dictionaries. The Deaf community is actively seeking 3D dictionaries of isolated signs to aid learning [40]. The current approach to creating such 3D signing dictionaries is fully manual, requiring an artist or a HamNoSys [21] expert, and the resulting avatars often move unnaturally [3]. We aim to automatically reconstruct expressive 3D signing avatars from monocular SL video, which we term Sign Language Capture (SLC). We focus on SLC of isolated signs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "3D reconstruction of human pose and shape has received significant attention, but accurate 3D hand-pose estimation" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12791" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "remains challenging from in-the-wild video. Challenges include the high number of degrees of freedom present in hands [5], frequent occurrence of self-contact and self-occlusions [37, 46], low resolution, and motion blur caused by fast motions [50] that cause hand pose to be unrecognizable in many frames (see Fig. 1). To address these issues, we exploit the linguistic nature of SL itself to develop novel priors that help disambiguate hand poses in SL videos, leading to accurate 3D reconstructions. This is a novel use of linguistic \"side information\" to improve 3D reconstruction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 553 + ], + "type": "text", + "content": "Based on hand movements and poses, Battison [4] defines five linguistic classes that contain all SL signs. We build on that work to define eight classes and formalize these as mathematical priors on 3D hand shape. We combine Battison's first two classes and place all one-handed signs in class 0, while two-handed signs are arranged in classes 1, 2, or 3, depending on how the non-dominant hand participates in the articulation of the sign. We then divide each of these four classes into two subclasses depending on whether the pose of the active hand(s) changes during the articulation of the sign. We introduce two class-dependent SL linguistic constraints that capture 1) symmetry and 2) hand-pose invariance. Under Battison's SL symmetry condition [4], when both hands actively move, the articulation of the fingers must be identical; the same is true for one class of two-handed signs in which only the dominant hand moves. We formalize this concept as a regularization term that encourages the pose of the two hands to be similar for such signs. Coupling the hand poses in this way effectively increases the image evidence for a pose, which improves estimates for challenging videos. Our invariance constraint uses the observation that hand pose is either static or transitions smoothly from one pose to another during the articulation of the sign; other significant changes to hand pose are not common in SL. Specifically, we extract a characteristic \"reference pose sequence\" (RPS) to describe each local hand pose during the sign articulation, and we penalize differences between the RPS and the estimated hand pose in each frame. These two priors of symmetry and hand-pose invariance are universally applicable to all sign languages." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 628 + ], + "type": "text", + "content": "The hands alone, however, are not sufficient to accurately reproduce SL. Information is conveyed holistically in SL through hand gestures, facial expressions, and upper-body movements in 3D space. To combine these, we use a 3D whole-body model, SMPL-X [41], that jointly models this information (see Fig. 1)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Our novel hand-pose constraints are formulated to be incorporated into the loss function for training a neural network regressor or into the objective function of optimization-based methods. In general, optimization-based methods are more computationally intensive but produce more accurate results when limited training data is available, so we take this approach here and build on the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "SMPLify-X method [41]. To appropriately incorporate our terms into the objective function, we need to know the class of the sign. We train a simple model that extracts features from the raw video and determines the class to which the depicted sign belongs. While SMPLify-X is a good foundation for the hands and body, we find that it does not capture expressive facial motions well. Consequently, we use a more expressive face regressor, SPECTRE [19], to capture the face parameters. We call our method SGNify." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 180, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 275 + ], + "type": "text", + "content": "To quantitatively evaluate SGNify, we capture a native German (DGS) signer with a frontal RGB camera synchronized with a 54-camera Vicon motion capture system and recover ground-truth meshes from the Vicon markers [34]. We run SGNify on the RGB video and compute 3D vertex-to-vertex (V2V) error between our resulting avatars and the ground-truth meshes. We find that SGNify reconstructs SMPL-X meshes more accurately than the competition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 276, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 418 + ], + "type": "text", + "content": "We conduct a perceptual evaluation in which we present proficient signers with a video of either an estimated SMPL-X avatar or the real-person source video and task them with identifying the sign being performed. Participants also rate their ease in recognizing the sign and the naturalness of the articulation. Our results show that SGNify reconstructs 3D signs that are as recognizable as the original videos and consistently more recognizable, easier to understand, and more natural than the existing state of the art. We also evaluate SGNify in a multi-view setting and on continuous signing videos. Despite not being designed for the latter, SGNify captures the meaning in continuous SL." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 419, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 563 + ], + "type": "text", + "content": "SGNify represents a step towards the automatic reconstruction of natural 3D avatars from sign-language videos. Our key contribution is the introduction of novel linguistic priors that are universal and helpful to constrain the problem of hand-pose estimation from SL video. SGNify is designed to work on video from different SL dictionaries across languages, backgrounds, people, trimming, image resolution, and framing, as visible in Sup. Mat. and in the video on our project page. This capability is critical to capture 3D signing at scale, which will enable progress on learning SL avatars. Our code and motion-capture dataset are available for research purposes at sgnify.is.tue.mpg.de." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 573, + 392, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 392, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 392, + 586 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Expressive 3D Humans From RGB Images: Until recently, human-posed estimation has focused on the estimation of 2D [12] or 3D [51] joints of the hands and body, as well as those of facial features [6] from single images. In addition to methods that estimate a sparse set of landmarks, there are multiple methods that estimate the parameters of morphable models for the hand [22, 32, 36, 58], face [11, 16, 18, 20], and body [8, 25, 27–29, 33, 39, 57]. The advent of expressive 3D body models like SMPL-X [41], Adam [26], and GHUM [54] has enabled research on esti" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12792" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 480 + ], + "type": "text", + "content": "mating the full 3D body surface [9, 17, 41, 44, 49, 53, 55]. Such body models are ideal for representing the expressiveness of SL but have rarely been applied to this domain [30]. Human Pose for Sign Language: To enable detailed 3D pose estimation from images, How2Sign [14] provides 3D skeleton reconstructions for three hours of data captured in a Panoptic Studio [24]. However, the skeletal representation lacks the richness of a full 3D body model and omits surface details that are important for communication [38]. Kratimenos et al. [30] use SMPLify-X to estimate 3D pose and shape on the GSLL sign-language dataset [48]. They compare SL recognition accuracy using features from raw RGB images, OpenPose [7] 2D skeletons, and SMPL-X bodies and observe the best automated recognition results with SMPL-X, illustrating the benefit of using a 3D model. They also highlight the importance of capturing the face and body; in an ablation study, they show that neglecting the face and body harms recognition accuracy [30]. However, their SMPL-X reconstructions use existing off-the-shelf methods and lack visual realism. SMPLify-X [41] and other recent 3D pose-reconstruction methods [17, 44], as well as keypoint detectors, struggle when applied to SL video due to challenging self-occlusion, hand-hand and hand-body interactions [38], motion blur [50], and cropping inherent to SL. SignPose [31] is a 3D-pose-lifting method for SL; it uses manually created synthetic SL animations to infer a textured avatar from single RGB images. SignPose requires all OpenPose keypoints above the pelvis to be detected, which is unrealistic in noisy SL videos. We address these challenges by incorporating sign-language knowledge in the form of linguistic constraints. Since the early 2000s, the integration of linguistic information has been known to be beneficial to both SLR [10] and SLP [35], but this strategy has not previously been applied to SLC." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 509, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 509, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 509, + 287, + 582 + ], + "type": "text", + "content": "We introduce SGNify, an offline method for reconstructing 3D body shape and pose of SL from monocular RGB video. SGNify centers around a key insight: SL signs follow universal linguistic rules that can be formulated as class-specific priors and used to improve hand-pose estimation. Our full pipeline is shown in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 588, + 275, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 275, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 275, + 601 + ], + "type": "text", + "content": "3.1. SMPLify-SL: Baseline for Sign-Language Video" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": "Our baseline method builds on SMPLify-X [41], which estimates SMPL-X [41] parameters from RGB images. SMPL-X is a 3D body model, representing whole-body pose and shape, including finger articulations and facial expressions. SMPL-X is a function, " + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "inline_equation", + "content": "M(\\theta, \\beta, \\psi)" + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": ", parameterized by body pose " + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": " (including hand pose " + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": "), body shape " + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": ", and facial expressions " + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 47, + 605, + 286, + 689 + ], + "type": "text", + "content": ", that outputs a 3D body mesh." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": "To create a strong baseline, we extend SMPLify-X to video by adapting it in the following ways: (1) We cope" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "with the upper-body framing typical of SL videos by changing the heuristic used for camera initialization and the estimation of the out-of-view lower-body joints. (2) Since human motion is locally smooth in time, we initialize " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\theta_t \\in \\mathbb{R}^{|\\theta|}" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\theta_{t-1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " and include a zero-velocity loss on the hands and body to encourage smooth reconstructions. (3) We estimate shape parameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "(\\beta)" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " over multiple frames by taking the median of the parameter estimates and not-optimizing them during the per-frame reconstruction. (4) To better capture the frequent hand-hand and hand-body interactions (mainly with the face and the chest), we employ the more robust self-contact loss of Müller et al. [39] instead of the original SMPLify-X interpenetration term. (5) For each frame, we pre-compute the facial expressions " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "(\\psi)" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " and jaw poses with SPECTRE [19]. These parameters are substituted into SMPL-X at the end of the optimization. SPECTRE can be swapped for any method whose expression parameters are consistent with those of SMPL-X, e.g., EMOCA [11]. We denote the baseline SMPLify-SL." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 308, + 433, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 433, + 320 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 433, + 320 + ], + "type": "text", + "content": "3.2. Linguistic Constraints" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 434 + ], + "type": "text", + "content": "State-of-the-art optimization- and regression-based human pose estimation methods struggle on SL video, particularly with the estimation of hand pose. We address this challenge by formulating linguistic constraints as additional losses on hand pose and integrating them into the SMPLify-SL objective function. First, we adapt the five sign-classification and morpheme-structure conditions introduced for American Sign Language (ASL) by Battison [4] to divide signs into four primary classes:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "type": "text", + "content": "Class 0: one-handed signs in which only the dominant hand articulates the sign." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 460, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 508 + ], + "type": "text", + "content": "Class 1: two-handed signs in which both hands are active. They share the same poses and perform the same movement in a synchronous or alternating pattern. This class includes all signs that follow Battison's symmetry condition [4]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 508, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 508, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 305, + 508, + 545, + 556 + ], + "type": "text", + "content": "Class 2: two-handed signs in which the dominant hand is active, the non-dominant hand is passive (its position and pose do not change during the articulation of the sign), and the two hands have the same initial pose." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 556, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 556, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 556, + 545, + 604 + ], + "type": "text", + "content": "Class 3: two-handed signs in which the dominant hand is active, the non-dominant hand is passive, and the two hands have different hand poses. All signs in this class follow Battison's dominance condition [4]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": "We further divide each class into two subclasses: subclass " + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": " contains signs in which the hand pose of the active hand(s) does not change throughout the articulation of the sign (static), and subclass " + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": " contains all signs in which the hand pose changes (transitioning)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Note that the division into these classes is not limited to ASL; Eccarius et al. [15] show that the phonological and prosodic properties of ASL can be successfully transferred to other sign-language lexicons." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12793" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 68, + 525, + 233 + ], + "blocks": [ + { + "bbox": [ + 70, + 68, + 525, + 233 + ], + "lines": [ + { + "bbox": [ + 70, + 68, + 525, + 233 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 525, + 233 + ], + "type": "image", + "image_path": "2b9b269b73bd003ac69d8400855935080979a542e74423eff972365f0d280248.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "text", + "content": "Figure 2. Given a video of a sign-language (SL) sign as input, our method preprocesses the data to first extract 2D keypoints. The hand keypoints are used to select candidate frames for estimating the reference hand poses " + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "inline_equation", + "content": "(\\theta_{ref,i}^{h},\\theta_{ref,f}^{h})" + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "text", + "content": " and, for static hand poses, also " + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\theta_{ref}^{h}" + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "text", + "content": ". The initial and final reference hand poses " + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "inline_equation", + "content": "(\\theta_{ref,i}^{h}" + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\theta_{ref,f}^{h})" + }, + { + "bbox": [ + 46, + 240, + 547, + 308 + ], + "type": "text", + "content": ", together with wrist-keypoint features detected across the sequence, are then fed into our sign-group classifier, which automatically classifies signs in monocular SL video into six groups based on linguistic rules universally applicable to SL [4]. Using the predicted group labels and the relevant reference hand poses, SGNify applies the appropriate linguistic constraints to improve SL 3D hand-pose estimation, especially when the video frame is ambiguous." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 321, + 281, + 467 + ], + "blocks": [ + { + "bbox": [ + 55, + 321, + 281, + 467 + ], + "lines": [ + { + "bbox": [ + 55, + 321, + 281, + 467 + ], + "spans": [ + { + "bbox": [ + 55, + 321, + 281, + 467 + ], + "type": "table", + "html": "
ClassHand-Pose SymmetryHand-Pose Invariance
DominantNon-dominant
0aXstaticX
0bXtransitioningX
1a✓staticstatic
1b✓transitioningtransitioning
2a✓staticstatic
2bXtransitioningstatic
3aXstaticstatic
3bXtransitioningstatic
", + "image_path": "edea10561f01ad102b4b5fde5ab40e753a2ed7f233978f5ff11d7222990c85c9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 475, + 278, + 486 + ], + "lines": [ + { + "bbox": [ + 55, + 475, + 278, + 486 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 278, + 486 + ], + "type": "text", + "content": "Table 1. Linguistic constraints defining the eight sign classes." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 499, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 547 + ], + "type": "text", + "content": "We then convert these linguistic classes into two 3D pose constraints: hand-pose symmetry and hand-pose invariance. Signs in the same class share the same constraints (see Tab. 1 and Tab. S.1 in Sup. Mat.)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 548, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 583 + ], + "type": "text", + "content": "Below we describe only the new terms added to the SMPLify-X objective. Please see Sup. Mat. for the full SGNify objective." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 597, + 174, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 174, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 174, + 609 + ], + "type": "text", + "content": "3.2.1 Hand-Pose Symmetry" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 640 + ], + "type": "text", + "content": "We encourage the left and right hand poses to match for the relevant classes (classes 1a, 1b, and 2a in Tab. 1):" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 117, + 645, + 287, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 645, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 117, + 645, + 287, + 660 + ], + "type": "interline_equation", + "content": "L _ {s} = \\lambda_ {s} \\| \\theta_ {t} ^ {r} - r \\left(\\theta_ {t} ^ {l}\\right) \\| _ {2} ^ {2}, \\tag {1}", + "image_path": "9ef6c28259e3cc2f52c0393af7c958547232eed8b87c71aef32c79dc7bd6ba26.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\theta_t^r" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " is the finger articulation of the right hand, and " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "r(\\theta_t^l)" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " is a reflection function to represent the articulation of the fingers of the left hand as if it were a right hand. This loss penalizes differences in finger poses between the hands." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 328, + 434, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 328, + 434, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 328, + 434, + 340 + ], + "type": "text", + "content": "3.2.2 Hand-Pose Invariance" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "text", + "content": "Each sign has a characteristic reference hand pose sequence (RPS). The RPS defines the hand pose that we expect at each time " + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "text", + "content": " during the articulation of the sign. The hand-posed-invariance constraint penalizes differences between the reference hand pose " + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\theta_{\\text{ref},t}^{h} \\in \\mathbf{RPS}^{h}" + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "text", + "content": " and the estimated hand pose " + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\theta_{t}^{h}" + }, + { + "bbox": [ + 304, + 347, + 547, + 422 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 378, + 430, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 430, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 378, + 430, + 545, + 445 + ], + "type": "interline_equation", + "content": "L _ {i} ^ {h} = \\lambda_ {i} \\| \\theta_ {\\text {r e f}, t} ^ {h} - \\theta_ {t} ^ {h} \\| _ {2} ^ {2}, \\tag {2}", + "image_path": "f3c90aaaf61a9586e60b98f1dd1e45cdc1b882193a29dce0fca04ba49f3b2052.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 454, + 511, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 454, + 511, + 466 + ], + "spans": [ + { + "bbox": [ + 305, + 454, + 511, + 466 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 454, + 511, + 466 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 454, + 511, + 466 + ], + "type": "text", + "content": " represents either the left or the right hand." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": "Throughout each sign, the hand pose either stays static or transitions between two poses. When static, only one hand pose, " + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{ref}^{h}" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": ", is representative of the RPS. Signs where the hand pose is transitioning are characterized by two reference hand poses, " + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{ref,i}^{h}" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{ref,f}^{h}" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": ", corresponding respectively to the initial and final poses. We interpolate " + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{ref,i}^{h}" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\theta_{ref,f}^{h}" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": " with spherical linear interpolation [45] to obtain intermediate poses. We presently do not consider signs with repeated hand-posed transitions, e.g., STORY in ASL, which occur in a small percentage of signs (" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\sim 3\\%" + }, + { + "bbox": [ + 304, + 466, + 545, + 589 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 597, + 402, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 402, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 402, + 609 + ], + "type": "text", + "content": "3.3. Automatization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 616, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 663 + ], + "type": "text", + "content": "To work fully automatically, SGNify must 1) estimate the poses needed to enforce the hand-pose-invariance constraint and 2) classify which sign group is present in a video sequence (see Fig. 2)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "text", + "content": "To estimate the reference hand poses " + }, + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\theta_{ref}^{h},\\theta_{ref,i}^{h}" + }, + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{ref,f}^{h})" + }, + { + "bbox": [ + 304, + 663, + 547, + 714 + ], + "type": "text", + "content": " , our method selects candidate frames in the core part of the sign using hand-keypoint detection confidences, and it uses SMPLify-X (adapted to SL cropping) to reconstruct" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12794" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": "a preliminary 3D hand pose for each candidate frame. With static hand poses, " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\theta_{ref}^{h}" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " is obtained by taking the average hand poses of these candidates. With transitioning hand poses, the core part of a sign is divided into two intervals, and " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\theta_{ref,i}^{h}" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\theta_{ref,f}^{h}" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " correspond to the average hand poses of the candidate frames in the first and second intervals, respectively (see Sup. Mat. for more details)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "content": "The constraints applied to each sign depend on its sign group; we have six sign groups because classes 1a & 2a share the same constraints, as do 2b & 3b (Tab. 1). There is insufficient paired data to train a CNN classifier, so we use an intuitive and interpretable decision tree trained on extracted 2D and 3D pose features. Our features are invariant to the handedness of the signer and include: 1) the minimum of the maximum height differences of each wrist across the sequence: " + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "inline_equation", + "content": "\\min (\\{w_r\\}_{\\max} - \\{w_r\\}_{\\min},\\{w_l\\}_{\\max} - \\{w_l\\}_{\\min})" + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "inline_equation", + "content": "w_{l}" + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "inline_equation", + "content": "w_{r}" + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "content": " are the heights of the left and right wrists, respectively. 2) the cosine distance between the initial poses of each hand: " + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "inline_equation", + "content": "\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,i}^{l})" + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "text", + "content": " , 3) the maximum of the two cosine distances between each initial and final hand pose: " + }, + { + "bbox": [ + 46, + 158, + 288, + 327 + ], + "type": "inline_equation", + "content": "\\max (\\mathrm{CosDist}(\\theta_{ref,i}^{r},\\theta_{ref,f}^{r}),\\mathrm{CosDist}(\\theta_{ref,i}^{l},\\theta_{ref,f}^{l}))" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 327, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 410 + ], + "type": "text", + "content": "We train our sign-group classifier on the over 3,000 videos from the Corpus-based Dictionary of Polish Sign Language (CDPSL) [1]; these are annotated with HamNoSys [21]. We construct a grammar to convert HamNoSys annotations into our group labels (see Sup. Mat.) Row 1 of Figure 3 shows a sample frame from CDPSL. This dataset is not used in our quantitative analysis or perceptual study." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 420, + 157, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 157, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 157, + 432 + ], + "type": "text", + "content": "3.4. SGNify Extensions" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "content": "First, we follow Huang et al. [23] to extend SGNify to work on multi-view videos. Second, we propose a baseline method for continuous SLC (CSLC). CSLC introduces additional challenges, such as the segmentation of sentences into signs; this is an active field of research. When a sentence is given as input, we use Renz et al. [43] to segment the input video and then process each segment with SGNify. The first frame of each segment is initialized from the last frame of the previous one. These extensions are not our main contribution and are described in Sup. Mat." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 572, + 100, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 100, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 100, + 583 + ], + "type": "text", + "content": "4. Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 593, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 676 + ], + "type": "text", + "content": "To quantitatively evaluate SGNify as a viable method for SLC, we collected motion-capture data with ground-truth SMPL-X bodies articulating signs. Our dataset represents the first publicly available expressive full-4D capture of isolated SL signs. The experimental procedure was reviewed by the ethics council of the University of Tübingen without objections or remarks (709/2021B02)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "In consultation with a Deaf DGS teacher and a DGS interpreter, we defined a German SL corpus consisting of 57 isolated signs. The selected signs cover a wide range of" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 72, + 425, + 137 + ], + "blocks": [ + { + "bbox": [ + 308, + 72, + 425, + 137 + ], + "lines": [ + { + "bbox": [ + 308, + 72, + 425, + 137 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 425, + 137 + ], + "type": "image", + "image_path": "8180a60f27e89700190d7f51d0def58152704b4c25915dd688001f597d5199ab.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 137, + 425, + 206 + ], + "blocks": [ + { + "bbox": [ + 308, + 137, + 425, + 206 + ], + "lines": [ + { + "bbox": [ + 308, + 137, + 425, + 206 + ], + "spans": [ + { + "bbox": [ + 308, + 137, + 425, + 206 + ], + "type": "image", + "image_path": "1018b7a0ce74a933d22405df86e6e28cf93ea5809723e32c5ab005dca291dd17.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 206, + 425, + 280 + ], + "blocks": [ + { + "bbox": [ + 308, + 206, + 425, + 280 + ], + "lines": [ + { + "bbox": [ + 308, + 206, + 425, + 280 + ], + "spans": [ + { + "bbox": [ + 308, + 206, + 425, + 280 + ], + "type": "image", + "image_path": "17f36ffde17a14fdd80203e2a15f187411df4217850c2d03755f229f209e3703.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 280, + 425, + 346 + ], + "blocks": [ + { + "bbox": [ + 308, + 280, + 425, + 346 + ], + "lines": [ + { + "bbox": [ + 308, + 280, + 425, + 346 + ], + "spans": [ + { + "bbox": [ + 308, + 280, + 425, + 346 + ], + "type": "image", + "image_path": "8982790361a65b1677898f628b735a5408ee237c513f279012fbfda33bd867fc.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 355, + 545, + 443 + ], + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 443 + ], + "type": "text", + "content": "Figure 3. Samples frames reconstructed by SGNify. The input videos are from diverse multilingual datasets. Row 1: Polish SL sign GDANSK (GDANSK, class 1a) from the dataset [1] used for training our sign-group classifier. Row 2: DGS sign BLUME (FLOWER, class 3b) from our captured dataset used in the quantitative evaluation. Row 3: ASL sign DOLL (class 0a) from the dataset [47] used in the perceptual study. Row 4: South African SL sign ARCHERY (class 2a) from the in-the-wild dataset [42]." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 426, + 72, + 545, + 137 + ], + "blocks": [ + { + "bbox": [ + 426, + 72, + 545, + 137 + ], + "lines": [ + { + "bbox": [ + 426, + 72, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 426, + 72, + 545, + 137 + ], + "type": "image", + "image_path": "1c0aff61dd4232689cd82d30a03298552a32374085a58e805ffda04294139c04.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 426, + 137, + 545, + 206 + ], + "blocks": [ + { + "bbox": [ + 426, + 137, + 545, + 206 + ], + "lines": [ + { + "bbox": [ + 426, + 137, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 426, + 137, + 545, + 206 + ], + "type": "image", + "image_path": "4d83b534e869607ada7e907922bac7bd5a7a7e82f3473a6a7b61e4a2e8fe221b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 426, + 206, + 545, + 280 + ], + "blocks": [ + { + "bbox": [ + 426, + 206, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 426, + 206, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 426, + 206, + 545, + 280 + ], + "type": "image", + "image_path": "2c582c2e1b48a0820e364b43ef70be0d1c7e1ad94db02ad98de7d68876bb6c05.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 426, + 280, + 545, + 346 + ], + "blocks": [ + { + "bbox": [ + 426, + 280, + 545, + 346 + ], + "lines": [ + { + "bbox": [ + 426, + 280, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 426, + 280, + 545, + 346 + ], + "type": "image", + "image_path": "8df943c8d11584a8ced6b3c7ef0d4d46d4302bdd441bfe0bf63d536efa777117.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 335, + 458, + 518, + 492 + ], + "blocks": [ + { + "bbox": [ + 335, + 458, + 518, + 492 + ], + "lines": [ + { + "bbox": [ + 335, + 458, + 518, + 492 + ], + "spans": [ + { + "bbox": [ + 335, + 458, + 518, + 492 + ], + "type": "table", + "html": "
Class0a0b1a1b2a2b3a3b
# Signs123143112102
", + "image_path": "9e532b24dd4baf01d05a2252ff005b1b7bc1c08b87c8a24efe2f8cd475011d34.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 335, + 501, + 515, + 512 + ], + "lines": [ + { + "bbox": [ + 335, + 501, + 515, + 512 + ], + "spans": [ + { + "bbox": [ + 335, + 501, + 515, + 512 + ], + "type": "text", + "content": "Table 2. Number of signs captured for each class." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 532, + 545, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 580 + ], + "type": "text", + "content": "challenges for SLC, such as self-contact and self-occlusion. Table 2 summarizes the number of signs collected for each of the eight classes. Signs of subclass " + }, + { + "bbox": [ + 304, + 532, + 545, + 580 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 532, + 545, + 580 + ], + "type": "text", + "content": " are less common, and this is reflected in our corpus." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "We captured a native right-handed DGS signer with a Vicon mocap system at 120 fps, synchronized with a frontal " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "4112 \\times 3008" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " RGB camera at 60 fps, framing an upper-body view as typically found in SL video. The hands start and end at rest at the signer's sides, and each sign lasts between 1.7 and 3.5 seconds after trimming. In total, our dataset comprises 16,608 mocap frames and 8,304 RGB frames. To obtain ground-truth SMPL-X meshes, we scanned the participant in a 4D body scanner in several poses. The SMPL-X mesh was registered to these scans and averaged to obtain a personalized body-shape mesh. MoSh++ was then used" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12795" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 279, + 155 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 279, + 155 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 279, + 155 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 279, + 155 + ], + "type": "table", + "html": "
MethodUpper BodyLeft HandRight Hand
FrankMocap [44]78.0720.4719.62
PIXIE [17]60.1125.0222.42
PyMAF-X [56]68.6121.4619.19
SMPLify-SL56.0722.2318.83
SGNify55.6319.2217.50
", + "image_path": "9baf3842e09d21239602ede9be77bbee50712c52efb2a0d59bbfd7c37adaec94.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 193, + 279, + 258 + ], + "blocks": [ + { + "bbox": [ + 47, + 158, + 286, + 180 + ], + "lines": [ + { + "bbox": [ + 47, + 158, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 286, + 180 + ], + "type": "text", + "content": "Table 3. Evaluation on our ground-truth mocap dataset: mean TR-V2V error (mm) for five methods and three body regions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 193, + 279, + 258 + ], + "lines": [ + { + "bbox": [ + 50, + 193, + 279, + 258 + ], + "spans": [ + { + "bbox": [ + 50, + 193, + 279, + 258 + ], + "type": "table", + "html": "
MethodSymInvLeft HandRight HandBoth Hands
SMPLify-SLXX20.3018.7819.54
SGNify✓X18.4418.3918.41
SGNifyX✓19.7617.1618.46
SGNify✓✓17.7217.2917.50
", + "image_path": "341c0a156eca8d5410b64081d9fab6e7dfe8b6e20b18bcf6b33f582ac8357ac8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 296, + 282, + 344 + ], + "blocks": [ + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "lines": [ + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "type": "text", + "content": "Table 4. Evaluating how the linguistic constraints of symmetry and invariance affect mean TR-V2V error (mm) in symmetric signs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 296, + 282, + 344 + ], + "lines": [ + { + "bbox": [ + 50, + 296, + 282, + 344 + ], + "spans": [ + { + "bbox": [ + 50, + 296, + 282, + 344 + ], + "type": "table", + "html": "
MethodInvLeft HandRight HandBoth Hands
SMPLify-SL✗26.0918.8920.50
SGNify✓22.2217.7018.60
", + "image_path": "bfc945a805b4f5cb859ac505affd349701499e63cac8d0e98d458e45e44e2fae.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 349, + 286, + 371 + ], + "lines": [ + { + "bbox": [ + 47, + 349, + 286, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 286, + 371 + ], + "type": "text", + "content": "Table 5. Evaluating how the linguistic constraint of hand-pose invariance affects mean TR-V2V error (mm) in asymmetric signs." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 388, + 286, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 286, + 472 + ], + "type": "text", + "content": "to fit this mesh to the mocap markers [34]. Marker-based mocap is useful for evaluating ground truth but is not practical for SLC at scale: it is expensive and requires expertise, the reflective markers attached to the signer can influence contact-heavy motions, and processing the resulting data is time consuming. If our monocular method can approach the performance of mocap, it will be widely applicable." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 503, + 181, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 181, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 181, + 514 + ], + "type": "text", + "content": "5.1.Quantitative Evaluation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 712 + ], + "type": "text", + "content": "We quantitatively evaluate SGNify, compare it with state-of-the-art methods, and quantify the improvement derived from each linguistic constraint. To emulate in-the-wild data, which might have very low resolution, lowramerate, and an occluded lower body, we pre-processed our high-quality video data to a resolution of " + }, + { + "bbox": [ + 46, + 521, + 286, + 712 + ], + "type": "inline_equation", + "content": "514 \\times 300" + }, + { + "bbox": [ + 46, + 521, + 286, + 712 + ], + "type": "text", + "content": " at 30 fps, and we cropped the input images above the pelvis (see Row 2 of Fig. 3). We used the synchronized meshes captured from the observed Vicon markers [34] as ground truth for evaluation. Since all tested methods estimate SMPL-X meshes with the same topology, we compute the mean pervertex error (TR-V2V) by considering the vertices above the pelvis. The prefix \"TR\" means that we translationally align the mesh reconstructed for each frame with the ground truth; i.e., we center the meshes before computing these errors. Since the starting and ending transitions are not part of" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "the sign itself, we manually annotate the expressive central portion of each sign from the raw videos and compute the quantitative results on only these central frames (in total, 2,872 RGB frames)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 121, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 288 + ], + "type": "text", + "content": "Table 3 shows the mean TR-V2V error across the 57 signs for four methods and three body regions. The columns labeled \"Upper Body\" report the error computed when considering the hands and the upper body (vertices above the pelvis). We include the head but not the face because our mocap system struggles to reconstruct face details using only 27 markers. We separately report the TR-V2V errors for the left and right hands because of the central role they play in SL. We provide a visualization of the vertices selected for each of these evaluations in Sup. Mat. This experiment compares SGNify with FrankMocap [44], PIXIE [17], PyMAF-X [56], and our baseline SMPLify-SL. SGNify achieves the lowest error for the upper body and both hands, beating the state-of-the-art methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 289, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 612 + ], + "type": "text", + "content": "Tables 4 and 5 show the improvements derived from each linguistic constraint. Table 4 reports the mean TR-V2V in symmetric signs (classes 1a, 1b, and 2a) when using no constraints, i.e., SMPLify-SL (Row 1), only one constraint (Rows 2 and 3), or both linguistic constraints (Row 4). When one linguistic constraint is used, the TR-V2V of both hands decreases. We observe that the symmetry constraint has the overall greater effect of the two. When the non-dominant hand is passive, it is often rotated at an angle difficult to capture from a frontal camera; this behavior might explain the greater effect of the symmetry constraint on the left hand. When both constraints are applied, we observe a more substantial decrease in the TR-V2V error of the left hand and a slight increase in the error of the right hand compared to when only the hand-pose invariance is applied to the right hand. We believe this happens because the symmetry constraint enforces symmetry between the two hands without knowing which hand reconstruction is more correct, and, for the same reason as above, detecting an accurate RPS for the non-dominant hand is often more challenging; overall, however, using both constraints greatly benefits the reconstruction. In Tab. 5, we separately evaluate performance on signs that do not present symmetry between the two hands (classes 0a, 0b, 2b, 3a, and 3b). As expected, the invariance prior included in SGNify improves the performance on all metrics. These quantitative results indicate that our linguistic constraints improve the reconstructions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "type": "text", + "content": "5.2. Perceptual Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "We conduct an online perceptual study to 1) compare SGNify with the best-performing state-of-the-art method for SL and 2) evaluate the improvement derived from the linguistic constraints (SGNify vs. SMPLify-SL). Even though FrankMocap has a lower hand error than PyMAF-X and PixIE, it has significant errors in the lower body when" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12796" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "content": "the full body is not seen, and higher errors in the upper body; these errors greatly affect the perceptual experience, making it unsuitable for the SL task, as already noticed in [31]. We thus use PyMAF-X since its hand-pose estimates are more accurate than pixIE (see Tab. 3)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": "Approval of all experimental procedures for this study was granted by the Ethics Council of the Max Planck Society under the Haptic Intelligence Department's framework agreement under protocol number F027A. No participants are employed by our institution, and all are compensated 20 USD for their time." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "text", + "content": "Our study involves 20 adult participants who all stated that they have an advanced level of proficiency (expert level) in ASL. We discarded responses from other potential participants who did not correctly recognize at least " + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "text", + "content": " of the signs presented via real-person video. 15 of the final 20 participants " + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "inline_equation", + "content": "(75\\%)" + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "text", + "content": " are Deaf, and one participant is left-handed. Participant ages are " + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "inline_equation", + "content": "46.75 \\pm 11.78" + }, + { + "bbox": [ + 46, + 206, + 286, + 289 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 292, + 286, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 286, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 286, + 482 + ], + "type": "text", + "content": "We used SGNify, SMPLify-SL, and PyMAF-X to reconstruct avatars from 50 videos taken from The American Sign Language Handshape Dictionary [47]; see Row 3 of Fig. 3 for an example. After responding to demographic questions, each participant evaluates the same six training videos to calibrate their responses to the quality of the presented reconstructions. We divide the remaining 44 signs into four batches (real-person RGB video, SGNify, SMPLify-SL, and PyMAF-X) that are balanced by sign class and sign frequency. We include real-person video to obtain an upper-bound on recognition performance and, as mentioned, to filter participants. We assign each participant to one of four surveys. Each survey contains all 44 test signs, and the four methods are rotated through the four sign batches across surveys. We further shuffle the questions in each survey for each user." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 484, + 286, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 614 + ], + "type": "text", + "content": "The participant enters the sign they believe the avatar or the real person is articulating in each video. They rate their ease in recognizing the presented sign using a visual analog scale (VAS) ranging from 0 to 100 with five standard labels ranging from \"very difficult\" to \"very easy.\" They also evaluate the naturalness of the articulation on a VAS-labeled scale from \"very unnatural\" to \"very natural.\" Participants are able to replay each video. We provide additional space for comments for each sign and at the end of the study. The self-reported participant carefulness is " + }, + { + "bbox": [ + 46, + 484, + 286, + 614 + ], + "type": "inline_equation", + "content": "84.45 \\pm 11.44" + }, + { + "bbox": [ + 46, + 484, + 286, + 614 + ], + "type": "text", + "content": " on a scale from 0 to 100." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "content": "The sign annotations submitted by participants are graded as either \"incorrect\" (no credit), \"partially correct\" (half credit), or \"completely correct\" (full credit). We calculate the rates at which each participant recognized the signs for each method. We visualize the resulting " + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "inline_equation", + "content": "20 \\times 4" + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "content": " matrix of recognition rates with box plots in the left plot of Fig. 4. Participants recognize signs in real-person videos with an average accuracy of " + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "inline_equation", + "content": "90.9\\%" + }, + { + "bbox": [ + 46, + 618, + 286, + 712 + ], + "type": "text", + "content": " and signs reconstructed" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "by SGNify with " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "86.2\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " accuracy. Signs reconstructed with SMPLify-SL and PyMAF-X are recognized less accurately, at " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "74.8\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "62.0\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", respectively. We evaluate the statistical significance of these recognition rates. Some distributions failed a Shapiro-Wilk normality test, so we used the non-parametric Friedman test which shows that the method used (real video, SGNify, SMPLify-SL, or PyMAF-X) has a statistically significant effect " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "(p < 0.001)" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " on recognition rate. Pairwise comparison with Wilcoxon signed-rank tests and a Bonferroni post-hoc correction reveal that the average sign recognition rate with real video and SGNify are both significantly higher than SMPLify-SL and PyMAF-X. Importantly, sign recognition rates with real video and SGNify are not significantly different from one another." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 241, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 241, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 241, + 545, + 348 + ], + "type": "text", + "content": "The central plot of Fig. 4 shows the participants' perceived easiness in recognizing the sign. These four distributions passed the normality test and were analyzed with a one-way repeated-measures ANOVA with a Bonferroni post-hoc correction for pairwise comparisons. As expected, real videos are perceived to be significantly easier to recognize than the three reconstruction methods. However, signs reconstructed with SGNify and SMPLify-SL are significantly easier to recognize than those by PyMAF-X." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 351, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 458 + ], + "type": "text", + "content": "The right plot of Fig. 4 shows the participants' perceived naturalness of the articulation of the signs. All four distributions passed the normality test, so they were analyzed in the same way as perceived easiness. All methods are statistically different one from another, with real video receiving the highest naturalness ratings, followed by SGNify, SMPLify-SL, and PyMAF-X. Nearly all participants reported in the comments that they want avatars with more expressive face motions and smoother hand and body motions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": "These results show that SGNify outperforms the state-of-the-art, PyMAF-X, in all qualitative metrics. Incorporating SL linguistic priors into our baseline SMPLify-SL yields statistically significant perceptual improvements, as judged by 20 expert signers. Most importantly, SGNify achieves a high sign-recognition rate that is not different from that of real-person video on the selected set of ASL signs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 545, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 712 + ], + "type": "text", + "content": "A few participants suggested having clothed (rather than \"nude\") avatars and introducing more human-like features. We thus conduct a second perceptual study to see whether these recommendations have a positive impact on the intelligibility of SGNify's reconstructions. Thirteen participants from the first study participated in this follow-up; the study design is the same. The tested methods are the real video and three different SGNify avatars: the solid purple avatar from the first study, the same avatar wearing a black long-sleeved t-shirt, and a fully textured human character adapted from Meshcapade [2] (see Sup. Mat.). This study comprises 24 signs (including the four for participant training) from the same ASL dataset [47] but different from those of the first study. Our results reveal that adding the" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12797" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 212, + 277 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 212, + 277 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 212, + 277 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 212, + 277 + ], + "type": "image", + "image_path": "6cd9a27685d9c0683b62630d990b89441ead75532f6cb62fcef41942b4b2f685.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "type": "text", + "content": "Figure 4. Box plots of the data from the perceptual study. The circle shows the mean, and the central line shows the median. The top and bottom box edges show the interquartile range (IQR), and the whiskers encompass the range up to 1.5 times the IQR. Outliers are marked with " + }, + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "type": "text", + "content": ". Statistically significant pairwise differences are indicated with a line and a " + }, + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 285, + 547, + 365 + ], + "type": "text", + "content": ". Left: Distribution of the rate at which participants recognized signs presented with each of the four methods. Real Video and SGNify achieve significantly higher recognition rates than both SMPLify-SL and PyMAF-X. Center: Distribution of the average easiness ratings participants assigned to recognizing signs presented by the four methods. All pairwise combinations except SGNify-SMPLify-SL are significantly different. Right: Distribution of the average articulation naturalness ratings participants assigned to the four methods. All pairwise combinations are significantly different." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 220, + 70, + 375, + 274 + ], + "blocks": [ + { + "bbox": [ + 220, + 70, + 375, + 274 + ], + "lines": [ + { + "bbox": [ + 220, + 70, + 375, + 274 + ], + "spans": [ + { + "bbox": [ + 220, + 70, + 375, + 274 + ], + "type": "image", + "image_path": "6b4c1dcb236fd10a733c6d33b854cc85b4f66dbd05644451c062db369301481e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 389, + 70, + 536, + 274 + ], + "blocks": [ + { + "bbox": [ + 389, + 70, + 536, + 274 + ], + "lines": [ + { + "bbox": [ + 389, + 70, + 536, + 274 + ], + "spans": [ + { + "bbox": [ + 389, + 70, + 536, + 274 + ], + "type": "image", + "image_path": "93566bfab244c6c47e6d718b7768b882168e09be02a1637a80a351f2e9c3ea85.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "content": "t-shirt and using a fully textured avatar do not benefit actual or perceived sign recognition or the perceived naturalness of the reconstruction. As in the previous study, recognition of SGNify's reconstructions were not statistically different from real video." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 454, + 117, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 117, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 117, + 466 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "Our results show that SGNify performs quantitatively better than the state of the art, in particular due to the inclusion of our novel linguistic constraints. However, we believe that a per-frame metric is not ideal for SL. To recognize a sign, the temporal evolution is crucial, and this is not captured by V2V. For example, the few slightly inaccurate frames of the SMPLify-SL reconstruction of DOLL (see video on our project page) confused many signers during the perceptual study. Small changes over time can disrupt perception, while overall V2V error remains small. In the end, what matters is whether the meaning is clear to a human. We think a perceptual study provides key insights that complement metric evaluation. The perceptual study indicated that SGNify significantly outperforms the state of the art and, most importantly, produces the first 3D avatars to achieve a sign-recognition accuracy that is not statistically different from the source videos. Our perceptual study also highlights the next challenge for SLC: the need for improvements in the face including facial expressions, tongue and eye movements, mouth morphemes, and eyebrows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 383, + 384, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 384, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 384, + 395 + ], + "type": "text", + "content": "7. Conclusions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "type": "text", + "content": "We present SGNify, which estimates 3D avatars of isolated SL signs from monocular RGB video. Quantitative and qualitative experiments show that SGNify outperforms the state of the art in estimating challenging SL hand poses by leveraging constraints derived from linguistics. SGNify represents a step towards the capture of realistic 3D avatars from SL videos in the wild. Future work should explore the use of our constraints in training regression methods, real-time processing, and continuous signing." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 517, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 686 + ], + "type": "text", + "content": "Acknowledgments We thank Galina Henz and Tsvetelina Alexiadis for trial coordination; Matvey Safroshkin, Markus Höschle, Senya Polikovsky, Tobias Bauch, Taylor McConnell (TM), and Bernard Javot for the capture setup; TM for data-cleaning coordination; Leyre Sánchez Vinuela, Andres Camilo Mendoza Patino, and Yasemin Fincan for data cleaning; Nima Ghorbani and Giorgio Becherini for MoSh++; Joachim Tesch for help with Blender; Benjamin Pellkofer and Joey Burns for IT support; Yao Feng, Anastasios Yiannakidis, and Radek Danček for discussions on facial methods; Haliza Mat Husin and Mayumi Mohan for help with statistics; and the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Maria-Paola Forte and Peter Kulits." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 689, + 545, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 702 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 702 + ], + "type": "text", + "content": "Disclosure: https://files.is.tue.mpg.de/black/CoI_CVPR_2023.txt" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12798" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 709 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 126 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 126 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 126 + ], + "type": "text", + "content": "[1] CDPSL: Corpus-based Dictionary of Polish Sign Language. https://www.slownikpjm.uw.edu.pl/.5" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 130, + 285, + 153 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 130, + 285, + 153 + ], + "spans": [ + { + "bbox": [ + 53, + 130, + 285, + 153 + ], + "type": "text", + "content": "[2] Meshcapade GmbH, Tübingen, Germany. https://meshcapade.com, 2022.7" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 157, + 287, + 216 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 157, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 54, + 157, + 287, + 216 + ], + "type": "text", + "content": "[3] Ahmed H. 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In International Conference on Computer Vision (ICCV), pages 813-822, 2019. 2" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12801" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_content_list.json b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a5dcd98fc2e7be4b04e81d7d1cb27e536805ad43 --- /dev/null +++ b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_content_list.json @@ -0,0 +1,1549 @@ +[ + { + "type": "text", + "text": "Recovering 3D Hand Mesh Sequence from a Single Blurry Image: A New Dataset and Temporal Unfolding", + "text_level": 1, + "bbox": [ + 153, + 130, + 818, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yeonguk Oh $^{1*}$ JoonKyu Park $^{1*}$ Jaeha Kim $^{1*}$ Gyeongsik Moon $^{3}$ Kyoung Mu Lee $^{1,2}$ $^{1}$ Dept. of ECE&ASRI, $^{2}$ IPAI, Seoul National University, Korea \n $^{3}$ Meta Reality Labs Research", + "bbox": [ + 140, + 200, + 851, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{namepllet, jkpark0825}@snu.ac.kr, jhkim97s2@gmail.com, mks0601$ and the folding $<(\\mathrm{c}) \\rightarrow (\\mathrm{b}) \\rightarrow (\\mathrm{a}) >$ make the same result blur image (d)." + ], + "image_footnote": [], + "bbox": [ + 274, + 316, + 370, + 391 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f9dbc4bbac6d3b33693703a42c80b52e2d104a7fc246e08c514de1d7077fc412.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 372, + 316, + 468, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Among the three sequential features, the hand feature at the middle of the motion $\\mathbf{F}_{\\mathrm{M}}$ can be specified as similar to the conventional deblurring approaches [25, 46]. However, we can not identify whether the hand at each end (i.e., $\\mathbf{F}_{\\mathrm{E1}}$ or $\\mathbf{F}_{\\mathrm{E2}}$ ) is come from the initial or final location of the motion due to the temporal ambiguity [12, 28, 33, 47]. For example, suppose that we obtain the blurry hand image shown in Figure 4d. Then we can not determine whether the blurry hand image comes from the motion of extending or folding. In that regard, Unfolder outputs hand features from both ends of the motion (i.e., $\\mathbf{F}_{\\mathrm{E1}}$ and $\\mathbf{F}_{\\mathrm{E2}}$ ) without considering temporal order. We note that exploiting the temporal information still benefits without explicitly considering the temporal order, and can further be stably optimized with the training loss introduced in Section 4.4.", + "bbox": [ + 75, + 474, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extracting temporal joint features. From produced three sequential hand features, we extract the corresponding joint features, which contain essential hand articulation information [21] that helps to recover 3D hand meshes. We first project the sequential hand features $\\mathbf{F}_{\\mathrm{E1}}$ , $\\mathbf{F}_{\\mathrm{E2}}$ , and $\\mathbf{F}_{\\mathrm{M}}$ into $dJ$ dimensional feature through $1 \\times 1$ convolution layer, and reshape them into 3D heatmaps with the dimension of $\\mathbb{R}^{J \\times h \\times w \\times d}$ , where $d = 32$ is a depth discretization size and $J = 21$ is a number of hand joints. Then, we perform a soft-argmax operation [41] on each heatmap to obtain the 3D joint coordinates of three temporal hands, $\\mathbf{J}_{\\mathrm{E1}}$ , $\\mathbf{J}_{\\mathrm{E2}}$ , and $\\mathbf{J}_{\\mathrm{M}}$ with dimension of $\\mathbb{R}^{J \\times 3}$ . Using 3D joint coordinates in each temporal hand, we perform grid sampling [10, 21]", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/71df2cf2c26d3eddebeb0eb9f27f2b5c53dd9aa2cb8285177bdaea560d588405.jpg", + "image_caption": [ + "Figure 5. Overall architecture of KTFormer. KTFormer refines temporal joint features $\\mathbf{F}_{\\mathrm{J_{E1}}}$ , $\\mathbf{F}_{\\mathrm{J_{E2}}}$ , and $\\mathbf{F}_{\\mathrm{J_M}}$ . First, kinematic and temporal positional embeddings are introduced. Then, the following self-attention mechanism refines joint features by leveraging attentive correlation between them, producing $\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}$ , $\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}$ , and $\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 324, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on the corresponding feature map. By doing so, we obtain temporal joint features $\\mathbf{F}_{\\mathrm{J_{E1}}}$ , $\\mathbf{F}_{\\mathrm{J_{E2}}}$ , and $\\mathbf{F}_{\\mathrm{J_M}}$ with a dimension of $\\mathbb{R}^{J\\times c}$ , which enable the following module to exploit temporal information effectively.", + "bbox": [ + 498, + 547, + 893, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. KTFormer", + "text_level": 1, + "bbox": [ + 500, + 619, + 620, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Kinematic-temporal positional embedding. The illustration of KTFormer is shown in Figure 5. KTFormer is the Transformer [42]-based module that refines the joint feature $\\mathbf{F}_{\\mathrm{J_{E1}}}$ , $\\mathbf{F}_{\\mathrm{J_{E2}}}$ , and $\\mathbf{F}_{\\mathrm{J_M}}$ by considering the correlation between not only joints at the same time step but also joints at different time steps. To utilize the temporal joint features as an input of Transformer, we first concatenate the three features along the joint dimension, producing $\\mathbf{F_J} \\in \\mathbb{R}^{3J \\times c}$ . Then, a learnable positional embedding, namely kinematic and temporal positional embeddings, is applied to $\\mathbf{F_J}$ . The kinematic positional embedding $\\in \\mathbb{R}^{J \\times c}$ is applied along the joints dimension, while the temporal positional embedding $\\in \\mathbb{R}^{3 \\times c}$ is applied along the temporal dimension. The kinematic and temporal positional embedding provide relative positions in kinematic and temporal space, respectively. Joint feature refinement with self-attention. KTFormer performs self-attention within $\\mathbf{F_J}$ by extracting query $\\mathbf{q}$ ,", + "bbox": [ + 496, + 642, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "557", + "bbox": [ + 485, + 944, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "key $\\mathbf{k}$ and value $\\mathbf{v}$ through three fully-connected layers. Following the formulation of the standard Transformer [42], refined joint features for sequential hands $\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}$ , $\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}$ , and $\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}$ are formulated as follows:", + "bbox": [ + 75, + 90, + 468, + 154 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {k} ^ {T}}{\\sqrt {d _ {\\mathbf {k}}}}\\right) \\mathbf {v}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 162, + 468, + 199 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} = \\mathbf {F} _ {\\mathrm {J}} + \\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 208, + 468, + 226 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 1}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 2}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {M}}} ^ {\\prime} = \\psi (\\mathbf {F} _ {\\mathrm {J}} + \\operatorname {M L P} (\\mathbf {R})), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 238, + 468, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_{\\mathbf{k}} = 512$ is the feature dimension of the key $\\mathbf{k}$ , and $\\mathbf{R}$ is the residual feature. MLP denotes multi-layer perceptron, and $\\psi$ denotes a dividing operation, which separates features in dimension $\\mathbb{R}^{3J\\times c}$ to three $\\mathbb{R}^{J\\times c}$ . Consequently, three joint features $\\mathbf{F}_{\\mathrm{JE_1}}^{\\prime},\\mathbf{F}_{\\mathrm{JE_2}}^{\\prime}$ , and $\\mathbf{F}_{\\mathrm{JM}}^{\\prime}$ are obtained by attentively utilizing kinematic and temporal information.", + "bbox": [ + 75, + 261, + 468, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Regressor", + "text_level": 1, + "bbox": [ + 76, + 361, + 191, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Regressor produces MANO [35] shape (i.e., $\\beta_{\\mathrm{E1}}$ , $\\beta_{\\mathrm{E2}}$ , and $\\beta_{\\mathrm{M}}$ ) and pose (i.e., $\\theta_{\\mathrm{E1}}$ , $\\theta_{\\mathrm{E2}}$ , and $\\theta_{\\mathrm{M}}$ ) parameters, which correspond to sequential hands. We describe the regression process of the middle hand (i.e., $\\beta_{\\mathrm{M}}$ and $\\theta_{\\mathrm{M}}$ ) as a representative procedure, and note that the process at different timesteps can be obtained in the same manner. First, the shape parameter $\\beta_{\\mathrm{M}}$ is obtained by forwarding the hand feature $\\mathbf{F}_{\\mathrm{M}}$ to a fully-connected layer after global average pooling [18]. Second, the pose parameter $\\theta_{\\mathrm{M}}$ is obtained by considering the kinematic correlation between hand joints. To this end, we first concatenate refined joint feature $\\mathbf{F}_{\\mathrm{J_M}}'$ with corresponding 3D coordinates $\\mathbf{J}_{\\mathrm{M}}$ . Then, we flatten the concatenated feature into one-dimensional vector $\\mathbf{f}_{\\mathrm{M}} \\in \\mathbb{R}^{J(c + 3)}$ . Instead of regressing poses of entire joints from $\\mathbf{f}_{\\mathrm{M}}$ at once, the Regressor gradually estimates pose for each joint along the hierarchy of hand kinematic tree, following [43]. In detail, for a specific joint, its ancestral pose parameters and $\\mathbf{f}_{\\mathrm{M}}$ are concatenated, and forwarded to a fully-connected layer to regress the pose parameters. By adopting the same process for both ends, three MANO parameters are obtained from the Regressor. Then, the MANO parameters are forwarded to the MANO layer to produce 3D hand meshes $\\mathbf{V}_{\\mathrm{E1}}$ , $\\mathbf{V}_{\\mathrm{E2}}$ , and $\\mathbf{V}_{\\mathrm{M}}$ , where each denotes to meshes at both ends and middle, respectively.", + "bbox": [ + 75, + 383, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Training loss", + "text_level": 1, + "bbox": [ + 76, + 756, + 212, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the training, a prediction on the middle of the motion can be simply supervised with GT of the middle frame. On the other hand, it is ambiguous to supervise both ends of motion as the temporal order is not uniquely determined, as shown in Figure 4. To resolve such temporal ambiguity during the loss calculation, we propose two items. First, we employ temporal order-invariant loss, which is invariant to GT temporal order [36]. To be specific, the temporal order", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in our loss function is determined in the direction that minimizes loss functions, not by the GT temporal order. Second, we propose to use a Unfolder-driven temporal ordering. It determines the temporal order based on the output of Unfolder, then uses the determined temporal order to supervise the outputs of Regressor rather than determining the temporal order of two modules separately. The effectiveness of the two items is demonstrated in the experimental section.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function $\\mathcal{L}$ is defined as follows:", + "bbox": [ + 517, + 210, + 843, + 226 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {U}} + \\mathcal {L} _ {\\mathrm {R}} \\\\ = \\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}}, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 227, + 890, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{U}}$ and $\\mathcal{L}_{\\mathrm{R}}$ are loss functions applied to outputs of the Unfolder and the Regressor, respectively. The subscripts M and E stand for prediction of the middle and both ends.", + "bbox": [ + 496, + 268, + 890, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To supervise outputs of Unfolder, we define $\\mathcal{L}_{\\mathrm{U,M}}$ and $\\mathcal{L}_{\\mathrm{U,E}}$ as follows:", + "bbox": [ + 500, + 315, + 890, + 344 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} = \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {M}}, \\mathbf {J} _ {\\text {m i d d l e}} ^ {*}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 352, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} = \\min (\\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}) + \\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*})), \\\\ \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}\\right)), \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 377, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{J}_{\\mathrm{middle}}^{*}, \\mathbf{J}_{\\mathrm{initial}}^{*}$ , and $\\mathbf{J}_{\\mathrm{final}}^{*}$ are GT 3D joint coordinates of the middle, initial and final frame, respectively. $\\mathcal{L}_{\\mathrm{joint}}$ is $L1$ distance between predicted and GT joint coordinates. The temporal order is determined to forward if the first term in min of Eq. 6 is selected as minimum and backward otherwise. Therefore, our loss function is invariant to the temporal order of GT.", + "bbox": [ + 496, + 434, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To supervise the outputs of the Regressor, we define the loss function $\\mathcal{L}_{\\mathrm{R,M}}$ and $\\mathcal{L}_{\\mathrm{R,E}}$ as follows:", + "bbox": [ + 496, + 540, + 890, + 570 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} = \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {M}}, \\Theta_ {\\text {m i d d l e}} ^ {*}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 578, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}} = \\mathbb {1} _ {\\mathbf {f}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right)\\right) \\\\ + \\mathbb {1} _ {\\mathbf {b}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right)\\right), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 602, + 890, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}_{\\mathbf{f}} = 1$ when the temporal order is determined to forward in Eq. 6 otherwise 0, and $\\mathbb{1}_{\\mathbf{b}} = 1 - \\mathbb{1}_{\\mathbf{f}}$ . In other words, the temporal order of Eq. 8 follows that of Eq. 6, which we call Unfolder-driven temporal ordering. $\\Theta_{\\bullet} = \\{\\theta_{\\bullet}, \\beta_{\\bullet}\\}$ is GT or predicted MANO parameters, where the superscript * denotes GT. $\\mathcal{L}_{\\mathrm{mesh}}$ is the summation of three $L1$ distances between GT and prediction of: 1) MANO parameters 2) 3D joint coordinates obtained by multiplying joint regression matrix to hand mesh 3) 2D joint coordinates projected from 3D joint coordinates.", + "bbox": [ + 496, + 659, + 890, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 821, + 632, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets and evaluation metrics", + "text_level": 1, + "bbox": [ + 500, + 847, + 779, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BlurHand. The BlurHand (BH) is our newly presented 3D hand pose dataset containing realistic blurry hand images as", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "558", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3ddeb2d0f024a9981b2e6919efafbaf7ca994a0f82d4d2c5c8aee2f1747a645b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsTrain setTest set
IH2.6MBH
I2L-MeshNet [22]IH2.6MBH22.2724.3029.1624.32
METRO [16]IH2.6MBH18.4420.1935.4320.54
Pose2Pose [21]IH2.6MBH16.8518.4025.3618.80
BlurHandNet (Ours)IH2.6MBH15.3316.1224.5716.80
", + "bbox": [ + 117, + 89, + 426, + 220 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/083823b5dc65b68c337cf79ff6bfc803477a9d86459916d1a85856b8cffb77b5.jpg", + "image_caption": [ + "Figure 6. Examples of deblurred images. Since the blurry hand undergoes challenging blur from complex articulation, even the state-of-the-art deblurring method [3] cannot fully restore and blur artifact remains, highlighted with red circles." + ], + "image_footnote": [], + "bbox": [ + 78, + 273, + 455, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "introduced in Section 3. We train and test the 3D hand mesh estimation networks on the train and test splits of the BH.", + "bbox": [ + 75, + 474, + 467, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "InterHand2.6M. InterHand2.6M [23] (IH2.6M) is a recently presented large-scale 3D hand dataset. It is captured under highly calibrated camera settings and provides accurate 3D annotations for hand images. We employ IH2.6M as a representative of sharp hand frames, as the hand images in IH2.6M do not contain blur. We use a subset of IH2.6M for training and testing purposes, where the subset is a set of the third sharp frame in Figure 2 for each image of BH.", + "bbox": [ + 75, + 505, + 467, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "YT-3D. YouTube-3D-hands (YT-3D) [13] is a 3D hand dataset with diverse and non-laboratory videos collected from youtube. We utilize the YT-3D as an additional training dataset when testing on YT-3D. Since YT-3D does not provide 3D GTs, we only provide a qualitative comparison of this dataset without quantitative evaluations.", + "bbox": [ + 75, + 625, + 467, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. We use mean per joint position error (MPJPE) and mean per vertex position error (MPVPE) as our evaluation metrics. The metrics measure Euclidean distance (mm) between estimated coordinates and groundtruth coordinates. Before calculating the metrics, we align the translation of the root joint (i.e., wrist).", + "bbox": [ + 75, + 715, + 467, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 816, + 225, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benefit of BlurHand dataset. Directly measuring how much synthesized blur is close to the real one is still an open research problem in the deblurring community [11, 48]. Hence, we justify the usefulness of the presented BlurHand", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9c75fd1d29cb1eddeaab5a6c8aeaf15ae288af3522372efdb575abe76aac45ef.jpg", + "table_caption": [ + "Table 1. Effectiveness of BlurHand on handling blurry hand. We calculate MPJPE (mm) on hand meshes located in the middle of the motion." + ], + "table_footnote": [], + "table_body": "
MethodsTrain setTest setMPIPE (mm)MPVPE (mm)
I2L-MeshNet [22]IH2.6MBH+Deblur26.5625.23
BH+DeblurBH+Deblur26.1325.00
BHBH24.3223.08
METRO [16]IH2.6MBH+Deblur26.0732.05
BH+DeblurBH+Deblur20.1126.55
BHBH20.5427.03
Pose2Pose [21]IH2.6MBH+Deblur22.4321.04
BH+DeblurBH+Deblur18.8117.43
BHBH18.8017.42
BlurHandNet (Ours)IH2.6MBH+Deblur21.3719.93
BH+DeblurBH+Deblur17.2815.82
BHBH16.8015.30
", + "bbox": [ + 521, + 89, + 870, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Effectiveness of BlurHand compared to deblurring baseline. MPJPE and MPVPE are calculated at hand meshes located in the middle of the motion.", + "bbox": [ + 498, + 252, + 890, + 292 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/94db369548dc3d2d65cfaa4b2a66c8171b38c52d7a8d67d448ae4655a4a5ee6d.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison on real-world blurry hand images. The captions below figures describe datasets used to train 3D hand mesh estimation networks. A setting with $\\mathbf{D}$ represents that the network is trained on deblurred BH and tested on (b)." + ], + "image_footnote": [], + "bbox": [ + 501, + 303, + 890, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "using indirect commonly used protocols [11], i.e., train the model with the presented dataset and test it on unseen blurry images. Table 1 shows that all 3D hand mesh recovery networks trained on InterHand2.6M suffer severe performance drops when they are tested on BlurHand, while networks trained on BlurHand perform well. These experimental results validate that training on BlurHand is necessary when handling the blurry hand. In addition, networks trained on BlurHand also perform well on InterHand2.6M, which consists of sharp images. This shows the generalizability of our dataset to sharp images.", + "bbox": [ + 496, + 521, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 shows that utilizing presented BlurHand is more valuable than applying deblurring methods [3]. The deblurring method [3], trained on our BlurHand as a pre-trained deblurring network, performs poorly on our BlurHand. Moreover, the networks trained on sharp images (IH2.6M) or deblurred images and tested on deblurred images perform worse than those trained and tested on our BlurHand. Such comparisons demonstrate the usefulness of our BlurHand dataset compared to applying deblurring methods. One reason is that, as Figure 6 shows, deblurring methods often fail to restore sharp hand images due to complicated hand motions. Another reason is that deblurring removes temporal information from the blurry image, which is helpful for reconstructing accurate 3D hand mesh sequences.", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "559", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/74400f70b77d2fa23f9db4087aeb138d25c13457afb86bbc92429e9ba6e95c62.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DeblurUnfolderKTFormerMPJPE
initialmiddlefinal
XXX-17.89-
XX✓-17.41-
X✓X18.9417.5519.05
X✓✓18.0816.8018.21
✓XX-17.28-
✓✓✓18.9517.2819.10
", + "bbox": [ + 117, + 89, + 426, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d257393d4e14c864395c2b7ef6956846a3d0c9cc41ee68d0641efd9a328d99b8.jpg", + "table_caption": [ + "Table 3. Ablation study on proposed Unfolder and KTFormer. (√ in Deblur): The experiments with the Deblur item checked are trained and tested on deblurred BlurHand. (Second row): We only employ features from a single time step when applying KTFormer, as temporal information does not exist without Unfolder." + ], + "table_footnote": [], + "table_body": "
# of unfoldingMPJPE
initialinitial*middlefinal*final
1--17.41--
3 (BlurHandNet)18.08-16.80-18.21
518.0617.1816.7817.3618.18
", + "bbox": [ + 109, + 272, + 436, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 7 provides a qualitative comparison of real-world blurry images in YT-3D, which further demonstrates the usefulness of our BlurHand. We train BlurHandNet on three different combinations of datasets: 1) InterHand2.6M and YT-3D (7b), 2) deblurred BlurHand and YT-3D (7c), and 3) BlurHand and YT-3D (7d). The comparison shows that networks trained on BlurHand produce the most robust 3D meshes, demonstrating the generalizability of BlurHand.", + "bbox": [ + 75, + 400, + 467, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Unfolder and KTFormer. Table 3 shows that using both Unfolder and KTFormer improves 3D mesh estimation accuracy by a large margin. As the proposed Unfolder allows a single image to be regarded as three sequential hands, we evaluate hands in both ends and middle of the motion. Since the temporal order of hand meshes in both ends (i.e., $\\mathbf{V}_{\\mathrm{E1}}$ and $\\mathbf{V}_{\\mathrm{E2}}$ ) is not determined, we report better MPJPE among the initial-final and final-initial pairs following [1, 36]. Solely employing one of Unfolder or KTFormer (the second and third rows) shows a slight improvement over the baseline network, which is designed without any of the proposed modules (the first row). On the other hand, our BlurHandNet (the fourth row) results in great performance boosts, by benefiting from the combination of two modules that effectively complement each other. In particular, KTFormer benefits from temporal information which is provided by Unfolder. Consequently, introducing both Unfolder and KTFormer, which have strong synergy, consistently improves the 3D errors in all time steps.", + "bbox": [ + 75, + 521, + 467, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the point of the baseline (the first row), using our two proposed modules, Unfolder and KTFormer, leads to more performance gain (the fourth row) than training and testing a network on deblurred BlurHand (the fifth row). This comparison shows that utilizing proposed modules is more effective than using deblurring methods. Interestingly, us", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c9e80f88be35b6c611087bb7a82028ed3deeb3cbc06f72f2eafbbdc3abd007a0.jpg", + "table_caption": [ + "Table 4. Ablation study on the number of unfolded hands. The initial* and final* denote hands between the initial and middle, and the middle and final, respectively." + ], + "table_footnote": [], + "table_body": "
KinematicTemporalMPJPE
initialmiddlefinal
XX18.9917.7919.06
✓X18.2816.9218.34
X✓18.7917.4118.92
✓✓18.0816.8018.21
", + "bbox": [ + 570, + 89, + 821, + 167 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/efb4d4b6e001ba5b05a4e620ea90da2085af5d7e2837292527952b9a095554b4.jpg", + "table_caption": [ + "Table 5. Ablation study on the kinematic and temporal positional embeddings." + ], + "table_footnote": [], + "table_body": "
Temporal order invariant lossUnfolder-driven temporal orderingMPJPE
initialmiddlefinal
XX18.7216.9818.86
✓X18.4417.1418.55
✓✓18.0816.8018.21
", + "bbox": [ + 540, + 205, + 849, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation study on proposed loss functions.", + "bbox": [ + 535, + 275, + 854, + 289 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing our two modules does not bring performance gain when training and testing on deblurred BlurHand (the last row) compared to the deblur baseline (the fifth row). This validates our statement that deblurring prohibits networks from utilizing temporal information.", + "bbox": [ + 498, + 308, + 890, + 382 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the number of unfolded hands. Table 4 shows that unfolding more sequential hands further improves the 3D errors. As our KTFormaler utilizes temporal information to enhance the joint feature, the number of hand sequences can affect the overall performance. Although unfolding a blurry hand into five sequential hands shows the best results, the performance is nearly saturated when a blurry hand is unfolded into three sequential hands. Considering the increased computational costs of producing additional hands and the temporal input size of KTFormaler, we design our Unfolder to produce three sequential hands. We note that our BlurHandNet can be easily extended if more number of unfolding is needed for some applications.", + "bbox": [ + 498, + 383, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the kinematic and temporal positional embeddings. Table 5 shows that our positional embedding setting, which uses both kinematic and temporal positional embedding, achieves the best performance. We design four variants with different positional embedding settings. The second and third rows, where either one of kinematic and temporal positional embedding is applied, achieve better results than a baseline without any positional embedding (the first row), but worse results than ours (the last row). This indicates that positional information of both kinematic and temporal dimensions is necessary for KTFounder.", + "bbox": [ + 498, + 582, + 890, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the proposed loss functions. Table 6 shows that two proposed items in our loss function, temporal order-invariant loss and Unfolder-driven temporal ordering as introduced in Section 4.4, are necessary for the high performance. We compare three variants for loss design at both ends of the motion, while keeping the loss function for the middle of the motion the same. In detail, the settings without temporal order-invariant loss are supervised with 3D meshes following the GT temporal order instead of determining the order based on Eq. 6. On the other hand,", + "bbox": [ + 498, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "560", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0cbb0ea66dfe221d581b38b8f92f2bae1c5405d01e793f5234fedbddf4b4269b.jpg", + "image_caption": [ + "Figure 8. Visual comparison of the BlurHandNet and state-of-the-art 3D hand mesh estimation methods [16,21] on BlurHand." + ], + "image_footnote": [], + "bbox": [ + 155, + 88, + 816, + 324 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8f8a8a8e1d3833a4b91e136ac4d0cc32122a51e790ca21305c05642c9d3b1ccb.jpg", + "image_caption": [ + "Figure 9. Visualization of attention map from KTFormer. The pixel at location $(i,j)$ represents the correlation between $i$ -th joint feature and $j$ -th joint feature. The attention map is obtained after performing a softmax operation across each row (query)." + ], + "image_footnote": [], + "bbox": [ + 94, + 347, + 455, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the setting without Unfolder-driven temporal ordering supervises Regressor with Regressor-driven temporal ordering, which indicates that Unfolder and Regressor can be supervised with different temporal ordering. Since inferring the temporal order of GT is ambiguous, the setting without temporal order-invariant loss degrades the performance as it forces to strictly follows the temporal order of GT. Utilizing the proposed Unfolder-driven temporal ordering performs the best, as it provides consistent temporal order to both Unfolder and Regressor, making the training stable.", + "bbox": [ + 75, + 566, + 468, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of attention map from KTFormer. Figure 9 shows a visualized attention map, obtained by the self-attention operation in KTFormer. Here, query and key are obtained from a combination of temporal joint features $\\mathbf{F}_{\\mathrm{JE1}}$ , $\\mathbf{F}_{\\mathrm{JC}}$ , and $\\mathbf{F}_{\\mathrm{JE1}}$ , as described in Section 4.2. The figure shows that our attention map produces two diagonal lines, representing a strong correlation between the corresponding query and key. Specifically, features from both ends of motion, $\\mathbf{F}_{\\mathrm{JE1}}$ and $\\mathbf{F}_{\\mathrm{JE2}}$ (the first and third queries), show high correlation with the middle hand feature $\\mathbf{F}_{\\mathrm{JM}}$ (the second key), and $\\mathbf{F}_{\\mathrm{JM}}$ (the second query) shows high correlation with $\\mathbf{F}_{\\mathrm{JE1}}$ and $\\mathbf{F}_{\\mathrm{JE2}}$ (the first and third keys). This indicates", + "bbox": [ + 75, + 719, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that temporal information is highly preferred to compensate for insufficient joint information in a certain time step. This is also consistent with the result in Table 3. In the second row of Table 3, solely employing KTFormer without Unfolder shows slight performance improvement over the baseline due to the lack of opportunity to exploit temporal information from both ends.", + "bbox": [ + 496, + 348, + 890, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Comparison with state-of-the-art methods", + "text_level": 1, + "bbox": [ + 498, + 462, + 859, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1 and 2 show that our BlurHandNet outperforms the previous state-of-the-art 3D hand mesh estimation methods in all settings. As the previous works [16,21,22] do not have a special module to address blurs, they fail to produce accurate 3D meshes from blurry hand images. On the contrary, by effectively handling the blur using temporal information, our BlurHandNet robustly estimates the 3D hand mesh, even under abrupt motion. Figure 8 further shows that our BlurHandNet produces much better results than previous methods on BlurHand.", + "bbox": [ + 496, + 484, + 890, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present the BlurHand dataset, containing realistic blurry hand images with 3D GTs, and the baseline network BlurHandNet. Our BlurHandNet regards a single blurry hand image as sequential hands to utilize the temporal information from sequential hands, which makes the network robust to the blurriness. Experimental results show that BlurHandNet achieves state-of-the-art performance in estimating 3D meshes from the newly proposed BlurHand and real-world test sets.", + "bbox": [ + 496, + 674, + 890, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported in part by the IITP grants [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University), No.2022-0-00156, No. 2021-0-02068, and No.2022-0-00156], and the NRF grant [No. 2021M3A9E4080782] funded by the Korea government (MSIT).", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "561", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] D. M. Argaw, J. Kim, F. Rameau, C. Zhang, and I. S. Kweon. Restoration of video frames from a single blurred image with motion understanding. In CVPR, 2019. 3, 7", + "[2] Mehrez Boulares and Mohamed Jemni. Automatic hand motion analysis for the sign language space management. 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In ICCV, 2019. 1, 2" + ], + "bbox": [ + 78, + 90, + 467, + 758 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "563", + "bbox": [ + 486, + 946, + 509, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_model.json b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..94a5b5feb12a62ff0da02e8d26b6b2a33a14cfea --- /dev/null +++ b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.131, + 0.819, + 0.177 + ], + "angle": 0, + "content": "Recovering 3D Hand Mesh Sequence from a Single Blurry Image: A New Dataset and Temporal Unfolding" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.202, + 0.852, + 0.256 + ], + "angle": 0, + "content": "Yeonguk Oh\\(^{1*}\\) JoonKyu Park\\(^{1*}\\) Jaeha Kim\\(^{1*}\\) Gyeongsik Moon\\(^{3}\\) Kyoung Mu Lee\\(^{1,2}\\) \n\\(^{1}\\)Dept. of ECE&ASRI, \\(^{2}\\)IPAI, Seoul National University, Korea \n\\(^{3}\\)Meta Reality Labs Research" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.26, + 0.9, + 0.275 + ], + "angle": 0, + "content": "{namepllet, jkpark0825}@snu.ac.kr, jhkim97s2@gmail.com, mks0601 \\) and the folding \\( <(\\mathrm{c}) \\rightarrow (\\mathrm{b}) \\rightarrow (\\mathrm{a}) > \\) make the same result blur image (d)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Among the three sequential features, the hand feature at the middle of the motion \\(\\mathbf{F}_{\\mathrm{M}}\\) can be specified as similar to the conventional deblurring approaches [25, 46]. However, we can not identify whether the hand at each end (i.e., \\(\\mathbf{F}_{\\mathrm{E1}}\\) or \\(\\mathbf{F}_{\\mathrm{E2}}\\)) is come from the initial or final location of the motion due to the temporal ambiguity [12, 28, 33, 47]. For example, suppose that we obtain the blurry hand image shown in Figure 4d. Then we can not determine whether the blurry hand image comes from the motion of extending or folding. In that regard, Unfolder outputs hand features from both ends of the motion (i.e., \\(\\mathbf{F}_{\\mathrm{E1}}\\) and \\(\\mathbf{F}_{\\mathrm{E2}}\\)) without considering temporal order. We note that exploiting the temporal information still benefits without explicitly considering the temporal order, and can further be stably optimized with the training loss introduced in Section 4.4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Extracting temporal joint features. From produced three sequential hand features, we extract the corresponding joint features, which contain essential hand articulation information [21] that helps to recover 3D hand meshes. We first project the sequential hand features \\(\\mathbf{F}_{\\mathrm{E1}}\\), \\(\\mathbf{F}_{\\mathrm{E2}}\\), and \\(\\mathbf{F}_{\\mathrm{M}}\\) into \\(dJ\\) dimensional feature through \\(1 \\times 1\\) convolution layer, and reshape them into 3D heatmaps with the dimension of \\(\\mathbb{R}^{J \\times h \\times w \\times d}\\), where \\(d = 32\\) is a depth discretization size and \\(J = 21\\) is a number of hand joints. Then, we perform a soft-argmax operation [41] on each heatmap to obtain the 3D joint coordinates of three temporal hands, \\(\\mathbf{J}_{\\mathrm{E1}}\\), \\(\\mathbf{J}_{\\mathrm{E2}}\\), and \\(\\mathbf{J}_{\\mathrm{M}}\\) with dimension of \\(\\mathbb{R}^{J \\times 3}\\). Using 3D joint coordinates in each temporal hand, we perform grid sampling [10, 21]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.325, + 0.891, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.461, + 0.893, + 0.533 + ], + "angle": 0, + "content": "Figure 5. Overall architecture of KTFormer. KTFormer refines temporal joint features \\(\\mathbf{F}_{\\mathrm{J_{E1}}}\\), \\(\\mathbf{F}_{\\mathrm{J_{E2}}}\\), and \\(\\mathbf{F}_{\\mathrm{J_M}}\\). First, kinematic and temporal positional embeddings are introduced. Then, the following self-attention mechanism refines joint features by leveraging attentive correlation between them, producing \\(\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}\\), \\(\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}\\), and \\(\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.894, + 0.609 + ], + "angle": 0, + "content": "on the corresponding feature map. By doing so, we obtain temporal joint features \\(\\mathbf{F}_{\\mathrm{J_{E1}}}\\), \\(\\mathbf{F}_{\\mathrm{J_{E2}}}\\), and \\(\\mathbf{F}_{\\mathrm{J_M}}\\) with a dimension of \\(\\mathbb{R}^{J\\times c}\\), which enable the following module to exploit temporal information effectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.622, + 0.635 + ], + "angle": 0, + "content": "4.2. KTFormer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Kinematic-temporal positional embedding. The illustration of KTFormer is shown in Figure 5. KTFormer is the Transformer [42]-based module that refines the joint feature \\(\\mathbf{F}_{\\mathrm{J_{E1}}}\\), \\(\\mathbf{F}_{\\mathrm{J_{E2}}}\\), and \\(\\mathbf{F}_{\\mathrm{J_M}}\\) by considering the correlation between not only joints at the same time step but also joints at different time steps. To utilize the temporal joint features as an input of Transformer, we first concatenate the three features along the joint dimension, producing \\(\\mathbf{F_J} \\in \\mathbb{R}^{3J \\times c}\\). Then, a learnable positional embedding, namely kinematic and temporal positional embeddings, is applied to \\(\\mathbf{F_J}\\). The kinematic positional embedding \\(\\in \\mathbb{R}^{J \\times c}\\) is applied along the joints dimension, while the temporal positional embedding \\(\\in \\mathbb{R}^{3 \\times c}\\) is applied along the temporal dimension. The kinematic and temporal positional embedding provide relative positions in kinematic and temporal space, respectively. Joint feature refinement with self-attention. KTFormer performs self-attention within \\(\\mathbf{F_J}\\) by extracting query \\(\\mathbf{q}\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.511, + 0.957 + ], + "angle": 0, + "content": "557" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.155 + ], + "angle": 0, + "content": "key \\(\\mathbf{k}\\) and value \\(\\mathbf{v}\\) through three fully-connected layers. Following the formulation of the standard Transformer [42], refined joint features for sequential hands \\(\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}\\), \\(\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}\\), and \\(\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}\\) are formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.164, + 0.47, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {k} ^ {T}}{\\sqrt {d _ {\\mathbf {k}}}}\\right) \\mathbf {v}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.209, + 0.469, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} = \\mathbf {F} _ {\\mathrm {J}} + \\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.239, + 0.469, + 0.257 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 1}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 2}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {M}}} ^ {\\prime} = \\psi (\\mathbf {F} _ {\\mathrm {J}} + \\operatorname {M L P} (\\mathbf {R})), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.469, + 0.354 + ], + "angle": 0, + "content": "where \\(d_{\\mathbf{k}} = 512\\) is the feature dimension of the key \\(\\mathbf{k}\\), and \\(\\mathbf{R}\\) is the residual feature. MLP denotes multi-layer perceptron, and \\(\\psi\\) denotes a dividing operation, which separates features in dimension \\(\\mathbb{R}^{3J\\times c}\\) to three \\(\\mathbb{R}^{J\\times c}\\). Consequently, three joint features \\(\\mathbf{F}_{\\mathrm{JE_1}}^{\\prime},\\mathbf{F}_{\\mathrm{JE_2}}^{\\prime}\\), and \\(\\mathbf{F}_{\\mathrm{JM}}^{\\prime}\\) are obtained by attentively utilizing kinematic and temporal information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.362, + 0.192, + 0.379 + ], + "angle": 0, + "content": "4.3. Regressor" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.749 + ], + "angle": 0, + "content": "The Regressor produces MANO [35] shape (i.e., \\(\\beta_{\\mathrm{E1}}\\), \\(\\beta_{\\mathrm{E2}}\\), and \\(\\beta_{\\mathrm{M}}\\)) and pose (i.e., \\(\\theta_{\\mathrm{E1}}\\), \\(\\theta_{\\mathrm{E2}}\\), and \\(\\theta_{\\mathrm{M}}\\)) parameters, which correspond to sequential hands. We describe the regression process of the middle hand (i.e., \\(\\beta_{\\mathrm{M}}\\) and \\(\\theta_{\\mathrm{M}}\\)) as a representative procedure, and note that the process at different timesteps can be obtained in the same manner. First, the shape parameter \\(\\beta_{\\mathrm{M}}\\) is obtained by forwarding the hand feature \\(\\mathbf{F}_{\\mathrm{M}}\\) to a fully-connected layer after global average pooling [18]. Second, the pose parameter \\(\\theta_{\\mathrm{M}}\\) is obtained by considering the kinematic correlation between hand joints. To this end, we first concatenate refined joint feature \\(\\mathbf{F}_{\\mathrm{J_M}}'\\) with corresponding 3D coordinates \\(\\mathbf{J}_{\\mathrm{M}}\\). Then, we flatten the concatenated feature into one-dimensional vector \\(\\mathbf{f}_{\\mathrm{M}} \\in \\mathbb{R}^{J(c + 3)}\\). Instead of regressing poses of entire joints from \\(\\mathbf{f}_{\\mathrm{M}}\\) at once, the Regressor gradually estimates pose for each joint along the hierarchy of hand kinematic tree, following [43]. In detail, for a specific joint, its ancestral pose parameters and \\(\\mathbf{f}_{\\mathrm{M}}\\) are concatenated, and forwarded to a fully-connected layer to regress the pose parameters. By adopting the same process for both ends, three MANO parameters are obtained from the Regressor. Then, the MANO parameters are forwarded to the MANO layer to produce 3D hand meshes \\(\\mathbf{V}_{\\mathrm{E1}}\\), \\(\\mathbf{V}_{\\mathrm{E2}}\\), and \\(\\mathbf{V}_{\\mathrm{M}}\\), where each denotes to meshes at both ends and middle, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.214, + 0.773 + ], + "angle": 0, + "content": "4.4. Training loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "During the training, a prediction on the middle of the motion can be simply supervised with GT of the middle frame. On the other hand, it is ambiguous to supervise both ends of motion as the temporal order is not uniquely determined, as shown in Figure 4. To resolve such temporal ambiguity during the loss calculation, we propose two items. First, we employ temporal order-invariant loss, which is invariant to GT temporal order [36]. To be specific, the temporal order" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "in our loss function is determined in the direction that minimizes loss functions, not by the GT temporal order. Second, we propose to use a Unfolder-driven temporal ordering. It determines the temporal order based on the output of Unfolder, then uses the determined temporal order to supervise the outputs of Regressor rather than determining the temporal order of two modules separately. The effectiveness of the two items is demonstrated in the experimental section." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.212, + 0.844, + 0.227 + ], + "angle": 0, + "content": "The overall loss function \\(\\mathcal{L}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.228, + 0.891, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {U}} + \\mathcal {L} _ {\\mathrm {R}} \\\\ = \\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}}, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.892, + 0.315 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{U}}\\) and \\(\\mathcal{L}_{\\mathrm{R}}\\) are loss functions applied to outputs of the Unfolder and the Regressor, respectively. The subscripts M and E stand for prediction of the middle and both ends." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.316, + 0.892, + 0.345 + ], + "angle": 0, + "content": "To supervise outputs of Unfolder, we define \\(\\mathcal{L}_{\\mathrm{U,M}}\\) and \\(\\mathcal{L}_{\\mathrm{U,E}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.353, + 0.891, + 0.371 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} = \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {M}}, \\mathbf {J} _ {\\text {m i d d l e}} ^ {*}\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.378, + 0.891, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} = \\min (\\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}) + \\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*})), \\\\ \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}\\right)), \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.892, + 0.54 + ], + "angle": 0, + "content": "where \\(\\mathbf{J}_{\\mathrm{middle}}^{*}, \\mathbf{J}_{\\mathrm{initial}}^{*}\\), and \\(\\mathbf{J}_{\\mathrm{final}}^{*}\\) are GT 3D joint coordinates of the middle, initial and final frame, respectively. \\(\\mathcal{L}_{\\mathrm{joint}}\\) is \\(L1\\) distance between predicted and GT joint coordinates. The temporal order is determined to forward if the first term in min of Eq. 6 is selected as minimum and backward otherwise. Therefore, our loss function is invariant to the temporal order of GT." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.571 + ], + "angle": 0, + "content": "To supervise the outputs of the Regressor, we define the loss function \\(\\mathcal{L}_{\\mathrm{R,M}}\\) and \\(\\mathcal{L}_{\\mathrm{R,E}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.579, + 0.891, + 0.596 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} = \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {M}}, \\Theta_ {\\text {m i d d l e}} ^ {*}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.603, + 0.891, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}} = \\mathbb {1} _ {\\mathbf {f}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right)\\right) \\\\ + \\mathbb {1} _ {\\mathbf {b}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right)\\right), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.811 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}_{\\mathbf{f}} = 1\\) when the temporal order is determined to forward in Eq. 6 otherwise 0, and \\(\\mathbb{1}_{\\mathbf{b}} = 1 - \\mathbb{1}_{\\mathbf{f}}\\). In other words, the temporal order of Eq. 8 follows that of Eq. 6, which we call Unfolder-driven temporal ordering. \\(\\Theta_{\\bullet} = \\{\\theta_{\\bullet}, \\beta_{\\bullet}\\}\\) is GT or predicted MANO parameters, where the superscript * denotes GT. \\(\\mathcal{L}_{\\mathrm{mesh}}\\) is the summation of three \\(L1\\) distances between GT and prediction of: 1) MANO parameters 2) 3D joint coordinates obtained by multiplying joint regression matrix to hand mesh 3) 2D joint coordinates projected from 3D joint coordinates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.823, + 0.633, + 0.839 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.78, + 0.862 + ], + "angle": 0, + "content": "5.1. Datasets and evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "BlurHand. The BlurHand (BH) is our newly presented 3D hand pose dataset containing realistic blurry hand images as" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "558" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.119, + 0.09, + 0.428, + 0.221 + ], + "angle": 0, + "content": "
MethodsTrain setTest set
IH2.6MBH
I2L-MeshNet [22]IH2.6MBH22.2724.3029.1624.32
METRO [16]IH2.6MBH18.4420.1935.4320.54
Pose2Pose [21]IH2.6MBH16.8518.4025.3618.80
BlurHandNet (Ours)IH2.6MBH15.3316.1224.5716.80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.223, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 1. Effectiveness of BlurHand on handling blurry hand. We calculate MPJPE (mm) on hand meshes located in the middle of the motion." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.274, + 0.457, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.401, + 0.468, + 0.456 + ], + "angle": 0, + "content": "Figure 6. Examples of deblurred images. Since the blurry hand undergoes challenging blur from complex articulation, even the state-of-the-art deblurring method [3] cannot fully restore and blur artifact remains, highlighted with red circles." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.468, + 0.505 + ], + "angle": 0, + "content": "introduced in Section 3. We train and test the 3D hand mesh estimation networks on the train and test splits of the BH." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.468, + 0.626 + ], + "angle": 0, + "content": "InterHand2.6M. InterHand2.6M [23] (IH2.6M) is a recently presented large-scale 3D hand dataset. It is captured under highly calibrated camera settings and provides accurate 3D annotations for hand images. We employ IH2.6M as a representative of sharp hand frames, as the hand images in IH2.6M do not contain blur. We use a subset of IH2.6M for training and testing purposes, where the subset is a set of the third sharp frame in Figure 2 for each image of BH." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.468, + 0.716 + ], + "angle": 0, + "content": "YT-3D. YouTube-3D-hands (YT-3D) [13] is a 3D hand dataset with diverse and non-laboratory videos collected from youtube. We utilize the YT-3D as an additional training dataset when testing on YT-3D. Since YT-3D does not provide 3D GTs, we only provide a qualitative comparison of this dataset without quantitative evaluations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.468, + 0.807 + ], + "angle": 0, + "content": "Evaluation metrics. We use mean per joint position error (MPJPE) and mean per vertex position error (MPVPE) as our evaluation metrics. The metrics measure Euclidean distance (mm) between estimated coordinates and groundtruth coordinates. Before calculating the metrics, we align the translation of the root joint (i.e., wrist)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.227, + 0.833 + ], + "angle": 0, + "content": "5.2. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Benefit of BlurHand dataset. Directly measuring how much synthesized blur is close to the real one is still an open research problem in the deblurring community [11, 48]. Hence, we justify the usefulness of the presented BlurHand" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.09, + 0.871, + 0.251 + ], + "angle": 0, + "content": "
MethodsTrain setTest setMPIPE (mm)MPVPE (mm)
I2L-MeshNet [22]IH2.6MBH+Deblur26.5625.23
BH+DeblurBH+Deblur26.1325.00
BHBH24.3223.08
METRO [16]IH2.6MBH+Deblur26.0732.05
BH+DeblurBH+Deblur20.1126.55
BHBH20.5427.03
Pose2Pose [21]IH2.6MBH+Deblur22.4321.04
BH+DeblurBH+Deblur18.8117.43
BHBH18.8017.42
BlurHandNet (Ours)IH2.6MBH+Deblur21.3719.93
BH+DeblurBH+Deblur17.2815.82
BHBH16.8015.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Table 2. Effectiveness of BlurHand compared to deblurring baseline. MPJPE and MPVPE are calculated at hand meshes located in the middle of the motion." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.304, + 0.892, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison on real-world blurry hand images. The captions below figures describe datasets used to train 3D hand mesh estimation networks. A setting with \\(\\mathbf{D}\\) represents that the network is trained on deblurred BH and tested on (b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.688 + ], + "angle": 0, + "content": "using indirect commonly used protocols [11], i.e., train the model with the presented dataset and test it on unseen blurry images. Table 1 shows that all 3D hand mesh recovery networks trained on InterHand2.6M suffer severe performance drops when they are tested on BlurHand, while networks trained on BlurHand perform well. These experimental results validate that training on BlurHand is necessary when handling the blurry hand. In addition, networks trained on BlurHand also perform well on InterHand2.6M, which consists of sharp images. This shows the generalizability of our dataset to sharp images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Table 2 shows that utilizing presented BlurHand is more valuable than applying deblurring methods [3]. The deblurring method [3], trained on our BlurHand as a pre-trained deblurring network, performs poorly on our BlurHand. Moreover, the networks trained on sharp images (IH2.6M) or deblurred images and tested on deblurred images perform worse than those trained and tested on our BlurHand. Such comparisons demonstrate the usefulness of our BlurHand dataset compared to applying deblurring methods. One reason is that, as Figure 6 shows, deblurring methods often fail to restore sharp hand images due to complicated hand motions. Another reason is that deblurring removes temporal information from the blurry image, which is helpful for reconstructing accurate 3D hand mesh sequences." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "559" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.119, + 0.09, + 0.428, + 0.196 + ], + "angle": 0, + "content": "
DeblurUnfolderKTFormerMPJPE
initialmiddlefinal
XXX-17.89-
XX✓-17.41-
X✓X18.9417.5519.05
X✓✓18.0816.8018.21
✓XX-17.28-
✓✓✓18.9517.2819.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.198, + 0.468, + 0.266 + ], + "angle": 0, + "content": "Table 3. Ablation study on proposed Unfolder and KTFormer. (√ in Deblur): The experiments with the Deblur item checked are trained and tested on deblurred BlurHand. (Second row): We only employ features from a single time step when applying KTFormer, as temporal information does not exist without Unfolder." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.273, + 0.437, + 0.34 + ], + "angle": 0, + "content": "
# of unfoldingMPJPE
initialinitial*middlefinal*final
1--17.41--
3 (BlurHandNet)18.08-16.80-18.21
518.0617.1816.7817.3618.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.342, + 0.468, + 0.384 + ], + "angle": 0, + "content": "Table 4. Ablation study on the number of unfolded hands. The initial* and final* denote hands between the initial and middle, and the middle and final, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.468, + 0.522 + ], + "angle": 0, + "content": "Figure 7 provides a qualitative comparison of real-world blurry images in YT-3D, which further demonstrates the usefulness of our BlurHand. We train BlurHandNet on three different combinations of datasets: 1) InterHand2.6M and YT-3D (7b), 2) deblurred BlurHand and YT-3D (7c), and 3) BlurHand and YT-3D (7d). The comparison shows that networks trained on BlurHand produce the most robust 3D meshes, demonstrating the generalizability of BlurHand." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.809 + ], + "angle": 0, + "content": "Effectiveness of Unfolder and KTFormer. Table 3 shows that using both Unfolder and KTFormer improves 3D mesh estimation accuracy by a large margin. As the proposed Unfolder allows a single image to be regarded as three sequential hands, we evaluate hands in both ends and middle of the motion. Since the temporal order of hand meshes in both ends (i.e., \\(\\mathbf{V}_{\\mathrm{E1}}\\) and \\(\\mathbf{V}_{\\mathrm{E2}}\\)) is not determined, we report better MPJPE among the initial-final and final-initial pairs following [1, 36]. Solely employing one of Unfolder or KTFormer (the second and third rows) shows a slight improvement over the baseline network, which is designed without any of the proposed modules (the first row). On the other hand, our BlurHandNet (the fourth row) results in great performance boosts, by benefiting from the combination of two modules that effectively complement each other. In particular, KTFormer benefits from temporal information which is provided by Unfolder. Consequently, introducing both Unfolder and KTFormer, which have strong synergy, consistently improves the 3D errors in all time steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In the point of the baseline (the first row), using our two proposed modules, Unfolder and KTFormer, leads to more performance gain (the fourth row) than training and testing a network on deblurred BlurHand (the fifth row). This comparison shows that utilizing proposed modules is more effective than using deblurring methods. Interestingly, us" + }, + { + "type": "table", + "bbox": [ + 0.571, + 0.09, + 0.822, + 0.169 + ], + "angle": 0, + "content": "
KinematicTemporalMPJPE
initialmiddlefinal
XX18.9917.7919.06
✓X18.2816.9218.34
X✓18.7917.4118.92
✓✓18.0816.8018.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.172, + 0.89, + 0.199 + ], + "angle": 0, + "content": "Table 5. Ablation study on the kinematic and temporal positional embeddings." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.206, + 0.851, + 0.274 + ], + "angle": 0, + "content": "
Temporal order invariant lossUnfolder-driven temporal orderingMPJPE
initialmiddlefinal
XX18.7216.9818.86
✓X18.4417.1418.55
✓✓18.0816.8018.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.276, + 0.855, + 0.29 + ], + "angle": 0, + "content": "Table 6. Ablation study on proposed loss functions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.309, + 0.892, + 0.383 + ], + "angle": 0, + "content": "ing our two modules does not bring performance gain when training and testing on deblurred BlurHand (the last row) compared to the deblur baseline (the fifth row). This validates our statement that deblurring prohibits networks from utilizing temporal information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Effect of the number of unfolded hands. Table 4 shows that unfolding more sequential hands further improves the 3D errors. As our KTFormaler utilizes temporal information to enhance the joint feature, the number of hand sequences can affect the overall performance. Although unfolding a blurry hand into five sequential hands shows the best results, the performance is nearly saturated when a blurry hand is unfolded into three sequential hands. Considering the increased computational costs of producing additional hands and the temporal input size of KTFormaler, we design our Unfolder to produce three sequential hands. We note that our BlurHandNet can be easily extended if more number of unfolding is needed for some applications." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.583, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Effect of the kinematic and temporal positional embeddings. Table 5 shows that our positional embedding setting, which uses both kinematic and temporal positional embedding, achieves the best performance. We design four variants with different positional embedding settings. The second and third rows, where either one of kinematic and temporal positional embedding is applied, achieve better results than a baseline without any positional embedding (the first row), but worse results than ours (the last row). This indicates that positional information of both kinematic and temporal dimensions is necessary for KTFounder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of the proposed loss functions. Table 6 shows that two proposed items in our loss function, temporal order-invariant loss and Unfolder-driven temporal ordering as introduced in Section 4.4, are necessary for the high performance. We compare three variants for loss design at both ends of the motion, while keeping the loss function for the middle of the motion the same. In detail, the settings without temporal order-invariant loss are supervised with 3D meshes following the GT temporal order instead of determining the order based on Eq. 6. On the other hand," + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "560" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.089, + 0.818, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.329, + 0.88, + 0.344 + ], + "angle": 0, + "content": "Figure 8. Visual comparison of the BlurHandNet and state-of-the-art 3D hand mesh estimation methods [16,21] on BlurHand." + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.348, + 0.456, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.498, + 0.471, + 0.555 + ], + "angle": 0, + "content": "Figure 9. Visualization of attention map from KTFormer. The pixel at location \\((i,j)\\) represents the correlation between \\(i\\)-th joint feature and \\(j\\)-th joint feature. The attention map is obtained after performing a softmax operation across each row (query)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.718 + ], + "angle": 0, + "content": "the setting without Unfolder-driven temporal ordering supervises Regressor with Regressor-driven temporal ordering, which indicates that Unfolder and Regressor can be supervised with different temporal ordering. Since inferring the temporal order of GT is ambiguous, the setting without temporal order-invariant loss degrades the performance as it forces to strictly follows the temporal order of GT. Utilizing the proposed Unfolder-driven temporal ordering performs the best, as it provides consistent temporal order to both Unfolder and Regressor, making the training stable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Visualization of attention map from KTFormer. Figure 9 shows a visualized attention map, obtained by the self-attention operation in KTFormer. Here, query and key are obtained from a combination of temporal joint features \\(\\mathbf{F}_{\\mathrm{JE1}}\\), \\(\\mathbf{F}_{\\mathrm{JC}}\\), and \\(\\mathbf{F}_{\\mathrm{JE1}}\\), as described in Section 4.2. The figure shows that our attention map produces two diagonal lines, representing a strong correlation between the corresponding query and key. Specifically, features from both ends of motion, \\(\\mathbf{F}_{\\mathrm{JE1}}\\) and \\(\\mathbf{F}_{\\mathrm{JE2}}\\) (the first and third queries), show high correlation with the middle hand feature \\(\\mathbf{F}_{\\mathrm{JM}}\\) (the second key), and \\(\\mathbf{F}_{\\mathrm{JM}}\\) (the second query) shows high correlation with \\(\\mathbf{F}_{\\mathrm{JE1}}\\) and \\(\\mathbf{F}_{\\mathrm{JE2}}\\) (the first and third keys). This indicates" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.454 + ], + "angle": 0, + "content": "that temporal information is highly preferred to compensate for insufficient joint information in a certain time step. This is also consistent with the result in Table 3. In the second row of Table 3, solely employing KTFormer without Unfolder shows slight performance improvement over the baseline due to the lack of opportunity to exploit temporal information from both ends." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.463, + 0.86, + 0.479 + ], + "angle": 0, + "content": "5.3. Comparison with state-of-the-art methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Table 1 and 2 show that our BlurHandNet outperforms the previous state-of-the-art 3D hand mesh estimation methods in all settings. As the previous works [16,21,22] do not have a special module to address blurs, they fail to produce accurate 3D meshes from blurry hand images. On the contrary, by effectively handling the blur using temporal information, our BlurHandNet robustly estimates the 3D hand mesh, even under abrupt motion. Figure 8 further shows that our BlurHandNet produces much better results than previous methods on BlurHand." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.619, + 0.665 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.809 + ], + "angle": 0, + "content": "We present the BlurHand dataset, containing realistic blurry hand images with 3D GTs, and the baseline network BlurHandNet. Our BlurHandNet regards a single blurry hand image as sequential hands to utilize the temporal information from sequential hands, which makes the network robust to the blurriness. Experimental results show that BlurHandNet achieves state-of-the-art performance in estimating 3D meshes from the newly proposed BlurHand and real-world test sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported in part by the IITP grants [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University), No.2022-0-00156, No. 2021-0-02068, and No.2022-0-00156], and the NRF grant [No. 2021M3A9E4080782] funded by the Korea government (MSIT)." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "561" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] D. M. Argaw, J. Kim, F. Rameau, C. Zhang, and I. S. Kweon. Restoration of video frames from a single blurred image with motion understanding. In CVPR, 2019. 3, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.469, + 0.199 + ], + "angle": 0, + "content": "[2] Mehrez Boulares and Mohamed Jemni. 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In ICCV, 2019. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.76 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.947, + 0.511, + 0.957 + ], + "angle": 0, + "content": "563" + } + ] +] \ No newline at end of file diff --git a/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_origin.pdf b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5191613bc950eba876d9000a90e1ac88be26f9dc --- /dev/null +++ b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/b7a63c82-2ead-41e3-b7d7-3cbeee09de5a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:769d2cd0ad3d3fd677d64b55ca99fd1516210086ef7a91dbd035e92b9b251f0f +size 3376549 diff --git a/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/full.md b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ec68b67efaa1236c65da9d14dacc3774c9bf27e3 --- /dev/null +++ b/2023/Recovering 3D Hand Mesh Sequence From a Single Blurry Image_ A New Dataset and Temporal Unfolding/full.md @@ -0,0 +1,313 @@ +# Recovering 3D Hand Mesh Sequence from a Single Blurry Image: A New Dataset and Temporal Unfolding + +Yeonguk Oh $^{1*}$ JoonKyu Park $^{1*}$ Jaeha Kim $^{1*}$ Gyeongsik Moon $^{3}$ Kyoung Mu Lee $^{1,2}$ $^{1}$ Dept. of ECE&ASRI, $^{2}$ IPAI, Seoul National University, Korea + $^{3}$ Meta Reality Labs Research + +{namepllet, jkpark0825}@snu.ac.kr, jhkim97s2@gmail.com, mks0601$ and the folding $<(\mathrm{c}) \rightarrow (\mathrm{b}) \rightarrow (\mathrm{a}) >$ make the same result blur image (d). + +![](images/f9dbc4bbac6d3b33693703a42c80b52e2d104a7fc246e08c514de1d7077fc412.jpg) +(d) + +Among the three sequential features, the hand feature at the middle of the motion $\mathbf{F}_{\mathrm{M}}$ can be specified as similar to the conventional deblurring approaches [25, 46]. However, we can not identify whether the hand at each end (i.e., $\mathbf{F}_{\mathrm{E1}}$ or $\mathbf{F}_{\mathrm{E2}}$ ) is come from the initial or final location of the motion due to the temporal ambiguity [12, 28, 33, 47]. For example, suppose that we obtain the blurry hand image shown in Figure 4d. Then we can not determine whether the blurry hand image comes from the motion of extending or folding. In that regard, Unfolder outputs hand features from both ends of the motion (i.e., $\mathbf{F}_{\mathrm{E1}}$ and $\mathbf{F}_{\mathrm{E2}}$ ) without considering temporal order. We note that exploiting the temporal information still benefits without explicitly considering the temporal order, and can further be stably optimized with the training loss introduced in Section 4.4. + +Extracting temporal joint features. From produced three sequential hand features, we extract the corresponding joint features, which contain essential hand articulation information [21] that helps to recover 3D hand meshes. We first project the sequential hand features $\mathbf{F}_{\mathrm{E1}}$ , $\mathbf{F}_{\mathrm{E2}}$ , and $\mathbf{F}_{\mathrm{M}}$ into $dJ$ dimensional feature through $1 \times 1$ convolution layer, and reshape them into 3D heatmaps with the dimension of $\mathbb{R}^{J \times h \times w \times d}$ , where $d = 32$ is a depth discretization size and $J = 21$ is a number of hand joints. Then, we perform a soft-argmax operation [41] on each heatmap to obtain the 3D joint coordinates of three temporal hands, $\mathbf{J}_{\mathrm{E1}}$ , $\mathbf{J}_{\mathrm{E2}}$ , and $\mathbf{J}_{\mathrm{M}}$ with dimension of $\mathbb{R}^{J \times 3}$ . Using 3D joint coordinates in each temporal hand, we perform grid sampling [10, 21] + +![](images/71df2cf2c26d3eddebeb0eb9f27f2b5c53dd9aa2cb8285177bdaea560d588405.jpg) +Figure 5. Overall architecture of KTFormer. KTFormer refines temporal joint features $\mathbf{F}_{\mathrm{J_{E1}}}$ , $\mathbf{F}_{\mathrm{J_{E2}}}$ , and $\mathbf{F}_{\mathrm{J_M}}$ . First, kinematic and temporal positional embeddings are introduced. Then, the following self-attention mechanism refines joint features by leveraging attentive correlation between them, producing $\mathbf{F}_{\mathrm{J_{E1}}}^{\prime}$ , $\mathbf{F}_{\mathrm{J_{E2}}}^{\prime}$ , and $\mathbf{F}_{\mathrm{J_M}}^{\prime}$ . + +on the corresponding feature map. By doing so, we obtain temporal joint features $\mathbf{F}_{\mathrm{J_{E1}}}$ , $\mathbf{F}_{\mathrm{J_{E2}}}$ , and $\mathbf{F}_{\mathrm{J_M}}$ with a dimension of $\mathbb{R}^{J\times c}$ , which enable the following module to exploit temporal information effectively. + +# 4.2. KTFormer + +Kinematic-temporal positional embedding. The illustration of KTFormer is shown in Figure 5. KTFormer is the Transformer [42]-based module that refines the joint feature $\mathbf{F}_{\mathrm{J_{E1}}}$ , $\mathbf{F}_{\mathrm{J_{E2}}}$ , and $\mathbf{F}_{\mathrm{J_M}}$ by considering the correlation between not only joints at the same time step but also joints at different time steps. To utilize the temporal joint features as an input of Transformer, we first concatenate the three features along the joint dimension, producing $\mathbf{F_J} \in \mathbb{R}^{3J \times c}$ . Then, a learnable positional embedding, namely kinematic and temporal positional embeddings, is applied to $\mathbf{F_J}$ . The kinematic positional embedding $\in \mathbb{R}^{J \times c}$ is applied along the joints dimension, while the temporal positional embedding $\in \mathbb{R}^{3 \times c}$ is applied along the temporal dimension. The kinematic and temporal positional embedding provide relative positions in kinematic and temporal space, respectively. Joint feature refinement with self-attention. KTFormer performs self-attention within $\mathbf{F_J}$ by extracting query $\mathbf{q}$ , + +key $\mathbf{k}$ and value $\mathbf{v}$ through three fully-connected layers. Following the formulation of the standard Transformer [42], refined joint features for sequential hands $\mathbf{F}_{\mathrm{J_{E1}}}^{\prime}$ , $\mathbf{F}_{\mathrm{J_{E2}}}^{\prime}$ , and $\mathbf{F}_{\mathrm{J_M}}^{\prime}$ are formulated as follows: + +$$ +\operatorname {A t t} (\mathbf {q}, \mathbf {k}, \mathbf {v}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {q} \mathbf {k} ^ {T}}{\sqrt {d _ {\mathbf {k}}}}\right) \mathbf {v}, \tag {1} +$$ + +$$ +\mathbf {R} = \mathbf {F} _ {\mathrm {J}} + \operatorname {A t t} (\mathbf {q}, \mathbf {k}, \mathbf {v}), \tag {2} +$$ + +$$ +\mathbf {F} _ {\mathrm {J} _ {\mathrm {E} 1}} ^ {\prime}, \mathbf {F} _ {\mathrm {J} _ {\mathrm {E} 2}} ^ {\prime}, \mathbf {F} _ {\mathrm {J} _ {\mathrm {M}}} ^ {\prime} = \psi (\mathbf {F} _ {\mathrm {J}} + \operatorname {M L P} (\mathbf {R})), \tag {3} +$$ + +where $d_{\mathbf{k}} = 512$ is the feature dimension of the key $\mathbf{k}$ , and $\mathbf{R}$ is the residual feature. MLP denotes multi-layer perceptron, and $\psi$ denotes a dividing operation, which separates features in dimension $\mathbb{R}^{3J\times c}$ to three $\mathbb{R}^{J\times c}$ . Consequently, three joint features $\mathbf{F}_{\mathrm{JE_1}}^{\prime},\mathbf{F}_{\mathrm{JE_2}}^{\prime}$ , and $\mathbf{F}_{\mathrm{JM}}^{\prime}$ are obtained by attentively utilizing kinematic and temporal information. + +# 4.3. Regressor + +The Regressor produces MANO [35] shape (i.e., $\beta_{\mathrm{E1}}$ , $\beta_{\mathrm{E2}}$ , and $\beta_{\mathrm{M}}$ ) and pose (i.e., $\theta_{\mathrm{E1}}$ , $\theta_{\mathrm{E2}}$ , and $\theta_{\mathrm{M}}$ ) parameters, which correspond to sequential hands. We describe the regression process of the middle hand (i.e., $\beta_{\mathrm{M}}$ and $\theta_{\mathrm{M}}$ ) as a representative procedure, and note that the process at different timesteps can be obtained in the same manner. First, the shape parameter $\beta_{\mathrm{M}}$ is obtained by forwarding the hand feature $\mathbf{F}_{\mathrm{M}}$ to a fully-connected layer after global average pooling [18]. Second, the pose parameter $\theta_{\mathrm{M}}$ is obtained by considering the kinematic correlation between hand joints. To this end, we first concatenate refined joint feature $\mathbf{F}_{\mathrm{J_M}}'$ with corresponding 3D coordinates $\mathbf{J}_{\mathrm{M}}$ . Then, we flatten the concatenated feature into one-dimensional vector $\mathbf{f}_{\mathrm{M}} \in \mathbb{R}^{J(c + 3)}$ . Instead of regressing poses of entire joints from $\mathbf{f}_{\mathrm{M}}$ at once, the Regressor gradually estimates pose for each joint along the hierarchy of hand kinematic tree, following [43]. In detail, for a specific joint, its ancestral pose parameters and $\mathbf{f}_{\mathrm{M}}$ are concatenated, and forwarded to a fully-connected layer to regress the pose parameters. By adopting the same process for both ends, three MANO parameters are obtained from the Regressor. Then, the MANO parameters are forwarded to the MANO layer to produce 3D hand meshes $\mathbf{V}_{\mathrm{E1}}$ , $\mathbf{V}_{\mathrm{E2}}$ , and $\mathbf{V}_{\mathrm{M}}$ , where each denotes to meshes at both ends and middle, respectively. + +# 4.4. Training loss + +During the training, a prediction on the middle of the motion can be simply supervised with GT of the middle frame. On the other hand, it is ambiguous to supervise both ends of motion as the temporal order is not uniquely determined, as shown in Figure 4. To resolve such temporal ambiguity during the loss calculation, we propose two items. First, we employ temporal order-invariant loss, which is invariant to GT temporal order [36]. To be specific, the temporal order + +in our loss function is determined in the direction that minimizes loss functions, not by the GT temporal order. Second, we propose to use a Unfolder-driven temporal ordering. It determines the temporal order based on the output of Unfolder, then uses the determined temporal order to supervise the outputs of Regressor rather than determining the temporal order of two modules separately. The effectiveness of the two items is demonstrated in the experimental section. + +The overall loss function $\mathcal{L}$ is defined as follows: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\mathrm {U}} + \mathcal {L} _ {\mathrm {R}} \\ = \mathcal {L} _ {\mathrm {U}, \mathrm {M}} + \mathcal {L} _ {\mathrm {U}, \mathrm {E}} + \mathcal {L} _ {\mathrm {R}, \mathrm {M}} + \mathcal {L} _ {\mathrm {R}, \mathrm {E}}, \tag {4} \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{U}}$ and $\mathcal{L}_{\mathrm{R}}$ are loss functions applied to outputs of the Unfolder and the Regressor, respectively. The subscripts M and E stand for prediction of the middle and both ends. + +To supervise outputs of Unfolder, we define $\mathcal{L}_{\mathrm{U,M}}$ and $\mathcal{L}_{\mathrm{U,E}}$ as follows: + +$$ +\mathcal {L} _ {\mathrm {U}, \mathrm {M}} = \mathcal {L} _ {\text {j o i n t}} \left(\mathbf {J} _ {\mathrm {M}}, \mathbf {J} _ {\text {m i d d l e}} ^ {*}\right), \tag {5} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {U}, \mathrm {E}} = \min (\mathcal {L} _ {\text {j o i n t}} (\mathbf {J} _ {\mathrm {E} 1}, \mathbf {J} _ {\text {i n i t i a l}} ^ {*}) + \mathcal {L} _ {\text {j o i n t}} (\mathbf {J} _ {\mathrm {E} 2}, \mathbf {J} _ {\text {f i n a l}} ^ {*})), \\ \mathcal {L} _ {\text {j o i n t}} \left(\mathbf {J} _ {\mathrm {E} 1}, \mathbf {J} _ {\text {f i n a l}} ^ {*}\right) + \mathcal {L} _ {\text {j o i n t}} \left(\mathbf {J} _ {\mathrm {E} 2}, \mathbf {J} _ {\text {i n i t i a l}} ^ {*}\right)), \tag {6} \\ \end{array} +$$ + +where $\mathbf{J}_{\mathrm{middle}}^{*}, \mathbf{J}_{\mathrm{initial}}^{*}$ , and $\mathbf{J}_{\mathrm{final}}^{*}$ are GT 3D joint coordinates of the middle, initial and final frame, respectively. $\mathcal{L}_{\mathrm{joint}}$ is $L1$ distance between predicted and GT joint coordinates. The temporal order is determined to forward if the first term in min of Eq. 6 is selected as minimum and backward otherwise. Therefore, our loss function is invariant to the temporal order of GT. + +To supervise the outputs of the Regressor, we define the loss function $\mathcal{L}_{\mathrm{R,M}}$ and $\mathcal{L}_{\mathrm{R,E}}$ as follows: + +$$ +\mathcal {L} _ {\mathrm {R}, \mathrm {M}} = \mathcal {L} _ {\text {m e s h}} \left(\Theta_ {\mathrm {M}}, \Theta_ {\text {m i d d l e}} ^ {*}\right), \tag {7} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {R}, \mathrm {E}} = \mathbb {1} _ {\mathbf {f}} \left(\mathcal {L} _ {\text {m e s h}} \left(\Theta_ {\mathrm {E} 1}, \Theta_ {\text {i n i t i a l}} ^ {*}\right) + \mathcal {L} _ {\text {m e s h}} \left(\Theta_ {\mathrm {E} 2}, \Theta_ {\text {f i n a l}} ^ {*}\right)\right) \\ + \mathbb {1} _ {\mathbf {b}} \left(\mathcal {L} _ {\text {m e s h}} \left(\Theta_ {\mathrm {E} 1}, \Theta_ {\text {f i n a l}} ^ {*}\right) + \mathcal {L} _ {\text {m e s h}} \left(\Theta_ {\mathrm {E} 2}, \Theta_ {\text {i n i t i a l}} ^ {*}\right)\right), \tag {8} \\ \end{array} +$$ + +where $\mathbb{1}_{\mathbf{f}} = 1$ when the temporal order is determined to forward in Eq. 6 otherwise 0, and $\mathbb{1}_{\mathbf{b}} = 1 - \mathbb{1}_{\mathbf{f}}$ . In other words, the temporal order of Eq. 8 follows that of Eq. 6, which we call Unfolder-driven temporal ordering. $\Theta_{\bullet} = \{\theta_{\bullet}, \beta_{\bullet}\}$ is GT or predicted MANO parameters, where the superscript * denotes GT. $\mathcal{L}_{\mathrm{mesh}}$ is the summation of three $L1$ distances between GT and prediction of: 1) MANO parameters 2) 3D joint coordinates obtained by multiplying joint regression matrix to hand mesh 3) 2D joint coordinates projected from 3D joint coordinates. + +# 5. Experiments + +# 5.1. Datasets and evaluation metrics + +BlurHand. The BlurHand (BH) is our newly presented 3D hand pose dataset containing realistic blurry hand images as + +
MethodsTrain setTest set
IH2.6MBH
I2L-MeshNet [22]IH2.6MBH22.2724.3029.1624.32
METRO [16]IH2.6MBH18.4420.1935.4320.54
Pose2Pose [21]IH2.6MBH16.8518.4025.3618.80
BlurHandNet (Ours)IH2.6MBH15.3316.1224.5716.80
+ +![](images/083823b5dc65b68c337cf79ff6bfc803477a9d86459916d1a85856b8cffb77b5.jpg) +Figure 6. Examples of deblurred images. Since the blurry hand undergoes challenging blur from complex articulation, even the state-of-the-art deblurring method [3] cannot fully restore and blur artifact remains, highlighted with red circles. + +introduced in Section 3. We train and test the 3D hand mesh estimation networks on the train and test splits of the BH. + +InterHand2.6M. InterHand2.6M [23] (IH2.6M) is a recently presented large-scale 3D hand dataset. It is captured under highly calibrated camera settings and provides accurate 3D annotations for hand images. We employ IH2.6M as a representative of sharp hand frames, as the hand images in IH2.6M do not contain blur. We use a subset of IH2.6M for training and testing purposes, where the subset is a set of the third sharp frame in Figure 2 for each image of BH. + +YT-3D. YouTube-3D-hands (YT-3D) [13] is a 3D hand dataset with diverse and non-laboratory videos collected from youtube. We utilize the YT-3D as an additional training dataset when testing on YT-3D. Since YT-3D does not provide 3D GTs, we only provide a qualitative comparison of this dataset without quantitative evaluations. + +Evaluation metrics. We use mean per joint position error (MPJPE) and mean per vertex position error (MPVPE) as our evaluation metrics. The metrics measure Euclidean distance (mm) between estimated coordinates and groundtruth coordinates. Before calculating the metrics, we align the translation of the root joint (i.e., wrist). + +# 5.2. Ablation study + +Benefit of BlurHand dataset. Directly measuring how much synthesized blur is close to the real one is still an open research problem in the deblurring community [11, 48]. Hence, we justify the usefulness of the presented BlurHand + +Table 1. Effectiveness of BlurHand on handling blurry hand. We calculate MPJPE (mm) on hand meshes located in the middle of the motion. + +
MethodsTrain setTest setMPIPE (mm)MPVPE (mm)
I2L-MeshNet [22]IH2.6MBH+Deblur26.5625.23
BH+DeblurBH+Deblur26.1325.00
BHBH24.3223.08
METRO [16]IH2.6MBH+Deblur26.0732.05
BH+DeblurBH+Deblur20.1126.55
BHBH20.5427.03
Pose2Pose [21]IH2.6MBH+Deblur22.4321.04
BH+DeblurBH+Deblur18.8117.43
BHBH18.8017.42
BlurHandNet (Ours)IH2.6MBH+Deblur21.3719.93
BH+DeblurBH+Deblur17.2815.82
BHBH16.8015.30
+ +Table 2. Effectiveness of BlurHand compared to deblurring baseline. MPJPE and MPVPE are calculated at hand meshes located in the middle of the motion. + +![](images/94db369548dc3d2d65cfaa4b2a66c8171b38c52d7a8d67d448ae4655a4a5ee6d.jpg) +Figure 7. Qualitative comparison on real-world blurry hand images. The captions below figures describe datasets used to train 3D hand mesh estimation networks. A setting with $\mathbf{D}$ represents that the network is trained on deblurred BH and tested on (b). + +using indirect commonly used protocols [11], i.e., train the model with the presented dataset and test it on unseen blurry images. Table 1 shows that all 3D hand mesh recovery networks trained on InterHand2.6M suffer severe performance drops when they are tested on BlurHand, while networks trained on BlurHand perform well. These experimental results validate that training on BlurHand is necessary when handling the blurry hand. In addition, networks trained on BlurHand also perform well on InterHand2.6M, which consists of sharp images. This shows the generalizability of our dataset to sharp images. + +Table 2 shows that utilizing presented BlurHand is more valuable than applying deblurring methods [3]. The deblurring method [3], trained on our BlurHand as a pre-trained deblurring network, performs poorly on our BlurHand. Moreover, the networks trained on sharp images (IH2.6M) or deblurred images and tested on deblurred images perform worse than those trained and tested on our BlurHand. Such comparisons demonstrate the usefulness of our BlurHand dataset compared to applying deblurring methods. One reason is that, as Figure 6 shows, deblurring methods often fail to restore sharp hand images due to complicated hand motions. Another reason is that deblurring removes temporal information from the blurry image, which is helpful for reconstructing accurate 3D hand mesh sequences. + +
DeblurUnfolderKTFormerMPJPE
initialmiddlefinal
XXX-17.89-
XX✓-17.41-
X✓X18.9417.5519.05
X✓✓18.0816.8018.21
✓XX-17.28-
✓✓✓18.9517.2819.10
+ +Table 3. Ablation study on proposed Unfolder and KTFormer. (√ in Deblur): The experiments with the Deblur item checked are trained and tested on deblurred BlurHand. (Second row): We only employ features from a single time step when applying KTFormer, as temporal information does not exist without Unfolder. + +
# of unfoldingMPJPE
initialinitial*middlefinal*final
1--17.41--
3 (BlurHandNet)18.08-16.80-18.21
518.0617.1816.7817.3618.18
+ +Figure 7 provides a qualitative comparison of real-world blurry images in YT-3D, which further demonstrates the usefulness of our BlurHand. We train BlurHandNet on three different combinations of datasets: 1) InterHand2.6M and YT-3D (7b), 2) deblurred BlurHand and YT-3D (7c), and 3) BlurHand and YT-3D (7d). The comparison shows that networks trained on BlurHand produce the most robust 3D meshes, demonstrating the generalizability of BlurHand. + +Effectiveness of Unfolder and KTFormer. Table 3 shows that using both Unfolder and KTFormer improves 3D mesh estimation accuracy by a large margin. As the proposed Unfolder allows a single image to be regarded as three sequential hands, we evaluate hands in both ends and middle of the motion. Since the temporal order of hand meshes in both ends (i.e., $\mathbf{V}_{\mathrm{E1}}$ and $\mathbf{V}_{\mathrm{E2}}$ ) is not determined, we report better MPJPE among the initial-final and final-initial pairs following [1, 36]. Solely employing one of Unfolder or KTFormer (the second and third rows) shows a slight improvement over the baseline network, which is designed without any of the proposed modules (the first row). On the other hand, our BlurHandNet (the fourth row) results in great performance boosts, by benefiting from the combination of two modules that effectively complement each other. In particular, KTFormer benefits from temporal information which is provided by Unfolder. Consequently, introducing both Unfolder and KTFormer, which have strong synergy, consistently improves the 3D errors in all time steps. + +In the point of the baseline (the first row), using our two proposed modules, Unfolder and KTFormer, leads to more performance gain (the fourth row) than training and testing a network on deblurred BlurHand (the fifth row). This comparison shows that utilizing proposed modules is more effective than using deblurring methods. Interestingly, us + +Table 4. Ablation study on the number of unfolded hands. The initial* and final* denote hands between the initial and middle, and the middle and final, respectively. + +
KinematicTemporalMPJPE
initialmiddlefinal
XX18.9917.7919.06
✓X18.2816.9218.34
X✓18.7917.4118.92
✓✓18.0816.8018.21
+ +Table 5. Ablation study on the kinematic and temporal positional embeddings. + +
Temporal order invariant lossUnfolder-driven temporal orderingMPJPE
initialmiddlefinal
XX18.7216.9818.86
✓X18.4417.1418.55
✓✓18.0816.8018.21
+ +Table 6. Ablation study on proposed loss functions. + +ing our two modules does not bring performance gain when training and testing on deblurred BlurHand (the last row) compared to the deblur baseline (the fifth row). This validates our statement that deblurring prohibits networks from utilizing temporal information. + +Effect of the number of unfolded hands. Table 4 shows that unfolding more sequential hands further improves the 3D errors. As our KTFormaler utilizes temporal information to enhance the joint feature, the number of hand sequences can affect the overall performance. Although unfolding a blurry hand into five sequential hands shows the best results, the performance is nearly saturated when a blurry hand is unfolded into three sequential hands. Considering the increased computational costs of producing additional hands and the temporal input size of KTFormaler, we design our Unfolder to produce three sequential hands. We note that our BlurHandNet can be easily extended if more number of unfolding is needed for some applications. + +Effect of the kinematic and temporal positional embeddings. Table 5 shows that our positional embedding setting, which uses both kinematic and temporal positional embedding, achieves the best performance. We design four variants with different positional embedding settings. The second and third rows, where either one of kinematic and temporal positional embedding is applied, achieve better results than a baseline without any positional embedding (the first row), but worse results than ours (the last row). This indicates that positional information of both kinematic and temporal dimensions is necessary for KTFounder. + +Effectiveness of the proposed loss functions. Table 6 shows that two proposed items in our loss function, temporal order-invariant loss and Unfolder-driven temporal ordering as introduced in Section 4.4, are necessary for the high performance. We compare three variants for loss design at both ends of the motion, while keeping the loss function for the middle of the motion the same. In detail, the settings without temporal order-invariant loss are supervised with 3D meshes following the GT temporal order instead of determining the order based on Eq. 6. On the other hand, + +![](images/0cbb0ea66dfe221d581b38b8f92f2bae1c5405d01e793f5234fedbddf4b4269b.jpg) +Figure 8. Visual comparison of the BlurHandNet and state-of-the-art 3D hand mesh estimation methods [16,21] on BlurHand. + +![](images/8f8a8a8e1d3833a4b91e136ac4d0cc32122a51e790ca21305c05642c9d3b1ccb.jpg) +Figure 9. Visualization of attention map from KTFormer. The pixel at location $(i,j)$ represents the correlation between $i$ -th joint feature and $j$ -th joint feature. The attention map is obtained after performing a softmax operation across each row (query). + +the setting without Unfolder-driven temporal ordering supervises Regressor with Regressor-driven temporal ordering, which indicates that Unfolder and Regressor can be supervised with different temporal ordering. Since inferring the temporal order of GT is ambiguous, the setting without temporal order-invariant loss degrades the performance as it forces to strictly follows the temporal order of GT. Utilizing the proposed Unfolder-driven temporal ordering performs the best, as it provides consistent temporal order to both Unfolder and Regressor, making the training stable. + +Visualization of attention map from KTFormer. Figure 9 shows a visualized attention map, obtained by the self-attention operation in KTFormer. Here, query and key are obtained from a combination of temporal joint features $\mathbf{F}_{\mathrm{JE1}}$ , $\mathbf{F}_{\mathrm{JC}}$ , and $\mathbf{F}_{\mathrm{JE1}}$ , as described in Section 4.2. The figure shows that our attention map produces two diagonal lines, representing a strong correlation between the corresponding query and key. Specifically, features from both ends of motion, $\mathbf{F}_{\mathrm{JE1}}$ and $\mathbf{F}_{\mathrm{JE2}}$ (the first and third queries), show high correlation with the middle hand feature $\mathbf{F}_{\mathrm{JM}}$ (the second key), and $\mathbf{F}_{\mathrm{JM}}$ (the second query) shows high correlation with $\mathbf{F}_{\mathrm{JE1}}$ and $\mathbf{F}_{\mathrm{JE2}}$ (the first and third keys). This indicates + +that temporal information is highly preferred to compensate for insufficient joint information in a certain time step. This is also consistent with the result in Table 3. In the second row of Table 3, solely employing KTFormer without Unfolder shows slight performance improvement over the baseline due to the lack of opportunity to exploit temporal information from both ends. + +# 5.3. Comparison with state-of-the-art methods + +Table 1 and 2 show that our BlurHandNet outperforms the previous state-of-the-art 3D hand mesh estimation methods in all settings. As the previous works [16,21,22] do not have a special module to address blurs, they fail to produce accurate 3D meshes from blurry hand images. On the contrary, by effectively handling the blur using temporal information, our BlurHandNet robustly estimates the 3D hand mesh, even under abrupt motion. Figure 8 further shows that our BlurHandNet produces much better results than previous methods on BlurHand. + +# 6. Conclusion + +We present the BlurHand dataset, containing realistic blurry hand images with 3D GTs, and the baseline network BlurHandNet. Our BlurHandNet regards a single blurry hand image as sequential hands to utilize the temporal information from sequential hands, which makes the network robust to the blurriness. Experimental results show that BlurHandNet achieves state-of-the-art performance in estimating 3D meshes from the newly proposed BlurHand and real-world test sets. + +Acknowledgments. This work was supported in part by the IITP grants [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University), No.2022-0-00156, No. 2021-0-02068, and No.2022-0-00156], and the NRF grant [No. 2021M3A9E4080782] funded by the Korea government (MSIT). + +# References + +[1] D. M. Argaw, J. Kim, F. Rameau, C. Zhang, and I. S. Kweon. Restoration of video frames from a single blurred image with motion understanding. In CVPR, 2019. 3, 7 +[2] Mehrez Boulares and Mohamed Jemni. Automatic hand motion analysis for the sign language space management. 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Freihand: A dataset for markerless capture of hand pose and shape from single RGB images. 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However, we can not identify whether the hand at each end (i.e., " + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "text", + "content": ") is come from the initial or final location of the motion due to the temporal ambiguity [12, 28, 33, 47]. For example, suppose that we obtain the blurry hand image shown in Figure 4d. Then we can not determine whether the blurry hand image comes from the motion of extending or folding. In that regard, Unfolder outputs hand features from both ends of the motion (i.e., " + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 376, + 287, + 555 + ], + "type": "text", + "content": ") without considering temporal order. We note that exploiting the temporal information still benefits without explicitly considering the temporal order, and can further be stably optimized with the training loss introduced in Section 4.4." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Extracting temporal joint features. From produced three sequential hand features, we extract the corresponding joint features, which contain essential hand articulation information [21] that helps to recover 3D hand meshes. We first project the sequential hand features " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "dJ" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " dimensional feature through " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " convolution layer, and reshape them into 3D heatmaps with the dimension of " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{J \\times h \\times w \\times d}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "d = 32" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " is a depth discretization size and " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "J = 21" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " is a number of hand joints. Then, we perform a soft-argmax operation [41] on each heatmap to obtain the 3D joint coordinates of three temporal hands, " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " with dimension of " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{J \\times 3}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ". Using 3D joint coordinates in each temporal hand, we perform grid sampling [10, 21]" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 257, + 545, + 363 + ], + "blocks": [ + { + "bbox": [ + 309, + 257, + 545, + 363 + ], + "lines": [ + { + "bbox": [ + 309, + 257, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 309, + 257, + 545, + 363 + ], + "type": "image", + "image_path": "71df2cf2c26d3eddebeb0eb9f27f2b5c53dd9aa2cb8285177bdaea560d588405.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "lines": [ + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": "Figure 5. Overall architecture of KTFormer. KTFormer refines temporal joint features " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E1}}}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E2}}}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": ". First, kinematic and temporal positional embeddings are introduced. Then, the following self-attention mechanism refines joint features by leveraging attentive correlation between them, producing " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}" + }, + { + "bbox": [ + 305, + 365, + 546, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "content": "on the corresponding feature map. By doing so, we obtain temporal joint features " + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E1}}}" + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E2}}}" + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}" + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "content": " with a dimension of " + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{J\\times c}" + }, + { + "bbox": [ + 305, + 434, + 547, + 482 + ], + "type": "text", + "content": ", which enable the following module to exploit temporal information effectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 491, + 380, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 380, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 380, + 502 + ], + "type": "text", + "content": "4.2. KTFormer" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": "Kinematic-temporal positional embedding. The illustration of KTFormer is shown in Figure 5. KTFormer is the Transformer [42]-based module that refines the joint feature " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E1}}}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E2}}}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": " by considering the correlation between not only joints at the same time step but also joints at different time steps. To utilize the temporal joint features as an input of Transformer, we first concatenate the three features along the joint dimension, producing " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_J} \\in \\mathbb{R}^{3J \\times c}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": ". Then, a learnable positional embedding, namely kinematic and temporal positional embeddings, is applied to " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_J}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": ". The kinematic positional embedding " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\in \\mathbb{R}^{J \\times c}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": " is applied along the joints dimension, while the temporal positional embedding " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\in \\mathbb{R}^{3 \\times c}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": " is applied along the temporal dimension. The kinematic and temporal positional embedding provide relative positions in kinematic and temporal space, respectively. Joint feature refinement with self-attention. KTFormer performs self-attention within " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F_J}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": " by extracting query " + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "text", + "content": "557" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": "key " + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{k}" + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": " through three fully-connected layers. Following the formulation of the standard Transformer [42], refined joint features for sequential hands " + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E1}}}^{\\prime}" + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_{E2}}}^{\\prime}" + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}^{\\prime}" + }, + { + "bbox": [ + 46, + 72, + 287, + 122 + ], + "type": "text", + "content": " are formulated as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 129, + 287, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 129, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 99, + 129, + 287, + 158 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {k} ^ {T}}{\\sqrt {d _ {\\mathbf {k}}}}\\right) \\mathbf {v}, \\tag {1}", + "image_path": "9764eebfb2fbd6a3e967dbdab827882678b77a0572f6d44e40aa42fa3a0925d5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 118, + 165, + 287, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 165, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 118, + 165, + 287, + 179 + ], + "type": "interline_equation", + "content": "\\mathbf {R} = \\mathbf {F} _ {\\mathrm {J}} + \\operatorname {A t t} (\\mathbf {q}, \\mathbf {k}, \\mathbf {v}), \\tag {2}", + "image_path": "95df4cf423d8d53a17b239a288e86320893730e10d0f077d4d91665c26223189.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 189, + 287, + 203 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 189, + 287, + 203 + ], + "spans": [ + { + "bbox": [ + 91, + 189, + 287, + 203 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 1}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {E} 2}} ^ {\\prime}, \\mathbf {F} _ {\\mathrm {J} _ {\\mathrm {M}}} ^ {\\prime} = \\psi (\\mathbf {F} _ {\\mathrm {J}} + \\operatorname {M L P} (\\mathbf {R})), \\tag {3}", + "image_path": "e3ce395ada1939b09b2b0192f6a7e4f84ddc44852a36aeb8accb00c492b15086.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "d_{\\mathbf{k}} = 512" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": " is the feature dimension of the key " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{k}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": " is the residual feature. MLP denotes multi-layer perceptron, and " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": " denotes a dividing operation, which separates features in dimension " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{3J\\times c}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": " to three " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{J\\times c}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": ". Consequently, three joint features " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE_1}}^{\\prime},\\mathbf{F}_{\\mathrm{JE_2}}^{\\prime}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JM}}^{\\prime}" + }, + { + "bbox": [ + 46, + 207, + 287, + 280 + ], + "type": "text", + "content": " are obtained by attentively utilizing kinematic and temporal information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 286, + 117, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 117, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 117, + 300 + ], + "type": "text", + "content": "4.3. Regressor" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": "The Regressor produces MANO [35] shape (i.e., " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ") and pose (i.e., " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ") parameters, which correspond to sequential hands. We describe the regression process of the middle hand (i.e., " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ") as a representative procedure, and note that the process at different timesteps can be obtained in the same manner. First, the shape parameter " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\beta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " is obtained by forwarding the hand feature " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " to a fully-connected layer after global average pooling [18]. Second, the pose parameter " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " is obtained by considering the kinematic correlation between hand joints. To this end, we first concatenate refined joint feature " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{J_M}}'" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " with corresponding 3D coordinates " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ". Then, we flatten the concatenated feature into one-dimensional vector " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{M}} \\in \\mathbb{R}^{J(c + 3)}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ". Instead of regressing poses of entire joints from " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " at once, the Regressor gradually estimates pose for each joint along the hierarchy of hand kinematic tree, following [43]. In detail, for a specific joint, its ancestral pose parameters and " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": " are concatenated, and forwarded to a fully-connected layer to regress the pose parameters. By adopting the same process for both ends, three MANO parameters are obtained from the Regressor. Then, the MANO parameters are forwarded to the MANO layer to produce 3D hand meshes " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\mathrm{E1}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\mathrm{E2}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 304, + 287, + 593 + ], + "type": "text", + "content": ", where each denotes to meshes at both ends and middle, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 599, + 130, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 130, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 130, + 612 + ], + "type": "text", + "content": "4.4. Training loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "During the training, a prediction on the middle of the motion can be simply supervised with GT of the middle frame. On the other hand, it is ambiguous to supervise both ends of motion as the temporal order is not uniquely determined, as shown in Figure 4. To resolve such temporal ambiguity during the loss calculation, we propose two items. First, we employ temporal order-invariant loss, which is invariant to GT temporal order [36]. To be specific, the temporal order" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "in our loss function is determined in the direction that minimizes loss functions, not by the GT temporal order. Second, we propose to use a Unfolder-driven temporal ordering. It determines the temporal order based on the output of Unfolder, then uses the determined temporal order to supervise the outputs of Regressor rather than determining the temporal order of two modules separately. The effectiveness of the two items is demonstrated in the experimental section." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 167, + 516, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 167, + 516, + 179 + ], + "spans": [ + { + "bbox": [ + 317, + 167, + 516, + 179 + ], + "type": "text", + "content": "The overall loss function " + }, + { + "bbox": [ + 317, + 167, + 516, + 179 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 317, + 167, + 516, + 179 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 355, + 180, + 545, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 180, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 355, + 180, + 545, + 208 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {U}} + \\mathcal {L} _ {\\mathrm {R}} \\\\ = \\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} + \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}}, \\tag {4} \\\\ \\end{array}", + "image_path": "5aaaa54dbf6c8c4964e6740bb05262ecaf28c5a8d1697f0b0909b3f2f50ecfe1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{U}}" + }, + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{R}}" + }, + { + "bbox": [ + 304, + 213, + 545, + 249 + ], + "type": "text", + "content": " are loss functions applied to outputs of the Unfolder and the Regressor, respectively. The subscripts M and E stand for prediction of the middle and both ends." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "text", + "content": "To supervise outputs of Unfolder, we define " + }, + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{U,M}}" + }, + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{U,E}}" + }, + { + "bbox": [ + 306, + 250, + 545, + 273 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 370, + 279, + 545, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 279, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 370, + 279, + 545, + 293 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {U}, \\mathrm {M}} = \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {M}}, \\mathbf {J} _ {\\text {m i d d l e}} ^ {*}\\right), \\tag {5}", + "image_path": "75fc3cd966ff84111751e4bdca05db00bc280f987d0ab172e9f787161b6ed55f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 299, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 299, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 318, + 299, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {U}, \\mathrm {E}} = \\min (\\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}) + \\mathcal {L} _ {\\text {j o i n t}} (\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*})), \\\\ \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 1}, \\mathbf {J} _ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {j o i n t}} \\left(\\mathbf {J} _ {\\mathrm {E} 2}, \\mathbf {J} _ {\\text {i n i t i a l}} ^ {*}\\right)), \\tag {6} \\\\ \\end{array}", + "image_path": "cda0fda16c89d5fc64cf89cff407f3b4660ea718b5b21668cf3cdc89df10f0aa.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{middle}}^{*}, \\mathbf{J}_{\\mathrm{initial}}^{*}" + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\mathrm{final}}^{*}" + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "content": " are GT 3D joint coordinates of the middle, initial and final frame, respectively. " + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{joint}}" + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 304, + 344, + 545, + 427 + ], + "type": "text", + "content": " distance between predicted and GT joint coordinates. The temporal order is determined to forward if the first term in min of Eq. 6 is selected as minimum and backward otherwise. Therefore, our loss function is invariant to the temporal order of GT." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "content": "To supervise the outputs of the Regressor, we define the loss function " + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{R,M}}" + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{R,E}}" + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 367, + 458, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 458, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 367, + 458, + 545, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R}, \\mathrm {M}} = \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {M}}, \\Theta_ {\\text {m i d d l e}} ^ {*}\\right), \\tag {7}", + "image_path": "4744b79de0f8d296c5654899843b094f0f7c873d167eed90a157cbea0432edd7.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 477, + 545, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 477, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 315, + 477, + 545, + 516 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R}, \\mathrm {E}} = \\mathbb {1} _ {\\mathbf {f}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right)\\right) \\\\ + \\mathbb {1} _ {\\mathbf {b}} \\left(\\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 1}, \\Theta_ {\\text {f i n a l}} ^ {*}\\right) + \\mathcal {L} _ {\\text {m e s h}} \\left(\\Theta_ {\\mathrm {E} 2}, \\Theta_ {\\text {i n i t i a l}} ^ {*}\\right)\\right), \\tag {8} \\\\ \\end{array}", + "image_path": "7a456847578c52b03f190d0b7da46b1b66963e8526730cb88b25dc5ef3c55571.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{\\mathbf{f}} = 1" + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": " when the temporal order is determined to forward in Eq. 6 otherwise 0, and " + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{\\mathbf{b}} = 1 - \\mathbb{1}_{\\mathbf{f}}" + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": ". In other words, the temporal order of Eq. 8 follows that of Eq. 6, which we call Unfolder-driven temporal ordering. " + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\Theta_{\\bullet} = \\{\\theta_{\\bullet}, \\beta_{\\bullet}\\}" + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": " is GT or predicted MANO parameters, where the superscript * denotes GT. " + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mesh}}" + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": " is the summation of three " + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 304, + 522, + 545, + 642 + ], + "type": "text", + "content": " distances between GT and prediction of: 1) MANO parameters 2) 3D joint coordinates obtained by multiplying joint regression matrix to hand mesh 3) 2D joint coordinates projected from 3D joint coordinates." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 651, + 387, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 387, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 387, + 664 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 671, + 477, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 477, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 477, + 682 + ], + "type": "text", + "content": "5.1. Datasets and evaluation metrics" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "BlurHand. The BlurHand (BH) is our newly presented 3D hand pose dataset containing realistic blurry hand images as" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "558" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 71, + 261, + 175 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 261, + 175 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 261, + 175 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 261, + 175 + ], + "type": "table", + "html": "
MethodsTrain setTest set
IH2.6MBH
I2L-MeshNet [22]IH2.6MBH22.2724.3029.1624.32
METRO [16]IH2.6MBH18.4420.1935.4320.54
Pose2Pose [21]IH2.6MBH16.8518.4025.3618.80
BlurHandNet (Ours)IH2.6MBH15.3316.1224.5716.80
", + "image_path": "3ddeb2d0f024a9981b2e6919efafbaf7ca994a0f82d4d2c5c8aee2f1747a645b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 217, + 279, + 316 + ], + "blocks": [ + { + "bbox": [ + 48, + 217, + 279, + 316 + ], + "lines": [ + { + "bbox": [ + 48, + 217, + 279, + 316 + ], + "spans": [ + { + "bbox": [ + 48, + 217, + 279, + 316 + ], + "type": "image", + "image_path": "083823b5dc65b68c337cf79ff6bfc803477a9d86459916d1a85856b8cffb77b5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 317, + 286, + 361 + ], + "lines": [ + { + "bbox": [ + 47, + 317, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 286, + 361 + ], + "type": "text", + "content": "Figure 6. Examples of deblurred images. Since the blurry hand undergoes challenging blur from complex articulation, even the state-of-the-art deblurring method [3] cannot fully restore and blur artifact remains, highlighted with red circles." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 376, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 286, + 399 + ], + "type": "text", + "content": "introduced in Section 3. We train and test the 3D hand mesh estimation networks on the train and test splits of the BH." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 286, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 286, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 286, + 495 + ], + "type": "text", + "content": "InterHand2.6M. InterHand2.6M [23] (IH2.6M) is a recently presented large-scale 3D hand dataset. It is captured under highly calibrated camera settings and provides accurate 3D annotations for hand images. We employ IH2.6M as a representative of sharp hand frames, as the hand images in IH2.6M do not contain blur. We use a subset of IH2.6M for training and testing purposes, where the subset is a set of the third sharp frame in Figure 2 for each image of BH." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 495, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 286, + 567 + ], + "type": "text", + "content": "YT-3D. YouTube-3D-hands (YT-3D) [13] is a 3D hand dataset with diverse and non-laboratory videos collected from youtube. We utilize the YT-3D as an additional training dataset when testing on YT-3D. Since YT-3D does not provide 3D GTs, we only provide a qualitative comparison of this dataset without quantitative evaluations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 567, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 286, + 639 + ], + "type": "text", + "content": "Evaluation metrics. We use mean per joint position error (MPJPE) and mean per vertex position error (MPVPE) as our evaluation metrics. The metrics measure Euclidean distance (mm) between estimated coordinates and groundtruth coordinates. Before calculating the metrics, we align the translation of the root joint (i.e., wrist)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 647, + 138, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 138, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 138, + 659 + ], + "type": "text", + "content": "5.2. Ablation study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Benefit of BlurHand dataset. Directly measuring how much synthesized blur is close to the real one is still an open research problem in the deblurring community [11, 48]. Hence, we justify the usefulness of the presented BlurHand" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 319, + 71, + 533, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 176, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 47, + 176, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 287, + 208 + ], + "type": "text", + "content": "Table 1. Effectiveness of BlurHand on handling blurry hand. We calculate MPJPE (mm) on hand meshes located in the middle of the motion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 71, + 533, + 198 + ], + "lines": [ + { + "bbox": [ + 319, + 71, + 533, + 198 + ], + "spans": [ + { + "bbox": [ + 319, + 71, + 533, + 198 + ], + "type": "table", + "html": "
MethodsTrain setTest setMPIPE (mm)MPVPE (mm)
I2L-MeshNet [22]IH2.6MBH+Deblur26.5625.23
BH+DeblurBH+Deblur26.1325.00
BHBH24.3223.08
METRO [16]IH2.6MBH+Deblur26.0732.05
BH+DeblurBH+Deblur20.1126.55
BHBH20.5427.03
Pose2Pose [21]IH2.6MBH+Deblur22.4321.04
BH+DeblurBH+Deblur18.8117.43
BHBH18.8017.42
BlurHandNet (Ours)IH2.6MBH+Deblur21.3719.93
BH+DeblurBH+Deblur17.2815.82
BHBH16.8015.30
", + "image_path": "9c75fd1d29cb1eddeaab5a6c8aeaf15ae288af3522372efdb575abe76aac45ef.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 200, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 232 + ], + "type": "text", + "content": "Table 2. Effectiveness of BlurHand compared to deblurring baseline. MPJPE and MPVPE are calculated at hand meshes located in the middle of the motion." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 240, + 545, + 353 + ], + "blocks": [ + { + "bbox": [ + 307, + 240, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 307, + 240, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 545, + 353 + ], + "type": "image", + "image_path": "94db369548dc3d2d65cfaa4b2a66c8171b38c52d7a8d67d448ae4655a4a5ee6d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 357, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 399 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison on real-world blurry hand images. The captions below figures describe datasets used to train 3D hand mesh estimation networks. A setting with " + }, + { + "bbox": [ + 305, + 357, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 305, + 357, + 545, + 399 + ], + "type": "text", + "content": " represents that the network is trained on deblurred BH and tested on (b)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 413, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 544 + ], + "type": "text", + "content": "using indirect commonly used protocols [11], i.e., train the model with the presented dataset and test it on unseen blurry images. Table 1 shows that all 3D hand mesh recovery networks trained on InterHand2.6M suffer severe performance drops when they are tested on BlurHand, while networks trained on BlurHand perform well. These experimental results validate that training on BlurHand is necessary when handling the blurry hand. In addition, networks trained on BlurHand also perform well on InterHand2.6M, which consists of sharp images. This shows the generalizability of our dataset to sharp images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Table 2 shows that utilizing presented BlurHand is more valuable than applying deblurring methods [3]. The deblurring method [3], trained on our BlurHand as a pre-trained deblurring network, performs poorly on our BlurHand. Moreover, the networks trained on sharp images (IH2.6M) or deblurred images and tested on deblurred images perform worse than those trained and tested on our BlurHand. Such comparisons demonstrate the usefulness of our BlurHand dataset compared to applying deblurring methods. One reason is that, as Figure 6 shows, deblurring methods often fail to restore sharp hand images due to complicated hand motions. Another reason is that deblurring removes temporal information from the blurry image, which is helpful for reconstructing accurate 3D hand mesh sequences." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "559" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 71, + 261, + 155 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 261, + 155 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 261, + 155 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 261, + 155 + ], + "type": "table", + "html": "
DeblurUnfolderKTFormerMPJPE
initialmiddlefinal
XXX-17.89-
XX✓-17.41-
X✓X18.9417.5519.05
X✓✓18.0816.8018.21
✓XX-17.28-
✓✓✓18.9517.2819.10
", + "image_path": "74400f70b77d2fa23f9db4087aeb138d25c13457afb86bbc92429e9ba6e95c62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 67, + 216, + 267, + 269 + ], + "blocks": [ + { + "bbox": [ + 47, + 156, + 286, + 210 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 210 + ], + "type": "text", + "content": "Table 3. Ablation study on proposed Unfolder and KTFormer. (√ in Deblur): The experiments with the Deblur item checked are trained and tested on deblurred BlurHand. (Second row): We only employ features from a single time step when applying KTFormer, as temporal information does not exist without Unfolder." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 216, + 267, + 269 + ], + "lines": [ + { + "bbox": [ + 67, + 216, + 267, + 269 + ], + "spans": [ + { + "bbox": [ + 67, + 216, + 267, + 269 + ], + "type": "table", + "html": "
# of unfoldingMPJPE
initialinitial*middlefinal*final
1--17.41--
3 (BlurHandNet)18.08-16.80-18.21
518.0617.1816.7817.3618.18
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KinematicTemporalMPJPE
initialmiddlefinal
XX18.9917.7919.06
✓X18.2816.9218.34
X✓18.7917.4118.92
✓✓18.0816.8018.21
", + "image_path": "c9e80f88be35b6c611087bb7a82028ed3deeb3cbc06f72f2eafbbdc3abd007a0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 331, + 163, + 520, + 217 + ], + "blocks": [ + { + "bbox": [ + 306, + 136, + 544, + 157 + ], + "lines": [ + { + "bbox": [ + 306, + 136, + 544, + 157 + ], + "spans": [ + { + "bbox": [ + 306, + 136, + 544, + 157 + ], + "type": "text", + "content": "Table 5. Ablation study on the kinematic and temporal positional embeddings." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 163, + 520, + 217 + ], + "lines": [ + { + "bbox": [ + 331, + 163, + 520, + 217 + ], + "spans": [ + { + "bbox": [ + 331, + 163, + 520, + 217 + ], + "type": "table", + "html": "
Temporal order invariant lossUnfolder-driven temporal orderingMPJPE
initialmiddlefinal
XX18.7216.9818.86
✓X18.4417.1418.55
✓✓18.0816.8018.21
", + "image_path": "efb4d4b6e001ba5b05a4e620ea90da2085af5d7e2837292527952b9a095554b4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 328, + 218, + 523, + 229 + ], + "lines": [ + { + "bbox": [ + 328, + 218, + 523, + 229 + ], + "spans": [ + { + "bbox": [ + 328, + 218, + 523, + 229 + ], + "type": "text", + "content": "Table 6. Ablation study on proposed loss functions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 244, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 244, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 244, + 545, + 303 + ], + "type": "text", + "content": "ing our two modules does not bring performance gain when training and testing on deblurred BlurHand (the last row) compared to the deblur baseline (the fifth row). This validates our statement that deblurring prohibits networks from utilizing temporal information." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": "Effect of the number of unfolded hands. Table 4 shows that unfolding more sequential hands further improves the 3D errors. As our KTFormaler utilizes temporal information to enhance the joint feature, the number of hand sequences can affect the overall performance. Although unfolding a blurry hand into five sequential hands shows the best results, the performance is nearly saturated when a blurry hand is unfolded into three sequential hands. Considering the increased computational costs of producing additional hands and the temporal input size of KTFormaler, we design our Unfolder to produce three sequential hands. We note that our BlurHandNet can be easily extended if more number of unfolding is needed for some applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 461, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 545, + 592 + ], + "type": "text", + "content": "Effect of the kinematic and temporal positional embeddings. Table 5 shows that our positional embedding setting, which uses both kinematic and temporal positional embedding, achieves the best performance. We design four variants with different positional embedding settings. The second and third rows, where either one of kinematic and temporal positional embedding is applied, achieve better results than a baseline without any positional embedding (the first row), but worse results than ours (the last row). This indicates that positional information of both kinematic and temporal dimensions is necessary for KTFounder." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of the proposed loss functions. Table 6 shows that two proposed items in our loss function, temporal order-invariant loss and Unfolder-driven temporal ordering as introduced in Section 4.4, are necessary for the high performance. We compare three variants for loss design at both ends of the motion, while keeping the loss function for the middle of the motion the same. In detail, the settings without temporal order-invariant loss are supervised with 3D meshes following the GT temporal order instead of determining the order based on Eq. 6. On the other hand," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "560" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 70, + 500, + 257 + ], + "blocks": [ + { + "bbox": [ + 95, + 70, + 500, + 257 + ], + "lines": [ + { + "bbox": [ + 95, + 70, + 500, + 257 + ], + "spans": [ + { + "bbox": [ + 95, + 70, + 500, + 257 + ], + "type": "image", + "image_path": "0cbb0ea66dfe221d581b38b8f92f2bae1c5405d01e793f5234fedbddf4b4269b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 260, + 538, + 272 + ], + "lines": [ + { + "bbox": [ + 54, + 260, + 538, + 272 + ], + "spans": [ + { + "bbox": [ + 54, + 260, + 538, + 272 + ], + "type": "text", + "content": "Figure 8. Visual comparison of the BlurHandNet and state-of-the-art 3D hand mesh estimation methods [16,21] on BlurHand." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 275, + 279, + 392 + ], + "blocks": [ + { + "bbox": [ + 58, + 275, + 279, + 392 + ], + "lines": [ + { + "bbox": [ + 58, + 275, + 279, + 392 + ], + "spans": [ + { + "bbox": [ + 58, + 275, + 279, + 392 + ], + "type": "image", + "image_path": "8f8a8a8e1d3833a4b91e136ac4d0cc32122a51e790ca21305c05642c9d3b1ccb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "lines": [ + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "text", + "content": "Figure 9. Visualization of attention map from KTFormer. The pixel at location " + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "text", + "content": " represents the correlation between " + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "text", + "content": "-th joint feature and " + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 394, + 288, + 439 + ], + "type": "text", + "content": "-th joint feature. The attention map is obtained after performing a softmax operation across each row (query)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 568 + ], + "type": "text", + "content": "the setting without Unfolder-driven temporal ordering supervises Regressor with Regressor-driven temporal ordering, which indicates that Unfolder and Regressor can be supervised with different temporal ordering. Since inferring the temporal order of GT is ambiguous, the setting without temporal order-invariant loss degrades the performance as it forces to strictly follows the temporal order of GT. Utilizing the proposed Unfolder-driven temporal ordering performs the best, as it provides consistent temporal order to both Unfolder and Regressor, making the training stable." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": "Visualization of attention map from KTFormer. Figure 9 shows a visualized attention map, obtained by the self-attention operation in KTFormer. Here, query and key are obtained from a combination of temporal joint features " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE1}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JC}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE1}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": ", as described in Section 4.2. The figure shows that our attention map produces two diagonal lines, representing a strong correlation between the corresponding query and key. Specifically, features from both ends of motion, " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE1}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE2}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " (the first and third queries), show high correlation with the middle hand feature " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JM}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " (the second key), and " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JM}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " (the second query) shows high correlation with " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE1}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{JE2}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": " (the first and third keys). This indicates" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 276, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 359 + ], + "type": "text", + "content": "that temporal information is highly preferred to compensate for insufficient joint information in a certain time step. This is also consistent with the result in Table 3. In the second row of Table 3, solely employing KTFormer without Unfolder shows slight performance improvement over the baseline due to the lack of opportunity to exploit temporal information from both ends." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 366, + 526, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 526, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 526, + 379 + ], + "type": "text", + "content": "5.3. Comparison with state-of-the-art methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 384, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 503 + ], + "type": "text", + "content": "Table 1 and 2 show that our BlurHandNet outperforms the previous state-of-the-art 3D hand mesh estimation methods in all settings. As the previous works [16,21,22] do not have a special module to address blurs, they fail to produce accurate 3D meshes from blurry hand images. On the contrary, by effectively handling the blur using temporal information, our BlurHandNet robustly estimates the 3D hand mesh, even under abrupt motion. Figure 8 further shows that our BlurHandNet produces much better results than previous methods on BlurHand." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 640 + ], + "type": "text", + "content": "We present the BlurHand dataset, containing realistic blurry hand images with 3D GTs, and the baseline network BlurHandNet. Our BlurHandNet regards a single blurry hand image as sequential hands to utilize the temporal information from sequential hands, which makes the network robust to the blurriness. Experimental results show that BlurHandNet achieves state-of-the-art performance in estimating 3D meshes from the newly proposed BlurHand and real-world test sets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was supported in part by the IITP grants [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University), No.2022-0-00156, No. 2021-0-02068, and No.2022-0-00156], and the NRF grant [No. 2021M3A9E4080782] funded by the Korea government (MSIT)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "561" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] D. 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In ICCV, 2019. 1, 2" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "text", + "content": "563" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_content_list.json b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..32e841a1b59c7fbb9947cd5a4cf56da86595ed77 --- /dev/null +++ b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_content_list.json @@ -0,0 +1,1464 @@ +[ + { + "type": "text", + "text": "Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Models", + "text_level": 1, + "bbox": [ + 153, + 131, + 816, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Paul Micaelli \nUniversity of Edinburgh \npaul.micaelli@ed.ac.uk", + "bbox": [ + 96, + 203, + 292, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Arash Vahdat NVIDIA \navahdat@nvidia.com", + "bbox": [ + 328, + 203, + 493, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hongxu Yin \nNVIDIA \ndanny@nvidia.com", + "bbox": [ + 529, + 203, + 684, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jan Kautz \nNVIDIA \njkautz@nvidia.com", + "bbox": [ + 720, + 203, + 872, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pavlo Molchanov \nNVIDIA", + "bbox": [ + 413, + 263, + 553, + 297 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pmolchanov@nvidia.com", + "bbox": [ + 387, + 303, + 576, + 315 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 351, + 313, + 367 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium Model (DEQ) can be naturally adapted to this form of computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching 3.92 NME with fewer parameters and a training memory cost of $\\mathcal{O}(1)$ in the number of recurrent modules. Furthermore, we show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labelled videos. This can lead to a \"flickering\" effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. By rephrasing DEQs as a constrained optimization, we emulate recurrence at inference time, despite not having access to temporal data at training time. This Recurrence without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we demonstrate by introducing a new metric, normalized mean flicker (NMF), and contributing a new facial landmark video dataset (WFLW-V) targeting landmark uncertainty. On the WFLW-V hard subset made up of 500 videos, our LDEQ with RwR improves the NME and NMF by 10 and $13\\%$ respectively, compared to the strongest previously published model using a hand-tuned conventional filter.", + "bbox": [ + 75, + 385, + 472, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 828, + 209, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The field of facial landmark detection has been fueled by important applications such as face recognition [49, 71], facial expression recognition [33, 37, 39, 43, 79], and face", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "alignment [55,87,89]. Early approaches to landmark detection relied on a statistical model of the global face appearance and shape [19,20,25], but this was then superseded by deep learning regression models [21,26,34,40,44,46,54,63, 68,69,73,75,77]. Both traditional and modern approaches have relied upon cascaded computation, an approach which starts with an initial guess of the landmarks and iteratively produces corrected landmarks which match the input face more finely. These iterations typically increase the training memory cost linearly, and do not have an obvious stopping criteria. To solve these issues, we adapt the recently proposed Deep Equilibrium Model [9-11] to the setting of landmark detection. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the WFLW dataset, while enjoying a natural stopping criteria and a memory cost that is constant in the number of cascaded iterations.", + "bbox": [ + 496, + 352, + 893, + 594 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, we explore the benefits of DEQs in landmark detection from facial videos. Since obtaining landmark annotation for videos is notoriously expensive, models are virtually always trained on still images and applied frame-wise on videos at inference time. When a sequence of frames have ambiguous landmarks (e.g., occluded faces or motion blur), this leads to flickering landmarks, which rapidly oscillate between different possible configurations across consecutive frames. This poor temporal coherence is particularly problematic in applications where high precision is required, which is typically the case for facial landmarks. These applications include face transforms [1, 2], face reenactment [84], video emotion recognition [33, 37, 39, 79], movie dubbing [28] or tiredness monitoring [35]. We propose to modify the DEQ objective at inference time to include a new recurrent loss term that encourages temporal coherence. We measure this improvement on our new WFLW-Video dataset (WFLW-V), demonstrating superiority over traditional filters, which typically reduce flickering at the cost of reducing landmark accuracy.", + "bbox": [ + 496, + 598, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22814", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/42c765552c189bfd97938713cc955b931477d682e7bdd882741ffa272c5e4cc7.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 133, + 87, + 872, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d678b5bd6312df57d1e05f64a4b01b4676f08b23d475dc97774e389a1c95e6d0.jpg", + "image_caption": [ + "(b)", + "Figure 1. (a) Common Stacked-Hourglass architecture [51], whereby each cascaded stage increases the memory cost and the number of backpropagation operations. (b) Our LDEQ model, which adapts an equilibrium model [9] to the landmark detection setting, enjoying a constant memory cost with the number of refining stages. At each stage, we compute landmark probability heatmaps, and encourage convergence to an equilibrium by lowering their entropy. We release our code here: https://github.com/polo5/LDEQ_RwR." + ], + "image_footnote": [], + "bbox": [ + 112, + 244, + 869, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 446, + 212, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Equilibrium Models [9] are part of the family of implicit models, which learn implicit functions such as the solution to an ODE [17, 24], or the solution to an optimization problem [3, 22, 72]. These functions are called implicit in the sense that the output cannot be written as a function of the input explicitly. In the case of DEQs, the output is the root of a function, and the model learned is agnostic to the root solver used. Early DEQ models were too slow to be competitive, and much work since has focused on better architecture design [10] and faster root solving [11, 27, 29]. Since the vanilla formulation of DEQs does not guarantee convergence or uniqueness of an equilibrium, another branch of research has focused on providing convergence guarantees [52, 56, 74], which usually comes at the cost of a performance drop. Most similar to our work is the recent use of DEQs for videos in the context of optical flow estimation [8], where slightly better performance than LSTM-based models was observed.", + "bbox": [ + 75, + 474, + 468, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A common theme throughout the development of landmark detection models has been the idea of cascaded compute, which has repeatedly enjoyed a better performance compared to single stage models [71]. This is true in traditional models like Cascaded Pose Regression (CPR) [7, 15, 23, 65, 78], but also in most modern landmark detection models [34, 40, 42, 69, 73, 75, 80], which usually rely on the Stacked-Hourglass backbone [51], or an RNN structure [41, 66]. In contrast to these methods, our DEQ-based model can directly solve for an infinite number of refine-", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ment stages at a constant memory cost and without gradient degradation. This is done by relying on the implicit function theorem, as opposed to tracking each forward operation in autograd. Furthermore, our model naturally supports adaptive compute, in the sense that the number of cascaded stages will be determined by how hard finding an equilibrium is for a specific input, while the number of stages in, say, the Stacked-Hourglass backbone, must be constant at all times.", + "bbox": [ + 496, + 449, + 890, + 584 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our recurrence without recurrence approach is most closely related to test time adaption methods. These have been most commonly developed in the context of domain adaptation [64,70], reinforcement learning [32], meta-learning [86], generative models [36, 50], pose estimation [45] or super resolution [6]. Typically, the methods above finetune a trained model at test time using a form of self-supervision. In contrast, our model doesn't need to be finetuned at test time: since DEQs solve for an objective function in the forward pass, this objective is simply modified at test time.", + "bbox": [ + 496, + 585, + 892, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. DEQs for landmark detection", + "text_level": 1, + "bbox": [ + 500, + 768, + 772, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consider learning a landmark detection model $F$ parameterized by $\\theta$ , which maps an input image $\\pmb{x}$ to landmarks $\\pmb{z}$ . Instead of directly having $\\pmb{z}$ as 2D landmarks, it is common for $\\pmb{z}$ to represent $L$ heatmaps of size $D\\times D$ , where $D$ is a hyperparameter (usually 64) and $L$ is the number of landmarks to learn. While typical machine learning models can explicitly write down the function $\\pmb{z} = F(\\pmb{x};\\pmb{\\theta})$ , in", + "bbox": [ + 496, + 794, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22815", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the DEQ approach this function is expressed implicitly by requiring its output to be a fixed point of another function $f(z, x; \\theta)$ :", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF: \\boldsymbol {x} \\rightarrow \\boldsymbol {z} ^ {*} \\quad \\text {s . t .} \\quad \\boldsymbol {z} ^ {*} = f (\\boldsymbol {z} ^ {*}, \\boldsymbol {x}; \\boldsymbol {\\theta}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 142, + 468, + 159 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z^{*}$ denotes the fixed point, or equivalently the root of $g(\\pmb{x},\\pmb{z};\\pmb{\\theta}) = f(\\pmb{z},\\pmb{x};\\pmb{\\theta}) - \\pmb{z}$ . The function $f$ must have inputs and outputs of similar shape, but beyond this restriction there is still limited understanding of its desired properties in machine learning. For simplicity, we build $f$ from the ubiquitous hourglass module $h$ (similar to a Unet):", + "bbox": [ + 76, + 164, + 468, + 255 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\boldsymbol {z}, \\boldsymbol {x}; \\boldsymbol {\\theta}) = \\sigma (h ([ \\boldsymbol {x}, \\boldsymbol {z} ]; \\boldsymbol {\\theta})) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 260, + 468, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h$ inputs the concatenation of $x$ and $z$ , and $\\sigma$ is a normalization function. For clarity, we omit from our notation that image $x$ is downsampled with a few convolutions to match the shape of $z$ .", + "bbox": [ + 76, + 282, + 468, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To evaluate $f$ in the forward pass, we must solve for its fixed point $z^{*}$ . When $f$ is a contraction mapping, $f \\circ f \\circ f \\circ \\dots \\circ f \\circ z^{(0)}$ converges to a unique $z^{*}$ for any initial heatmap $z^{(0)}$ . In practice, it is neither tractable or helpful to directly take an infinite number of fixed point iteration steps. Instead, it is common to achieve the same result by leveraging quasi Newtonian solvers like Broyden's method [13] or Anderson acceleration [4], which find $z^{*}$ in fewer iterations. Similarly to the original DEQ model, we use $z^{(0)} = 0$ when training our LDEQ on still images.", + "bbox": [ + 76, + 343, + 468, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Guaranteeing the existence of a unique fixed point by enforcing contraction restrictions on $f$ is cumbersome, and better performance can often be obtained by relying on regularization heuristics that are conducive to convergence, such as weight normalization and variational dropout [10]. In our landmark model, we did not find these tricks helpful, and instead used a simple normalization of the heatmaps to [0, 1] at each refining stage:", + "bbox": [ + 76, + 494, + 468, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma (z) = \\exp \\left(\\frac {z - \\operatorname* {m a x} (z)}{T}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 619, + 468, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T$ is a temperature hyperparameter. This layer also acts as an entropy regularizer, since it induces low-entropy (\"peaked\") heatmaps, which we found to improve convergence of root solvers.", + "bbox": [ + 76, + 657, + 468, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We contrast our model in Fig. 1 to the popular Stacked-Hourglass backbone [51]. Contrary to this model, our DEQ-based model uses a single hourglass module which updates $z$ until an equilibrium is found. The last predicted heatmaps, $z^{*}$ , are converted into 2D landmark points $\\hat{p} = \\Phi(z^{*})$ using the softargmax function $\\Phi(z)$ proposed in [48]. These points are trained to match the ground truth $p$ , and so the DEQ landmark training problem can be seen as a constrained optimization:", + "bbox": [ + 76, + 717, + 468, + 853 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {\\theta} ^ {*} = \\underset {\\boldsymbol {\\theta}} {\\arg \\min } \\mathcal {L} _ {\\text {M S E}} (\\Phi (\\boldsymbol {z} ^ {*}), \\boldsymbol {p}) \\tag {4} \\\\ \\text {s . t .} \\quad z ^ {*} = f \\left(z ^ {*}, x; \\theta\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 858, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To differentiate our loss function $\\mathcal{L}_{\\mathrm{MSE}}$ through this root solving process, the implicit function theorem is used [9] to derive", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {\\theta}} = - \\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {z} ^ {*}} \\mathcal {J} _ {\\boldsymbol {g} \\boldsymbol {z} ^ {*}} ^ {- 1} \\frac {\\partial f (\\boldsymbol {z} ^ {*} , \\boldsymbol {x} ; \\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 146, + 890, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the first two terms on the RHS can be expressed as the solution to a fixed point problem as well. Solving for this root in the backward pass means that we do not need to compute or store the expensive inverse Jacobian term $\\mathcal{I}_{gz^*}$ directly [9, 90]. Importantly, this backward-pass computation only depends on $z^*$ and doesn't depend on the operations done in the forward pass to reach an equilibrium. This means that these operations do not need to be tracked by autograd, and therefore that training requires a memory cost of O(1), despite differentiating through a potentially infinite recurrence.", + "bbox": [ + 498, + 189, + 890, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Recurrence without recurrence", + "text_level": 1, + "bbox": [ + 500, + 373, + 785, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Low temporal coherence (i.e. a large amount of flicker) is illustrated in Fig. 2. This can be a nuisance for many applications that require consistently precise landmarks for video. In this section, we describe how our LDEQ model can address this challenge by enabling recurrence at test time without recurrence at training time (RwR).", + "bbox": [ + 498, + 398, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall that in the DEQ formulation of Sec. 3, there is no guarantee that a unique fixed point solution exists. This can be a limitation for some applications, and DEQ variants have been proposed to allow provably unique solutions at the cost of additional model complexity [53, 74]. In this work, we instead propose a new paradigm: we leverage the potentially large solution space of DEQs after training to allow for some additional objective at inference time. This new objective is used to disambiguate which fixed point of $f(z, x; \\theta^*)$ is found, in light of extra information present at test time. We demonstrate this approach for the specific application of training a landmark model on face images and evaluating it on videos. In this case, DEQs allow us to include a recurrent loss term at inference time, which isn't achievable with conventional architectures.", + "bbox": [ + 498, + 491, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $f(\\pmb{z}, \\pmb{x}; \\pmb{\\theta}^*)$ be our DEQ model trained as per the formulation in Eq. (4). We would now like to do inference on a video of $N$ frames $\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N$ . Consider that a given frame $\\pmb{x}_n$ has a corresponding set of fixed points $\\mathcal{Z}_n^* = \\{z \\text { s.t. } f(\\pmb{z}, \\pmb{x}_n; \\pmb{\\theta}^*) = z\\}$ , representing plausible landmark heatmaps. If we select some $\\pmb{z}_n^* \\in \\mathcal{Z}_n^*$ at random for each frame $n$ , the corresponding heatmaps $\\pmb{z}_1^*, \\pmb{z}_2^*, \\dots, \\pmb{z}_N^*$ often exhibit some flickering artefacts, whereby landmarks rapidly change across contiguous frames (see Fig. 2). We propose to address this issue by choosing the fixed point at frame $n$ that is closest to the fixed point at frame $n - 1$ . This can be expressed by the following constrained optimization:", + "bbox": [ + 498, + 719, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22816", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/940ae187ce8860be61be775a2141fc6135f2f57afa6762279792835dee0190a7.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 106, + 101, + 890, + 213 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbdfcb43393c3cf82ea7defe20387d3e9d5418f3c7be6c79fd32e18b1c2a0a06.jpg", + "image_caption": [ + "(b)", + "Figure 2. Model predictions (▲) and ground truth landmarks (○) for (a) a model with high temporal coherence and (b) a model with the same accuracy but exhibiting a worse temporal coherence, due to ambiguity at the chin. This causes flickering around the ground truth, as illustrated in the landmark trajectory (right). This flickering is common when video frames are evaluated individually, as opposed to recurrently." + ], + "image_footnote": [], + "bbox": [ + 106, + 228, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {n} ^ {*} = \\underset {z} {\\arg \\min } \\| z - z _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {6a}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 464, + 467, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {s . t .} f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) = \\boldsymbol {z} \\tag {6b}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 494, + 467, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The problem above is equivalent to solving for the saddle point of a Lagrangian as follows:", + "bbox": [ + 75, + 525, + 467, + 555 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {z}} \\max _ {\\boldsymbol {\\lambda}} \\left\\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\right\\| _ {2} ^ {2} + \\boldsymbol {\\lambda} ^ {T} \\left(f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) - \\boldsymbol {z}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 569, + 468, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ are Lagrange multipliers. Effectively, we are using the set of fixed points $\\mathcal{Z}_n^*$ in Eq. (6b) as the trust region for the objective in Eq. (6a). In practice, adversarial optimization is notoriously unstable, as is typically observed in the context of GANs [5,30,62]. Furthermore, this objective breaks down if $\\mathcal{Z}_n^* = \\emptyset$ for any $x_{n}$ . We can remedy both of these problems by relaxing the inference time optimization problem to:", + "bbox": [ + 75, + 607, + 468, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {z}} \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} + \\frac {\\alpha}{2} \\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 741, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyperparameter that trades off fixed-point solver error vs. the shift in heatmaps across two consecutive frames. This objective can be more readily tackled with Newtonian optimizers like L-BFGS [47]. When doing so, our DEQ at inference time can be described as a form of OptNet [3], albeit without any of the practical limitations (e.g., quadratic programs) related to making gradient calculations cheap.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Converting our root solving problem into an optimization problem during the forward pass of each frame can significantly increase inference time. Thankfully, the objective in Eq. (8) can also be solved by using root solvers. First, note that it is equivalent to finding the MAP estimate given a log likelihood and prior:", + "bbox": [ + 496, + 438, + 890, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\log p \\left(\\boldsymbol {x} _ {n} \\mid \\boldsymbol {z}; \\boldsymbol {\\theta} ^ {*}\\right) \\propto - \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} \\tag {9a}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 537, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (z) = \\mathcal {N} (z; z _ {n - 1}, \\alpha^ {- 1} \\mathbb {1}) \\tag {9b}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 559, + 890, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It has been demonstrated in various settings that this prior, when centered on the initialization to a search algorithm, can be implemented by early stopping this algorithm [12, 31, 58, 61]. As such, we can approximate the solution to Eq. (6a-6b) by simply initializing the root solver with $z_{n}^{(0)} = z_{n - 1}^{*}$ (\"reuse\") and imposing a hard limit on the number of steps that it can take (\"early stopping\"). We call this approach Recurrence without Recurrence (RwR), and illustrate it in Fig. 3.", + "bbox": [ + 496, + 585, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Video landmark coherence", + "text_level": 1, + "bbox": [ + 498, + 737, + 750, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section we describe the metric (NMF) and the dataset (WFLW-V) that we contribute to measure the amount of temporal coherence in landmark videos. These are later used to benchmark the performance of our RwR paradigm against alternatives in Sec. 6.2.", + "bbox": [ + 496, + 762, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. NMF: a metric to track temporal coherence", + "text_level": 1, + "bbox": [ + 498, + 847, + 870, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The performance of a landmark detection model is typically measured with a single metric called the Normal-", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22817", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/321f9390505f323733d76ba50d0f136c0b04e99c5cd69308ef9337ea21a45553.jpg", + "image_caption": [ + "Figure 3. Recurrence without recurrence (RwR) on video data, from an LDEQ that was trained on still images. We use the initialization $\\mathbf{z}_1^{(0)} = \\mathbf{0}$ for the first frame, and then reuse $\\mathbf{z}_n^{(0)} = \\mathbf{z}_{n - 1}^*$ for $n > 1$ . Combined with early stopping, this is equivalent to regularizing the fixed point $\\mathbf{z}_n$ so that it is more temporally coherent with all its predecessors." + ], + "image_footnote": [], + "bbox": [ + 106, + 87, + 861, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ized Mean Error (NME). Consider a video sequence of $N$ frames, each containing $L$ ground truth landmarks. A single landmark point is a 2D vector denoted $\\pmb{p}_{n,l} \\in \\mathcal{R}^2$ , where $n$ and $l$ are the frame and landmark index respectively. Let $\\pmb{r}_{n,l} = \\pmb{p}_{n,l} - \\hat{\\pmb{p}}_{n,l}$ be the residual vector between ground truth landmarks and predicted landmarks $\\hat{\\pmb{p}}_{n,l}$ . The NME simply averages the $\\ell_2$ norm of this residual across all landmarks and all frames:", + "bbox": [ + 75, + 452, + 472, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {N M E} _ {n} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} \\right\\|}{d _ {0}} \\tag {10a}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 580, + 468, + 623 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {N M E} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathrm {N M E} _ {n} \\tag {10b}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 625, + 468, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $d_0$ is usually the inter-ocular distance, and aims to make the NME better correlate with the human perception of landmark error. We argue that this metric alone is insufficient to measure the performance of a landmark detector in videos. In Fig. 2 we show two models of equal NME but different coherence in time, with one model exhibiting flickering between plausible hypotheses when uncertain. This flickering is a nuisance for many applications, and yet is not captured by the NME. This is in contrast to random noise (jitter) which is unstructured and already reflected in the NME metric.", + "bbox": [ + 75, + 672, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To measure temporal coherence, we propose a new metric called the Normalized Mean Flicker (NMF). We design this metric to be orthogonal to the NME, by making it ag- nostic to the magnitude of $r_{n,l}$ , and only focusing on the", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "change of $\\pmb{r}_{n,l}$ across consecutive frames:", + "bbox": [ + 500, + 452, + 777, + 468 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {N M F} _ {n} = \\sqrt {\\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} - \\boldsymbol {r} _ {n - 1 , l} \\right\\| ^ {2}}{d _ {1} ^ {2}}} \\tag {11a}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 476, + 890, + 525 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {N M F} = \\sqrt {\\frac {1}{N} \\sum_ {n = 2} ^ {F} \\mathrm {N M F} _ {n} ^ {2}} \\tag {11b}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 527, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We replace the means in the NME with a root mean square to better represent the human perception of flicker. Indeed, this penalizes a short sudden changes in $\\boldsymbol{r}_{n,l}$ compared to the same change smoothed out in time and space. The value $d_1^2$ is chosen to be the face area. This prevents a long term issue with the NME score, namely the fact that large poses can have an artificially large NME due to having a small $d_0$ .", + "bbox": [ + 496, + 582, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. A new landmark video dataset: WFLW-V", + "text_level": 1, + "bbox": [ + 500, + 696, + 857, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to the tedious nature of producing landmark annotations for video data, there are few existing datasets for face landmark detection in videos. Shen et al. have proposed 300-VW [60], a dataset made up of $\\sim 100$ videos using the 68-point landmark scheme from the 300-W dataset [57]. Unfortunately, two major issues make this dataset unpopular: 1) it was labelled using fairly weak models from [18] and [67] which results in many labelling errors and high flicker (see Appendix B), and 2) it only contains 100 videos of little diversity, many of which being from the same speaker, or from different speakers in the same environment. Taken together, these two issues mean that the", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22818", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/be2e1e14b203fd4cb3c3954438f0f19d5de42f49aff49db4dce4ecfdaf8503c2.jpg", + "image_caption": [ + "Figure 4. Example of ground truth labels $(\\ast)$ obtained semi-automatically from an ensemble of 45 models $(\\triangle)$ . Ensembling these diverse models provides ground truth labels that do not flicker and can thus be used to measure flickering against. Note how landmark points with the most uncertainty are the most prone to having flickering predictions across consecutive frames." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 870, + 392 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "performance of modern models on 300-WV barely correlates with performance on real-world face videos.", + "bbox": [ + 75, + 470, + 468, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We propose a new video dataset for facial landmarks: WFLW-Video (WFLW-V). It consists of 1000 Youtube creative-commons videos (i.e., an order of magnitude more than its predecessor) and covers a wide range of people, expressions, poses, activities and background environments. Each video is 5s in length. These videos were collected by targeting challenging faces, where ground truth landmarks are subject to uncertainty. The dataset contains two subsets, hard and easy, made up of 500 videos each. This allows debugging temporal filters and smoothing techniques, whose optimal hyperparameters are often different for videos with little or a lot of flicker. This split was obtained by scraping 2000 videos, and selecting the top and bottom 500 videos based on the variance of predictions in the ensemble. To evaluate a landmark model on the WFLW-V dataset, we train it on the WFLW training set, and evaluate it on all WFLW-V videos. This pipeline best reflects the way large landmark models are trained in the industry, where labelled video data is scarce.", + "bbox": [ + 75, + 505, + 472, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Contrary to the 68-landmark scheme of the 300-VW dataset, we label videos semi-automatically using the more challenging 98-landmark scheme from the WFLW dataset [75], as it is considered the most relevant dataset for future research in face landmark detection [38]. To produce ground truth labels, we train an ensemble of 45 state-of-the-art models using a wide range of data augmentations", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of both the test and train set of WFLW (amounting to 10,000 images). We use a mix of large Unets, HRNets [63] and HRFormers [83] to promote landmark diversity. The heatmaps of these models are averaged to produce the ground truth heatmap, allowing uncertain models to weight less in the aggregated output. Ensembling models provide temporal coherence without the need for using hand-tuned filtering or smoothing, which are susceptible to misinterpreting signal for noise (e.g. closing eye landmarks mimic high frequency noise).", + "bbox": [ + 496, + 470, + 893, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide examples of annotated videos in Fig. 4. Note that regions of ambiguity, such as occluded parts of the face, correspond to a higher variance in landmark predictions. While the ground truth for some frames may be subjective (e.g. occluded mouth), having a temporally stable \"best guess\" is sufficient to measure flicker of individual models. We found that 45 models in the ensemble was enough to provide a low error on the mean for all videos in WFLW-V. While we manually checked that our Oracle was highly accurate and coherent in time, note that it is completely impractical to use it for real-world applications due to its computational cost ( $\\sim$ 2B parameters).", + "bbox": [ + 496, + 625, + 895, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We checked each frame manually for errors, which were rare. When we found an error in annotation, we corrected it by removing inaccurate models from the ensemble for the frames affected, rather than re-labeling the frame manually. We found this approach to be faster and less prone to human subjectivity when dealing with ambiguous faces, such", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22819", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5018cddf33ee067520cce034432625d18a05552e5c39738f9fe2874cd1415fc1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodParams (M)FullLarge posesExpressionsIlluminationMakeupOcclusionBlur
LAB [75]CVPR 201812.35.2710.245.515.235.156.796.32
Wing [26]CVPR 2018254.998.435.214.885.266.215.81
MHHN [69]TIP 2020-4.779.314.794.724.596.175.82
DecaFA [21]ICCV 2019104.628.114.654.414.635.745.38
HRNet [63]TPAMI 20209.74.607.944.854.554.295.445.42
AS [54]ICCV 2019354.398.424.684.244.375.604.86
LUVLI [40]CVPR 2020-4.377.564.774.304.335.294.94
AWing [73]ICCV 201924.24.367.384.584.324.275.194.96
SDFL [46]TIP 2021-4.357.424.634.294.225.195.08
SDL [44]ECCV 2020-4.217.364.494.124.054.984.82
ADNet [34]ICCV 202113.44.146.964.384.094.055.064.79
SLPT [77]CVPR 202219.54.126.994.374.024.035.014.79
HIH [42]-22.74.086.874.064.343.854.854.66
LDEQ (ours)-21.83.926.863.944.173.754.774.59
", + "bbox": [ + 99, + 88, + 870, + 320 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "as occluded ones. Occlusion has been characterized as one of the main remaining challenges in modern landmark detection [76], being most difficult in video data [60]. Finally, the stability of our oracle also depends on the stability of the face bounding box detector. We found the most popular detector, MTCNN [85] to be too jittery, and instead obtained stable detection by bootstrapping our oracle landmarks into the detector. More details about scraping and curating our dataset can be found in Appendix A.", + "bbox": [ + 75, + 385, + 470, + 522 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8e0113fe1695eb210fa8cbcd58d0924e6d9a673adc5dc0fa0894af925b3d5f2e.jpg", + "table_caption": [ + "Table 1. Performance of our model and previous state-of-the-art on the various WFLW subsets, using the NME metric (↓) for comparison. Models using pre-training on other datasets have been excluded for fair comparison [14,82,88]." + ], + "table_footnote": [], + "table_body": "
MetricMethodFullPoseExp.Illum.Mu.Occ.Blur
FR10(↓)LAB7.5628.836.376.737.7713.7210.74
HRNet4.6423.013.504.722.438.296.34
AS4.0818.104.462.724.377.744.40
LUVLi3.1215.953.182.153.406.393.23
AWing2.8413.502.232.582.915.983.75
SDFL2.7212.881.592.582.435.713.62
SDL3.0415.952.862.721.455.294.01
ADNet2.7212.722.152.441.945.793.54
SLPT2.7211.961.592.151.945.703.88
HIH2.6012.881.272.431.455.163.10
LDEQ2.4812.581.592.291.945.362.84
AUC10(↑)LAB0.5320.2350.4950.5430.5390.4490.463
HRNet0.5240.2510.5100.5330.5450.4590.452
AS0.5910.3110.5490.6090.5810.5160.551
LUVLi0.5570.3100.5490.5840.5880.5050.525
AWing0.5720.3120.5150.5780.5720.5020.512
SDFL0.5760.3150.5500.5850.5830.5040.515
SDL0.5890.3150.5660.5950.6040.5240.533
ADNet0.6020.3440.5230.5800.6010.5300.548
SLPT0.5960.3490.5730.6030.6080.5200.537
HIH0.6050.3580.6010.6130.6180.5390.561
LDEQ0.6240.3730.6140.6310.6310.5520.574
", + "bbox": [ + 81, + 587, + 465, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. ${\\mathrm{{AUC}}}_{10}$ and ${\\mathrm{{FR}}}_{10}$ on the WFLW test set.", + "bbox": [ + 125, + 882, + 418, + 895 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 383, + 632, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The aim of these experiments is to demonstrate that: 1) LDEQ is a state-of-the-art landmark detection model for high precision settings like faces, and 2) the LDEQ objective can be modified at inference time on videos to include a recurrence loss. This increases temporal coherence without decreasing accuracy, a common pitfall of popular filters.", + "bbox": [ + 498, + 410, + 890, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Landmark accuracy", + "text_level": 1, + "bbox": [ + 500, + 512, + 692, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare the performance of LDEQ to state-of-the-art models on the WFLW dataset [75], which is based on the WIDER Face dataset [81] and is made up of 7500 train images and 2500 test images. Each image is annotated with a face bounding box and 98 2D landmarks. Compared to previous datasets, WFLW uses denser facial landmarks, and introduces much more diversity in poses, expressions, occlusions and image quality (the test set is further divided into subsets reflecting these factors). This makes it uniquely appropriate for training landmark detectors meant to be deployed on real-world data, like the videos of WFLW-V.", + "bbox": [ + 496, + 537, + 890, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The common evaluation metrics for the WFLW test set are the Normalized Mean Error (see Eq. (10b)), the Area Under the Curve (AUC), and the Failure Rate (FR). The AUC is computed on the cumulative error distribution curve (CED), which plots the fraction of images with NME less or equal to some cutoff, vs. increasing cutoff values. We report $\\mathrm{AUC}_{10}$ , referring to a maximum NME cutoff of 10 for the CED curve. Higher AUC is better. The $\\mathrm{FR}_X$ metric is equal to the percentage of test images whose NME is larger than $X$ . We report $\\mathrm{FR}_{10}$ ; lower is better.", + "bbox": [ + 496, + 703, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We train our LDEQ for 60 epochs using the pre-cropped WFLW dataset as per [42], and the common data augmentations for face landmarks: rotations, flips, translations, blurs", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22820", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c3c5e3f8dd7467fc0bfa601545a00d73bfc43ee57fa708d077f97a1f70f855e.jpg", + "image_caption": [ + "Figure 5. NME (accuracy) vs NMF (temporal coherence) for various models, on the hard (left) and easy (right) WFLW-V subsets. We compare our RwR scheme (blue) to a conventional filter (exponential moving average) using three different smoothing coefficients (gray). For hard videos susceptible to flicker, RwR on LDEQ decreases NME by $12\\%$ without increasing NME, contrary to the conventional filter alternative. For easy videos that contain little to no flicker, conventional filters can increase both NME and NMF, while our model converges to the same fixed point with or without RwR. These results are given in tabular form in Appendix C." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 483, + 320 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d0915bcf4794321a252a0637f20f67ee4a924bccb16cf44ef45e128e82c29989.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 85, + 893, + 320 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and occlusions. We found the Anderson and fixed-point-iteration solvers to work best over the Broyden solver used in the original DEQ model [9, 10]. By setting a normalization temperature of $T = 2.5$ , convergence to fixed points only takes around 5 solver iterations. The NME, AUC and FR performance of LDEQ can be found in tables 1 and 2. We outperform all existing models on all three evaluation metrics, usually dominating individual subsets as well, which is important when applying LDEQ to video data.", + "bbox": [ + 75, + 428, + 472, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2. Landmark temporal coherence", + "text_level": 1, + "bbox": [ + 76, + 574, + 352, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluate the performance of LDEQ on the WFLW-V dataset, for both landmark accuracy (NME) and temporal coherence (NMF). We use RwR with early stopping after 2 solver iterations, allowing some adaptive compute (1 solver iteration) in cases where two consecutive frames are almost identical. Our baselines include previous state-of-the-art models that have publicly available weights [42, 46, 73, 77], as well as common architectures of comparable parameter count, which we trained with our own augmentation pipeline. We apply a conventional filtering algorithm, the exponential moving average, to our baselines. This was found to be more robust than more sophisticated filters like Savitzky-Golay filter [59] and One Euro filter [16].", + "bbox": [ + 75, + 598, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The NME vs. NMF results are shown in Fig. 5 for all models, for the hard and easy WFLW-V subsets. For videos that contain little uncertainty in landmarks (WFLW-V easy), there is little flickering and conventional filtering methods can mistakenly smooth out high frequency signal (e.g. eyes and mouth moving fast). For videos subject to more flickering (WFLW-hard), these same filtering tech-", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "niques do indeed improve the NMF metric, but beyond a certain smoothing factor this comes at the cost of increasing the NME. In contrast, LDEQ + RwR correctly smooths out flicker for WFLW-W hard without compromising performance on WFLW-V easy. This improvement comes from the fact that the RwR loss in Eq. (8) contains both a smoothing loss plus a log likelihood loss that constrains output landmarks to be plausible solutions, while conventional filters only optimize for the former.", + "bbox": [ + 496, + 428, + 893, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 577, + 617, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We adapt Deep Equilibrium Models to landmark detection, and demonstrate that our LDEQ model can reach state-of-the-art accuracy on the challenging WFLW facial dataset. We then bring the attention of the landmark community to a common problem in video applications, whereby landmarks flicker across consecutive frames. We contribute a new dataset and metric to effectively benchmark solutions to that problem. Since DEQs solve for an objective in the forward pass, we propose to change this objective at test time to take into account new information. This new paradigm can be used to tackle the flickering problem, by adding a recurrent loss term at inference that wasn't present at training time (RwR). We show how to solve for this objective cheaply in a way that leads to state-of-the-art video temporal coherence. We hope that our work brings attention to the potential of deep equilibrium models for computer vision applications, and in particular, the ability to add loss terms to the forward pass process, to leverage new information at inference time.", + "bbox": [ + 496, + 602, + 893, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22821", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mediapipe 3d face transform. https://developers. googleblog .com/2020/09/mediapipe-3d-face-transform.html. Accessed: 2022-11-09. 1", + "[2] Mediapipe face mesh. https://google.github.io/mediapipe/solutions/face_grid. Accessed: 2022-11-09. 1", + "[3] Brandon Amos and J. Zico Kolter. OptNet: Differentiable optimization as a layer in neural networks. 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In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 787-796, 2015. 1", + "[90] Matt Johnson Zico Kolter, David Duvenaud. http://implicit-layers-tutorial.org/deep_equilibrium_models/.3" + ], + "bbox": [ + 78, + 90, + 468, + 797 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "22825", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_model.json b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..078964962ef1151f9ac75f7c34e78a8f22971507 --- /dev/null +++ b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/75fbb2dc-eb4e-427c-bdb2-0594b83943c8_model.json @@ -0,0 +1,2435 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.132, + 0.817, + 0.177 + ], + "angle": 0, + "content": "Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Models" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.204, + 0.294, + 0.258 + ], + "angle": 0, + "content": "Paul Micaelli \nUniversity of Edinburgh \npaul.micaelli@ed.ac.uk" + }, + { + "type": "text", + "bbox": [ + 0.33, + 0.204, + 0.495, + 0.257 + ], + "angle": 0, + "content": "Arash Vahdat NVIDIA \navahdat@nvidia.com" + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.204, + 0.685, + 0.257 + ], + "angle": 0, + "content": "Hongxu Yin \nNVIDIA \ndanny@nvidia.com" + }, + { + "type": "text", + "bbox": [ + 0.721, + 0.204, + 0.874, + 0.257 + ], + "angle": 0, + "content": "Jan Kautz \nNVIDIA \njkautz@nvidia.com" + }, + { + "type": "text", + "bbox": [ + 0.414, + 0.265, + 0.555, + 0.298 + ], + "angle": 0, + "content": "Pavlo Molchanov \nNVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.388, + 0.304, + 0.578, + 0.316 + ], + "angle": 0, + "content": "pmolchanov@nvidia.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.352, + 0.314, + 0.368 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.473, + 0.794 + ], + "angle": 0, + "content": "Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium Model (DEQ) can be naturally adapted to this form of computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching 3.92 NME with fewer parameters and a training memory cost of \\(\\mathcal{O}(1)\\) in the number of recurrent modules. Furthermore, we show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labelled videos. This can lead to a \"flickering\" effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. By rephrasing DEQs as a constrained optimization, we emulate recurrence at inference time, despite not having access to temporal data at training time. This Recurrence without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we demonstrate by introducing a new metric, normalized mean flicker (NMF), and contributing a new facial landmark video dataset (WFLW-V) targeting landmark uncertainty. On the WFLW-V hard subset made up of 500 videos, our LDEQ with RwR improves the NME and NMF by 10 and \\(13\\%\\) respectively, compared to the strongest previously published model using a hand-tuned conventional filter." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.829, + 0.21, + 0.844 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The field of facial landmark detection has been fueled by important applications such as face recognition [49, 71], facial expression recognition [33, 37, 39, 43, 79], and face" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.895, + 0.595 + ], + "angle": 0, + "content": "alignment [55,87,89]. Early approaches to landmark detection relied on a statistical model of the global face appearance and shape [19,20,25], but this was then superseded by deep learning regression models [21,26,34,40,44,46,54,63, 68,69,73,75,77]. Both traditional and modern approaches have relied upon cascaded computation, an approach which starts with an initial guess of the landmarks and iteratively produces corrected landmarks which match the input face more finely. These iterations typically increase the training memory cost linearly, and do not have an obvious stopping criteria. To solve these issues, we adapt the recently proposed Deep Equilibrium Model [9-11] to the setting of landmark detection. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the WFLW dataset, while enjoying a natural stopping criteria and a memory cost that is constant in the number of cascaded iterations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Furthermore, we explore the benefits of DEQs in landmark detection from facial videos. Since obtaining landmark annotation for videos is notoriously expensive, models are virtually always trained on still images and applied frame-wise on videos at inference time. When a sequence of frames have ambiguous landmarks (e.g., occluded faces or motion blur), this leads to flickering landmarks, which rapidly oscillate between different possible configurations across consecutive frames. This poor temporal coherence is particularly problematic in applications where high precision is required, which is typically the case for facial landmarks. These applications include face transforms [1, 2], face reenactment [84], video emotion recognition [33, 37, 39, 79], movie dubbing [28] or tiredness monitoring [35]. We propose to modify the DEQ objective at inference time to include a new recurrent loss term that encourages temporal coherence. We measure this improvement on our new WFLW-Video dataset (WFLW-V), demonstrating superiority over traditional filters, which typically reduce flickering at the cost of reducing landmark accuracy." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22814" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.097, + 0.106, + 0.112 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.088, + 0.874, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.233, + 0.105, + 0.247 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.246, + 0.87, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.367, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Figure 1. (a) Common Stacked-Hourglass architecture [51], whereby each cascaded stage increases the memory cost and the number of backpropagation operations. (b) Our LDEQ model, which adapts an equilibrium model [9] to the landmark detection setting, enjoying a constant memory cost with the number of refining stages. At each stage, we compute landmark probability heatmaps, and encourage convergence to an equilibrium by lowering their entropy. We release our code here: https://github.com/polo5/LDEQ_RwR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.448, + 0.214, + 0.463 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.747 + ], + "angle": 0, + "content": "Deep Equilibrium Models [9] are part of the family of implicit models, which learn implicit functions such as the solution to an ODE [17, 24], or the solution to an optimization problem [3, 22, 72]. These functions are called implicit in the sense that the output cannot be written as a function of the input explicitly. In the case of DEQs, the output is the root of a function, and the model learned is agnostic to the root solver used. Early DEQ models were too slow to be competitive, and much work since has focused on better architecture design [10] and faster root solving [11, 27, 29]. Since the vanilla formulation of DEQs does not guarantee convergence or uniqueness of an equilibrium, another branch of research has focused on providing convergence guarantees [52, 56, 74], which usually comes at the cost of a performance drop. Most similar to our work is the recent use of DEQs for videos in the context of optical flow estimation [8], where slightly better performance than LSTM-based models was observed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "A common theme throughout the development of landmark detection models has been the idea of cascaded compute, which has repeatedly enjoyed a better performance compared to single stage models [71]. This is true in traditional models like Cascaded Pose Regression (CPR) [7, 15, 23, 65, 78], but also in most modern landmark detection models [34, 40, 42, 69, 73, 75, 80], which usually rely on the Stacked-Hourglass backbone [51], or an RNN structure [41, 66]. In contrast to these methods, our DEQ-based model can directly solve for an infinite number of refine-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.585 + ], + "angle": 0, + "content": "ment stages at a constant memory cost and without gradient degradation. This is done by relying on the implicit function theorem, as opposed to tracking each forward operation in autograd. Furthermore, our model naturally supports adaptive compute, in the sense that the number of cascaded stages will be determined by how hard finding an equilibrium is for a specific input, while the number of stages in, say, the Stacked-Hourglass backbone, must be constant at all times." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.893, + 0.751 + ], + "angle": 0, + "content": "Our recurrence without recurrence approach is most closely related to test time adaption methods. These have been most commonly developed in the context of domain adaptation [64,70], reinforcement learning [32], meta-learning [86], generative models [36, 50], pose estimation [45] or super resolution [6]. Typically, the methods above finetune a trained model at test time using a form of self-supervision. In contrast, our model doesn't need to be finetuned at test time: since DEQs solve for an objective function in the forward pass, this objective is simply modified at test time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.773, + 0.785 + ], + "angle": 0, + "content": "3. DEQs for landmark detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Consider learning a landmark detection model \\(F\\) parameterized by \\(\\theta\\), which maps an input image \\(\\pmb{x}\\) to landmarks \\(\\pmb{z}\\). Instead of directly having \\(\\pmb{z}\\) as 2D landmarks, it is common for \\(\\pmb{z}\\) to represent \\(L\\) heatmaps of size \\(D\\times D\\), where \\(D\\) is a hyperparameter (usually 64) and \\(L\\) is the number of landmarks to learn. While typical machine learning models can explicitly write down the function \\(\\pmb{z} = F(\\pmb{x};\\pmb{\\theta})\\), in" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22815" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "the DEQ approach this function is expressed implicitly by requiring its output to be a fixed point of another function \\( f(z, x; \\theta) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.143, + 0.469, + 0.16 + ], + "angle": 0, + "content": "\\[\nF: \\boldsymbol {x} \\rightarrow \\boldsymbol {z} ^ {*} \\quad \\text {s . t .} \\quad \\boldsymbol {z} ^ {*} = f (\\boldsymbol {z} ^ {*}, \\boldsymbol {x}; \\boldsymbol {\\theta}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.165, + 0.47, + 0.256 + ], + "angle": 0, + "content": "where \\( z^{*} \\) denotes the fixed point, or equivalently the root of \\( g(\\pmb{x},\\pmb{z};\\pmb{\\theta}) = f(\\pmb{z},\\pmb{x};\\pmb{\\theta}) - \\pmb{z} \\). The function \\( f \\) must have inputs and outputs of similar shape, but beyond this restriction there is still limited understanding of its desired properties in machine learning. For simplicity, we build \\( f \\) from the ubiquitous hourglass module \\( h \\) (similar to a Unet):" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.261, + 0.469, + 0.278 + ], + "angle": 0, + "content": "\\[\nf (\\boldsymbol {z}, \\boldsymbol {x}; \\boldsymbol {\\theta}) = \\sigma (h ([ \\boldsymbol {x}, \\boldsymbol {z} ]; \\boldsymbol {\\theta})) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.284, + 0.469, + 0.344 + ], + "angle": 0, + "content": "where \\( h \\) inputs the concatenation of \\( x \\) and \\( z \\), and \\( \\sigma \\) is a normalization function. For clarity, we omit from our notation that image \\( x \\) is downsampled with a few convolutions to match the shape of \\( z \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.344, + 0.469, + 0.495 + ], + "angle": 0, + "content": "To evaluate \\( f \\) in the forward pass, we must solve for its fixed point \\( z^{*} \\). When \\( f \\) is a contraction mapping, \\( f \\circ f \\circ f \\circ \\dots \\circ f \\circ z^{(0)} \\) converges to a unique \\( z^{*} \\) for any initial heatmap \\( z^{(0)} \\). In practice, it is neither tractable or helpful to directly take an infinite number of fixed point iteration steps. Instead, it is common to achieve the same result by leveraging quasi Newtonian solvers like Broyden's method [13] or Anderson acceleration [4], which find \\( z^{*} \\) in fewer iterations. Similarly to the original DEQ model, we use \\( z^{(0)} = 0 \\) when training our LDEQ on still images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.496, + 0.469, + 0.616 + ], + "angle": 0, + "content": "Guaranteeing the existence of a unique fixed point by enforcing contraction restrictions on \\( f \\) is cumbersome, and better performance can often be obtained by relying on regularization heuristics that are conducive to convergence, such as weight normalization and variational dropout [10]. In our landmark model, we did not find these tricks helpful, and instead used a simple normalization of the heatmaps to [0, 1] at each refining stage:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.621, + 0.469, + 0.655 + ], + "angle": 0, + "content": "\\[\n\\sigma (z) = \\exp \\left(\\frac {z - \\operatorname* {m a x} (z)}{T}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.469, + 0.717 + ], + "angle": 0, + "content": "where \\( T \\) is a temperature hyperparameter. This layer also acts as an entropy regularizer, since it induces low-entropy (\"peaked\") heatmaps, which we found to improve convergence of root solvers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.469, + 0.854 + ], + "angle": 0, + "content": "We contrast our model in Fig. 1 to the popular Stacked-Hourglass backbone [51]. Contrary to this model, our DEQ-based model uses a single hourglass module which updates \\( z \\) until an equilibrium is found. The last predicted heatmaps, \\( z^{*} \\), are converted into 2D landmark points \\( \\hat{p} = \\Phi(z^{*}) \\) using the softargmax function \\( \\Phi(z) \\) proposed in [48]. These points are trained to match the ground truth \\( p \\), and so the DEQ landmark training problem can be seen as a constrained optimization:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.859, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {\\theta} ^ {*} = \\underset {\\boldsymbol {\\theta}} {\\arg \\min } \\mathcal {L} _ {\\text {M S E}} (\\Phi (\\boldsymbol {z} ^ {*}), \\boldsymbol {p}) \\tag {4} \\\\ \\text {s . t .} \\quad z ^ {*} = f \\left(z ^ {*}, x; \\theta\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "To differentiate our loss function \\(\\mathcal{L}_{\\mathrm{MSE}}\\) through this root solving process, the implicit function theorem is used [9] to derive" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.147, + 0.892, + 0.179 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {\\theta}} = - \\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {z} ^ {*}} \\mathcal {J} _ {\\boldsymbol {g} \\boldsymbol {z} ^ {*}} ^ {- 1} \\frac {\\partial f (\\boldsymbol {z} ^ {*} , \\boldsymbol {x} ; \\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.19, + 0.892, + 0.355 + ], + "angle": 0, + "content": "where the first two terms on the RHS can be expressed as the solution to a fixed point problem as well. Solving for this root in the backward pass means that we do not need to compute or store the expensive inverse Jacobian term \\(\\mathcal{I}_{gz^*}\\) directly [9, 90]. Importantly, this backward-pass computation only depends on \\(z^*\\) and doesn't depend on the operations done in the forward pass to reach an equilibrium. This means that these operations do not need to be tracked by autograd, and therefore that training requires a memory cost of O(1), despite differentiating through a potentially infinite recurrence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.374, + 0.787, + 0.389 + ], + "angle": 0, + "content": "4. Recurrence without recurrence" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Low temporal coherence (i.e. a large amount of flicker) is illustrated in Fig. 2. This can be a nuisance for many applications that require consistently precise landmarks for video. In this section, we describe how our LDEQ model can address this challenge by enabling recurrence at test time without recurrence at training time (RwR)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.492, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Recall that in the DEQ formulation of Sec. 3, there is no guarantee that a unique fixed point solution exists. This can be a limitation for some applications, and DEQ variants have been proposed to allow provably unique solutions at the cost of additional model complexity [53, 74]. In this work, we instead propose a new paradigm: we leverage the potentially large solution space of DEQs after training to allow for some additional objective at inference time. This new objective is used to disambiguate which fixed point of \\( f(z, x; \\theta^*) \\) is found, in light of extra information present at test time. We demonstrate this approach for the specific application of training a landmark model on face images and evaluating it on videos. In this case, DEQs allow us to include a recurrent loss term at inference time, which isn't achievable with conventional architectures." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Let \\( f(\\pmb{z}, \\pmb{x}; \\pmb{\\theta}^*) \\) be our DEQ model trained as per the formulation in Eq. (4). We would now like to do inference on a video of \\( N \\) frames \\( \\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N \\). Consider that a given frame \\( \\pmb{x}_n \\) has a corresponding set of fixed points \\( \\mathcal{Z}_n^* = \\{z \\text { s.t. } f(\\pmb{z}, \\pmb{x}_n; \\pmb{\\theta}^*) = z\\} \\), representing plausible landmark heatmaps. If we select some \\( \\pmb{z}_n^* \\in \\mathcal{Z}_n^* \\) at random for each frame \\( n \\), the corresponding heatmaps \\( \\pmb{z}_1^*, \\pmb{z}_2^*, \\dots, \\pmb{z}_N^* \\) often exhibit some flickering artefacts, whereby landmarks rapidly change across contiguous frames (see Fig. 2). We propose to address this issue by choosing the fixed point at frame \\( n \\) that is closest to the fixed point at frame \\( n - 1 \\). This can be expressed by the following constrained optimization:" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22816" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.09, + 0.102, + 0.102 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.102, + 0.892, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.216, + 0.102, + 0.228 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.229, + 0.892, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.357, + 0.894, + 0.412 + ], + "angle": 0, + "content": "Figure 2. Model predictions (▲) and ground truth landmarks (○) for (a) a model with high temporal coherence and (b) a model with the same accuracy but exhibiting a worse temporal coherence, due to ambiguity at the chin. This causes flickering around the ground truth, as illustrated in the landmark trajectory (right). This flickering is common when video frames are evaluated individually, as opposed to recurrently." + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.465, + 0.468, + 0.492 + ], + "angle": 0, + "content": "\\[\nz _ {n} ^ {*} = \\underset {z} {\\arg \\min } \\| z - z _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {6a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.496, + 0.468, + 0.512 + ], + "angle": 0, + "content": "\\[\n\\text {s . t .} f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) = \\boldsymbol {z} \\tag {6b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.468, + 0.556 + ], + "angle": 0, + "content": "The problem above is equivalent to solving for the saddle point of a Lagrangian as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.57, + 0.469, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {z}} \\max _ {\\boldsymbol {\\lambda}} \\left\\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\right\\| _ {2} ^ {2} + \\boldsymbol {\\lambda} ^ {T} \\left(f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) - \\boldsymbol {z}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.729 + ], + "angle": 0, + "content": "where \\(\\lambda\\) are Lagrange multipliers. Effectively, we are using the set of fixed points \\(\\mathcal{Z}_n^*\\) in Eq. (6b) as the trust region for the objective in Eq. (6a). In practice, adversarial optimization is notoriously unstable, as is typically observed in the context of GANs [5,30,62]. Furthermore, this objective breaks down if \\(\\mathcal{Z}_n^* = \\emptyset\\) for any \\(x_{n}\\). We can remedy both of these problems by relaxing the inference time optimization problem to:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.742, + 0.469, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {z}} \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} + \\frac {\\alpha}{2} \\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyperparameter that trades off fixed-point solver error vs. the shift in heatmaps across two consecutive frames. This objective can be more readily tackled with Newtonian optimizers like L-BFGS [47]. When doing so, our DEQ at inference time can be described as a form of OptNet [3], albeit without any of the practical limitations (e.g., quadratic programs) related to making gradient calculations cheap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Converting our root solving problem into an optimization problem during the forward pass of each frame can significantly increase inference time. Thankfully, the objective in Eq. (8) can also be solved by using root solvers. First, note that it is equivalent to finding the MAP estimate given a log likelihood and prior:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.539, + 0.891, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\log p \\left(\\boldsymbol {x} _ {n} \\mid \\boldsymbol {z}; \\boldsymbol {\\theta} ^ {*}\\right) \\propto - \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} \\tag {9a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.56, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\np (z) = \\mathcal {N} (z; z _ {n - 1}, \\alpha^ {- 1} \\mathbb {1}) \\tag {9b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.726 + ], + "angle": 0, + "content": "It has been demonstrated in various settings that this prior, when centered on the initialization to a search algorithm, can be implemented by early stopping this algorithm [12, 31, 58, 61]. As such, we can approximate the solution to Eq. (6a-6b) by simply initializing the root solver with \\( z_{n}^{(0)} = z_{n - 1}^{*} \\) (\"reuse\") and imposing a hard limit on the number of steps that it can take (\"early stopping\"). We call this approach Recurrence without Recurrence (RwR), and illustrate it in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.738, + 0.75, + 0.754 + ], + "angle": 0, + "content": "5. Video landmark coherence" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.839 + ], + "angle": 0, + "content": "In this section we describe the metric (NMF) and the dataset (WFLW-V) that we contribute to measure the amount of temporal coherence in landmark videos. These are later used to benchmark the performance of our RwR paradigm against alternatives in Sec. 6.2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.848, + 0.871, + 0.864 + ], + "angle": 0, + "content": "5.1. NMF: a metric to track temporal coherence" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The performance of a landmark detection model is typically measured with a single metric called the Normal-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22817" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.088, + 0.862, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.895, + 0.429 + ], + "angle": 0, + "content": "Figure 3. Recurrence without recurrence (RwR) on video data, from an LDEQ that was trained on still images. We use the initialization \\( \\mathbf{z}_1^{(0)} = \\mathbf{0} \\) for the first frame, and then reuse \\( \\mathbf{z}_n^{(0)} = \\mathbf{z}_{n - 1}^* \\) for \\( n > 1 \\). Combined with early stopping, this is equivalent to regularizing the fixed point \\( \\mathbf{z}_n \\) so that it is more temporally coherent with all its predecessors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.573 + ], + "angle": 0, + "content": "ized Mean Error (NME). Consider a video sequence of \\( N \\) frames, each containing \\( L \\) ground truth landmarks. A single landmark point is a 2D vector denoted \\( \\pmb{p}_{n,l} \\in \\mathcal{R}^2 \\), where \\( n \\) and \\( l \\) are the frame and landmark index respectively. Let \\( \\pmb{r}_{n,l} = \\pmb{p}_{n,l} - \\hat{\\pmb{p}}_{n,l} \\) be the residual vector between ground truth landmarks and predicted landmarks \\( \\hat{\\pmb{p}}_{n,l} \\). The NME simply averages the \\( \\ell_2 \\) norm of this residual across all landmarks and all frames:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.581, + 0.47, + 0.624 + ], + "angle": 0, + "content": "\\[\n\\mathrm {N M E} _ {n} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} \\right\\|}{d _ {0}} \\tag {10a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.625, + 0.47, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\mathrm {N M E} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathrm {N M E} _ {n} \\tag {10b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Here \\( d_0 \\) is usually the inter-ocular distance, and aims to make the NME better correlate with the human perception of landmark error. We argue that this metric alone is insufficient to measure the performance of a landmark detector in videos. In Fig. 2 we show two models of equal NME but different coherence in time, with one model exhibiting flickering between plausible hypotheses when uncertain. This flickering is a nuisance for many applications, and yet is not captured by the NME. This is in contrast to random noise (jitter) which is unstructured and already reflected in the NME metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To measure temporal coherence, we propose a new metric called the Normalized Mean Flicker (NMF). We design this metric to be orthogonal to the NME, by making it ag- nostic to the magnitude of \\(r_{n,l}\\) , and only focusing on the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.453, + 0.779, + 0.469 + ], + "angle": 0, + "content": "change of \\( \\pmb{r}_{n,l} \\) across consecutive frames:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.477, + 0.892, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\mathrm {N M F} _ {n} = \\sqrt {\\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} - \\boldsymbol {r} _ {n - 1 , l} \\right\\| ^ {2}}{d _ {1} ^ {2}}} \\tag {11a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.528, + 0.892, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\mathrm {N M F} = \\sqrt {\\frac {1}{N} \\sum_ {n = 2} ^ {F} \\mathrm {N M F} _ {n} ^ {2}} \\tag {11b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.689 + ], + "angle": 0, + "content": "We replace the means in the NME with a root mean square to better represent the human perception of flicker. Indeed, this penalizes a short sudden changes in \\( \\boldsymbol{r}_{n,l} \\) compared to the same change smoothed out in time and space. The value \\( d_1^2 \\) is chosen to be the face area. This prevents a long term issue with the NME score, namely the fact that large poses can have an artificially large NME due to having a small \\( d_0 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.859, + 0.712 + ], + "angle": 0, + "content": "5.2. A new landmark video dataset: WFLW-V" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Due to the tedious nature of producing landmark annotations for video data, there are few existing datasets for face landmark detection in videos. Shen et al. have proposed 300-VW [60], a dataset made up of \\(\\sim 100\\) videos using the 68-point landmark scheme from the 300-W dataset [57]. Unfortunately, two major issues make this dataset unpopular: 1) it was labelled using fairly weak models from [18] and [67] which results in many labelling errors and high flicker (see Appendix B), and 2) it only contains 100 videos of little diversity, many of which being from the same speaker, or from different speakers in the same environment. Taken together, these two issues mean that the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22818" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.895, + 0.446 + ], + "angle": 0, + "content": "Figure 4. Example of ground truth labels \\((\\ast)\\) obtained semi-automatically from an ensemble of 45 models \\((\\triangle)\\). Ensembling these diverse models provides ground truth labels that do not flicker and can thus be used to measure flickering against. Note how landmark points with the most uncertainty are the most prone to having flickering predictions across consecutive frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.502 + ], + "angle": 0, + "content": "performance of modern models on 300-WV barely correlates with performance on real-world face videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.793 + ], + "angle": 0, + "content": "We propose a new video dataset for facial landmarks: WFLW-Video (WFLW-V). It consists of 1000 Youtube creative-commons videos (i.e., an order of magnitude more than its predecessor) and covers a wide range of people, expressions, poses, activities and background environments. Each video is 5s in length. These videos were collected by targeting challenging faces, where ground truth landmarks are subject to uncertainty. The dataset contains two subsets, hard and easy, made up of 500 videos each. This allows debugging temporal filters and smoothing techniques, whose optimal hyperparameters are often different for videos with little or a lot of flicker. This split was obtained by scraping 2000 videos, and selecting the top and bottom 500 videos based on the variance of predictions in the ensemble. To evaluate a landmark model on the WFLW-V dataset, we train it on the WFLW training set, and evaluate it on all WFLW-V videos. This pipeline best reflects the way large landmark models are trained in the industry, where labelled video data is scarce." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Contrary to the 68-landmark scheme of the 300-VW dataset, we label videos semi-automatically using the more challenging 98-landmark scheme from the WFLW dataset [75], as it is considered the most relevant dataset for future research in face landmark detection [38]. To produce ground truth labels, we train an ensemble of 45 state-of-the-art models using a wide range of data augmentations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.895, + 0.625 + ], + "angle": 0, + "content": "of both the test and train set of WFLW (amounting to 10,000 images). We use a mix of large Unets, HRNets [63] and HRFormers [83] to promote landmark diversity. The heatmaps of these models are averaged to produce the ground truth heatmap, allowing uncertain models to weight less in the aggregated output. Ensembling models provide temporal coherence without the need for using hand-tuned filtering or smoothing, which are susceptible to misinterpreting signal for noise (e.g. closing eye landmarks mimic high frequency noise)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.896, + 0.809 + ], + "angle": 0, + "content": "We provide examples of annotated videos in Fig. 4. Note that regions of ambiguity, such as occluded parts of the face, correspond to a higher variance in landmark predictions. While the ground truth for some frames may be subjective (e.g. occluded mouth), having a temporally stable \"best guess\" is sufficient to measure flicker of individual models. We found that 45 models in the ensemble was enough to provide a low error on the mean for all videos in WFLW-V. While we manually checked that our Oracle was highly accurate and coherent in time, note that it is completely impractical to use it for real-world applications due to its computational cost (\\(\\sim\\)2B parameters)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.897, + 0.903 + ], + "angle": 0, + "content": "We checked each frame manually for errors, which were rare. When we found an error in annotation, we corrected it by removing inaccurate models from the ensemble for the frames affected, rather than re-labeling the frame manually. We found this approach to be faster and less prone to human subjectivity when dealing with ambiguous faces, such" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22819" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.321 + ], + "angle": 0, + "content": "
MethodParams (M)FullLarge posesExpressionsIlluminationMakeupOcclusionBlur
LAB [75]CVPR 201812.35.2710.245.515.235.156.796.32
Wing [26]CVPR 2018254.998.435.214.885.266.215.81
MHHN [69]TIP 2020-4.779.314.794.724.596.175.82
DecaFA [21]ICCV 2019104.628.114.654.414.635.745.38
HRNet [63]TPAMI 20209.74.607.944.854.554.295.445.42
AS [54]ICCV 2019354.398.424.684.244.375.604.86
LUVLI [40]CVPR 2020-4.377.564.774.304.335.294.94
AWing [73]ICCV 201924.24.367.384.584.324.275.194.96
SDFL [46]TIP 2021-4.357.424.634.294.225.195.08
SDL [44]ECCV 2020-4.217.364.494.124.054.984.82
ADNet [34]ICCV 202113.44.146.964.384.094.055.064.79
SLPT [77]CVPR 202219.54.126.994.374.024.035.014.79
HIH [42]-22.74.086.874.064.343.854.854.66
LDEQ (ours)-21.83.926.863.944.173.754.774.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.331, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Table 1. Performance of our model and previous state-of-the-art on the various WFLW subsets, using the NME metric (↓) for comparison. Models using pre-training on other datasets have been excluded for fair comparison [14,82,88]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.471, + 0.523 + ], + "angle": 0, + "content": "as occluded ones. Occlusion has been characterized as one of the main remaining challenges in modern landmark detection [76], being most difficult in video data [60]. Finally, the stability of our oracle also depends on the stability of the face bounding box detector. We found the most popular detector, MTCNN [85] to be too jittery, and instead obtained stable detection by bootstrapping our oracle landmarks into the detector. More details about scraping and curating our dataset can be found in Appendix A." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.588, + 0.467, + 0.871 + ], + "angle": 0, + "content": "
MetricMethodFullPoseExp.Illum.Mu.Occ.Blur
FR10(↓)LAB7.5628.836.376.737.7713.7210.74
HRNet4.6423.013.504.722.438.296.34
AS4.0818.104.462.724.377.744.40
LUVLi3.1215.953.182.153.406.393.23
AWing2.8413.502.232.582.915.983.75
SDFL2.7212.881.592.582.435.713.62
SDL3.0415.952.862.721.455.294.01
ADNet2.7212.722.152.441.945.793.54
SLPT2.7211.961.592.151.945.703.88
HIH2.6012.881.272.431.455.163.10
LDEQ2.4812.581.592.291.945.362.84
AUC10(↑)LAB0.5320.2350.4950.5430.5390.4490.463
HRNet0.5240.2510.5100.5330.5450.4590.452
AS0.5910.3110.5490.6090.5810.5160.551
LUVLi0.5570.3100.5490.5840.5880.5050.525
AWing0.5720.3120.5150.5780.5720.5020.512
SDFL0.5760.3150.5500.5850.5830.5040.515
SDL0.5890.3150.5660.5950.6040.5240.533
ADNet0.6020.3440.5230.5800.6010.5300.548
SLPT0.5960.3490.5730.6030.6080.5200.537
HIH0.6050.3580.6010.6130.6180.5390.561
LDEQ0.6240.3730.6140.6310.6310.5520.574
" + }, + { + "type": "table_caption", + "bbox": [ + 0.127, + 0.883, + 0.419, + 0.896 + ], + "angle": 0, + "content": "Table 2. \\( {\\mathrm{{AUC}}}_{10} \\) and \\( {\\mathrm{{FR}}}_{10} \\) on the WFLW test set." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.633, + 0.403 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.892, + 0.502 + ], + "angle": 0, + "content": "The aim of these experiments is to demonstrate that: 1) LDEQ is a state-of-the-art landmark detection model for high precision settings like faces, and 2) the LDEQ objective can be modified at inference time on videos to include a recurrence loss. This increases temporal coherence without decreasing accuracy, a common pitfall of popular filters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.693, + 0.53 + ], + "angle": 0, + "content": "6.1. Landmark accuracy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.703 + ], + "angle": 0, + "content": "We compare the performance of LDEQ to state-of-the-art models on the WFLW dataset [75], which is based on the WIDER Face dataset [81] and is made up of 7500 train images and 2500 test images. Each image is annotated with a face bounding box and 98 2D landmarks. Compared to previous datasets, WFLW uses denser facial landmarks, and introduces much more diversity in poses, expressions, occlusions and image quality (the test set is further divided into subsets reflecting these factors). This makes it uniquely appropriate for training landmark detectors meant to be deployed on real-world data, like the videos of WFLW-V." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.854 + ], + "angle": 0, + "content": "The common evaluation metrics for the WFLW test set are the Normalized Mean Error (see Eq. (10b)), the Area Under the Curve (AUC), and the Failure Rate (FR). The AUC is computed on the cumulative error distribution curve (CED), which plots the fraction of images with NME less or equal to some cutoff, vs. increasing cutoff values. We report \\(\\mathrm{AUC}_{10}\\), referring to a maximum NME cutoff of 10 for the CED curve. Higher AUC is better. The \\(\\mathrm{FR}_X\\) metric is equal to the percentage of test images whose NME is larger than \\(X\\). We report \\(\\mathrm{FR}_{10}\\); lower is better." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We train our LDEQ for 60 epochs using the pre-cropped WFLW dataset as per [42], and the common data augmentations for face landmarks: rotations, flips, translations, blurs" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22820" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.077, + 0.086, + 0.485, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.087, + 0.895, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.332, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Figure 5. NME (accuracy) vs NMF (temporal coherence) for various models, on the hard (left) and easy (right) WFLW-V subsets. We compare our RwR scheme (blue) to a conventional filter (exponential moving average) using three different smoothing coefficients (gray). For hard videos susceptible to flicker, RwR on LDEQ decreases NME by \\(12\\%\\) without increasing NME, contrary to the conventional filter alternative. For easy videos that contain little to no flicker, conventional filters can increase both NME and NMF, while our model converges to the same fixed point with or without RwR. These results are given in tabular form in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.473, + 0.565 + ], + "angle": 0, + "content": "and occlusions. We found the Anderson and fixed-point-iteration solvers to work best over the Broyden solver used in the original DEQ model [9, 10]. By setting a normalization temperature of \\( T = 2.5 \\), convergence to fixed points only takes around 5 solver iterations. The NME, AUC and FR performance of LDEQ can be found in tables 1 and 2. We outperform all existing models on all three evaluation metrics, usually dominating individual subsets as well, which is important when applying LDEQ to video data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.353, + 0.592 + ], + "angle": 0, + "content": "6.2. Landmark temporal coherence" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.795 + ], + "angle": 0, + "content": "We evaluate the performance of LDEQ on the WFLW-V dataset, for both landmark accuracy (NME) and temporal coherence (NMF). We use RwR with early stopping after 2 solver iterations, allowing some adaptive compute (1 solver iteration) in cases where two consecutive frames are almost identical. Our baselines include previous state-of-the-art models that have publicly available weights [42, 46, 73, 77], as well as common architectures of comparable parameter count, which we trained with our own augmentation pipeline. We apply a conventional filtering algorithm, the exponential moving average, to our baselines. This was found to be more robust than more sophisticated filters like Savitzky-Golay filter [59] and One Euro filter [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The NME vs. NMF results are shown in Fig. 5 for all models, for the hard and easy WFLW-V subsets. For videos that contain little uncertainty in landmarks (WFLW-V easy), there is little flickering and conventional filtering methods can mistakenly smooth out high frequency signal (e.g. eyes and mouth moving fast). For videos subject to more flickering (WFLW-hard), these same filtering tech-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.895, + 0.565 + ], + "angle": 0, + "content": "niques do indeed improve the NMF metric, but beyond a certain smoothing factor this comes at the cost of increasing the NME. In contrast, LDEQ + RwR correctly smooths out flicker for WFLW-W hard without compromising performance on WFLW-V easy. This improvement comes from the fact that the RwR loss in Eq. (8) contains both a smoothing loss plus a log likelihood loss that constrains output landmarks to be plausible solutions, while conventional filters only optimize for the former." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.578, + 0.619, + 0.593 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.895, + 0.89 + ], + "angle": 0, + "content": "We adapt Deep Equilibrium Models to landmark detection, and demonstrate that our LDEQ model can reach state-of-the-art accuracy on the challenging WFLW facial dataset. We then bring the attention of the landmark community to a common problem in video applications, whereby landmarks flicker across consecutive frames. We contribute a new dataset and metric to effectively benchmark solutions to that problem. Since DEQs solve for an objective in the forward pass, we propose to change this objective at test time to take into account new information. This new paradigm can be used to tackle the flickering problem, by adding a recurrent loss term at inference that wasn't present at training time (RwR). We show how to solve for this objective cheaply in a way that leads to state-of-the-art video temporal coherence. We hope that our work brings attention to the potential of deep equilibrium models for computer vision applications, and in particular, the ability to add loss terms to the forward pass process, to leverage new information at inference time." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22821" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Mediapipe 3d face transform. https://developers. googleblog .com/2020/09/mediapipe-3d-face-transform.html. Accessed: 2022-11-09. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.468, + 0.198 + ], + "angle": 0, + "content": "[2] Mediapipe face mesh. https://google.github.io/mediapipe/solutions/face_grid. 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In this work, we show that the recently proposed Deep Equilibrium Model (DEQ) can be naturally adapted to this form of computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching 3.92 NME with fewer parameters and a training memory cost of $\mathcal{O}(1)$ in the number of recurrent modules. Furthermore, we show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labelled videos. This can lead to a "flickering" effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. By rephrasing DEQs as a constrained optimization, we emulate recurrence at inference time, despite not having access to temporal data at training time. This Recurrence without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we demonstrate by introducing a new metric, normalized mean flicker (NMF), and contributing a new facial landmark video dataset (WFLW-V) targeting landmark uncertainty. On the WFLW-V hard subset made up of 500 videos, our LDEQ with RwR improves the NME and NMF by 10 and $13\%$ respectively, compared to the strongest previously published model using a hand-tuned conventional filter. + +# 1. Introduction + +The field of facial landmark detection has been fueled by important applications such as face recognition [49, 71], facial expression recognition [33, 37, 39, 43, 79], and face + +alignment [55,87,89]. Early approaches to landmark detection relied on a statistical model of the global face appearance and shape [19,20,25], but this was then superseded by deep learning regression models [21,26,34,40,44,46,54,63, 68,69,73,75,77]. Both traditional and modern approaches have relied upon cascaded computation, an approach which starts with an initial guess of the landmarks and iteratively produces corrected landmarks which match the input face more finely. These iterations typically increase the training memory cost linearly, and do not have an obvious stopping criteria. To solve these issues, we adapt the recently proposed Deep Equilibrium Model [9-11] to the setting of landmark detection. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the WFLW dataset, while enjoying a natural stopping criteria and a memory cost that is constant in the number of cascaded iterations. + +Furthermore, we explore the benefits of DEQs in landmark detection from facial videos. Since obtaining landmark annotation for videos is notoriously expensive, models are virtually always trained on still images and applied frame-wise on videos at inference time. When a sequence of frames have ambiguous landmarks (e.g., occluded faces or motion blur), this leads to flickering landmarks, which rapidly oscillate between different possible configurations across consecutive frames. This poor temporal coherence is particularly problematic in applications where high precision is required, which is typically the case for facial landmarks. These applications include face transforms [1, 2], face reenactment [84], video emotion recognition [33, 37, 39, 79], movie dubbing [28] or tiredness monitoring [35]. We propose to modify the DEQ objective at inference time to include a new recurrent loss term that encourages temporal coherence. We measure this improvement on our new WFLW-Video dataset (WFLW-V), demonstrating superiority over traditional filters, which typically reduce flickering at the cost of reducing landmark accuracy. + +![](images/42c765552c189bfd97938713cc955b931477d682e7bdd882741ffa272c5e4cc7.jpg) +(a) + +![](images/d678b5bd6312df57d1e05f64a4b01b4676f08b23d475dc97774e389a1c95e6d0.jpg) +(b) +Figure 1. (a) Common Stacked-Hourglass architecture [51], whereby each cascaded stage increases the memory cost and the number of backpropagation operations. (b) Our LDEQ model, which adapts an equilibrium model [9] to the landmark detection setting, enjoying a constant memory cost with the number of refining stages. At each stage, we compute landmark probability heatmaps, and encourage convergence to an equilibrium by lowering their entropy. We release our code here: https://github.com/polo5/LDEQ_RwR. + +# 2. Related work + +Deep Equilibrium Models [9] are part of the family of implicit models, which learn implicit functions such as the solution to an ODE [17, 24], or the solution to an optimization problem [3, 22, 72]. These functions are called implicit in the sense that the output cannot be written as a function of the input explicitly. In the case of DEQs, the output is the root of a function, and the model learned is agnostic to the root solver used. Early DEQ models were too slow to be competitive, and much work since has focused on better architecture design [10] and faster root solving [11, 27, 29]. Since the vanilla formulation of DEQs does not guarantee convergence or uniqueness of an equilibrium, another branch of research has focused on providing convergence guarantees [52, 56, 74], which usually comes at the cost of a performance drop. Most similar to our work is the recent use of DEQs for videos in the context of optical flow estimation [8], where slightly better performance than LSTM-based models was observed. + +A common theme throughout the development of landmark detection models has been the idea of cascaded compute, which has repeatedly enjoyed a better performance compared to single stage models [71]. This is true in traditional models like Cascaded Pose Regression (CPR) [7, 15, 23, 65, 78], but also in most modern landmark detection models [34, 40, 42, 69, 73, 75, 80], which usually rely on the Stacked-Hourglass backbone [51], or an RNN structure [41, 66]. In contrast to these methods, our DEQ-based model can directly solve for an infinite number of refine- + +ment stages at a constant memory cost and without gradient degradation. This is done by relying on the implicit function theorem, as opposed to tracking each forward operation in autograd. Furthermore, our model naturally supports adaptive compute, in the sense that the number of cascaded stages will be determined by how hard finding an equilibrium is for a specific input, while the number of stages in, say, the Stacked-Hourglass backbone, must be constant at all times. + +Our recurrence without recurrence approach is most closely related to test time adaption methods. These have been most commonly developed in the context of domain adaptation [64,70], reinforcement learning [32], meta-learning [86], generative models [36, 50], pose estimation [45] or super resolution [6]. Typically, the methods above finetune a trained model at test time using a form of self-supervision. In contrast, our model doesn't need to be finetuned at test time: since DEQs solve for an objective function in the forward pass, this objective is simply modified at test time. + +# 3. DEQs for landmark detection + +Consider learning a landmark detection model $F$ parameterized by $\theta$ , which maps an input image $\pmb{x}$ to landmarks $\pmb{z}$ . Instead of directly having $\pmb{z}$ as 2D landmarks, it is common for $\pmb{z}$ to represent $L$ heatmaps of size $D\times D$ , where $D$ is a hyperparameter (usually 64) and $L$ is the number of landmarks to learn. While typical machine learning models can explicitly write down the function $\pmb{z} = F(\pmb{x};\pmb{\theta})$ , in + +the DEQ approach this function is expressed implicitly by requiring its output to be a fixed point of another function $f(z, x; \theta)$ : + +$$ +F: \boldsymbol {x} \rightarrow \boldsymbol {z} ^ {*} \quad \text {s . t .} \quad \boldsymbol {z} ^ {*} = f (\boldsymbol {z} ^ {*}, \boldsymbol {x}; \boldsymbol {\theta}) \tag {1} +$$ + +where $z^{*}$ denotes the fixed point, or equivalently the root of $g(\pmb{x},\pmb{z};\pmb{\theta}) = f(\pmb{z},\pmb{x};\pmb{\theta}) - \pmb{z}$ . The function $f$ must have inputs and outputs of similar shape, but beyond this restriction there is still limited understanding of its desired properties in machine learning. For simplicity, we build $f$ from the ubiquitous hourglass module $h$ (similar to a Unet): + +$$ +f (\boldsymbol {z}, \boldsymbol {x}; \boldsymbol {\theta}) = \sigma (h ([ \boldsymbol {x}, \boldsymbol {z} ]; \boldsymbol {\theta})) \tag {2} +$$ + +where $h$ inputs the concatenation of $x$ and $z$ , and $\sigma$ is a normalization function. For clarity, we omit from our notation that image $x$ is downsampled with a few convolutions to match the shape of $z$ . + +To evaluate $f$ in the forward pass, we must solve for its fixed point $z^{*}$ . When $f$ is a contraction mapping, $f \circ f \circ f \circ \dots \circ f \circ z^{(0)}$ converges to a unique $z^{*}$ for any initial heatmap $z^{(0)}$ . In practice, it is neither tractable or helpful to directly take an infinite number of fixed point iteration steps. Instead, it is common to achieve the same result by leveraging quasi Newtonian solvers like Broyden's method [13] or Anderson acceleration [4], which find $z^{*}$ in fewer iterations. Similarly to the original DEQ model, we use $z^{(0)} = 0$ when training our LDEQ on still images. + +Guaranteeing the existence of a unique fixed point by enforcing contraction restrictions on $f$ is cumbersome, and better performance can often be obtained by relying on regularization heuristics that are conducive to convergence, such as weight normalization and variational dropout [10]. In our landmark model, we did not find these tricks helpful, and instead used a simple normalization of the heatmaps to [0, 1] at each refining stage: + +$$ +\sigma (z) = \exp \left(\frac {z - \operatorname* {m a x} (z)}{T}\right) \tag {3} +$$ + +where $T$ is a temperature hyperparameter. This layer also acts as an entropy regularizer, since it induces low-entropy ("peaked") heatmaps, which we found to improve convergence of root solvers. + +We contrast our model in Fig. 1 to the popular Stacked-Hourglass backbone [51]. Contrary to this model, our DEQ-based model uses a single hourglass module which updates $z$ until an equilibrium is found. The last predicted heatmaps, $z^{*}$ , are converted into 2D landmark points $\hat{p} = \Phi(z^{*})$ using the softargmax function $\Phi(z)$ proposed in [48]. These points are trained to match the ground truth $p$ , and so the DEQ landmark training problem can be seen as a constrained optimization: + +$$ +\begin{array}{l} \boldsymbol {\theta} ^ {*} = \underset {\boldsymbol {\theta}} {\arg \min } \mathcal {L} _ {\text {M S E}} (\Phi (\boldsymbol {z} ^ {*}), \boldsymbol {p}) \tag {4} \\ \text {s . t .} \quad z ^ {*} = f \left(z ^ {*}, x; \theta\right) \\ \end{array} +$$ + +To differentiate our loss function $\mathcal{L}_{\mathrm{MSE}}$ through this root solving process, the implicit function theorem is used [9] to derive + +$$ +\frac {\partial \mathcal {L} _ {\mathrm {M S E}}}{\partial \boldsymbol {\theta}} = - \frac {\partial \mathcal {L} _ {\mathrm {M S E}}}{\partial \boldsymbol {z} ^ {*}} \mathcal {J} _ {\boldsymbol {g} \boldsymbol {z} ^ {*}} ^ {- 1} \frac {\partial f (\boldsymbol {z} ^ {*} , \boldsymbol {x} ; \boldsymbol {\theta})}{\partial \boldsymbol {\theta}} \tag {5} +$$ + +where the first two terms on the RHS can be expressed as the solution to a fixed point problem as well. Solving for this root in the backward pass means that we do not need to compute or store the expensive inverse Jacobian term $\mathcal{I}_{gz^*}$ directly [9, 90]. Importantly, this backward-pass computation only depends on $z^*$ and doesn't depend on the operations done in the forward pass to reach an equilibrium. This means that these operations do not need to be tracked by autograd, and therefore that training requires a memory cost of O(1), despite differentiating through a potentially infinite recurrence. + +# 4. Recurrence without recurrence + +Low temporal coherence (i.e. a large amount of flicker) is illustrated in Fig. 2. This can be a nuisance for many applications that require consistently precise landmarks for video. In this section, we describe how our LDEQ model can address this challenge by enabling recurrence at test time without recurrence at training time (RwR). + +Recall that in the DEQ formulation of Sec. 3, there is no guarantee that a unique fixed point solution exists. This can be a limitation for some applications, and DEQ variants have been proposed to allow provably unique solutions at the cost of additional model complexity [53, 74]. In this work, we instead propose a new paradigm: we leverage the potentially large solution space of DEQs after training to allow for some additional objective at inference time. This new objective is used to disambiguate which fixed point of $f(z, x; \theta^*)$ is found, in light of extra information present at test time. We demonstrate this approach for the specific application of training a landmark model on face images and evaluating it on videos. In this case, DEQs allow us to include a recurrent loss term at inference time, which isn't achievable with conventional architectures. + +Let $f(\pmb{z}, \pmb{x}; \pmb{\theta}^*)$ be our DEQ model trained as per the formulation in Eq. (4). We would now like to do inference on a video of $N$ frames $\pmb{x}_1, \pmb{x}_2, \dots, \pmb{x}_N$ . Consider that a given frame $\pmb{x}_n$ has a corresponding set of fixed points $\mathcal{Z}_n^* = \{z \text { s.t. } f(\pmb{z}, \pmb{x}_n; \pmb{\theta}^*) = z\}$ , representing plausible landmark heatmaps. If we select some $\pmb{z}_n^* \in \mathcal{Z}_n^*$ at random for each frame $n$ , the corresponding heatmaps $\pmb{z}_1^*, \pmb{z}_2^*, \dots, \pmb{z}_N^*$ often exhibit some flickering artefacts, whereby landmarks rapidly change across contiguous frames (see Fig. 2). We propose to address this issue by choosing the fixed point at frame $n$ that is closest to the fixed point at frame $n - 1$ . This can be expressed by the following constrained optimization: + +![](images/940ae187ce8860be61be775a2141fc6135f2f57afa6762279792835dee0190a7.jpg) +(a) + +![](images/cbdfcb43393c3cf82ea7defe20387d3e9d5418f3c7be6c79fd32e18b1c2a0a06.jpg) +(b) +Figure 2. Model predictions (▲) and ground truth landmarks (○) for (a) a model with high temporal coherence and (b) a model with the same accuracy but exhibiting a worse temporal coherence, due to ambiguity at the chin. This causes flickering around the ground truth, as illustrated in the landmark trajectory (right). This flickering is common when video frames are evaluated individually, as opposed to recurrently. + +$$ +z _ {n} ^ {*} = \underset {z} {\arg \min } \| z - z _ {n - 1} ^ {*} \| _ {2} ^ {2} \tag {6a} +$$ + +$$ +\text {s . t .} f \left(\boldsymbol {z}, \boldsymbol {x} _ {n}; \boldsymbol {\theta} ^ {*}\right) = \boldsymbol {z} \tag {6b} +$$ + +The problem above is equivalent to solving for the saddle point of a Lagrangian as follows: + +$$ +\min _ {\boldsymbol {z}} \max _ {\boldsymbol {\lambda}} \left\| \boldsymbol {z} - \boldsymbol {z} _ {n - 1} ^ {*} \right\| _ {2} ^ {2} + \boldsymbol {\lambda} ^ {T} \left(f \left(\boldsymbol {z}, \boldsymbol {x} _ {n}; \boldsymbol {\theta} ^ {*}\right) - \boldsymbol {z}\right) \tag {7} +$$ + +where $\lambda$ are Lagrange multipliers. Effectively, we are using the set of fixed points $\mathcal{Z}_n^*$ in Eq. (6b) as the trust region for the objective in Eq. (6a). In practice, adversarial optimization is notoriously unstable, as is typically observed in the context of GANs [5,30,62]. Furthermore, this objective breaks down if $\mathcal{Z}_n^* = \emptyset$ for any $x_{n}$ . We can remedy both of these problems by relaxing the inference time optimization problem to: + +$$ +\min _ {\boldsymbol {z}} \| f (\boldsymbol {z}, \boldsymbol {x} _ {n}; \boldsymbol {\theta} ^ {*}) - \boldsymbol {z} \| _ {2} ^ {2} + \frac {\alpha}{2} \| \boldsymbol {z} - \boldsymbol {z} _ {n - 1} ^ {*} \| _ {2} ^ {2} \tag {8} +$$ + +where $\alpha$ is a hyperparameter that trades off fixed-point solver error vs. the shift in heatmaps across two consecutive frames. This objective can be more readily tackled with Newtonian optimizers like L-BFGS [47]. When doing so, our DEQ at inference time can be described as a form of OptNet [3], albeit without any of the practical limitations (e.g., quadratic programs) related to making gradient calculations cheap. + +Converting our root solving problem into an optimization problem during the forward pass of each frame can significantly increase inference time. Thankfully, the objective in Eq. (8) can also be solved by using root solvers. First, note that it is equivalent to finding the MAP estimate given a log likelihood and prior: + +$$ +\log p \left(\boldsymbol {x} _ {n} \mid \boldsymbol {z}; \boldsymbol {\theta} ^ {*}\right) \propto - \| f (\boldsymbol {z}, \boldsymbol {x} _ {n}; \boldsymbol {\theta} ^ {*}) - \boldsymbol {z} \| _ {2} ^ {2} \tag {9a} +$$ + +$$ +p (z) = \mathcal {N} (z; z _ {n - 1}, \alpha^ {- 1} \mathbb {1}) \tag {9b} +$$ + +It has been demonstrated in various settings that this prior, when centered on the initialization to a search algorithm, can be implemented by early stopping this algorithm [12, 31, 58, 61]. As such, we can approximate the solution to Eq. (6a-6b) by simply initializing the root solver with $z_{n}^{(0)} = z_{n - 1}^{*}$ ("reuse") and imposing a hard limit on the number of steps that it can take ("early stopping"). We call this approach Recurrence without Recurrence (RwR), and illustrate it in Fig. 3. + +# 5. Video landmark coherence + +In this section we describe the metric (NMF) and the dataset (WFLW-V) that we contribute to measure the amount of temporal coherence in landmark videos. These are later used to benchmark the performance of our RwR paradigm against alternatives in Sec. 6.2. + +# 5.1. NMF: a metric to track temporal coherence + +The performance of a landmark detection model is typically measured with a single metric called the Normal- + +![](images/321f9390505f323733d76ba50d0f136c0b04e99c5cd69308ef9337ea21a45553.jpg) +Figure 3. Recurrence without recurrence (RwR) on video data, from an LDEQ that was trained on still images. We use the initialization $\mathbf{z}_1^{(0)} = \mathbf{0}$ for the first frame, and then reuse $\mathbf{z}_n^{(0)} = \mathbf{z}_{n - 1}^*$ for $n > 1$ . Combined with early stopping, this is equivalent to regularizing the fixed point $\mathbf{z}_n$ so that it is more temporally coherent with all its predecessors. + +ized Mean Error (NME). Consider a video sequence of $N$ frames, each containing $L$ ground truth landmarks. A single landmark point is a 2D vector denoted $\pmb{p}_{n,l} \in \mathcal{R}^2$ , where $n$ and $l$ are the frame and landmark index respectively. Let $\pmb{r}_{n,l} = \pmb{p}_{n,l} - \hat{\pmb{p}}_{n,l}$ be the residual vector between ground truth landmarks and predicted landmarks $\hat{\pmb{p}}_{n,l}$ . The NME simply averages the $\ell_2$ norm of this residual across all landmarks and all frames: + +$$ +\mathrm {N M E} _ {n} = \frac {1}{L} \sum_ {l = 1} ^ {L} \frac {\left\| \boldsymbol {r} _ {n , l} \right\|}{d _ {0}} \tag {10a} +$$ + +$$ +\mathrm {N M E} = \frac {1}{N} \sum_ {n = 1} ^ {N} \mathrm {N M E} _ {n} \tag {10b} +$$ + +Here $d_0$ is usually the inter-ocular distance, and aims to make the NME better correlate with the human perception of landmark error. We argue that this metric alone is insufficient to measure the performance of a landmark detector in videos. In Fig. 2 we show two models of equal NME but different coherence in time, with one model exhibiting flickering between plausible hypotheses when uncertain. This flickering is a nuisance for many applications, and yet is not captured by the NME. This is in contrast to random noise (jitter) which is unstructured and already reflected in the NME metric. + +To measure temporal coherence, we propose a new metric called the Normalized Mean Flicker (NMF). We design this metric to be orthogonal to the NME, by making it ag- nostic to the magnitude of $r_{n,l}$ , and only focusing on the + +change of $\pmb{r}_{n,l}$ across consecutive frames: + +$$ +\mathrm {N M F} _ {n} = \sqrt {\frac {1}{L} \sum_ {l = 1} ^ {L} \frac {\left\| \boldsymbol {r} _ {n , l} - \boldsymbol {r} _ {n - 1 , l} \right\| ^ {2}}{d _ {1} ^ {2}}} \tag {11a} +$$ + +$$ +\mathrm {N M F} = \sqrt {\frac {1}{N} \sum_ {n = 2} ^ {F} \mathrm {N M F} _ {n} ^ {2}} \tag {11b} +$$ + +We replace the means in the NME with a root mean square to better represent the human perception of flicker. Indeed, this penalizes a short sudden changes in $\boldsymbol{r}_{n,l}$ compared to the same change smoothed out in time and space. The value $d_1^2$ is chosen to be the face area. This prevents a long term issue with the NME score, namely the fact that large poses can have an artificially large NME due to having a small $d_0$ . + +# 5.2. A new landmark video dataset: WFLW-V + +Due to the tedious nature of producing landmark annotations for video data, there are few existing datasets for face landmark detection in videos. Shen et al. have proposed 300-VW [60], a dataset made up of $\sim 100$ videos using the 68-point landmark scheme from the 300-W dataset [57]. Unfortunately, two major issues make this dataset unpopular: 1) it was labelled using fairly weak models from [18] and [67] which results in many labelling errors and high flicker (see Appendix B), and 2) it only contains 100 videos of little diversity, many of which being from the same speaker, or from different speakers in the same environment. Taken together, these two issues mean that the + +![](images/be2e1e14b203fd4cb3c3954438f0f19d5de42f49aff49db4dce4ecfdaf8503c2.jpg) +Figure 4. Example of ground truth labels $(\ast)$ obtained semi-automatically from an ensemble of 45 models $(\triangle)$ . Ensembling these diverse models provides ground truth labels that do not flicker and can thus be used to measure flickering against. Note how landmark points with the most uncertainty are the most prone to having flickering predictions across consecutive frames. + +performance of modern models on 300-WV barely correlates with performance on real-world face videos. + +We propose a new video dataset for facial landmarks: WFLW-Video (WFLW-V). It consists of 1000 Youtube creative-commons videos (i.e., an order of magnitude more than its predecessor) and covers a wide range of people, expressions, poses, activities and background environments. Each video is 5s in length. These videos were collected by targeting challenging faces, where ground truth landmarks are subject to uncertainty. The dataset contains two subsets, hard and easy, made up of 500 videos each. This allows debugging temporal filters and smoothing techniques, whose optimal hyperparameters are often different for videos with little or a lot of flicker. This split was obtained by scraping 2000 videos, and selecting the top and bottom 500 videos based on the variance of predictions in the ensemble. To evaluate a landmark model on the WFLW-V dataset, we train it on the WFLW training set, and evaluate it on all WFLW-V videos. This pipeline best reflects the way large landmark models are trained in the industry, where labelled video data is scarce. + +Contrary to the 68-landmark scheme of the 300-VW dataset, we label videos semi-automatically using the more challenging 98-landmark scheme from the WFLW dataset [75], as it is considered the most relevant dataset for future research in face landmark detection [38]. To produce ground truth labels, we train an ensemble of 45 state-of-the-art models using a wide range of data augmentations + +of both the test and train set of WFLW (amounting to 10,000 images). We use a mix of large Unets, HRNets [63] and HRFormers [83] to promote landmark diversity. The heatmaps of these models are averaged to produce the ground truth heatmap, allowing uncertain models to weight less in the aggregated output. Ensembling models provide temporal coherence without the need for using hand-tuned filtering or smoothing, which are susceptible to misinterpreting signal for noise (e.g. closing eye landmarks mimic high frequency noise). + +We provide examples of annotated videos in Fig. 4. Note that regions of ambiguity, such as occluded parts of the face, correspond to a higher variance in landmark predictions. While the ground truth for some frames may be subjective (e.g. occluded mouth), having a temporally stable "best guess" is sufficient to measure flicker of individual models. We found that 45 models in the ensemble was enough to provide a low error on the mean for all videos in WFLW-V. While we manually checked that our Oracle was highly accurate and coherent in time, note that it is completely impractical to use it for real-world applications due to its computational cost ( $\sim$ 2B parameters). + +We checked each frame manually for errors, which were rare. When we found an error in annotation, we corrected it by removing inaccurate models from the ensemble for the frames affected, rather than re-labeling the frame manually. We found this approach to be faster and less prone to human subjectivity when dealing with ambiguous faces, such + +
MethodParams (M)FullLarge posesExpressionsIlluminationMakeupOcclusionBlur
LAB [75]CVPR 201812.35.2710.245.515.235.156.796.32
Wing [26]CVPR 2018254.998.435.214.885.266.215.81
MHHN [69]TIP 2020-4.779.314.794.724.596.175.82
DecaFA [21]ICCV 2019104.628.114.654.414.635.745.38
HRNet [63]TPAMI 20209.74.607.944.854.554.295.445.42
AS [54]ICCV 2019354.398.424.684.244.375.604.86
LUVLI [40]CVPR 2020-4.377.564.774.304.335.294.94
AWing [73]ICCV 201924.24.367.384.584.324.275.194.96
SDFL [46]TIP 2021-4.357.424.634.294.225.195.08
SDL [44]ECCV 2020-4.217.364.494.124.054.984.82
ADNet [34]ICCV 202113.44.146.964.384.094.055.064.79
SLPT [77]CVPR 202219.54.126.994.374.024.035.014.79
HIH [42]-22.74.086.874.064.343.854.854.66
LDEQ (ours)-21.83.926.863.944.173.754.774.59
+ +as occluded ones. Occlusion has been characterized as one of the main remaining challenges in modern landmark detection [76], being most difficult in video data [60]. Finally, the stability of our oracle also depends on the stability of the face bounding box detector. We found the most popular detector, MTCNN [85] to be too jittery, and instead obtained stable detection by bootstrapping our oracle landmarks into the detector. More details about scraping and curating our dataset can be found in Appendix A. + +Table 1. Performance of our model and previous state-of-the-art on the various WFLW subsets, using the NME metric (↓) for comparison. Models using pre-training on other datasets have been excluded for fair comparison [14,82,88]. + +
MetricMethodFullPoseExp.Illum.Mu.Occ.Blur
FR10(↓)LAB7.5628.836.376.737.7713.7210.74
HRNet4.6423.013.504.722.438.296.34
AS4.0818.104.462.724.377.744.40
LUVLi3.1215.953.182.153.406.393.23
AWing2.8413.502.232.582.915.983.75
SDFL2.7212.881.592.582.435.713.62
SDL3.0415.952.862.721.455.294.01
ADNet2.7212.722.152.441.945.793.54
SLPT2.7211.961.592.151.945.703.88
HIH2.6012.881.272.431.455.163.10
LDEQ2.4812.581.592.291.945.362.84
AUC10(↑)LAB0.5320.2350.4950.5430.5390.4490.463
HRNet0.5240.2510.5100.5330.5450.4590.452
AS0.5910.3110.5490.6090.5810.5160.551
LUVLi0.5570.3100.5490.5840.5880.5050.525
AWing0.5720.3120.5150.5780.5720.5020.512
SDFL0.5760.3150.5500.5850.5830.5040.515
SDL0.5890.3150.5660.5950.6040.5240.533
ADNet0.6020.3440.5230.5800.6010.5300.548
SLPT0.5960.3490.5730.6030.6080.5200.537
HIH0.6050.3580.6010.6130.6180.5390.561
LDEQ0.6240.3730.6140.6310.6310.5520.574
+ +Table 2. ${\mathrm{{AUC}}}_{10}$ and ${\mathrm{{FR}}}_{10}$ on the WFLW test set. + +# 6. Experiments + +The aim of these experiments is to demonstrate that: 1) LDEQ is a state-of-the-art landmark detection model for high precision settings like faces, and 2) the LDEQ objective can be modified at inference time on videos to include a recurrence loss. This increases temporal coherence without decreasing accuracy, a common pitfall of popular filters. + +# 6.1. Landmark accuracy + +We compare the performance of LDEQ to state-of-the-art models on the WFLW dataset [75], which is based on the WIDER Face dataset [81] and is made up of 7500 train images and 2500 test images. Each image is annotated with a face bounding box and 98 2D landmarks. Compared to previous datasets, WFLW uses denser facial landmarks, and introduces much more diversity in poses, expressions, occlusions and image quality (the test set is further divided into subsets reflecting these factors). This makes it uniquely appropriate for training landmark detectors meant to be deployed on real-world data, like the videos of WFLW-V. + +The common evaluation metrics for the WFLW test set are the Normalized Mean Error (see Eq. (10b)), the Area Under the Curve (AUC), and the Failure Rate (FR). The AUC is computed on the cumulative error distribution curve (CED), which plots the fraction of images with NME less or equal to some cutoff, vs. increasing cutoff values. We report $\mathrm{AUC}_{10}$ , referring to a maximum NME cutoff of 10 for the CED curve. Higher AUC is better. The $\mathrm{FR}_X$ metric is equal to the percentage of test images whose NME is larger than $X$ . We report $\mathrm{FR}_{10}$ ; lower is better. + +We train our LDEQ for 60 epochs using the pre-cropped WFLW dataset as per [42], and the common data augmentations for face landmarks: rotations, flips, translations, blurs + +![](images/9c3c5e3f8dd7467fc0bfa601545a00d73bfc43ee57fa708d077f97a1f70f855e.jpg) +Figure 5. NME (accuracy) vs NMF (temporal coherence) for various models, on the hard (left) and easy (right) WFLW-V subsets. We compare our RwR scheme (blue) to a conventional filter (exponential moving average) using three different smoothing coefficients (gray). For hard videos susceptible to flicker, RwR on LDEQ decreases NME by $12\%$ without increasing NME, contrary to the conventional filter alternative. For easy videos that contain little to no flicker, conventional filters can increase both NME and NMF, while our model converges to the same fixed point with or without RwR. These results are given in tabular form in Appendix C. + +![](images/d0915bcf4794321a252a0637f20f67ee4a924bccb16cf44ef45e128e82c29989.jpg) + +and occlusions. We found the Anderson and fixed-point-iteration solvers to work best over the Broyden solver used in the original DEQ model [9, 10]. By setting a normalization temperature of $T = 2.5$ , convergence to fixed points only takes around 5 solver iterations. The NME, AUC and FR performance of LDEQ can be found in tables 1 and 2. We outperform all existing models on all three evaluation metrics, usually dominating individual subsets as well, which is important when applying LDEQ to video data. + +# 6.2. Landmark temporal coherence + +We evaluate the performance of LDEQ on the WFLW-V dataset, for both landmark accuracy (NME) and temporal coherence (NMF). We use RwR with early stopping after 2 solver iterations, allowing some adaptive compute (1 solver iteration) in cases where two consecutive frames are almost identical. Our baselines include previous state-of-the-art models that have publicly available weights [42, 46, 73, 77], as well as common architectures of comparable parameter count, which we trained with our own augmentation pipeline. We apply a conventional filtering algorithm, the exponential moving average, to our baselines. This was found to be more robust than more sophisticated filters like Savitzky-Golay filter [59] and One Euro filter [16]. + +The NME vs. NMF results are shown in Fig. 5 for all models, for the hard and easy WFLW-V subsets. For videos that contain little uncertainty in landmarks (WFLW-V easy), there is little flickering and conventional filtering methods can mistakenly smooth out high frequency signal (e.g. eyes and mouth moving fast). For videos subject to more flickering (WFLW-hard), these same filtering tech- + +niques do indeed improve the NMF metric, but beyond a certain smoothing factor this comes at the cost of increasing the NME. In contrast, LDEQ + RwR correctly smooths out flicker for WFLW-W hard without compromising performance on WFLW-V easy. This improvement comes from the fact that the RwR loss in Eq. (8) contains both a smoothing loss plus a log likelihood loss that constrains output landmarks to be plausible solutions, while conventional filters only optimize for the former. + +# 7. Conclusion + +We adapt Deep Equilibrium Models to landmark detection, and demonstrate that our LDEQ model can reach state-of-the-art accuracy on the challenging WFLW facial dataset. We then bring the attention of the landmark community to a common problem in video applications, whereby landmarks flicker across consecutive frames. We contribute a new dataset and metric to effectively benchmark solutions to that problem. Since DEQs solve for an objective in the forward pass, we propose to change this objective at test time to take into account new information. This new paradigm can be used to tackle the flickering problem, by adding a recurrent loss term at inference that wasn't present at training time (RwR). We show how to solve for this objective cheaply in a way that leads to state-of-the-art video temporal coherence. We hope that our work brings attention to the potential of deep equilibrium models for computer vision applications, and in particular, the ability to add loss terms to the forward pass process, to leverage new information at inference time. + +# References + +[1] Mediapipe 3d face transform. https://developers. googleblog .com/2020/09/mediapipe-3d-face-transform.html. Accessed: 2022-11-09. 1 +[2] Mediapipe face mesh. https://google.github.io/mediapipe/solutions/face_grid. Accessed: 2022-11-09. 1 +[3] Brandon Amos and J. Zico Kolter. OptNet: Differentiable optimization as a layer in neural networks. 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In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 787-796, 2015. 1 +[90] Matt Johnson Zico Kolter, David Duvenaud. http://implicit-layers-tutorial.org/deep_equilibrium_models/.3 \ No newline at end of file diff --git a/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/images.zip b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fe16e7fa8c9097de7d219a7d5492beeb58939eff --- /dev/null +++ b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:37160672d04cd02202784096a85cb4135e4fcc94f142613b7ae3416e12359ad7 +size 687948 diff --git a/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/layout.json b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e412091285ade5c076e5266130b255150dcdd6c5 --- /dev/null +++ b/2023/Recurrence Without Recurrence_ Stable Video Landmark Detection With Deep Equilibrium Models/layout.json @@ -0,0 +1,9169 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 94, + 104, + 500, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 104, + 500, + 140 + ], + "spans": [ + { + "bbox": [ + 94, + 104, + 500, + 140 + ], + "type": "text", + "content": "Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 161, + 179, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 161, + 179, + 204 + ], + "spans": [ + { + "bbox": [ + 59, + 161, + 179, + 204 + ], + "type": "text", + "content": "Paul Micaelli \nUniversity of Edinburgh \npaul.micaelli@ed.ac.uk" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 201, + 161, + 302, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 201, + 161, + 302, + 203 + ], + "spans": [ + { + "bbox": [ + 201, + 161, + 302, + 203 + ], + "type": "text", + "content": "Arash Vahdat NVIDIA \navahdat@nvidia.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 324, + 161, + 419, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 161, + 419, + 203 + ], + "spans": [ + { + "bbox": [ + 324, + 161, + 419, + 203 + ], + "type": "text", + "content": "Hongxu Yin \nNVIDIA \ndanny@nvidia.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 441, + 161, + 534, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 441, + 161, + 534, + 203 + ], + "spans": [ + { + "bbox": [ + 441, + 161, + 534, + 203 + ], + "type": "text", + "content": "Jan Kautz \nNVIDIA \njkautz@nvidia.com" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 253, + 209, + 339, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 253, + 209, + 339, + 236 + ], + "spans": [ + { + "bbox": [ + 253, + 209, + 339, + 236 + ], + "type": "text", + "content": "Pavlo Molchanov \nNVIDIA" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 237, + 240, + 353, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 237, + 240, + 353, + 250 + ], + "spans": [ + { + "bbox": [ + 237, + 240, + 353, + 250 + ], + "type": "text", + "content": "pmolchanov@nvidia.com" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 278, + 192, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 278, + 192, + 291 + ], + "spans": [ + { + "bbox": [ + 143, + 278, + 192, + 291 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "text", + "content": "Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium Model (DEQ) can be naturally adapted to this form of computation. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching 3.92 NME with fewer parameters and a training memory cost of " + }, + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(1)" + }, + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "text", + "content": " in the number of recurrent modules. Furthermore, we show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labelled videos. This can lead to a \"flickering\" effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. By rephrasing DEQs as a constrained optimization, we emulate recurrence at inference time, despite not having access to temporal data at training time. This Recurrence without Recurrence (RwR) paradigm helps in reducing landmark flicker, which we demonstrate by introducing a new metric, normalized mean flicker (NMF), and contributing a new facial landmark video dataset (WFLW-V) targeting landmark uncertainty. On the WFLW-V hard subset made up of 500 videos, our LDEQ with RwR improves the NME and NMF by 10 and " + }, + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 46, + 305, + 289, + 628 + ], + "type": "text", + "content": " respectively, compared to the strongest previously published model using a hand-tuned conventional filter." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 656, + 128, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 128, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 128, + 668 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "The field of facial landmark detection has been fueled by important applications such as face recognition [49, 71], facial expression recognition [33, 37, 39, 43, 79], and face" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 279, + 547, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 547, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 547, + 471 + ], + "type": "text", + "content": "alignment [55,87,89]. Early approaches to landmark detection relied on a statistical model of the global face appearance and shape [19,20,25], but this was then superseded by deep learning regression models [21,26,34,40,44,46,54,63, 68,69,73,75,77]. Both traditional and modern approaches have relied upon cascaded computation, an approach which starts with an initial guess of the landmarks and iteratively produces corrected landmarks which match the input face more finely. These iterations typically increase the training memory cost linearly, and do not have an obvious stopping criteria. To solve these issues, we adapt the recently proposed Deep Equilibrium Model [9-11] to the setting of landmark detection. Our Landmark DEQ (LDEQ) achieves state-of-the-art performance on the WFLW dataset, while enjoying a natural stopping criteria and a memory cost that is constant in the number of cascaded iterations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": "Furthermore, we explore the benefits of DEQs in landmark detection from facial videos. Since obtaining landmark annotation for videos is notoriously expensive, models are virtually always trained on still images and applied frame-wise on videos at inference time. When a sequence of frames have ambiguous landmarks (e.g., occluded faces or motion blur), this leads to flickering landmarks, which rapidly oscillate between different possible configurations across consecutive frames. This poor temporal coherence is particularly problematic in applications where high precision is required, which is typically the case for facial landmarks. These applications include face transforms [1, 2], face reenactment [84], video emotion recognition [33, 37, 39, 79], movie dubbing [28] or tiredness monitoring [35]. We propose to modify the DEQ objective at inference time to include a new recurrent loss term that encourages temporal coherence. We measure this improvement on our new WFLW-Video dataset (WFLW-V), demonstrating superiority over traditional filters, which typically reduce flickering at the cost of reducing landmark accuracy." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22814" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 69, + 534, + 178 + ], + "blocks": [ + { + "bbox": [ + 52, + 76, + 64, + 88 + ], + "lines": [ + { + "bbox": [ + 52, + 76, + 64, + 88 + ], + "spans": [ + { + "bbox": [ + 52, + 76, + 64, + 88 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 82, + 69, + 534, + 178 + ], + "lines": [ + { + "bbox": [ + 82, + 69, + 534, + 178 + ], + "spans": [ + { + "bbox": [ + 82, + 69, + 534, + 178 + ], + "type": "image", + "image_path": "42c765552c189bfd97938713cc955b931477d682e7bdd882741ffa272c5e4cc7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 69, + 194, + 532, + 283 + ], + "blocks": [ + { + "bbox": [ + 52, + 184, + 64, + 195 + ], + "lines": [ + { + "bbox": [ + 52, + 184, + 64, + 195 + ], + "spans": [ + { + "bbox": [ + 52, + 184, + 64, + 195 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 69, + 194, + 532, + 283 + ], + "lines": [ + { + "bbox": [ + 69, + 194, + 532, + 283 + ], + "spans": [ + { + "bbox": [ + 69, + 194, + 532, + 283 + ], + "type": "image", + "image_path": "d678b5bd6312df57d1e05f64a4b01b4676f08b23d475dc97774e389a1c95e6d0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 290, + 546, + 335 + ], + "lines": [ + { + "bbox": [ + 45, + 290, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 45, + 290, + 546, + 335 + ], + "type": "text", + "content": "Figure 1. (a) Common Stacked-Hourglass architecture [51], whereby each cascaded stage increases the memory cost and the number of backpropagation operations. (b) Our LDEQ model, which adapts an equilibrium model [9] to the landmark detection setting, enjoying a constant memory cost with the number of refining stages. At each stage, we compute landmark probability heatmaps, and encourage convergence to an equilibrium by lowering their entropy. We release our code here: https://github.com/polo5/LDEQ_RwR." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 354, + 130, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 130, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 130, + 366 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": "Deep Equilibrium Models [9] are part of the family of implicit models, which learn implicit functions such as the solution to an ODE [17, 24], or the solution to an optimization problem [3, 22, 72]. These functions are called implicit in the sense that the output cannot be written as a function of the input explicitly. In the case of DEQs, the output is the root of a function, and the model learned is agnostic to the root solver used. Early DEQ models were too slow to be competitive, and much work since has focused on better architecture design [10] and faster root solving [11, 27, 29]. Since the vanilla formulation of DEQs does not guarantee convergence or uniqueness of an equilibrium, another branch of research has focused on providing convergence guarantees [52, 56, 74], which usually comes at the cost of a performance drop. Most similar to our work is the recent use of DEQs for videos in the context of optical flow estimation [8], where slightly better performance than LSTM-based models was observed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "A common theme throughout the development of landmark detection models has been the idea of cascaded compute, which has repeatedly enjoyed a better performance compared to single stage models [71]. This is true in traditional models like Cascaded Pose Regression (CPR) [7, 15, 23, 65, 78], but also in most modern landmark detection models [34, 40, 42, 69, 73, 75, 80], which usually rely on the Stacked-Hourglass backbone [51], or an RNN structure [41, 66]. In contrast to these methods, our DEQ-based model can directly solve for an infinite number of refine-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 356, + 545, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 463 + ], + "type": "text", + "content": "ment stages at a constant memory cost and without gradient degradation. This is done by relying on the implicit function theorem, as opposed to tracking each forward operation in autograd. Furthermore, our model naturally supports adaptive compute, in the sense that the number of cascaded stages will be determined by how hard finding an equilibrium is for a specific input, while the number of stages in, say, the Stacked-Hourglass backbone, must be constant at all times." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 464, + 546, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 546, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 546, + 594 + ], + "type": "text", + "content": "Our recurrence without recurrence approach is most closely related to test time adaption methods. These have been most commonly developed in the context of domain adaptation [64,70], reinforcement learning [32], meta-learning [86], generative models [36, 50], pose estimation [45] or super resolution [6]. Typically, the methods above finetune a trained model at test time using a form of self-supervision. In contrast, our model doesn't need to be finetuned at test time: since DEQs solve for an objective function in the forward pass, this objective is simply modified at test time." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 609, + 473, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 473, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 473, + 621 + ], + "type": "text", + "content": "3. DEQs for landmark detection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": "Consider learning a landmark detection model " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": ", which maps an input image " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " to landmarks " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": ". Instead of directly having " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " as 2D landmarks, it is common for " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " to represent " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " heatmaps of size " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "D\\times D" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " is a hyperparameter (usually 64) and " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " is the number of landmarks to learn. While typical machine learning models can explicitly write down the function " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z} = F(\\pmb{x};\\pmb{\\theta})" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": ", in" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22815" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "the DEQ approach this function is expressed implicitly by requiring its output to be a fixed point of another function " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "f(z, x; \\theta)" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 93, + 113, + 287, + 126 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 113, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 93, + 113, + 287, + 126 + ], + "type": "interline_equation", + "content": "F: \\boldsymbol {x} \\rightarrow \\boldsymbol {z} ^ {*} \\quad \\text {s . t .} \\quad \\boldsymbol {z} ^ {*} = f (\\boldsymbol {z} ^ {*}, \\boldsymbol {x}; \\boldsymbol {\\theta}) \\tag {1}", + "image_path": "4185bc5657a538fc85e42e3b13e4ef098f3800423fb92e82f6860b31ead04e47.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": " denotes the fixed point, or equivalently the root of " + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "inline_equation", + "content": "g(\\pmb{x},\\pmb{z};\\pmb{\\theta}) = f(\\pmb{z},\\pmb{x};\\pmb{\\theta}) - \\pmb{z}" + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": ". The function " + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": " must have inputs and outputs of similar shape, but beyond this restriction there is still limited understanding of its desired properties in machine learning. For simplicity, we build " + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": " from the ubiquitous hourglass module " + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 130, + 287, + 202 + ], + "type": "text", + "content": " (similar to a Unet):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 206, + 287, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 206, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 108, + 206, + 287, + 220 + ], + "type": "interline_equation", + "content": "f (\\boldsymbol {z}, \\boldsymbol {x}; \\boldsymbol {\\theta}) = \\sigma (h ([ \\boldsymbol {x}, \\boldsymbol {z} ]; \\boldsymbol {\\theta})) \\tag {2}", + "image_path": "b5d6b51511d949520db0bd9e0fa03b049aef3998b87a17bf321c34edd8c62e80.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": " inputs the concatenation of " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": " is a normalization function. For clarity, we omit from our notation that image " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": " is downsampled with a few convolutions to match the shape of " + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 224, + 287, + 272 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": "To evaluate " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " in the forward pass, we must solve for its fixed point " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " is a contraction mapping, " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "f \\circ f \\circ f \\circ \\dots \\circ f \\circ z^{(0)}" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " converges to a unique " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " for any initial heatmap " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "z^{(0)}" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": ". In practice, it is neither tractable or helpful to directly take an infinite number of fixed point iteration steps. Instead, it is common to achieve the same result by leveraging quasi Newtonian solvers like Broyden's method [13] or Anderson acceleration [4], which find " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " in fewer iterations. Similarly to the original DEQ model, we use " + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "inline_equation", + "content": "z^{(0)} = 0" + }, + { + "bbox": [ + 47, + 272, + 287, + 392 + ], + "type": "text", + "content": " when training our LDEQ on still images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 392, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 287, + 487 + ], + "type": "text", + "content": "Guaranteeing the existence of a unique fixed point by enforcing contraction restrictions on " + }, + { + "bbox": [ + 47, + 392, + 287, + 487 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 392, + 287, + 487 + ], + "type": "text", + "content": " is cumbersome, and better performance can often be obtained by relying on regularization heuristics that are conducive to convergence, such as weight normalization and variational dropout [10]. In our landmark model, we did not find these tricks helpful, and instead used a simple normalization of the heatmaps to [0, 1] at each refining stage:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 491, + 287, + 518 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 491, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 287, + 518 + ], + "type": "interline_equation", + "content": "\\sigma (z) = \\exp \\left(\\frac {z - \\operatorname* {m a x} (z)}{T}\\right) \\tag {3}", + "image_path": "4735afdab9aa305b90f9da3083e47c168a66b2d31d2571e777d0acb8818890e7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 521, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 567 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 521, + 287, + 567 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 521, + 287, + 567 + ], + "type": "text", + "content": " is a temperature hyperparameter. This layer also acts as an entropy regularizer, since it induces low-entropy (\"peaked\") heatmaps, which we found to improve convergence of root solvers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": "We contrast our model in Fig. 1 to the popular Stacked-Hourglass backbone [51]. Contrary to this model, our DEQ-based model uses a single hourglass module which updates " + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": " until an equilibrium is found. The last predicted heatmaps, " + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": ", are converted into 2D landmark points " + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\hat{p} = \\Phi(z^{*})" + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": " using the softargmax function " + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\Phi(z)" + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": " proposed in [48]. These points are trained to match the ground truth " + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 568, + 287, + 676 + ], + "type": "text", + "content": ", and so the DEQ landmark training problem can be seen as a constrained optimization:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 99, + 680, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 680, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 99, + 680, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {\\theta} ^ {*} = \\underset {\\boldsymbol {\\theta}} {\\arg \\min } \\mathcal {L} _ {\\text {M S E}} (\\Phi (\\boldsymbol {z} ^ {*}), \\boldsymbol {p}) \\tag {4} \\\\ \\text {s . t .} \\quad z ^ {*} = f \\left(z ^ {*}, x; \\theta\\right) \\\\ \\end{array}", + "image_path": "6ed64a71c65bb38f554ab09a8181c239ce7a7aedfe9255649c39764a01a7c9f3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "To differentiate our loss function " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MSE}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " through this root solving process, the implicit function theorem is used [9] to derive" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 116, + 545, + 141 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 116, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 347, + 116, + 545, + 141 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {\\theta}} = - \\frac {\\partial \\mathcal {L} _ {\\mathrm {M S E}}}{\\partial \\boldsymbol {z} ^ {*}} \\mathcal {J} _ {\\boldsymbol {g} \\boldsymbol {z} ^ {*}} ^ {- 1} \\frac {\\partial f (\\boldsymbol {z} ^ {*} , \\boldsymbol {x} ; \\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\tag {5}", + "image_path": "6cc3b01e4dff60f0bf2244692a75f133f921ddd7cd7ebe2621c9ab83b4b1233b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "text", + "content": "where the first two terms on the RHS can be expressed as the solution to a fixed point problem as well. Solving for this root in the backward pass means that we do not need to compute or store the expensive inverse Jacobian term " + }, + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{gz^*}" + }, + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "text", + "content": " directly [9, 90]. Importantly, this backward-pass computation only depends on " + }, + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "inline_equation", + "content": "z^*" + }, + { + "bbox": [ + 305, + 150, + 545, + 281 + ], + "type": "text", + "content": " and doesn't depend on the operations done in the forward pass to reach an equilibrium. This means that these operations do not need to be tracked by autograd, and therefore that training requires a memory cost of O(1), despite differentiating through a potentially infinite recurrence." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 296, + 481, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 481, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 481, + 308 + ], + "type": "text", + "content": "4. Recurrence without recurrence" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 316, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 545, + 388 + ], + "type": "text", + "content": "Low temporal coherence (i.e. a large amount of flicker) is illustrated in Fig. 2. This can be a nuisance for many applications that require consistently precise landmarks for video. In this section, we describe how our LDEQ model can address this challenge by enabling recurrence at test time without recurrence at training time (RwR)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 389, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 389, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 389, + 545, + 568 + ], + "type": "text", + "content": "Recall that in the DEQ formulation of Sec. 3, there is no guarantee that a unique fixed point solution exists. This can be a limitation for some applications, and DEQ variants have been proposed to allow provably unique solutions at the cost of additional model complexity [53, 74]. In this work, we instead propose a new paradigm: we leverage the potentially large solution space of DEQs after training to allow for some additional objective at inference time. This new objective is used to disambiguate which fixed point of " + }, + { + "bbox": [ + 305, + 389, + 545, + 568 + ], + "type": "inline_equation", + "content": "f(z, x; \\theta^*)" + }, + { + "bbox": [ + 305, + 389, + 545, + 568 + ], + "type": "text", + "content": " is found, in light of extra information present at test time. We demonstrate this approach for the specific application of training a landmark model on face images and evaluating it on videos. In this case, DEQs allow us to include a recurrent loss term at inference time, which isn't achievable with conventional architectures." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\pmb{z}, \\pmb{x}; \\pmb{\\theta}^*)" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " be our DEQ model trained as per the formulation in Eq. (4). We would now like to do inference on a video of " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " frames " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_N" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": ". Consider that a given frame " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}_n" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " has a corresponding set of fixed points " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_n^* = \\{z \\text { s.t. } f(\\pmb{z}, \\pmb{x}_n; \\pmb{\\theta}^*) = z\\}" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": ", representing plausible landmark heatmaps. If we select some " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z}_n^* \\in \\mathcal{Z}_n^*" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " at random for each frame " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": ", the corresponding heatmaps " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{z}_1^*, \\pmb{z}_2^*, \\dots, \\pmb{z}_N^*" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " often exhibit some flickering artefacts, whereby landmarks rapidly change across contiguous frames (see Fig. 2). We propose to address this issue by choosing the fixed point at frame " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": " that is closest to the fixed point at frame " + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": ". This can be expressed by the following constrained optimization:" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22816" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 80, + 545, + 169 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 62, + 80 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 62, + 80 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 62, + 80 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 80, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 65, + 80, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 65, + 80, + 545, + 169 + ], + "type": "image", + "image_path": "940ae187ce8860be61be775a2141fc6135f2f57afa6762279792835dee0190a7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 65, + 181, + 545, + 271 + ], + "blocks": [ + { + "bbox": [ + 51, + 171, + 62, + 180 + ], + "lines": [ + { + "bbox": [ + 51, + 171, + 62, + 180 + ], + "spans": [ + { + "bbox": [ + 51, + 171, + 62, + 180 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 181, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 65, + 181, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 65, + 181, + 545, + 271 + ], + "type": "image", + "image_path": "cbdfcb43393c3cf82ea7defe20387d3e9d5418f3c7be6c79fd32e18b1c2a0a06.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 282, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 45, + 282, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 45, + 282, + 547, + 326 + ], + "type": "text", + "content": "Figure 2. Model predictions (▲) and ground truth landmarks (○) for (a) a model with high temporal coherence and (b) a model with the same accuracy but exhibiting a worse temporal coherence, due to ambiguity at the chin. This causes flickering around the ground truth, as illustrated in the landmark trajectory (right). This flickering is common when video frames are evaluated individually, as opposed to recurrently." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 368, + 286, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 368, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 108, + 368, + 286, + 389 + ], + "type": "interline_equation", + "content": "z _ {n} ^ {*} = \\underset {z} {\\arg \\min } \\| z - z _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {6a}", + "image_path": "a5d12da762737329331f925a8eafc02278fb7e0fdbc92679f38058ceb060eacc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 127, + 392, + 286, + 405 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 392, + 286, + 405 + ], + "spans": [ + { + "bbox": [ + 127, + 392, + 286, + 405 + ], + "type": "interline_equation", + "content": "\\text {s . t .} f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) = \\boldsymbol {z} \\tag {6b}", + "image_path": "4873e47ceac126ca6c1764029eae8bc52bcf54a69bd37a0517bcc0bb63da7947.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 416, + 286, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 286, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 286, + 440 + ], + "type": "text", + "content": "The problem above is equivalent to solving for the saddle point of a Lagrangian as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 451, + 287, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 451, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 61, + 451, + 287, + 471 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {z}} \\max _ {\\boldsymbol {\\lambda}} \\left\\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\right\\| _ {2} ^ {2} + \\boldsymbol {\\lambda} ^ {T} \\left(f \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}\\right) - \\boldsymbol {z}\\right) \\tag {7}", + "image_path": "042f3e85a1ddbdc5364fa1a794c594c41af1eb897ae5f8e1db3815e3a1815356.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "content": " are Lagrange multipliers. Effectively, we are using the set of fixed points " + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_n^*" + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "content": " in Eq. (6b) as the trust region for the objective in Eq. (6a). In practice, adversarial optimization is notoriously unstable, as is typically observed in the context of GANs [5,30,62]. Furthermore, this objective breaks down if " + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_n^* = \\emptyset" + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 46, + 481, + 287, + 577 + ], + "type": "text", + "content": ". We can remedy both of these problems by relaxing the inference time optimization problem to:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 75, + 587, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 587, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 75, + 587, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {z}} \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} + \\frac {\\alpha}{2} \\| \\boldsymbol {z} - \\boldsymbol {z} _ {n - 1} ^ {*} \\| _ {2} ^ {2} \\tag {8}", + "image_path": "1906e4f9565762df2f439381ddbb9cb048e378f13b07536f704b0a3b62be105e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " is a hyperparameter that trades off fixed-point solver error vs. the shift in heatmaps across two consecutive frames. This objective can be more readily tackled with Newtonian optimizers like L-BFGS [47]. When doing so, our DEQ at inference time can be described as a form of OptNet [3], albeit without any of the practical limitations (e.g., quadratic programs) related to making gradient calculations cheap." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 347, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 419 + ], + "type": "text", + "content": "Converting our root solving problem into an optimization problem during the forward pass of each frame can significantly increase inference time. Thankfully, the objective in Eq. (8) can also be solved by using root solvers. First, note that it is equivalent to finding the MAP estimate given a log likelihood and prior:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 339, + 426, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 426, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 339, + 426, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\log p \\left(\\boldsymbol {x} _ {n} \\mid \\boldsymbol {z}; \\boldsymbol {\\theta} ^ {*}\\right) \\propto - \\| f (\\boldsymbol {z}, \\boldsymbol {x} _ {n}; \\boldsymbol {\\theta} ^ {*}) - \\boldsymbol {z} \\| _ {2} ^ {2} \\tag {9a}", + "image_path": "760bfaac11e9dbddf164c895d5c246b7aa7683169831d9652707c2f4eb65c465.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 383, + 443, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 443, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 383, + 443, + 545, + 456 + ], + "type": "interline_equation", + "content": "p (z) = \\mathcal {N} (z; z _ {n - 1}, \\alpha^ {- 1} \\mathbb {1}) \\tag {9b}", + "image_path": "696c5fa895470339d57643edf2c7ea01ac4e771bc6d0ab35551861d819e510e6.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 464, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 574 + ], + "type": "text", + "content": "It has been demonstrated in various settings that this prior, when centered on the initialization to a search algorithm, can be implemented by early stopping this algorithm [12, 31, 58, 61]. As such, we can approximate the solution to Eq. (6a-6b) by simply initializing the root solver with " + }, + { + "bbox": [ + 304, + 464, + 545, + 574 + ], + "type": "inline_equation", + "content": "z_{n}^{(0)} = z_{n - 1}^{*}" + }, + { + "bbox": [ + 304, + 464, + 545, + 574 + ], + "type": "text", + "content": " (\"reuse\") and imposing a hard limit on the number of steps that it can take (\"early stopping\"). We call this approach Recurrence without Recurrence (RwR), and illustrate it in Fig. 3." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 584, + 459, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 584, + 459, + 597 + ], + "spans": [ + { + "bbox": [ + 305, + 584, + 459, + 597 + ], + "type": "text", + "content": "5. Video landmark coherence" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "type": "text", + "content": "In this section we describe the metric (NMF) and the dataset (WFLW-V) that we contribute to measure the amount of temporal coherence in landmark videos. These are later used to benchmark the performance of our RwR paradigm against alternatives in Sec. 6.2." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 671, + 533, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 671, + 533, + 684 + ], + "spans": [ + { + "bbox": [ + 305, + 671, + 533, + 684 + ], + "type": "text", + "content": "5.1. NMF: a metric to track temporal coherence" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "The performance of a landmark detection model is typically measured with a single metric called the Normal-" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22817" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 69, + 527, + 295 + ], + "blocks": [ + { + "bbox": [ + 65, + 69, + 527, + 295 + ], + "lines": [ + { + "bbox": [ + 65, + 69, + 527, + 295 + ], + "spans": [ + { + "bbox": [ + 65, + 69, + 527, + 295 + ], + "type": "image", + "image_path": "321f9390505f323733d76ba50d0f136c0b04e99c5cd69308ef9337ea21a45553.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "text", + "content": "Figure 3. Recurrence without recurrence (RwR) on video data, from an LDEQ that was trained on still images. We use the initialization " + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_1^{(0)} = \\mathbf{0}" + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "text", + "content": " for the first frame, and then reuse " + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_n^{(0)} = \\mathbf{z}_{n - 1}^*" + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "inline_equation", + "content": "n > 1" + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "text", + "content": ". Combined with early stopping, this is equivalent to regularizing the fixed point " + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_n" + }, + { + "bbox": [ + 46, + 303, + 547, + 339 + ], + "type": "text", + "content": " so that it is more temporally coherent with all its predecessors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": "ized Mean Error (NME). Consider a video sequence of " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " frames, each containing " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " ground truth landmarks. A single landmark point is a 2D vector denoted " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{n,l} \\in \\mathcal{R}^2" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " are the frame and landmark index respectively. Let " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "\\pmb{r}_{n,l} = \\pmb{p}_{n,l} - \\hat{\\pmb{p}}_{n,l}" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " be the residual vector between ground truth landmarks and predicted landmarks " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{p}}_{n,l}" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": ". The NME simply averages the " + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 358, + 289, + 453 + ], + "type": "text", + "content": " norm of this residual across all landmarks and all frames:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 460, + 287, + 494 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 460, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 116, + 460, + 287, + 494 + ], + "type": "interline_equation", + "content": "\\mathrm {N M E} _ {n} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} \\right\\|}{d _ {0}} \\tag {10a}", + "image_path": "3c621ee1a3406bb4611107faa16ecc3ffe096c992ce4b726f4a000d291258521.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 121, + 495, + 287, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 495, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 121, + 495, + 287, + 528 + ], + "type": "interline_equation", + "content": "\\mathrm {N M E} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathrm {N M E} _ {n} \\tag {10b}", + "image_path": "c4d49a5f2fe61bee36ebcc40d18c3521027c66cea60b5285792ea8c1ded88930.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "inline_equation", + "content": "d_0" + }, + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "content": " is usually the inter-ocular distance, and aims to make the NME better correlate with the human perception of landmark error. We argue that this metric alone is insufficient to measure the performance of a landmark detector in videos. In Fig. 2 we show two models of equal NME but different coherence in time, with one model exhibiting flickering between plausible hypotheses when uncertain. This flickering is a nuisance for many applications, and yet is not captured by the NME. This is in contrast to random noise (jitter) which is unstructured and already reflected in the NME metric." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "To measure temporal coherence, we propose a new metric called the Normalized Mean Flicker (NMF). We design this metric to be orthogonal to the NME, by making it ag- nostic to the magnitude of " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "r_{n,l}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " , and only focusing on the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 358, + 476, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 476, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 476, + 371 + ], + "type": "text", + "content": "change of " + }, + { + "bbox": [ + 306, + 358, + 476, + 371 + ], + "type": "inline_equation", + "content": "\\pmb{r}_{n,l}" + }, + { + "bbox": [ + 306, + 358, + 476, + 371 + ], + "type": "text", + "content": " across consecutive frames:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 349, + 377, + 545, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 377, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 349, + 377, + 545, + 416 + ], + "type": "interline_equation", + "content": "\\mathrm {N M F} _ {n} = \\sqrt {\\frac {1}{L} \\sum_ {l = 1} ^ {L} \\frac {\\left\\| \\boldsymbol {r} _ {n , l} - \\boldsymbol {r} _ {n - 1 , l} \\right\\| ^ {2}}{d _ {1} ^ {2}}} \\tag {11a}", + "image_path": "d622740de12601a758dfa6935eeacaead5e13513d1700743290b7a169cbe1c5c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 355, + 418, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 418, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 355, + 418, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\mathrm {N M F} = \\sqrt {\\frac {1}{N} \\sum_ {n = 2} ^ {F} \\mathrm {N M F} _ {n} ^ {2}} \\tag {11b}", + "image_path": "e2903261e7f8f80a007c36111e7b100a65ecfaf285dbb32c42b7ce41c16faada.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "text", + "content": "We replace the means in the NME with a root mean square to better represent the human perception of flicker. Indeed, this penalizes a short sudden changes in " + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}_{n,l}" + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "text", + "content": " compared to the same change smoothed out in time and space. The value " + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "inline_equation", + "content": "d_1^2" + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "text", + "content": " is chosen to be the face area. This prevents a long term issue with the NME score, namely the fact that large poses can have an artificially large NME due to having a small " + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "inline_equation", + "content": "d_0" + }, + { + "bbox": [ + 304, + 461, + 545, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 552, + 525, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 525, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 525, + 563 + ], + "type": "text", + "content": "5.2. A new landmark video dataset: WFLW-V" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Due to the tedious nature of producing landmark annotations for video data, there are few existing datasets for face landmark detection in videos. Shen et al. have proposed 300-VW [60], a dataset made up of " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sim 100" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " videos using the 68-point landmark scheme from the 300-W dataset [57]. Unfortunately, two major issues make this dataset unpopular: 1) it was labelled using fairly weak models from [18] and [67] which results in many labelling errors and high flicker (see Appendix B), and 2) it only contains 100 videos of little diversity, many of which being from the same speaker, or from different speakers in the same environment. Taken together, these two issues mean that the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22818" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 533, + 311 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 311 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 311 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 311 + ], + "type": "image", + "image_path": "be2e1e14b203fd4cb3c3954438f0f19d5de42f49aff49db4dce4ecfdaf8503c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "text", + "content": "Figure 4. Example of ground truth labels " + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "inline_equation", + "content": "(\\ast)" + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "text", + "content": " obtained semi-automatically from an ensemble of 45 models " + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "inline_equation", + "content": "(\\triangle)" + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "text", + "content": ". Ensembling these diverse models provides ground truth labels that do not flicker and can thus be used to measure flickering against. Note how landmark points with the most uncertainty are the most prone to having flickering predictions across consecutive frames." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 373, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 397 + ], + "type": "text", + "content": "performance of modern models on 300-WV barely correlates with performance on real-world face videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 400, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 628 + ], + "type": "text", + "content": "We propose a new video dataset for facial landmarks: WFLW-Video (WFLW-V). It consists of 1000 Youtube creative-commons videos (i.e., an order of magnitude more than its predecessor) and covers a wide range of people, expressions, poses, activities and background environments. Each video is 5s in length. These videos were collected by targeting challenging faces, where ground truth landmarks are subject to uncertainty. The dataset contains two subsets, hard and easy, made up of 500 videos each. This allows debugging temporal filters and smoothing techniques, whose optimal hyperparameters are often different for videos with little or a lot of flicker. This split was obtained by scraping 2000 videos, and selecting the top and bottom 500 videos based on the variance of predictions in the ensemble. To evaluate a landmark model on the WFLW-V dataset, we train it on the WFLW training set, and evaluate it on all WFLW-V videos. This pipeline best reflects the way large landmark models are trained in the industry, where labelled video data is scarce." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Contrary to the 68-landmark scheme of the 300-VW dataset, we label videos semi-automatically using the more challenging 98-landmark scheme from the WFLW dataset [75], as it is considered the most relevant dataset for future research in face landmark detection [38]. To produce ground truth labels, we train an ensemble of 45 state-of-the-art models using a wide range of data augmentations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 495 + ], + "type": "text", + "content": "of both the test and train set of WFLW (amounting to 10,000 images). We use a mix of large Unets, HRNets [63] and HRFormers [83] to promote landmark diversity. The heatmaps of these models are averaged to produce the ground truth heatmap, allowing uncertain models to weight less in the aggregated output. Ensembling models provide temporal coherence without the need for using hand-tuned filtering or smoothing, which are susceptible to misinterpreting signal for noise (e.g. closing eye landmarks mimic high frequency noise)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 495, + 548, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 548, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 548, + 640 + ], + "type": "text", + "content": "We provide examples of annotated videos in Fig. 4. Note that regions of ambiguity, such as occluded parts of the face, correspond to a higher variance in landmark predictions. While the ground truth for some frames may be subjective (e.g. occluded mouth), having a temporally stable \"best guess\" is sufficient to measure flicker of individual models. We found that 45 models in the ensemble was enough to provide a low error on the mean for all videos in WFLW-V. While we manually checked that our Oracle was highly accurate and coherent in time, note that it is completely impractical to use it for real-world applications due to its computational cost (" + }, + { + "bbox": [ + 304, + 495, + 548, + 640 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 304, + 495, + 548, + 640 + ], + "type": "text", + "content": "2B parameters)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "We checked each frame manually for errors, which were rare. When we found an error in annotation, we corrected it by removing inaccurate models from the ensemble for the frames affected, rather than re-labeling the frame manually. We found this approach to be faster and less prone to human subjectivity when dealing with ambiguous faces, such" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22819" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 533, + 254 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 254 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 254 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 254 + ], + "type": "table", + "html": "
MethodParams (M)FullLarge posesExpressionsIlluminationMakeupOcclusionBlur
LAB [75]CVPR 201812.35.2710.245.515.235.156.796.32
Wing [26]CVPR 2018254.998.435.214.885.266.215.81
MHHN [69]TIP 2020-4.779.314.794.724.596.175.82
DecaFA [21]ICCV 2019104.628.114.654.414.635.745.38
HRNet [63]TPAMI 20209.74.607.944.854.554.295.445.42
AS [54]ICCV 2019354.398.424.684.244.375.604.86
LUVLI [40]CVPR 2020-4.377.564.774.304.335.294.94
AWing [73]ICCV 201924.24.367.384.584.324.275.194.96
SDFL [46]TIP 2021-4.357.424.634.294.225.195.08
SDL [44]ECCV 2020-4.217.364.494.124.054.984.82
ADNet [34]ICCV 202113.44.146.964.384.094.055.064.79
SLPT [77]CVPR 202219.54.126.994.374.024.035.014.79
HIH [42]-22.74.086.874.064.343.854.854.66
LDEQ (ours)-21.83.926.863.944.173.754.774.59
", + "image_path": "5018cddf33ee067520cce034432625d18a05552e5c39738f9fe2874cd1415fc1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 305, + 288, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 288, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 288, + 414 + ], + "type": "text", + "content": "as occluded ones. Occlusion has been characterized as one of the main remaining challenges in modern landmark detection [76], being most difficult in video data [60]. Finally, the stability of our oracle also depends on the stability of the face bounding box detector. We found the most popular detector, MTCNN [85] to be too jittery, and instead obtained stable detection by bootstrapping our oracle landmarks into the detector. More details about scraping and curating our dataset can be found in Appendix A." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 465, + 285, + 689 + ], + "blocks": [ + { + "bbox": [ + 46, + 262, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 545, + 285 + ], + "type": "text", + "content": "Table 1. Performance of our model and previous state-of-the-art on the various WFLW subsets, using the NME metric (↓) for comparison. Models using pre-training on other datasets have been excluded for fair comparison [14,82,88]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 465, + 285, + 689 + ], + "lines": [ + { + "bbox": [ + 50, + 465, + 285, + 689 + ], + "spans": [ + { + "bbox": [ + 50, + 465, + 285, + 689 + ], + "type": "table", + "html": "
MetricMethodFullPoseExp.Illum.Mu.Occ.Blur
FR10(↓)LAB7.5628.836.376.737.7713.7210.74
HRNet4.6423.013.504.722.438.296.34
AS4.0818.104.462.724.377.744.40
LUVLi3.1215.953.182.153.406.393.23
AWing2.8413.502.232.582.915.983.75
SDFL2.7212.881.592.582.435.713.62
SDL3.0415.952.862.721.455.294.01
ADNet2.7212.722.152.441.945.793.54
SLPT2.7211.961.592.151.945.703.88
HIH2.6012.881.272.431.455.163.10
LDEQ2.4812.581.592.291.945.362.84
AUC10(↑)LAB0.5320.2350.4950.5430.5390.4490.463
HRNet0.5240.2510.5100.5330.5450.4590.452
AS0.5910.3110.5490.6090.5810.5160.551
LUVLi0.5570.3100.5490.5840.5880.5050.525
AWing0.5720.3120.5150.5780.5720.5020.512
SDFL0.5760.3150.5500.5850.5830.5040.515
SDL0.5890.3150.5660.5950.6040.5240.533
ADNet0.6020.3440.5230.5800.6010.5300.548
SLPT0.5960.3490.5730.6030.6080.5200.537
HIH0.6050.3580.6010.6130.6180.5390.561
LDEQ0.6240.3730.6140.6310.6310.5520.574
", + "image_path": "8e0113fe1695eb210fa8cbcd58d0924e6d9a673adc5dc0fa0894af925b3d5f2e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "lines": [ + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "spans": [ + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "type": "text", + "content": "Table 2. " + }, + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "type": "inline_equation", + "content": "{\\mathrm{{AUC}}}_{10}" + }, + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "type": "inline_equation", + "content": "{\\mathrm{{FR}}}_{10}" + }, + { + "bbox": [ + 77, + 699, + 256, + 709 + ], + "type": "text", + "content": " on the WFLW test set." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 304, + 387, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 387, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 387, + 319 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 325, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 545, + 397 + ], + "type": "text", + "content": "The aim of these experiments is to demonstrate that: 1) LDEQ is a state-of-the-art landmark detection model for high precision settings like faces, and 2) the LDEQ objective can be modified at inference time on videos to include a recurrence loss. This increases temporal coherence without decreasing accuracy, a common pitfall of popular filters." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 406, + 424, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 424, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 424, + 419 + ], + "type": "text", + "content": "6.1. Landmark accuracy" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 426, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 556 + ], + "type": "text", + "content": "We compare the performance of LDEQ to state-of-the-art models on the WFLW dataset [75], which is based on the WIDER Face dataset [81] and is made up of 7500 train images and 2500 test images. Each image is annotated with a face bounding box and 98 2D landmarks. Compared to previous datasets, WFLW uses denser facial landmarks, and introduces much more diversity in poses, expressions, occlusions and image quality (the test set is further divided into subsets reflecting these factors). This makes it uniquely appropriate for training landmark detectors meant to be deployed on real-world data, like the videos of WFLW-V." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": "The common evaluation metrics for the WFLW test set are the Normalized Mean Error (see Eq. (10b)), the Area Under the Curve (AUC), and the Failure Rate (FR). The AUC is computed on the cumulative error distribution curve (CED), which plots the fraction of images with NME less or equal to some cutoff, vs. increasing cutoff values. We report " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{AUC}_{10}" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": ", referring to a maximum NME cutoff of 10 for the CED curve. Higher AUC is better. The " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{FR}_X" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": " metric is equal to the percentage of test images whose NME is larger than " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": ". We report " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{FR}_{10}" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": "; lower is better." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We train our LDEQ for 60 epochs using the pre-cropped WFLW dataset as per [42], and the common data augmentations for face landmarks: rotations, flips, translations, blurs" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22820" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 296, + 254 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 296, + 254 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 296, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 296, + 254 + ], + "type": "image", + "image_path": "9c3c5e3f8dd7467fc0bfa601545a00d73bfc43ee57fa708d077f97a1f70f855e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": "Figure 5. NME (accuracy) vs NMF (temporal coherence) for various models, on the hard (left) and easy (right) WFLW-V subsets. We compare our RwR scheme (blue) to a conventional filter (exponential moving average) using three different smoothing coefficients (gray). For hard videos susceptible to flicker, RwR on LDEQ decreases NME by " + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": " without increasing NME, contrary to the conventional filter alternative. For easy videos that contain little to no flicker, conventional filters can increase both NME and NMF, while our model converges to the same fixed point with or without RwR. These results are given in tabular form in Appendix C." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 68, + 547, + 254 + ], + "blocks": [ + { + "bbox": [ + 298, + 68, + 547, + 254 + ], + "lines": [ + { + "bbox": [ + 298, + 68, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 298, + 68, + 547, + 254 + ], + "type": "image", + "image_path": "d0915bcf4794321a252a0637f20f67ee4a924bccb16cf44ef45e128e82c29989.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 339, + 289, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 289, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 289, + 447 + ], + "type": "text", + "content": "and occlusions. We found the Anderson and fixed-point-iteration solvers to work best over the Broyden solver used in the original DEQ model [9, 10]. By setting a normalization temperature of " + }, + { + "bbox": [ + 46, + 339, + 289, + 447 + ], + "type": "inline_equation", + "content": "T = 2.5" + }, + { + "bbox": [ + 46, + 339, + 289, + 447 + ], + "type": "text", + "content": ", convergence to fixed points only takes around 5 solver iterations. The NME, AUC and FR performance of LDEQ can be found in tables 1 and 2. We outperform all existing models on all three evaluation metrics, usually dominating individual subsets as well, which is important when applying LDEQ to video data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 455, + 216, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 216, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 216, + 468 + ], + "type": "text", + "content": "6.2. Landmark temporal coherence" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "content": "We evaluate the performance of LDEQ on the WFLW-V dataset, for both landmark accuracy (NME) and temporal coherence (NMF). We use RwR with early stopping after 2 solver iterations, allowing some adaptive compute (1 solver iteration) in cases where two consecutive frames are almost identical. Our baselines include previous state-of-the-art models that have publicly available weights [42, 46, 73, 77], as well as common architectures of comparable parameter count, which we trained with our own augmentation pipeline. We apply a conventional filtering algorithm, the exponential moving average, to our baselines. This was found to be more robust than more sophisticated filters like Savitzky-Golay filter [59] and One Euro filter [16]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "The NME vs. NMF results are shown in Fig. 5 for all models, for the hard and easy WFLW-V subsets. For videos that contain little uncertainty in landmarks (WFLW-V easy), there is little flickering and conventional filtering methods can mistakenly smooth out high frequency signal (e.g. eyes and mouth moving fast). For videos subject to more flickering (WFLW-hard), these same filtering tech-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 339, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 447 + ], + "type": "text", + "content": "niques do indeed improve the NMF metric, but beyond a certain smoothing factor this comes at the cost of increasing the NME. In contrast, LDEQ + RwR correctly smooths out flicker for WFLW-W hard without compromising performance on WFLW-V easy. This improvement comes from the fact that the RwR loss in Eq. (8) contains both a smoothing loss plus a log likelihood loss that constrains output landmarks to be plausible solutions, while conventional filters only optimize for the former." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 457, + 378, + 469 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 378, + 469 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 378, + 469 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 477, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 547, + 704 + ], + "type": "text", + "content": "We adapt Deep Equilibrium Models to landmark detection, and demonstrate that our LDEQ model can reach state-of-the-art accuracy on the challenging WFLW facial dataset. We then bring the attention of the landmark community to a common problem in video applications, whereby landmarks flicker across consecutive frames. We contribute a new dataset and metric to effectively benchmark solutions to that problem. Since DEQs solve for an objective in the forward pass, we propose to change this objective at test time to take into account new information. This new paradigm can be used to tackle the flickering problem, by adding a recurrent loss term at inference that wasn't present at training time (RwR). We show how to solve for this objective cheaply in a way that leads to state-of-the-art video temporal coherence. We hope that our work brings attention to the potential of deep equilibrium models for computer vision applications, and in particular, the ability to add loss terms to the forward pass process, to leverage new information at inference time." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22821" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Mediapipe 3d face transform. https://developers. googleblog .com/2020/09/mediapipe-3d-face-transform.html. 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Both being appropriately absorbed into the recurrent framework, the homography-guided image warping progressively enhances the feature consistency and the attention-focusing mechanism in FocusFormer aggregates the intra-inter correspondence in a global $\\rightarrow$ nonlocal $\\rightarrow$ local manner. Thanks to the above strategies, RHWF ranks top in accuracy on a variety of datasets, including the challenging cross-resolution and cross-modal ones. Meanwhile, benefiting from the recurrent framework, RHWF achieves parameter efficiency despite the transformer architecture. Compared to previous state-of-the-art approaches LocalTrans and IHN, RHWF reduces the mean average corner error (MACE) by about $70\\%$ and $38.1\\%$ on the MSCOCO dataset, while saving the parameter costs by $86.5\\%$ and $24.6\\%$ . Similar to the previous works, RHWF can also be arranged in 1-scale for efficiency and 2-scale for accuracy, with the 1-scale RHWF already outperforming most of the previous methods. Source code is available at https://github.com/imdumpl78/RHWF.", + "bbox": [ + 73, + 324, + 473, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 666, + 209, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Homography is defined as a global projective mapping between two images captured from different perspectives. It has been widely applied in computer vision tasks ranging from the monocular camera system to the multi-camera system, such as image/video stitching [4, 17, 19], multiscale gigapixel photography [3, 34], multispectral image fusion [41, 49], planar object tracking [44, 45], SLAM [14, 31], and GPS-denied UAV localization [18, 48].", + "bbox": [ + 75, + 691, + 468, + 813 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep homography estimation was introduced in the pioneer [12] that uses a VGG-style network to predict the homography. Many following works have been presented to further improve the estimation accuracy, including cas-", + "bbox": [ + 75, + 814, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/402d7510d96acacb79a67d2ab3ebd3b1f232212f6f25c0d8b38b5316cdf8818a.jpg", + "image_caption": [ + "Figure 1. Illustration of the difference of warping and attention strategies in RHWF and previous approaches. Our RHWF deploys (c) and (f). Please see text for details." + ], + "image_footnote": [], + "bbox": [ + 506, + 290, + 880, + 412 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cading multiple similar networks [15, 21, 22, 34] or designing iterable architectures such as the IC-LK iterator [7, 48] and the trainable CNN iterator [6]. The cascading strategy has improved the accuracy to some extent but is limited by the fixed number of networks. Worse still, stacking more networks cannot guarantee better accuracy [22]. The IC-LK (inverse compositional Lucas-Kanade [1]) based deep methods use deep feature extractor combined with the untrainable iterator to improve the estimation performance, but is limited by the theoretical drawback of the untrainable iterator [6, 32]. IHN [6] avoids this limitation by designing an iterable and trainable network architecture, which further improves the estimation accuracy. However, the feature inconsistency caused by the homography deformation has long been neglected in most current works.", + "bbox": [ + 496, + 460, + 892, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It has been well investigated in [9] that standard convolution is unable to keep the equivariance under the spatial transformation except translation. However, besides translation, homography is composed of rotation, scaling, shearing, aspect ratio, and perspective transformations [37, 43], which leads to the inconsistency of the features from corresponding points [25]. The inconsistency will hinder the homography estimation performance. Many efforts have been made to acquire the transformation-equivariance by either applying group convolutions in the network [9] or pre-warping [16, 20, 25, 43] the input image. But the above strategies need to exhaustively explore the possible transformation dimensions and degrees, as is illustrated in Fig. 1a, which is redundant in computation when coping with", + "bbox": [ + 496, + 689, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9833", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the homography transformation with a DOF of 6.", + "bbox": [ + 76, + 90, + 403, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To cope with the above problem, homography-guided image warping, as shown in Fig. 1c, is adopted in our proposed recurrent homography estimation framework, dubbed RHWF. We note that homography-guided image warping has already been unconsciously employed in some of the previous cascading-based works [15, 22, 34]. However, the reason, effect, and technique of using homography-guided image warping, especially absorbing it properly in the recurrent framework, hasn't ever been investigated. Different from the previous works, our RHWF combines the homography-guided image warping with the recurrent trainable network, which significantly improves the accuracy without the cost of network parameters. Compared to the previous cascading-based SOTA method LocalTrans [34], RHWF reduces the mean average corner error (MACE) by about $70\\%$ on the MSCOCO dataset, while reducing the parameter cost of $86.5\\%$ .", + "bbox": [ + 75, + 106, + 468, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other side, transformer architecture [8, 13] has demonstrated its superior ability in computer vision and image processing tasks. The transformer architecture has also been introduced in the homography estimation task as in [21, 34]. Following their pioneer exploration, we propose a transformer structure, named FocusFormer, that is pretty compatible with the homography-guided image warping and the recurrent framework. As illustrated in Fig. 1d, Fig. 1e, and Fig. 1f, unlike the attention mechanism in previous works that is pure global or local, FocusFormer employs the attention focusing mechanism. The scope of the attention mechanism shrinks along with the recurrence procedure, which captures the intra/inter correspondence information in a global $\\rightarrow$ nonlocal $\\rightarrow$ local $^{1}$ manner. We note that compared to the most widely adopted global attention mechanism, the attention-focusing mechanism can save computation costs while improving the homography estimation performance simultaneously.", + "bbox": [ + 75, + 363, + 470, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce the homography-guided image warping and FocusFormer into the recurrent homography estimation framework, named RHWF. The three parts, i.e., recurrent estimation, homography-guided image warping, and the FocusFormer cooperate well, with each part facilitating the others. We evaluate RHWF on a variety of datasets including common RGB image data [24], cross-resolution data [34] and cross-modal data [6, 48], on which it outperforms all other competitors by a large gap. We show that though adopting the transformer, our RHWF reduces the parameter cost of $24.6\\%$ while achieving the accuracy gain of $38.1\\%$ (MSCOCO) and $34.1\\%$ (GoogleMap), compared to the previous SOTA method IHN [6]. In summary, our contributions are as follows: (1) We propose a novel Recurrent homography estimation framework using Homography-", + "bbox": [ + 75, + 637, + 468, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "guided image Warping and FocusFormer, dubbed RHWF. RHWF ranks top on a variety of datasets, including the challenge scenes such as the cross-resolution and cross-modal ones. The recurrent estimation, homography-guided image warping, and FocusFormer facilitate the functionality of each other. (2) The reason, effect, and technique of using homography-guided image warping properly in the recurrent framework is first fully investigated. With the assistance of homography-guided image warping, the extracted features gradually converge into consistency, and hence boosting the homography estimation accuracy. (3) The FocusFormer is proposed to be the fundamental block of the recurrent homography estimation. The attention mechanism in FocusFormer works in a global $\\rightarrow$ nonlocal $\\rightarrow$ local manner, which significantly saves the computational costs while achieving a better performance.", + "bbox": [ + 500, + 90, + 890, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 345, + 640, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section we briefly review the most relevant works including deep homography estimation, transformation-equivariant network, and transformer in deep homography estimation. The readers are referred to literature such as [50] for the basic knowledge and traditional methods for homography estimation.", + "bbox": [ + 498, + 371, + 890, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Homography Estimation. DeTone et al. [12] first propose to estimate the homography deformation between the concatenated input image pair with a VGG-style network. Many works [15,22,46] inherit the network as a basic structure, which is either modified or cascaded by multiple times to boost the estimation accuracy. The cascading strategy indeed improves the performance, but is exceeded by the recurrent estimation methods [6,7,38,48].", + "bbox": [ + 498, + 462, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recurrent homography estimation method mainly contains two types, including the IC-LK iterator based ones [7,38,48] and the deep iterator based ones [6]. CLKN [7] is the pioneer work introduced by Chang et al. to employ IC-LK to build an untrainable recurrent homography estimation framework. Zhao et al. [48] present a new loss function to directly enhance the similarity of the feature maps of CNNs, which further releases the potential of the IC-LK framework. However, the recurrent framework using IC-LK is unable to learn the implicit prior for the iterator through a large amount of image data. Cao et al. [6] propose IHN to make the whole network trainable, achieving a higher homography estimation accuracy.", + "bbox": [ + 498, + 584, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformation-Equivariant Under Homography. It has been well analyzed in previous works [9] that standard convolution is equivariant to translations, but may fail to equivary with more general transformations. Unfortunately, homography has the transformation of rotation, scaling, shearing, aspect ratio, and perspective [43]. The corresponding features extracted by standard CNNs are inconsistent under homography deformation, which reduce the", + "bbox": [ + 498, + 780, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1As in most of the works that refer to \"nonlocal\" [5], it denotes a relatively large neighborhood around a pixel.", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9834", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/103c7804ca25ac9119b1dcf96cada2e7ecfe541081066273907f94badff17c1c.jpg", + "image_caption": [ + "Figure 2. Architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. (a) Overall structure of RHWF. (b) Detailed structure of the proposed FocusFormer. (c) Detailed illustration of the attention-focusing mechanism." + ], + "image_footnote": [], + "bbox": [ + 250, + 90, + 718, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "estimation accuracy. Many efforts [9-11, 16, 25, 39] have been made to deal with this problem. Some methods design special network architectures to make CNNs equivariant to specific transformations [9-11, 39], among which the well-known group equivariant CNNs [9] produce rotation equivariant features using group convolution and subgroup pooling. However, the model becomes inefficient as it applies group convolutions directly on a large group [25]. The transformation is limited to rotation in this network. Other methods [16, 20, 25, 43] achieve transformation-equivariant by the predefined warping of the input image by different transformation dimensions and degrees. For example, GIFT [25] produces rotation and scale invariant features using warped images with predefined rotation angles and scale ratios. Warped convolution [20] achieves equivariance by warping the input image through a designed function. But the above two methods can only deal with the rotation/scaling of 2 DOF. When it comes to the homography transformation, the DOF of which increases from 2 to 6 (besides translation, which is equivariant in the standard convolution). The predefined warping will become burdensome and impracticable.", + "bbox": [ + 75, + 429, + 472, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer in Deep Homography Estimation. The performance of homography estimation networks can be boosted using the transformer. The transformer can be used either for feature enhancement or homography estimation. Shao et al. [34] adopt a multiscale transformer that works locally for the feature enhancement purpose. Hong et al. [21] employ a series of transformers to predict homography from the feature pyramids in a coarse-to-fine manner. The transformer shows powerful ability by significantly improv", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing the homography estimation accuracy, and a transformer structure suitable for the recurrent homography framework is urgently needed.", + "bbox": [ + 498, + 430, + 893, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 479, + 635, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 illustrates the architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. The details of FocusFormer are shown in Fig. 2b. The homography-guided image warping and the attention-focusing mechanism in FocusFormer are arranged in an interleaved manner, which are appropriately absorbed into the recurrent framework. We note that the whole network is tied despite the number of iteration, which means the framework won't raise the network parameters. Let's denote the paired input images as $I_{a}$ and $I_{b}$ , and we aim to obtain the homography matrix $\\mathbf{H}$ that relates them.", + "bbox": [ + 498, + 506, + 893, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Backbone", + "text_level": 1, + "bbox": [ + 500, + 696, + 612, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We employ convolutional neural network (CNN) with residual connections as our backbone. As illustrated in Fig. 2a, we use CNNs with shared weights for 2 input images. The input images are processed with a convolutional block of kernel size $3 \\times 3$ first. The produced feature maps are then continually processed by the basic blocks consisting of 2 residual layers, with each block accomplishing a $2 \\times 2$ down-sampling in the spatial dimension. Different from the previous works [6, 34] that use the max-pooling layer to perform down-sampling, RHWF uses convolution with stride 2 to reduce the inference computation, which reduces the inference computational cost at 1 time to 1.43 GFLOPs", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9835", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/23729feeb914b441c5b08e324169b9ba3e03e74df79980375a6a941c3e2c3914.jpg", + "image_caption": [ + "Figure 3. Illustration of the reason and effect of using homography-guided image warping. The red squares represent the feature extracted from the left-side ear of the cat in the images. The color of the squares exhibits the feature similarity, and the colors become consistent as the feature similarity grows. (a) The ideal homography-invariant situation. (b) The practical situation. (c) The effect of homography-guided image warping." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 459, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from 2.43 GFLOPs in [6]. Finally, the feature maps are projected by 1 linear convolutional layer of kernel size $1 \\times 1$ . RHWF only needs a dimension of 96 while achieving far better results than IHN [6] that needs 256. We stack 2 basic blocks to produce the feature maps of the spatial dimension $H / 4 \\times W / 4$ and $H / 2 \\times W / 2$ , where $H$ and $W$ denote the height and width of the image. We note that, during the recurrent estimation process, the feature map of $I_{a}$ is computed once but the one of $I_{b}$ is computed recurrently due to the homography-guided image warping. This operation raises the computational cost of the network, but we will show the tremendous benefits of doing so.", + "bbox": [ + 75, + 323, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Homography-Guided Image Warping", + "text_level": 1, + "bbox": [ + 76, + 516, + 403, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In previous recurrent methods [6, 7], the images of severe homography deformation are used directly to produce the feature maps for homography estimation. The defect that the standard convolution is lack of equivary under homography transformation is ignored. For the homography estimation task, we want the backbone network to extract homography equivariant feature maps, which can be formulated by", + "bbox": [ + 75, + 540, + 468, + 660 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\pi (I; \\mathbf {H})) = \\pi (\\phi (I); \\mathbf {H}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 662, + 468, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pi$ denotes the coordinate projection, $\\mathbf{H}$ denotes the homography matrix that relates $I_{a}$ and $I_{b}$ , and $\\phi$ denotes the backbone CNN. This ideal situation is illustrated in Fig. 3a. In the ideal situation, the homography deformation won't affect feature similarity, making 2 features absolutely match each other. Unfortunately, in practice, due to the lack of equivary under homography transformation, the similarity of corresponding features produced by the backbone CNN will be weakened as illustrated in Fig. 3b.", + "bbox": [ + 75, + 688, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To cope with the above problem, many strategies have been proposed [9, 10, 20, 25] to either employ the group convolution or pre-warp the image by multiple times. However, both of the above methods bring considerable computational costs. We propose to interleave the homography es", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "timation and image warping process, dubbed homographyguided image warping, in our RHWF. The whole process is designed under the inspiration of the alternate update of different variables in conventional optimization frameworks. For $I_{a}$ and $I_{b}$ related by homography $\\mathbf{H}$ , the interleaved image warping and homography estimation process can be expressed as", + "bbox": [ + 496, + 90, + 890, + 195 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {F} _ {b} ^ {n} = \\phi (\\mathcal {W} (I _ {b}; \\hat {\\mathbf {H}} ^ {n})), \\\\ \\hat {\\mathbf {\\Phi}} \\end{array} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 196, + 890, + 222 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {H}} ^ {n + 1} = \\psi (\\mathbf {F} _ {a}; \\mathbf {F} _ {b} ^ {n}),\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 219, + 763, + 236 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{W}$ denote the homography-guided image warping, $\\psi$ denotes the FocusFormer $^2$ designed for homography estimation. The feature consistency between $\\mathbf{F}_a$ and $\\mathbf{F}_b$ together with the homography $\\hat{\\mathbf{H}}$ are optimized alternatively. We note that the homography-guided image warping takes the advantage of the recurrent framework of RHWF, and hence the redundant pre-designed warping or complex group convolution is not required. They are replaced by the warping guided by the present estimated homography. Meanwhile, the homography-guided image warping facilitates the estimation accuracy of the recurrent framework by relieving the feature inconsistency caused by deformation, as shown in Fig. 3c. We note that the backbone network recurrently extracts the feature map of $\\mathbf{F}_b^n$ with tied weights, which won't bring additional parameter costs.", + "bbox": [ + 496, + 243, + 890, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. FocusFormer", + "text_level": 1, + "bbox": [ + 500, + 481, + 638, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core architecture of RHWF is our FocusFormer that achieves recurrent residual homography estimation. FocusFormer mainly contains two parts that accomplish attention mechanism and homography estimation.", + "bbox": [ + 496, + 503, + 890, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attention. Following previous works [23, 34, 36, 40], we interleave the self-attention layer and the cross-attention layer, which is shown in Fig. 2b. By adopting both self-attention and cross-attention, FocusFormer can capture the intra/inter correspondence information of the input image pair.", + "bbox": [ + 496, + 565, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As demonstrated in Fig. 2c, along with the network recurrence, the scope of attention mechanism shrinks in a global $\\rightarrow$ nonlocal $\\rightarrow$ local manner. This operation is deeply bounded with the homography-guided image warping process and the recurrent framework. At the first iteration, the deformation between the two images is large due to large homography deformation. Long range attention is needed to better capture the intra-inter correspondence. As the iteration continues, the deformation is continuously reduced, and hence the attention can focus on the local area to better improve the estimation accuracy. It is worth noting that the attention-focusing mechanism can reduce the computational cost to 3.18 GFLOPs from 7.14 GFLOPs, which", + "bbox": [ + 496, + 656, + 890, + 852 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "In practice, the FocusFormer predicts the residual translation of 4 corner points of an image $\\Delta \\mathbf{T}^{n + 1}$ , and some simple computation will produce $\\hat{\\mathbf{H}}^{n + 1}$ as will be detailed in Section 3.3.", + "bbox": [ + 500, + 862, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9836", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "works in the pure global manner.", + "bbox": [ + 76, + 90, + 297, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let us denote the coordinate index of the feature map as $\\mathbf{x} = (u, v)$ , the projected query, key, and value as $\\mathbf{Q}$ , $\\mathbf{K}$ , and $\\mathbf{V}$ . The self attention-focusing mechanism can be formulated as", + "bbox": [ + 76, + 106, + 468, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s e l f} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 171, + 468, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(\\mathbf{x})$ represents the region around $\\mathbf{x}$ that self-attention works within. If $\\mathcal{N}(\\mathbf{x})$ is set as the whole image, it would become the global self-attention, otherwise the nonlocal or local one of radius $R_{\\mathrm{A}}$ . The subscript \"i\" denotes that the query, key, and value are from the same image. The cross attention-focusing mechanism can be formulated as", + "bbox": [ + 76, + 218, + 468, + 308 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {c r o s s} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 316, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where subscripts “ $i$ ” and “ $j$ ” denote that the query is from one image, while the key and value are from another. As for other details, we only use 1 self-attention layer and 1 cross-attention layer. Considering that the whole attention block functions in the recurrent framework, the effectiveness of the attention layer would be fully motivated during the iterative inference process. The residual connecting, layer normalization, and feed-forward network are also adopted as in previous works [34, 40]. The multi-head attention is discarded as in [40] to improve efficiency.", + "bbox": [ + 75, + 362, + 468, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Homography Estimation. After capturing the intra/inter correspondence of the input image pair, the correlation within local areas is then computed as", + "bbox": [ + 76, + 513, + 468, + 559 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} (\\mathbf {x}, \\mathbf {r}) = \\operatorname {R e L U} \\left(\\mathbf {F} _ {a} ^ {\\prime} (\\mathbf {x}) ^ {\\top} \\mathbf {F} _ {b} ^ {\\prime n} (\\mathbf {x} + \\mathbf {r})\\right), \\quad \\| \\mathbf {r} \\| _ {\\infty} \\leq R _ {\\mathrm {C}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 566, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $R_{\\mathrm{C}}$ controls the radius of each local area, making the correlation volume having the size of $H \\times W \\times (2R_{\\mathrm{C}} + 1) \\times (2R_{\\mathrm{C}} + 1)$ . This correlation can also be interpreted as another layer of cross attention [34] for the homography estimation, while the mapping differs as the desired output is the residual homography.", + "bbox": [ + 76, + 598, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The architecture of the homography aggregator is similar to the previous correlation-based homography estimation works [6, 34]. The aggregator is composed of the basic blocks having 2 convolution layers and 1 max-pooling layer. The only difference is that the depth of the convolution layer of our RHWF (denoted as $D$ ) is set to be markedly lower than that of IHN [6] and LocalTrans [34], which also saves the network parameters. Like most previous works [6, 12, 34], we parameterize the residual homography in the form of the translation of the 4 corner points of an image, namely $\\mathbf{T}$ . At iteration $n$ , The parameterization of $\\hat{\\mathbf{H}}^n$ using $\\hat{\\mathbf{T}}^n$ can be easily established by a least square problem as", + "bbox": [ + 75, + 688, + 468, + 883 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} ^ {n} \\hat {\\mathbf {h}} ^ {n} = \\mathbf {b} ^ {n}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 883, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{b}^n$ is the coordinate of the projected 4 corner points, $\\mathbf{A}^n$ is composed of the projected 4 corner points and the original 4 corner points, $\\hat{\\mathbf{h}}^n$ is the vectorized $\\hat{\\mathbf{H}}^n$ . The original 4 corner points and the projected 4 corner points are related by $\\hat{\\mathbf{T}}^n$ . During the recurrent process, the homography estimator produces the present residual translation $\\Delta \\mathbf{T}$ and the translation $\\hat{\\mathbf{T}}$ is updated by", + "bbox": [ + 498, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {T}} ^ {n + 1} = \\hat {\\mathbf {T}} ^ {n} + \\Delta \\mathbf {T} ^ {n + 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 205, + 890, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which is equivalent to the homography update illustrated in Fig. 2a, which can be formulated as", + "bbox": [ + 498, + 234, + 890, + 265 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {H}} ^ {n + 1} = \\hat {\\mathbf {H}} ^ {n} \\Delta \\mathbf {H} ^ {n + 1}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 275, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Multiscale Refinement", + "text_level": 1, + "bbox": [ + 500, + 313, + 709, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The performance of our proposed RHWF can be further improved by multiscale refinement. As illustrated in Section 3.1, the feature map of the spatial dimension $H / 2 \\times W / 2$ can be adopted to construct an additional scale for a more accurate homography refinement. In the refinement scale, a FocusFormer with different weights is employed. The structures of the FocusFormer of the 2 levels are basically identical, except for the attention range of the additional scale, which further shrinks as the initial homography is given by the former scale. We will show that the accuracy of a single scale already outperforms most of the previous works except for the 2-scale IHN in [6].", + "bbox": [ + 498, + 335, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Supervision", + "text_level": 1, + "bbox": [ + 500, + 527, + 627, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the $L_{1}$ loss between the ground-truth translation $\\mathbf{T}_{\\mathrm{gt}}$ and the estimated one $\\hat{\\mathbf{T}}$ . The loss at each iteration is weight summed as the final loss", + "bbox": [ + 500, + 550, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\sum_ {n = 0} ^ {N - 1} \\gamma^ {(N - n - 1)} | \\hat {\\mathbf {T}} ^ {n} - \\mathbf {T} _ {\\mathrm {g t}} |, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 606, + 890, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N$ denotes the recurrent time within 1 scale, $\\gamma$ is less than 1 to produce a larger weight for the later estimations as in IHN [6]. If multiscale refinement is employed, the losses of the 2 scales are summed.", + "bbox": [ + 498, + 656, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 726, + 718, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our implementation, the recurrent time $N$ within one scale is set to 6. We set the attention range in the FocusFormer as $[G,4,2,1,1,1]$ for scale $H / 4 \\times W / 4$ and $[2,2,1,1,1,1]$ for scale $H / 2 \\times W / 2$ , where $G$ denotes the global attention, and others the radius of the attention area $R_{\\mathrm{A}}$ . The radius of correlation is set to $R_{\\mathrm{C}} = 8$ and $R_{\\mathrm{C}} = 4$ for the 2 scales. The depth of convolution layers is set to $D = 80$ and $D = 64$ for the 2 scales. The network is trained using AdamW [26] optimizer with the max learning rate of 0.0004 and the iteration of 120000.", + "bbox": [ + 498, + 750, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9837", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/209cd00e9735471a246f630830074b2afb43b0151d37976adaf1852f119d291e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 88, + 433, + 212 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e46063ff5bbcfe3f81c074501c5187e79b1dd99c7017c9a7f5e52a07a902b79d.jpg", + "image_caption": [ + "(a) Evaluation on MSCOCO.", + "(c) Evaluation on GoogleEarth.", + "Figure 4. Homography estimation evaluation on MSCOCO, cross-resolution MSCOCO, GoogleEarth, and GoogleMap datasets. MSCOCO contains common RGB images. Cross-resolution MSCOCO includes image pairs of $4 \\times$ and $8 \\times$ resolution gaps. GoogleEarth and GoogleMap are cross-modal datasets. The suffixes “-1” and “-2” denote the scale of the network." + ], + "image_footnote": [], + "bbox": [ + 125, + 222, + 433, + 344 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5c1b9b699fc11ea007fff9f3553e27dd03f3911a19eab712f25c642abb56bb7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 534, + 88, + 841, + 212 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5810584266e2dfed700884ac0cbd06e944a3f04da39488781867eec401b51cc6.jpg", + "image_caption": [ + "(b) Evaluation on $4\\times$ and $8\\times$ resolution gaps MSCOCO.", + "(d) Evaluation on GoogleMap." + ], + "image_footnote": [], + "bbox": [ + 534, + 224, + 839, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 415, + 209, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 441, + 370, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate our RHWF on MSCOCO [24] following [6, 7, 12, 15, 22, 34, 48], $4 \\times$ and $8 \\times$ cross-resolution MSCOCO following [34], and cross-modal GoogleEarth together with GoogleMap following [6, 48]. MSCOCO is a large-scale real world RGB dataset, which is most widely used for homography estimation evaluation. The cross-resolution MSCOCO is employed in [34] to meet the homography estimation requirement in multiscale gigapixel photography [3, 47]. The cross-modal GoogleEarth and GoogleMap datasets are employed in [48] for the homography estimation requirement in the navigation scenario [18, 48]. We note that all the methods included for comparison together with our RHWF are trained and evaluated on the same training and test subset of each dataset for totally fair comparison.", + "bbox": [ + 75, + 465, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental setup. Similar to most of the previous works [6, 7, 12, 15, 22, 34, 48], the input images of size $[128 \\times 128]$ are randomly perturbed in the corner points, with the perturbation range of $[-32, 32]$ . The average corner error (ACE) is adopted for the homography accuracy evaluation following [6, 7, 12, 15, 22, 34, 48], which is lower when achieving higher accuracy.", + "bbox": [ + 75, + 695, + 470, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation", + "text_level": 1, + "bbox": [ + 76, + 815, + 181, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation Study on MSCOCO Dataset. The ablation of the homography-guided image warping, the attention-focusing mechanism, and the multiscale refinement are shown in Table 1. Mean average corner error (MACE) and", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c3700e9a20b62202f7f83bce2ac0de8ba37e76cec40633fcb007f1781407e5d1.jpg", + "table_caption": [ + "Table 1. Ablation study of RHWF." + ], + "table_footnote": [], + "table_body": "
Ablation partSettingMACEParameters
WarpingFeature warping0.203(↑163.6%)0.94 M
Image warping0.0770.94 M
AttentionNo0.091(↑18.2%)0.85 M
Pure global0.085(↑10.4%)0.94 M
Pure local0.082(↑6.5%)0.94 M
Focus0.0770.94 M
Scale1 scale0.077(↑97.4%)0.94 M
2 scales0.0391.29 M
", + "bbox": [ + 504, + 419, + 885, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "network parameters are also listed. All the ablations are conducted on the 1-scale RHWF unless otherwise specially mentioned. It is observed that the proposed homography-guided image warping and attention-focusing mechanism yields significant gain in accuracy. The global attention has a range of the whole image, and the local has an attention radius of 1. We can also find the multiscale refinement very effective by increasing the accuracy by $97.4\\%$ .", + "bbox": [ + 496, + 563, + 890, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation without recurrence. We conduct the ablation with the compared methods with no recurrence and the RHWF w/ (RHWF) and w/o (RHWF-NF) FocusFormer in Table 2. It is observed that the FocusFormer is effective.", + "bbox": [ + 496, + 685, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2f31d5513d7085860a65c126d8cace82ef85088e41697b92107d8c59723694cb.jpg", + "table_caption": [ + "Table 2. MACEs of RHWF and the compared structures without recurrent processing." + ], + "table_footnote": [], + "table_body": "
DHN 4.191MHN 3.645LocalTrans 1.987IHN 1.027RHWF 0.945RHWF-NF 1.019
", + "bbox": [ + 501, + 773, + 890, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A Deeper Look at Warping. We further illustrate the average correlation value, which represents the feature similarity at each warping count in Fig. 5. The warping of feature or image is taken for comparison to evaluate the effectiveness of homography-guided image warping. It is observed that the image warping can significantly enhance the", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9838", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "feature similarity as the warping count increases, while the feature warping weakens it.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c84c2eee833400664d4dd1b79496627153cfff51e6016ed4881eea63ee3f1de.jpg", + "image_caption": [ + "Figure 5. The average correlation value at each warping count of feature warping and image warping." + ], + "image_footnote": [], + "bbox": [ + 165, + 137, + 380, + 242 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. MSCOCO Evaluation", + "text_level": 1, + "bbox": [ + 76, + 279, + 282, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate RHWF together with other homography estimation methods including IHN [6] (previous SOTA method), LocalTrans [34], MHN [22], UDHN [46], DHN [12], CLKN [7], AffNet [30], LFNet [33], PFNet [42], PWC [35], SIFT+ContextDesc+RANSAC [28], SIFT+GeoDesc+RANSAC [29], SIFT+MAGSAC [2], and SIFT+RANSAC [27]. The comparison is illustrated in Fig. 4a. Following previous works [6,7,22,34,48], we plot the fraction of the number of images w.r.t. corresponding ACEs of a dataset. It can be observed that our 1-scale RHWF already outperforms other competitors except for 2-scale IHN, while 2-scale RHWF outperforms all others with a large gap. We note that 2-scale RHWF reduces previous SOTA MACE by $38.1\\%$ . We also plot the result of 1-scale IHN, which is significantly exceeded by 1-scale RHWF. Please kindly note that CLKN performs IC- $\\mathsf{LK}$ iteration with 4 scales, LocalTrans and MHN cascade 3 scales of networks to improve the estimation accuracy, but our 1-scale RHWF already markedly outperforms them.", + "bbox": [ + 75, + 303, + 468, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We then plot the MACEs at each iteration for IHN and our RHWF that adopt the recurrent framework in Fig. 6. It is observed that RHWF exceeds IHN at the 3rd iteration, while a more iterations won't make IHN outperform the RHWF with only 3 iterations. What's more, RHWF continues to reduce MACEs obviously with more iterations.", + "bbox": [ + 75, + 590, + 468, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Cross-Resolution MSCOCO Evaluation", + "text_level": 1, + "bbox": [ + 76, + 694, + 418, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct the evaluation on $4\\times$ and $8\\times$ crossresolution MSCOCO following [34]. We compare our RHWF with LocalTrans [34] (previous SOTA method), MHN [22],UDHN [46],DHN [12],and SIFT+RANSAC [27]. The resolution gap dramatically increases the difficulty of homography estimation, while it is vital for multiscale gigapixel photography [3, 34]. The results of $4\\times$ and $8\\times$ resolution gap MSCOCO are plotted in Fig. 4b. It is observed that RHWF ranks top in both scenarios and is significantly more robust under the $8\\times$ resolution gap.", + "bbox": [ + 75, + 718, + 467, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further demonstrate the self- and cross-attention map of RHWF at each iteration in Fig. 7. It is observed that at the", + "bbox": [ + 76, + 869, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de4439919a814cd96d15b42f79022e5014e02bed19f4491a31e9b44729339f1c.jpg", + "image_caption": [ + "Figure 6. The MACE comparison of IHN and our RHWF at each iteration count." + ], + "image_footnote": [], + "bbox": [ + 588, + 90, + 802, + 194 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "1st iteration, the global attention in $I_{a}$ and $I_{b}(4\\downarrow)$ successfully captures the correspondence information. However, in $I_{b}(8\\downarrow)$ , the global attention becomes ambiguous as the resolution gap grows. Fortunately, as the recurrence continues, the homography-guided image warping corrects the deformation and the attention-focusing mechanism shrinks the attention range, which gradually clarifies the attention targets.", + "bbox": [ + 498, + 234, + 890, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Cross-Modal Datasets Evaluation", + "text_level": 1, + "bbox": [ + 500, + 376, + 792, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The cross-modal data further raises the challenge for homography estimation, while it can be employed for GPS-denied navigation [18]. GoogleEarth contains image pairs across different seasons and GoogleMap the image pairs cropped from satellite images and their corresponding map images. We include IHN [6] (previous SOTA method), the original LK [1], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], DHN+DLKFM [48], and MHN+DLKFM [48] for comparison. The results of both datasets are separately demonstrated in Fig. 4c and Fig. 4d. The MACEs of RHWF and IHN are also illustrated for a better comparison. RHWF outperforms IHN by $34.1\\%$ on GoogleMap3.", + "bbox": [ + 498, + 402, + 890, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further illustrate the homography estimation results of the above-mentioned methods except for CLKN, DHN+DLKFM, and LK, as they are outperformed by MHN+DLKFM in [48]. It can be observed in Fig. 8 that under the severe large deformation and modality gap, SIFT+RANSAC and SIFT+MAGSAC fail as in the experiment of [6]. MHN+DLKFM produces unstable results as the LK iterator is of theoretical drawback [32]. DHN, MHN, and IHN are not as accurate as RHWF, as they neither consider the feature inconsistency caused by homography deformation nor introduce an attention mechanism to capture the intra-inter correspondence information. On the contrary, our RHWF can produce promising results under large deformation and modality gaps.", + "bbox": [ + 498, + 603, + 890, + 815 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3We notice that the performance of RHWF on GoogleEarth is not that conspicuous compared to other datasets but still outperforms other methods. This is because GoogleEarth only contains about 8k image pairs of fixed homography deformations, which limits the ability of the model by disabling more deformation augmentation.", + "bbox": [ + 500, + 838, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9839", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e857bbd76eac5c5653f1d442d5a055f29650721ea44ff17c9e9fe375fb746d5.jpg", + "image_caption": [ + "Figure 7. The self- and cross-attention map of RHWF at each iteration. The 1st row: the image $I_{a}$ of the standard resolution with the self-attention map. The 2nd and 3rd row: the image $I_{b}$ with $4 \\times (I_{b}(4 \\downarrow))$ and $8 \\times (I_{b}(8 \\downarrow))$ downsampling and cross-attention maps. The red arrows denote the query point of attention, and the red and blue boxes separately highlight the self- and cross-attention maps." + ], + "image_footnote": [], + "bbox": [ + 228, + 85, + 738, + 286 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71d7889dc810c86b01802c16170e6a992ef3ce3f2b49baf98f0f23d51e00fa66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 334, + 236, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/df2b376f1898b8bcc48eb289f7dea032081669903205b2996b54d3912650b3fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 396, + 236, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7d5d18b0eb800730f24c1809ea47a59ff7c65a6fee05acc43b2d473bbcb81a8f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 238, + 335, + 318, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4ae48a1aeacf57cfdacef5e9194bbe85f7a58801e38de863ca029e5dac504f26.jpg", + "image_caption": [ + "SIFT+RANSAC" + ], + "image_footnote": [], + "bbox": [ + 238, + 396, + 318, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d4548234a08cc3e0d37a3221402480d964267de9dd0d980df8867ce42f5addc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 335, + 400, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/497b80f97c93a4f1285216e88a568f8958515e030f33ae1f6859b74e429fc06f.jpg", + "image_caption": [ + "SIFT+MAGSAC" + ], + "image_footnote": [], + "bbox": [ + 321, + 396, + 400, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/46b799ad855a23cd67241c1570d9ce56a9cb145055896442d928a0c173bc8649.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 401, + 335, + 480, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2da419619059e2b664c238b74ac07f4070f7358af21adbe9e642db61d10566b7.jpg", + "image_caption": [ + "DHN" + ], + "image_footnote": [], + "bbox": [ + 401, + 396, + 480, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3858be4ca6a4554bc02e8c0d2e541ffaaab3a07d992130f2fa1e95d777471ca8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 335, + 560, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a2e8c89ceb7de44c733a2272ad2638e5d9769902599bd639cd752fcd2f1cebc.jpg", + "image_caption": [ + "MHN" + ], + "image_footnote": [], + "bbox": [ + 482, + 396, + 560, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ef6b79ba1391b01c0de9ed1554ee221b11f4c16e51e2f9cedf5c1b150435713e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 563, + 335, + 642, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/da40639f92de3473730f0ed4c6aa83f0d1c2838c272a7c5641cc0c0a4747900f.jpg", + "image_caption": [ + "MHN+DLKFM" + ], + "image_footnote": [], + "bbox": [ + 563, + 396, + 642, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6815da309be443b1b116bee6ab96ef0f4317cd85bd7371a858f65c9c07de632.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 335, + 723, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ac3ac9828978d424e7fda49211d97bd3121f0d58c0af08e94cb90483363ea7dc.jpg", + "image_caption": [ + "IHN" + ], + "image_footnote": [], + "bbox": [ + 645, + 396, + 723, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe1a103e3e6cfc980fb6fe874840d0053a95bfd40b05b100c5fbb3eae097e4a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 335, + 803, + 395 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4a2a5e1aea095d13cca25fa86f1599b39d4adc49559a66ffd2b8cb09f0fcece8.jpg", + "image_caption": [ + "RHWF (Ours)" + ], + "image_footnote": [], + "bbox": [ + 725, + 396, + 803, + 455 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6839937d67a3b82e24dfea063db7ebc34e173a6980ee814b86f7cf358bbcebe1.jpg", + "table_caption": [ + "Table 3. Parameter comparison." + ], + "table_footnote": [], + "table_body": "
RHWFIHNLocalTransDHNMHNUDHNDLKFM
1.29 M1.71 M9.56 M34.19 M2.57 M21.29 M19.24 M
", + "bbox": [ + 83, + 506, + 460, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Parameter and FLOPs Comparison", + "text_level": 1, + "bbox": [ + 76, + 545, + 385, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct the parameter and FLOPs comparison in Table 3. It is observed that compared to previous methods, our RHWF owns the least parameter cost, which is reduced by $86.5\\%$ and $24.6\\%$ compared with previous SOTA works LocalTrans [34] and IHN [6].", + "bbox": [ + 75, + 569, + 468, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 4, we compare the FLOPs of models and MACEs on MSCOCO with the previous SOTA recurrent methods including IHN, its improved version IHN-mov, and DLKFM. Compared to IHN-mov and DLKFM, the computational costs spent on the homography-guided warping in RHWF are much more effective. We also take the RHWF of the recurrent time 3 (fewer FLOPs), namely RHWF-3, which outperforms IHN-mov and DLKFM.", + "bbox": [ + 75, + 645, + 468, + 765 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1e5335fb80069dccc12349df7e479d7b7f0b9d60fc96850aae2fb60628ce95b4.jpg", + "table_caption": [ + "Table 4. FLOPs of models with MACEs on MSCOCO." + ], + "table_footnote": [], + "table_body": "
FLOPs MACERHWF 16.96 G 0.077RHWF-3 9.64 G 0.176IHN 8.34 G 0.191IHN-mov 20.32 G 0.177DLKFM 110.51 G 0.550
", + "bbox": [ + 88, + 780, + 454, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Failure Case", + "text_level": 1, + "bbox": [ + 76, + 830, + 210, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 9 shows 2 failure cases, the left one is caused by the error accumulation, and the right the imperfect initial estimations.", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f7bccf02dbb0bfb065758aabb55b3c46ac062acecb72c8c61c3be6bebce3df73.jpg", + "image_caption": [ + "Figure 8. Homography estimation results of methods including IHN [6], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], MHN+DLKFM [48], and our RHWF.", + "Figure 9. Failure cases." + ], + "image_footnote": [], + "bbox": [ + 509, + 494, + 874, + 558 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 588, + 625, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a novel recurrent homography estimation framework, named RHWF. RHWF absorbs the homography-guided image warping and the FocusFormer, which facilitate the homography estimation by enhancing the feature consistency and capturing the intra/inter corresponding information in a global $\\rightarrow$ nonlocal $\\rightarrow$ local manner, into the recurrent framework. Experimentally, RHWF outperforms previous methods by a large gap with significantly fewer parameters. The computation cost is raised by the homography-guided image warping and attention operation, which is the limitation of our proposed framework.", + "bbox": [ + 496, + 618, + 890, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 790, + 633, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the \"Pioneer\" and \"Leading Goose\" R & D Program of Zhejiang under grant 2023C03136 and in part by the Ten Thousand Talents Program of Zhejiang Province under grant 2020R52003. We also thank the generous help from Jun Ma, Zhejiang University and Tianyu Guo, Peking University.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9840", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Simon Baker and Iain Matthews. Lucas-Kanade 20 years on: A unifying framework. International Journal of Computer Vision, 56(3):221-255, 2004. 1, 7", + "[2] Daniel Barath, Jiri Matas, and Jana Noskova. MAGSAC: marginalizing sample consensus. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10197-10205, 2019. 7, 8", + "[3] David J Brady, Michael E Gehm, Ronald A Stack, Daniel L Marks, David S Kittle, Dathon R Golish, EM Vera, and Steven D Feller. 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Springer, 2018. 7" + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[43] Xinrui Zhan, Yang Li, Wenyu Liu, and Jianke Zhu. Warped convolution networks for homography estimation. arXiv preprint arXiv:2206.11657, 2022. 1, 2, 3", + "[44] Xinrui Zhan, Yueran Liu, Jianke Zhu, and Yang Li. Homography decomposition networks for planar object tracking. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 3234-3242, 2022. 1", + "[45] Haoxian Zhang and Yonggen Ling. Hvc-net: Unifying homography, visibility, and confidence learning for planar object tracking. In Proceedings of the European Conference on Computer Vision, pages 701-718. Springer, 2022. 1", + "[46] Jirong Zhang, Chuan Wang, Shuaicheng Liu, Lanpeng Jia, Nianjin Ye, Jue Wang, Ji Zhou, and Jian Sun. Content-aware unsupervised deep homography estimation. 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Image and Vision Computing, 21(11):977-1000, 2003. 2" + ], + "bbox": [ + 501, + 92, + 890, + 570 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9842", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/b2d36598-87bb-4351-86c5-8b1cc41ad2e7_model.json b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/b2d36598-87bb-4351-86c5-8b1cc41ad2e7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..dde8e5d20b00232a77f9157bb8edb668f73b0dce --- /dev/null +++ b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/b2d36598-87bb-4351-86c5-8b1cc41ad2e7_model.json @@ -0,0 +1,2442 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.798, + 0.177 + ], + "angle": 0, + "content": "Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.203, + 0.893, + 0.223 + ], + "angle": 0, + "content": "Si-Yuan Cao\\(^{1,2}\\), Runmin Zhang\\(^{2}\\), Lun Luo\\(^{2*}\\), Beinan Yu\\(^{2}\\), Zehua Sheng\\(^{2}\\), Junwei Li\\(^{2}\\), Hui-Liang Shen\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.224, + 0.892, + 0.259 + ], + "angle": 0, + "content": "1Ningbo Innovation Center, Zhejiang University, 2College of Information Science and Electronic Engineering, Zhejiang University karlcao@hotmail.com, {runmin_zhang, luolun, yubeinan, shengzehua, lijunwei7788, shenhl}@zju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.325, + 0.474, + 0.657 + ], + "angle": 0, + "content": "We propose the Recurrent homography estimation framework using Homography-guided image Warping and Focus transformer (FocusFormer), named RHWF. Both being appropriately absorbed into the recurrent framework, the homography-guided image warping progressively enhances the feature consistency and the attention-focusing mechanism in FocusFormer aggregates the intra-inter correspondence in a global \\(\\rightarrow\\) nonlocal \\(\\rightarrow\\) local manner. Thanks to the above strategies, RHWF ranks top in accuracy on a variety of datasets, including the challenging cross-resolution and cross-modal ones. Meanwhile, benefiting from the recurrent framework, RHWF achieves parameter efficiency despite the transformer architecture. Compared to previous state-of-the-art approaches LocalTrans and IHN, RHWF reduces the mean average corner error (MACE) by about \\(70\\%\\) and \\(38.1\\%\\) on the MSCOCO dataset, while saving the parameter costs by \\(86.5\\%\\) and \\(24.6\\%\\). Similar to the previous works, RHWF can also be arranged in 1-scale for efficiency and 2-scale for accuracy, with the 1-scale RHWF already outperforming most of the previous methods. Source code is available at https://github.com/imdumpl78/RHWF." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.667, + 0.21, + 0.683 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.814 + ], + "angle": 0, + "content": "Homography is defined as a global projective mapping between two images captured from different perspectives. It has been widely applied in computer vision tasks ranging from the monocular camera system to the multi-camera system, such as image/video stitching [4, 17, 19], multiscale gigapixel photography [3, 34], multispectral image fusion [41, 49], planar object tracking [44, 45], SLAM [14, 31], and GPS-denied UAV localization [18, 48]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Deep homography estimation was introduced in the pioneer [12] that uses a VGG-style network to predict the homography. Many following works have been presented to further improve the estimation accuracy, including cas-" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.291, + 0.882, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.413, + 0.893, + 0.454 + ], + "angle": 0, + "content": "Figure 1. Illustration of the difference of warping and attention strategies in RHWF and previous approaches. Our RHWF deploys (c) and (f). Please see text for details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.893, + 0.688 + ], + "angle": 0, + "content": "cading multiple similar networks [15, 21, 22, 34] or designing iterable architectures such as the IC-LK iterator [7, 48] and the trainable CNN iterator [6]. The cascading strategy has improved the accuracy to some extent but is limited by the fixed number of networks. Worse still, stacking more networks cannot guarantee better accuracy [22]. The IC-LK (inverse compositional Lucas-Kanade [1]) based deep methods use deep feature extractor combined with the untrainable iterator to improve the estimation performance, but is limited by the theoretical drawback of the untrainable iterator [6, 32]. IHN [6] avoids this limitation by designing an iterable and trainable network architecture, which further improves the estimation accuracy. However, the feature inconsistency caused by the homography deformation has long been neglected in most current works." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.902 + ], + "angle": 0, + "content": "It has been well investigated in [9] that standard convolution is unable to keep the equivariance under the spatial transformation except translation. However, besides translation, homography is composed of rotation, scaling, shearing, aspect ratio, and perspective transformations [37, 43], which leads to the inconsistency of the features from corresponding points [25]. The inconsistency will hinder the homography estimation performance. Many efforts have been made to acquire the transformation-equivariance by either applying group convolutions in the network [9] or pre-warping [16, 20, 25, 43] the input image. But the above strategies need to exhaustively explore the possible transformation dimensions and degrees, as is illustrated in Fig. 1a, which is redundant in computation when coping with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9833" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.405, + 0.106 + ], + "angle": 0, + "content": "the homography transformation with a DOF of 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.47, + 0.363 + ], + "angle": 0, + "content": "To cope with the above problem, homography-guided image warping, as shown in Fig. 1c, is adopted in our proposed recurrent homography estimation framework, dubbed RHWF. We note that homography-guided image warping has already been unconsciously employed in some of the previous cascading-based works [15, 22, 34]. However, the reason, effect, and technique of using homography-guided image warping, especially absorbing it properly in the recurrent framework, hasn't ever been investigated. Different from the previous works, our RHWF combines the homography-guided image warping with the recurrent trainable network, which significantly improves the accuracy without the cost of network parameters. Compared to the previous cascading-based SOTA method LocalTrans [34], RHWF reduces the mean average corner error (MACE) by about \\(70\\%\\) on the MSCOCO dataset, while reducing the parameter cost of \\(86.5\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.471, + 0.636 + ], + "angle": 0, + "content": "On the other side, transformer architecture [8, 13] has demonstrated its superior ability in computer vision and image processing tasks. The transformer architecture has also been introduced in the homography estimation task as in [21, 34]. Following their pioneer exploration, we propose a transformer structure, named FocusFormer, that is pretty compatible with the homography-guided image warping and the recurrent framework. As illustrated in Fig. 1d, Fig. 1e, and Fig. 1f, unlike the attention mechanism in previous works that is pure global or local, FocusFormer employs the attention focusing mechanism. The scope of the attention mechanism shrinks along with the recurrence procedure, which captures the intra/inter correspondence information in a global \\(\\rightarrow\\) nonlocal \\(\\rightarrow\\) local\\(^{1}\\) manner. We note that compared to the most widely adopted global attention mechanism, the attention-focusing mechanism can save computation costs while improving the homography estimation performance simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.864 + ], + "angle": 0, + "content": "We introduce the homography-guided image warping and FocusFormer into the recurrent homography estimation framework, named RHWF. The three parts, i.e., recurrent estimation, homography-guided image warping, and the FocusFormer cooperate well, with each part facilitating the others. We evaluate RHWF on a variety of datasets including common RGB image data [24], cross-resolution data [34] and cross-modal data [6, 48], on which it outperforms all other competitors by a large gap. We show that though adopting the transformer, our RHWF reduces the parameter cost of \\(24.6\\%\\) while achieving the accuracy gain of \\(38.1\\%\\) (MSCOCO) and \\(34.1\\%\\) (GoogleMap), compared to the previous SOTA method IHN [6]. In summary, our contributions are as follows: (1) We propose a novel Recurrent homography estimation framework using Homography-" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.333 + ], + "angle": 0, + "content": "guided image Warping and FocusFormer, dubbed RHWF. RHWF ranks top on a variety of datasets, including the challenge scenes such as the cross-resolution and cross-modal ones. The recurrent estimation, homography-guided image warping, and FocusFormer facilitate the functionality of each other. (2) The reason, effect, and technique of using homography-guided image warping properly in the recurrent framework is first fully investigated. With the assistance of homography-guided image warping, the extracted features gradually converge into consistency, and hence boosting the homography estimation accuracy. (3) The FocusFormer is proposed to be the fundamental block of the recurrent homography estimation. The attention mechanism in FocusFormer works in a global \\(\\rightarrow\\) nonlocal \\(\\rightarrow\\) local manner, which significantly saves the computational costs while achieving a better performance." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.347, + 0.642, + 0.362 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.372, + 0.892, + 0.463 + ], + "angle": 0, + "content": "In this section we briefly review the most relevant works including deep homography estimation, transformation-equivariant network, and transformer in deep homography estimation. The readers are referred to literature such as [50] for the basic knowledge and traditional methods for homography estimation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Deep Homography Estimation. DeTone et al. [12] first propose to estimate the homography deformation between the concatenated input image pair with a VGG-style network. Many works [15,22,46] inherit the network as a basic structure, which is either modified or cascaded by multiple times to boost the estimation accuracy. The cascading strategy indeed improves the performance, but is exceeded by the recurrent estimation methods [6,7,38,48]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.78 + ], + "angle": 0, + "content": "The recurrent homography estimation method mainly contains two types, including the IC-LK iterator based ones [7,38,48] and the deep iterator based ones [6]. CLKN [7] is the pioneer work introduced by Chang et al. to employ IC-LK to build an untrainable recurrent homography estimation framework. Zhao et al. [48] present a new loss function to directly enhance the similarity of the feature maps of CNNs, which further releases the potential of the IC-LK framework. However, the recurrent framework using IC-LK is unable to learn the implicit prior for the iterator through a large amount of image data. Cao et al. [6] propose IHN to make the whole network trainable, achieving a higher homography estimation accuracy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Transformation-Equivariant Under Homography. It has been well analyzed in previous works [9] that standard convolution is equivariant to translations, but may fail to equivary with more general transformations. Unfortunately, homography has the transformation of rotation, scaling, shearing, aspect ratio, and perspective [43]. The corresponding features extracted by standard CNNs are inconsistent under homography deformation, which reduce the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "1As in most of the works that refer to \"nonlocal\" [5], it denotes a relatively large neighborhood around a pixel." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9834" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.25, + 0.092, + 0.72, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.895, + 0.422 + ], + "angle": 0, + "content": "Figure 2. Architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. (a) Overall structure of RHWF. (b) Detailed structure of the proposed FocusFormer. (c) Detailed illustration of the attention-focusing mechanism." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.473, + 0.763 + ], + "angle": 0, + "content": "estimation accuracy. Many efforts [9-11, 16, 25, 39] have been made to deal with this problem. Some methods design special network architectures to make CNNs equivariant to specific transformations [9-11, 39], among which the well-known group equivariant CNNs [9] produce rotation equivariant features using group convolution and subgroup pooling. However, the model becomes inefficient as it applies group convolutions directly on a large group [25]. The transformation is limited to rotation in this network. Other methods [16, 20, 25, 43] achieve transformation-equivariant by the predefined warping of the input image by different transformation dimensions and degrees. For example, GIFT [25] produces rotation and scale invariant features using warped images with predefined rotation angles and scale ratios. Warped convolution [20] achieves equivariance by warping the input image through a designed function. But the above two methods can only deal with the rotation/scaling of 2 DOF. When it comes to the homography transformation, the DOF of which increases from 2 to 6 (besides translation, which is equivariant in the standard convolution). The predefined warping will become burdensome and impracticable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Transformer in Deep Homography Estimation. The performance of homography estimation networks can be boosted using the transformer. The transformer can be used either for feature enhancement or homography estimation. Shao et al. [34] adopt a multiscale transformer that works locally for the feature enhancement purpose. Hong et al. [21] employ a series of transformers to predict homography from the feature pyramids in a coarse-to-fine manner. The transformer shows powerful ability by significantly improv" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.895, + 0.476 + ], + "angle": 0, + "content": "ing the homography estimation accuracy, and a transformer structure suitable for the recurrent homography framework is urgently needed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.481, + 0.637, + 0.499 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.895, + 0.688 + ], + "angle": 0, + "content": "Fig. 2 illustrates the architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. The details of FocusFormer are shown in Fig. 2b. The homography-guided image warping and the attention-focusing mechanism in FocusFormer are arranged in an interleaved manner, which are appropriately absorbed into the recurrent framework. We note that the whole network is tied despite the number of iteration, which means the framework won't raise the network parameters. Let's denote the paired input images as \\( I_{a} \\) and \\( I_{b} \\), and we aim to obtain the homography matrix \\( \\mathbf{H} \\) that relates them." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.613, + 0.711 + ], + "angle": 0, + "content": "3.1. Backbone" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We employ convolutional neural network (CNN) with residual connections as our backbone. As illustrated in Fig. 2a, we use CNNs with shared weights for 2 input images. The input images are processed with a convolutional block of kernel size \\(3 \\times 3\\) first. The produced feature maps are then continually processed by the basic blocks consisting of 2 residual layers, with each block accomplishing a \\(2 \\times 2\\) down-sampling in the spatial dimension. Different from the previous works [6, 34] that use the max-pooling layer to perform down-sampling, RHWF uses convolution with stride 2 to reduce the inference computation, which reduces the inference computational cost at 1 time to 1.43 GFLOPs" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9835" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.46, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.221, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Illustration of the reason and effect of using homography-guided image warping. The red squares represent the feature extracted from the left-side ear of the cat in the images. The color of the squares exhibits the feature similarity, and the colors become consistent as the feature similarity grows. (a) The ideal homography-invariant situation. (b) The practical situation. (c) The effect of homography-guided image warping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.506 + ], + "angle": 0, + "content": "from 2.43 GFLOPs in [6]. Finally, the feature maps are projected by 1 linear convolutional layer of kernel size \\( 1 \\times 1 \\). RHWF only needs a dimension of 96 while achieving far better results than IHN [6] that needs 256. We stack 2 basic blocks to produce the feature maps of the spatial dimension \\( H / 4 \\times W / 4 \\) and \\( H / 2 \\times W / 2 \\), where \\( H \\) and \\( W \\) denote the height and width of the image. We note that, during the recurrent estimation process, the feature map of \\( I_{a} \\) is computed once but the one of \\( I_{b} \\) is computed recurrently due to the homography-guided image warping. This operation raises the computational cost of the network, but we will show the tremendous benefits of doing so." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.517, + 0.405, + 0.535 + ], + "angle": 0, + "content": "3.2. Homography-Guided Image Warping" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.47, + 0.661 + ], + "angle": 0, + "content": "In previous recurrent methods [6, 7], the images of severe homography deformation are used directly to produce the feature maps for homography estimation. The defect that the standard convolution is lack of equivary under homography transformation is ignored. For the homography estimation task, we want the backbone network to extract homography equivariant feature maps, which can be formulated by" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.664, + 0.469, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\phi (\\pi (I; \\mathbf {H})) = \\pi (\\phi (I); \\mathbf {H}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\(\\pi\\) denotes the coordinate projection, \\(\\mathbf{H}\\) denotes the homography matrix that relates \\(I_{a}\\) and \\(I_{b}\\), and \\(\\phi\\) denotes the backbone CNN. This ideal situation is illustrated in Fig. 3a. In the ideal situation, the homography deformation won't affect feature similarity, making 2 features absolutely match each other. Unfortunately, in practice, due to the lack of equivary under homography transformation, the similarity of corresponding features produced by the backbone CNN will be weakened as illustrated in Fig. 3b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To cope with the above problem, many strategies have been proposed [9, 10, 20, 25] to either employ the group convolution or pre-warp the image by multiple times. However, both of the above methods bring considerable computational costs. We propose to interleave the homography es" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.196 + ], + "angle": 0, + "content": "timation and image warping process, dubbed homographyguided image warping, in our RHWF. The whole process is designed under the inspiration of the alternate update of different variables in conventional optimization frameworks. For \\( I_{a} \\) and \\( I_{b} \\) related by homography \\( \\mathbf{H} \\), the interleaved image warping and homography estimation process can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.198, + 0.892, + 0.223 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {F} _ {b} ^ {n} = \\phi (\\mathcal {W} (I _ {b}; \\hat {\\mathbf {H}} ^ {n})), \\\\ \\hat {\\mathbf {\\Phi}} \\end{array} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.22, + 0.764, + 0.237 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {H}} ^ {n + 1} = \\psi (\\mathbf {F} _ {a}; \\mathbf {F} _ {b} ^ {n}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.471 + ], + "angle": 0, + "content": "where \\(\\mathcal{W}\\) denote the homography-guided image warping, \\(\\psi\\) denotes the FocusFormer\\(^2\\) designed for homography estimation. The feature consistency between \\(\\mathbf{F}_a\\) and \\(\\mathbf{F}_b\\) together with the homography \\(\\hat{\\mathbf{H}}\\) are optimized alternatively. We note that the homography-guided image warping takes the advantage of the recurrent framework of RHWF, and hence the redundant pre-designed warping or complex group convolution is not required. They are replaced by the warping guided by the present estimated homography. Meanwhile, the homography-guided image warping facilitates the estimation accuracy of the recurrent framework by relieving the feature inconsistency caused by deformation, as shown in Fig. 3c. We note that the backbone network recurrently extracts the feature map of \\(\\mathbf{F}_b^n\\) with tied weights, which won't bring additional parameter costs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.64, + 0.496 + ], + "angle": 0, + "content": "3.3. FocusFormer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.566 + ], + "angle": 0, + "content": "The core architecture of RHWF is our FocusFormer that achieves recurrent residual homography estimation. FocusFormer mainly contains two parts that accomplish attention mechanism and homography estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Attention. Following previous works [23, 34, 36, 40], we interleave the self-attention layer and the cross-attention layer, which is shown in Fig. 2b. By adopting both self-attention and cross-attention, FocusFormer can capture the intra/inter correspondence information of the input image pair." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.853 + ], + "angle": 0, + "content": "As demonstrated in Fig. 2c, along with the network recurrence, the scope of attention mechanism shrinks in a global \\(\\rightarrow\\) nonlocal \\(\\rightarrow\\) local manner. This operation is deeply bounded with the homography-guided image warping process and the recurrent framework. At the first iteration, the deformation between the two images is large due to large homography deformation. Long range attention is needed to better capture the intra-inter correspondence. As the iteration continues, the deformation is continuously reduced, and hence the attention can focus on the local area to better improve the estimation accuracy. It is worth noting that the attention-focusing mechanism can reduce the computational cost to 3.18 GFLOPs from 7.14 GFLOPs, which" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In practice, the FocusFormer predicts the residual translation of 4 corner points of an image \\(\\Delta \\mathbf{T}^{n + 1}\\), and some simple computation will produce \\(\\hat{\\mathbf{H}}^{n + 1}\\) as will be detailed in Section 3.3." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9836" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.298, + 0.106 + ], + "angle": 0, + "content": "works in the pure global manner." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.107, + 0.469, + 0.166 + ], + "angle": 0, + "content": "Let us denote the coordinate index of the feature map as \\(\\mathbf{x} = (u, v)\\), the projected query, key, and value as \\(\\mathbf{Q}\\), \\(\\mathbf{K}\\), and \\(\\mathbf{V}\\). The self attention-focusing mechanism can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.172, + 0.469, + 0.219 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s e l f} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.219, + 0.469, + 0.309 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(\\mathbf{x})\\) represents the region around \\(\\mathbf{x}\\) that self-attention works within. If \\(\\mathcal{N}(\\mathbf{x})\\) is set as the whole image, it would become the global self-attention, otherwise the nonlocal or local one of radius \\(R_{\\mathrm{A}}\\). The subscript \"i\" denotes that the query, key, and value are from the same image. The cross attention-focusing mechanism can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.317, + 0.469, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\operatorname {c r o s s} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.469, + 0.514 + ], + "angle": 0, + "content": "where subscripts “\\(i\\)” and “\\(j\\)” denote that the query is from one image, while the key and value are from another. As for other details, we only use 1 self-attention layer and 1 cross-attention layer. Considering that the whole attention block functions in the recurrent framework, the effectiveness of the attention layer would be fully motivated during the iterative inference process. The residual connecting, layer normalization, and feed-forward network are also adopted as in previous works [34, 40]. The multi-head attention is discarded as in [40] to improve efficiency." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.515, + 0.469, + 0.56 + ], + "angle": 0, + "content": "Homography Estimation. After capturing the intra/inter correspondence of the input image pair, the correlation within local areas is then computed as" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.567, + 0.469, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} (\\mathbf {x}, \\mathbf {r}) = \\operatorname {R e L U} \\left(\\mathbf {F} _ {a} ^ {\\prime} (\\mathbf {x}) ^ {\\top} \\mathbf {F} _ {b} ^ {\\prime n} (\\mathbf {x} + \\mathbf {r})\\right), \\quad \\| \\mathbf {r} \\| _ {\\infty} \\leq R _ {\\mathrm {C}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.469, + 0.689 + ], + "angle": 0, + "content": "where \\( R_{\\mathrm{C}} \\) controls the radius of each local area, making the correlation volume having the size of \\( H \\times W \\times (2R_{\\mathrm{C}} + 1) \\times (2R_{\\mathrm{C}} + 1) \\). This correlation can also be interpreted as another layer of cross attention [34] for the homography estimation, while the mapping differs as the desired output is the residual homography." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.884 + ], + "angle": 0, + "content": "The architecture of the homography aggregator is similar to the previous correlation-based homography estimation works [6, 34]. The aggregator is composed of the basic blocks having 2 convolution layers and 1 max-pooling layer. The only difference is that the depth of the convolution layer of our RHWF (denoted as \\(D\\)) is set to be markedly lower than that of IHN [6] and LocalTrans [34], which also saves the network parameters. Like most previous works [6, 12, 34], we parameterize the residual homography in the form of the translation of the 4 corner points of an image, namely \\(\\mathbf{T}\\). At iteration \\(n\\), The parameterization of \\(\\hat{\\mathbf{H}}^n\\) using \\(\\hat{\\mathbf{T}}^n\\) can be easily established by a least square problem as" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.885, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} ^ {n} \\hat {\\mathbf {h}} ^ {n} = \\mathbf {b} ^ {n}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "where \\(\\mathbf{b}^n\\) is the coordinate of the projected 4 corner points, \\(\\mathbf{A}^n\\) is composed of the projected 4 corner points and the original 4 corner points, \\(\\hat{\\mathbf{h}}^n\\) is the vectorized \\(\\hat{\\mathbf{H}}^n\\). The original 4 corner points and the projected 4 corner points are related by \\(\\hat{\\mathbf{T}}^n\\). During the recurrent process, the homography estimator produces the present residual translation \\(\\Delta \\mathbf{T}\\) and the translation \\(\\hat{\\mathbf{T}}\\) is updated by" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.206, + 0.892, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {T}} ^ {n + 1} = \\hat {\\mathbf {T}} ^ {n} + \\Delta \\mathbf {T} ^ {n + 1}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.236, + 0.892, + 0.266 + ], + "angle": 0, + "content": "which is equivalent to the homography update illustrated in Fig. 2a, which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.276, + 0.892, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {H}} ^ {n + 1} = \\hat {\\mathbf {H}} ^ {n} \\Delta \\mathbf {H} ^ {n + 1}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.314, + 0.71, + 0.329 + ], + "angle": 0, + "content": "3.4. Multiscale Refinement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.892, + 0.518 + ], + "angle": 0, + "content": "The performance of our proposed RHWF can be further improved by multiscale refinement. As illustrated in Section 3.1, the feature map of the spatial dimension \\( H / 2 \\times W / 2 \\) can be adopted to construct an additional scale for a more accurate homography refinement. In the refinement scale, a FocusFormer with different weights is employed. The structures of the FocusFormer of the 2 levels are basically identical, except for the attention range of the additional scale, which further shrinks as the initial homography is given by the former scale. We will show that the accuracy of a single scale already outperforms most of the previous works except for the 2-scale IHN in [6]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.628, + 0.544 + ], + "angle": 0, + "content": "3.5. Supervision" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.551, + 0.892, + 0.596 + ], + "angle": 0, + "content": "We use the \\(L_{1}\\) loss between the ground-truth translation \\(\\mathbf{T}_{\\mathrm{gt}}\\) and the estimated one \\(\\hat{\\mathbf{T}}\\). The loss at each iteration is weight summed as the final loss" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.607, + 0.892, + 0.648 + ], + "angle": 0, + "content": "\\[\nL = \\sum_ {n = 0} ^ {N - 1} \\gamma^ {(N - n - 1)} | \\hat {\\mathbf {T}} ^ {n} - \\mathbf {T} _ {\\mathrm {g t}} |, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.657, + 0.892, + 0.717 + ], + "angle": 0, + "content": "where \\(N\\) denotes the recurrent time within 1 scale, \\(\\gamma\\) is less than 1 to produce a larger weight for the later estimations as in IHN [6]. If multiscale refinement is employed, the losses of the 2 scales are summed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.719, + 0.743 + ], + "angle": 0, + "content": "3.6. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In our implementation, the recurrent time \\( N \\) within one scale is set to 6. We set the attention range in the FocusFormer as \\( [G,4,2,1,1,1] \\) for scale \\( H / 4 \\times W / 4 \\) and \\( [2,2,1,1,1,1] \\) for scale \\( H / 2 \\times W / 2 \\), where \\( G \\) denotes the global attention, and others the radius of the attention area \\( R_{\\mathrm{A}} \\). The radius of correlation is set to \\( R_{\\mathrm{C}} = 8 \\) and \\( R_{\\mathrm{C}} = 4 \\) for the 2 scales. The depth of convolution layers is set to \\( D = 80 \\) and \\( D = 64 \\) for the 2 scales. The network is trained using AdamW [26] optimizer with the max learning rate of 0.0004 and the iteration of 120000." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9837" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.089, + 0.434, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.214, + 0.357, + 0.223 + ], + "angle": 0, + "content": "(a) Evaluation on MSCOCO." + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.223, + 0.434, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.346, + 0.364, + 0.357 + ], + "angle": 0, + "content": "(c) Evaluation on GoogleEarth." + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.089, + 0.842, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.214, + 0.84, + 0.225 + ], + "angle": 0, + "content": "(b) Evaluation on \\(4\\times\\) and \\(8\\times\\) resolution gaps MSCOCO." + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.225, + 0.841, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.609, + 0.346, + 0.771, + 0.357 + ], + "angle": 0, + "content": "(d) Evaluation on GoogleMap." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.36, + 0.895, + 0.403 + ], + "angle": 0, + "content": "Figure 4. Homography estimation evaluation on MSCOCO, cross-resolution MSCOCO, GoogleEarth, and GoogleMap datasets. MSCOCO contains common RGB images. Cross-resolution MSCOCO includes image pairs of \\(4 \\times\\) and \\(8 \\times\\) resolution gaps. GoogleEarth and GoogleMap are cross-modal datasets. The suffixes “-1” and “-2” denote the scale of the network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.416, + 0.21, + 0.433 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.443, + 0.371, + 0.459 + ], + "angle": 0, + "content": "4.1. Datasets and Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.47, + 0.693 + ], + "angle": 0, + "content": "Datasets. We evaluate our RHWF on MSCOCO [24] following [6, 7, 12, 15, 22, 34, 48], \\(4 \\times\\) and \\(8 \\times\\) cross-resolution MSCOCO following [34], and cross-modal GoogleEarth together with GoogleMap following [6, 48]. MSCOCO is a large-scale real world RGB dataset, which is most widely used for homography estimation evaluation. The cross-resolution MSCOCO is employed in [34] to meet the homography estimation requirement in multiscale gigapixel photography [3, 47]. The cross-modal GoogleEarth and GoogleMap datasets are employed in [48] for the homography estimation requirement in the navigation scenario [18, 48]. We note that all the methods included for comparison together with our RHWF are trained and evaluated on the same training and test subset of each dataset for totally fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.471, + 0.803 + ], + "angle": 0, + "content": "Experimental setup. Similar to most of the previous works [6, 7, 12, 15, 22, 34, 48], the input images of size \\([128 \\times 128]\\) are randomly perturbed in the corner points, with the perturbation range of \\([-32, 32]\\). The average corner error (ACE) is adopted for the homography accuracy evaluation following [6, 7, 12, 15, 22, 34, 48], which is lower when achieving higher accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.182, + 0.831 + ], + "angle": 0, + "content": "4.2. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Ablation Study on MSCOCO Dataset. The ablation of the homography-guided image warping, the attention-focusing mechanism, and the multiscale refinement are shown in Table 1. Mean average corner error (MACE) and" + }, + { + "type": "table_caption", + "bbox": [ + 0.592, + 0.405, + 0.8, + 0.419 + ], + "angle": 0, + "content": "Table 1. Ablation study of RHWF." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.42, + 0.887, + 0.557 + ], + "angle": 0, + "content": "
Ablation partSettingMACEParameters
WarpingFeature warping0.203(↑163.6%)0.94 M
Image warping0.0770.94 M
AttentionNo0.091(↑18.2%)0.85 M
Pure global0.085(↑10.4%)0.94 M
Pure local0.082(↑6.5%)0.94 M
Focus0.0770.94 M
Scale1 scale0.077(↑97.4%)0.94 M
2 scales0.0391.29 M
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.684 + ], + "angle": 0, + "content": "network parameters are also listed. All the ablations are conducted on the 1-scale RHWF unless otherwise specially mentioned. It is observed that the proposed homography-guided image warping and attention-focusing mechanism yields significant gain in accuracy. The global attention has a range of the whole image, and the local has an attention radius of 1. We can also find the multiscale refinement very effective by increasing the accuracy by \\(97.4\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.745 + ], + "angle": 0, + "content": "Ablation without recurrence. We conduct the ablation with the compared methods with no recurrence and the RHWF w/ (RHWF) and w/o (RHWF-NF) FocusFormer in Table 2. It is observed that the FocusFormer is effective." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.747, + 0.892, + 0.774 + ], + "angle": 0, + "content": "Table 2. MACEs of RHWF and the compared structures without recurrent processing." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.774, + 0.892, + 0.805 + ], + "angle": 0, + "content": "
DHN 4.191MHN 3.645LocalTrans 1.987IHN 1.027RHWF 0.945RHWF-NF 1.019
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "A Deeper Look at Warping. We further illustrate the average correlation value, which represents the feature similarity at each warping count in Fig. 5. The warping of feature or image is taken for comparison to evaluate the effectiveness of homography-guided image warping. It is observed that the image warping can significantly enhance the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9838" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "feature similarity as the warping count increases, while the feature warping weakens it." + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.138, + 0.381, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.244, + 0.471, + 0.273 + ], + "angle": 0, + "content": "Figure 5. The average correlation value at each warping count of feature warping and image warping." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.28, + 0.284, + 0.294 + ], + "angle": 0, + "content": "4.3. MSCOCO Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.47, + 0.59 + ], + "angle": 0, + "content": "We evaluate RHWF together with other homography estimation methods including IHN [6] (previous SOTA method), LocalTrans [34], MHN [22], UDHN [46], DHN [12], CLKN [7], AffNet [30], LFNet [33], PFNet [42], PWC [35], SIFT+ContextDesc+RANSAC [28], SIFT+GeoDesc+RANSAC [29], SIFT+MAGSAC [2], and SIFT+RANSAC [27]. The comparison is illustrated in Fig. 4a. Following previous works [6,7,22,34,48], we plot the fraction of the number of images w.r.t. corresponding ACEs of a dataset. It can be observed that our 1-scale RHWF already outperforms other competitors except for 2-scale IHN, while 2-scale RHWF outperforms all others with a large gap. We note that 2-scale RHWF reduces previous SOTA MACE by \\(38.1\\%\\). We also plot the result of 1-scale IHN, which is significantly exceeded by 1-scale RHWF. Please kindly note that CLKN performs IC- \\(\\mathsf{LK}\\) iteration with 4 scales, LocalTrans and MHN cascade 3 scales of networks to improve the estimation accuracy, but our 1-scale RHWF already markedly outperforms them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.682 + ], + "angle": 0, + "content": "We then plot the MACEs at each iteration for IHN and our RHWF that adopt the recurrent framework in Fig. 6. It is observed that RHWF exceeds IHN at the 3rd iteration, while a more iterations won't make IHN outperform the RHWF with only 3 iterations. What's more, RHWF continues to reduce MACEs obviously with more iterations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.419, + 0.71 + ], + "angle": 0, + "content": "4.4. Cross-Resolution MSCOCO Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.468, + 0.869 + ], + "angle": 0, + "content": "We conduct the evaluation on \\(4\\times\\) and \\(8\\times\\) crossresolution MSCOCO following [34]. We compare our RHWF with LocalTrans [34] (previous SOTA method), MHN [22],UDHN [46],DHN [12],and SIFT+RANSAC [27]. The resolution gap dramatically increases the difficulty of homography estimation, while it is vital for multiscale gigapixel photography [3, 34]. The results of \\(4\\times\\) and \\(8\\times\\) resolution gap MSCOCO are plotted in Fig. 4b. It is observed that RHWF ranks top in both scenarios and is significantly more robust under the \\(8\\times\\) resolution gap." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We further demonstrate the self- and cross-attention map of RHWF at each iteration in Fig. 7. It is observed that at the" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.092, + 0.803, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.196, + 0.892, + 0.223 + ], + "angle": 0, + "content": "Figure 6. The MACE comparison of IHN and our RHWF at each iteration count." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.235, + 0.892, + 0.356 + ], + "angle": 0, + "content": "1st iteration, the global attention in \\( I_{a} \\) and \\( I_{b}(4\\downarrow) \\) successfully captures the correspondence information. However, in \\( I_{b}(8\\downarrow) \\), the global attention becomes ambiguous as the resolution gap grows. Fortunately, as the recurrence continues, the homography-guided image warping corrects the deformation and the attention-focusing mechanism shrinks the attention range, which gradually clarifies the attention targets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.377, + 0.794, + 0.392 + ], + "angle": 0, + "content": "4.5. Cross-Modal Datasets Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.404, + 0.892, + 0.6 + ], + "angle": 0, + "content": "The cross-modal data further raises the challenge for homography estimation, while it can be employed for GPS-denied navigation [18]. GoogleEarth contains image pairs across different seasons and GoogleMap the image pairs cropped from satellite images and their corresponding map images. We include IHN [6] (previous SOTA method), the original LK [1], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], DHN+DLKFM [48], and MHN+DLKFM [48] for comparison. The results of both datasets are separately demonstrated in Fig. 4c and Fig. 4d. The MACEs of RHWF and IHN are also illustrated for a better comparison. RHWF outperforms IHN by \\(34.1\\%\\) on GoogleMap3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.604, + 0.892, + 0.816 + ], + "angle": 0, + "content": "We further illustrate the homography estimation results of the above-mentioned methods except for CLKN, DHN+DLKFM, and LK, as they are outperformed by MHN+DLKFM in [48]. It can be observed in Fig. 8 that under the severe large deformation and modality gap, SIFT+RANSAC and SIFT+MAGSAC fail as in the experiment of [6]. MHN+DLKFM produces unstable results as the LK iterator is of theoretical drawback [32]. DHN, MHN, and IHN are not as accurate as RHWF, as they neither consider the feature inconsistency caused by homography deformation nor introduce an attention mechanism to capture the intra-inter correspondence information. On the contrary, our RHWF can produce promising results under large deformation and modality gaps." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.839, + 0.894, + 0.901 + ], + "angle": 0, + "content": "3We notice that the performance of RHWF on GoogleEarth is not that conspicuous compared to other datasets but still outperforms other methods. This is because GoogleEarth only contains about 8k image pairs of fixed homography deformations, which limits the ability of the model by disabling more deformation augmentation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9839" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.229, + 0.087, + 0.74, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.289, + 0.895, + 0.332 + ], + "angle": 0, + "content": "Figure 7. The self- and cross-attention map of RHWF at each iteration. The 1st row: the image \\( I_{a} \\) of the standard resolution with the self-attention map. The 2nd and 3rd row: the image \\( I_{b} \\) with \\( 4 \\times (I_{b}(4 \\downarrow)) \\) and \\( 8 \\times (I_{b}(8 \\downarrow)) \\) downsampling and cross-attention maps. The red arrows denote the query point of attention, and the red and blue boxes separately highlight the self- and cross-attention maps." + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.335, + 0.238, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.397, + 0.238, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.336, + 0.319, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.397, + 0.319, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.458, + 0.307, + 0.465 + ], + "angle": 0, + "content": "SIFT+RANSAC" + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.336, + 0.401, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.397, + 0.401, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.458, + 0.39, + 0.465 + ], + "angle": 0, + "content": "SIFT+MAGSAC" + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.336, + 0.481, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.397, + 0.481, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.435, + 0.458, + 0.452, + 0.465 + ], + "angle": 0, + "content": "DHN" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.336, + 0.561, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.397, + 0.561, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.458, + 0.534, + 0.465 + ], + "angle": 0, + "content": "MHN" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.336, + 0.643, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.397, + 0.643, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.458, + 0.63, + 0.465 + ], + "angle": 0, + "content": "MHN+DLKFM" + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.336, + 0.725, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.397, + 0.725, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.458, + 0.696, + 0.465 + ], + "angle": 0, + "content": "IHN" + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.336, + 0.805, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.397, + 0.805, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.458, + 0.792, + 0.465 + ], + "angle": 0, + "content": "RHWF (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.467, + 0.892, + 0.494 + ], + "angle": 0, + "content": "Figure 8. Homography estimation results of methods including IHN [6], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], MHN+DLKFM [48], and our RHWF." + }, + { + "type": "table_caption", + "bbox": [ + 0.179, + 0.496, + 0.368, + 0.507 + ], + "angle": 0, + "content": "Table 3. Parameter comparison." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.507, + 0.461, + 0.544 + ], + "angle": 0, + "content": "
RHWFIHNLocalTransDHNMHNUDHNDLKFM
1.29 M1.71 M9.56 M34.19 M2.57 M21.29 M19.24 M
" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.546, + 0.387, + 0.563 + ], + "angle": 0, + "content": "4.6. Parameter and FLOPs Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.469, + 0.646 + ], + "angle": 0, + "content": "We conduct the parameter and FLOPs comparison in Table 3. It is observed that compared to previous methods, our RHWF owns the least parameter cost, which is reduced by \\(86.5\\%\\) and \\(24.6\\%\\) compared with previous SOTA works LocalTrans [34] and IHN [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.469, + 0.766 + ], + "angle": 0, + "content": "In Table 4, we compare the FLOPs of models and MACEs on MSCOCO with the previous SOTA recurrent methods including IHN, its improved version IHN-mov, and DLKFM. Compared to IHN-mov and DLKFM, the computational costs spent on the homography-guided warping in RHWF are much more effective. We also take the RHWF of the recurrent time 3 (fewer FLOPs), namely RHWF-3, which outperforms IHN-mov and DLKFM." + }, + { + "type": "table_caption", + "bbox": [ + 0.108, + 0.769, + 0.437, + 0.781 + ], + "angle": 0, + "content": "Table 4. FLOPs of models with MACEs on MSCOCO." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.781, + 0.455, + 0.821 + ], + "angle": 0, + "content": "
FLOPs MACERHWF 16.96 G 0.077RHWF-3 9.64 G 0.176IHN 8.34 G 0.191IHN-mov 20.32 G 0.177DLKFM 110.51 G 0.550
" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.832, + 0.212, + 0.847 + ], + "angle": 0, + "content": "4.7. Failure Case" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Fig. 9 shows 2 failure cases, the left one is caused by the error accumulation, and the right the imperfect initial estimations." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.496, + 0.875, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.56, + 0.766, + 0.571 + ], + "angle": 0, + "content": "Figure 9. Failure cases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.627, + 0.604 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.786 + ], + "angle": 0, + "content": "We have proposed a novel recurrent homography estimation framework, named RHWF. RHWF absorbs the homography-guided image warping and the FocusFormer, which facilitate the homography estimation by enhancing the feature consistency and capturing the intra/inter corresponding information in a global \\(\\rightarrow\\) nonlocal \\(\\rightarrow\\) local manner, into the recurrent framework. Experimentally, RHWF outperforms previous methods by a large gap with significantly fewer parameters. The computation cost is raised by the homography-guided image warping and attention operation, which is the limitation of our proposed framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.791, + 0.635, + 0.806 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the \"Pioneer\" and \"Leading Goose\" R & D Program of Zhejiang under grant 2023C03136 and in part by the Ten Thousand Talents Program of Zhejiang Province under grant 2020R52003. We also thank the generous help from Jun Ma, Zhejiang University and Tianyu Guo, Peking University." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9840" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Simon Baker and Iain Matthews. Lucas-Kanade 20 years on: A unifying framework. International Journal of Computer Vision, 56(3):221-255, 2004. 1, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.471, + 0.213 + ], + "angle": 0, + "content": "[2] Daniel Barath, Jiri Matas, and Jana Noskova. MAGSAC: marginalizing sample consensus. 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Both being appropriately absorbed into the recurrent framework, the homography-guided image warping progressively enhances the feature consistency and the attention-focusing mechanism in FocusFormer aggregates the intra-inter correspondence in a global $\rightarrow$ nonlocal $\rightarrow$ local manner. Thanks to the above strategies, RHWF ranks top in accuracy on a variety of datasets, including the challenging cross-resolution and cross-modal ones. Meanwhile, benefiting from the recurrent framework, RHWF achieves parameter efficiency despite the transformer architecture. Compared to previous state-of-the-art approaches LocalTrans and IHN, RHWF reduces the mean average corner error (MACE) by about $70\%$ and $38.1\%$ on the MSCOCO dataset, while saving the parameter costs by $86.5\%$ and $24.6\%$ . Similar to the previous works, RHWF can also be arranged in 1-scale for efficiency and 2-scale for accuracy, with the 1-scale RHWF already outperforming most of the previous methods. Source code is available at https://github.com/imdumpl78/RHWF. + +# 1. Introduction + +Homography is defined as a global projective mapping between two images captured from different perspectives. It has been widely applied in computer vision tasks ranging from the monocular camera system to the multi-camera system, such as image/video stitching [4, 17, 19], multiscale gigapixel photography [3, 34], multispectral image fusion [41, 49], planar object tracking [44, 45], SLAM [14, 31], and GPS-denied UAV localization [18, 48]. + +Deep homography estimation was introduced in the pioneer [12] that uses a VGG-style network to predict the homography. Many following works have been presented to further improve the estimation accuracy, including cas- + +![](images/402d7510d96acacb79a67d2ab3ebd3b1f232212f6f25c0d8b38b5316cdf8818a.jpg) +Figure 1. Illustration of the difference of warping and attention strategies in RHWF and previous approaches. Our RHWF deploys (c) and (f). Please see text for details. + +cading multiple similar networks [15, 21, 22, 34] or designing iterable architectures such as the IC-LK iterator [7, 48] and the trainable CNN iterator [6]. The cascading strategy has improved the accuracy to some extent but is limited by the fixed number of networks. Worse still, stacking more networks cannot guarantee better accuracy [22]. The IC-LK (inverse compositional Lucas-Kanade [1]) based deep methods use deep feature extractor combined with the untrainable iterator to improve the estimation performance, but is limited by the theoretical drawback of the untrainable iterator [6, 32]. IHN [6] avoids this limitation by designing an iterable and trainable network architecture, which further improves the estimation accuracy. However, the feature inconsistency caused by the homography deformation has long been neglected in most current works. + +It has been well investigated in [9] that standard convolution is unable to keep the equivariance under the spatial transformation except translation. However, besides translation, homography is composed of rotation, scaling, shearing, aspect ratio, and perspective transformations [37, 43], which leads to the inconsistency of the features from corresponding points [25]. The inconsistency will hinder the homography estimation performance. Many efforts have been made to acquire the transformation-equivariance by either applying group convolutions in the network [9] or pre-warping [16, 20, 25, 43] the input image. But the above strategies need to exhaustively explore the possible transformation dimensions and degrees, as is illustrated in Fig. 1a, which is redundant in computation when coping with + +the homography transformation with a DOF of 6. + +To cope with the above problem, homography-guided image warping, as shown in Fig. 1c, is adopted in our proposed recurrent homography estimation framework, dubbed RHWF. We note that homography-guided image warping has already been unconsciously employed in some of the previous cascading-based works [15, 22, 34]. However, the reason, effect, and technique of using homography-guided image warping, especially absorbing it properly in the recurrent framework, hasn't ever been investigated. Different from the previous works, our RHWF combines the homography-guided image warping with the recurrent trainable network, which significantly improves the accuracy without the cost of network parameters. Compared to the previous cascading-based SOTA method LocalTrans [34], RHWF reduces the mean average corner error (MACE) by about $70\%$ on the MSCOCO dataset, while reducing the parameter cost of $86.5\%$ . + +On the other side, transformer architecture [8, 13] has demonstrated its superior ability in computer vision and image processing tasks. The transformer architecture has also been introduced in the homography estimation task as in [21, 34]. Following their pioneer exploration, we propose a transformer structure, named FocusFormer, that is pretty compatible with the homography-guided image warping and the recurrent framework. As illustrated in Fig. 1d, Fig. 1e, and Fig. 1f, unlike the attention mechanism in previous works that is pure global or local, FocusFormer employs the attention focusing mechanism. The scope of the attention mechanism shrinks along with the recurrence procedure, which captures the intra/inter correspondence information in a global $\rightarrow$ nonlocal $\rightarrow$ local $^{1}$ manner. We note that compared to the most widely adopted global attention mechanism, the attention-focusing mechanism can save computation costs while improving the homography estimation performance simultaneously. + +We introduce the homography-guided image warping and FocusFormer into the recurrent homography estimation framework, named RHWF. The three parts, i.e., recurrent estimation, homography-guided image warping, and the FocusFormer cooperate well, with each part facilitating the others. We evaluate RHWF on a variety of datasets including common RGB image data [24], cross-resolution data [34] and cross-modal data [6, 48], on which it outperforms all other competitors by a large gap. We show that though adopting the transformer, our RHWF reduces the parameter cost of $24.6\%$ while achieving the accuracy gain of $38.1\%$ (MSCOCO) and $34.1\%$ (GoogleMap), compared to the previous SOTA method IHN [6]. In summary, our contributions are as follows: (1) We propose a novel Recurrent homography estimation framework using Homography- + +guided image Warping and FocusFormer, dubbed RHWF. RHWF ranks top on a variety of datasets, including the challenge scenes such as the cross-resolution and cross-modal ones. The recurrent estimation, homography-guided image warping, and FocusFormer facilitate the functionality of each other. (2) The reason, effect, and technique of using homography-guided image warping properly in the recurrent framework is first fully investigated. With the assistance of homography-guided image warping, the extracted features gradually converge into consistency, and hence boosting the homography estimation accuracy. (3) The FocusFormer is proposed to be the fundamental block of the recurrent homography estimation. The attention mechanism in FocusFormer works in a global $\rightarrow$ nonlocal $\rightarrow$ local manner, which significantly saves the computational costs while achieving a better performance. + +# 2. Related Work + +In this section we briefly review the most relevant works including deep homography estimation, transformation-equivariant network, and transformer in deep homography estimation. The readers are referred to literature such as [50] for the basic knowledge and traditional methods for homography estimation. + +Deep Homography Estimation. DeTone et al. [12] first propose to estimate the homography deformation between the concatenated input image pair with a VGG-style network. Many works [15,22,46] inherit the network as a basic structure, which is either modified or cascaded by multiple times to boost the estimation accuracy. The cascading strategy indeed improves the performance, but is exceeded by the recurrent estimation methods [6,7,38,48]. + +The recurrent homography estimation method mainly contains two types, including the IC-LK iterator based ones [7,38,48] and the deep iterator based ones [6]. CLKN [7] is the pioneer work introduced by Chang et al. to employ IC-LK to build an untrainable recurrent homography estimation framework. Zhao et al. [48] present a new loss function to directly enhance the similarity of the feature maps of CNNs, which further releases the potential of the IC-LK framework. However, the recurrent framework using IC-LK is unable to learn the implicit prior for the iterator through a large amount of image data. Cao et al. [6] propose IHN to make the whole network trainable, achieving a higher homography estimation accuracy. + +Transformation-Equivariant Under Homography. It has been well analyzed in previous works [9] that standard convolution is equivariant to translations, but may fail to equivary with more general transformations. Unfortunately, homography has the transformation of rotation, scaling, shearing, aspect ratio, and perspective [43]. The corresponding features extracted by standard CNNs are inconsistent under homography deformation, which reduce the + +![](images/103c7804ca25ac9119b1dcf96cada2e7ecfe541081066273907f94badff17c1c.jpg) +Figure 2. Architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. (a) Overall structure of RHWF. (b) Detailed structure of the proposed FocusFormer. (c) Detailed illustration of the attention-focusing mechanism. + +estimation accuracy. Many efforts [9-11, 16, 25, 39] have been made to deal with this problem. Some methods design special network architectures to make CNNs equivariant to specific transformations [9-11, 39], among which the well-known group equivariant CNNs [9] produce rotation equivariant features using group convolution and subgroup pooling. However, the model becomes inefficient as it applies group convolutions directly on a large group [25]. The transformation is limited to rotation in this network. Other methods [16, 20, 25, 43] achieve transformation-equivariant by the predefined warping of the input image by different transformation dimensions and degrees. For example, GIFT [25] produces rotation and scale invariant features using warped images with predefined rotation angles and scale ratios. Warped convolution [20] achieves equivariance by warping the input image through a designed function. But the above two methods can only deal with the rotation/scaling of 2 DOF. When it comes to the homography transformation, the DOF of which increases from 2 to 6 (besides translation, which is equivariant in the standard convolution). The predefined warping will become burdensome and impracticable. + +Transformer in Deep Homography Estimation. The performance of homography estimation networks can be boosted using the transformer. The transformer can be used either for feature enhancement or homography estimation. Shao et al. [34] adopt a multiscale transformer that works locally for the feature enhancement purpose. Hong et al. [21] employ a series of transformers to predict homography from the feature pyramids in a coarse-to-fine manner. The transformer shows powerful ability by significantly improv + +ing the homography estimation accuracy, and a transformer structure suitable for the recurrent homography framework is urgently needed. + +# 3. Methodology + +Fig. 2 illustrates the architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. The details of FocusFormer are shown in Fig. 2b. The homography-guided image warping and the attention-focusing mechanism in FocusFormer are arranged in an interleaved manner, which are appropriately absorbed into the recurrent framework. We note that the whole network is tied despite the number of iteration, which means the framework won't raise the network parameters. Let's denote the paired input images as $I_{a}$ and $I_{b}$ , and we aim to obtain the homography matrix $\mathbf{H}$ that relates them. + +# 3.1. Backbone + +We employ convolutional neural network (CNN) with residual connections as our backbone. As illustrated in Fig. 2a, we use CNNs with shared weights for 2 input images. The input images are processed with a convolutional block of kernel size $3 \times 3$ first. The produced feature maps are then continually processed by the basic blocks consisting of 2 residual layers, with each block accomplishing a $2 \times 2$ down-sampling in the spatial dimension. Different from the previous works [6, 34] that use the max-pooling layer to perform down-sampling, RHWF uses convolution with stride 2 to reduce the inference computation, which reduces the inference computational cost at 1 time to 1.43 GFLOPs + +![](images/23729feeb914b441c5b08e324169b9ba3e03e74df79980375a6a941c3e2c3914.jpg) +Figure 3. Illustration of the reason and effect of using homography-guided image warping. The red squares represent the feature extracted from the left-side ear of the cat in the images. The color of the squares exhibits the feature similarity, and the colors become consistent as the feature similarity grows. (a) The ideal homography-invariant situation. (b) The practical situation. (c) The effect of homography-guided image warping. + +from 2.43 GFLOPs in [6]. Finally, the feature maps are projected by 1 linear convolutional layer of kernel size $1 \times 1$ . RHWF only needs a dimension of 96 while achieving far better results than IHN [6] that needs 256. We stack 2 basic blocks to produce the feature maps of the spatial dimension $H / 4 \times W / 4$ and $H / 2 \times W / 2$ , where $H$ and $W$ denote the height and width of the image. We note that, during the recurrent estimation process, the feature map of $I_{a}$ is computed once but the one of $I_{b}$ is computed recurrently due to the homography-guided image warping. This operation raises the computational cost of the network, but we will show the tremendous benefits of doing so. + +# 3.2. Homography-Guided Image Warping + +In previous recurrent methods [6, 7], the images of severe homography deformation are used directly to produce the feature maps for homography estimation. The defect that the standard convolution is lack of equivary under homography transformation is ignored. For the homography estimation task, we want the backbone network to extract homography equivariant feature maps, which can be formulated by + +$$ +\phi (\pi (I; \mathbf {H})) = \pi (\phi (I); \mathbf {H}), \tag {1} +$$ + +where $\pi$ denotes the coordinate projection, $\mathbf{H}$ denotes the homography matrix that relates $I_{a}$ and $I_{b}$ , and $\phi$ denotes the backbone CNN. This ideal situation is illustrated in Fig. 3a. In the ideal situation, the homography deformation won't affect feature similarity, making 2 features absolutely match each other. Unfortunately, in practice, due to the lack of equivary under homography transformation, the similarity of corresponding features produced by the backbone CNN will be weakened as illustrated in Fig. 3b. + +To cope with the above problem, many strategies have been proposed [9, 10, 20, 25] to either employ the group convolution or pre-warp the image by multiple times. However, both of the above methods bring considerable computational costs. We propose to interleave the homography es + +timation and image warping process, dubbed homographyguided image warping, in our RHWF. The whole process is designed under the inspiration of the alternate update of different variables in conventional optimization frameworks. For $I_{a}$ and $I_{b}$ related by homography $\mathbf{H}$ , the interleaved image warping and homography estimation process can be expressed as + +$$ +\begin{array}{l} \mathbf {F} _ {b} ^ {n} = \phi (\mathcal {W} (I _ {b}; \hat {\mathbf {H}} ^ {n})), \\ \hat {\mathbf {\Phi}} \end{array} \tag {2} +$$ + +$$ +\hat {\mathbf {H}} ^ {n + 1} = \psi (\mathbf {F} _ {a}; \mathbf {F} _ {b} ^ {n}), +$$ + +where $\mathcal{W}$ denote the homography-guided image warping, $\psi$ denotes the FocusFormer $^2$ designed for homography estimation. The feature consistency between $\mathbf{F}_a$ and $\mathbf{F}_b$ together with the homography $\hat{\mathbf{H}}$ are optimized alternatively. We note that the homography-guided image warping takes the advantage of the recurrent framework of RHWF, and hence the redundant pre-designed warping or complex group convolution is not required. They are replaced by the warping guided by the present estimated homography. Meanwhile, the homography-guided image warping facilitates the estimation accuracy of the recurrent framework by relieving the feature inconsistency caused by deformation, as shown in Fig. 3c. We note that the backbone network recurrently extracts the feature map of $\mathbf{F}_b^n$ with tied weights, which won't bring additional parameter costs. + +# 3.3. FocusFormer + +The core architecture of RHWF is our FocusFormer that achieves recurrent residual homography estimation. FocusFormer mainly contains two parts that accomplish attention mechanism and homography estimation. + +Attention. Following previous works [23, 34, 36, 40], we interleave the self-attention layer and the cross-attention layer, which is shown in Fig. 2b. By adopting both self-attention and cross-attention, FocusFormer can capture the intra/inter correspondence information of the input image pair. + +As demonstrated in Fig. 2c, along with the network recurrence, the scope of attention mechanism shrinks in a global $\rightarrow$ nonlocal $\rightarrow$ local manner. This operation is deeply bounded with the homography-guided image warping process and the recurrent framework. At the first iteration, the deformation between the two images is large due to large homography deformation. Long range attention is needed to better capture the intra-inter correspondence. As the iteration continues, the deformation is continuously reduced, and hence the attention can focus on the local area to better improve the estimation accuracy. It is worth noting that the attention-focusing mechanism can reduce the computational cost to 3.18 GFLOPs from 7.14 GFLOPs, which + +works in the pure global manner. + +Let us denote the coordinate index of the feature map as $\mathbf{x} = (u, v)$ , the projected query, key, and value as $\mathbf{Q}$ , $\mathbf{K}$ , and $\mathbf{V}$ . The self attention-focusing mechanism can be formulated as + +$$ +\operatorname {s e l f} (\mathbf {x}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {i} \left(\mathcal {N} (\mathbf {x})\right) ^ {\top} \mathbf {K} _ {i} \left(\mathcal {N} (\mathbf {x})\right)}{\sqrt {D}}\right) \mathbf {V} _ {i} \left(\mathcal {N} (\mathbf {x})\right), \tag {3} +$$ + +where $\mathcal{N}(\mathbf{x})$ represents the region around $\mathbf{x}$ that self-attention works within. If $\mathcal{N}(\mathbf{x})$ is set as the whole image, it would become the global self-attention, otherwise the nonlocal or local one of radius $R_{\mathrm{A}}$ . The subscript "i" denotes that the query, key, and value are from the same image. The cross attention-focusing mechanism can be formulated as + +$$ +\operatorname {c r o s s} (\mathbf {x}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {i} \left(\mathcal {N} (\mathbf {x})\right) ^ {\top} \mathbf {K} _ {j} \left(\mathcal {N} (\mathbf {x})\right)}{\sqrt {D}}\right) \mathbf {V} _ {j} \left(\mathcal {N} (\mathbf {x})\right), \tag {4} +$$ + +where subscripts “ $i$ ” and “ $j$ ” denote that the query is from one image, while the key and value are from another. As for other details, we only use 1 self-attention layer and 1 cross-attention layer. Considering that the whole attention block functions in the recurrent framework, the effectiveness of the attention layer would be fully motivated during the iterative inference process. The residual connecting, layer normalization, and feed-forward network are also adopted as in previous works [34, 40]. The multi-head attention is discarded as in [40] to improve efficiency. + +Homography Estimation. After capturing the intra/inter correspondence of the input image pair, the correlation within local areas is then computed as + +$$ +\mathbf {C} (\mathbf {x}, \mathbf {r}) = \operatorname {R e L U} \left(\mathbf {F} _ {a} ^ {\prime} (\mathbf {x}) ^ {\top} \mathbf {F} _ {b} ^ {\prime n} (\mathbf {x} + \mathbf {r})\right), \quad \| \mathbf {r} \| _ {\infty} \leq R _ {\mathrm {C}} \tag {5} +$$ + +where $R_{\mathrm{C}}$ controls the radius of each local area, making the correlation volume having the size of $H \times W \times (2R_{\mathrm{C}} + 1) \times (2R_{\mathrm{C}} + 1)$ . This correlation can also be interpreted as another layer of cross attention [34] for the homography estimation, while the mapping differs as the desired output is the residual homography. + +The architecture of the homography aggregator is similar to the previous correlation-based homography estimation works [6, 34]. The aggregator is composed of the basic blocks having 2 convolution layers and 1 max-pooling layer. The only difference is that the depth of the convolution layer of our RHWF (denoted as $D$ ) is set to be markedly lower than that of IHN [6] and LocalTrans [34], which also saves the network parameters. Like most previous works [6, 12, 34], we parameterize the residual homography in the form of the translation of the 4 corner points of an image, namely $\mathbf{T}$ . At iteration $n$ , The parameterization of $\hat{\mathbf{H}}^n$ using $\hat{\mathbf{T}}^n$ can be easily established by a least square problem as + +$$ +\mathbf {A} ^ {n} \hat {\mathbf {h}} ^ {n} = \mathbf {b} ^ {n}, \tag {6} +$$ + +where $\mathbf{b}^n$ is the coordinate of the projected 4 corner points, $\mathbf{A}^n$ is composed of the projected 4 corner points and the original 4 corner points, $\hat{\mathbf{h}}^n$ is the vectorized $\hat{\mathbf{H}}^n$ . The original 4 corner points and the projected 4 corner points are related by $\hat{\mathbf{T}}^n$ . During the recurrent process, the homography estimator produces the present residual translation $\Delta \mathbf{T}$ and the translation $\hat{\mathbf{T}}$ is updated by + +$$ +\hat {\mathbf {T}} ^ {n + 1} = \hat {\mathbf {T}} ^ {n} + \Delta \mathbf {T} ^ {n + 1}, \tag {7} +$$ + +which is equivalent to the homography update illustrated in Fig. 2a, which can be formulated as + +$$ +\hat {\mathbf {H}} ^ {n + 1} = \hat {\mathbf {H}} ^ {n} \Delta \mathbf {H} ^ {n + 1}. \tag {8} +$$ + +# 3.4. Multiscale Refinement + +The performance of our proposed RHWF can be further improved by multiscale refinement. As illustrated in Section 3.1, the feature map of the spatial dimension $H / 2 \times W / 2$ can be adopted to construct an additional scale for a more accurate homography refinement. In the refinement scale, a FocusFormer with different weights is employed. The structures of the FocusFormer of the 2 levels are basically identical, except for the attention range of the additional scale, which further shrinks as the initial homography is given by the former scale. We will show that the accuracy of a single scale already outperforms most of the previous works except for the 2-scale IHN in [6]. + +# 3.5. Supervision + +We use the $L_{1}$ loss between the ground-truth translation $\mathbf{T}_{\mathrm{gt}}$ and the estimated one $\hat{\mathbf{T}}$ . The loss at each iteration is weight summed as the final loss + +$$ +L = \sum_ {n = 0} ^ {N - 1} \gamma^ {(N - n - 1)} | \hat {\mathbf {T}} ^ {n} - \mathbf {T} _ {\mathrm {g t}} |, \tag {9} +$$ + +where $N$ denotes the recurrent time within 1 scale, $\gamma$ is less than 1 to produce a larger weight for the later estimations as in IHN [6]. If multiscale refinement is employed, the losses of the 2 scales are summed. + +# 3.6. Implementation Details + +In our implementation, the recurrent time $N$ within one scale is set to 6. We set the attention range in the FocusFormer as $[G,4,2,1,1,1]$ for scale $H / 4 \times W / 4$ and $[2,2,1,1,1,1]$ for scale $H / 2 \times W / 2$ , where $G$ denotes the global attention, and others the radius of the attention area $R_{\mathrm{A}}$ . The radius of correlation is set to $R_{\mathrm{C}} = 8$ and $R_{\mathrm{C}} = 4$ for the 2 scales. The depth of convolution layers is set to $D = 80$ and $D = 64$ for the 2 scales. The network is trained using AdamW [26] optimizer with the max learning rate of 0.0004 and the iteration of 120000. + +![](images/209cd00e9735471a246f630830074b2afb43b0151d37976adaf1852f119d291e.jpg) + +![](images/e46063ff5bbcfe3f81c074501c5187e79b1dd99c7017c9a7f5e52a07a902b79d.jpg) +(a) Evaluation on MSCOCO. +(c) Evaluation on GoogleEarth. +Figure 4. Homography estimation evaluation on MSCOCO, cross-resolution MSCOCO, GoogleEarth, and GoogleMap datasets. MSCOCO contains common RGB images. Cross-resolution MSCOCO includes image pairs of $4 \times$ and $8 \times$ resolution gaps. GoogleEarth and GoogleMap are cross-modal datasets. The suffixes “-1” and “-2” denote the scale of the network. + +![](images/5c1b9b699fc11ea007fff9f3553e27dd03f3911a19eab712f25c642abb56bb7b.jpg) + +![](images/5810584266e2dfed700884ac0cbd06e944a3f04da39488781867eec401b51cc6.jpg) +(b) Evaluation on $4\times$ and $8\times$ resolution gaps MSCOCO. +(d) Evaluation on GoogleMap. + +# 4. Experiments + +# 4.1. Datasets and Experimental Setup + +Datasets. We evaluate our RHWF on MSCOCO [24] following [6, 7, 12, 15, 22, 34, 48], $4 \times$ and $8 \times$ cross-resolution MSCOCO following [34], and cross-modal GoogleEarth together with GoogleMap following [6, 48]. MSCOCO is a large-scale real world RGB dataset, which is most widely used for homography estimation evaluation. The cross-resolution MSCOCO is employed in [34] to meet the homography estimation requirement in multiscale gigapixel photography [3, 47]. The cross-modal GoogleEarth and GoogleMap datasets are employed in [48] for the homography estimation requirement in the navigation scenario [18, 48]. We note that all the methods included for comparison together with our RHWF are trained and evaluated on the same training and test subset of each dataset for totally fair comparison. + +Experimental setup. Similar to most of the previous works [6, 7, 12, 15, 22, 34, 48], the input images of size $[128 \times 128]$ are randomly perturbed in the corner points, with the perturbation range of $[-32, 32]$ . The average corner error (ACE) is adopted for the homography accuracy evaluation following [6, 7, 12, 15, 22, 34, 48], which is lower when achieving higher accuracy. + +# 4.2. Ablation + +Ablation Study on MSCOCO Dataset. The ablation of the homography-guided image warping, the attention-focusing mechanism, and the multiscale refinement are shown in Table 1. Mean average corner error (MACE) and + +Table 1. Ablation study of RHWF. + +
Ablation partSettingMACEParameters
WarpingFeature warping0.203(↑163.6%)0.94 M
Image warping0.0770.94 M
AttentionNo0.091(↑18.2%)0.85 M
Pure global0.085(↑10.4%)0.94 M
Pure local0.082(↑6.5%)0.94 M
Focus0.0770.94 M
Scale1 scale0.077(↑97.4%)0.94 M
2 scales0.0391.29 M
+ +network parameters are also listed. All the ablations are conducted on the 1-scale RHWF unless otherwise specially mentioned. It is observed that the proposed homography-guided image warping and attention-focusing mechanism yields significant gain in accuracy. The global attention has a range of the whole image, and the local has an attention radius of 1. We can also find the multiscale refinement very effective by increasing the accuracy by $97.4\%$ . + +Ablation without recurrence. We conduct the ablation with the compared methods with no recurrence and the RHWF w/ (RHWF) and w/o (RHWF-NF) FocusFormer in Table 2. It is observed that the FocusFormer is effective. + +Table 2. MACEs of RHWF and the compared structures without recurrent processing. + +
DHN 4.191MHN 3.645LocalTrans 1.987IHN 1.027RHWF 0.945RHWF-NF 1.019
+ +A Deeper Look at Warping. We further illustrate the average correlation value, which represents the feature similarity at each warping count in Fig. 5. The warping of feature or image is taken for comparison to evaluate the effectiveness of homography-guided image warping. It is observed that the image warping can significantly enhance the + +feature similarity as the warping count increases, while the feature warping weakens it. + +![](images/7c84c2eee833400664d4dd1b79496627153cfff51e6016ed4881eea63ee3f1de.jpg) +Figure 5. The average correlation value at each warping count of feature warping and image warping. + +# 4.3. MSCOCO Evaluation + +We evaluate RHWF together with other homography estimation methods including IHN [6] (previous SOTA method), LocalTrans [34], MHN [22], UDHN [46], DHN [12], CLKN [7], AffNet [30], LFNet [33], PFNet [42], PWC [35], SIFT+ContextDesc+RANSAC [28], SIFT+GeoDesc+RANSAC [29], SIFT+MAGSAC [2], and SIFT+RANSAC [27]. The comparison is illustrated in Fig. 4a. Following previous works [6,7,22,34,48], we plot the fraction of the number of images w.r.t. corresponding ACEs of a dataset. It can be observed that our 1-scale RHWF already outperforms other competitors except for 2-scale IHN, while 2-scale RHWF outperforms all others with a large gap. We note that 2-scale RHWF reduces previous SOTA MACE by $38.1\%$ . We also plot the result of 1-scale IHN, which is significantly exceeded by 1-scale RHWF. Please kindly note that CLKN performs IC- $\mathsf{LK}$ iteration with 4 scales, LocalTrans and MHN cascade 3 scales of networks to improve the estimation accuracy, but our 1-scale RHWF already markedly outperforms them. + +We then plot the MACEs at each iteration for IHN and our RHWF that adopt the recurrent framework in Fig. 6. It is observed that RHWF exceeds IHN at the 3rd iteration, while a more iterations won't make IHN outperform the RHWF with only 3 iterations. What's more, RHWF continues to reduce MACEs obviously with more iterations. + +# 4.4. Cross-Resolution MSCOCO Evaluation + +We conduct the evaluation on $4\times$ and $8\times$ crossresolution MSCOCO following [34]. We compare our RHWF with LocalTrans [34] (previous SOTA method), MHN [22],UDHN [46],DHN [12],and SIFT+RANSAC [27]. The resolution gap dramatically increases the difficulty of homography estimation, while it is vital for multiscale gigapixel photography [3, 34]. The results of $4\times$ and $8\times$ resolution gap MSCOCO are plotted in Fig. 4b. It is observed that RHWF ranks top in both scenarios and is significantly more robust under the $8\times$ resolution gap. + +We further demonstrate the self- and cross-attention map of RHWF at each iteration in Fig. 7. It is observed that at the + +![](images/de4439919a814cd96d15b42f79022e5014e02bed19f4491a31e9b44729339f1c.jpg) +Figure 6. The MACE comparison of IHN and our RHWF at each iteration count. + +1st iteration, the global attention in $I_{a}$ and $I_{b}(4\downarrow)$ successfully captures the correspondence information. However, in $I_{b}(8\downarrow)$ , the global attention becomes ambiguous as the resolution gap grows. Fortunately, as the recurrence continues, the homography-guided image warping corrects the deformation and the attention-focusing mechanism shrinks the attention range, which gradually clarifies the attention targets. + +# 4.5. Cross-Modal Datasets Evaluation + +The cross-modal data further raises the challenge for homography estimation, while it can be employed for GPS-denied navigation [18]. GoogleEarth contains image pairs across different seasons and GoogleMap the image pairs cropped from satellite images and their corresponding map images. We include IHN [6] (previous SOTA method), the original LK [1], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], DHN+DLKFM [48], and MHN+DLKFM [48] for comparison. The results of both datasets are separately demonstrated in Fig. 4c and Fig. 4d. The MACEs of RHWF and IHN are also illustrated for a better comparison. RHWF outperforms IHN by $34.1\%$ on GoogleMap3. + +We further illustrate the homography estimation results of the above-mentioned methods except for CLKN, DHN+DLKFM, and LK, as they are outperformed by MHN+DLKFM in [48]. It can be observed in Fig. 8 that under the severe large deformation and modality gap, SIFT+RANSAC and SIFT+MAGSAC fail as in the experiment of [6]. MHN+DLKFM produces unstable results as the LK iterator is of theoretical drawback [32]. DHN, MHN, and IHN are not as accurate as RHWF, as they neither consider the feature inconsistency caused by homography deformation nor introduce an attention mechanism to capture the intra-inter correspondence information. On the contrary, our RHWF can produce promising results under large deformation and modality gaps. + +![](images/8e857bbd76eac5c5653f1d442d5a055f29650721ea44ff17c9e9fe375fb746d5.jpg) +Figure 7. The self- and cross-attention map of RHWF at each iteration. The 1st row: the image $I_{a}$ of the standard resolution with the self-attention map. The 2nd and 3rd row: the image $I_{b}$ with $4 \times (I_{b}(4 \downarrow))$ and $8 \times (I_{b}(8 \downarrow))$ downsampling and cross-attention maps. The red arrows denote the query point of attention, and the red and blue boxes separately highlight the self- and cross-attention maps. + +![](images/71d7889dc810c86b01802c16170e6a992ef3ce3f2b49baf98f0f23d51e00fa66.jpg) + +![](images/df2b376f1898b8bcc48eb289f7dea032081669903205b2996b54d3912650b3fe.jpg) + +![](images/7d5d18b0eb800730f24c1809ea47a59ff7c65a6fee05acc43b2d473bbcb81a8f.jpg) + +![](images/4ae48a1aeacf57cfdacef5e9194bbe85f7a58801e38de863ca029e5dac504f26.jpg) +SIFT+RANSAC + +![](images/d4548234a08cc3e0d37a3221402480d964267de9dd0d980df8867ce42f5addc0.jpg) + +![](images/497b80f97c93a4f1285216e88a568f8958515e030f33ae1f6859b74e429fc06f.jpg) +SIFT+MAGSAC + +![](images/46b799ad855a23cd67241c1570d9ce56a9cb145055896442d928a0c173bc8649.jpg) + +![](images/2da419619059e2b664c238b74ac07f4070f7358af21adbe9e642db61d10566b7.jpg) +DHN + +![](images/3858be4ca6a4554bc02e8c0d2e541ffaaab3a07d992130f2fa1e95d777471ca8.jpg) + +![](images/0a2e8c89ceb7de44c733a2272ad2638e5d9769902599bd639cd752fcd2f1cebc.jpg) +MHN + +![](images/ef6b79ba1391b01c0de9ed1554ee221b11f4c16e51e2f9cedf5c1b150435713e.jpg) + +![](images/da40639f92de3473730f0ed4c6aa83f0d1c2838c272a7c5641cc0c0a4747900f.jpg) +MHN+DLKFM + +![](images/d6815da309be443b1b116bee6ab96ef0f4317cd85bd7371a858f65c9c07de632.jpg) + +![](images/ac3ac9828978d424e7fda49211d97bd3121f0d58c0af08e94cb90483363ea7dc.jpg) +IHN + +![](images/fe1a103e3e6cfc980fb6fe874840d0053a95bfd40b05b100c5fbb3eae097e4a6.jpg) + +![](images/4a2a5e1aea095d13cca25fa86f1599b39d4adc49559a66ffd2b8cb09f0fcece8.jpg) +RHWF (Ours) + +Table 3. Parameter comparison. + +
RHWFIHNLocalTransDHNMHNUDHNDLKFM
1.29 M1.71 M9.56 M34.19 M2.57 M21.29 M19.24 M
+ +# 4.6. Parameter and FLOPs Comparison + +We conduct the parameter and FLOPs comparison in Table 3. It is observed that compared to previous methods, our RHWF owns the least parameter cost, which is reduced by $86.5\%$ and $24.6\%$ compared with previous SOTA works LocalTrans [34] and IHN [6]. + +In Table 4, we compare the FLOPs of models and MACEs on MSCOCO with the previous SOTA recurrent methods including IHN, its improved version IHN-mov, and DLKFM. Compared to IHN-mov and DLKFM, the computational costs spent on the homography-guided warping in RHWF are much more effective. We also take the RHWF of the recurrent time 3 (fewer FLOPs), namely RHWF-3, which outperforms IHN-mov and DLKFM. + +Table 4. FLOPs of models with MACEs on MSCOCO. + +
FLOPs MACERHWF 16.96 G 0.077RHWF-3 9.64 G 0.176IHN 8.34 G 0.191IHN-mov 20.32 G 0.177DLKFM 110.51 G 0.550
+ +# 4.7. Failure Case + +Fig. 9 shows 2 failure cases, the left one is caused by the error accumulation, and the right the imperfect initial estimations. + +![](images/f7bccf02dbb0bfb065758aabb55b3c46ac062acecb72c8c61c3be6bebce3df73.jpg) +Figure 8. Homography estimation results of methods including IHN [6], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], MHN+DLKFM [48], and our RHWF. +Figure 9. Failure cases. + +# 5. Conclusions + +We have proposed a novel recurrent homography estimation framework, named RHWF. RHWF absorbs the homography-guided image warping and the FocusFormer, which facilitate the homography estimation by enhancing the feature consistency and capturing the intra/inter corresponding information in a global $\rightarrow$ nonlocal $\rightarrow$ local manner, into the recurrent framework. Experimentally, RHWF outperforms previous methods by a large gap with significantly fewer parameters. 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Rethinking planar homography estimation using perspective fields. In Asian Conference on Computer Vision, pages 571-586. Springer, 2018. 7 + +[43] Xinrui Zhan, Yang Li, Wenyu Liu, and Jianke Zhu. Warped convolution networks for homography estimation. arXiv preprint arXiv:2206.11657, 2022. 1, 2, 3 +[44] Xinrui Zhan, Yueran Liu, Jianke Zhu, and Yang Li. Homography decomposition networks for planar object tracking. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 3234-3242, 2022. 1 +[45] Haoxian Zhang and Yonggen Ling. Hvc-net: Unifying homography, visibility, and confidence learning for planar object tracking. In Proceedings of the European Conference on Computer Vision, pages 701-718. Springer, 2022. 1 +[46] Jirong Zhang, Chuan Wang, Shuaicheng Liu, Lanpeng Jia, Nianjin Ye, Jue Wang, Ji Zhou, and Jian Sun. Content-aware unsupervised deep homography estimation. In Proceedings of the European Conference on Computer Vision, pages 653-669. Springer, 2020. 2, 7 +[47] Jianing Zhang, Tianyi Zhu, Anke Zhang, Xiaoyun Yuan, Zihan Wang, Sebastian Beetschen, Lan Xu, Xing Lin, Qionghai Dai, and Lu Fang. Multiscale-vr: Multiscale gigapixel 3d panoramic videography for virtual reality. In 2020 IEEE International Conference on Computational Photography (ICCP), pages 1-12. IEEE, 2020. 6 +[48] Yiming Zhao, Xinming Huang, and Ziming Zhang. Deep Lucas-Kanade homography for multimodal image alignment. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15950-15959, 2021. 1, 2, 6, 7, 8 +[49] Yuan Zhou, Anand Ranganarajan, and Paul D Gader. An integrated approach to registration and fusion of hyperspectral and multispectral images. IEEE Transactions on Geoscience and Remote Sensing, 58(5):3020-3033, 2019. 1 +[50] Barbara Zitova and Jan Flusser. Image registration methods: A survey. Image and Vision Computing, 21(11):977-1000, 2003. 2 \ No newline at end of file diff --git a/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/images.zip b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2d2256bb221c197b2d1977e8a2bbb90d4cc56b55 --- /dev/null +++ b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1d2785af1347ac391cc8b74fd667b6fcb06890eefcc5044089ee5f72278ac7df +size 535654 diff --git a/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/layout.json b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..9aa80dfe7b32fc99e76d91fadc36cbd4a0e21a2b --- /dev/null +++ b/2023/Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer/layout.json @@ -0,0 +1,10136 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 106, + 103, + 488, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 103, + 488, + 140 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 488, + 140 + ], + "type": "text", + "content": "Recurrent Homography Estimation Using Homography-Guided Image Warping and Focus Transformer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "spans": [ + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": "Si-Yuan Cao" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Runmin Zhang" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Lun Luo" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Beinan Yu" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Zehua Sheng" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Junwei Li" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "text", + "content": ", Hui-Liang Shen" + }, + { + "bbox": [ + 54, + 160, + 546, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 177, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 177, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 53, + 177, + 545, + 205 + ], + "type": "text", + "content": "1Ningbo Innovation Center, Zhejiang University, 2College of Information Science and Electronic Engineering, Zhejiang University karlcao@hotmail.com, {runmin_zhang, luolun, yubeinan, shengzehua, lijunwei7788, shenhl}@zju.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "spans": [ + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": "We propose the Recurrent homography estimation framework using Homography-guided image Warping and Focus transformer (FocusFormer), named RHWF. Both being appropriately absorbed into the recurrent framework, the homography-guided image warping progressively enhances the feature consistency and the attention-focusing mechanism in FocusFormer aggregates the intra-inter correspondence in a global " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": " nonlocal " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": " local manner. Thanks to the above strategies, RHWF ranks top in accuracy on a variety of datasets, including the challenging cross-resolution and cross-modal ones. Meanwhile, benefiting from the recurrent framework, RHWF achieves parameter efficiency despite the transformer architecture. Compared to previous state-of-the-art approaches LocalTrans and IHN, RHWF reduces the mean average corner error (MACE) by about " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "38.1\\%" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": " on the MSCOCO dataset, while saving the parameter costs by " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "86.5\\%" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "inline_equation", + "content": "24.6\\%" + }, + { + "bbox": [ + 45, + 257, + 290, + 520 + ], + "type": "text", + "content": ". Similar to the previous works, RHWF can also be arranged in 1-scale for efficiency and 2-scale for accuracy, with the 1-scale RHWF already outperforming most of the previous methods. Source code is available at https://github.com/imdumpl78/RHWF." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 128, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 128, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 128, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 644 + ], + "type": "text", + "content": "Homography is defined as a global projective mapping between two images captured from different perspectives. It has been widely applied in computer vision tasks ranging from the monocular camera system to the multi-camera system, such as image/video stitching [4, 17, 19], multiscale gigapixel photography [3, 34], multispectral image fusion [41, 49], planar object tracking [44, 45], SLAM [14, 31], and GPS-denied UAV localization [18, 48]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "content": "Deep homography estimation was introduced in the pioneer [12] that uses a VGG-style network to predict the homography. Many following works have been presented to further improve the estimation accuracy, including cas-" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 230, + 539, + 327 + ], + "blocks": [ + { + "bbox": [ + 310, + 230, + 539, + 327 + ], + "lines": [ + { + "bbox": [ + 310, + 230, + 539, + 327 + ], + "spans": [ + { + "bbox": [ + 310, + 230, + 539, + 327 + ], + "type": "image", + "image_path": "402d7510d96acacb79a67d2ab3ebd3b1f232212f6f25c0d8b38b5316cdf8818a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 327, + 546, + 359 + ], + "lines": [ + { + "bbox": [ + 305, + 327, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 546, + 359 + ], + "type": "text", + "content": "Figure 1. Illustration of the difference of warping and attention strategies in RHWF and previous approaches. Our RHWF deploys (c) and (f). Please see text for details." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 544 + ], + "type": "text", + "content": "cading multiple similar networks [15, 21, 22, 34] or designing iterable architectures such as the IC-LK iterator [7, 48] and the trainable CNN iterator [6]. The cascading strategy has improved the accuracy to some extent but is limited by the fixed number of networks. Worse still, stacking more networks cannot guarantee better accuracy [22]. The IC-LK (inverse compositional Lucas-Kanade [1]) based deep methods use deep feature extractor combined with the untrainable iterator to improve the estimation performance, but is limited by the theoretical drawback of the untrainable iterator [6, 32]. IHN [6] avoids this limitation by designing an iterable and trainable network architecture, which further improves the estimation accuracy. However, the feature inconsistency caused by the homography deformation has long been neglected in most current works." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "content": "It has been well investigated in [9] that standard convolution is unable to keep the equivariance under the spatial transformation except translation. However, besides translation, homography is composed of rotation, scaling, shearing, aspect ratio, and perspective transformations [37, 43], which leads to the inconsistency of the features from corresponding points [25]. The inconsistency will hinder the homography estimation performance. Many efforts have been made to acquire the transformation-equivariance by either applying group convolutions in the network [9] or pre-warping [16, 20, 25, 43] the input image. But the above strategies need to exhaustively explore the possible transformation dimensions and degrees, as is illustrated in Fig. 1a, which is redundant in computation when coping with" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9833" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 247, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 247, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 247, + 83 + ], + "type": "text", + "content": "the homography transformation with a DOF of 6." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "text", + "content": "To cope with the above problem, homography-guided image warping, as shown in Fig. 1c, is adopted in our proposed recurrent homography estimation framework, dubbed RHWF. We note that homography-guided image warping has already been unconsciously employed in some of the previous cascading-based works [15, 22, 34]. However, the reason, effect, and technique of using homography-guided image warping, especially absorbing it properly in the recurrent framework, hasn't ever been investigated. Different from the previous works, our RHWF combines the homography-guided image warping with the recurrent trainable network, which significantly improves the accuracy without the cost of network parameters. Compared to the previous cascading-based SOTA method LocalTrans [34], RHWF reduces the mean average corner error (MACE) by about " + }, + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "text", + "content": " on the MSCOCO dataset, while reducing the parameter cost of " + }, + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "inline_equation", + "content": "86.5\\%" + }, + { + "bbox": [ + 46, + 84, + 287, + 287 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "text", + "content": "On the other side, transformer architecture [8, 13] has demonstrated its superior ability in computer vision and image processing tasks. The transformer architecture has also been introduced in the homography estimation task as in [21, 34]. Following their pioneer exploration, we propose a transformer structure, named FocusFormer, that is pretty compatible with the homography-guided image warping and the recurrent framework. As illustrated in Fig. 1d, Fig. 1e, and Fig. 1f, unlike the attention mechanism in previous works that is pure global or local, FocusFormer employs the attention focusing mechanism. The scope of the attention mechanism shrinks along with the recurrence procedure, which captures the intra/inter correspondence information in a global " + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "text", + "content": " nonlocal " + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "text", + "content": " local" + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 46, + 288, + 288, + 503 + ], + "type": "text", + "content": " manner. We note that compared to the most widely adopted global attention mechanism, the attention-focusing mechanism can save computation costs while improving the homography estimation performance simultaneously." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "text", + "content": "We introduce the homography-guided image warping and FocusFormer into the recurrent homography estimation framework, named RHWF. The three parts, i.e., recurrent estimation, homography-guided image warping, and the FocusFormer cooperate well, with each part facilitating the others. We evaluate RHWF on a variety of datasets including common RGB image data [24], cross-resolution data [34] and cross-modal data [6, 48], on which it outperforms all other competitors by a large gap. We show that though adopting the transformer, our RHWF reduces the parameter cost of " + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "inline_equation", + "content": "24.6\\%" + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "text", + "content": " while achieving the accuracy gain of " + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "inline_equation", + "content": "38.1\\%" + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "text", + "content": " (MSCOCO) and " + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "inline_equation", + "content": "34.1\\%" + }, + { + "bbox": [ + 46, + 505, + 287, + 684 + ], + "type": "text", + "content": " (GoogleMap), compared to the previous SOTA method IHN [6]. In summary, our contributions are as follows: (1) We propose a novel Recurrent homography estimation framework using Homography-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "text", + "content": "guided image Warping and FocusFormer, dubbed RHWF. RHWF ranks top on a variety of datasets, including the challenge scenes such as the cross-resolution and cross-modal ones. The recurrent estimation, homography-guided image warping, and FocusFormer facilitate the functionality of each other. (2) The reason, effect, and technique of using homography-guided image warping properly in the recurrent framework is first fully investigated. With the assistance of homography-guided image warping, the extracted features gradually converge into consistency, and hence boosting the homography estimation accuracy. (3) The FocusFormer is proposed to be the fundamental block of the recurrent homography estimation. The attention mechanism in FocusFormer works in a global " + }, + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "text", + "content": " nonlocal " + }, + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 306, + 72, + 545, + 263 + ], + "type": "text", + "content": " local manner, which significantly saves the computational costs while achieving a better performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "text", + "content": "In this section we briefly review the most relevant works including deep homography estimation, transformation-equivariant network, and transformer in deep homography estimation. The readers are referred to literature such as [50] for the basic knowledge and traditional methods for homography estimation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 366, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 545, + 461 + ], + "type": "text", + "content": "Deep Homography Estimation. DeTone et al. [12] first propose to estimate the homography deformation between the concatenated input image pair with a VGG-style network. Many works [15,22,46] inherit the network as a basic structure, which is either modified or cascaded by multiple times to boost the estimation accuracy. The cascading strategy indeed improves the performance, but is exceeded by the recurrent estimation methods [6,7,38,48]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 463, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 617 + ], + "type": "text", + "content": "The recurrent homography estimation method mainly contains two types, including the IC-LK iterator based ones [7,38,48] and the deep iterator based ones [6]. CLKN [7] is the pioneer work introduced by Chang et al. to employ IC-LK to build an untrainable recurrent homography estimation framework. Zhao et al. [48] present a new loss function to directly enhance the similarity of the feature maps of CNNs, which further releases the potential of the IC-LK framework. However, the recurrent framework using IC-LK is unable to learn the implicit prior for the iterator through a large amount of image data. Cao et al. [6] propose IHN to make the whole network trainable, achieving a higher homography estimation accuracy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": "Transformation-Equivariant Under Homography. It has been well analyzed in previous works [9] that standard convolution is equivariant to translations, but may fail to equivary with more general transformations. Unfortunately, homography has the transformation of rotation, scaling, shearing, aspect ratio, and perspective [43]. The corresponding features extracted by standard CNNs are inconsistent under homography deformation, which reduce the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "1As in most of the works that refer to \"nonlocal\" [5], it denotes a relatively large neighborhood around a pixel." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9834" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 153, + 72, + 440, + 299 + ], + "blocks": [ + { + "bbox": [ + 153, + 72, + 440, + 299 + ], + "lines": [ + { + "bbox": [ + 153, + 72, + 440, + 299 + ], + "spans": [ + { + "bbox": [ + 153, + 72, + 440, + 299 + ], + "type": "image", + "image_path": "103c7804ca25ac9119b1dcf96cada2e7ecfe541081066273907f94badff17c1c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 547, + 334 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 547, + 334 + ], + "type": "text", + "content": "Figure 2. Architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. (a) Overall structure of RHWF. (b) Detailed structure of the proposed FocusFormer. (c) Detailed illustration of the attention-focusing mechanism." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 340, + 289, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 289, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 289, + 604 + ], + "type": "text", + "content": "estimation accuracy. Many efforts [9-11, 16, 25, 39] have been made to deal with this problem. Some methods design special network architectures to make CNNs equivariant to specific transformations [9-11, 39], among which the well-known group equivariant CNNs [9] produce rotation equivariant features using group convolution and subgroup pooling. However, the model becomes inefficient as it applies group convolutions directly on a large group [25]. The transformation is limited to rotation in this network. Other methods [16, 20, 25, 43] achieve transformation-equivariant by the predefined warping of the input image by different transformation dimensions and degrees. For example, GIFT [25] produces rotation and scale invariant features using warped images with predefined rotation angles and scale ratios. Warped convolution [20] achieves equivariance by warping the input image through a designed function. But the above two methods can only deal with the rotation/scaling of 2 DOF. When it comes to the homography transformation, the DOF of which increases from 2 to 6 (besides translation, which is equivariant in the standard convolution). The predefined warping will become burdensome and impracticable." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Transformer in Deep Homography Estimation. The performance of homography estimation networks can be boosted using the transformer. The transformer can be used either for feature enhancement or homography estimation. Shao et al. [34] adopt a multiscale transformer that works locally for the feature enhancement purpose. Hong et al. [21] employ a series of transformers to predict homography from the feature pyramids in a coarse-to-fine manner. The transformer shows powerful ability by significantly improv" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 341, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 547, + 376 + ], + "type": "text", + "content": "ing the homography estimation accuracy, and a transformer structure suitable for the recurrent homography framework is urgently needed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 380, + 389, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 389, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 389, + 395 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "text", + "content": "Fig. 2 illustrates the architecture of Recurrent homography estimation using Homography-guided image Warping and FocusFormer, named RHWF. The details of FocusFormer are shown in Fig. 2b. The homography-guided image warping and the attention-focusing mechanism in FocusFormer are arranged in an interleaved manner, which are appropriately absorbed into the recurrent framework. We note that the whole network is tied despite the number of iteration, which means the framework won't raise the network parameters. Let's denote the paired input images as " + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "text", + "content": ", and we aim to obtain the homography matrix " + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 305, + 401, + 547, + 544 + ], + "type": "text", + "content": " that relates them." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 552, + 375, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 375, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 375, + 563 + ], + "type": "text", + "content": "3.1. Backbone" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "We employ convolutional neural network (CNN) with residual connections as our backbone. As illustrated in Fig. 2a, we use CNNs with shared weights for 2 input images. The input images are processed with a convolutional block of kernel size " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " first. The produced feature maps are then continually processed by the basic blocks consisting of 2 residual layers, with each block accomplishing a " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " down-sampling in the spatial dimension. Different from the previous works [6, 34] that use the max-pooling layer to perform down-sampling, RHWF uses convolution with stride 2 to reduce the inference computation, which reduces the inference computational cost at 1 time to 1.43 GFLOPs" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9835" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 281, + 175 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 281, + 175 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 281, + 175 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 281, + 175 + ], + "type": "image", + "image_path": "23729feeb914b441c5b08e324169b9ba3e03e74df79980375a6a941c3e2c3914.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 251 + ], + "type": "text", + "content": "Figure 3. Illustration of the reason and effect of using homography-guided image warping. The red squares represent the feature extracted from the left-side ear of the cat in the images. The color of the squares exhibits the feature similarity, and the colors become consistent as the feature similarity grows. (a) The ideal homography-invariant situation. (b) The practical situation. (c) The effect of homography-guided image warping." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": "from 2.43 GFLOPs in [6]. Finally, the feature maps are projected by 1 linear convolutional layer of kernel size " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": ". RHWF only needs a dimension of 96 while achieving far better results than IHN [6] that needs 256. We stack 2 basic blocks to produce the feature maps of the spatial dimension " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "H / 4 \\times W / 4" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "H / 2 \\times W / 2" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": " denote the height and width of the image. We note that, during the recurrent estimation process, the feature map of " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": " is computed once but the one of " + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 46, + 256, + 287, + 400 + ], + "type": "text", + "content": " is computed recurrently due to the homography-guided image warping. This operation raises the computational cost of the network, but we will show the tremendous benefits of doing so." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 409, + 247, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 409, + 247, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 409, + 247, + 423 + ], + "type": "text", + "content": "3.2. Homography-Guided Image Warping" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 428, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 287, + 523 + ], + "type": "text", + "content": "In previous recurrent methods [6, 7], the images of severe homography deformation are used directly to produce the feature maps for homography estimation. The defect that the standard convolution is lack of equivary under homography transformation is ignored. For the homography estimation task, we want the backbone network to extract homography equivariant feature maps, which can be formulated by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 525, + 287, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 525, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 111, + 525, + 287, + 539 + ], + "type": "interline_equation", + "content": "\\phi (\\pi (I; \\mathbf {H})) = \\pi (\\phi (I); \\mathbf {H}), \\tag {1}", + "image_path": "f13fc074d16150aed38a903adaab5faea4fcff8e0d0978ab41c8001f50d2aaf9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": " denotes the coordinate projection, " + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": " denotes the homography matrix that relates " + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 545, + 287, + 653 + ], + "type": "text", + "content": " denotes the backbone CNN. This ideal situation is illustrated in Fig. 3a. In the ideal situation, the homography deformation won't affect feature similarity, making 2 features absolutely match each other. Unfortunately, in practice, due to the lack of equivary under homography transformation, the similarity of corresponding features produced by the backbone CNN will be weakened as illustrated in Fig. 3b." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "To cope with the above problem, many strategies have been proposed [9, 10, 20, 25] to either employ the group convolution or pre-warp the image by multiple times. However, both of the above methods bring considerable computational costs. We propose to interleave the homography es" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": "timation and image warping process, dubbed homographyguided image warping, in our RHWF. The whole process is designed under the inspiration of the alternate update of different variables in conventional optimization frameworks. For " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " related by homography " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": ", the interleaved image warping and homography estimation process can be expressed as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 379, + 156, + 545, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 156, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 379, + 156, + 545, + 176 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {F} _ {b} ^ {n} = \\phi (\\mathcal {W} (I _ {b}; \\hat {\\mathbf {H}} ^ {n})), \\\\ \\hat {\\mathbf {\\Phi}} \\end{array} \\tag {2}", + "image_path": "2d2e548d86925dbe67e3ce5ef5910eb5f98c44ef602ec253bbc98b7636234d7e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 381, + 174, + 467, + 187 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 174, + 467, + 187 + ], + "spans": [ + { + "bbox": [ + 381, + 174, + 467, + 187 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {H}} ^ {n + 1} = \\psi (\\mathbf {F} _ {a}; \\mathbf {F} _ {b} ^ {n}),", + "image_path": "39771bb25ce74b753cdfeece53b1a2084b51cc9bcb675c8ab6dc748154b5a6aa.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " denote the homography-guided image warping, " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " denotes the FocusFormer" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " designed for homography estimation. The feature consistency between " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_a" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_b" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " together with the homography " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{H}}" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " are optimized alternatively. We note that the homography-guided image warping takes the advantage of the recurrent framework of RHWF, and hence the redundant pre-designed warping or complex group convolution is not required. They are replaced by the warping guided by the present estimated homography. Meanwhile, the homography-guided image warping facilitates the estimation accuracy of the recurrent framework by relieving the feature inconsistency caused by deformation, as shown in Fig. 3c. We note that the backbone network recurrently extracts the feature map of " + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_b^n" + }, + { + "bbox": [ + 304, + 193, + 545, + 373 + ], + "type": "text", + "content": " with tied weights, which won't bring additional parameter costs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 381, + 391, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 391, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 391, + 392 + ], + "type": "text", + "content": "3.3. FocusFormer" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 399, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 448 + ], + "type": "text", + "content": "The core architecture of RHWF is our FocusFormer that achieves recurrent residual homography estimation. FocusFormer mainly contains two parts that accomplish attention mechanism and homography estimation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 448, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 519 + ], + "type": "text", + "content": "Attention. Following previous works [23, 34, 36, 40], we interleave the self-attention layer and the cross-attention layer, which is shown in Fig. 2b. By adopting both self-attention and cross-attention, FocusFormer can capture the intra/inter correspondence information of the input image pair." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "text", + "content": "As demonstrated in Fig. 2c, along with the network recurrence, the scope of attention mechanism shrinks in a global " + }, + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "text", + "content": " nonlocal " + }, + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 520, + 545, + 675 + ], + "type": "text", + "content": " local manner. This operation is deeply bounded with the homography-guided image warping process and the recurrent framework. At the first iteration, the deformation between the two images is large due to large homography deformation. Long range attention is needed to better capture the intra-inter correspondence. As the iteration continues, the deformation is continuously reduced, and hence the attention can focus on the local area to better improve the estimation accuracy. It is worth noting that the attention-focusing mechanism can reduce the computational cost to 3.18 GFLOPs from 7.14 GFLOPs, which" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "In practice, the FocusFormer predicts the residual translation of 4 corner points of an image " + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{T}^{n + 1}" + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": ", and some simple computation will produce " + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{H}}^{n + 1}" + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": " as will be detailed in Section 3.3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9836" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 182, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 182, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 182, + 83 + ], + "type": "text", + "content": "works in the pure global manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "content": "Let us denote the coordinate index of the feature map as " + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = (u, v)" + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "content": ", the projected query, key, and value as " + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 47, + 84, + 287, + 131 + ], + "type": "text", + "content": ". The self attention-focusing mechanism can be formulated as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 136, + 287, + 173 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 136, + 287, + 173 + ], + "spans": [ + { + "bbox": [ + 52, + 136, + 287, + 173 + ], + "type": "interline_equation", + "content": "\\operatorname {s e l f} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {3}", + "image_path": "e0206196ae20037d9bec75a35d61cd1b7051e9cd070c7d8d6bc4f585d360f4dd.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "content": " represents the region around " + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "content": " that self-attention works within. If " + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "content": " is set as the whole image, it would become the global self-attention, otherwise the nonlocal or local one of radius " + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{A}}" + }, + { + "bbox": [ + 47, + 173, + 287, + 244 + ], + "type": "text", + "content": ". The subscript \"i\" denotes that the query, key, and value are from the same image. The cross attention-focusing mechanism can be formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 251, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 251, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 48, + 251, + 287, + 287 + ], + "type": "interline_equation", + "content": "\\operatorname {c r o s s} (\\mathbf {x}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} _ {i} \\left(\\mathcal {N} (\\mathbf {x})\\right) ^ {\\top} \\mathbf {K} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right)}{\\sqrt {D}}\\right) \\mathbf {V} _ {j} \\left(\\mathcal {N} (\\mathbf {x})\\right), \\tag {4}", + "image_path": "411fc04894443bbb4d0ab6f78b08c96e12e4b95a8efd4250dc5938d7a5822993.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "text", + "content": "where subscripts “" + }, + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "text", + "content": "” and “" + }, + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 287, + 287, + 407 + ], + "type": "text", + "content": "” denote that the query is from one image, while the key and value are from another. As for other details, we only use 1 self-attention layer and 1 cross-attention layer. Considering that the whole attention block functions in the recurrent framework, the effectiveness of the attention layer would be fully motivated during the iterative inference process. The residual connecting, layer normalization, and feed-forward network are also adopted as in previous works [34, 40]. The multi-head attention is discarded as in [40] to improve efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 407, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 287, + 443 + ], + "type": "text", + "content": "Homography Estimation. After capturing the intra/inter correspondence of the input image pair, the correlation within local areas is then computed as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 449, + 287, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 449, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 55, + 449, + 287, + 473 + ], + "type": "interline_equation", + "content": "\\mathbf {C} (\\mathbf {x}, \\mathbf {r}) = \\operatorname {R e L U} \\left(\\mathbf {F} _ {a} ^ {\\prime} (\\mathbf {x}) ^ {\\top} \\mathbf {F} _ {b} ^ {\\prime n} (\\mathbf {x} + \\mathbf {r})\\right), \\quad \\| \\mathbf {r} \\| _ {\\infty} \\leq R _ {\\mathrm {C}} \\tag {5}", + "image_path": "ab410222df0b7358642032d0868ef55756c7e3912e4d13f69f83d8f15db495a2.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{C}}" + }, + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "text", + "content": " controls the radius of each local area, making the correlation volume having the size of " + }, + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "inline_equation", + "content": "H \\times W \\times (2R_{\\mathrm{C}} + 1) \\times (2R_{\\mathrm{C}} + 1)" + }, + { + "bbox": [ + 47, + 474, + 287, + 545 + ], + "type": "text", + "content": ". This correlation can also be interpreted as another layer of cross attention [34] for the homography estimation, while the mapping differs as the desired output is the residual homography." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": "The architecture of the homography aggregator is similar to the previous correlation-based homography estimation works [6, 34]. The aggregator is composed of the basic blocks having 2 convolution layers and 1 max-pooling layer. The only difference is that the depth of the convolution layer of our RHWF (denoted as " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ") is set to be markedly lower than that of IHN [6] and LocalTrans [34], which also saves the network parameters. Like most previous works [6, 12, 34], we parameterize the residual homography in the form of the translation of the 4 corner points of an image, namely " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ". At iteration " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ", The parameterization of " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{H}}^n" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}^n" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": " can be easily established by a least square problem as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 138, + 700, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 700, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 138, + 700, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathbf {A} ^ {n} \\hat {\\mathbf {h}} ^ {n} = \\mathbf {b} ^ {n}, \\tag {6}", + "image_path": "3467e745bc320fd9192f6745e3813b6e9f6ba3fc7aa88973a0e642d91a0bfde8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{b}^n" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is the coordinate of the projected 4 corner points, " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^n" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is composed of the projected 4 corner points and the original 4 corner points, " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{h}}^n" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is the vectorized " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{H}}^n" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ". The original 4 corner points and the projected 4 corner points are related by " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}^n" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ". During the recurrent process, the homography estimator produces the present residual translation " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{T}" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " and the translation " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is updated by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 375, + 163, + 545, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 163, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 375, + 163, + 545, + 177 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {T}} ^ {n + 1} = \\hat {\\mathbf {T}} ^ {n} + \\Delta \\mathbf {T} ^ {n + 1}, \\tag {7}", + "image_path": "359bae94a08e7a26cfb7a19019288618423ce9e384ac12ca4ecee15c14fb6af4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 186, + 545, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 210 + ], + "type": "text", + "content": "which is equivalent to the homography update illustrated in Fig. 2a, which can be formulated as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 380, + 218, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 218, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 380, + 218, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {H}} ^ {n + 1} = \\hat {\\mathbf {H}} ^ {n} \\Delta \\mathbf {H} ^ {n + 1}. \\tag {8}", + "image_path": "7e7732cee3f53bfa5c5b8a62257c744734d08120abf0fbc19cb3fe3a66258de7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 248, + 434, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 248, + 434, + 260 + ], + "spans": [ + { + "bbox": [ + 306, + 248, + 434, + 260 + ], + "type": "text", + "content": "3.4. Multiscale Refinement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 266, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 410 + ], + "type": "text", + "content": "The performance of our proposed RHWF can be further improved by multiscale refinement. As illustrated in Section 3.1, the feature map of the spatial dimension " + }, + { + "bbox": [ + 305, + 266, + 545, + 410 + ], + "type": "inline_equation", + "content": "H / 2 \\times W / 2" + }, + { + "bbox": [ + 305, + 266, + 545, + 410 + ], + "type": "text", + "content": " can be adopted to construct an additional scale for a more accurate homography refinement. In the refinement scale, a FocusFormer with different weights is employed. The structures of the FocusFormer of the 2 levels are basically identical, except for the attention range of the additional scale, which further shrinks as the initial homography is given by the former scale. We will show that the accuracy of a single scale already outperforms most of the previous works except for the 2-scale IHN in [6]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 418, + 384, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 384, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 384, + 430 + ], + "type": "text", + "content": "3.5. Supervision" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "text", + "content": "We use the " + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "text", + "content": " loss between the ground-truth translation " + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{\\mathrm{gt}}" + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "text", + "content": " and the estimated one " + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{T}}" + }, + { + "bbox": [ + 306, + 436, + 545, + 472 + ], + "type": "text", + "content": ". The loss at each iteration is weight summed as the final loss" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 359, + 480, + 545, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 480, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 359, + 480, + 545, + 513 + ], + "type": "interline_equation", + "content": "L = \\sum_ {n = 0} ^ {N - 1} \\gamma^ {(N - n - 1)} | \\hat {\\mathbf {T}} ^ {n} - \\mathbf {T} _ {\\mathrm {g t}} |, \\tag {9}", + "image_path": "349c76df149627beeb7580955c9437237a0042cfaae4d5f69e2764f89f77d5bb.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "text", + "content": " denotes the recurrent time within 1 scale, " + }, + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 520, + 545, + 567 + ], + "type": "text", + "content": " is less than 1 to produce a larger weight for the later estimations as in IHN [6]. If multiscale refinement is employed, the losses of the 2 scales are summed." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "type": "text", + "content": "3.6. Implementation Details" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": "In our implementation, the recurrent time " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " within one scale is set to 6. We set the attention range in the FocusFormer as " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "[G,4,2,1,1,1]" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " for scale " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "H / 4 \\times W / 4" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "[2,2,1,1,1,1]" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " for scale " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "H / 2 \\times W / 2" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " denotes the global attention, and others the radius of the attention area " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{A}}" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": ". The radius of correlation is set to " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{C}} = 8" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{C}} = 4" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " for the 2 scales. The depth of convolution layers is set to " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "D = 80" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "inline_equation", + "content": "D = 64" + }, + { + "bbox": [ + 305, + 594, + 545, + 712 + ], + "type": "text", + "content": " for the 2 scales. The network is trained using AdamW [26] optimizer with the max learning rate of 0.0004 and the iteration of 120000." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9837" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 70, + 265, + 168 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 265, + 168 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 265, + 168 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 265, + 168 + ], + "type": "image", + "image_path": "209cd00e9735471a246f630830074b2afb43b0151d37976adaf1852f119d291e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 77, + 176, + 265, + 273 + ], + "blocks": [ + { + "bbox": [ + 124, + 169, + 218, + 176 + ], + "lines": [ + { + "bbox": [ + 124, + 169, + 218, + 176 + ], + "spans": [ + { + "bbox": [ + 124, + 169, + 218, + 176 + ], + "type": "text", + "content": "(a) Evaluation on MSCOCO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 77, + 176, + 265, + 273 + ], + "lines": [ + { + "bbox": [ + 77, + 176, + 265, + 273 + ], + "spans": [ + { + "bbox": [ + 77, + 176, + 265, + 273 + ], + "type": "image", + "image_path": "e46063ff5bbcfe3f81c074501c5187e79b1dd99c7017c9a7f5e52a07a902b79d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 274, + 222, + 282 + ], + "lines": [ + { + "bbox": [ + 121, + 274, + 222, + 282 + ], + "spans": [ + { + "bbox": [ + 121, + 274, + 222, + 282 + ], + "type": "text", + "content": "(c) Evaluation on GoogleEarth." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "type": "text", + "content": "Figure 4. Homography estimation evaluation on MSCOCO, cross-resolution MSCOCO, GoogleEarth, and GoogleMap datasets. MSCOCO contains common RGB images. Cross-resolution MSCOCO includes image pairs of " + }, + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 285, + 547, + 319 + ], + "type": "text", + "content": " resolution gaps. GoogleEarth and GoogleMap are cross-modal datasets. The suffixes “-1” and “-2” denote the scale of the network." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 327, + 70, + 515, + 168 + ], + "blocks": [ + { + "bbox": [ + 327, + 70, + 515, + 168 + ], + "lines": [ + { + "bbox": [ + 327, + 70, + 515, + 168 + ], + "spans": [ + { + "bbox": [ + 327, + 70, + 515, + 168 + ], + "type": "image", + "image_path": "5c1b9b699fc11ea007fff9f3553e27dd03f3911a19eab712f25c642abb56bb7b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 327, + 178, + 514, + 273 + ], + "blocks": [ + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "lines": [ + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "spans": [ + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "type": "text", + "content": "(b) Evaluation on " + }, + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 329, + 169, + 514, + 178 + ], + "type": "text", + "content": " resolution gaps MSCOCO." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 327, + 178, + 514, + 273 + ], + "lines": [ + { + "bbox": [ + 327, + 178, + 514, + 273 + ], + "spans": [ + { + "bbox": [ + 327, + 178, + 514, + 273 + ], + "type": "image", + "image_path": "5810584266e2dfed700884ac0cbd06e944a3f04da39488781867eec401b51cc6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 372, + 274, + 471, + 282 + ], + "lines": [ + { + "bbox": [ + 372, + 274, + 471, + 282 + ], + "spans": [ + { + "bbox": [ + 372, + 274, + 471, + 282 + ], + "type": "text", + "content": "(d) Evaluation on GoogleMap." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 329, + 128, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 329, + 128, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 329, + 128, + 342 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 350, + 227, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 227, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 227, + 363 + ], + "type": "text", + "content": "4.1. Datasets and Experimental Setup" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "text", + "content": "Datasets. We evaluate our RHWF on MSCOCO [24] following [6, 7, 12, 15, 22, 34, 48], " + }, + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 369, + 287, + 548 + ], + "type": "text", + "content": " cross-resolution MSCOCO following [34], and cross-modal GoogleEarth together with GoogleMap following [6, 48]. MSCOCO is a large-scale real world RGB dataset, which is most widely used for homography estimation evaluation. The cross-resolution MSCOCO is employed in [34] to meet the homography estimation requirement in multiscale gigapixel photography [3, 47]. The cross-modal GoogleEarth and GoogleMap datasets are employed in [48] for the homography estimation requirement in the navigation scenario [18, 48]. We note that all the methods included for comparison together with our RHWF are trained and evaluated on the same training and test subset of each dataset for totally fair comparison." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "text", + "content": "Experimental setup. Similar to most of the previous works [6, 7, 12, 15, 22, 34, 48], the input images of size " + }, + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "inline_equation", + "content": "[128 \\times 128]" + }, + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "text", + "content": " are randomly perturbed in the corner points, with the perturbation range of " + }, + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "inline_equation", + "content": "[-32, 32]" + }, + { + "bbox": [ + 46, + 551, + 288, + 635 + ], + "type": "text", + "content": ". The average corner error (ACE) is adopted for the homography accuracy evaluation following [6, 7, 12, 15, 22, 34, 48], which is lower when achieving higher accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 646, + 111, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 111, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 111, + 658 + ], + "type": "text", + "content": "4.2. Ablation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Ablation Study on MSCOCO Dataset. The ablation of the homography-guided image warping, the attention-focusing mechanism, and the multiscale refinement are shown in Table 1. Mean average corner error (MACE) and" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 309, + 332, + 542, + 441 + ], + "blocks": [ + { + "bbox": [ + 362, + 320, + 489, + 331 + ], + "lines": [ + { + "bbox": [ + 362, + 320, + 489, + 331 + ], + "spans": [ + { + "bbox": [ + 362, + 320, + 489, + 331 + ], + "type": "text", + "content": "Table 1. Ablation study of RHWF." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 332, + 542, + 441 + ], + "lines": [ + { + "bbox": [ + 309, + 332, + 542, + 441 + ], + "spans": [ + { + "bbox": [ + 309, + 332, + 542, + 441 + ], + "type": "table", + "html": "
Ablation partSettingMACEParameters
WarpingFeature warping0.203(↑163.6%)0.94 M
Image warping0.0770.94 M
AttentionNo0.091(↑18.2%)0.85 M
Pure global0.085(↑10.4%)0.94 M
Pure local0.082(↑6.5%)0.94 M
Focus0.0770.94 M
Scale1 scale0.077(↑97.4%)0.94 M
2 scales0.0391.29 M
", + "image_path": "c3700e9a20b62202f7f83bce2ac0de8ba37e76cec40633fcb007f1781407e5d1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 446, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 541 + ], + "type": "text", + "content": "network parameters are also listed. All the ablations are conducted on the 1-scale RHWF unless otherwise specially mentioned. It is observed that the proposed homography-guided image warping and attention-focusing mechanism yields significant gain in accuracy. The global attention has a range of the whole image, and the local has an attention radius of 1. We can also find the multiscale refinement very effective by increasing the accuracy by " + }, + { + "bbox": [ + 304, + 446, + 545, + 541 + ], + "type": "inline_equation", + "content": "97.4\\%" + }, + { + "bbox": [ + 304, + 446, + 545, + 541 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 543, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 590 + ], + "type": "text", + "content": "Ablation without recurrence. We conduct the ablation with the compared methods with no recurrence and the RHWF w/ (RHWF) and w/o (RHWF-NF) FocusFormer in Table 2. It is observed that the FocusFormer is effective." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 613, + 545, + 637 + ], + "blocks": [ + { + "bbox": [ + 305, + 591, + 545, + 613 + ], + "lines": [ + { + "bbox": [ + 305, + 591, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 591, + 545, + 613 + ], + "type": "text", + "content": "Table 2. MACEs of RHWF and the compared structures without recurrent processing." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 613, + 545, + 637 + ], + "lines": [ + { + "bbox": [ + 307, + 613, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 307, + 613, + 545, + 637 + ], + "type": "table", + "html": "
DHN 4.191MHN 3.645LocalTrans 1.987IHN 1.027RHWF 0.945RHWF-NF 1.019
", + "image_path": "2f31d5513d7085860a65c126d8cace82ef85088e41697b92107d8c59723694cb.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "A Deeper Look at Warping. We further illustrate the average correlation value, which represents the feature similarity at each warping count in Fig. 5. The warping of feature or image is taken for comparison to evaluate the effectiveness of homography-guided image warping. It is observed that the image warping can significantly enhance the" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9838" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "feature similarity as the warping count increases, while the feature warping weakens it." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 101, + 109, + 233, + 192 + ], + "blocks": [ + { + "bbox": [ + 101, + 109, + 233, + 192 + ], + "lines": [ + { + "bbox": [ + 101, + 109, + 233, + 192 + ], + "spans": [ + { + "bbox": [ + 101, + 109, + 233, + 192 + ], + "type": "image", + "image_path": "7c84c2eee833400664d4dd1b79496627153cfff51e6016ed4881eea63ee3f1de.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 193, + 288, + 216 + ], + "lines": [ + { + "bbox": [ + 47, + 193, + 288, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 193, + 288, + 216 + ], + "type": "text", + "content": "Figure 5. The average correlation value at each warping count of feature warping and image warping." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 221, + 173, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 173, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 173, + 232 + ], + "type": "text", + "content": "4.3. MSCOCO Evaluation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "text", + "content": "We evaluate RHWF together with other homography estimation methods including IHN [6] (previous SOTA method), LocalTrans [34], MHN [22], UDHN [46], DHN [12], CLKN [7], AffNet [30], LFNet [33], PFNet [42], PWC [35], SIFT+ContextDesc+RANSAC [28], SIFT+GeoDesc+RANSAC [29], SIFT+MAGSAC [2], and SIFT+RANSAC [27]. The comparison is illustrated in Fig. 4a. Following previous works [6,7,22,34,48], we plot the fraction of the number of images w.r.t. corresponding ACEs of a dataset. It can be observed that our 1-scale RHWF already outperforms other competitors except for 2-scale IHN, while 2-scale RHWF outperforms all others with a large gap. We note that 2-scale RHWF reduces previous SOTA MACE by " + }, + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "inline_equation", + "content": "38.1\\%" + }, + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "text", + "content": ". We also plot the result of 1-scale IHN, which is significantly exceeded by 1-scale RHWF. Please kindly note that CLKN performs IC- " + }, + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathsf{LK}" + }, + { + "bbox": [ + 46, + 240, + 287, + 467 + ], + "type": "text", + "content": " iteration with 4 scales, LocalTrans and MHN cascade 3 scales of networks to improve the estimation accuracy, but our 1-scale RHWF already markedly outperforms them." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 540 + ], + "type": "text", + "content": "We then plot the MACEs at each iteration for IHN and our RHWF that adopt the recurrent framework in Fig. 6. It is observed that RHWF exceeds IHN at the 3rd iteration, while a more iterations won't make IHN outperform the RHWF with only 3 iterations. What's more, RHWF continues to reduce MACEs obviously with more iterations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 550, + 256, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 256, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 256, + 562 + ], + "type": "text", + "content": "4.4. Cross-Resolution MSCOCO Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": "We conduct the evaluation on " + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": " crossresolution MSCOCO following [34]. We compare our RHWF with LocalTrans [34] (previous SOTA method), MHN [22],UDHN [46],DHN [12],and SIFT+RANSAC [27]. The resolution gap dramatically increases the difficulty of homography estimation, while it is vital for multiscale gigapixel photography [3, 34]. The results of " + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": " resolution gap MSCOCO are plotted in Fig. 4b. It is observed that RHWF ranks top in both scenarios and is significantly more robust under the " + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": " resolution gap." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "content": "We further demonstrate the self- and cross-attention map of RHWF at each iteration in Fig. 7. It is observed that at the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 360, + 72, + 491, + 154 + ], + "blocks": [ + { + "bbox": [ + 360, + 72, + 491, + 154 + ], + "lines": [ + { + "bbox": [ + 360, + 72, + 491, + 154 + ], + "spans": [ + { + "bbox": [ + 360, + 72, + 491, + 154 + ], + "type": "image", + "image_path": "de4439919a814cd96d15b42f79022e5014e02bed19f4491a31e9b44729339f1c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 155, + 545, + 176 + ], + "lines": [ + { + "bbox": [ + 306, + 155, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 306, + 155, + 545, + 176 + ], + "type": "text", + "content": "Figure 6. The MACE comparison of IHN and our RHWF at each iteration count." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": "1st iteration, the global attention in " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "I_{b}(4\\downarrow)" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": " successfully captures the correspondence information. However, in " + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "inline_equation", + "content": "I_{b}(8\\downarrow)" + }, + { + "bbox": [ + 305, + 186, + 545, + 281 + ], + "type": "text", + "content": ", the global attention becomes ambiguous as the resolution gap grows. Fortunately, as the recurrence continues, the homography-guided image warping corrects the deformation and the attention-focusing mechanism shrinks the attention range, which gradually clarifies the attention targets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 298, + 485, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 485, + 310 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 485, + 310 + ], + "type": "text", + "content": "4.5. Cross-Modal Datasets Evaluation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 319, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 475 + ], + "type": "text", + "content": "The cross-modal data further raises the challenge for homography estimation, while it can be employed for GPS-denied navigation [18]. GoogleEarth contains image pairs across different seasons and GoogleMap the image pairs cropped from satellite images and their corresponding map images. We include IHN [6] (previous SOTA method), the original LK [1], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], DHN+DLKFM [48], and MHN+DLKFM [48] for comparison. The results of both datasets are separately demonstrated in Fig. 4c and Fig. 4d. The MACEs of RHWF and IHN are also illustrated for a better comparison. RHWF outperforms IHN by " + }, + { + "bbox": [ + 305, + 319, + 545, + 475 + ], + "type": "inline_equation", + "content": "34.1\\%" + }, + { + "bbox": [ + 305, + 319, + 545, + 475 + ], + "type": "text", + "content": " on GoogleMap3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 478, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 478, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 305, + 478, + 545, + 646 + ], + "type": "text", + "content": "We further illustrate the homography estimation results of the above-mentioned methods except for CLKN, DHN+DLKFM, and LK, as they are outperformed by MHN+DLKFM in [48]. It can be observed in Fig. 8 that under the severe large deformation and modality gap, SIFT+RANSAC and SIFT+MAGSAC fail as in the experiment of [6]. MHN+DLKFM produces unstable results as the LK iterator is of theoretical drawback [32]. DHN, MHN, and IHN are not as accurate as RHWF, as they neither consider the feature inconsistency caused by homography deformation nor introduce an attention mechanism to capture the intra-inter correspondence information. On the contrary, our RHWF can produce promising results under large deformation and modality gaps." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 664, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 664, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 664, + 547, + 713 + ], + "type": "text", + "content": "3We notice that the performance of RHWF on GoogleEarth is not that conspicuous compared to other datasets but still outperforms other methods. This is because GoogleEarth only contains about 8k image pairs of fixed homography deformations, which limits the ability of the model by disabling more deformation augmentation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9839" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 140, + 68, + 452, + 227 + ], + "blocks": [ + { + "bbox": [ + 140, + 68, + 452, + 227 + ], + "lines": [ + { + "bbox": [ + 140, + 68, + 452, + 227 + ], + "spans": [ + { + "bbox": [ + 140, + 68, + 452, + 227 + ], + "type": "image", + "image_path": "8e857bbd76eac5c5653f1d442d5a055f29650721ea44ff17c9e9fe375fb746d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "text", + "content": "Figure 7. The self- and cross-attention map of RHWF at each iteration. The 1st row: the image " + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "inline_equation", + "content": "I_{a}" + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "text", + "content": " of the standard resolution with the self-attention map. The 2nd and 3rd row: the image " + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "inline_equation", + "content": "4 \\times (I_{b}(4 \\downarrow))" + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "inline_equation", + "content": "8 \\times (I_{b}(8 \\downarrow))" + }, + { + "bbox": [ + 45, + 228, + 547, + 262 + ], + "type": "text", + "content": " downsampling and cross-attention maps. The red arrows denote the query point of attention, and the red and blue boxes separately highlight the self- and cross-attention maps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 97, + 265, + 145, + 313 + ], + "blocks": [ + { + "bbox": [ + 97, + 265, + 145, + 313 + ], + "lines": [ + { + "bbox": [ + 97, + 265, + 145, + 313 + ], + "spans": [ + { + "bbox": [ + 97, + 265, + 145, + 313 + ], + "type": "image", + "image_path": "71d7889dc810c86b01802c16170e6a992ef3ce3f2b49baf98f0f23d51e00fa66.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 97, + 314, + 145, + 361 + ], + "blocks": [ + { + "bbox": [ + 97, + 314, + 145, + 361 + ], + "lines": [ + { + "bbox": [ + 97, + 314, + 145, + 361 + ], + "spans": [ + { + "bbox": [ + 97, + 314, + 145, + 361 + ], + "type": "image", + "image_path": 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Parameter comparison." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 401, + 282, + 430 + ], + "lines": [ + { + "bbox": [ + 51, + 401, + 282, + 430 + ], + "spans": [ + { + "bbox": [ + 51, + 401, + 282, + 430 + ], + "type": "table", + "html": "
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1.29 M1.71 M9.56 M34.19 M2.57 M21.29 M19.24 M
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FLOPs MACERHWF 16.96 G 0.077RHWF-3 9.64 G 0.176IHN 8.34 G 0.191IHN-mov 20.32 G 0.177DLKFM 110.51 G 0.550
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Failure Case" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "Fig. 9 shows 2 failure cases, the left one is caused by the error accumulation, and the right the imperfect initial estimations." + } + ] + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 312, + 392, + 535, + 442 + ], + "blocks": [ + { + "bbox": [ + 46, + 369, + 545, + 391 + ], + "lines": [ + { + "bbox": [ + 46, + 369, + 545, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 545, + 391 + ], + "type": "text", + "content": "Figure 8. Homography estimation results of methods including IHN [6], SIFT+RANSAC [27], SIFT+MAGSAC [2], CLKN [7], DHN [12], MHN [22], MHN+DLKFM [48], and our RHWF." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 392, + 535, + 442 + ], + "lines": [ + { + "bbox": [ + 312, + 392, + 535, + 442 + ], + "spans": [ + { + "bbox": [ + 312, + 392, + 535, + 442 + ], + "type": "image", + "image_path": "f7bccf02dbb0bfb065758aabb55b3c46ac062acecb72c8c61c3be6bebce3df73.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 443, + 468, + 452 + ], + "lines": [ + { + "bbox": [ + 383, + 443, + 468, + 452 + ], + "spans": [ + { + "bbox": [ + 383, + 443, + 468, + 452 + ], + "type": "text", + "content": "Figure 9. Failure cases." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 466, + 383, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 383, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 383, + 478 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "text", + "content": "We have proposed a novel recurrent homography estimation framework, named RHWF. RHWF absorbs the homography-guided image warping and the FocusFormer, which facilitate the homography estimation by enhancing the feature consistency and capturing the intra/inter corresponding information in a global " + }, + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "text", + "content": " nonlocal " + }, + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 490, + 545, + 622 + ], + "type": "text", + "content": " local manner, into the recurrent framework. Experimentally, RHWF outperforms previous methods by a large gap with significantly fewer parameters. The computation cost is raised by the homography-guided image warping and attention operation, which is the limitation of our proposed framework." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 626, + 388, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 626, + 388, + 638 + ], + "spans": [ + { + "bbox": [ + 306, + 626, + 388, + 638 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "This work was supported in part by the \"Pioneer\" and \"Leading Goose\" R & D Program of Zhejiang under grant 2023C03136 and in part by the Ten Thousand Talents Program of Zhejiang Province under grant 2020R52003. We also thank the generous help from Jun Ma, Zhejiang University and Tianyu Guo, Peking University." + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9840" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Simon Baker and Iain Matthews. 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Image and Vision Computing, 21(11):977-1000, 2003. 2" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9842" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_content_list.json b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b6cbdcefe23ca52f11b432490d68f30b15a1be64 --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_content_list.json @@ -0,0 +1,1567 @@ +[ + { + "type": "text", + "text": "Recurrent Vision Transformers for Object Detection with Event Cameras", + "text_level": 1, + "bbox": [ + 114, + 130, + 854, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mathias Gehrig and Davide Scaramuzza", + "bbox": [ + 323, + 181, + 645, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Robotics and Perception Group, University of Zurich, Switzerland", + "bbox": [ + 218, + 205, + 743, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 257, + 313, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present Recurrent Vision Transformers (RVTs), a novel backbone for object detection with event cameras. Event cameras provide visual information with submillisecond latency at a high-dynamic range and with strong robustness against motion blur. These unique properties offer great potential for low-latency object detection and tracking in time-critical scenarios. Prior work in event-based vision has achieved outstanding detection performance but at the cost of substantial inference time, typically beyond 40 milliseconds. By revisiting the high-level design of recurrent vision backbones, we reduce inference time by a factor of 6 while retaining similar performance. To achieve this, we explore a multi-stage design that utilizes three key concepts in each stage: first, a convolutional prior that can be regarded as a conditional positional embedding. Second, local and dilated global self-attention for spatial feature interaction. Third, recurrent temporal feature aggregation to minimize latency while retaining temporal information. RVTs can be trained from scratch to reach state-of-the-art performance on event-based object detection - achieving an mAP of $47.2\\%$ on the Gen1 automotive dataset. At the same time, RVTs offer fast inference ( $< 12$ ms on a T4 GPU) and favorable parameter efficiency ( $5 \\times$ fewer than prior art). Our study brings new insights into effective design choices that can be fruitful for research beyond event-based vision.", + "bbox": [ + 75, + 290, + 472, + 683 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Code: https://github.com/uzh-rpg/RVT", + "bbox": [ + 76, + 686, + 423, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 720, + 209, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Time matters for object detection. In 30 milliseconds, a human can run 0.3 meters, a car on public roads covers up to 1 meter, and a train can travel over 2 meters. Yet, during this time, an ordinary camera captures only a single frame.", + "bbox": [ + 75, + 748, + 468, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Frame-based sensors must strike a balance between latency and bandwidth. Given a fixed bandwidth, a frame-based camera must trade-off camera resolution and frame rate. However, in highly dynamic scenes, reducing the resolution or the frame rate may come at the cost of missing essential scene details, and, in safety-critical scenarios like", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/181205e9eb948670980454ac9a3440852946288e1cb82d95282f0f6648f9637e.jpg", + "image_caption": [ + "Figure 1. Detection performance vs inference time of our RVT models on the 1 Mpx detection dataset using a T4 GPU. The circle areas are proportional to the model size." + ], + "image_footnote": [], + "bbox": [ + 503, + 258, + 890, + 406 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "automotive, this may even cause fatalities.", + "bbox": [ + 500, + 489, + 779, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, event cameras have emerged as alternative sensor that offers a different trade-off. Instead of counterbalancing bandwidth requirements and perceptual latency, they provide visual information at sub-millisecond latency but sacrifice absolute intensity information. Instead of capturing intensity images, event cameras measure changes in intensity at the time they occur. This results in a stream of events, which encode time, location, and polarity of brightness changes [14]. The main advantages of event cameras are their sub-millisecond latency, very high dynamic range ( $>120$ dB), strong robustness to motion blur, and ability to provide events asynchronously in a continuous manner.", + "bbox": [ + 496, + 505, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we aim to utilize these outstanding properties of event cameras for object detection in time-critical scenarios. Therefore, our objective is to design an approach that reduces the processing latency as much as possible while maintaining high performance. This is challenging because event cameras asynchronously trigger binary events that are spread of pixel space and time. Hence, we need to develop detection algorithms that can continuously associate features in the spatio-temporal domain while simultaneously satisfying strict latency requirements.", + "bbox": [ + 496, + 703, + 893, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent work has shown that dynamic graph neural networks (GNNs) [28,43] and sparse neural networks [10, 34, 55, 57] can theoretically achieve low latency inference for", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13884", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "event-based object detection. Yet, to achieve this in practical scenarios they either require specialized hardware or their detection performance needs to be improved.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An alternative thread of research approaches the problem from the view of conventional, dense neural network designs [7,19,20,26,38]. These methods show impressive performance on event-based object detection, especially when using temporal recurrence in their architectures [26, 38]. Still, the processing latency of these approaches remains beyond 40 milliseconds such that the low-latency aspect of event cameras cannot be fully leveraged. This raises the question: How can we achieve both high accuracy and efficiency without requiring specialized hardware?", + "bbox": [ + 75, + 137, + 468, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We notice that common design choices yield a suboptimal trade-off between performance and compute. For example, prior work uses expensive convolutional LSTM (Conv-LSTM) cells [44] extensively in their feature extraction stage [26, 38] or relies on heavy backbones such as the VGG architecture [26]. Sparse neural networks instead struggle to model global mixing of features which is crucial to correctly locate and classify large objects in the scene.", + "bbox": [ + 75, + 287, + 468, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve our main objective, we fundamentally revisit the design of vision backbones for event-based object detection. In particular, we take inspiration from neural network design for conventional frame-based object detection and combine them with ideas that have proven successful in the event-based vision literature. Our study deliberately focuses on macro design of the object detection backbone to identify key components for both high performance and fast inference on GPUs. The resulting neural network is based on a single block that is repeated four times to form a multi-stage hierarchical backbone that can be used with off-the-shelf detection frameworks.", + "bbox": [ + 75, + 409, + 467, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We identify three key components that enable an excellent trade-off between detection performance and inference time. First, we find that interleaved local- and global self-attention [50] is ideally suited to mix both local and global features while offering linear complexity in the input resolution. Second, this attention mechanism is most effective when preceded by a simple convolution that also downsamples the spatial resolution from the previous stage. This convolution effectively provides a strong prior about the grid-structure of the pixel array and also acts as a conditional positional embedding for the transformer layers [9]. Third, temporal recurrence is paramount to achieve strong detection performance with events. Differently from prior work, we find that Conv-LSTM cells can be replaced by plain LSTM cells [18] that operate on each feature separately1. By doing so, we dramatically reduce the number of parameters and latency but also slightly improve the overall performance. Our full framework achieves competitive performance and higher efficiency compared to state-of-the", + "bbox": [ + 75, + 589, + 467, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "art methods. Specifically, we reduce parameter count (from 100M to 18.5 M) and inference time (from 72 ms to 12 ms) up to a factor of 6 compared to prior art [26]. At the same time, we train our networks from scratch, showing that these benefits do not originate from large-scale pretraining.", + "bbox": [ + 498, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our paper can be summarized as follows: (1) We reexamine predominant design choices in event-based object detection pipelines and reveal a set of key enablers for high performance in event-based object detection. (2) We propose a simple, composable stage design that unifies the crucial building blocks in a compact way. We build a 4-stage hierarchical backbone that is fast, lightweight and still offers performance comparable to the best reported so far. (3) We achieve state-of-the-art object detection performance of $47.2\\%$ mAP on the Gen1 detection dataset [11] and a highly competitive $47.4\\%$ mAP on the 1 Mpx detection dataset [38] while training the proposed architecture from scratch. In addition, we also provide insights into effective data augmentation techniques that contribute to these results.", + "bbox": [ + 496, + 167, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 395, + 640, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Object Detection for Event Cameras", + "text_level": 1, + "bbox": [ + 500, + 420, + 815, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object detection in the event camera literature can be broadly classified into three emerging research directions.", + "bbox": [ + 498, + 445, + 890, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent work explores graph neural networks to dynamically construct a spatio-temporal graph [28, 35, 43]. New nodes and node edges are established by sub-sampling events and finding existing nodes that are close in spacetime. The main challenge is to design the architecture such that information can propagate over vast distances in the space-time volume. This is relevant, for example, when large objects move slowly with respect to the camera. Furthermore, aggressive sub-sampling of events can lead to the removal of potentially crucial information, but is often required to maintain low-latency inference.", + "bbox": [ + 496, + 476, + 890, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A second line of work employs spiking neural networks (SNNs) that propagate information sparsely within the network [10, 55, 57]. SNNs are closely related to dense recurrent neural networks (RNNs) in that each spiking neuron has an internal state that is propagated in time. Differently from RNNs, neurons in SNNs only emit spikes whenever a threshold is reached. This spike generation mechanism is not differentiable, which leads to substantial difficulties in optimizing these networks [4,22,23,36,45,47,56]. One workaround is to avoid the aforementioned threshold and instead propagate features throughout the receptive field [34]. The downside of this mechanism is that the sparse-processing property is lost within deeper layers of the network. Overall, the design and training of SNNs still requires fundamental investigation before competitive performance can be reached.", + "bbox": [ + 496, + 643, + 890, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A third research direction is concerned with exploring", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "equivalent to $1\\times 1$ kernel in a Conv-LSTM cell", + "bbox": [ + 94, + 886, + 357, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13885", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/de9d57734048ced41688cc0f0e1b1fd82246ecc488a5ff55be7117e01dc5ede3.jpg", + "image_caption": [ + "Figure 2. Overview of the unrolled computation graph of our multi-stage recurrent backbone. Events are processed into a tensor representation before they are used as input to the first stage. Each stage also reuses the LSTM states (c: cell, h: hidden) from the previous timestep. Finally, the detection framework interfaces with the backbone from the second stage onwards. Specifically, the hidden states of the LSTMs are used as features for the detection framework." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 893, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dense neural networks for object detection with event cameras. The first step is the creation of a dense tensor (event representation) that enables compatibility with dense operations such as convolutions. Early work directly uses a single event representation generated from a short temporal window of events to infer detections [7, 19, 20]. These approaches discard relevant information from beyond the considered temporal window such that detecting slowly moving objects becomes difficult or impossible. Followup work addresses this issue by incorporating recurrent neural network layers [26,38] which drastically improved the detection performance. We follow this line of work but revamp dominant architecture choices to build a canonical framework that is fast, lightweight and highly performant.", + "bbox": [ + 75, + 366, + 472, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Vision Transformers for Spatio-Temporal Data", + "text_level": 1, + "bbox": [ + 76, + 589, + 468, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The success of attention-based models [52] in NLP has inspired the exploration of transformer-based architectures in computer vision [12]. Attention-based models have recently also been explored in video classification [1,5,13,48] where the models are applied directly to a set of frames. While these approaches have shown promising results in spatio-temporal modelling, they are optimized for offline processing of stored video data.", + "bbox": [ + 75, + 614, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In event-based vision, attention-based components have found applications in classification [42, 53] and image reconstruction [54], and monocular depth estimation [31], but their use in object detection has yet to be investigated.", + "bbox": [ + 75, + 736, + 468, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 813, + 168, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our object detection approach is designed to process a stream of events sequentially as they arrive. Incoming events are first processed into tensors that represent events in space and time. In every timestep, our network takes", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a36d8f2a5242130283d1965c6cd766b416279302438fcd34a1924a64685a07cc.jpg", + "image_caption": [ + "Figure 3. RVT block structure. The input is convolved with kernel size $k \\times k$ and stride $s$ . Block-SA applies self-attention in local windows while Grid-SA is a global operation using dilated attention. Finally, each block ends with an LSTM that reuses the (cell- and hidden) states from the previous timestep. The LSTM is applied to each feature separately. Normalization and activation layers are omitted for conciseness." + ], + "image_footnote": [], + "bbox": [ + 506, + 367, + 885, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a new event representation as input as well as the previous states of the recurrent neural network layers. After each pass through the backbone, the output of the RNNs are used as input to the detection framework. The following sections elaborate on each one of these steps. Fig. 2 shows an overview of the RVT architecture.", + "bbox": [ + 496, + 637, + 893, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event Processing Each pixel of an event camera can independently trigger an event when a significant log brightness change occurs. An event can be positive or negative depending on the sign of the brightness change. We characterize an event with polarity $p_k \\in \\{0,1\\}$ as a tuple $e_k = (x_k,y_k,t_k,p_k)$ that occurs at pixel $(x_k,y_k)$ at time $t_k$ . Modern event cameras can produce 10s of millions of events per second which renders event-by-event processing out of reach on conventional processing units.", + "bbox": [ + 496, + 750, + 890, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work we opt for a very simple preprocessing step", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13886", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to enable compatibility with convolutional neural network layers which, as we will show later in Sec. 4.2, are an important contributor to the performance of our model.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our preprocessing step starts with the creation of a 4-dimensional tensor $E$ . The first dimension consists of two components and represents the polarity. The second dimension has $T$ components and is associated with $T$ discretization steps of time. The 3rd and 4th dimension represent height and width of the event camera. We process set of events $\\mathcal{E}$ within a time duration $[t_a, t_b)$ the following way:", + "bbox": [ + 75, + 136, + 470, + 243 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} E (p, \\tau , x, y) = \\sum_ {e _ {k} \\in \\mathcal {E}} \\delta (p - p _ {k}) \\delta (x - x _ {k}, y - y _ {k}) \\delta (\\tau - \\tau_ {k}), \\\\ \\tau_ {k} = \\left\\lfloor \\frac {t _ {k} - t _ {a}}{t _ {b} - t _ {a}} \\cdot T \\right\\rfloor \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 250, + 470, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In words, we create $T$ 2-channel frames where each pixel contains the number of positive or negative events within one of the $T$ temporal frames. As a final step, we flatten the polarity and time dimension to retrieve a 3-dimensional tensor with shape $(2T, H, W)$ to directly enable compatibility with 2D convolutions. We implement the presented algorithm with byte tensors to save memory and bandwidth. Other, more sophisticated representations are possible [2,3,6,16,26,51,58], but their thorough evaluation is not our focus.", + "bbox": [ + 75, + 323, + 468, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Mixing Spatial and Temporal Features", + "text_level": 1, + "bbox": [ + 76, + 481, + 410, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The main difficulty of object detection with event cameras is that at any given time, the neural network should be able to efficiently (1) extract local- and global task-relevant features in pixel space because objects can cover both very small regions or large portions of the field of view; (2) extract features from very recent events (e.g. moving edges) as well as events from several seconds ago. This is necessary because some objects are moving slowly with respect to the camera such that they generate very few events over time. These observations motivate us to investigate transformer layers for spatial feature extraction and recurrent neural networks for efficient temporal feature extraction. Fig. 3 illustrates the components of a single stage.", + "bbox": [ + 75, + 505, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spatial Feature Extraction The spatial feature extraction stage should incorporate a prior about the fact that pixels are arranged in a 2D grid as early as possible in the computation graph. We enable this by using a convolution with overlapping kernels on the input features that at the same time spatially downsamples the input or features from the previous stage. This convolution also endows our model with a conditional positional embedding [9] such that we do not require absolute [12, 52] or relative [32] positional embeddings. Our ablation study in Sec. 4.2 shows that overlapping kernels lead to a substantial boost in detection performance.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a subsequent step, the resulting features are transformed through multi-axis self-attention. We quickly summarize the steps but refer to Tu et. al [50] for an elaborate explanation. Multi-axis attention consists of two stages using self-attention. The first stage performs local feature interaction while the second stage enables dilated global feature mixing. More specifically, the features are first grouped locally into non-overlapping windows: Let $X \\in \\mathbb{R}^{H \\times W \\times C}$ be the input feature tensor. We reshape the tensor to a shape $\\left(\\frac{H}{P} \\times \\frac{W}{P}, P \\times P, C\\right)$ where $P \\times P$ is the window size in which multi-head self-attention [52] is applied. This block attention (Block-SA in Fig. 3) is used to model local interactions. As a next step, we would ideally be able to extract features globally. One straightforward way to achieve this would be applying self-attention on the whole feature map. Unfortunately, global self-attention has quadratic complexity in the number of features. Instead, we use grid attention (Grid-SA in Fig. 3). Grid attention partitions the feature maps into a grid of shape $(G \\times G, \\frac{H}{G} \\times \\frac{W}{G}, C)$ using a $G \\times G$ uniform grid. The resulting windows are of size $\\frac{H}{G} \\times \\frac{W}{G}$ . Self-attention is then applied to these windows which corresponds to global, dilated mixing of features.", + "bbox": [ + 496, + 90, + 890, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We study alternative designs as part of our architecture in the ablation studies in Sec. 4.2.", + "bbox": [ + 498, + 425, + 890, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal Feature Extraction We opt for temporal feature aggregation with LSTM [18] cells at the end of the stage. Differently from prior work [26,38] we find that temporal and spatial feature aggregation can be completely separated. This means that we use plain LSTM cells such that the states of the LSTMs do not interact with each other. By avoiding Conv-LSTM units [44], we can drastically reduce the computational complexity and parameter count. I.e. a Conv-LSTM with kernel size $k \\times k$ and stride 1 demands $k^2$ the number of parameters and compute compared to the original LSTM cell. We examine this aspect in the experimental Sec. 4.2.", + "bbox": [ + 496, + 472, + 890, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model Details We apply LayerNorm [24] before and LayerScale [49] after each attention and MLP module, and add a residual connection after each module. We found that LayerScale enables a wider range of learning rates.", + "bbox": [ + 496, + 671, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Hierarchical Multi-Stage Design", + "text_level": 1, + "bbox": [ + 500, + 741, + 784, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We compose multiple RVT blocks together to form a multi-stage hierarchical backbone. The overall architecture is shown in Fig. 2.", + "bbox": [ + 496, + 763, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At first, a local temporal slice of events is processed into a 2D tensor format as formulated in the beginning of this section. Subsequently, each stage takes the previous features as input and optionally uses the LSTM state from the last timestep to compute features for the next stage. By saving the LSTM states for the following timestep, each re", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13887", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/e95e99fbdf2fc64362c36c7a841f0382e0a90440360fb7202f93c9c64dd50fd5.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. RVT parameters and architecture variation. All model variants share the same parameter set except the number of channels per stage. Each stage initially applies a 2D convolution with kernel and stride as indicated in the table." + ], + "table_body": "
StageSizeKernelStrideChannels
RVT-TRVT-SRVT-B
S11/474324864
S21/8326496128
S31/1632128192256
S41/3232256384512
", + "bbox": [ + 76, + 88, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "current stage can retain temporal information for the whole feature map.", + "bbox": [ + 75, + 290, + 467, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We follow prior work and use features from the second to the fourth stage for the object detection framework. To do so, we reshape the hidden states of the LSTMs into 2D feature maps.", + "bbox": [ + 75, + 321, + 467, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 398, + 209, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct ablations and evaluation our model on the Gen1 [11] and 1 Mpx [38] event camera datasets. We train three variants of our model on both datasets: the base model RVT-B and its small and tiny variants RVT-S and RVT-T. Parameter details for the models are shown in Tab. 1.", + "bbox": [ + 75, + 424, + 467, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 76, + 512, + 158, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details We initialize all layers randomly except LayerScale which is initialized to 1e-5 for each module. Our models are trained with mixed precision for 400k iterations with the ADAM optimizer [21] using a OneCycle learning rate schedule [46] with a linear decay from a maximum learning rate. We use a mixed batching strategy that applies backpropagation through time (BPTT) to half of the samples of the batch and truncated BPTT (TBPTT) to the other half. More details regarding this batching strategy can be found in the supplementary material. Our data augmentation includes random horizontal flipping, zooming in and zooming out. More details on data augmentation are available in Sec. 4.2 and the supplementary material. To construct event representations, we consider $50~\\mathrm{ms}$ time windows that are discretized into $T = 10$ bins. Finally, we use theYOLOX framework [15], which includes the IOU loss, class loss and regression loss. These losses are averaged both over the batch and sequence length for each optimization step.", + "bbox": [ + 73, + 535, + 467, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To compare against prior work on the Gen1 dataset, we train our models with a batch size of 8, sequence length of 21, and learning rate of 2e-4. The training takes approximately 2 days on a single A100 GPU.", + "bbox": [ + 75, + 824, + 467, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the 1 Mpx dataset, we train with a batch size of 24,", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4e26cb5e6e8dad672a57332a54e6230be43aef41aab314986c6121dab8458268.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Spatial Aggregation. Multi-axis attention leads to the best results on both the Gen1 and 1 Mpx dataset." + ], + "table_body": "
Block-typeGen11 MpxParams (M)
mAP\\( AP_{50} \\)mAP\\( AP_{50} \\)
multi-axis47.670.146.072.318.5
Swin46.768.744.471.718.5
ConvNeXt45.565.842.370.618.7
", + "bbox": [ + 501, + 88, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sequence length of 5, and learning rate of 3.5e-4. The training takes approximately 3 days on two A100 GPUs.", + "bbox": [ + 498, + 250, + 890, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets The Gen1 Automotive Detection dataset [11] consists of 39 hours of event camera recordings at a resolution of $304 \\times 240$ . In total, the Gen1 dataset contains 228k car and 28k pedestrian bounding boxes available at 1, 2 or 4 Hz. We follow the evaluation protocol of prior work [26,38] and remove bounding boxes with a side length of less than 10 pixels and a diagonal of less than 30 pixels.", + "bbox": [ + 496, + 297, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 1 MPx dataset [38] also features driving scenarios but provides recordings at a higher resolution of $720 \\times 1280$ over a period of several months at day and night. It consists of approximately 15 hours of event data labeled at a frequency of 30 or $60\\mathrm{Hz}$ with a total amount of 25 million bounding box labels for three classes (car, pedestrian, and two-wheeler). We follow the evaluation protocol of prior work [26, 38]. That is, we remove bounding boxes with a side length of less than 20 pixels and a diagonal of less than 60 pixels and halve the input resolution to nHD resolution $(640 \\times 360)$ . We provide qualitative examples of this dataset together with predictions of our base model in Fig. 4.", + "bbox": [ + 496, + 404, + 890, + 584 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For both datasets, mean average precision (mAP) is the main metric [29] that we consider.", + "bbox": [ + 498, + 585, + 890, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 625, + 663, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section examines the two main contributors to the final performance of the proposed model. First, we investigate key components and design choices of the proposed backbone. Second, we study the influence of different data augmentation techniques that are compatible with our sequential problem setting.", + "bbox": [ + 496, + 647, + 890, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unless stated otherwise, the ablation studies are performed on the Gen1 validation set using the best performing model after 400k iterations. To reduce the training time, we use BPTT with a sequence length of 11 instead 21.", + "bbox": [ + 496, + 738, + 890, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Model Components", + "text_level": 1, + "bbox": [ + 500, + 816, + 691, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial Interaction In Tab. 2, we study different spatial aggregation techniques. For a fair comparison, we keep the LSTM and convolutional downsampling layers identical and only exchange the attention and MLP modules. We", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13888", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9c0ec894169922d455831536e3134241b54c68855089c8f75ce12ccbd2db713e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Conv. kernel typemAPAP50AP75Params (M)
overlapping47.670.152.618.5
non-overlapping46.168.650.517.6
", + "bbox": [ + 83, + 88, + 462, + 150 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/61a42beed344f480f8e2b8ecadaa18c046298fb51b4bfcb22d8f5e3a7df087fb.jpg", + "table_caption": [ + "Table 3. Downsampling Strategy. The usage of overlapping kernels leads to higher performance at the expense of a slight increase in the number of parameters." + ], + "table_footnote": [], + "table_body": "
LSTM kernel sizemAPAP50AP75Params (M)
1 × 147.670.152.618.5
3 × 346.569.051.440.8
3 × 3 depth-sep46.367.251.218.6
", + "bbox": [ + 81, + 217, + 464, + 295 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "compare multi-axis attention with ConvNext blocks [33] and Swin transformer blocks [32]. ConvNext is a convolutional neural network architecture that has shown competitive performance with transformer-based models on a wide range of tasks, including object detection. We use the default kernel size of $7 \\times 7$ as originally suggested and place three ConvNeXt blocks in each stage to approximately match the number of parameters of the reference model. Swin, instead, is an attention-based model that applies local self-attention in windows that interact with each other through cyclic shifting.", + "bbox": [ + 75, + 359, + 467, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We find that our Swin variant achieves better performance than the ConvNext variant, however, both are outperformed by multi-axis self-attention [50] on both the Gen1 and 1 Mpx dataset. This experiment suggests that global interaction at every stage (multi-axis) is advantageous to purely local interaction (Swin, ConvNext).", + "bbox": [ + 75, + 527, + 467, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Convolutional Downsampling The original vision transformer [12] architecture does not perform local feature interaction with convolutional layers. Some popular hierarchical counterparts also choose to apply downsample features without overlapping kernels [8, 32]. In Tab. 3, we compare overlapping and non-overlapping convolutional kernels in both the input layer (patch embedding) and feature downsampling stage. While non-overlapping convolutions reduce the number of parameters, they cause a substantial drop in performance. Consequently, we choose overlapping kernels in all stages of the network.", + "bbox": [ + 75, + 638, + 467, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LSTM with Convolutions Prior state-of-the-art approaches on object detection with event cameras heavily rely on convolutional LSTM cells [26, 38]. We revisit this design choice and experiment with plain LSTM cells and a depthwise separable Conv-LSTM variant [39]. The depth-", + "bbox": [ + 75, + 824, + 467, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/15715d63bd932ed4eba15079be35707568795156fded0dc9104075edc6547bd4.jpg", + "table_caption": [ + "Table 4. LSTM kernel size. Conv-LSTM variants do not outperform the feature specific $(1\\times 1)$ LSTM." + ], + "table_footnote": [], + "table_body": "
S1S2S3S4mAP\\( AP_{50} \\)\\( AP_{75} \\)
32.054.831.4
✓39.863.541.6
✓✓44.268.447.5
✓✓✓46.970.050.8
✓✓✓✓47.670.152.6
", + "bbox": [ + 540, + 88, + 854, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. LSTM placement. LSTM cells contribute to the overall performance even in the early stages.", + "bbox": [ + 498, + 205, + 890, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "wise separable Conv-LSTM first applies a depthwise separable convolution on both the input and hidden state before a point-wise $(1 \\times 1)$ convolution is applied. Our results in Tab. 4 suggest that plain LSTM cells are sufficient in our model and even outperform both variations. This is to some degree surprising because both variants are a strict superset of the plain LSTM. We decide to use a plain LSTM cell based on these observations.", + "bbox": [ + 496, + 261, + 890, + 381 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LSTM Placement In this ablation we study the influence of using temporal recurrence only in a subset of stages or not at all. For all comparisons, we leave the model exactly the same but reset the states of the LSTMs at selected stages in each timestep. This way, we can simulate the absence of recurrent layers while keeping the number of parameters constant in the comparisons.", + "bbox": [ + 496, + 402, + 890, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results in Tab. 5 suggest that using no recurrence at all leads to a drastic decline of detection performance. Enabling the LSTMs in each stage, starting from the fourth consistently leads to enhanced performance. Surprisingly, we find that adding an LSTM to the first stage also leads to improvements, albeit the increase in mAP is not large. In general, this experiment suggests that the detection framework benefits from features that have been augmented with temporal information. Based on our observations, we decide to keep the LSTM also in the first stage.", + "bbox": [ + 496, + 508, + 890, + 659 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Data Augmentation", + "text_level": 1, + "bbox": [ + 500, + 680, + 689, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While data augmentation is not directly related to the model itself, it greatly influences the final result as we will illustrate next. Here, we investigate three data augmentation techniques that are suitable for object detection on spatiotemporal data: Random (1) horizontal flipping, (2) zoom-in, and (3) zoom-out.", + "bbox": [ + 496, + 703, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zoom-in augmentation randomly selects crops that contain at least one full bounding box at the final timestep of the BPTT sequence (i.e. during training). This crop is then applied to the rest of the sequence before the crops are rescaled to the default resolution. This procedure ensures that we have at least a single label to compute the loss function while maintaining the same resolution during training.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13889", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bd58266553e0b5ff98c21fdebccdeee75c39a20d4d38a2c90c6bd44222c51824.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
NVS-S [27]GNNYOLOv1 [40]8.6---0.9
Asynet [34]Sparse CNNYOLOv114.5---11.4
AEGNN [43]GNNYOLOv116.3---20.0
Spiking DenseNet [10]SNNSSD [30]18.9---8.2
Inception + SSD [19]CNNSSD30.119.434.045.2>60*
RRC-Events [7]CNNYOLOv3 [41]30.721.534.346.4>100*
MatrixLSTM [6]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [20]CNNYOLOv331.222.334.649.4>60*
RED [38]CNN + RNNSSD40.016.743.039.324.1
ASTMNet [26](T)CNN + RNNSSD46.735.648.372.3>100*
RVT-B (ours)Transformer + RNNYOLOX [15]47.210.2 (3.7)47.411.9 (6.1)18.5
RVT-S (ours)Transformer + RNNYOLOX46.59.5 (3.0)44.110.1 (5.0)9.9
RVT-T (ours)Transformer + RNNYOLOX44.19.4 (2.3)41.59.5 (3.5)4.4
", + "bbox": [ + 80, + 88, + 890, + 345 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5297aad1a1bb4e6750093b59c3b6486151d2f984800aa7e955a49a7f432283b9.jpg", + "table_caption": [ + "Table 6. Comparisons on test sets of Gen1 and 1 Mpx datasets. Best results in bold and second best underlined. Brackets $(\\cdot)$ in runtime indicate the inference time with JIT-compiled code using torch.compile. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for RVT to compare against indicated timings in prior work [26, 38] on comparable GPUs (Titan Xp)." + ], + "table_footnote": [], + "table_body": "
h-flipzoom-inzoom-outmAP\\( AP_{50} \\)\\( AP_{75} \\)
38.159.541.1
✓41.663.545.5
✓45.867.849.8
✓44.165.748.4
✓✓✓47.670.152.6
", + "bbox": [ + 93, + 434, + 452, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Data Augmentation. Data augmentation consistently improves the results.", + "bbox": [ + 76, + 551, + 468, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zoom-out augmentation resizes the full input to a lower resolution and randomly places the downscaled input in a zero-tensor initialized at the default resolution. This procedure is then applied in an identical way to the remaining BPTT sequence.", + "bbox": [ + 75, + 607, + 468, + 683 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7 shows that our model is performing poorly if no data augmentation is applied. Overall, we find that data augmentation is important to combat overfitting not only on the Gen1 sequence but also on the 1 Mpx dataset. The most effective augmentation is zoom-in, followed by zoom-out and horizontal flipping. Based on these results, we decide to apply all data augmentation techniques. We report the specific hyperparameters in the supplementary material.", + "bbox": [ + 75, + 684, + 468, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Benchmark Comparisons", + "text_level": 1, + "bbox": [ + 76, + 816, + 310, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we compare our proposed neural network architecture against prior work on both the Gen1 [11] and 1 Mpx dataset [38] and summarize the results in Tab. 6. We train three models, a base model (RVT-B) with approx-", + "bbox": [ + 76, + 840, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "imately 18.5 million parameters, a small variant (RVT-S) with 9.9 million parameters, and a tiny model (RVT-T) with 4.4 million parameters by adapting the channel dimensions in each stage. Their architectural hyperparameters are outlined in Tab. 1. To compare with prior work, we choose the models based on their best performance on the validation set and evaluate them on the test set.", + "bbox": [ + 496, + 436, + 890, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Tab. 6 we can draw multiple conclusions. First, we observe that models using recurrent layers consistently outperform other approaches, both sparse (GNNs, SNNs) and dense feed-forward models without recurrent layers (Inception+SSD, RRC-Events, YOLOv3 Events) by an mAP of more than 10 on both datasets. One notable exception is MatrixLSTM [6] which applies LSTM cells directly at the input. In contrast, RED [38] and ASTMNet [26] employ recurrent layers only in deeper layers.", + "bbox": [ + 496, + 542, + 892, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our base model achieves a new state-of-the-art performance of $47.2\\mathrm{mAP}$ on the Gen1 dataset and $47.4\\mathrm{mAP}$ on the 1 Mpx dataset. ASTMNet claims comparable results on both datasets albeit at the cost of using a much larger backbone and increased inference time. The RED model, also reports favorable results, but achieves 7.2 lower mAP on the Gen1 and 4.4 lower mAP on the 1 Mpx dataset compared to our model. Finally, our tiny model is amongst the smallest in our comparison. Still, it achieves 4.1 higher mAP on the Gen1 dataset than the RED model while using 5 times fewer parameters.", + "bbox": [ + 496, + 680, + 890, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inference Time We also compute the inference time of our model on a T4 GPU with a batch size of 1. Unfortu-", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13890", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/48cadbf752382fb16158d6cb7a8fec104fb6a57c4bef44514f43dc8744aa6b0b.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 292, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a2fdd206801126e6e2818c7bbb053972ff2dd99df03771f09d7fbff8bbddf24.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 292, + 88, + 491, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d22f74578784b71d475692b8970dba876093ad648efd1b4a748bca78ac0affd3.jpg", + "image_caption": [ + "(c)", + "Figure 4. Predictions on the 1 Mpx dataset. All examples are thematically picked to illustrate the behaviour of the model in different scenarios. (d) shows a scenario in which the model can still partially detect objects in absence of events due the temporal memory." + ], + "image_footnote": [], + "bbox": [ + 491, + 88, + 694, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/caa2226b1b6cc1af239209c50b0c3f41c3c2e26435db237a17986ee2ba9d8611.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 890, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "nately, both RED and ASTMNet are not open source such that we cannot directly compare inference time on the same GPU model. Instead, we use the timings provided by the authors that conducted their timing experiments on comparable GPUs (e.g. Titan Xp). We report the timing results of our models in Tab. 6 and also visualize them in Fig. 1.", + "bbox": [ + 75, + 340, + 468, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To compare against prior work we first compute the inference time in PyTorch eager mode. In eager mode, our base model achieves an inference time of 10.2 milliseconds (ms) on the Gen1 dataset $(304 \\times 240$ resolution). This implies a latency reduction of $6\\mathrm{ms}$ compared to RED and over 3 times lower inference time than ASTMNet. On the the 1 Mpx dataset, at a resolution of $640 \\times 360$ , our base model takes $11.9\\mathrm{ms}$ for a forward pass, which is 3 times faster than RED and over 5 times faster than ASTMNet.", + "bbox": [ + 75, + 433, + 468, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Even on a T4 GPU, most of the inference time is framework overhead. To overcome this partially, we use the JIT compilation feature torch.compile of PyTorch 2 [37]. As Tab. 6 shows, this almost halves the inference time for RVT-B on the 1 Mpx dataset and reduces the inference time by a factor of 2.7 on the Gen1 dataset. As expected, the small and tiny models benefit even more from JIT compilation. For example, RVT-T only takes $2.3\\mathrm{ms}$ for a forward pass on Gen1 and $3.5\\mathrm{ms}$ on 1 Mpx. On a RTX 3090 GPU, RVT-B completes a forward pass in $2.8\\mathrm{ms}$ on the 1 Mpx dataset, which shows the potential for low-latency inference if power consumption is less of a concern.", + "bbox": [ + 75, + 570, + 468, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 768, + 328, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We use a very simple event representation which does not leverage the full potential of event-based data. For example, we only have a weak prior on the order of events because we process the temporal dimension directly with fully connected layers. Recent work has shown substantial gains by introducing temporal convolutions in early layers [26]. Efficient low-level processing of event data is still an open", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "research problem that we have not addressed in this work.", + "bbox": [ + 498, + 340, + 880, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our approach currently only uses event streams to detect objects. Frames yield complementary information that, when properly incorporated, will yield significantly enhanced detection performance. For example, in Fig. 4 (d) we can see that our model can retain information over some period when no events are available. Still, the memory of the network will fade and detection performance deteriorates. High quality frames even at low frame-rate could provide the missing complementary information. Hence, we believe that a multi-modal extension of our method on a suitable dataset [17, 25] is a promising next step.", + "bbox": [ + 496, + 357, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 535, + 617, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced a novel backbone architecture for object detection with event cameras. The architecture consists of a stage design that is repeatedly applied to create a multistage hierarchical neural network. Each stage compactly incorporates convolutional priors, local- and sparse global attention and recurrent feature aggregation. Our experiments highlight that recurrent vision transformers can be trained from scratch to reach state-of-the-art performance in object detection with event cameras. The resulting canonical stage-design is directly compatible with existing detection frameworks, and paves the way to low-latency object detection with event cameras on conventional hardware. Nonetheless, we hope that this work also inspires novel designs in future neuromorphic systems.", + "bbox": [ + 496, + 560, + 890, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 784, + 669, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Centre of Competence in Research (NCCR) Robotics (grant agreement No. 51NF40-185543) through the Swiss National Science Foundation (SNSF), and the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT).", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13891", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In Int. Conf. Comput. Vis. 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(CVPR), 2019." + ], + "bbox": [ + 501, + 92, + 890, + 784 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13893", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_model.json b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bcd8d3a886820a33ea83472730309e52cee3e2ae --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.131, + 0.856, + 0.152 + ], + "angle": 0, + "content": "Recurrent Vision Transformers for Object Detection with Event Cameras" + }, + { + "type": "text", + "bbox": [ + 0.324, + 0.182, + 0.646, + 0.199 + ], + "angle": 0, + "content": "Mathias Gehrig and Davide Scaramuzza" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.206, + 0.745, + 0.223 + ], + "angle": 0, + "content": "Robotics and Perception Group, University of Zurich, Switzerland" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.258, + 0.314, + 0.274 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.684 + ], + "angle": 0, + "content": "We present Recurrent Vision Transformers (RVTs), a novel backbone for object detection with event cameras. Event cameras provide visual information with submillisecond latency at a high-dynamic range and with strong robustness against motion blur. These unique properties offer great potential for low-latency object detection and tracking in time-critical scenarios. Prior work in event-based vision has achieved outstanding detection performance but at the cost of substantial inference time, typically beyond 40 milliseconds. By revisiting the high-level design of recurrent vision backbones, we reduce inference time by a factor of 6 while retaining similar performance. To achieve this, we explore a multi-stage design that utilizes three key concepts in each stage: first, a convolutional prior that can be regarded as a conditional positional embedding. Second, local and dilated global self-attention for spatial feature interaction. Third, recurrent temporal feature aggregation to minimize latency while retaining temporal information. RVTs can be trained from scratch to reach state-of-the-art performance on event-based object detection - achieving an mAP of \\(47.2\\%\\) on the Gen1 automotive dataset. At the same time, RVTs offer fast inference (\\(< 12\\) ms on a T4 GPU) and favorable parameter efficiency (\\(5 \\times\\) fewer than prior art). Our study brings new insights into effective design choices that can be fruitful for research beyond event-based vision." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.688, + 0.424, + 0.704 + ], + "angle": 0, + "content": "Code: https://github.com/uzh-rpg/RVT" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.722, + 0.21, + 0.737 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Time matters for object detection. In 30 milliseconds, a human can run 0.3 meters, a car on public roads covers up to 1 meter, and a train can travel over 2 meters. Yet, during this time, an ordinary camera captures only a single frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Frame-based sensors must strike a balance between latency and bandwidth. Given a fixed bandwidth, a frame-based camera must trade-off camera resolution and frame rate. However, in highly dynamic scenes, reducing the resolution or the frame rate may come at the cost of missing essential scene details, and, in safety-critical scenarios like" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.259, + 0.891, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.418, + 0.895, + 0.461 + ], + "angle": 0, + "content": "Figure 1. Detection performance vs inference time of our RVT models on the 1 Mpx detection dataset using a T4 GPU. The circle areas are proportional to the model size." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.49, + 0.78, + 0.505 + ], + "angle": 0, + "content": "automotive, this may even cause fatalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.701 + ], + "angle": 0, + "content": "In recent years, event cameras have emerged as alternative sensor that offers a different trade-off. Instead of counterbalancing bandwidth requirements and perceptual latency, they provide visual information at sub-millisecond latency but sacrifice absolute intensity information. Instead of capturing intensity images, event cameras measure changes in intensity at the time they occur. This results in a stream of events, which encode time, location, and polarity of brightness changes [14]. The main advantages of event cameras are their sub-millisecond latency, very high dynamic range (\\(>120\\) dB), strong robustness to motion blur, and ability to provide events asynchronously in a continuous manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.854 + ], + "angle": 0, + "content": "In this work, we aim to utilize these outstanding properties of event cameras for object detection in time-critical scenarios. Therefore, our objective is to design an approach that reduces the processing latency as much as possible while maintaining high performance. This is challenging because event cameras asynchronously trigger binary events that are spread of pixel space and time. Hence, we need to develop detection algorithms that can continuously associate features in the spatio-temporal domain while simultaneously satisfying strict latency requirements." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Recent work has shown that dynamic graph neural networks (GNNs) [28,43] and sparse neural networks [10, 34, 55, 57] can theoretically achieve low latency inference for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13884" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "event-based object detection. Yet, to achieve this in practical scenarios they either require specialized hardware or their detection performance needs to be improved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.288 + ], + "angle": 0, + "content": "An alternative thread of research approaches the problem from the view of conventional, dense neural network designs [7,19,20,26,38]. These methods show impressive performance on event-based object detection, especially when using temporal recurrence in their architectures [26, 38]. Still, the processing latency of these approaches remains beyond 40 milliseconds such that the low-latency aspect of event cameras cannot be fully leveraged. This raises the question: How can we achieve both high accuracy and efficiency without requiring specialized hardware?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.47, + 0.409 + ], + "angle": 0, + "content": "We notice that common design choices yield a suboptimal trade-off between performance and compute. For example, prior work uses expensive convolutional LSTM (Conv-LSTM) cells [44] extensively in their feature extraction stage [26, 38] or relies on heavy backbones such as the VGG architecture [26]. Sparse neural networks instead struggle to model global mixing of features which is crucial to correctly locate and classify large objects in the scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.468, + 0.589 + ], + "angle": 0, + "content": "To achieve our main objective, we fundamentally revisit the design of vision backbones for event-based object detection. In particular, we take inspiration from neural network design for conventional frame-based object detection and combine them with ideas that have proven successful in the event-based vision literature. Our study deliberately focuses on macro design of the object detection backbone to identify key components for both high performance and fast inference on GPUs. The resulting neural network is based on a single block that is repeated four times to form a multi-stage hierarchical backbone that can be used with off-the-shelf detection frameworks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.468, + 0.877 + ], + "angle": 0, + "content": "We identify three key components that enable an excellent trade-off between detection performance and inference time. First, we find that interleaved local- and global self-attention [50] is ideally suited to mix both local and global features while offering linear complexity in the input resolution. Second, this attention mechanism is most effective when preceded by a simple convolution that also downsamples the spatial resolution from the previous stage. This convolution effectively provides a strong prior about the grid-structure of the pixel array and also acts as a conditional positional embedding for the transformer layers [9]. Third, temporal recurrence is paramount to achieve strong detection performance with events. Differently from prior work, we find that Conv-LSTM cells can be replaced by plain LSTM cells [18] that operate on each feature separately1. By doing so, we dramatically reduce the number of parameters and latency but also slightly improve the overall performance. Our full framework achieves competitive performance and higher efficiency compared to state-of-the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "art methods. Specifically, we reduce parameter count (from 100M to 18.5 M) and inference time (from 72 ms to 12 ms) up to a factor of 6 compared to prior art [26]. At the same time, we train our networks from scratch, showing that these benefits do not originate from large-scale pretraining." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.169, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Our paper can be summarized as follows: (1) We reexamine predominant design choices in event-based object detection pipelines and reveal a set of key enablers for high performance in event-based object detection. (2) We propose a simple, composable stage design that unifies the crucial building blocks in a compact way. We build a 4-stage hierarchical backbone that is fast, lightweight and still offers performance comparable to the best reported so far. (3) We achieve state-of-the-art object detection performance of \\(47.2\\%\\) mAP on the Gen1 detection dataset [11] and a highly competitive \\(47.4\\%\\) mAP on the 1 Mpx detection dataset [38] while training the proposed architecture from scratch. In addition, we also provide insights into effective data augmentation techniques that contribute to these results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.396, + 0.642, + 0.412 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.421, + 0.816, + 0.437 + ], + "angle": 0, + "content": "2.1. Object Detection for Event Cameras" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.891, + 0.476 + ], + "angle": 0, + "content": "Object detection in the event camera literature can be broadly classified into three emerging research directions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Recent work explores graph neural networks to dynamically construct a spatio-temporal graph [28, 35, 43]. New nodes and node edges are established by sub-sampling events and finding existing nodes that are close in spacetime. The main challenge is to design the architecture such that information can propagate over vast distances in the space-time volume. This is relevant, for example, when large objects move slowly with respect to the camera. Furthermore, aggressive sub-sampling of events can lead to the removal of potentially crucial information, but is often required to maintain low-latency inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.884 + ], + "angle": 0, + "content": "A second line of work employs spiking neural networks (SNNs) that propagate information sparsely within the network [10, 55, 57]. SNNs are closely related to dense recurrent neural networks (RNNs) in that each spiking neuron has an internal state that is propagated in time. Differently from RNNs, neurons in SNNs only emit spikes whenever a threshold is reached. This spike generation mechanism is not differentiable, which leads to substantial difficulties in optimizing these networks [4,22,23,36,45,47,56]. One workaround is to avoid the aforementioned threshold and instead propagate features throughout the receptive field [34]. The downside of this mechanism is that the sparse-processing property is lost within deeper layers of the network. Overall, the design and training of SNNs still requires fundamental investigation before competitive performance can be reached." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "A third research direction is concerned with exploring" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.358, + 0.9 + ], + "angle": 0, + "content": "equivalent to \\(1\\times 1\\) kernel in a Conv-LSTM cell" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13885" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.895, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.283, + 0.897, + 0.34 + ], + "angle": 0, + "content": "Figure 2. Overview of the unrolled computation graph of our multi-stage recurrent backbone. Events are processed into a tensor representation before they are used as input to the first stage. Each stage also reuses the LSTM states (c: cell, h: hidden) from the previous timestep. Finally, the detection framework interfaces with the backbone from the second stage onwards. Specifically, the hidden states of the LSTMs are used as features for the detection framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.579 + ], + "angle": 0, + "content": "dense neural networks for object detection with event cameras. The first step is the creation of a dense tensor (event representation) that enables compatibility with dense operations such as convolutions. Early work directly uses a single event representation generated from a short temporal window of events to infer detections [7, 19, 20]. These approaches discard relevant information from beyond the considered temporal window such that detecting slowly moving objects becomes difficult or impossible. Followup work addresses this issue by incorporating recurrent neural network layers [26,38] which drastically improved the detection performance. We follow this line of work but revamp dominant architecture choices to build a canonical framework that is fast, lightweight and highly performant." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.59, + 0.47, + 0.607 + ], + "angle": 0, + "content": "2.2. Vision Transformers for Spatio-Temporal Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.47, + 0.734 + ], + "angle": 0, + "content": "The success of attention-based models [52] in NLP has inspired the exploration of transformer-based architectures in computer vision [12]. Attention-based models have recently also been explored in video classification [1,5,13,48] where the models are applied directly to a set of frames. While these approaches have shown promising results in spatio-temporal modelling, they are optimized for offline processing of stored video data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.47, + 0.798 + ], + "angle": 0, + "content": "In event-based vision, attention-based components have found applications in classification [42, 53] and image reconstruction [54], and monocular depth estimation [31], but their use in object detection has yet to be investigated." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.814, + 0.169, + 0.83 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our object detection approach is designed to process a stream of events sequentially as they arrive. Incoming events are first processed into tensors that represent events in space and time. In every timestep, our network takes" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.368, + 0.887, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.512, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Figure 3. RVT block structure. The input is convolved with kernel size \\( k \\times k \\) and stride \\( s \\). Block-SA applies self-attention in local windows while Grid-SA is a global operation using dilated attention. Finally, each block ends with an LSTM that reuses the (cell- and hidden) states from the previous timestep. The LSTM is applied to each feature separately. Normalization and activation layers are omitted for conciseness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.894, + 0.728 + ], + "angle": 0, + "content": "a new event representation as input as well as the previous states of the recurrent neural network layers. After each pass through the backbone, the output of the RNNs are used as input to the detection framework. The following sections elaborate on each one of these steps. Fig. 2 shows an overview of the RVT architecture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Event Processing Each pixel of an event camera can independently trigger an event when a significant log brightness change occurs. An event can be positive or negative depending on the sign of the brightness change. We characterize an event with polarity \\( p_k \\in \\{0,1\\} \\) as a tuple \\( e_k = (x_k,y_k,t_k,p_k) \\) that occurs at pixel \\( (x_k,y_k) \\) at time \\( t_k \\). Modern event cameras can produce 10s of millions of events per second which renders event-by-event processing out of reach on conventional processing units." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this work we opt for a very simple preprocessing step" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13886" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "to enable compatibility with convolutional neural network layers which, as we will show later in Sec. 4.2, are an important contributor to the performance of our model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.244 + ], + "angle": 0, + "content": "Our preprocessing step starts with the creation of a 4-dimensional tensor \\( E \\). The first dimension consists of two components and represents the polarity. The second dimension has \\( T \\) components and is associated with \\( T \\) discretization steps of time. The 3rd and 4th dimension represent height and width of the event camera. We process set of events \\( \\mathcal{E} \\) within a time duration \\( [t_a, t_b) \\) the following way:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.25, + 0.472, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} E (p, \\tau , x, y) = \\sum_ {e _ {k} \\in \\mathcal {E}} \\delta (p - p _ {k}) \\delta (x - x _ {k}, y - y _ {k}) \\delta (\\tau - \\tau_ {k}), \\\\ \\tau_ {k} = \\left\\lfloor \\frac {t _ {k} - t _ {a}}{t _ {b} - t _ {a}} \\cdot T \\right\\rfloor \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.474 + ], + "angle": 0, + "content": "In words, we create \\( T \\) 2-channel frames where each pixel contains the number of positive or negative events within one of the \\( T \\) temporal frames. As a final step, we flatten the polarity and time dimension to retrieve a 3-dimensional tensor with shape \\( (2T, H, W) \\) to directly enable compatibility with 2D convolutions. We implement the presented algorithm with byte tensors to save memory and bandwidth. Other, more sophisticated representations are possible [2,3,6,16,26,51,58], but their thorough evaluation is not our focus." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.411, + 0.499 + ], + "angle": 0, + "content": "3.1. Mixing Spatial and Temporal Features" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.704 + ], + "angle": 0, + "content": "The main difficulty of object detection with event cameras is that at any given time, the neural network should be able to efficiently (1) extract local- and global task-relevant features in pixel space because objects can cover both very small regions or large portions of the field of view; (2) extract features from very recent events (e.g. moving edges) as well as events from several seconds ago. This is necessary because some objects are moving slowly with respect to the camera such that they generate very few events over time. These observations motivate us to investigate transformer layers for spatial feature extraction and recurrent neural networks for efficient temporal feature extraction. Fig. 3 illustrates the components of a single stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Spatial Feature Extraction The spatial feature extraction stage should incorporate a prior about the fact that pixels are arranged in a 2D grid as early as possible in the computation graph. We enable this by using a convolution with overlapping kernels on the input features that at the same time spatially downsamples the input or features from the previous stage. This convolution also endows our model with a conditional positional embedding [9] such that we do not require absolute [12, 52] or relative [32] positional embeddings. Our ablation study in Sec. 4.2 shows that overlapping kernels lead to a substantial boost in detection performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.426 + ], + "angle": 0, + "content": "In a subsequent step, the resulting features are transformed through multi-axis self-attention. We quickly summarize the steps but refer to Tu et. al [50] for an elaborate explanation. Multi-axis attention consists of two stages using self-attention. The first stage performs local feature interaction while the second stage enables dilated global feature mixing. More specifically, the features are first grouped locally into non-overlapping windows: Let \\( X \\in \\mathbb{R}^{H \\times W \\times C} \\) be the input feature tensor. We reshape the tensor to a shape \\( \\left(\\frac{H}{P} \\times \\frac{W}{P}, P \\times P, C\\right) \\) where \\( P \\times P \\) is the window size in which multi-head self-attention [52] is applied. This block attention (Block-SA in Fig. 3) is used to model local interactions. As a next step, we would ideally be able to extract features globally. One straightforward way to achieve this would be applying self-attention on the whole feature map. Unfortunately, global self-attention has quadratic complexity in the number of features. Instead, we use grid attention (Grid-SA in Fig. 3). Grid attention partitions the feature maps into a grid of shape \\( (G \\times G, \\frac{H}{G} \\times \\frac{W}{G}, C) \\) using a \\( G \\times G \\) uniform grid. The resulting windows are of size \\( \\frac{H}{G} \\times \\frac{W}{G} \\). Self-attention is then applied to these windows which corresponds to global, dilated mixing of features." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.455 + ], + "angle": 0, + "content": "We study alternative designs as part of our architecture in the ablation studies in Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Temporal Feature Extraction We opt for temporal feature aggregation with LSTM [18] cells at the end of the stage. Differently from prior work [26,38] we find that temporal and spatial feature aggregation can be completely separated. This means that we use plain LSTM cells such that the states of the LSTMs do not interact with each other. By avoiding Conv-LSTM units [44], we can drastically reduce the computational complexity and parameter count. I.e. a Conv-LSTM with kernel size \\( k \\times k \\) and stride 1 demands \\( k^2 \\) the number of parameters and compute compared to the original LSTM cell. We examine this aspect in the experimental Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Model Details We apply LayerNorm [24] before and LayerScale [49] after each attention and MLP module, and add a residual connection after each module. We found that LayerScale enables a wider range of learning rates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.785, + 0.759 + ], + "angle": 0, + "content": "3.2. Hierarchical Multi-Stage Design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.81 + ], + "angle": 0, + "content": "We compose multiple RVT blocks together to form a multi-stage hierarchical backbone. The overall architecture is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "At first, a local temporal slice of events is processed into a 2D tensor format as formulated in the beginning of this section. Subsequently, each stage takes the previous features as input and optionally uses the LSTM state from the last timestep to compute features for the next stage. By saving the LSTM states for the following timestep, each re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13887" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.468, + 0.197 + ], + "angle": 0, + "content": "
StageSizeKernelStrideChannels
RVT-TRVT-SRVT-B
S11/474324864
S21/8326496128
S31/1632128192256
S41/3232256384512
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.206, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 1. RVT parameters and architecture variation. All model variants share the same parameter set except the number of channels per stage. Each stage initially applies a 2D convolution with kernel and stride as indicated in the table." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.468, + 0.321 + ], + "angle": 0, + "content": "current stage can retain temporal information for the whole feature map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.468, + 0.382 + ], + "angle": 0, + "content": "We follow prior work and use features from the second to the fourth stage for the object detection framework. To do so, we reshape the hidden states of the LSTMs into 2D feature maps." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.21, + 0.416 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.468, + 0.5 + ], + "angle": 0, + "content": "We conduct ablations and evaluation our model on the Gen1 [11] and 1 Mpx [38] event camera datasets. We train three variants of our model on both datasets: the base model RVT-B and its small and tiny variants RVT-S and RVT-T. Parameter details for the models are shown in Tab. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.159, + 0.529 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.536, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Implementation Details We initialize all layers randomly except LayerScale which is initialized to 1e-5 for each module. Our models are trained with mixed precision for 400k iterations with the ADAM optimizer [21] using a OneCycle learning rate schedule [46] with a linear decay from a maximum learning rate. We use a mixed batching strategy that applies backpropagation through time (BPTT) to half of the samples of the batch and truncated BPTT (TBPTT) to the other half. More details regarding this batching strategy can be found in the supplementary material. Our data augmentation includes random horizontal flipping, zooming in and zooming out. More details on data augmentation are available in Sec. 4.2 and the supplementary material. To construct event representations, we consider \\(50~\\mathrm{ms}\\) time windows that are discretized into \\(T = 10\\) bins. Finally, we use theYOLOX framework [15], which includes the IOU loss, class loss and regression loss. These losses are averaged both over the batch and sequence length for each optimization step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.884 + ], + "angle": 0, + "content": "To compare against prior work on the Gen1 dataset, we train our models with a batch size of 8, sequence length of 21, and learning rate of 2e-4. The training takes approximately 2 days on a single A100 GPU." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "On the 1 Mpx dataset, we train with a batch size of 24," + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.892, + 0.187 + ], + "angle": 0, + "content": "
Block-typeGen11 MpxParams (M)
mAP\\( AP_{50} \\)mAP\\( AP_{50} \\)
multi-axis47.670.146.072.318.5
Swin46.768.744.471.718.5
ConvNeXt45.565.842.370.618.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.198, + 0.892, + 0.226 + ], + "angle": 0, + "content": "Table 2. Spatial Aggregation. Multi-axis attention leads to the best results on both the Gen1 and 1 Mpx dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.251, + 0.892, + 0.281 + ], + "angle": 0, + "content": "sequence length of 5, and learning rate of 3.5e-4. The training takes approximately 3 days on two A100 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Datasets The Gen1 Automotive Detection dataset [11] consists of 39 hours of event camera recordings at a resolution of \\(304 \\times 240\\). In total, the Gen1 dataset contains 228k car and 28k pedestrian bounding boxes available at 1, 2 or 4 Hz. We follow the evaluation protocol of prior work [26,38] and remove bounding boxes with a side length of less than 10 pixels and a diagonal of less than 30 pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.585 + ], + "angle": 0, + "content": "The 1 MPx dataset [38] also features driving scenarios but provides recordings at a higher resolution of \\(720 \\times 1280\\) over a period of several months at day and night. It consists of approximately 15 hours of event data labeled at a frequency of 30 or \\(60\\mathrm{Hz}\\) with a total amount of 25 million bounding box labels for three classes (car, pedestrian, and two-wheeler). We follow the evaluation protocol of prior work [26, 38]. That is, we remove bounding boxes with a side length of less than 20 pixels and a diagonal of less than 60 pixels and halve the input resolution to nHD resolution \\((640 \\times 360)\\). We provide qualitative examples of this dataset together with predictions of our base model in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.586, + 0.892, + 0.616 + ], + "angle": 0, + "content": "For both datasets, mean average precision (mAP) is the main metric [29] that we consider." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.665, + 0.64 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.738 + ], + "angle": 0, + "content": "This section examines the two main contributors to the final performance of the proposed model. First, we investigate key components and design choices of the proposed backbone. Second, we study the influence of different data augmentation techniques that are compatible with our sequential problem setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.739, + 0.892, + 0.799 + ], + "angle": 0, + "content": "Unless stated otherwise, the ablation studies are performed on the Gen1 validation set using the best performing model after 400k iterations. To reduce the training time, we use BPTT with a sequence length of 11 instead 21." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.692, + 0.832 + ], + "angle": 0, + "content": "4.2.1 Model Components" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Spatial Interaction In Tab. 2, we study different spatial aggregation techniques. For a fair comparison, we keep the LSTM and convolutional downsampling layers identical and only exchange the attention and MLP modules. We" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13888" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.464, + 0.151 + ], + "angle": 0, + "content": "
Conv. kernel typemAPAP50AP75Params (M)
overlapping47.670.152.618.5
non-overlapping46.168.650.517.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.161, + 0.47, + 0.203 + ], + "angle": 0, + "content": "Table 3. Downsampling Strategy. The usage of overlapping kernels leads to higher performance at the expense of a slight increase in the number of parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.218, + 0.465, + 0.296 + ], + "angle": 0, + "content": "
LSTM kernel sizemAPAP50AP75Params (M)
1 × 147.670.152.618.5
3 × 346.569.051.440.8
3 × 3 depth-sep46.367.251.218.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.306, + 0.468, + 0.334 + ], + "angle": 0, + "content": "Table 4. LSTM kernel size. Conv-LSTM variants do not outperform the feature specific \\((1\\times 1)\\) LSTM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.468, + 0.527 + ], + "angle": 0, + "content": "compare multi-axis attention with ConvNext blocks [33] and Swin transformer blocks [32]. ConvNext is a convolutional neural network architecture that has shown competitive performance with transformer-based models on a wide range of tasks, including object detection. We use the default kernel size of \\(7 \\times 7\\) as originally suggested and place three ConvNeXt blocks in each stage to approximately match the number of parameters of the reference model. Swin, instead, is an attention-based model that applies local self-attention in windows that interact with each other through cyclic shifting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.468, + 0.618 + ], + "angle": 0, + "content": "We find that our Swin variant achieves better performance than the ConvNext variant, however, both are outperformed by multi-axis self-attention [50] on both the Gen1 and 1 Mpx dataset. This experiment suggests that global interaction at every stage (multi-axis) is advantageous to purely local interaction (Swin, ConvNext)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.468, + 0.805 + ], + "angle": 0, + "content": "Convolutional Downsampling The original vision transformer [12] architecture does not perform local feature interaction with convolutional layers. Some popular hierarchical counterparts also choose to apply downsample features without overlapping kernels [8, 32]. In Tab. 3, we compare overlapping and non-overlapping convolutional kernels in both the input layer (patch embedding) and feature downsampling stage. While non-overlapping convolutions reduce the number of parameters, they cause a substantial drop in performance. Consequently, we choose overlapping kernels in all stages of the network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.902 + ], + "angle": 0, + "content": "LSTM with Convolutions Prior state-of-the-art approaches on object detection with event cameras heavily rely on convolutional LSTM cells [26, 38]. We revisit this design choice and experiment with plain LSTM cells and a depthwise separable Conv-LSTM variant [39]. The depth-" + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.089, + 0.855, + 0.197 + ], + "angle": 0, + "content": "
S1S2S3S4mAP\\( AP_{50} \\)\\( AP_{75} \\)
32.054.831.4
✓39.863.541.6
✓✓44.268.447.5
✓✓✓46.970.050.8
✓✓✓✓47.670.152.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.207, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Table 5. LSTM placement. LSTM cells contribute to the overall performance even in the early stages." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.382 + ], + "angle": 0, + "content": "wise separable Conv-LSTM first applies a depthwise separable convolution on both the input and hidden state before a point-wise \\((1 \\times 1)\\) convolution is applied. Our results in Tab. 4 suggest that plain LSTM cells are sufficient in our model and even outperform both variations. This is to some degree surprising because both variants are a strict superset of the plain LSTM. We decide to use a plain LSTM cell based on these observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.508 + ], + "angle": 0, + "content": "LSTM Placement In this ablation we study the influence of using temporal recurrence only in a subset of stages or not at all. For all comparisons, we leave the model exactly the same but reset the states of the LSTMs at selected stages in each timestep. This way, we can simulate the absence of recurrent layers while keeping the number of parameters constant in the comparisons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.66 + ], + "angle": 0, + "content": "The results in Tab. 5 suggest that using no recurrence at all leads to a drastic decline of detection performance. Enabling the LSTMs in each stage, starting from the fourth consistently leads to enhanced performance. Surprisingly, we find that adding an LSTM to the first stage also leads to improvements, albeit the increase in mAP is not large. In general, this experiment suggests that the detection framework benefits from features that have been augmented with temporal information. Based on our observations, we decide to keep the LSTM also in the first stage." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.691, + 0.696 + ], + "angle": 0, + "content": "4.2.2 Data Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.794 + ], + "angle": 0, + "content": "While data augmentation is not directly related to the model itself, it greatly influences the final result as we will illustrate next. Here, we investigate three data augmentation techniques that are suitable for object detection on spatiotemporal data: Random (1) horizontal flipping, (2) zoom-in, and (3) zoom-out." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Zoom-in augmentation randomly selects crops that contain at least one full bounding box at the final timestep of the BPTT sequence (i.e. during training). This crop is then applied to the rest of the sequence before the crops are rescaled to the default resolution. This procedure ensures that we have at least a single label to compute the loss function while maintaining the same resolution during training." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13889" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.891, + 0.346 + ], + "angle": 0, + "content": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
NVS-S [27]GNNYOLOv1 [40]8.6---0.9
Asynet [34]Sparse CNNYOLOv114.5---11.4
AEGNN [43]GNNYOLOv116.3---20.0
Spiking DenseNet [10]SNNSSD [30]18.9---8.2
Inception + SSD [19]CNNSSD30.119.434.045.2>60*
RRC-Events [7]CNNYOLOv3 [41]30.721.534.346.4>100*
MatrixLSTM [6]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [20]CNNYOLOv331.222.334.649.4>60*
RED [38]CNN + RNNSSD40.016.743.039.324.1
ASTMNet [26](T)CNN + RNNSSD46.735.648.372.3>100*
RVT-B (ours)Transformer + RNNYOLOX [15]47.210.2 (3.7)47.411.9 (6.1)18.5
RVT-S (ours)Transformer + RNNYOLOX46.59.5 (3.0)44.110.1 (5.0)9.9
RVT-T (ours)Transformer + RNNYOLOX44.19.4 (2.3)41.59.5 (3.5)4.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.355, + 0.893, + 0.412 + ], + "angle": 0, + "content": "Table 6. Comparisons on test sets of Gen1 and 1 Mpx datasets. Best results in bold and second best underlined. Brackets \\((\\cdot)\\) in runtime indicate the inference time with JIT-compiled code using torch.compile. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for RVT to compare against indicated timings in prior work [26, 38] on comparable GPUs (Titan Xp)." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.435, + 0.454, + 0.543 + ], + "angle": 0, + "content": "
h-flipzoom-inzoom-outmAP\\( AP_{50} \\)\\( AP_{75} \\)
38.159.541.1
✓41.663.545.5
✓45.867.849.8
✓44.165.748.4
✓✓✓47.670.152.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.553, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Table 7. Data Augmentation. Data augmentation consistently improves the results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Zoom-out augmentation resizes the full input to a lower resolution and randomly places the downscaled input in a zero-tensor initialized at the default resolution. This procedure is then applied in an identical way to the remaining BPTT sequence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.469, + 0.806 + ], + "angle": 0, + "content": "Table 7 shows that our model is performing poorly if no data augmentation is applied. Overall, we find that data augmentation is important to combat overfitting not only on the Gen1 sequence but also on the 1 Mpx dataset. The most effective augmentation is zoom-in, followed by zoom-out and horizontal flipping. Based on these results, we decide to apply all data augmentation techniques. We report the specific hyperparameters in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.312, + 0.833 + ], + "angle": 0, + "content": "4.3. Benchmark Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we compare our proposed neural network architecture against prior work on both the Gen1 [11] and 1 Mpx dataset [38] and summarize the results in Tab. 6. We train three models, a base model (RVT-B) with approx-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.543 + ], + "angle": 0, + "content": "imately 18.5 million parameters, a small variant (RVT-S) with 9.9 million parameters, and a tiny model (RVT-T) with 4.4 million parameters by adapting the channel dimensions in each stage. Their architectural hyperparameters are outlined in Tab. 1. To compare with prior work, we choose the models based on their best performance on the validation set and evaluate them on the test set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.893, + 0.68 + ], + "angle": 0, + "content": "From Tab. 6 we can draw multiple conclusions. First, we observe that models using recurrent layers consistently outperform other approaches, both sparse (GNNs, SNNs) and dense feed-forward models without recurrent layers (Inception+SSD, RRC-Events, YOLOv3 Events) by an mAP of more than 10 on both datasets. One notable exception is MatrixLSTM [6] which applies LSTM cells directly at the input. In contrast, RED [38] and ASTMNet [26] employ recurrent layers only in deeper layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Our base model achieves a new state-of-the-art performance of \\(47.2\\mathrm{mAP}\\) on the Gen1 dataset and \\(47.4\\mathrm{mAP}\\) on the 1 Mpx dataset. ASTMNet claims comparable results on both datasets albeit at the cost of using a much larger backbone and increased inference time. The RED model, also reports favorable results, but achieves 7.2 lower mAP on the Gen1 and 4.4 lower mAP on the 1 Mpx dataset compared to our model. Finally, our tiny model is amongst the smallest in our comparison. Still, it achieves 4.1 higher mAP on the Gen1 dataset than the RED model while using 5 times fewer parameters." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Inference Time We also compute the inference time of our model on a T4 GPU with a batch size of 1. Unfortu-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13890" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.293, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.274, + 0.205, + 0.287 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.089, + 0.493, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.274, + 0.404, + 0.287 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.089, + 0.695, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.274, + 0.602, + 0.287 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.892, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.274, + 0.801, + 0.287 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.3, + 0.894, + 0.329 + ], + "angle": 0, + "content": "Figure 4. Predictions on the 1 Mpx dataset. All examples are thematically picked to illustrate the behaviour of the model in different scenarios. (d) shows a scenario in which the model can still partially detect objects in absence of events due the temporal memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.432 + ], + "angle": 0, + "content": "nately, both RED and ASTMNet are not open source such that we cannot directly compare inference time on the same GPU model. Instead, we use the timings provided by the authors that conducted their timing experiments on comparable GPUs (e.g. Titan Xp). We report the timing results of our models in Tab. 6 and also visualize them in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.47, + 0.569 + ], + "angle": 0, + "content": "To compare against prior work we first compute the inference time in PyTorch eager mode. In eager mode, our base model achieves an inference time of 10.2 milliseconds (ms) on the Gen1 dataset \\((304 \\times 240\\) resolution). This implies a latency reduction of \\(6\\mathrm{ms}\\) compared to RED and over 3 times lower inference time than ASTMNet. On the the 1 Mpx dataset, at a resolution of \\(640 \\times 360\\), our base model takes \\(11.9\\mathrm{ms}\\) for a forward pass, which is 3 times faster than RED and over 5 times faster than ASTMNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.751 + ], + "angle": 0, + "content": "Even on a T4 GPU, most of the inference time is framework overhead. To overcome this partially, we use the JIT compilation feature torch.compile of PyTorch 2 [37]. As Tab. 6 shows, this almost halves the inference time for RVT-B on the 1 Mpx dataset and reduces the inference time by a factor of 2.7 on the Gen1 dataset. As expected, the small and tiny models benefit even more from JIT compilation. For example, RVT-T only takes \\(2.3\\mathrm{ms}\\) for a forward pass on Gen1 and \\(3.5\\mathrm{ms}\\) on 1 Mpx. On a RTX 3090 GPU, RVT-B completes a forward pass in \\(2.8\\mathrm{ms}\\) on the 1 Mpx dataset, which shows the potential for low-latency inference if power consumption is less of a concern." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.329, + 0.785 + ], + "angle": 0, + "content": "5. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We use a very simple event representation which does not leverage the full potential of event-based data. For example, we only have a weak prior on the order of events because we process the temporal dimension directly with fully connected layers. Recent work has shown substantial gains by introducing temporal convolutions in early layers [26]. Efficient low-level processing of event data is still an open" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.342, + 0.882, + 0.357 + ], + "angle": 0, + "content": "research problem that we have not addressed in this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.524 + ], + "angle": 0, + "content": "Our approach currently only uses event streams to detect objects. Frames yield complementary information that, when properly incorporated, will yield significantly enhanced detection performance. For example, in Fig. 4 (d) we can see that our model can retain information over some period when no events are available. Still, the memory of the network will fade and detection performance deteriorates. High quality frames even at low frame-rate could provide the missing complementary information. Hence, we believe that a multi-modal extension of our method on a suitable dataset [17, 25] is a promising next step." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.536, + 0.619, + 0.551 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.773 + ], + "angle": 0, + "content": "We introduced a novel backbone architecture for object detection with event cameras. The architecture consists of a stage design that is repeatedly applied to create a multistage hierarchical neural network. Each stage compactly incorporates convolutional priors, local- and sparse global attention and recurrent feature aggregation. Our experiments highlight that recurrent vision transformers can be trained from scratch to reach state-of-the-art performance in object detection with event cameras. The resulting canonical stage-design is directly compatible with existing detection frameworks, and paves the way to low-latency object detection with event cameras on conventional hardware. Nonetheless, we hope that this work also inspires novel designs in future neuromorphic systems." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.671, + 0.802 + ], + "angle": 0, + "content": "7. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported by the National Centre of Competence in Research (NCCR) Robotics (grant agreement No. 51NF40-185543) through the Swiss National Science Foundation (SNSF), and the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13891" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.157 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In Int. Conf. Comput. Vis. 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(CVPR), 2019." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.785 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "13893" + } + ] +] \ No newline at end of file diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_origin.pdf b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9edb447e6556b903809e314ffbfbcd402fdcd10c --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/6fcdd9e3-da92-40b0-9e0a-068ff912bee6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a744122270ac2343895062a7b9e7c0b04fc1464d66e8a123ba6e6ff7d27a9f1e +size 840984 diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/full.md b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d4ad283e5e9d50b84a5c13a6d67b874b6c2a5b41 --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/full.md @@ -0,0 +1,305 @@ +# Recurrent Vision Transformers for Object Detection with Event Cameras + +Mathias Gehrig and Davide Scaramuzza + +Robotics and Perception Group, University of Zurich, Switzerland + +# Abstract + +We present Recurrent Vision Transformers (RVTs), a novel backbone for object detection with event cameras. Event cameras provide visual information with submillisecond latency at a high-dynamic range and with strong robustness against motion blur. These unique properties offer great potential for low-latency object detection and tracking in time-critical scenarios. Prior work in event-based vision has achieved outstanding detection performance but at the cost of substantial inference time, typically beyond 40 milliseconds. By revisiting the high-level design of recurrent vision backbones, we reduce inference time by a factor of 6 while retaining similar performance. To achieve this, we explore a multi-stage design that utilizes three key concepts in each stage: first, a convolutional prior that can be regarded as a conditional positional embedding. Second, local and dilated global self-attention for spatial feature interaction. Third, recurrent temporal feature aggregation to minimize latency while retaining temporal information. RVTs can be trained from scratch to reach state-of-the-art performance on event-based object detection - achieving an mAP of $47.2\%$ on the Gen1 automotive dataset. At the same time, RVTs offer fast inference ( $< 12$ ms on a T4 GPU) and favorable parameter efficiency ( $5 \times$ fewer than prior art). Our study brings new insights into effective design choices that can be fruitful for research beyond event-based vision. + +Code: https://github.com/uzh-rpg/RVT + +# 1. Introduction + +Time matters for object detection. In 30 milliseconds, a human can run 0.3 meters, a car on public roads covers up to 1 meter, and a train can travel over 2 meters. Yet, during this time, an ordinary camera captures only a single frame. + +Frame-based sensors must strike a balance between latency and bandwidth. Given a fixed bandwidth, a frame-based camera must trade-off camera resolution and frame rate. However, in highly dynamic scenes, reducing the resolution or the frame rate may come at the cost of missing essential scene details, and, in safety-critical scenarios like + +![](images/181205e9eb948670980454ac9a3440852946288e1cb82d95282f0f6648f9637e.jpg) +Figure 1. Detection performance vs inference time of our RVT models on the 1 Mpx detection dataset using a T4 GPU. The circle areas are proportional to the model size. + +automotive, this may even cause fatalities. + +In recent years, event cameras have emerged as alternative sensor that offers a different trade-off. Instead of counterbalancing bandwidth requirements and perceptual latency, they provide visual information at sub-millisecond latency but sacrifice absolute intensity information. Instead of capturing intensity images, event cameras measure changes in intensity at the time they occur. This results in a stream of events, which encode time, location, and polarity of brightness changes [14]. The main advantages of event cameras are their sub-millisecond latency, very high dynamic range ( $>120$ dB), strong robustness to motion blur, and ability to provide events asynchronously in a continuous manner. + +In this work, we aim to utilize these outstanding properties of event cameras for object detection in time-critical scenarios. Therefore, our objective is to design an approach that reduces the processing latency as much as possible while maintaining high performance. This is challenging because event cameras asynchronously trigger binary events that are spread of pixel space and time. Hence, we need to develop detection algorithms that can continuously associate features in the spatio-temporal domain while simultaneously satisfying strict latency requirements. + +Recent work has shown that dynamic graph neural networks (GNNs) [28,43] and sparse neural networks [10, 34, 55, 57] can theoretically achieve low latency inference for + +event-based object detection. Yet, to achieve this in practical scenarios they either require specialized hardware or their detection performance needs to be improved. + +An alternative thread of research approaches the problem from the view of conventional, dense neural network designs [7,19,20,26,38]. These methods show impressive performance on event-based object detection, especially when using temporal recurrence in their architectures [26, 38]. Still, the processing latency of these approaches remains beyond 40 milliseconds such that the low-latency aspect of event cameras cannot be fully leveraged. This raises the question: How can we achieve both high accuracy and efficiency without requiring specialized hardware? + +We notice that common design choices yield a suboptimal trade-off between performance and compute. For example, prior work uses expensive convolutional LSTM (Conv-LSTM) cells [44] extensively in their feature extraction stage [26, 38] or relies on heavy backbones such as the VGG architecture [26]. Sparse neural networks instead struggle to model global mixing of features which is crucial to correctly locate and classify large objects in the scene. + +To achieve our main objective, we fundamentally revisit the design of vision backbones for event-based object detection. In particular, we take inspiration from neural network design for conventional frame-based object detection and combine them with ideas that have proven successful in the event-based vision literature. Our study deliberately focuses on macro design of the object detection backbone to identify key components for both high performance and fast inference on GPUs. The resulting neural network is based on a single block that is repeated four times to form a multi-stage hierarchical backbone that can be used with off-the-shelf detection frameworks. + +We identify three key components that enable an excellent trade-off between detection performance and inference time. First, we find that interleaved local- and global self-attention [50] is ideally suited to mix both local and global features while offering linear complexity in the input resolution. Second, this attention mechanism is most effective when preceded by a simple convolution that also downsamples the spatial resolution from the previous stage. This convolution effectively provides a strong prior about the grid-structure of the pixel array and also acts as a conditional positional embedding for the transformer layers [9]. Third, temporal recurrence is paramount to achieve strong detection performance with events. Differently from prior work, we find that Conv-LSTM cells can be replaced by plain LSTM cells [18] that operate on each feature separately1. By doing so, we dramatically reduce the number of parameters and latency but also slightly improve the overall performance. Our full framework achieves competitive performance and higher efficiency compared to state-of-the + +art methods. Specifically, we reduce parameter count (from 100M to 18.5 M) and inference time (from 72 ms to 12 ms) up to a factor of 6 compared to prior art [26]. At the same time, we train our networks from scratch, showing that these benefits do not originate from large-scale pretraining. + +Our paper can be summarized as follows: (1) We reexamine predominant design choices in event-based object detection pipelines and reveal a set of key enablers for high performance in event-based object detection. (2) We propose a simple, composable stage design that unifies the crucial building blocks in a compact way. We build a 4-stage hierarchical backbone that is fast, lightweight and still offers performance comparable to the best reported so far. (3) We achieve state-of-the-art object detection performance of $47.2\%$ mAP on the Gen1 detection dataset [11] and a highly competitive $47.4\%$ mAP on the 1 Mpx detection dataset [38] while training the proposed architecture from scratch. In addition, we also provide insights into effective data augmentation techniques that contribute to these results. + +# 2. Related Work + +# 2.1. Object Detection for Event Cameras + +Object detection in the event camera literature can be broadly classified into three emerging research directions. + +Recent work explores graph neural networks to dynamically construct a spatio-temporal graph [28, 35, 43]. New nodes and node edges are established by sub-sampling events and finding existing nodes that are close in spacetime. The main challenge is to design the architecture such that information can propagate over vast distances in the space-time volume. This is relevant, for example, when large objects move slowly with respect to the camera. Furthermore, aggressive sub-sampling of events can lead to the removal of potentially crucial information, but is often required to maintain low-latency inference. + +A second line of work employs spiking neural networks (SNNs) that propagate information sparsely within the network [10, 55, 57]. SNNs are closely related to dense recurrent neural networks (RNNs) in that each spiking neuron has an internal state that is propagated in time. Differently from RNNs, neurons in SNNs only emit spikes whenever a threshold is reached. This spike generation mechanism is not differentiable, which leads to substantial difficulties in optimizing these networks [4,22,23,36,45,47,56]. One workaround is to avoid the aforementioned threshold and instead propagate features throughout the receptive field [34]. The downside of this mechanism is that the sparse-processing property is lost within deeper layers of the network. Overall, the design and training of SNNs still requires fundamental investigation before competitive performance can be reached. + +A third research direction is concerned with exploring + +![](images/de9d57734048ced41688cc0f0e1b1fd82246ecc488a5ff55be7117e01dc5ede3.jpg) +Figure 2. Overview of the unrolled computation graph of our multi-stage recurrent backbone. Events are processed into a tensor representation before they are used as input to the first stage. Each stage also reuses the LSTM states (c: cell, h: hidden) from the previous timestep. Finally, the detection framework interfaces with the backbone from the second stage onwards. Specifically, the hidden states of the LSTMs are used as features for the detection framework. + +dense neural networks for object detection with event cameras. The first step is the creation of a dense tensor (event representation) that enables compatibility with dense operations such as convolutions. Early work directly uses a single event representation generated from a short temporal window of events to infer detections [7, 19, 20]. These approaches discard relevant information from beyond the considered temporal window such that detecting slowly moving objects becomes difficult or impossible. Followup work addresses this issue by incorporating recurrent neural network layers [26,38] which drastically improved the detection performance. We follow this line of work but revamp dominant architecture choices to build a canonical framework that is fast, lightweight and highly performant. + +# 2.2. Vision Transformers for Spatio-Temporal Data + +The success of attention-based models [52] in NLP has inspired the exploration of transformer-based architectures in computer vision [12]. Attention-based models have recently also been explored in video classification [1,5,13,48] where the models are applied directly to a set of frames. While these approaches have shown promising results in spatio-temporal modelling, they are optimized for offline processing of stored video data. + +In event-based vision, attention-based components have found applications in classification [42, 53] and image reconstruction [54], and monocular depth estimation [31], but their use in object detection has yet to be investigated. + +# 3. Method + +Our object detection approach is designed to process a stream of events sequentially as they arrive. Incoming events are first processed into tensors that represent events in space and time. In every timestep, our network takes + +![](images/a36d8f2a5242130283d1965c6cd766b416279302438fcd34a1924a64685a07cc.jpg) +Figure 3. RVT block structure. The input is convolved with kernel size $k \times k$ and stride $s$ . Block-SA applies self-attention in local windows while Grid-SA is a global operation using dilated attention. Finally, each block ends with an LSTM that reuses the (cell- and hidden) states from the previous timestep. The LSTM is applied to each feature separately. Normalization and activation layers are omitted for conciseness. + +a new event representation as input as well as the previous states of the recurrent neural network layers. After each pass through the backbone, the output of the RNNs are used as input to the detection framework. The following sections elaborate on each one of these steps. Fig. 2 shows an overview of the RVT architecture. + +Event Processing Each pixel of an event camera can independently trigger an event when a significant log brightness change occurs. An event can be positive or negative depending on the sign of the brightness change. We characterize an event with polarity $p_k \in \{0,1\}$ as a tuple $e_k = (x_k,y_k,t_k,p_k)$ that occurs at pixel $(x_k,y_k)$ at time $t_k$ . Modern event cameras can produce 10s of millions of events per second which renders event-by-event processing out of reach on conventional processing units. + +In this work we opt for a very simple preprocessing step + +to enable compatibility with convolutional neural network layers which, as we will show later in Sec. 4.2, are an important contributor to the performance of our model. + +Our preprocessing step starts with the creation of a 4-dimensional tensor $E$ . The first dimension consists of two components and represents the polarity. The second dimension has $T$ components and is associated with $T$ discretization steps of time. The 3rd and 4th dimension represent height and width of the event camera. We process set of events $\mathcal{E}$ within a time duration $[t_a, t_b)$ the following way: + +$$ +\begin{array}{l} E (p, \tau , x, y) = \sum_ {e _ {k} \in \mathcal {E}} \delta (p - p _ {k}) \delta (x - x _ {k}, y - y _ {k}) \delta (\tau - \tau_ {k}), \\ \tau_ {k} = \left\lfloor \frac {t _ {k} - t _ {a}}{t _ {b} - t _ {a}} \cdot T \right\rfloor \\ \end{array} +$$ + +In words, we create $T$ 2-channel frames where each pixel contains the number of positive or negative events within one of the $T$ temporal frames. As a final step, we flatten the polarity and time dimension to retrieve a 3-dimensional tensor with shape $(2T, H, W)$ to directly enable compatibility with 2D convolutions. We implement the presented algorithm with byte tensors to save memory and bandwidth. Other, more sophisticated representations are possible [2,3,6,16,26,51,58], but their thorough evaluation is not our focus. + +# 3.1. Mixing Spatial and Temporal Features + +The main difficulty of object detection with event cameras is that at any given time, the neural network should be able to efficiently (1) extract local- and global task-relevant features in pixel space because objects can cover both very small regions or large portions of the field of view; (2) extract features from very recent events (e.g. moving edges) as well as events from several seconds ago. This is necessary because some objects are moving slowly with respect to the camera such that they generate very few events over time. These observations motivate us to investigate transformer layers for spatial feature extraction and recurrent neural networks for efficient temporal feature extraction. Fig. 3 illustrates the components of a single stage. + +Spatial Feature Extraction The spatial feature extraction stage should incorporate a prior about the fact that pixels are arranged in a 2D grid as early as possible in the computation graph. We enable this by using a convolution with overlapping kernels on the input features that at the same time spatially downsamples the input or features from the previous stage. This convolution also endows our model with a conditional positional embedding [9] such that we do not require absolute [12, 52] or relative [32] positional embeddings. Our ablation study in Sec. 4.2 shows that overlapping kernels lead to a substantial boost in detection performance. + +In a subsequent step, the resulting features are transformed through multi-axis self-attention. We quickly summarize the steps but refer to Tu et. al [50] for an elaborate explanation. Multi-axis attention consists of two stages using self-attention. The first stage performs local feature interaction while the second stage enables dilated global feature mixing. More specifically, the features are first grouped locally into non-overlapping windows: Let $X \in \mathbb{R}^{H \times W \times C}$ be the input feature tensor. We reshape the tensor to a shape $\left(\frac{H}{P} \times \frac{W}{P}, P \times P, C\right)$ where $P \times P$ is the window size in which multi-head self-attention [52] is applied. This block attention (Block-SA in Fig. 3) is used to model local interactions. As a next step, we would ideally be able to extract features globally. One straightforward way to achieve this would be applying self-attention on the whole feature map. Unfortunately, global self-attention has quadratic complexity in the number of features. Instead, we use grid attention (Grid-SA in Fig. 3). Grid attention partitions the feature maps into a grid of shape $(G \times G, \frac{H}{G} \times \frac{W}{G}, C)$ using a $G \times G$ uniform grid. The resulting windows are of size $\frac{H}{G} \times \frac{W}{G}$ . Self-attention is then applied to these windows which corresponds to global, dilated mixing of features. + +We study alternative designs as part of our architecture in the ablation studies in Sec. 4.2. + +Temporal Feature Extraction We opt for temporal feature aggregation with LSTM [18] cells at the end of the stage. Differently from prior work [26,38] we find that temporal and spatial feature aggregation can be completely separated. This means that we use plain LSTM cells such that the states of the LSTMs do not interact with each other. By avoiding Conv-LSTM units [44], we can drastically reduce the computational complexity and parameter count. I.e. a Conv-LSTM with kernel size $k \times k$ and stride 1 demands $k^2$ the number of parameters and compute compared to the original LSTM cell. We examine this aspect in the experimental Sec. 4.2. + +Model Details We apply LayerNorm [24] before and LayerScale [49] after each attention and MLP module, and add a residual connection after each module. We found that LayerScale enables a wider range of learning rates. + +# 3.2. Hierarchical Multi-Stage Design + +We compose multiple RVT blocks together to form a multi-stage hierarchical backbone. The overall architecture is shown in Fig. 2. + +At first, a local temporal slice of events is processed into a 2D tensor format as formulated in the beginning of this section. Subsequently, each stage takes the previous features as input and optionally uses the LSTM state from the last timestep to compute features for the next stage. By saving the LSTM states for the following timestep, each re + +
StageSizeKernelStrideChannels
RVT-TRVT-SRVT-B
S11/474324864
S21/8326496128
S31/1632128192256
S41/3232256384512
+ +Table 1. RVT parameters and architecture variation. All model variants share the same parameter set except the number of channels per stage. Each stage initially applies a 2D convolution with kernel and stride as indicated in the table. + +current stage can retain temporal information for the whole feature map. + +We follow prior work and use features from the second to the fourth stage for the object detection framework. To do so, we reshape the hidden states of the LSTMs into 2D feature maps. + +# 4. Experiments + +We conduct ablations and evaluation our model on the Gen1 [11] and 1 Mpx [38] event camera datasets. We train three variants of our model on both datasets: the base model RVT-B and its small and tiny variants RVT-S and RVT-T. Parameter details for the models are shown in Tab. 1. + +# 4.1. Setup + +Implementation Details We initialize all layers randomly except LayerScale which is initialized to 1e-5 for each module. Our models are trained with mixed precision for 400k iterations with the ADAM optimizer [21] using a OneCycle learning rate schedule [46] with a linear decay from a maximum learning rate. We use a mixed batching strategy that applies backpropagation through time (BPTT) to half of the samples of the batch and truncated BPTT (TBPTT) to the other half. More details regarding this batching strategy can be found in the supplementary material. Our data augmentation includes random horizontal flipping, zooming in and zooming out. More details on data augmentation are available in Sec. 4.2 and the supplementary material. To construct event representations, we consider $50~\mathrm{ms}$ time windows that are discretized into $T = 10$ bins. Finally, we use theYOLOX framework [15], which includes the IOU loss, class loss and regression loss. These losses are averaged both over the batch and sequence length for each optimization step. + +To compare against prior work on the Gen1 dataset, we train our models with a batch size of 8, sequence length of 21, and learning rate of 2e-4. The training takes approximately 2 days on a single A100 GPU. + +On the 1 Mpx dataset, we train with a batch size of 24, + +
Block-typeGen11 MpxParams (M)
mAP\( AP_{50} \)mAP\( AP_{50} \)
multi-axis47.670.146.072.318.5
Swin46.768.744.471.718.5
ConvNeXt45.565.842.370.618.7
+ +Table 2. Spatial Aggregation. Multi-axis attention leads to the best results on both the Gen1 and 1 Mpx dataset. + +sequence length of 5, and learning rate of 3.5e-4. The training takes approximately 3 days on two A100 GPUs. + +Datasets The Gen1 Automotive Detection dataset [11] consists of 39 hours of event camera recordings at a resolution of $304 \times 240$ . In total, the Gen1 dataset contains 228k car and 28k pedestrian bounding boxes available at 1, 2 or 4 Hz. We follow the evaluation protocol of prior work [26,38] and remove bounding boxes with a side length of less than 10 pixels and a diagonal of less than 30 pixels. + +The 1 MPx dataset [38] also features driving scenarios but provides recordings at a higher resolution of $720 \times 1280$ over a period of several months at day and night. It consists of approximately 15 hours of event data labeled at a frequency of 30 or $60\mathrm{Hz}$ with a total amount of 25 million bounding box labels for three classes (car, pedestrian, and two-wheeler). We follow the evaluation protocol of prior work [26, 38]. That is, we remove bounding boxes with a side length of less than 20 pixels and a diagonal of less than 60 pixels and halve the input resolution to nHD resolution $(640 \times 360)$ . We provide qualitative examples of this dataset together with predictions of our base model in Fig. 4. + +For both datasets, mean average precision (mAP) is the main metric [29] that we consider. + +# 4.2. Ablation Studies + +This section examines the two main contributors to the final performance of the proposed model. First, we investigate key components and design choices of the proposed backbone. Second, we study the influence of different data augmentation techniques that are compatible with our sequential problem setting. + +Unless stated otherwise, the ablation studies are performed on the Gen1 validation set using the best performing model after 400k iterations. To reduce the training time, we use BPTT with a sequence length of 11 instead 21. + +# 4.2.1 Model Components + +Spatial Interaction In Tab. 2, we study different spatial aggregation techniques. For a fair comparison, we keep the LSTM and convolutional downsampling layers identical and only exchange the attention and MLP modules. We + +
Conv. kernel typemAPAP50AP75Params (M)
overlapping47.670.152.618.5
non-overlapping46.168.650.517.6
+ +Table 3. Downsampling Strategy. The usage of overlapping kernels leads to higher performance at the expense of a slight increase in the number of parameters. + +
LSTM kernel sizemAPAP50AP75Params (M)
1 × 147.670.152.618.5
3 × 346.569.051.440.8
3 × 3 depth-sep46.367.251.218.6
+ +compare multi-axis attention with ConvNext blocks [33] and Swin transformer blocks [32]. ConvNext is a convolutional neural network architecture that has shown competitive performance with transformer-based models on a wide range of tasks, including object detection. We use the default kernel size of $7 \times 7$ as originally suggested and place three ConvNeXt blocks in each stage to approximately match the number of parameters of the reference model. Swin, instead, is an attention-based model that applies local self-attention in windows that interact with each other through cyclic shifting. + +We find that our Swin variant achieves better performance than the ConvNext variant, however, both are outperformed by multi-axis self-attention [50] on both the Gen1 and 1 Mpx dataset. This experiment suggests that global interaction at every stage (multi-axis) is advantageous to purely local interaction (Swin, ConvNext). + +Convolutional Downsampling The original vision transformer [12] architecture does not perform local feature interaction with convolutional layers. Some popular hierarchical counterparts also choose to apply downsample features without overlapping kernels [8, 32]. In Tab. 3, we compare overlapping and non-overlapping convolutional kernels in both the input layer (patch embedding) and feature downsampling stage. While non-overlapping convolutions reduce the number of parameters, they cause a substantial drop in performance. Consequently, we choose overlapping kernels in all stages of the network. + +LSTM with Convolutions Prior state-of-the-art approaches on object detection with event cameras heavily rely on convolutional LSTM cells [26, 38]. We revisit this design choice and experiment with plain LSTM cells and a depthwise separable Conv-LSTM variant [39]. The depth- + +Table 4. LSTM kernel size. Conv-LSTM variants do not outperform the feature specific $(1\times 1)$ LSTM. + +
S1S2S3S4mAP\( AP_{50} \)\( AP_{75} \)
32.054.831.4
✓39.863.541.6
✓✓44.268.447.5
✓✓✓46.970.050.8
✓✓✓✓47.670.152.6
+ +Table 5. LSTM placement. LSTM cells contribute to the overall performance even in the early stages. + +wise separable Conv-LSTM first applies a depthwise separable convolution on both the input and hidden state before a point-wise $(1 \times 1)$ convolution is applied. Our results in Tab. 4 suggest that plain LSTM cells are sufficient in our model and even outperform both variations. This is to some degree surprising because both variants are a strict superset of the plain LSTM. We decide to use a plain LSTM cell based on these observations. + +LSTM Placement In this ablation we study the influence of using temporal recurrence only in a subset of stages or not at all. For all comparisons, we leave the model exactly the same but reset the states of the LSTMs at selected stages in each timestep. This way, we can simulate the absence of recurrent layers while keeping the number of parameters constant in the comparisons. + +The results in Tab. 5 suggest that using no recurrence at all leads to a drastic decline of detection performance. Enabling the LSTMs in each stage, starting from the fourth consistently leads to enhanced performance. Surprisingly, we find that adding an LSTM to the first stage also leads to improvements, albeit the increase in mAP is not large. In general, this experiment suggests that the detection framework benefits from features that have been augmented with temporal information. Based on our observations, we decide to keep the LSTM also in the first stage. + +# 4.2.2 Data Augmentation + +While data augmentation is not directly related to the model itself, it greatly influences the final result as we will illustrate next. Here, we investigate three data augmentation techniques that are suitable for object detection on spatiotemporal data: Random (1) horizontal flipping, (2) zoom-in, and (3) zoom-out. + +Zoom-in augmentation randomly selects crops that contain at least one full bounding box at the final timestep of the BPTT sequence (i.e. during training). This crop is then applied to the rest of the sequence before the crops are rescaled to the default resolution. This procedure ensures that we have at least a single label to compute the loss function while maintaining the same resolution during training. + +
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
NVS-S [27]GNNYOLOv1 [40]8.6---0.9
Asynet [34]Sparse CNNYOLOv114.5---11.4
AEGNN [43]GNNYOLOv116.3---20.0
Spiking DenseNet [10]SNNSSD [30]18.9---8.2
Inception + SSD [19]CNNSSD30.119.434.045.2>60*
RRC-Events [7]CNNYOLOv3 [41]30.721.534.346.4>100*
MatrixLSTM [6]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [20]CNNYOLOv331.222.334.649.4>60*
RED [38]CNN + RNNSSD40.016.743.039.324.1
ASTMNet [26](T)CNN + RNNSSD46.735.648.372.3>100*
RVT-B (ours)Transformer + RNNYOLOX [15]47.210.2 (3.7)47.411.9 (6.1)18.5
RVT-S (ours)Transformer + RNNYOLOX46.59.5 (3.0)44.110.1 (5.0)9.9
RVT-T (ours)Transformer + RNNYOLOX44.19.4 (2.3)41.59.5 (3.5)4.4
+ +Table 6. Comparisons on test sets of Gen1 and 1 Mpx datasets. Best results in bold and second best underlined. Brackets $(\cdot)$ in runtime indicate the inference time with JIT-compiled code using torch.compile. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for RVT to compare against indicated timings in prior work [26, 38] on comparable GPUs (Titan Xp). + +
h-flipzoom-inzoom-outmAP\( AP_{50} \)\( AP_{75} \)
38.159.541.1
✓41.663.545.5
✓45.867.849.8
✓44.165.748.4
✓✓✓47.670.152.6
+ +Table 7. Data Augmentation. Data augmentation consistently improves the results. + +Zoom-out augmentation resizes the full input to a lower resolution and randomly places the downscaled input in a zero-tensor initialized at the default resolution. This procedure is then applied in an identical way to the remaining BPTT sequence. + +Table 7 shows that our model is performing poorly if no data augmentation is applied. Overall, we find that data augmentation is important to combat overfitting not only on the Gen1 sequence but also on the 1 Mpx dataset. The most effective augmentation is zoom-in, followed by zoom-out and horizontal flipping. Based on these results, we decide to apply all data augmentation techniques. We report the specific hyperparameters in the supplementary material. + +# 4.3. Benchmark Comparisons + +In this section, we compare our proposed neural network architecture against prior work on both the Gen1 [11] and 1 Mpx dataset [38] and summarize the results in Tab. 6. We train three models, a base model (RVT-B) with approx- + +imately 18.5 million parameters, a small variant (RVT-S) with 9.9 million parameters, and a tiny model (RVT-T) with 4.4 million parameters by adapting the channel dimensions in each stage. Their architectural hyperparameters are outlined in Tab. 1. To compare with prior work, we choose the models based on their best performance on the validation set and evaluate them on the test set. + +From Tab. 6 we can draw multiple conclusions. First, we observe that models using recurrent layers consistently outperform other approaches, both sparse (GNNs, SNNs) and dense feed-forward models without recurrent layers (Inception+SSD, RRC-Events, YOLOv3 Events) by an mAP of more than 10 on both datasets. One notable exception is MatrixLSTM [6] which applies LSTM cells directly at the input. In contrast, RED [38] and ASTMNet [26] employ recurrent layers only in deeper layers. + +Our base model achieves a new state-of-the-art performance of $47.2\mathrm{mAP}$ on the Gen1 dataset and $47.4\mathrm{mAP}$ on the 1 Mpx dataset. ASTMNet claims comparable results on both datasets albeit at the cost of using a much larger backbone and increased inference time. The RED model, also reports favorable results, but achieves 7.2 lower mAP on the Gen1 and 4.4 lower mAP on the 1 Mpx dataset compared to our model. Finally, our tiny model is amongst the smallest in our comparison. Still, it achieves 4.1 higher mAP on the Gen1 dataset than the RED model while using 5 times fewer parameters. + +Inference Time We also compute the inference time of our model on a T4 GPU with a batch size of 1. Unfortu- + +![](images/48cadbf752382fb16158d6cb7a8fec104fb6a57c4bef44514f43dc8744aa6b0b.jpg) +(a) + +![](images/7a2fdd206801126e6e2818c7bbb053972ff2dd99df03771f09d7fbff8bbddf24.jpg) +(b) + +![](images/d22f74578784b71d475692b8970dba876093ad648efd1b4a748bca78ac0affd3.jpg) +(c) +Figure 4. Predictions on the 1 Mpx dataset. All examples are thematically picked to illustrate the behaviour of the model in different scenarios. (d) shows a scenario in which the model can still partially detect objects in absence of events due the temporal memory. + +![](images/caa2226b1b6cc1af239209c50b0c3f41c3c2e26435db237a17986ee2ba9d8611.jpg) +(d) + +nately, both RED and ASTMNet are not open source such that we cannot directly compare inference time on the same GPU model. Instead, we use the timings provided by the authors that conducted their timing experiments on comparable GPUs (e.g. Titan Xp). We report the timing results of our models in Tab. 6 and also visualize them in Fig. 1. + +To compare against prior work we first compute the inference time in PyTorch eager mode. In eager mode, our base model achieves an inference time of 10.2 milliseconds (ms) on the Gen1 dataset $(304 \times 240$ resolution). This implies a latency reduction of $6\mathrm{ms}$ compared to RED and over 3 times lower inference time than ASTMNet. On the the 1 Mpx dataset, at a resolution of $640 \times 360$ , our base model takes $11.9\mathrm{ms}$ for a forward pass, which is 3 times faster than RED and over 5 times faster than ASTMNet. + +Even on a T4 GPU, most of the inference time is framework overhead. To overcome this partially, we use the JIT compilation feature torch.compile of PyTorch 2 [37]. As Tab. 6 shows, this almost halves the inference time for RVT-B on the 1 Mpx dataset and reduces the inference time by a factor of 2.7 on the Gen1 dataset. As expected, the small and tiny models benefit even more from JIT compilation. For example, RVT-T only takes $2.3\mathrm{ms}$ for a forward pass on Gen1 and $3.5\mathrm{ms}$ on 1 Mpx. On a RTX 3090 GPU, RVT-B completes a forward pass in $2.8\mathrm{ms}$ on the 1 Mpx dataset, which shows the potential for low-latency inference if power consumption is less of a concern. + +# 5. Discussion and Limitations + +We use a very simple event representation which does not leverage the full potential of event-based data. For example, we only have a weak prior on the order of events because we process the temporal dimension directly with fully connected layers. Recent work has shown substantial gains by introducing temporal convolutions in early layers [26]. Efficient low-level processing of event data is still an open + +research problem that we have not addressed in this work. + +Our approach currently only uses event streams to detect objects. Frames yield complementary information that, when properly incorporated, will yield significantly enhanced detection performance. For example, in Fig. 4 (d) we can see that our model can retain information over some period when no events are available. Still, the memory of the network will fade and detection performance deteriorates. High quality frames even at low frame-rate could provide the missing complementary information. Hence, we believe that a multi-modal extension of our method on a suitable dataset [17, 25] is a promising next step. + +# 6. Conclusion + +We introduced a novel backbone architecture for object detection with event cameras. The architecture consists of a stage design that is repeatedly applied to create a multistage hierarchical neural network. Each stage compactly incorporates convolutional priors, local- and sparse global attention and recurrent feature aggregation. Our experiments highlight that recurrent vision transformers can be trained from scratch to reach state-of-the-art performance in object detection with event cameras. The resulting canonical stage-design is directly compatible with existing detection frameworks, and paves the way to low-latency object detection with event cameras on conventional hardware. Nonetheless, we hope that this work also inspires novel designs in future neuromorphic systems. + +# 7. Acknowledgment + +This work was supported by the National Centre of Competence in Research (NCCR) Robotics (grant agreement No. 51NF40-185543) through the Swiss National Science Foundation (SNSF), and the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT). + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In Int. Conf. Comput. Vis. 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(CVPR), 2019. \ No newline at end of file diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/images.zip b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..02cf3869c58988b1b78ecb6706025e550a3e77bb --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d2399520515c84ebfd2664c0ffc63339d27bf41efc182bb07f1364bdfbb6221f +size 421219 diff --git a/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/layout.json b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..90594b9144c34dba9ea42a025fc05d616e18ff1f --- /dev/null +++ b/2023/Recurrent Vision Transformers for Object Detection With Event Cameras/layout.json @@ -0,0 +1,7776 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 70, + 103, + 523, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 103, + 523, + 120 + ], + "spans": [ + { + "bbox": [ + 70, + 103, + 523, + 120 + ], + "type": "text", + "content": "Recurrent Vision Transformers for Object Detection with Event Cameras" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 198, + 144, + 395, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 144, + 395, + 157 + ], + "spans": [ + { + "bbox": [ + 198, + 144, + 395, + 157 + ], + "type": "text", + "content": "Mathias Gehrig and Davide Scaramuzza" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 163, + 455, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 163, + 455, + 176 + ], + "spans": [ + { + "bbox": [ + 134, + 163, + 455, + 176 + ], + "type": "text", + "content": "Robotics and Perception Group, University of Zurich, Switzerland" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "spans": [ + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 230, + 289, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 541 + ], + "type": "text", + "content": "We present Recurrent Vision Transformers (RVTs), a novel backbone for object detection with event cameras. Event cameras provide visual information with submillisecond latency at a high-dynamic range and with strong robustness against motion blur. These unique properties offer great potential for low-latency object detection and tracking in time-critical scenarios. Prior work in event-based vision has achieved outstanding detection performance but at the cost of substantial inference time, typically beyond 40 milliseconds. By revisiting the high-level design of recurrent vision backbones, we reduce inference time by a factor of 6 while retaining similar performance. To achieve this, we explore a multi-stage design that utilizes three key concepts in each stage: first, a convolutional prior that can be regarded as a conditional positional embedding. Second, local and dilated global self-attention for spatial feature interaction. Third, recurrent temporal feature aggregation to minimize latency while retaining temporal information. 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Our study brings new insights into effective design choices that can be fruitful for research beyond event-based vision." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 544, + 259, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 259, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 259, + 557 + ], + "type": "text", + "content": "Code: https://github.com/uzh-rpg/RVT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 593, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 640 + ], + "type": "text", + "content": "Time matters for object detection. In 30 milliseconds, a human can run 0.3 meters, a car on public roads covers up to 1 meter, and a train can travel over 2 meters. Yet, during this time, an ordinary camera captures only a single frame." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Frame-based sensors must strike a balance between latency and bandwidth. Given a fixed bandwidth, a frame-based camera must trade-off camera resolution and frame rate. However, in highly dynamic scenes, reducing the resolution or the frame rate may come at the cost of missing essential scene details, and, in safety-critical scenarios like" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 205, + 545, + 322 + ], + "blocks": [ + { + "bbox": [ + 308, + 205, + 545, + 322 + ], + "lines": [ + { + "bbox": [ + 308, + 205, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 308, + 205, + 545, + 322 + ], + "type": "image", + "image_path": "181205e9eb948670980454ac9a3440852946288e1cb82d95282f0f6648f9637e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 331, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 305, + 331, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 547, + 365 + ], + "type": "text", + "content": "Figure 1. Detection performance vs inference time of our RVT models on the 1 Mpx detection dataset using a T4 GPU. The circle areas are proportional to the model size." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 388, + 477, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 477, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 477, + 399 + ], + "type": "text", + "content": "automotive, this may even cause fatalities." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 400, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 555 + ], + "type": "text", + "content": "In recent years, event cameras have emerged as alternative sensor that offers a different trade-off. Instead of counterbalancing bandwidth requirements and perceptual latency, they provide visual information at sub-millisecond latency but sacrifice absolute intensity information. Instead of capturing intensity images, event cameras measure changes in intensity at the time they occur. This results in a stream of events, which encode time, location, and polarity of brightness changes [14]. 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This is challenging because event cameras asynchronously trigger binary events that are spread of pixel space and time. Hence, we need to develop detection algorithms that can continuously associate features in the spatio-temporal domain while simultaneously satisfying strict latency requirements." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Recent work has shown that dynamic graph neural networks (GNNs) [28,43] and sparse neural networks [10, 34, 55, 57] can theoretically achieve low latency inference for" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13884" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "event-based object detection. Yet, to achieve this in practical scenarios they either require specialized hardware or their detection performance needs to be improved." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 228 + ], + "type": "text", + "content": "An alternative thread of research approaches the problem from the view of conventional, dense neural network designs [7,19,20,26,38]. These methods show impressive performance on event-based object detection, especially when using temporal recurrence in their architectures [26, 38]. Still, the processing latency of these approaches remains beyond 40 milliseconds such that the low-latency aspect of event cameras cannot be fully leveraged. This raises the question: How can we achieve both high accuracy and efficiency without requiring specialized hardware?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 323 + ], + "type": "text", + "content": "We notice that common design choices yield a suboptimal trade-off between performance and compute. For example, prior work uses expensive convolutional LSTM (Conv-LSTM) cells [44] extensively in their feature extraction stage [26, 38] or relies on heavy backbones such as the VGG architecture [26]. Sparse neural networks instead struggle to model global mixing of features which is crucial to correctly locate and classify large objects in the scene." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 324, + 286, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 286, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 286, + 466 + ], + "type": "text", + "content": "To achieve our main objective, we fundamentally revisit the design of vision backbones for event-based object detection. In particular, we take inspiration from neural network design for conventional frame-based object detection and combine them with ideas that have proven successful in the event-based vision literature. Our study deliberately focuses on macro design of the object detection backbone to identify key components for both high performance and fast inference on GPUs. The resulting neural network is based on a single block that is repeated four times to form a multi-stage hierarchical backbone that can be used with off-the-shelf detection frameworks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 467, + 286, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 286, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 286, + 694 + ], + "type": "text", + "content": "We identify three key components that enable an excellent trade-off between detection performance and inference time. First, we find that interleaved local- and global self-attention [50] is ideally suited to mix both local and global features while offering linear complexity in the input resolution. Second, this attention mechanism is most effective when preceded by a simple convolution that also downsamples the spatial resolution from the previous stage. This convolution effectively provides a strong prior about the grid-structure of the pixel array and also acts as a conditional positional embedding for the transformer layers [9]. Third, temporal recurrence is paramount to achieve strong detection performance with events. Differently from prior work, we find that Conv-LSTM cells can be replaced by plain LSTM cells [18] that operate on each feature separately1. By doing so, we dramatically reduce the number of parameters and latency but also slightly improve the overall performance. Our full framework achieves competitive performance and higher efficiency compared to state-of-the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "art methods. Specifically, we reduce parameter count (from 100M to 18.5 M) and inference time (from 72 ms to 12 ms) up to a factor of 6 compared to prior art [26]. At the same time, we train our networks from scratch, showing that these benefits do not originate from large-scale pretraining." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "text", + "content": "Our paper can be summarized as follows: (1) We reexamine predominant design choices in event-based object detection pipelines and reveal a set of key enablers for high performance in event-based object detection. (2) We propose a simple, composable stage design that unifies the crucial building blocks in a compact way. We build a 4-stage hierarchical backbone that is fast, lightweight and still offers performance comparable to the best reported so far. (3) We achieve state-of-the-art object detection performance of " + }, + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "inline_equation", + "content": "47.2\\%" + }, + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "text", + "content": " mAP on the Gen1 detection dataset [11] and a highly competitive " + }, + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "inline_equation", + "content": "47.4\\%" + }, + { + "bbox": [ + 304, + 133, + 545, + 300 + ], + "type": "text", + "content": " mAP on the 1 Mpx detection dataset [38] while training the proposed architecture from scratch. In addition, we also provide insights into effective data augmentation techniques that contribute to these results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 313, + 392, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 313, + 392, + 326 + ], + "spans": [ + { + "bbox": [ + 306, + 313, + 392, + 326 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 333, + 499, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 333, + 499, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 333, + 499, + 346 + ], + "type": "text", + "content": "2.1. Object Detection for Event Cameras" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "content": "Object detection in the event camera literature can be broadly classified into three emerging research directions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 377, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 509 + ], + "type": "text", + "content": "Recent work explores graph neural networks to dynamically construct a spatio-temporal graph [28, 35, 43]. New nodes and node edges are established by sub-sampling events and finding existing nodes that are close in spacetime. The main challenge is to design the architecture such that information can propagate over vast distances in the space-time volume. This is relevant, for example, when large objects move slowly with respect to the camera. Furthermore, aggressive sub-sampling of events can lead to the removal of potentially crucial information, but is often required to maintain low-latency inference." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "type": "text", + "content": "A second line of work employs spiking neural networks (SNNs) that propagate information sparsely within the network [10, 55, 57]. SNNs are closely related to dense recurrent neural networks (RNNs) in that each spiking neuron has an internal state that is propagated in time. Differently from RNNs, neurons in SNNs only emit spikes whenever a threshold is reached. This spike generation mechanism is not differentiable, which leads to substantial difficulties in optimizing these networks [4,22,23,36,45,47,56]. One workaround is to avoid the aforementioned threshold and instead propagate features throughout the receptive field [34]. The downside of this mechanism is that the sparse-processing property is lost within deeper layers of the network. Overall, the design and training of SNNs still requires fundamental investigation before competitive performance can be reached." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "A third research direction is concerned with exploring" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 219, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 219, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 219, + 712 + ], + "type": "text", + "content": "equivalent to " + }, + { + "bbox": [ + 58, + 702, + 219, + 712 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 58, + 702, + 219, + 712 + ], + "type": "text", + "content": " kernel in a Conv-LSTM cell" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13885" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 547, + 214 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 547, + 214 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 547, + 214 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 547, + 214 + ], + "type": "image", + "image_path": "de9d57734048ced41688cc0f0e1b1fd82246ecc488a5ff55be7117e01dc5ede3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 224, + 548, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 548, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 548, + 269 + ], + "type": "text", + "content": "Figure 2. Overview of the unrolled computation graph of our multi-stage recurrent backbone. Events are processed into a tensor representation before they are used as input to the first stage. Each stage also reuses the LSTM states (c: cell, h: hidden) from the previous timestep. Finally, the detection framework interfaces with the backbone from the second stage onwards. Specifically, the hidden states of the LSTMs are used as features for the detection framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 290, + 289, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 289, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 289, + 458 + ], + "type": "text", + "content": "dense neural networks for object detection with event cameras. The first step is the creation of a dense tensor (event representation) that enables compatibility with dense operations such as convolutions. Early work directly uses a single event representation generated from a short temporal window of events to infer detections [7, 19, 20]. These approaches discard relevant information from beyond the considered temporal window such that detecting slowly moving objects becomes difficult or impossible. Followup work addresses this issue by incorporating recurrent neural network layers [26,38] which drastically improved the detection performance. We follow this line of work but revamp dominant architecture choices to build a canonical framework that is fast, lightweight and highly performant." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 467, + 287, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 287, + 480 + ], + "type": "text", + "content": "2.2. Vision Transformers for Spatio-Temporal Data" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 487, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 581 + ], + "type": "text", + "content": "The success of attention-based models [52] in NLP has inspired the exploration of transformer-based architectures in computer vision [12]. Attention-based models have recently also been explored in video classification [1,5,13,48] where the models are applied directly to a set of frames. While these approaches have shown promising results in spatio-temporal modelling, they are optimized for offline processing of stored video data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": "In event-based vision, attention-based components have found applications in classification [42, 53] and image reconstruction [54], and monocular depth estimation [31], but their use in object detection has yet to be investigated." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 644, + 103, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 103, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 103, + 657 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Our object detection approach is designed to process a stream of events sequentially as they arrive. Incoming events are first processed into tensors that represent events in space and time. In every timestep, our network takes" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 291, + 542, + 392 + ], + "blocks": [ + { + "bbox": [ + 310, + 291, + 542, + 392 + ], + "lines": [ + { + "bbox": [ + 310, + 291, + 542, + 392 + ], + "spans": [ + { + "bbox": [ + 310, + 291, + 542, + 392 + ], + "type": "image", + "image_path": "a36d8f2a5242130283d1965c6cd766b416279302438fcd34a1924a64685a07cc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "lines": [ + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "type": "text", + "content": "Figure 3. RVT block structure. The input is convolved with kernel size " + }, + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "type": "text", + "content": " and stride " + }, + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 405, + 547, + 483 + ], + "type": "text", + "content": ". Block-SA applies self-attention in local windows while Grid-SA is a global operation using dilated attention. Finally, each block ends with an LSTM that reuses the (cell- and hidden) states from the previous timestep. The LSTM is applied to each feature separately. Normalization and activation layers are omitted for conciseness." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 505, + 547, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 576 + ], + "type": "text", + "content": "a new event representation as input as well as the previous states of the recurrent neural network layers. After each pass through the backbone, the output of the RNNs are used as input to the detection framework. The following sections elaborate on each one of these steps. Fig. 2 shows an overview of the RVT architecture." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": "Event Processing Each pixel of an event camera can independently trigger an event when a significant log brightness change occurs. An event can be positive or negative depending on the sign of the brightness change. We characterize an event with polarity " + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "inline_equation", + "content": "p_k \\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": " as a tuple " + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "inline_equation", + "content": "e_k = (x_k,y_k,t_k,p_k)" + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": " that occurs at pixel " + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "inline_equation", + "content": "(x_k,y_k)" + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": ". Modern event cameras can produce 10s of millions of events per second which renders event-by-event processing out of reach on conventional processing units." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "In this work we opt for a very simple preprocessing step" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13886" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "to enable compatibility with convolutional neural network layers which, as we will show later in Sec. 4.2, are an important contributor to the performance of our model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": "Our preprocessing step starts with the creation of a 4-dimensional tensor " + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": ". The first dimension consists of two components and represents the polarity. The second dimension has " + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": " components and is associated with " + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": " discretization steps of time. The 3rd and 4th dimension represent height and width of the event camera. We process set of events " + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": " within a time duration " + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "inline_equation", + "content": "[t_a, t_b)" + }, + { + "bbox": [ + 46, + 108, + 288, + 193 + ], + "type": "text", + "content": " the following way:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 198, + 288, + 252 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 288, + 252 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} E (p, \\tau , x, y) = \\sum_ {e _ {k} \\in \\mathcal {E}} \\delta (p - p _ {k}) \\delta (x - x _ {k}, y - y _ {k}) \\delta (\\tau - \\tau_ {k}), \\\\ \\tau_ {k} = \\left\\lfloor \\frac {t _ {k} - t _ {a}}{t _ {b} - t _ {a}} \\cdot T \\right\\rfloor \\\\ \\end{array}", + "image_path": "fb198406fe6bc6b642da12158c0cf80396609963c3c2927957b9cb4ccc4d9d93.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "text", + "content": "In words, we create " + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "text", + "content": " 2-channel frames where each pixel contains the number of positive or negative events within one of the " + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "text", + "content": " temporal frames. As a final step, we flatten the polarity and time dimension to retrieve a 3-dimensional tensor with shape " + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "inline_equation", + "content": "(2T, H, W)" + }, + { + "bbox": [ + 46, + 256, + 287, + 375 + ], + "type": "text", + "content": " to directly enable compatibility with 2D convolutions. We implement the presented algorithm with byte tensors to save memory and bandwidth. Other, more sophisticated representations are possible [2,3,6,16,26,51,58], but their thorough evaluation is not our focus." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 381, + 251, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 251, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 251, + 395 + ], + "type": "text", + "content": "3.1. Mixing Spatial and Temporal Features" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 557 + ], + "type": "text", + "content": "The main difficulty of object detection with event cameras is that at any given time, the neural network should be able to efficiently (1) extract local- and global task-relevant features in pixel space because objects can cover both very small regions or large portions of the field of view; (2) extract features from very recent events (e.g. moving edges) as well as events from several seconds ago. This is necessary because some objects are moving slowly with respect to the camera such that they generate very few events over time. These observations motivate us to investigate transformer layers for spatial feature extraction and recurrent neural networks for efficient temporal feature extraction. Fig. 3 illustrates the components of a single stage." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Spatial Feature Extraction The spatial feature extraction stage should incorporate a prior about the fact that pixels are arranged in a 2D grid as early as possible in the computation graph. We enable this by using a convolution with overlapping kernels on the input features that at the same time spatially downsamples the input or features from the previous stage. This convolution also endows our model with a conditional positional embedding [9] such that we do not require absolute [12, 52] or relative [32] positional embeddings. Our ablation study in Sec. 4.2 shows that overlapping kernels lead to a substantial boost in detection performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": "In a subsequent step, the resulting features are transformed through multi-axis self-attention. We quickly summarize the steps but refer to Tu et. al [50] for an elaborate explanation. Multi-axis attention consists of two stages using self-attention. The first stage performs local feature interaction while the second stage enables dilated global feature mixing. More specifically, the features are first grouped locally into non-overlapping windows: Let " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": " be the input feature tensor. We reshape the tensor to a shape " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\left(\\frac{H}{P} \\times \\frac{W}{P}, P \\times P, C\\right)" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "P \\times P" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": " is the window size in which multi-head self-attention [52] is applied. This block attention (Block-SA in Fig. 3) is used to model local interactions. As a next step, we would ideally be able to extract features globally. One straightforward way to achieve this would be applying self-attention on the whole feature map. Unfortunately, global self-attention has quadratic complexity in the number of features. Instead, we use grid attention (Grid-SA in Fig. 3). Grid attention partitions the feature maps into a grid of shape " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "(G \\times G, \\frac{H}{G} \\times \\frac{W}{G}, C)" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": " using a " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "G \\times G" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": " uniform grid. The resulting windows are of size " + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\frac{H}{G} \\times \\frac{W}{G}" + }, + { + "bbox": [ + 304, + 72, + 545, + 337 + ], + "type": "text", + "content": ". Self-attention is then applied to these windows which corresponds to global, dilated mixing of features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "type": "text", + "content": "We study alternative designs as part of our architecture in the ablation studies in Sec. 4.2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "text", + "content": "Temporal Feature Extraction We opt for temporal feature aggregation with LSTM [18] cells at the end of the stage. Differently from prior work [26,38] we find that temporal and spatial feature aggregation can be completely separated. This means that we use plain LSTM cells such that the states of the LSTMs do not interact with each other. By avoiding Conv-LSTM units [44], we can drastically reduce the computational complexity and parameter count. I.e. a Conv-LSTM with kernel size " + }, + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "text", + "content": " and stride 1 demands " + }, + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "inline_equation", + "content": "k^2" + }, + { + "bbox": [ + 304, + 374, + 545, + 518 + ], + "type": "text", + "content": " the number of parameters and compute compared to the original LSTM cell. We examine this aspect in the experimental Sec. 4.2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 582 + ], + "type": "text", + "content": "Model Details We apply LayerNorm [24] before and LayerScale [49] after each attention and MLP module, and add a residual connection after each module. We found that LayerScale enables a wider range of learning rates." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 587, + 480, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 480, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 480, + 601 + ], + "type": "text", + "content": "3.2. Hierarchical Multi-Stage Design" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "content": "We compose multiple RVT blocks together to form a multi-stage hierarchical backbone. The overall architecture is shown in Fig. 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "At first, a local temporal slice of events is processed into a 2D tensor format as formulated in the beginning of this section. Subsequently, each stage takes the previous features as input and optionally uses the LSTM state from the last timestep to compute features for the next stage. By saving the LSTM states for the following timestep, each re" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13887" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 286, + 156 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 286, + 156 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 286, + 156 + ], + "type": "table", + "html": "
StageSizeKernelStrideChannels
RVT-TRVT-SRVT-B
S11/474324864
S21/8326496128
S31/1632128192256
S41/3232256384512
", + "image_path": "e95e99fbdf2fc64362c36c7a841f0382e0a90440360fb7202f93c9c64dd50fd5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 163, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 287, + 208 + ], + "type": "text", + "content": "Table 1. RVT parameters and architecture variation. All model variants share the same parameter set except the number of channels per stage. Each stage initially applies a 2D convolution with kernel and stride as indicated in the table." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "type": "text", + "content": "current stage can retain temporal information for the whole feature map." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 255, + 286, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 286, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 286, + 302 + ], + "type": "text", + "content": "We follow prior work and use features from the second to the fourth stage for the object detection framework. To do so, we reshape the hidden states of the LSTMs into 2D feature maps." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 316, + 128, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 128, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 128, + 329 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 336, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 286, + 396 + ], + "type": "text", + "content": "We conduct ablations and evaluation our model on the Gen1 [11] and 1 Mpx [38] event camera datasets. We train three variants of our model on both datasets: the base model RVT-B and its small and tiny variants RVT-S and RVT-T. Parameter details for the models are shown in Tab. 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 406, + 97, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 97, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 97, + 418 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "text", + "content": "Implementation Details We initialize all layers randomly except LayerScale which is initialized to 1e-5 for each module. Our models are trained with mixed precision for 400k iterations with the ADAM optimizer [21] using a OneCycle learning rate schedule [46] with a linear decay from a maximum learning rate. We use a mixed batching strategy that applies backpropagation through time (BPTT) to half of the samples of the batch and truncated BPTT (TBPTT) to the other half. More details regarding this batching strategy can be found in the supplementary material. Our data augmentation includes random horizontal flipping, zooming in and zooming out. More details on data augmentation are available in Sec. 4.2 and the supplementary material. To construct event representations, we consider " + }, + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "inline_equation", + "content": "50~\\mathrm{ms}" + }, + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "text", + "content": " time windows that are discretized into " + }, + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "inline_equation", + "content": "T = 10" + }, + { + "bbox": [ + 45, + 424, + 286, + 651 + ], + "type": "text", + "content": " bins. Finally, we use theYOLOX framework [15], which includes the IOU loss, class loss and regression loss. These losses are averaged both over the batch and sequence length for each optimization step." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "type": "text", + "content": "To compare against prior work on the Gen1 dataset, we train our models with a batch size of 8, sequence length of 21, and learning rate of 2e-4. The training takes approximately 2 days on a single A100 GPU." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "On the 1 Mpx dataset, we train with a batch size of 24," + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 148 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "type": "table", + "html": "
Block-typeGen11 MpxParams (M)
mAP\\( AP_{50} \\)mAP\\( AP_{50} \\)
multi-axis47.670.146.072.318.5
Swin46.768.744.471.718.5
ConvNeXt45.565.842.370.618.7
", + "image_path": "4e26cb5e6e8dad672a57332a54e6230be43aef41aab314986c6121dab8458268.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 156, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 305, + 156, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 305, + 156, + 545, + 178 + ], + "type": "text", + "content": "Table 2. Spatial Aggregation. Multi-axis attention leads to the best results on both the Gen1 and 1 Mpx dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "type": "text", + "content": "sequence length of 5, and learning rate of 3.5e-4. The training takes approximately 3 days on two A100 GPUs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 236, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 319 + ], + "type": "text", + "content": "Datasets The Gen1 Automotive Detection dataset [11] consists of 39 hours of event camera recordings at a resolution of " + }, + { + "bbox": [ + 304, + 236, + 545, + 319 + ], + "type": "inline_equation", + "content": "304 \\times 240" + }, + { + "bbox": [ + 304, + 236, + 545, + 319 + ], + "type": "text", + "content": ". In total, the Gen1 dataset contains 228k car and 28k pedestrian bounding boxes available at 1, 2 or 4 Hz. We follow the evaluation protocol of prior work [26,38] and remove bounding boxes with a side length of less than 10 pixels and a diagonal of less than 30 pixels." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "text", + "content": "The 1 MPx dataset [38] also features driving scenarios but provides recordings at a higher resolution of " + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "inline_equation", + "content": "720 \\times 1280" + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "text", + "content": " over a period of several months at day and night. It consists of approximately 15 hours of event data labeled at a frequency of 30 or " + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "inline_equation", + "content": "60\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "text", + "content": " with a total amount of 25 million bounding box labels for three classes (car, pedestrian, and two-wheeler). We follow the evaluation protocol of prior work [26, 38]. That is, we remove bounding boxes with a side length of less than 20 pixels and a diagonal of less than 60 pixels and halve the input resolution to nHD resolution " + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "inline_equation", + "content": "(640 \\times 360)" + }, + { + "bbox": [ + 304, + 320, + 545, + 463 + ], + "type": "text", + "content": ". We provide qualitative examples of this dataset together with predictions of our base model in Fig. 4." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 464, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 464, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 545, + 487 + ], + "type": "text", + "content": "For both datasets, mean average precision (mAP) is the main metric [29] that we consider." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 495, + 406, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 406, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 406, + 506 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 513, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 584 + ], + "type": "text", + "content": "This section examines the two main contributors to the final performance of the proposed model. First, we investigate key components and design choices of the proposed backbone. Second, we study the influence of different data augmentation techniques that are compatible with our sequential problem setting." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 585, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 585, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 545, + 632 + ], + "type": "text", + "content": "Unless stated otherwise, the ablation studies are performed on the Gen1 validation set using the best performing model after 400k iterations. To reduce the training time, we use BPTT with a sequence length of 11 instead 21." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 647, + 423, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 423, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 423, + 658 + ], + "type": "text", + "content": "4.2.1 Model Components" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Spatial Interaction In Tab. 2, we study different spatial aggregation techniques. For a fair comparison, we keep the LSTM and convolutional downsampling layers identical and only exchange the attention and MLP modules. We" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13888" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 283, + 119 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 283, + 119 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 283, + 119 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 283, + 119 + ], + "type": "table", + "html": "
Conv. kernel typemAPAP50AP75Params (M)
overlapping47.670.152.618.5
non-overlapping46.168.650.517.6
", + "image_path": "9c0ec894169922d455831536e3134241b54c68855089c8f75ce12ccbd2db713e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 172, + 284, + 234 + ], + "blocks": [ + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "lines": [ + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "type": "text", + "content": "Table 3. Downsampling Strategy. The usage of overlapping kernels leads to higher performance at the expense of a slight increase in the number of parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 172, + 284, + 234 + ], + "lines": [ + { + "bbox": [ + 50, + 172, + 284, + 234 + ], + "spans": [ + { + "bbox": [ + 50, + 172, + 284, + 234 + ], + "type": "table", + "html": "
LSTM kernel sizemAPAP50AP75Params (M)
1 × 147.670.152.618.5
3 × 346.569.051.440.8
3 × 3 depth-sep46.367.251.218.6
", + "image_path": "61a42beed344f480f8e2b8ecadaa18c046298fb51b4bfcb22d8f5e3a7df087fb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 286, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 286, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 286, + 417 + ], + "type": "text", + "content": "compare multi-axis attention with ConvNext blocks [33] and Swin transformer blocks [32]. ConvNext is a convolutional neural network architecture that has shown competitive performance with transformer-based models on a wide range of tasks, including object detection. We use the default kernel size of " + }, + { + "bbox": [ + 46, + 285, + 286, + 417 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 46, + 285, + 286, + 417 + ], + "type": "text", + "content": " as originally suggested and place three ConvNeXt blocks in each stage to approximately match the number of parameters of the reference model. Swin, instead, is an attention-based model that applies local self-attention in windows that interact with each other through cyclic shifting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 418, + 286, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 286, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 286, + 489 + ], + "type": "text", + "content": "We find that our Swin variant achieves better performance than the ConvNext variant, however, both are outperformed by multi-axis self-attention [50] on both the Gen1 and 1 Mpx dataset. This experiment suggests that global interaction at every stage (multi-axis) is advantageous to purely local interaction (Swin, ConvNext)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 506, + 286, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 286, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 286, + 637 + ], + "type": "text", + "content": "Convolutional Downsampling The original vision transformer [12] architecture does not perform local feature interaction with convolutional layers. Some popular hierarchical counterparts also choose to apply downsample features without overlapping kernels [8, 32]. In Tab. 3, we compare overlapping and non-overlapping convolutional kernels in both the input layer (patch embedding) and feature downsampling stage. While non-overlapping convolutions reduce the number of parameters, they cause a substantial drop in performance. Consequently, we choose overlapping kernels in all stages of the network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "content": "LSTM with Convolutions Prior state-of-the-art approaches on object detection with event cameras heavily rely on convolutional LSTM cells [26, 38]. We revisit this design choice and experiment with plain LSTM cells and a depthwise separable Conv-LSTM variant [39]. The depth-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 331, + 70, + 523, + 156 + ], + "blocks": [ + { + "bbox": [ + 47, + 242, + 286, + 264 + ], + "lines": [ + { + "bbox": [ + 47, + 242, + 286, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 286, + 264 + ], + "type": "text", + "content": "Table 4. LSTM kernel size. Conv-LSTM variants do not outperform the feature specific " + }, + { + "bbox": [ + 47, + 242, + 286, + 264 + ], + "type": "inline_equation", + "content": "(1\\times 1)" + }, + { + "bbox": [ + 47, + 242, + 286, + 264 + ], + "type": "text", + "content": " LSTM." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 70, + 523, + 156 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 523, + 156 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 523, + 156 + ], + "type": "table", + "html": "
S1S2S3S4mAP\\( AP_{50} \\)\\( AP_{75} \\)
32.054.831.4
✓39.863.541.6
✓✓44.268.447.5
✓✓✓46.970.050.8
✓✓✓✓47.670.152.6
", + "image_path": "15715d63bd932ed4eba15079be35707568795156fded0dc9104075edc6547bd4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "type": "text", + "content": "Table 5. LSTM placement. LSTM cells contribute to the overall performance even in the early stages." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 207, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 302 + ], + "type": "text", + "content": "wise separable Conv-LSTM first applies a depthwise separable convolution on both the input and hidden state before a point-wise " + }, + { + "bbox": [ + 304, + 207, + 545, + 302 + ], + "type": "inline_equation", + "content": "(1 \\times 1)" + }, + { + "bbox": [ + 304, + 207, + 545, + 302 + ], + "type": "text", + "content": " convolution is applied. Our results in Tab. 4 suggest that plain LSTM cells are sufficient in our model and even outperform both variations. This is to some degree surprising because both variants are a strict superset of the plain LSTM. We decide to use a plain LSTM cell based on these observations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": "LSTM Placement In this ablation we study the influence of using temporal recurrence only in a subset of stages or not at all. For all comparisons, we leave the model exactly the same but reset the states of the LSTMs at selected stages in each timestep. This way, we can simulate the absence of recurrent layers while keeping the number of parameters constant in the comparisons." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 522 + ], + "type": "text", + "content": "The results in Tab. 5 suggest that using no recurrence at all leads to a drastic decline of detection performance. Enabling the LSTMs in each stage, starting from the fourth consistently leads to enhanced performance. Surprisingly, we find that adding an LSTM to the first stage also leads to improvements, albeit the increase in mAP is not large. In general, this experiment suggests that the detection framework benefits from features that have been augmented with temporal information. Based on our observations, we decide to keep the LSTM also in the first stage." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 539, + 422, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 422, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 422, + 551 + ], + "type": "text", + "content": "4.2.2 Data Augmentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 628 + ], + "type": "text", + "content": "While data augmentation is not directly related to the model itself, it greatly influences the final result as we will illustrate next. Here, we investigate three data augmentation techniques that are suitable for object detection on spatiotemporal data: Random (1) horizontal flipping, (2) zoom-in, and (3) zoom-out." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Zoom-in augmentation randomly selects crops that contain at least one full bounding box at the final timestep of the BPTT sequence (i.e. during training). This crop is then applied to the rest of the sequence before the crops are rescaled to the default resolution. This procedure ensures that we have at least a single label to compute the loss function while maintaining the same resolution during training." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13889" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 545, + 274 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 274 + ], + "type": "table", + "html": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
NVS-S [27]GNNYOLOv1 [40]8.6---0.9
Asynet [34]Sparse CNNYOLOv114.5---11.4
AEGNN [43]GNNYOLOv116.3---20.0
Spiking DenseNet [10]SNNSSD [30]18.9---8.2
Inception + SSD [19]CNNSSD30.119.434.045.2>60*
RRC-Events [7]CNNYOLOv3 [41]30.721.534.346.4>100*
MatrixLSTM [6]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [20]CNNYOLOv331.222.334.649.4>60*
RED [38]CNN + RNNSSD40.016.743.039.324.1
ASTMNet [26](T)CNN + RNNSSD46.735.648.372.3>100*
RVT-B (ours)Transformer + RNNYOLOX [15]47.210.2 (3.7)47.411.9 (6.1)18.5
RVT-S (ours)Transformer + RNNYOLOX46.59.5 (3.0)44.110.1 (5.0)9.9
RVT-T (ours)Transformer + RNNYOLOX44.19.4 (2.3)41.59.5 (3.5)4.4
", + "image_path": "bd58266553e0b5ff98c21fdebccdeee75c39a20d4d38a2c90c6bd44222c51824.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 57, + 344, + 277, + 430 + ], + "blocks": [ + { + "bbox": [ + 46, + 281, + 546, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 546, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 546, + 326 + ], + "type": "text", + "content": "Table 6. Comparisons on test sets of Gen1 and 1 Mpx datasets. Best results in bold and second best underlined. Brackets " + }, + { + "bbox": [ + 46, + 281, + 546, + 326 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 46, + 281, + 546, + 326 + ], + "type": "text", + "content": " in runtime indicate the inference time with JIT-compiled code using torch.compile. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for RVT to compare against indicated timings in prior work [26, 38] on comparable GPUs (Titan Xp)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 344, + 277, + 430 + ], + "lines": [ + { + "bbox": [ + 57, + 344, + 277, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 344, + 277, + 430 + ], + "type": "table", + "html": "
h-flipzoom-inzoom-outmAP\\( AP_{50} \\)\\( AP_{75} \\)
38.159.541.1
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", + "image_path": "5297aad1a1bb4e6750093b59c3b6486151d2f984800aa7e955a49a7f432283b9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 437, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 47, + 437, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 287, + 460 + ], + "type": "text", + "content": "Table 7. Data Augmentation. Data augmentation consistently improves the results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 481, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 541 + ], + "type": "text", + "content": "Zoom-out augmentation resizes the full input to a lower resolution and randomly places the downscaled input in a zero-tensor initialized at the default resolution. This procedure is then applied in an identical way to the remaining BPTT sequence." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 542, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 638 + ], + "type": "text", + "content": "Table 7 shows that our model is performing poorly if no data augmentation is applied. Overall, we find that data augmentation is important to combat overfitting not only on the Gen1 sequence but also on the 1 Mpx dataset. The most effective augmentation is zoom-in, followed by zoom-out and horizontal flipping. Based on these results, we decide to apply all data augmentation techniques. We report the specific hyperparameters in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 190, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 190, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 190, + 659 + ], + "type": "text", + "content": "4.3. Benchmark Comparisons" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 715 + ], + "type": "text", + "content": "In this section, we compare our proposed neural network architecture against prior work on both the Gen1 [11] and 1 Mpx dataset [38] and summarize the results in Tab. 6. We train three models, a base model (RVT-B) with approx-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 346, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 430 + ], + "type": "text", + "content": "imately 18.5 million parameters, a small variant (RVT-S) with 9.9 million parameters, and a tiny model (RVT-T) with 4.4 million parameters by adapting the channel dimensions in each stage. Their architectural hyperparameters are outlined in Tab. 1. To compare with prior work, we choose the models based on their best performance on the validation set and evaluate them on the test set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 430, + 546, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 546, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 546, + 538 + ], + "type": "text", + "content": "From Tab. 6 we can draw multiple conclusions. First, we observe that models using recurrent layers consistently outperform other approaches, both sparse (GNNs, SNNs) and dense feed-forward models without recurrent layers (Inception+SSD, RRC-Events, YOLOv3 Events) by an mAP of more than 10 on both datasets. One notable exception is MatrixLSTM [6] which applies LSTM cells directly at the input. In contrast, RED [38] and ASTMNet [26] employ recurrent layers only in deeper layers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "text", + "content": "Our base model achieves a new state-of-the-art performance of " + }, + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "inline_equation", + "content": "47.2\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "text", + "content": " on the Gen1 dataset and " + }, + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "inline_equation", + "content": "47.4\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 539, + 545, + 671 + ], + "type": "text", + "content": " on the 1 Mpx dataset. ASTMNet claims comparable results on both datasets albeit at the cost of using a much larger backbone and increased inference time. The RED model, also reports favorable results, but achieves 7.2 lower mAP on the Gen1 and 4.4 lower mAP on the 1 Mpx dataset compared to our model. Finally, our tiny model is amongst the smallest in our comparison. Still, it achieves 4.1 higher mAP on the Gen1 dataset than the RED model while using 5 times fewer parameters." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Inference Time We also compute the inference time of our model on a T4 GPU with a batch size of 1. Unfortu-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13890" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 179, + 215 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 179, + 215 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 179, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 179, + 215 + ], + "type": "image", + "image_path": "48cadbf752382fb16158d6cb7a8fec104fb6a57c4bef44514f43dc8744aa6b0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 217, + 125, + 227 + ], + "lines": [ + { + "bbox": [ + 113, + 217, + 125, + 227 + ], + "spans": [ + { + "bbox": [ + 113, + 217, + 125, + 227 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 179, + 70, + 301, + 215 + ], + "blocks": [ + { + "bbox": [ + 179, + 70, + 301, + 215 + ], + "lines": [ + { + "bbox": [ + 179, + 70, + 301, + 215 + ], + "spans": [ + { + "bbox": [ + 179, + 70, + 301, + 215 + ], + "type": "image", + "image_path": "7a2fdd206801126e6e2818c7bbb053972ff2dd99df03771f09d7fbff8bbddf24.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 217, + 247, + 227 + ], + "lines": [ + { + "bbox": [ + 235, + 217, + 247, + 227 + ], + "spans": [ + { + "bbox": [ + 235, + 217, + 247, + 227 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 70, + 425, + 215 + ], + "blocks": [ + { + "bbox": [ + 301, + 70, + 425, + 215 + ], + "lines": [ + { + "bbox": [ + 301, + 70, + 425, + 215 + ], + "spans": [ + { + "bbox": [ + 301, + 70, + 425, + 215 + ], + "type": "image", + "image_path": "d22f74578784b71d475692b8970dba876093ad648efd1b4a748bca78ac0affd3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 217, + 368, + 227 + ], + "lines": [ + { + "bbox": [ + 358, + 217, + 368, + 227 + ], + "spans": [ + { + "bbox": [ + 358, + 217, + 368, + 227 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 237, + 547, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 547, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 547, + 260 + ], + "type": "text", + "content": "Figure 4. Predictions on the 1 Mpx dataset. All examples are thematically picked to illustrate the behaviour of the model in different scenarios. (d) shows a scenario in which the model can still partially detect objects in absence of events due the temporal memory." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 545, + 215 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 545, + 215 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 545, + 215 + ], + "type": "image", + "image_path": "caa2226b1b6cc1af239209c50b0c3f41c3c2e26435db237a17986ee2ba9d8611.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 217, + 490, + 227 + ], + "lines": [ + { + "bbox": [ + 478, + 217, + 490, + 227 + ], + "spans": [ + { + "bbox": [ + 478, + 217, + 490, + 227 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "content": "nately, both RED and ASTMNet are not open source such that we cannot directly compare inference time on the same GPU model. Instead, we use the timings provided by the authors that conducted their timing experiments on comparable GPUs (e.g. Titan Xp). We report the timing results of our models in Tab. 6 and also visualize them in Fig. 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "content": "To compare against prior work we first compute the inference time in PyTorch eager mode. In eager mode, our base model achieves an inference time of 10.2 milliseconds (ms) on the Gen1 dataset " + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "inline_equation", + "content": "(304 \\times 240" + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "content": " resolution). This implies a latency reduction of " + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "inline_equation", + "content": "6\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "content": " compared to RED and over 3 times lower inference time than ASTMNet. On the the 1 Mpx dataset, at a resolution of " + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "inline_equation", + "content": "640 \\times 360" + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "content": ", our base model takes " + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "inline_equation", + "content": "11.9\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 343, + 287, + 450 + ], + "type": "text", + "content": " for a forward pass, which is 3 times faster than RED and over 5 times faster than ASTMNet." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "text", + "content": "Even on a T4 GPU, most of the inference time is framework overhead. To overcome this partially, we use the JIT compilation feature torch.compile of PyTorch 2 [37]. As Tab. 6 shows, this almost halves the inference time for RVT-B on the 1 Mpx dataset and reduces the inference time by a factor of 2.7 on the Gen1 dataset. As expected, the small and tiny models benefit even more from JIT compilation. For example, RVT-T only takes " + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "inline_equation", + "content": "2.3\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "text", + "content": " for a forward pass on Gen1 and " + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "inline_equation", + "content": "3.5\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "text", + "content": " on 1 Mpx. On a RTX 3090 GPU, RVT-B completes a forward pass in " + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "inline_equation", + "content": "2.8\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 452, + 287, + 594 + ], + "type": "text", + "content": " on the 1 Mpx dataset, which shows the potential for low-latency inference if power consumption is less of a concern." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 609, + 201, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 201, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 201, + 621 + ], + "type": "text", + "content": "5. Discussion and Limitations" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "We use a very simple event representation which does not leverage the full potential of event-based data. For example, we only have a weak prior on the order of events because we process the temporal dimension directly with fully connected layers. Recent work has shown substantial gains by introducing temporal convolutions in early layers [26]. Efficient low-level processing of event data is still an open" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 270, + 539, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 539, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 539, + 282 + ], + "type": "text", + "content": "research problem that we have not addressed in this work." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 283, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 545, + 415 + ], + "type": "text", + "content": "Our approach currently only uses event streams to detect objects. Frames yield complementary information that, when properly incorporated, will yield significantly enhanced detection performance. For example, in Fig. 4 (d) we can see that our model can retain information over some period when no events are available. Still, the memory of the network will fade and detection performance deteriorates. High quality frames even at low frame-rate could provide the missing complementary information. Hence, we believe that a multi-modal extension of our method on a suitable dataset [17, 25] is a promising next step." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 424, + 378, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 424, + 378, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 424, + 378, + 436 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 444, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 612 + ], + "type": "text", + "content": "We introduced a novel backbone architecture for object detection with event cameras. The architecture consists of a stage design that is repeatedly applied to create a multistage hierarchical neural network. Each stage compactly incorporates convolutional priors, local- and sparse global attention and recurrent feature aggregation. Our experiments highlight that recurrent vision transformers can be trained from scratch to reach state-of-the-art performance in object detection with event cameras. The resulting canonical stage-design is directly compatible with existing detection frameworks, and paves the way to low-latency object detection with event cameras on conventional hardware. Nonetheless, we hope that this work also inspires novel designs in future neuromorphic systems." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 621, + 410, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 410, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 410, + 635 + ], + "type": "text", + "content": "7. Acknowledgment" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "This work was supported by the National Centre of Competence in Research (NCCR) Robotics (grant agreement No. 51NF40-185543) through the Swiss National Science Foundation (SNSF), and the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT)." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13891" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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However, previous approaches suffer from severe label bias due to over-reliance on sparse timestamp annotations, resulting in unsatisfactory performance. In this paper, we propose the Debiasing-TSTAS (D-TSTAS) framework by exploiting unannotated frames to alleviate this bias from two phases: 1) Initialization. To reduce the dependencies on annotated frames, we propose masked timestamp predictions (MTP) to ensure that initialized model captures more contextual information. 2) Refinement. To overcome the limitation of the expressiveness from sparsely annotated timestamps, we propose a center-oriented timestamp expansion (CTE) approach to progressively expand pseudo-timestamp groups which contain semantic-rich motion representation of action segments. Then, these pseudotimestamp groups and the model output are used to iteratively generate pseudo-labels for refining the model in a fully supervised setup. We further introduce segmental confidence loss to enable the model to have high confidence predictions within the pseudo-timestamp groups and more accurate action boundaries. Our D-TSTAS outperforms the state-of-the-art TSTAS method as well as achieves competitive results compared with fully supervised approaches on three benchmark datasets.", + "bbox": [ + 75, + 323, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 731, + 209, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Analyzing and understanding human actions in videos is very important for many applications, such as human-robot interaction [14] and healthcare [33]. Recently, several approaches have been very successful in locating and analyzing activities in videos, including action localization [12,29,37,50], action segmentation [7,11,20,23], and action recognition [9,27,39,41,47].", + "bbox": [ + 75, + 757, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf5bfc0152e64ea74b29cc542fe2e15daca8d2cc94da39d2250d9d1106a0584a.jpg", + "image_caption": [ + "(c) Representation bias during the refining phase.", + "Figure 1. (a) The TSTAS task aims to segment actions in videos by timestamp annotations. (b) An example of focus bias: existing initialization methods prefer to predict frames similar to the annotated timestamp, leading to incorrectly identifying dissimilar frames within the segment and similar frames outside the segment. (c) An example of representation bias: the frames of complex action share large semantic variance, e.g. the process of cutting cheese includes both taking out and cutting, resulting in the models that rely on sparse timestamps to produce biased pseudo-labels." + ], + "image_footnote": [], + "bbox": [ + 519, + 290, + 859, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the success of previous approaches, they rely on fully temporal supervision, where the start and end frames of each action are annotated. As a lightweight alternative, many researchers have started exploring timestamp supervised temporal action segmentation (TSTAS), where each action segment is annotated with only one frame in the untrimmed video, as shown in Fig. 1 (a).", + "bbox": [ + 496, + 611, + 892, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most previous approaches follow a two-step pipeline by initializing and then iteratively refining the model with generated pseudo-labels. However, relying only on supervised signals of sparse single-timestamp annotations, these methods fail to learn the semantics of entire action segments, which is referred to as label bias in this paper, including focus bias and representation bias. Specifically, to initialize the segmentation model, the previous methods [17, 28, 32] adopt the Naive approach proposed in [28] (referred to as Naive), which computes the loss at the annotated frames for training. However, utilizing only the annotated frames leads to focus bias, where the initialized model tends to fo", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work.", + "bbox": [ + 94, + 875, + 351, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 222, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6503", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cus on frames distributed over segments of various action categories similar to the annotated frames [51] (shown in Fig. 1 (b)).", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "During refining the segmentation model, to utilize the unlabeled frames, typical methods generate hard [17,28,51] or soft weighted [32] pseudo-labels that are used to refine the model like fully supervised methods. To generate pseudo-labels, the above methods depend on the timestamps that contain semantic or relative position information. Despite the success of such refined models, these approaches suffer from representation bias that single-frame fails to represent the entire action segment for complex actions with the large semantic variance of various frames (illustrated in Fig. 1 (c)). Moreover, when refining the segmentation model by these biased pseudo-labels, representation bias can be accumulated and expanded, resulting in unsatisfactory performance that is still a gap compared to fully supervised approaches.", + "bbox": [ + 75, + 138, + 468, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel framework called Debiasing-TSTAS (D-TSTAS) to reduce label bias, containing masked timestamp predictions and center-oriented timestamp expansion approaches. During the initialization phase, we aim to alleviate the focus bias problem by propagating timestamp supervision information to the contextual frames of the timestamps. In contrast to previous approaches, we propose the Masked Timestamp Predictions (MTP) approach that masks the input features of timestamps to remove the dependencies of the model on annotated frames. In this way, the initialized model is forced to reconstruct the annotated frames in corresponding output features and then predict their action categories by contextual information of timestamps. Furthermore, to capture the semantics of both timestamps and contextual frames, we adopt the Naive after our MTP.", + "bbox": [ + 75, + 368, + 468, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While our initialized model can reduce focus bias by capturing more contextual information, it does not guarantee that the generated pseudo-labels avoid representation bias during refining. Inspired by query expansion, we propose a Center-oriented Timestamp Expansion (CTE) approach for obtaining potential trustworthy unlabeled frames, which we refer to as pseudo-timestamps, to progressively expand the pseudo-timestamp groups that contain more semantics than single annotated timestamps. More specifically, it consists of three steps: 1) In the generating step, we generate pseudo-labels by current pseudotimestamp groups and the model output. 2) In the updating step, we choose the semantically dissimilar center frames of each segment in the pseudo-labels as pseudo-timestamps to expand the pseudo-timestamp groups. 3) In the segmenting step, the model is refined by pseudo-labels and our segmental confidence loss, which smooths the predicted probabilities in each action segment and maintains high confidence within pseudo-timestamp groups. The above steps are ex", + "bbox": [ + 75, + 613, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ecuted several times alternately to improve the model prediction in a lazy manner instead of generating pseudo-labels per epoch in previous methods [28, 51].", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarised as follows:", + "bbox": [ + 517, + 137, + 841, + 150 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We study the label bias in the TSTAS task and propose a novel D-TSTAS framework to reduce both focus and representation bias.", + "- Our masked timestamp predictions approach is the first attempt to alleviate the dependencies on timestamps, promoting the model to capture contextual information. Coupling MTP and Naive as a general solution is used to initialize the model in the TSTAS.", + "- Compared to sparsely annotated timestamps, our center-oriented timestamp expansion approach progressively expands pseudo-timestamp groups to contain semantic-rich motion representations of action segments.", + "- The proposed D-TSTAS not only outperforms state-of-the-art TSTAS approaches but also achieves competitive results compared with fully supervised approaches on three benchmark datasets." + ], + "bbox": [ + 517, + 160, + 890, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 459, + 640, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Temporal Action Segmentation", + "text_level": 1, + "bbox": [ + 500, + 484, + 774, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fully Supervised Action Segmentation has been attracting increasing attention. In contrast to action recognition where trimmed videos are classified [5, 22, 30, 39, 48], temporal action segmentation requires modeling long-range dependencies to predict all the frames in the video. To achieve a larger receptive field, many approaches utilized dilated temporal convolutional networks to capture local and global dependencies [7, 25]. Despite the success of these approaches, they suffer from an over-segmentation error. To alleviate this problem, current state-of-the-art methods follow the architecture that refines the initial predictions [1, 15, 26, 40, 49] or integrates text prompts [24]. The above fully supervised approaches rely on frame-wise annotations, which are expensive to obtain.", + "bbox": [ + 496, + 508, + 890, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Timestamp Supervised Action Segmentation only requires a single annotated frame for each action segment. Most previous methods [17, 28, 32, 51] apply a two-phase training scheme, initializing by Naive [28] (also called the warmup phase [51]) and then iteratively refining the learned model with generated pseudo-labels. Unlike these methods, UVAST [3] directly refines the model by generating pseudo-labels from the constrained k-medoids algorithm based on input features. Moreover, in the specific action field (surgical phase recognition), Ding et al. [6] generate only partial pseudo-labels. While the above methods for generating pseudo-labels are highly dependent on annotated", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6504", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/689744a32b046a8c7ba32e48426ba381aa91415b26b71a187054207d82b89eca.jpg", + "image_caption": [ + "Initialize Model with MTP Segmentation Model" + ], + "image_footnote": [], + "bbox": [ + 143, + 104, + 504, + 200 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dba19a30393561ee054a788130710be638b6c8aee159aa60927110c00f46eb80.jpg", + "image_caption": [ + "Refine Model with CTE" + ], + "image_footnote": [], + "bbox": [ + 511, + 104, + 830, + 200 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f9daa2bd03caa304a16ee017a4f0575402be7c7f89e13404cd4247057a34cd8.jpg", + "image_caption": [ + "Segmentation Model", + "Figure 2. The pipeline of our proposed framework consists of two phases: initialize the segmentation model (in Sec. 3.2) with masked timestamp predictions (MTP in Sec. 3.3) and refine the model with center-oriented timestamp expansion (CTE in Sec. 3.4). The overall losses are introduced in Sec. 3.5. GPL is the abbreviation for generating pseudo-labels." + ], + "image_footnote": [], + "bbox": [ + 140, + 213, + 506, + 318 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4e3e609e43e899c0c507d90cd2430d8d262074efb7d7214e4e65e3a11e73038f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 513, + 203, + 828, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "timesteps, the semantic representation of the timestamps is limited. Different from the previous solutions, we propose MTP to enable the initialized model to capture contextual information and CTE to enrich pseudo-timestamp groups instead of single timestamps.", + "bbox": [ + 75, + 380, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Self-Supervised Learning", + "text_level": 1, + "bbox": [ + 76, + 467, + 308, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In image and video tasks, self-supervised learning has been successful for its ability to learn information feature representations without human supervision. Most of the previous works were based on the spatial-temporal orders of videos by designing an auxiliary task related to the main task where the labels can be self-annotated [2,18,21,44,46]. Inspired by the success of the vision transformer, masked modeling is widely used in image [13, 42] and video modeling [10, 38]. Unlike these works, our proposed MTP predicts categories of annotated frames by using contextual information, aiming to address the problem of focus bias for timestamp supervised action segmentation.", + "bbox": [ + 75, + 491, + 468, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Debiasing-TSTAS Framework", + "text_level": 1, + "bbox": [ + 76, + 686, + 392, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present the details of our D-TSTAS. In Sec. 3.1, we first introduce the task of timestamp supervision and the pipeline of D-TSTAS, and the segmentation model is described in Sec. 3.2. Then, the masked timestamp predictions and the center-oriented timestamp expansion are proposed in Sec. 3.3 and Sec. 3.4, respectively. Finally, we provide the details of the loss functions in Sec. 3.5.", + "bbox": [ + 75, + 713, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem statement and pipeline", + "text_level": 1, + "bbox": [ + 76, + 830, + 357, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a video $X = \\{x_{t}\\}_{t=1}^{T}$ with $T$ frames and $N$ action segments ( $N \\ll T$ ), the fully supervised temporal action segmentation requires high-cost frame-wise annota", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tions for training and aims to predict a sequence of framewise action labels. In contrast to the fully supervised approaches, we consider efficient timestamp supervised segmentation, which provides a set of annotated timestamps $A_{Ts} = \\{(a_n,t_n)\\}_{n = 1}^N$ , where frame $t_n$ belongs to the $n$ -th action segment and $a_n$ is the label $n$ -th of action segment. While the annotation time of timestamp supervision is much less than that of the fully supervised setup, there is still a large gap in performance.", + "bbox": [ + 496, + 380, + 890, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve comparable performance to the fully supervised methods, we propose a framework named D-TSTAS, including an Initialization phase and a Refinement phase, as shown in Fig. 2. Specifically, following the previous [7, 16, 40, 49], we extract I3D [4] features $X' = \\{x_t'\\}_{t=1}^T$ as the input to our segmentation model. Then, to reduce focus bias, we initialize our model by masked timestamp predictions (MTP) and Naive [49] for capturing more contextual information. To further reduce representation bias, we propose the center-oriented timestamp expansion (CTE) to expand the progressive pseudo-timestamp groups and refine the segmentation model by generating pseudo-labels.", + "bbox": [ + 496, + 517, + 892, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. The segmentation model", + "text_level": 1, + "bbox": [ + 500, + 710, + 723, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The architecture of our segmentation model is shown in Fig. 2. We build a Transformer backbone of the cascaded encoder-decoder network structure [49], which contains an encoder and $H$ -1 decoders. The linear attention [45] is applied in our backbone to balance training efficiencies and performance, which is beneficial for modeling long sequences. More details of the segmentation model are described in the supplementary material. We also explore the effect of Temporal Convolutional Network (TCN) [17, 28] or our backbone and compare the different attentions in the backbone as illustrated in Sec. 4.7.", + "bbox": [ + 496, + 734, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6505", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Reducing the focus bias by MTP", + "text_level": 1, + "bbox": [ + 76, + 90, + 362, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As mentioned before, the previous initialization [17, 28, 32] suffers from focus bias. In this paper, we propose masked timestamp predictions (MTP) to reduce this bias as shown in Fig. 2. Specifically, given the input feature $X'$ , we mask the I3D feature $x_{t_n}'$ of annotated timestamps by a shared learnable token to reduce the dependency of the model on annotated timestamps. The input feature of the unannotated frames is used to generate output feature $F_h$ and predictions of timestamps $P_h$ , where $h = 1, \\dots, H$ , and $H$ denotes the total number of stages (encoder & decoder). To enable our model to involve the semantic information of annotated timestamps, Naive is employed to train the segmentation model after the MTP. The obtained output of our initialized model captures temporal feature representations at different distances from the timestamps by propagating the timestamp supervision information to contextual frames, which is superior to the feature representations obtained by using a Naive alone in typical approaches. Unlike the self-supervised methods [10, 13, 38, 43] that attain a generic pre-trained model by reconstructing input or handcrafted feature descriptor of input, the MTP maps to annotated frames with high-level semantic information (more analyses in Sec. 4.4).", + "bbox": [ + 76, + 113, + 473, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Reducing the representation bias by CTE", + "text_level": 1, + "bbox": [ + 76, + 469, + 431, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the limitation of the expressiveness of the single-frame timestamp, the model tends to produce expressiveness bias for complex action segments, generating incorrect pseudo-labels. Inspired by query expansion, we first propose to use progressive pseudo-timestamp groups $\\mathcal{G}$ to represent the action segments. Compared to the original single annotated frames, pseudo-timestamp groups provide a semantically richer representation of each action segment. We further propose the center-oriented timestamp expansion (CTE) to expand $\\mathcal{G}$ while refining the model. As illustrated in Alg.1, the annotated timestamp set $A_{T_s}$ is first used to initialize $\\mathcal{G} = \\{G_n\\}_{n=1}^N$ , where $G_n = \\{(a_n, t_n^1)\\}$ is the timestamp group of $n-th$ action segment and the $t_n^1$ indicates the first annotated timestamp of the group $G_n$ . Then, the generating step, the segmenting step, and updating step perform $M$ iterations to expand progressive pseudo-timestamp groups $\\mathcal{G}$ and refine the model by generated pseudo-labels $\\hat{Y}$ . The framework of the refined model with the proposed CTE approach is shown in Fig. 2 and we describe the process of the $m-th$ iteration as follows.", + "bbox": [ + 76, + 493, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generating step. Obtain output features of final decoder $F_{H} = \\{f_{t}\\}_{t = 1}^{T}$ and current timestamps groups $\\mathcal{G}$ , generating the frame-wise pseudo-labels can be reduced to estimate the action boundaries between the last timestamp $(a_{i}, t_{i}^{\\Omega(i)})$ of $G_{i}$ and the first timestamp $(a_{i + 1}, t_{i + 1}^{1})$ of $G_{i + 1}$ in temporal order, where $i = 1, \\dots, N - 1$ . Only $N - 1$ boundaries of pseudo-labels are required to be estimated, and $\\Omega(i)$", + "bbox": [ + 76, + 795, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "denotes the number of timestamps in the timestamps group $G_{i}$ . Specifically, the stamp-to-stamp energy function as proposed in [28] is used to detect the action change between $t_{i}^{\\Omega (i)}$ and $t_{i + 1}^{1}$ , and the boundaries of pseudo-label $t_{b_i}$ can be denoted by:", + "bbox": [ + 498, + 90, + 893, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt_{b_{i}} = \\operatorname *{arg min}_{\\hat{t}}\\sum_{\\substack{t = t_{i}^{\\Omega (j)}}}\\hat{t} d(f_{t},e_{i}) + \\sum_{t = \\hat{t} +1}^{t_{j + 1}^{1}}d(f_{t},e_{i + 1}),\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 185, + 851, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "s.t.", + "bbox": [ + 542, + 224, + 563, + 234 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {i} = \\frac {1}{\\hat {t} - t _ {i} ^ {\\Omega (i)} + 1} \\sum_ {t = t _ {i} ^ {\\Omega (i)}} ^ {\\hat {t}} f _ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 236, + 890, + 270 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {i + 1} = \\frac {1}{t _ {i + 1} ^ {1} - t} \\sum_ {t = \\hat {t} + 1} ^ {t _ {i + 1} ^ {1}} f _ {t},\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 271, + 704, + 304 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i} ^ {\\Omega (i)} \\leq \\hat {t} < t _ {i + 1} ^ {1},\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 304, + 668, + 320 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d(\\cdot, \\cdot)$ is the Euclidean distance, $e_i$ is the average of the embedding features between $t_i^{\\Omega(i)}$ and the estimate $\\hat{t}$ , and $e_{i+1}$ is the average of the segmentation feature between the estimate $\\hat{t}$ and $t_{i+1}^1$ . In Eq. (1), the pseudo-boundaries are estimated from the start of the video. The same argument holds if we estimate the pseudo-boundaries at the end of the video. The final pseudo-boundaries for $t_{b_i}$ are the average of these two estimates, which can be expressed as follows:", + "bbox": [ + 500, + 325, + 893, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r} t _ {b _ {i}} = \\frac {t _ {b _ {i} , F W} + t _ {b _ {i} , B W}}{2}, \\\\ s. t. \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 464, + 676, + 492 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {b _ {i}, F W} = \\arg \\min _ {\\hat {t}} \\sum_ {t = t _ {b _ {i - 1}}} ^ {\\hat {t}} d \\left(f _ {t}, e _ {i}\\right) + \\sum_ {t = \\hat {t} + 1} ^ {t _ {i + 1} ^ {1}} d \\left(f _ {t}, e _ {i + 1}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 493, + 890, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt_{b_{i},BW} = \\operatorname *{arg min}_{\\hat{t}}\\sum_{t = t_{i}^{\\Omega (i)}}^{\\hat{t}}d\\left(f_{t},e_{i}\\right) + \\sum_{t = \\hat{t} +1}^{t_{b_{i} + 1}}d\\left(f_{t},e_{i + 1}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 529, + 859, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i} ^ {\\Omega (i)} \\leq \\hat {t} < t _ {i + 1} ^ {1},\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 564, + 643, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "thus, we get the pseudo-boundaries $B = \\{t_{b_j}\\}_{j=0}^N$ , which $t_{b_0} = 0$ and $t_{b_N} = T$ . To generate the pseudo-labels $\\hat{Y} = \\{\\hat{y}_t\\}_{t=1}^T$ , we assign the frames between $t_{b_{n-1}}$ and $t_{b_n}$ to the same action label $a_n$ .", + "bbox": [ + 500, + 587, + 893, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Updating step. Our approach relies on the progressive pseudo-timestamp groups $\\mathcal{G}$ that contain more semantic and positional information to detect pseudo-boundaries. To enrich the $\\mathcal{G}$ , we need to find potentially trustworthy pseudo-timestamps that are not semantically similar to original timestamps. For finding potentially trustworthy pseudo timestamps, we intuitively choose the center frames of each segment in the pseudo-labels, which are expressed as $C = \\{(a_n, t_{c_n})\\}_{n=1}^N$ , and", + "bbox": [ + 498, + 651, + 893, + 789 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {c n} = \\frac {t _ {b _ {n - 1}} + t _ {b _ {n}}}{2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 796, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since adjacent frames usually have similar semantic information in the video, new pseudo-timesteps close to the $G_{n}$ might fail to reduce representation bias. To alleviate this problem, we keep a minimum temporal threshold $D$ between the new pseudo-timesteps and the latest", + "bbox": [ + 498, + 825, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6506", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Refine Model with Center-oriented Timestamp Expansion" + ], + "code_body": "Input: I3D features $X^{\\prime}$ , annotated timestamps $A_{Ts}$ and segmentation model $\\mathcal{M}$ \nOutput: Refined segmentation model $\\mathcal{M}$ \n1: Initialize $\\mathcal{G}$ and $R$ by $A_{Ts}$ \n2: for $m = 1,\\dots,M$ do \n3: D Generating step. \n4: $F_{H}\\gets ExtractFeature(X^{\\prime},\\mathcal{M})$ see Eq.2 \n5: $B\\gets$ EstimateBoundaries $(F_H,\\mathcal{G})$ \n6: $\\hat{Y}\\gets$ GeneratePseudoLabels(B, $\\mathcal{G}$ \n7: D Updating step. \n8: $(\\mathcal{G},R)\\gets$ Update $(\\hat{Y},\\mathcal{G},R)$ \n9: D Segmenting step. \n10: for $k = 1,\\ldots ,K$ do \n11: $\\mathcal{M}\\gets$ RefineModel $(\\mathcal{M},X^{\\prime},\\hat{Y},\\mathcal{G},\\mathcal{L}_{refine})$ \n12: end for \n13: end for", + "bbox": [ + 76, + 125, + 467, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "added pseudo-timesteps, i.e., $|t_{c_n} - t_{r_n}| > D$ , where $R = \\{t_{r_n}\\}_{n=1}^N$ denotes the location of the latest added pseudo-timesteps each iteration (initially, $t_{r_n} = t_n$ ). Besides, the value of the new pseudo timestamp $t_{c_n}$ is assigned to $t_{r_n}$ . Finally, we obtain the new pseudo-timestamp groups $\\mathcal{G}$ that are utilized for the next iteration.", + "bbox": [ + 76, + 311, + 467, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Segmenting step. To further improve the quality of the predictions, we refine the segmentation model with the pseudo-labels $\\hat{Y}$ , new pseudo-timestamp groups $\\mathcal{G}$ , and loss functions $\\mathcal{L}_{\\text{refine}}$ (described in Sec. 3.5) through $K$ training epochs.", + "bbox": [ + 76, + 402, + 468, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 491, + 228, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we use the same loss as baseline [28] to initialize the model with MTP and Naive, which can be formulated as follows:", + "bbox": [ + 76, + 515, + 467, + 558 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n i t}} = \\mathcal {L} _ {c e} + \\lambda \\mathcal {L} _ {\\text {t m s e}} + \\beta \\mathcal {L} _ {\\text {c o n f}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 575, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{ce}$ , $\\mathcal{L}_{tmse}$ , and $\\mathcal{L}_{conf}$ are the cross-entropy loss based on the annotated timestamps, smoothing loss [7], and confidence loss [28], respectively. $\\lambda$ and $\\beta$ are hyperparameters utilized to balance the contribution of each loss.", + "bbox": [ + 76, + 604, + 467, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the refinement of the model with CTE, we adapt weighted cross-entropy loss $\\mathcal{L}_{wce}$ to replace cross-entropy loss $\\mathcal{L}_{cls}$ , which can alleviate the imbalance problem in the frequency of different action segments for each action category [15]. Unlike the [15], to get the class weight, we calculate the median of class frequencies divided by each class frequency through pseudo-labels that approximate ground truth. The previous methods [17,28,32] typically apply confidence loss proposed in [28] so that the probability of prediction decreases monotonically with increasing distance from the timestamp. However, due to focus monotonicity outside the segments, the confidence loss leads to the blurring of the boundaries of the action segments.", + "bbox": [ + 76, + 666, + 467, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Segmental confidence loss. Unlike confidence loss $\\mathcal{L}_{conf}$ , we propose segmental confidence loss $\\mathcal{L}_{sconf}$ to smooth the predicted probabilities within the action seg", + "bbox": [ + 76, + 859, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ba939c01cc6aa707ca9dd3b181cdb33d7f1f8028122d7ab1b0e8f50bc9614466.jpg", + "image_caption": [ + "Figure 3. The segmental confidence loss penalizes decreasing predictions within the red range $(t_{b_{n-1}}$ to $t_n^{\\Omega(n)}$ and increasing predictions in the green range $(t_n^1$ to $t_{b_n}$ ) for label $a_n$ ." + ], + "image_footnote": [], + "bbox": [ + 535, + 90, + 861, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ments of pseudo-labels.", + "bbox": [ + 500, + 265, + 658, + 279 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {s c o n f} = \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {b _ {n - 1}}} ^ {t _ {n} ^ {\\Omega (n)}} \\delta_ {a _ {n}, 1}\\right) / T _ {1} + \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {n} ^ {1}} ^ {t _ {b _ {n}}} \\delta_ {a _ {n}, 2}\\right) / T _ {2}, \\\\ \\delta_ {a _ {n}, 1} = \\max \\left(0, p _ {a _ {n}, t - 1} - p _ {a _ {n}, t}\\right), \\\\ \\delta_ {a _ {n}, 2} = \\max \\left(0, p _ {a _ {n}, t} - p _ {a _ {n}, t - 1}\\right), \\\\ T _ {1} = \\sum_ {n = 1} ^ {N} \\left(t _ {n} ^ {\\Omega (n)} - t _ {b _ {n - 1}}\\right), \\\\ T _ {2} = \\sum_ {n = 1} ^ {N} \\left(t _ {b _ {n}} - t _ {n} ^ {1}\\right), \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 282, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_{a_n,t}$ is the probability of action $a_n$ at time $t$ . $\\delta_{a_n,1}$ and $\\delta_{a_n,2}$ are decreasing penalized predictions and increasing penalized predictions as illustrated in Fig. 3. $T_1$ and $T_2$ are the total sum of frames of $\\delta_{a_n,1}$ and $\\delta_{a_n,2}$ , respectively. The effect of our loss function is visualized as shown in Fig. 5, which can prevent boundary blur caused by prediction monotonicity outside the action segments and keeps consistent high confidence between $t_n^1$ and $t_n^{\\Omega(n)}$ .", + "bbox": [ + 498, + 411, + 890, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function to refine the segmentation model with CTE is as follows:", + "bbox": [ + 498, + 532, + 890, + 560 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {w c e} + \\lambda \\mathcal {L} _ {t m s e} + \\gamma \\mathcal {L} _ {s c o n f}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 571, + 890, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ and $\\gamma$ are hyper-parameters to balance the contribution of each loss.", + "bbox": [ + 498, + 598, + 888, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 641, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and evaluation", + "text_level": 1, + "bbox": [ + 500, + 666, + 718, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Following the previous works [17, 32, 51], we evaluate our approach on three datasets: 50Salads [36], Breakfast [19], and Georgia Tech Egocentric Activities (GTEA) [8]. We perform 4-fold cross-validation on Breakfast and GTEA, and 5-fold cross-validation on 50Salads.", + "bbox": [ + 498, + 688, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 50Salads dataset contains 50 videos (0.6M frames) with actors preparing different kinds of salads. It consists of 17 action classes which are recorded from the top view. On average, the video duration is 6.4 minutes long and each video has 20 action instances. The Breakfast dataset consists of 1712 third-person view videos (3.6M frames) related to breakfast preparation activities. There are 48 different action classes that were recorded in 18 different kitchens. The average video duration ranges from a few", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6507", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "seconds to several minutes and each video contains 6 action instances on average. The GTEA dataset contains 58 videos (32K frames) with actors performing various kinds of daily activities. It consists of 11 action classes. The average video duration is 1 minute long.", + "bbox": [ + 75, + 90, + 467, + 166 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For all datasets, our experimental results are reported for three random seeds used for annotating frames in videos. Only in Tab. 8, we use the same annotations that Li et al. [28] provide for a fair comparison.", + "bbox": [ + 75, + 167, + 467, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following previous works [7, 26], we use the standard metrics for fully supervised temporal action segmentation and report the frame-wise accuracy (Acc), segmental edit distance (Edit) and segmental F1 scores with overlapping thresholds of $10\\%$ , $25\\%$ , and $50\\%$ , denoted by $F1@{10,25,50}$ .", + "bbox": [ + 75, + 227, + 467, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 329, + 290, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We set $H = 4$ as in [49] and train our model for 290 epochs, including 80 epochs for MTP, 30 epochs for Naive, and 180 ( $K = 30$ , $M = 6$ ) epochs for CTE. $D$ is set to $\\{5, 20, 10\\}$ for GTEA, 50Salads, and Breakfast, which is related to the average action duration. The batch size is 8 and an AdamW optimizer with a learning rate of 0.0005 and weight decay of 0.05 is used. For the loss function, we set $\\lambda = 0.15$ , $\\beta = 0.075$ as in [28], and set $\\gamma = 1$ . All experiments in the comparison study use the above setting and are conducted with NVIDIA GeForce RTX 2080 Ti GPUs.", + "bbox": [ + 75, + 352, + 467, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Effectiveness of MTP", + "text_level": 1, + "bbox": [ + 76, + 513, + 276, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first compare the initialization of the MTP and Naive [28] on TCN backbone [28] and our backbone. As shown in Tab. 1, our approach outperforms Naive with a large margin F1 and edit scores. This is because the Naive initialized model by only using sparse timestamps, the model produces focus bias, incorrectly recognizing frames in various action categories similar to annotated frames. On the contrary, our approach reduces focus bias by masking the timestamps and predicting the category of annotated frames using contextual information. Moreover, we combine MTP and Naive to generate better initialized predictions by exploiting semantic information with annotated timestamps and the context of annotated frames. These are also reflected in the performance as illustrated in Fig. 4. We also evaluate the order of MTP and Naive in the supplementary.", + "bbox": [ + 75, + 537, + 467, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further explore the effectiveness of the MTP, we explore the impact of different initialization strategies on the refinement model, as shown in Tab. 2. To conduct a fair comparison, the same refinement approach in [28], containing 20 epochs of training, is used to refine the model. While our MTP gives an additional boost in performance, the best performance is achieved when MTP and Naive are combined. This illustrates that a good initialization model is beneficial for refining the model. While the MTP of the", + "bbox": [ + 75, + 763, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1a19a98e0ca06d3609ba8e57a2ce3064ae96a5190e627f4bedccd310cd7cd5ef.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
InitializationGTEA50Salads
F1@{10, 25, 50}EditAccF1@{10, 25, 50}EditAcc
TCNNaive59.755.339.651.156.547.943.334.0
MTP63.459.745.956.453.459.855.144.9
MTP+Naive74.468.152.167.262.860.255.745.5
oursNaive47.442.133.045.147.641.336.125.3
MTP67.662.747.361.060.555.451.140.9
MTP+Naive77.072.456.170.565.462.658.147.4
", + "bbox": [ + 504, + 88, + 888, + 178 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/80ad9b4a354aaa43169a5c0ae60af0011399aab00285f7f0de4f98fa3c14c452.jpg", + "table_caption": [ + "Table 1. Impact of different initialization strategies and backbones without refinement on GTEA and 50Salads datasets." + ], + "table_footnote": [], + "table_body": "
InitializationGTEA50Salads
F1@{10,25,50}EditAccF1@{10,25,50}EditAcc
TCNNaive78.973.055.472.366.473.970.960.166.8
MTP81.476.958.575.966.871.568.358.865.5
MTP+Naive84.079.060.479.567.872.069.058.664.6
oursNaive76.071.455.371.769.072.067.954.764.9
MTP82.679.661.677.570.273.969.458.267.0
MTP+Naive86.283.266.382.772.074.571.160.067.3
", + "bbox": [ + 506, + 213, + 887, + 304 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Impact of different initialization strategies and backbones with refinement [28] on GTEA and 50Salads datasets.", + "bbox": [ + 500, + 304, + 888, + 329 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22c2fdb7e8aee2f1906d6e634e4ed10dcaf2f28438d17e5cbb993076da821096.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of the different initialization strategies with TCN backbone [28] on the 50Salads dataset. Naive only correctly identifies frames close to the timestamp, which are also similar frames to annotated timestamps. MTP reduces this bias by directing the model to capture contextual information, but the boundaries of segments are not accurate. Adding Naive after MTP generates better predictions as the model exploits semantic information with annotated timestamps and the context of annotated frames." + ], + "image_footnote": [], + "bbox": [ + 513, + 339, + 879, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TCN backbone on 50Salads achieves good frame-wise accuracy, it suffers from over-segmentation during refining as evidenced by the low F1 and Edit scores. Meanwhile, our backbone based on Transformer can alleviate this problem.", + "bbox": [ + 498, + 556, + 888, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Impact of mapping target for MTP", + "text_level": 1, + "bbox": [ + 500, + 628, + 803, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our approach initializes the model by mapping the masked features to the label of timestamps (Feature-to-Label), which is described in Sec. 3.3. To analyze the impact of the mapping target, we train another model (Feature-to-Feature) that minimizes the $l_{2}$ distance between the output feature $f_{t_n}$ and the input I3D feature $x_{t_n}'$ . Specifically, we use an additional linear layer to adjust the dimensions of $f_{t_n}$ to match the dimensions of the $x_{t_n}'$ . For a fair comparison, the Feature-to-Feature model follows the same initialization method (MTP+Native) and refinement method [28] based on our backbone as Feature-to-Label. As shown in Tab. 2 and Tab. 3, compared to the Naive, Feature-to-Feature slightly improves the performance, which validates that the masking strategy achieves better initialization", + "bbox": [ + 496, + 652, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "Since there is no timestamp on the test set, we visualize the focus bias clearly by timestamps and predictions on the training set.", + "bbox": [ + 500, + 875, + 888, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6508", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f62b2e29e3a8c09385f15b9d761aa3f1b2fce0ff3e66e75996ac407ee9378797.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetTargetF1@{10,25,50}EditAcc
GTEAFeature-to-Feature75.672.456.865.571.2
Feature-to-Label86.283.266.382.772.0
50SaladsFeature-to-Feature72.369.158.965.875.9
Feature-to-Label74.571.160.067.377.6
", + "bbox": [ + 91, + 88, + 459, + 150 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8ae8b3e672e259e9b621dcde1e172a19466e2e69ef5c299422cf78e361b5408e.jpg", + "table_caption": [ + "Table 3. Impact of mapping target for MTP on GTEA and 50Salads datasets." + ], + "table_footnote": [], + "table_body": "
RefinementF1@{10, 25, 50}EditAcc
baseline [28] (epoch = 20)74.571.160.067.377.6
CTE (K = 10, M = 2)76.473.162.669.677.5
", + "bbox": [ + 91, + 184, + 459, + 224 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b0408ad36c58dc488ef201366807338969e2dde90c4f294ca0a31b975666bcaf.jpg", + "table_caption": [ + "Table 4. Comparison with the baseline in the refining phase on the 50Salads dataset." + ], + "table_footnote": [], + "table_body": "
Impact of KF1@{10, 25, 50}EditAccAccPLAccTS
CTE (K=10, M=6)80.177.866.372.978.087.197.3
CTE (K=20, M=6)82.880.669.675.779.187.397.2
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=40, M=6)83.581.371.276.780.087.297.0
Impact of MF1@{10, 25, 50}EditAccAccPLAccTi
CTE (K=30, M=2)81.078.468.074.179.788.697.9
CTE (K=30, M=4)83.280.670.476.379.887.897.4
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=30, M=8)83.781.970.377.879.286.497.0
CTE (K=30, M=10)83.781.069.576.578.885.696.4
", + "bbox": [ + 84, + 258, + 465, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of the model. However, it performed worse than Feature-to-Label. This is mainly because Feature-to-Label promotes the model to capture high-level semantic information, which is beneficial for the propagation of supervised signals of timestamps to unlabeled frames in the TSTAS task. We also discuss the number of masked frames with Feature-to-Label and Feature-to-Feature (please refer to the supplementary).", + "bbox": [ + 75, + 472, + 467, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Effectiveness of CTE", + "text_level": 1, + "bbox": [ + 76, + 603, + 272, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of the proposed CTE during the refining phase, we compare the CTE with the baseline that employs the refining approach [28] and perform the comparison experiments based on our initialized model. As shown in Tab. 4, our approach outperforms the baseline. This is because our method captures more semantic information within the action segment compared to the baseline by expanding the timestamp groups. As shown in Tab. 5, the addition of pseudo-labels is trustworthy, and pseudotimestamp groups are used to generate better pseudo-labels, as indicated by the high accuracy of pseudo-labels and timestamps. The effect of CTE can also be seen in the qualitative result, please refer to the supplementary.", + "bbox": [ + 75, + 626, + 467, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Ablation Study of CTE", + "text_level": 1, + "bbox": [ + 76, + 832, + 290, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The effect of the center-oriented timestamp expansion is controlled by two hyper-parameters: $K$ and $M$ . In this section, we study the impact of the two parameters with differ", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0e6ba8f00c44fe0b1e9a8f541aede64fc1e5458e0c9bd21f76ca24e8830b857e.jpg", + "table_caption": [ + "Table 5. Impact of epoch-per-segmentation step $K$ and the number of iterations $M$ in CTE on 50Salads dataset. AccPL and AccTS denote the accuracy of pseudo-labels and timestamps for each video, respectively." + ], + "table_footnote": [], + "table_body": "
StrategiesGTEA
F1@{10,25,50}EditAcc
Local attentionNaive69.762.745.462.059.8
MTP75.572.453.372.064.8
MTP+Naive77.473.654.971.166.3
MTP+Naive+CTE89.186.874.585.573.2
Linear attentionNaive47.442.133.045.147.6
MTP67.662.747.361.060.5
MTP+Naive77.072.456.170.565.4
MTP+Naive+CTE91.590.176.288.575.7
", + "bbox": [ + 516, + 88, + 880, + 199 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cbb0a6e009a9f393063e14987b971c4fd9b6e5d90f8a6aefe22da10a479100f6.jpg", + "table_caption": [ + "Table 6. Impact of different attention architectures in our backbone on the GTEA dataset." + ], + "table_footnote": [], + "table_body": "
LceLwceLconfLsconfF1@{10,25,50}EditAcc
✓✓82.579.968.576.278.7
✓✓83.881.170.676.679.4
✓✓82.980.465.876.875.6
✓✓84.282.171.577.680.0
", + "bbox": [ + 514, + 234, + 879, + 296 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Comparing different loss functions on the 50Salads dataset.", + "bbox": [ + 500, + 297, + 890, + 323 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cbf7328aba42b7f8d5a893447220bef2e68ca75d1ba304f5b4d82f5e1a7298cf.jpg", + "image_caption": [ + "Figure 5. Quality comparison of confidence loss [28] and segmental confidence loss." + ], + "image_footnote": [], + "bbox": [ + 519, + 335, + 696, + 391 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ea6da613492c348b5c7d4c54f5fb4dbc5e177f8bb1455248e9fae536e6d52dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 335, + 870, + 390 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ent values of $K$ and $M$ , as shown in Tab. 5.", + "bbox": [ + 500, + 441, + 787, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of epoch-per-segmentation stage $K$ . The parameter of $K$ affects the refinement model by using the same pseudo-labels in the segmenting step. Our default value is $K = 30$ . Increasing the value $K$ from 10 to 30 achieves better performance because sufficient training epochs lead to better convergence. However, setting $K = 40$ results in a slight drop in performance compared with a default value. This drop in performance is due to the over-fitting problem.", + "bbox": [ + 498, + 455, + 890, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of the number of iterations $M$ . This hyperparameter defines the number of times to supplement the timestamp groups and generate pseudo-labels. Reducing $M$ to 2 still improves the performance but is not as good as the default value of $M = 6$ . Increasing its value to $M = 10$ also causes a degradation in performance. This drop in performance is because adding the incorrect pseudo-timestamp results in a decrease in the accuracy of the pseudo-labels, which affects the predictions of the refinement model.", + "bbox": [ + 498, + 593, + 890, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.7. Impact of the backbones", + "text_level": 1, + "bbox": [ + 500, + 739, + 723, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our backbone with TCN [28] backbone as shown in Tab. 1 and Tab. 2. When the Naive is used alone, our backbone causes worse performance in the initialization and refinement phase compared with the TCN backbone. This is because the linear attention in our backbone with the Naive approach incorrectly identifies more frames with semantic similarity to timestamps by capturing global dependencies. In contrast, MTP can improve the performance of our backbone by a large margin, which indicates", + "bbox": [ + 498, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6509", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b1780e15f8ed734c8827899fe0013e5455492c0870f6aba875109002bfcc6363.jpg", + "table_caption": [], + "table_footnote": [ + "Table 8. Comparison with different levels of supervision on all three datasets. D-TSTAS uses the backbone that combines the cascaded encoder-decoder network structure [49] and the linear attention architecture [45]." + ], + "table_body": "
SupervisionMethodGTEA50SaladsBreakfast
F1@{10,25,50}EditAccF1@{10,25,50}EditAccF1@{10,25,50}EditAcc
FullyMS-TCN [7]87.585.474.681.479.276.374.064.567.980.752.648.137.961.766.3
MS-TCN++ [25]88.885.776.083.580.180.778.570.174.383.764.158.645.965.667.6
BCN [40]88.587.177.384.479.882.381.374.074.384.468.765.555.066.270.4
ASRF [16]89.487.879.883.777.384.983.577.379.384.574.368.956.172.467.6
ASFormer [49]90.188.879.284.679.785.183.476.079.685.676.070.657.475.073.5
ETSN [26]91.190.077.986.278.285.283.975.478.882.074.069.056.270.367.8
ICC [34]91.489.180.587.882.083.882.074.376.185.072.468.555.968.675.2
UVAST [3]92.791.381.092.180.289.187.681.783.987.476.971.558.077.169.7
DPRN [31]92.992.082.990.982.087.886.379.482.087.275.670.557.675.171.7
Br-Prompt+ ASFormer [23]94.192.083.091.681.289.287.881.383.888.1-----
SemiICC(5%) [34]77.971.654.671.468.252.949.036.645.661.360.253.535.656.665.3
ICC(10%) [34]83.781.966.676.473.367.364.949.256.968.664.659.042.261.968.8
TimestampLi et al. [28]78.973.055.472.366.473.970.960.166.875.670.563.647.469.964.1
Khan et al. [17]81.577.560.875.666.175.172.361.067.675.167.961.045.367.061.4
Zhao et al. [51]84.381.764.879.874.478.575.563.471.877.773.166.549.472.664.6
EM-TSS [32]-82.766.582.370.5-75.964.771.677.9-63.749.867.267.0
UVAST+ alignment decoder [3]70.863.549.288.255.375.770.658.278.467.872.064.148.674.360.2
UVAST+Viterbi [3]87.283.766.089.370.583.079.665.978.277.071.363.348.374.160.7
UVAST+FIFA [3]80.775.257.488.766.080.274.961.678.672.572.064.247.674.160.3
D-TSTAS91.590.176.288.575.784.282.171.577.680.076.769.350.775.865.7
", + "bbox": [ + 120, + 87, + 854, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that MTP is effective in alleviating focus bias. Moreover, MTP and transformer backbone are more complementary and can help to capture contextual information.", + "bbox": [ + 75, + 404, + 468, + 449 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further explore the impact of different attention architectures, including linear attention in Flowformer [45] and local attention in ASFormer [49]. The MTP and CTE are added to the local attention model separately by setting the batch size to 1. Tab. 6 shows that our MTP and CTE can improve the performance of the model. With both MTP and CTE, the linear attention model outperforms the local attention model. Moreover, we compare the training time for the linear attention model and local attention model in the supplementary. To balance training time and performance, we use linear attention in our backbone.", + "bbox": [ + 75, + 450, + 470, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.8. Comparing Different Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 628, + 395, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 7 shows the comparison of our loss function with the previous loss function [28]. Our proposed segmental confidence loss achieves better F1 and edit scores compared with the confidence loss [28]. This is because $\\mathcal{L}_{conf}$ blurs the boundaries of the action segmentation when it forces the predicted probabilities to remain monotonic between adjacent annotated timestamps. In contrast, our loss function truncates smoothing through the pseudo-labels at the action boundary. This effect can also be seen in the qualitative result shown in Fig. 5. Moreover, $\\mathcal{L}_{ce}$ replacing $\\mathcal{L}_{ce}$ also improves performance by alleviating the imbalance of segments for action categories.", + "bbox": [ + 75, + 652, + 468, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.9. Comparison with the state-of-the-Arts", + "text_level": 1, + "bbox": [ + 76, + 845, + 406, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our method with recent approaches under different levels of supervision on three datasets. By reduc", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing the label bias, D-TSTAS outperforms current state-of-the-art approaches under timestamp supervision and semi-supervised, as shown in Tab. 8. Please refer to the supplementary for the qualitative results of our method and the baseline. Our approach further reduces the gap to fully supervised approaches and only involves single-frame annotations for each action segment. Moreover, our approach performs better in rare annotation cases compared with other methods [28, 32] (please refer to the supplementary).", + "bbox": [ + 496, + 404, + 890, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Limitation", + "text_level": 1, + "bbox": [ + 500, + 554, + 750, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a Debiasing-TSTAS framework to alleviate the issue of label bias in the TSTAS task. Instead of the commonly used Naive, we additionally use masked timestamp prediction to initialize the model, which models contextual information of timestamps. Moreover, we utilize a center-oriented timestamp expansion to capture a more efficient representation of action segments. We further introduced a segmental confidence loss that improves prediction quality. Our approach outperforms state-of-the-art TSTAS methods on three datasets and achieves comparable performance to the fully supervised setup.", + "bbox": [ + 496, + 579, + 890, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation. The annotation frames for each action segment are essential to our approach, which limits the annotator not to miss any action segment [32, 35]. To release this limitation, we consider replacing the pseudo-labeling of hard weight in the cross-entropy loss with soft weight as mentioned in [32] and detecting pseudo-timesteps from the soft weight.", + "bbox": [ + 496, + 746, + 890, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments: This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant DUT22JC14.", + "bbox": [ + 496, + 851, + 890, + 895 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6510", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hyemin Ahn and Dongheui Lee. Refining action segmentation with hierarchical video representations. 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IEEE, 2022. 2, 5, 8", + "bbox": [ + 78, + 90, + 470, + 148 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6513", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_model.json b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d52ca8b0ecf36b0fab1eb914de39056d4dfdfb5a --- /dev/null +++ b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_model.json @@ -0,0 +1,2411 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.227, + 0.131, + 0.745, + 0.176 + ], + "angle": 0, + "content": "Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.136, + 0.203, + 0.834, + 0.223 + ], + "angle": 0, + "content": "Kaiyuan Liu\\(^{1*}\\) Yunheng Li\\(^{1*}\\) Shenglan Liu\\(^{1\\dagger}\\) Chenwei Tan\\(^{1}\\) Zihang Shao\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.223, + 0.764, + 0.258 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science, Dalian University of Technology, China {1154864382, liyunheng, liusl, tcw2000, 1317588161} \\(@\\) mail.dlut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.313, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.702 + ], + "angle": 0, + "content": "Timestamp supervised temporal action segmentation (TSTAS) is more cost-effective than fully supervised counterparts. However, previous approaches suffer from severe label bias due to over-reliance on sparse timestamp annotations, resulting in unsatisfactory performance. In this paper, we propose the Debiasing-TSTAS (D-TSTAS) framework by exploiting unannotated frames to alleviate this bias from two phases: 1) Initialization. To reduce the dependencies on annotated frames, we propose masked timestamp predictions (MTP) to ensure that initialized model captures more contextual information. 2) Refinement. To overcome the limitation of the expressiveness from sparsely annotated timestamps, we propose a center-oriented timestamp expansion (CTE) approach to progressively expand pseudo-timestamp groups which contain semantic-rich motion representation of action segments. Then, these pseudotimestamp groups and the model output are used to iteratively generate pseudo-labels for refining the model in a fully supervised setup. We further introduce segmental confidence loss to enable the model to have high confidence predictions within the pseudo-timestamp groups and more accurate action boundaries. Our D-TSTAS outperforms the state-of-the-art TSTAS method as well as achieves competitive results compared with fully supervised approaches on three benchmark datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.732, + 0.21, + 0.749 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Analyzing and understanding human actions in videos is very important for many applications, such as human-robot interaction [14] and healthcare [33]. Recently, several approaches have been very successful in locating and analyzing activities in videos, including action localization [12,29,37,50], action segmentation [7,11,20,23], and action recognition [9,27,39,41,47]." + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.291, + 0.861, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.453, + 0.776, + 0.462 + ], + "angle": 0, + "content": "(c) Representation bias during the refining phase." + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.463, + 0.893, + 0.588 + ], + "angle": 0, + "content": "Figure 1. (a) The TSTAS task aims to segment actions in videos by timestamp annotations. (b) An example of focus bias: existing initialization methods prefer to predict frames similar to the annotated timestamp, leading to incorrectly identifying dissimilar frames within the segment and similar frames outside the segment. (c) An example of representation bias: the frames of complex action share large semantic variance, e.g. the process of cutting cheese includes both taking out and cutting, resulting in the models that rely on sparse timestamps to produce biased pseudo-labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.893, + 0.718 + ], + "angle": 0, + "content": "Despite the success of previous approaches, they rely on fully temporal supervision, where the start and end frames of each action are annotated. As a lightweight alternative, many researchers have started exploring timestamp supervised temporal action segmentation (TSTAS), where each action segment is annotated with only one frame in the untrimmed video, as shown in Fig. 1 (a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Most previous approaches follow a two-step pipeline by initializing and then iteratively refining the model with generated pseudo-labels. However, relying only on supervised signals of sparse single-timestamp annotations, these methods fail to learn the semantics of entire action segments, which is referred to as label bias in this paper, including focus bias and representation bias. Specifically, to initialize the segmentation model, the previous methods [17, 28, 32] adopt the Naive approach proposed in [28] (referred to as Naive), which computes the loss at the annotated frames for training. However, utilizing only the annotated frames leads to focus bias, where the initialized model tends to fo" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.352, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.223, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.352, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6503" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "cus on frames distributed over segments of various action categories similar to the annotated frames [51] (shown in Fig. 1 (b))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.47, + 0.367 + ], + "angle": 0, + "content": "During refining the segmentation model, to utilize the unlabeled frames, typical methods generate hard [17,28,51] or soft weighted [32] pseudo-labels that are used to refine the model like fully supervised methods. To generate pseudo-labels, the above methods depend on the timestamps that contain semantic or relative position information. Despite the success of such refined models, these approaches suffer from representation bias that single-frame fails to represent the entire action segment for complex actions with the large semantic variance of various frames (illustrated in Fig. 1 (c)). Moreover, when refining the segmentation model by these biased pseudo-labels, representation bias can be accumulated and expanded, resulting in unsatisfactory performance that is still a gap compared to fully supervised approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.61 + ], + "angle": 0, + "content": "In this paper, we propose a novel framework called Debiasing-TSTAS (D-TSTAS) to reduce label bias, containing masked timestamp predictions and center-oriented timestamp expansion approaches. During the initialization phase, we aim to alleviate the focus bias problem by propagating timestamp supervision information to the contextual frames of the timestamps. In contrast to previous approaches, we propose the Masked Timestamp Predictions (MTP) approach that masks the input features of timestamps to remove the dependencies of the model on annotated frames. In this way, the initialized model is forced to reconstruct the annotated frames in corresponding output features and then predict their action categories by contextual information of timestamps. Furthermore, to capture the semantics of both timestamps and contextual frames, we adopt the Naive after our MTP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.901 + ], + "angle": 0, + "content": "While our initialized model can reduce focus bias by capturing more contextual information, it does not guarantee that the generated pseudo-labels avoid representation bias during refining. Inspired by query expansion, we propose a Center-oriented Timestamp Expansion (CTE) approach for obtaining potential trustworthy unlabeled frames, which we refer to as pseudo-timestamps, to progressively expand the pseudo-timestamp groups that contain more semantics than single annotated timestamps. More specifically, it consists of three steps: 1) In the generating step, we generate pseudo-labels by current pseudotimestamp groups and the model output. 2) In the updating step, we choose the semantically dissimilar center frames of each segment in the pseudo-labels as pseudo-timestamps to expand the pseudo-timestamp groups. 3) In the segmenting step, the model is refined by pseudo-labels and our segmental confidence loss, which smooths the predicted probabilities in each action segment and maintains high confidence within pseudo-timestamp groups. The above steps are ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "ecuted several times alternately to improve the model prediction in a lazy manner instead of generating pseudo-labels per epoch in previous methods [28, 51]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.138, + 0.842, + 0.151 + ], + "angle": 0, + "content": "Our contributions can be summarised as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.161, + 0.892, + 0.207 + ], + "angle": 0, + "content": "- We study the label bias in the TSTAS task and propose a novel D-TSTAS framework to reduce both focus and representation bias." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.216, + 0.892, + 0.291 + ], + "angle": 0, + "content": "- Our masked timestamp predictions approach is the first attempt to alleviate the dependencies on timestamps, promoting the model to capture contextual information. Coupling MTP and Naive as a general solution is used to initialize the model in the TSTAS." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.302, + 0.892, + 0.377 + ], + "angle": 0, + "content": "- Compared to sparsely annotated timestamps, our center-oriented timestamp expansion approach progressively expands pseudo-timestamp groups to contain semantic-rich motion representations of action segments." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.387, + 0.892, + 0.446 + ], + "angle": 0, + "content": "- The proposed D-TSTAS not only outperforms state-of-the-art TSTAS approaches but also achieves competitive results compared with fully supervised approaches on three benchmark datasets." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.161, + 0.892, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.46, + 0.642, + 0.476 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.776, + 0.502 + ], + "angle": 0, + "content": "2.1. Temporal Action Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Fully Supervised Action Segmentation has been attracting increasing attention. In contrast to action recognition where trimmed videos are classified [5, 22, 30, 39, 48], temporal action segmentation requires modeling long-range dependencies to predict all the frames in the video. To achieve a larger receptive field, many approaches utilized dilated temporal convolutional networks to capture local and global dependencies [7, 25]. Despite the success of these approaches, they suffer from an over-segmentation error. To alleviate this problem, current state-of-the-art methods follow the architecture that refines the initial predictions [1, 15, 26, 40, 49] or integrates text prompts [24]. The above fully supervised approaches rely on frame-wise annotations, which are expensive to obtain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Timestamp Supervised Action Segmentation only requires a single annotated frame for each action segment. Most previous methods [17, 28, 32, 51] apply a two-phase training scheme, initializing by Naive [28] (also called the warmup phase [51]) and then iteratively refining the learned model with generated pseudo-labels. Unlike these methods, UVAST [3] directly refines the model by generating pseudo-labels from the constrained k-medoids algorithm based on input features. Moreover, in the specific action field (surgical phase recognition), Ding et al. [6] generate only partial pseudo-labels. While the above methods for generating pseudo-labels are highly dependent on annotated" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6504" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.092, + 0.388, + 0.105 + ], + "angle": 0, + "content": "Initialize Model with MTP Segmentation Model" + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.106, + 0.505, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.092, + 0.642, + 0.104 + ], + "angle": 0, + "content": "Refine Model with CTE" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.105, + 0.831, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.203, + 0.258, + 0.214 + ], + "angle": 0, + "content": "Segmentation Model" + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.214, + 0.508, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.204, + 0.829, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.894, + 0.362 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our proposed framework consists of two phases: initialize the segmentation model (in Sec. 3.2) with masked timestamp predictions (MTP in Sec. 3.3) and refine the model with center-oriented timestamp expansion (CTE in Sec. 3.4). The overall losses are introduced in Sec. 3.5. GPL is the abbreviation for generating pseudo-labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.456 + ], + "angle": 0, + "content": "timesteps, the semantic representation of the timestamps is limited. Different from the previous solutions, we propose MTP to enable the initialized model to capture contextual information and CTE to enrich pseudo-timestamp groups instead of single timestamps." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.468, + 0.31, + 0.485 + ], + "angle": 0, + "content": "2.2. Self-Supervised Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.673 + ], + "angle": 0, + "content": "In image and video tasks, self-supervised learning has been successful for its ability to learn information feature representations without human supervision. Most of the previous works were based on the spatial-temporal orders of videos by designing an auxiliary task related to the main task where the labels can be self-annotated [2,18,21,44,46]. Inspired by the success of the vision transformer, masked modeling is widely used in image [13, 42] and video modeling [10, 38]. Unlike these works, our proposed MTP predicts categories of annotated frames by using contextual information, aiming to address the problem of focus bias for timestamp supervised action segmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.688, + 0.393, + 0.706 + ], + "angle": 0, + "content": "3. The Debiasing-TSTAS Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.469, + 0.82 + ], + "angle": 0, + "content": "In this section, we present the details of our D-TSTAS. In Sec. 3.1, we first introduce the task of timestamp supervision and the pipeline of D-TSTAS, and the segmentation model is described in Sec. 3.2. Then, the masked timestamp predictions and the center-oriented timestamp expansion are proposed in Sec. 3.3 and Sec. 3.4, respectively. Finally, we provide the details of the loss functions in Sec. 3.5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.358, + 0.849 + ], + "angle": 0, + "content": "3.1. Problem statement and pipeline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Given a video \\( X = \\{x_{t}\\}_{t=1}^{T} \\) with \\( T \\) frames and \\( N \\) action segments (\\( N \\ll T \\)), the fully supervised temporal action segmentation requires high-cost frame-wise annota" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.517 + ], + "angle": 0, + "content": "tions for training and aims to predict a sequence of framewise action labels. In contrast to the fully supervised approaches, we consider efficient timestamp supervised segmentation, which provides a set of annotated timestamps \\( A_{Ts} = \\{(a_n,t_n)\\}_{n = 1}^N \\), where frame \\( t_n \\) belongs to the \\( n \\)-th action segment and \\( a_n \\) is the label \\( n \\)-th of action segment. While the annotation time of timestamp supervision is much less than that of the fully supervised setup, there is still a large gap in performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.893, + 0.7 + ], + "angle": 0, + "content": "To achieve comparable performance to the fully supervised methods, we propose a framework named D-TSTAS, including an Initialization phase and a Refinement phase, as shown in Fig. 2. Specifically, following the previous [7, 16, 40, 49], we extract I3D [4] features \\( X' = \\{x_t'\\}_{t=1}^T \\) as the input to our segmentation model. Then, to reduce focus bias, we initialize our model by masked timestamp predictions (MTP) and Naive [49] for capturing more contextual information. To further reduce representation bias, we propose the center-oriented timestamp expansion (CTE) to expand the progressive pseudo-timestamp groups and refine the segmentation model by generating pseudo-labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.725, + 0.727 + ], + "angle": 0, + "content": "3.2. The segmentation model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.9 + ], + "angle": 0, + "content": "The architecture of our segmentation model is shown in Fig. 2. We build a Transformer backbone of the cascaded encoder-decoder network structure [49], which contains an encoder and \\( H \\)-1 decoders. The linear attention [45] is applied in our backbone to balance training efficiencies and performance, which is beneficial for modeling long sequences. More details of the segmentation model are described in the supplementary material. We also explore the effect of Temporal Convolutional Network (TCN) [17, 28] or our backbone and compare the different attentions in the backbone as illustrated in Sec. 4.7." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6505" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.364, + 0.108 + ], + "angle": 0, + "content": "3.3. Reducing the focus bias by MTP" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.474, + 0.462 + ], + "angle": 0, + "content": "As mentioned before, the previous initialization [17, 28, 32] suffers from focus bias. In this paper, we propose masked timestamp predictions (MTP) to reduce this bias as shown in Fig. 2. Specifically, given the input feature \\( X' \\), we mask the I3D feature \\( x_{t_n}' \\) of annotated timestamps by a shared learnable token to reduce the dependency of the model on annotated timestamps. The input feature of the unannotated frames is used to generate output feature \\( F_h \\) and predictions of timestamps \\( P_h \\), where \\( h = 1, \\dots, H \\), and \\( H \\) denotes the total number of stages (encoder & decoder). To enable our model to involve the semantic information of annotated timestamps, Naive is employed to train the segmentation model after the MTP. The obtained output of our initialized model captures temporal feature representations at different distances from the timestamps by propagating the timestamp supervision information to contextual frames, which is superior to the feature representations obtained by using a Naive alone in typical approaches. Unlike the self-supervised methods [10, 13, 38, 43] that attain a generic pre-trained model by reconstructing input or handcrafted feature descriptor of input, the MTP maps to annotated frames with high-level semantic information (more analyses in Sec. 4.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.433, + 0.487 + ], + "angle": 0, + "content": "3.4. Reducing the representation bias by CTE" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.494, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Due to the limitation of the expressiveness of the single-frame timestamp, the model tends to produce expressiveness bias for complex action segments, generating incorrect pseudo-labels. Inspired by query expansion, we first propose to use progressive pseudo-timestamp groups \\(\\mathcal{G}\\) to represent the action segments. Compared to the original single annotated frames, pseudo-timestamp groups provide a semantically richer representation of each action segment. We further propose the center-oriented timestamp expansion (CTE) to expand \\(\\mathcal{G}\\) while refining the model. As illustrated in Alg.1, the annotated timestamp set \\(A_{T_s}\\) is first used to initialize \\(\\mathcal{G} = \\{G_n\\}_{n=1}^N\\), where \\(G_n = \\{(a_n, t_n^1)\\}\\) is the timestamp group of \\(n-th\\) action segment and the \\(t_n^1\\) indicates the first annotated timestamp of the group \\(G_n\\). Then, the generating step, the segmenting step, and updating step perform \\(M\\) iterations to expand progressive pseudo-timestamp groups \\(\\mathcal{G}\\) and refine the model by generated pseudo-labels \\(\\hat{Y}\\). The framework of the refined model with the proposed CTE approach is shown in Fig. 2 and we describe the process of the \\(m-th\\) iteration as follows." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.471, + 0.904 + ], + "angle": 0, + "content": "Generating step. Obtain output features of final decoder \\( F_{H} = \\{f_{t}\\}_{t = 1}^{T} \\) and current timestamps groups \\( \\mathcal{G} \\), generating the frame-wise pseudo-labels can be reduced to estimate the action boundaries between the last timestamp \\( (a_{i}, t_{i}^{\\Omega(i)}) \\) of \\( G_{i} \\) and the first timestamp \\( (a_{i + 1}, t_{i + 1}^{1}) \\) of \\( G_{i + 1} \\) in temporal order, where \\( i = 1, \\dots, N - 1 \\). Only \\( N - 1 \\) boundaries of pseudo-labels are required to be estimated, and \\( \\Omega(i) \\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "denotes the number of timestamps in the timestamps group \\( G_{i} \\). Specifically, the stamp-to-stamp energy function as proposed in [28] is used to detect the action change between \\( t_{i}^{\\Omega (i)} \\) and \\( t_{i + 1}^{1} \\), and the boundaries of pseudo-label \\( t_{b_i} \\) can be denoted by:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.186, + 0.852, + 0.225 + ], + "angle": 0, + "content": "\\[\nt_{b_{i}} = \\operatorname *{arg min}_{\\hat{t}}\\sum_{\\substack{t = t_{i}^{\\Omega (j)}}}\\hat{t} d(f_{t},e_{i}) + \\sum_{t = \\hat{t} +1}^{t_{j + 1}^{1}}d(f_{t},e_{i + 1}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.226, + 0.564, + 0.235 + ], + "angle": 0, + "content": "s.t." + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.237, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\ne _ {i} = \\frac {1}{\\hat {t} - t _ {i} ^ {\\Omega (i)} + 1} \\sum_ {t = t _ {i} ^ {\\Omega (i)}} ^ {\\hat {t}} f _ {t}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.272, + 0.705, + 0.305 + ], + "angle": 0, + "content": "\\[\ne _ {i + 1} = \\frac {1}{t _ {i + 1} ^ {1} - t} \\sum_ {t = \\hat {t} + 1} ^ {t _ {i + 1} ^ {1}} f _ {t},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.305, + 0.669, + 0.321 + ], + "angle": 0, + "content": "\\[\nt _ {i} ^ {\\Omega (i)} \\leq \\hat {t} < t _ {i + 1} ^ {1},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.326, + 0.894, + 0.448 + ], + "angle": 0, + "content": "where \\(d(\\cdot, \\cdot)\\) is the Euclidean distance, \\(e_i\\) is the average of the embedding features between \\(t_i^{\\Omega(i)}\\) and the estimate \\(\\hat{t}\\), and \\(e_{i+1}\\) is the average of the segmentation feature between the estimate \\(\\hat{t}\\) and \\(t_{i+1}^1\\). In Eq. (1), the pseudo-boundaries are estimated from the start of the video. The same argument holds if we estimate the pseudo-boundaries at the end of the video. The final pseudo-boundaries for \\(t_{b_i}\\) are the average of these two estimates, which can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.465, + 0.678, + 0.493 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r} t _ {b _ {i}} = \\frac {t _ {b _ {i} , F W} + t _ {b _ {i} , B W}}{2}, \\\\ s. t. \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.494, + 0.891, + 0.53 + ], + "angle": 0, + "content": "\\[\nt _ {b _ {i}, F W} = \\arg \\min _ {\\hat {t}} \\sum_ {t = t _ {b _ {i - 1}}} ^ {\\hat {t}} d \\left(f _ {t}, e _ {i}\\right) + \\sum_ {t = \\hat {t} + 1} ^ {t _ {i + 1} ^ {1}} d \\left(f _ {t}, e _ {i + 1}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.53, + 0.861, + 0.565 + ], + "angle": 0, + "content": "\\[\nt_{b_{i},BW} = \\operatorname *{arg min}_{\\hat{t}}\\sum_{t = t_{i}^{\\Omega (i)}}^{\\hat{t}}d\\left(f_{t},e_{i}\\right) + \\sum_{t = \\hat{t} +1}^{t_{b_{i} + 1}}d\\left(f_{t},e_{i + 1}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.565, + 0.645, + 0.582 + ], + "angle": 0, + "content": "\\[\nt _ {i} ^ {\\Omega (i)} \\leq \\hat {t} < t _ {i + 1} ^ {1},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.588, + 0.894, + 0.652 + ], + "angle": 0, + "content": "thus, we get the pseudo-boundaries \\( B = \\{t_{b_j}\\}_{j=0}^N \\), which \\( t_{b_0} = 0 \\) and \\( t_{b_N} = T \\). To generate the pseudo-labels \\( \\hat{Y} = \\{\\hat{y}_t\\}_{t=1}^T \\), we assign the frames between \\( t_{b_{n-1}} \\) and \\( t_{b_n} \\) to the same action label \\( a_n \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.652, + 0.895, + 0.79 + ], + "angle": 0, + "content": "Updating step. Our approach relies on the progressive pseudo-timestamp groups \\(\\mathcal{G}\\) that contain more semantic and positional information to detect pseudo-boundaries. To enrich the \\(\\mathcal{G}\\), we need to find potentially trustworthy pseudo-timestamps that are not semantically similar to original timestamps. For finding potentially trustworthy pseudo timestamps, we intuitively choose the center frames of each segment in the pseudo-labels, which are expressed as \\(C = \\{(a_n, t_{c_n})\\}_{n=1}^N\\), and" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.797, + 0.892, + 0.825 + ], + "angle": 0, + "content": "\\[\nt _ {c n} = \\frac {t _ {b _ {n - 1}} + t _ {b _ {n}}}{2}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Since adjacent frames usually have similar semantic information in the video, new pseudo-timesteps close to the \\( G_{n} \\) might fail to reduce representation bias. To alleviate this problem, we keep a minimum temporal threshold \\( D \\) between the new pseudo-timesteps and the latest" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6506" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.078, + 0.091, + 0.468, + 0.121 + ], + "angle": 0, + "content": "Algorithm 1 Refine Model with Center-oriented Timestamp Expansion" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.125, + 0.468, + 0.282 + ], + "angle": 0, + "content": "Input: I3D features \\(X^{\\prime}\\) , annotated timestamps \\(A_{Ts}\\) and segmentation model \\(\\mathcal{M}\\) \nOutput: Refined segmentation model \\(\\mathcal{M}\\) \n1: Initialize \\(\\mathcal{G}\\) and \\(R\\) by \\(A_{Ts}\\) \n2: for \\(m = 1,\\dots,M\\) do \n3: D Generating step. \n4: \\(F_{H}\\gets ExtractFeature(X^{\\prime},\\mathcal{M})\\) see Eq.2 \n5: \\(B\\gets\\) EstimateBoundaries \\((F_H,\\mathcal{G})\\) \n6: \\(\\hat{Y}\\gets\\) GeneratePseudoLabels(B, \\(\\mathcal{G}\\) \n7: D Updating step. \n8: \\((\\mathcal{G},R)\\gets\\) Update \\((\\hat{Y},\\mathcal{G},R)\\) \n9: D Segmenting step. \n10: for \\(k = 1,\\ldots ,K\\) do \n11: \\(\\mathcal{M}\\gets\\) RefineModel \\((\\mathcal{M},X^{\\prime},\\hat{Y},\\mathcal{G},\\mathcal{L}_{refine})\\) \n12: end for \n13: end for" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.312, + 0.468, + 0.401 + ], + "angle": 0, + "content": "added pseudo-timesteps, i.e., \\( |t_{c_n} - t_{r_n}| > D \\), where \\( R = \\{t_{r_n}\\}_{n=1}^N \\) denotes the location of the latest added pseudo-timesteps each iteration (initially, \\( t_{r_n} = t_n \\)). Besides, the value of the new pseudo timestamp \\( t_{c_n} \\) is assigned to \\( t_{r_n} \\). Finally, we obtain the new pseudo-timestamp groups \\( \\mathcal{G} \\) that are utilized for the next iteration." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.403, + 0.469, + 0.479 + ], + "angle": 0, + "content": "Segmenting step. To further improve the quality of the predictions, we refine the segmentation model with the pseudo-labels \\(\\hat{Y}\\), new pseudo-timestamp groups \\(\\mathcal{G}\\), and loss functions \\(\\mathcal{L}_{\\text{refine}}\\) (described in Sec. 3.5) through \\(K\\) training epochs." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.492, + 0.229, + 0.506 + ], + "angle": 0, + "content": "3.5. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.516, + 0.468, + 0.559 + ], + "angle": 0, + "content": "As shown in Fig. 2, we use the same loss as baseline [28] to initialize the model with MTP and Naive, which can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.576, + 0.469, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n i t}} = \\mathcal {L} _ {c e} + \\lambda \\mathcal {L} _ {\\text {t m s e}} + \\beta \\mathcal {L} _ {\\text {c o n f}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.605, + 0.468, + 0.665 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{ce}\\), \\(\\mathcal{L}_{tmse}\\), and \\(\\mathcal{L}_{conf}\\) are the cross-entropy loss based on the annotated timestamps, smoothing loss [7], and confidence loss [28], respectively. \\(\\lambda\\) and \\(\\beta\\) are hyperparameters utilized to balance the contribution of each loss." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.667, + 0.468, + 0.862 + ], + "angle": 0, + "content": "During the refinement of the model with CTE, we adapt weighted cross-entropy loss \\(\\mathcal{L}_{wce}\\) to replace cross-entropy loss \\(\\mathcal{L}_{cls}\\), which can alleviate the imbalance problem in the frequency of different action segments for each action category [15]. Unlike the [15], to get the class weight, we calculate the median of class frequencies divided by each class frequency through pseudo-labels that approximate ground truth. The previous methods [17,28,32] typically apply confidence loss proposed in [28] so that the probability of prediction decreases monotonically with increasing distance from the timestamp. However, due to focus monotonicity outside the segments, the confidence loss leads to the blurring of the boundaries of the action segments." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.861, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Segmental confidence loss. Unlike confidence loss \\(\\mathcal{L}_{conf}\\), we propose segmental confidence loss \\(\\mathcal{L}_{sconf}\\) to smooth the predicted probabilities within the action seg" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.091, + 0.862, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.207, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Figure 3. The segmental confidence loss penalizes decreasing predictions within the red range \\((t_{b_{n-1}}\\) to \\(t_n^{\\Omega(n)}\\) and increasing predictions in the green range \\((t_n^1\\) to \\(t_{b_n}\\)) for label \\(a_n\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.266, + 0.659, + 0.28 + ], + "angle": 0, + "content": "ments of pseudo-labels." + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.284, + 0.891, + 0.41 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {s c o n f} = \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {b _ {n - 1}}} ^ {t _ {n} ^ {\\Omega (n)}} \\delta_ {a _ {n}, 1}\\right) / T _ {1} + \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {n} ^ {1}} ^ {t _ {b _ {n}}} \\delta_ {a _ {n}, 2}\\right) / T _ {2}, \\\\ \\delta_ {a _ {n}, 1} = \\max \\left(0, p _ {a _ {n}, t - 1} - p _ {a _ {n}, t}\\right), \\\\ \\delta_ {a _ {n}, 2} = \\max \\left(0, p _ {a _ {n}, t} - p _ {a _ {n}, t - 1}\\right), \\\\ T _ {1} = \\sum_ {n = 1} ^ {N} \\left(t _ {n} ^ {\\Omega (n)} - t _ {b _ {n - 1}}\\right), \\\\ T _ {2} = \\sum_ {n = 1} ^ {N} \\left(t _ {b _ {n}} - t _ {n} ^ {1}\\right), \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.412, + 0.892, + 0.532 + ], + "angle": 0, + "content": "where \\( p_{a_n,t} \\) is the probability of action \\( a_n \\) at time \\( t \\). \\( \\delta_{a_n,1} \\) and \\( \\delta_{a_n,2} \\) are decreasing penalized predictions and increasing penalized predictions as illustrated in Fig. 3. \\( T_1 \\) and \\( T_2 \\) are the total sum of frames of \\( \\delta_{a_n,1} \\) and \\( \\delta_{a_n,2} \\), respectively. The effect of our loss function is visualized as shown in Fig. 5, which can prevent boundary blur caused by prediction monotonicity outside the action segments and keeps consistent high confidence between \\( t_n^1 \\) and \\( t_n^{\\Omega(n)} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.533, + 0.892, + 0.561 + ], + "angle": 0, + "content": "The overall loss function to refine the segmentation model with CTE is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.573, + 0.891, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {w c e} + \\lambda \\mathcal {L} _ {t m s e} + \\gamma \\mathcal {L} _ {s c o n f}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.89, + 0.628 + ], + "angle": 0, + "content": "where \\(\\lambda\\) and \\(\\gamma\\) are hyper-parameters to balance the contribution of each loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.634, + 0.658 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.719, + 0.681 + ], + "angle": 0, + "content": "4.1. Datasets and evaluation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.689, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Datasets. Following the previous works [17, 32, 51], we evaluate our approach on three datasets: 50Salads [36], Breakfast [19], and Georgia Tech Egocentric Activities (GTEA) [8]. We perform 4-fold cross-validation on Breakfast and GTEA, and 5-fold cross-validation on 50Salads." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The 50Salads dataset contains 50 videos (0.6M frames) with actors preparing different kinds of salads. It consists of 17 action classes which are recorded from the top view. On average, the video duration is 6.4 minutes long and each video has 20 action instances. The Breakfast dataset consists of 1712 third-person view videos (3.6M frames) related to breakfast preparation activities. There are 48 different action classes that were recorded in 18 different kitchens. The average video duration ranges from a few" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6507" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.167 + ], + "angle": 0, + "content": "seconds to several minutes and each video contains 6 action instances on average. The GTEA dataset contains 58 videos (32K frames) with actors performing various kinds of daily activities. It consists of 11 action classes. The average video duration is 1 minute long." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.228 + ], + "angle": 0, + "content": "For all datasets, our experimental results are reported for three random seeds used for annotating frames in videos. Only in Tab. 8, we use the same annotations that Li et al. [28] provide for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.468, + 0.319 + ], + "angle": 0, + "content": "Evaluation Metrics. Following previous works [7, 26], we use the standard metrics for fully supervised temporal action segmentation and report the frame-wise accuracy (Acc), segmental edit distance (Edit) and segmental F1 scores with overlapping thresholds of \\(10\\%\\), \\(25\\%\\), and \\(50\\%\\), denoted by \\(F1@{10,25,50}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.292, + 0.345 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.468, + 0.502 + ], + "angle": 0, + "content": "We set \\( H = 4 \\) as in [49] and train our model for 290 epochs, including 80 epochs for MTP, 30 epochs for Naive, and 180 (\\( K = 30 \\), \\( M = 6 \\)) epochs for CTE. \\( D \\) is set to \\( \\{5, 20, 10\\} \\) for GTEA, 50Salads, and Breakfast, which is related to the average action duration. The batch size is 8 and an AdamW optimizer with a learning rate of 0.0005 and weight decay of 0.05 is used. For the loss function, we set \\( \\lambda = 0.15 \\), \\( \\beta = 0.075 \\) as in [28], and set \\( \\gamma = 1 \\). All experiments in the comparison study use the above setting and are conducted with NVIDIA GeForce RTX 2080 Ti GPUs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.277, + 0.529 + ], + "angle": 0, + "content": "4.3. Effectiveness of MTP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.468, + 0.764 + ], + "angle": 0, + "content": "We first compare the initialization of the MTP and Naive [28] on TCN backbone [28] and our backbone. As shown in Tab. 1, our approach outperforms Naive with a large margin F1 and edit scores. This is because the Naive initialized model by only using sparse timestamps, the model produces focus bias, incorrectly recognizing frames in various action categories similar to annotated frames. On the contrary, our approach reduces focus bias by masking the timestamps and predicting the category of annotated frames using contextual information. Moreover, we combine MTP and Naive to generate better initialized predictions by exploiting semantic information with annotated timestamps and the context of annotated frames. These are also reflected in the performance as illustrated in Fig. 4. We also evaluate the order of MTP and Naive in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.9 + ], + "angle": 0, + "content": "To further explore the effectiveness of the MTP, we explore the impact of different initialization strategies on the refinement model, as shown in Tab. 2. To conduct a fair comparison, the same refinement approach in [28], containing 20 epochs of training, is used to refine the model. While our MTP gives an additional boost in performance, the best performance is achieved when MTP and Naive are combined. This illustrates that a good initialization model is beneficial for refining the model. While the MTP of the" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.889, + 0.179 + ], + "angle": 0, + "content": "
InitializationGTEA50Salads
F1@{10, 25, 50}EditAccF1@{10, 25, 50}EditAcc
TCNNaive59.755.339.651.156.547.943.334.0
MTP63.459.745.956.453.459.855.144.9
MTP+Naive74.468.152.167.262.860.255.745.5
oursNaive47.442.133.045.147.641.336.125.3
MTP67.662.747.361.060.555.451.140.9
MTP+Naive77.072.456.170.565.462.658.147.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.179, + 0.89, + 0.204 + ], + "angle": 0, + "content": "Table 1. Impact of different initialization strategies and backbones without refinement on GTEA and 50Salads datasets." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.214, + 0.888, + 0.305 + ], + "angle": 0, + "content": "
InitializationGTEA50Salads
F1@{10,25,50}EditAccF1@{10,25,50}EditAcc
TCNNaive78.973.055.472.366.473.970.960.166.8
MTP81.476.958.575.966.871.568.358.865.5
MTP+Naive84.079.060.479.567.872.069.058.664.6
oursNaive76.071.455.371.769.072.067.954.764.9
MTP82.679.661.677.570.273.969.458.267.0
MTP+Naive86.283.266.382.772.074.571.160.067.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.305, + 0.89, + 0.33 + ], + "angle": 0, + "content": "Table 2. Impact of different initialization strategies and backbones with refinement [28] on GTEA and 50Salads datasets." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.34, + 0.88, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.413, + 0.892, + 0.535 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of the different initialization strategies with TCN backbone [28] on the 50Salads dataset. Naive only correctly identifies frames close to the timestamp, which are also similar frames to annotated timestamps. MTP reduces this bias by directing the model to capture contextual information, but the boundaries of segments are not accurate. Adding Naive after MTP generates better predictions as the model exploits semantic information with annotated timestamps and the context of annotated frames." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.557, + 0.89, + 0.618 + ], + "angle": 0, + "content": "TCN backbone on 50Salads achieves good frame-wise accuracy, it suffers from over-segmentation during refining as evidenced by the low F1 and Edit scores. Meanwhile, our backbone based on Transformer can alleviate this problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.629, + 0.804, + 0.645 + ], + "angle": 0, + "content": "4.4. Impact of mapping target for MTP" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Our approach initializes the model by mapping the masked features to the label of timestamps (Feature-to-Label), which is described in Sec. 3.3. To analyze the impact of the mapping target, we train another model (Feature-to-Feature) that minimizes the \\( l_{2} \\) distance between the output feature \\( f_{t_n} \\) and the input I3D feature \\( x_{t_n}' \\). Specifically, we use an additional linear layer to adjust the dimensions of \\( f_{t_n} \\) to match the dimensions of the \\( x_{t_n}' \\). For a fair comparison, the Feature-to-Feature model follows the same initialization method (MTP+Native) and refinement method [28] based on our backbone as Feature-to-Label. As shown in Tab. 2 and Tab. 3, compared to the Naive, Feature-to-Feature slightly improves the performance, which validates that the masking strategy achieves better initialization" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Since there is no timestamp on the test set, we visualize the focus bias clearly by timestamps and predictions on the training set." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6508" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.46, + 0.151 + ], + "angle": 0, + "content": "
DatasetTargetF1@{10,25,50}EditAcc
GTEAFeature-to-Feature75.672.456.865.571.2
Feature-to-Label86.283.266.382.772.0
50SaladsFeature-to-Feature72.369.158.965.875.9
Feature-to-Label74.571.160.067.377.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.152, + 0.468, + 0.177 + ], + "angle": 0, + "content": "Table 3. Impact of mapping target for MTP on GTEA and 50Salads datasets." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.185, + 0.46, + 0.226 + ], + "angle": 0, + "content": "
RefinementF1@{10, 25, 50}EditAcc
baseline [28] (epoch = 20)74.571.160.067.377.6
CTE (K = 10, M = 2)76.473.162.669.677.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.226, + 0.468, + 0.251 + ], + "angle": 0, + "content": "Table 4. Comparison with the baseline in the refining phase on the 50Salads dataset." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.26, + 0.467, + 0.399 + ], + "angle": 0, + "content": "
Impact of KF1@{10, 25, 50}EditAccAccPLAccTS
CTE (K=10, M=6)80.177.866.372.978.087.197.3
CTE (K=20, M=6)82.880.669.675.779.187.397.2
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=40, M=6)83.581.371.276.780.087.297.0
Impact of MF1@{10, 25, 50}EditAccAccPLAccTi
CTE (K=30, M=2)81.078.468.074.179.788.697.9
CTE (K=30, M=4)83.280.670.476.379.887.897.4
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=30, M=8)83.781.970.377.879.286.497.0
CTE (K=30, M=10)83.781.069.576.578.885.696.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.399, + 0.468, + 0.453 + ], + "angle": 0, + "content": "Table 5. Impact of epoch-per-segmentation step \\( K \\) and the number of iterations \\( M \\) in CTE on 50Salads dataset. AccPL and AccTS denote the accuracy of pseudo-labels and timestamps for each video, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.468, + 0.593 + ], + "angle": 0, + "content": "of the model. However, it performed worse than Feature-to-Label. This is mainly because Feature-to-Label promotes the model to capture high-level semantic information, which is beneficial for the propagation of supervised signals of timestamps to unlabeled frames in the TSTAS task. We also discuss the number of masked frames with Feature-to-Label and Feature-to-Feature (please refer to the supplementary)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.274, + 0.618 + ], + "angle": 0, + "content": "4.5. Effectiveness of CTE" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.468, + 0.822 + ], + "angle": 0, + "content": "To verify the effectiveness of the proposed CTE during the refining phase, we compare the CTE with the baseline that employs the refining approach [28] and perform the comparison experiments based on our initialized model. As shown in Tab. 4, our approach outperforms the baseline. This is because our method captures more semantic information within the action segment compared to the baseline by expanding the timestamp groups. As shown in Tab. 5, the addition of pseudo-labels is trustworthy, and pseudotimestamp groups are used to generate better pseudo-labels, as indicated by the high accuracy of pseudo-labels and timestamps. The effect of CTE can also be seen in the qualitative result, please refer to the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.291, + 0.849 + ], + "angle": 0, + "content": "4.6. Ablation Study of CTE" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The effect of the center-oriented timestamp expansion is controlled by two hyper-parameters: \\( K \\) and \\( M \\). In this section, we study the impact of the two parameters with differ" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.882, + 0.2 + ], + "angle": 0, + "content": "
StrategiesGTEA
F1@{10,25,50}EditAcc
Local attentionNaive69.762.745.462.059.8
MTP75.572.453.372.064.8
MTP+Naive77.473.654.971.166.3
MTP+Naive+CTE89.186.874.585.573.2
Linear attentionNaive47.442.133.045.147.6
MTP67.662.747.361.060.5
MTP+Naive77.072.456.170.565.4
MTP+Naive+CTE91.590.176.288.575.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.2, + 0.891, + 0.226 + ], + "angle": 0, + "content": "Table 6. Impact of different attention architectures in our backbone on the GTEA dataset." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.235, + 0.88, + 0.297 + ], + "angle": 0, + "content": "
LceLwceLconfLsconfF1@{10,25,50}EditAcc
✓✓82.579.968.576.278.7
✓✓83.881.170.676.679.4
✓✓82.980.465.876.875.6
✓✓84.282.171.577.680.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.298, + 0.891, + 0.324 + ], + "angle": 0, + "content": "Table 7. Comparing different loss functions on the 50Salads dataset." + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.336, + 0.697, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.337, + 0.872, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.393, + 0.891, + 0.419 + ], + "angle": 0, + "content": "Figure 5. Quality comparison of confidence loss [28] and segmental confidence loss." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.442, + 0.788, + 0.456 + ], + "angle": 0, + "content": "ent values of \\(K\\) and \\(M\\), as shown in Tab. 5." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.457, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Impact of epoch-per-segmentation stage \\( K \\). The parameter of \\( K \\) affects the refinement model by using the same pseudo-labels in the segmenting step. Our default value is \\( K = 30 \\). Increasing the value \\( K \\) from 10 to 30 achieves better performance because sufficient training epochs lead to better convergence. However, setting \\( K = 40 \\) results in a slight drop in performance compared with a default value. This drop in performance is due to the over-fitting problem." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.594, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Impact of the number of iterations \\( M \\). This hyperparameter defines the number of times to supplement the timestamp groups and generate pseudo-labels. Reducing \\( M \\) to 2 still improves the performance but is not as good as the default value of \\( M = 6 \\). Increasing its value to \\( M = 10 \\) also causes a degradation in performance. This drop in performance is because adding the incorrect pseudo-timestamp results in a decrease in the accuracy of the pseudo-labels, which affects the predictions of the refinement model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.724, + 0.757 + ], + "angle": 0, + "content": "4.7. Impact of the backbones" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We compare our backbone with TCN [28] backbone as shown in Tab. 1 and Tab. 2. When the Naive is used alone, our backbone causes worse performance in the initialization and refinement phase compared with the TCN backbone. This is because the linear attention in our backbone with the Naive approach incorrectly identifies more frames with semantic similarity to timestamps by capturing global dependencies. In contrast, MTP can improve the performance of our backbone by a large margin, which indicates" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6509" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.088, + 0.856, + 0.359 + ], + "angle": 0, + "content": "
SupervisionMethodGTEA50SaladsBreakfast
F1@{10,25,50}EditAccF1@{10,25,50}EditAccF1@{10,25,50}EditAcc
FullyMS-TCN [7]87.585.474.681.479.276.374.064.567.980.752.648.137.961.766.3
MS-TCN++ [25]88.885.776.083.580.180.778.570.174.383.764.158.645.965.667.6
BCN [40]88.587.177.384.479.882.381.374.074.384.468.765.555.066.270.4
ASRF [16]89.487.879.883.777.384.983.577.379.384.574.368.956.172.467.6
ASFormer [49]90.188.879.284.679.785.183.476.079.685.676.070.657.475.073.5
ETSN [26]91.190.077.986.278.285.283.975.478.882.074.069.056.270.367.8
ICC [34]91.489.180.587.882.083.882.074.376.185.072.468.555.968.675.2
UVAST [3]92.791.381.092.180.289.187.681.783.987.476.971.558.077.169.7
DPRN [31]92.992.082.990.982.087.886.379.482.087.275.670.557.675.171.7
Br-Prompt+ ASFormer [23]94.192.083.091.681.289.287.881.383.888.1-----
SemiICC(5%) [34]77.971.654.671.468.252.949.036.645.661.360.253.535.656.665.3
ICC(10%) [34]83.781.966.676.473.367.364.949.256.968.664.659.042.261.968.8
TimestampLi et al. [28]78.973.055.472.366.473.970.960.166.875.670.563.647.469.964.1
Khan et al. [17]81.577.560.875.666.175.172.361.067.675.167.961.045.367.061.4
Zhao et al. [51]84.381.764.879.874.478.575.563.471.877.773.166.549.472.664.6
EM-TSS [32]-82.766.582.370.5-75.964.771.677.9-63.749.867.267.0
UVAST+ alignment decoder [3]70.863.549.288.255.375.770.658.278.467.872.064.148.674.360.2
UVAST+Viterbi [3]87.283.766.089.370.583.079.665.978.277.071.363.348.374.160.7
UVAST+FIFA [3]80.775.257.488.766.080.274.961.678.672.572.064.247.674.160.3
D-TSTAS91.590.176.288.575.784.282.171.577.680.076.769.350.775.865.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.359, + 0.895, + 0.387 + ], + "angle": 0, + "content": "Table 8. Comparison with different levels of supervision on all three datasets. D-TSTAS uses the backbone that combines the cascaded encoder-decoder network structure [49] and the linear attention architecture [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.47, + 0.45 + ], + "angle": 0, + "content": "that MTP is effective in alleviating focus bias. Moreover, MTP and transformer backbone are more complementary and can help to capture contextual information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.471, + 0.618 + ], + "angle": 0, + "content": "We further explore the impact of different attention architectures, including linear attention in Flowformer [45] and local attention in ASFormer [49]. The MTP and CTE are added to the local attention model separately by setting the batch size to 1. Tab. 6 shows that our MTP and CTE can improve the performance of the model. With both MTP and CTE, the linear attention model outperforms the local attention model. Moreover, we compare the training time for the linear attention model and local attention model in the supplementary. To balance training time and performance, we use linear attention in our backbone." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.629, + 0.396, + 0.646 + ], + "angle": 0, + "content": "4.8. Comparing Different Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.47, + 0.835 + ], + "angle": 0, + "content": "Tab. 7 shows the comparison of our loss function with the previous loss function [28]. Our proposed segmental confidence loss achieves better F1 and edit scores compared with the confidence loss [28]. This is because \\(\\mathcal{L}_{conf}\\) blurs the boundaries of the action segmentation when it forces the predicted probabilities to remain monotonic between adjacent annotated timestamps. In contrast, our loss function truncates smoothing through the pseudo-labels at the action boundary. This effect can also be seen in the qualitative result shown in Fig. 5. Moreover, \\(\\mathcal{L}_{ce}\\) replacing \\(\\mathcal{L}_{ce}\\) also improves performance by alleviating the imbalance of segments for action categories." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.407, + 0.863 + ], + "angle": 0, + "content": "4.9. Comparison with the state-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We compare our method with recent approaches under different levels of supervision on three datasets. By reduc" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.542 + ], + "angle": 0, + "content": "ing the label bias, D-TSTAS outperforms current state-of-the-art approaches under timestamp supervision and semi-supervised, as shown in Tab. 8. Please refer to the supplementary for the qualitative results of our method and the baseline. Our approach further reduces the gap to fully supervised approaches and only involves single-frame annotations for each action segment. Moreover, our approach performs better in rare annotation cases compared with other methods [28, 32] (please refer to the supplementary)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.555, + 0.75, + 0.571 + ], + "angle": 0, + "content": "5. Conclusion and Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.746 + ], + "angle": 0, + "content": "In this paper, we propose a Debiasing-TSTAS framework to alleviate the issue of label bias in the TSTAS task. Instead of the commonly used Naive, we additionally use masked timestamp prediction to initialize the model, which models contextual information of timestamps. Moreover, we utilize a center-oriented timestamp expansion to capture a more efficient representation of action segments. We further introduced a segmental confidence loss that improves prediction quality. Our approach outperforms state-of-the-art TSTAS methods on three datasets and achieves comparable performance to the fully supervised setup." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Limitation. The annotation frames for each action segment are essential to our approach, which limits the annotator not to miss any action segment [32, 35]. To release this limitation, we consider replacing the pseudo-labeling of hard weight in the cross-entropy loss with soft weight as mentioned in [32] and detecting pseudo-timesteps from the soft weight." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.852, + 0.892, + 0.896 + ], + "angle": 0, + "content": "Acknowledgments: This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant DUT22JC14." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "6510" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Hyemin Ahn and Dongheui Lee. Refining action segmentation with hierarchical video representations. 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IEEE, 2022. 2, 5, 8" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.957 + ], + "angle": 0, + "content": "6513" + } + ] +] \ No newline at end of file diff --git a/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_origin.pdf b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f5b37b1d4c4b1d770c715b3690e0c66808b70652 --- /dev/null +++ b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/986159f2-45a0-4edb-a4fb-548f08a70e7e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dd7ebac17196867ac193541ce43055bf831104ac402c8f746b025cb5eb46c0e4 +size 1812146 diff --git a/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/full.md b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..de10e2170439d3edc9df050b6f6a3e77e2977fb5 --- /dev/null +++ b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/full.md @@ -0,0 +1,365 @@ +# Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation + +Kaiyuan Liu $^{1*}$ Yunheng Li $^{1*}$ Shenglan Liu $^{1\dagger}$ Chenwei Tan $^{1}$ Zihang Shao $^{1}$ + +$^{1}$ School of Computer Science, Dalian University of Technology, China {1154864382, liyunheng, liusl, tcw2000, 1317588161} $@$ mail.dlut.edu.cn + +# Abstract + +Timestamp supervised temporal action segmentation (TSTAS) is more cost-effective than fully supervised counterparts. However, previous approaches suffer from severe label bias due to over-reliance on sparse timestamp annotations, resulting in unsatisfactory performance. In this paper, we propose the Debiasing-TSTAS (D-TSTAS) framework by exploiting unannotated frames to alleviate this bias from two phases: 1) Initialization. To reduce the dependencies on annotated frames, we propose masked timestamp predictions (MTP) to ensure that initialized model captures more contextual information. 2) Refinement. To overcome the limitation of the expressiveness from sparsely annotated timestamps, we propose a center-oriented timestamp expansion (CTE) approach to progressively expand pseudo-timestamp groups which contain semantic-rich motion representation of action segments. Then, these pseudotimestamp groups and the model output are used to iteratively generate pseudo-labels for refining the model in a fully supervised setup. We further introduce segmental confidence loss to enable the model to have high confidence predictions within the pseudo-timestamp groups and more accurate action boundaries. Our D-TSTAS outperforms the state-of-the-art TSTAS method as well as achieves competitive results compared with fully supervised approaches on three benchmark datasets. + +# 1. Introduction + +Analyzing and understanding human actions in videos is very important for many applications, such as human-robot interaction [14] and healthcare [33]. Recently, several approaches have been very successful in locating and analyzing activities in videos, including action localization [12,29,37,50], action segmentation [7,11,20,23], and action recognition [9,27,39,41,47]. + +![](images/cf5bfc0152e64ea74b29cc542fe2e15daca8d2cc94da39d2250d9d1106a0584a.jpg) +(c) Representation bias during the refining phase. +Figure 1. (a) The TSTAS task aims to segment actions in videos by timestamp annotations. (b) An example of focus bias: existing initialization methods prefer to predict frames similar to the annotated timestamp, leading to incorrectly identifying dissimilar frames within the segment and similar frames outside the segment. (c) An example of representation bias: the frames of complex action share large semantic variance, e.g. the process of cutting cheese includes both taking out and cutting, resulting in the models that rely on sparse timestamps to produce biased pseudo-labels. + +Despite the success of previous approaches, they rely on fully temporal supervision, where the start and end frames of each action are annotated. As a lightweight alternative, many researchers have started exploring timestamp supervised temporal action segmentation (TSTAS), where each action segment is annotated with only one frame in the untrimmed video, as shown in Fig. 1 (a). + +Most previous approaches follow a two-step pipeline by initializing and then iteratively refining the model with generated pseudo-labels. However, relying only on supervised signals of sparse single-timestamp annotations, these methods fail to learn the semantics of entire action segments, which is referred to as label bias in this paper, including focus bias and representation bias. Specifically, to initialize the segmentation model, the previous methods [17, 28, 32] adopt the Naive approach proposed in [28] (referred to as Naive), which computes the loss at the annotated frames for training. However, utilizing only the annotated frames leads to focus bias, where the initialized model tends to fo + +cus on frames distributed over segments of various action categories similar to the annotated frames [51] (shown in Fig. 1 (b)). + +During refining the segmentation model, to utilize the unlabeled frames, typical methods generate hard [17,28,51] or soft weighted [32] pseudo-labels that are used to refine the model like fully supervised methods. To generate pseudo-labels, the above methods depend on the timestamps that contain semantic or relative position information. Despite the success of such refined models, these approaches suffer from representation bias that single-frame fails to represent the entire action segment for complex actions with the large semantic variance of various frames (illustrated in Fig. 1 (c)). Moreover, when refining the segmentation model by these biased pseudo-labels, representation bias can be accumulated and expanded, resulting in unsatisfactory performance that is still a gap compared to fully supervised approaches. + +In this paper, we propose a novel framework called Debiasing-TSTAS (D-TSTAS) to reduce label bias, containing masked timestamp predictions and center-oriented timestamp expansion approaches. During the initialization phase, we aim to alleviate the focus bias problem by propagating timestamp supervision information to the contextual frames of the timestamps. In contrast to previous approaches, we propose the Masked Timestamp Predictions (MTP) approach that masks the input features of timestamps to remove the dependencies of the model on annotated frames. In this way, the initialized model is forced to reconstruct the annotated frames in corresponding output features and then predict their action categories by contextual information of timestamps. Furthermore, to capture the semantics of both timestamps and contextual frames, we adopt the Naive after our MTP. + +While our initialized model can reduce focus bias by capturing more contextual information, it does not guarantee that the generated pseudo-labels avoid representation bias during refining. Inspired by query expansion, we propose a Center-oriented Timestamp Expansion (CTE) approach for obtaining potential trustworthy unlabeled frames, which we refer to as pseudo-timestamps, to progressively expand the pseudo-timestamp groups that contain more semantics than single annotated timestamps. More specifically, it consists of three steps: 1) In the generating step, we generate pseudo-labels by current pseudotimestamp groups and the model output. 2) In the updating step, we choose the semantically dissimilar center frames of each segment in the pseudo-labels as pseudo-timestamps to expand the pseudo-timestamp groups. 3) In the segmenting step, the model is refined by pseudo-labels and our segmental confidence loss, which smooths the predicted probabilities in each action segment and maintains high confidence within pseudo-timestamp groups. The above steps are ex + +ecuted several times alternately to improve the model prediction in a lazy manner instead of generating pseudo-labels per epoch in previous methods [28, 51]. + +Our contributions can be summarised as follows: + +- We study the label bias in the TSTAS task and propose a novel D-TSTAS framework to reduce both focus and representation bias. +- Our masked timestamp predictions approach is the first attempt to alleviate the dependencies on timestamps, promoting the model to capture contextual information. Coupling MTP and Naive as a general solution is used to initialize the model in the TSTAS. +- Compared to sparsely annotated timestamps, our center-oriented timestamp expansion approach progressively expands pseudo-timestamp groups to contain semantic-rich motion representations of action segments. +- The proposed D-TSTAS not only outperforms state-of-the-art TSTAS approaches but also achieves competitive results compared with fully supervised approaches on three benchmark datasets. + +# 2. Related Work + +# 2.1. Temporal Action Segmentation + +Fully Supervised Action Segmentation has been attracting increasing attention. In contrast to action recognition where trimmed videos are classified [5, 22, 30, 39, 48], temporal action segmentation requires modeling long-range dependencies to predict all the frames in the video. To achieve a larger receptive field, many approaches utilized dilated temporal convolutional networks to capture local and global dependencies [7, 25]. Despite the success of these approaches, they suffer from an over-segmentation error. To alleviate this problem, current state-of-the-art methods follow the architecture that refines the initial predictions [1, 15, 26, 40, 49] or integrates text prompts [24]. The above fully supervised approaches rely on frame-wise annotations, which are expensive to obtain. + +Timestamp Supervised Action Segmentation only requires a single annotated frame for each action segment. Most previous methods [17, 28, 32, 51] apply a two-phase training scheme, initializing by Naive [28] (also called the warmup phase [51]) and then iteratively refining the learned model with generated pseudo-labels. Unlike these methods, UVAST [3] directly refines the model by generating pseudo-labels from the constrained k-medoids algorithm based on input features. Moreover, in the specific action field (surgical phase recognition), Ding et al. [6] generate only partial pseudo-labels. While the above methods for generating pseudo-labels are highly dependent on annotated + +![](images/689744a32b046a8c7ba32e48426ba381aa91415b26b71a187054207d82b89eca.jpg) +Initialize Model with MTP Segmentation Model + +![](images/dba19a30393561ee054a788130710be638b6c8aee159aa60927110c00f46eb80.jpg) +Refine Model with CTE + +![](images/0f9daa2bd03caa304a16ee017a4f0575402be7c7f89e13404cd4247057a34cd8.jpg) +Segmentation Model +Figure 2. The pipeline of our proposed framework consists of two phases: initialize the segmentation model (in Sec. 3.2) with masked timestamp predictions (MTP in Sec. 3.3) and refine the model with center-oriented timestamp expansion (CTE in Sec. 3.4). The overall losses are introduced in Sec. 3.5. GPL is the abbreviation for generating pseudo-labels. + +![](images/4e3e609e43e899c0c507d90cd2430d8d262074efb7d7214e4e65e3a11e73038f.jpg) + +timesteps, the semantic representation of the timestamps is limited. Different from the previous solutions, we propose MTP to enable the initialized model to capture contextual information and CTE to enrich pseudo-timestamp groups instead of single timestamps. + +# 2.2. Self-Supervised Learning + +In image and video tasks, self-supervised learning has been successful for its ability to learn information feature representations without human supervision. Most of the previous works were based on the spatial-temporal orders of videos by designing an auxiliary task related to the main task where the labels can be self-annotated [2,18,21,44,46]. Inspired by the success of the vision transformer, masked modeling is widely used in image [13, 42] and video modeling [10, 38]. Unlike these works, our proposed MTP predicts categories of annotated frames by using contextual information, aiming to address the problem of focus bias for timestamp supervised action segmentation. + +# 3. The Debiasing-TSTAS Framework + +In this section, we present the details of our D-TSTAS. In Sec. 3.1, we first introduce the task of timestamp supervision and the pipeline of D-TSTAS, and the segmentation model is described in Sec. 3.2. Then, the masked timestamp predictions and the center-oriented timestamp expansion are proposed in Sec. 3.3 and Sec. 3.4, respectively. Finally, we provide the details of the loss functions in Sec. 3.5. + +# 3.1. Problem statement and pipeline + +Given a video $X = \{x_{t}\}_{t=1}^{T}$ with $T$ frames and $N$ action segments ( $N \ll T$ ), the fully supervised temporal action segmentation requires high-cost frame-wise annota + +tions for training and aims to predict a sequence of framewise action labels. In contrast to the fully supervised approaches, we consider efficient timestamp supervised segmentation, which provides a set of annotated timestamps $A_{Ts} = \{(a_n,t_n)\}_{n = 1}^N$ , where frame $t_n$ belongs to the $n$ -th action segment and $a_n$ is the label $n$ -th of action segment. While the annotation time of timestamp supervision is much less than that of the fully supervised setup, there is still a large gap in performance. + +To achieve comparable performance to the fully supervised methods, we propose a framework named D-TSTAS, including an Initialization phase and a Refinement phase, as shown in Fig. 2. Specifically, following the previous [7, 16, 40, 49], we extract I3D [4] features $X' = \{x_t'\}_{t=1}^T$ as the input to our segmentation model. Then, to reduce focus bias, we initialize our model by masked timestamp predictions (MTP) and Naive [49] for capturing more contextual information. To further reduce representation bias, we propose the center-oriented timestamp expansion (CTE) to expand the progressive pseudo-timestamp groups and refine the segmentation model by generating pseudo-labels. + +# 3.2. The segmentation model + +The architecture of our segmentation model is shown in Fig. 2. We build a Transformer backbone of the cascaded encoder-decoder network structure [49], which contains an encoder and $H$ -1 decoders. The linear attention [45] is applied in our backbone to balance training efficiencies and performance, which is beneficial for modeling long sequences. More details of the segmentation model are described in the supplementary material. We also explore the effect of Temporal Convolutional Network (TCN) [17, 28] or our backbone and compare the different attentions in the backbone as illustrated in Sec. 4.7. + +# 3.3. Reducing the focus bias by MTP + +As mentioned before, the previous initialization [17, 28, 32] suffers from focus bias. In this paper, we propose masked timestamp predictions (MTP) to reduce this bias as shown in Fig. 2. Specifically, given the input feature $X'$ , we mask the I3D feature $x_{t_n}'$ of annotated timestamps by a shared learnable token to reduce the dependency of the model on annotated timestamps. The input feature of the unannotated frames is used to generate output feature $F_h$ and predictions of timestamps $P_h$ , where $h = 1, \dots, H$ , and $H$ denotes the total number of stages (encoder & decoder). To enable our model to involve the semantic information of annotated timestamps, Naive is employed to train the segmentation model after the MTP. The obtained output of our initialized model captures temporal feature representations at different distances from the timestamps by propagating the timestamp supervision information to contextual frames, which is superior to the feature representations obtained by using a Naive alone in typical approaches. Unlike the self-supervised methods [10, 13, 38, 43] that attain a generic pre-trained model by reconstructing input or handcrafted feature descriptor of input, the MTP maps to annotated frames with high-level semantic information (more analyses in Sec. 4.4). + +# 3.4. Reducing the representation bias by CTE + +Due to the limitation of the expressiveness of the single-frame timestamp, the model tends to produce expressiveness bias for complex action segments, generating incorrect pseudo-labels. Inspired by query expansion, we first propose to use progressive pseudo-timestamp groups $\mathcal{G}$ to represent the action segments. Compared to the original single annotated frames, pseudo-timestamp groups provide a semantically richer representation of each action segment. We further propose the center-oriented timestamp expansion (CTE) to expand $\mathcal{G}$ while refining the model. As illustrated in Alg.1, the annotated timestamp set $A_{T_s}$ is first used to initialize $\mathcal{G} = \{G_n\}_{n=1}^N$ , where $G_n = \{(a_n, t_n^1)\}$ is the timestamp group of $n-th$ action segment and the $t_n^1$ indicates the first annotated timestamp of the group $G_n$ . Then, the generating step, the segmenting step, and updating step perform $M$ iterations to expand progressive pseudo-timestamp groups $\mathcal{G}$ and refine the model by generated pseudo-labels $\hat{Y}$ . The framework of the refined model with the proposed CTE approach is shown in Fig. 2 and we describe the process of the $m-th$ iteration as follows. + +Generating step. Obtain output features of final decoder $F_{H} = \{f_{t}\}_{t = 1}^{T}$ and current timestamps groups $\mathcal{G}$ , generating the frame-wise pseudo-labels can be reduced to estimate the action boundaries between the last timestamp $(a_{i}, t_{i}^{\Omega(i)})$ of $G_{i}$ and the first timestamp $(a_{i + 1}, t_{i + 1}^{1})$ of $G_{i + 1}$ in temporal order, where $i = 1, \dots, N - 1$ . Only $N - 1$ boundaries of pseudo-labels are required to be estimated, and $\Omega(i)$ + +denotes the number of timestamps in the timestamps group $G_{i}$ . Specifically, the stamp-to-stamp energy function as proposed in [28] is used to detect the action change between $t_{i}^{\Omega (i)}$ and $t_{i + 1}^{1}$ , and the boundaries of pseudo-label $t_{b_i}$ can be denoted by: + +$$ +t_{b_{i}} = \operatorname *{arg min}_{\hat{t}}\sum_{\substack{t = t_{i}^{\Omega (j)}}}\hat{t} d(f_{t},e_{i}) + \sum_{t = \hat{t} +1}^{t_{j + 1}^{1}}d(f_{t},e_{i + 1}), +$$ + +s.t. + +$$ +e _ {i} = \frac {1}{\hat {t} - t _ {i} ^ {\Omega (i)} + 1} \sum_ {t = t _ {i} ^ {\Omega (i)}} ^ {\hat {t}} f _ {t}, \tag {1} +$$ + +$$ +e _ {i + 1} = \frac {1}{t _ {i + 1} ^ {1} - t} \sum_ {t = \hat {t} + 1} ^ {t _ {i + 1} ^ {1}} f _ {t}, +$$ + +$$ +t _ {i} ^ {\Omega (i)} \leq \hat {t} < t _ {i + 1} ^ {1}, +$$ + +where $d(\cdot, \cdot)$ is the Euclidean distance, $e_i$ is the average of the embedding features between $t_i^{\Omega(i)}$ and the estimate $\hat{t}$ , and $e_{i+1}$ is the average of the segmentation feature between the estimate $\hat{t}$ and $t_{i+1}^1$ . In Eq. (1), the pseudo-boundaries are estimated from the start of the video. The same argument holds if we estimate the pseudo-boundaries at the end of the video. The final pseudo-boundaries for $t_{b_i}$ are the average of these two estimates, which can be expressed as follows: + +$$ +\begin{array}{r} t _ {b _ {i}} = \frac {t _ {b _ {i} , F W} + t _ {b _ {i} , B W}}{2}, \\ s. t. \end{array} +$$ + +$$ +t _ {b _ {i}, F W} = \arg \min _ {\hat {t}} \sum_ {t = t _ {b _ {i - 1}}} ^ {\hat {t}} d \left(f _ {t}, e _ {i}\right) + \sum_ {t = \hat {t} + 1} ^ {t _ {i + 1} ^ {1}} d \left(f _ {t}, e _ {i + 1}\right), \tag {2} +$$ + +$$ +t_{b_{i},BW} = \operatorname *{arg min}_{\hat{t}}\sum_{t = t_{i}^{\Omega (i)}}^{\hat{t}}d\left(f_{t},e_{i}\right) + \sum_{t = \hat{t} +1}^{t_{b_{i} + 1}}d\left(f_{t},e_{i + 1}\right), +$$ + +$$ +t _ {i} ^ {\Omega (i)} \leq \hat {t} < t _ {i + 1} ^ {1}, +$$ + +thus, we get the pseudo-boundaries $B = \{t_{b_j}\}_{j=0}^N$ , which $t_{b_0} = 0$ and $t_{b_N} = T$ . To generate the pseudo-labels $\hat{Y} = \{\hat{y}_t\}_{t=1}^T$ , we assign the frames between $t_{b_{n-1}}$ and $t_{b_n}$ to the same action label $a_n$ . + +Updating step. Our approach relies on the progressive pseudo-timestamp groups $\mathcal{G}$ that contain more semantic and positional information to detect pseudo-boundaries. To enrich the $\mathcal{G}$ , we need to find potentially trustworthy pseudo-timestamps that are not semantically similar to original timestamps. For finding potentially trustworthy pseudo timestamps, we intuitively choose the center frames of each segment in the pseudo-labels, which are expressed as $C = \{(a_n, t_{c_n})\}_{n=1}^N$ , and + +$$ +t _ {c n} = \frac {t _ {b _ {n - 1}} + t _ {b _ {n}}}{2}. \tag {3} +$$ + +Since adjacent frames usually have similar semantic information in the video, new pseudo-timesteps close to the $G_{n}$ might fail to reduce representation bias. To alleviate this problem, we keep a minimum temporal threshold $D$ between the new pseudo-timesteps and the latest + +Algorithm 1 Refine Model with Center-oriented Timestamp Expansion +Input: I3D features $X^{\prime}$ , annotated timestamps $A_{Ts}$ and segmentation model $\mathcal{M}$ +Output: Refined segmentation model $\mathcal{M}$ +1: Initialize $\mathcal{G}$ and $R$ by $A_{Ts}$ +2: for $m = 1,\dots,M$ do +3: D Generating step. +4: $F_{H}\gets ExtractFeature(X^{\prime},\mathcal{M})$ see Eq.2 +5: $B\gets$ EstimateBoundaries $(F_H,\mathcal{G})$ +6: $\hat{Y}\gets$ GeneratePseudoLabels(B, $\mathcal{G}$ +7: D Updating step. +8: $(\mathcal{G},R)\gets$ Update $(\hat{Y},\mathcal{G},R)$ +9: D Segmenting step. +10: for $k = 1,\ldots ,K$ do +11: $\mathcal{M}\gets$ RefineModel $(\mathcal{M},X^{\prime},\hat{Y},\mathcal{G},\mathcal{L}_{refine})$ +12: end for +13: end for + +added pseudo-timesteps, i.e., $|t_{c_n} - t_{r_n}| > D$ , where $R = \{t_{r_n}\}_{n=1}^N$ denotes the location of the latest added pseudo-timesteps each iteration (initially, $t_{r_n} = t_n$ ). Besides, the value of the new pseudo timestamp $t_{c_n}$ is assigned to $t_{r_n}$ . Finally, we obtain the new pseudo-timestamp groups $\mathcal{G}$ that are utilized for the next iteration. + +Segmenting step. To further improve the quality of the predictions, we refine the segmentation model with the pseudo-labels $\hat{Y}$ , new pseudo-timestamp groups $\mathcal{G}$ , and loss functions $\mathcal{L}_{\text{refine}}$ (described in Sec. 3.5) through $K$ training epochs. + +# 3.5. Loss Functions + +As shown in Fig. 2, we use the same loss as baseline [28] to initialize the model with MTP and Naive, which can be formulated as follows: + +$$ +\mathcal {L} _ {\text {i n i t}} = \mathcal {L} _ {c e} + \lambda \mathcal {L} _ {\text {t m s e}} + \beta \mathcal {L} _ {\text {c o n f}}, \tag {4} +$$ + +where $\mathcal{L}_{ce}$ , $\mathcal{L}_{tmse}$ , and $\mathcal{L}_{conf}$ are the cross-entropy loss based on the annotated timestamps, smoothing loss [7], and confidence loss [28], respectively. $\lambda$ and $\beta$ are hyperparameters utilized to balance the contribution of each loss. + +During the refinement of the model with CTE, we adapt weighted cross-entropy loss $\mathcal{L}_{wce}$ to replace cross-entropy loss $\mathcal{L}_{cls}$ , which can alleviate the imbalance problem in the frequency of different action segments for each action category [15]. Unlike the [15], to get the class weight, we calculate the median of class frequencies divided by each class frequency through pseudo-labels that approximate ground truth. The previous methods [17,28,32] typically apply confidence loss proposed in [28] so that the probability of prediction decreases monotonically with increasing distance from the timestamp. However, due to focus monotonicity outside the segments, the confidence loss leads to the blurring of the boundaries of the action segments. + +Segmental confidence loss. Unlike confidence loss $\mathcal{L}_{conf}$ , we propose segmental confidence loss $\mathcal{L}_{sconf}$ to smooth the predicted probabilities within the action seg + +![](images/ba939c01cc6aa707ca9dd3b181cdb33d7f1f8028122d7ab1b0e8f50bc9614466.jpg) +Figure 3. The segmental confidence loss penalizes decreasing predictions within the red range $(t_{b_{n-1}}$ to $t_n^{\Omega(n)}$ and increasing predictions in the green range $(t_n^1$ to $t_{b_n}$ ) for label $a_n$ . + +ments of pseudo-labels. + +$$ +\begin{array}{l} \mathcal {L} _ {s c o n f} = \left(\sum_ {n = 1} ^ {N} \sum_ {t = t _ {b _ {n - 1}}} ^ {t _ {n} ^ {\Omega (n)}} \delta_ {a _ {n}, 1}\right) / T _ {1} + \left(\sum_ {n = 1} ^ {N} \sum_ {t = t _ {n} ^ {1}} ^ {t _ {b _ {n}}} \delta_ {a _ {n}, 2}\right) / T _ {2}, \\ \delta_ {a _ {n}, 1} = \max \left(0, p _ {a _ {n}, t - 1} - p _ {a _ {n}, t}\right), \\ \delta_ {a _ {n}, 2} = \max \left(0, p _ {a _ {n}, t} - p _ {a _ {n}, t - 1}\right), \\ T _ {1} = \sum_ {n = 1} ^ {N} \left(t _ {n} ^ {\Omega (n)} - t _ {b _ {n - 1}}\right), \\ T _ {2} = \sum_ {n = 1} ^ {N} \left(t _ {b _ {n}} - t _ {n} ^ {1}\right), \tag {5} \\ \end{array} +$$ + +where $p_{a_n,t}$ is the probability of action $a_n$ at time $t$ . $\delta_{a_n,1}$ and $\delta_{a_n,2}$ are decreasing penalized predictions and increasing penalized predictions as illustrated in Fig. 3. $T_1$ and $T_2$ are the total sum of frames of $\delta_{a_n,1}$ and $\delta_{a_n,2}$ , respectively. The effect of our loss function is visualized as shown in Fig. 5, which can prevent boundary blur caused by prediction monotonicity outside the action segments and keeps consistent high confidence between $t_n^1$ and $t_n^{\Omega(n)}$ . + +The overall loss function to refine the segmentation model with CTE is as follows: + +$$ +\mathcal {L} _ {\text {r e f i n e}} = \mathcal {L} _ {w c e} + \lambda \mathcal {L} _ {t m s e} + \gamma \mathcal {L} _ {s c o n f}, \tag {6} +$$ + +where $\lambda$ and $\gamma$ are hyper-parameters to balance the contribution of each loss. + +# 4. Experiments + +# 4.1. Datasets and evaluation + +Datasets. Following the previous works [17, 32, 51], we evaluate our approach on three datasets: 50Salads [36], Breakfast [19], and Georgia Tech Egocentric Activities (GTEA) [8]. We perform 4-fold cross-validation on Breakfast and GTEA, and 5-fold cross-validation on 50Salads. + +The 50Salads dataset contains 50 videos (0.6M frames) with actors preparing different kinds of salads. It consists of 17 action classes which are recorded from the top view. On average, the video duration is 6.4 minutes long and each video has 20 action instances. The Breakfast dataset consists of 1712 third-person view videos (3.6M frames) related to breakfast preparation activities. There are 48 different action classes that were recorded in 18 different kitchens. The average video duration ranges from a few + +seconds to several minutes and each video contains 6 action instances on average. The GTEA dataset contains 58 videos (32K frames) with actors performing various kinds of daily activities. It consists of 11 action classes. The average video duration is 1 minute long. + +For all datasets, our experimental results are reported for three random seeds used for annotating frames in videos. Only in Tab. 8, we use the same annotations that Li et al. [28] provide for a fair comparison. + +Evaluation Metrics. Following previous works [7, 26], we use the standard metrics for fully supervised temporal action segmentation and report the frame-wise accuracy (Acc), segmental edit distance (Edit) and segmental F1 scores with overlapping thresholds of $10\%$ , $25\%$ , and $50\%$ , denoted by $F1@{10,25,50}$ . + +# 4.2. Implementation details + +We set $H = 4$ as in [49] and train our model for 290 epochs, including 80 epochs for MTP, 30 epochs for Naive, and 180 ( $K = 30$ , $M = 6$ ) epochs for CTE. $D$ is set to $\{5, 20, 10\}$ for GTEA, 50Salads, and Breakfast, which is related to the average action duration. The batch size is 8 and an AdamW optimizer with a learning rate of 0.0005 and weight decay of 0.05 is used. For the loss function, we set $\lambda = 0.15$ , $\beta = 0.075$ as in [28], and set $\gamma = 1$ . All experiments in the comparison study use the above setting and are conducted with NVIDIA GeForce RTX 2080 Ti GPUs. + +# 4.3. Effectiveness of MTP + +We first compare the initialization of the MTP and Naive [28] on TCN backbone [28] and our backbone. As shown in Tab. 1, our approach outperforms Naive with a large margin F1 and edit scores. This is because the Naive initialized model by only using sparse timestamps, the model produces focus bias, incorrectly recognizing frames in various action categories similar to annotated frames. On the contrary, our approach reduces focus bias by masking the timestamps and predicting the category of annotated frames using contextual information. Moreover, we combine MTP and Naive to generate better initialized predictions by exploiting semantic information with annotated timestamps and the context of annotated frames. These are also reflected in the performance as illustrated in Fig. 4. We also evaluate the order of MTP and Naive in the supplementary. + +To further explore the effectiveness of the MTP, we explore the impact of different initialization strategies on the refinement model, as shown in Tab. 2. To conduct a fair comparison, the same refinement approach in [28], containing 20 epochs of training, is used to refine the model. While our MTP gives an additional boost in performance, the best performance is achieved when MTP and Naive are combined. This illustrates that a good initialization model is beneficial for refining the model. While the MTP of the + +
InitializationGTEA50Salads
F1@{10, 25, 50}EditAccF1@{10, 25, 50}EditAcc
TCNNaive59.755.339.651.156.547.943.334.0
MTP63.459.745.956.453.459.855.144.9
MTP+Naive74.468.152.167.262.860.255.745.5
oursNaive47.442.133.045.147.641.336.125.3
MTP67.662.747.361.060.555.451.140.9
MTP+Naive77.072.456.170.565.462.658.147.4
+ +Table 1. Impact of different initialization strategies and backbones without refinement on GTEA and 50Salads datasets. + +
InitializationGTEA50Salads
F1@{10,25,50}EditAccF1@{10,25,50}EditAcc
TCNNaive78.973.055.472.366.473.970.960.166.8
MTP81.476.958.575.966.871.568.358.865.5
MTP+Naive84.079.060.479.567.872.069.058.664.6
oursNaive76.071.455.371.769.072.067.954.764.9
MTP82.679.661.677.570.273.969.458.267.0
MTP+Naive86.283.266.382.772.074.571.160.067.3
+ +Table 2. Impact of different initialization strategies and backbones with refinement [28] on GTEA and 50Salads datasets. + +![](images/22c2fdb7e8aee2f1906d6e634e4ed10dcaf2f28438d17e5cbb993076da821096.jpg) +Figure 4. Qualitative comparison of the different initialization strategies with TCN backbone [28] on the 50Salads dataset. Naive only correctly identifies frames close to the timestamp, which are also similar frames to annotated timestamps. MTP reduces this bias by directing the model to capture contextual information, but the boundaries of segments are not accurate. Adding Naive after MTP generates better predictions as the model exploits semantic information with annotated timestamps and the context of annotated frames. + +TCN backbone on 50Salads achieves good frame-wise accuracy, it suffers from over-segmentation during refining as evidenced by the low F1 and Edit scores. Meanwhile, our backbone based on Transformer can alleviate this problem. + +# 4.4. Impact of mapping target for MTP + +Our approach initializes the model by mapping the masked features to the label of timestamps (Feature-to-Label), which is described in Sec. 3.3. To analyze the impact of the mapping target, we train another model (Feature-to-Feature) that minimizes the $l_{2}$ distance between the output feature $f_{t_n}$ and the input I3D feature $x_{t_n}'$ . Specifically, we use an additional linear layer to adjust the dimensions of $f_{t_n}$ to match the dimensions of the $x_{t_n}'$ . For a fair comparison, the Feature-to-Feature model follows the same initialization method (MTP+Native) and refinement method [28] based on our backbone as Feature-to-Label. As shown in Tab. 2 and Tab. 3, compared to the Naive, Feature-to-Feature slightly improves the performance, which validates that the masking strategy achieves better initialization + +
DatasetTargetF1@{10,25,50}EditAcc
GTEAFeature-to-Feature75.672.456.865.571.2
Feature-to-Label86.283.266.382.772.0
50SaladsFeature-to-Feature72.369.158.965.875.9
Feature-to-Label74.571.160.067.377.6
+ +Table 3. Impact of mapping target for MTP on GTEA and 50Salads datasets. + +
RefinementF1@{10, 25, 50}EditAcc
baseline [28] (epoch = 20)74.571.160.067.377.6
CTE (K = 10, M = 2)76.473.162.669.677.5
+ +Table 4. Comparison with the baseline in the refining phase on the 50Salads dataset. + +
Impact of KF1@{10, 25, 50}EditAccAccPLAccTS
CTE (K=10, M=6)80.177.866.372.978.087.197.3
CTE (K=20, M=6)82.880.669.675.779.187.397.2
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=40, M=6)83.581.371.276.780.087.297.0
Impact of MF1@{10, 25, 50}EditAccAccPLAccTi
CTE (K=30, M=2)81.078.468.074.179.788.697.9
CTE (K=30, M=4)83.280.670.476.379.887.897.4
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=30, M=8)83.781.970.377.879.286.497.0
CTE (K=30, M=10)83.781.069.576.578.885.696.4
+ +of the model. However, it performed worse than Feature-to-Label. This is mainly because Feature-to-Label promotes the model to capture high-level semantic information, which is beneficial for the propagation of supervised signals of timestamps to unlabeled frames in the TSTAS task. We also discuss the number of masked frames with Feature-to-Label and Feature-to-Feature (please refer to the supplementary). + +# 4.5. Effectiveness of CTE + +To verify the effectiveness of the proposed CTE during the refining phase, we compare the CTE with the baseline that employs the refining approach [28] and perform the comparison experiments based on our initialized model. As shown in Tab. 4, our approach outperforms the baseline. This is because our method captures more semantic information within the action segment compared to the baseline by expanding the timestamp groups. As shown in Tab. 5, the addition of pseudo-labels is trustworthy, and pseudotimestamp groups are used to generate better pseudo-labels, as indicated by the high accuracy of pseudo-labels and timestamps. The effect of CTE can also be seen in the qualitative result, please refer to the supplementary. + +# 4.6. Ablation Study of CTE + +The effect of the center-oriented timestamp expansion is controlled by two hyper-parameters: $K$ and $M$ . In this section, we study the impact of the two parameters with differ + +Table 5. Impact of epoch-per-segmentation step $K$ and the number of iterations $M$ in CTE on 50Salads dataset. AccPL and AccTS denote the accuracy of pseudo-labels and timestamps for each video, respectively. + +
StrategiesGTEA
F1@{10,25,50}EditAcc
Local attentionNaive69.762.745.462.059.8
MTP75.572.453.372.064.8
MTP+Naive77.473.654.971.166.3
MTP+Naive+CTE89.186.874.585.573.2
Linear attentionNaive47.442.133.045.147.6
MTP67.662.747.361.060.5
MTP+Naive77.072.456.170.565.4
MTP+Naive+CTE91.590.176.288.575.7
+ +Table 6. Impact of different attention architectures in our backbone on the GTEA dataset. + +
LceLwceLconfLsconfF1@{10,25,50}EditAcc
✓✓82.579.968.576.278.7
✓✓83.881.170.676.679.4
✓✓82.980.465.876.875.6
✓✓84.282.171.577.680.0
+ +Table 7. Comparing different loss functions on the 50Salads dataset. + +![](images/cbf7328aba42b7f8d5a893447220bef2e68ca75d1ba304f5b4d82f5e1a7298cf.jpg) +Figure 5. Quality comparison of confidence loss [28] and segmental confidence loss. + +![](images/0ea6da613492c348b5c7d4c54f5fb4dbc5e177f8bb1455248e9fae536e6d52dc.jpg) + +ent values of $K$ and $M$ , as shown in Tab. 5. + +Impact of epoch-per-segmentation stage $K$ . The parameter of $K$ affects the refinement model by using the same pseudo-labels in the segmenting step. Our default value is $K = 30$ . Increasing the value $K$ from 10 to 30 achieves better performance because sufficient training epochs lead to better convergence. However, setting $K = 40$ results in a slight drop in performance compared with a default value. This drop in performance is due to the over-fitting problem. + +Impact of the number of iterations $M$ . This hyperparameter defines the number of times to supplement the timestamp groups and generate pseudo-labels. Reducing $M$ to 2 still improves the performance but is not as good as the default value of $M = 6$ . Increasing its value to $M = 10$ also causes a degradation in performance. This drop in performance is because adding the incorrect pseudo-timestamp results in a decrease in the accuracy of the pseudo-labels, which affects the predictions of the refinement model. + +# 4.7. Impact of the backbones + +We compare our backbone with TCN [28] backbone as shown in Tab. 1 and Tab. 2. When the Naive is used alone, our backbone causes worse performance in the initialization and refinement phase compared with the TCN backbone. This is because the linear attention in our backbone with the Naive approach incorrectly identifies more frames with semantic similarity to timestamps by capturing global dependencies. In contrast, MTP can improve the performance of our backbone by a large margin, which indicates + +
SupervisionMethodGTEA50SaladsBreakfast
F1@{10,25,50}EditAccF1@{10,25,50}EditAccF1@{10,25,50}EditAcc
FullyMS-TCN [7]87.585.474.681.479.276.374.064.567.980.752.648.137.961.766.3
MS-TCN++ [25]88.885.776.083.580.180.778.570.174.383.764.158.645.965.667.6
BCN [40]88.587.177.384.479.882.381.374.074.384.468.765.555.066.270.4
ASRF [16]89.487.879.883.777.384.983.577.379.384.574.368.956.172.467.6
ASFormer [49]90.188.879.284.679.785.183.476.079.685.676.070.657.475.073.5
ETSN [26]91.190.077.986.278.285.283.975.478.882.074.069.056.270.367.8
ICC [34]91.489.180.587.882.083.882.074.376.185.072.468.555.968.675.2
UVAST [3]92.791.381.092.180.289.187.681.783.987.476.971.558.077.169.7
DPRN [31]92.992.082.990.982.087.886.379.482.087.275.670.557.675.171.7
Br-Prompt+ ASFormer [23]94.192.083.091.681.289.287.881.383.888.1-----
SemiICC(5%) [34]77.971.654.671.468.252.949.036.645.661.360.253.535.656.665.3
ICC(10%) [34]83.781.966.676.473.367.364.949.256.968.664.659.042.261.968.8
TimestampLi et al. [28]78.973.055.472.366.473.970.960.166.875.670.563.647.469.964.1
Khan et al. [17]81.577.560.875.666.175.172.361.067.675.167.961.045.367.061.4
Zhao et al. [51]84.381.764.879.874.478.575.563.471.877.773.166.549.472.664.6
EM-TSS [32]-82.766.582.370.5-75.964.771.677.9-63.749.867.267.0
UVAST+ alignment decoder [3]70.863.549.288.255.375.770.658.278.467.872.064.148.674.360.2
UVAST+Viterbi [3]87.283.766.089.370.583.079.665.978.277.071.363.348.374.160.7
UVAST+FIFA [3]80.775.257.488.766.080.274.961.678.672.572.064.247.674.160.3
D-TSTAS91.590.176.288.575.784.282.171.577.680.076.769.350.775.865.7
+ +Table 8. Comparison with different levels of supervision on all three datasets. D-TSTAS uses the backbone that combines the cascaded encoder-decoder network structure [49] and the linear attention architecture [45]. + +that MTP is effective in alleviating focus bias. Moreover, MTP and transformer backbone are more complementary and can help to capture contextual information. + +We further explore the impact of different attention architectures, including linear attention in Flowformer [45] and local attention in ASFormer [49]. The MTP and CTE are added to the local attention model separately by setting the batch size to 1. Tab. 6 shows that our MTP and CTE can improve the performance of the model. With both MTP and CTE, the linear attention model outperforms the local attention model. Moreover, we compare the training time for the linear attention model and local attention model in the supplementary. To balance training time and performance, we use linear attention in our backbone. + +# 4.8. Comparing Different Loss Functions + +Tab. 7 shows the comparison of our loss function with the previous loss function [28]. Our proposed segmental confidence loss achieves better F1 and edit scores compared with the confidence loss [28]. This is because $\mathcal{L}_{conf}$ blurs the boundaries of the action segmentation when it forces the predicted probabilities to remain monotonic between adjacent annotated timestamps. In contrast, our loss function truncates smoothing through the pseudo-labels at the action boundary. This effect can also be seen in the qualitative result shown in Fig. 5. Moreover, $\mathcal{L}_{ce}$ replacing $\mathcal{L}_{ce}$ also improves performance by alleviating the imbalance of segments for action categories. + +# 4.9. Comparison with the state-of-the-Arts + +We compare our method with recent approaches under different levels of supervision on three datasets. By reduc + +ing the label bias, D-TSTAS outperforms current state-of-the-art approaches under timestamp supervision and semi-supervised, as shown in Tab. 8. Please refer to the supplementary for the qualitative results of our method and the baseline. Our approach further reduces the gap to fully supervised approaches and only involves single-frame annotations for each action segment. Moreover, our approach performs better in rare annotation cases compared with other methods [28, 32] (please refer to the supplementary). + +# 5. Conclusion and Limitation + +In this paper, we propose a Debiasing-TSTAS framework to alleviate the issue of label bias in the TSTAS task. Instead of the commonly used Naive, we additionally use masked timestamp prediction to initialize the model, which models contextual information of timestamps. Moreover, we utilize a center-oriented timestamp expansion to capture a more efficient representation of action segments. We further introduced a segmental confidence loss that improves prediction quality. Our approach outperforms state-of-the-art TSTAS methods on three datasets and achieves comparable performance to the fully supervised setup. + +Limitation. The annotation frames for each action segment are essential to our approach, which limits the annotator not to miss any action segment [32, 35]. To release this limitation, we consider replacing the pseudo-labeling of hard weight in the cross-entropy loss with soft weight as mentioned in [32] and detecting pseudo-timesteps from the soft weight. + +Acknowledgments: This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant DUT22JC14. + +# References + +[1] Hyemin Ahn and Dongheui Lee. Refining action segmentation with hierarchical video representations. 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IEEE, 2022. 2, 5, 8 \ No newline at end of file diff --git a/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/images.zip b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2bb64ee3d6d3b123ef29dd72a657688373547577 --- /dev/null +++ b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:407215d83044ae4a3d38cdd6a834cb3889a356353ce94de57ef744c443c4cf0e +size 633244 diff --git a/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/layout.json b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..12a25ecfe9d25666a428d4bf13ceb2ae4578aadd --- /dev/null +++ b/2023/Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation/layout.json @@ -0,0 +1,10547 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 138, + 103, + 455, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 103, + 455, + 139 + ], + "spans": [ + { + "bbox": [ + 138, + 103, + 455, + 139 + ], + "type": "text", + "content": "Reducing the Label Bias for Timestamp Supervised Temporal Action Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "spans": [ + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "content": "Kaiyuan Liu" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "content": " Yunheng Li" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "content": " Shenglan Liu" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "content": " Chenwei Tan" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "text", + "content": " Zihang Shao" + }, + { + "bbox": [ + 83, + 160, + 510, + 176 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "spans": [ + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "type": "text", + "content": "School of Computer Science, Dalian University of Technology, China {1154864382, liyunheng, liusl, tcw2000, 1317588161} " + }, + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "type": "inline_equation", + "content": "@" + }, + { + "bbox": [ + 125, + 176, + 467, + 204 + ], + "type": "text", + "content": " mail.dlut.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 256, + 290, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 555 + ], + "type": "text", + "content": "Timestamp supervised temporal action segmentation (TSTAS) is more cost-effective than fully supervised counterparts. However, previous approaches suffer from severe label bias due to over-reliance on sparse timestamp annotations, resulting in unsatisfactory performance. In this paper, we propose the Debiasing-TSTAS (D-TSTAS) framework by exploiting unannotated frames to alleviate this bias from two phases: 1) Initialization. To reduce the dependencies on annotated frames, we propose masked timestamp predictions (MTP) to ensure that initialized model captures more contextual information. 2) Refinement. To overcome the limitation of the expressiveness from sparsely annotated timestamps, we propose a center-oriented timestamp expansion (CTE) approach to progressively expand pseudo-timestamp groups which contain semantic-rich motion representation of action segments. Then, these pseudotimestamp groups and the model output are used to iteratively generate pseudo-labels for refining the model in a fully supervised setup. We further introduce segmental confidence loss to enable the model to have high confidence predictions within the pseudo-timestamp groups and more accurate action boundaries. Our D-TSTAS outperforms the state-of-the-art TSTAS method as well as achieves competitive results compared with fully supervised approaches on three benchmark datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 600, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 287, + 684 + ], + "type": "text", + "content": "Analyzing and understanding human actions in videos is very important for many applications, such as human-robot interaction [14] and healthcare [33]. Recently, several approaches have been very successful in locating and analyzing activities in videos, including action localization [12,29,37,50], action segmentation [7,11,20,23], and action recognition [9,27,39,41,47]." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 318, + 230, + 526, + 358 + ], + "blocks": [ + { + "bbox": [ + 318, + 230, + 526, + 358 + ], + "lines": [ + { + "bbox": [ + 318, + 230, + 526, + 358 + ], + "spans": [ + { + "bbox": [ + 318, + 230, + 526, + 358 + ], + "type": "image", + "image_path": "cf5bfc0152e64ea74b29cc542fe2e15daca8d2cc94da39d2250d9d1106a0584a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 358, + 474, + 365 + ], + "lines": [ + { + "bbox": [ + 370, + 358, + 474, + 365 + ], + "spans": [ + { + "bbox": [ + 370, + 358, + 474, + 365 + ], + "type": "text", + "content": "(c) Representation bias during the refining phase." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 366, + 546, + 465 + ], + "lines": [ + { + "bbox": [ + 305, + 366, + 546, + 465 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 546, + 465 + ], + "type": "text", + "content": "Figure 1. (a) The TSTAS task aims to segment actions in videos by timestamp annotations. (b) An example of focus bias: existing initialization methods prefer to predict frames similar to the annotated timestamp, leading to incorrectly identifying dissimilar frames within the segment and similar frames outside the segment. (c) An example of representation bias: the frames of complex action share large semantic variance, e.g. the process of cutting cheese includes both taking out and cutting, resulting in the models that rely on sparse timestamps to produce biased pseudo-labels." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 546, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 568 + ], + "type": "text", + "content": "Despite the success of previous approaches, they rely on fully temporal supervision, where the start and end frames of each action are annotated. As a lightweight alternative, many researchers have started exploring timestamp supervised temporal action segmentation (TSTAS), where each action segment is annotated with only one frame in the untrimmed video, as shown in Fig. 1 (a)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Most previous approaches follow a two-step pipeline by initializing and then iteratively refining the model with generated pseudo-labels. However, relying only on supervised signals of sparse single-timestamp annotations, these methods fail to learn the semantics of entire action segments, which is referred to as label bias in this paper, including focus bias and representation bias. Specifically, to initialize the segmentation model, the previous methods [17, 28, 32] adopt the Naive approach proposed in [28] (referred to as Naive), which computes the loss at the annotated frames for training. However, utilizing only the annotated frames leads to focus bias, where the initialized model tends to fo" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "type": "text", + "content": "*These authors contributed equally to this work." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6503" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "cus on frames distributed over segments of various action categories similar to the annotated frames [51] (shown in Fig. 1 (b))." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 290 + ], + "type": "text", + "content": "During refining the segmentation model, to utilize the unlabeled frames, typical methods generate hard [17,28,51] or soft weighted [32] pseudo-labels that are used to refine the model like fully supervised methods. To generate pseudo-labels, the above methods depend on the timestamps that contain semantic or relative position information. Despite the success of such refined models, these approaches suffer from representation bias that single-frame fails to represent the entire action segment for complex actions with the large semantic variance of various frames (illustrated in Fig. 1 (c)). Moreover, when refining the segmentation model by these biased pseudo-labels, representation bias can be accumulated and expanded, resulting in unsatisfactory performance that is still a gap compared to fully supervised approaches." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 292, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 483 + ], + "type": "text", + "content": "In this paper, we propose a novel framework called Debiasing-TSTAS (D-TSTAS) to reduce label bias, containing masked timestamp predictions and center-oriented timestamp expansion approaches. During the initialization phase, we aim to alleviate the focus bias problem by propagating timestamp supervision information to the contextual frames of the timestamps. In contrast to previous approaches, we propose the Masked Timestamp Predictions (MTP) approach that masks the input features of timestamps to remove the dependencies of the model on annotated frames. In this way, the initialized model is forced to reconstruct the annotated frames in corresponding output features and then predict their action categories by contextual information of timestamps. Furthermore, to capture the semantics of both timestamps and contextual frames, we adopt the Naive after our MTP." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": "While our initialized model can reduce focus bias by capturing more contextual information, it does not guarantee that the generated pseudo-labels avoid representation bias during refining. Inspired by query expansion, we propose a Center-oriented Timestamp Expansion (CTE) approach for obtaining potential trustworthy unlabeled frames, which we refer to as pseudo-timestamps, to progressively expand the pseudo-timestamp groups that contain more semantics than single annotated timestamps. More specifically, it consists of three steps: 1) In the generating step, we generate pseudo-labels by current pseudotimestamp groups and the model output. 2) In the updating step, we choose the semantically dissimilar center frames of each segment in the pseudo-labels as pseudo-timestamps to expand the pseudo-timestamp groups. 3) In the segmenting step, the model is refined by pseudo-labels and our segmental confidence loss, which smooths the predicted probabilities in each action segment and maintains high confidence within pseudo-timestamp groups. The above steps are ex" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "ecuted several times alternately to improve the model prediction in a lazy manner instead of generating pseudo-labels per epoch in previous methods [28, 51]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 109, + 515, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 109, + 515, + 119 + ], + "spans": [ + { + "bbox": [ + 317, + 109, + 515, + 119 + ], + "type": "text", + "content": "Our contributions can be summarised as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 127, + 545, + 353 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 127, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 127, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 317, + 127, + 545, + 163 + ], + "type": "text", + "content": "- We study the label bias in the TSTAS task and propose a novel D-TSTAS framework to reduce both focus and representation bias." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 171, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 171, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 317, + 171, + 545, + 230 + ], + "type": "text", + "content": "- Our masked timestamp predictions approach is the first attempt to alleviate the dependencies on timestamps, promoting the model to capture contextual information. Coupling MTP and Naive as a general solution is used to initialize the model in the TSTAS." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 239, + 545, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 239, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 317, + 239, + 545, + 298 + ], + "type": "text", + "content": "- Compared to sparsely annotated timestamps, our center-oriented timestamp expansion approach progressively expands pseudo-timestamp groups to contain semantic-rich motion representations of action segments." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 306, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 306, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 317, + 306, + 545, + 353 + ], + "type": "text", + "content": "- The proposed D-TSTAS not only outperforms state-of-the-art TSTAS approaches but also achieves competitive results compared with fully supervised approaches on three benchmark datasets." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 384, + 474, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 474, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 474, + 397 + ], + "type": "text", + "content": "2.1. Temporal Action Segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 403, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 569 + ], + "type": "text", + "content": "Fully Supervised Action Segmentation has been attracting increasing attention. In contrast to action recognition where trimmed videos are classified [5, 22, 30, 39, 48], temporal action segmentation requires modeling long-range dependencies to predict all the frames in the video. To achieve a larger receptive field, many approaches utilized dilated temporal convolutional networks to capture local and global dependencies [7, 25]. Despite the success of these approaches, they suffer from an over-segmentation error. To alleviate this problem, current state-of-the-art methods follow the architecture that refines the initial predictions [1, 15, 26, 40, 49] or integrates text prompts [24]. The above fully supervised approaches rely on frame-wise annotations, which are expensive to obtain." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Timestamp Supervised Action Segmentation only requires a single annotated frame for each action segment. Most previous methods [17, 28, 32, 51] apply a two-phase training scheme, initializing by Naive [28] (also called the warmup phase [51]) and then iteratively refining the learned model with generated pseudo-labels. Unlike these methods, UVAST [3] directly refines the model by generating pseudo-labels from the constrained k-medoids algorithm based on input features. Moreover, in the specific action field (surgical phase recognition), Ding et al. [6] generate only partial pseudo-labels. While the above methods for generating pseudo-labels are highly dependent on annotated" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6504" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 88, + 83, + 309, + 159 + ], + "blocks": [ + { + "bbox": [ + 88, + 72, + 237, + 83 + ], + "lines": [ + { + "bbox": [ + 88, + 72, + 237, + 83 + ], + "spans": [ + { + "bbox": [ + 88, + 72, + 237, + 83 + ], + "type": "text", + "content": "Initialize Model with MTP Segmentation Model" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 88, + 83, + 309, + 159 + ], + "lines": [ + { + "bbox": [ + 88, + 83, + 309, + 159 + ], + "spans": [ + { + "bbox": [ + 88, + 83, + 309, + 159 + ], + "type": "image", + "image_path": "689744a32b046a8c7ba32e48426ba381aa91415b26b71a187054207d82b89eca.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 313, + 83, + 508, + 159 + ], + "blocks": [ + { + "bbox": [ + 314, + 72, + 392, + 82 + ], + "lines": [ + { + "bbox": [ + 314, + 72, + 392, + 82 + ], + "spans": [ + { + "bbox": [ + 314, + 72, + 392, + 82 + ], + "type": "text", + "content": "Refine Model with CTE" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 83, + 508, + 159 + ], + "lines": [ + { + "bbox": [ + 313, + 83, + 508, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 83, + 508, + 159 + ], + "type": "image", + "image_path": "dba19a30393561ee054a788130710be638b6c8aee159aa60927110c00f46eb80.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 86, + 169, + 310, + 252 + ], + "blocks": [ + { + "bbox": [ + 86, + 160, + 157, + 169 + ], + "lines": [ + { + "bbox": [ + 86, + 160, + 157, + 169 + ], + "spans": [ + { + "bbox": [ + 86, + 160, + 157, + 169 + ], + "type": "text", + "content": "Segmentation Model" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 86, + 169, + 310, + 252 + ], + "lines": [ + { + "bbox": [ + 86, + 169, + 310, + 252 + ], + "spans": [ + { + "bbox": [ + 86, + 169, + 310, + 252 + ], + "type": "image", + "image_path": "0f9daa2bd03caa304a16ee017a4f0575402be7c7f89e13404cd4247057a34cd8.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 547, + 286 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 547, + 286 + ], + "type": "text", + "content": "Figure 2. The pipeline of our proposed framework consists of two phases: initialize the segmentation model (in Sec. 3.2) with masked timestamp predictions (MTP in Sec. 3.3) and refine the model with center-oriented timestamp expansion (CTE in Sec. 3.4). The overall losses are introduced in Sec. 3.5. GPL is the abbreviation for generating pseudo-labels." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 314, + 161, + 507, + 251 + ], + "blocks": [ + { + "bbox": [ + 314, + 161, + 507, + 251 + ], + "lines": [ + { + "bbox": [ + 314, + 161, + 507, + 251 + ], + "spans": [ + { + "bbox": [ + 314, + 161, + 507, + 251 + ], + "type": "image", + "image_path": "4e3e609e43e899c0c507d90cd2430d8d262074efb7d7214e4e65e3a11e73038f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 361 + ], + "type": "text", + "content": "timesteps, the semantic representation of the timestamps is limited. Different from the previous solutions, we propose MTP to enable the initialized model to capture contextual information and CTE to enrich pseudo-timestamp groups instead of single timestamps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 370, + 189, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 189, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 189, + 384 + ], + "type": "text", + "content": "2.2. Self-Supervised Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 389, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 533 + ], + "type": "text", + "content": "In image and video tasks, self-supervised learning has been successful for its ability to learn information feature representations without human supervision. Most of the previous works were based on the spatial-temporal orders of videos by designing an auxiliary task related to the main task where the labels can be self-annotated [2,18,21,44,46]. Inspired by the success of the vision transformer, masked modeling is widely used in image [13, 42] and video modeling [10, 38]. Unlike these works, our proposed MTP predicts categories of annotated frames by using contextual information, aiming to address the problem of focus bias for timestamp supervised action segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 544, + 240, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 240, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 240, + 559 + ], + "type": "text", + "content": "3. The Debiasing-TSTAS Framework" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "content": "In this section, we present the details of our D-TSTAS. In Sec. 3.1, we first introduce the task of timestamp supervision and the pipeline of D-TSTAS, and the segmentation model is described in Sec. 3.2. Then, the masked timestamp predictions and the center-oriented timestamp expansion are proposed in Sec. 3.3 and Sec. 3.4, respectively. Finally, we provide the details of the loss functions in Sec. 3.5." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 658, + 219, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 219, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 219, + 672 + ], + "type": "text", + "content": "3.1. Problem statement and pipeline" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Given a video " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "X = \\{x_{t}\\}_{t=1}^{T}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " frames and " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " action segments (" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "N \\ll T" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "), the fully supervised temporal action segmentation requires high-cost frame-wise annota" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": "tions for training and aims to predict a sequence of framewise action labels. In contrast to the fully supervised approaches, we consider efficient timestamp supervised segmentation, which provides a set of annotated timestamps " + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": "A_{Ts} = \\{(a_n,t_n)\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": ", where frame " + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": " belongs to the " + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": "-th action segment and " + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": "a_n" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": " is the label " + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": "-th of action segment. While the annotation time of timestamp supervision is much less than that of the fully supervised setup, there is still a large gap in performance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 410, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 546, + 554 + ], + "type": "text", + "content": "To achieve comparable performance to the fully supervised methods, we propose a framework named D-TSTAS, including an Initialization phase and a Refinement phase, as shown in Fig. 2. Specifically, following the previous [7, 16, 40, 49], we extract I3D [4] features " + }, + { + "bbox": [ + 304, + 410, + 546, + 554 + ], + "type": "inline_equation", + "content": "X' = \\{x_t'\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 410, + 546, + 554 + ], + "type": "text", + "content": " as the input to our segmentation model. Then, to reduce focus bias, we initialize our model by masked timestamp predictions (MTP) and Naive [49] for capturing more contextual information. To further reduce representation bias, we propose the center-oriented timestamp expansion (CTE) to expand the progressive pseudo-timestamp groups and refine the segmentation model by generating pseudo-labels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 563, + 443, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 443, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 443, + 575 + ], + "type": "text", + "content": "3.2. The segmentation model" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "content": "The architecture of our segmentation model is shown in Fig. 2. We build a Transformer backbone of the cascaded encoder-decoder network structure [49], which contains an encoder and " + }, + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "content": "-1 decoders. The linear attention [45] is applied in our backbone to balance training efficiencies and performance, which is beneficial for modeling long sequences. More details of the segmentation model are described in the supplementary material. We also explore the effect of Temporal Convolutional Network (TCN) [17, 28] or our backbone and compare the different attentions in the backbone as illustrated in Sec. 4.7." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6505" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 222, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 222, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 222, + 85 + ], + "type": "text", + "content": "3.3. Reducing the focus bias by MTP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": "As mentioned before, the previous initialization [17, 28, 32] suffers from focus bias. In this paper, we propose masked timestamp predictions (MTP) to reduce this bias as shown in Fig. 2. Specifically, given the input feature " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": ", we mask the I3D feature " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "x_{t_n}'" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": " of annotated timestamps by a shared learnable token to reduce the dependency of the model on annotated timestamps. The input feature of the unannotated frames is used to generate output feature " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "F_h" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": " and predictions of timestamps " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "P_h" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "h = 1, \\dots, H" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 90, + 290, + 365 + ], + "type": "text", + "content": " denotes the total number of stages (encoder & decoder). To enable our model to involve the semantic information of annotated timestamps, Naive is employed to train the segmentation model after the MTP. The obtained output of our initialized model captures temporal feature representations at different distances from the timestamps by propagating the timestamp supervision information to contextual frames, which is superior to the feature representations obtained by using a Naive alone in typical approaches. Unlike the self-supervised methods [10, 13, 38, 43] that attain a generic pre-trained model by reconstructing input or handcrafted feature descriptor of input, the MTP maps to annotated frames with high-level semantic information (more analyses in Sec. 4.4)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 372, + 264, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 264, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 264, + 385 + ], + "type": "text", + "content": "3.4. Reducing the representation bias by CTE" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": "Due to the limitation of the expressiveness of the single-frame timestamp, the model tends to produce expressiveness bias for complex action segments, generating incorrect pseudo-labels. Inspired by query expansion, we first propose to use progressive pseudo-timestamp groups " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " to represent the action segments. Compared to the original single annotated frames, pseudo-timestamp groups provide a semantically richer representation of each action segment. We further propose the center-oriented timestamp expansion (CTE) to expand " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " while refining the model. As illustrated in Alg.1, the annotated timestamp set " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "A_{T_s}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " is first used to initialize " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{G_n\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "G_n = \\{(a_n, t_n^1)\\}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " is the timestamp group of " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "n-th" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " action segment and the " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "t_n^1" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " indicates the first annotated timestamp of the group " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "G_n" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": ". Then, the generating step, the segmenting step, and updating step perform " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " iterations to expand progressive pseudo-timestamp groups " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " and refine the model by generated pseudo-labels " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": ". The framework of the refined model with the proposed CTE approach is shown in Fig. 2 and we describe the process of the " + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "inline_equation", + "content": "m-th" + }, + { + "bbox": [ + 47, + 391, + 287, + 628 + ], + "type": "text", + "content": " iteration as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": "Generating step. Obtain output features of final decoder " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "F_{H} = \\{f_{t}\\}_{t = 1}^{T}" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " and current timestamps groups " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": ", generating the frame-wise pseudo-labels can be reduced to estimate the action boundaries between the last timestamp " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "(a_{i}, t_{i}^{\\Omega(i)})" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " and the first timestamp " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "(a_{i + 1}, t_{i + 1}^{1})" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "G_{i + 1}" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " in temporal order, where " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N - 1" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": ". Only " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "N - 1" + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "text", + "content": " boundaries of pseudo-labels are required to be estimated, and " + }, + { + "bbox": [ + 47, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Omega(i)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 133 + ], + "type": "text", + "content": "denotes the number of timestamps in the timestamps group " + }, + { + "bbox": [ + 305, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 305, + 72, + 547, + 133 + ], + "type": "text", + "content": ". 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In Eq. (1), the pseudo-boundaries are estimated from the start of the video. The same argument holds if we estimate the pseudo-boundaries at the end of the video. The final pseudo-boundaries for " + }, + { + "bbox": [ + 306, + 258, + 547, + 354 + ], + "type": "inline_equation", + "content": "t_{b_i}" + }, + { + "bbox": [ + 306, + 258, + 547, + 354 + ], + "type": "text", + "content": " are the average of these two estimates, which can be expressed as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 368, + 414, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 368, + 414, + 390 + ], + "spans": [ + { + "bbox": [ + 317, + 368, + 414, + 390 + ], + "type": "interline_equation", + "content": "\\begin{array}{r} t _ {b _ {i}} = \\frac {t _ {b _ {i} , F W} + t _ {b _ {i} , B W}}{2}, \\\\ s. t. \\end{array}", + "image_path": "4fcee510517fe39491cc5e150a57084a56056d1dfc411ddbcd44904fac71852b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 332, + 391, + 545, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 391, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 332, + 391, + 545, + 419 + ], + "type": "interline_equation", + "content": "t _ {b _ {i}, F W} = \\arg \\min _ {\\hat {t}} \\sum_ {t = t _ {b _ {i - 1}}} ^ {\\hat {t}} d \\left(f _ {t}, e _ {i}\\right) + \\sum_ {t = \\hat {t} + 1} ^ {t _ {i + 1} ^ {1}} d \\left(f _ {t}, e _ {i + 1}\\right), \\tag {2}", + "image_path": "ce29808e072d471c4f82a72c6f90018897c0c7ff27e2c966c0edeb7a3b430db3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 332, + 419, + 526, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 419, + 526, + 447 + ], + "spans": [ + { + "bbox": [ + 332, + 419, + 526, + 447 + ], + "type": "interline_equation", + "content": "t_{b_{i},BW} = \\operatorname *{arg min}_{\\hat{t}}\\sum_{t = t_{i}^{\\Omega (i)}}^{\\hat{t}}d\\left(f_{t},e_{i}\\right) + \\sum_{t = \\hat{t} +1}^{t_{b_{i} + 1}}d\\left(f_{t},e_{i + 1}\\right),", + "image_path": "dbc6918f1dfdd83a85029aa76f7d16a03f058312e0664337facc190be8b20b26.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 332, + 447, + 394, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 447, + 394, + 460 + ], + "spans": [ + { + "bbox": [ + 332, + 447, + 394, + 460 + ], + "type": "interline_equation", + "content": "t _ {i} ^ {\\Omega (i)} \\leq \\hat {t} < t _ {i + 1} ^ {1},", + "image_path": "52e4a4ee61b8447a5107c8d72999d02041f6190e0d46cc3e415e410ad5b3c037.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": "thus, we get the pseudo-boundaries " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "B = \\{t_{b_j}\\}_{j=0}^N" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": ", which " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "t_{b_0} = 0" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "t_{b_N} = T" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": ". To generate the pseudo-labels " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "\\hat{Y} = \\{\\hat{y}_t\\}_{t=1}^T" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": ", we assign the frames between " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "t_{b_{n-1}}" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "t_{b_n}" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": " to the same action label " + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "inline_equation", + "content": "a_n" + }, + { + "bbox": [ + 306, + 465, + 547, + 516 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "spans": [ + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "text", + "content": "Updating step. Our approach relies on the progressive pseudo-timestamp groups " + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "text", + "content": " that contain more semantic and positional information to detect pseudo-boundaries. To enrich the " + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "text", + "content": ", we need to find potentially trustworthy pseudo-timestamps that are not semantically similar to original timestamps. For finding potentially trustworthy pseudo timestamps, we intuitively choose the center frames of each segment in the pseudo-labels, which are expressed as " + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "inline_equation", + "content": "C = \\{(a_n, t_{c_n})\\}_{n=1}^N" + }, + { + "bbox": [ + 305, + 516, + 547, + 625 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 387, + 631, + 545, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 631, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 387, + 631, + 545, + 653 + ], + "type": "interline_equation", + "content": "t _ {c n} = \\frac {t _ {b _ {n - 1}} + t _ {b _ {n}}}{2}. \\tag {3}", + "image_path": "97b8a82a2c44ae8bf14d887c9cbb6c286886b7f2ada74f1e4e73cb6251dbfd3b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "text", + "content": "Since adjacent frames usually have similar semantic information in the video, new pseudo-timesteps close to the " + }, + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "G_{n}" + }, + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "text", + "content": " might fail to reduce representation bias. To alleviate this problem, we keep a minimum temporal threshold " + }, + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 654, + 547, + 713 + ], + "type": "text", + "content": " between the new pseudo-timesteps and the latest" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6506" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 99, + 286, + 223 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "Algorithm 1 Refine Model with Center-oriented Timestamp Expansion" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "lines": [ + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": "Input: I3D features " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " , annotated timestamps " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "A_{Ts}" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " and segmentation model " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " \nOutput: Refined 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"content": " do \n3: D Generating step. \n4: " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "F_{H}\\gets ExtractFeature(X^{\\prime},\\mathcal{M})" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " see Eq.2 \n5: " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "B\\gets" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " EstimateBoundaries " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "(F_H,\\mathcal{G})" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "\\hat{Y}\\gets" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " GeneratePseudoLabels(B, " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": 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"text", + "content": " RefineModel " + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "inline_equation", + "content": "(\\mathcal{M},X^{\\prime},\\hat{Y},\\mathcal{G},\\mathcal{L}_{refine})" + }, + { + "bbox": [ + 47, + 99, + 286, + 223 + ], + "type": "text", + "content": " \n12: end for \n13: end for" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": "added pseudo-timesteps, i.e., " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "|t_{c_n} - t_{r_n}| > D" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "R = \\{t_{r_n}\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": " denotes the location of the latest added pseudo-timesteps each iteration (initially, " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "t_{r_n} = t_n" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": "). Besides, the value of the new pseudo timestamp " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "t_{c_n}" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": " is assigned to " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "t_{r_n}" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": ". Finally, we obtain the new pseudo-timestamp groups " + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 247, + 286, + 317 + ], + "type": "text", + "content": " that are utilized for the next iteration." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "content": "Segmenting step. To further improve the quality of the predictions, we refine the segmentation model with the pseudo-labels " + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "content": ", new pseudo-timestamp groups " + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "content": ", and loss functions " + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{refine}}" + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "content": " (described in Sec. 3.5) through " + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 319, + 287, + 379 + ], + "type": "text", + "content": " training epochs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 389, + 140, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 140, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 140, + 400 + ], + "type": "text", + "content": "3.5. Loss Functions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 408, + 286, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 286, + 442 + ], + "type": "text", + "content": "As shown in Fig. 2, we use the same loss as baseline [28] to initialize the model with MTP and Naive, which can be formulated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 96, + 456, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 456, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 96, + 456, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n i t}} = \\mathcal {L} _ {c e} + \\lambda \\mathcal {L} _ {\\text {t m s e}} + \\beta \\mathcal {L} _ {\\text {c o n f}}, \\tag {4}", + "image_path": "fcfdaa78e2d442c1f8faac30427f65614131c55adf0edbb3ce6033f3b899ef00.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tmse}" + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{conf}" + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": " are the cross-entropy loss based on the annotated timestamps, smoothing loss [7], and confidence loss [28], respectively. " + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 479, + 286, + 526 + ], + "type": "text", + "content": " are hyperparameters utilized to balance the contribution of each loss." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "text", + "content": "During the refinement of the model with CTE, we adapt weighted cross-entropy loss " + }, + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wce}" + }, + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "text", + "content": " to replace cross-entropy loss " + }, + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 528, + 286, + 682 + ], + "type": "text", + "content": ", which can alleviate the imbalance problem in the frequency of different action segments for each action category [15]. Unlike the [15], to get the class weight, we calculate the median of class frequencies divided by each class frequency through pseudo-labels that approximate ground truth. The previous methods [17,28,32] typically apply confidence loss proposed in [28] so that the probability of prediction decreases monotonically with increasing distance from the timestamp. However, due to focus monotonicity outside the segments, the confidence loss leads to the blurring of the boundaries of the action segments." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "text", + "content": "Segmental confidence loss. Unlike confidence loss " + }, + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{conf}" + }, + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "text", + "content": ", we propose segmental confidence loss " + }, + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sconf}" + }, + { + "bbox": [ + 47, + 681, + 286, + 713 + ], + "type": "text", + "content": " to smooth the predicted probabilities within the action seg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 328, + 72, + 527, + 163 + ], + "blocks": [ + { + "bbox": [ + 328, + 72, + 527, + 163 + ], + "lines": [ + { + "bbox": [ + 328, + 72, + 527, + 163 + ], + "spans": [ + { + "bbox": [ + 328, + 72, + 527, + 163 + ], + "type": "image", + "image_path": "ba939c01cc6aa707ca9dd3b181cdb33d7f1f8028122d7ab1b0e8f50bc9614466.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": "Figure 3. The segmental confidence loss penalizes decreasing predictions within the red range " + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "inline_equation", + "content": "(t_{b_{n-1}}" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "inline_equation", + "content": "t_n^{\\Omega(n)}" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": " and increasing predictions in the green range " + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "inline_equation", + "content": "(t_n^1" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "inline_equation", + "content": "t_{b_n}" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": ") for label " + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "inline_equation", + "content": "a_n" + }, + { + "bbox": [ + 305, + 163, + 545, + 196 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 210, + 403, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 210, + 403, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 210, + 403, + 221 + ], + "type": "text", + "content": "ments of pseudo-labels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 224, + 545, + 324 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 224, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 312, + 224, + 545, + 324 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {s c o n f} = \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {b _ {n - 1}}} ^ {t _ {n} ^ {\\Omega (n)}} \\delta_ {a _ {n}, 1}\\right) / T _ {1} + \\left(\\sum_ {n = 1} ^ {N} \\sum_ {t = t _ {n} ^ {1}} ^ {t _ {b _ {n}}} \\delta_ {a _ {n}, 2}\\right) / T _ {2}, \\\\ \\delta_ {a _ {n}, 1} = \\max \\left(0, p _ {a _ {n}, t - 1} - p _ {a _ {n}, t}\\right), \\\\ \\delta_ {a _ {n}, 2} = \\max \\left(0, p _ {a _ {n}, t} - p _ {a _ {n}, t - 1}\\right), \\\\ T _ {1} = \\sum_ {n = 1} ^ {N} \\left(t _ {n} ^ {\\Omega (n)} - t _ {b _ {n - 1}}\\right), \\\\ T _ {2} = \\sum_ {n = 1} ^ {N} \\left(t _ {b _ {n}} - t _ {n} ^ {1}\\right), \\tag {5} \\\\ \\end{array}", + "image_path": "36b15f4fbcb9a704b370feb15b2e3c582be0815a3af735013bbb1a1ce17b6954.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "p_{a_n,t}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " is the probability of action " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "a_n" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "\\delta_{a_n,1}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "\\delta_{a_n,2}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " are decreasing penalized predictions and increasing penalized predictions as illustrated in Fig. 3. " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "T_1" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "T_2" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " are the total sum of frames of " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "\\delta_{a_n,1}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "\\delta_{a_n,2}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": ", respectively. The effect of our loss function is visualized as shown in Fig. 5, which can prevent boundary blur caused by prediction monotonicity outside the action segments and keeps consistent high confidence between " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "t_n^1" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "inline_equation", + "content": "t_n^{\\Omega(n)}" + }, + { + "bbox": [ + 305, + 326, + 545, + 421 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 422, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 545, + 444 + ], + "type": "text", + "content": "The overall loss function to refine the segmentation model with CTE is as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 453, + 545, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 453, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 345, + 453, + 545, + 467 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {w c e} + \\lambda \\mathcal {L} _ {t m s e} + \\gamma \\mathcal {L} _ {s c o n f}, \\tag {6}", + "image_path": "56ef0914af6190948e1823f20a4f1584f8d255e28dd3ee93be28090a314fcd5e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 474, + 544, + 497 + ], + "type": "text", + "content": " are hyper-parameters to balance the contribution of each loss." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 528, + 440, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 440, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 440, + 539 + ], + "type": "text", + "content": "4.1. Datasets and evaluation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 545, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 545, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 545, + 545, + 605 + ], + "type": "text", + "content": "Datasets. Following the previous works [17, 32, 51], we evaluate our approach on three datasets: 50Salads [36], Breakfast [19], and Georgia Tech Egocentric Activities (GTEA) [8]. We perform 4-fold cross-validation on Breakfast and GTEA, and 5-fold cross-validation on 50Salads." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The 50Salads dataset contains 50 videos (0.6M frames) with actors preparing different kinds of salads. It consists of 17 action classes which are recorded from the top view. On average, the video duration is 6.4 minutes long and each video has 20 action instances. The Breakfast dataset consists of 1712 third-person view videos (3.6M frames) related to breakfast preparation activities. There are 48 different action classes that were recorded in 18 different kitchens. The average video duration ranges from a few" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6507" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "content": "seconds to several minutes and each video contains 6 action instances on average. The GTEA dataset contains 58 videos (32K frames) with actors performing various kinds of daily activities. It consists of 11 action classes. The average video duration is 1 minute long." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 180 + ], + "type": "text", + "content": "For all datasets, our experimental results are reported for three random seeds used for annotating frames in videos. Only in Tab. 8, we use the same annotations that Li et al. [28] provide for a fair comparison." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "content": "Evaluation Metrics. Following previous works [7, 26], we use the standard metrics for fully supervised temporal action segmentation and report the frame-wise accuracy (Acc), segmental edit distance (Edit) and segmental F1 scores with overlapping thresholds of " + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "inline_equation", + "content": "F1@{10,25,50}" + }, + { + "bbox": [ + 46, + 180, + 286, + 252 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 261, + 178, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 178, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 178, + 273 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": "We set " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "H = 4" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": " as in [49] and train our model for 290 epochs, including 80 epochs for MTP, 30 epochs for Naive, and 180 (" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "K = 30" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "M = 6" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": ") epochs for CTE. " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "\\{5, 20, 10\\}" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": " for GTEA, 50Salads, and Breakfast, which is related to the average action duration. The batch size is 8 and an AdamW optimizer with a learning rate of 0.0005 and weight decay of 0.05 is used. For the loss function, we set " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "\\lambda = 0.15" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "\\beta = 0.075" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": " as in [28], and set " + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "inline_equation", + "content": "\\gamma = 1" + }, + { + "bbox": [ + 46, + 279, + 286, + 397 + ], + "type": "text", + "content": ". All experiments in the comparison study use the above setting and are conducted with NVIDIA GeForce RTX 2080 Ti GPUs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 407, + 169, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 169, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 169, + 418 + ], + "type": "text", + "content": "4.3. Effectiveness of MTP" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 286, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 286, + 605 + ], + "type": "text", + "content": "We first compare the initialization of the MTP and Naive [28] on TCN backbone [28] and our backbone. As shown in Tab. 1, our approach outperforms Naive with a large margin F1 and edit scores. This is because the Naive initialized model by only using sparse timestamps, the model produces focus bias, incorrectly recognizing frames in various action categories similar to annotated frames. On the contrary, our approach reduces focus bias by masking the timestamps and predicting the category of annotated frames using contextual information. Moreover, we combine MTP and Naive to generate better initialized predictions by exploiting semantic information with annotated timestamps and the context of annotated frames. These are also reflected in the performance as illustrated in Fig. 4. We also evaluate the order of MTP and Naive in the supplementary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 712 + ], + "type": "text", + "content": "To further explore the effectiveness of the MTP, we explore the impact of different initialization strategies on the refinement model, as shown in Tab. 2. To conduct a fair comparison, the same refinement approach in [28], containing 20 epochs of training, is used to refine the model. While our MTP gives an additional boost in performance, the best performance is achieved when MTP and Naive are combined. This illustrates that a good initialization model is beneficial for refining the model. While the MTP of the" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 544, + 141 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 544, + 141 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 544, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 544, + 141 + ], + "type": "table", + "html": "
InitializationGTEA50Salads
F1@{10, 25, 50}EditAccF1@{10, 25, 50}EditAcc
TCNNaive59.755.339.651.156.547.943.334.0
MTP63.459.745.956.453.459.855.144.9
MTP+Naive74.468.152.167.262.860.255.745.5
oursNaive47.442.133.045.147.641.336.125.3
MTP67.662.747.361.060.555.451.140.9
MTP+Naive77.072.456.170.565.462.658.147.4
", + "image_path": "1a19a98e0ca06d3609ba8e57a2ce3064ae96a5190e627f4bedccd310cd7cd5ef.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 169, + 543, + 241 + ], + "blocks": [ + { + "bbox": [ + 306, + 141, + 544, + 161 + ], + "lines": [ + { + "bbox": [ + 306, + 141, + 544, + 161 + ], + "spans": [ + { + "bbox": [ + 306, + 141, + 544, + 161 + ], + "type": "text", + "content": "Table 1. Impact of different initialization strategies and backbones without refinement on GTEA and 50Salads datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 169, + 543, + 241 + ], + "lines": [ + { + "bbox": [ + 310, + 169, + 543, + 241 + ], + "spans": [ + { + "bbox": [ + 310, + 169, + 543, + 241 + ], + "type": "table", + "html": "
InitializationGTEA50Salads
F1@{10,25,50}EditAccF1@{10,25,50}EditAcc
TCNNaive78.973.055.472.366.473.970.960.166.8
MTP81.476.958.575.966.871.568.358.865.5
MTP+Naive84.079.060.479.567.872.069.058.664.6
oursNaive76.071.455.371.769.072.067.954.764.9
MTP82.679.661.677.570.273.969.458.267.0
MTP+Naive86.283.266.382.772.074.571.160.067.3
", + "image_path": "80ad9b4a354aaa43169a5c0ae60af0011399aab00285f7f0de4f98fa3c14c452.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 241, + 544, + 261 + ], + "lines": [ + { + "bbox": [ + 306, + 241, + 544, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 544, + 261 + ], + "type": "text", + "content": "Table 2. Impact of different initialization strategies and backbones with refinement [28] on GTEA and 50Salads datasets." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 314, + 269, + 538, + 327 + ], + "blocks": [ + { + "bbox": [ + 314, + 269, + 538, + 327 + ], + "lines": [ + { + "bbox": [ + 314, + 269, + 538, + 327 + ], + "spans": [ + { + "bbox": [ + 314, + 269, + 538, + 327 + ], + "type": "image", + "image_path": "22c2fdb7e8aee2f1906d6e634e4ed10dcaf2f28438d17e5cbb993076da821096.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 327, + 545, + 423 + ], + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 423 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of the different initialization strategies with TCN backbone [28] on the 50Salads dataset. Naive only correctly identifies frames close to the timestamp, which are also similar frames to annotated timestamps. MTP reduces this bias by directing the model to capture contextual information, but the boundaries of segments are not accurate. Adding Naive after MTP generates better predictions as the model exploits semantic information with annotated timestamps and the context of annotated frames." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 441, + 544, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 544, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 544, + 489 + ], + "type": "text", + "content": "TCN backbone on 50Salads achieves good frame-wise accuracy, it suffers from over-segmentation during refining as evidenced by the low F1 and Edit scores. Meanwhile, our backbone based on Transformer can alleviate this problem." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 498, + 492, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 492, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 492, + 510 + ], + "type": "text", + "content": "4.4. Impact of mapping target for MTP" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": "Our approach initializes the model by mapping the masked features to the label of timestamps (Feature-to-Label), which is described in Sec. 3.3. To analyze the impact of the mapping target, we train another model (Feature-to-Feature) that minimizes the " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " distance between the output feature " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "f_{t_n}" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " and the input I3D feature " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "x_{t_n}'" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": ". Specifically, we use an additional linear layer to adjust the dimensions of " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "f_{t_n}" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " to match the dimensions of the " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "x_{t_n}'" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": ". For a fair comparison, the Feature-to-Feature model follows the same initialization method (MTP+Native) and refinement method [28] based on our backbone as Feature-to-Label. As shown in Tab. 2 and Tab. 3, compared to the Naive, Feature-to-Feature slightly improves the performance, which validates that the masking strategy achieves better initialization" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 544, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 544, + 712 + ], + "type": "text", + "content": "Since there is no timestamp on the test set, we visualize the focus bias clearly by timestamps and predictions on the training set." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6508" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 281, + 119 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 281, + 119 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 281, + 119 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 281, + 119 + ], + "type": "table", + "html": "
DatasetTargetF1@{10,25,50}EditAcc
GTEAFeature-to-Feature75.672.456.865.571.2
Feature-to-Label86.283.266.382.772.0
50SaladsFeature-to-Feature72.369.158.965.875.9
Feature-to-Label74.571.160.067.377.6
", + "image_path": "f62b2e29e3a8c09385f15b9d761aa3f1b2fce0ff3e66e75996ac407ee9378797.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 146, + 281, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 120, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 47, + 120, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 286, + 140 + ], + "type": "text", + "content": "Table 3. Impact of mapping target for MTP on GTEA and 50Salads datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 146, + 281, + 178 + ], + "lines": [ + { + "bbox": [ + 56, + 146, + 281, + 178 + ], + "spans": [ + { + "bbox": [ + 56, + 146, + 281, + 178 + ], + "type": "table", + "html": "
RefinementF1@{10, 25, 50}EditAcc
baseline [28] (epoch = 20)74.571.160.067.377.6
CTE (K = 10, M = 2)76.473.162.669.677.5
", + "image_path": "8ae8b3e672e259e9b621dcde1e172a19466e2e69ef5c299422cf78e361b5408e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 52, + 205, + 285, + 316 + ], + "blocks": [ + { + "bbox": [ + 47, + 178, + 286, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 178, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 286, + 198 + ], + "type": "text", + "content": "Table 4. Comparison with the baseline in the refining phase on the 50Salads dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 205, + 285, + 316 + ], + "lines": [ + { + "bbox": [ + 52, + 205, + 285, + 316 + ], + "spans": [ + { + "bbox": [ + 52, + 205, + 285, + 316 + ], + "type": "table", + "html": "
Impact of KF1@{10, 25, 50}EditAccAccPLAccTS
CTE (K=10, M=6)80.177.866.372.978.087.197.3
CTE (K=20, M=6)82.880.669.675.779.187.397.2
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=40, M=6)83.581.371.276.780.087.297.0
Impact of MF1@{10, 25, 50}EditAccAccPLAccTi
CTE (K=30, M=2)81.078.468.074.179.788.697.9
CTE (K=30, M=4)83.280.670.476.379.887.897.4
CTE (K=30, M=6)84.482.271.277.580.287.497.2
CTE (K=30, M=8)83.781.970.377.879.286.497.0
CTE (K=30, M=10)83.781.069.576.578.885.696.4
", + "image_path": "b0408ad36c58dc488ef201366807338969e2dde90c4f294ca0a31b975666bcaf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 374, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 286, + 469 + ], + "type": "text", + "content": "of the model. However, it performed worse than Feature-to-Label. This is mainly because Feature-to-Label promotes the model to capture high-level semantic information, which is beneficial for the propagation of supervised signals of timestamps to unlabeled frames in the TSTAS task. We also discuss the number of masked frames with Feature-to-Label and Feature-to-Feature (please refer to the supplementary)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 478, + 167, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 167, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 167, + 489 + ], + "type": "text", + "content": "4.5. Effectiveness of CTE" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 496, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 286, + 651 + ], + "type": "text", + "content": "To verify the effectiveness of the proposed CTE during the refining phase, we compare the CTE with the baseline that employs the refining approach [28] and perform the comparison experiments based on our initialized model. As shown in Tab. 4, our approach outperforms the baseline. This is because our method captures more semantic information within the action segment compared to the baseline by expanding the timestamp groups. As shown in Tab. 5, the addition of pseudo-labels is trustworthy, and pseudotimestamp groups are used to generate better pseudo-labels, as indicated by the high accuracy of pseudo-labels and timestamps. The effect of CTE can also be seen in the qualitative result, please refer to the supplementary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 659, + 178, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 178, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 178, + 672 + ], + "type": "text", + "content": "4.6. Ablation Study of CTE" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "The effect of the center-oriented timestamp expansion is controlled by two hyper-parameters: " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": ". In this section, we study the impact of the two parameters with differ" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 539, + 158 + ], + "blocks": [ + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "lines": [ + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "type": "text", + "content": "Table 5. Impact of epoch-per-segmentation step " + }, + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "type": "text", + "content": " and the number of iterations " + }, + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 316, + 286, + 358 + ], + "type": "text", + "content": " in CTE on 50Salads dataset. AccPL and AccTS denote the accuracy of pseudo-labels and timestamps for each video, respectively." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 70, + 539, + 158 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 539, + 158 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 539, + 158 + ], + "type": "table", + "html": "
StrategiesGTEA
F1@{10,25,50}EditAcc
Local attentionNaive69.762.745.462.059.8
MTP75.572.453.372.064.8
MTP+Naive77.473.654.971.166.3
MTP+Naive+CTE89.186.874.585.573.2
Linear attentionNaive47.442.133.045.147.6
MTP67.662.747.361.060.5
MTP+Naive77.072.456.170.565.4
MTP+Naive+CTE91.590.176.288.575.7
", + "image_path": "0e6ba8f00c44fe0b1e9a8f541aede64fc1e5458e0c9bd21f76ca24e8830b857e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 186, + 538, + 235 + ], + "blocks": [ + { + "bbox": [ + 306, + 158, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 306, + 158, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 306, + 158, + 545, + 178 + ], + "type": "text", + "content": "Table 6. Impact of different attention architectures in our backbone on the GTEA dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 186, + 538, + 235 + ], + "lines": [ + { + "bbox": [ + 315, + 186, + 538, + 235 + ], + "spans": [ + { + "bbox": [ + 315, + 186, + 538, + 235 + ], + "type": "table", + "html": "
LceLwceLconfLsconfF1@{10,25,50}EditAcc
✓✓82.579.968.576.278.7
✓✓83.881.170.676.679.4
✓✓82.980.465.876.875.6
✓✓84.282.171.577.680.0
", + "image_path": "cbb0a6e009a9f393063e14987b971c4fd9b6e5d90f8a6aefe22da10a479100f6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 236, + 545, + 256 + ], + "lines": [ + { + "bbox": [ + 306, + 236, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 545, + 256 + ], + "type": "text", + "content": "Table 7. Comparing different loss functions on the 50Salads dataset." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 318, + 266, + 426, + 310 + ], + "blocks": [ + { + "bbox": [ + 318, + 266, + 426, + 310 + ], + "lines": [ + { + "bbox": [ + 318, + 266, + 426, + 310 + ], + "spans": [ + { + "bbox": [ + 318, + 266, + 426, + 310 + ], + "type": "image", + "image_path": "cbf7328aba42b7f8d5a893447220bef2e68ca75d1ba304f5b4d82f5e1a7298cf.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 311, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 306, + 311, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 545, + 331 + ], + "type": "text", + "content": "Figure 5. Quality comparison of confidence loss [28] and segmental confidence loss." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 429, + 266, + 533, + 309 + ], + "blocks": [ + { + "bbox": [ + 429, + 266, + 533, + 309 + ], + "lines": [ + { + "bbox": [ + 429, + 266, + 533, + 309 + ], + "spans": [ + { + "bbox": [ + 429, + 266, + 533, + 309 + ], + "type": "image", + "image_path": "0ea6da613492c348b5c7d4c54f5fb4dbc5e177f8bb1455248e9fae536e6d52dc.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "text", + "content": "ent values of " + }, + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 350, + 482, + 361 + ], + "type": "text", + "content": ", as shown in Tab. 5." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": "Impact of epoch-per-segmentation stage " + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": ". The parameter of " + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": " affects the refinement model by using the same pseudo-labels in the segmenting step. Our default value is " + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 30" + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": ". Increasing the value " + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": " from 10 to 30 achieves better performance because sufficient training epochs lead to better convergence. However, setting " + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 40" + }, + { + "bbox": [ + 305, + 361, + 545, + 469 + ], + "type": "text", + "content": " results in a slight drop in performance compared with a default value. This drop in performance is due to the over-fitting problem." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "content": "Impact of the number of iterations " + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "content": ". This hyperparameter defines the number of times to supplement the timestamp groups and generate pseudo-labels. Reducing " + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "content": " to 2 still improves the performance but is not as good as the default value of " + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "inline_equation", + "content": "M = 6" + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "content": ". Increasing its value to " + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "inline_equation", + "content": "M = 10" + }, + { + "bbox": [ + 305, + 470, + 545, + 577 + ], + "type": "text", + "content": " also causes a degradation in performance. This drop in performance is because adding the incorrect pseudo-timestamp results in a decrease in the accuracy of the pseudo-labels, which affects the predictions of the refinement model." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 443, + 599 + ], + "type": "text", + "content": "4.7. Impact of the backbones" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 545, + 713 + ], + "type": "text", + "content": "We compare our backbone with TCN [28] backbone as shown in Tab. 1 and Tab. 2. When the Naive is used alone, our backbone causes worse performance in the initialization and refinement phase compared with the TCN backbone. This is because the linear attention in our backbone with the Naive approach incorrectly identifies more frames with semantic similarity to timestamps by capturing global dependencies. In contrast, MTP can improve the performance of our backbone by a large margin, which indicates" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6509" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 69, + 523, + 284 + ], + "blocks": [ + { + "bbox": [ + 74, + 69, + 523, + 284 + ], + "lines": [ + { + "bbox": [ + 74, + 69, + 523, + 284 + ], + "spans": [ + { + "bbox": [ + 74, + 69, + 523, + 284 + ], + "type": "table", + "html": "
SupervisionMethodGTEA50SaladsBreakfast
F1@{10,25,50}EditAccF1@{10,25,50}EditAccF1@{10,25,50}EditAcc
FullyMS-TCN [7]87.585.474.681.479.276.374.064.567.980.752.648.137.961.766.3
MS-TCN++ [25]88.885.776.083.580.180.778.570.174.383.764.158.645.965.667.6
BCN [40]88.587.177.384.479.882.381.374.074.384.468.765.555.066.270.4
ASRF [16]89.487.879.883.777.384.983.577.379.384.574.368.956.172.467.6
ASFormer [49]90.188.879.284.679.785.183.476.079.685.676.070.657.475.073.5
ETSN [26]91.190.077.986.278.285.283.975.478.882.074.069.056.270.367.8
ICC [34]91.489.180.587.882.083.882.074.376.185.072.468.555.968.675.2
UVAST [3]92.791.381.092.180.289.187.681.783.987.476.971.558.077.169.7
DPRN [31]92.992.082.990.982.087.886.379.482.087.275.670.557.675.171.7
Br-Prompt+ ASFormer [23]94.192.083.091.681.289.287.881.383.888.1-----
SemiICC(5%) [34]77.971.654.671.468.252.949.036.645.661.360.253.535.656.665.3
ICC(10%) [34]83.781.966.676.473.367.364.949.256.968.664.659.042.261.968.8
TimestampLi et al. [28]78.973.055.472.366.473.970.960.166.875.670.563.647.469.964.1
Khan et al. [17]81.577.560.875.666.175.172.361.067.675.167.961.045.367.061.4
Zhao et al. [51]84.381.764.879.874.478.575.563.471.877.773.166.549.472.664.6
EM-TSS [32]-82.766.582.370.5-75.964.771.677.9-63.749.867.267.0
UVAST+ alignment decoder [3]70.863.549.288.255.375.770.658.278.467.872.064.148.674.360.2
UVAST+Viterbi [3]87.283.766.089.370.583.079.665.978.277.071.363.348.374.160.7
UVAST+FIFA [3]80.775.257.488.766.080.274.961.678.672.572.064.247.674.160.3
D-TSTAS91.590.176.288.575.784.282.171.577.680.076.769.350.775.865.7
", + "image_path": "b1780e15f8ed734c8827899fe0013e5455492c0870f6aba875109002bfcc6363.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 284, + 547, + 306 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 547, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 547, + 306 + ], + "type": "text", + "content": "Table 8. Comparison with different levels of supervision on all three datasets. D-TSTAS uses the backbone that combines the cascaded encoder-decoder network structure [49] and the linear attention architecture [45]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 320, + 287, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 356 + ], + "type": "text", + "content": "that MTP is effective in alleviating focus bias. Moreover, MTP and transformer backbone are more complementary and can help to capture contextual information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 288, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 288, + 489 + ], + "type": "text", + "content": "We further explore the impact of different attention architectures, including linear attention in Flowformer [45] and local attention in ASFormer [49]. The MTP and CTE are added to the local attention model separately by setting the batch size to 1. Tab. 6 shows that our MTP and CTE can improve the performance of the model. With both MTP and CTE, the linear attention model outperforms the local attention model. Moreover, we compare the training time for the linear attention model and local attention model in the supplementary. To balance training time and performance, we use linear attention in our backbone." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 498, + 242, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 242, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 242, + 511 + ], + "type": "text", + "content": "4.8. Comparing Different Loss Functions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "text", + "content": "Tab. 7 shows the comparison of our loss function with the previous loss function [28]. Our proposed segmental confidence loss achieves better F1 and edit scores compared with the confidence loss [28]. This is because " + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{conf}" + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "text", + "content": " blurs the boundaries of the action segmentation when it forces the predicted probabilities to remain monotonic between adjacent annotated timestamps. In contrast, our loss function truncates smoothing through the pseudo-labels at the action boundary. This effect can also be seen in the qualitative result shown in Fig. 5. Moreover, " + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "text", + "content": " replacing " + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 46, + 517, + 287, + 661 + ], + "type": "text", + "content": " also improves performance by alleviating the imbalance of segments for action categories." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 249, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 249, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 249, + 683 + ], + "type": "text", + "content": "4.9. Comparison with the state-of-the-Arts" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "We compare our method with recent approaches under different levels of supervision on three datasets. By reduc" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 320, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 429 + ], + "type": "text", + "content": "ing the label bias, D-TSTAS outperforms current state-of-the-art approaches under timestamp supervision and semi-supervised, as shown in Tab. 8. Please refer to the supplementary for the qualitative results of our method and the baseline. Our approach further reduces the gap to fully supervised approaches and only involves single-frame annotations for each action segment. Moreover, our approach performs better in rare annotation cases compared with other methods [28, 32] (please refer to the supplementary)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 439, + 459, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 459, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 459, + 452 + ], + "type": "text", + "content": "5. Conclusion and Limitation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "content": "In this paper, we propose a Debiasing-TSTAS framework to alleviate the issue of label bias in the TSTAS task. Instead of the commonly used Naive, we additionally use masked timestamp prediction to initialize the model, which models contextual information of timestamps. Moreover, we utilize a center-oriented timestamp expansion to capture a more efficient representation of action segments. We further introduced a segmental confidence loss that improves prediction quality. Our approach outperforms state-of-the-art TSTAS methods on three datasets and achieves comparable performance to the fully supervised setup." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 591, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 545, + 674 + ], + "type": "text", + "content": "Limitation. The annotation frames for each action segment are essential to our approach, which limits the annotator not to miss any action segment [32, 35]. To release this limitation, we consider replacing the pseudo-labeling of hard weight in the cross-entropy loss with soft weight as mentioned in [32] and detecting pseudo-timesteps from the soft weight." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 674, + 545, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 674, + 545, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 674, + 545, + 709 + ], + "type": "text", + "content": "Acknowledgments: This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant DUT22JC14." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "6510" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Hyemin Ahn and Dongheui Lee. 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